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- sage: L.<z12> = CyclotomicField(12)
- sage: R.<q> = L[[]]
- sage: chi = DirichletGroup(133, L)([-1, z12^2 - 1])
- sage: f = q - z12^2*q^2 + (z12^3 - z12)*q^3 + (-z12^3 + z12)*q^5 + z12*q^6 - z12^3*q^7 - q^8 - z12*q^10 + z12*q^13 + (z12^3 - z12)*q^14 + (z12^2 - 1)*q^15 + z12^2*q^16 + (z12^3 - z12)*q^17 + z12^3*q^19 + z12^2*q^21 + (z12^2 - 1)*q^23 + (-z12^3 + z12)*q^24 - z12^3*q^26 - z12^3*q^27 + (-z12^2 + 1)*q^29 + q^30 + z12*q^34 - z12^2*q^35 + O(q^38)
- sage: [hecke_operator_on_qexp(f, p, 1, chi) - f[p]*f for p in prime_range(38)] # this should return zero to available precision
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