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Query: /api/lfunc_lfunctions/?_offset=0
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  1. Lhash: dirichlet_L_3.2
    {'Lhash': 'dirichlet_L_3.2', 'a10': [1.0, 0.0], 'a2': [-1.0, 0.0], 'a3': [1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [1.0, 0.0], 'a7': [1.0, 0.0], 'a8': [-1.0, 0.0], 'a9': [1.0, 0.0], 'algebraic': True, 'analytic_conductor': 0.3223947743838751, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]]], 'bad_primes': [3], 'central_character': '3.2', 'coeff_info': ['x^2 - 1', -1, '\\\\zeta_{2}'], 'conductor': 3, 'conductor_radical': 3, 'conjugate': 'dirichlet_L_3.2', 'degree': 1, 'dirichlet_coefficients': [1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1], 'euler_factors': [[1, -1], [0], [1, -1], [1, 1], [1, -1], [1, 1], [1, -1], [1, 1], [1, -1], [1, -1], [1, 1], [1, 1], [1, -1], [1, 1], [1, -1], 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  2. Lhash: dirichlet_L_4.3
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  3. Lhash: dirichlet_L_5.2
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  4. Lhash: dirichlet_L_5.3
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  5. Lhash: dirichlet_L_5.4
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  6. Lhash: dirichlet_L_7.2
    {'Lhash': 'dirichlet_L_7.2', 'a10': [-0.5, 0.8660254037844386], 'a2': [-0.5, -0.8660254037844386], 'a3': [-0.5, 0.8660254037844386], 'a4': [-0.5, 0.8660254037844386], 'a5': [-0.5, -0.8660254037844386], 'a6': [1.0, 0.0], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, 0.0], 'a9': [-0.5, -0.8660254037844386], 'algebraic': True, 'analytic_conductor': 0.03250786333408151, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]]], 'bad_primes': [7], 'central_character': '7.2', 'coeff_info': ['x^3 - 1', '-0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{3}'], 'conductor': 7, 'conductor_radical': 7, 'conjugate': 'dirichlet_L_7.4', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 'a^1', 'a^1', 'a^2', 'a^0', 0, 'a^0', 'a^2', 'a^1', 'a^1', 'a^2', 'a^0', 0, 'a^0', 'a^2', 'a^1', 'a^1', 'a^2', 'a^0', 0, 'a^0', 'a^2', 'a^1', 'a^1', 'a^2', 'a^0', 0, 'a^0', 'a^2', 'a^1', 'a^1', 'a^2', 'a^0', 0, 'a^0', 'a^2', 'a^1', 'a^1', 'a^2', 'a^0', 0, 'a^0', 'a^2', 'a^1', 'a^1', 'a^2', 'a^0', 0, 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  7. Lhash: dirichlet_L_7.3
    {'Lhash': 'dirichlet_L_7.3', 'a10': [0.5, 0.8660254037844386], 'a2': [-0.5, 0.8660254037844386], 'a3': [0.5, 0.8660254037844386], 'a4': [-0.5, -0.8660254037844386], 'a5': [0.5, -0.8660254037844386], 'a6': [-1.0, -1.4081532572346456e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, 0.0], 'a9': [-0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 0.7522544735623752, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]]], 'bad_primes': [7], 'central_character': '7.3', 'coeff_info': ['x^6 - 1', '0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{6}'], 'conductor': 7, 'conductor_radical': 7, 'conjugate': 'dirichlet_L_7.5', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 'a^1', 'a^4', 'a^5', 'a^3', 0, 'a^0', 'a^2', 'a^1', 'a^4', 'a^5', 'a^3', 0, 'a^0', 'a^2', 'a^1', 'a^4', 'a^5', 'a^3', 0, 'a^0', 'a^2', 'a^1', 'a^4', 'a^5', 'a^3', 0, 'a^0', 'a^2', 'a^1', 'a^4', 'a^5', 'a^3', 0, 'a^0', 'a^2', 'a^1', 'a^4', 'a^5', 'a^3', 0, 'a^0', 'a^2', 'a^1', 'a^4', 'a^5', 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  8. Lhash: dirichlet_L_7.4
    {'Lhash': 'dirichlet_L_7.4', 'a10': [-0.5, -0.8660254037844386], 'a2': [-0.5, 0.8660254037844386], 'a3': [-0.5, -0.8660254037844386], 'a4': [-0.5, -0.8660254037844386], 'a5': [-0.5, 0.8660254037844386], 'a6': [1.0, 0.0], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, 0.0], 'a9': [-0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 0.03250786333408151, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]]], 'bad_primes': [7], 'central_character': '7.4', 'coeff_info': ['x^3 - 1', '-0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{3}'], 'conductor': 7, 'conductor_radical': 7, 'conjugate': 'dirichlet_L_7.2', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 'a^2', 'a^2', 'a^1', 'a^0', 0, 'a^0', 'a^1', 'a^2', 'a^2', 'a^1', 'a^0', 0, 'a^0', 'a^1', 'a^2', 'a^2', 'a^1', 'a^0', 0, 'a^0', 'a^1', 'a^2', 'a^2', 'a^1', 'a^0', 0, 'a^0', 'a^1', 'a^2', 'a^2', 'a^1', 'a^0', 0, 'a^0', 'a^1', 'a^2', 'a^2', 'a^1', 'a^0', 0, 'a^0', 'a^1', 'a^2', 'a^2', 'a^1', 'a^0', 0, 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  9. Lhash: dirichlet_L_7.5
    {'Lhash': 'dirichlet_L_7.5', 'a10': [0.5, -0.8660254037844386], 'a2': [-0.5, -0.8660254037844386], 'a3': [0.5, -0.8660254037844386], 'a4': [-0.5, 0.8660254037844386], 'a5': [0.5, 0.8660254037844386], 'a6': [-1.0, -1.4081532572346456e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, 0.0], 'a9': [-0.5, -0.8660254037844386], 'algebraic': True, 'analytic_conductor': 0.7522544735623752, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]]], 'bad_primes': [7], 'central_character': '7.5', 'coeff_info': ['x^6 - 1', '0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{6}'], 'conductor': 7, 'conductor_radical': 7, 'conjugate': 'dirichlet_L_7.3', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^4', 'a^5', 'a^2', 'a^1', 'a^3', 0, 'a^0', 'a^4', 'a^5', 'a^2', 'a^1', 'a^3', 0, 'a^0', 'a^4', 'a^5', 'a^2', 'a^1', 'a^3', 0, 'a^0', 'a^4', 'a^5', 'a^2', 'a^1', 'a^3', 0, 'a^0', 'a^4', 'a^5', 'a^2', 'a^1', 'a^3', 0, 'a^0', 'a^4', 'a^5', 'a^2', 'a^1', 'a^3', 0, 'a^0', 'a^4', 'a^5', 'a^2', 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  10. Lhash: dirichlet_L_7.6
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  11. Lhash: dirichlet_L_8.3
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  12. Lhash: dirichlet_L_8.5
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  13. Lhash: dirichlet_L_9.2
    {'Lhash': 'dirichlet_L_9.2', 'a10': [1.0, 0.0], 'a2': [0.5, 0.8660254037844386], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.5, 0.8660254037844386], 'a5': [0.5, -0.8660254037844386], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5, -0.8660254037844386], 'a8': [-1.0, -1.4081532572346456e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.9671843231516252, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]]], 'bad_primes': [3], 'central_character': '9.2', 'coeff_info': ['x^6 - 1', '0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{6}'], 'conductor': 9, 'conductor_radical': 3, 'conjugate': 'dirichlet_L_9.5', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 0, 'a^2', 'a^5', 0, 'a^4', 'a^3', 0, 'a^0', 'a^1', 0, 'a^2', 'a^5', 0, 'a^4', 'a^3', 0, 'a^0', 'a^1', 0, 'a^2', 'a^5', 0, 'a^4', 'a^3', 0, 'a^0', 'a^1', 0, 'a^2', 'a^5', 0, 'a^4', 'a^3', 0, 'a^0', 'a^1', 0, 'a^2', 'a^5', 0, 'a^4', 'a^3', 0, 'a^0', 'a^1', 0, 'a^2', 'a^5', 0, 'a^4', 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  14. Lhash: dirichlet_L_9.4
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  15. Lhash: dirichlet_L_9.5
    {'Lhash': 'dirichlet_L_9.5', 'a10': [1.0, 0.0], 'a2': [0.5, -0.8660254037844386], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.5, -0.8660254037844386], 'a5': [0.5, 0.8660254037844386], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5, 0.8660254037844386], 'a8': [-1.0, -1.4081532572346456e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.9671843231516252, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]]], 'bad_primes': [3], 'central_character': '9.5', 'coeff_info': ['x^6 - 1', '0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{6}'], 'conductor': 9, 'conductor_radical': 3, 'conjugate': 'dirichlet_L_9.2', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^5', 0, 'a^4', 'a^1', 0, 'a^2', 'a^3', 0, 'a^0', 'a^5', 0, 'a^4', 'a^1', 0, 'a^2', 'a^3', 0, 'a^0', 'a^5', 0, 'a^4', 'a^1', 0, 'a^2', 'a^3', 0, 'a^0', 'a^5', 0, 'a^4', 'a^1', 0, 'a^2', 'a^3', 0, 'a^0', 'a^5', 0, 'a^4', 'a^1', 0, 'a^2', 'a^3', 0, 'a^0', 'a^5', 0, 'a^4', 'a^1', 0, 'a^2', 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'data': '-0.138888888889', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(6)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.13627591877137772867946858379-0.413570612346262677133126917570*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.90199460774', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '5.91158995863', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '9.56544293454', 'prec': 44}}
  16. Lhash: dirichlet_L_9.7
    {'Lhash': 'dirichlet_L_9.7', 'a10': [1.0, 0.0], 'a2': [-0.5, -0.8660254037844386], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.5, 0.8660254037844386], 'a5': [-0.5, 0.8660254037844386], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5, -0.8660254037844386], 'a8': [1.0, 0.0], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.04179582428667622, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]]], 'bad_primes': [3], 'central_character': '9.7', 'coeff_info': ['x^3 - 1', '-0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{3}'], 'conductor': 9, 'conductor_radical': 3, 'conjugate': 'dirichlet_L_9.4', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 0, 'a^1', 'a^1', 0, 'a^2', 'a^0', 0, 'a^0', 'a^2', 0, 'a^1', 'a^1', 0, 'a^2', 'a^0', 0, 'a^0', 'a^2', 0, 'a^1', 'a^1', 0, 'a^2', 'a^0', 0, 'a^0', 'a^2', 0, 'a^1', 'a^1', 0, 'a^2', 'a^0', 0, 'a^0', 'a^2', 0, 'a^1', 'a^1', 0, 'a^2', 'a^0', 0, 'a^0', 'a^2', 0, 'a^1', 'a^1', 0, 'a^2', 'a^0', 0, 'a^0', 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False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.111111111111', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(3)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.589489817376260904257894655585-0.173097788506347289943761044262*I']], 'z1': {'__RealLiteral__': 0, 'data': '3.44409315515', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '7.53243305229', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '10.0165504226', 'prec': 44}}
  17. Lhash: dirichlet_L_11.10
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  18. Lhash: dirichlet_L_11.2
    {'Lhash': 'dirichlet_L_11.2', 'a10': [-1.0, -1.4081532572346456e-30], 'a2': [0.8090169943749475, 0.5877852522924731], 'a3': [0.30901699437494745, -0.9510565162951535], 'a4': [0.30901699437494745, 0.9510565162951535], 'a5': [-0.8090169943749475, 0.5877852522924731], 'a6': [0.8090169943749475, -0.5877852522924731], 'a7': [-0.30901699437494745, -0.9510565162951535], 'a8': [-0.30901699437494745, 0.9510565162951535], 'a9': [-0.8090169943749475, -0.5877852522924731], 'algebraic': True, 'analytic_conductor': 1.1821141727408753, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]]], 'bad_primes': [11], 'central_character': '11.2', 'coeff_info': ['x^10 - 1', '0.809016994374947 + 0.587785252292473*I', '\\\\zeta_{10}'], 'conductor': 11, 'conductor_radical': 11, 'conjugate': 'dirichlet_L_11.6', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 'a^8', 'a^2', 'a^4', 'a^9', 'a^7', 'a^3', 'a^6', 'a^5', 0, 'a^0', 'a^1', 'a^8', 'a^2', 'a^4', 'a^9', 'a^7', 'a^3', 'a^6', 'a^5', 0, 'a^0', 'a^1', 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  19. Lhash: dirichlet_L_11.3
    {'Lhash': 'dirichlet_L_11.3', 'a10': [1.0, 0.0], 'a2': [0.30901699437494745, -0.9510565162951535], 'a3': [-0.8090169943749475, 0.5877852522924731], 'a4': [-0.8090169943749475, -0.5877852522924731], 'a5': [0.30901699437494745, 0.9510565162951535], 'a6': [0.30901699437494745, 0.9510565162951535], 'a7': [-0.8090169943749475, -0.5877852522924731], 'a8': [-0.8090169943749475, 0.5877852522924731], 'a9': [0.30901699437494745, -0.9510565162951535], 'algebraic': True, 'analytic_conductor': 0.05108378523927094, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]]], 'bad_primes': [11], 'central_character': '11.3', 'coeff_info': ['x^5 - 1', '0.309016994374947 + 0.951056516295154*I', '\\\\zeta_{5}'], 'conductor': 11, 'conductor_radical': 11, 'conjugate': 'dirichlet_L_11.4', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^4', 'a^2', 'a^3', 'a^1', 'a^1', 'a^3', 'a^2', 'a^4', 'a^0', 0, 'a^0', 'a^4', 'a^2', 'a^3', 'a^1', 'a^1', 'a^3', 'a^2', 'a^4', 'a^0', 0, 'a^0', 'a^4', 'a^2', 'a^3', 'a^1', 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  20. Lhash: dirichlet_L_11.4
    {'Lhash': 'dirichlet_L_11.4', 'a10': [1.0, 0.0], 'a2': [0.30901699437494745, 0.9510565162951535], 'a3': [-0.8090169943749475, -0.5877852522924731], 'a4': [-0.8090169943749475, 0.5877852522924731], 'a5': [0.30901699437494745, -0.9510565162951535], 'a6': [0.30901699437494745, -0.9510565162951535], 'a7': [-0.8090169943749475, 0.5877852522924731], 'a8': [-0.8090169943749475, -0.5877852522924731], 'a9': [0.30901699437494745, 0.9510565162951535], 'algebraic': True, 'analytic_conductor': 0.05108378523927094, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]]], 'bad_primes': [11], 'central_character': '11.4', 'coeff_info': ['x^5 - 1', '0.309016994374947 + 0.951056516295154*I', '\\\\zeta_{5}'], 'conductor': 11, 'conductor_radical': 11, 'conjugate': 'dirichlet_L_11.3', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 'a^3', 'a^2', 'a^4', 'a^4', 'a^2', 'a^3', 'a^1', 'a^0', 0, 'a^0', 'a^1', 'a^3', 'a^2', 'a^4', 'a^4', 'a^2', 'a^3', 'a^1', 'a^0', 0, 'a^0', 'a^1', 'a^3', 'a^2', 'a^4', 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  21. Lhash: dirichlet_L_11.5
    {'Lhash': 'dirichlet_L_11.5', 'a10': [1.0, 0.0], 'a2': [-0.8090169943749475, 0.5877852522924731], 'a3': [0.30901699437494745, 0.9510565162951535], 'a4': [0.30901699437494745, -0.9510565162951535], 'a5': [-0.8090169943749475, -0.5877852522924731], 'a6': [-0.8090169943749475, -0.5877852522924731], 'a7': [0.30901699437494745, -0.9510565162951535], 'a8': [0.30901699437494745, 0.9510565162951535], 'a9': [-0.8090169943749475, 0.5877852522924731], 'algebraic': True, 'analytic_conductor': 0.05108378523927094, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]]], 'bad_primes': [11], 'central_character': '11.5', 'coeff_info': ['x^5 - 1', '0.309016994374947 + 0.951056516295154*I', '\\\\zeta_{5}'], 'conductor': 11, 'conductor_radical': 11, 'conjugate': 'dirichlet_L_11.9', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 'a^1', 'a^4', 'a^3', 'a^3', 'a^4', 'a^1', 'a^2', 'a^0', 0, 'a^0', 'a^2', 'a^1', 'a^4', 'a^3', 'a^3', 'a^4', 'a^1', 'a^2', 'a^0', 0, 'a^0', 'a^2', 'a^1', 'a^4', 'a^3', 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  22. Lhash: dirichlet_L_11.6
    {'Lhash': 'dirichlet_L_11.6', 'a10': [-1.0, -1.4081532572346456e-30], 'a2': [0.8090169943749475, -0.5877852522924731], 'a3': [0.30901699437494745, 0.9510565162951535], 'a4': [0.30901699437494745, -0.9510565162951535], 'a5': [-0.8090169943749475, -0.5877852522924731], 'a6': [0.8090169943749475, 0.5877852522924731], 'a7': [-0.30901699437494745, 0.9510565162951535], 'a8': [-0.30901699437494745, -0.9510565162951535], 'a9': [-0.8090169943749475, 0.5877852522924731], 'algebraic': True, 'analytic_conductor': 1.1821141727408753, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]]], 'bad_primes': [11], 'central_character': '11.6', 'coeff_info': ['x^10 - 1', '0.809016994374947 + 0.587785252292473*I', '\\\\zeta_{10}'], 'conductor': 11, 'conductor_radical': 11, 'conjugate': 'dirichlet_L_11.2', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^9', 'a^2', 'a^8', 'a^6', 'a^1', 'a^3', 'a^7', 'a^4', 'a^5', 0, 'a^0', 'a^9', 'a^2', 'a^8', 'a^6', 'a^1', 'a^3', 'a^7', 'a^4', 'a^5', 0, 'a^0', 'a^9', 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  23. Lhash: dirichlet_L_11.7
    {'Lhash': 'dirichlet_L_11.7', 'a10': [-1.0, -1.4081532572346456e-30], 'a2': [-0.30901699437494745, -0.9510565162951535], 'a3': [-0.8090169943749475, -0.5877852522924731], 'a4': [-0.8090169943749475, 0.5877852522924731], 'a5': [0.30901699437494745, -0.9510565162951535], 'a6': [-0.30901699437494745, 0.9510565162951535], 'a7': [0.8090169943749475, -0.5877852522924731], 'a8': [0.8090169943749475, 0.5877852522924731], 'a9': [0.30901699437494745, 0.9510565162951535], 'algebraic': True, 'analytic_conductor': 1.1821141727408753, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]]], 'bad_primes': [11], 'central_character': '11.7', 'coeff_info': ['x^10 - 1', '0.809016994374947 + 0.587785252292473*I', '\\\\zeta_{10}'], 'conductor': 11, 'conductor_radical': 11, 'conjugate': 'dirichlet_L_11.8', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^7', 'a^6', 'a^4', 'a^8', 'a^3', 'a^9', 'a^1', 'a^2', 'a^5', 0, 'a^0', 'a^7', 'a^6', 'a^4', 'a^8', 'a^3', 'a^9', 'a^1', 'a^2', 'a^5', 0, 'a^0', 'a^7', 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  24. Lhash: dirichlet_L_11.8
    {'Lhash': 'dirichlet_L_11.8', 'a10': [-1.0, -1.4081532572346456e-30], 'a2': [-0.30901699437494745, 0.9510565162951535], 'a3': [-0.8090169943749475, 0.5877852522924731], 'a4': [-0.8090169943749475, -0.5877852522924731], 'a5': [0.30901699437494745, 0.9510565162951535], 'a6': [-0.30901699437494745, -0.9510565162951535], 'a7': [0.8090169943749475, 0.5877852522924731], 'a8': [0.8090169943749475, -0.5877852522924731], 'a9': [0.30901699437494745, -0.9510565162951535], 'algebraic': True, 'analytic_conductor': 1.1821141727408753, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]]], 'bad_primes': [11], 'central_character': '11.8', 'coeff_info': ['x^10 - 1', '0.809016994374947 + 0.587785252292473*I', '\\\\zeta_{10}'], 'conductor': 11, 'conductor_radical': 11, 'conjugate': 'dirichlet_L_11.7', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^3', 'a^4', 'a^6', 'a^2', 'a^7', 'a^1', 'a^9', 'a^8', 'a^5', 0, 'a^0', 'a^3', 'a^4', 'a^6', 'a^2', 'a^7', 'a^1', 'a^9', 'a^8', 'a^5', 0, 'a^0', 'a^3', 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44}}
  25. Lhash: dirichlet_L_11.9
    {'Lhash': 'dirichlet_L_11.9', 'a10': [1.0, 0.0], 'a2': [-0.8090169943749475, -0.5877852522924731], 'a3': [0.30901699437494745, -0.9510565162951535], 'a4': [0.30901699437494745, 0.9510565162951535], 'a5': [-0.8090169943749475, 0.5877852522924731], 'a6': [-0.8090169943749475, 0.5877852522924731], 'a7': [0.30901699437494745, 0.9510565162951535], 'a8': [0.30901699437494745, -0.9510565162951535], 'a9': [-0.8090169943749475, -0.5877852522924731], 'algebraic': True, 'analytic_conductor': 0.05108378523927094, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]]], 'bad_primes': [11], 'central_character': '11.9', 'coeff_info': ['x^5 - 1', '0.309016994374947 + 0.951056516295154*I', '\\\\zeta_{5}'], 'conductor': 11, 'conductor_radical': 11, 'conjugate': 'dirichlet_L_11.5', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^3', 'a^4', 'a^1', 'a^2', 'a^2', 'a^1', 'a^4', 'a^3', 'a^0', 0, 'a^0', 'a^3', 'a^4', 'a^1', 'a^2', 'a^2', 'a^1', 'a^4', 'a^3', 'a^0', 0, 'a^0', 'a^3', 'a^4', 'a^1', 'a^2', 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  26. Lhash: dirichlet_L_12.11
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'values': [[1, '0.760345996300946347531094254881']], 'z1': {'__RealLiteral__': 0, 'data': '3.80462763305', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '6.6922233205', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '8.89059295873', 'prec': 44}}
  27. Lhash: dirichlet_L_13.10
    {'Lhash': 'dirichlet_L_13.10', 'a10': [-0.5, 0.8660254037844386], 'a2': [0.5, -0.8660254037844386], 'a3': [-0.5, 0.8660254037844386], 'a4': [-0.5, -0.8660254037844386], 'a5': [-1.0, -1.4081532572346456e-30], 'a6': [0.5, 0.8660254037844386], 'a7': [0.5, 0.8660254037844386], 'a8': [-1.0, -1.4081532572346456e-30], 'a9': [-0.5, -0.8660254037844386], 'algebraic': True, 'analytic_conductor': 0.06037174619186565, 'analytic_normalization': 0, 'bad_lfactors': [[13, [1]]], 'bad_primes': [13], 'central_character': '13.10', 'coeff_info': ['x^6 - 1', '0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{6}'], 'conductor': 13, 'conductor_radical': 13, 'conjugate': 'dirichlet_L_13.4', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^5', 'a^2', 'a^4', 'a^3', 'a^1', 'a^1', 'a^3', 'a^4', 'a^2', 'a^5', 'a^0', 0, 'a^0', 'a^5', 'a^2', 'a^4', 'a^3', 'a^1', 'a^1', 'a^3', 'a^4', 'a^2', 'a^5', 'a^0', 0, 'a^0', 'a^5', 'a^2', 'a^4', 'a^3', 'a^1', 'a^1', 'a^3', 'a^4', 'a^2', 'a^5', 'a^0', 0, 'a^0', 'a^5', 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  28. Lhash: dirichlet_L_13.11
    {'Lhash': 'dirichlet_L_13.11', 'a10': [0.5, -0.8660254037844386], 'a2': [-0.8660254037844386, -0.5], 'a3': [-0.5, 0.8660254037844386], 'a4': [0.5, 0.8660254037844386], 'a5': [-7.040766286173228e-31, 1.0], 'a6': [0.8660254037844386, -0.5], 'a7': [-0.8660254037844386, 0.5], 'a8': [2.9010907910729803e-30, -1.0], 'a9': [-0.5, -0.8660254037844386], 'algebraic': True, 'analytic_conductor': 1.3970440223301253, 'analytic_normalization': 0, 'bad_lfactors': [[13, [1]]], 'bad_primes': [13], 'central_character': '13.11', 'coeff_info': ['x^12 - 1', '0.866025403784439 + 0.500000000000000*I', '\\\\zeta_{12}'], 'conductor': 13, 'conductor_radical': 13, 'conjugate': 'dirichlet_L_13.6', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^7', 'a^4', 'a^2', 'a^3', 'a^11', 'a^5', 'a^9', 'a^8', 'a^10', 'a^1', 'a^6', 0, 'a^0', 'a^7', 'a^4', 'a^2', 'a^3', 'a^11', 'a^5', 'a^9', 'a^8', 'a^10', 'a^1', 'a^6', 0, 'a^0', 'a^7', 'a^4', 'a^2', 'a^3', 'a^11', 'a^5', 'a^9', 'a^8', 'a^10', 'a^1', 'a^6', 0, 'a^0', 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  29. Lhash: dirichlet_L_13.12
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  30. Lhash: dirichlet_L_13.2
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'prec': 44}}
  31. Lhash: dirichlet_L_13.3
    {'Lhash': 'dirichlet_L_13.3', 'a10': [-0.5, 0.8660254037844386], 'a2': [-0.5, 0.8660254037844386], 'a3': [-0.5, 0.8660254037844386], 'a4': [-0.5, -0.8660254037844386], 'a5': [1.0, 0.0], 'a6': [-0.5, -0.8660254037844386], 'a7': [-0.5, -0.8660254037844386], 'a8': [1.0, 0.0], 'a9': [-0.5, -0.8660254037844386], 'algebraic': True, 'analytic_conductor': 0.06037174619186565, 'analytic_normalization': 0, 'bad_lfactors': [[13, [1]]], 'bad_primes': [13], 'central_character': '13.3', 'coeff_info': ['x^3 - 1', '-0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{3}'], 'conductor': 13, 'conductor_radical': 13, 'conjugate': 'dirichlet_L_13.9', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 'a^1', 'a^2', 'a^0', 'a^2', 'a^2', 'a^0', 'a^2', 'a^1', 'a^1', 'a^0', 0, 'a^0', 'a^1', 'a^1', 'a^2', 'a^0', 'a^2', 'a^2', 'a^0', 'a^2', 'a^1', 'a^1', 'a^0', 0, 'a^0', 'a^1', 'a^1', 'a^2', 'a^0', 'a^2', 'a^2', 'a^0', 'a^2', 'a^1', 'a^1', 'a^0', 0, 'a^0', 'a^1', 'a^1', 'a^2', 'a^0', 'a^2', 'a^2', 'a^0', 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  32. Lhash: dirichlet_L_13.4
    {'Lhash': 'dirichlet_L_13.4', 'a10': [-0.5, -0.8660254037844386], 'a2': [0.5, 0.8660254037844386], 'a3': [-0.5, -0.8660254037844386], 'a4': [-0.5, 0.8660254037844386], 'a5': [-1.0, -1.4081532572346456e-30], 'a6': [0.5, -0.8660254037844386], 'a7': [0.5, -0.8660254037844386], 'a8': [-1.0, -1.4081532572346456e-30], 'a9': [-0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 0.06037174619186565, 'analytic_normalization': 0, 'bad_lfactors': [[13, [1]]], 'bad_primes': [13], 'central_character': '13.4', 'coeff_info': ['x^6 - 1', '0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{6}'], 'conductor': 13, 'conductor_radical': 13, 'conjugate': 'dirichlet_L_13.10', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 'a^4', 'a^2', 'a^3', 'a^5', 'a^5', 'a^3', 'a^2', 'a^4', 'a^1', 'a^0', 0, 'a^0', 'a^1', 'a^4', 'a^2', 'a^3', 'a^5', 'a^5', 'a^3', 'a^2', 'a^4', 'a^1', 'a^0', 0, 'a^0', 'a^1', 'a^4', 'a^2', 'a^3', 'a^5', 'a^5', 'a^3', 'a^2', 'a^4', 'a^1', 'a^0', 0, 'a^0', 'a^1', 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  33. Lhash: dirichlet_L_13.5
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  34. Lhash: dirichlet_L_13.6
    {'Lhash': 'dirichlet_L_13.6', 'a10': [0.5, 0.8660254037844386], 'a2': [-0.8660254037844386, 0.5], 'a3': [-0.5, -0.8660254037844386], 'a4': [0.5, -0.8660254037844386], 'a5': [2.9010907910729803e-30, -1.0], 'a6': [0.8660254037844386, 0.5], 'a7': [-0.8660254037844386, -0.5], 'a8': [-7.040766286173228e-31, 1.0], 'a9': [-0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 1.3970440223301253, 'analytic_normalization': 0, 'bad_lfactors': [[13, [1]]], 'bad_primes': [13], 'central_character': '13.6', 'coeff_info': ['x^12 - 1', '0.866025403784439 + 0.500000000000000*I', '\\\\zeta_{12}'], 'conductor': 13, 'conductor_radical': 13, 'conjugate': 'dirichlet_L_13.11', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^5', 'a^8', 'a^10', 'a^9', 'a^1', 'a^7', 'a^3', 'a^4', 'a^2', 'a^11', 'a^6', 0, 'a^0', 'a^5', 'a^8', 'a^10', 'a^9', 'a^1', 'a^7', 'a^3', 'a^4', 'a^2', 'a^11', 'a^6', 0, 'a^0', 'a^5', 'a^8', 'a^10', 'a^9', 'a^1', 'a^7', 'a^3', 'a^4', 'a^2', 'a^11', 'a^6', 0, 'a^0', 'a^5', 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  35. Lhash: dirichlet_L_13.7
    {'Lhash': 'dirichlet_L_13.7', 'a10': [0.5, 0.8660254037844386], 'a2': [0.8660254037844386, -0.5], 'a3': [-0.5, -0.8660254037844386], 'a4': [0.5, -0.8660254037844386], 'a5': [-7.040766286173228e-31, 1.0], 'a6': [-0.8660254037844386, -0.5], 'a7': [0.8660254037844386, 0.5], 'a8': [2.9010907910729803e-30, -1.0], 'a9': [-0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 1.3970440223301253, 'analytic_normalization': 0, 'bad_lfactors': [[13, [1]]], 'bad_primes': [13], 'central_character': '13.7', 'coeff_info': ['x^12 - 1', '0.866025403784439 + 0.500000000000000*I', '\\\\zeta_{12}'], 'conductor': 13, 'conductor_radical': 13, 'conjugate': 'dirichlet_L_13.2', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^11', 'a^8', 'a^10', 'a^3', 'a^7', 'a^1', 'a^9', 'a^4', 'a^2', 'a^5', 'a^6', 0, 'a^0', 'a^11', 'a^8', 'a^10', 'a^3', 'a^7', 'a^1', 'a^9', 'a^4', 'a^2', 'a^5', 'a^6', 0, 'a^0', 'a^11', 'a^8', 'a^10', 'a^3', 'a^7', 'a^1', 'a^9', 'a^4', 'a^2', 'a^5', 'a^6', 0, 'a^0', 'a^11', 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  36. Lhash: dirichlet_L_13.8
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'198.19371485903139535836624095635', '199.11511286598685180360841483669'], 'prelabel': '1-13-13.8-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3970440223301253, 'root_angle': 0.2032082395472503, 'root_number': '0.289784148688430089716825558519+0.957092026489052849592220722565*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.203208239547', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(4)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.08642943411465667904756436037+0.581439387881469050796952624011*I']], 'z1': {'__RealLiteral__': 0, 'data': '3.74382156415', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '6.72941969669', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '8.20662320146', 'prec': 44}}
  37. Lhash: dirichlet_L_13.9
    {'Lhash': 'dirichlet_L_13.9', 'a10': [-0.5, -0.8660254037844386], 'a2': [-0.5, -0.8660254037844386], 'a3': [-0.5, -0.8660254037844386], 'a4': [-0.5, 0.8660254037844386], 'a5': [1.0, 0.0], 'a6': [-0.5, 0.8660254037844386], 'a7': [-0.5, 0.8660254037844386], 'a8': [1.0, 0.0], 'a9': [-0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 0.06037174619186565, 'analytic_normalization': 0, 'bad_lfactors': [[13, [1]]], 'bad_primes': [13], 'central_character': '13.9', 'coeff_info': ['x^3 - 1', '-0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{3}'], 'conductor': 13, 'conductor_radical': 13, 'conjugate': 'dirichlet_L_13.3', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 'a^2', 'a^1', 'a^0', 'a^1', 'a^1', 'a^0', 'a^1', 'a^2', 'a^2', 'a^0', 0, 'a^0', 'a^2', 'a^2', 'a^1', 'a^0', 'a^1', 'a^1', 'a^0', 'a^1', 'a^2', 'a^2', 'a^0', 0, 'a^0', 'a^2', 'a^2', 'a^1', 'a^0', 'a^1', 'a^1', 'a^0', 'a^1', 'a^2', 'a^2', 'a^0', 0, 'a^0', 'a^2', 'a^2', 'a^1', 'a^0', 'a^1', 'a^1', 'a^0', 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  38. Lhash: dirichlet_L_15.14
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'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r1-0', 'st_group': 'mu(2)', 'symmetry_type': 'orthogonal', 'types': ['DIR'], 'values': [[1, '1.62231147038944475878118430812']], 'z1': {'__RealLiteral__': 0, 'data': '3.05701820981', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '5.34319209368', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '7.26763059827', 'prec': 44}}
  39. Lhash: dirichlet_L_15.2
    {'Lhash': 'dirichlet_L_15.2', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [2.9010907910729803e-30, -1.0], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-1.0, -1.4081532572346456e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-7.040766286173228e-31, 1.0], 'a8': [-7.040766286173228e-31, 1.0], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.06965970714446038, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '15.2', 'coeff_info': ['x^4 - 1', '6.12323399573677e-17 + 1.00000000000000*I', '\\\\zeta_{4}'], 'conductor': 15, 'conductor_radical': 15, 'conjugate': 'dirichlet_L_15.8', 'degree': 1, 'dirichlet_coefficients': [1, '-I', 0, -1, 0, 0, 'I', 'I', 0, 0, -1, 0, '-I', 1, 0, 1, '-I', 0, -1, 0, 0, 'I', 'I', 0, 0, -1, 0, '-I', 1, 0, 1, '-I', 0, -1, 0, 0, 'I', 'I', 0, 0, -1, 0, '-I', 1, 0, 1, '-I', 0, -1, 0, 0, 'I', 'I', 0, 0, -1, 0, '-I', 1, 0, 1, '-I', 0, 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  40. Lhash: dirichlet_L_15.8
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  41. Lhash: dirichlet_L_16.11
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  42. Lhash: dirichlet_L_16.13
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  43. Lhash: dirichlet_L_16.3
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  44. Lhash: dirichlet_L_16.5
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  45. Lhash: dirichlet_L_17.10
    {'Lhash': 'dirichlet_L_17.10', 'a10': [-0.9238795325112867, -0.3826834323650898], 'a2': [-0.7071067811865476, -0.7071067811865476], 'a3': [0.3826834323650898, 0.9238795325112867], 'a4': [-7.040766286173228e-31, 1.0], 'a5': [0.9238795325112867, -0.3826834323650898], 'a6': [0.3826834323650898, -0.9238795325112867], 'a7': [0.9238795325112867, 0.3826834323650898], 'a8': [0.7071067811865476, -0.7071067811865476], 'a9': [-0.7071067811865476, 0.7071067811865476], 'algebraic': True, 'analytic_conductor': 1.8269037215086255, 'analytic_normalization': 0, 'bad_lfactors': [[17, [1]]], 'bad_primes': [17], 'central_character': '17.10', 'coeff_info': ['x^16 - 1', '0.923879532511287 + 0.382683432365090*I', '\\\\zeta_{16}'], 'conductor': 17, 'conductor_radical': 17, 'conjugate': 'dirichlet_L_17.12', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^10', 'a^3', 'a^4', 'a^15', 'a^13', 'a^1', 'a^14', 'a^6', 'a^9', 'a^5', 'a^7', 'a^12', 'a^11', 'a^2', 'a^8', 0, 'a^0', 'a^10', 'a^3', 'a^4', 'a^15', 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  46. Lhash: dirichlet_L_17.11
    {'Lhash': 'dirichlet_L_17.11', 'a10': [-0.3826834323650898, 0.9238795325112867], 'a2': [0.7071067811865476, 0.7071067811865476], 'a3': [-0.9238795325112867, 0.3826834323650898], 'a4': [-7.040766286173228e-31, 1.0], 'a5': [0.3826834323650898, 0.9238795325112867], 'a6': [-0.9238795325112867, -0.3826834323650898], 'a7': [0.3826834323650898, -0.9238795325112867], 'a8': [-0.7071067811865476, 0.7071067811865476], 'a9': [0.7071067811865476, -0.7071067811865476], 'algebraic': True, 'analytic_conductor': 1.8269037215086255, 'analytic_normalization': 0, 'bad_lfactors': [[17, [1]]], 'bad_primes': [17], 'central_character': '17.11', 'coeff_info': ['x^16 - 1', '0.923879532511287 + 0.382683432365090*I', '\\\\zeta_{16}'], 'conductor': 17, 'conductor_radical': 17, 'conjugate': 'dirichlet_L_17.14', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 'a^7', 'a^4', 'a^3', 'a^9', 'a^13', 'a^6', 'a^14', 'a^5', 'a^1', 'a^11', 'a^12', 'a^15', 'a^10', 'a^8', 0, 'a^0', 'a^2', 'a^7', 'a^4', 'a^3', 'a^9', 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  47. Lhash: dirichlet_L_17.12
    {'Lhash': 'dirichlet_L_17.12', 'a10': [-0.9238795325112867, 0.3826834323650898], 'a2': [-0.7071067811865476, 0.7071067811865476], 'a3': [0.3826834323650898, -0.9238795325112867], 'a4': [2.9010907910729803e-30, -1.0], 'a5': [0.9238795325112867, 0.3826834323650898], 'a6': [0.3826834323650898, 0.9238795325112867], 'a7': [0.9238795325112867, -0.3826834323650898], 'a8': [0.7071067811865476, 0.7071067811865476], 'a9': [-0.7071067811865476, -0.7071067811865476], 'algebraic': True, 'analytic_conductor': 1.8269037215086255, 'analytic_normalization': 0, 'bad_lfactors': [[17, [1]]], 'bad_primes': [17], 'central_character': '17.12', 'coeff_info': ['x^16 - 1', '0.923879532511287 + 0.382683432365090*I', '\\\\zeta_{16}'], 'conductor': 17, 'conductor_radical': 17, 'conjugate': 'dirichlet_L_17.10', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^6', 'a^13', 'a^12', 'a^1', 'a^3', 'a^15', 'a^2', 'a^10', 'a^7', 'a^11', 'a^9', 'a^4', 'a^5', 'a^14', 'a^8', 0, 'a^0', 'a^6', 'a^13', 'a^12', 'a^1', 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  48. Lhash: dirichlet_L_17.13
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  49. Lhash: dirichlet_L_17.14
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  50. Lhash: dirichlet_L_17.15
    {'Lhash': 'dirichlet_L_17.15', 'a10': [0.7071067811865476, 0.7071067811865476], 'a2': [-7.040766286173228e-31, 1.0], 'a3': [-0.7071067811865476, 0.7071067811865476], 'a4': [-1.0, -1.4081532572346456e-30], 'a5': [0.7071067811865476, -0.7071067811865476], 'a6': [-0.7071067811865476, -0.7071067811865476], 'a7': [0.7071067811865476, 0.7071067811865476], 'a8': [2.9010907910729803e-30, -1.0], 'a9': [2.9010907910729803e-30, -1.0], 'algebraic': True, 'analytic_conductor': 0.07894766809705508, 'analytic_normalization': 0, 'bad_lfactors': [[17, [1]]], 'bad_primes': [17], 'central_character': '17.15', 'coeff_info': ['x^8 - 1', '0.707106781186548 + 0.707106781186547*I', '\\\\zeta_{8}'], 'conductor': 17, 'conductor_radical': 17, 'conjugate': 'dirichlet_L_17.8', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 'a^3', 'a^4', 'a^7', 'a^5', 'a^1', 'a^6', 'a^6', 'a^1', 'a^5', 'a^7', 'a^4', 'a^3', 'a^2', 'a^0', 0, 'a^0', 'a^2', 'a^3', 'a^4', 'a^7', 'a^5', 'a^1', 'a^6', 'a^6', 'a^1', 'a^5', 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  51. Lhash: dirichlet_L_17.16
    {'Lhash': 'dirichlet_L_17.16', 'a10': [-1.0, 0.0], 'a2': [1.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [-1.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [1.0, 0.0], 'a9': [1.0, 0.0], 'algebraic': True, 'analytic_conductor': 0.07894766809705508, 'analytic_normalization': 0, 'bad_lfactors': [[17, [1]]], 'bad_primes': [17], 'central_character': '17.16', 'coeff_info': ['x^2 - 1', -1, '\\\\zeta_{2}'], 'conductor': 17, 'conductor_radical': 17, 'conjugate': 'dirichlet_L_17.16', 'degree': 1, 'dirichlet_coefficients': [1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 0, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 0, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 0, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 0, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 0, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1], 'euler_factors': [[1, 1], [1, -1], [1, -1], [1, -1], [1, -1], [1, 1], [0], [1, 1], [1, -1], [1, -1], [1, -1], [1, 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  52. Lhash: dirichlet_L_17.2
    {'Lhash': 'dirichlet_L_17.2', 'a10': [-0.7071067811865476, -0.7071067811865476], 'a2': [-7.040766286173228e-31, 1.0], 'a3': [0.7071067811865476, -0.7071067811865476], 'a4': [-1.0, -1.4081532572346456e-30], 'a5': [-0.7071067811865476, 0.7071067811865476], 'a6': [0.7071067811865476, 0.7071067811865476], 'a7': [-0.7071067811865476, -0.7071067811865476], 'a8': [2.9010907910729803e-30, -1.0], 'a9': [2.9010907910729803e-30, -1.0], 'algebraic': True, 'analytic_conductor': 0.07894766809705508, 'analytic_normalization': 0, 'bad_lfactors': [[17, [1]]], 'bad_primes': [17], 'central_character': '17.2', 'coeff_info': ['x^8 - 1', '0.707106781186548 + 0.707106781186547*I', '\\\\zeta_{8}'], 'conductor': 17, 'conductor_radical': 17, 'conjugate': 'dirichlet_L_17.9', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 'a^7', 'a^4', 'a^3', 'a^1', 'a^5', 'a^6', 'a^6', 'a^5', 'a^1', 'a^3', 'a^4', 'a^7', 'a^2', 'a^0', 0, 'a^0', 'a^2', 'a^7', 'a^4', 'a^3', 'a^1', 'a^5', 'a^6', 'a^6', 'a^5', 'a^1', 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'0.739231464122773942105610997581+0.673451440306500482026900033760*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.117594474455', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(8)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.841281955743987032790172479875+0.260792083785577046009769093647*I']], 'z1': {'__RealLiteral__': 0, 'data': '3.73234531397', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '6.76194832104', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '7.64497211191', 'prec': 44}}
  53. Lhash: dirichlet_L_17.3
    {'Lhash': 'dirichlet_L_17.3', 'a10': [0.3826834323650898, 0.9238795325112867], 'a2': [0.7071067811865476, -0.7071067811865476], 'a3': [0.9238795325112867, 0.3826834323650898], 'a4': [2.9010907910729803e-30, -1.0], 'a5': [-0.3826834323650898, 0.9238795325112867], 'a6': [0.9238795325112867, -0.3826834323650898], 'a7': [-0.3826834323650898, -0.9238795325112867], 'a8': [-0.7071067811865476, -0.7071067811865476], 'a9': [0.7071067811865476, 0.7071067811865476], 'algebraic': True, 'analytic_conductor': 1.8269037215086255, 'analytic_normalization': 0, 'bad_lfactors': [[17, [1]]], 'bad_primes': [17], 'central_character': '17.3', 'coeff_info': ['x^16 - 1', '0.923879532511287 + 0.382683432365090*I', '\\\\zeta_{16}'], 'conductor': 17, 'conductor_radical': 17, 'conjugate': 'dirichlet_L_17.6', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^14', 'a^1', 'a^12', 'a^5', 'a^15', 'a^11', 'a^10', 'a^2', 'a^3', 'a^7', 'a^13', 'a^4', 'a^9', 'a^6', 'a^8', 0, 'a^0', 'a^14', 'a^1', 'a^12', 'a^5', 'a^15', 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  54. Lhash: dirichlet_L_17.4
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'prec': 44}}
  55. Lhash: dirichlet_L_17.5
    {'Lhash': 'dirichlet_L_17.5', 'a10': [0.9238795325112867, -0.3826834323650898], 'a2': [-0.7071067811865476, 0.7071067811865476], 'a3': [-0.3826834323650898, 0.9238795325112867], 'a4': [2.9010907910729803e-30, -1.0], 'a5': [-0.9238795325112867, -0.3826834323650898], 'a6': [-0.3826834323650898, -0.9238795325112867], 'a7': [-0.9238795325112867, 0.3826834323650898], 'a8': [0.7071067811865476, 0.7071067811865476], 'a9': [-0.7071067811865476, -0.7071067811865476], 'algebraic': True, 'analytic_conductor': 1.8269037215086255, 'analytic_normalization': 0, 'bad_lfactors': [[17, [1]]], 'bad_primes': [17], 'central_character': '17.5', 'coeff_info': ['x^16 - 1', '0.923879532511287 + 0.382683432365090*I', '\\\\zeta_{16}'], 'conductor': 17, 'conductor_radical': 17, 'conjugate': 'dirichlet_L_17.7', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^6', 'a^5', 'a^12', 'a^9', 'a^11', 'a^7', 'a^2', 'a^10', 'a^15', 'a^3', 'a^1', 'a^4', 'a^13', 'a^14', 'a^8', 0, 'a^0', 'a^6', 'a^5', 'a^12', 'a^9', 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  56. Lhash: dirichlet_L_17.6
    {'Lhash': 'dirichlet_L_17.6', 'a10': [0.3826834323650898, -0.9238795325112867], 'a2': [0.7071067811865476, 0.7071067811865476], 'a3': [0.9238795325112867, -0.3826834323650898], 'a4': [-7.040766286173228e-31, 1.0], 'a5': [-0.3826834323650898, -0.9238795325112867], 'a6': [0.9238795325112867, 0.3826834323650898], 'a7': [-0.3826834323650898, 0.9238795325112867], 'a8': [-0.7071067811865476, 0.7071067811865476], 'a9': [0.7071067811865476, -0.7071067811865476], 'algebraic': True, 'analytic_conductor': 1.8269037215086255, 'analytic_normalization': 0, 'bad_lfactors': [[17, [1]]], 'bad_primes': [17], 'central_character': '17.6', 'coeff_info': ['x^16 - 1', '0.923879532511287 + 0.382683432365090*I', '\\\\zeta_{16}'], 'conductor': 17, 'conductor_radical': 17, 'conjugate': 'dirichlet_L_17.3', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 'a^15', 'a^4', 'a^11', 'a^1', 'a^5', 'a^6', 'a^14', 'a^13', 'a^9', 'a^3', 'a^12', 'a^7', 'a^10', 'a^8', 0, 'a^0', 'a^2', 'a^15', 'a^4', 'a^11', 'a^1', 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  57. Lhash: dirichlet_L_17.7
    {'Lhash': 'dirichlet_L_17.7', 'a10': [0.9238795325112867, 0.3826834323650898], 'a2': [-0.7071067811865476, -0.7071067811865476], 'a3': [-0.3826834323650898, -0.9238795325112867], 'a4': [-7.040766286173228e-31, 1.0], 'a5': [-0.9238795325112867, 0.3826834323650898], 'a6': [-0.3826834323650898, 0.9238795325112867], 'a7': [-0.9238795325112867, -0.3826834323650898], 'a8': [0.7071067811865476, -0.7071067811865476], 'a9': [-0.7071067811865476, 0.7071067811865476], 'algebraic': True, 'analytic_conductor': 1.8269037215086255, 'analytic_normalization': 0, 'bad_lfactors': [[17, [1]]], 'bad_primes': [17], 'central_character': '17.7', 'coeff_info': ['x^16 - 1', '0.923879532511287 + 0.382683432365090*I', '\\\\zeta_{16}'], 'conductor': 17, 'conductor_radical': 17, 'conjugate': 'dirichlet_L_17.5', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^10', 'a^11', 'a^4', 'a^7', 'a^5', 'a^9', 'a^14', 'a^6', 'a^1', 'a^13', 'a^15', 'a^12', 'a^3', 'a^2', 'a^8', 0, 'a^0', 'a^10', 'a^11', 'a^4', 'a^7', 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  58. Lhash: dirichlet_L_17.8
    {'Lhash': 'dirichlet_L_17.8', 'a10': [0.7071067811865476, -0.7071067811865476], 'a2': [2.9010907910729803e-30, -1.0], 'a3': [-0.7071067811865476, -0.7071067811865476], 'a4': [-1.0, -1.4081532572346456e-30], 'a5': [0.7071067811865476, 0.7071067811865476], 'a6': [-0.7071067811865476, 0.7071067811865476], 'a7': [0.7071067811865476, -0.7071067811865476], 'a8': [-7.040766286173228e-31, 1.0], 'a9': [-7.040766286173228e-31, 1.0], 'algebraic': True, 'analytic_conductor': 0.07894766809705508, 'analytic_normalization': 0, 'bad_lfactors': [[17, [1]]], 'bad_primes': [17], 'central_character': '17.8', 'coeff_info': ['x^8 - 1', '0.707106781186548 + 0.707106781186547*I', '\\\\zeta_{8}'], 'conductor': 17, 'conductor_radical': 17, 'conjugate': 'dirichlet_L_17.15', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^6', 'a^5', 'a^4', 'a^1', 'a^3', 'a^7', 'a^2', 'a^2', 'a^7', 'a^3', 'a^1', 'a^4', 'a^5', 'a^6', 'a^0', 0, 'a^0', 'a^6', 'a^5', 'a^4', 'a^1', 'a^3', 'a^7', 'a^2', 'a^2', 'a^7', 'a^3', 'a^1', 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False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.23791074295', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(8)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.643250420835616101901074299374-0.415264723150863021988467960630*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.12217010146', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '5.0751153081', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '7.40782305439', 'prec': 44}}
  59. Lhash: dirichlet_L_17.9
    {'Lhash': 'dirichlet_L_17.9', 'a10': [-0.7071067811865476, 0.7071067811865476], 'a2': [2.9010907910729803e-30, -1.0], 'a3': [0.7071067811865476, 0.7071067811865476], 'a4': [-1.0, -1.4081532572346456e-30], 'a5': [-0.7071067811865476, -0.7071067811865476], 'a6': [0.7071067811865476, -0.7071067811865476], 'a7': [-0.7071067811865476, 0.7071067811865476], 'a8': [-7.040766286173228e-31, 1.0], 'a9': [-7.040766286173228e-31, 1.0], 'algebraic': True, 'analytic_conductor': 0.07894766809705508, 'analytic_normalization': 0, 'bad_lfactors': [[17, [1]]], 'bad_primes': [17], 'central_character': '17.9', 'coeff_info': ['x^8 - 1', '0.707106781186548 + 0.707106781186547*I', '\\\\zeta_{8}'], 'conductor': 17, 'conductor_radical': 17, 'conjugate': 'dirichlet_L_17.2', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^6', 'a^1', 'a^4', 'a^5', 'a^7', 'a^3', 'a^2', 'a^2', 'a^3', 'a^7', 'a^5', 'a^4', 'a^1', 'a^6', 'a^0', 0, 'a^0', 'a^6', 'a^1', 'a^4', 'a^5', 'a^7', 'a^3', 'a^2', 'a^2', 'a^3', 'a^7', 'a^5', 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  60. Lhash: dirichlet_L_19.10
    {'Lhash': 'dirichlet_L_19.10', 'a10': [0.9396926207859084, 0.3420201433256687], 'a2': [0.9396926207859084, -0.3420201433256687], 'a3': [-0.17364817766693036, 0.984807753012208], 'a4': [0.766044443118978, -0.6427876096865394], 'a5': [0.766044443118978, 0.6427876096865394], 'a6': [0.17364817766693036, 0.984807753012208], 'a7': [-0.5, -0.8660254037844386], 'a8': [0.5, -0.8660254037844386], 'a9': [-0.9396926207859084, -0.3420201433256687], 'algebraic': True, 'analytic_conductor': 2.041833571097875, 'analytic_normalization': 0, 'bad_lfactors': [[19, [1]]], 'bad_primes': [19], 'central_character': '19.10', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 19, 'conductor_radical': 19, 'conjugate': 'dirichlet_L_19.2', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^17', 'a^5', 'a^16', 'a^2', 'a^4', 'a^12', 'a^15', 'a^10', 'a^1', 'a^6', 'a^3', 'a^13', 'a^11', 'a^7', 'a^14', 'a^8', 'a^9', 0, 'a^0', 'a^17', 'a^5', 'a^16', 'a^2', 'a^4', 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'primitive': True, 'rational': False, 'root_analytic_conductor': 2.041833571097875, 'root_angle': 0.03146498178057028, 'root_number': '0.980520863497139550773243924705+0.196414959325464383126995692959*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0314649817806', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(18)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.66030163405372700266314201338+0.100076902141050771789623093101*I']], 'z1': {'__RealLiteral__': 0, 'data': '3.00729064822', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.84402088245', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '6.60288566905', 'prec': 44}}
  61. Lhash: dirichlet_L_19.11
    {'Lhash': 'dirichlet_L_19.11', 'a10': [-0.5, 0.8660254037844386], 'a2': [-0.5, -0.8660254037844386], 'a3': [-0.5, -0.8660254037844386], 'a4': [-0.5, 0.8660254037844386], 'a5': [-0.5, -0.8660254037844386], 'a6': [-0.5, 0.8660254037844386], 'a7': [1.0, 0.0], 'a8': [1.0, 0.0], 'a9': [-0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 0.08823562904964981, 'analytic_normalization': 0, 'bad_lfactors': [[19, [1]]], 'bad_primes': [19], 'central_character': '19.11', 'coeff_info': ['x^3 - 1', '-0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{3}'], 'conductor': 19, 'conductor_radical': 19, 'conjugate': 'dirichlet_L_19.7', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 'a^2', 'a^1', 'a^2', 'a^1', 'a^0', 'a^0', 'a^1', 'a^1', 'a^0', 'a^0', 'a^1', 'a^2', 'a^1', 'a^2', 'a^2', 'a^0', 0, 'a^0', 'a^2', 'a^2', 'a^1', 'a^2', 'a^1', 'a^0', 'a^0', 'a^1', 'a^1', 'a^0', 'a^0', 'a^1', 'a^2', 'a^1', 'a^2', 'a^2', 'a^0', 0, 'a^0', 'a^2', 'a^2', 'a^1', 'a^2', 'a^1', 'a^0', 'a^0', 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  62. Lhash: dirichlet_L_19.12
    {'Lhash': 'dirichlet_L_19.12', 'a10': [0.5, 0.8660254037844386], 'a2': [0.5, -0.8660254037844386], 'a3': [0.5, -0.8660254037844386], 'a4': [-0.5, -0.8660254037844386], 'a5': [-0.5, 0.8660254037844386], 'a6': [-0.5, -0.8660254037844386], 'a7': [1.0, 0.0], 'a8': [-1.0, -1.4081532572346456e-30], 'a9': [-0.5, -0.8660254037844386], 'algebraic': True, 'analytic_conductor': 2.041833571097875, 'analytic_normalization': 0, 'bad_lfactors': [[19, [1]]], 'bad_primes': [19], 'central_character': '19.12', 'coeff_info': ['x^6 - 1', '0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{6}'], 'conductor': 19, 'conductor_radical': 19, 'conjugate': 'dirichlet_L_19.8', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^5', 'a^5', 'a^4', 'a^2', 'a^4', 'a^0', 'a^3', 'a^4', 'a^1', 'a^0', 'a^3', 'a^1', 'a^5', 'a^1', 'a^2', 'a^2', 'a^3', 0, 'a^0', 'a^5', 'a^5', 'a^4', 'a^2', 'a^4', 'a^0', 'a^3', 'a^4', 'a^1', 'a^0', 'a^3', 'a^1', 'a^5', 'a^1', 'a^2', 'a^2', 'a^3', 0, 'a^0', 'a^5', 'a^5', 'a^4', 'a^2', 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  63. Lhash: dirichlet_L_19.13
    {'Lhash': 'dirichlet_L_19.13', 'a10': [-0.17364817766693036, -0.984807753012208], 'a2': [-0.17364817766693036, 0.984807753012208], 'a3': [-0.766044443118978, -0.6427876096865394], 'a4': [-0.9396926207859084, -0.3420201433256687], 'a5': [-0.9396926207859084, 0.3420201433256687], 'a6': [0.766044443118978, -0.6427876096865394], 'a7': [-0.5, -0.8660254037844386], 'a8': [0.5, -0.8660254037844386], 'a9': [0.17364817766693036, 0.984807753012208], 'algebraic': True, 'analytic_conductor': 2.041833571097875, 'analytic_normalization': 0, 'bad_lfactors': [[19, [1]]], 'bad_primes': [19], 'central_character': '19.13', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 19, 'conductor_radical': 19, 'conjugate': 'dirichlet_L_19.3', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^5', 'a^11', 'a^10', 'a^8', 'a^16', 'a^12', 'a^15', 'a^4', 'a^13', 'a^6', 'a^3', 'a^7', 'a^17', 'a^1', 'a^2', 'a^14', 'a^9', 0, 'a^0', 'a^5', 'a^11', 'a^10', 'a^8', 'a^16', 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'root_analytic_conductor': 2.041833571097875, 'root_angle': -0.38899276984789244, 'root_number': '-0.766463829517328185219963421674-0.642287473053641359390848193070*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.388992769848', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(18)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.400326194371313102047970018124+0.102312042792546814972428256028*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.0189563990802', 'prec': 50}, 'z2': {'__RealLiteral__': 0, 'data': '4.62408465986', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '6.80199131142', 'prec': 44}}
  64. Lhash: dirichlet_L_19.14
    {'Lhash': 'dirichlet_L_19.14', 'a10': [-0.766044443118978, -0.6427876096865394], 'a2': [-0.766044443118978, 0.6427876096865394], 'a3': [0.9396926207859084, 0.3420201433256687], 'a4': [0.17364817766693036, -0.984807753012208], 'a5': [0.17364817766693036, 0.984807753012208], 'a6': [-0.9396926207859084, 0.3420201433256687], 'a7': [-0.5, 0.8660254037844386], 'a8': [0.5, 0.8660254037844386], 'a9': [0.766044443118978, 0.6427876096865394], 'algebraic': True, 'analytic_conductor': 2.041833571097875, 'analytic_normalization': 0, 'bad_lfactors': [[19, [1]]], 'bad_primes': [19], 'central_character': '19.14', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 19, 'conductor_radical': 19, 'conjugate': 'dirichlet_L_19.15', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^7', 'a^1', 'a^14', 'a^4', 'a^8', 'a^6', 'a^3', 'a^2', 'a^11', 'a^12', 'a^15', 'a^17', 'a^13', 'a^5', 'a^10', 'a^16', 'a^9', 0, 'a^0', 'a^7', 'a^1', 'a^14', 'a^4', 'a^8', 'a^6', 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  65. Lhash: dirichlet_L_19.15
    {'Lhash': 'dirichlet_L_19.15', 'a10': [-0.766044443118978, 0.6427876096865394], 'a2': [-0.766044443118978, -0.6427876096865394], 'a3': [0.9396926207859084, -0.3420201433256687], 'a4': [0.17364817766693036, 0.984807753012208], 'a5': [0.17364817766693036, -0.984807753012208], 'a6': [-0.9396926207859084, -0.3420201433256687], 'a7': [-0.5, -0.8660254037844386], 'a8': [0.5, -0.8660254037844386], 'a9': [0.766044443118978, -0.6427876096865394], 'algebraic': True, 'analytic_conductor': 2.041833571097875, 'analytic_normalization': 0, 'bad_lfactors': [[19, [1]]], 'bad_primes': [19], 'central_character': '19.15', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 19, 'conductor_radical': 19, 'conjugate': 'dirichlet_L_19.14', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^11', 'a^17', 'a^4', 'a^14', 'a^10', 'a^12', 'a^15', 'a^16', 'a^7', 'a^6', 'a^3', 'a^1', 'a^5', 'a^13', 'a^8', 'a^2', 'a^9', 0, 'a^0', 'a^11', 'a^17', 'a^4', 'a^14', 'a^10', 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  66. Lhash: dirichlet_L_19.16
    {'Lhash': 'dirichlet_L_19.16', 'a10': [0.17364817766693036, -0.984807753012208], 'a2': [0.17364817766693036, 0.984807753012208], 'a3': [0.766044443118978, -0.6427876096865394], 'a4': [-0.9396926207859084, 0.3420201433256687], 'a5': [-0.9396926207859084, -0.3420201433256687], 'a6': [0.766044443118978, 0.6427876096865394], 'a7': [-0.5, 0.8660254037844386], 'a8': [-0.5, -0.8660254037844386], 'a9': [0.17364817766693036, -0.984807753012208], 'algebraic': True, 'analytic_conductor': 0.08823562904964981, 'analytic_normalization': 0, 'bad_lfactors': [[19, [1]]], 'bad_primes': [19], 'central_character': '19.16', 'coeff_info': ['x^9 - 1', '0.766044443118978 + 0.642787609686539*I', '\\\\zeta_{9}'], 'conductor': 19, 'conductor_radical': 19, 'conjugate': 'dirichlet_L_19.6', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 'a^8', 'a^4', 'a^5', 'a^1', 'a^3', 'a^6', 'a^7', 'a^7', 'a^6', 'a^3', 'a^1', 'a^5', 'a^4', 'a^8', 'a^2', 'a^0', 0, 'a^0', 'a^2', 'a^8', 'a^4', 'a^5', 'a^1', 'a^3', 'a^6', 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  67. Lhash: dirichlet_L_19.17
    {'Lhash': 'dirichlet_L_19.17', 'a10': [-0.9396926207859084, 0.3420201433256687], 'a2': [-0.9396926207859084, -0.3420201433256687], 'a3': [0.17364817766693036, 0.984807753012208], 'a4': [0.766044443118978, 0.6427876096865394], 'a5': [0.766044443118978, -0.6427876096865394], 'a6': [0.17364817766693036, -0.984807753012208], 'a7': [-0.5, 0.8660254037844386], 'a8': [-0.5, -0.8660254037844386], 'a9': [-0.9396926207859084, 0.3420201433256687], 'algebraic': True, 'analytic_conductor': 0.08823562904964981, 'analytic_normalization': 0, 'bad_lfactors': [[19, [1]]], 'bad_primes': [19], 'central_character': '19.17', 'coeff_info': ['x^9 - 1', '0.766044443118978 + 0.642787609686539*I', '\\\\zeta_{9}'], 'conductor': 19, 'conductor_radical': 19, 'conjugate': 'dirichlet_L_19.9', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^5', 'a^2', 'a^1', 'a^8', 'a^7', 'a^3', 'a^6', 'a^4', 'a^4', 'a^6', 'a^3', 'a^7', 'a^8', 'a^1', 'a^2', 'a^5', 'a^0', 0, 'a^0', 'a^5', 'a^2', 'a^1', 'a^8', 'a^7', 'a^3', 'a^6', 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'root_analytic_conductor': 0.08823562904964981, 'root_angle': 0.05304001234598393, 'root_number': '0.944980864034573771287316164987+0.327125612889713054142581920436*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.053040012346', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(9)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.680620362658866176300685916428+0.0715457394267178453903388447671*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.87454712438', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '5.65645229757', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '8.56898944616', 'prec': 44}}
  68. Lhash: dirichlet_L_19.18
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  69. Lhash: dirichlet_L_19.2
    {'Lhash': 'dirichlet_L_19.2', 'a10': [0.9396926207859084, -0.3420201433256687], 'a2': [0.9396926207859084, 0.3420201433256687], 'a3': [-0.17364817766693036, -0.984807753012208], 'a4': [0.766044443118978, 0.6427876096865394], 'a5': [0.766044443118978, -0.6427876096865394], 'a6': [0.17364817766693036, -0.984807753012208], 'a7': [-0.5, 0.8660254037844386], 'a8': [0.5, 0.8660254037844386], 'a9': [-0.9396926207859084, 0.3420201433256687], 'algebraic': True, 'analytic_conductor': 2.041833571097875, 'analytic_normalization': 0, 'bad_lfactors': [[19, [1]]], 'bad_primes': [19], 'central_character': '19.2', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 19, 'conductor_radical': 19, 'conjugate': 'dirichlet_L_19.10', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 'a^13', 'a^2', 'a^16', 'a^14', 'a^6', 'a^3', 'a^8', 'a^17', 'a^12', 'a^15', 'a^5', 'a^7', 'a^11', 'a^4', 'a^10', 'a^9', 0, 'a^0', 'a^1', 'a^13', 'a^2', 'a^16', 'a^14', 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  70. Lhash: dirichlet_L_19.3
    {'Lhash': 'dirichlet_L_19.3', 'a10': [-0.17364817766693036, 0.984807753012208], 'a2': [-0.17364817766693036, -0.984807753012208], 'a3': [-0.766044443118978, 0.6427876096865394], 'a4': [-0.9396926207859084, 0.3420201433256687], 'a5': [-0.9396926207859084, -0.3420201433256687], 'a6': [0.766044443118978, 0.6427876096865394], 'a7': [-0.5, 0.8660254037844386], 'a8': [0.5, 0.8660254037844386], 'a9': [0.17364817766693036, -0.984807753012208], 'algebraic': True, 'analytic_conductor': 2.041833571097875, 'analytic_normalization': 0, 'bad_lfactors': [[19, [1]]], 'bad_primes': [19], 'central_character': '19.3', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 19, 'conductor_radical': 19, 'conjugate': 'dirichlet_L_19.13', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^13', 'a^7', 'a^8', 'a^10', 'a^2', 'a^6', 'a^3', 'a^14', 'a^5', 'a^12', 'a^15', 'a^11', 'a^1', 'a^17', 'a^16', 'a^4', 'a^9', 0, 'a^0', 'a^13', 'a^7', 'a^8', 'a^10', 'a^2', 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  71. Lhash: dirichlet_L_19.4
    {'Lhash': 'dirichlet_L_19.4', 'a10': [0.766044443118978, -0.6427876096865394], 'a2': [0.766044443118978, 0.6427876096865394], 'a3': [-0.9396926207859084, 0.3420201433256687], 'a4': [0.17364817766693036, 0.984807753012208], 'a5': [0.17364817766693036, -0.984807753012208], 'a6': [-0.9396926207859084, -0.3420201433256687], 'a7': [-0.5, -0.8660254037844386], 'a8': [-0.5, 0.8660254037844386], 'a9': [0.766044443118978, -0.6427876096865394], 'algebraic': True, 'analytic_conductor': 0.08823562904964981, 'analytic_normalization': 0, 'bad_lfactors': [[19, [1]]], 'bad_primes': [19], 'central_character': '19.4', 'coeff_info': ['x^9 - 1', '0.766044443118978 + 0.642787609686539*I', '\\\\zeta_{9}'], 'conductor': 19, 'conductor_radical': 19, 'conjugate': 'dirichlet_L_19.5', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 'a^4', 'a^2', 'a^7', 'a^5', 'a^6', 'a^3', 'a^8', 'a^8', 'a^3', 'a^6', 'a^5', 'a^7', 'a^2', 'a^4', 'a^1', 'a^0', 0, 'a^0', 'a^1', 'a^4', 'a^2', 'a^7', 'a^5', 'a^6', 'a^3', 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  72. Lhash: dirichlet_L_19.5
    {'Lhash': 'dirichlet_L_19.5', 'a10': [0.766044443118978, 0.6427876096865394], 'a2': [0.766044443118978, -0.6427876096865394], 'a3': [-0.9396926207859084, -0.3420201433256687], 'a4': [0.17364817766693036, -0.984807753012208], 'a5': [0.17364817766693036, 0.984807753012208], 'a6': [-0.9396926207859084, 0.3420201433256687], 'a7': [-0.5, 0.8660254037844386], 'a8': [-0.5, -0.8660254037844386], 'a9': [0.766044443118978, 0.6427876096865394], 'algebraic': True, 'analytic_conductor': 0.08823562904964981, 'analytic_normalization': 0, 'bad_lfactors': [[19, [1]]], 'bad_primes': [19], 'central_character': '19.5', 'coeff_info': ['x^9 - 1', '0.766044443118978 + 0.642787609686539*I', '\\\\zeta_{9}'], 'conductor': 19, 'conductor_radical': 19, 'conjugate': 'dirichlet_L_19.4', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^8', 'a^5', 'a^7', 'a^2', 'a^4', 'a^3', 'a^6', 'a^1', 'a^1', 'a^6', 'a^3', 'a^4', 'a^2', 'a^7', 'a^5', 'a^8', 'a^0', 0, 'a^0', 'a^8', 'a^5', 'a^7', 'a^2', 'a^4', 'a^3', 'a^6', 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  73. Lhash: dirichlet_L_19.6
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  74. Lhash: dirichlet_L_19.7
    {'Lhash': 'dirichlet_L_19.7', 'a10': [-0.5, -0.8660254037844386], 'a2': [-0.5, 0.8660254037844386], 'a3': [-0.5, 0.8660254037844386], 'a4': [-0.5, -0.8660254037844386], 'a5': [-0.5, 0.8660254037844386], 'a6': [-0.5, -0.8660254037844386], 'a7': [1.0, 0.0], 'a8': [1.0, 0.0], 'a9': [-0.5, -0.8660254037844386], 'algebraic': True, 'analytic_conductor': 0.08823562904964981, 'analytic_normalization': 0, 'bad_lfactors': [[19, [1]]], 'bad_primes': [19], 'central_character': '19.7', 'coeff_info': ['x^3 - 1', '-0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{3}'], 'conductor': 19, 'conductor_radical': 19, 'conjugate': 'dirichlet_L_19.11', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 'a^1', 'a^2', 'a^1', 'a^2', 'a^0', 'a^0', 'a^2', 'a^2', 'a^0', 'a^0', 'a^2', 'a^1', 'a^2', 'a^1', 'a^1', 'a^0', 0, 'a^0', 'a^1', 'a^1', 'a^2', 'a^1', 'a^2', 'a^0', 'a^0', 'a^2', 'a^2', 'a^0', 'a^0', 'a^2', 'a^1', 'a^2', 'a^1', 'a^1', 'a^0', 0, 'a^0', 'a^1', 'a^1', 'a^2', 'a^1', 'a^2', 'a^0', 'a^0', 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  75. Lhash: dirichlet_L_19.8
    {'Lhash': 'dirichlet_L_19.8', 'a10': [0.5, -0.8660254037844386], 'a2': [0.5, 0.8660254037844386], 'a3': [0.5, 0.8660254037844386], 'a4': [-0.5, 0.8660254037844386], 'a5': [-0.5, -0.8660254037844386], 'a6': [-0.5, 0.8660254037844386], 'a7': [1.0, 0.0], 'a8': [-1.0, -1.4081532572346456e-30], 'a9': [-0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 2.041833571097875, 'analytic_normalization': 0, 'bad_lfactors': [[19, [1]]], 'bad_primes': [19], 'central_character': '19.8', 'coeff_info': ['x^6 - 1', '0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{6}'], 'conductor': 19, 'conductor_radical': 19, 'conjugate': 'dirichlet_L_19.12', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 'a^1', 'a^2', 'a^4', 'a^2', 'a^0', 'a^3', 'a^2', 'a^5', 'a^0', 'a^3', 'a^5', 'a^1', 'a^5', 'a^4', 'a^4', 'a^3', 0, 'a^0', 'a^1', 'a^1', 'a^2', 'a^4', 'a^2', 'a^0', 'a^3', 'a^2', 'a^5', 'a^0', 'a^3', 'a^5', 'a^1', 'a^5', 'a^4', 'a^4', 'a^3', 0, 'a^0', 'a^1', 'a^1', 'a^2', 'a^4', 'a^2', 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'sign_arg': {'__RealLiteral__': 0, 'data': '0.265580045271', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(6)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.17192436792164327728158615579+0.839288227447743058988005529230*I']], 'z1': {'__RealLiteral__': 0, 'data': '3.92233777169', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '5.21098682124', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '7.91237680847', 'prec': 44}}
  76. Lhash: dirichlet_L_19.9
    {'Lhash': 'dirichlet_L_19.9', 'a10': [-0.9396926207859084, -0.3420201433256687], 'a2': [-0.9396926207859084, 0.3420201433256687], 'a3': [0.17364817766693036, -0.984807753012208], 'a4': [0.766044443118978, -0.6427876096865394], 'a5': [0.766044443118978, 0.6427876096865394], 'a6': [0.17364817766693036, 0.984807753012208], 'a7': [-0.5, -0.8660254037844386], 'a8': [-0.5, 0.8660254037844386], 'a9': [-0.9396926207859084, -0.3420201433256687], 'algebraic': True, 'analytic_conductor': 0.08823562904964981, 'analytic_normalization': 0, 'bad_lfactors': [[19, [1]]], 'bad_primes': [19], 'central_character': '19.9', 'coeff_info': ['x^9 - 1', '0.766044443118978 + 0.642787609686539*I', '\\\\zeta_{9}'], 'conductor': 19, 'conductor_radical': 19, 'conjugate': 'dirichlet_L_19.17', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^4', 'a^7', 'a^8', 'a^1', 'a^2', 'a^6', 'a^3', 'a^5', 'a^5', 'a^3', 'a^6', 'a^2', 'a^1', 'a^8', 'a^7', 'a^4', 'a^0', 0, 'a^0', 'a^4', 'a^7', 'a^8', 'a^1', 'a^2', 'a^6', 'a^3', 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  77. Lhash: dirichlet_L_20.19
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  78. Lhash: dirichlet_L_20.3
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  79. Lhash: dirichlet_L_20.7
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  80. Lhash: dirichlet_L_21.11
    {'Lhash': 'dirichlet_L_21.11', 'a10': [-0.5, -0.8660254037844386], 'a2': [0.5, -0.8660254037844386], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.5, -0.8660254037844386], 'a5': [0.5, -0.8660254037844386], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-1.0, -1.4081532572346456e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 2.2567634206871254, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '21.11', 'coeff_info': ['x^6 - 1', '0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{6}'], 'conductor': 21, 'conductor_radical': 21, 'conjugate': 'dirichlet_L_21.2', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^5', 0, 'a^4', 'a^5', 0, 0, 'a^3', 0, 'a^4', 'a^1', 0, 'a^0', 0, 0, 'a^2', 'a^1', 0, 'a^2', 'a^3', 0, 'a^0', 'a^5', 0, 'a^4', 'a^5', 0, 0, 'a^3', 0, 'a^4', 'a^1', 0, 'a^0', 0, 0, 'a^2', 'a^1', 0, 'a^2', 'a^3', 0, 'a^0', 'a^5', 0, 'a^4', 'a^5', 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  81. Lhash: dirichlet_L_21.17
    {'Lhash': 'dirichlet_L_21.17', 'a10': [0.5, 0.8660254037844386], 'a2': [0.5, -0.8660254037844386], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.5, -0.8660254037844386], 'a5': [-0.5, 0.8660254037844386], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-1.0, -1.4081532572346456e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.09752359000224452, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '21.17', 'coeff_info': ['x^6 - 1', '0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{6}'], 'conductor': 21, 'conductor_radical': 21, 'conjugate': 'dirichlet_L_21.5', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^5', 0, 'a^4', 'a^2', 0, 0, 'a^3', 0, 'a^1', 'a^1', 0, 'a^3', 0, 0, 'a^2', 'a^4', 0, 'a^5', 'a^0', 0, 'a^0', 'a^5', 0, 'a^4', 'a^2', 0, 0, 'a^3', 0, 'a^1', 'a^1', 0, 'a^3', 0, 0, 'a^2', 'a^4', 0, 'a^5', 'a^0', 0, 'a^0', 'a^5', 0, 'a^4', 'a^2', 0, 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'data': '-0.146493713613', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(6)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.942430974157879462078946272271-0.360288869024044637674538393052*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.71366105453', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.61676697612', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '6.9630516643', 'prec': 40}}
  82. Lhash: dirichlet_L_21.2
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'spectral_label': 'r1-0', 'st_group': 'mu(6)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.14160874207759529299007116354+0.759377460712757134429918720611*I']], 'z1': {'__RealLiteral__': 0, 'data': '3.3812379813', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '5.70086521678', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '7.08050476258', 'prec': 44}}
  83. Lhash: dirichlet_L_21.20
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  84. Lhash: dirichlet_L_21.5
    {'Lhash': 'dirichlet_L_21.5', 'a10': [0.5, -0.8660254037844386], 'a2': [0.5, 0.8660254037844386], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.5, 0.8660254037844386], 'a5': [-0.5, -0.8660254037844386], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-1.0, -1.4081532572346456e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.09752359000224452, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '21.5', 'coeff_info': ['x^6 - 1', '0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{6}'], 'conductor': 21, 'conductor_radical': 21, 'conjugate': 'dirichlet_L_21.17', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 0, 'a^2', 'a^4', 0, 0, 'a^3', 0, 'a^5', 'a^5', 0, 'a^3', 0, 0, 'a^4', 'a^2', 0, 'a^1', 'a^0', 0, 'a^0', 'a^1', 0, 'a^2', 'a^4', 0, 0, 'a^3', 0, 'a^5', 'a^5', 0, 'a^3', 0, 0, 'a^4', 'a^2', 0, 'a^1', 'a^0', 0, 'a^0', 'a^1', 0, 'a^2', 'a^4', 0, 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  85. Lhash: dirichlet_L_23.10
    {'Lhash': 'dirichlet_L_23.10', 'a10': [-0.8412535328311812, 0.5406408174555976], 'a2': [-0.14231483827328514, 0.9898214418809327], 'a3': [0.41541501300188644, 0.9096319953545183], 'a4': [-0.9594929736144974, -0.28173255684142967], 'a5': [0.6548607339452851, 0.7557495743542583], 'a6': [-0.9594929736144974, 0.28173255684142967], 'a7': [-0.8412535328311812, -0.5406408174555976], 'a8': [0.41541501300188644, -0.9096319953545183], 'a9': [-0.6548607339452851, 0.7557495743542583], 'algebraic': True, 'analytic_conductor': 2.4716932702763756, 'analytic_normalization': 0, 'bad_lfactors': [[23, [1]]], 'bad_primes': [23], 'central_character': '23.10', 'coeff_info': ['x^22 - 1', '0.959492973614497 + 0.281732556841430*I', '\\\\zeta_{22}'], 'conductor': 23, 'conductor_radical': 23, 'conjugate': 'dirichlet_L_23.7', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^6', 'a^4', 'a^12', 'a^3', 'a^10', 'a^13', 'a^18', 'a^8', 'a^9', 'a^5', 'a^16', 'a^20', 'a^19', 'a^7', 'a^2', 'a^21', 'a^14', 'a^1', 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'prec': 40}}
  86. Lhash: dirichlet_L_23.11
    {'Lhash': 'dirichlet_L_23.11', 'a10': [0.14231483827328514, 0.9898214418809327], 'a2': [0.41541501300188644, -0.9096319953545183], 'a3': [-0.9594929736144974, -0.28173255684142967], 'a4': [-0.6548607339452851, -0.7557495743542583], 'a5': [-0.8412535328311812, 0.5406408174555976], 'a6': [-0.6548607339452851, 0.7557495743542583], 'a7': [0.14231483827328514, -0.9898214418809327], 'a8': [-0.9594929736144974, 0.28173255684142967], 'a9': [0.8412535328311812, 0.5406408174555976], 'algebraic': True, 'analytic_conductor': 2.4716932702763756, 'analytic_normalization': 0, 'bad_lfactors': [[23, [1]]], 'bad_primes': [23], 'central_character': '23.11', 'coeff_info': ['x^22 - 1', '0.959492973614497 + 0.281732556841430*I', '\\\\zeta_{22}'], 'conductor': 23, 'conductor_radical': 23, 'conjugate': 'dirichlet_L_23.21', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^18', 'a^12', 'a^14', 'a^9', 'a^8', 'a^17', 'a^10', 'a^2', 'a^5', 'a^15', 'a^4', 'a^16', 'a^13', 'a^21', 'a^6', 'a^19', 'a^20', 'a^3', 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  87. Lhash: dirichlet_L_23.12
    {'Lhash': 'dirichlet_L_23.12', 'a10': [-0.14231483827328514, -0.9898214418809327], 'a2': [0.41541501300188644, -0.9096319953545183], 'a3': [-0.9594929736144974, -0.28173255684142967], 'a4': [-0.6548607339452851, -0.7557495743542583], 'a5': [0.8412535328311812, -0.5406408174555976], 'a6': [-0.6548607339452851, 0.7557495743542583], 'a7': [-0.14231483827328514, 0.9898214418809327], 'a8': [-0.9594929736144974, 0.28173255684142967], 'a9': [0.8412535328311812, 0.5406408174555976], 'algebraic': True, 'analytic_conductor': 0.10681155095483924, 'analytic_normalization': 0, 'bad_lfactors': [[23, [1]]], 'bad_primes': [23], 'central_character': '23.12', 'coeff_info': ['x^11 - 1', '0.841253532831181 + 0.540640817455598*I', '\\\\zeta_{11}'], 'conductor': 23, 'conductor_radical': 23, 'conjugate': 'dirichlet_L_23.2', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^9', 'a^6', 'a^7', 'a^10', 'a^4', 'a^3', 'a^5', 'a^1', 'a^8', 'a^2', 'a^2', 'a^8', 'a^1', 'a^5', 'a^3', 'a^4', 'a^10', 'a^7', 'a^6', 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'prec': 44}}
  88. Lhash: dirichlet_L_23.13
    {'Lhash': 'dirichlet_L_23.13', 'a10': [0.8412535328311812, -0.5406408174555976], 'a2': [-0.14231483827328514, 0.9898214418809327], 'a3': [0.41541501300188644, 0.9096319953545183], 'a4': [-0.9594929736144974, -0.28173255684142967], 'a5': [-0.6548607339452851, -0.7557495743542583], 'a6': [-0.9594929736144974, 0.28173255684142967], 'a7': [0.8412535328311812, 0.5406408174555976], 'a8': [0.41541501300188644, -0.9096319953545183], 'a9': [-0.6548607339452851, 0.7557495743542583], 'algebraic': True, 'analytic_conductor': 0.10681155095483924, 'analytic_normalization': 0, 'bad_lfactors': [[23, [1]]], 'bad_primes': [23], 'central_character': '23.13', 'coeff_info': ['x^11 - 1', '0.841253532831181 + 0.540640817455598*I', '\\\\zeta_{11}'], 'conductor': 23, 'conductor_radical': 23, 'conjugate': 'dirichlet_L_23.16', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^3', 'a^2', 'a^6', 'a^7', 'a^5', 'a^1', 'a^9', 'a^4', 'a^10', 'a^8', 'a^8', 'a^10', 'a^4', 'a^9', 'a^1', 'a^5', 'a^7', 'a^6', 'a^2', 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'prec': 44}}
  89. Lhash: dirichlet_L_23.14
    {'Lhash': 'dirichlet_L_23.14', 'a10': [0.6548607339452851, -0.7557495743542583], 'a2': [0.8412535328311812, -0.5406408174555976], 'a3': [-0.14231483827328514, 0.9898214418809327], 'a4': [0.41541501300188644, -0.9096319953545183], 'a5': [0.9594929736144974, -0.28173255684142967], 'a6': [0.41541501300188644, 0.9096319953545183], 'a7': [0.6548607339452851, 0.7557495743542583], 'a8': [-0.14231483827328514, -0.9898214418809327], 'a9': [-0.9594929736144974, -0.28173255684142967], 'algebraic': True, 'analytic_conductor': 2.4716932702763756, 'analytic_normalization': 0, 'bad_lfactors': [[23, [1]]], 'bad_primes': [23], 'central_character': '23.14', 'coeff_info': ['x^22 - 1', '0.959492973614497 + 0.281732556841430*I', '\\\\zeta_{22}'], 'conductor': 23, 'conductor_radical': 23, 'conjugate': 'dirichlet_L_23.5', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^20', 'a^6', 'a^18', 'a^21', 'a^4', 'a^3', 'a^16', 'a^12', 'a^19', 'a^13', 'a^2', 'a^8', 'a^1', 'a^5', 'a^14', 'a^15', 'a^10', 'a^7', 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  90. Lhash: dirichlet_L_23.15
    {'Lhash': 'dirichlet_L_23.15', 'a10': [-0.41541501300188644, 0.9096319953545183], 'a2': [-0.9594929736144974, -0.28173255684142967], 'a3': [-0.6548607339452851, 0.7557495743542583], 'a4': [0.8412535328311812, 0.5406408174555976], 'a5': [0.14231483827328514, -0.9898214418809327], 'a6': [0.8412535328311812, -0.5406408174555976], 'a7': [-0.41541501300188644, -0.9096319953545183], 'a8': [-0.6548607339452851, -0.7557495743542583], 'a9': [-0.14231483827328514, -0.9898214418809327], 'algebraic': True, 'analytic_conductor': 2.4716932702763756, 'analytic_normalization': 0, 'bad_lfactors': [[23, [1]]], 'bad_primes': [23], 'central_character': '23.15', 'coeff_info': ['x^22 - 1', '0.959492973614497 + 0.281732556841430*I', '\\\\zeta_{22}'], 'conductor': 23, 'conductor_radical': 23, 'conjugate': 'dirichlet_L_23.20', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^12', 'a^8', 'a^2', 'a^17', 'a^20', 'a^15', 'a^14', 'a^16', 'a^7', 'a^21', 'a^10', 'a^18', 'a^5', 'a^3', 'a^4', 'a^9', 'a^6', 'a^13', 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{'__RealLiteral__': 0, 'data': '6.35513516932', 'prec': 44}}
  91. Lhash: dirichlet_L_23.16
    {'Lhash': 'dirichlet_L_23.16', 'a10': [0.8412535328311812, 0.5406408174555976], 'a2': [-0.14231483827328514, -0.9898214418809327], 'a3': [0.41541501300188644, -0.9096319953545183], 'a4': [-0.9594929736144974, 0.28173255684142967], 'a5': [-0.6548607339452851, 0.7557495743542583], 'a6': [-0.9594929736144974, -0.28173255684142967], 'a7': [0.8412535328311812, -0.5406408174555976], 'a8': [0.41541501300188644, 0.9096319953545183], 'a9': [-0.6548607339452851, -0.7557495743542583], 'algebraic': True, 'analytic_conductor': 0.10681155095483924, 'analytic_normalization': 0, 'bad_lfactors': [[23, [1]]], 'bad_primes': [23], 'central_character': '23.16', 'coeff_info': ['x^11 - 1', '0.841253532831181 + 0.540640817455598*I', '\\\\zeta_{11}'], 'conductor': 23, 'conductor_radical': 23, 'conjugate': 'dirichlet_L_23.13', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^8', 'a^9', 'a^5', 'a^4', 'a^6', 'a^10', 'a^2', 'a^7', 'a^1', 'a^3', 'a^3', 'a^1', 'a^7', 'a^2', 'a^10', 'a^6', 'a^4', 'a^5', 'a^9', 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  92. Lhash: dirichlet_L_23.17
    {'Lhash': 'dirichlet_L_23.17', 'a10': [0.9594929736144974, -0.28173255684142967], 'a2': [-0.6548607339452851, -0.7557495743542583], 'a3': [0.8412535328311812, 0.5406408174555976], 'a4': [-0.14231483827328514, 0.9898214418809327], 'a5': [-0.41541501300188644, 0.9096319953545183], 'a6': [-0.14231483827328514, -0.9898214418809327], 'a7': [0.9594929736144974, 0.28173255684142967], 'a8': [0.8412535328311812, -0.5406408174555976], 'a9': [0.41541501300188644, 0.9096319953545183], 'algebraic': True, 'analytic_conductor': 2.4716932702763756, 'analytic_normalization': 0, 'bad_lfactors': [[23, [1]]], 'bad_primes': [23], 'central_character': '23.17', 'coeff_info': ['x^22 - 1', '0.959492973614497 + 0.281732556841430*I', '\\\\zeta_{22}'], 'conductor': 23, 'conductor_radical': 23, 'conjugate': 'dirichlet_L_23.19', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^14', 'a^2', 'a^6', 'a^7', 'a^16', 'a^1', 'a^20', 'a^4', 'a^21', 'a^19', 'a^8', 'a^10', 'a^15', 'a^9', 'a^12', 'a^5', 'a^18', 'a^17', 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  93. Lhash: dirichlet_L_23.18
    {'Lhash': 'dirichlet_L_23.18', 'a10': [-0.6548607339452851, -0.7557495743542583], 'a2': [0.8412535328311812, 0.5406408174555976], 'a3': [-0.14231483827328514, -0.9898214418809327], 'a4': [0.41541501300188644, 0.9096319953545183], 'a5': [-0.9594929736144974, -0.28173255684142967], 'a6': [0.41541501300188644, -0.9096319953545183], 'a7': [-0.6548607339452851, 0.7557495743542583], 'a8': [-0.14231483827328514, 0.9898214418809327], 'a9': [-0.9594929736144974, 0.28173255684142967], 'algebraic': True, 'analytic_conductor': 0.10681155095483924, 'analytic_normalization': 0, 'bad_lfactors': [[23, [1]]], 'bad_primes': [23], 'central_character': '23.18', 'coeff_info': ['x^11 - 1', '0.841253532831181 + 0.540640817455598*I', '\\\\zeta_{11}'], 'conductor': 23, 'conductor_radical': 23, 'conjugate': 'dirichlet_L_23.9', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 'a^8', 'a^2', 'a^6', 'a^9', 'a^4', 'a^3', 'a^5', 'a^7', 'a^10', 'a^10', 'a^7', 'a^5', 'a^3', 'a^4', 'a^9', 'a^6', 'a^2', 'a^8', 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  94. Lhash: dirichlet_L_23.19
    {'Lhash': 'dirichlet_L_23.19', 'a10': [0.9594929736144974, 0.28173255684142967], 'a2': [-0.6548607339452851, 0.7557495743542583], 'a3': [0.8412535328311812, -0.5406408174555976], 'a4': [-0.14231483827328514, -0.9898214418809327], 'a5': [-0.41541501300188644, -0.9096319953545183], 'a6': [-0.14231483827328514, 0.9898214418809327], 'a7': [0.9594929736144974, -0.28173255684142967], 'a8': [0.8412535328311812, 0.5406408174555976], 'a9': [0.41541501300188644, -0.9096319953545183], 'algebraic': True, 'analytic_conductor': 2.4716932702763756, 'analytic_normalization': 0, 'bad_lfactors': [[23, [1]]], 'bad_primes': [23], 'central_character': '23.19', 'coeff_info': ['x^22 - 1', '0.959492973614497 + 0.281732556841430*I', '\\\\zeta_{22}'], 'conductor': 23, 'conductor_radical': 23, 'conjugate': 'dirichlet_L_23.17', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^8', 'a^20', 'a^16', 'a^15', 'a^6', 'a^21', 'a^2', 'a^18', 'a^1', 'a^3', 'a^14', 'a^12', 'a^7', 'a^13', 'a^10', 'a^17', 'a^4', 'a^5', 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  95. Lhash: dirichlet_L_23.2
    {'Lhash': 'dirichlet_L_23.2', 'a10': [-0.14231483827328514, 0.9898214418809327], 'a2': [0.41541501300188644, 0.9096319953545183], 'a3': [-0.9594929736144974, 0.28173255684142967], 'a4': [-0.6548607339452851, 0.7557495743542583], 'a5': [0.8412535328311812, 0.5406408174555976], 'a6': [-0.6548607339452851, -0.7557495743542583], 'a7': [-0.14231483827328514, -0.9898214418809327], 'a8': [-0.9594929736144974, -0.28173255684142967], 'a9': [0.8412535328311812, -0.5406408174555976], 'algebraic': True, 'analytic_conductor': 0.10681155095483924, 'analytic_normalization': 0, 'bad_lfactors': [[23, [1]]], 'bad_primes': [23], 'central_character': '23.2', 'coeff_info': ['x^11 - 1', '0.841253532831181 + 0.540640817455598*I', '\\\\zeta_{11}'], 'conductor': 23, 'conductor_radical': 23, 'conjugate': 'dirichlet_L_23.12', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 'a^5', 'a^4', 'a^1', 'a^7', 'a^8', 'a^6', 'a^10', 'a^3', 'a^9', 'a^9', 'a^3', 'a^10', 'a^6', 'a^8', 'a^7', 'a^1', 'a^4', 'a^5', 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  96. Lhash: dirichlet_L_23.20
    {'Lhash': 'dirichlet_L_23.20', 'a10': [-0.41541501300188644, -0.9096319953545183], 'a2': [-0.9594929736144974, 0.28173255684142967], 'a3': [-0.6548607339452851, -0.7557495743542583], 'a4': [0.8412535328311812, -0.5406408174555976], 'a5': [0.14231483827328514, 0.9898214418809327], 'a6': [0.8412535328311812, 0.5406408174555976], 'a7': [-0.41541501300188644, 0.9096319953545183], 'a8': [-0.6548607339452851, 0.7557495743542583], 'a9': [-0.14231483827328514, 0.9898214418809327], 'algebraic': True, 'analytic_conductor': 2.4716932702763756, 'analytic_normalization': 0, 'bad_lfactors': [[23, [1]]], 'bad_primes': [23], 'central_character': '23.20', 'coeff_info': ['x^22 - 1', '0.959492973614497 + 0.281732556841430*I', '\\\\zeta_{22}'], 'conductor': 23, 'conductor_radical': 23, 'conjugate': 'dirichlet_L_23.15', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^10', 'a^14', 'a^20', 'a^5', 'a^2', 'a^7', 'a^8', 'a^6', 'a^15', 'a^1', 'a^12', 'a^4', 'a^17', 'a^19', 'a^18', 'a^13', 'a^16', 'a^9', 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  97. Lhash: dirichlet_L_23.21
    {'Lhash': 'dirichlet_L_23.21', 'a10': [0.14231483827328514, -0.9898214418809327], 'a2': [0.41541501300188644, 0.9096319953545183], 'a3': [-0.9594929736144974, 0.28173255684142967], 'a4': [-0.6548607339452851, 0.7557495743542583], 'a5': [-0.8412535328311812, -0.5406408174555976], 'a6': [-0.6548607339452851, -0.7557495743542583], 'a7': [0.14231483827328514, 0.9898214418809327], 'a8': [-0.9594929736144974, -0.28173255684142967], 'a9': [0.8412535328311812, -0.5406408174555976], 'algebraic': True, 'analytic_conductor': 2.4716932702763756, 'analytic_normalization': 0, 'bad_lfactors': [[23, [1]]], 'bad_primes': [23], 'central_character': '23.21', 'coeff_info': ['x^22 - 1', '0.959492973614497 + 0.281732556841430*I', '\\\\zeta_{22}'], 'conductor': 23, 'conductor_radical': 23, 'conjugate': 'dirichlet_L_23.11', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^4', 'a^10', 'a^8', 'a^13', 'a^14', 'a^5', 'a^12', 'a^20', 'a^17', 'a^7', 'a^18', 'a^6', 'a^9', 'a^1', 'a^16', 'a^3', 'a^2', 'a^19', 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  98. Lhash: dirichlet_L_23.22
    {'Lhash': 'dirichlet_L_23.22', 'a10': [-1.0, 0.0], 'a2': [1.0, 0.0], 'a3': [1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [1.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [1.0, 0.0], 'a9': [1.0, 0.0], 'algebraic': True, 'analytic_conductor': 2.4716932702763756, 'analytic_normalization': 0, 'bad_lfactors': [[23, [1]]], 'bad_primes': [23], 'central_character': '23.22', 'coeff_info': ['x^2 - 1', -1, '\\\\zeta_{2}'], 'conductor': 23, 'conductor_radical': 23, 'conjugate': 'dirichlet_L_23.22', 'degree': 1, 'dirichlet_coefficients': [1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 0, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 0, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 0, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 0, 1, 1, 1, 1, -1, 1, -1, 1], 'euler_factors': [[1, 1], [1, 1], [1, -1], [1, -1], [1, -1], [1, 1], [1, -1], [1, -1], [0], [1, 1], [1, 1], [1, -1], [1, 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  99. Lhash: dirichlet_L_23.3
    {'Lhash': 'dirichlet_L_23.3', 'a10': [0.41541501300188644, 0.9096319953545183], 'a2': [-0.9594929736144974, 0.28173255684142967], 'a3': [-0.6548607339452851, -0.7557495743542583], 'a4': [0.8412535328311812, -0.5406408174555976], 'a5': [-0.14231483827328514, -0.9898214418809327], 'a6': [0.8412535328311812, 0.5406408174555976], 'a7': [0.41541501300188644, -0.9096319953545183], 'a8': [-0.6548607339452851, 0.7557495743542583], 'a9': [-0.14231483827328514, 0.9898214418809327], 'algebraic': True, 'analytic_conductor': 0.10681155095483924, 'analytic_normalization': 0, 'bad_lfactors': [[23, [1]]], 'bad_primes': [23], 'central_character': '23.3', 'coeff_info': ['x^11 - 1', '0.841253532831181 + 0.540640817455598*I', '\\\\zeta_{11}'], 'conductor': 23, 'conductor_radical': 23, 'conjugate': 'dirichlet_L_23.8', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^5', 'a^7', 'a^10', 'a^8', 'a^1', 'a^9', 'a^4', 'a^3', 'a^2', 'a^6', 'a^6', 'a^2', 'a^3', 'a^4', 'a^9', 'a^1', 'a^8', 'a^10', 'a^7', 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  100. Lhash: dirichlet_L_23.4
    {'Lhash': 'dirichlet_L_23.4', 'a10': [-0.9594929736144974, -0.28173255684142967], 'a2': [-0.6548607339452851, 0.7557495743542583], 'a3': [0.8412535328311812, -0.5406408174555976], 'a4': [-0.14231483827328514, -0.9898214418809327], 'a5': [0.41541501300188644, 0.9096319953545183], 'a6': [-0.14231483827328514, 0.9898214418809327], 'a7': [-0.9594929736144974, 0.28173255684142967], 'a8': [0.8412535328311812, 0.5406408174555976], 'a9': [0.41541501300188644, -0.9096319953545183], 'algebraic': True, 'analytic_conductor': 0.10681155095483924, 'analytic_normalization': 0, 'bad_lfactors': [[23, [1]]], 'bad_primes': [23], 'central_character': '23.4', 'coeff_info': ['x^11 - 1', '0.841253532831181 + 0.540640817455598*I', '\\\\zeta_{11}'], 'conductor': 23, 'conductor_radical': 23, 'conjugate': 'dirichlet_L_23.6', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^4', 'a^10', 'a^8', 'a^2', 'a^3', 'a^5', 'a^1', 'a^9', 'a^6', 'a^7', 'a^7', 'a^6', 'a^9', 'a^1', 'a^5', 'a^3', 'a^2', 'a^8', 'a^10', 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