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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_191.70', 'a10': [0.7891405093963936, 0.6142127126896678], 'a2': [-0.6772815716257411, 0.7357239106731316], 'a3': [0.24548548714079915, -0.9694002659393304], 'a4': [-0.08257934547233232, -0.9965844930066698], 'a5': [-0.08257934547233232, -0.9965844930066698], 'a6': [0.5469481581224269, 0.8371664782625285], 'a7': [-1.0, -1.4081532572346456e-30], 'a8': [0.7891405093963936, 0.6142127126896678], 'a9': [-0.8794737512064891, -0.47594739303707356], 'algebraic': True, 'analytic_conductor': 20.52580063577338, 'analytic_normalization': 0, 'bad_lfactors': [[191, [1]]], 'bad_primes': [191], 'central_character': '191.70', 'coeff_info': ['x^38 - 1', '0.986361303402722 + 0.164594590280734*I', '\\\\zeta_{38}'], 'conductor': 191, 'conductor_radical': 191, 'conjugate': 'dirichlet_L_191.161', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^14', 'a^30', 'a^28', 'a^28', 'a^6', 'a^19', 'a^4', 'a^22', 'a^4', 'a^21', 'a^20', 'a^8', 'a^33', 'a^20', 'a^18', 'a^26', 'a^36', 'a^15', 'a^18', 'a^11', 'a^35', 'a^34', 'a^34', 'a^18', 'a^22', 'a^14', 'a^9', 'a^1', 'a^34', 'a^3', 'a^32', 'a^13', 'a^2', 'a^9', 'a^12', 'a^35', 'a^29', 'a^0', 'a^32', 'a^5', 'a^25', 'a^6', 'a^11', 'a^12', 'a^10', 'a^21', 'a^10', 'a^0', 'a^32', 'a^18', 'a^36', 'a^21', 'a^28', 'a^11', 'a^23', 'a^7', 'a^15', 'a^22', 'a^10', 'a^31', 'a^17', 'a^3', 'a^8', 'a^36', 'a^27', 'a^12', 'a^16', 'a^26', 'a^23', 'a^5', 'a^26', 'a^17', 'a^11', 'a^10', 'a^5', 'a^2', 'a^14', 'a^18', 'a^8', 'a^6', 'a^19', 'a^23', 'a^1', 'a^16', 'a^20', 'a^31', 'a^25', 'a^13', 'a^26', 'a^27', 'a^24', 'a^33', 'a^35', 'a^5', 'a^24', 'a^16', 'a^14', 'a^5', 'a^8'], 'euler_factors': [[1, 'a^14'], [1, 'a^30'], [1, 'a^28'], [1, 'a^19'], [1, 'a^21'], [1, 'a^8'], [1, 'a^26'], [1, 'a^15'], [1, 'a^34'], [1, 'a^1'], [1, 'a^3'], [1, 'a^35'], [1, 'a^5'], [1, 'a^6'], [1, 'a^21'], [1, 'a^21'], [1, 'a^22'], [1, 'a^31'], [1, 'a^12'], [1, 'a^5'], [1, 'a^17'], [1, 'a^18'], [1, 'a^23'], [1, 'a^13'], [1, 'a^16'], [1, 'a^7']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-191-191.70-r1-0-0', 'leading_term': '0.0683730686745548945857373330112+0.0949676595283779686105542954696*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/191/70', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.11702022421903538, 0.5810274837474285, 0.658179800243695, 0.28756939647710833, -0.46887699871643107, -1.3555768416099778, -1.9424162468705066, -1.769674116386263, -0.5765200648474007, 1.4961558536943385, 3.8567396184345766, 5.64209119894773, 6.083991805539186, 4.899958309280515, 2.4933392379728114, -0.18318045202097838, -2.071760324133003, -2.542625398728566, -1.7141566159938653, -0.35474554859390306, 0.5958758658216874, 0.6013247962984392, -0.16779250745008054, -1.008259978625525, -1.2246161835505396, -0.6564772845370258, 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0.6027506838016459, 'root_number': '-0.317223935618693878631058310224+0.948350660183556133711137802948*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.301375341901', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(38)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.550482531665609794221984187160-0.113524255442982297594277286833*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.07165209189', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.59825426222', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.66431749781', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 20.52580063577338, 'bad_primes': [191], 'central_character': '191.70', 'conductor': 191, 'conductor_radical': 191, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/191/70'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-191-191.70-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-191-191.70-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 20.52580063577338, 'root_angle': 0.30137534190082294, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.07165209189', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_191.70', 'Lhash_array': ['dirichlet_L_191.70'], 'label': '1-191-191.70-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/191/70'}