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lfunc_lfunctions • Show schema
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{'Lhash': '8513935605435982321743373941292', 'a10': [-220.0, 298.496231131986], 'a2': [0.0, -6.6332495807108], 'a3': [0.0, 19.8997487421324], 'a4': [-12.0, 0.0], 'a5': [-45.0, -33.166247903554], 'a6': [132.0, 0.0], 'a7': [0.0, 59.6992462263972], 'a8': [0.0, -132.664991614216], 'a9': [-153.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8019190990649033, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [45.0, 33.166247903554]]]], 'bad_primes': [5], 'central_character': '5.4', 'coefficient_field': 'CDF', 'conductor': 5, 'conductor_radical': 5, 'conjugate': '5151107666939872653826102354558', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 6.6332495807108], [-32.0, 0]], [[1.0, 0], [0, -19.8997487421324], [-243.0, 0]], [[1.0, 0], [45.0, 33.166247903554]], [[1.0, 0], [0, -59.6992462263972], [-16807.0, 0]], [[1.0, 0], [-252.0, 0], [161051.0, 0]], [[1.0, 0], [0, -119.3984924527944], [-371293.0, 0]], [[1.0, 0], [0, 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'13.79103441325280814819768052363367', '15.33533538841285802399005921428510', '17.09272587952248977110949467302972', '18.56236613057734487804330711583467', '19.96105957672780268456689498557813', '22.80613211102536782471174831138607', '23.78022987484324488734829947865242'], 'prelabel': '2-5-5.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8954993573782749, 'root_angle': 0.10108678967805505, 'root_number': '0.8049844718999243 + 0.593295878967653*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.101086789678', 'prec': 47}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '6.71631094869763221321108390169', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '7.80950001073798191226471943289', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '11.66134790726682541804104153830', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8019190990649033, 'bad_primes': [5], 'central_character': '5.4', 'conductor': 5, 'conductor_radical': 5, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5/6/b/a/4/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, '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': '2-5-5.4-c5-0-1', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-5-5.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8954993573782749, 'root_angle': 0.10108678967805505, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '6.71631094869763221321108390169', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '8513935605435982321743373941292', 'Lhash_array': ['8513935605435982321743373941292'], 'factors': ['2-5-5.4-c5-0-1'], 'label': '2-5-5.4-c5-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5/6/b/a/4/1'}