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lfunc_lfunctions • Show schema
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{'Lhash': '455040885946413218556595251829', 'a10': [106.15517570560841, -4.1807324105168157e-60], 'a2': [-2.449489742783178, -1.4142135623730951], 'a3': [-7.807601775624837, 4.476757142537429], 'a4': [4.0, 6.928203230275509], 'a5': [-32.503251754279226, 18.765761149871288], 'a6': [25.455731131555822, 0.07584561912014157], 'a7': [-1.3545795572292725, 2.3462006160152535], 'a8': [0.0, -22.627416997969522], 'a9': [40.91729097348023, -69.90547403023281], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8606593355091985, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [2.449489742783178, 1.4142135623730951]]], [3, [[1.0, 0], [7.807601775624837, -4.476757142537429]]]], 'bad_primes': [2, 3], 'central_character': '18.11', 'coefficient_field': 'CDF', 'conductor': 18, 'conductor_radical': 6, 'conjugate': '4957984323404645206563894218626', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.449489742783178, 1.4142135623730951]], 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'5.06855817932564334022882027352659', '7.19077512983447310819691217661697', '8.386470627778484052063895364003422', '10.59000112693685631634310831085234', '11.88333079410378479230525637281171', '13.08589112422085762884385490644570', '15.47174465584957319815862863317551', '16.17232820206227241024900613929582', '17.44314304780314007451040536143909'], 'prelabel': '2-18-9.2-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3640598724063393, 'root_angle': -0.7758809680712324, 'root_number': '-0.7622004912389438 - 0.647341031570773*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.387940484036', 'prec': 50}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.35896396520025872083368777390', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.06855817932564334022882027353', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.19077512983447310819691217662', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8606593355091985, 'bad_primes': [2, 3], 'central_character': '9.2', 'conductor': 18, 'conductor_radical': 6, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/18/5/d/a/11/1'], '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': '2-18-9.2-c4-0-0', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-18-9.2-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3640598724063393, 'root_angle': -0.3879404840356162, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '0.35896396520025872083368777390', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '455040885946413218556595251829', 'Lhash_array': ['455040885946413218556595251829'], 'label': '2-18-9.2-c4-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/18/5/d/a/11/1'}