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lfunc_lfunctions • Show schema
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{'Lhash': '2178150599949439852114110334832', 'a10': [-11.070939766702542, 6.391810054487846], 'a2': [1.3660254037844386, 0.36602540378443865], 'a3': [0.8660254037844386, 1.5], 'a4': [1.7320508075688772, 1.0], 'a5': [-6.391810054487846, 6.391810054487846], 'a6': [0.6339745962155614, 2.366025403784439], 'a7': [9.231374910595195, -2.47353945232291], 'a8': [2.0, 2.0], 'a9': [-1.5, 2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.125346062010316, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.3660254037844386, -0.36602540378443865]]], [3, [[1.0, 0], [-0.8660254037844386, -1.5]]], [13, [[1.0, 0], [3.8131043084302583, 12.428203230275509]]]], 'bad_primes': [2, 3, 13], 'central_character': '78.67', 'coefficient_field': 'CDF', 'conductor': 78, 'conductor_radical': 78, 'conjugate': '4037796826693650383601305461679', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.3660254037844386, 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'4.99907588882584987091790229373126', '7.17778594003674267697699602591074', '8.121675137564520425107820526856938', '9.281532057421380435377050040135252', '11.33316130721313857469675100471135', '12.14420016705047371443888095094235', '12.53906028180152616612389977505395', '14.12061860648960629168347880918675'], 'prelabel': '2-78-13.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4578566671694155, 'root_angle': -0.3365494737091372, 'root_number': '0.49122447733351177 - 0.8710330147981867*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.168274736855', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.71825785398380507253526867395', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.23532752786441553675729096662', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.99907588882584987091790229373', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.125346062010316, 'bad_primes': [2, 3, 13], 'central_character': '13.2', 'conductor': 78, 'conductor_radical': 78, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/78/3/l/c/67/1'], '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': '2-78-13.2-c2-0-1', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-78-13.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4578566671694155, 'root_angle': -0.1682747368545686, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.71825785398380507253526867395', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2178150599949439852114110334832', 'Lhash_array': ['2178150599949439852114110334832'], 'label': '2-78-13.2-c2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/78/3/l/c/67/1'}