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lfunc_lfunctions • Show schema
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{'Lhash': '1014762598601589699748021487382', 'a10': [38.49939632308146, -4.763570738297253], 'a2': [-3.0048911362182094, 1.7348747063811036], 'a3': [-2.598076211353316, -1.5], 'a4': [2.019580493681841, -3.4980160250319847], 'a5': [-10.295625523822405, -4.358909849172913], 'a6': [10.409248238286622, 6.36515485563463e-61], 'a7': [-12.484528246352, 13.679786345774522], 'a8': [0.0, -13.743118838140505], 'a9': [4.5, 7.794228634059948], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.195200550602768, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [2.598076211353316, 1.5]]], [5, [[1.0, 0], [10.295625523822405, 4.358909849172913]]], [7, [[1.0, 0], [12.484528246352, -13.679786345774522]]]], 'bad_primes': [3, 5, 7], 'central_character': '105.4', 'coefficient_field': 'CDF', 'conductor': 105, 'conductor_radical': 105, 'conjugate': '912829927947732852731864807995', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'4.80372301376681817413895872864488', '6.78300744762435723009033950663548', '7.74574715798250042695225191082266', '9.295852796233365771104898637425218', '9.969468516650495807178750280792014', '11.12939175841224620394774867322579', '11.59097904786018244868996038706373', '12.91617103744662141419559985365603'], 'prelabel': '2-105-35.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.489015980383165, 'root_angle': -0.1168772086550714, 'root_number': '0.933343184413953 - 0.35898537589715496*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0584386043275', 'prec': 54}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.800506542117276298963137066731', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.21220153084981794686853918343', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.80372301376681817413895872864', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.195200550602768, 'bad_primes': [3, 5, 7], 'central_character': '35.4', 'conductor': 105, 'conductor_radical': 105, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/105/4/q/b/4/4'], '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': '2-105-35.4-c3-0-7', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-105-35.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.489015980383165, 'root_angle': -0.0584386043275357, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.800506542117276298963137066731', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1014762598601589699748021487382', 'Lhash_array': ['1014762598601589699748021487382'], 'label': '2-105-35.4-c3-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/105/4/q/b/4/4'}