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lfunc_lfunctions • Show schema
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{'Lhash': '1708397377803269098604773642620', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.8660254037844386, 0.5], 'a4': [0.5, 0.8660254037844386], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.8660254037844386, 0.5], 'a8': [0.0, 0.0], 'a9': [0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.48658838731717735, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.8660254037844386, -0.5]]], [5, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [3, 5, 13], 'central_character': '975.74', 'coefficient_field': 'CDF', 'conductor': 975, 'conductor_radical': 195, 'conjugate': '2976086099295221161625467564309', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.8660254037844386, -0.5], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 1.0]], 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'3.57494138434202337835865686999967', '4.66490929315396902704700856610145', '6.18999004559644605345422925578708', '6.58222945416412569508980364313661', '7.38687004474828700368709590706854', '8.415800432743590563584239387008887', '9.316273731660792870832350777994124', '10.00071826969149236424756583211621'], 'prelabel': '2-975-195.74-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6975588773122864, 'root_angle': -0.39554266625786655, 'root_number': '0.32230402756182605713543784566208 - 0.94663620985964067933133644787113*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1977713331289333', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.34768790193108976191285941272', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.47197013082709774899791691400', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.57494138434202337835865687000', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.48658838731717735, 'bad_primes': [3, 5, 13], 'central_character': '195.74', 'conductor': 975, 'conductor_radical': 195, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/975/1/y/a/74/2'], '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': '2-975-195.74-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-975-195.74-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6975588773122864, 'root_angle': -0.19777133312893327, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.34768790193108976191285941272', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1708397377803269098604773642620', 'Lhash_array': ['1708397377803269098604773642620'], 'label': '2-975-195.74-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/975/1/y/a/74/2'}