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lfunc_lfunctions • Show schema
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{'Lhash': '1307493130570025446250056191166', 'a10': [0.36534102436639504, -0.9308737486442042], 'a2': [-0.2225209339563144, 0.9749279121818236], 'a3': [-0.38747222055728137, 0.3595216807901484], 'a4': [-0.9009688679024191, -0.4338837391175581], 'a5': [-0.9888308262251285, -0.14904226617617444], 'a6': [-0.2642870412363061, -0.4577585832033332], 'a7': [1.565686167706318, -2.7118479911751487], 'a8': [0.6234898018587335, -0.7818314824680298], 'a9': [-0.20331139801385562, 2.7130020635550505], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.433567286915058, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.2225209339563144, -0.9749279121818236]]], [5, [[1.0, 0], [0.9888308262251285, 0.14904226617617444]]], [43, [[1.0, 0], [-4.907970433702363, 4.348772955892667]]]], 'bad_primes': [2, 5, 43], 'central_character': '430.271', 'coefficient_field': 'CDF', 'conductor': 430, 'conductor_radical': 430, 'conjugate': '1728798465786387546719018858832', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.2225209339563144, -0.9749279121818236]], [[1.0, 0], [0.38747222055728137, -0.3595216807901484], [0.22419028075927278, -2.9916113915435405]], [[1.0, 0], [0.9888308262251285, 0.14904226617617444]], [[1.0, 0], [-1.565686167706318, 2.7118479911751487], [-3.5, -6.06217782649107]], [[1.0, 0], [-2.806923005624402, 1.351742876455654], [6.858387820446069, -8.600146307148329]], [[1.0, 0], [-1.808955994351779, -4.609144703951662], [-9.529674333787742, 8.842245591021952]], [[1.0, 0], [-1.4089054867747857, 0.21235833370869478], [16.244737698364393, -5.010837964985372]], [[1.0, 0], [-0.08620860372493969, -1.1503738702638888], [-18.787785698277442, 2.8318030573473143]], [[1.0, 0], [-5.445001346195806, -3.7123390596559456], [8.402843560427085, 21.410096218816697]], [[1.0, 0], [-3.779162626313969, -3.506550475896244], [2.1671727140063033, 28.918910118254225]], [[1.0, 0], [4.980449879878342, -1.5362653312225507], 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'root_angle': -0.38765065088045786, 'root_number': '0.34567298766328014 - 0.938355042401298*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.19382532544', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.03143021455172485675256245680', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.71108351241866199493327898257', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.85197661756577203196919554655', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.433567286915058, 'bad_primes': [2, 5, 43], 'central_character': '43.13', 'conductor': 430, 'conductor_radical': 430, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/430/2/q/a/271/2'], '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': '2-430-43.13-c1-0-6', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-430-43.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8529887444113249, 'root_angle': -0.19382532544022893, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.03143021455172485675256245680', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1307493130570025446250056191166', 'Lhash_array': ['1307493130570025446250056191166'], 'label': '2-430-43.13-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/430/2/q/a/271/2'}