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lfunc_lfunctions • Show schema
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{'Lhash': '2717437273697129796280809077381', 'a10': [-2.8410062920856185, 0.0], 'a2': [2.0860641981309853, 0.0], 'a3': [1.0694041041897588, 0.0], 'a4': [2.3516638387238706, 0.0], 'a5': [-1.361897823964874, 0.0], 'a6': [2.2308456150845943, 0.0], 'a7': [4.4850007941877035, 0.0], 'a8': [0.7335933437391757, 0.0], 'a9': [-1.8563748619420992, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.833625618948815, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[13, [[1.0, 0], [0, 0]]], [31, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [13, 31], 'central_character': '5239.1', 'coefficient_field': 'CDF', 'conductor': 5239, 'conductor_radical': 403, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.0860641981309853, 0], [2.0, 0]], [[1.0, 0], [-1.0694041041897588, 0], [3.0, 0]], [[1.0, 0], [1.361897823964874, 0], [5.0, 0]], [[1.0, 0], [-4.4850007941877035, 0], [7.0, 0]], [[1.0, 0], [5.70282611940819, 0], [11.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'4.93443047699673375742916854432456', '5.40570775063789901872442974207586', '6.00676505070300949792971422937478', '7.41133312930009012682094113368538', '7.64825986994925859655979002312675'], 'prelabel': '2-5239-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.467891899139071, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.14368002761003622494947291246', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.35085590606153154510542486721', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.54794581436858311136225405330', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 41.833625618948815, 'bad_primes': [13, 31], 'central_character': '1.1', 'conductor': 5239, 'conductor_radical': 403, 'degree': 2, 'index': 383, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5239/2/a/m/1/15'], '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': '2-5239-1.1-c1-0-383', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-5239-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.467891899139071, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.14368002761003622494947291246', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2717437273697129796280809077381', 'Lhash_array': ['2717437273697129796280809077381'], 'label': '2-5239-1.1-c1-0-383', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5239/2/a/m/1/15'}