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lfunc_lfunctions • Show schema
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{'Lhash': '1747107260778196190106782212369', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-0.2984378812835757, -0.2984378812835757], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 49.046447584853446, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1800.1657', 'coefficient_field': 'CDF', 'conductor': 1800, 'conductor_radical': 30, 'conjugate': '68767388062192438086056627082', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.2984378812835757, 0.2984378812835757], [0, 49.0]], [[1.0, 0], [11.403124237432849, 0], [121.0, 0]], [[1.0, 0], [-1.5968757625671512, 1.5968757625671512], [0, -169.0]], [[1.0, 0], [-10.403124237432849, -10.403124237432849], [0, 289.0]], [[1.0, 0], [0, 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-1.1343441936272654, -0.9013578348724274, -0.5457241644507033], 'positive_zeros': ['1.37822461525569018074771707318228', '2.67354321871273166357406565722359', '3.44189286373947109683212035060451', '4.68164796391330076772356699047581', '5.36569402101479854844374968587095', '6.18743582859492781931150503333402', '7.32266558292740569696132102621414', '7.69181382778084544900462351574709', '8.752948461438179427575914693156422', '9.405305148389946954454979641424288'], 'prelabel': '2-1800-5.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.003316898788277, 'root_angle': 0.9262081911747834, 'root_number': '-0.973248989467730163788057748308152580741041127151910111 + 0.229752920547361183523937369381462718715990937285509726*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4631040955873917', 'prec': 60}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.37822461525569018074771707318', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.67354321871273166357406565722', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.44189286373947109683212035060', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 49.046447584853446, 'bad_primes': [2, 3, 5], 'central_character': '5.2', 'conductor': 1800, 'conductor_radical': 30, 'degree': 2, 'index': 39, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1800/3/v/k/1657/2'], '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': '2-1800-5.2-c2-0-39', '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': '2-1800-5.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.003316898788277, 'root_angle': 0.4631040955873917, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.37822461525569018074771707318', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1747107260778196190106782212369', 'Lhash_array': ['1747107260778196190106782212369'], 'label': '2-1800-5.2-c2-0-39', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1800/3/v/k/1657/2'}