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lfunc_lfunctions • Show schema
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{'Lhash': '303324110599436128973686442949', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, -1.7776732227038512], 'a6': [0, 0], 'a7': [-2.3924791513179655, -1.1296209587772652], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.19568209498026, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2.3924791513179655, 1.1296209587772652]]]], 'bad_primes': [2, 3, 7], 'central_character': '4032.1889', 'coefficient_field': 'CDF', 'conductor': 4032, 'conductor_radical': 42, 'conjugate': '875830751140825794886588638117', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.7776732227038512], [-5.0, 0]], [[1.0, 0], [2.3924791513179655, 1.1296209587772652]], [[1.0, 0], [3.852256210752564, 0], [11.0, 0]], [[1.0, 0], [6.593285049388693, 0], [13.0, 0]], [[1.0, 0], [4.5650715123951455, 0], [17.0, 0]], 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'2.39126813313895486917621851477077', '2.56679720757897757051762135390752', '3.54027476138313430583780624937923', '4.78086765237606658158385533190563', '5.23028019608463745736832622320442', '6.43452742648469949356142341057286', '6.74235053164422764778629235366972', '7.55648345879618518706213626399179', '8.263343648951607172626693677933360'], 'prelabel': '2-4032-168.125-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.674123905501206, 'root_angle': -0.24700576737123045, 'root_number': '0.71372691159797362788881606074239220878562693367965954256 - 0.70042408272475778576389483376043611407276726612205762811*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.12350288368561524', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.23928053246282948650036722029', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.39126813313895486917621851477', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.56679720757897757051762135391', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.19568209498026, 'bad_primes': [2, 3, 7], 'central_character': '168.125', 'conductor': 4032, 'conductor_radical': 42, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4032/2/i/c/1889/1'], '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': '2-4032-168.125-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': '2-4032-168.125-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.674123905501206, 'root_angle': -0.12350288368561523, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.23928053246282948650036722029', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '303324110599436128973686442949', 'Lhash_array': ['303324110599436128973686442949'], 'label': '2-4032-168.125-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4032/2/i/c/1889/1'}