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lfunc_lfunctions • Show schema
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{'Lhash': '1408838158885282797040599101306', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-3.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-18.42220510185596, 0.0], 'a6': [0.0, 0.0], 'a7': [-22.42220510185596, 0.0], 'a8': [0.0, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 45.31346688440881, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [3.0, 0]]]], 'bad_primes': [2, 3], 'central_character': '768.1', 'coefficient_field': 'CDF', 'conductor': 768, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [3.0, 0]], [[1.0, 0], [18.42220510185596, 0], [125.0, 0]], [[1.0, 0], [22.42220510185596, 0], [343.0, 0]], [[1.0, 0], [-53.688820407423826, 0], [1331.0, 0]], [[1.0, 0], [-7.155589796288085, 0], [2197.0, 0]], [[1.0, 0], [-39.688820407423826, 0], [4913.0, 0]], [[1.0, 0], [-125.68882040742383, 0], [6859.0, 0]], [[1.0, 0], [99.15558979628808, 0], 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'4.86525960549443810643976406669489', '6.15167787167665318345459511193069', '6.87231718350630663830168543731998', '7.62784892959693206614881267296641', '8.636709630530718719726098333068315', '9.582836305606770944345708164943389'], 'prelabel': '2-768-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.731527826905926, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.11137734532814784348255038158', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.33380969514049753298277033455', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.73501222903585859269929561342', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 45.31346688440881, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 768, 'conductor_radical': 6, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/768/4/a/e/1/1'], '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': '2-768-1.1-c3-0-20', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-768-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.731527826905926, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.11137734532814784348255038158', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1408838158885282797040599101306', 'Lhash_array': ['1408838158885282797040599101306'], 'label': '2-768-1.1-c3-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/768/4/a/e/1/1'}