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lfunc_lfunctions • Show schema
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{'Lhash': '944023610789905892680316704857', 'a10': [-0.7876529321965984, 0.0], 'a2': [0.7403713479004523, 0.0], 'a3': [-9.080494845101747, 0.0], 'a4': [-7.4518502672080675, 0.0], 'a5': [-1.0638619855160891, 0.0], 'a6': [-6.722938208071088, 0.0], 'a7': [0.0, 0.0], 'a8': [-11.4401072098888, 0.0], 'a9': [55.45538663191938, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 124.31702438209554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [43, [[1.0, 0], [43.0, 0]]]], 'bad_primes': [7, 43], 'central_character': '2107.1', 'coefficient_field': 'CDF', 'conductor': 2107, 'conductor_radical': 301, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7403713479004523, 0], [8.0, 0]], [[1.0, 0], [9.080494845101747, 0], [27.0, 0]], [[1.0, 0], [1.0638619855160891, 0], [125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [37.446273064355985, 0], [1331.0, 0]], [[1.0, 0], [-27.12503127484398, 0], [2197.0, 0]], [[1.0, 0], 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'2.21922265412846551652454011218928', '3.86410243816593339942110566840420', '4.43689436242186573165231599250844', '5.17300000504000123487578789705429', '5.98842051991126828631691216581939', '6.31361956486384929648399189445316', '7.56720083511725327994954315737724', '8.252137045193937061556297838848847'], 'prelabel': '2-2107-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.149754453892495, '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': '0.74470332015773328993660357547', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.21922265412846551652454011219', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.86410243816593339942110566840', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 124.31702438209554, 'bad_primes': [7, 43], 'central_character': '1.1', 'conductor': 2107, 'conductor_radical': 301, 'degree': 2, 'index': 168, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2107/4/a/h/1/17'], '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': '2-2107-1.1-c3-0-168', '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': '2-2107-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.149754453892495, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.74470332015773328993660357547', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '944023610789905892680316704857', 'Lhash_array': ['944023610789905892680316704857'], 'label': '2-2107-1.1-c3-0-168', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2107/4/a/h/1/17'}