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lfunc_lfunctions • Show schema
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{'Lhash': '1522071935840880515399185731280', 'a10': [4.325178578928116, 0.0], 'a2': [1.0, 0.0], 'a3': [-0.3522708605874692, 0.0], 'a4': [1.0, 0.0], 'a5': [4.325178578928116, 0.0], 'a6': [-0.3522708605874692, 0.0], 'a7': [1.0, 0.0], 'a8': [1.0, 0.0], 'a9': [-2.875905240780964, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 40.35639318155513, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7, 19], 'central_character': '5054.1', 'coefficient_field': 'CDF', 'conductor': 5054, 'conductor_radical': 266, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.3522708605874692, 0], [3.0, 0]], [[1.0, 0], [-4.325178578928116, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.352270860587469, 0], [11.0, 0]], [[1.0, 0], [-0.8015441987346218, 0], [13.0, 0]], [[1.0, 0], [-6.228176101368433, 0], [17.0, 0]], [[1.0, 0], [0, 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[109.0, 0]], [[1.0, 0], [1.4763656198065054, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 104, 'label': '2-5054-1.1-c1-0-104', 'leading_term': '4.7408130601550625676997845266803', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/5054/2/a/x/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [4.740813060155062, 4.732207404821833, 4.706274161432073, 4.662675616986494, 4.600885199792266, 4.520239263833016, 4.420004615591768, 4.299457469746234, 4.15796907973647, 3.995093232345278, 3.810651048896023, 3.6048090029288424, 3.378146649562825, 3.131711187367162, 2.8670565874560014, 2.5862656005235913, 2.2919534851605614, 1.9872527979294223, 1.6757790614296622, 1.3615775955261986, 1.0490522702296992, 0.7428774220719547, 0.44789466863253835, 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'5.47371668652524841200611848065425', '5.89578856850836512420273487148638', '6.44957194833157577845151288784344', '7.29267829314900472609553866763756', '8.314517626076476499838680070337051'], 'prelabel': '2-5054-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.352668193881617, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.20070304511893480588138578214', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.94329287585814635329165025848', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.84894352905872127055051205989', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 40.35639318155513, 'bad_primes': [2, 7, 19], 'central_character': '1.1', 'conductor': 5054, 'conductor_radical': 266, 'degree': 2, 'index': 104, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5054/2/a/x/1/2'], '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': '2-5054-1.1-c1-0-104', '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': '2-5054-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.352668193881617, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.20070304511893480588138578214', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1522071935840880515399185731280', 'Lhash_array': ['1522071935840880515399185731280'], 'label': '2-5054-1.1-c1-0-104', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5054/2/a/x/1/2'}