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lfunc_lfunctions • Show schema
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{'Lhash': '987448474414117898313037367386', 'a10': [-0.8562327314277113, 1.4830385939362731], 'a2': [-1.3712442840299355, -2.3750647695282567], 'a3': [-1.2067581530473561, 2.090166433526], 'a4': [-2.7606217729695404, 4.781537171264119], 'a5': [-0.31221013695362065, -0.5407638198417085], 'a6': [6.6190408782908365, 0], 'a7': [1.2723693850570286, 2.319714669516404], 'a8': [9.656970170092531, 0], 'a9': [-1.4125304798925322, -2.446574558413514], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.446302559117473, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-1.2723693850570286, -2.319714669516404]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [7, 13], 'central_character': '1183.508', 'coefficient_field': 'CDF', 'conductor': 1183, 'conductor_radical': 91, 'conjugate': '966231216387196244500092212579', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.3712442840299355, 2.3750647695282567], [-1.0, 1.7320508075688772]], [[1.0, 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[[1.0, 0], [0.8674458736428261, -1.5024603259653473], [-54.5, -94.39676901250381]], [[1.0, 0], [-3.4374698808125643, -1.0756812135268687e-70], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 26, 'label': '2-1183-7.4-c1-0-26', 'leading_term': '0.680141286518972920975458298472713716873515173078635689', '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/1183/2/e/l/508/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.6801412865189729, 0.6773946914743905, 0.6674532877555904, 0.6501469758289725, 0.6252256246512576, 0.5923902105437638, 0.5513331917727002, 0.5017860228361636, 0.4435715311568974, 0.37665889921072504, 0.3012191444662559, 0.21767919197484784, 0.12677283001422784, 0.029586992486909994, -0.07239808830047058, -0.17727626097029392, 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'4.24193461416245516888720470193176', '5.14203738541288703153415147904201', '6.19577450471968034717094888894822', '6.66162627380980647204796775395386', '7.37203887138811227163987373744069', '7.81379453557553181412868332563731', '8.656352347978506013994088798289721', '9.657130792229731585496723679786468'], 'prelabel': '2-1183-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0734837821464867, 'root_angle': 0.19381250782823675, 'root_number': '0.8202891433422365699046395177793653784158458389400362700 + 0.571949054824692988251784853744954755358012623055412821*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.09690625391411838', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.77895949738542816012124188879', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.67744385079222792761153488574', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.24193461416245516888720470193', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.446302559117473, 'bad_primes': [7, 13], 'central_character': '7.4', 'conductor': 1183, 'conductor_radical': 91, 'degree': 2, 'index': 26, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1183/2/e/l/508/1'], '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': '2-1183-7.4-c1-0-26', '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': '2-1183-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0734837821464867, 'root_angle': 0.09690625391411838, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.77895949738542816012124188879', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '987448474414117898313037367386', 'Lhash_array': ['987448474414117898313037367386'], 'label': '2-1183-7.4-c1-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1183/2/e/l/508/1'}