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lfunc_lfunctions • Show schema
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{'Lhash': '2967058124918813950605290629926', 'a10': [3.286329507638863, -0.5794685596950969], 'a2': [0.17364817766693036, -0.984807753012208], 'a3': [1.6773880645018282, 0.4317050857550911], 'a4': [-0.9396926207859084, -0.3420201433256687], 'a5': [1.1413302604290978, 3.13577911866921], 'a6': [0.7164218961074158, -1.5769399693006247], 'a7': [-1.0735637556113204, -1.8594669698832642], 'a8': [-0.5, 0.8660254037844386], 'a9': [2.627261437866379, 1.4482739164606562], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9102945830425968, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.17364817766693036, 0.984807753012208]]], [3, [[1.0, 0], [-1.6773880645018282, -0.4317050857550911]]], [19, [[1.0, 0], [-4.346397901811032, 0.3298867671378523]]]], 'bad_primes': [2, 3, 19], 'central_character': '114.59', 'coefficient_field': 'CDF', 'conductor': 114, 'conductor_radical': 114, 'conjugate': '3441513407524258239686844310762', 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[41.5, -71.88010851410841]], [[1.0, 0], [5.61887603967565, -4.714796812522693], [15.4546878123568, -87.64789001808651]], [[1.0, 0], [16.073409801423292, 2.8341758199748166], [91.15018421623311, 33.17595390258987]], [[1.0, 0], [3.6920727065600136, 4.400040912161924], [-17.538465944359967, 99.46558305423301]], [[1.0, 0], [0.9571265368244238, 0.5525972636841153], [51.5, 89.20061658979718]], [[1.0, 0], [3.476257393141273, 6.0210544251076215], [-53.5, 92.66471820493493]], [[1.0, 0], [-2.4288718565300904, -6.673270580565251], [-83.49884429996861, 70.06384945583278]], [[1.0, 0], [-2.330001761256047, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-114-57.2-c1-0-2', '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/114/2/l/b/59/3', 'plot_delta': {'__RealLiteral__': 0, 'data': 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{'__RealLiteral__': 0, 'data': '0.0594996434701', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.34059615826681349755095999868', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.53584581617290505220326034315', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.57881508231541731927475100820', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9102945830425968, 'bad_primes': [2, 3, 19], 'central_character': '57.2', 'conductor': 114, 'conductor_radical': 114, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/114/2/l/b/59/3'], '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': '2-114-57.2-c1-0-2', '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': '2-114-57.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9540935923915415, 'root_angle': 0.05949964347007176, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.34059615826681349755095999868', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2967058124918813950605290629926', 'Lhash_array': ['2967058124918813950605290629926'], 'label': '2-114-57.2-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/114/2/l/b/59/3'}