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lfunc_lfunctions • Show schema
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{'Lhash': '852634137536462594054196749990', 'a10': [3.4136473038210635, 5.049770657120267], 'a2': [-1.6022549791999419, -2.2053147853557165], 'a3': [-0.9510565162951535, 0.30901699437494745], 'a4': [-1.6781582953876277, 5.164840158488588], 'a5': [-2.234784618040114, -0.07574767964302408], 'a6': [2.2053147853557165, 1.6022549791999419], 'a7': [0.4625285464362922, 0.15028463480712775], 'a8': [8.893929820205834, -2.889812975498067], 'a9': [0.8090169943749475, -0.5877852522924731], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3175316333511269, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.9510565162951535, -0.30901699437494745]]], [5, [[1.0, 0], [2.234784618040114, 0.07574767964302408]]], [11, [[1.0, 0], [-3.0656829379956356, -1.2655386693746062]]]], 'bad_primes': [3, 5, 11], 'central_character': '165.124', 'coefficient_field': 'CDF', 'conductor': 165, 'conductor_radical': 165, 'conjugate': 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[-25.648410533120636, -78.93769085249775]], [[1.0, 0], [1.383537687403005, 0], [89.0, 0]], [[1.0, 0], [-0.8227406368179628, -1.132405337753184], [-29.974648454369902, 92.2524820806299]], [[1.0, 0], [-0.09160094574376013, 0.06655198268835338], [31.210716431869688, -96.05670814581052]], [[1.0, 0], [6.893546012112622, 2.239848876223196], [83.32875042061958, 60.54188098612473]], [[1.0, 0], [8.235003353964185, -2.675714788247008], [86.56481839811937, -62.893021995294625]], [[1.0, 0], [4.415733329237201, 0], [109.0, 0]], [[1.0, 0], [-17.465880371397734, 5.675008544714832], [91.41892036436906, -66.41973350904946]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-165-55.14-c1-0-0', '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/165/2/s/a/124/1', 'plot_delta': {'__RealLiteral__': 0, 'data': 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'0.0214851783576', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.67260973755935056253684694863', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.40721581348214180297179848456', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.73392295349008015950369209737', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3175316333511269, 'bad_primes': [3, 5, 11], 'central_character': '55.14', 'conductor': 165, 'conductor_radical': 165, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/165/2/s/a/124/1'], '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': '2-165-55.14-c1-0-0', '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': '2-165-55.14-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1478378079463696, 'root_angle': 0.021485178357584716, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.67260973755935056253684694863', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '852634137536462594054196749990', 'Lhash_array': ['852634137536462594054196749990'], 'label': '2-165-55.14-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/165/2/s/a/124/1'}