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lfunc_lfunctions • Show schema
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{'Lhash': '3037616291094434508117251204942', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.5, 0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [2.1374586088176875, -3.7021869095477244], 'a6': [0.0, 0.0], 'a7': [-1.5, -2.179449471770337], 'a8': [0.0, 0.0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.5, -0.8660254037844386]]], [7, [[1.0, 0], [1.5, 2.179449471770337]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.121', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': '2095081433605694502409400665947', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [-2.1374586088176875, 3.7021869095477244], [-2.5, -4.330127018922194]], [[1.0, 0], [1.5, 2.179449471770337]], [[1.0, 0], [-2.1374586088176875, 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[[1.0, 0], [-2.0, 0], [71.0, 0]], [[1.0, 0], [1.6374586088176875, 2.8361615057632856], [-36.5, 63.21985447626402]], [[1.0, 0], [-1.774917217635375, 3.0742468001732557], [-39.5, -68.41600689897065]], [[1.0, 0], [0.27491721763537486, 0], [83.0, 0]], [[1.0, 0], [2.274917217635375, -3.9402722039576945], [-44.5, -77.07626093681505]], [[1.0, 0], [-16.274917217635373, 0], [97.0, 0]], [[1.0, 0], [-3.0, -5.196152422706632], [-50.5, 87.4685657822283]], [[1.0, 0], [-5.912375826453062, 10.240535324858735], [-51.5, -89.20061658979718]], [[1.0, 0], [3.4123758264530624, -5.910408305936541], [-53.5, -92.66471820493493]], [[1.0, 0], [-2.9123758264530624, -5.044382902152103], [-54.5, 94.39676901250381]], [[1.0, 0], [-10.54983443527075, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-168-7.2-c1-0-3', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 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+ 0.371874752362654*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0606424574003', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.39625673710684810717946442515', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.27195594437754236239031944103', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.79316225419544392806601559543', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.341486753957511, 'bad_primes': [2, 3, 7], 'central_character': '7.2', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/q/c/121/2'], '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': '2-168-7.2-c1-0-3', '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': '2-168-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.060642457400302385, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.39625673710684810717946442515', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3037616291094434508117251204942', 'Lhash_array': ['3037616291094434508117251204942'], 'label': '2-168-7.2-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/q/c/121/2'}