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lfunc_lfunctions • Show schema
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{'Lhash': '1395385718455353883416053723621', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.5264397284942957, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.0193554789367, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '1380.1', 'coefficient_field': 'CDF', 'conductor': 1380, 'conductor_radical': 690, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.5264397284942957, 0], [7.0, 0]], [[1.0, 0], [3.5982107418842784, 0], [11.0, 0]], [[1.0, 0], [-5.598210741884278, 0], [13.0, 0]], [[1.0, 0], [-4.0717710133899825, 0], [17.0, 0]], [[1.0, 0], [1.5982107418842784, 0], [19.0, 0]], [[1.0, 0], [-1.0, 0]], 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0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-1380-1.1-c1-0-5', 'leading_term': '2.11126403560208362919106430342', '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/1380/2/a/j/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.1112640356020838, 2.1070365263830233, 2.0942177109360407, 2.0724082101372723, 2.040973263169048, 1.9990865573457504, 1.9457870464965923, 1.8800450528269688, 1.8008338293362383, 1.707203005536037, 1.598350806527041, 1.4736924809238983, 1.3329228858219924, 1.1760715932022088, 1.003549182648834, 0.8161835832942896, 0.6152454548588606, 0.40246169070512655, 0.18001621970259277, -0.04946259376425701, -0.2829284817527983, -0.5169580372066366, -0.7478057191982722, -0.9714727550616881, -1.1837891909787768, 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'6.25210672291659146773954580449264', '7.48946655346227699858853883078271', '7.989372098118033589802635454201386', '8.586356637424984742981632266419217', '9.495514595785548947709803492479502'], 'prelabel': '2-1380-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3195414561256347, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.10076524099316238344841236551', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.47009396817158378024093374842', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.49862922096268542721387489359', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.0193554789367, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 1380, 'conductor_radical': 690, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1380/2/a/j/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': '2-1380-1.1-c1-0-5', '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': '2-1380-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3195414561256347, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.10076524099316238344841236551', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1395385718455353883416053723621', 'Lhash_array': ['1395385718455353883416053723621'], 'label': '2-1380-1.1-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1380/2/a/j/1/2'}