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lfunc_lfunctions • Show schema
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{'Lhash': '878600003761095357958147462164', 'a10': [0.87053871919756, 0.0], 'a2': [1.367676394180129, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.12946128080243996, 0.0], 'a5': [0.6365092816560715, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [-2.9124139260740805, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 60.86996146082207, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7, 11], 'central_character': '7623.1', 'coefficient_field': 'CDF', 'conductor': 7623, 'conductor_radical': 231, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.367676394180129, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.6365092816560715, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.594855934365672, 0], [13.0, 0]], [[1.0, 0], [-1.4623342250481155, 0], [17.0, 0]], [[1.0, 0], [5.853778495970552, 0], [19.0, 0]], 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'3.69675929417969286816618255226313', '4.43479820599443244861896516794104', '5.00061506095793156474986931482527', '5.59242548594641137501371642050658', '6.33567660970279767286833926936881', '7.01842508533187378312603539544641', '7.82116225243411739036404377428191'], 'prelabel': '2-7623-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.80192037006416, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.69309319429416206093615435197', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.11361236339331091022617459059', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.75870396242534950895593793844', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 60.86996146082207, 'bad_primes': [3, 7, 11], 'central_character': '1.1', 'conductor': 7623, 'conductor_radical': 231, 'degree': 2, 'index': 78, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7623/2/a/cr/1/5'], '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': '2-7623-1.1-c1-0-78', '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': '2-7623-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.80192037006416, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.69309319429416206093615435197', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '878600003761095357958147462164', 'Lhash_array': ['878600003761095357958147462164'], 'label': '2-7623-1.1-c1-0-78', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7623/2/a/cr/1/5'}