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lfunc_lfunctions • Show schema
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{'Lhash': '1232689416068932859694957160562', 'a10': [-1.0, -0.20871215252208], 'a2': [0.0, 0.45685025174785665], 'a3': [0.0, 0.0], 'a4': [1.79128784747792, 0.0], 'a5': [-0.45685025174785665, 2.1889010593167337], 'a6': [0.0, 0.0], 'a7': [0.0, -1.0], 'a8': [0.0, 1.7320508075688772], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.545862991011, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.45685025174785665, -2.1889010593167337]]], [7, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [3, 5, 7], 'central_character': '945.379', 'coefficient_field': 'CDF', 'conductor': 945, 'conductor_radical': 105, 'conjugate': '2039436980236470936944606555996', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -0.45685025174785665], [-2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.45685025174785665, -2.1889010593167337]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [-1.7320508075688772, 0], [11.0, 0]], [[1.0, 0], 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'3.37335262069966511475326813110349', '4.51542583911330078155634383489060', '5.50199672602639983408678496720177', '6.45559798167401767684262435592542', '7.33510543513732264243742411312245', '8.246299532839084818803423509275755', '9.107425287089104097953038204547008', '9.823451266697743417535511845138937'], 'prelabel': '2-945-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.746973423790445, 'root_angle': -0.4345050597827727, 'root_number': '0.2043096436892199 - 0.9789063129307033*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.217252529891', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.972420488616498831440526230080', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.21497719604253992350322779417', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.37335262069966511475326813110', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.545862991011, 'bad_primes': [3, 5, 7], 'central_character': '5.4', 'conductor': 945, 'conductor_radical': 105, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/945/2/d/c/379/5'], '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': '2-945-5.4-c1-0-17', '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': '2-945-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.746973423790445, 'root_angle': -0.21725252989138635, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.972420488616498831440526230080', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1232689416068932859694957160562', 'Lhash_array': ['1232689416068932859694957160562'], 'label': '2-945-5.4-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/945/2/d/c/379/5'}