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lfunc_lfunctions • Show schema
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{'Lhash': '1791791089188790647988862142772', 'a10': [1.0724694340966112, -2.0421326164169742e-61], 'a2': [0.5, 0.8660254037844386], 'a3': [-1.6171973788691718, -0.6202198302043241], 'a4': [-0.5, 0.8660254037844386], 'a5': [0.5362347170483056, -0.928785774709986], 'a6': [-0.27147256054677005, -1.7106439281364723], 'a7': [-0.12195057329772192, -0.2112245889638068], 'a8': [-1.0, 0.0], 'a9': [2.2306547244426387, 2.0060357674582314], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.3058066436810094, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, -0.8660254037844386]]], [3, [[1.0, 0], [1.6171973788691718, 0.6202198302043241]]], [23, [[1.0, 0], [0.5, -0.8660254037844386]]]], 'bad_primes': [2, 3, 23], 'central_character': '414.139', 'coefficient_field': 'CDF', 'conductor': 414, 'conductor_radical': 138, 'conjugate': '1313364965415391283920084888933', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, 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'8.806112774025514548471110765503239', '9.777133568196975173795713841123104', '10.46709754694212677444243467055080', '11.20428029451783508925215700579484'], 'prelabel': '2-414-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8181877360935557, 'root_angle': 0.010917552371116001, 'root_number': '0.9994118640288525 + 0.034291777999607656*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.00545877618556', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.41347394058441208997029240118', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.21740010107713385842097365574', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.31614438339273500131975055632', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.3058066436810094, 'bad_primes': [2, 3, 23], 'central_character': '9.4', 'conductor': 414, 'conductor_radical': 138, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/414/2/e/d/139/1'], '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': '2-414-9.4-c1-0-13', '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': '2-414-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8181877360935557, 'root_angle': 0.005458776185558001, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.41347394058441208997029240118', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1791791089188790647988862142772', 'Lhash_array': ['1791791089188790647988862142772'], 'label': '2-414-9.4-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/414/2/e/d/139/1'}