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lfunc_lfunctions • Show schema
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{'Lhash': '1380838384602984393096401297869', 'a10': [-0.8228756555322952, 1.4252624436934813], 'a2': [0.5, 0.8660254037844386], 'a3': [-1.3228756555322954, 2.29128784747792], 'a4': [-0.5, 0.8660254037844386], 'a5': [0.8228756555322952, 1.4252624436934813], 'a6': [-2.6457513110645907, -8.123000456411799e-61], 'a7': [-1.3228756555322954, -2.29128784747792], 'a8': [-1.0, 0.0], 'a9': [-2.0, -3.4641016151377544], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.2296961911277184, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, -0.8660254037844386]]], [7, [[1.0, 0], [1.3228756555322954, 2.29128784747792]]], [11, [[1.0, 0], [0.5, -0.8660254037844386]]]], 'bad_primes': [2, 7, 11], 'central_character': '154.67', 'coefficient_field': 'CDF', 'conductor': 154, 'conductor_radical': 154, 'conjugate': '4531229191419164454850916425160', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], 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'11.72042628501259952489798890958973', '12.57413659309207540298850665839357'], 'prelabel': '2-154-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1089166745647385, 'root_angle': -0.8131603802793873, 'root_number': '-0.8326204335587601 - 0.5538440336596778*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.40658019014', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.08928941804182991840182327617', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.77152966487750449609004297313', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.02323960448957484868037720839', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.2296961911277184, 'bad_primes': [2, 7, 11], 'central_character': '7.4', 'conductor': 154, 'conductor_radical': 154, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/154/2/e/f/67/1'], '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': '2-154-7.4-c1-0-0', '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': '2-154-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1089166745647385, 'root_angle': -0.40658019013969365, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.08928941804182991840182327617', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1380838384602984393096401297869', 'Lhash_array': ['1380838384602984393096401297869'], 'label': '2-154-7.4-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/154/2/e/f/67/1'}