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lfunc_lfunctions • Show schema
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{'Lhash': '2404076721329119764641451754985', 'a10': [0.0, -3.4641016151377544], 'a2': [-1.0, 0.0], 'a3': [1.5, -0.8660254037844386], 'a4': [1.0, 0.0], 'a5': [0.0, 3.4641016151377544], 'a6': [-1.5, 0.8660254037844386], 'a7': [1.0, 0.0], 'a8': [-1.0, 0.0], 'a9': [1.5, -2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9102945830425968, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [3, [[1.0, 0], [-1.5, 0.8660254037844386]]], [19, [[1.0, 0], [4.0, 1.7320508075688772]]]], 'bad_primes': [2, 3, 19], 'central_character': '114.113', 'coefficient_field': 'CDF', 'conductor': 114, 'conductor_radical': 114, 'conjugate': '2851843150944079643063623399190', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.5, 0.8660254037844386]], [[1.0, 0], [0, -3.4641016151377544], [-5.0, 0]], [[1.0, 0], [-1.0, 0], [7.0, 0]], [[1.0, 0], [0, 3.4641016151377544], [-11.0, 0]], [[1.0, 0], [0, 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'9.930035272462788786741653902003775', '11.39982173113675917207642660543460', '12.66236941589837179367898930518125', '13.41443002050458089445793186249520'], 'prelabel': '2-114-57.56-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9540935923915415, 'root_angle': -0.036593197520163684, 'root_number': '0.9933992677987828 - 0.1147078669352809*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0182965987601', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.89648213860845155691770044950', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.13413131291149390841434116951', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.35039909813264016226809681016', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9102945830425968, 'bad_primes': [2, 3, 19], 'central_character': '57.56', 'conductor': 114, 'conductor_radical': 114, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/114/2/b/b/113/1'], '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': '2-114-57.56-c1-0-2', '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': '2-114-57.56-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9540935923915415, 'root_angle': -0.018296598760081842, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.89648213860845155691770044950', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2404076721329119764641451754985', 'Lhash_array': ['2404076721329119764641451754985'], 'label': '2-114-57.56-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/114/2/b/b/113/1'}