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lfunc_lfunctions • Show schema
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{'Lhash': '2086424549658933287612049258034', 'a10': [0, 0], 'a2': [-1.7320508075688772, -1.0], 'a3': [-0.8660254037844386, -1.5], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 3.4641016151377544], 'a7': [6.06217782649107, 3.5], 'a8': [0, 8.0], 'a9': [-1.5, 2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.30521387891559, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.8660254037844386, 1.5]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-6.06217782649107, -3.5]]]], 'bad_primes': [3, 5, 7], 'central_character': '525.124', 'coefficient_field': 'CDF', 'conductor': 525, 'conductor_radical': 105, 'conjugate': '175291267287114912355259196220', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.7320508075688772, 1.0], [2.0, 3.4641016151377544]], [[1.0, 0], [0.8660254037844386, 1.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [-6.06217782649107, -3.5]], [[1.0, 0], [5.0, 8.660254037844387], [-60.5, 104.78907385791707]], [[1.0, 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'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3869521891046038', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.64589875891928801117574003327', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.72863635681364083389026851569', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.47511321823972356152147722499', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.30521387891559, 'bad_primes': [3, 5, 7], 'central_character': '35.19', 'conductor': 525, 'conductor_radical': 105, 'degree': 2, 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/525/3/s/d/124/1'], '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': '2-525-35.19-c2-0-36', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-525-35.19-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.782223404152059, 'root_angle': -0.3869521891046038, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.64589875891928801117574003327', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2086424549658933287612049258034', 'Lhash_array': ['2086424549658933287612049258034'], 'label': '2-525-35.19-c2-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/525/3/s/d/124/1'}