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lfunc_lfunctions • Show schema
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{'Lhash': '1653140090389715052131572885444', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-10.0, 17.320508075688775], 'a4': [0, 0], 'a5': [37.0, 64.08587988004847], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [-78.5, -135.96598839415688], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 62.87045736668842, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7], 'central_character': '392.361', 'coefficient_field': 'CDF', 'conductor': 392, 'conductor_radical': 14, 'conjugate': '215443120620529753248532975567', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [10.0, -17.320508075688775], [-121.5, -210.4441731196186]], [[1.0, 0], [-37.0, -64.08587988004847], [-1562.5, 2706.329386826371]], [[1.0, 0], [0, 0]], [[1.0, 0], [62.0, -107.38715006927039], [-80525.5, -139474.25730488764]], [[1.0, 0], [-478.0, 0], [371293.0, 0]], [[1.0, 0], [-599.0, 1037.4984337337576], 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'0.6054643436493673635071294605077551469423497523567868621 + 0.7958724323465669471984178169629224157856347934855379281*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.14649371361272054', 'prec': 64}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.30409758816197589469217384022', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.65532519806933513359798353841', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.65707688917403336997711861529', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 62.87045736668842, 'bad_primes': [2, 7], 'central_character': '7.4', 'conductor': 392, 'conductor_radical': 14, 'degree': 2, 'index': 41, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/392/6/i/b/361/1'], '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': '2-392-7.4-c5-0-41', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-392-7.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.929089315090883, 'root_angle': 0.14649371361272054, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.30409758816197589469217384022', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1653140090389715052131572885444', 'Lhash_array': ['1653140090389715052131572885444'], 'label': '2-392-7.4-c5-0-41', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/392/6/i/b/361/1'}