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lfunc_lfunctions • Show schema
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{'Lhash': '1833512105216042530254166255228', 'a10': [-49687.89765945195, 50310.166230930205], 'a2': [-16.0, 16.0], 'a3': [326.1486309528985, 326.1486309528985], 'a4': [0.0, -512.0], 'a5': [3124.9394965744423, -19.445892858695412], 'a6': [-10436.756190492752, 0.0], 'a7': [-1507.1303400026477, 1507.1303400026477], 'a8': [8192.0, 8192.0], 'a9': [0.0, 153696.85894489993], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.353572526737245, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '5.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [16.0, -16.0]]], [5, [[1.0, 0], [-3124.9394965744423, 19.445892858695412]]]], 'bad_primes': [2, 5], 'central_character': '10.3', 'coefficient_field': 'CDF', 'conductor': 10, 'conductor_radical': 10, 'conjugate': '3396145029472641104879505618876', 'degree': 2, 'euler_factors': [[[1.0, 0], [16.0, -16.0]], [[1.0, 0], [-326.1486309528985, -326.1486309528985], [0, 59049.0]], [[1.0, 0], [-3124.9394965744423, 19.445892858695412]], [[1.0, 0], 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'18.42737129837583020962953988067104'], 'prelabel': '2-10-5.3-c10-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.520629390992901, 'root_angle': -0.2878862819950301, 'root_number': '-0.2358046948626566 - 0.9718004660838198*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.287886281995', 'prec': 50}, 'spectral_label': 'c10-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.44638601905441035155284825520', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.76067015636073612727335851885', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.87087864509810877173951289852', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.353572526737245, 'bad_primes': [2, 5], 'central_character': '5.3', 'conductor': 10, 'conductor_radical': 10, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/10/11/c/c/3/3'], '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': '2-10-5.3-c10-0-1', 'motivic_weight': 10, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [10], 'order_of_vanishing': 0, 'prelabel': '2-10-5.3-c10-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.520629390992901, 'root_angle': -0.2878862819950301, 'self_dual': False, 'spectral_label': 'c10-0', 'z1': {'__RealLiteral__': 0, 'data': '1.44638601905441035155284825520', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1833512105216042530254166255228', 'Lhash_array': ['1833512105216042530254166255228'], 'factors': ['2-10-5.3-c10-0-1'], 'label': '2-10-5.3-c10-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/10/11/c/c/3/3'}