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lfunc_lfunctions • Show schema
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{'Lhash': '2215248117773915996432683422840', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.3660254037844386, 1.3660254037844386], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.830444181021316, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0.8660254037844386, 0.5]]]], 'bad_primes': [2, 13], 'central_character': '1664.449', 'coefficient_field': 'CDF', 'conductor': 1664, 'conductor_radical': 26, 'conjugate': '36874837221953440941129453167', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [1.3660254037844386, -1.3660254037844386], [0, -1.0]], [[1.0, 0], [0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], [0, 0], [0.8660254037844386, -0.5]], [[1.0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], 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1.7971717494453745, 1.1085227553067623], 'positive_zeros': ['1.74752263547627394428401010208647', '3.11253171366067046380573896329045', '4.32173653278857551919963377260592', '4.78735313925148670847066592521094', '5.53727845418375049998595239591747', '6.95899687281277291026414748149587', '7.63088109770767674509761874159820', '8.315761603218261739950486559859402', '8.953890238485337355403477827879225', '9.627160228462341842120469354524834'], 'prelabel': '2-1664-104.85-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9112871013140239, 'root_angle': 0.41256204857686696, 'root_number': '-0.85284380225587800538335211690172 + 0.52216611241417884070227958465117*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.41256204857686696', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.74752263547627394428401010209', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.11253171366067046380573896329', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.32173653278857551919963377261', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.830444181021316, 'bad_primes': [2, 13], 'central_character': '104.85', 'conductor': 1664, 'conductor_radical': 26, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1664/1/bv/a/449/1'], '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': '2-1664-104.85-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1664-104.85-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9112871013140239, 'root_angle': 0.41256204857686696, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.74752263547627394428401010209', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2215248117773915996432683422840', 'Lhash_array': ['2215248117773915996432683422840'], 'factors': ['2-1664-104.85-c0-0-0'], 'label': '2-1664-104.85-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1664/1/bv/a/449/1'}