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lfunc_lfunctions • Show schema
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{'Lhash': '3733421386400977659080606984496', 'a10': [-1.4159101141686763, 2.452428256690797], 'a2': [1.5579924749153908, 0.0], 'a3': [-1.1984977837384674, -2.0758590541937223], 'a4': [0.427340551892985, 0.0], 'a5': [-0.9088042060315916, 1.5740950589790106], 'a6': [-1.8672505282673058, -3.2341727854188], 'a7': [-1.8050235406483286, -3.1263924812607717], 'a8': [-2.450191585755321, 0.0], 'a9': [-1.3727938752520366, 2.3777487402558988], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.217971201457601, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[13, [[1.0, 0], [0.5, -0.8660254037844386]]], [31, [[1.0, 0], [-3.743501016716535, 4.1214318067684035]]]], 'bad_primes': [13, 31], 'central_character': '403.118', 'coefficient_field': 'CDF', 'conductor': 403, 'conductor_radical': 403, 'conjugate': '476116375192134025412387036769', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.5579924749153908, 0], [2.0, 0]], [[1.0, 0], [1.1984977837384674, 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'9.946958687345720344533214642817510', '10.91633957790693824375248422250825', '12.01256255211702214782395780996449'], 'prelabel': '2-403-31.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7938704528080063, 'root_angle': 0.47018373376872863, 'root_number': '-0.9825029153579806 + 0.18624720484632437*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.470183733769', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.94515017444776012999834785096', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.06245449722067142572071366908', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.82293108800944802561752565751', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.217971201457601, 'bad_primes': [13, 31], 'central_character': '31.25', 'conductor': 403, 'conductor_radical': 403, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/403/2/h/b/118/13'], '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': '2-403-31.25-c1-0-30', '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': '2-403-31.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7938704528080063, 'root_angle': 0.47018373376872863, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.94515017444776012999834785096', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3733421386400977659080606984496', 'Lhash_array': ['3733421386400977659080606984496'], 'factors': ['2-403-31.25-c1-0-30'], 'label': '2-403-31.25-c1-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/403/2/h/b/118/13'}