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lfunc_lfunctions • Show schema
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{'Lhash': '1506097262734899089759631726934', 'a10': [0.8093239188491615, 0.0], 'a2': [1.0, 0.0], 'a3': [2.572815572515058, 0.0], 'a4': [1.0, 0.0], 'a5': [0.8093239188491615, 0.0], 'a6': [2.572815572515058, 0.0], 'a7': [-0.4024665640645603, 0.0], 'a8': [1.0, 0.0], 'a9': [3.619379970175984, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.02405234066265, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [-1.0, 0]]], [211, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 19, 211], 'central_character': '8018.1', 'coefficient_field': 'CDF', 'conductor': 8018, 'conductor_radical': 8018, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.572815572515058, 0], [3.0, 0]], [[1.0, 0], [-0.8093239188491615, 0], [5.0, 0]], [[1.0, 0], [0.4024665640645603, 0], [7.0, 0]], [[1.0, 0], [-5.266622209676793, 0], [11.0, 0]], [[1.0, 0], [2.391054656685436, 0], [13.0, 0]], [[1.0, 0], 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197, 'label': '2-8018-1.1-c1-0-197', 'leading_term': '6.92670274436673156515498316804', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/8018/2/a/k/1/41', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [6.9267027443667315, 6.915316133739711, 6.881043515720824, 6.823556901529855, 6.742343552043901, 6.636754608905857, 6.506068939239416, 6.349568440829104, 6.1666205831251055, 5.956763801828559, 5.719791481462215, 5.455830588787371, 5.16541149041019, 4.849526036150635, 4.509671565064804, 4.147879059478319, 3.766724215866712, 3.369320714171333, 2.9592954514575105, 2.5407459678103885, 2.118180738535051, 1.6964434416442407, 1.2806227345535863, 0.875949486345455, 0.48768380571696884, 0.1209945704504373, -0.219165509800002, -0.5281859926647902, -0.8019224533028659, 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'7.24507795574260298878303495376399', '7.82490372627497230309518299492748'], 'prelabel': '2-8018-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.001503130078914, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.18810125003194054619416186606', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.06738054536607696967316320691', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.79880128979375860364429019090', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.02405234066265, 'bad_primes': [2, 19, 211], 'central_character': '1.1', 'conductor': 8018, 'conductor_radical': 8018, 'degree': 2, 'index': 197, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8018/2/a/k/1/41'], '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': '2-8018-1.1-c1-0-197', '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': '2-8018-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.001503130078914, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.18810125003194054619416186606', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1506097262734899089759631726934', 'Lhash_array': ['1506097262734899089759631726934'], 'label': '2-8018-1.1-c1-0-197', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8018/2/a/k/1/41'}