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lfunc_lfunctions • Show schema
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{'Lhash': '2331783514605606862245202868418', 'a10': 3080, 'a2': 22, 'a3': 21, 'a4': 356, 'a5': 140, 'a6': 462, 'a7': -343, 'a8': 5016, 'a9': -1746, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.427037319055092, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[7, [1, 343]], [13, [1, 2197]]], 'bad_primes': [7, 13], 'central_character': '91.1', 'coefficient_field': '1.1.1.1', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'euler_factors': [[1, -22, 128], [1, -21, 2187], [1, -140, 78125], [1, 343], [1, -5051, 19487171], [1, 2197], [1, -27384, 410338673], [1, 32690, 893871739], [1, 23085, 3404825447], [1, 14068, 17249876309], [1, 203007, 27512614111], [1, -544041, 94931877133], [1, 352079, 194754273881], [1, -340412, 271818611107], [1, -406329, 506623120463], [1, 1909680, 1174711139837], [1, 2867214, 2488651484819], [1, 216419, 3142742836021], [1, -2538043, 6060711605323], [1, 2071872, 9095120158391], [1, -185913, 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'4.11416711914782565940976020985', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 28.427037319055092, 'bad_primes': [7, 13], 'central_character': '1.1', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'dirichlet_coefficients': [1, 22, 21, 356, 140, 462, -343, 5016, -1746, 3080, 5051, 7476, -2197, -7546, 2940, 64784, 27384, -38412, -32690, 49840, -7203, 111122, -23085, 105336, -58525, -48334, -82593, -122108, -14068, 64680, -203007, 783200, 106071, 602448, -48020, -621576, 544041, -719180, -46137, 702240, -352079, -158466, 340412, 1798156, -244440, -507870, 406329, 1360464, 117649, -1287550, 575064, -782132, -1909680, -1817046, 707140, -1720488, -686490, -309496, -2867214, 1046640, -216419, -4466154, 598878, 8938048, -307580, 2333562, 2538043, 9748704, -484785, -1056440, -2071872, -8757936, 185913, 11968902, -1229025, -11637640, -1732493, -1015014, -954631, 9069760, 2084049, -7745738, 5649672, -2564268, 3833760, 7489064, -295428, 25335816, -4673830, -5377680, 753571, -8218260, -4263147, 8939238, -4576600, 16447200, -13686645, 2588278, -8819046, -20834900], 'euler11': [1, -5051, 19487171], 'euler13': [1, 2197, 0], 'euler17': [1, -27384, 410338673], 'euler19': [1, 32690, 893871739], 'euler2': [1, -22, 128], 'euler23': [1, 23085, 3404825447], 'euler29': [1, 14068, 17249876309], 'euler3': [1, -21, 2187], 'euler31': [1, 203007, 27512614111], 'euler37': [1, -544041, 94931877133], 'euler41': [1, 352079, 194754273881], 'euler43': [1, -340412, 271818611107], 'euler47': [1, -406329, 506623120463], 'euler5': [1, -140, 78125], 'euler53': [1, 1909680, 1174711139837], 'euler59': [1, 2867214, 2488651484819], 'euler61': [1, 216419, 3142742836021], 'euler67': [1, -2538043, 6060711605323], 'euler7': [1, 343, 0], 'euler71': [1, 2071872, 9095120158391], 'euler73': [1, -185913, 11047398519097], 'euler79': [1, 954631, 19203908986159], 'euler83': [1, -5649672, 27136050989627], 'euler89': [1, 4673830, 44231334895529], 'euler97': [1, 13686645, 80798284478113], 'euler_factors': [[1, -22, 128], [1, -21, 2187], [1, -140, 78125], [1, 343, 0], [1, -5051, 19487171], [1, 2197, 0], [1, -27384, 410338673], [1, 32690, 893871739], [1, 23085, 3404825447], [1, 14068, 17249876309], [1, 203007, 27512614111], [1, -544041, 94931877133], [1, 352079, 194754273881], [1, -340412, 271818611107], [1, -406329, 506623120463], [1, 1909680, 1174711139837], [1, 2867214, 2488651484819], [1, 216419, 3142742836021], [1, -2538043, 6060711605323], [1, 2071872, 9095120158391], [1, -185913, 11047398519097], [1, 954631, 19203908986159], [1, -5649672, 27136050989627], [1, 4673830, 44231334895529], [1, 13686645, 80798284478113]], 'index': 31, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/91/8/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/91/8/a/a'], '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': '2-91-1.1-c7-0-31', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-91-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.331701165580746, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c7-0', 'trace_hash': 1191754241096160648, 'z1': {'__RealLiteral__': 0, 'data': '1.83945285411121143181725198345', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20742610
{'Lhash': '2331783514605606862245202868418', 'Lhash_array': ['2331783514605606862245202868418'], 'label': '2-91-1.1-c7-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/8/a/a'}
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id: 24562109
{'Lhash': '2331783514605606862245202868418', 'Lhash_array': ['2331783514605606862245202868418'], 'label': '2-91-1.1-c7-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/8/a/a/1/1'}