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lfunc_lfunctions • Show schema
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{'Lhash': '1624845737755732563343629690810', 'a10': 250, 'a2': 2, 'a3': 0, 'a4': -124, 'a5': 125, 'a6': 0, 'a7': 343, 'a8': -504, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 98.4012830274984, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, -125]], [7, [1, -343]]], 'bad_primes': [3, 5, 7], 'central_character': '315.1', 'coefficient_field': '1.1.1.1', 'conductor': 315, 'conductor_radical': 105, 'degree': 2, 'euler_factors': [[1, -2, 128], [1], [1, -125], [1, -343], [1, 2724, 19487171], [1, -2874, 62748517], [1, 9278, 410338673], [1, 4304, 893871739], [1, -41500, 3404825447], [1, -35498, 17249876309], [1, 52940, 27512614111], [1, 84098, 94931877133], [1, 180342, 194754273881], [1, 33452, 271818611107], [1, -136120, 506623120463], [1, -1270622, 1174711139837], [1, -1553252, 2488651484819], [1, -213598, 3142742836021], [1, -487228, 6060711605323], [1, 1086000, 9095120158391], [1, 5921978, 11047398519097], 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'positive_zeros': ['1.28177727953048994887417205121112', '2.71048883429078753857118637643491', '4.00425285494690616056593847641590', '5.01104748816947260210337486803296', '5.78613140817393934315282691278429', '7.08617885469246626824000488682015', '8.324389533298515320035954047280121', '8.941675942387986477726587270182164', '9.978714357961983819834016362633646'], 'prelabel': '2-315-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.91974208472672, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c7-0', 'trace_hash': 1208903960117537235, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.28177727953048994887417205121', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.71048883429078753857118637643', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.00425285494690616056593847642', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 98.4012830274984, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 315, 'conductor_radical': 105, 'degree': 2, 'dirichlet_coefficients': [1, 2, 0, -124, 125, 0, 343, -504, 0, 250, -2724, 0, 2874, 686, 0, 14864, -9278, 0, -4304, -15500, 0, -5448, 41500, 0, 15625, 5748, 0, -42532, 35498, 0, -52940, 94240, 0, -18556, 42875, 0, -84098, -8608, 0, -63000, -180342, 0, -33452, 337776, 0, 83000, 136120, 0, 117649, 31250, 0, -356376, 1270622, 0, -340500, -172872, 0, 70996, 1553252, 0, 213598, -105880, 0, -1714112, 359250, 0, 487228, 1150472, 0, 85750, -1086000, 0, -5921978, -168196, 0, 533696, -934332, 0, -5429824, 1858000, 0, -360684, -6933404, 0, -1159750, -66904, 0, 1372896, -262614, 0, 985782, -5146000, 0, 272240, -538000, 0, -522234, 235298, 0, -1937500], 'euler11': [1, 2724, 19487171], 'euler13': [1, -2874, 62748517], 'euler17': [1, 9278, 410338673], 'euler19': [1, 4304, 893871739], 'euler2': [1, -2, 128], 'euler23': [1, -41500, 3404825447], 'euler29': [1, -35498, 17249876309], 'euler3': [1, 0, 0], 'euler31': [1, 52940, 27512614111], 'euler37': [1, 84098, 94931877133], 'euler41': [1, 180342, 194754273881], 'euler43': [1, 33452, 271818611107], 'euler47': [1, -136120, 506623120463], 'euler5': [1, -125, 0], 'euler53': [1, -1270622, 1174711139837], 'euler59': [1, -1553252, 2488651484819], 'euler61': [1, -213598, 3142742836021], 'euler67': [1, -487228, 6060711605323], 'euler7': [1, -343, 0], 'euler71': [1, 1086000, 9095120158391], 'euler73': [1, 5921978, 11047398519097], 'euler79': [1, 5429824, 19203908986159], 'euler83': [1, 6933404, 27136050989627], 'euler89': [1, 262614, 44231334895529], 'euler97': [1, 522234, 80798284478113], 'euler_factors': [[1, -2, 128], [1, 0, 0], [1, -125, 0], [1, -343, 0], [1, 2724, 19487171], [1, -2874, 62748517], [1, 9278, 410338673], [1, 4304, 893871739], [1, -41500, 3404825447], [1, -35498, 17249876309], [1, 52940, 27512614111], [1, 84098, 94931877133], [1, 180342, 194754273881], [1, 33452, 271818611107], [1, -136120, 506623120463], [1, -1270622, 1174711139837], [1, -1553252, 2488651484819], [1, -213598, 3142742836021], [1, -487228, 6060711605323], [1, 1086000, 9095120158391], [1, 5921978, 11047398519097], [1, 5429824, 19203908986159], [1, 6933404, 27136050989627], [1, 262614, 44231334895529], [1, 522234, 80798284478113]], 'index': 56, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/315/8/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/315/8/a/b'], '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': '2-315-1.1-c7-0-56', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 1, 'prelabel': '2-315-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.91974208472672, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c7-0', 'trace_hash': 1208903960117537235, 'z1': {'__RealLiteral__': 0, 'data': '1.28177727953048994887417205121', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20875920
{'Lhash': '1624845737755732563343629690810', 'Lhash_array': ['1624845737755732563343629690810'], 'factors': ['2-315-1.1-c7-0-56'], 'label': '2-315-1.1-c7-0-56', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/315/8/a/b'}
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id: 24591916
{'Lhash': '1624845737755732563343629690810', 'Lhash_array': ['1624845737755732563343629690810'], 'factors': ['2-315-1.1-c7-0-56'], 'label': '2-315-1.1-c7-0-56', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/315/8/a/b/1/1'}