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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': 2, 'A4': 1, 'A5': 0, 'A6': 2, 'A7': -1, 'A8': 1, 'A9': 1, 'Lhash': '1427945667270373716', 'a10': [0.0, 0], 'a2': [0.7071067811865475, 0], 'a3': [1.1547005383792517, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.8164965809277261, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 206.7007506722865, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [7, [1, 1]], [43, [1]]], 'bad_primes': [2, 7, 43], 'central_character': '25886.1', 'coefficient_field': '1.1.1.1', 'conductor': 25886, 'conductor_radical': 602, 'degree': 2, 'euler_factors': [[1, -1], [1, -2, 3], [1, 0, 5], [1, 1], [1, 0, 11], [1, 4, 13], [1, -6, 17], [1, 2, 19], [1, 0, 23], [1, -6, 29], [1, 4, 31], [1, 2, 37], [1, -6, 41], [1], [1, 12, 47], [1, -6, 53], [1, 6, 59], [1, 8, 61], [1, 4, 67], [1, 0, 71], [1, 2, 73], [1, -8, 79], [1, 6, 83], [1, -6, 89], [1, 10, 97]], 'gamma_factors': [[], [0]], 'index': 3, 'label': '2-25886-1.1-c1-0-3', 'leading_term': '11.1163328022', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/Q/25886/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 2.672738379034541, 4.662998317555873, 5.230702444070805, 3.989901682218366, 1.457033413141248, -0.9849377509207751, -1.961204275168562, -1.202839921639006, 0.1946102794309054, 0.7914768670296541, 0.2219596597113646, -0.5058037927822158, -0.2910918764301773, 0.6013069299677825, 0.7729280150035219, -0.4360221494803578, -1.750573095570586, -1.303924198280221, 0.8232703403330783, 2.245137671252792, 1.101373242254313, -1.291740344523052, -1.777413467636909, 0.5176624643286601, 2.688343617680238, 1.669014182630942, -1.568675611612863, -3.143433741619886, -1.49229215840846, 0.6082977051695848, 0.2853530052498236, -1.090732769776482, -0.1373835524771574, 2.91773940067389, 4.047097780519222, 1.490007755151387, -1.205408447286832, -0.4043902668743285, 1.934396511920503, 1.398519263060492, -1.396861489994318, -1.139737348064681, 3.710229486594758, 7.526471232218881, 5.292266369890043, -0.02549094225478792, -1.966652766005061, 0.1275291874290662, 1.367095695360986, -0.2642160480040573, -1.411103723721699, 0.063569889740682, 1.465849570413031, 0.4227934012841255, -1.056952918678852, -0.6530983040275258, 0.1962835896103316, -0.3028848391778512, -0.6059079851697634, 0.6149865654067596, 0.9698756381348687, -1.075134596590907, -1.941240826747543, 1.226601137702582, 4.268130082444848, 2.44127854264592, -0.3664151848764577, 2.455217816659627, 7.638163940913679, 5.911828423109947, -1.993034765552507, -4.865532633671776, 1.430262209943375, 7.516284454616838, 5.71447997032174, 0.7252097269944666, -0.5351657957057079, 0.3651748732385159, -0.3750650904178673, -0.7986315969716633, 1.304674583208703, 2.614921036227393, 0.7089718679814653, -0.9266889025083384, -0.02806249714683502, -0.01561390596684426, -2.197955471879762, -2.073677204647787, 1.543229094245878, 2.942269723954058, -0.03685064118829434, -1.852334869487184, -0.170781072071622, -0.223453256792222, -3.744659558615255, -4.887762022050549, -1.582734648781256, 0.527404071142659, -0.8221520030282444, -1.14702853593344, 0.6186444301162835, 0.5290612916799956, -0.9394194056897404, -0.1325204733296908, 0.3757660024111045, -3.433163799124127, -6.510289501422604, -3.016989573706306, 0.9396850766563937, -1.872587927192565, -4.572466552569789, 1.382545802307047, 8.31244761903346, 5.018475111332542, -2.976739089479136, -4.004325387828636, -0.2267931047073025, 0.0890510631736982, -1.136573648688225, 1.183108132757846], 'positive_zeros': ['1.387508483491029', '2.211122507319805', '2.812278726005327', '3.335728854277714', '3.930055982342773', '4.661410877754398', '5.361339114783756', '5.955373721875272', '6.631974970536537', '7.403784360578705', '7.796451718187396', '8.263382181310590', '9.111253455995848', '9.540574385297172', '10.12301287452232', '10.57590522880014', '11.49857009597397', '11.98749477873573', '12.46925053256589', '12.99249522696100', '13.55642425960049', '14.15518306946598', '14.40839781564475', '14.89433156777703', '15.38861555891019', '15.92639445881062', '16.68345527262774', '16.85221628746017', '17.68687616765778', '18.20672488787916', '19.05916592319643', '19.37912198084853', '19.67574703005431'], 'prelabel': '2-25886-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 14.377091175626816, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1427945667270373716, 'z1': {'__RealLiteral__': 0, 'data': '1.387508483491029', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '2.211122507319805', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.812278726005327', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 206.7007506722865, 'bad_primes': [2, 7, 43], 'central_character': '1.1', 'conductor': 25886, 'conductor_radical': 602, 'degree': 2, 'dirichlet_coefficients': [1, 1, 2, 1, 0, 2, -1, 1, 1, 0, 0, 2, -4, -1, 0, 1, 6, 1, -2, 0, -2, 0, 0, 2, -5, -4, -4, -1, 6, 0, -4, 1, 0, 6, 0, 1, -2, -2, -8, 0, 6, -2, 0, 0, 0, 0, -12, 2, 1, -5, 12, -4, 6, -4, 0, -1, -4, 6, -6, 0, -8, -4, -1, 1, 0, 0, -4, 6, 0, 0, 0, 1, -2, -2, -10, -2, 0, -8, 8, 0, -11, 6, -6, -2, 0, 0, 12, 0, 6, 0, 4, 0, -8, -12, 0, 2, -10, 1, 0, -5], 'euler11': [1, 0, 11], 'euler13': [1, 4, 13], 'euler17': [1, -6, 17], 'euler19': [1, 2, 19], 'euler2': [1, -1, 0], 'euler23': [1, 0, 23], 'euler29': [1, -6, 29], 'euler3': [1, -2, 3], 'euler31': [1, 4, 31], 'euler37': [1, 2, 37], 'euler41': [1, -6, 41], 'euler43': [1, 0, 0], 'euler47': [1, 12, 47], 'euler5': [1, 0, 5], 'euler53': [1, -6, 53], 'euler59': [1, 6, 59], 'euler61': [1, 8, 61], 'euler67': [1, 4, 67], 'euler7': [1, 1, 0], 'euler71': [1, 0, 71], 'euler73': [1, 2, 73], 'euler79': [1, -8, 79], 'euler83': [1, 6, 83], 'euler89': [1, -6, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, -1, 0], [1, -2, 3], [1, 0, 5], [1, 1, 0], [1, 0, 11], [1, 4, 13], [1, -6, 17], [1, 2, 19], [1, 0, 23], [1, -6, 29], [1, 4, 31], [1, 2, 37], [1, -6, 41], [1, 0, 0], [1, 12, 47], [1, -6, 53], [1, 6, 59], [1, 8, 61], [1, 4, 67], [1, 0, 71], [1, 2, 73], [1, -8, 79], [1, 6, 83], [1, -6, 89], [1, 10, 97]], 'index': 3, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/25886/d'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-25886-1.1-c1-0-3', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-25886-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 14.377091175626816, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1427945667270373716, 'z1': {'__RealLiteral__': 0, 'data': '1.387508483491029', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1427945667270373716', 'Lhash_array': ['1427945667270373716'], 'label': '2-25886-1.1-c1-0-3', 'type': 'ECQ', 'url': 'EllipticCurve/Q/25886/d'}