-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1490155770597329676756107069605', 'a10': [0, 0.3719038373316331], 'a2': [0.3719038373316331, 0], 'a3': [-0.30592713297996027, 1.7048192248173006], 'a4': [-1.8616875357780063, 0], 'a5': [0, 1.0], 'a6': [-0.11377547469911203, 0.6340288116662942], 'a7': [0, -1.0], 'a8': [-1.4361764131315786, 0], 'a9': [-2.8128171786133236, -1.0431009153949502], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.222721433457888, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.30592713297996027, -1.7048192248173006]]], [5, [[1.0, 0], [0, -1.0]]], [7, [[1.0, 0], [0, 1.0]]], [11, [[1.0, 0], [1.9365461153258736, -2.692543248160792]]]], 'bad_primes': [3, 5, 7, 11], 'central_character': '1155.1121', 'coefficient_field': 'CDF', 'conductor': 1155, 'conductor_radical': 1155, 'conjugate': '467643529284035653114925186839', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.3719038373316331, 0], [2.0, 0]], [[1.0, 0], [0.30592713297996027, -1.7048192248173006]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [1.9365461153258736, -2.692543248160792]], [[1.0, 0], [0, 6.339347547524086], [-13.0, 0]], [[1.0, 0], [-1.5382509169333056, 0], [17.0, 0]], [[1.0, 0], [0, 1.5987028464814337], [-19.0, 0]], [[1.0, 0], [0, -0.20306006622173042], [-23.0, 0]], [[1.0, 0], [2.4077602311400597, 0], [29.0, 0]], [[1.0, 0], [5.919344815302013, 0], [31.0, 0]], [[1.0, 0], [-8.803082283771369, 0], [37.0, 0]], [[1.0, 0], [-9.290976508325475, 0], [41.0, 0]], [[1.0, 0], [0, 9.250803855426856], [-43.0, 0]], [[1.0, 0], [0, 4.56523699350002], [-47.0, 0]], [[1.0, 0], [0, -2.510509634997969], [-53.0, 0]], [[1.0, 0], [0, 4.956251107874754], [-59.0, 0]], [[1.0, 0], [0, -8.698936159306992], [-61.0, 0]], [[1.0, 0], [4.791522478429987, 0], [67.0, 0]], [[1.0, 0], [0, 13.979996795717556], [-71.0, 0]], [[1.0, 0], [0, -7.531401518889745], [-73.0, 0]], [[1.0, 0], [0, 6.74980219237915], [-79.0, 0]], [[1.0, 0], [-5.233635331858761, 0], [83.0, 0]], [[1.0, 0], [0, 10.609260792259638], [-89.0, 0]], [[1.0, 0], [-4.654513425836934, 0], [97.0, 0]], [[1.0, 0], [-8.788207808327364, 0], [101.0, 0]], [[1.0, 0], [15.74398323403428, 0], [103.0, 0]], [[1.0, 0], [12.649230107557036, 0], [107.0, 0]], [[1.0, 0], [0, 17.10078094414901], [-109.0, 0]], [[1.0, 0], [0, 12.866981678650967], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 54, 'label': '2-1155-33.32-c1-0-54', 'leading_term': '0.7733372699139860920488028482227843216563687855270934397', '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/1155/2/l/e/1121/24', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.7733372699139861, 0.8551483830723406, 0.9270875994751564, 0.9892312742865705, 1.0414298788744314, 1.083313795320231, 1.1143135344553272, 1.1336926441841997, 1.140591027977103, 1.1340761574811318, 1.1131996818734502, 1.0770571201139905, 1.0248485784511374, 0.955938691265053, 0.8699141937104762, 0.7666376821329927, 0.6462962062646183, 0.5094433819656444, 0.357033736690603, 0.1904480244336649, 0.011508292677696257, -0.17751843314863866, -0.37392885048679175, -0.5746052809770207, -0.7760513412022378, -0.9744416474003434, -1.1656854605253297, -1.3455037733193245, -1.509518899877544, -1.6533551631446075, -1.7727488016706505, -1.8636647504033808, -1.9224175093086875, -1.9457929170764907, -1.931167314228417, -1.8766203293464396, -1.781037371502663, -1.6441978770068222, -1.466845452336508, -1.2507362871675602, -0.99866258721109, -0.7144482967324356, -0.40291504052034693, -0.06981700438235247, 0.2782556241670335, 0.6340040393934809, 0.9895773514397131, 1.3367555079385858, 1.6671547554913642, 1.9724507535008855, 2.244613499326144, 2.4761473986327607, 2.660329159093498, 2.7914357373127077, 2.864954361440767, 2.877766712466823, 2.828299694673793, 2.71663586977704, 2.5445775687368606, 2.315659917473613, 2.0351094930385805, 1.7097470284803944, 1.3478344594168339, 0.958868594345379, 0.553325726154824, 0.1423635093065071, -0.26251167356790167, -0.6498019212388215, -1.0083882224143965, -1.3279015853536955, -1.5990817178787253, -1.814109856128561, -1.966902610195815, -2.0533544866145648, -2.0715180629001786, -2.021712607963754, -1.906554222158149, -1.7309032480309916, -1.5017276929693941, -1.2278846047337337, -0.9198246319487758, -0.5892282541839565, -0.24858524404747592, 0.08926831056877546, 0.41163877480035993, 0.7064711213517776, 0.9628329826835268, 1.1713667808441646, 1.3246905908272677, 1.4177296992125783, 1.4479629437024655, 1.4155708126274473, 1.323475861806285, 1.1772701497306395, 0.985028949783921, 0.7570147923634408, 0.5052807224553495, 0.24318631913435262, -0.015155701197086414, -0.2554807940757085, -0.4639974084408779, -0.6280089752543218, -0.736505857145581, -0.7807003646904828, -0.7544794695900969, -0.6547525690683834, -0.4816755098331178, -0.23873693891090342, 0.06730126516143638, 0.4266114387631024, 0.8266507880567872, 1.2526439095748425, 1.6881794220842539, 2.1158971157560957, 2.5182370550593594, 2.8782182423408935, 3.1802119880614446, 3.410674214462422, 3.55880164929661, 3.6170792779363414, 3.5816904687669995, 3.452766740181092, 3.2344609908378272, 2.934835888961716, 2.5655676702047896, 2.1414744379298587, 1.67988677476064, 1.1998866285634973, 0.721447607938952, 0.26451562118170563, -0.1519271200239008, -0.5107696022840992, -0.797605936793581, -1.0014529144815465, -1.1153128838675341, -1.1365501960831454, -1.0670578194165892, -0.9132005355711265, -0.6855319483928555, -0.39829385113839744, -0.06871775313479624, 0.2838410147897182, 0.6388967796044562, 0.9759070627419766, 1.2753731378146282, 1.5199116059528073, 1.6952408016579128, 1.7910285477378975, 1.8015533322589061, 1.7261391926616365, 1.5693351254536025, 1.3408222235861122, 1.0550453931091996, 0.7305807439453664, 0.38926385963788707, 0.05511738237936997, -0.2468720220945222, -0.49206789446240906, -0.6575234546893358, -0.7232771078969183, -0.6735350587507283, -0.49767603318671844, -0.1910205702573149, 0.24468193871396524, 0.8010817956692161, 1.4633908291654072, 2.210878225077423, 3.017683576596398, 3.8539133174516036, 4.686971001541966, 5.483058429716404, 6.208774184789188, 6.832729360824952, 7.327097621650468, 7.66901844252757, 7.841778490818638, 7.835706358459122, 7.648729808389319, 7.286561660370481, 6.762499556678045, 6.096845112493706, 5.315968279058767, 4.451062010755341, 3.5366494449673347, 2.60891978664964, 1.7039791034847618, 0.856107653820573, 0.09611580663995761, -0.5501140363771359, -1.0628216618478097, -1.429235551415894, -1.6440655299302938, -1.7095958856097866, -1.6353753991746607, -1.437523212411195, -1.1376910585243574, -0.7617418088921012, -0.3382204107022934, 0.1032948798367223, 0.5338662638114149, 0.9267991450283647, 1.2590821396156837, 1.5125823649006478, 1.6749286534364594, 1.7400340436899198, 1.7082305956878856, 1.5860129871964874, 1.3854110604788636, 1.1230340688878184, 0.8188494226210098, 0.49477499529501345, 0.1731754845096914, -0.12464083859451257, -0.3798288257931193, -0.5772266638784108, -0.7063116443825862, -0.7618305497364461, -0.7440647530878867, -0.6587138947069138, -0.5164070020275991, -0.3318745703392467, -0.12283782017866476, 0.09130940326884507, 0.29093612678286207, 0.4576284545586703, 0.5755615048919183, 0.632692502130962, 0.621689367497634, 0.5405259862100312, 0.39269707303914564, 0.18703086733824856, -0.06289484801314094, -0.33970046485834887, -0.6234572655261273, -0.8931639966490583, -1.1283487356033304, -1.3106863121627594, -1.4255175260521125, -1.4631599725452507, -1.4199114030781594, -1.2986646536627695, -1.109077239825916, -0.8672672896113571, -0.5950387757670511, -0.31867099769384893, -0.06733783732826971, 0.12875060580392772, 0.24036970531699797, 0.2413363209209087, 0.11046357057258378, -0.16671895474181628, -0.5966017085156902, -1.176591075585614, -1.894740400369072, -2.7299593187774063, -3.6528082054273785, -4.626846758317221], 'positive_zeros': ['1.17552563011372389659360154472134', '2.53144996920219277895313386330294', '3.82901121690141610993784574863258', '4.84762636804694471561764517577425', '5.73866673815668930099061099635242', '6.31613897597845335897489560122082', '7.59498059129994704495427208144198', '8.214742688841337045775259948715403', '9.092144225651240195594892141098970', '9.519991726541723017005874069436454'], 'prelabel': '2-1155-33.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.036893385263613, 'root_angle': 0.2549889786159732, 'root_number': '0.6959376610821243457063402662392902088139631768722001118 + 0.7181022015615480821746344067638624089548221902119097054*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1274944893079866', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.17552563011372389659360154472', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.53144996920219277895313386330', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.82901121690141610993784574863', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 9.222721433457888, 'bad_primes': [3, 5, 7, 11], 'central_character': '33.32', 'conductor': 1155, 'conductor_radical': 1155, 'degree': 2, 'index': 54, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1155/2/l/e/1121/24'], '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': '2-1155-33.32-c1-0-54', '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': '2-1155-33.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.036893385263613, 'root_angle': 0.1274944893079866, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.17552563011372389659360154472', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1490155770597329676756107069605', 'Lhash_array': ['1490155770597329676756107069605'], 'label': '2-1155-33.32-c1-0-54', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1155/2/l/e/1121/24'}