-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1091793021770699667574869191269', 'a10': [0.0, 0.0], 'a2': [0.0, 1.0], 'a3': [-1.0, 0.0], 'a4': [-1.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, -1.0], 'a7': [0.0, 0.0], 'a8': [0.0, -1.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5988780151596029, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.0]]], [3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1200.443', 'coefficient_field': 'CDF', 'conductor': 1200, 'conductor_radical': 30, 'conjugate': '1590983887486688267049443802790', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [-1.0, -1.0], [0, 1.0]], [[1.0, 0], [-1.0, 1.0], [0, -1.0]], [[1.0, 0], [1.0, -1.0], [0, -1.0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, -2.0], [-1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [-1.0, 1.0], [0, -1.0]], [[1.0, 0], [-2.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [1.0, -1.0], [0, -1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [1.0, 1.0], [0, 1.0]], [[1.0, 0], [-1.0, 1.0], [0, -1.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-1200-240.203-c0-0-0', 'leading_term': '0.69195505107107044910097905749721', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1200/1/bd/a/443/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.6919550510710705, 0.6660293547850625, 0.644554331943274, 0.6257398301943989, 0.6074774244828062, 0.5875610086255207, 0.5638671399824117, 0.5344789817722166, 0.49775932015285823, 0.45238771999663707, 0.3973769820731154, 0.3320799272472342, 0.2561928793234896, 0.1697586122785064, 0.07316921171698658, -0.03283199207408103, -0.14715087352833991, -0.26834699589903166, -0.39464374097124844, -0.5239455161077953, -0.6538632089101504, -0.7817487454357444, -0.9047392563482469, -1.0198109760389484, -1.1238426000093915, -1.2136874131153632, -1.2862530842706639, -1.3385876120978988, -1.3679695125853857, -1.371999977219281, -1.3486944124315965, -1.296570513116298, -1.214729838850378, -1.1029297649427543, -0.9616426836488022, -0.7920994437558159, -0.5963142462990991, -0.377088563918585, -0.13799212073813674, 0.1166804464593998, 0.3819779365188638, 0.6523858542870833, 0.9219436677485677, 1.1843842233294652, 1.4332925808842023, 1.662280635528443, 1.8651730493951297, 2.036199258719465, 2.1701856866846954, 2.2627418151534227, 2.3104334808958376, 2.310936691922014, 2.263165428791931, 2.167367318675503, 2.02518175214639, 1.839655950176245, 1.6152156670510196, 1.3575886086342277, 1.0736802184583487, 0.7714031901796901, 0.45946384836090903, 0.1471103369326847, -0.15615070323857308, -0.4408606722481131, -0.6979290566882576, -0.9189561355030677, -1.0965466981693148, -1.2246027226651146, -1.2985829978656056, -1.3157181849088897, -1.2751708086223674, -1.1781311481601993, -1.0278419301011046, -0.8295470710469405, -0.5903624033749084, -0.31906926109811745, -0.02583489959913805, 0.2781331437786292, 0.5809885986886284, 0.870690950904223, 1.1354774373042433, 1.3643451285320547, 1.5475242926433783, 1.6769235366698894, 1.7465272923387558, 1.7527270928155485, 1.6945697929500152, 1.5739083950134998, 1.3954443980210145, 1.166654497984627, 0.8975989009672718, 0.6006133116679028, 0.28989164252053823, -0.019028552481481123, -0.3098611948056124, -0.5662263622169892, -0.7723399530013626, -0.9137110234862058, -0.9778177905414454, -0.9547327554966533, -0.8376681209160366, -0.6234146732490982, -0.31265057320758777, 0.08989904555070018, 0.5754652554741193, 1.1314085002033443, 1.7415619515716567, 2.3867379181579276, 3.0453827862848795, 3.694358892151749, 4.309825270590408, 4.868183722320766, 5.347052380671078, 5.726226191017714, 5.988582635606717, 6.120891768274833, 6.114492215251765, 5.965799212957127, 5.676616868250761, 5.254234432820607, 4.71129519410728, 4.065436244064644, 3.3387074825222607, 2.556788294187095, 1.748029939363893, 0.9423603536971237, 0.1700953230784145, -0.5392945038611989, -1.1584079023449123, -1.6630747211442378, -2.0334023449599177, -2.25465827938427, -2.317946401069534, -2.220642800091378, -1.9665673445395946, -1.565878686167796, -1.0346928853506554, -0.394438588895678, 0.329025862343219, 1.1064964991469923, 1.9066620541965194, 2.6974416720056755, 3.4473616145948194, 4.126907887623047, 4.709792026897007, 5.174070659887085, 5.50306579084187, 5.686041798249885, 5.718606482374614, 5.602816632992136, 5.346982873488587, 4.965183272817876, 4.476509657484985, 3.9040839560796834, 3.2738935610159414, 2.613503964354213, 1.9507132970813252, 1.3122164967013425, 0.7223464355262943, 0.20195543259561807, -0.2325066954594721, -0.5696721724183507, -0.803659303689922, -0.9341825675604261, -0.9663660116141584, -0.9102731510242373, -0.7801818700597963, -0.5936466461690021, -0.3704019660320267, -0.13116941748408376, 0.10356389343660892, 0.31472656213711175, 0.4857372094790773, 0.6034116766304118, 0.6586526283123144, 0.6468838195829046, 0.5682062408031621, 0.42726971063768343, 0.23287029649875288, -0.0026997775086532766, -0.26450829145035915, -0.5359914242965708, -0.8000513166242035, -1.0401742566236332, -1.2414995948945464, -1.3917724067898891, -1.4821199757994519, -1.5076029918539209, -1.4675063317506545, -1.365350597584428, -1.2086232561268802, -1.0082461675358014, -0.7778133967933555, -0.5326483766135832, -0.2887417448564615, -0.061639683399742747, 0.1346432725360103, 0.2886135552910835, 0.3921219575489508, 0.44096290893501394, 0.4352053118371082, 0.37922766430807014, 0.2814494109072008, 0.1537706424527074, 0.010752125985037534, -0.13141411403538888, -0.25607805501959285, -0.3473717148986563, -0.39143224862579395, -0.37752308551469543, -0.29897240090799937, -0.15385801648546885, 0.05461736152451234, 0.3180976449717494, 0.6234065928812167, 0.9532339304447063, 1.2871414781155088, 1.6028337182231525, 1.8776174190587616, 2.0899594117855442, 2.221041538715171, 2.256208011352014, 2.186203400326097, 2.008109269246563, 1.725903661072462, 1.3505894184886191, 0.8998634472959879, 0.397327967080789, -0.12872524617235023, -0.6468975457580286, -1.1245466772099022, -1.52982260253216, -1.833752376276065, -2.012242461037741, -2.047866939134218, -1.9313185981372545, -1.6624165833789115, -1.2505884256504871, -0.7147744687693355, -0.08273730562774402, 0.6102042881778184, 1.3229605415605379, 2.010884066882647, 2.628290577909687, 3.131142845685324, 3.479738902034858, 3.641240167289264, 3.5918800199846297, 3.318708324644031, 2.820751920087221, 2.1095037489265667, 1.2086923227633053, 0.15332625590949495, -1.0119469652057498, -2.2350857630193657, -3.459381689344041, -4.626515788761648], 'positive_zeros': ['0.861272831468017989123779469564111', '2.25868528192296967182604056390163', '3.60230965685319239762687001590183', '4.45815436208753662970914316505514', '5.44554118987709071019299583271763', '6.02310815220676841352582560109297', '7.39631564949780711285228755408308', '8.059974699900014531791475717678148', '9.342109064604868001304213804416492', '9.934631146403040635609845463874249'], 'prelabel': '2-1200-240.203-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7738720922475515, 'root_angle': -0.5512081911747834, 'root_number': '-0.16018224300696722420136614681444 - 0.98708745763749672912388752601751*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2756040955873917', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.861272831468017989123779469564', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.25868528192296967182604056390', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.60230965685319239762687001590', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.5988780151596029, 'bad_primes': [2, 3, 5], 'central_character': '240.203', 'conductor': 1200, 'conductor_radical': 30, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1200/1/bd/a/443/1'], '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': '2-1200-240.203-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1200-240.203-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7738720922475515, 'root_angle': -0.2756040955873917, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.861272831468017989123779469564', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1091793021770699667574869191269', 'Lhash_array': ['1091793021770699667574869191269'], 'label': '2-1200-240.203-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1200/1/bd/a/443/1'}