-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '4190224356489224965345685717739', 'a10': [66.62890180830313, -38.468214394832955], 'a2': [-0.7320508075688773, 2.732050807568877], 'a3': [-4.747999609155196, -8.223776557373972], 'a4': [-6.928203230275509, -4.0], 'a5': [-19.234107197416478, -19.234107197416478], 'a6': [25.943552333058335, -6.9515538964375505], 'a7': [-5.114025012939635, -19.085801179468803], 'a8': [16.0, -16.0], 'a9': [-4.58700057707579, 7.944918053843026], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.6876190401799533, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7320508075688773, -2.732050807568877]]], [13, [[1.0, 0], [94.32822155887372, -140.22548490748758]]]], 'bad_primes': [2, 13], 'central_character': '26.11', 'coefficient_field': 'CDF', 'conductor': 26, 'conductor_radical': 26, 'conjugate': '748539341695893523952004927858', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7320508075688773, -2.732050807568877]], [[1.0, 0], [4.747999609155196, 8.223776557373972], [-40.5, 70.14805770653953]], [[1.0, 0], [19.234107197416478, 19.234107197416478], [0, 625.0]], [[1.0, 0], [5.114025012939635, 19.085801179468803], [-2079.3269944864373, 1200.5]], [[1.0, 0], [31.792862913275254, 8.518871942685497], [12679.477936807967, 7320.5]], [[1.0, 0], [94.32822155887372, -140.22548490748758]], [[1.0, 0], [186.16271301656064, 107.48109247318233], [41760.5, 72331.3077494801]], [[1.0, 0], [-407.7257241329254, 109.24977851481208], [112861.29664659183, -65160.5]], [[1.0, 0], [-833.2075410205216, 481.05259809902435], [139920.5, -242349.41502044108]], [[1.0, 0], [772.3932125464272, 1337.8242875517587], [-353640.5, 612523.3136140616]], [[1.0, 0], [-750.0403850885792, -750.0403850885792], [0, 923521.0]], [[1.0, 0], [-680.7347395366851, -182.40232371866543], [1623071.0367820472, 937080.5]], [[1.0, 0], [-146.9983422386386, 548.6052818629973], [-2447180.811023319, -1412880.5]], [[1.0, 0], [141.7555619233427, 81.84261183556858], [1709400.5, 2960768.5164836426]], [[1.0, 0], [1733.0067267519994, -1733.0067267519994], [0, -4879681.0]], [[1.0, 0], [4534.8479659067225, 0], [7890481.0, 0]], [[1.0, 0], [201.70806887872084, 752.7847613519888], [-10493942.45282681, 6058680.5]], [[1.0, 0], [1974.2303075457457, -3419.467198511562], [-6922920.5, -11990850.042760136]], [[1.0, 0], [-1784.270234166712, 6658.987168342987], [-17451382.700734083, -10075560.5]], [[1.0, 0], [-5330.869077002067, 1428.4020641387483], [22007161.298866346, -12705840.5]], [[1.0, 0], [2496.5753321181137, -2496.5753321181137], [0, -28398241.0]], [[1.0, 0], [-6710.047526180264, 0], [38950081.0, 0]], [[1.0, 0], [-1361.299826883053, -1361.299826883053], [0, 47458321.0]], [[1.0, 0], [-6033.513051694958, -1616.674949724303], [54336374.59636556, 31371120.5]], [[1.0, 0], [4670.758626764398, -1251.5260020822202], [76668606.32477103, -44264640.5]], [[1.0, 0], [-7300.501752564216, 4214.946652062285], [52030200.5, -90118950.7939956]], [[1.0, 0], [0, 2398.4450704788974], [-112550881.0, 0]], [[1.0, 0], [4706.1055996412315, 8151.21400436301], [-65539800.5, 113518264.3839281]], [[1.0, 0], [-14993.680145108603, -14993.680145108603], [0, 141158161.0]], [[1.0, 0], [-8782.457885283673, 15211.66327264524], [-81523680.5, -141203156.64601213]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-26-13.11-c4-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/26/5/f/b/11/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [0.638047947921199, 0.8025258697239385, 0.9570997082399978, 1.1018843452509512, 1.2362004897681513, 1.3584838155751837, 1.4662557833529855, 1.5561625368072778, 1.6240879651540285, 1.6653463875903922, 1.6749586754862336, 1.648012348957764, 1.5801008364575542, 1.4678295562775547, 1.3093670208051336, 1.1050084078928777, 0.8577079821934968, 0.5735267039485419, 0.26193391430101165, -0.06410113774801535, -0.38828925252389695, -0.6915236329081144, -0.9527366504104698, -1.1501154589102276, -1.2626454448579598, -1.2719092397211553, -1.1640252971949203, -0.9315684481447535, -0.5752809537751417, -0.10536243252603734, 0.45787351250531777, 1.0841642959762579, 1.73442227099515, 2.362876694714231, 2.9201912674050448, 3.3573974066296226, 3.6303618244949494, 3.7043958661564775, 3.5585299696801616, 3.1889359182409844, 2.6109961503569257, 1.8596020564938414, 0.9874132300423604, 0.0610191131793799, -0.8448045623835022, -1.6542870036130746, -2.298598847045361, -2.7236446588066094, -2.8967293099847047, -2.81114543740016, -2.4878955281252857, -1.9740619768630203, -1.3377472814970068, -0.6599791202300165, -0.024449053862066653, 0.4936432397984746, 0.8381080207166229, 0.9800562514252259, 0.922554986650554, 0.7006619477260005, 0.37648048699940184, 0.029630499295976626, -0.2556953895416603, -0.4052541814386546, -0.3685823996020714, -0.1297613813639057, 0.2869645320581226, 0.8181230540605416, 1.3689181361791323, 1.8273527743465534, 2.0826638776981117, 2.0452242344443903, 1.6645385580739602, 0.9419833002795793, -0.06443138936115987, -1.2448154156986102, -2.451627672461403, -3.5216191848389276, -4.302174156668273, -4.677651232389395, -4.590970513858507, -4.056196668535348, -3.1592185109443234, -2.0456376894675437, -0.8973224193345148, 0.09867187190295569, 0.7834139610953231, 1.0554681683861944, 0.8905389976136562, 0.34715870757571154, -0.4433093458798141, -1.3010659232213853, -2.0324404764672934, -2.46813297879804, -2.4975754633249396, -2.092291725470014, -1.3130787712620777, -0.2989729574570013, 0.7602978899166617, 1.6631054132266128, 2.2380669625886176, 2.3806234085107065, 2.0759890045138603, 1.403094055293228, 0.518139387461952, -0.37913052504791034, -1.0893432296537342, -1.4579639153975612, -1.4102259793725243, -0.9683059372687501, -0.24637721832682394, 0.5757861141971917, 1.2949043497785626, 1.7323234114266164, 1.7767776563321853, 1.411333736401693, 0.7176127152562725, -0.1442207105255445, -0.97522731242441, -1.5876355849646409, -1.8524686721722066, -1.7325200947819857, -1.291668881938747, -0.6773353443997002, -0.07980217778249464, 0.3215797021985721, 0.411297532565544, 0.17519892639849635, -0.2885354773417636, -0.7896339299452313, -1.093719815746848, -0.9868667351258903, -0.3403514314322991, 0.8419116507466337, 2.4073109180502277, 4.076489268829151, 5.500304506668987, 6.339383226936429, 6.347190494963072, 5.435555663325859, 3.705069774509032, 1.4310493018983288, -0.9931389488888925, -3.142519876391013, -4.6557632855090265, -5.315489599542826, -5.093290371445581, -4.1480465153419, -2.778284272497841, -1.3414663280894032, -0.1619311679593294, 0.5478437067389231, 0.7318089971855526, 0.48956142629829885, 0.03188999243956704, -0.39324927067568693, -0.5818342783118577, -0.43759466015476023, 0.0004940409405442394, 0.5750390108656277, 1.065819947610768, 1.26654144954341, 1.0583316255548536, 0.45618490058885475, -0.3874022166764028, -1.224152682441561, -1.7852447327912033, -1.8671013186424346, -1.4005397737532823, -0.48032894931188896, 0.6560987551156273, 1.6962810640406598, 2.34723288461032, 2.4279496353253185, 1.93042070674975, 1.0284245887841414, 0.02911395482568479, -0.7196040808064799, -0.9382786252271456, -0.5076944621512376, 0.486614101629583, 1.7730648363672845, 2.972364366981895, 3.712761505307794, 3.746913496949258, 3.0333293550138003, 1.7554414478497153, 0.27044359514294375, -0.9977222377704047, -1.6885346135783696, -1.6172038807352158, -0.8328194406801992, 0.39736558109998754, 1.6737539113074524, 2.5937274670875574, 2.88314591240572, 2.487136647245023, 1.5897724218525915, 0.5549924943768607, -0.1931060317124893, -0.3121634297579806, 0.34079943386372075, 1.655179258213311, 3.294835788863194, 4.8002375034318066, 5.731950800156166, 5.808748325517463, 4.995136151656038, 3.5097882876962694, 1.752731883573492, 0.17626453527913755, -0.8567609406562028, -1.1799282670534377, -0.8607224308901047, -0.1581671801337686, 0.5817667689396768, 1.0539269391990806, 1.098484160696228, 0.7451252776027305, 0.1826904375872959, -0.33199818420437843, -0.5894599542930988, -0.5211130964534483, -0.23321600173412757, 0.033941102288295145, 0.007597239964395769, -0.49382272544733025, -1.4642455849072993, -2.6819680533927666, -3.7670594114962044, -4.3088279856091045, -4.019839531599994, -2.8597087522617626, -1.0793249000318423, 0.8373992570582215, 2.320654073540851, 2.9036204704514157, 2.388049183116026, 0.926413721071427, -1.0124379939313293, -2.7870653503387746, -3.7904891115764556, -3.6505714401312743, -2.3543975859514443, -0.2527836642725689, 2.057355859788213, 3.932065578547608, 4.891347002008421, 4.768682400163126, 3.7482073221919943, 2.2795309189661945, 0.9044225771021706, 0.06080589212802619, -0.06383205327751702, 0.42223373509543605, 1.1833693904648108, 1.807736043390406], 'positive_zeros': ['3.30550417893922167901907340829357', '5.13260098668042408151671593155029', '7.57014967056757253442461289059086', '9.499526694989230731260494837712060', '10.73859210779971136293303180361084', '11.48804824714714505828700896385086', '12.99761141444058179631494732738517', '14.92170419826579683270852527363542', '15.72630762598155197559649682279816', '17.09969270189128609506678438253828'], 'prelabel': '2-26-13.11-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6393959375879743, 'root_angle': 0.5928661407131189, 'root_number': '-0.2876264006324024 + 0.957742686560043*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.296433070357', 'prec': 47}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.30550417893922167901907340829', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.13260098668042408151671593155', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.57014967056757253442461289059', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.6876190401799533, 'bad_primes': [2, 13], 'central_character': '13.11', 'conductor': 26, 'conductor_radical': 26, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/26/5/f/b/11/1'], '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': '2-26-13.11-c4-0-2', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-26-13.11-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6393959375879743, 'root_angle': 0.29643307035655947, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '3.30550417893922167901907340829', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '4190224356489224965345685717739', 'Lhash_array': ['4190224356489224965345685717739'], 'label': '2-26-13.11-c4-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/26/5/f/b/11/1'}