-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '990871769907538403557597446156', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-1.7320508075688772, 0], 'a6': [0, 0], 'a7': [-2.0, 1.7320508075688772], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24.1467615712352, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2.0, -1.7320508075688772]]]], 'bad_primes': [2, 3, 7], 'central_character': '3024.1889', 'coefficient_field': 'CDF', 'conductor': 3024, 'conductor_radical': 42, 'conjugate': '457660274111416966137336052250', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.7320508075688772, 0], [5.0, 0]], [[1.0, 0], [2.0, -1.7320508075688772]], [[1.0, 0], [0, -3.0], [-11.0, 0]], [[1.0, 0], [0, 3.4641016151377544], [-13.0, 0]], [[1.0, 0], [6.928203230275509, 0], [17.0, 0]], [[1.0, 0], [0, -1.7320508075688772], [-19.0, 0]], [[1.0, 0], [0, -3.0], [-23.0, 0]], [[1.0, 0], [0, 6.0], [-29.0, 0]], [[1.0, 0], [0, 5.196152422706632], [-31.0, 0]], [[1.0, 0], [-7.0, 0], [37.0, 0]], [[1.0, 0], [-12.12435565298214, 0], [41.0, 0]], [[1.0, 0], [-2.0, 0], [43.0, 0]], [[1.0, 0], [3.4641016151377544, 0], [47.0, 0]], [[1.0, 0], [0, -12.0], [-53.0, 0]], [[1.0, 0], [-3.4641016151377544, 0], [59.0, 0]], [[1.0, 0], [0, 6.928203230275509], [-61.0, 0]], [[1.0, 0], [2.0, 0], [67.0, 0]], [[1.0, 0], [0, 3.0], [-71.0, 0]], [[1.0, 0], [0, -3.4641016151377544], [-73.0, 0]], [[1.0, 0], [-10.0, 0], [79.0, 0]], [[1.0, 0], [17.320508075688775, 0], [83.0, 0]], [[1.0, 0], [-5.196152422706632, 0], [89.0, 0]], [[1.0, 0], [0, 13.856406460551018], [-97.0, 0]], [[1.0, 0], [0, 0], [101.0, 0]], [[1.0, 0], [0, 19.05255888325765], [-103.0, 0]], [[1.0, 0], [0, 0], [-107.0, 0]], [[1.0, 0], [-13.0, 0], [109.0, 0]], [[1.0, 0], [0, -12.0], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 30, 'label': '2-3024-21.20-c1-0-30', 'leading_term': '0.8206606186400232262748657660071031854342545168138234296', '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/3024/2/k/e/1889/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.8206606186400233, 0.8825913782356504, 0.9307963970720873, 0.964907828507028, 0.9844520868083879, 0.9888596992877839, 0.9774865438116657, 0.9496452582833926, 0.9046451253621344, 0.8418384198478438, 0.7606710497235135, 0.6607352969572422, 0.5418225337654256, 0.40397391743890315, 0.24752722231561258, 0.07315813133752716, -0.118085527769889, -0.32475795668483737, -0.5449991644620985, -0.776529372392412, -1.0166548819422299, -1.262286031576619, -1.509967629486112, -1.7559219797130423, -1.9961043193182104, -2.2262701571989023, -2.4420536566803515, -2.639055842058145, -2.812941043822511, -2.959539639868886, -3.074954813263976, -3.155670744461692, -3.1986594008340887, -3.201482892294425, -3.162388241124947, -3.0803913780197876, -2.955347234084239, -2.788002956996809, -2.5800315428096163, -2.3340435437719838, -2.0535749843905973, -1.743050186184017, -1.4077188558539881, -1.0535675176134982, -0.6872061502054674, -0.31573170134336415, 0.05342902739930401, 0.4126938304540205, 0.7545128330272853, 1.071564781470572, 1.3569565846791496, 1.6044203581233125, 1.8085019345475575, 1.9647346953491855, 2.069792660867032, 2.1216170674113073, 2.1195111585759374, 2.064198625838888, 1.9578420387659898, 1.804018690611388, 1.6076525253598437, 1.3749021745269707, 1.1130065768626958, 0.8300911362894493, 0.5349388432633134, 0.23673218962442638, -0.0552270069592861, -0.33181163880024783, -0.5843680824223049, -0.80500996563482, -0.9868968646953088, -1.1244878880368117, -1.2137604779499298, -1.2523854994945305, -1.239850780999207, -1.1775267033162413, -1.068669172222448, -0.9183573032250771, -0.7333653412711149, -0.5219706591830238, -0.2937020487944978, -0.059034852023882076, 0.1709583137222337, 0.3849904898400464, 0.5719645347438881, 0.7213847616187258, 0.8237614529235462, 0.8709932960384372, 0.8567129759068396, 0.7765819158178973, 0.6285214751505225, 0.41286976938466546, 0.13245562699340402, -0.20741602781176072, -0.5990699661208526, -1.032656876172765, -1.4964358194397325, -1.9771352903898363, -2.4603819711159995, -2.9311832859200657, -3.3744472981236084, -3.775521472036757, -4.120730450913133, -4.397892359080208, -4.5967932794906625, -4.7096005133240135, -4.731196990476911, -4.6594217298724105, -4.495204474159169, -4.242586440307993, -3.908623402583361, -3.503171899394995, -3.0385640534948366, -2.529181126265418, -1.990940296865841, -1.4407130743043364, -0.8956970350976525, -0.37276507075640214, 0.11218210495254478, 0.5448338976698471, 0.9130324731844423, 1.2072559857841174, 1.4210009854715806, 1.5510462825442701, 1.597585094329825, 1.5642175367749758, 1.4578012494009105, 1.2881639234683278, 1.067687488133219, 0.8107794369433455, 0.5332519884679817, 0.2516342252887458, -0.017554174488895017, -0.2585366929001038, -0.45698928975812947, -0.6006937371213029, -0.6801052146700265, -0.6888075698896655, -0.6238340755027387, -0.4858370511162939, -0.27909613819013185, -0.011362061307221094, 0.3064599284728372, 0.6607753777018559, 1.0358961619305878, 1.4147413311127235, 1.7796130295669659, 2.1130131659950893, 2.3984639089732824, 2.621294129522578, 2.7693546939361315, 2.8336280373372897, 2.80870164996547, 2.6930808313359433, 2.489323083130763, 2.203984522894052, 1.847377354306037, 1.4331463321551021, 0.9776808940808915, 0.49938777584407185, 0.0178560777505659, -0.44704746121265604, -0.8761111107545085, -1.2516946484097335, -1.558585511297411, -1.7847523997616546, -1.9219582144153229, -1.9662002275585544, -1.9179531011981468, -1.7821994320880106, -1.5682425189191047, -1.2893065401316381, -0.9619397990088467, -0.6052466200231195, -0.23998236452668287, 0.11244658867683269, 0.4310305819916078, 0.6962015733140485, 0.8908238097545931, 1.0010806231175358, 1.0172119104711685, 0.9340634316118487, 0.7514176941174, 0.47408651776748295, 0.11175689075067273, -0.3214061046538915, -0.8073833101477643, -1.325124830722965, -1.8515346126156422, -2.362569449080008, -2.834399087075593, -3.2445701817728567, -3.573115762641075, -3.803553747170607, -3.923722828339828, -3.9264115803748423, -3.809746539245761, -3.577316853230173, -3.2380262879967723, -2.805677250581845, -2.2983053579012465, -1.737296194751829, -1.1463275842362457, -0.550190292237172, 0.026452934413079277, 0.5603061529960756, 1.0306123429057124, 1.42019710721462, 1.7163282511770082, 1.911344611596504, 2.0030191980172463, 1.9946354209747066, 1.8947702249346412, 1.7167935301027843, 1.4781086897542988, 1.199172859432993, 0.9023484671178007, 0.610646673083754, 0.3464302462908601, 0.13014625372954153, -0.02084185974739636, -0.09325784804425967, -0.07869518293011979, 0.025866737313807273, 0.21784383670248347, 0.4891411970665899, 0.8265575319732544, 1.2124811393375574, 1.6258417779197052, 2.0432682560875666, 2.4403894446102714, 2.7932076421669434, 3.079468275056387, 3.2799491389342568, 3.379595900303154, 3.3684382406968685, 3.242232483107982, 3.002791204535206, 2.657977435847907, 2.221359654820997, 1.7115428631096454, 1.1512095309342982, 0.565921037102545, -0.01725555514065414, -0.5712198131534436, -1.0703271801923058, -1.491810988554858, -1.8170558475038046, -2.0326484688834565, -2.1311437813163883, -2.111499694440822, -1.9791522740632386, -1.7457233632227378, -1.42837369377239, -1.04883507749704, -0.6321741513128302, -0.20535626040489388], 'positive_zeros': ['0.78166000136720687015148149888064', '2.32852795461321131309851571246375', '3.34179720937903262778843681847526', '4.12612018602031606189479632410789', '4.69268245711063308092133663035143', '5.97999394463375606826302926303790', '6.69967744420730424624621056236191', '7.16210681859465324956638943808687', '8.126904193692300967873193914656734', '8.870124421908348015838614007021966'], 'prelabel': '2-3024-21.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.9139354463846185, 'root_angle': 0.27281447417149496, 'root_number': '0.6546536707079771437982924562468583555692080823954245576 + 0.7559289460184544544290330724683601216315026237378429087*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.13640723708574748', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.78166000136720687015148149888', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.32852795461321131309851571246', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.34179720937903262778843681848', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 24.1467615712352, 'bad_primes': [2, 3, 7], 'central_character': '21.20', 'conductor': 3024, 'conductor_radical': 42, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3024/2/k/e/1889/2'], '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': '2-3024-21.20-c1-0-30', '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': '2-3024-21.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.9139354463846185, 'root_angle': 0.13640723708574748, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.78166000136720687015148149888', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '990871769907538403557597446156', 'Lhash_array': ['990871769907538403557597446156'], 'label': '2-3024-21.20-c1-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3024/2/k/e/1889/2'}