-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1270392159442171155745917860996', 'a10': [125.99962625596777, 0.0], 'a2': [-1.722866782181628, 0.0], 'a3': [0.0, 0.0], 'a4': [-29.031730050855124, 0.0], 'a5': [-73.13370224505532, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [105.14954036369453, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 70.72926453752447, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '441.1', 'coefficient_field': 'CDF', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.722866782181628, 0], [32.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [73.13370224505532, 0], [3125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [193.0704129055728, 0], [161051.0, 0]], [[1.0, 0], [151.5003434469376, 0], [371293.0, 0]], [[1.0, 0], [-1760.1205121797293, 0], [1419857.0, 0]], [[1.0, 0], [1126.7909492870822, 0], [2476099.0, 0]], [[1.0, 0], [2413.3254946690445, 0], [6436343.0, 0]], [[1.0, 0], [-7729.106650194871, 0], [20511149.0, 0]], [[1.0, 0], [-8176.754180825752, 0], [28629151.0, 0]], [[1.0, 0], [-5932.376733425753, 0], [69343957.0, 0]], [[1.0, 0], [-4975.838722038296, 0], [115856201.0, 0]], [[1.0, 0], [5652.507680813682, 0], [147008443.0, 0]], [[1.0, 0], [-4720.9325545326865, 0], [229345007.0, 0]], [[1.0, 0], [-32072.115745682157, 0], [418195493.0, 0]], [[1.0, 0], [28566.931080707855, 0], [714924299.0, 0]], [[1.0, 0], [29003.65437237779, 0], [844596301.0, 0]], [[1.0, 0], [30517.384040684097, 0], [1350125107.0, 0]], [[1.0, 0], [56944.50353881482, 0], [1804229351.0, 0]], [[1.0, 0], [9726.786028454037, 0], [2073071593.0, 0]], [[1.0, 0], [98483.5215482197, 0], [3077056399.0, 0]], [[1.0, 0], [-50636.991775346156, 0], [3939040643.0, 0]], [[1.0, 0], [-59655.78977385894, 0], [5584059449.0, 0]], [[1.0, 0], [-134206.1565426406, 0], [8587340257.0, 0]], [[1.0, 0], [-135280.90844532484, 0], [10510100501.0, 0]], [[1.0, 0], [199409.56118008812, 0], [11592740743.0, 0]], [[1.0, 0], [93298.08250670826, 0], [14025517307.0, 0]], [[1.0, 0], [41818.73079796579, 0], [15386239549.0, 0]], [[1.0, 0], [-170560.04553562243, 0], [18424351793.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 38, 'label': '2-21e2-1.1-c5-0-38', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/441/6/a/be/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [-6.241246767933e-61, 0.1462823128654718, 0.2883040337030963, 0.42187431911874107, 0.5429412044470882, 0.6476594831669613, 0.7324566772912916, 0.7940964035438586, 0.8297383955089541, 0.8369943931675898, 0.8139790625977179, 0.7593550648813476, 0.6723713594913437, 0.5528938087853895, 0.40142715176150845, 0.2191274416487142, 0.007804097397966386, -0.2300891928619622, -0.4914753553324796, -0.7726870805407088, -1.0695125234067575, -1.3772536057297007, -1.6907967095955556, -2.004695257948346, -2.3132633635673825, -2.610679397087656, -2.891097986957678, -3.14876862901352, -3.3781587613083146, -3.574078862350172, -3.731806869766834, -3.8472090035012543, -3.916853924498983, -3.938117077290192, -3.909272062539297, -3.829565971564419, -3.699275795005186, -3.519743295779631, -3.2933861129459414, -3.0236833356832524, -2.715134349594713, -2.373190401705479, -2.0041590431630967, -1.6150823736214623, -1.2135908092854502, -0.807734905460429, -0.4057985596941162, -0.01609767699973322, 0.3532309329893793, 0.6944450630939223, 1.0004111829646123, 1.2648109163864671, 1.4823335972576412, 1.6488486057752654, 1.761551411121221, 1.8190776783101001, 1.8215804360478463, 1.7707661436485893, 1.6698865250721637, 1.5236842362440859, 1.3382917698603993, 1.121084444715284, 0.8804898327722673, 0.6257574999777421, 0.366694425407798, 0.11337286447087166, -0.1241813184581375, -0.3363107572592684, -0.514049219035102, -0.6494343216013482, -0.7357996804692045, -0.7680359775787451, -0.7428109592856423, -0.6587392607970866, -0.5164942094895997, -0.3188553573999993, -0.07068739661444294, 0.2211517304512071, 0.5479733642203634, 0.899488676416807, 1.2641021059089088, 1.629260110989448, 1.9818453741142865, 2.308604545323199, 2.596595893502216, 2.8336419323758175, 3.008771271555579, 3.1126336684061076, 3.137872562446354, 3.079440278636582, 2.9348425850278006, 2.7043013561864355, 2.3908266750787246, 2.0001927281197824, 1.5408152148318697, 1.023531590204681, 0.46128915442179347, -0.13125033959174662, -0.7381774215815331, -1.3428577074507262, -1.9284928332180222, -2.478699519554429, -2.9780854142925692, -3.412799802427846, -3.771037566646086, -4.0434759502717075, -4.223625707396515, -4.308081073867824, -4.296656573403939, -4.192402866335873, -4.001498504059544, -3.7330193936148204, -3.3985928073164597, -3.011947683086354, -2.588377539242972, -2.144136365417565, -1.6957911560398724, -1.2595571553415494, -0.8506432463484297, -0.4826351441355659, -0.16694309507978652, 0.08766136119130816, 0.27539828940280964, 0.3937049455976039, 0.4433222638690823, 0.4282363059140578, 0.355475021948793, 0.23476712173931663, 0.07807618345807225, -0.10097095558397384, -0.28773726209602957, -0.46728149776968786, -0.6250855361461118, -0.7477696948765232, -0.8237625556184398, -0.8438930769201591, -0.801875677265767, -0.6946632913809514, -0.5226490264545868, -0.28970374233100404, -0.003044367919148694, 0.32706428603407023, 0.6877634150950571, 1.0641912529740298, 1.4401856057434823, 1.7990661971933986, 2.124460444446157, 2.4011332251357995, 2.615779972696878, 2.7577431630255886, 2.8196149605391216, 2.797693404376529, 2.692265869226317, 2.507701370931986, 2.252342262832902, 1.938195574312822, 1.5804342172400574, 1.1967280386498678, 0.806433733353452, 0.42968047172854656, 0.08639431357716298, -0.204691295690225, -0.4269896905775066, -0.5669310319373403, -0.6147024141003775, -0.5648175834838542, -0.41648339979718796, -0.17373963936268974, 0.1546403324904052, 0.5554886248146144, 1.01180999984485, 1.5035535855183615, 2.0085544696244, 2.503600944484468, 2.9655756249225553, 3.3726136010273513, 3.705218546542599, 3.9472784814165682, 4.086926727867537, 4.11720038761882, 4.036458128516287, 3.8485307762712266, 3.5625916040488343, 3.1927476348823345, 2.7573679808499842, 2.278179462951306, 1.7791727145618572, 1.2853729425029927, 0.8215378625220754, 0.41085052326160865, 0.0736764229714374, -0.17354767544165742, -0.31923149936210327, -0.35730299492787204, -0.28759362020253465, -0.11591144758651084, 0.14620729891721443, 0.4820603898349394, 0.870630330554449, 1.2876823935506618, 1.7070543371601106, 2.102070646623691, 2.4470060218164345, 2.7185187024957997, 2.896974388140172, 2.967586065835445, 2.921303853262715, 2.7554016004094057, 2.473722853325811, 2.08656704958424, 1.6102165159085058, 1.0661248969427117, 0.47980693738654434, -0.12051303856545535, -0.7054220824656745, -1.2459264021797285, -1.7150570896063864, -2.0893835710125326, -2.3503483096584548, -2.4853450344972936, -2.48847610249223, -2.3609418517889993, -2.111035053862563, -1.753735716417148, -1.309924283123595, -0.8052534146922797, -0.2687387222605008, 0.2688541507448147, 0.7767358879064912, 1.2258353112851323, 1.5904564587883796, 1.8497543537307009, 1.9889422058269979, 2.0001573478979426, 1.8829322617001085, 1.6442395306768547, 1.2981042038693256, 0.8648024375463864, 0.36968990233494986, -0.15827417561903648, -0.6882227030759829, -1.1891975269110584, -1.6319804817384966, -1.9908298244964913, -2.2450177356408116, -2.3800754332333014, -2.3886690842892646, -2.271051184457054, -2.0350571783577753, -1.6956443329855053, -1.2739976240992454, -0.7962539609739371, -0.291919813559091, 0.20792327929089913, 0.6725170058346351, 1.0733127390869444, 1.3857302343159044], 'positive_zeros': ['1.00216270888322709782583949528494', '2.94014478315800471154889557590389', '4.09165414951758407511774919519333', '4.76595998783021677919650717204078', '6.04884527078206248051322163018026', '7.53911855263057160498065521025776', '8.027919406858157817466543334811264', '8.750612711784064299887338665389431', '10.01726790493519846061698238014310'], 'prelabel': '2-21e2-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.410069235001842, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.00216270888322709782583949528', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.94014478315800471154889557590', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.09165414951758407511774919519', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 70.72926453752447, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/6/a/be/1/3'], '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': '2-21e2-1.1-c5-0-38', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-21e2-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.410069235001842, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.00216270888322709782583949528', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1270392159442171155745917860996', 'Lhash_array': ['1270392159442171155745917860996'], 'label': '2-21e2-1.1-c5-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/6/a/be/1/3'}