-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3514340125169417419970635609208', 'a10': [-35.35006443103186, 0.0], 'a2': [-9.150224085424925, 0.0], 'a3': [9.094134095614637, 0.0], 'a4': [51.72660081349041, 0.0], 'a5': [3.863300406745202, 0.0], 'a6': [-83.21336483777706, 0.0], 'a7': [-226.37906575316458, 0.0], 'a8': [-180.50281788716282, 0.0], 'a9': [-160.29672505097938, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.6888278556985554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[23, [[1.0, 0], [529.0, 0]]]], 'bad_primes': [23], 'central_character': '23.1', 'coefficient_field': 'CDF', 'conductor': 23, 'conductor_radical': 23, 'conjugate': '3514340125169417419970635609208', 'degree': 2, 'euler_factors': [[[1.0, 0], [9.150224085424925, 0], [32.0, 0]], [[1.0, 0], [-9.094134095614637, 0], [243.0, 0]], [[1.0, 0], [-3.863300406745202, 0], [3125.0, 0]], [[1.0, 0], [226.37906575316458, 0], [16807.0, 0]], [[1.0, 0], [-18.32612185031121, 0], [161051.0, 0]], [[1.0, 0], [711.1851772924077, 0], [371293.0, 0]], [[1.0, 0], [-165.44091788487952, 0], [1419857.0, 0]], [[1.0, 0], [-213.25385163004574, 0], [2476099.0, 0]], [[1.0, 0], [529.0, 0]], [[1.0, 0], [-5475.819204989586, 0], [20511149.0, 0]], [[1.0, 0], [-6077.129256116049, 0], [28629151.0, 0]], [[1.0, 0], [-11499.694296460566, 0], [69343957.0, 0]], [[1.0, 0], [13182.974500992026, 0], [115856201.0, 0]], [[1.0, 0], [21455.220561641592, 0], [147008443.0, 0]], [[1.0, 0], [-12960.806155444645, 0], [229345007.0, 0]], [[1.0, 0], [29103.424119452764, 0], [418195493.0, 0]], [[1.0, 0], [-10506.192573178843, 0], [714924299.0, 0]], [[1.0, 0], [34103.26143209163, 0], [844596301.0, 0]], [[1.0, 0], [-12988.151709254184, 0], [1350125107.0, 0]], [[1.0, 0], [-45243.0262566206, 0], [1804229351.0, 0]], [[1.0, 0], [52589.20885644212, 0], [2073071593.0, 0]], [[1.0, 0], [-57603.3063109433, 0], [3077056399.0, 0]], [[1.0, 0], [40816.83375627411, 0], [3939040643.0, 0]], [[1.0, 0], [-54699.854221462614, 0], [5584059449.0, 0]], [[1.0, 0], [117496.89881176356, 0], [8587340257.0, 0]], [[1.0, 0], [141707.1273800574, 0], [10510100501.0, 0]], [[1.0, 0], [-60185.03246857353, 0], [11592740743.0, 0]], [[1.0, 0], [186998.88420044415, 0], [14025517307.0, 0]], [[1.0, 0], [63597.16130545042, 0], [15386239549.0, 0]], [[1.0, 0], [-42281.31885256607, 0], [18424351793.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-23-1.1-c5-0-4', '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/23/6/a/a/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [0.0, 0.17464400308660935, 0.3466325039117955, 0.5130984582527337, 0.6707668646074735, 0.81578849235804, 0.9436185336046125, 1.048954534013029, 1.125747203001094, 1.1672963756267771, 1.166442167432932, 1.1158578610733652, 1.008445958785767, 0.8378319190046333, 0.598941363139896, 0.288636253771762, -0.09362571395663365, -0.5451555924314286, -1.0594787927423115, -1.6259266415925198, -2.2294420243830757, -2.850664758941142, -3.4663526542085745, -4.050176407364372, -4.573900367992824, -5.0089274672200075, -5.328147095027815, -5.5079824104480215, -5.530492603787859, -5.385351000746552, -5.071497081269852, -4.598254839154797, -3.985725939014633, -3.2643066843596062, -2.473243299561593, -1.6582277674389414, -0.8681403144356067, -0.15115503097321464, 0.4494704118343217, 0.8995157373723355, 1.1773750431049246, 1.2766332136852891, 1.207239808847477, 0.9949924733799942, 0.6792105538531794, 0.3086895834691586, -0.06374297634999422, -0.38752921571263566, -0.6208176237425155, -0.73620591479726, -0.7249526262235906, -0.5989289977334824, -0.3898101913518135, -0.14533609700678665, 0.07712663398705644, 0.2190676887830169, 0.2303258517725635, 0.07827842016023003, -0.24470111175190826, -0.7168575763954151, -1.2867750504087405, -1.8777313175531125, -2.3965578830619743, -2.746158649503579, -2.840164628294417, -2.617684432898096, -2.0558555823407554, -1.17798524201558, -0.05551986866708974, 1.197127762872164, 2.4348285752524443, 3.4998572391056655, 4.24360897715871, 4.548837112706525, 4.348961335550585, 3.6411610492680944, 2.490698795800262, 1.0251467736580984, -0.5812495507284855, -2.131183821876424, -3.4325274665818, -4.326847925383232, -4.7135457584319065, -4.56543147920746, -3.932815715964401, -2.9350403689545805, -1.7405367308488249, -0.5385799494599706, 0.49247746284087707, 1.21490265574817, 1.5538220611204696, 1.5078501616556235, 1.1460399612732073, 0.5916622567983527, -0.004102139823784206, -0.4934124391336973, -0.7617178507000691, -0.7503062528180556, -0.46676321461340897, 0.018896419153225548, 0.5916449714372334, 1.1186661659481454, 1.4803922271515326, 1.598345365215022, 1.453295314067384, 1.089265060909643, 0.6020617424447249, 0.11462059347263794, -0.25528374534552095, -0.4272691014067171, -0.3824053443698722, -0.17248657140976498, 0.08889514828095033, 0.2526227103452839, 0.17244744593174538, -0.2531614904925415, -1.0459742728260946, -2.1292510476469055, -3.331622155369977, -4.41497996733955, -5.122061311677639, -5.234266327223534, -4.6269805875163, -3.3091766233719713, -1.4366979188054367, 0.7060285887885803, 2.754135327775238, 4.33155812335477, 5.127202730943775, 4.961442532311777, 3.827709121350642, 1.8989383966043751, -0.5037301313008986, -2.9740446723621456, -5.102107399507071, -6.556285313676494, -7.1472652736705, -6.859947021718457, -5.846367417602837, -4.382086344898614, -2.797178853879964, -1.3989758450669936, -0.40542097934651705, 0.09512712146958825, 0.1488841254256904, -0.09305908213874507, -0.4295353606509167, -0.6731802190962529, -0.7053294505757288, -0.5068103542792517, -0.1566395810758045, 0.1999813752782999, 0.40399922661628396, 0.3387925123729399, -0.02720432087044625, -0.6251460986790701, -1.3031220675874038, -1.8715930662228613, -2.16336876243639, -2.089467951617334, -1.672648969722967, -1.046507475995217, -0.4182252637402605, -0.004409130078738215, 0.04143589675331963, -0.312673743430364, -0.9525906907284631, -1.637900175585381, -2.0639692035941497, -1.950730811276897, -1.133367910549364, 0.3724493392973725, 2.35254677784527, 4.43272876475957, 6.166936530054382, 7.1531501762969185, 7.145555610528452, 6.130671701456856, 4.343746960114744, 2.217724237525749, 0.2760674922021277, -1.0027235016811988, -1.3119926396132904, -0.5995932766661297, 0.9175833461695133, 2.8122077556059115, 4.56244067671738, 5.692846464651858, 5.900633739862471, 5.131801522966889, 3.5864333528575303, 1.6531734618595186, -0.20638631573605518, -1.5883454190532476, -2.2534801460784486, -2.180069652073708, -1.5494190772017653, -0.6720035291208354, 0.11973218776598485, 0.5764412285194205, 0.6014784610143533, 0.2645970270103051, -0.24143508373243872, -0.683281500065159, -0.8778550832239251, -0.7589008538929394, -0.39618349968382355, 0.038378431875083135, 0.34385448231377475, 0.37445505782488103, 0.1021379558610139, -0.3672463059373719, -0.8320947482747443, -1.0747222218853592, -0.9531677210176253, -0.4693482376837106, 0.21551194895053163, 0.8291769295848588, 1.0879663071529104, 0.8145677262616455, 0.031089299287096327, -1.0106720776498357, -1.8805569967801616, -2.094190891666587, -1.2744372015182464, 0.7017590572770416, 3.6226564573802333, 6.960484583495335, 9.992260470465489, 11.99161016789731, 12.435394704017606, 11.161161977937326, 8.424435980185388, 4.835070213716571, 1.1898177637576692, -1.748519353695164, -3.4576649154336616, -3.7850456886094372, -2.961649177491503, -1.50016207928921, -0.014263146081968991, 0.9795805456730121, 1.2129648237871629, 0.7226026231889784, -0.1992241944600662, -1.136680780212415, -1.7134594082839802, -1.7273113923942782, -1.2097247196965897, -0.39393041317211164, 0.39104529493387485, 0.8558155074982534, 0.8618904503788869, 0.46654070360380573, -0.11359798201487571, -0.6025301827391971, -0.7858690809191272], 'positive_zeros': ['2.77232553239567056013537377254293', '6.54469224639957625151710339710667', '8.054824913865107838436730598268102', '9.426206077462713453649794813769981', '10.07161753068757523632361854977373', '11.96117264130566752377549293113680', '13.64776901001646144077118082940976', '15.37947389080488218696688756903573', '16.52216286400100048398235069591446'], 'prelabel': '2-23-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9206321500221106, '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': '2.77232553239567056013537377254', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.54469224639957625151710339711', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.054824913865107838436730598268', 'prec': 107}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.6888278556985554, 'bad_primes': [23], 'central_character': '1.1', 'conductor': 23, 'conductor_radical': 23, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/23/6/a/a/1/1'], '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': '2-23-1.1-c5-0-4', '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': '2-23-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9206321500221106, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '2.77232553239567056013537377254', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3514340125169417419970635609208', 'Lhash_array': ['3514340125169417419970635609208'], 'label': '2-23-1.1-c5-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/23/6/a/a/1/1'}