-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1883257745358861851825252341410', 'a10': [-2.447151918170408, -16.253938524730074], 'a2': [-1.9789860258503302, -0.28916139003870545], 'a3': [-1.0988014001519144, 1.3388933800061125], 'a4': [3.832771381021767, 1.1444927002041099], 'a5': [2.3857227266516707, 7.864673838794277], 'a6': [2.5616688869616038, -2.331920348891209], 'a7': [2.3613312200369765, -11.871213696481604], 'a8': [-7.254057903240977, -3.373224560628468], 'a9': [-0.5852709660483848, -2.9423558412096913], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.463242151435402, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.9789860258503302, 0.28916139003870545]]], [3, [[1.0, 0], [1.0988014001519144, -1.3388933800061125]]]], 'bad_primes': [2, 3], 'central_character': '384.235', 'coefficient_field': 'CDF', 'conductor': 384, 'conductor_radical': 6, 'conjugate': '476642760784984589741414322386', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.9789860258503302, 0.28916139003870545]], [[1.0, 0], [1.0988014001519144, -1.3388933800061125]], [[1.0, 0], [-2.3857227266516707, -7.864673838794277], [-20.78674030756363, 13.889255825490055]], [[1.0, 0], [-2.3613312200369765, 11.871213696481604], [-45.27009709305305, -18.7514881858894]], [[1.0, 0], [-0.9498801861885156, -0.09355503255887136], [118.67501892879089, 23.60592896395152]], [[1.0, 0], [23.623197304437138, 7.166018558502916], [140.51836447913016, 93.89136938031278]], [[1.0, 0], [5.564756749784253, 13.434511216636368], [-204.35385976291224, 204.35385976291224]], [[1.0, 0], [-16.774532411289037, 8.966174374201476], [200.5608541200764, -300.1605300412188]], [[1.0, 0], [19.38396025405431, 12.951948160035835], [202.4395357211325, 488.7322726984707]], [[1.0, 0], [-43.583871093528415, 4.292636627739358], [824.8404208191168, -164.07096081556386]], [[1.0, 0], [5.145907612385888, -5.145907612385888], [0, -961.0]], [[1.0, 0], [39.88663998912283, 21.319853249846314], [760.5756490038355, 1138.2818992421844]], [[1.0, 0], [25.745554066112156, 17.20262924837249], [643.2908498057159, 1553.041494151473]], [[1.0, 0], [22.044679525518394, 26.861519722301242], [-360.72200540782114, 1813.4719834655732]], [[1.0, 0], [-6.514987922969227, -15.728572202329229], [-1561.9988796410835, 1561.9988796410835]], [[1.0, 0], [-2.9483356904064513, -0.2903857197161452], [2755.0258526526745, 548.0087145433043]], [[1.0, 0], [12.85493817526318, 42.37705196705843], [-2894.34572042516, 1933.9399811412354]], [[1.0, 0], [-45.5846118122845, 55.54501020582797], [-725.9310882220133, -3649.5020283804206]], [[1.0, 0], [-46.80267207098552, -38.40996032276671], [875.7604555303998, 4402.745123730101]], [[1.0, 0], [-15.30759869113949, -3.0448706945523103], [4657.2767233893965, 1929.1071825524175]], [[1.0, 0], [-123.05701417773186, 24.477562012764785], [4923.3540287526475, -2039.3200110735634]], [[1.0, 0], [-36.13439661029113, 87.23615036473323], [-4413.053421385243, -4413.053421385243]], [[1.0, 0], [-34.58956891271182, -64.7125318562048], [-3827.32333527204, 5727.994159152234]], [[1.0, 0], [45.17382490901101, 67.60740668046769], [-3031.235467763876, 7318.049777021903]], [[1.0, 0], [16.331962523621545, 16.331962523621545], [0, 9409.0]], [[1.0, 0], [60.35614711135913, -112.9184090879552], [-5667.371947032962, -8481.821515098263]], [[1.0, 0], [5.505298094542453, 8.23926085348357], [-4059.8885339612375, 9801.43796041224]], [[1.0, 0], [-10.061923835834541, 8.257607487002767], [2233.5890967626524, -11229.010675336585]], [[1.0, 0], [29.672914328453338, 55.514118102836115], [-6600.729938505894, 9878.69046376654]], [[1.0, 0], [2.91305586866152, -7.032738986073179], [-9029.046488971026, -9029.046488971026]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 38, 'label': '2-384-128.107-c2-0-38', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/384/3/u/a/235/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.6034905266951553, 0.7514960042960702, 0.8694564937669379, 0.9546107167446344, 1.0037611192397642, 1.0135533784100297, 0.9810068095590913, 0.9042416043494919, 0.7833260925172109, 0.6211518407814575, 0.4242341459212587, 0.20332944437977896, -0.026239586160523454, -0.2446534497466004, -0.42814441987574536, -0.5500786588657295, -0.5825826121816298, -0.4986687839799357, -0.27475192355170086, 0.10662007988447372, 0.654058016408581, 1.3649311111651976, 2.2235846296386548, 3.2004785669840614, 4.252506642210798, 5.324671143431964, 6.353168283281642, 7.269788544862801, 8.007370482352908, 8.505882843751039, 8.71857018059394, 8.617503606261355, 8.197851202897535, 7.4802364631385, 6.510694249523321, 5.357957249135346, 4.108094756365176, 2.856850924179362, 1.7003528075731427, 0.7251353888883099, -0.0013828881278295881, -0.43878243118851556, -0.5787856780332882, -0.4468173915310734, -0.09953352573265492, 0.38163236411364343, 0.9003162299121024, 1.3573664328306718, 1.6637849115569106, 1.7527486699658346, 1.5890036023403102, 1.174184153750876, 0.5471095852102863, -0.22121373533514743, -1.0373833462029518, -1.7989330650957167, -2.4093439842837894, -2.7925103826738575, -2.904404449087607, -2.740011557582824, -2.334270333454756, -1.756664608214838, -1.1001432835010843, -0.466023221614295, 0.0527119309867275, 0.3869149680654629, 0.5028527228097982, 0.4076885094084427, 0.1476771858070781, -0.20086846505175934, -0.5464639546933551, -0.8006680029571935, -0.8963476089405565, -0.8025216578586577, -0.5327564621823528, -0.14513204506198438, 0.2667108963699565, 0.5902485940262253, 0.7157122609466039, 0.5587797522809569, 0.07995069485853068, -0.703408966286154, -1.7152014023827682, -2.8299536151035296, -3.8923050480311674, -4.743469704037135, -5.249936971329333, -5.328931824355386, -4.965455955895404, -4.217089953479363, -3.2049526187990622, -2.0918973805685157, -1.0516637324355942, -0.23475196821679636, 0.2622078892262717, 0.41714404618762607, 0.28850786108142273, 0.004496235046291213, -0.26313672651274733, -0.33606312115434334, -0.07001662565629652, 0.6092577066426481, 1.6826037077703413, 3.032323262531327, 4.45756268999461, 5.708318898472601, 6.532179626224068, 6.724930680091958, 6.1748735984606515, 4.891463394265846, 3.011643364811099, 0.7815372670924347, -1.4838761103120384, -3.4558566183731796, -4.851228096541673, -5.484201952967176, -5.300192435206783, -4.384589192226132, -2.94449646308155, -1.2670229368917705, 0.3373794653846476, 1.5948587401980607, 2.319019292801491, 2.4422930925670334, 2.0216720558582546, 1.2182543602792293, 0.25578341912107844, -0.6320873187206351, -1.2537325388837262, -1.4990524444806024, -1.3579916752305403, -0.9146100699196588, -0.3190751747401115, 0.2548318041607438, 0.6557590171992259, 0.7927871887574274, 0.6560178651758763, 0.3149154360091326, -0.10467606257016465, -0.4584023166834695, -0.6258393820781873, -0.5459730294369576, -0.2359795838968909, 0.212035719486835, 0.6557961323624524, 0.9426924787868324, 0.9540041804369399, 0.641287130954096, 0.04446166083775571, -0.7142122253776986, -1.459672986742542, -2.010002530944187, -2.2268262848082125, -2.0564181729425397, -1.5496338493388089, -0.8540037332224446, -0.17860621636658386, 0.2601663286461666, 0.2981650883525275, -0.12763422347651812, -0.9549076681570295, -2.004466997418644, -3.021060385936981, -3.737299731026001, -3.9447286451919186, -3.5531980802592584, -2.6217981529616288, -1.3513071254663709, -0.03790023855970183, 1.0017554280248104, 1.5156629318715937, 1.389792086938102, 0.6893182228317831, -0.345002265247217, -1.3469875123807504, -1.9112818110868122, -1.6953612109162668, -0.5119472463301462, 1.612108719298974, 4.426726400817831, 7.50339239015355, 10.324400568928843, 12.395628343661743, 13.355633421226736, 13.05445618985165, 11.582975142325415, 9.24611418264843, 6.487408219380001, 3.7846544426420587, 1.5433660216241072, 0.014645697969427733, -0.7430358116424677, -0.8508658860990308, -0.5521252649121814, -0.12840675378389832, 0.1855943213970366, 0.26459404630293804, 0.11588064632654337, -0.14147417901727968, -0.3328081439980843, -0.3005189145846396, 0.030413277300005995, 0.6151512157319557, 1.29226729592835, 1.8272789931904299, 1.9836284450615809, 1.5995167762252145, 0.6467064397609429, -0.7476551740676018, -2.32435513116658, -3.7552885375679828, -4.7290953889061935, -5.034791102876915, -4.619075055635964, -3.6004420837674593, -2.235797800625033, -0.8492511933900107, 0.25608471058829024, 0.8775181192853551, 0.9604964961942727, 0.6014661627325615, 0.00648598506839492, -0.5802789109924117, -0.9549957407150631, -1.0145968759739776, -0.7804272595133794, -0.3784994354571921, 0.015902208977758178, 0.24960675278345182, 0.25370061491825396, 0.07394292444696543, -0.14265699366505963, -0.20238416861844274, 0.05675635328125241, 0.6893683101520746, 1.5972942209669354, 2.5337900475564044, 3.161209677542495, 3.1485291008952965, 2.280664834674564, 0.5452819909522244, -1.8328533818324078, -4.425708940970096, -6.699610676800526, -8.152233698683581, -8.450892318362847, -7.531383307846769, -5.626284891614279, -3.211177517521527, -0.8811440621790131, 0.8090117433081181, 1.4956447894805573, 1.1045195216337922, -0.13270714496111258, -1.7492956482514048, -3.1813746798651628, -3.9328872280703155], 'positive_zeros': ['1.48562840976827350455822790406990', '2.34497052565570618593400519373466', '4.99970525555033215160804880142791', '5.52803462972049175925633509996114', '6.59048111479873586174343764479940', '7.985236016863544051645837816009989', '8.554988624579717563004305422040099', '9.418208333003246802184579960657599', '10.01519511407864806592065333208394', '11.67371970278745484558905108420504'], 'prelabel': '2-384-128.107-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.2346935173885334, 'root_angle': 0.4639082915762578, 'root_number': '0.11314265004726337 + 0.9935787541711439*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.231954145788', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.48562840976827350455822790407', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.34497052565570618593400519373', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.99970525555033215160804880143', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 10.463242151435402, 'bad_primes': [2, 3], 'central_character': '128.107', 'conductor': 384, 'conductor_radical': 6, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/384/3/u/a/235/3'], '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': '2-384-128.107-c2-0-38', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-384-128.107-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.2346935173885334, 'root_angle': 0.2319541457881289, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.48562840976827350455822790407', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1883257745358861851825252341410', 'Lhash_array': ['1883257745358861851825252341410'], 'label': '2-384-128.107-c2-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/384/3/u/a/235/3'}