-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1124831882082511871278090929663', 'a10': [0.0, 0.0], 'a2': [1.9617705019883533, 0.0], 'a3': [0.18770817325750477, 0.0], 'a4': [1.8485435024716357, 0.0], 'a5': [0.0, 0.0], 'a6': [0.3682403572786919, 0.0], 'a7': [0.6770674421921025, 0.0], 'a8': [-0.2971228891856171, 0.0], 'a9': [-2.9647656416923307, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 72.06498782420559, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 19], 'central_character': '9025.1', 'coefficient_field': 'CDF', 'conductor': 9025, 'conductor_radical': 95, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.9617705019883533, 0], [2.0, 0]], [[1.0, 0], [-0.18770817325750477, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.6770674421921025, 0], [7.0, 0]], [[1.0, 0], [-2.8406902395827394, 0], [11.0, 0]], [[1.0, 0], [-4.766629776372872, 0], [13.0, 0]], [[1.0, 0], [-5.183937071326238, 0], [17.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0509147803444947, 0], [23.0, 0]], [[1.0, 0], [1.426045243401764, 0], [29.0, 0]], [[1.0, 0], [-0.2710636374426865, 0], [31.0, 0]], [[1.0, 0], [-0.6037544281957674, 0], [37.0, 0]], [[1.0, 0], [-6.735634304559618, 0], [41.0, 0]], [[1.0, 0], [5.629441175891565, 0], [43.0, 0]], [[1.0, 0], [-7.8953758022203315, 0], [47.0, 0]], [[1.0, 0], [-6.888294304583311, 0], [53.0, 0]], [[1.0, 0], [10.12268094134529, 0], [59.0, 0]], [[1.0, 0], [7.471952996985774, 0], [61.0, 0]], [[1.0, 0], [-4.117332916631896, 0], [67.0, 0]], [[1.0, 0], [7.605464919232233, 0], [71.0, 0]], [[1.0, 0], [-16.127377623183293, 0], [73.0, 0]], [[1.0, 0], [-14.84676298691765, 0], [79.0, 0]], [[1.0, 0], [-14.181510735709132, 0], [83.0, 0]], [[1.0, 0], [-8.237884191015198, 0], [89.0, 0]], [[1.0, 0], [5.728466911172127, 0], [97.0, 0]], [[1.0, 0], [2.022314485736665, 0], [101.0, 0]], [[1.0, 0], [18.235841901379793, 0], [103.0, 0]], [[1.0, 0], [-6.213413198051228, 0], [107.0, 0]], [[1.0, 0], [-15.988517981914733, 0], [109.0, 0]], [[1.0, 0], [7.883919892208268, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 245, 'label': '2-95e2-1.1-c1-0-245', 'leading_term': '4.96149821738393372182636070282', '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/9025/2/a/cu/1/21', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [4.961498217383934, 4.947189547213816, 4.904190171966681, 4.832290742433373, 4.731177464620868, 4.600482415700686, 4.439849485311147, 4.249011940054463, 4.027877084983693, 3.776613299105303, 3.4957348148689737, 3.186179933202728, 2.849378846668008, 2.4873078192535707, 2.102527090610763, 1.698200499725306, 1.2780954380749268, 0.8465623372962956, 0.4084934711555489, -0.03073859028964119, -0.4653619912435067, -0.8893046483289366, -1.2963094181121377, -1.6800629331308654, -2.0343351907513245, -2.3531265446433958, -2.6308183691372866, -2.8623233582243612, -3.0432311997482135, -3.1699452468614546, -3.239805806781284, -3.251195792257341, -3.203624741472227, -3.0977876106613618, -2.935595279192193, -2.7201743727351273, -2.455834794777049, -2.1480042431029402, -1.8031299539893022, -1.4285489360863055, -1.032328997707302, -0.6230839017494735, -0.20976696587948432, 0.19855167485436417, 0.5929181465822034, 0.9647316356192932, 1.3059778492021172, 1.6094518543686926, 1.8689630204764136, 2.079515047521296, 2.2374545721355594, 2.3405826023799183, 2.3882240282542844, 2.3812516646862547, 2.3220626757293426, 2.214506762183224, 2.0637671214728606, 1.876196853673171, 1.659115131692414, 1.4205690148789298, 1.1690682014031513, 0.9133012254909559, 0.6618425553385282, 0.4228606877846983, 0.2038376274324481, 0.011310053303984843, -0.14935799900731742, -0.27416197701084033, -0.3605954497862904, -0.40773440472509154, -0.41626294063531816, -0.3884382090246329, -0.32799473074474594, -0.2399905685811354, -0.13060017695723852, -0.006860982996730195, 0.12361721605665432, 0.252969216587029, 0.3734055499526706, 0.47754470447988395, 0.5587329214311192, 0.6113381896132118, 0.6310057520212778, 0.6148636775334132, 0.5616688109916647, 0.4718856422747202, 0.34769325303839166, 0.19291841233254547, 0.012895985982843151, -0.18573902670650055, -0.39532044580295295, -0.6074706160397236, -0.8134581220208792, -1.0045787373327235, -1.1725433779006382, -1.309856042876, -1.4101646667088255, -1.468568504767184, -1.4818671301020852, -1.4487382947671188, -1.3698347354099543, -1.247793377071067, -1.0871541793338124, -0.8941899186021212, -0.6766523341790908, -0.443444097446026, -0.2042298029814384, 0.030997556536159883, 0.25237555359381125, 0.4506358273215246, 0.6175503124023508, 0.7463384641080815, 0.8320148541078145, 0.8716586336268094, 0.8645894395995114, 0.8124382490632064, 0.7191063156862814, 0.590610458779424, 0.4348183957005055, 0.2610832662601825, 0.07979173305316735, -0.0981552056215528, -0.261905531875602, -0.40123742854195116, -0.5071302557418172, -0.5722964973299147, -0.591646622607439, -0.5626609337908666, -0.4856459449208997, -0.363857552692537, -0.2034790386519573, -0.013448550570792833, 0.19486213677639164, 0.4081084090437311, 0.6115567328483928, 0.7897685391704281, 0.9273549818404958, 1.0097687277716754, 1.0240956237559748, 0.9598074399883199, 0.8094370646232947, 0.5691395858286861, 0.23910662779552827, -0.17619300746378136, -0.667966103144923, -1.2232524042187247, -1.8252884118914752, -2.454069514804723, -3.087092471576508, -3.7002508187637755, -4.268847281035984, -4.7686801590448376, -5.177155367665264, -5.474372623272764, -5.64413347233084, -5.674820546609099, -5.560101636848746, -5.29941878747472, -4.898231398258763, -4.367992927029845, -3.725852769894822, -2.994087716644475, -2.1992804425575456, -1.3712751733622304, -0.5419523137047756, 0.25612614503871295, 0.991140771462715, 1.6334435126301072, 2.1569240627992783, 2.5402476078356653, 2.7679019608512947, 2.830999435923184, 2.727789018076633, 2.463847066290832, 2.0519293833893846, 1.5114833408199861, 0.8678351128331679, 0.15108316042382613, -0.6052558923218262, -1.3657897007672386, -2.0949110850188366, -2.758500047621579, -3.325585785754457, -3.76988762434569, -4.0711578503792065, -4.216257371851967, -4.19990665887171, -4.025069062179074, -3.7029406899638904, -3.252539761292216, -2.6999078448330565, -2.0769546762127313, -1.4199963553780666, -0.768052723195372, -0.16098275654223215, 0.362453812656659, 0.7665153011827169, 1.0202833594659835, 1.0992648827881313, 0.9867093345185126, 0.6745731056021668, 0.16407899262695907, -0.5341618198798224, -1.4004766732544955, -2.4068965693136404, -3.518327024502851, -4.694071682413829, -5.88963769325292, -7.058737222151859, -8.155388977535326, -9.136017942778858, -9.961450895833131, -10.598709897128165, -11.022515530307283, -11.21642584311103, -11.173554962670181, -10.896836345512959, -10.398818497453261, -9.7010045817481, -8.832770396706055, -7.829916534512467, -6.732929001964296, -5.5850372057009485, -4.430168192764563, -3.310900848607194, -2.2665231207191647, -1.3312892807072756, -0.5329630779768978, 0.10828303051654337, 0.5805617246842265, 0.8805288447720124, 1.0132000805597767, 0.9913443474871314, 0.834494272318202, 0.5676342536082202, 0.21964314937199747, -0.17841912974980254, -0.5950846417861901, -1.0002117732053966, -1.3665863486544634, -1.6713038411226113, -1.8968606939514185, -2.031900351363768, -2.071580082576497, -2.0175468896098177, -1.8775334267560762, -1.6646066231629182, -1.3961213345200674, -1.0924477266071977, -0.7755532757344723, -0.46752756960761754, -0.18914010613129645, 0.04148207083440347, 0.20997856008645116, 0.30661638341251557, 0.3268390264811301, 0.27147506970523694], 'positive_zeros': ['0.887335896721064724493406842045513', '1.99269425681199690804036141311749', '3.04988119310639171616944253665984', '3.51812612008710219374463434865063', '4.12816234120879442064462666352718', '5.00932990701645659234921261609445', '5.64573861731849529439527659734448', '6.14374806784644335611334871893792', '6.68434093995437003121273900593476', '7.71901274072866546333487596028163'], 'prelabel': '2-95e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.489109954771795, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.887335896721064724493406842046', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.99269425681199690804036141312', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.04988119310639171616944253666', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 72.06498782420559, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 9025, 'conductor_radical': 95, 'degree': 2, 'index': 245, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9025/2/a/cu/1/21'], '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': '2-95e2-1.1-c1-0-245', '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': '2-95e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.489109954771795, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.887335896721064724493406842046', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1124831882082511871278090929663', 'Lhash_array': ['1124831882082511871278090929663'], 'label': '2-95e2-1.1-c1-0-245', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9025/2/a/cu/1/21'}