Table lfunc_lfunctions
L-functions
{'Lhash': '3615183878924887459261693291295', 'a10': [-2.0, 1.0], 'a2': [0.0, -1.0], 'a3': [0.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-1.0, -2.0], 'a6': [0.0, 0.0], 'a7': [0.0, 2.0], 'a8': [0.0, -3.0], 'a9': [3.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.758578819202164, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[5, [[1.0, 0], [1.0, 2.0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [5, 19], 'central_character': '95.39', 'coefficient_field': 'CDF', 'conductor': 95, 'conductor_radical': 95, 'conjugate': '2421654567487904000541084265122', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0], [-2.0, 0]], [[1.0, 0], [0, 0], [-3.0, 0]], [[1.0, 0], [1.0, 2.0]], [[1.0, 0], [0, -2.0], [-7.0, 0]], [[1.0, 0], [4.0, 0], [11.0, 0]], [[1.0, 0], [0, -2.0], [-13.0, 0]], [[1.0, 0], [0, -4.0], [-17.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, -6.0], [-23.0, 0]], [[1.0, 0], [-6.0, 0], [29.0, 0]], [[1.0, 0], [4.0, 0], [31.0, 0]], [[1.0, 0], [0, 10.0], [-37.0, 0]], [[1.0, 0], [10.0, 0], [41.0, 0]], [[1.0, 0], [0, 2.0], [-43.0, 0]], [[1.0, 0], [0, 6.0], [-47.0, 0]], [[1.0, 0], [0, 10.0], [-53.0, 0]], [[1.0, 0], [0, 0], [59.0, 0]], [[1.0, 0], [-2.0, 0], [61.0, 0]], [[1.0, 0], [0, -8.0], [-67.0, 0]], [[1.0, 0], [-4.0, 0], [71.0, 0]], [[1.0, 0], [0, 4.0], [-73.0, 0]], [[1.0, 0], [4.0, 0], [79.0, 0]], [[1.0, 0], [0, -18.0], [-83.0, 0]], [[1.0, 0], [-2.0, 0], [89.0, 0]], [[1.0, 0], [0, -6.0], [-97.0, 0]], [[1.0, 0], [6.0, 0], [101.0, 0]], [[1.0, 0], [0, 16.0], [-103.0, 0]], [[1.0, 0], [0, 4.0], [-107.0, 0]], [[1.0, 0], [6.0, 0], [109.0, 0]], [[1.0, 0], [0, 6.0], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 9597155, 'index': 5, 'label': '2-95-5.4-c1-0-5', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/95/2/b/a/39/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [1.0726779984714119, 1.1197353551135523, 1.1821193852183591, 1.2598374181227394, 1.3516878644812569, 1.4554127661211504, 1.5678550995882616, 1.6850786476589388, 1.8024478752776454, 1.9146890757560686, 2.015960491632373, 2.0999554459410397, 2.160055299336842, 2.1895415331290855, 2.1818693515274443, 2.1309988105728537, 2.0317733506692157, 1.8803296169013404, 1.6745167013390365, 1.4142977378963582, 1.102102572064948, 0.743097548773409, 0.3453378667179493, -0.08023005370706493, -0.519943754270202, -0.9577968521490529, -1.376016107614907, -1.7558372889546, -2.0784573331466296, -2.3261228014905573, -2.4832972948028775, -2.537834891243263, -2.482074514713411, -2.3137631514056753, -2.036715560022657, -1.6611257689323204, -1.2034618821987422, -0.6859004777200761, -0.1352892892803209, 0.4183348659356354, 0.943604489145124, 1.4099464794459504, 1.7898272246997864, 2.060942433635111, 2.2081602687027346, 2.2250259976333697, 2.1146541740151674, 1.8898710772993461, 1.5725247462982168, 1.191949367994888, 0.7826499782088994, 0.3813555813725402, 0.023665818268079546, -0.25942045709015327, -0.4447652496003862, -0.5197988658627778, -0.4843557057703419, -0.35137747660756635, -0.14631485431637664, 0.09482157316166599, 0.32867243856594386, 0.5087714661354377, 0.5904544196357749, 0.5359654363540141, 0.3192261188931183, -0.07027928502876844, -0.6250013928720752, -1.3185959834986436, -2.107193871480381, -2.932692514727132, -3.727865176654541, -4.422859767303422, -4.952465028010118, -5.2633823612915105, -5.320679195317406, -5.11262901786086, -4.653269083195343, -3.9822228610402672, -3.1616223644745785, -2.270296691315677, -1.3957304764624476, -0.6245983334652303, -0.03290829329836241, 0.3230957882259802, 0.41413941898782675, 0.24225532461364052, -0.15842956891203763, -0.7247442988219037, -1.3711873030875141, -1.9996608690086635, -2.511167713608409, -2.8181037879226722, -2.8556316068651606, -2.59065607602975, -2.0271572158241127, -1.2070429593697067, -0.20622675309071728, 0.8737555960675735, 1.917675759464575, 2.8106677900268737, 3.4526454638286546, 3.7712009498142933, 3.7312360023954327, 3.339954647780015, 2.6464292280626567, 1.7356678326061576, 0.717865653284183, -0.28578998359474017, -1.158872750747692, -1.8048730772774042, -2.15963421068898, -2.199287771970073, -1.9425200221017316, -1.4468025526459234, -0.799101531046896, -0.10240836296527212, 0.5399160070995743, 1.0396268732170586, 1.3365431159782475, 1.4069419230298044, 1.2660653793926766, 0.9643112716159359, 0.5776815916426268, 0.19399989509954993, -0.10287059707987634, -0.24819756407920449, -0.20836645579917146, 0.012423675298056583, 0.37203101942641204, 0.7970094476850023, 1.1950676099447382, 1.4713708308227451, 1.5459732247089444, 1.3693666419850314, 0.9333367516713438, 0.27501273099440166, -0.5269112495037707, -1.3634869229256399, -2.112732811744512, -2.660036540105261, -2.9183268593341336, -2.844482807889993, -2.448937148350848, -1.7964756228419514, -0.9976768296057296, -0.19204604513134368, 0.4746042337135397, 0.8748526480047729, 0.9222434874528745, 0.5877205624776776, -0.09319560115680493, -1.0241140664513042, -2.06214936700893, -3.0408714548962967, -3.798144139385371, -4.204163375625768, -4.1847943627721405, -3.7359555303929235, -2.9262272316297437, -1.8868484125694855, -0.790471125301392, 0.17791772322858906, 0.8529990091071994, 1.1184714952751507, 0.928484215191055, 0.31715458910980404, -0.6057978547906722, -1.6728330214273275, -2.6868983013166803, -3.4554175002812384, -3.823992600060796, -3.7037909948174574, -3.0876326064274555, -2.0517680311666098, -0.742905234604916, 0.647266765963469, 1.9154935933130326, 2.8822489541422303, 3.422460311698892, 3.4860429196132126, 3.104508612601331, 2.382529765152722, 1.4761853998893741, 0.562149957071304, -0.19618901243651093, -0.679125645943973, -0.8316906297651069, -0.6713730664903289, -0.28117267862080086, 0.21042199009532847, 0.6583103769568038, 0.9325106220980027, 0.9461728996165815, 0.6740756855229809, 0.15777632200743055, -0.5036340706281769, -1.1752007211154036, -1.7155939001716538, -2.0081168914269147, -1.986555936110312, -1.6502341660897775, -1.064893111756411, -0.3490500498081465, 0.3513655163424881, 0.8946838757431672, 1.1745766248606777, 1.1436346112832296, 0.8240294479803383, 0.3025750064684686, -0.2890971675870547, -0.8051925412665304, -1.1206308899440178, -1.1623644489679852, -0.9298636966673073, -0.4996366070185858, -0.012005396992897897, 0.3577515411243387, 0.438210140381532, 0.10241326956368595, -0.6986410503370845, -1.9174105906543548, -3.4109915525034276, -4.962860124769511, -6.321539233843762, -7.2487519959493865, -7.567286180201563, -7.198484978591824, -6.18113536529651, -4.667214777849634, -2.8947369587182914, -1.1428041012373622, 0.3221288582916924, 1.2977139322734244, 1.6841073679218985, 1.5011277894238257, 0.8804254836019042, 0.03423098104906844, -0.7926845152955029, -1.3775076535110595, -1.5685187846515385, -1.3181216500803907, -0.6924760823944074, 0.14445684019451935, 0.9690065711161305, 1.549635462070787, 1.7010242582434931, 1.3283067605915446, 0.4514694005495282, -0.7957056139580293, -2.1921161553973594, -3.4755056420830193, -4.398148926529006, -4.779717122072913, -4.545584457892626, -3.74210171801974, -2.525549547509549, -1.1274226130773668], 'positive_zeros': ['2.85187722726909546411289531009989', '4.78034076207371224866306495445015', '6.50918098564082978345606367110350', '7.32669114933864019521989753243754', '8.105993347947847675102235226929995', '10.25869934003058642049905339703221', '10.70752799236204843250226126333119', '12.02418282732934495801628845567859', '13.33833719146884021116825649847274', '14.39378607396707998210468115281473'], 'prelabel': '2-95-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8709643042066443, 'root_angle': 0.17620819117478337, 'root_number': '0.44721359549995804 + 0.8944271909999159*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.176208191175', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.85187722726909546411289531010', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '4.78034076207371224866306495445', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '6.50918098564082978345606367110', 'prec': 100}}