-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '711941089794104484758952921502', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [6.461740924470781, 0.0], 'a4': [0.0, 0.0], 'a5': [22.120528070724134, 0.0], 'a6': [0.0, 0.0], 'a7': [-246.7711562186821, 0.0], 'a8': [0.0, 0.0], 'a9': [-201.2459042250195, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 112.9102091483384, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-121.0, 0]]]], 'bad_primes': [2, 11], 'central_character': '704.1', 'coefficient_field': 'CDF', 'conductor': 704, 'conductor_radical': 22, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-6.461740924470781, 0], [243.0, 0]], [[1.0, 0], [-22.120528070724134, 0], [3125.0, 0]], [[1.0, 0], [246.7711562186821, 0], [16807.0, 0]], [[1.0, 0], [-121.0, 0]], [[1.0, 0], [-495.40323325045614, 0], [371293.0, 0]], [[1.0, 0], [-84.69460030842973, 0], [1419857.0, 0]], [[1.0, 0], [-2836.7586551952463, 0], [2476099.0, 0]], [[1.0, 0], [3455.0633682477674, 0], [6436343.0, 0]], [[1.0, 0], [4595.217513658935, 0], [20511149.0, 0]], [[1.0, 0], [-5528.64453392289, 0], [28629151.0, 0]], [[1.0, 0], [5559.8769694745815, 0], [69343957.0, 0]], [[1.0, 0], [20565.584724791657, 0], [115856201.0, 0]], [[1.0, 0], [-4693.521495147033, 0], [147008443.0, 0]], [[1.0, 0], [10991.267283170753, 0], [229345007.0, 0]], [[1.0, 0], [-1336.1521698667636, 0], [418195493.0, 0]], [[1.0, 0], [-41989.14884994913, 0], [714924299.0, 0]], [[1.0, 0], [-26059.971871741673, 0], [844596301.0, 0]], [[1.0, 0], [-27233.700974712, 0], [1350125107.0, 0]], [[1.0, 0], [34525.68264608649, 0], [1804229351.0, 0]], [[1.0, 0], [-52388.3527773948, 0], [2073071593.0, 0]], [[1.0, 0], [-8302.248254278198, 0], [3077056399.0, 0]], [[1.0, 0], [-21577.98830005544, 0], [3939040643.0, 0]], [[1.0, 0], [-86583.60040592865, 0], [5584059449.0, 0]], [[1.0, 0], [-64725.44732612694, 0], [8587340257.0, 0]], [[1.0, 0], [147550.5349178452, 0], [10510100501.0, 0]], [[1.0, 0], [-156376.77464739353, 0], [11592740743.0, 0]], [[1.0, 0], [-47460.29553837485, 0], [14025517307.0, 0]], [[1.0, 0], [-146610.64260127125, 0], [15386239549.0, 0]], [[1.0, 0], [-144172.8789071188, 0], [18424351793.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 21, 'label': '2-704-1.1-c5-0-21', 'leading_term': '1.6259083797920268475890156260696', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/704/6/a/bf/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.6259083797920268, 1.605625110704322, 1.54513212956484, 1.4454946160365587, 1.3084702438277396, 1.1364828719576245, 0.9325859781097832, 0.7004161129477928, 0.444136751975184, 0.16837303110741492, -0.12186202551935198, -0.4212490418988266, -0.7242507003296508, -1.0252059788273096, -1.3184290065973516, -1.5983111636669418, -1.8594248890186398, -2.0966275086907924, -2.3051632578159964, -2.480761555382156, -2.6197295047084364, -2.719036543227128, -2.7763891587772918, -2.790293632212643, -2.760104862721571, -2.686059486638756, -2.5692917149902024, -2.4118305901230443, -2.2165776961686543, -1.9872647483365435, -1.7283909265311608, -1.4451403017183158, -1.1432802188800961, -0.8290420362869118, -0.5089861633455844, -0.18985387306028698, 0.12159112641890356, 0.41872791093279915, 0.6952464944418527, 0.9453147345673812, 1.1637395720453376, 1.3461180614857007, 1.4889736472122141, 1.5898732657109487, 1.6475211218532775, 1.661825392201409, 1.633934653656159, 1.5662415131339513, 1.4623517127081993, 1.3270178887094475, 1.1660381519187024, 0.9861207040703059, 0.7947167843514388, 0.5998253161530377, 0.4097736643087482, 0.23297988038544465, 0.0777026719435577, -0.04821395425573623, -0.1375938883785727, -0.1841721362294023, -0.18282014491109447, -0.129745470341907, -0.02265843248829696, 0.13910092169330115, 0.3544812964366927, 0.6206886425656888, 0.93320785686504, 1.2858793003987181, 1.6710300393864095, 2.0796579118439134, 2.5016646907051467, 2.9261328112987077, 3.3416384224099165, 3.736591970931901, 4.0995962038003855, 4.419810426849581, 4.687309151107838, 4.893422926518377, 5.031049243516702, 5.094921893533554, 5.081828124794359, 4.990764298402181, 4.823022513897443, 4.582202789240881, 4.274147787796761, 3.9067997104531726, 3.489981728274663, 3.035109124130496, 2.55483803814298, 2.0626622661953977, 1.5724708387897002, 1.0980810100759995, 0.6527627240667602, 0.2487715204917105, -0.10309286278089186, -0.39388527908674686, -0.6168554430047524, -0.7677154165986173, -0.8448223045750384, -0.8492669576778284, -0.78486275361146, -0.6580321495149474, -0.47759255154085833, -0.25444698239280056, -0.0011888936973882254, 0.268365890417253, 0.5397038543800823, 0.7981761232404945, 1.0295774024388378, 1.220719182331949, 1.3599744181473798, 1.4377713545132456, 1.4470155432318343, 1.3834213820320467, 1.2457376206081172, 1.0358551405340235, 0.7587897845347414, 0.4225379237949114, 0.037807619645048834, -0.38236655026413824, -0.8231118899688108, -1.2682914473229854, -1.701141535673108, -2.104947864062762, -2.463732943421562, -2.762926250823694, -2.9899886331365, -3.1349636551418674, -3.1909310331371414, -3.1543408768612076, -3.0252120709852224, -2.8071835930869526, -2.5074136744218323, -2.136328212907254, -1.7072264679773732, -1.2357585127117505, -0.7392948958860215, -0.2362141922853813, 0.2548616649518466, 0.7158513925987027, 1.1299832498911522, 1.4825142989443743, 1.7613670235272034, 1.9576533480279066, 2.066060599309535, 2.085079739131168, 2.017063033172272, 1.8681059268891327, 1.6477559356108915, 1.3685594624501607, 1.0454652537820315, 0.6951103117945239, 0.3350201510934815, -0.017240005922029848, -0.34492341474687954, -0.6329284252331383, -0.8685532356036617, -1.0421410974821765, -1.147582770645449, -1.1826492256583345, -1.1491352535166608, -1.0528034322100612, -0.9031274236926774, -0.7128433860826293, -0.49732791232407864, -0.2738298701648799, -0.060591359562088026, 0.1241006953128983, 0.2628863953986566, 0.3402799909465737, 0.343544206841151, 0.26344618204170683, 0.09485425793853353, -0.16285817063688288, -0.5056266833483833, -0.9247423663028811, -1.4071341641147919, -1.9358786101808134, -2.49091686779146, -3.049948113115427, -3.589458684523634, -4.085838632272045, -4.516531771055042, -4.861162404815203, -5.1025817739727595, -5.227780046762175, -5.228615268789234, -5.102318881100376, -4.851747859592052, -4.485365734455596, -4.016948130544108, -3.465022364840155, -2.852064338777984, -2.2034887565074333, -1.5464799004110221, -0.9087191839788834, -0.31707196216363076, 0.20370077573198014, 0.6321404070820847, 0.9511365553017512, 1.1487659275376079, 1.218879077790015, 1.1614024793677526, 0.9823376299510106, 0.693454451153007, 0.31169217882583755, -0.14170357180721702, -0.6422646771963957, -1.1635502867630005, -1.6784981094280447, -2.160806733884249, -2.586276143597082, -2.9340351116929235, -3.187589560938297, -3.335635021619006, -3.3725885822422854, -3.2988105861263235, -3.1205030072847846, -2.8492890518824003, -2.5014961183353357, -2.097180834282755, -1.6589495337720968, -1.2106393952567813, -0.7759338227206912, -0.37698999373542863, -0.03315651136564299, 0.24014528801911933, 0.4323114237820411, 0.5381642137010861, 0.5582430857283089, 0.4987581510540252, 0.37120664121257296, 0.19167177708017077, -0.020157756426849943, -0.24219289435462052, -0.4513052742561051, -0.6247658115772247, -0.741676734268969, -0.7843123268594459, -0.7392878515234576, -0.5984851009583823, -0.3596763501133786, -0.026805404742338747, 0.3900959371821719, 0.8753564966733294, 1.4084583245273965, 1.9651315846256427, 2.5186914678024723, 3.041541650137797, 3.506757794916994, 3.8896585384893254, 4.1692707420173365, 4.329600665749616, 4.360632934762817, 4.258994197617538, 4.0282374167274595, 3.678724701133171], 'positive_zeros': ['0.56162249255901091311369490251042', '2.08624607986613895264076875894699', '3.31552693550102817731089447931582', '3.64236917900063615445330919695759', '5.48961937291403889921831847875125', '6.09401404798080714234353605052368', '6.91951309314448458916471192251567', '8.055214595563953741216061111779850', '8.961900971704783088623901552830395', '9.744557719340947110103431364614445'], 'prelabel': '2-704-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.625921567014242, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.56162249255901091311369490251', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.08624607986613895264076875895', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.31552693550102817731089447932', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 112.9102091483384, 'bad_primes': [2, 11], 'central_character': '1.1', 'conductor': 704, 'conductor_radical': 22, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/704/6/a/bf/1/4'], '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': '2-704-1.1-c5-0-21', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-704-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.625921567014242, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.56162249255901091311369490251', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '711941089794104484758952921502', 'Lhash_array': ['711941089794104484758952921502'], 'label': '2-704-1.1-c5-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/704/6/a/bf/1/4'}