-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '736661808456160985734491636032', 'a10': [0, 0], 'a2': [0, 0], 'a3': [1.3073939511507526, 2.2644727489013263], 'a4': [0, 0], 'a5': [0.04954969659078272, -0.08582259199485806], 'a6': [0, 0], 'a7': [-0.8414976307678783, 1.4575166509388005], 'a8': [0, 0], 'a9': [-1.9185578870111526, 3.323039737565306], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.093090815489845, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [79, [[1.0, 0], [-6.157975810308395, 6.409316181907136]]]], 'bad_primes': [2, 79], 'central_character': '1264.767', 'coefficient_field': 'CDF', 'conductor': 1264, 'conductor_radical': 158, 'conjugate': '2572409044074791035686427701887', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.3073939511507526, -2.2644727489013263], [-1.5, 2.598076211353316]], [[1.0, 0], [-0.04954969659078272, 0.08582259199485806], [-2.5, -4.330127018922194]], [[1.0, 0], [0.8414976307678783, -1.4575166509388005], [-3.5, -6.06217782649107]], [[1.0, 0], [2.7528212930535285, 1.5893421145753883], [5.5, 9.526279441628825]], [[1.0, 0], [-2.72281683219147, -4.7160570930593675], [-6.5, 11.258330249197702]], [[1.0, 0], [0, -3.0922165874404577], [-17.0, 0]], [[1.0, 0], [1.4521230909235114, 0.8383836574411607], [9.5, 16.454482671904334]], [[1.0, 0], [5.976784152696302, 3.4506979394474993], [11.5, 19.91858428704209]], [[1.0, 0], [1.5095864162160988, 0.871560123767367], [14.5, 25.11473670974872]], [[1.0, 0], [1.5583942875065175, 0.899739361395463], [15.5, 26.846787517317598]], [[1.0, 0], [3.6036961631091096, -2.080594949848666], [18.5, -32.04293994002423]], [[1.0, 0], [0, -3.9019575954799257], [-41.0, 0]], [[1.0, 0], [-1.9897545936794223, -3.4463560508463265], [-21.5, 37.239092362730865]], [[1.0, 0], [0.08339190457282175, -0.14443901566006265], [-23.5, -40.703193977868615]], [[1.0, 0], [0.4265257289606975, 0.24625474443176007], [26.5, 45.89934640057525]], [[1.0, 0], [4.2883362885498615, 7.42761633170971], [-29.5, 51.09549882328188]], [[1.0, 0], [0, 8.996526734672523], [-61.0, 0]], [[1.0, 0], [0, -15.275764434350478], [-67.0, 0]], [[1.0, 0], [-3.0710299909926664, 0], [71.0, 0]], [[1.0, 0], [-0.7532729977741325, 1.3047071041145153], [-36.5, -63.21985447626402]], [[1.0, 0], [-6.157975810308395, 6.409316181907136]], [[1.0, 0], [-5.116608858999268, -2.9540755020812517], [41.5, 71.88010851410841]], [[1.0, 0], [-1.5988456270293407, 0], [89.0, 0]], [[1.0, 0], [-15.60979075654637, 0], [97.0, 0]], [[1.0, 0], [18.61964025510357, 0], [101.0, 0]], [[1.0, 0], [4.435816554589285, 7.683059645603766], [-51.5, 89.20061658979718]], [[1.0, 0], [-2.0304720337042057, -3.51688072572339], [-53.5, 92.66471820493493]], [[1.0, 0], [-3.2624614494039736, 1.8835829960341608], [54.5, -94.39676901250381]], [[1.0, 0], [-11.75227886840846, 6.785181368267175], [56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-1264-316.135-c1-0-6', 'leading_term': '1.594976813845251975153096061868760400524710961000668264', '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/1264/2/n/i/767/13', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.594976813845252, 1.4344056851609603, 1.2745264555023872, 1.1149026673957974, 0.9551108162171681, 0.7948111298478255, 0.633811590470678, 0.47212196502778053, 0.309995608627581, 0.14795780310734982, -0.013179748689492505, -0.17231800575048106, -0.32808255469548697, -0.47884751988933166, -0.6227703587318476, -0.7578364266326023, -0.8819121549786281, -0.9928056264807128, -1.0883332388284817, -1.1663910161163693, -1.2250289642270829, -1.262526683721792, -1.2774682676923594, -1.2688143398039549, -1.2359689467179422, -1.1788389255807474, -1.0978833359757796, -0.9941505891543257, -0.8693010353534333, -0.725612989424919, -0.5659704893238616, -0.3938314910460459, -0.21317570324805274, -0.028431846831430685, 0.15561522311623527, 0.3339363898585227, 0.501387259665939, 0.6528516272922302, 0.783396058846738, 0.8884315420174649, 0.9638775424156819, 1.006323299188728, 1.013180822131129, 0.9828238432385603, 0.9147069514011422, 0.8094593183282445, 0.6689478194207982, 0.4963049706213492, 0.29591793869643246, 0.07337592663471719, -0.164625532544663, -0.4104234508793457, -0.6555679980075526, -0.8910418382166679, -1.1075135783489458, -1.295619152108187, -1.4462635080504764, -1.5509336768582556, -1.602013231304482, -1.593087378748791, -1.5192274936841024, -1.3772438501460522, -1.1658956822824353, -0.8860485035367943, -0.5407698522282628, -0.13535628795268595, 0.32271349477259736, 0.823902193950297, 1.3568141879769382, 1.9084698859565548, 2.464648545672272, 3.010291097495765, 3.5299517913161353, 4.008285026182444, 4.430551644196388, 4.783127378936813, 5.053995139133798, 5.2332024573783835, 5.31326579590345, 5.289504505165097, 5.160289075054099, 4.927190870800501, 4.59502374180752, 4.171771636337919, 3.668400523649617, 3.098557367787561, 2.4781634431822606, 1.8249137465508167, 1.1576984503725212, 0.4959660694891248, -0.14094890716827937, -0.7345088961563594, -1.2676402605553985, -1.7253578837079853, -2.0953214765221007, -2.3682997725089407, -2.538521807624314, -2.603898529935444, -2.566102903289308, -2.430502279833829, -2.205942898778414, -1.904392671601725, -1.5404546635716605, -1.1307695942473148, -0.693330974434967, -0.24674090861579845, 0.1905621158812065, 0.6010701528956193, 0.9689336102688088, 1.2806171358548104, 1.5254533121656324, 1.696067924921675, 1.7886559423428918, 1.8030938482784433, 1.7428813429486962, 1.6149133369860387, 1.4290912550190507, 1.1977905483585538, 0.9352086013005094, 0.6566235250425885, 0.3775993235454754, 0.11317629532131454, -0.12291291835410809, -0.31896165407285837, -0.46590437425794395, -0.557795506504081, -0.5921250493483236, -0.5699517810233835, -0.4958438756769796, -0.37762648671398863, -0.22594592356487173, -0.05366991628874256, 0.12484738713613752, 0.29459911466811695, 0.4408152236563338, 0.5498608891618921, 0.6100948638821466, 0.6126396418512373, 0.5520185395342482, 0.42662059217341186, 0.2389622307513889, -0.0042752939447015794, -0.2924423052509011, -0.6113481045275259, -0.9439039317285697, -1.2709537829375546, -1.572254212526832, -1.8275547909417211, -2.0177237218525508, -2.125858715216806, -2.1383219038442745, -2.0456395624173522, -1.8432126494516567, -1.5317925748418528, -1.117687751860343, -0.6126799114686895, -0.033644184452845595, 0.5981171730043908, 1.2578016622780979, 1.9182532812631508, 2.5512750834705873, 3.129042747229233, 3.625546756674673, 4.017986917288434, 4.288043094789557, 4.42295039939475, 4.4163154323296565, 4.268622332712562, 3.9873926564243707, 3.5869808350974246, 3.088006194233474, 2.516442232602452, 1.9024029990515283, 1.2786838662746765, 0.6791287739988634, 0.1369071978771189, -0.3172090270117709, -0.6564768368470445, -0.8596318213703281, -0.9120756555428094, -0.8067325649260975, -0.544523081214467, -0.13442335199826635, 0.4068995445865165, 1.055862672285974, 1.783116253640211, 2.5550089833021987, 3.3352936563646156, 4.08698277483002, 4.774254317803489, 5.364303897762391, 5.829041405194274, 6.146537961352165, 6.302142206086491, 6.28920296734884, 6.109357216794291, 5.7723666921295305, 5.295512263514145, 4.702580542223468, 4.022500868312773, 3.2877112437991913, 2.532347740702998, 1.7903623989734576, 1.0936789422205522, 0.4704934469798533, -0.056181537438088375, -0.46964555303193256, -0.7602474118380058, -0.9256907219070323, -0.9708938767741215, -0.9074179847226571, -0.7525028607807301, -0.5277754676161625, -0.2577155265500587, 0.032021892953057615, 0.3163181647494588, 0.5722266851203578, 0.780426768115011, 0.9264023277164434, 1.0012698830688007, 1.0022035106777725, 0.9324310337767227, 0.8008042857720359, 0.6209748643402024, 0.4102335259769201, 0.1880944685022935, -0.025276368646438212, -0.2106784522484771, -0.3514246470159469, -0.4347090954737567, -0.45269527549040894, -0.4032427358094356, -0.2902150776149693, -0.1233401517086323, 0.08237566809319537, 0.3076459436669079, 0.5302525223747556, 0.726655022567115, 0.8737523652373416, 0.9506740163792683, 0.9404735085294641, 0.8316003965790805, 0.6190390278472198, 0.3050227372650769, -0.10074087634233415, -0.5813657612497414, -1.113601247013257, -1.6691248808749424, -2.2162410032159676, -2.7218816540065993, -3.153782517502678, -3.482690778375804, -3.684455266014115, -3.7418527882651205, -3.6460181196564507, -3.3973680475084143, -3.0059408732630573], 'positive_zeros': ['0.58112370106047476429696827403717', '1.94259166995694030658559108800476', '2.88948343139979640057604130637847', '3.82657251375931996309083535053940', '5.26018093016248053905169236124502', '6.18509658507351246874644534257137', '7.11686923178371894501455801717932', '7.69338950655955467432908175986262', '8.260782029554398238898111836713287', '9.143852871557377337404326180319044'], 'prelabel': '2-1264-316.135-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1769625140202464, 'root_angle': -0.8600834030350523, 'root_number': '-0.90493858339755353784624061507862155370275098057280857834 - 0.42554219564977224527560598972193934340236276610269412424*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.43004170151752613', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.58112370106047476429696827404', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.94259166995694030658559108800', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.88948343139979640057604130638', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 10.093090815489845, 'bad_primes': [2, 79], 'central_character': '316.135', 'conductor': 1264, 'conductor_radical': 158, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1264/2/n/i/767/13'], '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': '2-1264-316.135-c1-0-6', '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': '2-1264-316.135-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1769625140202464, 'root_angle': -0.43004170151752613, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.58112370106047476429696827404', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '736661808456160985734491636032', 'Lhash_array': ['736661808456160985734491636032'], 'label': '2-1264-316.135-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1264/2/n/i/767/13'}