-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '671521859110638680057459104974', 'a10': [3.667291440549424, 0.0], 'a2': [-1.352223942185865, 0.0], 'a3': [2.9036732492685986, 0.0], 'a4': [-0.1714904101793184, 0.0], 'a5': [-2.7120444522090486, 0.0], 'a6': [-3.926416487945624, 0.0], 'a7': [-3.824424813896041, 0.0], 'a8': [2.936341322871479, 0.0], 'a9': [5.43131833851806, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.20770826531158, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [1.0, 0]]], [17, [[1.0, 0], [1.0, 0]]], [43, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [11, 17, 43], 'central_character': '8041.1', 'coefficient_field': 'CDF', 'conductor': 8041, 'conductor_radical': 8041, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.352223942185865, 0], [2.0, 0]], [[1.0, 0], [-2.9036732492685986, 0], [3.0, 0]], [[1.0, 0], [2.7120444522090486, 0], [5.0, 0]], [[1.0, 0], [3.824424813896041, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-6.556225360267064, 0], [13.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [4.533890291411961, 0], [19.0, 0]], [[1.0, 0], [5.045661022661377, 0], [23.0, 0]], [[1.0, 0], [-1.7823261216309807, 0], [29.0, 0]], [[1.0, 0], [-5.177707442899106, 0], [31.0, 0]], [[1.0, 0], [2.823599341096401, 0], [37.0, 0]], [[1.0, 0], [1.7487374324416107, 0], [41.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.9368136148724266, 0], [47.0, 0]], [[1.0, 0], [7.423534290004664, 0], [53.0, 0]], [[1.0, 0], [-7.839073004013918, 0], [59.0, 0]], [[1.0, 0], [4.436469721216533, 0], [61.0, 0]], [[1.0, 0], [7.0301602011564945, 0], [67.0, 0]], [[1.0, 0], [-9.18977971854414, 0], [71.0, 0]], [[1.0, 0], [11.405935463130039, 0], [73.0, 0]], [[1.0, 0], [-11.900622740917887, 0], [79.0, 0]], [[1.0, 0], [5.821343526804233, 0], [83.0, 0]], [[1.0, 0], [-16.102335900584883, 0], [89.0, 0]], [[1.0, 0], [-15.854581465101004, 0], [97.0, 0]], [[1.0, 0], [-7.311633537483655, 0], [101.0, 0]], [[1.0, 0], [16.628629558348912, 0], [103.0, 0]], [[1.0, 0], [-12.390476676727799, 0], [107.0, 0]], [[1.0, 0], [-3.65261814311196, 0], [109.0, 0]], [[1.0, 0], [8.034696472434211, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 117, 'label': '2-8041-1.1-c1-0-117', 'leading_term': '1.0191161370487936315358057921414', '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/8041/2/a/e/1/17', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.0191161370487936, 1.0093789938178508, 0.9801831423230323, 0.9315838711378787, 0.8637011197567169, 0.7767587186167729, 0.6711346921199073, 0.5474185540209461, 0.4064710508202013, 0.24948168792115902, 0.07801955766995401, -0.10592659112527379, -0.29992251850620216, -0.5010796848998502, -0.7060655210330163, -0.911134064449558, -1.112177478318072, -1.3047981947464171, -1.4844006548160698, -1.6463008562905275, -1.7858511763111589, -1.8985772241561394, -1.980322817145793, -2.0273985842096924, -2.036729212701004, -2.005993992348629, -1.9337551029300586, -1.8195680641591592, -1.664068938096426, -1.4690332609368386, -1.2374022897867059, -0.9732729798728322, -0.6818491478643784, -0.369352506865242, -0.0428936471609854, 0.2896954569109454, 0.6200642595297897, 0.939577036857186, 1.239570592457691, 1.5116285965262686, 1.7478636613924452, 1.9411972930525228, 2.0856272143601724, 2.176471283811286, 2.210577377186566, 2.1864891861130116, 2.104558929632047, 1.9669994651709806, 1.777870196904846, 1.5429934647569978, 1.2698006883351287, 0.9671103500715809, 0.6448428271694316, 0.3136800056296047, -0.015319594680934006, -0.3311369179752555, -0.6232242788189055, -0.881936023944371, -1.0989398785104227, -1.26759059702225, -1.383248004991624, -1.4435227929153882, -1.4484355106056217, -1.4004770722077735, -1.3045626476875163, -1.1678749753480189, -0.9995977374321534, -0.8105445217153864, -0.6126938459708431, -0.41864553163665247, -0.2410181517102971, -0.09181112093547997, 0.01824196927388196, 0.0803001333590925, 0.08799237464456758, 0.0379165434920185, -0.06996772908037276, -0.232076356120525, -0.4410883611797353, -0.6859981533881072, -0.9523404757181737, -1.2225887397839978, -1.4767197470244322, -1.692929945861003, -1.8484807389530435, -1.9206432964869449, -1.8877072074162737, -1.730012444682816, -1.4309608264873983, -0.9779616609036971, -0.36326673167912854, 0.4153476980196029, 1.3540896285834565, 2.442882085175543, 3.6653389426339524, 4.998999194255729, 6.415822316681224, 7.882936037779114, 9.363616348027865, 10.818468534086211, 12.206767887127523, 13.487910059036986, 14.622914271756155, 15.575918123188039, 16.31560087820621, 16.816473074372777, 17.059974071573947, 17.03532576071061, 16.740099809659256, 16.180467223486197, 15.371112168159039, 14.33480638797202, 13.101655493329442, 11.70804321477655, 10.19531370199415, 8.608244401976405, 6.993372341557472, 5.397244216207303, 3.8646651182185177, 2.437021735644743, 1.1507532943008485, 0.036037448877708766, -0.8842510171419724, -1.5952630519967934, -2.0905486849897836, -2.372065999822629, -2.4498279404110983, -2.3412062563968186, -2.06992816090144, -1.664815873306377, -1.15833139489466, -0.5849979684744616, 0.0202247915768954, 0.6235334611521672, 1.1937647705921988, 1.703700933622784, 2.13113615385151, 2.459657067973628, 2.6791052516127345, 2.785706886451226, 2.781872355260373, 2.675685936680186, 2.4801219617361627, 2.2120378758502692, 1.8910058406996826, 1.5380521834166228, 1.1743777245571163, 0.8201315813154393, 0.49330647620650137, 0.208815150382552, -0.022204321993303144, -0.19282100248790177, -0.30046432656047445, -0.346798250999692, -0.33733342785057985, -0.2808102990596398, -0.18839962382941045, -0.07277757461466931, 0.052860489802597256, 0.17578058248830333, 0.2846193800513709, 0.3701622439010722, 0.42593941894445464, 0.4486025786169313, 0.43805907245399023, 0.39735791640049767, 0.33233866911203563, 0.2510707409202282, 0.16312529705065557, 0.07873375472720062, 0.007895112909800942, -0.040501605489724486, -0.05947400845346301, -0.04460135456818015, 0.005513432176006359, 0.08901301309659237, 0.20080837594321674, 0.332859364413178, 0.474698662975831, 0.6141668327030221, 0.7383097411392249, 0.834376464464509, 0.8908464625481558, 0.8984102942914677, 0.8508288093797639, 0.7456017409875094, 0.5843876917408495, 0.373133058626666, 0.12188656300382095, -0.15570245283035383, -0.4431813258019423, -0.7223443874676556, -0.9744738272790326, -1.1816922532968053, -1.3283364793641894, -1.402256193372241, -1.395941665026653, -1.3073917583443608, -1.1406470118417398, -0.9059317870532723, -0.6193734012665211, -0.30229333531022895, 0.019905649804631158, 0.319204205243337, 0.566704375379372, 0.7345401618494165, 0.7978434768566247, 0.7366388302612131, 0.5375385739036788, 0.1951173692481692, -0.28714036303135354, -0.8964035732138677, -1.6106227748133268, -2.3992439548743576, -3.2244923092646602, -4.043172914959261, -4.808900396861836, -5.474638876212033, -5.995409145589027, -6.331003899852991, -6.448545284832986, -6.324722749569705, -5.947563301277353, -5.317610190535923, -4.448418568034648, -3.366315929637839, -2.1094188875229714, -0.7259433008151732, 0.7281107910130638, 2.191777532629092, 3.602291201025629, 4.898419175535172, 6.023767289635998, 6.929860763042055, 7.578814068253992, 7.945425167993843, 8.018562394214463, 7.801753926582903, 7.31293785387055, 6.583382187951415, 5.655835693444574, 4.582018676185071, 3.4196047723450316, 2.2288774937607267, 1.069266568380952, -0.004022560324564288, -0.943078040868624, -1.7098604820085455, -2.27813329121602, -2.6346279897697076, -2.7793774035239425, -2.725203618595766, -2.496402635762196, -2.126720102343473, -1.656758826845995, -1.1309958462413026, -0.5946120691991691], 'positive_zeros': ['0.52973734165371518273361532254025', '1.73313804326769311636259902424816', '2.73979033347501959332385399915104', '3.64618812533234321230525618704213', '3.82968804260071335470357856290557', '4.59533493166905722538168427700274', '6.14633032489779072175891986249694', '6.70144065371227141336617386760839', '7.61168433287161218701485858771549', '8.002225432872140133219774040488956'], 'prelabel': '2-8041-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.012971250747851, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.52973734165371518273361532254', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.73313804326769311636259902425', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.73979033347501959332385399915', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 64.20770826531158, 'bad_primes': [11, 17, 43], 'central_character': '1.1', 'conductor': 8041, 'conductor_radical': 8041, 'degree': 2, 'index': 117, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8041/2/a/e/1/17'], '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': '2-8041-1.1-c1-0-117', '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': '2-8041-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.012971250747851, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.52973734165371518273361532254', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '671521859110638680057459104974', 'Lhash_array': ['671521859110638680057459104974'], 'label': '2-8041-1.1-c1-0-117', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8041/2/a/e/1/17'}