-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1677417063279364856438876423833', 'a10': [0.0, 0.0], 'a2': [-0.2587123511011741, 0.0], 'a3': [0.0, 0.0], 'a4': [-7.933067919387703, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-14.517424702202348, 0.0], 'a8': [4.1220814616794845, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 39.82628925387493, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '675.1', 'coefficient_field': 'CDF', 'conductor': 675, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.2587123511011741, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [14.517424702202348, 0], [343.0, 0]], [[1.0, 0], [-49.28454578415786, 0], [1331.0, 0]], [[1.0, 0], [72.17999757094377, 0], [2197.0, 0]], [[1.0, 0], [-118.01681746170867, 0], [4913.0, 0]], [[1.0, 0], [-123.38909399737194, 0], [6859.0, 0]], [[1.0, 0], [91.48832584671794, 0], [12167.0, 0]], [[1.0, 0], [174.40016091016034, 0], [24389.0, 0]], [[1.0, 0], [46.295612696946236, 0], [29791.0, 0]], [[1.0, 0], [154.97665169343588, 0], [50653.0, 0]], [[1.0, 0], [-364.20256558157274, 0], [68921.0, 0]], [[1.0, 0], [125.71380554980259, 0], [79507.0, 0]], [[1.0, 0], [221.52317525112264, 0], [103823.0, 0]], [[1.0, 0], [13.679390330450087, 0], [148877.0, 0]], [[1.0, 0], [239.08695045557025, 0], [205379.0, 0]], [[1.0, 0], [54.54574326175159, 0], [226981.0, 0]], [[1.0, 0], [-76.0557687489941, 0], [300763.0, 0]], [[1.0, 0], [728.3030361667726, 0], [357911.0, 0]], [[1.0, 0], [-501.8151445051068, 0], [389017.0, 0]], [[1.0, 0], [-397.6096915216407, 0], [493039.0, 0]], [[1.0, 0], [1369.4613340971916, 0], [571787.0, 0]], [[1.0, 0], [1468.1304378107886, 0], [704969.0, 0]], [[1.0, 0], [335.0233483065641, 0], [912673.0, 0]], [[1.0, 0], [-1206.0861063403324, 0], [1030301.0, 0]], [[1.0, 0], [1061.1094546468964, 0], [1092727.0, 0]], [[1.0, 0], [475.57807563001234, 0], [1225043.0, 0]], [[1.0, 0], [-1320.4182809270255, 0], [1295029.0, 0]], [[1.0, 0], [68.17502731795865, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 47, 'label': '2-675-1.1-c3-0-47', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/675/4/a/q/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-1.0410180831031383e-60, 0.1686240457098304, 0.33485439942355294, 0.4963081616062117, 0.6506246438806684, 0.7954780084964692, 0.928591660938989, 1.0477548377935384, 1.1508417170446532, 1.2358332426125151, 1.300841703964647, 1.3441379503529987, 1.3641809530740439, 1.3596492636142432, 1.3294737559878216, 1.2728708931375778, 1.1893756247962421, 1.078872912195349, 0.9416267875800104, 0.7783057973463957, 0.5900036500139525, 0.37825389691665046, 0.14503751660706266, -0.10721764499247596, -0.375646506958115, -0.6569662283044047, -0.9475060999403344, -1.2432481972800553, -1.5398788744915153, -1.832850891415957, -2.117455652724927, -2.388904712880098, -2.6424193680393677, -2.873326826339844, -3.077161130958733, -3.249766716603925, -3.3874022205662575, -3.4868419551602434, -3.5454722899572095, -3.5613800996420917, -3.5334304154695455, -3.4613304825168645, -3.345677576687011, -3.1879881778851793, -2.990706429548848, -2.7571902374432318, -2.491673866945396, -2.1992064793355564, -1.8855666920853194, -1.5571539408574897, -1.220858144091556, -0.8839099042681594, -0.5537142007572375, -0.23767121357978438, 0.05701145934786408, 0.32351039170501356, 0.5555764980465312, 0.7477182611142857, 0.8953723526259431, 0.9950560083131228, 1.044495723123849, 1.0427272239652579, 0.9901622557939174, 0.8886184765656981, 0.7413096851771015, 0.5527946849527554, 0.3288842877379524, 0.07650725831071552, -0.1964626518411664, -0.4814150704280352, -0.7692419300838038, -1.0506008657448103, -1.3161958759731158, -1.5570670966364262, -1.7648808110381329, -1.9322103548794527, -2.0527983997474415, -2.1217912392759732, -2.1359361720646026, -2.0937338782155814, -1.9955388134403313, -1.8436020752013542, -1.6420528959751481, -1.3968168441177793, -1.1154709065588186, -0.8070378235153407, -0.48172426965770887, -0.15060964921218065, 0.1747056879406244, 0.4824821781692198, 0.7612405635270515, 1.0001658755515517, 1.1895018268664745, 1.3209212997115571, 1.3878588795657298, 1.3857921709646488, 1.3124599485252149, 1.16800701568704, 0.9550479226258931, 0.6786443688543751, 0.3461941020734472, -0.032767676799200604, -0.4468500949882385, -0.8831639943871369, -1.3277442201453427, -1.766023266812789, -2.183340300462518, -2.565467656248014, -2.8991356085854663, -3.1725356041412027, -3.375782290324648, -3.501315590547496, -3.5442257683523475, -3.502486850243241, -3.3770868745249945, -3.1720471030188016, -2.8943264485784637, -2.5536117842763764, -2.161999341472537, -1.7335768925675563, -1.2839206633212097, -0.82952474451764, -0.3871839988459506, 0.02664607051987977, 0.3964874391688896, 0.7084500195472174, 0.9507892567329935, 1.1143871733870825, 1.1931357264132358, 1.1842048550266164, 1.0881819663751866, 0.9090746623672348, 0.6541740655601491, 0.3337819294079462, -0.03918942499143478, -0.449729671486291, -0.8813357131231395, -1.316685327153206, -1.7383514654528571, -2.1295270838672717, -2.474729266879313, -2.760451659867155, -2.9757358510614864, -3.112635328585636, -3.1665498815437556, -3.1364136642190643, -3.0247263893585132, -2.837424002227119, -2.583592415408083, -2.2750351331641236, -1.9257125297523712, -1.5510768380068674, -1.1673322414243854, -0.7906535679668056, -0.4363997286082669, -0.11835906138303257, 0.15193696316984107, 0.3657976636887418, 0.5178248041402919, 0.6062077379111487, 0.6328447419227041, 0.603281199452697, 0.5264639025891773, 0.4143196179453865, 0.28117477212235875, 0.14304124056630602, 0.016800354109670353, -0.08067700358185655, -0.13343226717178563, -0.12729896050151282, -0.050716268312878066, 0.10456555981286954, 0.3429256948030017, 0.6644906089839476, 1.0649529262779958, 1.5356055093624368, 2.063594794002441, 2.632386654325744, 3.2224274075174546, 3.8119724753139317, 4.378046232258289, 4.89748916625478, 5.348043069153315, 5.709421888852199, 5.964315326742755, 6.0992743499635464, 6.10543247076666, 5.9790237562399655, 5.721667773285106, 5.340402631847752, 4.847459450614632, 4.2597843448978585, 3.5983267900689424, 2.8871252937508, 2.1522320816566296, 1.4205273821260849, 0.7184803825216461, 0.07091763743447586, -0.5001396204752834, -0.9765102840608327, -1.344706854958674, -1.5965625793447682, -1.7295980995580404, -1.747106342806394, -1.6579485615772842, -1.4760692522973062, -1.2197523427239387, -0.9106547781695074, -0.5726657070193047, -0.23064919428724134, 0.09086478462370823, 0.36897281891701894, 0.5836058312218699, 0.7185876798455344, 0.762487355521542, 0.7092179379914931, 0.5583485612003418, 0.3151107384534867, -0.009903263470222185, -0.4013356075460128, -0.8399210678561241, -1.3035629190357572, -1.7685687827090875, -2.2109792154985195, -2.607915931796744, -2.9388746258496896, -3.186889569332207, -3.3395034629701144, -3.3894861348845566, -3.335259106210465, -3.180999092192389, -2.936411319081714, -2.616182141737177, -2.239138807473617, -1.8271612848959635, -1.4039058706105088, -0.9934119196943892, -0.6186707976251381, -0.30023950881946715, -0.0549801474903324, 0.10499967072254818, 0.17314064594266626, 0.14890946246137438, 0.03792731730265823, -0.1482639895504932, -0.3927909172074677, -0.6743637956872166, -0.9684715363242672, -1.2487907587358351, -1.4887310717461784, -1.6630289676431567, -1.7492984322675265, -1.7294472815684208, -1.590874451666686, -1.327374728035222, -0.9396931338396989, -0.4356905684073319], 'positive_zeros': ['1.32324874297173100205937929990806', '3.15231960446786648172493864248015', '3.94257719189974779877219500002307', '5.12452559077187558901512581916565', '5.91313362681760704864163283228298', '7.20308636640991476464467929223803', '7.84571209656769414474315739518179', '9.106309948557660823742550032544554', '9.735319852133442835443044694697265'], 'prelabel': '2-675-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.310807337724305, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.32324874297173100205937929991', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.15231960446786648172493864248', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.94257719189974779877219500002', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 39.82628925387493, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 675, 'conductor_radical': 15, 'degree': 2, 'index': 47, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/675/4/a/q/1/2'], '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': '2-675-1.1-c3-0-47', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-675-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.310807337724305, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.32324874297173100205937929991', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1677417063279364856438876423833', 'Lhash_array': ['1677417063279364856438876423833'], 'label': '2-675-1.1-c3-0-47', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/675/4/a/q/1/2'}