-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2840918939594565524965705666510', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.42736734647120733, -1.678498481134302], 'a4': [0.0, 0.0], 'a5': [-0.045817439058354476, -0.17099301043846965], 'a6': [0.0, 0.0], 'a7': [-1.1743150761490875, -2.033973375984335], 'a8': [0.0, 0.0], 'a9': [-2.634714302340318, -1.434670883876637], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.599383156425752, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.42736734647120733, 1.678498481134302]]]], 'bad_primes': [2, 3], 'central_character': '576.527', 'coefficient_field': 'CDF', 'conductor': 576, 'conductor_radical': 6, 'conjugate': '771213558987530317089757194453', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.42736734647120733, 1.678498481134302]], [[1.0, 0], [0.045817439058354476, 0.17099301043846965], [-4.330127018922194, 2.5]], [[1.0, 0], [1.1743150761490875, 2.033973375984335], [-3.5, 6.06217782649107]], [[1.0, 0], [-0.09131881666465153, 0.34080646347954696], [-9.526279441628825, -5.5]], [[1.0, 0], [-0.39936225384373775, -1.4904402219700483], [-11.258330249197702, 6.5]], [[1.0, 0], [0, 3.5808051815866104], [-17.0, 0]], [[1.0, 0], [5.364623825910456, 5.364623825910456], [0, 19.0]], [[1.0, 0], [0.1650846660908833, 0.09531167640665096], [11.5, 19.91858428704209]], [[1.0, 0], [2.438789326377112, -9.101685674996059], [-25.11473670974872, -14.5]], [[1.0, 0], [3.439029336174999, 1.9855245129916557], [15.5, 26.846787517317598]], [[1.0, 0], [3.2831451034844394, 3.2831451034844394], [0, 37.0]], [[1.0, 0], [-4.255384064040981, 7.370541404637912], [-20.5, -35.50704155516198]], [[1.0, 0], [-4.094015776818749, -1.096988221198859], [37.239092362730865, 21.5]], [[1.0, 0], [-4.930299857331176, -8.539529849447183], [-23.5, 40.703193977868615]], [[1.0, 0], [-4.837350588824082, 4.837350588824082], [0, -53.0]], [[1.0, 0], [-2.6898522458296426, 0.7207437370290944], [51.09549882328188, -29.5]], [[1.0, 0], [7.973939160444323, 2.136610558535961], [52.827549630850754, 30.5]], [[1.0, 0], [11.454294811763827, -3.069169044680116], [58.023702053557386, -33.5]], [[1.0, 0], [0, -1.1363505870378119], [-71.0, 0]], [[1.0, 0], [0, 5.679612049206429], [-73.0, 0]], [[1.0, 0], [-12.862088148296596, 7.4259300547597356], [39.5, -68.41600689897065]], [[1.0, 0], [-12.363481465682616, -3.3127848743668107], [71.88010851410841, 41.5]], [[1.0, 0], [3.057186272077933, 0], [89.0, 0]], [[1.0, 0], [0.9967005780326615, 1.7263360410858382], [-48.5, 84.00446416709055]], [[1.0, 0], [-15.466310238966654, -4.1441853384203196], [87.4685657822283, 50.5]], [[1.0, 0], [-8.1214982475604, 14.066847598356212], [-51.5, -89.20061658979718]], [[1.0, 0], [2.0826175185547937, 2.0826175185547937], [0, 107.0]], [[1.0, 0], [-7.701912021138839, 7.701912021138839], [0, -109.0]], [[1.0, 0], [-10.313685088002593, -5.954608861895326], [56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 19, 'label': '2-24e2-144.59-c1-0-19', '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/576/2/y/a/527/14', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.1438925093289625, 1.3726476746662262, 1.6100069078679624, 1.8564328798031429, 2.108196004546177, 2.3572274107859355, 2.591539948262267, 2.796070063112317, 2.953835644003839, 3.047351447160419, 3.0602559206043933, 2.97908032666073, 2.795048315339244, 2.5057481683589584, 2.116484131830516, 1.641097509481864, 1.102059574959193, 0.5296810389001947, -0.03964260687726713, -0.5661277265905047, -1.0100964341170848, -1.3359938543095955, -1.5165361753165554, -1.5365079437799907, -1.3956867663586405, -1.1103976642413507, -0.7132970228046406, -0.2511573399857082, 0.21934247998614542, 0.637543769875416, 0.9458956939250078, 1.0974043573051857, 1.0624783044438653, 0.8341555952216657, 0.43079065931482585, -0.10447649690395702, -0.7077644301526387, -1.3018227266507407, -1.8060286019592535, -2.1478221869947367, -2.2740337519368112, -2.1603895764553243, -1.8175651636059877, -1.2925053494989174, -0.6643289106357138, -0.03491430451616452, 0.4848826186175816, 0.7916314303172011, 0.8060040302287033, 0.4871021194732336, -0.15805955986492734, -1.0718508048356266, -2.1511018055118094, -3.259755866154924, -4.247619859251816, -4.972591592302243, -5.322951392703724, -5.236036453231377, -4.7099671638562866, -3.8060578502726123, -2.6410000792461963, -1.3696326743240044, -0.160815703775844, 0.8297093238815438, 1.4848433016588118, 1.7454637098428916, 1.619903261514616, 1.1815548583639663, 0.5547081682528145, -0.10905542269510056, -0.6596892169194407, -0.9773359328299738, -0.995243419491159, -0.7122950526291592, -0.19240645683358584, 0.44941126373680246, 1.071805394437402, 1.5378031617465868, 1.7452100444200267, 1.6501991374546658, 1.2787728956214681, 0.7231399979561206, 0.12317114351212796, -0.36364915390810965, -0.5976699160910707, -0.49031332975913205, -0.027584621629241978, 0.7219205227847133, 1.617155656832011, 2.4716592478575934, 3.092393543259084, 3.3223689669496297, 3.0777397246542684, 2.370776750025144, 1.3128181307487874, 0.09547014558275606, -1.046877641188611, -1.885806477230045, -2.24857484281022, -2.057754100352939, -1.3515346288616306, -0.2793992519066916, 0.9267951052270423, 2.0007215714609785, 2.698359963662076, 2.851176589151951, 2.403673491962849, 1.42651148740426, 0.1017993079567737, -1.3165131395635823, -2.558366699395409, -3.396766202286437, -3.696715529902842, -3.4424849329716287, -2.736825097792765, -1.7724284539892168, -0.7826695146821678, 0.016228835452808777, 0.47727025139395873, 0.5560318388857838, 0.3169709506248747, -0.088771184478019, -0.4681885750907251, -0.6420140652531496, -0.4962804507110987, -0.015856385240618533, 0.7094582587267335, 1.5084956558885427, 2.176161061699819, 2.5322791582695383, 2.475829872233214, 2.0192329349462237, 1.2922144156466355, 0.5127099930486928, -0.06879332828075266, -0.23748840824506143, 0.12304425301789788, 0.9911101308972027, 2.2021970190565807, 3.482406231649964, 4.512965257141405, 5.010076581143348, 4.799561507894673, 3.8663177772967283, 2.364582869890337, 0.5849624392502036, -1.1144190650789276, -2.3955105983537535, -3.0240900485152564, -2.9276090813158477, -2.2115422711999586, -1.1295145619899498, -0.014843211855973634, 0.8083673819561292, 1.1107328029278836, 0.8166152938768475, 0.020726759247891857, -1.042002299665529, -2.0646590322666394, -2.755436103088362, -2.9190419803573913, -2.509544325505217, -1.6399271283334578, -0.546071660840148, 0.4839805826259353, 1.1945675652030794, 1.4358388013948606, 1.204480525706119, 0.6398613437600703, -0.022939060380400892, -0.5287463629957013, -0.6833110121011577, -0.4146745874630583, 0.20435566611174888, 0.9800395043812855, 1.6609223093089545, 2.021018334530848, 1.9367770852136206, 1.4328804424318382, 0.6809907815338032, -0.0500851962304285, -0.47902064546296996, -0.4059994513459329, 0.2133296230690549, 1.2385275307581964, 2.3714461481775575, 3.234537051233913, 3.4791530479350894, 2.892438654246529, 1.4704662466388845, -0.5658238424893363, -2.818977274778324, -4.8157497611327695, -6.132307436065813, -6.508046274284348, -5.914840913023325, -4.561252948196824, -2.8303159265569273, -1.1692471732154386, 0.03621227706503054, 0.5656238184698846, 0.41545959657796117, -0.21576349194631084, -1.0025948713616972, -1.6032962582400203, -1.7706288051788133, -1.4278813559560146, -0.6867718511682083, 0.1972331818292153, 0.9163903050250976, 1.2180936995197853, 0.9924078214334862, 0.31065448567916776, -0.597672777470235, -1.4218063420800509, -1.8744959888999975, -1.7892741946573811, -1.1770897534411529, -0.2227035076917127, 0.7784607190304115, 1.5219602666222396, 1.7998976413107344, 1.5738571808742676, 0.9891657428128534, 0.32410988151939496, -0.10988026384889238, -0.08356691492424403, 0.45926159017901697, 1.368441603850014, 2.32594494466761, 2.946425784774968, 2.9082479087634905, 2.0716446225159477, 0.5431458760350878, -1.3382018780763085, -3.092077730220618, -4.239007560195786, -4.448982205373659, -3.648616283164896, -2.0511105621196157, -0.09759716541144942, 1.6729754468095808, 2.784845928510276, 2.966374068942711, 2.226214769216843, 0.8410492393246323, -0.7399485173458915, -2.041616114143806, -2.711697755037505, -2.623567460621053, -1.900506366737805, -0.8562409663128653, 0.12512224762364563, 0.7265062127881707, 0.8044268357802232, 0.42840200392745514, -0.15865512162618925], 'positive_zeros': ['2.24108988634808591697441503999411', '3.44098373339593491268142897822104', '4.35227388523480307285147481406609', '5.63240080703539929660874018375830', '6.22415412467884086355588987075704', '7.76816568851204026148756944977742', '8.603692059519650053682575623552704', '9.288776500991284865357782371780829', '10.27772330157513393828592521034286', '10.75546790147094823202502990573398'], 'prelabel': '2-24e2-144.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.144617251731822, 'root_angle': 0.7794506274778723, 'root_number': '-0.7694119626934557 + 0.638752872137734*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.389725313739', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.24108988634808591697441503999', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.44098373339593491268142897822', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.35227388523480307285147481407', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.599383156425752, 'bad_primes': [2, 3], 'central_character': '144.59', 'conductor': 576, 'conductor_radical': 6, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/576/2/y/a/527/14'], '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': '2-24e2-144.59-c1-0-19', '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': '2-24e2-144.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.144617251731822, 'root_angle': 0.38972531373893615, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.24108988634808591697441503999', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2840918939594565524965705666510', 'Lhash_array': ['2840918939594565524965705666510'], 'label': '2-24e2-144.59-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/576/2/y/a/527/14'}