-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1322056188345533867140030170159', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 81.0], 'a4': [0, 0], 'a5': [0, -1783.680949816112], 'a6': [0, 0], 'a7': [4965.031159162499, 0], 'a8': [0, 0], 'a9': [-6561.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 197.77376108692732, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, -81.0]]]], 'bad_primes': [2, 3], 'central_character': '384.193', 'coefficient_field': 'CDF', 'conductor': 384, 'conductor_radical': 6, 'conjugate': '119617902028143709711285505001', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -81.0]], [[1.0, 0], [0, 1783.680949816112], [-1953125.0, 0]], [[1.0, 0], [-4965.031159162499, 0], [40353607.0, 0]], [[1.0, 0], [0, -53705.01919483569], [-2357947691.0, 0]], [[1.0, 0], [0, -54228.8675539935], [-10604499373.0, 0]], [[1.0, 0], [554662.4062964966, 0], [118587876497.0, 0]], [[1.0, 0], [0, -650851.7676459906], [-322687697779.0, 0]], [[1.0, 0], [183774.84915915132, 0], [1801152661463.0, 0]], [[1.0, 0], [0, 2024450.9347861346], [-14507145975869.0, 0]], [[1.0, 0], [-3431801.4475858225, 0], [26439622160671.0, 0]], [[1.0, 0], [0, -1300844.833415772], [-129961739795077.0, 0]], [[1.0, 0], [-157392.8800599473, 0], [327381934393961.0, 0]], [[1.0, 0], [0, 2101927.844482363], [-502592611936843.0, 0]], [[1.0, 0], [-47333162.919392414, 0], [1119130473102767.0, 0]], [[1.0, 0], [0, 100735274.43415989], [-3299763591802133.0, 0]], [[1.0, 0], [0, 18026288.68387502], [-8662995818654939.0, 0]], [[1.0, 0], [0, -54849808.95718276], [-11694146092834140, 0]], [[1.0, 0], [0, 213386683.07568368], [-27206534396294948, 0]], [[1.0, 0], [-164614583.1910386, 0], [45848500718449030, 0]], [[1.0, 0], [75850536.26488754, 0], [58871586708267910, 0]], [[1.0, 0], [425334994.77577114, 0], [119851595982618320, 0]], [[1.0, 0], [0, 106617994.33802322], [-186940255267540400, 0]], [[1.0, 0], [1027919341.6515884, 0], [350356403707485200, 0]], [[1.0, 0], [-624259136.2286962, 0], [760231058654565200, 0]], [[1.0, 0], [0, -525001751.82143605], [-1093685272684361000, 0]], [[1.0, 0], [1092987658.721474, 0], [1304773183829244700, 0]], [[1.0, 0], [0, -2508149966.695425], [-1838459212420154600, 0]], [[1.0, 0], [0, 1996333390.6131186], [-2171893279442309400, 0]], [[1.0, 0], [1756337655.7482662, 0], [3004041937984268300, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 58, 'label': '2-384-8.5-c9-0-58', 'leading_term': '0.510211776640571530098925452627210366042191359269439835', 'load_key': 'CMFs-workshop', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/384/10/d/b/193/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.5102117766405715, 0.8250867225891676, 1.1119797922615604, 1.363492099496833, 1.573160359163205, 1.735626583479649, 1.8467788382620074, 1.903859433250337, 1.905537708503543, 1.8519454384375367, 1.7446737883263541, 1.5867317054877161, 1.3824665883560545, 1.1374490298763498, 0.8583243554142695, 0.5526345479645485, 0.2286149535746531, -0.1050291328136628, -0.43936030552526417, -0.7654551485157338, -1.0746521140463037, -1.3587945300421913, -1.6104620861907273, -1.8231843194340174, -1.99162996261278, -2.111766533032249, -2.1809852136855055, -2.1981869073570053, -2.1638263069620267, -2.0799119040635534, -1.9499610273010668, -1.7789102355617983, -1.572982656089445, -1.339515121849938, -1.0867491901555422, -0.8235912797769765, -0.5593482107086994, -0.30344533477263325, -0.06513517403294594, 0.14679499136527413, 0.32430784826456444, 0.46038430227586874, 0.5492666816190858, 0.5866687953336635, 0.5699454881093358, 0.4982153262644699, 0.37243127501234585, 0.19539565883257254, -0.02828270066591989, -0.29228954396038165, -0.5887629936876647, -0.9085048626429274, -1.2412403716002425, -1.5759194846410953, -1.9010515059434696, -2.2050632263617587, -2.476669814319905, -2.7052468612790443, -2.8811915571215274, -2.9962609152602315, -3.0438753098443607, -3.019376334178041, -2.9202291329443435, -2.7461608795515713, -2.4992289283551723, -2.1838143205534313, -1.806538700538881, -1.3761052336957458, -0.9030667253207093, -0.39952673519646376, 0.12121802866513347, 0.645083463062466, 1.1576393930981093, 1.644572259319361, 2.092153776911546, 2.4876994972562163, 2.8200010759304632, 3.0797165036832217, 3.259703594651587, 3.3552836341146954, 3.364424229426459, 3.287833023703799, 3.1289569431171023, 2.8938849574834533, 2.5911558269351924, 2.2314758593930977, 1.8273551814266735, 1.3926742930330243, 0.9421956015053146, 0.49103708526379214, 0.05412711278271461, -0.35433935972313396, -0.7214225368476488, -1.035917144332974, -1.288770214151343, -1.4734200447233834, -1.5860417648810912, -1.6256882679690594, -1.5943191686098492, -1.4967147311341709, -1.340276265228529, -1.1347191041254647, -0.8916687868454526, -0.6241752692088377, -0.3461637044424031, -0.07184339231753759, 0.18490125398718937, 0.4111125532883539, 0.5953287395991541, 0.7280957676648809, 0.8023988513937896, 0.8139936968750437, 0.7616211804158219, 0.6470938172242194, 0.4752475971032325, 0.25375842497144835, -0.007171734979090149, -0.29524810055086587, -0.5966192794431142, -0.8964950727927413, -1.179820342843612, -1.4319762539882053, -1.6394782111622, -1.7906391349458983, -1.8761674018316077, -1.8896708550997583, -1.8280417088722465, -1.6917018153264745, -1.4846934733884893, -1.214607503032357, -0.8923474232264195, -0.5317359489025296, -0.1489773357626072, 0.23800398443366375, 0.6103218501290794, 0.9489521195534922, 1.235586099402571, 1.4534757044690683, 1.5882317527367467, 1.6285379112094411, 1.5667456787833052, 1.3993203436088584, 1.1271139219814732, 0.7554484354872096, 0.29400120647152295, -0.2435072134281651, -0.8398127237779196, -1.4747762807784537, -2.126194462812152, -2.7707178069762177, -3.384836932616507, -3.9458924182787736, -4.433062335511101, -4.82828141930459, -5.117048124387282, -5.2890802279989675, -5.33878603637181, -5.265526375727137, -5.073652049068342, -4.7723118897770425, -4.375037455594046, -3.8991212591088695, -3.3648156889370893, -2.7943889196175924, -2.2110816593819957, -1.6380141312401955, -1.0970959013441899, -0.6079918444815947, -0.1871955771021562, 0.15274286878264914, 0.40379534212944146, 0.5628091658349975, 0.6316161834936489, 0.6168894537243351, 0.5297524413306892, 0.3851581965254779, 0.20106799425093322, -0.0025304043874320556, -0.20471588583043535, -0.3847830744367076, -0.5233882351547825, -0.603632138977507, -0.6120224372988048, -0.539263527690775, -0.3808301495183678, -0.13729164813921335, 0.1856335218726314, 0.5772995484260154, 1.0226232343188684, 1.5028197949273476, 1.9963486597202318, 2.480021701203507, 2.9302168942584865, 3.3241338753334406, 3.6410246343657082, 3.863332873531188, 3.977679460571038, 3.9756387512500395, 3.854261025012527, 3.6163093618264313, 3.2701943238644535, 2.8296060086123918, 2.3128595442239623, 1.741986001754239, 1.1416151139340218, 0.5377082909908922, -0.04379050432349271, -0.5783129799443129, -1.043959278284259, -1.422653333665174, -1.7010955458813888, -1.8714579240936977, -1.9317805347228547, -1.8860443055107434, -1.7439131280063578, -1.5201567817157011, -1.2337844341527848, -0.9069353088664541, -0.5635875722192581, -0.22815769823458412, 0.07593017424217141, 0.32762256804778367, 0.5094822356274542, 0.6087270807916959, 0.6179994853900729, 0.5358178661082217, 0.36668011362194614, 0.12080846982987922, -0.18645373917945446, -0.5355624740534977, -0.903960242321055, -1.2674634574507555, -1.6017701520896113, -1.8839997994023747, -2.0941735361022866, -2.2165449652596534, -2.2406989415965026, -2.1623479867928417, -1.9837726239815845, -1.7138720623992048, -1.367814182127204, -0.9662973774489197, -0.5344601363566801, -0.10049587248606988, 0.30595083522113015, 0.6555159683193398, 0.920875772315192, 1.0784308562427347, 1.1098136054116805, 1.0031263819393805, 0.7538322068975771, 0.36523875380024357, -0.15146051925464024, -0.7775987198575992, -1.487885355799199, -2.2516515475180623, -3.034424492326832], 'positive_zeros': ['1.04291844149129832418222866307492', '2.39329298789251291737317427228295', '2.99271533915265434366917361266448', '4.36054738038520666202795540966249', '5.63299555897300501039036802395230', '6.57942930922355830307813028310542', '7.24837799969424103094384819302263', '8.273977175684807732198782638611614', '9.035153932060024957659613001578283', '10.53244790449334472225326188332735'], 'prelabel': '2-384-8.5-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 14.06320593203866, 'root_angle': 0.75, 'root_number': '-0.70710678118654752440084436210484903928483593768847403659 + 0.7071067811865475244008443621048490392848359376884740366*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.375', 'prec': 17}, 'spectral_label': 'c9-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.04291844149129832418222866307', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.39329298789251291737317427228', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.99271533915265434366917361266', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 197.77376108692732, 'bad_primes': [2, 3], 'central_character': '8.5', 'conductor': 384, 'conductor_radical': 6, 'degree': 2, 'index': 58, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/384/10/d/b/193/5'], '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': '2-384-8.5-c9-0-58', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'prelabel': '2-384-8.5-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 14.06320593203866, 'root_angle': 0.375, 'self_dual': False, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '1.04291844149129832418222866307', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1322056188345533867140030170159', 'Lhash_array': ['1322056188345533867140030170159'], 'label': '2-384-8.5-c9-0-58', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/384/10/d/b/193/5'}