-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '4468398274057084152281600955503', 'a10': [-1.5573834285615536e-57, -679389.7766267596], 'a2': [59.877809677809, -82.41473467795018], 'a3': [267.309381855222, -822.6936838683101], 'a4': [-1941.102791265221, -5974.100104641902], 'a5': [5395.471858789871, -3920.039764066976], 'a6': [-51796.18138541244, -71291.32760832722], 'a7': [477.55146554523776, -155.16587712053789], 'a8': [-211744.6378435132, -68800.00340706107], 'a9': [-175425.7913413737, -127454.29791850259], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.053931990039143, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '6.0', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [-1452596.0707749445, -1014097.1511103818]]]], 'bad_primes': [11], 'central_character': '11.7', 'coefficient_field': 'CDF', 'conductor': 11, 'conductor_radical': 11, 'conjugate': '1685163152048268457673703105243', 'degree': 2, 'euler_factors': [[[1.0, 0], [-59.877809677809, 82.41473467795018], [-1265.7336089597848, -3895.527490744949]], [[1.0, 0], [-267.309381855222, 822.6936838683101], [-429944.8005076164, -312373.1822635642]], [[1.0, 0], [-5395.471858789871, 3920.039764066976], [75443602.14232115, -232191532.29862148]], [[1.0, 0], [-477.55146554523776, 155.16587712053789], [11197836569.63345, -8135704489.492364]], [[1.0, 0], [-1452596.0707749445, -1014097.1511103818]], [[1.0, 0], [3356751.5377362287, -4620172.128053956], [-7199504239240.758, -22157795672934.727]], [[1.0, 0], [13841033.203647738, 19050547.862141956], [-180040172604748.34, 554106675255825.0]], [[1.0, 0], [33968236.62337699, 11036949.125235135], [1790609383428135.5, 1300953868105998.2]], [[1.0, 0], [-261039276.09773648, 0], [21914624432020320, 0]], [[1.0, 0], [-580103355.4705645, 188487006.0431855], [286242172474312200, -207967111611233300]], [[1.0, 0], [903630100.6086328, 656525697.6779346], [243401186027341700, 749111823165280900]], [[1.0, 0], [-364334263.9523411, -1121305566.1949835], [-5325720045879237000, 3869362105581927400]], [[1.0, 0], [1736794909.873041, 564318874.5348064], [18254247105410531000, 13262486838799510000]], [[1.0, 0], [0, 1401468911.4303107], [-39959630797262580000, 0]], [[1.0, 0], [4869955655.082212, -14988182346.420052], [-94000884436769050000, -68295640213429970000]], [[1.0, 0], [-6765526243.474121, -4915442540.220301], [151807350053343600000, 467214982081376350000]], [[1.0, 0], [-9914793135.627892, -30514595608.02017], [-1439400947703813000000, 1045786003358040600000]], [[1.0, 0], [192135021.787129, 264451170.2771394], [-820238942059664600000, 2524435888527076500000]], [[1.0, 0], [-165258858487.29712, 0], [8182718904632857000000, 0]], [[1.0, 0], [105897013657.26952, -76938684010.77083], [5070870839159273000000, -15606535700822557000000]], [[1.0, 0], [99570270863.86804, -32352342162.91621], [18528146075602186000000, -13461486089020618000000]], [[1.0, 0], [40335587108.346634, -55517172847.518456], [-18260281132081996000000, -56199366624400660000000]], [[1.0, 0], [-251275908252.89343, -345851617169.25586], [-33030828920115930000000, 101658438386693060000000]], [[1.0, 0], [-139926748816.92133, 0], [246990403565262140000000, 0]], [[1.0, 0], [228605272745.0791, 166091452775.5648], [214409080964827520000000, 659883298706325600000000]], [[1.0, 0], [-872500847632.4897, 1200894392277.1328], [-348208083997840840000000, -1071674287631492500000000]], [[1.0, 0], [-324459006340.4808, -998582142302.3389], [-1153464787373655100000000, 838041222583621600000000]], [[1.0, 0], [2319795410897.3057, 753747220231.2427], [1822061270057622300000000, 1323805001328323600000000]], [[1.0, 0], [0, -761349355440.0616], [-2812664781782894700000000, 0]], [[1.0, 0], [-840341961457.2549, 2586306620374.5547], [-3506702850565857500000000, -2547768754013723000000000]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-11-11.7-c12-0-10', 'load_key': 'CMFs-workshop', 'motivic_weight': 12, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [12], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/11/13/d/a/7/10', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [3.26025032060458, 3.7423897379091784, 4.185587334020001, 4.574458467242577, 4.895072172857454, 5.135445397736459, 5.2859968217458135, 5.339947466115208, 5.2936538630017, 5.146858328392055, 4.902840140141174, 4.568451484664091, 4.154023199976888, 3.6731278739148285, 3.1421919542603796, 2.579954297039698, 2.006776000463565, 1.4438152734663683, 0.9120911261670629, 0.4314703189778084, 0.019622562188864268, -0.309001446098877, -0.5441069032982818, -0.6803398008479251, -0.7178522737386653, -0.6625850850665528, -0.5262137489420605, -0.32572050041277184, -0.08257576789277617, 0.1784607015728558, 0.4308786691172565, 0.64822370302489, 0.8060670132227992, 0.884006959303018, 0.8675491188715998, 0.7497003440165346, 0.5321133412332446, 0.2256340633574391, -0.14986436716726567, -0.5664307045559595, -0.9897768871742778, -1.381750874239455, -1.7034056901113737, -1.9184568267886255, -1.9968572374817135, -1.9181736640748348, -1.6744272602129344, -1.2720712482268526, -0.7328221998268601, -0.09313985162351966, 0.5977401436050488, 1.2811827046795419, 1.8937548476922996, 2.37272278818224, 2.661987017510603, 2.717903094872959, 2.5143895718621248, 2.0467378031776136, 1.333617321586249, 0.41691398173857935, -0.6407625686909226, -1.760826939014679, -2.8553920163516966, -3.8352974886168525, -4.618722189084453, -5.139481654281144, -5.354078692629478, -5.2466493283100775, -4.831130850951274, -4.150260583268649, -3.271367098011171, -2.279301534877287, -1.267228541292938, -0.326304337458428, 0.4645328580872414, 1.0473833177714347, 1.3916547124953487, 1.4968952354974936, 1.3917242627988915, 1.1289036596602957, 0.7771302727192645, 0.41062052452699, 0.09792657161527639, -0.10839352740349473, -0.17967371322022022, -0.11531160152893752, 0.05758127526395103, 0.2891901050793685, 0.5160836566461575, 0.6731073045507102, 0.7062761729929754, 0.5845729823569025, 0.3085792439982512, -0.08577136296026425, -0.5293616962516542, -0.9281343900530447, -1.1765712510375306, -1.1746340675849583, -0.8456685379602594, -0.15239963566382195, 0.8917850462461014, 2.218531654284612, 3.708510451831225, 5.2037678755667445, 6.527152192717906, 7.506277821885688, 7.998572735376427, 7.913538194610841, 7.228547413810524, 5.99532987512563, 4.335634835217472, 2.426246999356998, 0.475273881515806, -1.3068574438428269, -2.737241832261419, -3.686416615772969, -4.096094845099955, -3.9856923416086967, -3.446448981933254, -2.6240395027577494, -1.6925769581700207, -0.8244667979098089, -0.16136984266572788, 0.2085985189865192, 0.2633791317588253, 0.046986556474486706, -0.3428636194764893, -0.7770749298395059, -1.123070555291755, -1.2727853771103987, -1.1651884132782848, -0.7988015757716496, -0.23163972159366122, 0.43147448490087437, 1.0616634300076995, 1.5341099581943956, 1.7556003836563834, 1.685540524883983, 1.3457332888895406, 0.8165010917720231, 0.2196381609400791, -0.3084101132603564, -0.6474506726046994, -0.7216942185893527, -0.5186311246487936, -0.09388357778227735, 0.439788183011881, 0.9376544819060706, 1.2573715566118617, 1.2951430208919201, 1.0154274638564629, 0.46685430467606126, -0.2203612887219931, -0.8563592401488975, -1.2294898997220647, -1.1528356793409535, -0.5097118313664464, 0.7119849639637615, 2.4049418370886726, 4.351749039801553, 6.258053387779105, 7.804056235218249, 8.704619216928702, 8.765901589299153, 7.926629950027281, 6.274869592834464, 4.036025212909006, 1.5337552791267657, -0.8687398057743512, -2.835287620974459, -4.117564564488775, -4.597665046982836, -4.303783940852432, -3.3961903017679567, -2.127144288782198, -0.7840768288534993, 0.3710972919212845, 1.1530670472327007, 1.4836651575425248, 1.3959615851832636, 1.012396943337001, 0.5036275871757507, 0.039232301456640195, -0.2569051617338759, -0.33529444552928117, -0.22679565482495828, -0.025169577285500375, 0.14813070157050634, 0.18645759379682406, 0.03525606931927013, -0.2870049579813907, -0.6909441918695601, -1.0416689000732096, -1.2009770724724995, -1.0746768283628212, -0.6511746463831893, -0.019088704618789705, 0.6432319661601887, 1.1059745619472359, 1.145782263872812, 0.6090832871157743, -0.5360429980878997, -2.174560121671392, -4.054859800688624, -5.83516327870345, -7.156804641120768, -7.727631444636498, -7.395081045896237, -6.189950727656001, -4.328353925760694, -2.1693858289280574, -0.13714269657668124, 1.374912638005847, 2.094184462851551, 1.9314245461657518, 0.9995813367091623, -0.4161308538445339, -1.9298011309542196, -3.15022123291484, -3.776100330399088, -3.667053710616865, -2.8725784446446903, -1.6121875274832707, -0.21266427648017597, 0.9803898473639583, 1.692936801367556, 1.7908468603731396, 1.3085352775534123, 0.43127927786896886, -0.5626214109495897, -1.38273707198877, -1.8072987145500339, -1.74125906262321, -1.2359291349597499, -0.46582989673567265, 0.3291482033555, 0.918233757918982, 1.1483261600569348, 0.9862282850662575, 0.5224663672864035, -0.06350211098522039, -0.5649803973754866, -0.8166208698829809, -0.7478190591931968, -0.4036616849998427, 0.07345976678758555, 0.4957212155081304, 0.6982361903587774, 0.6009827115154821, 0.24265014858337736, -0.2268097811479971, -0.5950037741893275, -0.6634993970471201, -0.32783344354556515, 0.365897510247265, 1.209415918100179, 1.8743958335213824], 'positive_zeros': ['3.52494470736067819587802959662921', '4.97795039544189408572620777431537', '6.61258708052222144290764163988919', '8.637436090346783675368192643451236', '10.44251956212542570107702497123884', '12.89978364217177490460015452391744', '14.48471759437789285262247716268911', '15.06726848845687900281700459921312', '16.31236567935842451617997352794354', '17.43193648179120803843399228332578'], 'prelabel': '2-11-11.7-c12-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1707935899454482, 'root_angle': 0.9161329340716494, 'root_number': '-0.965490488500383 + 0.2604383163347739*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.458066467036', 'prec': 47}, 'spectral_label': 'c12-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.52494470736067819587802959663', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.97795039544189408572620777432', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.61258708052222144290764163989', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 10.053931990039143, 'bad_primes': [11], 'central_character': '11.7', 'conductor': 11, 'conductor_radical': 11, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/11/13/d/a/7/10'], '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': '2-11-11.7-c12-0-10', 'motivic_weight': 12, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [12], 'order_of_vanishing': 0, 'prelabel': '2-11-11.7-c12-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1707935899454482, 'root_angle': 0.4580664670358247, 'self_dual': False, 'spectral_label': 'c12-0', 'z1': {'__RealLiteral__': 0, 'data': '3.52494470736067819587802959663', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '4468398274057084152281600955503', 'Lhash_array': ['4468398274057084152281600955503'], 'label': '2-11-11.7-c12-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/11/13/d/a/7/10'}