-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1546890358742483627726278523361', 'a10': [-1.0, 0], 'a2': [0.5, 0.8660254037844386], 'a3': [-0.5, 0.8660254037844386], 'a4': [-0.5, 0.8660254037844386], 'a5': [-0.5, 0.8660254037844386], 'a6': [-1.0, 0], 'a7': [1.5, -2.598076211353316], 'a8': [-1.0, 0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.863394624362128, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, -0.8660254037844386]]], [3, [[1.0, 0], [0.5, -0.8660254037844386]]], [5, [[1.0, 0], [0.5, -0.8660254037844386]]], [37, [[1.0, 0], [6.052343178074636, 0.6075706171412577]]]], 'bad_primes': [2, 3, 5, 37], 'central_character': '1110.211', 'coefficient_field': 'CDF', 'conductor': 1110, 'conductor_radical': 1110, 'conjugate': '1243520554742261882380069135854', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [-1.5, 2.598076211353316], [-3.5, -6.06217782649107]], [[1.0, 0], [-2.0, 0], [11.0, 0]], [[1.0, 0], [-3.2015621187164243, 5.545268253204709], [-6.5, -11.258330249197702]], [[1.0, 0], [-1.0, -1.7320508075688772], [-8.5, 14.722431864335457]], [[1.0, 0], [-0.3507810593582122, 0.6075706171412577], [-9.5, -16.454482671904334]], [[1.0, 0], [-5.4031242374328485, 0], [23.0, 0]], [[1.0, 0], [-4.701562118716424, 0], [29.0, 0]], [[1.0, 0], [1.7015621187164243, 0], [31.0, 0]], [[1.0, 0], [6.052343178074636, 0.6075706171412577]], [[1.0, 0], [-0.7015621187164244, 1.2151412342825154], [-20.5, -35.50704155516198]], [[1.0, 0], [-3.7015621187164243, 0], [43.0, 0]], [[1.0, 0], [8.0, 0], [47.0, 0]], [[1.0, 0], [-4.701562118716424, -8.143344464558025], [-26.5, 45.89934640057525]], [[1.0, 0], [1.0, 1.7320508075688772], [-29.5, 51.09549882328188]], [[1.0, 0], [1.7015621187164243, -2.947192041851393], [-30.5, -52.827549630850754]], [[1.0, 0], [-2.149218940641788, 3.7225564017809356], [-33.5, -58.023702053557386]], [[1.0, 0], [-1.3507810593582121, 2.339621424710135], [-35.5, -61.48780366869514]], [[1.0, 0], [-11.701562118716424, 0], [73.0, 0]], [[1.0, 0], [5.552343178074636, -9.61694048548372], [-39.5, -68.41600689897065]], [[1.0, 0], [-0.6492189406417879, -1.1244801904276196], [-41.5, 71.88010851410841]], [[1.0, 0], [5.701562118716424, 9.875395272126902], [-44.5, 77.07626093681505]], [[1.0, 0], [8.298437881283576, 0], [97.0, 0]], [[1.0, 0], [-16.806248474865697, 0], [101.0, 0]], [[1.0, 0], [-14.104686356149273, 0], [103.0, 0]], [[1.0, 0], [1.7015621187164243, -2.947192041851393], [-53.5, -92.66471820493493]], [[1.0, 0], [1.5523431780746366, 2.6887372552082116], [-54.5, 94.39676901250381]], [[1.0, 0], [-3.649218940641788, -6.320632613134252], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 17, 'label': '2-1110-37.26-c1-0-17', 'leading_term': '1.875433098065647769049151513164839379950483180691285159', '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/1110/2/i/k/211/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.8754330980656477, 1.8668731292165763, 1.8510275306688506, 1.8278978912593546, 1.7972731413754073, 1.7587762288079116, 1.711919484895425, 1.6561651738474954, 1.5909878252385832, 1.515935344480112, 1.4306864432729458, 1.3351025050284884, 1.229272508216935, 1.1135500272410928, 0.9885816084074223, 0.8553259969178731, 0.715063801545843, 0.5693972611726642, 0.4202398517866713, 0.2697955666683565, 0.12052783105257434, -0.024881817033713102, -0.16358493454415649, -0.2926266715143886, -0.40901467582067824, -0.5097952131884227, -0.5921349929468844, -0.6534068749772252, -0.6912773356183396, -0.7037933047400725, -0.6894657674961391, -0.6473473666385741, -0.5771011578848906, -0.47905767327936427, -0.35425754526523606, -0.20447714411741985, -0.032234987152545365, 0.15922291018958576, 0.36596005760071054, 0.5834095960904054, 0.8064575066196106, 1.0295481869006675, 1.2468108644208429, 1.45220449678, 1.6396780018607366, 1.8033418902451188, 1.9376466721736412, 2.0375628130840986, 2.0987565463924467, 2.1177555485553077, 2.0920983649642566, 2.02046156642274, 1.9027589293163645, 1.7402074753459302, 1.5353559779041386, 1.2920725319975443, 1.0154889738879673, 0.7119012968100144, 0.38862670259417403, 0.053819509801994354, -0.28375024617033495, -0.6149500955953036, -0.9305633717927987, -1.2215841253895305, -1.4795193027426372, -1.696687916578309, -1.8665064068042918, -1.9837492331425568, -2.0447739917547065, -2.0477010245856517, -1.992538596151289, -1.8812462342147522, -1.717730736590651, -1.5077715865689154, -1.2588750272669529, -0.9800587379334647, -0.6815718366929591, -0.3745576978669027, -0.0706697045856184, 0.21834755669611555, 0.48109712716779646, 0.706972439231242, 0.886586918612317, 1.0121729649350228, 1.0779331740225169, 1.0803277064701113, 1.0182834661568376, 0.8933131986353074, 0.709535690758918, 0.47359185677099014, 0.1944555110301295, -0.11685809299110621, -0.44767850078343707, -0.7841493220321909, -1.1117647520664375, -1.4159540176558034, -1.6826914931664598, -1.8991081108943573, -2.0540785023229176, -2.1387581567528855, -2.1470458317350567, -2.0759485122107573, -1.9258293597298042, -1.700523236987249, -1.4073094043839118, -1.0567366865087764, -0.6623025789625555, -0.23999415857406567, 0.19229500152061016, 0.6154517123400945, 1.0099082728998177, 1.356455749484354, 1.6370720472130365, 1.8357293998209732, 1.9391454087418682, 1.9374428541343915, 1.824686199757959, 1.5992669684181315, 1.2641158481927472, 0.8267263025022379, 0.29898233341590935, -0.3032084356855173, -0.9604664024865852, -1.650657732102278, -2.3497514533063177, -3.0327819506197313, -3.6748770052730984, -4.252307279280332, -4.743510775316001, -5.130045523891094, -5.397425639276735, -5.535799936779863, -5.540438401779547, -5.411999727407833, -5.156562577860926, -4.785413787434879, -4.314597901573149, -3.7642437867265253, -3.15769493684906, -2.5204800431077197, -1.8791688552475982, -1.2601648883995444, -0.688490738456687, -0.18662338523389715, 0.22656427177614197, 0.5367033100134029, 0.7346243494527396, 0.8168120063535772, 0.7855924671509057, 0.649040962510301, 0.42060941660981466, 0.11848833465344119, -0.23526961600791155, -0.6158245672985565, -0.9967726184038929, -1.351458620006446, -1.6543145257854062, -1.882156945221051, -2.0153785484829587, -2.0389723478457986, -1.9433354588539586, -1.7248094044191855, -1.3859268823977193, -0.9353495495628226, -0.38749705067669005, 0.23811656396728875, 0.9178075717775992, 1.6248631044892432, 2.330840400738567, 3.006958858684634, 3.625513481262951, 4.161236555484492, 4.59253654405378, 4.90254914094569, 5.079944989432121, 5.119451216360338, 5.022059054287669, 4.794906608280278, 4.450843373657991, 4.007700461851565, 3.4873066742214704, 2.9143046565683943, 2.3148325500107796, 1.7151441572680142, 1.1402441896443518, 0.6126143953646199, 0.1511012837678258, -0.2299730093608, -0.5214279434421282, -0.7195367908710958, -0.8260184705526322, -0.8477123450096666, -0.7959579857903707, -0.6857193945332427, -0.5345084232879914, -0.3611742301307752, -0.1846337704810535, -0.022622019174593184, 0.10946043844314168, 0.19953061561250401, 0.23957557159623144, 0.22612669973083094, 0.1604257028429912, 0.0482714086928921, -0.10044321950972106, -0.27247466613867816, -0.45220556317439103, -0.6227915272556229, -0.7674034339409753, -0.8704832988914931, -0.9189299291890716, -0.9031338489593332, -0.8177895828188522, -0.6624267556919515, -0.4416188816472997, -0.16484913721283728, 0.15396539958058897, 0.4972670018361198, 0.8449225031774817, 1.1754959167438097, 1.4676486713863075, 1.7015772713605792, 1.860393421223049, 1.931352979859794, 1.9068475859355796, 1.7850861053559306, 1.5704114780572387, 1.2732210249626466, 0.9094834633402914, 0.49987220507732577, 0.06856029566089979, -0.358254101327235, -0.7540030540054814, -1.0934819336483594, -1.3545489170026375, -1.519678476652354, -1.5772625662177904, -1.5225664669621135, -1.358265973133881, -1.0945176574895294, -0.7485428987513238, -0.34373739777947804, 0.09165089992800426, 0.5262032452394865, 0.9272731847178277, 1.2630737405112469, 1.5047782728239976, 1.6284998906304826, 1.6170181578395832, 1.4611343293401262, 1.1605568714152927, 0.7242464623449567, 0.1701824391868542, -0.4754512266001104, -1.1796251320463134, -1.9042976120944808, -2.608618397108504], 'positive_zeros': ['1.22028132867525132747550795302217', '2.11963342434973698590390563302773', '3.46636458552767120558125163373709', '4.58427764105156740825410417130178', '5.31059448628589767648630203124341', '6.30206461455360158164205152024205', '7.06113494864611259622950493717036', '8.403702484755230918526270387895443', '8.868050161988176318226963371372988', '9.646381504990794928182263394541393'], 'prelabel': '2-1110-37.26-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9771453817981626, 'root_angle': -0.25466209776125004, 'root_number': '0.6966747321668637142474717745108871415664475311524957179 - 0.7173871462189915130681998989300019163931562703313344058*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.12733104888062502', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.22028132867525132747550795302', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.11963342434973698590390563303', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.46636458552767120558125163374', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 8.863394624362128, 'bad_primes': [2, 3, 5, 37], 'central_character': '37.26', 'conductor': 1110, 'conductor_radical': 1110, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1110/2/i/k/211/2'], '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': '2-1110-37.26-c1-0-17', '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': '2-1110-37.26-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9771453817981626, 'root_angle': -0.12733104888062502, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.22028132867525132747550795302', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1546890358742483627726278523361', 'Lhash_array': ['1546890358742483627726278523361'], 'label': '2-1110-37.26-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1110/2/i/k/211/2'}