-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3985208786480808360797193849148', 'a10': [-1.0, 3.657796605117526e-61], 'a2': [-0.8090169943749475, -0.5877852522924731], 'a3': [1.0, -3.0776835371752536], 'a4': [0.30901699437494745, 0.9510565162951535], 'a5': [0.8090169943749475, -0.5877852522924731], 'a6': [-2.618033988749895, 1.902113032590307], 'a7': [0.8090169943749475, 2.48989828488278], 'a8': [0.30901699437494745, -0.9510565162951535], 'a9': [-6.045084971874737, -4.392011317473087], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8783544222340847, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8090169943749475, 0.5877852522924731]]], [5, [[1.0, 0], [-0.8090169943749475, 0.5877852522924731]]], [11, [[1.0, 0], [2.5450849718747373, -2.1266270208801]]]], 'bad_primes': [2, 5, 11], 'central_character': '110.81', 'coefficient_field': 'CDF', 'conductor': 110, 'conductor_radical': 110, 'conjugate': '2067797457757567003220040709590', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [-1.0, 3.0776835371752536], [-2.4270509831248424, -1.7633557568774194]], [[1.0, 0], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [-0.8090169943749475, -2.48989828488278], [-5.663118960624632, 4.114496766047312]], [[1.0, 0], [2.5450849718747373, -2.1266270208801]], [[1.0, 0], [-1.3090169943749475, -0.9510565162951535], [4.017220926874317, 12.363734711836996]], [[1.0, 0], [-4.23606797749979, 3.0776835371752536], [5.253288904374106, -16.167960777017612]], [[1.0, 0], [1.2639320225002102, -3.889982777757519], [-15.371322893124, -11.16791979355699]], [[1.0, 0], [-0.14589803375031546, 0], [23.0, 0]], [[1.0, 0], [0.38196601125010515, 1.1755705045849463], [-23.461492836873475, 17.04577231648172]], [[1.0, 0], [-5.854101966249685, -4.2532540417602], [9.57952682562337, 29.48275200514976]], [[1.0, 0], [0.2639320225002103, 0.8122992405822658], [-29.933628791873055, 21.748054334821507]], [[1.0, 0], [0.5729490168751578, -1.7633557568774194], [-33.16969676937284, -24.099195343991397]], [[1.0, 0], [9.23606797749979, 0], [43.0, 0]], [[1.0, 0], [-3.5, 10.771892380113387], [-38.02379873562253, -27.625906857746237]], [[1.0, 0], [0.7360679774997897, 0.5347846891564904], [16.377900701872214, 50.405995363643136]], [[1.0, 0], [-0.7360679774997897, -2.2653842965929876], [-47.7320026681219, 34.67932988525592]], [[1.0, 0], [7.23606797749979, -5.257311121191336], [18.850036656871794, -58.014447494004365]], [[1.0, 0], [-0.7639320225002103, 0], [67.0, 0]], [[1.0, 0], [10.70820393249937, -7.779965555515038], [21.940206600621266, -67.52501265695591]], [[1.0, 0], [0.5278640450004206, 1.6245984811645315], [-59.05824058937116, 42.90832341735054]], [[1.0, 0], [-1.2360679774997898, -0.8980559531591708], [24.412342555620846, 75.13346478731714]], [[1.0, 0], [12.70820393249937, -9.23305061152576], [25.648410533120636, -78.93769085249775]], [[1.0, 0], [12.034441853748634, 0], [89.0, 0]], [[1.0, 0], [-9.70820393249937, -7.053423027509678], [29.974648454369902, 92.2524820806299]], [[1.0, 0], [3.0, 2.1796275840160826], [31.210716431869688, 96.05670814581052]], [[1.0, 0], [3.5, 10.771892380113387], [-83.32875042061958, 60.54188098612473]], [[1.0, 0], [2.326237921249264, -7.159424153781643], [-86.56481839811937, -62.893021995294625]], [[1.0, 0], [-7.52786404500042, 0], [109.0, 0]], [[1.0, 0], [-1.9442719099991588, 5.983853649196697], [-91.41892036436906, -66.41973350904946]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-110-11.4-c1-0-3', '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/110/2/g/a/81/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.9669233616650321, 1.0384536065238585, 1.1256423192606493, 1.2296962115378924, 1.3505686997710542, 1.4870204203843804, 1.6367150803585597, 1.7963015180968118, 1.9614698199261473, 2.126996073263734, 2.2868011654091505, 2.4340487989956556, 2.561302512203102, 2.660754452895664, 2.724531266923519, 2.7450749471355262, 2.7155887884165897, 2.630530731137044, 2.4861285885981736, 2.2808843991985963, 2.0160290526517115, 1.6958841549340486, 1.3280865964313826, 0.9236331961384058, 0.4967086869122318, 0.06427051112473307, -0.35462159765068013, -0.7397248882138815, -1.0707539912610844, -1.3286917215419864, -1.4971967438111051, -1.5640140744252211, -1.5222785725771022, -1.3715927706560913, -1.1187606985720397, -0.7780703579741465, -0.3710400112006976, 0.0744227266599342, 0.5254562313696439, 0.9462307736580091, 1.3003864524298647, 1.5537712227436704, 1.6772803884228282, 1.64956457886406, 1.4593564707000217, 1.1071715672295703, 0.6061677796176193, -0.017997264591454325, -0.7283955362575376, -1.4791345659024433, -2.2186256735878405, -2.8935952752488316, -3.453525856290146, -3.8551408874917747, -4.066507891384321, -4.0703341192735, -3.866074420141209, -3.470560903834169, -2.9169938380756455, -2.2522926122677633, -1.5329796771880086, -0.8199408428146089, -0.17255227028167797, 0.357231402320856, 0.7301884230355608, 0.9239265713955505, 0.9352497490571262, 0.7804466982635503, 0.4933761688813854, 0.12147736847293371, -0.2799071120346454, -0.6542783534451497, -0.9510096807030582, -1.131783675543745, -1.1755845814272283, -1.0815242211426606, -0.8690144264973808, -0.5751157742943617, -0.24925642550543603, 0.05411818000273884, 0.2840828857165128, 0.401847545146037, 0.38824239319402004, 0.2489273426396123, 0.016399803765701056, -0.25175797330828625, -0.4784774770298052, -0.5762093059549832, -0.4583887937878477, -0.05199681104662545, 0.6904135420142946, 1.7809141561616224, 3.19014484916496, 4.846132651619223, 6.638541107421359, 8.42820716227532, 10.061096812426946, 11.38515387150987, 12.268026360727545, 12.613412626899606, 12.373824916847258, 11.557932810656501, 10.231289632716212, 8.51008643912371, 6.548511121820594, 4.5211852411098645, 2.6028770693263197, 0.9481322793887133, -0.3264541064143313, -1.1549074834339184, -1.5277344534742923, -1.4901651399404847, -1.1330528902025463, -0.5777779952397621, 0.04260523415848749, 0.6031668096851152, 1.004880984319212, 1.1877268430656878, 1.1371724766863351, 0.8831469454695766, 0.491804491637362, 0.051554404370121876, -0.3442245354927118, -0.61480621163742, -0.7070267388932393, -0.6048769159817556, -0.3320720749795139, 0.05289313136711567, 0.4683700398215374, 0.8258117020806817, 1.0477238017404633, 1.0839867864019515, 0.9234203903483751, 0.5982282922594958, 0.18018406163439427, -0.23110135769457874, -0.5260115725552573, -0.6058260649017477, -0.4029493779694267, 0.10333347056850391, 0.8787446771199142, 1.835472080575873, 2.843472947581645, 3.7501160224351486, 4.405064039565074, 4.686199082116023, 4.52200821027525, 3.906279680622865, 2.9021679539912646, 1.634480681685695, 0.2711180675365146, -1.0034163108761458, -2.017984470699358, -2.643044347608397, -2.8120851943746117, -2.5323104094860076, -1.8824744375399836, -0.9980886561798344, -0.0465454315869276, 0.8033691230131668, 1.411971673525362, 1.6934841504806533, 1.6304195967425954, 1.2747373752349285, 0.7354514919034589, 0.15499781195671639, -0.3210933787600277, -0.5752629001739503, -0.5434927576656071, -0.23009418126187267, 0.2915493625151565, 0.8928123303283172, 1.4158321880802782, 1.706749913652925, 1.649611249253628, 1.193984093173196, 0.37036181425981535, -0.7103329696654958, -1.8737610621448195, -2.9130073429840744, -3.6276745709074567, -3.8637830495589864, -3.5465819103245875, -2.699494623829077, -1.4449294890892206, 0.013873853656351475, 1.4270804325687334, 2.5424534317793475, 3.1512674006460744, 3.127175105097566, 2.450462143609232, 1.2128487888959136, -0.3982694606524457, -2.133247322251795, -3.7249153062054177, -4.936012655200296, -5.600218033354813, -5.648982201588832, -5.119254598562915, -4.141070212728214, -2.908025324346355, -1.6370752801782853, -0.5261217609222063, 0.281905036778297, 0.7213665625184604, 0.8086273560287954, 0.6290515011819758, 0.3100395329438155, -0.013170419005400946, -0.23079461933754608, -0.28319019817283614, -0.17143998368417065, 0.048203679605635735, 0.28414064197316163, 0.4381726937252095, 0.4356533747863626, 0.24912635220079934, -0.09091422786064833, -0.5013656297782247, -0.8671630687578556, -1.0724797966641824, -1.0348057929023355, -0.7330845820526327, -0.22207183680139997, 0.3719505949679778, 0.874640154375664, 1.1020572877067205, 0.905958330460845, 0.2154812670945577, -0.9351261268805078, -2.4005398514835705, -3.943417951084372, -5.276166569827842, -6.117722343470434, -6.253745525015362, -5.587138785604423, -4.167217469565134, -2.189968226940222, 0.032172978991571934, 2.125995752897032, 3.7278811770386313, 4.554545113141007, 4.459341961639578, 3.462056636165663, 1.7455728507618404, -0.38018006763160445, -2.539572129694943, -4.365012436050893, -5.567525291460303, -5.989372714892081, -5.627979994689859, -4.6268413579935705, -3.23642014896817, -1.7546355852506186, -0.4608396309758558, 0.4417487979956853, 0.8625906605132807], 'positive_zeros': ['3.14377541079798043747284821098830', '4.60448263139425405692379786558679', '5.87165781259701693233645598766886', '7.78732002411149714953887795001607', '8.662980336039716331505079858086679', '9.850950899887139770989817838847063', '10.50779665986759223933459870855893', '11.13612388410584567383626327299991', '13.46365730799103962294448377099727', '14.24129415487598630950886074539561'], 'prelabel': '2-110-11.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9372056456477866, 'root_angle': 0.5708685202784272, 'root_number': '-0.2208052509860023 + 0.975317917982136*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.285434260139', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.14377541079798043747284821099', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.60448263139425405692379786559', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.87165781259701693233645598767', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.8783544222340847, 'bad_primes': [2, 5, 11], 'central_character': '11.4', 'conductor': 110, 'conductor_radical': 110, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/110/2/g/a/81/1'], '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': '2-110-11.4-c1-0-3', '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': '2-110-11.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9372056456477866, 'root_angle': 0.2854342601392136, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.14377541079798043747284821099', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3985208786480808360797193849148', 'Lhash_array': ['3985208786480808360797193849148'], 'label': '2-110-11.4-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/110/2/g/a/81/1'}