-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1824701917508960977561887903113', 'a10': [0.2902846772544624, 0.9569403357322088], 'a2': [-0.0980171403295606, 0.9951847266721969], 'a3': [-0.48554359890621124, 1.1722059416028174], 'a4': [-0.9807852804032304, -0.19509032201612828], 'a5': [0.9238795325112867, -0.3826834323650898], 'a6': [-1.118969854527415, -0.5981018480381407], 'a7': [0.0, 0.0], 'a8': [0.2902846772544624, -0.9569403357322088], 'a9': [-0.4312074019036045, -0.4312074019036045], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5171576384043273, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.0980171403295606, -0.9951847266721969]]], [5, [[1.0, 0], [-0.9238795325112867, 0.3826834323650898]]], [19, [[1.0, 0], [0.9238795325112867, 0.3826834323650898]]]], 'bad_primes': [2, 5, 19], 'central_character': '3040.1709', 'coefficient_field': 'CDF', 'conductor': 3040, 'conductor_radical': 190, 'conjugate': '562932108885744814830030051898', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.0980171403295606, -0.9951847266721969]], [[1.0, 0], [0.48554359890621124, -1.1722059416028174], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [-0.9238795325112867, 0.3826834323650898]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0.6363792902864169, 1.5363555134228326], [-0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [1.6295780108358424, 0.6749933130331763], [0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0.9238795325112867, 0.3826834323650898]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.838861600080564, 0.76168141408046], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0.5916365870938927, 1.4283370725582065], [-0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0, 0], [-0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0.4252150473836282, -1.0265599343186735], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [-0.7324104244932061, 1.7681951800349338], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [-0.9427934736519953, 0], [1.0, 0]], [[1.0, 0], [-1.5363555134228326, 0.6363792902864169], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0.13861716919909145, -0.13861716919909145], [0, -1.0]], [[1.0, 0], [0.22217427330945994, 0.5363761438340849], [-0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0, 0], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, -1.546020906725474], [-1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-3040-3040.1709-c0-0-5', 'leading_term': '0.66139975054851265443390546591253', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3040/1/cn/a/1709/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.6613997505485126, 0.7158322151757921, 0.7718148954962937, 0.8298680448856138, 0.8894736758529703, 0.949274864008379, 1.007323114102961, 1.0613194207275147, 1.1088204043899823, 1.1474030986012647, 1.1747939961348062, 1.1889714404961595, 1.188249295571614, 1.1713470893984144, 1.1374491009058174, 1.086252728568277, 1.018005040162979, 0.933525567252475, 0.8342130563367595, 0.7220339162682923, 0.5994904285564304, 0.4695673532913615, 0.3356563202697332, 0.2014582996752916, 0.07086545747446342, -0.05217522615514946, -0.16381310831875767, -0.2604552835326168, -0.3389327440456812, -0.396664985609921, -0.431816111459669, -0.44343509839305684, -0.4315727876845944, -0.3973683857212517, -0.3430988292563846, -0.27218529896460214, -0.18915244786439608, -0.09953752627908183, -0.009748492409054016, 0.07312766073473327, 0.1415628306151072, 0.18786608231080398, 0.20449404333221738, 0.18438299552500945, 0.12129032114248654, 0.01013141759029354, -0.15270285855217638, -0.3690636267653794, -0.6388115127838028, -0.959648582061173, -1.3270273398711543, -1.7341470895794873, -2.172044888935855, -2.6297846971748284, -3.09474418453343, -3.5529942358371938, -3.9897616058591856, -4.389960683808103, -4.738776119533146, -5.0222743812761905, -5.228019373861941, -5.345665248543944, -5.367498652589177, -5.288903027885064, -5.108719251603526, -4.829479936598267, -4.457499027357684, -4.002803822976118, -3.4789030475803817, -2.9023918227561047, -2.2924020713484, -1.6699146483848093, -1.056956973569956, -0.47571673907397605, 0.05239199858890611, 0.5076697200380755, 0.8730361315760529, 1.1348548213952798, 1.28363557640882, 1.314575745611439, 1.2279078547264575, 1.0290284527110136, 0.7283926215353791, 0.34116931911348236, -0.11333572770852654, -0.6124710585040654, -1.1312144566725835, -1.6432913730507044, -2.122387345725639, -2.5433981192355257, -2.883656897388612, -3.1240768313200524, -3.2501486682398957, -3.252738528101885, -3.128638925411122, -2.8808371268829482, -2.5184782788591273, -2.056515844158776, -1.5150580213577312, -0.9184351515628514, -0.2940287675024859, 0.32908297934719, 0.9215971080625408, 1.4554998976278937, 1.9055436143734972, 2.2506056580237948, 2.474853743615838, 2.5686489343609002, 2.5291306171900194, 2.360443341183878, 2.0735840662371223, 1.685868849029181, 1.2200392325825828, 0.7030494213445647, 0.16459450796739059, -0.3645435921248716, -0.8542432942351381, -1.2767865408508505, -1.6084984859589684, -1.8311872682045267, -1.9332963102721274, -1.910695777661835, -1.7670587345887105, -1.513790193346979, -1.169502452619705, -0.759056450543436, -0.3122147923587737, 0.1380239072931776, 0.5573191947375047, 0.9120055391138966, 1.1711158918074187, 1.3082930233691112, 1.3034734290159957, 1.1442394156619204, 0.8267523587313875, 0.35620317144683716, -0.25325648831285047, -0.9791084007251522, -1.7915620569247366, -2.6550931231639727, -3.530342333552777, -4.376267712267121, -5.15242577424205, -5.821247403008056, -6.350172244492045, -6.713511984316351, -6.893927567092088, -6.883427518321779, -6.68382280052026, -6.306606408224331, -5.772261186799573, -5.109034945259536, -4.351255552457368, -3.537288165353357, -2.7072600673943747, -1.9006941827740949, -1.1541990406525573, -0.49936021497378447, 0.03903390490535432, 0.44432009122564886, 0.7087585249106069, 0.833752013115377, 0.829474597810059, 0.7139367702867827, 0.5115517918990234, 0.25130087315736127, -0.03537811131439285, -0.31683499469547355, -0.5634322924070211, -0.7495995104098594, -0.8555770872462842, -0.868731505587549, -0.7843526451983305, -0.6058803198342239, -0.34454670788885694, -0.018462303929551966, 0.3487877814276608, 0.7299356486713942, 1.0960813502143676, 1.4188546916597122, 1.6725320701873956, 1.8359553144389504, 1.8941135283988977, 1.839273121239617, 1.6715738672482643, 1.3990476845034825, 1.037059063329968, 0.6072086431290938, 0.13578119004226746, -0.3481468058984562, -0.8147991019910247, -1.235835206010682, -1.586369767716508, -1.846724617582442, -2.003782115330332, -2.051838488927346, -1.9928938006923786, -1.8363582560093694, -1.5981995213144031, -1.2995990962624082, -0.9652242115269846, -0.621252148246596, -0.2933038185122044, -0.004451204490593635, 0.22654195330679056, 0.38660477629813417, 0.4692571912588565, 0.47494801136535464, 0.4108051627860219, 0.2898181342440272, 0.12951985216000353, -0.04972246189082002, -0.22666384011940877, -0.38121909874366244, -0.4964054547469357, -0.5600192843418874, -0.565895381134945, -0.5146294934255047, -0.4136881251267793, -0.2768802950077729, -0.12322018010450513, 0.024737067121937833, 0.14295599103127513, 0.2082090774545557, 0.2003980466501644, 0.10470359216954526, -0.0866342193160211, -0.37307893130473224, -0.7452388024560587, -1.1850685838083457, -1.6668532810623296, -2.158929640086292, -2.6260364227461555, -3.0321261349071946, -3.3434237822413597, -3.5314867860785535, -3.5760076088007686, -3.4671087275746983, -3.206908563692937, -2.810185349773326, -2.3040306029778375, -1.7264603401642349, -1.1240347690254084, -0.5486195560971404, -0.05349731944734467, 0.31089957626939446, 0.5013200248714124, 0.4857530992709517, 0.24688342108965988, -0.21535800409384112, -0.8823932904092125, -1.7169168039199885, -2.6642105122033, -3.654829846146535, -4.60853004433619, -5.439204563117171, -6.060522444867789], 'positive_zeros': ['1.43943600640463496749605405664850', '2.23311602857593084641120276743131', '2.64100705752942285895055988210671', '4.32978046257333496282144650576298', '4.90790196765971972943704790464892', '5.88683945869376716748112407727272', '6.69764653200904700338107956086018', '7.42322255852609855744946757265843', '7.945869708573167685691703437633107', '9.253040933227427902877789536448070'], 'prelabel': '2-3040-3040.1709-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2317295313518821, 'root_angle': -0.015625, 'root_number': '0.99518472667219688624483695310913 - 0.098017140329560601994195563888964*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.015625', 'prec': 30}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.43943600640463496749605405665', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.23311602857593084641120276743', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.64100705752942285895055988211', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.5171576384043273, 'bad_primes': [2, 5, 19], 'central_character': '3040.1709', 'conductor': 3040, 'conductor_radical': 190, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3040/1/cn/a/1709/4'], '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': '2-3040-3040.1709-c0-0-5', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3040-3040.1709-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2317295313518821, 'root_angle': -0.015625, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.43943600640463496749605405665', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1824701917508960977561887903113', 'Lhash_array': ['1824701917508960977561887903113'], 'factors': ['2-3040-3040.1709-c0-0-5'], 'label': '2-3040-3040.1709-c0-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3040/1/cn/a/1709/4'}