-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1006056675478750730487431825491', 'a10': [-2.6755051310984745, 0.0], 'a2': [-1.0, 0.0], 'a3': [-0.3025127191860129, 0.0], 'a4': [1.0, 0.0], 'a5': [2.6755051310984745, 0.0], 'a6': [0.3025127191860129, 0.0], 'a7': [0.0, 0.0], 'a8': [-1.0, 0.0], 'a9': [-2.9084860547306843, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.083891532150474, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [41, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 7, 41], 'central_character': '4018.1', 'coefficient_field': 'CDF', 'conductor': 4018, 'conductor_radical': 574, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [0.3025127191860129, 0], [3.0, 0]], [[1.0, 0], [-2.6755051310984745, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.5318277113567245, 0], [11.0, 0]], [[1.0, 0], [-5.611292263616242, 0], [13.0, 0]], [[1.0, 0], [-1.23298092363221, 0], [17.0, 0]], [[1.0, 0], [-5.443979697548907, 0], [19.0, 0]], [[1.0, 0], [-4.320828937440027, 0], [23.0, 0]], [[1.0, 0], [2.6332744133317547, 0], [29.0, 0]], [[1.0, 0], [-0.8374987690942387, 0], [31.0, 0]], [[1.0, 0], [10.68648948642949, 0], [37.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0.19208115767791326, 0], [43.0, 0]], [[1.0, 0], [-9.248232608409495, 0], [47.0, 0]], [[1.0, 0], [-7.107713527219246, 0], [53.0, 0]], [[1.0, 0], [-5.341621511206538, 0], [59.0, 0]], [[1.0, 0], [-1.8594809188097512, 0], [61.0, 0]], [[1.0, 0], [15.874050620548033, 0], [67.0, 0]], [[1.0, 0], [-11.98019927662212, 0], [71.0, 0]], [[1.0, 0], [8.70958062703977, 0], [73.0, 0]], [[1.0, 0], [-10.741717494378653, 0], [79.0, 0]], [[1.0, 0], [8.341202043761454, 0], [83.0, 0]], [[1.0, 0], [2.043282316392021, 0], [89.0, 0]], [[1.0, 0], [-2.4067458630561096, 0], [97.0, 0]], [[1.0, 0], [-14.232040424223648, 0], [101.0, 0]], [[1.0, 0], [-12.440313766087408, 0], [103.0, 0]], [[1.0, 0], [-6.759365168647144, 0], [107.0, 0]], [[1.0, 0], [8.191169673310574, 0], [109.0, 0]], [[1.0, 0], [-12.286071458459727, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 29, 'label': '2-4018-1.1-c1-0-29', 'leading_term': '1.496848847120725296299521508907', '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/4018/2/a/bn/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.4968488471207253, 1.490641891382721, 1.4719869080960302, 1.4407877564812663, 1.3969044530943042, 1.3401820562130136, 1.2704882839385887, 1.187757396624761, 1.0920375932913626, 0.9835391000128714, 0.8626802298163359, 0.7301289196973764, 0.5868375521393153, 0.4340692059108121, 0.2734138268178638, 0.10679314951599905, -0.06354646697126537, -0.23505380132599332, -0.40490531383011513, -0.5700503216719882, -0.7272683085391748, -0.8732375112910552, -1.0046135554714086, -1.1181165354775147, -1.2106245636319706, -1.2792714571390407, -1.3215459068338749, -1.3353891918384722, -1.3192882852446695, -1.272361052934966, -1.1944301947090397, -1.0860826262485093, -0.9487111618205605, -0.7845356374924821, -0.5966010157316342, -0.3887505330744701, -0.16557258692746837, 0.06767920545333712, 0.30519251901650113, 0.5407282573176494, 0.7677758355615147, 0.9797287893623419, 1.1700767650189146, 1.3326090781326767, 1.4616242483056099, 1.5521392639382952, 1.6000918368949586, 1.602528603264614, 1.557772140603887, 1.4655598251949953, 1.3271479592969813, 1.1453752642683617, 0.9246807578693044, 0.6710722003375972, 0.3920426812152211, 0.09643449456477482, -0.20574882828734387, -0.5035796432393638, -0.7854879379300632, -1.039581335863958, -1.2539952736921147, -1.4172637062441398, -1.5186993708270666, -1.5487716200091821, -1.4994691688110113, -1.3646348466933964, -1.140259633668634, -0.8247239156013128, -0.4189750223724487, 0.07336829755058445, 0.645991791514815, 1.2899469277212108, 1.9937996326989986, 2.743865789888878, 3.52452965880297, 4.318638257423525, 5.107961722305896, 5.873706841042335, 6.597068459090666, 7.259801410396746, 7.844794110901346, 8.33662407253504, 8.722075409293513, 8.990598959192873, 9.134696952050751, 9.150216199619864, 9.036536527773213, 8.796644536117174, 8.437086655631326, 7.967799750543567, 7.401822025222732, 6.754891581826508, 6.044944450162763, 5.291528093991371, 4.515150107492239, 3.73658488268848, 2.97616330292746, 2.2530718749161203, 1.584688060798566, 0.9859778590281302, 0.46897989724170336, 0.04239747560641054, -0.2886837858919566, -0.5229396651075929, -0.6628046854065586, -0.7143211295412666, -0.6868437748959828, -0.5926104255078207, -0.446194081639353, -0.2638578434158734, -0.06283814903494311, 0.1394145178824604, 0.32600593669500094, 0.4813468711958656, 0.5918478939790611, 0.6465297053625362, 0.637521416853208, 0.5604236287308665, 0.414518616180731, 0.20281633665645502, -0.06806797732536131, -0.3882014692265407, -0.7447759451371708, -1.1226870551681571, -1.5052261334017438, -1.8748549157613017, -2.2140290409295322, -2.5060333863602433, -2.735791069501231, -2.8906084526024878, -2.9608207489186085, -2.940306778102198, -2.826846917081355, -2.6223051203737295, -2.332623751962482, -1.9676285332230605, -1.5406497787870752, -1.0679748501091781, -0.5681549842003609, -0.06119694596943869, 0.432324065301761, 0.8921894702264233, 1.2994570598792492, 1.6373317368781457, 1.8919452049436647, 2.053006299121254, 2.114289316014441, 2.073935066914774, 1.934548110028774, 1.7030833182809693, 1.3905251454892746, 1.0113731686316627, 0.5829571976382789, 0.12461395995267438, -0.343235372976955, -0.8000621409825652, -1.2262137075230457, -1.6038547235003138, -1.9178189140011594, -2.156328160646354, -2.311541918274288, -2.379908255634843, -2.3622976566292366, -2.2639116808763813, -2.0939701108022284, -1.8651917162526235, -1.5930946445488237, -1.295152111705074, -0.9898469983624676, -0.6956746918784846, -0.4301467207952868, -0.20884818423166362, -0.04459961370070575, 0.05323120460718719, 0.07922954663141328, 0.03221808460356027, -0.08469144460344626, -0.2642834134782048, -0.4956515845621208, -0.7648191430644481, -1.0555324980605685, -1.3501858886822298, -1.6308260807357997, -1.8801813876199378, -2.082657227816372, -2.225241608818181, -2.298268298657133, -2.2959928270378334, -2.216946491569221, -2.06404571680658, -1.8444477789215425, -1.5691583221203944, -1.2524104505403248, -0.9108486622124928, -0.5625627116735966, -0.22602593336475718, 0.08100096344631427, 0.3425365424513038, 0.5453522252643739, 0.679793591151631, 0.7403979906197424, 0.7262680591741958, 0.6411743056837926, 0.49337540943235103, 0.29516133495017544, 0.06214092739481177, -0.18768868149002102, -0.43503968415005123, -0.6605358899956183, -0.8459496057858934, -0.9753991938129566, -1.0364338522897736, -1.0209369702242188, -0.9257884017591927, -0.7532387637039063, -0.5109647337430949, -0.2117924640875932, 0.12690438139938892, 0.48410591796304486, 0.8363020694564449, 1.1588423267679524, 1.4274049499631116, 1.6195020668470541, 1.7159325271118, 1.702094844106636, 1.5690782055567905, 1.3144601680018153, 0.9427547759345203, 0.4654736959651767, -0.09921548107337903, -0.727226538204831, -1.3896570214151267, -2.0542030994156844, -2.68681465969375, -3.2535025077963384, -3.7221983833087173, -4.064562873357531, -4.257636661526991, -4.285237023144467, -4.139013834585458, -3.819097018284568, -3.334289382410025, -2.7017840390683334, -1.9464125847233136, -1.0994574503465715, -0.1970876768197865, 0.7214997111674496, 1.6161319871710886, 2.447792876543713, 3.1807141761269877, 3.7843067531919563, 4.23481821336603, 4.516618662341402, 4.623036170241915, 4.556688695425958, 4.329287932518441, 3.960921173253419], 'positive_zeros': ['0.793638779721809011715806770660764', '1.86432434692561275170696201251708', '2.80920937528952476318077630752115', '3.49685184631228161865213151069973', '5.13466400802671422085680640157708', '5.60154649202820523686107656026119', '6.08189376341844310843262569159562', '7.06477445753757918107979231701991', '7.78306532727044050861006221863008', '8.753298513419200206822986736101747'], 'prelabel': '2-4018-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.664264429928257, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.793638779721809011715806770661', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.86432434692561275170696201252', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.80920937528952476318077630752', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 32.083891532150474, 'bad_primes': [2, 7, 41], 'central_character': '1.1', 'conductor': 4018, 'conductor_radical': 574, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4018/2/a/bn/1/3'], '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': '2-4018-1.1-c1-0-29', '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': '2-4018-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.664264429928257, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.793638779721809011715806770661', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1006056675478750730487431825491', 'Lhash_array': ['1006056675478750730487431825491'], 'label': '2-4018-1.1-c1-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4018/2/a/bn/1/3'}