-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '989670196617008960583309549893', 'a10': [1.758266149674833, 0.9942853801083433], 'a2': [0.9033386153806949, 0.0], 'a3': [-1.7217998573143818, 0.18816283201571588], 'a4': [-1.1839793459620889, 0.0], 'a5': [1.946408710684692, 1.1006784866484653], 'a6': [-1.5553682990690516, 0.16997475213918706], 'a7': [0.0, 0.0], 'a8': [-2.876211493782124, 0.0], 'a9': [2.929189497295651, -0.6479574746330591], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.869004548564111, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.7217998573143818, -0.18816283201571588]]], [5, [[1.0, 0], [-1.946408710684692, -1.1006784866484653]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 7], 'central_character': '735.734', 'coefficient_field': 'CDF', 'conductor': 735, 'conductor_radical': 105, 'conjugate': '1701426485414142131483556646911', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.9033386153806949, 0], [2.0, 0]], [[1.0, 0], [1.7217998573143818, -0.18816283201571588]], [[1.0, 0], [-1.946408710684692, -1.1006784866484653]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 4.064373232612774], [-11.0, 0]], [[1.0, 0], [-2.88298107609703, 0], [13.0, 0]], [[1.0, 0], [0, -6.6686381961004635], [-17.0, 0]], [[1.0, 0], [0, -5.707013058977993], [-19.0, 0]], [[1.0, 0], [-1.631854630106873, 0], [23.0, 0]], [[1.0, 0], [0, -5.8970737295469595], [-29.0, 0]], [[1.0, 0], [0, 1.8706832337387331], [-31.0, 0]], [[1.0, 0], [0, 1.5997289456035335], [-37.0, 0]], [[1.0, 0], [-9.122440255968812, 0], [41.0, 0]], [[1.0, 0], [0, -7.533592604935644], [-43.0, 0]], [[1.0, 0], [0, -6.914461826375404], [-47.0, 0]], [[1.0, 0], [-1.51865003716415, 0], [53.0, 0]], [[1.0, 0], [0.9918503616767786, 0], [59.0, 0]], [[1.0, 0], [0, 6.164850089734321], [-61.0, 0]], [[1.0, 0], [0, 10.090268061057733], [-67.0, 0]], [[1.0, 0], [0, -4.812133961694693], [-71.0, 0]], [[1.0, 0], [0.5606186385317337, 0], [73.0, 0]], [[1.0, 0], [-3.7984752549010783, 0], [79.0, 0]], [[1.0, 0], [0, 4.004312514398473], [-83.0, 0]], [[1.0, 0], [-10.41094954388796, 0], [89.0, 0]], [[1.0, 0], [14.53702367471545, 0], [97.0, 0]], [[1.0, 0], [13.797338500569476, 0], [101.0, 0]], [[1.0, 0], [8.313585134440881, 0], [103.0, 0]], [[1.0, 0], [-10.737072925813342, 0], [107.0, 0]], [[1.0, 0], [-0.5366751731160411, 0], [109.0, 0]], [[1.0, 0], [-12.102849975863059, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 23, 'label': '2-735-105.104-c1-0-23', '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/735/2/g/c/734/22', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.3942200046018847, 1.259464270408672, 1.099230305869327, 0.9073761261347264, 0.6771939904495936, 0.40357341056216284, 0.08491858368741712, -0.27537333648673096, -0.6679575357129883, -1.077161537723491, -1.481235741871531, -1.8532907577861393, -2.162951230754513, -2.3786977958250546, -2.470785571999595, -2.4145312103217944, -2.193666059281077, -1.8033771976105903, -1.2526175284534695, -0.5652752644245108, 0.22013827708857334, 1.052493000214272, 1.871760744693365, 2.6142516313252036, 3.2189276827672444, 3.6341388452839674, 3.8239681298849013, 3.7733072353904786, 3.4908382905641684, 3.0092833435135193, 2.382593666305219, 1.6801567690321233, 0.9785502985790805, 0.3518027382070991, -0.1385424485841601, -0.4520893003336968, -0.5755511731912165, -0.5248665512673679, -0.34283011883880826, -0.09227534560726691, 0.15440615280977046, 0.32792142740398667, 0.3748976664738122, 0.2686260151045362, 0.015627263387926228, -0.34352528696235685, -0.7398093632289133, -1.0873602845430368, -1.2995018768603914, -1.3066292970551447, -1.0727453083751384, -0.6073556806738158, 0.030055128199755428, 0.7346464610804229, 1.3700780893416318, 1.7899982991202668, 1.863939317274571, 1.503218756531185, 0.6819900344095698, -0.5509833650352115, -2.0729265455588948, -3.701064978634525, -5.218636098796021, -6.409081739877951, -7.092724707161999, -7.159303917666886, -6.59003194225106, -5.464393700134388, -3.9495191911954635, -2.2731954213368657, -0.6848274697231563, 0.5887421715445708, 1.384270121347475, 1.6319310944105303, 1.367709039912516, 0.7253823770221086, -0.09086410055003037, -0.8481752354570897, -1.3329531189575565, -1.395262755664017, -0.9804329206802397, -0.14099357915843624, 0.9739218499500938, 2.1498304202497263, 3.1524268208867348, 3.777750311806229, 3.8961354076970935, 3.480247992019235, 2.610872648821979, 1.4589996719606177, 0.24809306468383957, -0.7950140284671605, -1.489440217666416, -1.738475171930997, -1.54787948187936, -1.020089173451838, -0.3258762686078557, 0.3395302332007883, 0.8050223312435211, 0.9648220296829287, 0.8020143049901262, 0.38848976389860734, -0.13862720837129303, -0.6178824136472247, -0.9108908363047188, -0.9434473994472257, -0.7289335137051741, -0.36704930220917154, -0.017371969483285777, 0.14589961472856058, -0.013780016351411541, -0.5502896379934499, -1.4101038979341394, -2.4359820497229983, -3.3999057054999815, -4.058151582439231, -4.214953736543789, -3.7781019185181877, -2.791052308497744, -1.4315857386168338, 0.024523952972336255, 1.2671032589877786, 2.0270679840802406, 2.144576571401025, 1.6117453769102281, 0.5778640313270715, -0.6854265381417355, -1.850967352078255, -2.618132989452477, -2.7887995480031798, -2.3170631699339803, -1.319206478500488, -0.040944028111303814, 1.209413511475967, 2.1437512225963316, 2.5701263763019315, 2.440798149962735, 1.8588233405765149, 1.0413782137330256, 0.2504035515904474, -0.28915670000919785, -0.45922552950119305, -0.2852452823697791, 0.0723751185353673, 0.37080967375013285, 0.3668346635592997, -0.0957319838498759, -1.019987432688517, -2.233025782912295, -3.416100897186444, -4.182549317860349, -4.1837163125129635, -3.213808273360476, -1.2833368370013385, 1.3616791128478658, 4.2831710656616, 6.948157765907642, 8.855142393142508, 9.656398741698105, 9.243076111817926, 7.769746812948885, 5.611506951180981, 3.2653786161774803, 1.223192987944751, -0.14913904086786833, -0.693326884739598, -0.4803455002935998, 0.2314476847803646, 1.0869083039531748, 1.7449988629889672, 1.9766738433627784, 1.7216293541424799, 1.0893317611547448, 0.3073663592694146, -0.36365939796920715, -0.7197021182563679, -0.6781225830874382, -0.2976589113051513, 0.2511398005411995, 0.7530116869685647, 1.0281913562824403, 0.9972660020449134, 0.7078840799656176, 0.3140127581480248, 0.015208402112630566, -0.022305206686366867, 0.2659519052685653, 0.8104528932528225, 1.4249594916585595, 1.869387591534931, 1.937591484498465, 1.539349542557491, 0.7461718228905251, -0.2183464885304552, -1.044380394882425, -1.4388223581599155, -1.2318117851885753, -0.4497060523261257, 0.6736589951091171, 1.7563301842358388, 2.3836272648830445, 2.2449543125845204, 1.2478651118586115, -0.4300977078806906, -2.3731533700736462, -4.037800246956341, -4.911324847621446, -4.670406343951297, -3.2896530534435606, -1.0638337672970444, 1.466277426561659, 3.664275691849549, 4.979952006585649, 5.107010877957899, 4.0679536399454985, 2.199970952680353, 0.04687654211706507, -1.808154146963537, -2.9157368732093385, -3.084810345768211, -2.4205929829939747, -1.2668575401495035, -0.0749344356056707, 0.7544983546356209, 1.0029067788550234, 0.6951957147142697, 0.07241817283316959, -0.5114744957381653, -0.7300114296011433, -0.4105540175725213, 0.3987571341488421, 1.4450627637611522, 2.3634194620386935, 2.8119456607689077, 2.6000429087060586, 1.7626639826853183, 0.5529927967244231, -0.6446067349949292, -1.4504921482843889, -1.6255484150142092, -1.1574822014551267, -0.2656572391183595, 0.6782129993462527, 1.285632759134348, 1.2944882036142478, 0.6678169410216326, -0.3882706789932468, -1.4950066536048365, -2.235209390112912, -2.3034490115250867, -1.6180401881141846, -0.3542161684044794, 1.11382627699641, 2.3413483694565533, 2.9657352981231235, 2.828464659026842, 2.0228433653767017], 'positive_zeros': ['0.78071212717355042395536443365968', '2.46607569338126127032676182817293', '4.21015215750301770779993251881157', '4.91960982918596494997159263218275', '5.50613996065507503794445161791635', '6.49455637363522219523233914068709', '7.32355678411049488845248228785368', '8.812166034336102150520445074095063', '9.486289922181187083616511300426021', '10.14215259670028953302245313985822'], 'prelabel': '2-735-105.104-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.422602845817719, 'root_angle': -0.16039363191635433, 'root_number': '0.5337369138710983 - 0.8456505819612233*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.160393631916', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.78071212717355042395536443366', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.46607569338126127032676182817', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.21015215750301770779993251881', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.869004548564111, 'bad_primes': [3, 5, 7], 'central_character': '105.104', 'conductor': 735, 'conductor_radical': 105, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/735/2/g/c/734/22'], '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': '2-735-105.104-c1-0-23', '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': '2-735-105.104-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.422602845817719, 'root_angle': -0.16039363191635433, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.78071212717355042395536443366', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '989670196617008960583309549893', 'Lhash_array': ['989670196617008960583309549893'], 'factors': ['2-735-105.104-c1-0-23'], 'label': '2-735-105.104-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/735/2/g/c/734/22'}