-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3540235527401457536557761487695', 'a10': [-0.21209833929354477, 1.0234561546972942], 'a2': [-0.18625644421436163, -0.09490239845955661], 'a3': [1.7107263879541725, 0.2709524415045372], 'a4': [-2.3254560113918914, -3.2007156109308066], 'a5': [-1.3186840569563867, -4.822973393864935], 'a6': [-0.2929197774767694, -0.21281867563073983], 'a7': [5.113194739828776, -5.113194739828776], 'a8': [0.2601801311661406, 1.6427126972385715], 'a9': [2.853169548885461, 0.9270509831248422], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.043601982702227, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.7107263879541725, -0.2709524415045372]]], [5, [[1.0, 0], [1.3186840569563867, 4.822973393864935]]]], 'bad_primes': [3, 5], 'central_character': '75.58', 'coefficient_field': 'CDF', 'conductor': 75, 'conductor_radical': 15, 'conjugate': '1696607867996699193191441717761', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.18625644421436163, 0.09490239845955661], [2.3511410091698925, 3.23606797749979]], [[1.0, 0], [-1.7107263879541725, -0.2709524415045372]], [[1.0, 0], [1.3186840569563867, 4.822973393864935]], [[1.0, 0], [-5.113194739828776, 5.113194739828776], [0, -49.0]], [[1.0, 0], [-3.215307618954492, -9.895699325810403], [-97.89105631936864, 71.12201552738925]], [[1.0, 0], [-3.7835461598838656, 1.9278130577977466], [99.33570763742796, -136.72387204936612]], [[1.0, 0], [11.449606968485726, -1.8134395916395223], [274.8553332092994, -89.30591137435981]], [[1.0, 0], [-18.475279692403163, 25.429040944271936], [-111.55513496935602, -343.33140238255044]], [[1.0, 0], [16.0059762486984, -31.413497136561396], [-310.9383984627183, -427.96999002434717]], [[1.0, 0], [-21.7753539169067, -29.971203443091532], [-259.8832922693308, 799.8385302042242]], [[1.0, 0], [-33.960959103554195, -24.67408108058294], [296.9653315943245, 913.9653121596426]], [[1.0, 0], [7.7369157383524225, 15.184552108298602], [-804.6780103883957, 1107.544265299303]], [[1.0, 0], [-10.414906737028245, 32.05378700576746], [-1359.9575675442866, -988.0670091036474]], [[1.0, 0], [4.349659940398333, 4.349659940398333], [0, 1849.0]], [[1.0, 0], [-7.650131425755561, 48.30102887682732], [-2100.8838444959943, -682.6185405742589]], [[1.0, 0], [-20.9646519207133, -3.320474661060891], [2671.517754273086, 868.0287371992273]], [[1.0, 0], [31.217007267197914, 10.143020518558375], [2816.188157419192, 2046.080463230099]], [[1.0, 0], [-28.93911850227724, -89.06544859482244], [-3010.3522360691795, 2187.1489237802925]], [[1.0, 0], [122.48236375476081, -19.399300632924064], [4269.292701648945, -1387.177287749139]], [[1.0, 0], [-24.039398062623288, 17.4656450401455], [1557.7546686441099, -4794.275898643869]], [[1.0, 0], [-17.16633409845249, 33.69082764263415], [-3132.3076094665894, -4311.251563024095]], [[1.0, 0], [5.941264194440423, 8.177448621970528], [-1928.575061894047, 5935.543718198053]], [[1.0, 0], [10.743853780398195, 67.83402307943629], [-6551.828340757313, 2128.8180742490126]], [[1.0, 0], [86.36638109107652, -28.06213830884801], [6408.223612443959, -4655.84698340868]], [[1.0, 0], [13.503685847217543, -85.2589169715657], [-8948.4907618211, -2907.5409000738805]], [[1.0, 0], [73.97410041144198, 0], [10201.0, 0]], [[1.0, 0], [125.18792073272114, 19.82781876064445], [10089.758581375285, 3278.3612933238173]], [[1.0, 0], [120.65198517241849, -120.65198517241849], [0, -11449.0]], [[1.0, 0], [-35.100017313306466, -11.404686963209292], [9611.93091016875, 6983.476582486874]], [[1.0, 0], [-146.44904244761597, 74.61951418115021], [7505.429886522589, -10330.338001173704]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 8, 'label': '2-75-25.8-c2-0-8', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/75/3/k/a/58/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.275281336134181, 1.3508121244854228, 1.4270065251854058, 1.5040808304060103, 1.5814830121851047, 1.6578982579794894, 1.7312909764504205, 1.7989772265827821, 1.8577230672116425, 1.903866904086879, 1.9334661573136331, 1.942469621995563, 1.9269164827853402, 1.8831612136232372, 1.8081208795073254, 1.6995380303934349, 1.5562487921774324, 1.3784422461686339, 1.1678940664926503, 0.9281549757453914, 0.6646732054799127, 0.3848301206729681, 0.09786976196941957, -0.18529351409499514, -0.4523997496330689, -0.6903036259257561, -0.8855643962919706, -1.0251493266278449, -1.0972233328005145, -1.0919863591664711, -1.0025097917171701, -0.8255148624174524, -0.5620306337094758, -0.21786775576402895, 0.19615239102502843, 0.6642647405003264, 1.166160926289292, 1.6777403968751925, 2.172205316414437, 2.6214647403009046, 2.997784609001724, 3.275592080260078, 3.4333182213210733, 3.455144818108971, 3.332511598789197, 3.065241676785881, 2.6621569665442206, 2.141082241941732, 1.5281757698150757, 0.8565741656421338, 0.1643961090626282, -0.5077905140709981, -1.1198758483700504, -1.6352779080658644, -2.0239274492631667, -2.264903451274822, -2.3484608111351517, -2.2772229272286397, -2.066367869897454, -1.742715163586328, -1.3427155760572145, -0.9094510617077739, -0.48885657504191604, -0.12546917622553821, 0.14191809433354585, 0.2842794293873883, 0.285636633267241, 0.14521801093872305, -0.12179859860502806, -0.4851304129283815, -0.9018421871089278, -1.3202600270970866, -1.685034522794567, -1.9428953535728035, -2.0485311975300506, -1.9699734074654411, -1.6928704421116747, -1.223117158427426, -0.5874460399473418, 0.16821435579544813, 0.9825730235392077, 1.7847128858076895, 2.5012065207023118, 3.063896792500637, 3.41750574414628, 3.5262016001017398, 3.3783197195410843, 2.9885985088030718, 2.3975432191942807, 1.6678451625695985, 0.8781274756600254, 0.11462122361004562, -0.5383442988415538, -1.0079639649050913, -1.241550037037357, -1.2130226121448646, -0.9264293253247103, -0.4159520739643789, 0.25772961478161893, 1.0143984310754117, 1.7638287814184368, 2.4167733195457832, 2.8960604495781466, 3.1463868647645747, 3.141501443843699, 2.887766541844009, 2.423520967072143, 1.8142048673698974, 1.1437730491930664, 0.5034443741274071, -0.020763016913439774, -0.3600395062585007, -0.47266309975686854, -0.3503097851719779, -0.01979844710393846, 0.4601231635137004, 1.0066593151578902, 1.5245475428778659, 1.9198076874648091, 2.1137552063260383, 2.055262573910914, 1.729427087965197, 1.1612533747123457, 0.41363148660634835, -0.42030182010103573, -1.2295032669742827, -1.9004224027808427, -2.3333047108022043, -2.4570301951555518, -2.240251884842305, -1.6970721129810473, -0.8862515199839135, 0.09611664655362494, 1.1295519227421762, 2.085958360835266, 2.8477946184754686, 3.3249314631516644, 3.4676123006717106, 3.2734644906133483, 2.787378952350713, 2.094158495358843, 1.3049678331754109, 0.5396219592475074, -0.09254069697492144, -0.510162772582741, -0.6729019951549563, -0.5878029470501134, -0.3078476594582416, 0.0772202677238968, 0.45642731680564547, 0.7169982720686181, 0.76450789056384, 0.5403755756239945, 0.033674275696345506, -0.7149039188999468, -1.6178207221146064, -2.5536447376231326, -3.3862211487093568, -3.9869786779590775, -4.256668576708484, -4.142818555964948, -3.6498099674708224, -2.8396632261775223, -1.823159773852478, -0.7425835902302587, 0.2511527093942537, 1.0231870984101203, 1.4769718182778038, 1.570217002384976, 1.321621098395292, 0.8070450309743712, 0.1456183924962765, -0.5219380532908423, -1.059049974335798, -1.358549615404612, -1.3628977778897096, -1.0756033452074796, -0.5615736748992616, 0.06392140914658401, 0.6559278853728092, 1.0665820199266205, 1.1732289665806013, 0.9027614227296976, 0.2476093256044326, -0.7297810258849271, -1.9051144140526513, -3.1119085057041733, -4.169362207115518, -4.913559054270682, -5.226410680537471, -5.057039019068631, -4.431577575408568, -3.4494267794289493, -2.266459889937735, -1.0680916423101008, -0.03703630616625931, 0.6783767465424171, 0.9895082034328044, 0.8816592052984471, 0.4146393417713812, -0.29040209247139254, -1.0753231846655866, -1.7758084808248782, -2.252695181917785, -2.417732444959299, -2.2487799255214056, -1.7915275370527508, -1.1474951078714741, -0.45082538170967484, 0.1613332663215141, 0.5787146314373846, 0.7418387888791481, 0.6548408843230658, 0.3843630246735866, 0.04451335288964954, -0.2291749401998323, -0.31146095103767624, -0.11811969466028258, 0.3709931231498413, 1.1018067966847176, 1.9515687147979852, 2.7495962484469594, 3.3096016661820395, 3.467396553409736, 3.1164306737195364, 2.2337809731372786, 0.8908923749214419, -0.7537189811941539, -2.4790212068033366, -4.038990874597158, -5.206086210202737, -5.812282851163071, -5.779596560099347, -5.133979635721903, -3.999722080816943, -2.575370165535446, -1.0959024088273064, 0.21129933124094824, 1.1678740115162856, 1.6750316042685451, 1.727222993819249, 1.4064528440549235, 0.8588232254303944, 0.25863761757376125, -0.23198810722539667, -0.4991422505294334, -0.5008914969972996, -0.27365828525469627, 0.08008926562387172, 0.41994463908937657, 0.6049946712124233, 0.5319192374734197, 0.1648245109001078, -0.45040042629136656, -1.1910331732594626, -1.881286681982359, -2.3301016428934975], 'positive_zeros': ['2.79275340284149993610176549620286', '4.19312299970740479883245216187366', '6.27994617627242077039760486857020', '7.927291670019961255215638880505833', '8.449363931700458395552849376418528', '9.848363430368325872947122346278028', '11.39511397709659921766262347289864', '12.20479551244662203551713857162586', '13.74417519405202052644255813949156', '14.25588006824901896100210469900833'], 'prelabel': '2-75-25.8-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4295460757534983, 'root_angle': 0.3600899173994717, 'root_number': '0.4255236755587179 + 0.9049472921330828*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1800449587', 'prec': 40}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.79275340284149993610176549620', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.19312299970740479883245216187', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.27994617627242077039760486857', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.043601982702227, 'bad_primes': [3, 5], 'central_character': '25.8', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/3/k/a/58/5'], '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': '2-75-25.8-c2-0-8', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-75-25.8-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4295460757534983, 'root_angle': 0.18004495869973586, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.79275340284149993610176549620', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3540235527401457536557761487695', 'Lhash_array': ['3540235527401457536557761487695'], 'label': '2-75-25.8-c2-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/3/k/a/58/5'}