-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '743323087831140882973529122143', 'a10': [8.740819988684676, 5.046514773405159], 'a2': [-0.36602540378443865, -1.3660254037844386], 'a3': [-0.8660254037844386, 1.5], 'a4': [-1.7320508075688772, 1.0], 'a5': [-5.046514773405159, 5.046514773405159], 'a6': [2.366025403784439, 0.6339745962155614], 'a7': [-1.3471526076397582, 5.027641977260479], 'a8': [2.0, 2.0], 'a9': [-1.5, -2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.125346062010316, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.36602540378443865, 1.3660254037844386]]], [3, [[1.0, 0], [0.8660254037844386, -1.5]]], [13, [[1.0, 0], [-12.921309358305395, -1.4282032302755092]]]], 'bad_primes': [2, 3, 13], 'central_character': '78.19', 'coefficient_field': 'CDF', 'conductor': 78, 'conductor_radical': 78, 'conjugate': '3682625916534639708535561757238', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.36602540378443865, 1.3660254037844386]], [[1.0, 0], [0.8660254037844386, -1.5]], [[1.0, 0], [5.046514773405159, -5.046514773405159], [0, -25.0]], [[1.0, 0], [1.3471526076397582, -5.027641977260479], [-42.4352447854375, -24.5]], [[1.0, 0], [7.32323314695208, -1.9622544077106392], [104.78907385791707, -60.5]], [[1.0, 0], [-12.921309358305395, -1.4282032302755092]], [[1.0, 0], [13.996790256941232, -8.08105062263575], [144.5, -250.28134169370276]], [[1.0, 0], [-9.876641792327352, -2.6464381921855904], [312.63517076618234, 180.5]], [[1.0, 0], [8.291907040780258, 4.787334762089834], [264.5, 458.12743860196804]], [[1.0, 0], [-16.587972596324434, 28.731211331394142], [-420.5, -728.3273645827129]], [[1.0, 0], [34.23120104545126, -34.23120104545126], [0, -961.0]], [[1.0, 0], [-63.22666715442229, 16.941534404138842], [1185.5887777808964, -684.5]], [[1.0, 0], [-14.096239289869088, -52.60788122544006], [-1455.7887037616413, 840.5]], [[1.0, 0], [40.74315186790725, -23.523069698570055], [924.5, -1601.280971597427]], [[1.0, 0], [-47.821385939524966, -47.821385939524966], [0, 2209.0]], [[1.0, 0], [-67.51768604542347, 0], [2809.0, 0]], [[1.0, 0], [19.491753878341118, -72.74421580259677], [-3014.634430573631, -1740.5]], [[1.0, 0], [35.25973117249081, 61.071645851974225], [-1860.5, 3222.4805274818964]], [[1.0, 0], [-11.184053917058764, -41.73945745305302], [-3887.5880375883453, 2244.5]], [[1.0, 0], [106.79677468585442, 28.61610953132326], [4365.634060477355, 2520.5]], [[1.0, 0], [36.838541395658716, 36.838541395658716], [0, 5329.0]], [[1.0, 0], [13.386692315262959, 0], [6241.0, 0]], [[1.0, 0], [-93.12370224766073, 93.12370224766073], [0, -6889.0]], [[1.0, 0], [-48.613739264439225, 13.026012176963652], [6859.787223376538, -3960.5]], [[1.0, 0], [52.541904107053284, 14.078560774278415], [8148.433024207783, 4704.5]], [[1.0, 0], [-19.5286188506842, -11.274853350344122], [5100.5, 8834.325144005059]], [[1.0, 0], [0, 109.38519081020277], [-10609.0, 0]], [[1.0, 0], [-16.437495470848226, 28.47057730469243], [-5724.5, -9915.124847928038]], [[1.0, 0], [150.08590798176704, -150.08590798176704], [0, -11881.0]], [[1.0, 0], [-59.39383563612256, -102.87314097815924], [-6384.5, 11058.278380923497]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-78-13.6-c2-0-0', '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/78/3/l/c/19/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.620548769730058, 0.503675133489871, 0.3807186778411329, 0.2491920835194357, 0.10648555903125148, -0.049939548914953086, -0.2223578961020091, -0.41259375852241015, -0.6218440020952982, -0.8505121161571011, -1.0980556892623683, -1.3628516718577066, -1.6420862699299597, -1.9316786563309476, -2.226249373676553, -2.5191450176930132, -2.8025303448988064, -3.0675572408789287, -3.304616977921177, -3.5036779133460714, -3.654705343050714, -3.748153836405387, -3.7755153565010877, -3.7298992459721054, -3.606613272333698, -3.4037090032478043, -3.1224504976259757, -2.7676633313604575, -2.347921946512091, -1.875537712245397, -1.366318207478184, -0.8390801039921674, -0.3149133444392237, 0.1837875906833527, 0.6344896853363029, 1.0158288067382044, 1.3089837837158669, 1.499026642198304, 1.5761477999681939, 1.536651134551685, 1.3836181873884101, 1.1271542610967602, 0.7841520085180047, 0.3775396615913051, -0.06498026101789581, -0.5126525881310662, -0.9337576260551858, -1.2979299041832555, -1.5785365529615256, -1.7549204173067166, -1.8143040637840315, -1.7531597054366717, -1.5778782137271683, -1.304617554022858, -0.9582749552990444, -0.5706036843035421, -0.1775783661258514, 0.18380516666980687, 0.4790369220292771, 0.6795934844180653, 0.766090251848129, 0.7307456145051155, 0.5788550686404308, 0.329045724272085, 0.012185268275964167, -0.3310534066309064, -0.6538310453573084, -0.9077050169375674, -1.0477149407591229, -1.0374985677841624, -0.8538991124921192, -0.49053289623261903, 0.04014752532408107, 0.7066362178730671, 1.4601720317723943, 2.2385151769503073, 2.9714451385117977, 3.5875124869781607, 4.021401520389999, 4.221143138306618, 4.154376618443514, 3.8129064672538173, 3.214938255024108, 2.404596752192615, 1.448611626217174, 0.4303720868796899, -0.5581327623849608, -1.4256943233149246, -2.0915901693166474, -2.494522440652297, -2.599723743370234, -2.403322585348244, -1.9333373579489312, -1.2470385212337785, -0.4248431570441842, 0.4386651573103141, 1.2456188196901643, 1.9063998429665454, 2.350436891632675, 2.5349096603421604, 2.4502104142893626, 2.1213759094794846, 1.6051853396939417, 0.9831647004477988, 0.35127648113339516, -0.1924659598412145, -0.560903199191773, -0.689474369935193, -0.5452188834790705, -0.1317666304466554, 0.5104530351432168, 1.3089295506490861, 2.1681949830516563, 2.9822112821773166, 3.6483946309855093, 4.081377101701402, 4.2245908808137855, 4.058016863295872, 3.600941667081082, 2.909252246643216, 2.0675726547363933, 1.1773028375879135, 0.3422422638199071, -0.3461260515397454, -0.8215205161072602, -1.0519725346060935, -1.0437513160685952, -0.8394488215544526, -0.5104550930928327, -0.14492853981348428, 0.16690537741637126, 0.3478299256996516, 0.3466748859251213, 0.14716863340463923, -0.22892582757871555, -0.7250363688632283, -1.2589939911661525, -1.7368612495558262, -2.069198271501344, -2.1871077094407996, -2.055340719124817, -1.680135606004168, -1.1102542570907894, -0.4307648561887024, 0.2496750822724893, 0.8161498879978718, 1.1666816974676173, 1.2301032386102448, 0.97950034935568, 0.4387283959814535, -0.3194298721940288, -1.1835408108625574, -2.0208729872730458, -2.6991991193603377, -3.1095366620660014, -3.185991126323863, -2.919179199541169, -2.360637065519141, -1.6170330069450387, -0.8346829578800876, -0.17653775662065468, 0.2048149981635477, 0.19376176447363197, -0.2666061160754615, -1.1614941223088069, -2.4026702041124635, -3.838723832358995, -5.27605659928029, -6.507497537929766, -7.344060462032705, -7.644706631334101, -7.339179491999255, -6.440029268491045, -5.0416850537659155, -3.3065761480962177, -1.440488674327957, 0.33881316337085626, 1.8344998897292633, 2.8996408335255173, 3.457410372593367, 3.5092508695069955, 3.129819513605449, 2.4498753562225435, 1.6303892740332193, 0.8326942086769749, 0.19014913184030643, -0.21356070732871682, -0.3556653262244275, -0.2732854988542123, -0.05068733588376064, 0.20239162334039282, 0.376842113987625, 0.3893675756579087, 0.2016175089564858, -0.17064545173303677, -0.6602514543965764, -1.1626991839057683, -1.558760553609743, -1.7409766980726085, -1.6385231221188454, -1.235146615226635, -0.5761893965234008, 0.2371241594182913, 1.0653745840824613, 1.7573446340753112, 2.1799650191090785, 2.2457552828002476, 1.9320337692330063, 1.287685210754174, 0.4257010979599896, -0.4974244314285493, -1.3116284199342654, -1.866698313948239, -2.0624455195990232, -1.86937702338644, -1.3353896444182218, -0.5767708303358833, 0.24501317838220543, 0.9562759305814897, 1.4072037006038247, 1.5036352868035745, 1.2277727615105722, 0.6431895259168767, -0.11734286013861345, -0.8791264008158297, -1.4625892614011933, -1.7225806804039323, -1.5816606520386725, -1.0501364774863673, -0.22815088468040798, 0.7112549697125299, 1.5552221896597678, 2.0939401998527125, 2.1646890078028838, 1.6879330303363613, 0.6877207193778864, -0.7083182116257837, -2.2899820196007465, -3.8027795125113286, -4.99608777984185, -5.671580445597905, -5.7220718394293275, -5.152724591402922, -4.080085376489553, -2.708937656828031, -1.2915544375447918, -0.07762803808752304, 0.7348487222037845, 1.0376227312903739, 0.831303146211245, 0.22169329835243048, -0.6057279110825672, -1.4275994987981593, -2.0317128674848326, -2.2627284803479144, -2.054768588372466, -1.4439606283926614], 'positive_zeros': ['0.58637852393815146177077860458714', '4.07782171265526942671399339259866', '5.48194545019363236179987928243606', '7.05929287176955074829966941921582', '8.004506963733916866823379855516144', '8.991646381230845683881086648886935', '10.67827587004579113226311145835180', '11.81135874209172499871172197024756', '13.07699273258995417750644189957167', '13.65420465080990901863736648426840'], 'prelabel': '2-78-13.6-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4578566671694155, 'root_angle': -0.5360013707210651, 'root_number': '-0.11286066360838728 - 0.9936108245233012*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.268000685361', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.58637852393815146177077860459', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.07782171265526942671399339260', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.48194545019363236179987928244', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.125346062010316, 'bad_primes': [2, 3, 13], 'central_character': '13.6', 'conductor': 78, 'conductor_radical': 78, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/78/3/l/c/19/1'], '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': '2-78-13.6-c2-0-0', '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': '2-78-13.6-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4578566671694155, 'root_angle': -0.26800068536053256, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.58637852393815146177077860459', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '743323087831140882973529122143', 'Lhash_array': ['743323087831140882973529122143'], 'label': '2-78-13.6-c2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/78/3/l/c/19/1'}