-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1045.388', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.20791169081775934, -0.9781476007338057], 'a3': [0.4067366430758002, -0.9135454576426009], 'a4': [-0.9135454576426009, 0.4067366430758002], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.9781476007338057, -0.20791169081775934], 'a7': [-0.5877852522924731, 0.8090169943749475], 'a8': [0.5877852522924731, 0.8090169943749475], 'a9': [-0.6691306063588582, -0.7431448254773942], 'algebraic': True, 'analytic_conductor': 4.852959597730739, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]], [19, [1]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.388', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': 'dirichlet_L_1045.202', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^43', 'a^49', 'a^26', 0, 'a^32', 'a^21', 'a^9', 'a^38', 0, 0, 'a^15', 'a^53', 'a^4', 0, 'a^52', 'a^37', 'a^21', 0, 0, 'a^10', 0, 'a^35', 'a^58', 0, 'a^36', 'a^27', 'a^47', 'a^56', 0, 'a^18', 'a^35', 0, 'a^20', 0, 'a^4', 'a^51', 0, 'a^42', 0, 'a^34', 'a^53', 'a^55', 0, 0, 'a^18', 'a^29', 'a^41', 'a^42', 0, 'a^26', 'a^19', 'a^53', 'a^10', 0, 'a^30', 0, 'a^39', 'a^16', 0, 'a^32', 'a^1', 'a^59', 'a^18', 0, 0, 'a^35', 'a^3', 'a^24', 0, 'a^22', 'a^47', 'a^31', 'a^34', 0, 0, 0, 'a^25', 'a^28', 0, 'a^16', 'a^17', 'a^27', 'a^36', 0, 'a^38', 'a^45', 0, 'a^20', 0, 'a^14', 'a^1', 'a^7', 'a^12', 0, 'a^24', 'a^43', 'a^25', 0, 0], 'euler_factors': [[1, 'a^43'], [1, 'a^49'], [0], [1, 'a^21'], [0], [1, 'a^53'], [1, 'a^37'], [0], [1, 'a^35'], [1, 'a^56'], [1, 'a^18'], [1, 'a^51'], [1, 'a^34'], [1, 'a^55'], [1, 'a^29'], [1, 'a^53'], [1, 'a^16'], [1, 'a^32'], [1, 'a^35'], [1, 'a^22'], [1, 'a^31'], [1, 'a^28'], [1, 'a^27'], [1, 'a^20'], [1, 'a^43'], [1, 'a^8']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1045-1045.388-r0-0-0', 'leading_term': '-0.262036703239938716342069942012-0.477918557097529713712454380877*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/1045/388', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-0.545040715050757, 0.17705827451718337, 0.8679974206872868, 1.1482874957928757, 0.6954660327404331, -0.21776301140689147, -0.8655159977237036, -0.7180100291480012, -0.014585193245461061, 0.3606489208386078, -0.2551369037132142, -1.4464639180583567, -1.8297376753624937, -0.2958430775208385, 2.6551285935040965, 4.916883559846144, 4.466137349626053, 1.3571323536272397, -1.9837683650170441, -2.7620368926214605, -0.41298144920889973, 2.7628098917083705, 3.732912075779276, 1.637180381237001, -1.4664610102678062, -2.802403670890165, -1.7034792658467899, -0.046334647806556765, 0.0957144404564132, -1.1436560086109155, -1.7364832244908812, -0.378144432076045, 1.7581011003019067, 2.306043195960995, 0.5369690166749225, -1.7046723754486748, -2.149070536924845, -0.7260517544982731, 0.5581857277589993, 0.27023053106404854, -0.7198926703951111, -0.668766784477886, 0.4233053055005484, 0.698481231541093, -0.774900568525989, -2.0961151547521664, -0.5733169214206507, 3.414561592965067, 5.883782922808026, 3.525757446010272, -1.9797507092854492, -5.161359516814278, -2.6200544796419223, 3.1732515731880415, 6.678237955884262, 5.333029992166797, 1.7210724947621492, -0.23247753033047736, 0.19026653561223672, 0.7124723971056948, -0.11437653565705229, -1.0907264970341237, -0.7057335395931266, 0.2996840948799129, 0.10399425517221542, -1.1492039621240508, -1.2769453471174634, 0.6017837227249425, 2.2591622158251496, 1.1953113701075937, -1.6280788215913118, -2.7476113120318613, -0.9736823240699898, 0.7214085044713231, -0.713814638923324, -3.8130075819454294, -4.181703302210746, -0.5045348980544699, 3.314414953330274, 3.132106231490274, -0.02383934224687747, -1.5969599116315971, 0.12715672219017854, 1.8789785253817846, 0.3983444126450993, -2.6986144262578584, -3.1591409121862633, -0.14413674499312348, 2.5997748826587572, 1.9559307832056965, -0.5698673449173643, -1.5320215983944276, -0.49042272012865523, 0.04279864974077839, -1.0488242358920346, -1.8722321351409517, -0.8976293905076574, 0.4357780102941842, 0.1866096911764583, -0.6993835832557956, 0.06924366352030466, 1.958963454319292, 2.035925661254689, 0.17597652760080218, 0.7350012031198856, 6.606140465251999, 13.550407958363873, 13.986845322626888, 6.4322404013550605, -2.1054394860099275, -4.452761130018833, -1.2962285489757654, 1.3744121197218067, 0.7395483730047406, -0.4963004938797554, 0.23296049722204515, 1.3401948855040091, 0.39911544527756504, -1.5103940253047121, -1.6467713484441653, -0.2065309689041499, 0.18583941565360856, -0.8248023146953368, -0.5490757907675661, 1.9916618327618467, 3.703238958365799, 1.879218427076779, -1.373571736208609, -2.094196172786114, -0.4128808485304447, -0.006413873793853357, -1.913628841317816, -2.845293463069457, -0.9062783003203809, 0.7755839098145053, -0.9271571195344321, -3.2531400051489694, -0.986528021097722, 5.176565778764337, 8.456496262104368, 5.22171584511459, 0.1320332552231112, -0.5526572541526124, 2.5119991412557514, 3.7956817122699116, 1.5229731749598798, -0.4471570996488923, 0.6452918621784276, 2.443166406078405, 1.9106033922209378, 0.0916529462912212, -0.36604781720949675, 0.2025317659460688, -0.23248855448362982, -1.2089748089941617, -0.6837673280668799, 0.6189221769174675, -0.06626229454536971, -2.142729540902625, -1.402883837107512, 3.046274787542427, 5.838332515022355, 2.7567054900509884, -2.1622737286484237, -1.7221249252336266, 3.8856172973786083, 7.152287715456711, 4.1317985107343, -0.3166243683353565, -0.3847696043624751, 2.460625813094551, 3.0668063667105736, 0.9240368406776549, -0.20528604712629103, 0.699961923193188, 0.7765467170440361, -0.7653898354154112, -0.8145113044377191, 1.878856368571965, 3.696671071262575, 1.7067366616726023, -1.4329528749253426, -1.6442504115326337, 0.30871142279406255, 0.8283890985834028, -0.255788846810724, -0.17228557994606625, 1.0035580461232032, 0.25323719056759986, -2.3524544482737983, -2.8701777642819515, -0.4136928730669015, 0.42909177820491756, -2.644097887289507, -4.3309299239807, 0.7038509807413984, 8.334343100114582, 9.53516967303964, 3.2129718803898983, -2.279780037657388, -1.2113693149883185, 2.44797733782582, 2.603477424405164, -0.06769230194428758, -1.1362120883992957, -0.09878575361785129, 0.27579581215048327, -0.22068971451767477, 0.507410287518437, 1.9383993176154206, 1.4853001231129401, -0.32866351253873205, -0.298824452788479, 1.5516988765936737, 1.6854871657469424, -0.2667963844059036, -0.06370485609982098, 3.579712077259832, 5.511624657711057, 2.1682950984100824, -1.7961556129927356, -0.3460009238589178, 4.145678463685233, 4.567836595225408, 0.45889716459191243, -1.6599044609072269, 0.8250044775038954, 2.9500338651663287, 1.2271392561000767, -0.7252812683814166, 0.7269187167215103, 2.5558012437549333, 0.5897518443265498, -2.860073962692173, -2.8032624480076, 0.061708322596609994, 0.9670692344198375, -0.746504144388899, -1.3442213675431378, 0.10003844316187901, 0.4481618787466487, -1.1688977459775343, -1.7120943735766425, -0.13153781830760974, 0.727621866232209, -0.16400063723568475, -0.036042459645454175, 1.6551678427122911, 1.2563056087139648, -1.4762920298290416, -0.0722322722675122, 8.693996308823316, 16.809377133621805, 14.46441081923026, 4.22468372476316, -2.369351639891425, -0.8191082485487684, 2.2683570163516382, 1.3528588324904178, -0.6433352596417037, 0.2227973772414041, 1.8853193527697616, 1.1587922461962636, -0.3096829005442755, 0.08572840166595926, 0.746838197236477, -0.5183384304998264, -1.7438810386539503, -0.6590681058000829, 0.39022695433334714, -1.254260835818315, -2.7056719399862166, -0.024449576417118125, 4.1807052637188455, 4.3149307967065225, 1.0074893504771987, -0.39065298024365935, 0.7099162951423023, 0.036314778927954317, -2.280135421871751, -0.9599166298917301, 4.207458159424043, 6.016915527610097, 1.2409921969042441, -3.5803482350944766, -2.644705278043182, 0.06068114957958693, -1.499525207854179, -4.854095480528892, -3.8984558892257697, 0.20033120860982057, 1.3167067198581366, -1.0981994622526676, -2.0119941081103256, -0.05571922883910205, 1.0283593525960777, -0.08452304269435582, -0.5727893490496896, 0.3729048712911558, 0.365039890116725, -0.6649839837397777, -0.2566523677434495, 0.7792774552424457, -0.8129730981524352, -3.446268225408491, -1.8598945930772415, 3.0005992372321337, 3.7485943881457326, -0.9239728879489484, -2.4327605729601482, 4.07868531274668, 10.815681982573615, 8.957698700181773, 2.0174933865173554, -0.7051655068657463, 1.5827955598036116, 2.5624308397297524, 0.6202050536866868, -0.21477005654276635, 0.8856031803862299, 0.781540125799225, -0.3593749195992385, 0.7055348668098491, 3.045742521146831, 2.389508825295911, -0.7211257575655382, -1.2874395052275087, 1.24850276452579, 2.1446726942473493, 0.1378886898619783, -0.7157572168946014, 0.8188854447647183, 1.094935344801553, -0.643417546269561, -0.5124366408466134, 1.7744197058942561, 1.3159710016625397, -2.41504646433688, -3.218374015051266, 0.6678653537887659, 2.1999205669093054, -2.162567198772609, -4.825315871516959, 0.814194193608995, 8.549788855478843, 8.596472246611027, 2.4090786875778547, -1.2283310196296449, -0.2146397359920597, 0.5176705878249164, -0.5545519610087791, -0.36358851642544393, 1.1793523642999932, 1.0758846619572622, -0.2828001484404508, -0.03218021307211592, 1.0268498241154091, 0.21086246065131514, -0.951259964787928, 0.4355809948294294, 2.009769354568646, 0.16645865260851778, -1.9030429427397706, 0.9150356634343824, 5.075830189312685, 2.8733169000174223, -3.7835396059091044, -5.220137914794616, 0.231021284252507, 3.786223398053632, 1.134057887484914, -1.6876594174081765, -0.4003044712727556, 0.6531295018595602, -1.7468191503204757, -3.262675736815289, -0.7411261104734348, 1.5926982688814073, 0.32488182035544855, -0.9271110682394389, 0.8828012771148087, 2.1282972907029243, -0.21616718273376953, -2.4457953312594163, -1.0768738463890115, 0.864581532101659, 0.13394398083780232, -0.7504319094242137, 0.731336540403622, 1.909730872299281, 0.710789526556461, -0.11485643514977542, 0.5627742887652176, -0.8594806766612957, -4.309810627529667, -3.2862334399969115, 3.1673644004853996, 5.152587662830234, -3.173690454432215, -12.315475995494861, -10.873253664810315, -2.4358069787174874, 1.7294407696077674, 0.1725141963640252, -0.1978784174094568, 1.9927250248266517, 2.081164081614973, -0.23255241871195376, -0.7987037153935085, 0.5209437079478475, 0.4619615241561361, -0.5952230529041717, -0.23752330489670948, 0.08206410159851861, -1.6196819051267148, -2.2085865401976803, 1.1563333389071322, 4.205232046278082, 2.2439696352657466, -1.0669126004219898, -0.22315903604367252, 2.0017967688174734, 0.37120415288584274, -2.2094470930043153, -0.342466236311493, 2.637860489333905, 0.4173666206259822, -3.7425532845625087, -2.1659794255867175, 3.1550834948946767, 3.9274234453447043, 0.13779677397492965, -1.1356829100266495, 0.7034875512289377, -0.10531542721436096, -3.325391319784164, -2.8091193083230244, 1.464427840157356, 2.963599954422657, 0.2589194842660666, -1.4440388111112012, -0.3426996103285411, 0.19687366442054938, -0.5069991930382084, -0.00420720236706659, 0.8385044956608658, -0.48270992611809377, -1.8739747673181946, -0.3523934635840777, 1.2516821558495455, -0.09998891015799635, -0.07511716688921197, 5.073615764391615, 8.550504403318659, 2.9109520085786373, -5.271279127714217, -4.111319483754561, 4.22344326202719, 7.126813764761716, 1.8351681283931809, -2.4017962256472276, -1.1170906125931148, 0.5209565015504238, -0.3642839850614637, -0.5112742681141859, 0.7658434392663311, 0.302438959414339, -1.2527789266160687, -0.47509678356335494, 1.0285854405665735, -0.6913536877802365, -3.4135669030765854, -2.3402949400082242, 0.5987277140828597, 0.5001413008165957, -1.0212422639498697, 0.27302997208160007, 2.0980278856502332, 0.29471060578024, -2.115832994785931, -0.5653335510168083, 1.7451380514482633, 0.38252963319084937, -0.7084505643805736, 2.978871204921155, 5.9739250724562, 2.042795591908206, -2.976208777487184, -0.44038692672537194, 5.447583070818186, 4.7635449250103665, -1.0330343874776986, -2.7866403613007265, 0.2758943880422179, 1.416312493382194, -0.49686404272522533, -1.0121130663698448, 0.05876286694733298, -0.3605003825195481, -1.133189646680504, 0.32026759664737453, 1.8198554361161265, 0.811373200337727, -0.232216695061361, 0.599132313472552, 0.4609022526724146, -1.009339237387032, 0.9421391383832398, 5.707239099124191, 4.8621784100240015, -3.128200977615591, -7.587669208660452, -2.6709464805812955, 2.7173839477953847, 0.6272165691023582, -3.0189895744865414, -0.8325028182005231, 2.9327347299547273, 1.9423139925563606, -0.6205439674584476, 0.06072418402886098, 1.058174416752887, -0.865679273531177, -2.046853970364421, 0.13779198773645468, 1.5688971468733224, 0.015348657608745452, -0.25147063040091766, 2.271597807892434, 2.591654354413171, -0.8089185105390373, -2.6213476559465723, -0.8422664510260011, 0.15330299243773368, -0.9927617287558332, -0.7399999336888277, 0.8139829094657351, 0.37251527514952143, -0.15026502414541032, 2.7994522632878827, 4.685438116435346, -0.27226313388226214, -5.7743188414001505, -1.7167698595344576, 7.474644245303362, 8.774603689103708, 2.038127953539318, -1.0901103478097456, 2.3238652644386084, 3.8600250272235277, 0.5800051798510679, -1.3790774411931388, 0.18315839650970062, 0.92674710369806, -0.06639612704644861, 0.33960202459197686, 1.5335150724429256, 0.8408180864004301, -0.1286847457730859, 0.5690240533923899, 0.09395129509920662, -2.6721176447630435, -2.7894732287797863, 1.2881112368939749, 3.0057590975022497, -0.4915589442592014, -2.4961061384803, 0.4538564108450164, 2.0908215443366003, -0.28189193848659094, 0.48211085462907455, 6.844218861493732, 9.839164249897681, 4.715366708022654, -0.5849638782616424, -0.022717767563428165, 1.3503407347667986, -0.4102565301911959, -0.7894861247502162, 1.9777839639639723, 2.058674786149973, -1.972452093589045, -3.397069740684098, -0.04136890943033536, 1.984865865412658, 0.2970591069340863, -0.3814794591054198, 1.359726046015616, 1.6278027477786026, 0.08012116316950343, -0.17114269380103764, -0.0853889136331368, -1.9878201275489094, -2.9692302541547955, -0.5882729585404716, 0.8083156063146636, -1.3240313503611467, -1.5264919294257673, 1.7924720449067033, -0.2135593810402264, -10.523968350607024, -16.35357990801767, -8.291993310022647, 3.50489738062897, 5.511904462817956, 0.7213155733507688, -0.8125741709690711, 0.7711567840086322, 0.2686428896916457, -0.9638796907258272, 0.043565621896871506, 0.7369275385741649, -0.5793282859149841, -0.5257921845788966, 1.5602044078196728, 1.6048379194682352, -0.2754191378297857, 0.34298780235582793, 2.3648498962125353, 0.8786683536116777, -2.1547579788492723, -1.1833954546614383, 1.5069907987219637, 0.2831058295204518, -2.1597753327236973, -0.4965179569372594, 1.7509993148185465, -0.5429791732221229, -2.8556704920394127, -0.02448784975613078, 2.5144732287426175, -0.47358226789448865, -2.430181766373953, 2.5908884787469058, 7.272103474289262, 3.994137538127178, -1.1982243957184018, -0.2670037833223919, 2.8876541648568894, 1.8803951477221945, -0.3353948636022382], 'positive_zeros': ['0.23599237083766466386472012410', '1.489804907174227117864078672708', '2.50650238116396044413446888865', '3.04369353329089854099568192561', '4.09835365110235946395329728150', '5.42616750782543793043010359960', '6.28841096341314255852783826794', '7.34529121661961895269379029219', '8.45103707509079429720225570067', '8.78409396487679854362273006424', '9.74122221180939435115002231931', '10.69240286159558397733668206625', '11.70280590293182084246964773605', '12.26929027040967267861864241484', '13.00929912679882581250111367714', '13.61783785198854772988241726115', '14.42739301688641003519100440606', '15.514807108031126293153349156543', '16.394996812087347079975434379969', '17.7313100742300899862791237461', '18.058539472903690774517720026289', '18.72117423849834613321178864081', '19.57614871328059287974094271269', '20.03077240537905054095198607622', '20.85588916196066320012481073704', '21.69722494812062032181890297272', '22.632666558589042565940205268884', '23.03967857264729662415509499582', '24.0963114275013817411604743285', '24.99759562929399440289396881441', '25.60922366678479328382014931121', '26.290300619362284596633778417301', '27.19978587097090614150271420183', '28.05018947595111592514073385046', '28.91131470729926321185117555002', '29.09039225788527520072444418728', '30.18124257310073817312332431591', '30.68102797550605008525011041603', '31.23745886303095065717296818237', '32.2279854446825039353329841876', '32.40067362806460170973474431454', '33.96945826790004719393365286582', '34.79927888917544726944821400530', '35.45765006323142644717281286366', '35.88559438388383944718387869376', '36.62460050490915360027436595104', '37.55439459989885823535242384690', '37.88603758108153307462658633507', '38.52401029144738299800667823982', '39.54443478027776590588052735541', '40.40839245071805583804559959651', '40.6230582219666238295468403389', '41.678150085586684074440924493112', '42.08018521755527050539096653951', '42.86922462300235295715978010636', '44.074615024807950059079095684751', '44.44643592883477546540610290604', '45.50239583644020517180845208007', '45.83281777059461314972082947245', '46.896138172386894776644464034300', '47.373753924557067221342272800802', '47.73613943248038812011562503901', '48.581480315585277455139248047628', '49.05164561131744994819971469966', '49.80324633632515162330919778194', '50.78184032291217768239153005700', '51.36097270964394020993288495480', '52.466903383922501886692983447580', '52.860835568401415504494198857867', '53.91687564016585208216824526412', '54.17457384640227291971168774123', '54.85419945907006151311247396689', '55.430981533853197927682967800433', '56.40259739898665028780969541379', '57.13508790631430609294488752078', '57.7361461067995321458066505797', '58.17190982738552604499589318239', '58.78456408263452235249108834977', '59.74167013750063818098350159504', '60.07012614733451811800515225328', '60.90894075250967745766850349842', '62.01980928357560761601632543510', '62.59649216575419785823776927322', '63.42896112979748877384184701671', '64.091776357006862609760615706321', '64.52988549502880997733886560970', '64.87207234087458449989094751204', '65.87117358075833908765857413898', '66.308548118980583708566158489806', '67.14131308094305807042756453701', '67.50828660961010946478855573665', '68.57692667489337331830833347923', '69.08771786940667974586571725101', '70.03493569021706018487617122398', '70.54907815454302080268370442609', '71.39524767459275291681153185905', '71.78161719580442771190251892551', '72.549003001974573701892127439891', '73.43005197113039944048215794641', '73.942445664342167117957781271570', '74.6666423215900912415715686086', '75.10724052553703545400126232229', '75.96122665715662101877414519198', '76.51085209669162242735444068600', '76.88344887283176470666777945578', '77.64284970457740512942987634894', '78.12907544227612560942899531717', '79.52533925259666775909586927612', '80.06555011768598423864056227288', '80.80020189146519785655878081353', '81.21440431698622489025557381996', '82.09102551784090836750936955624', '82.47515489260862585471981074426', '83.03507198980590511210783669433', '83.87463227027211191095561308889', '84.19264220372469447937351112294', '85.001707116404647999109537040954', '86.06314560389051785237931710969', '86.381549626852607322672232804402', '86.88011597262625178944540518985', '87.56653659063620797664985290237', '88.499262508627052453566661330437', '89.35851413188291065467504000197', '89.50785351558126696789889713436', '90.60731604487684034642393340699', '91.1235571606412586082308197693', '91.88297199187966111198661490185', '92.48034769865551586313920375868', '93.01024653909937840599029807764', '93.544895182070355168229945517788', '94.121773285339043836962190391569', '94.59206868169471258775601692192', '95.43319194566521583801280309050', '96.19303407759812612141693767320', '96.71604547229441938627069788875', '97.94708901616160735888074383412', '98.25815985006068513600225903494', '99.17682567598385722662610037981', '99.45708947166765122562642255837', '100.18575857339552577329203433615', '100.51546042176317354459634864008', '101.484852571499116561123619137783', '102.04714917341147260571393602843', '102.8328670852675511019398923229', '103.291842515772569951303285964155', '103.94832436130931983130419070817', '104.45117602889710249927123203869', '105.11970126374909356501891991070', '105.88914024450075817126775676313', '106.43668369594532460720937113471', '107.15763279818725156283491172806', '108.27140421260359389124185510280', '108.790516788831548149342515098444', '109.227214773957217878129593516402', '109.76349984587541625459113015371', '110.54467675342678112273961923186', '110.945863146491787210692108039121', '111.60209817855818955485718297395', '112.127170145261508501260038158180', '112.82936034315736152932560199478', '113.37632623913363335918252567439', '114.19687368314295076253041784230', '114.98834806371092752280315102698', '115.71373934123126116868649728712', '116.30703529651077873693458825829', '116.68644780254788118635376177252', '117.56816986057725968269160722798', '118.1714084485102090188212337053', '118.63744795983284759535662062503', '119.3543535928707949236562931735', '120.13555478470990740491822880010', '120.65182743657197253966638892091', '121.13572688850329696229005142398', '122.04593539842110201500399028914', '122.26078354980322759353170501318', '122.71218431164775804019741774234', '123.605968459870753315349537832', '124.2839151066456362695647772618', '125.42835839568240011181529237775', '125.96537762841207739953526645880', '126.286600619192992732747520396747', '127.153464984216416691547250660816', '127.68828067745872083387258807543', '128.24615225490926993089238387885', '128.83534432748764357863800839133', '129.09188027788825704850809985020', '129.91661465453461270782519801589', '130.806878786590525803591812973777', '131.2754598478494707262149819100', '131.90970610405690043127597327307', '132.52812782513263760007639956558', '133.152535166065423812791313418315', '133.87445474494944326018280944091', '134.69987059652242101366104567547', '135.19184943116944578438514230386', '135.613439638359521882461629529181', '136.45714862081542927477428973699', '137.21403735958485719891640333105', '137.89966454498319080242711159767', '138.2204710690889764028099635335', '138.75108386712766128355551280270', '139.30077653087096695226035141630', '140.04507236191124860547452047262', '140.6084736764194395401199239676', '140.9457014895825935803856048325', '141.971416707551851738774820106472', '142.65799438131082736455787482283', '143.53204267649345461582100546661', '144.21326113733696907256531379368', '144.59602187055208355859761937076', '145.124773056266895657175234001', '145.6795546854362745544838040941', '146.32387681372574812918746483106', '146.802430766124672917537760723570', '147.73164942853964673767483967013', '148.20936390270680553790124395432', '148.71529242609591828199564043368', '149.40363116318737143440800248831', '150.05707896476082209594424161536', '150.67422961679205165339492283740', '151.0367828041975129023520455197', '151.97499095057845784786441526646', '152.52221358721597196448089059979', '153.37800449831863898985405358244', '154.03563857753580926362045455784', '154.61133288596190972748317043825', '155.28664980488238360195689866896', '155.51569914866377676792927589342', '156.203717280282056813173044078561', '157.04591622303687497206663193319', '157.32362221410208618085546348411', '157.90271598095605148746848252784', '158.36190684604132798008414113005', '159.26344174821504715234077631024', '160.11796277940632640405443673404', '160.6660099147578967686381006883', '161.30670576744915310768249401762', '162.07999056826845621022633424450', '162.48949868655171292250729430481', '163.01787209347849906093875709230', '163.73446372832587774191437133706', '164.37768328120748443253594681527', '164.73027621660991531220053442068', '165.557916195456344578627812610144', '166.40164394987041159445494654741', '166.62692875776862775286368529910', '167.32276978141585003557269257776', '167.90113162874234400503168164510', '168.158918687732084092027799237891', '169.050840853176210545296952922247', '169.74519127868226788363326121116', '170.73653664680067309627791712022', '171.0738801567515470861126601134', '171.92571562411439486492761222370', '172.47070888295990123283448680510', '173.09808747200870562247749149858', '173.34509784420996242055516996670', '174.275168362979065106761633348088', '174.49020275794156692828433533320', '175.01382189940402311214109385532', '175.847670775171699761151898849209', '176.526441994035809309975483986235', '177.149341318045933998153028628200', '177.776262120104095493353104764798', '178.086444389638152867833717906189', '179.31438485381706147622000792332', '179.69057463891136601851924599707', '180.25466603004256350102484189779', '180.7300493045845432884408410244', '181.42120323204796634049986605747', '182.19086790556237569604347952941', '182.86058640466296738844271533769', '183.21264594849373873542972247678', '184.08374887673616302576564755940', '184.478229042480717404127955442044', '184.6519677683394954013037806814', '185.69157250681126942519657959800', '186.088427857017857894328932229663', '186.70971862426130797586160164683', '187.17798805471705083537118765496', '188.326668070107070004969272815320', '189.12194532069004660204916172936', '189.532617421385312648631669385493', '190.04960219302497684344272311907', '190.61634203435053795188680403821', '191.12954642819665694824972884625', '191.6496440044495693493911148755', '192.44082478737883719316805770027', '192.75919083753039005003117650540', '193.51591398002375639815532186651', '194.178435032360715226263781888739', '194.71612489450876776988861108847', '195.35990225328731418273109568265', '195.89149429192418419801456205522', '196.56429965194117018406058305036', '197.15301054077378508506656552361', '197.68967184155677444326862268047', '198.64900583917180172611853022319', '199.08553173690877464411732129551', '199.917898473245725935295950462258'], 'prelabel': '1-1045-1045.388-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': 0.6807177584963197, 'root_number': '-0.537729310242950776317025244595+0.843117541571541727648908162015*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.340358879248', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.529264021564283949591126571393-0.559444601532369021731825402547*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.235992370838', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.48980490717', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.50650238116', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.852959597730739, 'bad_primes': [5, 11, 19], 'central_character': '1045.388', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1045/388'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-1045-1045.388-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-1045-1045.388-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': 0.34035887924815983, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.235992370838', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1045.388', 'Lhash_array': ['dirichlet_L_1045.388'], 'label': '1-1045-1045.388-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1045/388'}
Lfunction data - 1-1045-1045.388-r0-0-0