-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_29.20', 'a10': [-0.2225209339563144, -0.9749279121818236], 'a2': [0.6234898018587335, -0.7818314824680298], 'a3': [-0.2225209339563144, 0.9749279121818236], 'a4': [-0.2225209339563144, -0.9749279121818236], 'a5': [0.6234898018587335, -0.7818314824680298], 'a6': [0.6234898018587335, 0.7818314824680298], 'a7': [-0.2225209339563144, 0.9749279121818236], 'a8': [-0.9009688679024191, -0.4338837391175581], 'a9': [-0.9009688679024191, -0.4338837391175581], 'algebraic': True, 'analytic_conductor': 0.1346754338126234, 'analytic_normalization': 0, 'bad_lfactors': [[29, [1]]], 'bad_primes': [29], 'central_character': '29.20', 'coeff_info': ['x^7 - 1', '0.623489801858734 + 0.781831482468030*I', '\\\\zeta_{7}'], 'conductor': 29, 'conductor_radical': 29, 'conjugate': 'dirichlet_L_29.16', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^6', 'a^2', 'a^5', 'a^6', 'a^1', 'a^2', 'a^4', 'a^4', 'a^5', 'a^3', 'a^0', 'a^3', 'a^1', 'a^1', 'a^3', 'a^0', 'a^3', 'a^5', 'a^4', 'a^4', 'a^2', 'a^1', 'a^6', 'a^5', 'a^2', 'a^6', 'a^0', 0, 'a^0', 'a^6', 'a^2', 'a^5', 'a^6', 'a^1', 'a^2', 'a^4', 'a^4', 'a^5', 'a^3', 'a^0', 'a^3', 'a^1', 'a^1', 'a^3', 'a^0', 'a^3', 'a^5', 'a^4', 'a^4', 'a^2', 'a^1', 'a^6', 'a^5', 'a^2', 'a^6', 'a^0', 0, 'a^0', 'a^6', 'a^2', 'a^5', 'a^6', 'a^1', 'a^2', 'a^4', 'a^4', 'a^5', 'a^3', 'a^0', 'a^3', 'a^1', 'a^1', 'a^3', 'a^0', 'a^3', 'a^5', 'a^4', 'a^4', 'a^2', 'a^1', 'a^6', 'a^5', 'a^2', 'a^6', 'a^0', 0, 'a^0', 'a^6', 'a^2', 'a^5', 'a^6', 'a^1', 'a^2', 'a^4', 'a^4', 'a^5', 'a^3', 'a^0', 'a^3'], 'euler_factors': [[1, 'a^6'], [1, 'a^2'], [1, 'a^6'], [1, 'a^2'], [1, 'a^3'], [1, 'a^3'], [1, 'a^0'], [1, 'a^5'], [1, 'a^1'], [0], [1, 'a^6'], [1, 'a^4'], [1, 'a^0'], [1, 'a^1'], [1, 'a^3'], [1, 'a^6'], [1, 'a^0'], [1, 'a^2'], [1, 'a^4'], [1, 'a^3'], [1, 'a^1'], [1, 'a^4'], [1, 'a^5'], [1, 'a^6'], [1, 'a^5'], [1, 'a^1']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-29-29.20-r0-0-0', 'leading_term': '0.867002582186451739302133912500-0.241978947103727455901303307473*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/29/20', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.9001373719379745, 1.0118380655751742, 1.2691657042460884, 1.4973189763712011, 1.6001311783496672, 1.5257394754517106, 1.2548447153570936, 0.8039442533448491, 0.2287175274067512, -0.37966575860749924, -0.9084523213638342, -1.247053702979248, -1.3166664607640268, -1.0986500953771783, -0.6528426187177687, -0.11767379667027697, 0.31253420981393054, 0.43168877339917455, 0.07896610774016612, -0.8058350360241129, -2.1459572428553058, -3.72529040520377, -5.226924082258664, -6.307728896171093, -6.691431434611731, -6.2536249260347425, -5.070629057136144, -3.412022752576217, -1.6728661574987487, -0.26164850946066753, 0.5228427477200843, 0.5850034693413184, 0.061828986292596436, -0.7264222341237481, -1.3915548798801185, -1.6203765020841407, -1.2932859683898978, -0.5317747872540084, 0.3477388289041809, 0.9608238637197766, 1.016142449126269, 0.44648092871306455, -0.5472604031991337, -1.5641911717005421, -2.163215160752594, -2.0529504854519702, -1.2318425189456348, -0.013090124633474424, 1.0864878723261597, 1.5566831572884023, 1.1193959638948123, -0.12841926135544993, -1.723951426190079, -3.0078174203248347, -3.3911126149988005, -2.6100398993231106, -0.8559919896742403, 1.2826162559146843, 3.0501474327840272, 3.831040079892456, 3.401739773727212, 2.0147595053098555, 0.2755914195341956, -1.1324885252130068, -1.7490669977520916, -1.522497489834644, -0.7944665268650621, -0.09391399108666418, 0.15438786693994544, -0.14316095536087783, -0.7057827844460887, -1.0452482497277849, -0.758609986285326, 0.20904072095903026, 1.4801093504635734, 2.3994963606591275, 2.3646686893947946, 1.16675131688794, -0.840344670711679, -2.8483964336438485, -3.9476886812108205, -3.5602998167552395, -1.7375156946597448, 0.8367870106021855, 3.150811573885714, 4.333506978036786, 4.054353712915502, 2.651922748049093, 0.9268367416519216, -0.29021501907189523, -0.5658360650860892, -0.06006829499157306, 0.6092981251837651, 0.752680778696388, 0.02486213647723317, -1.365264014134808, -2.770920000403348, -3.4824886540268496, -3.1434526944686385, -1.9625416763600314, -0.5934584351345943, 0.2515640121769359, 0.2270453042863948, -0.4393141868068483, -1.0932198599102585, -1.0777320748733954, -0.1851663923709982, 1.1436631967321318, 2.016013671365596, 1.5906718787550338, -0.3926144806045137, -3.3730733081729665, -6.181608575783344, -7.612848107055352, -7.049397341493181, -4.7890204575122475, -1.885978716034372, 0.4078615350458404, 1.2876784813317315, 0.7645104937777515, -0.43860547278948303, -1.3802673143207274, -1.4741887660592476, -0.7957408759223941, 0.0498992765111526, 0.39089468918225295, -0.031374269172112335, -0.8853024581579474, -1.4926486531306418, -1.3296201249708508, -0.4441743166119685, 0.5076416559201863, 0.6588744996045507, -0.4763620998724366, -2.6022886386659305, -4.717719715127354, -5.659677605284629, -4.799062013381011, -2.4555139268292505, 0.24533554234800264, 2.0080732463135225, 2.1193247296498914, 0.8535112951381798, -0.7220453574477854, -1.424074898408135, -0.6898687678317282, 1.0876496714687036, 2.8320359819858467, 3.4808810194360795, 2.656996322033926, 0.884434447458925, -0.7780702181710033, -1.4318649735364892, -0.8968818451149293, 0.23000358238170138, 1.037773443893031, 0.9529934229146846, 0.1248469270560564, -0.7205883832939337, -0.8451129688237276, -0.07066142325611152, 1.0644479063784917, 1.697558358393189, 1.3176082995918807, 0.23695015282078075, -0.5126308385766085, 0.15855312301927899, 2.5987636488692254, 6.028391933609105, 8.871729807576147, 9.642221488772059, 7.835191853157844, 4.2536697820649945, 0.5480385461417809, -1.7419064873971002, -2.033088077254966, -0.9075859564787055, 0.4111027425717691, 0.9236185927811851, 0.4640784062337875, -0.3376818301807344, -0.6615414401112967, -0.19208972079478284, 0.6205698923230323, 0.9225588051061192, 0.15873966229319728, -1.42607405952179, -2.88620207656618, -3.2274495750525323, -2.1426986299932107, -0.2770368384325707, 1.202359828276689, 1.445488997810988, 0.5623170177761011, -0.41977893714727904, -0.288572928082542, 1.4350397478318675, 4.058877940597373, 6.10704067376042, 6.2954103847132075, 4.424723024595566, 1.5574798277119306, -0.6631790716162627, -1.0915774624380763, 0.1894309821781627, 1.9849740669963345, 2.8543627528086284, 2.1046702141550866, 0.21522684002747328, -1.5783207725141235, -2.202050896781855, -1.4783984079184775, -0.1566775998478389, 0.7368807805274482, 0.6964057558116556, 0.057304023425719344, -0.39064072577607883, -0.16081672282996373, 0.44035830718212476, 0.5226630006385735, -0.6106827781996601, -2.7307648448801203, -4.622791414841526, -4.836310615036004, -2.750172427517065, 0.8351602952407653, 4.06964497937982, 5.194233326299286, 3.677998799198055, 0.5523045660071778, -2.299047110028521, -3.3917499437911998, -2.5521258677398735, -0.8679851513933718, 0.22981007215221372, 0.03793650207255513, -0.9908038593030506, -1.7364008840049852, -1.3847467434147922, -0.09781259875182685, 1.1400833335762726, 1.3531370898898178, 0.3955037823709562, -0.9093985279610026, -1.4303071976806077, -0.6573108011786164, 0.8596659557124324, 1.9340847489690967, 1.7016862001658106, 0.3412013565407172, -1.045678503006541, -1.328456054627292, -0.3099145292077417, 1.0396192023182738, 1.3170218886168705, -0.1458654122503684, -2.6012970423990507, -4.277864230728262, -3.617351951844308, -0.456653224414952, 3.7411393498324426, 6.808929156496145, 7.293524193765515, 5.3448585580344075, 2.4603428999079098, 0.3328247662733459, -0.2984923040077623, 0.046732951555624166, 0.2687670712197897, -0.2822350891542057, -1.2893180759293215, -1.852727497951315, -1.3879001295734494, -0.22329889569830252, 0.6438947497811945, 0.43699127726653103, -0.6437849885623959, -1.4963549506489962, -1.0302733623607805, 0.8109989342538014, 2.8032128215537617, 3.264810304029943, 1.3685802696347735, -2.0893594202944787, -5.121916504315406, -5.917749809659054, -4.125987675250179, -1.078591116979661, 1.218878080265391, 1.5458492822788488, 0.25618015330053134, -1.1740106425821444, -1.4246536408156873, -0.3849642524620122, 0.8489820660153067, 0.9797094601608718, -0.351799222746095, -2.244283062157588, -3.281755511658114, -2.7012391928864123, -0.9984297427940036, 0.5213573598957945, 0.8412906128474973, 0.033349799232701115, -0.9122184739061321, -1.0502755233903536, -0.3639445159234133, 0.23892933928694712, -0.1603958986230357, -1.4738295913422215, -2.4388193432888703, -1.559754161565408, 1.5543831787516835, 5.586721159591869, 8.246391266832408, 7.867487013202161, 4.657662035203258, 0.6024513780143177, -1.933326408700688, -1.844571153207841, 0.07541397116541933, 1.9289550071556847, 2.2416897643628, 0.9911361847483399, -0.6175082587203591, -1.3185502081425058, -0.8393924263978758, 0.036690569507092596, 0.3608057816013877, -0.013901363900010877, -0.2963139097911796, 0.4218650950930414, 2.158522572433239, 3.817137702022465, 4.029760822298671, 2.3739300012916518, -0.12266733217708105, -1.707460783179599, -1.3114302743627473, 0.5426643199551453, 2.1431860309456034, 2.0169580971002903, 0.19991926360672557, -1.7385047520341184, -1.9772141535597418, 0.01770030935444822, 2.9872566445527653, 4.848711901251604, 4.349518876089088, 2.0423415398098874, -0.2110682045712434, -0.7683506506344268, 0.5167182621874612, 2.3039705151537495, 2.9859192322772046, 2.029670069796054, 0.30714193730177064, -0.79561656094141, -0.6323982890081017, 0.21562213505769365, 0.6091153835303085, 0.0010038348626566034, -1.0323302905437184, -1.3821485707828132, -0.554531619272649, 0.7463319657622625, 1.226407980560006, 0.31304895813727923, -1.0450754118061882, -0.9403311634258249, 1.9032809821912522, 6.822251532924773, 11.373863210751708, 12.970642919533532, 10.74501944921999, 6.160134658315034, 1.884320843027988, -0.1453897999702295, 0.0786075194763077, 1.0480488330972957, 1.2639743466934499, 0.49198528568030125, -0.28846306818986894, -0.05623082844141884, 1.1306054072551366, 2.1253513064902383, 1.7803401998540536, 0.08332270892563534, -1.74977398147476, -2.339869469819668, -1.390351017430822, 0.052342518342753296, 0.5874387411365016, -0.20603362547489606, -1.3429870268542632, -1.3507075671250404, 0.2849564860556918, 2.4979848285878608, 3.489855660455281, 2.3496844257463203, -0.009704935927236034, -1.5107675474769666, -0.6720213275132866, 2.041704918173776, 4.49256433778868, 4.591240475491033, 2.0245046780033755, -1.4768768981594147, -3.5453116435772727, -3.046236238473147, -0.8414001647177031, 1.1186831641413948, 1.4858879708285597, 0.492217935180816, -0.547885383454963, -0.6085477861568531, 0.14071978772202823, 0.6944449450647483, 0.3813511990016146, -0.38216072611974855, -0.5405439701801628, 0.38626793468705434, 1.571691453834066, 1.477435398948567, -0.6622793007747839, -3.84838326366286, -5.866309391132738, -5.054748563831318, -1.7956141783059294, 1.6375550092236515, 2.8438777602425303, 1.2129062878604298, -1.6379375249587171, -3.2722997637837925, -2.4592666960658986, -0.07575839520764963, 1.8240953519616445, 1.860127922420436, 0.4250754627926102, -0.8819789492271, -0.8541945711755448, 0.22894506523309224, 1.0026157777121945, 0.45840899353377984, -0.9994631193984361, -1.9071915902831391, -1.1559928360784566, 0.9025060793217685, 2.7315299794639842, 3.0063967367049953, 1.793183935107413, 0.37930429090519496, -0.06345280059521484, 0.34688329049442984, 0.3848070276983709, -0.8741007519912466, -2.8022289289044973, -3.4590606052182586, -1.279101653042457, 3.268388886592086, 7.644497240879922, 9.043500153704214, 6.582208250440993, 2.0083520676577207, -1.6913548587912457, -2.593039773452049, -1.1081790582363893, 0.7446167895485845, 1.2624619130621726, 0.40176824562467867, -0.5563641287174462, -0.4998985245148657, 0.4002678468585624, 0.9986483995486972, 0.4835440314417916, -0.7153523844576634, -1.3710843279088287, -0.8006323926583612, 0.299858546623578, 0.45706703057893844, -1.0584588421166374, -3.304675185799485, -4.360407271246235, -3.108616856718, -0.44616186431024196, 1.3154507567188203, 0.43554470309865695, -2.651443965328636, -5.6098422154608745, -6.164785417004625, -4.009176322709253, -0.9502631621465474, 0.797975433523655, 0.5796488279864687, -0.27560803736149847, 0.10865398653362501, 2.261816453212021, 4.810850690699505, 5.751242997651462, 4.302684876367875, 1.5965830222803907, -0.39946312063667194, -0.6343229699773844, 0.26782554824803473, 0.8770319336886916, 0.4858605092952589, -0.26357740911382543, -0.2354933563812086, 0.8197879555578088, 1.8633298054373957, 1.629912349420669, 0.08713902276868218, -1.2840739204293814, -0.8475600135361154, 1.415238106233914, 3.5091762991613193, 2.99822546795104, -0.7507945598756173, -5.716833787328028, -8.664793097742841, -7.708595794471719, -3.778315758082955, 0.26112686955620307, 1.9956501762701369, 1.2229742322401935, -0.35322603166183586, -0.9840965678300437, -0.42656087608426074, 0.20109695707275005, -0.10673690003874034, -1.0729768194875253, -1.4770644751156623, -0.5837213093383296, 0.9042436196468775, 1.4400708443149886, 0.22386347067588236, -1.8445149644551888, -2.900350267938249, -1.8891353004275553, 0.3684851391938359, 1.930814591179283, 1.6215022631477873, 0.1903855008831155, -0.4491955939688731, 0.788444241061526, 2.9069981847083533, 3.6292307800794434, 1.5830277863655, -2.2048252237256967, -5.004461803134896, -4.710211988204381, -1.6730464805726328, 1.6500286244117666, 2.88092335465227, 1.7022489525077102, -0.14181217637573998, -0.6846788950169636, 0.42699334101662084, 1.8148738262941035, 1.9226378723270179, 0.5869597320914391, -0.9242024269579728, -1.3213765221244604, -0.6045660121303899, 0.08558385785952274, -0.15714160812728584, -0.9543402558426511, -1.119759431183821, -0.19770981272620886, 0.6404648285933348, -0.4988710528003974, -4.224236552409851, -8.741746313147745, -10.949915720597602, -8.974007712695592, -3.8733193914700346, 1.1134987698893728, 3.1839583203810355, 2.1218520567066883, 0.1038543767718756, -0.5190197769431595, 0.689330372048471, 2.1838631585357953, 2.2521818398839297, 0.782489047423266, -0.7516754789479385, -0.9418199200685845, 0.058797422820176956, 0.7433837618664082, -0.09684514947447517, -2.0364146214046546, -3.4033841355025802, -2.988795706359082, -1.2909193126734495, 0.011633358119697505, -0.18638112187797082, -1.2765983979921547, -1.6277281146520595, -0.40384752675092705, 1.4198413065156732, 1.9931974964517607, 0.5919817956451356, -1.4039952161911349, -1.7070789924028356, 0.5582137521071922, 3.7139957629215745, 4.837536785969422, 2.416513050169171, -2.1371282517787304, -5.592049196214987, -5.636055554852806, -2.7350227197169565, 0.5222032848740311, 1.8313778585927023, 1.007140893808047, -0.34632988380400787, -0.7200394131007793, -0.10757665160738425, 0.39002514228649277, 0.10014218634113957, -0.35864739060408235, 0.146638558383405, 1.7574320638206036, 3.158511734971076, 2.817738249973297, 0.6896918385736869, -1.4978621924674784, -1.8619170939285958, -0.3382122499962852, 1.0634851140165753, 0.15744006179887307, -3.1439585758834783, -6.469776971220583, -7.03347885279657, -4.194363515681075, -0.08243168526166991, 2.3221747118013796, 1.808488599975109, -0.22850382692463406, -1.4172022863016303, -0.7762858624738819], 'positive_zeros': ['2.61651033357808942884242111086', '4.76049809736198473232714243615', '5.66282989807631649012267817691', '9.14032345328068345315784728183', '10.02645301479179505306856722472', '11.74763329073383371968176783727', '12.96277523568800026875007687731', '14.69076706307787309494151081602', '15.91086718365607048026202776731', '17.62570589298972592738392630703', '19.42733449376387309090769850350', '20.99954262032163585143748860372', '21.463178604150063307236876344128', '22.75725135996340718917740299621', '24.25221451545722138060684098177', '25.83854410020353207462493594906', '27.71427759350211912667125558644', '28.46364549863046286890333186446', '29.38177252567326692571952768931', '31.43322853231579063423886782330', '32.00319791325642011574843912590', '33.17066664678966439088990420063', '34.32700190206809129728835216859', '36.49248713724828751864705575186', '37.39027899654660773251304173249', '38.72780071816477043056734052584', '39.36150569203568719640840043588', '40.75651237622737445381019954089', '41.468349974954245373685812673103', '43.406444825475927380262072880383', '44.53578799878215570061841634235', '45.44679427046008175032617219922', '47.025969116859286844884175509920', '48.06197851327675478080047010533', '49.1023095315405920473925910520', '50.019993877026123951616363208795', '51.31893416573502454994062318016', '51.841750653955332393247197424912', '54.11858335336491429558760164541', '55.20213671241420840837898967109', '56.11244767548530434432755182312', '56.94925829007319940531409095234', '57.84954534977765085689797895652', '59.42220453936206196273689171301', '60.46893994150051578616938553306', '61.01561276435769226430313968022', '63.00760136498033047405126074516', '63.7164153120635111060736536637', '65.032677089364705513116568327135', '66.2899822961808105632713841091', '67.214435076134948558304662073335', '67.89860154510381642218029157137', '68.624870830879221692489678109485', '70.24340927939421605114893334462', '71.61518544836243763023532498351', '73.022133687944261660151106941330', '73.4524654644535830892386595448', '74.70848466446684407355495510714', '75.71565005830645700244660206469', '76.70323830055215264540214143283', '77.87957744522306156592651641020', '78.81687396362154263159005488953', '79.66642826095807944482675849404', '80.97243343296824514136512158009', '82.90230023073753347062237351988', '83.4062382370843888357946990902', '83.95248492728705767496923955358', '85.37264934642812740851212114514', '86.079898519799548362904389039475', '87.068088956485219161087871046094', '88.256832598639597001763316927869', '89.80875891306271771437680960934', '90.67373653360804069277984577573', '91.649061363466644248013210679521', '92.4380439153148378929115906544', '93.9332814867743303147901107929', '94.69716662292053651002597883626', '95.77211259082689281701356388509', '96.19348821565777578616477616336', '97.366669861470351962998944948053', '99.116630585806049208212396176727', '99.98938651990420776895085288495', '101.11993097012790690839131254201', '102.17179205270322470081145436956', '102.8039717904001708797073385283', '103.317830597664571956007870973972', '104.98367353780184981967261255154', '105.8552004075126706889882972451', '106.90312611357145473763672707331', '107.81053194866643223652954381143', '109.336002583469116243280407394442', '109.90656546092016697689449196344', '111.31230084908977891406829525581', '112.10814734979339455260070515635', '112.81281434524890463786449141537', '113.87919345132775027405581093669', '114.75447857575447324130219040162', '115.454471052682820421329348048987', '117.76356976447333046204160333424', '118.096705641573292188623900672365', '119.227589775445570850701907972934', '119.70777802019659045816648648487', '120.95031336313008669616492263334', '122.17385964495070084057239202565', '122.75779025050431407019885175', '123.70888643117512182577393785869', '124.998677207608898172615695145208', '125.71610384055605469210657330518', '127.05154780035071085699770427535', '128.23869473141007630175554611917', '129.18830220215665164053663635214', '129.94802898453872394355457757610', '130.77804740560712154566547813194', '131.46354146554291613155507609809', '132.42670506215501414670242136627', '133.899859144399530687081010024174', '134.82071171954483503929587173524', '135.94704674980346103135931572138', '136.95707233174180600177572733663', '137.7529779727856646394183610770', '138.54425718928381854730928497012', '139.56139334989429701508935389434', '141.0994425577054354972380609362', '141.33157188105592037429608246468', '142.01134837962788309046077119026', '143.224338315474294778138025836192', '144.83393153268484950578093928228', '145.7961401915370347307488979735', '146.67213469778477346968827165132', '147.373710821228439402773683073517', '148.25556553297990140241055211930', '149.28072970445795531517553293601', '149.820633662632731819239926057059', '151.3051789310816170332892139849', '151.93028706542992043702572352353', '153.563680606122780673852856071603', '154.25359237059430950560508582587', '154.66077280770195789754448570040', '156.47425399998875459777823595802', '157.10469073698147372137799371522', '158.000000617106853665951436243091', '158.53125383409576727501547972401', '159.70281497548695404747114451022', '160.449434876125460986098770812325', '161.51319932028710508816472128260', '163.099760727199683261598372649777', '163.98475386886416429317845826416', '164.861052362450257851459523265717', '165.26761743028016666786304521054', '166.3702923919248245575233107375', '167.22291767240691378542303664507', '168.38716104533141483573325005918', '169.421388935307150400042897024061', '169.85627509014505896882728323063', '171.07388684136395876667189598609', '172.3316948854230834751155132191', '173.407832604909217848870131409816', '173.973119243989519092329532163594', '175.108442768850626014666149397160', '176.18191221348876752407916742970', '176.48043661813409923675631647884', '177.55208978994489215022052635960', '178.05433444869135372187136553226', '179.91743041174527310066952642842', '180.95854888484932851870359378184', '181.42467922653348022597115908444', '182.63900904857648354858379791949', '183.4214036084900783614674930188', '184.04324002710886916910073075701', '185.61912976623605661467286153730', '185.85938137950121188234976186152', '186.942104583910042242243058824081', '187.898887969917035124820198862717', '188.693149560500056316204733804628', '189.85813692534612580758079093507', '191.18993981648575706304333509871', '192.09438856917934048955610020013', '192.85794165460465057983132517975', '193.49111041202325102373873479491', '194.02025928742991452803625819879', '195.3981667561791928498102647504', '196.30633067102899695969628637411', '196.895388764017897885260926807527', '198.444541739510924418491598608893', '199.33945808875646981788402736803'], 'prelabel': '1-29-29.20-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1346754338126234, 'root_angle': -0.17327030693518589, 'root_number': '0.855466814433927086815600629088-0.517857634299494477268943562671*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0866351534676', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(7)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.10793530482631361559388332074-0.246557535716147291485849070194*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.61651033358', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.76049809736', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.66282989808', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.1346754338126234, 'bad_primes': [29], 'central_character': '29.20', 'conductor': 29, 'conductor_radical': 29, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/29/20'], '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': '1-29-29.20-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': '1-29-29.20-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1346754338126234, 'root_angle': -0.08663515346759294, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.61651033358', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_29.20', 'Lhash_array': ['dirichlet_L_29.20'], 'label': '1-29-29.20-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/29/20'}