{'Lhash': 'dirichlet_L_13.12', 'a10': [1.0, 0.0], 'a2': [-1.0, 0.0], 'a3': [1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [-1.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [-1.0, 0.0], 'a9': [1.0, 0.0], 'algebraic': True, 'analytic_conductor': 0.06037174619186565, 'analytic_normalization': 0, 'bad_lfactors': [[13, [1]]], 'bad_primes': [13], 'central_character': '13.12', 'coeff_info': ['x^2 - 1', -1, '\\\\zeta_{2}'], 'conductor': 13, 'conductor_radical': 13, 'conjugate': 'dirichlet_L_13.12', 'degree': 1, 'dirichlet_coefficients': [1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 0, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 0, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 0, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 0, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 0, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 0, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 0, 1, -1, 1, 1, -1, -1, -1, -1, 1], 'euler_factors': [[1, -1], [1, 1], [1, -1], [1, -1], [1, -1], [0], [1, 1], [1, -1], [1, 1], [1, 1], [1, -1], [1, -1], [1, -1], [1, 1], [1, -1], [1, 1], [1, -1], [1, 1], [1, -1], [1, -1], [1, -1], [1, 1], [1, -1], [1, -1], [1, -1], [1, 1]], 'gamma_factors': [[0], []], 'id': 29, 'index': 0, 'label': '1-13-13.12-r0-0-0', 'leading_term': '0.439592973509005225245051817779', '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/13/12', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.4395929735090052, 0.5157291132882211, 0.6883547598609389, 0.8841543361711011, 1.0591354553791705, 1.179755738479735, 1.2140527905297034, 1.1316105940922045, 0.9072201493663735, 0.5260493526553759, -0.011020720260863414, -0.6831070490849674, -1.4472690908243326, -2.239715542041706, -2.9809218337300063, -3.5846863607995383, -3.9703523764471487, -4.076569909961, -3.874251455830357, -3.375991975620023, -2.639358500240599, -1.7622090942663435, -0.8695496989006699, -0.09319963930930861, 0.45261777928319946, 0.6951457065482636, 0.6211068191152925, 0.28397251364047427, -0.20270335483415883, -0.6862938456686787, -1.0074817325164576, -1.037828405896641, -0.7141439156161656, -0.060849404497171154, 0.8067087278328477, 1.7011733235381608, 2.4022359285308843, 2.708282452685209, 2.488831247383617, 1.7243162606236908, 0.5215243939837448, -0.9018459735608602, -2.262457919346456, -3.2772054196147273, -3.733895164111063, -3.5481198162896233, -2.7898359587612336, -1.6702151541422323, -0.4897905479401604, 0.4399517602764407, 0.8808356322049028, 0.7342644502773488, 0.06938589369990526, -0.8968407731176896, -1.8637172247000229, -2.537298985267035, -2.7203756953120477, -2.3736620573413107, -1.627536750931485, -0.738499562475803, -0.0022903804770883947, 0.3493173026899388, 0.23391753055054937, -0.2442007790098193, -0.8206607921102352, -1.1565264537270896, -0.9570594323888645, -0.08467922453097933, 1.3736813946554938, 3.1116290114828615, 4.684291765404342, 5.642613539212697, 5.678360054560492, 4.730915618481008, 3.0174585198425294, 0.9727859914525595, -0.8840469003144942, -2.112759107431353, -2.489013574638121, -2.0676501372171296, -1.149097674466119, -0.16057552172922104, 0.5048975186559957, 0.6322505050578271, 0.2568578519785888, -0.3620719920765333, -0.8573752562720329, -0.9141017571412255, -0.4102714293274756, 0.5196888515197333, 1.52759275569861, 2.1870369984240887, 2.17011856839043, 1.3942350793070184, 0.07651286162161919, -1.331990935320033, -2.3123435235266587, -2.481901015660391, -1.7554953970063014, -0.39586607038433086, 1.0726814927576211, 2.0589491971080984, 2.1340846632581587, 1.2045647891803255, -0.44235806382649784, -2.242454280902234, -3.5690569037032938, -3.9736907145112714, -3.355827966760713, -1.9925819016275157, -0.41646633171612524, 0.8072988919280437, 1.309953477736934, 1.0579542412016156, 0.34332062541805897, -0.3677952708006641, -0.6590918351042009, -0.35867645829313227, 0.38532555327840307, 1.184346032425326, 1.6091652311625413, 1.4177077799170077, 0.7020684476368229, -0.1207029838554668, -0.47965879456683735, 0.08729977628084422, 1.6960358600753334, 4.016257879617555, 6.364288250392374, 7.958759237058397, 8.234243059904752, 7.077273847270405, 4.879081642339033, 2.3780897436107367, 0.3583109744706409, -0.6650706652560532, -0.6350575904359094, 0.06448767605808489, 0.8202796774842561, 1.0936765858646713, 0.6739529931793378, -0.23728814560690303, -1.1472302293280596, -1.535959517990897, -1.1316218701764797, -0.05906146214926784, 1.213652031612698, 2.1061415815524214, 2.2196712346746255, 1.5453304417240463, 0.4772506367748096, -0.38250374698797984, -0.535019708642012, 0.14345048751545098, 1.310157152993416, 2.3011971764368875, 2.4521185284841795, 1.441041619502685, -0.5167826270889084, -2.727455116220179, -4.313165669510634, -4.609222875705644, -3.4749291479404785, -1.3670109827250576, 0.8630682649286712, 2.352947753040887, 2.6109521568710425, 1.713546959400319, 0.22848526284643705, -1.0901280338043866, -1.6762283304306116, -1.4058308657949166, -0.6070193909892628, 0.1684437585930734, 0.4808401284816815, 0.2590166027967094, -0.1645398003890269, -0.2608299297059269, 0.3601125617409472, 1.6741445549741334, 3.1906627167560306, 4.168307019025343, 3.9973808438291405, 2.549879470922302, 0.30407911461765924, -1.8386103540861292, -2.9668866308488626, -2.600017927891148, -0.9302680390125055, 1.262243153582912, 2.9852973852805196, 3.5132117703469685, 2.7256387426291977, 1.135423888089875, -0.4036789515230781, -1.1515337027343249, -0.85718850611814, 0.14031340221007224, 1.131709331442119, 1.4501630311937332, 0.8462799608168973, -0.3808261502210484, -1.564865457340207, -2.059238716839016, -1.6074678831959452, -0.485228935202286, 0.6675073950900038, 1.2275155211139175, 0.9608312328107659, 0.16582689620503932, -0.5051646665613386, -0.4515633143434231, 0.4742561036249464, 1.8104804736028721, 2.6839023903409367, 2.272863852056212, 0.2884785906853391, -2.796061376396333, -5.91035640240357, -7.875867674142088, -7.969357984595268, -6.264780628065761, -3.573636125892343, -1.019555752078375, 0.5207544432840904, 0.8105110015054255, 0.2788928517808389, -0.3119862663850723, -0.3513625353573833, 0.26983072475203684, 1.1395321402455927, 1.6319774435115608, 1.342505266941978, 0.3757836828002606, -0.6956679841075479, -1.1831066036582758, -0.7301313338235339, 0.4222940659314796, 1.5320413602822014, 1.7757250995534097, 0.754115757571536, -1.219501986666617, -3.2350278828532546, -4.259774515785564, -3.711089637812436, -1.798880844534753, 0.5674693589188139, 2.2662184191933012, 2.574029708386967, 1.5543171671976448, 0.001621126168349946, -1.0249679516303123, -0.8095544029907495, 0.6214473390644031, 2.5343910342114393, 3.927849562164233, 4.11120551660643, 3.08111628597981, 1.4820805600023204, 0.19033584123790484, -0.2146614235701948, 0.23394124919880877, 0.9731950888065531, 1.3252787805519648, 0.96924801854487, 0.15970702883498938, -0.4548640952175471, -0.30186982342747687, 0.6631911115321942, 1.8300942209979056, 2.2447479821080867, 1.1923390454235767, -1.2982952414965876, -4.353983403580889, -6.654735261133162, -7.124447271314635, -5.523378162822219, -2.5953530381922327, 0.3232927220758789, 2.0121708230795914, 1.9870198977310292, 0.6824718110729899, -0.8878573186518078, -1.7686807422033535, -1.6043355827715076, -0.7656333889174625, -0.012015696550545204, 0.06942314792979273, -0.5259970948766404, -1.2271405082032052, -1.2985259401007718, -0.3773282843000539, 1.2280028053495664, 2.6872092304008675, 3.1608009975487694, 2.346381856387152, 0.6963653184089306, -0.8503912431899012, -1.4656859335338206, -0.9784060640916628, -0.009289138859989061, 0.41263156093891024, -0.4742142103094757, -2.6204927454494342, -5.111458777615774, -6.659568782089168, -6.357977530140417, -4.236407371364653, -1.273526276740887, 1.1490280332645855, 2.0225818910879236, 1.2492679839471288, -0.37427038324930323, -1.696445634277918, -1.9212504160135984, -1.0445072856929254, 0.23838976372499168, 1.0600923434802616, 0.9745866715918923, 0.21949604522468127, -0.513172740248505, -0.6195229692205708, -0.04754470324586146, 0.6538147427139502, 0.7470644853861944, -0.1009733909775589, -1.4690632426749113, -2.3506511627589246, -1.773059633929399, 0.5189324360296746, 3.7727007757935676, 6.556477429216469, 7.539974023439711, 6.259335837893591, 3.3913222763176885, 0.3597111525946248, -1.4865824304420694, -1.616900460868548, -0.5323517737858567, 0.6594303204541399, 1.0101387061670775, 0.33202402988865043, -0.7456037709675699, -1.2743727146803656, -0.681642680619323, 0.8163721593856111, 2.3587478028005737, 3.031218507600992, 2.489504345294142, 1.1818455472044707, 0.018882585957513964, -0.27539895262148534, 0.3259666936752434, 1.1445073386414555, 1.3025820252202742, 0.3911890013132945, -1.1793920020666775, -2.416170610620454, -2.430761684351993, -1.114126593192784, 0.6814605832055157, 1.6174001968247091, 0.7216362227946832, -1.9310985167297414, -5.171645487047362, -7.379812249261361, -7.426927516576514, -5.326364206860883, -2.187461878685835, 0.4815631508515, 1.6613468919391687, 1.3342170424195716, 0.32561558613026115, -0.36714372576199544, -0.2693944081274401, 0.3276442480941454, 0.7089516269585286, 0.3754299928470491, -0.5117149856190705, -1.2212353626256203, -1.0157358731340609, 0.23040301185714324, 1.8348607737233795, 2.715431596983657, 2.1453691896955505, 0.32722509176306824, -1.6455283161036431, -2.4575206048249587, -1.444369173650226, 0.9218437941481901, 3.2840434995630856, 4.245984638995237, 3.2619377820952997, 0.9796594365443062, -1.1923502413619858, -2.002293893959118, -1.1428404608004659, 0.6102587850031149, 1.9811385308076037, 2.080770433843804, 0.9847603440037711, -0.38106065762689656, -0.940544254696728, -0.24191721069884664, 1.2402838936144227, 2.473598647221986, 2.621467754270487, 1.6286910390195388, 0.21957943200962238, -0.6728957407938272, -0.6089140715351478, 0.058272101040323356, 0.5154339489591051, 0.20701883929818943, -0.6154922593293436, -0.9631348844760632, 0.1980804987105509, 3.101185121282796, 6.800371203987775, 9.588158582888148, 9.986955530485004, 7.676650078167659, 3.733596651257131, 0.004266225489152575, -1.985120418896666, -1.8734562507805437, -0.5303811966270164, 0.6553257439253543, 0.7422449479760088, -0.20886393056338973, -1.3354787000651986, -1.7229990982162904, -1.118704497252972, -0.08320781269140774, 0.5061697805493244, 0.19375313257738233, -0.6582778515126767, -1.1332315649746598, -0.49088910945109127, 1.194608886328611, 2.99769133909262, 3.7696138075774055, 2.9887731126976176, 1.198999032739996, -0.31835171040095667, -0.43595710071627447, 0.9946354697434976, 2.9926074226003987, 4.1089220335395895, 3.4497520782293933, 1.3372022375635535, -0.8753546055042944, -1.720607341228176, -0.6307342802275854, 1.6637674981076307, 3.6284728609222876, 3.961579609715847, 2.4456860203927895, 0.032860268296860395, -1.8636735102188682, -2.338346126126152, -1.5292226029275533, -0.3727807623231591, 0.18591449470220694, -0.09685353361251572, -0.6657539498819345, -0.721432900332627, 0.04235878305645995, 1.128359378009712, 1.6198529907944963, 0.9683082887330199, -0.4492425526190076, -1.4892122286481044, -1.0620541120108888, 0.9701829209493438, 3.5124267834310805, 4.847943257431512, 3.7691057038308067, 0.4484786177789907, -3.5794102054825485, -6.343361546461786, -6.647543680581861, -4.74832296747866, -2.056752045271003, -0.11695909058712363, 0.39396697608049847, -0.047694912959545914, -0.3817873762285248, 0.09944883110911408, 1.1812974626199015, 1.9419976761866258, 1.552317499987952, 0.008158173034320983, -1.7927051042478719, -2.698628470379489, -2.1736448222661497, -0.7060757942183158, 0.5714178009553671, 0.7618527481807063, -0.10303643168202468, -1.1091263435850651, -1.2251522188638069, -0.19416042012670606, 1.164843669896604, 1.5251953810845644, 0.09726623941090545, -2.640495507874802, -5.1170953970390824, -5.683581858581365, -3.763530659401913, -0.30692759200096875, 2.7989440964067125, 3.958385716211454, 2.872837788189243, 0.6300177614860965, -1.145609283289208, -1.4324588871339081, -0.4169586766078414, 0.8247222558604237, 1.2539674696989924, 0.6584092741243879, -0.28987295590198203, -0.6939590736465574, -0.22709393026837313, 0.6068641888863192, 0.9612882130091954, 0.4671327318953934, -0.32326752159019695, -0.2904649539633364, 1.3279438745819094, 4.167424270463722, 6.778751881909904, 7.538525522488614, 5.800436744769861, 2.4296136905493437, -0.715310646158553, -2.015188495623821, -1.1599964531499993, 0.715748327838203, 1.917778936888153, 1.4330124643122364, -0.3876438367891182, -2.183263024461433, -2.666584395903459, -1.5940661820970987, 0.1052090649564277, 1.1029897004108755, 0.7149285092377009, -0.6055528106686958, -1.6866789481428928, -1.6077617055265652, -0.43143930564426686, 0.879888738171248, 1.2757598303537359, 0.4831342873479407, -0.7850240336041004, -1.4465798006949446, -0.9784821855286889, 0.12497899063967592, 0.7717374997961324, 0.25349459844853156, -1.0175168024566477, -1.6708804550450087, -0.39520281284351466, 2.937643237087444, 6.932814119877103, 9.453933024264941, 9.017447377003638, 5.805112342510232, 1.555798324185887, -1.5872926780970524, -2.4396003423811203, -1.3854169125842433, 0.13842320853444523, 0.8146225185130008, 0.351951332430028, -0.5219057187951934, -0.8730868073466581, -0.4436888656907693, 0.14052512109221615, -0.01686820116455797, -1.2036112021441716, -2.7332772393363833, -3.4404156685838903, -2.649204029224798, -0.8039726697948714, 0.8027171806252913, 1.0363024724031642, -0.1322751116691763, -1.5269149822942145, -1.649955756965957, 0.10962398171004953, 2.8966073297775212, 4.93168361991703, 4.7989222816284105, 2.5050512560602543, -0.5079753319714753, -2.417453267902439, -2.3398755075352606, -0.91314560866934, 0.2848698872837512, 0.005236957729250433, -1.7110144240553733, -3.609858791004963, -4.240969552010825, -3.086767378234793, -0.9194805844326522, 0.8549555147745398, 1.2952611099345719, 0.569074940804619, -0.34292659163900585, -0.5764599912291819, -0.12545354189598018, 0.23879780808083467, -0.21782667654963087, -1.3820014696446363, -2.2443341732164352, -1.7280816555433085, 0.2646732180408802, 2.5014714563091247, 3.1625754635262053, 1.191736569069466, -2.7768022930533243, -6.68368724383423, -8.377540009484784, -7.060023721737271, -3.779315937020316, -0.6209261944128963, 0.774135309549445, 0.24946913658975256, -1.000379599139299, -1.538097958835697, -0.8322440603361765, 0.4535478419268305, 1.1839057063823926, 0.8087841159115019, -0.16251746016682192, -0.6548894518435093, -0.03299958896277843, 1.2741383263911292, 2.0924110899618373], 'positive_zeros': ['3.119341479008603413901599756715', '7.23159073941876201502754170862', '8.62542663503259159734490395156', '10.33642072623153902983172482625', '12.61701279102317873036853708840', '15.14833241700574422460628551477', '16.2748260574985884178954092949', '18.75125235623423291645518570775', '19.54804144334703986992466920641', '20.95918191740503118143937053273', '23.59202788517293715038687724139', '25.37170440577142621541053358349', '26.38431352575075899278988900685', '27.64980842472696812713008959723', '29.39145603391187839555762592893', '31.01874209224480391870730181195', '32.4234172849637336609819268055', '34.46644233774365394408596282416', '35.76319303421611596021350693284', '36.727547051537073200591290509603', '38.38532547892825026671651055760', '39.03678471619023999728500556745', '41.95272842208549146545251634782', '42.788261511645281673975244898140', '43.988308502403416504944841263', '45.32698188727387053950164420235', '47.02559251326658098497994034690', '47.76652470997699267368858481270', '49.30119556332343034607225149729', '51.12271994979953048808616054124', '52.54738524937692657347833357772', '53.98183008250945615328163821430', '54.8720854891482010321476987726', '55.49277369335127708797923520112', '57.54040496135948335366399264156', '58.883400102740923662426791057907', '60.531614188445863108551984291736', '61.52343977416719653772010880272', '62.722702441405187473421873654031', '64.18437876525375531611663934439', '65.37454732465903796376915515385', '66.12012319500561418096447203181', '67.53296727756918506154927050238', '69.8624705457876281205817833485', '70.753412683414055538776475587391', '71.45557754022086650302209696699', '72.91506366211967736249244136539', '73.95844615009451377698755788496', '75.13098178400531220168973467820', '76.79727368306604215649350952211', '78.12534784738865814895037766891', '78.9498189561804193101718266493', '81.01368387655506426476974661653', '81.44891693397052238846948068527', '82.87434825609780863037099687227', '83.559922019154150837752933365888', '84.8547328750741405694312729873', '86.83523716162051650644835015383', '87.942131499461431910345533391566', '89.38307144213592295005879982074', '89.74498492853128459109074446666', '91.01838484656466561888612570777', '92.62677852942711066499359310313', '93.75335504725111287969261674658', '94.26628115398115249284217755843', '96.39549447911899517601052805072', '97.430578226759162009264522131068', '98.689039192977017293332781202366', '99.76733399335025764943645799601', '100.644355054682655421619353735180', '101.53657860185280409341031001503', '102.75613506123149449596273441737', '104.73210009233907807832190161655', '105.75084360044031420443621742233', '106.65831266439654624232614811456', '107.65656339818687497081601932745', '109.382466939343902075454981540683', '109.87065352675849405180278058931', '111.021182912312893486542659788818', '112.37672192726394429190891442199', '113.22836990452727715788658946232', '115.243668123069431740403919153665', '116.36198515819085951958649552100', '117.02693555414770957645175534505', '117.95634238446428480975176407306', '119.016406863888405376231497414188', '120.36041863061835280967076324548', '121.4514129084815663971899302915', '122.93932107600894068569802150800', '123.95749916742054421477955758215', '125.21563813126225045003465105328', '125.9952106459024530564510895783', '127.55575822126878068056085803904', '128.41186091077999261612579632262', '129.14833594186988828193617223385', '129.96904287142675338808019360197', '132.187939601680256638182552854675', '133.24173613454202851020108138960', '134.00787104735014996457980134203', '135.34066245715714642645745899754', '136.015726312025292612743968912541', '136.9817245213540492999111797395', '138.66273727299633146284165716435', '139.19121177776375790152995953242', '140.800791089640488285653711603322', '141.65713370519611130665671223046', '143.12932650072584165424250639119', '144.52169283532495376647206563073', '144.943114436013256213892039728903', '145.92499741726093013099832418288', '147.09300198516085271286868395388', '147.9985296693995301694882477653', '149.40964503232622469195293018536', '151.2815555700313266008861770394', '151.84884556958476114043536345700', '152.46371863127955665581465871446', '153.75136018645334022500379206407', '155.14945513912760322632318470869', '155.90880567718488258046110183853', '156.91751246066497306571858797616', '157.82568038778197795314160532889', '159.40166721825027462395331566832', '160.71588736746547339847901353499', '161.65883523865890125545773995904', '162.70991217766035423818996047000', '163.52269557497054130414474319618', '164.54724284335057780491232499610', '165.088935728772374220807609356360', '167.10335643660296193292543506481', '168.00734144848757835069818930025', '169.00378733592774298347687762115', '170.29157927113461163567406113426', '171.11724380425160133542283597942', '172.28060438314590887258913659408', '173.24296083998284529592332875965', '174.339031773328338912278356933024', '175.0688815625309690576338411349', '175.98531191366887525964138689425', '177.94363650214689943165413394607', '179.029220154872368089040153383809', '179.81008716272467406011130007792', '180.839716759895420211687911259713', '181.2424039010023483903418927547', '182.94703347139351418877767764794', '183.7230380245977028096966894677', '184.67382020782877260271592990404', '186.193762578089388178209742019589', '187.393213557863651875288671884834', '187.813946056291932235636153770084', '189.51459824403891977329935676855', '190.49134645733840416285231002290', '191.32158169255437367825868442029', '191.79038234673076433835281248106', '193.0903956940942897608478488940', '194.16738670154704908929247896731', '196.027429508490264989481342097159', '196.62656333195458603891168923495', '197.700463017830176253336153710081', '198.696375218511702719509847521651', '199.384077760336411133597488007867'], 'prelabel': '1-13-13.12-r0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.06037174619186565, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(2)', 'symmetry_type': 'orthogonal', 'types': ['DIR'], 'values': [[1, '0.662735391071845589713696515477']], 'z1': {'__RealLiteral__': 0, 'data': '3.11934147901', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '7.23159073942', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '8.62542663503', 'prec': 44}}
