{'Lhash': 'dirichlet_L_12.11', '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': 0.0557277657155683, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '12.11', 'coeff_info': ['x^2 - 1', -1, '\\\\zeta_{2}'], 'conductor': 12, 'conductor_radical': 6, 'conjugate': 'dirichlet_L_12.11', 'degree': 1, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 0, 0], 'euler_factors': [[0], [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], [1, 1], [1, -1], [1, 1], [1, -1]], 'gamma_factors': [[0], []], 'id': 26, 'index': 0, 'label': '1-12-12.11-r0-0-0', 'leading_term': '0.498557002457815436156756553987', '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/12/11', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.4985570024578156, 0.5869027447924686, 0.7916737672964158, 1.0362068597522947, 1.2782637943341755, 1.4879245697730688, 1.63670768056328, 1.6962843942684989, 1.641095430186484, 1.452653697486016, 1.1243436443147914, 0.6657040001854155, 0.10517840334527777, -0.5096217889658917, -1.1148704407096444, -1.636989769584175, -2.0022999171173153, -2.148807738376676, -2.0383902585417983, -1.6671219379446656, -1.0713465727718054, -0.3274323601980899, 0.455981445302976, 1.153105492183281, 1.6417524838667217, 1.826437450605497, 1.6594203819937, 1.1549445879087012, 0.3926103087844318, -0.4924203868912496, -1.3320799893731203, -1.9576149299413779, -2.2353661603695714, -2.0984158135695212, -1.566320683483886, -0.7469694607833447, 0.18183658725156238, 1.0088109036808912, 1.5366147851632375, 1.6297248622652492, 1.2508678111517235, 0.475796271578283, -0.5192845612998148, -1.4967480050577477, -2.2150518331113123, -2.4910293614302756, -2.250709447310048, -1.5540740980687089, -0.5850728430039277, 0.3928451149267202, 1.105693296224559, 1.344649180816178, 1.0274082558981283, 0.22664403233047817, -0.8447430641867084, -1.8899102629943014, -2.6117321863343586, -2.8004759762318114, -2.3993339081480443, -1.5266884497979536, -0.4459458965380371, 0.5105216215854804, 1.0420140682244365, 0.9743638609215537, 0.31870174535749435, -0.7263770949506921, -1.8326372818687107, -2.6440787352326316, -2.8916181536001746, -2.4834349795891804, -1.5399862804870408, -0.3596282012973781, 0.6765329965866864, 1.2308843421876232, 1.1249023564115532, 0.40403198863134726, -0.672541404793332, -1.7165723803022943, -2.3431015650525495, -2.3056754091474754, -1.5866693966787317, -0.40892189670640117, 0.8382792647470024, 1.735162067082891, 1.982211310720872, 1.511210624740201, 0.5145417506473068, -0.6207351658611462, -1.4526334187391752, -1.6480445036699924, -1.1099254499435132, -0.018791957651014386, 1.2298174457546152, 2.1712157776794725, 2.4474132118861958, 1.9461675875075342, 0.8484347550911214, -0.4367984136890409, -1.4279903463077672, -1.7583183551025257, -1.321794343460211, -0.319253446386148, 0.816734527126159, 1.5911904940645214, 1.6447480040961282, 0.9012533870978315, -0.39610998349536247, -1.7776514419497063, -2.7342204755965285, -2.9240458812936496, -2.3146564385083135, -1.199663779178133, -0.08053555078585506, 0.5404271717426186, 0.3712197450029117, -0.54332788780836, -1.834934651804648, -2.9626272931890143, -3.4397838942663244, -3.0421982097704805, -1.9076079340409988, -0.481588334217418, 0.6700396731685614, 1.1037646210612353, 0.6915517831551614, -0.3206703407121009, -1.4174974215303433, -2.038783178984799, -1.8278116533642967, -0.7934679870702539, 0.6873319792423731, 2.031146633686257, 2.704397643226449, 2.461464618162231, 1.4570451556519235, 0.1797924595437076, -0.765906806881049, -0.9335363978972422, -0.23965967230528717, 0.9943383084645879, 2.1859865143651396, 2.757997541039771, 2.4062358482851804, 1.2452953612249553, -0.2380511407975347, -1.4051450049903478, -1.7595413673418638, -1.1784375760455559, 0.028231042758314756, 1.2615563191090442, 1.9154909345869435, 1.6652825336972246, 0.6254510399713588, -0.7000804282403174, -1.655127547619293, -1.7449078561072755, -0.8766548305541157, 0.5898951890973424, 2.0094516017853414, 2.7580090075653096, 2.5327302343277593, 1.4988773917808076, 0.20998722165748884, -0.6627409367314252, -0.6616078506552799, 0.2280984476177684, 1.5650537558069912, 2.6648810585015186, 2.9368135135973823, 2.178498545834735, 0.6815343155089166, -0.9075516627675834, -1.9046520379230234, -1.9270174015060908, -1.083750518492489, 0.07994589021830528, 0.8595981330771447, 0.7517892601707381, -0.28410496891106046, -1.7974441475212934, -3.0688078084202237, -3.473054767241332, -2.798857135033796, -1.3601920037533823, 0.16011461606743416, 1.057409965946206, 0.9658439934075873, 0.046112672883549075, -1.0990207564324734, -1.740478848234171, -1.4077419004661378, -0.14227711560314643, 1.5149967812013847, 2.7990095067398286, 3.1171559684044134, 2.3598816072605766, 0.9604448744867168, -0.3305159074978053, -0.8393220207233324, -0.32501827903885566, 0.8930481136984625, 2.106156945357665, 2.597308831765716, 2.030418498610773, 0.638572757818508, -0.8923450703021134, -1.7855885505085825, -1.5886657183454842, -0.4180331484713552, 1.1007992551627577, 2.1683765801832138, 2.242343894618661, 1.3307937440015807, -0.013325165494893574, -0.9964090270178422, -1.0230520182228944, -0.029702233596990285, 1.4717642152689008, 2.6678487760420593, 2.887082980423988, 1.9703186293702277, 0.3621363188380333, -1.1299589283746188, -1.7780409418785097, -1.3338224380857429, -0.16313926599845924, 0.9623621355602333, 1.302554597316829, 0.5717255325897678, -0.8910343667444454, -2.302639738938081, -2.869910838356364, -2.234490121995531, -0.677709957223935, 1.0326356091786206, 2.070051893449442, 2.0114260419363514, 1.0712905867819946, -0.02671011802803013, -0.47040247539611163, 0.1667743182157277, 1.6697218163019554, 3.2931064426036025, 4.180034646582115, 3.8502698557631625, 2.4776233579888745, 0.79476616662179, -0.32280360578247924, -0.3558686994605297, 0.5644559688567525, 1.7395340889258322, 2.3171570036315274, 1.7975723910818924, 0.3364943394454204, -1.3342378640300523, -2.325647656907642, -2.1079980377163055, -0.8226294342889416, 0.7956058112042373, 1.8430345175818243, 1.7719584565442945, 0.7072987136947901, -0.6329351635560028, -1.3686152745394529, -0.9864786337309651, 0.34674770890349055, 1.8754211917429235, 2.6995783201696937, 2.3109878663619607, 0.9013913505796428, -0.743318614507237, -1.7033214178448146, -1.4670803400734553, -0.23161117713824728, 1.2205674934469593, 1.9960848739725685, 1.6328707985820223, 0.3826741088770848, -0.9389429139019182, -1.447583255403627, -0.7323940986368458, 0.8833138115635039, 2.524286167252999, 3.2816872787131595, 2.7553944367626864, 1.2907844001368898, -0.23576542696608255, -0.9539543885798474, -0.5322334356573833, 0.6206106582706232, 1.6108274361839103, 1.6178112571054526, 0.41289474903643564, -1.4820546215301706, -3.0977366711782763, -3.5994909921024734, -2.7915999773992963, -1.2322003469240952, 0.11421706646147303, 0.4736947585967803, -0.26019560133406017, -1.4664529831826894, -2.193207630150484, -1.7654322017333328, -0.22449908422997408, 1.6776926120902744, 2.9306845667266, 2.8845548442135804, 1.6499476813658762, 0.02713399421538646, -0.9939878264216006, -0.8510603050192012, 0.2440574416888628, 1.4486259960449401, 1.8336942708616182, 0.9867594890707877, -0.7102384584644724, -2.3071810418295065, -2.876974392123583, -2.09915151795218, -0.46502145109311316, 1.0286620351940254, 1.5058947345822993, 0.7607306638031931, -0.6204925177291365, -1.6433992176883296, -1.5519345996576468, -0.32284879481946627, 1.3108969517595108, 2.326264987845524, 2.0691360662028746, 0.6827638091031094, -0.972538487289307, -1.8607654263738587, -1.427063128274841, 0.052482612648687435, 1.654879222293821, 2.4107465923524916, 1.9334086541072368, 0.6679160092374916, -0.40385361635841444, -0.41254405854698917, 0.816967681395965, 2.6326775726012874, 3.962377595697771, 3.9993278661423437, 2.7213908666538926, 0.9040674443238614, -0.38319300762079933, -0.4697207753858843, 0.4879457901050602, 1.623888263849852, 1.95073385916809, 1.0310342312847767, -0.7122247288319814, -2.254934244527063, -2.6345588141693774, -1.5814802386675146, 0.2983988771811342, 1.9132219803241877, 2.3923737901828304, 1.6449501114463683, 0.39956839760015145, -0.30141585341478033, 0.1829574798854965, 1.6454661973931977, 3.1535188681290984, 3.6637584646042387, 2.7207513809225734, 0.7725203054093347, -1.111360809853702, -1.9349011581871767, -1.4219528133076325, -0.18172896516166867, 0.7178122968615314, 0.4827128864980703, -0.8614595134022428, -2.4807379499482676, -3.2958751214096704, -2.71927802217846, -1.0672008198915357, 0.6351166042032551, 1.3285672935662636, 0.6225386067727359, -0.9498860186307745, -2.2979498820381368, -2.514056199720115, -1.4873888780264657, 0.027257707935157686, 0.9335770316990446, 0.5543681649328274, -0.8914383446426478, -2.4246310813450638, -2.9662118958696126, -2.0741937957471066, -0.2528409080310993, 1.380031368895627, 1.8435855779540264, 0.9506622943132669, -0.5789307358567352, -1.6266291781051456, -1.455570670522964, -0.22495282620283538, 1.1187985510601852, 1.5020535583192671, 0.48106312662935075, -1.4285070540437932, -3.081904125584864, -3.4724798618455472, -2.4088452679177643, -0.6344902237229177, 0.6935770642969101, 0.8064687579716652, -0.1512020733106756, -1.2383088100112674, -1.3960858617412693, -0.21538756094688366, 1.7458800347408203, 3.3222164802582697, 3.531784571570354, 2.2504263872804806, 0.29766713484195917, -1.1276781016828337, -1.2701575572908759, -0.3243197721221617, 0.7290572275802729, 0.8415738796885146, -0.3359700184450792, -2.181442752378384, -3.520423613733788, -3.4455890118830226, -1.9604629224600618, 0.00854206272702222, 1.244812358494047, 1.076876716170006, -0.17082687279167666, -1.4294008747749427, -1.6608723069889053, -0.6073215136395884, 1.0195277881080498, 2.0454349415866244, 1.6787464767043943, 0.09146841189372441, -1.6812925424585683, -2.4576249170610365, -1.7353053494631792, -0.04130005987374609, 1.4458686950091444, 1.7334732073009904, 0.7151552059293259, -0.7656999708508418, -1.5352997305674219, -0.9472954868379027, 0.6382847587483362, 2.1028321475863794, 2.3700633588354276, 1.1867384270109833, -0.6794761616754612, -1.9716571638050515, -1.827231171584868, -0.38086795524757144, 1.3463090247429115, 2.1911287881696095, 1.6888425444769797, 0.4013275680131855, -0.505940429213514, -0.13269397178775488, 1.4726718332261115, 3.315317941400267, 4.1469653177654715, 3.3527010034570996, 1.3906175430001178, -0.5355689051490243, -1.3353979314921907, -0.799877439112431, 0.2783848937125971, 0.7191730495282905, -0.14729914845692654, -1.9578756076487092, -3.5568386007398747, -3.829028558382987, -2.5193324531479693, -0.43772673855073985, 1.1048788402465688, 1.2226130061234508, 0.06861016637209794, -1.3102922482059935, -1.7695845822946599, -0.9271342792677373, 0.5477134575913791, 1.4314948017896083, 0.8655150568677259, -0.9826706030069794, -3.008215784251437, -3.9499113213508483, -3.2929410165781423, -1.6301027715527325, -0.21480691252855003, -0.034929678462127176, -1.0913600249881847, -2.4146956798224917, -2.807006802031229, -1.7566227982558416, 0.15696393757136906, 1.6742182538400554, 1.782024961548412, 0.4685375325545488, -1.2571233278802654, -2.0996974022026706, -1.4249290783963797, 0.28335934417051856, 1.7957125632775015, 2.060746597067391, 0.9897540372462165, -0.48540062845545057, -1.1255071749267067, -0.3339344870619546, 1.371707126248271, 2.725660862036334, 2.649759763986696, 1.0608585052540778, -1.0558462364979861, -2.365611351194604, -2.159098150204584, -0.8540503405007133, 0.3510972765645966, 0.4083774158137967, -0.7687523740804989, -2.2305286669945725, -2.712775071521549, -1.6123633345708144, 0.5229109958653932, 2.366507221086035, 2.773934590517433, 1.6122313929724355, -0.1655001944769696, -1.2552462966499967, -0.9893324094994798, 0.1731152441173276, 1.0244989508915938, 0.5667865748265469, -1.1833481909554573, -3.161937501140943, -4.031037292077122, -3.176110914785106, -1.170671931283284, 0.6473790743011859, 1.1689274602506148, 0.3234475191743457, -0.9085986216501785, -1.2865934260871035, -0.2952672468308068, 1.4339215751624639, 2.593200127911474, 2.203779237359867, 0.38526312405603313, -1.70545801583817, -2.7263709887548817, -2.146798967382735, -0.627807286999084, 0.5038439671929327, 0.28377681064403315, -1.1503353081793237, -2.676575454511816, -3.0724731821972555, -1.9808184072121882, -0.20772553058675292, 0.8833878518289859, 0.4192067587518321, -1.3021261513287712, -3.0248936378585634, -3.4849383005132633, -2.3654106108616677, -0.5233204552345356, 0.6865184219276926, 0.4651438908611918, -0.8174816009954443, -1.9268213462272805, -1.7491481047566504, -0.18958355994465254, 1.7213567439296593, 2.603440584678483, 1.7878188465584584, -0.15942882424631066, -1.860395520921904, -2.169754588292382, -1.0314219130346776, 0.5161111061783801, 1.1857903072855387, 0.4742033574493515, -0.9317369970189932, -1.6964379384799717, -0.904278303251815, 1.183199647538745, 3.281292756695764, 4.036297403458256, 3.0412424803860807, 1.1231759177199205, -0.32028310037483465, -0.41365147009836856, 0.5321062128719352, 1.3041182305450385, 0.7937881704188242, -1.0733282727920403, -3.2249507239288153, -4.245211263974372, -3.4680607419157914, -1.501593468530968, 0.232744879664056, 0.5882926280124458, -0.44374546249712044, -1.772117517524038, -2.1093518985699533, -1.0220820116491962, 0.7079835195898736, 1.7020747527345563, 1.0928713113132158, -0.7582593045631111, -2.5112930278181764, -2.8755075908663716, -1.6070509612892316, 0.3121002942005143, 1.4558181466091373, 1.0769271610179034, -0.3187354426798148, -1.4013951441495651, -1.1047039051893717, 0.4993474204550664, 2.2409412966584474, 2.7810950142297286, 1.6895370464687116, -0.19115850581341812, -1.3924617904007612, -0.968766273784597, 0.76390532545217, 2.4871510215339048, 2.929857124948024, 1.86938512080649, 0.28427951348906877, -0.4612794327338732, 0.2568878300154669], 'positive_zeros': ['3.80462763305086509714431754003', '6.69222332050013115991012819444', '8.890592958726741509335625537170', '11.18839274507490915416358679559', '12.966178808028845374957099032698', '15.181480875888216735397832429452', '16.632633274523762123171390835505', '18.884369457120650808166588937461', '20.10392819124581857313303938476', '22.285839107226887658739733010514', '23.561319713137844716347932732028', '25.411633892392695962033821338368', '27.013943985850672344345415796374', '28.44220325774560811850882430583', '30.20400655643888185431053894859', '31.648077614940686366898633770299', '33.037132879506503601921758064941', '35.02737848501270258165386682011', '35.77804457652351027241685311662', '37.92681682137521283528523170529', '38.97399882227494028953955236153', '40.48415475080402043184282320936', '42.23514301791452202974955316843', '43.192847102617221657447923692506', '44.94882250215854377900265729379', '46.24336997904449113816991169202', '47.64640050097841353818233520547', '48.94372801181154403766149113430', '50.68247370870381801555606155660', '51.50144965428900306753636761351', '53.25295350194411129650859250323', '54.66474663458226693914040487807', '55.557957047761764710160536729866', '57.46281800853182310573545241255', '58.4499112517594547977125199801', '59.71528623182713343644290733806', '61.46861264432186164192945362931', '62.2828462419935942660484451728', '63.8743468141202336874645947752', '65.086085807259905157303652991367', '66.5592866751383944322760290281', '67.506740139102626184102913412', '69.130110327778964003742597389702', '70.352174860587656928597706943583', '71.38283522451618660002829391551', '72.930733922802756141741555609484', '74.365706132513364465657113079764', '74.95209974202992946324880844421', '77.06556608767700799168009130985', '77.64991492365901467880022859140', '79.12312383473225418471486973220', '80.46802427720213289191557128686', '81.72189933639796160588096848307', '82.74288223441881030979894122497', '84.22753294357007561191441171883', '85.36022988019767139163795929351', '86.645200071803277171205150425210', '87.654412874552796936707537571389', '89.31875093075840174547246787967', '90.15544169801626687714070021027', '91.32296823341590663447741370663', '93.08914855026156623507463708939', '93.67247342044831372724634442732', '95.03674524411889006793818486917', '96.56829223271701624166080163588', '97.441444672758210542785855739833', '98.62790439635903725202155211983', '100.08505583887374266104543537310', '101.11336635511982525297240624949', '102.24919913404026990916013150324', '103.56092168370775440653723385902', '104.677966713700396811797677440657', '106.10587718178267475714802765333', '106.700615353102109448468627087712', '108.627335793089180658337975467911', '109.242758268488454635792949971959', '110.50430095355178412450499841117', '111.82724607888611055187855823251', '113.25071655974607861820446038147', '113.69175951315446006527762139519', '115.42896349854255711595571965950', '116.60910343349908286253786891853', '117.323346635251388569324996804676', '118.932970521591422335250168676593', '119.820719294585806494405428239347', '121.24386645193378507682716984506', '122.01326276247324424705652154680', '123.47881240350289174319867374162', '124.56991786460242258430826386081', '125.67224158442230184038347431682', '126.64877180740398885437873469436', '128.24782038194791088578435986220', '129.023302421761594782113169987058', '130.03770681674868023344629470339', '131.6134263190101663342059228146', '132.5845863258591779344841858438', '133.37198234674291741727184770050', '134.99850631391482269284362369511', '135.900818048318346613560625637048', '136.992740889892560819282607389544', '138.14004891365196362702433685637', '139.382173613883381492258711826389', '140.45989505926904582841325168427', '141.44733637874455722851406983148', '142.698776730960020056843353939229', '143.81535774117711890018104766203', '145.10360590300294645117859199553', '145.66063254874701159188970911891', '147.39966045150305701429286192935', '148.35226438799103017084859446108', '149.030364258093647226737326321317', '150.6951564803123412129703956722', '151.57692066180193751766167299924', '152.69608126403180534175546303446', '153.60158051849211075963530565973', '155.4121205037183433208333741144', '155.60253390371395150421962108891', '157.162390817613308090503826528301', '158.20697283636030515577382473650', '159.32700904093304856075045076552', '160.514463082130980711688036409142', '161.318569620087972096660605542318', '162.65355203117156893514809465046', '163.94739846121791050173520052605', '164.51389052266277880161592497008', '165.864975253692154556958267068878', '167.15639397377296674061623508778', '168.08152860035635912279540052632', '168.87136921206239137990516715268', '170.4945656894738917826546028766', '171.32798543753789901144358219616', '172.24454201166452276011035537763', '173.491801737386694088717678932', '174.826306825533831876226094667144', '175.39241005309027882774732090894', '176.91551819384757748366309905262', '177.59172318861264364562164689671', '179.16441244773858007145966471142', '179.81756493983324194267354437815', '180.96728716330586923884987869815', '182.16356084948894077503661362806', '183.32489488820142021424836995920', '184.17111658810491530838194741292', '185.15003897463843483483633355191', '186.77883927267960007572175264672', '187.34565507954039615850656276163', '188.27860890521110893871723578934', '189.94352248505514513774359284127', '190.521423586704370274888727398852', '191.74537755074612104272802997570', '192.69656274057560979455151354305', '194.00867785169739925766362812533', '194.93372256881282365942695885512', '195.854666432101248695008797401891', '197.15459967867528481963077611312', '198.0023662129029902802670413745', '199.446024271340080373272008456882', '199.93475544005386038383301741410'], 'prelabel': '1-12-12.11-r0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.0557277657155683, '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, '0.760345996300946347531094254881']], 'z1': {'__RealLiteral__': 0, 'data': '3.80462763305', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '6.6922233205', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '8.89059295873', 'prec': 44}}
