Formats: - HTML - YAML - JSON - 2026-09-21T00:59:31.994875
Query: /api/lfunc_lfunctions/?_offset=0
Show schema

{'Lhash': 'dirichlet_L_231.194', 'a10': [-0.5, 0.8660254037844386], 'a2': [0.6691306063588582, -0.7431448254773942], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.10452846326765347, -0.9945218953682733], 'a5': [-0.9781476007338057, 0.20791169081775934], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.8090169943749475, -0.5877852522924731], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 24.82439762755838, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [11, [1]]], 'bad_primes': [3, 7, 11], 'central_character': '231.194', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 231, 'conductor_radical': 231, 'conjugate': 'dirichlet_L_231.206', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^26', 0, 'a^22', 'a^14', 0, 0, 'a^18', 0, 'a^10', 0, 0, 'a^6', 0, 0, 'a^14', 'a^19', 0, 'a^8', 'a^6', 0, 0, 'a^5', 0, 'a^28', 'a^2', 0, 0, 'a^12', 0, 'a^1', 'a^10', 0, 'a^15', 0, 0, 'a^2', 'a^4', 0, 'a^2', 'a^3', 0, 'a^15', 0, 0, 'a^1', 'a^8', 0, 0, 'a^24', 0, 'a^28', 'a^1', 0, 0, 0, 0, 'a^8', 'a^22', 0, 'a^14', 'a^27', 0, 'a^6', 'a^20', 0, 'a^10', 'a^11', 0, 0, 'a^9', 0, 'a^22', 'a^28', 0, 'a^0', 0, 0, 'a^11', 'a^28', 0, 'a^29', 'a^9', 0, 'a^3', 'a^11', 0, 0, 'a^20', 0, 0, 'a^27', 0, 'a^4', 'a^22', 0, 'a^21', 0, 0, 'a^20'], 'euler_factors': [[1, 'a^26'], [0], [1, 'a^14'], [0], [0], [1, 'a^6'], [1, 'a^19'], [1, 'a^8'], [1, 'a^5'], [1, 'a^12'], [1, 'a^1'], [1, 'a^2'], [1, 'a^3'], [1, 'a^15'], [1, 'a^8'], [1, 'a^1'], [1, 'a^22'], [1, 'a^14'], [1, 'a^10'], [1, 'a^9'], [1, 'a^22'], [1, 'a^11'], [1, 'a^9'], [1, 'a^20'], [1, 'a^21'], [1, 'a^1']], 'gamma_factors': [[1], []], 'id': 9828, 'index': 0, 'label': '1-231-231.194-r1-0-0', 'leading_term': '1.17477057633538666914010158786+0.459840773468131042143312308168*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/231/194', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 14}, 'plot_values': [1.2615623028479988, 1.8410041789241407, 1.834928842768936, 1.2530858207362434, 0.25086558092125266, -0.8360958406568512, -1.5807449596794665, -1.6586946002850373, -1.0417558205360746, -0.059366559880247013, 0.7464365277925223, 0.9252761973327498, 0.41454034005458906, -0.37381184640197845, -0.7767132815685753, -0.3180553645035355, 0.9080235898848145, 2.195186882518967, 2.6217997215414686, 1.6828977355339467, -0.25920048338264134, -2.0677738172310796, -2.496311469045847, -1.038082131559669, 1.6233912504617454, 3.9404574319253207, 4.463930422226034, 2.820637765240679, 0.010135162728105357, -2.2364493069678013, -2.6208793320536943, -1.1409753025572327, 0.9807539209461625, 2.2483731662067132, 1.9951652208985178, 0.7873477851130694, -0.16602461781851013, -0.08482506911340851, 0.7383708536230033, 1.268064908904403, 0.7310737949334656, -0.60831034530705, -1.6296963879531146, -1.3730094956060994, 0.017813895640015804, 1.3281403172088218, 1.3364112034923696, -0.01226126845642799, -1.43727142820318, -1.4310183891839112, 0.2681333414430055, 2.1978989781337597, 2.263838780240501, -0.4251425893092401, -4.572201303071384, -7.5230382072687405, -7.317570493239812, -4.2487441992591455, -0.5809003246703743, 1.3325065994979948, 0.8883399102920265, -0.5478702365152135, -1.1312538231962832, -0.27657455880842124, 0.9689503238501227, 1.1698591289317382, 0.048614009571558266, -1.2282167975378389, -1.281202644002318, 0.025629049823836656, 1.424709365213218, 1.5618388617738017, 0.4184662391510132, -0.6797619217543165, -0.523725157129626, 0.585614408207032, 1.0718293119107138, -0.16324847710003962, -2.265683843073926, -2.9261611727425785, -0.5928725428774382, 3.722841933935096, 6.980472228990029, 6.696377910791755, 3.1980411033037197, -0.6481948440066582, -2.0309814410670506, -0.6389776306099018, 1.3565376953343173, 1.6431299667675883, 0.017988949840298373, -1.6640749300340485, -1.6238940152255297, -0.03746014215923207, 1.2821384197709136, 0.9289102656241536, -0.6172921836602219, -1.654618213233371, -1.2271368819657786, -0.1304791426830249, 0.1682396245570476, -0.6009389081788789, -1.0942975640148342, 0.027854182066696397, 2.2900174551611547, 3.621513626620181, 2.596903676410971, 0.26544136616898845, -0.6510772904730051, 1.4034979049555827, 4.934897190360873, 6.663585447314149, 4.81856730484623, 1.0428658874739778, -1.1785118949089273, -0.005868365640681126, 2.976462791568304, 4.511889801902561, 3.0296841189177144, 0.0543115123740762, -1.6694135935891223, -1.1047720643942893, 0.29945494738675815, 0.6004353173689103, -0.37475094342606124, -1.0993296212780157, -0.4686292381485085, 0.7313703888961842, 0.8255733132571325, -0.5425505804716942, -1.7931408418531705, -1.2656060438360592, 0.6549134302203405, 1.8229304742660033, 0.8624888824575734, -1.0580515016232823, -1.5068019986201284, 0.18785259650745537, 1.775168102403088, 0.44867188636003597, -3.727776534119285, -7.317762328804363, -6.821843560598391, -2.3508405147029934, 2.3704108436515146, 3.728123741069937, 1.6451854834507644, -0.8854799874229948, -1.339143661467314, -0.15117965764236613, 0.43687118299967653, -0.5885675405946293, -1.8731159701381048, -1.6478256609546162, -0.12159797651641308, 0.753550974021142, -0.20254148680009693, -1.8509370409275983, -2.154657056201292, -0.765648557115476, 0.5509868468097896, 0.23973068107586937, -0.9727910580033465, -1.0525990292339185, 0.42232798462884225, 1.219929347772879, -0.993957630560806, -5.368803405775146, -8.048866780711869, -6.12680218085792, -1.0260105000608444, 2.722059554763741, 2.144099437384701, -1.2511317677948113, -3.4937128877856867, -2.6215807543312866, -0.43267148336029587, 0.20271833520075844, -1.0853481535542056, -2.0213888717537465, -0.8282800845946579, 1.479716276404536, 2.465859391964946, 1.361197108688615, -0.13397329680996697, -0.22429137769323987, 0.6827502625089462, 0.77779514821537, -0.4434570918502417, -1.3472377272053864, -0.45815504175884814, 1.2001097143967303, 1.1145733854834787, -1.3451346756412472, -3.6033438468855543, -2.7414601110615227, 0.7128534646490737, 2.930369035964436, 1.1006658777491245, -3.130196405521387, -5.390362464167226, -3.585193256890324, -0.23351045387971237, 0.623734915017926, -1.8479189462302785, -4.559029504885899, -4.3981914920103655, -1.7928596295412031, 0.27013153244496285, 0.11641670950225602, -0.8920771164679963, -0.6603685121018548, 0.7253446184622575, 1.3794848223759755, 0.5135824650524744, -0.3406146560380091, 0.4651761562363015, 2.171956474168634, 2.439962009354036, 0.5861245811802647, -1.2189890500526843, -0.6831575492087146, 1.4578103843779215, 2.2646853886986014, 0.606853259117657, -0.9428203124606138, 0.7749426660510044, 5.064281476336088, 7.46261971809792, 4.7545160093294605, -1.0482084184076474, -4.739530725495388, -3.6313427092668413, -0.13607580791295598, 1.599067876788001, 0.5245619874043457, -0.8745670509178344, -0.4414259486108495, 0.9122239749934608, 0.9615710306800438, -0.45020284888103657, -1.2225672172626685, -0.11563914928047558, 1.357833221330776, 0.9949779994788637, -0.9760699634195483, -2.1462164364159135, -1.2433929637686658, 0.16402250628095072, 0.051610900430585874, -0.9601984198076112, -0.39806827575296116, 2.1821382405108807, 3.7291765509278356, 1.304587995868443, -3.5849752440725267, -5.922045704948744, -2.8705180001161947, 2.677841583964399, 5.288040120248686, 3.10969986466727, -0.5065971742428782, -1.5587320532428492, -0.06736808285913373, 0.8430906423870085, -0.3857221881344083, -1.7948710449683956, -0.9825716703978693, 1.3918839432983998, 2.527852470462232, 1.3226494134013247, -0.3211504883234019, -0.37795262137260865, 0.5142280821545935, 0.31392766734967603, -1.1413112228951163, -1.7975703527784925, -0.5836209267654564, 0.6452446695849298, -0.36179117810683764, -2.6059087818655082, -2.573867389406425, 1.0221358185301086, 4.8565542263854, 4.719137373433159, 0.9077674093003775, -1.8666891428411894, -0.2731310845580965, 3.5162696252426553, 4.705489002981131, 1.9687198000554065, -1.130437808114366, -0.9704022758075148, 1.623949018956571, 2.9413451600085327, 1.4341352076031781, -0.6538742138724857, -0.8152220833918016, 0.3747947541348432, 0.6330239560653022, -0.4098965536061379, -0.8150505866604631, 0.43162774776209745, 1.6259157522403778, 0.8561892886398432, -0.8946531343692882, -0.9012749488467537, 1.2781232208695716, 2.815090579552496, 1.4684178133986894, -1.0686698343892873, -1.4046278384528317, 0.5279209076072018, 0.8748712662895801, -2.890148539949074, -7.813778698220876, -8.456119041003136, -3.593688173828055, 2.06472186788185, 3.4806124173991164, 0.9896024004516588, -0.9967962603452014, 0.012624670033559458, 2.003520330369158, 2.076245368726201, 0.5485504934005662, -0.11272629179025409, 0.6696917199285004, 0.8144671735254804, -0.9479756246431732, -2.8204933124975504, -2.428792489215249, -0.3547715848385136, 0.640964444398172, -0.3763031471857066, -1.2794601632997458, -0.3180602894660133, 0.9974293829825807, 0.18487648676049212, -1.9576290968962933, -1.8204274548147452, 1.7414346190427699, 4.7416177340217605, 2.55716162591498, -3.8287996362394145, -8.347295682038887, -6.931322645750067, -2.118568685377931, 0.6253020380608776, -0.32462003041508647, -1.7523132941425168, -0.8985151087650651, 0.8142062897858569, 0.5000812379306395, -1.6061361528030127, -2.511448496626988, -0.9330036502722603, 0.9128723502399194, 0.7004881964896688, -0.6899371341238223, -0.8203093849411649, 0.4548587223528389, 0.9319902161747526, -0.22071636845923737, -0.9532407656596742, 0.3460321474085297, 1.8043134632404179, 0.4794360366502404, -2.844096764685798, -3.859078511043053, -0.5210463667477699, 3.5187817981803655, 3.2099858050808856, -1.2560807071553555, -4.578441440857696, -3.278711617307036, -0.05709748201078599, 0.22790163964504118, -2.816172444355198, -4.967075733894456, -3.455272784472441, -0.5034644563644843, 0.24682980284978664, -1.2230709423043353, -1.9413015243874243, -0.6654130128789739, 0.5793738097519912, 0.032821798455935254, -1.056555741898972, -0.7096672526902746, 0.3392443467190208, -0.27208579740836064, -2.4888225285992935, -3.375530722242232, -1.4229804512674404, 0.8493309602758652, 0.36179620916920285, -1.8630877252531255, -2.0647257116039737, 0.42468173084541366, 1.570001794053633, -1.7323726157100956, -6.543680121313173, -7.033643693038861, -2.1124549493224594, 2.9065205716928264, 3.030858378554885, -0.408240394519811, -2.3114072982762814, -0.7710109931520306, 1.2474698462606761, 0.9467288363394674, -0.5092798639357191, -0.5911044436952035, 0.3814108518959547, 0.06291595385700278, -1.728161088231004, -2.3808702578354293, -0.5342575313023296, 1.6206885082195537, 1.5453438899980387, 0.14073358680060394, 0.15256512872918768, 1.663668877182607, 1.8971015998352454, -0.12973232742335172, -1.523324660045493, 0.1005567839388413, 2.13026930913703, -0.14214503661177777, -6.48073008573495, -10.717369843634133, -8.120415205722976, -1.4446728380848066, 2.61998402415311, 1.7050450487644184, -0.38459947731872035, 0.08108990373708597, 1.8537218675482305, 1.6444514116527085, -0.42885791705872855, -1.2327940320331083, 0.2931695198145476, 1.5128759502146554, 0.28558810738001006, -1.7595255897047024, -1.8839044582023967, -0.43380824773729465, 0.03947246867312812, -0.9167458769668257, -1.0220495295111585, 0.6736969896313835, 1.8398504925948593, 0.6453498317244062, -0.629808386049427, 1.448912163181196, 5.734949906135547, 7.018831242321809, 3.090310186328293, -1.6128399655816514, -1.5848505543045561, 2.4064404355177538, 4.58913874748389, 2.2470243988798404, -0.8902386371765013, -0.4100409615589723, 2.5660193453943205, 3.510678118593126, 1.2171244339997374, -0.912136457607568, -0.30142381414714825, 1.2590085634274473, 0.9375526373837484, -0.716116786711398, -1.097700033085273, 0.050503975137995934, 0.4900742918003385, -0.40003730434300055, -0.3480467724020399, 1.8590441883772018, 3.694446207310184, 2.3641364078342857, -0.6875069102262817, -1.6537274385721732, -0.21730790766694577, -0.20581262981831008, -3.4682723639616935, -6.238064660970384, -4.1917056695296955, 0.7899996390151864, 2.487031012225673, -1.2033833272282604, -5.231800081495995, -4.247657700460449, 0.376377536226417, 3.020786201592018, 1.5992674902350552, -0.5740219413255154, -0.49984253189576494, 0.49564529577987404, -0.05182253795044366, -1.3688964219505015, -0.9916889776372176, 0.7756668548719297, 1.1358132744267813, -0.5812965779022912, -1.641421371295553, -0.2566671614842531, 1.4553511703455442, 0.8402061662883189, -0.9837560412964645, -1.0164420974706463, 0.4667763074037463, 0.15672655321752818, -2.4628520643699563, -3.13784682798578, 1.0543261679594904, 6.222273389808871, 5.832752435338611, -0.45795908792653156, -5.879566375899385, -5.181687811867284, -0.8315011636375066, 1.423268301230175, 0.4560121338004609, -0.13507296512825648, 1.4375047474188611, 2.586589410121776, 1.1031102288096668, -1.0263077693561011, -0.8247600156638276, 0.9360861958357296, 1.1565010488078915, -0.5288123230887388, -1.3335584212464284, -0.01601410029466243, 1.1953560518934536, 0.5423268741028618, -0.25251458056943205, 0.8188519775220735, 2.0101670507508023, 0.2887199484426902, -3.0472671135988976, -3.1164461917207813, 1.342048673263548, 5.112133648399468, 3.266883395975748, -1.783062827707403, -3.4988931261400893, -0.29581977115258257, 2.647168788331774, 1.1830075330958951, -2.1492088762888493, -2.575792340951465, -0.2622490858790125, 0.582204016003382, -1.4743742398410102, -3.1779151297458967, -1.9934770438970526, 0.16534236040848752, 0.4272889005347459, -0.568502150071942, -0.40980918758268964, 0.6395355141200693, 0.252188901791931, -1.4607252840397797, -1.6023210497104556, 0.6303256660470599, 2.0293955552822336, 0.2500935898161845, -2.136349364705142, -1.4631446808510864, 0.9358792477563982, 0.3862400509702618, -3.6074141468234675, -5.780577680686528, -2.7257884408661304, 1.5377579179289196, 0.9134470239307166, -4.022130636286301, -6.779653348399569, -4.0458451281781525, 0.24186114818378673, 1.1646425975003025, -0.5744452104840466, -1.0727381365287068, 0.3530854836790682, 0.977641045566392, -0.07035608498811155, -0.3924987419082649, 1.1927416049757575, 2.3112895201389194, 1.0082104279945532, -0.7395545172645807, -0.13969527882909205, 1.7263896126252978, 1.60718844318463, -0.47724737853695615, -1.2210808488596625, 0.2957763149897254, 0.8533099361423624, -1.2247485457444502, -2.208922558992825, 1.7221094112725766, 7.473615088943511, 7.897853596667998, 1.5557640628142033, -4.791823110928998, -4.997278860545914, -1.0814955280589427, 0.8568912836022454, -0.5881069156047254, -1.597090985082331, -0.16633150478521164, 1.0495207082728295, -0.14243808371578448, -1.601479964876244, -0.5633544214215456, 1.6451166346123134, 1.83194553559523, 0.210878681124793, -0.1402632497073738, 1.460633214672829, 2.2883860107107656, 1.0050007585790461, -0.15612541931222956, 0.3201973232257679, 0.07140625844796922, -3.035499068828503, -6.084742962310691, -4.550294263726172, 0.3172500505331013, 2.1553726439046064, -1.5262116729082826, -5.3322374198483065, -3.5321891570174833, 1.7733498286478668, 3.9602065919723284, 1.401660122077233, -1.0846142280656859, -0.2190179492347564], 'positive_zeros': ['1.31997720104922816572255819115', '2.83138445145136414284850988261', '3.91194193564392128659698213942', '4.78361003037088080527830017965', '6.21155959039288133130073250945', '7.31742180102221474782273026935', '8.75112314970598966971803057747', '9.85213926715956713352658589329', '11.16748712944976309302181795223', '11.60382069896253202139015957903', '12.67902082686731704646057210971', '13.746521491929765441166635363167', '14.685208198854810503514581014101', '15.58595862343116372907856531805', '16.52668273998037643736655820718', '18.18818571074889685520800122761', '18.94051870020023833197732480072', '19.75159481248469025641826608818', '20.635323193759298218568796779045', '21.557585462380445864785494922928', '22.59628038198550363162650771679', '23.28209498928514886977532061615', '24.036248690766260292154628436955', '25.0477216006165107875112026233', '26.49891832503322764642981289451', '27.27775267169172864529117406409', '28.127750920988681655504375627755', '29.06902196054821364891635066969', '29.882654968924221726783490452374', '30.98748583459583426006834640451', '31.34907775942317362623329179242', '32.18302983045047728691810488853', '33.47955305582517142576108427187', '33.90255399863541594136860438202', '35.41373046658463127641635102981', '35.938206913338212211448417471237', '37.193716723728592933331361507428', '38.04820084263111454998358698764', '38.649433073488079182145639784648', '39.49005312183773980655630829341', '40.20948471148397479102632682059', '41.14889814496983257490316778375', '42.0105639429883394739780184159', '42.785663101199102298734864227686', '43.47985620939230779421022928431', '44.82725982569656953238310218129', '45.80804477911841514991987704303', '46.60183601894876330087247122083', '47.05466311486937863212889481456', '48.14993182084680717019141151433', '48.71053542772276839976073398113', '49.83506426109376524384830632333', '50.37641137209534506358510922901', '51.172213414167163790455247853923', '51.78287147351170716951271968963', '53.188755033625351247075616585939', '53.95393495500164152778412041572', '55.09206753524607502444156711576', '55.39048004273638694173985342003', '56.36201245416143054355963080642', '57.45991352705611659860345626672', '57.89892999907039443811244436461', '58.65408213389206305560507652612', '59.45640150139949318294583168483', '60.16582870853439328627135265319', '61.18921043832979914447895750503', '61.961092973381608486331192929808', '63.15424214345948658741016409309', '63.55191716266690276088040332863', '64.93173195759216187727236902342', '65.34748954631763531439584606308', '66.09478521060979704059249110669', '67.01343100161252657637130376264', '67.39559898838076655651881442217', '68.51713876408572849483099615521', '69.16865724243873055056407172151', '70.086376938771723890618144741531', '70.54812951176742055518490438023', '71.81827937022388225174734288809', '72.826139977840480819470817190996', '73.5301544855728210349192356064', '74.16086420824233135556870208256', '74.90980934952827273497368635386', '75.645804326242201627671606176504', '76.41776982713511176671174260227', '77.44712633699042665144492488055', '77.82933320555016076039104498675', '78.49815747357008176742438216645', '79.46210189736020178060354712734', '80.471499266106939050504657927807', '81.50948689991720578129653501109', '82.199665879353366906347029527322', '82.745204445695920103355970912697', '83.57149770050991601710918398678', '84.605999635839143652070437561085', '85.12937706267488512245942680405', '85.70491580046910223178762094541', '86.67254235966722181095519267392', '87.13014037265345083927743157629', '88.05352878768102152401670549390', '89.13321722182394508075615148219', '89.711407298797468066043638008228', '90.79714994217026174700909284685', '91.37815684103011061263795131007', '92.38098128285230630589966624402', '93.02618654749553670346461957308', '93.640851385655714763981447717807', '94.29231762416688868611895192762', '95.1441955421412323368418918123', '95.77525332386688369560230837105', '96.73184545238663902565516812613', '97.41990539596990126778034487570', '97.921317965939519330597827288786', '99.243858055995725170698880535705', '100.11098204922079546714032241256', '100.623116922291535299658324010310', '101.71537282084926546517345508240', '101.9525009091090265247254379773', '102.67651326597333841642317032074', '103.81048628760876647842318745654', '104.29248253044037480504857877814', '105.059986338223874845609476100462', '105.65322489108740862465997036211', '106.432109101433960502398110427350', '107.32301042684832114297391848873', '108.62261938248445397932077265262', '109.00745054350279370681574164120', '109.83335600561746660877473372174', '110.39702325849830432013983860294', '111.381884542892495768833123988077', '112.02823040387543402534034677784', '112.708833945635726685070149930211', '113.38937098048022657677672169366', '114.00586641425373812320820696724', '114.73652564623652895327180378457', '115.65960289851717151278967473029', '116.48385485155002109626309878219', '117.50773611656487958456821140192', '117.84723381613148030096310916662', '119.14596739121075507801077153416', '119.45044792165873455348450786481', '120.43939012278542577606725681437', '120.94575009479590766793924566620', '121.75014985077454543962491249169', '122.13367851453788263527342184757', '123.29115253496116498376791762334', '123.80422248195541797337761871901', '124.63943026963343000915820476443', '125.19359646805459654389751757268', '126.36026298847027854332742185559', '127.15159297351633949918534389391', '127.90992146277772161361235846432', '128.62857561593218294498576180059', '129.243853267791004492711691489346', '129.70171303296053094776858642937', '130.68969735289282612533984163326', '131.610597583346331090922615955408', '131.82434802470857257258652857840', '132.79552870440629737595906526958', '133.425681533204800607939253974334', '134.05346076084991487224396212713', '135.38866948961466043302752863435', '136.16672313830775755766641530706', '136.547359997320844488686677075071', '137.43574897045551473717382194189', '138.078561086226191420581067166141', '138.79009692714363940049691193518', '139.8207170920452397564201552637', '140.02266602825272860044433739057', '140.832119672641572172990305284470', '141.670291845270879329897320790046', '142.04341128455470329313659927754', '143.30741627005906829890763968800', '143.88810492632175736985567717825', '144.884319832948798436438915363022', '145.36131734491531172543109222206', '146.389618041405571425979564227434', '146.9290867166792127498845560388', '147.67474742373194602437917810760', '148.42428336688430313035966228995', '148.93857047326925348277258963279', '149.445932371246430400769894165217', '150.54791328262498856981481433849', '151.30284791489826087092683895495', '151.52104260967484080247785021955', '152.7588158369106478200953238532', '153.36136598689557094951712993165', '154.349402971381978392010777474295', '155.203303355952208742730842430618', '155.75924282974291703668267825865', '156.237952286404154558437051186576', '157.05008419739752877257223507975', '157.72218029745953609662941926734', '158.474665603746952367276768498918', '159.19812605292250740512618198345', '159.895104347777264570912589713655', '160.3372916619698179485040721910', '161.19218356154222685101266771423', '162.16773040595928483642901568134', '163.19458176167233425629413977240', '163.86337179608724528962096526104', '164.11319144153204895482570248100', '165.14038277078194306231424800925', '165.770913406940539923049019298106', '166.47347090970556507350342548424', '167.190309640213997529967807807041', '167.96047770790660946152887019972', '168.263741211461854678932446409957', '169.08972549771838261338316227701', '169.920934966049899686402774075024', '170.82333331118475508057271994595', '171.58471610745236872582372886741', '172.29201759929294134507127206430', '173.163170204224960504668675420099', '173.56130368992686761926292143539', '174.65475403727789952306587615192', '175.13277693458753032256921150996', '175.74071395675429328149050591935', '176.30121320198874661266181025563', '177.11103800534953124884231853231', '177.839638319687390405601057061619', '178.61513819803287517941258353017', '179.10197402922057693364385735958', '180.17633564405217050053606059054', '180.69443010909478083042181923862', '181.85133589602651178734852187797', '182.4028899417933053853777552236', '183.05543704292764402723584734225', '183.73154600020644824841856777966', '184.16987239833407104058663508641', '185.14991124579585436073962090499', '185.64880356406530565529469341246', '186.49194730293891215636070349940', '187.13529691635289738412510799675', '187.65869721857690997381530056709', '188.34021070275845153291261005524', '189.437757925022130074601052083462', '190.4158308376361097555198619883', '190.84494748610255269222795396949', '191.58917546519223210255645081252', '192.164584455818648301948888797009', '192.888180630360359916959497821021', '193.79953925863384977277600152276', '194.10432832528685083513842708198', '195.22408755337409207232782105097', '195.493390973728555939904607737671', '195.9501886578654442190398847329', '197.16562022642874514016315131399', '197.7150829562882477873138034660', '198.64331769893363115878119247208', '199.50896255390530844217822647338'], 'prelabel': '1-231-231.194-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 24.82439762755838, 'root_angle': 0.11876043991348892, 'root_number': '0.734277981302568228482636648641+0.678848912626532284009873687743*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.118760439913', 'prec': 40}, 'spectral_label': 'r1-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.05982430235985814067674559520-0.277319654603184827844111246030*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.31997720105', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.83138445145', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.91194193564', 'prec': 40}}