Formats: - HTML - YAML - JSON - 2025-12-24T17:11:32.206840
Query: /api/lfunc_lfunctions/?_offset=0
Show schema

{'Lhash': 'dirichlet_L_17.10', 'a10': [-0.9238795325112867, -0.3826834323650898], 'a2': [-0.7071067811865476, -0.7071067811865476], 'a3': [0.3826834323650898, 0.9238795325112867], 'a4': [-7.040766286173228e-31, 1.0], 'a5': [0.9238795325112867, -0.3826834323650898], 'a6': [0.3826834323650898, -0.9238795325112867], 'a7': [0.9238795325112867, 0.3826834323650898], 'a8': [0.7071067811865476, -0.7071067811865476], 'a9': [-0.7071067811865476, 0.7071067811865476], 'algebraic': True, 'analytic_conductor': 1.8269037215086255, 'analytic_normalization': 0, 'bad_lfactors': [[17, [1]]], 'bad_primes': [17], 'central_character': '17.10', 'coeff_info': ['x^16 - 1', '0.923879532511287 + 0.382683432365090*I', '\\\\zeta_{16}'], 'conductor': 17, 'conductor_radical': 17, 'conjugate': 'dirichlet_L_17.12', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^10', 'a^3', 'a^4', 'a^15', 'a^13', 'a^1', 'a^14', 'a^6', 'a^9', 'a^5', 'a^7', 'a^12', 'a^11', 'a^2', 'a^8', 0, 'a^0', 'a^10', 'a^3', 'a^4', 'a^15', 'a^13', 'a^1', 'a^14', 'a^6', 'a^9', 'a^5', 'a^7', 'a^12', 'a^11', 'a^2', 'a^8', 0, 'a^0', 'a^10', 'a^3', 'a^4', 'a^15', 'a^13', 'a^1', 'a^14', 'a^6', 'a^9', 'a^5', 'a^7', 'a^12', 'a^11', 'a^2', 'a^8', 0, 'a^0', 'a^10', 'a^3', 'a^4', 'a^15', 'a^13', 'a^1', 'a^14', 'a^6', 'a^9', 'a^5', 'a^7', 'a^12', 'a^11', 'a^2', 'a^8', 0, 'a^0', 'a^10', 'a^3', 'a^4', 'a^15', 'a^13', 'a^1', 'a^14', 'a^6', 'a^9', 'a^5', 'a^7', 'a^12', 'a^11', 'a^2', 'a^8', 0, 'a^0', 'a^10', 'a^3', 'a^4', 'a^15', 'a^13', 'a^1', 'a^14', 'a^6', 'a^9', 'a^5', 'a^7', 'a^12', 'a^11', 'a^2'], 'euler_factors': [[1, 'a^10'], [1, 'a^3'], [1, 'a^15'], [1, 'a^1'], [1, 'a^5'], [1, 'a^12'], [0], [1, 'a^10'], [1, 'a^13'], [1, 'a^7'], [1, 'a^11'], [1, 'a^3'], [1, 'a^1'], [1, 'a^6'], [1, 'a^12'], [1, 'a^10'], [1, 'a^14'], [1, 'a^9'], [1, 'a^8'], [1, 'a^3'], [1, 'a^15'], [1, 'a^5'], [1, 'a^2'], [1, 'a^4'], [1, 'a^7'], [1, 'a^8']], 'gamma_factors': [[1], []], 'id': 45, 'index': 0, 'label': '1-17-17.10-r1-0-0', 'leading_term': '1.11731282579527724151206153958+0.0851931097269587695208765374609*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/17/10', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.1205560301170026, 1.1626616469297388, 1.1851786858592321, 1.1676659282360182, 1.0823649348851039, 0.9041388756118867, 0.6187357502646137, 0.22910394944673984, -0.24038284012947292, -0.742537788896048, -1.2098284852175716, -1.561426840489444, -1.714793603887242, -1.6006647203089779, -1.1791512677667342, -0.4537375421691918, 0.5204210567748078, 1.6370787319758393, 2.7502013428622587, 3.695689807590848, 4.320638195164114, 4.514793853318598, 4.237277761390681, 3.531484365256266, 2.522779224341769, 1.3970767435780087, 0.3630100099786518, -0.3948687215462865, -0.7609188112927441, -0.7192958342260907, -0.3610798591516349, 0.13685984311846416, 0.558364782457669, 0.7093045875459852, 0.47753748445035005, -0.12623943997655873, -0.9609347086731482, -1.7866111175076977, -2.329687759916682, -2.36533878642624, -1.793410072178244, -0.6835535103485112, 0.7276813955783453, 2.09167155143469, 3.0421919881732187, 3.3033555141488495, 2.778023680181694, 1.587036650179969, 0.04308824734679151, -1.4368167396429103, -2.455824656713344, -2.760110339714611, -2.3196584814366323, -1.338192075297994, -0.18605309249726423, 0.7238912059597713, 1.0763569486860212, 0.7612403406214168, -0.09034051883291018, -1.1563291328737155, -2.0440184286101446, -2.437289607915218, -2.2157832011042036, -1.499349940208371, -0.5979712176656595, 0.11653525852682978, 0.36883817648925543, 0.10553483354320442, -0.46571232247732103, -0.9451713380975103, -0.897432350025616, -0.03736446574659849, 1.6283681685735534, 3.7654215245574516, 5.804102812859425, 7.132131181522134, 7.317766378333921, 6.276941932533832, 4.3160065842862245, 2.0284859154873085, 0.08212733983900197, -1.0220788308084399, -1.1237420864812355, -0.44016591994750653, 0.5475431029424831, 1.3107792356702421, 1.4999703037500454, 1.084229815131745, 0.3442112463409218, -0.2774079010812853, -0.3995337755322446, 0.10267556781167458, 1.024029518477173, 1.9147518174543017, 2.29023503190989, 1.8702385925981029, 0.7344446765834309, -0.6847551076253288, -1.778544226091785, -2.0338114311429747, -1.2786594153055153, 0.21541790574231678, 1.830503878691387, 2.8639868978925414, 2.8421376530614824, 1.7433010211630535, 0.02441962743036623, -1.5682430911723686, -2.323947421197353, -1.8825165894946205, -0.3952862146437088, 1.5434075869092378, 3.1636509995323125, 3.862402552311467, 3.4613700129354403, 2.2609890388688756, 0.8692854326355829, -0.10661229130340508, -0.35213069937742486, 0.02435619024668572, 0.5846191859411777, 0.8249379040070828, 0.47050663629002965, -0.3586920495821664, -1.2039553481596839, -1.5230248074566484, -1.013194789876128, 0.17200684117988296, 1.439600373816262, 2.017352049544745, 1.338749436568926, -0.6391171255283041, -3.3535780477970136, -5.847311474752036, -7.182763160664251, -6.8640412582906, -5.060013508672369, -2.5168844185874084, -0.20209960304046076, 1.1438216352497244, 1.3250077282868244, 0.7230669307263368, 0.03849809733582195, -0.11491370546503202, 0.45605995028503243, 1.4386529953477583, 2.2170354156611705, 2.245586494637377, 1.3810091597846488, -0.015311102512661502, -1.2652572226552383, -1.7491992467408577, -1.2570862723404335, -0.11297793081978288, 1.00524696910596, 1.4568621353969926, 1.0214040834537914, 0.0512514113498883, -0.7061439001444009, -0.5313062993048224, 0.8284299534915192, 2.954331914472119, 4.916047887579439, 5.727689717264494, 4.86418107416959, 2.559277213350743, -0.2827580982512129, -2.5235517312210964, -3.347456701524869, -2.6443788857316837, -1.0187872636146682, 0.5700881648294933, 1.330854648678959, 1.0349942723896057, 0.0736712731311896, -0.8367335417724353, -1.1118722769622567, -0.6422290955249144, 0.1802947336912273, 0.7588196154034603, 0.7191512673755496, 0.19400523764605596, -0.22607765621041495, 0.13940307488512357, 1.5912036912464882, 3.7722572015314597, 5.773732762128808, 6.593531313882032, 5.698872759879892, 3.366806647814786, 0.5901194011154096, -1.4190930674468718, -1.860821065695018, -0.7603292779976888, 1.071758578731751, 2.5100430927517787, 2.745772007924389, 1.7176273340590242, 0.09993682052563044, -1.1325142076247559, -1.2958793942977143, -0.39056100430147594, 0.9323117070616969, 1.7982699821856905, 1.6592074556202792, 0.6238676440743485, -0.6313955902460933, -1.3077320235799288, -0.9977831705113214, 0.060477536327440164, 1.1524362038855194, 1.5688267739220887, 1.0868710885369117, 0.1306293517784552, -0.5077503521577358, -0.2191815869086054, 0.9529678659616706, 2.2450805918138057, 2.584212198769433, 1.250530211725823, -1.610600871645036, -4.9579198002520135, -7.3548617289522005, -7.728521404912987, -5.949017288915848, -2.8898756292331265, 0.06393545048228379, 1.7662702856167545, 1.8766825008962613, 0.924812373943124, -0.13199426083215227, -0.5531572811516074, -0.24697775378957865, 0.26883738806728735, 0.3210321646846805, -0.37917363301234885, -1.4874979299402729, -2.2437877397793877, -2.0085603079134917, -0.7481017845871597, 0.8783358314336963, 1.9139239531049053, 1.7381631683323853, 0.5192419606552109, -0.834602387203651, -1.224141103035896, -0.07403217137911322, 2.2474766245784488, 4.59249518358583, 5.70141123275741, 4.966559420535528, 2.8102419811898827, 0.431817018947831, -0.9230430518289442, -0.7127636849917952, 0.6013166304632982, 1.8894674741563517, 2.0975005285228714, 0.9176238576304665, -1.0401560890130759, -2.6704265225213275, -3.095069455919891, -2.2050871521060937, -0.6744466589143064, 0.5390283007099542, 0.8466037787691176, 0.38284601758732156, -0.17288493872490562, -0.16311907508196483, 0.5131030214978206, 1.2972562500592286, 1.392898949833093, 0.4224310600877077, -1.1596206545831411, -2.230724196109264, -1.6850493467915966, 0.791907286493805, 4.385212962018387, 7.514144303260935, 8.708193784704319, 7.4591337161907365, 4.510613799708728, 1.399189979849886, -0.46078549694183873, -0.5676376608218954, 0.48940605617977645, 1.541169164554397, 1.6644677030409605, 0.7597622721903109, -0.48773367970001447, -1.1935602906809848, -0.9607141634550964, -0.16810381902242907, 0.3389536312748208, -0.08161619133367509, -1.339663261156637, -2.6254579477037003, -2.971993348021993, -1.9694484123445566, -0.10956025643456051, 1.5098031860158634, 1.9328720591185056, 1.023481631785664, -0.42146993894527024, -1.2288866091347246, -0.7049777554090432, 0.8122061613191257, 2.1144803059639425, 1.9216737322121562, -0.21280216315727216, -3.5127019618768602, -6.392691487570382, -7.4189770413191125, -6.185816620440838, -3.531042138996712, -0.9612583189560278, 0.31113318741407914, 0.06887444699084108, -0.918574316434688, -1.5558370754792792, -1.2312998954731431, -0.196375699006327, 0.7258324469134142, 0.8425920921103032, 0.1501640893636596, -0.6808088428317156, -0.8760488988288633, -0.2330626052049365, 0.6439718214427034, 0.7704768721517388, -0.41865126638610256, -2.4958428157675887, -4.166954095537321, -4.076596209020168, -1.7645894766704129, 1.903290228398932, 5.171730315471063, 6.445481682563115, 5.262101910329104, 2.5365029872540146, -0.07946747095462062, -1.2738713467347798, -0.8504351718342409, 0.3042603448297627, 0.9889082920020628, 0.604542740571299, -0.44566499685698147, -1.1379774751606802, -0.6727594326973994, 0.8693973631970925, 2.5550533812098495, 3.2805691395574326, 2.5867324896113875, 0.9863098320982272, -0.44073152964653206, -0.869844931271591, -0.33743872321271895, 0.3404098862495253, 0.27603677072588517, -0.7078842857910381, -1.85085257054223, -1.9979414853264212, -0.5333833489017442, 2.0061432259918726, 4.147942433657219, 4.438103561017004, 2.48090316035091, -0.6914012435612392, -3.2199998385953137, -3.605923003687078, -1.670755043156728, 1.3667395116847096, 3.733953575852243, 4.261452773472391, 3.049567418693403, 1.2222878872029816, 0.01634591886814432, -0.08632844734365992, 0.44371844217122014, 0.7381985828781953, 0.3402136200773182, -0.4029711433192608, -0.6752974668131184, 0.034223528401907656, 1.3756422897710598, 2.2949565059364008, 1.82863293088018, -0.07158405370441462, -2.3584036839973845, -3.558265210056903, -2.83638687059151, -0.6650686868380598, 1.4381979365562971, 1.9553898858128367, 0.4522802461997117, -2.0944072123899597, -3.9806080621610085, -3.980041189527362, -2.1945428425592164, 0.0643880341676143, 1.2590387978491033, 0.7347697110365887, -0.8613775403243799, -2.136111400896267, -2.0285443739687707, -0.5838013002725453, 1.1478173529528066, 1.9705015455360604, 1.4685873699411602, 0.27873142794855293, -0.47734301371462684, -0.11909532209641657, 1.0605316110082752, 2.076847795584783, 2.10126460086593, 1.1622253988765114, 0.10230657130439125, -0.19401789151608145, 0.3309568744912826, 0.6952113239713653, -0.42557999473789165, -3.573305508203487, -7.831971790562174, -11.194742203216887, -11.797311426377721, -9.16700774449215, -4.583353308601351, -0.2722962132369531, 1.9998145766429793, 1.9402041199954296, 0.6702765990506159, -0.28276451913470824, -0.13523540299481054, 0.7189767327324043, 1.2434243559160274, 0.7515141420278718, -0.4821096326676103, -1.475756879073999, -1.4133639058113316, -0.3782696254011487, 0.6859632597477502, 0.7704142663511832, -0.3083889102065761, -1.6825173112623855, -2.0984330742169144, -0.9602828521537115, 1.1041572390220546, 2.655561058100619, 2.551950060772537, 0.8883757029455821, -1.0028047395642983, -1.5383932291752647, -0.11682406531668234, 2.3671991820071203, 4.153917937678453, 3.9359028587540985, 1.8572527303440396, -0.5769881259238689, -1.6169528811696217, -0.5573205226362328, 1.7772678752872362, 3.696188230579977, 3.914609556140484, 2.4458600160558426, 0.46176448174430373, -0.7007503407567408, -0.5529410110620324, 0.3104353234700089, 0.8760578155743959, 0.6534308367843, 0.06767686165954295, -0.021449446829709663, 0.7725095142435727, 1.8619029320432385, 2.0908107127487963, 0.7604714821654369, -1.5905987552943537, -3.3801665191761616, -3.105895877031941, -0.5645869378365035, 2.8176998832279194, 4.881913820156637, 4.241835224933338, 1.2794469157021113, -2.127021723885254, -3.940040881044639, -3.3563907988044326, -1.2287499952341217, 0.7393083131349295, 1.3319989858167747, 0.6301160714404922, -0.291135275605418, -0.4340729993760589, 0.22483867741079833, 0.763162960666327, 0.20440270103199315, -1.5246204025861814, -3.416837369816279, -4.160106410218751, -3.2148978788650986, -1.2748324799635453, 0.29494378715753516, 0.5780234395381019, -0.1637936688105035, -0.7826394897596647, -0.3214567003895512, 1.0493074008575998, 2.0746227172959, 1.4651723657578721, -0.8899031609441339, -3.5880687107055214, -4.6221383852079345, -2.884514603559559, 0.9057036099019362, 4.613042968329681, 6.157141451386562, 4.936128804983273, 2.1341731917655857, -0.2732491268140588, -0.9944990274509783, -0.22722026434140155, 0.7612564986560619, 0.8272674530856263, -0.11924451439380807, -1.1888391010309762, -1.4359449605008463, -0.7581927123903314, 0.03748270971531616, 0.03984263052991591, -0.8470065245839461, -1.7421768520338297, -1.5854423962275435, -0.21464796459028984, 1.265169034745019, 1.2480615805138846, -1.0236466708107068, -4.642325986128606, -7.5007130534047874, -7.764595749099678, -5.228254778546816, -1.4759992714788017, 1.2955076033086186, 1.8736829491551075, 0.7974903811992132, -0.2699752441109585, 0.00014842232213561882, 1.5260501083513465, 2.9768769433435223, 2.979556535128412, 1.3197209482831709, -0.8725658933060828, -2.076385800827299, -1.632482694825113, -0.22718120629150523, 0.773430293771941, 0.5256530769331884, -0.6095471779353564, -1.4784317036875658, -1.2399294702669221, -0.15418781098819748, 0.664596324409064, 0.31222429061663415, -0.998247495856562, -2.051739891264437, -1.735081901176264, -0.18160568172044023, 1.1039382845660268, 0.371191593411297, -2.8572284130206174, -7.144355367028734, -9.991680684067438, -9.596510915125162, -6.161773147500658, -1.7343981983202168, 1.2894046014015803, 1.8103333326538187, 0.5694038704145714, -0.729103533941694, -0.8858797796681912, -0.03200317553270997, 0.783004484866725, 0.7398936971905755, 0.03884337381250602, -0.3708777042920597, 0.18264441921995736, 1.3151349445847353, 1.8293178111830297, 0.8053630582376528, -1.4464068571231818, -3.4830229069693868, -3.8730889866524563, -2.426593948340101, -0.41368489003717723, 0.48200714118378135, -0.3789147484249469, -1.9804630398241132, -2.460133256429814, -0.7008345103607733, 2.6305269292187807, 5.5030942078943275, 6.089674614018543, 4.1978090367147844, 1.3838589136609065, -0.3312160083384212, -0.06315955159635957, 1.339418760834525, 2.1521772290580468, 1.3039741538267953, -0.7371344429871988, -2.4356017525185614, -2.544945152726414, -1.1405581355731398, 0.5413575291121873, 1.2459342301360907, 0.7575930117556757, -0.06417243006035406, -0.24041796778016944, 0.32856832736967956, 0.7965553387371325, 0.3204886433675645, -0.8835081709853985, -1.453829491680831, 0.006659484424071159, 3.526821074049, 7.352001160170795, 9.03563583251782, 7.266185671272289, 2.9591236590492183, -1.3232177291167806, -3.2107643046656174, -2.176544289025915, 0.2852684246955503, 2.0160440373426223, 1.9035312190374394, 0.5489898112770947, -0.5481200029883587, -0.4506021469742198, 0.4344502307214373, 0.8858536020379337, 0.133100999443787, -1.3606564379046673], 'positive_zeros': ['2.345022443715306518815975574733', '4.84126687487047368130114228786', '8.2571959790708365471446385471', '9.60263413453277681184895574948', '10.88353387145199816664488206161', '12.96775964740942140200901487855', '15.0085048360268982488406590296', '16.92921271966480724773767472939', '18.09712616600168233542405898077', '20.2477382945753211790833811886', '21.00300263712762854430034066777', '22.19645290154881894732101226664', '25.01643976790543863355011486029', '26.07813875152469597260856160604', '27.65169401472526661775545503446', '28.39414315973199275513059497665', '30.16129926751069219733768534744', '31.52206490240973849857305490686', '33.12926773536538763144517949619', '34.44066071816064924019371288843', '36.51404791064985371718647034533', '37.17373731623919123251814561241', '38.31460750405404610307143793420', '39.64749815727321169037916371478', '40.85324334857053755903505284524', '43.15898124803132144413696441171', '44.40058061367629632793226327403', '44.79114718808932357723997866055', '46.55919074806908282978658290802', '47.84066786293070721699165484920', '49.0785734256007455449540429801', '49.84126550091138463337920067392', '51.84289557159289394846968085358', '53.31265611514156318056762506085', '54.39678620665739375661845404714', '55.556243851426007503832655751548', '56.67020786698174054907165168577', '57.13381825007521638618484345397', '59.44954610248355761971562720381', '60.44629543111460147689434675136', '61.89491311164056012084907126345', '62.90555456430642759234918239930', '64.211527377463857575275843519918', '65.29689723896376107265427754306', '66.60751143706513717593769256161', '67.2625134598394549471649018848', '68.58978183064552274999255604655', '70.61694616095510405032520791087', '71.827410350480537596853175934642', '72.639174955821707253029192474227', '73.305649345820207292680287685193', '74.8289026353119126598128186719', '76.04712315945630519811088284016', '76.887163586440301683305081622676', '78.82087928264072806722740021090', '79.560658755668480429696966464984', '80.77663022112285101356276934726', '82.337750112649511551802557559156', '83.31839970949721780048517261447', '83.85194302952904074071040749543', '85.08767163701692667136906686503', '86.16996586912183919036212816000', '88.32655329245763753081888048814', '88.937963623357680037322815133970', '90.18537876562103038015709440323', '91.31946056525445316700544437335', '91.846115201527501238221934877942', '93.45523055370630736842874866068', '94.59305003531133901157988282527', '95.47038668289745469246463245313', '96.5395196760722377747764214446', '98.62564380404668650702663497614', '99.0884266502550555784840125971', '100.3675781539640351319180045439', '101.301272483438052341927198313671', '102.26499181954362078169402352192', '103.046311450489719977003970451464', '104.53129503001153172624970661441', '106.23802662879139787637571291663', '107.10495745719579790694111090817', '107.99818889588082080000608756443', '108.9047197074608112240777888722', '110.50935427455584792196653259565', '111.38586645029630378783392794017', '111.98948137046853233821123594160', '113.196997941952942546773836586635', '114.620593094402311359050144982367', '115.79905376307114747620621867929', '117.50808177465573225652023233112', '117.8773490462255089519201459924', '118.8916067174656210173123522305', '119.67820599182023115223397521935', '120.92790335735483907467019534691', '122.27411543336762859041199216896', '123.18435767798342957368417962040', '124.67722497211773469565854895218', '125.4666878640199646086251883554', '126.66190781711710685721655130263', '127.89322436958700832257452751730', '128.476606511395025207659343489273', '130.04458657727787259803349349698', '130.46489721694273398700966485682', '131.1806709681060338348205117383', '133.462579420496960767158008580147', '134.55684933350732133443739587569', '135.05887971526160177373686544886', '136.13562089359168752126867083202', '137.28339155455532226885560270508', '138.055678172271964188183602928820', '139.21309998056256606423660832844', '140.44708230342314185383434650249', '141.26628464930899852829417601273', '142.728933775172248435058319106964', '143.52019681124945909884401251539', '145.08982881886020959309472674779', '145.83054794920148456507088279739', '146.92488156090671254620624081933', '147.20454853188192482375645144409', '148.54507825029619233290209093262', '149.739792286199792932260568241179', '151.048673577164301757519205621812', '152.36304421173773482279391872059', '153.32085230252290519114701970817', '153.97410125975942489261322311942', '154.7355543033954214502148271713', '156.4831971670856574361655582203', '157.13077088489876889858546162405', '157.89746287770314657484925368364', '158.96171975988794990246145297949', '160.24425282188488672775522831503', '161.82752005186466531053294976729', '162.56269532685537008722344251290', '163.40619727965745372991237702487', '164.665634378791146563554613809650', '165.022427457469502235064716408308', '166.289475052643104101074823352547', '167.07897831800577877056406812540', '168.89029158094564071941696903429', '169.88932648417860794963948757516', '170.31245557129943043221389867066', '171.74489541279730934683342300167', '172.863864521132050385090017477960', '173.59470349213154980478975541098', '174.72983667707910199578043280449', '175.40037384084209373985143011384', '176.59534897726801275742524723754', '177.23839793777772993839797407964', '179.2120955815478671449280145126', '180.11717444031468096822650985870', '180.94721635739684753292698980521', '181.89187176431484560078900549860', '182.43873365164384220251773390700', '183.560781972839615189336608229296', '185.085839090080262519534880423267', '185.53955810964801349896436582478', '186.6356645550542688249901138821', '188.33941561570250788236945660510', '188.767438020182028539623118957122', '189.89430215492858763831448840914', '191.13793036413384924726294291529', '192.156482176984578141863180074126', '192.661736592430462196131208800232', '193.528625910645740809162402675424', '194.37421276895795584282054777933', '196.14042704658508503217167274191', '197.15126457003908855778024458176', '198.24998962637823246177618199281', '198.91785712902482214841952728360', '199.71851761130170001358903692267'], 'prelabel': '1-17-17.10-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8269037215086255, 'root_angle': 0.0242236897094665, 'root_number': '0.988439628677424743605117878677+0.151614974392487671610104139829*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0242236897095', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(16)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.990332400616956436705408562878+0.0107451137885021533335659654254*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.34502244372', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.84126687487', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '8.25719597907', 'prec': 44}}