-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_287.18', 'a10': [0.6691306063588582, -0.7431448254773942], 'a2': [-0.10452846326765347, -0.9945218953682733], 'a3': [-0.5, -0.8660254037844386], 'a4': [-0.9781476007338057, 0.20791169081775934], 'a5': [0.6691306063588582, 0.7431448254773942], 'a6': [-0.8090169943749475, 0.5877852522924731], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.30901699437494745, 0.9510565162951535], 'a9': [-0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [41, [1]]], 'bad_primes': [7, 41], 'central_character': '287.18', 'coeff_info': ['x^15 - 1', '0.913545457642601 + 0.406736643075800*I', '\\\\zeta_{15}'], 'conductor': 287, 'conductor_radical': 287, 'conjugate': 'dirichlet_L_287.16', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^11', 'a^10', 'a^7', 'a^2', 'a^6', 0, 'a^3', 'a^5', 'a^13', 'a^13', 'a^2', 'a^6', 0, 'a^12', 'a^14', 'a^13', 'a^1', 'a^14', 'a^9', 0, 'a^9', 'a^11', 'a^13', 'a^4', 'a^2', 'a^0', 0, 'a^12', 'a^8', 'a^13', 'a^10', 'a^8', 'a^9', 0, 'a^12', 'a^2', 'a^10', 'a^1', 'a^5', 0, 0, 'a^6', 'a^5', 'a^7', 'a^7', 'a^11', 'a^9', 0, 'a^0', 'a^8', 'a^13', 'a^7', 'a^11', 'a^0', 0, 'a^9', 'a^8', 'a^1', 'a^4', 'a^14', 'a^9', 0, 'a^6', 'a^8', 'a^4', 'a^7', 'a^5', 'a^6', 0, 'a^3', 'a^8', 'a^10', 'a^13', 'a^14', 'a^6', 0, 'a^12', 'a^5', 'a^1', 'a^10', 0, 'a^0', 0, 'a^0', 'a^2', 'a^7', 'a^1', 'a^14', 'a^3', 0, 'a^3', 'a^8', 'a^7', 'a^1', 'a^5', 'a^12', 0, 'a^3', 'a^11'], 'euler_factors': [[1, 'a^11'], [1, 'a^10'], [1, 'a^2'], [0], [1, 'a^13'], [1, 'a^6'], [1, 'a^13'], [1, 'a^14'], [1, 'a^11'], [1, 'a^12'], [1, 'a^13'], [1, 'a^2'], [0], [1, 'a^6'], [1, 'a^11'], [1, 'a^7'], [1, 'a^1'], [1, 'a^14'], [1, 'a^7'], [1, 'a^3'], [1, 'a^10'], [1, 'a^5'], [1, 'a^0'], [1, 'a^14'], [1, 'a^12'], [1, 'a^4']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-287-287.18-r0-0-0', 'leading_term': '0.558166743573119023870600394169-0.827245371910972320389307125125*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/287/18', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.9979403884897848, 0.8282991502647827, 0.5194361595795999, -0.04626522793782547, -0.6508034664532445, -0.9510198760237178, -0.7304498118939768, -0.08963291105054697, 0.5382069355234339, 0.601056852885092, -0.21267639904779528, -1.684491317558399, -3.073409761625059, -3.4944008830590647, -2.4877751056245705, -0.41438092243738833, 1.6447332463788138, 2.508763341650225, 1.6823376041238984, -0.23708653287857862, -1.8814753037091663, -2.023393217306043, -0.4720490321848713, 1.7153405026951711, 2.931564336437223, 2.176912141134431, -0.17022110688417472, -2.583774324789143, -3.4948531793613773, -2.4477207855593583, -0.4053748521804511, 1.045064714710802, 0.9492328076504628, -0.3227065751061897, -1.5096092308709956, -1.6183975985063146, -0.7769533506331183, -0.022706199700392376, -0.2382618206353741, -1.2485475849073628, -1.968348124906858, -1.4987272597635963, -0.11386747131315154, 0.902665016259486, 0.5475738259914363, -0.6734038999793671, -0.8746546359223918, 1.6020603405914768, 6.436695801787202, 11.107200502273713, 12.627823133318724, 9.902546356176332, 4.667547228314543, 0.14553848625984106, -1.4565665698684365, -0.44723349845467875, 1.0735764034984954, 1.335072197087432, 0.36548157929196323, -0.47618778712432175, -0.2272758387503132, 0.5793737186505166, 0.581325826031339, -0.7581842218748595, -2.357160563364834, -2.5270947849159255, -0.7748273388119449, 1.545714696618675, 2.5156847825768427, 1.581091295883758, 0.07607344330268487, -0.2725804109653772, 0.7155898370660385, 1.4344862877119104, 0.31679541186188964, -2.206384488947507, -3.847124934967886, -2.7695202437855206, 0.28716321562967567, 2.437174255265163, 1.4123966190046475, -2.089260518500013, -4.9559109447094265, -4.667841535191897, -1.738307049631141, 0.8923132665191486, 0.8463021118014626, -1.4238322967624992, -3.352272154514721, -3.0311798754047405, -1.0223979396691831, 0.5803471834483188, 0.5530120688733794, -0.3540634512796127, -0.67812925040689, -0.14263468833023307, 0.16858208316889547, -0.5052298391269764, -1.3024811281496858, -0.6640151725149259, 1.4733230766549696, 2.9947740041411004, 1.6814087602711574, -2.038291578868882, -4.9235297889423535, -3.971681773358167, 0.37965950742386634, 4.448460125163541, 4.9100217629232095, 2.0564649430552855, -0.7470231566427777, -0.7413277310836656, 1.4681406186000852, 2.9760067998838076, 2.022479675918695, -0.18174869751776165, -1.1703949245570164, -0.21964220665820994, 0.978583625055386, 0.6195135302139606, -0.8978008471886455, -1.5156178822137736, -0.19519733088935445, 1.6605281743516995, 1.8611920390701875, 0.1322857433402735, -1.5062654421036004, -1.189134292551087, 0.5569705291186664, 1.5859139454798337, 0.9176380343477619, -0.061807010594754186, 0.3902587773650528, 1.7231133196860156, 1.4432735346414738, -1.5659733115985688, -4.8046393150880915, -4.221118790741717, 1.2636105001487201, 7.924179524044064, 10.538587766374363, 7.464647110239029, 1.9986422694023789, -1.3041188309083123, -1.076604306108548, 0.42107585353123356, 0.7094899303499972, -0.11418955836262096, -0.30135084756673025, 0.7005674669527813, 1.4470528423751847, 0.6413698895558916, -0.9094568091479311, -1.321357354980205, -0.27515071594049206, 0.4244018628481111, -0.6684605016104537, -2.396779493441245, -2.2448138950058594, 0.24477569540979477, 2.380259526901507, 1.3970166245937623, -1.884394806332823, -3.5763259745724545, -1.1978305879447038, 3.1989898231622282, 5.190543948410998, 2.9821402307708693, -0.7219680402479898, -2.121129824431647, -0.6902165665090763, 0.7890886563109495, 0.2388727300935826, -0.9941768078720243, -0.14699036088804382, 3.0078535028795987, 5.516283544237207, 4.765734046333824, 1.6243849343800525, -0.7615453595630313, -0.7937123250160946, 0.08310722290441117, -0.154895347243276, -1.309834167342451, -1.5868871828563917, -0.45829668240842086, 0.5199381786698755, 0.17561809247560228, -0.19426363810318298, 1.489636617712087, 4.625471706460014, 5.74295410734524, 2.6601898959739785, -2.077744971264065, -3.397596678945012, 0.4812689870440168, 5.6179493376834655, 6.585604602316014, 2.5028213067747713, -2.2788389266641365, -3.406989128258135, -1.15520232619337, 0.8487597731075507, 0.47223028387545074, -0.8622188133375357, -0.9345932530750909, 0.08769378590732735, 0.3726072519628954, -0.4958939377067023, -0.8563862826186149, 0.2967347113630438, 1.373456306356412, 0.22376666988061536, -2.512742567991312, -3.6812267731440116, -1.597662091445835, 1.5452065820793264, 2.3291373515058833, 0.4380097630317348, -1.1839802448000296, -0.5822282381151388, 0.4541664356951909, -0.8968698779650714, -3.972750817265173, -4.785942790551145, -1.148665505234078, 3.951487531834541, 5.536273655122942, 2.592013890313571, -0.8215918815201461, -0.7079577276745824, 2.143195162558202, 3.7245843030002987, 2.1712223243066333, -0.25232016296026827, -0.6926921396396195, 0.5128740608030051, 0.8708481786409701, -0.4111882174380686, -1.441961340531832, -0.6798053069930222, 0.7529239085100226, 0.8896024064787091, -0.04146637640271413, -0.10729849433748417, 1.0186004382705247, 1.2173578915546344, -0.6204997495253365, -1.8339637803704516, 1.208334003630621, 7.65780103867302, 11.669348232586218, 8.618515553940316, 0.7328608514359991, -5.125259552455999, -5.008023391008766, -1.52070039105191, 0.43692930856221335, -0.29525887013973523, -0.9731513922507378, 0.20614868414406448, 1.5704843926979515, 0.9540479410367277, -0.7600966274186091, -0.9367600715786457, 0.7244400565519818, 1.5453253154192583, -0.24846585095612567, -2.8061788751041314, -3.144841266443378, -1.2663512386598124, 0.075635873692926, -0.48339899401924974, -1.0682196695214077, 0.26405234225701185, 2.2015669505902276, 1.9388844455689456, -0.4041343432062198, -1.4751398420291526, 0.548917332676151, 2.9479931085324353, 2.054685229215277, -1.1935458817190852, -1.8343511916210644, 2.527738610687542, 7.930922081946941, 8.568105443638787, 3.9256708605014308, -0.7762584335476221, -1.195791275925696, 1.3123161876913798, 2.5025830841939256, 1.0274857539743991, -0.6809701310052193, -0.6267279055939651, 0.17194605814024488, 0.040887670056045614, -0.48836723165924856, 0.035244739624874635, 0.9584862596135394, 0.13083358371995218, -2.3939728690633473, -3.570161442719414, -1.505255637865242, 1.3129534842191106, 1.0310684916369184, -2.035492410726905, -3.424744829329426, -0.679302928895088, 2.860048702707112, 2.307298377384136, -2.064209286554764, -5.000767705748187, -3.200123382154642, 0.5350522107572963, 1.4443280759508708, -0.8344209474024153, -2.4654321549792946, -1.2443513940659536, 0.6325064626579808, 0.4399268001516328, -0.8717927252996257, -0.47319725357342696, 1.5902793017566346, 2.157338894517524, -0.3245775770654803, -3.2692731125078365, -3.4575187197731423, -1.346469636771923, 0.0871791518326957, -0.14315086321749146, -0.1430942628774483, 1.148591405329378, 1.9614027544691681, 0.8105415155076408, -0.47000604805675145, 0.5927400005881202, 2.2411374712026975, -0.43595265640097924, -8.501414178483651, -15.875175493210213, -15.524320605622538, -7.865909532564543, -0.34307389267987726, 1.3569844629733225, -0.9948218532618632, -2.2239658376754456, -0.9081237592980143, 0.1067809204579062, -0.9009293523569551, -1.9868586497776535, -1.1027192285010021, 0.5354362899064816, 0.5862470243916482, -0.5647343583185613, -0.5861770356035791, 0.7736864993205096, 1.1754365207329727, -0.27377617488356903, -1.0664276461350122, 0.9016459356843046, 3.4625234278767207, 2.767745974659813, -0.9356361570654589, -3.140757715281747, -1.3768108696575054, 1.124049872498579, 0.060055654472095474, -3.6015491429872624, -4.952887695153913, -2.2607185239481082, 0.6468546012948841, 0.21395741935402518, -1.5728831154258218, -0.37718188832993116, 3.6570770465451523, 5.71281651273531, 3.0908134393226923, -0.99160706433464, -1.9613633677870874, 0.10166286620161225, 1.490273209401113, 0.5890637941517036, -0.4883030169739451, -0.007213256926855277, 0.6865576288396941, -0.04527133643608824, -1.0209209664751995, -0.24492284999932773, 1.3773292387456344, 1.1973177810284708, -0.646728148279536, -1.0125356121289009, 0.9846093611644682, 1.5224358626994272, -2.5949210843424604, -8.098894867168422, -8.382014128817696, -2.3786225240613956, 3.2390860940845, 2.2825964231336755, -3.2848519688885967, -6.494829366486241, -4.446167078022554, -0.8191545738114946, 0.3592592687521963, -0.2773331496089918, -0.1626345580481901, 0.5048548714001471, -0.23956759749411163, -1.9292111879995244, -1.9234055071091554, 0.07769295015040065, 0.9749456849134864, -1.0185126480733948, -3.2333186498279938, -2.2993031316489683, 0.7602897868601817, 2.040012936701021, 0.5514617764697078, -0.7372252815623138, -0.02057180943824336, 0.5703869403824403, -0.8326926042850482, -1.711630417194482, 1.3727901246643734, 6.480192034698256, 7.529327064123257, 2.511768210099812, -3.1512636620373695, -3.608804458710483, -0.23558437557640732, 0.9325338787731619, -2.0433691259464846, -4.799892239084575, -3.558510356886945, -0.37725409428176115, 0.5595213514553223, -0.8852724072558835, -1.4931009163069902, -0.18175592780758884, 0.7427497482854428, -0.11233935498441062, -1.0128717300745491, -0.40951983881367593, 0.35294592847595696, -0.2684549986532201, -0.8501437787545364, 0.4726342281202185, 1.6431535700205984, -1.3019095622013022, -7.544548583202243, -10.698074458408982, -6.7926398686641045, -0.12977565536081834, 2.0286223474599203, -1.0946725631516638, -3.54309763242009, -1.5063604809482631, 1.8377410977263235, 1.956027763754735, -0.2683514896063023, -0.7199426767594699, 1.1490861179339302, 1.8797430721732207, 0.0635102970102185, -1.2768420797259439, 0.28851801692633644, 2.5716627782374957, 2.281298798361646, 0.2224929108757775, -0.24726256295552512, 1.2373812123400039, 1.66900585503379, -0.1057077038705967, -1.388756573129494, -0.1983380179419036, 1.3212176931513193, 0.47796771258293513, -1.3903184053881588, -1.2384894569217262, 0.21378112864050766, -0.5300682894172519, -3.2027109699176104, -2.7346156374237602, 3.0585147052524198, 8.414413448999692, 6.174611234779325, -2.3606026862155263, -8.505368336519384, -7.063992732844059, -1.9307619484130025, 0.4856164246907106, -0.5068279769103569, -1.1931393566138793, -0.18838987170594168, 0.3696586939685307, -0.4671201975416666, -0.8008391693748319, 0.26468765809487543, 0.7248048014950577, -0.5871505032507803, -1.328271530199147, 0.6608149424904607, 3.205217079211925, 2.69840021569665, -0.0812996450852612, -0.957749271652512, 0.8845860383399687, 1.3706664846646006, -1.6784474885011218, -4.179939646872262, -1.533082372283625, 3.929102572852586, 5.668096865877959, 2.2298415777794314, -0.9138462729226238, 0.36268368619067104, 3.2089187859231565, 2.9654130806853787, 0.3542227337635079, -0.49773062391620104, 0.7901041226495947, 0.4594128289673628, -2.6795562465739478, -4.755946630201394, -2.747031651016079, 0.7894938075629898, 1.6397503922272574, -0.015155753202347997, -0.8215982504291177, 0.09912330841730163, 0.5467925592658871, -0.2179067111982952, -0.35186871025617955, 0.4601462334694943, -0.28821983618519914, -3.1935927417437693, -4.5206313329101695, -1.8091379159582068, 0.8055121604288387, -2.492258183446073, -9.919113216597797, -12.88194849522773, -7.171801989785984, 1.2264139931008011, 4.1891855110983345, 1.6067014272962366, -0.5005796629418171, 0.4616200729297657, 1.1911550138217422, -0.7195765795221114, -2.7436611892484133, -2.031234936404794, -0.03475348101867023, 0.41464796986085, -0.19125996841793663, 0.25489198575288957, 0.9752350750623788, -0.4409937887013374, -3.008756032881695, -2.8722511424113537, 0.5383155735954298, 2.964322464821245, 1.6844843155891847, -0.26763647952376096, 0.8759172768903327, 3.4323227334931907, 3.1559234967962375, 0.432298653182432, -0.364721137965115, 1.5178044380525726, 1.5508508468991826, -2.36970203159646, -5.385419920948912, -2.544894451792266, 3.1604604505718985, 4.511731977528154, 0.29834420502667053, -3.3748876717062, -2.2279588957777228, 0.8215747678462231, 1.3159393563163884, -0.11299431872752648, -0.16929514896424858, 1.1238997571573475, 1.1293581902724559, -0.2267180611842953, -0.36681923059378413, 1.08661222122489, 1.5430499705034206, 0.20563758866157708, -0.4078454801434801, 0.7391168631337977, 0.8022174840377778, -1.829111016826257, -3.5740043386690425, -1.0274756717083817, 2.1173580971467247, -0.9801506016751522, -9.734193364494372, -15.186961252110619, -11.462463825372645, -3.3400976052598423, 0.8300170592322891, -0.1404680367582869, -1.152866105804682, 0.1743037592291567, 1.0840634707414007, -0.10171744601388161, -0.9976865147262854, -0.0625832203340444, 0.17487301897041896, -2.2862187247101136, -4.650233530760193, -3.357051616973256, 0.03800122736954398, 1.1565948033021805, -0.41279865946608585, -1.0483117502043586, 0.5360842987958253, 1.5113085447873138, 0.3934364774002725, -0.29988034840233674, 0.9893522873753192, 1.4363870947151214, -1.1548011216528693, -3.338708488215187, -0.8097408969180425, 3.835607301209463, 3.8021482845449346, -1.6082568121427332, -5.283557573619293, -2.6754854408894526, 1.5075007788890287, 0.6427497569238283, -3.948883035551651, -5.606763845999014, -2.4766061140883293, 0.6725517345980999, 0.4318137238349646], 'positive_zeros': ['0.91484666992465354332572351824', '2.22610218206742601679324804442', '3.0678072500387786557062756555', '4.74444208780875670592904570394', '5.901302589473140197992224963318', '6.94238167020421387178635081836', '8.10515060364937481617399998871', '9.441069843683996947857474925468', '10.243390266655737999274683282383', '11.58582966657547559786982114092', '11.7303191814084287243012352478', '13.14993274443500380534809170494', '13.89336911083154011073178845617', '14.53257301573731998720613153704', '16.57688427880115235896038522293', '17.26987356565850422173905375355', '18.22851482496778424103686761433', '18.83787649130528636321736064307', '19.54147644351924844158587246197', '20.724225665419709297706019199211', '21.896864087107998815861347078163', '22.30448830942134306969266265480', '23.169875881668780158250398290380', '24.34679170835303353729543120024', '25.13931338268685453579025782041', '26.42792446470189616699038271851', '27.01123512472300047335355644124', '28.29044639428615654563359391407', '28.94092633634885838440885562021', '29.761371656314712044245080012585', '30.12844300085675795930328432242', '31.049014792038467762180127501303', '32.02811859086872950705206704397', '33.10103198116616984372506346283', '34.26537641451148407580426723762', '34.80916989940415307850294168613', '35.90916044578727261079986393868', '36.60883624004973273672635968475', '37.32189291677264927513961729661', '38.15530757572896357524079480165', '39.0820969713353471224171951731', '39.904955023037469506164737322139', '40.90013066086983292829037916484', '41.12196276903866553683202382389', '42.05148311457403280651366923790', '43.06731453205363748108007285051', '44.52080958013495835130218957259', '45.213761754491910671419880191245', '45.89446449982590302637873960057', '46.37291689823557654021034210247', '47.31243440022022236433597144737', '48.19724814937418316932785228393', '48.61835483874856351153537809966', '49.661397449245300712963676418602', '50.45329839967757435390132131234', '51.3362461129998227015378457146', '52.431121430181453719808647392460', '53.23637179078222963091141295388', '53.80225728056879035021324292291', '54.39433858492150704422405851833', '55.80239677340268980854737124909', '56.51982492761030771996374424127', '56.81744231362980564085498532076', '57.92121537294059425926966966655', '58.51073890974165348161603174135', '58.83056461356931232763918185043', '60.16718765532703491797118588962', '60.90989618455426431886862633499', '62.02194234215924489118819122030', '62.95463244514993707822595055575', '63.54145504579227781664955261139', '64.34678786244277210166086785571', '64.84539689880341503601810648041', '65.56476275480586051692137285949', '66.2786870161474559578711469581', '67.33571746426130089058285854204', '68.18518814465397342440227659105', '68.88178616378769784843354219004', '69.24926155639541994812924672905', '70.37925540741725530282350122250', '71.46303233457266700868955298182', '71.9658004609316454178428070285', '73.08247409090602939185966979464', '73.62711363965137242996675369969', '74.29377996806811459143613994575', '75.13607164086713173869412917634', '75.92170590385666550529006729125', '76.29046814514055113852837112313', '77.101434549251467972699337691077', '77.73547656082760784760766768112', '79.091462151227198730217154741', '80.18132995688154331811232513376', '80.55099345411609851581715752353', '81.21286161515800329861218043025', '82.04146061025574217248349174632', '82.691175886260590621632731117155', '83.40867713356031396517667365396', '84.63928618798762816427695456357', '84.8309758608367721999624305911', '85.58517915904970106619263480384', '86.51051652695066115371958600526', '87.128094586086375121155444083340', '88.00855729562494943473694554450', '88.604920041493802194947158503482', '89.92835575288173124120090976663', '90.47261239567158679130460155047', '91.4083137041930828737736530083', '92.1004230568395909141440345974', '92.520408107037867629674560304836', '93.11455252290403141315514284185', '93.76973715492712339590904694488', '94.83418105050108226168299002131', '95.43056570281669124280628108178', '96.30128627816496509555425000193', '97.05260334204818839638930494751', '98.0719566786744369002491340557', '98.65409046439597598449330006473', '99.55658668791936800921723634787', '100.09913087136429545894593121369', '100.7055029085195769205079615544', '101.532289582524207748046057731575', '102.7668196505671133906129424072', '103.03928777472441125168368673165', '103.48933774687647926053206407893', '104.52650126199264970307291188680', '104.9011002830574107978128046262', '105.60067872402808058442897609766', '107.21020488658127196274040992930', '107.69655309673329379615003154761', '108.65025211664902693419144531496', '108.83761805889985490307794375084', '109.88045789169242793312121729126', '110.47188789404783346683205953122', '111.084492076032325803536551571963', '111.825791357059206340222067808436', '112.39809972079732289762630814415', '113.36314350581920549460834894139', '114.2050769853011297318012169547', '114.69357683729117616766388328125', '115.8373482394259321340104853166', '116.28407147374276685596805616195', '116.90998809934454273284622382896', '118.03596222399731089503318467729', '118.73657266757440434473900103867', '119.50459703867886429526701783645', '120.00226277776426052205761304894', '120.61381081628918743481817820838', '121.294873206322622139683743751611', '122.079025729939833568020742802809', '122.67742609153274411977246783232', '123.28197708507673041242001172643', '124.48106634204978060312120657002', '125.13743915145740685375777402279', '126.37083234660904845656326339524', '126.75117614509381464031481502417', '127.25278854540579971289959974275', '127.76241799910957971530518665871', '128.73833039079335109780257644036', '129.25533267289046762594599807129', '130.23260316855106102522669261990', '131.028724704687032782187775399372', '131.56782912582323011448701338085', '132.04395641849937950559661322048', '132.71783232104573400833528507452', '133.86960786884530108815550435865', '134.71130539210938302174470034968', '135.1343354112295101561576537888', '136.30090029833840051931528162451', '136.70861502656986953509265259626', '137.536365672195066085187640128976', '138.09823168778676243893869464248', '138.87139622367850757247513067765', '139.29276657791797684091863665662', '139.92237444435630915033221496768', '140.539685403925124090744662255466', '141.88272679495771896637290288211', '142.41367874934498716842171413547', '143.25007272108558119897717452426', '144.02137400584147484707864453841', '144.51460336929110207943516694878', '145.32128296841047764203098758096', '145.9021477650717064869791508876', '146.918916518354936896145462637119', '147.257969733322938337501570321957', '148.1095784613871464837489689621', '148.781204252180213588314387018587', '149.44844752854028110676016540178', '150.24995646493119327405766504626', '150.53883855594885179057225648198', '151.42189135572152346786035606774', '152.419208907514395863187772984671', '153.616718626077793863842567718502', '153.95495234923185764662888336454', '154.73876731555411244730467892625', '155.170112639540517933880781517520', '155.87162426764705374843846997176', '156.449997855546474884026358782169', '157.1149838319494185693078357857', '158.11483401943981680881639820469', '158.62064533306805042450786726262', '159.23362415211643655357485065574', '160.087815493335157519265905618485', '161.11458588735021442475137913798', '161.52312498855653155244550642719', '162.55268508393410232780509876198', '162.95077001351002969943717719767', '163.49836614887182999570289736992', '164.60583233605141246106695580324', '165.30978760727528278328906158202', '165.90960486443536581625909311627', '166.483621001283888373218690042187', '167.01002773273965353632573055357', '167.4537712612135160507381747866', '168.597994088894700536536948497382', '168.90881025586626864350682667459', '170.25828533169699442060305635700', '171.11752752025081461980425952981', '171.471272741337335711635397992627', '172.10051947640791991137794308996', '173.13238574752283664561942719576', '173.6315032365059463159765245217', '173.97588096843726080725309879169', '174.630279699402078610340104735305', '175.58114561758952323474398304094', '176.48609117143647683390569034303', '176.74656952468553117919261836482', '177.87450597225039619362535841876', '178.206735889377295520247632210271', '178.89964546627090059346679764159', '179.82167072833323921758320185945', '180.64313041911540106075250486132', '181.46447802922327095013299841047', '182.15864985471794679176772048003', '182.54711807095119409274549046432', '183.381574122157087729948470512780', '183.844801054105350103872912933321', '184.73345215787272247119938005186', '185.14045198314090003812065695877', '185.74694215283454383078981503446', '186.64061410683192762846088056902', '187.13998433653216528170082225017', '188.63110908216703541633322448985', '189.03941453013376020270062923571', '189.65651036582881693092978202122', '190.29272205267524815360992182556', '190.95399705653615928215855028906', '191.28991833554247041050248606995', '192.49583491617099823237601069289', '193.0543552322645101699387665337', '193.66264527899819589259457843330', '194.46597357232237288524494216037', '194.79833059484635350643038421440', '195.51494884267552774415943161620', '196.301946631365138468877899419522', '197.10511048773030525477474233339', '197.98691541915319920084652923937', '198.487263778513237212310683243320', '199.588717565614820115891444700069'], 'prelabel': '1-287-287.18-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': -0.6221256002965527, 'root_number': '-0.374325132533106449411798142622-0.927297522456558864510319586859*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.311062800148', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(15)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.715054495657790224918248877389-0.553513559109898944267653295287*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.914846669925', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.22610218207', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.06780725004', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'bad_primes': [7, 41], 'central_character': '287.18', 'conductor': 287, 'conductor_radical': 287, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/287/18'], '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': '1-287-287.18-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': '1-287-287.18-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': -0.31106280014827636, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.914846669925', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_287.18', 'Lhash_array': ['dirichlet_L_287.18'], 'label': '1-287-287.18-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/287/18'}