Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(146,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.146");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.o (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 146.8 | ||
Character | \(\chi\) | \(=\) | 441.146 |
Dual form | 441.2.o.e.293.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.02035 | − | 0.589100i | −0.721498 | − | 0.416557i | 0.0938059 | − | 0.995591i | \(-0.470097\pi\) |
−0.815304 | + | 0.579034i | \(0.803430\pi\) | |||||||
\(3\) | 1.61957 | − | 0.613991i | 0.935061 | − | 0.354488i | ||||
\(4\) | −0.305921 | − | 0.529871i | −0.152961 | − | 0.264936i | ||||
\(5\) | −2.16601 | − | 3.75164i | −0.968670 | − | 1.67778i | −0.699415 | − | 0.714716i | \(-0.746556\pi\) |
−0.269254 | − | 0.963069i | \(-0.586777\pi\) | |||||||
\(6\) | −2.01424 | − | 0.327604i | −0.822308 | − | 0.133744i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.07728i | 1.08798i | ||||||||
\(9\) | 2.24603 | − | 1.98880i | 0.748677 | − | 0.662935i | ||||
\(10\) | 5.10399i | 1.61402i | ||||||||
\(11\) | −1.87238 | − | 1.08102i | −0.564545 | − | 0.325940i | 0.190423 | − | 0.981702i | \(-0.439014\pi\) |
−0.754968 | + | 0.655762i | \(0.772347\pi\) | |||||||
\(12\) | −0.820798 | − | 0.670332i | −0.236944 | − | 0.193508i | ||||
\(13\) | 2.25256 | − | 1.30052i | 0.624748 | − | 0.360698i | −0.153967 | − | 0.988076i | \(-0.549205\pi\) |
0.778715 | + | 0.627378i | \(0.215872\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.81148 | − | 4.74614i | −1.50052 | − | 1.22545i | ||||
\(16\) | 1.20098 | − | 2.08016i | 0.300245 | − | 0.520040i | ||||
\(17\) | −1.17115 | −0.284046 | −0.142023 | − | 0.989863i | \(-0.545361\pi\) | ||||
−0.142023 | + | 0.989863i | \(0.545361\pi\) | |||||||
\(18\) | −3.46335 | + | 0.706143i | −0.816319 | + | 0.166440i | ||||
\(19\) | 2.41658i | 0.554402i | 0.960812 | + | 0.277201i | \(0.0894067\pi\) | ||||
−0.960812 | + | 0.277201i | \(0.910593\pi\) | |||||||
\(20\) | −1.32526 | + | 2.29541i | −0.296337 | + | 0.513270i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.27366 | + | 2.20604i | 0.271545 | + | 0.470330i | ||||
\(23\) | −3.16186 | + | 1.82550i | −0.659294 | + | 0.380644i | −0.792008 | − | 0.610511i | \(-0.790964\pi\) |
0.132714 | + | 0.991154i | \(0.457631\pi\) | |||||||
\(24\) | 1.88942 | + | 4.98387i | 0.385676 | + | 1.01733i | ||||
\(25\) | −6.88321 | + | 11.9221i | −1.37664 | + | 2.38441i | ||||
\(26\) | −3.06454 | −0.601006 | ||||||||
\(27\) | 2.41650 | − | 4.60006i | 0.465056 | − | 0.885281i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.589262 | + | 0.340210i | 0.109423 | + | 0.0631755i | 0.553713 | − | 0.832708i | \(-0.313211\pi\) |
−0.444290 | + | 0.895883i | \(0.646544\pi\) | |||||||
\(30\) | 3.13380 | + | 8.26629i | 0.572152 | + | 1.50921i | ||||
\(31\) | 5.67723 | − | 3.27775i | 1.01966 | − | 0.588702i | 0.105655 | − | 0.994403i | \(-0.466306\pi\) |
0.914006 | + | 0.405701i | \(0.132973\pi\) | |||||||
\(32\) | 2.87915 | − | 1.66228i | 0.508967 | − | 0.293852i | ||||
\(33\) | −3.69620 | − | 0.601166i | −0.643425 | − | 0.104650i | ||||
\(34\) | 1.19499 | + | 0.689926i | 0.204939 | + | 0.118321i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.74092 | − | 0.581689i | −0.290153 | − | 0.0969482i | ||||
\(37\) | −5.10692 | −0.839572 | −0.419786 | − | 0.907623i | \(-0.637895\pi\) | ||||
−0.419786 | + | 0.907623i | \(0.637895\pi\) | |||||||
\(38\) | 1.42361 | − | 2.46576i | 0.230940 | − | 0.399999i | ||||
\(39\) | 2.84968 | − | 3.48933i | 0.456314 | − | 0.558740i | ||||
\(40\) | 11.5448 | − | 6.66541i | 1.82540 | − | 1.05389i | ||||
\(41\) | −3.68473 | − | 6.38214i | −0.575458 | − | 0.996723i | −0.995992 | − | 0.0894458i | \(-0.971490\pi\) |
0.420534 | − | 0.907277i | \(-0.361843\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.12577 | + | 3.68194i | −0.324176 | + | 0.561490i | −0.981345 | − | 0.192253i | \(-0.938420\pi\) |
0.657169 | + | 0.753743i | \(0.271754\pi\) | |||||||
\(44\) | 1.32283i | 0.199424i | ||||||||
\(45\) | −12.3262 | − | 4.11853i | −1.83748 | − | 0.613954i | ||||
\(46\) | 4.30162 | 0.634239 | ||||||||
\(47\) | 3.57157 | − | 6.18614i | 0.520967 | − | 0.902341i | −0.478736 | − | 0.877959i | \(-0.658905\pi\) |
0.999703 | − | 0.0243819i | \(-0.00776176\pi\) | |||||||
\(48\) | 0.667877 | − | 4.10636i | 0.0963998 | − | 0.592703i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 14.0466 | − | 8.10980i | 1.98649 | − | 1.14690i | ||||
\(51\) | −1.89677 | + | 0.719077i | −0.265600 | + | 0.100691i | ||||
\(52\) | −1.37821 | − | 0.795711i | −0.191124 | − | 0.110345i | ||||
\(53\) | − | 3.23289i | − | 0.444071i | −0.975039 | − | 0.222036i | \(-0.928730\pi\) | ||
0.975039 | − | 0.222036i | \(-0.0712702\pi\) | |||||||
\(54\) | −5.17558 | + | 3.27011i | −0.704307 | + | 0.445006i | ||||
\(55\) | 9.36601i | 1.26291i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.48376 | + | 3.91383i | 0.196528 | + | 0.518399i | ||||
\(58\) | −0.400836 | − | 0.694269i | −0.0526324 | − | 0.0911619i | ||||
\(59\) | 2.91810 | + | 5.05430i | 0.379905 | + | 0.658014i | 0.991048 | − | 0.133506i | \(-0.0426234\pi\) |
−0.611143 | + | 0.791520i | \(0.709290\pi\) | |||||||
\(60\) | −0.736989 | + | 4.53129i | −0.0951448 | + | 0.584986i | ||||
\(61\) | 6.21638 | + | 3.58903i | 0.795925 | + | 0.459528i | 0.842044 | − | 0.539408i | \(-0.181352\pi\) |
−0.0461190 | + | 0.998936i | \(0.514685\pi\) | |||||||
\(62\) | −7.72370 | −0.980911 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.72092 | −1.09012 | ||||||||
\(65\) | −9.75814 | − | 5.63387i | −1.21035 | − | 0.698795i | ||||
\(66\) | 3.41727 | + | 2.79083i | 0.420637 | + | 0.343528i | ||||
\(67\) | −3.32682 | − | 5.76221i | −0.406435 | − | 0.703966i | 0.588052 | − | 0.808823i | \(-0.299895\pi\) |
−0.994487 | + | 0.104857i | \(0.966562\pi\) | |||||||
\(68\) | 0.358281 | + | 0.620560i | 0.0434479 | + | 0.0752540i | ||||
\(69\) | −4.00003 | + | 4.89789i | −0.481547 | + | 0.589637i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.95976i | − | 0.232580i | −0.993215 | − | 0.116290i | \(-0.962900\pi\) | ||
0.993215 | − | 0.116290i | \(-0.0371003\pi\) | |||||||
\(72\) | 6.12010 | + | 6.91166i | 0.721261 | + | 0.814546i | ||||
\(73\) | − | 11.9069i | − | 1.39360i | −0.717266 | − | 0.696799i | \(-0.754607\pi\) | ||
0.717266 | − | 0.696799i | \(-0.245393\pi\) | |||||||
\(74\) | 5.21085 | + | 3.00849i | 0.605749 | + | 0.349729i | ||||
\(75\) | −3.82782 | + | 23.5349i | −0.441998 | + | 2.71757i | ||||
\(76\) | 1.28048 | − | 0.739283i | 0.146881 | − | 0.0848016i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.96324 | + | 1.88160i | −0.561977 | + | 0.213049i | ||||
\(79\) | 4.87702 | − | 8.44725i | 0.548708 | − | 0.950390i | −0.449656 | − | 0.893202i | \(-0.648453\pi\) |
0.998363 | − | 0.0571879i | \(-0.0182134\pi\) | |||||||
\(80\) | −10.4054 | −1.16335 | ||||||||
\(81\) | 1.08931 | − | 8.93383i | 0.121034 | − | 0.992648i | ||||
\(82\) | 8.68270i | 0.958844i | ||||||||
\(83\) | 0.796736 | − | 1.37999i | 0.0874531 | − | 0.151473i | −0.818981 | − | 0.573821i | \(-0.805461\pi\) |
0.906434 | + | 0.422348i | \(0.138794\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.53673 | + | 4.39374i | 0.275147 | + | 0.476568i | ||||
\(86\) | 4.33806 | − | 2.50458i | 0.467785 | − | 0.270076i | ||||
\(87\) | 1.16324 | + | 0.189194i | 0.124712 | + | 0.0202838i | ||||
\(88\) | 3.32660 | − | 5.76184i | 0.354617 | − | 0.614214i | ||||
\(89\) | −6.09921 | −0.646515 | −0.323258 | − | 0.946311i | \(-0.604778\pi\) | ||||
−0.323258 | + | 0.946311i | \(0.604778\pi\) | |||||||
\(90\) | 10.1508 | + | 11.4637i | 1.06999 | + | 1.20838i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.93456 | + | 1.11692i | 0.201692 | + | 0.116447i | ||||
\(93\) | 7.18218 | − | 8.79432i | 0.744757 | − | 0.911929i | ||||
\(94\) | −7.28851 | + | 4.20802i | −0.751753 | + | 0.434025i | ||||
\(95\) | 9.06614 | − | 5.23434i | 0.930166 | − | 0.537032i | ||||
\(96\) | 3.64237 | − | 4.45995i | 0.371748 | − | 0.455192i | ||||
\(97\) | −2.36387 | − | 1.36478i | −0.240014 | − | 0.138572i | 0.375169 | − | 0.926956i | \(-0.377585\pi\) |
−0.615183 | + | 0.788384i | \(0.710918\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.35537 | + | 1.29580i | −0.638738 | + | 0.130233i | ||||
\(100\) | 8.42288 | 0.842288 | ||||||||
\(101\) | 7.99849 | − | 13.8538i | 0.795880 | − | 1.37850i | −0.126400 | − | 0.991979i | \(-0.540342\pi\) |
0.922279 | − | 0.386524i | \(-0.126324\pi\) | |||||||
\(102\) | 2.35898 | + | 0.383675i | 0.233574 | + | 0.0379895i | ||||
\(103\) | −2.61251 | + | 1.50834i | −0.257419 | + | 0.148621i | −0.623156 | − | 0.782097i | \(-0.714150\pi\) |
0.365738 | + | 0.930718i | \(0.380817\pi\) | |||||||
\(104\) | 4.00205 | + | 6.93175i | 0.392433 | + | 0.679714i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.90450 | + | 3.29868i | −0.184981 | + | 0.320397i | ||||
\(107\) | 11.8484i | 1.14543i | 0.819754 | + | 0.572716i | \(0.194110\pi\) | ||||
−0.819754 | + | 0.572716i | \(0.805890\pi\) | |||||||
\(108\) | −3.17670 | + | 0.126820i | −0.305678 | + | 0.0122033i | ||||
\(109\) | 7.16157 | 0.685954 | 0.342977 | − | 0.939344i | \(-0.388565\pi\) | ||||
0.342977 | + | 0.939344i | \(0.388565\pi\) | |||||||
\(110\) | 5.51752 | − | 9.55662i | 0.526075 | − | 0.911188i | ||||
\(111\) | −8.27102 | + | 3.13560i | −0.785051 | + | 0.297618i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.46102 | − | 1.42087i | 0.231514 | − | 0.133664i | −0.379756 | − | 0.925086i | \(-0.623992\pi\) |
0.611270 | + | 0.791422i | \(0.290659\pi\) | |||||||
\(114\) | 0.791682 | − | 4.86756i | 0.0741478 | − | 0.455889i | ||||
\(115\) | 13.6973 | + | 7.90812i | 1.27728 | + | 0.737436i | ||||
\(116\) | − | 0.416310i | − | 0.0386535i | ||||||
\(117\) | 2.47285 | − | 7.40090i | 0.228615 | − | 0.684214i | ||||
\(118\) | − | 6.87623i | − | 0.633008i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 14.6052 | − | 17.8835i | 1.33327 | − | 1.63254i | ||||
\(121\) | −3.16279 | − | 5.47811i | −0.287526 | − | 0.498010i | ||||
\(122\) | −4.22859 | − | 7.32414i | −0.382839 | − | 0.663096i | ||||
\(123\) | −9.88626 | − | 8.07395i | −0.891414 | − | 0.728003i | ||||
\(124\) | −3.47357 | − | 2.00547i | −0.311936 | − | 0.180096i | ||||
\(125\) | 37.9763 | 3.39670 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.5344 | 1.64466 | 0.822332 | − | 0.569009i | \(-0.192673\pi\) | ||||
0.822332 | + | 0.569009i | \(0.192673\pi\) | |||||||
\(128\) | 3.14011 | + | 1.81294i | 0.277549 | + | 0.160243i | ||||
\(129\) | −1.18216 | + | 7.26836i | −0.104083 | + | 0.639944i | ||||
\(130\) | 6.63783 | + | 11.4971i | 0.582176 | + | 1.00836i | ||||
\(131\) | 3.35221 | + | 5.80619i | 0.292884 | + | 0.507289i | 0.974490 | − | 0.224429i | \(-0.0720518\pi\) |
−0.681607 | + | 0.731719i | \(0.738718\pi\) | |||||||
\(132\) | 0.812205 | + | 2.14242i | 0.0706933 | + | 0.186474i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 7.83931i | 0.677214i | ||||||||
\(135\) | −22.4919 | + | 0.897922i | −1.93580 | + | 0.0772808i | ||||
\(136\) | − | 3.60396i | − | 0.309037i | ||||||
\(137\) | 11.8181 | + | 6.82316i | 1.00969 | + | 0.582942i | 0.911099 | − | 0.412187i | \(-0.135235\pi\) |
0.0985856 | + | 0.995129i | \(0.468568\pi\) | |||||||
\(138\) | 6.96678 | − | 2.64115i | 0.593052 | − | 0.224830i | ||||
\(139\) | 7.74126 | − | 4.46942i | 0.656605 | − | 0.379091i | −0.134377 | − | 0.990930i | \(-0.542903\pi\) |
0.790982 | + | 0.611839i | \(0.209570\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.98618 | − | 12.2118i | 0.167267 | − | 1.02842i | ||||
\(142\) | −1.15449 | + | 1.99964i | −0.0968830 | + | 0.167806i | ||||
\(143\) | −5.62354 | −0.470264 | ||||||||
\(144\) | −1.43959 | − | 7.06062i | −0.119966 | − | 0.588385i | ||||
\(145\) | − | 2.94760i | − | 0.244785i | ||||||
\(146\) | −7.01436 | + | 12.1492i | −0.580513 | + | 1.00548i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.56231 | + | 2.70601i | 0.128421 | + | 0.222432i | ||||
\(149\) | −3.29003 | + | 1.89950i | −0.269530 | + | 0.155613i | −0.628674 | − | 0.777669i | \(-0.716402\pi\) |
0.359144 | + | 0.933282i | \(0.383069\pi\) | |||||||
\(150\) | 17.7701 | − | 21.7589i | 1.45092 | − | 1.77661i | ||||
\(151\) | 1.91083 | − | 3.30965i | 0.155501 | − | 0.269336i | −0.777740 | − | 0.628586i | \(-0.783634\pi\) |
0.933241 | + | 0.359250i | \(0.116967\pi\) | |||||||
\(152\) | −7.43648 | −0.603178 | ||||||||
\(153\) | −2.63044 | + | 2.32919i | −0.212659 | + | 0.188304i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −24.5939 | − | 14.1993i | −1.97543 | − | 1.14051i | ||||
\(156\) | −2.72067 | − | 0.442503i | −0.217828 | − | 0.0354286i | ||||
\(157\) | −18.6081 | + | 10.7434i | −1.48509 | + | 0.857417i | −0.999856 | − | 0.0169675i | \(-0.994599\pi\) |
−0.485234 | + | 0.874384i | \(0.661265\pi\) | |||||||
\(158\) | −9.95256 | + | 5.74611i | −0.791783 | + | 0.457136i | ||||
\(159\) | −1.98496 | − | 5.23590i | −0.157418 | − | 0.415234i | ||||
\(160\) | −12.4725 | − | 7.20102i | −0.986041 | − | 0.569291i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −6.37441 | + | 8.47394i | −0.500821 | + | 0.665776i | ||||
\(163\) | 12.5175 | 0.980447 | 0.490223 | − | 0.871597i | \(-0.336915\pi\) | ||||
0.490223 | + | 0.871597i | \(0.336915\pi\) | |||||||
\(164\) | −2.25448 | + | 3.90487i | −0.176045 | + | 0.304919i | ||||
\(165\) | 5.75064 | + | 15.1689i | 0.447687 | + | 1.18090i | ||||
\(166\) | −1.62590 | + | 0.938715i | −0.126194 | + | 0.0728584i | ||||
\(167\) | −7.70819 | − | 13.3510i | −0.596477 | − | 1.03313i | −0.993337 | − | 0.115250i | \(-0.963233\pi\) |
0.396859 | − | 0.917880i | \(-0.370100\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.11731 | + | 5.39935i | −0.239793 | + | 0.415334i | ||||
\(170\) | − | 5.97755i | − | 0.458457i | ||||||
\(171\) | 4.80611 | + | 5.42771i | 0.367532 | + | 0.415068i | ||||
\(172\) | 2.60127 | 0.198345 | ||||||||
\(173\) | −4.30737 | + | 7.46059i | −0.327483 | + | 0.567218i | −0.982012 | − | 0.188820i | \(-0.939534\pi\) |
0.654528 | + | 0.756037i | \(0.272867\pi\) | |||||||
\(174\) | −1.07546 | − | 0.878309i | −0.0815302 | − | 0.0665844i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.49739 | + | 2.59657i | −0.339004 | + | 0.195724i | ||||
\(177\) | 7.82938 | + | 6.39413i | 0.588492 | + | 0.480612i | ||||
\(178\) | 6.22334 | + | 3.59305i | 0.466459 | + | 0.269310i | ||||
\(179\) | 19.1384i | 1.43047i | 0.698882 | + | 0.715237i | \(0.253681\pi\) | ||||
−0.698882 | + | 0.715237i | \(0.746319\pi\) | |||||||
\(180\) | 1.58856 | + | 7.79125i | 0.118404 | + | 0.580725i | ||||
\(181\) | − | 7.69817i | − | 0.572200i | −0.958200 | − | 0.286100i | \(-0.907641\pi\) | ||
0.958200 | − | 0.286100i | \(-0.0923590\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.2715 | + | 1.99589i | 0.907135 | + | 0.147541i | ||||
\(184\) | −5.61758 | − | 9.72993i | −0.414133 | − | 0.717300i | ||||
\(185\) | 11.0616 | + | 19.1593i | 0.813268 | + | 1.40862i | ||||
\(186\) | −12.5091 | + | 4.74228i | −0.917211 | + | 0.347721i | ||||
\(187\) | 2.19285 | + | 1.26604i | 0.160357 | + | 0.0925820i | ||||
\(188\) | −4.37047 | −0.318750 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −12.3342 | −0.894817 | ||||||||
\(191\) | 16.1203 | + | 9.30704i | 1.16642 | + | 0.673433i | 0.952834 | − | 0.303491i | \(-0.0981521\pi\) |
0.213587 | + | 0.976924i | \(0.431485\pi\) | |||||||
\(192\) | −14.1242 | + | 5.35456i | −1.01932 | + | 0.386432i | ||||
\(193\) | −9.05721 | − | 15.6875i | −0.651952 | − | 1.12921i | −0.982649 | − | 0.185477i | \(-0.940617\pi\) |
0.330696 | − | 0.943737i | \(-0.392716\pi\) | |||||||
\(194\) | 1.60799 | + | 2.78511i | 0.115447 | + | 0.199959i | ||||
\(195\) | −19.2632 | − | 3.13305i | −1.37946 | − | 0.224362i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.5945i | 1.18231i | 0.806559 | + | 0.591154i | \(0.201328\pi\) | ||||
−0.806559 | + | 0.591154i | \(0.798672\pi\) | |||||||
\(198\) | 7.24807 | + | 2.42178i | 0.515098 | + | 0.172108i | ||||
\(199\) | − | 2.71887i | − | 0.192735i | −0.995346 | − | 0.0963677i | \(-0.969278\pi\) | ||
0.995346 | − | 0.0963677i | \(-0.0307225\pi\) | |||||||
\(200\) | −36.6875 | − | 21.1815i | −2.59420 | − | 1.49776i | ||||
\(201\) | −8.92596 | − | 7.28969i | −0.629589 | − | 0.514175i | ||||
\(202\) | −16.3225 | + | 9.42383i | −1.14845 | + | 0.663058i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.961279 | + | 0.785061i | 0.0673030 | + | 0.0549653i | ||||
\(205\) | −15.9623 | + | 27.6476i | −1.11486 | + | 1.93099i | ||||
\(206\) | 3.55425 | 0.247636 | ||||||||
\(207\) | −3.47108 | + | 10.3885i | −0.241256 | + | 0.722048i | ||||
\(208\) | − | 6.24759i | − | 0.433192i | ||||||
\(209\) | 2.61237 | − | 4.52476i | 0.180702 | − | 0.312984i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.9445 | − | 24.1526i | −0.959979 | − | 1.66273i | −0.722539 | − | 0.691330i | \(-0.757025\pi\) |
−0.237440 | − | 0.971402i | \(-0.576308\pi\) | |||||||
\(212\) | −1.71301 | + | 0.989010i | −0.117650 | + | 0.0679255i | ||||
\(213\) | −1.20327 | − | 3.17397i | −0.0824469 | − | 0.217477i | ||||
\(214\) | 6.97992 | − | 12.0896i | 0.477138 | − | 0.826427i | ||||
\(215\) | 18.4177 | 1.25608 | ||||||||
\(216\) | 14.1556 | + | 7.43624i | 0.963169 | + | 0.505972i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7.30732 | − | 4.21888i | −0.494914 | − | 0.285739i | ||||
\(219\) | −7.31073 | − | 19.2841i | −0.494013 | − | 1.30310i | ||||
\(220\) | 4.96278 | − | 2.86526i | 0.334590 | − | 0.193176i | ||||
\(221\) | −2.63809 | + | 1.52310i | −0.177457 | + | 0.102455i | ||||
\(222\) | 10.2865 | + | 1.67305i | 0.690387 | + | 0.112288i | ||||
\(223\) | 6.64349 | + | 3.83562i | 0.444881 | + | 0.256852i | 0.705666 | − | 0.708545i | \(-0.250648\pi\) |
−0.260785 | + | 0.965397i | \(0.583981\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.25076 | + | 40.4667i | 0.550051 | + | 2.69778i | ||||
\(226\) | −3.34815 | −0.222715 | ||||||||
\(227\) | 1.16439 | − | 2.01677i | 0.0772829 | − | 0.133858i | −0.824794 | − | 0.565434i | \(-0.808709\pi\) |
0.902077 | + | 0.431576i | \(0.142042\pi\) | |||||||
\(228\) | 1.61991 | − | 1.98352i | 0.107281 | − | 0.131362i | ||||
\(229\) | −10.3653 | + | 5.98443i | −0.684961 | + | 0.395463i | −0.801722 | − | 0.597698i | \(-0.796082\pi\) |
0.116760 | + | 0.993160i | \(0.462749\pi\) | |||||||
\(230\) | −9.31735 | − | 16.1381i | −0.614368 | − | 1.06412i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.04692 | + | 1.81332i | −0.0687337 | + | 0.119050i | ||||
\(233\) | 2.52779i | 0.165601i | 0.996566 | + | 0.0828007i | \(0.0263865\pi\) | ||||
−0.996566 | + | 0.0828007i | \(0.973614\pi\) | |||||||
\(234\) | −6.88305 | + | 6.09477i | −0.449959 | + | 0.398428i | ||||
\(235\) | −30.9442 | −2.01858 | ||||||||
\(236\) | 1.78542 | − | 3.09244i | 0.116221 | − | 0.201301i | ||||
\(237\) | 2.71216 | − | 16.6754i | 0.176174 | − | 1.08318i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.4587 | − | 10.0798i | 1.12931 | − | 0.652006i | 0.185546 | − | 0.982636i | \(-0.440595\pi\) |
0.943761 | + | 0.330630i | \(0.107261\pi\) | |||||||
\(240\) | −16.8522 | + | 6.38879i | −1.08781 | + | 0.412395i | ||||
\(241\) | −18.1254 | − | 10.4647i | −1.16756 | − | 0.674091i | −0.214455 | − | 0.976734i | \(-0.568798\pi\) |
−0.953104 | + | 0.302643i | \(0.902131\pi\) | |||||||
\(242\) | 7.45280i | 0.479084i | ||||||||
\(243\) | −3.72107 | − | 15.1378i | −0.238707 | − | 0.971092i | ||||
\(244\) | − | 4.39184i | − | 0.281159i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.33110 | + | 14.0623i | 0.339899 | + | 0.896578i | ||||
\(247\) | 3.14280 | + | 5.44349i | 0.199972 | + | 0.346361i | ||||
\(248\) | 10.0865 | + | 17.4704i | 0.640496 | + | 1.10937i | ||||
\(249\) | 0.443072 | − | 2.72418i | 0.0280786 | − | 0.172638i | ||||
\(250\) | −38.7492 | − | 22.3718i | −2.45071 | − | 1.41492i | ||||
\(251\) | −25.5747 | −1.61426 | −0.807130 | − | 0.590374i | \(-0.798980\pi\) | ||||
−0.807130 | + | 0.590374i | \(0.798980\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.89363 | 0.496268 | ||||||||
\(254\) | −18.9116 | − | 10.9186i | −1.18662 | − | 0.685096i | ||||
\(255\) | 6.80613 | + | 5.55846i | 0.426217 | + | 0.348084i | ||||
\(256\) | 6.58491 | + | 11.4054i | 0.411557 | + | 0.712837i | ||||
\(257\) | 5.93725 | + | 10.2836i | 0.370355 | + | 0.641474i | 0.989620 | − | 0.143708i | \(-0.0459026\pi\) |
−0.619265 | + | 0.785182i | \(0.712569\pi\) | |||||||
\(258\) | 5.48801 | − | 6.71988i | 0.341669 | − | 0.418361i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 6.89408i | 0.427553i | ||||||||
\(261\) | 2.00011 | − | 0.407803i | 0.123804 | − | 0.0252424i | ||||
\(262\) | − | 7.89915i | − | 0.488011i | ||||||
\(263\) | 19.3705 | + | 11.1836i | 1.19444 | + | 0.689608i | 0.959309 | − | 0.282357i | \(-0.0911162\pi\) |
0.235127 | + | 0.971965i | \(0.424450\pi\) | |||||||
\(264\) | 1.84995 | − | 11.3742i | 0.113857 | − | 0.700034i | ||||
\(265\) | −12.1286 | + | 7.00247i | −0.745056 | + | 0.430158i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.87812 | + | 3.74486i | −0.604531 | + | 0.229182i | ||||
\(268\) | −2.03549 | + | 3.52557i | −0.124337 | + | 0.215358i | ||||
\(269\) | 4.22669 | 0.257706 | 0.128853 | − | 0.991664i | \(-0.458870\pi\) | ||||
0.128853 | + | 0.991664i | \(0.458870\pi\) | |||||||
\(270\) | 23.4786 | + | 12.3338i | 1.42887 | + | 0.750612i | ||||
\(271\) | − | 22.3943i | − | 1.36036i | −0.733046 | − | 0.680179i | \(-0.761902\pi\) | ||
0.733046 | − | 0.680179i | \(-0.238098\pi\) | |||||||
\(272\) | −1.40653 | + | 2.43619i | −0.0852836 | + | 0.147715i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.03905 | − | 13.9240i | −0.485657 | − | 0.841183i | ||||
\(275\) | 25.7760 | − | 14.8818i | 1.55435 | − | 0.897405i | ||||
\(276\) | 3.81894 | + | 0.621130i | 0.229873 | + | 0.0373877i | ||||
\(277\) | −5.69230 | + | 9.85935i | −0.342017 | + | 0.592391i | −0.984807 | − | 0.173651i | \(-0.944443\pi\) |
0.642790 | + | 0.766042i | \(0.277777\pi\) | |||||||
\(278\) | −10.5317 | −0.631652 | ||||||||
\(279\) | 6.23243 | − | 18.6528i | 0.373126 | − | 1.11672i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.702700 | − | 0.405704i | −0.0419196 | − | 0.0242023i | 0.478894 | − | 0.877873i | \(-0.341038\pi\) |
−0.520813 | + | 0.853671i | \(0.674371\pi\) | |||||||
\(282\) | −9.22059 | + | 11.2903i | −0.549078 | + | 0.672326i | ||||
\(283\) | 15.8740 | − | 9.16486i | 0.943611 | − | 0.544794i | 0.0525206 | − | 0.998620i | \(-0.483274\pi\) |
0.891090 | + | 0.453826i | \(0.149941\pi\) | |||||||
\(284\) | −1.03842 | + | 0.599532i | −0.0616188 | + | 0.0355757i | ||||
\(285\) | 11.4694 | − | 14.0439i | 0.679391 | − | 0.831890i | ||||
\(286\) | 5.73799 | + | 3.31283i | 0.339294 | + | 0.195892i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 3.16071 | − | 9.45959i | 0.186247 | − | 0.557412i | ||||
\(289\) | −15.6284 | −0.919318 | ||||||||
\(290\) | −1.73643 | + | 3.00759i | −0.101967 | + | 0.176612i | ||||
\(291\) | −4.66642 | − | 0.758967i | −0.273550 | − | 0.0444914i | ||||
\(292\) | −6.30913 | + | 3.64258i | −0.369214 | + | 0.213166i | ||||
\(293\) | 6.23639 | + | 10.8017i | 0.364334 | + | 0.631044i | 0.988669 | − | 0.150112i | \(-0.0479634\pi\) |
−0.624335 | + | 0.781156i | \(0.714630\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.6413 | − | 21.8954i | 0.736004 | − | 1.27480i | ||||
\(296\) | − | 15.7154i | − | 0.913438i | ||||||
\(297\) | −9.49737 | + | 6.00078i | −0.551093 | + | 0.348200i | ||||
\(298\) | 4.47599 | 0.259287 | ||||||||
\(299\) | −4.74819 | + | 8.22411i | −0.274595 | + | 0.475613i | ||||
\(300\) | 13.6415 | − | 5.17157i | 0.787590 | − | 0.298581i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3.89943 | + | 2.25134i | −0.224387 | + | 0.129550i | ||||
\(303\) | 4.44804 | − | 27.3482i | 0.255533 | − | 1.57111i | ||||
\(304\) | 5.02688 | + | 2.90227i | 0.288311 | + | 0.166457i | ||||
\(305\) | − | 31.0955i | − | 1.78052i | ||||||
\(306\) | 4.05611 | − | 0.827001i | 0.231872 | − | 0.0472765i | ||||
\(307\) | 21.3241i | 1.21703i | 0.793543 | + | 0.608514i | \(0.208234\pi\) | ||||
−0.793543 | + | 0.608514i | \(0.791766\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.30505 | + | 4.04692i | −0.188018 | + | 0.230221i | ||||
\(310\) | 16.7296 | + | 28.9765i | 0.950178 | + | 1.64576i | ||||
\(311\) | −3.92094 | − | 6.79126i | −0.222336 | − | 0.385097i | 0.733181 | − | 0.680034i | \(-0.238035\pi\) |
−0.955517 | + | 0.294936i | \(0.904702\pi\) | |||||||
\(312\) | 10.7376 | + | 8.76925i | 0.607899 | + | 0.496461i | ||||
\(313\) | 8.57593 | + | 4.95131i | 0.484740 | + | 0.279865i | 0.722390 | − | 0.691486i | \(-0.243044\pi\) |
−0.237650 | + | 0.971351i | \(0.576377\pi\) | |||||||
\(314\) | 25.3158 | 1.42865 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.96794 | −0.335723 | ||||||||
\(317\) | 20.8358 | + | 12.0296i | 1.17025 | + | 0.675647i | 0.953740 | − | 0.300632i | \(-0.0971977\pi\) |
0.216515 | + | 0.976279i | \(0.430531\pi\) | |||||||
\(318\) | −1.05911 | + | 6.51180i | −0.0593919 | + | 0.365164i | ||||
\(319\) | −0.735549 | − | 1.27401i | −0.0411828 | − | 0.0713308i | ||||
\(320\) | 18.8896 | + | 32.7178i | 1.05596 | + | 1.82898i | ||||
\(321\) | 7.27483 | + | 19.1894i | 0.406042 | + | 1.07105i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 2.83018i | − | 0.157476i | ||||||
\(324\) | −5.06703 | + | 2.15586i | −0.281501 | + | 0.119770i | ||||
\(325\) | 35.8069i | 1.98621i | ||||||||
\(326\) | −12.7723 | − | 7.37407i | −0.707390 | − | 0.408412i | ||||
\(327\) | 11.5987 | − | 4.39713i | 0.641408 | − | 0.243162i | ||||
\(328\) | 19.6396 | − | 11.3389i | 1.08442 | − | 0.626088i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 3.06835 | − | 18.8654i | 0.168907 | − | 1.03850i | ||||
\(331\) | 4.53686 | − | 7.85807i | 0.249368 | − | 0.431918i | −0.713982 | − | 0.700164i | \(-0.753110\pi\) |
0.963351 | + | 0.268245i | \(0.0864437\pi\) | |||||||
\(332\) | −0.974954 | −0.0535075 | ||||||||
\(333\) | −11.4703 | + | 10.1567i | −0.628568 | + | 0.556581i | ||||
\(334\) | 18.1636i | 0.993867i | ||||||||
\(335\) | −14.4118 | + | 24.9620i | −0.787403 | + | 1.36382i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.02012 | + | 6.96304i | 0.218990 | + | 0.379301i | 0.954499 | − | 0.298213i | \(-0.0963906\pi\) |
−0.735510 | + | 0.677514i | \(0.763057\pi\) | |||||||
\(338\) | 6.36152 | − | 3.67282i | 0.346021 | − | 0.199775i | ||||
\(339\) | 3.11340 | − | 3.81225i | 0.169097 | − | 0.207053i | ||||
\(340\) | 1.55208 | − | 2.68828i | 0.0841733 | − | 0.145792i | ||||
\(341\) | −14.1733 | −0.767525 | ||||||||
\(342\) | −1.70645 | − | 8.36946i | −0.0922743 | − | 0.452568i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −11.3303 | − | 6.54157i | −0.610891 | − | 0.352698i | ||||
\(345\) | 27.0392 | + | 4.39778i | 1.45574 | + | 0.236769i | ||||
\(346\) | 8.79007 | − | 5.07495i | 0.472557 | − | 0.272831i | ||||
\(347\) | −30.6345 | + | 17.6868i | −1.64454 | + | 0.949478i | −0.665356 | + | 0.746526i | \(0.731720\pi\) |
−0.979189 | + | 0.202952i | \(0.934946\pi\) | |||||||
\(348\) | −0.255611 | − | 0.674245i | −0.0137022 | − | 0.0361433i | ||||
\(349\) | 21.1868 | + | 12.2322i | 1.13411 | + | 0.654776i | 0.944964 | − | 0.327174i | \(-0.106096\pi\) |
0.189141 | + | 0.981950i | \(0.439430\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.539130 | − | 13.5046i | −0.0287766 | − | 0.720823i | ||||
\(352\) | −7.18783 | −0.383112 | ||||||||
\(353\) | −0.485949 | + | 0.841688i | −0.0258644 | + | 0.0447985i | −0.878668 | − | 0.477433i | \(-0.841567\pi\) |
0.852803 | + | 0.522232i | \(0.174900\pi\) | |||||||
\(354\) | −4.22194 | − | 11.1365i | −0.224394 | − | 0.591901i | ||||
\(355\) | −7.35231 | + | 4.24486i | −0.390220 | + | 0.225294i | ||||
\(356\) | 1.86588 | + | 3.23180i | 0.0988914 | + | 0.171285i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.2745 | − | 19.5279i | 0.595874 | − | 1.03208i | ||||
\(359\) | − | 15.9210i | − | 0.840276i | −0.907460 | − | 0.420138i | \(-0.861982\pi\) | ||
0.907460 | − | 0.420138i | \(-0.138018\pi\) | |||||||
\(360\) | 12.6738 | − | 37.9311i | 0.667970 | − | 1.99915i | ||||
\(361\) | 13.1601 | 0.692639 | ||||||||
\(362\) | −4.53499 | + | 7.85484i | −0.238354 | + | 0.412841i | ||||
\(363\) | −8.48588 | − | 6.93028i | −0.445393 | − | 0.363745i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −44.6704 | + | 25.7905i | −2.33816 | + | 1.34994i | ||||
\(366\) | −11.3455 | − | 9.26566i | −0.593037 | − | 0.484324i | ||||
\(367\) | −21.3983 | − | 12.3543i | −1.11698 | − | 0.644891i | −0.176355 | − | 0.984327i | \(-0.556431\pi\) |
−0.940629 | + | 0.339435i | \(0.889764\pi\) | |||||||
\(368\) | 8.76958i | 0.457146i | ||||||||
\(369\) | −20.9688 | − | 7.00627i | −1.09159 | − | 0.364732i | ||||
\(370\) | − | 26.0657i | − | 1.35509i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −6.85704 | − | 1.11526i | −0.355521 | − | 0.0578235i | ||||
\(373\) | 4.71810 | + | 8.17200i | 0.244294 | + | 0.423130i | 0.961933 | − | 0.273286i | \(-0.0881104\pi\) |
−0.717639 | + | 0.696416i | \(0.754777\pi\) | |||||||
\(374\) | −1.49165 | − | 2.58361i | −0.0771314 | − | 0.133595i | ||||
\(375\) | 61.5054 | − | 23.3171i | 3.17612 | − | 1.20409i | ||||
\(376\) | 19.0364 | + | 10.9907i | 0.981730 | + | 0.566802i | ||||
\(377\) | 1.76980 | 0.0911492 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.8031 | 1.06858 | 0.534292 | − | 0.845300i | \(-0.320578\pi\) | ||||
0.534292 | + | 0.845300i | \(0.320578\pi\) | |||||||
\(380\) | −5.54705 | − | 3.20259i | −0.284558 | − | 0.164289i | ||||
\(381\) | 30.0178 | − | 11.3800i | 1.53786 | − | 0.583013i | ||||
\(382\) | −10.9656 | − | 18.9929i | −0.561047 | − | 0.971761i | ||||
\(383\) | −3.23008 | − | 5.59467i | −0.165050 | − | 0.285874i | 0.771623 | − | 0.636080i | \(-0.219445\pi\) |
−0.936673 | + | 0.350205i | \(0.886112\pi\) | |||||||
\(384\) | 6.19876 | + | 1.00819i | 0.316329 | + | 0.0514492i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 21.3424i | 1.08630i | ||||||||
\(387\) | 2.54811 | + | 12.4975i | 0.129528 | + | 0.635283i | ||||
\(388\) | 1.67006i | 0.0847845i | ||||||||
\(389\) | −0.0445846 | − | 0.0257409i | −0.00226053 | − | 0.00130512i | 0.498869 | − | 0.866677i | \(-0.333749\pi\) |
−0.501130 | + | 0.865372i | \(0.667082\pi\) | |||||||
\(390\) | 17.8095 | + | 14.5447i | 0.901820 | + | 0.736502i | ||||
\(391\) | 3.70303 | − | 2.13794i | 0.187270 | − | 0.108120i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.99409 | + | 7.34533i | 0.453692 | + | 0.370523i | ||||
\(394\) | 9.77582 | − | 16.9322i | 0.492499 | − | 0.853033i | ||||
\(395\) | −42.2547 | −2.12607 | ||||||||
\(396\) | 2.63085 | + | 2.97111i | 0.132205 | + | 0.149304i | ||||
\(397\) | 12.7131i | 0.638052i | 0.947746 | + | 0.319026i | \(0.103356\pi\) | ||||
−0.947746 | + | 0.319026i | \(0.896644\pi\) | |||||||
\(398\) | −1.60169 | + | 2.77420i | −0.0802853 | + | 0.139058i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.5332 | + | 28.6364i | 0.826660 | + | 1.43182i | ||||
\(401\) | −2.19725 | + | 1.26858i | −0.109725 | + | 0.0633500i | −0.553858 | − | 0.832611i | \(-0.686845\pi\) |
0.444133 | + | 0.895961i | \(0.353512\pi\) | |||||||
\(402\) | 4.81327 | + | 12.6963i | 0.240064 | + | 0.633236i | ||||
\(403\) | 8.52554 | − | 14.7667i | 0.424687 | − | 0.735580i | ||||
\(404\) | −9.78764 | −0.486953 | ||||||||
\(405\) | −35.8760 | + | 15.2641i | −1.78269 | + | 0.758478i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.56210 | + | 5.52068i | 0.473976 | + | 0.273650i | ||||
\(408\) | −2.21280 | − | 5.83687i | −0.109550 | − | 0.288968i | ||||
\(409\) | −0.0495655 | + | 0.0286167i | −0.00245086 | + | 0.00141500i | −0.501225 | − | 0.865317i | \(-0.667117\pi\) |
0.498774 | + | 0.866732i | \(0.333784\pi\) | |||||||
\(410\) | 32.5744 | − | 18.8068i | 1.60873 | − | 0.928803i | ||||
\(411\) | 23.3296 | + | 3.79443i | 1.15076 | + | 0.187165i | ||||
\(412\) | 1.59845 | + | 0.922864i | 0.0787499 | + | 0.0454663i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 9.66157 | − | 8.55508i | 0.474840 | − | 0.420459i | ||||
\(415\) | −6.90295 | −0.338853 | ||||||||
\(416\) | 4.32364 | − | 7.48876i | 0.211984 | − | 0.367167i | ||||
\(417\) | 9.79335 | − | 11.9916i | 0.479583 | − | 0.587232i | ||||
\(418\) | −5.33108 | + | 3.07790i | −0.260752 | + | 0.150545i | ||||
\(419\) | 3.08007 | + | 5.33484i | 0.150471 | + | 0.260624i | 0.931401 | − | 0.363995i | \(-0.118588\pi\) |
−0.780930 | + | 0.624619i | \(0.785254\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.0693 | − | 26.1007i | 0.734431 | − | 1.27207i | −0.220542 | − | 0.975378i | \(-0.570783\pi\) |
0.954973 | − | 0.296694i | \(-0.0958842\pi\) | |||||||
\(422\) | 32.8588i | 1.59954i | ||||||||
\(423\) | −4.28117 | − | 20.9974i | −0.208157 | − | 1.02093i | ||||
\(424\) | 9.94849 | 0.483141 | ||||||||
\(425\) | 8.06128 | − | 13.9626i | 0.391030 | − | 0.677283i | ||||
\(426\) | −0.642025 | + | 3.94741i | −0.0311062 | + | 0.191253i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6.27815 | − | 3.62469i | 0.303466 | − | 0.175206i | ||||
\(429\) | −9.10773 | + | 3.45280i | −0.439725 | + | 0.166703i | ||||
\(430\) | −18.7926 | − | 10.8499i | −0.906258 | − | 0.523228i | ||||
\(431\) | − | 8.07140i | − | 0.388785i | −0.980924 | − | 0.194393i | \(-0.937726\pi\) | ||
0.980924 | − | 0.194393i | \(-0.0622736\pi\) | |||||||
\(432\) | −6.66668 | − | 10.5513i | −0.320751 | − | 0.507650i | ||||
\(433\) | 28.4938i | 1.36933i | 0.728860 | + | 0.684663i | \(0.240051\pi\) | ||||
−0.728860 | + | 0.684663i | \(0.759949\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.80980 | − | 4.77385i | −0.0867731 | − | 0.228889i | ||||
\(436\) | −2.19088 | − | 3.79471i | −0.104924 | − | 0.181734i | ||||
\(437\) | −4.41147 | − | 7.64090i | −0.211029 | − | 0.365514i | ||||
\(438\) | −3.90076 | + | 23.9833i | −0.186385 | + | 1.14597i | ||||
\(439\) | 1.77067 | + | 1.02230i | 0.0845096 | + | 0.0487916i | 0.541659 | − | 0.840598i | \(-0.317796\pi\) |
−0.457150 | + | 0.889390i | \(0.651130\pi\) | |||||||
\(440\) | −28.8218 | −1.37402 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.58904 | 0.170713 | ||||||||
\(443\) | −21.1324 | − | 12.2008i | −1.00403 | − | 0.579677i | −0.0945924 | − | 0.995516i | \(-0.530155\pi\) |
−0.909438 | + | 0.415839i | \(0.863488\pi\) | |||||||
\(444\) | 4.19175 | + | 3.42333i | 0.198931 | + | 0.162464i | ||||
\(445\) | 13.2110 | + | 22.8821i | 0.626260 | + | 1.08471i | ||||
\(446\) | −4.51913 | − | 7.82737i | −0.213987 | − | 0.370637i | ||||
\(447\) | −4.16217 | + | 5.09643i | −0.196864 | + | 0.241053i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 0.293539i | − | 0.0138529i | −0.999976 | − | 0.00692647i | \(-0.997795\pi\) | ||
0.999976 | − | 0.00692647i | \(-0.00220478\pi\) | |||||||
\(450\) | 15.4203 | − | 46.1508i | 0.726918 | − | 2.17557i | ||||
\(451\) | 15.9331i | 0.750259i | ||||||||
\(452\) | −1.50576 | − | 0.869351i | −0.0708250 | − | 0.0408908i | ||||
\(453\) | 1.06263 | − | 6.53345i | 0.0499267 | − | 0.306968i | ||||
\(454\) | −2.37616 | + | 1.37188i | −0.111519 | + | 0.0643855i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −12.0439 | + | 4.56593i | −0.564008 | + | 0.213819i | ||||
\(457\) | −8.27470 | + | 14.3322i | −0.387074 | + | 0.670432i | −0.992055 | − | 0.125808i | \(-0.959848\pi\) |
0.604981 | + | 0.796240i | \(0.293181\pi\) | |||||||
\(458\) | 14.1017 | 0.658931 | ||||||||
\(459\) | −2.83009 | + | 5.38737i | −0.132097 | + | 0.251461i | ||||
\(460\) | − | 9.67705i | − | 0.451195i | ||||||
\(461\) | 10.0560 | − | 17.4175i | 0.468354 | − | 0.811213i | −0.530992 | − | 0.847377i | \(-0.678180\pi\) |
0.999346 | + | 0.0361638i | \(0.0115138\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.34602 | + | 16.1878i | 0.434346 | + | 0.752310i | 0.997242 | − | 0.0742181i | \(-0.0236461\pi\) |
−0.562896 | + | 0.826528i | \(0.690313\pi\) | |||||||
\(464\) | 1.41538 | − | 0.817173i | 0.0657076 | − | 0.0379363i | ||||
\(465\) | −48.5498 | − | 7.89636i | −2.25144 | − | 0.366185i | ||||
\(466\) | 1.48912 | − | 2.57924i | 0.0689824 | − | 0.119481i | ||||
\(467\) | 29.3605 | 1.35864 | 0.679322 | − | 0.733841i | \(-0.262274\pi\) | ||||
0.679322 | + | 0.733841i | \(0.262274\pi\) | |||||||
\(468\) | −4.67802 | + | 0.953804i | −0.216242 | + | 0.0440896i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 31.5740 | + | 18.2293i | 1.45640 | + | 0.840853i | ||||
\(471\) | −23.5409 | + | 28.8249i | −1.08471 | + | 1.32818i | ||||
\(472\) | −15.5535 | + | 8.97981i | −0.715907 | + | 0.413329i | ||||
\(473\) | 7.96050 | − | 4.59599i | 0.366024 | − | 0.211324i | ||||
\(474\) | −12.5908 | + | 15.4170i | −0.578316 | + | 0.708127i | ||||
\(475\) | −28.8106 | − | 16.6338i | −1.32192 | − | 0.763212i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.42958 | − | 7.26117i | −0.294390 | − | 0.332466i | ||||
\(478\) | −23.7520 | −1.08639 | ||||||||
\(479\) | 10.9660 | − | 18.9938i | 0.501051 | − | 0.867847i | −0.498948 | − | 0.866632i | \(-0.666280\pi\) |
0.999999 | − | 0.00121455i | \(-0.000386605\pi\) | |||||||
\(480\) | −24.6215 | − | 4.00456i | −1.12381 | − | 0.182782i | ||||
\(481\) | −11.5036 | + | 6.64163i | −0.524521 | + | 0.302832i | ||||
\(482\) | 12.3295 | + | 21.3554i | 0.561594 | + | 0.972710i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.93513 | + | 3.35174i | −0.0879604 | + | 0.152352i | ||||
\(485\) | 11.8245i | 0.536923i | ||||||||
\(486\) | −5.12089 | + | 17.6380i | −0.232288 | + | 0.800075i | ||||
\(487\) | 1.07779 | 0.0488394 | 0.0244197 | − | 0.999702i | \(-0.492226\pi\) | ||||
0.0244197 | + | 0.999702i | \(0.492226\pi\) | |||||||
\(488\) | −11.0444 | + | 19.1295i | −0.499957 | + | 0.865952i | ||||
\(489\) | 20.2730 | − | 7.68563i | 0.916777 | − | 0.347556i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.3708 | − | 9.45168i | 0.738804 | − | 0.426549i | −0.0828305 | − | 0.996564i | \(-0.526396\pi\) |
0.821634 | + | 0.570015i | \(0.193063\pi\) | |||||||
\(492\) | −1.25374 | + | 7.70844i | −0.0565228 | + | 0.347523i | ||||
\(493\) | −0.690115 | − | 0.398438i | −0.0310812 | − | 0.0179448i | ||||
\(494\) | − | 7.40570i | − | 0.333198i | ||||||
\(495\) | 18.6272 | + | 21.0363i | 0.837229 | + | 0.945513i | ||||
\(496\) | − | 15.7461i | − | 0.707020i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −2.05690 | + | 2.51860i | −0.0921721 | + | 0.112861i | ||||
\(499\) | 8.34290 | + | 14.4503i | 0.373479 | + | 0.646885i | 0.990098 | − | 0.140377i | \(-0.0448314\pi\) |
−0.616619 | + | 0.787262i | \(0.711498\pi\) | |||||||
\(500\) | −11.6178 | − | 20.1225i | −0.519562 | − | 0.899908i | ||||
\(501\) | −20.6813 | − | 16.8901i | −0.923974 | − | 0.754595i | ||||
\(502\) | 26.0952 | + | 15.0661i | 1.16468 | + | 0.672431i | ||||
\(503\) | 21.2386 | 0.946981 | 0.473491 | − | 0.880799i | \(-0.342994\pi\) | ||||
0.473491 | + | 0.880799i | \(0.342994\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −69.2993 | −3.08378 | ||||||||
\(506\) | −8.05428 | − | 4.65014i | −0.358056 | − | 0.206724i | ||||
\(507\) | −1.73357 | + | 10.6586i | −0.0769905 | + | 0.473367i | ||||
\(508\) | −5.67007 | − | 9.82085i | −0.251569 | − | 0.435730i | ||||
\(509\) | −5.72252 | − | 9.91170i | −0.253646 | − | 0.439328i | 0.710881 | − | 0.703313i | \(-0.248297\pi\) |
−0.964527 | + | 0.263984i | \(0.914963\pi\) | |||||||
\(510\) | −3.67016 | − | 9.68108i | −0.162517 | − | 0.428685i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 22.7685i | − | 1.00623i | ||||||
\(513\) | 11.1164 | + | 5.83967i | 0.490801 | + | 0.257828i | ||||
\(514\) | − | 13.9905i | − | 0.617096i | ||||||
\(515\) | 11.3175 | + | 6.53414i | 0.498707 | + | 0.287929i | ||||
\(516\) | 4.21295 | − | 1.59716i | 0.185465 | − | 0.0703108i | ||||
\(517\) | −13.3747 | + | 7.72188i | −0.588218 | + | 0.339608i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.39537 | + | 14.7276i | −0.105145 | + | 0.646472i | ||||
\(520\) | 17.3370 | − | 30.0285i | 0.760276 | − | 1.31684i | ||||
\(521\) | 20.7998 | 0.911254 | 0.455627 | − | 0.890171i | \(-0.349415\pi\) | ||||
0.455627 | + | 0.890171i | \(0.349415\pi\) | |||||||
\(522\) | −2.28106 | − | 0.762164i | −0.0998391 | − | 0.0333590i | ||||
\(523\) | − | 14.9338i | − | 0.653009i | −0.945196 | − | 0.326505i | \(-0.894129\pi\) | ||
0.945196 | − | 0.326505i | \(-0.105871\pi\) | |||||||
\(524\) | 2.05102 | − | 3.55248i | 0.0895994 | − | 0.155191i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.1765 | − | 22.8223i | −0.574522 | − | 0.995101i | ||||
\(527\) | −6.64890 | + | 3.83875i | −0.289631 | + | 0.167218i | ||||
\(528\) | −5.68959 | + | 6.96669i | −0.247607 | + | 0.303186i | ||||
\(529\) | −4.83508 | + | 8.37460i | −0.210221 | + | 0.364113i | ||||
\(530\) | 16.5006 | 0.716742 | ||||||||
\(531\) | 16.6062 | + | 5.54858i | 0.720647 | + | 0.240788i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.6002 | − | 9.58410i | −0.719033 | − | 0.415134i | ||||
\(534\) | 12.2853 | + | 1.99813i | 0.531635 | + | 0.0864675i | ||||
\(535\) | 44.4511 | − | 25.6639i | 1.92179 | − | 1.10955i | ||||
\(536\) | 17.7319 | − | 10.2375i | 0.765902 | − | 0.442194i | ||||
\(537\) | 11.7508 | + | 30.9961i | 0.507085 | + | 1.33758i | ||||
\(538\) | −4.31272 | − | 2.48995i | −0.185934 | − | 0.107349i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 7.35654 | + | 11.6431i | 0.316575 | + | 0.501041i | ||||
\(541\) | 31.1677 | 1.34000 | 0.670002 | − | 0.742360i | \(-0.266293\pi\) | ||||
0.670002 | + | 0.742360i | \(0.266293\pi\) | |||||||
\(542\) | −13.1925 | + | 22.8501i | −0.566667 | + | 0.981496i | ||||
\(543\) | −4.72660 | − | 12.4677i | −0.202838 | − | 0.535042i | ||||
\(544\) | −3.37192 | + | 1.94678i | −0.144570 | + | 0.0834675i | ||||
\(545\) | −15.5120 | − | 26.8676i | −0.664462 | − | 1.15088i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.7410 | + | 27.2642i | −0.673035 | + | 1.16573i | 0.304004 | + | 0.952671i | \(0.401677\pi\) |
−0.977039 | + | 0.213061i | \(0.931657\pi\) | |||||||
\(548\) | − | 8.34940i | − | 0.356669i | ||||||
\(549\) | 21.1000 | − | 4.30209i | 0.900528 | − | 0.183609i | ||||
\(550\) | −35.0674 | −1.49528 | ||||||||
\(551\) | −0.822146 | + | 1.42400i | −0.0350246 | + | 0.0606644i | ||||
\(552\) | −15.0722 | − | 12.3092i | −0.641514 | − | 0.523914i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 11.6163 | − | 6.70667i | 0.493529 | − | 0.284939i | ||||
\(555\) | 29.6788 | + | 24.2382i | 1.25979 | + | 1.02885i | ||||
\(556\) | −4.73643 | − | 2.73458i | −0.200870 | − | 0.115972i | ||||
\(557\) | 27.2389i | 1.15415i | 0.816692 | + | 0.577074i | \(0.195806\pi\) | ||||
−0.816692 | + | 0.577074i | \(0.804194\pi\) | |||||||
\(558\) | −17.3477 | + | 15.3609i | −0.734385 | + | 0.650280i | ||||
\(559\) | 11.0584i | 0.467720i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.32881 | + | 0.704057i | 0.182762 | + | 0.0297253i | ||||
\(562\) | 0.478001 | + | 0.827922i | 0.0201633 | + | 0.0349238i | ||||
\(563\) | 14.1871 | + | 24.5728i | 0.597916 | + | 1.03562i | 0.993128 | + | 0.117031i | \(0.0373377\pi\) |
−0.395212 | + | 0.918590i | \(0.629329\pi\) | |||||||
\(564\) | −7.07830 | + | 2.68343i | −0.298050 | + | 0.112993i | ||||
\(565\) | −10.6612 | − | 6.15525i | −0.448521 | − | 0.258953i | ||||
\(566\) | −21.5961 | −0.907751 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.03071 | 0.253043 | ||||||||
\(569\) | 29.4616 | + | 17.0097i | 1.23509 | + | 0.713082i | 0.968087 | − | 0.250613i | \(-0.0806321\pi\) |
0.267007 | + | 0.963695i | \(0.413965\pi\) | |||||||
\(570\) | −19.9761 | + | 7.57309i | −0.836708 | + | 0.317202i | ||||
\(571\) | 22.3455 | + | 38.7035i | 0.935130 | + | 1.61969i | 0.774402 | + | 0.632693i | \(0.218051\pi\) |
0.160727 | + | 0.986999i | \(0.448616\pi\) | |||||||
\(572\) | 1.72036 | + | 2.97975i | 0.0719319 | + | 0.124590i | ||||
\(573\) | 31.8224 | + | 5.17573i | 1.32940 | + | 0.216219i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 50.2613i | − | 2.09604i | ||||||
\(576\) | −19.5875 | + | 17.3442i | −0.816144 | + | 0.722675i | ||||
\(577\) | 7.34738i | 0.305875i | 0.988236 | + | 0.152938i | \(0.0488734\pi\) | ||||
−0.988236 | + | 0.152938i | \(0.951127\pi\) | |||||||
\(578\) | 15.9465 | + | 9.20670i | 0.663286 | + | 0.382948i | ||||
\(579\) | −24.3008 | − | 19.8461i | −1.00991 | − | 0.824775i | ||||
\(580\) | −1.56185 | + | 0.901733i | −0.0648522 | + | 0.0374424i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 4.31428 | + | 3.52340i | 0.178833 | + | 0.146050i | ||||
\(583\) | −3.49482 | + | 6.05320i | −0.144741 | + | 0.250698i | ||||
\(584\) | 36.6408 | 1.51621 | ||||||||
\(585\) | −33.1217 | + | 6.75320i | −1.36942 | + | 0.279211i | ||||
\(586\) | − | 14.6954i | − | 0.607063i | ||||||
\(587\) | 13.1328 | − | 22.7466i | 0.542048 | − | 0.938855i | −0.456738 | − | 0.889601i | \(-0.650982\pi\) |
0.998786 | − | 0.0492535i | \(-0.0156842\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.92095 | + | 13.7195i | 0.326377 | + | 0.565302i | ||||
\(590\) | −25.7971 | + | 14.8940i | −1.06205 | + | 0.613175i | ||||
\(591\) | 10.1889 | + | 26.8760i | 0.419114 | + | 1.10553i | ||||
\(592\) | −6.13331 | + | 10.6232i | −0.252078 | + | 0.436611i | ||||
\(593\) | 9.12418 | 0.374685 | 0.187343 | − | 0.982295i | \(-0.440013\pi\) | ||||
0.187343 | + | 0.982295i | \(0.440013\pi\) | |||||||
\(594\) | 13.2257 | − | 0.527997i | 0.542658 | − | 0.0216640i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.01298 | + | 1.16220i | 0.0824550 | + | 0.0476054i | ||||
\(597\) | −1.66936 | − | 4.40340i | −0.0683223 | − | 0.180219i | ||||
\(598\) | 9.68966 | − | 5.59433i | 0.396240 | − | 0.228769i | ||||
\(599\) | −20.0987 | + | 11.6040i | −0.821210 | + | 0.474126i | −0.850834 | − | 0.525435i | \(-0.823903\pi\) |
0.0296234 | + | 0.999561i | \(0.490569\pi\) | |||||||
\(600\) | −72.4233 | − | 11.7792i | −2.95667 | − | 0.480886i | ||||
\(601\) | 19.0021 | + | 10.9709i | 0.775111 | + | 0.447510i | 0.834695 | − | 0.550713i | \(-0.185644\pi\) |
−0.0595840 | + | 0.998223i | \(0.518977\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −18.9320 | − | 6.32572i | −0.770973 | − | 0.257603i | ||||
\(604\) | −2.33825 | −0.0951421 | ||||||||
\(605\) | −13.7013 | + | 23.7313i | −0.557036 | + | 0.964815i | ||||
\(606\) | −20.6494 | + | 25.2845i | −0.838825 | + | 1.02711i | ||||
\(607\) | 38.6289 | − | 22.3024i | 1.56790 | − | 0.905226i | 0.571484 | − | 0.820613i | \(-0.306368\pi\) |
0.996414 | − | 0.0846136i | \(-0.0269656\pi\) | |||||||
\(608\) | 4.01703 | + | 6.95770i | 0.162912 | + | 0.282172i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −18.3184 | + | 31.7283i | −0.741689 | + | 1.28464i | ||||
\(611\) | − | 18.5795i | − | 0.751647i | ||||||
\(612\) | 2.03888 | + | 0.681247i | 0.0824169 | + | 0.0275378i | ||||
\(613\) | 11.6560 | 0.470780 | 0.235390 | − | 0.971901i | \(-0.424363\pi\) | ||||
0.235390 | + | 0.971901i | \(0.424363\pi\) | |||||||
\(614\) | 12.5620 | − | 21.7580i | 0.506961 | − | 0.878083i | ||||
\(615\) | −8.87681 | + | 54.5780i | −0.357947 | + | 2.20080i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 36.6143 | − | 21.1393i | 1.47403 | − | 0.851034i | 0.474462 | − | 0.880276i | \(-0.342643\pi\) |
0.999572 | + | 0.0292416i | \(0.00930923\pi\) | |||||||
\(618\) | 5.75636 | − | 2.18227i | 0.231555 | − | 0.0877839i | ||||
\(619\) | 30.0633 | + | 17.3571i | 1.20835 | + | 0.697640i | 0.962398 | − | 0.271643i | \(-0.0875670\pi\) |
0.245949 | + | 0.969283i | \(0.420900\pi\) | |||||||
\(620\) | 17.3755i | 0.697815i | ||||||||
\(621\) | 0.756764 | + | 18.9561i | 0.0303679 | + | 0.760681i | ||||
\(622\) | 9.23930i | 0.370462i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.83596 | − | 10.1184i | −0.153561 | − | 0.405061i | ||||
\(625\) | −47.8410 | − | 82.8631i | −1.91364 | − | 3.31452i | ||||
\(626\) | −5.83364 | − | 10.1042i | −0.233159 | − | 0.403844i | ||||
\(627\) | 1.45277 | − | 8.93215i | 0.0580179 | − | 0.356716i | ||||
\(628\) | 11.3852 | + | 6.57327i | 0.454321 | + | 0.262302i | ||||
\(629\) | 5.98098 | 0.238477 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.8860 | −0.512982 | −0.256491 | − | 0.966547i | \(-0.582566\pi\) | ||||
−0.256491 | + | 0.966547i | \(0.582566\pi\) | |||||||
\(632\) | 25.9945 | + | 15.0079i | 1.03401 | + | 0.596984i | ||||
\(633\) | −37.4136 | − | 30.5551i | −1.48706 | − | 1.21446i | ||||
\(634\) | −14.1732 | − | 24.5488i | −0.562891 | − | 0.974956i | ||||
\(635\) | −40.1457 | − | 69.5345i | −1.59314 | − | 2.75939i | ||||
\(636\) | −2.16711 | + | 2.65355i | −0.0859315 | + | 0.105220i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.73325i | 0.0686200i | ||||||||
\(639\) | −3.89758 | − | 4.40168i | −0.154186 | − | 0.174128i | ||||
\(640\) | − | 15.7074i | − | 0.620890i | ||||||
\(641\) | −16.5666 | − | 9.56474i | −0.654342 | − | 0.377785i | 0.135776 | − | 0.990740i | \(-0.456647\pi\) |
−0.790118 | + | 0.612955i | \(0.789981\pi\) | |||||||
\(642\) | 3.88160 | − | 23.8656i | 0.153195 | − | 0.941899i | ||||
\(643\) | 9.77521 | − | 5.64372i | 0.385497 | − | 0.222567i | −0.294710 | − | 0.955587i | \(-0.595223\pi\) |
0.680207 | + | 0.733020i | \(0.261890\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 29.8289 | − | 11.3083i | 1.17451 | − | 0.445265i | ||||
\(646\) | −1.66726 | + | 2.88778i | −0.0655976 | + | 0.113618i | ||||
\(647\) | 5.08677 | 0.199982 | 0.0999909 | − | 0.994988i | \(-0.468119\pi\) | ||||
0.0999909 | + | 0.994988i | \(0.468119\pi\) | |||||||
\(648\) | 27.4919 | + | 3.35211i | 1.07998 | + | 0.131683i | ||||
\(649\) | − | 12.6181i | − | 0.495305i | ||||||
\(650\) | 21.0939 | − | 36.5356i | 0.827369 | − | 1.43305i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.82937 | − | 6.63267i | −0.149970 | − | 0.259755i | ||||
\(653\) | −32.9044 | + | 18.9974i | −1.28765 | + | 0.743424i | −0.978234 | − | 0.207503i | \(-0.933466\pi\) |
−0.309414 | + | 0.950927i | \(0.600133\pi\) | |||||||
\(654\) | −14.4251 | − | 2.34616i | −0.564066 | − | 0.0917421i | ||||
\(655\) | 14.5218 | − | 25.1526i | 0.567415 | − | 0.982792i | ||||
\(656\) | −17.7012 | −0.691115 | ||||||||
\(657\) | −23.6805 | − | 26.7433i | −0.923865 | − | 1.04335i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.97949 | + | 5.76166i | 0.388746 | + | 0.224442i | 0.681617 | − | 0.731710i | \(-0.261277\pi\) |
−0.292871 | + | 0.956152i | \(0.594611\pi\) | |||||||
\(660\) | 6.27834 | − | 7.68760i | 0.244384 | − | 0.299239i | ||||
\(661\) | −38.0928 | + | 21.9929i | −1.48164 | + | 0.855424i | −0.999783 | − | 0.0208274i | \(-0.993370\pi\) |
−0.481854 | + | 0.876251i | \(0.660037\pi\) | |||||||
\(662\) | −9.25838 | + | 5.34533i | −0.359837 | + | 0.207752i | ||||
\(663\) | −3.33741 | + | 4.08654i | −0.129614 | + | 0.158708i | ||||
\(664\) | 4.24660 | + | 2.45178i | 0.164800 | + | 0.0951473i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 17.6870 | − | 3.60621i | 0.685358 | − | 0.139738i | ||||
\(667\) | −2.48422 | −0.0961894 | ||||||||
\(668\) | −4.71620 | + | 8.16869i | −0.182475 | + | 0.316056i | ||||
\(669\) | 13.1147 | + | 2.13303i | 0.507042 | + | 0.0824675i | ||||
\(670\) | 29.4103 | − | 16.9800i | 1.13622 | − | 0.655996i | ||||
\(671\) | −7.75962 | − | 13.4401i | −0.299557 | − | 0.518848i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.9316 | + | 37.9866i | −0.845400 | + | 1.46428i | 0.0398735 | + | 0.999205i | \(0.487305\pi\) |
−0.885273 | + | 0.465071i | \(0.846029\pi\) | |||||||
\(674\) | − | 9.47301i | − | 0.364887i | ||||||
\(675\) | 38.2089 | + | 60.4728i | 1.47066 | + | 2.32760i | ||||
\(676\) | 3.81461 | 0.146716 | ||||||||
\(677\) | 0.738999 | − | 1.27998i | 0.0284020 | − | 0.0491938i | −0.851475 | − | 0.524395i | \(-0.824291\pi\) |
0.879877 | + | 0.475201i | \(0.157625\pi\) | |||||||
\(678\) | −5.42257 | + | 2.05573i | −0.208252 | + | 0.0789499i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −13.5208 | + | 7.80621i | −0.518497 | + | 0.299355i | ||||
\(681\) | 0.647526 | − | 3.98123i | 0.0248132 | − | 0.152561i | ||||
\(682\) | 14.4617 | + | 8.34948i | 0.553768 | + | 0.319718i | ||||
\(683\) | − | 10.3259i | − | 0.395111i | −0.980292 | − | 0.197555i | \(-0.936700\pi\) | ||
0.980292 | − | 0.197555i | \(-0.0633002\pi\) | |||||||
\(684\) | 1.40570 | − | 4.20707i | 0.0537483 | − | 0.160861i | ||||
\(685\) | − | 59.1162i | − | 2.25871i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13.1130 | + | 16.0565i | −0.500294 | + | 0.612592i | ||||
\(688\) | 5.10601 | + | 8.84388i | 0.194665 | + | 0.337170i | ||||
\(689\) | −4.20442 | − | 7.28228i | −0.160176 | − | 0.277433i | ||||
\(690\) | −24.9988 | − | 20.4161i | −0.951688 | − | 0.777228i | ||||
\(691\) | 6.58166 | + | 3.79992i | 0.250378 | + | 0.144556i | 0.619937 | − | 0.784651i | \(-0.287158\pi\) |
−0.369559 | + | 0.929207i | \(0.620491\pi\) | |||||||
\(692\) | 5.27087 | 0.200368 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 41.6773 | 1.58205 | ||||||||
\(695\) | −33.5353 | − | 19.3616i | −1.27207 | − | 0.734428i | ||||
\(696\) | −0.582203 | + | 3.57960i | −0.0220683 | + | 0.135685i | ||||
\(697\) | 4.31538 | + | 7.47446i | 0.163457 | + | 0.283115i | ||||
\(698\) | −14.4120 | − | 24.9624i | −0.545503 | − | 0.944839i | ||||
\(699\) | 1.55204 | + | 4.09395i | 0.0587036 | + | 0.154847i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.35907i | 0.240179i | 0.992763 | + | 0.120089i | \(0.0383181\pi\) | ||||
−0.992763 | + | 0.120089i | \(0.961682\pi\) | |||||||
\(702\) | −7.40547 | + | 14.0971i | −0.279501 | + | 0.532059i | ||||
\(703\) | − | 12.3413i | − | 0.465460i | ||||||
\(704\) | 16.3289 | + | 9.42749i | 0.615419 | + | 0.355312i | ||||
\(705\) | −50.1164 | + | 18.9995i | −1.88749 | + | 0.715561i | ||||
\(706\) | 0.991677 | − | 0.572545i | 0.0373223 | − | 0.0215480i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0.992890 | − | 6.10466i | 0.0373151 | − | 0.229427i | ||||
\(709\) | 23.8048 | − | 41.2311i | 0.894007 | − | 1.54847i | 0.0589776 | − | 0.998259i | \(-0.481216\pi\) |
0.835029 | − | 0.550206i | \(-0.185451\pi\) | |||||||
\(710\) | 10.0026 | 0.375390 | ||||||||
\(711\) | −5.84599 | − | 28.6722i | −0.219242 | − | 1.07529i | ||||
\(712\) | − | 18.7690i | − | 0.703396i | ||||||
\(713\) | −11.9671 | + | 20.7276i | −0.448171 | + | 0.776255i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.1806 | + | 21.0975i | 0.455530 | + | 0.789002i | ||||
\(716\) | 10.1409 | − | 5.85486i | 0.378983 | − | 0.218806i | ||||
\(717\) | 22.0867 | − | 27.0444i | 0.824843 | − | 1.00999i | ||||
\(718\) | −9.37904 | + | 16.2450i | −0.350023 | + | 0.606257i | ||||
\(719\) | −14.1470 | −0.527594 | −0.263797 | − | 0.964578i | \(-0.584975\pi\) | ||||
−0.263797 | + | 0.964578i | \(0.584975\pi\) | |||||||
\(720\) | −23.3708 | + | 20.6942i | −0.870977 | + | 0.771228i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −13.4280 | − | 7.75264i | −0.499737 | − | 0.288524i | ||||
\(723\) | −35.7806 | − | 5.81952i | −1.33070 | − | 0.216430i | ||||
\(724\) | −4.07904 | + | 2.35503i | −0.151596 | + | 0.0875241i | ||||
\(725\) | −8.11202 | + | 4.68348i | −0.301273 | + | 0.173940i | ||||
\(726\) | 4.57595 | + | 12.0704i | 0.169829 | + | 0.447973i | ||||
\(727\) | −40.1828 | − | 23.1996i | −1.49030 | − | 0.860424i | −0.490360 | − | 0.871520i | \(-0.663135\pi\) |
−0.999938 | + | 0.0110955i | \(0.996468\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.3210 | − | 22.2321i | −0.567446 | − | 0.823411i | ||||
\(730\) | 60.7728 | 2.24930 | ||||||||
\(731\) | 2.48960 | − | 4.31211i | 0.0920811 | − | 0.159489i | ||||
\(732\) | −2.69655 | − | 7.11290i | −0.0996673 | − | 0.262900i | ||||
\(733\) | −22.8893 | + | 13.2151i | −0.845436 | + | 0.488112i | −0.859108 | − | 0.511794i | \(-0.828981\pi\) |
0.0136726 | + | 0.999907i | \(0.495648\pi\) | |||||||
\(734\) | 14.5559 | + | 25.2115i | 0.537268 | + | 0.930575i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.06899 | + | 10.5118i | −0.223706 | + | 0.387470i | ||||
\(737\) | 14.3854i | 0.529894i | ||||||||
\(738\) | 17.2682 | + | 19.5016i | 0.635651 | + | 0.717865i | ||||
\(739\) | −46.2670 | −1.70196 | −0.850979 | − | 0.525200i | \(-0.823991\pi\) | ||||
−0.850979 | + | 0.525200i | \(0.823991\pi\) | |||||||
\(740\) | 6.76798 | − | 11.7225i | 0.248796 | − | 0.430927i | ||||
\(741\) | 8.43225 | + | 6.88648i | 0.309766 | + | 0.252981i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −36.5640 | + | 21.1102i | −1.34140 | + | 0.774458i | −0.987013 | − | 0.160640i | \(-0.948644\pi\) |
−0.354388 | + | 0.935098i | \(0.615311\pi\) | |||||||
\(744\) | 27.0626 | + | 22.1015i | 0.992161 | + | 0.810282i | ||||
\(745\) | 14.2525 | + | 8.22868i | 0.522171 | + | 0.301476i | ||||
\(746\) | − | 11.1177i | − | 0.407050i | ||||||
\(747\) | −0.955031 | − | 4.68404i | −0.0349428 | − | 0.171380i | ||||
\(748\) | − | 1.54923i | − | 0.0566456i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −76.4932 | − | 12.4412i | −2.79314 | − | 0.454288i | ||||
\(751\) | 8.02320 | + | 13.8966i | 0.292771 | + | 0.507094i | 0.974464 | − | 0.224544i | \(-0.0720894\pi\) |
−0.681693 | + | 0.731638i | \(0.738756\pi\) | |||||||
\(752\) | −8.57877 | − | 14.8589i | −0.312836 | − | 0.541847i | ||||
\(753\) | −41.4201 | + | 15.7026i | −1.50943 | + | 0.572235i | ||||
\(754\) | −1.80582 | − | 1.04259i | −0.0657639 | − | 0.0379688i | ||||
\(755\) | −16.5555 | −0.602516 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.0149 | 0.909183 | 0.454591 | − | 0.890700i | \(-0.349785\pi\) | ||||
0.454591 | + | 0.890700i | \(0.349785\pi\) | |||||||
\(758\) | −21.2265 | − | 12.2551i | −0.770981 | − | 0.445126i | ||||
\(759\) | 12.7843 | − | 4.84661i | 0.464041 | − | 0.175921i | ||||
\(760\) | 16.1075 | + | 27.8990i | 0.584281 | + | 1.01200i | ||||
\(761\) | −3.00365 | − | 5.20247i | −0.108882 | − | 0.188589i | 0.806436 | − | 0.591322i | \(-0.201394\pi\) |
−0.915318 | + | 0.402733i | \(0.868060\pi\) | |||||||
\(762\) | −37.3327 | − | 6.07196i | −1.35242 | − | 0.219964i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 11.3889i | − | 0.412035i | ||||||
\(765\) | 14.4359 | + | 4.82343i | 0.521930 | + | 0.174391i | ||||
\(766\) | 7.61138i | 0.275010i | ||||||||
\(767\) | 13.1464 | + | 7.59008i | 0.474689 | + | 0.274062i | ||||
\(768\) | 17.6675 | + | 14.4288i | 0.637523 | + | 0.520654i | ||||
\(769\) | −28.9946 | + | 16.7400i | −1.04557 | + | 0.603661i | −0.921406 | − | 0.388600i | \(-0.872959\pi\) |
−0.124166 | + | 0.992262i | \(0.539625\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.9298 | + | 13.0096i | 0.573699 | + | 0.468531i | ||||
\(772\) | −5.54159 | + | 9.59831i | −0.199446 | + | 0.345451i | ||||
\(773\) | −36.2016 | −1.30208 | −0.651040 | − | 0.759043i | \(-0.725667\pi\) | ||||
−0.651040 | + | 0.759043i | \(0.725667\pi\) | |||||||
\(774\) | 4.76230 | − | 14.2529i | 0.171177 | − | 0.512311i | ||||
\(775\) | 90.2458i | 3.24172i | ||||||||
\(776\) | 4.19980 | − | 7.27427i | 0.150764 | − | 0.261131i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.0303280 | + | 0.0525296i | 0.00108731 | + | 0.00188328i | ||||
\(779\) | 15.4230 | − | 8.90445i | 0.552585 | − | 0.319035i | ||||
\(780\) | 4.23290 | + | 11.1655i | 0.151562 | + | 0.399788i | ||||
\(781\) | −2.11854 | + | 3.66942i | −0.0758073 | + | 0.131302i | ||||
\(782\) | −5.03785 | −0.180153 | ||||||||
\(783\) | 2.98894 | − | 1.88852i | 0.106816 | − | 0.0674901i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 80.6108 | + | 46.5407i | 2.87712 | + | 1.66111i | ||||
\(786\) | −4.85000 | − | 12.7932i | −0.172994 | − | 0.456320i | ||||
\(787\) | −14.1930 | + | 8.19433i | −0.505926 | + | 0.292096i | −0.731157 | − | 0.682209i | \(-0.761019\pi\) |
0.225232 | + | 0.974305i | \(0.427686\pi\) | |||||||
\(788\) | 8.79294 | − | 5.07661i | 0.313236 | − | 0.180847i | ||||
\(789\) | 38.2385 | + | 6.21929i | 1.36133 | + | 0.221412i | ||||
\(790\) | 43.1147 | + | 24.8923i | 1.53395 | + | 0.885628i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −3.98753 | − | 19.5572i | −0.141691 | − | 0.694935i | ||||
\(793\) | 18.6703 | 0.663004 | ||||||||
\(794\) | 7.48929 | − | 12.9718i | 0.265785 | − | 0.460353i | ||||
\(795\) | −15.3438 | + | 18.7879i | −0.544187 | + | 0.666337i | ||||
\(796\) | −1.44065 | + | 0.831760i | −0.0510625 | + | 0.0294809i | ||||
\(797\) | 23.3328 | + | 40.4137i | 0.826492 | + | 1.43153i | 0.900774 | + | 0.434288i | \(0.143000\pi\) |
−0.0742821 | + | 0.997237i | \(0.523667\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.18285 | + | 7.24491i | −0.147979 | + | 0.256306i | ||||
\(800\) | 45.7672i | 1.61811i | ||||||||
\(801\) | −13.6990 | + | 12.1301i | −0.484031 | + | 0.428598i | ||||
\(802\) | 2.98929 | 0.105555 | ||||||||
\(803\) | −12.8716 | + | 22.2943i | −0.454229 | + | 0.786748i | ||||
\(804\) | −1.13195 | + | 6.95968i | −0.0399209 | + | 0.245449i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −17.3981 | + | 10.0448i | −0.612822 | + | 0.353813i | ||||
\(807\) | 6.84544 | − | 2.59515i | 0.240971 | − | 0.0913536i | ||||
\(808\) | 42.6319 | + | 24.6136i | 1.49979 | + | 0.865902i | ||||
\(809\) | − | 29.8980i | − | 1.05116i | −0.850744 | − | 0.525580i | \(-0.823849\pi\) | ||
0.850744 | − | 0.525580i | \(-0.176151\pi\) | |||||||
\(810\) | 45.5982 | + | 5.55983i | 1.60216 | + | 0.195352i | ||||
\(811\) | − | 25.3404i | − | 0.889821i | −0.895575 | − | 0.444911i | \(-0.853235\pi\) | ||
0.895575 | − | 0.444911i | \(-0.146765\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.7499 | − | 36.2693i | −0.482230 | − | 1.27202i | ||||
\(814\) | −6.50447 | − | 11.2661i | −0.227982 | − | 0.394876i | ||||
\(815\) | −27.1131 | − | 46.9612i | −0.949729 | − | 1.64498i | ||||
\(816\) | −0.782186 | + | 4.80918i | −0.0273820 | + | 0.168355i | ||||
\(817\) | −8.89769 | − | 5.13709i | −0.311291 | − | 0.179724i | ||||
\(818\) | 0.0674323 | 0.00235772 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 19.5329 | 0.682117 | ||||||||
\(821\) | 9.23012 | + | 5.32901i | 0.322133 | + | 0.185984i | 0.652343 | − | 0.757924i | \(-0.273786\pi\) |
−0.330210 | + | 0.943908i | \(0.607119\pi\) | |||||||
\(822\) | −21.5691 | − | 17.6151i | −0.752308 | − | 0.614397i | ||||
\(823\) | −8.55239 | − | 14.8132i | −0.298118 | − | 0.516355i | 0.677588 | − | 0.735442i | \(-0.263025\pi\) |
−0.975705 | + | 0.219087i | \(0.929692\pi\) | |||||||
\(824\) | −4.64156 | − | 8.03943i | −0.161697 | − | 0.280067i | ||||
\(825\) | 32.6088 | − | 39.9283i | 1.13529 | − | 1.39013i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 18.3221i | − | 0.637121i | −0.947903 | − | 0.318560i | \(-0.896801\pi\) | ||
0.947903 | − | 0.318560i | \(-0.103199\pi\) | |||||||
\(828\) | 6.56643 | − | 1.33883i | 0.228199 | − | 0.0465276i | ||||
\(829\) | 7.73341i | 0.268592i | 0.990941 | + | 0.134296i | \(0.0428774\pi\) | ||||
−0.990941 | + | 0.134296i | \(0.957123\pi\) | |||||||
\(830\) | 7.04344 | + | 4.06653i | 0.244481 | + | 0.141151i | ||||
\(831\) | −3.16554 | + | 19.4629i | −0.109811 | + | 0.675162i | ||||
\(832\) | −19.6444 | + | 11.3417i | −0.681047 | + | 0.393203i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −17.0569 | + | 6.46639i | −0.590633 | + | 0.223913i | ||||
\(835\) | −33.3920 | + | 57.8367i | −1.15558 | + | 2.00152i | ||||
\(836\) | −3.19672 | −0.110561 | ||||||||
\(837\) | −1.35879 | − | 34.0363i | −0.0469668 | − | 1.17647i | ||||
\(838\) | − | 7.25788i | − | 0.250719i | ||||||
\(839\) | 9.73588 | − | 16.8630i | 0.336120 | − | 0.582177i | −0.647579 | − | 0.761998i | \(-0.724219\pi\) |
0.983699 | + | 0.179821i | \(0.0575519\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.2685 | − | 24.7138i | −0.492018 | − | 0.852200i | ||||
\(842\) | −30.7519 | + | 17.7546i | −1.05978 | + | 0.611865i | ||||
\(843\) | −1.38717 | − | 0.225616i | −0.0477768 | − | 0.00777063i | ||||
\(844\) | −8.53184 | + | 14.7776i | −0.293678 | + | 0.508665i | ||||
\(845\) | 27.0085 | 0.929122 | ||||||||
\(846\) | −8.00128 | + | 23.9468i | −0.275090 | + | 0.823307i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.72493 | − | 3.88264i | −0.230935 | − | 0.133330i | ||||
\(849\) | 20.0820 | − | 24.5896i | 0.689211 | − | 0.843914i | ||||
\(850\) | −16.4507 | + | 9.49781i | −0.564254 | + | 0.325772i | ||||
\(851\) | 16.1474 | − | 9.32269i | 0.553525 | − | 0.319578i | ||||
\(852\) | −1.31369 | + | 1.60856i | −0.0450062 | + | 0.0551085i | ||||
\(853\) | 0.812274 | + | 0.468967i | 0.0278117 | + | 0.0160571i | 0.513841 | − | 0.857885i | \(-0.328222\pi\) |
−0.486030 | + | 0.873942i | \(0.661555\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.95275 | − | 29.7873i | 0.340377 | − | 1.01870i | ||||
\(856\) | −36.4609 | −1.24621 | ||||||||
\(857\) | 9.00087 | − | 15.5900i | 0.307464 | − | 0.532543i | −0.670343 | − | 0.742051i | \(-0.733853\pi\) |
0.977807 | + | 0.209509i | \(0.0671864\pi\) | |||||||
\(858\) | 11.3271 | + | 1.84230i | 0.386702 | + | 0.0628950i | ||||
\(859\) | 23.1160 | − | 13.3460i | 0.788709 | − | 0.455361i | −0.0507989 | − | 0.998709i | \(-0.516177\pi\) |
0.839508 | + | 0.543348i | \(0.182843\pi\) | |||||||
\(860\) | −5.63438 | − | 9.75903i | −0.192131 | − | 0.332780i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.75486 | + | 8.23566i | −0.161951 | + | 0.280508i | ||||
\(863\) | − | 27.7596i | − | 0.944946i | −0.881345 | − | 0.472473i | \(-0.843361\pi\) | ||
0.881345 | − | 0.472473i | \(-0.156639\pi\) | |||||||
\(864\) | −0.689099 | − | 17.2611i | −0.0234436 | − | 0.587236i | ||||
\(865\) | 37.3193 | 1.26889 | ||||||||
\(866\) | 16.7857 | − | 29.0737i | 0.570402 | − | 0.987966i | ||||
\(867\) | −25.3113 | + | 9.59569i | −0.859618 | + | 0.325887i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.2633 | + | 10.5443i | −0.619540 | + | 0.357692i | ||||
\(870\) | −0.965646 | + | 5.93716i | −0.0327385 | + | 0.201289i | ||||
\(871\) | −14.9877 | − | 8.65316i | −0.507839 | − | 0.293201i | ||||
\(872\) | 22.0381i | 0.746305i | ||||||||
\(873\) | −8.02360 | + | 1.63593i | −0.271558 | + | 0.0553680i | ||||
\(874\) | 10.3952i | 0.351623i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −7.98158 | + | 9.77316i | −0.269673 | + | 0.330205i | ||||
\(877\) | −6.90978 | − | 11.9681i | −0.233327 | − | 0.404134i | 0.725458 | − | 0.688266i | \(-0.241628\pi\) |
−0.958785 | + | 0.284132i | \(0.908295\pi\) | |||||||
\(878\) | −1.20447 | − | 2.08621i | −0.0406490 | − | 0.0704061i | ||||
\(879\) | 16.7325 | + | 13.6651i | 0.564372 | + | 0.460913i | ||||
\(880\) | 19.4828 | + | 11.2484i | 0.656765 | + | 0.379184i | ||||
\(881\) | −43.9006 | −1.47905 | −0.739525 | − | 0.673129i | \(-0.764950\pi\) | ||||
−0.739525 | + | 0.673129i | \(0.764950\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.96743 | 0.268125 | 0.134063 | − | 0.990973i | \(-0.457198\pi\) | ||||
0.134063 | + | 0.990973i | \(0.457198\pi\) | |||||||
\(884\) | 1.61410 | + | 0.931899i | 0.0542880 | + | 0.0313432i | ||||
\(885\) | 7.02994 | − | 43.2228i | 0.236309 | − | 1.45292i | ||||
\(886\) | 14.3750 | + | 24.8982i | 0.482937 | + | 0.836472i | ||||
\(887\) | 10.6080 | + | 18.3736i | 0.356181 | + | 0.616924i | 0.987319 | − | 0.158747i | \(-0.0507453\pi\) |
−0.631138 | + | 0.775670i | \(0.717412\pi\) | |||||||
\(888\) | −9.64910 | − | 25.4522i | −0.323803 | − | 0.854120i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 31.1303i | − | 1.04349i | ||||||
\(891\) | −11.6973 | + | 15.5500i | −0.391873 | + | 0.520944i | ||||
\(892\) | − | 4.69359i | − | 0.157153i | ||||||
\(893\) | 14.9493 | + | 8.63098i | 0.500259 | + | 0.288825i | ||||
\(894\) | 7.24919 | − | 2.74822i | 0.242449 | − | 0.0919141i | ||||
\(895\) | 71.8005 | − | 41.4541i | 2.40003 | − | 1.38566i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.64052 | + | 16.2349i | −0.0881643 | + | 0.542067i | ||||
\(898\) | −0.172924 | + | 0.299513i | −0.00577054 | + | 0.00999487i | ||||
\(899\) | 4.46050 | 0.148766 | ||||||||
\(900\) | 18.9180 | − | 16.7515i | 0.630602 | − | 0.558382i | ||||
\(901\) | 3.78621i | 0.126137i | ||||||||
\(902\) | 9.38618 | − | 16.2573i | 0.312526 | − | 0.541310i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.37242 | + | 7.57325i | 0.145424 | + | 0.251883i | ||||
\(905\) | −28.8808 | + | 16.6743i | −0.960029 | + | 0.554273i | ||||
\(906\) | −4.93311 | + | 6.04042i | −0.163892 | + | 0.200680i | ||||
\(907\) | −1.88344 | + | 3.26221i | −0.0625385 | + | 0.108320i | −0.895599 | − | 0.444861i | \(-0.853253\pi\) |
0.833061 | + | 0.553181i | \(0.186586\pi\) | |||||||
\(908\) | −1.42484 | −0.0472850 | ||||||||
\(909\) | −9.58763 | − | 47.0235i | −0.318002 | − | 1.55967i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.0013 | + | 23.0947i | 1.32530 | + | 0.765163i | 0.984569 | − | 0.174998i | \(-0.0559917\pi\) |
0.340732 | + | 0.940160i | \(0.389325\pi\) | |||||||
\(912\) | 9.92336 | + | 1.61398i | 0.328595 | + | 0.0534442i | ||||
\(913\) | −2.98359 | + | 1.72258i | −0.0987423 | + | 0.0570089i | ||||
\(914\) | 16.8862 | − | 9.74926i | 0.558546 | − | 0.322477i | ||||
\(915\) | −19.0923 | − | 50.3614i | −0.631173 | − | 1.66490i | ||||
\(916\) | 6.34196 | + | 3.66153i | 0.209544 | + | 0.120980i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 6.06139 | − | 3.82980i | 0.200056 | − | 0.126402i | ||||
\(919\) | 1.21522 | 0.0400864 | 0.0200432 | − | 0.999799i | \(-0.493620\pi\) | ||||
0.0200432 | + | 0.999799i | \(0.493620\pi\) | |||||||
\(920\) | −24.3355 | + | 42.1503i | −0.802316 | + | 1.38965i | ||||
\(921\) | 13.0928 | + | 34.5359i | 0.431421 | + | 1.13800i | ||||
\(922\) | −20.5213 | + | 11.8480i | −0.675833 | + | 0.390192i | ||||
\(923\) | −2.54870 | − | 4.41447i | −0.0838914 | − | 0.145304i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 35.1520 | − | 60.8850i | 1.15579 | − | 2.00189i | ||||
\(926\) | − | 22.0230i | − | 0.723720i | ||||||
\(927\) | −2.86800 | + | 8.58355i | −0.0941976 | + | 0.281921i | ||||
\(928\) | 2.26210 | 0.0742570 | ||||||||
\(929\) | −9.44516 | + | 16.3595i | −0.309886 | + | 0.536737i | −0.978337 | − | 0.207018i | \(-0.933624\pi\) |
0.668452 | + | 0.743756i | \(0.266957\pi\) | |||||||
\(930\) | 44.8862 | + | 36.6578i | 1.47188 | + | 1.20206i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.33941 | − | 0.773306i | 0.0438737 | − | 0.0253305i | ||||
\(933\) | −10.5200 | − | 8.59152i | −0.344410 | − | 0.281274i | ||||
\(934\) | −29.9581 | − | 17.2963i | −0.980258 | − | 0.565952i | ||||
\(935\) | − | 10.9690i | − | 0.358725i | ||||||
\(936\) | 22.7746 | + | 7.60963i | 0.744412 | + | 0.248729i | ||||
\(937\) | 27.0448i | 0.883516i | 0.897134 | + | 0.441758i | \(0.145645\pi\) | ||||
−0.897134 | + | 0.441758i | \(0.854355\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.9294 | + | 2.75347i | 0.552470 | + | 0.0898562i | ||||
\(940\) | 9.46650 | + | 16.3965i | 0.308763 | + | 0.534793i | ||||
\(941\) | −8.16024 | − | 14.1339i | −0.266016 | − | 0.460754i | 0.701813 | − | 0.712361i | \(-0.252374\pi\) |
−0.967829 | + | 0.251607i | \(0.919041\pi\) | |||||||
\(942\) | 41.0007 | − | 15.5437i | 1.33588 | − | 0.506440i | ||||
\(943\) | 23.3012 | + | 13.4530i | 0.758793 | + | 0.438089i | ||||
\(944\) | 14.0184 | 0.456259 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.8300 | −0.352114 | ||||||||
\(947\) | −24.8567 | − | 14.3510i | −0.807734 | − | 0.466345i | 0.0384343 | − | 0.999261i | \(-0.487763\pi\) |
−0.846168 | + | 0.532916i | \(0.821096\pi\) | |||||||
\(948\) | −9.66551 | + | 3.66426i | −0.313921 | + | 0.119010i | ||||
\(949\) | −15.4851 | − | 26.8210i | −0.502668 | − | 0.870647i | ||||
\(950\) | 19.5980 | + | 33.9447i | 0.635842 | + | 1.10131i | ||||
\(951\) | 41.1311 | + | 6.68975i | 1.33377 | + | 0.216930i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 34.5757i | − | 1.12002i | −0.828486 | − | 0.560009i | \(-0.810798\pi\) | ||
0.828486 | − | 0.560009i | \(-0.189202\pi\) | |||||||
\(954\) | 2.28288 | + | 11.1966i | 0.0739110 | + | 0.362504i | ||||
\(955\) | − | 80.6366i | − | 2.60934i | ||||||
\(956\) | −10.6820 | − | 6.16723i | −0.345479 | − | 0.199462i | ||||
\(957\) | −1.97350 | − | 1.61173i | −0.0637943 | − | 0.0520998i | ||||
\(958\) | −22.3785 | + | 12.9202i | −0.723015 | + | 0.417433i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 50.6815 | + | 41.3907i | 1.63574 | + | 1.33588i | ||||
\(961\) | 5.98731 | − | 10.3703i | 0.193139 | − | 0.334527i | ||||
\(962\) | 15.6503 | 0.504587 | ||||||||
\(963\) | 23.5642 | + | 26.6120i | 0.759347 | + | 0.857559i | ||||
\(964\) | 12.8055i | 0.412437i | ||||||||
\(965\) | −39.2360 | + | 67.9588i | −1.26305 | + | 2.18767i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.25000 | − | 9.09327i | −0.168829 | − | 0.292420i | 0.769180 | − | 0.639033i | \(-0.220665\pi\) |
−0.938008 | + | 0.346613i | \(0.887332\pi\) | |||||||
\(968\) | 16.8577 | − | 9.73277i | 0.541826 | − | 0.312823i | ||||
\(969\) | −1.73771 | − | 4.58369i | −0.0558232 | − | 0.147249i | ||||
\(970\) | 6.96583 | − | 12.0652i | 0.223659 | − | 0.387389i | ||||
\(971\) | −22.8312 | −0.732689 | −0.366345 | − | 0.930479i | \(-0.619391\pi\) | ||||
−0.366345 | + | 0.930479i | \(0.619391\pi\) | |||||||
\(972\) | −6.88274 | + | 6.60267i | −0.220764 | + | 0.211781i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.09973 | − | 0.634927i | −0.0352375 | − | 0.0203444i | ||||
\(975\) | 21.9851 | + | 57.9919i | 0.704087 | + | 1.85723i | ||||
\(976\) | 14.9315 | − | 8.62071i | 0.477946 | − | 0.275942i | ||||
\(977\) | −8.88551 | + | 5.13005i | −0.284273 | + | 0.164125i | −0.635356 | − | 0.772219i | \(-0.719147\pi\) |
0.351083 | + | 0.936344i | \(0.385813\pi\) | |||||||
\(978\) | −25.2132 | − | 4.10079i | −0.806230 | − | 0.131129i | ||||
\(979\) | 11.4201 | + | 6.59337i | 0.364987 | + | 0.210725i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.0851 | − | 14.2430i | 0.513558 | − | 0.454743i | ||||
\(982\) | −22.2720 | −0.710727 | ||||||||
\(983\) | −16.9599 | + | 29.3754i | −0.540937 | + | 0.936930i | 0.457913 | + | 0.888997i | \(0.348597\pi\) |
−0.998851 | + | 0.0479337i | \(0.984736\pi\) | |||||||
\(984\) | 24.8458 | − | 30.4228i | 0.792054 | − | 0.969842i | ||||
\(985\) | 62.2566 | − | 35.9438i | 1.98366 | − | 1.14527i | ||||
\(986\) | 0.469440 | + | 0.813095i | 0.0149500 | + | 0.0258942i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.92290 | − | 3.33056i | 0.0611756 | − | 0.105959i | ||||
\(989\) | − | 15.5224i | − | 0.493583i | ||||||
\(990\) | −6.61374 | − | 32.4377i | −0.210199 | − | 1.03094i | ||||
\(991\) | 22.8556 | 0.726031 | 0.363015 | − | 0.931783i | \(-0.381747\pi\) | ||||
0.363015 | + | 0.931783i | \(0.381747\pi\) | |||||||
\(992\) | 10.8971 | − | 18.8743i | 0.345982 | − | 0.599259i | ||||
\(993\) | 2.52299 | − | 15.5123i | 0.0800647 | − | 0.492268i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.2002 | + | 5.88910i | −0.323369 | + | 0.186697i | ||||
\(996\) | −1.57901 | + | 0.598612i | −0.0500328 | + | 0.0189678i | ||||
\(997\) | −5.65867 | − | 3.26704i | −0.179212 | − | 0.103468i | 0.407710 | − | 0.913111i | \(-0.366327\pi\) |
−0.586922 | + | 0.809643i | \(0.699661\pi\) | |||||||
\(998\) | − | 19.6592i | − | 0.622302i | ||||||
\(999\) | −12.3409 | + | 23.4921i | −0.390448 | + | 0.743257i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 441.2.o.e.146.8 | yes | 48 | |
3.2 | odd | 2 | 1323.2.o.e.440.18 | 48 | |||
7.2 | even | 3 | 441.2.i.d.227.17 | 48 | |||
7.3 | odd | 6 | 441.2.s.d.362.18 | 48 | |||
7.4 | even | 3 | 441.2.s.d.362.17 | 48 | |||
7.5 | odd | 6 | 441.2.i.d.227.18 | 48 | |||
7.6 | odd | 2 | inner | 441.2.o.e.146.7 | ✓ | 48 | |
9.4 | even | 3 | 1323.2.o.e.881.17 | 48 | |||
9.5 | odd | 6 | inner | 441.2.o.e.293.7 | yes | 48 | |
21.2 | odd | 6 | 1323.2.i.d.521.1 | 48 | |||
21.5 | even | 6 | 1323.2.i.d.521.20 | 48 | |||
21.11 | odd | 6 | 1323.2.s.d.656.7 | 48 | |||
21.17 | even | 6 | 1323.2.s.d.656.8 | 48 | |||
21.20 | even | 2 | 1323.2.o.e.440.17 | 48 | |||
63.4 | even | 3 | 1323.2.i.d.1097.20 | 48 | |||
63.5 | even | 6 | 441.2.s.d.374.17 | 48 | |||
63.13 | odd | 6 | 1323.2.o.e.881.18 | 48 | |||
63.23 | odd | 6 | 441.2.s.d.374.18 | 48 | |||
63.31 | odd | 6 | 1323.2.i.d.1097.1 | 48 | |||
63.32 | odd | 6 | 441.2.i.d.68.8 | 48 | |||
63.40 | odd | 6 | 1323.2.s.d.962.7 | 48 | |||
63.41 | even | 6 | inner | 441.2.o.e.293.8 | yes | 48 | |
63.58 | even | 3 | 1323.2.s.d.962.8 | 48 | |||
63.59 | even | 6 | 441.2.i.d.68.7 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.i.d.68.7 | 48 | 63.59 | even | 6 | |||
441.2.i.d.68.8 | 48 | 63.32 | odd | 6 | |||
441.2.i.d.227.17 | 48 | 7.2 | even | 3 | |||
441.2.i.d.227.18 | 48 | 7.5 | odd | 6 | |||
441.2.o.e.146.7 | ✓ | 48 | 7.6 | odd | 2 | inner | |
441.2.o.e.146.8 | yes | 48 | 1.1 | even | 1 | trivial | |
441.2.o.e.293.7 | yes | 48 | 9.5 | odd | 6 | inner | |
441.2.o.e.293.8 | yes | 48 | 63.41 | even | 6 | inner | |
441.2.s.d.362.17 | 48 | 7.4 | even | 3 | |||
441.2.s.d.362.18 | 48 | 7.3 | odd | 6 | |||
441.2.s.d.374.17 | 48 | 63.5 | even | 6 | |||
441.2.s.d.374.18 | 48 | 63.23 | odd | 6 | |||
1323.2.i.d.521.1 | 48 | 21.2 | odd | 6 | |||
1323.2.i.d.521.20 | 48 | 21.5 | even | 6 | |||
1323.2.i.d.1097.1 | 48 | 63.31 | odd | 6 | |||
1323.2.i.d.1097.20 | 48 | 63.4 | even | 3 | |||
1323.2.o.e.440.17 | 48 | 21.20 | even | 2 | |||
1323.2.o.e.440.18 | 48 | 3.2 | odd | 2 | |||
1323.2.o.e.881.17 | 48 | 9.4 | even | 3 | |||
1323.2.o.e.881.18 | 48 | 63.13 | odd | 6 | |||
1323.2.s.d.656.7 | 48 | 21.11 | odd | 6 | |||
1323.2.s.d.656.8 | 48 | 21.17 | even | 6 | |||
1323.2.s.d.962.7 | 48 | 63.40 | odd | 6 | |||
1323.2.s.d.962.8 | 48 | 63.58 | even | 3 |