Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [275,3,Mod(24,275)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(275, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("275.24");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 275 = 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 275.q (of order \(10\), degree \(4\), not 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: | \(7.49320726991\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{10})\) |
Twist minimal: | no (minimal twist has level 55) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 24.3 | ||
Character | \(\chi\) | \(=\) | 275.24 |
Dual form | 275.3.q.f.149.3 |
$q$-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 \(\left(\mathbb{Z}/275\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) |
\(\chi(n)\) | \(e\left(\frac{1}{10}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0941972 | + | 0.289909i | −0.0470986 | + | 0.144955i | −0.971840 | − | 0.235641i | \(-0.924281\pi\) |
0.924742 | + | 0.380596i | \(0.124281\pi\) | |||||||
\(3\) | 3.03467 | + | 4.17687i | 1.01156 | + | 1.39229i | 0.917957 | + | 0.396679i | \(0.129837\pi\) |
0.0935994 | + | 0.995610i | \(0.470163\pi\) | |||||||
\(4\) | 3.16089 | + | 2.29652i | 0.790223 | + | 0.574131i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.49677 | + | 0.486330i | −0.249462 | + | 0.0810550i | ||||
\(7\) | −8.17974 | − | 5.94293i | −1.16853 | − | 0.848990i | −0.177701 | − | 0.984084i | \(-0.556866\pi\) |
−0.990833 | + | 0.135095i | \(0.956866\pi\) | |||||||
\(8\) | −1.94998 | + | 1.41674i | −0.243747 | + | 0.177093i | ||||
\(9\) | −5.45583 | + | 16.7913i | −0.606203 | + | 1.86570i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50807 | + | 10.8961i | −0.137097 | + | 0.990558i | ||||
\(12\) | 20.1718i | 1.68099i | ||||||||
\(13\) | 1.49891 | − | 4.61316i | 0.115301 | − | 0.354859i | −0.876709 | − | 0.481021i | \(-0.840266\pi\) |
0.992010 | + | 0.126162i | \(0.0402661\pi\) | |||||||
\(14\) | 2.49342 | − | 1.81157i | 0.178101 | − | 0.129398i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.60237 | + | 14.1646i | 0.287648 | + | 0.885290i | ||||
\(17\) | −0.883556 | − | 2.71930i | −0.0519739 | − | 0.159959i | 0.921701 | − | 0.387902i | \(-0.126800\pi\) |
−0.973675 | + | 0.227943i | \(0.926800\pi\) | |||||||
\(18\) | −4.35403 | − | 3.16339i | −0.241891 | − | 0.175744i | ||||
\(19\) | 12.5616 | + | 17.2895i | 0.661136 | + | 0.909975i | 0.999518 | − | 0.0310333i | \(-0.00987978\pi\) |
−0.338383 | + | 0.941009i | \(0.609880\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 52.2005i | − | 2.48574i | ||||||
\(22\) | −3.01683 | − | 1.46359i | −0.137129 | − | 0.0665267i | ||||
\(23\) | 12.1155i | 0.526762i | 0.964692 | + | 0.263381i | \(0.0848376\pi\) | ||||
−0.964692 | + | 0.263381i | \(0.915162\pi\) | |||||||
\(24\) | −11.8351 | − | 3.84545i | −0.493128 | − | 0.160227i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.19620 | + | 0.869094i | 0.0460079 | + | 0.0334267i | ||||
\(27\) | −42.4999 | + | 13.8091i | −1.57407 | + | 0.511447i | ||||
\(28\) | −12.2072 | − | 37.5699i | −0.435972 | − | 1.34178i | ||||
\(29\) | 28.0610 | − | 38.6227i | 0.967622 | − | 1.33182i | 0.0243833 | − | 0.999703i | \(-0.492238\pi\) |
0.943239 | − | 0.332115i | \(-0.107762\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.63737 | − | 29.6608i | 0.310883 | − | 0.956800i | −0.666533 | − | 0.745476i | \(-0.732222\pi\) |
0.977416 | − | 0.211324i | \(-0.0677776\pi\) | |||||||
\(32\) | −14.1812 | −0.443163 | ||||||||
\(33\) | −50.0882 | + | 26.7672i | −1.51782 | + | 0.811127i | ||||
\(34\) | 0.871580 | 0.0256347 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −55.8070 | + | 40.5461i | −1.55019 | + | 1.12628i | ||||
\(37\) | 11.6773 | − | 16.0724i | 0.315602 | − | 0.434389i | −0.621516 | − | 0.783402i | \(-0.713483\pi\) |
0.937118 | + | 0.349012i | \(0.113483\pi\) | |||||||
\(38\) | −6.19566 | + | 2.01309i | −0.163044 | + | 0.0529761i | ||||
\(39\) | 23.8172 | − | 7.73869i | 0.610699 | − | 0.198428i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 23.5474 | + | 32.4102i | 0.574326 | + | 0.790493i | 0.993059 | − | 0.117617i | \(-0.0375255\pi\) |
−0.418733 | + | 0.908110i | \(0.637526\pi\) | |||||||
\(42\) | 15.1334 | + | 4.91714i | 0.360319 | + | 0.117075i | ||||
\(43\) | 28.7133 | 0.667752 | 0.333876 | − | 0.942617i | \(-0.391643\pi\) | ||||
0.333876 | + | 0.942617i | \(0.391643\pi\) | |||||||
\(44\) | −29.7901 | + | 30.9782i | −0.677047 | + | 0.704050i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.51240 | − | 1.14125i | −0.0763566 | − | 0.0248098i | ||||
\(47\) | 2.31141 | + | 3.18139i | 0.0491790 | + | 0.0676891i | 0.832898 | − | 0.553426i | \(-0.186680\pi\) |
−0.783719 | + | 0.621115i | \(0.786680\pi\) | |||||||
\(48\) | −45.1971 | + | 62.2085i | −0.941607 | + | 1.29601i | ||||
\(49\) | 16.4479 | + | 50.6214i | 0.335671 | + | 1.03309i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.67687 | − | 11.9427i | 0.170135 | − | 0.234170i | ||||
\(52\) | 15.3321 | − | 11.1394i | 0.294848 | − | 0.214220i | ||||
\(53\) | 59.9100 | + | 19.4659i | 1.13038 | + | 0.367282i | 0.813719 | − | 0.581258i | \(-0.197439\pi\) |
0.316658 | + | 0.948540i | \(0.397439\pi\) | |||||||
\(54\) | − | 13.6219i | − | 0.252257i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 24.3699 | 0.435177 | ||||||||
\(57\) | −34.0958 | + | 104.936i | −0.598172 | + | 1.84098i | ||||
\(58\) | 8.55381 | + | 11.7733i | 0.147479 | + | 0.202988i | ||||
\(59\) | −41.4758 | − | 30.1339i | −0.702979 | − | 0.510744i | 0.177922 | − | 0.984045i | \(-0.443063\pi\) |
−0.880901 | + | 0.473300i | \(0.843063\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 31.6001 | − | 10.2675i | 0.518035 | − | 0.168320i | −0.0383184 | − | 0.999266i | \(-0.512200\pi\) |
0.556353 | + | 0.830946i | \(0.312200\pi\) | |||||||
\(62\) | 7.69112 | + | 5.58793i | 0.124050 | + | 0.0901279i | ||||
\(63\) | 144.417 | − | 104.925i | 2.29233 | − | 1.66548i | ||||
\(64\) | −17.0737 | + | 52.5473i | −0.266776 | + | 0.821052i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.04189 | − | 17.0424i | −0.0460892 | − | 0.258218i | ||||
\(67\) | − | 90.1298i | − | 1.34522i | −0.739997 | − | 0.672611i | \(-0.765173\pi\) | ||
0.739997 | − | 0.672611i | \(-0.234827\pi\) | |||||||
\(68\) | 3.45212 | − | 10.6245i | 0.0507665 | − | 0.156243i | ||||
\(69\) | −50.6049 | + | 36.7666i | −0.733405 | + | 0.532850i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.85591 | + | 5.71191i | 0.0261396 | + | 0.0804494i | 0.963275 | − | 0.268516i | \(-0.0865331\pi\) |
−0.937136 | + | 0.348965i | \(0.886533\pi\) | |||||||
\(72\) | −13.1502 | − | 40.4722i | −0.182642 | − | 0.562114i | ||||
\(73\) | −105.902 | − | 76.9424i | −1.45071 | − | 1.05401i | −0.985664 | − | 0.168722i | \(-0.946036\pi\) |
−0.465051 | − | 0.885284i | \(-0.653964\pi\) | |||||||
\(74\) | 3.55957 | + | 4.89933i | 0.0481023 | + | 0.0662072i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 83.4983i | 1.09866i | ||||||||
\(77\) | 77.0905 | − | 80.1652i | 1.00118 | − | 1.04111i | ||||
\(78\) | 7.63380i | 0.0978693i | ||||||||
\(79\) | −85.4604 | − | 27.7678i | −1.08178 | − | 0.351491i | −0.286714 | − | 0.958016i | \(-0.592563\pi\) |
−0.795064 | + | 0.606525i | \(0.792563\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −58.1000 | − | 42.2121i | −0.717284 | − | 0.521137i | ||||
\(82\) | −11.6141 | + | 3.77365i | −0.141636 | + | 0.0460202i | ||||
\(83\) | 27.3155 | + | 84.0686i | 0.329103 | + | 1.01287i | 0.969554 | + | 0.244876i | \(0.0787473\pi\) |
−0.640451 | + | 0.767999i | \(0.721253\pi\) | |||||||
\(84\) | 119.880 | − | 165.000i | 1.42714 | − | 1.96429i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.70472 | + | 8.32426i | −0.0314502 | + | 0.0967937i | ||||
\(87\) | 246.478 | 2.83308 | ||||||||
\(88\) | −12.4963 | − | 23.3837i | −0.142003 | − | 0.265724i | ||||
\(89\) | 118.531 | 1.33180 | 0.665902 | − | 0.746039i | \(-0.268047\pi\) | ||||
0.665902 | + | 0.746039i | \(0.268047\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −39.6764 | + | 28.8266i | −0.436004 | + | 0.316775i | ||||
\(92\) | −27.8236 | + | 38.2959i | −0.302430 | + | 0.416260i | ||||
\(93\) | 153.135 | − | 49.7567i | 1.64662 | − | 0.535018i | ||||
\(94\) | −1.14004 | + | 0.370422i | −0.0121281 | + | 0.00394066i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −43.0353 | − | 59.2330i | −0.448284 | − | 0.617010i | ||||
\(97\) | −63.5544 | − | 20.6501i | −0.655200 | − | 0.212887i | −0.0374942 | − | 0.999297i | \(-0.511938\pi\) |
−0.617705 | + | 0.786410i | \(0.711938\pi\) | |||||||
\(98\) | −16.2250 | −0.165561 | ||||||||
\(99\) | −174.733 | − | 84.7699i | −1.76498 | − | 0.856262i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.3073 | + | 3.99890i | 0.121855 | + | 0.0395931i | 0.369310 | − | 0.929306i | \(-0.379594\pi\) |
−0.247455 | + | 0.968899i | \(0.579594\pi\) | |||||||
\(102\) | 2.64496 | + | 3.64047i | 0.0259310 | + | 0.0356909i | ||||
\(103\) | −66.4251 | + | 91.4263i | −0.644904 | + | 0.887634i | −0.998865 | − | 0.0476260i | \(-0.984834\pi\) |
0.353961 | + | 0.935260i | \(0.384834\pi\) | |||||||
\(104\) | 3.61282 | + | 11.1191i | 0.0347387 | + | 0.106915i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.2867 | + | 15.5348i | −0.106478 | + | 0.146555i | ||||
\(107\) | 12.9688 | − | 9.42241i | 0.121204 | − | 0.0880599i | −0.525532 | − | 0.850774i | \(-0.676134\pi\) |
0.646736 | + | 0.762714i | \(0.276134\pi\) | |||||||
\(108\) | −166.051 | − | 53.9531i | −1.53751 | − | 0.499566i | ||||
\(109\) | − | 156.813i | − | 1.43865i | −0.694671 | − | 0.719327i | \(-0.744450\pi\) | ||
0.694671 | − | 0.719327i | \(-0.255550\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 102.569 | 0.924045 | ||||||||
\(112\) | 46.5333 | − | 143.215i | 0.415476 | − | 1.27870i | ||||
\(113\) | 18.8099 | + | 25.8896i | 0.166459 | + | 0.229112i | 0.884095 | − | 0.467307i | \(-0.154776\pi\) |
−0.717636 | + | 0.696419i | \(0.754776\pi\) | |||||||
\(114\) | −27.2102 | − | 19.7694i | −0.238686 | − | 0.173416i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 177.396 | − | 57.6394i | 1.52928 | − | 0.496892i | ||||
\(117\) | 69.2833 | + | 50.3372i | 0.592165 | + | 0.430233i | ||||
\(118\) | 12.6430 | − | 9.18568i | 0.107144 | − | 0.0778447i | ||||
\(119\) | −8.93338 | + | 27.4941i | −0.0750704 | + | 0.231043i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −116.451 | − | 32.8642i | −0.962409 | − | 0.271605i | ||||
\(122\) | 10.1283i | 0.0830192i | ||||||||
\(123\) | −63.9145 | + | 196.709i | −0.519630 | + | 1.59926i | ||||
\(124\) | 98.5794 | − | 71.6221i | 0.794995 | − | 0.577598i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 16.8151 | + | 51.7514i | 0.133453 | + | 0.410726i | ||||
\(127\) | 33.3284 | + | 102.574i | 0.262428 | + | 0.807671i | 0.992275 | + | 0.124060i | \(0.0395915\pi\) |
−0.729846 | + | 0.683611i | \(0.760408\pi\) | |||||||
\(128\) | −59.5170 | − | 43.2416i | −0.464977 | − | 0.337825i | ||||
\(129\) | 87.1355 | + | 119.932i | 0.675469 | + | 0.929703i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 48.6741i | 0.371558i | 0.982592 | + | 0.185779i | \(0.0594808\pi\) | ||||
−0.982592 | + | 0.185779i | \(0.940519\pi\) | |||||||
\(132\) | −219.795 | − | 30.4205i | −1.66511 | − | 0.230458i | ||||
\(133\) | − | 216.076i | − | 1.62463i | ||||||
\(134\) | 26.1295 | + | 8.48998i | 0.194996 | + | 0.0633580i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.57546 | + | 4.05081i | 0.0409961 | + | 0.0297854i | ||||
\(137\) | 71.4507 | − | 23.2157i | 0.521538 | − | 0.169458i | −0.0364052 | − | 0.999337i | \(-0.511591\pi\) |
0.557943 | + | 0.829879i | \(0.311591\pi\) | |||||||
\(138\) | −5.89214 | − | 18.1341i | −0.0426967 | − | 0.131407i | ||||
\(139\) | 28.3745 | − | 39.0542i | 0.204133 | − | 0.280965i | −0.694660 | − | 0.719338i | \(-0.744445\pi\) |
0.898793 | + | 0.438373i | \(0.144445\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.27385 | + | 19.3089i | −0.0444954 | + | 0.136943i | ||||
\(142\) | −1.83076 | −0.0128926 | ||||||||
\(143\) | 48.0052 | + | 23.2892i | 0.335700 | + | 0.162862i | ||||
\(144\) | −262.953 | −1.82606 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 32.2820 | − | 23.4542i | 0.221110 | − | 0.160646i | ||||
\(147\) | −161.525 | + | 222.320i | −1.09881 | + | 1.51238i | ||||
\(148\) | 73.8213 | − | 23.9860i | 0.498793 | − | 0.162068i | ||||
\(149\) | −114.600 | + | 37.2357i | −0.769126 | + | 0.249904i | −0.667191 | − | 0.744887i | \(-0.732503\pi\) |
−0.101935 | + | 0.994791i | \(0.532503\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −45.4102 | − | 62.5018i | −0.300730 | − | 0.413919i | 0.631733 | − | 0.775186i | \(-0.282344\pi\) |
−0.932462 | + | 0.361268i | \(0.882344\pi\) | |||||||
\(152\) | −48.9896 | − | 15.9177i | −0.322300 | − | 0.104722i | ||||
\(153\) | 50.4812 | 0.329943 | ||||||||
\(154\) | 15.9789 | + | 29.9006i | 0.103759 | + | 0.194160i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 93.0559 | + | 30.2357i | 0.596512 | + | 0.193819i | ||||
\(157\) | −31.8599 | − | 43.8515i | −0.202930 | − | 0.279309i | 0.695407 | − | 0.718616i | \(-0.255224\pi\) |
−0.898337 | + | 0.439307i | \(0.855224\pi\) | |||||||
\(158\) | 16.1003 | − | 22.1601i | 0.101900 | − | 0.140254i | ||||
\(159\) | 100.501 | + | 309.309i | 0.632079 | + | 1.94534i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 72.0017 | − | 99.1018i | 0.447215 | − | 0.615539i | ||||
\(162\) | 17.7105 | − | 12.8675i | 0.109324 | − | 0.0794287i | ||||
\(163\) | 193.205 | + | 62.7761i | 1.18531 | + | 0.385129i | 0.834336 | − | 0.551257i | \(-0.185852\pi\) |
0.350971 | + | 0.936386i | \(0.385852\pi\) | |||||||
\(164\) | 156.522i | 0.954404i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −26.9453 | −0.162321 | ||||||||
\(167\) | −41.0093 | + | 126.214i | −0.245565 | + | 0.755771i | 0.749978 | + | 0.661462i | \(0.230064\pi\) |
−0.995543 | + | 0.0943081i | \(0.969936\pi\) | |||||||
\(168\) | 73.9546 | + | 101.790i | 0.440206 | + | 0.605891i | ||||
\(169\) | 117.689 | + | 85.5063i | 0.696387 | + | 0.505954i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −358.848 | + | 116.597i | −2.09853 | + | 0.681852i | ||||
\(172\) | 90.7598 | + | 65.9408i | 0.527673 | + | 0.383377i | ||||
\(173\) | −90.4855 | + | 65.7416i | −0.523037 | + | 0.380009i | −0.817747 | − | 0.575578i | \(-0.804777\pi\) |
0.294709 | + | 0.955587i | \(0.404777\pi\) | |||||||
\(174\) | −23.2175 | + | 71.4562i | −0.133434 | + | 0.410668i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −161.281 | + | 28.7868i | −0.916367 | + | 0.163562i | ||||
\(177\) | − | 264.685i | − | 1.49540i | ||||||
\(178\) | −11.1652 | + | 34.3631i | −0.0627261 | + | 0.193051i | ||||
\(179\) | −38.7619 | + | 28.1621i | −0.216547 | + | 0.157330i | −0.690771 | − | 0.723074i | \(-0.742729\pi\) |
0.474224 | + | 0.880404i | \(0.342729\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.09873 | + | 6.45923i | 0.0115952 | + | 0.0356864i | 0.956687 | − | 0.291119i | \(-0.0940277\pi\) |
−0.945092 | + | 0.326806i | \(0.894028\pi\) | |||||||
\(182\) | −4.61968 | − | 14.2179i | −0.0253829 | − | 0.0781204i | ||||
\(183\) | 138.782 | + | 100.831i | 0.758371 | + | 0.550989i | ||||
\(184\) | −17.1646 | − | 23.6250i | −0.0932857 | − | 0.128397i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 49.0823i | 0.263883i | ||||||||
\(187\) | 30.9624 | − | 5.52645i | 0.165574 | − | 0.0295532i | ||||
\(188\) | 15.3642i | 0.0817246i | ||||||||
\(189\) | 429.705 | + | 139.619i | 2.27357 | + | 0.738728i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 60.7195 | + | 44.1153i | 0.317903 | + | 0.230970i | 0.735280 | − | 0.677763i | \(-0.237051\pi\) |
−0.417377 | + | 0.908733i | \(0.637051\pi\) | |||||||
\(192\) | −271.296 | + | 88.1494i | −1.41300 | + | 0.459112i | ||||
\(193\) | −117.250 | − | 360.857i | −0.607511 | − | 1.86973i | −0.478513 | − | 0.878081i | \(-0.658824\pi\) |
−0.128998 | − | 0.991645i | \(-0.541176\pi\) | |||||||
\(194\) | 11.9733 | − | 16.4798i | 0.0617180 | − | 0.0849475i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −64.2633 | + | 197.782i | −0.327874 | + | 1.00909i | ||||
\(197\) | −91.4898 | −0.464415 | −0.232208 | − | 0.972666i | \(-0.574595\pi\) | ||||
−0.232208 | + | 0.972666i | \(0.574595\pi\) | |||||||
\(198\) | 41.0349 | − | 42.6715i | 0.207247 | − | 0.215513i | ||||
\(199\) | −24.0213 | −0.120710 | −0.0603551 | − | 0.998177i | \(-0.519223\pi\) | ||||
−0.0603551 | + | 0.998177i | \(0.519223\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 376.460 | − | 273.514i | 1.87294 | − | 1.36077i | ||||
\(202\) | −2.31864 | + | 3.19133i | −0.0114784 | + | 0.0157987i | ||||
\(203\) | −459.064 | + | 149.159i | −2.26140 | + | 0.734773i | ||||
\(204\) | 54.8533 | − | 17.8229i | 0.268889 | − | 0.0873673i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −20.2483 | − | 27.8693i | −0.0982926 | − | 0.135288i | ||||
\(207\) | −203.436 | − | 66.1002i | −0.982781 | − | 0.319325i | ||||
\(208\) | 72.2423 | 0.347319 | ||||||||
\(209\) | −207.333 | + | 110.799i | −0.992023 | + | 0.530138i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −349.688 | − | 113.620i | −1.65729 | − | 0.538486i | −0.676987 | − | 0.735995i | \(-0.736715\pi\) |
−0.980301 | + | 0.197509i | \(0.936715\pi\) | |||||||
\(212\) | 144.665 | + | 199.115i | 0.682383 | + | 0.939219i | ||||
\(213\) | −18.2258 | + | 25.0856i | −0.0855671 | + | 0.117773i | ||||
\(214\) | 1.51002 | + | 4.64735i | 0.00705615 | + | 0.0217166i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 63.3100 | − | 87.1387i | 0.293102 | − | 0.403420i | ||||
\(217\) | −255.103 | + | 185.343i | −1.17559 | + | 0.854117i | ||||
\(218\) | 45.4616 | + | 14.7714i | 0.208540 | + | 0.0677586i | ||||
\(219\) | − | 675.834i | − | 3.08600i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.8690 | −0.0627555 | ||||||||
\(222\) | −9.66172 | + | 29.7357i | −0.0435212 | + | 0.133945i | ||||
\(223\) | −104.183 | − | 143.396i | −0.467190 | − | 0.643032i | 0.508790 | − | 0.860891i | \(-0.330093\pi\) |
−0.975980 | + | 0.217858i | \(0.930093\pi\) | |||||||
\(224\) | 115.999 | + | 84.2779i | 0.517851 | + | 0.376241i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.27747 | + | 3.01443i | −0.0410508 | + | 0.0133382i | ||||
\(227\) | 14.9656 | + | 10.8732i | 0.0659279 | + | 0.0478994i | 0.620261 | − | 0.784395i | \(-0.287027\pi\) |
−0.554333 | + | 0.832295i | \(0.687027\pi\) | |||||||
\(228\) | −348.761 | + | 253.390i | −1.52966 | + | 1.11136i | ||||
\(229\) | 41.3284 | − | 127.196i | 0.180473 | − | 0.555440i | −0.819368 | − | 0.573268i | \(-0.805675\pi\) |
0.999841 | + | 0.0178283i | \(0.00567522\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 568.784 | + | 78.7219i | 2.46227 | + | 0.340787i | ||||
\(232\) | 115.069i | 0.495985i | ||||||||
\(233\) | −13.6070 | + | 41.8780i | −0.0583991 | + | 0.179734i | −0.976001 | − | 0.217767i | \(-0.930123\pi\) |
0.917602 | + | 0.397501i | \(0.130123\pi\) | |||||||
\(234\) | −21.1195 | + | 15.3442i | −0.0902544 | + | 0.0655736i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −61.8973 | − | 190.500i | −0.262277 | − | 0.807204i | ||||
\(237\) | −143.362 | − | 441.223i | −0.604903 | − | 1.86170i | ||||
\(238\) | −7.12930 | − | 5.17974i | −0.0299550 | − | 0.0217636i | ||||
\(239\) | −97.2433 | − | 133.844i | −0.406876 | − | 0.560017i | 0.555577 | − | 0.831465i | \(-0.312497\pi\) |
−0.962453 | + | 0.271448i | \(0.912497\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 68.3979i | − | 0.283809i | −0.989880 | − | 0.141904i | \(-0.954677\pi\) | ||
0.989880 | − | 0.141904i | \(-0.0453225\pi\) | |||||||
\(242\) | 20.4970 | − | 30.6646i | 0.0846985 | − | 0.126713i | ||||
\(243\) | 31.4080i | 0.129251i | ||||||||
\(244\) | 123.464 | + | 40.1160i | 0.506001 | + | 0.164410i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −51.0071 | − | 37.0588i | −0.207346 | − | 0.150645i | ||||
\(247\) | 98.5880 | − | 32.0332i | 0.399142 | − | 0.129689i | ||||
\(248\) | 23.2290 | + | 71.4915i | 0.0936653 | + | 0.288272i | ||||
\(249\) | −268.250 | + | 369.214i | −1.07731 | + | 1.48279i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 104.767 | − | 322.440i | 0.417399 | − | 1.28462i | −0.492688 | − | 0.870206i | \(-0.663986\pi\) |
0.910087 | − | 0.414417i | \(-0.136014\pi\) | |||||||
\(252\) | 697.449 | 2.76766 | ||||||||
\(253\) | −132.012 | − | 18.2710i | −0.521788 | − | 0.0722175i | ||||
\(254\) | −32.8767 | −0.129436 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −160.655 | + | 116.723i | −0.627559 | + | 0.455949i | ||||
\(257\) | −148.075 | + | 203.807i | −0.576167 | + | 0.793025i | −0.993269 | − | 0.115835i | \(-0.963046\pi\) |
0.417102 | + | 0.908860i | \(0.363046\pi\) | |||||||
\(258\) | −42.9772 | + | 13.9641i | −0.166578 | + | 0.0541246i | ||||
\(259\) | −191.034 | + | 62.0708i | −0.737584 | + | 0.239656i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 495.430 | + | 681.901i | 1.89820 | + | 2.61265i | ||||
\(262\) | −14.1111 | − | 4.58496i | −0.0538590 | − | 0.0174999i | ||||
\(263\) | 424.803 | 1.61522 | 0.807610 | − | 0.589717i | \(-0.200761\pi\) | ||||
0.807610 | + | 0.589717i | \(0.200761\pi\) | |||||||
\(264\) | 59.7486 | − | 123.157i | 0.226320 | − | 0.466505i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 62.6425 | + | 20.3538i | 0.235498 | + | 0.0765180i | ||||
\(267\) | 359.701 | + | 495.086i | 1.34720 | + | 1.85426i | ||||
\(268\) | 206.985 | − | 284.891i | 0.772333 | − | 1.06303i | ||||
\(269\) | −154.300 | − | 474.888i | −0.573608 | − | 1.76538i | −0.640872 | − | 0.767648i | \(-0.721427\pi\) |
0.0672640 | − | 0.997735i | \(-0.478573\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −138.031 | + | 189.983i | −0.509339 | + | 0.701045i | −0.983808 | − | 0.179227i | \(-0.942640\pi\) |
0.474468 | + | 0.880273i | \(0.342640\pi\) | |||||||
\(272\) | 34.4515 | − | 25.0305i | 0.126660 | − | 0.0920239i | ||||
\(273\) | −240.809 | − | 78.2437i | −0.882086 | − | 0.286607i | ||||
\(274\) | 22.9011i | 0.0835806i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −244.392 | −0.885479 | ||||||||
\(277\) | −42.0248 | + | 129.339i | −0.151714 | + | 0.466928i | −0.997813 | − | 0.0660976i | \(-0.978945\pi\) |
0.846099 | + | 0.533026i | \(0.178945\pi\) | |||||||
\(278\) | 8.64937 | + | 11.9048i | 0.0311128 | + | 0.0428232i | ||||
\(279\) | 445.464 | + | 323.648i | 1.59664 | + | 1.16003i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −287.964 | + | 93.5652i | −1.02478 | + | 0.332972i | −0.772726 | − | 0.634740i | \(-0.781107\pi\) |
−0.252057 | + | 0.967712i | \(0.581107\pi\) | |||||||
\(282\) | −5.00685 | − | 3.63769i | −0.0177548 | − | 0.0128996i | ||||
\(283\) | −8.61523 | + | 6.25933i | −0.0304425 | + | 0.0221178i | −0.602902 | − | 0.797815i | \(-0.705989\pi\) |
0.572460 | + | 0.819933i | \(0.305989\pi\) | |||||||
\(284\) | −7.25119 | + | 22.3169i | −0.0255324 | + | 0.0785805i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −11.2737 | + | 11.7234i | −0.0394186 | + | 0.0409908i | ||||
\(287\) | − | 405.047i | − | 1.41131i | ||||||
\(288\) | 77.3703 | − | 238.121i | 0.268647 | − | 0.826810i | ||||
\(289\) | 227.192 | − | 165.065i | 0.786131 | − | 0.571158i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −106.614 | − | 328.124i | −0.366371 | − | 1.12757i | ||||
\(292\) | −158.045 | − | 486.414i | −0.541251 | − | 1.66580i | ||||
\(293\) | 267.010 | + | 193.994i | 0.911296 | + | 0.662095i | 0.941342 | − | 0.337453i | \(-0.109565\pi\) |
−0.0300463 | + | 0.999549i | \(0.509565\pi\) | |||||||
\(294\) | −49.2374 | − | 67.7695i | −0.167474 | − | 0.230509i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 47.8845i | 0.161772i | ||||||||
\(297\) | −86.3727 | − | 483.910i | −0.290817 | − | 1.62933i | ||||
\(298\) | − | 36.7310i | − | 0.123259i | ||||||
\(299\) | 55.8909 | + | 18.1600i | 0.186926 | + | 0.0607359i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −234.868 | − | 170.641i | −0.780291 | − | 0.566914i | ||||
\(302\) | 22.3973 | − | 7.27734i | 0.0741634 | − | 0.0240971i | ||||
\(303\) | 20.6459 | + | 63.5415i | 0.0681382 | + | 0.209708i | ||||
\(304\) | −187.087 | + | 257.503i | −0.615418 | + | 0.847050i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4.75519 | + | 14.6350i | −0.0155398 | + | 0.0478267i | ||||
\(307\) | 111.473 | 0.363104 | 0.181552 | − | 0.983381i | \(-0.441888\pi\) | ||||
0.181552 | + | 0.983381i | \(0.441888\pi\) | |||||||
\(308\) | 427.776 | − | 76.3534i | 1.38888 | − | 0.247901i | ||||
\(309\) | −583.454 | −1.88820 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −327.747 | + | 238.122i | −1.05385 | + | 0.765665i | −0.972940 | − | 0.231057i | \(-0.925782\pi\) |
−0.0809071 | + | 0.996722i | \(0.525782\pi\) | |||||||
\(312\) | −35.4794 | + | 48.8331i | −0.113716 | + | 0.156516i | ||||
\(313\) | 161.450 | − | 52.4582i | 0.515814 | − | 0.167598i | −0.0395307 | − | 0.999218i | \(-0.512586\pi\) |
0.555345 | + | 0.831620i | \(0.312586\pi\) | |||||||
\(314\) | 15.7141 | − | 5.10581i | 0.0500448 | − | 0.0162605i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −206.362 | − | 284.033i | −0.653044 | − | 0.898838i | ||||
\(317\) | −367.389 | − | 119.372i | −1.15895 | − | 0.376567i | −0.334445 | − | 0.942415i | \(-0.608549\pi\) |
−0.824510 | + | 0.565848i | \(0.808549\pi\) | |||||||
\(318\) | −99.1383 | −0.311756 | ||||||||
\(319\) | 378.520 | + | 364.003i | 1.18658 | + | 1.14107i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 78.7123 | + | 25.5752i | 0.245210 | + | 0.0796735i | ||||
\(322\) | 21.9482 | + | 30.2091i | 0.0681620 | + | 0.0938170i | ||||
\(323\) | 35.9167 | − | 49.4350i | 0.111197 | − | 0.153050i | ||||
\(324\) | −86.7068 | − | 266.856i | −0.267613 | − | 0.823630i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −36.3987 | + | 50.0986i | −0.111653 | + | 0.153677i | ||||
\(327\) | 654.988 | − | 475.877i | 2.00302 | − | 1.45528i | ||||
\(328\) | −91.8337 | − | 29.8386i | −0.279981 | − | 0.0909713i | ||||
\(329\) | − | 39.7595i | − | 0.120849i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 118.966 | 0.359413 | 0.179706 | − | 0.983720i | \(-0.442485\pi\) | ||||
0.179706 | + | 0.983720i | \(0.442485\pi\) | |||||||
\(332\) | −106.724 | + | 328.463i | −0.321458 | + | 0.989346i | ||||
\(333\) | 206.168 | + | 283.765i | 0.619122 | + | 0.852148i | ||||
\(334\) | −32.7275 | − | 23.7780i | −0.0979867 | − | 0.0711915i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 739.402 | − | 240.246i | 2.20060 | − | 0.715018i | ||||
\(337\) | 358.847 | + | 260.717i | 1.06483 | + | 0.773642i | 0.974975 | − | 0.222313i | \(-0.0713607\pi\) |
0.0898516 | + | 0.995955i | \(0.471361\pi\) | |||||||
\(338\) | −35.8751 | + | 26.0648i | −0.106139 | + | 0.0771147i | ||||
\(339\) | −51.0556 | + | 157.133i | −0.150606 | + | 0.463519i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 308.654 | + | 149.741i | 0.905144 | + | 0.439122i | ||||
\(342\) | − | 115.016i | − | 0.336305i | ||||||
\(343\) | 13.2053 | − | 40.6417i | 0.0384993 | − | 0.118489i | ||||
\(344\) | −55.9903 | + | 40.6793i | −0.162763 | + | 0.118254i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.5356 | − | 32.4252i | −0.0304497 | − | 0.0937146i | ||||
\(347\) | 163.076 | + | 501.898i | 0.469961 | + | 1.44639i | 0.852635 | + | 0.522507i | \(0.175003\pi\) |
−0.382674 | + | 0.923883i | \(0.624997\pi\) | |||||||
\(348\) | 779.091 | + | 566.042i | 2.23877 | + | 1.62656i | ||||
\(349\) | −318.255 | − | 438.040i | −0.911905 | − | 1.25513i | −0.966512 | − | 0.256622i | \(-0.917390\pi\) |
0.0546065 | − | 0.998508i | \(-0.482610\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 216.758i | 0.617543i | ||||||||
\(352\) | 21.3862 | − | 154.520i | 0.0607563 | − | 0.438978i | ||||
\(353\) | − | 216.813i | − | 0.614201i | −0.951677 | − | 0.307101i | \(-0.900641\pi\) | ||
0.951677 | − | 0.307101i | \(-0.0993588\pi\) | |||||||
\(354\) | 76.7347 | + | 24.9326i | 0.216765 | + | 0.0704311i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 374.662 | + | 272.208i | 1.05242 | + | 0.764630i | ||||
\(357\) | −141.949 | + | 46.1221i | −0.397616 | + | 0.129193i | ||||
\(358\) | −4.51321 | − | 13.8902i | −0.0126067 | − | 0.0387995i | ||||
\(359\) | 329.315 | − | 453.263i | 0.917311 | − | 1.26257i | −0.0472967 | − | 0.998881i | \(-0.515061\pi\) |
0.964608 | − | 0.263689i | \(-0.0849394\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −29.5795 | + | 91.0363i | −0.0819376 | + | 0.252178i | ||||
\(362\) | −2.07029 | −0.00571902 | ||||||||
\(363\) | −216.123 | − | 586.134i | −0.595379 | − | 1.61469i | ||||
\(364\) | −191.614 | −0.526411 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −42.3047 | + | 30.7362i | −0.115587 | + | 0.0839786i | ||||
\(367\) | 18.1911 | − | 25.0380i | 0.0495671 | − | 0.0682233i | −0.783514 | − | 0.621374i | \(-0.786575\pi\) |
0.833081 | + | 0.553151i | \(0.186575\pi\) | |||||||
\(368\) | −171.612 | + | 55.7602i | −0.466337 | + | 0.151522i | ||||
\(369\) | −672.680 | + | 218.567i | −1.82298 | + | 0.592323i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −374.364 | − | 515.267i | −1.00907 | − | 1.38886i | ||||
\(372\) | 598.312 | + | 194.403i | 1.60837 | + | 0.522590i | ||||
\(373\) | −483.806 | −1.29707 | −0.648534 | − | 0.761186i | \(-0.724617\pi\) | ||||
−0.648534 | + | 0.761186i | \(0.724617\pi\) | |||||||
\(374\) | −1.31440 | + | 9.49685i | −0.00351444 | + | 0.0253927i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.01440 | − | 2.92896i | −0.0239745 | − | 0.00778977i | ||||
\(377\) | −136.112 | − | 187.342i | −0.361040 | − | 0.496928i | ||||
\(378\) | −80.9540 | + | 111.424i | −0.214164 | + | 0.294771i | ||||
\(379\) | −25.3368 | − | 77.9786i | −0.0668517 | − | 0.205748i | 0.912050 | − | 0.410078i | \(-0.134499\pi\) |
−0.978902 | + | 0.204330i | \(0.934499\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −327.298 | + | 450.487i | −0.859050 | + | 1.18238i | ||||
\(382\) | −18.5090 | + | 13.4476i | −0.0484530 | + | 0.0352031i | ||||
\(383\) | −693.283 | − | 225.261i | −1.81014 | − | 0.588150i | −0.999998 | − | 0.00191562i | \(-0.999390\pi\) |
−0.810141 | − | 0.586234i | \(-0.800610\pi\) | |||||||
\(384\) | − | 379.819i | − | 0.989111i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 115.660 | 0.299638 | ||||||||
\(387\) | −156.655 | + | 482.135i | −0.404793 | + | 1.24583i | ||||
\(388\) | −153.465 | − | 211.227i | −0.395529 | − | 0.544399i | ||||
\(389\) | 193.321 | + | 140.456i | 0.496969 | + | 0.361069i | 0.807858 | − | 0.589377i | \(-0.200627\pi\) |
−0.310889 | + | 0.950446i | \(0.600627\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 32.9458 | − | 10.7047i | 0.0842604 | − | 0.0273779i | ||||
\(392\) | −103.790 | − | 75.4082i | −0.264772 | − | 0.192368i | ||||
\(393\) | −203.305 | + | 147.710i | −0.517316 | + | 0.375852i | ||||
\(394\) | 8.61808 | − | 26.5237i | 0.0218733 | − | 0.0673191i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −357.635 | − | 669.226i | −0.903120 | − | 1.68997i | ||||
\(397\) | − | 354.733i | − | 0.893535i | −0.894650 | − | 0.446768i | \(-0.852575\pi\) | ||
0.894650 | − | 0.446768i | \(-0.147425\pi\) | |||||||
\(398\) | 2.26274 | − | 6.96401i | 0.00568528 | − | 0.0174975i | ||||
\(399\) | 902.522 | − | 655.721i | 2.26196 | − | 1.64341i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 79.1417 | + | 243.573i | 0.197361 | + | 0.607414i | 0.999941 | + | 0.0108700i | \(0.00346008\pi\) |
−0.802580 | + | 0.596545i | \(0.796540\pi\) | |||||||
\(402\) | 43.8328 | + | 134.904i | 0.109037 | + | 0.335581i | ||||
\(403\) | −122.384 | − | 88.9175i | −0.303684 | − | 0.220639i | ||||
\(404\) | 29.7187 | + | 40.9042i | 0.0735610 | + | 0.101248i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 147.137i | − | 0.362407i | ||||||
\(407\) | 157.517 | + | 151.476i | 0.387020 | + | 0.372176i | ||||
\(408\) | 35.5808i | 0.0872079i | ||||||||
\(409\) | −261.500 | − | 84.9666i | −0.639365 | − | 0.207742i | −0.0286458 | − | 0.999590i | \(-0.509119\pi\) |
−0.610719 | + | 0.791847i | \(0.709119\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 313.798 | + | 227.988i | 0.763500 | + | 0.554715i | ||||
\(412\) | −419.925 | + | 136.442i | −1.01924 | + | 0.331170i | ||||
\(413\) | 160.177 | + | 492.975i | 0.387839 | + | 1.19364i | ||||
\(414\) | 38.3261 | − | 52.7514i | 0.0925752 | − | 0.127419i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −21.2563 | + | 65.4202i | −0.0510969 | + | 0.157260i | ||||
\(417\) | 249.232 | 0.597678 | ||||||||
\(418\) | −12.5914 | − | 70.5446i | −0.0301231 | − | 0.168767i | ||||
\(419\) | −44.0757 | −0.105193 | −0.0525963 | − | 0.998616i | \(-0.516750\pi\) | ||||
−0.0525963 | + | 0.998616i | \(0.516750\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 65.8608 | − | 47.8507i | 0.156439 | − | 0.113660i | −0.506812 | − | 0.862057i | \(-0.669176\pi\) |
0.663251 | + | 0.748397i | \(0.269176\pi\) | |||||||
\(422\) | 65.8792 | − | 90.6750i | 0.156112 | − | 0.214870i | ||||
\(423\) | −66.0303 | + | 21.4546i | −0.156100 | + | 0.0507200i | ||||
\(424\) | −144.401 | + | 46.9188i | −0.340569 | + | 0.110658i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.55574 | − | 7.64682i | −0.0130416 | − | 0.0179503i | ||||
\(427\) | −319.500 | − | 103.812i | −0.748243 | − | 0.243119i | ||||
\(428\) | 62.6319 | 0.146336 | ||||||||
\(429\) | 48.4038 | + | 271.186i | 0.112829 | + | 0.632136i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 690.547 | + | 224.372i | 1.60220 | + | 0.520585i | 0.967649 | − | 0.252299i | \(-0.0811866\pi\) |
0.634547 | + | 0.772884i | \(0.281187\pi\) | |||||||
\(432\) | −391.201 | − | 538.442i | −0.905558 | − | 1.24639i | ||||
\(433\) | −204.033 | + | 280.828i | −0.471208 | + | 0.648563i | −0.976786 | − | 0.214218i | \(-0.931280\pi\) |
0.505577 | + | 0.862781i | \(0.331280\pi\) | |||||||
\(434\) | −29.7027 | − | 91.4156i | −0.0684394 | − | 0.210635i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 360.126 | − | 495.670i | 0.825976 | − | 1.13686i | ||||
\(437\) | −209.472 | + | 152.190i | −0.479340 | + | 0.348261i | ||||
\(438\) | 195.930 | + | 63.6617i | 0.447330 | + | 0.145346i | ||||
\(439\) | 72.1914i | 0.164445i | 0.996614 | + | 0.0822226i | \(0.0262018\pi\) | ||||
−0.996614 | + | 0.0822226i | \(0.973798\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −939.738 | −2.13092 | ||||||||
\(442\) | 1.30642 | − | 4.02074i | 0.00295569 | − | 0.00909669i | ||||
\(443\) | −220.886 | − | 304.024i | −0.498614 | − | 0.686284i | 0.483333 | − | 0.875436i | \(-0.339426\pi\) |
−0.981948 | + | 0.189153i | \(0.939426\pi\) | |||||||
\(444\) | 324.210 | + | 235.552i | 0.730202 | + | 0.530523i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 51.3857 | − | 16.6962i | 0.115214 | − | 0.0374355i | ||||
\(447\) | −503.301 | − | 365.670i | −1.12595 | − | 0.818053i | ||||
\(448\) | 451.943 | − | 328.356i | 1.00880 | − | 0.732937i | ||||
\(449\) | −34.6764 | + | 106.723i | −0.0772302 | + | 0.237690i | −0.982217 | − | 0.187750i | \(-0.939881\pi\) |
0.904987 | + | 0.425440i | \(0.139881\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −388.657 | + | 207.699i | −0.861767 | + | 0.460529i | ||||
\(452\) | 125.032i | 0.276619i | ||||||||
\(453\) | 123.256 | − | 379.344i | 0.272089 | − | 0.837405i | ||||
\(454\) | −4.56195 | + | 3.31445i | −0.0100483 | + | 0.00730055i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −82.1812 | − | 252.928i | −0.180222 | − | 0.554666i | ||||
\(457\) | −57.6949 | − | 177.567i | −0.126247 | − | 0.388549i | 0.867879 | − | 0.496775i | \(-0.165483\pi\) |
−0.994126 | + | 0.108227i | \(0.965483\pi\) | |||||||
\(458\) | 32.9822 | + | 23.9630i | 0.0720136 | + | 0.0523209i | ||||
\(459\) | 75.1021 | + | 103.369i | 0.163621 | + | 0.225205i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 559.922i | − | 1.21458i | −0.794479 | − | 0.607291i | \(-0.792256\pi\) | ||
0.794479 | − | 0.607291i | \(-0.207744\pi\) | |||||||
\(462\) | −76.4000 | + | 157.480i | −0.165368 | + | 0.340866i | ||||
\(463\) | 648.611i | 1.40089i | 0.713708 | + | 0.700444i | \(0.247014\pi\) | ||||
−0.713708 | + | 0.700444i | \(0.752986\pi\) | |||||||
\(464\) | 676.224 | + | 219.719i | 1.45738 | + | 0.473532i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.8591 | − | 7.88958i | −0.0233028 | − | 0.0169304i | ||||
\(467\) | 856.339 | − | 278.242i | 1.83370 | − | 0.595806i | 0.834722 | − | 0.550671i | \(-0.185628\pi\) |
0.998981 | − | 0.0451348i | \(-0.0143717\pi\) | |||||||
\(468\) | 103.396 | + | 318.221i | 0.220932 | + | 0.679960i | ||||
\(469\) | −535.635 | + | 737.238i | −1.14208 | + | 1.57194i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 86.4772 | − | 266.149i | 0.183603 | − | 0.565073i | ||||
\(472\) | 123.569 | 0.261798 | ||||||||
\(473\) | −43.3016 | + | 312.864i | −0.0915468 | + | 0.661447i | ||||
\(474\) | 141.419 | 0.298352 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −91.3783 | + | 66.3902i | −0.191971 | + | 0.139475i | ||||
\(477\) | −653.718 | + | 899.765i | −1.37048 | + | 1.88630i | ||||
\(478\) | 47.9626 | − | 15.5840i | 0.100340 | − | 0.0326025i | ||||
\(479\) | 441.790 | − | 143.546i | 0.922317 | − | 0.299679i | 0.190900 | − | 0.981609i | \(-0.438859\pi\) |
0.731417 | + | 0.681930i | \(0.238859\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −56.6415 | − | 77.9603i | −0.117758 | − | 0.162080i | ||||
\(482\) | 19.8292 | + | 6.44289i | 0.0411394 | + | 0.0133670i | ||||
\(483\) | 632.437 | 1.30939 | ||||||||
\(484\) | −292.617 | − | 371.314i | −0.604581 | − | 0.767177i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −9.10546 | − | 2.95854i | −0.0187355 | − | 0.00608753i | ||||
\(487\) | −19.3672 | − | 26.6567i | −0.0397685 | − | 0.0547366i | 0.788670 | − | 0.614817i | \(-0.210770\pi\) |
−0.828438 | + | 0.560081i | \(0.810770\pi\) | |||||||
\(488\) | −47.0731 | + | 64.7906i | −0.0964613 | + | 0.132768i | ||||
\(489\) | 324.106 | + | 997.496i | 0.662794 | + | 2.03987i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −469.003 | + | 645.528i | −0.955200 | + | 1.31472i | −0.00602158 | + | 0.999982i | \(0.501917\pi\) |
−0.949179 | + | 0.314738i | \(0.898083\pi\) | |||||||
\(492\) | −653.773 | + | 474.994i | −1.32881 | + | 0.965434i | ||||
\(493\) | −129.820 | − | 42.1812i | −0.263327 | − | 0.0855603i | ||||
\(494\) | 31.5990i | 0.0639656i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 464.489 | 0.936470 | ||||||||
\(497\) | 18.7646 | − | 57.7514i | 0.0377557 | − | 0.116200i | ||||
\(498\) | −81.7701 | − | 112.547i | −0.164197 | − | 0.225998i | ||||
\(499\) | 479.816 | + | 348.607i | 0.961555 | + | 0.698611i | 0.953511 | − | 0.301357i | \(-0.0974396\pi\) |
0.00804363 | + | 0.999968i | \(0.497440\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −651.627 | + | 211.727i | −1.30065 | + | 0.422608i | ||||
\(502\) | 83.6096 | + | 60.7459i | 0.166553 | + | 0.121008i | ||||
\(503\) | 634.532 | − | 461.015i | 1.26150 | − | 0.916530i | 0.262665 | − | 0.964887i | \(-0.415398\pi\) |
0.998830 | + | 0.0483569i | \(0.0153985\pi\) | |||||||
\(504\) | −132.958 | + | 409.203i | −0.263806 | + | 0.811910i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 17.7321 | − | 36.5505i | 0.0350437 | − | 0.0722342i | ||||
\(507\) | 751.056i | 1.48137i | ||||||||
\(508\) | −130.217 | + | 400.766i | −0.256332 | + | 0.788909i | ||||
\(509\) | −639.768 | + | 464.819i | −1.25691 | + | 0.913200i | −0.998602 | − | 0.0528625i | \(-0.983165\pi\) |
−0.258310 | + | 0.966062i | \(0.583165\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 408.989 | + | 1258.74i | 0.800369 | + | 2.46328i | ||||
\(512\) | −109.640 | − | 337.436i | −0.214140 | − | 0.659055i | ||||
\(513\) | −772.619 | − | 561.340i | −1.50608 | − | 1.09423i | ||||
\(514\) | −45.1374 | − | 62.1263i | −0.0878160 | − | 0.120868i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 579.200i | 1.12248i | ||||||||
\(517\) | −38.1506 | + | 20.3877i | −0.0737922 | + | 0.0394346i | ||||
\(518\) | − | 61.2295i | − | 0.118204i | ||||||
\(519\) | −549.187 | − | 178.442i | −1.05816 | − | 0.343818i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −514.280 | − | 373.646i | −0.987101 | − | 0.717171i | −0.0278170 | − | 0.999613i | \(-0.508856\pi\) |
−0.959284 | + | 0.282442i | \(0.908856\pi\) | |||||||
\(522\) | −244.357 | + | 79.3966i | −0.468118 | + | 0.152101i | ||||
\(523\) | −58.7556 | − | 180.831i | −0.112343 | − | 0.345757i | 0.879040 | − | 0.476747i | \(-0.158184\pi\) |
−0.991384 | + | 0.130990i | \(0.958184\pi\) | |||||||
\(524\) | −111.781 | + | 153.854i | −0.213323 | + | 0.293614i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −40.0152 | + | 123.154i | −0.0760746 | + | 0.234134i | ||||
\(527\) | −89.1719 | −0.169207 | ||||||||
\(528\) | −609.672 | − | 586.289i | −1.15468 | − | 1.11040i | ||||
\(529\) | 382.214 | 0.722522 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 732.273 | − | 532.027i | 1.37905 | − | 1.00193i | ||||
\(532\) | 496.225 | − | 682.995i | 0.932753 | − | 1.28382i | ||||
\(533\) | 184.809 | − | 60.0480i | 0.346733 | − | 0.112660i | ||||
\(534\) | −177.413 | + | 57.6449i | −0.332234 | + | 0.107949i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 127.691 | + | 175.751i | 0.238229 | + | 0.327894i | ||||
\(537\) | −235.259 | − | 76.4403i | −0.438099 | − | 0.142347i | ||||
\(538\) | 152.209 | 0.282917 | ||||||||
\(539\) | −576.382 | + | 102.878i | −1.06936 | + | 0.190868i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.6026 | + | 12.2178i | 0.0695058 | + | 0.0225838i | 0.343563 | − | 0.939129i | \(-0.388366\pi\) |
−0.274058 | + | 0.961713i | \(0.588366\pi\) | |||||||
\(542\) | −42.0758 | − | 57.9123i | −0.0776306 | − | 0.106849i | ||||
\(543\) | −20.6104 | + | 28.3678i | −0.0379565 | + | 0.0522427i | ||||
\(544\) | 12.5299 | + | 38.5630i | 0.0230329 | + | 0.0708879i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 45.3671 | − | 62.4425i | 0.0830900 | − | 0.114364i | ||||
\(547\) | −478.368 | + | 347.554i | −0.874529 | + | 0.635383i | −0.931799 | − | 0.362976i | \(-0.881761\pi\) |
0.0572690 | + | 0.998359i | \(0.481761\pi\) | |||||||
\(548\) | 279.164 | + | 90.7057i | 0.509423 | + | 0.165521i | ||||
\(549\) | 586.626i | 1.06853i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1020.26 | 1.85165 | ||||||||
\(552\) | 46.5896 | − | 143.388i | 0.0844015 | − | 0.259761i | ||||
\(553\) | 534.022 | + | 735.018i | 0.965682 | + | 1.32915i | ||||
\(554\) | −33.5380 | − | 24.3668i | −0.0605379 | − | 0.0439833i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 179.378 | − | 58.2834i | 0.322622 | − | 0.104826i | ||||
\(557\) | 176.596 | + | 128.305i | 0.317049 | + | 0.230350i | 0.734915 | − | 0.678159i | \(-0.237222\pi\) |
−0.417866 | + | 0.908509i | \(0.637222\pi\) | |||||||
\(558\) | −135.790 | + | 98.6573i | −0.243351 | + | 0.176805i | ||||
\(559\) | 43.0386 | − | 132.459i | 0.0769921 | − | 0.236957i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 117.044 | + | 112.555i | 0.208634 | + | 0.200632i | ||||
\(562\) | − | 92.2970i | − | 0.164229i | ||||||
\(563\) | −115.865 | + | 356.595i | −0.205799 | + | 0.633383i | 0.793881 | + | 0.608073i | \(0.208057\pi\) |
−0.999680 | + | 0.0253101i | \(0.991943\pi\) | |||||||
\(564\) | −64.1743 | + | 46.6254i | −0.113784 | + | 0.0826691i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.00311 | − | 3.08725i | −0.00177227 | − | 0.00545450i | ||||
\(567\) | 224.379 | + | 690.568i | 0.395730 | + | 1.21793i | ||||
\(568\) | −11.7113 | − | 8.50874i | −0.0206184 | − | 0.0149802i | ||||
\(569\) | 131.674 | + | 181.234i | 0.231413 | + | 0.318513i | 0.908894 | − | 0.417028i | \(-0.136928\pi\) |
−0.677480 | + | 0.735541i | \(0.736928\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 176.017i | − | 0.308262i | −0.988050 | − | 0.154131i | \(-0.950742\pi\) | ||
0.988050 | − | 0.154131i | \(-0.0492577\pi\) | |||||||
\(572\) | 98.2549 | + | 183.860i | 0.171774 | + | 0.321433i | ||||
\(573\) | 387.492i | 0.676252i | ||||||||
\(574\) | 117.427 | + | 38.1543i | 0.204577 | + | 0.0664710i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −789.188 | − | 573.378i | −1.37012 | − | 0.995449i | ||||
\(577\) | −635.162 | + | 206.377i | −1.10080 | + | 0.357672i | −0.802411 | − | 0.596772i | \(-0.796450\pi\) |
−0.298391 | + | 0.954444i | \(0.596450\pi\) | |||||||
\(578\) | 26.4529 | + | 81.4137i | 0.0457663 | + | 0.140854i | ||||
\(579\) | 1151.44 | − | 1584.82i | 1.98867 | − | 2.73716i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 276.180 | − | 849.994i | 0.475352 | − | 1.46298i | ||||
\(582\) | 105.169 | 0.180703 | ||||||||
\(583\) | −302.452 | + | 623.432i | −0.518785 | + | 1.06935i | ||||
\(584\) | 315.514 | 0.540264 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −81.3922 | + | 59.1349i | −0.138895 | + | 0.100913i | ||||
\(587\) | −57.4195 | + | 79.0311i | −0.0978185 | + | 0.134636i | −0.855121 | − | 0.518429i | \(-0.826517\pi\) |
0.757302 | + | 0.653065i | \(0.226517\pi\) | |||||||
\(588\) | −1021.13 | + | 331.784i | −1.73661 | + | 0.564259i | ||||
\(589\) | 633.882 | − | 205.961i | 1.07620 | − | 0.349679i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −277.641 | − | 382.141i | −0.469782 | − | 0.646600i | ||||
\(592\) | 281.403 | + | 91.4335i | 0.475343 | + | 0.154448i | ||||
\(593\) | −479.081 | −0.807893 | −0.403947 | − | 0.914783i | \(-0.632362\pi\) | ||||
−0.403947 | + | 0.914783i | \(0.632362\pi\) | |||||||
\(594\) | 148.426 | + | 20.5427i | 0.249875 | + | 0.0345837i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −447.751 | − | 145.483i | −0.751259 | − | 0.244099i | ||||
\(597\) | −72.8968 | − | 100.334i | −0.122105 | − | 0.168063i | ||||
\(598\) | −10.5295 | + | 14.4927i | −0.0176079 | + | 0.0242352i | ||||
\(599\) | −146.829 | − | 451.894i | −0.245124 | − | 0.754414i | −0.995616 | − | 0.0935345i | \(-0.970183\pi\) |
0.750492 | − | 0.660879i | \(-0.229817\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 316.409 | − | 435.499i | 0.526470 | − | 0.724624i | −0.460117 | − | 0.887858i | \(-0.652193\pi\) |
0.986587 | + | 0.163234i | \(0.0521926\pi\) | |||||||
\(602\) | 71.5943 | − | 52.0163i | 0.118927 | − | 0.0864059i | ||||
\(603\) | 1513.40 | + | 491.733i | 2.50978 | + | 0.815477i | ||||
\(604\) | − | 301.847i | − | 0.499747i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −20.3660 | −0.0336073 | ||||||||
\(607\) | 127.052 | − | 391.027i | 0.209312 | − | 0.644196i | −0.790197 | − | 0.612853i | \(-0.790022\pi\) |
0.999509 | − | 0.0313426i | \(-0.00997830\pi\) | |||||||
\(608\) | −178.138 | − | 245.186i | −0.292991 | − | 0.403267i | ||||
\(609\) | −2016.13 | − | 1464.80i | −3.31055 | − | 2.40526i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.1408 | − | 5.89431i | 0.0296904 | − | 0.00964700i | ||||
\(612\) | 159.566 | + | 115.931i | 0.260728 | + | 0.189430i | ||||
\(613\) | 201.079 | − | 146.092i | 0.328025 | − | 0.238324i | −0.411567 | − | 0.911379i | \(-0.635019\pi\) |
0.739592 | + | 0.673056i | \(0.235019\pi\) | |||||||
\(614\) | −10.5004 | + | 32.3170i | −0.0171017 | + | 0.0526336i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −36.7514 | + | 265.538i | −0.0596614 | + | 0.431067i | ||||
\(617\) | − | 1141.96i | − | 1.85082i | −0.378964 | − | 0.925411i | \(-0.623720\pi\) | ||
0.378964 | − | 0.925411i | \(-0.376280\pi\) | |||||||
\(618\) | 54.9597 | − | 169.149i | 0.0889316 | − | 0.273703i | ||||
\(619\) | 4.57281 | − | 3.32234i | 0.00738742 | − | 0.00536727i | −0.584085 | − | 0.811692i | \(-0.698547\pi\) |
0.591473 | + | 0.806325i | \(0.298547\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −167.304 | − | 514.909i | −0.269411 | − | 0.829161i | ||||
\(622\) | −38.1609 | − | 117.447i | −0.0613519 | − | 0.188822i | ||||
\(623\) | −969.549 | − | 704.418i | −1.55626 | − | 1.13069i | ||||
\(624\) | 219.232 | + | 301.746i | 0.351333 | + | 0.483568i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 51.7472i | 0.0826633i | ||||||||
\(627\) | −1091.98 | − | 529.763i | −1.74159 | − | 0.844917i | ||||
\(628\) | − | 211.777i | − | 0.337224i | ||||||
\(629\) | −54.0233 | − | 17.5532i | −0.0858876 | − | 0.0279066i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 601.402 | + | 436.944i | 0.953094 | + | 0.692463i | 0.951537 | − | 0.307536i | \(-0.0995043\pi\) |
0.00155713 | + | 0.999999i | \(0.499504\pi\) | |||||||
\(632\) | 205.986 | − | 66.9288i | 0.325927 | − | 0.105900i | ||||
\(633\) | −586.610 | − | 1805.40i | −0.926714 | − | 2.85213i | ||||
\(634\) | 69.2140 | − | 95.2649i | 0.109170 | − | 0.150260i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −392.664 | + | 1208.49i | −0.617396 | + | 1.90015i | ||||
\(637\) | 258.179 | 0.405304 | ||||||||
\(638\) | −141.183 | + | 75.4485i | −0.221290 | + | 0.118258i | ||||
\(639\) | −106.036 | −0.165940 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −292.789 | + | 212.724i | −0.456769 | + | 0.331862i | −0.792263 | − | 0.610180i | \(-0.791097\pi\) |
0.335493 | + | 0.942043i | \(0.391097\pi\) | |||||||
\(642\) | −14.8290 | + | 20.4103i | −0.0230981 | + | 0.0317918i | ||||
\(643\) | 615.565 | − | 200.009i | 0.957333 | − | 0.311056i | 0.211641 | − | 0.977347i | \(-0.432119\pi\) |
0.745692 | + | 0.666291i | \(0.232119\pi\) | |||||||
\(644\) | 455.179 | − | 147.897i | 0.706800 | − | 0.229653i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10.9484 | + | 15.0692i | 0.0169480 | + | 0.0233269i | ||||
\(647\) | 694.892 | + | 225.784i | 1.07402 | + | 0.348971i | 0.792053 | − | 0.610453i | \(-0.209012\pi\) |
0.281969 | + | 0.959423i | \(0.409012\pi\) | |||||||
\(648\) | 173.097 | 0.267125 | ||||||||
\(649\) | 390.891 | − | 406.482i | 0.602298 | − | 0.626320i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1548.31 | − | 503.076i | −2.37835 | − | 0.772774i | ||||
\(652\) | 466.534 | + | 642.128i | 0.715542 | + | 0.984859i | ||||
\(653\) | −176.964 | + | 243.570i | −0.271001 | + | 0.373001i | −0.922727 | − | 0.385453i | \(-0.874045\pi\) |
0.651726 | + | 0.758454i | \(0.274045\pi\) | |||||||
\(654\) | 76.2630 | + | 234.713i | 0.116610 | + | 0.358889i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −350.705 | + | 482.704i | −0.534611 | + | 0.735829i | ||||
\(657\) | 1869.75 | − | 1358.45i | 2.84589 | − | 2.06766i | ||||
\(658\) | 11.5266 | + | 3.74523i | 0.0175177 | + | 0.00569184i | ||||
\(659\) | 596.433i | 0.905057i | 0.891750 | + | 0.452529i | \(0.149478\pi\) | ||||
−0.891750 | + | 0.452529i | \(0.850522\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 882.175 | 1.33461 | 0.667303 | − | 0.744786i | \(-0.267449\pi\) | ||||
0.667303 | + | 0.744786i | \(0.267449\pi\) | |||||||
\(662\) | −11.2062 | + | 34.4892i | −0.0169278 | + | 0.0520985i | ||||
\(663\) | −42.0877 | − | 57.9288i | −0.0634807 | − | 0.0873737i | ||||
\(664\) | −172.368 | − | 125.233i | −0.259591 | − | 0.188604i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −101.687 | + | 33.0400i | −0.152683 | + | 0.0496096i | ||||
\(667\) | 467.934 | + | 339.974i | 0.701551 | + | 0.509707i | ||||
\(668\) | −419.479 | + | 304.769i | −0.627962 | + | 0.456241i | ||||
\(669\) | 282.784 | − | 870.320i | 0.422697 | − | 1.30093i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 64.2210 | + | 359.803i | 0.0957094 | + | 0.536220i | ||||
\(672\) | 740.266i | 1.10159i | ||||||||
\(673\) | 124.617 | − | 383.533i | 0.185167 | − | 0.569886i | −0.814784 | − | 0.579764i | \(-0.803145\pi\) |
0.999951 | + | 0.00987877i | \(0.00314456\pi\) | |||||||
\(674\) | −109.387 | + | 79.4741i | −0.162295 | + | 0.117914i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 175.636 | + | 540.553i | 0.259817 | + | 0.799634i | ||||
\(677\) | −193.523 | − | 595.604i | −0.285854 | − | 0.879769i | −0.986141 | − | 0.165908i | \(-0.946945\pi\) |
0.700287 | − | 0.713861i | \(-0.253055\pi\) | |||||||
\(678\) | −40.7450 | − | 29.6029i | −0.0600958 | − | 0.0436622i | ||||
\(679\) | 397.136 | + | 546.611i | 0.584884 | + | 0.805024i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 95.5059i | 0.140244i | ||||||||
\(682\) | −72.4855 | + | 75.3765i | −0.106284 | + | 0.110523i | ||||
\(683\) | − | 935.585i | − | 1.36982i | −0.728629 | − | 0.684909i | \(-0.759842\pi\) | ||
0.728629 | − | 0.684909i | \(-0.240158\pi\) | |||||||
\(684\) | −1402.05 | − | 455.553i | −2.04978 | − | 0.666013i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 10.5385 | + | 7.65666i | 0.0153622 | + | 0.0111613i | ||||
\(687\) | 656.698 | − | 213.374i | 0.955892 | − | 0.310588i | ||||
\(688\) | 132.149 | + | 406.714i | 0.192078 | + | 0.591154i | ||||
\(689\) | 179.599 | − | 247.197i | 0.260666 | − | 0.358776i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 255.366 | − | 785.937i | 0.369561 | − | 1.13739i | −0.577515 | − | 0.816380i | \(-0.695977\pi\) |
0.947076 | − | 0.321011i | \(-0.104023\pi\) | |||||||
\(692\) | −436.992 | −0.631491 | ||||||||
\(693\) | 925.486 | + | 1731.82i | 1.33548 | + | 2.49902i | ||||
\(694\) | −160.866 | −0.231795 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −480.626 | + | 349.195i | −0.690555 | + | 0.501718i | ||||
\(697\) | 67.3278 | − | 92.6687i | 0.0965965 | − | 0.132954i | ||||
\(698\) | 156.971 | − | 51.0029i | 0.224886 | − | 0.0730700i | ||||
\(699\) | −216.212 | + | 70.2514i | −0.309316 | + | 0.100503i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −139.111 | − | 191.469i | −0.198446 | − | 0.273138i | 0.698184 | − | 0.715919i | \(-0.253992\pi\) |
−0.896630 | + | 0.442781i | \(0.853992\pi\) | |||||||
\(702\) | −62.8400 | − | 20.4180i | −0.0895157 | − | 0.0290854i | ||||
\(703\) | 424.570 | 0.603940 | ||||||||
\(704\) | −546.814 | − | 265.282i | −0.776725 | − | 0.376821i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 62.8561 | + | 20.4232i | 0.0890313 | + | 0.0289280i | ||||
\(707\) | −76.9057 | − | 105.852i | −0.108778 | − | 0.149719i | ||||
\(708\) | 607.856 | − | 836.642i | 0.858554 | − | 1.18170i | ||||
\(709\) | 278.848 | + | 858.205i | 0.393297 | + | 1.21044i | 0.930280 | + | 0.366851i | \(0.119564\pi\) |
−0.536982 | + | 0.843593i | \(0.680436\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 932.515 | − | 1283.50i | 1.31155 | − | 1.80520i | ||||
\(712\) | −231.132 | + | 167.927i | −0.324623 | + | 0.235853i | ||||
\(713\) | 359.356 | + | 116.762i | 0.504006 | + | 0.163761i | ||||
\(714\) | − | 45.4969i | − | 0.0637212i | ||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −187.197 | −0.261449 | ||||||||
\(717\) | 263.947 | − | 812.345i | 0.368127 | − | 1.13298i | ||||
\(718\) | 100.385 | + | 138.167i | 0.139811 | + | 0.192434i | ||||
\(719\) | −318.157 | − | 231.154i | −0.442499 | − | 0.321494i | 0.344128 | − | 0.938923i | \(-0.388174\pi\) |
−0.786627 | + | 0.617428i | \(0.788174\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1086.68 | − | 353.084i | 1.50718 | − | 0.489714i | ||||
\(722\) | −23.6060 | − | 17.1507i | −0.0326952 | − | 0.0237545i | ||||
\(723\) | 285.689 | − | 207.565i | 0.395144 | − | 0.287089i | ||||
\(724\) | −8.19991 | + | 25.2367i | −0.0113258 | + | 0.0348574i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 190.284 | − | 7.44370i | 0.262099 | − | 0.0102530i | ||||
\(727\) | 1284.55i | 1.76691i | 0.468514 | + | 0.883456i | \(0.344790\pi\) | ||||
−0.468514 | + | 0.883456i | \(0.655210\pi\) | |||||||
\(728\) | 36.5282 | − | 112.422i | 0.0501761 | − | 0.154426i | ||||
\(729\) | −654.087 | + | 475.222i | −0.897238 | + | 0.651882i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.3698 | − | 78.0803i | −0.0347056 | − | 0.106813i | ||||
\(732\) | 207.114 | + | 637.432i | 0.282943 | + | 0.870809i | ||||
\(733\) | 339.175 | + | 246.425i | 0.462722 | + | 0.336187i | 0.794598 | − | 0.607136i | \(-0.207682\pi\) |
−0.331876 | + | 0.943323i | \(0.607682\pi\) | |||||||
\(734\) | 5.54518 | + | 7.63228i | 0.00755474 | + | 0.0103982i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 171.813i | − | 0.233441i | ||||||
\(737\) | 982.066 | + | 135.922i | 1.33252 | + | 0.184426i | ||||
\(738\) | − | 215.605i | − | 0.292147i | ||||||
\(739\) | 269.243 | + | 87.4823i | 0.364334 | + | 0.118379i | 0.485462 | − | 0.874258i | \(-0.338651\pi\) |
−0.121128 | + | 0.992637i | \(0.538651\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 432.981 | + | 314.579i | 0.584319 | + | 0.424533i | ||||
\(742\) | 184.645 | − | 59.9947i | 0.248847 | − | 0.0808554i | ||||
\(743\) | 3.47057 | + | 10.6813i | 0.00467102 | + | 0.0143759i | 0.953365 | − | 0.301820i | \(-0.0975942\pi\) |
−0.948694 | + | 0.316196i | \(0.897594\pi\) | |||||||
\(744\) | −228.118 | + | 313.978i | −0.306610 | + | 0.422013i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 45.5732 | − | 140.260i | 0.0610901 | − | 0.188016i | ||||
\(747\) | −1560.65 | −2.08923 | ||||||||
\(748\) | 110.560 | + | 53.6373i | 0.147808 | + | 0.0717076i | ||||
\(749\) | −162.078 | −0.216393 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −700.813 | + | 509.171i | −0.933174 | + | 0.677990i | −0.946768 | − | 0.321917i | \(-0.895673\pi\) |
0.0135942 | + | 0.999908i | \(0.495673\pi\) | |||||||
\(752\) | −34.4252 | + | 47.3822i | −0.0457782 | + | 0.0630083i | ||||
\(753\) | 1664.72 | − | 540.902i | 2.21079 | − | 0.718329i | ||||
\(754\) | 67.1335 | − | 21.8130i | 0.0890365 | − | 0.0289297i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1037.61 | + | 1428.15i | 1.37250 | + | 1.88909i | ||||
\(757\) | 117.605 | + | 38.2121i | 0.155356 | + | 0.0504783i | 0.385663 | − | 0.922640i | \(-0.373973\pi\) |
−0.230306 | + | 0.973118i | \(0.573973\pi\) | |||||||
\(758\) | 24.9934 | 0.0329728 | ||||||||
\(759\) | −324.299 | − | 606.845i | −0.427271 | − | 0.799532i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 627.999 | + | 204.049i | 0.825228 | + | 0.268133i | 0.691034 | − | 0.722822i | \(-0.257155\pi\) |
0.134194 | + | 0.990955i | \(0.457155\pi\) | |||||||
\(762\) | −99.7698 | − | 137.321i | −0.130932 | − | 0.180212i | ||||
\(763\) | −931.931 | + | 1282.69i | −1.22140 | + | 1.68112i | ||||
\(764\) | 90.6160 | + | 278.887i | 0.118607 | + | 0.365036i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 130.611 | − | 179.770i | 0.170510 | − | 0.234687i | ||||
\(767\) | −201.181 | + | 146.167i | −0.262296 | + | 0.190569i | ||||
\(768\) | −975.071 | − | 316.820i | −1.26962 | − | 0.412526i | ||||
\(769\) | − | 753.219i | − | 0.979479i | −0.871869 | − | 0.489739i | \(-0.837092\pi\) | ||
0.871869 | − | 0.489739i | \(-0.162908\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1300.63 | −1.68695 | ||||||||
\(772\) | 458.103 | − | 1409.90i | 0.593398 | − | 1.82629i | ||||
\(773\) | −97.8922 | − | 134.737i | −0.126639 | − | 0.174304i | 0.740989 | − | 0.671517i | \(-0.234357\pi\) |
−0.867629 | + | 0.497213i | \(0.834357\pi\) | |||||||
\(774\) | −125.019 | − | 90.8315i | −0.161523 | − | 0.117353i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 153.185 | − | 49.7729i | 0.197404 | − | 0.0641404i | ||||
\(777\) | −838.988 | − | 609.560i | −1.07978 | − | 0.784505i | ||||
\(778\) | −58.9297 | + | 42.8149i | −0.0757451 | + | 0.0550320i | ||||
\(779\) | −264.565 | + | 814.247i | −0.339621 | + | 1.04525i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −65.0365 | + | 11.6083i | −0.0832734 | + | 0.0148634i | ||||
\(782\) | 10.5596i | 0.0135034i | ||||||||
\(783\) | −659.249 | + | 2028.96i | −0.841953 | + | 2.59126i | ||||
\(784\) | −641.335 | + | 465.957i | −0.818030 | + | 0.594333i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −23.6717 | − | 72.8539i | −0.0301166 | − | 0.0926894i | ||||
\(787\) | 107.043 | + | 329.445i | 0.136014 | + | 0.418609i | 0.995746 | − | 0.0921365i | \(-0.0293696\pi\) |
−0.859732 | + | 0.510745i | \(0.829370\pi\) | |||||||
\(788\) | −289.190 | − | 210.108i | −0.366992 | − | 0.266635i | ||||
\(789\) | 1289.14 | + | 1774.34i | 1.63389 | + | 2.24885i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 323.556i | − | 0.409047i | ||||||
\(792\) | 460.822 | − | 82.2517i | 0.581846 | − | 0.103853i | ||||
\(793\) | − | 161.167i | − | 0.203236i | ||||||
\(794\) | 102.840 | + | 33.4149i | 0.129522 | + | 0.0420843i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −75.9289 | − | 55.1656i | −0.0953880 | − | 0.0693035i | ||||
\(797\) | −42.8487 | + | 13.9224i | −0.0537625 | + | 0.0174685i | −0.335775 | − | 0.941942i | \(-0.608998\pi\) |
0.282012 | + | 0.959411i | \(0.408998\pi\) | |||||||
\(798\) | 105.084 | + | 323.417i | 0.131685 | + | 0.405284i | ||||
\(799\) | 6.60890 | − | 9.09636i | 0.00827146 | − | 0.0113847i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −646.683 | + | 1990.28i | −0.807344 | + | 2.48475i | ||||
\(802\) | −78.0690 | −0.0973429 | ||||||||
\(803\) | 998.082 | − | 1037.89i | 1.24294 | − | 1.29252i | ||||
\(804\) | 1818.08 | 2.26130 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 37.3063 | − | 27.1046i | 0.0462857 | − | 0.0336285i | ||||
\(807\) | 1515.29 | − | 2085.62i | 1.87769 | − | 2.58441i | ||||
\(808\) | −29.6644 | + | 9.63856i | −0.0367134 | + | 0.0119289i | ||||
\(809\) | 1187.16 | − | 385.731i | 1.46744 | − | 0.476800i | 0.537106 | − | 0.843515i | \(-0.319518\pi\) |
0.930333 | + | 0.366715i | \(0.119518\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −62.7425 | − | 86.3577i | −0.0773644 | − | 0.106483i | 0.768581 | − | 0.639753i | \(-0.220963\pi\) |
−0.845945 | + | 0.533270i | \(0.820963\pi\) | |||||||
\(812\) | −1793.60 | − | 582.776i | −2.20887 | − | 0.717704i | ||||
\(813\) | −1212.41 | −1.49128 | ||||||||
\(814\) | −58.7518 | + | 31.3971i | −0.0721767 | + | 0.0385713i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 209.098 | + | 67.9401i | 0.256248 | + | 0.0832599i | ||||
\(817\) | 360.685 | + | 496.440i | 0.441475 | + | 0.607638i | ||||
\(818\) | 49.2652 | − | 67.8077i | 0.0602264 | − | 0.0828945i | ||||
\(819\) | −267.568 | − | 823.491i | −0.326701 | − | 1.00548i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −361.534 | + | 497.608i | −0.440358 | + | 0.606100i | −0.970292 | − | 0.241939i | \(-0.922217\pi\) |
0.529934 | + | 0.848039i | \(0.322217\pi\) | |||||||
\(822\) | −95.6547 | + | 69.4972i | −0.116368 | + | 0.0845465i | ||||
\(823\) | 363.528 | + | 118.117i | 0.441711 | + | 0.143521i | 0.521425 | − | 0.853297i | \(-0.325401\pi\) |
−0.0797139 | + | 0.996818i | \(0.525401\pi\) | |||||||
\(824\) | − | 272.386i | − | 0.330566i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −158.006 | −0.191291 | ||||||||
\(827\) | −295.494 | + | 909.438i | −0.357309 | + | 1.09968i | 0.597350 | + | 0.801981i | \(0.296220\pi\) |
−0.954659 | + | 0.297703i | \(0.903780\pi\) | |||||||
\(828\) | −491.238 | − | 676.131i | −0.593282 | − | 0.816583i | ||||
\(829\) | −591.020 | − | 429.401i | −0.712931 | − | 0.517975i | 0.171187 | − | 0.985239i | \(-0.445240\pi\) |
−0.884118 | + | 0.467264i | \(0.845240\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −667.764 | + | 216.970i | −0.803566 | + | 0.261095i | ||||
\(832\) | 216.817 | + | 157.527i | 0.260598 | + | 0.189335i | ||||
\(833\) | 123.122 | − | 89.4537i | 0.147806 | − | 0.107387i | ||||
\(834\) | −23.4769 | + | 72.2545i | −0.0281498 | + | 0.0866361i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −909.809 | − | 125.921i | −1.08829 | − | 0.150623i | ||||
\(837\) | 1393.66i | 1.66507i | ||||||||
\(838\) | 4.15181 | − | 12.7780i | 0.00495443 | − | 0.0152482i | ||||
\(839\) | −739.591 | + | 537.345i | −0.881515 | + | 0.640458i | −0.933652 | − | 0.358182i | \(-0.883397\pi\) |
0.0521367 | + | 0.998640i | \(0.483397\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −444.409 | − | 1367.75i | −0.528429 | − | 1.62634i | ||||
\(842\) | 7.66845 | + | 23.6010i | 0.00910742 | + | 0.0280297i | ||||
\(843\) | −1264.68 | − | 918.847i | −1.50022 | − | 1.08997i | ||||
\(844\) | −844.394 | − | 1162.21i | −1.00047 | − | 1.37702i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 21.1638i | − | 0.0250163i | ||||||
\(847\) | 757.233 | + | 960.883i | 0.894018 | + | 1.13445i | ||||
\(848\) | 938.193i | 1.10636i | ||||||||
\(849\) | −52.2888 | − | 16.9896i | −0.0615887 | − | 0.0200114i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 194.726 | + | 141.476i | 0.228820 | + | 0.166247i | ||||
\(852\) | −115.220 | + | 37.4371i | −0.135234 | + | 0.0439403i | ||||
\(853\) | 338.270 | + | 1041.09i | 0.396565 | + | 1.22050i | 0.927736 | + | 0.373237i | \(0.121752\pi\) |
−0.531171 | + | 0.847265i | \(0.678248\pi\) | |||||||
\(854\) | 60.1920 | − | 82.8472i | 0.0704824 | − | 0.0970107i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11.9398 | + | 36.7470i | −0.0139484 | + | 0.0429287i | ||||
\(857\) | −1161.22 | −1.35499 | −0.677494 | − | 0.735528i | \(-0.736934\pi\) | ||||
−0.677494 | + | 0.735528i | \(0.736934\pi\) | |||||||
\(858\) | −83.1789 | − | 11.5123i | −0.0969451 | − | 0.0134176i | ||||
\(859\) | 465.631 | 0.542061 | 0.271031 | − | 0.962571i | \(-0.412636\pi\) | ||||
0.271031 | + | 0.962571i | \(0.412636\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1691.83 | − | 1229.19i | 1.96496 | − | 1.42763i | ||||
\(862\) | −130.095 | + | 179.061i | −0.150922 | + | 0.207727i | ||||
\(863\) | 738.720 | − | 240.025i | 0.855990 | − | 0.278128i | 0.152037 | − | 0.988375i | \(-0.451417\pi\) |
0.703953 | + | 0.710247i | \(0.251417\pi\) | |||||||
\(864\) | 602.700 | − | 195.829i | 0.697570 | − | 0.226654i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −62.1952 | − | 85.6043i | −0.0718189 | − | 0.0988502i | ||||
\(867\) | 1378.91 | + | 448.034i | 1.59043 | + | 0.516763i | ||||
\(868\) | −1232.00 | −1.41935 | ||||||||
\(869\) | 431.442 | − | 889.313i | 0.496480 | − | 1.02337i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −415.783 | − | 135.096i | −0.477363 | − | 0.155105i | ||||
\(872\) | 222.164 | + | 305.782i | 0.254775 | + | 0.350668i | ||||
\(873\) | 693.484 | − | 954.498i | 0.794368 | − | 1.09335i | ||||
\(874\) | −24.3897 | − | 75.0637i | −0.0279058 | − | 0.0858852i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1552.07 | − | 2136.24i | 1.77177 | − | 2.43863i | ||||
\(877\) | −1120.57 | + | 814.144i | −1.27773 | + | 0.928329i | −0.999482 | − | 0.0321793i | \(-0.989755\pi\) |
−0.278253 | + | 0.960508i | \(0.589755\pi\) | |||||||
\(878\) | −20.9290 | − | 6.80023i | −0.0238371 | − | 0.00774514i | ||||
\(879\) | 1703.97i | 1.93853i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1570.42 | −1.78255 | −0.891273 | − | 0.453467i | \(-0.850187\pi\) | ||||
−0.891273 | + | 0.453467i | \(0.850187\pi\) | |||||||
\(882\) | 88.5206 | − | 272.439i | 0.100364 | − | 0.308887i | ||||
\(883\) | 643.690 | + | 885.963i | 0.728981 | + | 1.00336i | 0.999177 | + | 0.0405507i | \(0.0129112\pi\) |
−0.270197 | + | 0.962805i | \(0.587089\pi\) | |||||||
\(884\) | −43.8383 | − | 31.8504i | −0.0495908 | − | 0.0360299i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 108.946 | − | 35.3987i | 0.122964 | − | 0.0399534i | ||||
\(887\) | −716.448 | − | 520.530i | −0.807720 | − | 0.586843i | 0.105449 | − | 0.994425i | \(-0.466372\pi\) |
−0.913169 | + | 0.407582i | \(0.866372\pi\) | |||||||
\(888\) | −200.007 | + | 145.314i | −0.225233 | + | 0.163642i | ||||
\(889\) | 336.974 | − | 1037.10i | 0.379048 | − | 1.16659i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 547.567 | − | 569.407i | 0.614554 | − | 0.639065i | ||||
\(892\) | − | 692.520i | − | 0.776368i | ||||||
\(893\) | −25.9697 | + | 79.9265i | −0.0290814 | + | 0.0895033i | ||||
\(894\) | 153.421 | − | 111.467i | 0.171611 | − | 0.124683i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 229.852 | + | 707.411i | 0.256531 | + | 0.789521i | ||||
\(897\) | 93.7583 | + | 288.558i | 0.104524 | + | 0.321693i | ||||
\(898\) | −27.6735 | − | 20.1060i | −0.0308168 | − | 0.0223897i | ||||
\(899\) | −875.145 | − | 1204.53i | −0.973465 | − | 1.33986i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 180.113i | − | 0.199903i | ||||||
\(902\) | −23.6034 | − | 132.240i | −0.0261678 | − | 0.146607i | ||||
\(903\) | − | 1498.85i | − | 1.65986i | ||||||
\(904\) | −73.3577 | − | 23.8354i | −0.0811479 | − | 0.0263666i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 98.3650 | + | 71.4664i | 0.108571 | + | 0.0788812i | ||||
\(907\) | 297.496 | − | 96.6622i | 0.327999 | − | 0.106573i | −0.140388 | − | 0.990097i | \(-0.544835\pi\) |
0.468388 | + | 0.883523i | \(0.344835\pi\) | |||||||
\(908\) | 22.3343 | + | 68.7378i | 0.0245972 | + | 0.0757025i | ||||
\(909\) | −134.294 | + | 184.839i | −0.147738 | + | 0.203344i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −140.671 | + | 432.942i | −0.154414 | + | 0.475238i | −0.998101 | − | 0.0615976i | \(-0.980380\pi\) |
0.843687 | + | 0.536836i | \(0.180380\pi\) | |||||||
\(912\) | −1643.30 | −1.80187 | ||||||||
\(913\) | −957.216 | + | 170.853i | −1.04843 | + | 0.187133i | ||||
\(914\) | 56.9129 | 0.0622680 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 422.743 | − | 307.141i | 0.461510 | − | 0.335306i | ||||
\(917\) | 289.267 | − | 398.141i | 0.315449 | − | 0.434178i | ||||
\(918\) | −37.0421 | + | 12.0357i | −0.0403509 | + | 0.0131108i | ||||
\(919\) | −981.783 | + | 319.001i | −1.06832 | + | 0.347117i | −0.789832 | − | 0.613324i | \(-0.789832\pi\) |
−0.278485 | + | 0.960441i | \(0.589832\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 338.284 | + | 465.607i | 0.367300 | + | 0.505545i | ||||
\(922\) | 162.327 | + | 52.7431i | 0.176059 | + | 0.0572051i | ||||
\(923\) | 29.1318 | 0.0315621 | ||||||||
\(924\) | 1617.08 | + | 1555.06i | 1.75008 | + | 1.68296i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −188.038 | − | 61.0973i | −0.203065 | − | 0.0659798i | ||||
\(927\) | −1172.76 | − | 1614.17i | −1.26512 | − | 1.74129i | ||||
\(928\) | −397.939 | + | 547.717i | −0.428814 | + | 0.590212i | ||||
\(929\) | 431.640 | + | 1328.45i | 0.464629 | + | 1.42998i | 0.859449 | + | 0.511222i | \(0.170807\pi\) |
−0.394820 | + | 0.918758i | \(0.629193\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −668.609 | + | 920.262i | −0.718162 | + | 0.988466i | ||||
\(932\) | −139.184 | + | 101.123i | −0.149339 | + | 0.108501i | ||||
\(933\) | −1989.21 | − | 646.332i | −2.13205 | − | 0.692746i | ||||
\(934\) | 274.470i | 0.293865i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −206.416 | −0.220530 | ||||||||
\(937\) | −370.868 | + | 1141.42i | −0.395804 | + | 1.21816i | 0.532530 | + | 0.846411i | \(0.321241\pi\) |
−0.928334 | + | 0.371748i | \(0.878759\pi\) | |||||||
\(938\) | −163.277 | − | 224.731i | −0.174069 | − | 0.239586i | ||||
\(939\) | 709.058 | + | 515.161i | 0.755120 | + | 0.548627i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.9217 | − | 9.72215i | 0.0317978 | − | 0.0103317i | −0.293075 | − | 0.956089i | \(-0.594679\pi\) |
0.324873 | + | 0.945758i | \(0.394679\pi\) | |||||||
\(942\) | 69.0133 | + | 50.1411i | 0.0732625 | + | 0.0532283i | ||||
\(943\) | −392.667 | + | 285.289i | −0.416401 | + | 0.302533i | ||||
\(944\) | 235.949 | − | 726.177i | 0.249946 | − | 0.769255i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −86.6233 | − | 42.0245i | −0.0915680 | − | 0.0444233i | ||||
\(947\) | − | 540.682i | − | 0.570942i | −0.958387 | − | 0.285471i | \(-0.907850\pi\) | ||
0.958387 | − | 0.285471i | \(-0.0921501\pi\) | |||||||
\(948\) | 560.127 | − | 1723.89i | 0.590851 | − | 1.81845i | ||||
\(949\) | −513.685 | + | 373.214i | −0.541291 | + | 0.393271i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −616.304 | − | 1896.79i | −0.648059 | − | 1.99452i | ||||
\(952\) | −21.5322 | − | 66.2692i | −0.0226178 | − | 0.0696105i | ||||
\(953\) | 462.279 | + | 335.865i | 0.485077 | + | 0.352429i | 0.803288 | − | 0.595591i | \(-0.203082\pi\) |
−0.318211 | + | 0.948020i | \(0.603082\pi\) | |||||||
\(954\) | −199.272 | − | 274.274i | −0.208880 | − | 0.287499i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 646.388i | − | 0.676138i | ||||||
\(957\) | −371.705 | + | 2685.66i | −0.388407 | + | 2.80633i | ||||
\(958\) | 141.601i | 0.147809i | ||||||||
\(959\) | −722.418 | − | 234.728i | −0.753303 | − | 0.244763i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.41808 | − | 6.84263i | −0.00980029 | − | 0.00712033i | ||||
\(962\) | 27.9369 | − | 9.07724i | 0.0290404 | − | 0.00943580i | ||||
\(963\) | 87.4590 | + | 269.171i | 0.0908193 | + | 0.279513i | ||||
\(964\) | 157.077 | − | 216.198i | 0.162943 | − | 0.224272i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −59.5738 | + | 183.349i | −0.0616705 | + | 0.189802i | ||||
\(967\) | −1228.33 | −1.27025 | −0.635125 | − | 0.772410i | \(-0.719051\pi\) | ||||
−0.635125 | + | 0.772410i | \(0.719051\pi\) | |||||||
\(968\) | 273.638 | − | 100.897i | 0.282684 | − | 0.104233i | ||||
\(969\) | 315.479 | 0.325571 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1282.98 | + | 932.137i | −1.32129 | + | 0.959976i | −0.321379 | + | 0.946951i | \(0.604146\pi\) |
−0.999915 | + | 0.0130253i | \(0.995854\pi\) | |||||||
\(972\) | −72.1291 | + | 99.2772i | −0.0742069 | + | 0.102137i | ||||
\(973\) | −464.193 | + | 150.825i | −0.477074 | + | 0.155011i | ||||
\(974\) | 9.55237 | − | 3.10375i | 0.00980736 | − | 0.00318660i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 290.871 | + | 400.350i | 0.298024 | + | 0.410194i | ||||
\(977\) | 895.345 | + | 290.915i | 0.916422 | + | 0.297764i | 0.728998 | − | 0.684515i | \(-0.239986\pi\) |
0.187424 | + | 0.982279i | \(0.439986\pi\) | |||||||
\(978\) | −319.713 | −0.326905 | ||||||||
\(979\) | −178.752 | + | 1291.52i | −0.182586 | + | 1.31923i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2633.10 | + | 855.547i | 2.68410 | + | 0.872117i | ||||
\(982\) | −142.966 | − | 196.775i | −0.145586 | − | 0.200382i | ||||
\(983\) | 410.154 | − | 564.528i | 0.417247 | − | 0.574291i | −0.547720 | − | 0.836662i | \(-0.684504\pi\) |
0.964967 | + | 0.262370i | \(0.0845042\pi\) | |||||||
\(984\) | −154.053 | − | 474.127i | −0.156558 | − | 0.481837i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 24.4574 | − | 33.6628i | 0.0248047 | − | 0.0341408i | ||||
\(987\) | 166.070 | − | 120.657i | 0.168257 | − | 0.122246i | ||||
\(988\) | 385.191 | + | 125.156i | 0.389870 | + | 0.126676i | ||||
\(989\) | 347.877i | 0.351746i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1202.24 | 1.21315 | 0.606577 | − | 0.795025i | \(-0.292542\pi\) | ||||
0.606577 | + | 0.795025i | \(0.292542\pi\) | |||||||
\(992\) | −136.670 | + | 420.626i | −0.137772 | + | 0.424018i | ||||
\(993\) | 361.021 | + | 496.903i | 0.363566 | + | 0.500406i | ||||
\(994\) | 14.9751 | + | 10.8800i | 0.0150655 | + | 0.0109457i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1695.82 | + | 551.004i | −1.70263 | + | 0.553217i | ||||
\(997\) | −655.602 | − | 476.323i | −0.657575 | − | 0.477756i | 0.208268 | − | 0.978072i | \(-0.433217\pi\) |
−0.865843 | + | 0.500316i | \(0.833217\pi\) | |||||||
\(998\) | −146.262 | + | 106.265i | −0.146555 | + | 0.106478i | ||||
\(999\) | −274.339 | + | 844.329i | −0.274614 | + | 0.845174i |
(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 | 275.3.q.f.24.3 | 24 | ||
5.2 | odd | 4 | 275.3.x.f.101.2 | 12 | |||
5.3 | odd | 4 | 55.3.i.d.46.2 | yes | 12 | ||
5.4 | even | 2 | inner | 275.3.q.f.24.4 | 24 | ||
11.6 | odd | 10 | inner | 275.3.q.f.149.4 | 24 | ||
55.17 | even | 20 | 275.3.x.f.226.2 | 12 | |||
55.18 | even | 20 | 605.3.c.d.241.5 | 12 | |||
55.28 | even | 20 | 55.3.i.d.6.2 | ✓ | 12 | ||
55.39 | odd | 10 | inner | 275.3.q.f.149.3 | 24 | ||
55.48 | odd | 20 | 605.3.c.d.241.8 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.3.i.d.6.2 | ✓ | 12 | 55.28 | even | 20 | ||
55.3.i.d.46.2 | yes | 12 | 5.3 | odd | 4 | ||
275.3.q.f.24.3 | 24 | 1.1 | even | 1 | trivial | ||
275.3.q.f.24.4 | 24 | 5.4 | even | 2 | inner | ||
275.3.q.f.149.3 | 24 | 55.39 | odd | 10 | inner | ||
275.3.q.f.149.4 | 24 | 11.6 | odd | 10 | inner | ||
275.3.x.f.101.2 | 12 | 5.2 | odd | 4 | |||
275.3.x.f.226.2 | 12 | 55.17 | even | 20 | |||
605.3.c.d.241.5 | 12 | 55.18 | even | 20 | |||
605.3.c.d.241.8 | 12 | 55.48 | odd | 20 |