Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [11,5,Mod(2,11)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(11, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("11.2");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 11 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 11.d (of order \(10\), degree \(4\), 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: | \(1.13706959392\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 115x^{10} + 5030x^{8} + 102975x^{6} + 953170x^{4} + 2910655x^{2} + 73205 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 7.2 | ||
Root | \(0.159251i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 11.7 |
Dual form | 11.5.d.a.8.2 |
$q$-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 \(\left(\mathbb{Z}/11\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{7}{10}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.02443 | − | 1.41001i | 0.256107 | − | 0.352501i | −0.661531 | − | 0.749918i | \(-0.730093\pi\) |
0.917638 | + | 0.397416i | \(0.130093\pi\) | |||||||
\(3\) | 2.68168 | − | 8.25338i | 0.297965 | − | 0.917042i | −0.684244 | − | 0.729253i | \(-0.739868\pi\) |
0.982209 | − | 0.187789i | \(-0.0601322\pi\) | |||||||
\(4\) | 4.00561 | + | 12.3280i | 0.250351 | + | 0.770500i | ||||
\(5\) | −8.06057 | + | 5.85635i | −0.322423 | + | 0.234254i | −0.737209 | − | 0.675665i | \(-0.763857\pi\) |
0.414786 | + | 0.909919i | \(0.363857\pi\) | |||||||
\(6\) | −8.89011 | − | 12.2362i | −0.246948 | − | 0.339894i | ||||
\(7\) | −56.0338 | + | 18.2065i | −1.14355 | + | 0.371561i | −0.818709 | − | 0.574208i | \(-0.805310\pi\) |
−0.324839 | + | 0.945769i | \(0.605310\pi\) | |||||||
\(8\) | 48.0070 | + | 15.5984i | 0.750109 | + | 0.243725i | ||||
\(9\) | 4.60358 | + | 3.34469i | 0.0568343 | + | 0.0412925i | ||||
\(10\) | 17.3649i | 0.173649i | ||||||||
\(11\) | −16.1117 | − | 119.923i | −0.133155 | − | 0.991095i | ||||
\(12\) | 112.489 | 0.781177 | ||||||||
\(13\) | 75.0662 | − | 103.320i | 0.444178 | − | 0.611359i | −0.526956 | − | 0.849893i | \(-0.676667\pi\) |
0.971134 | + | 0.238533i | \(0.0766667\pi\) | |||||||
\(14\) | −31.7314 | + | 97.6593i | −0.161895 | + | 0.498262i | ||||
\(15\) | 26.7187 | + | 82.2318i | 0.118750 | + | 0.365475i | ||||
\(16\) | −96.6156 | + | 70.1954i | −0.377405 | + | 0.274201i | ||||
\(17\) | 22.8472 | + | 31.4465i | 0.0790560 | + | 0.108811i | 0.846714 | − | 0.532049i | \(-0.178578\pi\) |
−0.767658 | + | 0.640860i | \(0.778578\pi\) | |||||||
\(18\) | 9.43207 | − | 3.06467i | 0.0291113 | − | 0.00945885i | ||||
\(19\) | −560.182 | − | 182.014i | −1.55175 | − | 0.504194i | −0.597162 | − | 0.802121i | \(-0.703705\pi\) |
−0.954589 | + | 0.297927i | \(0.903705\pi\) | |||||||
\(20\) | −104.485 | − | 75.9125i | −0.261212 | − | 0.189781i | ||||
\(21\) | 511.293i | 1.15939i | ||||||||
\(22\) | −185.597 | − | 100.135i | −0.383464 | − | 0.206889i | ||||
\(23\) | 973.600 | 1.84045 | 0.920227 | − | 0.391386i | \(-0.128004\pi\) | ||||
0.920227 | + | 0.391386i | \(0.128004\pi\) | |||||||
\(24\) | 257.479 | − | 354.390i | 0.447013 | − | 0.615260i | ||||
\(25\) | −162.460 | + | 499.999i | −0.259935 | + | 0.799999i | ||||
\(26\) | −68.7814 | − | 211.687i | −0.101748 | − | 0.313147i | ||||
\(27\) | 608.630 | − | 442.196i | 0.834884 | − | 0.606579i | ||||
\(28\) | −448.900 | − | 617.857i | −0.572576 | − | 0.788083i | ||||
\(29\) | −141.677 | + | 46.0337i | −0.168463 | + | 0.0547369i | −0.392034 | − | 0.919951i | \(-0.628228\pi\) |
0.223571 | + | 0.974688i | \(0.428228\pi\) | |||||||
\(30\) | 143.319 | + | 46.5671i | 0.159243 | + | 0.0517412i | ||||
\(31\) | 140.685 | + | 102.214i | 0.146394 | + | 0.106362i | 0.658572 | − | 0.752518i | \(-0.271161\pi\) |
−0.512177 | + | 0.858880i | \(0.671161\pi\) | |||||||
\(32\) | 1015.78i | 0.991972i | ||||||||
\(33\) | −1032.97 | − | 188.618i | −0.948551 | − | 0.173203i | ||||
\(34\) | 67.7450 | 0.0586029 | ||||||||
\(35\) | 345.041 | − | 474.909i | 0.281666 | − | 0.387680i | ||||
\(36\) | −22.7933 | + | 70.1504i | −0.0175874 | + | 0.0541284i | ||||
\(37\) | 442.232 | + | 1361.05i | 0.323033 | + | 0.994194i | 0.972321 | + | 0.233651i | \(0.0750672\pi\) |
−0.649287 | + | 0.760543i | \(0.724933\pi\) | |||||||
\(38\) | −830.507 | + | 603.399i | −0.575144 | + | 0.417866i | ||||
\(39\) | −651.433 | − | 896.620i | −0.428292 | − | 0.589494i | ||||
\(40\) | −478.314 | + | 155.414i | −0.298946 | + | 0.0971334i | ||||
\(41\) | −561.211 | − | 182.349i | −0.333856 | − | 0.108476i | 0.137292 | − | 0.990531i | \(-0.456160\pi\) |
−0.471148 | + | 0.882054i | \(0.656160\pi\) | |||||||
\(42\) | 720.925 | + | 523.783i | 0.408688 | + | 0.296929i | ||||
\(43\) | − | 1171.41i | − | 0.633535i | −0.948503 | − | 0.316767i | \(-0.897403\pi\) | ||
0.948503 | − | 0.316767i | \(-0.102597\pi\) | |||||||
\(44\) | 1413.87 | − | 678.988i | 0.730304 | − | 0.350717i | ||||
\(45\) | −56.6952 | −0.0279976 | ||||||||
\(46\) | 997.384 | − | 1372.78i | 0.471353 | − | 0.648762i | ||||
\(47\) | −151.299 | + | 465.650i | −0.0684920 | + | 0.210797i | −0.979444 | − | 0.201715i | \(-0.935348\pi\) |
0.910952 | + | 0.412512i | \(0.135348\pi\) | |||||||
\(48\) | 320.256 | + | 985.647i | 0.139000 | + | 0.427798i | ||||
\(49\) | 865.865 | − | 629.088i | 0.360627 | − | 0.262011i | ||||
\(50\) | 538.573 | + | 741.283i | 0.215429 | + | 0.296513i | ||||
\(51\) | 320.808 | − | 104.237i | 0.123340 | − | 0.0400757i | ||||
\(52\) | 1574.41 | + | 511.557i | 0.582253 | + | 0.189185i | ||||
\(53\) | −1804.69 | − | 1311.18i | −0.642467 | − | 0.466780i | 0.218230 | − | 0.975897i | \(-0.429972\pi\) |
−0.860697 | + | 0.509118i | \(0.829972\pi\) | |||||||
\(54\) | − | 1311.17i | − | 0.449647i | ||||||
\(55\) | 832.178 | + | 872.289i | 0.275100 | + | 0.288360i | ||||
\(56\) | −2974.01 | −0.948345 | ||||||||
\(57\) | −3004.46 | + | 4135.29i | −0.924734 | + | 1.27279i | ||||
\(58\) | −80.2304 | + | 246.924i | −0.0238497 | + | 0.0734019i | ||||
\(59\) | −1488.77 | − | 4581.97i | −0.427685 | − | 1.31628i | −0.900400 | − | 0.435063i | \(-0.856726\pi\) |
0.472715 | − | 0.881215i | \(-0.343274\pi\) | |||||||
\(60\) | −906.729 | + | 658.778i | −0.251869 | + | 0.182994i | ||||
\(61\) | 2838.11 | + | 3906.32i | 0.762727 | + | 1.04980i | 0.996982 | + | 0.0776287i | \(0.0247349\pi\) |
−0.234255 | + | 0.972175i | \(0.575265\pi\) | |||||||
\(62\) | 288.243 | − | 93.6559i | 0.0749852 | − | 0.0243642i | ||||
\(63\) | −318.851 | − | 103.601i | −0.0803354 | − | 0.0261026i | ||||
\(64\) | −113.596 | − | 82.5323i | −0.0277334 | − | 0.0201495i | ||||
\(65\) | 1272.43i | 0.301167i | ||||||||
\(66\) | −1324.16 | + | 1263.27i | −0.303985 | + | 0.290007i | ||||
\(67\) | 187.188 | 0.0416992 | 0.0208496 | − | 0.999783i | \(-0.493363\pi\) | ||||
0.0208496 | + | 0.999783i | \(0.493363\pi\) | |||||||
\(68\) | −296.155 | + | 407.623i | −0.0640474 | + | 0.0881537i | ||||
\(69\) | 2610.89 | − | 8035.49i | 0.548391 | − | 1.68777i | ||||
\(70\) | −316.153 | − | 973.020i | −0.0645211 | − | 0.198576i | ||||
\(71\) | −537.618 | + | 390.602i | −0.106649 | + | 0.0774850i | −0.639832 | − | 0.768515i | \(-0.720996\pi\) |
0.533183 | + | 0.846000i | \(0.320996\pi\) | |||||||
\(72\) | 168.832 | + | 232.377i | 0.0325679 | + | 0.0448258i | ||||
\(73\) | 5025.08 | − | 1632.75i | 0.942969 | − | 0.306389i | 0.203113 | − | 0.979155i | \(-0.434894\pi\) |
0.739855 | + | 0.672766i | \(0.234894\pi\) | |||||||
\(74\) | 2372.13 | + | 770.750i | 0.433186 | + | 0.140751i | ||||
\(75\) | 3691.02 | + | 2681.68i | 0.656181 | + | 0.476743i | ||||
\(76\) | − | 7635.00i | − | 1.32185i | ||||||
\(77\) | 3086.17 | + | 6426.38i | 0.520521 | + | 1.08389i | ||||
\(78\) | −1931.59 | −0.317486 | ||||||||
\(79\) | −5015.11 | + | 6902.71i | −0.803575 | + | 1.10603i | 0.188708 | + | 0.982033i | \(0.439570\pi\) |
−0.992283 | + | 0.123993i | \(0.960430\pi\) | |||||||
\(80\) | 367.689 | − | 1131.63i | 0.0574514 | − | 0.176817i | ||||
\(81\) | −1875.02 | − | 5770.73i | −0.285783 | − | 0.879550i | ||||
\(82\) | −832.034 | + | 604.508i | −0.123741 | + | 0.0899030i | ||||
\(83\) | −136.132 | − | 187.370i | −0.0197608 | − | 0.0271985i | 0.799022 | − | 0.601301i | \(-0.205351\pi\) |
−0.818783 | + | 0.574103i | \(0.805351\pi\) | |||||||
\(84\) | −6303.22 | + | 2048.04i | −0.893313 | + | 0.290255i | ||||
\(85\) | −368.323 | − | 119.675i | −0.0509789 | − | 0.0165641i | ||||
\(86\) | −1651.69 | − | 1200.02i | −0.223322 | − | 0.162253i | ||||
\(87\) | 1292.76i | 0.170797i | ||||||||
\(88\) | 1097.13 | − | 6008.44i | 0.141674 | − | 0.775883i | ||||
\(89\) | −6640.75 | −0.838372 | −0.419186 | − | 0.907900i | \(-0.637685\pi\) | ||||
−0.419186 | + | 0.907900i | \(0.637685\pi\) | |||||||
\(90\) | −58.0802 | + | 79.9405i | −0.00717039 | + | 0.00986919i | ||||
\(91\) | −2325.16 | + | 7156.09i | −0.280782 | + | 0.864158i | ||||
\(92\) | 3899.86 | + | 12002.5i | 0.460759 | + | 1.41807i | ||||
\(93\) | 1220.88 | − | 887.020i | 0.141158 | − | 0.102558i | ||||
\(94\) | 501.574 | + | 690.357i | 0.0567648 | + | 0.0781301i | ||||
\(95\) | 5581.33 | − | 1813.48i | 0.618429 | − | 0.200940i | ||||
\(96\) | 8383.61 | + | 2724.00i | 0.909680 | + | 0.295573i | ||||
\(97\) | −5913.27 | − | 4296.24i | −0.628470 | − | 0.456610i | 0.227400 | − | 0.973801i | \(-0.426978\pi\) |
−0.855870 | + | 0.517191i | \(0.826978\pi\) | |||||||
\(98\) | − | 1865.33i | − | 0.194224i | ||||||
\(99\) | 326.933 | − | 605.961i | 0.0333571 | − | 0.0618265i | ||||
\(100\) | −6814.74 | −0.681474 | ||||||||
\(101\) | 9028.83 | − | 12427.1i | 0.885092 | − | 1.21823i | −0.0898920 | − | 0.995952i | \(-0.528652\pi\) |
0.974984 | − | 0.222274i | \(-0.0713478\pi\) | |||||||
\(102\) | 181.671 | − | 559.125i | 0.0174616 | − | 0.0537413i | ||||
\(103\) | −282.605 | − | 869.770i | −0.0266383 | − | 0.0819841i | 0.936854 | − | 0.349722i | \(-0.113724\pi\) |
−0.963492 | + | 0.267738i | \(0.913724\pi\) | |||||||
\(104\) | 5215.32 | − | 3789.15i | 0.482186 | − | 0.350329i | ||||
\(105\) | −2994.31 | − | 4121.31i | −0.271593 | − | 0.373815i | ||||
\(106\) | −3697.55 | + | 1201.41i | −0.329081 | + | 0.106925i | ||||
\(107\) | −7928.10 | − | 2576.00i | −0.692471 | − | 0.224998i | −0.0584239 | − | 0.998292i | \(-0.518608\pi\) |
−0.634047 | + | 0.773294i | \(0.718608\pi\) | |||||||
\(108\) | 7889.33 | + | 5731.93i | 0.676383 | + | 0.491421i | ||||
\(109\) | 3099.23i | 0.260856i | 0.991458 | + | 0.130428i | \(0.0416351\pi\) | ||||
−0.991458 | + | 0.130428i | \(0.958365\pi\) | |||||||
\(110\) | 2082.44 | − | 279.778i | 0.172102 | − | 0.0231221i | ||||
\(111\) | 12419.2 | 1.00797 | ||||||||
\(112\) | 4135.73 | − | 5692.35i | 0.329698 | − | 0.453791i | ||||
\(113\) | −1541.47 | + | 4744.16i | −0.120720 | + | 0.371538i | −0.993097 | − | 0.117296i | \(-0.962577\pi\) |
0.872377 | + | 0.488833i | \(0.162577\pi\) | |||||||
\(114\) | 2752.92 | + | 8472.62i | 0.211828 | + | 0.651940i | ||||
\(115\) | −7847.77 | + | 5701.74i | −0.593404 | + | 0.431134i | ||||
\(116\) | −1135.01 | − | 1562.20i | −0.0843496 | − | 0.116097i | ||||
\(117\) | 691.145 | − | 224.567i | 0.0504891 | − | 0.0164049i | ||||
\(118\) | −7985.74 | − | 2594.72i | −0.573523 | − | 0.186349i | ||||
\(119\) | −1852.75 | − | 1346.10i | −0.130834 | − | 0.0950567i | ||||
\(120\) | 4364.47i | 0.303088i | ||||||||
\(121\) | −14121.8 | + | 3864.31i | −0.964540 | + | 0.263938i | ||||
\(122\) | 8415.37 | 0.565397 | ||||||||
\(123\) | −3009.98 | + | 4142.89i | −0.198955 | + | 0.273837i | ||||
\(124\) | −696.560 | + | 2143.79i | −0.0453018 | + | 0.139424i | ||||
\(125\) | −3542.94 | − | 10904.1i | −0.226748 | − | 0.697860i | ||||
\(126\) | −472.718 | + | 343.450i | −0.0297757 | + | 0.0216333i | ||||
\(127\) | −6612.92 | − | 9101.91i | −0.410002 | − | 0.564319i | 0.553217 | − | 0.833037i | \(-0.313400\pi\) |
−0.963219 | + | 0.268718i | \(0.913400\pi\) | |||||||
\(128\) | −15689.8 | + | 5097.91i | −0.957627 | + | 0.311152i | ||||
\(129\) | −9668.06 | − | 3141.34i | −0.580978 | − | 0.188771i | ||||
\(130\) | 1794.13 | + | 1303.51i | 0.106162 | + | 0.0771310i | ||||
\(131\) | 27358.8i | 1.59424i | 0.603818 | + | 0.797122i | \(0.293645\pi\) | ||||
−0.603818 | + | 0.797122i | \(0.706355\pi\) | |||||||
\(132\) | −1812.40 | − | 13490.0i | −0.104017 | − | 0.774221i | ||||
\(133\) | 34703.0 | 1.96184 | ||||||||
\(134\) | 191.760 | − | 263.935i | 0.0106795 | − | 0.0146990i | ||||
\(135\) | −2316.26 | + | 7128.71i | −0.127092 | + | 0.391150i | ||||
\(136\) | 606.310 | + | 1866.03i | 0.0327806 | + | 0.100888i | ||||
\(137\) | 20807.3 | − | 15117.4i | 1.10860 | − | 0.805445i | 0.126158 | − | 0.992010i | \(-0.459736\pi\) |
0.982443 | + | 0.186565i | \(0.0597355\pi\) | |||||||
\(138\) | −8655.41 | − | 11913.2i | −0.454495 | − | 0.625559i | ||||
\(139\) | 20596.8 | − | 6692.32i | 1.06603 | − | 0.346375i | 0.277092 | − | 0.960843i | \(-0.410629\pi\) |
0.788942 | + | 0.614468i | \(0.210629\pi\) | |||||||
\(140\) | 7236.78 | + | 2351.37i | 0.369223 | + | 0.119968i | ||||
\(141\) | 3437.45 | + | 2497.45i | 0.172901 | + | 0.125620i | ||||
\(142\) | 1158.19i | 0.0574384i | ||||||||
\(143\) | −13599.8 | − | 7337.47i | −0.665060 | − | 0.358818i | ||||
\(144\) | −679.559 | −0.0327720 | ||||||||
\(145\) | 872.410 | − | 1200.77i | 0.0414939 | − | 0.0571115i | ||||
\(146\) | 2845.65 | − | 8758.02i | 0.133498 | − | 0.410866i | ||||
\(147\) | −2870.12 | − | 8833.32i | −0.132821 | − | 0.408780i | ||||
\(148\) | −15007.6 | + | 10903.7i | −0.685155 | + | 0.497794i | ||||
\(149\) | 21517.4 | + | 29616.2i | 0.969211 | + | 1.33400i | 0.942445 | + | 0.334362i | \(0.108521\pi\) |
0.0267658 | + | 0.999642i | \(0.491479\pi\) | |||||||
\(150\) | 7562.37 | − | 2457.16i | 0.336105 | − | 0.109207i | ||||
\(151\) | −8685.35 | − | 2822.04i | −0.380920 | − | 0.123768i | 0.112297 | − | 0.993675i | \(-0.464179\pi\) |
−0.493217 | + | 0.869906i | \(0.664179\pi\) | |||||||
\(152\) | −24053.5 | − | 17475.9i | −1.04110 | − | 0.756401i | ||||
\(153\) | 221.183i | 0.00944863i | ||||||||
\(154\) | 12222.8 | + | 2231.86i | 0.515382 | + | 0.0941076i | ||||
\(155\) | −1732.60 | −0.0721165 | ||||||||
\(156\) | 8444.15 | − | 11622.4i | 0.346982 | − | 0.477580i | ||||
\(157\) | −2087.92 | + | 6425.96i | −0.0847061 | + | 0.260699i | −0.984435 | − | 0.175752i | \(-0.943764\pi\) |
0.899728 | + | 0.436450i | \(0.143764\pi\) | |||||||
\(158\) | 4595.23 | + | 14142.7i | 0.184074 | + | 0.566522i | ||||
\(159\) | −15661.3 | + | 11378.6i | −0.619489 | + | 0.450085i | ||||
\(160\) | −5948.76 | − | 8187.76i | −0.232373 | − | 0.319834i | ||||
\(161\) | −54554.5 | + | 17725.8i | −2.10465 | + | 0.683841i | ||||
\(162\) | −10057.6 | − | 3267.91i | −0.383234 | − | 0.124520i | ||||
\(163\) | 19475.3 | + | 14149.6i | 0.733009 | + | 0.532562i | 0.890514 | − | 0.454956i | \(-0.150345\pi\) |
−0.157505 | + | 0.987518i | \(0.550345\pi\) | |||||||
\(164\) | − | 7649.03i | − | 0.284393i | ||||||
\(165\) | 9430.97 | − | 4529.07i | 0.346408 | − | 0.166357i | ||||
\(166\) | −403.651 | −0.0146484 | ||||||||
\(167\) | 12349.4 | − | 16997.5i | 0.442805 | − | 0.609469i | −0.528028 | − | 0.849227i | \(-0.677068\pi\) |
0.970833 | + | 0.239758i | \(0.0770683\pi\) | |||||||
\(168\) | −7975.35 | + | 24545.6i | −0.282573 | + | 0.869672i | ||||
\(169\) | 3785.80 | + | 11651.5i | 0.132551 | + | 0.407951i | ||||
\(170\) | −546.063 | + | 396.738i | −0.0188949 | + | 0.0137280i | ||||
\(171\) | −1970.06 | − | 2711.55i | −0.0673731 | − | 0.0927312i | ||||
\(172\) | 14441.1 | − | 4692.20i | 0.488139 | − | 0.158606i | ||||
\(173\) | 6450.49 | + | 2095.89i | 0.215526 | + | 0.0700288i | 0.414790 | − | 0.909917i | \(-0.363855\pi\) |
−0.199264 | + | 0.979946i | \(0.563855\pi\) | |||||||
\(174\) | 1822.80 | + | 1324.34i | 0.0602062 | + | 0.0437424i | ||||
\(175\) | − | 30974.7i | − | 1.01142i | ||||||
\(176\) | 9974.65 | + | 10455.4i | 0.322012 | + | 0.337533i | ||||
\(177\) | −41809.1 | −1.33452 | ||||||||
\(178\) | −6802.97 | + | 9363.49i | −0.214713 | + | 0.295527i | ||||
\(179\) | 11829.4 | − | 36407.2i | 0.369196 | − | 1.13627i | −0.578116 | − | 0.815955i | \(-0.696212\pi\) |
0.947312 | − | 0.320313i | \(-0.103788\pi\) | |||||||
\(180\) | −227.099 | − | 698.938i | −0.00700922 | − | 0.0215722i | ||||
\(181\) | 17836.1 | − | 12958.7i | 0.544430 | − | 0.395551i | −0.281298 | − | 0.959620i | \(-0.590765\pi\) |
0.825727 | + | 0.564069i | \(0.190765\pi\) | |||||||
\(182\) | 7708.17 | + | 10609.4i | 0.232707 | + | 0.320293i | ||||
\(183\) | 39851.2 | − | 12948.5i | 1.18998 | − | 0.386648i | ||||
\(184\) | 46739.6 | + | 15186.6i | 1.38054 | + | 0.448565i | ||||
\(185\) | −11535.4 | − | 8380.99i | −0.337047 | − | 0.244879i | ||||
\(186\) | − | 2630.14i | − | 0.0760243i | ||||||
\(187\) | 3403.03 | − | 3246.55i | 0.0973157 | − | 0.0928408i | ||||
\(188\) | −6346.58 | −0.179566 | ||||||||
\(189\) | −26053.1 | + | 35859.0i | −0.729349 | + | 1.00386i | ||||
\(190\) | 3160.65 | − | 9727.48i | 0.0875526 | − | 0.269459i | ||||
\(191\) | −1356.85 | − | 4175.95i | −0.0371933 | − | 0.114469i | 0.930736 | − | 0.365691i | \(-0.119167\pi\) |
−0.967929 | + | 0.251222i | \(0.919167\pi\) | |||||||
\(192\) | −985.799 | + | 716.225i | −0.0267415 | + | 0.0194288i | ||||
\(193\) | −11047.4 | − | 15205.4i | −0.296582 | − | 0.408210i | 0.634556 | − | 0.772877i | \(-0.281183\pi\) |
−0.931138 | + | 0.364666i | \(0.881183\pi\) | |||||||
\(194\) | −12115.5 | + | 3936.55i | −0.321911 | + | 0.104595i | ||||
\(195\) | 10501.8 | + | 3412.26i | 0.276183 | + | 0.0897372i | ||||
\(196\) | 11223.7 | + | 8154.51i | 0.292162 | + | 0.212268i | ||||
\(197\) | − | 13912.0i | − | 0.358474i | −0.983806 | − | 0.179237i | \(-0.942637\pi\) | ||
0.983806 | − | 0.179237i | \(-0.0573629\pi\) | |||||||
\(198\) | −519.489 | − | 1081.74i | −0.0132509 | − | 0.0275926i | ||||
\(199\) | −42834.8 | −1.08166 | −0.540830 | − | 0.841132i | \(-0.681890\pi\) | ||||
−0.540830 | + | 0.841132i | \(0.681890\pi\) | |||||||
\(200\) | −15598.4 | + | 21469.3i | −0.389960 | + | 0.536734i | ||||
\(201\) | 501.978 | − | 1544.93i | 0.0124249 | − | 0.0382399i | ||||
\(202\) | −8272.91 | − | 25461.4i | −0.202747 | − | 0.623992i | ||||
\(203\) | 7100.61 | − | 5158.89i | 0.172307 | − | 0.125188i | ||||
\(204\) | 2570.07 | + | 3537.39i | 0.0617567 | + | 0.0850008i | ||||
\(205\) | 5591.58 | − | 1816.82i | 0.133054 | − | 0.0432318i | ||||
\(206\) | −1515.89 | − | 492.542i | −0.0357218 | − | 0.0116067i | ||||
\(207\) | 4482.04 | + | 3256.39i | 0.104601 | + | 0.0759970i | ||||
\(208\) | 15251.6i | 0.352524i | ||||||||
\(209\) | −12802.1 | + | 70111.0i | −0.293082 | + | 1.60507i | ||||
\(210\) | −8878.53 | −0.201327 | ||||||||
\(211\) | −25464.9 | + | 35049.5i | −0.571975 | + | 0.787257i | −0.992787 | − | 0.119891i | \(-0.961745\pi\) |
0.420812 | + | 0.907148i | \(0.361745\pi\) | |||||||
\(212\) | 8935.40 | − | 27500.3i | 0.198812 | − | 0.611880i | ||||
\(213\) | 1782.07 | + | 5484.63i | 0.0392794 | + | 0.120889i | ||||
\(214\) | −11753.9 | + | 8539.74i | −0.256659 | + | 0.186474i | ||||
\(215\) | 6860.16 | + | 9442.20i | 0.148408 | + | 0.204266i | ||||
\(216\) | 36116.1 | − | 11734.8i | 0.774093 | − | 0.251518i | ||||
\(217\) | −9744.06 | − | 3166.04i | −0.206929 | − | 0.0672352i | ||||
\(218\) | 4369.93 | + | 3174.94i | 0.0919521 | + | 0.0668071i | ||||
\(219\) | − | 45852.4i | − | 0.956035i | ||||||
\(220\) | −7420.20 | + | 13753.1i | −0.153310 | + | 0.284156i | ||||
\(221\) | 4964.09 | 0.101638 | ||||||||
\(222\) | 12722.6 | − | 17511.1i | 0.258148 | − | 0.355311i | ||||
\(223\) | 945.780 | − | 2910.81i | 0.0190187 | − | 0.0585335i | −0.941097 | − | 0.338137i | \(-0.890203\pi\) |
0.960115 | + | 0.279604i | \(0.0902031\pi\) | |||||||
\(224\) | −18493.8 | − | 56918.0i | −0.368578 | − | 1.13437i | ||||
\(225\) | −2420.24 | + | 1758.41i | −0.0478072 | + | 0.0347340i | ||||
\(226\) | 5110.17 | + | 7033.54i | 0.100050 | + | 0.137707i | ||||
\(227\) | 64.7787 | − | 21.0479i | 0.00125713 | − | 0.000408467i | −0.308388 | − | 0.951261i | \(-0.599790\pi\) |
0.309645 | + | 0.950852i | \(0.399790\pi\) | |||||||
\(228\) | −63014.6 | − | 20474.7i | −1.21219 | − | 0.393865i | ||||
\(229\) | 11009.2 | + | 7998.63i | 0.209934 | + | 0.152526i | 0.687784 | − | 0.725915i | \(-0.258584\pi\) |
−0.477850 | + | 0.878442i | \(0.658584\pi\) | |||||||
\(230\) | 16906.4i | 0.319592i | ||||||||
\(231\) | 61315.5 | − | 8237.79i | 1.14907 | − | 0.154379i | ||||
\(232\) | −7519.55 | −0.139706 | ||||||||
\(233\) | 30700.4 | − | 42255.4i | 0.565499 | − | 0.778343i | −0.426514 | − | 0.904481i | \(-0.640258\pi\) |
0.992013 | + | 0.126138i | \(0.0402584\pi\) | |||||||
\(234\) | 391.389 | − | 1204.57i | 0.00714787 | − | 0.0219989i | ||||
\(235\) | −1507.45 | − | 4639.46i | −0.0272966 | − | 0.0840102i | ||||
\(236\) | 50523.1 | − | 36707.2i | 0.907122 | − | 0.659063i | ||||
\(237\) | 43521.7 | + | 59902.5i | 0.774835 | + | 1.06647i | ||||
\(238\) | −3796.01 | + | 1233.40i | −0.0670153 | + | 0.0217746i | ||||
\(239\) | 78576.7 | + | 25531.1i | 1.37562 | + | 0.446965i | 0.901226 | − | 0.433348i | \(-0.142668\pi\) |
0.474392 | + | 0.880314i | \(0.342668\pi\) | |||||||
\(240\) | −8353.74 | − | 6069.35i | −0.145030 | − | 0.105371i | ||||
\(241\) | − | 24514.3i | − | 0.422070i | −0.977478 | − | 0.211035i | \(-0.932317\pi\) | ||
0.977478 | − | 0.211035i | \(-0.0676835\pi\) | |||||||
\(242\) | −9018.11 | + | 23870.6i | −0.153987 | + | 0.407598i | ||||
\(243\) | 8280.78 | 0.140236 | ||||||||
\(244\) | −36788.8 | + | 50635.4i | −0.617925 | + | 0.850501i | ||||
\(245\) | −3295.21 | + | 10141.6i | −0.0548973 | + | 0.168957i | ||||
\(246\) | 2757.98 | + | 8488.19i | 0.0455744 | + | 0.140264i | ||||
\(247\) | −60856.3 | + | 44214.7i | −0.997498 | + | 0.724725i | ||||
\(248\) | 5159.49 | + | 7101.42i | 0.0838886 | + | 0.115463i | ||||
\(249\) | −1911.50 | + | 621.085i | −0.0308302 | + | 0.0100173i | ||||
\(250\) | −19004.3 | − | 6174.86i | −0.304068 | − | 0.0987978i | ||||
\(251\) | −86430.5 | − | 62795.5i | −1.37189 | − | 0.996737i | −0.997587 | − | 0.0694317i | \(-0.977881\pi\) |
−0.374305 | − | 0.927306i | \(-0.622119\pi\) | |||||||
\(252\) | − | 4345.78i | − | 0.0684332i | ||||||
\(253\) | −15686.4 | − | 116757.i | −0.245065 | − | 1.82406i | ||||
\(254\) | −19608.2 | −0.303928 | ||||||||
\(255\) | −1975.45 | + | 2718.98i | −0.0303799 | + | 0.0418143i | ||||
\(256\) | −8190.72 | + | 25208.4i | −0.124980 | + | 0.384650i | ||||
\(257\) | 27704.0 | + | 85264.0i | 0.419446 | + | 1.29092i | 0.908214 | + | 0.418507i | \(0.137446\pi\) |
−0.488768 | + | 0.872414i | \(0.662554\pi\) | |||||||
\(258\) | −14333.5 | + | 10413.9i | −0.215335 | + | 0.156450i | ||||
\(259\) | −49560.0 | − | 68213.4i | −0.738808 | − | 1.01688i | ||||
\(260\) | −15686.5 | + | 5096.86i | −0.232049 | + | 0.0753973i | ||||
\(261\) | −806.191 | − | 261.947i | −0.0118347 | − | 0.00384532i | ||||
\(262\) | 38576.1 | + | 28027.2i | 0.561973 | + | 0.408297i | ||||
\(263\) | 109118.i | 1.57756i | 0.614675 | + | 0.788781i | \(0.289287\pi\) | ||||
−0.614675 | + | 0.788781i | \(0.710713\pi\) | |||||||
\(264\) | −46647.7 | − | 25167.7i | −0.669303 | − | 0.361107i | ||||
\(265\) | 22225.6 | 0.316491 | ||||||||
\(266\) | 35550.7 | − | 48931.4i | 0.502441 | − | 0.691551i | ||||
\(267\) | −17808.4 | + | 54808.6i | −0.249806 | + | 0.768822i | ||||
\(268\) | 749.801 | + | 2307.65i | 0.0104394 | + | 0.0321292i | ||||
\(269\) | 7596.38 | − | 5519.09i | 0.104979 | − | 0.0762716i | −0.534057 | − | 0.845448i | \(-0.679333\pi\) |
0.639036 | + | 0.769177i | \(0.279333\pi\) | |||||||
\(270\) | 7678.67 | + | 10568.8i | 0.105332 | + | 0.144976i | ||||
\(271\) | −77397.0 | + | 25147.8i | −1.05387 | + | 0.342422i | −0.784185 | − | 0.620527i | \(-0.786919\pi\) |
−0.269682 | + | 0.962949i | \(0.586919\pi\) | |||||||
\(272\) | −4414.79 | − | 1434.45i | −0.0596722 | − | 0.0193887i | ||||
\(273\) | 52826.6 | + | 38380.8i | 0.708806 | + | 0.514978i | ||||
\(274\) | − | 44825.1i | − | 0.597063i | ||||||
\(275\) | 62578.7 | + | 11426.7i | 0.827487 | + | 0.151097i | ||||
\(276\) | 109520. | 1.43772 | ||||||||
\(277\) | 28294.2 | − | 38943.7i | 0.368755 | − | 0.507548i | −0.583807 | − | 0.811893i | \(-0.698437\pi\) |
0.952562 | + | 0.304344i | \(0.0984374\pi\) | |||||||
\(278\) | 11663.8 | − | 35897.5i | 0.150921 | − | 0.464488i | ||||
\(279\) | 305.780 | + | 941.095i | 0.00392827 | + | 0.0120900i | ||||
\(280\) | 23972.2 | − | 17416.8i | 0.305768 | − | 0.222153i | ||||
\(281\) | −51179.9 | − | 70443.1i | −0.648167 | − | 0.892126i | 0.350851 | − | 0.936431i | \(-0.385892\pi\) |
−0.999018 | + | 0.0443056i | \(0.985892\pi\) | |||||||
\(282\) | 7042.84 | − | 2288.36i | 0.0885625 | − | 0.0287757i | ||||
\(283\) | 8915.84 | + | 2896.93i | 0.111324 | + | 0.0361714i | 0.364149 | − | 0.931341i | \(-0.381360\pi\) |
−0.252825 | + | 0.967512i | \(0.581360\pi\) | |||||||
\(284\) | −6968.83 | − | 5063.15i | −0.0864019 | − | 0.0627747i | ||||
\(285\) | − | 50928.0i | − | 0.626999i | ||||||
\(286\) | −24277.9 | + | 11659.1i | −0.296810 | + | 0.142539i | ||||
\(287\) | 34766.8 | 0.422085 | ||||||||
\(288\) | −3397.47 | + | 4676.22i | −0.0409610 | + | 0.0563780i | ||||
\(289\) | 25342.5 | − | 77996.3i | 0.303427 | − | 0.933852i | ||||
\(290\) | −799.369 | − | 2460.21i | −0.00950499 | − | 0.0292533i | ||||
\(291\) | −51316.1 | + | 37283.3i | −0.605993 | + | 0.440279i | ||||
\(292\) | 40257.0 | + | 55409.0i | 0.472146 | + | 0.649853i | ||||
\(293\) | −74010.8 | + | 24047.6i | −0.862105 | + | 0.280115i | −0.706507 | − | 0.707706i | \(-0.749730\pi\) |
−0.155597 | + | 0.987821i | \(0.549730\pi\) | |||||||
\(294\) | −15395.3 | − | 5002.23i | −0.178112 | − | 0.0578720i | ||||
\(295\) | 38833.9 | + | 28214.5i | 0.446239 | + | 0.324212i | ||||
\(296\) | 72238.1i | 0.824485i | ||||||||
\(297\) | −62835.3 | − | 65864.0i | −0.712346 | − | 0.746681i | ||||
\(298\) | 63802.1 | 0.718460 | ||||||||
\(299\) | 73084.4 | − | 100592.i | 0.817490 | − | 1.12518i | ||||
\(300\) | −18275.0 | + | 56244.6i | −0.203055 | + | 0.624940i | ||||
\(301\) | 21327.2 | + | 65638.4i | 0.235397 | + | 0.724477i | ||||
\(302\) | −12876.6 | + | 9355.41i | −0.141185 | + | 0.102577i | ||||
\(303\) | −78353.2 | − | 107844.i | −0.853437 | − | 1.17466i | ||||
\(304\) | 66898.9 | − | 21736.8i | 0.723888 | − | 0.235206i | ||||
\(305\) | −45753.5 | − | 14866.2i | −0.491841 | − | 0.159809i | ||||
\(306\) | 311.869 | + | 226.586i | 0.00333065 | + | 0.00241986i | ||||
\(307\) | 153965.i | 1.63360i | 0.576921 | + | 0.816800i | \(0.304254\pi\) | ||||
−0.576921 | + | 0.816800i | \(0.695746\pi\) | |||||||
\(308\) | −66862.5 | + | 63787.9i | −0.704824 | + | 0.672414i | ||||
\(309\) | −7936.40 | −0.0831202 | ||||||||
\(310\) | −1774.92 | + | 2442.97i | −0.0184695 | + | 0.0254212i | ||||
\(311\) | −25689.2 | + | 79063.2i | −0.265601 | + | 0.817436i | 0.725953 | + | 0.687744i | \(0.241399\pi\) |
−0.991554 | + | 0.129692i | \(0.958601\pi\) | |||||||
\(312\) | −17287.5 | − | 53205.3i | −0.177591 | − | 0.546570i | ||||
\(313\) | 82353.8 | − | 59833.6i | 0.840611 | − | 0.610740i | −0.0819302 | − | 0.996638i | \(-0.526108\pi\) |
0.922541 | + | 0.385898i | \(0.126108\pi\) | |||||||
\(314\) | 6921.71 | + | 9526.92i | 0.0702027 | + | 0.0966258i | ||||
\(315\) | 3176.85 | − | 1032.22i | 0.0320166 | − | 0.0104028i | ||||
\(316\) | −105185. | − | 34176.7i | −1.05337 | − | 0.342260i | ||||
\(317\) | −92619.0 | − | 67291.6i | −0.921683 | − | 0.669642i | 0.0222593 | − | 0.999752i | \(-0.492914\pi\) |
−0.943942 | + | 0.330110i | \(0.892914\pi\) | |||||||
\(318\) | 33739.1i | 0.333641i | ||||||||
\(319\) | 7803.14 | + | 16248.6i | 0.0766811 | + | 0.159674i | ||||
\(320\) | 1398.99 | 0.0136620 | ||||||||
\(321\) | −42521.3 | + | 58525.6i | −0.412664 | + | 0.567984i | ||||
\(322\) | −30893.7 | + | 95081.1i | −0.297960 | + | 0.917027i | ||||
\(323\) | −7074.88 | − | 21774.2i | −0.0678132 | − | 0.208708i | ||||
\(324\) | 63631.0 | − | 46230.6i | 0.606148 | − | 0.440392i | ||||
\(325\) | 39464.6 | + | 54318.3i | 0.373629 | + | 0.514256i | ||||
\(326\) | 39902.2 | − | 12965.0i | 0.375458 | − | 0.121994i | ||||
\(327\) | 25579.1 | + | 8311.16i | 0.239216 | + | 0.0777259i | ||||
\(328\) | −24097.7 | − | 17508.0i | −0.223990 | − | 0.162738i | ||||
\(329\) | − | 28846.8i | − | 0.266505i | ||||||
\(330\) | 3275.33 | − | 17937.4i | 0.0300765 | − | 0.164715i | ||||
\(331\) | 3500.96 | 0.0319545 | 0.0159772 | − | 0.999872i | \(-0.494914\pi\) | ||||
0.0159772 | + | 0.999872i | \(0.494914\pi\) | |||||||
\(332\) | 1764.61 | − | 2428.77i | 0.0160093 | − | 0.0220349i | ||||
\(333\) | −2516.45 | + | 7744.84i | −0.0226934 | + | 0.0698431i | ||||
\(334\) | −11315.5 | − | 34825.4i | −0.101433 | − | 0.312179i | ||||
\(335\) | −1508.84 | + | 1096.24i | −0.0134448 | + | 0.00976820i | ||||
\(336\) | −35890.4 | − | 49398.8i | −0.317906 | − | 0.437561i | ||||
\(337\) | 128354. | − | 41704.6i | 1.13018 | − | 0.367218i | 0.316536 | − | 0.948580i | \(-0.397480\pi\) |
0.813645 | + | 0.581362i | \(0.197480\pi\) | |||||||
\(338\) | 20307.0 | + | 6598.13i | 0.177751 | + | 0.0577547i | ||||
\(339\) | 35021.6 | + | 25444.7i | 0.304745 | + | 0.221410i | ||||
\(340\) | − | 5020.06i | − | 0.0434261i | ||||||
\(341\) | 9991.03 | − | 18518.1i | 0.0859214 | − | 0.159253i | ||||
\(342\) | −5841.49 | −0.0499426 | ||||||||
\(343\) | 46084.3 | − | 63429.7i | 0.391710 | − | 0.539143i | ||||
\(344\) | 18272.1 | − | 56235.7i | 0.154408 | − | 0.475220i | ||||
\(345\) | 26013.4 | + | 80060.9i | 0.218554 | + | 0.672639i | ||||
\(346\) | 9563.29 | − | 6948.13i | 0.0798831 | − | 0.0580385i | ||||
\(347\) | 54879.0 | + | 75534.5i | 0.455772 | + | 0.627316i | 0.973625 | − | 0.228153i | \(-0.0732687\pi\) |
−0.517853 | + | 0.855469i | \(0.673269\pi\) | |||||||
\(348\) | −15937.2 | + | 5178.31i | −0.131599 | + | 0.0427592i | ||||
\(349\) | −52327.1 | − | 17002.1i | −0.429612 | − | 0.139589i | 0.0862261 | − | 0.996276i | \(-0.472519\pi\) |
−0.515838 | + | 0.856686i | \(0.672519\pi\) | |||||||
\(350\) | −43674.5 | − | 31731.4i | −0.356526 | − | 0.259032i | ||||
\(351\) | − | 96077.5i | − | 0.779843i | ||||||
\(352\) | 121815. | − | 16365.9i | 0.983139 | − | 0.132086i | ||||
\(353\) | −3735.78 | −0.0299801 | −0.0149900 | − | 0.999888i | \(-0.504772\pi\) | ||||
−0.0149900 | + | 0.999888i | \(0.504772\pi\) | |||||||
\(354\) | −42830.5 | + | 58951.1i | −0.341780 | + | 0.470419i | ||||
\(355\) | 2046.00 | − | 6296.95i | 0.0162349 | − | 0.0499659i | ||||
\(356\) | −26600.2 | − | 81867.1i | −0.209887 | − | 0.645966i | ||||
\(357\) | −16078.3 | + | 11681.6i | −0.126155 | + | 0.0916570i | ||||
\(358\) | −39215.9 | − | 53976.1i | −0.305982 | − | 0.421148i | ||||
\(359\) | −81956.4 | + | 26629.2i | −0.635907 | + | 0.206619i | −0.609190 | − | 0.793024i | \(-0.708505\pi\) |
−0.0267172 | + | 0.999643i | \(0.508505\pi\) | |||||||
\(360\) | −2721.76 | − | 884.355i | −0.0210013 | − | 0.00682372i | ||||
\(361\) | 175243. | + | 127321.i | 1.34470 | + | 0.976982i | ||||
\(362\) | − | 38424.2i | − | 0.293216i | ||||||
\(363\) | −5976.66 | + | 126916.i | −0.0453571 | + | 0.963168i | ||||
\(364\) | −97534.0 | −0.736128 | ||||||||
\(365\) | −30943.1 | + | 42589.5i | −0.232262 | + | 0.319681i | ||||
\(366\) | 22567.4 | − | 69455.2i | 0.168469 | − | 0.518493i | ||||
\(367\) | 7826.17 | + | 24086.5i | 0.0581055 | + | 0.178830i | 0.975897 | − | 0.218233i | \(-0.0700293\pi\) |
−0.917791 | + | 0.397063i | \(0.870029\pi\) | |||||||
\(368\) | −94065.0 | + | 68342.2i | −0.694596 | + | 0.504654i | ||||
\(369\) | −1973.68 | − | 2716.54i | −0.0144952 | − | 0.0199509i | ||||
\(370\) | −23634.5 | + | 7679.31i | −0.172640 | + | 0.0560943i | ||||
\(371\) | 124996. | + | 40613.6i | 0.908129 | + | 0.295069i | ||||
\(372\) | 15825.6 | + | 11497.9i | 0.114360 | + | 0.0830872i | ||||
\(373\) | − | 192208.i | − | 1.38151i | −0.723089 | − | 0.690755i | \(-0.757278\pi\) | ||
0.723089 | − | 0.690755i | \(-0.242722\pi\) | |||||||
\(374\) | −1091.49 | − | 8124.15i | −0.00780325 | − | 0.0580811i | ||||
\(375\) | −99496.4 | −0.707530 | ||||||||
\(376\) | −14526.8 | + | 19994.4i | −0.102753 | + | 0.141427i | ||||
\(377\) | −5878.97 | + | 18093.6i | −0.0413637 | + | 0.127304i | ||||
\(378\) | 23871.8 | + | 73469.9i | 0.167071 | + | 0.514193i | ||||
\(379\) | −106632. | + | 77472.8i | −0.742352 | + | 0.539350i | −0.893447 | − | 0.449169i | \(-0.851720\pi\) |
0.151095 | + | 0.988519i | \(0.451720\pi\) | |||||||
\(380\) | 44713.2 | + | 61542.5i | 0.309648 | + | 0.426195i | ||||
\(381\) | −92855.2 | + | 30170.5i | −0.639671 | + | 0.207842i | ||||
\(382\) | −7278.10 | − | 2364.80i | −0.0498760 | − | 0.0162057i | ||||
\(383\) | −142062. | − | 103214.i | −0.968454 | − | 0.703623i | −0.0133552 | − | 0.999911i | \(-0.504251\pi\) |
−0.955099 | + | 0.296288i | \(0.904251\pi\) | |||||||
\(384\) | 143164.i | 0.970896i | ||||||||
\(385\) | −62511.4 | − | 33726.6i | −0.421733 | − | 0.227537i | ||||
\(386\) | −32757.0 | −0.219852 | ||||||||
\(387\) | 3917.99 | − | 5392.66i | 0.0261602 | − | 0.0360065i | ||||
\(388\) | 29277.8 | − | 90108.0i | 0.194480 | − | 0.598549i | ||||
\(389\) | 7643.41 | + | 23524.0i | 0.0505112 | + | 0.155458i | 0.973130 | − | 0.230254i | \(-0.0739558\pi\) |
−0.922619 | + | 0.385712i | \(0.873956\pi\) | |||||||
\(390\) | 15569.7 | − | 11312.0i | 0.102365 | − | 0.0743724i | ||||
\(391\) | 22244.0 | + | 30616.3i | 0.145499 | + | 0.200262i | ||||
\(392\) | 51380.3 | − | 16694.5i | 0.334368 | − | 0.108643i | ||||
\(393\) | 225803. | + | 73367.7i | 1.46199 | + | 0.475029i | ||||
\(394\) | −19616.0 | − | 14251.9i | −0.126363 | − | 0.0918078i | ||||
\(395\) | − | 85010.0i | − | 0.544849i | ||||||
\(396\) | 8779.86 | + | 1603.18i | 0.0559883 | + | 0.0102233i | ||||
\(397\) | −191822. | −1.21708 | −0.608539 | − | 0.793524i | \(-0.708244\pi\) | ||||
−0.608539 | + | 0.793524i | \(0.708244\pi\) | |||||||
\(398\) | −43881.2 | + | 60397.3i | −0.277021 | + | 0.381286i | ||||
\(399\) | 93062.5 | − | 286417.i | 0.584559 | − | 1.79909i | ||||
\(400\) | −19401.5 | − | 59711.7i | −0.121259 | − | 0.373198i | ||||
\(401\) | 91171.9 | − | 66240.3i | 0.566986 | − | 0.411939i | −0.267023 | − | 0.963690i | \(-0.586040\pi\) |
0.834009 | + | 0.551751i | \(0.186040\pi\) | |||||||
\(402\) | −1664.12 | − | 2290.46i | −0.0102975 | − | 0.0141733i | ||||
\(403\) | 21121.3 | − | 6862.74i | 0.130050 | − | 0.0422559i | ||||
\(404\) | 189367. | + | 61529.2i | 1.16023 | + | 0.376980i | ||||
\(405\) | 48909.2 | + | 35534.6i | 0.298181 | + | 0.216641i | ||||
\(406\) | − | 15296.8i | − | 0.0928002i | ||||||
\(407\) | 156096. | − | 74962.5i | 0.942328 | − | 0.452538i | ||||
\(408\) | 17027.0 | 0.102286 | ||||||||
\(409\) | −159737. | + | 219859.i | −0.954902 | + | 1.31431i | −0.00558643 | + | 0.999984i | \(0.501778\pi\) |
−0.949315 | + | 0.314325i | \(0.898222\pi\) | |||||||
\(410\) | 3166.46 | − | 9745.36i | 0.0188368 | − | 0.0579736i | ||||
\(411\) | −68970.9 | − | 212271.i | −0.408303 | − | 1.25663i | ||||
\(412\) | 9590.52 | − | 6967.92i | 0.0564999 | − | 0.0410496i | ||||
\(413\) | 166843. | + | 229640.i | 0.978156 | + | 1.34632i | ||||
\(414\) | 9183.06 | − | 2983.76i | 0.0535781 | − | 0.0174086i | ||||
\(415\) | 2194.61 | + | 713.072i | 0.0127427 | + | 0.00414035i | ||||
\(416\) | 104950. | + | 76250.6i | 0.606451 | + | 0.440613i | ||||
\(417\) | − | 187940.i | − | 1.08081i | ||||||
\(418\) | 85742.0 | + | 89874.8i | 0.490728 | + | 0.514381i | ||||
\(419\) | 36389.5 | 0.207275 | 0.103638 | − | 0.994615i | \(-0.466952\pi\) | ||||
0.103638 | + | 0.994615i | \(0.466952\pi\) | |||||||
\(420\) | 38813.5 | − | 53422.2i | 0.220031 | − | 0.302847i | ||||
\(421\) | −44837.8 | + | 137997.i | −0.252976 | + | 0.778581i | 0.741245 | + | 0.671234i | \(0.234236\pi\) |
−0.994222 | + | 0.107347i | \(0.965764\pi\) | |||||||
\(422\) | 23332.9 | + | 71811.3i | 0.131022 | + | 0.403244i | ||||
\(423\) | −2253.97 | + | 1637.61i | −0.0125970 | + | 0.00915227i | ||||
\(424\) | −66185.3 | − | 91096.3i | −0.368155 | − | 0.506721i | ||||
\(425\) | −19435.0 | + | 6314.80i | −0.107598 | + | 0.0349608i | ||||
\(426\) | 9558.96 | + | 3105.89i | 0.0526734 | + | 0.0171146i | ||||
\(427\) | −230150. | − | 167214.i | −1.26228 | − | 0.917101i | ||||
\(428\) | − | 108056.i | − | 0.589877i | ||||||
\(429\) | −97029.3 | + | 92567.5i | −0.527216 | + | 0.502972i | ||||
\(430\) | 20341.3 | 0.110012 | ||||||||
\(431\) | 487.457 | − | 670.927i | 0.00262411 | − | 0.00361178i | −0.807703 | − | 0.589590i | \(-0.799289\pi\) |
0.810327 | + | 0.585978i | \(0.199289\pi\) | |||||||
\(432\) | −27763.1 | + | 85446.1i | −0.148765 | + | 0.457851i | ||||
\(433\) | −45127.5 | − | 138888.i | −0.240694 | − | 0.740781i | −0.996315 | − | 0.0857711i | \(-0.972665\pi\) |
0.755621 | − | 0.655009i | \(-0.227335\pi\) | |||||||
\(434\) | −14446.2 | + | 10495.8i | −0.0766964 | + | 0.0557232i | ||||
\(435\) | −7570.87 | − | 10420.4i | −0.0400099 | − | 0.0550689i | ||||
\(436\) | −38207.3 | + | 12414.3i | −0.200990 | + | 0.0653055i | ||||
\(437\) | −545393. | − | 177209.i | −2.85592 | − | 0.927946i | ||||
\(438\) | −64652.1 | − | 46972.5i | −0.337004 | − | 0.244847i | ||||
\(439\) | 325054.i | 1.68666i | 0.537398 | + | 0.843329i | \(0.319407\pi\) | ||||
−0.537398 | + | 0.843329i | \(0.680593\pi\) | |||||||
\(440\) | 26344.0 | + | 54856.6i | 0.136075 | + | 0.283350i | ||||
\(441\) | 6090.18 | 0.0313150 | ||||||||
\(442\) | 5085.36 | − | 6999.39i | 0.0260302 | − | 0.0358274i | ||||
\(443\) | −3613.23 | + | 11120.4i | −0.0184115 | + | 0.0566647i | −0.959840 | − | 0.280548i | \(-0.909484\pi\) |
0.941429 | + | 0.337212i | \(0.109484\pi\) | |||||||
\(444\) | 49746.5 | + | 153104.i | 0.252346 | + | 0.776641i | ||||
\(445\) | 53528.2 | − | 38890.5i | 0.270310 | − | 0.196392i | ||||
\(446\) | −3135.38 | − | 4315.48i | −0.0157623 | − | 0.0216950i | ||||
\(447\) | 302137. | − | 98170.2i | 1.51213 | − | 0.491320i | ||||
\(448\) | 7867.84 | + | 2556.42i | 0.0392012 | + | 0.0127372i | ||||
\(449\) | 284422. | + | 206645.i | 1.41082 | + | 1.02502i | 0.993203 | + | 0.116395i | \(0.0371340\pi\) |
0.417615 | + | 0.908624i | \(0.362866\pi\) | |||||||
\(450\) | 5213.91i | 0.0257477i | ||||||||
\(451\) | −12825.6 | + | 70239.8i | −0.0630559 | + | 0.345327i | ||||
\(452\) | −64660.6 | −0.316492 | ||||||||
\(453\) | −46582.8 | + | 64115.7i | −0.227002 | + | 0.312441i | ||||
\(454\) | 36.6836 | − | 112.900i | 0.000177975 | − | 0.000547752i | ||||
\(455\) | −23166.5 | − | 71299.1i | −0.111902 | − | 0.344399i | ||||
\(456\) | −208739. | + | 151658.i | −1.00386 | + | 0.729349i | ||||
\(457\) | 90965.8 | + | 125204.i | 0.435558 | + | 0.599494i | 0.969218 | − | 0.246205i | \(-0.0791837\pi\) |
−0.533660 | + | 0.845699i | \(0.679184\pi\) | |||||||
\(458\) | 22556.2 | − | 7328.96i | 0.107531 | − | 0.0349391i | ||||
\(459\) | 27811.0 | + | 9036.34i | 0.132005 | + | 0.0428911i | ||||
\(460\) | −101726. | − | 73908.4i | −0.480748 | − | 0.349284i | ||||
\(461\) | − | 116794.i | − | 0.549564i | −0.961507 | − | 0.274782i | \(-0.911394\pi\) | ||
0.961507 | − | 0.274782i | \(-0.0886057\pi\) | |||||||
\(462\) | 51198.0 | − | 94894.2i | 0.239866 | − | 0.444586i | ||||
\(463\) | 39611.3 | 0.184781 | 0.0923904 | − | 0.995723i | \(-0.470549\pi\) | ||||
0.0923904 | + | 0.995723i | \(0.470549\pi\) | |||||||
\(464\) | 10456.9 | − | 14392.7i | 0.0485698 | − | 0.0668506i | ||||
\(465\) | −4646.28 | + | 14299.8i | −0.0214882 | + | 0.0661338i | ||||
\(466\) | −28130.1 | − | 86575.4i | −0.129538 | − | 0.398678i | ||||
\(467\) | 77040.8 | − | 55973.4i | 0.353254 | − | 0.256654i | −0.396979 | − | 0.917828i | \(-0.629941\pi\) |
0.750233 | + | 0.661174i | \(0.229941\pi\) | |||||||
\(468\) | 5536.92 | + | 7620.92i | 0.0252800 | + | 0.0347949i | ||||
\(469\) | −10488.8 | + | 3408.03i | −0.0476850 | + | 0.0154938i | ||||
\(470\) | −8085.95 | − | 2627.28i | −0.0366046 | − | 0.0118935i | ||||
\(471\) | 47436.7 | + | 34464.8i | 0.213832 | + | 0.155358i | ||||
\(472\) | − | 243189.i | − | 1.09159i | ||||||
\(473\) | −140478. | + | 18873.3i | −0.627893 | + | 0.0843581i | ||||
\(474\) | 129048. | 0.574372 | ||||||||
\(475\) | 182014. | − | 250521.i | 0.806710 | − | 1.11034i | ||||
\(476\) | 9173.33 | − | 28232.6i | 0.0404868 | − | 0.124605i | ||||
\(477\) | −3922.52 | − | 12072.3i | −0.0172396 | − | 0.0530582i | ||||
\(478\) | 116495. | − | 84638.7i | 0.509862 | − | 0.370436i | ||||
\(479\) | −206359. | − | 284028.i | −0.899398 | − | 1.23791i | −0.970660 | − | 0.240457i | \(-0.922703\pi\) |
0.0712622 | − | 0.997458i | \(-0.477297\pi\) | |||||||
\(480\) | −83529.4 | + | 27140.3i | −0.362541 | + | 0.117797i | ||||
\(481\) | 173820. | + | 56477.6i | 0.751294 | + | 0.244110i | ||||
\(482\) | −34565.2 | − | 25113.1i | −0.148780 | − | 0.108095i | ||||
\(483\) | 497794.i | 2.13381i | ||||||||
\(484\) | −104206. | − | 158615.i | −0.444837 | − | 0.677101i | ||||
\(485\) | 72824.7 | 0.309596 | ||||||||
\(486\) | 8483.07 | − | 11675.9i | 0.0359154 | − | 0.0494333i | ||||
\(487\) | −50720.6 | + | 156102.i | −0.213858 | + | 0.658189i | 0.785374 | + | 0.619021i | \(0.212471\pi\) |
−0.999233 | + | 0.0391673i | \(0.987529\pi\) | |||||||
\(488\) | 75316.6 | + | 231801.i | 0.316265 | + | 0.973363i | ||||
\(489\) | 169009. | − | 122792.i | 0.706793 | − | 0.513515i | ||||
\(490\) | 10924.0 | + | 15035.6i | 0.0454978 | + | 0.0626224i | ||||
\(491\) | 172324. | − | 55991.5i | 0.714797 | − | 0.232252i | 0.0710312 | − | 0.997474i | \(-0.477371\pi\) |
0.643766 | + | 0.765222i | \(0.277371\pi\) | |||||||
\(492\) | −63130.4 | − | 20512.3i | −0.260800 | − | 0.0847391i | ||||
\(493\) | −4684.52 | − | 3403.51i | −0.0192740 | − | 0.0140034i | ||||
\(494\) | 131103.i | 0.537227i | ||||||||
\(495\) | 913.455 | + | 6799.03i | 0.00372801 | + | 0.0277483i | ||||
\(496\) | −20767.3 | −0.0844143 | ||||||||
\(497\) | 23013.3 | − | 31675.1i | 0.0931678 | − | 0.128234i | ||||
\(498\) | −1082.47 | + | 3331.48i | −0.00436471 | + | 0.0134332i | ||||
\(499\) | 35889.1 | + | 110455.i | 0.144132 | + | 0.443594i | 0.996898 | − | 0.0786994i | \(-0.0250767\pi\) |
−0.852766 | + | 0.522293i | \(0.825077\pi\) | |||||||
\(500\) | 120234. | − | 87354.8i | 0.480934 | − | 0.349419i | ||||
\(501\) | −107169. | − | 147506.i | −0.426968 | − | 0.587671i | ||||
\(502\) | −177084. | + | 57538.0i | −0.702703 | + | 0.228322i | ||||
\(503\) | 61308.6 | + | 19920.4i | 0.242318 | + | 0.0787339i | 0.427658 | − | 0.903941i | \(-0.359339\pi\) |
−0.185340 | + | 0.982674i | \(0.559339\pi\) | |||||||
\(504\) | −13691.1 | − | 9947.15i | −0.0538985 | − | 0.0391595i | ||||
\(505\) | 153046.i | 0.600120i | ||||||||
\(506\) | −180697. | − | 97491.0i | −0.705748 | − | 0.380771i | ||||
\(507\) | 106317. | 0.413604 | ||||||||
\(508\) | 85719.5 | − | 117983.i | 0.332164 | − | 0.457184i | ||||
\(509\) | −44701.3 | + | 137576.i | −0.172538 | + | 0.531017i | −0.999512 | − | 0.0312225i | \(-0.990060\pi\) |
0.826975 | + | 0.562239i | \(0.190060\pi\) | |||||||
\(510\) | 1810.06 | + | 5570.79i | 0.00695910 | + | 0.0214179i | ||||
\(511\) | −251848. | + | 182978.i | −0.964487 | + | 0.700741i | ||||
\(512\) | −127996. | − | 176171.i | −0.488265 | − | 0.672038i | ||||
\(513\) | −421430. | + | 136931.i | −1.60137 | + | 0.520315i | ||||
\(514\) | 148603. | + | 48284.2i | 0.562474 | + | 0.182759i | ||||
\(515\) | 7371.64 | + | 5355.81i | 0.0277939 | + | 0.0201934i | ||||
\(516\) | − | 131771.i | − | 0.494903i | ||||||
\(517\) | 58279.6 | + | 10641.7i | 0.218040 | + | 0.0398135i | ||||
\(518\) | −146952. | −0.547666 | ||||||||
\(519\) | 34596.4 | − | 47617.8i | 0.128439 | − | 0.176781i | ||||
\(520\) | −19847.9 | + | 61085.5i | −0.0734019 | + | 0.225908i | ||||
\(521\) | 33121.1 | + | 101936.i | 0.122020 | + | 0.375538i | 0.993346 | − | 0.115166i | \(-0.0367399\pi\) |
−0.871327 | + | 0.490703i | \(0.836740\pi\) | |||||||
\(522\) | −1195.23 | + | 868.387i | −0.00438643 | + | 0.00318693i | ||||
\(523\) | −118355. | − | 162901.i | −0.432695 | − | 0.595554i | 0.535874 | − | 0.844298i | \(-0.319982\pi\) |
−0.968569 | + | 0.248744i | \(0.919982\pi\) | |||||||
\(524\) | −337280. | + | 109589.i | −1.22837 | + | 0.399120i | ||||
\(525\) | −255646. | − | 83064.4i | −0.927513 | − | 0.301367i | ||||
\(526\) | 153857. | + | 111784.i | 0.556093 | + | 0.404025i | ||||
\(527\) | 6759.33i | 0.0243379i | ||||||||
\(528\) | 113041. | − | 54286.4i | 0.405480 | − | 0.194726i | ||||
\(529\) | 668056. | 2.38727 | ||||||||
\(530\) | 22768.5 | − | 31338.2i | 0.0810557 | − | 0.111564i | ||||
\(531\) | 8471.60 | − | 26072.9i | 0.0300453 | − | 0.0924699i | ||||
\(532\) | 139007. | + | 427818.i | 0.491148 | + | 1.51160i | ||||
\(533\) | −60968.2 | + | 44296.0i | −0.214609 | + | 0.155923i | ||||
\(534\) | 59037.0 | + | 81257.4i | 0.207034 | + | 0.284958i | ||||
\(535\) | 78991.0 | − | 25665.7i | 0.275975 | − | 0.0896698i | ||||
\(536\) | 8986.31 | + | 2919.83i | 0.0312789 | + | 0.0101631i | ||||
\(537\) | −268759. | − | 195265.i | −0.931998 | − | 0.677136i | ||||
\(538\) | − | 16364.8i | − | 0.0565389i | ||||||
\(539\) | −89392.3 | − | 93701.0i | −0.307697 | − | 0.322528i | ||||
\(540\) | −97160.7 | −0.333199 | ||||||||
\(541\) | 90406.1 | − | 124433.i | 0.308890 | − | 0.425150i | −0.626145 | − | 0.779707i | \(-0.715368\pi\) |
0.935035 | + | 0.354557i | \(0.115368\pi\) | |||||||
\(542\) | −43829.2 | + | 134892.i | −0.149199 | + | 0.459186i | ||||
\(543\) | −59122.0 | − | 181959.i | −0.200516 | − | 0.617125i | ||||
\(544\) | −31942.7 | + | 23207.7i | −0.107938 | + | 0.0784213i | ||||
\(545\) | −18150.2 | − | 24981.6i | −0.0611065 | − | 0.0841059i | ||||
\(546\) | 108234. | − | 35167.4i | 0.363061 | − | 0.117966i | ||||
\(547\) | −150147. | − | 48785.9i | −0.501815 | − | 0.163049i | 0.0471619 | − | 0.998887i | \(-0.484982\pi\) |
−0.548976 | + | 0.835838i | \(0.684982\pi\) | |||||||
\(548\) | 269713. | + | 195958.i | 0.898134 | + | 0.652533i | ||||
\(549\) | 27475.6i | 0.0911598i | ||||||||
\(550\) | 80219.1 | − | 76530.4i | 0.265187 | − | 0.252993i | ||||
\(551\) | 87743.8 | 0.289010 | ||||||||
\(552\) | 250682. | − | 345034.i | 0.822706 | − | 1.13236i | ||||
\(553\) | 155342. | − | 478093.i | 0.507970 | − | 1.56337i | ||||
\(554\) | −25925.4 | − | 79790.0i | −0.0844705 | − | 0.259974i | ||||
\(555\) | −100106. | + | 72731.2i | −0.324993 | + | 0.236121i | ||||
\(556\) | 165006. | + | 227111.i | 0.533765 | + | 0.734664i | ||||
\(557\) | 553427. | − | 179819.i | 1.78382 | − | 0.579597i | 0.784630 | − | 0.619964i | \(-0.212853\pi\) |
0.999185 | + | 0.0403674i | \(0.0128528\pi\) | |||||||
\(558\) | 1640.20 | + | 532.933i | 0.00526779 | + | 0.00171161i | ||||
\(559\) | −121029. | − | 87932.9i | −0.387317 | − | 0.281403i | ||||
\(560\) | 70103.9i | 0.223546i | ||||||||
\(561\) | −17669.1 | − | 36792.7i | −0.0561422 | − | 0.116906i | ||||
\(562\) | −151755. | −0.480476 | ||||||||
\(563\) | −228448. | + | 314432.i | −0.720728 | + | 0.991997i | 0.278771 | + | 0.960358i | \(0.410073\pi\) |
−0.999499 | + | 0.0316397i | \(0.989927\pi\) | |||||||
\(564\) | −17019.5 | + | 52380.7i | −0.0535043 | + | 0.164669i | ||||
\(565\) | −15358.3 | − | 47268.1i | −0.0481113 | − | 0.148071i | ||||
\(566\) | 13218.3 | − | 9603.68i | 0.0412614 | − | 0.0299781i | ||||
\(567\) | 210130. | + | 289218.i | 0.653613 | + | 0.899622i | ||||
\(568\) | −31902.2 | + | 10365.6i | −0.0988835 | + | 0.0321292i | ||||
\(569\) | −194357. | − | 63150.3i | −0.600309 | − | 0.195052i | −0.00693101 | − | 0.999976i | \(-0.502206\pi\) |
−0.593378 | + | 0.804924i | \(0.702206\pi\) | |||||||
\(570\) | −71808.7 | − | 52172.1i | −0.221018 | − | 0.160579i | ||||
\(571\) | 68721.2i | 0.210775i | 0.994431 | + | 0.105387i | \(0.0336083\pi\) | ||||
−0.994431 | + | 0.105387i | \(0.966392\pi\) | |||||||
\(572\) | 35980.8 | − | 197049.i | 0.109971 | − | 0.602259i | ||||
\(573\) | −38104.3 | −0.116055 | ||||||||
\(574\) | 35616.1 | − | 49021.3i | 0.108099 | − | 0.148786i | ||||
\(575\) | −158171. | + | 486799.i | −0.478399 | + | 1.47236i | ||||
\(576\) | −246.902 | − | 759.887i | −0.000744184 | − | 0.00229036i | ||||
\(577\) | 194489. | − | 141305.i | 0.584177 | − | 0.424429i | −0.256051 | − | 0.966663i | \(-0.582421\pi\) |
0.840227 | + | 0.542234i | \(0.182421\pi\) | |||||||
\(578\) | −84013.5 | − | 115635.i | −0.251474 | − | 0.346125i | ||||
\(579\) | −155122. | + | 50402.1i | −0.462717 | + | 0.150346i | ||||
\(580\) | 18297.6 | + | 5945.26i | 0.0543925 | + | 0.0176732i | ||||
\(581\) | 11039.4 | + | 8020.58i | 0.0327034 | + | 0.0237604i | ||||
\(582\) | 110550.i | 0.326372i | ||||||||
\(583\) | −128164. | + | 237548.i | −0.377076 | + | 0.698900i | ||||
\(584\) | 266707. | 0.782004 | ||||||||
\(585\) | −4255.89 | + | 5857.73i | −0.0124359 | + | 0.0171166i | ||||
\(586\) | −41911.6 | + | 128991.i | −0.122050 | + | 0.375633i | ||||
\(587\) | −143863. | − | 442766.i | −0.417517 | − | 1.28499i | −0.909980 | − | 0.414652i | \(-0.863903\pi\) |
0.492463 | − | 0.870334i | \(-0.336097\pi\) | |||||||
\(588\) | 97400.7 | − | 70765.7i | 0.281713 | − | 0.204677i | ||||
\(589\) | −60204.8 | − | 82864.8i | −0.173540 | − | 0.238858i | ||||
\(590\) | 79565.2 | − | 25852.3i | 0.228570 | − | 0.0742669i | ||||
\(591\) | −114821. | − | 37307.6i | −0.328736 | − | 0.106813i | ||||
\(592\) | −138266. | − | 100456.i | −0.394523 | − | 0.286638i | ||||
\(593\) | − | 54204.4i | − | 0.154143i | −0.997026 | − | 0.0770717i | \(-0.975443\pi\) | ||
0.997026 | − | 0.0770717i | \(-0.0245570\pi\) | |||||||
\(594\) | −157239. | + | 21125.2i | −0.445643 | + | 0.0598725i | ||||
\(595\) | 22817.4 | 0.0644514 | ||||||||
\(596\) | −278918. | + | 383898.i | −0.785208 | + | 1.08075i | ||||
\(597\) | −114869. | + | 353532.i | −0.322297 | + | 0.991927i | ||||
\(598\) | −66965.6 | − | 206099.i | −0.187262 | − | 0.576332i | ||||
\(599\) | −344600. | + | 250367.i | −0.960421 | + | 0.697787i | −0.953249 | − | 0.302187i | \(-0.902283\pi\) |
−0.00717284 | + | 0.999974i | \(0.502283\pi\) | |||||||
\(600\) | 135365. | + | 186313.i | 0.376013 | + | 0.517537i | ||||
\(601\) | −178462. | + | 57985.7i | −0.494078 | + | 0.160536i | −0.545449 | − | 0.838144i | \(-0.683641\pi\) |
0.0513708 | + | 0.998680i | \(0.483641\pi\) | |||||||
\(602\) | 114399. | + | 37170.4i | 0.315666 | + | 0.102566i | ||||
\(603\) | 861.732 | + | 626.085i | 0.00236994 | + | 0.00172186i | ||||
\(604\) | − | 118377.i | − | 0.324484i | ||||||
\(605\) | 91199.3 | − | 113851.i | 0.249161 | − | 0.311047i | ||||
\(606\) | −232328. | −0.632639 | ||||||||
\(607\) | −197925. | + | 272420.i | −0.537183 | + | 0.739369i | −0.988204 | − | 0.153144i | \(-0.951060\pi\) |
0.451021 | + | 0.892513i | \(0.351060\pi\) | |||||||
\(608\) | 184886. | − | 569021.i | 0.500147 | − | 1.53929i | ||||
\(609\) | −23536.7 | − | 72438.5i | −0.0634616 | − | 0.195315i | ||||
\(610\) | −67832.7 | + | 49283.4i | −0.182297 | + | 0.132447i | ||||
\(611\) | 36753.4 | + | 50586.7i | 0.0984498 | + | 0.135505i | ||||
\(612\) | −2726.74 | + | 885.973i | −0.00728017 | + | 0.00236547i | ||||
\(613\) | 253103. | + | 82238.3i | 0.673561 | + | 0.218853i | 0.625774 | − | 0.780004i | \(-0.284783\pi\) |
0.0477869 | + | 0.998858i | \(0.484783\pi\) | |||||||
\(614\) | 217092. | + | 157726.i | 0.575846 | + | 0.418377i | ||||
\(615\) | − | 51021.6i | − | 0.134897i | ||||||
\(616\) | 47916.3 | + | 356651.i | 0.126276 | + | 0.939900i | ||||
\(617\) | −266633. | −0.700396 | −0.350198 | − | 0.936676i | \(-0.613886\pi\) | ||||
−0.350198 | + | 0.936676i | \(0.613886\pi\) | |||||||
\(618\) | −8130.27 | + | 11190.4i | −0.0212877 | + | 0.0293000i | ||||
\(619\) | 190706. | − | 586932.i | 0.497717 | − | 1.53182i | −0.314962 | − | 0.949104i | \(-0.601992\pi\) |
0.812679 | − | 0.582711i | \(-0.198008\pi\) | |||||||
\(620\) | −6940.12 | − | 21359.5i | −0.0180544 | − | 0.0555658i | ||||
\(621\) | 592563. | − | 430522.i | 1.53657 | − | 1.11638i | ||||
\(622\) | 85162.8 | + | 117217.i | 0.220125 | + | 0.302976i | ||||
\(623\) | 372106. | − | 120905.i | 0.958719 | − | 0.311507i | ||||
\(624\) | 125877. | + | 40900.0i | 0.323279 | + | 0.105040i | ||||
\(625\) | −173412. | − | 125991.i | −0.443934 | − | 0.322537i | ||||
\(626\) | − | 177415.i | − | 0.452731i | ||||||
\(627\) | 544321. | + | 293676.i | 1.38459 | + | 0.747022i | ||||
\(628\) | −87582.6 | −0.222075 | ||||||||
\(629\) | −32696.5 | + | 45002.8i | −0.0826418 | + | 0.113747i | ||||
\(630\) | 1799.02 | − | 5536.81i | 0.00453267 | − | 0.0139501i | ||||
\(631\) | 24299.7 | + | 74786.9i | 0.0610299 | + | 0.187831i | 0.976923 | − | 0.213591i | \(-0.0685161\pi\) |
−0.915893 | + | 0.401422i | \(0.868516\pi\) | |||||||
\(632\) | −348432. | + | 253150.i | −0.872335 | + | 0.633789i | ||||
\(633\) | 220987. | + | 304163.i | 0.551519 | + | 0.759100i | ||||
\(634\) | −189763. | + | 61657.8i | −0.472099 | + | 0.153394i | ||||
\(635\) | 106608. | + | 34639.0i | 0.264388 | + | 0.0859049i | ||||
\(636\) | −203009. | − | 147494.i | −0.501880 | − | 0.364637i | ||||
\(637\) | − | 136684.i | − | 0.336852i | ||||||
\(638\) | 30904.4 | + | 5643.07i | 0.0759240 | + | 0.0138635i | ||||
\(639\) | −3781.41 | −0.00926087 | ||||||||
\(640\) | 96613.3 | − | 132977.i | 0.235872 | − | 0.324650i | ||||
\(641\) | 169464. | − | 521557.i | 0.412441 | − | 1.26936i | −0.502079 | − | 0.864822i | \(-0.667431\pi\) |
0.914520 | − | 0.404541i | \(-0.132569\pi\) | |||||||
\(642\) | 38961.3 | + | 119911.i | 0.0945287 | + | 0.290929i | ||||
\(643\) | 103495. | − | 75193.8i | 0.250322 | − | 0.181870i | −0.455548 | − | 0.890211i | \(-0.650556\pi\) |
0.705870 | + | 0.708342i | \(0.250556\pi\) | |||||||
\(644\) | −437049. | − | 601546.i | −1.05380 | − | 1.45043i | ||||
\(645\) | 96326.9 | − | 31298.5i | 0.231541 | − | 0.0752323i | ||||
\(646\) | −37949.5 | − | 12330.5i | −0.0909371 | − | 0.0295473i | ||||
\(647\) | 575751. | + | 418308.i | 1.37539 | + | 0.999281i | 0.997294 | + | 0.0735150i | \(0.0234217\pi\) |
0.378098 | + | 0.925766i | \(0.376578\pi\) | |||||||
\(648\) | − | 306283.i | − | 0.729411i | ||||||
\(649\) | −525494. | + | 252360.i | −1.24761 | + | 0.599145i | ||||
\(650\) | 117018. | 0.276965 | ||||||||
\(651\) | −52261.0 | + | 71931.1i | −0.123315 | + | 0.169728i | ||||
\(652\) | −96426.4 | + | 296770.i | −0.226830 | + | 0.698111i | ||||
\(653\) | 74638.0 | + | 229712.i | 0.175039 | + | 0.538713i | 0.999635 | − | 0.0270077i | \(-0.00859788\pi\) |
−0.824597 | + | 0.565721i | \(0.808598\pi\) | |||||||
\(654\) | 37922.8 | − | 27552.5i | 0.0886634 | − | 0.0644177i | ||||
\(655\) | −160223. | − | 220528.i | −0.373458 | − | 0.514021i | ||||
\(656\) | 67021.8 | − | 21776.7i | 0.155743 | − | 0.0506040i | ||||
\(657\) | 28594.4 | + | 9290.88i | 0.0662445 | + | 0.0215241i | ||||
\(658\) | −40674.1 | − | 29551.5i | −0.0939434 | − | 0.0682539i | ||||
\(659\) | − | 165208.i | − | 0.380418i | −0.981744 | − | 0.190209i | \(-0.939084\pi\) | ||
0.981744 | − | 0.190209i | \(-0.0609165\pi\) | |||||||
\(660\) | 93611.2 | + | 98123.3i | 0.214902 | + | 0.225260i | ||||
\(661\) | −782672. | −1.79133 | −0.895667 | − | 0.444725i | \(-0.853302\pi\) | ||||
−0.895667 | + | 0.444725i | \(0.853302\pi\) | |||||||
\(662\) | 3586.49 | − | 4936.38i | 0.00818377 | − | 0.0112640i | ||||
\(663\) | 13312.1 | − | 40970.5i | 0.0302845 | − | 0.0932061i | ||||
\(664\) | −3612.63 | − | 11118.5i | −0.00819384 | − | 0.0252180i | ||||
\(665\) | −279726. | + | 203233.i | −0.632542 | + | 0.459569i | ||||
\(666\) | 8342.34 | + | 11482.2i | 0.0188079 | + | 0.0258868i | ||||
\(667\) | −137937. | + | 44818.4i | −0.310048 | + | 0.100741i | ||||
\(668\) | 259012. | + | 84158.0i | 0.580452 | + | 0.188600i | ||||
\(669\) | −21487.7 | − | 15611.8i | −0.0480108 | − | 0.0348819i | ||||
\(670\) | 3250.49i | 0.00724100i | ||||||||
\(671\) | 422729. | − | 403291.i | 0.938895 | − | 0.895721i | ||||
\(672\) | −519360. | −1.15009 | ||||||||
\(673\) | −198195. | + | 272792.i | −0.437586 | + | 0.602285i | −0.969673 | − | 0.244404i | \(-0.921408\pi\) |
0.532088 | + | 0.846689i | \(0.321408\pi\) | |||||||
\(674\) | 72685.4 | − | 223703.i | 0.160003 | − | 0.492437i | ||||
\(675\) | 122220. | + | 376154.i | 0.268246 | + | 0.825577i | ||||
\(676\) | −128475. | + | 93342.8i | −0.281142 | + | 0.204262i | ||||
\(677\) | 439699. | + | 605194.i | 0.959353 | + | 1.32044i | 0.947245 | + | 0.320510i | \(0.103854\pi\) |
0.0121078 | + | 0.999927i | \(0.496146\pi\) | |||||||
\(678\) | 71754.3 | − | 23314.4i | 0.156095 | − | 0.0507183i | ||||
\(679\) | 409563. | + | 133075.i | 0.888344 | + | 0.288640i | ||||
\(680\) | −15815.3 | − | 11490.5i | −0.0342027 | − | 0.0248497i | ||||
\(681\) | − | 591.087i | − | 0.00127455i | ||||||
\(682\) | −15875.5 | − | 33057.9i | −0.0341318 | − | 0.0710733i | ||||
\(683\) | −591342. | −1.26764 | −0.633822 | − | 0.773479i | \(-0.718515\pi\) | ||||
−0.633822 | + | 0.773479i | \(0.718515\pi\) | |||||||
\(684\) | 25536.7 | − | 35148.3i | 0.0545825 | − | 0.0751263i | ||||
\(685\) | −79186.1 | + | 243710.i | −0.168759 | + | 0.519388i | ||||
\(686\) | −42226.0 | − | 129958.i | −0.0897288 | − | 0.276157i | ||||
\(687\) | 95538.9 | − | 69413.1i | 0.202426 | − | 0.147071i | ||||
\(688\) | 82227.3 | + | 113176.i | 0.173716 | + | 0.239099i | ||||
\(689\) | −270942. | + | 88034.5i | −0.570740 | + | 0.185445i | ||||
\(690\) | 139535. | + | 45337.7i | 0.293080 | + | 0.0952273i | ||||
\(691\) | −187294. | − | 136077.i | −0.392253 | − | 0.284989i | 0.374125 | − | 0.927378i | \(-0.377943\pi\) |
−0.766378 | + | 0.642390i | \(0.777943\pi\) | |||||||
\(692\) | 87917.0i | 0.183595i | ||||||||
\(693\) | −7286.86 | + | 39906.6i | −0.0151731 | + | 0.0830957i | ||||
\(694\) | 162724. | 0.337856 | ||||||||
\(695\) | −126830. | + | 174566.i | −0.262574 | + | 0.361402i | ||||
\(696\) | −20165.1 | + | 62061.7i | −0.0416276 | + | 0.128116i | ||||
\(697\) | −7087.88 | − | 21814.3i | −0.0145899 | − | 0.0449030i | ||||
\(698\) | −77578.5 | + | 56364.1i | −0.159232 | + | 0.115689i | ||||
\(699\) | −266421. | − | 366698.i | −0.545274 | − | 0.750505i | ||||
\(700\) | 381856. | − | 124073.i | 0.779298 | − | 0.253209i | ||||
\(701\) | 46147.3 | + | 14994.2i | 0.0939097 | + | 0.0305131i | 0.355595 | − | 0.934640i | \(-0.384278\pi\) |
−0.261685 | + | 0.965153i | \(0.584278\pi\) | |||||||
\(702\) | −135470. | − | 98424.5i | −0.274896 | − | 0.199723i | ||||
\(703\) | − | 842929.i | − | 1.70561i | ||||||
\(704\) | −8067.26 | + | 14952.4i | −0.0162772 | + | 0.0301694i | ||||
\(705\) | −42333.8 | −0.0851743 | ||||||||
\(706\) | −3827.05 | + | 5267.48i | −0.00767811 | + | 0.0105680i | ||||
\(707\) | −279666. | + | 860722.i | −0.559500 | + | 1.72196i | ||||
\(708\) | −167471. | − | 515423.i | −0.334098 | − | 1.02825i | ||||
\(709\) | 472771. | − | 343488.i | 0.940499 | − | 0.683313i | −0.00804160 | − | 0.999968i | \(-0.502560\pi\) |
0.948541 | + | 0.316655i | \(0.102560\pi\) | |||||||
\(710\) | −6782.75 | − | 9335.66i | −0.0134552 | − | 0.0185195i | ||||
\(711\) | −46174.9 | + | 15003.1i | −0.0913412 | + | 0.0296785i | ||||
\(712\) | −318802. | − | 103585.i | −0.628871 | − | 0.204332i | ||||
\(713\) | 136971. | + | 99515.1i | 0.269432 | + | 0.195754i | ||||
\(714\) | 34637.5i | 0.0679439i | ||||||||
\(715\) | 152593. | − | 20501.0i | 0.298485 | − | 0.0401017i | ||||
\(716\) | 496212. | 0.967923 | ||||||||
\(717\) | 421436. | − | 580057.i | 0.819772 | − | 1.12832i | ||||
\(718\) | −46411.1 | + | 142839.i | −0.0900270 | + | 0.277075i | ||||
\(719\) | −81167.1 | − | 249807.i | −0.157008 | − | 0.483221i | 0.841351 | − | 0.540490i | \(-0.181761\pi\) |
−0.998359 | + | 0.0572683i | \(0.981761\pi\) | |||||||
\(720\) | 5477.64 | − | 3979.74i | 0.0105664 | − | 0.00767696i | ||||
\(721\) | 31670.9 | + | 43591.3i | 0.0609242 | + | 0.0838550i | ||||
\(722\) | 359047. | − | 116662.i | 0.688775 | − | 0.223797i | ||||
\(723\) | −202325. | − | 65739.5i | −0.387056 | − | 0.125762i | ||||
\(724\) | 231199. | + | 167976.i | 0.441071 | + | 0.320457i | ||||
\(725\) | − | 78317.1i | − | 0.148998i | ||||||
\(726\) | 172829. | + | 138443.i | 0.327902 | + | 0.262663i | ||||
\(727\) | 172573. | 0.326516 | 0.163258 | − | 0.986583i | \(-0.447800\pi\) | ||||
0.163258 | + | 0.986583i | \(0.447800\pi\) | |||||||
\(728\) | −223247. | + | 307274.i | −0.421234 | + | 0.579779i | ||||
\(729\) | 174083. | − | 535773.i | 0.327568 | − | 1.00815i | ||||
\(730\) | 28352.4 | + | 87259.8i | 0.0532040 | + | 0.163745i | ||||
\(731\) | 36836.6 | − | 26763.3i | 0.0689357 | − | 0.0500847i | ||||
\(732\) | 319257. | + | 439420.i | 0.595825 | + | 0.820082i | ||||
\(733\) | −174118. | + | 56574.4i | −0.324068 | + | 0.105296i | −0.466533 | − | 0.884504i | \(-0.654497\pi\) |
0.142465 | + | 0.989800i | \(0.454497\pi\) | |||||||
\(734\) | 41979.4 | + | 13639.9i | 0.0779191 | + | 0.0253175i | ||||
\(735\) | 74865.9 | + | 54393.2i | 0.138583 | + | 0.100686i | ||||
\(736\) | 988963.i | 1.82568i | ||||||||
\(737\) | −3015.91 | − | 22448.0i | −0.00555243 | − | 0.0413279i | ||||
\(738\) | −5852.22 | −0.0107450 | ||||||||
\(739\) | 177886. | − | 244839.i | 0.325726 | − | 0.448323i | −0.614479 | − | 0.788933i | \(-0.710634\pi\) |
0.940205 | + | 0.340610i | \(0.110634\pi\) | |||||||
\(740\) | 57114.4 | − | 175780.i | 0.104299 | − | 0.321001i | ||||
\(741\) | 201723. | + | 620840.i | 0.367383 | + | 1.13069i | ||||
\(742\) | 185315. | − | 134639.i | 0.336591 | − | 0.244547i | ||||
\(743\) | −271424. | − | 373583.i | −0.491666 | − | 0.676721i | 0.489028 | − | 0.872268i | \(-0.337352\pi\) |
−0.980694 | + | 0.195547i | \(0.937352\pi\) | |||||||
\(744\) | 72446.8 | − | 23539.4i | 0.130880 | − | 0.0425255i | ||||
\(745\) | −346886. | − | 112710.i | −0.624991 | − | 0.203072i | ||||
\(746\) | −271014. | − | 196904.i | −0.486984 | − | 0.353815i | ||||
\(747\) | − | 1317.89i | − | 0.00236178i | ||||||
\(748\) | 53654.7 | + | 28948.2i | 0.0958969 | + | 0.0517390i | ||||
\(749\) | 491142. | 0.875474 | ||||||||
\(750\) | −101927. | + | 140290.i | −0.181203 | + | 0.249405i | ||||
\(751\) | 185329. | − | 570383.i | 0.328596 | − | 1.01132i | −0.641195 | − | 0.767378i | \(-0.721561\pi\) |
0.969791 | − | 0.243937i | \(-0.0784390\pi\) | |||||||
\(752\) | −18068.6 | − | 55609.5i | −0.0319514 | − | 0.0983362i | ||||
\(753\) | −750054. | + | 544946.i | −1.32283 | + | 0.961089i | ||||
\(754\) | 19489.5 | + | 26825.0i | 0.0342814 | + | 0.0471843i | ||||
\(755\) | 86535.8 | − | 28117.2i | 0.151811 | − | 0.0493262i | ||||
\(756\) | −546428. | − | 177545.i | −0.956069 | − | 0.310646i | ||||
\(757\) | −506946. | − | 368318.i | −0.884647 | − | 0.642734i | 0.0498296 | − | 0.998758i | \(-0.484132\pi\) |
−0.934477 | + | 0.356024i | \(0.884132\pi\) | |||||||
\(758\) | 229717.i | 0.399812i | ||||||||
\(759\) | −1.00570e6 | − | 183639.i | −1.74576 | − | 0.318773i | ||||
\(760\) | 296230. | 0.512864 | ||||||||
\(761\) | 23646.8 | − | 32547.1i | 0.0408323 | − | 0.0562008i | −0.788113 | − | 0.615531i | \(-0.788942\pi\) |
0.828945 | + | 0.559330i | \(0.188942\pi\) | |||||||
\(762\) | −52583.0 | + | 161834.i | −0.0905598 | + | 0.278715i | ||||
\(763\) | −56426.1 | − | 173662.i | −0.0969240 | − | 0.298301i | ||||
\(764\) | 46046.1 | − | 33454.5i | 0.0788871 | − | 0.0573149i | ||||
\(765\) | −1295.32 | − | 1782.86i | −0.00221338 | − | 0.00304646i | ||||
\(766\) | −291064. | + | 94572.4i | −0.496056 | + | 0.161178i | ||||
\(767\) | −585164. | − | 190131.i | −0.994688 | − | 0.323194i | ||||
\(768\) | 186090. | + | 135202.i | 0.315501 | + | 0.229225i | ||||
\(769\) | 816302.i | 1.38038i | 0.723629 | + | 0.690189i | \(0.242473\pi\) | ||||
−0.723629 | + | 0.690189i | \(0.757527\pi\) | |||||||
\(770\) | −111593. | + | 53590.9i | −0.188216 | + | 0.0903878i | ||||
\(771\) | 778009. | 1.30881 | ||||||||
\(772\) | 143201. | − | 197099.i | 0.240277 | − | 0.330712i | ||||
\(773\) | −131828. | + | 405724.i | −0.220621 | + | 0.679002i | 0.778085 | + | 0.628159i | \(0.216191\pi\) |
−0.998707 | + | 0.0508439i | \(0.983809\pi\) | |||||||
\(774\) | −3589.97 | − | 11048.8i | −0.00599251 | − | 0.0184430i | ||||
\(775\) | −73962.3 | + | 53736.7i | −0.123142 | + | 0.0894680i | ||||
\(776\) | −216864. | − | 298487.i | −0.360134 | − | 0.495681i | ||||
\(777\) | −695895. | + | 226110.i | −1.15266 | + | 0.374523i | ||||
\(778\) | 40999.1 | + | 13321.4i | 0.0677353 | + | 0.0220085i | ||||
\(779\) | 281190. | + | 204297.i | 0.463367 | + | 0.336656i | ||||
\(780\) | 143135.i | 0.235264i | ||||||||
\(781\) | 55503.9 | + | 58179.2i | 0.0909959 | + | 0.0953818i | ||||
\(782\) | 65956.5 | 0.107856 | ||||||||
\(783\) | −65873.1 | + | 90666.6i | −0.107445 | + | 0.147885i | ||||
\(784\) | −39497.0 | + | 121559.i | −0.0642588 | + | 0.197768i | ||||
\(785\) | −20802.8 | − | 64024.5i | −0.0337585 | − | 0.103898i | ||||
\(786\) | 334768. | − | 243223.i | 0.541874 | − | 0.393695i | ||||
\(787\) | 459337. | + | 632224.i | 0.741621 | + | 1.02075i | 0.998524 | + | 0.0543170i | \(0.0172982\pi\) |
−0.256902 | + | 0.966437i | \(0.582702\pi\) | |||||||
\(788\) | 171507. | − | 55726.1i | 0.276204 | − | 0.0897442i | ||||
\(789\) | 900595. | + | 292621.i | 1.44669 | + | 0.470058i | ||||
\(790\) | −119865. | − | 87086.7i | −0.192060 | − | 0.139540i | ||||
\(791\) | − | 293899.i | − | 0.469726i | ||||||
\(792\) | 25147.1 | − | 23990.7i | 0.0400901 | − | 0.0382466i | ||||
\(793\) | 616646. | 0.980594 | ||||||||
\(794\) | −196508. | + | 270471.i | −0.311703 | + | 0.429022i | ||||
\(795\) | 59602.0 | − | 183436.i | 0.0943033 | − | 0.290236i | ||||
\(796\) | −171580. | − | 528067.i | −0.270794 | − | 0.833419i | ||||
\(797\) | −246599. | + | 179164.i | −0.388217 | + | 0.282056i | −0.764724 | − | 0.644358i | \(-0.777125\pi\) |
0.376508 | + | 0.926414i | \(0.377125\pi\) | |||||||
\(798\) | −308513. | − | 424632.i | −0.484471 | − | 0.666818i | ||||
\(799\) | −18099.8 | + | 5880.98i | −0.0283518 | + | 0.00921204i | ||||
\(800\) | −507889. | − | 165023.i | −0.793576 | − | 0.257849i | ||||
\(801\) | −30571.2 | − | 22211.3i | −0.0476483 | − | 0.0346185i | ||||
\(802\) | − | 196411.i | − | 0.305364i | ||||||
\(803\) | −276766. | − | 576314.i | −0.429221 | − | 0.893775i | ||||
\(804\) | 21056.6 | 0.0325744 | ||||||||
\(805\) | 335932. | − | 462371.i | 0.518394 | − | 0.713508i | ||||
\(806\) | 11960.8 | − | 36811.6i | 0.0184116 | − | 0.0566649i | ||||
\(807\) | −25180.0 | − | 77496.2i | −0.0386642 | − | 0.118996i | ||||
\(808\) | 627290. | − | 455753.i | 0.960828 | − | 0.698082i | ||||
\(809\) | −427633. | − | 588586.i | −0.653392 | − | 0.899317i | 0.345848 | − | 0.938290i | \(-0.387591\pi\) |
−0.999240 | + | 0.0389736i | \(0.987591\pi\) | |||||||
\(810\) | 100208. | − | 32559.5i | 0.152733 | − | 0.0496259i | ||||
\(811\) | 924592. | + | 300418.i | 1.40575 | + | 0.456756i | 0.911046 | − | 0.412304i | \(-0.135276\pi\) |
0.494706 | + | 0.869061i | \(0.335276\pi\) | |||||||
\(812\) | 92041.1 | + | 66871.8i | 0.139595 | + | 0.101422i | ||||
\(813\) | 706225.i | 1.06847i | ||||||||
\(814\) | 54211.3 | − | 296889.i | 0.0818166 | − | 0.448070i | ||||
\(815\) | −239848. | −0.361094 | ||||||||
\(816\) | −23678.2 | + | 32590.2i | −0.0355605 | + | 0.0489448i | ||||
\(817\) | −213212. | + | 656200.i | −0.319425 | + | 0.983088i | ||||
\(818\) | 146363. | + | 450460.i | 0.218739 | + | 0.673208i | ||||
\(819\) | −34639.0 | + | 25166.7i | −0.0516413 | + | 0.0375196i | ||||
\(820\) | 44795.4 | + | 61655.6i | 0.0666202 | + | 0.0916948i | ||||
\(821\) | 120294. | − | 39086.0i | 0.178468 | − | 0.0579876i | −0.218420 | − | 0.975855i | \(-0.570090\pi\) |
0.396888 | + | 0.917867i | \(0.370090\pi\) | |||||||
\(822\) | −369959. | − | 120207.i | −0.547532 | − | 0.177904i | ||||
\(823\) | 671667. | + | 487995.i | 0.991641 | + | 0.720469i | 0.960280 | − | 0.279039i | \(-0.0900158\pi\) |
0.0313612 | + | 0.999508i | \(0.490016\pi\) | |||||||
\(824\) | − | 46163.2i | − | 0.0679895i | ||||||
\(825\) | 262125. | − | 485843.i | 0.385125 | − | 0.713818i | ||||
\(826\) | 494712. | 0.725091 | ||||||||
\(827\) | 736162. | − | 1.01324e6i | 1.07637 | − | 1.48150i | 0.212919 | − | 0.977070i | \(-0.431703\pi\) |
0.863453 | − | 0.504429i | \(-0.168297\pi\) | |||||||
\(828\) | −22191.5 | + | 68298.5i | −0.0323688 | + | 0.0996209i | ||||
\(829\) | 164951. | + | 507668.i | 0.240020 | + | 0.738705i | 0.996416 | + | 0.0845907i | \(0.0269583\pi\) |
−0.756396 | + | 0.654114i | \(0.773042\pi\) | |||||||
\(830\) | 3253.66 | − | 2363.92i | 0.00472298 | − | 0.00343144i | ||||
\(831\) | −245541. | − | 337958.i | −0.355567 | − | 0.489396i | ||||
\(832\) | −17054.4 | + | 5541.32i | −0.0246371 | + | 0.00800509i | ||||
\(833\) | 39565.2 | + | 12855.5i | 0.0570194 | + | 0.0185267i | ||||
\(834\) | −264997. | − | 192531.i | −0.380985 | − | 0.276802i | ||||
\(835\) | 209332.i | 0.300236i | ||||||||
\(836\) | −915609. | + | 123013.i | −1.31008 | + | 0.176010i | ||||
\(837\) | 130823. | 0.186739 | ||||||||
\(838\) | 37278.4 | − | 51309.4i | 0.0530847 | − | 0.0730649i | ||||
\(839\) | −247517. | + | 761779.i | −0.351626 | + | 1.08219i | 0.606314 | + | 0.795225i | \(0.292647\pi\) |
−0.957940 | + | 0.286968i | \(0.907353\pi\) | |||||||
\(840\) | −79461.8 | − | 244558.i | −0.112616 | − | 0.346596i | ||||
\(841\) | −554249. | + | 402685.i | −0.783633 | + | 0.569343i | ||||
\(842\) | 148643. | + | 204589.i | 0.209662 | + | 0.288575i | ||||
\(843\) | −718642. | + | 233501.i | −1.01125 | + | 0.328574i | ||||
\(844\) | −534092. | − | 173537.i | −0.749776 | − | 0.243617i | ||||
\(845\) | −98751.0 | − | 71746.8i | −0.138302 | − | 0.100482i | ||||
\(846\) | 4855.72i | 0.00678443i | ||||||||
\(847\) | 720945. | − | 473641.i | 1.00493 | − | 0.660211i | ||||
\(848\) | 266400. | 0.370461 | ||||||||
\(849\) | 47818.9 | − | 65817.1i | 0.0663414 | − | 0.0913111i | ||||
\(850\) | −11005.8 | + | 33872.4i | −0.0152330 | + | 0.0468823i | ||||
\(851\) | 430557. | + | 1.32512e6i | 0.594528 | + | 1.82977i | ||||
\(852\) | −60476.3 | + | 43938.6i | −0.0833117 | + | 0.0605295i | ||||
\(853\) | −441124. | − | 607155.i | −0.606265 | − | 0.834453i | 0.389998 | − | 0.920816i | \(-0.372476\pi\) |
−0.996264 | + | 0.0863629i | \(0.972476\pi\) | |||||||
\(854\) | −471546. | + | 153214.i | −0.646559 | + | 0.210080i | ||||
\(855\) | 31759.6 | + | 10319.3i | 0.0434453 | + | 0.0141162i | ||||
\(856\) | −340423. | − | 247332.i | −0.464591 | − | 0.337545i | ||||
\(857\) | − | 918487.i | − | 1.25058i | −0.780392 | − | 0.625290i | \(-0.784981\pi\) | ||
0.780392 | − | 0.625290i | \(-0.215019\pi\) | |||||||
\(858\) | 31121.1 | + | 231641.i | 0.0422747 | + | 0.314659i | ||||
\(859\) | −997172. | −1.35140 | −0.675700 | − | 0.737177i | \(-0.736158\pi\) | ||||
−0.675700 | + | 0.737177i | \(0.736158\pi\) | |||||||
\(860\) | −88924.4 | + | 122394.i | −0.120233 | + | 0.165487i | ||||
\(861\) | 93233.5 | − | 286943.i | 0.125767 | − | 0.387070i | ||||
\(862\) | −446.646 | − | 1374.63i | −0.000601103 | − | 0.00185000i | ||||
\(863\) | 141638. | − | 102906.i | 0.190178 | − | 0.138172i | −0.488622 | − | 0.872495i | \(-0.662500\pi\) |
0.678800 | + | 0.734323i | \(0.262500\pi\) | |||||||
\(864\) | 449173. | + | 618234.i | 0.601709 | + | 0.828182i | ||||
\(865\) | −64268.9 | + | 20882.2i | −0.0858952 | + | 0.0279090i | ||||
\(866\) | −242063. | − | 78651.0i | −0.322770 | − | 0.104874i | ||||
\(867\) | −575772. | − | 418323.i | −0.765971 | − | 0.556510i | ||||
\(868\) | − | 132807.i | − | 0.176271i | ||||||
\(869\) | 908592. | + | 490210.i | 1.20318 | + | 0.649147i | ||||
\(870\) | −22448.7 | −0.0296587 | ||||||||
\(871\) | 14051.5 | − | 19340.2i | 0.0185219 | − | 0.0254932i | ||||
\(872\) | −48343.1 | + | 148785.i | −0.0635772 | + | 0.195670i | ||||
\(873\) | −12852.6 | − | 39556.2i | −0.0168641 | − | 0.0519022i | ||||
\(874\) | −808582. | + | 587469.i | −1.05853 | + | 0.769063i | ||||
\(875\) | 397049. | + | 546492.i | 0.518595 | + | 0.713785i | ||||
\(876\) | 565268. | − | 183667.i | 0.736625 | − | 0.239344i | ||||
\(877\) | −637584. | − | 207164.i | −0.828969 | − | 0.269348i | −0.136358 | − | 0.990660i | \(-0.543540\pi\) |
−0.692611 | + | 0.721311i | \(0.743540\pi\) | |||||||
\(878\) | 458328. | + | 332995.i | 0.594549 | + | 0.431965i | ||||
\(879\) | 675327.i | 0.874051i | ||||||||
\(880\) | −141632. | − | 25861.7i | −0.182893 | − | 0.0333958i | ||||
\(881\) | −1.11426e6 | −1.43561 | −0.717805 | − | 0.696244i | \(-0.754853\pi\) | ||||
−0.717805 | + | 0.696244i | \(0.754853\pi\) | |||||||
\(882\) | 6238.96 | − | 8587.19i | 0.00802001 | − | 0.0110386i | ||||
\(883\) | 135169. | − | 416006.i | 0.173362 | − | 0.533554i | −0.826193 | − | 0.563388i | \(-0.809498\pi\) |
0.999555 | + | 0.0298335i | \(0.00949771\pi\) | |||||||
\(884\) | 19884.2 | + | 61197.3i | 0.0254451 | + | 0.0783119i | ||||
\(885\) | 337005. | − | 244849.i | 0.430279 | − | 0.312616i | ||||
\(886\) | 11978.3 | + | 16486.7i | 0.0152591 | + | 0.0210023i | ||||
\(887\) | 733230. | − | 238241.i | 0.931950 | − | 0.302809i | 0.196590 | − | 0.980486i | \(-0.437013\pi\) |
0.735360 | + | 0.677677i | \(0.237013\pi\) | |||||||
\(888\) | 596208. | + | 193720.i | 0.756088 | + | 0.245668i | ||||
\(889\) | 536261. | + | 389617.i | 0.678536 | + | 0.492985i | ||||
\(890\) | − | 115316.i | − | 0.145582i | ||||||
\(891\) | −661831. | + | 317834.i | −0.833665 | + | 0.400354i | ||||
\(892\) | 39672.9 | 0.0498614 | ||||||||
\(893\) | 169510. | − | 233310.i | 0.212565 | − | 0.292571i | ||||
\(894\) | 171097. | − | 526583.i | 0.214076 | − | 0.658858i | ||||
\(895\) | 117861. | + | 362740.i | 0.147138 | + | 0.452844i | ||||
\(896\) | 786342. | − | 571311.i | 0.979480 | − | 0.711634i | ||||
\(897\) | −634235. | − | 872949.i | −0.788252 | − | 1.08494i | ||||
\(898\) | 582741. | − | 189344.i | 0.722641 | − | 0.234800i | ||||
\(899\) | −24637.1 | − | 8005.08i | −0.0304839 | − | 0.00990481i | ||||
\(900\) | −31372.2 | − | 22793.2i | −0.0387311 | − | 0.0281398i | ||||
\(901\) | − | 86708.0i | − | 0.106809i | ||||||
\(902\) | 85899.6 | + | 90039.9i | 0.105579 | + | 0.110668i | ||||
\(903\) | 598931. | 0.734516 | ||||||||
\(904\) | −148003. | + | 203708.i | −0.181106 | + | 0.249271i | ||||
\(905\) | −67878.4 | + | 208908.i | −0.0828771 | + | 0.255070i | ||||
\(906\) | 42682.7 | + | 131364.i | 0.0519991 | + | 0.160037i | ||||
\(907\) | 241833. | − | 175702.i | 0.293969 | − | 0.213581i | −0.431018 | − | 0.902343i | \(-0.641846\pi\) |
0.724987 | + | 0.688762i | \(0.241846\pi\) | |||||||
\(908\) | 518.957 | + | 714.283i | 0.000629447 | + | 0.000866360i | ||||
\(909\) | 83129.8 | − | 27010.5i | 0.100607 | − | 0.0326892i | ||||
\(910\) | −124265. | − | 40376.0i | −0.150060 | − | 0.0487574i | ||||
\(911\) | −763082. | − | 554411.i | −0.919463 | − | 0.668029i | 0.0239274 | − | 0.999714i | \(-0.492383\pi\) |
−0.943390 | + | 0.331685i | \(0.892383\pi\) | |||||||
\(912\) | − | 610433.i | − | 0.733919i | ||||||
\(913\) | −20276.6 | + | 19344.2i | −0.0243250 | + | 0.0232065i | ||||
\(914\) | 269726. | 0.322872 | ||||||||
\(915\) | −245393. | + | 337755.i | −0.293103 | + | 0.403422i | ||||
\(916\) | −54508.7 | + | 167761.i | −0.0649643 | + | 0.199940i | ||||
\(917\) | −498108. | − | 1.53302e6i | −0.592359 | − | 1.82309i | ||||
\(918\) | 41231.7 | − | 29956.6i | 0.0489267 | − | 0.0355473i | ||||
\(919\) | 23459.5 | + | 32289.3i | 0.0277772 | + | 0.0382320i | 0.822680 | − | 0.568505i | \(-0.192478\pi\) |
−0.794903 | + | 0.606737i | \(0.792478\pi\) | |||||||
\(920\) | −465686. | + | 151311.i | −0.550196 | + | 0.178770i | ||||
\(921\) | 1.27073e6 | + | 412886.i | 1.49808 | + | 0.486756i | ||||
\(922\) | −164680. | − | 119647.i | −0.193722 | − | 0.140747i | ||||
\(923\) | 84867.5i | 0.0996180i | ||||||||
\(924\) | 347162. | + | 722900.i | 0.406619 | + | 0.846709i | ||||
\(925\) | −752370. | −0.879322 | ||||||||
\(926\) | 40578.9 | − | 55852.1i | 0.0473237 | − | 0.0651355i | ||||
\(927\) | 1608.12 | − | 4949.28i | 0.00187136 | − | 0.00575947i | ||||
\(928\) | −46760.1 | − | 143913.i | −0.0542975 | − | 0.167110i | ||||
\(929\) | 602349. | − | 437632.i | 0.697938 | − | 0.507082i | −0.181322 | − | 0.983424i | \(-0.558038\pi\) |
0.879260 | + | 0.476342i | \(0.158038\pi\) | |||||||
\(930\) | 15403.0 | + | 21200.4i | 0.0178090 | + | 0.0245120i | ||||
\(931\) | −599545. | + | 194804.i | −0.691707 | + | 0.224749i | ||||
\(932\) | 643899. | + | 209215.i | 0.741286 | + | 0.240859i | ||||
\(933\) | 583648. | + | 424045.i | 0.670483 | + | 0.487134i | ||||
\(934\) | − | 165969.i | − | 0.190253i | ||||||
\(935\) | −8417.46 | + | 46098.4i | −0.00962849 | + | 0.0527306i | ||||
\(936\) | 36682.7 | 0.0418706 | ||||||||
\(937\) | −447603. | + | 616073.i | −0.509816 | + | 0.701702i | −0.983888 | − | 0.178784i | \(-0.942784\pi\) |
0.474072 | + | 0.880486i | \(0.342784\pi\) | |||||||
\(938\) | −5939.73 | + | 18280.6i | −0.00675089 | + | 0.0207771i | ||||
\(939\) | −272982. | − | 840152.i | −0.309601 | − | 0.952855i | ||||
\(940\) | 51157.1 | − | 37167.8i | 0.0578962 | − | 0.0420640i | ||||
\(941\) | 745350. | + | 1.02589e6i | 0.841746 | + | 1.15856i | 0.985621 | + | 0.168968i | \(0.0540435\pi\) |
−0.143875 | + | 0.989596i | \(0.545956\pi\) | |||||||
\(942\) | 97191.1 | − | 31579.3i | 0.109528 | − | 0.0355878i | ||||
\(943\) | −546395. | − | 177535.i | −0.614446 | − | 0.199646i | ||||
\(944\) | 465471. | + | 338185.i | 0.522335 | + | 0.379498i | ||||
\(945\) | − | 441620.i | − | 0.494521i | ||||||
\(946\) | −117298. | + | 217409.i | −0.131072 | + | 0.242938i | ||||
\(947\) | −334276. | −0.372740 | −0.186370 | − | 0.982480i | \(-0.559672\pi\) | ||||
−0.186370 | + | 0.982480i | \(0.559672\pi\) | |||||||
\(948\) | −564147. | + | 776482.i | −0.627734 | + | 0.864002i | ||||
\(949\) | 208518. | − | 641754.i | 0.231533 | − | 0.712584i | ||||
\(950\) | −166775. | − | 513281.i | −0.184792 | − | 0.568732i | ||||
\(951\) | −803758. | + | 583965.i | −0.888719 | + | 0.645692i | ||||
\(952\) | −67947.7 | − | 93522.0i | −0.0749723 | − | 0.103191i | ||||
\(953\) | 593076. | − | 192702.i | 0.653017 | − | 0.212178i | 0.0362728 | − | 0.999342i | \(-0.488451\pi\) |
0.616744 | + | 0.787164i | \(0.288451\pi\) | |||||||
\(954\) | −21040.3 | − | 6836.41i | −0.0231183 | − | 0.00751158i | ||||
\(955\) | 35392.8 | + | 25714.4i | 0.0388068 | + | 0.0281948i | ||||
\(956\) | 1.07096e6i | 1.17181i | ||||||||
\(957\) | 155031. | − | 20828.6i | 0.169276 | − | 0.0227424i | ||||
\(958\) | −611881. | −0.666709 | ||||||||
\(959\) | −890679. | + | 1.22591e6i | −0.968465 | + | 1.33298i | ||||
\(960\) | 3751.64 | − | 11546.4i | 0.00407079 | − | 0.0125286i | ||||
\(961\) | −276039. | − | 849561.i | −0.298899 | − | 0.919915i | ||||
\(962\) | 257700. | − | 187230.i | 0.278461 | − | 0.202314i | ||||
\(963\) | −27881.7 | − | 38375.9i | −0.0300654 | − | 0.0413814i | ||||
\(964\) | 302212. | − | 98194.6i | 0.325205 | − | 0.105666i | ||||
\(965\) | 178097. | + | 57867.1i | 0.191250 | + | 0.0621408i | ||||
\(966\) | 701893. | + | 509955.i | 0.752171 | + | 0.546484i | ||||
\(967\) | − | 183055.i | − | 0.195762i | −0.995198 | − | 0.0978809i | \(-0.968794\pi\) | ||
0.995198 | − | 0.0978809i | \(-0.0312064\pi\) | |||||||
\(968\) | −738223. | − | 34764.1i | −0.787838 | − | 0.0371006i | ||||
\(969\) | −198684. | −0.211599 | ||||||||
\(970\) | 74603.7 | − | 102683.i | 0.0792897 | − | 0.109133i | ||||
\(971\) | 254131. | − | 782134.i | 0.269537 | − | 0.829551i | −0.721076 | − | 0.692856i | \(-0.756352\pi\) |
0.990613 | − | 0.136695i | \(-0.0436479\pi\) | |||||||
\(972\) | 33169.6 | + | 102085.i | 0.0351081 | + | 0.108052i | ||||
\(973\) | −1.03228e6 | + | 749993.i | −1.09036 | + | 0.792194i | ||||
\(974\) | 168145. | + | 231432.i | 0.177242 | + | 0.243952i | ||||
\(975\) | 554141. | − | 180051.i | 0.582923 | − | 0.189403i | ||||
\(976\) | −548411. | − | 178190.i | −0.575714 | − | 0.187061i | ||||
\(977\) | −1.07719e6 | − | 782623.i | −1.12850 | − | 0.819905i | −0.143027 | − | 0.989719i | \(-0.545683\pi\) |
−0.985476 | + | 0.169814i | \(0.945683\pi\) | |||||||
\(978\) | − | 364096.i | − | 0.380660i | ||||||
\(979\) | 106994. | + | 796375.i | 0.111633 | + | 0.830907i | ||||
\(980\) | −138225. | −0.143925 | ||||||||
\(981\) | −10366.0 | + | 14267.5i | −0.0107714 | + | 0.0148256i | ||||
\(982\) | 97585.4 | − | 300337.i | 0.101196 | − | 0.311448i | ||||
\(983\) | 443474. | + | 1.36487e6i | 0.458945 | + | 1.41249i | 0.866440 | + | 0.499281i | \(0.166402\pi\) |
−0.407495 | + | 0.913207i | \(0.633598\pi\) | |||||||
\(984\) | −209123. | + | 151937.i | −0.215979 | + | 0.156918i | ||||
\(985\) | 81473.6 | + | 112139.i | 0.0839739 | + | 0.115580i | ||||
\(986\) | −9597.92 | + | 3118.55i | −0.00987241 | + | 0.00320774i | ||||
\(987\) | −238083. | − | 77357.9i | −0.244396 | − | 0.0794092i | ||||
\(988\) | −788846. | − | 573130.i | −0.808125 | − | 0.587137i | ||||
\(989\) | − | 1.14048e6i | − | 1.16599i | ||||||
\(990\) | 10522.4 | + | 5677.14i | 0.0107361 | + | 0.00579241i | ||||
\(991\) | −519599. | −0.529079 | −0.264540 | − | 0.964375i | \(-0.585220\pi\) | ||||
−0.264540 | + | 0.964375i | \(0.585220\pi\) | |||||||
\(992\) | −103826. | + | 142905.i | −0.105508 | + | 0.145219i | ||||
\(993\) | 9388.48 | − | 28894.8i | 0.00952131 | − | 0.0293036i | ||||
\(994\) | −21086.5 | − | 64897.7i | −0.0213419 | − | 0.0656835i | ||||
\(995\) | 345273. | − | 250855.i | 0.348752 | − | 0.253383i | ||||
\(996\) | −15313.5 | − | 21077.2i | −0.0154367 | − | 0.0212468i | ||||
\(997\) | 356006. | − | 115673.i | 0.358152 | − | 0.116370i | −0.124414 | − | 0.992230i | \(-0.539705\pi\) |
0.482565 | + | 0.875860i | \(0.339705\pi\) | |||||||
\(998\) | 192508. | + | 62549.7i | 0.193281 | + | 0.0628007i | ||||
\(999\) | 871008. | + | 632824.i | 0.872752 | + | 0.634092i |
(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 | 11.5.d.a.7.2 | ✓ | 12 | |
3.2 | odd | 2 | 99.5.k.a.73.2 | 12 | |||
4.3 | odd | 2 | 176.5.n.a.161.1 | 12 | |||
11.2 | odd | 10 | 121.5.d.e.94.2 | 12 | |||
11.3 | even | 5 | 121.5.d.d.118.2 | 12 | |||
11.4 | even | 5 | 121.5.d.e.112.2 | 12 | |||
11.5 | even | 5 | 121.5.b.b.120.7 | 12 | |||
11.6 | odd | 10 | 121.5.b.b.120.6 | 12 | |||
11.7 | odd | 10 | 121.5.d.c.112.2 | 12 | |||
11.8 | odd | 10 | inner | 11.5.d.a.8.2 | yes | 12 | |
11.9 | even | 5 | 121.5.d.c.94.2 | 12 | |||
11.10 | odd | 2 | 121.5.d.d.40.2 | 12 | |||
33.8 | even | 10 | 99.5.k.a.19.2 | 12 | |||
44.19 | even | 10 | 176.5.n.a.129.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
11.5.d.a.7.2 | ✓ | 12 | 1.1 | even | 1 | trivial | |
11.5.d.a.8.2 | yes | 12 | 11.8 | odd | 10 | inner | |
99.5.k.a.19.2 | 12 | 33.8 | even | 10 | |||
99.5.k.a.73.2 | 12 | 3.2 | odd | 2 | |||
121.5.b.b.120.6 | 12 | 11.6 | odd | 10 | |||
121.5.b.b.120.7 | 12 | 11.5 | even | 5 | |||
121.5.d.c.94.2 | 12 | 11.9 | even | 5 | |||
121.5.d.c.112.2 | 12 | 11.7 | odd | 10 | |||
121.5.d.d.40.2 | 12 | 11.10 | odd | 2 | |||
121.5.d.d.118.2 | 12 | 11.3 | even | 5 | |||
121.5.d.e.94.2 | 12 | 11.2 | odd | 10 | |||
121.5.d.e.112.2 | 12 | 11.4 | even | 5 | |||
176.5.n.a.129.1 | 12 | 44.19 | even | 10 | |||
176.5.n.a.161.1 | 12 | 4.3 | odd | 2 |