Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,3,Mod(22,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.22");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.l (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.86104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 22.9 | ||
Character | \(\chi\) | \(=\) | 105.22 |
Dual form | 105.3.l.a.43.9 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.08980 | + | 2.08980i | 1.04490 | + | 1.04490i | 0.998943 | + | 0.0459576i | \(0.0146339\pi\) |
0.0459576 | + | 0.998943i | \(0.485366\pi\) | |||||||
\(3\) | −1.22474 | + | 1.22474i | −0.408248 | + | 0.408248i | ||||
\(4\) | 4.73454i | 1.18364i | ||||||||
\(5\) | 0.137153 | + | 4.99812i | 0.0274307 | + | 0.999624i | ||||
\(6\) | −5.11895 | −0.853158 | ||||||||
\(7\) | −1.87083 | − | 1.87083i | −0.267261 | − | 0.267261i | ||||
\(8\) | −1.53505 | + | 1.53505i | −0.191882 | + | 0.191882i | ||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | −10.1585 | + | 10.7317i | −1.01585 | + | 1.07317i | ||||
\(11\) | 2.70159 | 0.245599 | 0.122800 | − | 0.992431i | \(-0.460813\pi\) | ||||
0.122800 | + | 0.992431i | \(0.460813\pi\) | |||||||
\(12\) | −5.79861 | − | 5.79861i | −0.483217 | − | 0.483217i | ||||
\(13\) | −2.37916 | + | 2.37916i | −0.183012 | + | 0.183012i | −0.792667 | − | 0.609655i | \(-0.791308\pi\) |
0.609655 | + | 0.792667i | \(0.291308\pi\) | |||||||
\(14\) | − | 7.81932i | − | 0.558523i | ||||||
\(15\) | −6.28940 | − | 5.95344i | −0.419293 | − | 0.396896i | ||||
\(16\) | 12.5223 | 0.782642 | ||||||||
\(17\) | 16.3715 | + | 16.3715i | 0.963027 | + | 0.963027i | 0.999340 | − | 0.0363138i | \(-0.0115616\pi\) |
−0.0363138 | + | 0.999340i | \(0.511562\pi\) | |||||||
\(18\) | 6.26941 | − | 6.26941i | 0.348300 | − | 0.348300i | ||||
\(19\) | − | 9.18722i | − | 0.483538i | −0.970334 | − | 0.241769i | \(-0.922272\pi\) | ||
0.970334 | − | 0.241769i | \(-0.0777276\pi\) | |||||||
\(20\) | −23.6638 | + | 0.649359i | −1.18319 | + | 0.0324679i | ||||
\(21\) | 4.58258 | 0.218218 | ||||||||
\(22\) | 5.64579 | + | 5.64579i | 0.256627 | + | 0.256627i | ||||
\(23\) | 21.4530 | − | 21.4530i | 0.932740 | − | 0.932740i | −0.0651365 | − | 0.997876i | \(-0.520748\pi\) |
0.997876 | + | 0.0651365i | \(0.0207483\pi\) | |||||||
\(24\) | − | 3.76010i | − | 0.156671i | ||||||
\(25\) | −24.9624 | + | 1.37102i | −0.998495 | + | 0.0548407i | ||||
\(26\) | −9.94394 | −0.382459 | ||||||||
\(27\) | 3.67423 | + | 3.67423i | 0.136083 | + | 0.136083i | ||||
\(28\) | 8.85752 | − | 8.85752i | 0.316340 | − | 0.316340i | ||||
\(29\) | − | 52.3515i | − | 1.80523i | −0.430453 | − | 0.902613i | \(-0.641646\pi\) | ||
0.430453 | − | 0.902613i | \(-0.358354\pi\) | |||||||
\(30\) | −0.702081 | − | 25.5851i | −0.0234027 | − | 0.852837i | ||||
\(31\) | −5.01849 | −0.161887 | −0.0809434 | − | 0.996719i | \(-0.525793\pi\) | ||||
−0.0809434 | + | 0.996719i | \(0.525793\pi\) | |||||||
\(32\) | 32.3093 | + | 32.3093i | 1.00966 | + | 1.00966i | ||||
\(33\) | −3.30876 | + | 3.30876i | −0.100265 | + | 0.100265i | ||||
\(34\) | 68.4262i | 2.01253i | ||||||||
\(35\) | 9.09403 | − | 9.60721i | 0.259830 | − | 0.274492i | ||||
\(36\) | 14.2036 | 0.394545 | ||||||||
\(37\) | 23.2257 | + | 23.2257i | 0.627721 | + | 0.627721i | 0.947494 | − | 0.319773i | \(-0.103607\pi\) |
−0.319773 | + | 0.947494i | \(0.603607\pi\) | |||||||
\(38\) | 19.1995 | − | 19.1995i | 0.505249 | − | 0.505249i | ||||
\(39\) | − | 5.82772i | − | 0.149429i | ||||||
\(40\) | −7.88291 | − | 7.46184i | −0.197073 | − | 0.186546i | ||||
\(41\) | −60.5336 | −1.47643 | −0.738215 | − | 0.674566i | \(-0.764331\pi\) | ||||
−0.738215 | + | 0.674566i | \(0.764331\pi\) | |||||||
\(42\) | 9.57668 | + | 9.57668i | 0.228016 | + | 0.228016i | ||||
\(43\) | −8.78639 | + | 8.78639i | −0.204335 | + | 0.204335i | −0.801854 | − | 0.597520i | \(-0.796153\pi\) |
0.597520 | + | 0.801854i | \(0.296153\pi\) | |||||||
\(44\) | 12.7908i | 0.290700i | ||||||||
\(45\) | 14.9944 | − | 0.411460i | 0.333208 | − | 0.00914356i | ||||
\(46\) | 89.6651 | 1.94924 | ||||||||
\(47\) | 2.24235 | + | 2.24235i | 0.0477096 | + | 0.0477096i | 0.730559 | − | 0.682850i | \(-0.239260\pi\) |
−0.682850 | + | 0.730559i | \(0.739260\pi\) | |||||||
\(48\) | −15.3366 | + | 15.3366i | −0.319512 | + | 0.319512i | ||||
\(49\) | 7.00000i | 0.142857i | ||||||||
\(50\) | −55.0316 | − | 49.3013i | −1.10063 | − | 0.986025i | ||||
\(51\) | −40.1017 | −0.786308 | ||||||||
\(52\) | −11.2642 | − | 11.2642i | −0.216620 | − | 0.216620i | ||||
\(53\) | −25.6733 | + | 25.6733i | −0.484401 | + | 0.484401i | −0.906534 | − | 0.422133i | \(-0.861282\pi\) |
0.422133 | + | 0.906534i | \(0.361282\pi\) | |||||||
\(54\) | 15.3568i | 0.284386i | ||||||||
\(55\) | 0.370533 | + | 13.5029i | 0.00673696 | + | 0.245507i | ||||
\(56\) | 5.74364 | 0.102565 | ||||||||
\(57\) | 11.2520 | + | 11.2520i | 0.197404 | + | 0.197404i | ||||
\(58\) | 109.404 | − | 109.404i | 1.88628 | − | 1.88628i | ||||
\(59\) | − | 100.980i | − | 1.71152i | −0.517374 | − | 0.855759i | \(-0.673091\pi\) | ||
0.517374 | − | 0.855759i | \(-0.326909\pi\) | |||||||
\(60\) | 28.1868 | − | 29.7774i | 0.469781 | − | 0.496291i | ||||
\(61\) | −82.1567 | −1.34683 | −0.673415 | − | 0.739264i | \(-0.735173\pi\) | ||||
−0.673415 | + | 0.739264i | \(0.735173\pi\) | |||||||
\(62\) | −10.4877 | − | 10.4877i | −0.169156 | − | 0.169156i | ||||
\(63\) | −5.61249 | + | 5.61249i | −0.0890871 | + | 0.0890871i | ||||
\(64\) | 84.9509i | 1.32736i | ||||||||
\(65\) | −12.2176 | − | 11.5650i | −0.187963 | − | 0.177923i | ||||
\(66\) | −13.8293 | −0.209535 | ||||||||
\(67\) | −65.1606 | − | 65.1606i | −0.972546 | − | 0.972546i | 0.0270874 | − | 0.999633i | \(-0.491377\pi\) |
−0.999633 | + | 0.0270874i | \(0.991377\pi\) | |||||||
\(68\) | −77.5114 | + | 77.5114i | −1.13987 | + | 1.13987i | ||||
\(69\) | 52.5489i | 0.761579i | ||||||||
\(70\) | 39.0819 | − | 1.07245i | 0.558313 | − | 0.0153207i | ||||
\(71\) | −22.8905 | −0.322402 | −0.161201 | − | 0.986922i | \(-0.551537\pi\) | ||||
−0.161201 | + | 0.986922i | \(0.551537\pi\) | |||||||
\(72\) | 4.60516 | + | 4.60516i | 0.0639605 | + | 0.0639605i | ||||
\(73\) | −5.38609 | + | 5.38609i | −0.0737820 | + | 0.0737820i | −0.743035 | − | 0.669253i | \(-0.766614\pi\) |
0.669253 | + | 0.743035i | \(0.266614\pi\) | |||||||
\(74\) | 97.0741i | 1.31181i | ||||||||
\(75\) | 28.8934 | − | 32.2517i | 0.385245 | − | 0.430023i | ||||
\(76\) | 43.4973 | 0.572333 | ||||||||
\(77\) | −5.05422 | − | 5.05422i | −0.0656392 | − | 0.0656392i | ||||
\(78\) | 12.1788 | − | 12.1788i | 0.156138 | − | 0.156138i | ||||
\(79\) | 117.836i | 1.49159i | 0.666175 | + | 0.745795i | \(0.267930\pi\) | ||||
−0.666175 | + | 0.745795i | \(0.732070\pi\) | |||||||
\(80\) | 1.71747 | + | 62.5878i | 0.0214684 | + | 0.782347i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | −126.503 | − | 126.503i | −1.54272 | − | 1.54272i | ||||
\(83\) | 85.5086 | − | 85.5086i | 1.03022 | − | 1.03022i | 0.0306951 | − | 0.999529i | \(-0.490228\pi\) |
0.999529 | − | 0.0306951i | \(-0.00977210\pi\) | |||||||
\(84\) | 21.6964i | 0.258291i | ||||||||
\(85\) | −79.5811 | + | 84.0719i | −0.936248 | + | 0.989081i | ||||
\(86\) | −36.7236 | −0.427019 | ||||||||
\(87\) | 64.1173 | + | 64.1173i | 0.736980 | + | 0.736980i | ||||
\(88\) | −4.14709 | + | 4.14709i | −0.0471260 | + | 0.0471260i | ||||
\(89\) | 119.010i | 1.33719i | 0.743629 | + | 0.668593i | \(0.233103\pi\) | ||||
−0.743629 | + | 0.668593i | \(0.766897\pi\) | |||||||
\(90\) | 32.1951 | + | 30.4754i | 0.357723 | + | 0.338615i | ||||
\(91\) | 8.90199 | 0.0978241 | ||||||||
\(92\) | 101.570 | + | 101.570i | 1.10402 | + | 1.10402i | ||||
\(93\) | 6.14637 | − | 6.14637i | 0.0660900 | − | 0.0660900i | ||||
\(94\) | 9.37213i | 0.0997035i | ||||||||
\(95\) | 45.9188 | − | 1.26006i | 0.483356 | − | 0.0132638i | ||||
\(96\) | −79.1412 | −0.824388 | ||||||||
\(97\) | −55.1059 | − | 55.1059i | −0.568102 | − | 0.568102i | 0.363494 | − | 0.931596i | \(-0.381584\pi\) |
−0.931596 | + | 0.363494i | \(0.881584\pi\) | |||||||
\(98\) | −14.6286 | + | 14.6286i | −0.149272 | + | 0.149272i | ||||
\(99\) | − | 8.10478i | − | 0.0818664i | ||||||
\(100\) | −6.49114 | − | 118.185i | −0.0649114 | − | 1.18185i | ||||
\(101\) | 128.322 | 1.27052 | 0.635259 | − | 0.772299i | \(-0.280893\pi\) | ||||
0.635259 | + | 0.772299i | \(0.280893\pi\) | |||||||
\(102\) | −83.8046 | − | 83.8046i | −0.821614 | − | 0.821614i | ||||
\(103\) | 10.5985 | − | 10.5985i | 0.102898 | − | 0.102898i | −0.653783 | − | 0.756682i | \(-0.726819\pi\) |
0.756682 | + | 0.653783i | \(0.226819\pi\) | |||||||
\(104\) | − | 7.30426i | − | 0.0702333i | ||||||
\(105\) | 0.628516 | + | 22.9043i | 0.00598586 | + | 0.218136i | ||||
\(106\) | −107.304 | −1.01230 | ||||||||
\(107\) | 138.356 | + | 138.356i | 1.29305 | + | 1.29305i | 0.932894 | + | 0.360151i | \(0.117275\pi\) |
0.360151 | + | 0.932894i | \(0.382725\pi\) | |||||||
\(108\) | −17.3958 | + | 17.3958i | −0.161072 | + | 0.161072i | ||||
\(109\) | − | 161.387i | − | 1.48061i | −0.672271 | − | 0.740305i | \(-0.734681\pi\) | ||
0.672271 | − | 0.740305i | \(-0.265319\pi\) | |||||||
\(110\) | −27.4440 | + | 28.9927i | −0.249491 | + | 0.263570i | ||||
\(111\) | −56.8911 | −0.512532 | ||||||||
\(112\) | −23.4270 | − | 23.4270i | −0.209170 | − | 0.209170i | ||||
\(113\) | −34.2178 | + | 34.2178i | −0.302812 | + | 0.302812i | −0.842113 | − | 0.539301i | \(-0.818689\pi\) |
0.539301 | + | 0.842113i | \(0.318689\pi\) | |||||||
\(114\) | 47.0289i | 0.412534i | ||||||||
\(115\) | 110.167 | + | 104.282i | 0.957975 | + | 0.906803i | ||||
\(116\) | 247.861 | 2.13673 | ||||||||
\(117\) | 7.13747 | + | 7.13747i | 0.0610040 | + | 0.0610040i | ||||
\(118\) | 211.027 | − | 211.027i | 1.78837 | − | 1.78837i | ||||
\(119\) | − | 61.2564i | − | 0.514759i | ||||||
\(120\) | 18.7934 | − | 0.515710i | 0.156612 | − | 0.00429758i | ||||
\(121\) | −113.701 | −0.939681 | ||||||||
\(122\) | −171.691 | − | 171.691i | −1.40730 | − | 1.40730i | ||||
\(123\) | 74.1383 | − | 74.1383i | 0.602750 | − | 0.602750i | ||||
\(124\) | − | 23.7603i | − | 0.191615i | ||||||
\(125\) | −10.2762 | − | 124.577i | −0.0822095 | − | 0.996615i | ||||
\(126\) | −23.4580 | −0.186174 | ||||||||
\(127\) | −13.3778 | − | 13.3778i | −0.105337 | − | 0.105337i | 0.652474 | − | 0.757811i | \(-0.273731\pi\) |
−0.757811 | + | 0.652474i | \(0.773731\pi\) | |||||||
\(128\) | −48.2934 | + | 48.2934i | −0.377292 | + | 0.377292i | ||||
\(129\) | − | 21.5222i | − | 0.166838i | ||||||
\(130\) | −1.36384 | − | 49.7010i | −0.0104911 | − | 0.382315i | ||||
\(131\) | 27.9162 | 0.213101 | 0.106550 | − | 0.994307i | \(-0.466019\pi\) | ||||
0.106550 | + | 0.994307i | \(0.466019\pi\) | |||||||
\(132\) | −15.6655 | − | 15.6655i | −0.118678 | − | 0.118678i | ||||
\(133\) | −17.1877 | + | 17.1877i | −0.129231 | + | 0.129231i | ||||
\(134\) | − | 272.345i | − | 2.03243i | ||||||
\(135\) | −17.8603 | + | 18.8682i | −0.132299 | + | 0.139764i | ||||
\(136\) | −50.2621 | −0.369574 | ||||||||
\(137\) | 69.2726 | + | 69.2726i | 0.505639 | + | 0.505639i | 0.913185 | − | 0.407546i | \(-0.133615\pi\) |
−0.407546 | + | 0.913185i | \(0.633615\pi\) | |||||||
\(138\) | −109.817 | + | 109.817i | −0.795775 | + | 0.795775i | ||||
\(139\) | − | 233.891i | − | 1.68267i | −0.540513 | − | 0.841335i | \(-0.681770\pi\) | ||
0.540513 | − | 0.841335i | \(-0.318230\pi\) | |||||||
\(140\) | 45.4858 | + | 43.0561i | 0.324898 | + | 0.307544i | ||||
\(141\) | −5.49261 | −0.0389547 | ||||||||
\(142\) | −47.8367 | − | 47.8367i | −0.336878 | − | 0.336878i | ||||
\(143\) | −6.42751 | + | 6.42751i | −0.0449477 | + | 0.0449477i | ||||
\(144\) | − | 37.5668i | − | 0.260881i | ||||||
\(145\) | 261.659 | − | 7.18019i | 1.80455 | − | 0.0495186i | ||||
\(146\) | −22.5117 | −0.154190 | ||||||||
\(147\) | −8.57321 | − | 8.57321i | −0.0583212 | − | 0.0583212i | ||||
\(148\) | −109.963 | + | 109.963i | −0.742993 | + | 0.742993i | ||||
\(149\) | 127.594i | 0.856336i | 0.903699 | + | 0.428168i | \(0.140841\pi\) | ||||
−0.903699 | + | 0.428168i | \(0.859159\pi\) | |||||||
\(150\) | 127.781 | − | 7.01817i | 0.851874 | − | 0.0467878i | ||||
\(151\) | 49.1914 | 0.325771 | 0.162886 | − | 0.986645i | \(-0.447920\pi\) | ||||
0.162886 | + | 0.986645i | \(0.447920\pi\) | |||||||
\(152\) | 14.1029 | + | 14.1029i | 0.0927821 | + | 0.0927821i | ||||
\(153\) | 49.1144 | − | 49.1144i | 0.321009 | − | 0.321009i | ||||
\(154\) | − | 21.1246i | − | 0.137173i | ||||||
\(155\) | −0.688303 | − | 25.0830i | −0.00444067 | − | 0.161826i | ||||
\(156\) | 27.5916 | 0.176869 | ||||||||
\(157\) | 130.828 | + | 130.828i | 0.833301 | + | 0.833301i | 0.987967 | − | 0.154666i | \(-0.0494302\pi\) |
−0.154666 | + | 0.987967i | \(0.549430\pi\) | |||||||
\(158\) | −246.253 | + | 246.253i | −1.55856 | + | 1.55856i | ||||
\(159\) | − | 62.8864i | − | 0.395512i | ||||||
\(160\) | −157.054 | + | 165.917i | −0.981589 | + | 1.03698i | ||||
\(161\) | −80.2698 | −0.498570 | ||||||||
\(162\) | −18.8082 | − | 18.8082i | −0.116100 | − | 0.116100i | ||||
\(163\) | −35.5824 | + | 35.5824i | −0.218297 | + | 0.218297i | −0.807780 | − | 0.589483i | \(-0.799331\pi\) |
0.589483 | + | 0.807780i | \(0.299331\pi\) | |||||||
\(164\) | − | 286.599i | − | 1.74756i | ||||||
\(165\) | −16.9914 | − | 16.0838i | −0.102978 | − | 0.0974774i | ||||
\(166\) | 357.392 | 2.15296 | ||||||||
\(167\) | 27.7479 | + | 27.7479i | 0.166155 | + | 0.166155i | 0.785287 | − | 0.619132i | \(-0.212515\pi\) |
−0.619132 | + | 0.785287i | \(0.712515\pi\) | |||||||
\(168\) | −7.03449 | + | 7.03449i | −0.0418720 | + | 0.0418720i | ||||
\(169\) | 157.679i | 0.933013i | ||||||||
\(170\) | −342.002 | + | 9.38488i | −2.01178 | + | 0.0552052i | ||||
\(171\) | −27.5617 | −0.161179 | ||||||||
\(172\) | −41.5995 | − | 41.5995i | −0.241858 | − | 0.241858i | ||||
\(173\) | −190.785 | + | 190.785i | −1.10280 | + | 1.10280i | −0.108732 | + | 0.994071i | \(0.534679\pi\) |
−0.994071 | + | 0.108732i | \(0.965321\pi\) | |||||||
\(174\) | 267.985i | 1.54014i | ||||||||
\(175\) | 49.2653 | + | 44.1354i | 0.281516 | + | 0.252202i | ||||
\(176\) | 33.8301 | 0.192216 | ||||||||
\(177\) | 123.674 | + | 123.674i | 0.698724 | + | 0.698724i | ||||
\(178\) | −248.706 | + | 248.706i | −1.39723 | + | 1.39723i | ||||
\(179\) | − | 180.379i | − | 1.00770i | −0.863791 | − | 0.503851i | \(-0.831916\pi\) | ||
0.863791 | − | 0.503851i | \(-0.168084\pi\) | |||||||
\(180\) | 1.94808 | + | 70.9914i | 0.0108226 | + | 0.394397i | ||||
\(181\) | −20.8061 | −0.114951 | −0.0574754 | − | 0.998347i | \(-0.518305\pi\) | ||||
−0.0574754 | + | 0.998347i | \(0.518305\pi\) | |||||||
\(182\) | 18.6034 | + | 18.6034i | 0.102217 | + | 0.102217i | ||||
\(183\) | 100.621 | − | 100.621i | 0.549841 | − | 0.549841i | ||||
\(184\) | 65.8630i | 0.357951i | ||||||||
\(185\) | −112.899 | + | 119.270i | −0.610266 | + | 0.644704i | ||||
\(186\) | 25.6894 | 0.138115 | ||||||||
\(187\) | 44.2290 | + | 44.2290i | 0.236519 | + | 0.236519i | ||||
\(188\) | −10.6165 | + | 10.6165i | −0.0564708 | + | 0.0564708i | ||||
\(189\) | − | 13.7477i | − | 0.0727393i | ||||||
\(190\) | 98.5946 | + | 93.3280i | 0.518919 | + | 0.491200i | ||||
\(191\) | 221.603 | 1.16022 | 0.580112 | − | 0.814536i | \(-0.303009\pi\) | ||||
0.580112 | + | 0.814536i | \(0.303009\pi\) | |||||||
\(192\) | −104.043 | − | 104.043i | −0.541891 | − | 0.541891i | ||||
\(193\) | −188.688 | + | 188.688i | −0.977659 | + | 0.977659i | −0.999756 | − | 0.0220973i | \(-0.992966\pi\) |
0.0220973 | + | 0.999756i | \(0.492966\pi\) | |||||||
\(194\) | − | 230.321i | − | 1.18722i | ||||||
\(195\) | 29.1276 | − | 0.799292i | 0.149373 | − | 0.00409893i | ||||
\(196\) | −33.1418 | −0.169091 | ||||||||
\(197\) | 85.7353 | + | 85.7353i | 0.435205 | + | 0.435205i | 0.890394 | − | 0.455190i | \(-0.150429\pi\) |
−0.455190 | + | 0.890394i | \(0.650429\pi\) | |||||||
\(198\) | 16.9374 | − | 16.9374i | 0.0855423 | − | 0.0855423i | ||||
\(199\) | − | 106.621i | − | 0.535783i | −0.963449 | − | 0.267892i | \(-0.913673\pi\) | ||
0.963449 | − | 0.267892i | \(-0.0863269\pi\) | |||||||
\(200\) | 36.2140 | − | 40.4231i | 0.181070 | − | 0.202116i | ||||
\(201\) | 159.610 | 0.794080 | ||||||||
\(202\) | 268.168 | + | 268.168i | 1.32756 | + | 1.32756i | ||||
\(203\) | −97.9408 | + | 97.9408i | −0.482467 | + | 0.482467i | ||||
\(204\) | − | 189.863i | − | 0.930703i | ||||||
\(205\) | −8.30239 | − | 302.554i | −0.0404995 | − | 1.47587i | ||||
\(206\) | 44.2976 | 0.215037 | ||||||||
\(207\) | −64.3590 | − | 64.3590i | −0.310913 | − | 0.310913i | ||||
\(208\) | −29.7924 | + | 29.7924i | −0.143233 | + | 0.143233i | ||||
\(209\) | − | 24.8201i | − | 0.118757i | ||||||
\(210\) | −46.5519 | + | 49.1788i | −0.221676 | + | 0.234185i | ||||
\(211\) | −210.119 | −0.995827 | −0.497913 | − | 0.867227i | \(-0.665900\pi\) | ||||
−0.497913 | + | 0.867227i | \(0.665900\pi\) | |||||||
\(212\) | −121.551 | − | 121.551i | −0.573355 | − | 0.573355i | ||||
\(213\) | 28.0351 | − | 28.0351i | 0.131620 | − | 0.131620i | ||||
\(214\) | 578.273i | 2.70221i | ||||||||
\(215\) | −45.1205 | − | 42.7103i | −0.209863 | − | 0.198653i | ||||
\(216\) | −11.2803 | −0.0522235 | ||||||||
\(217\) | 9.38874 | + | 9.38874i | 0.0432661 | + | 0.0432661i | ||||
\(218\) | 337.266 | − | 337.266i | 1.54709 | − | 1.54709i | ||||
\(219\) | − | 13.1932i | − | 0.0602428i | ||||||
\(220\) | −63.9300 | + | 1.75430i | −0.290591 | + | 0.00797410i | ||||
\(221\) | −77.9005 | −0.352491 | ||||||||
\(222\) | −118.891 | − | 118.891i | −0.535545 | − | 0.535545i | ||||
\(223\) | −138.303 | + | 138.303i | −0.620191 | + | 0.620191i | −0.945580 | − | 0.325389i | \(-0.894505\pi\) |
0.325389 | + | 0.945580i | \(0.394505\pi\) | |||||||
\(224\) | − | 120.890i | − | 0.539688i | ||||||
\(225\) | 4.11305 | + | 74.8871i | 0.0182802 | + | 0.332832i | ||||
\(226\) | −143.017 | −0.632818 | ||||||||
\(227\) | −286.401 | − | 286.401i | −1.26168 | − | 1.26168i | −0.950280 | − | 0.311397i | \(-0.899203\pi\) |
−0.311397 | − | 0.950280i | \(-0.600797\pi\) | |||||||
\(228\) | −53.2731 | + | 53.2731i | −0.233654 | + | 0.233654i | ||||
\(229\) | − | 210.860i | − | 0.920787i | −0.887715 | − | 0.460394i | \(-0.847708\pi\) | ||
0.887715 | − | 0.460394i | \(-0.152292\pi\) | |||||||
\(230\) | 12.2979 | + | 448.157i | 0.0534690 | + | 1.94851i | ||||
\(231\) | 12.3803 | 0.0535942 | ||||||||
\(232\) | 80.3624 | + | 80.3624i | 0.346389 | + | 0.346389i | ||||
\(233\) | 217.881 | − | 217.881i | 0.935112 | − | 0.935112i | −0.0629077 | − | 0.998019i | \(-0.520037\pi\) |
0.998019 | + | 0.0629077i | \(0.0200374\pi\) | |||||||
\(234\) | 29.8318i | 0.127486i | ||||||||
\(235\) | −10.9000 | + | 11.5151i | −0.0463829 | + | 0.0490003i | ||||
\(236\) | 478.092 | 2.02581 | ||||||||
\(237\) | −144.319 | − | 144.319i | −0.608939 | − | 0.608939i | ||||
\(238\) | 128.014 | − | 128.014i | 0.537873 | − | 0.537873i | ||||
\(239\) | 103.424i | 0.432737i | 0.976312 | + | 0.216369i | \(0.0694213\pi\) | ||||
−0.976312 | + | 0.216369i | \(0.930579\pi\) | |||||||
\(240\) | −78.7575 | − | 74.5506i | −0.328156 | − | 0.310627i | ||||
\(241\) | −13.3346 | −0.0553304 | −0.0276652 | − | 0.999617i | \(-0.508807\pi\) | ||||
−0.0276652 | + | 0.999617i | \(0.508807\pi\) | |||||||
\(242\) | −237.613 | − | 237.613i | −0.981874 | − | 0.981874i | ||||
\(243\) | 11.0227 | − | 11.0227i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | − | 388.974i | − | 1.59416i | ||||||
\(245\) | −34.9868 | + | 0.960074i | −0.142803 | + | 0.00391867i | ||||
\(246\) | 309.869 | 1.25963 | ||||||||
\(247\) | 21.8579 | + | 21.8579i | 0.0884934 | + | 0.0884934i | ||||
\(248\) | 7.70365 | − | 7.70365i | 0.0310631 | − | 0.0310631i | ||||
\(249\) | 209.452i | 0.841174i | ||||||||
\(250\) | 238.866 | − | 281.816i | 0.955463 | − | 1.12726i | ||||
\(251\) | −324.833 | −1.29416 | −0.647078 | − | 0.762424i | \(-0.724009\pi\) | ||||
−0.647078 | + | 0.762424i | \(0.724009\pi\) | |||||||
\(252\) | −26.5726 | − | 26.5726i | −0.105447 | − | 0.105447i | ||||
\(253\) | 57.9573 | − | 57.9573i | 0.229080 | − | 0.229080i | ||||
\(254\) | − | 55.9141i | − | 0.220134i | ||||||
\(255\) | −5.50009 | − | 200.433i | −0.0215690 | − | 0.786012i | ||||
\(256\) | 137.956 | 0.538891 | ||||||||
\(257\) | 45.5488 | + | 45.5488i | 0.177233 | + | 0.177233i | 0.790148 | − | 0.612916i | \(-0.210003\pi\) |
−0.612916 | + | 0.790148i | \(0.710003\pi\) | |||||||
\(258\) | 44.9771 | − | 44.9771i | 0.174330 | − | 0.174330i | ||||
\(259\) | − | 86.9025i | − | 0.335531i | ||||||
\(260\) | 54.7550 | − | 57.8449i | 0.210596 | − | 0.222480i | ||||
\(261\) | −157.055 | −0.601742 | ||||||||
\(262\) | 58.3393 | + | 58.3393i | 0.222669 | + | 0.222669i | ||||
\(263\) | −186.483 | + | 186.483i | −0.709062 | + | 0.709062i | −0.966338 | − | 0.257276i | \(-0.917175\pi\) |
0.257276 | + | 0.966338i | \(0.417175\pi\) | |||||||
\(264\) | − | 10.1582i | − | 0.0384782i | ||||||
\(265\) | −131.839 | − | 124.797i | −0.497506 | − | 0.470931i | ||||
\(266\) | −71.8379 | −0.270067 | ||||||||
\(267\) | −145.756 | − | 145.756i | −0.545904 | − | 0.545904i | ||||
\(268\) | 308.506 | − | 308.506i | 1.15114 | − | 1.15114i | ||||
\(269\) | 489.403i | 1.81934i | 0.415330 | + | 0.909671i | \(0.363666\pi\) | ||||
−0.415330 | + | 0.909671i | \(0.636334\pi\) | |||||||
\(270\) | −76.7553 | + | 2.10624i | −0.284279 | + | 0.00780090i | ||||
\(271\) | 35.3651 | 0.130499 | 0.0652493 | − | 0.997869i | \(-0.479216\pi\) | ||||
0.0652493 | + | 0.997869i | \(0.479216\pi\) | |||||||
\(272\) | 205.008 | + | 205.008i | 0.753705 | + | 0.753705i | ||||
\(273\) | −10.9027 | + | 10.9027i | −0.0399365 | + | 0.0399365i | ||||
\(274\) | 289.532i | 1.05669i | ||||||||
\(275\) | −67.4382 | + | 3.70393i | −0.245230 | + | 0.0134688i | ||||
\(276\) | −248.795 | −0.901432 | ||||||||
\(277\) | −88.7149 | − | 88.7149i | −0.320270 | − | 0.320270i | 0.528600 | − | 0.848871i | \(-0.322717\pi\) |
−0.848871 | + | 0.528600i | \(0.822717\pi\) | |||||||
\(278\) | 488.786 | − | 488.786i | 1.75822 | − | 1.75822i | ||||
\(279\) | 15.0555i | 0.0539623i | ||||||||
\(280\) | 0.787760 | + | 28.7074i | 0.00281343 | + | 0.102526i | ||||
\(281\) | −31.7224 | −0.112891 | −0.0564456 | − | 0.998406i | \(-0.517977\pi\) | ||||
−0.0564456 | + | 0.998406i | \(0.517977\pi\) | |||||||
\(282\) | −11.4785 | − | 11.4785i | −0.0407038 | − | 0.0407038i | ||||
\(283\) | −111.462 | + | 111.462i | −0.393859 | + | 0.393859i | −0.876060 | − | 0.482202i | \(-0.839837\pi\) |
0.482202 | + | 0.876060i | \(0.339837\pi\) | |||||||
\(284\) | − | 108.376i | − | 0.381607i | ||||||
\(285\) | −54.6956 | + | 57.7821i | −0.191914 | + | 0.202744i | ||||
\(286\) | −26.8645 | −0.0939317 | ||||||||
\(287\) | 113.248 | + | 113.248i | 0.394593 | + | 0.394593i | ||||
\(288\) | 96.9278 | − | 96.9278i | 0.336555 | − | 0.336555i | ||||
\(289\) | 247.049i | 0.854841i | ||||||||
\(290\) | 561.821 | + | 531.811i | 1.93731 | + | 1.83383i | ||||
\(291\) | 134.981 | 0.463854 | ||||||||
\(292\) | −25.5007 | − | 25.5007i | −0.0873311 | − | 0.0873311i | ||||
\(293\) | 10.3345 | − | 10.3345i | 0.0352712 | − | 0.0352712i | −0.689251 | − | 0.724522i | \(-0.742060\pi\) |
0.724522 | + | 0.689251i | \(0.242060\pi\) | |||||||
\(294\) | − | 35.8326i | − | 0.121880i | ||||||
\(295\) | 504.708 | − | 13.8497i | 1.71087 | − | 0.0469481i | ||||
\(296\) | −71.3053 | −0.240896 | ||||||||
\(297\) | 9.92628 | + | 9.92628i | 0.0334218 | + | 0.0334218i | ||||
\(298\) | −266.646 | + | 266.646i | −0.894786 | + | 0.894786i | ||||
\(299\) | 102.080i | 0.341405i | ||||||||
\(300\) | 152.697 | + | 136.797i | 0.508990 | + | 0.455990i | ||||
\(301\) | 32.8756 | 0.109221 | ||||||||
\(302\) | 102.800 | + | 102.800i | 0.340399 | + | 0.340399i | ||||
\(303\) | −157.162 | + | 157.162i | −0.518687 | + | 0.518687i | ||||
\(304\) | − | 115.045i | − | 0.378437i | ||||||
\(305\) | −11.2681 | − | 410.629i | −0.0369445 | − | 1.34632i | ||||
\(306\) | 205.279 | 0.670845 | ||||||||
\(307\) | 296.667 | + | 296.667i | 0.966341 | + | 0.966341i | 0.999452 | − | 0.0331110i | \(-0.0105415\pi\) |
−0.0331110 | + | 0.999452i | \(0.510541\pi\) | |||||||
\(308\) | 23.9294 | − | 23.9294i | 0.0776929 | − | 0.0776929i | ||||
\(309\) | 25.9610i | 0.0840160i | ||||||||
\(310\) | 50.9801 | − | 53.8570i | 0.164452 | − | 0.173732i | ||||
\(311\) | −36.8400 | −0.118457 | −0.0592284 | − | 0.998244i | \(-0.518864\pi\) | ||||
−0.0592284 | + | 0.998244i | \(0.518864\pi\) | |||||||
\(312\) | 8.94586 | + | 8.94586i | 0.0286726 | + | 0.0286726i | ||||
\(313\) | −90.5345 | + | 90.5345i | −0.289248 | + | 0.289248i | −0.836783 | − | 0.547535i | \(-0.815566\pi\) |
0.547535 | + | 0.836783i | \(0.315566\pi\) | |||||||
\(314\) | 546.810i | 1.74143i | ||||||||
\(315\) | −28.8216 | − | 27.2821i | −0.0914973 | − | 0.0866098i | ||||
\(316\) | −557.898 | −1.76550 | ||||||||
\(317\) | 2.40123 | + | 2.40123i | 0.00757485 | + | 0.00757485i | 0.710884 | − | 0.703309i | \(-0.248295\pi\) |
−0.703309 | + | 0.710884i | \(0.748295\pi\) | |||||||
\(318\) | 131.420 | − | 131.420i | 0.413271 | − | 0.413271i | ||||
\(319\) | − | 141.433i | − | 0.443362i | ||||||
\(320\) | −424.595 | + | 11.6513i | −1.32686 | + | 0.0364103i | ||||
\(321\) | −338.901 | −1.05577 | ||||||||
\(322\) | −167.748 | − | 167.748i | −0.520957 | − | 0.520957i | ||||
\(323\) | 150.408 | − | 150.408i | 0.465660 | − | 0.465660i | ||||
\(324\) | − | 42.6109i | − | 0.131515i | ||||||
\(325\) | 56.1276 | − | 62.6513i | 0.172700 | − | 0.192773i | ||||
\(326\) | −148.720 | −0.456198 | ||||||||
\(327\) | 197.657 | + | 197.657i | 0.604457 | + | 0.604457i | ||||
\(328\) | 92.9223 | − | 92.9223i | 0.283300 | − | 0.283300i | ||||
\(329\) | − | 8.39010i | − | 0.0255018i | ||||||
\(330\) | −1.89674 | − | 69.1205i | −0.00574769 | − | 0.209456i | ||||
\(331\) | −288.021 | −0.870154 | −0.435077 | − | 0.900393i | \(-0.643279\pi\) | ||||
−0.435077 | + | 0.900393i | \(0.643279\pi\) | |||||||
\(332\) | 404.844 | + | 404.844i | 1.21941 | + | 1.21941i | ||||
\(333\) | 69.6770 | − | 69.6770i | 0.209240 | − | 0.209240i | ||||
\(334\) | 115.975i | 0.347232i | ||||||||
\(335\) | 316.743 | − | 334.617i | 0.945502 | − | 0.998857i | ||||
\(336\) | 57.3842 | 0.170786 | ||||||||
\(337\) | −354.146 | − | 354.146i | −1.05088 | − | 1.05088i | −0.998634 | − | 0.0522432i | \(-0.983363\pi\) |
−0.0522432 | − | 0.998634i | \(-0.516637\pi\) | |||||||
\(338\) | −329.518 | + | 329.518i | −0.974906 | + | 0.974906i | ||||
\(339\) | − | 83.8162i | − | 0.247245i | ||||||
\(340\) | −398.042 | − | 376.780i | −1.17071 | − | 1.10818i | ||||
\(341\) | −13.5579 | −0.0397593 | ||||||||
\(342\) | −57.5984 | − | 57.5984i | −0.168416 | − | 0.168416i | ||||
\(343\) | 13.0958 | − | 13.0958i | 0.0381802 | − | 0.0381802i | ||||
\(344\) | − | 26.9751i | − | 0.0784161i | ||||||
\(345\) | −262.646 | + | 7.20727i | −0.761292 | + | 0.0208906i | ||||
\(346\) | −797.405 | −2.30464 | ||||||||
\(347\) | −440.033 | − | 440.033i | −1.26811 | − | 1.26811i | −0.947064 | − | 0.321044i | \(-0.895966\pi\) |
−0.321044 | − | 0.947064i | \(-0.604034\pi\) | |||||||
\(348\) | −303.566 | + | 303.566i | −0.872316 | + | 0.872316i | ||||
\(349\) | − | 429.577i | − | 1.23088i | −0.788184 | − | 0.615440i | \(-0.788978\pi\) | ||
0.788184 | − | 0.615440i | \(-0.211022\pi\) | |||||||
\(350\) | 10.7204 | + | 195.189i | 0.0306298 | + | 0.557683i | ||||
\(351\) | −17.4832 | −0.0498096 | ||||||||
\(352\) | 87.2865 | + | 87.2865i | 0.247973 | + | 0.247973i | ||||
\(353\) | 240.557 | − | 240.557i | 0.681463 | − | 0.681463i | −0.278867 | − | 0.960330i | \(-0.589959\pi\) |
0.960330 | + | 0.278867i | \(0.0899587\pi\) | |||||||
\(354\) | 516.909i | 1.46020i | ||||||||
\(355\) | −3.13952 | − | 114.410i | −0.00884371 | − | 0.322281i | ||||
\(356\) | −563.456 | −1.58274 | ||||||||
\(357\) | 75.0234 | + | 75.0234i | 0.210150 | + | 0.210150i | ||||
\(358\) | 376.956 | − | 376.956i | 1.05295 | − | 1.05295i | ||||
\(359\) | − | 53.5007i | − | 0.149027i | −0.997220 | − | 0.0745135i | \(-0.976260\pi\) | ||
0.997220 | − | 0.0745135i | \(-0.0237404\pi\) | |||||||
\(360\) | −22.3855 | + | 23.6487i | −0.0621820 | + | 0.0656909i | ||||
\(361\) | 276.595 | 0.766191 | ||||||||
\(362\) | −43.4806 | − | 43.4806i | −0.120112 | − | 0.120112i | ||||
\(363\) | 139.255 | − | 139.255i | 0.383623 | − | 0.383623i | ||||
\(364\) | 42.1469i | 0.115788i | ||||||||
\(365\) | −27.6590 | − | 26.1816i | −0.0757781 | − | 0.0717304i | ||||
\(366\) | 420.556 | 1.14906 | ||||||||
\(367\) | 1.26172 | + | 1.26172i | 0.00343792 | + | 0.00343792i | 0.708824 | − | 0.705386i | \(-0.249226\pi\) |
−0.705386 | + | 0.708824i | \(0.749226\pi\) | |||||||
\(368\) | 268.640 | − | 268.640i | 0.730001 | − | 0.730001i | ||||
\(369\) | 181.601i | 0.492143i | ||||||||
\(370\) | −485.188 | + | 13.3140i | −1.31132 | + | 0.0359839i | ||||
\(371\) | 96.0606 | 0.258923 | ||||||||
\(372\) | 29.1003 | + | 29.1003i | 0.0782266 | + | 0.0782266i | ||||
\(373\) | −48.6449 | + | 48.6449i | −0.130415 | + | 0.130415i | −0.769301 | − | 0.638886i | \(-0.779396\pi\) |
0.638886 | + | 0.769301i | \(0.279396\pi\) | |||||||
\(374\) | 184.860i | 0.494277i | ||||||||
\(375\) | 165.161 | + | 139.989i | 0.440428 | + | 0.373305i | ||||
\(376\) | −6.88425 | −0.0183092 | ||||||||
\(377\) | 124.553 | + | 124.553i | 0.330378 | + | 0.330378i | ||||
\(378\) | 28.7300 | − | 28.7300i | 0.0760054 | − | 0.0760054i | ||||
\(379\) | 482.025i | 1.27183i | 0.771758 | + | 0.635917i | \(0.219378\pi\) | ||||
−0.771758 | + | 0.635917i | \(0.780622\pi\) | |||||||
\(380\) | 5.96581 | + | 217.405i | 0.0156995 | + | 0.572118i | ||||
\(381\) | 32.7689 | 0.0860076 | ||||||||
\(382\) | 463.106 | + | 463.106i | 1.21232 | + | 1.21232i | ||||
\(383\) | −75.2958 | + | 75.2958i | −0.196595 | + | 0.196595i | −0.798539 | − | 0.601944i | \(-0.794393\pi\) |
0.601944 | + | 0.798539i | \(0.294393\pi\) | |||||||
\(384\) | − | 118.294i | − | 0.308058i | ||||||
\(385\) | 24.5684 | − | 25.9548i | 0.0638139 | − | 0.0674150i | ||||
\(386\) | −788.641 | −2.04311 | ||||||||
\(387\) | 26.3592 | + | 26.3592i | 0.0681115 | + | 0.0681115i | ||||
\(388\) | 260.901 | − | 260.901i | 0.672426 | − | 0.672426i | ||||
\(389\) | 270.881i | 0.696353i | 0.937429 | + | 0.348176i | \(0.113199\pi\) | ||||
−0.937429 | + | 0.348176i | \(0.886801\pi\) | |||||||
\(390\) | 62.5414 | + | 59.2007i | 0.160363 | + | 0.151797i | ||||
\(391\) | 702.434 | 1.79651 | ||||||||
\(392\) | −10.7454 | − | 10.7454i | −0.0274117 | − | 0.0274117i | ||||
\(393\) | −34.1902 | + | 34.1902i | −0.0869979 | + | 0.0869979i | ||||
\(394\) | 358.340i | 0.909492i | ||||||||
\(395\) | −588.957 | + | 16.1616i | −1.49103 | + | 0.0409153i | ||||
\(396\) | 38.3724 | 0.0969001 | ||||||||
\(397\) | −62.2126 | − | 62.2126i | −0.156707 | − | 0.156707i | 0.624399 | − | 0.781106i | \(-0.285344\pi\) |
−0.781106 | + | 0.624399i | \(0.785344\pi\) | |||||||
\(398\) | 222.817 | − | 222.817i | 0.559841 | − | 0.559841i | ||||
\(399\) | − | 42.1012i | − | 0.105517i | ||||||
\(400\) | −312.586 | + | 17.1683i | −0.781464 | + | 0.0429206i | ||||
\(401\) | 520.801 | 1.29876 | 0.649378 | − | 0.760466i | \(-0.275029\pi\) | ||||
0.649378 | + | 0.760466i | \(0.275029\pi\) | |||||||
\(402\) | 333.554 | + | 333.554i | 0.829735 | + | 0.829735i | ||||
\(403\) | 11.9398 | − | 11.9398i | 0.0296273 | − | 0.0296273i | ||||
\(404\) | 607.547i | 1.50383i | ||||||||
\(405\) | −1.23438 | − | 44.9831i | −0.00304785 | − | 0.111069i | ||||
\(406\) | −409.354 | −1.00826 | ||||||||
\(407\) | 62.7463 | + | 62.7463i | 0.154168 | + | 0.154168i | ||||
\(408\) | 61.5582 | − | 61.5582i | 0.150878 | − | 0.150878i | ||||
\(409\) | − | 575.516i | − | 1.40713i | −0.710631 | − | 0.703564i | \(-0.751591\pi\) | ||
0.710631 | − | 0.703564i | \(-0.248409\pi\) | |||||||
\(410\) | 614.928 | − | 649.629i | 1.49982 | − | 1.58446i | ||||
\(411\) | −169.682 | −0.412853 | ||||||||
\(412\) | 50.1791 | + | 50.1791i | 0.121794 | + | 0.121794i | ||||
\(413\) | −188.916 | + | 188.916i | −0.457423 | + | 0.457423i | ||||
\(414\) | − | 268.995i | − | 0.649747i | ||||||
\(415\) | 439.110 | + | 415.654i | 1.05810 | + | 1.00158i | ||||
\(416\) | −153.738 | −0.369562 | ||||||||
\(417\) | 286.457 | + | 286.457i | 0.686947 | + | 0.686947i | ||||
\(418\) | 51.8692 | − | 51.8692i | 0.124089 | − | 0.124089i | ||||
\(419\) | − | 113.474i | − | 0.270822i | −0.990790 | − | 0.135411i | \(-0.956765\pi\) | ||
0.990790 | − | 0.135411i | \(-0.0432355\pi\) | |||||||
\(420\) | −108.441 | + | 2.97574i | −0.258193 | + | 0.00708509i | ||||
\(421\) | 737.737 | 1.75234 | 0.876172 | − | 0.481999i | \(-0.160089\pi\) | ||||
0.876172 | + | 0.481999i | \(0.160089\pi\) | |||||||
\(422\) | −439.108 | − | 439.108i | −1.04054 | − | 1.04054i | ||||
\(423\) | 6.72705 | − | 6.72705i | 0.0159032 | − | 0.0159032i | ||||
\(424\) | − | 78.8196i | − | 0.185895i | ||||||
\(425\) | −431.116 | − | 386.225i | −1.01439 | − | 0.908764i | ||||
\(426\) | 117.176 | 0.275060 | ||||||||
\(427\) | 153.701 | + | 153.701i | 0.359956 | + | 0.359956i | ||||
\(428\) | −655.052 | + | 655.052i | −1.53049 | + | 1.53049i | ||||
\(429\) | − | 15.7441i | − | 0.0366996i | ||||||
\(430\) | −5.03677 | − | 183.549i | −0.0117134 | − | 0.426858i | ||||
\(431\) | 626.096 | 1.45266 | 0.726329 | − | 0.687347i | \(-0.241225\pi\) | ||||
0.726329 | + | 0.687347i | \(0.241225\pi\) | |||||||
\(432\) | 46.0097 | + | 46.0097i | 0.106504 | + | 0.106504i | ||||
\(433\) | 99.3139 | − | 99.3139i | 0.229362 | − | 0.229362i | −0.583064 | − | 0.812426i | \(-0.698146\pi\) |
0.812426 | + | 0.583064i | \(0.198146\pi\) | |||||||
\(434\) | 39.2412i | 0.0904176i | ||||||||
\(435\) | −311.672 | + | 329.260i | −0.716487 | + | 0.756919i | ||||
\(436\) | 764.092 | 1.75250 | ||||||||
\(437\) | −197.094 | − | 197.094i | −0.451015 | − | 0.451015i | ||||
\(438\) | 27.5711 | − | 27.5711i | 0.0629477 | − | 0.0629477i | ||||
\(439\) | 249.762i | 0.568933i | 0.958686 | + | 0.284467i | \(0.0918165\pi\) | ||||
−0.958686 | + | 0.284467i | \(0.908183\pi\) | |||||||
\(440\) | −21.2964 | − | 20.1588i | −0.0484009 | − | 0.0458155i | ||||
\(441\) | 21.0000 | 0.0476190 | ||||||||
\(442\) | −162.797 | − | 162.797i | −0.368318 | − | 0.368318i | ||||
\(443\) | −213.838 | + | 213.838i | −0.482704 | + | 0.482704i | −0.905994 | − | 0.423290i | \(-0.860875\pi\) |
0.423290 | + | 0.905994i | \(0.360875\pi\) | |||||||
\(444\) | − | 269.353i | − | 0.606651i | ||||||
\(445\) | −594.824 | + | 16.3226i | −1.33668 | + | 0.0366799i | ||||
\(446\) | −578.050 | −1.29608 | ||||||||
\(447\) | −156.270 | − | 156.270i | −0.349598 | − | 0.349598i | ||||
\(448\) | 158.929 | − | 158.929i | 0.354751 | − | 0.354751i | ||||
\(449\) | 540.540i | 1.20387i | 0.798544 | + | 0.601937i | \(0.205604\pi\) | ||||
−0.798544 | + | 0.601937i | \(0.794396\pi\) | |||||||
\(450\) | −147.904 | + | 165.095i | −0.328675 | + | 0.366877i | ||||
\(451\) | −163.537 | −0.362610 | ||||||||
\(452\) | −162.006 | − | 162.006i | −0.358420 | − | 0.358420i | ||||
\(453\) | −60.2470 | + | 60.2470i | −0.132995 | + | 0.132995i | ||||
\(454\) | − | 1197.04i | − | 2.63666i | ||||||
\(455\) | 1.22094 | + | 44.4932i | 0.00268338 | + | 0.0977873i | ||||
\(456\) | −34.5448 | −0.0757562 | ||||||||
\(457\) | −236.212 | − | 236.212i | −0.516876 | − | 0.516876i | 0.399749 | − | 0.916625i | \(-0.369097\pi\) |
−0.916625 | + | 0.399749i | \(0.869097\pi\) | |||||||
\(458\) | 440.656 | − | 440.656i | 0.962131 | − | 0.962131i | ||||
\(459\) | 120.305i | 0.262103i | ||||||||
\(460\) | −493.729 | + | 521.591i | −1.07332 | + | 1.13389i | ||||
\(461\) | 156.987 | 0.340536 | 0.170268 | − | 0.985398i | \(-0.445537\pi\) | ||||
0.170268 | + | 0.985398i | \(0.445537\pi\) | |||||||
\(462\) | 25.8723 | + | 25.8723i | 0.0560006 | + | 0.0560006i | ||||
\(463\) | −269.161 | + | 269.161i | −0.581342 | + | 0.581342i | −0.935272 | − | 0.353930i | \(-0.884845\pi\) |
0.353930 | + | 0.935272i | \(0.384845\pi\) | |||||||
\(464\) | − | 655.560i | − | 1.41284i | ||||||
\(465\) | 31.5633 | + | 29.8773i | 0.0678781 | + | 0.0642523i | ||||
\(466\) | 910.656 | 1.95420 | ||||||||
\(467\) | 114.700 | + | 114.700i | 0.245610 | + | 0.245610i | 0.819166 | − | 0.573556i | \(-0.194436\pi\) |
−0.573556 | + | 0.819166i | \(0.694436\pi\) | |||||||
\(468\) | −33.7927 | + | 33.7927i | −0.0722066 | + | 0.0722066i | ||||
\(469\) | 243.808i | 0.519848i | ||||||||
\(470\) | −46.8430 | + | 1.28542i | −0.0996660 | + | 0.00273494i | ||||
\(471\) | −320.462 | −0.680387 | ||||||||
\(472\) | 155.009 | + | 155.009i | 0.328409 | + | 0.328409i | ||||
\(473\) | −23.7372 | + | 23.7372i | −0.0501844 | + | 0.0501844i | ||||
\(474\) | − | 603.195i | − | 1.27256i | ||||||
\(475\) | 12.5958 | + | 229.335i | 0.0265176 | + | 0.482810i | ||||
\(476\) | 290.021 | 0.609288 | ||||||||
\(477\) | 77.0198 | + | 77.0198i | 0.161467 | + | 0.161467i | ||||
\(478\) | −216.136 | + | 216.136i | −0.452168 | + | 0.452168i | ||||
\(479\) | − | 158.331i | − | 0.330546i | −0.986248 | − | 0.165273i | \(-0.947149\pi\) | ||
0.986248 | − | 0.165273i | \(-0.0528505\pi\) | |||||||
\(480\) | −10.8545 | − | 395.557i | −0.0226135 | − | 0.824077i | ||||
\(481\) | −110.515 | −0.229761 | ||||||||
\(482\) | −27.8667 | − | 27.8667i | −0.0578148 | − | 0.0578148i | ||||
\(483\) | 98.3101 | − | 98.3101i | 0.203541 | − | 0.203541i | ||||
\(484\) | − | 538.324i | − | 1.11224i | ||||||
\(485\) | 267.868 | − | 282.984i | 0.552305 | − | 0.583472i | ||||
\(486\) | 46.0705 | 0.0947953 | ||||||||
\(487\) | 220.865 | + | 220.865i | 0.453521 | + | 0.453521i | 0.896521 | − | 0.443000i | \(-0.146086\pi\) |
−0.443000 | + | 0.896521i | \(0.646086\pi\) | |||||||
\(488\) | 126.115 | − | 126.115i | 0.258432 | − | 0.258432i | ||||
\(489\) | − | 87.1588i | − | 0.178239i | ||||||
\(490\) | −75.1219 | − | 71.1092i | −0.153310 | − | 0.145121i | ||||
\(491\) | 925.802 | 1.88554 | 0.942772 | − | 0.333439i | \(-0.108209\pi\) | ||||
0.942772 | + | 0.333439i | \(0.108209\pi\) | |||||||
\(492\) | 351.011 | + | 351.011i | 0.713437 | + | 0.713437i | ||||
\(493\) | 857.071 | − | 857.071i | 1.73848 | − | 1.73848i | ||||
\(494\) | 91.3572i | 0.184934i | ||||||||
\(495\) | 40.5086 | − | 1.11160i | 0.0818356 | − | 0.00224565i | ||||
\(496\) | −62.8429 | −0.126699 | ||||||||
\(497\) | 42.8243 | + | 42.8243i | 0.0861656 | + | 0.0861656i | ||||
\(498\) | −437.714 | + | 437.714i | −0.878944 | + | 0.878944i | ||||
\(499\) | − | 114.955i | − | 0.230370i | −0.993344 | − | 0.115185i | \(-0.963254\pi\) | ||
0.993344 | − | 0.115185i | \(-0.0367461\pi\) | |||||||
\(500\) | 589.815 | − | 48.6531i | 1.17963 | − | 0.0973061i | ||||
\(501\) | −67.9683 | −0.135665 | ||||||||
\(502\) | −678.837 | − | 678.837i | −1.35226 | − | 1.35226i | ||||
\(503\) | −46.4397 | + | 46.4397i | −0.0923254 | + | 0.0923254i | −0.751761 | − | 0.659436i | \(-0.770795\pi\) |
0.659436 | + | 0.751761i | \(0.270795\pi\) | |||||||
\(504\) | − | 17.2309i | − | 0.0341883i | ||||||
\(505\) | 17.5998 | + | 641.370i | 0.0348512 | + | 1.27004i | ||||
\(506\) | 242.239 | 0.478732 | ||||||||
\(507\) | −193.117 | − | 193.117i | −0.380901 | − | 0.380901i | ||||
\(508\) | 63.3380 | − | 63.3380i | 0.124681 | − | 0.124681i | ||||
\(509\) | − | 185.083i | − | 0.363621i | −0.983334 | − | 0.181811i | \(-0.941804\pi\) | ||
0.983334 | − | 0.181811i | \(-0.0581958\pi\) | |||||||
\(510\) | 407.371 | − | 430.360i | 0.798767 | − | 0.843842i | ||||
\(511\) | 20.1529 | 0.0394381 | ||||||||
\(512\) | 481.475 | + | 481.475i | 0.940380 | + | 0.940380i | ||||
\(513\) | 33.7560 | − | 33.7560i | 0.0658012 | − | 0.0658012i | ||||
\(514\) | 190.376i | 0.370381i | ||||||||
\(515\) | 54.4262 | + | 51.5190i | 0.105682 | + | 0.100037i | ||||
\(516\) | 101.898 | 0.197476 | ||||||||
\(517\) | 6.05791 | + | 6.05791i | 0.0117174 | + | 0.0117174i | ||||
\(518\) | 181.609 | − | 181.609i | 0.350597 | − | 0.350597i | ||||
\(519\) | − | 467.326i | − | 0.900435i | ||||||
\(520\) | 36.5076 | − | 1.00180i | 0.0702069 | − | 0.00192655i | ||||
\(521\) | −275.217 | −0.528248 | −0.264124 | − | 0.964489i | \(-0.585083\pi\) | ||||
−0.264124 | + | 0.964489i | \(0.585083\pi\) | |||||||
\(522\) | −328.213 | − | 328.213i | −0.628761 | − | 0.628761i | ||||
\(523\) | −424.281 | + | 424.281i | −0.811245 | + | 0.811245i | −0.984821 | − | 0.173576i | \(-0.944468\pi\) |
0.173576 | + | 0.984821i | \(0.444468\pi\) | |||||||
\(524\) | 132.170i | 0.252233i | ||||||||
\(525\) | −114.392 | + | 6.28279i | −0.217889 | + | 0.0119672i | ||||
\(526\) | −779.426 | −1.48180 | ||||||||
\(527\) | −82.1600 | − | 82.1600i | −0.155901 | − | 0.155901i | ||||
\(528\) | −41.4332 | + | 41.4332i | −0.0784719 | + | 0.0784719i | ||||
\(529\) | − | 391.464i | − | 0.740007i | ||||||
\(530\) | −14.7171 | − | 536.318i | −0.0277681 | − | 1.01192i | ||||
\(531\) | −302.939 | −0.570506 | ||||||||
\(532\) | −81.3760 | − | 81.3760i | −0.152962 | − | 0.152962i | ||||
\(533\) | 144.019 | − | 144.019i | 0.270205 | − | 0.270205i | ||||
\(534\) | − | 609.204i | − | 1.14083i | ||||||
\(535\) | −672.543 | + | 710.495i | −1.25709 | + | 1.32803i | ||||
\(536\) | 200.050 | 0.373227 | ||||||||
\(537\) | 220.918 | + | 220.918i | 0.411392 | + | 0.411392i | ||||
\(538\) | −1022.76 | + | 1022.76i | −1.90103 | + | 1.90103i | ||||
\(539\) | 18.9111i | 0.0350856i | ||||||||
\(540\) | −89.3323 | − | 84.5605i | −0.165430 | − | 0.156594i | ||||
\(541\) | −484.593 | −0.895735 | −0.447868 | − | 0.894100i | \(-0.647816\pi\) | ||||
−0.447868 | + | 0.894100i | \(0.647816\pi\) | |||||||
\(542\) | 73.9061 | + | 73.9061i | 0.136358 | + | 0.136358i | ||||
\(543\) | 25.4821 | − | 25.4821i | 0.0469284 | − | 0.0469284i | ||||
\(544\) | 1057.90i | 1.94467i | ||||||||
\(545\) | 806.629 | − | 22.1347i | 1.48005 | − | 0.0406142i | ||||
\(546\) | −45.5688 | −0.0834594 | ||||||||
\(547\) | −367.275 | − | 367.275i | −0.671436 | − | 0.671436i | 0.286611 | − | 0.958047i | \(-0.407471\pi\) |
−0.958047 | + | 0.286611i | \(0.907471\pi\) | |||||||
\(548\) | −327.974 | + | 327.974i | −0.598493 | + | 0.598493i | ||||
\(549\) | 246.470i | 0.448944i | ||||||||
\(550\) | −148.673 | − | 133.192i | −0.270314 | − | 0.242167i | ||||
\(551\) | −480.965 | −0.872895 | ||||||||
\(552\) | −80.6654 | − | 80.6654i | −0.146133 | − | 0.146133i | ||||
\(553\) | 220.450 | − | 220.450i | 0.398644 | − | 0.398644i | ||||
\(554\) | − | 370.793i | − | 0.669302i | ||||||
\(555\) | −7.80280 | − | 284.348i | −0.0140591 | − | 0.512339i | ||||
\(556\) | 1107.37 | 1.99167 | ||||||||
\(557\) | 532.387 | + | 532.387i | 0.955811 | + | 0.955811i | 0.999064 | − | 0.0432528i | \(-0.0137721\pi\) |
−0.0432528 | + | 0.999064i | \(0.513772\pi\) | |||||||
\(558\) | −31.4630 | + | 31.4630i | −0.0563853 | + | 0.0563853i | ||||
\(559\) | − | 41.8084i | − | 0.0747914i | ||||||
\(560\) | 113.878 | − | 120.304i | 0.203353 | − | 0.214829i | ||||
\(561\) | −108.338 | −0.193117 | ||||||||
\(562\) | −66.2936 | − | 66.2936i | −0.117960 | − | 0.117960i | ||||
\(563\) | −724.535 | + | 724.535i | −1.28692 | + | 1.28692i | −0.350268 | + | 0.936649i | \(0.613910\pi\) |
−0.936649 | + | 0.350268i | \(0.886090\pi\) | |||||||
\(564\) | − | 26.0050i | − | 0.0461082i | ||||||
\(565\) | −175.718 | − | 166.332i | −0.311005 | − | 0.294392i | ||||
\(566\) | −465.867 | −0.823087 | ||||||||
\(567\) | 16.8375 | + | 16.8375i | 0.0296957 | + | 0.0296957i | ||||
\(568\) | 35.1382 | − | 35.1382i | 0.0618630 | − | 0.0618630i | ||||
\(569\) | − | 63.5327i | − | 0.111657i | −0.998440 | − | 0.0558284i | \(-0.982220\pi\) | ||
0.998440 | − | 0.0558284i | \(-0.0177800\pi\) | |||||||
\(570\) | −235.056 | + | 6.45018i | −0.412379 | + | 0.0113161i | ||||
\(571\) | 186.947 | 0.327403 | 0.163701 | − | 0.986510i | \(-0.447657\pi\) | ||||
0.163701 | + | 0.986510i | \(0.447657\pi\) | |||||||
\(572\) | −30.4314 | − | 30.4314i | −0.0532017 | − | 0.0532017i | ||||
\(573\) | −271.407 | + | 271.407i | −0.473660 | + | 0.473660i | ||||
\(574\) | 473.332i | 0.824620i | ||||||||
\(575\) | −506.106 | + | 564.931i | −0.880184 | + | 0.982488i | ||||
\(576\) | 254.853 | 0.442452 | ||||||||
\(577\) | 650.925 | + | 650.925i | 1.12812 | + | 1.12812i | 0.990483 | + | 0.137637i | \(0.0439506\pi\) |
0.137637 | + | 0.990483i | \(0.456049\pi\) | |||||||
\(578\) | −516.283 | + | 516.283i | −0.893224 | + | 0.893224i | ||||
\(579\) | − | 462.190i | − | 0.798255i | ||||||
\(580\) | 33.9949 | + | 1238.84i | 0.0586120 | + | 2.13593i | ||||
\(581\) | −319.944 | −0.550678 | ||||||||
\(582\) | 282.084 | + | 282.084i | 0.484681 | + | 0.484681i | ||||
\(583\) | −69.3587 | + | 69.3587i | −0.118969 | + | 0.118969i | ||||
\(584\) | − | 16.5359i | − | 0.0283148i | ||||||
\(585\) | −34.6950 | + | 36.6529i | −0.0593077 | + | 0.0626545i | ||||
\(586\) | 43.1939 | 0.0737098 | ||||||||
\(587\) | −451.044 | − | 451.044i | −0.768389 | − | 0.768389i | 0.209434 | − | 0.977823i | \(-0.432838\pi\) |
−0.977823 | + | 0.209434i | \(0.932838\pi\) | |||||||
\(588\) | 40.5903 | − | 40.5903i | 0.0690311 | − | 0.0690311i | ||||
\(589\) | 46.1060i | 0.0782785i | ||||||||
\(590\) | 1083.68 | + | 1025.80i | 1.83675 | + | 1.73864i | ||||
\(591\) | −210.008 | −0.355343 | ||||||||
\(592\) | 290.838 | + | 290.838i | 0.491281 | + | 0.491281i | ||||
\(593\) | 459.882 | − | 459.882i | 0.775518 | − | 0.775518i | −0.203547 | − | 0.979065i | \(-0.565247\pi\) |
0.979065 | + | 0.203547i | \(0.0652471\pi\) | |||||||
\(594\) | 41.4879i | 0.0698450i | ||||||||
\(595\) | 306.167 | − | 8.40152i | 0.514566 | − | 0.0141202i | ||||
\(596\) | −604.100 | −1.01359 | ||||||||
\(597\) | 130.583 | + | 130.583i | 0.218733 | + | 0.218733i | ||||
\(598\) | −213.327 | + | 213.327i | −0.356735 | + | 0.356735i | ||||
\(599\) | 415.835i | 0.694216i | 0.937825 | + | 0.347108i | \(0.112836\pi\) | ||||
−0.937825 | + | 0.347108i | \(0.887164\pi\) | |||||||
\(600\) | 5.15516 | + | 93.8609i | 0.00859193 | + | 0.156435i | ||||
\(601\) | −693.471 | −1.15386 | −0.576931 | − | 0.816793i | \(-0.695750\pi\) | ||||
−0.576931 | + | 0.816793i | \(0.695750\pi\) | |||||||
\(602\) | 68.7036 | + | 68.7036i | 0.114126 | + | 0.114126i | ||||
\(603\) | −195.482 | + | 195.482i | −0.324182 | + | 0.324182i | ||||
\(604\) | 232.899i | 0.385594i | ||||||||
\(605\) | −15.5945 | − | 568.293i | −0.0257761 | − | 0.939327i | ||||
\(606\) | −656.875 | −1.08395 | ||||||||
\(607\) | 247.205 | + | 247.205i | 0.407257 | + | 0.407257i | 0.880781 | − | 0.473524i | \(-0.157018\pi\) |
−0.473524 | + | 0.880781i | \(0.657018\pi\) | |||||||
\(608\) | 296.833 | − | 296.833i | 0.488211 | − | 0.488211i | ||||
\(609\) | − | 239.905i | − | 0.393933i | ||||||
\(610\) | 834.585 | − | 881.681i | 1.36817 | − | 1.44538i | ||||
\(611\) | −10.6698 | −0.0174629 | ||||||||
\(612\) | 232.534 | + | 232.534i | 0.379958 | + | 0.379958i | ||||
\(613\) | 512.566 | − | 512.566i | 0.836159 | − | 0.836159i | −0.152192 | − | 0.988351i | \(-0.548633\pi\) |
0.988351 | + | 0.152192i | \(0.0486331\pi\) | |||||||
\(614\) | 1239.95i | 2.01946i | ||||||||
\(615\) | 380.720 | + | 360.383i | 0.619057 | + | 0.585989i | ||||
\(616\) | 15.5170 | 0.0251899 | ||||||||
\(617\) | −700.942 | − | 700.942i | −1.13605 | − | 1.13605i | −0.989152 | − | 0.146897i | \(-0.953072\pi\) |
−0.146897 | − | 0.989152i | \(-0.546928\pi\) | |||||||
\(618\) | −54.2532 | + | 54.2532i | −0.0877884 | + | 0.0877884i | ||||
\(619\) | 354.521i | 0.572732i | 0.958120 | + | 0.286366i | \(0.0924473\pi\) | ||||
−0.958120 | + | 0.286366i | \(0.907553\pi\) | |||||||
\(620\) | 118.757 | − | 3.25880i | 0.191543 | − | 0.00525613i | ||||
\(621\) | 157.647 | 0.253860 | ||||||||
\(622\) | −76.9884 | − | 76.9884i | −0.123776 | − | 0.123776i | ||||
\(623\) | 222.646 | − | 222.646i | 0.357378 | − | 0.357378i | ||||
\(624\) | − | 72.9763i | − | 0.116949i | ||||||
\(625\) | 621.241 | − | 68.4477i | 0.993985 | − | 0.109516i | ||||
\(626\) | −378.398 | −0.604470 | ||||||||
\(627\) | 30.3983 | + | 30.3983i | 0.0484822 | + | 0.0484822i | ||||
\(628\) | −619.412 | + | 619.412i | −0.986325 | + | 0.986325i | ||||
\(629\) | 760.476i | 1.20902i | ||||||||
\(630\) | −3.21734 | − | 117.246i | −0.00510689 | − | 0.186104i | ||||
\(631\) | 930.684 | 1.47494 | 0.737468 | − | 0.675383i | \(-0.236021\pi\) | ||||
0.737468 | + | 0.675383i | \(0.236021\pi\) | |||||||
\(632\) | −180.884 | − | 180.884i | −0.286209 | − | 0.286209i | ||||
\(633\) | 257.343 | − | 257.343i | 0.406545 | − | 0.406545i | ||||
\(634\) | 10.0362i | 0.0158299i | ||||||||
\(635\) | 65.0292 | − | 68.6989i | 0.102408 | − | 0.108187i | ||||
\(636\) | 297.738 | 0.468142 | ||||||||
\(637\) | −16.6541 | − | 16.6541i | −0.0261446 | − | 0.0261446i | ||||
\(638\) | 295.566 | − | 295.566i | 0.463270 | − | 0.463270i | ||||
\(639\) | 68.6716i | 0.107467i | ||||||||
\(640\) | −248.000 | − | 234.753i | −0.387500 | − | 0.366801i | ||||
\(641\) | −499.986 | −0.780009 | −0.390005 | − | 0.920813i | \(-0.627527\pi\) | ||||
−0.390005 | + | 0.920813i | \(0.627527\pi\) | |||||||
\(642\) | −708.236 | − | 708.236i | −1.10317 | − | 1.10317i | ||||
\(643\) | −385.589 | + | 385.589i | −0.599672 | + | 0.599672i | −0.940225 | − | 0.340554i | \(-0.889386\pi\) |
0.340554 | + | 0.940225i | \(0.389386\pi\) | |||||||
\(644\) | − | 380.041i | − | 0.590126i | ||||||
\(645\) | 107.570 | − | 2.95184i | 0.166776 | − | 0.00457649i | ||||
\(646\) | 628.647 | 0.973137 | ||||||||
\(647\) | −84.6226 | − | 84.6226i | −0.130792 | − | 0.130792i | 0.638680 | − | 0.769472i | \(-0.279481\pi\) |
−0.769472 | + | 0.638680i | \(0.779481\pi\) | |||||||
\(648\) | 13.8155 | − | 13.8155i | 0.0213202 | − | 0.0213202i | ||||
\(649\) | − | 272.806i | − | 0.420348i | ||||||
\(650\) | 248.224 | − | 13.6333i | 0.381884 | − | 0.0209743i | ||||
\(651\) | −22.9976 | −0.0353266 | ||||||||
\(652\) | −168.467 | − | 168.467i | −0.258384 | − | 0.258384i | ||||
\(653\) | −132.499 | + | 132.499i | −0.202907 | + | 0.202907i | −0.801244 | − | 0.598337i | \(-0.795828\pi\) |
0.598337 | + | 0.801244i | \(0.295828\pi\) | |||||||
\(654\) | 826.130i | 1.26320i | ||||||||
\(655\) | 3.82880 | + | 139.528i | 0.00584549 | + | 0.213020i | ||||
\(656\) | −758.018 | −1.15552 | ||||||||
\(657\) | 16.1583 | + | 16.1583i | 0.0245940 | + | 0.0245940i | ||||
\(658\) | 17.5337 | − | 17.5337i | 0.0266469 | − | 0.0266469i | ||||
\(659\) | − | 921.339i | − | 1.39809i | −0.715080 | − | 0.699043i | \(-0.753610\pi\) | ||
0.715080 | − | 0.699043i | \(-0.246390\pi\) | |||||||
\(660\) | 76.1493 | − | 80.4465i | 0.115378 | − | 0.121889i | ||||
\(661\) | 705.918 | 1.06795 | 0.533977 | − | 0.845499i | \(-0.320697\pi\) | ||||
0.533977 | + | 0.845499i | \(0.320697\pi\) | |||||||
\(662\) | −601.907 | − | 601.907i | −0.909224 | − | 0.909224i | ||||
\(663\) | 95.4083 | − | 95.4083i | 0.143904 | − | 0.143904i | ||||
\(664\) | 262.520i | 0.395362i | ||||||||
\(665\) | −88.2636 | − | 83.5489i | −0.132727 | − | 0.125637i | ||||
\(666\) | 291.222 | 0.437271 | ||||||||
\(667\) | −1123.10 | − | 1123.10i | −1.68381 | − | 1.68381i | ||||
\(668\) | −131.374 | + | 131.374i | −0.196667 | + | 0.196667i | ||||
\(669\) | − | 338.771i | − | 0.506384i | ||||||
\(670\) | 1361.21 | − | 37.3531i | 2.03166 | − | 0.0557509i | ||||
\(671\) | −221.954 | −0.330781 | ||||||||
\(672\) | 148.060 | + | 148.060i | 0.220327 | + | 0.220327i | ||||
\(673\) | 480.376 | − | 480.376i | 0.713783 | − | 0.713783i | −0.253542 | − | 0.967324i | \(-0.581595\pi\) |
0.967324 | + | 0.253542i | \(0.0815955\pi\) | |||||||
\(674\) | − | 1480.19i | − | 2.19613i | ||||||
\(675\) | −96.7551 | − | 86.6802i | −0.143341 | − | 0.128415i | ||||
\(676\) | −746.539 | −1.10435 | ||||||||
\(677\) | 146.784 | + | 146.784i | 0.216815 | + | 0.216815i | 0.807155 | − | 0.590340i | \(-0.201006\pi\) |
−0.590340 | + | 0.807155i | \(0.701006\pi\) | |||||||
\(678\) | 175.159 | − | 175.159i | 0.258347 | − | 0.258347i | ||||
\(679\) | 206.187i | 0.303663i | ||||||||
\(680\) | −6.89361 | − | 251.216i | −0.0101377 | − | 0.369435i | ||||
\(681\) | 701.536 | 1.03016 | ||||||||
\(682\) | −28.3334 | − | 28.3334i | −0.0415445 | − | 0.0415445i | ||||
\(683\) | −88.7069 | + | 88.7069i | −0.129878 | + | 0.129878i | −0.769058 | − | 0.639179i | \(-0.779274\pi\) |
0.639179 | + | 0.769058i | \(0.279274\pi\) | |||||||
\(684\) | − | 130.492i | − | 0.190778i | ||||||
\(685\) | −336.731 | + | 355.733i | −0.491579 | + | 0.519319i | ||||
\(686\) | 54.7353 | 0.0797890 | ||||||||
\(687\) | 258.250 | + | 258.250i | 0.375910 | + | 0.375910i | ||||
\(688\) | −110.025 | + | 110.025i | −0.159921 | + | 0.159921i | ||||
\(689\) | − | 122.161i | − | 0.177303i | ||||||
\(690\) | −563.940 | − | 533.816i | −0.817304 | − | 0.773646i | ||||
\(691\) | −664.952 | −0.962304 | −0.481152 | − | 0.876637i | \(-0.659781\pi\) | ||||
−0.481152 | + | 0.876637i | \(0.659781\pi\) | |||||||
\(692\) | −903.280 | − | 903.280i | −1.30532 | − | 1.30532i | ||||
\(693\) | −15.1626 | + | 15.1626i | −0.0218797 | + | 0.0218797i | ||||
\(694\) | − | 1839.17i | − | 2.65009i | ||||||
\(695\) | 1169.02 | − | 32.0790i | 1.68204 | − | 0.0461568i | ||||
\(696\) | −196.847 | −0.282826 | ||||||||
\(697\) | −991.023 | − | 991.023i | −1.42184 | − | 1.42184i | ||||
\(698\) | 897.731 | − | 897.731i | 1.28615 | − | 1.28615i | ||||
\(699\) | 533.697i | 0.763515i | ||||||||
\(700\) | −208.961 | + | 233.249i | −0.298516 | + | 0.333212i | ||||
\(701\) | −137.923 | −0.196751 | −0.0983757 | − | 0.995149i | \(-0.531365\pi\) | ||||
−0.0983757 | + | 0.995149i | \(0.531365\pi\) | |||||||
\(702\) | −36.5364 | − | 36.5364i | −0.0520461 | − | 0.0520461i | ||||
\(703\) | 213.380 | − | 213.380i | 0.303527 | − | 0.303527i | ||||
\(704\) | 229.503i | 0.325998i | ||||||||
\(705\) | −0.753330 | − | 27.4527i | −0.00106855 | − | 0.0389400i | ||||
\(706\) | 1005.43 | 1.42412 | ||||||||
\(707\) | −240.069 | − | 240.069i | −0.339560 | − | 0.339560i | ||||
\(708\) | −585.541 | + | 585.541i | −0.827035 | + | 0.827035i | ||||
\(709\) | 371.525i | 0.524013i | 0.965066 | + | 0.262006i | \(0.0843842\pi\) | ||||
−0.965066 | + | 0.262006i | \(0.915616\pi\) | |||||||
\(710\) | 232.533 | − | 245.655i | 0.327511 | − | 0.345992i | ||||
\(711\) | 353.507 | 0.497197 | ||||||||
\(712\) | −182.686 | − | 182.686i | −0.256581 | − | 0.256581i | ||||
\(713\) | −107.662 | + | 107.662i | −0.150998 | + | 0.150998i | ||||
\(714\) | 313.568i | 0.439171i | ||||||||
\(715\) | −33.0070 | − | 31.2439i | −0.0461637 | − | 0.0436978i | ||||
\(716\) | 854.010 | 1.19275 | ||||||||
\(717\) | −126.668 | − | 126.668i | −0.176664 | − | 0.176664i | ||||
\(718\) | 111.806 | − | 111.806i | 0.155718 | − | 0.155718i | ||||
\(719\) | 85.5943i | 0.119046i | 0.998227 | + | 0.0595232i | \(0.0189580\pi\) | ||||
−0.998227 | + | 0.0595232i | \(0.981042\pi\) | |||||||
\(720\) | 187.763 | − | 5.15241i | 0.260782 | − | 0.00715613i | ||||
\(721\) | −39.6560 | −0.0550014 | ||||||||
\(722\) | 578.029 | + | 578.029i | 0.800594 | + | 0.800594i | ||||
\(723\) | 16.3315 | − | 16.3315i | 0.0225886 | − | 0.0225886i | ||||
\(724\) | − | 98.5073i | − | 0.136060i | ||||||
\(725\) | 71.7749 | + | 1306.82i | 0.0989999 | + | 1.80251i | ||||
\(726\) | 582.032 | 0.801696 | ||||||||
\(727\) | 589.673 | + | 589.673i | 0.811104 | + | 0.811104i | 0.984799 | − | 0.173695i | \(-0.0555707\pi\) |
−0.173695 | + | 0.984799i | \(0.555571\pi\) | |||||||
\(728\) | −13.6650 | + | 13.6650i | −0.0187706 | + | 0.0187706i | ||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | −3.08756 | − | 112.516i | −0.00422953 | − | 0.154132i | ||||
\(731\) | −287.692 | −0.393559 | ||||||||
\(732\) | 476.394 | + | 476.394i | 0.650812 | + | 0.650812i | ||||
\(733\) | 1019.17 | − | 1019.17i | 1.39040 | − | 1.39040i | 0.565992 | − | 0.824411i | \(-0.308493\pi\) |
0.824411 | − | 0.565992i | \(-0.191507\pi\) | |||||||
\(734\) | 5.27347i | 0.00718457i | ||||||||
\(735\) | 41.6741 | − | 44.0258i | 0.0566994 | − | 0.0598990i | ||||
\(736\) | 1386.26 | 1.88351 | ||||||||
\(737\) | −176.037 | − | 176.037i | −0.238857 | − | 0.238857i | ||||
\(738\) | −379.510 | + | 379.510i | −0.514241 | + | 0.514241i | ||||
\(739\) | 54.4746i | 0.0737139i | 0.999321 | + | 0.0368570i | \(0.0117346\pi\) | ||||
−0.999321 | + | 0.0368570i | \(0.988265\pi\) | |||||||
\(740\) | −564.690 | − | 534.526i | −0.763094 | − | 0.722333i | ||||
\(741\) | −53.5406 | −0.0722545 | ||||||||
\(742\) | 200.748 | + | 200.748i | 0.270549 | + | 0.270549i | ||||
\(743\) | 247.895 | − | 247.895i | 0.333641 | − | 0.333641i | −0.520326 | − | 0.853968i | \(-0.674190\pi\) |
0.853968 | + | 0.520326i | \(0.174190\pi\) | |||||||
\(744\) | 18.8700i | 0.0253629i | ||||||||
\(745\) | −637.730 | + | 17.5000i | −0.856014 | + | 0.0234899i | ||||
\(746\) | −203.316 | −0.272542 | ||||||||
\(747\) | −256.526 | − | 256.526i | −0.343408 | − | 0.343408i | ||||
\(748\) | −209.404 | + | 209.404i | −0.279952 | + | 0.279952i | ||||
\(749\) | − | 517.680i | − | 0.691162i | ||||||
\(750\) | 52.6033 | + | 637.703i | 0.0701377 | + | 0.850270i | ||||
\(751\) | −1361.29 | −1.81263 | −0.906316 | − | 0.422600i | \(-0.861117\pi\) | ||||
−0.906316 | + | 0.422600i | \(0.861117\pi\) | |||||||
\(752\) | 28.0793 | + | 28.0793i | 0.0373395 | + | 0.0373395i | ||||
\(753\) | 397.838 | − | 397.838i | 0.528337 | − | 0.528337i | ||||
\(754\) | 520.580i | 0.690425i | ||||||||
\(755\) | 6.74677 | + | 245.865i | 0.00893612 | + | 0.325648i | ||||
\(756\) | 65.0892 | 0.0860969 | ||||||||
\(757\) | 178.475 | + | 178.475i | 0.235767 | + | 0.235767i | 0.815095 | − | 0.579328i | \(-0.196685\pi\) |
−0.579328 | + | 0.815095i | \(0.696685\pi\) | |||||||
\(758\) | −1007.34 | + | 1007.34i | −1.32894 | + | 1.32894i | ||||
\(759\) | 141.966i | 0.187043i | ||||||||
\(760\) | −68.5536 | + | 72.4221i | −0.0902021 | + | 0.0952922i | ||||
\(761\) | 815.185 | 1.07120 | 0.535601 | − | 0.844471i | \(-0.320085\pi\) | ||||
0.535601 | + | 0.844471i | \(0.320085\pi\) | |||||||
\(762\) | 68.4805 | + | 68.4805i | 0.0898694 | + | 0.0898694i | ||||
\(763\) | −301.927 | + | 301.927i | −0.395710 | + | 0.395710i | ||||
\(764\) | 1049.19i | 1.37328i | ||||||||
\(765\) | 252.216 | + | 238.743i | 0.329694 | + | 0.312083i | ||||
\(766\) | −314.707 | −0.410844 | ||||||||
\(767\) | 240.246 | + | 240.246i | 0.313229 | + | 0.313229i | ||||
\(768\) | −168.961 | + | 168.961i | −0.220001 | + | 0.220001i | ||||
\(769\) | 327.202i | 0.425490i | 0.977108 | + | 0.212745i | \(0.0682403\pi\) | ||||
−0.977108 | + | 0.212745i | \(0.931760\pi\) | |||||||
\(770\) | 105.583 | − | 2.89731i | 0.137121 | − | 0.00376274i | ||||
\(771\) | −111.571 | −0.144710 | ||||||||
\(772\) | −893.352 | − | 893.352i | −1.15719 | − | 1.15719i | ||||
\(773\) | 224.127 | − | 224.127i | 0.289944 | − | 0.289944i | −0.547114 | − | 0.837058i | \(-0.684274\pi\) |
0.837058 | + | 0.547114i | \(0.184274\pi\) | |||||||
\(774\) | 110.171i | 0.142340i | ||||||||
\(775\) | 125.274 | − | 6.88044i | 0.161643 | − | 0.00887799i | ||||
\(776\) | 169.181 | 0.218017 | ||||||||
\(777\) | 106.433 | + | 106.433i | 0.136980 | + | 0.136980i | ||||
\(778\) | −566.088 | + | 566.088i | −0.727620 | + | 0.727620i | ||||
\(779\) | 556.136i | 0.713910i | ||||||||
\(780\) | 3.78428 | + | 137.906i | 0.00485165 | + | 0.176803i | ||||
\(781\) | −61.8409 | −0.0791817 | ||||||||
\(782\) | 1467.95 | + | 1467.95i | 1.87717 | + | 1.87717i | ||||
\(783\) | 192.352 | − | 192.352i | 0.245660 | − | 0.245660i | ||||
\(784\) | 87.6559i | 0.111806i | ||||||||
\(785\) | −635.951 | + | 671.838i | −0.810129 | + | 0.855845i | ||||
\(786\) | −142.901 | −0.181808 | ||||||||
\(787\) | −309.705 | − | 309.705i | −0.393526 | − | 0.393526i | 0.482416 | − | 0.875942i | \(-0.339759\pi\) |
−0.875942 | + | 0.482416i | \(0.839759\pi\) | |||||||
\(788\) | −405.918 | + | 405.918i | −0.515124 | + | 0.515124i | ||||
\(789\) | − | 456.789i | − | 0.578947i | ||||||
\(790\) | −1264.58 | − | 1197.03i | −1.60073 | − | 1.51523i | ||||
\(791\) | 128.031 | 0.161860 | ||||||||
\(792\) | 12.4413 | + | 12.4413i | 0.0157087 | + | 0.0157087i | ||||
\(793\) | 195.464 | − | 195.464i | 0.246486 | − | 0.246486i | ||||
\(794\) | − | 260.024i | − | 0.327486i | ||||||
\(795\) | 314.314 | − | 8.62508i | 0.395363 | − | 0.0108492i | ||||
\(796\) | 504.801 | 0.634173 | ||||||||
\(797\) | −138.230 | − | 138.230i | −0.173438 | − | 0.173438i | 0.615050 | − | 0.788488i | \(-0.289136\pi\) |
−0.788488 | + | 0.615050i | \(0.789136\pi\) | |||||||
\(798\) | 87.9831 | − | 87.9831i | 0.110254 | − | 0.110254i | ||||
\(799\) | 73.4210i | 0.0918911i | ||||||||
\(800\) | −850.813 | − | 762.220i | −1.06352 | − | 0.952774i | ||||
\(801\) | 357.029 | 0.445728 | ||||||||
\(802\) | 1088.37 | + | 1088.37i | 1.35707 | + | 1.35707i | ||||
\(803\) | −14.5510 | + | 14.5510i | −0.0181208 | + | 0.0181208i | ||||
\(804\) | 755.681i | 0.939902i | ||||||||
\(805\) | −11.0093 | − | 401.198i | −0.0136761 | − | 0.498383i | ||||
\(806\) | 49.9036 | 0.0619151 | ||||||||
\(807\) | −599.394 | − | 599.394i | −0.742743 | − | 0.742743i | ||||
\(808\) | −196.981 | + | 196.981i | −0.243789 | + | 0.243789i | ||||
\(809\) | 814.512i | 1.00681i | 0.864050 | + | 0.503407i | \(0.167920\pi\) | ||||
−0.864050 | + | 0.503407i | \(0.832080\pi\) | |||||||
\(810\) | 91.4261 | − | 96.5853i | 0.112872 | − | 0.119241i | ||||
\(811\) | 255.277 | 0.314769 | 0.157384 | − | 0.987537i | \(-0.449694\pi\) | ||||
0.157384 | + | 0.987537i | \(0.449694\pi\) | |||||||
\(812\) | −463.705 | − | 463.705i | −0.571065 | − | 0.571065i | ||||
\(813\) | −43.3133 | + | 43.3133i | −0.0532759 | + | 0.0532759i | ||||
\(814\) | 262.255i | 0.322180i | ||||||||
\(815\) | −182.725 | − | 172.965i | −0.224203 | − | 0.212227i | ||||
\(816\) | −502.164 | −0.615397 | ||||||||
\(817\) | 80.7225 | + | 80.7225i | 0.0988036 | + | 0.0988036i | ||||
\(818\) | 1202.71 | − | 1202.71i | 1.47031 | − | 1.47031i | ||||
\(819\) | − | 26.7060i | − | 0.0326080i | ||||||
\(820\) | 1432.46 | − | 39.3080i | 1.74690 | − | 0.0479366i | ||||
\(821\) | −340.619 | −0.414883 | −0.207441 | − | 0.978247i | \(-0.566514\pi\) | ||||
−0.207441 | + | 0.978247i | \(0.566514\pi\) | |||||||
\(822\) | −354.603 | − | 354.603i | −0.431390 | − | 0.431390i | ||||
\(823\) | −109.226 | + | 109.226i | −0.132717 | + | 0.132717i | −0.770345 | − | 0.637628i | \(-0.779916\pi\) |
0.637628 | + | 0.770345i | \(0.279916\pi\) | |||||||
\(824\) | 32.5385i | 0.0394885i | ||||||||
\(825\) | 78.0582 | − | 87.1309i | 0.0946160 | − | 0.105613i | ||||
\(826\) | −789.592 | −0.955922 | ||||||||
\(827\) | −543.650 | − | 543.650i | −0.657376 | − | 0.657376i | 0.297383 | − | 0.954758i | \(-0.403886\pi\) |
−0.954758 | + | 0.297383i | \(0.903886\pi\) | |||||||
\(828\) | 304.711 | − | 304.711i | 0.368008 | − | 0.368008i | ||||
\(829\) | − | 419.953i | − | 0.506578i | −0.967391 | − | 0.253289i | \(-0.918488\pi\) | ||
0.967391 | − | 0.253289i | \(-0.0815123\pi\) | |||||||
\(830\) | 49.0175 | + | 1786.29i | 0.0590573 | + | 2.15215i | ||||
\(831\) | 217.306 | 0.261500 | ||||||||
\(832\) | −202.112 | − | 202.112i | −0.242923 | − | 0.242923i | ||||
\(833\) | −114.600 | + | 114.600i | −0.137575 | + | 0.137575i | ||||
\(834\) | 1197.28i | 1.43558i | ||||||||
\(835\) | −134.882 | + | 142.493i | −0.161535 | + | 0.170650i | ||||
\(836\) | 117.512 | 0.140565 | ||||||||
\(837\) | −18.4391 | − | 18.4391i | −0.0220300 | − | 0.0220300i | ||||
\(838\) | 237.139 | − | 237.139i | 0.282982 | − | 0.282982i | ||||
\(839\) | − | 762.801i | − | 0.909178i | −0.890701 | − | 0.454589i | \(-0.849786\pi\) | ||
0.890701 | − | 0.454589i | \(-0.150214\pi\) | |||||||
\(840\) | −36.1240 | − | 34.1944i | −0.0430048 | − | 0.0407077i | ||||
\(841\) | −1899.68 | −2.25884 | ||||||||
\(842\) | 1541.72 | + | 1541.72i | 1.83103 | + | 1.83103i | ||||
\(843\) | 38.8519 | − | 38.8519i | 0.0460876 | − | 0.0460876i | ||||
\(844\) | − | 994.820i | − | 1.17870i | ||||||
\(845\) | −788.099 | + | 21.6262i | −0.932662 | + | 0.0255932i | ||||
\(846\) | 28.1164 | 0.0332345 | ||||||||
\(847\) | 212.716 | + | 212.716i | 0.251140 | + | 0.251140i | ||||
\(848\) | −321.487 | + | 321.487i | −0.379113 | + | 0.379113i | ||||
\(849\) | − | 273.025i | − | 0.321584i | ||||||
\(850\) | −93.8135 | − | 1708.08i | −0.110369 | − | 2.00951i | ||||
\(851\) | 996.522 | 1.17100 | ||||||||
\(852\) | 132.733 | + | 132.733i | 0.155790 | + | 0.155790i | ||||
\(853\) | −594.088 | + | 594.088i | −0.696469 | + | 0.696469i | −0.963647 | − | 0.267178i | \(-0.913909\pi\) |
0.267178 | + | 0.963647i | \(0.413909\pi\) | |||||||
\(854\) | 642.410i | 0.752236i | ||||||||
\(855\) | −3.78018 | − | 137.757i | −0.00442126 | − | 0.161119i | ||||
\(856\) | −424.767 | −0.496223 | ||||||||
\(857\) | 346.747 | + | 346.747i | 0.404605 | + | 0.404605i | 0.879852 | − | 0.475247i | \(-0.157641\pi\) |
−0.475247 | + | 0.879852i | \(0.657641\pi\) | |||||||
\(858\) | 32.9021 | − | 32.9021i | 0.0383475 | − | 0.0383475i | ||||
\(859\) | − | 1031.74i | − | 1.20110i | −0.799588 | − | 0.600549i | \(-0.794949\pi\) | ||
0.799588 | − | 0.600549i | \(-0.205051\pi\) | |||||||
\(860\) | 202.214 | − | 213.625i | 0.235132 | − | 0.248401i | ||||
\(861\) | −277.400 | −0.322183 | ||||||||
\(862\) | 1308.42 | + | 1308.42i | 1.51788 | + | 1.51788i | ||||
\(863\) | −695.429 | + | 695.429i | −0.805828 | + | 0.805828i | −0.983999 | − | 0.178172i | \(-0.942982\pi\) |
0.178172 | + | 0.983999i | \(0.442982\pi\) | |||||||
\(864\) | 237.424i | 0.274796i | ||||||||
\(865\) | −979.732 | − | 927.399i | −1.13264 | − | 1.07214i | ||||
\(866\) | 415.093 | 0.479322 | ||||||||
\(867\) | −302.572 | − | 302.572i | −0.348987 | − | 0.348987i | ||||
\(868\) | −44.4514 | + | 44.4514i | −0.0512113 | + | 0.0512113i | ||||
\(869\) | 318.344i | 0.366334i | ||||||||
\(870\) | −1339.42 | + | 36.7550i | −1.53956 | + | 0.0422472i | ||||
\(871\) | 310.055 | 0.355975 | ||||||||
\(872\) | 247.737 | + | 247.737i | 0.284102 | + | 0.284102i | ||||
\(873\) | −165.318 | + | 165.318i | −0.189367 | + | 0.189367i | ||||
\(874\) | − | 823.774i | − | 0.942533i | ||||||
\(875\) | −213.837 | + | 252.287i | −0.244385 | + | 0.288328i | ||||
\(876\) | 62.4636 | 0.0713055 | ||||||||
\(877\) | 1168.49 | + | 1168.49i | 1.33237 | + | 1.33237i | 0.903247 | + | 0.429121i | \(0.141177\pi\) |
0.429121 | + | 0.903247i | \(0.358823\pi\) | |||||||
\(878\) | −521.953 | + | 521.953i | −0.594479 | + | 0.594479i | ||||
\(879\) | 25.3141i | 0.0287988i | ||||||||
\(880\) | 4.63991 | + | 169.087i | 0.00527262 | + | 0.192144i | ||||
\(881\) | −303.523 | −0.344522 | −0.172261 | − | 0.985051i | \(-0.555107\pi\) | ||||
−0.172261 | + | 0.985051i | \(0.555107\pi\) | |||||||
\(882\) | 43.8858 | + | 43.8858i | 0.0497572 | + | 0.0497572i | ||||
\(883\) | 720.863 | − | 720.863i | 0.816379 | − | 0.816379i | −0.169202 | − | 0.985581i | \(-0.554119\pi\) |
0.985581 | + | 0.169202i | \(0.0541190\pi\) | |||||||
\(884\) | − | 368.824i | − | 0.417221i | ||||||
\(885\) | −601.176 | + | 635.101i | −0.679295 | + | 0.717628i | ||||
\(886\) | −893.757 | −1.00876 | ||||||||
\(887\) | 975.650 | + | 975.650i | 1.09994 | + | 1.09994i | 0.994416 | + | 0.105527i | \(0.0336530\pi\) |
0.105527 | + | 0.994416i | \(0.466347\pi\) | |||||||
\(888\) | 87.3307 | − | 87.3307i | 0.0983454 | − | 0.0983454i | ||||
\(889\) | 50.0553i | 0.0563052i | ||||||||
\(890\) | −1277.17 | − | 1208.95i | −1.43503 | − | 1.35837i | ||||
\(891\) | −24.3143 | −0.0272888 | ||||||||
\(892\) | −654.799 | − | 654.799i | −0.734080 | − | 0.734080i | ||||
\(893\) | 20.6010 | − | 20.6010i | 0.0230694 | − | 0.0230694i | ||||
\(894\) | − | 653.147i | − | 0.730590i | ||||||
\(895\) | 901.554 | − | 24.7395i | 1.00732 | − | 0.0276419i | ||||
\(896\) | 180.697 | 0.201671 | ||||||||
\(897\) | −125.022 | − | 125.022i | −0.139378 | − | 0.139378i | ||||
\(898\) | −1129.62 | + | 1129.62i | −1.25793 | + | 1.25793i | ||||
\(899\) | 262.726i | 0.292242i | ||||||||
\(900\) | −354.556 | + | 19.4734i | −0.393952 | + | 0.0216371i | ||||
\(901\) | −840.617 | −0.932983 | ||||||||
\(902\) | −341.760 | − | 341.760i | −0.378892 | − | 0.378892i | ||||
\(903\) | −40.2643 | + | 40.2643i | −0.0445895 | + | 0.0445895i | ||||
\(904\) | − | 105.052i | − | 0.116208i | ||||||
\(905\) | −2.85362 | − | 103.991i | −0.00315318 | − | 0.114907i | ||||
\(906\) | −251.808 | −0.277934 | ||||||||
\(907\) | −265.891 | − | 265.891i | −0.293155 | − | 0.293155i | 0.545171 | − | 0.838325i | \(-0.316465\pi\) |
−0.838325 | + | 0.545171i | \(0.816465\pi\) | |||||||
\(908\) | 1355.98 | − | 1355.98i | 1.49337 | − | 1.49337i | ||||
\(909\) | − | 384.967i | − | 0.423506i | ||||||
\(910\) | −90.4305 | + | 95.5335i | −0.0993742 | + | 0.104982i | ||||
\(911\) | 916.932 | 1.00651 | 0.503256 | − | 0.864138i | \(-0.332135\pi\) | ||||
0.503256 | + | 0.864138i | \(0.332135\pi\) | |||||||
\(912\) | 140.901 | + | 140.901i | 0.154496 | + | 0.154496i | ||||
\(913\) | 231.009 | − | 231.009i | 0.253022 | − | 0.253022i | ||||
\(914\) | − | 987.274i | − | 1.08017i | ||||||
\(915\) | 516.716 | + | 489.115i | 0.564717 | + | 0.534552i | ||||
\(916\) | 998.327 | 1.08988 | ||||||||
\(917\) | −52.2264 | − | 52.2264i | −0.0569535 | − | 0.0569535i | ||||
\(918\) | −251.414 | + | 251.414i | −0.273871 | + | 0.273871i | ||||
\(919\) | − | 421.767i | − | 0.458941i | −0.973316 | − | 0.229470i | \(-0.926301\pi\) | ||
0.973316 | − | 0.229470i | \(-0.0736994\pi\) | |||||||
\(920\) | −329.191 | + | 9.03334i | −0.357816 | + | 0.00981884i | ||||
\(921\) | −726.682 | −0.789014 | ||||||||
\(922\) | 328.072 | + | 328.072i | 0.355827 | + | 0.355827i | ||||
\(923\) | 54.4602 | − | 54.4602i | 0.0590035 | − | 0.0590035i | ||||
\(924\) | 58.6148i | 0.0634360i | ||||||||
\(925\) | −611.611 | − | 547.925i | −0.661201 | − | 0.592352i | ||||
\(926\) | −1124.99 | −1.21489 | ||||||||
\(927\) | −31.7955 | − | 31.7955i | −0.0342994 | − | 0.0342994i | ||||
\(928\) | 1691.44 | − | 1691.44i | 1.82267 | − | 1.82267i | ||||
\(929\) | 416.476i | 0.448305i | 0.974554 | + | 0.224153i | \(0.0719614\pi\) | ||||
−0.974554 | + | 0.224153i | \(0.928039\pi\) | |||||||
\(930\) | 3.52339 | + | 128.399i | 0.00378859 | + | 0.138063i | ||||
\(931\) | 64.3106 | 0.0690769 | ||||||||
\(932\) | 1031.57 | + | 1031.57i | 1.10683 | + | 1.10683i | ||||
\(933\) | 45.1196 | − | 45.1196i | 0.0483598 | − | 0.0483598i | ||||
\(934\) | 479.401i | 0.513277i | ||||||||
\(935\) | −214.996 | + | 227.128i | −0.229942 | + | 0.242918i | ||||
\(936\) | −21.9128 | −0.0234111 | ||||||||
\(937\) | 877.123 | + | 877.123i | 0.936097 | + | 0.936097i | 0.998077 | − | 0.0619806i | \(-0.0197417\pi\) |
−0.0619806 | + | 0.998077i | \(0.519742\pi\) | |||||||
\(938\) | −509.511 | + | 509.511i | −0.543189 | + | 0.543189i | ||||
\(939\) | − | 221.763i | − | 0.236170i | ||||||
\(940\) | −54.5186 | − | 51.6064i | −0.0579985 | − | 0.0549005i | ||||
\(941\) | 1322.22 | 1.40513 | 0.702563 | − | 0.711621i | \(-0.252039\pi\) | ||||
0.702563 | + | 0.711621i | \(0.252039\pi\) | |||||||
\(942\) | −669.703 | − | 669.703i | −0.710937 | − | 0.710937i | ||||
\(943\) | −1298.63 | + | 1298.63i | −1.37713 | + | 1.37713i | ||||
\(944\) | − | 1264.49i | − | 1.33951i | ||||||
\(945\) | 68.7128 | − | 1.88555i | 0.0727119 | − | 0.00199529i | ||||
\(946\) | −99.2122 | −0.104876 | ||||||||
\(947\) | −445.898 | − | 445.898i | −0.470853 | − | 0.470853i | 0.431338 | − | 0.902191i | \(-0.358042\pi\) |
−0.902191 | + | 0.431338i | \(0.858042\pi\) | |||||||
\(948\) | 683.283 | − | 683.283i | 0.720763 | − | 0.720763i | ||||
\(949\) | − | 25.6287i | − | 0.0270060i | ||||||
\(950\) | −452.942 | + | 505.588i | −0.476781 | + | 0.532197i | ||||
\(951\) | −5.88178 | −0.00618484 | ||||||||
\(952\) | 94.0317 | + | 94.0317i | 0.0987728 | + | 0.0987728i | ||||
\(953\) | 568.485 | − | 568.485i | 0.596521 | − | 0.596521i | −0.342864 | − | 0.939385i | \(-0.611397\pi\) |
0.939385 | + | 0.342864i | \(0.111397\pi\) | |||||||
\(954\) | 321.912i | 0.337434i | ||||||||
\(955\) | 30.3936 | + | 1107.60i | 0.0318257 | + | 1.15979i | ||||
\(956\) | −489.667 | −0.512204 | ||||||||
\(957\) | 173.219 | + | 173.219i | 0.181002 | + | 0.181002i | ||||
\(958\) | 330.881 | − | 330.881i | 0.345388 | − | 0.345388i | ||||
\(959\) | − | 259.194i | − | 0.270275i | ||||||
\(960\) | 505.750 | − | 534.290i | 0.526823 | − | 0.556552i | ||||
\(961\) | −935.815 | −0.973793 | ||||||||
\(962\) | −230.955 | − | 230.955i | −0.240078 | − | 0.240078i | ||||
\(963\) | 415.067 | − | 415.067i | 0.431015 | − | 0.431015i | ||||
\(964\) | − | 63.1334i | − | 0.0654911i | ||||||
\(965\) | −968.965 | − | 917.206i | −1.00411 | − | 0.950473i | ||||
\(966\) | 410.897 | 0.425359 | ||||||||
\(967\) | −721.223 | − | 721.223i | −0.745836 | − | 0.745836i | 0.227858 | − | 0.973694i | \(-0.426828\pi\) |
−0.973694 | + | 0.227858i | \(0.926828\pi\) | |||||||
\(968\) | 174.538 | − | 174.538i | 0.180307 | − | 0.180307i | ||||
\(969\) | 368.423i | 0.380210i | ||||||||
\(970\) | 1151.17 | − | 31.5893i | 1.18677 | − | 0.0325663i | ||||
\(971\) | 670.576 | 0.690604 | 0.345302 | − | 0.938492i | \(-0.387777\pi\) | ||||
0.345302 | + | 0.938492i | \(0.387777\pi\) | |||||||
\(972\) | 52.1875 | + | 52.1875i | 0.0536908 | + | 0.0536908i | ||||
\(973\) | −437.570 | + | 437.570i | −0.449713 | + | 0.449713i | ||||
\(974\) | 923.127i | 0.947769i | ||||||||
\(975\) | 7.98991 | + | 145.474i | 0.00819478 | + | 0.149204i | ||||
\(976\) | −1028.79 | −1.05409 | ||||||||
\(977\) | −787.654 | − | 787.654i | −0.806196 | − | 0.806196i | 0.177860 | − | 0.984056i | \(-0.443083\pi\) |
−0.984056 | + | 0.177860i | \(0.943083\pi\) | |||||||
\(978\) | 182.145 | − | 182.145i | 0.186242 | − | 0.186242i | ||||
\(979\) | 321.515i | 0.328412i | ||||||||
\(980\) | −4.54551 | − | 165.647i | −0.00463828 | − | 0.169027i | ||||
\(981\) | −484.160 | −0.493537 | ||||||||
\(982\) | 1934.74 | + | 1934.74i | 1.97021 | + | 1.97021i | ||||
\(983\) | −585.387 | + | 585.387i | −0.595510 | + | 0.595510i | −0.939115 | − | 0.343604i | \(-0.888352\pi\) |
0.343604 | + | 0.939115i | \(0.388352\pi\) | |||||||
\(984\) | 227.612i | 0.231313i | ||||||||
\(985\) | −416.756 | + | 440.274i | −0.423103 | + | 0.446979i | ||||
\(986\) | 3582.22 | 3.63308 | ||||||||
\(987\) | 10.2757 | + | 10.2757i | 0.0104111 | + | 0.0104111i | ||||
\(988\) | −103.487 | + | 103.487i | −0.104744 | + | 0.104744i | ||||
\(989\) | 376.989i | 0.381182i | ||||||||
\(990\) | 86.9780 | + | 82.3320i | 0.0878566 | + | 0.0831636i | ||||
\(991\) | −1406.48 | −1.41925 | −0.709627 | − | 0.704577i | \(-0.751137\pi\) | ||||
−0.709627 | + | 0.704577i | \(0.751137\pi\) | |||||||
\(992\) | −162.144 | − | 162.144i | −0.163451 | − | 0.163451i | ||||
\(993\) | 352.752 | − | 352.752i | 0.355239 | − | 0.355239i | ||||
\(994\) | 178.989i | 0.180069i | ||||||||
\(995\) | 532.904 | − | 14.6234i | 0.535582 | − | 0.0146969i | ||||
\(996\) | −991.662 | −0.995644 | ||||||||
\(997\) | 718.536 | + | 718.536i | 0.720698 | + | 0.720698i | 0.968747 | − | 0.248049i | \(-0.0797894\pi\) |
−0.248049 | + | 0.968747i | \(0.579789\pi\) | |||||||
\(998\) | 240.232 | − | 240.232i | 0.240714 | − | 0.240714i | ||||
\(999\) | 170.673i | 0.170844i |
(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 | 105.3.l.a.22.9 | ✓ | 24 | |
3.2 | odd | 2 | 315.3.o.b.127.4 | 24 | |||
5.2 | odd | 4 | 525.3.l.e.43.4 | 24 | |||
5.3 | odd | 4 | inner | 105.3.l.a.43.9 | yes | 24 | |
5.4 | even | 2 | 525.3.l.e.232.4 | 24 | |||
15.8 | even | 4 | 315.3.o.b.253.4 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.l.a.22.9 | ✓ | 24 | 1.1 | even | 1 | trivial | |
105.3.l.a.43.9 | yes | 24 | 5.3 | odd | 4 | inner | |
315.3.o.b.127.4 | 24 | 3.2 | odd | 2 | |||
315.3.o.b.253.4 | 24 | 15.8 | even | 4 | |||
525.3.l.e.43.4 | 24 | 5.2 | odd | 4 | |||
525.3.l.e.232.4 | 24 | 5.4 | even | 2 |