Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,3,Mod(43,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.43");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.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: | \(14.3052138789\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.4 | ||
Character | \(\chi\) | \(=\) | 525.43 |
Dual form | 525.3.l.e.232.4 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
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 | −0.0459576 | + | 0.998943i | \(0.514634\pi\) |
−0.998943 | + | 0.0459576i | \(0.985366\pi\) | |||||||
\(3\) | 1.22474 | + | 1.22474i | 0.408248 | + | 0.408248i | ||||
\(4\) | − | 4.73454i | − | 1.18364i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −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 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 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 | \(-0.208692\pi\) |
−0.609655 | + | 0.792667i | \(0.708692\pi\) | |||||||
\(14\) | 7.81932i | 0.558523i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 12.5223 | 0.782642 | ||||||||
\(17\) | −16.3715 | + | 16.3715i | −0.963027 | + | 0.963027i | −0.999340 | − | 0.0363138i | \(-0.988438\pi\) |
0.0363138 | + | 0.999340i | \(0.488438\pi\) | |||||||
\(18\) | −6.26941 | − | 6.26941i | −0.348300 | − | 0.348300i | ||||
\(19\) | 9.18722i | 0.483538i | 0.970334 | + | 0.241769i | \(0.0777276\pi\) | ||||
−0.970334 | + | 0.241769i | \(0.922272\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 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 | \(-0.479252\pi\) |
−0.997876 | + | 0.0651365i | \(0.979252\pi\) | |||||||
\(24\) | 3.76010i | 0.156671i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −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 | \(0.358354\pi\) | ||||
−0.430453 | + | 0.902613i | \(0.641646\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −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 | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 14.2036 | 0.394545 | ||||||||
\(37\) | −23.2257 | + | 23.2257i | −0.627721 | + | 0.627721i | −0.947494 | − | 0.319773i | \(-0.896393\pi\) |
0.319773 | + | 0.947494i | \(0.396393\pi\) | |||||||
\(38\) | −19.1995 | − | 19.1995i | −0.505249 | − | 0.505249i | ||||
\(39\) | 5.82772i | 0.149429i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −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 | \(-0.203847\pi\) |
−0.597520 | + | 0.801854i | \(0.703847\pi\) | |||||||
\(44\) | − | 12.7908i | − | 0.290700i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 89.6651 | 1.94924 | ||||||||
\(47\) | −2.24235 | + | 2.24235i | −0.0477096 | + | 0.0477096i | −0.730559 | − | 0.682850i | \(-0.760740\pi\) |
0.682850 | + | 0.730559i | \(0.260740\pi\) | |||||||
\(48\) | 15.3366 | + | 15.3366i | 0.319512 | + | 0.319512i | ||||
\(49\) | − | 7.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −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 | \(-0.138718\pi\) |
−0.422133 | + | 0.906534i | \(0.638718\pi\) | |||||||
\(54\) | − | 15.3568i | − | 0.284386i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 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 | \(0.326909\pi\) | ||||
−0.517374 | + | 0.855759i | \(0.673091\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −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 | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −13.8293 | −0.209535 | ||||||||
\(67\) | 65.1606 | − | 65.1606i | 0.972546 | − | 0.972546i | −0.0270874 | − | 0.999633i | \(-0.508623\pi\) |
0.999633 | + | 0.0270874i | \(0.00862323\pi\) | |||||||
\(68\) | 77.5114 | + | 77.5114i | 1.13987 | + | 1.13987i | ||||
\(69\) | − | 52.5489i | − | 0.761579i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −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 | \(-0.233386\pi\) |
−0.669253 | + | 0.743035i | \(0.733386\pi\) | |||||||
\(74\) | − | 97.0741i | − | 1.31181i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 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 | \(-0.732070\pi\) | ||
0.666175 | − | 0.745795i | \(-0.267930\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 126.503 | − | 126.503i | 1.54272 | − | 1.54272i | ||||
\(83\) | −85.5086 | − | 85.5086i | −1.03022 | − | 1.03022i | −0.999529 | − | 0.0306951i | \(-0.990228\pi\) |
−0.0306951 | − | 0.999529i | \(-0.509772\pi\) | |||||||
\(84\) | − | 21.6964i | − | 0.258291i | ||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −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 | \(-0.766897\pi\) | ||
0.743629 | − | 0.668593i | \(-0.233103\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 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 | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −79.1412 | −0.824388 | ||||||||
\(97\) | 55.1059 | − | 55.1059i | 0.568102 | − | 0.568102i | −0.363494 | − | 0.931596i | \(-0.618416\pi\) |
0.931596 | + | 0.363494i | \(0.118416\pi\) | |||||||
\(98\) | 14.6286 | + | 14.6286i | 0.149272 | + | 0.149272i | ||||
\(99\) | 8.10478i | 0.0818664i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 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 | \(-0.273181\pi\) |
−0.756682 | + | 0.653783i | \(0.773181\pi\) | |||||||
\(104\) | 7.30426i | 0.0702333i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −107.304 | −1.01230 | ||||||||
\(107\) | −138.356 | + | 138.356i | −1.29305 | + | 1.29305i | −0.360151 | + | 0.932894i | \(0.617275\pi\) |
−0.932894 | + | 0.360151i | \(0.882725\pi\) | |||||||
\(108\) | 17.3958 | + | 17.3958i | 0.161072 | + | 0.161072i | ||||
\(109\) | 161.387i | 1.48061i | 0.672271 | + | 0.740305i | \(0.265319\pi\) | ||||
−0.672271 | + | 0.740305i | \(0.734681\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −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 | \(-0.181311\pi\) |
−0.539301 | + | 0.842113i | \(0.681311\pi\) | |||||||
\(114\) | − | 47.0289i | − | 0.412534i | ||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 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 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −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 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −23.4580 | −0.186174 | ||||||||
\(127\) | 13.3778 | − | 13.3778i | 0.105337 | − | 0.105337i | −0.652474 | − | 0.757811i | \(-0.726269\pi\) |
0.757811 | + | 0.652474i | \(0.226269\pi\) | |||||||
\(128\) | 48.2934 | + | 48.2934i | 0.377292 | + | 0.377292i | ||||
\(129\) | 21.5222i | 0.166838i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 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 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −50.2621 | −0.369574 | ||||||||
\(137\) | −69.2726 | + | 69.2726i | −0.505639 | + | 0.505639i | −0.913185 | − | 0.407546i | \(-0.866385\pi\) |
0.407546 | + | 0.913185i | \(0.366385\pi\) | |||||||
\(138\) | 109.817 | + | 109.817i | 0.795775 | + | 0.795775i | ||||
\(139\) | 233.891i | 1.68267i | 0.540513 | + | 0.841335i | \(0.318230\pi\) | ||||
−0.540513 | + | 0.841335i | \(0.681770\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −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 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −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 | \(-0.859159\pi\) | ||
0.903699 | − | 0.428168i | \(-0.140841\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 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 | 0 | ||||||||
\(156\) | 27.5916 | 0.176869 | ||||||||
\(157\) | −130.828 | + | 130.828i | −0.833301 | + | 0.833301i | −0.987967 | − | 0.154666i | \(-0.950570\pi\) |
0.154666 | + | 0.987967i | \(0.450570\pi\) | |||||||
\(158\) | 246.253 | + | 246.253i | 1.55856 | + | 1.55856i | ||||
\(159\) | 62.8864i | 0.395512i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −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 | \(-0.200669\pi\) |
−0.589483 | + | 0.807780i | \(0.700669\pi\) | |||||||
\(164\) | 286.599i | 1.74756i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 357.392 | 2.15296 | ||||||||
\(167\) | −27.7479 | + | 27.7479i | −0.166155 | + | 0.166155i | −0.785287 | − | 0.619132i | \(-0.787485\pi\) |
0.619132 | + | 0.785287i | \(0.287485\pi\) | |||||||
\(168\) | 7.03449 | + | 7.03449i | 0.0418720 | + | 0.0418720i | ||||
\(169\) | − | 157.679i | − | 0.933013i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −27.5617 | −0.161179 | ||||||||
\(172\) | 41.5995 | − | 41.5995i | 0.241858 | − | 0.241858i | ||||
\(173\) | 190.785 | + | 190.785i | 1.10280 | + | 1.10280i | 0.994071 | + | 0.108732i | \(0.0346790\pi\) |
0.108732 | + | 0.994071i | \(0.465321\pi\) | |||||||
\(174\) | − | 267.985i | − | 1.54014i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 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 | \(0.168084\pi\) | ||||
−0.863791 | + | 0.503851i | \(0.831916\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −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 | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 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 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 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 | \(-0.00703437\pi\) |
−0.0220973 | + | 0.999756i | \(0.507034\pi\) | |||||||
\(194\) | 230.321i | 1.18722i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −33.1418 | −0.169091 | ||||||||
\(197\) | −85.7353 | + | 85.7353i | −0.435205 | + | 0.435205i | −0.890394 | − | 0.455190i | \(-0.849571\pi\) |
0.455190 | + | 0.890394i | \(0.349571\pi\) | |||||||
\(198\) | −16.9374 | − | 16.9374i | −0.0855423 | − | 0.0855423i | ||||
\(199\) | 106.621i | 0.535783i | 0.963449 | + | 0.267892i | \(0.0863269\pi\) | ||||
−0.963449 | + | 0.267892i | \(0.913673\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 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 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 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 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −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 | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −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 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −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 | \(-0.105495\pi\) |
−0.325389 | + | 0.945580i | \(0.605495\pi\) | |||||||
\(224\) | 120.890i | 0.539688i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −143.017 | −0.632818 | ||||||||
\(227\) | 286.401 | − | 286.401i | 1.26168 | − | 1.26168i | 0.311397 | − | 0.950280i | \(-0.399203\pi\) |
0.950280 | − | 0.311397i | \(-0.100797\pi\) | |||||||
\(228\) | 53.2731 | + | 53.2731i | 0.233654 | + | 0.233654i | ||||
\(229\) | 210.860i | 0.920787i | 0.887715 | + | 0.460394i | \(0.152292\pi\) | ||||
−0.887715 | + | 0.460394i | \(0.847708\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 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 | \(-0.479963\pi\) |
−0.998019 | + | 0.0629077i | \(0.979963\pi\) | |||||||
\(234\) | − | 29.8318i | − | 0.127486i | ||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 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 | \(-0.930579\pi\) | ||
0.976312 | − | 0.216369i | \(-0.0694213\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −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 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 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 | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −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 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 137.956 | 0.538891 | ||||||||
\(257\) | −45.5488 | + | 45.5488i | −0.177233 | + | 0.177233i | −0.790148 | − | 0.612916i | \(-0.789997\pi\) |
0.612916 | + | 0.790148i | \(0.289997\pi\) | |||||||
\(258\) | −44.9771 | − | 44.9771i | −0.174330 | − | 0.174330i | ||||
\(259\) | 86.9025i | 0.335531i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −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 | \(-0.0828250\pi\) |
−0.257276 | + | 0.966338i | \(0.582825\pi\) | |||||||
\(264\) | 10.1582i | 0.0384782i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −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 | \(-0.636334\pi\) | ||
0.415330 | − | 0.909671i | \(-0.363666\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 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 | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −248.795 | −0.901432 | ||||||||
\(277\) | 88.7149 | − | 88.7149i | 0.320270 | − | 0.320270i | −0.528600 | − | 0.848871i | \(-0.677283\pi\) |
0.848871 | + | 0.528600i | \(0.177283\pi\) | |||||||
\(278\) | −488.786 | − | 488.786i | −1.75822 | − | 1.75822i | ||||
\(279\) | − | 15.0555i | − | 0.0539623i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −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 | \(-0.160163\pi\) |
−0.482202 | + | 0.876060i | \(0.660163\pi\) | |||||||
\(284\) | 108.376i | 0.381607i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −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 | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 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 | \(-0.257940\pi\) |
−0.724522 | + | 0.689251i | \(0.757940\pi\) | |||||||
\(294\) | 35.8326i | 0.121880i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −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 | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 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 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 205.279 | 0.670845 | ||||||||
\(307\) | −296.667 | + | 296.667i | −0.966341 | + | 0.966341i | −0.999452 | − | 0.0331110i | \(-0.989459\pi\) |
0.0331110 | + | 0.999452i | \(0.489459\pi\) | |||||||
\(308\) | −23.9294 | − | 23.9294i | −0.0776929 | − | 0.0776929i | ||||
\(309\) | − | 25.9610i | − | 0.0840160i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −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 | \(-0.184434\pi\) |
−0.547535 | + | 0.836783i | \(0.684434\pi\) | |||||||
\(314\) | − | 546.810i | − | 1.74143i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −557.898 | −1.76550 | ||||||||
\(317\) | −2.40123 | + | 2.40123i | −0.00757485 | + | 0.00757485i | −0.710884 | − | 0.703309i | \(-0.751705\pi\) |
0.703309 | + | 0.710884i | \(0.251705\pi\) | |||||||
\(318\) | −131.420 | − | 131.420i | −0.413271 | − | 0.413271i | ||||
\(319\) | 141.433i | 0.443362i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −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 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −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 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −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 | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 57.3842 | 0.170786 | ||||||||
\(337\) | 354.146 | − | 354.146i | 1.05088 | − | 1.05088i | 0.0522432 | − | 0.998634i | \(-0.483363\pi\) |
0.998634 | − | 0.0522432i | \(-0.0166371\pi\) | |||||||
\(338\) | 329.518 | + | 329.518i | 0.974906 | + | 0.974906i | ||||
\(339\) | 83.8162i | 0.247245i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −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 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −797.405 | −2.30464 | ||||||||
\(347\) | 440.033 | − | 440.033i | 1.26811 | − | 1.26811i | 0.321044 | − | 0.947064i | \(-0.395966\pi\) |
0.947064 | − | 0.321044i | \(-0.104034\pi\) | |||||||
\(348\) | 303.566 | + | 303.566i | 0.872316 | + | 0.872316i | ||||
\(349\) | 429.577i | 1.23088i | 0.788184 | + | 0.615440i | \(0.211022\pi\) | ||||
−0.788184 | + | 0.615440i | \(0.788978\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −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 | \(-0.410041\pi\) |
−0.960330 | + | 0.278867i | \(0.910041\pi\) | |||||||
\(354\) | − | 516.909i | − | 1.46020i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −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 | \(0.0237404\pi\) | ||||
−0.997220 | + | 0.0745135i | \(0.976260\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 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 | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 420.556 | 1.14906 | ||||||||
\(367\) | −1.26172 | + | 1.26172i | −0.00343792 | + | 0.00343792i | −0.708824 | − | 0.705386i | \(-0.750774\pi\) |
0.705386 | + | 0.708824i | \(0.250774\pi\) | |||||||
\(368\) | −268.640 | − | 268.640i | −0.730001 | − | 0.730001i | ||||
\(369\) | − | 181.601i | − | 0.492143i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 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 | \(-0.220604\pi\) |
−0.638886 | + | 0.769301i | \(0.720604\pi\) | |||||||
\(374\) | − | 184.860i | − | 0.494277i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −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 | \(-0.780622\pi\) | ||
0.771758 | − | 0.635917i | \(-0.219378\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 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 | \(-0.205607\pi\) |
−0.601944 | + | 0.798539i | \(0.705607\pi\) | |||||||
\(384\) | 118.294i | 0.308058i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −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 | \(-0.886801\pi\) | ||
0.937429 | − | 0.348176i | \(-0.113199\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 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 | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 38.3724 | 0.0969001 | ||||||||
\(397\) | 62.2126 | − | 62.2126i | 0.156707 | − | 0.156707i | −0.624399 | − | 0.781106i | \(-0.714656\pi\) |
0.781106 | + | 0.624399i | \(0.214656\pi\) | |||||||
\(398\) | −222.817 | − | 222.817i | −0.559841 | − | 0.559841i | ||||
\(399\) | 42.1012i | 0.105517i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 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 | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −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 | \(0.248409\pi\) | ||||
−0.710631 | + | 0.703564i | \(0.751591\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −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 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −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 | \(0.0432355\pi\) | ||||
−0.990790 | + | 0.135411i | \(0.956765\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 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 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 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 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 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 | \(-0.301854\pi\) |
−0.812426 | + | 0.583064i | \(0.801854\pi\) | |||||||
\(434\) | − | 39.2412i | − | 0.0904176i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 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 | \(-0.908183\pi\) | ||
0.958686 | − | 0.284467i | \(-0.0918165\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 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 | \(-0.139125\pi\) |
−0.423290 | + | 0.905994i | \(0.639125\pi\) | |||||||
\(444\) | 269.353i | 0.606651i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −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 | \(-0.794396\pi\) | ||
0.798544 | − | 0.601937i | \(-0.205604\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −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 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −34.5448 | −0.0757562 | ||||||||
\(457\) | 236.212 | − | 236.212i | 0.516876 | − | 0.516876i | −0.399749 | − | 0.916625i | \(-0.630903\pi\) |
0.916625 | + | 0.399749i | \(0.130903\pi\) | |||||||
\(458\) | −440.656 | − | 440.656i | −0.962131 | − | 0.962131i | ||||
\(459\) | − | 120.305i | − | 0.262103i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 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 | \(-0.115155\pi\) |
−0.353930 | + | 0.935272i | \(0.615155\pi\) | |||||||
\(464\) | 655.560i | 1.41284i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 910.656 | 1.95420 | ||||||||
\(467\) | −114.700 | + | 114.700i | −0.245610 | + | 0.245610i | −0.819166 | − | 0.573556i | \(-0.805564\pi\) |
0.573556 | + | 0.819166i | \(0.305564\pi\) | |||||||
\(468\) | 33.7927 | + | 33.7927i | 0.0722066 | + | 0.0722066i | ||||
\(469\) | − | 243.808i | − | 0.519848i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −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 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 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 | \(0.0528505\pi\) | ||||
−0.986248 | + | 0.165273i | \(0.947149\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −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 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 46.0705 | 0.0947953 | ||||||||
\(487\) | −220.865 | + | 220.865i | −0.453521 | + | 0.453521i | −0.896521 | − | 0.443000i | \(-0.853914\pi\) |
0.443000 | + | 0.896521i | \(0.353914\pi\) | |||||||
\(488\) | −126.115 | − | 126.115i | −0.258432 | − | 0.258432i | ||||
\(489\) | 87.1588i | 0.178239i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 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 | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −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 | \(0.0367461\pi\) | ||||
−0.993344 | + | 0.115185i | \(0.963254\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −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 | \(-0.229205\pi\) |
−0.659436 | + | 0.751761i | \(0.729205\pi\) | |||||||
\(504\) | 17.2309i | 0.0341883i | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 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 | \(0.0581958\pi\) | ||||
−0.983334 | + | 0.181811i | \(0.941804\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 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 | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 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 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −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 | \(-0.0555321\pi\) |
−0.173576 | + | 0.984821i | \(0.555532\pi\) | |||||||
\(524\) | − | 132.170i | − | 0.252233i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −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 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −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 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 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 | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −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 | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −45.5688 | −0.0834594 | ||||||||
\(547\) | 367.275 | − | 367.275i | 0.671436 | − | 0.671436i | −0.286611 | − | 0.958047i | \(-0.592529\pi\) |
0.958047 | + | 0.286611i | \(0.0925288\pi\) | |||||||
\(548\) | 327.974 | + | 327.974i | 0.598493 | + | 0.598493i | ||||
\(549\) | − | 246.470i | − | 0.448944i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −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 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1107.37 | 1.99167 | ||||||||
\(557\) | −532.387 | + | 532.387i | −0.955811 | + | 0.955811i | −0.999064 | − | 0.0432528i | \(-0.986228\pi\) |
0.0432528 | + | 0.999064i | \(0.486228\pi\) | |||||||
\(558\) | 31.4630 | + | 31.4630i | 0.0563853 | + | 0.0563853i | ||||
\(559\) | 41.8084i | 0.0747914i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −108.338 | −0.193117 | ||||||||
\(562\) | 66.2936 | − | 66.2936i | 0.117960 | − | 0.117960i | ||||
\(563\) | 724.535 | + | 724.535i | 1.28692 | + | 1.28692i | 0.936649 | + | 0.350268i | \(0.113910\pi\) |
0.350268 | + | 0.936649i | \(0.386090\pi\) | |||||||
\(564\) | 26.0050i | 0.0461082i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −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 | \(0.0177800\pi\) | ||||
−0.998440 | + | 0.0558284i | \(0.982220\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 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 | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 254.853 | 0.442452 | ||||||||
\(577\) | −650.925 | + | 650.925i | −1.12812 | + | 1.12812i | −0.137637 | + | 0.990483i | \(0.543951\pi\) |
−0.990483 | + | 0.137637i | \(0.956049\pi\) | |||||||
\(578\) | 516.283 | + | 516.283i | 0.893224 | + | 0.893224i | ||||
\(579\) | 462.190i | 0.798255i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −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 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 43.1939 | 0.0737098 | ||||||||
\(587\) | 451.044 | − | 451.044i | 0.768389 | − | 0.768389i | −0.209434 | − | 0.977823i | \(-0.567162\pi\) |
0.977823 | + | 0.209434i | \(0.0671621\pi\) | |||||||
\(588\) | −40.5903 | − | 40.5903i | −0.0690311 | − | 0.0690311i | ||||
\(589\) | − | 46.1060i | − | 0.0782785i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −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 | \(-0.434753\pi\) |
−0.979065 | + | 0.203547i | \(0.934753\pi\) | |||||||
\(594\) | − | 41.4879i | − | 0.0698450i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −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 | \(-0.887164\pi\) | ||
0.937825 | − | 0.347108i | \(-0.112836\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −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 | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −656.875 | −1.08395 | ||||||||
\(607\) | −247.205 | + | 247.205i | −0.407257 | + | 0.407257i | −0.880781 | − | 0.473524i | \(-0.842982\pi\) |
0.473524 | + | 0.880781i | \(0.342982\pi\) | |||||||
\(608\) | −296.833 | − | 296.833i | −0.488211 | − | 0.488211i | ||||
\(609\) | 239.905i | 0.393933i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −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 | \(-0.451367\pi\) |
−0.988351 | + | 0.152192i | \(0.951367\pi\) | |||||||
\(614\) | − | 1239.95i | − | 2.01946i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 15.5170 | 0.0251899 | ||||||||
\(617\) | 700.942 | − | 700.942i | 1.13605 | − | 1.13605i | 0.146897 | − | 0.989152i | \(-0.453072\pi\) |
0.989152 | − | 0.146897i | \(-0.0469284\pi\) | |||||||
\(618\) | 54.2532 | + | 54.2532i | 0.0877884 | + | 0.0877884i | ||||
\(619\) | − | 354.521i | − | 0.572732i | −0.958120 | − | 0.286366i | \(-0.907553\pi\) | ||
0.958120 | − | 0.286366i | \(-0.0924473\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 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 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −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 | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 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 | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 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 | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −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 | \(-0.110614\pi\) |
−0.340554 | + | 0.940225i | \(0.610614\pi\) | |||||||
\(644\) | 380.041i | 0.590126i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 628.647 | 0.973137 | ||||||||
\(647\) | 84.6226 | − | 84.6226i | 0.130792 | − | 0.130792i | −0.638680 | − | 0.769472i | \(-0.720519\pi\) |
0.769472 | + | 0.638680i | \(0.220519\pi\) | |||||||
\(648\) | −13.8155 | − | 13.8155i | −0.0213202 | − | 0.0213202i | ||||
\(649\) | 272.806i | 0.420348i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −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 | \(-0.204172\pi\) |
−0.598337 | + | 0.801244i | \(0.704172\pi\) | |||||||
\(654\) | − | 826.130i | − | 1.26320i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −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 | \(0.246390\pi\) | ||||
−0.715080 | + | 0.699043i | \(0.753610\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 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 | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 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 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −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 | \(-0.418405\pi\) |
−0.967324 | + | 0.253542i | \(0.918405\pi\) | |||||||
\(674\) | 1480.19i | 2.19613i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −746.539 | −1.10435 | ||||||||
\(677\) | −146.784 | + | 146.784i | −0.216815 | + | 0.216815i | −0.807155 | − | 0.590340i | \(-0.798994\pi\) |
0.590340 | + | 0.807155i | \(0.298994\pi\) | |||||||
\(678\) | −175.159 | − | 175.159i | −0.258347 | − | 0.258347i | ||||
\(679\) | − | 206.187i | − | 0.303663i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 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 | \(-0.220726\pi\) |
−0.639179 | + | 0.769058i | \(0.720726\pi\) | |||||||
\(684\) | 130.492i | 0.190778i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 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 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −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 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −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 | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −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 | 0 | ||||||||
\(706\) | 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 | \(-0.915616\pi\) | ||
0.965066 | − | 0.262006i | \(-0.0843842\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 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 | ||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 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 | \(-0.981042\pi\) | ||
0.998227 | − | 0.0595232i | \(-0.0189580\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −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 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 582.032 | 0.801696 | ||||||||
\(727\) | −589.673 | + | 589.673i | −0.811104 | + | 0.811104i | −0.984799 | − | 0.173695i | \(-0.944429\pi\) |
0.173695 | + | 0.984799i | \(0.444429\pi\) | |||||||
\(728\) | 13.6650 | + | 13.6650i | 0.0187706 | + | 0.0187706i | ||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −287.692 | −0.393559 | ||||||||
\(732\) | −476.394 | + | 476.394i | −0.650812 | + | 0.650812i | ||||
\(733\) | −1019.17 | − | 1019.17i | −1.39040 | − | 1.39040i | −0.824411 | − | 0.565992i | \(-0.808493\pi\) |
−0.565992 | − | 0.824411i | \(-0.691507\pi\) | |||||||
\(734\) | − | 5.27347i | − | 0.00718457i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 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 | \(-0.988265\pi\) | ||
0.999321 | − | 0.0368570i | \(-0.0117346\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −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 | \(-0.325810\pi\) |
−0.853968 | + | 0.520326i | \(0.825810\pi\) | |||||||
\(744\) | − | 18.8700i | − | 0.0253629i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −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 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −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 | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 65.0892 | 0.0860969 | ||||||||
\(757\) | −178.475 | + | 178.475i | −0.235767 | + | 0.235767i | −0.815095 | − | 0.579328i | \(-0.803315\pi\) |
0.579328 | + | 0.815095i | \(0.303315\pi\) | |||||||
\(758\) | 1007.34 | + | 1007.34i | 1.32894 | + | 1.32894i | ||||
\(759\) | − | 141.966i | − | 0.187043i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 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 | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −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 | \(-0.931760\pi\) | ||
0.977108 | − | 0.212745i | \(-0.0682403\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −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 | \(-0.315726\pi\) |
−0.837058 | + | 0.547114i | \(0.815726\pi\) | |||||||
\(774\) | − | 110.171i | − | 0.142340i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 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 | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −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 | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −142.901 | −0.181808 | ||||||||
\(787\) | 309.705 | − | 309.705i | 0.393526 | − | 0.393526i | −0.482416 | − | 0.875942i | \(-0.660241\pi\) |
0.875942 | + | 0.482416i | \(0.160241\pi\) | |||||||
\(788\) | 405.918 | + | 405.918i | 0.515124 | + | 0.515124i | ||||
\(789\) | 456.789i | 0.578947i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 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 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 504.801 | 0.634173 | ||||||||
\(797\) | 138.230 | − | 138.230i | 0.173438 | − | 0.173438i | −0.615050 | − | 0.788488i | \(-0.710864\pi\) |
0.788488 | + | 0.615050i | \(0.210864\pi\) | |||||||
\(798\) | −87.9831 | − | 87.9831i | −0.110254 | − | 0.110254i | ||||
\(799\) | − | 73.4210i | − | 0.0918911i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 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 | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 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 | \(-0.832080\pi\) | ||
0.864050 | − | 0.503407i | \(-0.167920\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 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 | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −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 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −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 | \(-0.220084\pi\) |
−0.637628 | + | 0.770345i | \(0.720084\pi\) | |||||||
\(824\) | − | 32.5385i | − | 0.0394885i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −789.592 | −0.955922 | ||||||||
\(827\) | 543.650 | − | 543.650i | 0.657376 | − | 0.657376i | −0.297383 | − | 0.954758i | \(-0.596114\pi\) |
0.954758 | + | 0.297383i | \(0.0961137\pi\) | |||||||
\(828\) | −304.711 | − | 304.711i | −0.368008 | − | 0.368008i | ||||
\(829\) | 419.953i | 0.506578i | 0.967391 | + | 0.253289i | \(0.0815123\pi\) | ||||
−0.967391 | + | 0.253289i | \(0.918488\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 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 | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 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 | \(0.150214\pi\) | ||||
−0.890701 | + | 0.454589i | \(0.849786\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −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 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 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 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 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 | \(-0.0860911\pi\) |
−0.267178 | + | 0.963647i | \(0.586091\pi\) | |||||||
\(854\) | − | 642.410i | − | 0.752236i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −424.767 | −0.496223 | ||||||||
\(857\) | −346.747 | + | 346.747i | −0.404605 | + | 0.404605i | −0.879852 | − | 0.475247i | \(-0.842359\pi\) |
0.475247 | + | 0.879852i | \(0.342359\pi\) | |||||||
\(858\) | −32.9021 | − | 32.9021i | −0.0383475 | − | 0.0383475i | ||||
\(859\) | 1031.74i | 1.20110i | 0.799588 | + | 0.600549i | \(0.205051\pi\) | ||||
−0.799588 | + | 0.600549i | \(0.794949\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −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 | \(-0.0570182\pi\) |
−0.178172 | + | 0.983999i | \(0.557018\pi\) | |||||||
\(864\) | − | 237.424i | − | 0.274796i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 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 | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 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 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 62.4636 | 0.0713055 | ||||||||
\(877\) | −1168.49 | + | 1168.49i | −1.33237 | + | 1.33237i | −0.429121 | + | 0.903247i | \(0.641177\pi\) |
−0.903247 | + | 0.429121i | \(0.858823\pi\) | |||||||
\(878\) | 521.953 | + | 521.953i | 0.594479 | + | 0.594479i | ||||
\(879\) | − | 25.3141i | − | 0.0287988i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −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 | \(-0.445881\pi\) |
−0.985581 | + | 0.169202i | \(0.945881\pi\) | |||||||
\(884\) | 368.824i | 0.417221i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −893.757 | −1.00876 | ||||||||
\(887\) | −975.650 | + | 975.650i | −1.09994 | + | 1.09994i | −0.105527 | + | 0.994416i | \(0.533653\pi\) |
−0.994416 | + | 0.105527i | \(0.966347\pi\) | |||||||
\(888\) | −87.3307 | − | 87.3307i | −0.0983454 | − | 0.0983454i | ||||
\(889\) | − | 50.0553i | − | 0.0563052i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −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 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 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 | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −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 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −251.808 | −0.277934 | ||||||||
\(907\) | 265.891 | − | 265.891i | 0.293155 | − | 0.293155i | −0.545171 | − | 0.838325i | \(-0.683535\pi\) |
0.838325 | + | 0.545171i | \(0.183535\pi\) | |||||||
\(908\) | −1355.98 | − | 1355.98i | −1.49337 | − | 1.49337i | ||||
\(909\) | 384.967i | 0.423506i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 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 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 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 | \(0.0736994\pi\) | ||||
−0.973316 | + | 0.229470i | \(0.926301\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −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 | ||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −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 | \(-0.928039\pi\) | ||
0.974554 | − | 0.224153i | \(-0.0719614\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 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 | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −21.9128 | −0.0234111 | ||||||||
\(937\) | −877.123 | + | 877.123i | −0.936097 | + | 0.936097i | −0.998077 | − | 0.0619806i | \(-0.980258\pi\) |
0.0619806 | + | 0.998077i | \(0.480258\pi\) | |||||||
\(938\) | 509.511 | + | 509.511i | 0.543189 | + | 0.543189i | ||||
\(939\) | 221.763i | 0.236170i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 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 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −99.2122 | −0.104876 | ||||||||
\(947\) | 445.898 | − | 445.898i | 0.470853 | − | 0.470853i | −0.431338 | − | 0.902191i | \(-0.641958\pi\) |
0.902191 | + | 0.431338i | \(0.141958\pi\) | |||||||
\(948\) | −683.283 | − | 683.283i | −0.720763 | − | 0.720763i | ||||
\(949\) | 25.6287i | 0.0270060i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −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 | \(-0.388603\pi\) |
−0.939385 | + | 0.342864i | \(0.888603\pi\) | |||||||
\(954\) | − | 321.912i | − | 0.337434i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −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 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −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 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 410.897 | 0.425359 | ||||||||
\(967\) | 721.223 | − | 721.223i | 0.745836 | − | 0.745836i | −0.227858 | − | 0.973694i | \(-0.573172\pi\) |
0.973694 | + | 0.227858i | \(0.0731723\pi\) | |||||||
\(968\) | −174.538 | − | 174.538i | −0.180307 | − | 0.180307i | ||||
\(969\) | − | 368.423i | − | 0.380210i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 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 | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1028.79 | −1.05409 | ||||||||
\(977\) | 787.654 | − | 787.654i | 0.806196 | − | 0.806196i | −0.177860 | − | 0.984056i | \(-0.556917\pi\) |
0.984056 | + | 0.177860i | \(0.0569173\pi\) | |||||||
\(978\) | −182.145 | − | 182.145i | −0.186242 | − | 0.186242i | ||||
\(979\) | − | 321.515i | − | 0.328412i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −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 | \(-0.111648\pi\) |
−0.343604 | + | 0.939115i | \(0.611648\pi\) | |||||||
\(984\) | − | 227.612i | − | 0.231313i | ||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 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 | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −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 | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −991.662 | −0.995644 | ||||||||
\(997\) | −718.536 | + | 718.536i | −0.720698 | + | 0.720698i | −0.968747 | − | 0.248049i | \(-0.920211\pi\) |
0.248049 | + | 0.968747i | \(0.420211\pi\) | |||||||
\(998\) | −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 | 525.3.l.e.43.4 | 24 | ||
5.2 | odd | 4 | inner | 525.3.l.e.232.4 | 24 | ||
5.3 | odd | 4 | 105.3.l.a.22.9 | ✓ | 24 | ||
5.4 | even | 2 | 105.3.l.a.43.9 | yes | 24 | ||
15.8 | even | 4 | 315.3.o.b.127.4 | 24 | |||
15.14 | odd | 2 | 315.3.o.b.253.4 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.l.a.22.9 | ✓ | 24 | 5.3 | odd | 4 | ||
105.3.l.a.43.9 | yes | 24 | 5.4 | even | 2 | ||
315.3.o.b.127.4 | 24 | 15.8 | even | 4 | |||
315.3.o.b.253.4 | 24 | 15.14 | odd | 2 | |||
525.3.l.e.43.4 | 24 | 1.1 | even | 1 | trivial | ||
525.3.l.e.232.4 | 24 | 5.2 | odd | 4 | inner |