Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(104,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.104");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.g (of order \(2\), degree \(1\), 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: | \(6.19520055060\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 104.4 | ||
Character | \(\chi\) | \(=\) | 105.104 |
Dual form | 105.4.g.b.104.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.11138 | −1.80715 | −0.903573 | − | 0.428435i | \(-0.859065\pi\) | ||||
−0.903573 | + | 0.428435i | \(0.859065\pi\) | |||||||
\(3\) | 1.51783 | + | 4.96953i | 0.292107 | + | 0.956386i | ||||
\(4\) | 18.1262 | 2.26578 | ||||||||
\(5\) | 10.9509 | − | 2.25323i | 0.979481 | − | 0.201535i | ||||
\(6\) | −7.75821 | − | 25.4011i | −0.527879 | − | 1.72833i | ||||
\(7\) | 11.4695 | − | 14.5413i | 0.619295 | − | 0.785158i | ||||
\(8\) | −51.7589 | −2.28744 | ||||||||
\(9\) | −22.3924 | + | 15.0858i | −0.829347 | + | 0.558733i | ||||
\(10\) | −55.9744 | + | 11.5171i | −1.77007 | + | 0.364204i | ||||
\(11\) | − | 55.4308i | − | 1.51936i | −0.650294 | − | 0.759682i | \(-0.725354\pi\) | ||
0.650294 | − | 0.759682i | \(-0.274646\pi\) | |||||||
\(12\) | 27.5125 | + | 90.0786i | 0.661848 | + | 2.16695i | ||||
\(13\) | 20.9550 | 0.447066 | 0.223533 | − | 0.974696i | \(-0.428241\pi\) | ||||
0.223533 | + | 0.974696i | \(0.428241\pi\) | |||||||
\(14\) | −58.6250 | + | 74.3263i | −1.11916 | + | 1.41890i | ||||
\(15\) | 27.8192 | + | 51.0009i | 0.478859 | + | 0.877892i | ||||
\(16\) | 119.550 | 1.86796 | ||||||||
\(17\) | − | 96.8237i | − | 1.38136i | −0.723158 | − | 0.690682i | \(-0.757310\pi\) | ||
0.723158 | − | 0.690682i | \(-0.242690\pi\) | |||||||
\(18\) | 114.456 | − | 77.1093i | 1.49875 | − | 1.00971i | ||||
\(19\) | − | 33.1970i | − | 0.400838i | −0.979710 | − | 0.200419i | \(-0.935770\pi\) | ||
0.979710 | − | 0.200419i | \(-0.0642303\pi\) | |||||||
\(20\) | 198.499 | − | 40.8425i | 2.21928 | − | 0.456634i | ||||
\(21\) | 89.6723 | + | 34.9267i | 0.931814 | + | 0.362935i | ||||
\(22\) | 283.328i | 2.74571i | ||||||||
\(23\) | 111.288 | 1.00892 | 0.504460 | − | 0.863435i | \(-0.331692\pi\) | ||||
0.504460 | + | 0.863435i | \(0.331692\pi\) | |||||||
\(24\) | −78.5612 | − | 257.217i | −0.668177 | − | 2.18767i | ||||
\(25\) | 114.846 | − | 49.3500i | 0.918767 | − | 0.394800i | ||||
\(26\) | −107.109 | −0.807914 | ||||||||
\(27\) | −108.957 | − | 88.3818i | −0.776623 | − | 0.629966i | ||||
\(28\) | 207.899 | − | 263.579i | 1.40318 | − | 1.77899i | ||||
\(29\) | 156.784i | 1.00393i | 0.864888 | + | 0.501965i | \(0.167389\pi\) | ||||
−0.864888 | + | 0.501965i | \(0.832611\pi\) | |||||||
\(30\) | −142.194 | − | 260.685i | −0.865367 | − | 1.58648i | ||||
\(31\) | 80.4962i | 0.466372i | 0.972432 | + | 0.233186i | \(0.0749152\pi\) | ||||
−0.972432 | + | 0.233186i | \(0.925085\pi\) | |||||||
\(32\) | −196.992 | −1.08824 | ||||||||
\(33\) | 275.465 | − | 84.1346i | 1.45310 | − | 0.443817i | ||||
\(34\) | 494.903i | 2.49633i | ||||||||
\(35\) | 92.8368 | − | 185.085i | 0.448351 | − | 0.893858i | ||||
\(36\) | −405.889 | + | 273.448i | −1.87911 | + | 1.26596i | ||||
\(37\) | 180.365i | 0.801402i | 0.916209 | + | 0.400701i | \(0.131233\pi\) | ||||
−0.916209 | + | 0.400701i | \(0.868767\pi\) | |||||||
\(38\) | 169.683i | 0.724372i | ||||||||
\(39\) | 31.8061 | + | 104.136i | 0.130591 | + | 0.427568i | ||||
\(40\) | −566.808 | + | 116.625i | −2.24050 | + | 0.461000i | ||||
\(41\) | −36.5837 | −0.139351 | −0.0696757 | − | 0.997570i | \(-0.522196\pi\) | ||||
−0.0696757 | + | 0.997570i | \(0.522196\pi\) | |||||||
\(42\) | −458.349 | − | 178.524i | −1.68392 | − | 0.655876i | ||||
\(43\) | − | 52.5826i | − | 0.186483i | −0.995644 | − | 0.0932416i | \(-0.970277\pi\) | ||
0.995644 | − | 0.0932416i | \(-0.0297229\pi\) | |||||||
\(44\) | − | 1004.75i | − | 3.44254i | ||||||
\(45\) | −211.226 | + | 215.659i | −0.699726 | + | 0.714412i | ||||
\(46\) | −568.835 | −1.82326 | ||||||||
\(47\) | 259.660i | 0.805858i | 0.915231 | + | 0.402929i | \(0.132008\pi\) | ||||
−0.915231 | + | 0.402929i | \(0.867992\pi\) | |||||||
\(48\) | 181.456 | + | 594.105i | 0.545644 | + | 1.78649i | ||||
\(49\) | −79.9009 | − | 333.564i | −0.232947 | − | 0.972489i | ||||
\(50\) | −587.021 | + | 252.247i | −1.66035 | + | 0.713461i | ||||
\(51\) | 481.168 | − | 146.962i | 1.32112 | − | 0.403506i | ||||
\(52\) | 379.834 | 1.01295 | ||||||||
\(53\) | −191.690 | −0.496804 | −0.248402 | − | 0.968657i | \(-0.579905\pi\) | ||||
−0.248402 | + | 0.968657i | \(0.579905\pi\) | |||||||
\(54\) | 556.921 | + | 451.753i | 1.40347 | + | 1.13844i | ||||
\(55\) | −124.898 | − | 607.019i | −0.306206 | − | 1.48819i | ||||
\(56\) | −593.648 | + | 752.643i | −1.41660 | + | 1.79600i | ||||
\(57\) | 164.973 | − | 50.3875i | 0.383356 | − | 0.117087i | ||||
\(58\) | − | 801.380i | − | 1.81425i | ||||||
\(59\) | 705.237 | 1.55617 | 0.778085 | − | 0.628159i | \(-0.216191\pi\) | ||||
0.778085 | + | 0.628159i | \(0.216191\pi\) | |||||||
\(60\) | 504.256 | + | 924.453i | 1.08499 | + | 1.98911i | ||||
\(61\) | − | 427.079i | − | 0.896423i | −0.893928 | − | 0.448212i | \(-0.852061\pi\) | ||
0.893928 | − | 0.448212i | \(-0.147939\pi\) | |||||||
\(62\) | − | 411.447i | − | 0.842803i | ||||||
\(63\) | −37.4617 | + | 498.642i | −0.0749164 | + | 0.997190i | ||||
\(64\) | 50.5057 | 0.0986440 | ||||||||
\(65\) | 229.476 | − | 47.2164i | 0.437893 | − | 0.0900996i | ||||
\(66\) | −1408.00 | + | 430.044i | −2.62596 | + | 0.802041i | ||||
\(67\) | 306.444i | 0.558777i | 0.960178 | + | 0.279388i | \(0.0901317\pi\) | ||||
−0.960178 | + | 0.279388i | \(0.909868\pi\) | |||||||
\(68\) | − | 1755.05i | − | 3.12986i | ||||||
\(69\) | 168.916 | + | 553.048i | 0.294712 | + | 0.964916i | ||||
\(70\) | −474.524 | + | 946.038i | −0.810235 | + | 1.61533i | ||||
\(71\) | 513.791i | 0.858814i | 0.903111 | + | 0.429407i | \(0.141277\pi\) | ||||
−0.903111 | + | 0.429407i | \(0.858723\pi\) | |||||||
\(72\) | 1159.00 | − | 780.824i | 1.89708 | − | 1.27807i | ||||
\(73\) | 360.633 | 0.578204 | 0.289102 | − | 0.957298i | \(-0.406643\pi\) | ||||
0.289102 | + | 0.957298i | \(0.406643\pi\) | |||||||
\(74\) | − | 921.916i | − | 1.44825i | ||||||
\(75\) | 419.563 | + | 495.825i | 0.645959 | + | 0.763372i | ||||
\(76\) | − | 601.736i | − | 0.908208i | ||||||
\(77\) | −806.038 | − | 635.764i | −1.19294 | − | 0.940935i | ||||
\(78\) | −162.573 | − | 532.280i | −0.235997 | − | 0.772677i | ||||
\(79\) | 85.9838 | 0.122455 | 0.0612274 | − | 0.998124i | \(-0.480499\pi\) | ||||
0.0612274 | + | 0.998124i | \(0.480499\pi\) | |||||||
\(80\) | 1309.18 | − | 269.373i | 1.82963 | − | 0.376460i | ||||
\(81\) | 273.837 | − | 675.614i | 0.375634 | − | 0.926768i | ||||
\(82\) | 186.993 | 0.251828 | ||||||||
\(83\) | 886.893i | 1.17288i | 0.809992 | + | 0.586440i | \(0.199471\pi\) | ||||
−0.809992 | + | 0.586440i | \(0.800529\pi\) | |||||||
\(84\) | 1625.42 | + | 633.089i | 2.11128 | + | 0.822329i | ||||
\(85\) | −218.166 | − | 1060.31i | −0.278394 | − | 1.35302i | ||||
\(86\) | 268.770i | 0.337002i | ||||||||
\(87\) | −779.140 | + | 237.971i | −0.960145 | + | 0.293255i | ||||
\(88\) | 2869.03i | 3.47545i | ||||||||
\(89\) | −1417.80 | −1.68861 | −0.844305 | − | 0.535863i | \(-0.819986\pi\) | ||||
−0.844305 | + | 0.535863i | \(0.819986\pi\) | |||||||
\(90\) | 1079.65 | − | 1102.31i | 1.26451 | − | 1.29105i | ||||
\(91\) | 240.343 | − | 304.713i | 0.276866 | − | 0.351018i | ||||
\(92\) | 2017.23 | 2.28598 | ||||||||
\(93\) | −400.028 | + | 122.180i | −0.446032 | + | 0.136231i | ||||
\(94\) | − | 1327.22i | − | 1.45630i | ||||||
\(95\) | −74.8006 | − | 363.538i | −0.0807830 | − | 0.392613i | ||||
\(96\) | −299.001 | − | 978.958i | −0.317882 | − | 1.04078i | ||||
\(97\) | −1055.44 | −1.10478 | −0.552392 | − | 0.833584i | \(-0.686285\pi\) | ||||
−0.552392 | + | 0.833584i | \(0.686285\pi\) | |||||||
\(98\) | 408.404 | + | 1704.97i | 0.420970 | + | 1.75743i | ||||
\(99\) | 836.218 | + | 1241.23i | 0.848920 | + | 1.26008i | ||||
\(100\) | 2081.72 | − | 894.528i | 2.08172 | − | 0.894528i | ||||
\(101\) | 740.746 | 0.729772 | 0.364886 | − | 0.931052i | \(-0.381108\pi\) | ||||
0.364886 | + | 0.931052i | \(0.381108\pi\) | |||||||
\(102\) | −2459.43 | + | 751.179i | −2.38745 | + | 0.729194i | ||||
\(103\) | 935.584 | 0.895008 | 0.447504 | − | 0.894282i | \(-0.352313\pi\) | ||||
0.447504 | + | 0.894282i | \(0.352313\pi\) | |||||||
\(104\) | −1084.61 | −1.02264 | ||||||||
\(105\) | 1060.69 | + | 180.427i | 0.985839 | + | 0.167694i | ||||
\(106\) | 979.799 | 0.897797 | ||||||||
\(107\) | −794.752 | −0.718052 | −0.359026 | − | 0.933328i | \(-0.616891\pi\) | ||||
−0.359026 | + | 0.933328i | \(0.616891\pi\) | |||||||
\(108\) | −1974.98 | − | 1602.03i | −1.75965 | − | 1.42736i | ||||
\(109\) | −202.134 | −0.177623 | −0.0888117 | − | 0.996048i | \(-0.528307\pi\) | ||||
−0.0888117 | + | 0.996048i | \(0.528307\pi\) | |||||||
\(110\) | 638.403 | + | 3102.70i | 0.553358 | + | 2.68937i | ||||
\(111\) | −896.330 | + | 273.764i | −0.766449 | + | 0.234095i | ||||
\(112\) | 1371.17 | − | 1738.41i | 1.15682 | − | 1.46665i | ||||
\(113\) | −1457.83 | −1.21364 | −0.606818 | − | 0.794841i | \(-0.707554\pi\) | ||||
−0.606818 | + | 0.794841i | \(0.707554\pi\) | |||||||
\(114\) | −843.242 | + | 257.550i | −0.692779 | + | 0.211594i | ||||
\(115\) | 1218.71 | − | 250.758i | 0.988218 | − | 0.203333i | ||||
\(116\) | 2841.89i | 2.27468i | ||||||||
\(117\) | −469.232 | + | 316.123i | −0.370773 | + | 0.249791i | ||||
\(118\) | −3604.73 | −2.81223 | ||||||||
\(119\) | −1407.95 | − | 1110.52i | −1.08459 | − | 0.855472i | ||||
\(120\) | −1439.89 | − | 2639.75i | −1.09536 | − | 2.00813i | ||||
\(121\) | −1741.57 | −1.30847 | ||||||||
\(122\) | 2182.96i | 1.61997i | ||||||||
\(123\) | −55.5278 | − | 181.803i | −0.0407055 | − | 0.133274i | ||||
\(124\) | 1459.09i | 1.05669i | ||||||||
\(125\) | 1146.47 | − | 799.203i | 0.820349 | − | 0.571863i | ||||
\(126\) | 191.481 | − | 2548.75i | 0.135385 | − | 1.80207i | ||||
\(127\) | 1189.69i | 0.831242i | 0.909538 | + | 0.415621i | \(0.136436\pi\) | ||||
−0.909538 | + | 0.415621i | \(0.863564\pi\) | |||||||
\(128\) | 1317.78 | 0.909975 | ||||||||
\(129\) | 261.311 | − | 79.8116i | 0.178350 | − | 0.0544730i | ||||
\(130\) | −1172.94 | + | 241.341i | −0.791337 | + | 0.162823i | ||||
\(131\) | 531.346 | 0.354381 | 0.177190 | − | 0.984177i | \(-0.443299\pi\) | ||||
0.177190 | + | 0.984177i | \(0.443299\pi\) | |||||||
\(132\) | 4993.13 | − | 1525.04i | 3.29239 | − | 1.00559i | ||||
\(133\) | −482.729 | − | 380.753i | −0.314721 | − | 0.248237i | ||||
\(134\) | − | 1566.35i | − | 1.00979i | ||||||
\(135\) | −1392.33 | − | 722.357i | −0.887648 | − | 0.460523i | ||||
\(136\) | 5011.48i | 3.15979i | ||||||||
\(137\) | 1269.32 | 0.791572 | 0.395786 | − | 0.918343i | \(-0.370472\pi\) | ||||
0.395786 | + | 0.918343i | \(0.370472\pi\) | |||||||
\(138\) | −863.396 | − | 2826.84i | −0.532588 | − | 1.74374i | ||||
\(139\) | − | 1566.53i | − | 0.955910i | −0.878384 | − | 0.477955i | \(-0.841378\pi\) | ||
0.878384 | − | 0.477955i | \(-0.158622\pi\) | |||||||
\(140\) | 1682.78 | − | 3354.88i | 1.01586 | − | 2.02528i | ||||
\(141\) | −1290.39 | + | 394.120i | −0.770711 | + | 0.235397i | ||||
\(142\) | − | 2626.18i | − | 1.55200i | ||||||
\(143\) | − | 1161.55i | − | 0.679257i | ||||||
\(144\) | −2677.00 | + | 1803.50i | −1.54919 | + | 1.04369i | ||||
\(145\) | 353.270 | + | 1716.93i | 0.202327 | + | 0.983331i | ||||
\(146\) | −1843.33 | −1.04490 | ||||||||
\(147\) | 1536.38 | − | 903.363i | 0.862029 | − | 0.506858i | ||||
\(148\) | 3269.34i | 1.81580i | ||||||||
\(149\) | 1112.59i | 0.611723i | 0.952076 | + | 0.305862i | \(0.0989445\pi\) | ||||
−0.952076 | + | 0.305862i | \(0.901055\pi\) | |||||||
\(150\) | −2144.54 | − | 2534.35i | −1.16734 | − | 1.37952i | ||||
\(151\) | 1252.15 | 0.674822 | 0.337411 | − | 0.941357i | \(-0.390449\pi\) | ||||
0.337411 | + | 0.941357i | \(0.390449\pi\) | |||||||
\(152\) | 1718.24i | 0.916892i | ||||||||
\(153\) | 1460.66 | + | 2168.11i | 0.771815 | + | 1.14563i | ||||
\(154\) | 4119.96 | + | 3249.63i | 2.15582 | + | 1.70041i | ||||
\(155\) | 181.377 | + | 881.509i | 0.0939905 | + | 0.456803i | ||||
\(156\) | 576.524 | + | 1887.59i | 0.295890 | + | 0.968773i | ||||
\(157\) | −226.625 | −0.115202 | −0.0576009 | − | 0.998340i | \(-0.518345\pi\) | ||||
−0.0576009 | + | 0.998340i | \(0.518345\pi\) | |||||||
\(158\) | −439.496 | −0.221294 | ||||||||
\(159\) | −290.953 | − | 952.607i | −0.145120 | − | 0.475136i | ||||
\(160\) | −2157.25 | + | 443.869i | −1.06591 | + | 0.219318i | ||||
\(161\) | 1276.42 | − | 1618.28i | 0.624819 | − | 0.792161i | ||||
\(162\) | −1399.69 | + | 3453.32i | −0.678825 | + | 1.67480i | ||||
\(163\) | 1843.89i | 0.886042i | 0.896511 | + | 0.443021i | \(0.146093\pi\) | ||||
−0.896511 | + | 0.443021i | \(0.853907\pi\) | |||||||
\(164\) | −663.123 | −0.315739 | ||||||||
\(165\) | 2827.02 | − | 1542.04i | 1.33384 | − | 0.727561i | ||||
\(166\) | − | 4533.24i | − | 2.11957i | ||||||
\(167\) | − | 2144.68i | − | 0.993774i | −0.867815 | − | 0.496887i | \(-0.834476\pi\) | ||
0.867815 | − | 0.496887i | \(-0.165524\pi\) | |||||||
\(168\) | −4641.34 | − | 1807.77i | −2.13147 | − | 0.830192i | ||||
\(169\) | −1757.89 | −0.800132 | ||||||||
\(170\) | 1115.13 | + | 5419.65i | 0.503098 | + | 2.44511i | ||||
\(171\) | 500.804 | + | 743.360i | 0.223962 | + | 0.332434i | ||||
\(172\) | − | 953.123i | − | 0.422529i | ||||||
\(173\) | − | 3462.67i | − | 1.52175i | −0.648901 | − | 0.760873i | \(-0.724771\pi\) | ||
0.648901 | − | 0.760873i | \(-0.275229\pi\) | |||||||
\(174\) | 3982.48 | − | 1216.36i | 1.73512 | − | 0.529954i | ||||
\(175\) | 599.610 | − | 2236.03i | 0.259007 | − | 0.965875i | ||||
\(176\) | − | 6626.72i | − | 2.83811i | ||||||
\(177\) | 1070.43 | + | 3504.69i | 0.454568 | + | 1.48830i | ||||
\(178\) | 7246.90 | 3.05156 | ||||||||
\(179\) | − | 3089.42i | − | 1.29002i | −0.764173 | − | 0.645011i | \(-0.776853\pi\) | ||
0.764173 | − | 0.645011i | \(-0.223147\pi\) | |||||||
\(180\) | −3828.72 | + | 3909.08i | −1.58542 | + | 1.61870i | ||||
\(181\) | 2791.07i | 1.14618i | 0.819493 | + | 0.573090i | \(0.194255\pi\) | ||||
−0.819493 | + | 0.573090i | \(0.805745\pi\) | |||||||
\(182\) | −1228.48 | + | 1557.51i | −0.500337 | + | 0.634340i | ||||
\(183\) | 2122.38 | − | 648.233i | 0.857326 | − | 0.261851i | ||||
\(184\) | −5760.14 | −2.30784 | ||||||||
\(185\) | 406.405 | + | 1975.17i | 0.161511 | + | 0.784958i | ||||
\(186\) | 2044.69 | − | 624.507i | 0.806045 | − | 0.246188i | ||||
\(187\) | −5367.01 | −2.09880 | ||||||||
\(188\) | 4706.65i | 1.82589i | ||||||||
\(189\) | −2534.87 | + | 570.687i | −0.975582 | + | 0.219637i | ||||
\(190\) | 382.334 | + | 1858.18i | 0.145987 | + | 0.709509i | ||||
\(191\) | 3188.41i | 1.20788i | 0.797029 | + | 0.603941i | \(0.206404\pi\) | ||||
−0.797029 | + | 0.603941i | \(0.793596\pi\) | |||||||
\(192\) | 76.6591 | + | 250.989i | 0.0288146 | + | 0.0943417i | ||||
\(193\) | − | 1762.45i | − | 0.657327i | −0.944447 | − | 0.328664i | \(-0.893402\pi\) | ||
0.944447 | − | 0.328664i | \(-0.106598\pi\) | |||||||
\(194\) | 5394.77 | 1.99651 | ||||||||
\(195\) | 582.950 | + | 1068.72i | 0.214082 | + | 0.392476i | ||||
\(196\) | −1448.30 | − | 6046.25i | −0.527806 | − | 2.20344i | ||||
\(197\) | −1135.69 | −0.410735 | −0.205367 | − | 0.978685i | \(-0.565839\pi\) | ||||
−0.205367 | + | 0.978685i | \(0.565839\pi\) | |||||||
\(198\) | −4274.23 | − | 6344.38i | −1.53412 | − | 2.27715i | ||||
\(199\) | 1200.54i | 0.427658i | 0.976871 | + | 0.213829i | \(0.0685935\pi\) | ||||
−0.976871 | + | 0.213829i | \(0.931407\pi\) | |||||||
\(200\) | −5944.29 | + | 2554.30i | −2.10162 | + | 0.903081i | ||||
\(201\) | −1522.88 | + | 465.130i | −0.534406 | + | 0.163223i | ||||
\(202\) | −3786.23 | −1.31880 | ||||||||
\(203\) | 2279.84 | + | 1798.23i | 0.788244 | + | 0.621729i | ||||
\(204\) | 8721.75 | − | 2663.86i | 2.99336 | − | 0.914254i | ||||
\(205\) | −400.625 | + | 82.4315i | −0.136492 | + | 0.0280842i | ||||
\(206\) | −4782.13 | −1.61741 | ||||||||
\(207\) | −2492.00 | + | 1678.87i | −0.836744 | + | 0.563717i | ||||
\(208\) | 2505.16 | 0.835103 | ||||||||
\(209\) | −1840.14 | −0.609019 | ||||||||
\(210\) | −5421.61 | − | 922.233i | −1.78155 | − | 0.303048i | ||||
\(211\) | −835.608 | −0.272633 | −0.136317 | − | 0.990665i | \(-0.543526\pi\) | ||||
−0.136317 | + | 0.990665i | \(0.543526\pi\) | |||||||
\(212\) | −3474.61 | −1.12565 | ||||||||
\(213\) | −2553.30 | + | 779.848i | −0.821357 | + | 0.250865i | ||||
\(214\) | 4062.28 | 1.29762 | ||||||||
\(215\) | −118.481 | − | 575.829i | −0.0375829 | − | 0.182657i | ||||
\(216\) | 5639.50 | + | 4574.54i | 1.77648 | + | 1.44101i | ||||
\(217\) | 1170.52 | + | 923.252i | 0.366176 | + | 0.288822i | ||||
\(218\) | 1033.19 | 0.320991 | ||||||||
\(219\) | 547.380 | + | 1792.17i | 0.168897 | + | 0.552986i | ||||
\(220\) | −2263.93 | − | 11002.9i | −0.693793 | − | 3.37190i | ||||
\(221\) | − | 2028.94i | − | 0.617562i | ||||||
\(222\) | 4581.48 | − | 1399.31i | 1.38509 | − | 0.423044i | ||||
\(223\) | 2734.39 | 0.821115 | 0.410557 | − | 0.911835i | \(-0.365334\pi\) | ||||
0.410557 | + | 0.911835i | \(0.365334\pi\) | |||||||
\(224\) | −2259.40 | + | 2864.53i | −0.673941 | + | 0.854440i | ||||
\(225\) | −1827.19 | + | 2837.61i | −0.541389 | + | 0.840772i | ||||
\(226\) | 7451.50 | 2.19322 | ||||||||
\(227\) | − | 2207.95i | − | 0.645579i | −0.946471 | − | 0.322790i | \(-0.895379\pi\) | ||
0.946471 | − | 0.322790i | \(-0.104621\pi\) | |||||||
\(228\) | 2990.34 | − | 913.333i | 0.868597 | − | 0.265294i | ||||
\(229\) | − | 1720.95i | − | 0.496610i | −0.968682 | − | 0.248305i | \(-0.920126\pi\) | ||
0.968682 | − | 0.248305i | \(-0.0798735\pi\) | |||||||
\(230\) | −6229.27 | + | 1281.72i | −1.78585 | + | 0.367452i | ||||
\(231\) | 1936.01 | − | 4970.61i | 0.551430 | − | 1.41577i | ||||
\(232\) | − | 8114.94i | − | 2.29643i | ||||||
\(233\) | 2915.58 | 0.819767 | 0.409884 | − | 0.912138i | \(-0.365569\pi\) | ||||
0.409884 | + | 0.912138i | \(0.365569\pi\) | |||||||
\(234\) | 2398.42 | − | 1615.82i | 0.670041 | − | 0.451409i | ||||
\(235\) | 585.075 | + | 2843.52i | 0.162409 | + | 0.789323i | ||||
\(236\) | 12783.3 | 3.52593 | ||||||||
\(237\) | 130.509 | + | 427.299i | 0.0357699 | + | 0.117114i | ||||
\(238\) | 7196.55 | + | 5676.29i | 1.96001 | + | 1.54596i | ||||
\(239\) | 6597.22i | 1.78552i | 0.450536 | + | 0.892758i | \(0.351233\pi\) | ||||
−0.450536 | + | 0.892758i | \(0.648767\pi\) | |||||||
\(240\) | 3325.77 | + | 6097.14i | 0.894489 | + | 1.63987i | ||||
\(241\) | 5492.27i | 1.46800i | 0.679149 | + | 0.734000i | \(0.262349\pi\) | ||||
−0.679149 | + | 0.734000i | \(0.737651\pi\) | |||||||
\(242\) | 8901.83 | 2.36459 | ||||||||
\(243\) | 3773.12 | + | 335.372i | 0.996073 | + | 0.0885356i | ||||
\(244\) | − | 7741.31i | − | 2.03109i | ||||||
\(245\) | −1626.59 | − | 3472.80i | −0.424158 | − | 0.905588i | ||||
\(246\) | 283.824 | + | 929.266i | 0.0735607 | + | 0.240845i | ||||
\(247\) | − | 695.643i | − | 0.179201i | ||||||
\(248\) | − | 4166.39i | − | 1.06680i | ||||||
\(249\) | −4407.44 | + | 1346.15i | −1.12173 | + | 0.342606i | ||||
\(250\) | −5860.06 | + | 4085.03i | −1.48249 | + | 1.03344i | ||||
\(251\) | 3852.51 | 0.968798 | 0.484399 | − | 0.874847i | \(-0.339038\pi\) | ||||
0.484399 | + | 0.874847i | \(0.339038\pi\) | |||||||
\(252\) | −679.039 | + | 9038.48i | −0.169744 | + | 2.25941i | ||||
\(253\) | − | 6168.78i | − | 1.53292i | ||||||
\(254\) | − | 6080.95i | − | 1.50218i | ||||||
\(255\) | 4938.10 | − | 2693.56i | 1.21269 | − | 0.661478i | ||||
\(256\) | −7139.74 | −1.74310 | ||||||||
\(257\) | 445.140i | 0.108043i | 0.998540 | + | 0.0540215i | \(0.0172040\pi\) | ||||
−0.998540 | + | 0.0540215i | \(0.982796\pi\) | |||||||
\(258\) | −1335.66 | + | 407.947i | −0.322304 | + | 0.0984406i | ||||
\(259\) | 2622.75 | + | 2068.70i | 0.629227 | + | 0.496304i | ||||
\(260\) | 4159.54 | − | 855.854i | 0.992167 | − | 0.204146i | ||||
\(261\) | −2365.21 | − | 3510.76i | −0.560929 | − | 0.832607i | ||||
\(262\) | −2715.91 | −0.640418 | ||||||||
\(263\) | −5539.14 | −1.29870 | −0.649350 | − | 0.760490i | \(-0.724959\pi\) | ||||
−0.649350 | + | 0.760490i | \(0.724959\pi\) | |||||||
\(264\) | −14257.7 | + | 4354.71i | −3.32388 | + | 1.01520i | ||||
\(265\) | −2099.18 | + | 431.922i | −0.486610 | + | 0.100124i | ||||
\(266\) | 2467.41 | + | 1946.18i | 0.568747 | + | 0.448600i | ||||
\(267\) | −2151.98 | − | 7045.78i | −0.493254 | − | 1.61496i | ||||
\(268\) | 5554.66i | 1.26606i | ||||||||
\(269\) | −6822.25 | −1.54632 | −0.773160 | − | 0.634211i | \(-0.781325\pi\) | ||||
−0.773160 | + | 0.634211i | \(0.781325\pi\) | |||||||
\(270\) | 7116.71 | + | 3692.24i | 1.60411 | + | 0.832232i | ||||
\(271\) | − | 3566.70i | − | 0.799490i | −0.916626 | − | 0.399745i | \(-0.869099\pi\) | ||
0.916626 | − | 0.399745i | \(-0.130901\pi\) | |||||||
\(272\) | − | 11575.2i | − | 2.58034i | ||||||
\(273\) | 1879.08 | + | 731.888i | 0.416583 | + | 0.162256i | ||||
\(274\) | −6487.98 | −1.43049 | ||||||||
\(275\) | −2735.51 | − | 6366.00i | −0.599845 | − | 1.39594i | ||||
\(276\) | 3061.81 | + | 10024.7i | 0.667751 | + | 2.18628i | ||||
\(277\) | 4554.17i | 0.987847i | 0.869505 | + | 0.493923i | \(0.164438\pi\) | ||||
−0.869505 | + | 0.493923i | \(0.835562\pi\) | |||||||
\(278\) | 8007.14i | 1.72747i | ||||||||
\(279\) | −1214.35 | − | 1802.50i | −0.260578 | − | 0.386785i | ||||
\(280\) | −4805.12 | + | 9579.77i | −1.02558 | + | 2.04465i | ||||
\(281\) | 4934.61i | 1.04759i | 0.851843 | + | 0.523797i | \(0.175485\pi\) | ||||
−0.851843 | + | 0.523797i | \(0.824515\pi\) | |||||||
\(282\) | 6595.67 | − | 2014.50i | 1.39279 | − | 0.425396i | ||||
\(283\) | −456.724 | −0.0959344 | −0.0479672 | − | 0.998849i | \(-0.515274\pi\) | ||||
−0.0479672 | + | 0.998849i | \(0.515274\pi\) | |||||||
\(284\) | 9313.08i | 1.94588i | ||||||||
\(285\) | 1693.08 | − | 923.513i | 0.351892 | − | 0.191945i | ||||
\(286\) | 5937.12i | 1.22752i | ||||||||
\(287\) | −419.596 | + | 531.975i | −0.0862996 | + | 0.109413i | ||||
\(288\) | 4411.12 | − | 2971.79i | 0.902528 | − | 0.608035i | ||||
\(289\) | −4461.83 | −0.908168 | ||||||||
\(290\) | −1805.70 | − | 8775.86i | −0.365635 | − | 1.77702i | ||||
\(291\) | −1601.99 | − | 5245.05i | −0.322715 | − | 1.05660i | ||||
\(292\) | 6536.90 | 1.31008 | ||||||||
\(293\) | − | 2102.29i | − | 0.419171i | −0.977790 | − | 0.209585i | \(-0.932789\pi\) | ||
0.977790 | − | 0.209585i | \(-0.0672114\pi\) | |||||||
\(294\) | −7853.01 | + | 4617.43i | −1.55781 | + | 0.915966i | ||||
\(295\) | 7723.00 | − | 1589.06i | 1.52424 | − | 0.313623i | ||||
\(296\) | − | 9335.50i | − | 1.83316i | ||||||
\(297\) | −4899.07 | + | 6039.58i | −0.957148 | + | 1.17997i | ||||
\(298\) | − | 5686.86i | − | 1.10547i | ||||||
\(299\) | 2332.04 | 0.451054 | ||||||||
\(300\) | 7605.08 | + | 8987.42i | 1.46360 | + | 1.72963i | ||||
\(301\) | −764.622 | − | 603.097i | −0.146419 | − | 0.115488i | ||||
\(302\) | −6400.19 | −1.21950 | ||||||||
\(303\) | 1124.33 | + | 3681.16i | 0.213171 | + | 0.697944i | ||||
\(304\) | − | 3968.69i | − | 0.748750i | ||||||
\(305\) | −962.308 | − | 4676.91i | −0.180661 | − | 0.878030i | ||||
\(306\) | −7466.01 | − | 11082.0i | −1.39478 | − | 2.07032i | ||||
\(307\) | 2780.68 | 0.516944 | 0.258472 | − | 0.966019i | \(-0.416781\pi\) | ||||
0.258472 | + | 0.966019i | \(0.416781\pi\) | |||||||
\(308\) | −14610.4 | − | 11524.0i | −2.70294 | − | 2.13195i | ||||
\(309\) | 1420.06 | + | 4649.41i | 0.261438 | + | 0.855973i | ||||
\(310\) | −927.085 | − | 4505.72i | −0.169854 | − | 0.825510i | ||||
\(311\) | −440.562 | −0.0803280 | −0.0401640 | − | 0.999193i | \(-0.512788\pi\) | ||||
−0.0401640 | + | 0.999193i | \(0.512788\pi\) | |||||||
\(312\) | −1646.25 | − | 5389.97i | −0.298719 | − | 0.978036i | ||||
\(313\) | −6998.87 | −1.26390 | −0.631948 | − | 0.775010i | \(-0.717745\pi\) | ||||
−0.631948 | + | 0.775010i | \(0.717745\pi\) | |||||||
\(314\) | 1158.37 | 0.208186 | ||||||||
\(315\) | 713.315 | + | 5545.00i | 0.127590 | + | 0.991827i | ||||
\(316\) | 1558.56 | 0.277455 | ||||||||
\(317\) | −10112.3 | −1.79168 | −0.895839 | − | 0.444379i | \(-0.853424\pi\) | ||||
−0.895839 | + | 0.444379i | \(0.853424\pi\) | |||||||
\(318\) | 1487.17 | + | 4869.14i | 0.262253 | + | 0.858640i | ||||
\(319\) | 8690.64 | 1.52534 | ||||||||
\(320\) | 553.085 | − | 113.801i | 0.0966199 | − | 0.0198802i | ||||
\(321\) | −1206.30 | − | 3949.54i | −0.209748 | − | 0.686735i | ||||
\(322\) | −6524.26 | + | 8271.62i | −1.12914 | + | 1.43155i | ||||
\(323\) | −3214.26 | −0.553703 | ||||||||
\(324\) | 4963.63 | − | 12246.3i | 0.851102 | − | 2.09985i | ||||
\(325\) | 2406.59 | − | 1034.13i | 0.410750 | − | 0.176502i | ||||
\(326\) | − | 9424.84i | − | 1.60121i | ||||||
\(327\) | −306.806 | − | 1004.51i | −0.0518850 | − | 0.169877i | ||||
\(328\) | 1893.53 | 0.318758 | ||||||||
\(329\) | 3775.81 | + | 2978.17i | 0.632726 | + | 0.499064i | ||||
\(330\) | −14450.0 | + | 7881.94i | −2.41044 | + | 1.31481i | ||||
\(331\) | 5030.87 | 0.835413 | 0.417706 | − | 0.908582i | \(-0.362834\pi\) | ||||
0.417706 | + | 0.908582i | \(0.362834\pi\) | |||||||
\(332\) | 16076.0i | 2.65748i | ||||||||
\(333\) | −2720.96 | − | 4038.81i | −0.447770 | − | 0.664641i | ||||
\(334\) | 10962.3i | 1.79589i | ||||||||
\(335\) | 690.489 | + | 3355.84i | 0.112613 | + | 0.547311i | ||||
\(336\) | 10720.3 | + | 4175.47i | 1.74059 | + | 0.677948i | ||||
\(337\) | 3231.43i | 0.522335i | 0.965293 | + | 0.261168i | \(0.0841075\pi\) | ||||
−0.965293 | + | 0.261168i | \(0.915892\pi\) | |||||||
\(338\) | 8985.24 | 1.44595 | ||||||||
\(339\) | −2212.73 | − | 7244.71i | −0.354511 | − | 1.16070i | ||||
\(340\) | −3954.53 | − | 19219.4i | −0.630778 | − | 3.06564i | ||||
\(341\) | 4461.97 | 0.708590 | ||||||||
\(342\) | −2559.80 | − | 3799.60i | −0.404731 | − | 0.600756i | ||||
\(343\) | −5766.89 | − | 2663.95i | −0.907821 | − | 0.419357i | ||||
\(344\) | 2721.62i | 0.426569i | ||||||||
\(345\) | 3095.94 | + | 5675.79i | 0.483130 | + | 0.885722i | ||||
\(346\) | 17699.0i | 2.75002i | ||||||||
\(347\) | 8184.28 | 1.26615 | 0.633077 | − | 0.774089i | \(-0.281792\pi\) | ||||
0.633077 | + | 0.774089i | \(0.281792\pi\) | |||||||
\(348\) | −14122.8 | + | 4313.51i | −2.17547 | + | 0.664449i | ||||
\(349\) | 11214.5i | 1.72005i | 0.510248 | + | 0.860027i | \(0.329554\pi\) | ||||
−0.510248 | + | 0.860027i | \(0.670446\pi\) | |||||||
\(350\) | −3064.84 | + | 11429.2i | −0.468064 | + | 1.74548i | ||||
\(351\) | −2283.19 | − | 1852.04i | −0.347202 | − | 0.281637i | ||||
\(352\) | 10919.4i | 1.65343i | ||||||||
\(353\) | 804.207i | 0.121257i | 0.998160 | + | 0.0606284i | \(0.0193105\pi\) | ||||
−0.998160 | + | 0.0606284i | \(0.980690\pi\) | |||||||
\(354\) | −5471.38 | − | 17913.8i | −0.821470 | − | 2.68957i | ||||
\(355\) | 1157.69 | + | 5626.49i | 0.173081 | + | 0.841192i | ||||
\(356\) | −25699.3 | −3.82601 | ||||||||
\(357\) | 3381.73 | − | 8682.41i | 0.501345 | − | 1.28718i | ||||
\(358\) | 15791.2i | 2.33126i | ||||||||
\(359\) | 4210.90i | 0.619060i | 0.950890 | + | 0.309530i | \(0.100172\pi\) | ||||
−0.950890 | + | 0.309530i | \(0.899828\pi\) | |||||||
\(360\) | 10932.8 | − | 11162.3i | 1.60058 | − | 1.63417i | ||||
\(361\) | 5756.96 | 0.839329 | ||||||||
\(362\) | − | 14266.2i | − | 2.07131i | ||||||
\(363\) | −2643.41 | − | 8654.79i | −0.382213 | − | 1.25140i | ||||
\(364\) | 4356.51 | − | 5523.29i | 0.627316 | − | 0.795328i | ||||
\(365\) | 3949.27 | − | 812.590i | 0.566340 | − | 0.116528i | ||||
\(366\) | −10848.3 | + | 3313.37i | −1.54931 | + | 0.473203i | ||||
\(367\) | 12710.6 | 1.80787 | 0.903935 | − | 0.427670i | \(-0.140666\pi\) | ||||
0.903935 | + | 0.427670i | \(0.140666\pi\) | |||||||
\(368\) | 13304.4 | 1.88462 | ||||||||
\(369\) | 819.195 | − | 551.894i | 0.115571 | − | 0.0778603i | ||||
\(370\) | −2077.29 | − | 10095.8i | −0.291873 | − | 1.41853i | ||||
\(371\) | −2198.59 | + | 2787.43i | −0.307668 | + | 0.390070i | ||||
\(372\) | −7250.99 | + | 2214.65i | −1.01061 | + | 0.308668i | ||||
\(373\) | 10529.6i | 1.46167i | 0.682555 | + | 0.730835i | \(0.260869\pi\) | ||||
−0.682555 | + | 0.730835i | \(0.739131\pi\) | |||||||
\(374\) | 27432.8 | 3.79283 | ||||||||
\(375\) | 5711.81 | + | 4484.37i | 0.786551 | + | 0.617525i | ||||
\(376\) | − | 13439.7i | − | 1.84335i | ||||||
\(377\) | 3285.39i | 0.448823i | ||||||||
\(378\) | 12956.7 | − | 2917.00i | 1.76302 | − | 0.396916i | ||||
\(379\) | −7340.38 | −0.994855 | −0.497428 | − | 0.867505i | \(-0.665722\pi\) | ||||
−0.497428 | + | 0.867505i | \(0.665722\pi\) | |||||||
\(380\) | −1355.85 | − | 6589.57i | −0.183036 | − | 0.889573i | ||||
\(381\) | −5912.19 | + | 1805.75i | −0.794988 | + | 0.242811i | ||||
\(382\) | − | 16297.2i | − | 2.18282i | ||||||
\(383\) | 12222.6i | 1.63067i | 0.578991 | + | 0.815334i | \(0.303447\pi\) | ||||
−0.578991 | + | 0.815334i | \(0.696553\pi\) | |||||||
\(384\) | 2000.17 | + | 6548.76i | 0.265810 | + | 0.870287i | ||||
\(385\) | −10259.4 | − | 5146.01i | −1.35810 | − | 0.681208i | ||||
\(386\) | 9008.57i | 1.18789i | ||||||||
\(387\) | 793.251 | + | 1177.45i | 0.104194 | + | 0.154659i | ||||
\(388\) | −19131.2 | −2.50319 | ||||||||
\(389\) | − | 1069.72i | − | 0.139426i | −0.997567 | − | 0.0697131i | \(-0.977792\pi\) | ||
0.997567 | − | 0.0697131i | \(-0.0222084\pi\) | |||||||
\(390\) | −2979.68 | − | 5462.65i | −0.386877 | − | 0.709261i | ||||
\(391\) | − | 10775.3i | − | 1.39369i | ||||||
\(392\) | 4135.58 | + | 17264.9i | 0.532853 | + | 2.22451i | ||||
\(393\) | 806.493 | + | 2640.54i | 0.103517 | + | 0.338925i | ||||
\(394\) | 5804.95 | 0.742257 | ||||||||
\(395\) | 941.603 | − | 193.742i | 0.119942 | − | 0.0246790i | ||||
\(396\) | 15157.5 | + | 22498.7i | 1.92346 | + | 2.85506i | ||||
\(397\) | 11929.8 | 1.50816 | 0.754082 | − | 0.656780i | \(-0.228082\pi\) | ||||
0.754082 | + | 0.656780i | \(0.228082\pi\) | |||||||
\(398\) | − | 6136.40i | − | 0.772839i | ||||||
\(399\) | 1159.46 | − | 2976.85i | 0.145478 | − | 0.373506i | ||||
\(400\) | 13729.8 | − | 5899.77i | 1.71622 | − | 0.737471i | ||||
\(401\) | − | 5198.65i | − | 0.647402i | −0.946159 | − | 0.323701i | \(-0.895073\pi\) | ||
0.946159 | − | 0.323701i | \(-0.104927\pi\) | |||||||
\(402\) | 7784.02 | − | 2377.45i | 0.965750 | − | 0.294967i | ||||
\(403\) | 1686.80i | 0.208499i | ||||||||
\(404\) | 13426.9 | 1.65350 | ||||||||
\(405\) | 1476.46 | − | 8015.62i | 0.181150 | − | 0.983456i | ||||
\(406\) | −11653.1 | − | 9191.44i | −1.42447 | − | 1.12355i | ||||
\(407\) | 9997.79 | 1.21762 | ||||||||
\(408\) | −24904.7 | + | 7606.59i | −3.02198 | + | 0.922996i | ||||
\(409\) | − | 16413.0i | − | 1.98428i | −0.125136 | − | 0.992140i | \(-0.539937\pi\) | ||
0.125136 | − | 0.992140i | \(-0.460063\pi\) | |||||||
\(410\) | 2047.75 | − | 421.339i | 0.246661 | − | 0.0507523i | ||||
\(411\) | 1926.61 | + | 6307.92i | 0.231223 | + | 0.757048i | ||||
\(412\) | 16958.6 | 2.02789 | ||||||||
\(413\) | 8088.72 | − | 10255.1i | 0.963729 | − | 1.22184i | ||||
\(414\) | 12737.6 | − | 8581.33i | 1.51212 | − | 1.01872i | ||||
\(415\) | 1998.38 | + | 9712.30i | 0.236377 | + | 1.14881i | ||||
\(416\) | −4127.97 | −0.486515 | ||||||||
\(417\) | 7784.92 | − | 2377.73i | 0.914219 | − | 0.279228i | ||||
\(418\) | 9405.64 | 1.10059 | ||||||||
\(419\) | −8997.49 | −1.04906 | −0.524530 | − | 0.851392i | \(-0.675759\pi\) | ||||
−0.524530 | + | 0.851392i | \(0.675759\pi\) | |||||||
\(420\) | 19226.3 | + | 3270.46i | 2.23369 | + | 0.379958i | ||||
\(421\) | 2279.63 | 0.263901 | 0.131950 | − | 0.991256i | \(-0.457876\pi\) | ||||
0.131950 | + | 0.991256i | \(0.457876\pi\) | |||||||
\(422\) | 4271.11 | 0.492688 | ||||||||
\(423\) | −3917.18 | − | 5814.41i | −0.450260 | − | 0.668336i | ||||
\(424\) | 9921.64 | 1.13641 | ||||||||
\(425\) | −4778.25 | − | 11119.8i | −0.545363 | − | 1.26915i | ||||
\(426\) | 13050.9 | − | 3986.10i | 1.48431 | − | 0.453350i | ||||
\(427\) | −6210.29 | − | 4898.38i | −0.703834 | − | 0.555150i | ||||
\(428\) | −14405.8 | −1.62694 | ||||||||
\(429\) | 5772.35 | − | 1763.04i | 0.649631 | − | 0.198416i | ||||
\(430\) | 605.601 | + | 2943.28i | 0.0679178 | + | 0.330087i | ||||
\(431\) | 14695.9i | 1.64240i | 0.570638 | + | 0.821202i | \(0.306696\pi\) | ||||
−0.570638 | + | 0.821202i | \(0.693304\pi\) | |||||||
\(432\) | −13025.8 | − | 10566.0i | −1.45070 | − | 1.17675i | ||||
\(433\) | −3577.42 | −0.397043 | −0.198522 | − | 0.980097i | \(-0.563614\pi\) | ||||
−0.198522 | + | 0.980097i | \(0.563614\pi\) | |||||||
\(434\) | −5982.98 | − | 4719.09i | −0.661734 | − | 0.521944i | ||||
\(435\) | −7996.11 | + | 4361.59i | −0.881342 | + | 0.480741i | ||||
\(436\) | −3663.93 | −0.402455 | ||||||||
\(437\) | − | 3694.43i | − | 0.404413i | ||||||
\(438\) | −2797.87 | − | 9160.48i | −0.305222 | − | 0.999326i | ||||
\(439\) | − | 7413.92i | − | 0.806030i | −0.915193 | − | 0.403015i | \(-0.867962\pi\) | ||
0.915193 | − | 0.403015i | \(-0.132038\pi\) | |||||||
\(440\) | 6464.60 | + | 31418.6i | 0.700427 | + | 3.40414i | ||||
\(441\) | 6821.25 | + | 6263.92i | 0.736557 | + | 0.676376i | ||||
\(442\) | 10370.7i | 1.11602i | ||||||||
\(443\) | 5151.58 | 0.552503 | 0.276252 | − | 0.961085i | \(-0.410908\pi\) | ||||
0.276252 | + | 0.961085i | \(0.410908\pi\) | |||||||
\(444\) | −16247.1 | + | 4962.30i | −1.73660 | + | 0.530406i | ||||
\(445\) | −15526.2 | + | 3194.63i | −1.65396 | + | 0.340314i | ||||
\(446\) | −13976.5 | −1.48387 | ||||||||
\(447\) | −5529.04 | + | 1688.72i | −0.585043 | + | 0.178689i | ||||
\(448\) | 579.276 | − | 734.421i | 0.0610897 | − | 0.0774511i | ||||
\(449\) | − | 5031.60i | − | 0.528855i | −0.964406 | − | 0.264427i | \(-0.914817\pi\) | ||
0.964406 | − | 0.264427i | \(-0.0851830\pi\) | |||||||
\(450\) | 9339.45 | − | 14504.1i | 0.978369 | − | 1.51940i | ||||
\(451\) | 2027.86i | 0.211726i | ||||||||
\(452\) | −26424.9 | −2.74982 | ||||||||
\(453\) | 1900.55 | + | 6222.57i | 0.197120 | + | 0.645391i | ||||
\(454\) | 11285.7i | 1.16666i | ||||||||
\(455\) | 1945.39 | − | 3878.44i | 0.200443 | − | 0.399614i | ||||
\(456\) | −8538.84 | + | 2608.00i | −0.876903 | + | 0.267830i | ||||
\(457\) | 1781.33i | 0.182335i | 0.995836 | + | 0.0911673i | \(0.0290598\pi\) | ||||
−0.995836 | + | 0.0911673i | \(0.970940\pi\) | |||||||
\(458\) | 8796.44i | 0.897447i | ||||||||
\(459\) | −8557.45 | + | 10549.6i | −0.870213 | + | 1.07280i | ||||
\(460\) | 22090.5 | − | 4545.28i | 2.23908 | − | 0.460706i | ||||
\(461\) | 17966.1 | 1.81511 | 0.907556 | − | 0.419931i | \(-0.137946\pi\) | ||||
0.907556 | + | 0.419931i | \(0.137946\pi\) | |||||||
\(462\) | −9895.71 | + | 25406.7i | −0.996515 | + | 2.55850i | ||||
\(463\) | − | 7730.37i | − | 0.775941i | −0.921672 | − | 0.387971i | \(-0.873176\pi\) | ||
0.921672 | − | 0.387971i | \(-0.126824\pi\) | |||||||
\(464\) | 18743.4i | 1.87530i | ||||||||
\(465\) | −4105.38 | + | 2239.34i | −0.409425 | + | 0.223326i | ||||
\(466\) | −14902.6 | −1.48144 | ||||||||
\(467\) | 7613.81i | 0.754443i | 0.926123 | + | 0.377222i | \(0.123121\pi\) | ||||
−0.926123 | + | 0.377222i | \(0.876879\pi\) | |||||||
\(468\) | −8505.39 | + | 5730.10i | −0.840089 | + | 0.565970i | ||||
\(469\) | 4456.10 | + | 3514.76i | 0.438728 | + | 0.346048i | ||||
\(470\) | −2990.54 | − | 14534.3i | −0.293497 | − | 1.42642i | ||||
\(471\) | −343.979 | − | 1126.22i | −0.0336512 | − | 0.110177i | ||||
\(472\) | −36502.3 | −3.55965 | ||||||||
\(473\) | −2914.70 | −0.283336 | ||||||||
\(474\) | −667.081 | − | 2184.09i | −0.0646414 | − | 0.211642i | ||||
\(475\) | −1638.27 | − | 3812.54i | −0.158251 | − | 0.368277i | ||||
\(476\) | −25520.7 | − | 20129.5i | −2.45744 | − | 1.93831i | ||||
\(477\) | 4292.39 | − | 2891.79i | 0.412023 | − | 0.277581i | ||||
\(478\) | − | 33720.9i | − | 3.22669i | ||||||
\(479\) | 1660.45 | 0.158388 | 0.0791939 | − | 0.996859i | \(-0.474765\pi\) | ||||
0.0791939 | + | 0.996859i | \(0.474765\pi\) | |||||||
\(480\) | −5480.16 | − | 10046.8i | −0.521112 | − | 0.955356i | ||||
\(481\) | 3779.55i | 0.358280i | ||||||||
\(482\) | − | 28073.1i | − | 2.65289i | ||||||
\(483\) | 9979.45 | + | 3886.92i | 0.940126 | + | 0.366172i | ||||
\(484\) | −31568.1 | −2.96470 | ||||||||
\(485\) | −11558.1 | + | 2378.16i | −1.08212 | + | 0.222653i | ||||
\(486\) | −19285.8 | − | 1714.21i | −1.80005 | − | 0.159997i | ||||
\(487\) | − | 1783.16i | − | 0.165920i | −0.996553 | − | 0.0829599i | \(-0.973563\pi\) | ||
0.996553 | − | 0.0829599i | \(-0.0264373\pi\) | |||||||
\(488\) | 22105.1i | 2.05051i | ||||||||
\(489\) | −9163.28 | + | 2798.72i | −0.847398 | + | 0.258819i | ||||
\(490\) | 8314.10 | + | 17750.8i | 0.766516 | + | 1.63653i | ||||
\(491\) | − | 4975.18i | − | 0.457284i | −0.973511 | − | 0.228642i | \(-0.926571\pi\) | ||
0.973511 | − | 0.228642i | \(-0.0734286\pi\) | |||||||
\(492\) | −1006.51 | − | 3295.41i | −0.0922295 | − | 0.301968i | ||||
\(493\) | 15180.4 | 1.38679 | ||||||||
\(494\) | 3555.69i | 0.323842i | ||||||||
\(495\) | 11954.1 | + | 11708.4i | 1.08545 | + | 1.06314i | ||||
\(496\) | 9623.28i | 0.871166i | ||||||||
\(497\) | 7471.21 | + | 5892.93i | 0.674305 | + | 0.531859i | ||||
\(498\) | 22528.1 | − | 6880.70i | 2.02712 | − | 0.619140i | ||||
\(499\) | −7878.69 | −0.706811 | −0.353406 | − | 0.935470i | \(-0.614976\pi\) | ||||
−0.353406 | + | 0.935470i | \(0.614976\pi\) | |||||||
\(500\) | 20781.2 | − | 14486.5i | 1.85873 | − | 1.29571i | ||||
\(501\) | 10658.0 | − | 3255.26i | 0.950431 | − | 0.290288i | ||||
\(502\) | −19691.6 | −1.75076 | ||||||||
\(503\) | − | 3798.11i | − | 0.336678i | −0.985729 | − | 0.168339i | \(-0.946160\pi\) | ||
0.985729 | − | 0.168339i | \(-0.0538404\pi\) | |||||||
\(504\) | 1938.98 | − | 25809.1i | 0.171367 | − | 2.28101i | ||||
\(505\) | 8111.86 | − | 1669.07i | 0.714798 | − | 0.147075i | ||||
\(506\) | 31531.0i | 2.77020i | ||||||||
\(507\) | −2668.18 | − | 8735.88i | −0.233724 | − | 0.765234i | ||||
\(508\) | 21564.5i | 1.88341i | ||||||||
\(509\) | −12066.4 | −1.05075 | −0.525377 | − | 0.850870i | \(-0.676076\pi\) | ||||
−0.525377 | + | 0.850870i | \(0.676076\pi\) | |||||||
\(510\) | −25240.5 | + | 13767.8i | −2.19151 | + | 1.19539i | ||||
\(511\) | 4136.28 | − | 5244.08i | 0.358079 | − | 0.453982i | ||||
\(512\) | 25951.6 | 2.24006 | ||||||||
\(513\) | −2934.01 | + | 3617.05i | −0.252514 | + | 0.311300i | ||||
\(514\) | − | 2275.28i | − | 0.195249i | ||||||
\(515\) | 10245.5 | − | 2108.09i | 0.876644 | − | 0.180376i | ||||
\(516\) | 4736.57 | − | 1446.68i | 0.404101 | − | 0.123424i | ||||
\(517\) | 14393.2 | 1.22439 | ||||||||
\(518\) | −13405.9 | − | 10573.9i | −1.13711 | − | 0.896894i | ||||
\(519\) | 17207.8 | − | 5255.75i | 1.45538 | − | 0.444512i | ||||
\(520\) | −11877.4 | + | 2443.87i | −1.00165 | + | 0.206098i | ||||
\(521\) | 671.033 | 0.0564270 | 0.0282135 | − | 0.999602i | \(-0.491018\pi\) | ||||
0.0282135 | + | 0.999602i | \(0.491018\pi\) | |||||||
\(522\) | 12089.5 | + | 17944.8i | 1.01368 | + | 1.50464i | ||||
\(523\) | −8833.34 | −0.738538 | −0.369269 | − | 0.929323i | \(-0.620392\pi\) | ||||
−0.369269 | + | 0.929323i | \(0.620392\pi\) | |||||||
\(524\) | 9631.28 | 0.802947 | ||||||||
\(525\) | 12022.1 | − | 414.141i | 0.999407 | − | 0.0344278i | ||||
\(526\) | 28312.6 | 2.34694 | ||||||||
\(527\) | 7793.94 | 0.644230 | ||||||||
\(528\) | 32931.7 | − | 10058.2i | 2.71433 | − | 0.829032i | ||||
\(529\) | 218.010 | 0.0179181 | ||||||||
\(530\) | 10729.7 | − | 2207.72i | 0.879376 | − | 0.180938i | ||||
\(531\) | −15791.9 | + | 10639.1i | −1.29061 | + | 0.869484i | ||||
\(532\) | −8750.04 | − | 6901.61i | −0.713087 | − | 0.562449i | ||||
\(533\) | −766.609 | −0.0622993 | ||||||||
\(534\) | 10999.6 | + | 36013.7i | 0.891382 | + | 2.91847i | ||||
\(535\) | −8703.27 | + | 1790.76i | −0.703318 | + | 0.144713i | ||||
\(536\) | − | 15861.2i | − | 1.27817i | ||||||
\(537\) | 15352.9 | − | 4689.22i | 1.23376 | − | 0.376824i | ||||
\(538\) | 34871.1 | 2.79443 | ||||||||
\(539\) | −18489.7 | + | 4428.97i | −1.47757 | + | 0.353932i | ||||
\(540\) | −25237.6 | − | 13093.6i | −2.01121 | − | 1.04344i | ||||
\(541\) | −16688.3 | −1.32623 | −0.663113 | − | 0.748519i | \(-0.730765\pi\) | ||||
−0.663113 | + | 0.748519i | \(0.730765\pi\) | |||||||
\(542\) | 18230.8i | 1.44480i | ||||||||
\(543\) | −13870.3 | + | 4236.37i | −1.09619 | + | 0.334807i | ||||
\(544\) | 19073.5i | 1.50325i | ||||||||
\(545\) | −2213.56 | + | 455.456i | −0.173979 | + | 0.0357974i | ||||
\(546\) | −9604.69 | − | 3740.96i | −0.752826 | − | 0.293220i | ||||
\(547\) | − | 19572.5i | − | 1.52991i | −0.644086 | − | 0.764953i | \(-0.722762\pi\) | ||
0.644086 | − | 0.764953i | \(-0.277238\pi\) | |||||||
\(548\) | 23008.0 | 1.79352 | ||||||||
\(549\) | 6442.82 | + | 9563.30i | 0.500862 | + | 0.743446i | ||||
\(550\) | 13982.2 | + | 32539.0i | 1.08401 | + | 2.52267i | ||||
\(551\) | 5204.75 | 0.402413 | ||||||||
\(552\) | −8742.92 | − | 28625.2i | −0.674136 | − | 2.20719i | ||||
\(553\) | 986.192 | − | 1250.32i | 0.0758357 | − | 0.0961464i | ||||
\(554\) | − | 23278.1i | − | 1.78518i | ||||||
\(555\) | −9198.80 | + | 5017.61i | −0.703544 | + | 0.383758i | ||||
\(556\) | − | 28395.3i | − | 2.16588i | ||||||
\(557\) | −23150.1 | −1.76104 | −0.880521 | − | 0.474008i | \(-0.842807\pi\) | ||||
−0.880521 | + | 0.474008i | \(0.842807\pi\) | |||||||
\(558\) | 6207.00 | + | 9213.27i | 0.470902 | + | 0.698976i | ||||
\(559\) | − | 1101.87i | − | 0.0833704i | ||||||
\(560\) | 11098.6 | − | 22126.8i | 0.837502 | − | 1.66969i | ||||
\(561\) | −8146.22 | − | 26671.5i | −0.613073 | − | 2.00726i | ||||
\(562\) | − | 25222.7i | − | 1.89316i | ||||||
\(563\) | 5111.84i | 0.382661i | 0.981526 | + | 0.191331i | \(0.0612803\pi\) | ||||
−0.981526 | + | 0.191331i | \(0.938720\pi\) | |||||||
\(564\) | −23389.8 | + | 7143.91i | −1.74626 | + | 0.533356i | ||||
\(565\) | −15964.6 | + | 3284.82i | −1.18873 | + | 0.244590i | ||||
\(566\) | 2334.49 | 0.173367 | ||||||||
\(567\) | −6683.55 | − | 11730.9i | −0.495032 | − | 0.868875i | ||||
\(568\) | − | 26593.2i | − | 1.96448i | ||||||
\(569\) | − | 1896.42i | − | 0.139723i | −0.997557 | − | 0.0698613i | \(-0.977744\pi\) | ||
0.997557 | − | 0.0698613i | \(-0.0222557\pi\) | |||||||
\(570\) | −8653.97 | + | 4720.43i | −0.635921 | + | 0.346872i | ||||
\(571\) | −17070.6 | −1.25111 | −0.625554 | − | 0.780181i | \(-0.715127\pi\) | ||||
−0.625554 | + | 0.780181i | \(0.715127\pi\) | |||||||
\(572\) | − | 21054.5i | − | 1.53904i | ||||||
\(573\) | −15844.9 | + | 4839.47i | −1.15520 | + | 0.352831i | ||||
\(574\) | 2144.72 | − | 2719.13i | 0.155956 | − | 0.197725i | ||||
\(575\) | 12781.0 | − | 5492.06i | 0.926962 | − | 0.398321i | ||||
\(576\) | −1130.94 | + | 761.919i | −0.0818101 | + | 0.0551157i | ||||
\(577\) | 4537.92 | 0.327411 | 0.163705 | − | 0.986509i | \(-0.447655\pi\) | ||||
0.163705 | + | 0.986509i | \(0.447655\pi\) | |||||||
\(578\) | 22806.1 | 1.64119 | ||||||||
\(579\) | 8758.56 | − | 2675.11i | 0.628658 | − | 0.192010i | ||||
\(580\) | 6403.44 | + | 31121.4i | 0.458428 | + | 2.22801i | ||||
\(581\) | 12896.6 | + | 10172.2i | 0.920897 | + | 0.726359i | ||||
\(582\) | 8188.35 | + | 26809.5i | 0.583193 | + | 1.90943i | ||||
\(583\) | 10625.5i | 0.754826i | ||||||||
\(584\) | −18665.9 | −1.32261 | ||||||||
\(585\) | −4426.23 | + | 4519.13i | −0.312824 | + | 0.319389i | ||||
\(586\) | 10745.6i | 0.757503i | ||||||||
\(587\) | 15763.7i | 1.10841i | 0.832380 | + | 0.554205i | \(0.186978\pi\) | ||||
−0.832380 | + | 0.554205i | \(0.813022\pi\) | |||||||
\(588\) | 27848.7 | − | 16374.5i | 1.95316 | − | 1.14843i | ||||
\(589\) | 2672.23 | 0.186940 | ||||||||
\(590\) | −39475.2 | + | 8122.31i | −2.75452 | + | 0.566763i | ||||
\(591\) | −1723.79 | − | 5643.85i | −0.119978 | − | 0.392821i | ||||
\(592\) | 21562.6i | 1.49699i | ||||||||
\(593\) | − | 2405.31i | − | 0.166567i | −0.996526 | − | 0.0832834i | \(-0.973459\pi\) | ||
0.996526 | − | 0.0832834i | \(-0.0265407\pi\) | |||||||
\(594\) | 25041.0 | − | 30870.6i | 1.72971 | − | 2.13238i | ||||
\(595\) | −17920.6 | − | 8988.80i | −1.23474 | − | 0.619336i | ||||
\(596\) | 20167.0i | 1.38603i | ||||||||
\(597\) | −5966.10 | + | 1822.21i | −0.409006 | + | 0.124922i | ||||
\(598\) | −11919.9 | −0.815120 | ||||||||
\(599\) | − | 8892.20i | − | 0.606553i | −0.952903 | − | 0.303277i | \(-0.901919\pi\) | ||
0.952903 | − | 0.303277i | \(-0.0980806\pi\) | |||||||
\(600\) | −21716.1 | − | 25663.3i | −1.47759 | − | 1.74617i | ||||
\(601\) | 2916.97i | 0.197980i | 0.995088 | + | 0.0989898i | \(0.0315611\pi\) | ||||
−0.995088 | + | 0.0989898i | \(0.968439\pi\) | |||||||
\(602\) | 3908.27 | + | 3082.66i | 0.264600 | + | 0.208704i | ||||
\(603\) | −4622.95 | − | 6862.00i | −0.312207 | − | 0.463420i | ||||
\(604\) | 22696.6 | 1.52900 | ||||||||
\(605\) | −19071.8 | + | 3924.17i | −1.28162 | + | 0.263703i | ||||
\(606\) | −5746.86 | − | 18815.8i | −0.385232 | − | 1.26129i | ||||
\(607\) | −12105.3 | −0.809458 | −0.404729 | − | 0.914437i | \(-0.632634\pi\) | ||||
−0.404729 | + | 0.914437i | \(0.632634\pi\) | |||||||
\(608\) | 6539.55i | 0.436207i | ||||||||
\(609\) | −5475.93 | + | 14059.1i | −0.364361 | + | 0.935477i | ||||
\(610\) | 4918.72 | + | 23905.5i | 0.326481 | + | 1.58673i | ||||
\(611\) | 5441.17i | 0.360272i | ||||||||
\(612\) | 26476.3 | + | 39299.7i | 1.74876 | + | 2.59574i | ||||
\(613\) | − | 11262.7i | − | 0.742083i | −0.928616 | − | 0.371041i | \(-0.879001\pi\) | ||
0.928616 | − | 0.371041i | \(-0.120999\pi\) | |||||||
\(614\) | −14213.1 | −0.934194 | ||||||||
\(615\) | −1017.73 | − | 1865.80i | −0.0667296 | − | 0.122335i | ||||
\(616\) | 41719.6 | + | 32906.4i | 2.72878 | + | 2.15233i | ||||
\(617\) | −5183.80 | −0.338236 | −0.169118 | − | 0.985596i | \(-0.554092\pi\) | ||||
−0.169118 | + | 0.985596i | \(0.554092\pi\) | |||||||
\(618\) | −7258.46 | − | 23764.9i | −0.472456 | − | 1.54687i | ||||
\(619\) | 26124.4i | 1.69633i | 0.529734 | + | 0.848164i | \(0.322292\pi\) | ||||
−0.529734 | + | 0.848164i | \(0.677708\pi\) | |||||||
\(620\) | 3287.67 | + | 15978.4i | 0.212961 | + | 1.03501i | ||||
\(621\) | −12125.6 | − | 9835.83i | −0.783550 | − | 0.635585i | ||||
\(622\) | 2251.88 | 0.145164 | ||||||||
\(623\) | −16261.4 | + | 20616.7i | −1.04575 | + | 1.32583i | ||||
\(624\) | 3802.41 | + | 12449.4i | 0.243939 | + | 0.798680i | ||||
\(625\) | 10754.2 | − | 11335.3i | 0.688266 | − | 0.725459i | ||||
\(626\) | 35773.9 | 2.28405 | ||||||||
\(627\) | −2793.02 | − | 9144.61i | −0.177899 | − | 0.582457i | ||||
\(628\) | −4107.86 | −0.261021 | ||||||||
\(629\) | 17463.6 | 1.10703 | ||||||||
\(630\) | −3646.02 | − | 28342.6i | −0.230573 | − | 1.79238i | ||||
\(631\) | −10304.6 | −0.650110 | −0.325055 | − | 0.945695i | \(-0.605383\pi\) | ||||
−0.325055 | + | 0.945695i | \(0.605383\pi\) | |||||||
\(632\) | −4450.42 | −0.280108 | ||||||||
\(633\) | −1268.31 | − | 4152.58i | −0.0796380 | − | 0.260743i | ||||
\(634\) | 51687.7 | 3.23782 | ||||||||
\(635\) | 2680.64 | + | 13028.2i | 0.167525 | + | 0.814186i | ||||
\(636\) | −5273.87 | − | 17267.2i | −0.328809 | − | 1.07655i | ||||
\(637\) | −1674.32 | − | 6989.82i | −0.104143 | − | 0.434767i | ||||
\(638\) | −44421.1 | −2.75650 | ||||||||
\(639\) | −7750.95 | − | 11505.0i | −0.479848 | − | 0.712255i | ||||
\(640\) | 14431.0 | − | 2969.27i | 0.891303 | − | 0.183392i | ||||
\(641\) | 23841.8i | 1.46910i | 0.678552 | + | 0.734552i | \(0.262608\pi\) | ||||
−0.678552 | + | 0.734552i | \(0.737392\pi\) | |||||||
\(642\) | 6165.85 | + | 20187.6i | 0.379045 | + | 1.24103i | ||||
\(643\) | 8773.65 | 0.538101 | 0.269050 | − | 0.963126i | \(-0.413290\pi\) | ||||
0.269050 | + | 0.963126i | \(0.413290\pi\) | |||||||
\(644\) | 23136.6 | − | 29333.2i | 1.41570 | − | 1.79486i | ||||
\(645\) | 2681.76 | − | 1462.81i | 0.163712 | − | 0.0892991i | ||||
\(646\) | 16429.3 | 1.00062 | ||||||||
\(647\) | 8008.70i | 0.486638i | 0.969946 | + | 0.243319i | \(0.0782362\pi\) | ||||
−0.969946 | + | 0.243319i | \(0.921764\pi\) | |||||||
\(648\) | −14173.5 | + | 34969.0i | −0.859240 | + | 2.11993i | ||||
\(649\) | − | 39091.8i | − | 2.36439i | ||||||
\(650\) | −12301.0 | + | 5285.82i | −0.742285 | + | 0.318964i | ||||
\(651\) | −2811.47 | + | 7218.28i | −0.169263 | + | 0.434573i | ||||
\(652\) | 33422.8i | 2.00757i | ||||||||
\(653\) | 4305.61 | 0.258027 | 0.129014 | − | 0.991643i | \(-0.458819\pi\) | ||||
0.129014 | + | 0.991643i | \(0.458819\pi\) | |||||||
\(654\) | 1568.20 | + | 5134.44i | 0.0937638 | + | 0.306992i | ||||
\(655\) | 5818.73 | − | 1197.25i | 0.347109 | − | 0.0714202i | ||||
\(656\) | −4373.56 | −0.260303 | ||||||||
\(657\) | −8075.43 | + | 5440.44i | −0.479532 | + | 0.323062i | ||||
\(658\) | −19299.6 | − | 15222.6i | −1.14343 | − | 0.901882i | ||||
\(659\) | − | 24759.2i | − | 1.46355i | −0.681545 | − | 0.731777i | \(-0.738691\pi\) | ||
0.681545 | − | 0.731777i | \(-0.261309\pi\) | |||||||
\(660\) | 51243.1 | − | 27951.3i | 3.02218 | − | 1.64849i | ||||
\(661\) | − | 10995.7i | − | 0.647022i | −0.946224 | − | 0.323511i | \(-0.895137\pi\) | ||
0.946224 | − | 0.323511i | \(-0.104863\pi\) | |||||||
\(662\) | −25714.7 | −1.50971 | ||||||||
\(663\) | 10082.9 | − | 3079.59i | 0.590627 | − | 0.180394i | ||||
\(664\) | − | 45904.5i | − | 2.68289i | ||||||
\(665\) | −6144.26 | − | 3081.90i | −0.358292 | − | 0.179716i | ||||
\(666\) | 13907.8 | + | 20643.9i | 0.809186 | + | 1.20110i | ||||
\(667\) | 17448.1i | 1.01288i | ||||||||
\(668\) | − | 38874.9i | − | 2.25167i | ||||||
\(669\) | 4150.35 | + | 13588.6i | 0.239853 | + | 0.785302i | ||||
\(670\) | −3529.35 | − | 17153.0i | −0.203509 | − | 0.989071i | ||||
\(671\) | −23673.3 | −1.36199 | ||||||||
\(672\) | −17664.7 | − | 6880.29i | −1.01404 | − | 0.394960i | ||||
\(673\) | 18477.5i | 1.05833i | 0.848520 | + | 0.529163i | \(0.177494\pi\) | ||||
−0.848520 | + | 0.529163i | \(0.822506\pi\) | |||||||
\(674\) | − | 16517.0i | − | 0.943936i | ||||||
\(675\) | −16874.9 | − | 4773.25i | −0.962246 | − | 0.272181i | ||||
\(676\) | −31863.9 | −1.81292 | ||||||||
\(677\) | − | 6639.83i | − | 0.376942i | −0.982079 | − | 0.188471i | \(-0.939647\pi\) | ||
0.982079 | − | 0.188471i | \(-0.0603531\pi\) | |||||||
\(678\) | 11310.1 | + | 37030.4i | 0.640653 | + | 2.09756i | ||||
\(679\) | −12105.4 | + | 15347.6i | −0.684187 | + | 0.867430i | ||||
\(680\) | 11292.0 | + | 54880.4i | 0.636809 | + | 3.09495i | ||||
\(681\) | 10972.4 | − | 3351.29i | 0.617423 | − | 0.188578i | ||||
\(682\) | −22806.8 | −1.28052 | ||||||||
\(683\) | 6422.87 | 0.359830 | 0.179915 | − | 0.983682i | \(-0.442418\pi\) | ||||
0.179915 | + | 0.983682i | \(0.442418\pi\) | |||||||
\(684\) | 9077.67 | + | 13474.3i | 0.507446 | + | 0.753220i | ||||
\(685\) | 13900.2 | − | 2860.07i | 0.775330 | − | 0.159530i | ||||
\(686\) | 29476.8 | + | 13616.4i | 1.64057 | + | 0.757840i | ||||
\(687\) | 8552.32 | − | 2612.11i | 0.474951 | − | 0.145063i | ||||
\(688\) | − | 6286.23i | − | 0.348343i | ||||||
\(689\) | −4016.85 | −0.222104 | ||||||||
\(690\) | −15824.5 | − | 29011.1i | −0.873086 | − | 1.60063i | ||||
\(691\) | 33292.1i | 1.83284i | 0.400221 | + | 0.916419i | \(0.368933\pi\) | ||||
−0.400221 | + | 0.916419i | \(0.631067\pi\) | |||||||
\(692\) | − | 62765.1i | − | 3.44793i | ||||||
\(693\) | 27640.1 | + | 2076.53i | 1.51509 | + | 0.113825i | ||||
\(694\) | −41833.0 | −2.28812 | ||||||||
\(695\) | −3529.76 | − | 17155.0i | −0.192650 | − | 0.936296i | ||||
\(696\) | 40327.4 | − | 12317.1i | 2.19627 | − | 0.670803i | ||||
\(697\) | 3542.17i | 0.192495i | ||||||||
\(698\) | − | 57321.6i | − | 3.10839i | ||||||
\(699\) | 4425.35 | + | 14489.0i | 0.239460 | + | 0.784014i | ||||
\(700\) | 10868.7 | − | 40530.8i | 0.586852 | − | 2.18846i | ||||
\(701\) | − | 21719.6i | − | 1.17024i | −0.810946 | − | 0.585121i | \(-0.801047\pi\) | ||
0.810946 | − | 0.585121i | \(-0.198953\pi\) | |||||||
\(702\) | 11670.3 | + | 9466.47i | 0.627444 | + | 0.508958i | ||||
\(703\) | 5987.59 | 0.321232 | ||||||||
\(704\) | − | 2799.57i | − | 0.149876i | ||||||
\(705\) | −13242.9 | + | 7223.53i | −0.707457 | + | 0.385892i | ||||
\(706\) | − | 4110.61i | − | 0.219129i | ||||||
\(707\) | 8495.99 | − | 10771.4i | 0.451944 | − | 0.572987i | ||||
\(708\) | 19402.8 | + | 63526.8i | 1.02995 | + | 3.37215i | ||||
\(709\) | 9450.02 | 0.500568 | 0.250284 | − | 0.968172i | \(-0.419476\pi\) | ||||
0.250284 | + | 0.968172i | \(0.419476\pi\) | |||||||
\(710\) | −5917.40 | − | 28759.1i | −0.312783 | − | 1.52016i | ||||
\(711\) | −1925.38 | + | 1297.13i | −0.101558 | + | 0.0684196i | ||||
\(712\) | 73383.6 | 3.86259 | ||||||||
\(713\) | 8958.26i | 0.470532i | ||||||||
\(714\) | −17285.3 | + | 44379.1i | −0.906004 | + | 2.32611i | ||||
\(715\) | −2617.24 | − | 12720.1i | −0.136894 | − | 0.665319i | ||||
\(716\) | − | 55999.4i | − | 2.92290i | ||||||
\(717\) | −32785.0 | + | 10013.5i | −1.70764 | + | 0.521562i | ||||
\(718\) | − | 21523.5i | − | 1.11873i | ||||||
\(719\) | 29056.2 | 1.50711 | 0.753555 | − | 0.657385i | \(-0.228338\pi\) | ||||
0.753555 | + | 0.657385i | \(0.228338\pi\) | |||||||
\(720\) | −25251.9 | + | 25781.9i | −1.30706 | + | 1.33449i | ||||
\(721\) | 10730.7 | − | 13604.6i | 0.554274 | − | 0.702723i | ||||
\(722\) | −29426.0 | −1.51679 | ||||||||
\(723\) | −27294.0 | + | 8336.34i | −1.40398 | + | 0.428813i | ||||
\(724\) | 50591.4i | 2.59698i | ||||||||
\(725\) | 7737.27 | + | 18005.9i | 0.396352 | + | 0.922378i | ||||
\(726\) | 13511.5 | + | 44237.9i | 0.690714 | + | 2.26146i | ||||
\(727\) | 3457.74 | 0.176397 | 0.0881983 | − | 0.996103i | \(-0.471889\pi\) | ||||
0.0881983 | + | 0.996103i | \(0.471889\pi\) | |||||||
\(728\) | −12439.9 | + | 15771.6i | −0.633314 | + | 0.802932i | ||||
\(729\) | 4060.32 | + | 19259.7i | 0.206286 | + | 0.978492i | ||||
\(730\) | −20186.2 | + | 4153.45i | −1.02346 | + | 0.210584i | ||||
\(731\) | −5091.25 | −0.257601 | ||||||||
\(732\) | 38470.7 | − | 11750.0i | 1.94251 | − | 0.593296i | ||||
\(733\) | −22212.1 | −1.11927 | −0.559634 | − | 0.828740i | \(-0.689058\pi\) | ||||
−0.559634 | + | 0.828740i | \(0.689058\pi\) | |||||||
\(734\) | −64968.7 | −3.26708 | ||||||||
\(735\) | 14789.3 | − | 13354.5i | 0.742192 | − | 0.670187i | ||||
\(736\) | −21922.9 | −1.09794 | ||||||||
\(737\) | 16986.4 | 0.848986 | ||||||||
\(738\) | −4187.22 | + | 2820.94i | −0.208853 | + | 0.140705i | ||||
\(739\) | −35565.7 | −1.77037 | −0.885186 | − | 0.465237i | \(-0.845969\pi\) | ||||
−0.885186 | + | 0.465237i | \(0.845969\pi\) | |||||||
\(740\) | 7366.58 | + | 35802.3i | 0.365947 | + | 1.77854i | ||||
\(741\) | 3457.01 | − | 1055.87i | 0.171385 | − | 0.0523459i | ||||
\(742\) | 11237.8 | − | 14247.6i | 0.556001 | − | 0.704913i | ||||
\(743\) | 20992.4 | 1.03652 | 0.518262 | − | 0.855222i | \(-0.326579\pi\) | ||||
0.518262 | + | 0.855222i | \(0.326579\pi\) | |||||||
\(744\) | 20705.0 | − | 6323.88i | 1.02027 | − | 0.311619i | ||||
\(745\) | 2506.92 | + | 12183.9i | 0.123284 | + | 0.599172i | ||||
\(746\) | − | 53820.8i | − | 2.64145i | ||||||
\(747\) | −13379.5 | − | 19859.6i | −0.655328 | − | 0.972725i | ||||
\(748\) | −97283.6 | −4.75540 | ||||||||
\(749\) | −9115.41 | + | 11556.8i | −0.444686 | + | 0.563785i | ||||
\(750\) | −29195.2 | − | 22921.3i | −1.42141 | − | 1.11596i | ||||
\(751\) | 5971.01 | 0.290127 | 0.145063 | − | 0.989422i | \(-0.453661\pi\) | ||||
0.145063 | + | 0.989422i | \(0.453661\pi\) | |||||||
\(752\) | 31042.3i | 1.50531i | ||||||||
\(753\) | 5847.46 | + | 19145.1i | 0.282992 | + | 0.926545i | ||||
\(754\) | − | 16792.9i | − | 0.811089i | ||||||
\(755\) | 13712.2 | − | 2821.38i | 0.660976 | − | 0.136001i | ||||
\(756\) | −45947.6 | + | 10344.4i | −2.21045 | + | 0.497648i | ||||
\(757\) | 23358.2i | 1.12149i | 0.827988 | + | 0.560745i | \(0.189485\pi\) | ||||
−0.827988 | + | 0.560745i | \(0.810515\pi\) | |||||||
\(758\) | 37519.5 | 1.79785 | ||||||||
\(759\) | 30655.9 | − | 9363.17i | 1.46606 | − | 0.447775i | ||||
\(760\) | 3871.59 | + | 18816.3i | 0.184786 | + | 0.898079i | ||||
\(761\) | −428.292 | −0.0204015 | −0.0102008 | − | 0.999948i | \(-0.503247\pi\) | ||||
−0.0102008 | + | 0.999948i | \(0.503247\pi\) | |||||||
\(762\) | 30219.4 | − | 9229.85i | 1.43666 | − | 0.438796i | ||||
\(763\) | −2318.38 | + | 2939.30i | −0.110001 | + | 0.139463i | ||||
\(764\) | 57793.8i | 2.73679i | ||||||||
\(765\) | 20880.9 | + | 20451.6i | 0.986863 | + | 0.966576i | ||||
\(766\) | − | 62474.4i | − | 2.94686i | ||||||
\(767\) | 14778.2 | 0.695711 | ||||||||
\(768\) | −10836.9 | − | 35481.1i | −0.509171 | − | 1.66708i | ||||
\(769\) | 16393.0i | 0.768720i | 0.923183 | + | 0.384360i | \(0.125578\pi\) | ||||
−0.923183 | + | 0.384360i | \(0.874422\pi\) | |||||||
\(770\) | 52439.6 | + | 26303.2i | 2.45428 | + | 1.23104i | ||||
\(771\) | −2212.13 | + | 675.647i | −0.103331 | + | 0.0315601i | ||||
\(772\) | − | 31946.6i | − | 1.48936i | ||||||
\(773\) | − | 22894.4i | − | 1.06527i | −0.846344 | − | 0.532636i | \(-0.821201\pi\) | ||
0.846344 | − | 0.532636i | \(-0.178799\pi\) | |||||||
\(774\) | −4054.61 | − | 6018.39i | −0.188294 | − | 0.279492i | ||||
\(775\) | 3972.49 | + | 9244.66i | 0.184124 | + | 0.428488i | ||||
\(776\) | 54628.5 | 2.52713 | ||||||||
\(777\) | −6299.57 | + | 16173.8i | −0.290857 | + | 0.746758i | ||||
\(778\) | 5467.73i | 0.251963i | ||||||||
\(779\) | 1214.47i | 0.0558573i | ||||||||
\(780\) | 10566.7 | + | 19371.9i | 0.485061 | + | 0.889262i | ||||
\(781\) | 28479.8 | 1.30485 | ||||||||
\(782\) | 55076.7i | 2.51859i | ||||||||
\(783\) | 13856.8 | − | 17082.7i | 0.632442 | − | 0.779675i | ||||
\(784\) | −9552.12 | − | 39877.4i | −0.435136 | − | 1.81657i | ||||
\(785\) | −2481.76 | + | 510.640i | −0.112838 | + | 0.0232172i | ||||
\(786\) | −4122.29 | − | 13496.8i | −0.187070 | − | 0.612486i | ||||
\(787\) | 37222.3 | 1.68594 | 0.842969 | − | 0.537963i | \(-0.180806\pi\) | ||||
0.842969 | + | 0.537963i | \(0.180806\pi\) | |||||||
\(788\) | −20585.8 | −0.930632 | ||||||||
\(789\) | −8407.48 | − | 27526.9i | −0.379359 | − | 1.24206i | ||||
\(790\) | −4812.89 | + | 990.286i | −0.216753 | + | 0.0445985i | ||||
\(791\) | −16720.5 | + | 21198.7i | −0.751598 | + | 0.952896i | ||||
\(792\) | −43281.7 | − | 64244.5i | −1.94185 | − | 2.88236i | ||||
\(793\) | − | 8949.42i | − | 0.400761i | ||||||
\(794\) | −60977.9 | −2.72547 | ||||||||
\(795\) | −5332.65 | − | 9776.35i | −0.237899 | − | 0.436140i | ||||
\(796\) | 21761.2i | 0.968976i | ||||||||
\(797\) | − | 10475.1i | − | 0.465554i | −0.972530 | − | 0.232777i | \(-0.925219\pi\) | ||
0.972530 | − | 0.232777i | \(-0.0747812\pi\) | |||||||
\(798\) | −5926.45 | + | 15215.8i | −0.262900 | + | 0.674981i | ||||
\(799\) | 25141.3 | 1.11318 | ||||||||
\(800\) | −22623.7 | + | 9721.57i | −0.999838 | + | 0.429637i | ||||
\(801\) | 31747.9 | − | 21388.6i | 1.40044 | − | 0.943483i | ||||
\(802\) | 26572.3i | 1.16995i | ||||||||
\(803\) | − | 19990.2i | − | 0.878502i | ||||||
\(804\) | −27604.0 | + | 8431.04i | −1.21084 | + | 0.369825i | ||||
\(805\) | 10331.6 | − | 20597.7i | 0.452350 | − | 0.901830i | ||||
\(806\) | − | 8621.85i | − | 0.376789i | ||||||
\(807\) | −10355.0 | − | 33903.4i | −0.451691 | − | 1.47888i | ||||
\(808\) | −38340.2 | −1.66931 | ||||||||
\(809\) | − | 8052.55i | − | 0.349954i | −0.984573 | − | 0.174977i | \(-0.944015\pi\) | ||
0.984573 | − | 0.174977i | \(-0.0559850\pi\) | |||||||
\(810\) | −7546.72 | + | 40970.9i | −0.327364 | + | 1.77725i | ||||
\(811\) | − | 11903.9i | − | 0.515416i | −0.966223 | − | 0.257708i | \(-0.917033\pi\) | ||
0.966223 | − | 0.257708i | \(-0.0829672\pi\) | |||||||
\(812\) | 41324.9 | + | 32595.1i | 1.78598 | + | 1.40870i | ||||
\(813\) | 17724.8 | − | 5413.66i | 0.764621 | − | 0.233537i | ||||
\(814\) | −51102.5 | −2.20042 | ||||||||
\(815\) | 4154.72 | + | 20192.4i | 0.178569 | + | 0.867862i | ||||
\(816\) | 57523.4 | − | 17569.2i | 2.46780 | − | 0.753734i | ||||
\(817\) | −1745.59 | −0.0747495 | ||||||||
\(818\) | 83893.0i | 3.58588i | ||||||||
\(819\) | −785.010 | + | 10449.0i | −0.0334926 | + | 0.445810i | ||||
\(820\) | −7261.81 | + | 1494.17i | −0.309260 | + | 0.0636325i | ||||
\(821\) | − | 16286.9i | − | 0.692346i | −0.938171 | − | 0.346173i | \(-0.887481\pi\) | ||
0.938171 | − | 0.346173i | \(-0.112519\pi\) | |||||||
\(822\) | −9847.65 | − | 32242.2i | −0.417855 | − | 1.36810i | ||||
\(823\) | 6282.68i | 0.266100i | 0.991109 | + | 0.133050i | \(0.0424771\pi\) | ||||
−0.991109 | + | 0.133050i | \(0.957523\pi\) | |||||||
\(824\) | −48424.8 | −2.04728 | ||||||||
\(825\) | 27483.9 | − | 23256.7i | 1.15984 | − | 0.981447i | ||||
\(826\) | −41344.5 | + | 52417.7i | −1.74160 | + | 2.20804i | ||||
\(827\) | −11366.9 | −0.477953 | −0.238977 | − | 0.971025i | \(-0.576812\pi\) | ||||
−0.238977 | + | 0.971025i | \(0.576812\pi\) | |||||||
\(828\) | −45170.5 | + | 30431.5i | −1.89587 | + | 1.27726i | ||||
\(829\) | − | 9728.24i | − | 0.407570i | −0.979016 | − | 0.203785i | \(-0.934676\pi\) | ||
0.979016 | − | 0.203785i | \(-0.0653244\pi\) | |||||||
\(830\) | −10214.5 | − | 49643.3i | −0.427167 | − | 2.07608i | ||||
\(831\) | −22632.1 | + | 6912.46i | −0.944762 | + | 0.288557i | ||||
\(832\) | 1058.35 | 0.0441004 | ||||||||
\(833\) | −32296.9 | + | 7736.30i | −1.34336 | + | 0.321785i | ||||
\(834\) | −39791.7 | + | 12153.5i | −1.65213 | + | 0.504605i | ||||
\(835\) | −4832.46 | − | 23486.2i | −0.200280 | − | 0.973383i | ||||
\(836\) | −33354.7 | −1.37990 | ||||||||
\(837\) | 7114.40 | − | 8770.64i | 0.293799 | − | 0.362195i | ||||
\(838\) | 45989.6 | 1.89580 | ||||||||
\(839\) | 12992.1 | 0.534610 | 0.267305 | − | 0.963612i | \(-0.413867\pi\) | ||||
0.267305 | + | 0.963612i | \(0.413867\pi\) | |||||||
\(840\) | −54900.3 | − | 9338.72i | −2.25505 | − | 0.383591i | ||||
\(841\) | −192.087 | −0.00787596 | ||||||||
\(842\) | −11652.0 | −0.476907 | ||||||||
\(843\) | −24522.7 | + | 7489.91i | −1.00190 | + | 0.306010i | ||||
\(844\) | −15146.4 | −0.617726 | ||||||||
\(845\) | −19250.5 | + | 3960.93i | −0.783714 | + | 0.161255i | ||||
\(846\) | 20022.2 | + | 29719.7i | 0.813685 | + | 1.20778i | ||||
\(847\) | −19975.0 | + | 25324.8i | −0.810328 | + | 1.02736i | ||||
\(848\) | −22916.4 | −0.928011 | ||||||||
\(849\) | −693.230 | − | 2269.70i | −0.0280231 | − | 0.0917503i | ||||
\(850\) | 24423.5 | + | 56837.5i | 0.985550 | + | 2.29354i | ||||
\(851\) | 20072.5i | 0.808550i | ||||||||
\(852\) | −46281.6 | + | 14135.7i | −1.86101 | + | 0.568404i | ||||
\(853\) | −10335.1 | −0.414849 | −0.207424 | − | 0.978251i | \(-0.566508\pi\) | ||||
−0.207424 | + | 0.978251i | \(0.566508\pi\) | |||||||
\(854\) | 31743.2 | + | 25037.5i | 1.27193 | + | 1.00324i | ||||
\(855\) | 7159.23 | + | 7012.06i | 0.286363 | + | 0.280476i | ||||
\(856\) | 41135.4 | 1.64250 | ||||||||
\(857\) | − | 21299.4i | − | 0.848977i | −0.905433 | − | 0.424489i | \(-0.860454\pi\) | ||
0.905433 | − | 0.424489i | \(-0.139546\pi\) | |||||||
\(858\) | −29504.7 | + | 9011.55i | −1.17398 | + | 0.358566i | ||||
\(859\) | − | 12245.3i | − | 0.486386i | −0.969978 | − | 0.243193i | \(-0.921805\pi\) | ||
0.969978 | − | 0.243193i | \(-0.0781948\pi\) | |||||||
\(860\) | −2147.61 | − | 10437.6i | −0.0851545 | − | 0.413859i | ||||
\(861\) | −3280.54 | − | 1277.75i | −0.129850 | − | 0.0505755i | ||||
\(862\) | − | 75116.3i | − | 2.96806i | ||||||
\(863\) | 24644.7 | 0.972092 | 0.486046 | − | 0.873933i | \(-0.338439\pi\) | ||||
0.486046 | + | 0.873933i | \(0.338439\pi\) | |||||||
\(864\) | 21463.7 | + | 17410.5i | 0.845151 | + | 0.685553i | ||||
\(865\) | −7802.21 | − | 37919.5i | −0.306685 | − | 1.49052i | ||||
\(866\) | 18285.5 | 0.717515 | ||||||||
\(867\) | −6772.31 | − | 22173.2i | −0.265282 | − | 0.868559i | ||||
\(868\) | 21217.1 | + | 16735.0i | 0.829673 | + | 0.654406i | ||||
\(869\) | − | 4766.15i | − | 0.186054i | ||||||
\(870\) | 40871.1 | − | 22293.7i | 1.59271 | − | 0.868768i | ||||
\(871\) | 6421.52i | 0.249810i | ||||||||
\(872\) | 10462.2 | 0.406303 | ||||||||
\(873\) | 23633.9 | − | 15922.2i | 0.916250 | − | 0.617280i | ||||
\(874\) | 18883.6i | 0.730833i | ||||||||
\(875\) | 1527.99 | − | 25837.7i | 0.0590349 | − | 0.998256i | ||||
\(876\) | 9921.91 | + | 32485.3i | 0.382683 | + | 1.25294i | ||||
\(877\) | 41124.6i | 1.58344i | 0.610883 | + | 0.791721i | \(0.290815\pi\) | ||||
−0.610883 | + | 0.791721i | \(0.709185\pi\) | |||||||
\(878\) | 37895.4i | 1.45661i | ||||||||
\(879\) | 10447.4 | − | 3190.92i | 0.400889 | − | 0.122443i | ||||
\(880\) | −14931.6 | − | 72568.8i | −0.571980 | − | 2.77988i | ||||
\(881\) | 40650.0 | 1.55452 | 0.777261 | − | 0.629179i | \(-0.216609\pi\) | ||||
0.777261 | + | 0.629179i | \(0.216609\pi\) | |||||||
\(882\) | −34866.0 | − | 32017.3i | −1.33106 | − | 1.22231i | ||||
\(883\) | − | 31725.7i | − | 1.20912i | −0.796559 | − | 0.604561i | \(-0.793349\pi\) | ||
0.796559 | − | 0.604561i | \(-0.206651\pi\) | |||||||
\(884\) | − | 36776.9i | − | 1.39926i | ||||||
\(885\) | 19619.1 | + | 35967.7i | 0.745186 | + | 1.36615i | ||||
\(886\) | −26331.7 | −0.998454 | ||||||||
\(887\) | − | 6747.77i | − | 0.255432i | −0.991811 | − | 0.127716i | \(-0.959235\pi\) | ||
0.991811 | − | 0.127716i | \(-0.0407646\pi\) | |||||||
\(888\) | 46393.0 | − | 14169.7i | 1.75321 | − | 0.535478i | ||||
\(889\) | 17299.7 | + | 13645.1i | 0.652657 | + | 0.514784i | ||||
\(890\) | 79360.3 | − | 16329.0i | 2.98895 | − | 0.614998i | ||||
\(891\) | −37449.8 | − | 15179.0i | −1.40810 | − | 0.570725i | ||||
\(892\) | 49564.2 | 1.86046 | ||||||||
\(893\) | 8619.95 | 0.323019 | ||||||||
\(894\) | 28261.0 | − | 8631.70i | 1.05726 | − | 0.322916i | ||||
\(895\) | −6961.18 | − | 33832.0i | −0.259985 | − | 1.26355i | ||||
\(896\) | 15114.3 | − | 19162.3i | 0.563543 | − | 0.714474i | ||||
\(897\) | 3539.64 | + | 11589.1i | 0.131756 | + | 0.431381i | ||||
\(898\) | 25718.4i | 0.955718i | ||||||||
\(899\) | −12620.5 | −0.468205 | ||||||||
\(900\) | −33120.0 | + | 51435.0i | −1.22667 | + | 1.90500i | ||||
\(901\) | 18560.1i | 0.686268i | ||||||||
\(902\) | − | 10365.2i | − | 0.382619i | ||||||
\(903\) | 1836.54 | − | 4715.21i | 0.0676812 | − | 0.173768i | ||||
\(904\) | 75455.4 | 2.77612 | ||||||||
\(905\) | 6288.92 | + | 30564.8i | 0.230996 | + | 1.12266i | ||||
\(906\) | −9714.41 | − | 31805.9i | −0.356225 | − | 1.16631i | ||||
\(907\) | 49852.4i | 1.82505i | 0.409020 | + | 0.912525i | \(0.365871\pi\) | ||||
−0.409020 | + | 0.912525i | \(0.634129\pi\) | |||||||
\(908\) | − | 40021.7i | − | 1.46274i | ||||||
\(909\) | −16587.1 | + | 11174.7i | −0.605234 | + | 0.407748i | ||||
\(910\) | −9943.64 | + | 19824.2i | −0.362229 | + | 0.722160i | ||||
\(911\) | 14687.9i | 0.534175i | 0.963672 | + | 0.267087i | \(0.0860612\pi\) | ||||
−0.963672 | + | 0.267087i | \(0.913939\pi\) | |||||||
\(912\) | 19722.5 | − | 6023.80i | 0.716093 | − | 0.218715i | ||||
\(913\) | 49161.1 | 1.78203 | ||||||||
\(914\) | − | 9105.03i | − | 0.329505i | ||||||
\(915\) | 21781.4 | − | 11881.0i | 0.786963 | − | 0.429260i | ||||
\(916\) | − | 31194.3i | − | 1.12521i | ||||||
\(917\) | 6094.27 | − | 7726.47i | 0.219466 | − | 0.278245i | ||||
\(918\) | 43740.4 | − | 53923.2i | 1.57260 | − | 1.93870i | ||||
\(919\) | 48920.4 | 1.75597 | 0.877984 | − | 0.478689i | \(-0.158888\pi\) | ||||
0.877984 | + | 0.478689i | \(0.158888\pi\) | |||||||
\(920\) | −63078.9 | + | 12978.9i | −2.26049 | + | 0.465112i | ||||
\(921\) | 4220.61 | + | 13818.7i | 0.151003 | + | 0.494398i | ||||
\(922\) | −91831.7 | −3.28017 | ||||||||
\(923\) | 10766.5i | 0.383947i | ||||||||
\(924\) | 35092.6 | − | 90098.2i | 1.24942 | − | 3.20781i | ||||
\(925\) | 8901.03 | + | 20714.2i | 0.316394 | + | 0.736302i | ||||
\(926\) | 39512.8i | 1.40224i | ||||||||
\(927\) | −20950.0 | + | 14114.0i | −0.742273 | + | 0.500071i | ||||
\(928\) | − | 30885.1i | − | 1.09252i | ||||||
\(929\) | 34688.5 | 1.22507 | 0.612537 | − | 0.790442i | \(-0.290149\pi\) | ||||
0.612537 | + | 0.790442i | \(0.290149\pi\) | |||||||
\(930\) | 20984.2 | − | 11446.1i | 0.739890 | − | 0.403583i | ||||
\(931\) | −11073.3 | + | 2652.47i | −0.389811 | + | 0.0933741i | ||||
\(932\) | 52848.3 | 1.85741 | ||||||||
\(933\) | −668.699 | − | 2189.39i | −0.0234643 | − | 0.0768245i | ||||
\(934\) | − | 38917.1i | − | 1.36339i | ||||||
\(935\) | −58773.8 | + | 12093.1i | −2.05573 | + | 0.422982i | ||||
\(936\) | 24286.9 | − | 16362.1i | 0.848122 | − | 0.571382i | ||||
\(937\) | −29779.4 | −1.03826 | −0.519130 | − | 0.854695i | \(-0.673744\pi\) | ||||
−0.519130 | + | 0.854695i | \(0.673744\pi\) | |||||||
\(938\) | −22776.8 | − | 17965.3i | −0.792846 | − | 0.625359i | ||||
\(939\) | −10623.1 | − | 34781.1i | −0.369193 | − | 1.20877i | ||||
\(940\) | 10605.2 | + | 51542.3i | 0.367982 | + | 1.78843i | ||||
\(941\) | 18023.5 | 0.624389 | 0.312195 | − | 0.950018i | \(-0.398936\pi\) | ||||
0.312195 | + | 0.950018i | \(0.398936\pi\) | |||||||
\(942\) | 1758.21 | + | 5756.54i | 0.0608127 | + | 0.199107i | ||||
\(943\) | −4071.32 | −0.140594 | ||||||||
\(944\) | 84310.8 | 2.90687 | ||||||||
\(945\) | −26473.3 | + | 11961.2i | −0.911299 | + | 0.411744i | ||||
\(946\) | 14898.1 | 0.512029 | ||||||||
\(947\) | −34592.1 | −1.18700 | −0.593501 | − | 0.804833i | \(-0.702255\pi\) | ||||
−0.593501 | + | 0.804833i | \(0.702255\pi\) | |||||||
\(948\) | 2365.63 | + | 7745.30i | 0.0810465 | + | 0.265354i | ||||
\(949\) | 7557.05 | 0.258495 | ||||||||
\(950\) | 8373.84 | + | 19487.3i | 0.285982 | + | 0.665529i | ||||
\(951\) | −15348.7 | − | 50253.2i | −0.523361 | − | 1.71354i | ||||
\(952\) | 72873.7 | + | 57479.2i | 2.48093 | + | 1.95684i | ||||
\(953\) | −41901.5 | −1.42426 | −0.712132 | − | 0.702046i | \(-0.752270\pi\) | ||||
−0.712132 | + | 0.702046i | \(0.752270\pi\) | |||||||
\(954\) | −21940.0 | + | 14781.1i | −0.744586 | + | 0.501629i | ||||
\(955\) | 7184.24 | + | 34916.1i | 0.243431 | + | 1.18310i | ||||
\(956\) | 119582.i | 4.04558i | ||||||||
\(957\) | 13190.9 | + | 43188.3i | 0.445561 | + | 1.45881i | ||||
\(958\) | −8487.17 | −0.286230 | ||||||||
\(959\) | 14558.5 | − | 18457.6i | 0.490217 | − | 0.621509i | ||||
\(960\) | 1405.03 | + | 2575.84i | 0.0472365 | + | 0.0865988i | ||||
\(961\) | 23311.4 | 0.782497 | ||||||||
\(962\) | − | 19318.7i | − | 0.647464i | ||||||
\(963\) | 17796.4 | − | 11989.5i | 0.595514 | − | 0.401200i | ||||
\(964\) | 99554.0i | 3.32616i | ||||||||
\(965\) | −3971.22 | − | 19300.5i | −0.132475 | − | 0.643840i | ||||
\(966\) | −51008.8 | − | 19867.5i | −1.69894 | − | 0.661726i | ||||
\(967\) | − | 1876.37i | − | 0.0623993i | −0.999513 | − | 0.0311996i | \(-0.990067\pi\) | ||
0.999513 | − | 0.0311996i | \(-0.00993277\pi\) | |||||||
\(968\) | 90141.8 | 2.99304 | ||||||||
\(969\) | −4878.70 | − | 15973.3i | −0.161740 | − | 0.529554i | ||||
\(970\) | 59077.8 | − | 12155.7i | 1.95554 | − | 0.402366i | ||||
\(971\) | −42968.7 | −1.42011 | −0.710057 | − | 0.704144i | \(-0.751331\pi\) | ||||
−0.710057 | + | 0.704144i | \(0.751331\pi\) | |||||||
\(972\) | 68392.3 | + | 6079.02i | 2.25688 | + | 0.200602i | ||||
\(973\) | −22779.5 | − | 17967.4i | −0.750541 | − | 0.591991i | ||||
\(974\) | 9114.43i | 0.299841i | ||||||||
\(975\) | 8791.93 | + | 10390.0i | 0.288787 | + | 0.341278i | ||||
\(976\) | − | 51057.0i | − | 1.67448i | ||||||
\(977\) | 18443.6 | 0.603954 | 0.301977 | − | 0.953315i | \(-0.402353\pi\) | ||||
0.301977 | + | 0.953315i | \(0.402353\pi\) | |||||||
\(978\) | 46837.0 | − | 14305.3i | 1.53137 | − | 0.467723i | ||||
\(979\) | 78589.6i | 2.56561i | ||||||||
\(980\) | −29483.8 | − | 62948.7i | −0.961047 | − | 2.05186i | ||||
\(981\) | 4526.27 | − | 3049.36i | 0.147312 | − | 0.0992442i | ||||
\(982\) | 25430.0i | 0.826379i | ||||||||
\(983\) | − | 17892.5i | − | 0.580550i | −0.956943 | − | 0.290275i | \(-0.906253\pi\) | ||
0.956943 | − | 0.290275i | \(-0.0937468\pi\) | |||||||
\(984\) | 2874.06 | + | 9409.94i | 0.0931113 | + | 0.304855i | ||||
\(985\) | −12436.9 | + | 2558.98i | −0.402307 | + | 0.0827775i | ||||
\(986\) | −77592.6 | −2.50614 | ||||||||
\(987\) | −9069.08 | + | 23284.3i | −0.292474 | + | 0.750911i | ||||
\(988\) | − | 12609.4i | − | 0.406029i | ||||||
\(989\) | − | 5851.81i | − | 0.188146i | ||||||
\(990\) | −61102.1 | − | 59846.1i | −1.96157 | − | 1.92125i | ||||
\(991\) | 26347.5 | 0.844557 | 0.422278 | − | 0.906466i | \(-0.361230\pi\) | ||||
0.422278 | + | 0.906466i | \(0.361230\pi\) | |||||||
\(992\) | − | 15857.1i | − | 0.507524i | ||||||
\(993\) | 7636.01 | + | 25001.0i | 0.244030 | + | 0.798977i | ||||
\(994\) | −38188.2 | − | 30121.0i | −1.21857 | − | 0.961147i | ||||
\(995\) | 2705.09 | + | 13147.0i | 0.0861881 | + | 0.418883i | ||||
\(996\) | −79890.1 | + | 24400.6i | −2.54158 | + | 0.776269i | ||||
\(997\) | −37680.0 | −1.19693 | −0.598463 | − | 0.801150i | \(-0.704222\pi\) | ||||
−0.598463 | + | 0.801150i | \(0.704222\pi\) | |||||||
\(998\) | 40271.0 | 1.27731 | ||||||||
\(999\) | 15941.0 | − | 19652.1i | 0.504856 | − | 0.622387i |
(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 | 105.4.g.b.104.4 | yes | 40 | |
3.2 | odd | 2 | inner | 105.4.g.b.104.39 | yes | 40 | |
5.4 | even | 2 | inner | 105.4.g.b.104.37 | yes | 40 | |
7.6 | odd | 2 | inner | 105.4.g.b.104.1 | ✓ | 40 | |
15.14 | odd | 2 | inner | 105.4.g.b.104.2 | yes | 40 | |
21.20 | even | 2 | inner | 105.4.g.b.104.38 | yes | 40 | |
35.34 | odd | 2 | inner | 105.4.g.b.104.40 | yes | 40 | |
105.104 | even | 2 | inner | 105.4.g.b.104.3 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.g.b.104.1 | ✓ | 40 | 7.6 | odd | 2 | inner | |
105.4.g.b.104.2 | yes | 40 | 15.14 | odd | 2 | inner | |
105.4.g.b.104.3 | yes | 40 | 105.104 | even | 2 | inner | |
105.4.g.b.104.4 | yes | 40 | 1.1 | even | 1 | trivial | |
105.4.g.b.104.37 | yes | 40 | 5.4 | even | 2 | inner | |
105.4.g.b.104.38 | yes | 40 | 21.20 | even | 2 | inner | |
105.4.g.b.104.39 | yes | 40 | 3.2 | odd | 2 | inner | |
105.4.g.b.104.40 | yes | 40 | 35.34 | odd | 2 | inner |