Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [136,4,Mod(101,136)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(136, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("136.101");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 136 = 2^{3} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 136.h (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: | \(8.02425976078\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 101.19 | ||
Character | \(\chi\) | \(=\) | 136.101 |
Dual form | 136.4.h.a.101.17 |
$q$-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 \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).
\(n\) | \(69\) | \(103\) | \(105\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.64670 | + | 2.29965i | −0.582197 | + | 0.813047i | ||||
\(3\) | −3.96792 | −0.763627 | −0.381813 | − | 0.924239i | \(-0.624700\pi\) | ||||
−0.381813 | + | 0.924239i | \(0.624700\pi\) | |||||||
\(4\) | −2.57674 | − | 7.57367i | −0.322092 | − | 0.946708i | ||||
\(5\) | 5.58507 | 0.499543 | 0.249772 | − | 0.968305i | \(-0.419644\pi\) | ||||
0.249772 | + | 0.968305i | \(0.419644\pi\) | |||||||
\(6\) | 6.53398 | − | 9.12481i | 0.444581 | − | 0.620865i | ||||
\(7\) | − | 3.60918i | − | 0.194877i | −0.995242 | − | 0.0974387i | \(-0.968935\pi\) | ||
0.995242 | − | 0.0974387i | \(-0.0310650\pi\) | |||||||
\(8\) | 21.6599 | + | 6.54599i | 0.957240 | + | 0.289295i | ||||
\(9\) | −11.2556 | −0.416875 | ||||||||
\(10\) | −9.19694 | + | 12.8437i | −0.290833 | + | 0.406153i | ||||
\(11\) | 50.2528 | 1.37744 | 0.688718 | − | 0.725029i | \(-0.258174\pi\) | ||||
0.688718 | + | 0.725029i | \(0.258174\pi\) | |||||||
\(12\) | 10.2243 | + | 30.0517i | 0.245958 | + | 0.722932i | ||||
\(13\) | 45.3934i | 0.968450i | 0.874943 | + | 0.484225i | \(0.160898\pi\) | ||||
−0.874943 | + | 0.484225i | \(0.839102\pi\) | |||||||
\(14\) | 8.29983 | + | 5.94324i | 0.158445 | + | 0.113457i | ||||
\(15\) | −22.1611 | −0.381465 | ||||||||
\(16\) | −50.7208 | + | 39.0307i | −0.792513 | + | 0.609855i | ||||
\(17\) | −59.0292 | − | 37.7962i | −0.842158 | − | 0.539231i | ||||
\(18\) | 18.5347 | − | 25.8839i | 0.242703 | − | 0.338939i | ||||
\(19\) | 85.4733i | 1.03205i | 0.856574 | + | 0.516024i | \(0.172588\pi\) | ||||
−0.856574 | + | 0.516024i | \(0.827412\pi\) | |||||||
\(20\) | −14.3913 | − | 42.2994i | −0.160899 | − | 0.472922i | ||||
\(21\) | 14.3209i | 0.148813i | ||||||||
\(22\) | −82.7515 | + | 115.564i | −0.801940 | + | 1.11992i | ||||
\(23\) | 176.742i | 1.60231i | 0.598455 | + | 0.801156i | \(0.295782\pi\) | ||||
−0.598455 | + | 0.801156i | \(0.704218\pi\) | |||||||
\(24\) | −85.9446 | − | 25.9740i | −0.730974 | − | 0.220913i | ||||
\(25\) | −93.8070 | −0.750456 | ||||||||
\(26\) | −104.389 | − | 74.7494i | −0.787396 | − | 0.563829i | ||||
\(27\) | 151.795 | 1.08196 | ||||||||
\(28\) | −27.3347 | + | 9.29991i | −0.184492 | + | 0.0627685i | ||||
\(29\) | −211.680 | −1.35545 | −0.677724 | − | 0.735316i | \(-0.737034\pi\) | ||||
−0.677724 | + | 0.735316i | \(0.737034\pi\) | |||||||
\(30\) | 36.4927 | − | 50.9627i | 0.222088 | − | 0.310149i | ||||
\(31\) | 3.22438i | 0.0186811i | 0.999956 | + | 0.00934057i | \(0.00297324\pi\) | ||||
−0.999956 | + | 0.00934057i | \(0.997027\pi\) | |||||||
\(32\) | −6.23469 | − | 180.912i | −0.0344421 | − | 0.999407i | ||||
\(33\) | −199.399 | −1.05185 | ||||||||
\(34\) | 184.121 | − | 73.5071i | 0.928723 | − | 0.370775i | ||||
\(35\) | − | 20.1575i | − | 0.0973497i | ||||||
\(36\) | 29.0028 | + | 85.2463i | 0.134272 | + | 0.394659i | ||||
\(37\) | 355.514 | 1.57963 | 0.789814 | − | 0.613347i | \(-0.210177\pi\) | ||||
0.789814 | + | 0.613347i | \(0.210177\pi\) | |||||||
\(38\) | −196.558 | − | 140.749i | −0.839104 | − | 0.600856i | ||||
\(39\) | − | 180.117i | − | 0.739534i | ||||||
\(40\) | 120.972 | + | 36.5598i | 0.478183 | + | 0.144515i | ||||
\(41\) | 412.291i | 1.57046i | 0.619203 | + | 0.785231i | \(0.287456\pi\) | ||||
−0.619203 | + | 0.785231i | \(0.712544\pi\) | |||||||
\(42\) | −32.9331 | − | 23.5823i | −0.120992 | − | 0.0866388i | ||||
\(43\) | 464.709i | 1.64808i | 0.566532 | + | 0.824040i | \(0.308285\pi\) | ||||
−0.566532 | + | 0.824040i | \(0.691715\pi\) | |||||||
\(44\) | −129.488 | − | 380.598i | −0.443662 | − | 1.30403i | ||||
\(45\) | −62.8633 | −0.208247 | ||||||||
\(46\) | −406.443 | − | 291.041i | −1.30276 | − | 0.932862i | ||||
\(47\) | 180.837 | 0.561231 | 0.280615 | − | 0.959820i | \(-0.409461\pi\) | ||||
0.280615 | + | 0.959820i | \(0.409461\pi\) | |||||||
\(48\) | 201.256 | − | 154.871i | 0.605184 | − | 0.465701i | ||||
\(49\) | 329.974 | 0.962023 | ||||||||
\(50\) | 154.472 | − | 215.723i | 0.436914 | − | 0.610157i | ||||
\(51\) | 234.223 | + | 149.972i | 0.643094 | + | 0.411771i | ||||
\(52\) | 343.794 | − | 116.967i | 0.916840 | − | 0.311930i | ||||
\(53\) | 81.8134i | 0.212037i | 0.994364 | + | 0.106018i | \(0.0338102\pi\) | ||||
−0.994364 | + | 0.106018i | \(0.966190\pi\) | |||||||
\(54\) | −249.962 | + | 349.075i | −0.629916 | + | 0.879687i | ||||
\(55\) | 280.665 | 0.688089 | ||||||||
\(56\) | 23.6257 | − | 78.1743i | 0.0563770 | − | 0.186544i | ||||
\(57\) | − | 339.151i | − | 0.788099i | ||||||
\(58\) | 348.574 | − | 486.789i | 0.789139 | − | 1.10204i | ||||
\(59\) | 297.123i | 0.655629i | 0.944742 | + | 0.327815i | \(0.106312\pi\) | ||||
−0.944742 | + | 0.327815i | \(0.893688\pi\) | |||||||
\(60\) | 57.1033 | + | 167.841i | 0.122867 | + | 0.361136i | ||||
\(61\) | −303.899 | −0.637874 | −0.318937 | − | 0.947776i | \(-0.603326\pi\) | ||||
−0.318937 | + | 0.947776i | \(0.603326\pi\) | |||||||
\(62\) | −7.41493 | − | 5.30959i | −0.0151887 | − | 0.0108761i | ||||
\(63\) | 40.6235i | 0.0812394i | ||||||||
\(64\) | 426.300 | + | 283.571i | 0.832617 | + | 0.553849i | ||||
\(65\) | 253.525i | 0.483783i | ||||||||
\(66\) | 328.351 | − | 458.547i | 0.612382 | − | 0.855201i | ||||
\(67\) | 3.06619i | 0.00559097i | 0.999996 | + | 0.00279549i | \(0.000889832\pi\) | ||||
−0.999996 | + | 0.00279549i | \(0.999110\pi\) | |||||||
\(68\) | −134.153 | + | 544.458i | −0.239242 | + | 0.970960i | ||||
\(69\) | − | 701.297i | − | 1.22357i | ||||||
\(70\) | 46.3551 | + | 33.1934i | 0.0791499 | + | 0.0566767i | ||||
\(71\) | − | 680.135i | − | 1.13686i | −0.822731 | − | 0.568431i | \(-0.807551\pi\) | ||
0.822731 | − | 0.568431i | \(-0.192449\pi\) | |||||||
\(72\) | −243.795 | − | 73.6791i | −0.399049 | − | 0.120600i | ||||
\(73\) | − | 186.773i | − | 0.299453i | −0.988727 | − | 0.149727i | \(-0.952161\pi\) | ||
0.988727 | − | 0.149727i | \(-0.0478393\pi\) | |||||||
\(74\) | −585.427 | + | 817.557i | −0.919655 | + | 1.28431i | ||||
\(75\) | 372.219 | 0.573068 | ||||||||
\(76\) | 647.346 | − | 220.242i | 0.977048 | − | 0.332415i | ||||
\(77\) | − | 181.371i | − | 0.268431i | ||||||
\(78\) | 414.206 | + | 296.600i | 0.601276 | + | 0.430555i | ||||
\(79\) | − | 808.517i | − | 1.15146i | −0.817640 | − | 0.575730i | \(-0.804718\pi\) | ||
0.817640 | − | 0.575730i | \(-0.195282\pi\) | |||||||
\(80\) | −283.279 | + | 217.989i | −0.395895 | + | 0.304649i | ||||
\(81\) | −298.410 | −0.409341 | ||||||||
\(82\) | −948.122 | − | 678.920i | −1.27686 | − | 0.914319i | ||||
\(83\) | 282.350i | 0.373397i | 0.982417 | + | 0.186699i | \(0.0597788\pi\) | ||||
−0.982417 | + | 0.186699i | \(0.940221\pi\) | |||||||
\(84\) | 108.462 | − | 36.9013i | 0.140883 | − | 0.0479317i | ||||
\(85\) | −329.682 | − | 211.094i | −0.420694 | − | 0.269369i | ||||
\(86\) | −1068.67 | − | 765.237i | −1.33997 | − | 0.959508i | ||||
\(87\) | 839.930 | 1.03506 | ||||||||
\(88\) | 1088.47 | + | 328.955i | 1.31854 | + | 0.398485i | ||||
\(89\) | −1117.41 | −1.33084 | −0.665422 | − | 0.746468i | \(-0.731748\pi\) | ||||
−0.665422 | + | 0.746468i | \(0.731748\pi\) | |||||||
\(90\) | 103.517 | − | 144.563i | 0.121241 | − | 0.169315i | ||||
\(91\) | 163.833 | 0.188729 | ||||||||
\(92\) | 1338.58 | − | 455.417i | 1.51692 | − | 0.516093i | ||||
\(93\) | − | 12.7941i | − | 0.0142654i | ||||||
\(94\) | −297.786 | + | 415.862i | −0.326747 | + | 0.456307i | ||||
\(95\) | 477.374i | 0.515553i | ||||||||
\(96\) | 24.7387 | + | 717.844i | 0.0263009 | + | 0.763173i | ||||
\(97\) | 954.348i | 0.998963i | 0.866325 | + | 0.499481i | \(0.166476\pi\) | ||||
−0.866325 | + | 0.499481i | \(0.833524\pi\) | |||||||
\(98\) | −543.369 | + | 758.823i | −0.560087 | + | 0.782170i | ||||
\(99\) | −565.626 | −0.574218 | ||||||||
\(100\) | 241.716 | + | 710.463i | 0.241716 | + | 0.710463i | ||||
\(101\) | − | 1602.71i | − | 1.57897i | −0.613771 | − | 0.789484i | \(-0.710348\pi\) | ||
0.613771 | − | 0.789484i | \(-0.289652\pi\) | |||||||
\(102\) | −730.579 | + | 291.670i | −0.709197 | + | 0.283134i | ||||
\(103\) | −292.616 | −0.279926 | −0.139963 | − | 0.990157i | \(-0.544698\pi\) | ||||
−0.139963 | + | 0.990157i | \(0.544698\pi\) | |||||||
\(104\) | −297.145 | + | 983.214i | −0.280168 | + | 0.927039i | ||||
\(105\) | 79.9833i | 0.0743388i | ||||||||
\(106\) | −188.142 | − | 134.722i | −0.172396 | − | 0.123447i | ||||
\(107\) | 191.142 | 0.172695 | 0.0863476 | − | 0.996265i | \(-0.472480\pi\) | ||||
0.0863476 | + | 0.996265i | \(0.472480\pi\) | |||||||
\(108\) | −391.137 | − | 1149.65i | −0.348492 | − | 1.02430i | ||||
\(109\) | −458.741 | −0.403114 | −0.201557 | − | 0.979477i | \(-0.564600\pi\) | ||||
−0.201557 | + | 0.979477i | \(0.564600\pi\) | |||||||
\(110\) | −462.172 | + | 645.431i | −0.400604 | + | 0.559449i | ||||
\(111\) | −1410.65 | −1.20625 | ||||||||
\(112\) | 140.869 | + | 183.061i | 0.118847 | + | 0.154443i | ||||
\(113\) | 1139.90i | 0.948963i | 0.880265 | + | 0.474482i | \(0.157364\pi\) | ||||
−0.880265 | + | 0.474482i | \(0.842636\pi\) | |||||||
\(114\) | 779.927 | + | 558.481i | 0.640762 | + | 0.458829i | ||||
\(115\) | 987.114i | 0.800425i | ||||||||
\(116\) | 545.445 | + | 1603.19i | 0.436580 | + | 1.28321i | ||||
\(117\) | − | 510.930i | − | 0.403722i | ||||||
\(118\) | −683.278 | − | 489.273i | −0.533058 | − | 0.381706i | ||||
\(119\) | −136.413 | + | 213.047i | −0.105084 | + | 0.164117i | ||||
\(120\) | −480.006 | − | 145.066i | −0.365153 | − | 0.110356i | ||||
\(121\) | 1194.35 | 0.897331 | ||||||||
\(122\) | 500.432 | − | 698.861i | 0.371369 | − | 0.518622i | ||||
\(123\) | − | 1635.94i | − | 1.19925i | ||||||
\(124\) | 24.4204 | − | 8.30838i | 0.0176856 | − | 0.00601706i | ||||
\(125\) | −1222.05 | −0.874429 | ||||||||
\(126\) | −93.4197 | − | 66.8949i | −0.0660515 | − | 0.0472974i | ||||
\(127\) | 1900.13 | 1.32763 | 0.663815 | − | 0.747897i | \(-0.268936\pi\) | ||||
0.663815 | + | 0.747897i | \(0.268936\pi\) | |||||||
\(128\) | −1354.10 | + | 513.382i | −0.935053 | + | 0.354508i | ||||
\(129\) | − | 1843.93i | − | 1.25852i | ||||||
\(130\) | −583.017 | − | 417.480i | −0.393339 | − | 0.281657i | ||||
\(131\) | −851.725 | −0.568058 | −0.284029 | − | 0.958816i | \(-0.591671\pi\) | ||||
−0.284029 | + | 0.958816i | \(0.591671\pi\) | |||||||
\(132\) | 513.800 | + | 1510.18i | 0.338792 | + | 0.995792i | ||||
\(133\) | 308.488 | 0.201123 | ||||||||
\(134\) | −7.05116 | − | 5.04911i | −0.00454573 | − | 0.00325505i | ||||
\(135\) | 847.786 | 0.540487 | ||||||||
\(136\) | −1031.15 | − | 1205.07i | −0.650151 | − | 0.759805i | ||||
\(137\) | −1042.37 | −0.650043 | −0.325022 | − | 0.945707i | \(-0.605372\pi\) | ||||
−0.325022 | + | 0.945707i | \(0.605372\pi\) | |||||||
\(138\) | 1612.73 | + | 1154.83i | 0.994819 | + | 0.712358i | ||||
\(139\) | 669.165 | 0.408330 | 0.204165 | − | 0.978936i | \(-0.434552\pi\) | ||||
0.204165 | + | 0.978936i | \(0.434552\pi\) | |||||||
\(140\) | −152.666 | + | 51.9406i | −0.0921617 | + | 0.0313556i | ||||
\(141\) | −717.549 | −0.428571 | ||||||||
\(142\) | 1564.07 | + | 1119.98i | 0.924322 | + | 0.661878i | ||||
\(143\) | 2281.14i | 1.33398i | ||||||||
\(144\) | 570.894 | − | 439.315i | 0.330378 | − | 0.254233i | ||||
\(145\) | −1182.25 | −0.677106 | ||||||||
\(146\) | 429.511 | + | 307.559i | 0.243470 | + | 0.174341i | ||||
\(147\) | −1309.31 | −0.734626 | ||||||||
\(148\) | −916.068 | − | 2692.55i | −0.508786 | − | 1.49545i | ||||
\(149\) | 1322.92i | 0.727367i | 0.931523 | + | 0.363684i | \(0.118481\pi\) | ||||
−0.931523 | + | 0.363684i | \(0.881519\pi\) | |||||||
\(150\) | −612.934 | + | 855.971i | −0.333639 | + | 0.465932i | ||||
\(151\) | 266.561 | 0.143658 | 0.0718292 | − | 0.997417i | \(-0.477116\pi\) | ||||
0.0718292 | + | 0.997417i | \(0.477116\pi\) | |||||||
\(152\) | −559.507 | + | 1851.34i | −0.298566 | + | 0.987918i | ||||
\(153\) | 664.410 | + | 425.420i | 0.351074 | + | 0.224792i | ||||
\(154\) | 417.090 | + | 298.665i | 0.218247 | + | 0.156280i | ||||
\(155\) | 18.0084i | 0.00933204i | ||||||||
\(156\) | −1364.15 | + | 464.115i | −0.700123 | + | 0.238198i | ||||
\(157\) | − | 422.085i | − | 0.214561i | −0.994229 | − | 0.107280i | \(-0.965786\pi\) | ||
0.994229 | − | 0.107280i | \(-0.0342142\pi\) | |||||||
\(158\) | 1859.30 | + | 1331.39i | 0.936191 | + | 0.670377i | ||||
\(159\) | − | 324.629i | − | 0.161917i | ||||||
\(160\) | −34.8211 | − | 1010.40i | −0.0172053 | − | 0.499247i | ||||
\(161\) | 637.892 | 0.312254 | ||||||||
\(162\) | 491.392 | − | 686.236i | 0.238317 | − | 0.332814i | ||||
\(163\) | 3335.56 | 1.60283 | 0.801415 | − | 0.598108i | \(-0.204081\pi\) | ||||
0.801415 | + | 0.598108i | \(0.204081\pi\) | |||||||
\(164\) | 3122.55 | − | 1062.37i | 1.48677 | − | 0.505834i | ||||
\(165\) | −1113.66 | −0.525443 | ||||||||
\(166\) | −649.306 | − | 464.947i | −0.303590 | − | 0.217391i | ||||
\(167\) | − | 3909.11i | − | 1.81135i | −0.423968 | − | 0.905677i | \(-0.639363\pi\) | ||
0.423968 | − | 0.905677i | \(-0.360637\pi\) | |||||||
\(168\) | −93.7447 | + | 310.190i | −0.0430509 | + | 0.142450i | ||||
\(169\) | 136.443 | 0.0621041 | ||||||||
\(170\) | 1028.33 | − | 410.542i | 0.463937 | − | 0.185218i | ||||
\(171\) | − | 962.054i | − | 0.430235i | ||||||
\(172\) | 3519.55 | − | 1197.43i | 1.56025 | − | 0.530834i | ||||
\(173\) | 1124.10 | 0.494008 | 0.247004 | − | 0.969014i | \(-0.420554\pi\) | ||||
0.247004 | + | 0.969014i | \(0.420554\pi\) | |||||||
\(174\) | −1383.11 | + | 1931.54i | −0.602607 | + | 0.841550i | ||||
\(175\) | 338.566i | 0.146247i | ||||||||
\(176\) | −2548.87 | + | 1961.40i | −1.09164 | + | 0.840036i | ||||
\(177\) | − | 1178.96i | − | 0.500656i | ||||||
\(178\) | 1840.04 | − | 2569.64i | 0.774814 | − | 1.08204i | ||||
\(179\) | − | 103.033i | − | 0.0430226i | −0.999769 | − | 0.0215113i | \(-0.993152\pi\) | ||
0.999769 | − | 0.0215113i | \(-0.00684778\pi\) | |||||||
\(180\) | 161.982 | + | 476.106i | 0.0670748 | + | 0.197149i | ||||
\(181\) | 2314.03 | 0.950278 | 0.475139 | − | 0.879911i | \(-0.342398\pi\) | ||||
0.475139 | + | 0.879911i | \(0.342398\pi\) | |||||||
\(182\) | −269.784 | + | 376.757i | −0.109878 | + | 0.153446i | ||||
\(183\) | 1205.85 | 0.487098 | ||||||||
\(184\) | −1156.95 | + | 3828.20i | −0.463541 | + | 1.53380i | ||||
\(185\) | 1985.57 | 0.789092 | ||||||||
\(186\) | 29.4218 | + | 21.0680i | 0.0115985 | + | 0.00830529i | ||||
\(187\) | −2966.38 | − | 1899.37i | −1.16002 | − | 0.742756i | ||||
\(188\) | −465.971 | − | 1369.60i | −0.180768 | − | 0.531322i | ||||
\(189\) | − | 547.856i | − | 0.210850i | ||||||
\(190\) | −1097.79 | − | 786.093i | −0.419169 | − | 0.300154i | ||||
\(191\) | −4926.83 | −1.86646 | −0.933228 | − | 0.359284i | \(-0.883021\pi\) | ||||
−0.933228 | + | 0.359284i | \(0.883021\pi\) | |||||||
\(192\) | −1691.52 | − | 1125.19i | −0.635809 | − | 0.422934i | ||||
\(193\) | − | 4824.36i | − | 1.79930i | −0.436611 | − | 0.899651i | \(-0.643821\pi\) | ||
0.436611 | − | 0.899651i | \(-0.356179\pi\) | |||||||
\(194\) | −2194.66 | − | 1571.53i | −0.812204 | − | 0.581594i | ||||
\(195\) | − | 1005.97i | − | 0.369429i | ||||||
\(196\) | −850.256 | − | 2499.11i | −0.309860 | − | 0.910755i | ||||
\(197\) | 43.7756 | 0.0158319 | 0.00791595 | − | 0.999969i | \(-0.497480\pi\) | ||||
0.00791595 | + | 0.999969i | \(0.497480\pi\) | |||||||
\(198\) | 931.419 | − | 1300.74i | 0.334308 | − | 0.466867i | ||||
\(199\) | 3511.51i | 1.25088i | 0.780274 | + | 0.625438i | \(0.215080\pi\) | ||||
−0.780274 | + | 0.625438i | \(0.784920\pi\) | |||||||
\(200\) | −2031.85 | − | 614.060i | −0.718367 | − | 0.217103i | ||||
\(201\) | − | 12.1664i | − | 0.00426941i | ||||||
\(202\) | 3685.67 | + | 2639.19i | 1.28378 | + | 0.919271i | ||||
\(203\) | 763.991i | 0.264146i | ||||||||
\(204\) | 532.309 | − | 2160.37i | 0.182691 | − | 0.741451i | ||||
\(205\) | 2302.67i | 0.784514i | ||||||||
\(206\) | 481.852 | − | 672.914i | 0.162972 | − | 0.227593i | ||||
\(207\) | − | 1989.34i | − | 0.667964i | ||||||
\(208\) | −1771.74 | − | 2302.39i | −0.590614 | − | 0.767509i | ||||
\(209\) | 4295.27i | 1.42158i | ||||||||
\(210\) | −183.933 | − | 131.709i | −0.0604410 | − | 0.0432799i | ||||
\(211\) | −2959.42 | −0.965569 | −0.482785 | − | 0.875739i | \(-0.660375\pi\) | ||||
−0.482785 | + | 0.875739i | \(0.660375\pi\) | |||||||
\(212\) | 619.627 | − | 210.812i | 0.200737 | − | 0.0682954i | ||||
\(213\) | 2698.72i | 0.868138i | ||||||||
\(214\) | −314.754 | + | 439.558i | −0.100543 | + | 0.140409i | ||||
\(215\) | 2595.43i | 0.823287i | ||||||||
\(216\) | 3287.86 | + | 993.650i | 1.03570 | + | 0.313006i | ||||
\(217\) | 11.6374 | 0.00364053 | ||||||||
\(218\) | 755.411 | − | 1054.94i | 0.234692 | − | 0.327751i | ||||
\(219\) | 741.098i | 0.228670i | ||||||||
\(220\) | −723.201 | − | 2125.67i | −0.221628 | − | 0.651420i | ||||
\(221\) | 1715.70 | − | 2679.53i | 0.522219 | − | 0.815588i | ||||
\(222\) | 2322.93 | − | 3244.00i | 0.702273 | − | 0.980735i | ||||
\(223\) | 1816.62 | 0.545515 | 0.272757 | − | 0.962083i | \(-0.412064\pi\) | ||||
0.272757 | + | 0.962083i | \(0.412064\pi\) | |||||||
\(224\) | −652.943 | + | 22.5021i | −0.194762 | + | 0.00671198i | ||||
\(225\) | 1055.86 | 0.312846 | ||||||||
\(226\) | −2621.37 | − | 1877.08i | −0.771552 | − | 0.552484i | ||||
\(227\) | 3744.84 | 1.09495 | 0.547475 | − | 0.836822i | \(-0.315589\pi\) | ||||
0.547475 | + | 0.836822i | \(0.315589\pi\) | |||||||
\(228\) | −2568.62 | + | 873.904i | −0.746100 | + | 0.253841i | ||||
\(229\) | 3032.89i | 0.875193i | 0.899171 | + | 0.437596i | \(0.144170\pi\) | ||||
−0.899171 | + | 0.437596i | \(0.855830\pi\) | |||||||
\(230\) | −2270.01 | − | 1625.48i | −0.650783 | − | 0.466005i | ||||
\(231\) | 719.667i | 0.204981i | ||||||||
\(232\) | −4584.96 | − | 1385.66i | −1.29749 | − | 0.392124i | ||||
\(233\) | − | 2090.43i | − | 0.587761i | −0.955842 | − | 0.293881i | \(-0.905053\pi\) | ||
0.955842 | − | 0.293881i | \(-0.0949468\pi\) | |||||||
\(234\) | 1174.96 | + | 841.350i | 0.328245 | + | 0.235046i | ||||
\(235\) | 1009.99 | 0.280359 | ||||||||
\(236\) | 2250.31 | − | 765.608i | 0.620690 | − | 0.211173i | ||||
\(237\) | 3208.13i | 0.879285i | ||||||||
\(238\) | −265.300 | − | 664.527i | −0.0722557 | − | 0.180987i | ||||
\(239\) | −102.308 | −0.0276894 | −0.0138447 | − | 0.999904i | \(-0.504407\pi\) | ||||
−0.0138447 | + | 0.999904i | \(0.504407\pi\) | |||||||
\(240\) | 1124.03 | − | 864.963i | 0.302316 | − | 0.232638i | ||||
\(241\) | 970.078i | 0.259287i | 0.991561 | + | 0.129644i | \(0.0413833\pi\) | ||||
−0.991561 | + | 0.129644i | \(0.958617\pi\) | |||||||
\(242\) | −1966.73 | + | 2746.57i | −0.522424 | + | 0.729572i | ||||
\(243\) | −2914.41 | −0.769379 | ||||||||
\(244\) | 783.070 | + | 2301.63i | 0.205454 | + | 0.603881i | ||||
\(245\) | 1842.93 | 0.480572 | ||||||||
\(246\) | 3762.07 | + | 2693.90i | 0.975045 | + | 0.698198i | ||||
\(247\) | −3879.92 | −0.999487 | ||||||||
\(248\) | −21.1068 | + | 69.8396i | −0.00540436 | + | 0.0178823i | ||||
\(249\) | − | 1120.34i | − | 0.285136i | ||||||
\(250\) | 2012.36 | − | 2810.29i | 0.509090 | − | 0.710952i | ||||
\(251\) | 2165.36i | 0.544528i | 0.962223 | + | 0.272264i | \(0.0877724\pi\) | ||||
−0.962223 | + | 0.272264i | \(0.912228\pi\) | |||||||
\(252\) | 307.669 | − | 104.676i | 0.0769100 | − | 0.0261666i | ||||
\(253\) | 8881.77i | 2.20708i | ||||||||
\(254\) | −3128.95 | + | 4369.62i | −0.772943 | + | 1.07943i | ||||
\(255\) | 1308.15 | + | 837.605i | 0.321253 | + | 0.205698i | ||||
\(256\) | 1049.21 | − | 3959.34i | 0.256154 | − | 0.966636i | ||||
\(257\) | 4668.83 | 1.13320 | 0.566602 | − | 0.823991i | \(-0.308258\pi\) | ||||
0.566602 | + | 0.823991i | \(0.308258\pi\) | |||||||
\(258\) | 4240.38 | + | 3036.40i | 1.02323 | + | 0.732705i | ||||
\(259\) | − | 1283.11i | − | 0.307834i | ||||||
\(260\) | 1920.11 | − | 653.267i | 0.458001 | − | 0.155823i | ||||
\(261\) | 2382.59 | 0.565052 | ||||||||
\(262\) | 1402.54 | − | 1958.67i | 0.330722 | − | 0.461858i | ||||
\(263\) | −1721.64 | −0.403654 | −0.201827 | − | 0.979421i | \(-0.564688\pi\) | ||||
−0.201827 | + | 0.979421i | \(0.564688\pi\) | |||||||
\(264\) | −4318.96 | − | 1305.27i | −1.00687 | − | 0.304294i | ||||
\(265\) | 456.933i | 0.105921i | ||||||||
\(266\) | −507.989 | + | 709.414i | −0.117093 | + | 0.163522i | ||||
\(267\) | 4433.79 | 1.01627 | ||||||||
\(268\) | 23.2223 | − | 7.90078i | 0.00529302 | − | 0.00180081i | ||||
\(269\) | 1654.44 | 0.374992 | 0.187496 | − | 0.982265i | \(-0.439963\pi\) | ||||
0.187496 | + | 0.982265i | \(0.439963\pi\) | |||||||
\(270\) | −1396.05 | + | 1949.61i | −0.314670 | + | 0.439442i | ||||
\(271\) | −6057.17 | −1.35774 | −0.678869 | − | 0.734259i | \(-0.737530\pi\) | ||||
−0.678869 | + | 0.734259i | \(0.737530\pi\) | |||||||
\(272\) | 4469.22 | − | 386.897i | 0.996274 | − | 0.0862465i | ||||
\(273\) | −650.075 | −0.144118 | ||||||||
\(274\) | 1716.48 | − | 2397.09i | 0.378453 | − | 0.528516i | ||||
\(275\) | −4714.07 | −1.03371 | ||||||||
\(276\) | −5311.39 | + | 1807.06i | −1.15836 | + | 0.394102i | ||||
\(277\) | 6390.39 | 1.38614 | 0.693071 | − | 0.720869i | \(-0.256257\pi\) | ||||
0.693071 | + | 0.720869i | \(0.256257\pi\) | |||||||
\(278\) | −1101.92 | + | 1538.84i | −0.237729 | + | 0.331992i | ||||
\(279\) | − | 36.2924i | − | 0.00778770i | ||||||
\(280\) | 131.951 | − | 436.609i | 0.0281627 | − | 0.0931870i | ||||
\(281\) | −7615.33 | −1.61670 | −0.808349 | − | 0.588703i | \(-0.799639\pi\) | ||||
−0.808349 | + | 0.588703i | \(0.799639\pi\) | |||||||
\(282\) | 1181.59 | − | 1650.11i | 0.249513 | − | 0.348448i | ||||
\(283\) | 1672.36 | 0.351278 | 0.175639 | − | 0.984455i | \(-0.443801\pi\) | ||||
0.175639 | + | 0.984455i | \(0.443801\pi\) | |||||||
\(284\) | −5151.12 | + | 1752.53i | −1.07628 | + | 0.366174i | ||||
\(285\) | − | 1894.18i | − | 0.393690i | ||||||
\(286\) | −5245.82 | − | 3756.37i | −1.08459 | − | 0.776639i | ||||
\(287\) | 1488.03 | 0.306048 | ||||||||
\(288\) | 70.1752 | + | 2036.27i | 0.0143580 | + | 0.416627i | ||||
\(289\) | 2055.89 | + | 4462.16i | 0.418460 | + | 0.908235i | ||||
\(290\) | 1946.81 | − | 2718.75i | 0.394209 | − | 0.550519i | ||||
\(291\) | − | 3786.78i | − | 0.762834i | ||||||
\(292\) | −1414.55 | + | 481.264i | −0.283495 | + | 0.0964515i | ||||
\(293\) | − | 1783.03i | − | 0.355514i | −0.984074 | − | 0.177757i | \(-0.943116\pi\) | ||
0.984074 | − | 0.177757i | \(-0.0568841\pi\) | |||||||
\(294\) | 2156.04 | − | 3010.95i | 0.427697 | − | 0.597286i | ||||
\(295\) | 1659.45i | 0.327515i | ||||||||
\(296\) | 7700.40 | + | 2327.19i | 1.51208 | + | 0.456978i | ||||
\(297\) | 7628.14 | 1.49033 | ||||||||
\(298\) | −3042.24 | − | 2178.45i | −0.591384 | − | 0.423471i | ||||
\(299\) | −8022.90 | −1.55176 | ||||||||
\(300\) | −959.111 | − | 2819.06i | −0.184581 | − | 0.542529i | ||||
\(301\) | 1677.22 | 0.321173 | ||||||||
\(302\) | −438.947 | + | 612.996i | −0.0836375 | + | 0.116801i | ||||
\(303\) | 6359.43i | 1.20574i | ||||||||
\(304\) | −3336.08 | − | 4335.28i | −0.629400 | − | 0.817912i | ||||
\(305\) | −1697.30 | −0.318646 | ||||||||
\(306\) | −2072.40 | + | 827.367i | −0.387161 | + | 0.154567i | ||||
\(307\) | 7946.57i | 1.47731i | 0.674082 | + | 0.738656i | \(0.264539\pi\) | ||||
−0.674082 | + | 0.738656i | \(0.735461\pi\) | |||||||
\(308\) | −1373.65 | + | 467.347i | −0.254126 | + | 0.0864596i | ||||
\(309\) | 1161.08 | 0.213759 | ||||||||
\(310\) | −41.4129 | − | 29.6544i | −0.00758739 | − | 0.00543309i | ||||
\(311\) | − | 9967.26i | − | 1.81734i | −0.417520 | − | 0.908668i | \(-0.637101\pi\) | ||
0.417520 | − | 0.908668i | \(-0.362899\pi\) | |||||||
\(312\) | 1179.05 | − | 3901.32i | 0.213943 | − | 0.707912i | ||||
\(313\) | 8854.42i | 1.59898i | 0.600678 | + | 0.799491i | \(0.294897\pi\) | ||||
−0.600678 | + | 0.799491i | \(0.705103\pi\) | |||||||
\(314\) | 970.645 | + | 695.048i | 0.174448 | + | 0.124917i | ||||
\(315\) | 226.885i | 0.0405826i | ||||||||
\(316\) | −6123.44 | + | 2083.34i | −1.09010 | + | 0.370876i | ||||
\(317\) | −8924.75 | −1.58127 | −0.790637 | − | 0.612285i | \(-0.790250\pi\) | ||||
−0.790637 | + | 0.612285i | \(0.790250\pi\) | |||||||
\(318\) | 746.532 | + | 534.568i | 0.131646 | + | 0.0942675i | ||||
\(319\) | −10637.5 | −1.86704 | ||||||||
\(320\) | 2380.91 | + | 1583.76i | 0.415928 | + | 0.276672i | ||||
\(321\) | −758.435 | −0.131875 | ||||||||
\(322\) | −1050.42 | + | 1466.93i | −0.181794 | + | 0.253878i | ||||
\(323\) | 3230.57 | − | 5045.42i | 0.556512 | − | 0.869147i | ||||
\(324\) | 768.924 | + | 2260.05i | 0.131846 | + | 0.387527i | ||||
\(325\) | − | 4258.22i | − | 0.726780i | ||||||
\(326\) | −5492.68 | + | 7670.61i | −0.933164 | + | 1.30318i | ||||
\(327\) | 1820.25 | 0.307829 | ||||||||
\(328\) | −2698.85 | + | 8930.16i | −0.454326 | + | 1.50331i | ||||
\(329\) | − | 652.675i | − | 0.109371i | ||||||
\(330\) | 1833.86 | − | 2561.02i | 0.305912 | − | 0.427210i | ||||
\(331\) | − | 203.773i | − | 0.0338380i | −0.999857 | − | 0.0169190i | \(-0.994614\pi\) | ||
0.999857 | − | 0.0169190i | \(-0.00538574\pi\) | |||||||
\(332\) | 2138.43 | − | 727.543i | 0.353498 | − | 0.120268i | ||||
\(333\) | −4001.53 | −0.658506 | ||||||||
\(334\) | 8989.57 | + | 6437.14i | 1.47272 | + | 1.05457i | ||||
\(335\) | 17.1249i | 0.00279293i | ||||||||
\(336\) | −558.956 | − | 726.370i | −0.0907547 | − | 0.117937i | ||||
\(337\) | − | 8219.48i | − | 1.32862i | −0.747459 | − | 0.664308i | \(-0.768726\pi\) | ||
0.747459 | − | 0.664308i | \(-0.231274\pi\) | |||||||
\(338\) | −224.680 | + | 313.770i | −0.0361568 | + | 0.0504935i | ||||
\(339\) | − | 4523.03i | − | 0.724653i | ||||||
\(340\) | −749.254 | + | 3040.84i | −0.119512 | + | 0.485037i | ||||
\(341\) | 162.034i | 0.0257321i | ||||||||
\(342\) | 2212.38 | + | 1584.22i | 0.349801 | + | 0.250481i | ||||
\(343\) | − | 2428.88i | − | 0.382354i | ||||||
\(344\) | −3041.98 | + | 10065.5i | −0.476781 | + | 1.57761i | ||||
\(345\) | − | 3916.79i | − | 0.611226i | ||||||
\(346\) | −1851.05 | + | 2585.02i | −0.287610 | + | 0.401652i | ||||
\(347\) | 3076.83 | 0.476002 | 0.238001 | − | 0.971265i | \(-0.423508\pi\) | ||||
0.238001 | + | 0.971265i | \(0.423508\pi\) | |||||||
\(348\) | −2164.28 | − | 6361.35i | −0.333384 | − | 0.979897i | ||||
\(349\) | 6679.79i | 1.02453i | 0.858827 | + | 0.512265i | \(0.171194\pi\) | ||||
−0.858827 | + | 0.512265i | \(0.828806\pi\) | |||||||
\(350\) | −778.583 | − | 557.518i | −0.118906 | − | 0.0851446i | ||||
\(351\) | 6890.49i | 1.04783i | ||||||||
\(352\) | −313.311 | − | 9091.34i | −0.0474418 | − | 1.37662i | ||||
\(353\) | −5558.14 | −0.838045 | −0.419022 | − | 0.907976i | \(-0.637627\pi\) | ||||
−0.419022 | + | 0.907976i | \(0.637627\pi\) | |||||||
\(354\) | 2711.19 | + | 1941.40i | 0.407057 | + | 0.291481i | ||||
\(355\) | − | 3798.60i | − | 0.567912i | ||||||
\(356\) | 2879.27 | + | 8462.88i | 0.428655 | + | 1.25992i | ||||
\(357\) | 541.277 | − | 845.353i | 0.0802449 | − | 0.125324i | ||||
\(358\) | 236.939 | + | 169.665i | 0.0349794 | + | 0.0250476i | ||||
\(359\) | 13509.2 | 1.98604 | 0.993018 | − | 0.117963i | \(-0.0376365\pi\) | ||||
0.993018 | + | 0.117963i | \(0.0376365\pi\) | |||||||
\(360\) | −1361.61 | − | 411.503i | −0.199342 | − | 0.0602447i | ||||
\(361\) | −446.681 | −0.0651233 | ||||||||
\(362\) | −3810.52 | + | 5321.45i | −0.553250 | + | 0.772621i | ||||
\(363\) | −4739.07 | −0.685225 | ||||||||
\(364\) | −422.154 | − | 1240.81i | −0.0607882 | − | 0.178671i | ||||
\(365\) | − | 1043.14i | − | 0.149590i | ||||||
\(366\) | −1985.67 | + | 2773.02i | −0.283587 | + | 0.396034i | ||||
\(367\) | 2183.01i | 0.310497i | 0.987875 | + | 0.155248i | \(0.0496178\pi\) | ||||
−0.987875 | + | 0.155248i | \(0.950382\pi\) | |||||||
\(368\) | −6898.36 | − | 8964.49i | −0.977179 | − | 1.26985i | ||||
\(369\) | − | 4640.58i | − | 0.654686i | ||||||
\(370\) | −3269.65 | + | 4566.11i | −0.459408 | + | 0.641570i | ||||
\(371\) | 295.279 | 0.0413211 | ||||||||
\(372\) | −96.8981 | + | 32.9670i | −0.0135052 | + | 0.00459478i | ||||
\(373\) | − | 10025.2i | − | 1.39165i | −0.718209 | − | 0.695827i | \(-0.755038\pi\) | ||
0.718209 | − | 0.695827i | \(-0.244962\pi\) | |||||||
\(374\) | 9252.62 | − | 3693.94i | 1.27926 | − | 0.510719i | ||||
\(375\) | 4849.00 | 0.667737 | ||||||||
\(376\) | 3916.92 | + | 1183.76i | 0.537233 | + | 0.162361i | ||||
\(377\) | − | 9608.87i | − | 1.31268i | ||||||
\(378\) | 1259.87 | + | 902.156i | 0.171431 | + | 0.122756i | ||||
\(379\) | −2116.32 | −0.286829 | −0.143415 | − | 0.989663i | \(-0.545808\pi\) | ||||
−0.143415 | + | 0.989663i | \(0.545808\pi\) | |||||||
\(380\) | 3615.47 | − | 1230.07i | 0.488078 | − | 0.166056i | ||||
\(381\) | −7539.55 | −1.01381 | ||||||||
\(382\) | 8113.03 | − | 11330.0i | 1.08665 | − | 1.51752i | ||||
\(383\) | −5242.21 | −0.699385 | −0.349693 | − | 0.936864i | \(-0.613714\pi\) | ||||
−0.349693 | + | 0.936864i | \(0.613714\pi\) | |||||||
\(384\) | 5372.97 | − | 2037.06i | 0.714031 | − | 0.270712i | ||||
\(385\) | − | 1012.97i | − | 0.134093i | ||||||
\(386\) | 11094.3 | + | 7944.29i | 1.46292 | + | 1.04755i | ||||
\(387\) | − | 5230.58i | − | 0.687042i | ||||||
\(388\) | 7227.92 | − | 2459.11i | 0.945726 | − | 0.321758i | ||||
\(389\) | − | 6794.48i | − | 0.885588i | −0.896623 | − | 0.442794i | \(-0.853987\pi\) | ||
0.896623 | − | 0.442794i | \(-0.146013\pi\) | |||||||
\(390\) | 2313.37 | + | 1656.53i | 0.300364 | + | 0.215081i | ||||
\(391\) | 6680.17 | − | 10432.9i | 0.864017 | − | 1.34940i | ||||
\(392\) | 7147.19 | + | 2160.01i | 0.920887 | + | 0.278308i | ||||
\(393\) | 3379.58 | 0.433784 | ||||||||
\(394\) | −72.0855 | + | 100.668i | −0.00921729 | + | 0.0128721i | ||||
\(395\) | − | 4515.62i | − | 0.575204i | ||||||
\(396\) | 1457.47 | + | 4283.87i | 0.184951 | + | 0.543617i | ||||
\(397\) | 1568.70 | 0.198315 | 0.0991574 | − | 0.995072i | \(-0.468385\pi\) | ||||
0.0991574 | + | 0.995072i | \(0.468385\pi\) | |||||||
\(398\) | −8075.22 | − | 5782.41i | −1.01702 | − | 0.728256i | ||||
\(399\) | −1224.06 | −0.153583 | ||||||||
\(400\) | 4757.97 | − | 3661.36i | 0.594746 | − | 0.457670i | ||||
\(401\) | 5584.03i | 0.695394i | 0.937607 | + | 0.347697i | \(0.113036\pi\) | ||||
−0.937607 | + | 0.347697i | \(0.886964\pi\) | |||||||
\(402\) | 27.9784 | + | 20.0345i | 0.00347124 | + | 0.00248564i | ||||
\(403\) | −146.365 | −0.0180918 | ||||||||
\(404\) | −12138.4 | + | 4129.77i | −1.49482 | + | 0.508573i | ||||
\(405\) | −1666.64 | −0.204484 | ||||||||
\(406\) | −1756.91 | − | 1258.07i | −0.214763 | − | 0.153785i | ||||
\(407\) | 17865.6 | 2.17584 | ||||||||
\(408\) | 4091.52 | + | 4781.60i | 0.496472 | + | 0.580208i | ||||
\(409\) | 3024.68 | 0.365674 | 0.182837 | − | 0.983143i | \(-0.441472\pi\) | ||||
0.182837 | + | 0.983143i | \(0.441472\pi\) | |||||||
\(410\) | −5295.32 | − | 3791.81i | −0.637847 | − | 0.456742i | ||||
\(411\) | 4136.05 | 0.496390 | ||||||||
\(412\) | 753.996 | + | 2216.18i | 0.0901620 | + | 0.265008i | ||||
\(413\) | 1072.37 | 0.127767 | ||||||||
\(414\) | 4574.77 | + | 3275.85i | 0.543086 | + | 0.388887i | ||||
\(415\) | 1576.94i | 0.186528i | ||||||||
\(416\) | 8212.20 | − | 283.013i | 0.967876 | − | 0.0333555i | ||||
\(417\) | −2655.19 | −0.311812 | ||||||||
\(418\) | −9877.61 | − | 7073.04i | −1.15581 | − | 0.827640i | ||||
\(419\) | 7564.25 | 0.881952 | 0.440976 | − | 0.897519i | \(-0.354632\pi\) | ||||
0.440976 | + | 0.897519i | \(0.354632\pi\) | |||||||
\(420\) | 605.767 | − | 206.096i | 0.0703772 | − | 0.0239440i | ||||
\(421\) | 2210.99i | 0.255955i | 0.991777 | + | 0.127977i | \(0.0408485\pi\) | ||||
−0.991777 | + | 0.127977i | \(0.959151\pi\) | |||||||
\(422\) | 4873.29 | − | 6805.63i | 0.562152 | − | 0.785054i | ||||
\(423\) | −2035.44 | −0.233963 | ||||||||
\(424\) | −535.550 | + | 1772.07i | −0.0613410 | + | 0.202970i | ||||
\(425\) | 5537.35 | + | 3545.55i | 0.632003 | + | 0.404669i | ||||
\(426\) | −6206.10 | − | 4443.99i | −0.705837 | − | 0.505427i | ||||
\(427\) | 1096.83i | 0.124307i | ||||||||
\(428\) | −492.523 | − | 1447.64i | −0.0556238 | − | 0.163492i | ||||
\(429\) | − | 9051.40i | − | 1.01866i | ||||||
\(430\) | −5968.57 | − | 4273.90i | −0.669372 | − | 0.479316i | ||||
\(431\) | 1387.02i | 0.155013i | 0.996992 | + | 0.0775064i | \(0.0246958\pi\) | ||||
−0.996992 | + | 0.0775064i | \(0.975304\pi\) | |||||||
\(432\) | −7699.18 | + | 5924.68i | −0.857470 | + | 0.659841i | ||||
\(433\) | 3801.82 | 0.421949 | 0.210974 | − | 0.977492i | \(-0.432336\pi\) | ||||
0.210974 | + | 0.977492i | \(0.432336\pi\) | |||||||
\(434\) | −19.1633 | + | 26.7618i | −0.00211951 | + | 0.00295993i | ||||
\(435\) | 4691.06 | 0.517056 | ||||||||
\(436\) | 1182.06 | + | 3474.35i | 0.129840 | + | 0.381632i | ||||
\(437\) | −15106.7 | −1.65366 | ||||||||
\(438\) | −1704.26 | − | 1220.37i | −0.185920 | − | 0.133131i | ||||
\(439\) | − | 4754.35i | − | 0.516886i | −0.966027 | − | 0.258443i | \(-0.916791\pi\) | ||
0.966027 | − | 0.258443i | \(-0.0832094\pi\) | |||||||
\(440\) | 6079.17 | + | 1837.23i | 0.658667 | + | 0.199061i | ||||
\(441\) | −3714.06 | −0.401043 | ||||||||
\(442\) | 3336.73 | + | 8357.89i | 0.359077 | + | 0.899422i | ||||
\(443\) | 12346.2i | 1.32412i | 0.749452 | + | 0.662059i | \(0.230317\pi\) | ||||
−0.749452 | + | 0.662059i | \(0.769683\pi\) | |||||||
\(444\) | 3634.88 | + | 10683.8i | 0.388522 | + | 1.14196i | ||||
\(445\) | −6240.80 | −0.664814 | ||||||||
\(446\) | −2991.43 | + | 4177.58i | −0.317597 | + | 0.443530i | ||||
\(447\) | − | 5249.24i | − | 0.555437i | ||||||
\(448\) | 1023.46 | − | 1538.59i | 0.107933 | − | 0.162258i | ||||
\(449\) | − | 9274.67i | − | 0.974830i | −0.873170 | − | 0.487415i | \(-0.837940\pi\) | ||
0.873170 | − | 0.487415i | \(-0.162060\pi\) | |||||||
\(450\) | −1738.68 | + | 2428.09i | −0.182138 | + | 0.254359i | ||||
\(451\) | 20718.8i | 2.16321i | ||||||||
\(452\) | 8633.23 | − | 2937.23i | 0.898391 | − | 0.305654i | ||||
\(453\) | −1057.69 | −0.109701 | ||||||||
\(454\) | −6166.64 | + | 8611.80i | −0.637477 | + | 0.890247i | ||||
\(455\) | 915.017 | 0.0942783 | ||||||||
\(456\) | 2220.08 | − | 7345.97i | 0.227993 | − | 0.754400i | ||||
\(457\) | −6107.91 | −0.625199 | −0.312600 | − | 0.949885i | \(-0.601200\pi\) | ||||
−0.312600 | + | 0.949885i | \(0.601200\pi\) | |||||||
\(458\) | −6974.58 | − | 4994.27i | −0.711573 | − | 0.509535i | ||||
\(459\) | −8960.35 | − | 5737.28i | −0.911184 | − | 0.583428i | ||||
\(460\) | 7476.07 | − | 2543.54i | 0.757769 | − | 0.257811i | ||||
\(461\) | − | 19516.5i | − | 1.97175i | −0.167487 | − | 0.985874i | \(-0.553565\pi\) | ||
0.167487 | − | 0.985874i | \(-0.446435\pi\) | |||||||
\(462\) | −1654.98 | − | 1185.08i | −0.166659 | − | 0.119339i | ||||
\(463\) | 564.749 | 0.0566871 | 0.0283435 | − | 0.999598i | \(-0.490977\pi\) | ||||
0.0283435 | + | 0.999598i | \(0.490977\pi\) | |||||||
\(464\) | 10736.6 | − | 8262.03i | 1.07421 | − | 0.826627i | ||||
\(465\) | − | 71.4558i | − | 0.00712620i | ||||||
\(466\) | 4807.24 | + | 3442.31i | 0.477878 | + | 0.342193i | ||||
\(467\) | 4243.88i | 0.420521i | 0.977645 | + | 0.210261i | \(0.0674313\pi\) | ||||
−0.977645 | + | 0.210261i | \(0.932569\pi\) | |||||||
\(468\) | −3869.61 | + | 1316.53i | −0.382207 | + | 0.130036i | ||||
\(469\) | 11.0664 | 0.00108955 | ||||||||
\(470\) | −1663.15 | + | 2322.62i | −0.163224 | + | 0.227945i | ||||
\(471\) | 1674.80i | 0.163844i | ||||||||
\(472\) | −1944.96 | + | 6435.65i | −0.189670 | + | 0.627595i | ||||
\(473\) | 23352.9i | 2.27012i | ||||||||
\(474\) | −7377.56 | − | 5282.84i | −0.714900 | − | 0.511917i | ||||
\(475\) | − | 8018.00i | − | 0.774507i | ||||||
\(476\) | 1965.05 | + | 484.182i | 0.189218 | + | 0.0466228i | ||||
\(477\) | − | 920.860i | − | 0.0883926i | ||||||
\(478\) | 168.471 | − | 235.273i | 0.0161207 | − | 0.0225128i | ||||
\(479\) | 8871.92i | 0.846280i | 0.906064 | + | 0.423140i | \(0.139072\pi\) | ||||
−0.906064 | + | 0.423140i | \(0.860928\pi\) | |||||||
\(480\) | 138.167 | + | 4009.21i | 0.0131384 | + | 0.381238i | ||||
\(481\) | 16138.0i | 1.52979i | ||||||||
\(482\) | −2230.84 | − | 1597.43i | −0.210813 | − | 0.150956i | ||||
\(483\) | −2531.11 | −0.238446 | ||||||||
\(484\) | −3077.52 | − | 9045.59i | −0.289023 | − | 0.849510i | ||||
\(485\) | 5330.10i | 0.499025i | ||||||||
\(486\) | 4799.16 | − | 6702.10i | 0.447931 | − | 0.625542i | ||||
\(487\) | 636.492i | 0.0592242i | 0.999561 | + | 0.0296121i | \(0.00942720\pi\) | ||||
−0.999561 | + | 0.0296121i | \(0.990573\pi\) | |||||||
\(488\) | −6582.42 | − | 1989.32i | −0.610599 | − | 0.184534i | ||||
\(489\) | −13235.2 | −1.22396 | ||||||||
\(490\) | −3034.75 | + | 4238.07i | −0.279788 | + | 0.390728i | ||||
\(491\) | 3844.10i | 0.353323i | 0.984272 | + | 0.176662i | \(0.0565298\pi\) | ||||
−0.984272 | + | 0.176662i | \(0.943470\pi\) | |||||||
\(492\) | −12390.0 | + | 4215.38i | −1.13534 | + | 0.386268i | ||||
\(493\) | 12495.3 | + | 8000.71i | 1.14150 | + | 0.730900i | ||||
\(494\) | 6389.07 | − | 8922.44i | 0.581899 | − | 0.812631i | ||||
\(495\) | −3159.06 | −0.286847 | ||||||||
\(496\) | −125.850 | − | 163.543i | −0.0113928 | − | 0.0148051i | ||||
\(497\) | −2454.73 | −0.221549 | ||||||||
\(498\) | 2576.39 | + | 1844.87i | 0.231829 | + | 0.166005i | ||||
\(499\) | 9286.78 | 0.833133 | 0.416567 | − | 0.909105i | \(-0.363233\pi\) | ||||
0.416567 | + | 0.909105i | \(0.363233\pi\) | |||||||
\(500\) | 3148.91 | + | 9255.41i | 0.281647 | + | 0.827829i | ||||
\(501\) | 15511.0i | 1.38320i | ||||||||
\(502\) | −4979.57 | − | 3565.71i | −0.442727 | − | 0.317023i | ||||
\(503\) | − | 3479.75i | − | 0.308458i | −0.988035 | − | 0.154229i | \(-0.950711\pi\) | ||
0.988035 | − | 0.154229i | \(-0.0492894\pi\) | |||||||
\(504\) | −265.921 | + | 879.900i | −0.0235021 | + | 0.0777656i | ||||
\(505\) | − | 8951.25i | − | 0.788763i | ||||||
\(506\) | −20424.9 | − | 14625.6i | −1.79446 | − | 1.28496i | ||||
\(507\) | −541.393 | −0.0474243 | ||||||||
\(508\) | −4896.13 | − | 14390.9i | −0.427620 | − | 1.25688i | ||||
\(509\) | − | 13024.0i | − | 1.13414i | −0.823670 | − | 0.567070i | \(-0.808077\pi\) | ||
0.823670 | − | 0.567070i | \(-0.191923\pi\) | |||||||
\(510\) | −4080.33 | + | 1629.00i | −0.354275 | + | 0.141438i | ||||
\(511\) | −674.095 | −0.0583566 | ||||||||
\(512\) | 7377.35 | + | 8932.66i | 0.636789 | + | 0.771038i | ||||
\(513\) | 12974.4i | 1.11664i | ||||||||
\(514\) | −7688.18 | + | 10736.7i | −0.659749 | + | 0.921349i | ||||
\(515\) | −1634.28 | −0.139835 | ||||||||
\(516\) | −13965.3 | + | 4751.32i | −1.19145 | + | 0.405359i | ||||
\(517\) | 9087.59 | 0.773060 | ||||||||
\(518\) | 2950.71 | + | 2112.91i | 0.250283 | + | 0.179220i | ||||
\(519\) | −4460.32 | −0.377238 | ||||||||
\(520\) | −1659.57 | + | 5491.32i | −0.139956 | + | 0.463096i | ||||
\(521\) | − | 8878.51i | − | 0.746592i | −0.927712 | − | 0.373296i | \(-0.878228\pi\) | ||
0.927712 | − | 0.373296i | \(-0.121772\pi\) | |||||||
\(522\) | −3923.42 | + | 5479.11i | −0.328972 | + | 0.459414i | ||||
\(523\) | 13119.8i | 1.09692i | 0.836177 | + | 0.548459i | \(0.184785\pi\) | ||||
−0.836177 | + | 0.548459i | \(0.815215\pi\) | |||||||
\(524\) | 2194.67 | + | 6450.68i | 0.182967 | + | 0.537785i | ||||
\(525\) | − | 1343.40i | − | 0.111678i | ||||||
\(526\) | 2835.04 | − | 3959.17i | 0.235006 | − | 0.328190i | ||||
\(527\) | 121.869 | − | 190.333i | 0.0100735 | − | 0.0157325i | ||||
\(528\) | 10113.7 | − | 7782.69i | 0.833602 | − | 0.641474i | ||||
\(529\) | −19070.6 | −1.56741 | ||||||||
\(530\) | −1050.78 | − | 752.433i | −0.0861192 | − | 0.0616672i | ||||
\(531\) | − | 3344.30i | − | 0.273315i | ||||||
\(532\) | −794.894 | − | 2336.39i | −0.0647801 | − | 0.190405i | ||||
\(533\) | −18715.3 | −1.52091 | ||||||||
\(534\) | −7301.13 | + | 10196.1i | −0.591668 | + | 0.826274i | ||||
\(535\) | 1067.54 | 0.0862687 | ||||||||
\(536\) | −20.0713 | + | 66.4134i | −0.00161744 | + | 0.00535190i | ||||
\(537\) | 408.826i | 0.0328532i | ||||||||
\(538\) | −2724.36 | + | 3804.62i | −0.218319 | + | 0.304886i | ||||
\(539\) | 16582.1 | 1.32513 | ||||||||
\(540\) | −2184.52 | − | 6420.85i | −0.174087 | − | 0.511684i | ||||
\(541\) | 10188.3 | 0.809664 | 0.404832 | − | 0.914391i | \(-0.367330\pi\) | ||||
0.404832 | + | 0.914391i | \(0.367330\pi\) | |||||||
\(542\) | 9974.36 | − | 13929.4i | 0.790472 | − | 1.10391i | ||||
\(543\) | −9181.88 | −0.725658 | ||||||||
\(544\) | −6469.76 | + | 10914.7i | −0.509906 | + | 0.860230i | ||||
\(545\) | −2562.10 | −0.201373 | ||||||||
\(546\) | 1070.48 | − | 1494.94i | 0.0839054 | − | 0.117175i | ||||
\(547\) | 4399.60 | 0.343900 | 0.171950 | − | 0.985106i | \(-0.444993\pi\) | ||||
0.171950 | + | 0.985106i | \(0.444993\pi\) | |||||||
\(548\) | 2685.92 | + | 7894.58i | 0.209374 | + | 0.615401i | ||||
\(549\) | 3420.57 | 0.265914 | ||||||||
\(550\) | 7762.67 | − | 10840.7i | 0.601821 | − | 0.840452i | ||||
\(551\) | − | 18093.0i | − | 1.39889i | ||||||
\(552\) | 4590.68 | − | 15190.0i | 0.353972 | − | 1.17125i | ||||
\(553\) | −2918.08 | −0.224393 | ||||||||
\(554\) | −10523.1 | + | 14695.6i | −0.807009 | + | 1.12700i | ||||
\(555\) | −7878.59 | −0.602572 | ||||||||
\(556\) | −1724.26 | − | 5068.03i | −0.131520 | − | 0.386569i | ||||
\(557\) | − | 11164.3i | − | 0.849273i | −0.905364 | − | 0.424637i | \(-0.860402\pi\) | ||
0.905364 | − | 0.424637i | \(-0.139598\pi\) | |||||||
\(558\) | 83.4596 | + | 59.7627i | 0.00633177 | + | 0.00453398i | ||||
\(559\) | −21094.7 | −1.59608 | ||||||||
\(560\) | 786.762 | + | 1022.40i | 0.0593692 | + | 0.0771509i | ||||
\(561\) | 11770.4 | + | 7536.54i | 0.885821 | + | 0.567189i | ||||
\(562\) | 12540.2 | − | 17512.6i | 0.941238 | − | 1.31445i | ||||
\(563\) | 7510.92i | 0.562252i | 0.959671 | + | 0.281126i | \(0.0907078\pi\) | ||||
−0.959671 | + | 0.281126i | \(0.909292\pi\) | |||||||
\(564\) | 1848.94 | + | 5434.47i | 0.138039 | + | 0.405732i | ||||
\(565\) | 6366.42i | 0.474048i | ||||||||
\(566\) | −2753.88 | + | 3845.84i | −0.204513 | + | 0.285605i | ||||
\(567\) | 1077.01i | 0.0797713i | ||||||||
\(568\) | 4452.16 | − | 14731.6i | 0.328888 | − | 1.08825i | ||||
\(569\) | −7281.16 | −0.536454 | −0.268227 | − | 0.963356i | \(-0.586438\pi\) | ||||
−0.268227 | + | 0.963356i | \(0.586438\pi\) | |||||||
\(570\) | 4355.94 | + | 3119.15i | 0.320089 | + | 0.229205i | ||||
\(571\) | 6333.20 | 0.464161 | 0.232081 | − | 0.972697i | \(-0.425447\pi\) | ||||
0.232081 | + | 0.972697i | \(0.425447\pi\) | |||||||
\(572\) | 17276.6 | − | 5877.92i | 1.26289 | − | 0.429664i | ||||
\(573\) | 19549.3 | 1.42528 | ||||||||
\(574\) | −2450.34 | + | 3421.94i | −0.178180 | + | 0.248831i | ||||
\(575\) | − | 16579.6i | − | 1.20247i | ||||||
\(576\) | −4798.27 | − | 3191.76i | −0.347097 | − | 0.230886i | ||||
\(577\) | 7726.62 | 0.557476 | 0.278738 | − | 0.960367i | \(-0.410084\pi\) | ||||
0.278738 | + | 0.960367i | \(0.410084\pi\) | |||||||
\(578\) | −13646.8 | − | 2620.03i | −0.982065 | − | 0.188545i | ||||
\(579\) | 19142.7i | 1.37399i | ||||||||
\(580\) | 3046.34 | + | 8953.95i | 0.218091 | + | 0.641021i | ||||
\(581\) | 1019.05 | 0.0727667 | ||||||||
\(582\) | 8708.25 | + | 6235.70i | 0.620221 | + | 0.444120i | ||||
\(583\) | 4111.36i | 0.292067i | ||||||||
\(584\) | 1222.61 | − | 4045.47i | 0.0866302 | − | 0.286648i | ||||
\(585\) | − | 2853.58i | − | 0.201677i | ||||||
\(586\) | 4100.33 | + | 2936.12i | 0.289050 | + | 0.206979i | ||||
\(587\) | 18469.0i | 1.29864i | 0.760517 | + | 0.649318i | \(0.224945\pi\) | ||||
−0.760517 | + | 0.649318i | \(0.775055\pi\) | |||||||
\(588\) | 3373.75 | + | 9916.27i | 0.236617 | + | 0.695477i | ||||
\(589\) | −275.598 | −0.0192798 | ||||||||
\(590\) | −3816.15 | − | 2732.62i | −0.266285 | − | 0.190679i | ||||
\(591\) | −173.698 | −0.0120897 | ||||||||
\(592\) | −18032.0 | + | 13876.0i | −1.25188 | + | 0.963344i | ||||
\(593\) | 4888.22 | 0.338508 | 0.169254 | − | 0.985572i | \(-0.445864\pi\) | ||||
0.169254 | + | 0.985572i | \(0.445864\pi\) | |||||||
\(594\) | −12561.3 | + | 17542.0i | −0.867669 | + | 1.21171i | ||||
\(595\) | −761.877 | + | 1189.88i | −0.0524940 | + | 0.0819838i | ||||
\(596\) | 10019.3 | − | 3408.82i | 0.688605 | − | 0.234279i | ||||
\(597\) | − | 13933.4i | − | 0.955202i | ||||||
\(598\) | 13211.3 | − | 18449.8i | 0.903431 | − | 1.26165i | ||||
\(599\) | 13200.8 | 0.900453 | 0.450227 | − | 0.892914i | \(-0.351343\pi\) | ||||
0.450227 | + | 0.892914i | \(0.351343\pi\) | |||||||
\(600\) | 8062.21 | + | 2436.54i | 0.548564 | + | 0.165786i | ||||
\(601\) | 407.078i | 0.0276291i | 0.999905 | + | 0.0138145i | \(0.00439744\pi\) | ||||
−0.999905 | + | 0.0138145i | \(0.995603\pi\) | |||||||
\(602\) | −2761.88 | + | 3857.00i | −0.186986 | + | 0.261129i | ||||
\(603\) | − | 34.5119i | − | 0.00233073i | ||||||
\(604\) | −686.858 | − | 2018.84i | −0.0462713 | − | 0.136003i | ||||
\(605\) | 6670.51 | 0.448256 | ||||||||
\(606\) | −14624.4 | − | 10472.1i | −0.980325 | − | 0.701980i | ||||
\(607\) | 21194.5i | 1.41723i | 0.705595 | + | 0.708615i | \(0.250680\pi\) | ||||
−0.705595 | + | 0.708615i | \(0.749320\pi\) | |||||||
\(608\) | 15463.1 | − | 532.899i | 1.03144 | − | 0.0355459i | ||||
\(609\) | − | 3031.46i | − | 0.201709i | ||||||
\(610\) | 2794.95 | − | 3903.18i | 0.185515 | − | 0.259074i | ||||
\(611\) | 8208.82i | 0.543524i | ||||||||
\(612\) | 1509.98 | − | 6128.21i | 0.0997339 | − | 0.404769i | ||||
\(613\) | 25367.0i | 1.67139i | 0.549191 | + | 0.835697i | \(0.314936\pi\) | ||||
−0.549191 | + | 0.835697i | \(0.685064\pi\) | |||||||
\(614\) | −18274.3 | − | 13085.6i | −1.20113 | − | 0.860087i | ||||
\(615\) | − | 9136.81i | − | 0.599076i | ||||||
\(616\) | 1187.26 | − | 3928.48i | 0.0776557 | − | 0.256953i | ||||
\(617\) | − | 2919.48i | − | 0.190492i | −0.995454 | − | 0.0952461i | \(-0.969636\pi\) | ||
0.995454 | − | 0.0952461i | \(-0.0303638\pi\) | |||||||
\(618\) | −1911.95 | + | 2670.07i | −0.124450 | + | 0.173796i | ||||
\(619\) | 596.827 | 0.0387537 | 0.0193768 | − | 0.999812i | \(-0.493832\pi\) | ||||
0.0193768 | + | 0.999812i | \(0.493832\pi\) | |||||||
\(620\) | 136.389 | − | 46.4029i | 0.00883472 | − | 0.00300578i | ||||
\(621\) | 26828.5i | 1.73364i | ||||||||
\(622\) | 22921.2 | + | 16413.1i | 1.47758 | + | 1.05805i | ||||
\(623\) | 4032.93i | 0.259351i | ||||||||
\(624\) | 7030.11 | + | 9135.70i | 0.451009 | + | 0.586091i | ||||
\(625\) | 4900.64 | 0.313641 | ||||||||
\(626\) | −20362.0 | − | 14580.6i | −1.30005 | − | 0.930923i | ||||
\(627\) | − | 17043.3i | − | 1.08556i | ||||||
\(628\) | −3196.73 | + | 1087.60i | −0.203126 | + | 0.0691084i | ||||
\(629\) | −20985.7 | − | 13437.1i | −1.33030 | − | 0.851784i | ||||
\(630\) | −521.755 | − | 373.612i | −0.0329956 | − | 0.0236271i | ||||
\(631\) | 21069.5 | 1.32926 | 0.664632 | − | 0.747171i | \(-0.268588\pi\) | ||||
0.664632 | + | 0.747171i | \(0.268588\pi\) | |||||||
\(632\) | 5292.55 | − | 17512.4i | 0.333111 | − | 1.10222i | ||||
\(633\) | 11742.8 | 0.737334 | ||||||||
\(634\) | 14696.4 | − | 20523.8i | 0.920613 | − | 1.28565i | ||||
\(635\) | 10612.3 | 0.663209 | ||||||||
\(636\) | −2458.63 | + | 836.484i | −0.153288 | + | 0.0521521i | ||||
\(637\) | 14978.6i | 0.931671i | ||||||||
\(638\) | 17516.8 | − | 24462.5i | 1.08699 | − | 1.51800i | ||||
\(639\) | 7655.34i | 0.473929i | ||||||||
\(640\) | −7562.74 | + | 2867.27i | −0.467100 | + | 0.177092i | ||||
\(641\) | − | 5527.94i | − | 0.340625i | −0.985390 | − | 0.170312i | \(-0.945522\pi\) | ||
0.985390 | − | 0.170312i | \(-0.0544776\pi\) | |||||||
\(642\) | 1248.92 | − | 1744.13i | 0.0767770 | − | 0.107220i | ||||
\(643\) | −11206.4 | −0.687307 | −0.343653 | − | 0.939097i | \(-0.611665\pi\) | ||||
−0.343653 | + | 0.939097i | \(0.611665\pi\) | |||||||
\(644\) | −1643.68 | − | 4831.18i | −0.100575 | − | 0.295614i | ||||
\(645\) | − | 10298.5i | − | 0.628684i | ||||||
\(646\) | 6282.89 | + | 15737.5i | 0.382658 | + | 0.958486i | ||||
\(647\) | 26877.0 | 1.63315 | 0.816573 | − | 0.577242i | \(-0.195871\pi\) | ||||
0.816573 | + | 0.577242i | \(0.195871\pi\) | |||||||
\(648\) | −6463.51 | − | 1953.39i | −0.391838 | − | 0.118420i | ||||
\(649\) | 14931.3i | 0.903087i | ||||||||
\(650\) | 9792.39 | + | 7012.02i | 0.590906 | + | 0.423129i | ||||
\(651\) | −46.1761 | −0.00278001 | ||||||||
\(652\) | −8594.87 | − | 25262.4i | −0.516260 | − | 1.51741i | ||||
\(653\) | 12384.8 | 0.742195 | 0.371097 | − | 0.928594i | \(-0.378982\pi\) | ||||
0.371097 | + | 0.928594i | \(0.378982\pi\) | |||||||
\(654\) | −2997.41 | + | 4185.93i | −0.179217 | + | 0.250279i | ||||
\(655\) | −4756.94 | −0.283769 | ||||||||
\(656\) | −16092.0 | − | 20911.7i | −0.957754 | − | 1.24461i | ||||
\(657\) | 2102.24i | 0.124834i | ||||||||
\(658\) | 1500.92 | + | 1074.76i | 0.0889240 | + | 0.0636756i | ||||
\(659\) | − | 22390.6i | − | 1.32354i | −0.749705 | − | 0.661772i | \(-0.769805\pi\) | ||
0.749705 | − | 0.661772i | \(-0.230195\pi\) | |||||||
\(660\) | 2869.60 | + | 8434.47i | 0.169241 | + | 0.497441i | ||||
\(661\) | 16036.4i | 0.943636i | 0.881696 | + | 0.471818i | \(0.156402\pi\) | ||||
−0.881696 | + | 0.471818i | \(0.843598\pi\) | |||||||
\(662\) | 468.605 | + | 335.553i | 0.0275119 | + | 0.0197004i | ||||
\(663\) | −6807.75 | + | 10632.2i | −0.398780 | + | 0.622805i | ||||
\(664\) | −1848.26 | + | 6115.67i | −0.108022 | + | 0.357431i | ||||
\(665\) | 1722.93 | 0.100470 | ||||||||
\(666\) | 6589.34 | − | 9202.11i | 0.383381 | − | 0.535397i | ||||
\(667\) | − | 37412.7i | − | 2.17185i | ||||||
\(668\) | −29606.3 | + | 10072.8i | −1.71482 | + | 0.583423i | ||||
\(669\) | −7208.20 | −0.416570 | ||||||||
\(670\) | −39.3812 | − | 28.1996i | −0.00227079 | − | 0.00162604i | ||||
\(671\) | −15271.8 | −0.878631 | ||||||||
\(672\) | 2590.83 | − | 89.2865i | 0.148725 | − | 0.00512545i | ||||
\(673\) | − | 29521.8i | − | 1.69091i | −0.534048 | − | 0.845454i | \(-0.679330\pi\) | ||
0.534048 | − | 0.845454i | \(-0.320670\pi\) | |||||||
\(674\) | 18901.9 | + | 13535.0i | 1.08023 | + | 0.773517i | ||||
\(675\) | −14239.5 | −0.811966 | ||||||||
\(676\) | −351.577 | − | 1033.37i | −0.0200032 | − | 0.0587944i | ||||
\(677\) | −12136.9 | −0.689008 | −0.344504 | − | 0.938785i | \(-0.611953\pi\) | ||||
−0.344504 | + | 0.938785i | \(0.611953\pi\) | |||||||
\(678\) | 10401.4 | + | 7448.09i | 0.589178 | + | 0.421891i | ||||
\(679\) | 3444.41 | 0.194675 | ||||||||
\(680\) | −5759.05 | − | 6730.37i | −0.324778 | − | 0.379556i | ||||
\(681\) | −14859.2 | −0.836133 | ||||||||
\(682\) | −372.621 | − | 266.822i | −0.0209214 | − | 0.0149812i | ||||
\(683\) | −4710.94 | −0.263923 | −0.131961 | − | 0.991255i | \(-0.542127\pi\) | ||||
−0.131961 | + | 0.991255i | \(0.542127\pi\) | |||||||
\(684\) | −7286.28 | + | 2478.96i | −0.407307 | + | 0.138575i | ||||
\(685\) | −5821.72 | −0.324725 | ||||||||
\(686\) | 5585.57 | + | 3999.65i | 0.310872 | + | 0.222605i | ||||
\(687\) | − | 12034.3i | − | 0.668320i | ||||||
\(688\) | −18137.9 | − | 23570.4i | −1.00509 | − | 1.30612i | ||||
\(689\) | −3713.79 | −0.205347 | ||||||||
\(690\) | 9007.23 | + | 6449.79i | 0.496955 | + | 0.355854i | ||||
\(691\) | 7822.50 | 0.430654 | 0.215327 | − | 0.976542i | \(-0.430918\pi\) | ||||
0.215327 | + | 0.976542i | \(0.430918\pi\) | |||||||
\(692\) | −2896.50 | − | 8513.52i | −0.159116 | − | 0.467681i | ||||
\(693\) | 2041.45i | 0.111902i | ||||||||
\(694\) | −5066.62 | + | 7075.61i | −0.277127 | + | 0.387012i | ||||
\(695\) | 3737.33 | 0.203979 | ||||||||
\(696\) | 18192.8 | + | 5498.17i | 0.990798 | + | 0.299436i | ||||
\(697\) | 15583.0 | − | 24337.2i | 0.846842 | − | 1.32258i | ||||
\(698\) | −15361.2 | − | 10999.6i | −0.832992 | − | 0.596479i | ||||
\(699\) | 8294.64i | 0.448830i | ||||||||
\(700\) | 2564.19 | − | 872.397i | 0.138453 | − | 0.0471050i | ||||
\(701\) | − | 19853.3i | − | 1.06969i | −0.844951 | − | 0.534843i | \(-0.820371\pi\) | ||
0.844951 | − | 0.534843i | \(-0.179629\pi\) | |||||||
\(702\) | −15845.7 | − | 11346.6i | −0.851933 | − | 0.610042i | ||||
\(703\) | 30387.0i | 1.63025i | ||||||||
\(704\) | 21422.8 | + | 14250.2i | 1.14688 | + | 0.762892i | ||||
\(705\) | −4007.56 | −0.214090 | ||||||||
\(706\) | 9152.60 | − | 12781.7i | 0.487907 | − | 0.681370i | ||||
\(707\) | −5784.47 | −0.307705 | ||||||||
\(708\) | −8929.05 | + | 3037.87i | −0.473975 | + | 0.161257i | ||||
\(709\) | −20864.8 | −1.10521 | −0.552605 | − | 0.833443i | \(-0.686366\pi\) | ||||
−0.552605 | + | 0.833443i | \(0.686366\pi\) | |||||||
\(710\) | 8735.43 | + | 6255.16i | 0.461739 | + | 0.330637i | ||||
\(711\) | 9100.35i | 0.480014i | ||||||||
\(712\) | −24202.9 | − | 7314.55i | −1.27394 | − | 0.385006i | ||||
\(713\) | −569.882 | −0.0299330 | ||||||||
\(714\) | 1052.69 | + | 2636.79i | 0.0551764 | + | 0.138206i | ||||
\(715\) | 12740.3i | 0.666380i | ||||||||
\(716\) | −780.337 | + | 265.489i | −0.0407298 | + | 0.0138572i | ||||
\(717\) | 405.951 | 0.0211444 | ||||||||
\(718\) | −22245.6 | + | 31066.3i | −1.15626 | + | 1.61474i | ||||
\(719\) | 25691.2i | 1.33257i | 0.745697 | + | 0.666286i | \(0.232117\pi\) | ||||
−0.745697 | + | 0.666286i | \(0.767883\pi\) | |||||||
\(720\) | 3188.48 | − | 2453.60i | 0.165038 | − | 0.127000i | ||||
\(721\) | 1056.10i | 0.0545512i | ||||||||
\(722\) | 735.550 | − | 1027.21i | 0.0379146 | − | 0.0529483i | ||||
\(723\) | − | 3849.19i | − | 0.197999i | ||||||
\(724\) | −5962.65 | − | 17525.7i | −0.306077 | − | 0.899636i | ||||
\(725\) | 19857.1 | 1.01721 | ||||||||
\(726\) | 7803.85 | − | 10898.2i | 0.398936 | − | 0.557121i | ||||
\(727\) | −4195.31 | −0.214024 | −0.107012 | − | 0.994258i | \(-0.534128\pi\) | ||||
−0.107012 | + | 0.994258i | \(0.534128\pi\) | |||||||
\(728\) | 3548.60 | + | 1072.45i | 0.180659 | + | 0.0545983i | ||||
\(729\) | 19621.2 | 0.996859 | ||||||||
\(730\) | 2398.84 | + | 1717.74i | 0.121624 | + | 0.0870908i | ||||
\(731\) | 17564.2 | − | 27431.4i | 0.888696 | − | 1.38794i | ||||
\(732\) | −3107.16 | − | 9132.70i | −0.156890 | − | 0.461140i | ||||
\(733\) | 434.712i | 0.0219051i | 0.999940 | + | 0.0109526i | \(0.00348638\pi\) | ||||
−0.999940 | + | 0.0109526i | \(0.996514\pi\) | |||||||
\(734\) | −5020.16 | − | 3594.77i | −0.252449 | − | 0.180770i | ||||
\(735\) | −7312.58 | −0.366978 | ||||||||
\(736\) | 31974.7 | − | 1101.93i | 1.60136 | − | 0.0551870i | ||||
\(737\) | 154.085i | 0.00770121i | ||||||||
\(738\) | 10671.7 | + | 7641.66i | 0.532291 | + | 0.381156i | ||||
\(739\) | − | 32433.4i | − | 1.61445i | −0.590241 | − | 0.807227i | \(-0.700967\pi\) | ||
0.590241 | − | 0.807227i | \(-0.299033\pi\) | |||||||
\(740\) | −5116.30 | − | 15038.1i | −0.254161 | − | 0.747040i | ||||
\(741\) | 15395.2 | 0.763235 | ||||||||
\(742\) | −486.237 | + | 679.038i | −0.0240570 | + | 0.0335960i | ||||
\(743\) | − | 26343.4i | − | 1.30073i | −0.759621 | − | 0.650366i | \(-0.774615\pi\) | ||
0.759621 | − | 0.650366i | \(-0.225385\pi\) | |||||||
\(744\) | 83.7499 | − | 277.118i | 0.00412691 | − | 0.0136554i | ||||
\(745\) | 7388.59i | 0.363352i | ||||||||
\(746\) | 23054.5 | + | 16508.6i | 1.13148 | + | 0.810217i | ||||
\(747\) | − | 3178.03i | − | 0.155660i | ||||||
\(748\) | −6741.57 | + | 27360.6i | −0.329541 | + | 1.33744i | ||||
\(749\) | − | 689.865i | − | 0.0336544i | ||||||
\(750\) | −7984.87 | + | 11151.0i | −0.388755 | + | 0.542902i | ||||
\(751\) | 7794.47i | 0.378727i | 0.981907 | + | 0.189364i | \(0.0606425\pi\) | ||||
−0.981907 | + | 0.189364i | \(0.939357\pi\) | |||||||
\(752\) | −9172.23 | + | 7058.22i | −0.444783 | + | 0.342270i | ||||
\(753\) | − | 8591.99i | − | 0.415816i | ||||||
\(754\) | 22097.0 | + | 15823.0i | 1.06728 | + | 0.764242i | ||||
\(755\) | 1488.76 | 0.0717636 | ||||||||
\(756\) | −4149.28 | + | 1411.68i | −0.199613 | + | 0.0679132i | ||||
\(757\) | − | 8502.18i | − | 0.408213i | −0.978949 | − | 0.204106i | \(-0.934571\pi\) | ||
0.978949 | − | 0.204106i | \(-0.0654288\pi\) | |||||||
\(758\) | 3484.96 | − | 4866.79i | 0.166991 | − | 0.233206i | ||||
\(759\) | − | 35242.2i | − | 1.68539i | ||||||
\(760\) | −3124.88 | + | 10339.9i | −0.149147 | + | 0.493508i | ||||
\(761\) | −7693.97 | −0.366500 | −0.183250 | − | 0.983066i | \(-0.558662\pi\) | ||||
−0.183250 | + | 0.983066i | \(0.558662\pi\) | |||||||
\(762\) | 12415.4 | − | 17338.3i | 0.590240 | − | 0.824279i | ||||
\(763\) | 1655.68i | 0.0785578i | ||||||||
\(764\) | 12695.2 | + | 37314.2i | 0.601171 | + | 1.76699i | ||||
\(765\) | 3710.77 | + | 2376.00i | 0.175377 | + | 0.112293i | ||||
\(766\) | 8632.37 | − | 12055.2i | 0.407180 | − | 0.568634i | ||||
\(767\) | −13487.4 | −0.634944 | ||||||||
\(768\) | −4163.16 | + | 15710.3i | −0.195606 | + | 0.738149i | ||||
\(769\) | 32455.6 | 1.52195 | 0.760974 | − | 0.648783i | \(-0.224722\pi\) | ||||
0.760974 | + | 0.648783i | \(0.224722\pi\) | |||||||
\(770\) | 2329.47 | + | 1668.06i | 0.109024 | + | 0.0780686i | ||||
\(771\) | −18525.5 | −0.865345 | ||||||||
\(772\) | −36538.1 | + | 12431.1i | −1.70341 | + | 0.579541i | ||||
\(773\) | 38959.3i | 1.81277i | 0.422458 | + | 0.906383i | \(0.361167\pi\) | ||||
−0.422458 | + | 0.906383i | \(0.638833\pi\) | |||||||
\(774\) | 12028.5 | + | 8613.21i | 0.558598 | + | 0.399994i | ||||
\(775\) | − | 302.469i | − | 0.0140194i | ||||||
\(776\) | −6247.16 | + | 20671.1i | −0.288995 | + | 0.956247i | ||||
\(777\) | 5091.30i | 0.235070i | ||||||||
\(778\) | 15624.9 | + | 11188.5i | 0.720025 | + | 0.515587i | ||||
\(779\) | −35239.8 | −1.62079 | ||||||||
\(780\) | −7618.85 | + | 2592.11i | −0.349742 | + | 0.118990i | ||||
\(781\) | − | 34178.7i | − | 1.56595i | ||||||
\(782\) | 12991.8 | + | 32541.9i | 0.594098 | + | 1.48810i | ||||
\(783\) | −32132.0 | −1.46655 | ||||||||
\(784\) | −16736.5 | + | 12879.1i | −0.762416 | + | 0.586694i | ||||
\(785\) | − | 2357.37i | − | 0.107182i | ||||||
\(786\) | −5565.16 | + | 7771.83i | −0.252548 | + | 0.352687i | ||||
\(787\) | −17362.0 | −0.786390 | −0.393195 | − | 0.919455i | \(-0.628630\pi\) | ||||
−0.393195 | + | 0.919455i | \(0.628630\pi\) | |||||||
\(788\) | −112.798 | − | 331.542i | −0.00509933 | − | 0.0149882i | ||||
\(789\) | 6831.34 | 0.308241 | ||||||||
\(790\) | 10384.3 | + | 7435.88i | 0.467668 | + | 0.334882i | ||||
\(791\) | 4114.11 | 0.184931 | ||||||||
\(792\) | −12251.4 | − | 3702.59i | −0.549665 | − | 0.166118i | ||||
\(793\) | − | 13795.0i | − | 0.617750i | ||||||
\(794\) | −2583.19 | + | 3607.46i | −0.115458 | + | 0.161239i | ||||
\(795\) | − | 1813.07i | − | 0.0808844i | ||||||
\(796\) | 26595.0 | − | 9048.24i | 1.18421 | − | 0.402897i | ||||
\(797\) | 30076.1i | 1.33670i | 0.743847 | + | 0.668350i | \(0.232999\pi\) | ||||
−0.743847 | + | 0.668350i | \(0.767001\pi\) | |||||||
\(798\) | 2015.66 | − | 2814.90i | 0.0894154 | − | 0.124870i | ||||
\(799\) | −10674.7 | − | 6834.97i | −0.472645 | − | 0.302633i | ||||
\(800\) | 584.858 | + | 16970.8i | 0.0258473 | + | 0.750011i | ||||
\(801\) | 12577.1 | 0.554795 | ||||||||
\(802\) | −12841.3 | − | 9195.23i | −0.565388 | − | 0.404856i | ||||
\(803\) | − | 9385.85i | − | 0.412477i | ||||||
\(804\) | −92.1443 | + | 31.3497i | −0.00404189 | + | 0.00137515i | ||||
\(805\) | 3562.67 | 0.155985 | ||||||||
\(806\) | 241.020 | − | 336.589i | 0.0105330 | − | 0.0147095i | ||||
\(807\) | −6564.67 | −0.286354 | ||||||||
\(808\) | 10491.3 | − | 34714.5i | 0.456787 | − | 1.51145i | ||||
\(809\) | 9812.44i | 0.426436i | 0.977005 | + | 0.213218i | \(0.0683945\pi\) | ||||
−0.977005 | + | 0.213218i | \(0.931606\pi\) | |||||||
\(810\) | 2744.46 | − | 3832.67i | 0.119050 | − | 0.166255i | ||||
\(811\) | −25891.9 | −1.12107 | −0.560535 | − | 0.828131i | \(-0.689404\pi\) | ||||
−0.560535 | + | 0.828131i | \(0.689404\pi\) | |||||||
\(812\) | 5786.22 | − | 1968.61i | 0.250069 | − | 0.0850795i | ||||
\(813\) | 24034.4 | 1.03680 | ||||||||
\(814\) | −29419.3 | + | 41084.6i | −1.26677 | + | 1.76906i | ||||
\(815\) | 18629.3 | 0.800683 | ||||||||
\(816\) | −17733.5 | + | 1535.17i | −0.760781 | + | 0.0658601i | ||||
\(817\) | −39720.2 | −1.70090 | ||||||||
\(818\) | −4980.75 | + | 6955.69i | −0.212895 | + | 0.297310i | ||||
\(819\) | −1844.04 | −0.0786763 | ||||||||
\(820\) | 17439.6 | − | 5933.38i | 0.742706 | − | 0.252686i | ||||
\(821\) | −23472.8 | −0.997813 | −0.498907 | − | 0.866656i | \(-0.666265\pi\) | ||||
−0.498907 | + | 0.866656i | \(0.666265\pi\) | |||||||
\(822\) | −6810.85 | + | 9511.45i | −0.288997 | + | 0.403589i | ||||
\(823\) | 11678.8i | 0.494649i | 0.968933 | + | 0.247324i | \(0.0795513\pi\) | ||||
−0.968933 | + | 0.247324i | \(0.920449\pi\) | |||||||
\(824\) | −6338.03 | − | 1915.46i | −0.267956 | − | 0.0809810i | ||||
\(825\) | 18705.1 | 0.789365 | ||||||||
\(826\) | −1765.87 | + | 2466.07i | −0.0743858 | + | 0.103881i | ||||
\(827\) | 3225.66 | 0.135631 | 0.0678157 | − | 0.997698i | \(-0.478397\pi\) | ||||
0.0678157 | + | 0.997698i | \(0.478397\pi\) | |||||||
\(828\) | −15066.6 | + | 5126.00i | −0.632367 | + | 0.215146i | ||||
\(829\) | − | 2726.47i | − | 0.114227i | −0.998368 | − | 0.0571134i | \(-0.981810\pi\) | ||
0.998368 | − | 0.0571134i | \(-0.0181897\pi\) | |||||||
\(830\) | −3626.41 | − | 2596.76i | −0.151656 | − | 0.108596i | ||||
\(831\) | −25356.6 | −1.05850 | ||||||||
\(832\) | −12872.2 | + | 19351.2i | −0.536375 | + | 0.806348i | ||||
\(833\) | −19478.1 | − | 12471.8i | −0.810175 | − | 0.518753i | ||||
\(834\) | 4372.32 | − | 6106.01i | 0.181536 | − | 0.253518i | ||||
\(835\) | − | 21832.6i | − | 0.904850i | ||||||
\(836\) | 32531.0 | − | 11067.8i | 1.34582 | − | 0.457880i | ||||
\(837\) | 489.445i | 0.0202123i | ||||||||
\(838\) | −12456.1 | + | 17395.1i | −0.513470 | + | 0.717069i | ||||
\(839\) | 734.014i | 0.0302038i | 0.999886 | + | 0.0151019i | \(0.00480727\pi\) | ||||
−0.999886 | + | 0.0151019i | \(0.995193\pi\) | |||||||
\(840\) | −523.570 | + | 1732.43i | −0.0215058 | + | 0.0711601i | ||||
\(841\) | 20419.5 | 0.837242 | ||||||||
\(842\) | −5084.49 | − | 3640.84i | −0.208103 | − | 0.149016i | ||||
\(843\) | 30217.0 | 1.23455 | ||||||||
\(844\) | 7625.66 | + | 22413.7i | 0.311003 | + | 0.914113i | ||||
\(845\) | 762.041 | 0.0310237 | ||||||||
\(846\) | 3351.76 | − | 4680.78i | 0.136213 | − | 0.190223i | ||||
\(847\) | − | 4310.61i | − | 0.174869i | ||||||
\(848\) | −3193.24 | − | 4149.64i | −0.129312 | − | 0.168042i | ||||
\(849\) | −6635.80 | −0.268245 | ||||||||
\(850\) | −17271.9 | + | 6895.48i | −0.696966 | + | 0.278251i | ||||
\(851\) | 62834.2i | 2.53106i | ||||||||
\(852\) | 20439.2 | − | 6953.90i | 0.821873 | − | 0.279621i | ||||
\(853\) | 44819.1 | 1.79904 | 0.899518 | − | 0.436883i | \(-0.143918\pi\) | ||||
0.899518 | + | 0.436883i | \(0.143918\pi\) | |||||||
\(854\) | −2522.31 | − | 1806.15i | −0.101068 | − | 0.0723714i | ||||
\(855\) | − | 5373.13i | − | 0.214921i | ||||||
\(856\) | 4140.11 | + | 1251.21i | 0.165311 | + | 0.0499598i | ||||
\(857\) | 24869.7i | 0.991288i | 0.868526 | + | 0.495644i | \(0.165068\pi\) | ||||
−0.868526 | + | 0.495644i | \(0.834932\pi\) | |||||||
\(858\) | 20815.0 | + | 14905.0i | 0.828220 | + | 0.593062i | ||||
\(859\) | − | 32702.9i | − | 1.29896i | −0.760378 | − | 0.649481i | \(-0.774986\pi\) | ||
0.760378 | − | 0.649481i | \(-0.225014\pi\) | |||||||
\(860\) | 19656.9 | − | 6687.74i | 0.779413 | − | 0.265175i | ||||
\(861\) | −5904.38 | −0.233706 | ||||||||
\(862\) | −3189.66 | − | 2284.01i | −0.126033 | − | 0.0902480i | ||||
\(863\) | 28968.1 | 1.14263 | 0.571313 | − | 0.820733i | \(-0.306434\pi\) | ||||
0.571313 | + | 0.820733i | \(0.306434\pi\) | |||||||
\(864\) | −946.395 | − | 27461.6i | −0.0372651 | − | 1.08132i | ||||
\(865\) | 6278.15 | 0.246778 | ||||||||
\(866\) | −6260.47 | + | 8742.84i | −0.245657 | + | 0.343064i | ||||
\(867\) | −8157.61 | − | 17705.5i | −0.319547 | − | 0.693553i | ||||
\(868\) | −29.9864 | − | 88.1375i | −0.00117259 | − | 0.00344652i | ||||
\(869\) | − | 40630.3i | − | 1.58606i | ||||||
\(870\) | −7724.79 | + | 10787.8i | −0.301029 | + | 0.420391i | ||||
\(871\) | −139.185 | −0.00541458 | ||||||||
\(872\) | −9936.28 | − | 3002.92i | −0.385877 | − | 0.116619i | ||||
\(873\) | − | 10741.8i | − | 0.416442i | ||||||
\(874\) | 24876.2 | − | 34740.0i | 0.962759 | − | 1.34451i | ||||
\(875\) | 4410.60i | 0.170406i | ||||||||
\(876\) | 5612.83 | − | 1909.62i | 0.216484 | − | 0.0736530i | ||||
\(877\) | −43317.7 | −1.66789 | −0.833943 | − | 0.551851i | \(-0.813922\pi\) | ||||
−0.833943 | + | 0.551851i | \(0.813922\pi\) | |||||||
\(878\) | 10933.3 | + | 7829.01i | 0.420253 | + | 0.300930i | ||||
\(879\) | 7074.91i | 0.271480i | ||||||||
\(880\) | −14235.6 | + | 10954.6i | −0.545320 | + | 0.419635i | ||||
\(881\) | 38749.8i | 1.48185i | 0.671585 | + | 0.740927i | \(0.265614\pi\) | ||||
−0.671585 | + | 0.740927i | \(0.734386\pi\) | |||||||
\(882\) | 6115.95 | − | 8541.02i | 0.233486 | − | 0.326067i | ||||
\(883\) | − | 15267.3i | − | 0.581865i | −0.956744 | − | 0.290932i | \(-0.906035\pi\) | ||
0.956744 | − | 0.290932i | \(-0.0939654\pi\) | |||||||
\(884\) | −24714.8 | − | 6089.66i | −0.940326 | − | 0.231694i | ||||
\(885\) | − | 6584.57i | − | 0.250099i | ||||||
\(886\) | −28391.8 | − | 20330.5i | −1.07657 | − | 0.770898i | ||||
\(887\) | 23837.0i | 0.902330i | 0.892440 | + | 0.451165i | \(0.148991\pi\) | ||||
−0.892440 | + | 0.451165i | \(0.851009\pi\) | |||||||
\(888\) | −30554.6 | − | 9234.12i | −1.15467 | − | 0.348960i | ||||
\(889\) | − | 6857.90i | − | 0.258725i | ||||||
\(890\) | 10276.7 | − | 14351.6i | 0.387053 | − | 0.540525i | ||||
\(891\) | −14995.9 | −0.563841 | ||||||||
\(892\) | −4680.95 | − | 13758.5i | −0.175706 | − | 0.516443i | ||||
\(893\) | 15456.8i | 0.579217i | ||||||||
\(894\) | 12071.4 | + | 8643.93i | 0.451597 | + | 0.323374i | ||||
\(895\) | − | 575.445i | − | 0.0214916i | ||||||
\(896\) | 1852.89 | + | 4887.19i | 0.0690856 | + | 0.182221i | ||||
\(897\) | 31834.2 | 1.18497 | ||||||||
\(898\) | 21328.5 | + | 15272.6i | 0.792583 | + | 0.567544i | ||||
\(899\) | − | 682.537i | − | 0.0253213i | ||||||
\(900\) | −2720.67 | − | 7996.70i | −0.100765 | − | 0.296174i | ||||
\(901\) | 3092.24 | − | 4829.38i | 0.114337 | − | 0.178568i | ||||
\(902\) | −47645.8 | − | 34117.7i | −1.75879 | − | 1.25942i | ||||
\(903\) | −6655.06 | −0.245256 | ||||||||
\(904\) | −7461.78 | + | 24690.1i | −0.274530 | + | 0.908386i | ||||
\(905\) | 12924.0 | 0.474705 | ||||||||
\(906\) | 1741.70 | − | 2432.32i | 0.0638678 | − | 0.0891924i | ||||
\(907\) | −8219.18 | −0.300897 | −0.150448 | − | 0.988618i | \(-0.548072\pi\) | ||||
−0.150448 | + | 0.988618i | \(0.548072\pi\) | |||||||
\(908\) | −9649.47 | − | 28362.2i | −0.352675 | − | 1.03660i | ||||
\(909\) | 18039.5i | 0.658231i | ||||||||
\(910\) | −1506.76 | + | 2104.21i | −0.0548886 | + | 0.0766528i | ||||
\(911\) | 2137.80i | 0.0777480i | 0.999244 | + | 0.0388740i | \(0.0123771\pi\) | ||||
−0.999244 | + | 0.0388740i | \(0.987623\pi\) | |||||||
\(912\) | 13237.3 | + | 17202.0i | 0.480626 | + | 0.624579i | ||||
\(913\) | 14188.9i | 0.514331i | ||||||||
\(914\) | 10057.9 | − | 14046.0i | 0.363989 | − | 0.508317i | ||||
\(915\) | 6734.74 | 0.243327 | ||||||||
\(916\) | 22970.1 | − | 7814.97i | 0.828552 | − | 0.281893i | ||||
\(917\) | 3074.03i | 0.110702i | ||||||||
\(918\) | 27948.8 | − | 11158.0i | 1.00484 | − | 0.401165i | ||||
\(919\) | 4777.02 | 0.171468 | 0.0857341 | − | 0.996318i | \(-0.472676\pi\) | ||||
0.0857341 | + | 0.996318i | \(0.472676\pi\) | |||||||
\(920\) | −6461.64 | + | 21380.8i | −0.231559 | + | 0.766199i | ||||
\(921\) | − | 31531.4i | − | 1.12811i | ||||||
\(922\) | 44881.1 | + | 32138.0i | 1.60313 | + | 1.14795i | ||||
\(923\) | 30873.6 | 1.10099 | ||||||||
\(924\) | 5450.52 | − | 1854.39i | 0.194057 | − | 0.0660228i | ||||
\(925\) | −33349.8 | −1.18544 | ||||||||
\(926\) | −929.974 | + | 1298.72i | −0.0330031 | + | 0.0460893i | ||||
\(927\) | 3293.58 | 0.116694 | ||||||||
\(928\) | 1319.76 | + | 38295.5i | 0.0466845 | + | 1.35464i | ||||
\(929\) | − | 2478.09i | − | 0.0875173i | −0.999042 | − | 0.0437586i | \(-0.986067\pi\) | ||
0.999042 | − | 0.0437586i | \(-0.0139333\pi\) | |||||||
\(930\) | 164.323 | + | 117.666i | 0.00579394 | + | 0.00414885i | ||||
\(931\) | 28203.9i | 0.992854i | ||||||||
\(932\) | −15832.2 | + | 5386.48i | −0.556439 | + | 0.189313i | ||||
\(933\) | 39549.3i | 1.38777i | ||||||||
\(934\) | −9759.43 | − | 6988.42i | −0.341904 | − | 0.244827i | ||||
\(935\) | −16567.4 | − | 10608.1i | −0.579480 | − | 0.371039i | ||||
\(936\) | 3344.54 | − | 11066.7i | 0.116795 | − | 0.386459i | ||||
\(937\) | −43983.1 | −1.53348 | −0.766738 | − | 0.641960i | \(-0.778121\pi\) | ||||
−0.766738 | + | 0.641960i | \(0.778121\pi\) | |||||||
\(938\) | −18.2231 | + | 25.4489i | −0.000634335 | + | 0.000885859i | ||||
\(939\) | − | 35133.6i | − | 1.22102i | ||||||
\(940\) | −2602.48 | − | 7649.32i | −0.0903016 | − | 0.265418i | ||||
\(941\) | 44283.1 | 1.53410 | 0.767051 | − | 0.641587i | \(-0.221723\pi\) | ||||
0.767051 | + | 0.641587i | \(0.221723\pi\) | |||||||
\(942\) | −3851.44 | − | 2757.90i | −0.133213 | − | 0.0953897i | ||||
\(943\) | −72868.9 | −2.51637 | ||||||||
\(944\) | −11596.9 | − | 15070.3i | −0.399839 | − | 0.519595i | ||||
\(945\) | − | 3059.81i | − | 0.105329i | ||||||
\(946\) | −53703.5 | − | 38455.3i | −1.84572 | − | 1.32166i | ||||
\(947\) | 38659.4 | 1.32657 | 0.663285 | − | 0.748367i | \(-0.269162\pi\) | ||||
0.663285 | + | 0.748367i | \(0.269162\pi\) | |||||||
\(948\) | 24297.3 | − | 8266.52i | 0.832426 | − | 0.283211i | ||||
\(949\) | 8478.23 | 0.290005 | ||||||||
\(950\) | 18438.5 | + | 13203.3i | 0.629711 | + | 0.450916i | ||||
\(951\) | 35412.7 | 1.20750 | ||||||||
\(952\) | −4349.30 | + | 3721.61i | −0.148069 | + | 0.126700i | ||||
\(953\) | −21138.8 | −0.718524 | −0.359262 | − | 0.933237i | \(-0.616972\pi\) | ||||
−0.359262 | + | 0.933237i | \(0.616972\pi\) | |||||||
\(954\) | 2117.65 | + | 1516.38i | 0.0718674 | + | 0.0514620i | ||||
\(955\) | −27516.7 | −0.932376 | ||||||||
\(956\) | 263.622 | + | 774.849i | 0.00891856 | + | 0.0262138i | ||||
\(957\) | 42208.9 | 1.42572 | ||||||||
\(958\) | −20402.3 | − | 14609.4i | −0.688066 | − | 0.492702i | ||||
\(959\) | 3762.11i | 0.126679i | ||||||||
\(960\) | −9447.27 | − | 6284.23i | −0.317614 | − | 0.211274i | ||||
\(961\) | 29780.6 | 0.999651 | ||||||||
\(962\) | −37111.7 | − | 26574.5i | −1.24379 | − | 0.890640i | ||||
\(963\) | −2151.42 | −0.0719922 | ||||||||
\(964\) | 7347.05 | − | 2499.64i | 0.245469 | − | 0.0835144i | ||||
\(965\) | − | 26944.4i | − | 0.898829i | ||||||
\(966\) | 4167.98 | − | 5820.65i | 0.138823 | − | 0.193868i | ||||
\(967\) | 15325.8 | 0.509662 | 0.254831 | − | 0.966986i | \(-0.417980\pi\) | ||||
0.254831 | + | 0.966986i | \(0.417980\pi\) | |||||||
\(968\) | 25869.4 | + | 7818.18i | 0.858961 | + | 0.259593i | ||||
\(969\) | −12818.6 | + | 20019.8i | −0.424968 | + | 0.663704i | ||||
\(970\) | −12257.3 | − | 8777.09i | −0.405731 | − | 0.290531i | ||||
\(971\) | 40479.0i | 1.33783i | 0.743338 | + | 0.668915i | \(0.233241\pi\) | ||||
−0.743338 | + | 0.668915i | \(0.766759\pi\) | |||||||
\(972\) | 7509.66 | + | 22072.7i | 0.247811 | + | 0.728378i | ||||
\(973\) | − | 2415.14i | − | 0.0795743i | ||||||
\(974\) | −1463.71 | − | 1048.11i | −0.0481521 | − | 0.0344802i | ||||
\(975\) | 16896.3i | 0.554988i | ||||||||
\(976\) | 15414.0 | − | 11861.4i | 0.505524 | − | 0.389011i | ||||
\(977\) | 11827.3 | 0.387296 | 0.193648 | − | 0.981071i | \(-0.437968\pi\) | ||||
0.193648 | + | 0.981071i | \(0.437968\pi\) | |||||||
\(978\) | 21794.5 | − | 30436.4i | 0.712589 | − | 0.995141i | ||||
\(979\) | −56152.9 | −1.83315 | ||||||||
\(980\) | −4748.74 | − | 13957.7i | −0.154789 | − | 0.454962i | ||||
\(981\) | 5163.42 | 0.168048 | ||||||||
\(982\) | −8840.06 | − | 6330.08i | −0.287268 | − | 0.205704i | ||||
\(983\) | − | 20465.6i | − | 0.664040i | −0.943272 | − | 0.332020i | \(-0.892270\pi\) | ||
0.943272 | − | 0.332020i | \(-0.107730\pi\) | |||||||
\(984\) | 10708.8 | − | 35434.2i | 0.346936 | − | 1.14797i | ||||
\(985\) | 244.490 | 0.00790872 | ||||||||
\(986\) | −38974.9 | + | 15560.0i | −1.25884 | + | 0.502567i | ||||
\(987\) | 2589.76i | 0.0835187i | ||||||||
\(988\) | 9997.54 | + | 29385.2i | 0.321927 | + | 0.946223i | ||||
\(989\) | −82133.4 | −2.64074 | ||||||||
\(990\) | 5202.03 | − | 7264.72i | 0.167002 | − | 0.233220i | ||||
\(991\) | − | 25049.8i | − | 0.802961i | −0.915868 | − | 0.401480i | \(-0.868496\pi\) | ||
0.915868 | − | 0.401480i | \(-0.131504\pi\) | |||||||
\(992\) | 583.329 | − | 20.1030i | 0.0186701 | − | 0.000643418i | ||||
\(993\) | 808.554i | 0.0258396i | ||||||||
\(994\) | 4042.21 | − | 5645.01i | 0.128985 | − | 0.180129i | ||||
\(995\) | 19612.0i | 0.624867i | ||||||||
\(996\) | −8485.11 | + | 2886.83i | −0.269941 | + | 0.0918401i | ||||
\(997\) | −9705.23 | −0.308292 | −0.154146 | − | 0.988048i | \(-0.549263\pi\) | ||||
−0.154146 | + | 0.988048i | \(0.549263\pi\) | |||||||
\(998\) | −15292.6 | + | 21356.3i | −0.485048 | + | 0.677377i | ||||
\(999\) | 53965.4 | 1.70910 |
(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 | 136.4.h.a.101.19 | yes | 52 | |
4.3 | odd | 2 | 544.4.h.a.305.38 | 52 | |||
8.3 | odd | 2 | 544.4.h.a.305.16 | 52 | |||
8.5 | even | 2 | inner | 136.4.h.a.101.18 | yes | 52 | |
17.16 | even | 2 | inner | 136.4.h.a.101.20 | yes | 52 | |
68.67 | odd | 2 | 544.4.h.a.305.15 | 52 | |||
136.67 | odd | 2 | 544.4.h.a.305.37 | 52 | |||
136.101 | even | 2 | inner | 136.4.h.a.101.17 | ✓ | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
136.4.h.a.101.17 | ✓ | 52 | 136.101 | even | 2 | inner | |
136.4.h.a.101.18 | yes | 52 | 8.5 | even | 2 | inner | |
136.4.h.a.101.19 | yes | 52 | 1.1 | even | 1 | trivial | |
136.4.h.a.101.20 | yes | 52 | 17.16 | even | 2 | inner | |
544.4.h.a.305.15 | 52 | 68.67 | odd | 2 | |||
544.4.h.a.305.16 | 52 | 8.3 | odd | 2 | |||
544.4.h.a.305.37 | 52 | 136.67 | odd | 2 | |||
544.4.h.a.305.38 | 52 | 4.3 | odd | 2 |