Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(76,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.76");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 151.1 | ||
Character | \(\chi\) | \(=\) | 225.151 |
Dual form | 225.4.e.f.76.1 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.42567 | + | 4.20138i | −0.857603 | + | 1.48541i | 0.0166066 | + | 0.999862i | \(0.494714\pi\) |
−0.874209 | + | 0.485549i | \(0.838620\pi\) | |||||||
\(3\) | 4.79753 | + | 1.99591i | 0.923286 | + | 0.384113i | ||||
\(4\) | −7.76772 | − | 13.4541i | −0.970965 | − | 1.68176i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −20.0228 | + | 15.3148i | −1.36238 | + | 1.04204i | ||||
\(7\) | 8.11924 | − | 14.0629i | 0.438398 | − | 0.759327i | −0.559169 | − | 0.829054i | \(-0.688880\pi\) |
0.997566 | + | 0.0697271i | \(0.0222129\pi\) | |||||||
\(8\) | 36.5569 | 1.61560 | ||||||||
\(9\) | 19.0327 | + | 19.1509i | 0.704914 | + | 0.709293i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −29.7592 | + | 51.5445i | −0.815704 | + | 1.41284i | 0.0931172 | + | 0.995655i | \(0.470317\pi\) |
−0.908821 | + | 0.417186i | \(0.863016\pi\) | |||||||
\(12\) | −10.4127 | − | 80.0501i | −0.250491 | − | 1.92571i | ||||
\(13\) | 13.5395 | + | 23.4511i | 0.288860 | + | 0.500321i | 0.973538 | − | 0.228525i | \(-0.0733903\pi\) |
−0.684678 | + | 0.728846i | \(0.740057\pi\) | |||||||
\(14\) | 39.3891 | + | 68.2240i | 0.751942 | + | 1.30240i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −26.5331 | + | 45.9567i | −0.414580 | + | 0.718074i | ||||
\(17\) | −78.9077 | −1.12576 | −0.562880 | − | 0.826538i | \(-0.690307\pi\) | ||||
−0.562880 | + | 0.826538i | \(0.690307\pi\) | |||||||
\(18\) | −126.627 | + | 33.5097i | −1.65813 | + | 0.438796i | ||||
\(19\) | −142.290 | −1.71809 | −0.859044 | − | 0.511902i | \(-0.828941\pi\) | ||||
−0.859044 | + | 0.511902i | \(0.828941\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 67.0207 | − | 51.2621i | 0.696434 | − | 0.532681i | ||||
\(22\) | −144.372 | − | 250.060i | −1.39910 | − | 2.42331i | ||||
\(23\) | 42.8140 | + | 74.1561i | 0.388145 | + | 0.672288i | 0.992200 | − | 0.124655i | \(-0.0397825\pi\) |
−0.604055 | + | 0.796943i | \(0.706449\pi\) | |||||||
\(24\) | 175.383 | + | 72.9643i | 1.49166 | + | 0.620574i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −131.369 | −0.990910 | ||||||||
\(27\) | 53.0864 | + | 129.865i | 0.378388 | + | 0.925647i | ||||
\(28\) | −252.272 | −1.70267 | ||||||||
\(29\) | −113.004 | + | 195.729i | −0.723600 | + | 1.25331i | 0.235948 | + | 0.971766i | \(0.424180\pi\) |
−0.959548 | + | 0.281546i | \(0.909153\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 75.3561 | + | 130.521i | 0.436592 | + | 0.756200i | 0.997424 | − | 0.0717300i | \(-0.0228520\pi\) |
−0.560832 | + | 0.827930i | \(0.689519\pi\) | |||||||
\(32\) | 17.5066 | + | 30.3223i | 0.0967112 | + | 0.167509i | ||||
\(33\) | −245.649 | + | 187.890i | −1.29582 | + | 0.991133i | ||||
\(34\) | 191.404 | − | 331.521i | 0.965455 | − | 1.67222i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 109.817 | − | 404.826i | 0.508414 | − | 1.87419i | ||||
\(37\) | −234.171 | −1.04047 | −0.520237 | − | 0.854022i | \(-0.674156\pi\) | ||||
−0.520237 | + | 0.854022i | \(0.674156\pi\) | |||||||
\(38\) | 345.149 | − | 597.816i | 1.47344 | − | 2.55207i | ||||
\(39\) | 18.1499 | + | 139.531i | 0.0745208 | + | 0.572894i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −36.9290 | − | 63.9629i | −0.140667 | − | 0.243642i | 0.787081 | − | 0.616850i | \(-0.211591\pi\) |
−0.927748 | + | 0.373207i | \(0.878258\pi\) | |||||||
\(42\) | 52.8017 | + | 405.924i | 0.193988 | + | 1.49132i | ||||
\(43\) | 133.539 | − | 231.296i | 0.473592 | − | 0.820285i | −0.525951 | − | 0.850515i | \(-0.676290\pi\) |
0.999543 | + | 0.0302295i | \(0.00962383\pi\) | |||||||
\(44\) | 924.645 | 3.16808 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −415.410 | −1.33150 | ||||||||
\(47\) | 133.013 | − | 230.385i | 0.412806 | − | 0.715001i | −0.582389 | − | 0.812910i | \(-0.697882\pi\) |
0.995195 | + | 0.0979088i | \(0.0312154\pi\) | |||||||
\(48\) | −219.019 | + | 167.521i | −0.658598 | + | 0.503742i | ||||
\(49\) | 39.6560 | + | 68.6862i | 0.115615 | + | 0.200251i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −378.563 | − | 157.493i | −1.03940 | − | 0.432420i | ||||
\(52\) | 210.342 | − | 364.323i | 0.560946 | − | 0.971588i | ||||
\(53\) | 603.281 | 1.56353 | 0.781765 | − | 0.623574i | \(-0.214320\pi\) | ||||
0.781765 | + | 0.623574i | \(0.214320\pi\) | |||||||
\(54\) | −674.380 | − | 91.9724i | −1.69947 | − | 0.231775i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 296.814 | − | 514.097i | 0.708276 | − | 1.22677i | ||||
\(57\) | −682.643 | − | 283.999i | −1.58629 | − | 0.659940i | ||||
\(58\) | −548.222 | − | 949.548i | −1.24112 | − | 2.14969i | ||||
\(59\) | −254.360 | − | 440.565i | −0.561270 | − | 0.972148i | −0.997386 | − | 0.0722573i | \(-0.976980\pi\) |
0.436116 | − | 0.899890i | \(-0.356354\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −39.1519 | + | 67.8131i | −0.0821786 | + | 0.142337i | −0.904185 | − | 0.427140i | \(-0.859521\pi\) |
0.822007 | + | 0.569478i | \(0.192854\pi\) | |||||||
\(62\) | −731.155 | −1.49769 | ||||||||
\(63\) | 423.849 | − | 112.164i | 0.847618 | − | 0.224308i | ||||
\(64\) | −594.391 | −1.16092 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −193.533 | − | 1487.82i | −0.360943 | − | 2.77482i | ||||
\(67\) | 244.101 | + | 422.796i | 0.445101 | + | 0.770937i | 0.998059 | − | 0.0622718i | \(-0.0198346\pi\) |
−0.552959 | + | 0.833209i | \(0.686501\pi\) | |||||||
\(68\) | 612.933 | + | 1061.63i | 1.09307 | + | 1.89326i | ||||
\(69\) | 57.3928 | + | 441.219i | 0.100135 | + | 0.769805i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −73.2487 | −0.122437 | −0.0612184 | − | 0.998124i | \(-0.519499\pi\) | ||||
−0.0612184 | + | 0.998124i | \(0.519499\pi\) | |||||||
\(72\) | 695.776 | + | 700.098i | 1.13886 | + | 1.14594i | ||||
\(73\) | −115.831 | −0.185712 | −0.0928558 | − | 0.995680i | \(-0.529600\pi\) | ||||
−0.0928558 | + | 0.995680i | \(0.529600\pi\) | |||||||
\(74\) | 568.021 | − | 983.842i | 0.892313 | − | 1.54553i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1105.27 | + | 1914.39i | 1.66820 | + | 2.88941i | ||||
\(77\) | 483.244 | + | 837.004i | 0.715205 | + | 1.23877i | ||||
\(78\) | −630.249 | − | 262.202i | −0.914893 | − | 0.380622i | ||||
\(79\) | −391.371 | + | 677.875i | −0.557376 | + | 0.965404i | 0.440338 | + | 0.897832i | \(0.354859\pi\) |
−0.997714 | + | 0.0675718i | \(0.978475\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.51465 | + | 728.986i | −0.00619293 | + | 0.999981i | ||||
\(82\) | 358.310 | 0.482545 | ||||||||
\(83\) | −135.732 | + | 235.095i | −0.179501 | + | 0.310904i | −0.941710 | − | 0.336427i | \(-0.890782\pi\) |
0.762209 | + | 0.647331i | \(0.224115\pi\) | |||||||
\(84\) | −1210.28 | − | 503.512i | −1.57206 | − | 0.654020i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 647.840 | + | 1122.09i | 0.812307 | + | 1.40696i | ||||
\(87\) | −932.801 | + | 713.471i | −1.14950 | + | 0.879220i | ||||
\(88\) | −1087.91 | + | 1884.31i | −1.31785 | + | 2.28259i | ||||
\(89\) | 211.511 | 0.251911 | 0.125955 | − | 0.992036i | \(-0.459800\pi\) | ||||
0.125955 | + | 0.992036i | \(0.459800\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 439.722 | 0.506543 | ||||||||
\(92\) | 665.135 | − | 1152.05i | 0.753751 | − | 1.30553i | ||||
\(93\) | 101.016 | + | 776.581i | 0.112633 | + | 0.865889i | ||||
\(94\) | 645.289 | + | 1117.67i | 0.708047 | + | 1.22637i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 23.4678 | + | 180.414i | 0.0249498 | + | 0.191806i | ||||
\(97\) | 833.050 | − | 1442.89i | 0.871994 | − | 1.51034i | 0.0120642 | − | 0.999927i | \(-0.496160\pi\) |
0.859930 | − | 0.510411i | \(-0.170507\pi\) | |||||||
\(98\) | −384.769 | −0.396607 | ||||||||
\(99\) | −1553.52 | + | 411.113i | −1.57712 | + | 0.417358i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 228.292 | − | 395.413i | 0.224910 | − | 0.389555i | −0.731383 | − | 0.681967i | \(-0.761125\pi\) |
0.956292 | + | 0.292412i | \(0.0944580\pi\) | |||||||
\(102\) | 1579.95 | − | 1208.46i | 1.53371 | − | 1.17309i | ||||
\(103\) | 82.9660 | + | 143.701i | 0.0793678 | + | 0.137469i | 0.902977 | − | 0.429688i | \(-0.141377\pi\) |
−0.823610 | + | 0.567157i | \(0.808043\pi\) | |||||||
\(104\) | 494.963 | + | 857.300i | 0.466683 | + | 0.808319i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1463.36 | + | 2534.61i | −1.34089 | + | 2.32248i | ||||
\(107\) | −452.071 | −0.408443 | −0.204221 | − | 0.978925i | \(-0.565466\pi\) | ||||
−0.204221 | + | 0.978925i | \(0.565466\pi\) | |||||||
\(108\) | 1334.85 | − | 1722.98i | 1.18931 | − | 1.53513i | ||||
\(109\) | −463.243 | −0.407070 | −0.203535 | − | 0.979068i | \(-0.565243\pi\) | ||||
−0.203535 | + | 0.979068i | \(0.565243\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1123.44 | − | 467.385i | −0.960655 | − | 0.399660i | ||||
\(112\) | 430.857 | + | 746.267i | 0.363502 | + | 0.629604i | ||||
\(113\) | 475.041 | + | 822.795i | 0.395470 | + | 0.684974i | 0.993161 | − | 0.116753i | \(-0.0372485\pi\) |
−0.597691 | + | 0.801726i | \(0.703915\pi\) | |||||||
\(114\) | 2849.05 | − | 2179.15i | 2.34069 | − | 1.79032i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3511.14 | 2.81036 | ||||||||
\(117\) | −191.417 | + | 705.632i | −0.151252 | + | 0.557570i | ||||
\(118\) | 2467.97 | 1.92539 | ||||||||
\(119\) | −640.670 | + | 1109.67i | −0.493531 | + | 0.854820i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1105.72 | − | 1915.17i | −0.830746 | − | 1.43889i | ||||
\(122\) | −189.939 | − | 328.984i | −0.140953 | − | 0.244138i | ||||
\(123\) | −49.5038 | − | 380.571i | −0.0362895 | − | 0.278983i | ||||
\(124\) | 1170.69 | − | 2027.69i | 0.847831 | − | 1.46849i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −556.871 | + | 2052.82i | −0.393730 | + | 1.45143i | ||||
\(127\) | −210.383 | −0.146996 | −0.0734979 | − | 0.997295i | \(-0.523416\pi\) | ||||
−0.0734979 | + | 0.997295i | \(0.523416\pi\) | |||||||
\(128\) | 1301.74 | − | 2254.68i | 0.898896 | − | 1.55693i | ||||
\(129\) | 1102.30 | − | 843.118i | 0.752343 | − | 0.575445i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 462.388 | + | 800.879i | 0.308389 | + | 0.534146i | 0.978010 | − | 0.208557i | \(-0.0668767\pi\) |
−0.669621 | + | 0.742703i | \(0.733543\pi\) | |||||||
\(132\) | 4436.02 | + | 1845.51i | 2.92504 | + | 1.21690i | ||||
\(133\) | −1155.29 | + | 2001.02i | −0.753205 | + | 1.30459i | ||||
\(134\) | −2368.44 | −1.52688 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2884.62 | −1.81878 | ||||||||
\(137\) | −968.837 | + | 1678.07i | −0.604185 | + | 1.04648i | 0.387995 | + | 0.921661i | \(0.373168\pi\) |
−0.992180 | + | 0.124817i | \(0.960166\pi\) | |||||||
\(138\) | −1992.95 | − | 829.122i | −1.22935 | − | 0.511446i | ||||
\(139\) | 985.256 | + | 1706.51i | 0.601211 | + | 1.04133i | 0.992638 | + | 0.121119i | \(0.0386481\pi\) |
−0.391427 | + | 0.920209i | \(0.628019\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1097.96 | − | 839.797i | 0.655780 | − | 0.501586i | ||||
\(142\) | 177.677 | − | 307.745i | 0.105002 | − | 0.181869i | ||||
\(143\) | −1611.70 | −0.942498 | ||||||||
\(144\) | −1385.11 | + | 366.546i | −0.801568 | + | 0.212121i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 280.966 | − | 486.648i | 0.159267 | − | 0.275858i | ||||
\(147\) | 53.1594 | + | 408.674i | 0.0298266 | + | 0.229298i | ||||
\(148\) | 1818.98 | + | 3150.56i | 1.01026 | + | 1.74983i | ||||
\(149\) | −798.166 | − | 1382.46i | −0.438848 | − | 0.760106i | 0.558753 | − | 0.829334i | \(-0.311280\pi\) |
−0.997601 | + | 0.0692276i | \(0.977947\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1836.48 | − | 3180.88i | 0.989741 | − | 1.71428i | 0.371141 | − | 0.928576i | \(-0.378967\pi\) |
0.618600 | − | 0.785706i | \(-0.287700\pi\) | |||||||
\(152\) | −5201.70 | −2.77575 | ||||||||
\(153\) | −1501.82 | − | 1511.15i | −0.793564 | − | 0.798494i | ||||
\(154\) | −4688.76 | −2.45345 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1736.28 | − | 1328.03i | 0.891114 | − | 0.681586i | ||||
\(157\) | 525.779 | + | 910.676i | 0.267272 | + | 0.462929i | 0.968156 | − | 0.250346i | \(-0.0805444\pi\) |
−0.700884 | + | 0.713275i | \(0.747211\pi\) | |||||||
\(158\) | −1898.67 | − | 3288.60i | −0.956014 | − | 1.65587i | ||||
\(159\) | 2894.26 | + | 1204.10i | 1.44358 | + | 0.600573i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1390.47 | 0.680648 | ||||||||
\(162\) | −3051.79 | − | 1787.24i | −1.48007 | − | 0.866785i | ||||
\(163\) | 1998.77 | 0.960463 | 0.480232 | − | 0.877142i | \(-0.340553\pi\) | ||||
0.480232 | + | 0.877142i | \(0.340553\pi\) | |||||||
\(164\) | −573.708 | + | 993.691i | −0.273165 | + | 0.473136i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −658.483 | − | 1140.53i | −0.307881 | − | 0.533265i | ||||
\(167\) | 1240.51 | + | 2148.63i | 0.574813 | + | 0.995606i | 0.996062 | + | 0.0886604i | \(0.0282586\pi\) |
−0.421249 | + | 0.906945i | \(0.638408\pi\) | |||||||
\(168\) | 2450.07 | − | 1873.98i | 1.12516 | − | 0.860601i | ||||
\(169\) | 731.863 | − | 1267.62i | 0.333119 | − | 0.576980i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2708.17 | − | 2724.99i | −1.21110 | − | 1.21863i | ||||
\(172\) | −4149.16 | −1.83936 | ||||||||
\(173\) | −1313.04 | + | 2274.25i | −0.577042 | + | 0.999466i | 0.418774 | + | 0.908090i | \(0.362460\pi\) |
−0.995816 | + | 0.0913761i | \(0.970873\pi\) | |||||||
\(174\) | −734.899 | − | 5649.69i | −0.320187 | − | 2.46151i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1579.21 | − | 2735.27i | −0.676349 | − | 1.17147i | ||||
\(177\) | −340.974 | − | 2621.31i | −0.144798 | − | 1.11316i | ||||
\(178\) | −513.054 | + | 888.636i | −0.216039 | + | 0.374191i | ||||
\(179\) | −3231.72 | −1.34944 | −0.674720 | − | 0.738074i | \(-0.735736\pi\) | ||||
−0.674720 | + | 0.738074i | \(0.735736\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 337.854 | 0.138743 | 0.0693714 | − | 0.997591i | \(-0.477901\pi\) | ||||
0.0693714 | + | 0.997591i | \(0.477901\pi\) | |||||||
\(182\) | −1066.62 | + | 1847.44i | −0.434412 | + | 0.752424i | ||||
\(183\) | −323.182 | + | 247.192i | −0.130548 | + | 0.0998523i | ||||
\(184\) | 1565.15 | + | 2710.92i | 0.627088 | + | 1.08615i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3507.74 | − | 1459.32i | −1.38280 | − | 0.575283i | ||||
\(187\) | 2348.23 | − | 4067.26i | 0.918288 | − | 1.59052i | ||||
\(188\) | −4132.82 | −1.60328 | ||||||||
\(189\) | 2257.30 | + | 307.852i | 0.868753 | + | 0.118481i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −505.253 | + | 875.124i | −0.191407 | + | 0.331527i | −0.945717 | − | 0.324992i | \(-0.894639\pi\) |
0.754309 | + | 0.656519i | \(0.227972\pi\) | |||||||
\(192\) | −2851.61 | − | 1186.35i | −1.07186 | − | 0.445925i | ||||
\(193\) | −746.079 | − | 1292.25i | −0.278259 | − | 0.481958i | 0.692693 | − | 0.721232i | \(-0.256424\pi\) |
−0.970952 | + | 0.239274i | \(0.923091\pi\) | |||||||
\(194\) | 4041.41 | + | 6999.92i | 1.49565 | + | 2.59054i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 616.073 | − | 1067.07i | 0.224516 | − | 0.388874i | ||||
\(197\) | 3313.50 | 1.19836 | 0.599181 | − | 0.800613i | \(-0.295493\pi\) | ||||
0.599181 | + | 0.800613i | \(0.295493\pi\) | |||||||
\(198\) | 2041.08 | − | 7524.15i | 0.732593 | − | 2.70060i | ||||
\(199\) | 2165.17 | 0.771279 | 0.385640 | − | 0.922649i | \(-0.373981\pi\) | ||||
0.385640 | + | 0.922649i | \(0.373981\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 327.222 | + | 2515.58i | 0.114828 | + | 0.882764i | ||||
\(202\) | 1107.52 | + | 1918.28i | 0.385766 | + | 0.668167i | ||||
\(203\) | 1835.02 | + | 3178.35i | 0.634449 | + | 1.09890i | ||||
\(204\) | 821.645 | + | 6316.57i | 0.281993 | + | 2.16788i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −804.991 | −0.272264 | ||||||||
\(207\) | −605.291 | + | 2231.32i | −0.203240 | + | 0.749214i | ||||
\(208\) | −1436.98 | −0.479023 | ||||||||
\(209\) | 4234.45 | − | 7334.29i | 1.40145 | − | 2.42738i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1279.85 | + | 2216.77i | 0.417576 | + | 0.723263i | 0.995695 | − | 0.0926897i | \(-0.0295464\pi\) |
−0.578119 | + | 0.815952i | \(0.696213\pi\) | |||||||
\(212\) | −4686.12 | − | 8116.59i | −1.51813 | − | 2.62948i | ||||
\(213\) | −351.413 | − | 146.198i | −0.113044 | − | 0.0470296i | ||||
\(214\) | 1096.57 | − | 1899.32i | 0.350282 | − | 0.606706i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1940.67 | + | 4747.45i | 0.611325 | + | 1.49548i | ||||
\(217\) | 2447.34 | 0.765604 | ||||||||
\(218\) | 1123.67 | − | 1946.26i | 0.349104 | − | 0.604666i | ||||
\(219\) | −555.701 | − | 231.188i | −0.171465 | − | 0.0713343i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1068.37 | − | 1850.47i | −0.325188 | − | 0.563242i | ||||
\(222\) | 4688.76 | − | 3586.30i | 1.41752 | − | 1.08422i | ||||
\(223\) | 707.218 | − | 1224.94i | 0.212371 | − | 0.367838i | −0.740085 | − | 0.672514i | \(-0.765215\pi\) |
0.952456 | + | 0.304675i | \(0.0985480\pi\) | |||||||
\(224\) | 568.561 | 0.169592 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4609.16 | −1.35662 | ||||||||
\(227\) | 813.532 | − | 1409.08i | 0.237868 | − | 0.411999i | −0.722234 | − | 0.691648i | \(-0.756885\pi\) |
0.960102 | + | 0.279649i | \(0.0902181\pi\) | |||||||
\(228\) | 1481.63 | + | 11390.4i | 0.430366 | + | 3.30853i | ||||
\(229\) | 3309.78 | + | 5732.71i | 0.955093 | + | 1.65427i | 0.734154 | + | 0.678983i | \(0.237579\pi\) |
0.220939 | + | 0.975288i | \(0.429088\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 647.796 | + | 4980.07i | 0.184510 | + | 1.41846i | ||||
\(232\) | −4131.09 | + | 7155.26i | −1.16905 | + | 2.02485i | ||||
\(233\) | 1911.28 | 0.537390 | 0.268695 | − | 0.963225i | \(-0.413408\pi\) | ||||
0.268695 | + | 0.963225i | \(0.413408\pi\) | |||||||
\(234\) | −2500.31 | − | 2515.84i | −0.698506 | − | 0.702845i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3951.60 | + | 6844.37i | −1.08995 | + | 1.88784i | ||||
\(237\) | −3230.60 | + | 2470.99i | −0.885442 | + | 0.677248i | ||||
\(238\) | −3108.11 | − | 5383.40i | −0.846507 | − | 1.46619i | ||||
\(239\) | −1443.35 | − | 2499.95i | −0.390637 | − | 0.676603i | 0.601897 | − | 0.798574i | \(-0.294412\pi\) |
−0.992534 | + | 0.121971i | \(0.961079\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 644.326 | − | 1116.01i | 0.172219 | − | 0.298291i | −0.766977 | − | 0.641675i | \(-0.778240\pi\) |
0.939195 | + | 0.343384i | \(0.111573\pi\) | |||||||
\(242\) | 10728.5 | 2.84980 | ||||||||
\(243\) | −1476.65 | + | 3488.32i | −0.389824 | + | 0.920889i | ||||
\(244\) | 1216.48 | 0.319170 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1719.00 | + | 715.154i | 0.445527 | + | 0.185352i | ||||
\(247\) | −1926.54 | − | 3336.87i | −0.496287 | − | 0.859595i | ||||
\(248\) | 2754.79 | + | 4771.43i | 0.705359 | + | 1.22172i | ||||
\(249\) | −1120.41 | + | 856.968i | −0.285153 | + | 0.218105i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4356.21 | 1.09546 | 0.547732 | − | 0.836654i | \(-0.315491\pi\) | ||||
0.547732 | + | 0.836654i | \(0.315491\pi\) | |||||||
\(252\) | −4801.41 | − | 4831.23i | −1.20024 | − | 1.20769i | ||||
\(253\) | −5096.45 | −1.26645 | ||||||||
\(254\) | 510.319 | − | 883.898i | 0.126064 | − | 0.218349i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3937.62 | + | 6820.15i | 0.961332 | + | 1.66508i | ||||
\(257\) | −1618.26 | − | 2802.91i | −0.392780 | − | 0.680314i | 0.600035 | − | 0.799973i | \(-0.295153\pi\) |
−0.992815 | + | 0.119659i | \(0.961820\pi\) | |||||||
\(258\) | 868.439 | + | 6676.31i | 0.209561 | + | 1.61104i | ||||
\(259\) | −1901.29 | + | 3293.13i | −0.456141 | + | 0.790060i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5899.17 | + | 1561.12i | −1.39904 | + | 0.370232i | ||||
\(262\) | −4486.40 | −1.05790 | ||||||||
\(263\) | −690.768 | + | 1196.44i | −0.161956 | + | 0.280517i | −0.935570 | − | 0.353141i | \(-0.885114\pi\) |
0.773614 | + | 0.633657i | \(0.218447\pi\) | |||||||
\(264\) | −8980.17 | + | 6868.67i | −2.09353 | + | 1.60128i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −5604.70 | − | 9707.62i | −1.29190 | − | 2.23764i | ||||
\(267\) | 1014.73 | + | 422.156i | 0.232586 | + | 0.0967623i | ||||
\(268\) | 3792.22 | − | 6568.32i | 0.864354 | − | 1.49710i | ||||
\(269\) | 721.063 | 0.163435 | 0.0817175 | − | 0.996656i | \(-0.473959\pi\) | ||||
0.0817175 | + | 0.996656i | \(0.473959\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3816.82 | 0.855554 | 0.427777 | − | 0.903884i | \(-0.359297\pi\) | ||||
0.427777 | + | 0.903884i | \(0.359297\pi\) | |||||||
\(272\) | 2093.67 | − | 3626.34i | 0.466718 | − | 0.808379i | ||||
\(273\) | 2109.58 | + | 877.646i | 0.467684 | + | 0.194570i | ||||
\(274\) | −4700.15 | − | 8140.90i | −1.03630 | − | 1.79493i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5490.39 | − | 4199.44i | 1.19740 | − | 0.915856i | ||||
\(277\) | 964.393 | − | 1670.38i | 0.209187 | − | 0.362322i | −0.742272 | − | 0.670099i | \(-0.766252\pi\) |
0.951459 | + | 0.307777i | \(0.0995850\pi\) | |||||||
\(278\) | −9559.61 | −2.06240 | ||||||||
\(279\) | −1065.36 | + | 3927.29i | −0.228607 | + | 0.842727i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2471.93 | + | 4281.50i | −0.524778 | + | 0.908943i | 0.474805 | + | 0.880091i | \(0.342518\pi\) |
−0.999584 | + | 0.0288518i | \(0.990815\pi\) | |||||||
\(282\) | 865.019 | + | 6650.01i | 0.182664 | + | 1.40426i | ||||
\(283\) | −3171.79 | − | 5493.70i | −0.666231 | − | 1.15395i | −0.978950 | − | 0.204100i | \(-0.934573\pi\) |
0.312719 | − | 0.949846i | \(-0.398760\pi\) | |||||||
\(284\) | 568.975 | + | 985.494i | 0.118882 | + | 0.205909i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3909.45 | − | 6771.37i | 0.808289 | − | 1.40000i | ||||
\(287\) | −1199.34 | −0.246672 | ||||||||
\(288\) | −247.503 | + | 912.382i | −0.0506397 | + | 0.186676i | ||||
\(289\) | 1313.43 | 0.267337 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6876.46 | − | 5259.60i | 1.38524 | − | 1.05953i | ||||
\(292\) | 899.739 | + | 1558.39i | 0.180319 | + | 0.312322i | ||||
\(293\) | 753.429 | + | 1304.98i | 0.150225 | + | 0.260197i | 0.931310 | − | 0.364228i | \(-0.118667\pi\) |
−0.781085 | + | 0.624424i | \(0.785334\pi\) | |||||||
\(294\) | −1845.94 | − | 767.964i | −0.366182 | − | 0.152342i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8560.58 | −1.68099 | ||||||||
\(297\) | −8273.62 | − | 1128.36i | −1.61644 | − | 0.220452i | ||||
\(298\) | 7744.34 | 1.50543 | ||||||||
\(299\) | −1159.36 | + | 2008.07i | −0.224240 | + | 0.388394i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2168.46 | − | 3755.89i | −0.415243 | − | 0.719222i | ||||
\(302\) | 8909.40 | + | 15431.5i | 1.69761 | + | 2.94035i | ||||
\(303\) | 1884.45 | − | 1441.36i | 0.357289 | − | 0.273280i | ||||
\(304\) | 3775.41 | − | 6539.20i | 0.712285 | − | 1.23371i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 9991.86 | − | 2644.18i | 1.86666 | − | 0.493979i | ||||
\(307\) | 8239.13 | 1.53170 | 0.765850 | − | 0.643019i | \(-0.222319\pi\) | ||||
0.765850 | + | 0.643019i | \(0.222319\pi\) | |||||||
\(308\) | 7507.41 | − | 13003.2i | 1.38888 | − | 2.40561i | ||||
\(309\) | 111.217 | + | 855.005i | 0.0204755 | + | 0.157409i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 402.948 | + | 697.927i | 0.0734698 | + | 0.127253i | 0.900420 | − | 0.435022i | \(-0.143259\pi\) |
−0.826950 | + | 0.562275i | \(0.809926\pi\) | |||||||
\(312\) | 663.504 | + | 5100.83i | 0.120396 | + | 0.925569i | ||||
\(313\) | −2030.70 | + | 3517.28i | −0.366716 | + | 0.635171i | −0.989050 | − | 0.147581i | \(-0.952851\pi\) |
0.622334 | + | 0.782752i | \(0.286185\pi\) | |||||||
\(314\) | −5101.46 | −0.916853 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12160.2 | 2.16477 | ||||||||
\(317\) | −503.804 | + | 872.615i | −0.0892633 | + | 0.154609i | −0.907200 | − | 0.420700i | \(-0.861785\pi\) |
0.817937 | + | 0.575308i | \(0.195118\pi\) | |||||||
\(318\) | −12079.4 | + | 9239.16i | −2.13012 | + | 1.62926i | ||||
\(319\) | −6725.85 | − | 11649.5i | −1.18049 | − | 2.04466i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2168.83 | − | 902.295i | −0.377110 | − | 0.156888i | ||||
\(322\) | −3372.81 | + | 5841.89i | −0.583726 | + | 1.01104i | ||||
\(323\) | 11227.8 | 1.93416 | ||||||||
\(324\) | 9842.91 | − | 5601.82i | 1.68774 | − | 0.960531i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4848.34 | + | 8397.57i | −0.823696 | + | 1.42668i | ||||
\(327\) | −2222.42 | − | 924.591i | −0.375842 | − | 0.156361i | ||||
\(328\) | −1350.01 | − | 2338.29i | −0.227262 | − | 0.393629i | ||||
\(329\) | −2159.92 | − | 3741.10i | −0.361946 | − | 0.626910i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4647.21 | + | 8049.20i | −0.771702 | + | 1.33663i | 0.164927 | + | 0.986306i | \(0.447261\pi\) |
−0.936629 | + | 0.350322i | \(0.886072\pi\) | |||||||
\(332\) | 4217.32 | 0.697155 | ||||||||
\(333\) | −4456.91 | − | 4484.59i | −0.733444 | − | 0.738001i | ||||
\(334\) | −12036.3 | −1.97185 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 577.570 | + | 4440.19i | 0.0937769 | + | 0.720930i | ||||
\(337\) | 1697.85 | + | 2940.77i | 0.274445 | + | 0.475352i | 0.969995 | − | 0.243125i | \(-0.0781726\pi\) |
−0.695550 | + | 0.718478i | \(0.744839\pi\) | |||||||
\(338\) | 3550.51 | + | 6149.67i | 0.571368 | + | 0.989639i | ||||
\(339\) | 636.799 | + | 4895.53i | 0.102024 | + | 0.784332i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8970.16 | −1.42452 | ||||||||
\(342\) | 18017.8 | − | 4768.11i | 2.84881 | − | 0.753889i | ||||
\(343\) | 6857.70 | 1.07954 | ||||||||
\(344\) | 4881.76 | − | 8455.46i | 0.765136 | − | 1.32525i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6369.98 | − | 11033.1i | −0.989746 | − | 1.71429i | ||||
\(347\) | 4086.81 | + | 7078.56i | 0.632252 | + | 1.09509i | 0.987090 | + | 0.160165i | \(0.0512026\pi\) |
−0.354838 | + | 0.934928i | \(0.615464\pi\) | |||||||
\(348\) | 16844.8 | + | 7007.93i | 2.59476 | + | 1.07950i | ||||
\(349\) | 2787.95 | − | 4828.88i | 0.427609 | − | 0.740641i | −0.569051 | − | 0.822302i | \(-0.692689\pi\) |
0.996660 | + | 0.0816612i | \(0.0260225\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2326.71 | + | 3003.24i | −0.353819 | + | 0.456698i | ||||
\(352\) | −2083.93 | −0.315551 | ||||||||
\(353\) | 1611.89 | − | 2791.87i | 0.243037 | − | 0.420953i | −0.718541 | − | 0.695485i | \(-0.755190\pi\) |
0.961578 | + | 0.274532i | \(0.0885230\pi\) | |||||||
\(354\) | 11840.2 | + | 4925.86i | 1.77768 | + | 0.739566i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1642.95 | − | 2845.68i | −0.244597 | − | 0.423654i | ||||
\(357\) | −5288.45 | + | 4044.98i | −0.784018 | + | 0.599672i | ||||
\(358\) | 7839.07 | − | 13577.7i | 1.15728 | − | 2.00447i | ||||
\(359\) | −2593.48 | −0.381278 | −0.190639 | − | 0.981660i | \(-0.561056\pi\) | ||||
−0.190639 | + | 0.981660i | \(0.561056\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13387.6 | 1.95182 | ||||||||
\(362\) | −819.520 | + | 1419.45i | −0.118986 | + | 0.206090i | ||||
\(363\) | −1482.24 | − | 11395.0i | −0.214318 | − | 1.64761i | ||||
\(364\) | −3415.64 | − | 5916.06i | −0.491835 | − | 0.851883i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −254.616 | − | 1957.41i | −0.0363634 | − | 0.279551i | ||||
\(367\) | 884.083 | − | 1531.28i | 0.125746 | − | 0.217798i | −0.796278 | − | 0.604930i | \(-0.793201\pi\) |
0.922024 | + | 0.387132i | \(0.126534\pi\) | |||||||
\(368\) | −4543.96 | −0.643669 | ||||||||
\(369\) | 522.090 | − | 1924.61i | 0.0736556 | − | 0.271521i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4898.18 | − | 8483.90i | 0.685447 | − | 1.18723i | ||||
\(372\) | 9663.52 | − | 7391.34i | 1.34686 | − | 1.03017i | ||||
\(373\) | −1514.74 | − | 2623.61i | −0.210269 | − | 0.364197i | 0.741529 | − | 0.670920i | \(-0.234101\pi\) |
−0.951799 | + | 0.306723i | \(0.900767\pi\) | |||||||
\(374\) | 11392.1 | + | 19731.6i | 1.57505 | + | 2.72807i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4862.53 | − | 8422.15i | 0.666931 | − | 1.15516i | ||||
\(377\) | −6120.10 | −0.836077 | ||||||||
\(378\) | −6768.86 | + | 8737.02i | −0.921038 | + | 1.18885i | ||||
\(379\) | 9435.84 | 1.27886 | 0.639428 | − | 0.768851i | \(-0.279171\pi\) | ||||
0.639428 | + | 0.768851i | \(0.279171\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1009.32 | − | 419.906i | −0.135719 | − | 0.0564630i | ||||
\(382\) | −2451.15 | − | 4245.52i | −0.328303 | − | 0.568638i | ||||
\(383\) | −4849.33 | − | 8399.29i | −0.646969 | − | 1.12058i | −0.983843 | − | 0.179034i | \(-0.942703\pi\) |
0.336874 | − | 0.941550i | \(-0.390631\pi\) | |||||||
\(384\) | 10745.3 | − | 8218.75i | 1.42798 | − | 1.09222i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7238.96 | 0.954542 | ||||||||
\(387\) | 6971.12 | − | 1844.79i | 0.915664 | − | 0.242315i | ||||
\(388\) | −25883.6 | −3.38670 | ||||||||
\(389\) | −6379.36 | + | 11049.4i | −0.831481 | + | 1.44017i | 0.0653822 | + | 0.997860i | \(0.479173\pi\) |
−0.896863 | + | 0.442308i | \(0.854160\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3378.36 | − | 5851.49i | −0.436959 | − | 0.756835i | ||||
\(392\) | 1449.70 | + | 2510.95i | 0.186788 | + | 0.323526i | ||||
\(393\) | 619.838 | + | 4765.13i | 0.0795590 | + | 0.611626i | ||||
\(394\) | −8037.46 | + | 13921.3i | −1.02772 | + | 1.78006i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 17598.5 | + | 17707.8i | 2.23322 | + | 2.24710i | ||||
\(397\) | −14088.8 | −1.78111 | −0.890553 | − | 0.454879i | \(-0.849682\pi\) | ||||
−0.890553 | + | 0.454879i | \(0.849682\pi\) | |||||||
\(398\) | −5251.97 | + | 9096.68i | −0.661451 | + | 1.14567i | ||||
\(399\) | −9536.40 | + | 7294.11i | −1.19653 | + | 0.915193i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3582.63 | + | 6205.30i | 0.446155 | + | 0.772763i | 0.998132 | − | 0.0610961i | \(-0.0194596\pi\) |
−0.551977 | + | 0.833860i | \(0.686126\pi\) | |||||||
\(402\) | −11362.6 | − | 4727.19i | −1.40974 | − | 0.586494i | ||||
\(403\) | −2040.57 | + | 3534.37i | −0.252228 | + | 0.436872i | ||||
\(404\) | −7093.22 | −0.873517 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −17804.6 | −2.17642 | ||||||||
\(407\) | 6968.76 | − | 12070.2i | 0.848719 | − | 1.47002i | ||||
\(408\) | −13839.1 | − | 5757.45i | −1.67926 | − | 0.698618i | ||||
\(409\) | −1019.82 | − | 1766.39i | −0.123293 | − | 0.213550i | 0.797771 | − | 0.602960i | \(-0.206012\pi\) |
−0.921065 | + | 0.389410i | \(0.872679\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7997.31 | + | 6116.91i | −0.959802 | + | 0.734123i | ||||
\(412\) | 1288.91 | − | 2232.46i | 0.154127 | − | 0.266955i | ||||
\(413\) | −8260.85 | −0.984237 | ||||||||
\(414\) | −7906.37 | − | 7955.49i | −0.938591 | − | 0.944422i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −474.061 | + | 821.099i | −0.0558721 | + | 0.0967732i | ||||
\(417\) | 1320.75 | + | 10153.5i | 0.155102 | + | 1.19238i | ||||
\(418\) | 20542.7 | + | 35581.1i | 2.40378 | + | 4.16346i | ||||
\(419\) | −6596.83 | − | 11426.0i | −0.769156 | − | 1.33222i | −0.938021 | − | 0.346578i | \(-0.887344\pi\) |
0.168865 | − | 0.985639i | \(-0.445990\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5621.08 | + | 9735.99i | −0.650724 | + | 1.12709i | 0.332224 | + | 0.943201i | \(0.392201\pi\) |
−0.982948 | + | 0.183886i | \(0.941132\pi\) | |||||||
\(422\) | −12418.0 | −1.43246 | ||||||||
\(423\) | 6943.66 | − | 1837.52i | 0.798138 | − | 0.211214i | ||||
\(424\) | 22054.1 | 2.52604 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1466.64 | − | 1121.79i | 0.166805 | − | 0.127584i | ||||
\(427\) | 635.768 | + | 1101.18i | 0.0720538 | + | 0.124801i | ||||
\(428\) | 3511.56 | + | 6082.21i | 0.396584 | + | 0.686903i | ||||
\(429\) | −7732.19 | − | 3216.81i | −0.870195 | − | 0.362026i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5546.88 | −0.619916 | −0.309958 | − | 0.950750i | \(-0.600315\pi\) | ||||
−0.309958 | + | 0.950750i | \(0.600315\pi\) | |||||||
\(432\) | −7376.70 | − | 1006.04i | −0.821555 | − | 0.112044i | ||||
\(433\) | 4484.74 | 0.497744 | 0.248872 | − | 0.968536i | \(-0.419940\pi\) | ||||
0.248872 | + | 0.968536i | \(0.419940\pi\) | |||||||
\(434\) | −5936.42 | + | 10282.2i | −0.656584 | + | 1.13724i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3598.34 | + | 6232.50i | 0.395250 | + | 0.684594i | ||||
\(437\) | −6092.03 | − | 10551.7i | −0.666868 | − | 1.15505i | ||||
\(438\) | 2319.25 | − | 1773.93i | 0.253009 | − | 0.193519i | ||||
\(439\) | −2634.86 | + | 4563.71i | −0.286458 | + | 0.496159i | −0.972962 | − | 0.230967i | \(-0.925811\pi\) |
0.686504 | + | 0.727126i | \(0.259144\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −560.643 | + | 2066.73i | −0.0605381 | + | 0.223165i | ||||
\(442\) | 10366.1 | 1.11553 | ||||||||
\(443\) | 3700.66 | − | 6409.74i | 0.396894 | − | 0.687440i | −0.596447 | − | 0.802652i | \(-0.703422\pi\) |
0.993341 | + | 0.115212i | \(0.0367549\pi\) | |||||||
\(444\) | 2438.36 | + | 18745.4i | 0.260630 | + | 2.00365i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3430.95 | + | 5942.58i | 0.364261 | + | 0.630918i | ||||
\(447\) | −1069.95 | − | 8225.49i | −0.113215 | − | 0.870363i | ||||
\(448\) | −4826.00 | + | 8358.87i | −0.508944 | + | 0.881517i | ||||
\(449\) | −938.733 | −0.0986672 | −0.0493336 | − | 0.998782i | \(-0.515710\pi\) | ||||
−0.0493336 | + | 0.998782i | \(0.515710\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4395.91 | 0.458970 | ||||||||
\(452\) | 7379.97 | − | 12782.5i | 0.767974 | − | 1.33017i | ||||
\(453\) | 15159.4 | − | 11594.9i | 1.57229 | − | 1.20260i | ||||
\(454\) | 3946.71 | + | 6835.91i | 0.407992 | + | 0.706663i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −24955.3 | − | 10382.1i | −2.56281 | − | 1.06620i | ||||
\(457\) | −2153.58 | + | 3730.11i | −0.220438 | + | 0.381810i | −0.954941 | − | 0.296795i | \(-0.904082\pi\) |
0.734503 | + | 0.678605i | \(0.237415\pi\) | |||||||
\(458\) | −32113.7 | −3.27636 | ||||||||
\(459\) | −4188.93 | − | 10247.3i | −0.425975 | − | 1.04206i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2621.39 | + | 4540.38i | −0.264838 | + | 0.458713i | −0.967521 | − | 0.252790i | \(-0.918652\pi\) |
0.702683 | + | 0.711503i | \(0.251985\pi\) | |||||||
\(462\) | −22494.5 | − | 9358.35i | −2.26523 | − | 0.942402i | ||||
\(463\) | −4274.77 | − | 7404.13i | −0.429083 | − | 0.743194i | 0.567709 | − | 0.823230i | \(-0.307830\pi\) |
−0.996792 | + | 0.0800354i | \(0.974497\pi\) | |||||||
\(464\) | −5996.72 | − | 10386.6i | −0.599980 | − | 1.03920i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4636.12 | + | 8029.99i | −0.460867 | + | 0.798245i | ||||
\(467\) | −12706.2 | −1.25904 | −0.629522 | − | 0.776983i | \(-0.716749\pi\) | ||||
−0.629522 | + | 0.776983i | \(0.716749\pi\) | |||||||
\(468\) | 10980.5 | − | 2905.80i | 1.08456 | − | 0.287010i | ||||
\(469\) | 7927.67 | 0.780524 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 704.814 | + | 5418.41i | 0.0689514 | + | 0.530079i | ||||
\(472\) | −9298.63 | − | 16105.7i | −0.906788 | − | 1.57060i | ||||
\(473\) | 7948.01 | + | 13766.4i | 0.772622 | + | 1.33822i | ||||
\(474\) | −2545.20 | − | 19566.7i | −0.246635 | − | 1.89606i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 19906.2 | 1.91680 | ||||||||
\(477\) | 11482.1 | + | 11553.4i | 1.10215 | + | 1.10900i | ||||
\(478\) | 14004.3 | 1.34005 | ||||||||
\(479\) | 9178.08 | − | 15896.9i | 0.875485 | − | 1.51638i | 0.0192388 | − | 0.999815i | \(-0.493876\pi\) |
0.856246 | − | 0.516569i | \(-0.172791\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3170.57 | − | 5491.58i | −0.300552 | − | 0.520571i | ||||
\(482\) | 3125.84 | + | 5414.11i | 0.295390 | + | 0.511631i | ||||
\(483\) | 6670.82 | + | 2775.25i | 0.628433 | + | 0.261446i | ||||
\(484\) | −17177.9 | + | 29753.0i | −1.61325 | + | 2.79423i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −11073.9 | − | 14665.5i | −1.03359 | − | 1.36881i | ||||
\(487\) | 15195.3 | 1.41389 | 0.706945 | − | 0.707268i | \(-0.250073\pi\) | ||||
0.706945 | + | 0.707268i | \(0.250073\pi\) | |||||||
\(488\) | −1431.27 | + | 2479.04i | −0.132768 | + | 0.229961i | ||||
\(489\) | 9589.15 | + | 3989.36i | 0.886782 | + | 0.368927i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3971.95 | − | 6879.62i | −0.365075 | − | 0.632328i | 0.623713 | − | 0.781653i | \(-0.285623\pi\) |
−0.988788 | + | 0.149325i | \(0.952290\pi\) | |||||||
\(492\) | −4735.70 | + | 3622.20i | −0.433947 | + | 0.331913i | ||||
\(493\) | 8916.92 | − | 15444.6i | 0.814600 | − | 1.41093i | ||||
\(494\) | 18692.6 | 1.70247 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7997.73 | −0.724009 | ||||||||
\(497\) | −594.723 | + | 1030.09i | −0.0536760 | + | 0.0929696i | ||||
\(498\) | −882.705 | − | 6785.98i | −0.0794277 | − | 0.610617i | ||||
\(499\) | 9578.93 | + | 16591.2i | 0.859343 | + | 1.48843i | 0.872557 | + | 0.488512i | \(0.162460\pi\) |
−0.0132143 | + | 0.999913i | \(0.504206\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1662.93 | + | 12784.1i | 0.148291 | + | 1.14002i | ||||
\(502\) | −10566.7 | + | 18302.1i | −0.939474 | + | 1.62722i | ||||
\(503\) | −11203.5 | −0.993119 | −0.496559 | − | 0.868003i | \(-0.665403\pi\) | ||||
−0.496559 | + | 0.868003i | \(0.665403\pi\) | |||||||
\(504\) | 15494.6 | − | 4100.38i | 1.36941 | − | 0.362392i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 12362.3 | − | 21412.1i | 1.08611 | − | 1.88119i | ||||
\(507\) | 6041.20 | − | 4620.74i | 0.529190 | − | 0.404762i | ||||
\(508\) | 1634.19 | + | 2830.51i | 0.142728 | + | 0.247212i | ||||
\(509\) | −3544.02 | − | 6138.42i | −0.308617 | − | 0.534540i | 0.669443 | − | 0.742863i | \(-0.266533\pi\) |
−0.978060 | + | 0.208323i | \(0.933199\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −940.456 | + | 1628.92i | −0.0814155 | + | 0.141016i | ||||
\(512\) | −17377.5 | −1.49997 | ||||||||
\(513\) | −7553.68 | − | 18478.5i | −0.650104 | − | 1.59034i | ||||
\(514\) | 15701.5 | 1.34740 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −19905.7 | − | 8281.36i | −1.69826 | − | 0.706524i | ||||
\(517\) | 7916.71 | + | 13712.1i | 0.673455 | + | 1.16646i | ||||
\(518\) | −9223.80 | − | 15976.1i | −0.782376 | − | 1.35511i | ||||
\(519\) | −10838.5 | + | 8290.07i | −0.916683 | + | 0.701144i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9739.55 | −0.818997 | −0.409499 | − | 0.912311i | \(-0.634296\pi\) | ||||
−0.409499 | + | 0.912311i | \(0.634296\pi\) | |||||||
\(522\) | 7750.58 | − | 28571.4i | 0.649873 | − | 2.39566i | ||||
\(523\) | −14153.1 | −1.18331 | −0.591656 | − | 0.806190i | \(-0.701526\pi\) | ||||
−0.591656 | + | 0.806190i | \(0.701526\pi\) | |||||||
\(524\) | 7183.40 | − | 12442.0i | 0.598871 | − | 1.03727i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3351.14 | − | 5804.35i | −0.277789 | − | 0.481144i | ||||
\(527\) | −5946.18 | − | 10299.1i | −0.491498 | − | 0.851300i | ||||
\(528\) | −2116.95 | − | 16274.5i | −0.174486 | − | 1.34140i | ||||
\(529\) | 2417.42 | − | 4187.09i | 0.198686 | − | 0.344135i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3596.07 | − | 13256.4i | 0.293891 | − | 1.08338i | ||||
\(532\) | 35895.9 | 2.92534 | ||||||||
\(533\) | 1000.00 | − | 1732.05i | 0.0812661 | − | 0.140757i | ||||
\(534\) | −4235.03 | + | 3239.25i | −0.343198 | + | 0.262502i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8923.59 | + | 15456.1i | 0.719106 | + | 1.24553i | ||||
\(537\) | −15504.3 | − | 6450.22i | −1.24592 | − | 0.518338i | ||||
\(538\) | −1749.06 | + | 3029.46i | −0.140162 | + | 0.242768i | ||||
\(539\) | −4720.52 | −0.377231 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12175.5 | −0.967592 | −0.483796 | − | 0.875181i | \(-0.660742\pi\) | ||||
−0.483796 | + | 0.875181i | \(0.660742\pi\) | |||||||
\(542\) | −9258.33 | + | 16035.9i | −0.733725 | + | 1.27085i | ||||
\(543\) | 1620.86 | + | 674.326i | 0.128099 | + | 0.0532930i | ||||
\(544\) | −1381.41 | − | 2392.66i | −0.108874 | − | 0.188575i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −8804.47 | + | 6734.27i | −0.690103 | + | 0.527839i | ||||
\(547\) | −609.617 | + | 1055.89i | −0.0476515 | + | 0.0825348i | −0.888867 | − | 0.458165i | \(-0.848507\pi\) |
0.841216 | + | 0.540699i | \(0.181840\pi\) | |||||||
\(548\) | 30102.6 | 2.34657 | ||||||||
\(549\) | −2043.85 | + | 540.870i | −0.158888 | + | 0.0420470i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16079.4 | − | 27850.4i | 1.24321 | − | 2.15330i | ||||
\(552\) | 2098.10 | + | 16129.6i | 0.161778 | + | 1.24370i | ||||
\(553\) | 6355.27 | + | 11007.7i | 0.488705 | + | 0.846461i | ||||
\(554\) | 4678.59 | + | 8103.56i | 0.358798 | + | 0.621457i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15306.4 | − | 26511.4i | 1.16751 | − | 2.02218i | ||||
\(557\) | −12672.4 | −0.963995 | −0.481998 | − | 0.876172i | \(-0.660089\pi\) | ||||
−0.481998 | + | 0.876172i | \(0.660089\pi\) | |||||||
\(558\) | −13915.8 | − | 14002.3i | −1.05574 | − | 1.06230i | ||||
\(559\) | 7232.19 | 0.547208 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 19383.6 | − | 14825.9i | 1.45878 | − | 1.11578i | ||||
\(562\) | −11992.1 | − | 20771.0i | −0.900102 | − | 1.55902i | ||||
\(563\) | 4116.80 | + | 7130.50i | 0.308175 | + | 0.533774i | 0.977963 | − | 0.208778i | \(-0.0669486\pi\) |
−0.669788 | + | 0.742552i | \(0.733615\pi\) | |||||||
\(564\) | −19827.3 | − | 8248.74i | −1.48029 | − | 0.615842i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 30774.8 | 2.28545 | ||||||||
\(567\) | 10215.0 | + | 5982.30i | 0.756597 | + | 0.443092i | ||||
\(568\) | −2677.75 | −0.197809 | ||||||||
\(569\) | −1974.55 | + | 3420.02i | −0.145479 | + | 0.251977i | −0.929552 | − | 0.368692i | \(-0.879806\pi\) |
0.784073 | + | 0.620669i | \(0.213139\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1955.13 | + | 3386.38i | 0.143292 | + | 0.248189i | 0.928734 | − | 0.370746i | \(-0.120898\pi\) |
−0.785442 | + | 0.618935i | \(0.787565\pi\) | |||||||
\(572\) | 12519.2 | + | 21684.0i | 0.915133 | + | 1.58506i | ||||
\(573\) | −4170.64 | + | 3190.00i | −0.304068 | + | 0.232572i | ||||
\(574\) | 2909.20 | − | 5038.88i | 0.211547 | − | 0.366409i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −11312.8 | − | 11383.1i | −0.818348 | − | 0.823432i | ||||
\(577\) | −18788.9 | −1.35562 | −0.677810 | − | 0.735237i | \(-0.737071\pi\) | ||||
−0.677810 | + | 0.735237i | \(0.737071\pi\) | |||||||
\(578\) | −3185.94 | + | 5518.21i | −0.229269 | + | 0.397106i | ||||
\(579\) | −1000.13 | − | 7688.71i | −0.0717858 | − | 0.551868i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2204.09 | + | 3817.59i | 0.157385 | + | 0.272599i | ||||
\(582\) | 5417.56 | + | 41648.6i | 0.385851 | + | 2.96631i | ||||
\(583\) | −17953.2 | + | 31095.8i | −1.27538 | + | 2.20902i | ||||
\(584\) | −4234.41 | −0.300036 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7310.27 | −0.515332 | ||||||||
\(587\) | 2200.11 | − | 3810.70i | 0.154699 | − | 0.267946i | −0.778251 | − | 0.627954i | \(-0.783893\pi\) |
0.932949 | + | 0.360008i | \(0.117226\pi\) | |||||||
\(588\) | 5085.41 | − | 3889.68i | 0.356664 | − | 0.272802i | ||||
\(589\) | −10722.4 | − | 18571.8i | −0.750103 | − | 1.29922i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15896.7 | + | 6613.46i | 1.10643 | + | 0.460307i | ||||
\(592\) | 6213.30 | − | 10761.7i | 0.431360 | − | 0.747137i | ||||
\(593\) | −13311.2 | −0.921798 | −0.460899 | − | 0.887453i | \(-0.652473\pi\) | ||||
−0.460899 | + | 0.887453i | \(0.652473\pi\) | |||||||
\(594\) | 24809.7 | − | 32023.6i | 1.71373 | − | 2.21203i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12399.9 | + | 21477.2i | −0.852211 | + | 1.47607i | ||||
\(597\) | 10387.5 | + | 4321.48i | 0.712111 | + | 0.296259i | ||||
\(598\) | −5624.45 | − | 9741.84i | −0.384617 | − | 0.666176i | ||||
\(599\) | 7966.01 | + | 13797.5i | 0.543377 | + | 0.941156i | 0.998707 | + | 0.0508333i | \(0.0161877\pi\) |
−0.455331 | + | 0.890322i | \(0.650479\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11754.9 | + | 20360.2i | −0.797828 | + | 1.38188i | 0.123201 | + | 0.992382i | \(0.460684\pi\) |
−0.921028 | + | 0.389496i | \(0.872649\pi\) | |||||||
\(602\) | 21039.9 | 1.42445 | ||||||||
\(603\) | −3451.03 | + | 12721.7i | −0.233062 | + | 0.859151i | ||||
\(604\) | −57061.2 | −3.84402 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1484.65 | + | 11413.5i | 0.0995208 | + | 0.765087i | ||||
\(607\) | 4876.00 | + | 8445.49i | 0.326048 | + | 0.564731i | 0.981724 | − | 0.190311i | \(-0.0609497\pi\) |
−0.655676 | + | 0.755042i | \(0.727616\pi\) | |||||||
\(608\) | −2491.02 | − | 4314.57i | −0.166158 | − | 0.287795i | ||||
\(609\) | 2459.87 | + | 18910.8i | 0.163676 | + | 1.25830i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7203.71 | 0.476973 | ||||||||
\(612\) | −8665.44 | + | 31943.9i | −0.572353 | + | 2.10989i | ||||
\(613\) | −24076.3 | −1.58635 | −0.793176 | − | 0.608992i | \(-0.791574\pi\) | ||||
−0.793176 | + | 0.608992i | \(0.791574\pi\) | |||||||
\(614\) | −19985.4 | + | 34615.7i | −1.31359 | + | 2.27520i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 17665.9 | + | 30598.3i | 1.15549 | + | 2.00136i | ||||
\(617\) | −3324.25 | − | 5757.76i | −0.216903 | − | 0.375687i | 0.736957 | − | 0.675940i | \(-0.236262\pi\) |
−0.953860 | + | 0.300253i | \(0.902929\pi\) | |||||||
\(618\) | −3861.97 | − | 1606.69i | −0.251378 | − | 0.104580i | ||||
\(619\) | 4100.83 | − | 7102.85i | 0.266278 | − | 0.461208i | −0.701619 | − | 0.712552i | \(-0.747539\pi\) |
0.967898 | + | 0.251344i | \(0.0808726\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7357.41 | + | 9496.71i | −0.475431 | + | 0.613671i | ||||
\(622\) | −3909.67 | −0.252031 | ||||||||
\(623\) | 1717.30 | − | 2974.46i | 0.110437 | − | 0.191283i | ||||
\(624\) | −6893.97 | − | 2868.09i | −0.442275 | − | 0.183999i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −9851.62 | − | 17063.5i | −0.628994 | − | 1.08945i | ||||
\(627\) | 34953.5 | − | 26734.9i | 2.22633 | − | 1.70285i | ||||
\(628\) | 8168.21 | − | 14147.7i | 0.519024 | − | 0.898975i | ||||
\(629\) | 18477.9 | 1.17132 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28159.1 | 1.77654 | 0.888269 | − | 0.459323i | \(-0.151908\pi\) | ||||
0.888269 | + | 0.459323i | \(0.151908\pi\) | |||||||
\(632\) | −14307.3 | + | 24781.0i | −0.900498 | + | 1.55971i | ||||
\(633\) | 1715.66 | + | 13189.5i | 0.107727 | + | 0.828175i | ||||
\(634\) | −2444.12 | − | 4233.35i | −0.153105 | − | 0.265186i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −6281.81 | − | 48292.7i | −0.391651 | − | 3.01090i | ||||
\(637\) | −1073.85 | + | 1859.95i | −0.0667932 | + | 0.115689i | ||||
\(638\) | 65258.6 | 4.04955 | ||||||||
\(639\) | −1394.12 | − | 1402.78i | −0.0863075 | − | 0.0868436i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5777.99 | + | 10007.8i | −0.356032 | + | 0.616666i | −0.987294 | − | 0.158904i | \(-0.949204\pi\) |
0.631262 | + | 0.775570i | \(0.282537\pi\) | |||||||
\(642\) | 9051.74 | − | 6923.40i | 0.556454 | − | 0.425615i | ||||
\(643\) | 6901.87 | + | 11954.4i | 0.423302 | + | 0.733180i | 0.996260 | − | 0.0864042i | \(-0.0275376\pi\) |
−0.572958 | + | 0.819585i | \(0.694204\pi\) | |||||||
\(644\) | −10800.8 | − | 18707.5i | −0.660885 | − | 1.14469i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −27234.9 | + | 47172.3i | −1.65874 | + | 2.87302i | ||||
\(647\) | 24257.1 | 1.47395 | 0.736974 | − | 0.675921i | \(-0.236254\pi\) | ||||
0.736974 | + | 0.675921i | \(0.236254\pi\) | |||||||
\(648\) | −165.041 | + | 26649.5i | −0.0100053 | + | 1.61557i | ||||
\(649\) | 30278.3 | 1.83132 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11741.2 | + | 4884.67i | 0.706871 | + | 0.294079i | ||||
\(652\) | −15525.9 | − | 26891.6i | −0.932576 | − | 1.61527i | ||||
\(653\) | −3249.10 | − | 5627.61i | −0.194712 | − | 0.337252i | 0.752094 | − | 0.659056i | \(-0.229044\pi\) |
−0.946806 | + | 0.321804i | \(0.895711\pi\) | |||||||
\(654\) | 9275.41 | − | 7094.49i | 0.554583 | − | 0.424184i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3919.37 | 0.233271 | ||||||||
\(657\) | −2204.57 | − | 2218.26i | −0.130911 | − | 0.131724i | ||||
\(658\) | 20957.0 | 1.24162 | ||||||||
\(659\) | −1901.37 | + | 3293.26i | −0.112393 | + | 0.194670i | −0.916734 | − | 0.399497i | \(-0.869185\pi\) |
0.804342 | + | 0.594167i | \(0.202518\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4837.05 | − | 8378.01i | −0.284628 | − | 0.492991i | 0.687891 | − | 0.725814i | \(-0.258537\pi\) |
−0.972519 | + | 0.232824i | \(0.925204\pi\) | |||||||
\(662\) | −22545.1 | − | 39049.3i | −1.32363 | − | 2.29259i | ||||
\(663\) | −1432.17 | − | 11010.1i | −0.0838926 | − | 0.644942i | ||||
\(664\) | −4961.95 | + | 8594.35i | −0.290002 | + | 0.502298i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 29652.4 | − | 7847.02i | 1.72524 | − | 0.456555i | ||||
\(667\) | −19352.7 | −1.12345 | ||||||||
\(668\) | 19271.9 | − | 33379.9i | 1.11625 | − | 1.93340i | ||||
\(669\) | 5837.77 | − | 4465.14i | 0.337371 | − | 0.258045i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2330.26 | − | 4036.13i | −0.134067 | − | 0.232210i | ||||
\(672\) | 2727.69 | + | 1134.80i | 0.156582 | + | 0.0651425i | ||||
\(673\) | −1016.47 | + | 1760.57i | −0.0582198 | + | 0.100840i | −0.893666 | − | 0.448732i | \(-0.851876\pi\) |
0.835447 | + | 0.549572i | \(0.185209\pi\) | |||||||
\(674\) | −16473.7 | −0.941458 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −22739.6 | −1.29379 | ||||||||
\(677\) | 4499.50 | − | 7793.36i | 0.255435 | − | 0.442427i | −0.709578 | − | 0.704627i | \(-0.751114\pi\) |
0.965014 | + | 0.262199i | \(0.0844478\pi\) | |||||||
\(678\) | −22112.6 | − | 9199.48i | −1.25255 | − | 0.521097i | ||||
\(679\) | −13527.5 | − | 23430.3i | −0.764561 | − | 1.32426i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6715.34 | − | 5136.37i | 0.377875 | − | 0.289025i | ||||
\(682\) | 21758.6 | − | 37687.0i | 1.22167 | − | 2.11600i | ||||
\(683\) | 23826.0 | 1.33481 | 0.667407 | − | 0.744693i | \(-0.267404\pi\) | ||||
0.667407 | + | 0.744693i | \(0.267404\pi\) | |||||||
\(684\) | −15626.0 | + | 57602.9i | −0.873500 | + | 3.22003i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −16634.5 | + | 28811.8i | −0.925814 | + | 1.60356i | ||||
\(687\) | 4436.81 | + | 34108.9i | 0.246397 | + | 1.89423i | ||||
\(688\) | 7086.39 | + | 12274.0i | 0.392684 | + | 0.680148i | ||||
\(689\) | 8168.13 | + | 14147.6i | 0.451642 | + | 0.782266i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2939.49 | − | 5091.35i | 0.161828 | − | 0.280295i | −0.773696 | − | 0.633557i | \(-0.781594\pi\) |
0.935524 | + | 0.353262i | \(0.114928\pi\) | |||||||
\(692\) | 40797.2 | 2.24115 | ||||||||
\(693\) | −6831.95 | + | 25185.0i | −0.374494 | + | 1.38052i | ||||
\(694\) | −39653.0 | −2.16888 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −34100.3 | + | 26082.3i | −1.85714 | + | 1.42047i | ||||
\(697\) | 2913.98 | + | 5047.17i | 0.158357 | + | 0.274283i | ||||
\(698\) | 13525.3 | + | 23426.5i | 0.733438 | + | 1.27035i | ||||
\(699\) | 9169.41 | + | 3814.74i | 0.496164 | + | 0.206419i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24961.0 | −1.34489 | −0.672443 | − | 0.740148i | \(-0.734755\pi\) | ||||
−0.672443 | + | 0.740148i | \(0.734755\pi\) | |||||||
\(702\) | −6973.93 | − | 17060.2i | −0.374949 | − | 0.917233i | ||||
\(703\) | 33320.3 | 1.78762 | ||||||||
\(704\) | 17688.6 | − | 30637.6i | 0.946966 | − | 1.64019i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7819.80 | + | 13544.3i | 0.416859 | + | 0.722020i | ||||
\(707\) | −3707.11 | − | 6420.90i | −0.197200 | − | 0.341560i | ||||
\(708\) | −32618.7 | + | 24949.1i | −1.73148 | + | 1.32436i | ||||
\(709\) | 5754.43 | − | 9966.96i | 0.304813 | − | 0.527951i | −0.672407 | − | 0.740182i | \(-0.734739\pi\) |
0.977220 | + | 0.212231i | \(0.0680728\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20430.8 | + | 5406.66i | −1.07766 | + | 0.285184i | ||||
\(712\) | 7732.17 | 0.406988 | ||||||||
\(713\) | −6452.60 | + | 11176.2i | −0.338922 | + | 0.587031i | ||||
\(714\) | −4166.46 | − | 32030.5i | −0.218384 | − | 1.67887i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 25103.1 | + | 43479.8i | 1.31026 | + | 2.26943i | ||||
\(717\) | −1934.83 | − | 14874.4i | −0.100777 | − | 0.774747i | ||||
\(718\) | 6290.92 | − | 10896.2i | 0.326985 | − | 0.566355i | ||||
\(719\) | 16503.6 | 0.856022 | 0.428011 | − | 0.903773i | \(-0.359214\pi\) | ||||
0.428011 | + | 0.903773i | \(0.359214\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2694.48 | 0.139179 | ||||||||
\(722\) | −32473.8 | + | 56246.2i | −1.67389 | + | 2.89926i | ||||
\(723\) | 5318.62 | − | 4068.06i | 0.273585 | − | 0.209257i | ||||
\(724\) | −2624.35 | − | 4545.51i | −0.134714 | − | 0.233332i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 51470.2 | + | 21413.1i | 2.63118 | + | 1.09465i | ||||
\(727\) | 19224.0 | − | 33296.9i | 0.980713 | − | 1.69865i | 0.321090 | − | 0.947049i | \(-0.395951\pi\) |
0.659623 | − | 0.751597i | \(-0.270716\pi\) | |||||||
\(728\) | 16074.9 | 0.818372 | ||||||||
\(729\) | −14046.7 | + | 13788.1i | −0.713645 | + | 0.700508i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10537.2 | + | 18251.0i | −0.533151 | + | 0.923445i | ||||
\(732\) | 5836.13 | + | 2428.00i | 0.294685 | + | 0.122597i | ||||
\(733\) | −17220.7 | − | 29827.1i | −0.867750 | − | 1.50299i | −0.864290 | − | 0.502993i | \(-0.832232\pi\) |
−0.00345985 | − | 0.999994i | \(-0.501101\pi\) | |||||||
\(734\) | 4288.98 | + | 7428.73i | 0.215680 | + | 0.373569i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1499.06 | + | 2596.44i | −0.0750760 | + | 0.130035i | ||||
\(737\) | −29057.1 | −1.45228 | ||||||||
\(738\) | 6819.59 | + | 6861.96i | 0.340153 | + | 0.342266i | ||||
\(739\) | 4619.83 | 0.229964 | 0.114982 | − | 0.993368i | \(-0.463319\pi\) | ||||
0.114982 | + | 0.993368i | \(0.463319\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2582.56 | − | 19854.0i | −0.128033 | − | 0.984283i | ||||
\(742\) | 23762.7 | + | 41158.2i | 1.17568 | + | 2.03634i | ||||
\(743\) | −296.537 | − | 513.617i | −0.0146418 | − | 0.0253604i | 0.858612 | − | 0.512627i | \(-0.171327\pi\) |
−0.873253 | + | 0.487266i | \(0.837994\pi\) | |||||||
\(744\) | 3692.83 | + | 28389.4i | 0.181970 | + | 1.39893i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 14697.1 | 0.721310 | ||||||||
\(747\) | −7085.64 | + | 1875.09i | −0.347055 | + | 0.0918422i | ||||
\(748\) | −72961.6 | −3.56650 | ||||||||
\(749\) | −3670.48 | + | 6357.45i | −0.179060 | + | 0.310142i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11099.8 | + | 19225.4i | 0.539331 | + | 0.934150i | 0.998940 | + | 0.0460280i | \(0.0146563\pi\) |
−0.459609 | + | 0.888122i | \(0.652010\pi\) | |||||||
\(752\) | 7058.48 | + | 12225.6i | 0.342282 | + | 0.592850i | ||||
\(753\) | 20899.1 | + | 8694.61i | 1.01143 | + | 0.420783i | ||||
\(754\) | 14845.3 | − | 25712.8i | 0.717022 | − | 1.24192i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −13392.2 | − | 32761.2i | −0.644272 | − | 1.57608i | ||||
\(757\) | 9329.48 | 0.447934 | 0.223967 | − | 0.974597i | \(-0.428099\pi\) | ||||
0.223967 | + | 0.974597i | \(0.428099\pi\) | |||||||
\(758\) | −22888.2 | + | 39643.5i | −1.09675 | + | 1.89963i | ||||
\(759\) | −24450.4 | − | 10172.1i | −1.16929 | − | 0.486459i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11435.9 | − | 19807.5i | −0.544745 | − | 0.943526i | −0.998623 | − | 0.0524619i | \(-0.983293\pi\) |
0.453878 | − | 0.891064i | \(-0.350040\pi\) | |||||||
\(762\) | 4212.45 | − | 3221.98i | 0.200264 | − | 0.153176i | ||||
\(763\) | −3761.18 | + | 6514.55i | −0.178458 | + | 0.309099i | ||||
\(764\) | 15698.7 | 0.743400 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 47051.4 | 2.21937 | ||||||||
\(767\) | 6887.83 | − | 11930.1i | 0.324257 | − | 0.561630i | ||||
\(768\) | 5278.43 | + | 40579.0i | 0.248006 | + | 1.90660i | ||||
\(769\) | 6416.15 | + | 11113.1i | 0.300874 | + | 0.521130i | 0.976334 | − | 0.216267i | \(-0.0693882\pi\) |
−0.675460 | + | 0.737397i | \(0.736055\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2169.30 | − | 16677.0i | −0.101330 | − | 0.778997i | ||||
\(772\) | −11590.7 | + | 20075.6i | −0.540359 | + | 0.935929i | ||||
\(773\) | −10821.5 | −0.503523 | −0.251762 | − | 0.967789i | \(-0.581010\pi\) | ||||
−0.251762 | + | 0.967789i | \(0.581010\pi\) | |||||||
\(774\) | −9158.96 | + | 33763.2i | −0.425338 | + | 1.56795i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 30453.7 | − | 52747.4i | 1.40880 | − | 2.44011i | ||||
\(777\) | −15694.3 | + | 12004.1i | −0.724621 | + | 0.554241i | ||||
\(778\) | −30948.4 | − | 53604.2i | −1.42616 | − | 2.47018i | ||||
\(779\) | 5254.64 | + | 9101.31i | 0.241678 | + | 0.418598i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2179.82 | − | 3775.57i | 0.0998723 | − | 0.172984i | ||||
\(782\) | 32779.1 | 1.49895 | ||||||||
\(783\) | −31417.3 | − | 4284.71i | −1.43393 | − | 0.195560i | ||||
\(784\) | −4208.79 | −0.191727 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −21523.6 | − | 8954.45i | −0.976746 | − | 0.406354i | ||||
\(787\) | 6993.16 | + | 12112.5i | 0.316746 | + | 0.548620i | 0.979807 | − | 0.199945i | \(-0.0640763\pi\) |
−0.663061 | + | 0.748565i | \(0.730743\pi\) | |||||||
\(788\) | −25738.4 | − | 44580.2i | −1.16357 | − | 2.01536i | ||||
\(789\) | −5701.98 | + | 4361.27i | −0.257282 | + | 0.196788i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15427.9 | 0.693492 | ||||||||
\(792\) | −56791.9 | + | 15029.0i | −2.54800 | + | 0.674284i | ||||
\(793\) | −2120.39 | −0.0949525 | ||||||||
\(794\) | 34174.9 | − | 59192.6i | 1.52748 | − | 2.64568i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −16818.4 | − | 29130.3i | −0.748885 | − | 1.29711i | ||||
\(797\) | 10069.6 | + | 17441.0i | 0.447532 | + | 0.775148i | 0.998225 | − | 0.0595602i | \(-0.0189698\pi\) |
−0.550693 | + | 0.834708i | \(0.685636\pi\) | |||||||
\(798\) | −7513.17 | − | 57759.1i | −0.333288 | − | 2.56222i | ||||
\(799\) | −10495.7 | + | 18179.1i | −0.464721 | + | 0.804920i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4025.61 | + | 4050.62i | 0.177575 | + | 0.178679i | ||||
\(802\) | −34761.1 | −1.53050 | ||||||||
\(803\) | 3447.03 | − | 5970.43i | 0.151486 | − | 0.262381i | ||||
\(804\) | 31303.1 | − | 23942.8i | 1.37310 | − | 1.05025i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9899.48 | − | 17146.4i | −0.432623 | − | 0.749326i | ||||
\(807\) | 3459.33 | + | 1439.18i | 0.150897 | + | 0.0627775i | ||||
\(808\) | 8345.64 | − | 14455.1i | 0.363364 | − | 0.629366i | ||||
\(809\) | 4443.65 | 0.193115 | 0.0965576 | − | 0.995327i | \(-0.469217\pi\) | ||||
0.0965576 | + | 0.995327i | \(0.469217\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3871.68 | 0.167636 | 0.0838181 | − | 0.996481i | \(-0.473289\pi\) | ||||
0.0838181 | + | 0.996481i | \(0.473289\pi\) | |||||||
\(812\) | 28507.8 | − | 49377.0i | 1.23205 | − | 2.13398i | ||||
\(813\) | 18311.3 | + | 7618.03i | 0.789921 | + | 0.328630i | ||||
\(814\) | 33807.8 | + | 58556.8i | 1.45573 | + | 2.52139i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 17282.3 | − | 13218.7i | 0.741423 | − | 0.567093i | ||||
\(817\) | −19001.3 | + | 32911.2i | −0.813672 | + | 1.40932i | ||||
\(818\) | 9895.00 | 0.422947 | ||||||||
\(819\) | 8369.09 | + | 8421.08i | 0.357069 | + | 0.359287i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16596.6 | − | 28746.2i | 0.705513 | − | 1.22198i | −0.260994 | − | 0.965341i | \(-0.584050\pi\) |
0.966506 | − | 0.256643i | \(-0.0826165\pi\) | |||||||
\(822\) | −6300.62 | − | 48437.3i | −0.267347 | − | 2.05529i | ||||
\(823\) | −3072.38 | − | 5321.52i | −0.130129 | − | 0.225391i | 0.793597 | − | 0.608444i | \(-0.208206\pi\) |
−0.923726 | + | 0.383053i | \(0.874873\pi\) | |||||||
\(824\) | 3032.98 | + | 5253.28i | 0.128227 | + | 0.222095i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 20038.1 | − | 34707.0i | 0.844084 | − | 1.46200i | ||||
\(827\) | 138.554 | 0.00582585 | 0.00291293 | − | 0.999996i | \(-0.499073\pi\) | ||||
0.00291293 | + | 0.999996i | \(0.499073\pi\) | |||||||
\(828\) | 34722.0 | − | 9188.60i | 1.45734 | − | 0.385659i | ||||
\(829\) | −21615.2 | −0.905580 | −0.452790 | − | 0.891617i | \(-0.649571\pi\) | ||||
−0.452790 | + | 0.891617i | \(0.649571\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7960.63 | − | 6088.85i | 0.332312 | − | 0.254176i | ||||
\(832\) | −8047.76 | − | 13939.1i | −0.335344 | − | 0.580832i | ||||
\(833\) | −3129.16 | − | 5419.87i | −0.130155 | − | 0.225435i | ||||
\(834\) | −45862.6 | − | 19080.1i | −1.90418 | − | 0.792195i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −131568. | −5.44304 | ||||||||
\(837\) | −12949.6 | + | 16715.0i | −0.534773 | + | 0.690267i | ||||
\(838\) | 64006.8 | 2.63852 | ||||||||
\(839\) | −6484.88 | + | 11232.1i | −0.266845 | + | 0.462189i | −0.968045 | − | 0.250775i | \(-0.919315\pi\) |
0.701200 | + | 0.712964i | \(0.252648\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13345.5 | − | 23115.0i | −0.547193 | − | 0.947765i | ||||
\(842\) | −27269.7 | − | 47232.6i | −1.11612 | − | 1.93318i | ||||
\(843\) | −20404.6 | + | 15606.9i | −0.833657 | + | 0.637640i | ||||
\(844\) | 19883.0 | − | 34438.4i | 0.810903 | − | 1.40453i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9122.88 | + | 33630.2i | −0.370746 | + | 1.36670i | ||||
\(847\) | −35910.5 | −1.45679 | ||||||||
\(848\) | −16006.9 | + | 27724.8i | −0.648208 | + | 1.12273i | ||||
\(849\) | −4251.83 | − | 32686.8i | −0.171876 | − | 1.32133i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10025.8 | − | 17365.2i | −0.403855 | − | 0.699497i | ||||
\(852\) | 762.719 | + | 5863.56i | 0.0306694 | + | 0.235777i | ||||
\(853\) | −19772.3 | + | 34246.6i | −0.793658 | + | 1.37466i | 0.130030 | + | 0.991510i | \(0.458493\pi\) |
−0.923688 | + | 0.383146i | \(0.874841\pi\) | |||||||
\(854\) | −6168.64 | −0.247174 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16526.3 | −0.659881 | ||||||||
\(857\) | 7419.10 | − | 12850.3i | 0.295719 | − | 0.512201i | −0.679433 | − | 0.733738i | \(-0.737774\pi\) |
0.975152 | + | 0.221537i | \(0.0711073\pi\) | |||||||
\(858\) | 32270.8 | − | 24683.0i | 1.28404 | − | 0.982124i | ||||
\(859\) | 12244.8 | + | 21208.7i | 0.486366 | + | 0.842411i | 0.999877 | − | 0.0156718i | \(-0.00498870\pi\) |
−0.513511 | + | 0.858083i | \(0.671655\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5753.88 | − | 2393.78i | −0.227749 | − | 0.0947500i | ||||
\(862\) | 13454.9 | − | 23304.6i | 0.531642 | − | 0.920831i | ||||
\(863\) | 10016.3 | 0.395084 | 0.197542 | − | 0.980294i | \(-0.436704\pi\) | ||||
0.197542 | + | 0.980294i | \(0.436704\pi\) | |||||||
\(864\) | −3008.44 | + | 3883.19i | −0.118460 | + | 0.152904i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −10878.5 | + | 18842.1i | −0.426866 | + | 0.739354i | ||||
\(867\) | 6301.22 | + | 2621.49i | 0.246829 | + | 0.102688i | ||||
\(868\) | −19010.2 | − | 32926.7i | −0.743374 | − | 1.28756i | ||||
\(869\) | −23293.8 | − | 40346.1i | −0.909308 | − | 1.57497i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6610.03 | + | 11448.9i | −0.257144 | + | 0.445386i | ||||
\(872\) | −16934.7 | −0.657663 | ||||||||
\(873\) | 43487.8 | − | 11508.3i | 1.68595 | − | 0.446159i | ||||
\(874\) | 59108.9 | 2.28763 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1206.11 | + | 9272.25i | 0.0465192 | + | 0.357626i | ||||
\(877\) | 16957.1 | + | 29370.5i | 0.652907 | + | 1.13087i | 0.982414 | + | 0.186715i | \(0.0597841\pi\) |
−0.329507 | + | 0.944153i | \(0.606883\pi\) | |||||||
\(878\) | −12782.6 | − | 22140.1i | −0.491334 | − | 0.851015i | ||||
\(879\) | 1009.98 | + | 7764.45i | 0.0387552 | + | 0.297939i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37237.1 | 1.42401 | 0.712004 | − | 0.702176i | \(-0.247788\pi\) | ||||
0.712004 | + | 0.702176i | \(0.247788\pi\) | |||||||
\(882\) | −7323.18 | − | 7368.67i | −0.279574 | − | 0.281311i | ||||
\(883\) | 36907.3 | 1.40660 | 0.703302 | − | 0.710892i | \(-0.251708\pi\) | ||||
0.703302 | + | 0.710892i | \(0.251708\pi\) | |||||||
\(884\) | −16597.6 | + | 28747.9i | −0.631492 | + | 1.09378i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 17953.2 | + | 31095.8i | 0.680754 | + | 1.17910i | ||||
\(887\) | 7791.52 | + | 13495.3i | 0.294942 | + | 0.510855i | 0.974971 | − | 0.222330i | \(-0.0713663\pi\) |
−0.680029 | + | 0.733185i | \(0.738033\pi\) | |||||||
\(888\) | −41069.7 | − | 17086.2i | −1.55204 | − | 0.645691i | ||||
\(889\) | −1708.15 | + | 2958.60i | −0.0644426 | + | 0.111618i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −37440.9 | − | 21926.8i | −1.40776 | − | 0.824438i | ||||
\(892\) | −21973.9 | −0.824820 | ||||||||
\(893\) | −18926.4 | + | 32781.5i | −0.709237 | + | 1.22843i | ||||
\(894\) | 37153.7 | + | 15457.0i | 1.38994 | + | 0.578255i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −21138.3 | − | 36612.6i | −0.788148 | − | 1.36511i | ||||
\(897\) | −9570.02 | + | 7319.82i | −0.356225 | + | 0.272466i | ||||
\(898\) | 2277.05 | − | 3943.97i | 0.0846172 | − | 0.146561i | ||||
\(899\) | −34062.3 | −1.26367 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −47603.5 | −1.76016 | ||||||||
\(902\) | −10663.0 | + | 18468.9i | −0.393614 | + | 0.681759i | ||||
\(903\) | −2906.86 | − | 22347.1i | −0.107125 | − | 0.823548i | ||||
\(904\) | 17366.0 | + | 30078.8i | 0.638922 | + | 1.10665i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 11943.2 | + | 91815.6i | 0.437953 | + | 3.36685i | ||||
\(907\) | −13559.3 | + | 23485.4i | −0.496394 | + | 0.859779i | −0.999991 | − | 0.00415907i | \(-0.998676\pi\) |
0.503598 | + | 0.863938i | \(0.332009\pi\) | |||||||
\(908\) | −25277.1 | −0.923845 | ||||||||
\(909\) | 11917.5 | − | 3153.77i | 0.434850 | − | 0.115076i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10366.8 | − | 17955.8i | 0.377021 | − | 0.653020i | −0.613606 | − | 0.789612i | \(-0.710282\pi\) |
0.990627 | + | 0.136593i | \(0.0436151\pi\) | |||||||
\(912\) | 31164.3 | − | 23836.7i | 1.13153 | − | 0.865472i | ||||
\(913\) | −8078.58 | − | 13992.5i | −0.292839 | − | 0.507212i | ||||
\(914\) | −10447.7 | − | 18096.0i | −0.378097 | − | 0.654883i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 51418.9 | − | 89060.1i | 1.85472 | − | 3.21248i | ||||
\(917\) | 15016.9 | 0.540789 | ||||||||
\(918\) | 53213.8 | + | 7257.34i | 1.91320 | + | 0.260924i | ||||
\(919\) | −48056.4 | −1.72495 | −0.862477 | − | 0.506096i | \(-0.831088\pi\) | ||||
−0.862477 | + | 0.506096i | \(0.831088\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 39527.5 | + | 16444.6i | 1.41420 | + | 0.588346i | ||||
\(922\) | −12717.2 | − | 22026.9i | −0.454251 | − | 0.786786i | ||||
\(923\) | −991.751 | − | 1717.76i | −0.0353672 | − | 0.0612577i | ||||
\(924\) | 61970.3 | − | 47399.3i | 2.20636 | − | 1.68758i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 41476.7 | 1.47193 | ||||||||
\(927\) | −1172.95 | + | 4323.90i | −0.0415584 | + | 0.153199i | ||||
\(928\) | −7913.29 | −0.279921 | ||||||||
\(929\) | −17838.8 | + | 30897.6i | −0.630001 | + | 1.09119i | 0.357550 | + | 0.933894i | \(0.383612\pi\) |
−0.987551 | + | 0.157299i | \(0.949721\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5642.67 | − | 9773.38i | −0.198637 | − | 0.344049i | ||||
\(932\) | −14846.2 | − | 25714.4i | −0.521786 | − | 0.903760i | ||||
\(933\) | 540.158 | + | 4152.58i | 0.0189539 | + | 0.145712i | ||||
\(934\) | 30821.0 | − | 53383.6i | 1.07976 | − | 1.87020i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6997.62 | + | 25795.7i | −0.244364 | + | 0.900811i | ||||
\(937\) | 33519.2 | 1.16865 | 0.584324 | − | 0.811520i | \(-0.301360\pi\) | ||||
0.584324 | + | 0.811520i | \(0.301360\pi\) | |||||||
\(938\) | −19229.9 | + | 33307.1i | −0.669380 | + | 1.15940i | ||||
\(939\) | −16762.6 | + | 12821.2i | −0.582562 | + | 0.445584i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26137.5 | + | 45271.5i | 0.905482 | + | 1.56834i | 0.820269 | + | 0.571978i | \(0.193824\pi\) |
0.0852134 | + | 0.996363i | \(0.472843\pi\) | |||||||
\(942\) | −24474.4 | − | 10182.1i | −0.846518 | − | 0.352176i | ||||
\(943\) | 3162.16 | − | 5477.02i | 0.109198 | − | 0.189137i | ||||
\(944\) | 26995.9 | 0.930765 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −77116.9 | −2.65041 | ||||||||
\(947\) | −14234.3 | + | 24654.6i | −0.488440 | + | 0.846004i | −0.999912 | − | 0.0132968i | \(-0.995767\pi\) |
0.511471 | + | 0.859300i | \(0.329101\pi\) | |||||||
\(948\) | 58339.2 | + | 24270.8i | 1.99870 | + | 0.831517i | ||||
\(949\) | −1568.29 | − | 2716.36i | −0.0536447 | − | 0.0929154i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4158.68 | + | 3180.85i | −0.141803 | + | 0.108461i | ||||
\(952\) | −23420.9 | + | 40566.2i | −0.797349 | + | 1.38105i | ||||
\(953\) | −492.737 | −0.0167485 | −0.00837424 | − | 0.999965i | \(-0.502666\pi\) | ||||
−0.00837424 | + | 0.999965i | \(0.502666\pi\) | |||||||
\(954\) | −76391.8 | + | 20215.8i | −2.59253 | + | 0.686070i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −22423.0 | + | 38837.8i | −0.758590 | + | 1.31392i | ||||
\(957\) | −9016.09 | − | 69313.1i | −0.304544 | − | 2.34125i | ||||
\(958\) | 44525.9 | + | 77121.1i | 1.50164 | + | 2.60091i | ||||
\(959\) | 15732.4 | + | 27249.4i | 0.529746 | + | 0.917547i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3538.42 | − | 6128.72i | 0.118775 | − | 0.205724i | ||||
\(962\) | 30762.9 | 1.03102 | ||||||||
\(963\) | −8604.13 | − | 8657.58i | −0.287917 | − | 0.289706i | ||||
\(964\) | −20019.8 | −0.668873 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −27841.1 | + | 21294.8i | −0.927300 | + | 0.709264i | ||||
\(967\) | −11603.2 | − | 20097.3i | −0.385866 | − | 0.668340i | 0.606023 | − | 0.795447i | \(-0.292764\pi\) |
−0.991889 | + | 0.127108i | \(0.959431\pi\) | |||||||
\(968\) | −40421.8 | − | 70012.6i | −1.34216 | − | 2.32468i | ||||
\(969\) | 53865.8 | + | 22409.7i | 1.78578 | + | 0.742935i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −47923.0 | −1.58385 | −0.791927 | − | 0.610615i | \(-0.790922\pi\) | ||||
−0.791927 | + | 0.610615i | \(0.790922\pi\) | |||||||
\(972\) | 58402.4 | − | 7229.34i | 1.92722 | − | 0.238561i | ||||
\(973\) | 31998.1 | 1.05428 | ||||||||
\(974\) | −36858.7 | + | 63841.2i | −1.21256 | + | 2.10021i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2077.65 | − | 3598.59i | −0.0681392 | − | 0.118021i | ||||
\(977\) | 12164.2 | + | 21069.1i | 0.398330 | + | 0.689929i | 0.993520 | − | 0.113657i | \(-0.0362564\pi\) |
−0.595190 | + | 0.803585i | \(0.702923\pi\) | |||||||
\(978\) | −40020.9 | + | 30610.8i | −1.30851 | + | 1.00084i | ||||
\(979\) | −6294.39 | + | 10902.2i | −0.205485 | + | 0.355910i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8816.75 | − | 8871.52i | −0.286949 | − | 0.288732i | ||||
\(982\) | 38538.5 | 1.25236 | ||||||||
\(983\) | 12686.3 | − | 21973.3i | 0.411627 | − | 0.712958i | −0.583441 | − | 0.812155i | \(-0.698294\pi\) |
0.995068 | + | 0.0991972i | \(0.0316275\pi\) | |||||||
\(984\) | −1809.71 | − | 13912.5i | −0.0586294 | − | 0.450726i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 43258.9 | + | 74926.7i | 1.39721 | + | 2.42003i | ||||
\(987\) | −2895.41 | − | 22259.0i | −0.0933757 | − | 0.717845i | ||||
\(988\) | −29929.7 | + | 51839.7i | −0.963755 | + | 1.66927i | ||||
\(989\) | 22869.3 | 0.735290 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32297.1 | 1.03527 | 0.517635 | − | 0.855602i | \(-0.326813\pi\) | ||||
0.517635 | + | 0.855602i | \(0.326813\pi\) | |||||||
\(992\) | −2638.46 | + | 4569.94i | −0.0844467 | + | 0.146266i | ||||
\(993\) | −38360.6 | + | 29340.9i | −1.22592 | + | 0.937668i | ||||
\(994\) | −2885.20 | − | 4997.32i | −0.0920654 | − | 0.159462i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 20232.7 | + | 8417.40i | 0.643674 | + | 0.267787i | ||||
\(997\) | 12728.6 | − | 22046.6i | 0.404332 | − | 0.700323i | −0.589912 | − | 0.807468i | \(-0.700838\pi\) |
0.994243 | + | 0.107145i | \(0.0341709\pi\) | |||||||
\(998\) | −92941.2 | −2.94790 | ||||||||
\(999\) | −12431.3 | − | 30410.6i | −0.393703 | − | 0.963111i |
(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 | 225.4.e.f.151.1 | yes | 24 | |
5.2 | odd | 4 | 225.4.k.e.124.2 | 48 | |||
5.3 | odd | 4 | 225.4.k.e.124.23 | 48 | |||
5.4 | even | 2 | 225.4.e.e.151.12 | yes | 24 | ||
9.2 | odd | 6 | 2025.4.a.bj.1.1 | 12 | |||
9.4 | even | 3 | inner | 225.4.e.f.76.1 | yes | 24 | |
9.7 | even | 3 | 2025.4.a.bf.1.12 | 12 | |||
45.4 | even | 6 | 225.4.e.e.76.12 | ✓ | 24 | ||
45.13 | odd | 12 | 225.4.k.e.49.2 | 48 | |||
45.22 | odd | 12 | 225.4.k.e.49.23 | 48 | |||
45.29 | odd | 6 | 2025.4.a.be.1.12 | 12 | |||
45.34 | even | 6 | 2025.4.a.bi.1.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.4.e.e.76.12 | ✓ | 24 | 45.4 | even | 6 | ||
225.4.e.e.151.12 | yes | 24 | 5.4 | even | 2 | ||
225.4.e.f.76.1 | yes | 24 | 9.4 | even | 3 | inner | |
225.4.e.f.151.1 | yes | 24 | 1.1 | even | 1 | trivial | |
225.4.k.e.49.2 | 48 | 45.13 | odd | 12 | |||
225.4.k.e.49.23 | 48 | 45.22 | odd | 12 | |||
225.4.k.e.124.2 | 48 | 5.2 | odd | 4 | |||
225.4.k.e.124.23 | 48 | 5.3 | odd | 4 | |||
2025.4.a.be.1.12 | 12 | 45.29 | odd | 6 | |||
2025.4.a.bf.1.12 | 12 | 9.7 | even | 3 | |||
2025.4.a.bi.1.1 | 12 | 45.34 | even | 6 | |||
2025.4.a.bj.1.1 | 12 | 9.2 | odd | 6 |