Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,4,Mod(109,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.109");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.e (of order \(3\), degree \(2\), not 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: | \(19.1166188419\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 12) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 109.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.109 |
Dual form | 324.4.e.h.217.1 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 9.00000 | − | 15.5885i | 0.804984 | − | 1.39427i | −0.111317 | − | 0.993785i | \(-0.535507\pi\) |
0.916302 | − | 0.400489i | \(-0.131160\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.00000 | − | 6.92820i | −0.215980 | − | 0.374088i | 0.737595 | − | 0.675243i | \(-0.235961\pi\) |
−0.953575 | + | 0.301155i | \(0.902628\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −18.0000 | − | 31.1769i | −0.493382 | − | 0.854563i | 0.506589 | − | 0.862188i | \(-0.330906\pi\) |
−0.999971 | + | 0.00762479i | \(0.997573\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.00000 | − | 8.66025i | 0.106673 | − | 0.184763i | −0.807747 | − | 0.589529i | \(-0.799313\pi\) |
0.914421 | + | 0.404765i | \(0.132647\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 18.0000 | 0.256802 | 0.128401 | − | 0.991722i | \(-0.459015\pi\) | ||||
0.128401 | + | 0.991722i | \(0.459015\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −100.000 | −1.20745 | −0.603726 | − | 0.797192i | \(-0.706318\pi\) | ||||
−0.603726 | + | 0.797192i | \(0.706318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −36.0000 | + | 62.3538i | −0.326370 | + | 0.565290i | −0.981789 | − | 0.189976i | \(-0.939159\pi\) |
0.655418 | + | 0.755266i | \(0.272492\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −99.5000 | − | 172.339i | −0.796000 | − | 1.37871i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 117.000 | + | 202.650i | 0.749185 | + | 1.29763i | 0.948214 | + | 0.317632i | \(0.102888\pi\) |
−0.199029 | + | 0.979994i | \(0.563779\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.00000 | − | 13.8564i | 0.0463498 | − | 0.0802801i | −0.841920 | − | 0.539603i | \(-0.818574\pi\) |
0.888270 | + | 0.459323i | \(0.151908\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −144.000 | −0.695441 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −226.000 | −1.00417 | −0.502083 | − | 0.864819i | \(-0.667433\pi\) | ||||
−0.502083 | + | 0.864819i | \(0.667433\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −45.0000 | + | 77.9423i | −0.171410 | + | 0.296891i | −0.938913 | − | 0.344154i | \(-0.888166\pi\) |
0.767503 | + | 0.641045i | \(0.221499\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −226.000 | − | 391.443i | −0.801504 | − | 1.38825i | −0.918626 | − | 0.395128i | \(-0.870700\pi\) |
0.117122 | − | 0.993118i | \(-0.462633\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −216.000 | − | 374.123i | −0.670358 | − | 1.16109i | −0.977803 | − | 0.209528i | \(-0.932807\pi\) |
0.307444 | − | 0.951566i | \(-0.400526\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 139.500 | − | 241.621i | 0.406706 | − | 0.704435i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 414.000 | 1.07297 | 0.536484 | − | 0.843911i | \(-0.319752\pi\) | ||||
0.536484 | + | 0.843911i | \(0.319752\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −648.000 | −1.58866 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 342.000 | − | 592.361i | 0.754654 | − | 1.30710i | −0.190892 | − | 0.981611i | \(-0.561138\pi\) |
0.945546 | − | 0.325489i | \(-0.105529\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −211.000 | − | 365.463i | −0.442882 | − | 0.767094i | 0.555020 | − | 0.831837i | \(-0.312710\pi\) |
−0.997902 | + | 0.0647433i | \(0.979377\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −90.0000 | − | 155.885i | −0.171740 | − | 0.297463i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −166.000 | + | 287.520i | −0.302688 | + | 0.524272i | −0.976744 | − | 0.214409i | \(-0.931218\pi\) |
0.674056 | + | 0.738681i | \(0.264551\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −360.000 | −0.601748 | −0.300874 | − | 0.953664i | \(-0.597278\pi\) | ||||
−0.300874 | + | 0.953664i | \(0.597278\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 26.0000 | 0.0416859 | 0.0208429 | − | 0.999783i | \(-0.493365\pi\) | ||||
0.0208429 | + | 0.999783i | \(0.493365\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −144.000 | + | 249.415i | −0.213121 | + | 0.369137i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −256.000 | − | 443.405i | −0.364585 | − | 0.631481i | 0.624124 | − | 0.781325i | \(-0.285456\pi\) |
−0.988710 | + | 0.149845i | \(0.952123\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 594.000 | + | 1028.84i | 0.785542 | + | 1.36060i | 0.928675 | + | 0.370895i | \(0.120949\pi\) |
−0.143133 | + | 0.989703i | \(0.545718\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 162.000 | − | 280.592i | 0.206722 | − | 0.358053i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −630.000 | −0.750336 | −0.375168 | − | 0.926957i | \(-0.622415\pi\) | ||||
−0.375168 | + | 0.926957i | \(0.622415\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −80.0000 | −0.0921569 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −900.000 | + | 1558.85i | −0.971979 | + | 1.68352i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 527.000 | + | 912.791i | 0.551637 | + | 0.955462i | 0.998157 | + | 0.0606889i | \(0.0193298\pi\) |
−0.446520 | + | 0.894774i | \(0.647337\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −279.000 | − | 483.242i | −0.274867 | − | 0.476083i | 0.695235 | − | 0.718783i | \(-0.255300\pi\) |
−0.970101 | + | 0.242700i | \(0.921967\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00000 | + | 6.92820i | −0.00382652 | + | 0.00662773i | −0.867932 | − | 0.496682i | \(-0.834551\pi\) |
0.864106 | + | 0.503310i | \(0.167885\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1764.00 | 1.59376 | 0.796880 | − | 0.604138i | \(-0.206482\pi\) | ||||
0.796880 | + | 0.604138i | \(0.206482\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1622.00 | 1.42532 | 0.712658 | − | 0.701512i | \(-0.247491\pi\) | ||||
0.712658 | + | 0.701512i | \(0.247491\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 567.000 | − | 982.073i | 0.472025 | − | 0.817572i | −0.527462 | − | 0.849578i | \(-0.676856\pi\) |
0.999488 | + | 0.0320065i | \(0.0101897\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 648.000 | + | 1122.37i | 0.525446 | + | 0.910099i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −72.0000 | − | 124.708i | −0.0554641 | − | 0.0960667i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.5000 | − | 30.3109i | 0.0131480 | − | 0.0227730i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1332.00 | −0.953102 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −592.000 | −0.413634 | −0.206817 | − | 0.978380i | \(-0.566310\pi\) | ||||
−0.206817 | + | 0.978380i | \(0.566310\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 954.000 | − | 1652.38i | 0.636270 | − | 1.10205i | −0.349975 | − | 0.936759i | \(-0.613810\pi\) |
0.986245 | − | 0.165293i | \(-0.0528569\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 400.000 | + | 692.820i | 0.260785 | + | 0.451693i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −477.000 | − | 826.188i | −0.297466 | − | 0.515226i | 0.678089 | − | 0.734979i | \(-0.262808\pi\) |
−0.975556 | + | 0.219753i | \(0.929475\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1282.00 | + | 2220.49i | −0.782286 | + | 1.35496i | 0.148320 | + | 0.988939i | \(0.452613\pi\) |
−0.930607 | + | 0.366021i | \(0.880720\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −360.000 | −0.210522 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4212.00 | 2.41233 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 369.000 | − | 639.127i | 0.202884 | − | 0.351405i | −0.746573 | − | 0.665304i | \(-0.768302\pi\) |
0.949456 | + | 0.313899i | \(0.101635\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1220.00 | + | 2113.10i | 0.657498 | + | 1.13882i | 0.981261 | + | 0.192682i | \(0.0617185\pi\) |
−0.323763 | + | 0.946138i | \(0.604948\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −144.000 | − | 249.415i | −0.0746217 | − | 0.129249i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1277.00 | − | 2211.83i | 0.649145 | − | 1.12435i | −0.334183 | − | 0.942508i | \(-0.608460\pi\) |
0.983328 | − | 0.181843i | \(-0.0582063\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 576.000 | 0.281958 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −820.000 | −0.394033 | −0.197016 | − | 0.980400i | \(-0.563125\pi\) | ||||
−0.197016 | + | 0.980400i | \(0.563125\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −972.000 | + | 1683.55i | −0.450393 | + | 0.780103i | −0.998410 | − | 0.0563635i | \(-0.982049\pi\) |
0.548017 | + | 0.836467i | \(0.315383\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1048.50 | + | 1816.06i | 0.477242 | + | 0.826607i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 621.000 | + | 1075.60i | 0.272912 | + | 0.472697i | 0.969606 | − | 0.244671i | \(-0.0786799\pi\) |
−0.696694 | + | 0.717368i | \(0.745347\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −796.000 | + | 1378.71i | −0.343840 | + | 0.595548i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1116.00 | 0.465999 | 0.232999 | − | 0.972477i | \(-0.425146\pi\) | ||||
0.232999 | + | 0.972477i | \(0.425146\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1070.00 | 0.439406 | 0.219703 | − | 0.975567i | \(-0.429491\pi\) | ||||
0.219703 | + | 0.975567i | \(0.429491\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2034.00 | + | 3522.99i | −0.808339 | + | 1.40008i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −324.000 | − | 561.184i | −0.126702 | − | 0.219454i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 288.000 | + | 498.831i | 0.109104 | + | 0.188974i | 0.915408 | − | 0.402528i | \(-0.131868\pi\) |
−0.806303 | + | 0.591502i | \(0.798535\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 671.000 | − | 1162.21i | 0.250257 | − | 0.433458i | −0.713339 | − | 0.700819i | \(-0.752818\pi\) |
0.963597 | + | 0.267361i | \(0.0861515\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1422.00 | 0.514281 | 0.257140 | − | 0.966374i | \(-0.417220\pi\) | ||||
0.257140 | + | 0.966374i | \(0.417220\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 872.000 | 0.310625 | 0.155313 | − | 0.987865i | \(-0.450361\pi\) | ||||
0.155313 | + | 0.987865i | \(0.450361\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 936.000 | − | 1621.20i | 0.323617 | − | 0.560522i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 810.000 | + | 1402.96i | 0.275965 | + | 0.477986i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1800.00 | + | 3117.69i | 0.595735 | + | 1.03184i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −670.000 | + | 1160.47i | −0.218600 | + | 0.378627i | −0.954380 | − | 0.298594i | \(-0.903482\pi\) |
0.735780 | + | 0.677221i | \(0.236816\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8136.00 | −2.58079 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −128.000 | −0.0400424 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 90.0000 | − | 155.885i | 0.0273939 | − | 0.0474477i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2440.00 | − | 4226.20i | −0.732711 | − | 1.26909i | −0.955720 | − | 0.294276i | \(-0.904922\pi\) |
0.223010 | − | 0.974816i | \(-0.428412\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1350.00 | − | 2338.27i | −0.394725 | − | 0.683684i | 0.598341 | − | 0.801242i | \(-0.295827\pi\) |
−0.993066 | + | 0.117557i | \(0.962494\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −127.000 | + | 219.970i | −0.0366480 | + | 0.0634762i | −0.883768 | − | 0.467926i | \(-0.845001\pi\) |
0.847120 | + | 0.531402i | \(0.178335\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4410.00 | 1.23995 | 0.619976 | − | 0.784621i | \(-0.287142\pi\) | ||||
0.619976 | + | 0.784621i | \(0.287142\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7776.00 | −2.15851 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1944.00 | − | 3367.11i | 0.526138 | − | 0.911297i | −0.473399 | − | 0.880848i | \(-0.656973\pi\) |
0.999536 | − | 0.0304489i | \(-0.00969368\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2569.00 | − | 4449.64i | −0.686655 | − | 1.18932i | −0.972914 | − | 0.231169i | \(-0.925745\pi\) |
0.286259 | − | 0.958152i | \(-0.407588\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2511.00 | − | 4349.18i | −0.654783 | − | 1.13412i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −500.000 | + | 866.025i | −0.128803 | + | 0.223093i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4788.00 | 1.20405 | 0.602024 | − | 0.798478i | \(-0.294361\pi\) | ||||
0.602024 | + | 0.798478i | \(0.294361\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2592.00 | 0.644101 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2943.00 | − | 5097.43i | 0.714316 | − | 1.23723i | −0.248906 | − | 0.968528i | \(-0.580071\pi\) |
0.963223 | − | 0.268705i | \(-0.0865955\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 904.000 | + | 1565.77i | 0.216880 | + | 0.375647i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1116.00 | − | 1932.97i | −0.261656 | − | 0.453201i | 0.705026 | − | 0.709181i | \(-0.250935\pi\) |
−0.966682 | + | 0.255980i | \(0.917602\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3726.00 | − | 6453.62i | 0.863722 | − | 1.49601i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −666.000 | −0.150954 | −0.0754772 | − | 0.997148i | \(-0.524048\pi\) | ||||
−0.0754772 | + | 0.997148i | \(0.524048\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5536.00 | −1.24092 | −0.620458 | − | 0.784240i | \(-0.713053\pi\) | ||||
−0.620458 | + | 0.784240i | \(0.713053\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3582.00 | + | 6204.21i | −0.785464 | + | 1.36046i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1063.00 | − | 1841.17i | −0.230576 | − | 0.399369i | 0.727402 | − | 0.686212i | \(-0.240728\pi\) |
−0.957978 | + | 0.286843i | \(0.907394\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1467.00 | + | 2540.92i | 0.311437 | + | 0.539425i | 0.978674 | − | 0.205421i | \(-0.0658563\pi\) |
−0.667236 | + | 0.744846i | \(0.732523\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1018.00 | + | 1763.23i | −0.213830 | + | 0.370364i | −0.952910 | − | 0.303253i | \(-0.901927\pi\) |
0.739080 | + | 0.673617i | \(0.235260\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 720.000 | 0.148085 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4589.00 | −0.934053 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1143.00 | + | 1979.73i | −0.227900 | + | 0.394735i | −0.957186 | − | 0.289475i | \(-0.906519\pi\) |
0.729285 | + | 0.684210i | \(0.239853\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6156.00 | − | 10662.5i | −1.21497 | − | 2.10439i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 360.000 | + | 623.538i | 0.0696299 | + | 0.120603i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1808.00 | + | 3131.55i | −0.346217 | + | 0.599666i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7596.00 | −1.42605 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1244.00 | 0.231267 | 0.115633 | − | 0.993292i | \(-0.463110\pi\) | ||||
0.115633 | + | 0.993292i | \(0.463110\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −612.000 | + | 1060.02i | −0.111586 | + | 0.193273i | −0.916410 | − | 0.400241i | \(-0.868926\pi\) |
0.804824 | + | 0.593514i | \(0.202260\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −949.000 | − | 1643.72i | −0.171376 | − | 0.296832i | 0.767525 | − | 0.641019i | \(-0.221488\pi\) |
−0.938901 | + | 0.344187i | \(0.888155\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4581.00 | + | 7934.52i | 0.811655 | + | 1.40583i | 0.911705 | + | 0.410845i | \(0.134766\pi\) |
−0.100050 | + | 0.994982i | \(0.531900\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4212.00 | − | 7295.40i | 0.739269 | − | 1.28045i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1800.00 | −0.310076 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1990.00 | −0.339647 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1728.00 | + | 2992.98i | −0.289568 | + | 0.501546i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2174.00 | + | 3765.48i | 0.361009 | + | 0.625285i | 0.988127 | − | 0.153639i | \(-0.0490992\pi\) |
−0.627119 | + | 0.778924i | \(0.715766\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2988.00 | + | 5175.37i | 0.487319 | + | 0.844061i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3577.00 | + | 6195.55i | −0.578195 | + | 1.00146i | 0.417492 | + | 0.908681i | \(0.362909\pi\) |
−0.995686 | + | 0.0927819i | \(0.970424\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −576.000 | −0.0914726 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4976.00 | −0.783320 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 918.000 | − | 1590.02i | 0.142020 | − | 0.245985i | −0.786237 | − | 0.617925i | \(-0.787974\pi\) |
0.928257 | + | 0.371939i | \(0.121307\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2947.00 | − | 5104.35i | −0.452004 | − | 0.782893i | 0.546507 | − | 0.837455i | \(-0.315957\pi\) |
−0.998510 | + | 0.0545613i | \(0.982624\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5553.00 | − | 9618.08i | −0.837270 | − | 1.45019i | −0.892169 | − | 0.451703i | \(-0.850817\pi\) |
0.0548984 | − | 0.998492i | \(-0.482516\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3240.00 | + | 5611.84i | −0.484398 | + | 0.839002i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13176.0 | 1.93705 | 0.968527 | − | 0.248907i | \(-0.0800713\pi\) | ||||
0.968527 | + | 0.248907i | \(0.0800713\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3141.00 | 0.457938 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 234.000 | − | 405.300i | 0.0335565 | − | 0.0581216i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3056.00 | + | 5293.15i | 0.434665 | + | 0.752861i | 0.997268 | − | 0.0738656i | \(-0.0235336\pi\) |
−0.562604 | + | 0.826727i | \(0.690200\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1656.00 | − | 2868.28i | −0.231739 | − | 0.401384i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6809.00 | − | 11793.5i | 0.945192 | − | 1.63712i | 0.189826 | − | 0.981818i | \(-0.439208\pi\) |
0.755366 | − | 0.655303i | \(-0.227459\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2340.00 | 0.319671 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 692.000 | 0.0937880 | 0.0468940 | − | 0.998900i | \(-0.485068\pi\) | ||||
0.0468940 | + | 0.998900i | \(0.485068\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4032.00 | − | 6983.63i | 0.537926 | − | 0.931715i | −0.461090 | − | 0.887353i | \(-0.652541\pi\) |
0.999016 | − | 0.0443613i | \(-0.0141253\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2592.00 | + | 4489.48i | 0.343118 | + | 0.594298i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6327.00 | − | 10958.7i | −0.824657 | − | 1.42835i | −0.902181 | − | 0.431358i | \(-0.858035\pi\) |
0.0775239 | − | 0.996990i | \(-0.475299\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −648.000 | + | 1122.37i | −0.0838127 | + | 0.145168i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9216.00 | −1.17394 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −106.000 | −0.0134005 | −0.00670024 | − | 0.999978i | \(-0.502133\pi\) | ||||
−0.00670024 | + | 0.999978i | \(0.502133\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2007.00 | − | 3476.23i | 0.249937 | − | 0.432904i | −0.713571 | − | 0.700583i | \(-0.752923\pi\) |
0.963508 | + | 0.267679i | \(0.0862567\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −80.0000 | − | 138.564i | −0.00988855 | − | 0.0171275i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4068.00 | + | 7045.98i | 0.495438 | + | 0.858124i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1957.00 | + | 3389.62i | −0.236595 | + | 0.409795i | −0.959735 | − | 0.280907i | \(-0.909365\pi\) |
0.723140 | + | 0.690702i | \(0.242698\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5472.00 | −0.651960 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 21384.0 | 2.52940 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2214.00 | + | 3834.76i | −0.258141 | + | 0.447113i | −0.965744 | − | 0.259497i | \(-0.916443\pi\) |
0.707603 | + | 0.706610i | \(0.249776\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7745.00 | + | 13414.7i | 0.896599 | + | 1.55296i | 0.831813 | + | 0.555056i | \(0.187303\pi\) |
0.0647860 | + | 0.997899i | \(0.479364\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1791.00 | − | 3102.10i | −0.204415 | − | 0.354057i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1688.00 | + | 2923.70i | −0.191307 | + | 0.331353i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6768.00 | 0.756388 | 0.378194 | − | 0.925726i | \(-0.376545\pi\) | ||||
0.378194 | + | 0.925726i | \(0.376545\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1298.00 | 0.144060 | 0.0720299 | − | 0.997402i | \(-0.477052\pi\) | ||||
0.0720299 | + | 0.997402i | \(0.477052\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3600.00 | − | 6235.38i | 0.394076 | − | 0.682560i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1124.00 | + | 1946.83i | 0.122200 | + | 0.211656i | 0.920635 | − | 0.390425i | \(-0.127672\pi\) |
−0.798435 | + | 0.602081i | \(0.794339\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4806.00 | + | 8324.24i | 0.515440 | + | 0.892768i | 0.999839 | + | 0.0179214i | \(0.00570486\pi\) |
−0.484399 | + | 0.874847i | \(0.660962\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5670.00 | + | 9820.73i | −0.604008 | + | 1.04617i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 162.000 | 0.0170273 | 0.00851364 | − | 0.999964i | \(-0.497290\pi\) | ||||
0.00851364 | + | 0.999964i | \(0.497290\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3240.00 | 0.338283 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −720.000 | + | 1247.08i | −0.0741849 | + | 0.128492i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −685.000 | − | 1186.45i | −0.0701159 | − | 0.121444i | 0.828836 | − | 0.559492i | \(-0.189004\pi\) |
−0.898952 | + | 0.438047i | \(0.855670\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7677.00 | + | 13297.0i | 0.775604 | + | 1.34339i | 0.934454 | + | 0.356083i | \(0.115888\pi\) |
−0.158850 | + | 0.987303i | \(0.550779\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6512.00 | − | 11279.1i | 0.653646 | − | 1.13215i | −0.328585 | − | 0.944474i | \(-0.606572\pi\) |
0.982231 | − | 0.187674i | \(-0.0600950\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14436.0 | −1.43045 | −0.715223 | − | 0.698896i | \(-0.753675\pi\) | ||||
−0.715223 | + | 0.698896i | \(0.753675\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2656.00 | 0.261498 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8136.00 | + | 14092.0i | −0.790896 | + | 1.36987i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9950.00 | + | 17233.9i | 0.961131 | + | 1.66473i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6048.00 | − | 10475.4i | −0.576911 | − | 0.999238i | −0.995831 | − | 0.0912156i | \(-0.970925\pi\) |
0.418921 | − | 0.908023i | \(-0.362409\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1130.00 | + | 1957.22i | −0.107118 | + | 0.185533i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18972.0 | 1.77624 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6056.00 | 0.563498 | 0.281749 | − | 0.959488i | \(-0.409085\pi\) | ||||
0.281749 | + | 0.959488i | \(0.409085\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3762.00 | + | 6515.98i | −0.345777 | + | 0.598904i | −0.985495 | − | 0.169706i | \(-0.945718\pi\) |
0.639717 | + | 0.768610i | \(0.279051\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2106.00 | + | 3647.70i | 0.192392 | + | 0.333233i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1440.00 | + | 2494.15i | 0.129965 | + | 0.225107i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2638.00 | + | 4569.15i | −0.236660 | + | 0.409906i | −0.959754 | − | 0.280843i | \(-0.909386\pi\) |
0.723094 | + | 0.690749i | \(0.242719\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4968.00 | 0.440382 | 0.220191 | − | 0.975457i | \(-0.429332\pi\) | ||||
0.220191 | + | 0.975457i | \(0.429332\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10044.0 | −0.885054 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5499.00 | + | 9524.55i | −0.478858 | + | 0.829407i | −0.999706 | − | 0.0242426i | \(-0.992283\pi\) |
0.520848 | + | 0.853650i | \(0.325616\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −104.000 | − | 180.133i | −0.00900331 | − | 0.0155942i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 72.0000 | + | 124.708i | 0.00616058 | + | 0.0106704i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7776.00 | + | 13468.4i | −0.661486 | + | 1.14573i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8838.00 | −0.743186 | −0.371593 | − | 0.928396i | \(-0.621188\pi\) | ||||
−0.371593 | + | 0.928396i | \(0.621188\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22436.0 | 1.87583 | 0.937914 | − | 0.346869i | \(-0.112755\pi\) | ||||
0.937914 | + | 0.346869i | \(0.112755\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 144.000 | − | 249.415i | 0.0119027 | − | 0.0206161i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3491.50 | + | 6047.46i | 0.286965 | + | 0.497038i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 450.000 | + | 779.423i | 0.0365697 | + | 0.0633406i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15876.0 | − | 27498.0i | 1.28295 | − | 2.22214i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10044.0 | −0.802645 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4762.00 | −0.378437 | −0.189218 | − | 0.981935i | \(-0.560595\pi\) | ||||
−0.189218 | + | 0.981935i | \(0.560595\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14598.0 | − | 25284.5i | 1.14736 | − | 1.98728i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3002.00 | + | 5199.62i | 0.234655 | + | 0.406434i | 0.959172 | − | 0.282822i | \(-0.0912706\pi\) |
−0.724517 | + | 0.689257i | \(0.757937\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11700.0 | − | 20265.0i | −0.904604 | − | 1.56682i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2048.00 | + | 3547.24i | −0.157486 | + | 0.272774i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5274.00 | −0.401197 | −0.200598 | − | 0.979674i | \(-0.564289\pi\) | ||||
−0.200598 | + | 0.979674i | \(0.564289\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4520.00 | −0.341996 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6210.00 | − | 10756.0i | 0.464867 | − | 0.805174i | −0.534328 | − | 0.845277i | \(-0.679435\pi\) |
0.999196 | + | 0.0401033i | \(0.0127687\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10206.0 | − | 17677.3i | −0.759946 | − | 1.31627i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10683.0 | + | 18503.5i | 0.787091 | + | 1.36328i | 0.927742 | + | 0.373222i | \(0.121747\pi\) |
−0.140651 | + | 0.990059i | \(0.544920\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10570.0 | + | 18307.8i | −0.774677 | + | 1.34178i | 0.160298 | + | 0.987069i | \(0.448754\pi\) |
−0.934976 | + | 0.354712i | \(0.884579\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14328.0 | 1.03916 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3266.00 | 0.235642 | 0.117821 | − | 0.993035i | \(-0.462409\pi\) | ||||
0.117821 | + | 0.993035i | \(0.462409\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4752.00 | − | 8230.71i | 0.339322 | − | 0.587723i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7452.00 | − | 12907.2i | −0.529383 | − | 0.916918i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8514.00 | − | 14746.7i | −0.598655 | − | 1.03690i | −0.993020 | − | 0.117947i | \(-0.962369\pi\) |
0.394365 | − | 0.918954i | \(-0.370965\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −800.000 | + | 1385.64i | −0.0559651 | + | 0.0969343i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9522.00 | 0.659396 | 0.329698 | − | 0.944086i | \(-0.393053\pi\) | ||||
0.329698 | + | 0.944086i | \(0.393053\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2592.00 | −0.178591 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5148.00 | − | 8916.60i | 0.351155 | − | 0.608218i | −0.635297 | − | 0.772268i | \(-0.719123\pi\) |
0.986452 | + | 0.164050i | \(0.0524558\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1691.00 | + | 2928.90i | 0.114771 | + | 0.198789i | 0.917688 | − | 0.397301i | \(-0.130053\pi\) |
−0.802917 | + | 0.596091i | \(0.796720\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −315.000 | − | 545.596i | −0.0211679 | − | 0.0366639i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10328.0 | − | 17888.6i | 0.690611 | − | 1.19617i | −0.281028 | − | 0.959700i | \(-0.590675\pi\) |
0.971638 | − | 0.236473i | \(-0.0759914\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4320.00 | −0.286037 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22114.0 | −1.45706 | −0.728529 | − | 0.685015i | \(-0.759795\pi\) | ||||
−0.728529 | + | 0.685015i | \(0.759795\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9981.00 | + | 17287.6i | −0.651248 | + | 1.12799i | 0.331573 | + | 0.943430i | \(0.392421\pi\) |
−0.982820 | + | 0.184565i | \(0.940912\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 302.000 | + | 523.079i | 0.0196097 | + | 0.0339650i | 0.875664 | − | 0.482921i | \(-0.160424\pi\) |
−0.856054 | + | 0.516886i | \(0.827091\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2520.00 | + | 4364.77i | 0.162057 | + | 0.280691i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 449.500 | − | 778.557i | 0.0287680 | − | 0.0498276i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4068.00 | −0.257872 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 152.000 | 0.00958958 | 0.00479479 | − | 0.999989i | \(-0.498474\pi\) | ||||
0.00479479 | + | 0.999989i | \(0.498474\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5328.00 | + | 9228.37i | −0.332969 | + | 0.576719i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1395.00 | − | 2416.21i | −0.0867691 | − | 0.150288i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2097.00 | − | 3632.11i | −0.129215 | − | 0.223806i | 0.794158 | − | 0.607711i | \(-0.207912\pi\) |
−0.923372 | + | 0.383905i | \(0.874579\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3626.00 | − | 6280.42i | 0.222388 | − | 0.385187i | −0.733145 | − | 0.680073i | \(-0.761948\pi\) |
0.955533 | + | 0.294885i | \(0.0952815\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6696.00 | −0.406873 | −0.203437 | − | 0.979088i | \(-0.565211\pi\) | ||||
−0.203437 | + | 0.979088i | \(0.565211\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24624.0 | −1.48933 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14211.0 | + | 24614.2i | −0.851638 | + | 1.47508i | 0.0280919 | + | 0.999605i | \(0.491057\pi\) |
−0.879730 | + | 0.475474i | \(0.842276\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17172.0 | − | 29742.8i | −1.02437 | − | 1.77427i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9954.00 | + | 17240.8i | 0.588396 | + | 1.01913i | 0.994443 | + | 0.105279i | \(0.0335736\pi\) |
−0.406047 | + | 0.913852i | \(0.633093\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7159.00 | + | 12399.8i | −0.421260 | + | 0.729644i | −0.996063 | − | 0.0886482i | \(-0.971745\pi\) |
0.574803 | + | 0.818292i | \(0.305079\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14400.0 | 0.839711 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16848.0 | −0.978047 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7596.00 | + | 13156.7i | −0.437020 | + | 0.756941i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15025.0 | − | 26024.1i | −0.860581 | − | 1.49057i | −0.871369 | − | 0.490629i | \(-0.836767\pi\) |
0.0107875 | − | 0.999942i | \(-0.496566\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11079.0 | − | 19189.4i | −0.628952 | − | 1.08938i | −0.987762 | − | 0.155966i | \(-0.950151\pi\) |
0.358810 | − | 0.933411i | \(-0.383183\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4216.00 | − | 7302.33i | 0.238285 | − | 0.412721i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3132.00 | −0.175465 | −0.0877325 | − | 0.996144i | \(-0.527962\pi\) | ||||
−0.0877325 | + | 0.996144i | \(0.527962\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17172.0 | −0.957822 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2070.00 | − | 3585.35i | 0.114457 | − | 0.198245i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10466.0 | + | 18127.6i | 0.576187 | + | 0.997986i | 0.995912 | + | 0.0903340i | \(0.0287934\pi\) |
−0.419724 | + | 0.907652i | \(0.637873\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 23076.0 | + | 39968.8i | 1.25946 | + | 2.18144i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −810.000 | + | 1402.96i | −0.0440186 | + | 0.0762424i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21834.0 | −1.17640 | −0.588202 | − | 0.808714i | \(-0.700164\pi\) | ||||
−0.588202 | + | 0.808714i | \(0.700164\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22600.0 | 1.21248 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2232.00 | + | 3865.94i | −0.118731 | + | 0.205649i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6223.00 | − | 10778.6i | −0.329633 | − | 0.570941i | 0.652806 | − | 0.757525i | \(-0.273592\pi\) |
−0.982439 | + | 0.186584i | \(0.940258\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 576.000 | + | 997.661i | 0.0302544 | + | 0.0524021i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3240.00 | + | 5611.84i | −0.169467 | + | 0.293526i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12528.0 | −0.649813 | −0.324907 | − | 0.945746i | \(-0.605333\pi\) | ||||
−0.324907 | + | 0.945746i | \(0.605333\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 64.0000 | 0.00330580 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 23283.0 | − | 40327.3i | 1.19270 | − | 2.06582i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5788.00 | − | 10025.1i | −0.295275 | − | 0.511432i | 0.679774 | − | 0.733422i | \(-0.262078\pi\) |
−0.975049 | + | 0.221990i | \(0.928745\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4068.00 | − | 7045.98i | −0.205828 | − | 0.356505i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14669.0 | − | 25407.5i | 0.739170 | − | 1.28028i | −0.213699 | − | 0.976900i | \(-0.568551\pi\) |
0.952869 | − | 0.303381i | \(-0.0981155\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11952.0 | 0.597364 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2540.00 | 0.126435 | 0.0632175 | − | 0.998000i | \(-0.479864\pi\) | ||||
0.0632175 | + | 0.998000i | \(0.479864\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9396.00 | − | 16274.3i | 0.463938 | − | 0.803564i | −0.535215 | − | 0.844716i | \(-0.679769\pi\) |
0.999153 | + | 0.0411519i | \(0.0131028\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6642.00 | − | 11504.3i | −0.326636 | − | 0.565751i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7056.00 | − | 12221.4i | −0.344220 | − | 0.596206i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2416.00 | + | 4184.63i | −0.117392 | + | 0.203328i | −0.918733 | − | 0.394879i | \(-0.870787\pi\) |
0.801342 | + | 0.598207i | \(0.204120\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 43920.0 | 2.11710 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20818.0 | −0.999529 | −0.499764 | − | 0.866161i | \(-0.666580\pi\) | ||||
−0.499764 | + | 0.866161i | \(0.666580\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6021.00 | + | 10428.7i | −0.286808 | + | 0.496766i | −0.973046 | − | 0.230611i | \(-0.925928\pi\) |
0.686238 | + | 0.727377i | \(0.259261\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6488.00 | − | 11237.5i | −0.307839 | − | 0.533193i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3420.00 | − | 5923.61i | −0.161003 | − | 0.278865i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6529.00 | + | 11308.6i | −0.306166 | + | 0.530295i | −0.977520 | − | 0.210841i | \(-0.932380\pi\) |
0.671354 | + | 0.741137i | \(0.265713\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11826.0 | −0.550261 | −0.275130 | − | 0.961407i | \(-0.588721\pi\) | ||||
−0.275130 | + | 0.961407i | \(0.588721\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3184.00 | −0.147578 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4500.00 | − | 7794.23i | 0.206969 | − | 0.358482i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6480.00 | + | 11223.7i | 0.296892 | + | 0.514232i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22986.0 | − | 39812.9i | −1.04510 | − | 1.81017i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5998.00 | + | 10388.8i | −0.271672 | + | 0.470549i | −0.969290 | − | 0.245920i | \(-0.920910\pi\) |
0.697618 | + | 0.716470i | \(0.254243\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9072.00 | −0.407792 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4220.00 | −0.188974 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3483.00 | + | 6032.73i | −0.154798 | + | 0.268118i | −0.932986 | − | 0.359914i | \(-0.882806\pi\) |
0.778187 | + | 0.628032i | \(0.216139\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3888.00 | − | 6734.21i | −0.172150 | − | 0.298172i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −468.000 | − | 810.600i | −0.0205671 | − | 0.0356232i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5184.00 | − | 8978.95i | 0.226971 | − | 0.393126i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −40806.0 | −1.77338 | −0.886689 | − | 0.462367i | \(-0.847000\pi\) | ||||
−0.886689 | + | 0.462367i | \(0.847000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17980.0 | −0.778500 | −0.389250 | − | 0.921132i | \(-0.627266\pi\) | ||||
−0.389250 | + | 0.921132i | \(0.627266\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7380.00 | + | 12782.5i | −0.317190 | + | 0.549390i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22600.0 | + | 39144.3i | 0.967777 | + | 1.67624i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6417.00 | + | 11114.6i | 0.272783 | + | 0.472474i | 0.969573 | − | 0.244801i | \(-0.0787226\pi\) |
−0.696790 | + | 0.717275i | \(0.745389\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18932.0 | − | 32791.2i | 0.801857 | − | 1.38886i | −0.116536 | − | 0.993186i | \(-0.537179\pi\) |
0.918393 | − | 0.395670i | \(-0.129488\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 42516.0 | 1.78770 | 0.893849 | − | 0.448368i | \(-0.147995\pi\) | ||||
0.893849 | + | 0.448368i | \(0.147995\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45638.0 | 1.91203 | 0.956015 | − | 0.293317i | \(-0.0947591\pi\) | ||||
0.956015 | + | 0.293317i | \(0.0947591\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2511.00 | − | 4349.18i | 0.104443 | − | 0.180901i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17496.0 | + | 30304.0i | 0.725119 | + | 1.25594i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8748.00 | − | 15152.0i | −0.359970 | − | 0.623486i | 0.627986 | − | 0.778225i | \(-0.283880\pi\) |
−0.987955 | + | 0.154739i | \(0.950546\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15183.5 | + | 26298.6i | −0.622555 | + | 1.07830i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 37746.0 | 1.53669 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −280.000 | −0.0113588 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8136.00 | − | 14092.0i | 0.327730 | − | 0.567646i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16087.0 | − | 27863.5i | −0.645731 | − | 1.11844i | −0.984132 | − | 0.177437i | \(-0.943219\pi\) |
0.338401 | − | 0.941002i | \(-0.390114\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19467.0 | + | 33717.8i | 0.775939 | + | 1.34397i | 0.934265 | + | 0.356579i | \(0.116057\pi\) |
−0.158326 | + | 0.987387i | \(0.550610\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14890.0 | + | 25790.2i | −0.591432 | + | 1.02439i | 0.402608 | + | 0.915373i | \(0.368104\pi\) |
−0.994040 | + | 0.109018i | \(0.965229\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −48096.0 | −1.89711 | −0.948556 | − | 0.316611i | \(-0.897455\pi\) | ||||
−0.948556 | + | 0.316611i | \(0.897455\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22356.0 | 0.878759 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9216.00 | + | 15962.6i | −0.359760 | + | 0.623122i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1660.00 | + | 2875.20i | 0.0645774 | + | 0.111851i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5328.00 | + | 9228.37i | 0.205851 | + | 0.356544i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10651.0 | + | 18448.1i | −0.410101 | + | 0.710316i | −0.994900 | − | 0.100862i | \(-0.967840\pi\) |
0.584799 | + | 0.811178i | \(0.301173\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7470.00 | −0.285665 | −0.142832 | − | 0.989747i | \(-0.545621\pi\) | ||||
−0.142832 | + | 0.989747i | \(0.545621\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 764.000 | 0.0291174 | 0.0145587 | − | 0.999894i | \(-0.495366\pi\) | ||||
0.0145587 | + | 0.999894i | \(0.495366\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16164.0 | + | 27996.9i | −0.611876 | + | 1.05980i | 0.379048 | + | 0.925377i | \(0.376252\pi\) |
−0.990924 | + | 0.134423i | \(0.957082\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2368.00 | + | 4101.50i | 0.0893365 | + | 0.154735i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 21600.0 | + | 37412.3i | 0.809425 | + | 1.40197i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10044.0 | − | 17396.7i | 0.375122 | − | 0.649730i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3744.00 | 0.138898 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7452.00 | 0.275541 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9630.00 | − | 16679.6i | 0.353715 | − | 0.612652i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18158.0 | + | 31450.6i | 0.664748 | + | 1.15138i | 0.979354 | + | 0.202155i | \(0.0647944\pi\) |
−0.314605 | + | 0.949223i | \(0.601872\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6696.00 | + | 11597.8i | 0.243522 | + | 0.421792i | 0.961715 | − | 0.274052i | \(-0.0883639\pi\) |
−0.718193 | + | 0.695844i | \(0.755031\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21384.0 | − | 37038.2i | 0.775145 | − | 1.34259i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15264.0 | −0.549686 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38072.0 | 1.36657 | 0.683286 | − | 0.730151i | \(-0.260550\pi\) | ||||
0.683286 | + | 0.730151i | \(0.260550\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1800.00 | + | 3117.69i | −0.0641904 | + | 0.111181i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22487.0 | + | 38948.6i | 0.799317 | + | 1.38446i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6399.00 | + | 11083.4i | 0.225990 | + | 0.391426i | 0.956616 | − | 0.291352i | \(-0.0941051\pi\) |
−0.730626 | + | 0.682778i | \(0.760772\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13950.0 | + | 24162.1i | −0.491077 | + | 0.850570i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11664.0 | −0.407972 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34874.0 | 1.21588 | 0.607942 | − | 0.793981i | \(-0.291995\pi\) | ||||
0.607942 | + | 0.793981i | \(0.291995\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8595.00 | + | 14887.0i | −0.297757 | + | 0.515730i | −0.975622 | − | 0.219456i | \(-0.929572\pi\) |
0.677866 | + | 0.735186i | \(0.262905\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3240.00 | − | 5611.84i | −0.111886 | − | 0.193793i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20142.0 | − | 34887.0i | −0.691158 | − | 1.19712i | −0.971459 | − | 0.237209i | \(-0.923767\pi\) |
0.280300 | − | 0.959912i | \(-0.409566\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 130.000 | − | 225.167i | 0.00444676 | − | 0.00770202i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15498.0 | 0.526789 | 0.263394 | − | 0.964688i | \(-0.415158\pi\) | ||||
0.263394 | + | 0.964688i | \(0.415158\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10368.0 | 0.351310 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3816.00 | + | 6609.51i | −0.128493 | + | 0.222557i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14767.5 | + | 25578.1i | 0.495703 | + | 0.858583i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12078.0 | − | 20919.7i | −0.402906 | − | 0.697854i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18580.0 | + | 32181.5i | −0.617883 | + | 1.07020i | 0.371989 | + | 0.928237i | \(0.378676\pi\) |
−0.989871 | + | 0.141967i | \(0.954657\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18468.0 | 0.610367 | 0.305183 | − | 0.952294i | \(-0.401282\pi\) | ||||
0.305183 | + | 0.952294i | \(0.401282\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20512.0 | 0.675832 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5193.00 | + | 8994.54i | −0.170050 | + | 0.294535i | −0.938437 | − | 0.345450i | \(-0.887726\pi\) |
0.768387 | + | 0.639985i | \(0.221060\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11340.0 | + | 19641.5i | 0.370202 | + | 0.641209i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22068.0 | − | 38222.9i | −0.716032 | − | 1.24020i | −0.962560 | − | 0.271069i | \(-0.912623\pi\) |
0.246528 | − | 0.969136i | \(-0.420710\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12798.0 | − | 22166.8i | 0.413988 | − | 0.717048i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32544.0 | 1.04635 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28432.0 | −0.911375 | −0.455687 | − | 0.890140i | \(-0.650606\pi\) | ||||
−0.455687 | + | 0.890140i | \(0.650606\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7848.00 | − | 13593.1i | 0.250049 | − | 0.433097i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19889.0 | + | 34448.8i | 0.631786 | + | 1.09429i | 0.987186 | + | 0.159572i | \(0.0510113\pi\) |
−0.355400 | + | 0.934714i | \(0.615655\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))