Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(13,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.13");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.v (of order \(8\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.10355792167\) |
Analytic rank: | \(0\) |
Dimension: | \(240\) |
Relative dimension: | \(60\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 13.6 | ||
Character | \(\chi\) | \(=\) | 224.13 |
Dual form | 224.3.v.b.69.6 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{7}{8}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.91469 | − | 0.577879i | −0.957347 | − | 0.288939i | ||||
\(3\) | 2.09916 | + | 0.869500i | 0.699719 | + | 0.289833i | 0.704043 | − | 0.710157i | \(-0.251376\pi\) |
−0.00432364 | + | 0.999991i | \(0.501376\pi\) | |||||||
\(4\) | 3.33211 | + | 2.21292i | 0.833028 | + | 0.553231i | ||||
\(5\) | 0.289108 | + | 0.697967i | 0.0578215 | + | 0.139593i | 0.950150 | − | 0.311793i | \(-0.100930\pi\) |
−0.892329 | + | 0.451387i | \(0.850930\pi\) | |||||||
\(6\) | −3.51678 | − | 2.87788i | −0.586130 | − | 0.479647i | ||||
\(7\) | −5.35156 | − | 4.51230i | −0.764508 | − | 0.644614i | ||||
\(8\) | −5.10118 | − | 6.16263i | −0.637647 | − | 0.770328i | ||||
\(9\) | −2.71353 | − | 2.71353i | −0.301503 | − | 0.301503i | ||||
\(10\) | −0.150212 | − | 1.50346i | −0.0150212 | − | 0.150346i | ||||
\(11\) | −4.20281 | − | 10.1465i | −0.382073 | − | 0.922407i | −0.991565 | − | 0.129614i | \(-0.958626\pi\) |
0.609491 | − | 0.792793i | \(-0.291374\pi\) | |||||||
\(12\) | 5.07050 | + | 7.54254i | 0.422541 | + | 0.628545i | ||||
\(13\) | 5.80299 | − | 14.0096i | 0.446384 | − | 1.07767i | −0.527283 | − | 0.849690i | \(-0.676789\pi\) |
0.973667 | − | 0.227976i | \(-0.0732106\pi\) | |||||||
\(14\) | 7.63904 | + | 11.7322i | 0.545645 | + | 0.838016i | ||||
\(15\) | 1.71652i | 0.114435i | ||||||||
\(16\) | 6.20595 | + | 14.7474i | 0.387872 | + | 0.921713i | ||||
\(17\) | 6.67995 | 0.392938 | 0.196469 | − | 0.980510i | \(-0.437052\pi\) | ||||
0.196469 | + | 0.980510i | \(0.437052\pi\) | |||||||
\(18\) | 3.62749 | + | 6.76367i | 0.201527 | + | 0.375759i | ||||
\(19\) | 4.52161 | − | 10.9161i | 0.237980 | − | 0.574534i | −0.759094 | − | 0.650981i | \(-0.774358\pi\) |
0.997074 | + | 0.0764475i | \(0.0243577\pi\) | |||||||
\(20\) | −0.581209 | + | 2.96548i | −0.0290604 | + | 0.148274i | ||||
\(21\) | −7.31032 | − | 14.1252i | −0.348110 | − | 0.672629i | ||||
\(22\) | 2.18366 | + | 21.8561i | 0.0992575 | + | 0.993460i | ||||
\(23\) | 23.1208 | + | 23.1208i | 1.00525 | + | 1.00525i | 0.999986 | + | 0.00526649i | \(0.00167638\pi\) |
0.00526649 | + | 0.999986i | \(0.498324\pi\) | |||||||
\(24\) | −5.34978 | − | 17.3718i | −0.222907 | − | 0.723825i | ||||
\(25\) | 17.2741 | − | 17.2741i | 0.690964 | − | 0.690964i | ||||
\(26\) | −19.2068 | + | 23.4708i | −0.738724 | + | 0.902722i | ||||
\(27\) | −11.1622 | − | 26.9480i | −0.413415 | − | 0.998072i | ||||
\(28\) | −7.84662 | − | 26.8781i | −0.280236 | − | 0.959931i | ||||
\(29\) | −12.5246 | + | 30.2370i | −0.431882 | + | 1.04265i | 0.546799 | + | 0.837264i | \(0.315846\pi\) |
−0.978680 | + | 0.205390i | \(0.934154\pi\) | |||||||
\(30\) | 0.991942 | − | 3.28662i | 0.0330647 | − | 0.109554i | ||||
\(31\) | − | 43.5456i | − | 1.40470i | −0.711834 | − | 0.702348i | \(-0.752135\pi\) | ||
0.711834 | − | 0.702348i | \(-0.247865\pi\) | |||||||
\(32\) | −3.36029 | − | 31.8231i | −0.105009 | − | 0.994471i | ||||
\(33\) | − | 24.9534i | − | 0.756163i | ||||||
\(34\) | −12.7901 | − | 3.86020i | −0.376178 | − | 0.113535i | ||||
\(35\) | 1.60226 | − | 5.03975i | 0.0457789 | − | 0.143993i | ||||
\(36\) | −3.03695 | − | 15.0466i | −0.0843598 | − | 0.417961i | ||||
\(37\) | −37.6230 | + | 15.5839i | −1.01684 | + | 0.421187i | −0.827944 | − | 0.560810i | \(-0.810490\pi\) |
−0.188892 | + | 0.981998i | \(0.560490\pi\) | |||||||
\(38\) | −14.9657 | + | 18.2881i | −0.393834 | + | 0.481267i | ||||
\(39\) | 24.3628 | − | 24.3628i | 0.624686 | − | 0.624686i | ||||
\(40\) | 2.82652 | − | 5.34212i | 0.0706631 | − | 0.133553i | ||||
\(41\) | 33.6938 | − | 33.6938i | 0.821800 | − | 0.821800i | −0.164566 | − | 0.986366i | \(-0.552622\pi\) |
0.986366 | + | 0.164566i | \(0.0526223\pi\) | |||||||
\(42\) | 5.83438 | + | 31.2699i | 0.138914 | + | 0.744522i | ||||
\(43\) | 2.11801 | + | 5.11333i | 0.0492560 | + | 0.118915i | 0.946592 | − | 0.322433i | \(-0.104501\pi\) |
−0.897336 | + | 0.441347i | \(0.854501\pi\) | |||||||
\(44\) | 8.44913 | − | 43.1097i | 0.192026 | − | 0.979766i | ||||
\(45\) | 1.10945 | − | 2.67845i | 0.0246545 | − | 0.0595212i | ||||
\(46\) | −30.9083 | − | 57.6303i | −0.671919 | − | 1.25283i | ||||
\(47\) | −80.2362 | −1.70715 | −0.853577 | − | 0.520967i | \(-0.825571\pi\) | ||||
−0.853577 | + | 0.520967i | \(0.825571\pi\) | |||||||
\(48\) | 0.204400 | + | 36.3532i | 0.00425833 | + | 0.757359i | ||||
\(49\) | 8.27831 | + | 48.2956i | 0.168945 | + | 0.985625i | ||||
\(50\) | −43.0569 | + | 23.0923i | −0.861139 | + | 0.461846i | ||||
\(51\) | 14.0223 | + | 5.80821i | 0.274946 | + | 0.113886i | ||||
\(52\) | 50.3385 | − | 33.8402i | 0.968047 | − | 0.650772i | ||||
\(53\) | −2.85046 | − | 6.88163i | −0.0537823 | − | 0.129842i | 0.894705 | − | 0.446658i | \(-0.147386\pi\) |
−0.948487 | + | 0.316816i | \(0.897386\pi\) | |||||||
\(54\) | 5.79958 | + | 58.0475i | 0.107400 | + | 1.07495i | ||||
\(55\) | 5.86685 | − | 5.86685i | 0.106670 | − | 0.106670i | ||||
\(56\) | −0.508375 | + | 55.9977i | −0.00907812 | + | 0.999959i | ||||
\(57\) | 18.9832 | − | 18.9832i | 0.333038 | − | 0.333038i | ||||
\(58\) | 41.4540 | − | 50.6569i | 0.714725 | − | 0.873395i | ||||
\(59\) | −8.20694 | − | 19.8133i | −0.139101 | − | 0.335819i | 0.838943 | − | 0.544220i | \(-0.183174\pi\) |
−0.978044 | + | 0.208401i | \(0.933174\pi\) | |||||||
\(60\) | −3.79853 | + | 5.71965i | −0.0633088 | + | 0.0953274i | ||||
\(61\) | 82.3062 | + | 34.0923i | 1.34928 | + | 0.558891i | 0.936092 | − | 0.351755i | \(-0.114415\pi\) |
0.413189 | + | 0.910645i | \(0.364415\pi\) | |||||||
\(62\) | −25.1641 | + | 83.3765i | −0.405872 | + | 1.34478i | ||||
\(63\) | 2.27735 | + | 26.7658i | 0.0361483 | + | 0.424855i | ||||
\(64\) | −11.9559 | + | 62.8733i | −0.186812 | + | 0.982396i | ||||
\(65\) | 11.4560 | 0.176246 | ||||||||
\(66\) | −14.4200 | + | 47.7781i | −0.218485 | + | 0.723911i | ||||
\(67\) | 17.9668 | − | 43.3756i | 0.268161 | − | 0.647397i | −0.731236 | − | 0.682124i | \(-0.761056\pi\) |
0.999397 | + | 0.0347271i | \(0.0110562\pi\) | |||||||
\(68\) | 22.2583 | + | 14.7822i | 0.327328 | + | 0.217385i | ||||
\(69\) | 28.4307 | + | 68.6378i | 0.412039 | + | 0.994750i | ||||
\(70\) | −5.98021 | + | 8.72367i | −0.0854315 | + | 0.124624i | ||||
\(71\) | −87.4287 | + | 87.4287i | −1.23139 | + | 1.23139i | −0.267960 | + | 0.963430i | \(0.586350\pi\) |
−0.963430 | + | 0.267960i | \(0.913650\pi\) | |||||||
\(72\) | −2.88027 | + | 30.5646i | −0.0400037 | + | 0.424509i | ||||
\(73\) | −12.3360 | + | 12.3360i | −0.168986 | + | 0.168986i | −0.786534 | − | 0.617548i | \(-0.788126\pi\) |
0.617548 | + | 0.786534i | \(0.288126\pi\) | |||||||
\(74\) | 81.0421 | − | 8.09699i | 1.09516 | − | 0.109419i | ||||
\(75\) | 51.2809 | − | 21.2412i | 0.683745 | − | 0.283216i | ||||
\(76\) | 39.2231 | − | 26.3678i | 0.516093 | − | 0.346945i | ||||
\(77\) | −23.2924 | + | 73.2638i | −0.302498 | + | 0.951478i | ||||
\(78\) | −60.7260 | + | 32.5685i | −0.778538 | + | 0.417545i | ||||
\(79\) | − | 68.3729i | − | 0.865480i | −0.901519 | − | 0.432740i | \(-0.857547\pi\) | ||
0.901519 | − | 0.432740i | \(-0.142453\pi\) | |||||||
\(80\) | −8.49903 | + | 8.59514i | −0.106238 | + | 0.107439i | ||||
\(81\) | − | 31.7360i | − | 0.391802i | ||||||
\(82\) | −83.9843 | + | 45.0424i | −1.02420 | + | 0.549298i | ||||
\(83\) | −10.3384 | + | 24.9591i | −0.124559 | + | 0.300712i | −0.973842 | − | 0.227226i | \(-0.927035\pi\) |
0.849283 | + | 0.527938i | \(0.177035\pi\) | |||||||
\(84\) | 6.89917 | − | 63.2439i | 0.0821330 | − | 0.752904i | ||||
\(85\) | 1.93122 | + | 4.66238i | 0.0227203 | + | 0.0548516i | ||||
\(86\) | −1.10046 | − | 11.0144i | −0.0127960 | − | 0.128075i | ||||
\(87\) | −52.5821 | + | 52.5821i | −0.604392 | + | 0.604392i | ||||
\(88\) | −41.0897 | + | 77.6593i | −0.466928 | + | 0.882492i | ||||
\(89\) | 82.5918 | + | 82.5918i | 0.927998 | + | 0.927998i | 0.997576 | − | 0.0695783i | \(-0.0221654\pi\) |
−0.0695783 | + | 0.997576i | \(0.522165\pi\) | |||||||
\(90\) | −3.67208 | + | 4.48730i | −0.0408009 | + | 0.0498588i | ||||
\(91\) | −94.2707 | + | 48.7886i | −1.03594 | + | 0.536138i | ||||
\(92\) | 25.8766 | + | 128.206i | 0.281267 | + | 1.39354i | ||||
\(93\) | 37.8629 | − | 91.4090i | 0.407128 | − | 0.982893i | ||||
\(94\) | 153.628 | + | 46.3668i | 1.63434 | + | 0.493264i | ||||
\(95\) | 8.92634 | 0.0939615 | ||||||||
\(96\) | 20.6164 | − | 69.7234i | 0.214754 | − | 0.726286i | ||||
\(97\) | − | 94.9539i | − | 0.978906i | −0.872030 | − | 0.489453i | \(-0.837196\pi\) | ||
0.872030 | − | 0.489453i | \(-0.162804\pi\) | |||||||
\(98\) | 12.0586 | − | 97.2553i | 0.123047 | − | 0.992401i | ||||
\(99\) | −16.1283 | + | 38.9372i | −0.162912 | + | 0.393305i | ||||
\(100\) | 95.7855 | − | 19.3330i | 0.957855 | − | 0.193330i | ||||
\(101\) | 30.7044 | + | 74.1270i | 0.304004 | + | 0.733931i | 0.999876 | + | 0.0157648i | \(0.00501829\pi\) |
−0.695872 | + | 0.718166i | \(0.744982\pi\) | |||||||
\(102\) | −23.4919 | − | 19.2241i | −0.230313 | − | 0.188472i | ||||
\(103\) | −116.227 | − | 116.227i | −1.12842 | − | 1.12842i | −0.990434 | − | 0.137984i | \(-0.955938\pi\) |
−0.137984 | − | 0.990434i | \(-0.544062\pi\) | |||||||
\(104\) | −115.938 | + | 35.7041i | −1.11479 | + | 0.343308i | ||||
\(105\) | 7.74546 | − | 9.18607i | 0.0737663 | − | 0.0874864i | ||||
\(106\) | 1.48102 | + | 14.8234i | 0.0139719 | + | 0.139844i | ||||
\(107\) | −29.4921 | − | 71.2003i | −0.275627 | − | 0.665423i | 0.724078 | − | 0.689719i | \(-0.242266\pi\) |
−0.999705 | + | 0.0242955i | \(0.992266\pi\) | |||||||
\(108\) | 22.4400 | − | 114.495i | 0.207778 | − | 1.06014i | ||||
\(109\) | 162.294 | + | 67.2242i | 1.48893 | + | 0.616736i | 0.971084 | − | 0.238737i | \(-0.0767333\pi\) |
0.517848 | + | 0.855473i | \(0.326733\pi\) | |||||||
\(110\) | −14.6235 | + | 7.84290i | −0.132941 | + | 0.0712991i | ||||
\(111\) | −92.5267 | −0.833574 | ||||||||
\(112\) | 33.3332 | − | 106.925i | 0.297618 | − | 0.954685i | ||||
\(113\) | 75.2992i | 0.666364i | 0.942862 | + | 0.333182i | \(0.108122\pi\) | ||||
−0.942862 | + | 0.333182i | \(0.891878\pi\) | |||||||
\(114\) | −47.3169 | + | 25.3770i | −0.415061 | + | 0.222605i | ||||
\(115\) | −9.45317 | + | 22.8220i | −0.0822015 | + | 0.198452i | ||||
\(116\) | −108.645 | + | 73.0371i | −0.936598 | + | 0.629630i | ||||
\(117\) | −53.7621 | + | 22.2690i | −0.459505 | + | 0.190333i | ||||
\(118\) | 4.26410 | + | 42.6791i | 0.0361365 | + | 0.361687i | ||||
\(119\) | −35.7481 | − | 30.1419i | −0.300404 | − | 0.253293i | ||||
\(120\) | 10.5783 | − | 8.75629i | 0.0881524 | − | 0.0729691i | ||||
\(121\) | 0.272532 | − | 0.272532i | 0.00225233 | − | 0.00225233i | ||||
\(122\) | −137.890 | − | 112.839i | −1.13025 | − | 0.924913i | ||||
\(123\) | 100.025 | − | 41.4319i | 0.813215 | − | 0.336845i | ||||
\(124\) | 96.3630 | − | 145.099i | 0.777121 | − | 1.17015i | ||||
\(125\) | 34.5000 | + | 14.2904i | 0.276000 | + | 0.114323i | ||||
\(126\) | 11.1070 | − | 52.5644i | 0.0881507 | − | 0.417178i | ||||
\(127\) | 58.6231 | 0.461600 | 0.230800 | − | 0.973001i | \(-0.425866\pi\) | ||||
0.230800 | + | 0.973001i | \(0.425866\pi\) | |||||||
\(128\) | 59.2251 | − | 113.474i | 0.462696 | − | 0.886517i | ||||
\(129\) | 12.5753i | 0.0974829i | ||||||||
\(130\) | −21.9347 | − | 6.62016i | −0.168728 | − | 0.0509243i | ||||
\(131\) | 38.7012 | + | 16.0306i | 0.295429 | + | 0.122371i | 0.525475 | − | 0.850809i | \(-0.323888\pi\) |
−0.230046 | + | 0.973180i | \(0.573888\pi\) | |||||||
\(132\) | 55.2199 | − | 83.1475i | 0.418333 | − | 0.629905i | ||||
\(133\) | −73.4545 | + | 38.0155i | −0.552290 | + | 0.285830i | ||||
\(134\) | −59.4667 | + | 72.6685i | −0.443782 | + | 0.542302i | ||||
\(135\) | 15.5817 | − | 15.5817i | 0.115420 | − | 0.115420i | ||||
\(136\) | −34.0756 | − | 41.1660i | −0.250556 | − | 0.302691i | ||||
\(137\) | −32.4767 | − | 32.4767i | −0.237056 | − | 0.237056i | 0.578574 | − | 0.815630i | \(-0.303609\pi\) |
−0.815630 | + | 0.578574i | \(0.803609\pi\) | |||||||
\(138\) | −14.7718 | − | 147.850i | −0.107042 | − | 1.07138i | ||||
\(139\) | 167.633 | − | 69.4357i | 1.20599 | − | 0.499538i | 0.313060 | − | 0.949733i | \(-0.398646\pi\) |
0.892930 | + | 0.450196i | \(0.148646\pi\) | |||||||
\(140\) | 16.4915 | − | 13.2473i | 0.117796 | − | 0.0946238i | ||||
\(141\) | −168.428 | − | 69.7654i | −1.19453 | − | 0.494790i | ||||
\(142\) | 217.922 | − | 116.876i | 1.53467 | − | 0.823071i | ||||
\(143\) | −166.537 | −1.16460 | ||||||||
\(144\) | 23.1775 | − | 56.8575i | 0.160955 | − | 0.394844i | ||||
\(145\) | −24.7254 | −0.170520 | ||||||||
\(146\) | 30.7483 | − | 16.4909i | 0.210605 | − | 0.112952i | ||||
\(147\) | −24.6156 | + | 108.578i | −0.167453 | + | 0.738627i | ||||
\(148\) | −159.850 | − | 31.3292i | −1.08007 | − | 0.211684i | ||||
\(149\) | 7.34358 | + | 17.7290i | 0.0492858 | + | 0.118986i | 0.946605 | − | 0.322396i | \(-0.104488\pi\) |
−0.897319 | + | 0.441382i | \(0.854488\pi\) | |||||||
\(150\) | −110.462 | + | 11.0364i | −0.736414 | + | 0.0735757i | ||||
\(151\) | −99.6942 | − | 99.6942i | −0.660226 | − | 0.660226i | 0.295207 | − | 0.955433i | \(-0.404611\pi\) |
−0.955433 | + | 0.295207i | \(0.904611\pi\) | |||||||
\(152\) | −90.3376 | + | 27.8202i | −0.594327 | + | 0.183027i | ||||
\(153\) | −18.1262 | − | 18.1262i | −0.118472 | − | 0.118472i | ||||
\(154\) | 86.9354 | − | 126.818i | 0.564515 | − | 0.823491i | ||||
\(155\) | 30.3934 | − | 12.5894i | 0.196086 | − | 0.0812217i | ||||
\(156\) | 135.092 | − | 27.2666i | 0.865977 | − | 0.174786i | ||||
\(157\) | 156.442 | + | 64.8003i | 0.996444 | + | 0.412741i | 0.820492 | − | 0.571658i | \(-0.193700\pi\) |
0.175952 | + | 0.984399i | \(0.443700\pi\) | |||||||
\(158\) | −39.5112 | + | 130.913i | −0.250071 | + | 0.828565i | ||||
\(159\) | − | 16.9241i | − | 0.106441i | ||||||
\(160\) | 21.2400 | − | 11.5457i | 0.132750 | − | 0.0721604i | ||||
\(161\) | −19.4043 | − | 228.060i | −0.120524 | − | 1.41652i | ||||
\(162\) | −18.3395 | + | 60.7647i | −0.113207 | + | 0.375091i | ||||
\(163\) | −79.1127 | + | 190.995i | −0.485354 | + | 1.17175i | 0.471679 | + | 0.881770i | \(0.343648\pi\) |
−0.957033 | + | 0.289978i | \(0.906352\pi\) | |||||||
\(164\) | 186.833 | − | 37.7098i | 1.13923 | − | 0.229938i | ||||
\(165\) | 17.4167 | − | 7.21422i | 0.105555 | − | 0.0437225i | ||||
\(166\) | 34.2182 | − | 41.8147i | 0.206134 | − | 0.251896i | ||||
\(167\) | 115.583 | + | 115.583i | 0.692115 | + | 0.692115i | 0.962697 | − | 0.270582i | \(-0.0872162\pi\) |
−0.270582 | + | 0.962697i | \(0.587216\pi\) | |||||||
\(168\) | −49.7571 | + | 117.106i | −0.296173 | + | 0.697059i | ||||
\(169\) | −43.0945 | − | 43.0945i | −0.254997 | − | 0.254997i | ||||
\(170\) | −1.00341 | − | 10.0431i | −0.00590241 | − | 0.0590768i | ||||
\(171\) | −41.8908 | + | 17.3517i | −0.244975 | + | 0.101472i | ||||
\(172\) | −4.25795 | + | 21.7252i | −0.0247555 | + | 0.126309i | ||||
\(173\) | −42.8385 | + | 103.421i | −0.247621 | + | 0.597811i | −0.998001 | − | 0.0631963i | \(-0.979871\pi\) |
0.750380 | + | 0.661007i | \(0.229871\pi\) | |||||||
\(174\) | 131.065 | − | 70.2926i | 0.753245 | − | 0.403980i | ||||
\(175\) | −170.389 | + | 14.4974i | −0.973652 | + | 0.0828423i | ||||
\(176\) | 123.552 | − | 124.949i | 0.701999 | − | 0.709938i | ||||
\(177\) | − | 48.7272i | − | 0.275295i | ||||||
\(178\) | −110.410 | − | 205.866i | −0.620282 | − | 1.15655i | ||||
\(179\) | 118.584 | + | 49.1190i | 0.662479 | + | 0.274408i | 0.688481 | − | 0.725254i | \(-0.258278\pi\) |
−0.0260023 | + | 0.999662i | \(0.508278\pi\) | |||||||
\(180\) | 9.62403 | − | 6.46978i | 0.0534668 | − | 0.0359432i | ||||
\(181\) | −234.591 | + | 97.1707i | −1.29608 | + | 0.536855i | −0.920792 | − | 0.390053i | \(-0.872457\pi\) |
−0.375289 | + | 0.926908i | \(0.622457\pi\) | |||||||
\(182\) | 208.694 | − | 38.9383i | 1.14667 | − | 0.213946i | ||||
\(183\) | 143.130 | + | 143.130i | 0.782133 | + | 0.782133i | ||||
\(184\) | 24.5415 | − | 260.428i | 0.133378 | − | 1.41537i | ||||
\(185\) | −21.7542 | − | 21.7542i | −0.117590 | − | 0.117590i | ||||
\(186\) | −125.319 | + | 153.140i | −0.673759 | + | 0.823335i | ||||
\(187\) | −28.0745 | − | 67.7779i | −0.150131 | − | 0.362449i | ||||
\(188\) | −267.356 | − | 177.557i | −1.42211 | − | 0.944449i | ||||
\(189\) | −61.8621 | + | 194.581i | −0.327312 | + | 1.02953i | ||||
\(190\) | −17.0912 | − | 5.15834i | −0.0899538 | − | 0.0271492i | ||||
\(191\) | 84.8434 | 0.444206 | 0.222103 | − | 0.975023i | \(-0.428708\pi\) | ||||
0.222103 | + | 0.975023i | \(0.428708\pi\) | |||||||
\(192\) | −79.7658 | + | 121.585i | −0.415447 | + | 0.633257i | ||||
\(193\) | 209.730 | 1.08668 | 0.543341 | − | 0.839512i | \(-0.317159\pi\) | ||||
0.543341 | + | 0.839512i | \(0.317159\pi\) | |||||||
\(194\) | −54.8718 | + | 181.808i | −0.282844 | + | 0.937153i | ||||
\(195\) | 24.0479 | + | 9.96096i | 0.123322 | + | 0.0510818i | ||||
\(196\) | −79.2903 | + | 179.246i | −0.404542 | + | 0.914519i | ||||
\(197\) | 28.7414 | − | 11.9051i | 0.145895 | − | 0.0604319i | −0.308541 | − | 0.951211i | \(-0.599841\pi\) |
0.454436 | + | 0.890779i | \(0.349841\pi\) | |||||||
\(198\) | 53.3817 | − | 65.2326i | 0.269605 | − | 0.329458i | ||||
\(199\) | 167.527 | + | 167.527i | 0.841844 | + | 0.841844i | 0.989099 | − | 0.147254i | \(-0.0470436\pi\) |
−0.147254 | + | 0.989099i | \(0.547044\pi\) | |||||||
\(200\) | −194.572 | − | 18.3356i | −0.972860 | − | 0.0916778i | ||||
\(201\) | 75.4302 | − | 75.4302i | 0.375275 | − | 0.375275i | ||||
\(202\) | −15.9532 | − | 159.674i | −0.0789761 | − | 0.790466i | ||||
\(203\) | 203.464 | − | 105.300i | 1.00229 | − | 0.518721i | ||||
\(204\) | 33.8706 | + | 50.3838i | 0.166033 | + | 0.246979i | ||||
\(205\) | 33.2583 | + | 13.7760i | 0.162236 | + | 0.0672002i | ||||
\(206\) | 155.374 | + | 289.705i | 0.754244 | + | 1.40633i | ||||
\(207\) | − | 125.478i | − | 0.606173i | ||||||
\(208\) | 242.619 | − | 1.36415i | 1.16644 | − | 0.00655843i | ||||
\(209\) | −129.764 | −0.620879 | ||||||||
\(210\) | −20.1386 | + | 13.1126i | −0.0958982 | + | 0.0624408i | ||||
\(211\) | 52.9763 | + | 21.9435i | 0.251073 | + | 0.103998i | 0.504671 | − | 0.863312i | \(-0.331614\pi\) |
−0.253598 | + | 0.967310i | \(0.581614\pi\) | |||||||
\(212\) | 5.73044 | − | 29.2382i | 0.0270304 | − | 0.137916i | ||||
\(213\) | −259.546 | + | 107.507i | −1.21853 | + | 0.504730i | ||||
\(214\) | 15.3233 | + | 153.370i | 0.0716042 | + | 0.716681i | ||||
\(215\) | −2.95660 | + | 2.95660i | −0.0137516 | + | 0.0137516i | ||||
\(216\) | −109.130 | + | 206.255i | −0.505230 | + | 0.954884i | ||||
\(217\) | −196.491 | + | 233.037i | −0.905487 | + | 1.07390i | ||||
\(218\) | −271.895 | − | 222.500i | −1.24723 | − | 1.02064i | ||||
\(219\) | −36.6213 | + | 15.1690i | −0.167221 | + | 0.0692650i | ||||
\(220\) | 32.5319 | − | 6.56612i | 0.147872 | − | 0.0298460i | ||||
\(221\) | 38.7636 | − | 93.5837i | 0.175401 | − | 0.423456i | ||||
\(222\) | 177.160 | + | 53.4692i | 0.798020 | + | 0.240852i | ||||
\(223\) | − | 91.0173i | − | 0.408149i | −0.978955 | − | 0.204075i | \(-0.934581\pi\) | ||
0.978955 | − | 0.204075i | \(-0.0654185\pi\) | |||||||
\(224\) | −125.612 | + | 185.466i | −0.560770 | + | 0.827972i | ||||
\(225\) | −93.7475 | −0.416655 | ||||||||
\(226\) | 43.5138 | − | 144.175i | 0.192539 | − | 0.637942i | ||||
\(227\) | 257.066 | + | 106.480i | 1.13245 | + | 0.469076i | 0.868613 | − | 0.495492i | \(-0.165012\pi\) |
0.263836 | + | 0.964568i | \(0.415012\pi\) | |||||||
\(228\) | 105.262 | − | 21.2458i | 0.461677 | − | 0.0931832i | ||||
\(229\) | 126.804 | + | 306.132i | 0.553729 | + | 1.33682i | 0.914659 | + | 0.404227i | \(0.132459\pi\) |
−0.360930 | + | 0.932593i | \(0.617541\pi\) | |||||||
\(230\) | 31.2883 | − | 38.2343i | 0.136036 | − | 0.166236i | ||||
\(231\) | −112.597 | + | 133.539i | −0.487434 | + | 0.578093i | ||||
\(232\) | 250.229 | − | 77.0600i | 1.07857 | − | 0.332155i | ||||
\(233\) | −77.9402 | − | 77.9402i | −0.334507 | − | 0.334507i | 0.519788 | − | 0.854295i | \(-0.326011\pi\) |
−0.854295 | + | 0.519788i | \(0.826011\pi\) | |||||||
\(234\) | 115.807 | − | 11.5704i | 0.494901 | − | 0.0494460i | ||||
\(235\) | −23.1969 | − | 56.0023i | −0.0987102 | − | 0.238308i | ||||
\(236\) | 16.4989 | − | 84.1815i | 0.0699104 | − | 0.356701i | ||||
\(237\) | 59.4502 | − | 143.526i | 0.250845 | − | 0.605593i | ||||
\(238\) | 51.0283 | + | 78.3706i | 0.214405 | + | 0.329288i | ||||
\(239\) | − | 23.1041i | − | 0.0966699i | −0.998831 | − | 0.0483350i | \(-0.984609\pi\) | ||
0.998831 | − | 0.0483350i | \(-0.0153915\pi\) | |||||||
\(240\) | −25.3143 | + | 10.6527i | −0.105476 | + | 0.0443861i | ||||
\(241\) | −29.4277 | −0.122107 | −0.0610534 | − | 0.998135i | \(-0.519446\pi\) | ||||
−0.0610534 | + | 0.998135i | \(0.519446\pi\) | |||||||
\(242\) | −0.679307 | + | 0.364326i | −0.00280705 | + | 0.00150548i | ||||
\(243\) | −72.8654 | + | 175.913i | −0.299858 | + | 0.723921i | ||||
\(244\) | 198.810 | + | 295.737i | 0.814794 | + | 1.21204i | ||||
\(245\) | −31.3155 | + | 19.7406i | −0.127818 | + | 0.0805740i | ||||
\(246\) | −215.461 | + | 21.5269i | −0.875857 | + | 0.0875076i | ||||
\(247\) | −126.692 | − | 126.692i | −0.512925 | − | 0.512925i | ||||
\(248\) | −268.355 | + | 222.134i | −1.08208 | + | 0.895701i | ||||
\(249\) | −43.4038 | + | 43.4038i | −0.174313 | + | 0.174313i | ||||
\(250\) | −57.7989 | − | 47.2985i | −0.231196 | − | 0.189194i | ||||
\(251\) | 75.0350 | + | 181.151i | 0.298944 | + | 0.721715i | 0.999963 | + | 0.00857265i | \(0.00272879\pi\) |
−0.701019 | + | 0.713143i | \(0.747271\pi\) | |||||||
\(252\) | −51.6424 | + | 94.2264i | −0.204930 | + | 0.373914i | ||||
\(253\) | 137.422 | − | 331.767i | 0.543172 | − | 1.31133i | ||||
\(254\) | −112.245 | − | 33.8771i | −0.441911 | − | 0.133374i | ||||
\(255\) | 11.4663i | 0.0449658i | ||||||||
\(256\) | −178.972 | + | 183.043i | −0.699111 | + | 0.715013i | ||||
\(257\) | − | 476.031i | − | 1.85226i | −0.377205 | − | 0.926130i | \(-0.623115\pi\) | ||
0.377205 | − | 0.926130i | \(-0.376885\pi\) | |||||||
\(258\) | 7.26699 | − | 24.0778i | 0.0281666 | − | 0.0933250i | ||||
\(259\) | 271.661 | + | 86.3677i | 1.04888 | + | 0.333466i | ||||
\(260\) | 38.1726 | + | 25.3512i | 0.146818 | + | 0.0975044i | ||||
\(261\) | 116.035 | − | 48.0631i | 0.444577 | − | 0.184150i | ||||
\(262\) | −64.8373 | − | 53.0582i | −0.247471 | − | 0.202512i | ||||
\(263\) | 228.327 | − | 228.327i | 0.868163 | − | 0.868163i | −0.124106 | − | 0.992269i | \(-0.539606\pi\) |
0.992269 | + | 0.124106i | \(0.0396063\pi\) | |||||||
\(264\) | −153.778 | + | 127.292i | −0.582494 | + | 0.482166i | ||||
\(265\) | 3.97906 | − | 3.97906i | 0.0150153 | − | 0.0150153i | ||||
\(266\) | 162.611 | − | 30.3402i | 0.611321 | − | 0.114061i | ||||
\(267\) | 101.560 | + | 245.187i | 0.380374 | + | 0.918303i | ||||
\(268\) | 155.854 | − | 104.773i | 0.581545 | − | 0.390946i | ||||
\(269\) | 155.951 | − | 376.498i | 0.579742 | − | 1.39962i | −0.313303 | − | 0.949653i | \(-0.601436\pi\) |
0.893045 | − | 0.449967i | \(-0.148564\pi\) | |||||||
\(270\) | −38.8386 | + | 20.8299i | −0.143847 | + | 0.0771477i | ||||
\(271\) | −244.080 | −0.900664 | −0.450332 | − | 0.892861i | \(-0.648694\pi\) | ||||
−0.450332 | + | 0.892861i | \(0.648694\pi\) | |||||||
\(272\) | 41.4554 | + | 98.5119i | 0.152410 | + | 0.362176i | ||||
\(273\) | −240.311 | + | 20.4466i | −0.880259 | + | 0.0748960i | ||||
\(274\) | 43.4153 | + | 80.9505i | 0.158450 | + | 0.295440i | ||||
\(275\) | −247.871 | − | 102.671i | −0.901349 | − | 0.373351i | ||||
\(276\) | −57.1558 | + | 291.624i | −0.207086 | + | 1.05661i | ||||
\(277\) | 19.5040 | + | 47.0868i | 0.0704115 | + | 0.169988i | 0.955167 | − | 0.296066i | \(-0.0956750\pi\) |
−0.884756 | + | 0.466055i | \(0.845675\pi\) | |||||||
\(278\) | −361.091 | + | 36.0769i | −1.29889 | + | 0.129773i | ||||
\(279\) | −118.162 | + | 118.162i | −0.423520 | + | 0.423520i | ||||
\(280\) | −39.2315 | + | 15.8345i | −0.140113 | + | 0.0565519i | ||||
\(281\) | 243.350 | − | 243.350i | 0.866014 | − | 0.866014i | −0.126014 | − | 0.992028i | \(-0.540219\pi\) |
0.992028 | + | 0.126014i | \(0.0402185\pi\) | |||||||
\(282\) | 282.173 | + | 230.911i | 1.00061 | + | 0.818832i | ||||
\(283\) | −194.439 | − | 469.416i | −0.687062 | − | 1.65871i | −0.750619 | − | 0.660736i | \(-0.770244\pi\) |
0.0635567 | − | 0.997978i | \(-0.479756\pi\) | |||||||
\(284\) | −484.795 | + | 97.8494i | −1.70703 | + | 0.344540i | ||||
\(285\) | 18.7378 | + | 7.76145i | 0.0657467 | + | 0.0272332i | ||||
\(286\) | 318.868 | + | 96.2384i | 1.11492 | + | 0.336498i | ||||
\(287\) | −332.351 | + | 28.2778i | −1.15802 | + | 0.0985288i | ||||
\(288\) | −77.2346 | + | 95.4710i | −0.268176 | + | 0.331497i | ||||
\(289\) | −244.378 | −0.845600 | ||||||||
\(290\) | 47.3415 | + | 14.2883i | 0.163247 | + | 0.0492699i | ||||
\(291\) | 82.5624 | − | 199.323i | 0.283720 | − | 0.684960i | ||||
\(292\) | −68.4035 | + | 13.8063i | −0.234258 | + | 0.0472819i | ||||
\(293\) | −59.1298 | − | 142.752i | −0.201808 | − | 0.487208i | 0.790281 | − | 0.612745i | \(-0.209935\pi\) |
−0.992089 | + | 0.125537i | \(0.959935\pi\) | |||||||
\(294\) | 109.876 | − | 193.669i | 0.373729 | − | 0.658739i | ||||
\(295\) | 11.4564 | − | 11.4564i | 0.0388351 | − | 0.0388351i | ||||
\(296\) | 287.959 | + | 152.360i | 0.972836 | + | 0.514729i | ||||
\(297\) | −226.514 | + | 226.514i | −0.762674 | + | 0.762674i | ||||
\(298\) | −3.81553 | − | 38.1893i | −0.0128038 | − | 0.128152i | ||||
\(299\) | 458.084 | − | 189.745i | 1.53205 | − | 0.634597i | ||||
\(300\) | 217.879 | + | 42.7024i | 0.726263 | + | 0.142341i | ||||
\(301\) | 11.7382 | − | 36.9214i | 0.0389974 | − | 0.122662i | ||||
\(302\) | 133.273 | + | 248.495i | 0.441301 | + | 0.822831i | ||||
\(303\) | 182.302i | 0.601656i | ||||||||
\(304\) | 189.046 | − | 1.06293i | 0.621861 | − | 0.00349648i | ||||
\(305\) | 67.3034i | 0.220667i | ||||||||
\(306\) | 24.2314 | + | 45.1809i | 0.0791877 | + | 0.147650i | ||||
\(307\) | −55.8272 | + | 134.779i | −0.181848 | + | 0.439019i | −0.988347 | − | 0.152216i | \(-0.951359\pi\) |
0.806500 | + | 0.591234i | \(0.201359\pi\) | |||||||
\(308\) | −239.740 | + | 192.579i | −0.778376 | + | 0.625256i | ||||
\(309\) | −142.920 | − | 345.039i | −0.462523 | − | 1.11663i | ||||
\(310\) | −65.4692 | + | 6.54108i | −0.211191 | + | 0.0211003i | ||||
\(311\) | 378.064 | − | 378.064i | 1.21564 | − | 1.21564i | 0.246494 | − | 0.969144i | \(-0.420721\pi\) |
0.969144 | − | 0.246494i | \(-0.0792786\pi\) | |||||||
\(312\) | −274.417 | − | 25.8598i | −0.879543 | − | 0.0828840i | ||||
\(313\) | 5.84131 | + | 5.84131i | 0.0186623 | + | 0.0186623i | 0.716376 | − | 0.697714i | \(-0.245799\pi\) |
−0.697714 | + | 0.716376i | \(0.745799\pi\) | |||||||
\(314\) | −262.092 | − | 214.477i | −0.834686 | − | 0.683048i | ||||
\(315\) | −18.0233 | + | 9.32772i | −0.0572168 | + | 0.0296118i | ||||
\(316\) | 151.304 | − | 227.826i | 0.478810 | − | 0.720969i | ||||
\(317\) | −181.823 | + | 438.960i | −0.573575 | + | 1.38473i | 0.324918 | + | 0.945742i | \(0.394663\pi\) |
−0.898492 | + | 0.438989i | \(0.855337\pi\) | |||||||
\(318\) | −9.78007 | + | 32.4045i | −0.0307549 | + | 0.101901i | ||||
\(319\) | 359.437 | 1.12676 | ||||||||
\(320\) | −47.3401 | + | 9.83229i | −0.147938 | + | 0.0307259i | ||||
\(321\) | − | 175.104i | − | 0.545495i | ||||||
\(322\) | −94.6379 | + | 447.879i | −0.293906 | + | 1.39093i | ||||
\(323\) | 30.2041 | − | 72.9192i | 0.0935112 | − | 0.225756i | ||||
\(324\) | 70.2292 | − | 105.748i | 0.216757 | − | 0.326382i | ||||
\(325\) | −141.763 | − | 342.245i | −0.436193 | − | 1.05306i | ||||
\(326\) | 261.849 | − | 319.980i | 0.803217 | − | 0.981533i | ||||
\(327\) | 282.228 | + | 282.228i | 0.863084 | + | 0.863084i | ||||
\(328\) | −379.521 | − | 35.7642i | −1.15708 | − | 0.109037i | ||||
\(329\) | 429.389 | + | 362.050i | 1.30513 | + | 1.10046i | ||||
\(330\) | −37.5165 | + | 3.74831i | −0.113686 | + | 0.0113585i | ||||
\(331\) | 190.224 | + | 459.241i | 0.574694 | + | 1.38743i | 0.897519 | + | 0.440975i | \(0.145367\pi\) |
−0.322826 | + | 0.946458i | \(0.604633\pi\) | |||||||
\(332\) | −89.6812 | + | 60.2884i | −0.270124 | + | 0.181592i | ||||
\(333\) | 144.378 | + | 59.8035i | 0.433569 | + | 0.179590i | ||||
\(334\) | −154.513 | − | 288.099i | −0.462615 | − | 0.862573i | ||||
\(335\) | 35.4691 | 0.105878 | ||||||||
\(336\) | 162.943 | − | 195.469i | 0.484949 | − | 0.581752i | ||||
\(337\) | − | 336.033i | − | 0.997129i | −0.866853 | − | 0.498565i | \(-0.833861\pi\) | ||
0.866853 | − | 0.498565i | \(-0.166139\pi\) | |||||||
\(338\) | 57.6094 | + | 107.416i | 0.170442 | + | 0.317799i | ||||
\(339\) | −65.4726 | + | 158.065i | −0.193135 | + | 0.466268i | ||||
\(340\) | −3.88244 | + | 19.8092i | −0.0114189 | + | 0.0582625i | ||||
\(341\) | −441.834 | + | 183.014i | −1.29570 | + | 0.536697i | ||||
\(342\) | 90.2352 | − | 9.01548i | 0.263846 | − | 0.0263610i | ||||
\(343\) | 173.623 | − | 295.811i | 0.506188 | − | 0.862423i | ||||
\(344\) | 20.7072 | − | 39.1365i | 0.0601953 | − | 0.113769i | ||||
\(345\) | −39.6874 | + | 39.6874i | −0.115036 | + | 0.115036i | ||||
\(346\) | 141.788 | − | 173.265i | 0.409791 | − | 0.500765i | ||||
\(347\) | −142.386 | + | 58.9781i | −0.410333 | + | 0.169966i | −0.578295 | − | 0.815828i | \(-0.696282\pi\) |
0.167961 | + | 0.985794i | \(0.446282\pi\) | |||||||
\(348\) | −291.569 | + | 58.8494i | −0.837843 | + | 0.169107i | ||||
\(349\) | −114.510 | − | 47.4314i | −0.328108 | − | 0.135907i | 0.212548 | − | 0.977151i | \(-0.431824\pi\) |
−0.540656 | + | 0.841244i | \(0.681824\pi\) | |||||||
\(350\) | 334.621 | + | 70.7062i | 0.956060 | + | 0.202018i | ||||
\(351\) | −442.305 | −1.26013 | ||||||||
\(352\) | −308.769 | + | 167.841i | −0.877186 | + | 0.476822i | ||||
\(353\) | − | 371.003i | − | 1.05100i | −0.850794 | − | 0.525499i | \(-0.823878\pi\) | ||
0.850794 | − | 0.525499i | \(-0.176122\pi\) | |||||||
\(354\) | −28.1584 | + | 93.2977i | −0.0795435 | + | 0.263553i | ||||
\(355\) | −86.2987 | − | 35.7461i | −0.243095 | − | 0.100693i | ||||
\(356\) | 92.4360 | + | 457.975i | 0.259652 | + | 1.28645i | ||||
\(357\) | −48.8325 | − | 94.3556i | −0.136786 | − | 0.264301i | ||||
\(358\) | −198.667 | − | 162.575i | −0.554935 | − | 0.454120i | ||||
\(359\) | −82.3766 | + | 82.3766i | −0.229461 | + | 0.229461i | −0.812468 | − | 0.583006i | \(-0.801876\pi\) |
0.583006 | + | 0.812468i | \(0.301876\pi\) | |||||||
\(360\) | −22.1658 | + | 6.82614i | −0.0615718 | + | 0.0189615i | ||||
\(361\) | 156.548 | + | 156.548i | 0.433652 | + | 0.433652i | ||||
\(362\) | 505.323 | − | 50.4872i | 1.39592 | − | 0.139467i | ||||
\(363\) | 0.809055 | − | 0.335122i | 0.00222880 | − | 0.000923200i | ||||
\(364\) | −422.086 | − | 46.0447i | −1.15958 | − | 0.126496i | ||||
\(365\) | −12.1765 | − | 5.04369i | −0.0333604 | − | 0.0138183i | ||||
\(366\) | −191.339 | − | 356.763i | −0.522784 | − | 0.974762i | ||||
\(367\) | 72.0402 | 0.196295 | 0.0981474 | − | 0.995172i | \(-0.468708\pi\) | ||||
0.0981474 | + | 0.995172i | \(0.468708\pi\) | |||||||
\(368\) | −197.486 | + | 484.459i | −0.536645 | + | 1.31646i | ||||
\(369\) | −182.858 | −0.495551 | ||||||||
\(370\) | 29.0813 | + | 54.2238i | 0.0785981 | + | 0.146551i | ||||
\(371\) | −15.7975 | + | 49.6896i | −0.0425810 | + | 0.133934i | ||||
\(372\) | 328.444 | − | 220.798i | 0.882915 | − | 0.593542i | ||||
\(373\) | 99.9056 | + | 241.193i | 0.267843 | + | 0.646631i | 0.999381 | − | 0.0351696i | \(-0.0111972\pi\) |
−0.731538 | + | 0.681801i | \(0.761197\pi\) | |||||||
\(374\) | 14.5868 | + | 145.998i | 0.0390020 | + | 0.390368i | ||||
\(375\) | 59.9955 | + | 59.9955i | 0.159988 | + | 0.159988i | ||||
\(376\) | 409.299 | + | 494.466i | 1.08856 | + | 1.31507i | ||||
\(377\) | 350.929 | + | 350.929i | 0.930847 | + | 0.930847i | ||||
\(378\) | 230.891 | − | 336.814i | 0.610823 | − | 0.891042i | ||||
\(379\) | 454.762 | − | 188.368i | 1.19990 | − | 0.497014i | 0.308933 | − | 0.951084i | \(-0.400028\pi\) |
0.890966 | + | 0.454069i | \(0.150028\pi\) | |||||||
\(380\) | 29.7436 | + | 19.7533i | 0.0782726 | + | 0.0519824i | ||||
\(381\) | 123.059 | + | 50.9728i | 0.322990 | + | 0.133787i | ||||
\(382\) | −162.449 | − | 49.0292i | −0.425260 | − | 0.128349i | ||||
\(383\) | − | 348.756i | − | 0.910590i | −0.890341 | − | 0.455295i | \(-0.849534\pi\) | ||
0.890341 | − | 0.455295i | \(-0.150466\pi\) | |||||||
\(384\) | 222.989 | − | 186.704i | 0.580700 | − | 0.486208i | ||||
\(385\) | −57.8697 | + | 4.92379i | −0.150311 | + | 0.0127891i | ||||
\(386\) | −401.568 | − | 121.198i | −1.04033 | − | 0.313985i | ||||
\(387\) | 8.12788 | − | 19.6224i | 0.0210023 | − | 0.0507040i | ||||
\(388\) | 210.126 | − | 316.397i | 0.541561 | − | 0.815457i | ||||
\(389\) | 63.3197 | − | 26.2279i | 0.162775 | − | 0.0674238i | −0.299808 | − | 0.954000i | \(-0.596923\pi\) |
0.462583 | + | 0.886576i | \(0.346923\pi\) | |||||||
\(390\) | −40.2881 | − | 32.9689i | −0.103303 | − | 0.0845357i | ||||
\(391\) | 154.446 | + | 154.446i | 0.395002 | + | 0.395002i | ||||
\(392\) | 255.399 | − | 297.381i | 0.651528 | − | 0.758625i | ||||
\(393\) | 67.3014 | + | 67.3014i | 0.171250 | + | 0.171250i | ||||
\(394\) | −61.9107 | + | 6.18555i | −0.157134 | + | 0.0156994i | ||||
\(395\) | 47.7221 | − | 19.7671i | 0.120815 | − | 0.0500434i | ||||
\(396\) | −139.906 | + | 94.0524i | −0.353299 | + | 0.237506i | ||||
\(397\) | 40.9820 | − | 98.9394i | 0.103229 | − | 0.249218i | −0.863823 | − | 0.503795i | \(-0.831937\pi\) |
0.967052 | + | 0.254578i | \(0.0819365\pi\) | |||||||
\(398\) | −223.953 | − | 417.573i | −0.562696 | − | 1.04918i | ||||
\(399\) | −187.247 | + | 15.9317i | −0.469291 | + | 0.0399292i | ||||
\(400\) | 361.950 | + | 147.546i | 0.904876 | + | 0.368865i | ||||
\(401\) | − | 228.115i | − | 0.568866i | −0.958696 | − | 0.284433i | \(-0.908195\pi\) | ||
0.958696 | − | 0.284433i | \(-0.0918053\pi\) | |||||||
\(402\) | −188.015 | + | 100.836i | −0.467700 | + | 0.250837i | ||||
\(403\) | −610.058 | − | 252.694i | −1.51379 | − | 0.627033i | ||||
\(404\) | −61.7268 | + | 314.946i | −0.152789 | + | 0.779570i | ||||
\(405\) | 22.1507 | − | 9.17511i | 0.0546930 | − | 0.0226546i | ||||
\(406\) | −450.423 | + | 84.0403i | −1.10942 | + | 0.206996i | ||||
\(407\) | 316.244 | + | 316.244i | 0.777013 | + | 0.777013i | ||||
\(408\) | −35.7362 | − | 116.043i | −0.0875888 | − | 0.284418i | ||||
\(409\) | 257.465 | + | 257.465i | 0.629499 | + | 0.629499i | 0.947942 | − | 0.318443i | \(-0.103160\pi\) |
−0.318443 | + | 0.947942i | \(0.603160\pi\) | |||||||
\(410\) | −55.7187 | − | 45.5962i | −0.135899 | − | 0.111210i | ||||
\(411\) | −39.9352 | − | 96.4121i | −0.0971659 | − | 0.234579i | ||||
\(412\) | −130.080 | − | 644.483i | −0.315729 | − | 1.56428i | ||||
\(413\) | −45.4837 | + | 143.064i | −0.110130 | + | 0.346402i | ||||
\(414\) | −72.5110 | + | 240.252i | −0.175147 | + | 0.580319i | ||||
\(415\) | −20.4095 | −0.0491796 | ||||||||
\(416\) | −465.330 | − | 137.592i | −1.11858 | − | 0.330751i | ||||
\(417\) | 412.262 | 0.988637 | ||||||||
\(418\) | 248.458 | + | 74.9877i | 0.594397 | + | 0.179396i | ||||
\(419\) | −201.431 | − | 83.4352i | −0.480741 | − | 0.199129i | 0.129134 | − | 0.991627i | \(-0.458780\pi\) |
−0.609875 | + | 0.792498i | \(0.708780\pi\) | |||||||
\(420\) | 46.1368 | − | 13.4689i | 0.109850 | − | 0.0320688i | ||||
\(421\) | 18.7520 | − | 7.76732i | 0.0445415 | − | 0.0184497i | −0.360301 | − | 0.932836i | \(-0.617326\pi\) |
0.404843 | + | 0.914386i | \(0.367326\pi\) | |||||||
\(422\) | −88.7528 | − | 72.6290i | −0.210315 | − | 0.172107i | ||||
\(423\) | 217.723 | + | 217.723i | 0.514712 | + | 0.514712i | ||||
\(424\) | −27.8682 | + | 52.6708i | −0.0657268 | + | 0.124223i | ||||
\(425\) | 115.390 | − | 115.390i | 0.271506 | − | 0.271506i | ||||
\(426\) | 559.077 | − | 55.8579i | 1.31239 | − | 0.131122i | ||||
\(427\) | −286.631 | − | 553.837i | −0.671268 | − | 1.29704i | ||||
\(428\) | 59.2896 | − | 302.511i | 0.138527 | − | 0.706802i | ||||
\(429\) | −349.588 | − | 144.804i | −0.814891 | − | 0.337539i | ||||
\(430\) | 7.36955 | − | 3.95244i | 0.0171385 | − | 0.00919171i | ||||
\(431\) | 7.68510i | 0.0178309i | 0.999960 | + | 0.00891543i | \(0.00283791\pi\) | ||||
−0.999960 | + | 0.00891543i | \(0.997162\pi\) | |||||||
\(432\) | 328.140 | − | 331.851i | 0.759584 | − | 0.768174i | ||||
\(433\) | −582.001 | −1.34411 | −0.672057 | − | 0.740500i | \(-0.734589\pi\) | ||||
−0.672057 | + | 0.740500i | \(0.734589\pi\) | |||||||
\(434\) | 510.887 | − | 332.646i | 1.17716 | − | 0.766466i | ||||
\(435\) | −51.9025 | − | 21.4987i | −0.119316 | − | 0.0494223i | ||||
\(436\) | 392.019 | + | 583.142i | 0.899125 | + | 1.33748i | ||||
\(437\) | 356.933 | − | 147.847i | 0.816781 | − | 0.338322i | ||||
\(438\) | 78.8845 | − | 7.88142i | 0.180102 | − | 0.0179941i | ||||
\(439\) | −47.5409 | + | 47.5409i | −0.108294 | + | 0.108294i | −0.759177 | − | 0.650884i | \(-0.774399\pi\) |
0.650884 | + | 0.759177i | \(0.274399\pi\) | |||||||
\(440\) | −66.0830 | − | 6.22735i | −0.150189 | − | 0.0141531i | ||||
\(441\) | 108.588 | − | 153.515i | 0.246232 | − | 0.348107i | ||||
\(442\) | −128.301 | + | 156.784i | −0.290273 | + | 0.354714i | ||||
\(443\) | −515.473 | + | 213.516i | −1.16360 | + | 0.481977i | −0.879071 | − | 0.476692i | \(-0.841836\pi\) |
−0.284525 | + | 0.958669i | \(0.591836\pi\) | |||||||
\(444\) | −308.310 | − | 204.754i | −0.694391 | − | 0.461159i | ||||
\(445\) | −33.7685 | + | 81.5243i | −0.0758842 | + | 0.183201i | ||||
\(446\) | −52.5969 | + | 174.270i | −0.117930 | + | 0.390741i | ||||
\(447\) | 43.6012i | 0.0975418i | ||||||||
\(448\) | 347.686 | − | 282.521i | 0.776085 | − | 0.630628i | ||||
\(449\) | 191.980 | 0.427573 | 0.213787 | − | 0.976880i | \(-0.431420\pi\) | ||||
0.213787 | + | 0.976880i | \(0.431420\pi\) | |||||||
\(450\) | 179.498 | + | 54.1746i | 0.398884 | + | 0.120388i | ||||
\(451\) | −483.482 | − | 200.265i | −1.07202 | − | 0.444046i | ||||
\(452\) | −166.631 | + | 250.905i | −0.368653 | + | 0.555100i | ||||
\(453\) | −122.590 | − | 295.958i | −0.270618 | − | 0.653329i | ||||
\(454\) | −430.670 | − | 352.430i | −0.948612 | − | 0.776277i | ||||
\(455\) | −61.3072 | − | 51.6927i | −0.134741 | − | 0.113610i | ||||
\(456\) | −213.823 | − | 20.1496i | −0.468909 | − | 0.0441878i | ||||
\(457\) | −514.716 | − | 514.716i | −1.12629 | − | 1.12629i | −0.990775 | − | 0.135519i | \(-0.956730\pi\) |
−0.135519 | − | 0.990775i | \(-0.543270\pi\) | |||||||
\(458\) | −65.8838 | − | 659.426i | −0.143851 | − | 1.43979i | ||||
\(459\) | −74.5629 | − | 180.011i | −0.162447 | − | 0.392181i | ||||
\(460\) | −82.0023 | + | 55.1263i | −0.178266 | + | 0.119840i | ||||
\(461\) | 251.467 | − | 607.096i | 0.545482 | − | 1.31691i | −0.375325 | − | 0.926893i | \(-0.622469\pi\) |
0.920807 | − | 0.390018i | \(-0.127531\pi\) | |||||||
\(462\) | 292.759 | − | 190.620i | 0.633677 | − | 0.412597i | ||||
\(463\) | 682.752i | 1.47463i | 0.675551 | + | 0.737313i | \(0.263906\pi\) | ||||
−0.675551 | + | 0.737313i | \(0.736094\pi\) | |||||||
\(464\) | −523.644 | + | 2.94425i | −1.12854 | + | 0.00634536i | ||||
\(465\) | 74.7470 | 0.160746 | ||||||||
\(466\) | 104.192 | + | 194.272i | 0.223588 | + | 0.416892i | ||||
\(467\) | −145.725 | + | 351.812i | −0.312046 | + | 0.753345i | 0.687583 | + | 0.726106i | \(0.258672\pi\) |
−0.999629 | + | 0.0272393i | \(0.991328\pi\) | |||||||
\(468\) | −228.421 | − | 44.7686i | −0.488079 | − | 0.0956593i | ||||
\(469\) | −291.874 | + | 151.056i | −0.622333 | + | 0.322080i | ||||
\(470\) | 12.0525 | + | 120.632i | 0.0256436 | + | 0.256664i | ||||
\(471\) | 272.052 | + | 272.052i | 0.577605 | + | 0.577605i | ||||
\(472\) | −80.2370 | + | 151.648i | −0.169994 | + | 0.321287i | ||||
\(473\) | 42.9807 | − | 42.9807i | 0.0908682 | − | 0.0908682i | ||||
\(474\) | −196.769 | + | 240.453i | −0.415125 | + | 0.507284i | ||||
\(475\) | −110.460 | − | 266.673i | −0.232547 | − | 0.561417i | ||||
\(476\) | −52.4150 | − | 179.544i | −0.110116 | − | 0.377193i | ||||
\(477\) | −10.9387 | + | 26.4083i | −0.0229322 | + | 0.0553633i | ||||
\(478\) | −13.3514 | + | 44.2373i | −0.0279317 | + | 0.0925467i | ||||
\(479\) | 281.780i | 0.588268i | 0.955764 | + | 0.294134i | \(0.0950312\pi\) | ||||
−0.955764 | + | 0.294134i | \(0.904969\pi\) | |||||||
\(480\) | 54.6250 | − | 5.76801i | 0.113802 | − | 0.0120167i | ||||
\(481\) | 617.518i | 1.28382i | ||||||||
\(482\) | 56.3451 | + | 17.0057i | 0.116899 | + | 0.0352815i | ||||
\(483\) | 157.566 | − | 495.607i | 0.326223 | − | 1.02610i | ||||
\(484\) | 1.51120 | − | 0.305016i | 0.00312232 | − | 0.000630197i | ||||
\(485\) | 66.2747 | − | 27.4519i | 0.136649 | − | 0.0566018i | ||||
\(486\) | 241.171 | − | 294.712i | 0.496237 | − | 0.606403i | ||||
\(487\) | 469.750 | − | 469.750i | 0.964578 | − | 0.964578i | −0.0348154 | − | 0.999394i | \(-0.511084\pi\) |
0.999394 | + | 0.0348154i | \(0.0110843\pi\) | |||||||
\(488\) | −209.760 | − | 681.133i | −0.429836 | − | 1.39576i | ||||
\(489\) | −332.140 | + | 332.140i | −0.679223 | + | 0.679223i | ||||
\(490\) | 71.3672 | − | 19.7007i | 0.145647 | − | 0.0402056i | ||||
\(491\) | 104.088 | + | 251.291i | 0.211992 | + | 0.511795i | 0.993729 | − | 0.111814i | \(-0.0356660\pi\) |
−0.781737 | + | 0.623608i | \(0.785666\pi\) | |||||||
\(492\) | 424.981 | + | 83.2927i | 0.863783 | + | 0.169294i | ||||
\(493\) | −83.6634 | + | 201.981i | −0.169703 | + | 0.409699i | ||||
\(494\) | 169.364 | + | 315.790i | 0.342843 | + | 0.639251i | ||||
\(495\) | −31.8397 | −0.0643226 | ||||||||
\(496\) | 642.185 | − | 270.242i | 1.29473 | − | 0.544842i | ||||
\(497\) | 862.384 | − | 73.3751i | 1.73518 | − | 0.147636i | ||||
\(498\) | 108.187 | − | 58.0230i | 0.217243 | − | 0.116512i | ||||
\(499\) | 305.440 | + | 126.517i | 0.612104 | + | 0.253542i | 0.667128 | − | 0.744943i | \(-0.267523\pi\) |
−0.0550239 | + | 0.998485i | \(0.517523\pi\) | |||||||
\(500\) | 83.3344 | + | 123.963i | 0.166669 | + | 0.247926i | ||||
\(501\) | 142.128 | + | 343.127i | 0.283688 | + | 0.684884i | ||||
\(502\) | −38.9861 | − | 390.209i | −0.0776616 | − | 0.777309i | ||||
\(503\) | 20.6455 | − | 20.6455i | 0.0410447 | − | 0.0410447i | −0.686287 | − | 0.727331i | \(-0.740760\pi\) |
0.727331 | + | 0.686287i | \(0.240760\pi\) | |||||||
\(504\) | 153.331 | − | 150.572i | 0.304228 | − | 0.298754i | ||||
\(505\) | −42.8614 | + | 42.8614i | −0.0848740 | + | 0.0848740i | ||||
\(506\) | −454.843 | + | 555.819i | −0.898899 | + | 1.09846i | ||||
\(507\) | −52.9915 | − | 127.933i | −0.104520 | − | 0.252333i | ||||
\(508\) | 195.339 | + | 129.728i | 0.384525 | + | 0.255371i | ||||
\(509\) | 164.659 | + | 68.2039i | 0.323495 | + | 0.133996i | 0.538520 | − | 0.842612i | \(-0.318983\pi\) |
−0.215026 | + | 0.976608i | \(0.568983\pi\) | |||||||
\(510\) | 6.62612 | − | 21.9544i | 0.0129924 | − | 0.0430479i | ||||
\(511\) | 121.680 | − | 10.3531i | 0.238122 | − | 0.0202604i | ||||
\(512\) | 448.454 | − | 247.048i | 0.875887 | − | 0.482516i | ||||
\(513\) | −344.639 | −0.671810 | ||||||||
\(514\) | −275.088 | + | 911.454i | −0.535191 | + | 1.77326i | ||||
\(515\) | 47.5206 | − | 114.725i | 0.0922730 | − | 0.222767i | ||||
\(516\) | −27.8281 | + | 41.9023i | −0.0539305 | + | 0.0812060i | ||||
\(517\) | 337.217 | + | 814.115i | 0.652258 | + | 1.57469i | ||||
\(518\) | −470.237 | − | 322.355i | −0.907794 | − | 0.622306i | ||||
\(519\) | −179.849 | + | 179.849i | −0.346531 | + | 0.346531i | ||||
\(520\) | −58.4389 | − | 70.5988i | −0.112383 | − | 0.135767i | ||||
\(521\) | −261.960 | + | 261.960i | −0.502803 | + | 0.502803i | −0.912308 | − | 0.409505i | \(-0.865701\pi\) |
0.409505 | + | 0.912308i | \(0.365701\pi\) | |||||||
\(522\) | −249.946 | + | 24.9723i | −0.478823 | + | 0.0478396i | ||||
\(523\) | −651.942 | + | 270.043i | −1.24654 | + | 0.516335i | −0.905754 | − | 0.423804i | \(-0.860694\pi\) |
−0.340790 | + | 0.940140i | \(0.610694\pi\) | |||||||
\(524\) | 93.4824 | + | 139.058i | 0.178402 | + | 0.265379i | ||||
\(525\) | −370.279 | − | 117.721i | −0.705294 | − | 0.224230i | ||||
\(526\) | −569.121 | + | 305.231i | −1.08198 | + | 0.580287i | ||||
\(527\) | − | 290.882i | − | 0.551959i | ||||||
\(528\) | 367.998 | − | 154.860i | 0.696966 | − | 0.293295i | ||||
\(529\) | 540.144i | 1.02107i | ||||||||
\(530\) | −9.91810 | + | 5.31927i | −0.0187134 | + | 0.0100364i | ||||
\(531\) | −31.4942 | + | 76.0337i | −0.0593111 | + | 0.143190i | ||||
\(532\) | −328.884 | − | 35.8774i | −0.618203 | − | 0.0674387i | ||||
\(533\) | −276.514 | − | 667.563i | −0.518787 | − | 1.25246i | ||||
\(534\) | −52.7677 | − | 528.147i | −0.0988158 | − | 0.989040i | ||||
\(535\) | 41.1691 | − | 41.1691i | 0.0769515 | − | 0.0769515i | ||||
\(536\) | −358.960 | + | 110.544i | −0.669701 | + | 0.206239i | ||||
\(537\) | 206.217 | + | 206.217i | 0.384017 | + | 0.384017i | ||||
\(538\) | −516.168 | + | 630.758i | −0.959420 | + | 1.17241i | ||||
\(539\) | 455.239 | − | 286.973i | 0.844598 | − | 0.532417i | ||||
\(540\) | 86.4011 | − | 17.4389i | 0.160002 | − | 0.0322943i | ||||
\(541\) | −65.5708 | + | 158.302i | −0.121203 | + | 0.292610i | −0.972823 | − | 0.231550i | \(-0.925620\pi\) |
0.851620 | + | 0.524159i | \(0.175620\pi\) | |||||||
\(542\) | 467.339 | + | 141.049i | 0.862248 | + | 0.260237i | ||||
\(543\) | −576.933 | −1.06249 | ||||||||
\(544\) | −22.4465 | − | 212.576i | −0.0412620 | − | 0.390766i | ||||
\(545\) | 132.711i | 0.243506i | ||||||||
\(546\) | 471.937 | + | 99.7214i | 0.864354 | + | 0.182640i | ||||
\(547\) | −164.242 | + | 396.515i | −0.300260 | + | 0.724891i | 0.699686 | + | 0.714451i | \(0.253323\pi\) |
−0.999945 | + | 0.0104405i | \(0.996677\pi\) | |||||||
\(548\) | −36.3476 | − | 180.084i | −0.0663277 | − | 0.328621i | ||||
\(549\) | −130.830 | − | 315.850i | −0.238305 | − | 0.575320i | ||||
\(550\) | 415.265 | + | 339.824i | 0.755028 | + | 0.617862i | ||||
\(551\) | 273.440 | + | 273.440i | 0.496261 | + | 0.496261i | ||||
\(552\) | 277.959 | − | 525.341i | 0.503549 | − | 0.951705i | ||||
\(553\) | −308.519 | + | 365.902i | −0.557901 | + | 0.661666i | ||||
\(554\) | −10.1337 | − | 101.428i | −0.0182919 | − | 0.183082i | ||||
\(555\) | −26.7502 | − | 64.5806i | −0.0481985 | − | 0.116362i | ||||
\(556\) | 712.227 | + | 139.590i | 1.28098 | + | 0.251062i | ||||
\(557\) | 50.3084 | + | 20.8384i | 0.0903203 | + | 0.0374119i | 0.427386 | − | 0.904069i | \(-0.359434\pi\) |
−0.337066 | + | 0.941481i | \(0.609434\pi\) | |||||||
\(558\) | 294.528 | − | 157.961i | 0.527828 | − | 0.283084i | ||||
\(559\) | 83.9267 | 0.150137 | ||||||||
\(560\) | 84.2669 | − | 7.64722i | 0.150477 | − | 0.0136558i | ||||
\(561\) | − | 166.687i | − | 0.297125i | ||||||
\(562\) | −606.568 | + | 325.314i | −1.07930 | + | 0.578851i | ||||
\(563\) | −286.196 | + | 690.939i | −0.508341 | + | 1.22724i | 0.436496 | + | 0.899706i | \(0.356219\pi\) |
−0.944838 | + | 0.327539i | \(0.893781\pi\) | |||||||
\(564\) | −406.837 | − | 605.185i | −0.721343 | − | 1.07302i | ||||
\(565\) | −52.5564 | + | 21.7696i | −0.0930201 | + | 0.0385302i | ||||
\(566\) | 101.025 | + | 1011.15i | 0.178489 | + | 1.78648i | ||||
\(567\) | −143.202 | + | 169.837i | −0.252561 | + | 0.299536i | ||||
\(568\) | 984.780 | + | 92.8011i | 1.73377 | + | 0.163382i | ||||
\(569\) | −636.268 | + | 636.268i | −1.11822 | + | 1.11822i | −0.126219 | + | 0.992002i | \(0.540284\pi\) |
−0.992002 | + | 0.126219i | \(0.959716\pi\) | |||||||
\(570\) | −31.3920 | − | 25.6890i | −0.0550737 | − | 0.0450684i | ||||
\(571\) | 876.195 | − | 362.932i | 1.53449 | − | 0.635608i | 0.554062 | − | 0.832475i | \(-0.313077\pi\) |
0.980430 | + | 0.196868i | \(0.0630769\pi\) | |||||||
\(572\) | −554.921 | − | 368.534i | −0.970142 | − | 0.644291i | ||||
\(573\) | 178.100 | + | 73.7713i | 0.310820 | + | 0.128746i | ||||
\(574\) | 652.692 | + | 137.915i | 1.13709 | + | 0.240270i | ||||
\(575\) | 798.782 | 1.38919 | ||||||||
\(576\) | 203.051 | − | 138.166i | 0.352520 | − | 0.239871i | ||||
\(577\) | 1068.87i | 1.85247i | 0.376951 | + | 0.926233i | \(0.376972\pi\) | ||||
−0.376951 | + | 0.926233i | \(0.623028\pi\) | |||||||
\(578\) | 467.910 | + | 141.221i | 0.809533 | + | 0.244327i | ||||
\(579\) | 440.256 | + | 182.360i | 0.760373 | + | 0.314957i | ||||
\(580\) | −82.3877 | − | 54.7153i | −0.142048 | − | 0.0943368i | ||||
\(581\) | 167.949 | − | 86.9200i | 0.289069 | − | 0.149604i | ||||
\(582\) | −273.266 | + | 333.932i | −0.469530 | + | 0.573767i | ||||
\(583\) | −57.8443 | + | 57.8443i | −0.0992184 | + | 0.0992184i | ||||
\(584\) | 138.950 | + | 13.0940i | 0.237928 | + | 0.0224213i | ||||
\(585\) | −31.0861 | − | 31.0861i | −0.0531386 | − | 0.0531386i | ||||
\(586\) | 30.7222 | + | 307.496i | 0.0524270 | + | 0.524738i | ||||
\(587\) | −17.5961 | + | 7.28853i | −0.0299763 | + | 0.0124166i | −0.397621 | − | 0.917550i | \(-0.630164\pi\) |
0.367645 | + | 0.929966i | \(0.380164\pi\) | |||||||
\(588\) | −322.297 | + | 307.322i | −0.548124 | + | 0.522657i | ||||
\(589\) | −475.350 | − | 196.896i | −0.807045 | − | 0.334289i | ||||
\(590\) | −28.5558 | + | 15.3150i | −0.0483997 | + | 0.0259577i | ||||
\(591\) | 70.6842 | 0.119601 | ||||||||
\(592\) | −463.309 | − | 458.128i | −0.782616 | − | 0.773865i | ||||
\(593\) | 137.536 | 0.231933 | 0.115966 | − | 0.993253i | \(-0.463004\pi\) | ||||
0.115966 | + | 0.993253i | \(0.463004\pi\) | |||||||
\(594\) | 564.603 | − | 302.808i | 0.950510 | − | 0.509777i | ||||
\(595\) | 10.7030 | − | 33.6653i | 0.0179883 | − | 0.0565803i | ||||
\(596\) | −14.7632 | + | 75.3257i | −0.0247705 | + | 0.126385i | ||||
\(597\) | 206.001 | + | 497.330i | 0.345060 | + | 0.833049i | ||||
\(598\) | −986.741 | + | 98.5861i | −1.65007 | + | 0.164860i | ||||
\(599\) | −689.523 | − | 689.523i | −1.15112 | − | 1.15112i | −0.986328 | − | 0.164795i | \(-0.947304\pi\) |
−0.164795 | − | 0.986328i | \(-0.552696\pi\) | |||||||
\(600\) | −392.495 | − | 207.670i | −0.654158 | − | 0.346116i | ||||
\(601\) | 789.713 | + | 789.713i | 1.31400 | + | 1.31400i | 0.918441 | + | 0.395557i | \(0.129448\pi\) |
0.395557 | + | 0.918441i | \(0.370552\pi\) | |||||||
\(602\) | −43.8112 | + | 63.9099i | −0.0727760 | + | 0.106163i | ||||
\(603\) | −166.454 | + | 68.9476i | −0.276044 | + | 0.114341i | ||||
\(604\) | −111.577 | − | 552.808i | −0.184730 | − | 0.915245i | ||||
\(605\) | 0.269010 | + | 0.111427i | 0.000444644 | + | 0.000184178i | ||||
\(606\) | 105.348 | − | 349.052i | 0.173842 | − | 0.575994i | ||||
\(607\) | − | 45.3017i | − | 0.0746322i | −0.999304 | − | 0.0373161i | \(-0.988119\pi\) | ||
0.999304 | − | 0.0373161i | \(-0.0118808\pi\) | |||||||
\(608\) | −362.579 | − | 107.210i | −0.596347 | − | 0.176333i | ||||
\(609\) | 518.662 | − | 44.1299i | 0.851662 | − | 0.0724628i | ||||
\(610\) | 38.8932 | − | 128.865i | 0.0637593 | − | 0.211255i | ||||
\(611\) | −465.610 | + | 1124.08i | −0.762045 | + | 1.83974i | ||||
\(612\) | −20.2867 | − | 100.511i | −0.0331482 | − | 0.164233i | ||||
\(613\) | −213.873 | + | 88.5890i | −0.348895 | + | 0.144517i | −0.550247 | − | 0.835002i | \(-0.685467\pi\) |
0.201352 | + | 0.979519i | \(0.435467\pi\) | |||||||
\(614\) | 184.778 | − | 225.799i | 0.300941 | − | 0.367751i | ||||
\(615\) | 57.8362 | + | 57.8362i | 0.0940426 | + | 0.0940426i | ||||
\(616\) | 570.316 | − | 230.189i | 0.925837 | − | 0.373684i | ||||
\(617\) | −214.537 | − | 214.537i | −0.347709 | − | 0.347709i | 0.511546 | − | 0.859256i | \(-0.329073\pi\) |
−0.859256 | + | 0.511546i | \(0.829073\pi\) | |||||||
\(618\) | 74.2571 | + | 743.234i | 0.120157 | + | 1.20264i | ||||
\(619\) | −482.960 | + | 200.048i | −0.780226 | + | 0.323180i | −0.737007 | − | 0.675886i | \(-0.763761\pi\) |
−0.0432191 | + | 0.999066i | \(0.513761\pi\) | |||||||
\(620\) | 129.133 | + | 25.3091i | 0.208280 | + | 0.0408211i | ||||
\(621\) | 364.979 | − | 881.138i | 0.587728 | − | 1.41890i | ||||
\(622\) | −942.351 | + | 505.402i | −1.51503 | + | 0.812543i | ||||
\(623\) | −69.3158 | − | 814.674i | −0.111261 | − | 1.30766i | ||||
\(624\) | 510.482 | + | 208.094i | 0.818080 | + | 0.333483i | ||||
\(625\) | − | 582.520i | − | 0.932032i | ||||||
\(626\) | −7.80877 | − | 14.5599i | −0.0124741 | − | 0.0232586i | ||||
\(627\) | −272.395 | − | 112.830i | −0.434441 | − | 0.179951i | ||||
\(628\) | 377.884 | + | 562.115i | 0.601725 | + | 0.895088i | ||||
\(629\) | −251.319 | + | 104.100i | −0.399554 | + | 0.165501i | ||||
\(630\) | 39.8994 | − | 7.44447i | 0.0633324 | − | 0.0118166i | ||||
\(631\) | −362.669 | − | 362.669i | −0.574752 | − | 0.574752i | 0.358701 | − | 0.933453i | \(-0.383220\pi\) |
−0.933453 | + | 0.358701i | \(0.883220\pi\) | |||||||
\(632\) | −421.357 | + | 348.783i | −0.666704 | + | 0.551871i | ||||
\(633\) | 92.1258 | + | 92.1258i | 0.145538 | + | 0.145538i | ||||
\(634\) | 601.801 | − | 735.403i | 0.949214 | − | 1.15994i | ||||
\(635\) | 16.9484 | + | 40.9170i | 0.0266904 | + | 0.0644363i | ||||
\(636\) | 37.4517 | − | 56.3930i | 0.0588863 | − | 0.0886682i | ||||
\(637\) | 724.644 | + | 164.283i | 1.13759 | + | 0.257901i | ||||
\(638\) | −688.212 | − | 207.711i | −1.07870 | − | 0.325566i | ||||
\(639\) | 474.480 | 0.742536 | ||||||||
\(640\) | 96.3237 | + | 8.53098i | 0.150506 | + | 0.0133297i | ||||
\(641\) | −724.389 | −1.13009 | −0.565046 | − | 0.825059i | \(-0.691142\pi\) | ||||
−0.565046 | + | 0.825059i | \(0.691142\pi\) | |||||||
\(642\) | −101.189 | + | 335.271i | −0.157615 | + | 0.522228i | ||||
\(643\) | −1122.10 | − | 464.789i | −1.74510 | − | 0.722844i | −0.998330 | − | 0.0577611i | \(-0.981604\pi\) |
−0.746770 | − | 0.665083i | \(-0.768396\pi\) | |||||||
\(644\) | 440.022 | − | 802.863i | 0.683265 | − | 1.24668i | ||||
\(645\) | −8.77714 | + | 3.63561i | −0.0136080 | + | 0.00563661i | ||||
\(646\) | −99.9701 | + | 122.164i | −0.154753 | + | 0.189108i | ||||
\(647\) | −25.0563 | − | 25.0563i | −0.0387269 | − | 0.0387269i | 0.687478 | − | 0.726205i | \(-0.258718\pi\) |
−0.726205 | + | 0.687478i | \(0.758718\pi\) | |||||||
\(648\) | −195.577 | + | 161.891i | −0.301816 | + | 0.249832i | ||||
\(649\) | −166.543 | + | 166.543i | −0.256615 | + | 0.256615i | ||||
\(650\) | 73.6560 | + | 737.217i | 0.113317 | + | 1.13418i | ||||
\(651\) | −615.090 | + | 318.332i | −0.944839 | + | 0.488989i | ||||
\(652\) | −686.270 | + | 461.347i | −1.05256 | + | 0.707587i | ||||
\(653\) | 1138.50 | + | 471.581i | 1.74349 | + | 0.722176i | 0.998480 | + | 0.0551197i | \(0.0175540\pi\) |
0.745007 | + | 0.667056i | \(0.232446\pi\) | |||||||
\(654\) | −377.288 | − | 703.475i | −0.576892 | − | 1.07565i | ||||
\(655\) | 31.6467i | 0.0483156i | ||||||||
\(656\) | 705.999 | + | 287.794i | 1.07622 | + | 0.438711i | ||||
\(657\) | 66.9481 | 0.101900 | ||||||||
\(658\) | −612.927 | − | 941.349i | −0.931501 | − | 1.43062i | ||||
\(659\) | 1026.06 | + | 425.007i | 1.55699 | + | 0.644928i | 0.984564 | − | 0.175026i | \(-0.0560011\pi\) |
0.572429 | + | 0.819954i | \(0.306001\pi\) | |||||||
\(660\) | 73.9988 | + | 14.5031i | 0.112119 | + | 0.0219744i | ||||
\(661\) | 426.275 | − | 176.569i | 0.644895 | − | 0.267124i | −0.0361718 | − | 0.999346i | \(-0.511516\pi\) |
0.681067 | + | 0.732221i | \(0.261516\pi\) | |||||||
\(662\) | −98.8350 | − | 989.232i | −0.149298 | − | 1.49431i | ||||
\(663\) | 162.742 | − | 162.742i | 0.245463 | − | 0.245463i | ||||
\(664\) | 206.552 | − | 63.6091i | 0.311072 | − | 0.0957969i | ||||
\(665\) | −47.7698 | − | 40.2783i | −0.0718343 | − | 0.0605689i | ||||
\(666\) | −241.881 | − | 197.939i | −0.363185 | − | 0.297205i | ||||
\(667\) | −988.682 | + | 409.525i | −1.48228 | + | 0.613981i | ||||
\(668\) | 129.360 | + | 640.913i | 0.193652 | + | 0.959450i | ||||
\(669\) | 79.1395 | − | 191.060i | 0.118295 | − | 0.285590i | ||||
\(670\) | −67.9125 | − | 20.4968i | −0.101362 | − | 0.0305923i | ||||
\(671\) | − | 978.401i | − | 1.45812i | ||||||
\(672\) | −424.943 | + | 280.102i | −0.632355 | + | 0.416818i | ||||
\(673\) | 209.915 | 0.311910 | 0.155955 | − | 0.987764i | \(-0.450155\pi\) | ||||
0.155955 | + | 0.987764i | \(0.450155\pi\) | |||||||
\(674\) | −194.186 | + | 643.400i | −0.288110 | + | 0.954599i | ||||
\(675\) | −658.318 | − | 272.684i | −0.975287 | − | 0.403977i | ||||
\(676\) | −48.2310 | − | 238.961i | −0.0713476 | − | 0.353492i | ||||
\(677\) | −5.00322 | − | 12.0788i | −0.00739028 | − | 0.0178417i | 0.920141 | − | 0.391586i | \(-0.128074\pi\) |
−0.927532 | + | 0.373745i | \(0.878074\pi\) | |||||||
\(678\) | 216.702 | − | 264.811i | 0.319620 | − | 0.390576i | ||||
\(679\) | −428.460 | + | 508.151i | −0.631017 | + | 0.748382i | ||||
\(680\) | 18.8810 | − | 35.6851i | 0.0277662 | − | 0.0524780i | ||||
\(681\) | 447.037 | + | 447.037i | 0.656442 | + | 0.656442i | ||||
\(682\) | 951.737 | − | 95.0889i | 1.39551 | − | 0.139427i | ||||
\(683\) | 155.013 | + | 374.233i | 0.226958 | + | 0.547926i | 0.995804 | − | 0.0915081i | \(-0.0291687\pi\) |
−0.768846 | + | 0.639434i | \(0.779169\pi\) | |||||||
\(684\) | −177.983 | − | 34.8831i | −0.260209 | − | 0.0509987i | ||||
\(685\) | 13.2784 | − | 32.0569i | 0.0193845 | − | 0.0467984i | ||||
\(686\) | −503.377 | + | 466.055i | −0.733786 | + | 0.679381i | ||||
\(687\) | 752.875i | 1.09589i | ||||||||
\(688\) | −62.2641 | + | 62.9682i | −0.0905001 | + | 0.0915236i | ||||
\(689\) | −112.950 | −0.163934 | ||||||||
\(690\) | 98.9237 | − | 53.0548i | 0.143368 | − | 0.0768909i | ||||
\(691\) | 254.787 | − | 615.111i | 0.368722 | − | 0.890175i | −0.625238 | − | 0.780434i | \(-0.714998\pi\) |
0.993960 | − | 0.109740i | \(-0.0350019\pi\) | |||||||
\(692\) | −371.606 | + | 249.813i | −0.537003 | + | 0.361001i | ||||
\(693\) | 262.008 | − | 135.599i | 0.378078 | − | 0.195669i | ||||
\(694\) | 306.707 | − | 30.6434i | 0.441941 | − | 0.0441547i | ||||
\(695\) | 96.9277 | + | 96.9277i | 0.139464 | + | 0.139464i | ||||
\(696\) | 592.274 | + | 55.8132i | 0.850969 | + | 0.0801913i | ||||
\(697\) | 225.073 | − | 225.073i | 0.322917 | − | 0.322917i | ||||
\(698\) | 191.841 | + | 156.989i | 0.274844 | + | 0.224913i | ||||
\(699\) | −95.8399 | − | 231.378i | −0.137110 | − | 0.331013i | ||||
\(700\) | −599.838 | − | 328.751i | −0.856911 | − | 0.469644i | ||||
\(701\) | 529.921 | − | 1279.34i | 0.755949 | − | 1.82502i | 0.233490 | − | 0.972359i | \(-0.424985\pi\) |
0.522459 | − | 0.852664i | \(-0.325015\pi\) | |||||||
\(702\) | 846.880 | + | 255.599i | 1.20638 | + | 0.364101i | ||||
\(703\) | 481.162i | 0.684441i | ||||||||
\(704\) | 688.191 | − | 142.934i | 0.977544 | − | 0.203031i | ||||
\(705\) | − | 137.727i | − | 0.195358i | ||||||
\(706\) | −214.394 | + | 710.357i | −0.303675 | + | 1.00617i | ||||
\(707\) | 170.167 | − | 535.243i | 0.240689 | − | 0.757062i | ||||
\(708\) | 107.830 | − | 162.365i | 0.152302 | − | 0.229328i | ||||
\(709\) | 296.905 | − | 122.982i | 0.418766 | − | 0.173458i | −0.163343 | − | 0.986569i | \(-0.552228\pi\) |
0.582109 | + | 0.813111i | \(0.302228\pi\) | |||||||
\(710\) | 144.579 | + | 118.313i | 0.203632 | + | 0.166638i | ||||
\(711\) | −185.532 | + | 185.532i | −0.260945 | + | 0.260945i | ||||
\(712\) | 87.6670 | − | 930.298i | 0.123128 | − | 1.30660i | ||||
\(713\) | 1006.81 | − | 1006.81i | 1.41207 | − | 1.41207i | ||||
\(714\) | 38.9733 | + | 208.881i | 0.0545845 | + | 0.292551i | ||||
\(715\) | −48.1472 | − | 116.238i | −0.0673388 | − | 0.162570i | ||||
\(716\) | 286.438 | + | 426.087i | 0.400053 | + | 0.595093i | ||||
\(717\) | 20.0890 | − | 48.4992i | 0.0280182 | − | 0.0676418i | ||||
\(718\) | 205.330 | − | 110.122i | 0.285974 | − | 0.153374i | ||||
\(719\) | 161.235 | 0.224249 | 0.112124 | − | 0.993694i | \(-0.464234\pi\) | ||||
0.112124 | + | 0.993694i | \(0.464234\pi\) | |||||||
\(720\) | 46.3855 | − | 0.260808i | 0.0644243 | − | 0.000362233i | ||||
\(721\) | 97.5444 | + | 1146.45i | 0.135290 | + | 1.59008i | ||||
\(722\) | −209.277 | − | 390.209i | −0.289857 | − | 0.540455i | ||||
\(723\) | −61.7735 | − | 25.5874i | −0.0854405 | − | 0.0353906i | ||||
\(724\) | −996.714 | − | 195.347i | −1.37668 | − | 0.269817i | ||||
\(725\) | 305.966 | + | 738.667i | 0.422022 | + | 1.01885i | ||||
\(726\) | −1.74275 | + | 0.174120i | −0.00240049 | + | 0.000239835i | ||||
\(727\) | 164.695 | − | 164.695i | 0.226541 | − | 0.226541i | −0.584705 | − | 0.811246i | \(-0.698790\pi\) |
0.811246 | + | 0.584705i | \(0.198790\pi\) | |||||||
\(728\) | 781.558 | + | 332.076i | 1.07357 | + | 0.456148i | ||||
\(729\) | −507.879 | + | 507.879i | −0.696679 | + | 0.696679i | ||||
\(730\) | 20.3997 | + | 16.6937i | 0.0279448 | + | 0.0228681i | ||||
\(731\) | 14.1482 | + | 34.1568i | 0.0193546 | + | 0.0467261i | ||||
\(732\) | 160.190 | + | 793.663i | 0.218839 | + | 1.08424i | ||||
\(733\) | −641.487 | − | 265.713i | −0.875153 | − | 0.362500i | −0.100538 | − | 0.994933i | \(-0.532056\pi\) |
−0.774615 | + | 0.632433i | \(0.782056\pi\) | |||||||
\(734\) | −137.935 | − | 41.6305i | −0.187922 | − | 0.0567173i | ||||
\(735\) | −82.9006 | + | 14.2099i | −0.112790 | + | 0.0193332i | ||||
\(736\) | 658.083 | − | 813.468i | 0.894134 | − | 1.10526i | ||||
\(737\) | −515.621 | −0.699621 | ||||||||
\(738\) | 350.118 | + | 105.670i | 0.474414 | + | 0.143184i | ||||
\(739\) | −187.738 | + | 453.240i | −0.254044 | + | 0.613316i | −0.998523 | − | 0.0543296i | \(-0.982698\pi\) |
0.744479 | + | 0.667646i | \(0.232698\pi\) | |||||||
\(740\) | −24.3470 | − | 120.628i | −0.0329014 | − | 0.163010i | ||||
\(741\) | −155.788 | − | 376.106i | −0.210241 | − | 0.507566i | ||||
\(742\) | 58.9620 | − | 86.0113i | 0.0794636 | − | 0.115918i | ||||
\(743\) | −319.731 | + | 319.731i | −0.430324 | + | 0.430324i | −0.888738 | − | 0.458415i | \(-0.848417\pi\) |
0.458415 | + | 0.888738i | \(0.348417\pi\) | |||||||
\(744\) | −756.465 | + | 232.959i | −1.01675 | + | 0.313117i | ||||
\(745\) | −10.2512 | + | 10.2512i | −0.0137600 | + | 0.0137600i | ||||
\(746\) | −51.9082 | − | 519.545i | −0.0695820 | − | 0.696441i | ||||
\(747\) | 95.7807 | − | 39.6737i | 0.128220 | − | 0.0531107i | ||||
\(748\) | 56.4398 | − | 287.970i | 0.0754542 | − | 0.384987i | ||||
\(749\) | −163.448 | + | 514.109i | −0.218222 | + | 0.686394i | ||||
\(750\) | −80.2030 | − | 149.543i | −0.106937 | − | 0.199391i | ||||
\(751\) | − | 1241.02i | − | 1.65249i | −0.563311 | − | 0.826245i | \(-0.690473\pi\) | ||
0.563311 | − | 0.826245i | \(-0.309527\pi\) | |||||||
\(752\) | −497.942 | − | 1183.28i | −0.662157 | − | 1.57351i | ||||
\(753\) | 445.506i | 0.591642i | ||||||||
\(754\) | −469.128 | − | 874.718i | −0.622186 | − | 1.16010i | ||||
\(755\) | 40.7609 | − | 98.4056i | 0.0539880 | − | 0.130339i | ||||
\(756\) | −636.723 | + | 511.469i | −0.842227 | + | 0.676546i | ||||
\(757\) | −226.507 | − | 546.837i | −0.299217 | − | 0.722374i | −0.999960 | − | 0.00895973i | \(-0.997148\pi\) |
0.700743 | − | 0.713414i | \(-0.252852\pi\) | |||||||
\(758\) | −979.584 | + | 97.8711i | −1.29233 | + | 0.129118i | ||||
\(759\) | 576.943 | − | 576.943i | 0.760135 | − | 0.760135i | ||||
\(760\) | −45.5349 | − | 55.0097i | −0.0599143 | − | 0.0723812i | ||||
\(761\) | −480.917 | − | 480.917i | −0.631954 | − | 0.631954i | 0.316604 | − | 0.948558i | \(-0.397457\pi\) |
−0.948558 | + | 0.316604i | \(0.897457\pi\) | |||||||
\(762\) | −206.165 | − | 168.711i | −0.270557 | − | 0.221405i | ||||
\(763\) | −565.188 | − | 1092.07i | −0.740744 | − | 1.43129i | ||||
\(764\) | 282.708 | + | 187.752i | 0.370036 | + | 0.245748i | ||||
\(765\) | 7.41108 | − | 17.8919i | 0.00968769 | − | 0.0233881i | ||||
\(766\) | −201.539 | + | 667.761i | −0.263105 | + | 0.871751i | ||||
\(767\) | −325.202 | −0.423993 | ||||||||
\(768\) | −534.847 | + | 228.621i | −0.696416 | + | 0.297683i | ||||
\(769\) | 237.047i | 0.308254i | 0.988051 | + | 0.154127i | \(0.0492565\pi\) | ||||
−0.988051 | + | 0.154127i | \(0.950744\pi\) | |||||||
\(770\) | 113.648 | + | 24.0141i | 0.147595 | + | 0.0311872i | ||||
\(771\) | 413.909 | − | 999.264i | 0.536846 | − | 1.29606i | ||||
\(772\) | 698.843 | + | 464.115i | 0.905237 | + | 0.601186i | ||||
\(773\) | −256.268 | − | 618.685i | −0.331523 | − | 0.800368i | −0.998472 | − | 0.0552644i | \(-0.982400\pi\) |
0.666948 | − | 0.745104i | \(-0.267600\pi\) | |||||||
\(774\) | −26.9018 | + | 32.8740i | −0.0347568 | + | 0.0424729i | ||||
\(775\) | −752.210 | − | 752.210i | −0.970594 | − | 0.970594i | ||||
\(776\) | −585.166 | + | 484.377i | −0.754079 | + | 0.624197i | ||||
\(777\) | 495.162 | + | 417.508i | 0.637274 | + | 0.537334i | ||||
\(778\) | −136.394 | + | 13.6273i | −0.175314 | + | 0.0175158i | ||||
\(779\) | −215.456 | − | 520.157i | −0.276580 | − | 0.667724i | ||||
\(780\) | 58.0874 | + | 86.4071i | 0.0744710 | + | 0.110778i | ||||
\(781\) | 1254.54 | + | 519.647i | 1.60632 | + | 0.665361i | ||||
\(782\) | −206.466 | − | 384.967i | −0.264023 | − | 0.492286i | ||||
\(783\) | 954.626 | 1.21919 | ||||||||
\(784\) | −660.861 | + | 421.804i | −0.842935 | + | 0.538015i | ||||
\(785\) | 127.926i | 0.162962i | ||||||||
\(786\) | −89.9696 | − | 167.754i | −0.114465 | − | 0.213427i | ||||
\(787\) | 221.730 | − | 535.303i | 0.281741 | − | 0.680182i | −0.718136 | − | 0.695903i | \(-0.755004\pi\) |
0.999876 | + | 0.0157208i | \(0.00500430\pi\) | |||||||
\(788\) | 122.115 | + | 23.9334i | 0.154968 | + | 0.0303724i | ||||
\(789\) | 677.824 | − | 280.764i | 0.859093 | − | 0.355848i | ||||
\(790\) | −102.796 | + | 10.2705i | −0.130122 | + | 0.0130006i | ||||
\(791\) | 339.772 | − | 402.968i | 0.429548 | − | 0.509441i | ||||
\(792\) | 322.229 | − | 99.2328i | 0.406854 | − | 0.125294i | ||||
\(793\) | 955.243 | − | 955.243i | 1.20459 | − | 1.20459i | ||||
\(794\) | −135.643 | + | 165.756i | −0.170835 | + | 0.208761i | ||||
\(795\) | 11.8125 | − | 4.89288i | 0.0148585 | − | 0.00615457i | ||||
\(796\) | 187.495 | + | 928.943i | 0.235546 | + | 1.16701i | ||||
\(797\) | −435.570 | − | 180.419i | −0.546512 | − | 0.226373i | 0.0923060 | − | 0.995731i | \(-0.470576\pi\) |
−0.638818 | + | 0.769358i | \(0.720576\pi\) | |||||||
\(798\) | 367.728 | + | 77.7017i | 0.460812 | + | 0.0973705i | ||||
\(799\) | −535.974 | −0.670806 | ||||||||
\(800\) | −607.761 | − | 491.669i | −0.759701 | − | 0.614586i | ||||
\(801\) | − | 448.230i | − | 0.559589i | ||||||
\(802\) | −131.823 | + | 436.771i | −0.164368 | + | 0.544602i | ||||
\(803\) | 177.013 | + | 73.3210i | 0.220439 | + | 0.0913088i | ||||
\(804\) | 418.263 | − | 84.4207i | 0.520228 | − | 0.105001i | ||||
\(805\) | 153.569 | − | 79.4775i | 0.190769 | − | 0.0987299i | ||||
\(806\) | 1022.05 | + | 836.372i | 1.26805 | + | 1.03768i | ||||
\(807\) | 654.730 | − | 654.730i | 0.811313 | − | 0.811313i | ||||
\(808\) | 300.189 | − | 567.355i | 0.371520 | − | 0.702172i | ||||
\(809\) | −1044.08 | − | 1044.08i | −1.29058 | − | 1.29058i | −0.934431 | − | 0.356145i | \(-0.884091\pi\) |
−0.356145 | − | 0.934431i | \(-0.615909\pi\) | |||||||
\(810\) | −47.7139 | + | 4.76714i | −0.0589060 | + | 0.00588535i | ||||
\(811\) | 94.3340 | − | 39.0744i | 0.116318 | − | 0.0481806i | −0.323765 | − | 0.946137i | \(-0.604949\pi\) |
0.440084 | + | 0.897957i | \(0.354949\pi\) | |||||||
\(812\) | 910.987 | + | 99.3780i | 1.12191 | + | 0.122387i | ||||
\(813\) | −512.362 | − | 212.227i | −0.630212 | − | 0.261042i | ||||
\(814\) | −422.760 | − | 788.262i | −0.519361 | − | 0.968380i | ||||
\(815\) | −156.180 | −0.191632 | ||||||||
\(816\) | 1.36538 | + | 242.838i | 0.00167326 | + | 0.297595i | ||||
\(817\) | 65.3946 | 0.0800424 | ||||||||
\(818\) | −344.184 | − | 641.751i | −0.420762 | − | 0.784536i | ||||
\(819\) | 388.195 | + | 123.417i | 0.473987 | + | 0.150692i | ||||
\(820\) | 80.3352 | + | 119.501i | 0.0979697 | + | 0.145733i | ||||
\(821\) | −191.944 | − | 463.393i | −0.233793 | − | 0.564425i | 0.762825 | − | 0.646605i | \(-0.223812\pi\) |
−0.996618 | + | 0.0821799i | \(0.973812\pi\) | |||||||
\(822\) | 20.7492 | + | 207.677i | 0.0252424 | + | 0.252649i | ||||
\(823\) | 428.028 | + | 428.028i | 0.520082 | + | 0.520082i | 0.917596 | − | 0.397514i | \(-0.130127\pi\) |
−0.397514 | + | 0.917596i | \(0.630127\pi\) | |||||||
\(824\) | −123.369 | + | 1309.16i | −0.149720 | + | 1.58879i | ||||
\(825\) | −431.047 | − | 431.047i | −0.522482 | − | 0.522482i | ||||
\(826\) | 169.761 | − | 247.640i | 0.205522 | − | 0.299807i | ||||
\(827\) | −68.1155 | + | 28.2144i | −0.0823646 | + | 0.0341165i | −0.423485 | − | 0.905903i | \(-0.639193\pi\) |
0.341121 | + | 0.940019i | \(0.389193\pi\) | |||||||
\(828\) | 277.673 | − | 418.107i | 0.335354 | − | 0.504960i | ||||
\(829\) | −268.930 | − | 111.394i | −0.324403 | − | 0.134372i | 0.214538 | − | 0.976716i | \(-0.431175\pi\) |
−0.538941 | + | 0.842344i | \(0.681175\pi\) | |||||||
\(830\) | 39.0780 | + | 11.7942i | 0.0470820 | + | 0.0142099i | ||||
\(831\) | 115.801i | 0.139352i | ||||||||
\(832\) | 811.453 | + | 532.352i | 0.975304 | + | 0.639846i | ||||
\(833\) | 55.2986 | + | 322.612i | 0.0663849 | + | 0.387290i | ||||
\(834\) | −789.355 | − | 238.237i | −0.946469 | − | 0.285656i | ||||
\(835\) | −47.2573 | + | 114.089i | −0.0565956 | + | 0.136634i | ||||
\(836\) | −432.388 | − | 287.157i | −0.517210 | − | 0.343489i | ||||
\(837\) | −1173.46 | + | 486.065i | −1.40199 | + | 0.580723i | ||||
\(838\) | 337.463 | + | 276.155i | 0.402700 | + | 0.329541i | ||||
\(839\) | −287.697 | − | 287.697i | −0.342904 | − | 0.342904i | 0.514554 | − | 0.857458i | \(-0.327958\pi\) |
−0.857458 | + | 0.514554i | \(0.827958\pi\) | |||||||
\(840\) | −96.1213 | − | 0.872637i | −0.114430 | − | 0.00103885i | ||||
\(841\) | −162.733 | − | 162.733i | −0.193500 | − | 0.193500i | ||||
\(842\) | −40.3929 | + | 4.03569i | −0.0479726 | + | 0.00479298i | ||||
\(843\) | 722.423 | − | 299.237i | 0.856966 | − | 0.354967i | ||||
\(844\) | 127.964 | + | 190.351i | 0.151616 | + | 0.225534i | ||||
\(845\) | 17.6196 | − | 42.5375i | 0.0208516 | − | 0.0503402i | ||||
\(846\) | −291.056 | − | 542.691i | −0.344038 | − | 0.641479i | ||||
\(847\) | −2.68822 | + | 0.228725i | −0.00317381 | + | 0.000270041i | ||||
\(848\) | 83.7964 | − | 84.7440i | 0.0988165 | − | 0.0999340i | ||||
\(849\) | − | 1154.44i | − | 1.35977i | ||||||
\(850\) | −287.618 | + | 154.255i | −0.338374 | + | 0.181477i | ||||
\(851\) | −1230.19 | − | 509.560i | −1.44558 | − | 0.598778i | ||||
\(852\) | −1102.74 | − | 216.128i | −1.29430 | − | 0.253671i | ||||
\(853\) | 1248.25 | − | 517.044i | 1.46337 | − | 0.606148i | 0.498034 | − | 0.867157i | \(-0.334055\pi\) |
0.965336 | + | 0.261010i | \(0.0840555\pi\) | |||||||
\(854\) | 228.761 | + | 1226.07i | 0.267870 | + | 1.43568i | ||||
\(855\) | −24.2219 | − | 24.2219i | −0.0283297 | − | 0.0283297i | ||||
\(856\) | −288.336 | + | 544.954i | −0.336841 | + | 0.636629i | ||||
\(857\) | 23.1448 | + | 23.1448i | 0.0270068 | + | 0.0270068i | 0.720481 | − | 0.693474i | \(-0.243921\pi\) |
−0.693474 | + | 0.720481i | \(0.743921\pi\) | |||||||
\(858\) | 585.676 | + | 479.275i | 0.682606 | + | 0.558596i | ||||
\(859\) | 250.080 | + | 603.746i | 0.291129 | + | 0.702848i | 0.999997 | − | 0.00249369i | \(-0.000793768\pi\) |
−0.708868 | + | 0.705341i | \(0.750794\pi\) | |||||||
\(860\) | −16.3945 | + | 3.30900i | −0.0190633 | + | 0.00384768i | ||||
\(861\) | −722.245 | − | 229.620i | −0.838844 | − | 0.266689i | ||||
\(862\) | 4.44106 | − | 14.7146i | 0.00515204 | − | 0.0170703i | ||||
\(863\) | 888.240 | 1.02925 | 0.514624 | − | 0.857416i | \(-0.327932\pi\) | ||||
0.514624 | + | 0.857416i | \(0.327932\pi\) | |||||||
\(864\) | −820.059 | + | 445.769i | −0.949142 | + | 0.515936i | ||||
\(865\) | −84.5696 | −0.0977683 | ||||||||
\(866\) | 1114.35 | + | 336.326i | 1.28678 | + | 0.388367i | ||||
\(867\) | −512.989 | − | 212.487i | −0.591682 | − | 0.245083i | ||||
\(868\) | −1170.42 | + | 341.686i | −1.34841 | + | 0.393647i | ||||
\(869\) | −693.744 | + | 287.358i | −0.798325 | + | 0.330677i | ||||
\(870\) | 86.9537 | + | 71.1568i | 0.0999468 | + | 0.0817894i | ||||
\(871\) | −503.416 | − | 503.416i | −0.577975 | − | 0.577975i | ||||
\(872\) | −413.611 | − | 1343.08i | −0.474325 | − | 1.54023i | ||||
\(873\) | −257.660 | + | 257.660i | −0.295143 | + | 0.295143i | ||||
\(874\) | −768.856 | + | 76.8170i | −0.879698 | + | 0.0878914i | ||||
\(875\) | −120.146 | − | 232.150i | −0.137310 | − | 0.265314i | ||||
\(876\) | −155.594 | − | 30.4951i | −0.177619 | − | 0.0348118i | ||||
\(877\) | 192.920 | + | 79.9101i | 0.219977 | + | 0.0911175i | 0.489950 | − | 0.871750i | \(-0.337015\pi\) |
−0.269973 | + | 0.962868i | \(0.587015\pi\) | |||||||
\(878\) | 118.499 | − | 63.5535i | 0.134965 | − | 0.0723844i | ||||
\(879\) | − | 351.072i | − | 0.399400i | ||||||
\(880\) | 122.930 | + | 50.1114i | 0.139693 | + | 0.0569448i | ||||
\(881\) | −134.274 | −0.152411 | −0.0762054 | − | 0.997092i | \(-0.524280\pi\) | ||||
−0.0762054 | + | 0.997092i | \(0.524280\pi\) | |||||||
\(882\) | −296.626 | + | 231.184i | −0.336311 | + | 0.262113i | ||||
\(883\) | 491.420 | + | 203.553i | 0.556535 | + | 0.230524i | 0.643180 | − | 0.765715i | \(-0.277615\pi\) |
−0.0866454 | + | 0.996239i | \(0.527615\pi\) | |||||||
\(884\) | 336.258 | − | 226.050i | 0.380383 | − | 0.255713i | ||||
\(885\) | 34.0100 | − | 14.0874i | 0.0384294 | − | 0.0159180i | ||||
\(886\) | 1110.36 | − | 110.937i | 1.25323 | − | 0.125211i | ||||
\(887\) | −952.918 | + | 952.918i | −1.07432 | + | 1.07432i | −0.0773081 | + | 0.997007i | \(0.524633\pi\) |
−0.997007 | + | 0.0773081i | \(0.975367\pi\) | |||||||
\(888\) | 471.995 | + | 570.208i | 0.531526 | + | 0.642126i | ||||
\(889\) | −313.725 | − | 264.525i | −0.352897 | − | 0.297554i | ||||
\(890\) | 111.768 | − | 136.580i | 0.125581 | − | 0.153461i | ||||
\(891\) | −322.008 | + | 133.380i | −0.361401 | + | 0.149697i | ||||
\(892\) | 201.414 | − | 303.280i | 0.225801 | − | 0.340000i | ||||
\(893\) | −362.797 | + | 875.870i | −0.406268 | + | 0.980817i | ||||
\(894\) | 25.1962 | − | 83.4829i | 0.0281836 | − | 0.0933814i | ||||
\(895\) | 96.9683i | 0.108344i | ||||||||
\(896\) | −828.976 | + | 340.022i | −0.925196 | + | 0.379489i | ||||
\(897\) | 1126.57 | 1.25594 | ||||||||
\(898\) | −367.584 | − | 110.941i | −0.409336 | − | 0.123543i | ||||
\(899\) | 1316.69 | + | 545.389i | 1.46461 | + | 0.606662i | ||||
\(900\) | −312.377 | − | 207.456i | −0.347086 | − | 0.230506i | ||||
\(901\) | −19.0409 | − | 45.9689i | −0.0211331 | − | 0.0510199i | ||||
\(902\) | 809.992 | + | 662.840i | 0.897996 | + | 0.734856i | ||||
\(903\) | 56.7435 | − | 67.2974i | 0.0628389 | − | 0.0745264i | ||||
\(904\) | 464.041 | − | 384.115i | 0.513319 | − | 0.424905i | ||||
\(905\) | −135.644 | − | 135.644i | −0.149883 | − | 0.149883i | ||||
\(906\) | 63.6943 | + | 637.511i | 0.0703027 | + | 0.703655i | ||||
\(907\) | 15.0924 | + | 36.4363i | 0.0166399 | + | 0.0401723i | 0.931981 | − | 0.362507i | \(-0.118079\pi\) |
−0.915341 | + | 0.402679i | \(0.868079\pi\) | |||||||
\(908\) | 620.940 | + | 923.671i | 0.683855 | + | 1.01726i | ||||
\(909\) | 117.828 | − | 284.463i | 0.129624 | − | 0.312941i | ||||
\(910\) | 87.5125 | + | 134.404i | 0.0961676 | + | 0.147697i | ||||
\(911\) | 1382.27i | 1.51731i | 0.651492 | + | 0.758655i | \(0.274143\pi\) | ||||
−0.651492 | + | 0.758655i | \(0.725857\pi\) | |||||||
\(912\) | 397.761 | + | 162.144i | 0.436141 | + | 0.177789i | ||||
\(913\) | 296.697 | 0.324969 | ||||||||
\(914\) | 688.081 | + | 1282.97i | 0.752824 | + | 1.40368i | ||||
\(915\) | −58.5202 | + | 141.280i | −0.0639566 | + | 0.154405i | ||||
\(916\) | −254.921 | + | 1300.67i | −0.278298 | + | 1.41995i | ||||
\(917\) | −134.777 | − | 260.420i | −0.146976 | − | 0.283991i | ||||
\(918\) | 38.7409 | + | 387.754i | 0.0422014 | + | 0.422390i | ||||
\(919\) | 577.562 | + | 577.562i | 0.628468 | + | 0.628468i | 0.947682 | − | 0.319215i | \(-0.103419\pi\) |
−0.319215 | + | 0.947682i | \(0.603419\pi\) | |||||||
\(920\) | 188.866 | − | 58.1626i | 0.205289 | − | 0.0632202i | ||||
\(921\) | −234.380 | + | 234.380i | −0.254484 | + | 0.254484i | ||||
\(922\) | −832.311 | + | 1017.09i | −0.902724 | + | 1.10313i | ||||
\(923\) | 717.498 | + | 1732.19i | 0.777354 | + | 1.87670i | ||||
\(924\) | −670.699 | + | 195.800i | −0.725865 | + | 0.211905i | ||||
\(925\) | −380.704 | + | 919.101i | −0.411572 | + | 0.993622i | ||||
\(926\) | 394.548 | − | 1307.26i | 0.426077 | − | 1.41173i | ||||
\(927\) | 630.771i | 0.680443i | ||||||||
\(928\) | 1004.32 | + | 296.965i | 1.08224 | + | 0.320006i | ||||
\(929\) | − | 290.266i | − | 0.312450i | −0.987722 | − | 0.156225i | \(-0.950068\pi\) | ||
0.987722 | − | 0.156225i | \(-0.0499325\pi\) | |||||||
\(930\) | −143.118 | − | 43.1947i | −0.153890 | − | 0.0464459i | ||||
\(931\) | 564.633 | + | 128.007i | 0.606480 | + | 0.137494i | ||||
\(932\) | −87.2300 | − | 432.181i | −0.0935944 | − | 0.463714i | ||||
\(933\) | 1122.34 | − | 464.889i | 1.20294 | − | 0.498273i | ||||
\(934\) | 482.324 | − | 589.401i | 0.516407 | − | 0.631051i | ||||
\(935\) | 39.1902 | − | 39.1902i | 0.0419147 | − | 0.0419147i | ||||
\(936\) | 411.486 | + | 217.718i | 0.439621 | + | 0.232604i | ||||
\(937\) | −200.099 | + | 200.099i | −0.213553 | + | 0.213553i | −0.805775 | − | 0.592222i | \(-0.798251\pi\) |
0.592222 | + | 0.805775i | \(0.298251\pi\) | |||||||
\(938\) | 646.141 | − | 120.558i | 0.688850 | − | 0.128526i | ||||
\(939\) | 7.18282 | + | 17.3409i | 0.00764944 | + | 0.0184674i | ||||
\(940\) | 46.6340 | − | 237.939i | 0.0496106 | − | 0.253126i | ||||
\(941\) | −659.745 | + | 1592.76i | −0.701110 | + | 1.69263i | 0.0199910 | + | 0.999800i | \(0.493636\pi\) |
−0.721101 | + | 0.692830i | \(0.756364\pi\) | |||||||
\(942\) | −363.684 | − | 678.110i | −0.386076 | − | 0.719862i | ||||
\(943\) | 1558.06 | 1.65223 | ||||||||
\(944\) | 241.263 | − | 243.992i | 0.255575 | − | 0.258466i | ||||
\(945\) | −153.696 | + | 13.0771i | −0.162641 | + | 0.0138382i | ||||
\(946\) | −107.132 | + | 57.4573i | −0.113248 | + | 0.0607371i | ||||
\(947\) | 1437.45 | + | 595.412i | 1.51790 | + | 0.628735i | 0.977170 | − | 0.212461i | \(-0.0681479\pi\) |
0.540730 | + | 0.841196i | \(0.318148\pi\) | |||||||
\(948\) | 515.706 | − | 346.685i | 0.543993 | − | 0.365701i | ||||
\(949\) | 101.237 | + | 244.408i | 0.106678 | + | 0.257543i | ||||
\(950\) | 57.3918 | + | 574.430i | 0.0604124 | + | 0.604663i | ||||
\(951\) | −763.351 | + | 763.351i | −0.802682 | + | 0.802682i | ||||
\(952\) | −3.39592 | + | 374.062i | −0.00356714 | + | 0.392922i | ||||
\(953\) | 1001.05 | − | 1001.05i | 1.05042 | − | 1.05042i | 0.0517586 | − | 0.998660i | \(-0.483517\pi\) |
0.998660 | − | 0.0517586i | \(-0.0164827\pi\) | |||||||
\(954\) | 36.2050 | − | 44.2426i | 0.0379507 | − | 0.0463759i | ||||
\(955\) | 24.5289 | + | 59.2179i | 0.0256847 | + | 0.0620083i | ||||
\(956\) | 51.1276 | − | 76.9855i | 0.0534808 | − | 0.0805288i | ||||
\(957\) | 754.515 | + | 312.530i | 0.788417 | + | 0.326573i | ||||
\(958\) | 162.835 | − | 539.523i | 0.169974 | − | 0.563177i | ||||
\(959\) | 27.2563 | + | 320.345i | 0.0284215 | + | 0.334041i | ||||
\(960\) | −107.923 | − | 20.5227i | −0.112420 | − | 0.0213778i | ||||
\(961\) | −935.218 | −0.973171 | ||||||||
\(962\) | 356.850 | − | 1182.36i | 0.370946 | − | 1.22906i | ||||
\(963\) | −113.176 | + | 273.232i | −0.117525 | + | 0.283730i | ||||
\(964\) | −98.0566 | − | 65.1213i | −0.101718 | − | 0.0675532i | ||||
\(965\) | 60.6344 | + | 146.384i | 0.0628336 | + | 0.151694i | ||||
\(966\) | −588.091 | + | 857.882i | −0.608790 | + | 0.888076i | ||||
\(967\) | −777.227 | + | 777.227i | −0.803751 | + | 0.803751i | −0.983680 | − | 0.179929i | \(-0.942413\pi\) |
0.179929 | + | 0.983680i | \(0.442413\pi\) | |||||||
\(968\) | −3.06975 | − | 0.289279i | −0.00317123 | − | 0.000298842i | ||||
\(969\) | 126.806 | − | 126.806i | 0.130863 | − | 0.130863i | ||||
\(970\) | −142.760 | + | 14.2633i | −0.147175 | + | 0.0147044i | ||||
\(971\) | −91.5375 | + | 37.9161i | −0.0942714 | + | 0.0390485i | −0.429321 | − | 0.903152i | \(-0.641247\pi\) |
0.335049 | + | 0.942201i | \(0.391247\pi\) | |||||||
\(972\) | −632.077 | + | 424.916i | −0.650285 | + | 0.437156i | ||||
\(973\) | −1210.41 | − | 384.820i | −1.24400 | − | 0.395498i | ||||
\(974\) | −1170.89 | + | 627.969i | −1.20214 | + | 0.644732i | ||||
\(975\) | − | 841.689i | − | 0.863271i | ||||||
\(976\) | 8.01435 | + | 1425.38i | 0.00821142 | + | 1.46043i | ||||
\(977\) | 1551.42i | 1.58794i | 0.607958 | + | 0.793970i | \(0.291989\pi\) | ||||
−0.607958 | + | 0.793970i | \(0.708011\pi\) | |||||||
\(978\) | 827.884 | − | 444.010i | 0.846507 | − | 0.453998i | ||||
\(979\) | 490.899 | − | 1185.13i | 0.501429 | − | 1.21056i | ||||
\(980\) | −148.031 | − | 3.52070i | −0.151052 | − | 0.00359255i | ||||
\(981\) | −257.973 | − | 622.803i | −0.262970 | − | 0.634865i | ||||
\(982\) | −54.0814 | − | 541.296i | −0.0550727 | − | 0.551218i | ||||
\(983\) | −546.422 | + | 546.422i | −0.555872 | + | 0.555872i | −0.928129 | − | 0.372258i | \(-0.878584\pi\) |
0.372258 | + | 0.928129i | \(0.378584\pi\) | |||||||
\(984\) | −765.577 | − | 405.068i | −0.778025 | − | 0.411654i | ||||
\(985\) | 16.6187 | + | 16.6187i | 0.0168718 | + | 0.0168718i | ||||
\(986\) | 276.911 | − | 338.385i | 0.280842 | − | 0.343190i | ||||
\(987\) | 586.552 | + | 1133.35i | 0.594278 | + | 1.14828i | ||||
\(988\) | −141.793 | − | 702.514i | −0.143515 | − | 0.711046i | ||||
\(989\) | −69.2542 | + | 167.194i | −0.0700245 | + | 0.169054i | ||||
\(990\) | 60.9633 | + | 18.3995i | 0.0615791 | + | 0.0185853i | ||||
\(991\) | −182.571 | −0.184229 | −0.0921145 | − | 0.995748i | \(-0.529363\pi\) | ||||
−0.0921145 | + | 0.995748i | \(0.529363\pi\) | |||||||
\(992\) | −1385.75 | + | 146.326i | −1.39693 | + | 0.147506i | ||||
\(993\) | 1129.42i | 1.13738i | ||||||||
\(994\) | −1693.60 | − | 357.862i | −1.70383 | − | 0.360022i | ||||
\(995\) | −68.4951 | + | 165.362i | −0.0688393 | + | 0.166193i | ||||
\(996\) | −240.676 | + | 48.5772i | −0.241642 | + | 0.0487723i | ||||
\(997\) | 127.707 | + | 308.312i | 0.128091 | + | 0.309240i | 0.974895 | − | 0.222666i | \(-0.0714760\pi\) |
−0.846804 | + | 0.531906i | \(0.821476\pi\) | |||||||
\(998\) | −511.712 | − | 418.749i | −0.512738 | − | 0.419588i | ||||
\(999\) | 839.910 | + | 839.910i | 0.840751 | + | 0.840751i |
(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 | 224.3.v.b.13.6 | yes | 240 | |
7.6 | odd | 2 | inner | 224.3.v.b.13.5 | ✓ | 240 | |
32.5 | even | 8 | inner | 224.3.v.b.69.5 | yes | 240 | |
224.69 | odd | 8 | inner | 224.3.v.b.69.6 | yes | 240 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.v.b.13.5 | ✓ | 240 | 7.6 | odd | 2 | inner | |
224.3.v.b.13.6 | yes | 240 | 1.1 | even | 1 | trivial | |
224.3.v.b.69.5 | yes | 240 | 32.5 | even | 8 | inner | |
224.3.v.b.69.6 | yes | 240 | 224.69 | odd | 8 | inner |