Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1680,3,Mod(769,1680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1680.769");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.bd (of order \(2\), degree \(1\), 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: | \(45.7766844125\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 96 x^{14} - 532 x^{13} + 3236 x^{12} - 12864 x^{11} + 49526 x^{10} - 141436 x^{9} + \cdots + 33750 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 769.5 | ||
Root | \(0.500000 + 4.96598i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1680.769 |
Dual form | 1680.3.bd.a.769.6 |
$q$-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 \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(421\) | \(1121\) | \(1471\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.38028 | − | 4.80571i | −0.276057 | − | 0.961141i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.24961 | + | 4.63050i | −0.749945 | + | 0.661501i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.7671 | −1.06973 | −0.534867 | − | 0.844936i | \(-0.679638\pi\) | ||||
−0.534867 | + | 0.844936i | \(0.679638\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −24.8280 | −1.90985 | −0.954925 | − | 0.296848i | \(-0.904065\pi\) | ||||
−0.954925 | + | 0.296848i | \(0.904065\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.39072 | + | 8.32373i | 0.159381 | + | 0.554915i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.26100 | −0.427118 | −0.213559 | − | 0.976930i | \(-0.568506\pi\) | ||||
−0.213559 | + | 0.976930i | \(0.568506\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 23.0050i | 1.21079i | 0.795925 | + | 0.605395i | \(0.206985\pi\) | ||||
−0.795925 | + | 0.605395i | \(0.793015\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.09260 | − | 8.02027i | 0.432981 | − | 0.381918i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 26.4223i | 1.14880i | 0.818576 | + | 0.574398i | \(0.194764\pi\) | ||||
−0.818576 | + | 0.574398i | \(0.805236\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −21.1896 | + | 13.2665i | −0.847586 | + | 0.530659i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 57.0861 | 1.96849 | 0.984243 | − | 0.176819i | \(-0.0565806\pi\) | ||||
0.984243 | + | 0.176819i | \(0.0565806\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 10.2222i | − | 0.329749i | −0.986315 | − | 0.164874i | \(-0.947278\pi\) | ||
0.986315 | − | 0.164874i | \(-0.0527219\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 20.3812 | 0.617612 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 29.4988 | + | 18.8367i | 0.842823 | + | 0.538191i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 14.2196i | − | 0.384314i | −0.981364 | − | 0.192157i | \(-0.938452\pi\) | ||
0.981364 | − | 0.192157i | \(-0.0615482\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 43.0034 | 1.10265 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 16.2271i | 0.395782i | 0.980224 | + | 0.197891i | \(0.0634093\pi\) | ||||
−0.980224 | + | 0.197891i | \(0.936591\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 82.3114i | − | 1.91422i | −0.289725 | − | 0.957110i | \(-0.593564\pi\) | ||
0.289725 | − | 0.957110i | \(-0.406436\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.14085 | − | 14.4171i | −0.0920188 | − | 0.320380i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −51.6631 | −1.09922 | −0.549608 | − | 0.835423i | \(-0.685223\pi\) | ||||
−0.549608 | + | 0.835423i | \(0.685223\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.11686 | − | 48.6167i | 0.124834 | − | 0.992178i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.5764 | 0.246597 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 64.8273i | 1.22316i | 0.791184 | + | 0.611579i | \(0.209465\pi\) | ||||
−0.791184 | + | 0.611579i | \(0.790535\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 16.2419 | + | 56.5491i | 0.295307 | + | 1.02817i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 39.8459i | − | 0.699050i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 81.7685i | − | 1.38591i | −0.720982 | − | 0.692953i | \(-0.756309\pi\) | ||
0.720982 | − | 0.692953i | \(-0.243691\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 13.1240i | − | 0.215148i | −0.994197 | − | 0.107574i | \(-0.965692\pi\) | ||
0.994197 | − | 0.107574i | \(-0.0343083\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −15.7488 | + | 13.8915i | −0.249982 | + | 0.220500i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 34.2697 | + | 119.316i | 0.527226 | + | 1.83564i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 22.4035i | 0.334381i | 0.985925 | + | 0.167190i | \(0.0534695\pi\) | ||||
−0.985925 | + | 0.167190i | \(0.946531\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 45.7648i | − | 0.663257i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −91.5022 | −1.28876 | −0.644382 | − | 0.764704i | \(-0.722885\pi\) | ||||
−0.644382 | + | 0.764704i | \(0.722885\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 71.9256 | 0.985282 | 0.492641 | − | 0.870233i | \(-0.336032\pi\) | ||||
0.492641 | + | 0.870233i | \(0.336032\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 36.7015 | − | 22.9782i | 0.489354 | − | 0.306376i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 61.7726 | − | 54.4875i | 0.802242 | − | 0.707630i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −45.2802 | −0.573167 | −0.286584 | − | 0.958055i | \(-0.592520\pi\) | ||||
−0.286584 | + | 0.958055i | \(0.592520\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 17.7328 | 0.213648 | 0.106824 | − | 0.994278i | \(-0.465932\pi\) | ||||
0.106824 | + | 0.994278i | \(0.465932\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.0222 | + | 34.8943i | 0.117909 | + | 0.410521i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −98.8761 | −1.13651 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 77.5800i | 0.871686i | 0.900023 | + | 0.435843i | \(0.143550\pi\) | ||||
−0.900023 | + | 0.435843i | \(0.856450\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 130.338 | − | 114.966i | 1.43228 | − | 1.26337i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 17.7054i | 0.190381i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 110.555 | − | 31.7534i | 1.16374 | − | 0.334247i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.15741 | 0.0634785 | 0.0317392 | − | 0.999496i | \(-0.489895\pi\) | ||||
0.0317392 | + | 0.999496i | \(0.489895\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −35.3012 | −0.356578 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 142.983i | − | 1.41568i | −0.706374 | − | 0.707839i | \(-0.749670\pi\) | ||
0.706374 | − | 0.707839i | \(-0.250330\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.5292 | 0.141060 | 0.0705302 | − | 0.997510i | \(-0.477531\pi\) | ||||
0.0705302 | + | 0.997510i | \(0.477531\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −51.0934 | − | 32.6261i | −0.486604 | − | 0.310725i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 78.4228i | 0.732923i | 0.930433 | + | 0.366462i | \(0.119431\pi\) | ||||
−0.930433 | + | 0.366462i | \(0.880569\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −74.7424 | −0.685710 | −0.342855 | − | 0.939388i | \(-0.611394\pi\) | ||||
−0.342855 | + | 0.939388i | \(0.611394\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 24.6291i | 0.221884i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 85.2417i | − | 0.754351i | −0.926142 | − | 0.377175i | \(-0.876895\pi\) | ||
0.926142 | − | 0.377175i | \(-0.123105\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 126.978 | − | 36.4702i | 1.10415 | − | 0.317132i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −74.4841 | −0.636617 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 38.1175 | − | 33.6221i | 0.320315 | − | 0.282539i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.4642 | 0.144332 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 28.1061i | − | 0.228505i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 93.0025 | + | 83.5197i | 0.744020 | + | 0.668158i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 66.7734i | 0.525775i | 0.964827 | + | 0.262887i | \(0.0846747\pi\) | ||||
−0.964827 | + | 0.262887i | \(0.915325\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 142.568i | 1.10518i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 28.8330i | − | 0.220099i | −0.993926 | − | 0.110049i | \(-0.964899\pi\) | ||
0.993926 | − | 0.110049i | \(-0.0351009\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −106.525 | − | 120.767i | −0.800939 | − | 0.908026i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.17216 | + | 24.9712i | 0.0531271 | + | 0.184972i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 119.450i | − | 0.871897i | −0.899972 | − | 0.435948i | \(-0.856413\pi\) | ||
0.899972 | − | 0.435948i | \(-0.143587\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 200.948i | − | 1.44567i | −0.691021 | − | 0.722834i | \(-0.742839\pi\) | ||
0.691021 | − | 0.722834i | \(-0.257161\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 89.4832 | 0.634633 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 292.154 | 2.04303 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −78.7950 | − | 274.339i | −0.543414 | − | 1.89199i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.5947 | + | 84.2066i | −0.0720729 | + | 0.572834i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.70484 | −0.0382875 | −0.0191438 | − | 0.999817i | \(-0.506094\pi\) | ||||
−0.0191438 | + | 0.999817i | \(0.506094\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 216.490 | 1.43371 | 0.716854 | − | 0.697223i | \(-0.245581\pi\) | ||||
0.716854 | + | 0.697223i | \(0.245581\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −21.7830 | −0.142373 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −49.1250 | + | 14.1095i | −0.316935 | + | 0.0910293i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 108.287 | 0.689726 | 0.344863 | − | 0.938653i | \(-0.387925\pi\) | ||||
0.344863 | + | 0.938653i | \(0.387925\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 112.284i | − | 0.706190i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −122.349 | − | 138.707i | −0.759929 | − | 0.861533i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 234.395i | − | 1.43800i | −0.695008 | − | 0.719002i | \(-0.744599\pi\) | ||
0.695008 | − | 0.719002i | \(-0.255401\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −28.1318 | − | 97.9460i | −0.170496 | − | 0.593612i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 41.8830 | 0.250796 | 0.125398 | − | 0.992106i | \(-0.459979\pi\) | ||||
0.125398 | + | 0.992106i | \(0.459979\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 447.432 | 2.64753 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 69.0151i | 0.403597i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.0301 | −0.0753183 | −0.0376592 | − | 0.999291i | \(-0.511990\pi\) | ||||
−0.0376592 | + | 0.999291i | \(0.511990\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 49.8070 | − | 167.763i | 0.284611 | − | 0.958643i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 141.627i | 0.800154i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 24.1573 | 0.134957 | 0.0674786 | − | 0.997721i | \(-0.478505\pi\) | ||||
0.0674786 | + | 0.997721i | \(0.478505\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 43.5107i | 0.240390i | 0.992750 | + | 0.120195i | \(0.0383521\pi\) | ||||
−0.992750 | + | 0.120195i | \(0.961648\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 22.7315i | 0.124216i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −68.3353 | + | 19.6271i | −0.369380 | + | 0.106092i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 85.4408 | 0.456903 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 27.2778 | − | 24.0608i | 0.144327 | − | 0.127306i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 246.572 | 1.29095 | 0.645477 | − | 0.763780i | \(-0.276659\pi\) | ||||
0.645477 | + | 0.763780i | \(0.276659\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 161.875i | 0.838733i | 0.907817 | + | 0.419366i | \(0.137748\pi\) | ||||
−0.907817 | + | 0.419366i | \(0.862252\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −59.3569 | − | 206.662i | −0.304394 | − | 1.05980i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 44.8380i | 0.227604i | 0.993503 | + | 0.113802i | \(0.0363029\pi\) | ||||
−0.993503 | + | 0.113802i | \(0.963697\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 114.767i | 0.576718i | 0.957522 | + | 0.288359i | \(0.0931097\pi\) | ||||
−0.957522 | + | 0.288359i | \(0.906890\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 38.8040i | − | 0.193055i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −299.680 | + | 264.338i | −1.47626 | + | 1.30216i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 77.9826 | − | 22.3980i | 0.380403 | − | 0.109258i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 79.2669i | 0.382932i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 270.702i | − | 1.29522i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 219.602 | 1.04077 | 0.520384 | − | 0.853932i | \(-0.325789\pi\) | ||||
0.520384 | + | 0.853932i | \(0.325789\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 158.486 | 0.744068 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −395.565 | + | 113.613i | −1.83984 | + | 0.528433i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 47.3340 | + | 53.6626i | 0.218129 | + | 0.247293i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −124.579 | −0.568853 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 180.277 | 0.815731 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.57102 | −0.0160136 | −0.00800678 | − | 0.999968i | \(-0.502549\pi\) | ||||
−0.00800678 | + | 0.999968i | \(0.502549\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −63.5689 | + | 39.7994i | −0.282529 | + | 0.176886i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 68.0647 | 0.299844 | 0.149922 | − | 0.988698i | \(-0.452098\pi\) | ||||
0.149922 | + | 0.988698i | \(0.452098\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 180.019i | 0.786109i | 0.919515 | + | 0.393054i | \(0.128582\pi\) | ||||
−0.919515 | + | 0.393054i | \(0.871418\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −106.993 | + | 94.3752i | −0.463175 | + | 0.408550i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 115.207i | 0.494449i | 0.968958 | + | 0.247225i | \(0.0795185\pi\) | ||||
−0.968958 | + | 0.247225i | \(0.920481\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 71.3097 | + | 248.278i | 0.303446 | + | 1.05650i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 78.4276 | 0.330918 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.6873 | −0.0656374 | −0.0328187 | − | 0.999461i | \(-0.510448\pi\) | ||||
−0.0328187 | + | 0.999461i | \(0.510448\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 303.442i | 1.25909i | 0.776962 | + | 0.629547i | \(0.216760\pi\) | ||||
−0.776962 | + | 0.629547i | \(0.783240\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −242.081 | + | 37.7089i | −0.988084 | + | 0.153914i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 571.170i | − | 2.31243i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −30.7141 | −0.123350 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 80.5241i | 0.320813i | 0.987051 | + | 0.160407i | \(0.0512805\pi\) | ||||
−0.987051 | + | 0.160407i | \(0.948719\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 310.913i | − | 1.22891i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −17.3590 | − | 60.4386i | −0.0680746 | − | 0.237014i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −39.1012 | −0.152145 | −0.0760723 | − | 0.997102i | \(-0.524238\pi\) | ||||
−0.0760723 | + | 0.997102i | \(0.524238\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 65.8439 | + | 74.6474i | 0.254224 | + | 0.288214i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 171.258 | 0.656162 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 79.1644i | 0.301005i | 0.988610 | + | 0.150503i | \(0.0480892\pi\) | ||||
−0.988610 | + | 0.150503i | \(0.951911\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 311.541 | − | 89.4801i | 1.17563 | − | 0.337661i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 134.373i | − | 0.503268i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 53.2775i | − | 0.198058i | −0.995085 | − | 0.0990288i | \(-0.968426\pi\) | ||
0.995085 | − | 0.0990288i | \(-0.0315736\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 237.638i | 0.876892i | 0.898757 | + | 0.438446i | \(0.144471\pi\) | ||||
−0.898757 | + | 0.438446i | \(0.855529\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −225.751 | + | 199.128i | −0.826928 | + | 0.729405i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 249.340 | − | 156.108i | 0.906692 | − | 0.567664i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 168.185i | 0.607167i | 0.952805 | + | 0.303583i | \(0.0981831\pi\) | ||||
−0.952805 | + | 0.303583i | \(0.901817\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 30.6666i | − | 0.109916i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 128.175 | 0.456140 | 0.228070 | − | 0.973645i | \(-0.426758\pi\) | ||||
0.228070 | + | 0.973645i | \(0.426758\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 72.7293 | 0.256994 | 0.128497 | − | 0.991710i | \(-0.458985\pi\) | ||||
0.128497 | + | 0.991710i | \(0.458985\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −191.488 | + | 54.9986i | −0.671886 | + | 0.192977i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −75.1396 | − | 85.1859i | −0.261810 | − | 0.296815i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −236.278 | −0.817570 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.6649 | −0.0366493 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 273.216 | 0.932477 | 0.466238 | − | 0.884659i | \(-0.345609\pi\) | ||||
0.466238 | + | 0.884659i | \(0.345609\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −392.955 | + | 112.864i | −1.33205 | + | 0.382589i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 61.1436 | 0.205871 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 656.014i | − | 2.19403i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 381.143 | + | 432.103i | 1.26626 | + | 1.43556i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 247.655i | 0.817342i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −63.0703 | + | 18.1149i | −0.206788 | + | 0.0593931i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 336.086 | 1.09474 | 0.547372 | − | 0.836889i | \(-0.315628\pi\) | ||||
0.547372 | + | 0.836889i | \(0.315628\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −25.1653 | −0.0814412 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 497.276i | 1.59896i | 0.600693 | + | 0.799480i | \(0.294891\pi\) | ||||
−0.600693 | + | 0.799480i | \(0.705109\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 252.024 | 0.805188 | 0.402594 | − | 0.915379i | \(-0.368109\pi\) | ||||
0.402594 | + | 0.915379i | \(0.368109\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 88.4964 | + | 56.5101i | 0.280941 | + | 0.179397i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 270.203i | 0.852377i | 0.904634 | + | 0.426188i | \(0.140144\pi\) | ||||
−0.904634 | + | 0.426188i | \(0.859856\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −671.737 | −2.10576 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 135.832i | − | 0.423153i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 167.040i | − | 0.517150i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 526.097 | − | 329.380i | 1.61876 | − | 1.01348i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 129.458 | 0.395895 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 271.211 | − | 239.226i | 0.824351 | − | 0.727132i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 306.813 | 0.926926 | 0.463463 | − | 0.886116i | \(-0.346607\pi\) | ||||
0.463463 | + | 0.886116i | \(0.346607\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 42.6588i | − | 0.128105i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 107.665 | − | 30.9232i | 0.321387 | − | 0.0923080i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 485.903i | − | 1.44185i | −0.693014 | − | 0.720924i | \(-0.743718\pi\) | ||
0.693014 | − | 0.720924i | \(-0.256282\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 147.643i | 0.435525i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 120.286i | 0.352744i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 193.009 | + | 283.543i | 0.562708 | + | 0.826656i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −219.932 | + | 63.1683i | −0.637484 | + | 0.183097i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 8.02712i | − | 0.0231329i | −0.999933 | − | 0.0115665i | \(-0.996318\pi\) | ||
0.999933 | − | 0.0115665i | \(-0.00368180\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 649.899i | − | 1.86217i | −0.364798 | − | 0.931087i | \(-0.618862\pi\) | ||
0.364798 | − | 0.931087i | \(-0.381138\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 129.010 | 0.367551 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −396.496 | −1.12322 | −0.561608 | − | 0.827403i | \(-0.689817\pi\) | ||||
−0.561608 | + | 0.827403i | \(0.689817\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 126.299 | + | 439.733i | 0.355772 | + | 1.23868i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −66.0214 | + | 58.2352i | −0.184934 | + | 0.163124i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −398.981 | −1.11137 | −0.555684 | − | 0.831394i | \(-0.687543\pi\) | ||||
−0.555684 | + | 0.831394i | \(0.687543\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −168.231 | −0.466014 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −30.2489 | −0.0833303 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −99.2777 | − | 345.653i | −0.271994 | − | 0.946996i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −506.200 | −1.37929 | −0.689646 | − | 0.724147i | \(-0.742234\pi\) | ||||
−0.689646 | + | 0.724147i | \(0.742234\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 48.6812i | 0.131927i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −300.183 | − | 340.318i | −0.809119 | − | 0.917300i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 278.751i | − | 0.747322i | −0.927565 | − | 0.373661i | \(-0.878102\pi\) | ||
0.927565 | − | 0.373661i | \(-0.121898\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −161.085 | − | 144.660i | −0.429560 | − | 0.385761i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1417.34 | −3.75951 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 515.959 | 1.36137 | 0.680685 | − | 0.732576i | \(-0.261682\pi\) | ||||
0.680685 | + | 0.732576i | \(0.261682\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 115.655i | − | 0.303556i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −238.715 | −0.623276 | −0.311638 | − | 0.950201i | \(-0.600878\pi\) | ||||
−0.311638 | + | 0.950201i | \(0.600878\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −347.115 | − | 221.653i | −0.901597 | − | 0.575722i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 246.934i | − | 0.638073i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −170.748 | −0.438941 | −0.219471 | − | 0.975619i | \(-0.570433\pi\) | ||||
−0.219471 | + | 0.975619i | \(0.570433\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 191.852i | − | 0.490671i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 49.9402i | 0.127074i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 62.4995 | + | 217.603i | 0.158227 | + | 0.550895i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −80.7184 | −0.203321 | −0.101660 | − | 0.994819i | \(-0.532416\pi\) | ||||
−0.101660 | + | 0.994819i | \(0.532416\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 184.506 | + | 209.175i | 0.462422 | + | 0.524249i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 469.375 | 1.17051 | 0.585255 | − | 0.810849i | \(-0.300994\pi\) | ||||
0.585255 | + | 0.810849i | \(0.300994\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 253.798i | 0.629770i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −12.4225 | − | 43.2514i | −0.0306729 | − | 0.106793i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 167.323i | 0.411114i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 671.238i | 1.64117i | 0.571525 | + | 0.820585i | \(0.306352\pi\) | ||||
−0.571525 | + | 0.820585i | \(0.693648\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 206.893i | 0.503390i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 378.629 | + | 429.253i | 0.916778 | + | 1.03935i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24.4763 | − | 85.2185i | −0.0589789 | − | 0.205346i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 348.052i | 0.834657i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 16.1628i | − | 0.0385747i | −0.999814 | − | 0.0192874i | \(-0.993860\pi\) | ||
0.999814 | − | 0.0192874i | \(-0.00613974\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −463.356 | −1.10061 | −0.550304 | − | 0.834964i | \(-0.685488\pi\) | ||||
−0.550304 | + | 0.834964i | \(0.685488\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −154.989 | −0.366405 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 153.858 | − | 96.3279i | 0.362019 | − | 0.226654i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 60.7709 | + | 68.8961i | 0.142321 | + | 0.161349i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −506.025 | −1.17955 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −425.457 | −0.987140 | −0.493570 | − | 0.869706i | \(-0.664308\pi\) | ||||
−0.493570 | + | 0.869706i | \(0.664308\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 480.947 | 1.11073 | 0.555366 | − | 0.831606i | \(-0.312578\pi\) | ||||
0.555366 | + | 0.831606i | \(0.312578\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 136.477 | + | 475.169i | 0.313740 | + | 1.09234i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −607.845 | −1.39095 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 73.3796i | − | 0.167152i | −0.996501 | − | 0.0835759i | \(-0.973366\pi\) | ||
0.996501 | − | 0.0835759i | \(-0.0266341\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.3506 | − | 145.850i | 0.0416113 | − | 0.330726i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 72.4361i | 0.163513i | 0.996652 | + | 0.0817563i | \(0.0260529\pi\) | ||||
−0.996652 | + | 0.0817563i | \(0.973947\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 372.827 | − | 107.082i | 0.837813 | − | 0.240635i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.88107 | 0.0221053 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −721.760 | −1.60748 | −0.803742 | − | 0.594978i | \(-0.797161\pi\) | ||||
−0.803742 | + | 0.594978i | \(0.797161\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 190.945i | − | 0.423382i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −374.972 | −0.827752 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −732.397 | − | 467.678i | −1.60966 | − | 1.02786i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 622.396i | − | 1.36192i | −0.732322 | − | 0.680958i | \(-0.761564\pi\) | ||
0.732322 | − | 0.680958i | \(-0.238436\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 37.7293 | 0.0821989 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 600.196i | 1.30194i | 0.759102 | + | 0.650971i | \(0.225638\pi\) | ||||
−0.759102 | + | 0.650971i | \(0.774362\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 127.513i | − | 0.275406i | −0.990474 | − | 0.137703i | \(-0.956028\pi\) | ||
0.990474 | − | 0.137703i | \(-0.0439720\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 85.0869 | − | 24.4384i | 0.182983 | − | 0.0525558i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.4438 | 0.0245048 | 0.0122524 | − | 0.999925i | \(-0.496100\pi\) | ||||
0.0122524 | + | 0.999925i | \(0.496100\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −103.740 | − | 117.610i | −0.221193 | − | 0.250767i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −187.559 | −0.398214 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 968.566i | 2.04771i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −305.195 | − | 487.468i | −0.642517 | − | 1.02625i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 194.482i | 0.407719i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 205.867i | − | 0.429784i | −0.976638 | − | 0.214892i | \(-0.931060\pi\) | ||
0.976638 | − | 0.214892i | \(-0.0689400\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 353.045i | 0.733981i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 211.914 | + | 240.247i | 0.438745 | + | 0.497406i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.49897 | − | 29.5907i | −0.0175236 | − | 0.0610118i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 603.451i | − | 1.23912i | −0.784950 | − | 0.619559i | \(-0.787311\pi\) | ||
0.784950 | − | 0.619559i | \(-0.212689\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 405.983i | 0.830232i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 522.576 | 1.06431 | 0.532154 | − | 0.846647i | \(-0.321383\pi\) | ||||
0.532154 | + | 0.846647i | \(0.321383\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −414.503 | −0.840776 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 48.7257 | + | 169.647i | 0.0984358 | + | 0.342722i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 480.351 | − | 423.701i | 0.966501 | − | 0.852518i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −124.569 | −0.249636 | −0.124818 | − | 0.992180i | \(-0.539835\pi\) | ||||
−0.124818 | + | 0.992180i | \(0.539835\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −72.5435 | −0.144797 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −33.8355 | −0.0672673 | −0.0336337 | − | 0.999434i | \(-0.510708\pi\) | ||||
−0.0336337 | + | 0.999434i | \(0.510708\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −687.137 | + | 197.358i | −1.36067 | + | 0.390807i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −774.975 | −1.52855 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 630.938i | 1.23956i | 0.784774 | + | 0.619782i | \(0.212779\pi\) | ||||
−0.784774 | + | 0.619782i | \(0.787221\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −377.582 | + | 333.052i | −0.738907 | + | 0.651765i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 119.538i | − | 0.233017i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −20.0544 | − | 69.8232i | −0.0389406 | − | 0.135579i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 607.924 | 1.17587 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.5687 | 0.0434850 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 492.821i | 0.945914i | 0.881086 | + | 0.472957i | \(0.156813\pi\) | ||||
−0.881086 | + | 0.472957i | \(0.843187\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −331.944 | −0.634692 | −0.317346 | − | 0.948310i | \(-0.602792\pi\) | ||||
−0.317346 | + | 0.948310i | \(0.602792\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −86.2682 | + | 290.573i | −0.164320 | + | 0.553473i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 74.2235i | 0.140842i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −169.138 | −0.319731 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 245.306i | − | 0.461969i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 402.887i | − | 0.755885i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 376.877 | − | 108.246i | 0.704443 | − | 0.202328i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −41.8417 | −0.0779175 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −71.9776 | + | 572.077i | −0.133539 | + | 1.06137i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −96.8104 | −0.178947 | −0.0894735 | − | 0.995989i | \(-0.528518\pi\) | ||||
−0.0894735 | + | 0.995989i | \(0.528518\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 75.3627i | − | 0.138789i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 103.166 | + | 359.190i | 0.189295 | + | 0.659065i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 772.034i | − | 1.41140i | −0.708512 | − | 0.705699i | \(-0.750633\pi\) | ||
0.708512 | − | 0.705699i | \(-0.249367\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 39.3721i | − | 0.0717161i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1313.27i | 2.38343i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 237.704 | − | 209.670i | 0.429844 | − | 0.379150i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 118.360 | − | 33.9951i | 0.213261 | − | 0.0612524i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 42.3682i | 0.0760650i | 0.999277 | + | 0.0380325i | \(0.0121090\pi\) | ||||
−0.999277 | + | 0.0380325i | \(0.987891\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2043.63i | 3.65587i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −147.988 | −0.263793 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 370.393 | 0.657891 | 0.328946 | − | 0.944349i | \(-0.393307\pi\) | ||||
0.328946 | + | 0.944349i | \(0.393307\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −409.646 | + | 117.658i | −0.725038 | + | 0.208244i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −47.2465 | + | 41.6745i | −0.0833272 | + | 0.0735001i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −419.012 | −0.736401 | −0.368201 | − | 0.929746i | \(-0.620026\pi\) | ||||
−0.368201 | + | 0.929746i | \(0.620026\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 113.210 | 0.198266 | 0.0991329 | − | 0.995074i | \(-0.468393\pi\) | ||||
0.0991329 | + | 0.995074i | \(0.468393\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −427.075 | −0.745332 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −350.531 | − | 559.879i | −0.609618 | − | 0.973702i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 604.749 | 1.04809 | 0.524046 | − | 0.851690i | \(-0.324422\pi\) | ||||
0.524046 | + | 0.851690i | \(0.324422\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 280.376i | − | 0.484242i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −93.0902 | + | 82.1117i | −0.160224 | + | 0.141328i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 762.829i | − | 1.30845i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 102.809 | + | 357.949i | 0.175742 | + | 0.611878i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −458.151 | −0.780496 | −0.390248 | − | 0.920710i | \(-0.627611\pi\) | ||||
−0.390248 | + | 0.920710i | \(0.627611\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 235.162 | 0.399257 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 77.6616i | − | 0.131407i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 780.457 | 1.31612 | 0.658059 | − | 0.752967i | \(-0.271378\pi\) | ||||
0.658059 | + | 0.752967i | \(0.271378\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −214.191 | − | 136.773i | −0.359985 | − | 0.229871i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 198.782i | − | 0.332968i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.7391 | 0.0195977 | 0.00979887 | − | 0.999952i | \(-0.496881\pi\) | ||||
0.00979887 | + | 0.999952i | \(0.496881\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 182.878i | 0.304290i | 0.988358 | + | 0.152145i | \(0.0486181\pi\) | ||||
−0.988358 | + | 0.152145i | \(0.951382\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 67.2106i | 0.111460i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −24.1056 | − | 83.9279i | −0.0398439 | − | 0.138724i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 777.171 | 1.28035 | 0.640174 | − | 0.768230i | \(-0.278862\pi\) | ||||
0.640174 | + | 0.768230i | \(0.278862\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 519.061 | − | 457.846i | 0.852317 | − | 0.751800i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1282.69 | 2.09934 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 106.169i | − | 0.173196i | −0.996243 | − | 0.0865978i | \(-0.972400\pi\) | ||
0.996243 | − | 0.0865978i | \(-0.0275995\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −135.070 | + | 38.7944i | −0.219626 | + | 0.0630803i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 680.569i | − | 1.10303i | −0.834165 | − | 0.551515i | \(-0.814050\pi\) | ||
0.834165 | − | 0.551515i | \(-0.185950\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 861.054i | − | 1.39104i | −0.718507 | − | 0.695520i | \(-0.755174\pi\) | ||
0.718507 | − | 0.695520i | \(-0.244826\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 137.294i | − | 0.221086i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −359.235 | − | 407.265i | −0.576621 | − | 0.653716i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 273.002 | − | 562.223i | 0.436803 | − | 0.899557i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 468.870i | 0.747798i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 103.249i | 0.164147i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 489.247 | 0.775352 | 0.387676 | − | 0.921796i | \(-0.373278\pi\) | ||||
0.387676 | + | 0.921796i | \(0.373278\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −380.362 | −0.600888 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 320.893 | − | 92.1661i | 0.505344 | − | 0.145144i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −151.870 | + | 1207.06i | −0.238414 | + | 1.89491i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −274.507 | −0.429588 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 962.813 | 1.50205 | 0.751024 | − | 0.660275i | \(-0.229560\pi\) | ||||
0.751024 | + | 0.660275i | \(0.229560\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 581.069 | 0.903684 | 0.451842 | − | 0.892098i | \(-0.350767\pi\) | ||||
0.451842 | + | 0.892098i | \(0.350767\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 685.138 | − | 196.784i | 1.06223 | − | 0.305091i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 339.036 | 0.524012 | 0.262006 | − | 0.965066i | \(-0.415616\pi\) | ||||
0.262006 | + | 0.965066i | \(0.415616\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 962.177i | 1.48255i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −81.9849 | − | 92.9464i | −0.125937 | − | 0.142775i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 289.383i | 0.443159i | 0.975142 | + | 0.221580i | \(0.0711213\pi\) | ||||
−0.975142 | + | 0.221580i | \(0.928879\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −138.563 | + | 39.7976i | −0.211546 | + | 0.0607598i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 215.777 | 0.328427 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −62.6627 | −0.0950875 | −0.0475438 | − | 0.998869i | \(-0.515139\pi\) | ||||
−0.0475438 | + | 0.998869i | \(0.515139\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 148.826i | 0.225153i | 0.993643 | + | 0.112577i | \(0.0359104\pi\) | ||||
−0.993643 | + | 0.112577i | \(0.964090\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −312.248 | −0.470962 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −433.339 | + | 678.620i | −0.651637 | + | 1.02048i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1508.35i | 2.26139i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.18519 | 0.00924543 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 154.432i | 0.230152i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 833.049i | − | 1.23781i | −0.785464 | − | 0.618907i | \(-0.787576\pi\) | ||
0.785464 | − | 0.618907i | \(-0.212424\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 110.105 | − | 68.9346i | 0.163118 | − | 0.102125i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 391.042 | 0.577611 | 0.288805 | − | 0.957388i | \(-0.406742\pi\) | ||||
0.288805 | + | 0.957388i | \(0.406742\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −32.3240 | + | 28.5119i | −0.0476053 | + | 0.0419910i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −117.891 | −0.173115 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 992.775i | 1.45355i | 0.686875 | + | 0.726775i | \(0.258982\pi\) | ||||
−0.686875 | + | 0.726775i | \(0.741018\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −574.041 | + | 164.875i | −0.838016 | + | 0.240693i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 311.802i | − | 0.453860i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1609.54i | − | 2.33605i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 697.871i | 1.00994i | 0.863136 | + | 0.504972i | \(0.168497\pi\) | ||||
−0.863136 | + | 0.504972i | \(0.831503\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 185.318 | − | 163.463i | 0.267414 | − | 0.235877i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −965.697 | + | 277.365i | −1.38949 | + | 0.399086i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 117.825i | − | 0.169046i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 199.544i | − | 0.285470i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −222.920 | −0.318003 | −0.159002 | − | 0.987278i | \(-0.550828\pi\) | ||||
−0.159002 | + | 0.987278i | \(0.550828\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 327.122 | 0.465323 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −123.512 | − | 430.030i | −0.175194 | − | 0.609972i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 662.085 | + | 750.608i | 0.936472 | + | 1.06168i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −267.679 | −0.377544 | −0.188772 | − | 0.982021i | \(-0.560451\pi\) | ||||
−0.188772 | + | 0.982021i | \(0.560451\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −135.841 | −0.191056 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 270.094 | 0.378814 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −403.255 | − | 1404.00i | −0.563992 | − | 1.96364i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 27.1713 | 0.0378958 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 217.258i | 0.302167i | 0.988521 | + | 0.151083i | \(0.0482762\pi\) | ||||
−0.988521 | + | 0.151083i | \(0.951724\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −76.2728 | + | 67.2776i | −0.105787 | + | 0.0933115i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 525.577i | − | 0.726939i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1209.63 | + | 757.331i | −1.66846 | + | 1.04459i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −771.678 | −1.06146 | −0.530728 | − | 0.847543i | \(-0.678081\pi\) | ||||
−0.530728 | + | 0.847543i | \(0.678081\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 597.664i | 0.817598i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1103.98 | −1.50611 | −0.753053 | − | 0.657960i | \(-0.771420\pi\) | ||||
−0.753053 | + | 0.657960i | \(0.771420\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 419.296 | − | 65.3138i | 0.570471 | − | 0.0888623i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 263.624i | − | 0.357699i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −264.136 | −0.357423 | −0.178712 | − | 0.983901i | \(-0.557193\pi\) | ||||
−0.178712 | + | 0.983901i | \(0.557193\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 989.295i | 1.33508i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1069.03i | − | 1.43880i | −0.694595 | − | 0.719401i | \(-0.744417\pi\) | ||
0.694595 | − | 0.719401i | \(-0.255583\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.87429 | + | 27.4158i | 0.0105695 | + | 0.0367997i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 53.1983 | 0.0712160 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −363.137 | − | 411.689i | −0.484829 | − | 0.549652i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −987.190 | −1.31450 | −0.657250 | − | 0.753673i | \(-0.728280\pi\) | ||||
−0.657250 | + | 0.753673i | \(0.728280\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 139.472i | − | 0.185222i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −298.817 | − | 1040.39i | −0.395785 | − | 1.37800i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1173.09i | − | 1.54966i | −0.632169 | − | 0.774830i | \(-0.717835\pi\) | ||
0.632169 | − | 0.774830i | \(-0.282165\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 538.518i | 0.709509i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 271.712i | 0.357045i | 0.983936 | + | 0.178523i | \(0.0571318\pi\) | ||||
−0.983936 | + | 0.178523i | \(0.942868\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 392.369 | − | 346.095i | 0.514245 | − | 0.453598i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 30.0667 | + | 104.683i | 0.0393029 | + | 0.136840i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2030.15i | 2.64687i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1031.82i | − | 1.34177i | −0.741563 | − | 0.670883i | \(-0.765915\pi\) | ||
0.741563 | − | 0.670883i | \(-0.234085\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 67.7252 | 0.0878407 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −877.988 | −1.13582 | −0.567910 | − | 0.823091i | \(-0.692248\pi\) | ||||
−0.567910 | + | 0.823091i | \(0.692248\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 135.613 | + | 216.605i | 0.174984 | + | 0.279490i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −114.045 | − | 129.293i | −0.146776 | − | 0.166400i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −373.304 | −0.479210 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1076.71 | 1.37863 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −296.628 | −0.378835 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −149.467 | − | 520.396i | −0.190403 | − | 0.662924i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −142.727 | −0.181356 | −0.0906780 | − | 0.995880i | \(-0.528903\pi\) | ||||
−0.0906780 | + | 0.995880i | \(0.528903\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 137.117i | − | 0.173786i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 394.712 | + | 447.486i | 0.499004 | + | 0.565721i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 325.844i | 0.410901i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −539.605 | + | 154.984i | −0.678749 | + | 0.194948i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 317.415 | 0.398262 | 0.199131 | − | 0.979973i | \(-0.436188\pi\) | ||||
0.199131 | + | 0.979973i | \(0.436188\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 375.126 | 0.469495 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 232.740i | 0.290562i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −846.354 | −1.05399 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −497.709 | + | 779.426i | −0.618272 | + | 0.968231i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 92.2793i | 0.114349i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1392.39 | −1.72112 | −0.860560 | − | 0.509350i | \(-0.829886\pi\) | ||||
−0.860560 | + | 0.509350i | \(0.829886\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1087.46i | 1.34089i | 0.741958 | + | 0.670447i | \(0.233898\pi\) | ||||
−0.741958 | + | 0.670447i | \(0.766102\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 411.601i | − | 0.506274i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1126.43 | + | 323.531i | −1.38212 | + | 0.396970i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1893.58 | 2.31772 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 391.013 | − | 344.899i | 0.477427 | − | 0.421122i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 172.333 | 0.209906 | 0.104953 | − | 0.994477i | \(-0.466531\pi\) | ||||
0.104953 | + | 0.994477i | \(0.466531\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 215.439i | − | 0.261773i | −0.991397 | − | 0.130886i | \(-0.958218\pi\) | ||
0.991397 | − | 0.130886i | \(-0.0417823\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −431.870 | + | 270.386i | −0.523479 | + | 0.327741i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 797.435i | − | 0.964250i | −0.876102 | − | 0.482125i | \(-0.839865\pi\) | ||
0.876102 | − | 0.482125i | \(-0.160135\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 389.170i | − | 0.469445i | −0.972062 | − | 0.234723i | \(-0.924582\pi\) | ||
0.972062 | − | 0.234723i | \(-0.0754182\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 291.305i | − | 0.350548i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −44.4146 | + | 353.006i | −0.0533188 | + | 0.423777i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −57.8104 | − | 201.277i | −0.0692340 | − | 0.241051i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 53.1162i | 0.0634602i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 280.262i | 0.334043i | 0.985953 | + | 0.167021i | \(0.0534149\pi\) | ||||
−0.985953 | + | 0.167021i | \(0.946585\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2417.83 | 2.87494 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −222.006 | −0.263353 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −617.582 | − | 2150.23i | −0.730867 | − | 2.54465i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −91.6804 | + | 80.8681i | −0.108241 | + | 0.0954760i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −125.971 | −0.148376 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 375.715 | 0.441498 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −245.874 | −0.288246 | −0.144123 | − | 0.989560i | \(-0.546036\pi\) | ||||
−0.144123 | + | 0.989560i | \(0.546036\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 331.666 | − | 95.2603i | 0.387914 | − | 0.111416i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 798.850 | 0.932147 | 0.466074 | − | 0.884746i | \(-0.345668\pi\) | ||||
0.466074 | + | 0.884746i | \(0.345668\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1274.93i | − | 1.48420i | −0.670287 | − | 0.742102i | \(-0.733829\pi\) | ||
0.670287 | − | 0.742102i | \(-0.266171\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 130.146 | + | 147.546i | 0.151156 | + | 0.171366i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 736.114i | 0.852971i | 0.904494 | + | 0.426486i | \(0.140249\pi\) | ||||
−0.904494 | + | 0.426486i | \(0.859751\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.9852 | + | 62.6187i | 0.0207921 | + | 0.0723915i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 409.245 | 0.472024 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 532.816 | 0.613137 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 556.236i | − | 0.638617i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 18.4722 | 0.0211595 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −874.965 | − | 7.79790i | −0.999960 | − | 0.00891189i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1103.15i | 1.25787i | 0.777457 | + | 0.628936i | \(0.216509\pi\) | ||||
−0.777457 | + | 0.628936i | \(0.783491\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −473.223 | −0.538366 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 269.425i | 0.305817i | 0.988240 | + | 0.152909i | \(0.0488640\pi\) | ||||
−0.988240 | + | 0.152909i | \(0.951136\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1077.49i | − | 1.22026i | −0.792302 | − | 0.610129i | \(-0.791118\pi\) | ||
0.792302 | − | 0.610129i | \(-0.208882\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 680.619 | − | 195.486i | 0.769061 | − | 0.220888i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 500.908 | 0.564721 | 0.282361 | − | 0.959308i | \(-0.408883\pi\) | ||||
0.282361 | + | 0.959308i | \(0.408883\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −309.194 | − | 350.534i | −0.347800 | − | 0.394302i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −105.904 | −0.118859 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 1188.51i | − | 1.33092i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −33.3439 | − | 116.093i | −0.0372558 | − | 0.129713i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1136.25i | 1.26672i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 583.546i | − | 0.649106i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 470.712i | − | 0.522433i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −660.160 | − | 748.425i | −0.731074 | − | 0.828820i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 209.100 | − | 60.0570i | 0.231049 | − | 0.0663614i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 789.727i | − | 0.870702i | −0.900261 | − | 0.435351i | \(-0.856624\pi\) | ||
0.900261 | − | 0.435351i | \(-0.143376\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 428.950i | − | 0.471893i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −885.912 | −0.972461 | −0.486231 | − | 0.873830i | \(-0.661629\pi\) | ||||
−0.486231 | + | 0.873830i | \(0.661629\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −208.663 | −0.228547 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 109.241 | − | 31.3759i | 0.119389 | − | 0.0342906i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 133.511 | + | 151.362i | 0.145596 | + | 0.165062i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1411.37 | 1.53577 | 0.767883 | − | 0.640590i | \(-0.221310\pi\) | ||||
0.767883 | + | 0.640590i | \(0.221310\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −582.119 | −0.632051 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2271.82 | 2.46134 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 188.644 | + | 301.308i | 0.203939 | + | 0.325739i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 43.5877 | 0.0470201 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1394.66i | 1.50125i | 0.660727 | + | 0.750627i | \(0.270248\pi\) | ||||
−0.660727 | + | 0.750627i | \(0.729752\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1118.43 | + | 140.719i | 1.20132 | + | 0.151148i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 861.308i | − | 0.923160i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −117.933 | − | 410.604i | −0.126131 | − | 0.439148i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −448.660 | −0.478826 | −0.239413 | − | 0.970918i | \(-0.576955\pi\) | ||||
−0.239413 | + | 0.970918i | \(0.576955\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −436.518 | −0.464876 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1061.98i | 1.12856i | 0.825583 | + | 0.564281i | \(0.190847\pi\) | ||||
−0.825583 | + | 0.564281i | \(0.809153\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −428.757 | −0.454673 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −153.280 | − | 97.8783i | −0.162201 | − | 0.103575i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 470.708i | − | 0.497051i | −0.968625 | − | 0.248526i | \(-0.920054\pi\) | ||
0.968625 | − | 0.248526i | \(-0.0799460\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1785.77 | −1.88174 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 468.006i | − | 0.492120i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 625.282i | 0.656119i | 0.944657 | + | 0.328060i | \(0.106395\pi\) | ||||
−0.944657 | + | 0.328060i | \(0.893605\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −340.339 | − | 1184.95i | −0.356376 | − | 1.24079i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1163.48 | 1.21576 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 553.113 | + | 627.065i | 0.576760 | + | 0.653874i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 856.506 | 0.891266 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 235.268i | 0.244308i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 777.926 | − | 223.434i | 0.806141 | − | 0.231538i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 593.257i | 0.613503i | 0.951790 | + | 0.306751i | \(0.0992420\pi\) | ||||
−0.951790 | + | 0.306751i | \(0.900758\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 289.321i | 0.298577i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1633.10i | − | 1.68187i | −0.541133 | − | 0.840937i | \(-0.682004\pi\) | ||
0.541133 | − | 0.840937i | \(-0.317996\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 930.490 | + | 1054.90i | 0.956311 | + | 1.08417i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −911.227 | + | 570.504i | −0.934592 | + | 0.585132i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1137.81i | 1.16459i | 0.812977 | + | 0.582296i | \(0.197846\pi\) | ||||
−0.812977 | + | 0.582296i | \(0.802154\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 912.891i | − | 0.932472i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −224.227 | −0.228570 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −746.446 | −0.759355 | −0.379677 | − | 0.925119i | \(-0.623965\pi\) | ||||
−0.379677 | + | 0.925119i | \(0.623965\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 215.478 | − | 61.8891i | 0.218760 | − | 0.0628315i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −469.752 | + | 414.352i | −0.475939 | + | 0.419810i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2174.86 | 2.19905 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 765.218 | 0.772168 | 0.386084 | − | 0.922464i | \(-0.373828\pi\) | ||||
0.386084 | + | 0.922464i | \(0.373828\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −531.415 | −0.535161 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 551.536 | − | 158.411i | 0.554308 | − | 0.159207i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1799.05 | −1.80446 | −0.902230 | − | 0.431255i | \(-0.858071\pi\) | ||||
−0.902230 | + | 0.431255i | \(0.858071\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 73.8872i | 0.0739612i |
(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 | 1680.3.bd.a.769.5 | 16 | ||
4.3 | odd | 2 | 210.3.h.a.139.7 | yes | 16 | ||
5.4 | even | 2 | inner | 1680.3.bd.a.769.11 | 16 | ||
7.6 | odd | 2 | inner | 1680.3.bd.a.769.12 | 16 | ||
12.11 | even | 2 | 630.3.h.e.559.13 | 16 | |||
20.3 | even | 4 | 1050.3.f.e.601.5 | 16 | |||
20.7 | even | 4 | 1050.3.f.e.601.12 | 16 | |||
20.19 | odd | 2 | 210.3.h.a.139.10 | yes | 16 | ||
28.27 | even | 2 | 210.3.h.a.139.2 | ✓ | 16 | ||
35.34 | odd | 2 | inner | 1680.3.bd.a.769.6 | 16 | ||
60.59 | even | 2 | 630.3.h.e.559.4 | 16 | |||
84.83 | odd | 2 | 630.3.h.e.559.12 | 16 | |||
140.27 | odd | 4 | 1050.3.f.e.601.16 | 16 | |||
140.83 | odd | 4 | 1050.3.f.e.601.1 | 16 | |||
140.139 | even | 2 | 210.3.h.a.139.15 | yes | 16 | ||
420.419 | odd | 2 | 630.3.h.e.559.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.h.a.139.2 | ✓ | 16 | 28.27 | even | 2 | ||
210.3.h.a.139.7 | yes | 16 | 4.3 | odd | 2 | ||
210.3.h.a.139.10 | yes | 16 | 20.19 | odd | 2 | ||
210.3.h.a.139.15 | yes | 16 | 140.139 | even | 2 | ||
630.3.h.e.559.4 | 16 | 60.59 | even | 2 | |||
630.3.h.e.559.5 | 16 | 420.419 | odd | 2 | |||
630.3.h.e.559.12 | 16 | 84.83 | odd | 2 | |||
630.3.h.e.559.13 | 16 | 12.11 | even | 2 | |||
1050.3.f.e.601.1 | 16 | 140.83 | odd | 4 | |||
1050.3.f.e.601.5 | 16 | 20.3 | even | 4 | |||
1050.3.f.e.601.12 | 16 | 20.7 | even | 4 | |||
1050.3.f.e.601.16 | 16 | 140.27 | odd | 4 | |||
1680.3.bd.a.769.5 | 16 | 1.1 | even | 1 | trivial | ||
1680.3.bd.a.769.6 | 16 | 35.34 | odd | 2 | inner | ||
1680.3.bd.a.769.11 | 16 | 5.4 | even | 2 | inner | ||
1680.3.bd.a.769.12 | 16 | 7.6 | odd | 2 | inner |