Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,4,Mod(45,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.45");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.48414516044\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2 x^{9} + 90 x^{8} - 212 x^{7} + 7012 x^{6} - 14448 x^{5} + 100896 x^{4} - 25920 x^{3} + \cdots + 1016064 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 45.1 | ||
Root | \(-4.43560 + 7.68268i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.45 |
Dual form | 76.4.e.a.49.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.93560 | − | 6.81665i | −0.757406 | − | 1.31187i | −0.944169 | − | 0.329461i | \(-0.893133\pi\) |
0.186763 | − | 0.982405i | \(-0.440200\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.0670670 | + | 0.116164i | 0.00599866 | + | 0.0103900i | 0.869009 | − | 0.494796i | \(-0.164757\pi\) |
−0.863010 | + | 0.505186i | \(0.831424\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −9.41300 | −0.508254 | −0.254127 | − | 0.967171i | \(-0.581788\pi\) | ||||
−0.254127 | + | 0.967171i | \(0.581788\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −17.4778 | + | 30.2725i | −0.647327 | + | 1.12120i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −47.5639 | −1.30373 | −0.651867 | − | 0.758334i | \(-0.726014\pi\) | ||||
−0.651867 | + | 0.758334i | \(0.726014\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −22.2514 | + | 38.5406i | −0.474725 | + | 0.822248i | −0.999581 | − | 0.0289429i | \(-0.990786\pi\) |
0.524856 | + | 0.851191i | \(0.324119\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.527898 | − | 0.914345i | 0.00908684 | − | 0.0157389i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.963494 | − | 1.66882i | −0.0137460 | − | 0.0238087i | 0.859071 | − | 0.511857i | \(-0.171042\pi\) |
−0.872817 | + | 0.488048i | \(0.837709\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −42.7995 | − | 70.9028i | −0.516783 | − | 0.856116i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 37.0458 | + | 64.1651i | 0.384955 | + | 0.666761i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 77.1861 | − | 133.690i | 0.699757 | − | 1.21201i | −0.268794 | − | 0.963198i | \(-0.586625\pi\) |
0.968551 | − | 0.248817i | \(-0.0800417\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 62.4910 | − | 108.238i | 0.499928 | − | 0.865901i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 62.6206 | 0.446346 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −26.5445 | + | 45.9764i | −0.169972 | + | 0.294400i | −0.938410 | − | 0.345525i | \(-0.887701\pi\) |
0.768438 | + | 0.639924i | \(0.221034\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 11.3029 | 0.0654859 | 0.0327430 | − | 0.999464i | \(-0.489576\pi\) | ||||
0.0327430 | + | 0.999464i | \(0.489576\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 187.192 | + | 324.227i | 0.987455 | + | 1.71032i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.631302 | − | 1.09345i | −0.00304884 | − | 0.00528075i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −148.199 | −0.658480 | −0.329240 | − | 0.944246i | \(-0.606792\pi\) | ||||
−0.329240 | + | 0.944246i | \(0.606792\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 350.290 | 1.43824 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −131.426 | − | 227.637i | −0.500617 | − | 0.867094i | −1.00000 | 0.000712775i | \(-0.999773\pi\) | |
0.499383 | − | 0.866382i | \(-0.333560\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 114.553 | + | 198.412i | 0.406261 | + | 0.703665i | 0.994467 | − | 0.105046i | \(-0.0334990\pi\) |
−0.588206 | + | 0.808711i | \(0.700166\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.68875 | −0.0155324 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 176.617 | − | 305.910i | 0.548134 | − | 0.949395i | −0.450269 | − | 0.892893i | \(-0.648672\pi\) |
0.998402 | − | 0.0565023i | \(-0.0179948\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −254.396 | −0.741678 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.58385 | + | 13.1356i | −0.0208226 | + | 0.0360657i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 110.311 | − | 191.065i | 0.285894 | − | 0.495184i | −0.686931 | − | 0.726722i | \(-0.741043\pi\) |
0.972826 | + | 0.231539i | \(0.0743760\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.18997 | − | 5.52519i | −0.00782065 | − | 0.0135458i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −314.878 | + | 570.794i | −0.731695 | + | 1.32638i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −421.722 | − | 730.444i | −0.930569 | − | 1.61179i | −0.782351 | − | 0.622838i | \(-0.785980\pi\) |
−0.148218 | − | 0.988955i | \(-0.547354\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 74.9309 | − | 129.784i | 0.157277 | − | 0.272412i | −0.776609 | − | 0.629983i | \(-0.783062\pi\) |
0.933886 | + | 0.357571i | \(0.116395\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 164.519 | − | 284.955i | 0.329007 | − | 0.569856i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.96934 | −0.0113909 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −459.082 | + | 795.154i | −0.837102 | + | 1.44990i | 0.0552050 | + | 0.998475i | \(0.482419\pi\) |
−0.892307 | + | 0.451429i | \(0.850915\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1215.09 | −2.12000 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 493.025 | + | 853.944i | 0.824102 | + | 1.42739i | 0.902604 | + | 0.430473i | \(0.141653\pi\) |
−0.0785015 | + | 0.996914i | \(0.525014\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 461.416 | + | 799.196i | 0.739790 | + | 1.28135i | 0.952590 | + | 0.304257i | \(0.0984083\pi\) |
−0.212800 | + | 0.977096i | \(0.568258\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −983.757 | −1.51459 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 447.719 | 0.662627 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −540.151 | − | 935.568i | −0.769262 | − | 1.33240i | −0.937964 | − | 0.346733i | \(-0.887291\pi\) |
0.168702 | − | 0.985667i | \(-0.446042\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 225.452 | + | 390.494i | 0.309262 | + | 0.535658i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −316.723 | −0.418853 | −0.209427 | − | 0.977824i | \(-0.567160\pi\) | ||||
−0.209427 | + | 0.977824i | \(0.567160\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.129237 | − | 0.223846i | 0.000164915 | − | 0.000285641i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 417.873 | 0.514951 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 508.710 | − | 881.112i | 0.605879 | − | 1.04941i | −0.386033 | − | 0.922485i | \(-0.626155\pi\) |
0.991912 | − | 0.126928i | \(-0.0405117\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 209.452 | − | 362.782i | 0.241281 | − | 0.417911i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −44.4837 | − | 77.0481i | −0.0495994 | − | 0.0859087i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.36588 | − | 9.72698i | 0.00579503 | − | 0.0105049i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 537.224 | + | 930.499i | 0.562338 | + | 0.973998i | 0.997292 | + | 0.0735455i | \(0.0234314\pi\) |
−0.434954 | + | 0.900453i | \(0.643235\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 831.315 | − | 1439.88i | 0.843942 | − | 1.46175i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 642.035 | − | 1112.04i | 0.632523 | − | 1.09556i | −0.354511 | − | 0.935052i | \(-0.615353\pi\) |
0.987034 | − | 0.160510i | \(-0.0513140\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 491.614 | 0.470293 | 0.235147 | − | 0.971960i | \(-0.424443\pi\) | ||||
0.235147 | + | 0.971960i | \(0.424443\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.96910 | + | 8.60673i | −0.00461842 | + | 0.00799934i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 302.381 | 0.273199 | 0.136600 | − | 0.990626i | \(-0.456383\pi\) | ||||
0.136600 | + | 0.990626i | \(0.456383\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 392.757 | + | 680.274i | 0.345131 | + | 0.597784i | 0.985378 | − | 0.170385i | \(-0.0545012\pi\) |
−0.640247 | + | 0.768169i | \(0.721168\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 583.251 | + | 1010.22i | 0.498736 | + | 0.863837i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −171.809 | −0.143030 | −0.0715150 | − | 0.997440i | \(-0.522783\pi\) | ||||
−0.0715150 | + | 0.997440i | \(0.522783\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 20.7066 | 0.0167904 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −777.813 | − | 1347.21i | −0.614605 | − | 1.06453i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.06936 | + | 15.7086i | 0.00698645 | + | 0.0121009i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 931.327 | 0.699720 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1034.48 | + | 1791.77i | −0.758341 | + | 1.31348i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 33.5311 | 0.0239929 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1367.41 | + | 2368.43i | −0.955420 | + | 1.65484i | −0.222015 | + | 0.975043i | \(0.571263\pi\) |
−0.733405 | + | 0.679792i | \(0.762070\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 901.672 | − | 1561.74i | 0.615409 | − | 1.06592i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 648.315 | + | 1122.91i | 0.432393 | + | 0.748927i | 0.997079 | − | 0.0763788i | \(-0.0243358\pi\) |
−0.564685 | + | 0.825306i | \(0.691003\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 402.871 | + | 667.408i | 0.262657 | + | 0.435125i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.19978 | + | 7.27423i | 0.00267748 | + | 0.00463753i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1042.84 | − | 1806.25i | 0.650334 | − | 1.12641i | −0.332708 | − | 0.943030i | \(-0.607962\pi\) |
0.983042 | − | 0.183382i | \(-0.0587044\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −234.329 | + | 405.869i | −0.142989 | + | 0.247665i | −0.928621 | − | 0.371030i | \(-0.879005\pi\) |
0.785632 | + | 0.618694i | \(0.212338\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2780.38 | −1.66064 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1058.36 | − | 1833.14i | 0.618915 | − | 1.07199i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.12103 | −0.00407841 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1001.20 | + | 1734.13i | 0.561751 | + | 0.972982i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1211.56 | − | 2098.49i | −0.666141 | − | 1.15379i | −0.978975 | − | 0.203982i | \(-0.934612\pi\) |
0.312834 | − | 0.949808i | \(-0.398722\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3484.73 | −1.87804 | −0.939018 | − | 0.343867i | \(-0.888263\pi\) | ||||
−0.939018 | + | 0.343867i | \(0.888263\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 67.3592 | 0.0355926 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.758053 | + | 1.31299i | 0.000392828 | + | 0.000680397i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1665.86 | − | 2885.36i | −0.846817 | − | 1.46673i | −0.884034 | − | 0.467423i | \(-0.845182\pi\) |
0.0372162 | − | 0.999307i | \(-0.488151\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1736.56 | −0.866152 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −726.552 | + | 1258.43i | −0.355654 | + | 0.616011i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2610.26 | 1.25430 | 0.627151 | − | 0.778897i | \(-0.284221\pi\) | ||||
0.627151 | + | 0.778897i | \(0.284221\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −25.1089 | + | 43.4899i | −0.0118468 | + | 0.0205193i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 97.3470 | − | 168.610i | 0.0451074 | − | 0.0781284i | −0.842590 | − | 0.538555i | \(-0.818970\pi\) |
0.887698 | + | 0.460427i | \(0.152304\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 108.250 | + | 187.495i | 0.0492718 | + | 0.0853413i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2894.45 | − | 56.4205i | 1.29441 | − | 0.0252315i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 292.376 | + | 506.410i | 0.128491 | + | 0.222553i | 0.923092 | − | 0.384579i | \(-0.125653\pi\) |
−0.794601 | + | 0.607132i | \(0.792320\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −588.228 | + | 1018.84i | −0.254090 | + | 0.440098i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3319.46 | + | 5749.47i | −1.40964 | + | 2.44156i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1465.40 | −0.611894 | −0.305947 | − | 0.952048i | \(-0.598973\pi\) | ||||
−0.305947 | + | 0.952048i | \(0.598973\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1179.10 | − | 2042.26i | 0.484210 | − | 0.838676i | −0.515626 | − | 0.856814i | \(-0.672441\pi\) |
0.999835 | + | 0.0181381i | \(0.00577387\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1179.59 | −0.476491 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.93926 | − | 17.2153i | −0.00394999 | − | 0.00684159i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 45.8276 | + | 79.3756i | 0.0179211 | + | 0.0310402i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −589.448 | −0.226857 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4343.02 | −1.64529 | −0.822643 | − | 0.568558i | \(-0.807501\pi\) | ||||
−0.822643 | + | 0.568558i | \(0.807501\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 401.381 | + | 695.212i | 0.149700 | + | 0.259287i | 0.931116 | − | 0.364722i | \(-0.118836\pi\) |
−0.781417 | + | 0.624009i | \(0.785503\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 23.4929 | + | 40.6909i | 0.00862750 | + | 0.0149433i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −160.829 | −0.0581654 | −0.0290827 | − | 0.999577i | \(-0.509259\pi\) | ||||
−0.0290827 | + | 0.999577i | \(0.509259\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 709.541 | − | 1228.96i | 0.252754 | − | 0.437782i | −0.711529 | − | 0.702657i | \(-0.751997\pi\) |
0.964283 | + | 0.264874i | \(0.0853304\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7227.05 | 2.53610 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 249.863 | − | 432.775i | 0.0863888 | − | 0.149630i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.6287 | − | 30.5338i | 0.00600606 | − | 0.0104028i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2698.09 | + | 4673.23i | 0.905944 | + | 1.56914i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2035.71 | + | 3372.41i | 0.673747 | + | 1.11615i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1451.84 | − | 2514.65i | −0.473689 | − | 0.820454i | 0.525857 | − | 0.850573i | \(-0.323745\pi\) |
−0.999546 | + | 0.0301189i | \(0.990411\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3880.69 | − | 6721.55i | 1.24836 | − | 2.16222i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15.3655 | + | 26.6138i | −0.00487404 | + | 0.00844209i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −106.394 | −0.0332835 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3631.89 | − | 6290.62i | 1.12064 | − | 1.94101i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 85.7564 | 0.0261022 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1786.34 | − | 3094.04i | −0.536423 | − | 0.929112i | −0.999093 | − | 0.0425814i | \(-0.986442\pi\) |
0.462670 | − | 0.886531i | \(-0.346892\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2184.42 | + | 3783.52i | 0.647234 | + | 1.12104i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 193.355 | 0.0565349 | 0.0282674 | − | 0.999600i | \(-0.491001\pi\) | ||||
0.0282674 | + | 0.999600i | \(0.491001\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 830.109 | 0.239542 | 0.119771 | − | 0.992802i | \(-0.461784\pi\) | ||||
0.119771 | + | 0.992802i | \(0.461784\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1762.04 | − | 3051.95i | −0.501878 | − | 0.869278i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2541.17 | − | 4401.43i | −0.714496 | − | 1.23754i | −0.963154 | − | 0.268952i | \(-0.913323\pi\) |
0.248658 | − | 0.968591i | \(-0.420011\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 47.3808 | 0.0131523 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4251.63 | + | 7364.04i | −1.16529 | + | 2.01834i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6668.03 | 1.80468 | 0.902341 | − | 0.431023i | \(-0.141847\pi\) | ||||
0.902341 | + | 0.431023i | \(0.141847\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 89.9899 | − | 155.867i | 0.0240529 | − | 0.0416609i | −0.853748 | − | 0.520686i | \(-0.825676\pi\) |
0.877801 | + | 0.479025i | \(0.159010\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2619.95 | − | 4537.90i | 0.691647 | − | 1.19797i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −17.0616 | − | 29.5515i | −0.00444907 | − | 0.00770602i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3684.98 | − | 71.8301i | 0.949270 | − | 0.0185038i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1246.49 | + | 2158.99i | 0.317242 | + | 0.549479i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2513.33 | + | 4353.22i | −0.632032 | + | 1.09471i | 0.355103 | + | 0.934827i | \(0.384446\pi\) |
−0.987136 | + | 0.159885i | \(0.948888\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3671.27 | + | 6358.83i | −0.912296 | + | 1.58014i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.03450 | −0.000499630 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1871.36 | + | 3241.29i | −0.454210 | + | 0.786715i | −0.998642 | − | 0.0520895i | \(-0.983412\pi\) |
0.544432 | + | 0.838805i | \(0.316745\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1395.00 | 0.334675 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −927.879 | − | 1607.13i | −0.220055 | − | 0.381146i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 125.709 | + | 217.734i | 0.0294735 | + | 0.0510497i | 0.880386 | − | 0.474258i | \(-0.157284\pi\) |
−0.850912 | + | 0.525308i | \(0.823950\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 29.5930 | 0.00685993 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8008.32 | −1.83558 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1085.34 | − | 1879.87i | −0.246002 | − | 0.426088i | 0.716411 | − | 0.697679i | \(-0.245784\pi\) |
−0.962413 | + | 0.271591i | \(0.912450\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −670.094 | − | 1160.64i | −0.150204 | − | 0.260161i | 0.781098 | − | 0.624408i | \(-0.214660\pi\) |
−0.931302 | + | 0.364247i | \(0.881326\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3297.28 | −0.730991 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2972.32 | + | 5148.20i | −0.651773 | + | 1.12890i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 191.769 | 0.0415967 | 0.0207984 | − | 0.999784i | \(-0.493379\pi\) | ||||
0.0207984 | + | 0.999784i | \(0.493379\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −197.551 | + | 342.168i | −0.0423908 | + | 0.0734231i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −142.001 | + | 245.953i | −0.0301461 | + | 0.0522146i | −0.880705 | − | 0.473665i | \(-0.842931\pi\) |
0.850559 | + | 0.525880i | \(0.176264\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −44.9188 | − | 77.8016i | −0.00943514 | − | 0.0163421i | 0.861269 | − | 0.508149i | \(-0.169670\pi\) |
−0.870704 | + | 0.491807i | \(0.836337\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −87.4234 | + | 1.70411i | −0.0181702 | + | 0.000354186i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1237.11 | + | 2142.74i | 0.254441 | + | 0.440704i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2454.64 | − | 4251.57i | 0.499622 | − | 0.865371i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4228.59 | − | 7324.14i | 0.851837 | − | 1.47542i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5957.69 | −1.18789 | −0.593946 | − | 0.804505i | \(-0.702431\pi\) | ||||
−0.593946 | + | 0.804505i | \(0.702431\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 56.5673 | − | 97.9775i | 0.0111643 | − | 0.0193372i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2978.48 | −0.581916 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3435.00 | + | 5949.59i | 0.664385 | + | 1.15075i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1078.29 | − | 1867.65i | −0.206484 | − | 0.357641i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10107.2 | −1.91631 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 20.1016 | 0.00377381 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1127.36 | − | 1952.64i | −0.209582 | − | 0.363006i | 0.742001 | − | 0.670399i | \(-0.233877\pi\) |
−0.951583 | + | 0.307392i | \(0.900544\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1934.80 | − | 3351.16i | −0.356203 | − | 0.616961i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5929.03 | 1.08104 | 0.540521 | − | 0.841330i | \(-0.318227\pi\) | ||||
0.540521 | + | 0.841330i | \(0.318227\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3020.55 | − | 5231.75i | 0.545469 | − | 0.944780i | −0.453108 | − | 0.891456i | \(-0.649685\pi\) |
0.998577 | − | 0.0533246i | \(-0.0169818\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 44.1352 | 0.00789439 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3084.14 | + | 5341.88i | −0.546443 | + | 0.946467i | 0.452072 | + | 0.891982i | \(0.350685\pi\) |
−0.998515 | + | 0.0544850i | \(0.982648\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1262.56 | − | 2186.82i | 0.221598 | − | 0.383819i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1190.05 | − | 2061.23i | −0.206923 | − | 0.358401i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −77.0870 | + | 139.739i | −0.0132794 | + | 0.0240721i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2781.02 | + | 4816.88i | 0.474657 | + | 0.822130i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3091.46 | − | 5354.57i | 0.522808 | − | 0.905530i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1662.50 | + | 2879.53i | −0.278591 | + | 0.482534i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6863.00 | −1.13965 | −0.569826 | − | 0.821765i | \(-0.692989\pi\) | ||||
−0.569826 | + | 0.821765i | \(0.692989\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2590.20 | − | 4486.35i | 0.426252 | − | 0.738290i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −123.157 | −0.0200860 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3914.15 | + | 6779.50i | 0.632692 | + | 1.09585i | 0.986999 | + | 0.160725i | \(0.0513833\pi\) |
−0.354308 | + | 0.935129i | \(0.615283\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 676.169 | + | 1171.16i | 0.108332 | + | 0.187636i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −537.611 | −0.0853762 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5623.28 | 0.885215 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −81.4927 | − | 141.149i | −0.0127172 | − | 0.0220268i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5492.82 | + | 9513.84i | 0.849769 | + | 1.47184i | 0.881414 | + | 0.472344i | \(0.156592\pi\) |
−0.0316451 | + | 0.999499i | \(0.510075\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2768.56 | 0.424635 | 0.212318 | − | 0.977201i | \(-0.431899\pi\) | ||||
0.212318 | + | 0.977201i | \(0.431899\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1393.40 | + | 2413.43i | −0.211892 | + | 0.367007i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7098.29 | −1.07027 | −0.535133 | − | 0.844768i | \(-0.679739\pi\) | ||||
−0.535133 | + | 0.844768i | \(0.679739\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −66.1314 | + | 114.543i | −0.00988701 | + | 0.0171248i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 71.3867 | − | 123.645i | 0.0105832 | − | 0.0183306i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3319.66 | + | 5749.82i | 0.488036 | + | 0.845304i | 0.999905 | − | 0.0137598i | \(-0.00438002\pi\) |
−0.511869 | + | 0.859064i | \(0.671047\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3195.41 | + | 6069.21i | −0.465871 | + | 0.884853i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3665.33 | − | 6348.53i | −0.529972 | − | 0.917938i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −61.8916 | + | 107.199i | −0.00887549 | + | 0.0153728i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5043.80 | − | 8736.12i | 0.717396 | − | 1.24257i | −0.244633 | − | 0.969616i | \(-0.578667\pi\) |
0.962028 | − | 0.272950i | \(-0.0879993\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9188.17 | 1.29625 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1038.36 | + | 1798.49i | −0.145307 | + | 0.251679i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3174.01 | 0.440600 | 0.220300 | − | 0.975432i | \(-0.429296\pi\) | ||||
0.220300 | + | 0.975432i | \(0.429296\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −131.965 | − | 228.570i | −0.0181724 | − | 0.0314755i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1181.30 | − | 2046.08i | −0.161380 | − | 0.279518i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2129.14 | −0.288567 | −0.144283 | − | 0.989536i | \(-0.546088\pi\) | ||||
−0.144283 | + | 0.989536i | \(0.546088\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 21526.3 | 2.89456 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1432.60 | − | 2481.34i | −0.191129 | − | 0.331046i | 0.754495 | − | 0.656305i | \(-0.227882\pi\) |
−0.945625 | + | 0.325260i | \(0.894548\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 30.0272 | + | 52.0086i | 0.00397488 | + | 0.00688469i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8008.58 | −1.05194 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6416.83 | − | 11114.3i | 0.836365 | − | 1.44863i | −0.0565491 | − | 0.998400i | \(-0.518010\pi\) |
0.892914 | − | 0.450227i | \(-0.148657\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −297.473 | −0.0384754 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5103.01 | − | 8838.68i | 0.654995 | − | 1.13448i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 72.4526 | − | 125.492i | 0.00922908 | − | 0.0159852i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1933.68 | − | 3349.23i | −0.244454 | − | 0.423408i | 0.717524 | − | 0.696534i | \(-0.245276\pi\) |
−0.961978 | + | 0.273127i | \(0.911942\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2963.95 | − | 5372.88i | 0.371887 | − | 0.674137i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −934.292 | − | 1618.24i | −0.116350 | − | 0.201524i | 0.801969 | − | 0.597366i | \(-0.203786\pi\) |
−0.918319 | + | 0.395842i | \(0.870453\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −251.506 | + | 435.621i | −0.0310878 | + | 0.0538457i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −30.2408 | + | 52.3786i | −0.00371031 | + | 0.00642645i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7048.92 | 0.858482 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3666.90 | + | 6351.26i | −0.443317 | + | 0.767848i | −0.997933 | − | 0.0642584i | \(-0.979532\pi\) |
0.554616 | + | 0.832106i | \(0.312865\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16416.8 | −1.97027 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3969.67 | + | 6875.67i | 0.472965 | + | 0.819200i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21.2416 | − | 36.7916i | −0.00251256 | − | 0.00435188i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3688.89 | 0.433204 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1286.23 | 0.149968 | 0.0749840 | − | 0.997185i | \(-0.476109\pi\) | ||||
0.0749840 | + | 0.997185i | \(0.476109\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −757.659 | − | 1312.30i | −0.0877103 | − | 0.151919i | 0.818833 | − | 0.574032i | \(-0.194622\pi\) |
−0.906543 | + | 0.422114i | \(0.861288\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6173.78 | + | 10693.3i | 0.709644 | + | 1.22914i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −240.839 | −0.0274880 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −705.324 | + | 1221.66i | −0.0799368 | + | 0.138455i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −16661.2 | −1.87508 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3663.73 | + | 6345.76i | −0.409456 | + | 0.709199i | −0.994829 | − | 0.101566i | \(-0.967615\pi\) |
0.585373 | + | 0.810764i | \(0.300948\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3511.74 | − | 6082.50i | 0.389753 | − | 0.675073i | −0.602663 | − | 0.797996i | \(-0.705894\pi\) |
0.992416 | + | 0.122923i | \(0.0392269\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 28.0255 | + | 48.5416i | 0.00308901 | + | 0.00535033i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12782.5 | + | 249.166i | −1.39925 | + | 0.0272751i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7556.49 | − | 13088.2i | −0.821530 | − | 1.42293i | −0.904543 | − | 0.426383i | \(-0.859788\pi\) |
0.0830132 | − | 0.996548i | \(-0.473546\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4446.28 | − | 7701.19i | 0.480108 | − | 0.831572i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 983.331 | − | 1703.18i | 0.105462 | − | 0.182665i | −0.808465 | − | 0.588544i | \(-0.799701\pi\) |
0.913927 | + | 0.405879i | \(0.133035\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 136.471 | 0.0145378 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9536.43 | + | 16517.6i | −1.00908 | + | 1.74777i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8276.44 | −0.869909 | −0.434954 | − | 0.900452i | \(-0.643236\pi\) | ||||
−0.434954 | + | 0.900452i | \(0.643236\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6251.14 | + | 10827.3i | 0.652671 | + | 1.13046i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13714.5 | + | 23754.2i | 1.42244 | + | 2.46373i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 56.1894 | 0.00578945 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16789.0 | −1.71850 | −0.859251 | − | 0.511555i | \(-0.829070\pi\) | ||||
−0.859251 | + | 0.511555i | \(0.829070\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −60.3346 | − | 104.503i | −0.00613547 | − | 0.0106269i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5237.00 | − | 9070.75i | −0.529092 | − | 0.916414i | −0.999424 | − | 0.0339251i | \(-0.989199\pi\) |
0.470332 | − | 0.882489i | \(-0.344134\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3416.87 | −0.342970 | −0.171485 | − | 0.985187i | \(-0.554857\pi\) | ||||
−0.171485 | + | 0.985187i | \(0.554857\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.96678 | − | 10.3348i | 0.000595060 | − | 0.00103067i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5081.31 | 0.503501 | 0.251751 | − | 0.967792i | \(-0.418994\pi\) | ||||
0.251751 | + | 0.967792i | \(0.418994\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4321.34 | − | 7484.78i | 0.425461 | − | 0.736919i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13112.3 | + | 22711.2i | −1.28277 | + | 2.22182i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5448.61 | − | 9437.27i | −0.529656 | − | 0.917391i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10348.9 | + | 201.728i | −0.999666 | + | 0.0194861i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3856.00 | + | 6678.79i | 0.370135 | + | 0.641092i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5528.06 | + | 9574.89i | −0.527315 | + | 0.913336i | 0.472179 | + | 0.881503i | \(0.343468\pi\) |
−0.999493 | + | 0.0318328i | \(0.989866\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3297.63 | − | 5711.67i | 0.312597 | − | 0.541434i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11437.7 | 1.07750 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −72.0600 | + | 124.812i | −0.00674655 | + | 0.0116854i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18123.1 | 1.68632 | 0.843158 | − | 0.537667i | \(-0.180694\pi\) | ||||
0.843158 | + | 0.537667i | \(0.180694\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10272.9 | − | 17793.2i | −0.950016 | − | 1.64548i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7620.44 | − | 13199.0i | −0.700419 | − | 1.21316i | −0.968320 | − | 0.249714i | \(-0.919663\pi\) |
0.267901 | − | 0.963446i | \(-0.413670\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 102.302 | 0.00934571 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 223.015 | 0.0202501 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4640.84 | − | 8038.17i | −0.418853 | − | 0.725475i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4334.55 | + | 7507.67i | 0.388860 | + | 0.673526i | 0.992297 | − | 0.123885i | \(-0.0395355\pi\) |
−0.603436 | + | 0.797411i | \(0.706202\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1532.47 | −0.136659 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8232.19 | − | 14258.6i | 0.729732 | − | 1.26393i | −0.227265 | − | 0.973833i | \(-0.572978\pi\) |
0.956997 | − | 0.290099i | \(-0.0936883\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 172.237 | 0.0151772 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 852.058 | − | 1475.81i | 0.0746376 | − | 0.129276i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4912.20 | − | 8508.18i | 0.427759 | − | 0.740900i | −0.568915 | − | 0.822397i | \(-0.692637\pi\) |
0.996674 | + | 0.0814962i | \(0.0259699\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4343.31 | − | 7522.83i | −0.376001 | − | 0.651253i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2680.13 | − | 4439.98i | −0.230664 | − | 0.382124i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 32.9711 | + | 57.1076i | 0.00282113 | + | 0.00488634i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8400.61 | + | 14550.3i | −0.714620 | + | 1.23776i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2301.35 | − | 3986.05i | 0.194639 | − | 0.337125i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10650.5 | 0.895595 | 0.447798 | − | 0.894135i | \(-0.352208\pi\) | ||||
0.447798 | + | 0.894135i | \(0.352208\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5825.64 | + | 10090.3i | −0.487070 | + | 0.843629i | −0.999889 | − | 0.0148670i | \(-0.995268\pi\) |
0.512820 | + | 0.858496i | \(0.328601\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9260.10 | 0.769798 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.8903 | − | 18.8625i | −0.000900168 | − | 0.00155914i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5831.88 | − | 10101.1i | −0.479320 | − | 0.830206i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 29483.2 | 2.40953 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11697.7 | 0.950622 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 20.2798 | + | 35.1257i | 0.00163883 | + | 0.00283853i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5767.22 | + | 9989.12i | 0.463452 | + | 0.802723i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12100.0 | 0.966950 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4978.81 | + | 8623.56i | −0.395667 | + | 0.685316i | −0.993186 | − | 0.116539i | \(-0.962820\pi\) |
0.597519 | + | 0.801855i | \(0.296153\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −18561.9 | −1.46697 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −52.6820 | + | 91.2480i | −0.00414064 | + | 0.00717180i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −193.113 | + | 334.481i | −0.0150949 | + | 0.0261451i | −0.873474 | − | 0.486870i | \(-0.838138\pi\) |
0.858379 | + | 0.513016i | \(0.171472\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2619.26 | + | 4536.69i | 0.203620 | + | 0.352680i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4395.94 | − | 85.6885i | 0.339879 | − | 0.00662515i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5084.43 | + | 8806.50i | 0.390980 | + | 0.677198i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −78.2338 | + | 135.505i | −0.00598350 | + | 0.0103637i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4092.54 | − | 7088.49i | 0.311322 | − | 0.539226i | −0.667327 | − | 0.744765i | \(-0.732561\pi\) |
0.978649 | + | 0.205539i | \(0.0658948\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10195.9 | −0.771450 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 360.717 | − | 624.781i | 0.0271471 | − | 0.0470201i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9871.86 | 0.738986 | 0.369493 | − | 0.929234i | \(-0.379531\pi\) | ||||
0.369493 | + | 0.929234i | \(0.379531\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.5227 | − | 19.9579i | −0.000857988 | − | 0.00148608i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2122.18 | − | 3675.72i | −0.157184 | − | 0.272250i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12867.7 | −0.948054 | −0.474027 | − | 0.880510i | \(-0.657200\pi\) | ||||
−0.474027 | + | 0.880510i | \(0.657200\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2729.67 | 0.200058 | 0.100029 | − | 0.994985i | \(-0.468106\pi\) | ||||
0.100029 | + | 0.994985i | \(0.468106\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17092.4 | + | 29604.8i | 1.24615 | + | 2.15839i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9646.87 | − | 16708.9i | −0.699656 | − | 1.21184i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8624.00 | 0.622222 | 0.311111 | − | 0.950374i | \(-0.399299\pi\) | ||||
0.311111 | + | 0.950374i | \(0.399299\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3159.35 | − | 5472.15i | 0.226767 | − | 0.392772i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2981.31 | 0.212884 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5246.83 | + | 9087.78i | −0.372730 | + | 0.645587i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 104.331 | − | 180.707i | 0.00737361 | − | 0.0127715i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1995.20 | + | 3455.80i | 0.140291 | + | 0.242991i | 0.927606 | − | 0.373559i | \(-0.121863\pi\) |
−0.787315 | + | 0.616551i | \(0.788529\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −483.759 | − | 801.408i | −0.0338420 | − | 0.0560636i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 632.958 | + | 1096.32i | 0.0440548 | + | 0.0763052i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9617.19 | + | 16657.5i | −0.665987 | + | 1.15352i | 0.313029 | + | 0.949743i | \(0.398656\pi\) |
−0.979017 | + | 0.203780i | \(0.934677\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.21651 | + | 2.10706i | −8.38186e−5 | + | 0.000145178i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11169.9 | −0.765749 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11156.9 | − | 19324.3i | 0.761033 | − | 1.31815i | −0.181286 | − | 0.983430i | \(-0.558026\pi\) |
0.942319 | − | 0.334717i | \(-0.108641\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10725.0 | 0.727923 | 0.363962 | − | 0.931414i | \(-0.381424\pi\) | ||||
0.363962 | + | 0.931414i | \(0.381424\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16047.5 | − | 27795.2i | −1.08376 | − | 1.87712i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 62.4613 | + | 108.186i | 0.00419738 | + | 0.00727007i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25360.0 | 1.69577 | 0.847884 | − | 0.530181i | \(-0.177876\pi\) | ||||
0.847884 | + | 0.530181i | \(0.177876\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3933.44 | −0.261726 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7859.97 | + | 13613.9i | 0.520426 | + | 0.901404i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3946.86 | + | 6836.16i | 0.260052 | + | 0.450424i | 0.966256 | − | 0.257585i | \(-0.0829268\pi\) |
−0.706203 | + | 0.708009i | \(0.749593\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −277.518 | −0.0181961 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6594.61 | − | 11422.2i | 0.430290 | − | 0.745284i | −0.566608 | − | 0.823987i | \(-0.691745\pi\) |
0.996898 | + | 0.0787034i | \(0.0250780\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1559.76 | −0.101280 | −0.0506399 | − | 0.998717i | \(-0.516126\pi\) | ||||
−0.0506399 | + | 0.998717i | \(0.516126\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4833.44 | − | 8371.77i | 0.312334 | − | 0.540978i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4788.49 | + | 8293.91i | −0.307940 | + | 0.533368i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7809.13 | − | 13525.8i | −0.499784 | − | 0.865651i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 14976.8 | − | 27149.2i | 0.953935 | − | 1.72924i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 142.789 | + | 247.317i | 0.00905144 | + | 0.0156776i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3801.01 | + | 6583.54i | −0.239803 | + | 0.415351i | −0.960658 | − | 0.277735i | \(-0.910416\pi\) |
0.720855 | + | 0.693086i | \(0.243750\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11427.7 | + | 19793.3i | −0.717550 | + | 1.24283i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −366.833 | −0.0229249 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5660.66 | − | 9804.55i | 0.352093 | − | 0.609843i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −34468.0 | −2.13386 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9450.80 | − | 16369.3i | −0.582346 | − | 1.00865i | −0.995201 | − | 0.0978565i | \(-0.968801\pi\) |
0.412854 | − | 0.910797i | \(-0.364532\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14237.5 | − | 24660.1i | −0.873210 | − | 1.51244i | −0.858658 | − | 0.512549i | \(-0.828701\pi\) |
−0.0145519 | − | 0.999894i | \(-0.504632\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 241.890 | 0.0147665 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18625.7 | −1.13177 | −0.565883 | − | 0.824485i | \(-0.691465\pi\) | ||||
−0.565883 | + | 0.824485i | \(0.691465\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20058.8 | + | 34742.8i | 1.21321 | + | 2.10135i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 418.725 | + | 725.253i | 0.0252091 | + | 0.0436635i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3276.84 | 0.196374 | 0.0981872 | − | 0.995168i | \(-0.468696\pi\) | ||||
0.0981872 | + | 0.995168i | \(0.468696\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −86.9611 | + | 150.621i | −0.00518756 | + | 0.00898512i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −32258.2 | −1.91554 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3275.97 | − | 5674.15i | 0.193648 | − | 0.335408i | −0.752809 | − | 0.658239i | \(-0.771301\pi\) |
0.946456 | + | 0.322832i | \(0.104635\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13591.2 | + | 23540.7i | −0.799754 | + | 1.38522i | 0.120021 | + | 0.992771i | \(0.461704\pi\) |
−0.919776 | + | 0.392444i | \(0.871630\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −337.502 | − | 584.571i | −0.0197700 | − | 0.0342426i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −50.5090 | + | 91.5600i | −0.00294535 | + | 0.00533916i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4097.73 | + | 7097.47i | 0.237878 | + | 0.412017i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14060.6 | + | 24353.8i | −0.812580 | + | 1.40743i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3564.01 | + | 6173.04i | −0.205048 | + | 0.355153i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14256.8 | −0.816582 | −0.408291 | − | 0.912852i | \(-0.633875\pi\) | ||||
−0.408291 | + | 0.912852i | \(0.633875\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3913.23 | − | 6777.91i | 0.223141 | − | 0.386492i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27947.0 | 1.58655 | 0.793273 | − | 0.608866i | \(-0.208375\pi\) | ||||
0.793273 | + | 0.608866i | \(0.208375\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5056.88 | − | 8758.78i | −0.285811 | − | 0.495039i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −760.967 | − | 1318.03i | −0.0428199 | − | 0.0741662i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10455.7 | 0.585761 | 0.292880 | − | 0.956149i | \(-0.405386\pi\) | ||||
0.292880 | + | 0.956149i | \(0.405386\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 279.760 | 0.0156045 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3266.97 | − | 5658.56i | −0.181431 | − | 0.314247i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4909.16 | + | 8502.91i | 0.271443 | + | 0.470152i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6684.98 | −0.368030 | −0.184015 | − | 0.982923i | \(-0.558909\pi\) | ||||
−0.184015 | + | 0.982923i | \(0.558909\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7825.16 | + | 13553.6i | −0.428937 | + | 0.742940i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −62.8630 | −0.00343098 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −253.256 | + | 438.653i | −0.0137629 | + | 0.0238381i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −20002.0 | + | 34644.5i | −1.08233 | + | 1.87464i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1109.57 | − | 1921.83i | −0.0597829 | − | 0.103547i | 0.834585 | − | 0.550879i | \(-0.185708\pi\) |
−0.894368 | + | 0.447332i | \(0.852374\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6342.84 | + | 10507.7i | 0.340291 | + | 0.563735i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −186.472 | − | 322.978i | −0.00996160 | − | 0.0172540i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6043.47 | + | 10467.6i | −0.321482 | + | 0.556824i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10880.2 | + | 18845.0i | −0.576323 | + | 0.998220i | 0.419574 | + | 0.907721i | \(0.362180\pi\) |
−0.995897 | + | 0.0904991i | \(0.971154\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 37762.7 | 1.99186 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 872.428 | − | 1511.09i | 0.0458242 | − | 0.0793699i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 283.925 | 0.0148506 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −26242.7 | − | 45453.7i | −1.36688 | − | 2.36750i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8761.18 | − | 15174.8i | −0.454433 | − | 0.787100i | 0.544223 | − | 0.838941i | \(-0.316825\pi\) |
−0.998655 | + | 0.0518405i | \(0.983491\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4627.56 | −0.239028 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1416.66 | −0.0728714 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3317.58 | + | 5746.22i | 0.169947 | + | 0.294357i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8678.76 | − | 15032.1i | −0.442748 | − | 0.766861i | 0.555145 | − | 0.831754i | \(-0.312663\pi\) |
−0.997892 | + | 0.0648925i | \(0.979330\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29069.9 | −1.47691 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 220.743 | − | 382.338i | 0.0111689 | − | 0.0193451i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31302.6 | 1.57734 | 0.788669 | − | 0.614818i | \(-0.210770\pi\) | ||||
0.788669 | + | 0.614818i | \(0.210770\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −134.295 | + | 232.605i | −0.00673951 | + | 0.0116732i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21835.8 | − | 37820.7i | 1.09136 | − | 1.89029i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8352.91 | + | 14467.7i | 0.415787 | + | 0.720165i | 0.995511 | − | 0.0946487i | \(-0.0301728\pi\) |
−0.579724 | + | 0.814813i | \(0.696839\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −14992.2 | − | 24836.5i | −0.743257 | − | 1.23130i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5866.80 | + | 10161.6i | 0.289679 | + | 0.501740i | 0.973733 | − | 0.227692i | \(-0.0731180\pi\) |
−0.684054 | + | 0.729432i | \(0.739785\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 162.512 | − | 281.478i | 0.00799190 | − | 0.0138424i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5535.62 | − | 9587.98i | 0.271135 | − | 0.469620i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2846.31 | −0.138855 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5718.63 | + | 9904.95i | −0.277864 | + | 0.481274i | −0.970854 | − | 0.239673i | \(-0.922960\pi\) |
0.692990 | + | 0.720947i | \(0.256293\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 39565.8 | 1.91482 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −233.711 | − | 404.799i | −0.0112657 | − | 0.0195128i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13329.0 | + | 23086.5i | 0.639960 | + | 1.10844i | 0.985441 | + | 0.170018i | \(0.0543826\pi\) |
−0.345481 | + | 0.938426i | \(0.612284\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 57794.6 | 2.76391 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29934.0 | −1.42590 | −0.712948 | − | 0.701217i | \(-0.752640\pi\) | ||||
−0.712948 | + | 0.701217i | \(0.752640\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3697.02 | − | 6403.42i | −0.175414 | − | 0.303826i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.51758 | + | 7.82468i | 0.000213508 | + | 0.000369806i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 37535.6 | 1.76706 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15271.1 | − | 26450.3i | 0.716112 | − | 1.24034i | −0.246418 | − | 0.969164i | \(-0.579253\pi\) |
0.962529 | − | 0.271178i | \(-0.0874132\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 29459.6 | 1.37609 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5386.26 | − | 9329.28i | 0.250621 | − | 0.434089i | −0.713076 | − | 0.701087i | \(-0.752698\pi\) |
0.963697 | + | 0.266998i | \(0.0860317\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 706.331 | − | 1223.40i | 0.0327383 | − | 0.0567043i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5490.14 | − | 9509.20i | −0.253485 | − | 0.439048i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10515.1 | + | 19061.2i | −0.483623 | + | 0.876686i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23450.2 | − | 40616.9i | −1.07441 | − | 1.86093i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1662.23 | + | 2879.07i | −0.0758663 | + | 0.131404i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 223.449 | − | 387.025i | 0.0101595 | − | 0.0175968i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9202.56 | −0.416818 | −0.208409 | − | 0.978042i | \(-0.566829\pi\) | ||||
−0.208409 | + | 0.978042i | \(0.566829\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 989.479 | − | 1713.83i | 0.0446469 | − | 0.0773306i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1617.23 | 0.0726956 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3334.63 | + | 5775.76i | 0.149327 | + | 0.258642i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −116.466 | − | 201.725i | −0.00519575 | − | 0.00899931i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23453.4 | 1.04236 | 0.521181 | − | 0.853446i | \(-0.325492\pi\) | ||||
0.521181 | + | 0.853446i | \(0.325492\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −680.679 | −0.0301385 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17782.3 | + | 30799.9i | 0.784404 | + | 1.35863i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21946.7 | − | 38012.9i | −0.964488 | − | 1.67054i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −194.911 | −0.00853379 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8542.94 | + | 14796.8i | −0.372646 | + | 0.645443i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22322.4 | −0.970105 | −0.485052 | − | 0.874485i | \(-0.661199\pi\) | ||||
−0.485052 | + | 0.874485i | \(0.661199\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8031.11 | + | 13910.3i | −0.347732 | + | 0.602289i | −0.985846 | − | 0.167652i | \(-0.946381\pi\) |
0.638114 | + | 0.769942i | \(0.279715\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5274.44 | + | 9135.60i | −0.227531 | + | 0.394095i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 175.062 | + | 303.217i | 0.00752413 | + | 0.0130322i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9165.16 | − | 16614.1i | 0.392470 | − | 0.711449i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7321.55 | + | 12681.3i | 0.312376 | + | 0.541050i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15725.2 | + | 27236.8i | −0.668467 | + | 1.15782i | 0.309865 | + | 0.950780i | \(0.399716\pi\) |
−0.978333 | + | 0.207039i | \(0.933617\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4638.10 | + | 8033.42i | −0.196445 | + | 0.340252i | −0.947373 | − | 0.320132i | \(-0.896273\pi\) |
0.750929 | + | 0.660383i | \(0.229606\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 46791.4 | 1.97463 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16678.2 | + | 28887.5i | −0.701281 | + | 1.21465i | 0.266737 | + | 0.963769i | \(0.414055\pi\) |
−0.968017 | + | 0.250884i | \(0.919279\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28257.5 | 1.18386 | 0.591932 | − | 0.805988i | \(-0.298365\pi\) | ||||
0.591932 | + | 0.805988i | \(0.298365\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −754.726 | − | 1307.22i | −0.0315056 | − | 0.0545693i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 245.109 | + | 424.540i | 0.0101951 | + | 0.0176584i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 26.1151 | 0.00108234 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 707.796 | 0.0292294 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4415.75 | − | 7648.30i | −0.181703 | − | 0.314718i | 0.760758 | − | 0.649036i | \(-0.224827\pi\) |
−0.942460 | + | 0.334318i | \(0.891494\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10785.3 | + | 18680.7i | 0.442219 | + | 0.765946i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2235.43 | 0.0913314 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14.5200 | + | 25.1495i | −0.000591130 | + | 0.00102387i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8766.58 | −0.355635 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −353.564 | + | 612.392i | −0.0142925 | + | 0.0247553i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11438.9 | + | 19812.7i | −0.460776 | + | 0.798087i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16810.4 | − | 29116.6i | −0.674770 | − | 1.16874i | −0.976536 | − | 0.215354i | \(-0.930909\pi\) |
0.301766 | − | 0.953382i | \(-0.402424\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 200.676 | + | 332.445i | 0.00802687 | + | 0.0132975i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11754.4 | + | 20359.2i | 0.468520 | + | 0.811500i | 0.999353 | − | 0.0359766i | \(-0.0114542\pi\) |
−0.530833 | + | 0.847476i | \(0.678121\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5258.38 | + | 9107.79i | −0.208863 | + | 0.361762i | −0.951357 | − | 0.308091i | \(-0.900310\pi\) |
0.742493 | + | 0.669853i | \(0.233643\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9737.55 | − | 16865.9i | 0.385430 | − | 0.667584i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9794.63 | −0.386342 | −0.193171 | − | 0.981165i | \(-0.561877\pi\) | ||||
−0.193171 | + | 0.981165i | \(0.561877\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −39.2175 | + | 67.9268i | −0.00154154 | + | 0.00267003i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −38641.9 | −1.51367 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25691.7 | + | 44499.3i | 1.00291 | + | 1.73709i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20430.5 | − | 35386.6i | −0.794787 | − | 1.37661i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −37558.0 | −1.45607 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −315.628 | −0.0121945 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24459.4 | − | 42364.9i | −0.941773 | − | 1.63120i | −0.762087 | − | 0.647474i | \(-0.775825\pi\) |
−0.179686 | − | 0.983724i | \(-0.557508\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 23447.1 | + | 40611.5i | 0.899716 | + | 1.55835i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37028.4 | −1.41603 | −0.708013 | − | 0.706199i | \(-0.750408\pi\) | ||||
−0.708013 | + | 0.706199i | \(0.750408\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16940.7 | − | 29342.1i | 0.645639 | − | 1.11828i | −0.338515 | − | 0.940961i | \(-0.609925\pi\) |
0.984154 | − | 0.177318i | \(-0.0567421\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −890.505 | −0.0338237 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15256.1 | − | 26424.4i | 0.577509 | − | 1.00027i | −0.418256 | − | 0.908329i | \(-0.637358\pi\) |
0.995764 | − | 0.0919448i | \(-0.0293083\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12871.5 | − | 22294.0i | 0.485596 | − | 0.841077i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10723.4 | − | 18573.4i | −0.403195 | − | 0.698354i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −29249.0 | + | 570.141i | −1.09606 | + | 0.0213651i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −98.2800 | − | 170.226i | −0.00367055 | − | 0.00635757i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 27037.5 | − | 46830.4i | 1.00642 | − | 1.74317i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −300.030 | + | 519.667i | −0.0111308 | + | 0.0192790i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −425.137 | −0.0157196 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8487.43 | + | 14700.7i | −0.312784 | + | 0.541758i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 316.315 | 0.0116184 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4101.70 | − | 7104.35i | −0.150160 | − | 0.260084i | 0.781126 | − | 0.624373i | \(-0.214645\pi\) |
−0.931286 | + | 0.364289i | \(0.881312\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 22442.8 | + | 38872.0i | 0.818899 | + | 1.41837i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26297.5 | −0.956395 | −0.478198 | − | 0.878252i | \(-0.658710\pi\) | ||||
−0.478198 | + | 0.878252i | \(0.658710\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15064.6 | 0.546073 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −79.1117 | − | 137.025i | −0.00285831 | − | 0.00495073i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6102.59 | − | 10570.0i | −0.219766 | − | 0.380645i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 39244.1 | 1.40864 | 0.704321 | − | 0.709882i | \(-0.251252\pi\) | ||||
0.704321 | + | 0.709882i | \(0.251252\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8873.63 | + | 15369.6i | −0.317477 | + | 0.549886i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −43881.9 | −1.56489 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9261.10 | + | 16040.7i | −0.329192 | + | 0.570178i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8592.36 | + | 14882.4i | −0.304434 | + | 0.527295i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22995.1 | + | 39828.6i | 0.812103 | + | 1.40660i | 0.911390 | + | 0.411544i | \(0.135010\pi\) |
−0.0992873 | + | 0.995059i | \(0.531656\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10888.0 | + | 18037.3i | 0.383287 | + | 0.634963i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −23334.3 | − | 40416.1i | −0.818788 | − | 1.41818i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.14704 | + | 10.6470i | −0.000215005 | + | 0.000372399i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 286.074 | − | 495.494i | 0.00997399 | − | 0.0172755i | −0.860995 | − | 0.508613i | \(-0.830158\pi\) |
0.870969 | + | 0.491337i | \(0.163492\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −47550.7 | −1.65257 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27767.8 | − | 48095.2i | 0.961960 | − | 1.66616i | 0.244389 | − | 0.969677i | \(-0.421413\pi\) |
0.717570 | − | 0.696486i | \(-0.245254\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −40577.1 | −1.40124 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −39.5325 | − | 68.4723i | −0.00136084 | − | 0.00235704i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1469.65 | − | 2545.51i | −0.0504300 | − | 0.0873473i | 0.839708 | − | 0.543037i | \(-0.182726\pi\) |
−0.890138 | + | 0.455690i | \(0.849393\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −41068.6 | −1.40479 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 48551.7 | 1.65552 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11592.8 | + | 20079.4i | 0.394049 | + | 0.682513i | 0.992979 | − | 0.118288i | \(-0.0377407\pi\) |
−0.598930 | + | 0.800801i | \(0.704407\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −291.273 | − | 504.500i | −0.00986951 | − | 0.0170945i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −19875.7 | −0.671358 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9816.24 | + | 17002.2i | −0.330535 | + | 0.572503i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29663.2 | −0.995712 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5284.97 | + | 9153.84i | −0.176849 | + | 0.306312i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −53.8389 | + | 93.2516i | −0.00179599 | + | 0.00311075i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8276.81 | + | 14335.9i | 0.275247 | + | 0.476742i | 0.970198 | − | 0.242315i | \(-0.0779069\pi\) |
−0.694950 | + | 0.719058i | \(0.744574\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1255.94 | − | 24.4815i | 0.0416372 | − | 0.000811620i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10422.0 | + | 18051.4i | 0.344445 | + | 0.596597i | 0.985253 | − | 0.171105i | \(-0.0547337\pi\) |
−0.640807 | + | 0.767702i | \(0.721400\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2205.74 | − | 3820.45i | 0.0726749 | − | 0.125877i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 21890.0 | − | 37914.6i | 0.719016 | − | 1.24537i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6747.90 | 0.220967 | 0.110483 | − | 0.993878i | \(-0.464760\pi\) | ||||
0.110483 | + | 0.993878i | \(0.464760\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −24196.3 | + | 41909.2i | −0.789904 | + | 1.36815i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −27458.1 | −0.893650 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10992.1 | + | 19038.9i | 0.356658 | + | 0.617750i | 0.987400 | − | 0.158243i | \(-0.0505829\pi\) |
−0.630742 | + | 0.775992i | \(0.717250\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.7863 | − | 18.6825i | −0.000348915 | − | 0.000604338i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 26171.7 | 0.844026 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 35367.7 | 1.13714 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4924.35 | + | 8529.22i | 0.157848 | + | 0.273400i | 0.934092 | − | 0.357032i | \(-0.116211\pi\) |
−0.776245 | + | 0.630432i | \(0.782878\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27010.0 | + | 46782.7i | 0.863179 | + | 1.49507i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 190.347 | 0.00606473 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20176.0 | − | 34945.8i | 0.640902 | − | 1.11008i | −0.344330 | − | 0.938849i | \(-0.611894\pi\) |
0.985232 | − | 0.171226i | \(-0.0547729\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9280.31 | −0.293910 |
(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 | 76.4.e.a.45.1 | ✓ | 10 | |
3.2 | odd | 2 | 684.4.k.c.577.3 | 10 | |||
4.3 | odd | 2 | 304.4.i.f.273.5 | 10 | |||
19.7 | even | 3 | 1444.4.a.f.1.5 | 5 | |||
19.11 | even | 3 | inner | 76.4.e.a.49.1 | yes | 10 | |
19.12 | odd | 6 | 1444.4.a.g.1.1 | 5 | |||
57.11 | odd | 6 | 684.4.k.c.505.3 | 10 | |||
76.11 | odd | 6 | 304.4.i.f.49.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.4.e.a.45.1 | ✓ | 10 | 1.1 | even | 1 | trivial | |
76.4.e.a.49.1 | yes | 10 | 19.11 | even | 3 | inner | |
304.4.i.f.49.5 | 10 | 76.11 | odd | 6 | |||
304.4.i.f.273.5 | 10 | 4.3 | odd | 2 | |||
684.4.k.c.505.3 | 10 | 57.11 | odd | 6 | |||
684.4.k.c.577.3 | 10 | 3.2 | odd | 2 | |||
1444.4.a.f.1.5 | 5 | 19.7 | even | 3 | |||
1444.4.a.g.1.1 | 5 | 19.12 | odd | 6 |