Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [169,4,Mod(23,169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(169, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("169.23");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 169 = 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 169.e (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.97132279097\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.1731891456.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 13) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 23.3 | ||
Root | \(1.35234 + 0.780776i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 169.23 |
Dual form | 169.4.e.g.147.3 |
$q$-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 \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.379706 | − | 0.219224i | 0.134246 | − | 0.0775072i | −0.431373 | − | 0.902174i | \(-0.641971\pi\) |
0.565619 | + | 0.824667i | \(0.308637\pi\) | |||||||
\(3\) | 1.84233 | + | 3.19101i | 0.354556 | + | 0.614110i | 0.987042 | − | 0.160462i | \(-0.0512985\pi\) |
−0.632486 | + | 0.774572i | \(0.717965\pi\) | |||||||
\(4\) | −3.90388 | + | 6.76172i | −0.487985 | + | 0.845215i | ||||
\(5\) | 17.8078i | 1.59277i | 0.604787 | + | 0.796387i | \(0.293258\pi\) | ||||
−0.604787 | + | 0.796387i | \(0.706742\pi\) | |||||||
\(6\) | 1.39909 | + | 0.807764i | 0.0951959 | + | 0.0549614i | ||||
\(7\) | −4.70983 | − | 2.71922i | −0.254307 | − | 0.146824i | 0.367428 | − | 0.930052i | \(-0.380239\pi\) |
−0.621735 | + | 0.783228i | \(0.713572\pi\) | |||||||
\(8\) | 6.93087i | 0.306304i | ||||||||
\(9\) | 6.71165 | − | 11.6249i | 0.248579 | − | 0.430552i | ||||
\(10\) | 3.90388 | + | 6.76172i | 0.123452 | + | 0.213824i | ||||
\(11\) | −19.4191 | + | 11.2116i | −0.532281 | + | 0.307313i | −0.741945 | − | 0.670461i | \(-0.766096\pi\) |
0.209664 | + | 0.977774i | \(0.432763\pi\) | |||||||
\(12\) | −28.7689 | −0.692073 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −2.38447 | −0.0455198 | ||||||||
\(15\) | −56.8247 | + | 32.8078i | −0.978139 | + | 0.564729i | ||||
\(16\) | −29.7116 | − | 51.4621i | −0.464244 | − | 0.804095i | ||||
\(17\) | 33.9924 | − | 58.8766i | 0.484963 | − | 0.839981i | −0.514888 | − | 0.857258i | \(-0.672166\pi\) |
0.999851 | + | 0.0172769i | \(0.00549968\pi\) | |||||||
\(18\) | − | 5.88540i | − | 0.0770668i | ||||||
\(19\) | −69.9816 | − | 40.4039i | −0.844993 | − | 0.487857i | 0.0139650 | − | 0.999902i | \(-0.495555\pi\) |
−0.858958 | + | 0.512045i | \(0.828888\pi\) | |||||||
\(20\) | −120.411 | − | 69.5194i | −1.34624 | − | 0.777251i | ||||
\(21\) | − | 20.0388i | − | 0.208230i | ||||||
\(22\) | −4.91571 | + | 8.51427i | −0.0476379 | + | 0.0825113i | ||||
\(23\) | 70.2656 | + | 121.704i | 0.637017 | + | 1.10335i | 0.986084 | + | 0.166248i | \(0.0531653\pi\) |
−0.349067 | + | 0.937098i | \(0.613501\pi\) | |||||||
\(24\) | −22.1165 | + | 12.7689i | −0.188104 | + | 0.108602i | ||||
\(25\) | −192.116 | −1.53693 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 148.946 | 1.06165 | ||||||||
\(28\) | 36.7733 | − | 21.2311i | 0.248196 | − | 0.143296i | ||||
\(29\) | 53.3466 | + | 92.3990i | 0.341594 | + | 0.591657i | 0.984729 | − | 0.174095i | \(-0.0557001\pi\) |
−0.643135 | + | 0.765753i | \(0.722367\pi\) | |||||||
\(30\) | −14.3845 | + | 24.9146i | −0.0875411 | + | 0.151626i | ||||
\(31\) | 276.155i | 1.59997i | 0.600023 | + | 0.799983i | \(0.295158\pi\) | ||||
−0.600023 | + | 0.799983i | \(0.704842\pi\) | |||||||
\(32\) | −70.5819 | − | 40.7505i | −0.389913 | − | 0.225117i | ||||
\(33\) | −71.5529 | − | 41.3111i | −0.377447 | − | 0.217919i | ||||
\(34\) | − | 29.8078i | − | 0.150353i | ||||||
\(35\) | 48.4233 | − | 83.8716i | 0.233858 | − | 0.405054i | ||||
\(36\) | 52.4029 | + | 90.7646i | 0.242606 | + | 0.420206i | ||||
\(37\) | −3.71670 | + | 2.14584i | −0.0165141 | + | 0.00953442i | −0.508234 | − | 0.861219i | \(-0.669702\pi\) |
0.491720 | + | 0.870753i | \(0.336368\pi\) | |||||||
\(38\) | −35.4299 | −0.151250 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −123.423 | −0.487873 | ||||||||
\(41\) | −197.254 | + | 113.884i | −0.751362 | + | 0.433799i | −0.826186 | − | 0.563398i | \(-0.809494\pi\) |
0.0748237 | + | 0.997197i | \(0.476161\pi\) | |||||||
\(42\) | −4.39298 | − | 7.60887i | −0.0161393 | − | 0.0279541i | ||||
\(43\) | 13.7647 | − | 23.8411i | 0.0488162 | − | 0.0845521i | −0.840585 | − | 0.541680i | \(-0.817788\pi\) |
0.889401 | + | 0.457128i | \(0.151122\pi\) | |||||||
\(44\) | − | 175.076i | − | 0.599856i | ||||||
\(45\) | 207.014 | + | 119.519i | 0.685773 | + | 0.395931i | ||||
\(46\) | 53.3606 | + | 30.8078i | 0.171035 | + | 0.0987469i | ||||
\(47\) | 318.617i | 0.988832i | 0.869225 | + | 0.494416i | \(0.164618\pi\) | ||||
−0.869225 | + | 0.494416i | \(0.835382\pi\) | |||||||
\(48\) | 109.477 | − | 189.620i | 0.329202 | − | 0.570194i | ||||
\(49\) | −156.712 | − | 271.433i | −0.456885 | − | 0.791348i | ||||
\(50\) | −72.9479 | + | 42.1165i | −0.206328 | + | 0.119123i | ||||
\(51\) | 250.501 | 0.687787 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −67.6562 | −0.175345 | −0.0876726 | − | 0.996149i | \(-0.527943\pi\) | ||||
−0.0876726 | + | 0.996149i | \(0.527943\pi\) | |||||||
\(54\) | 56.5558 | − | 32.6525i | 0.142523 | − | 0.0822859i | ||||
\(55\) | −199.654 | − | 345.811i | −0.489480 | − | 0.847804i | ||||
\(56\) | 18.8466 | − | 32.6432i | 0.0449729 | − | 0.0778953i | ||||
\(57\) | − | 297.749i | − | 0.691892i | ||||||
\(58\) | 40.5121 | + | 23.3897i | 0.0917155 | + | 0.0529519i | ||||
\(59\) | 252.113 | + | 145.557i | 0.556310 | + | 0.321186i | 0.751663 | − | 0.659547i | \(-0.229252\pi\) |
−0.195353 | + | 0.980733i | \(0.562585\pi\) | |||||||
\(60\) | − | 512.311i | − | 1.10232i | ||||||
\(61\) | −331.655 | + | 574.444i | −0.696133 | + | 1.20574i | 0.273664 | + | 0.961825i | \(0.411764\pi\) |
−0.969797 | + | 0.243912i | \(0.921569\pi\) | |||||||
\(62\) | 60.5398 | + | 104.858i | 0.124009 | + | 0.214790i | ||||
\(63\) | −63.2215 | + | 36.5009i | −0.126431 | + | 0.0729950i | ||||
\(64\) | 439.652 | 0.858696 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −36.2255 | −0.0675613 | ||||||||
\(67\) | 368.149 | − | 212.551i | 0.671291 | − | 0.387570i | −0.125275 | − | 0.992122i | \(-0.539981\pi\) |
0.796566 | + | 0.604552i | \(0.206648\pi\) | |||||||
\(68\) | 265.405 | + | 459.695i | 0.473310 | + | 0.819796i | ||||
\(69\) | −258.905 | + | 448.436i | −0.451717 | + | 0.782397i | ||||
\(70\) | − | 42.4621i | − | 0.0725028i | ||||||
\(71\) | −132.470 | − | 76.4815i | −0.221427 | − | 0.127841i | 0.385184 | − | 0.922840i | \(-0.374138\pi\) |
−0.606611 | + | 0.794999i | \(0.707471\pi\) | |||||||
\(72\) | 80.5708 | + | 46.5175i | 0.131880 | + | 0.0761409i | ||||
\(73\) | 117.268i | 0.188016i | 0.995571 | + | 0.0940081i | \(0.0299680\pi\) | ||||
−0.995571 | + | 0.0940081i | \(0.970032\pi\) | |||||||
\(74\) | −0.940837 | + | 1.62958i | −0.00147797 | + | 0.00255993i | ||||
\(75\) | −353.942 | − | 613.045i | −0.544929 | − | 0.943845i | ||||
\(76\) | 546.400 | − | 315.464i | 0.824689 | − | 0.476134i | ||||
\(77\) | 121.948 | 0.180484 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 202.462 | 0.288339 | 0.144169 | − | 0.989553i | \(-0.453949\pi\) | ||||
0.144169 | + | 0.989553i | \(0.453949\pi\) | |||||||
\(80\) | 916.425 | − | 529.098i | 1.28074 | − | 0.739437i | ||||
\(81\) | 93.1932 | + | 161.415i | 0.127837 | + | 0.221420i | ||||
\(82\) | −49.9323 | + | 86.4853i | −0.0672452 | + | 0.116472i | ||||
\(83\) | − | 336.155i | − | 0.444552i | −0.974984 | − | 0.222276i | \(-0.928651\pi\) | ||
0.974984 | − | 0.222276i | \(-0.0713486\pi\) | |||||||
\(84\) | 135.497 | + | 78.2292i | 0.175999 | + | 0.101613i | ||||
\(85\) | 1048.46 | + | 605.329i | 1.33790 | + | 0.772437i | ||||
\(86\) | − | 12.0702i | − | 0.0151344i | ||||||
\(87\) | −196.564 | + | 340.459i | −0.242228 | + | 0.419552i | ||||
\(88\) | −77.7065 | − | 134.592i | −0.0941311 | − | 0.163040i | ||||
\(89\) | 621.974 | − | 359.097i | 0.740777 | − | 0.427688i | −0.0815748 | − | 0.996667i | \(-0.525995\pi\) |
0.822352 | + | 0.568979i | \(0.192662\pi\) | |||||||
\(90\) | 104.806 | 0.122750 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1097.23 | −1.24342 | ||||||||
\(93\) | −881.214 | + | 508.769i | −0.982555 | + | 0.567278i | ||||
\(94\) | 69.8485 | + | 120.981i | 0.0766417 | + | 0.132747i | ||||
\(95\) | 719.503 | − | 1246.22i | 0.777047 | − | 1.34588i | ||||
\(96\) | − | 300.303i | − | 0.319266i | ||||||
\(97\) | 657.632 | + | 379.684i | 0.688376 | + | 0.397434i | 0.803003 | − | 0.595975i | \(-0.203234\pi\) |
−0.114628 | + | 0.993409i | \(0.536567\pi\) | |||||||
\(98\) | −119.009 | − | 68.7098i | −0.122670 | − | 0.0708238i | ||||
\(99\) | 300.994i | 0.305566i | ||||||||
\(100\) | 750.000 | − | 1299.04i | 0.750000 | − | 1.29904i | ||||
\(101\) | −174.348 | − | 301.980i | −0.171766 | − | 0.297507i | 0.767272 | − | 0.641322i | \(-0.221614\pi\) |
−0.939037 | + | 0.343816i | \(0.888280\pi\) | |||||||
\(102\) | 95.1168 | − | 54.9157i | 0.0923330 | − | 0.0533085i | ||||
\(103\) | 580.303 | 0.555136 | 0.277568 | − | 0.960706i | \(-0.410472\pi\) | ||||
0.277568 | + | 0.960706i | \(0.410472\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 356.847 | 0.331663 | ||||||||
\(106\) | −25.6895 | + | 14.8318i | −0.0235395 | + | 0.0135905i | ||||
\(107\) | −285.747 | − | 494.928i | −0.258170 | − | 0.447163i | 0.707582 | − | 0.706631i | \(-0.249786\pi\) |
−0.965752 | + | 0.259468i | \(0.916453\pi\) | |||||||
\(108\) | −581.468 | + | 1007.13i | −0.518072 | + | 0.897327i | ||||
\(109\) | − | 176.004i | − | 0.154661i | −0.997005 | − | 0.0773307i | \(-0.975360\pi\) | ||
0.997005 | − | 0.0773307i | \(-0.0246397\pi\) | |||||||
\(110\) | −151.620 | − | 87.5379i | −0.131422 | − | 0.0758765i | ||||
\(111\) | −13.6948 | − | 7.90668i | −0.0117104 | − | 0.00676098i | ||||
\(112\) | 323.170i | 0.272649i | ||||||||
\(113\) | −632.441 | + | 1095.42i | −0.526505 | + | 0.911933i | 0.473018 | + | 0.881053i | \(0.343165\pi\) |
−0.999523 | + | 0.0308807i | \(0.990169\pi\) | |||||||
\(114\) | −65.2736 | − | 113.057i | −0.0536266 | − | 0.0928840i | ||||
\(115\) | −2167.27 | + | 1251.27i | −1.75738 | + | 1.01462i | ||||
\(116\) | −833.035 | −0.666770 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 127.638 | 0.0995768 | ||||||||
\(119\) | −320.197 | + | 184.866i | −0.246659 | + | 0.142409i | ||||
\(120\) | −227.386 | − | 393.845i | −0.172979 | − | 0.299608i | ||||
\(121\) | −414.098 | + | 717.239i | −0.311118 | + | 0.538872i | ||||
\(122\) | 290.827i | 0.215821i | ||||||||
\(123\) | −726.812 | − | 419.625i | −0.532801 | − | 0.307613i | ||||
\(124\) | −1867.29 | − | 1078.08i | −1.35232 | − | 0.780760i | ||||
\(125\) | − | 1195.19i | − | 0.855211i | ||||||
\(126\) | −16.0037 | + | 27.7193i | −0.0113153 | + | 0.0195986i | ||||
\(127\) | 1302.05 | + | 2255.22i | 0.909752 | + | 1.57574i | 0.814408 | + | 0.580293i | \(0.197062\pi\) |
0.0953448 | + | 0.995444i | \(0.469605\pi\) | |||||||
\(128\) | 731.594 | − | 422.386i | 0.505190 | − | 0.291672i | ||||
\(129\) | 101.436 | 0.0692323 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2131.70 | 1.42174 | 0.710870 | − | 0.703324i | \(-0.248302\pi\) | ||||
0.710870 | + | 0.703324i | \(0.248302\pi\) | |||||||
\(132\) | 558.668 | − | 322.547i | 0.368377 | − | 0.212683i | ||||
\(133\) | 219.734 | + | 380.591i | 0.143259 | + | 0.248131i | ||||
\(134\) | 93.1922 | − | 161.414i | 0.0600790 | − | 0.104060i | ||||
\(135\) | 2652.40i | 1.69098i | ||||||||
\(136\) | 408.066 | + | 235.597i | 0.257290 | + | 0.148546i | ||||
\(137\) | −595.812 | − | 343.992i | −0.371560 | − | 0.214520i | 0.302580 | − | 0.953124i | \(-0.402152\pi\) |
−0.674140 | + | 0.738604i | \(0.735485\pi\) | |||||||
\(138\) | 227.032i | 0.140045i | ||||||||
\(139\) | 339.790 | − | 588.534i | 0.207343 | − | 0.359128i | −0.743534 | − | 0.668698i | \(-0.766852\pi\) |
0.950877 | + | 0.309570i | \(0.100185\pi\) | |||||||
\(140\) | 378.078 | + | 654.850i | 0.228239 | + | 0.395321i | ||||
\(141\) | −1016.71 | + | 586.998i | −0.607252 | + | 0.350597i | ||||
\(142\) | −67.0662 | −0.0396343 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −797.656 | −0.461607 | ||||||||
\(145\) | −1645.42 | + | 949.983i | −0.942377 | + | 0.544082i | ||||
\(146\) | 25.7079 | + | 44.5274i | 0.0145726 | + | 0.0252405i | ||||
\(147\) | 577.429 | − | 1000.14i | 0.323983 | − | 0.561155i | ||||
\(148\) | − | 33.5084i | − | 0.0186106i | ||||||
\(149\) | −1710.80 | − | 987.731i | −0.940632 | − | 0.543074i | −0.0504739 | − | 0.998725i | \(-0.516073\pi\) |
−0.890159 | + | 0.455651i | \(0.849407\pi\) | |||||||
\(150\) | −268.788 | − | 155.185i | −0.146310 | − | 0.0844719i | ||||
\(151\) | 1803.24i | 0.971824i | 0.874008 | + | 0.485912i | \(0.161513\pi\) | ||||
−0.874008 | + | 0.485912i | \(0.838487\pi\) | |||||||
\(152\) | 280.034 | − | 485.033i | 0.149433 | − | 0.258825i | ||||
\(153\) | −456.290 | − | 790.318i | −0.241104 | − | 0.417604i | ||||
\(154\) | 46.3044 | − | 26.7339i | 0.0242293 | − | 0.0139888i | ||||
\(155\) | −4917.71 | −2.54839 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −397.168 | −0.201894 | −0.100947 | − | 0.994892i | \(-0.532187\pi\) | ||||
−0.100947 | + | 0.994892i | \(0.532187\pi\) | |||||||
\(158\) | 76.8762 | − | 44.3845i | 0.0387085 | − | 0.0223483i | ||||
\(159\) | −124.645 | − | 215.892i | −0.0621698 | − | 0.107681i | ||||
\(160\) | 725.675 | − | 1256.91i | 0.358560 | − | 0.621044i | ||||
\(161\) | − | 764.272i | − | 0.374118i | ||||||
\(162\) | 70.7721 | + | 40.8603i | 0.0343233 | + | 0.0198166i | ||||
\(163\) | −815.270 | − | 470.696i | −0.391760 | − | 0.226183i | 0.291162 | − | 0.956674i | \(-0.405958\pi\) |
−0.682922 | + | 0.730491i | \(0.739291\pi\) | |||||||
\(164\) | − | 1778.37i | − | 0.846750i | ||||||
\(165\) | 735.658 | − | 1274.20i | 0.347096 | − | 0.601189i | ||||
\(166\) | −73.6932 | − | 127.640i | −0.0344560 | − | 0.0596796i | ||||
\(167\) | 3187.35 | − | 1840.22i | 1.47691 | − | 0.852696i | 0.477252 | − | 0.878766i | \(-0.341633\pi\) |
0.999660 | + | 0.0260704i | \(0.00829942\pi\) | |||||||
\(168\) | 138.886 | 0.0637817 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 530.810 | 0.239478 | ||||||||
\(171\) | −939.383 | + | 542.353i | −0.420096 | + | 0.242543i | ||||
\(172\) | 107.471 | + | 186.146i | 0.0476431 | + | 0.0825203i | ||||
\(173\) | 711.387 | − | 1232.16i | 0.312634 | − | 0.541499i | −0.666297 | − | 0.745686i | \(-0.732122\pi\) |
0.978932 | + | 0.204187i | \(0.0654552\pi\) | |||||||
\(174\) | 172.366i | 0.0750978i | ||||||||
\(175\) | 904.837 | + | 522.408i | 0.390853 | + | 0.225659i | ||||
\(176\) | 1153.95 | + | 666.233i | 0.494217 | + | 0.285336i | ||||
\(177\) | 1072.66i | 0.455514i | ||||||||
\(178\) | 157.445 | − | 272.703i | 0.0662978 | − | 0.114831i | ||||
\(179\) | 583.946 | + | 1011.42i | 0.243833 | + | 0.422331i | 0.961803 | − | 0.273743i | \(-0.0882617\pi\) |
−0.717970 | + | 0.696074i | \(0.754928\pi\) | |||||||
\(180\) | −1616.31 | + | 933.179i | −0.669294 | + | 0.386417i | ||||
\(181\) | 1133.96 | 0.465673 | 0.232836 | − | 0.972516i | \(-0.425199\pi\) | ||||
0.232836 | + | 0.972516i | \(0.425199\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2444.07 | −0.987274 | ||||||||
\(184\) | −843.512 | + | 487.002i | −0.337959 | + | 0.195121i | ||||
\(185\) | −38.2126 | − | 66.1861i | −0.0151862 | − | 0.0263032i | ||||
\(186\) | −223.068 | + | 386.366i | −0.0879364 | + | 0.152310i | ||||
\(187\) | 1524.44i | 0.596141i | ||||||||
\(188\) | −2154.40 | − | 1243.84i | −0.835776 | − | 0.482536i | ||||
\(189\) | −701.511 | − | 405.018i | −0.269986 | − | 0.155877i | ||||
\(190\) | − | 630.928i | − | 0.240907i | ||||||
\(191\) | −1341.06 | + | 2322.78i | −0.508040 | + | 0.879952i | 0.491916 | + | 0.870642i | \(0.336297\pi\) |
−0.999957 | + | 0.00930919i | \(0.997037\pi\) | |||||||
\(192\) | 809.985 | + | 1402.93i | 0.304456 | + | 0.527334i | ||||
\(193\) | −1706.65 | + | 985.333i | −0.636514 | + | 0.367491i | −0.783270 | − | 0.621681i | \(-0.786450\pi\) |
0.146757 | + | 0.989173i | \(0.453117\pi\) | |||||||
\(194\) | 332.943 | 0.123216 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2447.14 | 0.891813 | ||||||||
\(197\) | 3478.00 | − | 2008.02i | 1.25785 | − | 0.726222i | 0.285197 | − | 0.958469i | \(-0.407941\pi\) |
0.972657 | + | 0.232247i | \(0.0746077\pi\) | |||||||
\(198\) | 65.9851 | + | 114.290i | 0.0236836 | + | 0.0410212i | ||||
\(199\) | −2113.03 | + | 3659.87i | −0.752707 | + | 1.30373i | 0.193800 | + | 0.981041i | \(0.437919\pi\) |
−0.946506 | + | 0.322685i | \(0.895415\pi\) | |||||||
\(200\) | − | 1331.53i | − | 0.470768i | ||||||
\(201\) | 1356.50 | + | 783.177i | 0.476021 | + | 0.274831i | ||||
\(202\) | −132.402 | − | 76.4426i | −0.0461178 | − | 0.0266261i | ||||
\(203\) | − | 580.245i | − | 0.200617i | ||||||
\(204\) | −977.926 | + | 1693.82i | −0.335630 | + | 0.581328i | ||||
\(205\) | −2028.03 | − | 3512.65i | −0.690944 | − | 1.19675i | ||||
\(206\) | 220.345 | − | 127.216i | 0.0745250 | − | 0.0430270i | ||||
\(207\) | 1886.39 | 0.633398 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1811.98 | 0.599699 | ||||||||
\(210\) | 135.497 | − | 78.2292i | 0.0445247 | − | 0.0257063i | ||||
\(211\) | −682.334 | − | 1181.84i | −0.222625 | − | 0.385597i | 0.732980 | − | 0.680251i | \(-0.238129\pi\) |
−0.955604 | + | 0.294654i | \(0.904796\pi\) | |||||||
\(212\) | 264.122 | − | 457.473i | 0.0855659 | − | 0.148204i | ||||
\(213\) | − | 563.617i | − | 0.181307i | ||||||
\(214\) | −217.000 | − | 125.285i | −0.0693168 | − | 0.0400201i | ||||
\(215\) | 424.557 | + | 245.118i | 0.134672 | + | 0.0777532i | ||||
\(216\) | 1032.33i | 0.325189i | ||||||||
\(217\) | 750.928 | − | 1300.65i | 0.234914 | − | 0.406883i | ||||
\(218\) | −38.5842 | − | 66.8297i | −0.0119874 | − | 0.0207628i | ||||
\(219\) | −374.203 | + | 216.046i | −0.115463 | + | 0.0666624i | ||||
\(220\) | 3117.71 | 0.955436 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −6.93332 | −0.00209610 | ||||||||
\(223\) | 917.527 | − | 529.734i | 0.275525 | − | 0.159075i | −0.355871 | − | 0.934535i | \(-0.615816\pi\) |
0.631396 | + | 0.775461i | \(0.282482\pi\) | |||||||
\(224\) | 221.619 | + | 383.856i | 0.0661052 | + | 0.114498i | ||||
\(225\) | −1289.42 | + | 2233.34i | −0.382050 | + | 0.661729i | ||||
\(226\) | 554.584i | 0.163232i | ||||||||
\(227\) | 3000.08 | + | 1732.10i | 0.877190 | + | 0.506446i | 0.869731 | − | 0.493526i | \(-0.164292\pi\) |
0.00745930 | + | 0.999972i | \(0.497626\pi\) | |||||||
\(228\) | 2013.30 | + | 1162.38i | 0.584797 | + | 0.337633i | ||||
\(229\) | − | 2324.64i | − | 0.670815i | −0.942073 | − | 0.335407i | \(-0.891126\pi\) | ||
0.942073 | − | 0.335407i | \(-0.108874\pi\) | |||||||
\(230\) | −548.617 | + | 950.233i | −0.157282 | + | 0.272420i | ||||
\(231\) | 224.668 | + | 389.137i | 0.0639917 | + | 0.110837i | ||||
\(232\) | −640.405 | + | 369.738i | −0.181227 | + | 0.104631i | ||||
\(233\) | 3731.01 | 1.04904 | 0.524521 | − | 0.851398i | \(-0.324245\pi\) | ||||
0.524521 | + | 0.851398i | \(0.324245\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5673.86 | −1.57499 | ||||||||
\(236\) | −1968.44 | + | 1136.48i | −0.542942 | + | 0.313468i | ||||
\(237\) | 373.002 | + | 646.058i | 0.102232 | + | 0.177072i | ||||
\(238\) | −81.0540 | + | 140.390i | −0.0220754 | + | 0.0382357i | ||||
\(239\) | − | 6044.47i | − | 1.63592i | −0.575278 | − | 0.817958i | \(-0.695106\pi\) | ||
0.575278 | − | 0.817958i | \(-0.304894\pi\) | |||||||
\(240\) | 3376.71 | + | 1949.55i | 0.908191 | + | 0.524344i | ||||
\(241\) | 4480.78 | + | 2586.98i | 1.19765 | + | 0.691461i | 0.960030 | − | 0.279898i | \(-0.0903008\pi\) |
0.237616 | + | 0.971359i | \(0.423634\pi\) | |||||||
\(242\) | 363.120i | 0.0964556i | ||||||||
\(243\) | 1667.39 | − | 2888.00i | 0.440176 | − | 0.762408i | ||||
\(244\) | −2589.49 | − | 4485.12i | −0.679405 | − | 1.17676i | ||||
\(245\) | 4833.61 | − | 2790.68i | 1.26044 | − | 0.727715i | ||||
\(246\) | −367.967 | −0.0953688 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1914.00 | −0.490076 | ||||||||
\(249\) | 1072.67 | − | 619.309i | 0.273004 | − | 0.157619i | ||||
\(250\) | −262.015 | − | 453.823i | −0.0662851 | − | 0.114809i | ||||
\(251\) | 2810.37 | − | 4867.70i | 0.706728 | − | 1.22409i | −0.259337 | − | 0.965787i | \(-0.583504\pi\) |
0.966064 | − | 0.258301i | \(-0.0831628\pi\) | |||||||
\(252\) | − | 569.981i | − | 0.142482i | ||||||
\(253\) | −2729.00 | − | 1575.59i | −0.678144 | − | 0.391527i | ||||
\(254\) | 988.796 | + | 570.882i | 0.244262 | + | 0.141025i | ||||
\(255\) | 4460.86i | 1.09549i | ||||||||
\(256\) | −1573.42 | + | 2725.24i | −0.384135 | + | 0.665341i | ||||
\(257\) | −837.070 | − | 1449.85i | −0.203171 | − | 0.351903i | 0.746377 | − | 0.665523i | \(-0.231791\pi\) |
−0.949549 | + | 0.313620i | \(0.898458\pi\) | |||||||
\(258\) | 38.5160 | − | 22.2372i | 0.00929420 | − | 0.00536601i | ||||
\(259\) | 23.3401 | 0.00559954 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1432.17 | 0.339653 | ||||||||
\(262\) | 809.422 | − | 467.320i | 0.190864 | − | 0.110195i | ||||
\(263\) | 3154.59 | + | 5463.91i | 0.739622 | + | 1.28106i | 0.952666 | + | 0.304020i | \(0.0983289\pi\) |
−0.213044 | + | 0.977043i | \(0.568338\pi\) | |||||||
\(264\) | 286.322 | − | 495.924i | 0.0667496 | − | 0.115614i | ||||
\(265\) | − | 1204.81i | − | 0.279285i | ||||||
\(266\) | 166.869 | + | 96.3419i | 0.0384639 | + | 0.0222072i | ||||
\(267\) | 2291.76 | + | 1323.15i | 0.525294 | + | 0.303279i | ||||
\(268\) | 3319.09i | 0.756514i | ||||||||
\(269\) | 1241.37 | − | 2150.11i | 0.281366 | − | 0.487340i | −0.690356 | − | 0.723470i | \(-0.742546\pi\) |
0.971721 | + | 0.236131i | \(0.0758793\pi\) | |||||||
\(270\) | 581.468 | + | 1007.13i | 0.131063 | + | 0.227008i | ||||
\(271\) | 2455.81 | − | 1417.86i | 0.550478 | − | 0.317819i | −0.198837 | − | 0.980033i | \(-0.563716\pi\) |
0.749315 | + | 0.662214i | \(0.230383\pi\) | |||||||
\(272\) | −4039.88 | −0.900566 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −301.645 | −0.0665075 | ||||||||
\(275\) | 3730.74 | − | 2153.94i | 0.818080 | − | 0.472318i | ||||
\(276\) | −2021.47 | − | 3501.28i | −0.440863 | − | 0.763596i | ||||
\(277\) | −1918.76 | + | 3323.38i | −0.416198 | + | 0.720876i | −0.995553 | − | 0.0941989i | \(-0.969971\pi\) |
0.579355 | + | 0.815075i | \(0.303304\pi\) | |||||||
\(278\) | − | 297.960i | − | 0.0642822i | ||||||
\(279\) | 3210.28 | + | 1853.46i | 0.688869 | + | 0.397719i | ||||
\(280\) | 581.303 | + | 335.616i | 0.124070 | + | 0.0716317i | ||||
\(281\) | − | 9122.13i | − | 1.93659i | −0.249819 | − | 0.968293i | \(-0.580371\pi\) | ||
0.249819 | − | 0.968293i | \(-0.419629\pi\) | |||||||
\(282\) | −257.368 | + | 445.774i | −0.0543476 | + | 0.0941328i | ||||
\(283\) | 1063.92 | + | 1842.77i | 0.223476 | + | 0.387072i | 0.955861 | − | 0.293819i | \(-0.0949262\pi\) |
−0.732385 | + | 0.680891i | \(0.761593\pi\) | |||||||
\(284\) | 1034.29 | − | 597.150i | 0.216106 | − | 0.124769i | ||||
\(285\) | 5302.24 | 1.10203 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1238.71 | 0.254769 | ||||||||
\(288\) | −947.441 | + | 547.005i | −0.193849 | + | 0.111919i | ||||
\(289\) | 145.530 | + | 252.066i | 0.0296215 | + | 0.0513059i | ||||
\(290\) | −416.518 | + | 721.430i | −0.0843405 | + | 0.146082i | ||||
\(291\) | 2798.01i | 0.563651i | ||||||||
\(292\) | −792.934 | − | 457.800i | −0.158914 | − | 0.0917491i | ||||
\(293\) | −7166.16 | − | 4137.38i | −1.42884 | − | 0.824944i | −0.431815 | − | 0.901962i | \(-0.642127\pi\) |
−0.997030 | + | 0.0770183i | \(0.975460\pi\) | |||||||
\(294\) | − | 506.344i | − | 0.100444i | ||||||
\(295\) | −2592.05 | + | 4489.56i | −0.511576 | + | 0.886076i | ||||
\(296\) | −14.8725 | − | 25.7600i | −0.00292043 | − | 0.00505834i | ||||
\(297\) | −2892.40 | + | 1669.93i | −0.565099 | + | 0.326260i | ||||
\(298\) | −866.136 | −0.168369 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 5526.99 | 1.06367 | ||||||||
\(301\) | −129.659 | + | 74.8585i | −0.0248286 | + | 0.0143348i | ||||
\(302\) | 395.312 | + | 684.701i | 0.0753234 | + | 0.130464i | ||||
\(303\) | 642.414 | − | 1112.69i | 0.121801 | − | 0.210966i | ||||
\(304\) | 4801.86i | 0.905940i | ||||||||
\(305\) | −10229.6 | − | 5906.04i | −1.92047 | − | 1.10878i | ||||
\(306\) | −346.513 | − | 200.059i | −0.0647347 | − | 0.0373746i | ||||
\(307\) | − | 3610.49i | − | 0.671211i | −0.942003 | − | 0.335605i | \(-0.891059\pi\) | ||
0.942003 | − | 0.335605i | \(-0.108941\pi\) | |||||||
\(308\) | −476.070 | + | 824.578i | −0.0880734 | + | 0.152548i | ||||
\(309\) | 1069.11 | + | 1851.75i | 0.196827 | + | 0.340914i | ||||
\(310\) | −1867.29 | + | 1078.08i | −0.342112 | + | 0.197518i | ||||
\(311\) | −3331.06 | −0.607354 | −0.303677 | − | 0.952775i | \(-0.598214\pi\) | ||||
−0.303677 | + | 0.952775i | \(0.598214\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −358.125 | −0.0646724 | −0.0323362 | − | 0.999477i | \(-0.510295\pi\) | ||||
−0.0323362 | + | 0.999477i | \(0.510295\pi\) | |||||||
\(314\) | −150.807 | + | 87.0685i | −0.0271036 | + | 0.0156483i | ||||
\(315\) | −650.000 | − | 1125.83i | −0.116265 | − | 0.201376i | ||||
\(316\) | −790.388 | + | 1368.99i | −0.140705 | + | 0.243708i | ||||
\(317\) | − | 3047.46i | − | 0.539944i | −0.962868 | − | 0.269972i | \(-0.912986\pi\) | ||
0.962868 | − | 0.269972i | \(-0.0870144\pi\) | |||||||
\(318\) | −94.6570 | − | 54.6503i | −0.0166921 | − | 0.00963721i | ||||
\(319\) | −2071.89 | − | 1196.21i | −0.363647 | − | 0.209952i | ||||
\(320\) | 7829.23i | 1.36771i | ||||||||
\(321\) | 1052.88 | − | 1823.64i | 0.183072 | − | 0.317089i | ||||
\(322\) | −167.546 | − | 290.199i | −0.0289969 | − | 0.0502241i | ||||
\(323\) | −4757.69 | + | 2746.85i | −0.819581 | + | 0.473185i | ||||
\(324\) | −1455.26 | −0.249530 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −412.751 | −0.0701232 | ||||||||
\(327\) | 561.629 | − | 324.257i | 0.0949791 | − | 0.0548362i | ||||
\(328\) | −789.318 | − | 1367.14i | −0.132874 | − | 0.230145i | ||||
\(329\) | 866.392 | − | 1500.63i | 0.145185 | − | 0.251467i | ||||
\(330\) | − | 645.094i | − | 0.107610i | ||||||
\(331\) | 6663.87 | + | 3847.39i | 1.10658 | + | 0.638887i | 0.937942 | − | 0.346791i | \(-0.112729\pi\) |
0.168641 | + | 0.985677i | \(0.446062\pi\) | |||||||
\(332\) | 2272.99 | + | 1312.31i | 0.375742 | + | 0.216935i | ||||
\(333\) | 57.6084i | 0.00948025i | ||||||||
\(334\) | 806.838 | − | 1397.48i | 0.132180 | − | 0.228943i | ||||
\(335\) | 3785.05 | + | 6555.90i | 0.617312 | + | 1.06922i | ||||
\(336\) | −1031.24 | + | 595.386i | −0.167437 | + | 0.0966696i | ||||
\(337\) | −4712.21 | −0.761693 | −0.380846 | − | 0.924638i | \(-0.624367\pi\) | ||||
−0.380846 | + | 0.924638i | \(0.624367\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4660.66 | −0.746703 | ||||||||
\(340\) | −8186.13 | + | 4726.27i | −1.30575 | + | 0.753876i | ||||
\(341\) | −3096.16 | − | 5362.70i | −0.491690 | − | 0.851632i | ||||
\(342\) | −237.793 | + | 411.870i | −0.0375976 | + | 0.0651210i | ||||
\(343\) | 3569.92i | 0.561976i | ||||||||
\(344\) | 165.240 | + | 95.4013i | 0.0258986 | + | 0.0149526i | ||||
\(345\) | −7985.65 | − | 4610.52i | −1.24618 | − | 0.719484i | ||||
\(346\) | − | 623.811i | − | 0.0969257i | ||||||
\(347\) | 2630.99 | − | 4557.01i | 0.407029 | − | 0.704995i | −0.587526 | − | 0.809205i | \(-0.699898\pi\) |
0.994555 | + | 0.104210i | \(0.0332315\pi\) | |||||||
\(348\) | −1534.72 | − | 2658.22i | −0.236408 | − | 0.409470i | ||||
\(349\) | 43.5909 | − | 25.1672i | 0.00668587 | − | 0.00386009i | −0.496653 | − | 0.867949i | \(-0.665438\pi\) |
0.503339 | + | 0.864089i | \(0.332105\pi\) | |||||||
\(350\) | 458.096 | 0.0699608 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1827.52 | 0.276725 | ||||||||
\(353\) | −7844.14 | + | 4528.82i | −1.18272 | + | 0.682846i | −0.956643 | − | 0.291263i | \(-0.905925\pi\) |
−0.226081 | + | 0.974109i | \(0.572591\pi\) | |||||||
\(354\) | 235.152 | + | 407.295i | 0.0353056 | + | 0.0611511i | ||||
\(355\) | 1361.96 | − | 2358.99i | 0.203621 | − | 0.352683i | ||||
\(356\) | 5607.49i | 0.834821i | ||||||||
\(357\) | −1179.82 | − | 681.168i | −0.174909 | − | 0.100984i | ||||
\(358\) | 443.456 | + | 256.029i | 0.0654675 | + | 0.0377977i | ||||
\(359\) | 7177.86i | 1.05525i | 0.849479 | + | 0.527623i | \(0.176917\pi\) | ||||
−0.849479 | + | 0.527623i | \(0.823083\pi\) | |||||||
\(360\) | −828.373 | + | 1434.78i | −0.121275 | + | 0.210055i | ||||
\(361\) | −164.553 | − | 285.014i | −0.0239908 | − | 0.0415532i | ||||
\(362\) | 430.573 | − | 248.591i | 0.0625150 | − | 0.0360930i | ||||
\(363\) | −3051.62 | −0.441235 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2088.28 | −0.299467 | ||||||||
\(366\) | −928.030 | + | 535.798i | −0.132538 | + | 0.0765209i | ||||
\(367\) | −2002.07 | − | 3467.69i | −0.284761 | − | 0.493221i | 0.687790 | − | 0.725910i | \(-0.258581\pi\) |
−0.972551 | + | 0.232689i | \(0.925248\pi\) | |||||||
\(368\) | 4175.41 | − | 7232.03i | 0.591463 | − | 1.02444i | ||||
\(369\) | 3057.41i | 0.431334i | ||||||||
\(370\) | −29.0191 | − | 16.7542i | −0.00407738 | − | 0.00235408i | ||||
\(371\) | 318.649 | + | 183.972i | 0.0445915 | + | 0.0257449i | ||||
\(372\) | − | 7944.70i | − | 1.10729i | ||||||
\(373\) | 5007.09 | − | 8672.53i | 0.695060 | − | 1.20388i | −0.275101 | − | 0.961415i | \(-0.588711\pi\) |
0.970161 | − | 0.242464i | \(-0.0779555\pi\) | |||||||
\(374\) | 334.194 | + | 578.841i | 0.0462053 | + | 0.0800299i | ||||
\(375\) | 3813.87 | − | 2201.94i | 0.525194 | − | 0.303221i | ||||
\(376\) | −2208.30 | −0.302883 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −355.158 | −0.0483263 | ||||||||
\(379\) | 7074.66 | − | 4084.56i | 0.958842 | − | 0.553587i | 0.0630252 | − | 0.998012i | \(-0.479925\pi\) |
0.895816 | + | 0.444425i | \(0.146592\pi\) | |||||||
\(380\) | 5617.71 | + | 9730.16i | 0.758375 | + | 1.31354i | ||||
\(381\) | −4797.62 | + | 8309.73i | −0.645117 | + | 1.11738i | ||||
\(382\) | 1175.97i | 0.157507i | ||||||||
\(383\) | −6330.86 | − | 3655.12i | −0.844626 | − | 0.487645i | 0.0142079 | − | 0.999899i | \(-0.495477\pi\) |
−0.858834 | + | 0.512254i | \(0.828811\pi\) | |||||||
\(384\) | 2695.67 | + | 1556.35i | 0.358237 | + | 0.206828i | ||||
\(385\) | 2171.62i | 0.287470i | ||||||||
\(386\) | −432.017 | + | 748.275i | −0.0569665 | + | 0.0986689i | ||||
\(387\) | −184.767 | − | 320.027i | −0.0242694 | − | 0.0420358i | ||||
\(388\) | −5134.64 | + | 2964.48i | −0.671834 | + | 0.387884i | ||||
\(389\) | −8785.47 | −1.14509 | −0.572546 | − | 0.819872i | \(-0.694044\pi\) | ||||
−0.572546 | + | 0.819872i | \(0.694044\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9553.99 | 1.23572 | ||||||||
\(392\) | 1881.26 | − | 1086.15i | 0.242393 | − | 0.139946i | ||||
\(393\) | 3927.30 | + | 6802.29i | 0.504087 | + | 0.873104i | ||||
\(394\) | 880.412 | − | 1524.92i | 0.112575 | − | 0.194986i | ||||
\(395\) | 3605.40i | 0.459259i | ||||||||
\(396\) | −2035.24 | − | 1175.05i | −0.258269 | − | 0.149112i | ||||
\(397\) | −9757.33 | − | 5633.40i | −1.23352 | − | 0.712171i | −0.265756 | − | 0.964040i | \(-0.585621\pi\) |
−0.967761 | + | 0.251869i | \(0.918955\pi\) | |||||||
\(398\) | 1852.90i | 0.233361i | ||||||||
\(399\) | −809.646 | + | 1402.35i | −0.101586 | + | 0.175953i | ||||
\(400\) | 5708.10 | + | 9886.71i | 0.713512 | + | 1.23584i | ||||
\(401\) | 1365.06 | − | 788.117i | 0.169995 | − | 0.0981464i | −0.412589 | − | 0.910917i | \(-0.635375\pi\) |
0.582583 | + | 0.812771i | \(0.302042\pi\) | |||||||
\(402\) | 686.763 | 0.0852055 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 2722.54 | 0.335276 | ||||||||
\(405\) | −2874.45 | + | 1659.56i | −0.352672 | + | 0.203616i | ||||
\(406\) | −127.203 | − | 220.323i | −0.0155493 | − | 0.0269321i | ||||
\(407\) | 48.1168 | − | 83.3407i | 0.00586010 | − | 0.0101500i | ||||
\(408\) | 1736.19i | 0.210672i | ||||||||
\(409\) | 5850.68 | + | 3377.89i | 0.707329 | + | 0.408377i | 0.810071 | − | 0.586331i | \(-0.199428\pi\) |
−0.102742 | + | 0.994708i | \(0.532762\pi\) | |||||||
\(410\) | −1540.11 | − | 889.183i | −0.185514 | − | 0.107106i | ||||
\(411\) | − | 2534.99i | − | 0.304238i | ||||||
\(412\) | −2265.43 | + | 3923.85i | −0.270898 | + | 0.469209i | ||||
\(413\) | −791.606 | − | 1371.10i | −0.0943157 | − | 0.163360i | ||||
\(414\) | 716.275 | − | 413.542i | 0.0850314 | − | 0.0490929i | ||||
\(415\) | 5986.17 | 0.708072 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2504.02 | 0.294059 | ||||||||
\(418\) | 688.019 | − | 397.228i | 0.0805074 | − | 0.0464810i | ||||
\(419\) | −5378.09 | − | 9315.13i | −0.627057 | − | 1.08610i | −0.988139 | − | 0.153561i | \(-0.950926\pi\) |
0.361082 | − | 0.932534i | \(-0.382408\pi\) | |||||||
\(420\) | −1393.09 | + | 2412.90i | −0.161847 | + | 0.280327i | ||||
\(421\) | − | 7886.03i | − | 0.912925i | −0.889743 | − | 0.456463i | \(-0.849116\pi\) | ||
0.889743 | − | 0.456463i | \(-0.150884\pi\) | |||||||
\(422\) | −518.173 | − | 299.167i | −0.0597731 | − | 0.0345100i | ||||
\(423\) | 3703.90 | + | 2138.45i | 0.425744 | + | 0.245803i | ||||
\(424\) | − | 468.916i | − | 0.0537089i | ||||||
\(425\) | −6530.50 | + | 11311.2i | −0.745355 | + | 1.29099i | ||||
\(426\) | −123.558 | − | 214.009i | −0.0140526 | − | 0.0243398i | ||||
\(427\) | 3124.08 | − | 1803.69i | 0.354063 | − | 0.204418i | ||||
\(428\) | 4462.08 | 0.503932 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 214.943 | 0.0241057 | ||||||||
\(431\) | 12197.6 | − | 7042.31i | 1.36320 | − | 0.787044i | 0.373152 | − | 0.927770i | \(-0.378277\pi\) |
0.990049 | + | 0.140726i | \(0.0449438\pi\) | |||||||
\(432\) | −4425.43 | − | 7665.07i | −0.492867 | − | 0.853671i | ||||
\(433\) | 932.072 | − | 1614.40i | 0.103447 | − | 0.179175i | −0.809656 | − | 0.586905i | \(-0.800346\pi\) |
0.913103 | + | 0.407730i | \(0.133679\pi\) | |||||||
\(434\) | − | 658.485i | − | 0.0728301i | ||||||
\(435\) | −6062.81 | − | 3500.36i | −0.668252 | − | 0.385815i | ||||
\(436\) | 1190.09 | + | 687.098i | 0.130722 | + | 0.0754725i | ||||
\(437\) | − | 11356.0i | − | 1.24309i | ||||||
\(438\) | −94.7249 | + | 164.068i | −0.0103336 | + | 0.0178984i | ||||
\(439\) | 3077.24 | + | 5329.94i | 0.334553 | + | 0.579463i | 0.983399 | − | 0.181457i | \(-0.0580813\pi\) |
−0.648846 | + | 0.760920i | \(0.724748\pi\) | |||||||
\(440\) | 2396.77 | − | 1383.78i | 0.259686 | − | 0.149930i | ||||
\(441\) | −4207.17 | −0.454289 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14539.3 | −1.55933 | −0.779663 | − | 0.626200i | \(-0.784609\pi\) | ||||
−0.779663 | + | 0.626200i | \(0.784609\pi\) | |||||||
\(444\) | 106.926 | − | 61.7335i | 0.0114290 | − | 0.00659852i | ||||
\(445\) | 6394.72 | + | 11076.0i | 0.681210 | + | 1.17989i | ||||
\(446\) | 232.261 | − | 402.287i | 0.0246589 | − | 0.0427104i | ||||
\(447\) | − | 7278.90i | − | 0.770202i | ||||||
\(448\) | −2070.69 | − | 1195.51i | −0.218373 | − | 0.126077i | ||||
\(449\) | 6100.17 | + | 3521.93i | 0.641169 | + | 0.370179i | 0.785065 | − | 0.619414i | \(-0.212630\pi\) |
−0.143896 | + | 0.989593i | \(0.545963\pi\) | |||||||
\(450\) | 1130.68i | 0.118446i | ||||||||
\(451\) | 2553.66 | − | 4423.08i | 0.266624 | − | 0.461806i | ||||
\(452\) | −4937.95 | − | 8552.78i | −0.513853 | − | 0.890020i | ||||
\(453\) | −5754.15 | + | 3322.16i | −0.596807 | + | 0.344567i | ||||
\(454\) | 1518.87 | 0.157013 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2063.66 | 0.211929 | ||||||||
\(457\) | −12210.0 | + | 7049.43i | −1.24980 | + | 0.721572i | −0.971069 | − | 0.238798i | \(-0.923247\pi\) |
−0.278730 | + | 0.960370i | \(0.589913\pi\) | |||||||
\(458\) | −509.616 | − | 882.681i | −0.0519930 | − | 0.0900545i | ||||
\(459\) | 5063.04 | − | 8769.44i | 0.514863 | − | 0.891770i | ||||
\(460\) | − | 19539.3i | − | 1.98049i | ||||||
\(461\) | 12513.8 | + | 7224.85i | 1.26426 | + | 0.729924i | 0.973897 | − | 0.226991i | \(-0.0728889\pi\) |
0.290368 | + | 0.956915i | \(0.406222\pi\) | |||||||
\(462\) | 170.616 | + | 98.5051i | 0.0171813 | + | 0.00991964i | ||||
\(463\) | 15806.5i | 1.58659i | 0.608840 | + | 0.793293i | \(0.291635\pi\) | ||||
−0.608840 | + | 0.793293i | \(0.708365\pi\) | |||||||
\(464\) | 3170.03 | − | 5490.65i | 0.317166 | − | 0.549347i | ||||
\(465\) | −9060.04 | − | 15692.4i | −0.903547 | − | 1.56499i | ||||
\(466\) | 1416.69 | − | 817.926i | 0.140830 | − | 0.0813083i | ||||
\(467\) | 15071.3 | 1.49340 | 0.746699 | − | 0.665162i | \(-0.231638\pi\) | ||||
0.746699 | + | 0.665162i | \(0.231638\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2311.89 | −0.227619 | ||||||||
\(470\) | −2154.40 | + | 1243.84i | −0.211437 | + | 0.122073i | ||||
\(471\) | −731.713 | − | 1267.36i | −0.0715830 | − | 0.123985i | ||||
\(472\) | −1008.84 | + | 1747.36i | −0.0983804 | + | 0.170400i | ||||
\(473\) | 617.299i | 0.0600073i | ||||||||
\(474\) | 283.262 | + | 163.542i | 0.0274487 | + | 0.0158475i | ||||
\(475\) | 13444.6 | + | 7762.25i | 1.29870 | + | 0.749803i | ||||
\(476\) | − | 2886.78i | − | 0.277973i | ||||||
\(477\) | −454.085 | + | 786.498i | −0.0435872 | + | 0.0754953i | ||||
\(478\) | −1325.09 | − | 2295.12i | −0.126795 | − | 0.219616i | ||||
\(479\) | −339.954 | + | 196.272i | −0.0324277 | + | 0.0187222i | −0.516126 | − | 0.856513i | \(-0.672626\pi\) |
0.483698 | + | 0.875235i | \(0.339293\pi\) | |||||||
\(480\) | 5347.73 | 0.508519 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 2268.51 | 0.214373 | ||||||||
\(483\) | 2438.80 | − | 1408.04i | 0.229750 | − | 0.132646i | ||||
\(484\) | −3233.18 | − | 5600.03i | −0.303642 | − | 0.525923i | ||||
\(485\) | −6761.33 | + | 11711.0i | −0.633023 | + | 1.09643i | ||||
\(486\) | − | 1462.12i | − | 0.136467i | ||||||
\(487\) | 8225.41 | + | 4748.94i | 0.765357 | + | 0.441879i | 0.831216 | − | 0.555950i | \(-0.187645\pi\) |
−0.0658588 | + | 0.997829i | \(0.520979\pi\) | |||||||
\(488\) | −3981.40 | − | 2298.66i | −0.369322 | − | 0.213228i | ||||
\(489\) | − | 3468.71i | − | 0.320778i | ||||||
\(490\) | 1223.57 | − | 2119.28i | 0.112806 | − | 0.195386i | ||||
\(491\) | −946.912 | − | 1640.10i | −0.0870337 | − | 0.150747i | 0.819222 | − | 0.573476i | \(-0.194405\pi\) |
−0.906256 | + | 0.422729i | \(0.861072\pi\) | |||||||
\(492\) | 5674.78 | − | 3276.34i | 0.519998 | − | 0.300221i | ||||
\(493\) | 7253.52 | 0.662641 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5360.04 | −0.486699 | ||||||||
\(496\) | 14211.5 | − | 8205.03i | 1.28652 | − | 0.742775i | ||||
\(497\) | 415.941 | + | 720.430i | 0.0375402 | + | 0.0650216i | ||||
\(498\) | 271.534 | − | 470.311i | 0.0244332 | − | 0.0423196i | ||||
\(499\) | 13370.1i | 1.19945i | 0.800205 | + | 0.599727i | \(0.204724\pi\) | ||||
−0.800205 | + | 0.599727i | \(0.795276\pi\) | |||||||
\(500\) | 8081.57 | + | 4665.90i | 0.722838 | + | 0.417330i | ||||
\(501\) | 11744.3 | + | 6780.57i | 1.04730 | + | 0.604658i | ||||
\(502\) | − | 2464.39i | − | 0.219106i | ||||||
\(503\) | −2777.36 | + | 4810.52i | −0.246195 | + | 0.426423i | −0.962467 | − | 0.271399i | \(-0.912514\pi\) |
0.716272 | + | 0.697822i | \(0.245847\pi\) | |||||||
\(504\) | −252.983 | − | 438.180i | −0.0223587 | − | 0.0387263i | ||||
\(505\) | 5377.60 | − | 3104.76i | 0.473861 | − | 0.273584i | ||||
\(506\) | −1381.62 | −0.121385 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −20332.3 | −1.77578 | ||||||||
\(509\) | −1903.13 | + | 1098.78i | −0.165727 | + | 0.0956824i | −0.580569 | − | 0.814211i | \(-0.697170\pi\) |
0.414843 | + | 0.909893i | \(0.363837\pi\) | |||||||
\(510\) | 977.926 | + | 1693.82i | 0.0849084 | + | 0.147066i | ||||
\(511\) | 318.878 | − | 552.313i | 0.0276053 | − | 0.0478139i | ||||
\(512\) | 8137.89i | 0.702437i | ||||||||
\(513\) | −10423.5 | − | 6018.00i | −0.897091 | − | 0.517936i | ||||
\(514\) | −635.682 | − | 367.011i | −0.0545500 | − | 0.0314945i | ||||
\(515\) | 10333.9i | 0.884206i | ||||||||
\(516\) | −395.996 | + | 685.884i | −0.0337844 | + | 0.0585162i | ||||
\(517\) | −3572.23 | − | 6187.28i | −0.303881 | − | 0.526337i | ||||
\(518\) | 8.86237 | − | 5.11669i | 0.000751718 | − | 0.000434005i | ||||
\(519\) | 5242.44 | 0.443386 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17005.2 | 1.42997 | 0.714983 | − | 0.699142i | \(-0.246435\pi\) | ||||
0.714983 | + | 0.699142i | \(0.246435\pi\) | |||||||
\(522\) | 543.805 | − | 313.966i | 0.0455972 | − | 0.0263255i | ||||
\(523\) | 7243.11 | + | 12545.4i | 0.605581 | + | 1.04890i | 0.991959 | + | 0.126557i | \(0.0403928\pi\) |
−0.386378 | + | 0.922341i | \(0.626274\pi\) | |||||||
\(524\) | −8321.92 | + | 14414.0i | −0.693788 | + | 1.20168i | ||||
\(525\) | 3849.79i | 0.320035i | ||||||||
\(526\) | 2395.64 | + | 1383.12i | 0.198583 | + | 0.114652i | ||||
\(527\) | 16259.1 | + | 9387.19i | 1.34394 | + | 0.775925i | ||||
\(528\) | 4909.68i | 0.404671i | ||||||||
\(529\) | −3791.02 | + | 6566.23i | −0.311582 | + | 0.539675i | ||||
\(530\) | −264.122 | − | 457.473i | −0.0216466 | − | 0.0374931i | ||||
\(531\) | 3384.18 | − | 1953.86i | 0.276574 | − | 0.159680i | ||||
\(532\) | −3431.27 | −0.279632 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 1160.26 | 0.0940252 | ||||||||
\(535\) | 8813.56 | − | 5088.51i | 0.712230 | − | 0.411206i | ||||
\(536\) | 1473.16 | + | 2551.59i | 0.118714 | + | 0.205619i | ||||
\(537\) | −2151.64 | + | 3726.75i | −0.172905 | + | 0.299481i | ||||
\(538\) | − | 1088.55i | − | 0.0872315i | ||||||
\(539\) | 6086.41 | + | 3513.99i | 0.486383 | + | 0.280813i | ||||
\(540\) | −17934.8 | − | 10354.6i | −1.42924 | − | 0.825172i | ||||
\(541\) | − | 15266.7i | − | 1.21325i | −0.794990 | − | 0.606623i | \(-0.792524\pi\) | ||
0.794990 | − | 0.606623i | \(-0.207476\pi\) | |||||||
\(542\) | 621.657 | − | 1076.74i | 0.0492665 | − | 0.0853321i | ||||
\(543\) | 2089.13 | + | 3618.48i | 0.165107 | + | 0.285974i | ||||
\(544\) | −4798.50 | + | 2770.41i | −0.378187 | + | 0.218347i | ||||
\(545\) | 3134.23 | 0.246341 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15260.5 | 1.19286 | 0.596430 | − | 0.802665i | \(-0.296586\pi\) | ||||
0.596430 | + | 0.802665i | \(0.296586\pi\) | |||||||
\(548\) | 4651.96 | − | 2685.81i | 0.362631 | − | 0.209365i | ||||
\(549\) | 4451.91 | + | 7710.93i | 0.346089 | + | 0.599443i | ||||
\(550\) | 944.390 | − | 1635.73i | 0.0732162 | − | 0.126814i | ||||
\(551\) | − | 8621.64i | − | 0.666595i | ||||||
\(552\) | −3108.05 | − | 1794.44i | −0.239651 | − | 0.138363i | ||||
\(553\) | −953.563 | − | 550.540i | −0.0733266 | − | 0.0423351i | ||||
\(554\) | 1682.55i | 0.129033i | ||||||||
\(555\) | 140.800 | − | 243.873i | 0.0107687 | − | 0.0186520i | ||||
\(556\) | 2653.00 | + | 4595.13i | 0.202360 | + | 0.350498i | ||||
\(557\) | −9043.12 | + | 5221.05i | −0.687916 | + | 0.397169i | −0.802831 | − | 0.596207i | \(-0.796674\pi\) |
0.114915 | + | 0.993375i | \(0.463341\pi\) | |||||||
\(558\) | 1625.29 | 0.123304 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −5754.94 | −0.434269 | ||||||||
\(561\) | −4864.51 | + | 2808.53i | −0.366096 | + | 0.211366i | ||||
\(562\) | −1999.79 | − | 3463.73i | −0.150099 | − | 0.259980i | ||||
\(563\) | 3572.63 | − | 6187.98i | 0.267440 | − | 0.463219i | −0.700760 | − | 0.713397i | \(-0.747156\pi\) |
0.968200 | + | 0.250178i | \(0.0804891\pi\) | |||||||
\(564\) | − | 9166.29i | − | 0.684344i | ||||||
\(565\) | −19507.0 | − | 11262.4i | −1.45250 | − | 0.838604i | ||||
\(566\) | 807.958 | + | 466.475i | 0.0600018 | + | 0.0346420i | ||||
\(567\) | − | 1013.65i | − | 0.0750783i | ||||||
\(568\) | 530.083 | − | 918.131i | 0.0391581 | − | 0.0678238i | ||||
\(569\) | 2219.43 | + | 3844.17i | 0.163521 | + | 0.283226i | 0.936129 | − | 0.351657i | \(-0.114382\pi\) |
−0.772608 | + | 0.634883i | \(0.781048\pi\) | |||||||
\(570\) | 2013.30 | − | 1162.38i | 0.147943 | − | 0.0854151i | ||||
\(571\) | −10117.3 | −0.741497 | −0.370748 | − | 0.928733i | \(-0.620899\pi\) | ||||
−0.370748 | + | 0.928733i | \(0.620899\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9882.70 | −0.720516 | ||||||||
\(574\) | 470.346 | − | 271.554i | 0.0342018 | − | 0.0197464i | ||||
\(575\) | −13499.2 | − | 23381.3i | −0.979052 | − | 1.69577i | ||||
\(576\) | 2950.79 | − | 5110.92i | 0.213454 | − | 0.369714i | ||||
\(577\) | − | 3105.60i | − | 0.224069i | −0.993704 | − | 0.112035i | \(-0.964263\pi\) | ||
0.993704 | − | 0.112035i | \(-0.0357368\pi\) | |||||||
\(578\) | 110.518 | + | 63.8074i | 0.00795316 | + | 0.00459176i | ||||
\(579\) | −6288.41 | − | 3630.62i | −0.451360 | − | 0.260593i | ||||
\(580\) | − | 14834.5i | − | 1.06202i | ||||||
\(581\) | −914.081 | + | 1583.24i | −0.0652711 | + | 0.113053i | ||||
\(582\) | 613.390 | + | 1062.42i | 0.0436870 | + | 0.0756682i | ||||
\(583\) | 1313.83 | − | 758.538i | 0.0933329 | − | 0.0538858i | ||||
\(584\) | −812.769 | −0.0575901 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3628.05 | −0.255757 | ||||||||
\(587\) | −17028.1 | + | 9831.16i | −1.19731 | + | 0.691270i | −0.959956 | − | 0.280152i | \(-0.909615\pi\) |
−0.237359 | + | 0.971422i | \(0.576282\pi\) | |||||||
\(588\) | 4508.43 | + | 7808.83i | 0.316198 | + | 0.547671i | ||||
\(589\) | 11157.7 | − | 19325.8i | 0.780555 | − | 1.35196i | ||||
\(590\) | 2272.95i | 0.158603i | ||||||||
\(591\) | 12815.2 | + | 7398.88i | 0.891960 | + | 0.514974i | ||||
\(592\) | 220.859 | + | 127.513i | 0.0153332 | + | 0.00885261i | ||||
\(593\) | 6395.51i | 0.442888i | 0.975173 | + | 0.221444i | \(0.0710769\pi\) | ||||
−0.975173 | + | 0.221444i | \(0.928923\pi\) | |||||||
\(594\) | −732.176 | + | 1268.17i | −0.0505750 | + | 0.0875985i | ||||
\(595\) | −3292.05 | − | 5702.00i | −0.226825 | − | 0.392872i | ||||
\(596\) | 13357.5 | − | 7711.97i | 0.918029 | − | 0.530025i | ||||
\(597\) | −15571.6 | −1.06751 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8878.48 | 0.605618 | 0.302809 | − | 0.953051i | \(-0.402076\pi\) | ||||
0.302809 | + | 0.953051i | \(0.402076\pi\) | |||||||
\(600\) | 4248.94 | − | 2453.12i | 0.289103 | − | 0.166914i | ||||
\(601\) | −9550.29 | − | 16541.6i | −0.648194 | − | 1.12270i | −0.983554 | − | 0.180615i | \(-0.942191\pi\) |
0.335360 | − | 0.942090i | \(-0.391142\pi\) | |||||||
\(602\) | −32.8215 | + | 56.8485i | −0.00222210 | + | 0.00384879i | ||||
\(603\) | − | 5706.26i | − | 0.385368i | ||||||
\(604\) | −12193.0 | − | 7039.63i | −0.821401 | − | 0.474236i | ||||
\(605\) | −12772.4 | − | 7374.16i | −0.858302 | − | 0.495541i | ||||
\(606\) | − | 563.330i | − | 0.0377619i | ||||||
\(607\) | −8297.88 | + | 14372.4i | −0.554861 | + | 0.961047i | 0.443053 | + | 0.896495i | \(0.353895\pi\) |
−0.997914 | + | 0.0645522i | \(0.979438\pi\) | |||||||
\(608\) | 3292.95 | + | 5703.56i | 0.219650 | + | 0.380444i | ||||
\(609\) | 1851.57 | − | 1069.00i | 0.123201 | − | 0.0711300i | ||||
\(610\) | −5178.97 | −0.343755 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 7125.21 | 0.470620 | ||||||||
\(613\) | −14262.7 | + | 8234.58i | −0.939748 | + | 0.542564i | −0.889881 | − | 0.456192i | \(-0.849213\pi\) |
−0.0498668 | + | 0.998756i | \(0.515880\pi\) | |||||||
\(614\) | −791.505 | − | 1370.93i | −0.0520237 | − | 0.0901077i | ||||
\(615\) | 7472.59 | − | 12942.9i | 0.489958 | − | 0.848631i | ||||
\(616\) | 845.205i | 0.0552829i | ||||||||
\(617\) | 8760.69 | + | 5057.99i | 0.571624 | + | 0.330027i | 0.757798 | − | 0.652489i | \(-0.226275\pi\) |
−0.186174 | + | 0.982517i | \(0.559609\pi\) | |||||||
\(618\) | 811.895 | + | 468.748i | 0.0528466 | + | 0.0305110i | ||||
\(619\) | 18854.8i | 1.22430i | 0.790743 | + | 0.612148i | \(0.209694\pi\) | ||||
−0.790743 | + | 0.612148i | \(0.790306\pi\) | |||||||
\(620\) | 19198.2 | − | 33252.2i | 1.24357 | − | 2.15393i | ||||
\(621\) | 10465.8 | + | 18127.3i | 0.676292 | + | 1.17137i | ||||
\(622\) | −1264.83 | + | 730.247i | −0.0815352 | + | 0.0470743i | ||||
\(623\) | −3905.86 | −0.251180 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2730.82 | −0.174773 | ||||||||
\(626\) | −135.983 | + | 78.5095i | −0.00868204 | + | 0.00501258i | ||||
\(627\) | 3338.26 | + | 5782.03i | 0.212627 | + | 0.368281i | ||||
\(628\) | 1550.50 | − | 2685.54i | 0.0985215 | − | 0.170644i | ||||
\(629\) | 291.769i | 0.0184954i | ||||||||
\(630\) | −493.618 | − | 284.991i | −0.0312162 | − | 0.0180227i | ||||
\(631\) | −16407.9 | − | 9473.12i | −1.03517 | − | 0.597653i | −0.116705 | − | 0.993167i | \(-0.537233\pi\) |
−0.918460 | + | 0.395514i | \(0.870567\pi\) | |||||||
\(632\) | 1403.24i | 0.0883194i | ||||||||
\(633\) | 2514.17 | − | 4354.66i | 0.157866 | − | 0.273432i | ||||
\(634\) | −668.074 | − | 1157.14i | −0.0418496 | − | 0.0724856i | ||||
\(635\) | −40160.5 | + | 23186.7i | −2.50979 | + | 1.44903i | ||||
\(636\) | 1946.40 | 0.121352 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1048.95 | −0.0650912 | ||||||||
\(639\) | −1778.18 | + | 1026.63i | −0.110084 | + | 0.0635571i | ||||
\(640\) | 7521.75 | + | 13028.1i | 0.464568 | + | 0.804655i | ||||
\(641\) | −11793.5 | + | 20426.9i | −0.726698 | + | 1.25868i | 0.231573 | + | 0.972818i | \(0.425613\pi\) |
−0.958271 | + | 0.285861i | \(0.907721\pi\) | |||||||
\(642\) | − | 923.263i | − | 0.0567575i | ||||||
\(643\) | −23515.2 | − | 13576.5i | −1.44222 | − | 0.832669i | −0.444226 | − | 0.895915i | \(-0.646521\pi\) |
−0.997998 | + | 0.0632461i | \(0.979855\pi\) | |||||||
\(644\) | 5167.79 | + | 2983.63i | 0.316211 | + | 0.182564i | ||||
\(645\) | 1806.35i | 0.110272i | ||||||||
\(646\) | −1204.35 | + | 2085.99i | −0.0733506 | + | 0.127047i | ||||
\(647\) | 3428.36 | + | 5938.09i | 0.208319 | + | 0.360820i | 0.951185 | − | 0.308620i | \(-0.0998673\pi\) |
−0.742866 | + | 0.669440i | \(0.766534\pi\) | |||||||
\(648\) | −1118.75 | + | 645.910i | −0.0678219 | + | 0.0391570i | ||||
\(649\) | −6527.75 | −0.394817 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5533.83 | 0.333161 | ||||||||
\(652\) | 6365.44 | − | 3675.09i | 0.382346 | − | 0.220748i | ||||
\(653\) | 4036.95 | + | 6992.20i | 0.241926 | + | 0.419029i | 0.961263 | − | 0.275633i | \(-0.0888874\pi\) |
−0.719337 | + | 0.694662i | \(0.755554\pi\) | |||||||
\(654\) | 142.169 | − | 246.245i | 0.00850041 | − | 0.0147231i | ||||
\(655\) | 37960.9i | 2.26451i | ||||||||
\(656\) | 11721.5 | + | 6767.39i | 0.697632 | + | 0.402778i | ||||
\(657\) | 1363.23 | + | 787.061i | 0.0809508 | + | 0.0467370i | ||||
\(658\) | − | 759.734i | − | 0.0450114i | ||||||
\(659\) | −2652.86 | + | 4594.89i | −0.156815 | + | 0.271611i | −0.933718 | − | 0.358008i | \(-0.883456\pi\) |
0.776904 | + | 0.629620i | \(0.216789\pi\) | |||||||
\(660\) | 5743.84 | + | 9948.63i | 0.338756 | + | 0.586742i | ||||
\(661\) | 22385.3 | − | 12924.2i | 1.31723 | − | 0.760502i | 0.333946 | − | 0.942592i | \(-0.391620\pi\) |
0.983282 | + | 0.182091i | \(0.0582865\pi\) | |||||||
\(662\) | 3373.75 | 0.198073 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2329.85 | 0.136168 | ||||||||
\(665\) | −6777.48 | + | 3912.98i | −0.395217 | + | 0.228179i | ||||
\(666\) | 12.6291 | + | 21.8743i | 0.000734788 | + | 0.00127269i | ||||
\(667\) | −7496.86 | + | 12984.9i | −0.435202 | + | 0.753792i | ||||
\(668\) | 28735.9i | 1.66441i | ||||||||
\(669\) | 3380.77 | + | 1951.89i | 0.195379 | + | 0.112802i | ||||
\(670\) | 2874.42 | + | 1659.55i | 0.165744 | + | 0.0956923i | ||||
\(671\) | − | 14873.6i | − | 0.855722i | ||||||
\(672\) | −816.591 | + | 1414.38i | −0.0468760 | + | 0.0811917i | ||||
\(673\) | −7264.55 | − | 12582.6i | −0.416089 | − | 0.720687i | 0.579453 | − | 0.815005i | \(-0.303266\pi\) |
−0.995542 | + | 0.0943186i | \(0.969933\pi\) | |||||||
\(674\) | −1789.26 | + | 1033.03i | −0.102255 | + | 0.0590367i | ||||
\(675\) | −28615.0 | −1.63169 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12058.1 | 0.684535 | 0.342267 | − | 0.939603i | \(-0.388805\pi\) | ||||
0.342267 | + | 0.939603i | \(0.388805\pi\) | |||||||
\(678\) | −1769.68 | + | 1021.73i | −0.100242 | + | 0.0578749i | ||||
\(679\) | −2064.89 | − | 3576.50i | −0.116706 | − | 0.202140i | ||||
\(680\) | −4195.46 | + | 7266.74i | −0.236601 | + | 0.409804i | ||||
\(681\) | 12764.4i | 0.718255i | ||||||||
\(682\) | −2351.26 | − | 1357.50i | −0.132015 | − | 0.0762190i | ||||
\(683\) | −26005.7 | − | 15014.4i | −1.45693 | − | 0.841156i | −0.458067 | − | 0.888918i | \(-0.651458\pi\) |
−0.998859 | + | 0.0477615i | \(0.984791\pi\) | |||||||
\(684\) | − | 8469.13i | − | 0.473429i | ||||||
\(685\) | 6125.74 | − | 10610.1i | 0.341682 | − | 0.591811i | ||||
\(686\) | 782.611 | + | 1355.52i | 0.0435572 | + | 0.0754433i | ||||
\(687\) | 7417.94 | − | 4282.75i | 0.411954 | − | 0.237842i | ||||
\(688\) | −1635.89 | −0.0906505 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −4042.94 | −0.223061 | ||||||||
\(691\) | −389.448 | + | 224.848i | −0.0214404 | + | 0.0123786i | −0.510682 | − | 0.859770i | \(-0.670607\pi\) |
0.489241 | + | 0.872148i | \(0.337274\pi\) | |||||||
\(692\) | 5554.34 | + | 9620.40i | 0.305122 | + | 0.528487i | ||||
\(693\) | 818.471 | − | 1417.63i | 0.0448646 | − | 0.0777077i | ||||
\(694\) | − | 2307.10i | − | 0.126191i | ||||||
\(695\) | 10480.5 | + | 6050.90i | 0.572010 | + | 0.330250i | ||||
\(696\) | −2359.68 | − | 1362.36i | −0.128510 | − | 0.0741955i | ||||
\(697\) | 15484.8i | 0.841506i | ||||||||
\(698\) | 11.0345 | − | 19.1123i | 0.000598370 | − | 0.00103641i | ||||
\(699\) | 6873.75 | + | 11905.7i | 0.371944 | + | 0.644227i | ||||
\(700\) | −7064.75 | + | 4078.84i | −0.381461 | + | 0.220236i | ||||
\(701\) | 26986.0 | 1.45399 | 0.726994 | − | 0.686644i | \(-0.240917\pi\) | ||||
0.726994 | + | 0.686644i | \(0.240917\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 346.801 | 0.0186057 | ||||||||
\(704\) | −8537.67 | + | 4929.23i | −0.457068 | + | 0.263888i | ||||
\(705\) | −10453.1 | − | 18105.3i | −0.558422 | − | 0.967215i | ||||
\(706\) | −1985.65 | + | 3439.24i | −0.105851 | + | 0.183339i | ||||
\(707\) | 1896.37i | 0.100877i | ||||||||
\(708\) | −7253.01 | − | 4187.53i | −0.385007 | − | 0.222284i | ||||
\(709\) | 7879.85 | + | 4549.44i | 0.417396 | + | 0.240984i | 0.693963 | − | 0.720011i | \(-0.255863\pi\) |
−0.276566 | + | 0.960995i | \(0.589197\pi\) | |||||||
\(710\) | − | 1194.30i | − | 0.0631285i | ||||||
\(711\) | 1358.85 | − | 2353.60i | 0.0716751 | − | 0.124145i | ||||
\(712\) | 2488.85 | + | 4310.82i | 0.131002 | + | 0.226903i | ||||
\(713\) | −33609.1 | + | 19404.2i | −1.76532 | + | 1.01921i | ||||
\(714\) | −597.312 | −0.0313079 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9118.62 | −0.475948 | ||||||||
\(717\) | 19287.9 | − | 11135.9i | 1.00463 | − | 0.580025i | ||||
\(718\) | 1573.56 | + | 2725.48i | 0.0817892 | + | 0.141663i | ||||
\(719\) | −3146.78 | + | 5450.38i | −0.163220 | + | 0.282705i | −0.936022 | − | 0.351942i | \(-0.885521\pi\) |
0.772802 | + | 0.634647i | \(0.218855\pi\) | |||||||
\(720\) | − | 14204.5i | − | 0.735235i | ||||||
\(721\) | −2733.13 | − | 1577.97i | −0.141175 | − | 0.0815074i | ||||
\(722\) | −124.963 | − | 72.1476i | −0.00644135 | − | 0.00371892i | ||||
\(723\) | 19064.3i | 0.980648i | ||||||||
\(724\) | −4426.86 | + | 7667.54i | −0.227242 | + | 0.393594i | ||||
\(725\) | −10248.8 | − | 17751.4i | −0.525006 | − | 0.909337i | ||||
\(726\) | −1158.72 | + | 668.987i | −0.0592343 | + | 0.0341989i | ||||
\(727\) | −18070.7 | −0.921878 | −0.460939 | − | 0.887432i | \(-0.652487\pi\) | ||||
−0.460939 | + | 0.887432i | \(0.652487\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17319.9 | 0.879944 | ||||||||
\(730\) | −792.934 | + | 457.800i | −0.0402025 | + | 0.0232109i | ||||
\(731\) | −935.790 | − | 1620.84i | −0.0473481 | − | 0.0820093i | ||||
\(732\) | 9541.37 | − | 16526.1i | 0.481775 | − | 0.834459i | ||||
\(733\) | − | 34771.5i | − | 1.75214i | −0.482188 | − | 0.876068i | \(-0.660158\pi\) | ||
0.482188 | − | 0.876068i | \(-0.339842\pi\) | |||||||
\(734\) | −1520.40 | − | 877.803i | −0.0764563 | − | 0.0441421i | ||||
\(735\) | 17810.2 | + | 10282.7i | 0.893794 | + | 0.516032i | ||||
\(736\) | − | 11453.4i | − | 0.573613i | ||||||
\(737\) | −4766.09 | + | 8255.10i | −0.238210 | + | 0.412592i | ||||
\(738\) | 670.256 | + | 1160.92i | 0.0334315 | + | 0.0579051i | ||||
\(739\) | 20465.4 | − | 11815.7i | 1.01872 | − | 0.588158i | 0.104986 | − | 0.994474i | \(-0.466520\pi\) |
0.913733 | + | 0.406316i | \(0.133187\pi\) | |||||||
\(740\) | 596.710 | 0.0296425 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 161.324 | 0.00798167 | ||||||||
\(743\) | −28148.3 | + | 16251.4i | −1.38985 | + | 0.802431i | −0.993298 | − | 0.115581i | \(-0.963127\pi\) |
−0.396553 | + | 0.918012i | \(0.629794\pi\) | |||||||
\(744\) | −3526.21 | − | 6107.58i | −0.173760 | − | 0.300961i | ||||
\(745\) | 17589.3 | − | 30465.5i | 0.864995 | − | 1.49822i | ||||
\(746\) | − | 4390.69i | − | 0.215489i | ||||||
\(747\) | −3907.78 | − | 2256.16i | −0.191403 | − | 0.110507i | ||||
\(748\) | −10307.9 | − | 5951.25i | −0.503868 | − | 0.290908i | ||||
\(749\) | 3108.04i | 0.151622i | ||||||||
\(750\) | 965.435 | − | 1672.18i | 0.0470036 | − | 0.0814126i | ||||
\(751\) | 1010.43 | + | 1750.12i | 0.0490960 | + | 0.0850368i | 0.889529 | − | 0.456879i | \(-0.151033\pi\) |
−0.840433 | + | 0.541915i | \(0.817699\pi\) | |||||||
\(752\) | 16396.7 | − | 9466.65i | 0.795115 | − | 0.459060i | ||||
\(753\) | 20710.5 | 1.00230 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −32111.6 | −1.54790 | ||||||||
\(756\) | 5477.23 | − | 3162.28i | 0.263499 | − | 0.152131i | ||||
\(757\) | −6284.11 | − | 10884.4i | −0.301717 | − | 0.522589i | 0.674808 | − | 0.737993i | \(-0.264226\pi\) |
−0.976525 | + | 0.215404i | \(0.930893\pi\) | |||||||
\(758\) | 1790.86 | − | 3101.87i | 0.0858141 | − | 0.148634i | ||||
\(759\) | − | 11611.0i | − | 0.555273i | ||||||
\(760\) | 8637.36 | + | 4986.78i | 0.412250 | + | 0.238013i | ||||
\(761\) | 7538.59 | + | 4352.40i | 0.359098 | + | 0.207325i | 0.668685 | − | 0.743546i | \(-0.266857\pi\) |
−0.309587 | + | 0.950871i | \(0.600191\pi\) | |||||||
\(762\) | 4207.01i | 0.200005i | ||||||||
\(763\) | −478.593 | + | 828.948i | −0.0227081 | + | 0.0393315i | ||||
\(764\) | −10470.7 | − | 18135.8i | −0.495832 | − | 0.858807i | ||||
\(765\) | 14073.8 | − | 8125.51i | 0.665149 | − | 0.384024i | ||||
\(766\) | −3205.16 | −0.151184 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −11595.0 | −0.544790 | ||||||||
\(769\) | 18979.7 | − | 10957.9i | 0.890020 | − | 0.513853i | 0.0160706 | − | 0.999871i | \(-0.494884\pi\) |
0.873949 | + | 0.486018i | \(0.161551\pi\) | |||||||
\(770\) | 476.070 | + | 824.578i | 0.0222810 | + | 0.0385918i | ||||
\(771\) | 3084.32 | − | 5342.19i | 0.144071 | − | 0.249539i | ||||
\(772\) | − | 15386.5i | − | 0.717322i | ||||||
\(773\) | −19985.7 | − | 11538.8i | −0.929930 | − | 0.536896i | −0.0431408 | − | 0.999069i | \(-0.513736\pi\) |
−0.886790 | + | 0.462173i | \(0.847070\pi\) | |||||||
\(774\) | −140.315 | − | 81.0108i | −0.00651616 | − | 0.00376211i | ||||
\(775\) | − | 53054.0i | − | 2.45904i | ||||||
\(776\) | −2631.54 | + | 4557.96i | −0.121736 | + | 0.210852i | ||||
\(777\) | 43.0001 | + | 74.4783i | 0.00198535 | + | 0.00343873i | ||||
\(778\) | −3335.90 | + | 1925.98i | −0.153725 | + | 0.0887530i | ||||
\(779\) | 18405.5 | 0.846528 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3429.94 | 0.157148 | ||||||||
\(782\) | 3627.71 | − | 2094.46i | 0.165891 | − | 0.0957772i | ||||
\(783\) | 7945.76 | + | 13762.5i | 0.362654 | + | 0.628136i | ||||
\(784\) | −9312.32 | + | 16129.4i | −0.424213 | + | 0.734758i | ||||
\(785\) | − | 7072.67i | − | 0.321572i | ||||||
\(786\) | 2982.44 | + | 1721.91i | 0.135344 | + | 0.0781408i | ||||
\(787\) | 14308.8 | + | 8261.21i | 0.648100 | + | 0.374181i | 0.787728 | − | 0.616023i | \(-0.211257\pi\) |
−0.139628 | + | 0.990204i | \(0.544591\pi\) | |||||||
\(788\) | 31356.4i | 1.41754i | ||||||||
\(789\) | −11623.6 | + | 20132.7i | −0.524475 | + | 0.908418i | ||||
\(790\) | 790.388 | + | 1368.99i | 0.0355959 | + | 0.0616539i | ||||
\(791\) | 5957.39 | − | 3439.50i | 0.267788 | − | 0.154607i | ||||
\(792\) | −2086.15 | −0.0935962 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −4939.89 | −0.220794 | ||||||||
\(795\) | 3844.55 | − | 2219.65i | 0.171512 | − | 0.0990224i | ||||
\(796\) | −16498.0 | − | 28575.4i | −0.734620 | − | 1.27240i | ||||
\(797\) | −5859.68 | + | 10149.3i | −0.260427 | + | 0.451073i | −0.966356 | − | 0.257210i | \(-0.917197\pi\) |
0.705928 | + | 0.708283i | \(0.250530\pi\) | |||||||
\(798\) | 709.974i | 0.0314948i | ||||||||
\(799\) | 18759.1 | + | 10830.6i | 0.830600 | + | 0.479547i | ||||
\(800\) | 13559.9 | + | 7828.84i | 0.599270 | + | 0.345989i | ||||
\(801\) | − | 9640.53i | − | 0.425258i | ||||||
\(802\) | 345.548 | − | 598.506i | 0.0152141 | − | 0.0263516i | ||||
\(803\) | −1314.77 | − | 2277.24i | −0.0577797 | − | 0.100077i | ||||
\(804\) | −10591.2 | + | 6114.86i | −0.464583 | + | 0.268227i | ||||
\(805\) | 13610.0 | 0.595886 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9148.01 | 0.399040 | ||||||||
\(808\) | 2092.99 | − | 1208.39i | 0.0911275 | − | 0.0526125i | ||||
\(809\) | 12048.0 | + | 20867.8i | 0.523592 | + | 0.906888i | 0.999623 | + | 0.0274594i | \(0.00874171\pi\) |
−0.476031 | + | 0.879429i | \(0.657925\pi\) | |||||||
\(810\) | −727.630 | + | 1260.29i | −0.0315634 | + | 0.0546693i | ||||
\(811\) | − | 16622.6i | − | 0.719729i | −0.933005 | − | 0.359864i | \(-0.882823\pi\) | ||
0.933005 | − | 0.359864i | \(-0.117177\pi\) | |||||||
\(812\) | 3923.46 | + | 2265.21i | 0.169564 | + | 0.0978981i | ||||
\(813\) | 9048.81 | + | 5224.33i | 0.390351 | + | 0.225369i | ||||
\(814\) | − | 42.1933i | − | 0.00181680i | ||||||
\(815\) | 8382.05 | − | 14518.1i | 0.360258 | − | 0.623985i | ||||
\(816\) | −7442.80 | − | 12891.3i | −0.319301 | − | 0.553046i | ||||
\(817\) | −1926.55 | + | 1112.29i | −0.0824987 | + | 0.0476306i | ||||
\(818\) | 2962.05 | 0.126609 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 31668.7 | 1.34868 | ||||||||
\(821\) | 32913.8 | − | 19002.8i | 1.39915 | − | 0.807797i | 0.404842 | − | 0.914387i | \(-0.367326\pi\) |
0.994303 | + | 0.106590i | \(0.0339931\pi\) | |||||||
\(822\) | −555.729 | − | 962.552i | −0.0235806 | − | 0.0408429i | ||||
\(823\) | −7929.75 | + | 13734.7i | −0.335861 | + | 0.581728i | −0.983650 | − | 0.180092i | \(-0.942361\pi\) |
0.647789 | + | 0.761820i | \(0.275694\pi\) | |||||||
\(824\) | 4022.01i | 0.170040i | ||||||||
\(825\) | 13746.5 | + | 7936.54i | 0.580111 | + | 0.334927i | ||||
\(826\) | −601.155 | − | 347.077i | −0.0253231 | − | 0.0146203i | ||||
\(827\) | 12201.0i | 0.513023i | 0.966541 | + | 0.256512i | \(0.0825732\pi\) | ||||
−0.966541 | + | 0.256512i | \(0.917427\pi\) | |||||||
\(828\) | −7364.25 | + | 12755.3i | −0.309089 | + | 0.535357i | ||||
\(829\) | −2715.71 | − | 4703.74i | −0.113776 | − | 0.197066i | 0.803514 | − | 0.595286i | \(-0.202961\pi\) |
−0.917290 | + | 0.398220i | \(0.869628\pi\) | |||||||
\(830\) | 2272.99 | − | 1312.31i | 0.0950561 | − | 0.0548807i | ||||
\(831\) | −14139.9 | −0.590263 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21308.0 | −0.886290 | ||||||||
\(834\) | 950.793 | − | 548.941i | 0.0394763 | − | 0.0227917i | ||||
\(835\) | 32770.1 | + | 56759.5i | 1.35815 | + | 2.35239i | ||||
\(836\) | −7073.74 | + | 12252.1i | −0.292644 | + | 0.506874i | ||||
\(837\) | 41132.2i | 1.69861i | ||||||||
\(838\) | −4084.19 | − | 2358.01i | −0.168361 | − | 0.0972030i | ||||
\(839\) | 6894.34 | + | 3980.45i | 0.283694 | + | 0.163791i | 0.635095 | − | 0.772434i | \(-0.280961\pi\) |
−0.351401 | + | 0.936225i | \(0.614294\pi\) | |||||||
\(840\) | 2473.26i | 0.101590i | ||||||||
\(841\) | 6502.78 | − | 11263.2i | 0.266628 | − | 0.461813i | ||||
\(842\) | −1728.80 | − | 2994.38i | −0.0707583 | − | 0.122557i | ||||
\(843\) | 29108.8 | − | 16806.0i | 1.18928 | − | 0.686629i | ||||
\(844\) | 10655.0 | 0.434550 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1875.19 | 0.0762062 | ||||||||
\(847\) | 3900.67 | − | 2252.05i | 0.158239 | − | 0.0913593i | ||||
\(848\) | 2010.18 | + | 3481.73i | 0.0814030 | + | 0.140994i | ||||
\(849\) | −3920.20 | + | 6789.98i | −0.158470 | + | 0.274478i | ||||
\(850\) | 5726.56i | 0.231082i | ||||||||
\(851\) | −522.313 | − | 301.557i | −0.0210395 | − | 0.0121472i | ||||
\(852\) | 3811.02 | + | 2200.29i | 0.153243 | + | 0.0884751i | ||||
\(853\) | 13576.7i | 0.544969i | 0.962160 | + | 0.272485i | \(0.0878454\pi\) | ||||
−0.962160 | + | 0.272485i | \(0.912155\pi\) | |||||||
\(854\) | 790.823 | − | 1369.75i | 0.0316878 | − | 0.0548849i | ||||
\(855\) | −9658.10 | − | 16728.3i | −0.386316 | − | 0.669118i | ||||
\(856\) | 3430.28 | − | 1980.47i | 0.136968 | − | 0.0790785i | ||||
\(857\) | 31223.9 | 1.24456 | 0.622281 | − | 0.782794i | \(-0.286206\pi\) | ||||
0.622281 | + | 0.782794i | \(0.286206\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11815.8 | −0.469323 | −0.234661 | − | 0.972077i | \(-0.575398\pi\) | ||||
−0.234661 | + | 0.972077i | \(0.575398\pi\) | |||||||
\(860\) | −3314.84 | + | 1913.83i | −0.131436 | + | 0.0758848i | ||||
\(861\) | 2282.11 | + | 3952.73i | 0.0903300 | + | 0.156456i | ||||
\(862\) | 3087.68 | − | 5348.02i | 0.122003 | − | 0.211316i | ||||
\(863\) | 1790.84i | 0.0706384i | 0.999376 | + | 0.0353192i | \(0.0112448\pi\) | ||||
−0.999376 | + | 0.0353192i | \(0.988755\pi\) | |||||||
\(864\) | −10512.9 | − | 6069.62i | −0.413953 | − | 0.238996i | ||||
\(865\) | 21942.0 | + | 12668.2i | 0.862485 | + | 0.497956i | ||||
\(866\) | − | 817.328i | − | 0.0320715i | ||||||
\(867\) | −536.230 | + | 928.777i | −0.0210050 | + | 0.0363817i | ||||
\(868\) | 5863.07 | + | 10155.1i | 0.229269 | + | 0.397106i | ||||
\(869\) | −3931.64 | + | 2269.93i | −0.153477 | + | 0.0886102i | ||||
\(870\) | −3069.45 | −0.119614 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 1219.86 | 0.0473734 | ||||||||
\(873\) | 8827.59 | − | 5096.61i | 0.342232 | − | 0.197588i | ||||
\(874\) | −2489.51 | − | 4311.95i | −0.0963488 | − | 0.166881i | ||||
\(875\) | −3250.00 | + | 5629.17i | −0.125566 | + | 0.217486i | ||||
\(876\) | − | 3373.68i | − | 0.130121i | ||||||
\(877\) | 37708.9 | + | 21771.2i | 1.45193 | + | 0.838270i | 0.998591 | − | 0.0530701i | \(-0.0169007\pi\) |
0.453335 | + | 0.891340i | \(0.350234\pi\) | |||||||
\(878\) | 2336.90 | + | 1349.21i | 0.0898251 | + | 0.0518606i | ||||
\(879\) | − | 30489.7i | − | 1.16996i | ||||||
\(880\) | −11864.1 | + | 20549.3i | −0.454477 | + | 0.787176i | ||||
\(881\) | −510.020 | − | 883.380i | −0.0195040 | − | 0.0337819i | 0.856109 | − | 0.516796i | \(-0.172875\pi\) |
−0.875613 | + | 0.483014i | \(0.839542\pi\) | |||||||
\(882\) | −1597.49 | + | 922.311i | −0.0609867 | + | 0.0352107i | ||||
\(883\) | 34781.9 | 1.32560 | 0.662800 | − | 0.748797i | \(-0.269368\pi\) | ||||
0.662800 | + | 0.748797i | \(0.269368\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −19101.6 | −0.725531 | ||||||||
\(886\) | −5520.65 | + | 3187.35i | −0.209334 | + | 0.120859i | ||||
\(887\) | −24892.5 | − | 43115.2i | −0.942288 | − | 1.63209i | −0.761091 | − | 0.648645i | \(-0.775336\pi\) |
−0.181197 | − | 0.983447i | \(-0.557997\pi\) | |||||||
\(888\) | 54.8002 | − | 94.9167i | 0.00207092 | − | 0.00358693i | ||||
\(889\) | − | 14162.3i | − | 0.534295i | ||||||
\(890\) | 4856.23 | + | 2803.75i | 0.182900 | + | 0.105597i | ||||
\(891\) | −3619.46 | − | 2089.70i | −0.136090 | − | 0.0785718i | ||||
\(892\) | 8272.08i | 0.310504i | ||||||||
\(893\) | 12873.4 | − | 22297.3i | 0.482409 | − | 0.835557i | ||||
\(894\) | −1595.71 | − | 2763.85i | −0.0596962 | − | 0.103397i | ||||
\(895\) | −18011.2 | + | 10398.8i | −0.672679 | + | 0.388371i | ||||
\(896\) | −4594.25 | −0.171298 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3088.36 | 0.114766 | ||||||||
\(899\) | −25516.5 | + | 14731.9i | −0.946632 | + | 0.546538i | ||||
\(900\) | −10067.5 | − | 17437.4i | −0.372869 | − | 0.645828i | ||||
\(901\) | −2299.80 | + | 3983.37i | −0.0850360 | + | 0.147287i | ||||
\(902\) | − | 2239.29i | − | 0.0826611i | ||||||
\(903\) | −477.748 | − | 275.828i | −0.0176063 | − | 0.0101650i | ||||
\(904\) | −7592.22 | − | 4383.37i | −0.279329 | − | 0.161271i | ||||
\(905\) | 20193.3i | 0.741712i | ||||||||
\(906\) | −1456.59 | + | 2522.89i | −0.0534128 | + | 0.0925137i | ||||
\(907\) | 8694.93 | + | 15060.1i | 0.318314 | + | 0.551335i | 0.980136 | − | 0.198325i | \(-0.0635502\pi\) |
−0.661823 | + | 0.749660i | \(0.730217\pi\) | |||||||
\(908\) | −23423.9 | + | 13523.8i | −0.856112 | + | 0.494276i | ||||
\(909\) | −4680.66 | −0.170790 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20419.5 | 0.742621 | 0.371311 | − | 0.928509i | \(-0.378909\pi\) | ||||
0.371311 | + | 0.928509i | \(0.378909\pi\) | |||||||
\(912\) | −15322.8 | + | 8846.61i | −0.556347 | + | 0.321207i | ||||
\(913\) | 3768.85 | + | 6527.85i | 0.136616 | + | 0.236627i | ||||
\(914\) | −3090.80 | + | 5353.43i | −0.111854 | + | 0.193737i | ||||
\(915\) | − | 43523.5i | − | 1.57250i | ||||||
\(916\) | 15718.6 | + | 9075.12i | 0.566983 | + | 0.327348i | ||||
\(917\) | −10040.0 | − | 5796.58i | −0.361558 | − | 0.208746i | ||||
\(918\) | − | 4439.75i | − | 0.159623i | ||||||
\(919\) | 16615.9 | − | 28779.6i | 0.596417 | − | 1.03303i | −0.396928 | − | 0.917850i | \(-0.629924\pi\) |
0.993345 | − | 0.115175i | \(-0.0367430\pi\) | |||||||
\(920\) | −8672.41 | − | 15021.1i | −0.310784 | − | 0.538293i | ||||
\(921\) | 11521.1 | − | 6651.71i | 0.412197 | − | 0.237982i | ||||
\(922\) | 6335.43 | 0.226297 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −3508.31 | −0.124908 | ||||||||
\(925\) | 714.039 | − | 412.251i | 0.0253810 | − | 0.0146538i | ||||
\(926\) | 3465.15 | + | 6001.82i | 0.122972 | + | 0.212994i | ||||
\(927\) | 3894.79 | − | 6745.97i | 0.137995 | − | 0.239015i | ||||
\(928\) | − | 8695.59i | − | 0.307594i | ||||||
\(929\) | −21843.6 | − | 12611.4i | −0.771438 | − | 0.445390i | 0.0619492 | − | 0.998079i | \(-0.480268\pi\) |
−0.833387 | + | 0.552689i | \(0.813602\pi\) | |||||||
\(930\) | −6880.31 | − | 3972.35i | −0.242596 | − | 0.140063i | ||||
\(931\) | 25327.0i | 0.891579i | ||||||||
\(932\) | −14565.4 | + | 25228.1i | −0.511917 | + | 0.886666i | ||||
\(933\) | −6136.91 | − | 10629.4i | −0.215341 | − | 0.372982i | ||||
\(934\) | 5722.67 | − | 3303.99i | 0.200483 | − | 0.115749i | ||||
\(935\) | −27146.9 | −0.949519 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26979.4 | −0.940639 | −0.470319 | − | 0.882496i | \(-0.655861\pi\) | ||||
−0.470319 | + | 0.882496i | \(0.655861\pi\) | |||||||
\(938\) | −877.840 | + | 506.821i | −0.0305570 | + | 0.0176421i | ||||
\(939\) | −659.785 | − | 1142.78i | −0.0229300 | − | 0.0397159i | ||||
\(940\) | 22150.1 | − | 38365.1i | 0.768571 | − | 1.33120i | ||||
\(941\) | − | 7641.67i | − | 0.264730i | −0.991201 | − | 0.132365i | \(-0.957743\pi\) | ||
0.991201 | − | 0.132365i | \(-0.0422572\pi\) | |||||||
\(942\) | −555.672 | − | 320.818i | −0.0192195 | − | 0.0110964i | ||||
\(943\) | −27720.3 | − | 16004.3i | −0.957261 | − | 0.552675i | ||||
\(944\) | − | 17299.0i | − | 0.596434i | ||||||
\(945\) | 7212.46 | − | 12492.3i | 0.248276 | − | 0.430027i | ||||
\(946\) | 135.327 | + | 234.392i | 0.00465100 | + | 0.00805577i | ||||
\(947\) | −2484.90 | + | 1434.66i | −0.0852677 | + | 0.0492293i | −0.542028 | − | 0.840361i | \(-0.682343\pi\) |
0.456760 | + | 0.889590i | \(0.349010\pi\) | |||||||
\(948\) | −5824.62 | −0.199552 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 6806.67 | 0.232461 | ||||||||
\(951\) | 9724.46 | − | 5614.42i | 0.331585 | − | 0.191441i | ||||
\(952\) | −1281.28 | − | 2219.25i | −0.0436204 | − | 0.0755527i | ||||
\(953\) | 6156.79 | − | 10663.9i | 0.209274 | − | 0.362473i | −0.742212 | − | 0.670165i | \(-0.766223\pi\) |
0.951486 | + | 0.307692i | \(0.0995567\pi\) | |||||||
\(954\) | 398.184i | 0.0135133i | ||||||||
\(955\) | −41363.6 | − | 23881.3i | −1.40156 | − | 0.809194i | ||||
\(956\) | 40871.0 | + | 23596.9i | 1.38270 | + | 0.798303i | ||||
\(957\) | − | 8815.22i | − | 0.297759i | ||||||
\(958\) | −86.0551 | + | 149.052i | −0.00290221 | + | 0.00502677i | ||||
\(959\) | 1870.78 | + | 3240.29i | 0.0629935 | + | 0.109108i | ||||
\(960\) | −24983.1 | + | 14424.0i | −0.839924 | + | 0.484930i | ||||
\(961\) | −46470.7 | −1.55989 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7671.32 | −0.256703 | ||||||||
\(964\) | −34984.9 | + | 20198.5i | −1.16887 | + | 0.674845i | ||||
\(965\) | −17546.6 | − | 30391.6i | −0.585331 | − | 1.01382i | ||||
\(966\) | 617.351 | − | 1069.28i | 0.0205621 | − | 0.0356145i | ||||
\(967\) | 17838.0i | 0.593207i | 0.955001 | + | 0.296603i | \(0.0958540\pi\) | ||||
−0.955001 | + | 0.296603i | \(0.904146\pi\) | |||||||
\(968\) | −4971.09 | − | 2870.06i | −0.165059 | − | 0.0952967i | ||||
\(969\) | −17530.5 | − | 10121.2i | −0.581176 | − | 0.335542i | ||||
\(970\) | 5928.97i | 0.196255i | ||||||||
\(971\) | −20762.7 | + | 35962.0i | −0.686206 | + | 1.18854i | 0.286851 | + | 0.957975i | \(0.407392\pi\) |
−0.973056 | + | 0.230568i | \(0.925942\pi\) | |||||||
\(972\) | 13018.6 | + | 22548.8i | 0.429599 | + | 0.744088i | ||||
\(973\) | −3200.71 | + | 1847.93i | −0.105457 | + | 0.0608859i | ||||
\(974\) | 4164.32 | 0.136995 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 39416.1 | 1.29270 | ||||||||
\(977\) | 27413.5 | − | 15827.2i | 0.897682 | − | 0.518277i | 0.0212344 | − | 0.999775i | \(-0.493240\pi\) |
0.876447 | + | 0.481498i | \(0.159907\pi\) | |||||||
\(978\) | −760.423 | − | 1317.09i | −0.0248626 | − | 0.0430633i | ||||
\(979\) | −8052.14 | + | 13946.7i | −0.262868 | + | 0.455300i | ||||
\(980\) | 43578.0i | 1.42046i | ||||||||
\(981\) | −2046.03 | − | 1181.27i | −0.0665899 | − | 0.0384457i | ||||
\(982\) | −719.097 | − | 415.171i | −0.0233679 | − | 0.0134915i | ||||
\(983\) | − | 39913.2i | − | 1.29505i | −0.762045 | − | 0.647525i | \(-0.775804\pi\) | ||
0.762045 | − | 0.647525i | \(-0.224196\pi\) | |||||||
\(984\) | 2908.37 | − | 5037.44i | 0.0942230 | − | 0.163199i | ||||
\(985\) | 35758.4 | + | 61935.4i | 1.15671 | + | 2.00348i | ||||
\(986\) | 2754.21 | − | 1590.14i | 0.0889572 | − | 0.0513595i | ||||
\(987\) | 6384.72 | 0.205905 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3868.74 | 0.124387 | ||||||||
\(990\) | −2035.24 | + | 1175.05i | −0.0653376 | + | 0.0377227i | ||||
\(991\) | 1350.47 | + | 2339.08i | 0.0432887 | + | 0.0749781i | 0.886858 | − | 0.462042i | \(-0.152883\pi\) |
−0.843569 | + | 0.537020i | \(0.819550\pi\) | |||||||
\(992\) | 11253.5 | − | 19491.6i | 0.360179 | − | 0.623848i | ||||
\(993\) | 28352.6i | 0.906085i | ||||||||
\(994\) | 315.871 | + | 182.368i | 0.0100793 | + | 0.00581928i | ||||
\(995\) | −65174.2 | − | 37628.3i | −2.07654 | − | 1.19889i | ||||
\(996\) | 9670.83i | 0.307663i | ||||||||
\(997\) | 4864.54 | − | 8425.63i | 0.154525 | − | 0.267645i | −0.778361 | − | 0.627817i | \(-0.783949\pi\) |
0.932886 | + | 0.360172i | \(0.117282\pi\) | |||||||
\(998\) | 2931.04 | + | 5076.71i | 0.0929664 | + | 0.161022i | ||||
\(999\) | −553.588 | + | 319.614i | −0.0175323 | + | 0.0101223i |
(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 | 169.4.e.g.23.3 | 8 | ||
13.2 | odd | 12 | 169.4.a.j.1.1 | 2 | |||
13.3 | even | 3 | 169.4.b.e.168.3 | 4 | |||
13.4 | even | 6 | inner | 169.4.e.g.147.3 | 8 | ||
13.5 | odd | 4 | 169.4.c.f.146.2 | 4 | |||
13.6 | odd | 12 | 169.4.c.f.22.2 | 4 | |||
13.7 | odd | 12 | 13.4.c.b.9.1 | yes | 4 | ||
13.8 | odd | 4 | 13.4.c.b.3.1 | ✓ | 4 | ||
13.9 | even | 3 | inner | 169.4.e.g.147.2 | 8 | ||
13.10 | even | 6 | 169.4.b.e.168.2 | 4 | |||
13.11 | odd | 12 | 169.4.a.f.1.2 | 2 | |||
13.12 | even | 2 | inner | 169.4.e.g.23.2 | 8 | ||
39.2 | even | 12 | 1521.4.a.l.1.2 | 2 | |||
39.8 | even | 4 | 117.4.g.d.55.2 | 4 | |||
39.11 | even | 12 | 1521.4.a.t.1.1 | 2 | |||
39.20 | even | 12 | 117.4.g.d.100.2 | 4 | |||
52.7 | even | 12 | 208.4.i.e.113.1 | 4 | |||
52.47 | even | 4 | 208.4.i.e.81.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.4.c.b.3.1 | ✓ | 4 | 13.8 | odd | 4 | ||
13.4.c.b.9.1 | yes | 4 | 13.7 | odd | 12 | ||
117.4.g.d.55.2 | 4 | 39.8 | even | 4 | |||
117.4.g.d.100.2 | 4 | 39.20 | even | 12 | |||
169.4.a.f.1.2 | 2 | 13.11 | odd | 12 | |||
169.4.a.j.1.1 | 2 | 13.2 | odd | 12 | |||
169.4.b.e.168.2 | 4 | 13.10 | even | 6 | |||
169.4.b.e.168.3 | 4 | 13.3 | even | 3 | |||
169.4.c.f.22.2 | 4 | 13.6 | odd | 12 | |||
169.4.c.f.146.2 | 4 | 13.5 | odd | 4 | |||
169.4.e.g.23.2 | 8 | 13.12 | even | 2 | inner | ||
169.4.e.g.23.3 | 8 | 1.1 | even | 1 | trivial | ||
169.4.e.g.147.2 | 8 | 13.9 | even | 3 | inner | ||
169.4.e.g.147.3 | 8 | 13.4 | even | 6 | inner | ||
208.4.i.e.81.1 | 4 | 52.47 | even | 4 | |||
208.4.i.e.113.1 | 4 | 52.7 | even | 12 | |||
1521.4.a.l.1.2 | 2 | 39.2 | even | 12 | |||
1521.4.a.t.1.1 | 2 | 39.11 | even | 12 |