Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(1,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.a (trivial) |
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: | yes |
Analytic conductor: | \(79.2985670477\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{137}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 34 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 672) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-5.35235\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.70470 | 0.599687 | 0.299843 | − | 0.953988i | \(-0.403066\pi\) | ||||
0.299843 | + | 0.953988i | \(0.403066\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.704700 | 0.0193159 | 0.00965796 | − | 0.999953i | \(-0.496926\pi\) | ||||
0.00965796 | + | 0.999953i | \(0.496926\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −35.4094 | −0.755446 | −0.377723 | − | 0.925919i | \(-0.623293\pi\) | ||||
−0.377723 | + | 0.925919i | \(0.623293\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −20.1141 | −0.346229 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 26.7047 | 0.380991 | 0.190495 | − | 0.981688i | \(-0.438991\pi\) | ||||
0.190495 | + | 0.981688i | \(0.438991\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 30.8188 | 0.372122 | 0.186061 | − | 0.982538i | \(-0.440428\pi\) | ||||
0.186061 | + | 0.982538i | \(0.440428\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.88590 | 0.0533607 | 0.0266803 | − | 0.999644i | \(-0.491506\pi\) | ||||
0.0266803 | + | 0.999644i | \(0.491506\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −80.0470 | −0.640376 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −252.094 | −1.61423 | −0.807115 | − | 0.590394i | \(-0.798972\pi\) | ||||
−0.807115 | + | 0.590394i | \(0.798972\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −37.6376 | −0.218062 | −0.109031 | − | 0.994038i | \(-0.534775\pi\) | ||||
−0.109031 | + | 0.994038i | \(0.534775\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.11410 | −0.0111520 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 46.9329 | 0.226660 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 139.866 | 0.621454 | 0.310727 | − | 0.950499i | \(-0.399428\pi\) | ||||
0.310727 | + | 0.950499i | \(0.399428\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 106.228 | 0.436157 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −46.7047 | −0.177904 | −0.0889518 | − | 0.996036i | \(-0.528352\pi\) | ||||
−0.0889518 | + | 0.996036i | \(0.528352\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −254.094 | −0.901139 | −0.450569 | − | 0.892741i | \(-0.648779\pi\) | ||||
−0.450569 | + | 0.892741i | \(0.648779\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 60.3423 | 0.199896 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 607.960 | 1.88681 | 0.943405 | − | 0.331643i | \(-0.107603\pi\) | ||||
0.943405 | + | 0.331643i | \(0.107603\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −80.1141 | −0.219965 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −298.685 | −0.774103 | −0.387052 | − | 0.922058i | \(-0.626507\pi\) | ||||
−0.387052 | + | 0.922058i | \(0.626507\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.72480 | 0.0115835 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −92.4564 | −0.214845 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −178.591 | −0.394077 | −0.197038 | − | 0.980396i | \(-0.563132\pi\) | ||||
−0.197038 | + | 0.980396i | \(0.563132\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −390.188 | −0.818991 | −0.409496 | − | 0.912312i | \(-0.634295\pi\) | ||||
−0.409496 | + | 0.912312i | \(0.634295\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −237.409 | −0.453031 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −349.141 | −0.636632 | −0.318316 | − | 0.947985i | \(-0.603117\pi\) | ||||
−0.318316 | + | 0.947985i | \(0.603117\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −17.6577 | −0.0308078 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 348.477 | 0.582487 | 0.291243 | − | 0.956649i | \(-0.405931\pi\) | ||||
0.291243 | + | 0.956649i | \(0.405931\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −646.416 | −1.03640 | −0.518201 | − | 0.855259i | \(-0.673398\pi\) | ||||
−0.518201 | + | 0.855259i | \(0.673398\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 240.141 | 0.369721 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.93290 | 0.00730073 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1047.50 | 1.49181 | 0.745907 | − | 0.666050i | \(-0.232016\pi\) | ||||
0.745907 | + | 0.666050i | \(0.232016\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −278.819 | −0.368727 | −0.184363 | − | 0.982858i | \(-0.559022\pi\) | ||||
−0.184363 | + | 0.982858i | \(0.559022\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 179.047 | 0.228475 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 756.282 | 0.931976 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 439.309 | 0.523221 | 0.261610 | − | 0.965174i | \(-0.415746\pi\) | ||||
0.261610 | + | 0.965174i | \(0.415746\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −247.866 | −0.285532 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 112.913 | 0.125898 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 206.631 | 0.223157 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −154.309 | −0.161522 | −0.0807612 | − | 0.996733i | \(-0.525735\pi\) | ||||
−0.0807612 | + | 0.996733i | \(0.525735\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.34230 | 0.00643864 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −166.060 | −0.163600 | −0.0818001 | − | 0.996649i | \(-0.526067\pi\) | ||||
−0.0818001 | + | 0.996649i | \(0.526067\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 42.4428 | 0.0406021 | 0.0203010 | − | 0.999794i | \(-0.493538\pi\) | ||||
0.0203010 | + | 0.999794i | \(0.493538\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −140.799 | −0.130862 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −293.470 | −0.265148 | −0.132574 | − | 0.991173i | \(-0.542324\pi\) | ||||
−0.132574 | + | 0.991173i | \(0.542324\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1176.01 | 1.03341 | 0.516705 | − | 0.856164i | \(-0.327158\pi\) | ||||
0.516705 | + | 0.856164i | \(0.327158\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −419.597 | −0.358797 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −182.537 | −0.151961 | −0.0759806 | − | 0.997109i | \(-0.524209\pi\) | ||||
−0.0759806 | + | 0.997109i | \(0.524209\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 39.4632 | 0.0319997 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −318.685 | −0.251815 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 186.933 | 0.144001 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1330.50 | −0.999627 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 140.114 | 0.102713 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1374.78 | −0.983711 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1374.59 | 0.960435 | 0.480217 | − | 0.877150i | \(-0.340558\pi\) | ||||
0.480217 | + | 0.877150i | \(0.340558\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 762.282 | 0.520273 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1316.91 | −0.878315 | −0.439157 | − | 0.898410i | \(-0.644723\pi\) | ||||
−0.439157 | + | 0.898410i | \(0.644723\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 215.732 | 0.140649 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −181.027 | −0.115410 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2266.98 | −1.41373 | −0.706866 | − | 0.707348i | \(-0.749891\pi\) | ||||
−0.706866 | + | 0.707348i | \(0.749891\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1162.93 | −0.709627 | −0.354813 | − | 0.934937i | \(-0.615456\pi\) | ||||
−0.354813 | + | 0.934937i | \(0.615456\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1823.88 | −1.08935 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −24.9530 | −0.0145921 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1690.21 | −0.968032 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 54.0674 | 0.0297273 | 0.0148637 | − | 0.999890i | \(-0.495269\pi\) | ||||
0.0148637 | + | 0.999890i | \(0.495269\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −862.014 | −0.464567 | −0.232284 | − | 0.972648i | \(-0.574620\pi\) | ||||
−0.232284 | + | 0.972648i | \(0.574620\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 240.342 | 0.126997 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −252.349 | −0.130769 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1459.75 | −0.742040 | −0.371020 | − | 0.928625i | \(-0.620992\pi\) | ||||
−0.371020 | + | 0.928625i | \(0.620992\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 896.054 | 0.446929 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 41.2013 | 0.0201684 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1067.77 | −0.513094 | −0.256547 | − | 0.966532i | \(-0.582585\pi\) | ||||
−0.256547 | + | 0.966532i | \(0.582585\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −14.1744 | −0.00668773 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2082.86 | −0.965129 | −0.482564 | − | 0.875861i | \(-0.660295\pi\) | ||||
−0.482564 | + | 0.875861i | \(0.660295\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −943.174 | −0.429301 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 277.369 | 0.124041 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2210.17 | −0.971306 | −0.485653 | − | 0.874152i | \(-0.661418\pi\) | ||||
−0.485653 | + | 0.874152i | \(0.661418\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −560.329 | −0.242039 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 535.772 | 0.227520 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −934.718 | −0.390302 | −0.195151 | − | 0.980773i | \(-0.562520\pi\) | ||||
−0.195151 | + | 0.980773i | \(0.562520\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.85221 | −0.00240327 | −0.00120163 | − | 0.999999i | \(-0.500382\pi\) | ||||
−0.00120163 | + | 0.999999i | \(0.500382\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1170.56 | 0.472845 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 937.758 | 0.372678 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.8188 | 0.00735918 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2377.34 | 0.900618 | 0.450309 | − | 0.892873i | \(-0.351314\pi\) | ||||
0.450309 | + | 0.892873i | \(0.351314\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2233.85 | −0.833141 | −0.416570 | − | 0.909103i | \(-0.636768\pi\) | ||||
−0.416570 | + | 0.909103i | \(0.636768\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 712.228 | 0.261558 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2358.95 | −0.853139 | −0.426570 | − | 0.904455i | \(-0.640278\pi\) | ||||
−0.426570 | + | 0.904455i | \(0.640278\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 367.759 | 0.131004 | 0.0655018 | − | 0.997852i | \(-0.479135\pi\) | ||||
0.0655018 | + | 0.997852i | \(0.479135\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1047.42 | 0.367560 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1764.66 | −0.610122 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −313.141 | −0.106686 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 52.9731 | 0.0177869 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.7180 | 0.00718787 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1873.13 | −0.611144 | −0.305572 | − | 0.952169i | \(-0.598848\pi\) | ||||
−0.305572 | + | 0.952169i | \(0.598848\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1045.43 | −0.336299 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1703.62 | −0.540401 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −263.463 | −0.0824196 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1939.25 | 0.598367 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −945.597 | −0.287818 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3352.83 | −1.00683 | −0.503413 | − | 0.864046i | \(-0.667923\pi\) | ||||
−0.503413 | + | 0.864046i | \(0.667923\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −720.423 | −0.213459 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1006.08 | 0.294167 | 0.147084 | − | 0.989124i | \(-0.453011\pi\) | ||||
0.147084 | + | 0.989124i | \(0.453011\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1550.82 | −0.447515 | −0.223758 | − | 0.974645i | \(-0.571832\pi\) | ||||
−0.223758 | + | 0.974645i | \(0.571832\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.7987 | −0.00421508 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 592.215 | 0.166512 | 0.0832559 | − | 0.996528i | \(-0.473468\pi\) | ||||
0.0832559 | + | 0.996528i | \(0.473468\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4076.19 | 1.13149 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3142.51 | −0.861299 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5096.56 | −1.37937 | −0.689684 | − | 0.724111i | \(-0.742251\pi\) | ||||
−0.689684 | + | 0.724111i | \(0.742251\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4499.44 | −1.20263 | −0.601316 | − | 0.799011i | \(-0.705357\pi\) | ||||
−0.601316 | + | 0.799011i | \(0.705357\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 328.530 | 0.0856695 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1091.28 | −0.281118 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 836.456 | 0.212885 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1602.75 | 0.403047 | 0.201523 | − | 0.979484i | \(-0.435411\pi\) | ||||
0.201523 | + | 0.979484i | \(0.435411\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.14779 | 0.00103071 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −537.141 | −0.131910 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4953.82 | −1.20238 | −0.601188 | − | 0.799107i | \(-0.705306\pi\) | ||||
−0.601188 | + | 0.799107i | \(0.705306\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 979.061 | 0.234888 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2268.85 | −0.538077 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3675.40 | −0.861730 | −0.430865 | − | 0.902416i | \(-0.641792\pi\) | ||||
−0.430865 | + | 0.902416i | \(0.641792\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2002.59 | −0.464219 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1317.93 | −0.302082 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1989.64 | −0.450969 | −0.225485 | − | 0.974247i | \(-0.572397\pi\) | ||||
−0.225485 | + | 0.974247i | \(0.572397\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1638.85 | 0.367354 | 0.183677 | − | 0.982987i | \(-0.441200\pi\) | ||||
0.183677 | + | 0.982987i | \(0.441200\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 743.597 | 0.164852 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −56.4091 | −0.0123694 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7810.87 | 1.69426 | 0.847130 | − | 0.531386i | \(-0.178329\pi\) | ||||
0.847130 | + | 0.531386i | \(0.178329\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −338.738 | −0.0726872 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3018.34 | 0.640779 | 0.320389 | − | 0.947286i | \(-0.396186\pi\) | ||||
0.320389 | + | 0.947286i | \(0.396186\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7348.13 | 1.54347 | 0.771734 | − | 0.635946i | \(-0.219390\pi\) | ||||
0.771734 | + | 0.635946i | \(0.219390\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −619.892 | −0.128839 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −326.933 | −0.0672413 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4199.86 | −0.854846 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 462.926 | 0.0932550 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4211.91 | −0.839804 | −0.419902 | − | 0.907569i | \(-0.637936\pi\) | ||||
−0.419902 | + | 0.907569i | \(0.637936\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1197.40 | −0.236322 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −19.0269 | −0.00371735 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −208.416 | −0.0403111 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1778.66 | −0.340598 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 498.181 | 0.0944546 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2616.09 | −0.491138 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7553.16 | 1.40417 | 0.702087 | − | 0.712091i | \(-0.252252\pi\) | ||||
0.702087 | + | 0.712091i | \(0.252252\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −127.328 | −0.0234416 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2656.58 | −0.484375 | −0.242188 | − | 0.970229i | \(-0.577865\pi\) | ||||
−0.242188 | + | 0.970229i | \(0.577865\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10819.2 | −1.95379 | −0.976893 | − | 0.213731i | \(-0.931439\pi\) | ||||
−0.976893 | + | 0.213731i | \(0.931439\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 422.396 | 0.0755534 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1704.91 | −0.302074 | −0.151037 | − | 0.988528i | \(-0.548261\pi\) | ||||
−0.151037 | + | 0.988528i | \(0.548261\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −177.651 | −0.0311803 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 880.409 | 0.153083 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 823.007 | 0.141775 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2834.42 | 0.483770 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3528.04 | −0.596639 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4255.72 | 0.713147 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −75.1144 | −0.0124733 | −0.00623665 | − | 0.999981i | \(-0.501985\pi\) | ||||
−0.00623665 | + | 0.999981i | \(0.501985\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1258.79 | 0.207151 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2340.89 | −0.381780 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1474.97 | −0.238417 | −0.119208 | − | 0.992869i | \(-0.538036\pi\) | ||||
−0.119208 | + | 0.992869i | \(0.538036\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 547.610 | 0.0877349 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −26.5232 | −0.00421206 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −118.390 | −0.0184750 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −73.8327 | −0.0114223 | −0.00571116 | − | 0.999984i | \(-0.501818\pi\) | ||||
−0.00571116 | + | 0.999984i | \(0.501818\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3803.45 | −0.583364 | −0.291682 | − | 0.956515i | \(-0.594215\pi\) | ||||
−0.291682 | + | 0.956515i | \(0.594215\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 956.054 | 0.145386 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7569.15 | 1.14126 | 0.570631 | − | 0.821207i | \(-0.306699\pi\) | ||||
0.570631 | + | 0.821207i | \(0.306699\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2336.43 | 0.349309 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −560.799 | −0.0831390 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5094.05 | −0.748896 | −0.374448 | − | 0.927248i | \(-0.622168\pi\) | ||||
−0.374448 | + | 0.927248i | \(0.622168\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5909.20 | −0.861525 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3991.51 | 0.577135 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4334.03 | −0.621516 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8647.95 | 1.23003 | 0.615013 | − | 0.788517i | \(-0.289151\pi\) | ||||
0.615013 | + | 0.788517i | \(0.289151\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −420.342 | −0.0593012 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2090.79 | −0.292584 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13760.1 | 1.91011 | 0.955053 | − | 0.296436i | \(-0.0957982\pi\) | ||||
0.955053 | + | 0.296436i | \(0.0957982\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4124.34 | 0.567946 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8926.50 | 1.21946 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2462.66 | 0.333768 | 0.166884 | − | 0.985977i | \(-0.446629\pi\) | ||||
0.166884 | + | 0.985977i | \(0.446629\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4123.77 | −0.554507 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2553.40 | −0.340659 | −0.170330 | − | 0.985387i | \(-0.554483\pi\) | ||||
−0.170330 | + | 0.985387i | \(0.554483\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 33.0736 | 0.00437815 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2286.85 | −0.300380 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5247.13 | 0.683907 | 0.341954 | − | 0.939717i | \(-0.388911\pi\) | ||||
0.341954 | + | 0.939717i | \(0.388911\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 157.181 | 0.0203299 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3950.74 | 0.507095 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7023.20 | 0.894621 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11500.6 | 1.45390 | 0.726952 | − | 0.686688i | \(-0.240936\pi\) | ||||
0.726952 | + | 0.686688i | \(0.240936\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −647.195 | −0.0812037 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −288.322 | −0.0359055 | −0.0179528 | − | 0.999839i | \(-0.505715\pi\) | ||||
−0.0179528 | + | 0.999839i | \(0.505715\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1332.72 | 0.164734 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 543.081 | 0.0666318 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 98.5634 | 0.0120039 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13567.8 | 1.64030 | 0.820151 | − | 0.572147i | \(-0.193889\pi\) | ||||
0.820151 | + | 0.572147i | \(0.193889\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6800.94 | 0.816218 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1250.13 | −0.148947 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1869.40 | −0.221121 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3488.78 | 0.409703 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12094.2 | −1.41012 | −0.705059 | − | 0.709148i | \(-0.749080\pi\) | ||||
−0.705059 | + | 0.709148i | \(0.749080\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2030.79 | −0.235094 | −0.117547 | − | 0.993067i | \(-0.537503\pi\) | ||||
−0.117547 | + | 0.993067i | \(0.537503\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5471.64 | 0.628937 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2137.63 | −0.243977 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2731.32 | −0.309550 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 74.8590 | 0.00842477 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11236.7 | −1.25580 | −0.627902 | − | 0.778292i | \(-0.716086\pi\) | ||||
−0.627902 | + | 0.778292i | \(0.716086\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2847.80 | −0.316066 | −0.158033 | − | 0.987434i | \(-0.550515\pi\) | ||||
−0.158033 | + | 0.987434i | \(0.550515\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5070.64 | 0.558894 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 181.396 | 0.0198567 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 596.831 | 0.0648866 | 0.0324433 | − | 0.999474i | \(-0.489671\pi\) | ||||
0.0324433 | + | 0.999474i | \(0.489671\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10883.5 | −1.16725 | −0.583624 | − | 0.812024i | \(-0.698366\pi\) | ||||
−0.583624 | + | 0.812024i | \(0.698366\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2945.43 | 0.313768 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −162.202 | −0.0171631 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6593.68 | −0.693040 | −0.346520 | − | 0.938043i | \(-0.612637\pi\) | ||||
−0.346520 | + | 0.938043i | \(0.612637\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −32.9128 | −0.00343637 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2586.04 | 0.268218 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1661.87 | −0.171230 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14848.9 | 1.51992 | 0.759960 | − | 0.649970i | \(-0.225218\pi\) | ||||
0.759960 | + | 0.649970i | \(0.225218\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −721.027 | −0.0733217 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1723.59 | −0.174134 | −0.0870668 | − | 0.996202i | \(-0.527749\pi\) | ||||
−0.0870668 | + | 0.996202i | \(0.527749\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17899.2 | 1.79664 | 0.898321 | − | 0.439339i | \(-0.144787\pi\) | ||||
0.898321 | + | 0.439339i | \(0.144787\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 757.046 | 0.0754993 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17921.1 | −1.77579 | −0.887893 | − | 0.460051i | \(-0.847831\pi\) | ||||
−0.887893 | + | 0.460051i | \(0.847831\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2443.99 | −0.240624 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4379.24 | 0.428417 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −179.060 | −0.0174063 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2466.95 | −0.238298 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2688.16 | −0.258034 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1507.10 | 0.143760 | 0.0718801 | − | 0.997413i | \(-0.477100\pi\) | ||||
0.0718801 | + | 0.997413i | \(0.477100\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4952.56 | −0.469475 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −123.604 | −0.0116442 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1034.59 | −0.0968628 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7618.50 | 0.708885 | 0.354443 | − | 0.935078i | \(-0.384671\pi\) | ||||
0.354443 | + | 0.935078i | \(0.384671\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3203.32 | 0.296235 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7346.20 | 0.675212 | 0.337606 | − | 0.941287i | \(-0.390383\pi\) | ||||
0.337606 | + | 0.941287i | \(0.390383\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6732.09 | −0.615007 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 42.5232 | 0.00386116 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2439.34 | 0.220159 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18775.3 | 1.68436 | 0.842182 | − | 0.539193i | \(-0.181271\pi\) | ||||
0.842182 | + | 0.539193i | \(0.181271\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6248.58 | 0.557217 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2556.27 | −0.226597 | −0.113299 | − | 0.993561i | \(-0.536142\pi\) | ||||
−0.113299 | + | 0.993561i | \(0.536142\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1113.38 | −0.0981088 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2829.52 | 0.247857 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1902.18 | −0.165644 | −0.0828219 | − | 0.996564i | \(-0.526393\pi\) | ||||
−0.0828219 | + | 0.996564i | \(0.526393\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4524.91 | −0.391723 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −832.108 | −0.0716149 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 284.566 | 0.0243485 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 428.429 | 0.0364454 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6630.50 | 0.560784 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14253.1 | 1.19854 | 0.599272 | − | 0.800545i | \(-0.295457\pi\) | ||||
0.599272 | + | 0.800545i | \(0.295457\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10544.3 | −0.881591 | −0.440796 | − | 0.897608i | \(-0.645304\pi\) | ||||
−0.440796 | + | 0.897608i | \(0.645304\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1680.99 | 0.139741 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1005.10 | −0.0830795 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12132.4 | −0.997153 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1607.32 | −0.131359 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1653.79 | 0.134397 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1967.63 | −0.159005 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2804.15 | 0.225341 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 34.5303 | 0.00275942 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7563.14 | 0.601044 | 0.300522 | − | 0.953775i | \(-0.402839\pi\) | ||||
0.300522 | + | 0.953775i | \(0.402839\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.5566 | 0.00138753 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7884.82 | 0.619722 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9059.07 | 0.708113 | 0.354057 | − | 0.935224i | \(-0.384802\pi\) | ||||
0.354057 | + | 0.935224i | \(0.384802\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3511.69 | −0.272997 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7769.23 | −0.600691 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7332.52 | 0.563853 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2813.27 | −0.215166 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23719.2 | 1.80434 | 0.902169 | − | 0.431384i | \(-0.141974\pi\) | ||||
0.902169 | + | 0.431384i | \(0.141974\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8997.32 | 0.680762 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −56.4564 | −0.00424883 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14719.8 | −1.10189 | −0.550947 | − | 0.834540i | \(-0.685733\pi\) | ||||
−0.550947 | + | 0.834540i | \(0.685733\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1223.85 | −0.0911291 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 567.000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5184.65 | −0.381989 | −0.190994 | − | 0.981591i | \(-0.561171\pi\) | ||||
−0.190994 | + | 0.981591i | \(0.561171\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13173.6 | −0.965496 | −0.482748 | − | 0.875759i | \(-0.660361\pi\) | ||||
−0.482748 | + | 0.875759i | \(0.660361\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7132.01 | −0.519972 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −471.149 | −0.0341709 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2354.29 | 0.169862 | 0.0849311 | − | 0.996387i | \(-0.472933\pi\) | ||||
0.0849311 | + | 0.996387i | \(0.472933\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6701.56 | 0.481014 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1951.73 | −0.139366 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −210.483 | −0.0149525 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2136.68 | −0.151010 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17138.5 | −1.20508 | −0.602541 | − | 0.798088i | \(-0.705845\pi\) | ||||
−0.602541 | + | 0.798088i | \(0.705845\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1159.95 | −0.0811455 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7076.86 | 0.492560 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20553.0 | −1.42329 | −0.711645 | − | 0.702540i | \(-0.752049\pi\) | ||||
−0.711645 | + | 0.702540i | \(0.752049\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1253.33 | 0.0863554 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1103.28 | −0.0756350 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19280.3 | 1.31514 | 0.657571 | − | 0.753392i | \(-0.271584\pi\) | ||||
0.657571 | + | 0.753392i | \(0.271584\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24736.4 | 1.67890 | 0.839451 | − | 0.543436i | \(-0.182877\pi\) | ||||
0.839451 | + | 0.543436i | \(0.182877\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3142.27 | −0.212211 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8920.63 | −0.599463 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4926.07 | 0.329395 | 0.164698 | − | 0.986344i | \(-0.447335\pi\) | ||||
0.164698 | + | 0.986344i | \(0.447335\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5293.97 | 0.352254 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −21527.5 | −1.42538 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28344.4 | 1.86757 | 0.933784 | − | 0.357837i | \(-0.116486\pi\) | ||||
0.933784 | + | 0.357837i | \(0.116486\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 939.423 | 0.0615954 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21881.8 | 1.42776 | 0.713879 | − | 0.700269i | \(-0.246937\pi\) | ||||
0.713879 | + | 0.700269i | \(0.246937\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8355.39 | −0.542538 | −0.271269 | − | 0.962504i | \(-0.587443\pi\) | ||||
−0.271269 | + | 0.962504i | \(0.587443\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −158.919 | −0.0102693 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3075.16 | 0.197759 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 788.397 | 0.0504574 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −65.1540 | −0.00414992 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3735.07 | 0.236768 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10780.0 | 0.680100 | 0.340050 | − | 0.940407i | \(-0.389556\pi\) | ||||
0.340050 | + | 0.940407i | \(0.389556\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5619.38 | 0.352844 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9216.22 | 0.575960 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1735.06 | −0.107921 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3136.29 | 0.194162 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20161.7 | −1.24234 | −0.621171 | − | 0.783675i | \(-0.713343\pi\) | ||||
−0.621171 | + | 0.783675i | \(0.713343\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18277.8 | −1.12100 | −0.560502 | − | 0.828153i | \(-0.689392\pi\) | ||||
−0.560502 | + | 0.828153i | \(0.689392\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5110.87 | 0.312001 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2534.86 | −0.154027 | −0.0770136 | − | 0.997030i | \(-0.524538\pi\) | ||||
−0.0770136 | + | 0.997030i | \(0.524538\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −125.853 | −0.00761195 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 790.390 | 0.0475850 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16869.8 | 1.01098 | 0.505488 | − | 0.862833i | \(-0.331312\pi\) | ||||
0.505488 | + | 0.862833i | \(0.331312\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8829.51 | −0.526713 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5817.75 | −0.345467 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7724.65 | 0.456616 | 0.228308 | − | 0.973589i | \(-0.426681\pi\) | ||||
0.228308 | + | 0.973589i | \(0.426681\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6387.26 | −0.375848 | −0.187924 | − | 0.982184i | \(-0.560176\pi\) | ||||
−0.187924 | + | 0.982184i | \(0.560176\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2836.79 | 0.166172 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1446.42 | 0.0843453 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1483.80 | −0.0861364 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10058.5 | 0.581291 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −274.965 | −0.0158196 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14558.1 | 0.833837 | 0.416919 | − | 0.908944i | \(-0.363110\pi\) | ||||
0.416919 | + | 0.908944i | \(0.363110\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2161.27 | 0.123240 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32914.0 | 1.86852 | 0.934259 | − | 0.356595i | \(-0.116063\pi\) | ||||
0.934259 | + | 0.356595i | \(0.116063\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1080.16 | −0.0610497 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3018.24 | −0.169837 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −27334.4 | −1.53137 | −0.765683 | − | 0.643218i | \(-0.777599\pi\) | ||||
−0.765683 | + | 0.643218i | \(0.777599\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15199.4 | −0.847796 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4652.46 | 0.258373 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10576.2 | 0.584794 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25255.2 | −1.39038 | −0.695190 | − | 0.718826i | \(-0.744680\pi\) | ||||
−0.695190 | + | 0.718826i | \(0.744680\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 44.3961 | 0.00243358 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7797.07 | −0.425554 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1247.23 | −0.0677796 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1776.64 | −0.0961357 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16418.5 | −0.884620 | −0.442310 | − | 0.896862i | \(-0.645841\pi\) | ||||
−0.442310 | + | 0.896862i | \(0.645841\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4310.50 | 0.231257 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12228.6 | −0.653269 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1162.42 | −0.0618351 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13186.2 | 0.698475 | 0.349238 | − | 0.937034i | \(-0.386441\pi\) | ||||
0.349238 | + | 0.937034i | \(0.386441\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9427.53 | 0.497271 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −221.531 | −0.0116359 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −167.302 | −0.00875071 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15289.7 | 0.796378 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17244.2 | −0.894438 | −0.447219 | − | 0.894425i | \(-0.647585\pi\) | ||||
−0.447219 | + | 0.894425i | \(0.647585\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 297.100 | 0.0153461 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13498.3 | 0.694340 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 20179.4 | 1.03371 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3297.69 | −0.168232 | −0.0841160 | − | 0.996456i | \(-0.526807\pi\) | ||||
−0.0841160 | + | 0.996456i | \(0.526807\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6785.50 | −0.343325 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14191.5 | −0.715112 | −0.357556 | − | 0.933892i | \(-0.616390\pi\) | ||||
−0.357556 | + | 0.933892i | \(0.616390\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −985.591 | −0.0494613 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −246.040 | −0.0122971 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31437.7 | 1.56489 | 0.782446 | − | 0.622718i | \(-0.213972\pi\) | ||||
0.782446 | + | 0.622718i | \(0.213972\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3273.83 | 0.162304 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9095.98 | −0.449124 | −0.224562 | − | 0.974460i | \(-0.572095\pi\) | ||||
−0.224562 | + | 0.974460i | \(0.572095\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 362.506 | 0.0178271 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2509.37 | −0.122909 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2054.29 | −0.100216 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19791.9 | −0.961676 | −0.480838 | − | 0.876810i | \(-0.659667\pi\) | ||||
−0.480838 | + | 0.876810i | \(0.659667\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4808.25 | −0.232699 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5779.54 | −0.278595 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11194.5 | −0.537479 | −0.268739 | − | 0.963213i | \(-0.586607\pi\) | ||||
−0.268739 | + | 0.963213i | \(0.586607\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12.4434 | −0.000595080 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24445.6 | 1.16446 | 0.582230 | − | 0.813024i | \(-0.302180\pi\) | ||||
0.582230 | + | 0.813024i | \(0.302180\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8232.10 | 0.390592 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1611.42 | 0.0761583 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6323.79 | 0.297704 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33296.7 | 1.56139 | 0.780695 | − | 0.624912i | \(-0.214865\pi\) | ||||
0.780695 | + | 0.624912i | \(0.214865\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14861.5 | 0.694192 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31129.8 | 1.44846 | 0.724230 | − | 0.689559i | \(-0.242195\pi\) | ||||
0.724230 | + | 0.689559i | \(0.242195\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3012.78 | 0.139641 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2937.18 | −0.135612 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1439.38 | −0.0662018 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 245.571 | 0.0112513 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6806.54 | 0.310659 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9787.15 | −0.444992 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22918.3 | 1.03805 | 0.519027 | − | 0.854758i | \(-0.326294\pi\) | ||||
0.519027 | + | 0.854758i | \(0.326294\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11026.2 | 0.497520 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1277.76 | −0.0574359 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13816.3 | 0.618704 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6007.77 | 0.268017 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −40462.6 | −1.79832 | −0.899158 | − | 0.437624i | \(-0.855820\pi\) | ||||
−0.899158 | + | 0.437624i | \(0.855820\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16235.4 | 0.718857 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3953.78 | 0.174407 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −455.529 | −0.0200190 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 276.242 | 0.0120947 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5968.93 | 0.260367 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8286.03 | −0.360100 | −0.180050 | − | 0.983657i | \(-0.557626\pi\) | ||||
−0.180050 | + | 0.983657i | \(0.557626\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15527.8 | −0.672323 | −0.336162 | − | 0.941804i | \(-0.609129\pi\) | ||||
−0.336162 | + | 0.941804i | \(0.609129\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4916.54 | −0.212092 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7159.09 | −0.307696 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7830.87 | −0.335334 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2230.79 | −0.0951773 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13165.6 | 0.559663 | 0.279831 | − | 0.960049i | \(-0.409721\pi\) | ||||
0.279831 | + | 0.960049i | \(0.409721\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9659.67 | 0.409131 | 0.204565 | − | 0.978853i | \(-0.434422\pi\) | ||||
0.204565 | + | 0.978853i | \(0.434422\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 169.227 | 0.00714150 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31937.7 | 1.34290 | 0.671452 | − | 0.741048i | \(-0.265671\pi\) | ||||
0.671452 | + | 0.741048i | \(0.265671\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29987.5 | −1.25635 | −0.628173 | − | 0.778074i | \(-0.716197\pi\) | ||||
−0.628173 | + | 0.778074i | \(0.716197\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23432.6 | −0.978181 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1308.53 | 0.0544272 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13964.9 | −0.578775 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1016.22 | 0.0419660 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25864.3 | −1.06428 | −0.532141 | − | 0.846656i | \(-0.678613\pi\) | ||||
−0.532141 | + | 0.846656i | \(0.678613\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 39162.4 | 1.60574 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9055.01 | −0.369954 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6323.70 | −0.257446 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9313.52 | −0.377823 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −22044.4 | −0.891121 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 823.236 | 0.0331612 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9652.50 | 0.387451 | 0.193725 | − | 0.981056i | \(-0.437943\pi\) | ||||
0.193725 | + | 0.981056i | \(0.437943\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1859.68 | 0.0743855 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7058.37 | 0.281341 | 0.140671 | − | 0.990056i | \(-0.455074\pi\) | ||||
0.140671 | + | 0.990056i | \(0.455074\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5146.18 | 0.204407 | 0.102203 | − | 0.994764i | \(-0.467411\pi\) | ||||
0.102203 | + | 0.994764i | \(0.467411\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 980.799 | 0.0388218 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23233.4 | −0.916426 | −0.458213 | − | 0.888842i | \(-0.651510\pi\) | ||||
−0.458213 | + | 0.888842i | \(0.651510\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14818.5 | −0.582479 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12599.6 | 0.493546 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 738.176 | 0.0288158 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12362.9 | 0.480941 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1388.78 | −0.0538408 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9623.45 | −0.371808 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17998.3 | −0.692997 | −0.346498 | − | 0.938051i | \(-0.612629\pi\) | ||||
−0.346498 | + | 0.938051i | \(0.612629\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12635.7 | 0.484861 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10400.3 | 0.397723 | 0.198861 | − | 0.980028i | \(-0.436276\pi\) | ||||
0.198861 | + | 0.980028i | \(0.436276\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35365.0 | 1.34782 | 0.673912 | − | 0.738812i | \(-0.264613\pi\) | ||||
0.673912 | + | 0.738812i | \(0.264613\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3592.19 | 0.136441 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −39216.8 | −1.48452 | −0.742261 | − | 0.670111i | \(-0.766246\pi\) | ||||
−0.742261 | + | 0.670111i | \(0.766246\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9622.13 | 0.363010 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 57.0807 | 0.00214621 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18736.6 | 0.702123 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6267.01 | −0.234059 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 625.249 | 0.0232736 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9488.21 | 0.352002 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7976.28 | −0.294926 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5335.97 | 0.196645 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −39.2373 | −0.00144121 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42804.2 | 1.56702 | 0.783511 | − | 0.621378i | \(-0.213427\pi\) | ||||
0.783511 | + | 0.621378i | \(0.213427\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1494.54 | −0.0545334 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32448.5 | 1.18010 | 0.590048 | − | 0.807368i | \(-0.299109\pi\) | ||||
0.590048 | + | 0.807368i | \(0.299109\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −196.484 | −0.00712230 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7848.28 | 0.283559 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9218.39 | −0.331972 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21991.6 | −0.789375 | −0.394688 | − | 0.918815i | \(-0.629147\pi\) | ||||
−0.394688 | + | 0.918815i | \(0.629147\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22659.5 | −0.810700 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12339.3 | −0.440037 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11195.8 | −0.397964 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 381.985 | 0.0135340 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1281.57 | −0.0452606 | −0.0226303 | − | 0.999744i | \(-0.507204\pi\) | ||||
−0.0226303 | + | 0.999744i | \(0.507204\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1510.12 | 0.0531603 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7969.73 | 0.279654 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 126.174 | 0.00441320 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23582.2 | 0.822194 | 0.411097 | − | 0.911592i | \(-0.365146\pi\) | ||||
0.411097 | + | 0.911592i | \(0.365146\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 32457.5 | 1.12802 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27439.5 | −0.950586 | −0.475293 | − | 0.879828i | \(-0.657658\pi\) | ||||
−0.475293 | + | 0.879828i | \(0.657658\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −274.899 | −0.00949305 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1267.19 | −0.0436208 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17543.6 | 0.601996 | 0.300998 | − | 0.953625i | \(-0.402680\pi\) | ||||
0.300998 | + | 0.953625i | \(0.402680\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22889.2 | 0.782945 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5114.74 | 0.174403 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13884.1 | −0.471930 | −0.235965 | − | 0.971762i | \(-0.575825\pi\) | ||||
−0.235965 | + | 0.971762i | \(0.575825\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15939.3 | 0.540088 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 532.952 | 0.0180020 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15868.9 | −0.534340 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28374.4 | −0.952449 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2641.23 | −0.0883825 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −14977.3 | −0.499623 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39807.7 | 1.32382 | 0.661908 | − | 0.749585i | \(-0.269747\pi\) | ||||
0.661908 | + | 0.749585i | \(0.269747\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2469.02 | −0.0818538 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20963.7 | −0.692851 | −0.346425 | − | 0.938077i | \(-0.612605\pi\) | ||||
−0.346425 | + | 0.938077i | \(0.612605\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8140.48 | −0.268214 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8503.25 | −0.279305 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −38199.7 | −1.25089 | −0.625443 | − | 0.780270i | \(-0.715082\pi\) | ||||
−0.625443 | + | 0.780270i | \(0.715082\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 309.581 | 0.0101065 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10584.1 | 0.344470 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18877.5 | 0.612510 | 0.306255 | − | 0.951950i | \(-0.400924\pi\) | ||||
0.306255 | + | 0.951950i | \(0.400924\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15816.1 | −0.511616 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12767.2 | −0.411736 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1495.57 | −0.0480854 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1894.95 | −0.0607418 | −0.0303709 | − | 0.999539i | \(-0.509669\pi\) | ||||
−0.0303709 | + | 0.999539i | \(0.509669\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 225.343 | 0.00720146 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2465.71 | 0.0785611 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −60576.0 | −1.92424 | −0.962118 | − | 0.272635i | \(-0.912105\pi\) | ||||
−0.962118 | + | 0.272635i | \(0.912105\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3776.38 | −0.119599 |
(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 | 1344.4.a.be.1.2 | 2 | ||
4.3 | odd | 2 | 1344.4.a.bm.1.2 | 2 | |||
8.3 | odd | 2 | 672.4.a.h.1.1 | ✓ | 2 | ||
8.5 | even | 2 | 672.4.a.m.1.1 | yes | 2 | ||
24.5 | odd | 2 | 2016.4.a.j.1.2 | 2 | |||
24.11 | even | 2 | 2016.4.a.i.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.4.a.h.1.1 | ✓ | 2 | 8.3 | odd | 2 | ||
672.4.a.m.1.1 | yes | 2 | 8.5 | even | 2 | ||
1344.4.a.be.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1344.4.a.bm.1.2 | 2 | 4.3 | odd | 2 | |||
2016.4.a.i.1.2 | 2 | 24.11 | even | 2 | |||
2016.4.a.j.1.2 | 2 | 24.5 | odd | 2 |