Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [414,4,Mod(1,414)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(414, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("414.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 414 = 2 \cdot 3^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 414.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: | \(24.4267907424\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - 2 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 138) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 414.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 7.31371 | 0.654158 | 0.327079 | − | 0.944997i | \(-0.393936\pi\) | ||||
0.327079 | + | 0.944997i | \(0.393936\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 17.3137 | 0.934852 | 0.467426 | − | 0.884032i | \(-0.345181\pi\) | ||||
0.467426 | + | 0.884032i | \(0.345181\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −14.6274 | −0.462560 | ||||||||
\(11\) | −69.2548 | −1.89828 | −0.949142 | − | 0.314849i | \(-0.898046\pi\) | ||||
−0.949142 | + | 0.314849i | \(0.898046\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.25483 | −0.0694407 | −0.0347203 | − | 0.999397i | \(-0.511054\pi\) | ||||
−0.0347203 | + | 0.999397i | \(0.511054\pi\) | |||||||
\(14\) | −34.6274 | −0.661040 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −85.9411 | −1.22610 | −0.613052 | − | 0.790042i | \(-0.710059\pi\) | ||||
−0.613052 | + | 0.790042i | \(0.710059\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −19.9411 | −0.240779 | −0.120390 | − | 0.992727i | \(-0.538414\pi\) | ||||
−0.120390 | + | 0.992727i | \(0.538414\pi\) | |||||||
\(20\) | 29.2548 | 0.327079 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 138.510 | 1.34229 | ||||||||
\(23\) | −23.0000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −71.5097 | −0.572077 | ||||||||
\(26\) | 6.50967 | 0.0491020 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 69.2548 | 0.467426 | ||||||||
\(29\) | 47.1371 | 0.301832 | 0.150916 | − | 0.988547i | \(-0.451778\pi\) | ||||
0.150916 | + | 0.988547i | \(0.451778\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 109.137 | 0.632310 | 0.316155 | − | 0.948708i | \(-0.397608\pi\) | ||||
0.316155 | + | 0.948708i | \(0.397608\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 171.882 | 0.866987 | ||||||||
\(35\) | 126.627 | 0.611541 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 86.9016 | 0.386123 | 0.193061 | − | 0.981187i | \(-0.438158\pi\) | ||||
0.193061 | + | 0.981187i | \(0.438158\pi\) | |||||||
\(38\) | 39.8823 | 0.170257 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −58.5097 | −0.231280 | ||||||||
\(41\) | −65.7645 | −0.250505 | −0.125252 | − | 0.992125i | \(-0.539974\pi\) | ||||
−0.125252 | + | 0.992125i | \(0.539974\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −398.451 | −1.41310 | −0.706549 | − | 0.707665i | \(-0.749749\pi\) | ||||
−0.706549 | + | 0.707665i | \(0.749749\pi\) | |||||||
\(44\) | −277.019 | −0.949142 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 46.0000 | 0.147442 | ||||||||
\(47\) | 164.118 | 0.509341 | 0.254671 | − | 0.967028i | \(-0.418033\pi\) | ||||
0.254671 | + | 0.967028i | \(0.418033\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −43.2355 | −0.126051 | ||||||||
\(50\) | 143.019 | 0.404520 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −13.0193 | −0.0347203 | ||||||||
\(53\) | −631.862 | −1.63760 | −0.818801 | − | 0.574077i | \(-0.805361\pi\) | ||||
−0.818801 | + | 0.574077i | \(0.805361\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −506.510 | −1.24178 | ||||||||
\(56\) | −138.510 | −0.330520 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −94.2742 | −0.213428 | ||||||||
\(59\) | 665.450 | 1.46838 | 0.734188 | − | 0.678946i | \(-0.237563\pi\) | ||||
0.734188 | + | 0.678946i | \(0.237563\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −490.431 | −1.02940 | −0.514698 | − | 0.857371i | \(-0.672096\pi\) | ||||
−0.514698 | + | 0.857371i | \(0.672096\pi\) | |||||||
\(62\) | −218.274 | −0.447110 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −23.8049 | −0.0454252 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 83.4701 | 0.152201 | 0.0761007 | − | 0.997100i | \(-0.475753\pi\) | ||||
0.0761007 | + | 0.997100i | \(0.475753\pi\) | |||||||
\(68\) | −343.765 | −0.613052 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −253.255 | −0.432425 | ||||||||
\(71\) | −969.568 | −1.62066 | −0.810328 | − | 0.585977i | \(-0.800711\pi\) | ||||
−0.810328 | + | 0.585977i | \(0.800711\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 462.313 | 0.741228 | 0.370614 | − | 0.928787i | \(-0.379147\pi\) | ||||
0.370614 | + | 0.928787i | \(0.379147\pi\) | |||||||
\(74\) | −173.803 | −0.273030 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −79.7645 | −0.120390 | ||||||||
\(77\) | −1199.06 | −1.77461 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −857.314 | −1.22095 | −0.610477 | − | 0.792034i | \(-0.709022\pi\) | ||||
−0.610477 | + | 0.792034i | \(0.709022\pi\) | |||||||
\(80\) | 117.019 | 0.163539 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 131.529 | 0.177134 | ||||||||
\(83\) | 1195.61 | 1.58114 | 0.790571 | − | 0.612370i | \(-0.209784\pi\) | ||||
0.790571 | + | 0.612370i | \(0.209784\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −628.548 | −0.802066 | ||||||||
\(86\) | 796.902 | 0.999211 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 554.039 | 0.671145 | ||||||||
\(89\) | 382.960 | 0.456109 | 0.228055 | − | 0.973648i | \(-0.426764\pi\) | ||||
0.228055 | + | 0.973648i | \(0.426764\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −56.3532 | −0.0649168 | ||||||||
\(92\) | −92.0000 | −0.104257 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −328.235 | −0.360159 | ||||||||
\(95\) | −145.844 | −0.157508 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −817.724 | −0.855952 | −0.427976 | − | 0.903790i | \(-0.640773\pi\) | ||||
−0.427976 | + | 0.903790i | \(0.640773\pi\) | |||||||
\(98\) | 86.4710 | 0.0891315 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −286.039 | −0.286039 | ||||||||
\(101\) | −530.548 | −0.522688 | −0.261344 | − | 0.965246i | \(-0.584166\pi\) | ||||
−0.261344 | + | 0.965246i | \(0.584166\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1427.12 | −1.36522 | −0.682612 | − | 0.730781i | \(-0.739156\pi\) | ||||
−0.682612 | + | 0.730781i | \(0.739156\pi\) | |||||||
\(104\) | 26.0387 | 0.0245510 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1263.72 | 1.15796 | ||||||||
\(107\) | −1085.49 | −0.980732 | −0.490366 | − | 0.871517i | \(-0.663137\pi\) | ||||
−0.490366 | + | 0.871517i | \(0.663137\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −100.432 | −0.0882539 | −0.0441269 | − | 0.999026i | \(-0.514051\pi\) | ||||
−0.0441269 | + | 0.999026i | \(0.514051\pi\) | |||||||
\(110\) | 1013.02 | 0.878069 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 277.019 | 0.233713 | ||||||||
\(113\) | −2289.43 | −1.90594 | −0.952971 | − | 0.303062i | \(-0.901991\pi\) | ||||
−0.952971 | + | 0.303062i | \(0.901991\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −168.215 | −0.136401 | ||||||||
\(116\) | 188.548 | 0.150916 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1330.90 | −1.03830 | ||||||||
\(119\) | −1487.96 | −1.14623 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3465.23 | 2.60348 | ||||||||
\(122\) | 980.861 | 0.727893 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 436.548 | 0.316155 | ||||||||
\(125\) | −1437.21 | −1.02839 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 313.531 | 0.219066 | 0.109533 | − | 0.993983i | \(-0.465065\pi\) | ||||
0.109533 | + | 0.993983i | \(0.465065\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 47.6098 | 0.0321204 | ||||||||
\(131\) | 517.568 | 0.345192 | 0.172596 | − | 0.984993i | \(-0.444785\pi\) | ||||
0.172596 | + | 0.984993i | \(0.444785\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −345.255 | −0.225093 | ||||||||
\(134\) | −166.940 | −0.107623 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 687.529 | 0.433494 | ||||||||
\(137\) | 435.038 | 0.271298 | 0.135649 | − | 0.990757i | \(-0.456688\pi\) | ||||
0.135649 | + | 0.990757i | \(0.456688\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 124.626 | 0.0760476 | 0.0380238 | − | 0.999277i | \(-0.487894\pi\) | ||||
0.0380238 | + | 0.999277i | \(0.487894\pi\) | |||||||
\(140\) | 506.510 | 0.305771 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1939.14 | 1.14598 | ||||||||
\(143\) | 225.413 | 0.131818 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 344.747 | 0.197446 | ||||||||
\(146\) | −924.626 | −0.524127 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 347.606 | 0.193061 | ||||||||
\(149\) | 2790.29 | 1.53416 | 0.767079 | − | 0.641553i | \(-0.221709\pi\) | ||||
0.767079 | + | 0.641553i | \(0.221709\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2883.14 | 1.55382 | 0.776908 | − | 0.629614i | \(-0.216787\pi\) | ||||
0.776908 | + | 0.629614i | \(0.216787\pi\) | |||||||
\(152\) | 159.529 | 0.0851284 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2398.12 | 1.25484 | ||||||||
\(155\) | 798.197 | 0.413630 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1524.86 | 0.775142 | 0.387571 | − | 0.921840i | \(-0.373314\pi\) | ||||
0.387571 | + | 0.921840i | \(0.373314\pi\) | |||||||
\(158\) | 1714.63 | 0.863345 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −234.039 | −0.115640 | ||||||||
\(161\) | −398.215 | −0.194930 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1796.74 | −0.863385 | −0.431693 | − | 0.902021i | \(-0.642083\pi\) | ||||
−0.431693 | + | 0.902021i | \(0.642083\pi\) | |||||||
\(164\) | −263.058 | −0.125252 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2391.21 | −1.11804 | ||||||||
\(167\) | 1339.61 | 0.620730 | 0.310365 | − | 0.950618i | \(-0.399549\pi\) | ||||
0.310365 | + | 0.950618i | \(0.399549\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2186.41 | −0.995178 | ||||||||
\(170\) | 1257.10 | 0.567147 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1593.80 | −0.706549 | ||||||||
\(173\) | 1753.65 | 0.770678 | 0.385339 | − | 0.922775i | \(-0.374085\pi\) | ||||
0.385339 | + | 0.922775i | \(0.374085\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1238.10 | −0.534808 | ||||||||
\(176\) | −1108.08 | −0.474571 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −765.921 | −0.322518 | ||||||||
\(179\) | 4375.18 | 1.82690 | 0.913452 | − | 0.406945i | \(-0.133406\pi\) | ||||
0.913452 | + | 0.406945i | \(0.133406\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3619.02 | −1.48619 | −0.743093 | − | 0.669188i | \(-0.766642\pi\) | ||||
−0.743093 | + | 0.669188i | \(0.766642\pi\) | |||||||
\(182\) | 112.706 | 0.0459031 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 184.000 | 0.0737210 | ||||||||
\(185\) | 635.573 | 0.252585 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5951.84 | 2.32749 | ||||||||
\(188\) | 656.471 | 0.254671 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 291.687 | 0.111375 | ||||||||
\(191\) | −537.369 | −0.203574 | −0.101787 | − | 0.994806i | \(-0.532456\pi\) | ||||
−0.101787 | + | 0.994806i | \(0.532456\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −334.784 | −0.124861 | −0.0624307 | − | 0.998049i | \(-0.519885\pi\) | ||||
−0.0624307 | + | 0.998049i | \(0.519885\pi\) | |||||||
\(194\) | 1635.45 | 0.605249 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −172.942 | −0.0630255 | ||||||||
\(197\) | 1674.19 | 0.605488 | 0.302744 | − | 0.953072i | \(-0.402097\pi\) | ||||
0.302744 | + | 0.953072i | \(0.402097\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 767.231 | 0.273304 | 0.136652 | − | 0.990619i | \(-0.456366\pi\) | ||||
0.136652 | + | 0.990619i | \(0.456366\pi\) | |||||||
\(200\) | 572.077 | 0.202260 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1061.10 | 0.369597 | ||||||||
\(203\) | 816.118 | 0.282169 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −480.982 | −0.163870 | ||||||||
\(206\) | 2854.23 | 0.965359 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −52.0773 | −0.0173602 | ||||||||
\(209\) | 1381.02 | 0.457067 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4779.40 | −1.55937 | −0.779687 | − | 0.626170i | \(-0.784622\pi\) | ||||
−0.779687 | + | 0.626170i | \(0.784622\pi\) | |||||||
\(212\) | −2527.45 | −0.818801 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2170.98 | 0.693482 | ||||||||
\(215\) | −2914.15 | −0.924389 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1889.57 | 0.591116 | ||||||||
\(218\) | 200.865 | 0.0624049 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2026.04 | −0.620889 | ||||||||
\(221\) | 279.724 | 0.0851415 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −797.410 | −0.239455 | −0.119728 | − | 0.992807i | \(-0.538202\pi\) | ||||
−0.119728 | + | 0.992807i | \(0.538202\pi\) | |||||||
\(224\) | −554.039 | −0.165260 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4578.86 | 1.34770 | ||||||||
\(227\) | 5898.63 | 1.72469 | 0.862347 | − | 0.506317i | \(-0.168994\pi\) | ||||
0.862347 | + | 0.506317i | \(0.168994\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −168.826 | −0.0487176 | −0.0243588 | − | 0.999703i | \(-0.507754\pi\) | ||||
−0.0243588 | + | 0.999703i | \(0.507754\pi\) | |||||||
\(230\) | 336.431 | 0.0964503 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −377.097 | −0.106714 | ||||||||
\(233\) | −4184.67 | −1.17660 | −0.588298 | − | 0.808644i | \(-0.700202\pi\) | ||||
−0.588298 | + | 0.808644i | \(0.700202\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1200.31 | 0.333190 | ||||||||
\(236\) | 2661.80 | 0.734188 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2975.92 | 0.810505 | ||||||||
\(239\) | −2573.96 | −0.696635 | −0.348317 | − | 0.937377i | \(-0.613247\pi\) | ||||
−0.348317 | + | 0.937377i | \(0.613247\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1092.40 | −0.291981 | −0.145990 | − | 0.989286i | \(-0.546637\pi\) | ||||
−0.145990 | + | 0.989286i | \(0.546637\pi\) | |||||||
\(242\) | −6930.46 | −1.84094 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1961.72 | −0.514698 | ||||||||
\(245\) | −316.212 | −0.0824573 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 64.9051 | 0.0167199 | ||||||||
\(248\) | −873.097 | −0.223555 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2874.43 | 0.727179 | ||||||||
\(251\) | 5504.11 | 1.38413 | 0.692065 | − | 0.721836i | \(-0.256701\pi\) | ||||
0.692065 | + | 0.721836i | \(0.256701\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1592.86 | 0.395819 | ||||||||
\(254\) | −627.061 | −0.154903 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −3654.39 | −0.886984 | −0.443492 | − | 0.896278i | \(-0.646260\pi\) | ||||
−0.443492 | + | 0.896278i | \(0.646260\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1504.59 | 0.360968 | ||||||||
\(260\) | −95.2196 | −0.0227126 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1035.14 | −0.244087 | ||||||||
\(263\) | 5352.43 | 1.25492 | 0.627462 | − | 0.778648i | \(-0.284094\pi\) | ||||
0.627462 | + | 0.778648i | \(0.284094\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4621.25 | −1.07125 | ||||||||
\(266\) | 690.510 | 0.159165 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 333.881 | 0.0761007 | ||||||||
\(269\) | −4423.21 | −1.00256 | −0.501279 | − | 0.865286i | \(-0.667137\pi\) | ||||
−0.501279 | + | 0.865286i | \(0.667137\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3179.72 | −0.712747 | −0.356374 | − | 0.934344i | \(-0.615987\pi\) | ||||
−0.356374 | + | 0.934344i | \(0.615987\pi\) | |||||||
\(272\) | −1375.06 | −0.306526 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −870.076 | −0.191836 | ||||||||
\(275\) | 4952.39 | 1.08596 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1135.26 | 0.246249 | 0.123125 | − | 0.992391i | \(-0.460708\pi\) | ||||
0.123125 | + | 0.992391i | \(0.460708\pi\) | |||||||
\(278\) | −249.251 | −0.0537738 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1013.02 | −0.216212 | ||||||||
\(281\) | 2869.86 | 0.609257 | 0.304629 | − | 0.952471i | \(-0.401468\pi\) | ||||
0.304629 | + | 0.952471i | \(0.401468\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 857.505 | 0.180118 | 0.0900590 | − | 0.995936i | \(-0.471294\pi\) | ||||
0.0900590 | + | 0.995936i | \(0.471294\pi\) | |||||||
\(284\) | −3878.27 | −0.810328 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −450.826 | −0.0932094 | ||||||||
\(287\) | −1138.63 | −0.234185 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2472.88 | 0.503333 | ||||||||
\(290\) | −689.494 | −0.139615 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1849.25 | 0.370614 | ||||||||
\(293\) | −8823.46 | −1.75929 | −0.879645 | − | 0.475631i | \(-0.842220\pi\) | ||||
−0.879645 | + | 0.475631i | \(0.842220\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4866.91 | 0.960550 | ||||||||
\(296\) | −695.213 | −0.136515 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5580.58 | −1.08481 | ||||||||
\(299\) | 74.8612 | 0.0144794 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6898.66 | −1.32104 | ||||||||
\(302\) | −5766.27 | −1.09871 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −319.058 | −0.0601948 | ||||||||
\(305\) | −3586.87 | −0.673388 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8123.41 | 1.51019 | 0.755094 | − | 0.655617i | \(-0.227591\pi\) | ||||
0.755094 | + | 0.655617i | \(0.227591\pi\) | |||||||
\(308\) | −4796.23 | −0.887307 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1596.39 | −0.292481 | ||||||||
\(311\) | −3416.66 | −0.622961 | −0.311481 | − | 0.950252i | \(-0.600825\pi\) | ||||
−0.311481 | + | 0.950252i | \(0.600825\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5325.14 | 0.961644 | 0.480822 | − | 0.876818i | \(-0.340338\pi\) | ||||
0.480822 | + | 0.876818i | \(0.340338\pi\) | |||||||
\(314\) | −3049.73 | −0.548108 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3429.25 | −0.610477 | ||||||||
\(317\) | 952.315 | 0.168730 | 0.0843649 | − | 0.996435i | \(-0.473114\pi\) | ||||
0.0843649 | + | 0.996435i | \(0.473114\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3264.47 | −0.572963 | ||||||||
\(320\) | 468.077 | 0.0817697 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 796.431 | 0.137836 | ||||||||
\(323\) | 1713.76 | 0.295221 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 232.752 | 0.0397254 | ||||||||
\(326\) | 3593.49 | 0.610506 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 526.116 | 0.0885668 | ||||||||
\(329\) | 2841.49 | 0.476159 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5728.43 | 0.951248 | 0.475624 | − | 0.879649i | \(-0.342222\pi\) | ||||
0.475624 | + | 0.879649i | \(0.342222\pi\) | |||||||
\(332\) | 4782.43 | 0.790571 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2679.21 | −0.438922 | ||||||||
\(335\) | 610.476 | 0.0995638 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6304.39 | −1.01906 | −0.509528 | − | 0.860454i | \(-0.670180\pi\) | ||||
−0.509528 | + | 0.860454i | \(0.670180\pi\) | |||||||
\(338\) | 4372.81 | 0.703697 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2514.19 | −0.401033 | ||||||||
\(341\) | −7558.27 | −1.20030 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6687.17 | −1.05269 | ||||||||
\(344\) | 3187.61 | 0.499605 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3507.29 | −0.544952 | ||||||||
\(347\) | −9338.30 | −1.44469 | −0.722344 | − | 0.691534i | \(-0.756935\pi\) | ||||
−0.722344 | + | 0.691534i | \(0.756935\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4224.27 | 0.647908 | 0.323954 | − | 0.946073i | \(-0.394988\pi\) | ||||
0.323954 | + | 0.946073i | \(0.394988\pi\) | |||||||
\(350\) | 2476.20 | 0.378166 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2216.15 | 0.335572 | ||||||||
\(353\) | 6291.13 | 0.948564 | 0.474282 | − | 0.880373i | \(-0.342708\pi\) | ||||
0.474282 | + | 0.880373i | \(0.342708\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7091.14 | −1.06016 | ||||||||
\(356\) | 1531.84 | 0.228055 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8750.35 | −1.29182 | ||||||||
\(359\) | −12068.0 | −1.77416 | −0.887079 | − | 0.461618i | \(-0.847269\pi\) | ||||
−0.887079 | + | 0.461618i | \(0.847269\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6461.35 | −0.942025 | ||||||||
\(362\) | 7238.04 | 1.05089 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −225.413 | −0.0324584 | ||||||||
\(365\) | 3381.22 | 0.484880 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8119.00 | 1.15479 | 0.577395 | − | 0.816465i | \(-0.304069\pi\) | ||||
0.577395 | + | 0.816465i | \(0.304069\pi\) | |||||||
\(368\) | −368.000 | −0.0521286 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1271.15 | −0.178605 | ||||||||
\(371\) | −10939.9 | −1.53092 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5256.30 | 0.729654 | 0.364827 | − | 0.931075i | \(-0.381128\pi\) | ||||
0.364827 | + | 0.931075i | \(0.381128\pi\) | |||||||
\(374\) | −11903.7 | −1.64579 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1312.94 | −0.180079 | ||||||||
\(377\) | −153.423 | −0.0209594 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3375.35 | 0.457467 | 0.228734 | − | 0.973489i | \(-0.426542\pi\) | ||||
0.228734 | + | 0.973489i | \(0.426542\pi\) | |||||||
\(380\) | −583.374 | −0.0787539 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1074.74 | 0.143949 | ||||||||
\(383\) | 8034.61 | 1.07193 | 0.535966 | − | 0.844240i | \(-0.319948\pi\) | ||||
0.535966 | + | 0.844240i | \(0.319948\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8769.56 | −1.16088 | ||||||||
\(386\) | 669.568 | 0.0882904 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3270.90 | −0.427976 | ||||||||
\(389\) | −26.5264 | −0.00345743 | −0.00172872 | − | 0.999999i | \(-0.500550\pi\) | ||||
−0.00172872 | + | 0.999999i | \(0.500550\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1976.65 | 0.255661 | ||||||||
\(392\) | 345.884 | 0.0445658 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3348.38 | −0.428145 | ||||||||
\(395\) | −6270.14 | −0.798696 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9160.19 | 1.15803 | 0.579014 | − | 0.815318i | \(-0.303438\pi\) | ||||
0.579014 | + | 0.815318i | \(0.303438\pi\) | |||||||
\(398\) | −1534.46 | −0.193255 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1144.15 | −0.143019 | ||||||||
\(401\) | −4494.80 | −0.559750 | −0.279875 | − | 0.960036i | \(-0.590293\pi\) | ||||
−0.279875 | + | 0.960036i | \(0.590293\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −355.223 | −0.0439080 | ||||||||
\(404\) | −2122.19 | −0.261344 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1632.24 | −0.199523 | ||||||||
\(407\) | −6018.35 | −0.732970 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7988.04 | −0.965729 | −0.482864 | − | 0.875695i | \(-0.660404\pi\) | ||||
−0.482864 | + | 0.875695i | \(0.660404\pi\) | |||||||
\(410\) | 961.965 | 0.115873 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5708.47 | −0.682612 | ||||||||
\(413\) | 11521.4 | 1.37272 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8744.32 | 1.03432 | ||||||||
\(416\) | 104.155 | 0.0122755 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2762.04 | −0.323196 | ||||||||
\(419\) | 12558.9 | 1.46430 | 0.732150 | − | 0.681143i | \(-0.238517\pi\) | ||||
0.732150 | + | 0.681143i | \(0.238517\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12609.7 | −1.45976 | −0.729879 | − | 0.683577i | \(-0.760423\pi\) | ||||
−0.729879 | + | 0.683577i | \(0.760423\pi\) | |||||||
\(422\) | 9558.81 | 1.10264 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5054.90 | 0.578980 | ||||||||
\(425\) | 6145.62 | 0.701427 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8491.17 | −0.962334 | ||||||||
\(428\) | −4341.96 | −0.490366 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5828.31 | 0.653642 | ||||||||
\(431\) | 1715.05 | 0.191673 | 0.0958364 | − | 0.995397i | \(-0.469447\pi\) | ||||
0.0958364 | + | 0.995397i | \(0.469447\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16686.2 | 1.85194 | 0.925969 | − | 0.377601i | \(-0.123251\pi\) | ||||
0.925969 | + | 0.377601i | \(0.123251\pi\) | |||||||
\(434\) | −3779.14 | −0.417982 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −401.729 | −0.0441269 | ||||||||
\(437\) | 458.646 | 0.0502060 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11447.0 | 1.24450 | 0.622249 | − | 0.782819i | \(-0.286219\pi\) | ||||
0.622249 | + | 0.782819i | \(0.286219\pi\) | |||||||
\(440\) | 4052.08 | 0.439035 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −559.448 | −0.0602042 | ||||||||
\(443\) | −12008.1 | −1.28786 | −0.643932 | − | 0.765082i | \(-0.722698\pi\) | ||||
−0.643932 | + | 0.765082i | \(0.722698\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2800.86 | 0.298368 | ||||||||
\(446\) | 1594.82 | 0.169320 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1108.08 | 0.116857 | ||||||||
\(449\) | −3225.83 | −0.339057 | −0.169528 | − | 0.985525i | \(-0.554224\pi\) | ||||
−0.169528 | + | 0.985525i | \(0.554224\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4554.51 | 0.475529 | ||||||||
\(452\) | −9157.72 | −0.952971 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11797.3 | −1.21954 | ||||||||
\(455\) | −412.151 | −0.0424658 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1318.20 | 0.134929 | 0.0674645 | − | 0.997722i | \(-0.478509\pi\) | ||||
0.0674645 | + | 0.997722i | \(0.478509\pi\) | |||||||
\(458\) | 337.652 | 0.0344486 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −672.861 | −0.0682007 | ||||||||
\(461\) | 7837.18 | 0.791787 | 0.395894 | − | 0.918296i | \(-0.370435\pi\) | ||||
0.395894 | + | 0.918296i | \(0.370435\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15812.5 | 1.58719 | 0.793594 | − | 0.608448i | \(-0.208208\pi\) | ||||
0.793594 | + | 0.608448i | \(0.208208\pi\) | |||||||
\(464\) | 754.193 | 0.0754581 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8369.34 | 0.831979 | ||||||||
\(467\) | 8142.16 | 0.806797 | 0.403399 | − | 0.915024i | \(-0.367829\pi\) | ||||
0.403399 | + | 0.915024i | \(0.367829\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1445.18 | 0.142286 | ||||||||
\(470\) | −2400.62 | −0.235601 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5323.60 | −0.519149 | ||||||||
\(473\) | 27594.6 | 2.68246 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1425.98 | 0.137744 | ||||||||
\(476\) | −5951.84 | −0.573114 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5147.92 | 0.492595 | ||||||||
\(479\) | 2216.85 | 0.211463 | 0.105731 | − | 0.994395i | \(-0.466282\pi\) | ||||
0.105731 | + | 0.994395i | \(0.466282\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −282.850 | −0.0268126 | ||||||||
\(482\) | 2184.79 | 0.206462 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 13860.9 | 1.30174 | ||||||||
\(485\) | −5980.60 | −0.559928 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −85.0055 | −0.00790958 | −0.00395479 | − | 0.999992i | \(-0.501259\pi\) | ||||
−0.00395479 | + | 0.999992i | \(0.501259\pi\) | |||||||
\(488\) | 3923.44 | 0.363947 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 632.424 | 0.0583061 | ||||||||
\(491\) | 1200.29 | 0.110322 | 0.0551611 | − | 0.998477i | \(-0.482433\pi\) | ||||
0.0551611 | + | 0.998477i | \(0.482433\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4051.01 | −0.370078 | ||||||||
\(494\) | −129.810 | −0.0118227 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1746.19 | 0.158077 | ||||||||
\(497\) | −16786.8 | −1.51507 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18846.0 | −1.69071 | −0.845353 | − | 0.534208i | \(-0.820610\pi\) | ||||
−0.845353 | + | 0.534208i | \(0.820610\pi\) | |||||||
\(500\) | −5748.86 | −0.514193 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −11008.2 | −0.978727 | ||||||||
\(503\) | 8489.56 | 0.752546 | 0.376273 | − | 0.926509i | \(-0.377205\pi\) | ||||
0.376273 | + | 0.926509i | \(0.377205\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3880.28 | −0.341921 | ||||||||
\(506\) | −3185.72 | −0.279887 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1254.12 | 0.109533 | ||||||||
\(509\) | −7158.36 | −0.623357 | −0.311679 | − | 0.950188i | \(-0.600891\pi\) | ||||
−0.311679 | + | 0.950188i | \(0.600891\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8004.35 | 0.692939 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7308.79 | 0.627192 | ||||||||
\(515\) | −10437.5 | −0.893072 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11365.9 | −0.966874 | ||||||||
\(518\) | −3009.18 | −0.255243 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 190.439 | 0.0160602 | ||||||||
\(521\) | 4283.35 | 0.360186 | 0.180093 | − | 0.983650i | \(-0.442360\pi\) | ||||
0.180093 | + | 0.983650i | \(0.442360\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19831.0 | 1.65803 | 0.829014 | − | 0.559228i | \(-0.188902\pi\) | ||||
0.829014 | + | 0.559228i | \(0.188902\pi\) | |||||||
\(524\) | 2070.27 | 0.172596 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10704.9 | −0.887365 | ||||||||
\(527\) | −9379.36 | −0.775278 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 9242.51 | 0.757489 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1381.02 | −0.112547 | ||||||||
\(533\) | 214.053 | 0.0173952 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7938.96 | −0.641554 | ||||||||
\(536\) | −667.761 | −0.0538114 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8846.43 | 0.708916 | ||||||||
\(539\) | 2994.27 | 0.239281 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15713.7 | −1.24877 | −0.624384 | − | 0.781117i | \(-0.714650\pi\) | ||||
−0.624384 | + | 0.781117i | \(0.714650\pi\) | |||||||
\(542\) | 6359.45 | 0.503988 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2750.12 | 0.216747 | ||||||||
\(545\) | −734.533 | −0.0577320 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21143.1 | 1.65267 | 0.826337 | − | 0.563176i | \(-0.190421\pi\) | ||||
0.826337 | + | 0.563176i | \(0.190421\pi\) | |||||||
\(548\) | 1740.15 | 0.135649 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −9904.78 | −0.767893 | ||||||||
\(551\) | −939.967 | −0.0726750 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14843.3 | −1.14141 | ||||||||
\(554\) | −2270.52 | −0.174125 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 498.503 | 0.0380238 | ||||||||
\(557\) | −3746.75 | −0.285018 | −0.142509 | − | 0.989794i | \(-0.545517\pi\) | ||||
−0.142509 | + | 0.989794i | \(0.545517\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1296.89 | 0.0981264 | ||||||||
\(560\) | 2026.04 | 0.152885 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5739.71 | −0.430810 | ||||||||
\(563\) | 16060.2 | 1.20223 | 0.601116 | − | 0.799162i | \(-0.294723\pi\) | ||||
0.601116 | + | 0.799162i | \(0.294723\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16744.2 | −1.24679 | ||||||||
\(566\) | −1715.01 | −0.127363 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7756.54 | 0.572988 | ||||||||
\(569\) | −17547.1 | −1.29282 | −0.646409 | − | 0.762991i | \(-0.723730\pi\) | ||||
−0.646409 | + | 0.762991i | \(0.723730\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5551.81 | −0.406893 | −0.203446 | − | 0.979086i | \(-0.565214\pi\) | ||||
−0.203446 | + | 0.979086i | \(0.565214\pi\) | |||||||
\(572\) | 901.652 | 0.0659090 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2277.25 | 0.165594 | ||||||||
\(575\) | 1644.72 | 0.119286 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1394.14 | 0.100587 | 0.0502937 | − | 0.998734i | \(-0.483984\pi\) | ||||
0.0502937 | + | 0.998734i | \(0.483984\pi\) | |||||||
\(578\) | −4945.75 | −0.355910 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1378.99 | 0.0987230 | ||||||||
\(581\) | 20700.4 | 1.47814 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 43759.5 | 3.10863 | ||||||||
\(584\) | −3698.50 | −0.262064 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17646.9 | 1.24401 | ||||||||
\(587\) | 26307.6 | 1.84980 | 0.924900 | − | 0.380210i | \(-0.124148\pi\) | ||||
0.924900 | + | 0.380210i | \(0.124148\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2176.32 | −0.152247 | ||||||||
\(590\) | −9733.81 | −0.679211 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1390.43 | 0.0965306 | ||||||||
\(593\) | −10657.9 | −0.738056 | −0.369028 | − | 0.929418i | \(-0.620309\pi\) | ||||
−0.369028 | + | 0.929418i | \(0.620309\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10882.5 | −0.749814 | ||||||||
\(596\) | 11161.2 | 0.767079 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −149.722 | −0.0102385 | ||||||||
\(599\) | −5018.67 | −0.342333 | −0.171166 | − | 0.985242i | \(-0.554754\pi\) | ||||
−0.171166 | + | 0.985242i | \(0.554754\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7715.55 | 0.523667 | 0.261833 | − | 0.965113i | \(-0.415673\pi\) | ||||
0.261833 | + | 0.965113i | \(0.415673\pi\) | |||||||
\(602\) | 13797.3 | 0.934114 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 11532.5 | 0.776908 | ||||||||
\(605\) | 25343.7 | 1.70309 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26998.5 | 1.80533 | 0.902664 | − | 0.430346i | \(-0.141608\pi\) | ||||
0.902664 | + | 0.430346i | \(0.141608\pi\) | |||||||
\(608\) | 638.116 | 0.0425642 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7173.73 | 0.476157 | ||||||||
\(611\) | −534.176 | −0.0353690 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3756.96 | 0.247540 | 0.123770 | − | 0.992311i | \(-0.460501\pi\) | ||||
0.123770 | + | 0.992311i | \(0.460501\pi\) | |||||||
\(614\) | −16246.8 | −1.06786 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9592.46 | 0.627421 | ||||||||
\(617\) | −14186.2 | −0.925632 | −0.462816 | − | 0.886454i | \(-0.653161\pi\) | ||||
−0.462816 | + | 0.886454i | \(0.653161\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25670.2 | −1.66684 | −0.833418 | − | 0.552643i | \(-0.813619\pi\) | ||||
−0.833418 | + | 0.552643i | \(0.813619\pi\) | |||||||
\(620\) | 3192.79 | 0.206815 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6833.32 | 0.440500 | ||||||||
\(623\) | 6630.47 | 0.426395 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1572.66 | −0.100650 | ||||||||
\(626\) | −10650.3 | −0.679985 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6099.45 | 0.387571 | ||||||||
\(629\) | −7468.42 | −0.473427 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −948.530 | −0.0598421 | −0.0299211 | − | 0.999552i | \(-0.509526\pi\) | ||||
−0.0299211 | + | 0.999552i | \(0.509526\pi\) | |||||||
\(632\) | 6858.51 | 0.431672 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1904.63 | −0.119310 | ||||||||
\(635\) | 2293.07 | 0.143304 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 140.724 | 0.00875307 | ||||||||
\(638\) | 6528.94 | 0.405146 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −936.155 | −0.0578199 | ||||||||
\(641\) | 28678.3 | 1.76712 | 0.883560 | − | 0.468318i | \(-0.155140\pi\) | ||||
0.883560 | + | 0.468318i | \(0.155140\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7606.41 | 0.466513 | 0.233256 | − | 0.972415i | \(-0.425062\pi\) | ||||
0.233256 | + | 0.972415i | \(0.425062\pi\) | |||||||
\(644\) | −1592.86 | −0.0974651 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3427.53 | −0.208753 | ||||||||
\(647\) | −546.880 | −0.0332304 | −0.0166152 | − | 0.999862i | \(-0.505289\pi\) | ||||
−0.0166152 | + | 0.999862i | \(0.505289\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −46085.6 | −2.78739 | ||||||||
\(650\) | −465.504 | −0.0280901 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7186.97 | −0.431693 | ||||||||
\(653\) | −2615.66 | −0.156751 | −0.0783756 | − | 0.996924i | \(-0.524973\pi\) | ||||
−0.0783756 | + | 0.996924i | \(0.524973\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3785.34 | 0.225810 | ||||||||
\(656\) | −1052.23 | −0.0626262 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5682.97 | −0.336695 | ||||||||
\(659\) | −5101.12 | −0.301535 | −0.150767 | − | 0.988569i | \(-0.548174\pi\) | ||||
−0.150767 | + | 0.988569i | \(0.548174\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33184.1 | −1.95267 | −0.976334 | − | 0.216268i | \(-0.930611\pi\) | ||||
−0.976334 | + | 0.216268i | \(0.930611\pi\) | |||||||
\(662\) | −11456.9 | −0.672634 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9564.85 | −0.559018 | ||||||||
\(665\) | −2525.09 | −0.147246 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1084.15 | −0.0629364 | ||||||||
\(668\) | 5358.43 | 0.310365 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1220.95 | −0.0704022 | ||||||||
\(671\) | 33964.7 | 1.95409 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22540.9 | −1.29107 | −0.645533 | − | 0.763733i | \(-0.723365\pi\) | ||||
−0.645533 | + | 0.763733i | \(0.723365\pi\) | |||||||
\(674\) | 12608.8 | 0.720582 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8745.62 | −0.497589 | ||||||||
\(677\) | −30165.0 | −1.71246 | −0.856229 | − | 0.516596i | \(-0.827199\pi\) | ||||
−0.856229 | + | 0.516596i | \(0.827199\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14157.8 | −0.800188 | ||||||||
\(680\) | 5028.39 | 0.283573 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 15116.5 | 0.848742 | ||||||||
\(683\) | −417.726 | −0.0234024 | −0.0117012 | − | 0.999932i | \(-0.503725\pi\) | ||||
−0.0117012 | + | 0.999932i | \(0.503725\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3181.74 | 0.177472 | ||||||||
\(686\) | 13374.3 | 0.744365 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6375.21 | −0.353274 | ||||||||
\(689\) | 2056.61 | 0.113716 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5421.98 | −0.298498 | −0.149249 | − | 0.988800i | \(-0.547686\pi\) | ||||
−0.149249 | + | 0.988800i | \(0.547686\pi\) | |||||||
\(692\) | 7014.59 | 0.385339 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 18676.6 | 1.02155 | ||||||||
\(695\) | 911.476 | 0.0497471 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5651.88 | 0.307145 | ||||||||
\(698\) | −8448.54 | −0.458140 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4952.39 | −0.267404 | ||||||||
\(701\) | −14840.0 | −0.799572 | −0.399786 | − | 0.916608i | \(-0.630916\pi\) | ||||
−0.399786 | + | 0.916608i | \(0.630916\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1732.92 | −0.0929703 | ||||||||
\(704\) | −4432.31 | −0.237285 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12582.3 | −0.670736 | ||||||||
\(707\) | −9185.76 | −0.488637 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15302.4 | 0.810569 | 0.405284 | − | 0.914191i | \(-0.367173\pi\) | ||||
0.405284 | + | 0.914191i | \(0.367173\pi\) | |||||||
\(710\) | 14182.3 | 0.749649 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3063.68 | −0.161259 | ||||||||
\(713\) | −2510.15 | −0.131846 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1648.60 | 0.0862298 | ||||||||
\(716\) | 17500.7 | 0.913452 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 24135.9 | 1.25452 | ||||||||
\(719\) | −26125.2 | −1.35508 | −0.677542 | − | 0.735484i | \(-0.736955\pi\) | ||||
−0.677542 | + | 0.735484i | \(0.736955\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24708.7 | −1.27628 | ||||||||
\(722\) | 12922.7 | 0.666112 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −14476.1 | −0.743093 | ||||||||
\(725\) | −3370.76 | −0.172671 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4928.32 | −0.251419 | −0.125709 | − | 0.992067i | \(-0.540121\pi\) | ||||
−0.125709 | + | 0.992067i | \(0.540121\pi\) | |||||||
\(728\) | 450.826 | 0.0229515 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6762.44 | −0.342862 | ||||||||
\(731\) | 34243.3 | 1.73261 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16142.2 | 0.813405 | 0.406703 | − | 0.913561i | \(-0.366679\pi\) | ||||
0.406703 | + | 0.913561i | \(0.366679\pi\) | |||||||
\(734\) | −16238.0 | −0.816560 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 736.000 | 0.0368605 | ||||||||
\(737\) | −5780.71 | −0.288922 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1612.09 | −0.0802457 | −0.0401229 | − | 0.999195i | \(-0.512775\pi\) | ||||
−0.0401229 | + | 0.999195i | \(0.512775\pi\) | |||||||
\(740\) | 2542.29 | 0.126293 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 21879.8 | 1.08252 | ||||||||
\(743\) | 33768.1 | 1.66734 | 0.833668 | − | 0.552265i | \(-0.186236\pi\) | ||||
0.833668 | + | 0.552265i | \(0.186236\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20407.4 | 1.00358 | ||||||||
\(746\) | −10512.6 | −0.515943 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 23807.4 | 1.16375 | ||||||||
\(749\) | −18793.9 | −0.916840 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12656.6 | −0.614977 | −0.307488 | − | 0.951552i | \(-0.599489\pi\) | ||||
−0.307488 | + | 0.951552i | \(0.599489\pi\) | |||||||
\(752\) | 2625.88 | 0.127335 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 306.847 | 0.0148206 | ||||||||
\(755\) | 21086.4 | 1.01644 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35451.3 | −1.70211 | −0.851056 | − | 0.525075i | \(-0.824037\pi\) | ||||
−0.851056 | + | 0.525075i | \(0.824037\pi\) | |||||||
\(758\) | −6750.70 | −0.323478 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1166.75 | 0.0556874 | ||||||||
\(761\) | −4234.99 | −0.201732 | −0.100866 | − | 0.994900i | \(-0.532161\pi\) | ||||
−0.100866 | + | 0.994900i | \(0.532161\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1738.86 | −0.0825043 | ||||||||
\(764\) | −2149.48 | −0.101787 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16069.2 | −0.757970 | ||||||||
\(767\) | −2165.93 | −0.101965 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23381.4 | 1.09643 | 0.548216 | − | 0.836337i | \(-0.315307\pi\) | ||||
0.548216 | + | 0.836337i | \(0.315307\pi\) | |||||||
\(770\) | 17539.1 | 0.820865 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1339.14 | −0.0624307 | ||||||||
\(773\) | −8976.44 | −0.417672 | −0.208836 | − | 0.977951i | \(-0.566967\pi\) | ||||
−0.208836 | + | 0.977951i | \(0.566967\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7804.36 | −0.361730 | ||||||||
\(776\) | 6541.79 | 0.302625 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 53.0528 | 0.00244478 | ||||||||
\(779\) | 1311.42 | 0.0603163 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 67147.2 | 3.07646 | ||||||||
\(782\) | −3953.29 | −0.180779 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −691.768 | −0.0315128 | ||||||||
\(785\) | 11152.4 | 0.507065 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33632.8 | −1.52335 | −0.761677 | − | 0.647957i | \(-0.775624\pi\) | ||||
−0.761677 | + | 0.647957i | \(0.775624\pi\) | |||||||
\(788\) | 6696.77 | 0.302744 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 12540.3 | 0.564764 | ||||||||
\(791\) | −39638.5 | −1.78177 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1596.27 | 0.0714820 | ||||||||
\(794\) | −18320.4 | −0.818849 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3068.92 | 0.136652 | ||||||||
\(797\) | −38371.3 | −1.70537 | −0.852686 | − | 0.522424i | \(-0.825028\pi\) | ||||
−0.852686 | + | 0.522424i | \(0.825028\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14104.5 | −0.624506 | ||||||||
\(800\) | 2288.31 | 0.101130 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8989.60 | 0.395803 | ||||||||
\(803\) | −32017.4 | −1.40706 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2912.43 | −0.127515 | ||||||||
\(806\) | 710.446 | 0.0310476 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4244.39 | 0.184798 | ||||||||
\(809\) | 15249.5 | 0.662722 | 0.331361 | − | 0.943504i | \(-0.392492\pi\) | ||||
0.331361 | + | 0.943504i | \(0.392492\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9708.02 | 0.420339 | 0.210169 | − | 0.977665i | \(-0.432598\pi\) | ||||
0.210169 | + | 0.977665i | \(0.432598\pi\) | |||||||
\(812\) | 3264.47 | 0.141084 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 12036.7 | 0.518288 | ||||||||
\(815\) | −13140.9 | −0.564790 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7945.56 | 0.340245 | ||||||||
\(818\) | 15976.1 | 0.682873 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1923.93 | −0.0819348 | ||||||||
\(821\) | −9028.52 | −0.383797 | −0.191899 | − | 0.981415i | \(-0.561464\pi\) | ||||
−0.191899 | + | 0.981415i | \(0.561464\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42539.1 | 1.80172 | 0.900862 | − | 0.434105i | \(-0.142935\pi\) | ||||
0.900862 | + | 0.434105i | \(0.142935\pi\) | |||||||
\(824\) | 11416.9 | 0.482679 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −23042.8 | −0.970656 | ||||||||
\(827\) | −21526.4 | −0.905134 | −0.452567 | − | 0.891730i | \(-0.649492\pi\) | ||||
−0.452567 | + | 0.891730i | \(0.649492\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38550.4 | 1.61509 | 0.807546 | − | 0.589804i | \(-0.200795\pi\) | ||||
0.807546 | + | 0.589804i | \(0.200795\pi\) | |||||||
\(830\) | −17488.6 | −0.731373 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −208.309 | −0.00868008 | ||||||||
\(833\) | 3715.71 | 0.154552 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9797.49 | 0.406055 | ||||||||
\(836\) | 5524.08 | 0.228534 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −25117.8 | −1.03542 | ||||||||
\(839\) | −30566.4 | −1.25777 | −0.628884 | − | 0.777499i | \(-0.716488\pi\) | ||||
−0.628884 | + | 0.777499i | \(0.716488\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22167.1 | −0.908897 | ||||||||
\(842\) | 25219.3 | 1.03220 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −19117.6 | −0.779687 | ||||||||
\(845\) | −15990.7 | −0.651004 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 59996.0 | 2.43387 | ||||||||
\(848\) | −10109.8 | −0.409401 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −12291.2 | −0.495984 | ||||||||
\(851\) | −1998.74 | −0.0805121 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20617.3 | 0.827576 | 0.413788 | − | 0.910373i | \(-0.364205\pi\) | ||||
0.413788 | + | 0.910373i | \(0.364205\pi\) | |||||||
\(854\) | 16982.3 | 0.680473 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8683.92 | 0.346741 | ||||||||
\(857\) | −1553.09 | −0.0619048 | −0.0309524 | − | 0.999521i | \(-0.509854\pi\) | ||||
−0.0309524 | + | 0.999521i | \(0.509854\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34732.9 | −1.37959 | −0.689797 | − | 0.724003i | \(-0.742300\pi\) | ||||
−0.689797 | + | 0.724003i | \(0.742300\pi\) | |||||||
\(860\) | −11656.6 | −0.462194 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3430.10 | −0.135533 | ||||||||
\(863\) | −9162.01 | −0.361389 | −0.180694 | − | 0.983539i | \(-0.557834\pi\) | ||||
−0.180694 | + | 0.983539i | \(0.557834\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12825.7 | 0.504145 | ||||||||
\(866\) | −33372.5 | −1.30952 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7558.27 | 0.295558 | ||||||||
\(869\) | 59373.1 | 2.31772 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −271.681 | −0.0105690 | ||||||||
\(872\) | 803.459 | 0.0312025 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −917.292 | −0.0355010 | ||||||||
\(875\) | −24883.5 | −0.961390 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5772.11 | −0.222247 | −0.111123 | − | 0.993807i | \(-0.535445\pi\) | ||||
−0.111123 | + | 0.993807i | \(0.535445\pi\) | |||||||
\(878\) | −22894.0 | −0.879993 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8104.15 | −0.310444 | ||||||||
\(881\) | −9412.65 | −0.359955 | −0.179977 | − | 0.983671i | \(-0.557602\pi\) | ||||
−0.179977 | + | 0.983671i | \(0.557602\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45232.2 | −1.72388 | −0.861940 | − | 0.507011i | \(-0.830750\pi\) | ||||
−0.861940 | + | 0.507011i | \(0.830750\pi\) | |||||||
\(884\) | 1118.90 | 0.0425708 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24016.3 | 0.910658 | ||||||||
\(887\) | −31353.8 | −1.18687 | −0.593437 | − | 0.804880i | \(-0.702229\pi\) | ||||
−0.593437 | + | 0.804880i | \(0.702229\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5428.38 | 0.204794 | ||||||||
\(890\) | −5601.72 | −0.210978 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3189.64 | −0.119728 | ||||||||
\(893\) | −3272.69 | −0.122639 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 31998.8 | 1.19508 | ||||||||
\(896\) | −2216.15 | −0.0826301 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6451.66 | 0.239749 | ||||||||
\(899\) | 5144.40 | 0.190851 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 54302.9 | 2.00787 | ||||||||
\(902\) | −9109.02 | −0.336250 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 18315.4 | 0.673852 | ||||||||
\(905\) | −26468.5 | −0.972200 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8652.83 | −0.316772 | −0.158386 | − | 0.987377i | \(-0.550629\pi\) | ||||
−0.158386 | + | 0.987377i | \(0.550629\pi\) | |||||||
\(908\) | 23594.5 | 0.862347 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 824.302 | 0.0300279 | ||||||||
\(911\) | −23107.3 | −0.840370 | −0.420185 | − | 0.907438i | \(-0.638035\pi\) | ||||
−0.420185 | + | 0.907438i | \(0.638035\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −82801.5 | −3.00146 | ||||||||
\(914\) | −2636.39 | −0.0954092 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −675.304 | −0.0243588 | ||||||||
\(917\) | 8961.02 | 0.322703 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42056.1 | −1.50958 | −0.754790 | − | 0.655966i | \(-0.772261\pi\) | ||||
−0.754790 | + | 0.655966i | \(0.772261\pi\) | |||||||
\(920\) | 1345.72 | 0.0482252 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −15674.4 | −0.559878 | ||||||||
\(923\) | 3155.78 | 0.112539 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6214.30 | −0.220892 | ||||||||
\(926\) | −31624.9 | −1.12231 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1508.39 | −0.0533569 | ||||||||
\(929\) | −1263.92 | −0.0446369 | −0.0223185 | − | 0.999751i | \(-0.507105\pi\) | ||||
−0.0223185 | + | 0.999751i | \(0.507105\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 862.164 | 0.0303505 | ||||||||
\(932\) | −16738.7 | −0.588298 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −16284.3 | −0.570492 | ||||||||
\(935\) | 43530.0 | 1.52255 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27756.8 | −0.967743 | −0.483871 | − | 0.875139i | \(-0.660770\pi\) | ||||
−0.483871 | + | 0.875139i | \(0.660770\pi\) | |||||||
\(938\) | −2890.35 | −0.100611 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4801.24 | 0.166595 | ||||||||
\(941\) | 7081.47 | 0.245323 | 0.122662 | − | 0.992449i | \(-0.460857\pi\) | ||||
0.122662 | + | 0.992449i | \(0.460857\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1512.58 | 0.0522338 | ||||||||
\(944\) | 10647.2 | 0.367094 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −55189.3 | −1.89678 | ||||||||
\(947\) | 34048.7 | 1.16836 | 0.584179 | − | 0.811625i | \(-0.301417\pi\) | ||||
0.584179 | + | 0.811625i | \(0.301417\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1504.75 | −0.0514713 | ||||||||
\(950\) | −2851.97 | −0.0974000 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 11903.7 | 0.405252 | ||||||||
\(953\) | 10453.3 | 0.355314 | 0.177657 | − | 0.984092i | \(-0.443148\pi\) | ||||
0.177657 | + | 0.984092i | \(0.443148\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3930.16 | −0.133170 | ||||||||
\(956\) | −10295.8 | −0.348317 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4433.71 | −0.149527 | ||||||||
\(959\) | 7532.12 | 0.253623 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17880.1 | −0.600185 | ||||||||
\(962\) | 565.700 | 0.0189594 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4369.58 | −0.145990 | ||||||||
\(965\) | −2448.51 | −0.0816791 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22280.5 | −0.740945 | −0.370473 | − | 0.928843i | \(-0.620804\pi\) | ||||
−0.370473 | + | 0.928843i | \(0.620804\pi\) | |||||||
\(968\) | −27721.9 | −0.920469 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 11961.2 | 0.395929 | ||||||||
\(971\) | 39430.9 | 1.30319 | 0.651595 | − | 0.758567i | \(-0.274100\pi\) | ||||
0.651595 | + | 0.758567i | \(0.274100\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2157.73 | 0.0710933 | ||||||||
\(974\) | 170.011 | 0.00559292 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7846.89 | −0.257349 | ||||||||
\(977\) | −56586.0 | −1.85297 | −0.926483 | − | 0.376337i | \(-0.877183\pi\) | ||||
−0.926483 | + | 0.376337i | \(0.877183\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −26521.9 | −0.865825 | ||||||||
\(980\) | −1264.85 | −0.0412286 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2400.57 | −0.0780095 | ||||||||
\(983\) | −42422.5 | −1.37647 | −0.688235 | − | 0.725488i | \(-0.741614\pi\) | ||||
−0.688235 | + | 0.725488i | \(0.741614\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12244.5 | 0.396085 | ||||||||
\(986\) | 8102.03 | 0.261685 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 259.620 | 0.00835994 | ||||||||
\(989\) | 9164.37 | 0.294651 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23798.6 | −0.762853 | −0.381426 | − | 0.924399i | \(-0.624567\pi\) | ||||
−0.381426 | + | 0.924399i | \(0.624567\pi\) | |||||||
\(992\) | −3492.39 | −0.111778 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 33573.6 | 1.07132 | ||||||||
\(995\) | 5611.31 | 0.178784 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35708.9 | −1.13431 | −0.567157 | − | 0.823610i | \(-0.691957\pi\) | ||||
−0.567157 | + | 0.823610i | \(0.691957\pi\) | |||||||
\(998\) | 37692.0 | 1.19551 | ||||||||
\(999\) | 0 | 0 |
(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 | 414.4.a.g.1.2 | 2 | ||
3.2 | odd | 2 | 138.4.a.e.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 1104.4.a.p.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
138.4.a.e.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
414.4.a.g.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1104.4.a.p.1.1 | 2 | 12.11 | even | 2 |