Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 6 x^{17} - 11 x^{16} + 123 x^{15} - 35 x^{14} - 982 x^{13} + 988 x^{12} + 3872 x^{11} - 5421 x^{10} - 7882 x^{9} + 13376 x^{8} + 7948 x^{7} - 15795 x^{6} - 3858 x^{5} + \cdots + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2\cdot 5 \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.90615\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.90615 | −1.34785 | −0.673926 | − | 0.738798i | \(-0.735394\pi\) | ||||
−0.673926 | + | 0.738798i | \(0.735394\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.63341 | 0.816707 | ||||||||
\(5\) | −1.97979 | −0.885391 | −0.442695 | − | 0.896672i | \(-0.645978\pi\) | ||||
−0.442695 | + | 0.896672i | \(0.645978\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0.698768 | 0.247052 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.77379 | 1.19338 | ||||||||
\(11\) | 5.17880 | 1.56147 | 0.780734 | − | 0.624863i | \(-0.214845\pi\) | ||||
0.780734 | + | 0.624863i | \(0.214845\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.58823 | −0.440497 | −0.220248 | − | 0.975444i | \(-0.570687\pi\) | ||||
−0.220248 | + | 0.975444i | \(0.570687\pi\) | |||||||
\(14\) | −1.90615 | −0.509440 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.59879 | −1.14970 | ||||||||
\(17\) | 8.13644 | 1.97338 | 0.986688 | − | 0.162624i | \(-0.0519957\pi\) | ||||
0.986688 | + | 0.162624i | \(0.0519957\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.36350 | 1.00106 | 0.500528 | − | 0.865721i | \(-0.333139\pi\) | ||||
0.500528 | + | 0.865721i | \(0.333139\pi\) | |||||||
\(20\) | −3.23382 | −0.723105 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −9.87159 | −2.10463 | ||||||||
\(23\) | 7.89668 | 1.64657 | 0.823286 | − | 0.567627i | \(-0.192138\pi\) | ||||
0.823286 | + | 0.567627i | \(0.192138\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.08042 | −0.216084 | ||||||||
\(26\) | 3.02741 | 0.593725 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.63341 | 0.308686 | ||||||||
\(29\) | −2.09112 | −0.388311 | −0.194155 | − | 0.980971i | \(-0.562197\pi\) | ||||
−0.194155 | + | 0.980971i | \(0.562197\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.621893 | −0.111695 | −0.0558476 | − | 0.998439i | \(-0.517786\pi\) | ||||
−0.0558476 | + | 0.998439i | \(0.517786\pi\) | |||||||
\(32\) | 7.36845 | 1.30257 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −15.5093 | −2.65982 | ||||||||
\(35\) | −1.97979 | −0.334646 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.803128 | 0.132033 | 0.0660167 | − | 0.997819i | \(-0.478971\pi\) | ||||
0.0660167 | + | 0.997819i | \(0.478971\pi\) | |||||||
\(38\) | −8.31749 | −1.34927 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.38342 | −0.218737 | ||||||||
\(41\) | 2.54636 | 0.397674 | 0.198837 | − | 0.980033i | \(-0.436284\pi\) | ||||
0.198837 | + | 0.980033i | \(0.436284\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.6823 | 1.78153 | 0.890764 | − | 0.454467i | \(-0.150170\pi\) | ||||
0.890764 | + | 0.454467i | \(0.150170\pi\) | |||||||
\(44\) | 8.45913 | 1.27526 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −15.0523 | −2.21934 | ||||||||
\(47\) | 10.9388 | 1.59559 | 0.797794 | − | 0.602930i | \(-0.206000\pi\) | ||||
0.797794 | + | 0.602930i | \(0.206000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.05944 | 0.291249 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.59424 | −0.359757 | ||||||||
\(53\) | 11.9325 | 1.63905 | 0.819524 | − | 0.573045i | \(-0.194238\pi\) | ||||
0.819524 | + | 0.573045i | \(0.194238\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.2530 | −1.38251 | ||||||||
\(56\) | 0.698768 | 0.0933768 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.98599 | 0.523386 | ||||||||
\(59\) | −5.22205 | −0.679853 | −0.339927 | − | 0.940452i | \(-0.610402\pi\) | ||||
−0.339927 | + | 0.940452i | \(0.610402\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.63485 | 0.721469 | 0.360735 | − | 0.932669i | \(-0.382526\pi\) | ||||
0.360735 | + | 0.932669i | \(0.382526\pi\) | |||||||
\(62\) | 1.18542 | 0.150549 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.84781 | −0.605976 | ||||||||
\(65\) | 3.14437 | 0.390011 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.63507 | 0.932772 | 0.466386 | − | 0.884581i | \(-0.345556\pi\) | ||||
0.466386 | + | 0.884581i | \(0.345556\pi\) | |||||||
\(68\) | 13.2902 | 1.61167 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.77379 | 0.451054 | ||||||||
\(71\) | 2.26392 | 0.268678 | 0.134339 | − | 0.990935i | \(-0.457109\pi\) | ||||
0.134339 | + | 0.990935i | \(0.457109\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.81158 | 0.446112 | 0.223056 | − | 0.974806i | \(-0.428397\pi\) | ||||
0.223056 | + | 0.974806i | \(0.428397\pi\) | |||||||
\(74\) | −1.53088 | −0.177962 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.12740 | 0.817569 | ||||||||
\(77\) | 5.17880 | 0.590180 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.3567 | 1.39024 | 0.695120 | − | 0.718893i | \(-0.255351\pi\) | ||||
0.695120 | + | 0.718893i | \(0.255351\pi\) | |||||||
\(80\) | 9.10465 | 1.01793 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.85374 | −0.536006 | ||||||||
\(83\) | 1.82793 | 0.200642 | 0.100321 | − | 0.994955i | \(-0.468013\pi\) | ||||
0.100321 | + | 0.994955i | \(0.468013\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16.1085 | −1.74721 | ||||||||
\(86\) | −22.2682 | −2.40124 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.61878 | 0.385763 | ||||||||
\(89\) | −11.2636 | −1.19394 | −0.596971 | − | 0.802263i | \(-0.703629\pi\) | ||||
−0.596971 | + | 0.802263i | \(0.703629\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.58823 | −0.166492 | ||||||||
\(92\) | 12.8986 | 1.34477 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −20.8510 | −2.15062 | ||||||||
\(95\) | −8.63883 | −0.886325 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.9449 | −1.51743 | −0.758713 | − | 0.651425i | \(-0.774172\pi\) | ||||
−0.758713 | + | 0.651425i | \(0.774172\pi\) | |||||||
\(98\) | −1.90615 | −0.192550 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.76477 | −0.176477 | ||||||||
\(101\) | 6.73317 | 0.669975 | 0.334988 | − | 0.942223i | \(-0.391268\pi\) | ||||
0.334988 | + | 0.942223i | \(0.391268\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.36518 | −0.725713 | −0.362856 | − | 0.931845i | \(-0.618198\pi\) | ||||
−0.362856 | + | 0.931845i | \(0.618198\pi\) | |||||||
\(104\) | −1.10981 | −0.108825 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −22.7451 | −2.20920 | ||||||||
\(107\) | −2.36070 | −0.228218 | −0.114109 | − | 0.993468i | \(-0.536401\pi\) | ||||
−0.114109 | + | 0.993468i | \(0.536401\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.6315 | 1.40144 | 0.700720 | − | 0.713436i | \(-0.252862\pi\) | ||||
0.700720 | + | 0.713436i | \(0.252862\pi\) | |||||||
\(110\) | 19.5437 | 1.86342 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.59879 | −0.434544 | ||||||||
\(113\) | −5.00346 | −0.470686 | −0.235343 | − | 0.971912i | \(-0.575621\pi\) | ||||
−0.235343 | + | 0.971912i | \(0.575621\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.6338 | −1.45786 | ||||||||
\(116\) | −3.41566 | −0.317136 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.95402 | 0.916342 | ||||||||
\(119\) | 8.13644 | 0.745866 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.8200 | 1.43818 | ||||||||
\(122\) | −10.7409 | −0.972434 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.01581 | −0.0912223 | ||||||||
\(125\) | 12.0380 | 1.07671 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | −5.49624 | −0.485803 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.99365 | −0.525678 | ||||||||
\(131\) | −7.45485 | −0.651334 | −0.325667 | − | 0.945485i | \(-0.605589\pi\) | ||||
−0.325667 | + | 0.945485i | \(0.605589\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.36350 | 0.378363 | ||||||||
\(134\) | −14.5536 | −1.25724 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.68548 | 0.487526 | ||||||||
\(137\) | 18.5476 | 1.58463 | 0.792315 | − | 0.610112i | \(-0.208876\pi\) | ||||
0.792315 | + | 0.610112i | \(0.208876\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.7225 | −1.41838 | −0.709192 | − | 0.705015i | \(-0.750940\pi\) | ||||
−0.709192 | + | 0.705015i | \(0.750940\pi\) | |||||||
\(140\) | −3.23382 | −0.273308 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.31538 | −0.362138 | ||||||||
\(143\) | −8.22515 | −0.687821 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.13998 | 0.343807 | ||||||||
\(146\) | −7.26546 | −0.601294 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.31184 | 0.107833 | ||||||||
\(149\) | −7.51285 | −0.615477 | −0.307739 | − | 0.951471i | \(-0.599572\pi\) | ||||
−0.307739 | + | 0.951471i | \(0.599572\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.1145 | −1.47414 | −0.737069 | − | 0.675817i | \(-0.763791\pi\) | ||||
−0.737069 | + | 0.675817i | \(0.763791\pi\) | |||||||
\(152\) | 3.04907 | 0.247312 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −9.87159 | −0.795475 | ||||||||
\(155\) | 1.23122 | 0.0988939 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.3027 | −1.06167 | −0.530837 | − | 0.847474i | \(-0.678122\pi\) | ||||
−0.530837 | + | 0.847474i | \(0.678122\pi\) | |||||||
\(158\) | −23.5538 | −1.87384 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −14.5880 | −1.15328 | ||||||||
\(161\) | 7.89668 | 0.622346 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.37885 | −0.499630 | −0.249815 | − | 0.968294i | \(-0.580370\pi\) | ||||
−0.249815 | + | 0.968294i | \(0.580370\pi\) | |||||||
\(164\) | 4.15925 | 0.324783 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.48432 | −0.270435 | ||||||||
\(167\) | −4.71885 | −0.365156 | −0.182578 | − | 0.983191i | \(-0.558444\pi\) | ||||
−0.182578 | + | 0.983191i | \(0.558444\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.4775 | −0.805963 | ||||||||
\(170\) | 30.7052 | 2.35498 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 19.0820 | 1.45499 | ||||||||
\(173\) | 12.6074 | 0.958521 | 0.479261 | − | 0.877673i | \(-0.340905\pi\) | ||||
0.479261 | + | 0.877673i | \(0.340905\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.08042 | −0.0816719 | ||||||||
\(176\) | −23.8162 | −1.79521 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 21.4702 | 1.60926 | ||||||||
\(179\) | −19.5887 | −1.46413 | −0.732064 | − | 0.681235i | \(-0.761443\pi\) | ||||
−0.732064 | + | 0.681235i | \(0.761443\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.2615 | −0.911393 | −0.455696 | − | 0.890135i | \(-0.650610\pi\) | ||||
−0.455696 | + | 0.890135i | \(0.650610\pi\) | |||||||
\(182\) | 3.02741 | 0.224407 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.51795 | 0.406788 | ||||||||
\(185\) | −1.59003 | −0.116901 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 42.1370 | 3.08136 | ||||||||
\(188\) | 17.8676 | 1.30313 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 16.4669 | 1.19464 | ||||||||
\(191\) | 8.08753 | 0.585193 | 0.292597 | − | 0.956236i | \(-0.405481\pi\) | ||||
0.292597 | + | 0.956236i | \(0.405481\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.91124 | −0.497482 | −0.248741 | − | 0.968570i | \(-0.580017\pi\) | ||||
−0.248741 | + | 0.968570i | \(0.580017\pi\) | |||||||
\(194\) | 28.4873 | 2.04527 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.63341 | 0.116672 | ||||||||
\(197\) | 23.8478 | 1.69908 | 0.849542 | − | 0.527521i | \(-0.176878\pi\) | ||||
0.849542 | + | 0.527521i | \(0.176878\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.6886 | −1.75013 | −0.875064 | − | 0.484008i | \(-0.839181\pi\) | ||||
−0.875064 | + | 0.484008i | \(0.839181\pi\) | |||||||
\(200\) | −0.754961 | −0.0533838 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −12.8344 | −0.903028 | ||||||||
\(203\) | −2.09112 | −0.146768 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.04126 | −0.352097 | ||||||||
\(206\) | 14.0392 | 0.978154 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.30394 | 0.506437 | ||||||||
\(209\) | 22.5977 | 1.56312 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.8302 | 1.43401 | 0.717004 | − | 0.697069i | \(-0.245513\pi\) | ||||
0.717004 | + | 0.697069i | \(0.245513\pi\) | |||||||
\(212\) | 19.4906 | 1.33862 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.49985 | 0.307604 | ||||||||
\(215\) | −23.1285 | −1.57735 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.621893 | −0.0422168 | ||||||||
\(218\) | −27.8898 | −1.88893 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −16.7473 | −1.12911 | ||||||||
\(221\) | −12.9226 | −0.869265 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.589818 | −0.0394971 | −0.0197486 | − | 0.999805i | \(-0.506287\pi\) | ||||
−0.0197486 | + | 0.999805i | \(0.506287\pi\) | |||||||
\(224\) | 7.36845 | 0.492325 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.53735 | 0.634415 | ||||||||
\(227\) | −26.8903 | −1.78477 | −0.892385 | − | 0.451275i | \(-0.850969\pi\) | ||||
−0.892385 | + | 0.451275i | \(0.850969\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.08930 | 0.270228 | 0.135114 | − | 0.990830i | \(-0.456860\pi\) | ||||
0.135114 | + | 0.990830i | \(0.456860\pi\) | |||||||
\(230\) | 29.8004 | 1.96498 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.46121 | −0.0959329 | ||||||||
\(233\) | −17.8233 | −1.16764 | −0.583822 | − | 0.811881i | \(-0.698444\pi\) | ||||
−0.583822 | + | 0.811881i | \(0.698444\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −21.6566 | −1.41272 | ||||||||
\(236\) | −8.52977 | −0.555241 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −15.5093 | −1.00532 | ||||||||
\(239\) | −12.7795 | −0.826639 | −0.413319 | − | 0.910586i | \(-0.635631\pi\) | ||||
−0.413319 | + | 0.910586i | \(0.635631\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.622612 | 0.0401060 | 0.0200530 | − | 0.999799i | \(-0.493617\pi\) | ||||
0.0200530 | + | 0.999799i | \(0.493617\pi\) | |||||||
\(242\) | −30.1554 | −1.93846 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.20405 | 0.589229 | ||||||||
\(245\) | −1.97979 | −0.126484 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.93025 | −0.440961 | ||||||||
\(248\) | −0.434558 | −0.0275945 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −22.9462 | −1.45125 | ||||||||
\(251\) | −4.77595 | −0.301455 | −0.150728 | − | 0.988575i | \(-0.548162\pi\) | ||||
−0.150728 | + | 0.988575i | \(0.548162\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 40.8954 | 2.57107 | ||||||||
\(254\) | −1.90615 | −0.119603 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.1723 | 1.26077 | ||||||||
\(257\) | 9.29252 | 0.579651 | 0.289826 | − | 0.957079i | \(-0.406403\pi\) | ||||
0.289826 | + | 0.957079i | \(0.406403\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.803128 | 0.0499040 | ||||||||
\(260\) | 5.13606 | 0.318525 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 14.2101 | 0.877902 | ||||||||
\(263\) | −13.5268 | −0.834101 | −0.417050 | − | 0.908883i | \(-0.636936\pi\) | ||||
−0.417050 | + | 0.908883i | \(0.636936\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −23.6238 | −1.45120 | ||||||||
\(266\) | −8.31749 | −0.509978 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12.4712 | 0.761802 | ||||||||
\(269\) | 4.24141 | 0.258603 | 0.129302 | − | 0.991605i | \(-0.458726\pi\) | ||||
0.129302 | + | 0.991605i | \(0.458726\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.865289 | −0.0525626 | −0.0262813 | − | 0.999655i | \(-0.508367\pi\) | ||||
−0.0262813 | + | 0.999655i | \(0.508367\pi\) | |||||||
\(272\) | −37.4177 | −2.26878 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −35.3546 | −2.13585 | ||||||||
\(275\) | −5.59527 | −0.337408 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −31.0536 | −1.86583 | −0.932914 | − | 0.360100i | \(-0.882743\pi\) | ||||
−0.932914 | + | 0.360100i | \(0.882743\pi\) | |||||||
\(278\) | 31.8756 | 1.91177 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.38342 | −0.0826749 | ||||||||
\(281\) | −30.2059 | −1.80194 | −0.900968 | − | 0.433886i | \(-0.857142\pi\) | ||||
−0.900968 | + | 0.433886i | \(0.857142\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.4665 | −1.03827 | −0.519137 | − | 0.854691i | \(-0.673747\pi\) | ||||
−0.519137 | + | 0.854691i | \(0.673747\pi\) | |||||||
\(284\) | 3.69792 | 0.219431 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 15.6784 | 0.927082 | ||||||||
\(287\) | 2.54636 | 0.150307 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 49.2016 | 2.89421 | ||||||||
\(290\) | −7.89144 | −0.463401 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.22590 | 0.364343 | ||||||||
\(293\) | 19.7297 | 1.15262 | 0.576312 | − | 0.817230i | \(-0.304491\pi\) | ||||
0.576312 | + | 0.817230i | \(0.304491\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.3386 | 0.601935 | ||||||||
\(296\) | 0.561200 | 0.0326191 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 14.3206 | 0.829572 | ||||||||
\(299\) | −12.5418 | −0.725309 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.6823 | 0.673354 | ||||||||
\(302\) | 34.5290 | 1.98692 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −20.0668 | −1.15091 | ||||||||
\(305\) | −11.1558 | −0.638782 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.1755 | 0.694894 | 0.347447 | − | 0.937700i | \(-0.387049\pi\) | ||||
0.347447 | + | 0.937700i | \(0.387049\pi\) | |||||||
\(308\) | 8.45913 | 0.482004 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.34689 | −0.133294 | ||||||||
\(311\) | 33.0092 | 1.87178 | 0.935890 | − | 0.352293i | \(-0.114598\pi\) | ||||
0.935890 | + | 0.352293i | \(0.114598\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 34.5663 | 1.95380 | 0.976902 | − | 0.213686i | \(-0.0685469\pi\) | ||||
0.976902 | + | 0.213686i | \(0.0685469\pi\) | |||||||
\(314\) | 25.3570 | 1.43098 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 20.1837 | 1.13542 | ||||||||
\(317\) | −34.6280 | −1.94490 | −0.972452 | − | 0.233104i | \(-0.925112\pi\) | ||||
−0.972452 | + | 0.233104i | \(0.925112\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.8295 | −0.606335 | ||||||||
\(320\) | 9.59766 | 0.536526 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −15.0523 | −0.838831 | ||||||||
\(323\) | 35.5033 | 1.97546 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.71596 | 0.0951841 | ||||||||
\(326\) | 12.1591 | 0.673428 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.77931 | 0.0982460 | ||||||||
\(329\) | 10.9388 | 0.603076 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.6892 | 1.52194 | 0.760968 | − | 0.648789i | \(-0.224724\pi\) | ||||
0.760968 | + | 0.648789i | \(0.224724\pi\) | |||||||
\(332\) | 2.98577 | 0.163865 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.99484 | 0.492176 | ||||||||
\(335\) | −15.1159 | −0.825868 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.9563 | −1.52288 | −0.761440 | − | 0.648236i | \(-0.775507\pi\) | ||||
−0.761440 | + | 0.648236i | \(0.775507\pi\) | |||||||
\(338\) | 19.9717 | 1.08632 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −26.3118 | −1.42696 | ||||||||
\(341\) | −3.22066 | −0.174409 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 8.16318 | 0.440129 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −24.0316 | −1.29195 | ||||||||
\(347\) | −30.4685 | −1.63563 | −0.817816 | − | 0.575480i | \(-0.804815\pi\) | ||||
−0.817816 | + | 0.575480i | \(0.804815\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.92375 | 0.477677 | 0.238839 | − | 0.971059i | \(-0.423233\pi\) | ||||
0.238839 | + | 0.971059i | \(0.423233\pi\) | |||||||
\(350\) | 2.05944 | 0.110082 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 38.1598 | 2.03392 | ||||||||
\(353\) | 7.92953 | 0.422046 | 0.211023 | − | 0.977481i | \(-0.432320\pi\) | ||||
0.211023 | + | 0.977481i | \(0.432320\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.48210 | −0.237885 | ||||||||
\(356\) | −18.3982 | −0.975101 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 37.3390 | 1.97343 | ||||||||
\(359\) | 29.9988 | 1.58328 | 0.791639 | − | 0.610989i | \(-0.209228\pi\) | ||||
0.791639 | + | 0.610989i | \(0.209228\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.0401162 | 0.00211138 | ||||||||
\(362\) | 23.3723 | 1.22842 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.59424 | −0.135975 | ||||||||
\(365\) | −7.54615 | −0.394984 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.24810 | 0.169549 | 0.0847747 | − | 0.996400i | \(-0.472983\pi\) | ||||
0.0847747 | + | 0.996400i | \(0.472983\pi\) | |||||||
\(368\) | −36.3152 | −1.89306 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.03084 | 0.157566 | ||||||||
\(371\) | 11.9325 | 0.619502 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.4551 | −0.748459 | −0.374230 | − | 0.927336i | \(-0.622093\pi\) | ||||
−0.374230 | + | 0.927336i | \(0.622093\pi\) | |||||||
\(374\) | −80.3196 | −4.15323 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.64368 | 0.394193 | ||||||||
\(377\) | 3.32118 | 0.171050 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.92309 | 0.509715 | 0.254857 | − | 0.966979i | \(-0.417971\pi\) | ||||
0.254857 | + | 0.966979i | \(0.417971\pi\) | |||||||
\(380\) | −14.1108 | −0.723868 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −15.4161 | −0.788754 | ||||||||
\(383\) | 11.7627 | 0.601048 | 0.300524 | − | 0.953774i | \(-0.402838\pi\) | ||||
0.300524 | + | 0.953774i | \(0.402838\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.2530 | −0.522539 | ||||||||
\(386\) | 13.1739 | 0.670533 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −24.4113 | −1.23929 | ||||||||
\(389\) | −5.27688 | −0.267548 | −0.133774 | − | 0.991012i | \(-0.542710\pi\) | ||||
−0.133774 | + | 0.991012i | \(0.542710\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 64.2509 | 3.24931 | ||||||||
\(392\) | 0.698768 | 0.0352931 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −45.4575 | −2.29012 | ||||||||
\(395\) | −24.4638 | −1.23091 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.83225 | 0.393089 | 0.196545 | − | 0.980495i | \(-0.437028\pi\) | ||||
0.196545 | + | 0.980495i | \(0.437028\pi\) | |||||||
\(398\) | 47.0602 | 2.35891 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.96861 | 0.248431 | ||||||||
\(401\) | 5.22847 | 0.261097 | 0.130549 | − | 0.991442i | \(-0.458326\pi\) | ||||
0.130549 | + | 0.991442i | \(0.458326\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.987710 | 0.0492014 | ||||||||
\(404\) | 10.9981 | 0.547174 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.98599 | 0.197821 | ||||||||
\(407\) | 4.15925 | 0.206166 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.44012 | 0.417337 | 0.208668 | − | 0.977986i | \(-0.433087\pi\) | ||||
0.208668 | + | 0.977986i | \(0.433087\pi\) | |||||||
\(410\) | 9.60940 | 0.474575 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −12.0304 | −0.592695 | ||||||||
\(413\) | −5.22205 | −0.256960 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.61893 | −0.177646 | ||||||||
\(416\) | −11.7028 | −0.573778 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −43.0747 | −2.10685 | ||||||||
\(419\) | −11.7497 | −0.574008 | −0.287004 | − | 0.957929i | \(-0.592659\pi\) | ||||
−0.287004 | + | 0.957929i | \(0.592659\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.2927 | −0.745319 | −0.372659 | − | 0.927968i | \(-0.621554\pi\) | ||||
−0.372659 | + | 0.927968i | \(0.621554\pi\) | |||||||
\(422\) | −39.7055 | −1.93283 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.33801 | 0.404930 | ||||||||
\(425\) | −8.79075 | −0.426414 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.63485 | 0.272690 | ||||||||
\(428\) | −3.85600 | −0.186387 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 44.0863 | 2.12603 | ||||||||
\(431\) | −23.8777 | −1.15015 | −0.575074 | − | 0.818102i | \(-0.695027\pi\) | ||||
−0.575074 | + | 0.818102i | \(0.695027\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −38.8940 | −1.86913 | −0.934563 | − | 0.355797i | \(-0.884209\pi\) | ||||
−0.934563 | + | 0.355797i | \(0.884209\pi\) | |||||||
\(434\) | 1.18542 | 0.0569021 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 23.8992 | 1.14457 | ||||||||
\(437\) | 34.4572 | 1.64831 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.95880 | 0.141216 | 0.0706080 | − | 0.997504i | \(-0.477506\pi\) | ||||
0.0706080 | + | 0.997504i | \(0.477506\pi\) | |||||||
\(440\) | −7.16444 | −0.341551 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 24.6324 | 1.17164 | ||||||||
\(443\) | −10.8531 | −0.515646 | −0.257823 | − | 0.966192i | \(-0.583005\pi\) | ||||
−0.257823 | + | 0.966192i | \(0.583005\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 22.2996 | 1.05710 | ||||||||
\(446\) | 1.12428 | 0.0532363 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.84781 | −0.229037 | ||||||||
\(449\) | 19.8143 | 0.935097 | 0.467548 | − | 0.883967i | \(-0.345137\pi\) | ||||
0.467548 | + | 0.883967i | \(0.345137\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.1871 | 0.620955 | ||||||||
\(452\) | −8.17272 | −0.384412 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 51.2569 | 2.40561 | ||||||||
\(455\) | 3.14437 | 0.147410 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.1030 | −1.22105 | −0.610523 | − | 0.791998i | \(-0.709041\pi\) | ||||
−0.610523 | + | 0.791998i | \(0.709041\pi\) | |||||||
\(458\) | −7.79482 | −0.364228 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −25.5365 | −1.19064 | ||||||||
\(461\) | 10.0670 | 0.468867 | 0.234434 | − | 0.972132i | \(-0.424676\pi\) | ||||
0.234434 | + | 0.972132i | \(0.424676\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.8067 | −0.641650 | −0.320825 | − | 0.947138i | \(-0.603960\pi\) | ||||
−0.320825 | + | 0.947138i | \(0.603960\pi\) | |||||||
\(464\) | 9.61661 | 0.446440 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 33.9740 | 1.57381 | ||||||||
\(467\) | 23.7068 | 1.09702 | 0.548510 | − | 0.836144i | \(-0.315195\pi\) | ||||
0.548510 | + | 0.836144i | \(0.315195\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.63507 | 0.352555 | ||||||||
\(470\) | 41.2807 | 1.90414 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.64900 | −0.167959 | ||||||||
\(473\) | 60.5001 | 2.78180 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.71440 | −0.216312 | ||||||||
\(476\) | 13.2902 | 0.609154 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 24.3597 | 1.11419 | ||||||||
\(479\) | 0.638921 | 0.0291930 | 0.0145965 | − | 0.999893i | \(-0.495354\pi\) | ||||
0.0145965 | + | 0.999893i | \(0.495354\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.27556 | −0.0581603 | ||||||||
\(482\) | −1.18679 | −0.0540569 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 25.8406 | 1.17457 | ||||||||
\(485\) | 29.5879 | 1.34352 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.9657 | 0.723473 | 0.361736 | − | 0.932280i | \(-0.382184\pi\) | ||||
0.361736 | + | 0.932280i | \(0.382184\pi\) | |||||||
\(488\) | 3.93745 | 0.178240 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.77379 | 0.170482 | ||||||||
\(491\) | −2.20827 | −0.0996578 | −0.0498289 | − | 0.998758i | \(-0.515868\pi\) | ||||
−0.0498289 | + | 0.998758i | \(0.515868\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.0143 | −0.766284 | ||||||||
\(494\) | 13.2101 | 0.594351 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.85995 | 0.128416 | ||||||||
\(497\) | 2.26392 | 0.101551 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −43.3268 | −1.93957 | −0.969787 | − | 0.243955i | \(-0.921555\pi\) | ||||
−0.969787 | + | 0.243955i | \(0.921555\pi\) | |||||||
\(500\) | 19.6630 | 0.879356 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.10368 | 0.406317 | ||||||||
\(503\) | −30.7833 | −1.37256 | −0.686279 | − | 0.727338i | \(-0.740757\pi\) | ||||
−0.686279 | + | 0.727338i | \(0.740757\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.3303 | −0.593190 | ||||||||
\(506\) | −77.9528 | −3.46542 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.63341 | 0.0724710 | ||||||||
\(509\) | −12.3751 | −0.548517 | −0.274258 | − | 0.961656i | \(-0.588432\pi\) | ||||
−0.274258 | + | 0.961656i | \(0.588432\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.81158 | 0.168615 | ||||||||
\(512\) | −27.4590 | −1.21353 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −17.7129 | −0.781285 | ||||||||
\(515\) | 14.5815 | 0.642539 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 56.6499 | 2.49146 | ||||||||
\(518\) | −1.53088 | −0.0672632 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.19719 | 0.0963530 | ||||||||
\(521\) | −16.4426 | −0.720362 | −0.360181 | − | 0.932882i | \(-0.617285\pi\) | ||||
−0.360181 | + | 0.932882i | \(0.617285\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −35.5760 | −1.55563 | −0.777815 | − | 0.628493i | \(-0.783672\pi\) | ||||
−0.777815 | + | 0.628493i | \(0.783672\pi\) | |||||||
\(524\) | −12.1769 | −0.531949 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 25.7842 | 1.12424 | ||||||||
\(527\) | −5.05999 | −0.220417 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 39.3576 | 1.71120 | ||||||||
\(530\) | 45.0305 | 1.95600 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.12740 | 0.309012 | ||||||||
\(533\) | −4.04421 | −0.175174 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.67370 | 0.202062 | ||||||||
\(536\) | 5.33514 | 0.230443 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.08478 | −0.348559 | ||||||||
\(539\) | 5.17880 | 0.223067 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.04038 | 0.388676 | 0.194338 | − | 0.980935i | \(-0.437744\pi\) | ||||
0.194338 | + | 0.980935i | \(0.437744\pi\) | |||||||
\(542\) | 1.64937 | 0.0708466 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 59.9529 | 2.57046 | ||||||||
\(545\) | −28.9673 | −1.24082 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.9287 | 1.70723 | 0.853614 | − | 0.520906i | \(-0.174406\pi\) | ||||
0.853614 | + | 0.520906i | \(0.174406\pi\) | |||||||
\(548\) | 30.2960 | 1.29418 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 10.6654 | 0.454776 | ||||||||
\(551\) | −9.12459 | −0.388721 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.3567 | 0.525462 | ||||||||
\(554\) | 59.1928 | 2.51486 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −27.3148 | −1.15841 | ||||||||
\(557\) | 11.8703 | 0.502961 | 0.251481 | − | 0.967862i | \(-0.419082\pi\) | ||||
0.251481 | + | 0.967862i | \(0.419082\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.5541 | −0.784757 | ||||||||
\(560\) | 9.10465 | 0.384742 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 57.5771 | 2.42874 | ||||||||
\(563\) | −32.5540 | −1.37199 | −0.685993 | − | 0.727608i | \(-0.740632\pi\) | ||||
−0.685993 | + | 0.727608i | \(0.740632\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.90581 | 0.416741 | ||||||||
\(566\) | 33.2937 | 1.39944 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.58195 | 0.0663773 | ||||||||
\(569\) | 28.7488 | 1.20521 | 0.602607 | − | 0.798038i | \(-0.294129\pi\) | ||||
0.602607 | + | 0.798038i | \(0.294129\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.04241 | 0.169169 | 0.0845847 | − | 0.996416i | \(-0.473044\pi\) | ||||
0.0845847 | + | 0.996416i | \(0.473044\pi\) | |||||||
\(572\) | −13.4351 | −0.561749 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.85374 | −0.202591 | ||||||||
\(575\) | −8.53172 | −0.355797 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.23459 | 0.301180 | 0.150590 | − | 0.988596i | \(-0.451883\pi\) | ||||
0.150590 | + | 0.988596i | \(0.451883\pi\) | |||||||
\(578\) | −93.7858 | −3.90097 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.76231 | 0.280790 | ||||||||
\(581\) | 1.82793 | 0.0758354 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 61.7958 | 2.55932 | ||||||||
\(584\) | 2.66341 | 0.110213 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −37.6079 | −1.55357 | ||||||||
\(587\) | 16.9970 | 0.701543 | 0.350771 | − | 0.936461i | \(-0.385919\pi\) | ||||
0.350771 | + | 0.936461i | \(0.385919\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.71363 | −0.111813 | ||||||||
\(590\) | −19.7069 | −0.811320 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.69342 | −0.151798 | ||||||||
\(593\) | 30.9750 | 1.27199 | 0.635996 | − | 0.771692i | \(-0.280590\pi\) | ||||
0.635996 | + | 0.771692i | \(0.280590\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.1085 | −0.660383 | ||||||||
\(596\) | −12.2716 | −0.502665 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 23.9065 | 0.977610 | ||||||||
\(599\) | 17.4383 | 0.712511 | 0.356256 | − | 0.934389i | \(-0.384053\pi\) | ||||
0.356256 | + | 0.934389i | \(0.384053\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.0703960 | −0.00287151 | −0.00143576 | − | 0.999999i | \(-0.500457\pi\) | ||||
−0.00143576 | + | 0.999999i | \(0.500457\pi\) | |||||||
\(602\) | −22.2682 | −0.907582 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −29.5885 | −1.20394 | ||||||||
\(605\) | −31.3204 | −1.27335 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.9613 | 0.972558 | 0.486279 | − | 0.873804i | \(-0.338354\pi\) | ||||
0.486279 | + | 0.873804i | \(0.338354\pi\) | |||||||
\(608\) | 32.1522 | 1.30394 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 21.2647 | 0.860984 | ||||||||
\(611\) | −17.3734 | −0.702851 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.5676 | −1.11344 | −0.556722 | − | 0.830699i | \(-0.687941\pi\) | ||||
−0.556722 | + | 0.830699i | \(0.687941\pi\) | |||||||
\(614\) | −23.2084 | −0.936615 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.61878 | 0.145805 | ||||||||
\(617\) | −1.96872 | −0.0792576 | −0.0396288 | − | 0.999214i | \(-0.512618\pi\) | ||||
−0.0396288 | + | 0.999214i | \(0.512618\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.3570 | −0.416282 | −0.208141 | − | 0.978099i | \(-0.566741\pi\) | ||||
−0.208141 | + | 0.978099i | \(0.566741\pi\) | |||||||
\(620\) | 2.01109 | 0.0807673 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −62.9205 | −2.52288 | ||||||||
\(623\) | −11.2636 | −0.451268 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18.4306 | −0.737224 | ||||||||
\(626\) | −65.8887 | −2.63344 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −21.7289 | −0.867077 | ||||||||
\(629\) | 6.53461 | 0.260552 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.137455 | 0.00547200 | 0.00273600 | − | 0.999996i | \(-0.499129\pi\) | ||||
0.00273600 | + | 0.999996i | \(0.499129\pi\) | |||||||
\(632\) | 8.63448 | 0.343461 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 66.0063 | 2.62144 | ||||||||
\(635\) | −1.97979 | −0.0785657 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.58823 | −0.0629281 | ||||||||
\(638\) | 20.6427 | 0.817251 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 10.8814 | 0.430126 | ||||||||
\(641\) | 23.6488 | 0.934072 | 0.467036 | − | 0.884238i | \(-0.345322\pi\) | ||||
0.467036 | + | 0.884238i | \(0.345322\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.2588 | −0.522878 | −0.261439 | − | 0.965220i | \(-0.584197\pi\) | ||||
−0.261439 | + | 0.965220i | \(0.584197\pi\) | |||||||
\(644\) | 12.8986 | 0.508274 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −67.6747 | −2.66263 | ||||||||
\(647\) | −41.9389 | −1.64879 | −0.824394 | − | 0.566016i | \(-0.808484\pi\) | ||||
−0.824394 | + | 0.566016i | \(0.808484\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.0440 | −1.06157 | ||||||||
\(650\) | −3.27087 | −0.128294 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.4193 | −0.408051 | ||||||||
\(653\) | −6.75287 | −0.264260 | −0.132130 | − | 0.991232i | \(-0.542182\pi\) | ||||
−0.132130 | + | 0.991232i | \(0.542182\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.7591 | 0.576685 | ||||||||
\(656\) | −11.7101 | −0.457204 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −20.8510 | −0.812857 | ||||||||
\(659\) | 22.6213 | 0.881202 | 0.440601 | − | 0.897703i | \(-0.354765\pi\) | ||||
0.440601 | + | 0.897703i | \(0.354765\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.5296 | 0.681822 | 0.340911 | − | 0.940095i | \(-0.389264\pi\) | ||||
0.340911 | + | 0.940095i | \(0.389264\pi\) | |||||||
\(662\) | −52.7798 | −2.05135 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.27730 | 0.0495689 | ||||||||
\(665\) | −8.63883 | −0.334999 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16.5129 | −0.639382 | ||||||||
\(668\) | −7.70784 | −0.298225 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 28.8131 | 1.11315 | ||||||||
\(671\) | 29.1818 | 1.12655 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.0213 | 1.23433 | 0.617165 | − | 0.786834i | \(-0.288281\pi\) | ||||
0.617165 | + | 0.786834i | \(0.288281\pi\) | |||||||
\(674\) | 53.2890 | 2.05262 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −17.1141 | −0.658236 | ||||||||
\(677\) | 1.28783 | 0.0494953 | 0.0247476 | − | 0.999694i | \(-0.492122\pi\) | ||||
0.0247476 | + | 0.999694i | \(0.492122\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.9449 | −0.573533 | ||||||||
\(680\) | −11.2561 | −0.431651 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.13907 | 0.235077 | ||||||||
\(683\) | 3.44389 | 0.131777 | 0.0658883 | − | 0.997827i | \(-0.479012\pi\) | ||||
0.0658883 | + | 0.997827i | \(0.479012\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −36.7205 | −1.40302 | ||||||||
\(686\) | −1.90615 | −0.0727772 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −53.7242 | −2.04822 | ||||||||
\(689\) | −18.9515 | −0.721995 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.4991 | −1.12220 | −0.561100 | − | 0.827748i | \(-0.689622\pi\) | ||||
−0.561100 | + | 0.827748i | \(0.689622\pi\) | |||||||
\(692\) | 20.5931 | 0.782831 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 58.0775 | 2.20459 | ||||||||
\(695\) | 33.1071 | 1.25582 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.7183 | 0.784760 | ||||||||
\(698\) | −17.0100 | −0.643839 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.76477 | −0.0667020 | ||||||||
\(701\) | 16.7240 | 0.631658 | 0.315829 | − | 0.948816i | \(-0.397717\pi\) | ||||
0.315829 | + | 0.948816i | \(0.397717\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.50445 | 0.132173 | ||||||||
\(704\) | −25.1059 | −0.946213 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15.1149 | −0.568856 | ||||||||
\(707\) | 6.73317 | 0.253227 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −39.6390 | −1.48867 | −0.744337 | − | 0.667804i | \(-0.767234\pi\) | ||||
−0.744337 | + | 0.667804i | \(0.767234\pi\) | |||||||
\(710\) | 8.54355 | 0.320634 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7.87066 | −0.294965 | ||||||||
\(713\) | −4.91089 | −0.183914 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.2841 | 0.608991 | ||||||||
\(716\) | −31.9965 | −1.19576 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −57.1823 | −2.13403 | ||||||||
\(719\) | −22.3146 | −0.832194 | −0.416097 | − | 0.909320i | \(-0.636602\pi\) | ||||
−0.416097 | + | 0.909320i | \(0.636602\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.36518 | −0.274294 | ||||||||
\(722\) | −0.0764676 | −0.00284583 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −20.0282 | −0.744341 | ||||||||
\(725\) | 2.25928 | 0.0839076 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −43.5620 | −1.61563 | −0.807813 | − | 0.589439i | \(-0.799349\pi\) | ||||
−0.807813 | + | 0.589439i | \(0.799349\pi\) | |||||||
\(728\) | −1.10981 | −0.0411321 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 14.3841 | 0.532380 | ||||||||
\(731\) | 95.0520 | 3.51562 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −41.1695 | −1.52063 | −0.760315 | − | 0.649554i | \(-0.774956\pi\) | ||||
−0.760315 | + | 0.649554i | \(0.774956\pi\) | |||||||
\(734\) | −6.19137 | −0.228528 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 58.1863 | 2.14478 | ||||||||
\(737\) | 39.5405 | 1.45649 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.29123 | 0.304998 | 0.152499 | − | 0.988304i | \(-0.451268\pi\) | ||||
0.152499 | + | 0.988304i | \(0.451268\pi\) | |||||||
\(740\) | −2.59718 | −0.0954741 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −22.7451 | −0.834997 | ||||||||
\(743\) | −13.1999 | −0.484256 | −0.242128 | − | 0.970244i | \(-0.577845\pi\) | ||||
−0.242128 | + | 0.970244i | \(0.577845\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.8739 | 0.544938 | ||||||||
\(746\) | 27.5537 | 1.00881 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 68.8272 | 2.51657 | ||||||||
\(749\) | −2.36070 | −0.0862581 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.2608 | −0.374421 | −0.187210 | − | 0.982320i | \(-0.559945\pi\) | ||||
−0.187210 | + | 0.982320i | \(0.559945\pi\) | |||||||
\(752\) | −50.3052 | −1.83444 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.33068 | −0.230550 | ||||||||
\(755\) | 35.8630 | 1.30519 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.2390 | 0.662909 | 0.331455 | − | 0.943471i | \(-0.392461\pi\) | ||||
0.331455 | + | 0.943471i | \(0.392461\pi\) | |||||||
\(758\) | −18.9149 | −0.687021 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.03653 | −0.218968 | ||||||||
\(761\) | 7.43533 | 0.269530 | 0.134765 | − | 0.990878i | \(-0.456972\pi\) | ||||
0.134765 | + | 0.990878i | \(0.456972\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.6315 | 0.529694 | ||||||||
\(764\) | 13.2103 | 0.477931 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −22.4216 | −0.810124 | ||||||||
\(767\) | 8.29383 | 0.299473 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.0750 | 0.363313 | 0.181657 | − | 0.983362i | \(-0.441854\pi\) | ||||
0.181657 | + | 0.983362i | \(0.441854\pi\) | |||||||
\(770\) | 19.5437 | 0.704306 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −11.2889 | −0.406297 | ||||||||
\(773\) | 10.0743 | 0.362346 | 0.181173 | − | 0.983451i | \(-0.442011\pi\) | ||||
0.181173 | + | 0.983451i | \(0.442011\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.671904 | 0.0241355 | ||||||||
\(776\) | −10.4430 | −0.374883 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.0585 | 0.360616 | ||||||||
\(779\) | 11.1110 | 0.398094 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.7244 | 0.419532 | ||||||||
\(782\) | −122.472 | −4.37959 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.59879 | −0.164242 | ||||||||
\(785\) | 26.3367 | 0.939996 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.6451 | −0.415103 | −0.207551 | − | 0.978224i | \(-0.566549\pi\) | ||||
−0.207551 | + | 0.978224i | \(0.566549\pi\) | |||||||
\(788\) | 38.9533 | 1.38765 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 46.6317 | 1.65908 | ||||||||
\(791\) | −5.00346 | −0.177902 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.94946 | −0.317805 | ||||||||
\(794\) | −14.9295 | −0.529827 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −40.3267 | −1.42934 | ||||||||
\(797\) | 2.79683 | 0.0990688 | 0.0495344 | − | 0.998772i | \(-0.484226\pi\) | ||||
0.0495344 | + | 0.998772i | \(0.484226\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 89.0029 | 3.14870 | ||||||||
\(800\) | −7.96100 | −0.281464 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.96625 | −0.351920 | ||||||||
\(803\) | 19.7394 | 0.696590 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15.6338 | −0.551019 | ||||||||
\(806\) | −1.88273 | −0.0663162 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.70492 | 0.165519 | ||||||||
\(809\) | −7.01169 | −0.246518 | −0.123259 | − | 0.992375i | \(-0.539335\pi\) | ||||
−0.123259 | + | 0.992375i | \(0.539335\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −45.4030 | −1.59431 | −0.797157 | − | 0.603772i | \(-0.793664\pi\) | ||||
−0.797157 | + | 0.603772i | \(0.793664\pi\) | |||||||
\(812\) | −3.41566 | −0.119866 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.92815 | −0.277882 | ||||||||
\(815\) | 12.6288 | 0.442368 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 50.9755 | 1.78341 | ||||||||
\(818\) | −16.0881 | −0.562509 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.23446 | −0.287560 | ||||||||
\(821\) | −1.36322 | −0.0475767 | −0.0237883 | − | 0.999717i | \(-0.507573\pi\) | ||||
−0.0237883 | + | 0.999717i | \(0.507573\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.3554 | 1.19755 | 0.598777 | − | 0.800916i | \(-0.295654\pi\) | ||||
0.598777 | + | 0.800916i | \(0.295654\pi\) | |||||||
\(824\) | −5.14655 | −0.179289 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.95402 | 0.346345 | ||||||||
\(827\) | −23.6447 | −0.822208 | −0.411104 | − | 0.911588i | \(-0.634857\pi\) | ||||
−0.411104 | + | 0.911588i | \(0.634857\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −42.8712 | −1.48898 | −0.744489 | − | 0.667635i | \(-0.767307\pi\) | ||||
−0.744489 | + | 0.667635i | \(0.767307\pi\) | |||||||
\(830\) | 6.89823 | 0.239441 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 7.69945 | 0.266930 | ||||||||
\(833\) | 8.13644 | 0.281911 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.34235 | 0.323305 | ||||||||
\(836\) | 36.9114 | 1.27661 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 22.3966 | 0.773679 | ||||||||
\(839\) | 7.78248 | 0.268681 | 0.134340 | − | 0.990935i | \(-0.457108\pi\) | ||||
0.134340 | + | 0.990935i | \(0.457108\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.6272 | −0.849215 | ||||||||
\(842\) | 29.1501 | 1.00458 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 34.0243 | 1.17116 | ||||||||
\(845\) | 20.7433 | 0.713592 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.8200 | 0.543582 | ||||||||
\(848\) | −54.8748 | −1.88441 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 16.7565 | 0.574744 | ||||||||
\(851\) | 6.34205 | 0.217403 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.6778 | 1.11887 | 0.559433 | − | 0.828876i | \(-0.311019\pi\) | ||||
0.559433 | + | 0.828876i | \(0.311019\pi\) | |||||||
\(854\) | −10.7409 | −0.367546 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.64958 | −0.0563815 | ||||||||
\(857\) | 1.01476 | 0.0346634 | 0.0173317 | − | 0.999850i | \(-0.494483\pi\) | ||||
0.0173317 | + | 0.999850i | \(0.494483\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.0846 | −1.02647 | −0.513237 | − | 0.858247i | \(-0.671554\pi\) | ||||
−0.513237 | + | 0.858247i | \(0.671554\pi\) | |||||||
\(860\) | −37.7784 | −1.28823 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 45.5145 | 1.55023 | ||||||||
\(863\) | −28.5365 | −0.971393 | −0.485696 | − | 0.874128i | \(-0.661434\pi\) | ||||
−0.485696 | + | 0.874128i | \(0.661434\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.9600 | −0.848666 | ||||||||
\(866\) | 74.1379 | 2.51931 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.01581 | −0.0344788 | ||||||||
\(869\) | 63.9931 | 2.17082 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.1263 | −0.410883 | ||||||||
\(872\) | 10.2240 | 0.346228 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −65.6806 | −2.22168 | ||||||||
\(875\) | 12.0380 | 0.406958 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.59332 | −0.155105 | −0.0775527 | − | 0.996988i | \(-0.524711\pi\) | ||||
−0.0775527 | + | 0.996988i | \(0.524711\pi\) | |||||||
\(878\) | −5.63993 | −0.190338 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 47.1512 | 1.58947 | ||||||||
\(881\) | 32.7435 | 1.10316 | 0.551578 | − | 0.834123i | \(-0.314026\pi\) | ||||
0.551578 | + | 0.834123i | \(0.314026\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41.4437 | 1.39469 | 0.697346 | − | 0.716735i | \(-0.254364\pi\) | ||||
0.697346 | + | 0.716735i | \(0.254364\pi\) | |||||||
\(884\) | −21.1079 | −0.709935 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 20.6876 | 0.695015 | ||||||||
\(887\) | −29.0254 | −0.974578 | −0.487289 | − | 0.873241i | \(-0.662014\pi\) | ||||
−0.487289 | + | 0.873241i | \(0.662014\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −42.5065 | −1.42482 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.963418 | −0.0322576 | ||||||||
\(893\) | 47.7314 | 1.59727 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 38.7816 | 1.29633 | ||||||||
\(896\) | −5.49624 | −0.183616 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −37.7691 | −1.26037 | ||||||||
\(899\) | 1.30045 | 0.0433725 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 97.0877 | 3.23446 | ||||||||
\(902\) | −25.1366 | −0.836956 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.49625 | −0.116284 | ||||||||
\(905\) | 24.2753 | 0.806939 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −55.9269 | −1.85702 | −0.928512 | − | 0.371303i | \(-0.878911\pi\) | ||||
−0.928512 | + | 0.371303i | \(0.878911\pi\) | |||||||
\(908\) | −43.9229 | −1.45763 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5.99365 | −0.198688 | ||||||||
\(911\) | 44.3323 | 1.46880 | 0.734398 | − | 0.678719i | \(-0.237465\pi\) | ||||
0.734398 | + | 0.678719i | \(0.237465\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.46650 | 0.313296 | ||||||||
\(914\) | 49.7562 | 1.64579 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.67952 | 0.220697 | ||||||||
\(917\) | −7.45485 | −0.246181 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.7427 | 0.651250 | 0.325625 | − | 0.945499i | \(-0.394425\pi\) | ||||
0.325625 | + | 0.945499i | \(0.394425\pi\) | |||||||
\(920\) | −10.9244 | −0.360167 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −19.1892 | −0.631964 | ||||||||
\(923\) | −3.59563 | −0.118352 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.867714 | −0.0285303 | ||||||||
\(926\) | 26.3176 | 0.864850 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −15.4083 | −0.505802 | ||||||||
\(929\) | 24.0010 | 0.787449 | 0.393724 | − | 0.919229i | \(-0.371186\pi\) | ||||
0.393724 | + | 0.919229i | \(0.371186\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.36350 | 0.143008 | ||||||||
\(932\) | −29.1129 | −0.953624 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −45.1888 | −1.47862 | ||||||||
\(935\) | −83.4226 | −2.72821 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39.2507 | −1.28226 | −0.641132 | − | 0.767431i | \(-0.721535\pi\) | ||||
−0.641132 | + | 0.767431i | \(0.721535\pi\) | |||||||
\(938\) | −14.5536 | −0.475192 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −35.3742 | −1.15378 | ||||||||
\(941\) | 2.24962 | 0.0733355 | 0.0366677 | − | 0.999328i | \(-0.488326\pi\) | ||||
0.0366677 | + | 0.999328i | \(0.488326\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.1078 | 0.654799 | ||||||||
\(944\) | 24.0151 | 0.781625 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −115.322 | −3.74946 | ||||||||
\(947\) | 46.7613 | 1.51954 | 0.759769 | − | 0.650193i | \(-0.225312\pi\) | ||||
0.759769 | + | 0.650193i | \(0.225312\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.05368 | −0.196511 | ||||||||
\(950\) | 8.98636 | 0.291556 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.68548 | 0.184267 | ||||||||
\(953\) | 9.10879 | 0.295063 | 0.147531 | − | 0.989057i | \(-0.452867\pi\) | ||||
0.147531 | + | 0.989057i | \(0.452867\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.0116 | −0.518124 | ||||||||
\(956\) | −20.8743 | −0.675122 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.21788 | −0.0393479 | ||||||||
\(959\) | 18.5476 | 0.598934 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6132 | −0.987524 | ||||||||
\(962\) | 2.43140 | 0.0783915 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.01698 | 0.0327548 | ||||||||
\(965\) | 13.6828 | 0.440466 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.219150 | −0.00704739 | −0.00352370 | − | 0.999994i | \(-0.501122\pi\) | ||||
−0.00352370 | + | 0.999994i | \(0.501122\pi\) | |||||||
\(968\) | 11.0545 | 0.355306 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −56.3989 | −1.81086 | ||||||||
\(971\) | 21.5646 | 0.692041 | 0.346020 | − | 0.938227i | \(-0.387533\pi\) | ||||
0.346020 | + | 0.938227i | \(0.387533\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.7225 | −0.536099 | ||||||||
\(974\) | −30.4330 | −0.975135 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −25.9135 | −0.829471 | ||||||||
\(977\) | −29.3741 | −0.939760 | −0.469880 | − | 0.882730i | \(-0.655703\pi\) | ||||
−0.469880 | + | 0.882730i | \(0.655703\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −58.3321 | −1.86430 | ||||||||
\(980\) | −3.23382 | −0.103301 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.20930 | 0.134324 | ||||||||
\(983\) | 10.1660 | 0.324246 | 0.162123 | − | 0.986771i | \(-0.448166\pi\) | ||||
0.162123 | + | 0.986771i | \(0.448166\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −47.2137 | −1.50435 | ||||||||
\(986\) | 32.4318 | 1.03284 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −11.3200 | −0.360136 | ||||||||
\(989\) | 92.2511 | 2.93341 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35.1411 | 1.11629 | 0.558147 | − | 0.829742i | \(-0.311512\pi\) | ||||
0.558147 | + | 0.829742i | \(0.311512\pi\) | |||||||
\(992\) | −4.58238 | −0.145491 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.31538 | −0.136875 | ||||||||
\(995\) | 48.8783 | 1.54955 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.96104 | 0.0937769 | 0.0468885 | − | 0.998900i | \(-0.485069\pi\) | ||||
0.0468885 | + | 0.998900i | \(0.485069\pi\) | |||||||
\(998\) | 82.5874 | 2.61426 | ||||||||
\(999\) | 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 | 8001.2.a.u.1.3 | 18 | ||
3.2 | odd | 2 | 2667.2.a.p.1.16 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.p.1.16 | ✓ | 18 | 3.2 | odd | 2 | ||
8001.2.a.u.1.3 | 18 | 1.1 | even | 1 | trivial |