Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4023,2,Mod(1,4023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4023, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4023 = 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4023.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: | \(32.1238167332\) |
Analytic rank: | \(1\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 4023.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.51871 | −1.78100 | −0.890498 | − | 0.454987i | \(-0.849644\pi\) | ||||
−0.890498 | + | 0.454987i | \(0.849644\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.34389 | 2.17195 | ||||||||
\(5\) | 3.54254 | 1.58427 | 0.792135 | − | 0.610346i | \(-0.208970\pi\) | ||||
0.792135 | + | 0.610346i | \(0.208970\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.81300 | 1.44118 | 0.720589 | − | 0.693362i | \(-0.243871\pi\) | ||||
0.720589 | + | 0.693362i | \(0.243871\pi\) | |||||||
\(8\) | −5.90358 | −2.08723 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −8.92261 | −2.82158 | ||||||||
\(11\) | −2.43666 | −0.734680 | −0.367340 | − | 0.930087i | \(-0.619731\pi\) | ||||
−0.367340 | + | 0.930087i | \(0.619731\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.859287 | −0.238323 | −0.119162 | − | 0.992875i | \(-0.538021\pi\) | ||||
−0.119162 | + | 0.992875i | \(0.538021\pi\) | |||||||
\(14\) | −9.60384 | −2.56673 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 6.18161 | 1.54540 | ||||||||
\(17\) | −5.04387 | −1.22332 | −0.611659 | − | 0.791121i | \(-0.709498\pi\) | ||||
−0.611659 | + | 0.791121i | \(0.709498\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.23507 | −1.43042 | −0.715212 | − | 0.698908i | \(-0.753670\pi\) | ||||
−0.715212 | + | 0.698908i | \(0.753670\pi\) | |||||||
\(20\) | 15.3884 | 3.44095 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.13723 | 1.30846 | ||||||||
\(23\) | −6.49720 | −1.35476 | −0.677380 | − | 0.735633i | \(-0.736885\pi\) | ||||
−0.677380 | + | 0.735633i | \(0.736885\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.54956 | 1.50991 | ||||||||
\(26\) | 2.16429 | 0.424453 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 16.5633 | 3.13016 | ||||||||
\(29\) | 1.60049 | 0.297204 | 0.148602 | − | 0.988897i | \(-0.452523\pi\) | ||||
0.148602 | + | 0.988897i | \(0.452523\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.29467 | 0.412134 | 0.206067 | − | 0.978538i | \(-0.433934\pi\) | ||||
0.206067 | + | 0.978538i | \(0.433934\pi\) | |||||||
\(32\) | −3.76251 | −0.665125 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 12.7040 | 2.17873 | ||||||||
\(35\) | 13.5077 | 2.28322 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.904111 | −0.148635 | −0.0743175 | − | 0.997235i | \(-0.523678\pi\) | ||||
−0.0743175 | + | 0.997235i | \(0.523678\pi\) | |||||||
\(38\) | 15.7043 | 2.54758 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −20.9136 | −3.30674 | ||||||||
\(41\) | −7.92721 | −1.23802 | −0.619011 | − | 0.785382i | \(-0.712466\pi\) | ||||
−0.619011 | + | 0.785382i | \(0.712466\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.50374 | −0.686814 | −0.343407 | − | 0.939187i | \(-0.611581\pi\) | ||||
−0.343407 | + | 0.939187i | \(0.611581\pi\) | |||||||
\(44\) | −10.5846 | −1.59568 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 16.3646 | 2.41282 | ||||||||
\(47\) | −2.73389 | −0.398779 | −0.199389 | − | 0.979920i | \(-0.563896\pi\) | ||||
−0.199389 | + | 0.979920i | \(0.563896\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.53897 | 1.07700 | ||||||||
\(50\) | −19.0151 | −2.68915 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.73265 | −0.517626 | ||||||||
\(53\) | −13.3347 | −1.83166 | −0.915832 | − | 0.401562i | \(-0.868467\pi\) | ||||
−0.915832 | + | 0.401562i | \(0.868467\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.63194 | −1.16393 | ||||||||
\(56\) | −22.5103 | −3.00807 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.03118 | −0.529319 | ||||||||
\(59\) | −5.37203 | −0.699379 | −0.349689 | − | 0.936866i | \(-0.613713\pi\) | ||||
−0.349689 | + | 0.936866i | \(0.613713\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.31743 | 0.168680 | 0.0843400 | − | 0.996437i | \(-0.473122\pi\) | ||||
0.0843400 | + | 0.996437i | \(0.473122\pi\) | |||||||
\(62\) | −5.77959 | −0.734009 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.88654 | −0.360818 | ||||||||
\(65\) | −3.04406 | −0.377569 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.24840 | 0.152516 | 0.0762581 | − | 0.997088i | \(-0.475703\pi\) | ||||
0.0762581 | + | 0.997088i | \(0.475703\pi\) | |||||||
\(68\) | −21.9100 | −2.65698 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −34.0219 | −4.06640 | ||||||||
\(71\) | 2.94792 | 0.349853 | 0.174927 | − | 0.984581i | \(-0.444031\pi\) | ||||
0.174927 | + | 0.984581i | \(0.444031\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.46161 | 0.288109 | 0.144055 | − | 0.989570i | \(-0.453986\pi\) | ||||
0.144055 | + | 0.989570i | \(0.453986\pi\) | |||||||
\(74\) | 2.27719 | 0.264718 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −27.0845 | −3.10680 | ||||||||
\(77\) | −9.29097 | −1.05880 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.5158 | −1.18312 | −0.591562 | − | 0.806259i | \(-0.701489\pi\) | ||||
−0.591562 | + | 0.806259i | \(0.701489\pi\) | |||||||
\(80\) | 21.8986 | 2.44833 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 19.9663 | 2.20491 | ||||||||
\(83\) | 7.75670 | 0.851409 | 0.425704 | − | 0.904862i | \(-0.360026\pi\) | ||||
0.425704 | + | 0.904862i | \(0.360026\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −17.8681 | −1.93807 | ||||||||
\(86\) | 11.3436 | 1.22321 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 14.3850 | 1.53345 | ||||||||
\(89\) | −0.331629 | −0.0351526 | −0.0175763 | − | 0.999846i | \(-0.505595\pi\) | ||||
−0.0175763 | + | 0.999846i | \(0.505595\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.27646 | −0.343467 | ||||||||
\(92\) | −28.2231 | −2.94247 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.88587 | 0.710223 | ||||||||
\(95\) | −22.0880 | −2.26618 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.4028 | −1.86852 | −0.934260 | − | 0.356591i | \(-0.883939\pi\) | ||||
−0.934260 | + | 0.356591i | \(0.883939\pi\) | |||||||
\(98\) | −18.9885 | −1.91813 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 32.7945 | 3.27945 | ||||||||
\(101\) | −10.4299 | −1.03781 | −0.518906 | − | 0.854832i | \(-0.673660\pi\) | ||||
−0.518906 | + | 0.854832i | \(0.673660\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.94376 | 0.979787 | 0.489894 | − | 0.871782i | \(-0.337036\pi\) | ||||
0.489894 | + | 0.871782i | \(0.337036\pi\) | |||||||
\(104\) | 5.07287 | 0.497436 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 33.5863 | 3.26219 | ||||||||
\(107\) | 5.63676 | 0.544926 | 0.272463 | − | 0.962166i | \(-0.412162\pi\) | ||||
0.272463 | + | 0.962166i | \(0.412162\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.1052 | 1.06368 | 0.531841 | − | 0.846844i | \(-0.321500\pi\) | ||||
0.531841 | + | 0.846844i | \(0.321500\pi\) | |||||||
\(110\) | 21.7414 | 2.07296 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 23.5705 | 2.22720 | ||||||||
\(113\) | −19.5556 | −1.83963 | −0.919816 | − | 0.392349i | \(-0.871662\pi\) | ||||
−0.919816 | + | 0.392349i | \(0.871662\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −23.0166 | −2.14631 | ||||||||
\(116\) | 6.95237 | 0.645511 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 13.5306 | 1.24559 | ||||||||
\(119\) | −19.2323 | −1.76302 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.06270 | −0.460246 | ||||||||
\(122\) | −3.31823 | −0.300418 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.96778 | 0.895133 | ||||||||
\(125\) | 9.03190 | 0.807838 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.0860 | 1.78235 | 0.891174 | − | 0.453662i | \(-0.149883\pi\) | ||||
0.891174 | + | 0.453662i | \(0.149883\pi\) | |||||||
\(128\) | 14.7954 | 1.30774 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.66709 | 0.672448 | ||||||||
\(131\) | 6.31752 | 0.551965 | 0.275982 | − | 0.961163i | \(-0.410997\pi\) | ||||
0.275982 | + | 0.961163i | \(0.410997\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −23.7743 | −2.06150 | ||||||||
\(134\) | −3.14435 | −0.271631 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 29.7769 | 2.55335 | ||||||||
\(137\) | −6.45572 | −0.551549 | −0.275775 | − | 0.961222i | \(-0.588934\pi\) | ||||
−0.275775 | + | 0.961222i | \(0.588934\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.4023 | −1.30640 | −0.653202 | − | 0.757184i | \(-0.726575\pi\) | ||||
−0.653202 | + | 0.757184i | \(0.726575\pi\) | |||||||
\(140\) | 58.6759 | 4.95902 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.42494 | −0.623087 | ||||||||
\(143\) | 2.09379 | 0.175091 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.66981 | 0.470852 | ||||||||
\(146\) | −6.20007 | −0.513121 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.92736 | −0.322827 | ||||||||
\(149\) | −1.00000 | −0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.0141 | 1.54735 | 0.773674 | − | 0.633584i | \(-0.218417\pi\) | ||||
0.773674 | + | 0.633584i | \(0.218417\pi\) | |||||||
\(152\) | 36.8092 | 2.98562 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 23.4013 | 1.88573 | ||||||||
\(155\) | 8.12893 | 0.652932 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.4113 | −1.38958 | −0.694788 | − | 0.719215i | \(-0.744502\pi\) | ||||
−0.694788 | + | 0.719215i | \(0.744502\pi\) | |||||||
\(158\) | 26.4863 | 2.10714 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −13.3288 | −1.05374 | ||||||||
\(161\) | −24.7738 | −1.95245 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.4329 | −1.60043 | −0.800215 | − | 0.599713i | \(-0.795281\pi\) | ||||
−0.800215 | + | 0.599713i | \(0.795281\pi\) | |||||||
\(164\) | −34.4349 | −2.68892 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −19.5369 | −1.51636 | ||||||||
\(167\) | 10.3545 | 0.801255 | 0.400628 | − | 0.916241i | \(-0.368792\pi\) | ||||
0.400628 | + | 0.916241i | \(0.368792\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.2616 | −0.943202 | ||||||||
\(170\) | 45.0045 | 3.45169 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −19.5637 | −1.49172 | ||||||||
\(173\) | 20.7152 | 1.57494 | 0.787472 | − | 0.616350i | \(-0.211389\pi\) | ||||
0.787472 | + | 0.616350i | \(0.211389\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 28.7865 | 2.17605 | ||||||||
\(176\) | −15.0625 | −1.13538 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.835277 | 0.0626067 | ||||||||
\(179\) | −15.2082 | −1.13671 | −0.568357 | − | 0.822782i | \(-0.692421\pi\) | ||||
−0.568357 | + | 0.822782i | \(0.692421\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.03982 | 0.0772892 | 0.0386446 | − | 0.999253i | \(-0.487696\pi\) | ||||
0.0386446 | + | 0.999253i | \(0.487696\pi\) | |||||||
\(182\) | 8.25246 | 0.611713 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 38.3567 | 2.82770 | ||||||||
\(185\) | −3.20285 | −0.235478 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.2902 | 0.898748 | ||||||||
\(188\) | −11.8757 | −0.866126 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 55.6331 | 4.03605 | ||||||||
\(191\) | 13.0784 | 0.946322 | 0.473161 | − | 0.880976i | \(-0.343113\pi\) | ||||
0.473161 | + | 0.880976i | \(0.343113\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.1240 | 1.08865 | 0.544325 | − | 0.838874i | \(-0.316786\pi\) | ||||
0.544325 | + | 0.838874i | \(0.316786\pi\) | |||||||
\(194\) | 46.3513 | 3.32783 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 32.7485 | 2.33918 | ||||||||
\(197\) | 19.2160 | 1.36909 | 0.684543 | − | 0.728972i | \(-0.260002\pi\) | ||||
0.684543 | + | 0.728972i | \(0.260002\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.3009 | −1.01377 | −0.506883 | − | 0.862015i | \(-0.669202\pi\) | ||||
−0.506883 | + | 0.862015i | \(0.669202\pi\) | |||||||
\(200\) | −44.5694 | −3.15153 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 26.2698 | 1.84834 | ||||||||
\(203\) | 6.10268 | 0.428324 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −28.0824 | −1.96136 | ||||||||
\(206\) | −25.0454 | −1.74500 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.31178 | −0.368306 | ||||||||
\(209\) | 15.1927 | 1.05090 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.92394 | 0.614349 | 0.307175 | − | 0.951653i | \(-0.400616\pi\) | ||||
0.307175 | + | 0.951653i | \(0.400616\pi\) | |||||||
\(212\) | −57.9245 | −3.97827 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −14.1974 | −0.970511 | ||||||||
\(215\) | −15.9547 | −1.08810 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.74956 | 0.593959 | ||||||||
\(218\) | −27.9707 | −1.89441 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −37.4962 | −2.52800 | ||||||||
\(221\) | 4.33414 | 0.291546 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.01768 | −0.0681491 | −0.0340746 | − | 0.999419i | \(-0.510848\pi\) | ||||
−0.0340746 | + | 0.999419i | \(0.510848\pi\) | |||||||
\(224\) | −14.3465 | −0.958564 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 49.2548 | 3.27638 | ||||||||
\(227\) | 0.986066 | 0.0654475 | 0.0327238 | − | 0.999464i | \(-0.489582\pi\) | ||||
0.0327238 | + | 0.999464i | \(0.489582\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.2376 | 1.07301 | 0.536505 | − | 0.843897i | \(-0.319744\pi\) | ||||
0.536505 | + | 0.843897i | \(0.319744\pi\) | |||||||
\(230\) | 57.9720 | 3.82256 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.44864 | −0.620334 | ||||||||
\(233\) | −5.54175 | −0.363052 | −0.181526 | − | 0.983386i | \(-0.558104\pi\) | ||||
−0.181526 | + | 0.983386i | \(0.558104\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.68490 | −0.631773 | ||||||||
\(236\) | −23.3355 | −1.51901 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 48.4405 | 3.13993 | ||||||||
\(239\) | 4.34193 | 0.280856 | 0.140428 | − | 0.990091i | \(-0.455152\pi\) | ||||
0.140428 | + | 0.990091i | \(0.455152\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.1086 | −0.715566 | −0.357783 | − | 0.933805i | \(-0.616467\pi\) | ||||
−0.357783 | + | 0.933805i | \(0.616467\pi\) | |||||||
\(242\) | 12.7515 | 0.819696 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.72279 | 0.366364 | ||||||||
\(245\) | 26.7071 | 1.70625 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.35772 | 0.340903 | ||||||||
\(248\) | −13.5467 | −0.860219 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −22.7487 | −1.43876 | ||||||||
\(251\) | 28.3565 | 1.78984 | 0.894922 | − | 0.446222i | \(-0.147231\pi\) | ||||
0.894922 | + | 0.446222i | \(0.147231\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.8315 | 0.995315 | ||||||||
\(254\) | −50.5909 | −3.17435 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −31.4922 | −1.96826 | ||||||||
\(257\) | 24.5994 | 1.53447 | 0.767234 | − | 0.641368i | \(-0.221633\pi\) | ||||
0.767234 | + | 0.641368i | \(0.221633\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.44738 | −0.214210 | ||||||||
\(260\) | −13.2230 | −0.820059 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −15.9120 | −0.983046 | ||||||||
\(263\) | −4.51251 | −0.278253 | −0.139126 | − | 0.990275i | \(-0.544429\pi\) | ||||
−0.139126 | + | 0.990275i | \(0.544429\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −47.2387 | −2.90185 | ||||||||
\(266\) | 59.8806 | 3.67151 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.42291 | 0.331257 | ||||||||
\(269\) | 27.6112 | 1.68348 | 0.841741 | − | 0.539881i | \(-0.181531\pi\) | ||||
0.841741 | + | 0.539881i | \(0.181531\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.25459 | −0.136957 | −0.0684784 | − | 0.997653i | \(-0.521814\pi\) | ||||
−0.0684784 | + | 0.997653i | \(0.521814\pi\) | |||||||
\(272\) | −31.1793 | −1.89052 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.2601 | 0.982307 | ||||||||
\(275\) | −18.3957 | −1.10930 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.57741 | 0.515366 | 0.257683 | − | 0.966229i | \(-0.417041\pi\) | ||||
0.257683 | + | 0.966229i | \(0.417041\pi\) | |||||||
\(278\) | 38.7938 | 2.32670 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −79.7437 | −4.76560 | ||||||||
\(281\) | 29.5805 | 1.76462 | 0.882312 | − | 0.470666i | \(-0.155986\pi\) | ||||
0.882312 | + | 0.470666i | \(0.155986\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.8967 | 1.18274 | 0.591368 | − | 0.806402i | \(-0.298588\pi\) | ||||
0.591368 | + | 0.806402i | \(0.298588\pi\) | |||||||
\(284\) | 12.8054 | 0.759862 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.27364 | −0.311837 | ||||||||
\(287\) | −30.2265 | −1.78421 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.44065 | 0.496509 | ||||||||
\(290\) | −14.2806 | −0.838585 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 10.6929 | 0.625757 | ||||||||
\(293\) | −27.2289 | −1.59073 | −0.795365 | − | 0.606131i | \(-0.792721\pi\) | ||||
−0.795365 | + | 0.606131i | \(0.792721\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −19.0306 | −1.10801 | ||||||||
\(296\) | 5.33749 | 0.310235 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.51871 | 0.145905 | ||||||||
\(299\) | 5.58296 | 0.322871 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.1728 | −0.989821 | ||||||||
\(302\) | −47.8910 | −2.75582 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −38.5428 | −2.21058 | ||||||||
\(305\) | 4.66705 | 0.267235 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.04427 | −0.173746 | −0.0868728 | − | 0.996219i | \(-0.527687\pi\) | ||||
−0.0868728 | + | 0.996219i | \(0.527687\pi\) | |||||||
\(308\) | −40.3590 | −2.29967 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −20.4744 | −1.16287 | ||||||||
\(311\) | −16.1735 | −0.917115 | −0.458558 | − | 0.888665i | \(-0.651634\pi\) | ||||
−0.458558 | + | 0.888665i | \(0.651634\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.7255 | −1.11495 | −0.557476 | − | 0.830193i | \(-0.688230\pi\) | ||||
−0.557476 | + | 0.830193i | \(0.688230\pi\) | |||||||
\(314\) | 43.8541 | 2.47483 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −45.6797 | −2.56968 | ||||||||
\(317\) | −12.7244 | −0.714673 | −0.357337 | − | 0.933976i | \(-0.616315\pi\) | ||||
−0.357337 | + | 0.933976i | \(0.616315\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.89985 | −0.218350 | ||||||||
\(320\) | −10.2257 | −0.571633 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 62.3981 | 3.47731 | ||||||||
\(323\) | 31.4489 | 1.74986 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.48724 | −0.359847 | ||||||||
\(326\) | 51.4646 | 2.85036 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 46.7989 | 2.58404 | ||||||||
\(329\) | −10.4243 | −0.574711 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.1086 | 1.70988 | 0.854942 | − | 0.518723i | \(-0.173593\pi\) | ||||
0.854942 | + | 0.518723i | \(0.173593\pi\) | |||||||
\(332\) | 33.6943 | 1.84921 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −26.0800 | −1.42703 | ||||||||
\(335\) | 4.42250 | 0.241627 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.6804 | −1.23548 | −0.617741 | − | 0.786382i | \(-0.711952\pi\) | ||||
−0.617741 | + | 0.786382i | \(0.711952\pi\) | |||||||
\(338\) | 30.8835 | 1.67984 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −77.6171 | −4.20938 | ||||||||
\(341\) | −5.59131 | −0.302787 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.05511 | 0.110965 | ||||||||
\(344\) | 26.5882 | 1.43354 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −52.1754 | −2.80497 | ||||||||
\(347\) | −24.2199 | −1.30019 | −0.650095 | − | 0.759853i | \(-0.725271\pi\) | ||||
−0.650095 | + | 0.759853i | \(0.725271\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −31.2438 | −1.67244 | −0.836220 | − | 0.548394i | \(-0.815239\pi\) | ||||
−0.836220 | + | 0.548394i | \(0.815239\pi\) | |||||||
\(350\) | −72.5047 | −3.87554 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9.16796 | 0.488654 | ||||||||
\(353\) | −16.8284 | −0.895688 | −0.447844 | − | 0.894112i | \(-0.647808\pi\) | ||||
−0.447844 | + | 0.894112i | \(0.647808\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.4431 | 0.554262 | ||||||||
\(356\) | −1.44056 | −0.0763496 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 38.3050 | 2.02448 | ||||||||
\(359\) | 8.82572 | 0.465804 | 0.232902 | − | 0.972500i | \(-0.425178\pi\) | ||||
0.232902 | + | 0.972500i | \(0.425178\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.8761 | 1.04611 | ||||||||
\(362\) | −2.61900 | −0.137652 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −14.2326 | −0.745991 | ||||||||
\(365\) | 8.72032 | 0.456443 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.3302 | −1.32223 | −0.661113 | − | 0.750286i | \(-0.729916\pi\) | ||||
−0.661113 | + | 0.750286i | \(0.729916\pi\) | |||||||
\(368\) | −40.1632 | −2.09365 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.06704 | 0.419385 | ||||||||
\(371\) | −50.8453 | −2.63975 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.2292 | −0.736760 | −0.368380 | − | 0.929675i | \(-0.620088\pi\) | ||||
−0.368380 | + | 0.929675i | \(0.620088\pi\) | |||||||
\(374\) | −30.9554 | −1.60067 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 16.1397 | 0.832343 | ||||||||
\(377\) | −1.37528 | −0.0708307 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.53201 | 0.386893 | 0.193447 | − | 0.981111i | \(-0.438033\pi\) | ||||
0.193447 | + | 0.981111i | \(0.438033\pi\) | |||||||
\(380\) | −95.9477 | −4.92201 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −32.9407 | −1.68539 | ||||||||
\(383\) | 36.0995 | 1.84460 | 0.922298 | − | 0.386479i | \(-0.126309\pi\) | ||||
0.922298 | + | 0.386479i | \(0.126309\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −32.9136 | −1.67743 | ||||||||
\(386\) | −38.0930 | −1.93888 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −79.9397 | −4.05833 | ||||||||
\(389\) | 16.6283 | 0.843089 | 0.421544 | − | 0.906808i | \(-0.361488\pi\) | ||||
0.421544 | + | 0.906808i | \(0.361488\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 32.7711 | 1.65730 | ||||||||
\(392\) | −44.5069 | −2.24794 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −48.3996 | −2.43834 | ||||||||
\(395\) | −37.2528 | −1.87439 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −37.3483 | −1.87446 | −0.937229 | − | 0.348715i | \(-0.886618\pi\) | ||||
−0.937229 | + | 0.348715i | \(0.886618\pi\) | |||||||
\(398\) | 36.0199 | 1.80551 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 46.6684 | 2.33342 | ||||||||
\(401\) | −12.7934 | −0.638873 | −0.319436 | − | 0.947608i | \(-0.603494\pi\) | ||||
−0.319436 | + | 0.947608i | \(0.603494\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.97178 | −0.0982212 | ||||||||
\(404\) | −45.3062 | −2.25407 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15.3709 | −0.762844 | ||||||||
\(407\) | 2.20301 | 0.109199 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.9878 | 1.38391 | 0.691954 | − | 0.721942i | \(-0.256750\pi\) | ||||
0.691954 | + | 0.721942i | \(0.256750\pi\) | |||||||
\(410\) | 70.7314 | 3.49318 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 43.1946 | 2.12805 | ||||||||
\(413\) | −20.4836 | −1.00793 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 27.4784 | 1.34886 | ||||||||
\(416\) | 3.23308 | 0.158515 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −38.2660 | −1.87165 | ||||||||
\(419\) | −26.3038 | −1.28503 | −0.642513 | − | 0.766275i | \(-0.722108\pi\) | ||||
−0.642513 | + | 0.766275i | \(0.722108\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.74782 | 0.280131 | 0.140066 | − | 0.990142i | \(-0.455269\pi\) | ||||
0.140066 | + | 0.990142i | \(0.455269\pi\) | |||||||
\(422\) | −22.4768 | −1.09415 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 78.7225 | 3.82310 | ||||||||
\(425\) | −38.0790 | −1.84710 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.02337 | 0.243098 | ||||||||
\(428\) | 24.4855 | 1.18355 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 40.1851 | 1.93790 | ||||||||
\(431\) | 8.62945 | 0.415666 | 0.207833 | − | 0.978164i | \(-0.433359\pi\) | ||||
0.207833 | + | 0.978164i | \(0.433359\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.5910 | 0.893425 | 0.446712 | − | 0.894678i | \(-0.352595\pi\) | ||||
0.446712 | + | 0.894678i | \(0.352595\pi\) | |||||||
\(434\) | −22.0376 | −1.05784 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 48.2397 | 2.31026 | ||||||||
\(437\) | 40.5105 | 1.93788 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.84186 | 0.135635 | 0.0678173 | − | 0.997698i | \(-0.478397\pi\) | ||||
0.0678173 | + | 0.997698i | \(0.478397\pi\) | |||||||
\(440\) | 50.9594 | 2.42939 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10.9164 | −0.519241 | ||||||||
\(443\) | 29.6998 | 1.41108 | 0.705541 | − | 0.708670i | \(-0.250704\pi\) | ||||
0.705541 | + | 0.708670i | \(0.250704\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.17481 | −0.0556913 | ||||||||
\(446\) | 2.56325 | 0.121373 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −11.0064 | −0.520003 | ||||||||
\(449\) | −7.67404 | −0.362161 | −0.181080 | − | 0.983468i | \(-0.557959\pi\) | ||||
−0.181080 | + | 0.983468i | \(0.557959\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.3159 | 0.909550 | ||||||||
\(452\) | −84.9472 | −3.99558 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.48361 | −0.116562 | ||||||||
\(455\) | −11.6070 | −0.544144 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.83854 | −0.366672 | −0.183336 | − | 0.983050i | \(-0.558690\pi\) | ||||
−0.183336 | + | 0.983050i | \(0.558690\pi\) | |||||||
\(458\) | −40.8977 | −1.91103 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −99.9815 | −4.66166 | ||||||||
\(461\) | 22.5521 | 1.05035 | 0.525177 | − | 0.850993i | \(-0.323999\pi\) | ||||
0.525177 | + | 0.850993i | \(0.323999\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.11066 | −0.144565 | −0.0722823 | − | 0.997384i | \(-0.523028\pi\) | ||||
−0.0722823 | + | 0.997384i | \(0.523028\pi\) | |||||||
\(464\) | 9.89363 | 0.459300 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 13.9581 | 0.646595 | ||||||||
\(467\) | 9.43684 | 0.436685 | 0.218342 | − | 0.975872i | \(-0.429935\pi\) | ||||
0.218342 | + | 0.975872i | \(0.429935\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.76015 | 0.219803 | ||||||||
\(470\) | 24.3934 | 1.12519 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 31.7142 | 1.45976 | ||||||||
\(473\) | 10.9741 | 0.504588 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −47.0720 | −2.15981 | ||||||||
\(476\) | −83.5430 | −3.82919 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −10.9361 | −0.500204 | ||||||||
\(479\) | 21.7130 | 0.992094 | 0.496047 | − | 0.868296i | \(-0.334784\pi\) | ||||
0.496047 | + | 0.868296i | \(0.334784\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.776891 | 0.0354232 | ||||||||
\(482\) | 27.9792 | 1.27442 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −21.9918 | −0.999629 | ||||||||
\(485\) | −65.1926 | −2.96024 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.9987 | −1.40468 | −0.702342 | − | 0.711840i | \(-0.747862\pi\) | ||||
−0.702342 | + | 0.711840i | \(0.747862\pi\) | |||||||
\(488\) | −7.77757 | −0.352074 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −67.2674 | −3.03883 | ||||||||
\(491\) | −14.9510 | −0.674731 | −0.337366 | − | 0.941374i | \(-0.609536\pi\) | ||||
−0.337366 | + | 0.941374i | \(0.609536\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.07269 | −0.363576 | ||||||||
\(494\) | −13.4945 | −0.607147 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 14.1847 | 0.636913 | ||||||||
\(497\) | 11.2404 | 0.504201 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.3098 | −0.640596 | −0.320298 | − | 0.947317i | \(-0.603783\pi\) | ||||
−0.320298 | + | 0.947317i | \(0.603783\pi\) | |||||||
\(500\) | 39.2336 | 1.75458 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −71.4217 | −3.18771 | ||||||||
\(503\) | 38.7190 | 1.72640 | 0.863198 | − | 0.504866i | \(-0.168458\pi\) | ||||
0.863198 | + | 0.504866i | \(0.168458\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −36.9482 | −1.64417 | ||||||||
\(506\) | −39.8748 | −1.77265 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 87.2515 | 3.87116 | ||||||||
\(509\) | 26.9274 | 1.19354 | 0.596768 | − | 0.802414i | \(-0.296451\pi\) | ||||
0.596768 | + | 0.802414i | \(0.296451\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.38610 | 0.415217 | ||||||||
\(512\) | 49.7288 | 2.19773 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −61.9587 | −2.73288 | ||||||||
\(515\) | 35.2261 | 1.55225 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.66155 | 0.292975 | ||||||||
\(518\) | 8.68294 | 0.381506 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 17.9708 | 0.788073 | ||||||||
\(521\) | 37.0750 | 1.62429 | 0.812143 | − | 0.583458i | \(-0.198301\pi\) | ||||
0.812143 | + | 0.583458i | \(0.198301\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.3357 | −0.714310 | −0.357155 | − | 0.934045i | \(-0.616253\pi\) | ||||
−0.357155 | + | 0.934045i | \(0.616253\pi\) | |||||||
\(524\) | 27.4426 | 1.19884 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.3657 | 0.495567 | ||||||||
\(527\) | −11.5740 | −0.504171 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.2136 | 0.835375 | ||||||||
\(530\) | 118.981 | 5.16818 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −103.273 | −4.47746 | ||||||||
\(533\) | 6.81175 | 0.295050 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.9684 | 0.863310 | ||||||||
\(536\) | −7.37002 | −0.318336 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −69.5445 | −2.99827 | ||||||||
\(539\) | −18.3699 | −0.791247 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.3725 | 0.832889 | 0.416445 | − | 0.909161i | \(-0.363276\pi\) | ||||
0.416445 | + | 0.909161i | \(0.363276\pi\) | |||||||
\(542\) | 5.67866 | 0.243919 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 18.9776 | 0.813660 | ||||||||
\(545\) | 39.3405 | 1.68516 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.0673 | −0.644232 | −0.322116 | − | 0.946700i | \(-0.604394\pi\) | ||||
−0.322116 | + | 0.946700i | \(0.604394\pi\) | |||||||
\(548\) | −28.0429 | −1.19794 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 46.3334 | 1.97566 | ||||||||
\(551\) | −9.97919 | −0.425128 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −40.0969 | −1.70509 | ||||||||
\(554\) | −21.6040 | −0.917865 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −66.9058 | −2.83744 | ||||||||
\(557\) | 17.9877 | 0.762164 | 0.381082 | − | 0.924541i | \(-0.375552\pi\) | ||||
0.381082 | + | 0.924541i | \(0.375552\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.87000 | 0.163684 | ||||||||
\(560\) | 83.4993 | 3.52849 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −74.5046 | −3.14279 | ||||||||
\(563\) | −31.6510 | −1.33393 | −0.666965 | − | 0.745089i | \(-0.732407\pi\) | ||||
−0.666965 | + | 0.745089i | \(0.732407\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −69.2763 | −2.91447 | ||||||||
\(566\) | −50.1140 | −2.10645 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −17.4033 | −0.730224 | ||||||||
\(569\) | 28.5709 | 1.19776 | 0.598878 | − | 0.800840i | \(-0.295613\pi\) | ||||
0.598878 | + | 0.800840i | \(0.295613\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.2318 | 1.09777 | 0.548883 | − | 0.835899i | \(-0.315053\pi\) | ||||
0.548883 | + | 0.835899i | \(0.315053\pi\) | |||||||
\(572\) | 9.09519 | 0.380289 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 76.1316 | 3.17767 | ||||||||
\(575\) | −49.0510 | −2.04557 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.7950 | 1.19875 | 0.599376 | − | 0.800467i | \(-0.295415\pi\) | ||||
0.599376 | + | 0.800467i | \(0.295415\pi\) | |||||||
\(578\) | −21.2595 | −0.884280 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 24.6290 | 1.02266 | ||||||||
\(581\) | 29.5763 | 1.22703 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 32.4921 | 1.34569 | ||||||||
\(584\) | −14.5323 | −0.601350 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 68.5817 | 2.83308 | ||||||||
\(587\) | 15.5798 | 0.643048 | 0.321524 | − | 0.946901i | \(-0.395805\pi\) | ||||
0.321524 | + | 0.946901i | \(0.395805\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.3074 | −0.589526 | ||||||||
\(590\) | 47.9326 | 1.97335 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.58886 | −0.229701 | ||||||||
\(593\) | −6.82097 | −0.280104 | −0.140052 | − | 0.990144i | \(-0.544727\pi\) | ||||
−0.140052 | + | 0.990144i | \(0.544727\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −68.1311 | −2.79310 | ||||||||
\(596\) | −4.34389 | −0.177933 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −14.0619 | −0.575032 | ||||||||
\(599\) | 7.40614 | 0.302607 | 0.151303 | − | 0.988487i | \(-0.451653\pi\) | ||||
0.151303 | + | 0.988487i | \(0.451653\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.0323 | 1.18425 | 0.592127 | − | 0.805845i | \(-0.298289\pi\) | ||||
0.592127 | + | 0.805845i | \(0.298289\pi\) | |||||||
\(602\) | 43.2532 | 1.76287 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 82.5953 | 3.36075 | ||||||||
\(605\) | −17.9348 | −0.729153 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −38.5152 | −1.56328 | −0.781641 | − | 0.623728i | \(-0.785617\pi\) | ||||
−0.781641 | + | 0.623728i | \(0.785617\pi\) | |||||||
\(608\) | 23.4595 | 0.951410 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −11.7549 | −0.475944 | ||||||||
\(611\) | 2.34920 | 0.0950383 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.0901 | −0.609485 | −0.304742 | − | 0.952435i | \(-0.598570\pi\) | ||||
−0.304742 | + | 0.952435i | \(0.598570\pi\) | |||||||
\(614\) | 7.66763 | 0.309440 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 54.8500 | 2.20997 | ||||||||
\(617\) | −22.5652 | −0.908442 | −0.454221 | − | 0.890889i | \(-0.650082\pi\) | ||||
−0.454221 | + | 0.890889i | \(0.650082\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.705183 | 0.0283437 | 0.0141719 | − | 0.999900i | \(-0.495489\pi\) | ||||
0.0141719 | + | 0.999900i | \(0.495489\pi\) | |||||||
\(620\) | 35.3112 | 1.41813 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 40.7363 | 1.63338 | ||||||||
\(623\) | −1.26450 | −0.0506612 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.75195 | −0.230078 | ||||||||
\(626\) | 49.6828 | 1.98572 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −75.6330 | −3.01808 | ||||||||
\(629\) | 4.56022 | 0.181828 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.0301 | 1.23529 | 0.617645 | − | 0.786457i | \(-0.288087\pi\) | ||||
0.617645 | + | 0.786457i | \(0.288087\pi\) | |||||||
\(632\) | 62.0811 | 2.46945 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 32.0490 | 1.27283 | ||||||||
\(635\) | 71.1555 | 2.82372 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.47814 | −0.256673 | ||||||||
\(638\) | 9.82260 | 0.388880 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 52.4132 | 2.07181 | ||||||||
\(641\) | −47.6989 | −1.88399 | −0.941996 | − | 0.335624i | \(-0.891053\pi\) | ||||
−0.941996 | + | 0.335624i | \(0.891053\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.51878 | 0.296512 | 0.148256 | − | 0.988949i | \(-0.452634\pi\) | ||||
0.148256 | + | 0.988949i | \(0.452634\pi\) | |||||||
\(644\) | −107.615 | −4.24062 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −79.2106 | −3.11650 | ||||||||
\(647\) | −44.3497 | −1.74357 | −0.871783 | − | 0.489892i | \(-0.837036\pi\) | ||||
−0.871783 | + | 0.489892i | \(0.837036\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.0898 | 0.513819 | ||||||||
\(650\) | 16.3395 | 0.640887 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −88.7584 | −3.47605 | ||||||||
\(653\) | −22.8452 | −0.894000 | −0.447000 | − | 0.894534i | \(-0.647508\pi\) | ||||
−0.447000 | + | 0.894534i | \(0.647508\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.3800 | 0.874461 | ||||||||
\(656\) | −49.0029 | −1.91324 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 26.2558 | 1.02356 | ||||||||
\(659\) | −0.270041 | −0.0105193 | −0.00525964 | − | 0.999986i | \(-0.501674\pi\) | ||||
−0.00525964 | + | 0.999986i | \(0.501674\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.272894 | −0.0106144 | −0.00530718 | − | 0.999986i | \(-0.501689\pi\) | ||||
−0.00530718 | + | 0.999986i | \(0.501689\pi\) | |||||||
\(662\) | −78.3535 | −3.04530 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −45.7923 | −1.77709 | ||||||||
\(665\) | −84.2214 | −3.26597 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.3987 | −0.402640 | ||||||||
\(668\) | 44.9788 | 1.74028 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −11.1390 | −0.430336 | ||||||||
\(671\) | −3.21013 | −0.123926 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.7981 | 0.763160 | 0.381580 | − | 0.924336i | \(-0.375380\pi\) | ||||
0.381580 | + | 0.924336i | \(0.375380\pi\) | |||||||
\(674\) | 57.1254 | 2.20039 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −53.2632 | −2.04858 | ||||||||
\(677\) | −23.6048 | −0.907205 | −0.453603 | − | 0.891204i | \(-0.649861\pi\) | ||||
−0.453603 | + | 0.891204i | \(0.649861\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −70.1699 | −2.69287 | ||||||||
\(680\) | 105.486 | 4.04519 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 14.0829 | 0.539261 | ||||||||
\(683\) | −11.2704 | −0.431248 | −0.215624 | − | 0.976476i | \(-0.569179\pi\) | ||||
−0.215624 | + | 0.976476i | \(0.569179\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.8696 | −0.873803 | ||||||||
\(686\) | −5.17621 | −0.197629 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −27.8403 | −1.06140 | ||||||||
\(689\) | 11.4584 | 0.436528 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.3062 | 1.22899 | 0.614493 | − | 0.788922i | \(-0.289361\pi\) | ||||
0.614493 | + | 0.788922i | \(0.289361\pi\) | |||||||
\(692\) | 89.9844 | 3.42069 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 61.0027 | 2.31563 | ||||||||
\(695\) | −54.5631 | −2.06970 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 39.9838 | 1.51450 | ||||||||
\(698\) | 78.6939 | 2.97861 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 125.045 | 4.72627 | ||||||||
\(701\) | −8.35579 | −0.315594 | −0.157797 | − | 0.987472i | \(-0.550439\pi\) | ||||
−0.157797 | + | 0.987472i | \(0.550439\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.63720 | 0.212611 | ||||||||
\(704\) | 7.03352 | 0.265086 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 42.3859 | 1.59522 | ||||||||
\(707\) | −39.7691 | −1.49567 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 51.8270 | 1.94640 | 0.973201 | − | 0.229955i | \(-0.0738579\pi\) | ||||
0.973201 | + | 0.229955i | \(0.0738579\pi\) | |||||||
\(710\) | −26.3031 | −0.987138 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.95780 | 0.0733716 | ||||||||
\(713\) | −14.9089 | −0.558343 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.41732 | 0.277392 | ||||||||
\(716\) | −66.0627 | −2.46888 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −22.2294 | −0.829594 | ||||||||
\(719\) | −16.7450 | −0.624484 | −0.312242 | − | 0.950003i | \(-0.601080\pi\) | ||||
−0.312242 | + | 0.950003i | \(0.601080\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 37.9156 | 1.41205 | ||||||||
\(722\) | −50.0621 | −1.86312 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.51687 | 0.167868 | ||||||||
\(725\) | 12.0830 | 0.448752 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.13040 | −0.190276 | −0.0951379 | − | 0.995464i | \(-0.530329\pi\) | ||||
−0.0951379 | + | 0.995464i | \(0.530329\pi\) | |||||||
\(728\) | 19.3429 | 0.716894 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −21.9640 | −0.812922 | ||||||||
\(731\) | 22.7163 | 0.840192 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.8555 | −0.511763 | −0.255882 | − | 0.966708i | \(-0.582366\pi\) | ||||
−0.255882 | + | 0.966708i | \(0.582366\pi\) | |||||||
\(734\) | 63.7994 | 2.35488 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 24.4458 | 0.901085 | ||||||||
\(737\) | −3.04192 | −0.112051 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.2565 | 0.450864 | 0.225432 | − | 0.974259i | \(-0.427621\pi\) | ||||
0.225432 | + | 0.974259i | \(0.427621\pi\) | |||||||
\(740\) | −13.9128 | −0.511445 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 128.064 | 4.70139 | ||||||||
\(743\) | −6.73262 | −0.246996 | −0.123498 | − | 0.992345i | \(-0.539411\pi\) | ||||
−0.123498 | + | 0.992345i | \(0.539411\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.54254 | −0.129788 | ||||||||
\(746\) | 35.8392 | 1.31217 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 53.3872 | 1.95203 | ||||||||
\(749\) | 21.4930 | 0.785336 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.9110 | −1.01849 | −0.509244 | − | 0.860622i | \(-0.670075\pi\) | ||||
−0.509244 | + | 0.860622i | \(0.670075\pi\) | |||||||
\(752\) | −16.8998 | −0.616273 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.46394 | 0.126149 | ||||||||
\(755\) | 67.3582 | 2.45142 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.28185 | 0.228318 | 0.114159 | − | 0.993463i | \(-0.463583\pi\) | ||||
0.114159 | + | 0.993463i | \(0.463583\pi\) | |||||||
\(758\) | −18.9709 | −0.689056 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 130.398 | 4.73003 | ||||||||
\(761\) | 8.56141 | 0.310351 | 0.155175 | − | 0.987887i | \(-0.450406\pi\) | ||||
0.155175 | + | 0.987887i | \(0.450406\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 42.3440 | 1.53296 | ||||||||
\(764\) | 56.8113 | 2.05536 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −90.9240 | −3.28522 | ||||||||
\(767\) | 4.61612 | 0.166678 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.9571 | 0.503304 | 0.251652 | − | 0.967818i | \(-0.419026\pi\) | ||||
0.251652 | + | 0.967818i | \(0.419026\pi\) | |||||||
\(770\) | 82.8998 | 2.98750 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 65.6971 | 2.36449 | ||||||||
\(773\) | −28.6210 | −1.02943 | −0.514713 | − | 0.857362i | \(-0.672102\pi\) | ||||
−0.514713 | + | 0.857362i | \(0.672102\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.3237 | 0.622286 | ||||||||
\(776\) | 108.642 | 3.90003 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −41.8819 | −1.50154 | ||||||||
\(779\) | 49.4267 | 1.77090 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.18306 | −0.257030 | ||||||||
\(782\) | −82.5407 | −2.95165 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 46.6030 | 1.66439 | ||||||||
\(785\) | −61.6803 | −2.20146 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.4572 | 0.907451 | 0.453725 | − | 0.891142i | \(-0.350095\pi\) | ||||
0.453725 | + | 0.891142i | \(0.350095\pi\) | |||||||
\(788\) | 83.4724 | 2.97358 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 93.8288 | 3.33828 | ||||||||
\(791\) | −74.5654 | −2.65124 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.13205 | −0.0402004 | ||||||||
\(794\) | 94.0695 | 3.33840 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −62.1217 | −2.20184 | ||||||||
\(797\) | 11.8383 | 0.419333 | 0.209666 | − | 0.977773i | \(-0.432762\pi\) | ||||
0.209666 | + | 0.977773i | \(0.432762\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.7894 | 0.487833 | ||||||||
\(800\) | −28.4053 | −1.00428 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 32.2229 | 1.13783 | ||||||||
\(803\) | −5.99809 | −0.211668 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −87.7622 | −3.09321 | ||||||||
\(806\) | 4.96633 | 0.174932 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 61.5736 | 2.16615 | ||||||||
\(809\) | 38.7147 | 1.36114 | 0.680569 | − | 0.732684i | \(-0.261733\pi\) | ||||
0.680569 | + | 0.732684i | \(0.261733\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 52.7892 | 1.85368 | 0.926840 | − | 0.375455i | \(-0.122514\pi\) | ||||
0.926840 | + | 0.375455i | \(0.122514\pi\) | |||||||
\(812\) | 26.5094 | 0.930297 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −5.54874 | −0.194483 | ||||||||
\(815\) | −72.3844 | −2.53551 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 28.0811 | 0.982434 | ||||||||
\(818\) | −70.4931 | −2.46473 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −121.987 | −4.25997 | ||||||||
\(821\) | −27.1384 | −0.947136 | −0.473568 | − | 0.880757i | \(-0.657034\pi\) | ||||
−0.473568 | + | 0.880757i | \(0.657034\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.3029 | −0.672856 | −0.336428 | − | 0.941709i | \(-0.609219\pi\) | ||||
−0.336428 | + | 0.941709i | \(0.609219\pi\) | |||||||
\(824\) | −58.7038 | −2.04504 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 51.5921 | 1.79512 | ||||||||
\(827\) | 28.5457 | 0.992633 | 0.496316 | − | 0.868142i | \(-0.334686\pi\) | ||||
0.496316 | + | 0.868142i | \(0.334686\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −51.5908 | −1.79182 | −0.895912 | − | 0.444232i | \(-0.853477\pi\) | ||||
−0.895912 | + | 0.444232i | \(0.853477\pi\) | |||||||
\(830\) | −69.2101 | −2.40232 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.48037 | 0.0859914 | ||||||||
\(833\) | −38.0256 | −1.31751 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 36.6812 | 1.26941 | ||||||||
\(836\) | 65.9956 | 2.28250 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 66.2517 | 2.28863 | ||||||||
\(839\) | −43.8462 | −1.51374 | −0.756870 | − | 0.653565i | \(-0.773273\pi\) | ||||
−0.756870 | + | 0.653565i | \(0.773273\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.4384 | −0.911670 | ||||||||
\(842\) | −14.4771 | −0.498913 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 38.7646 | 1.33433 | ||||||||
\(845\) | −43.4372 | −1.49429 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.3041 | −0.663296 | ||||||||
\(848\) | −82.4300 | −2.83066 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 95.9099 | 3.28968 | ||||||||
\(851\) | 5.87419 | 0.201365 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.31118 | −0.147612 | −0.0738061 | − | 0.997273i | \(-0.523515\pi\) | ||||
−0.0738061 | + | 0.997273i | \(0.523515\pi\) | |||||||
\(854\) | −12.6524 | −0.432957 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −33.2771 | −1.13739 | ||||||||
\(857\) | 14.3215 | 0.489212 | 0.244606 | − | 0.969623i | \(-0.421341\pi\) | ||||
0.244606 | + | 0.969623i | \(0.421341\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.8911 | 0.405720 | 0.202860 | − | 0.979208i | \(-0.434976\pi\) | ||||
0.202860 | + | 0.979208i | \(0.434976\pi\) | |||||||
\(860\) | −69.3053 | −2.36329 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −21.7351 | −0.740299 | ||||||||
\(863\) | −18.9929 | −0.646526 | −0.323263 | − | 0.946309i | \(-0.604780\pi\) | ||||
−0.323263 | + | 0.946309i | \(0.604780\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 73.3842 | 2.49514 | ||||||||
\(866\) | −46.8252 | −1.59119 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 38.0071 | 1.29005 | ||||||||
\(869\) | 25.6235 | 0.869218 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.07273 | −0.0363482 | ||||||||
\(872\) | −65.5603 | −2.22015 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −102.034 | −3.45136 | ||||||||
\(875\) | 34.4387 | 1.16424 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −53.0314 | −1.79074 | −0.895372 | − | 0.445319i | \(-0.853090\pi\) | ||||
−0.895372 | + | 0.445319i | \(0.853090\pi\) | |||||||
\(878\) | −7.15781 | −0.241565 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −53.3593 | −1.79874 | ||||||||
\(881\) | 2.62841 | 0.0885533 | 0.0442766 | − | 0.999019i | \(-0.485902\pi\) | ||||
0.0442766 | + | 0.999019i | \(0.485902\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.1139 | −0.374011 | −0.187006 | − | 0.982359i | \(-0.559878\pi\) | ||||
−0.187006 | + | 0.982359i | \(0.559878\pi\) | |||||||
\(884\) | 18.8270 | 0.633221 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −74.8052 | −2.51313 | ||||||||
\(887\) | −20.8917 | −0.701473 | −0.350737 | − | 0.936474i | \(-0.614069\pi\) | ||||
−0.350737 | + | 0.936474i | \(0.614069\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 76.5881 | 2.56868 | ||||||||
\(890\) | 2.95900 | 0.0991859 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.42071 | −0.148016 | ||||||||
\(893\) | 17.0460 | 0.570422 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −53.8755 | −1.80086 | ||||||||
\(896\) | 56.4148 | 1.88469 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 19.3287 | 0.645006 | ||||||||
\(899\) | 3.67260 | 0.122488 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 67.2586 | 2.24071 | ||||||||
\(902\) | −48.6511 | −1.61990 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 115.448 | 3.83974 | ||||||||
\(905\) | 3.68360 | 0.122447 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.86295 | −0.128267 | −0.0641335 | − | 0.997941i | \(-0.520428\pi\) | ||||
−0.0641335 | + | 0.997941i | \(0.520428\pi\) | |||||||
\(908\) | 4.28336 | 0.142148 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 29.2346 | 0.969118 | ||||||||
\(911\) | −33.9317 | −1.12421 | −0.562103 | − | 0.827067i | \(-0.690008\pi\) | ||||
−0.562103 | + | 0.827067i | \(0.690008\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.9004 | −0.625513 | ||||||||
\(914\) | 19.7430 | 0.653040 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 70.5343 | 2.33052 | ||||||||
\(917\) | 24.0887 | 0.795480 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 53.1931 | 1.75468 | 0.877339 | − | 0.479871i | \(-0.159316\pi\) | ||||
0.877339 | + | 0.479871i | \(0.159316\pi\) | |||||||
\(920\) | 135.880 | 4.47984 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −56.8021 | −1.87068 | ||||||||
\(923\) | −2.53311 | −0.0833782 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.82564 | −0.224426 | ||||||||
\(926\) | 7.83485 | 0.257469 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.02188 | −0.197678 | ||||||||
\(929\) | −26.3041 | −0.863010 | −0.431505 | − | 0.902111i | \(-0.642017\pi\) | ||||
−0.431505 | + | 0.902111i | \(0.642017\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −47.0060 | −1.54056 | ||||||||
\(932\) | −24.0728 | −0.788530 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −23.7686 | −0.777734 | ||||||||
\(935\) | 43.5384 | 1.42386 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.5656 | −0.541174 | −0.270587 | − | 0.962695i | \(-0.587218\pi\) | ||||
−0.270587 | + | 0.962695i | \(0.587218\pi\) | |||||||
\(938\) | −11.9894 | −0.391468 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −42.0701 | −1.37218 | ||||||||
\(941\) | −52.1923 | −1.70142 | −0.850711 | − | 0.525634i | \(-0.823828\pi\) | ||||
−0.850711 | + | 0.525634i | \(0.823828\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 51.5047 | 1.67722 | ||||||||
\(944\) | −33.2078 | −1.08082 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −27.6405 | −0.898669 | ||||||||
\(947\) | 21.4194 | 0.696037 | 0.348018 | − | 0.937488i | \(-0.386855\pi\) | ||||
0.348018 | + | 0.937488i | \(0.386855\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.11523 | −0.0686632 | ||||||||
\(950\) | 118.561 | 3.84662 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 113.539 | 3.67983 | ||||||||
\(953\) | −28.4814 | −0.922604 | −0.461302 | − | 0.887243i | \(-0.652617\pi\) | ||||
−0.461302 | + | 0.887243i | \(0.652617\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 46.3308 | 1.49923 | ||||||||
\(956\) | 18.8609 | 0.610005 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −54.6888 | −1.76692 | ||||||||
\(959\) | −24.6157 | −0.794881 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.7345 | −0.830146 | ||||||||
\(962\) | −1.95676 | −0.0630886 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −48.2544 | −1.55417 | ||||||||
\(965\) | 53.5774 | 1.72472 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.0595 | −1.48117 | −0.740587 | − | 0.671961i | \(-0.765452\pi\) | ||||
−0.740587 | + | 0.671961i | \(0.765452\pi\) | |||||||
\(968\) | 29.8881 | 0.960639 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 164.201 | 5.27218 | ||||||||
\(971\) | 11.9120 | 0.382273 | 0.191137 | − | 0.981563i | \(-0.438783\pi\) | ||||
0.191137 | + | 0.981563i | \(0.438783\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −58.7289 | −1.88276 | ||||||||
\(974\) | 78.0766 | 2.50174 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.14386 | 0.260679 | ||||||||
\(977\) | 5.22896 | 0.167289 | 0.0836447 | − | 0.996496i | \(-0.473344\pi\) | ||||
0.0836447 | + | 0.996496i | \(0.473344\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.808067 | 0.0258259 | ||||||||
\(980\) | 116.013 | 3.70589 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 37.6573 | 1.20169 | ||||||||
\(983\) | 31.5001 | 1.00470 | 0.502349 | − | 0.864665i | \(-0.332469\pi\) | ||||
0.502349 | + | 0.864665i | \(0.332469\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 68.0735 | 2.16900 | ||||||||
\(986\) | 20.3327 | 0.647526 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 23.2733 | 0.740424 | ||||||||
\(989\) | 29.2617 | 0.930468 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.3670 | 0.996407 | 0.498203 | − | 0.867060i | \(-0.333993\pi\) | ||||
0.498203 | + | 0.867060i | \(0.333993\pi\) | |||||||
\(992\) | −8.63371 | −0.274121 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −28.3113 | −0.897980 | ||||||||
\(995\) | −50.6615 | −1.60608 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46.0663 | 1.45894 | 0.729468 | − | 0.684015i | \(-0.239768\pi\) | ||||
0.729468 | + | 0.684015i | \(0.239768\pi\) | |||||||
\(998\) | 36.0423 | 1.14090 | ||||||||
\(999\) | 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 | 4023.2.a.e.1.3 | ✓ | 25 | |
3.2 | odd | 2 | 4023.2.a.f.1.23 | yes | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4023.2.a.e.1.3 | ✓ | 25 | 1.1 | even | 1 | trivial | |
4023.2.a.f.1.23 | yes | 25 | 3.2 | odd | 2 |