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: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5 x^{11} - 3 x^{10} + 41 x^{9} - 11 x^{8} - 123 x^{7} + 44 x^{6} + 159 x^{5} - 39 x^{4} - 71 x^{3} + 16 x^{2} + 7 x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 889) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.94650\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.946499 | −0.669276 | −0.334638 | − | 0.942347i | \(-0.608614\pi\) | ||||
−0.334638 | + | 0.942347i | \(0.608614\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.10414 | −0.552070 | ||||||||
\(5\) | 2.90523 | 1.29926 | 0.649629 | − | 0.760252i | \(-0.274924\pi\) | ||||
0.649629 | + | 0.760252i | \(0.274924\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.93806 | 1.03876 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.74979 | −0.869561 | ||||||||
\(11\) | 4.94698 | 1.49157 | 0.745786 | − | 0.666186i | \(-0.232074\pi\) | ||||
0.745786 | + | 0.666186i | \(0.232074\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.17643 | 0.603632 | 0.301816 | − | 0.953366i | \(-0.402407\pi\) | ||||
0.301816 | + | 0.953366i | \(0.402407\pi\) | |||||||
\(14\) | −0.946499 | −0.252962 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.572592 | −0.143148 | ||||||||
\(17\) | 3.30137 | 0.800701 | 0.400350 | − | 0.916362i | \(-0.368888\pi\) | ||||
0.400350 | + | 0.916362i | \(0.368888\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.52914 | −0.809640 | −0.404820 | − | 0.914397i | \(-0.632666\pi\) | ||||
−0.404820 | + | 0.914397i | \(0.632666\pi\) | |||||||
\(20\) | −3.20778 | −0.717281 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.68231 | −0.998272 | ||||||||
\(23\) | −0.742903 | −0.154906 | −0.0774530 | − | 0.996996i | \(-0.524679\pi\) | ||||
−0.0774530 | + | 0.996996i | \(0.524679\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.44035 | 0.688070 | ||||||||
\(26\) | −2.05998 | −0.403996 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.10414 | −0.208663 | ||||||||
\(29\) | −0.319007 | −0.0592381 | −0.0296191 | − | 0.999561i | \(-0.509429\pi\) | ||||
−0.0296191 | + | 0.999561i | \(0.509429\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.09600 | −1.27448 | −0.637240 | − | 0.770665i | \(-0.719924\pi\) | ||||
−0.637240 | + | 0.770665i | \(0.719924\pi\) | |||||||
\(32\) | −5.33417 | −0.942957 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.12475 | −0.535889 | ||||||||
\(35\) | 2.90523 | 0.491073 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.44695 | 0.895474 | 0.447737 | − | 0.894165i | \(-0.352230\pi\) | ||||
0.447737 | + | 0.894165i | \(0.352230\pi\) | |||||||
\(38\) | 3.34032 | 0.541872 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 8.53575 | 1.34962 | ||||||||
\(41\) | −4.63255 | −0.723482 | −0.361741 | − | 0.932279i | \(-0.617818\pi\) | ||||
−0.361741 | + | 0.932279i | \(0.617818\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.59387 | 0.395562 | 0.197781 | − | 0.980246i | \(-0.436627\pi\) | ||||
0.197781 | + | 0.980246i | \(0.436627\pi\) | |||||||
\(44\) | −5.46216 | −0.823452 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.703156 | 0.103675 | ||||||||
\(47\) | 2.05606 | 0.299907 | 0.149954 | − | 0.988693i | \(-0.452088\pi\) | ||||
0.149954 | + | 0.988693i | \(0.452088\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.25629 | −0.460508 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.40308 | −0.333247 | ||||||||
\(53\) | 8.76118 | 1.20344 | 0.601720 | − | 0.798707i | \(-0.294482\pi\) | ||||
0.601720 | + | 0.798707i | \(0.294482\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.3721 | 1.93794 | ||||||||
\(56\) | 2.93806 | 0.392615 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.301940 | 0.0396466 | ||||||||
\(59\) | 12.4619 | 1.62240 | 0.811199 | − | 0.584770i | \(-0.198815\pi\) | ||||
0.811199 | + | 0.584770i | \(0.198815\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.4232 | 1.33455 | 0.667277 | − | 0.744809i | \(-0.267460\pi\) | ||||
0.667277 | + | 0.744809i | \(0.267460\pi\) | |||||||
\(62\) | 6.71636 | 0.852978 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.19397 | 0.774246 | ||||||||
\(65\) | 6.32301 | 0.784273 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.00987 | 0.367714 | 0.183857 | − | 0.982953i | \(-0.441142\pi\) | ||||
0.183857 | + | 0.982953i | \(0.441142\pi\) | |||||||
\(68\) | −3.64518 | −0.442043 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.74979 | −0.328663 | ||||||||
\(71\) | 15.6703 | 1.85972 | 0.929859 | − | 0.367916i | \(-0.119928\pi\) | ||||
0.929859 | + | 0.367916i | \(0.119928\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.60269 | 0.772787 | 0.386393 | − | 0.922334i | \(-0.373721\pi\) | ||||
0.386393 | + | 0.922334i | \(0.373721\pi\) | |||||||
\(74\) | −5.15553 | −0.599319 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.89666 | 0.446978 | ||||||||
\(77\) | 4.94698 | 0.563761 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.76302 | 0.310865 | 0.155432 | − | 0.987847i | \(-0.450323\pi\) | ||||
0.155432 | + | 0.987847i | \(0.450323\pi\) | |||||||
\(80\) | −1.66351 | −0.185986 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.38470 | 0.484209 | ||||||||
\(83\) | −11.9081 | −1.30709 | −0.653544 | − | 0.756888i | \(-0.726719\pi\) | ||||
−0.653544 | + | 0.756888i | \(0.726719\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.59124 | 1.04032 | ||||||||
\(86\) | −2.45510 | −0.264740 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 14.5346 | 1.54939 | ||||||||
\(89\) | −10.9952 | −1.16549 | −0.582746 | − | 0.812654i | \(-0.698022\pi\) | ||||
−0.582746 | + | 0.812654i | \(0.698022\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.17643 | 0.228151 | ||||||||
\(92\) | 0.820269 | 0.0855190 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.94606 | −0.200721 | ||||||||
\(95\) | −10.2529 | −1.05193 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.7659 | −1.60078 | −0.800391 | − | 0.599478i | \(-0.795375\pi\) | ||||
−0.800391 | + | 0.599478i | \(0.795375\pi\) | |||||||
\(98\) | −0.946499 | −0.0956108 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.79863 | −0.379863 | ||||||||
\(101\) | −11.5305 | −1.14733 | −0.573665 | − | 0.819090i | \(-0.694479\pi\) | ||||
−0.573665 | + | 0.819090i | \(0.694479\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.90350 | 0.680222 | 0.340111 | − | 0.940385i | \(-0.389535\pi\) | ||||
0.340111 | + | 0.940385i | \(0.389535\pi\) | |||||||
\(104\) | 6.39448 | 0.627030 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.29244 | −0.805433 | ||||||||
\(107\) | −0.262006 | −0.0253290 | −0.0126645 | − | 0.999920i | \(-0.504031\pi\) | ||||
−0.0126645 | + | 0.999920i | \(0.504031\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.3229 | −0.988753 | −0.494377 | − | 0.869248i | \(-0.664604\pi\) | ||||
−0.494377 | + | 0.869248i | \(0.664604\pi\) | |||||||
\(110\) | −13.6032 | −1.29701 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.572592 | −0.0541049 | ||||||||
\(113\) | 9.52058 | 0.895621 | 0.447811 | − | 0.894128i | \(-0.352204\pi\) | ||||
0.447811 | + | 0.894128i | \(0.352204\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.15830 | −0.201263 | ||||||||
\(116\) | 0.352229 | 0.0327036 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.7951 | −1.08583 | ||||||||
\(119\) | 3.30137 | 0.302636 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.4726 | 1.22479 | ||||||||
\(122\) | −9.86555 | −0.893185 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.83499 | 0.703603 | ||||||||
\(125\) | −4.53114 | −0.405277 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | 4.80576 | 0.424773 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.98472 | −0.524895 | ||||||||
\(131\) | 2.11923 | 0.185158 | 0.0925791 | − | 0.995705i | \(-0.470489\pi\) | ||||
0.0925791 | + | 0.995705i | \(0.470489\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.52914 | −0.306015 | ||||||||
\(134\) | −2.84883 | −0.246102 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.69965 | 0.831738 | ||||||||
\(137\) | −1.54986 | −0.132414 | −0.0662069 | − | 0.997806i | \(-0.521090\pi\) | ||||
−0.0662069 | + | 0.997806i | \(0.521090\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.95651 | 0.844500 | 0.422250 | − | 0.906479i | \(-0.361240\pi\) | ||||
0.422250 | + | 0.906479i | \(0.361240\pi\) | |||||||
\(140\) | −3.20778 | −0.271107 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −14.8319 | −1.24466 | ||||||||
\(143\) | 10.7667 | 0.900360 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.926788 | −0.0769656 | ||||||||
\(146\) | −6.24944 | −0.517207 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.01420 | −0.494365 | ||||||||
\(149\) | −7.29141 | −0.597335 | −0.298668 | − | 0.954357i | \(-0.596542\pi\) | ||||
−0.298668 | + | 0.954357i | \(0.596542\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.8054 | −1.20485 | −0.602424 | − | 0.798176i | \(-0.705798\pi\) | ||||
−0.602424 | + | 0.798176i | \(0.705798\pi\) | |||||||
\(152\) | −10.3688 | −0.841023 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.68231 | −0.377311 | ||||||||
\(155\) | −20.6155 | −1.65588 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.6316 | −1.72639 | −0.863196 | − | 0.504868i | \(-0.831541\pi\) | ||||
−0.863196 | + | 0.504868i | \(0.831541\pi\) | |||||||
\(158\) | −2.61520 | −0.208054 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −15.4970 | −1.22514 | ||||||||
\(161\) | −0.742903 | −0.0585489 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.35133 | −0.262496 | −0.131248 | − | 0.991350i | \(-0.541898\pi\) | ||||
−0.131248 | + | 0.991350i | \(0.541898\pi\) | |||||||
\(164\) | 5.11498 | 0.399413 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.2710 | 0.874802 | ||||||||
\(167\) | 9.37694 | 0.725609 | 0.362805 | − | 0.931865i | \(-0.381819\pi\) | ||||
0.362805 | + | 0.931865i | \(0.381819\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.26317 | −0.635629 | ||||||||
\(170\) | −9.07810 | −0.696258 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.86400 | −0.218378 | ||||||||
\(173\) | 7.49955 | 0.570180 | 0.285090 | − | 0.958501i | \(-0.407977\pi\) | ||||
0.285090 | + | 0.958501i | \(0.407977\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.44035 | 0.260066 | ||||||||
\(176\) | −2.83261 | −0.213516 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 10.4070 | 0.780035 | ||||||||
\(179\) | 8.83499 | 0.660358 | 0.330179 | − | 0.943918i | \(-0.392891\pi\) | ||||
0.330179 | + | 0.943918i | \(0.392891\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.61913 | −0.269008 | −0.134504 | − | 0.990913i | \(-0.542944\pi\) | ||||
−0.134504 | + | 0.990913i | \(0.542944\pi\) | |||||||
\(182\) | −2.05998 | −0.152696 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.18270 | −0.160911 | ||||||||
\(185\) | 15.8246 | 1.16345 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.3318 | 1.19430 | ||||||||
\(188\) | −2.27018 | −0.165570 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.70440 | 0.704031 | ||||||||
\(191\) | 7.37068 | 0.533324 | 0.266662 | − | 0.963790i | \(-0.414079\pi\) | ||||
0.266662 | + | 0.963790i | \(0.414079\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.10872 | 0.439715 | 0.219858 | − | 0.975532i | \(-0.429441\pi\) | ||||
0.219858 | + | 0.975532i | \(0.429441\pi\) | |||||||
\(194\) | 14.9224 | 1.07136 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.10414 | −0.0788672 | ||||||||
\(197\) | 23.9507 | 1.70642 | 0.853210 | − | 0.521568i | \(-0.174653\pi\) | ||||
0.853210 | + | 0.521568i | \(0.174653\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.99542 | 0.637669 | 0.318834 | − | 0.947810i | \(-0.396709\pi\) | ||||
0.318834 | + | 0.947810i | \(0.396709\pi\) | |||||||
\(200\) | 10.1080 | 0.714741 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.9136 | 0.767880 | ||||||||
\(203\) | −0.319007 | −0.0223899 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.4586 | −0.939990 | ||||||||
\(206\) | −6.53415 | −0.455256 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.24620 | −0.0864087 | ||||||||
\(209\) | −17.4586 | −1.20764 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.24920 | 0.567898 | 0.283949 | − | 0.958839i | \(-0.408355\pi\) | ||||
0.283949 | + | 0.958839i | \(0.408355\pi\) | |||||||
\(212\) | −9.67357 | −0.664383 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.247988 | 0.0169521 | ||||||||
\(215\) | 7.53579 | 0.513936 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.09600 | −0.481708 | ||||||||
\(218\) | 9.77060 | 0.661748 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −15.8688 | −1.06988 | ||||||||
\(221\) | 7.18519 | 0.483328 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.19009 | 0.347554 | 0.173777 | − | 0.984785i | \(-0.444403\pi\) | ||||
0.173777 | + | 0.984785i | \(0.444403\pi\) | |||||||
\(224\) | −5.33417 | −0.356404 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.01122 | −0.599417 | ||||||||
\(227\) | 3.74134 | 0.248321 | 0.124161 | − | 0.992262i | \(-0.460376\pi\) | ||||
0.124161 | + | 0.992262i | \(0.460376\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.06533 | −0.599054 | −0.299527 | − | 0.954088i | \(-0.596829\pi\) | ||||
−0.299527 | + | 0.954088i | \(0.596829\pi\) | |||||||
\(230\) | 2.04283 | 0.134700 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.937263 | −0.0615343 | ||||||||
\(233\) | 5.38719 | 0.352927 | 0.176463 | − | 0.984307i | \(-0.443534\pi\) | ||||
0.176463 | + | 0.984307i | \(0.443534\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.97333 | 0.389657 | ||||||||
\(236\) | −13.7597 | −0.895678 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.12475 | −0.202547 | ||||||||
\(239\) | −20.2277 | −1.30842 | −0.654212 | − | 0.756311i | \(-0.727000\pi\) | ||||
−0.654212 | + | 0.756311i | \(0.727000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.7927 | −0.695221 | −0.347610 | − | 0.937639i | \(-0.613007\pi\) | ||||
−0.347610 | + | 0.937639i | \(0.613007\pi\) | |||||||
\(242\) | −12.7518 | −0.819719 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −11.5087 | −0.736768 | ||||||||
\(245\) | 2.90523 | 0.185608 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.68090 | −0.488724 | ||||||||
\(248\) | −20.8485 | −1.32388 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.28872 | 0.271242 | ||||||||
\(251\) | 4.47720 | 0.282599 | 0.141299 | − | 0.989967i | \(-0.454872\pi\) | ||||
0.141299 | + | 0.989967i | \(0.454872\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.67513 | −0.231053 | ||||||||
\(254\) | −0.946499 | −0.0593886 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.9366 | −1.05854 | ||||||||
\(257\) | −14.0925 | −0.879064 | −0.439532 | − | 0.898227i | \(-0.644856\pi\) | ||||
−0.439532 | + | 0.898227i | \(0.644856\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.44695 | 0.338457 | ||||||||
\(260\) | −6.98149 | −0.432974 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.00585 | −0.123922 | ||||||||
\(263\) | 26.2405 | 1.61806 | 0.809028 | − | 0.587770i | \(-0.199994\pi\) | ||||
0.809028 | + | 0.587770i | \(0.199994\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.4532 | 1.56358 | ||||||||
\(266\) | 3.34032 | 0.204808 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.32332 | −0.203004 | ||||||||
\(269\) | −25.1525 | −1.53357 | −0.766787 | − | 0.641901i | \(-0.778146\pi\) | ||||
−0.766787 | + | 0.641901i | \(0.778146\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.8886 | −1.75486 | −0.877428 | − | 0.479709i | \(-0.840742\pi\) | ||||
−0.877428 | + | 0.479709i | \(0.840742\pi\) | |||||||
\(272\) | −1.89034 | −0.114619 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.46694 | 0.0886213 | ||||||||
\(275\) | 17.0194 | 1.02631 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.0555 | 0.784431 | 0.392216 | − | 0.919873i | \(-0.371709\pi\) | ||||
0.392216 | + | 0.919873i | \(0.371709\pi\) | |||||||
\(278\) | −9.42382 | −0.565203 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8.53575 | 0.510108 | ||||||||
\(281\) | 18.9153 | 1.12839 | 0.564197 | − | 0.825640i | \(-0.309186\pi\) | ||||
0.564197 | + | 0.825640i | \(0.309186\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.0469 | 1.13222 | 0.566112 | − | 0.824328i | \(-0.308447\pi\) | ||||
0.566112 | + | 0.824328i | \(0.308447\pi\) | |||||||
\(284\) | −17.3022 | −1.02670 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10.1907 | −0.602589 | ||||||||
\(287\) | −4.63255 | −0.273451 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.10093 | −0.358878 | ||||||||
\(290\) | 0.877204 | 0.0515112 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.29030 | −0.426633 | ||||||||
\(293\) | −19.7793 | −1.15552 | −0.577759 | − | 0.816207i | \(-0.696073\pi\) | ||||
−0.577759 | + | 0.816207i | \(0.696073\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 36.2046 | 2.10791 | ||||||||
\(296\) | 16.0035 | 0.930185 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.90131 | 0.399782 | ||||||||
\(299\) | −1.61687 | −0.0935061 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.59387 | 0.149508 | ||||||||
\(302\) | 14.0133 | 0.806375 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.02076 | 0.115898 | ||||||||
\(305\) | 30.2818 | 1.73393 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.97628 | 0.455230 | 0.227615 | − | 0.973751i | \(-0.426907\pi\) | ||||
0.227615 | + | 0.973751i | \(0.426907\pi\) | |||||||
\(308\) | −5.46216 | −0.311236 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 19.5126 | 1.10824 | ||||||||
\(311\) | −8.94253 | −0.507084 | −0.253542 | − | 0.967324i | \(-0.581596\pi\) | ||||
−0.253542 | + | 0.967324i | \(0.581596\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.35550 | 0.189664 | 0.0948320 | − | 0.995493i | \(-0.469769\pi\) | ||||
0.0948320 | + | 0.995493i | \(0.469769\pi\) | |||||||
\(314\) | 20.4743 | 1.15543 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.05077 | −0.171619 | ||||||||
\(317\) | 32.1693 | 1.80681 | 0.903405 | − | 0.428788i | \(-0.141059\pi\) | ||||
0.903405 | + | 0.428788i | \(0.141059\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.57812 | −0.0883579 | ||||||||
\(320\) | 17.9949 | 1.00595 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.703156 | 0.0391854 | ||||||||
\(323\) | −11.6510 | −0.648279 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.48766 | 0.415341 | ||||||||
\(326\) | 3.17202 | 0.175682 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −13.6107 | −0.751526 | ||||||||
\(329\) | 2.05606 | 0.113354 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.65680 | −0.475821 | −0.237910 | − | 0.971287i | \(-0.576462\pi\) | ||||
−0.237910 | + | 0.971287i | \(0.576462\pi\) | |||||||
\(332\) | 13.1483 | 0.721604 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.87526 | −0.485632 | ||||||||
\(335\) | 8.74435 | 0.477755 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.57382 | 0.467046 | 0.233523 | − | 0.972351i | \(-0.424975\pi\) | ||||
0.233523 | + | 0.972351i | \(0.424975\pi\) | |||||||
\(338\) | 7.82108 | 0.425411 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −10.5901 | −0.574328 | ||||||||
\(341\) | −35.1038 | −1.90098 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 7.62096 | 0.410895 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.09831 | −0.381607 | ||||||||
\(347\) | 7.60641 | 0.408333 | 0.204167 | − | 0.978936i | \(-0.434552\pi\) | ||||
0.204167 | + | 0.978936i | \(0.434552\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.7137 | 1.69760 | 0.848798 | − | 0.528718i | \(-0.177327\pi\) | ||||
0.848798 | + | 0.528718i | \(0.177327\pi\) | |||||||
\(350\) | −3.25629 | −0.174056 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −26.3881 | −1.40649 | ||||||||
\(353\) | −9.13856 | −0.486397 | −0.243198 | − | 0.969977i | \(-0.578197\pi\) | ||||
−0.243198 | + | 0.969977i | \(0.578197\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 45.5257 | 2.41625 | ||||||||
\(356\) | 12.1403 | 0.643433 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.36230 | −0.441962 | ||||||||
\(359\) | −20.8619 | −1.10105 | −0.550525 | − | 0.834819i | \(-0.685572\pi\) | ||||
−0.550525 | + | 0.834819i | \(0.685572\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.54519 | −0.344484 | ||||||||
\(362\) | 3.42550 | 0.180041 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.40308 | −0.125956 | ||||||||
\(365\) | 19.1823 | 1.00405 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −33.9477 | −1.77206 | −0.886028 | − | 0.463631i | \(-0.846546\pi\) | ||||
−0.886028 | + | 0.463631i | \(0.846546\pi\) | |||||||
\(368\) | 0.425381 | 0.0221745 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −14.9780 | −0.778669 | ||||||||
\(371\) | 8.76118 | 0.454858 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.1597 | −1.30272 | −0.651360 | − | 0.758769i | \(-0.725801\pi\) | ||||
−0.651360 | + | 0.758769i | \(0.725801\pi\) | |||||||
\(374\) | −15.4581 | −0.799317 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.04084 | 0.311533 | ||||||||
\(377\) | −0.694295 | −0.0357580 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.6120 | 1.57243 | 0.786216 | − | 0.617951i | \(-0.212037\pi\) | ||||
0.786216 | + | 0.617951i | \(0.212037\pi\) | |||||||
\(380\) | 11.3207 | 0.580739 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.97634 | −0.356941 | ||||||||
\(383\) | 38.1453 | 1.94913 | 0.974567 | − | 0.224098i | \(-0.0719435\pi\) | ||||
0.974567 | + | 0.224098i | \(0.0719435\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.3721 | 0.732471 | ||||||||
\(386\) | −5.78189 | −0.294291 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 17.4077 | 0.883744 | ||||||||
\(389\) | 12.6250 | 0.640115 | 0.320057 | − | 0.947398i | \(-0.396298\pi\) | ||||
0.320057 | + | 0.947398i | \(0.396298\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.45260 | −0.124033 | ||||||||
\(392\) | 2.93806 | 0.148395 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −22.6693 | −1.14206 | ||||||||
\(395\) | 8.02722 | 0.403893 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.5214 | −1.43145 | −0.715723 | − | 0.698384i | \(-0.753903\pi\) | ||||
−0.715723 | + | 0.698384i | \(0.753903\pi\) | |||||||
\(398\) | −8.51415 | −0.426776 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.96992 | −0.0984959 | ||||||||
\(401\) | −37.6239 | −1.87885 | −0.939424 | − | 0.342758i | \(-0.888639\pi\) | ||||
−0.939424 | + | 0.342758i | \(0.888639\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.4439 | −0.769317 | ||||||||
\(404\) | 12.7313 | 0.633407 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.301940 | 0.0149850 | ||||||||
\(407\) | 26.9460 | 1.33566 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.0228 | −0.495597 | −0.247799 | − | 0.968812i | \(-0.579707\pi\) | ||||
−0.247799 | + | 0.968812i | \(0.579707\pi\) | |||||||
\(410\) | 12.7386 | 0.629112 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.62243 | −0.375530 | ||||||||
\(413\) | 12.4619 | 0.613209 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −34.5959 | −1.69824 | ||||||||
\(416\) | −11.6094 | −0.569199 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 16.5245 | 0.808241 | ||||||||
\(419\) | −15.8944 | −0.776492 | −0.388246 | − | 0.921556i | \(-0.626919\pi\) | ||||
−0.388246 | + | 0.921556i | \(0.626919\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.9881 | 1.21784 | 0.608922 | − | 0.793230i | \(-0.291602\pi\) | ||||
0.608922 | + | 0.793230i | \(0.291602\pi\) | |||||||
\(422\) | −7.80785 | −0.380080 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 25.7409 | 1.25009 | ||||||||
\(425\) | 11.3579 | 0.550938 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.4232 | 0.504414 | ||||||||
\(428\) | 0.289291 | 0.0139834 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.13261 | −0.343965 | ||||||||
\(431\) | 21.3467 | 1.02823 | 0.514117 | − | 0.857720i | \(-0.328120\pi\) | ||||
0.514117 | + | 0.857720i | \(0.328120\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.8838 | 0.667213 | 0.333607 | − | 0.942712i | \(-0.391734\pi\) | ||||
0.333607 | + | 0.942712i | \(0.391734\pi\) | |||||||
\(434\) | 6.71636 | 0.322395 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.3979 | 0.545861 | ||||||||
\(437\) | 2.62181 | 0.125418 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.27790 | 0.251900 | 0.125950 | − | 0.992037i | \(-0.459802\pi\) | ||||
0.125950 | + | 0.992037i | \(0.459802\pi\) | |||||||
\(440\) | 42.2262 | 2.01306 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.80077 | −0.323480 | ||||||||
\(443\) | −1.78515 | −0.0848152 | −0.0424076 | − | 0.999100i | \(-0.513503\pi\) | ||||
−0.0424076 | + | 0.999100i | \(0.513503\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −31.9436 | −1.51427 | ||||||||
\(446\) | −4.91241 | −0.232609 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.19397 | 0.292638 | ||||||||
\(449\) | 40.5984 | 1.91596 | 0.957979 | − | 0.286837i | \(-0.0926038\pi\) | ||||
0.957979 | + | 0.286837i | \(0.0926038\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.9171 | −1.07913 | ||||||||
\(452\) | −10.5121 | −0.494446 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.54117 | −0.166195 | ||||||||
\(455\) | 6.32301 | 0.296427 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.95828 | −0.372273 | −0.186136 | − | 0.982524i | \(-0.559597\pi\) | ||||
−0.186136 | + | 0.982524i | \(0.559597\pi\) | |||||||
\(458\) | 8.58032 | 0.400932 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.38307 | 0.111111 | ||||||||
\(461\) | 23.4497 | 1.09216 | 0.546080 | − | 0.837733i | \(-0.316120\pi\) | ||||
0.546080 | + | 0.837733i | \(0.316120\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.8328 | −0.503441 | −0.251721 | − | 0.967800i | \(-0.580996\pi\) | ||||
−0.251721 | + | 0.967800i | \(0.580996\pi\) | |||||||
\(464\) | 0.182661 | 0.00847983 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.09897 | −0.236205 | ||||||||
\(467\) | 34.7902 | 1.60990 | 0.804948 | − | 0.593345i | \(-0.202193\pi\) | ||||
0.804948 | + | 0.593345i | \(0.202193\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.00987 | 0.138983 | ||||||||
\(470\) | −5.65374 | −0.260788 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 36.6138 | 1.68529 | ||||||||
\(473\) | 12.8318 | 0.590009 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.1415 | −0.557089 | ||||||||
\(476\) | −3.64518 | −0.167077 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 19.1455 | 0.875696 | ||||||||
\(479\) | −10.0138 | −0.457543 | −0.228772 | − | 0.973480i | \(-0.573471\pi\) | ||||
−0.228772 | + | 0.973480i | \(0.573471\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.8549 | 0.540536 | ||||||||
\(482\) | 10.2153 | 0.465294 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −14.8757 | −0.676168 | ||||||||
\(485\) | −45.8035 | −2.07983 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.0140 | −1.45069 | −0.725347 | − | 0.688384i | \(-0.758320\pi\) | ||||
−0.725347 | + | 0.688384i | \(0.758320\pi\) | |||||||
\(488\) | 30.6240 | 1.38629 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.74979 | −0.124223 | ||||||||
\(491\) | −12.2449 | −0.552604 | −0.276302 | − | 0.961071i | \(-0.589109\pi\) | ||||
−0.276302 | + | 0.961071i | \(0.589109\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.05316 | −0.0474320 | ||||||||
\(494\) | 7.26996 | 0.327091 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.06312 | 0.182439 | ||||||||
\(497\) | 15.6703 | 0.702907 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.5460 | −0.785465 | −0.392732 | − | 0.919653i | \(-0.628470\pi\) | ||||
−0.392732 | + | 0.919653i | \(0.628470\pi\) | |||||||
\(500\) | 5.00302 | 0.223742 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.23767 | −0.189136 | ||||||||
\(503\) | −1.16673 | −0.0520218 | −0.0260109 | − | 0.999662i | \(-0.508280\pi\) | ||||
−0.0260109 | + | 0.999662i | \(0.508280\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −33.4988 | −1.49068 | ||||||||
\(506\) | 3.47850 | 0.154638 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.10414 | −0.0489883 | ||||||||
\(509\) | −28.2068 | −1.25025 | −0.625123 | − | 0.780526i | \(-0.714951\pi\) | ||||
−0.625123 | + | 0.780526i | \(0.714951\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.60269 | 0.292086 | ||||||||
\(512\) | 6.41893 | 0.283679 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 13.3385 | 0.588336 | ||||||||
\(515\) | 20.0562 | 0.883783 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.1713 | 0.447333 | ||||||||
\(518\) | −5.15553 | −0.226521 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 18.5774 | 0.814674 | ||||||||
\(521\) | −24.2587 | −1.06279 | −0.531397 | − | 0.847123i | \(-0.678333\pi\) | ||||
−0.531397 | + | 0.847123i | \(0.678333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 38.2576 | 1.67289 | 0.836443 | − | 0.548053i | \(-0.184631\pi\) | ||||
0.836443 | + | 0.548053i | \(0.184631\pi\) | |||||||
\(524\) | −2.33993 | −0.102220 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.8366 | −1.08293 | ||||||||
\(527\) | −23.4266 | −1.02048 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.4481 | −0.976004 | ||||||||
\(530\) | −24.0914 | −1.04646 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.89666 | 0.168942 | ||||||||
\(533\) | −10.0824 | −0.436717 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.761186 | −0.0329089 | ||||||||
\(536\) | 8.84318 | 0.381967 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 23.8068 | 1.02638 | ||||||||
\(539\) | 4.94698 | 0.213082 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.38204 | 0.360372 | 0.180186 | − | 0.983633i | \(-0.442330\pi\) | ||||
0.180186 | + | 0.983633i | \(0.442330\pi\) | |||||||
\(542\) | 27.3430 | 1.17448 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −17.6101 | −0.755026 | ||||||||
\(545\) | −29.9903 | −1.28465 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.8688 | −0.977798 | −0.488899 | − | 0.872340i | \(-0.662601\pi\) | ||||
−0.488899 | + | 0.872340i | \(0.662601\pi\) | |||||||
\(548\) | 1.71127 | 0.0731017 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −16.1088 | −0.686881 | ||||||||
\(551\) | 1.12582 | 0.0479615 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.76302 | 0.117496 | ||||||||
\(554\) | −12.3570 | −0.525000 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.9934 | −0.466223 | ||||||||
\(557\) | −21.8641 | −0.926413 | −0.463206 | − | 0.886250i | \(-0.653301\pi\) | ||||
−0.463206 | + | 0.886250i | \(0.653301\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.64537 | 0.238774 | ||||||||
\(560\) | −1.66351 | −0.0702962 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −17.9033 | −0.755206 | ||||||||
\(563\) | 24.1831 | 1.01920 | 0.509599 | − | 0.860412i | \(-0.329794\pi\) | ||||
0.509599 | + | 0.860412i | \(0.329794\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 27.6595 | 1.16364 | ||||||||
\(566\) | −18.0279 | −0.757770 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 46.0402 | 1.93181 | ||||||||
\(569\) | −31.8186 | −1.33391 | −0.666953 | − | 0.745099i | \(-0.732402\pi\) | ||||
−0.666953 | + | 0.745099i | \(0.732402\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.5806 | 1.78194 | 0.890972 | − | 0.454058i | \(-0.150024\pi\) | ||||
0.890972 | + | 0.454058i | \(0.150024\pi\) | |||||||
\(572\) | −11.8880 | −0.497062 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.38470 | 0.183014 | ||||||||
\(575\) | −2.55585 | −0.106586 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.6971 | 0.778372 | 0.389186 | − | 0.921159i | \(-0.372756\pi\) | ||||
0.389186 | + | 0.921159i | \(0.372756\pi\) | |||||||
\(578\) | 5.77452 | 0.240188 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.02330 | 0.0424904 | ||||||||
\(581\) | −11.9081 | −0.494033 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 43.3414 | 1.79502 | ||||||||
\(584\) | 19.3991 | 0.802742 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.7211 | 0.773360 | ||||||||
\(587\) | 21.6873 | 0.895131 | 0.447565 | − | 0.894251i | \(-0.352291\pi\) | ||||
0.447565 | + | 0.894251i | \(0.352291\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 25.0428 | 1.03187 | ||||||||
\(590\) | −34.2676 | −1.41077 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.11889 | −0.128185 | ||||||||
\(593\) | −37.1088 | −1.52388 | −0.761939 | − | 0.647649i | \(-0.775752\pi\) | ||||
−0.761939 | + | 0.647649i | \(0.775752\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.59124 | 0.393203 | ||||||||
\(596\) | 8.05074 | 0.329771 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.53037 | 0.0625814 | ||||||||
\(599\) | 26.1898 | 1.07009 | 0.535043 | − | 0.844825i | \(-0.320295\pi\) | ||||
0.535043 | + | 0.844825i | \(0.320295\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.5840 | 0.513311 | 0.256655 | − | 0.966503i | \(-0.417379\pi\) | ||||
0.256655 | + | 0.966503i | \(0.417379\pi\) | |||||||
\(602\) | −2.45510 | −0.100062 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 16.3473 | 0.665161 | ||||||||
\(605\) | 39.1411 | 1.59131 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −44.5936 | −1.81000 | −0.904999 | − | 0.425413i | \(-0.860129\pi\) | ||||
−0.904999 | + | 0.425413i | \(0.860129\pi\) | |||||||
\(608\) | 18.8250 | 0.763455 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −28.6617 | −1.16048 | ||||||||
\(611\) | 4.47486 | 0.181034 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.8923 | 0.641885 | 0.320942 | − | 0.947099i | \(-0.396000\pi\) | ||||
0.320942 | + | 0.947099i | \(0.396000\pi\) | |||||||
\(614\) | −7.54954 | −0.304675 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 14.5346 | 0.585614 | ||||||||
\(617\) | 25.7330 | 1.03597 | 0.517985 | − | 0.855390i | \(-0.326682\pi\) | ||||
0.517985 | + | 0.855390i | \(0.326682\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −33.1354 | −1.33182 | −0.665912 | − | 0.746030i | \(-0.731957\pi\) | ||||
−0.665912 | + | 0.746030i | \(0.731957\pi\) | |||||||
\(620\) | 22.7624 | 0.914161 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.46409 | 0.339379 | ||||||||
\(623\) | −10.9952 | −0.440515 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.3657 | −1.21463 | ||||||||
\(626\) | −3.17598 | −0.126938 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 23.8844 | 0.953090 | ||||||||
\(629\) | 17.9824 | 0.717007 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.5658 | 0.778902 | 0.389451 | − | 0.921047i | \(-0.372665\pi\) | ||||
0.389451 | + | 0.921047i | \(0.372665\pi\) | |||||||
\(632\) | 8.11795 | 0.322915 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −30.4482 | −1.20925 | ||||||||
\(635\) | 2.90523 | 0.115290 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.17643 | 0.0862331 | ||||||||
\(638\) | 1.49369 | 0.0591358 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 13.9618 | 0.551890 | ||||||||
\(641\) | 11.2433 | 0.444085 | 0.222043 | − | 0.975037i | \(-0.428728\pi\) | ||||
0.222043 | + | 0.975037i | \(0.428728\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.66730 | 0.262933 | 0.131466 | − | 0.991321i | \(-0.458031\pi\) | ||||
0.131466 | + | 0.991321i | \(0.458031\pi\) | |||||||
\(644\) | 0.820269 | 0.0323231 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.0277 | 0.433877 | ||||||||
\(647\) | 3.29425 | 0.129510 | 0.0647551 | − | 0.997901i | \(-0.479373\pi\) | ||||
0.0647551 | + | 0.997901i | \(0.479373\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 61.6487 | 2.41992 | ||||||||
\(650\) | −7.08706 | −0.277977 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.70033 | 0.144916 | ||||||||
\(653\) | −44.1351 | −1.72714 | −0.863570 | − | 0.504230i | \(-0.831777\pi\) | ||||
−0.863570 | + | 0.504230i | \(0.831777\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.15685 | 0.240568 | ||||||||
\(656\) | 2.65256 | 0.103565 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.94606 | −0.0758653 | ||||||||
\(659\) | −26.9020 | −1.04795 | −0.523976 | − | 0.851733i | \(-0.675552\pi\) | ||||
−0.523976 | + | 0.851733i | \(0.675552\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.1836 | 0.746157 | 0.373079 | − | 0.927800i | \(-0.378302\pi\) | ||||
0.373079 | + | 0.927800i | \(0.378302\pi\) | |||||||
\(662\) | 8.19364 | 0.318455 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −34.9869 | −1.35775 | ||||||||
\(665\) | −10.2529 | −0.397592 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.236991 | 0.00917634 | ||||||||
\(668\) | −10.3535 | −0.400587 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8.27651 | −0.319750 | ||||||||
\(671\) | 51.5634 | 1.99058 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.61017 | 0.0620673 | 0.0310337 | − | 0.999518i | \(-0.490120\pi\) | ||||
0.0310337 | + | 0.999518i | \(0.490120\pi\) | |||||||
\(674\) | −8.11511 | −0.312582 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.12370 | 0.350912 | ||||||||
\(677\) | 19.9709 | 0.767545 | 0.383773 | − | 0.923428i | \(-0.374625\pi\) | ||||
0.383773 | + | 0.923428i | \(0.374625\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.7659 | −0.605039 | ||||||||
\(680\) | 28.1797 | 1.08064 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 33.2257 | 1.27228 | ||||||||
\(683\) | −2.10058 | −0.0803765 | −0.0401882 | − | 0.999192i | \(-0.512796\pi\) | ||||
−0.0401882 | + | 0.999192i | \(0.512796\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.50271 | −0.172040 | ||||||||
\(686\) | −0.946499 | −0.0361375 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.48523 | −0.0566239 | ||||||||
\(689\) | 19.0680 | 0.726435 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.0483 | 0.610505 | 0.305252 | − | 0.952271i | \(-0.401259\pi\) | ||||
0.305252 | + | 0.952271i | \(0.401259\pi\) | |||||||
\(692\) | −8.28055 | −0.314779 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.19945 | −0.273287 | ||||||||
\(695\) | 28.9259 | 1.09722 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.2938 | −0.579293 | ||||||||
\(698\) | −30.0170 | −1.13616 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.79863 | −0.143575 | ||||||||
\(701\) | 29.4967 | 1.11408 | 0.557038 | − | 0.830487i | \(-0.311938\pi\) | ||||
0.557038 | + | 0.830487i | \(0.311938\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.2230 | −0.725011 | ||||||||
\(704\) | 30.6415 | 1.15484 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.64964 | 0.325533 | ||||||||
\(707\) | −11.5305 | −0.433650 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.1469 | −1.09464 | −0.547318 | − | 0.836925i | \(-0.684351\pi\) | ||||
−0.547318 | + | 0.836925i | \(0.684351\pi\) | |||||||
\(710\) | −43.0900 | −1.61714 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −32.3047 | −1.21067 | ||||||||
\(713\) | 5.27164 | 0.197425 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 31.2798 | 1.16980 | ||||||||
\(716\) | −9.75507 | −0.364564 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 19.7458 | 0.736905 | ||||||||
\(719\) | 22.4686 | 0.837937 | 0.418968 | − | 0.908001i | \(-0.362392\pi\) | ||||
0.418968 | + | 0.908001i | \(0.362392\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.90350 | 0.257100 | ||||||||
\(722\) | 6.19502 | 0.230555 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.99603 | 0.148511 | ||||||||
\(725\) | −1.09750 | −0.0407600 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.54240 | −0.0572045 | −0.0286023 | − | 0.999591i | \(-0.509106\pi\) | ||||
−0.0286023 | + | 0.999591i | \(0.509106\pi\) | |||||||
\(728\) | 6.39448 | 0.236995 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −18.1560 | −0.671985 | ||||||||
\(731\) | 8.56334 | 0.316727 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.5101 | 1.08998 | 0.544990 | − | 0.838442i | \(-0.316533\pi\) | ||||
0.544990 | + | 0.838442i | \(0.316533\pi\) | |||||||
\(734\) | 32.1315 | 1.18599 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.96277 | 0.146070 | ||||||||
\(737\) | 14.8898 | 0.548471 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.659012 | 0.0242421 | 0.0121211 | − | 0.999927i | \(-0.496142\pi\) | ||||
0.0121211 | + | 0.999927i | \(0.496142\pi\) | |||||||
\(740\) | −17.4726 | −0.642307 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.29244 | −0.304425 | ||||||||
\(743\) | 9.62625 | 0.353153 | 0.176576 | − | 0.984287i | \(-0.443498\pi\) | ||||
0.176576 | + | 0.984287i | \(0.443498\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.1832 | −0.776093 | ||||||||
\(746\) | 23.8136 | 0.871879 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −18.0326 | −0.659339 | ||||||||
\(749\) | −0.262006 | −0.00957347 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −52.8305 | −1.92781 | −0.963906 | − | 0.266242i | \(-0.914218\pi\) | ||||
−0.963906 | + | 0.266242i | \(0.914218\pi\) | |||||||
\(752\) | −1.17729 | −0.0429312 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.657149 | 0.0239320 | ||||||||
\(755\) | −43.0131 | −1.56541 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.2632 | 0.954551 | 0.477276 | − | 0.878754i | \(-0.341624\pi\) | ||||
0.477276 | + | 0.878754i | \(0.341624\pi\) | |||||||
\(758\) | −28.9742 | −1.05239 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −30.1238 | −1.09271 | ||||||||
\(761\) | 23.8727 | 0.865386 | 0.432693 | − | 0.901541i | \(-0.357563\pi\) | ||||
0.432693 | + | 0.901541i | \(0.357563\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.3229 | −0.373714 | ||||||||
\(764\) | −8.13827 | −0.294432 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −36.1045 | −1.30451 | ||||||||
\(767\) | 27.1223 | 0.979331 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.6177 | 1.53683 | 0.768416 | − | 0.639950i | \(-0.221045\pi\) | ||||
0.768416 | + | 0.639950i | \(0.221045\pi\) | |||||||
\(770\) | −13.6032 | −0.490225 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.74488 | −0.242754 | ||||||||
\(773\) | 52.5536 | 1.89022 | 0.945110 | − | 0.326751i | \(-0.105954\pi\) | ||||
0.945110 | + | 0.326751i | \(0.105954\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24.4127 | −0.876931 | ||||||||
\(776\) | −46.3211 | −1.66283 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.9496 | −0.428413 | ||||||||
\(779\) | 16.3489 | 0.585760 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 77.5205 | 2.77390 | ||||||||
\(782\) | 2.32138 | 0.0830125 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.572592 | −0.0204497 | ||||||||
\(785\) | −62.8448 | −2.24303 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.10111 | −0.0392504 | −0.0196252 | − | 0.999807i | \(-0.506247\pi\) | ||||
−0.0196252 | + | 0.999807i | \(0.506247\pi\) | |||||||
\(788\) | −26.4450 | −0.942063 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −7.59775 | −0.270316 | ||||||||
\(791\) | 9.52058 | 0.338513 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.6853 | 0.805579 | ||||||||
\(794\) | 26.9954 | 0.958032 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.93221 | −0.352038 | ||||||||
\(797\) | −46.4625 | −1.64579 | −0.822893 | − | 0.568197i | \(-0.807641\pi\) | ||||
−0.822893 | + | 0.568197i | \(0.807641\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.78783 | 0.240136 | ||||||||
\(800\) | −18.3514 | −0.648820 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 35.6110 | 1.25747 | ||||||||
\(803\) | 32.6634 | 1.15267 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.15830 | −0.0760702 | ||||||||
\(806\) | 14.6177 | 0.514885 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −33.8774 | −1.19180 | ||||||||
\(809\) | −9.63649 | −0.338801 | −0.169401 | − | 0.985547i | \(-0.554183\pi\) | ||||
−0.169401 | + | 0.985547i | \(0.554183\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.3426 | 1.13570 | 0.567850 | − | 0.823132i | \(-0.307775\pi\) | ||||
0.567850 | + | 0.823132i | \(0.307775\pi\) | |||||||
\(812\) | 0.352229 | 0.0123608 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −25.5043 | −0.893927 | ||||||||
\(815\) | −9.73636 | −0.341050 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.15413 | −0.320262 | ||||||||
\(818\) | 9.48660 | 0.331691 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 14.8602 | 0.518940 | ||||||||
\(821\) | −9.19978 | −0.321075 | −0.160537 | − | 0.987030i | \(-0.551323\pi\) | ||||
−0.160537 | + | 0.987030i | \(0.551323\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.0062 | 0.941379 | 0.470689 | − | 0.882299i | \(-0.344005\pi\) | ||||
0.470689 | + | 0.882299i | \(0.344005\pi\) | |||||||
\(824\) | 20.2829 | 0.706589 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.7951 | −0.410406 | ||||||||
\(827\) | −18.8167 | −0.654320 | −0.327160 | − | 0.944969i | \(-0.606092\pi\) | ||||
−0.327160 | + | 0.944969i | \(0.606092\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39.6289 | 1.37637 | 0.688184 | − | 0.725536i | \(-0.258408\pi\) | ||||
0.688184 | + | 0.725536i | \(0.258408\pi\) | |||||||
\(830\) | 32.7449 | 1.13659 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 13.4807 | 0.467360 | ||||||||
\(833\) | 3.30137 | 0.114386 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 27.2421 | 0.942753 | ||||||||
\(836\) | 19.2767 | 0.666700 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 15.0440 | 0.519687 | ||||||||
\(839\) | −15.2610 | −0.526870 | −0.263435 | − | 0.964677i | \(-0.584855\pi\) | ||||
−0.263435 | + | 0.964677i | \(0.584855\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8982 | −0.996491 | ||||||||
\(842\) | −23.6512 | −0.815074 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9.10827 | −0.313520 | ||||||||
\(845\) | −24.0064 | −0.825845 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.4726 | 0.462926 | ||||||||
\(848\) | −5.01658 | −0.172270 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −10.7502 | −0.368729 | ||||||||
\(851\) | −4.04656 | −0.138714 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.84519 | 0.200136 | 0.100068 | − | 0.994981i | \(-0.468094\pi\) | ||||
0.100068 | + | 0.994981i | \(0.468094\pi\) | |||||||
\(854\) | −9.86555 | −0.337592 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.769789 | −0.0263109 | ||||||||
\(857\) | −28.1450 | −0.961416 | −0.480708 | − | 0.876881i | \(-0.659620\pi\) | ||||
−0.480708 | + | 0.876881i | \(0.659620\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.0135 | 0.785211 | 0.392606 | − | 0.919707i | \(-0.371574\pi\) | ||||
0.392606 | + | 0.919707i | \(0.371574\pi\) | |||||||
\(860\) | −8.32057 | −0.283729 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −20.2046 | −0.688172 | ||||||||
\(863\) | 15.7017 | 0.534492 | 0.267246 | − | 0.963628i | \(-0.413886\pi\) | ||||
0.267246 | + | 0.963628i | \(0.413886\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.7879 | 0.740810 | ||||||||
\(866\) | −13.1410 | −0.446549 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.83499 | 0.265937 | ||||||||
\(869\) | 13.6686 | 0.463677 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.55075 | 0.221964 | ||||||||
\(872\) | −30.3293 | −1.02708 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.48154 | −0.0839392 | ||||||||
\(875\) | −4.53114 | −0.153180 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.1043 | −1.52306 | −0.761532 | − | 0.648127i | \(-0.775553\pi\) | ||||
−0.761532 | + | 0.648127i | \(0.775553\pi\) | |||||||
\(878\) | −4.99552 | −0.168591 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8.22936 | −0.277412 | ||||||||
\(881\) | −15.6070 | −0.525812 | −0.262906 | − | 0.964821i | \(-0.584681\pi\) | ||||
−0.262906 | + | 0.964821i | \(0.584681\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.1214 | −0.609835 | −0.304917 | − | 0.952379i | \(-0.598629\pi\) | ||||
−0.304917 | + | 0.952379i | \(0.598629\pi\) | |||||||
\(884\) | −7.93346 | −0.266831 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.68964 | 0.0567647 | ||||||||
\(887\) | −32.4870 | −1.09081 | −0.545404 | − | 0.838173i | \(-0.683624\pi\) | ||||
−0.545404 | + | 0.838173i | \(0.683624\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | 30.2346 | 1.01347 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.73058 | −0.191874 | ||||||||
\(893\) | −7.25612 | −0.242817 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25.6677 | 0.857975 | ||||||||
\(896\) | 4.80576 | 0.160549 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −38.4264 | −1.28230 | ||||||||
\(899\) | 2.26368 | 0.0754978 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.9239 | 0.963595 | ||||||||
\(902\) | 21.6910 | 0.722232 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 27.9721 | 0.930338 | ||||||||
\(905\) | −10.5144 | −0.349511 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.2443 | 1.10386 | 0.551930 | − | 0.833890i | \(-0.313892\pi\) | ||||
0.551930 | + | 0.833890i | \(0.313892\pi\) | |||||||
\(908\) | −4.13096 | −0.137091 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5.98472 | −0.198392 | ||||||||
\(911\) | 6.23541 | 0.206588 | 0.103294 | − | 0.994651i | \(-0.467062\pi\) | ||||
0.103294 | + | 0.994651i | \(0.467062\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −58.9094 | −1.94962 | ||||||||
\(914\) | 7.53250 | 0.249153 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.0094 | 0.330720 | ||||||||
\(917\) | 2.11923 | 0.0699832 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.51224 | 0.115858 | 0.0579290 | − | 0.998321i | \(-0.481550\pi\) | ||||
0.0579290 | + | 0.998321i | \(0.481550\pi\) | |||||||
\(920\) | −6.34123 | −0.209064 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −22.1951 | −0.730956 | ||||||||
\(923\) | 34.1052 | 1.12259 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.7394 | 0.616149 | ||||||||
\(926\) | 10.2532 | 0.336941 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.70164 | 0.0558590 | ||||||||
\(929\) | −9.88716 | −0.324387 | −0.162194 | − | 0.986759i | \(-0.551857\pi\) | ||||
−0.162194 | + | 0.986759i | \(0.551857\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.52914 | −0.115663 | ||||||||
\(932\) | −5.94822 | −0.194840 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −32.9288 | −1.07746 | ||||||||
\(935\) | 47.4477 | 1.55171 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.5089 | 0.408648 | 0.204324 | − | 0.978903i | \(-0.434500\pi\) | ||||
0.204324 | + | 0.978903i | \(0.434500\pi\) | |||||||
\(938\) | −2.84883 | −0.0930177 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.59539 | −0.215118 | ||||||||
\(941\) | 21.9212 | 0.714612 | 0.357306 | − | 0.933987i | \(-0.383695\pi\) | ||||
0.357306 | + | 0.933987i | \(0.383695\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.44153 | 0.112072 | ||||||||
\(944\) | −7.13557 | −0.232243 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.1453 | −0.394878 | ||||||||
\(947\) | 37.2266 | 1.20970 | 0.604851 | − | 0.796339i | \(-0.293233\pi\) | ||||
0.604851 | + | 0.796339i | \(0.293233\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.3703 | 0.466479 | ||||||||
\(950\) | 11.4919 | 0.372846 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9.69965 | 0.314367 | ||||||||
\(953\) | −52.1922 | −1.69067 | −0.845336 | − | 0.534235i | \(-0.820600\pi\) | ||||
−0.845336 | + | 0.534235i | \(0.820600\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.4135 | 0.692925 | ||||||||
\(956\) | 22.3343 | 0.722342 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.47807 | 0.306222 | ||||||||
\(959\) | −1.54986 | −0.0500477 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.3533 | 0.624299 | ||||||||
\(962\) | −11.2206 | −0.361768 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11.9167 | 0.383811 | ||||||||
\(965\) | 17.7472 | 0.571303 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35.6045 | −1.14496 | −0.572482 | − | 0.819917i | \(-0.694019\pi\) | ||||
−0.572482 | + | 0.819917i | \(0.694019\pi\) | |||||||
\(968\) | 39.5835 | 1.27226 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 43.3529 | 1.39198 | ||||||||
\(971\) | −42.4387 | −1.36192 | −0.680962 | − | 0.732319i | \(-0.738438\pi\) | ||||
−0.680962 | + | 0.732319i | \(0.738438\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.95651 | 0.319191 | ||||||||
\(974\) | 30.3012 | 0.970913 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.96825 | −0.191039 | ||||||||
\(977\) | −4.99648 | −0.159852 | −0.0799258 | − | 0.996801i | \(-0.525468\pi\) | ||||
−0.0799258 | + | 0.996801i | \(0.525468\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −54.3932 | −1.73841 | ||||||||
\(980\) | −3.20778 | −0.102469 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 11.5898 | 0.369844 | ||||||||
\(983\) | −7.70508 | −0.245754 | −0.122877 | − | 0.992422i | \(-0.539212\pi\) | ||||
−0.122877 | + | 0.992422i | \(0.539212\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 69.5823 | 2.21708 | ||||||||
\(986\) | 0.996816 | 0.0317451 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.48080 | 0.269810 | ||||||||
\(989\) | −1.92699 | −0.0612749 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.7733 | −1.19991 | −0.599954 | − | 0.800034i | \(-0.704815\pi\) | ||||
−0.599954 | + | 0.800034i | \(0.704815\pi\) | |||||||
\(992\) | 37.8513 | 1.20178 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −14.8319 | −0.470439 | ||||||||
\(995\) | 26.1338 | 0.828496 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.61397 | −0.272807 | −0.136404 | − | 0.990653i | \(-0.543554\pi\) | ||||
−0.136404 | + | 0.990653i | \(0.543554\pi\) | |||||||
\(998\) | 16.6072 | 0.525692 | ||||||||
\(999\) | 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.n.1.3 | 12 | ||
3.2 | odd | 2 | 889.2.a.a.1.10 | ✓ | 12 | ||
21.20 | even | 2 | 6223.2.a.i.1.10 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
889.2.a.a.1.10 | ✓ | 12 | 3.2 | odd | 2 | ||
6223.2.a.i.1.10 | 12 | 21.20 | even | 2 | |||
8001.2.a.n.1.3 | 12 | 1.1 | even | 1 | trivial |