Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, 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("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.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: | \(64.2476334663\) |
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: | \( x^{12} - 5 x^{11} - 23 x^{10} + 142 x^{9} + 104 x^{8} - 1302 x^{7} + 607 x^{6} + 4323 x^{5} - 4461 x^{4} + \cdots - 553 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.72799\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8046.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.72799 | −1.66721 | −0.833603 | − | 0.552364i | \(-0.813726\pi\) | ||||
−0.833603 | + | 0.552364i | \(0.813726\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.68331 | −1.01420 | −0.507098 | − | 0.861889i | \(-0.669282\pi\) | ||||
−0.507098 | + | 0.861889i | \(0.669282\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.72799 | −1.17889 | ||||||||
\(11\) | −3.03613 | −0.915427 | −0.457714 | − | 0.889100i | \(-0.651331\pi\) | ||||
−0.457714 | + | 0.889100i | \(0.651331\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.51763 | −0.420914 | −0.210457 | − | 0.977603i | \(-0.567495\pi\) | ||||
−0.210457 | + | 0.977603i | \(0.567495\pi\) | |||||||
\(14\) | −2.68331 | −0.717144 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.16608 | −0.767886 | −0.383943 | − | 0.923357i | \(-0.625434\pi\) | ||||
−0.383943 | + | 0.923357i | \(0.625434\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.34640 | −1.68538 | −0.842690 | − | 0.538400i | \(-0.819029\pi\) | ||||
−0.842690 | + | 0.538400i | \(0.819029\pi\) | |||||||
\(20\) | −3.72799 | −0.833603 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.03613 | −0.647305 | ||||||||
\(23\) | −4.36415 | −0.909989 | −0.454995 | − | 0.890494i | \(-0.650359\pi\) | ||||
−0.454995 | + | 0.890494i | \(0.650359\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.89789 | 1.77958 | ||||||||
\(26\) | −1.51763 | −0.297631 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.68331 | −0.507098 | ||||||||
\(29\) | 3.00007 | 0.557100 | 0.278550 | − | 0.960422i | \(-0.410146\pi\) | ||||
0.278550 | + | 0.960422i | \(0.410146\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.76116 | −0.316313 | −0.158157 | − | 0.987414i | \(-0.550555\pi\) | ||||
−0.158157 | + | 0.987414i | \(0.550555\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.16608 | −0.542978 | ||||||||
\(35\) | 10.0033 | 1.69087 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.0054 | −1.80928 | −0.904639 | − | 0.426178i | \(-0.859860\pi\) | ||||
−0.904639 | + | 0.426178i | \(0.859860\pi\) | |||||||
\(38\) | −7.34640 | −1.19174 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.72799 | −0.589446 | ||||||||
\(41\) | 7.36102 | 1.14960 | 0.574799 | − | 0.818295i | \(-0.305080\pi\) | ||||
0.574799 | + | 0.818295i | \(0.305080\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.31638 | −0.658243 | −0.329121 | − | 0.944288i | \(-0.606752\pi\) | ||||
−0.329121 | + | 0.944288i | \(0.606752\pi\) | |||||||
\(44\) | −3.03613 | −0.457714 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.36415 | −0.643459 | ||||||||
\(47\) | −4.55389 | −0.664254 | −0.332127 | − | 0.943235i | \(-0.607766\pi\) | ||||
−0.332127 | + | 0.943235i | \(0.607766\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.200143 | 0.0285918 | ||||||||
\(50\) | 8.89789 | 1.25835 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.51763 | −0.210457 | ||||||||
\(53\) | 10.4838 | 1.44006 | 0.720031 | − | 0.693942i | \(-0.244128\pi\) | ||||
0.720031 | + | 0.693942i | \(0.244128\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.3186 | 1.52621 | ||||||||
\(56\) | −2.68331 | −0.358572 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.00007 | 0.393929 | ||||||||
\(59\) | 3.61539 | 0.470684 | 0.235342 | − | 0.971913i | \(-0.424379\pi\) | ||||
0.235342 | + | 0.971913i | \(0.424379\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.93968 | −0.248351 | −0.124176 | − | 0.992260i | \(-0.539629\pi\) | ||||
−0.124176 | + | 0.992260i | \(0.539629\pi\) | |||||||
\(62\) | −1.76116 | −0.223667 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.65770 | 0.701751 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.348084 | 0.0425252 | 0.0212626 | − | 0.999774i | \(-0.493231\pi\) | ||||
0.0212626 | + | 0.999774i | \(0.493231\pi\) | |||||||
\(68\) | −3.16608 | −0.383943 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 10.0033 | 1.19563 | ||||||||
\(71\) | 1.77899 | 0.211127 | 0.105564 | − | 0.994413i | \(-0.466335\pi\) | ||||
0.105564 | + | 0.994413i | \(0.466335\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.05505 | −1.05981 | −0.529907 | − | 0.848056i | \(-0.677773\pi\) | ||||
−0.529907 | + | 0.848056i | \(0.677773\pi\) | |||||||
\(74\) | −11.0054 | −1.27935 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.34640 | −0.842690 | ||||||||
\(77\) | 8.14687 | 0.928422 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.59998 | 0.967573 | 0.483786 | − | 0.875186i | \(-0.339261\pi\) | ||||
0.483786 | + | 0.875186i | \(0.339261\pi\) | |||||||
\(80\) | −3.72799 | −0.416802 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.36102 | 0.812889 | ||||||||
\(83\) | −0.134921 | −0.0148095 | −0.00740474 | − | 0.999973i | \(-0.502357\pi\) | ||||
−0.00740474 | + | 0.999973i | \(0.502357\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.8031 | 1.28022 | ||||||||
\(86\) | −4.31638 | −0.465448 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.03613 | −0.323652 | ||||||||
\(89\) | −13.2087 | −1.40011 | −0.700057 | − | 0.714087i | \(-0.746842\pi\) | ||||
−0.700057 | + | 0.714087i | \(0.746842\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.07226 | 0.426889 | ||||||||
\(92\) | −4.36415 | −0.454995 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.55389 | −0.469698 | ||||||||
\(95\) | 27.3873 | 2.80988 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.9196 | −1.10871 | −0.554357 | − | 0.832279i | \(-0.687036\pi\) | ||||
−0.554357 | + | 0.832279i | \(0.687036\pi\) | |||||||
\(98\) | 0.200143 | 0.0202175 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.89789 | 0.889789 | ||||||||
\(101\) | 7.12802 | 0.709265 | 0.354632 | − | 0.935006i | \(-0.384606\pi\) | ||||
0.354632 | + | 0.935006i | \(0.384606\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.1181 | 1.19403 | 0.597015 | − | 0.802230i | \(-0.296353\pi\) | ||||
0.597015 | + | 0.802230i | \(0.296353\pi\) | |||||||
\(104\) | −1.51763 | −0.148816 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.4838 | 1.01828 | ||||||||
\(107\) | 2.99883 | 0.289908 | 0.144954 | − | 0.989438i | \(-0.453697\pi\) | ||||
0.144954 | + | 0.989438i | \(0.453697\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.6605 | −1.02109 | −0.510543 | − | 0.859852i | \(-0.670556\pi\) | ||||
−0.510543 | + | 0.859852i | \(0.670556\pi\) | |||||||
\(110\) | 11.3186 | 1.07919 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.68331 | −0.253549 | ||||||||
\(113\) | 4.55326 | 0.428335 | 0.214168 | − | 0.976797i | \(-0.431296\pi\) | ||||
0.214168 | + | 0.976797i | \(0.431296\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16.2695 | 1.51714 | ||||||||
\(116\) | 3.00007 | 0.278550 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.61539 | 0.332824 | ||||||||
\(119\) | 8.49556 | 0.778787 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.78193 | −0.161993 | ||||||||
\(122\) | −1.93968 | −0.175611 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.76116 | −0.158157 | ||||||||
\(125\) | −14.5313 | −1.29972 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.85022 | 0.874066 | 0.437033 | − | 0.899446i | \(-0.356029\pi\) | ||||
0.437033 | + | 0.899446i | \(0.356029\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.65770 | 0.496213 | ||||||||
\(131\) | 9.08179 | 0.793479 | 0.396740 | − | 0.917931i | \(-0.370142\pi\) | ||||
0.396740 | + | 0.917931i | \(0.370142\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 19.7127 | 1.70930 | ||||||||
\(134\) | 0.348084 | 0.0300699 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.16608 | −0.271489 | ||||||||
\(137\) | −12.2378 | −1.04555 | −0.522775 | − | 0.852471i | \(-0.675103\pi\) | ||||
−0.522775 | + | 0.852471i | \(0.675103\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.30626 | 0.619709 | 0.309855 | − | 0.950784i | \(-0.399720\pi\) | ||||
0.309855 | + | 0.950784i | \(0.399720\pi\) | |||||||
\(140\) | 10.0033 | 0.845436 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.77899 | 0.149289 | ||||||||
\(143\) | 4.60771 | 0.385316 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.1842 | −0.928800 | ||||||||
\(146\) | −9.05505 | −0.749401 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −11.0054 | −0.904639 | ||||||||
\(149\) | −1.00000 | −0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.8449 | −1.69634 | −0.848168 | − | 0.529728i | \(-0.822294\pi\) | ||||
−0.848168 | + | 0.529728i | \(0.822294\pi\) | |||||||
\(152\) | −7.34640 | −0.595872 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 8.14687 | 0.656493 | ||||||||
\(155\) | 6.56558 | 0.527360 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.4371 | −1.15220 | −0.576101 | − | 0.817378i | \(-0.695427\pi\) | ||||
−0.576101 | + | 0.817378i | \(0.695427\pi\) | |||||||
\(158\) | 8.59998 | 0.684177 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.72799 | −0.294723 | ||||||||
\(161\) | 11.7104 | 0.922906 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.9863 | 1.80043 | 0.900214 | − | 0.435448i | \(-0.143410\pi\) | ||||
0.900214 | + | 0.435448i | \(0.143410\pi\) | |||||||
\(164\) | 7.36102 | 0.574799 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.134921 | −0.0104719 | ||||||||
\(167\) | 11.1508 | 0.862874 | 0.431437 | − | 0.902143i | \(-0.358007\pi\) | ||||
0.431437 | + | 0.902143i | \(0.358007\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.6968 | −0.822831 | ||||||||
\(170\) | 11.8031 | 0.905256 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.31638 | −0.329121 | ||||||||
\(173\) | 9.79349 | 0.744585 | 0.372293 | − | 0.928115i | \(-0.378572\pi\) | ||||
0.372293 | + | 0.928115i | \(0.378572\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −23.8758 | −1.80484 | ||||||||
\(176\) | −3.03613 | −0.228857 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −13.2087 | −0.990031 | ||||||||
\(179\) | 18.3388 | 1.37071 | 0.685354 | − | 0.728210i | \(-0.259647\pi\) | ||||
0.685354 | + | 0.728210i | \(0.259647\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.4340 | 0.849885 | 0.424943 | − | 0.905220i | \(-0.360294\pi\) | ||||
0.424943 | + | 0.905220i | \(0.360294\pi\) | |||||||
\(182\) | 4.07226 | 0.301856 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.36415 | −0.321730 | ||||||||
\(185\) | 41.0280 | 3.01644 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.61261 | 0.702944 | ||||||||
\(188\) | −4.55389 | −0.332127 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 27.3873 | 1.98688 | ||||||||
\(191\) | −1.34890 | −0.0976029 | −0.0488015 | − | 0.998808i | \(-0.515540\pi\) | ||||
−0.0488015 | + | 0.998808i | \(0.515540\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.26527 | −0.522965 | −0.261483 | − | 0.965208i | \(-0.584211\pi\) | ||||
−0.261483 | + | 0.965208i | \(0.584211\pi\) | |||||||
\(194\) | −10.9196 | −0.783979 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.200143 | 0.0142959 | ||||||||
\(197\) | −4.47541 | −0.318859 | −0.159430 | − | 0.987209i | \(-0.550966\pi\) | ||||
−0.159430 | + | 0.987209i | \(0.550966\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.6122 | 1.31939 | 0.659693 | − | 0.751536i | \(-0.270687\pi\) | ||||
0.659693 | + | 0.751536i | \(0.270687\pi\) | |||||||
\(200\) | 8.89789 | 0.629176 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.12802 | 0.501526 | ||||||||
\(203\) | −8.05012 | −0.565008 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −27.4418 | −1.91662 | ||||||||
\(206\) | 12.1181 | 0.844306 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.51763 | −0.105229 | ||||||||
\(209\) | 22.3046 | 1.54284 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.66630 | 0.321241 | 0.160621 | − | 0.987016i | \(-0.448650\pi\) | ||||
0.160621 | + | 0.987016i | \(0.448650\pi\) | |||||||
\(212\) | 10.4838 | 0.720031 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.99883 | 0.204996 | ||||||||
\(215\) | 16.0914 | 1.09743 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.72573 | 0.320804 | ||||||||
\(218\) | −10.6605 | −0.722017 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 11.3186 | 0.763103 | ||||||||
\(221\) | 4.80493 | 0.323214 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.01396 | −0.469690 | −0.234845 | − | 0.972033i | \(-0.575458\pi\) | ||||
−0.234845 | + | 0.972033i | \(0.575458\pi\) | |||||||
\(224\) | −2.68331 | −0.179286 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.55326 | 0.302879 | ||||||||
\(227\) | −28.9841 | −1.92374 | −0.961871 | − | 0.273504i | \(-0.911817\pi\) | ||||
−0.961871 | + | 0.273504i | \(0.911817\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.49235 | −0.0986172 | −0.0493086 | − | 0.998784i | \(-0.515702\pi\) | ||||
−0.0493086 | + | 0.998784i | \(0.515702\pi\) | |||||||
\(230\) | 16.2695 | 1.07278 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.00007 | 0.196964 | ||||||||
\(233\) | 16.5298 | 1.08291 | 0.541453 | − | 0.840731i | \(-0.317874\pi\) | ||||
0.541453 | + | 0.840731i | \(0.317874\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.9769 | 1.10745 | ||||||||
\(236\) | 3.61539 | 0.235342 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 8.49556 | 0.550685 | ||||||||
\(239\) | −6.51060 | −0.421136 | −0.210568 | − | 0.977579i | \(-0.567531\pi\) | ||||
−0.210568 | + | 0.977579i | \(0.567531\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.15693 | −0.203356 | −0.101678 | − | 0.994817i | \(-0.532421\pi\) | ||||
−0.101678 | + | 0.994817i | \(0.532421\pi\) | |||||||
\(242\) | −1.78193 | −0.114547 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.93968 | −0.124176 | ||||||||
\(245\) | −0.746129 | −0.0476685 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.1491 | 0.709400 | ||||||||
\(248\) | −1.76116 | −0.111834 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −14.5313 | −0.919038 | ||||||||
\(251\) | −20.0049 | −1.26269 | −0.631347 | − | 0.775500i | \(-0.717498\pi\) | ||||
−0.631347 | + | 0.775500i | \(0.717498\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.2501 | 0.833029 | ||||||||
\(254\) | 9.85022 | 0.618058 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.28291 | 0.391917 | 0.195959 | − | 0.980612i | \(-0.437218\pi\) | ||||
0.195959 | + | 0.980612i | \(0.437218\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 29.5309 | 1.83496 | ||||||||
\(260\) | 5.65770 | 0.350875 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.08179 | 0.561075 | ||||||||
\(263\) | −22.9242 | −1.41357 | −0.706785 | − | 0.707429i | \(-0.749855\pi\) | ||||
−0.706785 | + | 0.707429i | \(0.749855\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −39.0835 | −2.40088 | ||||||||
\(266\) | 19.7127 | 1.20866 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.348084 | 0.0212626 | ||||||||
\(269\) | 5.77491 | 0.352102 | 0.176051 | − | 0.984381i | \(-0.443668\pi\) | ||||
0.176051 | + | 0.984381i | \(0.443668\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −32.1746 | −1.95447 | −0.977233 | − | 0.212171i | \(-0.931947\pi\) | ||||
−0.977233 | + | 0.212171i | \(0.931947\pi\) | |||||||
\(272\) | −3.16608 | −0.191972 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.2378 | −0.739315 | ||||||||
\(275\) | −27.0151 | −1.62907 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.3691 | 0.743185 | 0.371593 | − | 0.928396i | \(-0.378812\pi\) | ||||
0.371593 | + | 0.928396i | \(0.378812\pi\) | |||||||
\(278\) | 7.30626 | 0.438201 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 10.0033 | 0.597814 | ||||||||
\(281\) | 7.67646 | 0.457939 | 0.228970 | − | 0.973434i | \(-0.426464\pi\) | ||||
0.228970 | + | 0.973434i | \(0.426464\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.14480 | −0.246383 | −0.123191 | − | 0.992383i | \(-0.539313\pi\) | ||||
−0.123191 | + | 0.992383i | \(0.539313\pi\) | |||||||
\(284\) | 1.77899 | 0.105564 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.60771 | 0.272460 | ||||||||
\(287\) | −19.7519 | −1.16592 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.97596 | −0.410351 | ||||||||
\(290\) | −11.1842 | −0.656761 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.05505 | −0.529907 | ||||||||
\(293\) | 12.7783 | 0.746517 | 0.373259 | − | 0.927727i | \(-0.378240\pi\) | ||||
0.373259 | + | 0.927727i | \(0.378240\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.4781 | −0.784728 | ||||||||
\(296\) | −11.0054 | −0.639676 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.00000 | −0.0579284 | ||||||||
\(299\) | 6.62316 | 0.383027 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.5822 | 0.667586 | ||||||||
\(302\) | −20.8449 | −1.19949 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.34640 | −0.421345 | ||||||||
\(305\) | 7.23112 | 0.414053 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.6013 | 1.00456 | 0.502281 | − | 0.864705i | \(-0.332494\pi\) | ||||
0.502281 | + | 0.864705i | \(0.332494\pi\) | |||||||
\(308\) | 8.14687 | 0.464211 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.56558 | 0.372900 | ||||||||
\(311\) | 10.6147 | 0.601903 | 0.300951 | − | 0.953639i | \(-0.402696\pi\) | ||||
0.300951 | + | 0.953639i | \(0.402696\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.2722 | −0.976284 | −0.488142 | − | 0.872764i | \(-0.662325\pi\) | ||||
−0.488142 | + | 0.872764i | \(0.662325\pi\) | |||||||
\(314\) | −14.4371 | −0.814731 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.59998 | 0.483786 | ||||||||
\(317\) | −7.28092 | −0.408937 | −0.204469 | − | 0.978873i | \(-0.565547\pi\) | ||||
−0.204469 | + | 0.978873i | \(0.565547\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.10861 | −0.509984 | ||||||||
\(320\) | −3.72799 | −0.208401 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 11.7104 | 0.652593 | ||||||||
\(323\) | 23.2593 | 1.29418 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.5037 | −0.749049 | ||||||||
\(326\) | 22.9863 | 1.27309 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.36102 | 0.406444 | ||||||||
\(329\) | 12.2195 | 0.673683 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.05357 | −0.387699 | −0.193850 | − | 0.981031i | \(-0.562097\pi\) | ||||
−0.193850 | + | 0.981031i | \(0.562097\pi\) | |||||||
\(332\) | −0.134921 | −0.00740474 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 11.1508 | 0.610144 | ||||||||
\(335\) | −1.29765 | −0.0708984 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.20317 | −0.120015 | −0.0600073 | − | 0.998198i | \(-0.519112\pi\) | ||||
−0.0600073 | + | 0.998198i | \(0.519112\pi\) | |||||||
\(338\) | −10.6968 | −0.581829 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 11.8031 | 0.640112 | ||||||||
\(341\) | 5.34710 | 0.289562 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.2461 | 0.985197 | ||||||||
\(344\) | −4.31638 | −0.232724 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.79349 | 0.526501 | ||||||||
\(347\) | 8.47386 | 0.454901 | 0.227450 | − | 0.973790i | \(-0.426961\pi\) | ||||
0.227450 | + | 0.973790i | \(0.426961\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.7803 | 1.64763 | 0.823816 | − | 0.566857i | \(-0.191841\pi\) | ||||
0.823816 | + | 0.566857i | \(0.191841\pi\) | |||||||
\(350\) | −23.8758 | −1.27621 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.03613 | −0.161826 | ||||||||
\(353\) | −25.4586 | −1.35502 | −0.677511 | − | 0.735513i | \(-0.736941\pi\) | ||||
−0.677511 | + | 0.735513i | \(0.736941\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.63205 | −0.351993 | ||||||||
\(356\) | −13.2087 | −0.700057 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 18.3388 | 0.969237 | ||||||||
\(359\) | −0.739243 | −0.0390157 | −0.0195079 | − | 0.999810i | \(-0.506210\pi\) | ||||
−0.0195079 | + | 0.999810i | \(0.506210\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 34.9696 | 1.84050 | ||||||||
\(362\) | 11.4340 | 0.600960 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.07226 | 0.213445 | ||||||||
\(365\) | 33.7571 | 1.76693 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.3186 | −1.26942 | −0.634711 | − | 0.772750i | \(-0.718881\pi\) | ||||
−0.634711 | + | 0.772750i | \(0.718881\pi\) | |||||||
\(368\) | −4.36415 | −0.227497 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 41.0280 | 2.13295 | ||||||||
\(371\) | −28.1313 | −1.46050 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.50837 | 0.129879 | 0.0649393 | − | 0.997889i | \(-0.479315\pi\) | ||||
0.0649393 | + | 0.997889i | \(0.479315\pi\) | |||||||
\(374\) | 9.61261 | 0.497056 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.55389 | −0.234849 | ||||||||
\(377\) | −4.55300 | −0.234491 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.3360 | 1.66099 | 0.830494 | − | 0.557028i | \(-0.188059\pi\) | ||||
0.830494 | + | 0.557028i | \(0.188059\pi\) | |||||||
\(380\) | 27.3873 | 1.40494 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.34890 | −0.0690157 | ||||||||
\(383\) | −6.93966 | −0.354600 | −0.177300 | − | 0.984157i | \(-0.556736\pi\) | ||||
−0.177300 | + | 0.984157i | \(0.556736\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −30.3714 | −1.54787 | ||||||||
\(386\) | −7.26527 | −0.369792 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10.9196 | −0.554357 | ||||||||
\(389\) | −23.9613 | −1.21489 | −0.607444 | − | 0.794362i | \(-0.707805\pi\) | ||||
−0.607444 | + | 0.794362i | \(0.707805\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.8172 | 0.698768 | ||||||||
\(392\) | 0.200143 | 0.0101087 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.47541 | −0.225468 | ||||||||
\(395\) | −32.0606 | −1.61314 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.7734 | −0.942209 | −0.471105 | − | 0.882077i | \(-0.656145\pi\) | ||||
−0.471105 | + | 0.882077i | \(0.656145\pi\) | |||||||
\(398\) | 18.6122 | 0.932946 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.89789 | 0.444894 | ||||||||
\(401\) | 37.4767 | 1.87150 | 0.935748 | − | 0.352670i | \(-0.114726\pi\) | ||||
0.935748 | + | 0.352670i | \(0.114726\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.67278 | 0.133141 | ||||||||
\(404\) | 7.12802 | 0.354632 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.05012 | −0.399521 | ||||||||
\(407\) | 33.4138 | 1.65626 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.66375 | 0.378948 | 0.189474 | − | 0.981886i | \(-0.439322\pi\) | ||||
0.189474 | + | 0.981886i | \(0.439322\pi\) | |||||||
\(410\) | −27.4418 | −1.35525 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.1181 | 0.597015 | ||||||||
\(413\) | −9.70122 | −0.477366 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.502983 | 0.0246905 | ||||||||
\(416\) | −1.51763 | −0.0744078 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 22.3046 | 1.09095 | ||||||||
\(419\) | 35.3284 | 1.72591 | 0.862953 | − | 0.505285i | \(-0.168613\pi\) | ||||
0.862953 | + | 0.505285i | \(0.168613\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.0077 | 1.07259 | 0.536296 | − | 0.844030i | \(-0.319823\pi\) | ||||
0.536296 | + | 0.844030i | \(0.319823\pi\) | |||||||
\(422\) | 4.66630 | 0.227152 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10.4838 | 0.509139 | ||||||||
\(425\) | −28.1714 | −1.36651 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.20477 | 0.251876 | ||||||||
\(428\) | 2.99883 | 0.144954 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 16.0914 | 0.775997 | ||||||||
\(431\) | 33.2706 | 1.60259 | 0.801295 | − | 0.598269i | \(-0.204145\pi\) | ||||
0.801295 | + | 0.598269i | \(0.204145\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −33.4569 | −1.60783 | −0.803917 | − | 0.594741i | \(-0.797254\pi\) | ||||
−0.803917 | + | 0.594741i | \(0.797254\pi\) | |||||||
\(434\) | 4.72573 | 0.226842 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.6605 | −0.510543 | ||||||||
\(437\) | 32.0608 | 1.53368 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.8073 | −0.706713 | −0.353356 | − | 0.935489i | \(-0.614960\pi\) | ||||
−0.353356 | + | 0.935489i | \(0.614960\pi\) | |||||||
\(440\) | 11.3186 | 0.539595 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.80493 | 0.228547 | ||||||||
\(443\) | 34.0503 | 1.61778 | 0.808889 | − | 0.587962i | \(-0.200070\pi\) | ||||
0.808889 | + | 0.587962i | \(0.200070\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 49.2417 | 2.33428 | ||||||||
\(446\) | −7.01396 | −0.332121 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.68331 | −0.126774 | ||||||||
\(449\) | −12.2168 | −0.576546 | −0.288273 | − | 0.957548i | \(-0.593081\pi\) | ||||
−0.288273 | + | 0.957548i | \(0.593081\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.3490 | −1.05237 | ||||||||
\(452\) | 4.55326 | 0.214168 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −28.9841 | −1.36029 | ||||||||
\(455\) | −15.1813 | −0.711712 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.68028 | −0.265712 | −0.132856 | − | 0.991135i | \(-0.542415\pi\) | ||||
−0.132856 | + | 0.991135i | \(0.542415\pi\) | |||||||
\(458\) | −1.49235 | −0.0697329 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 16.2695 | 0.758570 | ||||||||
\(461\) | −2.69247 | −0.125401 | −0.0627004 | − | 0.998032i | \(-0.519971\pi\) | ||||
−0.0627004 | + | 0.998032i | \(0.519971\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.31923 | 0.340153 | 0.170077 | − | 0.985431i | \(-0.445598\pi\) | ||||
0.170077 | + | 0.985431i | \(0.445598\pi\) | |||||||
\(464\) | 3.00007 | 0.139275 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16.5298 | 0.765730 | ||||||||
\(467\) | −41.8088 | −1.93468 | −0.967341 | − | 0.253479i | \(-0.918425\pi\) | ||||
−0.967341 | + | 0.253479i | \(0.918425\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.934017 | −0.0431289 | ||||||||
\(470\) | 16.9769 | 0.783084 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.61539 | 0.166412 | ||||||||
\(473\) | 13.1051 | 0.602573 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −65.3674 | −2.99926 | ||||||||
\(476\) | 8.49556 | 0.389393 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.51060 | −0.297788 | ||||||||
\(479\) | 24.8975 | 1.13759 | 0.568797 | − | 0.822478i | \(-0.307409\pi\) | ||||
0.568797 | + | 0.822478i | \(0.307409\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.7021 | 0.761551 | ||||||||
\(482\) | −3.15693 | −0.143794 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.78193 | −0.0809967 | ||||||||
\(485\) | 40.7080 | 1.84845 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.5846 | 1.52186 | 0.760932 | − | 0.648832i | \(-0.224742\pi\) | ||||
0.760932 | + | 0.648832i | \(0.224742\pi\) | |||||||
\(488\) | −1.93968 | −0.0878054 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.746129 | −0.0337067 | ||||||||
\(491\) | 4.55572 | 0.205597 | 0.102798 | − | 0.994702i | \(-0.467220\pi\) | ||||
0.102798 | + | 0.994702i | \(0.467220\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.49846 | −0.427789 | ||||||||
\(494\) | 11.1491 | 0.501622 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.76116 | −0.0790784 | ||||||||
\(497\) | −4.77358 | −0.214124 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.32927 | 0.372869 | 0.186435 | − | 0.982467i | \(-0.440307\pi\) | ||||
0.186435 | + | 0.982467i | \(0.440307\pi\) | |||||||
\(500\) | −14.5313 | −0.649858 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −20.0049 | −0.892860 | ||||||||
\(503\) | 10.0572 | 0.448429 | 0.224214 | − | 0.974540i | \(-0.428018\pi\) | ||||
0.224214 | + | 0.974540i | \(0.428018\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −26.5732 | −1.18249 | ||||||||
\(506\) | 13.2501 | 0.589040 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.85022 | 0.437033 | ||||||||
\(509\) | −32.6070 | −1.44528 | −0.722640 | − | 0.691224i | \(-0.757072\pi\) | ||||
−0.722640 | + | 0.691224i | \(0.757072\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.2975 | 1.07486 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.28291 | 0.277127 | ||||||||
\(515\) | −45.1760 | −1.99069 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.8262 | 0.608076 | ||||||||
\(518\) | 29.5309 | 1.29751 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.65770 | 0.248106 | ||||||||
\(521\) | −32.9185 | −1.44219 | −0.721094 | − | 0.692838i | \(-0.756360\pi\) | ||||
−0.721094 | + | 0.692838i | \(0.756360\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −43.1958 | −1.88882 | −0.944409 | − | 0.328772i | \(-0.893365\pi\) | ||||
−0.944409 | + | 0.328772i | \(0.893365\pi\) | |||||||
\(524\) | 9.08179 | 0.396740 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.9242 | −0.999545 | ||||||||
\(527\) | 5.57596 | 0.242893 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.95416 | −0.171920 | ||||||||
\(530\) | −39.0835 | −1.69768 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 19.7127 | 0.854652 | ||||||||
\(533\) | −11.1713 | −0.483882 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.1796 | −0.483336 | ||||||||
\(536\) | 0.348084 | 0.0150349 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.77491 | 0.248974 | ||||||||
\(539\) | −0.607659 | −0.0261737 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.8775 | −0.768612 | −0.384306 | − | 0.923206i | \(-0.625559\pi\) | ||||
−0.384306 | + | 0.923206i | \(0.625559\pi\) | |||||||
\(542\) | −32.1746 | −1.38202 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.16608 | −0.135744 | ||||||||
\(545\) | 39.7420 | 1.70236 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.2678 | 1.59346 | 0.796728 | − | 0.604338i | \(-0.206563\pi\) | ||||
0.796728 | + | 0.604338i | \(0.206563\pi\) | |||||||
\(548\) | −12.2378 | −0.522775 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −27.0151 | −1.15193 | ||||||||
\(551\) | −22.0397 | −0.938924 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −23.0764 | −0.981308 | ||||||||
\(554\) | 12.3691 | 0.525511 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.30626 | 0.309855 | ||||||||
\(557\) | −8.96823 | −0.379996 | −0.189998 | − | 0.981784i | \(-0.560848\pi\) | ||||
−0.189998 | + | 0.981784i | \(0.560848\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.55067 | 0.277064 | ||||||||
\(560\) | 10.0033 | 0.422718 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.67646 | 0.323812 | ||||||||
\(563\) | 6.43248 | 0.271097 | 0.135548 | − | 0.990771i | \(-0.456720\pi\) | ||||
0.135548 | + | 0.990771i | \(0.456720\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.9745 | −0.714123 | ||||||||
\(566\) | −4.14480 | −0.174219 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.77899 | 0.0746447 | ||||||||
\(569\) | −0.866264 | −0.0363157 | −0.0181578 | − | 0.999835i | \(-0.505780\pi\) | ||||
−0.0181578 | + | 0.999835i | \(0.505780\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 38.7345 | 1.62099 | 0.810493 | − | 0.585748i | \(-0.199199\pi\) | ||||
0.810493 | + | 0.585748i | \(0.199199\pi\) | |||||||
\(572\) | 4.60771 | 0.192658 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −19.7519 | −0.824428 | ||||||||
\(575\) | −38.8317 | −1.61940 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.58882 | 0.399188 | 0.199594 | − | 0.979879i | \(-0.436038\pi\) | ||||
0.199594 | + | 0.979879i | \(0.436038\pi\) | |||||||
\(578\) | −6.97596 | −0.290162 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −11.1842 | −0.464400 | ||||||||
\(581\) | 0.362034 | 0.0150197 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −31.8302 | −1.31827 | ||||||||
\(584\) | −9.05505 | −0.374701 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.7783 | 0.527867 | ||||||||
\(587\) | −4.71487 | −0.194604 | −0.0973018 | − | 0.995255i | \(-0.531021\pi\) | ||||
−0.0973018 | + | 0.995255i | \(0.531021\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.9382 | 0.533108 | ||||||||
\(590\) | −13.4781 | −0.554886 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −11.0054 | −0.452320 | ||||||||
\(593\) | −47.8498 | −1.96496 | −0.982478 | − | 0.186379i | \(-0.940325\pi\) | ||||
−0.982478 | + | 0.186379i | \(0.940325\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −31.6713 | −1.29840 | ||||||||
\(596\) | −1.00000 | −0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.62316 | 0.270841 | ||||||||
\(599\) | 12.1155 | 0.495027 | 0.247513 | − | 0.968884i | \(-0.420387\pi\) | ||||
0.247513 | + | 0.968884i | \(0.420387\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.9338 | −0.731536 | −0.365768 | − | 0.930706i | \(-0.619194\pi\) | ||||
−0.365768 | + | 0.930706i | \(0.619194\pi\) | |||||||
\(602\) | 11.5822 | 0.472055 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −20.8449 | −0.848168 | ||||||||
\(605\) | 6.64300 | 0.270076 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.8665 | −1.29342 | −0.646710 | − | 0.762736i | \(-0.723856\pi\) | ||||
−0.646710 | + | 0.762736i | \(0.723856\pi\) | |||||||
\(608\) | −7.34640 | −0.297936 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.23112 | 0.292779 | ||||||||
\(611\) | 6.91112 | 0.279594 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.75657 | −0.394064 | −0.197032 | − | 0.980397i | \(-0.563130\pi\) | ||||
−0.197032 | + | 0.980397i | \(0.563130\pi\) | |||||||
\(614\) | 17.6013 | 0.710332 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.14687 | 0.328247 | ||||||||
\(617\) | −17.3527 | −0.698595 | −0.349298 | − | 0.937012i | \(-0.613580\pi\) | ||||
−0.349298 | + | 0.937012i | \(0.613580\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.61009 | 0.265682 | 0.132841 | − | 0.991137i | \(-0.457590\pi\) | ||||
0.132841 | + | 0.991137i | \(0.457590\pi\) | |||||||
\(620\) | 6.56558 | 0.263680 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10.6147 | 0.425610 | ||||||||
\(623\) | 35.4429 | 1.41999 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.68294 | 0.387318 | ||||||||
\(626\) | −17.2722 | −0.690337 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14.4371 | −0.576101 | ||||||||
\(629\) | 34.8440 | 1.38932 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.83702 | 0.232368 | 0.116184 | − | 0.993228i | \(-0.462934\pi\) | ||||
0.116184 | + | 0.993228i | \(0.462934\pi\) | |||||||
\(632\) | 8.59998 | 0.342089 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.28092 | −0.289162 | ||||||||
\(635\) | −36.7215 | −1.45725 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.303742 | −0.0120347 | ||||||||
\(638\) | −9.10861 | −0.360613 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.72799 | −0.147362 | ||||||||
\(641\) | 8.97358 | 0.354435 | 0.177218 | − | 0.984172i | \(-0.443290\pi\) | ||||
0.177218 | + | 0.984172i | \(0.443290\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.5976 | 0.496799 | 0.248400 | − | 0.968658i | \(-0.420095\pi\) | ||||
0.248400 | + | 0.968658i | \(0.420095\pi\) | |||||||
\(644\) | 11.7104 | 0.461453 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 23.2593 | 0.915123 | ||||||||
\(647\) | −30.1280 | −1.18445 | −0.592226 | − | 0.805772i | \(-0.701751\pi\) | ||||
−0.592226 | + | 0.805772i | \(0.701751\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.9768 | −0.430877 | ||||||||
\(650\) | −13.5037 | −0.529658 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 22.9863 | 0.900214 | ||||||||
\(653\) | 24.2342 | 0.948356 | 0.474178 | − | 0.880429i | \(-0.342745\pi\) | ||||
0.474178 | + | 0.880429i | \(0.342745\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −33.8568 | −1.32289 | ||||||||
\(656\) | 7.36102 | 0.287399 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 12.2195 | 0.476366 | ||||||||
\(659\) | 0.635814 | 0.0247678 | 0.0123839 | − | 0.999923i | \(-0.496058\pi\) | ||||
0.0123839 | + | 0.999923i | \(0.496058\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.3171 | 0.906929 | 0.453464 | − | 0.891274i | \(-0.350188\pi\) | ||||
0.453464 | + | 0.891274i | \(0.350188\pi\) | |||||||
\(662\) | −7.05357 | −0.274145 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.134921 | −0.00523594 | ||||||||
\(665\) | −73.4885 | −2.84976 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.0928 | −0.506955 | ||||||||
\(668\) | 11.1508 | 0.431437 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.29765 | −0.0501327 | ||||||||
\(671\) | 5.88913 | 0.227347 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −43.9800 | −1.69530 | −0.847652 | − | 0.530553i | \(-0.821984\pi\) | ||||
−0.847652 | + | 0.530553i | \(0.821984\pi\) | |||||||
\(674\) | −2.20317 | −0.0848631 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.6968 | −0.411416 | ||||||||
\(677\) | −29.1623 | −1.12080 | −0.560399 | − | 0.828223i | \(-0.689352\pi\) | ||||
−0.560399 | + | 0.828223i | \(0.689352\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 29.3006 | 1.12445 | ||||||||
\(680\) | 11.8031 | 0.452628 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.34710 | 0.204751 | ||||||||
\(683\) | −9.47599 | −0.362589 | −0.181294 | − | 0.983429i | \(-0.558029\pi\) | ||||
−0.181294 | + | 0.983429i | \(0.558029\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 45.6225 | 1.74315 | ||||||||
\(686\) | 18.2461 | 0.696640 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.31638 | −0.164561 | ||||||||
\(689\) | −15.9105 | −0.606143 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.8611 | −1.70660 | −0.853299 | − | 0.521422i | \(-0.825402\pi\) | ||||
−0.853299 | + | 0.521422i | \(0.825402\pi\) | |||||||
\(692\) | 9.79349 | 0.372293 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.47386 | 0.321663 | ||||||||
\(695\) | −27.2377 | −1.03318 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −23.3055 | −0.882760 | ||||||||
\(698\) | 30.7803 | 1.16505 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −23.8758 | −0.902419 | ||||||||
\(701\) | 23.7948 | 0.898716 | 0.449358 | − | 0.893352i | \(-0.351653\pi\) | ||||
0.449358 | + | 0.893352i | \(0.351653\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 80.8501 | 3.04932 | ||||||||
\(704\) | −3.03613 | −0.114428 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −25.4586 | −0.958145 | ||||||||
\(707\) | −19.1267 | −0.719333 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.0140 | −1.08964 | −0.544822 | − | 0.838552i | \(-0.683403\pi\) | ||||
−0.544822 | + | 0.838552i | \(0.683403\pi\) | |||||||
\(710\) | −6.63205 | −0.248896 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −13.2087 | −0.495015 | ||||||||
\(713\) | 7.68597 | 0.287842 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17.1775 | −0.642402 | ||||||||
\(716\) | 18.3388 | 0.685354 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.739243 | −0.0275883 | ||||||||
\(719\) | 13.9547 | 0.520423 | 0.260211 | − | 0.965552i | \(-0.416208\pi\) | ||||
0.260211 | + | 0.965552i | \(0.416208\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.5165 | −1.21098 | ||||||||
\(722\) | 34.9696 | 1.30143 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11.4340 | 0.424943 | ||||||||
\(725\) | 26.6943 | 0.991402 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.70803 | 0.137523 | 0.0687616 | − | 0.997633i | \(-0.478095\pi\) | ||||
0.0687616 | + | 0.997633i | \(0.478095\pi\) | |||||||
\(728\) | 4.07226 | 0.150928 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 33.7571 | 1.24941 | ||||||||
\(731\) | 13.6660 | 0.505455 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.1030 | 0.557842 | 0.278921 | − | 0.960314i | \(-0.410023\pi\) | ||||
0.278921 | + | 0.960314i | \(0.410023\pi\) | |||||||
\(734\) | −24.3186 | −0.897617 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.36415 | −0.160865 | ||||||||
\(737\) | −1.05683 | −0.0389288 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −46.4878 | −1.71008 | −0.855041 | − | 0.518561i | \(-0.826468\pi\) | ||||
−0.855041 | + | 0.518561i | \(0.826468\pi\) | |||||||
\(740\) | 41.0280 | 1.50822 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −28.1313 | −1.03273 | ||||||||
\(743\) | −34.4107 | −1.26240 | −0.631202 | − | 0.775618i | \(-0.717438\pi\) | ||||
−0.631202 | + | 0.775618i | \(0.717438\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.72799 | 0.136583 | ||||||||
\(746\) | 2.50837 | 0.0918381 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.61261 | 0.351472 | ||||||||
\(749\) | −8.04678 | −0.294023 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.1491 | −0.662269 | −0.331135 | − | 0.943584i | \(-0.607431\pi\) | ||||
−0.331135 | + | 0.943584i | \(0.607431\pi\) | |||||||
\(752\) | −4.55389 | −0.166063 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.55300 | −0.165810 | ||||||||
\(755\) | 77.7096 | 2.82814 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.0081 | 0.690861 | 0.345430 | − | 0.938444i | \(-0.387733\pi\) | ||||
0.345430 | + | 0.938444i | \(0.387733\pi\) | |||||||
\(758\) | 32.3360 | 1.17450 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 27.3873 | 0.993441 | ||||||||
\(761\) | −0.514324 | −0.0186442 | −0.00932212 | − | 0.999957i | \(-0.502967\pi\) | ||||
−0.00932212 | + | 0.999957i | \(0.502967\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.6053 | 1.03558 | ||||||||
\(764\) | −1.34890 | −0.0488015 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.93966 | −0.250740 | ||||||||
\(767\) | −5.48682 | −0.198118 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.5648 | −0.813706 | −0.406853 | − | 0.913494i | \(-0.633374\pi\) | ||||
−0.406853 | + | 0.913494i | \(0.633374\pi\) | |||||||
\(770\) | −30.3714 | −1.09451 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.26527 | −0.261483 | ||||||||
\(773\) | 22.3684 | 0.804534 | 0.402267 | − | 0.915522i | \(-0.368222\pi\) | ||||
0.402267 | + | 0.915522i | \(0.368222\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.6706 | −0.562904 | ||||||||
\(776\) | −10.9196 | −0.391989 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −23.9613 | −0.859056 | ||||||||
\(779\) | −54.0770 | −1.93751 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.40124 | −0.193272 | ||||||||
\(782\) | 13.8172 | 0.494104 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.200143 | 0.00714795 | ||||||||
\(785\) | 53.8212 | 1.92096 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.81781 | −0.243029 | −0.121514 | − | 0.992590i | \(-0.538775\pi\) | ||||
−0.121514 | + | 0.992590i | \(0.538775\pi\) | |||||||
\(788\) | −4.47541 | −0.159430 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −32.0606 | −1.14066 | ||||||||
\(791\) | −12.2178 | −0.434415 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.94372 | 0.104535 | ||||||||
\(794\) | −18.7734 | −0.666242 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.6122 | 0.659693 | ||||||||
\(797\) | 18.6309 | 0.659941 | 0.329970 | − | 0.943991i | \(-0.392961\pi\) | ||||
0.329970 | + | 0.943991i | \(0.392961\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.4180 | 0.510071 | ||||||||
\(800\) | 8.89789 | 0.314588 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 37.4767 | 1.32335 | ||||||||
\(803\) | 27.4923 | 0.970182 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −43.6561 | −1.53868 | ||||||||
\(806\) | 2.67278 | 0.0941448 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.12802 | 0.250763 | ||||||||
\(809\) | −34.1985 | −1.20236 | −0.601178 | − | 0.799115i | \(-0.705302\pi\) | ||||
−0.601178 | + | 0.799115i | \(0.705302\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.8426 | −0.450965 | −0.225482 | − | 0.974247i | \(-0.572396\pi\) | ||||
−0.225482 | + | 0.974247i | \(0.572396\pi\) | |||||||
\(812\) | −8.05012 | −0.282504 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 33.4138 | 1.17115 | ||||||||
\(815\) | −85.6927 | −3.00168 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31.7099 | 1.10939 | ||||||||
\(818\) | 7.66375 | 0.267957 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −27.4418 | −0.958309 | ||||||||
\(821\) | 28.4301 | 0.992217 | 0.496108 | − | 0.868261i | \(-0.334762\pi\) | ||||
0.496108 | + | 0.868261i | \(0.334762\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.4052 | −0.432418 | −0.216209 | − | 0.976347i | \(-0.569369\pi\) | ||||
−0.216209 | + | 0.976347i | \(0.569369\pi\) | |||||||
\(824\) | 12.1181 | 0.422153 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.70122 | −0.337549 | ||||||||
\(827\) | −30.7034 | −1.06766 | −0.533831 | − | 0.845591i | \(-0.679248\pi\) | ||||
−0.533831 | + | 0.845591i | \(0.679248\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.3653 | 0.637854 | 0.318927 | − | 0.947779i | \(-0.396678\pi\) | ||||
0.318927 | + | 0.947779i | \(0.396678\pi\) | |||||||
\(830\) | 0.502983 | 0.0174588 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.51763 | −0.0526143 | ||||||||
\(833\) | −0.633667 | −0.0219553 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −41.5700 | −1.43859 | ||||||||
\(836\) | 22.3046 | 0.771421 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 35.3284 | 1.22040 | ||||||||
\(839\) | 36.6263 | 1.26448 | 0.632239 | − | 0.774773i | \(-0.282136\pi\) | ||||
0.632239 | + | 0.774773i | \(0.282136\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.9996 | −0.689640 | ||||||||
\(842\) | 22.0077 | 0.758437 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.66630 | 0.160621 | ||||||||
\(845\) | 39.8775 | 1.37183 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.78146 | 0.164293 | ||||||||
\(848\) | 10.4838 | 0.360016 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −28.1714 | −0.966270 | ||||||||
\(851\) | 48.0293 | 1.64642 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.5200 | 0.565633 | 0.282816 | − | 0.959174i | \(-0.408731\pi\) | ||||
0.282816 | + | 0.959174i | \(0.408731\pi\) | |||||||
\(854\) | 5.20477 | 0.178104 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.99883 | 0.102498 | ||||||||
\(857\) | −38.7649 | −1.32418 | −0.662092 | − | 0.749423i | \(-0.730331\pi\) | ||||
−0.662092 | + | 0.749423i | \(0.730331\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.3944 | −1.07116 | −0.535581 | − | 0.844484i | \(-0.679907\pi\) | ||||
−0.535581 | + | 0.844484i | \(0.679907\pi\) | |||||||
\(860\) | 16.0914 | 0.548713 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 33.2706 | 1.13320 | ||||||||
\(863\) | 13.2569 | 0.451269 | 0.225635 | − | 0.974212i | \(-0.427554\pi\) | ||||
0.225635 | + | 0.974212i | \(0.427554\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −36.5100 | −1.24138 | ||||||||
\(866\) | −33.4569 | −1.13691 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.72573 | 0.160402 | ||||||||
\(869\) | −26.1106 | −0.885742 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.528262 | −0.0178995 | ||||||||
\(872\) | −10.6605 | −0.361009 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 32.0608 | 1.08447 | ||||||||
\(875\) | 38.9919 | 1.31817 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.3016 | 0.955679 | 0.477839 | − | 0.878447i | \(-0.341420\pi\) | ||||
0.477839 | + | 0.878447i | \(0.341420\pi\) | |||||||
\(878\) | −14.8073 | −0.499721 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 11.3186 | 0.381551 | ||||||||
\(881\) | 41.8860 | 1.41118 | 0.705588 | − | 0.708622i | \(-0.250683\pi\) | ||||
0.705588 | + | 0.708622i | \(0.250683\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42.1014 | −1.41682 | −0.708412 | − | 0.705799i | \(-0.750588\pi\) | ||||
−0.708412 | + | 0.705799i | \(0.750588\pi\) | |||||||
\(884\) | 4.80493 | 0.161607 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 34.0503 | 1.14394 | ||||||||
\(887\) | 33.1791 | 1.11405 | 0.557023 | − | 0.830497i | \(-0.311944\pi\) | ||||
0.557023 | + | 0.830497i | \(0.311944\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −26.4312 | −0.886473 | ||||||||
\(890\) | 49.2417 | 1.65059 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.01396 | −0.234845 | ||||||||
\(893\) | 33.4547 | 1.11952 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −68.3669 | −2.28525 | ||||||||
\(896\) | −2.68331 | −0.0896430 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.2168 | −0.407680 | ||||||||
\(899\) | −5.28361 | −0.176218 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −33.1925 | −1.10580 | ||||||||
\(902\) | −22.3490 | −0.744140 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.55326 | 0.151439 | ||||||||
\(905\) | −42.6259 | −1.41693 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.3574 | −1.14082 | −0.570410 | − | 0.821360i | \(-0.693216\pi\) | ||||
−0.570410 | + | 0.821360i | \(0.693216\pi\) | |||||||
\(908\) | −28.9841 | −0.961871 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −15.1813 | −0.503257 | ||||||||
\(911\) | 37.7454 | 1.25056 | 0.625280 | − | 0.780400i | \(-0.284985\pi\) | ||||
0.625280 | + | 0.780400i | \(0.284985\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.409637 | 0.0135570 | ||||||||
\(914\) | −5.68028 | −0.187887 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.49235 | −0.0493086 | ||||||||
\(917\) | −24.3692 | −0.804743 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −49.5954 | −1.63600 | −0.818000 | − | 0.575218i | \(-0.804917\pi\) | ||||
−0.818000 | + | 0.575218i | \(0.804917\pi\) | |||||||
\(920\) | 16.2695 | 0.536390 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.69247 | −0.0886717 | ||||||||
\(923\) | −2.69984 | −0.0888665 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −97.9249 | −3.21975 | ||||||||
\(926\) | 7.31923 | 0.240525 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.00007 | 0.0984822 | ||||||||
\(929\) | 6.32218 | 0.207424 | 0.103712 | − | 0.994607i | \(-0.466928\pi\) | ||||
0.103712 | + | 0.994607i | \(0.466928\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.47033 | −0.0481881 | ||||||||
\(932\) | 16.5298 | 0.541453 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −41.8088 | −1.36803 | ||||||||
\(935\) | −35.8357 | −1.17195 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.2690 | −0.923506 | −0.461753 | − | 0.887008i | \(-0.652779\pi\) | ||||
−0.461753 | + | 0.887008i | \(0.652779\pi\) | |||||||
\(938\) | −0.934017 | −0.0304967 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 16.9769 | 0.553724 | ||||||||
\(941\) | 4.80946 | 0.156784 | 0.0783920 | − | 0.996923i | \(-0.475021\pi\) | ||||
0.0783920 | + | 0.996923i | \(0.475021\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −32.1246 | −1.04612 | ||||||||
\(944\) | 3.61539 | 0.117671 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13.1051 | 0.426083 | ||||||||
\(947\) | −21.3831 | −0.694856 | −0.347428 | − | 0.937707i | \(-0.612945\pi\) | ||||
−0.347428 | + | 0.937707i | \(0.612945\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.7422 | 0.446091 | ||||||||
\(950\) | −65.3674 | −2.12080 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 8.49556 | 0.275343 | ||||||||
\(953\) | 47.7187 | 1.54576 | 0.772881 | − | 0.634551i | \(-0.218815\pi\) | ||||
0.772881 | + | 0.634551i | \(0.218815\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.02868 | 0.162724 | ||||||||
\(956\) | −6.51060 | −0.210568 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 24.8975 | 0.804400 | ||||||||
\(959\) | 32.8379 | 1.06039 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.8983 | −0.899946 | ||||||||
\(962\) | 16.7021 | 0.538498 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.15693 | −0.101678 | ||||||||
\(965\) | 27.0848 | 0.871891 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.82754 | 0.251717 | 0.125858 | − | 0.992048i | \(-0.459832\pi\) | ||||
0.125858 | + | 0.992048i | \(0.459832\pi\) | |||||||
\(968\) | −1.78193 | −0.0572733 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 40.7080 | 1.30705 | ||||||||
\(971\) | −1.90224 | −0.0610456 | −0.0305228 | − | 0.999534i | \(-0.509717\pi\) | ||||
−0.0305228 | + | 0.999534i | \(0.509717\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.6050 | −0.628506 | ||||||||
\(974\) | 33.5846 | 1.07612 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.93968 | −0.0620878 | ||||||||
\(977\) | 35.6734 | 1.14129 | 0.570646 | − | 0.821196i | \(-0.306693\pi\) | ||||
0.570646 | + | 0.821196i | \(0.306693\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 40.1032 | 1.28170 | ||||||||
\(980\) | −0.746129 | −0.0238342 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.55572 | 0.145379 | ||||||||
\(983\) | 9.95422 | 0.317490 | 0.158745 | − | 0.987320i | \(-0.449255\pi\) | ||||
0.158745 | + | 0.987320i | \(0.449255\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.6843 | 0.531605 | ||||||||
\(986\) | −9.49846 | −0.302493 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11.1491 | 0.354700 | ||||||||
\(989\) | 18.8374 | 0.598993 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.3371 | −0.328370 | −0.164185 | − | 0.986430i | \(-0.552499\pi\) | ||||
−0.164185 | + | 0.986430i | \(0.552499\pi\) | |||||||
\(992\) | −1.76116 | −0.0559168 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.77358 | −0.151409 | ||||||||
\(995\) | −69.3861 | −2.19969 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −54.6167 | −1.72973 | −0.864863 | − | 0.502007i | \(-0.832595\pi\) | ||||
−0.864863 | + | 0.502007i | \(0.832595\pi\) | |||||||
\(998\) | 8.32927 | 0.263658 | ||||||||
\(999\) | 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 | 8046.2.a.p.1.1 | yes | 12 | |
3.2 | odd | 2 | 8046.2.a.i.1.12 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.i.1.12 | ✓ | 12 | 3.2 | odd | 2 | ||
8046.2.a.p.1.1 | yes | 12 | 1.1 | even | 1 | trivial |