Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8379,2,Mod(1,8379)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8379, 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("8379.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8379 = 3^{2} \cdot 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8379.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: | \(66.9066518536\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 13x^{6} - x^{5} + 51x^{4} + 3x^{3} - 65x^{2} - 6x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 399) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.28285\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8379.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.28285 | −1.61422 | −0.807110 | − | 0.590402i | \(-0.798969\pi\) | ||||
−0.807110 | + | 0.590402i | \(0.798969\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.21141 | 1.60570 | ||||||||
\(5\) | −2.54525 | −1.13827 | −0.569136 | − | 0.822244i | \(-0.692722\pi\) | ||||
−0.569136 | + | 0.822244i | \(0.692722\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.76546 | −0.977737 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.81043 | 1.83742 | ||||||||
\(11\) | −3.29628 | −0.993866 | −0.496933 | − | 0.867789i | \(-0.665541\pi\) | ||||
−0.496933 | + | 0.867789i | \(0.665541\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.96243 | 1.37633 | 0.688166 | − | 0.725553i | \(-0.258416\pi\) | ||||
0.688166 | + | 0.725553i | \(0.258416\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.109683 | −0.0274207 | ||||||||
\(17\) | 5.59636 | 1.35732 | 0.678658 | − | 0.734454i | \(-0.262562\pi\) | ||||
0.678658 | + | 0.734454i | \(0.262562\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −8.17384 | −1.82773 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 7.52492 | 1.60432 | ||||||||
\(23\) | 5.81981 | 1.21351 | 0.606757 | − | 0.794887i | \(-0.292470\pi\) | ||||
0.606757 | + | 0.794887i | \(0.292470\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.47831 | 0.295662 | ||||||||
\(26\) | −11.3285 | −2.22170 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.32850 | 1.73226 | 0.866129 | − | 0.499820i | \(-0.166601\pi\) | ||||
0.866129 | + | 0.499820i | \(0.166601\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.42307 | 1.15362 | 0.576809 | − | 0.816879i | \(-0.304298\pi\) | ||||
0.576809 | + | 0.816879i | \(0.304298\pi\) | |||||||
\(32\) | 5.78131 | 1.02200 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −12.7757 | −2.19101 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.70048 | 1.26595 | 0.632976 | − | 0.774171i | \(-0.281833\pi\) | ||||
0.632976 | + | 0.774171i | \(0.281833\pi\) | |||||||
\(38\) | −2.28285 | −0.370327 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.03879 | 1.11293 | ||||||||
\(41\) | 6.13136 | 0.957558 | 0.478779 | − | 0.877936i | \(-0.341080\pi\) | ||||
0.478779 | + | 0.877936i | \(0.341080\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.62835 | −0.705816 | −0.352908 | − | 0.935658i | \(-0.614807\pi\) | ||||
−0.352908 | + | 0.935658i | \(0.614807\pi\) | |||||||
\(44\) | −10.5857 | −1.59585 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −13.2858 | −1.95888 | ||||||||
\(47\) | −6.31439 | −0.921049 | −0.460524 | − | 0.887647i | \(-0.652339\pi\) | ||||
−0.460524 | + | 0.887647i | \(0.652339\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.37477 | −0.477264 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 15.9364 | 2.20998 | ||||||||
\(53\) | 9.16420 | 1.25880 | 0.629400 | − | 0.777082i | \(-0.283301\pi\) | ||||
0.629400 | + | 0.777082i | \(0.283301\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.38987 | 1.13129 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −21.2956 | −2.79624 | ||||||||
\(59\) | 9.81110 | 1.27730 | 0.638649 | − | 0.769499i | \(-0.279494\pi\) | ||||
0.638649 | + | 0.769499i | \(0.279494\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.81589 | 0.232501 | 0.116251 | − | 0.993220i | \(-0.462912\pi\) | ||||
0.116251 | + | 0.993220i | \(0.462912\pi\) | |||||||
\(62\) | −14.6629 | −1.86219 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.9785 | −1.62231 | ||||||||
\(65\) | −12.6307 | −1.56664 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.36328 | 0.410891 | 0.205445 | − | 0.978669i | \(-0.434136\pi\) | ||||
0.205445 | + | 0.978669i | \(0.434136\pi\) | |||||||
\(68\) | 17.9722 | 2.17945 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.01667 | −0.239335 | −0.119667 | − | 0.992814i | \(-0.538183\pi\) | ||||
−0.119667 | + | 0.992814i | \(0.538183\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.72568 | 0.553099 | 0.276550 | − | 0.961000i | \(-0.410809\pi\) | ||||
0.276550 | + | 0.961000i | \(0.410809\pi\) | |||||||
\(74\) | −17.5791 | −2.04352 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.21141 | 0.368374 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.8985 | −1.45120 | −0.725599 | − | 0.688117i | \(-0.758437\pi\) | ||||
−0.725599 | + | 0.688117i | \(0.758437\pi\) | |||||||
\(80\) | 0.279170 | 0.0312122 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −13.9970 | −1.54571 | ||||||||
\(83\) | −0.743338 | −0.0815919 | −0.0407960 | − | 0.999167i | \(-0.512989\pi\) | ||||
−0.0407960 | + | 0.999167i | \(0.512989\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.2442 | −1.54500 | ||||||||
\(86\) | 10.5658 | 1.13934 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 9.11573 | 0.971740 | ||||||||
\(89\) | −11.4048 | −1.20891 | −0.604455 | − | 0.796639i | \(-0.706609\pi\) | ||||
−0.604455 | + | 0.796639i | \(0.706609\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 18.6898 | 1.94854 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 14.4148 | 1.48677 | ||||||||
\(95\) | −2.54525 | −0.261137 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.9210 | 1.71807 | 0.859035 | − | 0.511918i | \(-0.171065\pi\) | ||||
0.859035 | + | 0.511918i | \(0.171065\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.74746 | 0.474746 | ||||||||
\(101\) | −10.8587 | −1.08048 | −0.540242 | − | 0.841510i | \(-0.681667\pi\) | ||||
−0.540242 | + | 0.841510i | \(0.681667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.17582 | −0.411456 | −0.205728 | − | 0.978609i | \(-0.565956\pi\) | ||||
−0.205728 | + | 0.978609i | \(0.565956\pi\) | |||||||
\(104\) | −13.7234 | −1.34569 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −20.9205 | −2.03198 | ||||||||
\(107\) | 3.64747 | 0.352614 | 0.176307 | − | 0.984335i | \(-0.443585\pi\) | ||||
0.176307 | + | 0.984335i | \(0.443585\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.1717 | 1.35740 | 0.678701 | − | 0.734414i | \(-0.262543\pi\) | ||||
0.678701 | + | 0.734414i | \(0.262543\pi\) | |||||||
\(110\) | −19.1528 | −1.82615 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.20761 | 0.866179 | 0.433089 | − | 0.901351i | \(-0.357423\pi\) | ||||
0.433089 | + | 0.901351i | \(0.357423\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.8129 | −1.38131 | ||||||||
\(116\) | 29.9576 | 2.78149 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −22.3973 | −2.06184 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.134531 | −0.0122300 | ||||||||
\(122\) | −4.14542 | −0.375308 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 20.6271 | 1.85237 | ||||||||
\(125\) | 8.96359 | 0.801728 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.26815 | −0.467472 | −0.233736 | − | 0.972300i | \(-0.575095\pi\) | ||||
−0.233736 | + | 0.972300i | \(0.575095\pi\) | |||||||
\(128\) | 18.0653 | 1.59677 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 28.8339 | 2.52890 | ||||||||
\(131\) | −7.93634 | −0.693402 | −0.346701 | − | 0.937976i | \(-0.612698\pi\) | ||||
−0.346701 | + | 0.937976i | \(0.612698\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −7.67788 | −0.663268 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −15.4765 | −1.32710 | ||||||||
\(137\) | −8.19651 | −0.700275 | −0.350138 | − | 0.936698i | \(-0.613865\pi\) | ||||
−0.350138 | + | 0.936698i | \(0.613865\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.20860 | −0.781063 | −0.390531 | − | 0.920590i | \(-0.627709\pi\) | ||||
−0.390531 | + | 0.920590i | \(0.627709\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.60376 | 0.386339 | ||||||||
\(143\) | −16.3576 | −1.36789 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −23.7434 | −1.97178 | ||||||||
\(146\) | −10.7880 | −0.892823 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 24.7294 | 2.03274 | ||||||||
\(149\) | −4.79529 | −0.392845 | −0.196423 | − | 0.980519i | \(-0.562932\pi\) | ||||
−0.196423 | + | 0.980519i | \(0.562932\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.66081 | 0.623428 | 0.311714 | − | 0.950176i | \(-0.399097\pi\) | ||||
0.311714 | + | 0.950176i | \(0.399097\pi\) | |||||||
\(152\) | −2.76546 | −0.224308 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.3483 | −1.31313 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.93606 | 0.393940 | 0.196970 | − | 0.980409i | \(-0.436890\pi\) | ||||
0.196970 | + | 0.980409i | \(0.436890\pi\) | |||||||
\(158\) | 29.4454 | 2.34255 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −14.7149 | −1.16331 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.55111 | 0.199818 | 0.0999090 | − | 0.994997i | \(-0.468145\pi\) | ||||
0.0999090 | + | 0.994997i | \(0.468145\pi\) | |||||||
\(164\) | 19.6903 | 1.53755 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.69693 | 0.131707 | ||||||||
\(167\) | −1.94706 | −0.150668 | −0.0753340 | − | 0.997158i | \(-0.524002\pi\) | ||||
−0.0753340 | + | 0.997158i | \(0.524002\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.6258 | 0.894289 | ||||||||
\(170\) | 32.5173 | 2.49396 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −14.8635 | −1.13333 | ||||||||
\(173\) | 15.0694 | 1.14571 | 0.572853 | − | 0.819658i | \(-0.305836\pi\) | ||||
0.572853 | + | 0.819658i | \(0.305836\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.361545 | 0.0272525 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 26.0355 | 1.95145 | ||||||||
\(179\) | −23.3572 | −1.74580 | −0.872901 | − | 0.487897i | \(-0.837764\pi\) | ||||
−0.872901 | + | 0.487897i | \(0.837764\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.8279 | −1.62246 | −0.811228 | − | 0.584730i | \(-0.801200\pi\) | ||||
−0.811228 | + | 0.584730i | \(0.801200\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −16.0944 | −1.18650 | ||||||||
\(185\) | −19.5997 | −1.44100 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.4472 | −1.34899 | ||||||||
\(188\) | −20.2781 | −1.47893 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.81043 | 0.421533 | ||||||||
\(191\) | 10.7351 | 0.776763 | 0.388381 | − | 0.921499i | \(-0.373034\pi\) | ||||
0.388381 | + | 0.921499i | \(0.373034\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.0206 | 1.29715 | 0.648575 | − | 0.761151i | \(-0.275365\pi\) | ||||
0.648575 | + | 0.761151i | \(0.275365\pi\) | |||||||
\(194\) | −38.6282 | −2.77334 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.39251 | 0.241706 | 0.120853 | − | 0.992670i | \(-0.461437\pi\) | ||||
0.120853 | + | 0.992670i | \(0.461437\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.110913 | −0.00786243 | −0.00393121 | − | 0.999992i | \(-0.501251\pi\) | ||||
−0.00393121 | + | 0.999992i | \(0.501251\pi\) | |||||||
\(200\) | −4.08821 | −0.289080 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 24.7888 | 1.74414 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.6059 | −1.08996 | ||||||||
\(206\) | 9.53277 | 0.664180 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.544293 | −0.0377399 | ||||||||
\(209\) | −3.29628 | −0.228009 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.6596 | 0.802681 | 0.401340 | − | 0.915929i | \(-0.368544\pi\) | ||||
0.401340 | + | 0.915929i | \(0.368544\pi\) | |||||||
\(212\) | 29.4300 | 2.02126 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.32662 | −0.569196 | ||||||||
\(215\) | 11.7803 | 0.803410 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −32.3519 | −2.19115 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 26.9433 | 1.81652 | ||||||||
\(221\) | 27.7716 | 1.86812 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.8313 | −0.926214 | −0.463107 | − | 0.886302i | \(-0.653265\pi\) | ||||
−0.463107 | + | 0.886302i | \(0.653265\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −21.0196 | −1.39820 | ||||||||
\(227\) | 13.7904 | 0.915299 | 0.457650 | − | 0.889133i | \(-0.348691\pi\) | ||||
0.457650 | + | 0.889133i | \(0.348691\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.9644 | −0.922797 | −0.461398 | − | 0.887193i | \(-0.652652\pi\) | ||||
−0.461398 | + | 0.887193i | \(0.652652\pi\) | |||||||
\(230\) | 33.8156 | 2.22973 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −25.7976 | −1.69369 | ||||||||
\(233\) | 16.9838 | 1.11264 | 0.556322 | − | 0.830967i | \(-0.312212\pi\) | ||||
0.556322 | + | 0.830967i | \(0.312212\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.0717 | 1.04840 | ||||||||
\(236\) | 31.5074 | 2.05096 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.74352 | −0.177463 | −0.0887317 | − | 0.996056i | \(-0.528281\pi\) | ||||
−0.0887317 | + | 0.996056i | \(0.528281\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.93214 | −0.639786 | −0.319893 | − | 0.947454i | \(-0.603647\pi\) | ||||
−0.319893 | + | 0.947454i | \(0.603647\pi\) | |||||||
\(242\) | 0.307113 | 0.0197420 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.83157 | 0.373328 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.96243 | 0.315752 | ||||||||
\(248\) | −17.7628 | −1.12794 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −20.4625 | −1.29416 | ||||||||
\(251\) | 0.0936224 | 0.00590940 | 0.00295470 | − | 0.999996i | \(-0.499059\pi\) | ||||
0.00295470 | + | 0.999996i | \(0.499059\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.1837 | −1.20607 | ||||||||
\(254\) | 12.0264 | 0.754603 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.2835 | −0.955219 | ||||||||
\(257\) | 10.6649 | 0.665260 | 0.332630 | − | 0.943057i | \(-0.392064\pi\) | ||||
0.332630 | + | 0.943057i | \(0.392064\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −40.5621 | −2.51556 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 18.1175 | 1.11930 | ||||||||
\(263\) | −2.71193 | −0.167225 | −0.0836124 | − | 0.996498i | \(-0.526646\pi\) | ||||
−0.0836124 | + | 0.996498i | \(0.526646\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −23.3252 | −1.43286 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10.8009 | 0.659768 | ||||||||
\(269\) | −0.765987 | −0.0467030 | −0.0233515 | − | 0.999727i | \(-0.507434\pi\) | ||||
−0.0233515 | + | 0.999727i | \(0.507434\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.61998 | −0.341389 | −0.170695 | − | 0.985324i | \(-0.554601\pi\) | ||||
−0.170695 | + | 0.985324i | \(0.554601\pi\) | |||||||
\(272\) | −0.613824 | −0.0372186 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 18.7114 | 1.13040 | ||||||||
\(275\) | −4.87293 | −0.293849 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −28.3556 | −1.70373 | −0.851863 | − | 0.523765i | \(-0.824527\pi\) | ||||
−0.851863 | + | 0.523765i | \(0.824527\pi\) | |||||||
\(278\) | 21.0218 | 1.26081 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.7742 | 1.83583 | 0.917916 | − | 0.396774i | \(-0.129870\pi\) | ||||
0.917916 | + | 0.396774i | \(0.129870\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.4003 | 0.915452 | 0.457726 | − | 0.889093i | \(-0.348664\pi\) | ||||
0.457726 | + | 0.889093i | \(0.348664\pi\) | |||||||
\(284\) | −6.47635 | −0.384301 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 37.3419 | 2.20807 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.3193 | 0.842309 | ||||||||
\(290\) | 54.2026 | 3.18289 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 15.1761 | 0.888113 | ||||||||
\(293\) | −3.63257 | −0.212217 | −0.106109 | − | 0.994355i | \(-0.533839\pi\) | ||||
−0.106109 | + | 0.994355i | \(0.533839\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24.9717 | −1.45391 | ||||||||
\(296\) | −21.2954 | −1.23777 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.9469 | 0.634138 | ||||||||
\(299\) | 28.8804 | 1.67020 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −17.4885 | −1.00635 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.109683 | −0.00629074 | ||||||||
\(305\) | −4.62191 | −0.264650 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.4805 | −1.16888 | −0.584442 | − | 0.811436i | \(-0.698686\pi\) | ||||
−0.584442 | + | 0.811436i | \(0.698686\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 37.3208 | 2.11968 | ||||||||
\(311\) | −22.8687 | −1.29676 | −0.648382 | − | 0.761315i | \(-0.724554\pi\) | ||||
−0.648382 | + | 0.761315i | \(0.724554\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.4524 | 1.21256 | 0.606279 | − | 0.795252i | \(-0.292661\pi\) | ||||
0.606279 | + | 0.795252i | \(0.292661\pi\) | |||||||
\(314\) | −11.2683 | −0.635906 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −41.4224 | −2.33019 | ||||||||
\(317\) | −22.6472 | −1.27199 | −0.635996 | − | 0.771692i | \(-0.719411\pi\) | ||||
−0.635996 | + | 0.771692i | \(0.719411\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −30.7493 | −1.72163 | ||||||||
\(320\) | 33.0336 | 1.84663 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.59636 | 0.311390 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.33603 | 0.406930 | ||||||||
\(326\) | −5.82379 | −0.322550 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −16.9560 | −0.936240 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.7069 | 1.57787 | 0.788937 | − | 0.614474i | \(-0.210632\pi\) | ||||
0.788937 | + | 0.614474i | \(0.210632\pi\) | |||||||
\(332\) | −2.38716 | −0.131012 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.44485 | 0.243211 | ||||||||
\(335\) | −8.56041 | −0.467705 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.9822 | 1.52428 | 0.762142 | − | 0.647409i | \(-0.224148\pi\) | ||||
0.762142 | + | 0.647409i | \(0.224148\pi\) | |||||||
\(338\) | −26.5399 | −1.44358 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −45.7438 | −2.48080 | ||||||||
\(341\) | −21.1723 | −1.14654 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 12.7995 | 0.690103 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −34.4012 | −1.84942 | ||||||||
\(347\) | −18.1162 | −0.972531 | −0.486265 | − | 0.873811i | \(-0.661641\pi\) | ||||
−0.486265 | + | 0.873811i | \(0.661641\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.1254 | 0.863170 | 0.431585 | − | 0.902072i | \(-0.357954\pi\) | ||||
0.431585 | + | 0.902072i | \(0.357954\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −19.0568 | −1.01573 | ||||||||
\(353\) | −19.0378 | −1.01328 | −0.506641 | − | 0.862157i | \(-0.669113\pi\) | ||||
−0.506641 | + | 0.862157i | \(0.669113\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.13294 | 0.272428 | ||||||||
\(356\) | −36.6256 | −1.94115 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 53.3211 | 2.81811 | ||||||||
\(359\) | 5.17164 | 0.272948 | 0.136474 | − | 0.990644i | \(-0.456423\pi\) | ||||
0.136474 | + | 0.990644i | \(0.456423\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 49.8299 | 2.61900 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.0281 | −0.629577 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.62784 | −0.293771 | −0.146886 | − | 0.989153i | \(-0.546925\pi\) | ||||
−0.146886 | + | 0.989153i | \(0.546925\pi\) | |||||||
\(368\) | −0.638332 | −0.0332754 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 44.7431 | 2.32609 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.59456 | 0.186119 | 0.0930596 | − | 0.995661i | \(-0.470335\pi\) | ||||
0.0930596 | + | 0.995661i | \(0.470335\pi\) | |||||||
\(374\) | 42.1122 | 2.17757 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 17.4622 | 0.900544 | ||||||||
\(377\) | 46.2920 | 2.38416 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.82165 | 0.453138 | 0.226569 | − | 0.973995i | \(-0.427249\pi\) | ||||
0.226569 | + | 0.973995i | \(0.427249\pi\) | |||||||
\(380\) | −8.17384 | −0.419309 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −24.5066 | −1.25387 | ||||||||
\(383\) | −31.3248 | −1.60062 | −0.800311 | − | 0.599586i | \(-0.795332\pi\) | ||||
−0.800311 | + | 0.599586i | \(0.795332\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −41.1383 | −2.09388 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 54.3403 | 2.75871 | ||||||||
\(389\) | 0.245826 | 0.0124639 | 0.00623193 | − | 0.999981i | \(-0.498016\pi\) | ||||
0.00623193 | + | 0.999981i | \(0.498016\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 32.5697 | 1.64712 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.74458 | −0.390166 | ||||||||
\(395\) | 32.8300 | 1.65186 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.79530 | 0.0901037 | 0.0450519 | − | 0.998985i | \(-0.485655\pi\) | ||||
0.0450519 | + | 0.998985i | \(0.485655\pi\) | |||||||
\(398\) | 0.253198 | 0.0126917 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.162145 | −0.00810726 | ||||||||
\(401\) | 24.5023 | 1.22359 | 0.611793 | − | 0.791018i | \(-0.290448\pi\) | ||||
0.611793 | + | 0.791018i | \(0.290448\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 31.8741 | 1.58776 | ||||||||
\(404\) | −34.8718 | −1.73493 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −25.3830 | −1.25819 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.1049 | −1.34025 | −0.670125 | − | 0.742248i | \(-0.733760\pi\) | ||||
−0.670125 | + | 0.742248i | \(0.733760\pi\) | |||||||
\(410\) | 35.6259 | 1.75944 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −13.4103 | −0.660676 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.89198 | 0.0928738 | ||||||||
\(416\) | 28.6894 | 1.40661 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.52492 | 0.368056 | ||||||||
\(419\) | −24.5949 | −1.20154 | −0.600771 | − | 0.799421i | \(-0.705140\pi\) | ||||
−0.600771 | + | 0.799421i | \(0.705140\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.1191 | 0.834334 | 0.417167 | − | 0.908830i | \(-0.363023\pi\) | ||||
0.417167 | + | 0.908830i | \(0.363023\pi\) | |||||||
\(422\) | −26.6171 | −1.29570 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −25.3432 | −1.23078 | ||||||||
\(425\) | 8.27317 | 0.401308 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 11.7135 | 0.566193 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −26.8927 | −1.29688 | ||||||||
\(431\) | 19.6284 | 0.945467 | 0.472733 | − | 0.881206i | \(-0.343267\pi\) | ||||
0.472733 | + | 0.881206i | \(0.343267\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.0095 | −1.44216 | −0.721082 | − | 0.692850i | \(-0.756355\pi\) | ||||
−0.721082 | + | 0.692850i | \(0.756355\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 45.5111 | 2.17959 | ||||||||
\(437\) | 5.81981 | 0.278399 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.6440 | 0.555739 | 0.277869 | − | 0.960619i | \(-0.410372\pi\) | ||||
0.277869 | + | 0.960619i | \(0.410372\pi\) | |||||||
\(440\) | −23.2018 | −1.10610 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −63.3984 | −3.01555 | ||||||||
\(443\) | 19.3379 | 0.918771 | 0.459386 | − | 0.888237i | \(-0.348070\pi\) | ||||
0.459386 | + | 0.888237i | \(0.348070\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 29.0282 | 1.37607 | ||||||||
\(446\) | 31.5749 | 1.49511 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 34.8975 | 1.64692 | 0.823458 | − | 0.567377i | \(-0.192042\pi\) | ||||
0.823458 | + | 0.567377i | \(0.192042\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20.2107 | −0.951684 | ||||||||
\(452\) | 29.5694 | 1.39083 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −31.4814 | −1.47749 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.11205 | −0.145576 | −0.0727878 | − | 0.997347i | \(-0.523190\pi\) | ||||
−0.0727878 | + | 0.997347i | \(0.523190\pi\) | |||||||
\(458\) | 31.8787 | 1.48960 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −47.5702 | −2.21797 | ||||||||
\(461\) | 21.6573 | 1.00868 | 0.504341 | − | 0.863505i | \(-0.331736\pi\) | ||||
0.504341 | + | 0.863505i | \(0.331736\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.4240 | −1.27450 | −0.637252 | − | 0.770656i | \(-0.719929\pi\) | ||||
−0.637252 | + | 0.770656i | \(0.719929\pi\) | |||||||
\(464\) | −1.02317 | −0.0474997 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −38.7714 | −1.79605 | ||||||||
\(467\) | −27.2546 | −1.26119 | −0.630595 | − | 0.776112i | \(-0.717189\pi\) | ||||
−0.630595 | + | 0.776112i | \(0.717189\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −36.6893 | −1.69235 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −27.1322 | −1.24886 | ||||||||
\(473\) | 15.2563 | 0.701487 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.47831 | 0.0678296 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.26304 | 0.286465 | ||||||||
\(479\) | −35.5989 | −1.62655 | −0.813277 | − | 0.581877i | \(-0.802318\pi\) | ||||
−0.813277 | + | 0.581877i | \(0.802318\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 38.2132 | 1.74237 | ||||||||
\(482\) | 22.6736 | 1.03275 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.432032 | −0.0196378 | ||||||||
\(485\) | −43.0683 | −1.95563 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.5604 | 0.976996 | 0.488498 | − | 0.872565i | \(-0.337545\pi\) | ||||
0.488498 | + | 0.872565i | \(0.337545\pi\) | |||||||
\(488\) | −5.02178 | −0.227325 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.06065 | −0.183255 | −0.0916273 | − | 0.995793i | \(-0.529207\pi\) | ||||
−0.0916273 | + | 0.995793i | \(0.529207\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 52.2056 | 2.35122 | ||||||||
\(494\) | −11.3285 | −0.509693 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.704500 | −0.0316330 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.6822 | −0.612498 | −0.306249 | − | 0.951951i | \(-0.599074\pi\) | ||||
−0.306249 | + | 0.951951i | \(0.599074\pi\) | |||||||
\(500\) | 28.7857 | 1.28734 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.213726 | −0.00953906 | ||||||||
\(503\) | 16.8353 | 0.750650 | 0.375325 | − | 0.926893i | \(-0.377531\pi\) | ||||
0.375325 | + | 0.926893i | \(0.377531\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 27.6382 | 1.22988 | ||||||||
\(506\) | 43.7936 | 1.94686 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −16.9182 | −0.750622 | ||||||||
\(509\) | 4.18134 | 0.185335 | 0.0926673 | − | 0.995697i | \(-0.470461\pi\) | ||||
0.0926673 | + | 0.995697i | \(0.470461\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.24076 | −0.0548342 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −24.3464 | −1.07387 | ||||||||
\(515\) | 10.6285 | 0.468348 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.8140 | 0.915399 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 34.9295 | 1.53176 | ||||||||
\(521\) | −12.7717 | −0.559538 | −0.279769 | − | 0.960067i | \(-0.590258\pi\) | ||||
−0.279769 | + | 0.960067i | \(0.590258\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.9317 | 1.13391 | 0.566957 | − | 0.823747i | \(-0.308120\pi\) | ||||
0.566957 | + | 0.823747i | \(0.308120\pi\) | |||||||
\(524\) | −25.4868 | −1.11340 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.19093 | 0.269937 | ||||||||
\(527\) | 35.9458 | 1.56583 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.8702 | 0.472616 | ||||||||
\(530\) | 53.2480 | 2.31294 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 30.4265 | 1.31792 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.28372 | −0.401370 | ||||||||
\(536\) | −9.30103 | −0.401743 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.74863 | 0.0753889 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.8312 | −0.981590 | −0.490795 | − | 0.871275i | \(-0.663294\pi\) | ||||
−0.490795 | + | 0.871275i | \(0.663294\pi\) | |||||||
\(542\) | 12.8296 | 0.551077 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 32.3543 | 1.38718 | ||||||||
\(545\) | −36.0706 | −1.54509 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.0599 | −0.900455 | −0.450227 | − | 0.892914i | \(-0.648657\pi\) | ||||
−0.450227 | + | 0.892914i | \(0.648657\pi\) | |||||||
\(548\) | −26.3223 | −1.12443 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 11.1242 | 0.474336 | ||||||||
\(551\) | 9.32850 | 0.397407 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 64.7317 | 2.75019 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −29.5725 | −1.25416 | ||||||||
\(557\) | −43.5536 | −1.84543 | −0.922713 | − | 0.385488i | \(-0.874033\pi\) | ||||
−0.922713 | + | 0.385488i | \(0.874033\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.9679 | −0.971437 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −70.2528 | −2.96344 | ||||||||
\(563\) | −21.5381 | −0.907724 | −0.453862 | − | 0.891072i | \(-0.649954\pi\) | ||||
−0.453862 | + | 0.891072i | \(0.649954\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −23.4357 | −0.985947 | ||||||||
\(566\) | −35.1566 | −1.47774 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.57702 | 0.234007 | ||||||||
\(569\) | −13.8224 | −0.579464 | −0.289732 | − | 0.957108i | \(-0.593566\pi\) | ||||
−0.289732 | + | 0.957108i | \(0.593566\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.37170 | −0.266647 | −0.133324 | − | 0.991073i | \(-0.542565\pi\) | ||||
−0.133324 | + | 0.991073i | \(0.542565\pi\) | |||||||
\(572\) | −52.5308 | −2.19642 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.60349 | 0.358790 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.3947 | −0.765780 | −0.382890 | − | 0.923794i | \(-0.625071\pi\) | ||||
−0.382890 | + | 0.923794i | \(0.625071\pi\) | |||||||
\(578\) | −32.6887 | −1.35967 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −76.2496 | −3.16609 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −30.2078 | −1.25108 | ||||||||
\(584\) | −13.0687 | −0.540786 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.29262 | 0.342565 | ||||||||
\(587\) | −28.7021 | −1.18466 | −0.592331 | − | 0.805695i | \(-0.701792\pi\) | ||||
−0.592331 | + | 0.805695i | \(0.701792\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.42307 | 0.264658 | ||||||||
\(590\) | 57.0068 | 2.34693 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.844610 | −0.0347133 | ||||||||
\(593\) | 32.6544 | 1.34096 | 0.670478 | − | 0.741930i | \(-0.266089\pi\) | ||||
0.670478 | + | 0.741930i | \(0.266089\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −15.3996 | −0.630793 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −65.9297 | −2.69606 | ||||||||
\(599\) | −9.27154 | −0.378825 | −0.189412 | − | 0.981898i | \(-0.560658\pi\) | ||||
−0.189412 | + | 0.981898i | \(0.560658\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.44868 | −0.263047 | −0.131524 | − | 0.991313i | \(-0.541987\pi\) | ||||
−0.131524 | + | 0.991313i | \(0.541987\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 24.6020 | 1.00104 | ||||||||
\(605\) | 0.342414 | 0.0139211 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.77185 | 0.396627 | 0.198314 | − | 0.980139i | \(-0.436454\pi\) | ||||
0.198314 | + | 0.980139i | \(0.436454\pi\) | |||||||
\(608\) | 5.78131 | 0.234463 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10.5511 | 0.427203 | ||||||||
\(611\) | −31.3348 | −1.26767 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −44.6639 | −1.80396 | −0.901979 | − | 0.431781i | \(-0.857885\pi\) | ||||
−0.901979 | + | 0.431781i | \(0.857885\pi\) | |||||||
\(614\) | 46.7539 | 1.88683 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.1695 | 1.01329 | 0.506643 | − | 0.862156i | \(-0.330886\pi\) | ||||
0.506643 | + | 0.862156i | \(0.330886\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 39.4836 | 1.58698 | 0.793490 | − | 0.608583i | \(-0.208262\pi\) | ||||
0.793490 | + | 0.608583i | \(0.208262\pi\) | |||||||
\(620\) | −52.5012 | −2.10850 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 52.2058 | 2.09326 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.2062 | −1.20825 | ||||||||
\(626\) | −48.9725 | −1.95734 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.8517 | 0.632551 | ||||||||
\(629\) | 43.0947 | 1.71830 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.92164 | 0.235737 | 0.117868 | − | 0.993029i | \(-0.462394\pi\) | ||||
0.117868 | + | 0.993029i | \(0.462394\pi\) | |||||||
\(632\) | 35.6704 | 1.41889 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 51.7001 | 2.05327 | ||||||||
\(635\) | 13.4088 | 0.532110 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 70.1962 | 2.77909 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −45.9809 | −1.81755 | ||||||||
\(641\) | 15.1334 | 0.597733 | 0.298867 | − | 0.954295i | \(-0.403391\pi\) | ||||
0.298867 | + | 0.954295i | \(0.403391\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.5709 | −0.574619 | −0.287310 | − | 0.957838i | \(-0.592761\pi\) | ||||
−0.287310 | + | 0.957838i | \(0.592761\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.7757 | −0.502651 | ||||||||
\(647\) | −2.91875 | −0.114748 | −0.0573739 | − | 0.998353i | \(-0.518273\pi\) | ||||
−0.0573739 | + | 0.998353i | \(0.518273\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −32.3402 | −1.26946 | ||||||||
\(650\) | −16.7471 | −0.656873 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.19264 | 0.320848 | ||||||||
\(653\) | 27.7398 | 1.08554 | 0.542770 | − | 0.839881i | \(-0.317375\pi\) | ||||
0.542770 | + | 0.839881i | \(0.317375\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.2000 | 0.789279 | ||||||||
\(656\) | −0.672504 | −0.0262569 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.7834 | −0.575880 | −0.287940 | − | 0.957648i | \(-0.592970\pi\) | ||||
−0.287940 | + | 0.957648i | \(0.592970\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.2532 | −1.37119 | −0.685596 | − | 0.727983i | \(-0.740458\pi\) | ||||
−0.685596 | + | 0.727983i | \(0.740458\pi\) | |||||||
\(662\) | −65.5335 | −2.54703 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.05567 | 0.0797755 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 54.2901 | 2.10212 | ||||||||
\(668\) | −6.25280 | −0.241928 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 19.5421 | 0.754979 | ||||||||
\(671\) | −5.98570 | −0.231075 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.4607 | −0.865796 | −0.432898 | − | 0.901443i | \(-0.642509\pi\) | ||||
−0.432898 | + | 0.901443i | \(0.642509\pi\) | |||||||
\(674\) | −63.8791 | −2.46053 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 37.3350 | 1.43596 | ||||||||
\(677\) | −9.28643 | −0.356906 | −0.178453 | − | 0.983948i | \(-0.557109\pi\) | ||||
−0.178453 | + | 0.983948i | \(0.557109\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 39.3916 | 1.51060 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 48.3331 | 1.85077 | ||||||||
\(683\) | −19.2391 | −0.736162 | −0.368081 | − | 0.929794i | \(-0.619985\pi\) | ||||
−0.368081 | + | 0.929794i | \(0.619985\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.8622 | 0.797103 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.507649 | 0.0193540 | ||||||||
\(689\) | 45.4767 | 1.73253 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.0706 | −0.877646 | −0.438823 | − | 0.898573i | \(-0.644605\pi\) | ||||
−0.438823 | + | 0.898573i | \(0.644605\pi\) | |||||||
\(692\) | 48.3940 | 1.83967 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 41.3567 | 1.56988 | ||||||||
\(695\) | 23.4382 | 0.889062 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 34.3133 | 1.29971 | ||||||||
\(698\) | −36.8118 | −1.39335 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.6485 | 0.704344 | 0.352172 | − | 0.935935i | \(-0.385443\pi\) | ||||
0.352172 | + | 0.935935i | \(0.385443\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.70048 | 0.290429 | ||||||||
\(704\) | 42.7808 | 1.61236 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 43.4605 | 1.63566 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 44.5115 | 1.67166 | 0.835832 | − | 0.548986i | \(-0.184986\pi\) | ||||
0.835832 | + | 0.548986i | \(0.184986\pi\) | |||||||
\(710\) | −11.7177 | −0.439759 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 31.5396 | 1.18200 | ||||||||
\(713\) | 37.3811 | 1.39993 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 41.6342 | 1.55703 | ||||||||
\(716\) | −75.0096 | −2.80324 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −11.8061 | −0.440599 | ||||||||
\(719\) | 23.7966 | 0.887465 | 0.443733 | − | 0.896159i | \(-0.353654\pi\) | ||||
0.443733 | + | 0.896159i | \(0.353654\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.28285 | −0.0849589 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −70.0983 | −2.60518 | ||||||||
\(725\) | 13.7904 | 0.512164 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.5209 | 1.05778 | 0.528891 | − | 0.848689i | \(-0.322608\pi\) | ||||
0.528891 | + | 0.848689i | \(0.322608\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 27.4582 | 1.01628 | ||||||||
\(731\) | −25.9019 | −0.958016 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.2788 | 0.601270 | 0.300635 | − | 0.953739i | \(-0.402801\pi\) | ||||
0.300635 | + | 0.953739i | \(0.402801\pi\) | |||||||
\(734\) | 12.8475 | 0.474211 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 33.6461 | 1.24021 | ||||||||
\(737\) | −11.0863 | −0.408370 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 52.4917 | 1.93094 | 0.965470 | − | 0.260516i | \(-0.0838927\pi\) | ||||
0.965470 | + | 0.260516i | \(0.0838927\pi\) | |||||||
\(740\) | −62.9425 | −2.31381 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.9433 | 1.17189 | 0.585944 | − | 0.810352i | \(-0.300724\pi\) | ||||
0.585944 | + | 0.810352i | \(0.300724\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.2052 | 0.447165 | ||||||||
\(746\) | −8.20584 | −0.300437 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −59.2414 | −2.16608 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.80983 | −0.248494 | −0.124247 | − | 0.992251i | \(-0.539652\pi\) | ||||
−0.124247 | + | 0.992251i | \(0.539652\pi\) | |||||||
\(752\) | 0.692580 | 0.0252558 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −105.678 | −3.84856 | ||||||||
\(755\) | −19.4987 | −0.709630 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.00239 | 0.327198 | 0.163599 | − | 0.986527i | \(-0.447690\pi\) | ||||
0.163599 | + | 0.986527i | \(0.447690\pi\) | |||||||
\(758\) | −20.1385 | −0.731464 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.03879 | 0.255324 | ||||||||
\(761\) | 5.17963 | 0.187762 | 0.0938808 | − | 0.995583i | \(-0.470073\pi\) | ||||
0.0938808 | + | 0.995583i | \(0.470073\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 34.4747 | 1.24725 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 71.5098 | 2.58375 | ||||||||
\(767\) | 48.6870 | 1.75798 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.5253 | −1.49744 | −0.748720 | − | 0.662886i | \(-0.769331\pi\) | ||||
−0.748720 | + | 0.662886i | \(0.769331\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 57.8714 | 2.08284 | ||||||||
\(773\) | −2.83802 | −0.102076 | −0.0510382 | − | 0.998697i | \(-0.516253\pi\) | ||||
−0.0510382 | + | 0.998697i | \(0.516253\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.49531 | 0.341082 | ||||||||
\(776\) | −46.7944 | −1.67982 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.561183 | −0.0201194 | ||||||||
\(779\) | 6.13136 | 0.219679 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.64752 | 0.237867 | ||||||||
\(782\) | −74.3519 | −2.65882 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.5635 | −0.448411 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.4975 | 1.47923 | 0.739614 | − | 0.673032i | \(-0.235008\pi\) | ||||
0.739614 | + | 0.673032i | \(0.235008\pi\) | |||||||
\(788\) | 10.8947 | 0.388108 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −74.9461 | −2.66646 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.01126 | 0.319999 | ||||||||
\(794\) | −4.09841 | −0.145447 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.356187 | −0.0126247 | ||||||||
\(797\) | −34.7178 | −1.22977 | −0.614884 | − | 0.788618i | \(-0.710797\pi\) | ||||
−0.614884 | + | 0.788618i | \(0.710797\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −35.3376 | −1.25016 | ||||||||
\(800\) | 8.54658 | 0.302167 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −55.9351 | −1.97514 | ||||||||
\(803\) | −15.5772 | −0.549706 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −72.7638 | −2.56299 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 30.0293 | 1.05643 | ||||||||
\(809\) | 36.8670 | 1.29617 | 0.648087 | − | 0.761566i | \(-0.275569\pi\) | ||||
0.648087 | + | 0.761566i | \(0.275569\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.4803 | 1.59703 | 0.798515 | − | 0.601974i | \(-0.205619\pi\) | ||||
0.798515 | + | 0.601974i | \(0.205619\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 57.9455 | 2.03099 | ||||||||
\(815\) | −6.49321 | −0.227447 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.62835 | −0.161925 | ||||||||
\(818\) | 61.8764 | 2.16346 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −50.1168 | −1.75015 | ||||||||
\(821\) | −25.5522 | −0.891776 | −0.445888 | − | 0.895089i | \(-0.647112\pi\) | ||||
−0.445888 | + | 0.895089i | \(0.647112\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.55183 | 0.263240 | 0.131620 | − | 0.991300i | \(-0.457982\pi\) | ||||
0.131620 | + | 0.991300i | \(0.457982\pi\) | |||||||
\(824\) | 11.5481 | 0.402296 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.8901 | 1.07415 | 0.537077 | − | 0.843533i | \(-0.319528\pi\) | ||||
0.537077 | + | 0.843533i | \(0.319528\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.3786 | −0.916167 | −0.458084 | − | 0.888909i | \(-0.651464\pi\) | ||||
−0.458084 | + | 0.888909i | \(0.651464\pi\) | |||||||
\(830\) | −4.31911 | −0.149919 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −64.4049 | −2.23284 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.95576 | 0.171501 | ||||||||
\(836\) | −10.5857 | −0.366114 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 56.1466 | 1.93955 | ||||||||
\(839\) | −2.55457 | −0.0881935 | −0.0440968 | − | 0.999027i | \(-0.514041\pi\) | ||||
−0.0440968 | + | 0.999027i | \(0.514041\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 58.0208 | 2.00072 | ||||||||
\(842\) | −39.0803 | −1.34680 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 37.4437 | 1.28887 | ||||||||
\(845\) | −29.5905 | −1.01794 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.00515 | −0.0345171 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −18.8864 | −0.647798 | ||||||||
\(851\) | 44.8153 | 1.53625 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 52.1083 | 1.78416 | 0.892078 | − | 0.451882i | \(-0.149247\pi\) | ||||
0.892078 | + | 0.451882i | \(0.149247\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.0869 | −0.344764 | ||||||||
\(857\) | −7.45507 | −0.254660 | −0.127330 | − | 0.991860i | \(-0.540641\pi\) | ||||
−0.127330 | + | 0.991860i | \(0.540641\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.9401 | 1.02154 | 0.510772 | − | 0.859716i | \(-0.329360\pi\) | ||||
0.510772 | + | 0.859716i | \(0.329360\pi\) | |||||||
\(860\) | 37.8314 | 1.29004 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −44.8087 | −1.52619 | ||||||||
\(863\) | 14.3896 | 0.489828 | 0.244914 | − | 0.969545i | \(-0.421240\pi\) | ||||
0.244914 | + | 0.969545i | \(0.421240\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −38.3555 | −1.30413 | ||||||||
\(866\) | 68.5071 | 2.32797 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 42.5172 | 1.44230 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.6901 | 0.565522 | ||||||||
\(872\) | −39.1913 | −1.32718 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −13.2858 | −0.449397 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 54.7996 | 1.85045 | 0.925226 | − | 0.379416i | \(-0.123875\pi\) | ||||
0.925226 | + | 0.379416i | \(0.123875\pi\) | |||||||
\(878\) | −26.5816 | −0.897084 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.920224 | −0.0310207 | ||||||||
\(881\) | −20.3805 | −0.686638 | −0.343319 | − | 0.939219i | \(-0.611551\pi\) | ||||
−0.343319 | + | 0.939219i | \(0.611551\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.1615 | −0.678488 | −0.339244 | − | 0.940698i | \(-0.610171\pi\) | ||||
−0.339244 | + | 0.940698i | \(0.610171\pi\) | |||||||
\(884\) | 89.1858 | 2.99964 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −44.1455 | −1.48310 | ||||||||
\(887\) | −45.0043 | −1.51110 | −0.755549 | − | 0.655092i | \(-0.772630\pi\) | ||||
−0.755549 | + | 0.655092i | \(0.772630\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −66.2670 | −2.22128 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −44.4180 | −1.48723 | ||||||||
\(893\) | −6.31439 | −0.211303 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 59.4501 | 1.98720 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −79.6659 | −2.65848 | ||||||||
\(899\) | 59.9176 | 1.99836 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 51.2862 | 1.70859 | ||||||||
\(902\) | 46.1380 | 1.53623 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −25.4633 | −0.846895 | ||||||||
\(905\) | 55.5575 | 1.84680 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.8676 | −0.858919 | −0.429459 | − | 0.903086i | \(-0.641296\pi\) | ||||
−0.429459 | + | 0.903086i | \(0.641296\pi\) | |||||||
\(908\) | 44.2865 | 1.46970 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.50711 | 0.281853 | 0.140927 | − | 0.990020i | \(-0.454992\pi\) | ||||
0.140927 | + | 0.990020i | \(0.454992\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.45025 | 0.0810915 | ||||||||
\(914\) | 7.10435 | 0.234991 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −44.8455 | −1.48174 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.7168 | 0.914292 | 0.457146 | − | 0.889392i | \(-0.348872\pi\) | ||||
0.457146 | + | 0.889392i | \(0.348872\pi\) | |||||||
\(920\) | 40.9644 | 1.35056 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −49.4404 | −1.62823 | ||||||||
\(923\) | −10.0076 | −0.329404 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.3837 | 0.374294 | ||||||||
\(926\) | 62.6050 | 2.05733 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 53.9309 | 1.77037 | ||||||||
\(929\) | −19.6853 | −0.645855 | −0.322928 | − | 0.946424i | \(-0.604667\pi\) | ||||
−0.322928 | + | 0.946424i | \(0.604667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 54.5418 | 1.78658 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 62.2181 | 2.03584 | ||||||||
\(935\) | 46.9527 | 1.53552 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39.0825 | −1.27677 | −0.638385 | − | 0.769717i | \(-0.720397\pi\) | ||||
−0.638385 | + | 0.769717i | \(0.720397\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 51.6128 | 1.68343 | ||||||||
\(941\) | 46.1337 | 1.50392 | 0.751958 | − | 0.659210i | \(-0.229109\pi\) | ||||
0.751958 | + | 0.659210i | \(0.229109\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 35.6833 | 1.16201 | ||||||||
\(944\) | −1.07611 | −0.0350244 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −34.8279 | −1.13235 | ||||||||
\(947\) | −9.84967 | −0.320071 | −0.160036 | − | 0.987111i | \(-0.551161\pi\) | ||||
−0.160036 | + | 0.987111i | \(0.551161\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23.4509 | 0.761248 | ||||||||
\(950\) | −3.37477 | −0.109492 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23.5275 | −0.762131 | −0.381066 | − | 0.924548i | \(-0.624443\pi\) | ||||
−0.381066 | + | 0.924548i | \(0.624443\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −27.3235 | −0.884167 | ||||||||
\(956\) | −8.81055 | −0.284954 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 81.2669 | 2.62561 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.2559 | 0.330835 | ||||||||
\(962\) | −87.2349 | −2.81257 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −31.8961 | −1.02731 | ||||||||
\(965\) | −45.8669 | −1.47651 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.3664 | 0.622783 | 0.311391 | − | 0.950282i | \(-0.399205\pi\) | ||||
0.311391 | + | 0.950282i | \(0.399205\pi\) | |||||||
\(968\) | 0.372039 | 0.0119578 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 98.3184 | 3.15681 | ||||||||
\(971\) | −39.1062 | −1.25498 | −0.627488 | − | 0.778626i | \(-0.715917\pi\) | ||||
−0.627488 | + | 0.778626i | \(0.715917\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −49.2192 | −1.57709 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.199172 | −0.00637535 | ||||||||
\(977\) | −43.2545 | −1.38383 | −0.691917 | − | 0.721977i | \(-0.743234\pi\) | ||||
−0.691917 | + | 0.721977i | \(0.743234\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 37.5935 | 1.20149 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9.26986 | 0.295813 | ||||||||
\(983\) | −0.143918 | −0.00459027 | −0.00229513 | − | 0.999997i | \(-0.500731\pi\) | ||||
−0.00229513 | + | 0.999997i | \(0.500731\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.63478 | −0.275127 | ||||||||
\(986\) | −119.178 | −3.79539 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 15.9364 | 0.507004 | ||||||||
\(989\) | −26.9361 | −0.856518 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.6827 | 0.402880 | 0.201440 | − | 0.979501i | \(-0.435438\pi\) | ||||
0.201440 | + | 0.979501i | \(0.435438\pi\) | |||||||
\(992\) | 37.1338 | 1.17900 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.282302 | 0.00894958 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.3602 | 0.708156 | 0.354078 | − | 0.935216i | \(-0.384795\pi\) | ||||
0.354078 | + | 0.935216i | \(0.384795\pi\) | |||||||
\(998\) | 31.2343 | 0.988706 | ||||||||
\(999\) | 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 | 8379.2.a.cq.1.2 | 8 | ||
3.2 | odd | 2 | 2793.2.a.bn.1.7 | 8 | |||
7.3 | odd | 6 | 1197.2.j.m.856.7 | 16 | |||
7.5 | odd | 6 | 1197.2.j.m.172.7 | 16 | |||
7.6 | odd | 2 | 8379.2.a.cr.1.2 | 8 | |||
21.5 | even | 6 | 399.2.j.g.172.2 | yes | 16 | ||
21.17 | even | 6 | 399.2.j.g.58.2 | ✓ | 16 | ||
21.20 | even | 2 | 2793.2.a.bm.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
399.2.j.g.58.2 | ✓ | 16 | 21.17 | even | 6 | ||
399.2.j.g.172.2 | yes | 16 | 21.5 | even | 6 | ||
1197.2.j.m.172.7 | 16 | 7.5 | odd | 6 | |||
1197.2.j.m.856.7 | 16 | 7.3 | odd | 6 | |||
2793.2.a.bm.1.7 | 8 | 21.20 | even | 2 | |||
2793.2.a.bn.1.7 | 8 | 3.2 | odd | 2 | |||
8379.2.a.cq.1.2 | 8 | 1.1 | even | 1 | trivial | ||
8379.2.a.cr.1.2 | 8 | 7.6 | odd | 2 |