Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5290,2,Mod(1,5290)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5290, 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("5290.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5290 = 2 \cdot 5 \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5290.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: | \(42.2408626693\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 5 x^{14} - 24 x^{13} + 142 x^{12} + 184 x^{11} - 1488 x^{10} - 426 x^{9} + 7165 x^{8} + \cdots - 32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 230) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(1.31120\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5290.1 |
$q$-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 | ||||||||
\(3\) | 1.31120 | 0.757022 | 0.378511 | − | 0.925597i | \(-0.376436\pi\) | ||||
0.378511 | + | 0.925597i | \(0.376436\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.31120 | 0.535295 | ||||||||
\(7\) | 3.61614 | 1.36677 | 0.683387 | − | 0.730056i | \(-0.260506\pi\) | ||||
0.683387 | + | 0.730056i | \(0.260506\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.28075 | −0.426918 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 3.14951 | 0.949612 | 0.474806 | − | 0.880091i | \(-0.342518\pi\) | ||||
0.474806 | + | 0.880091i | \(0.342518\pi\) | |||||||
\(12\) | 1.31120 | 0.378511 | ||||||||
\(13\) | 3.52217 | 0.976874 | 0.488437 | − | 0.872599i | \(-0.337567\pi\) | ||||
0.488437 | + | 0.872599i | \(0.337567\pi\) | |||||||
\(14\) | 3.61614 | 0.966455 | ||||||||
\(15\) | 1.31120 | 0.338550 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.96756 | −1.20481 | −0.602405 | − | 0.798190i | \(-0.705791\pi\) | ||||
−0.602405 | + | 0.798190i | \(0.705791\pi\) | |||||||
\(18\) | −1.28075 | −0.301877 | ||||||||
\(19\) | 1.16157 | 0.266482 | 0.133241 | − | 0.991084i | \(-0.457462\pi\) | ||||
0.133241 | + | 0.991084i | \(0.457462\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 4.74149 | 1.03468 | ||||||||
\(22\) | 3.14951 | 0.671477 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | 1.31120 | 0.267648 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 3.52217 | 0.690754 | ||||||||
\(27\) | −5.61293 | −1.08021 | ||||||||
\(28\) | 3.61614 | 0.683387 | ||||||||
\(29\) | 5.04510 | 0.936852 | 0.468426 | − | 0.883503i | \(-0.344821\pi\) | ||||
0.468426 | + | 0.883503i | \(0.344821\pi\) | |||||||
\(30\) | 1.31120 | 0.239391 | ||||||||
\(31\) | 6.15794 | 1.10600 | 0.553000 | − | 0.833181i | \(-0.313483\pi\) | ||||
0.553000 | + | 0.833181i | \(0.313483\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.12963 | 0.718877 | ||||||||
\(34\) | −4.96756 | −0.851930 | ||||||||
\(35\) | 3.61614 | 0.611240 | ||||||||
\(36\) | −1.28075 | −0.213459 | ||||||||
\(37\) | 0.957846 | 0.157469 | 0.0787344 | − | 0.996896i | \(-0.474912\pi\) | ||||
0.0787344 | + | 0.996896i | \(0.474912\pi\) | |||||||
\(38\) | 1.16157 | 0.188431 | ||||||||
\(39\) | 4.61827 | 0.739515 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 2.20177 | 0.343859 | 0.171930 | − | 0.985109i | \(-0.445000\pi\) | ||||
0.171930 | + | 0.985109i | \(0.445000\pi\) | |||||||
\(42\) | 4.74149 | 0.731628 | ||||||||
\(43\) | −8.45052 | −1.28869 | −0.644346 | − | 0.764734i | \(-0.722870\pi\) | ||||
−0.644346 | + | 0.764734i | \(0.722870\pi\) | |||||||
\(44\) | 3.14951 | 0.474806 | ||||||||
\(45\) | −1.28075 | −0.190923 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.16026 | −0.898567 | −0.449283 | − | 0.893389i | \(-0.648321\pi\) | ||||
−0.449283 | + | 0.893389i | \(0.648321\pi\) | |||||||
\(48\) | 1.31120 | 0.189255 | ||||||||
\(49\) | 6.07649 | 0.868071 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −6.51347 | −0.912068 | ||||||||
\(52\) | 3.52217 | 0.488437 | ||||||||
\(53\) | −12.3701 | −1.69916 | −0.849579 | − | 0.527461i | \(-0.823144\pi\) | ||||
−0.849579 | + | 0.527461i | \(0.823144\pi\) | |||||||
\(54\) | −5.61293 | −0.763822 | ||||||||
\(55\) | 3.14951 | 0.424679 | ||||||||
\(56\) | 3.61614 | 0.483228 | ||||||||
\(57\) | 1.52305 | 0.201733 | ||||||||
\(58\) | 5.04510 | 0.662455 | ||||||||
\(59\) | 7.95193 | 1.03525 | 0.517626 | − | 0.855607i | \(-0.326816\pi\) | ||||
0.517626 | + | 0.855607i | \(0.326816\pi\) | |||||||
\(60\) | 1.31120 | 0.169275 | ||||||||
\(61\) | 8.77820 | 1.12393 | 0.561967 | − | 0.827160i | \(-0.310045\pi\) | ||||
0.561967 | + | 0.827160i | \(0.310045\pi\) | |||||||
\(62\) | 6.15794 | 0.782060 | ||||||||
\(63\) | −4.63139 | −0.583500 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.52217 | 0.436871 | ||||||||
\(66\) | 4.12963 | 0.508323 | ||||||||
\(67\) | −15.5122 | −1.89512 | −0.947561 | − | 0.319575i | \(-0.896460\pi\) | ||||
−0.947561 | + | 0.319575i | \(0.896460\pi\) | |||||||
\(68\) | −4.96756 | −0.602405 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.61614 | 0.432212 | ||||||||
\(71\) | 1.07941 | 0.128102 | 0.0640510 | − | 0.997947i | \(-0.479598\pi\) | ||||
0.0640510 | + | 0.997947i | \(0.479598\pi\) | |||||||
\(72\) | −1.28075 | −0.150938 | ||||||||
\(73\) | −2.34692 | −0.274686 | −0.137343 | − | 0.990524i | \(-0.543856\pi\) | ||||
−0.137343 | + | 0.990524i | \(0.543856\pi\) | |||||||
\(74\) | 0.957846 | 0.111347 | ||||||||
\(75\) | 1.31120 | 0.151404 | ||||||||
\(76\) | 1.16157 | 0.133241 | ||||||||
\(77\) | 11.3891 | 1.29790 | ||||||||
\(78\) | 4.61827 | 0.522916 | ||||||||
\(79\) | −7.30901 | −0.822328 | −0.411164 | − | 0.911561i | \(-0.634878\pi\) | ||||
−0.411164 | + | 0.911561i | \(0.634878\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −3.51741 | −0.390823 | ||||||||
\(82\) | 2.20177 | 0.243145 | ||||||||
\(83\) | 14.6609 | 1.60924 | 0.804622 | − | 0.593788i | \(-0.202368\pi\) | ||||
0.804622 | + | 0.593788i | \(0.202368\pi\) | |||||||
\(84\) | 4.74149 | 0.517339 | ||||||||
\(85\) | −4.96756 | −0.538808 | ||||||||
\(86\) | −8.45052 | −0.911243 | ||||||||
\(87\) | 6.61514 | 0.709218 | ||||||||
\(88\) | 3.14951 | 0.335738 | ||||||||
\(89\) | −1.58594 | −0.168109 | −0.0840546 | − | 0.996461i | \(-0.526787\pi\) | ||||
−0.0840546 | + | 0.996461i | \(0.526787\pi\) | |||||||
\(90\) | −1.28075 | −0.135003 | ||||||||
\(91\) | 12.7367 | 1.33517 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.07430 | 0.837266 | ||||||||
\(94\) | −6.16026 | −0.635383 | ||||||||
\(95\) | 1.16157 | 0.119174 | ||||||||
\(96\) | 1.31120 | 0.133824 | ||||||||
\(97\) | 0.135127 | 0.0137200 | 0.00686002 | − | 0.999976i | \(-0.497816\pi\) | ||||
0.00686002 | + | 0.999976i | \(0.497816\pi\) | |||||||
\(98\) | 6.07649 | 0.613819 | ||||||||
\(99\) | −4.03374 | −0.405406 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 12.9048 | 1.28407 | 0.642036 | − | 0.766675i | \(-0.278090\pi\) | ||||
0.642036 | + | 0.766675i | \(0.278090\pi\) | |||||||
\(102\) | −6.51347 | −0.644930 | ||||||||
\(103\) | 6.73469 | 0.663588 | 0.331794 | − | 0.943352i | \(-0.392346\pi\) | ||||
0.331794 | + | 0.943352i | \(0.392346\pi\) | |||||||
\(104\) | 3.52217 | 0.345377 | ||||||||
\(105\) | 4.74149 | 0.462722 | ||||||||
\(106\) | −12.3701 | −1.20149 | ||||||||
\(107\) | 15.0699 | 1.45686 | 0.728432 | − | 0.685118i | \(-0.240250\pi\) | ||||
0.728432 | + | 0.685118i | \(0.240250\pi\) | |||||||
\(108\) | −5.61293 | −0.540104 | ||||||||
\(109\) | −12.7003 | −1.21646 | −0.608232 | − | 0.793759i | \(-0.708121\pi\) | ||||
−0.608232 | + | 0.793759i | \(0.708121\pi\) | |||||||
\(110\) | 3.14951 | 0.300294 | ||||||||
\(111\) | 1.25593 | 0.119207 | ||||||||
\(112\) | 3.61614 | 0.341693 | ||||||||
\(113\) | −14.0869 | −1.32518 | −0.662592 | − | 0.748980i | \(-0.730544\pi\) | ||||
−0.662592 | + | 0.748980i | \(0.730544\pi\) | |||||||
\(114\) | 1.52305 | 0.142646 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.04510 | 0.468426 | ||||||||
\(117\) | −4.51103 | −0.417045 | ||||||||
\(118\) | 7.95193 | 0.732034 | ||||||||
\(119\) | −17.9634 | −1.64670 | ||||||||
\(120\) | 1.31120 | 0.119696 | ||||||||
\(121\) | −1.08061 | −0.0982374 | ||||||||
\(122\) | 8.77820 | 0.794741 | ||||||||
\(123\) | 2.88697 | 0.260309 | ||||||||
\(124\) | 6.15794 | 0.553000 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −4.63139 | −0.412597 | ||||||||
\(127\) | −3.35646 | −0.297838 | −0.148919 | − | 0.988849i | \(-0.547579\pi\) | ||||
−0.148919 | + | 0.988849i | \(0.547579\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −11.0803 | −0.975568 | ||||||||
\(130\) | 3.52217 | 0.308915 | ||||||||
\(131\) | 16.9660 | 1.48233 | 0.741163 | − | 0.671325i | \(-0.234275\pi\) | ||||
0.741163 | + | 0.671325i | \(0.234275\pi\) | |||||||
\(132\) | 4.12963 | 0.359438 | ||||||||
\(133\) | 4.20039 | 0.364220 | ||||||||
\(134\) | −15.5122 | −1.34005 | ||||||||
\(135\) | −5.61293 | −0.483084 | ||||||||
\(136\) | −4.96756 | −0.425965 | ||||||||
\(137\) | −14.4268 | −1.23257 | −0.616284 | − | 0.787524i | \(-0.711363\pi\) | ||||
−0.616284 | + | 0.787524i | \(0.711363\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.0105 | 0.933901 | 0.466950 | − | 0.884283i | \(-0.345353\pi\) | ||||
0.466950 | + | 0.884283i | \(0.345353\pi\) | |||||||
\(140\) | 3.61614 | 0.305620 | ||||||||
\(141\) | −8.07734 | −0.680235 | ||||||||
\(142\) | 1.07941 | 0.0905818 | ||||||||
\(143\) | 11.0931 | 0.927651 | ||||||||
\(144\) | −1.28075 | −0.106729 | ||||||||
\(145\) | 5.04510 | 0.418973 | ||||||||
\(146\) | −2.34692 | −0.194233 | ||||||||
\(147\) | 7.96750 | 0.657148 | ||||||||
\(148\) | 0.957846 | 0.0787344 | ||||||||
\(149\) | −1.23855 | −0.101466 | −0.0507331 | − | 0.998712i | \(-0.516156\pi\) | ||||
−0.0507331 | + | 0.998712i | \(0.516156\pi\) | |||||||
\(150\) | 1.31120 | 0.107059 | ||||||||
\(151\) | −22.7286 | −1.84963 | −0.924813 | − | 0.380422i | \(-0.875779\pi\) | ||||
−0.924813 | + | 0.380422i | \(0.875779\pi\) | |||||||
\(152\) | 1.16157 | 0.0942156 | ||||||||
\(153\) | 6.36222 | 0.514355 | ||||||||
\(154\) | 11.3891 | 0.917757 | ||||||||
\(155\) | 6.15794 | 0.494618 | ||||||||
\(156\) | 4.61827 | 0.369757 | ||||||||
\(157\) | −16.1780 | −1.29114 | −0.645571 | − | 0.763700i | \(-0.723381\pi\) | ||||
−0.645571 | + | 0.763700i | \(0.723381\pi\) | |||||||
\(158\) | −7.30901 | −0.581474 | ||||||||
\(159\) | −16.2196 | −1.28630 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −3.51741 | −0.276354 | ||||||||
\(163\) | −11.6751 | −0.914466 | −0.457233 | − | 0.889347i | \(-0.651159\pi\) | ||||
−0.457233 | + | 0.889347i | \(0.651159\pi\) | |||||||
\(164\) | 2.20177 | 0.171930 | ||||||||
\(165\) | 4.12963 | 0.321492 | ||||||||
\(166\) | 14.6609 | 1.13791 | ||||||||
\(167\) | 6.79041 | 0.525457 | 0.262729 | − | 0.964870i | \(-0.415378\pi\) | ||||
0.262729 | + | 0.964870i | \(0.415378\pi\) | |||||||
\(168\) | 4.74149 | 0.365814 | ||||||||
\(169\) | −0.594330 | −0.0457177 | ||||||||
\(170\) | −4.96756 | −0.380995 | ||||||||
\(171\) | −1.48768 | −0.113766 | ||||||||
\(172\) | −8.45052 | −0.644346 | ||||||||
\(173\) | −3.77075 | −0.286685 | −0.143342 | − | 0.989673i | \(-0.545785\pi\) | ||||
−0.143342 | + | 0.989673i | \(0.545785\pi\) | |||||||
\(174\) | 6.61514 | 0.501493 | ||||||||
\(175\) | 3.61614 | 0.273355 | ||||||||
\(176\) | 3.14951 | 0.237403 | ||||||||
\(177\) | 10.4266 | 0.783709 | ||||||||
\(178\) | −1.58594 | −0.118871 | ||||||||
\(179\) | 11.5561 | 0.863741 | 0.431871 | − | 0.901936i | \(-0.357854\pi\) | ||||
0.431871 | + | 0.901936i | \(0.357854\pi\) | |||||||
\(180\) | −1.28075 | −0.0954617 | ||||||||
\(181\) | −16.2020 | −1.20428 | −0.602142 | − | 0.798389i | \(-0.705686\pi\) | ||||
−0.602142 | + | 0.798389i | \(0.705686\pi\) | |||||||
\(182\) | 12.7367 | 0.944105 | ||||||||
\(183\) | 11.5100 | 0.850842 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.957846 | 0.0704222 | ||||||||
\(186\) | 8.07430 | 0.592036 | ||||||||
\(187\) | −15.6454 | −1.14410 | ||||||||
\(188\) | −6.16026 | −0.449283 | ||||||||
\(189\) | −20.2971 | −1.47640 | ||||||||
\(190\) | 1.16157 | 0.0842690 | ||||||||
\(191\) | 3.85033 | 0.278600 | 0.139300 | − | 0.990250i | \(-0.455515\pi\) | ||||
0.139300 | + | 0.990250i | \(0.455515\pi\) | |||||||
\(192\) | 1.31120 | 0.0946277 | ||||||||
\(193\) | 17.6774 | 1.27245 | 0.636225 | − | 0.771504i | \(-0.280495\pi\) | ||||
0.636225 | + | 0.771504i | \(0.280495\pi\) | |||||||
\(194\) | 0.135127 | 0.00970154 | ||||||||
\(195\) | 4.61827 | 0.330721 | ||||||||
\(196\) | 6.07649 | 0.434035 | ||||||||
\(197\) | −26.5330 | −1.89040 | −0.945200 | − | 0.326491i | \(-0.894134\pi\) | ||||
−0.945200 | + | 0.326491i | \(0.894134\pi\) | |||||||
\(198\) | −4.03374 | −0.286666 | ||||||||
\(199\) | −8.64754 | −0.613008 | −0.306504 | − | 0.951869i | \(-0.599159\pi\) | ||||
−0.306504 | + | 0.951869i | \(0.599159\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −20.3397 | −1.43465 | ||||||||
\(202\) | 12.9048 | 0.907976 | ||||||||
\(203\) | 18.2438 | 1.28047 | ||||||||
\(204\) | −6.51347 | −0.456034 | ||||||||
\(205\) | 2.20177 | 0.153779 | ||||||||
\(206\) | 6.73469 | 0.469228 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.52217 | 0.244218 | ||||||||
\(209\) | 3.65836 | 0.253054 | ||||||||
\(210\) | 4.74149 | 0.327194 | ||||||||
\(211\) | −0.497276 | −0.0342339 | −0.0171170 | − | 0.999853i | \(-0.505449\pi\) | ||||
−0.0171170 | + | 0.999853i | \(0.505449\pi\) | |||||||
\(212\) | −12.3701 | −0.849579 | ||||||||
\(213\) | 1.41532 | 0.0969760 | ||||||||
\(214\) | 15.0699 | 1.03016 | ||||||||
\(215\) | −8.45052 | −0.576321 | ||||||||
\(216\) | −5.61293 | −0.381911 | ||||||||
\(217\) | 22.2680 | 1.51165 | ||||||||
\(218\) | −12.7003 | −0.860170 | ||||||||
\(219\) | −3.07728 | −0.207944 | ||||||||
\(220\) | 3.14951 | 0.212340 | ||||||||
\(221\) | −17.4966 | −1.17695 | ||||||||
\(222\) | 1.25593 | 0.0842924 | ||||||||
\(223\) | −3.53102 | −0.236454 | −0.118227 | − | 0.992987i | \(-0.537721\pi\) | ||||
−0.118227 | + | 0.992987i | \(0.537721\pi\) | |||||||
\(224\) | 3.61614 | 0.241614 | ||||||||
\(225\) | −1.28075 | −0.0853836 | ||||||||
\(226\) | −14.0869 | −0.937047 | ||||||||
\(227\) | 12.8244 | 0.851183 | 0.425592 | − | 0.904915i | \(-0.360066\pi\) | ||||
0.425592 | + | 0.904915i | \(0.360066\pi\) | |||||||
\(228\) | 1.52305 | 0.100866 | ||||||||
\(229\) | 13.3800 | 0.884178 | 0.442089 | − | 0.896971i | \(-0.354238\pi\) | ||||
0.442089 | + | 0.896971i | \(0.354238\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.9333 | 0.982542 | ||||||||
\(232\) | 5.04510 | 0.331227 | ||||||||
\(233\) | 28.4249 | 1.86218 | 0.931090 | − | 0.364791i | \(-0.118859\pi\) | ||||
0.931090 | + | 0.364791i | \(0.118859\pi\) | |||||||
\(234\) | −4.51103 | −0.294895 | ||||||||
\(235\) | −6.16026 | −0.401851 | ||||||||
\(236\) | 7.95193 | 0.517626 | ||||||||
\(237\) | −9.58358 | −0.622520 | ||||||||
\(238\) | −17.9634 | −1.16440 | ||||||||
\(239\) | 14.6017 | 0.944503 | 0.472251 | − | 0.881464i | \(-0.343442\pi\) | ||||
0.472251 | + | 0.881464i | \(0.343442\pi\) | |||||||
\(240\) | 1.31120 | 0.0846376 | ||||||||
\(241\) | −21.3303 | −1.37400 | −0.687002 | − | 0.726655i | \(-0.741074\pi\) | ||||
−0.687002 | + | 0.726655i | \(0.741074\pi\) | |||||||
\(242\) | −1.08061 | −0.0694643 | ||||||||
\(243\) | 12.2267 | 0.784346 | ||||||||
\(244\) | 8.77820 | 0.561967 | ||||||||
\(245\) | 6.07649 | 0.388213 | ||||||||
\(246\) | 2.88697 | 0.184066 | ||||||||
\(247\) | 4.09124 | 0.260319 | ||||||||
\(248\) | 6.15794 | 0.391030 | ||||||||
\(249\) | 19.2234 | 1.21823 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 17.0976 | 1.07919 | 0.539594 | − | 0.841925i | \(-0.318578\pi\) | ||||
0.539594 | + | 0.841925i | \(0.318578\pi\) | |||||||
\(252\) | −4.63139 | −0.291750 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −3.35646 | −0.210603 | ||||||||
\(255\) | −6.51347 | −0.407889 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −29.9543 | −1.86850 | −0.934248 | − | 0.356623i | \(-0.883928\pi\) | ||||
−0.934248 | + | 0.356623i | \(0.883928\pi\) | |||||||
\(258\) | −11.0803 | −0.689831 | ||||||||
\(259\) | 3.46371 | 0.215224 | ||||||||
\(260\) | 3.52217 | 0.218436 | ||||||||
\(261\) | −6.46154 | −0.399959 | ||||||||
\(262\) | 16.9660 | 1.04816 | ||||||||
\(263\) | 2.46654 | 0.152093 | 0.0760467 | − | 0.997104i | \(-0.475770\pi\) | ||||
0.0760467 | + | 0.997104i | \(0.475770\pi\) | |||||||
\(264\) | 4.12963 | 0.254161 | ||||||||
\(265\) | −12.3701 | −0.759887 | ||||||||
\(266\) | 4.20039 | 0.257543 | ||||||||
\(267\) | −2.07948 | −0.127262 | ||||||||
\(268\) | −15.5122 | −0.947561 | ||||||||
\(269\) | 4.08349 | 0.248975 | 0.124487 | − | 0.992221i | \(-0.460271\pi\) | ||||
0.124487 | + | 0.992221i | \(0.460271\pi\) | |||||||
\(270\) | −5.61293 | −0.341592 | ||||||||
\(271\) | 12.9062 | 0.783999 | 0.391999 | − | 0.919965i | \(-0.371784\pi\) | ||||
0.391999 | + | 0.919965i | \(0.371784\pi\) | |||||||
\(272\) | −4.96756 | −0.301203 | ||||||||
\(273\) | 16.7003 | 1.01075 | ||||||||
\(274\) | −14.4268 | −0.871557 | ||||||||
\(275\) | 3.14951 | 0.189922 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.8828 | 0.894218 | 0.447109 | − | 0.894479i | \(-0.352454\pi\) | ||||
0.447109 | + | 0.894479i | \(0.352454\pi\) | |||||||
\(278\) | 11.0105 | 0.660368 | ||||||||
\(279\) | −7.88681 | −0.472171 | ||||||||
\(280\) | 3.61614 | 0.216106 | ||||||||
\(281\) | 18.4841 | 1.10267 | 0.551335 | − | 0.834284i | \(-0.314118\pi\) | ||||
0.551335 | + | 0.834284i | \(0.314118\pi\) | |||||||
\(282\) | −8.07734 | −0.480999 | ||||||||
\(283\) | 12.8751 | 0.765344 | 0.382672 | − | 0.923884i | \(-0.375004\pi\) | ||||
0.382672 | + | 0.923884i | \(0.375004\pi\) | |||||||
\(284\) | 1.07941 | 0.0640510 | ||||||||
\(285\) | 1.52305 | 0.0902176 | ||||||||
\(286\) | 11.0931 | 0.655948 | ||||||||
\(287\) | 7.96193 | 0.469978 | ||||||||
\(288\) | −1.28075 | −0.0754691 | ||||||||
\(289\) | 7.67668 | 0.451569 | ||||||||
\(290\) | 5.04510 | 0.296259 | ||||||||
\(291\) | 0.177178 | 0.0103864 | ||||||||
\(292\) | −2.34692 | −0.137343 | ||||||||
\(293\) | −16.7824 | −0.980437 | −0.490218 | − | 0.871600i | \(-0.663083\pi\) | ||||
−0.490218 | + | 0.871600i | \(0.663083\pi\) | |||||||
\(294\) | 7.96750 | 0.464674 | ||||||||
\(295\) | 7.95193 | 0.462979 | ||||||||
\(296\) | 0.957846 | 0.0556737 | ||||||||
\(297\) | −17.6779 | −1.02578 | ||||||||
\(298\) | −1.23855 | −0.0717474 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.31120 | 0.0757022 | ||||||||
\(301\) | −30.5583 | −1.76135 | ||||||||
\(302\) | −22.7286 | −1.30788 | ||||||||
\(303\) | 16.9207 | 0.972070 | ||||||||
\(304\) | 1.16157 | 0.0666205 | ||||||||
\(305\) | 8.77820 | 0.502638 | ||||||||
\(306\) | 6.36222 | 0.363704 | ||||||||
\(307\) | 0.364016 | 0.0207755 | 0.0103877 | − | 0.999946i | \(-0.496693\pi\) | ||||
0.0103877 | + | 0.999946i | \(0.496693\pi\) | |||||||
\(308\) | 11.3891 | 0.648952 | ||||||||
\(309\) | 8.83052 | 0.502351 | ||||||||
\(310\) | 6.15794 | 0.349748 | ||||||||
\(311\) | −7.29349 | −0.413576 | −0.206788 | − | 0.978386i | \(-0.566301\pi\) | ||||
−0.206788 | + | 0.978386i | \(0.566301\pi\) | |||||||
\(312\) | 4.61827 | 0.261458 | ||||||||
\(313\) | 25.9726 | 1.46806 | 0.734030 | − | 0.679117i | \(-0.237637\pi\) | ||||
0.734030 | + | 0.679117i | \(0.237637\pi\) | |||||||
\(314\) | −16.1780 | −0.912976 | ||||||||
\(315\) | −4.63139 | −0.260949 | ||||||||
\(316\) | −7.30901 | −0.411164 | ||||||||
\(317\) | −10.0369 | −0.563726 | −0.281863 | − | 0.959455i | \(-0.590952\pi\) | ||||
−0.281863 | + | 0.959455i | \(0.590952\pi\) | |||||||
\(318\) | −16.2196 | −0.909551 | ||||||||
\(319\) | 15.8896 | 0.889646 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 19.7597 | 1.10288 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.77016 | −0.321060 | ||||||||
\(324\) | −3.51741 | −0.195412 | ||||||||
\(325\) | 3.52217 | 0.195375 | ||||||||
\(326\) | −11.6751 | −0.646625 | ||||||||
\(327\) | −16.6526 | −0.920890 | ||||||||
\(328\) | 2.20177 | 0.121573 | ||||||||
\(329\) | −22.2764 | −1.22814 | ||||||||
\(330\) | 4.12963 | 0.227329 | ||||||||
\(331\) | −28.1837 | −1.54912 | −0.774558 | − | 0.632502i | \(-0.782028\pi\) | ||||
−0.774558 | + | 0.632502i | \(0.782028\pi\) | |||||||
\(332\) | 14.6609 | 0.804622 | ||||||||
\(333\) | −1.22676 | −0.0672263 | ||||||||
\(334\) | 6.79041 | 0.371554 | ||||||||
\(335\) | −15.5122 | −0.847524 | ||||||||
\(336\) | 4.74149 | 0.258669 | ||||||||
\(337\) | 22.5355 | 1.22759 | 0.613793 | − | 0.789467i | \(-0.289643\pi\) | ||||
0.613793 | + | 0.789467i | \(0.289643\pi\) | |||||||
\(338\) | −0.594330 | −0.0323273 | ||||||||
\(339\) | −18.4708 | −1.00319 | ||||||||
\(340\) | −4.96756 | −0.269404 | ||||||||
\(341\) | 19.3945 | 1.05027 | ||||||||
\(342\) | −1.48768 | −0.0804446 | ||||||||
\(343\) | −3.33953 | −0.180318 | ||||||||
\(344\) | −8.45052 | −0.455622 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.77075 | −0.202717 | ||||||||
\(347\) | 15.9837 | 0.858050 | 0.429025 | − | 0.903293i | \(-0.358857\pi\) | ||||
0.429025 | + | 0.903293i | \(0.358857\pi\) | |||||||
\(348\) | 6.61514 | 0.354609 | ||||||||
\(349\) | −20.6925 | −1.10765 | −0.553823 | − | 0.832635i | \(-0.686831\pi\) | ||||
−0.553823 | + | 0.832635i | \(0.686831\pi\) | |||||||
\(350\) | 3.61614 | 0.193291 | ||||||||
\(351\) | −19.7697 | −1.05523 | ||||||||
\(352\) | 3.14951 | 0.167869 | ||||||||
\(353\) | 10.7261 | 0.570893 | 0.285447 | − | 0.958395i | \(-0.407858\pi\) | ||||
0.285447 | + | 0.958395i | \(0.407858\pi\) | |||||||
\(354\) | 10.4266 | 0.554166 | ||||||||
\(355\) | 1.07941 | 0.0572890 | ||||||||
\(356\) | −1.58594 | −0.0840546 | ||||||||
\(357\) | −23.5536 | −1.24659 | ||||||||
\(358\) | 11.5561 | 0.610757 | ||||||||
\(359\) | 15.2290 | 0.803756 | 0.401878 | − | 0.915693i | \(-0.368358\pi\) | ||||
0.401878 | + | 0.915693i | \(0.368358\pi\) | |||||||
\(360\) | −1.28075 | −0.0675016 | ||||||||
\(361\) | −17.6508 | −0.928987 | ||||||||
\(362\) | −16.2020 | −0.851557 | ||||||||
\(363\) | −1.41690 | −0.0743679 | ||||||||
\(364\) | 12.7367 | 0.667583 | ||||||||
\(365\) | −2.34692 | −0.122843 | ||||||||
\(366\) | 11.5100 | 0.601636 | ||||||||
\(367\) | −15.5272 | −0.810516 | −0.405258 | − | 0.914202i | \(-0.632818\pi\) | ||||
−0.405258 | + | 0.914202i | \(0.632818\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.81993 | −0.146800 | ||||||||
\(370\) | 0.957846 | 0.0497960 | ||||||||
\(371\) | −44.7319 | −2.32236 | ||||||||
\(372\) | 8.07430 | 0.418633 | ||||||||
\(373\) | −20.7074 | −1.07219 | −0.536094 | − | 0.844159i | \(-0.680101\pi\) | ||||
−0.536094 | + | 0.844159i | \(0.680101\pi\) | |||||||
\(374\) | −15.6454 | −0.809003 | ||||||||
\(375\) | 1.31120 | 0.0677101 | ||||||||
\(376\) | −6.16026 | −0.317691 | ||||||||
\(377\) | 17.7697 | 0.915186 | ||||||||
\(378\) | −20.2971 | −1.04397 | ||||||||
\(379\) | −5.07433 | −0.260651 | −0.130325 | − | 0.991471i | \(-0.541602\pi\) | ||||
−0.130325 | + | 0.991471i | \(0.541602\pi\) | |||||||
\(380\) | 1.16157 | 0.0595872 | ||||||||
\(381\) | −4.40100 | −0.225470 | ||||||||
\(382\) | 3.85033 | 0.197000 | ||||||||
\(383\) | 1.77390 | 0.0906422 | 0.0453211 | − | 0.998972i | \(-0.485569\pi\) | ||||
0.0453211 | + | 0.998972i | \(0.485569\pi\) | |||||||
\(384\) | 1.31120 | 0.0669119 | ||||||||
\(385\) | 11.3891 | 0.580441 | ||||||||
\(386\) | 17.6774 | 0.899757 | ||||||||
\(387\) | 10.8230 | 0.550166 | ||||||||
\(388\) | 0.135127 | 0.00686002 | ||||||||
\(389\) | 5.06064 | 0.256585 | 0.128292 | − | 0.991736i | \(-0.459050\pi\) | ||||
0.128292 | + | 0.991736i | \(0.459050\pi\) | |||||||
\(390\) | 4.61827 | 0.233855 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 6.07649 | 0.306909 | ||||||||
\(393\) | 22.2458 | 1.12215 | ||||||||
\(394\) | −26.5330 | −1.33672 | ||||||||
\(395\) | −7.30901 | −0.367756 | ||||||||
\(396\) | −4.03374 | −0.202703 | ||||||||
\(397\) | −2.38213 | −0.119556 | −0.0597779 | − | 0.998212i | \(-0.519039\pi\) | ||||
−0.0597779 | + | 0.998212i | \(0.519039\pi\) | |||||||
\(398\) | −8.64754 | −0.433462 | ||||||||
\(399\) | 5.50756 | 0.275723 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 16.3779 | 0.817876 | 0.408938 | − | 0.912562i | \(-0.365899\pi\) | ||||
0.408938 | + | 0.912562i | \(0.365899\pi\) | |||||||
\(402\) | −20.3397 | −1.01445 | ||||||||
\(403\) | 21.6893 | 1.08042 | ||||||||
\(404\) | 12.9048 | 0.642036 | ||||||||
\(405\) | −3.51741 | −0.174781 | ||||||||
\(406\) | 18.2438 | 0.905426 | ||||||||
\(407\) | 3.01674 | 0.149534 | ||||||||
\(408\) | −6.51347 | −0.322465 | ||||||||
\(409\) | −40.0872 | −1.98218 | −0.991092 | − | 0.133176i | \(-0.957483\pi\) | ||||
−0.991092 | + | 0.133176i | \(0.957483\pi\) | |||||||
\(410\) | 2.20177 | 0.108738 | ||||||||
\(411\) | −18.9165 | −0.933081 | ||||||||
\(412\) | 6.73469 | 0.331794 | ||||||||
\(413\) | 28.7553 | 1.41496 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.6609 | 0.719676 | ||||||||
\(416\) | 3.52217 | 0.172689 | ||||||||
\(417\) | 14.4370 | 0.706983 | ||||||||
\(418\) | 3.65836 | 0.178936 | ||||||||
\(419\) | −27.3306 | −1.33519 | −0.667595 | − | 0.744525i | \(-0.732676\pi\) | ||||
−0.667595 | + | 0.744525i | \(0.732676\pi\) | |||||||
\(420\) | 4.74149 | 0.231361 | ||||||||
\(421\) | 29.9565 | 1.45999 | 0.729996 | − | 0.683451i | \(-0.239522\pi\) | ||||
0.729996 | + | 0.683451i | \(0.239522\pi\) | |||||||
\(422\) | −0.497276 | −0.0242070 | ||||||||
\(423\) | 7.88978 | 0.383614 | ||||||||
\(424\) | −12.3701 | −0.600743 | ||||||||
\(425\) | −4.96756 | −0.240962 | ||||||||
\(426\) | 1.41532 | 0.0685724 | ||||||||
\(427\) | 31.7432 | 1.53616 | ||||||||
\(428\) | 15.0699 | 0.728432 | ||||||||
\(429\) | 14.5453 | 0.702252 | ||||||||
\(430\) | −8.45052 | −0.407520 | ||||||||
\(431\) | 11.1446 | 0.536814 | 0.268407 | − | 0.963306i | \(-0.413503\pi\) | ||||
0.268407 | + | 0.963306i | \(0.413503\pi\) | |||||||
\(432\) | −5.61293 | −0.270052 | ||||||||
\(433\) | −15.9555 | −0.766771 | −0.383386 | − | 0.923588i | \(-0.625242\pi\) | ||||
−0.383386 | + | 0.923588i | \(0.625242\pi\) | |||||||
\(434\) | 22.2680 | 1.06890 | ||||||||
\(435\) | 6.61514 | 0.317172 | ||||||||
\(436\) | −12.7003 | −0.608232 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −3.07728 | −0.147038 | ||||||||
\(439\) | −19.6094 | −0.935903 | −0.467952 | − | 0.883754i | \(-0.655008\pi\) | ||||
−0.467952 | + | 0.883754i | \(0.655008\pi\) | |||||||
\(440\) | 3.14951 | 0.150147 | ||||||||
\(441\) | −7.78249 | −0.370595 | ||||||||
\(442\) | −17.4966 | −0.832228 | ||||||||
\(443\) | −21.8222 | −1.03680 | −0.518401 | − | 0.855138i | \(-0.673472\pi\) | ||||
−0.518401 | + | 0.855138i | \(0.673472\pi\) | |||||||
\(444\) | 1.25593 | 0.0596037 | ||||||||
\(445\) | −1.58594 | −0.0751808 | ||||||||
\(446\) | −3.53102 | −0.167198 | ||||||||
\(447\) | −1.62399 | −0.0768121 | ||||||||
\(448\) | 3.61614 | 0.170847 | ||||||||
\(449\) | −10.8162 | −0.510449 | −0.255225 | − | 0.966882i | \(-0.582149\pi\) | ||||
−0.255225 | + | 0.966882i | \(0.582149\pi\) | |||||||
\(450\) | −1.28075 | −0.0603753 | ||||||||
\(451\) | 6.93450 | 0.326533 | ||||||||
\(452\) | −14.0869 | −0.662592 | ||||||||
\(453\) | −29.8017 | −1.40021 | ||||||||
\(454\) | 12.8244 | 0.601878 | ||||||||
\(455\) | 12.7367 | 0.597104 | ||||||||
\(456\) | 1.52305 | 0.0713232 | ||||||||
\(457\) | −21.9582 | −1.02716 | −0.513581 | − | 0.858041i | \(-0.671681\pi\) | ||||
−0.513581 | + | 0.858041i | \(0.671681\pi\) | |||||||
\(458\) | 13.3800 | 0.625208 | ||||||||
\(459\) | 27.8826 | 1.30145 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 37.0763 | 1.72682 | 0.863408 | − | 0.504507i | \(-0.168326\pi\) | ||||
0.863408 | + | 0.504507i | \(0.168326\pi\) | |||||||
\(462\) | 14.9333 | 0.694762 | ||||||||
\(463\) | −28.3719 | −1.31855 | −0.659277 | − | 0.751900i | \(-0.729137\pi\) | ||||
−0.659277 | + | 0.751900i | \(0.729137\pi\) | |||||||
\(464\) | 5.04510 | 0.234213 | ||||||||
\(465\) | 8.07430 | 0.374437 | ||||||||
\(466\) | 28.4249 | 1.31676 | ||||||||
\(467\) | −9.50192 | −0.439696 | −0.219848 | − | 0.975534i | \(-0.570556\pi\) | ||||
−0.219848 | + | 0.975534i | \(0.570556\pi\) | |||||||
\(468\) | −4.51103 | −0.208522 | ||||||||
\(469\) | −56.0945 | −2.59020 | ||||||||
\(470\) | −6.16026 | −0.284152 | ||||||||
\(471\) | −21.2126 | −0.977423 | ||||||||
\(472\) | 7.95193 | 0.366017 | ||||||||
\(473\) | −26.6150 | −1.22376 | ||||||||
\(474\) | −9.58358 | −0.440188 | ||||||||
\(475\) | 1.16157 | 0.0532964 | ||||||||
\(476\) | −17.9634 | −0.823352 | ||||||||
\(477\) | 15.8430 | 0.725401 | ||||||||
\(478\) | 14.6017 | 0.667864 | ||||||||
\(479\) | −5.70246 | −0.260552 | −0.130276 | − | 0.991478i | \(-0.541586\pi\) | ||||
−0.130276 | + | 0.991478i | \(0.541586\pi\) | |||||||
\(480\) | 1.31120 | 0.0598478 | ||||||||
\(481\) | 3.37369 | 0.153827 | ||||||||
\(482\) | −21.3303 | −0.971568 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.08061 | −0.0491187 | ||||||||
\(485\) | 0.135127 | 0.00613579 | ||||||||
\(486\) | 12.2267 | 0.554617 | ||||||||
\(487\) | 18.9032 | 0.856584 | 0.428292 | − | 0.903640i | \(-0.359115\pi\) | ||||
0.428292 | + | 0.903640i | \(0.359115\pi\) | |||||||
\(488\) | 8.77820 | 0.397371 | ||||||||
\(489\) | −15.3084 | −0.692271 | ||||||||
\(490\) | 6.07649 | 0.274508 | ||||||||
\(491\) | 7.56954 | 0.341609 | 0.170804 | − | 0.985305i | \(-0.445363\pi\) | ||||
0.170804 | + | 0.985305i | \(0.445363\pi\) | |||||||
\(492\) | 2.88697 | 0.130154 | ||||||||
\(493\) | −25.0619 | −1.12873 | ||||||||
\(494\) | 4.09124 | 0.184073 | ||||||||
\(495\) | −4.03374 | −0.181303 | ||||||||
\(496\) | 6.15794 | 0.276500 | ||||||||
\(497\) | 3.90329 | 0.175086 | ||||||||
\(498\) | 19.2234 | 0.861420 | ||||||||
\(499\) | 21.0387 | 0.941823 | 0.470911 | − | 0.882181i | \(-0.343925\pi\) | ||||
0.470911 | + | 0.882181i | \(0.343925\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 8.90358 | 0.397783 | ||||||||
\(502\) | 17.0976 | 0.763102 | ||||||||
\(503\) | −11.1353 | −0.496497 | −0.248249 | − | 0.968696i | \(-0.579855\pi\) | ||||
−0.248249 | + | 0.968696i | \(0.579855\pi\) | |||||||
\(504\) | −4.63139 | −0.206298 | ||||||||
\(505\) | 12.9048 | 0.574254 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.779286 | −0.0346093 | ||||||||
\(508\) | −3.35646 | −0.148919 | ||||||||
\(509\) | 37.7982 | 1.67537 | 0.837687 | − | 0.546150i | \(-0.183907\pi\) | ||||
0.837687 | + | 0.546150i | \(0.183907\pi\) | |||||||
\(510\) | −6.51347 | −0.288421 | ||||||||
\(511\) | −8.48680 | −0.375434 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −6.51979 | −0.287856 | ||||||||
\(514\) | −29.9543 | −1.32123 | ||||||||
\(515\) | 6.73469 | 0.296766 | ||||||||
\(516\) | −11.0803 | −0.487784 | ||||||||
\(517\) | −19.4018 | −0.853290 | ||||||||
\(518\) | 3.46371 | 0.152187 | ||||||||
\(519\) | −4.94421 | −0.217027 | ||||||||
\(520\) | 3.52217 | 0.154457 | ||||||||
\(521\) | −37.2834 | −1.63342 | −0.816708 | − | 0.577051i | \(-0.804203\pi\) | ||||
−0.816708 | + | 0.577051i | \(0.804203\pi\) | |||||||
\(522\) | −6.46154 | −0.282814 | ||||||||
\(523\) | 3.08580 | 0.134932 | 0.0674662 | − | 0.997722i | \(-0.478509\pi\) | ||||
0.0674662 | + | 0.997722i | \(0.478509\pi\) | |||||||
\(524\) | 16.9660 | 0.741163 | ||||||||
\(525\) | 4.74149 | 0.206936 | ||||||||
\(526\) | 2.46654 | 0.107546 | ||||||||
\(527\) | −30.5900 | −1.33252 | ||||||||
\(528\) | 4.12963 | 0.179719 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | −12.3701 | −0.537321 | ||||||||
\(531\) | −10.1845 | −0.441968 | ||||||||
\(532\) | 4.20039 | 0.182110 | ||||||||
\(533\) | 7.75502 | 0.335907 | ||||||||
\(534\) | −2.07948 | −0.0899881 | ||||||||
\(535\) | 15.0699 | 0.651529 | ||||||||
\(536\) | −15.5122 | −0.670027 | ||||||||
\(537\) | 15.1523 | 0.653871 | ||||||||
\(538\) | 4.08349 | 0.176052 | ||||||||
\(539\) | 19.1380 | 0.824330 | ||||||||
\(540\) | −5.61293 | −0.241542 | ||||||||
\(541\) | 25.1062 | 1.07940 | 0.539700 | − | 0.841857i | \(-0.318537\pi\) | ||||
0.539700 | + | 0.841857i | \(0.318537\pi\) | |||||||
\(542\) | 12.9062 | 0.554371 | ||||||||
\(543\) | −21.2440 | −0.911669 | ||||||||
\(544\) | −4.96756 | −0.212982 | ||||||||
\(545\) | −12.7003 | −0.544019 | ||||||||
\(546\) | 16.7003 | 0.714708 | ||||||||
\(547\) | −27.9394 | −1.19460 | −0.597301 | − | 0.802017i | \(-0.703760\pi\) | ||||
−0.597301 | + | 0.802017i | \(0.703760\pi\) | |||||||
\(548\) | −14.4268 | −0.616284 | ||||||||
\(549\) | −11.2427 | −0.479827 | ||||||||
\(550\) | 3.14951 | 0.134295 | ||||||||
\(551\) | 5.86023 | 0.249654 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −26.4304 | −1.12394 | ||||||||
\(554\) | 14.8828 | 0.632308 | ||||||||
\(555\) | 1.25593 | 0.0533112 | ||||||||
\(556\) | 11.0105 | 0.466950 | ||||||||
\(557\) | −6.99671 | −0.296460 | −0.148230 | − | 0.988953i | \(-0.547358\pi\) | ||||
−0.148230 | + | 0.988953i | \(0.547358\pi\) | |||||||
\(558\) | −7.88681 | −0.333875 | ||||||||
\(559\) | −29.7642 | −1.25889 | ||||||||
\(560\) | 3.61614 | 0.152810 | ||||||||
\(561\) | −20.5142 | −0.866111 | ||||||||
\(562\) | 18.4841 | 0.779706 | ||||||||
\(563\) | 20.4404 | 0.861460 | 0.430730 | − | 0.902481i | \(-0.358256\pi\) | ||||
0.430730 | + | 0.902481i | \(0.358256\pi\) | |||||||
\(564\) | −8.07734 | −0.340117 | ||||||||
\(565\) | −14.0869 | −0.592640 | ||||||||
\(566\) | 12.8751 | 0.541180 | ||||||||
\(567\) | −12.7195 | −0.534167 | ||||||||
\(568\) | 1.07941 | 0.0452909 | ||||||||
\(569\) | 5.96631 | 0.250121 | 0.125060 | − | 0.992149i | \(-0.460088\pi\) | ||||
0.125060 | + | 0.992149i | \(0.460088\pi\) | |||||||
\(570\) | 1.52305 | 0.0637934 | ||||||||
\(571\) | 6.74153 | 0.282124 | 0.141062 | − | 0.990001i | \(-0.454948\pi\) | ||||
0.141062 | + | 0.990001i | \(0.454948\pi\) | |||||||
\(572\) | 11.0931 | 0.463825 | ||||||||
\(573\) | 5.04855 | 0.210906 | ||||||||
\(574\) | 7.96193 | 0.332324 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.28075 | −0.0533647 | ||||||||
\(577\) | 36.2809 | 1.51039 | 0.755196 | − | 0.655499i | \(-0.227541\pi\) | ||||
0.755196 | + | 0.655499i | \(0.227541\pi\) | |||||||
\(578\) | 7.67668 | 0.319308 | ||||||||
\(579\) | 23.1786 | 0.963272 | ||||||||
\(580\) | 5.04510 | 0.209487 | ||||||||
\(581\) | 53.0159 | 2.19947 | ||||||||
\(582\) | 0.177178 | 0.00734427 | ||||||||
\(583\) | −38.9596 | −1.61354 | ||||||||
\(584\) | −2.34692 | −0.0971163 | ||||||||
\(585\) | −4.51103 | −0.186508 | ||||||||
\(586\) | −16.7824 | −0.693274 | ||||||||
\(587\) | −27.0407 | −1.11609 | −0.558045 | − | 0.829811i | \(-0.688448\pi\) | ||||
−0.558045 | + | 0.829811i | \(0.688448\pi\) | |||||||
\(588\) | 7.96750 | 0.328574 | ||||||||
\(589\) | 7.15287 | 0.294729 | ||||||||
\(590\) | 7.95193 | 0.327376 | ||||||||
\(591\) | −34.7901 | −1.43107 | ||||||||
\(592\) | 0.957846 | 0.0393672 | ||||||||
\(593\) | −22.3090 | −0.916120 | −0.458060 | − | 0.888921i | \(-0.651455\pi\) | ||||
−0.458060 | + | 0.888921i | \(0.651455\pi\) | |||||||
\(594\) | −17.6779 | −0.725335 | ||||||||
\(595\) | −17.9634 | −0.736428 | ||||||||
\(596\) | −1.23855 | −0.0507331 | ||||||||
\(597\) | −11.3387 | −0.464060 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.9530 | 0.978693 | 0.489347 | − | 0.872089i | \(-0.337235\pi\) | ||||
0.489347 | + | 0.872089i | \(0.337235\pi\) | |||||||
\(600\) | 1.31120 | 0.0535295 | ||||||||
\(601\) | 0.908172 | 0.0370451 | 0.0185226 | − | 0.999828i | \(-0.494104\pi\) | ||||
0.0185226 | + | 0.999828i | \(0.494104\pi\) | |||||||
\(602\) | −30.5583 | −1.24546 | ||||||||
\(603\) | 19.8674 | 0.809061 | ||||||||
\(604\) | −22.7286 | −0.924813 | ||||||||
\(605\) | −1.08061 | −0.0439331 | ||||||||
\(606\) | 16.9207 | 0.687357 | ||||||||
\(607\) | 31.1358 | 1.26376 | 0.631882 | − | 0.775065i | \(-0.282283\pi\) | ||||
0.631882 | + | 0.775065i | \(0.282283\pi\) | |||||||
\(608\) | 1.16157 | 0.0471078 | ||||||||
\(609\) | 23.9213 | 0.969340 | ||||||||
\(610\) | 8.77820 | 0.355419 | ||||||||
\(611\) | −21.6975 | −0.877786 | ||||||||
\(612\) | 6.36222 | 0.257178 | ||||||||
\(613\) | 16.0906 | 0.649895 | 0.324948 | − | 0.945732i | \(-0.394653\pi\) | ||||
0.324948 | + | 0.945732i | \(0.394653\pi\) | |||||||
\(614\) | 0.364016 | 0.0146905 | ||||||||
\(615\) | 2.88697 | 0.116414 | ||||||||
\(616\) | 11.3891 | 0.458879 | ||||||||
\(617\) | −22.3451 | −0.899580 | −0.449790 | − | 0.893134i | \(-0.648501\pi\) | ||||
−0.449790 | + | 0.893134i | \(0.648501\pi\) | |||||||
\(618\) | 8.83052 | 0.355216 | ||||||||
\(619\) | 13.2003 | 0.530564 | 0.265282 | − | 0.964171i | \(-0.414535\pi\) | ||||
0.265282 | + | 0.964171i | \(0.414535\pi\) | |||||||
\(620\) | 6.15794 | 0.247309 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7.29349 | −0.292442 | ||||||||
\(623\) | −5.73499 | −0.229767 | ||||||||
\(624\) | 4.61827 | 0.184879 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 25.9726 | 1.03808 | ||||||||
\(627\) | 4.79685 | 0.191568 | ||||||||
\(628\) | −16.1780 | −0.645571 | ||||||||
\(629\) | −4.75816 | −0.189720 | ||||||||
\(630\) | −4.63139 | −0.184519 | ||||||||
\(631\) | 27.8956 | 1.11051 | 0.555253 | − | 0.831682i | \(-0.312622\pi\) | ||||
0.555253 | + | 0.831682i | \(0.312622\pi\) | |||||||
\(632\) | −7.30901 | −0.290737 | ||||||||
\(633\) | −0.652029 | −0.0259158 | ||||||||
\(634\) | −10.0369 | −0.398614 | ||||||||
\(635\) | −3.35646 | −0.133197 | ||||||||
\(636\) | −16.2196 | −0.643150 | ||||||||
\(637\) | 21.4024 | 0.847995 | ||||||||
\(638\) | 15.8896 | 0.629075 | ||||||||
\(639\) | −1.38245 | −0.0546890 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 15.9297 | 0.629185 | 0.314593 | − | 0.949227i | \(-0.398132\pi\) | ||||
0.314593 | + | 0.949227i | \(0.398132\pi\) | |||||||
\(642\) | 19.7597 | 0.779852 | ||||||||
\(643\) | 21.7301 | 0.856952 | 0.428476 | − | 0.903553i | \(-0.359051\pi\) | ||||
0.428476 | + | 0.903553i | \(0.359051\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.0803 | −0.436287 | ||||||||
\(646\) | −5.77016 | −0.227024 | ||||||||
\(647\) | −19.8277 | −0.779507 | −0.389753 | − | 0.920919i | \(-0.627440\pi\) | ||||
−0.389753 | + | 0.920919i | \(0.627440\pi\) | |||||||
\(648\) | −3.51741 | −0.138177 | ||||||||
\(649\) | 25.0446 | 0.983088 | ||||||||
\(650\) | 3.52217 | 0.138151 | ||||||||
\(651\) | 29.1978 | 1.14435 | ||||||||
\(652\) | −11.6751 | −0.457233 | ||||||||
\(653\) | 6.98897 | 0.273500 | 0.136750 | − | 0.990606i | \(-0.456334\pi\) | ||||
0.136750 | + | 0.990606i | \(0.456334\pi\) | |||||||
\(654\) | −16.6526 | −0.651168 | ||||||||
\(655\) | 16.9660 | 0.662916 | ||||||||
\(656\) | 2.20177 | 0.0859648 | ||||||||
\(657\) | 3.00583 | 0.117268 | ||||||||
\(658\) | −22.2764 | −0.868424 | ||||||||
\(659\) | −16.7329 | −0.651820 | −0.325910 | − | 0.945401i | \(-0.605671\pi\) | ||||
−0.325910 | + | 0.945401i | \(0.605671\pi\) | |||||||
\(660\) | 4.12963 | 0.160746 | ||||||||
\(661\) | −1.88913 | −0.0734786 | −0.0367393 | − | 0.999325i | \(-0.511697\pi\) | ||||
−0.0367393 | + | 0.999325i | \(0.511697\pi\) | |||||||
\(662\) | −28.1837 | −1.09539 | ||||||||
\(663\) | −22.9415 | −0.890975 | ||||||||
\(664\) | 14.6609 | 0.568953 | ||||||||
\(665\) | 4.20039 | 0.162884 | ||||||||
\(666\) | −1.22676 | −0.0475362 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 6.79041 | 0.262729 | ||||||||
\(669\) | −4.62987 | −0.179001 | ||||||||
\(670\) | −15.5122 | −0.599290 | ||||||||
\(671\) | 27.6470 | 1.06730 | ||||||||
\(672\) | 4.74149 | 0.182907 | ||||||||
\(673\) | 34.6587 | 1.33600 | 0.667998 | − | 0.744163i | \(-0.267152\pi\) | ||||
0.667998 | + | 0.744163i | \(0.267152\pi\) | |||||||
\(674\) | 22.5355 | 0.868034 | ||||||||
\(675\) | −5.61293 | −0.216042 | ||||||||
\(676\) | −0.594330 | −0.0228589 | ||||||||
\(677\) | −24.6522 | −0.947460 | −0.473730 | − | 0.880670i | \(-0.657093\pi\) | ||||
−0.473730 | + | 0.880670i | \(0.657093\pi\) | |||||||
\(678\) | −18.4708 | −0.709365 | ||||||||
\(679\) | 0.488638 | 0.0187522 | ||||||||
\(680\) | −4.96756 | −0.190497 | ||||||||
\(681\) | 16.8153 | 0.644364 | ||||||||
\(682\) | 19.3945 | 0.742653 | ||||||||
\(683\) | 17.8802 | 0.684169 | 0.342084 | − | 0.939669i | \(-0.388867\pi\) | ||||
0.342084 | + | 0.939669i | \(0.388867\pi\) | |||||||
\(684\) | −1.48768 | −0.0568829 | ||||||||
\(685\) | −14.4268 | −0.551221 | ||||||||
\(686\) | −3.33953 | −0.127504 | ||||||||
\(687\) | 17.5439 | 0.669342 | ||||||||
\(688\) | −8.45052 | −0.322173 | ||||||||
\(689\) | −43.5694 | −1.65986 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.8803 | −0.680197 | −0.340099 | − | 0.940390i | \(-0.610460\pi\) | ||||
−0.340099 | + | 0.940390i | \(0.610460\pi\) | |||||||
\(692\) | −3.77075 | −0.143342 | ||||||||
\(693\) | −14.5866 | −0.554099 | ||||||||
\(694\) | 15.9837 | 0.606733 | ||||||||
\(695\) | 11.0105 | 0.417653 | ||||||||
\(696\) | 6.61514 | 0.250746 | ||||||||
\(697\) | −10.9374 | −0.414285 | ||||||||
\(698\) | −20.6925 | −0.783223 | ||||||||
\(699\) | 37.2708 | 1.40971 | ||||||||
\(700\) | 3.61614 | 0.136677 | ||||||||
\(701\) | 41.4364 | 1.56503 | 0.782516 | − | 0.622631i | \(-0.213936\pi\) | ||||
0.782516 | + | 0.622631i | \(0.213936\pi\) | |||||||
\(702\) | −19.7697 | −0.746158 | ||||||||
\(703\) | 1.11260 | 0.0419626 | ||||||||
\(704\) | 3.14951 | 0.118701 | ||||||||
\(705\) | −8.07734 | −0.304210 | ||||||||
\(706\) | 10.7261 | 0.403683 | ||||||||
\(707\) | 46.6655 | 1.75504 | ||||||||
\(708\) | 10.4266 | 0.391854 | ||||||||
\(709\) | −38.3664 | −1.44088 | −0.720440 | − | 0.693517i | \(-0.756060\pi\) | ||||
−0.720440 | + | 0.693517i | \(0.756060\pi\) | |||||||
\(710\) | 1.07941 | 0.0405094 | ||||||||
\(711\) | 9.36104 | 0.351066 | ||||||||
\(712\) | −1.58594 | −0.0594356 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −23.5536 | −0.881473 | ||||||||
\(715\) | 11.0931 | 0.414858 | ||||||||
\(716\) | 11.5561 | 0.431871 | ||||||||
\(717\) | 19.1457 | 0.715009 | ||||||||
\(718\) | 15.2290 | 0.568341 | ||||||||
\(719\) | −2.34937 | −0.0876167 | −0.0438084 | − | 0.999040i | \(-0.513949\pi\) | ||||
−0.0438084 | + | 0.999040i | \(0.513949\pi\) | |||||||
\(720\) | −1.28075 | −0.0477309 | ||||||||
\(721\) | 24.3536 | 0.906975 | ||||||||
\(722\) | −17.6508 | −0.656893 | ||||||||
\(723\) | −27.9683 | −1.04015 | ||||||||
\(724\) | −16.2020 | −0.602142 | ||||||||
\(725\) | 5.04510 | 0.187370 | ||||||||
\(726\) | −1.41690 | −0.0525860 | ||||||||
\(727\) | −49.7210 | −1.84405 | −0.922024 | − | 0.387132i | \(-0.873466\pi\) | ||||
−0.922024 | + | 0.387132i | \(0.873466\pi\) | |||||||
\(728\) | 12.7367 | 0.472052 | ||||||||
\(729\) | 26.5839 | 0.984591 | ||||||||
\(730\) | −2.34692 | −0.0868634 | ||||||||
\(731\) | 41.9785 | 1.55263 | ||||||||
\(732\) | 11.5100 | 0.425421 | ||||||||
\(733\) | 41.8260 | 1.54488 | 0.772439 | − | 0.635089i | \(-0.219036\pi\) | ||||
0.772439 | + | 0.635089i | \(0.219036\pi\) | |||||||
\(734\) | −15.5272 | −0.573121 | ||||||||
\(735\) | 7.96750 | 0.293886 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −48.8559 | −1.79963 | ||||||||
\(738\) | −2.81993 | −0.103803 | ||||||||
\(739\) | −5.30005 | −0.194966 | −0.0974828 | − | 0.995237i | \(-0.531079\pi\) | ||||
−0.0974828 | + | 0.995237i | \(0.531079\pi\) | |||||||
\(740\) | 0.957846 | 0.0352111 | ||||||||
\(741\) | 5.36443 | 0.197067 | ||||||||
\(742\) | −44.7319 | −1.64216 | ||||||||
\(743\) | −49.2260 | −1.80593 | −0.902963 | − | 0.429718i | \(-0.858613\pi\) | ||||
−0.902963 | + | 0.429718i | \(0.858613\pi\) | |||||||
\(744\) | 8.07430 | 0.296018 | ||||||||
\(745\) | −1.23855 | −0.0453770 | ||||||||
\(746\) | −20.7074 | −0.758151 | ||||||||
\(747\) | −18.7770 | −0.687015 | ||||||||
\(748\) | −15.6454 | −0.572051 | ||||||||
\(749\) | 54.4950 | 1.99120 | ||||||||
\(750\) | 1.31120 | 0.0478783 | ||||||||
\(751\) | −40.0566 | −1.46169 | −0.730844 | − | 0.682545i | \(-0.760873\pi\) | ||||
−0.730844 | + | 0.682545i | \(0.760873\pi\) | |||||||
\(752\) | −6.16026 | −0.224642 | ||||||||
\(753\) | 22.4183 | 0.816969 | ||||||||
\(754\) | 17.7697 | 0.647135 | ||||||||
\(755\) | −22.7286 | −0.827178 | ||||||||
\(756\) | −20.2971 | −0.738200 | ||||||||
\(757\) | −41.0244 | −1.49106 | −0.745529 | − | 0.666473i | \(-0.767803\pi\) | ||||
−0.745529 | + | 0.666473i | \(0.767803\pi\) | |||||||
\(758\) | −5.07433 | −0.184308 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.16157 | 0.0421345 | ||||||||
\(761\) | −46.3560 | −1.68040 | −0.840202 | − | 0.542273i | \(-0.817564\pi\) | ||||
−0.840202 | + | 0.542273i | \(0.817564\pi\) | |||||||
\(762\) | −4.40100 | −0.159431 | ||||||||
\(763\) | −45.9260 | −1.66263 | ||||||||
\(764\) | 3.85033 | 0.139300 | ||||||||
\(765\) | 6.36222 | 0.230027 | ||||||||
\(766\) | 1.77390 | 0.0640937 | ||||||||
\(767\) | 28.0080 | 1.01131 | ||||||||
\(768\) | 1.31120 | 0.0473139 | ||||||||
\(769\) | 19.0095 | 0.685500 | 0.342750 | − | 0.939427i | \(-0.388642\pi\) | ||||
0.342750 | + | 0.939427i | \(0.388642\pi\) | |||||||
\(770\) | 11.3891 | 0.410433 | ||||||||
\(771\) | −39.2761 | −1.41449 | ||||||||
\(772\) | 17.6774 | 0.636225 | ||||||||
\(773\) | 23.9067 | 0.859864 | 0.429932 | − | 0.902861i | \(-0.358538\pi\) | ||||
0.429932 | + | 0.902861i | \(0.358538\pi\) | |||||||
\(774\) | 10.8230 | 0.389026 | ||||||||
\(775\) | 6.15794 | 0.221200 | ||||||||
\(776\) | 0.135127 | 0.00485077 | ||||||||
\(777\) | 4.54162 | 0.162930 | ||||||||
\(778\) | 5.06064 | 0.181433 | ||||||||
\(779\) | 2.55751 | 0.0916322 | ||||||||
\(780\) | 4.61827 | 0.165361 | ||||||||
\(781\) | 3.39960 | 0.121647 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −28.3178 | −1.01200 | ||||||||
\(784\) | 6.07649 | 0.217018 | ||||||||
\(785\) | −16.1780 | −0.577417 | ||||||||
\(786\) | 22.2458 | 0.793482 | ||||||||
\(787\) | −27.9989 | −0.998054 | −0.499027 | − | 0.866586i | \(-0.666309\pi\) | ||||
−0.499027 | + | 0.866586i | \(0.666309\pi\) | |||||||
\(788\) | −26.5330 | −0.945200 | ||||||||
\(789\) | 3.23413 | 0.115138 | ||||||||
\(790\) | −7.30901 | −0.260043 | ||||||||
\(791\) | −50.9403 | −1.81123 | ||||||||
\(792\) | −4.03374 | −0.143333 | ||||||||
\(793\) | 30.9183 | 1.09794 | ||||||||
\(794\) | −2.38213 | −0.0845387 | ||||||||
\(795\) | −16.2196 | −0.575251 | ||||||||
\(796\) | −8.64754 | −0.306504 | ||||||||
\(797\) | 2.48986 | 0.0881954 | 0.0440977 | − | 0.999027i | \(-0.485959\pi\) | ||||
0.0440977 | + | 0.999027i | \(0.485959\pi\) | |||||||
\(798\) | 5.50756 | 0.194965 | ||||||||
\(799\) | 30.6015 | 1.08260 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 2.03120 | 0.0717689 | ||||||||
\(802\) | 16.3779 | 0.578325 | ||||||||
\(803\) | −7.39164 | −0.260845 | ||||||||
\(804\) | −20.3397 | −0.717324 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 21.6893 | 0.763973 | ||||||||
\(807\) | 5.35427 | 0.188479 | ||||||||
\(808\) | 12.9048 | 0.453988 | ||||||||
\(809\) | −32.5826 | −1.14554 | −0.572771 | − | 0.819715i | \(-0.694132\pi\) | ||||
−0.572771 | + | 0.819715i | \(0.694132\pi\) | |||||||
\(810\) | −3.51741 | −0.123589 | ||||||||
\(811\) | 19.2096 | 0.674540 | 0.337270 | − | 0.941408i | \(-0.390496\pi\) | ||||
0.337270 | + | 0.941408i | \(0.390496\pi\) | |||||||
\(812\) | 18.2438 | 0.640233 | ||||||||
\(813\) | 16.9227 | 0.593504 | ||||||||
\(814\) | 3.01674 | 0.105737 | ||||||||
\(815\) | −11.6751 | −0.408962 | ||||||||
\(816\) | −6.51347 | −0.228017 | ||||||||
\(817\) | −9.81585 | −0.343413 | ||||||||
\(818\) | −40.0872 | −1.40162 | ||||||||
\(819\) | −16.3125 | −0.570006 | ||||||||
\(820\) | 2.20177 | 0.0768893 | ||||||||
\(821\) | −34.4281 | −1.20155 | −0.600774 | − | 0.799419i | \(-0.705141\pi\) | ||||
−0.600774 | + | 0.799419i | \(0.705141\pi\) | |||||||
\(822\) | −18.9165 | −0.659788 | ||||||||
\(823\) | −56.5034 | −1.96959 | −0.984793 | − | 0.173732i | \(-0.944417\pi\) | ||||
−0.984793 | + | 0.173732i | \(0.944417\pi\) | |||||||
\(824\) | 6.73469 | 0.234614 | ||||||||
\(825\) | 4.12963 | 0.143775 | ||||||||
\(826\) | 28.7553 | 1.00053 | ||||||||
\(827\) | −33.4116 | −1.16184 | −0.580918 | − | 0.813962i | \(-0.697306\pi\) | ||||
−0.580918 | + | 0.813962i | \(0.697306\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.4187 | −1.57746 | −0.788728 | − | 0.614742i | \(-0.789260\pi\) | ||||
−0.788728 | + | 0.614742i | \(0.789260\pi\) | |||||||
\(830\) | 14.6609 | 0.508887 | ||||||||
\(831\) | 19.5143 | 0.676943 | ||||||||
\(832\) | 3.52217 | 0.122109 | ||||||||
\(833\) | −30.1854 | −1.04586 | ||||||||
\(834\) | 14.4370 | 0.499913 | ||||||||
\(835\) | 6.79041 | 0.234992 | ||||||||
\(836\) | 3.65836 | 0.126527 | ||||||||
\(837\) | −34.5641 | −1.19471 | ||||||||
\(838\) | −27.3306 | −0.944122 | ||||||||
\(839\) | −21.0551 | −0.726901 | −0.363451 | − | 0.931613i | \(-0.618401\pi\) | ||||
−0.363451 | + | 0.931613i | \(0.618401\pi\) | |||||||
\(840\) | 4.74149 | 0.163597 | ||||||||
\(841\) | −3.54692 | −0.122308 | ||||||||
\(842\) | 29.9565 | 1.03237 | ||||||||
\(843\) | 24.2364 | 0.834746 | ||||||||
\(844\) | −0.497276 | −0.0171170 | ||||||||
\(845\) | −0.594330 | −0.0204456 | ||||||||
\(846\) | 7.88978 | 0.271256 | ||||||||
\(847\) | −3.90765 | −0.134268 | ||||||||
\(848\) | −12.3701 | −0.424790 | ||||||||
\(849\) | 16.8818 | 0.579382 | ||||||||
\(850\) | −4.96756 | −0.170386 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 1.41532 | 0.0484880 | ||||||||
\(853\) | 7.65046 | 0.261947 | 0.130973 | − | 0.991386i | \(-0.458190\pi\) | ||||
0.130973 | + | 0.991386i | \(0.458190\pi\) | |||||||
\(854\) | 31.7432 | 1.08623 | ||||||||
\(855\) | −1.48768 | −0.0508776 | ||||||||
\(856\) | 15.0699 | 0.515079 | ||||||||
\(857\) | −12.5359 | −0.428219 | −0.214110 | − | 0.976810i | \(-0.568685\pi\) | ||||
−0.214110 | + | 0.976810i | \(0.568685\pi\) | |||||||
\(858\) | 14.5453 | 0.496567 | ||||||||
\(859\) | 42.6589 | 1.45550 | 0.727751 | − | 0.685842i | \(-0.240566\pi\) | ||||
0.727751 | + | 0.685842i | \(0.240566\pi\) | |||||||
\(860\) | −8.45052 | −0.288160 | ||||||||
\(861\) | 10.4397 | 0.355783 | ||||||||
\(862\) | 11.1446 | 0.379585 | ||||||||
\(863\) | 44.3134 | 1.50844 | 0.754222 | − | 0.656619i | \(-0.228014\pi\) | ||||
0.754222 | + | 0.656619i | \(0.228014\pi\) | |||||||
\(864\) | −5.61293 | −0.190956 | ||||||||
\(865\) | −3.77075 | −0.128209 | ||||||||
\(866\) | −15.9555 | −0.542189 | ||||||||
\(867\) | 10.0657 | 0.341848 | ||||||||
\(868\) | 22.2680 | 0.755825 | ||||||||
\(869\) | −23.0198 | −0.780892 | ||||||||
\(870\) | 6.61514 | 0.224274 | ||||||||
\(871\) | −54.6367 | −1.85129 | ||||||||
\(872\) | −12.7003 | −0.430085 | ||||||||
\(873\) | −0.173064 | −0.00585733 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.61614 | 0.122248 | ||||||||
\(876\) | −3.07728 | −0.103972 | ||||||||
\(877\) | 47.3057 | 1.59740 | 0.798701 | − | 0.601729i | \(-0.205521\pi\) | ||||
0.798701 | + | 0.601729i | \(0.205521\pi\) | |||||||
\(878\) | −19.6094 | −0.661784 | ||||||||
\(879\) | −22.0051 | −0.742212 | ||||||||
\(880\) | 3.14951 | 0.106170 | ||||||||
\(881\) | −48.0057 | −1.61735 | −0.808676 | − | 0.588254i | \(-0.799815\pi\) | ||||
−0.808676 | + | 0.588254i | \(0.799815\pi\) | |||||||
\(882\) | −7.78249 | −0.262050 | ||||||||
\(883\) | −40.9247 | −1.37723 | −0.688613 | − | 0.725129i | \(-0.741780\pi\) | ||||
−0.688613 | + | 0.725129i | \(0.741780\pi\) | |||||||
\(884\) | −17.4966 | −0.588474 | ||||||||
\(885\) | 10.4266 | 0.350485 | ||||||||
\(886\) | −21.8222 | −0.733130 | ||||||||
\(887\) | −44.1551 | −1.48258 | −0.741292 | − | 0.671183i | \(-0.765787\pi\) | ||||
−0.741292 | + | 0.671183i | \(0.765787\pi\) | |||||||
\(888\) | 1.25593 | 0.0421462 | ||||||||
\(889\) | −12.1375 | −0.407077 | ||||||||
\(890\) | −1.58594 | −0.0531608 | ||||||||
\(891\) | −11.0781 | −0.371130 | ||||||||
\(892\) | −3.53102 | −0.118227 | ||||||||
\(893\) | −7.15556 | −0.239452 | ||||||||
\(894\) | −1.62399 | −0.0543143 | ||||||||
\(895\) | 11.5561 | 0.386277 | ||||||||
\(896\) | 3.61614 | 0.120807 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −10.8162 | −0.360942 | ||||||||
\(899\) | 31.0675 | 1.03616 | ||||||||
\(900\) | −1.28075 | −0.0426918 | ||||||||
\(901\) | 61.4490 | 2.04716 | ||||||||
\(902\) | 6.93450 | 0.230894 | ||||||||
\(903\) | −40.0681 | −1.33338 | ||||||||
\(904\) | −14.0869 | −0.468523 | ||||||||
\(905\) | −16.2020 | −0.538572 | ||||||||
\(906\) | −29.8017 | −0.990096 | ||||||||
\(907\) | 0.832231 | 0.0276338 | 0.0138169 | − | 0.999905i | \(-0.495602\pi\) | ||||
0.0138169 | + | 0.999905i | \(0.495602\pi\) | |||||||
\(908\) | 12.8244 | 0.425592 | ||||||||
\(909\) | −16.5278 | −0.548193 | ||||||||
\(910\) | 12.7367 | 0.422216 | ||||||||
\(911\) | −26.3756 | −0.873862 | −0.436931 | − | 0.899495i | \(-0.643935\pi\) | ||||
−0.436931 | + | 0.899495i | \(0.643935\pi\) | |||||||
\(912\) | 1.52305 | 0.0504331 | ||||||||
\(913\) | 46.1746 | 1.52816 | ||||||||
\(914\) | −21.9582 | −0.726313 | ||||||||
\(915\) | 11.5100 | 0.380508 | ||||||||
\(916\) | 13.3800 | 0.442089 | ||||||||
\(917\) | 61.3515 | 2.02600 | ||||||||
\(918\) | 27.8826 | 0.920262 | ||||||||
\(919\) | −14.7025 | −0.484990 | −0.242495 | − | 0.970153i | \(-0.577966\pi\) | ||||
−0.242495 | + | 0.970153i | \(0.577966\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.477298 | 0.0157275 | ||||||||
\(922\) | 37.0763 | 1.22104 | ||||||||
\(923\) | 3.80185 | 0.125140 | ||||||||
\(924\) | 14.9333 | 0.491271 | ||||||||
\(925\) | 0.957846 | 0.0314938 | ||||||||
\(926\) | −28.3719 | −0.932358 | ||||||||
\(927\) | −8.62547 | −0.283298 | ||||||||
\(928\) | 5.04510 | 0.165614 | ||||||||
\(929\) | −9.14220 | −0.299946 | −0.149973 | − | 0.988690i | \(-0.547919\pi\) | ||||
−0.149973 | + | 0.988690i | \(0.547919\pi\) | |||||||
\(930\) | 8.07430 | 0.264767 | ||||||||
\(931\) | 7.05826 | 0.231325 | ||||||||
\(932\) | 28.4249 | 0.931090 | ||||||||
\(933\) | −9.56323 | −0.313086 | ||||||||
\(934\) | −9.50192 | −0.310912 | ||||||||
\(935\) | −15.6454 | −0.511658 | ||||||||
\(936\) | −4.51103 | −0.147448 | ||||||||
\(937\) | −16.8071 | −0.549065 | −0.274532 | − | 0.961578i | \(-0.588523\pi\) | ||||
−0.274532 | + | 0.961578i | \(0.588523\pi\) | |||||||
\(938\) | −56.0945 | −1.83155 | ||||||||
\(939\) | 34.0553 | 1.11135 | ||||||||
\(940\) | −6.16026 | −0.200926 | ||||||||
\(941\) | −19.2847 | −0.628664 | −0.314332 | − | 0.949313i | \(-0.601780\pi\) | ||||
−0.314332 | + | 0.949313i | \(0.601780\pi\) | |||||||
\(942\) | −21.2126 | −0.691143 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 7.95193 | 0.258813 | ||||||||
\(945\) | −20.2971 | −0.660266 | ||||||||
\(946\) | −26.6150 | −0.865327 | ||||||||
\(947\) | 45.1096 | 1.46586 | 0.732932 | − | 0.680302i | \(-0.238151\pi\) | ||||
0.732932 | + | 0.680302i | \(0.238151\pi\) | |||||||
\(948\) | −9.58358 | −0.311260 | ||||||||
\(949\) | −8.26625 | −0.268334 | ||||||||
\(950\) | 1.16157 | 0.0376862 | ||||||||
\(951\) | −13.1603 | −0.426753 | ||||||||
\(952\) | −17.9634 | −0.582198 | ||||||||
\(953\) | 26.5479 | 0.859970 | 0.429985 | − | 0.902836i | \(-0.358519\pi\) | ||||
0.429985 | + | 0.902836i | \(0.358519\pi\) | |||||||
\(954\) | 15.8430 | 0.512936 | ||||||||
\(955\) | 3.85033 | 0.124594 | ||||||||
\(956\) | 14.6017 | 0.472251 | ||||||||
\(957\) | 20.8344 | 0.673482 | ||||||||
\(958\) | −5.70246 | −0.184238 | ||||||||
\(959\) | −52.1695 | −1.68464 | ||||||||
\(960\) | 1.31120 | 0.0423188 | ||||||||
\(961\) | 6.92026 | 0.223234 | ||||||||
\(962\) | 3.37369 | 0.108772 | ||||||||
\(963\) | −19.3008 | −0.621961 | ||||||||
\(964\) | −21.3303 | −0.687002 | ||||||||
\(965\) | 17.6774 | 0.569056 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.555100 | 0.0178508 | 0.00892541 | − | 0.999960i | \(-0.497159\pi\) | ||||
0.00892541 | + | 0.999960i | \(0.497159\pi\) | |||||||
\(968\) | −1.08061 | −0.0347322 | ||||||||
\(969\) | −7.56583 | −0.243050 | ||||||||
\(970\) | 0.135127 | 0.00433866 | ||||||||
\(971\) | 36.1945 | 1.16154 | 0.580768 | − | 0.814069i | \(-0.302752\pi\) | ||||
0.580768 | + | 0.814069i | \(0.302752\pi\) | |||||||
\(972\) | 12.2267 | 0.392173 | ||||||||
\(973\) | 39.8157 | 1.27643 | ||||||||
\(974\) | 18.9032 | 0.605697 | ||||||||
\(975\) | 4.61827 | 0.147903 | ||||||||
\(976\) | 8.77820 | 0.280983 | ||||||||
\(977\) | 19.5359 | 0.625010 | 0.312505 | − | 0.949916i | \(-0.398832\pi\) | ||||
0.312505 | + | 0.949916i | \(0.398832\pi\) | |||||||
\(978\) | −15.3084 | −0.489509 | ||||||||
\(979\) | −4.99493 | −0.159639 | ||||||||
\(980\) | 6.07649 | 0.194106 | ||||||||
\(981\) | 16.2659 | 0.519330 | ||||||||
\(982\) | 7.56954 | 0.241554 | ||||||||
\(983\) | −12.1376 | −0.387129 | −0.193565 | − | 0.981088i | \(-0.562005\pi\) | ||||
−0.193565 | + | 0.981088i | \(0.562005\pi\) | |||||||
\(984\) | 2.88697 | 0.0920331 | ||||||||
\(985\) | −26.5330 | −0.845413 | ||||||||
\(986\) | −25.0619 | −0.798133 | ||||||||
\(987\) | −29.2088 | −0.929727 | ||||||||
\(988\) | 4.09124 | 0.130160 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −4.03374 | −0.128201 | ||||||||
\(991\) | 16.6514 | 0.528950 | 0.264475 | − | 0.964393i | \(-0.414801\pi\) | ||||
0.264475 | + | 0.964393i | \(0.414801\pi\) | |||||||
\(992\) | 6.15794 | 0.195515 | ||||||||
\(993\) | −36.9545 | −1.17272 | ||||||||
\(994\) | 3.90329 | 0.123805 | ||||||||
\(995\) | −8.64754 | −0.274146 | ||||||||
\(996\) | 19.2234 | 0.609116 | ||||||||
\(997\) | 20.4518 | 0.647714 | 0.323857 | − | 0.946106i | \(-0.395020\pi\) | ||||
0.323857 | + | 0.946106i | \(0.395020\pi\) | |||||||
\(998\) | 21.0387 | 0.665969 | ||||||||
\(999\) | −5.37632 | −0.170099 |
(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 | 5290.2.a.bl.1.10 | 15 | ||
23.15 | odd | 22 | 230.2.g.d.41.2 | ✓ | 30 | ||
23.20 | odd | 22 | 230.2.g.d.101.2 | yes | 30 | ||
23.22 | odd | 2 | 5290.2.a.bk.1.10 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.2.g.d.41.2 | ✓ | 30 | 23.15 | odd | 22 | ||
230.2.g.d.101.2 | yes | 30 | 23.20 | odd | 22 | ||
5290.2.a.bk.1.10 | 15 | 23.22 | odd | 2 | |||
5290.2.a.bl.1.10 | 15 | 1.1 | even | 1 | trivial |