Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1450,2,Mod(1,1450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1450, 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("1450.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1450 = 2 \cdot 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1450.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: | \(11.5783082931\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 290) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1450.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.381966 | 0.220528 | 0.110264 | − | 0.993902i | \(-0.464830\pi\) | ||||
0.110264 | + | 0.993902i | \(0.464830\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.381966 | −0.155937 | ||||||||
\(7\) | 2.61803 | 0.989524 | 0.494762 | − | 0.869029i | \(-0.335255\pi\) | ||||
0.494762 | + | 0.869029i | \(0.335255\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.85410 | −0.951367 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 0.381966 | 0.110264 | ||||||||
\(13\) | 0.381966 | 0.105938 | 0.0529692 | − | 0.998596i | \(-0.483131\pi\) | ||||
0.0529692 | + | 0.998596i | \(0.483131\pi\) | |||||||
\(14\) | −2.61803 | −0.699699 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.38197 | 0.820247 | 0.410124 | − | 0.912030i | \(-0.365486\pi\) | ||||
0.410124 | + | 0.912030i | \(0.365486\pi\) | |||||||
\(18\) | 2.85410 | 0.672718 | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −2.00000 | −0.426401 | ||||||||
\(23\) | 4.85410 | 1.01215 | 0.506075 | − | 0.862489i | \(-0.331096\pi\) | ||||
0.506075 | + | 0.862489i | \(0.331096\pi\) | |||||||
\(24\) | −0.381966 | −0.0779685 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.381966 | −0.0749097 | ||||||||
\(27\) | −2.23607 | −0.430331 | ||||||||
\(28\) | 2.61803 | 0.494762 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.85410 | −0.692217 | −0.346109 | − | 0.938194i | \(-0.612497\pi\) | ||||
−0.346109 | + | 0.938194i | \(0.612497\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.763932 | 0.132983 | ||||||||
\(34\) | −3.38197 | −0.580002 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.85410 | −0.475684 | ||||||||
\(37\) | 8.94427 | 1.47043 | 0.735215 | − | 0.677834i | \(-0.237081\pi\) | ||||
0.735215 | + | 0.677834i | \(0.237081\pi\) | |||||||
\(38\) | 2.00000 | 0.324443 | ||||||||
\(39\) | 0.145898 | 0.0233624 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.70820 | 1.20382 | 0.601910 | − | 0.798564i | \(-0.294407\pi\) | ||||
0.601910 | + | 0.798564i | \(0.294407\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | 3.38197 | 0.515745 | 0.257872 | − | 0.966179i | \(-0.416979\pi\) | ||||
0.257872 | + | 0.966179i | \(0.416979\pi\) | |||||||
\(44\) | 2.00000 | 0.301511 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.85410 | −0.715698 | ||||||||
\(47\) | 1.52786 | 0.222862 | 0.111431 | − | 0.993772i | \(-0.464457\pi\) | ||||
0.111431 | + | 0.993772i | \(0.464457\pi\) | |||||||
\(48\) | 0.381966 | 0.0551320 | ||||||||
\(49\) | −0.145898 | −0.0208426 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.29180 | 0.180888 | ||||||||
\(52\) | 0.381966 | 0.0529692 | ||||||||
\(53\) | 9.38197 | 1.28871 | 0.644356 | − | 0.764726i | \(-0.277125\pi\) | ||||
0.644356 | + | 0.764726i | \(0.277125\pi\) | |||||||
\(54\) | 2.23607 | 0.304290 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.61803 | −0.349850 | ||||||||
\(57\) | −0.763932 | −0.101185 | ||||||||
\(58\) | 1.00000 | 0.131306 | ||||||||
\(59\) | 2.85410 | 0.371572 | 0.185786 | − | 0.982590i | \(-0.440517\pi\) | ||||
0.185786 | + | 0.982590i | \(0.440517\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.8541 | −1.38973 | −0.694863 | − | 0.719142i | \(-0.744535\pi\) | ||||
−0.694863 | + | 0.719142i | \(0.744535\pi\) | |||||||
\(62\) | 3.85410 | 0.489471 | ||||||||
\(63\) | −7.47214 | −0.941401 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.763932 | −0.0940335 | ||||||||
\(67\) | −8.94427 | −1.09272 | −0.546358 | − | 0.837552i | \(-0.683986\pi\) | ||||
−0.546358 | + | 0.837552i | \(0.683986\pi\) | |||||||
\(68\) | 3.38197 | 0.410124 | ||||||||
\(69\) | 1.85410 | 0.223208 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.70820 | −0.677439 | −0.338720 | − | 0.940887i | \(-0.609994\pi\) | ||||
−0.338720 | + | 0.940887i | \(0.609994\pi\) | |||||||
\(72\) | 2.85410 | 0.336359 | ||||||||
\(73\) | −5.56231 | −0.651019 | −0.325509 | − | 0.945539i | \(-0.605536\pi\) | ||||
−0.325509 | + | 0.945539i | \(0.605536\pi\) | |||||||
\(74\) | −8.94427 | −1.03975 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.00000 | −0.229416 | ||||||||
\(77\) | 5.23607 | 0.596705 | ||||||||
\(78\) | −0.145898 | −0.0165197 | ||||||||
\(79\) | 6.56231 | 0.738317 | 0.369159 | − | 0.929366i | \(-0.379646\pi\) | ||||
0.369159 | + | 0.929366i | \(0.379646\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.70820 | 0.856467 | ||||||||
\(82\) | −7.70820 | −0.851229 | ||||||||
\(83\) | 14.9443 | 1.64035 | 0.820173 | − | 0.572115i | \(-0.193877\pi\) | ||||
0.820173 | + | 0.572115i | \(0.193877\pi\) | |||||||
\(84\) | 1.00000 | 0.109109 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.38197 | −0.364687 | ||||||||
\(87\) | −0.381966 | −0.0409511 | ||||||||
\(88\) | −2.00000 | −0.213201 | ||||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 4.85410 | 0.506075 | ||||||||
\(93\) | −1.47214 | −0.152653 | ||||||||
\(94\) | −1.52786 | −0.157587 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.381966 | −0.0389842 | ||||||||
\(97\) | 7.14590 | 0.725556 | 0.362778 | − | 0.931876i | \(-0.381828\pi\) | ||||
0.362778 | + | 0.931876i | \(0.381828\pi\) | |||||||
\(98\) | 0.145898 | 0.0147379 | ||||||||
\(99\) | −5.70820 | −0.573696 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.8541 | 1.08002 | 0.540012 | − | 0.841657i | \(-0.318420\pi\) | ||||
0.540012 | + | 0.841657i | \(0.318420\pi\) | |||||||
\(102\) | −1.29180 | −0.127907 | ||||||||
\(103\) | 7.41641 | 0.730760 | 0.365380 | − | 0.930858i | \(-0.380939\pi\) | ||||
0.365380 | + | 0.930858i | \(0.380939\pi\) | |||||||
\(104\) | −0.381966 | −0.0374548 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.38197 | −0.911257 | ||||||||
\(107\) | −14.1803 | −1.37087 | −0.685433 | − | 0.728136i | \(-0.740387\pi\) | ||||
−0.685433 | + | 0.728136i | \(0.740387\pi\) | |||||||
\(108\) | −2.23607 | −0.215166 | ||||||||
\(109\) | 19.4164 | 1.85975 | 0.929877 | − | 0.367870i | \(-0.119913\pi\) | ||||
0.929877 | + | 0.367870i | \(0.119913\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.41641 | 0.324271 | ||||||||
\(112\) | 2.61803 | 0.247381 | ||||||||
\(113\) | 4.09017 | 0.384771 | 0.192385 | − | 0.981319i | \(-0.438378\pi\) | ||||
0.192385 | + | 0.981319i | \(0.438378\pi\) | |||||||
\(114\) | 0.763932 | 0.0715488 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | −1.09017 | −0.100786 | ||||||||
\(118\) | −2.85410 | −0.262741 | ||||||||
\(119\) | 8.85410 | 0.811654 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 10.8541 | 0.982684 | ||||||||
\(123\) | 2.94427 | 0.265476 | ||||||||
\(124\) | −3.85410 | −0.346109 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 7.47214 | 0.665671 | ||||||||
\(127\) | −8.29180 | −0.735778 | −0.367889 | − | 0.929870i | \(-0.619919\pi\) | ||||
−0.367889 | + | 0.929870i | \(0.619919\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 1.29180 | 0.113736 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21.4164 | 1.87116 | 0.935580 | − | 0.353114i | \(-0.114877\pi\) | ||||
0.935580 | + | 0.353114i | \(0.114877\pi\) | |||||||
\(132\) | 0.763932 | 0.0664917 | ||||||||
\(133\) | −5.23607 | −0.454025 | ||||||||
\(134\) | 8.94427 | 0.772667 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.38197 | −0.290001 | ||||||||
\(137\) | −4.85410 | −0.414714 | −0.207357 | − | 0.978265i | \(-0.566486\pi\) | ||||
−0.207357 | + | 0.978265i | \(0.566486\pi\) | |||||||
\(138\) | −1.85410 | −0.157832 | ||||||||
\(139\) | −5.56231 | −0.471789 | −0.235894 | − | 0.971779i | \(-0.575802\pi\) | ||||
−0.235894 | + | 0.971779i | \(0.575802\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.583592 | 0.0491473 | ||||||||
\(142\) | 5.70820 | 0.479022 | ||||||||
\(143\) | 0.763932 | 0.0638832 | ||||||||
\(144\) | −2.85410 | −0.237842 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 5.56231 | 0.460340 | ||||||||
\(147\) | −0.0557281 | −0.00459638 | ||||||||
\(148\) | 8.94427 | 0.735215 | ||||||||
\(149\) | −21.4164 | −1.75450 | −0.877250 | − | 0.480033i | \(-0.840625\pi\) | ||||
−0.877250 | + | 0.480033i | \(0.840625\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.29180 | 0.349261 | 0.174631 | − | 0.984634i | \(-0.444127\pi\) | ||||
0.174631 | + | 0.984634i | \(0.444127\pi\) | |||||||
\(152\) | 2.00000 | 0.162221 | ||||||||
\(153\) | −9.65248 | −0.780356 | ||||||||
\(154\) | −5.23607 | −0.421934 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.145898 | 0.0116812 | ||||||||
\(157\) | 9.70820 | 0.774799 | 0.387400 | − | 0.921912i | \(-0.373373\pi\) | ||||
0.387400 | + | 0.921912i | \(0.373373\pi\) | |||||||
\(158\) | −6.56231 | −0.522069 | ||||||||
\(159\) | 3.58359 | 0.284197 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.7082 | 1.00155 | ||||||||
\(162\) | −7.70820 | −0.605614 | ||||||||
\(163\) | 7.41641 | 0.580898 | 0.290449 | − | 0.956890i | \(-0.406195\pi\) | ||||
0.290449 | + | 0.956890i | \(0.406195\pi\) | |||||||
\(164\) | 7.70820 | 0.601910 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.9443 | −1.15990 | ||||||||
\(167\) | 2.61803 | 0.202590 | 0.101295 | − | 0.994856i | \(-0.467701\pi\) | ||||
0.101295 | + | 0.994856i | \(0.467701\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | −12.8541 | −0.988777 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.70820 | 0.436517 | ||||||||
\(172\) | 3.38197 | 0.257872 | ||||||||
\(173\) | 17.5066 | 1.33100 | 0.665500 | − | 0.746398i | \(-0.268218\pi\) | ||||
0.665500 | + | 0.746398i | \(0.268218\pi\) | |||||||
\(174\) | 0.381966 | 0.0289568 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.00000 | 0.150756 | ||||||||
\(177\) | 1.09017 | 0.0819422 | ||||||||
\(178\) | −2.00000 | −0.149906 | ||||||||
\(179\) | 9.14590 | 0.683597 | 0.341798 | − | 0.939773i | \(-0.388964\pi\) | ||||
0.341798 | + | 0.939773i | \(0.388964\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | −1.00000 | −0.0741249 | ||||||||
\(183\) | −4.14590 | −0.306474 | ||||||||
\(184\) | −4.85410 | −0.357849 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.47214 | 0.107942 | ||||||||
\(187\) | 6.76393 | 0.494628 | ||||||||
\(188\) | 1.52786 | 0.111431 | ||||||||
\(189\) | −5.85410 | −0.425823 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.2705 | 1.68379 | 0.841897 | − | 0.539637i | \(-0.181439\pi\) | ||||
0.841897 | + | 0.539637i | \(0.181439\pi\) | |||||||
\(192\) | 0.381966 | 0.0275660 | ||||||||
\(193\) | −2.56231 | −0.184439 | −0.0922194 | − | 0.995739i | \(-0.529396\pi\) | ||||
−0.0922194 | + | 0.995739i | \(0.529396\pi\) | |||||||
\(194\) | −7.14590 | −0.513046 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.145898 | −0.0104213 | ||||||||
\(197\) | 9.38197 | 0.668437 | 0.334219 | − | 0.942496i | \(-0.391528\pi\) | ||||
0.334219 | + | 0.942496i | \(0.391528\pi\) | |||||||
\(198\) | 5.70820 | 0.405664 | ||||||||
\(199\) | 19.1246 | 1.35571 | 0.677854 | − | 0.735197i | \(-0.262910\pi\) | ||||
0.677854 | + | 0.735197i | \(0.262910\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.41641 | −0.240975 | ||||||||
\(202\) | −10.8541 | −0.763692 | ||||||||
\(203\) | −2.61803 | −0.183750 | ||||||||
\(204\) | 1.29180 | 0.0904438 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −7.41641 | −0.516726 | ||||||||
\(207\) | −13.8541 | −0.962927 | ||||||||
\(208\) | 0.381966 | 0.0264846 | ||||||||
\(209\) | −4.00000 | −0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.4164 | −0.785938 | −0.392969 | − | 0.919552i | \(-0.628552\pi\) | ||||
−0.392969 | + | 0.919552i | \(0.628552\pi\) | |||||||
\(212\) | 9.38197 | 0.644356 | ||||||||
\(213\) | −2.18034 | −0.149394 | ||||||||
\(214\) | 14.1803 | 0.969348 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.23607 | 0.152145 | ||||||||
\(217\) | −10.0902 | −0.684965 | ||||||||
\(218\) | −19.4164 | −1.31505 | ||||||||
\(219\) | −2.12461 | −0.143568 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.29180 | 0.0868956 | ||||||||
\(222\) | −3.41641 | −0.229294 | ||||||||
\(223\) | −26.5623 | −1.77874 | −0.889372 | − | 0.457185i | \(-0.848858\pi\) | ||||
−0.889372 | + | 0.457185i | \(0.848858\pi\) | |||||||
\(224\) | −2.61803 | −0.174925 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.09017 | −0.272074 | ||||||||
\(227\) | 16.4721 | 1.09329 | 0.546647 | − | 0.837363i | \(-0.315904\pi\) | ||||
0.546647 | + | 0.837363i | \(0.315904\pi\) | |||||||
\(228\) | −0.763932 | −0.0505926 | ||||||||
\(229\) | −8.14590 | −0.538296 | −0.269148 | − | 0.963099i | \(-0.586742\pi\) | ||||
−0.269148 | + | 0.963099i | \(0.586742\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.00000 | 0.131590 | ||||||||
\(232\) | 1.00000 | 0.0656532 | ||||||||
\(233\) | −11.2361 | −0.736099 | −0.368050 | − | 0.929806i | \(-0.619974\pi\) | ||||
−0.368050 | + | 0.929806i | \(0.619974\pi\) | |||||||
\(234\) | 1.09017 | 0.0712666 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.85410 | 0.185786 | ||||||||
\(237\) | 2.50658 | 0.162820 | ||||||||
\(238\) | −8.85410 | −0.573926 | ||||||||
\(239\) | 5.70820 | 0.369233 | 0.184617 | − | 0.982811i | \(-0.440896\pi\) | ||||
0.184617 | + | 0.982811i | \(0.440896\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.85410 | −0.570343 | −0.285171 | − | 0.958477i | \(-0.592051\pi\) | ||||
−0.285171 | + | 0.958477i | \(0.592051\pi\) | |||||||
\(242\) | 7.00000 | 0.449977 | ||||||||
\(243\) | 9.65248 | 0.619207 | ||||||||
\(244\) | −10.8541 | −0.694863 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.94427 | −0.187720 | ||||||||
\(247\) | −0.763932 | −0.0486078 | ||||||||
\(248\) | 3.85410 | 0.244736 | ||||||||
\(249\) | 5.70820 | 0.361743 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −29.1246 | −1.83833 | −0.919165 | − | 0.393874i | \(-0.871135\pi\) | ||||
−0.919165 | + | 0.393874i | \(0.871135\pi\) | |||||||
\(252\) | −7.47214 | −0.470700 | ||||||||
\(253\) | 9.70820 | 0.610350 | ||||||||
\(254\) | 8.29180 | 0.520274 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.29180 | 0.142958 | 0.0714792 | − | 0.997442i | \(-0.477228\pi\) | ||||
0.0714792 | + | 0.997442i | \(0.477228\pi\) | |||||||
\(258\) | −1.29180 | −0.0804237 | ||||||||
\(259\) | 23.4164 | 1.45502 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.85410 | 0.176664 | ||||||||
\(262\) | −21.4164 | −1.32311 | ||||||||
\(263\) | −21.5967 | −1.33171 | −0.665856 | − | 0.746080i | \(-0.731934\pi\) | ||||
−0.665856 | + | 0.746080i | \(0.731934\pi\) | |||||||
\(264\) | −0.763932 | −0.0470168 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.23607 | 0.321044 | ||||||||
\(267\) | 0.763932 | 0.0467519 | ||||||||
\(268\) | −8.94427 | −0.546358 | ||||||||
\(269\) | 3.27051 | 0.199407 | 0.0997033 | − | 0.995017i | \(-0.468211\pi\) | ||||
0.0997033 | + | 0.995017i | \(0.468211\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.4164 | 1.42245 | 0.711223 | − | 0.702967i | \(-0.248142\pi\) | ||||
0.711223 | + | 0.702967i | \(0.248142\pi\) | |||||||
\(272\) | 3.38197 | 0.205062 | ||||||||
\(273\) | 0.381966 | 0.0231176 | ||||||||
\(274\) | 4.85410 | 0.293247 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.85410 | 0.111604 | ||||||||
\(277\) | −30.0000 | −1.80253 | −0.901263 | − | 0.433273i | \(-0.857359\pi\) | ||||
−0.901263 | + | 0.433273i | \(0.857359\pi\) | |||||||
\(278\) | 5.56231 | 0.333605 | ||||||||
\(279\) | 11.0000 | 0.658553 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.5623 | −1.04768 | −0.523840 | − | 0.851817i | \(-0.675501\pi\) | ||||
−0.523840 | + | 0.851817i | \(0.675501\pi\) | |||||||
\(282\) | −0.583592 | −0.0347524 | ||||||||
\(283\) | −6.76393 | −0.402074 | −0.201037 | − | 0.979584i | \(-0.564431\pi\) | ||||
−0.201037 | + | 0.979584i | \(0.564431\pi\) | |||||||
\(284\) | −5.70820 | −0.338720 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.763932 | −0.0451722 | ||||||||
\(287\) | 20.1803 | 1.19121 | ||||||||
\(288\) | 2.85410 | 0.168180 | ||||||||
\(289\) | −5.56231 | −0.327194 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.72949 | 0.160006 | ||||||||
\(292\) | −5.56231 | −0.325509 | ||||||||
\(293\) | −19.4164 | −1.13432 | −0.567159 | − | 0.823608i | \(-0.691958\pi\) | ||||
−0.567159 | + | 0.823608i | \(0.691958\pi\) | |||||||
\(294\) | 0.0557281 | 0.00325013 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8.94427 | −0.519875 | ||||||||
\(297\) | −4.47214 | −0.259500 | ||||||||
\(298\) | 21.4164 | 1.24062 | ||||||||
\(299\) | 1.85410 | 0.107225 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.85410 | 0.510342 | ||||||||
\(302\) | −4.29180 | −0.246965 | ||||||||
\(303\) | 4.14590 | 0.238176 | ||||||||
\(304\) | −2.00000 | −0.114708 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 9.65248 | 0.551795 | ||||||||
\(307\) | −24.0000 | −1.36975 | −0.684876 | − | 0.728659i | \(-0.740144\pi\) | ||||
−0.684876 | + | 0.728659i | \(0.740144\pi\) | |||||||
\(308\) | 5.23607 | 0.298353 | ||||||||
\(309\) | 2.83282 | 0.161153 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −34.5623 | −1.95985 | −0.979924 | − | 0.199370i | \(-0.936110\pi\) | ||||
−0.979924 | + | 0.199370i | \(0.936110\pi\) | |||||||
\(312\) | −0.145898 | −0.00825985 | ||||||||
\(313\) | −12.7639 | −0.721460 | −0.360730 | − | 0.932670i | \(-0.617472\pi\) | ||||
−0.360730 | + | 0.932670i | \(0.617472\pi\) | |||||||
\(314\) | −9.70820 | −0.547866 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.56231 | 0.369159 | ||||||||
\(317\) | −20.1803 | −1.13344 | −0.566720 | − | 0.823910i | \(-0.691788\pi\) | ||||
−0.566720 | + | 0.823910i | \(0.691788\pi\) | |||||||
\(318\) | −3.58359 | −0.200958 | ||||||||
\(319\) | −2.00000 | −0.111979 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.41641 | −0.302314 | ||||||||
\(322\) | −12.7082 | −0.708201 | ||||||||
\(323\) | −6.76393 | −0.376355 | ||||||||
\(324\) | 7.70820 | 0.428234 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −7.41641 | −0.410757 | ||||||||
\(327\) | 7.41641 | 0.410128 | ||||||||
\(328\) | −7.70820 | −0.425614 | ||||||||
\(329\) | 4.00000 | 0.220527 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.1246 | 1.49090 | 0.745452 | − | 0.666560i | \(-0.232234\pi\) | ||||
0.745452 | + | 0.666560i | \(0.232234\pi\) | |||||||
\(332\) | 14.9443 | 0.820173 | ||||||||
\(333\) | −25.5279 | −1.39892 | ||||||||
\(334\) | −2.61803 | −0.143252 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.00000 | 0.0545545 | ||||||||
\(337\) | 8.61803 | 0.469454 | 0.234727 | − | 0.972061i | \(-0.424580\pi\) | ||||
0.234727 | + | 0.972061i | \(0.424580\pi\) | |||||||
\(338\) | 12.8541 | 0.699171 | ||||||||
\(339\) | 1.56231 | 0.0848528 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.70820 | −0.417423 | ||||||||
\(342\) | −5.70820 | −0.308664 | ||||||||
\(343\) | −18.7082 | −1.01015 | ||||||||
\(344\) | −3.38197 | −0.182343 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.5066 | −0.941159 | ||||||||
\(347\) | −6.00000 | −0.322097 | −0.161048 | − | 0.986947i | \(-0.551488\pi\) | ||||
−0.161048 | + | 0.986947i | \(0.551488\pi\) | |||||||
\(348\) | −0.381966 | −0.0204755 | ||||||||
\(349\) | −24.8328 | −1.32927 | −0.664635 | − | 0.747168i | \(-0.731413\pi\) | ||||
−0.664635 | + | 0.747168i | \(0.731413\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.854102 | −0.0455886 | ||||||||
\(352\) | −2.00000 | −0.106600 | ||||||||
\(353\) | −3.05573 | −0.162640 | −0.0813200 | − | 0.996688i | \(-0.525914\pi\) | ||||
−0.0813200 | + | 0.996688i | \(0.525914\pi\) | |||||||
\(354\) | −1.09017 | −0.0579419 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.00000 | 0.106000 | ||||||||
\(357\) | 3.38197 | 0.178993 | ||||||||
\(358\) | −9.14590 | −0.483376 | ||||||||
\(359\) | 0.270510 | 0.0142770 | 0.00713848 | − | 0.999975i | \(-0.497728\pi\) | ||||
0.00713848 | + | 0.999975i | \(0.497728\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 10.0000 | 0.525588 | ||||||||
\(363\) | −2.67376 | −0.140336 | ||||||||
\(364\) | 1.00000 | 0.0524142 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.14590 | 0.216710 | ||||||||
\(367\) | 35.1246 | 1.83349 | 0.916745 | − | 0.399473i | \(-0.130807\pi\) | ||||
0.916745 | + | 0.399473i | \(0.130807\pi\) | |||||||
\(368\) | 4.85410 | 0.253038 | ||||||||
\(369\) | −22.0000 | −1.14527 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.5623 | 1.27521 | ||||||||
\(372\) | −1.47214 | −0.0763267 | ||||||||
\(373\) | 15.2705 | 0.790677 | 0.395339 | − | 0.918535i | \(-0.370627\pi\) | ||||
0.395339 | + | 0.918535i | \(0.370627\pi\) | |||||||
\(374\) | −6.76393 | −0.349755 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.52786 | −0.0787936 | ||||||||
\(377\) | −0.381966 | −0.0196723 | ||||||||
\(378\) | 5.85410 | 0.301103 | ||||||||
\(379\) | 26.0000 | 1.33553 | 0.667765 | − | 0.744372i | \(-0.267251\pi\) | ||||
0.667765 | + | 0.744372i | \(0.267251\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.16718 | −0.162260 | ||||||||
\(382\) | −23.2705 | −1.19062 | ||||||||
\(383\) | −7.85410 | −0.401326 | −0.200663 | − | 0.979660i | \(-0.564310\pi\) | ||||
−0.200663 | + | 0.979660i | \(0.564310\pi\) | |||||||
\(384\) | −0.381966 | −0.0194921 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.56231 | 0.130418 | ||||||||
\(387\) | −9.65248 | −0.490663 | ||||||||
\(388\) | 7.14590 | 0.362778 | ||||||||
\(389\) | −20.8328 | −1.05627 | −0.528133 | − | 0.849162i | \(-0.677108\pi\) | ||||
−0.528133 | + | 0.849162i | \(0.677108\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.4164 | 0.830213 | ||||||||
\(392\) | 0.145898 | 0.00736896 | ||||||||
\(393\) | 8.18034 | 0.412644 | ||||||||
\(394\) | −9.38197 | −0.472657 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5.70820 | −0.286848 | ||||||||
\(397\) | −1.96556 | −0.0986485 | −0.0493243 | − | 0.998783i | \(-0.515707\pi\) | ||||
−0.0493243 | + | 0.998783i | \(0.515707\pi\) | |||||||
\(398\) | −19.1246 | −0.958630 | ||||||||
\(399\) | −2.00000 | −0.100125 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.9787 | 1.09756 | 0.548782 | − | 0.835965i | \(-0.315092\pi\) | ||||
0.548782 | + | 0.835965i | \(0.315092\pi\) | |||||||
\(402\) | 3.41641 | 0.170395 | ||||||||
\(403\) | −1.47214 | −0.0733323 | ||||||||
\(404\) | 10.8541 | 0.540012 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.61803 | 0.129931 | ||||||||
\(407\) | 17.8885 | 0.886702 | ||||||||
\(408\) | −1.29180 | −0.0639534 | ||||||||
\(409\) | −7.12461 | −0.352289 | −0.176145 | − | 0.984364i | \(-0.556363\pi\) | ||||
−0.176145 | + | 0.984364i | \(0.556363\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.85410 | −0.0914561 | ||||||||
\(412\) | 7.41641 | 0.365380 | ||||||||
\(413\) | 7.47214 | 0.367680 | ||||||||
\(414\) | 13.8541 | 0.680892 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.381966 | −0.0187274 | ||||||||
\(417\) | −2.12461 | −0.104043 | ||||||||
\(418\) | 4.00000 | 0.195646 | ||||||||
\(419\) | −21.8541 | −1.06764 | −0.533821 | − | 0.845597i | \(-0.679245\pi\) | ||||
−0.533821 | + | 0.845597i | \(0.679245\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | 11.4164 | 0.555742 | ||||||||
\(423\) | −4.36068 | −0.212024 | ||||||||
\(424\) | −9.38197 | −0.455629 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.18034 | 0.105638 | ||||||||
\(427\) | −28.4164 | −1.37517 | ||||||||
\(428\) | −14.1803 | −0.685433 | ||||||||
\(429\) | 0.291796 | 0.0140880 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.4164 | −1.60961 | −0.804806 | − | 0.593538i | \(-0.797731\pi\) | ||||
−0.804806 | + | 0.593538i | \(0.797731\pi\) | |||||||
\(432\) | −2.23607 | −0.107583 | ||||||||
\(433\) | −16.4721 | −0.791600 | −0.395800 | − | 0.918337i | \(-0.629533\pi\) | ||||
−0.395800 | + | 0.918337i | \(0.629533\pi\) | |||||||
\(434\) | 10.0902 | 0.484344 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 19.4164 | 0.929877 | ||||||||
\(437\) | −9.70820 | −0.464406 | ||||||||
\(438\) | 2.12461 | 0.101518 | ||||||||
\(439\) | −37.1246 | −1.77186 | −0.885931 | − | 0.463818i | \(-0.846479\pi\) | ||||
−0.885931 | + | 0.463818i | \(0.846479\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.416408 | 0.0198289 | ||||||||
\(442\) | −1.29180 | −0.0614445 | ||||||||
\(443\) | −1.90983 | −0.0907388 | −0.0453694 | − | 0.998970i | \(-0.514446\pi\) | ||||
−0.0453694 | + | 0.998970i | \(0.514446\pi\) | |||||||
\(444\) | 3.41641 | 0.162136 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 26.5623 | 1.25776 | ||||||||
\(447\) | −8.18034 | −0.386917 | ||||||||
\(448\) | 2.61803 | 0.123690 | ||||||||
\(449\) | −4.58359 | −0.216313 | −0.108157 | − | 0.994134i | \(-0.534495\pi\) | ||||
−0.108157 | + | 0.994134i | \(0.534495\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.4164 | 0.725930 | ||||||||
\(452\) | 4.09017 | 0.192385 | ||||||||
\(453\) | 1.63932 | 0.0770220 | ||||||||
\(454\) | −16.4721 | −0.773076 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.763932 | 0.0357744 | ||||||||
\(457\) | −14.2918 | −0.668542 | −0.334271 | − | 0.942477i | \(-0.608490\pi\) | ||||
−0.334271 | + | 0.942477i | \(0.608490\pi\) | |||||||
\(458\) | 8.14590 | 0.380633 | ||||||||
\(459\) | −7.56231 | −0.352978 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.1459 | −1.12459 | −0.562293 | − | 0.826938i | \(-0.690081\pi\) | ||||
−0.562293 | + | 0.826938i | \(0.690081\pi\) | |||||||
\(462\) | −2.00000 | −0.0930484 | ||||||||
\(463\) | −17.8885 | −0.831351 | −0.415676 | − | 0.909513i | \(-0.636455\pi\) | ||||
−0.415676 | + | 0.909513i | \(0.636455\pi\) | |||||||
\(464\) | −1.00000 | −0.0464238 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.2361 | 0.520501 | ||||||||
\(467\) | 34.7984 | 1.61028 | 0.805138 | − | 0.593087i | \(-0.202091\pi\) | ||||
0.805138 | + | 0.593087i | \(0.202091\pi\) | |||||||
\(468\) | −1.09017 | −0.0503931 | ||||||||
\(469\) | −23.4164 | −1.08127 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.70820 | 0.170865 | ||||||||
\(472\) | −2.85410 | −0.131371 | ||||||||
\(473\) | 6.76393 | 0.311006 | ||||||||
\(474\) | −2.50658 | −0.115131 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 8.85410 | 0.405827 | ||||||||
\(477\) | −26.7771 | −1.22604 | ||||||||
\(478\) | −5.70820 | −0.261087 | ||||||||
\(479\) | −18.9787 | −0.867160 | −0.433580 | − | 0.901115i | \(-0.642750\pi\) | ||||
−0.433580 | + | 0.901115i | \(0.642750\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.41641 | 0.155775 | ||||||||
\(482\) | 8.85410 | 0.403293 | ||||||||
\(483\) | 4.85410 | 0.220869 | ||||||||
\(484\) | −7.00000 | −0.318182 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −9.65248 | −0.437845 | ||||||||
\(487\) | 38.5623 | 1.74742 | 0.873712 | − | 0.486443i | \(-0.161706\pi\) | ||||
0.873712 | + | 0.486443i | \(0.161706\pi\) | |||||||
\(488\) | 10.8541 | 0.491342 | ||||||||
\(489\) | 2.83282 | 0.128104 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.29180 | −0.283945 | −0.141972 | − | 0.989871i | \(-0.545344\pi\) | ||||
−0.141972 | + | 0.989871i | \(0.545344\pi\) | |||||||
\(492\) | 2.94427 | 0.132738 | ||||||||
\(493\) | −3.38197 | −0.152316 | ||||||||
\(494\) | 0.763932 | 0.0343709 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.85410 | −0.173054 | ||||||||
\(497\) | −14.9443 | −0.670342 | ||||||||
\(498\) | −5.70820 | −0.255791 | ||||||||
\(499\) | 28.5623 | 1.27862 | 0.639312 | − | 0.768947i | \(-0.279219\pi\) | ||||
0.639312 | + | 0.768947i | \(0.279219\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 29.1246 | 1.29990 | ||||||||
\(503\) | 32.9443 | 1.46891 | 0.734456 | − | 0.678656i | \(-0.237437\pi\) | ||||
0.734456 | + | 0.678656i | \(0.237437\pi\) | |||||||
\(504\) | 7.47214 | 0.332835 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −9.70820 | −0.431582 | ||||||||
\(507\) | −4.90983 | −0.218053 | ||||||||
\(508\) | −8.29180 | −0.367889 | ||||||||
\(509\) | −21.1246 | −0.936332 | −0.468166 | − | 0.883641i | \(-0.655085\pi\) | ||||
−0.468166 | + | 0.883641i | \(0.655085\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.5623 | −0.644198 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 4.47214 | 0.197450 | ||||||||
\(514\) | −2.29180 | −0.101087 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.29180 | 0.0568682 | ||||||||
\(517\) | 3.05573 | 0.134391 | ||||||||
\(518\) | −23.4164 | −1.02886 | ||||||||
\(519\) | 6.68692 | 0.293523 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −36.3951 | −1.59450 | −0.797250 | − | 0.603650i | \(-0.793713\pi\) | ||||
−0.797250 | + | 0.603650i | \(0.793713\pi\) | |||||||
\(522\) | −2.85410 | −0.124921 | ||||||||
\(523\) | −11.1246 | −0.486445 | −0.243223 | − | 0.969970i | \(-0.578205\pi\) | ||||
−0.243223 | + | 0.969970i | \(0.578205\pi\) | |||||||
\(524\) | 21.4164 | 0.935580 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.5967 | 0.941663 | ||||||||
\(527\) | −13.0344 | −0.567789 | ||||||||
\(528\) | 0.763932 | 0.0332459 | ||||||||
\(529\) | 0.562306 | 0.0244481 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.14590 | −0.353502 | ||||||||
\(532\) | −5.23607 | −0.227012 | ||||||||
\(533\) | 2.94427 | 0.127531 | ||||||||
\(534\) | −0.763932 | −0.0330586 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8.94427 | 0.386334 | ||||||||
\(537\) | 3.49342 | 0.150752 | ||||||||
\(538\) | −3.27051 | −0.141002 | ||||||||
\(539\) | −0.291796 | −0.0125685 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.5623 | −1.18500 | −0.592498 | − | 0.805572i | \(-0.701858\pi\) | ||||
−0.592498 | + | 0.805572i | \(0.701858\pi\) | |||||||
\(542\) | −23.4164 | −1.00582 | ||||||||
\(543\) | −3.81966 | −0.163917 | ||||||||
\(544\) | −3.38197 | −0.145001 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.381966 | −0.0163466 | ||||||||
\(547\) | −14.8328 | −0.634205 | −0.317103 | − | 0.948391i | \(-0.602710\pi\) | ||||
−0.317103 | + | 0.948391i | \(0.602710\pi\) | |||||||
\(548\) | −4.85410 | −0.207357 | ||||||||
\(549\) | 30.9787 | 1.32214 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.00000 | 0.0852029 | ||||||||
\(552\) | −1.85410 | −0.0789158 | ||||||||
\(553\) | 17.1803 | 0.730582 | ||||||||
\(554\) | 30.0000 | 1.27458 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.56231 | −0.235894 | ||||||||
\(557\) | −7.79837 | −0.330428 | −0.165214 | − | 0.986258i | \(-0.552831\pi\) | ||||
−0.165214 | + | 0.986258i | \(0.552831\pi\) | |||||||
\(558\) | −11.0000 | −0.465667 | ||||||||
\(559\) | 1.29180 | 0.0546372 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.58359 | 0.109079 | ||||||||
\(562\) | 17.5623 | 0.740821 | ||||||||
\(563\) | 33.3262 | 1.40453 | 0.702267 | − | 0.711914i | \(-0.252171\pi\) | ||||
0.702267 | + | 0.711914i | \(0.252171\pi\) | |||||||
\(564\) | 0.583592 | 0.0245737 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.76393 | 0.284309 | ||||||||
\(567\) | 20.1803 | 0.847495 | ||||||||
\(568\) | 5.70820 | 0.239511 | ||||||||
\(569\) | 12.0000 | 0.503066 | 0.251533 | − | 0.967849i | \(-0.419065\pi\) | ||||
0.251533 | + | 0.967849i | \(0.419065\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.85410 | −0.286835 | −0.143418 | − | 0.989662i | \(-0.545809\pi\) | ||||
−0.143418 | + | 0.989662i | \(0.545809\pi\) | |||||||
\(572\) | 0.763932 | 0.0319416 | ||||||||
\(573\) | 8.88854 | 0.371324 | ||||||||
\(574\) | −20.1803 | −0.842311 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.85410 | −0.118921 | ||||||||
\(577\) | −28.0344 | −1.16709 | −0.583545 | − | 0.812081i | \(-0.698335\pi\) | ||||
−0.583545 | + | 0.812081i | \(0.698335\pi\) | |||||||
\(578\) | 5.56231 | 0.231361 | ||||||||
\(579\) | −0.978714 | −0.0406740 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 39.1246 | 1.62316 | ||||||||
\(582\) | −2.72949 | −0.113141 | ||||||||
\(583\) | 18.7639 | 0.777123 | ||||||||
\(584\) | 5.56231 | 0.230170 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 19.4164 | 0.802084 | ||||||||
\(587\) | 12.6525 | 0.522224 | 0.261112 | − | 0.965309i | \(-0.415911\pi\) | ||||
0.261112 | + | 0.965309i | \(0.415911\pi\) | |||||||
\(588\) | −0.0557281 | −0.00229819 | ||||||||
\(589\) | 7.70820 | 0.317611 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.58359 | 0.147409 | ||||||||
\(592\) | 8.94427 | 0.367607 | ||||||||
\(593\) | 43.3050 | 1.77832 | 0.889161 | − | 0.457595i | \(-0.151289\pi\) | ||||
0.889161 | + | 0.457595i | \(0.151289\pi\) | |||||||
\(594\) | 4.47214 | 0.183494 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −21.4164 | −0.877250 | ||||||||
\(597\) | 7.30495 | 0.298972 | ||||||||
\(598\) | −1.85410 | −0.0758199 | ||||||||
\(599\) | 23.5623 | 0.962730 | 0.481365 | − | 0.876520i | \(-0.340141\pi\) | ||||
0.481365 | + | 0.876520i | \(0.340141\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.70820 | 0.232842 | 0.116421 | − | 0.993200i | \(-0.462858\pi\) | ||||
0.116421 | + | 0.993200i | \(0.462858\pi\) | |||||||
\(602\) | −8.85410 | −0.360866 | ||||||||
\(603\) | 25.5279 | 1.03957 | ||||||||
\(604\) | 4.29180 | 0.174631 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4.14590 | −0.168416 | ||||||||
\(607\) | 0.763932 | 0.0310070 | 0.0155035 | − | 0.999880i | \(-0.495065\pi\) | ||||
0.0155035 | + | 0.999880i | \(0.495065\pi\) | |||||||
\(608\) | 2.00000 | 0.0811107 | ||||||||
\(609\) | −1.00000 | −0.0405220 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.583592 | 0.0236096 | ||||||||
\(612\) | −9.65248 | −0.390178 | ||||||||
\(613\) | 13.7426 | 0.555060 | 0.277530 | − | 0.960717i | \(-0.410484\pi\) | ||||
0.277530 | + | 0.960717i | \(0.410484\pi\) | |||||||
\(614\) | 24.0000 | 0.968561 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.23607 | −0.210967 | ||||||||
\(617\) | 32.6180 | 1.31315 | 0.656576 | − | 0.754260i | \(-0.272004\pi\) | ||||
0.656576 | + | 0.754260i | \(0.272004\pi\) | |||||||
\(618\) | −2.83282 | −0.113953 | ||||||||
\(619\) | −7.41641 | −0.298091 | −0.149045 | − | 0.988830i | \(-0.547620\pi\) | ||||
−0.149045 | + | 0.988830i | \(0.547620\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.8541 | −0.435560 | ||||||||
\(622\) | 34.5623 | 1.38582 | ||||||||
\(623\) | 5.23607 | 0.209779 | ||||||||
\(624\) | 0.145898 | 0.00584060 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 12.7639 | 0.510149 | ||||||||
\(627\) | −1.52786 | −0.0610170 | ||||||||
\(628\) | 9.70820 | 0.387400 | ||||||||
\(629\) | 30.2492 | 1.20612 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.8328 | −1.38667 | −0.693336 | − | 0.720614i | \(-0.743860\pi\) | ||||
−0.693336 | + | 0.720614i | \(0.743860\pi\) | |||||||
\(632\) | −6.56231 | −0.261035 | ||||||||
\(633\) | −4.36068 | −0.173321 | ||||||||
\(634\) | 20.1803 | 0.801464 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.58359 | 0.142099 | ||||||||
\(637\) | −0.0557281 | −0.00220803 | ||||||||
\(638\) | 2.00000 | 0.0791808 | ||||||||
\(639\) | 16.2918 | 0.644493 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.291796 | 0.0115253 | 0.00576263 | − | 0.999983i | \(-0.498166\pi\) | ||||
0.00576263 | + | 0.999983i | \(0.498166\pi\) | |||||||
\(642\) | 5.41641 | 0.213769 | ||||||||
\(643\) | −16.5836 | −0.653993 | −0.326997 | − | 0.945026i | \(-0.606037\pi\) | ||||
−0.326997 | + | 0.945026i | \(0.606037\pi\) | |||||||
\(644\) | 12.7082 | 0.500773 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.76393 | 0.266123 | ||||||||
\(647\) | 13.5279 | 0.531835 | 0.265918 | − | 0.963996i | \(-0.414325\pi\) | ||||
0.265918 | + | 0.963996i | \(0.414325\pi\) | |||||||
\(648\) | −7.70820 | −0.302807 | ||||||||
\(649\) | 5.70820 | 0.224067 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.85410 | −0.151054 | ||||||||
\(652\) | 7.41641 | 0.290449 | ||||||||
\(653\) | 37.3050 | 1.45986 | 0.729928 | − | 0.683524i | \(-0.239554\pi\) | ||||
0.729928 | + | 0.683524i | \(0.239554\pi\) | |||||||
\(654\) | −7.41641 | −0.290004 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 7.70820 | 0.300955 | ||||||||
\(657\) | 15.8754 | 0.619358 | ||||||||
\(658\) | −4.00000 | −0.155936 | ||||||||
\(659\) | 40.5410 | 1.57925 | 0.789627 | − | 0.613587i | \(-0.210274\pi\) | ||||
0.789627 | + | 0.613587i | \(0.210274\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.8328 | 1.12147 | 0.560733 | − | 0.827996i | \(-0.310519\pi\) | ||||
0.560733 | + | 0.827996i | \(0.310519\pi\) | |||||||
\(662\) | −27.1246 | −1.05423 | ||||||||
\(663\) | 0.493422 | 0.0191629 | ||||||||
\(664\) | −14.9443 | −0.579950 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 25.5279 | 0.989185 | ||||||||
\(667\) | −4.85410 | −0.187952 | ||||||||
\(668\) | 2.61803 | 0.101295 | ||||||||
\(669\) | −10.1459 | −0.392263 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −21.7082 | −0.838036 | ||||||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | 26.9443 | 1.03863 | 0.519313 | − | 0.854584i | \(-0.326188\pi\) | ||||
0.519313 | + | 0.854584i | \(0.326188\pi\) | |||||||
\(674\) | −8.61803 | −0.331954 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.8541 | −0.494389 | ||||||||
\(677\) | 32.9443 | 1.26615 | 0.633076 | − | 0.774090i | \(-0.281792\pi\) | ||||
0.633076 | + | 0.774090i | \(0.281792\pi\) | |||||||
\(678\) | −1.56231 | −0.0600000 | ||||||||
\(679\) | 18.7082 | 0.717955 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.29180 | 0.241102 | ||||||||
\(682\) | 7.70820 | 0.295162 | ||||||||
\(683\) | −23.7771 | −0.909805 | −0.454902 | − | 0.890541i | \(-0.650326\pi\) | ||||
−0.454902 | + | 0.890541i | \(0.650326\pi\) | |||||||
\(684\) | 5.70820 | 0.218259 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 18.7082 | 0.714283 | ||||||||
\(687\) | −3.11146 | −0.118709 | ||||||||
\(688\) | 3.38197 | 0.128936 | ||||||||
\(689\) | 3.58359 | 0.136524 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.5623 | −0.515934 | −0.257967 | − | 0.966154i | \(-0.583053\pi\) | ||||
−0.257967 | + | 0.966154i | \(0.583053\pi\) | |||||||
\(692\) | 17.5066 | 0.665500 | ||||||||
\(693\) | −14.9443 | −0.567686 | ||||||||
\(694\) | 6.00000 | 0.227757 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.381966 | 0.0144784 | ||||||||
\(697\) | 26.0689 | 0.987429 | ||||||||
\(698\) | 24.8328 | 0.939936 | ||||||||
\(699\) | −4.29180 | −0.162331 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.12461 | −0.344632 | −0.172316 | − | 0.985042i | \(-0.555125\pi\) | ||||
−0.172316 | + | 0.985042i | \(0.555125\pi\) | |||||||
\(702\) | 0.854102 | 0.0322360 | ||||||||
\(703\) | −17.8885 | −0.674679 | ||||||||
\(704\) | 2.00000 | 0.0753778 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.05573 | 0.115004 | ||||||||
\(707\) | 28.4164 | 1.06871 | ||||||||
\(708\) | 1.09017 | 0.0409711 | ||||||||
\(709\) | 12.2918 | 0.461628 | 0.230814 | − | 0.972998i | \(-0.425861\pi\) | ||||
0.230814 | + | 0.972998i | \(0.425861\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −18.7295 | −0.702411 | ||||||||
\(712\) | −2.00000 | −0.0749532 | ||||||||
\(713\) | −18.7082 | −0.700628 | ||||||||
\(714\) | −3.38197 | −0.126567 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.14590 | 0.341798 | ||||||||
\(717\) | 2.18034 | 0.0814263 | ||||||||
\(718\) | −0.270510 | −0.0100953 | ||||||||
\(719\) | 8.29180 | 0.309232 | 0.154616 | − | 0.987975i | \(-0.450586\pi\) | ||||
0.154616 | + | 0.987975i | \(0.450586\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.4164 | 0.723105 | ||||||||
\(722\) | 15.0000 | 0.558242 | ||||||||
\(723\) | −3.38197 | −0.125777 | ||||||||
\(724\) | −10.0000 | −0.371647 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.67376 | 0.0992326 | ||||||||
\(727\) | −32.9443 | −1.22184 | −0.610918 | − | 0.791694i | \(-0.709199\pi\) | ||||
−0.610918 | + | 0.791694i | \(0.709199\pi\) | |||||||
\(728\) | −1.00000 | −0.0370625 | ||||||||
\(729\) | −19.4377 | −0.719915 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.4377 | 0.423038 | ||||||||
\(732\) | −4.14590 | −0.153237 | ||||||||
\(733\) | 12.0000 | 0.443230 | 0.221615 | − | 0.975134i | \(-0.428867\pi\) | ||||
0.221615 | + | 0.975134i | \(0.428867\pi\) | |||||||
\(734\) | −35.1246 | −1.29647 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.85410 | −0.178925 | ||||||||
\(737\) | −17.8885 | −0.658933 | ||||||||
\(738\) | 22.0000 | 0.809831 | ||||||||
\(739\) | 28.2918 | 1.04073 | 0.520365 | − | 0.853944i | \(-0.325796\pi\) | ||||
0.520365 | + | 0.853944i | \(0.325796\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.291796 | −0.0107194 | ||||||||
\(742\) | −24.5623 | −0.901711 | ||||||||
\(743\) | −25.4164 | −0.932438 | −0.466219 | − | 0.884669i | \(-0.654384\pi\) | ||||
−0.466219 | + | 0.884669i | \(0.654384\pi\) | |||||||
\(744\) | 1.47214 | 0.0539711 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −15.2705 | −0.559093 | ||||||||
\(747\) | −42.6525 | −1.56057 | ||||||||
\(748\) | 6.76393 | 0.247314 | ||||||||
\(749\) | −37.1246 | −1.35650 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.00000 | −0.145962 | −0.0729810 | − | 0.997333i | \(-0.523251\pi\) | ||||
−0.0729810 | + | 0.997333i | \(0.523251\pi\) | |||||||
\(752\) | 1.52786 | 0.0557155 | ||||||||
\(753\) | −11.1246 | −0.405403 | ||||||||
\(754\) | 0.381966 | 0.0139104 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5.85410 | −0.212912 | ||||||||
\(757\) | 32.0689 | 1.16556 | 0.582782 | − | 0.812629i | \(-0.301964\pi\) | ||||
0.582782 | + | 0.812629i | \(0.301964\pi\) | |||||||
\(758\) | −26.0000 | −0.944363 | ||||||||
\(759\) | 3.70820 | 0.134599 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.85410 | −0.357211 | −0.178605 | − | 0.983921i | \(-0.557159\pi\) | ||||
−0.178605 | + | 0.983921i | \(0.557159\pi\) | |||||||
\(762\) | 3.16718 | 0.114735 | ||||||||
\(763\) | 50.8328 | 1.84027 | ||||||||
\(764\) | 23.2705 | 0.841897 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.85410 | 0.283780 | ||||||||
\(767\) | 1.09017 | 0.0393638 | ||||||||
\(768\) | 0.381966 | 0.0137830 | ||||||||
\(769\) | −18.5836 | −0.670141 | −0.335071 | − | 0.942193i | \(-0.608760\pi\) | ||||
−0.335071 | + | 0.942193i | \(0.608760\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.875388 | 0.0315263 | ||||||||
\(772\) | −2.56231 | −0.0922194 | ||||||||
\(773\) | 6.76393 | 0.243282 | 0.121641 | − | 0.992574i | \(-0.461184\pi\) | ||||
0.121641 | + | 0.992574i | \(0.461184\pi\) | |||||||
\(774\) | 9.65248 | 0.346951 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7.14590 | −0.256523 | ||||||||
\(777\) | 8.94427 | 0.320874 | ||||||||
\(778\) | 20.8328 | 0.746893 | ||||||||
\(779\) | −15.4164 | −0.552350 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.4164 | −0.408511 | ||||||||
\(782\) | −16.4164 | −0.587050 | ||||||||
\(783\) | 2.23607 | 0.0799106 | ||||||||
\(784\) | −0.145898 | −0.00521064 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −8.18034 | −0.291783 | ||||||||
\(787\) | −41.7771 | −1.48919 | −0.744596 | − | 0.667515i | \(-0.767358\pi\) | ||||
−0.744596 | + | 0.667515i | \(0.767358\pi\) | |||||||
\(788\) | 9.38197 | 0.334219 | ||||||||
\(789\) | −8.24922 | −0.293680 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.7082 | 0.380740 | ||||||||
\(792\) | 5.70820 | 0.202832 | ||||||||
\(793\) | −4.14590 | −0.147225 | ||||||||
\(794\) | 1.96556 | 0.0697550 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 19.1246 | 0.677854 | ||||||||
\(797\) | −35.2361 | −1.24813 | −0.624063 | − | 0.781374i | \(-0.714519\pi\) | ||||
−0.624063 | + | 0.781374i | \(0.714519\pi\) | |||||||
\(798\) | 2.00000 | 0.0707992 | ||||||||
\(799\) | 5.16718 | 0.182802 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.70820 | −0.201689 | ||||||||
\(802\) | −21.9787 | −0.776095 | ||||||||
\(803\) | −11.1246 | −0.392579 | ||||||||
\(804\) | −3.41641 | −0.120487 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.47214 | 0.0518538 | ||||||||
\(807\) | 1.24922 | 0.0439748 | ||||||||
\(808\) | −10.8541 | −0.381846 | ||||||||
\(809\) | −39.4164 | −1.38581 | −0.692904 | − | 0.721030i | \(-0.743669\pi\) | ||||
−0.692904 | + | 0.721030i | \(0.743669\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 48.3951 | 1.69938 | 0.849691 | − | 0.527280i | \(-0.176788\pi\) | ||||
0.849691 | + | 0.527280i | \(0.176788\pi\) | |||||||
\(812\) | −2.61803 | −0.0918750 | ||||||||
\(813\) | 8.94427 | 0.313689 | ||||||||
\(814\) | −17.8885 | −0.626993 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.29180 | 0.0452219 | ||||||||
\(817\) | −6.76393 | −0.236640 | ||||||||
\(818\) | 7.12461 | 0.249106 | ||||||||
\(819\) | −2.85410 | −0.0997304 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.00000 | −0.279202 | −0.139601 | − | 0.990208i | \(-0.544582\pi\) | ||||
−0.139601 | + | 0.990208i | \(0.544582\pi\) | |||||||
\(822\) | 1.85410 | 0.0646692 | ||||||||
\(823\) | 5.23607 | 0.182518 | 0.0912589 | − | 0.995827i | \(-0.470911\pi\) | ||||
0.0912589 | + | 0.995827i | \(0.470911\pi\) | |||||||
\(824\) | −7.41641 | −0.258363 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.47214 | −0.259989 | ||||||||
\(827\) | 25.2016 | 0.876346 | 0.438173 | − | 0.898891i | \(-0.355626\pi\) | ||||
0.438173 | + | 0.898891i | \(0.355626\pi\) | |||||||
\(828\) | −13.8541 | −0.481463 | ||||||||
\(829\) | −0.729490 | −0.0253362 | −0.0126681 | − | 0.999920i | \(-0.504032\pi\) | ||||
−0.0126681 | + | 0.999920i | \(0.504032\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.4590 | −0.397508 | ||||||||
\(832\) | 0.381966 | 0.0132423 | ||||||||
\(833\) | −0.493422 | −0.0170961 | ||||||||
\(834\) | 2.12461 | 0.0735693 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.00000 | −0.138343 | ||||||||
\(837\) | 8.61803 | 0.297883 | ||||||||
\(838\) | 21.8541 | 0.754937 | ||||||||
\(839\) | −38.8328 | −1.34066 | −0.670329 | − | 0.742064i | \(-0.733847\pi\) | ||||
−0.670329 | + | 0.742064i | \(0.733847\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 10.0000 | 0.344623 | ||||||||
\(843\) | −6.70820 | −0.231043 | ||||||||
\(844\) | −11.4164 | −0.392969 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.36068 | 0.149923 | ||||||||
\(847\) | −18.3262 | −0.629697 | ||||||||
\(848\) | 9.38197 | 0.322178 | ||||||||
\(849\) | −2.58359 | −0.0886687 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 43.4164 | 1.48830 | ||||||||
\(852\) | −2.18034 | −0.0746972 | ||||||||
\(853\) | −8.83282 | −0.302430 | −0.151215 | − | 0.988501i | \(-0.548319\pi\) | ||||
−0.151215 | + | 0.988501i | \(0.548319\pi\) | |||||||
\(854\) | 28.4164 | 0.972389 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14.1803 | 0.484674 | ||||||||
\(857\) | 21.8197 | 0.745345 | 0.372673 | − | 0.927963i | \(-0.378441\pi\) | ||||
0.372673 | + | 0.927963i | \(0.378441\pi\) | |||||||
\(858\) | −0.291796 | −0.00996175 | ||||||||
\(859\) | 27.7082 | 0.945392 | 0.472696 | − | 0.881226i | \(-0.343281\pi\) | ||||
0.472696 | + | 0.881226i | \(0.343281\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.70820 | 0.262695 | ||||||||
\(862\) | 33.4164 | 1.13817 | ||||||||
\(863\) | 30.9230 | 1.05263 | 0.526315 | − | 0.850289i | \(-0.323573\pi\) | ||||
0.526315 | + | 0.850289i | \(0.323573\pi\) | |||||||
\(864\) | 2.23607 | 0.0760726 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 16.4721 | 0.559746 | ||||||||
\(867\) | −2.12461 | −0.0721556 | ||||||||
\(868\) | −10.0902 | −0.342483 | ||||||||
\(869\) | 13.1246 | 0.445222 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.41641 | −0.115761 | ||||||||
\(872\) | −19.4164 | −0.657523 | ||||||||
\(873\) | −20.3951 | −0.690270 | ||||||||
\(874\) | 9.70820 | 0.328385 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.12461 | −0.0717840 | ||||||||
\(877\) | −42.2705 | −1.42737 | −0.713687 | − | 0.700465i | \(-0.752976\pi\) | ||||
−0.713687 | + | 0.700465i | \(0.752976\pi\) | |||||||
\(878\) | 37.1246 | 1.25289 | ||||||||
\(879\) | −7.41641 | −0.250149 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.5836 | −0.491334 | −0.245667 | − | 0.969354i | \(-0.579007\pi\) | ||||
−0.245667 | + | 0.969354i | \(0.579007\pi\) | |||||||
\(882\) | −0.416408 | −0.0140212 | ||||||||
\(883\) | −33.7082 | −1.13437 | −0.567186 | − | 0.823590i | \(-0.691968\pi\) | ||||
−0.567186 | + | 0.823590i | \(0.691968\pi\) | |||||||
\(884\) | 1.29180 | 0.0434478 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.90983 | 0.0641620 | ||||||||
\(887\) | 24.0000 | 0.805841 | 0.402921 | − | 0.915235i | \(-0.367995\pi\) | ||||
0.402921 | + | 0.915235i | \(0.367995\pi\) | |||||||
\(888\) | −3.41641 | −0.114647 | ||||||||
\(889\) | −21.7082 | −0.728070 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.4164 | 0.516469 | ||||||||
\(892\) | −26.5623 | −0.889372 | ||||||||
\(893\) | −3.05573 | −0.102256 | ||||||||
\(894\) | 8.18034 | 0.273591 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.61803 | −0.0874624 | ||||||||
\(897\) | 0.708204 | 0.0236462 | ||||||||
\(898\) | 4.58359 | 0.152956 | ||||||||
\(899\) | 3.85410 | 0.128541 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31.7295 | 1.05706 | ||||||||
\(902\) | −15.4164 | −0.513310 | ||||||||
\(903\) | 3.38197 | 0.112545 | ||||||||
\(904\) | −4.09017 | −0.136037 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.63932 | −0.0544628 | ||||||||
\(907\) | −7.74265 | −0.257090 | −0.128545 | − | 0.991704i | \(-0.541031\pi\) | ||||
−0.128545 | + | 0.991704i | \(0.541031\pi\) | |||||||
\(908\) | 16.4721 | 0.546647 | ||||||||
\(909\) | −30.9787 | −1.02750 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.8541 | 0.425875 | 0.212938 | − | 0.977066i | \(-0.431697\pi\) | ||||
0.212938 | + | 0.977066i | \(0.431697\pi\) | |||||||
\(912\) | −0.763932 | −0.0252963 | ||||||||
\(913\) | 29.8885 | 0.989166 | ||||||||
\(914\) | 14.2918 | 0.472731 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.14590 | −0.269148 | ||||||||
\(917\) | 56.0689 | 1.85156 | ||||||||
\(918\) | 7.56231 | 0.249593 | ||||||||
\(919\) | −52.5410 | −1.73317 | −0.866584 | − | 0.499031i | \(-0.833689\pi\) | ||||
−0.866584 | + | 0.499031i | \(0.833689\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.16718 | −0.302069 | ||||||||
\(922\) | 24.1459 | 0.795203 | ||||||||
\(923\) | −2.18034 | −0.0717668 | ||||||||
\(924\) | 2.00000 | 0.0657952 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 17.8885 | 0.587854 | ||||||||
\(927\) | −21.1672 | −0.695222 | ||||||||
\(928\) | 1.00000 | 0.0328266 | ||||||||
\(929\) | 34.1459 | 1.12029 | 0.560145 | − | 0.828394i | \(-0.310745\pi\) | ||||
0.560145 | + | 0.828394i | \(0.310745\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.291796 | 0.00956323 | ||||||||
\(932\) | −11.2361 | −0.368050 | ||||||||
\(933\) | −13.2016 | −0.432202 | ||||||||
\(934\) | −34.7984 | −1.13864 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.09017 | 0.0356333 | ||||||||
\(937\) | 44.0689 | 1.43967 | 0.719834 | − | 0.694146i | \(-0.244218\pi\) | ||||
0.719834 | + | 0.694146i | \(0.244218\pi\) | |||||||
\(938\) | 23.4164 | 0.764573 | ||||||||
\(939\) | −4.87539 | −0.159102 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.7082 | −0.707667 | −0.353834 | − | 0.935308i | \(-0.615122\pi\) | ||||
−0.353834 | + | 0.935308i | \(0.615122\pi\) | |||||||
\(942\) | −3.70820 | −0.120820 | ||||||||
\(943\) | 37.4164 | 1.21845 | ||||||||
\(944\) | 2.85410 | 0.0928931 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.76393 | −0.219914 | ||||||||
\(947\) | 60.1591 | 1.95491 | 0.977453 | − | 0.211152i | \(-0.0677214\pi\) | ||||
0.977453 | + | 0.211152i | \(0.0677214\pi\) | |||||||
\(948\) | 2.50658 | 0.0814099 | ||||||||
\(949\) | −2.12461 | −0.0689678 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.70820 | −0.249956 | ||||||||
\(952\) | −8.85410 | −0.286963 | ||||||||
\(953\) | −2.83282 | −0.0917639 | −0.0458820 | − | 0.998947i | \(-0.514610\pi\) | ||||
−0.0458820 | + | 0.998947i | \(0.514610\pi\) | |||||||
\(954\) | 26.7771 | 0.866940 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.70820 | 0.184617 | ||||||||
\(957\) | −0.763932 | −0.0246944 | ||||||||
\(958\) | 18.9787 | 0.613174 | ||||||||
\(959\) | −12.7082 | −0.410369 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.1459 | −0.520835 | ||||||||
\(962\) | −3.41641 | −0.110149 | ||||||||
\(963\) | 40.4721 | 1.30420 | ||||||||
\(964\) | −8.85410 | −0.285171 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.85410 | −0.156178 | ||||||||
\(967\) | 33.7082 | 1.08398 | 0.541991 | − | 0.840384i | \(-0.317671\pi\) | ||||
0.541991 | + | 0.840384i | \(0.317671\pi\) | |||||||
\(968\) | 7.00000 | 0.224989 | ||||||||
\(969\) | −2.58359 | −0.0829969 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.70820 | 0.0548189 | 0.0274094 | − | 0.999624i | \(-0.491274\pi\) | ||||
0.0274094 | + | 0.999624i | \(0.491274\pi\) | |||||||
\(972\) | 9.65248 | 0.309603 | ||||||||
\(973\) | −14.5623 | −0.466846 | ||||||||
\(974\) | −38.5623 | −1.23562 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.8541 | −0.347431 | ||||||||
\(977\) | −33.0557 | −1.05755 | −0.528773 | − | 0.848763i | \(-0.677348\pi\) | ||||
−0.528773 | + | 0.848763i | \(0.677348\pi\) | |||||||
\(978\) | −2.83282 | −0.0905835 | ||||||||
\(979\) | 4.00000 | 0.127841 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −55.4164 | −1.76931 | ||||||||
\(982\) | 6.29180 | 0.200779 | ||||||||
\(983\) | −3.59675 | −0.114718 | −0.0573592 | − | 0.998354i | \(-0.518268\pi\) | ||||
−0.0573592 | + | 0.998354i | \(0.518268\pi\) | |||||||
\(984\) | −2.94427 | −0.0938600 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.38197 | 0.107704 | ||||||||
\(987\) | 1.52786 | 0.0486324 | ||||||||
\(988\) | −0.763932 | −0.0243039 | ||||||||
\(989\) | 16.4164 | 0.522011 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.4164 | −1.31564 | −0.657818 | − | 0.753177i | \(-0.728520\pi\) | ||||
−0.657818 | + | 0.753177i | \(0.728520\pi\) | |||||||
\(992\) | 3.85410 | 0.122368 | ||||||||
\(993\) | 10.3607 | 0.328786 | ||||||||
\(994\) | 14.9443 | 0.474004 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 5.70820 | 0.180871 | ||||||||
\(997\) | 17.1246 | 0.542342 | 0.271171 | − | 0.962531i | \(-0.412589\pi\) | ||||
0.271171 | + | 0.962531i | \(0.412589\pi\) | |||||||
\(998\) | −28.5623 | −0.904124 | ||||||||
\(999\) | −20.0000 | −0.632772 |
(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 | 1450.2.a.k.1.1 | 2 | ||
5.2 | odd | 4 | 290.2.b.a.59.2 | ✓ | 4 | ||
5.3 | odd | 4 | 290.2.b.a.59.3 | yes | 4 | ||
5.4 | even | 2 | 1450.2.a.l.1.2 | 2 | |||
15.2 | even | 4 | 2610.2.e.e.2089.3 | 4 | |||
15.8 | even | 4 | 2610.2.e.e.2089.2 | 4 | |||
20.3 | even | 4 | 2320.2.d.d.929.2 | 4 | |||
20.7 | even | 4 | 2320.2.d.d.929.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
290.2.b.a.59.2 | ✓ | 4 | 5.2 | odd | 4 | ||
290.2.b.a.59.3 | yes | 4 | 5.3 | odd | 4 | ||
1450.2.a.k.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1450.2.a.l.1.2 | 2 | 5.4 | even | 2 | |||
2320.2.d.d.929.2 | 4 | 20.3 | even | 4 | |||
2320.2.d.d.929.3 | 4 | 20.7 | even | 4 | |||
2610.2.e.e.2089.2 | 4 | 15.8 | even | 4 | |||
2610.2.e.e.2089.3 | 4 | 15.2 | even | 4 |