Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5586,2,Mod(1,5586)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5586, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5586.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5586.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: | \(44.6044345691\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.404.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 798) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.86620\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5586.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.34889 | −1.05046 | −0.525229 | − | 0.850961i | \(-0.676020\pi\) | ||||
−0.525229 | + | 0.850961i | \(0.676020\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.34889 | 0.742786 | ||||||||
\(11\) | −2.21509 | −0.667876 | −0.333938 | − | 0.942595i | \(-0.608378\pi\) | ||||
−0.333938 | + | 0.942595i | \(0.608378\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −5.73240 | −1.58988 | −0.794940 | − | 0.606688i | \(-0.792498\pi\) | ||||
−0.794940 | + | 0.606688i | \(0.792498\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.34889 | −0.606482 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.34889 | 1.29730 | 0.648649 | − | 0.761088i | \(-0.275334\pi\) | ||||
0.648649 | + | 0.761088i | \(0.275334\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −2.34889 | −0.525229 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.21509 | 0.472259 | ||||||||
\(23\) | 4.83159 | 1.00746 | 0.503728 | − | 0.863862i | \(-0.331961\pi\) | ||||
0.503728 | + | 0.863862i | \(0.331961\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0.517304 | 0.103461 | ||||||||
\(26\) | 5.73240 | 1.12422 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.24970 | 0.603454 | 0.301727 | − | 0.953394i | \(-0.402437\pi\) | ||||
0.301727 | + | 0.953394i | \(0.402437\pi\) | |||||||
\(30\) | 2.34889 | 0.428847 | ||||||||
\(31\) | 9.76700 | 1.75421 | 0.877103 | − | 0.480302i | \(-0.159473\pi\) | ||||
0.877103 | + | 0.480302i | \(0.159473\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.21509 | −0.385598 | ||||||||
\(34\) | −5.34889 | −0.917328 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −8.11590 | −1.33425 | −0.667123 | − | 0.744948i | \(-0.732474\pi\) | ||||
−0.667123 | + | 0.744948i | \(0.732474\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | −5.73240 | −0.917918 | ||||||||
\(40\) | 2.34889 | 0.371393 | ||||||||
\(41\) | −1.86620 | −0.291451 | −0.145726 | − | 0.989325i | \(-0.546552\pi\) | ||||
−0.145726 | + | 0.989325i | \(0.546552\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.08129 | −1.38488 | −0.692442 | − | 0.721474i | \(-0.743465\pi\) | ||||
−0.692442 | + | 0.721474i | \(0.743465\pi\) | |||||||
\(44\) | −2.21509 | −0.333938 | ||||||||
\(45\) | −2.34889 | −0.350152 | ||||||||
\(46\) | −4.83159 | −0.712379 | ||||||||
\(47\) | −1.03461 | −0.150913 | −0.0754566 | − | 0.997149i | \(-0.524041\pi\) | ||||
−0.0754566 | + | 0.997149i | \(0.524041\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.517304 | −0.0731578 | ||||||||
\(51\) | 5.34889 | 0.748995 | ||||||||
\(52\) | −5.73240 | −0.794940 | ||||||||
\(53\) | −4.73240 | −0.650045 | −0.325022 | − | 0.945706i | \(-0.605372\pi\) | ||||
−0.325022 | + | 0.945706i | \(0.605372\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 5.20302 | 0.701575 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | −3.24970 | −0.426707 | ||||||||
\(59\) | −9.63320 | −1.25414 | −0.627068 | − | 0.778964i | \(-0.715745\pi\) | ||||
−0.627068 | + | 0.778964i | \(0.715745\pi\) | |||||||
\(60\) | −2.34889 | −0.303241 | ||||||||
\(61\) | 3.30221 | 0.422805 | 0.211402 | − | 0.977399i | \(-0.432197\pi\) | ||||
0.211402 | + | 0.977399i | \(0.432197\pi\) | |||||||
\(62\) | −9.76700 | −1.24041 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 13.4648 | 1.67010 | ||||||||
\(66\) | 2.21509 | 0.272659 | ||||||||
\(67\) | −10.6978 | −1.30694 | −0.653471 | − | 0.756951i | \(-0.726688\pi\) | ||||
−0.653471 | + | 0.756951i | \(0.726688\pi\) | |||||||
\(68\) | 5.34889 | 0.648649 | ||||||||
\(69\) | 4.83159 | 0.581655 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.34889 | −0.634797 | −0.317398 | − | 0.948292i | \(-0.602809\pi\) | ||||
−0.317398 | + | 0.948292i | \(0.602809\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −13.9821 | −1.63648 | −0.818240 | − | 0.574876i | \(-0.805050\pi\) | ||||
−0.818240 | + | 0.574876i | \(0.805050\pi\) | |||||||
\(74\) | 8.11590 | 0.943454 | ||||||||
\(75\) | 0.517304 | 0.0597331 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.73240 | 0.649066 | ||||||||
\(79\) | 1.58652 | 0.178497 | 0.0892487 | − | 0.996009i | \(-0.471553\pi\) | ||||
0.0892487 | + | 0.996009i | \(0.471553\pi\) | |||||||
\(80\) | −2.34889 | −0.262614 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.86620 | 0.206087 | ||||||||
\(83\) | −2.30221 | −0.252701 | −0.126350 | − | 0.991986i | \(-0.540326\pi\) | ||||
−0.126350 | + | 0.991986i | \(0.540326\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.5640 | −1.36276 | ||||||||
\(86\) | 9.08129 | 0.979261 | ||||||||
\(87\) | 3.24970 | 0.348404 | ||||||||
\(88\) | 2.21509 | 0.236130 | ||||||||
\(89\) | 17.3310 | 1.83708 | 0.918541 | − | 0.395326i | \(-0.129369\pi\) | ||||
0.918541 | + | 0.395326i | \(0.129369\pi\) | |||||||
\(90\) | 2.34889 | 0.247595 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.83159 | 0.503728 | ||||||||
\(93\) | 9.76700 | 1.01279 | ||||||||
\(94\) | 1.03461 | 0.106712 | ||||||||
\(95\) | −2.34889 | −0.240991 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 8.33099 | 0.845884 | 0.422942 | − | 0.906157i | \(-0.360997\pi\) | ||||
0.422942 | + | 0.906157i | \(0.360997\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.21509 | −0.222625 | ||||||||
\(100\) | 0.517304 | 0.0517304 | ||||||||
\(101\) | 14.7670 | 1.46937 | 0.734686 | − | 0.678407i | \(-0.237330\pi\) | ||||
0.734686 | + | 0.678407i | \(0.237330\pi\) | |||||||
\(102\) | −5.34889 | −0.529619 | ||||||||
\(103\) | 16.6107 | 1.63670 | 0.818349 | − | 0.574722i | \(-0.194890\pi\) | ||||
0.818349 | + | 0.574722i | \(0.194890\pi\) | |||||||
\(104\) | 5.73240 | 0.562108 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.73240 | 0.459651 | ||||||||
\(107\) | 0.884101 | 0.0854693 | 0.0427346 | − | 0.999086i | \(-0.486393\pi\) | ||||
0.0427346 | + | 0.999086i | \(0.486393\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 12.4769 | 1.19507 | 0.597534 | − | 0.801844i | \(-0.296147\pi\) | ||||
0.597534 | + | 0.801844i | \(0.296147\pi\) | |||||||
\(110\) | −5.20302 | −0.496088 | ||||||||
\(111\) | −8.11590 | −0.770327 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.9700 | 1.03197 | 0.515986 | − | 0.856597i | \(-0.327425\pi\) | ||||
0.515986 | + | 0.856597i | \(0.327425\pi\) | |||||||
\(114\) | −1.00000 | −0.0936586 | ||||||||
\(115\) | −11.3489 | −1.05829 | ||||||||
\(116\) | 3.24970 | 0.301727 | ||||||||
\(117\) | −5.73240 | −0.529960 | ||||||||
\(118\) | 9.63320 | 0.886808 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.34889 | 0.214424 | ||||||||
\(121\) | −6.09337 | −0.553942 | ||||||||
\(122\) | −3.30221 | −0.298968 | ||||||||
\(123\) | −1.86620 | −0.168269 | ||||||||
\(124\) | 9.76700 | 0.877103 | ||||||||
\(125\) | 10.5294 | 0.941776 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.10382 | −0.541627 | −0.270813 | − | 0.962632i | \(-0.587293\pi\) | ||||
−0.270813 | + | 0.962632i | \(0.587293\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −9.08129 | −0.799563 | ||||||||
\(130\) | −13.4648 | −1.18094 | ||||||||
\(131\) | 16.1280 | 1.40911 | 0.704554 | − | 0.709651i | \(-0.251147\pi\) | ||||
0.704554 | + | 0.709651i | \(0.251147\pi\) | |||||||
\(132\) | −2.21509 | −0.192799 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 10.6978 | 0.924148 | ||||||||
\(135\) | −2.34889 | −0.202161 | ||||||||
\(136\) | −5.34889 | −0.458664 | ||||||||
\(137\) | 4.00000 | 0.341743 | 0.170872 | − | 0.985293i | \(-0.445342\pi\) | ||||
0.170872 | + | 0.985293i | \(0.445342\pi\) | |||||||
\(138\) | −4.83159 | −0.411292 | ||||||||
\(139\) | 17.1505 | 1.45469 | 0.727344 | − | 0.686274i | \(-0.240755\pi\) | ||||
0.727344 | + | 0.686274i | \(0.240755\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.03461 | −0.0871297 | ||||||||
\(142\) | 5.34889 | 0.448869 | ||||||||
\(143\) | 12.6978 | 1.06184 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −7.63320 | −0.633903 | ||||||||
\(146\) | 13.9821 | 1.15717 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.11590 | −0.667123 | ||||||||
\(149\) | 16.6978 | 1.36794 | 0.683968 | − | 0.729512i | \(-0.260253\pi\) | ||||
0.683968 | + | 0.729512i | \(0.260253\pi\) | |||||||
\(150\) | −0.517304 | −0.0422377 | ||||||||
\(151\) | −6.56982 | −0.534644 | −0.267322 | − | 0.963607i | \(-0.586139\pi\) | ||||
−0.267322 | + | 0.963607i | \(0.586139\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 5.34889 | 0.432432 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −22.9417 | −1.84272 | ||||||||
\(156\) | −5.73240 | −0.458959 | ||||||||
\(157\) | 2.36097 | 0.188426 | 0.0942129 | − | 0.995552i | \(-0.469967\pi\) | ||||
0.0942129 | + | 0.995552i | \(0.469967\pi\) | |||||||
\(158\) | −1.58652 | −0.126217 | ||||||||
\(159\) | −4.73240 | −0.375303 | ||||||||
\(160\) | 2.34889 | 0.185696 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 9.80161 | 0.767722 | 0.383861 | − | 0.923391i | \(-0.374594\pi\) | ||||
0.383861 | + | 0.923391i | \(0.374594\pi\) | |||||||
\(164\) | −1.86620 | −0.145726 | ||||||||
\(165\) | 5.20302 | 0.405054 | ||||||||
\(166\) | 2.30221 | 0.178686 | ||||||||
\(167\) | 4.72032 | 0.365269 | 0.182635 | − | 0.983181i | \(-0.441537\pi\) | ||||
0.182635 | + | 0.983181i | \(0.441537\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.8604 | 1.52772 | ||||||||
\(170\) | 12.5640 | 0.963614 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | −9.08129 | −0.692442 | ||||||||
\(173\) | −10.3431 | −0.786369 | −0.393184 | − | 0.919460i | \(-0.628627\pi\) | ||||
−0.393184 | + | 0.919460i | \(0.628627\pi\) | |||||||
\(174\) | −3.24970 | −0.246359 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.21509 | −0.166969 | ||||||||
\(177\) | −9.63320 | −0.724076 | ||||||||
\(178\) | −17.3310 | −1.29901 | ||||||||
\(179\) | 16.8604 | 1.26020 | 0.630102 | − | 0.776513i | \(-0.283013\pi\) | ||||
0.630102 | + | 0.776513i | \(0.283013\pi\) | |||||||
\(180\) | −2.34889 | −0.175076 | ||||||||
\(181\) | −24.6620 | −1.83311 | −0.916555 | − | 0.399908i | \(-0.869042\pi\) | ||||
−0.916555 | + | 0.399908i | \(0.869042\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.30221 | 0.244107 | ||||||||
\(184\) | −4.83159 | −0.356190 | ||||||||
\(185\) | 19.0634 | 1.40157 | ||||||||
\(186\) | −9.76700 | −0.716152 | ||||||||
\(187\) | −11.8483 | −0.866433 | ||||||||
\(188\) | −1.03461 | −0.0754566 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.34889 | 0.170407 | ||||||||
\(191\) | 18.6978 | 1.35292 | 0.676462 | − | 0.736477i | \(-0.263512\pi\) | ||||
0.676462 | + | 0.736477i | \(0.263512\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 4.77908 | 0.344006 | 0.172003 | − | 0.985096i | \(-0.444976\pi\) | ||||
0.172003 | + | 0.985096i | \(0.444976\pi\) | |||||||
\(194\) | −8.33099 | −0.598130 | ||||||||
\(195\) | 13.4648 | 0.964234 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.87827 | 0.347563 | 0.173781 | − | 0.984784i | \(-0.444401\pi\) | ||||
0.173781 | + | 0.984784i | \(0.444401\pi\) | |||||||
\(198\) | 2.21509 | 0.157420 | ||||||||
\(199\) | 2.06922 | 0.146683 | 0.0733414 | − | 0.997307i | \(-0.476634\pi\) | ||||
0.0733414 | + | 0.997307i | \(0.476634\pi\) | |||||||
\(200\) | −0.517304 | −0.0365789 | ||||||||
\(201\) | −10.6978 | −0.754564 | ||||||||
\(202\) | −14.7670 | −1.03900 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 5.34889 | 0.374498 | ||||||||
\(205\) | 4.38350 | 0.306157 | ||||||||
\(206\) | −16.6107 | −1.15732 | ||||||||
\(207\) | 4.83159 | 0.335819 | ||||||||
\(208\) | −5.73240 | −0.397470 | ||||||||
\(209\) | −2.21509 | −0.153221 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.06459 | −0.555189 | −0.277594 | − | 0.960698i | \(-0.589537\pi\) | ||||
−0.277594 | + | 0.960698i | \(0.589537\pi\) | |||||||
\(212\) | −4.73240 | −0.325022 | ||||||||
\(213\) | −5.34889 | −0.366500 | ||||||||
\(214\) | −0.884101 | −0.0604359 | ||||||||
\(215\) | 21.3310 | 1.45476 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −12.4769 | −0.845040 | ||||||||
\(219\) | −13.9821 | −0.944823 | ||||||||
\(220\) | 5.20302 | 0.350787 | ||||||||
\(221\) | −30.6620 | −2.06255 | ||||||||
\(222\) | 8.11590 | 0.544703 | ||||||||
\(223\) | −3.31892 | −0.222251 | −0.111126 | − | 0.993806i | \(-0.535446\pi\) | ||||
−0.111126 | + | 0.993806i | \(0.535446\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.517304 | 0.0344869 | ||||||||
\(226\) | −10.9700 | −0.729715 | ||||||||
\(227\) | −3.58189 | −0.237738 | −0.118869 | − | 0.992910i | \(-0.537927\pi\) | ||||
−0.118869 | + | 0.992910i | \(0.537927\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | −7.39558 | −0.488713 | −0.244357 | − | 0.969685i | \(-0.578577\pi\) | ||||
−0.244357 | + | 0.969685i | \(0.578577\pi\) | |||||||
\(230\) | 11.3489 | 0.748324 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.24970 | −0.213353 | ||||||||
\(233\) | 26.0934 | 1.70943 | 0.854717 | − | 0.519095i | \(-0.173731\pi\) | ||||
0.854717 | + | 0.519095i | \(0.173731\pi\) | |||||||
\(234\) | 5.73240 | 0.374738 | ||||||||
\(235\) | 2.43018 | 0.158528 | ||||||||
\(236\) | −9.63320 | −0.627068 | ||||||||
\(237\) | 1.58652 | 0.103056 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.89498 | −0.122576 | −0.0612880 | − | 0.998120i | \(-0.519521\pi\) | ||||
−0.0612880 | + | 0.998120i | \(0.519521\pi\) | |||||||
\(240\) | −2.34889 | −0.151620 | ||||||||
\(241\) | 4.36680 | 0.281290 | 0.140645 | − | 0.990060i | \(-0.455082\pi\) | ||||
0.140645 | + | 0.990060i | \(0.455082\pi\) | |||||||
\(242\) | 6.09337 | 0.391696 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 3.30221 | 0.211402 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.86620 | 0.118984 | ||||||||
\(247\) | −5.73240 | −0.364744 | ||||||||
\(248\) | −9.76700 | −0.620205 | ||||||||
\(249\) | −2.30221 | −0.145897 | ||||||||
\(250\) | −10.5294 | −0.665936 | ||||||||
\(251\) | −4.98210 | −0.314467 | −0.157234 | − | 0.987561i | \(-0.550258\pi\) | ||||
−0.157234 | + | 0.987561i | \(0.550258\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.7024 | −0.672855 | ||||||||
\(254\) | 6.10382 | 0.382988 | ||||||||
\(255\) | −12.5640 | −0.786787 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.4648 | 0.839911 | 0.419955 | − | 0.907545i | \(-0.362046\pi\) | ||||
0.419955 | + | 0.907545i | \(0.362046\pi\) | |||||||
\(258\) | 9.08129 | 0.565376 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 13.4648 | 0.835051 | ||||||||
\(261\) | 3.24970 | 0.201151 | ||||||||
\(262\) | −16.1280 | −0.996390 | ||||||||
\(263\) | 24.2272 | 1.49391 | 0.746956 | − | 0.664874i | \(-0.231515\pi\) | ||||
0.746956 | + | 0.664874i | \(0.231515\pi\) | |||||||
\(264\) | 2.21509 | 0.136330 | ||||||||
\(265\) | 11.1159 | 0.682844 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.3310 | 1.06064 | ||||||||
\(268\) | −10.6978 | −0.653471 | ||||||||
\(269\) | 18.3777 | 1.12051 | 0.560253 | − | 0.828321i | \(-0.310704\pi\) | ||||
0.560253 | + | 0.828321i | \(0.310704\pi\) | |||||||
\(270\) | 2.34889 | 0.142949 | ||||||||
\(271\) | 24.4181 | 1.48329 | 0.741647 | − | 0.670790i | \(-0.234045\pi\) | ||||
0.741647 | + | 0.670790i | \(0.234045\pi\) | |||||||
\(272\) | 5.34889 | 0.324324 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.00000 | −0.241649 | ||||||||
\(275\) | −1.14588 | −0.0690989 | ||||||||
\(276\) | 4.83159 | 0.290828 | ||||||||
\(277\) | −5.33099 | −0.320308 | −0.160154 | − | 0.987092i | \(-0.551199\pi\) | ||||
−0.160154 | + | 0.987092i | \(0.551199\pi\) | |||||||
\(278\) | −17.1505 | −1.02862 | ||||||||
\(279\) | 9.76700 | 0.584735 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.56982 | −0.212957 | −0.106479 | − | 0.994315i | \(-0.533958\pi\) | ||||
−0.106479 | + | 0.994315i | \(0.533958\pi\) | |||||||
\(282\) | 1.03461 | 0.0616100 | ||||||||
\(283\) | 12.0467 | 0.716101 | 0.358050 | − | 0.933702i | \(-0.383442\pi\) | ||||
0.358050 | + | 0.933702i | \(0.383442\pi\) | |||||||
\(284\) | −5.34889 | −0.317398 | ||||||||
\(285\) | −2.34889 | −0.139136 | ||||||||
\(286\) | −12.6978 | −0.750836 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 11.6107 | 0.682981 | ||||||||
\(290\) | 7.63320 | 0.448237 | ||||||||
\(291\) | 8.33099 | 0.488371 | ||||||||
\(292\) | −13.9821 | −0.818240 | ||||||||
\(293\) | 24.5761 | 1.43575 | 0.717874 | − | 0.696173i | \(-0.245115\pi\) | ||||
0.717874 | + | 0.696173i | \(0.245115\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 22.6274 | 1.31742 | ||||||||
\(296\) | 8.11590 | 0.471727 | ||||||||
\(297\) | −2.21509 | −0.128533 | ||||||||
\(298\) | −16.6978 | −0.967277 | ||||||||
\(299\) | −27.6966 | −1.60174 | ||||||||
\(300\) | 0.517304 | 0.0298666 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6.56982 | 0.378050 | ||||||||
\(303\) | 14.7670 | 0.848342 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −7.75655 | −0.444139 | ||||||||
\(306\) | −5.34889 | −0.305776 | ||||||||
\(307\) | 29.6227 | 1.69066 | 0.845330 | − | 0.534245i | \(-0.179404\pi\) | ||||
0.845330 | + | 0.534245i | \(0.179404\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.6107 | 0.944948 | ||||||||
\(310\) | 22.9417 | 1.30300 | ||||||||
\(311\) | 21.8903 | 1.24129 | 0.620644 | − | 0.784093i | \(-0.286871\pi\) | ||||
0.620644 | + | 0.784093i | \(0.286871\pi\) | |||||||
\(312\) | 5.73240 | 0.324533 | ||||||||
\(313\) | 27.7491 | 1.56847 | 0.784236 | − | 0.620463i | \(-0.213055\pi\) | ||||
0.784236 | + | 0.620463i | \(0.213055\pi\) | |||||||
\(314\) | −2.36097 | −0.133237 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.58652 | 0.0892487 | ||||||||
\(317\) | −11.9296 | −0.670032 | −0.335016 | − | 0.942212i | \(-0.608742\pi\) | ||||
−0.335016 | + | 0.942212i | \(0.608742\pi\) | |||||||
\(318\) | 4.73240 | 0.265380 | ||||||||
\(319\) | −7.19839 | −0.403032 | ||||||||
\(320\) | −2.34889 | −0.131307 | ||||||||
\(321\) | 0.884101 | 0.0493457 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.34889 | 0.297620 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −2.96539 | −0.164490 | ||||||||
\(326\) | −9.80161 | −0.542861 | ||||||||
\(327\) | 12.4769 | 0.689972 | ||||||||
\(328\) | 1.86620 | 0.103044 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −5.20302 | −0.286417 | ||||||||
\(331\) | −25.6678 | −1.41083 | −0.705415 | − | 0.708794i | \(-0.749239\pi\) | ||||
−0.705415 | + | 0.708794i | \(0.749239\pi\) | |||||||
\(332\) | −2.30221 | −0.126350 | ||||||||
\(333\) | −8.11590 | −0.444749 | ||||||||
\(334\) | −4.72032 | −0.258285 | ||||||||
\(335\) | 25.1280 | 1.37289 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.7266 | 0.747734 | 0.373867 | − | 0.927482i | \(-0.378032\pi\) | ||||
0.373867 | + | 0.927482i | \(0.378032\pi\) | |||||||
\(338\) | −19.8604 | −1.08026 | ||||||||
\(339\) | 10.9700 | 0.595810 | ||||||||
\(340\) | −12.5640 | −0.681378 | ||||||||
\(341\) | −21.6348 | −1.17159 | ||||||||
\(342\) | −1.00000 | −0.0540738 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 9.08129 | 0.489630 | ||||||||
\(345\) | −11.3489 | −0.611004 | ||||||||
\(346\) | 10.3431 | 0.556047 | ||||||||
\(347\) | −12.8783 | −0.691342 | −0.345671 | − | 0.938356i | \(-0.612349\pi\) | ||||
−0.345671 | + | 0.938356i | \(0.612349\pi\) | |||||||
\(348\) | 3.24970 | 0.174202 | ||||||||
\(349\) | −2.76237 | −0.147866 | −0.0739332 | − | 0.997263i | \(-0.523555\pi\) | ||||
−0.0739332 | + | 0.997263i | \(0.523555\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.73240 | −0.305973 | ||||||||
\(352\) | 2.21509 | 0.118065 | ||||||||
\(353\) | −28.0109 | −1.49087 | −0.745434 | − | 0.666579i | \(-0.767758\pi\) | ||||
−0.745434 | + | 0.666579i | \(0.767758\pi\) | |||||||
\(354\) | 9.63320 | 0.511999 | ||||||||
\(355\) | 12.5640 | 0.666827 | ||||||||
\(356\) | 17.3310 | 0.918541 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −16.8604 | −0.891098 | ||||||||
\(359\) | −18.0000 | −0.950004 | −0.475002 | − | 0.879985i | \(-0.657553\pi\) | ||||
−0.475002 | + | 0.879985i | \(0.657553\pi\) | |||||||
\(360\) | 2.34889 | 0.123798 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 24.6620 | 1.29621 | ||||||||
\(363\) | −6.09337 | −0.319819 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 32.8425 | 1.71905 | ||||||||
\(366\) | −3.30221 | −0.172609 | ||||||||
\(367\) | −30.3131 | −1.58233 | −0.791165 | − | 0.611603i | \(-0.790525\pi\) | ||||
−0.791165 | + | 0.611603i | \(0.790525\pi\) | |||||||
\(368\) | 4.83159 | 0.251864 | ||||||||
\(369\) | −1.86620 | −0.0971504 | ||||||||
\(370\) | −19.0634 | −0.991058 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 9.76700 | 0.506396 | ||||||||
\(373\) | 18.5236 | 0.959113 | 0.479557 | − | 0.877511i | \(-0.340798\pi\) | ||||
0.479557 | + | 0.877511i | \(0.340798\pi\) | |||||||
\(374\) | 11.8483 | 0.612661 | ||||||||
\(375\) | 10.5294 | 0.543735 | ||||||||
\(376\) | 1.03461 | 0.0533558 | ||||||||
\(377\) | −18.6286 | −0.959420 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.17304 | −0.471187 | −0.235594 | − | 0.971852i | \(-0.575703\pi\) | ||||
−0.235594 | + | 0.971852i | \(0.575703\pi\) | |||||||
\(380\) | −2.34889 | −0.120496 | ||||||||
\(381\) | −6.10382 | −0.312708 | ||||||||
\(382\) | −18.6978 | −0.956662 | ||||||||
\(383\) | 6.43018 | 0.328567 | 0.164284 | − | 0.986413i | \(-0.447469\pi\) | ||||
0.164284 | + | 0.986413i | \(0.447469\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.77908 | −0.243249 | ||||||||
\(387\) | −9.08129 | −0.461628 | ||||||||
\(388\) | 8.33099 | 0.422942 | ||||||||
\(389\) | 23.9883 | 1.21626 | 0.608129 | − | 0.793838i | \(-0.291920\pi\) | ||||
0.608129 | + | 0.793838i | \(0.291920\pi\) | |||||||
\(390\) | −13.4648 | −0.681816 | ||||||||
\(391\) | 25.8437 | 1.30697 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.1280 | 0.813549 | ||||||||
\(394\) | −4.87827 | −0.245764 | ||||||||
\(395\) | −3.72657 | −0.187504 | ||||||||
\(396\) | −2.21509 | −0.111313 | ||||||||
\(397\) | 15.3598 | 0.770885 | 0.385442 | − | 0.922732i | \(-0.374049\pi\) | ||||
0.385442 | + | 0.922732i | \(0.374049\pi\) | |||||||
\(398\) | −2.06922 | −0.103720 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.517304 | 0.0258652 | ||||||||
\(401\) | −30.9988 | −1.54801 | −0.774003 | − | 0.633182i | \(-0.781749\pi\) | ||||
−0.774003 | + | 0.633182i | \(0.781749\pi\) | |||||||
\(402\) | 10.6978 | 0.533557 | ||||||||
\(403\) | −55.9883 | −2.78898 | ||||||||
\(404\) | 14.7670 | 0.734686 | ||||||||
\(405\) | −2.34889 | −0.116717 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.9775 | 0.891110 | ||||||||
\(408\) | −5.34889 | −0.264810 | ||||||||
\(409\) | 23.5189 | 1.16294 | 0.581468 | − | 0.813569i | \(-0.302479\pi\) | ||||
0.581468 | + | 0.813569i | \(0.302479\pi\) | |||||||
\(410\) | −4.38350 | −0.216486 | ||||||||
\(411\) | 4.00000 | 0.197305 | ||||||||
\(412\) | 16.6107 | 0.818349 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −4.83159 | −0.237460 | ||||||||
\(415\) | 5.40765 | 0.265451 | ||||||||
\(416\) | 5.73240 | 0.281054 | ||||||||
\(417\) | 17.1505 | 0.839864 | ||||||||
\(418\) | 2.21509 | 0.108344 | ||||||||
\(419\) | −23.5403 | −1.15002 | −0.575008 | − | 0.818148i | \(-0.695001\pi\) | ||||
−0.575008 | + | 0.818148i | \(0.695001\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.05876 | −0.441497 | −0.220748 | − | 0.975331i | \(-0.570850\pi\) | ||||
−0.220748 | + | 0.975331i | \(0.570850\pi\) | |||||||
\(422\) | 8.06459 | 0.392578 | ||||||||
\(423\) | −1.03461 | −0.0503044 | ||||||||
\(424\) | 4.73240 | 0.229825 | ||||||||
\(425\) | 2.76700 | 0.134219 | ||||||||
\(426\) | 5.34889 | 0.259155 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.884101 | 0.0427346 | ||||||||
\(429\) | 12.6978 | 0.613055 | ||||||||
\(430\) | −21.3310 | −1.02867 | ||||||||
\(431\) | 8.09175 | 0.389766 | 0.194883 | − | 0.980827i | \(-0.437567\pi\) | ||||
0.194883 | + | 0.980827i | \(0.437567\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −34.7733 | −1.67110 | −0.835548 | − | 0.549418i | \(-0.814850\pi\) | ||||
−0.835548 | + | 0.549418i | \(0.814850\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.63320 | −0.365984 | ||||||||
\(436\) | 12.4769 | 0.597534 | ||||||||
\(437\) | 4.83159 | 0.231126 | ||||||||
\(438\) | 13.9821 | 0.668090 | ||||||||
\(439\) | −15.4815 | −0.738892 | −0.369446 | − | 0.929252i | \(-0.620452\pi\) | ||||
−0.369446 | + | 0.929252i | \(0.620452\pi\) | |||||||
\(440\) | −5.20302 | −0.248044 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 30.6620 | 1.45844 | ||||||||
\(443\) | −29.9024 | −1.42071 | −0.710353 | − | 0.703845i | \(-0.751465\pi\) | ||||
−0.710353 | + | 0.703845i | \(0.751465\pi\) | |||||||
\(444\) | −8.11590 | −0.385164 | ||||||||
\(445\) | −40.7087 | −1.92978 | ||||||||
\(446\) | 3.31892 | 0.157155 | ||||||||
\(447\) | 16.6978 | 0.789778 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.36560 | 0.206025 | 0.103013 | − | 0.994680i | \(-0.467152\pi\) | ||||
0.103013 | + | 0.994680i | \(0.467152\pi\) | |||||||
\(450\) | −0.517304 | −0.0243859 | ||||||||
\(451\) | 4.13380 | 0.194653 | ||||||||
\(452\) | 10.9700 | 0.515986 | ||||||||
\(453\) | −6.56982 | −0.308677 | ||||||||
\(454\) | 3.58189 | 0.168106 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.00000 | −0.0468293 | ||||||||
\(457\) | −25.8425 | −1.20886 | −0.604430 | − | 0.796658i | \(-0.706599\pi\) | ||||
−0.604430 | + | 0.796658i | \(0.706599\pi\) | |||||||
\(458\) | 7.39558 | 0.345573 | ||||||||
\(459\) | 5.34889 | 0.249665 | ||||||||
\(460\) | −11.3489 | −0.529145 | ||||||||
\(461\) | −24.7912 | −1.15464 | −0.577320 | − | 0.816518i | \(-0.695901\pi\) | ||||
−0.577320 | + | 0.816518i | \(0.695901\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.9642 | 0.556023 | 0.278012 | − | 0.960578i | \(-0.410325\pi\) | ||||
0.278012 | + | 0.960578i | \(0.410325\pi\) | |||||||
\(464\) | 3.24970 | 0.150864 | ||||||||
\(465\) | −22.9417 | −1.06389 | ||||||||
\(466\) | −26.0934 | −1.20875 | ||||||||
\(467\) | 13.5068 | 0.625022 | 0.312511 | − | 0.949914i | \(-0.398830\pi\) | ||||
0.312511 | + | 0.949914i | \(0.398830\pi\) | |||||||
\(468\) | −5.73240 | −0.264980 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2.43018 | −0.112096 | ||||||||
\(471\) | 2.36097 | 0.108788 | ||||||||
\(472\) | 9.63320 | 0.443404 | ||||||||
\(473\) | 20.1159 | 0.924930 | ||||||||
\(474\) | −1.58652 | −0.0728713 | ||||||||
\(475\) | 0.517304 | 0.0237355 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.73240 | −0.216682 | ||||||||
\(478\) | 1.89498 | 0.0866743 | ||||||||
\(479\) | −8.59277 | −0.392614 | −0.196307 | − | 0.980543i | \(-0.562895\pi\) | ||||
−0.196307 | + | 0.980543i | \(0.562895\pi\) | |||||||
\(480\) | 2.34889 | 0.107212 | ||||||||
\(481\) | 46.5236 | 2.12129 | ||||||||
\(482\) | −4.36680 | −0.198902 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.09337 | −0.276971 | ||||||||
\(485\) | −19.5686 | −0.888565 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −18.4648 | −0.836720 | −0.418360 | − | 0.908281i | \(-0.637395\pi\) | ||||
−0.418360 | + | 0.908281i | \(0.637395\pi\) | |||||||
\(488\) | −3.30221 | −0.149484 | ||||||||
\(489\) | 9.80161 | 0.443244 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.7912 | −1.16394 | −0.581969 | − | 0.813211i | \(-0.697718\pi\) | ||||
−0.581969 | + | 0.813211i | \(0.697718\pi\) | |||||||
\(492\) | −1.86620 | −0.0841347 | ||||||||
\(493\) | 17.3823 | 0.782860 | ||||||||
\(494\) | 5.73240 | 0.257913 | ||||||||
\(495\) | 5.20302 | 0.233858 | ||||||||
\(496\) | 9.76700 | 0.438551 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.30221 | 0.103165 | ||||||||
\(499\) | −10.3610 | −0.463821 | −0.231910 | − | 0.972737i | \(-0.574498\pi\) | ||||
−0.231910 | + | 0.972737i | \(0.574498\pi\) | |||||||
\(500\) | 10.5294 | 0.470888 | ||||||||
\(501\) | 4.72032 | 0.210888 | ||||||||
\(502\) | 4.98210 | 0.222362 | ||||||||
\(503\) | −10.5881 | −0.472102 | −0.236051 | − | 0.971741i | \(-0.575853\pi\) | ||||
−0.236051 | + | 0.971741i | \(0.575853\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −34.6861 | −1.54351 | ||||||||
\(506\) | 10.7024 | 0.475781 | ||||||||
\(507\) | 19.8604 | 0.882030 | ||||||||
\(508\) | −6.10382 | −0.270813 | ||||||||
\(509\) | 13.2497 | 0.587283 | 0.293641 | − | 0.955916i | \(-0.405133\pi\) | ||||
0.293641 | + | 0.955916i | \(0.405133\pi\) | |||||||
\(510\) | 12.5640 | 0.556343 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | −13.4648 | −0.593907 | ||||||||
\(515\) | −39.0167 | −1.71928 | ||||||||
\(516\) | −9.08129 | −0.399782 | ||||||||
\(517\) | 2.29175 | 0.100791 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.3431 | −0.454010 | ||||||||
\(520\) | −13.4648 | −0.590470 | ||||||||
\(521\) | 28.0934 | 1.23079 | 0.615396 | − | 0.788218i | \(-0.288996\pi\) | ||||
0.615396 | + | 0.788218i | \(0.288996\pi\) | |||||||
\(522\) | −3.24970 | −0.142236 | ||||||||
\(523\) | 36.1672 | 1.58148 | 0.790741 | − | 0.612151i | \(-0.209696\pi\) | ||||
0.790741 | + | 0.612151i | \(0.209696\pi\) | |||||||
\(524\) | 16.1280 | 0.704554 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.2272 | −1.05635 | ||||||||
\(527\) | 52.2427 | 2.27573 | ||||||||
\(528\) | −2.21509 | −0.0963995 | ||||||||
\(529\) | 0.344264 | 0.0149680 | ||||||||
\(530\) | −11.1159 | −0.482844 | ||||||||
\(531\) | −9.63320 | −0.418045 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.6978 | 0.463373 | ||||||||
\(534\) | −17.3310 | −0.749985 | ||||||||
\(535\) | −2.07666 | −0.0897818 | ||||||||
\(536\) | 10.6978 | 0.462074 | ||||||||
\(537\) | 16.8604 | 0.727579 | ||||||||
\(538\) | −18.3777 | −0.792318 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.34889 | −0.101080 | ||||||||
\(541\) | 27.5986 | 1.18656 | 0.593278 | − | 0.804998i | \(-0.297833\pi\) | ||||
0.593278 | + | 0.804998i | \(0.297833\pi\) | |||||||
\(542\) | −24.4181 | −1.04885 | ||||||||
\(543\) | −24.6620 | −1.05835 | ||||||||
\(544\) | −5.34889 | −0.229332 | ||||||||
\(545\) | −29.3068 | −1.25537 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.3551 | −1.16962 | −0.584811 | − | 0.811170i | \(-0.698831\pi\) | ||||
−0.584811 | + | 0.811170i | \(0.698831\pi\) | |||||||
\(548\) | 4.00000 | 0.170872 | ||||||||
\(549\) | 3.30221 | 0.140935 | ||||||||
\(550\) | 1.14588 | 0.0488603 | ||||||||
\(551\) | 3.24970 | 0.138442 | ||||||||
\(552\) | −4.83159 | −0.205646 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 5.33099 | 0.226492 | ||||||||
\(555\) | 19.0634 | 0.809196 | ||||||||
\(556\) | 17.1505 | 0.727344 | ||||||||
\(557\) | 28.4694 | 1.20629 | 0.603144 | − | 0.797632i | \(-0.293914\pi\) | ||||
0.603144 | + | 0.797632i | \(0.293914\pi\) | |||||||
\(558\) | −9.76700 | −0.413470 | ||||||||
\(559\) | 52.0576 | 2.20180 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.8483 | −0.500235 | ||||||||
\(562\) | 3.56982 | 0.150584 | ||||||||
\(563\) | −10.1233 | −0.426648 | −0.213324 | − | 0.976982i | \(-0.568429\pi\) | ||||
−0.213324 | + | 0.976982i | \(0.568429\pi\) | |||||||
\(564\) | −1.03461 | −0.0435649 | ||||||||
\(565\) | −25.7674 | −1.08404 | ||||||||
\(566\) | −12.0467 | −0.506360 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.34889 | 0.224435 | ||||||||
\(569\) | 2.23180 | 0.0935618 | 0.0467809 | − | 0.998905i | \(-0.485104\pi\) | ||||
0.0467809 | + | 0.998905i | \(0.485104\pi\) | |||||||
\(570\) | 2.34889 | 0.0983844 | ||||||||
\(571\) | −7.08129 | −0.296343 | −0.148171 | − | 0.988962i | \(-0.547339\pi\) | ||||
−0.148171 | + | 0.988962i | \(0.547339\pi\) | |||||||
\(572\) | 12.6978 | 0.530921 | ||||||||
\(573\) | 18.6978 | 0.781111 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.49940 | 0.104232 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 6.53401 | 0.272014 | 0.136007 | − | 0.990708i | \(-0.456573\pi\) | ||||
0.136007 | + | 0.990708i | \(0.456573\pi\) | |||||||
\(578\) | −11.6107 | −0.482940 | ||||||||
\(579\) | 4.77908 | 0.198612 | ||||||||
\(580\) | −7.63320 | −0.316951 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −8.33099 | −0.345331 | ||||||||
\(583\) | 10.4827 | 0.434149 | ||||||||
\(584\) | 13.9821 | 0.578583 | ||||||||
\(585\) | 13.4648 | 0.556701 | ||||||||
\(586\) | −24.5761 | −1.01523 | ||||||||
\(587\) | 24.8529 | 1.02579 | 0.512895 | − | 0.858451i | \(-0.328573\pi\) | ||||
0.512895 | + | 0.858451i | \(0.328573\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.76700 | 0.402442 | ||||||||
\(590\) | −22.6274 | −0.931554 | ||||||||
\(591\) | 4.87827 | 0.200665 | ||||||||
\(592\) | −8.11590 | −0.333561 | ||||||||
\(593\) | −32.0576 | −1.31645 | −0.658223 | − | 0.752823i | \(-0.728692\pi\) | ||||
−0.658223 | + | 0.752823i | \(0.728692\pi\) | |||||||
\(594\) | 2.21509 | 0.0908863 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.6978 | 0.683968 | ||||||||
\(597\) | 2.06922 | 0.0846874 | ||||||||
\(598\) | 27.6966 | 1.13260 | ||||||||
\(599\) | 19.5565 | 0.799059 | 0.399529 | − | 0.916720i | \(-0.369174\pi\) | ||||
0.399529 | + | 0.916720i | \(0.369174\pi\) | |||||||
\(600\) | −0.517304 | −0.0211188 | ||||||||
\(601\) | 46.9479 | 1.91505 | 0.957523 | − | 0.288358i | \(-0.0931095\pi\) | ||||
0.957523 | + | 0.288358i | \(0.0931095\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.6978 | −0.435648 | ||||||||
\(604\) | −6.56982 | −0.267322 | ||||||||
\(605\) | 14.3127 | 0.581893 | ||||||||
\(606\) | −14.7670 | −0.599869 | ||||||||
\(607\) | −4.17929 | −0.169632 | −0.0848160 | − | 0.996397i | \(-0.527030\pi\) | ||||
−0.0848160 | + | 0.996397i | \(0.527030\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.75655 | 0.314053 | ||||||||
\(611\) | 5.93078 | 0.239934 | ||||||||
\(612\) | 5.34889 | 0.216216 | ||||||||
\(613\) | 30.2606 | 1.22221 | 0.611107 | − | 0.791548i | \(-0.290725\pi\) | ||||
0.611107 | + | 0.791548i | \(0.290725\pi\) | |||||||
\(614\) | −29.6227 | −1.19548 | ||||||||
\(615\) | 4.38350 | 0.176760 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.2889 | −0.857060 | −0.428530 | − | 0.903527i | \(-0.640968\pi\) | ||||
−0.428530 | + | 0.903527i | \(0.640968\pi\) | |||||||
\(618\) | −16.6107 | −0.668179 | ||||||||
\(619\) | 7.44064 | 0.299065 | 0.149532 | − | 0.988757i | \(-0.452223\pi\) | ||||
0.149532 | + | 0.988757i | \(0.452223\pi\) | |||||||
\(620\) | −22.9417 | −0.921359 | ||||||||
\(621\) | 4.83159 | 0.193885 | ||||||||
\(622\) | −21.8903 | −0.877723 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −5.73240 | −0.229480 | ||||||||
\(625\) | −27.3189 | −1.09276 | ||||||||
\(626\) | −27.7491 | −1.10908 | ||||||||
\(627\) | −2.21509 | −0.0884623 | ||||||||
\(628\) | 2.36097 | 0.0942129 | ||||||||
\(629\) | −43.4111 | −1.73091 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.6499 | 0.981297 | 0.490649 | − | 0.871357i | \(-0.336760\pi\) | ||||
0.490649 | + | 0.871357i | \(0.336760\pi\) | |||||||
\(632\) | −1.58652 | −0.0631084 | ||||||||
\(633\) | −8.06459 | −0.320538 | ||||||||
\(634\) | 11.9296 | 0.473784 | ||||||||
\(635\) | 14.3372 | 0.568956 | ||||||||
\(636\) | −4.73240 | −0.187652 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 7.19839 | 0.284987 | ||||||||
\(639\) | −5.34889 | −0.211599 | ||||||||
\(640\) | 2.34889 | 0.0928482 | ||||||||
\(641\) | 13.4602 | 0.531644 | 0.265822 | − | 0.964022i | \(-0.414357\pi\) | ||||
0.265822 | + | 0.964022i | \(0.414357\pi\) | |||||||
\(642\) | −0.884101 | −0.0348927 | ||||||||
\(643\) | 12.6511 | 0.498911 | 0.249455 | − | 0.968386i | \(-0.419748\pi\) | ||||
0.249455 | + | 0.968386i | \(0.419748\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 21.3310 | 0.839907 | ||||||||
\(646\) | −5.34889 | −0.210449 | ||||||||
\(647\) | −8.02878 | −0.315644 | −0.157822 | − | 0.987468i | \(-0.550447\pi\) | ||||
−0.157822 | + | 0.987468i | \(0.550447\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 21.3384 | 0.837607 | ||||||||
\(650\) | 2.96539 | 0.116312 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.80161 | 0.383861 | ||||||||
\(653\) | −12.0392 | −0.471132 | −0.235566 | − | 0.971858i | \(-0.575694\pi\) | ||||
−0.235566 | + | 0.971858i | \(0.575694\pi\) | |||||||
\(654\) | −12.4769 | −0.487884 | ||||||||
\(655\) | −37.8829 | −1.48021 | ||||||||
\(656\) | −1.86620 | −0.0728628 | ||||||||
\(657\) | −13.9821 | −0.545494 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −44.8183 | −1.74587 | −0.872937 | − | 0.487833i | \(-0.837787\pi\) | ||||
−0.872937 | + | 0.487833i | \(0.837787\pi\) | |||||||
\(660\) | 5.20302 | 0.202527 | ||||||||
\(661\) | 47.7433 | 1.85700 | 0.928499 | − | 0.371335i | \(-0.121100\pi\) | ||||
0.928499 | + | 0.371335i | \(0.121100\pi\) | |||||||
\(662\) | 25.6678 | 0.997608 | ||||||||
\(663\) | −30.6620 | −1.19081 | ||||||||
\(664\) | 2.30221 | 0.0893431 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.11590 | 0.314485 | ||||||||
\(667\) | 15.7012 | 0.607954 | ||||||||
\(668\) | 4.72032 | 0.182635 | ||||||||
\(669\) | −3.31892 | −0.128317 | ||||||||
\(670\) | −25.1280 | −0.970778 | ||||||||
\(671\) | −7.31470 | −0.282381 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.4181 | −1.17253 | −0.586266 | − | 0.810119i | \(-0.699403\pi\) | ||||
−0.586266 | + | 0.810119i | \(0.699403\pi\) | |||||||
\(674\) | −13.7266 | −0.528728 | ||||||||
\(675\) | 0.517304 | 0.0199110 | ||||||||
\(676\) | 19.8604 | 0.763860 | ||||||||
\(677\) | −2.03461 | −0.0781963 | −0.0390982 | − | 0.999235i | \(-0.512449\pi\) | ||||
−0.0390982 | + | 0.999235i | \(0.512449\pi\) | |||||||
\(678\) | −10.9700 | −0.421301 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 12.5640 | 0.481807 | ||||||||
\(681\) | −3.58189 | −0.137258 | ||||||||
\(682\) | 21.6348 | 0.828440 | ||||||||
\(683\) | −13.9521 | −0.533863 | −0.266932 | − | 0.963716i | \(-0.586010\pi\) | ||||
−0.266932 | + | 0.963716i | \(0.586010\pi\) | |||||||
\(684\) | 1.00000 | 0.0382360 | ||||||||
\(685\) | −9.39558 | −0.358987 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.39558 | −0.282159 | ||||||||
\(688\) | −9.08129 | −0.346221 | ||||||||
\(689\) | 27.1280 | 1.03349 | ||||||||
\(690\) | 11.3489 | 0.432045 | ||||||||
\(691\) | 17.8841 | 0.680343 | 0.340172 | − | 0.940363i | \(-0.389515\pi\) | ||||
0.340172 | + | 0.940363i | \(0.389515\pi\) | |||||||
\(692\) | −10.3431 | −0.393184 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.8783 | 0.488853 | ||||||||
\(695\) | −40.2847 | −1.52809 | ||||||||
\(696\) | −3.24970 | −0.123180 | ||||||||
\(697\) | −9.98210 | −0.378099 | ||||||||
\(698\) | 2.76237 | 0.104557 | ||||||||
\(699\) | 26.0934 | 0.986942 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35.5282 | −1.34188 | −0.670940 | − | 0.741511i | \(-0.734109\pi\) | ||||
−0.670940 | + | 0.741511i | \(0.734109\pi\) | |||||||
\(702\) | 5.73240 | 0.216355 | ||||||||
\(703\) | −8.11590 | −0.306097 | ||||||||
\(704\) | −2.21509 | −0.0834844 | ||||||||
\(705\) | 2.43018 | 0.0915261 | ||||||||
\(706\) | 28.0109 | 1.05420 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −9.63320 | −0.362038 | ||||||||
\(709\) | 5.16841 | 0.194104 | 0.0970519 | − | 0.995279i | \(-0.469059\pi\) | ||||
0.0970519 | + | 0.995279i | \(0.469059\pi\) | |||||||
\(710\) | −12.5640 | −0.471518 | ||||||||
\(711\) | 1.58652 | 0.0594992 | ||||||||
\(712\) | −17.3310 | −0.649506 | ||||||||
\(713\) | 47.1902 | 1.76729 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −29.8258 | −1.11542 | ||||||||
\(716\) | 16.8604 | 0.630102 | ||||||||
\(717\) | −1.89498 | −0.0707693 | ||||||||
\(718\) | 18.0000 | 0.671754 | ||||||||
\(719\) | −14.9537 | −0.557680 | −0.278840 | − | 0.960338i | \(-0.589950\pi\) | ||||
−0.278840 | + | 0.960338i | \(0.589950\pi\) | |||||||
\(720\) | −2.34889 | −0.0875381 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 4.36680 | 0.162403 | ||||||||
\(724\) | −24.6620 | −0.916555 | ||||||||
\(725\) | 1.68108 | 0.0624339 | ||||||||
\(726\) | 6.09337 | 0.226146 | ||||||||
\(727\) | 0.511476 | 0.0189696 | 0.00948479 | − | 0.999955i | \(-0.496981\pi\) | ||||
0.00948479 | + | 0.999955i | \(0.496981\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −32.8425 | −1.21555 | ||||||||
\(731\) | −48.5749 | −1.79661 | ||||||||
\(732\) | 3.30221 | 0.122053 | ||||||||
\(733\) | 29.4360 | 1.08724 | 0.543622 | − | 0.839330i | \(-0.317053\pi\) | ||||
0.543622 | + | 0.839330i | \(0.317053\pi\) | |||||||
\(734\) | 30.3131 | 1.11888 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.83159 | −0.178095 | ||||||||
\(737\) | 23.6966 | 0.872875 | ||||||||
\(738\) | 1.86620 | 0.0686957 | ||||||||
\(739\) | −24.4077 | −0.897850 | −0.448925 | − | 0.893569i | \(-0.648193\pi\) | ||||
−0.448925 | + | 0.893569i | \(0.648193\pi\) | |||||||
\(740\) | 19.0634 | 0.700784 | ||||||||
\(741\) | −5.73240 | −0.210585 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.25595 | 0.229508 | 0.114754 | − | 0.993394i | \(-0.463392\pi\) | ||||
0.114754 | + | 0.993394i | \(0.463392\pi\) | |||||||
\(744\) | −9.76700 | −0.358076 | ||||||||
\(745\) | −39.2213 | −1.43696 | ||||||||
\(746\) | −18.5236 | −0.678195 | ||||||||
\(747\) | −2.30221 | −0.0842335 | ||||||||
\(748\) | −11.8483 | −0.433217 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −10.5294 | −0.384479 | ||||||||
\(751\) | −10.6211 | −0.387570 | −0.193785 | − | 0.981044i | \(-0.562076\pi\) | ||||
−0.193785 | + | 0.981044i | \(0.562076\pi\) | |||||||
\(752\) | −1.03461 | −0.0377283 | ||||||||
\(753\) | −4.98210 | −0.181558 | ||||||||
\(754\) | 18.6286 | 0.678413 | ||||||||
\(755\) | 15.4318 | 0.561621 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.9837 | −0.799012 | −0.399506 | − | 0.916731i | \(-0.630818\pi\) | ||||
−0.399506 | + | 0.916731i | \(0.630818\pi\) | |||||||
\(758\) | 9.17304 | 0.333180 | ||||||||
\(759\) | −10.7024 | −0.388473 | ||||||||
\(760\) | 2.34889 | 0.0852033 | ||||||||
\(761\) | 16.0241 | 0.580875 | 0.290437 | − | 0.956894i | \(-0.406199\pi\) | ||||
0.290437 | + | 0.956894i | \(0.406199\pi\) | |||||||
\(762\) | 6.10382 | 0.221118 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 18.6978 | 0.676462 | ||||||||
\(765\) | −12.5640 | −0.454252 | ||||||||
\(766\) | −6.43018 | −0.232332 | ||||||||
\(767\) | 55.2213 | 1.99393 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −40.4469 | −1.45855 | −0.729276 | − | 0.684220i | \(-0.760143\pi\) | ||||
−0.729276 | + | 0.684220i | \(0.760143\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.4648 | 0.484923 | ||||||||
\(772\) | 4.77908 | 0.172003 | ||||||||
\(773\) | 20.0421 | 0.720863 | 0.360431 | − | 0.932786i | \(-0.382630\pi\) | ||||
0.360431 | + | 0.932786i | \(0.382630\pi\) | |||||||
\(774\) | 9.08129 | 0.326420 | ||||||||
\(775\) | 5.05251 | 0.181492 | ||||||||
\(776\) | −8.33099 | −0.299065 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −23.9883 | −0.860024 | ||||||||
\(779\) | −1.86620 | −0.0668635 | ||||||||
\(780\) | 13.4648 | 0.482117 | ||||||||
\(781\) | 11.8483 | 0.423965 | ||||||||
\(782\) | −25.8437 | −0.924168 | ||||||||
\(783\) | 3.24970 | 0.116135 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.54567 | −0.197933 | ||||||||
\(786\) | −16.1280 | −0.575266 | ||||||||
\(787\) | −25.0680 | −0.893578 | −0.446789 | − | 0.894639i | \(-0.647433\pi\) | ||||
−0.446789 | + | 0.894639i | \(0.647433\pi\) | |||||||
\(788\) | 4.87827 | 0.173781 | ||||||||
\(789\) | 24.2272 | 0.862510 | ||||||||
\(790\) | 3.72657 | 0.132585 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2.21509 | 0.0787099 | ||||||||
\(793\) | −18.9296 | −0.672209 | ||||||||
\(794\) | −15.3598 | −0.545098 | ||||||||
\(795\) | 11.1159 | 0.394240 | ||||||||
\(796\) | 2.06922 | 0.0733414 | ||||||||
\(797\) | 43.9358 | 1.55629 | 0.778144 | − | 0.628087i | \(-0.216162\pi\) | ||||
0.778144 | + | 0.628087i | \(0.216162\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.53401 | −0.195779 | ||||||||
\(800\) | −0.517304 | −0.0182895 | ||||||||
\(801\) | 17.3310 | 0.612360 | ||||||||
\(802\) | 30.9988 | 1.09461 | ||||||||
\(803\) | 30.9716 | 1.09297 | ||||||||
\(804\) | −10.6978 | −0.377282 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 55.9883 | 1.97211 | ||||||||
\(807\) | 18.3777 | 0.646925 | ||||||||
\(808\) | −14.7670 | −0.519501 | ||||||||
\(809\) | 8.29014 | 0.291466 | 0.145733 | − | 0.989324i | \(-0.453446\pi\) | ||||
0.145733 | + | 0.989324i | \(0.453446\pi\) | |||||||
\(810\) | 2.34889 | 0.0825317 | ||||||||
\(811\) | −7.26178 | −0.254995 | −0.127498 | − | 0.991839i | \(-0.540695\pi\) | ||||
−0.127498 | + | 0.991839i | \(0.540695\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 24.4181 | 0.856381 | ||||||||
\(814\) | −17.9775 | −0.630110 | ||||||||
\(815\) | −23.0230 | −0.806459 | ||||||||
\(816\) | 5.34889 | 0.187249 | ||||||||
\(817\) | −9.08129 | −0.317714 | ||||||||
\(818\) | −23.5189 | −0.822320 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.38350 | 0.153079 | ||||||||
\(821\) | 54.6562 | 1.90751 | 0.953756 | − | 0.300580i | \(-0.0971804\pi\) | ||||
0.953756 | + | 0.300580i | \(0.0971804\pi\) | |||||||
\(822\) | −4.00000 | −0.139516 | ||||||||
\(823\) | 35.8833 | 1.25081 | 0.625407 | − | 0.780299i | \(-0.284933\pi\) | ||||
0.625407 | + | 0.780299i | \(0.284933\pi\) | |||||||
\(824\) | −16.6107 | −0.578660 | ||||||||
\(825\) | −1.14588 | −0.0398943 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 44.5177 | 1.54803 | 0.774016 | − | 0.633166i | \(-0.218245\pi\) | ||||
0.774016 | + | 0.633166i | \(0.218245\pi\) | |||||||
\(828\) | 4.83159 | 0.167909 | ||||||||
\(829\) | −1.20885 | −0.0419850 | −0.0209925 | − | 0.999780i | \(-0.506683\pi\) | ||||
−0.0209925 | + | 0.999780i | \(0.506683\pi\) | |||||||
\(830\) | −5.40765 | −0.187702 | ||||||||
\(831\) | −5.33099 | −0.184930 | ||||||||
\(832\) | −5.73240 | −0.198735 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −17.1505 | −0.593873 | ||||||||
\(835\) | −11.0875 | −0.383700 | ||||||||
\(836\) | −2.21509 | −0.0766106 | ||||||||
\(837\) | 9.76700 | 0.337597 | ||||||||
\(838\) | 23.5403 | 0.813185 | ||||||||
\(839\) | −20.0708 | −0.692922 | −0.346461 | − | 0.938064i | \(-0.612617\pi\) | ||||
−0.346461 | + | 0.938064i | \(0.612617\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.4394 | −0.635843 | ||||||||
\(842\) | 9.05876 | 0.312185 | ||||||||
\(843\) | −3.56982 | −0.122951 | ||||||||
\(844\) | −8.06459 | −0.277594 | ||||||||
\(845\) | −46.6499 | −1.60481 | ||||||||
\(846\) | 1.03461 | 0.0355706 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4.73240 | −0.162511 | ||||||||
\(849\) | 12.0467 | 0.413441 | ||||||||
\(850\) | −2.76700 | −0.0949075 | ||||||||
\(851\) | −39.2127 | −1.34419 | ||||||||
\(852\) | −5.34889 | −0.183250 | ||||||||
\(853\) | −51.5628 | −1.76548 | −0.882738 | − | 0.469865i | \(-0.844302\pi\) | ||||
−0.882738 | + | 0.469865i | \(0.844302\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.34889 | −0.0803305 | ||||||||
\(856\) | −0.884101 | −0.0302180 | ||||||||
\(857\) | −6.92032 | −0.236394 | −0.118197 | − | 0.992990i | \(-0.537711\pi\) | ||||
−0.118197 | + | 0.992990i | \(0.537711\pi\) | |||||||
\(858\) | −12.6978 | −0.433495 | ||||||||
\(859\) | 37.2306 | 1.27029 | 0.635146 | − | 0.772392i | \(-0.280940\pi\) | ||||
0.635146 | + | 0.772392i | \(0.280940\pi\) | |||||||
\(860\) | 21.3310 | 0.727381 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.09175 | −0.275606 | ||||||||
\(863\) | −20.6511 | −0.702972 | −0.351486 | − | 0.936193i | \(-0.614323\pi\) | ||||
−0.351486 | + | 0.936193i | \(0.614323\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 24.2948 | 0.826047 | ||||||||
\(866\) | 34.7733 | 1.18164 | ||||||||
\(867\) | 11.6107 | 0.394319 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.51429 | −0.119214 | ||||||||
\(870\) | 7.63320 | 0.258790 | ||||||||
\(871\) | 61.3240 | 2.07788 | ||||||||
\(872\) | −12.4769 | −0.422520 | ||||||||
\(873\) | 8.33099 | 0.281961 | ||||||||
\(874\) | −4.83159 | −0.163431 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −13.9821 | −0.472411 | ||||||||
\(877\) | 0.927971 | 0.0313353 | 0.0156677 | − | 0.999877i | \(-0.495013\pi\) | ||||
0.0156677 | + | 0.999877i | \(0.495013\pi\) | |||||||
\(878\) | 15.4815 | 0.522475 | ||||||||
\(879\) | 24.5761 | 0.828930 | ||||||||
\(880\) | 5.20302 | 0.175394 | ||||||||
\(881\) | −37.0346 | −1.24773 | −0.623864 | − | 0.781533i | \(-0.714438\pi\) | ||||
−0.623864 | + | 0.781533i | \(0.714438\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.7087 | 0.831513 | 0.415756 | − | 0.909476i | \(-0.363517\pi\) | ||||
0.415756 | + | 0.909476i | \(0.363517\pi\) | |||||||
\(884\) | −30.6620 | −1.03127 | ||||||||
\(885\) | 22.6274 | 0.760611 | ||||||||
\(886\) | 29.9024 | 1.00459 | ||||||||
\(887\) | 24.0801 | 0.808530 | 0.404265 | − | 0.914642i | \(-0.367527\pi\) | ||||
0.404265 | + | 0.914642i | \(0.367527\pi\) | |||||||
\(888\) | 8.11590 | 0.272352 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 40.7087 | 1.36456 | ||||||||
\(891\) | −2.21509 | −0.0742084 | ||||||||
\(892\) | −3.31892 | −0.111126 | ||||||||
\(893\) | −1.03461 | −0.0346218 | ||||||||
\(894\) | −16.6978 | −0.558458 | ||||||||
\(895\) | −39.6032 | −1.32379 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −27.6966 | −0.924762 | ||||||||
\(898\) | −4.36560 | −0.145682 | ||||||||
\(899\) | 31.7398 | 1.05858 | ||||||||
\(900\) | 0.517304 | 0.0172435 | ||||||||
\(901\) | −25.3131 | −0.843301 | ||||||||
\(902\) | −4.13380 | −0.137641 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10.9700 | −0.364858 | ||||||||
\(905\) | 57.9284 | 1.92560 | ||||||||
\(906\) | 6.56982 | 0.218267 | ||||||||
\(907\) | 7.29758 | 0.242312 | 0.121156 | − | 0.992633i | \(-0.461340\pi\) | ||||
0.121156 | + | 0.992633i | \(0.461340\pi\) | |||||||
\(908\) | −3.58189 | −0.118869 | ||||||||
\(909\) | 14.7670 | 0.489791 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.73240 | 0.189923 | 0.0949614 | − | 0.995481i | \(-0.469727\pi\) | ||||
0.0949614 | + | 0.995481i | \(0.469727\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | 5.09961 | 0.168773 | ||||||||
\(914\) | 25.8425 | 0.854793 | ||||||||
\(915\) | −7.75655 | −0.256423 | ||||||||
\(916\) | −7.39558 | −0.244357 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −5.34889 | −0.176540 | ||||||||
\(919\) | 29.4376 | 0.971058 | 0.485529 | − | 0.874221i | \(-0.338627\pi\) | ||||
0.485529 | + | 0.874221i | \(0.338627\pi\) | |||||||
\(920\) | 11.3489 | 0.374162 | ||||||||
\(921\) | 29.6227 | 0.976103 | ||||||||
\(922\) | 24.7912 | 0.816453 | ||||||||
\(923\) | 30.6620 | 1.00925 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.19839 | −0.138042 | ||||||||
\(926\) | −11.9642 | −0.393168 | ||||||||
\(927\) | 16.6107 | 0.545566 | ||||||||
\(928\) | −3.24970 | −0.106677 | ||||||||
\(929\) | −38.0467 | −1.24827 | −0.624136 | − | 0.781316i | \(-0.714549\pi\) | ||||
−0.624136 | + | 0.781316i | \(0.714549\pi\) | |||||||
\(930\) | 22.9417 | 0.752287 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 26.0934 | 0.854717 | ||||||||
\(933\) | 21.8903 | 0.716658 | ||||||||
\(934\) | −13.5068 | −0.441957 | ||||||||
\(935\) | 27.8304 | 0.910151 | ||||||||
\(936\) | 5.73240 | 0.187369 | ||||||||
\(937\) | −13.1533 | −0.429700 | −0.214850 | − | 0.976647i | \(-0.568926\pi\) | ||||
−0.214850 | + | 0.976647i | \(0.568926\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.7491 | 0.905558 | ||||||||
\(940\) | 2.43018 | 0.0792639 | ||||||||
\(941\) | −8.95493 | −0.291922 | −0.145961 | − | 0.989290i | \(-0.546627\pi\) | ||||
−0.145961 | + | 0.989290i | \(0.546627\pi\) | |||||||
\(942\) | −2.36097 | −0.0769245 | ||||||||
\(943\) | −9.01671 | −0.293624 | ||||||||
\(944\) | −9.63320 | −0.313534 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −20.1159 | −0.654024 | ||||||||
\(947\) | 15.0859 | 0.490227 | 0.245113 | − | 0.969494i | \(-0.421175\pi\) | ||||
0.245113 | + | 0.969494i | \(0.421175\pi\) | |||||||
\(948\) | 1.58652 | 0.0515278 | ||||||||
\(949\) | 80.1509 | 2.60181 | ||||||||
\(950\) | −0.517304 | −0.0167836 | ||||||||
\(951\) | −11.9296 | −0.386843 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −47.2906 | −1.53189 | −0.765946 | − | 0.642905i | \(-0.777729\pi\) | ||||
−0.765946 | + | 0.642905i | \(0.777729\pi\) | |||||||
\(954\) | 4.73240 | 0.153217 | ||||||||
\(955\) | −43.9191 | −1.42119 | ||||||||
\(956\) | −1.89498 | −0.0612880 | ||||||||
\(957\) | −7.19839 | −0.232691 | ||||||||
\(958\) | 8.59277 | 0.277620 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2.34889 | −0.0758102 | ||||||||
\(961\) | 64.3944 | 2.07724 | ||||||||
\(962\) | −46.5236 | −1.49998 | ||||||||
\(963\) | 0.884101 | 0.0284898 | ||||||||
\(964\) | 4.36680 | 0.140645 | ||||||||
\(965\) | −11.2256 | −0.361363 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.0863 | 1.44988 | 0.724939 | − | 0.688813i | \(-0.241868\pi\) | ||||
0.724939 | + | 0.688813i | \(0.241868\pi\) | |||||||
\(968\) | 6.09337 | 0.195848 | ||||||||
\(969\) | 5.34889 | 0.171831 | ||||||||
\(970\) | 19.5686 | 0.628310 | ||||||||
\(971\) | −45.8441 | −1.47121 | −0.735603 | − | 0.677413i | \(-0.763101\pi\) | ||||
−0.735603 | + | 0.677413i | \(0.763101\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 18.4648 | 0.591650 | ||||||||
\(975\) | −2.96539 | −0.0949685 | ||||||||
\(976\) | 3.30221 | 0.105701 | ||||||||
\(977\) | 32.6169 | 1.04351 | 0.521754 | − | 0.853096i | \(-0.325278\pi\) | ||||
0.521754 | + | 0.853096i | \(0.325278\pi\) | |||||||
\(978\) | −9.80161 | −0.313421 | ||||||||
\(979\) | −38.3897 | −1.22694 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.4769 | 0.398356 | ||||||||
\(982\) | 25.7912 | 0.823029 | ||||||||
\(983\) | 21.1730 | 0.675315 | 0.337658 | − | 0.941269i | \(-0.390365\pi\) | ||||
0.337658 | + | 0.941269i | \(0.390365\pi\) | |||||||
\(984\) | 1.86620 | 0.0594922 | ||||||||
\(985\) | −11.4585 | −0.365100 | ||||||||
\(986\) | −17.3823 | −0.553565 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.73240 | −0.182372 | ||||||||
\(989\) | −43.8771 | −1.39521 | ||||||||
\(990\) | −5.20302 | −0.165363 | ||||||||
\(991\) | −51.1718 | −1.62553 | −0.812764 | − | 0.582594i | \(-0.802038\pi\) | ||||
−0.812764 | + | 0.582594i | \(0.802038\pi\) | |||||||
\(992\) | −9.76700 | −0.310103 | ||||||||
\(993\) | −25.6678 | −0.814543 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.86037 | −0.154084 | ||||||||
\(996\) | −2.30221 | −0.0729484 | ||||||||
\(997\) | −21.7082 | −0.687507 | −0.343754 | − | 0.939060i | \(-0.611698\pi\) | ||||
−0.343754 | + | 0.939060i | \(0.611698\pi\) | |||||||
\(998\) | 10.3610 | 0.327971 | ||||||||
\(999\) | −8.11590 | −0.256776 |
(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 | 5586.2.a.bt.1.1 | 3 | ||
7.3 | odd | 6 | 798.2.j.j.457.1 | ✓ | 6 | ||
7.5 | odd | 6 | 798.2.j.j.571.1 | yes | 6 | ||
7.6 | odd | 2 | 5586.2.a.bs.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
798.2.j.j.457.1 | ✓ | 6 | 7.3 | odd | 6 | ||
798.2.j.j.571.1 | yes | 6 | 7.5 | odd | 6 | ||
5586.2.a.bs.1.3 | 3 | 7.6 | odd | 2 | |||
5586.2.a.bt.1.1 | 3 | 1.1 | even | 1 | trivial |