Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8036,2,Mod(1,8036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8036, 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("8036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8036.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1677830643\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 14x^{6} - 4x^{5} + 60x^{4} + 31x^{3} - 75x^{2} - 60x - 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1148) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(1.71291\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8036.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.71291 | 0.988948 | 0.494474 | − | 0.869192i | \(-0.335361\pi\) | ||||
0.494474 | + | 0.869192i | \(0.335361\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.15120 | −0.962045 | −0.481023 | − | 0.876708i | \(-0.659735\pi\) | ||||
−0.481023 | + | 0.876708i | \(0.659735\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.0659453 | −0.0219818 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.02769 | −0.912882 | −0.456441 | − | 0.889754i | \(-0.650876\pi\) | ||||
−0.456441 | + | 0.889754i | \(0.650876\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.848387 | −0.235300 | −0.117650 | − | 0.993055i | \(-0.537536\pi\) | ||||
−0.117650 | + | 0.993055i | \(0.537536\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.68481 | −0.951413 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.76096 | 1.15470 | 0.577351 | − | 0.816496i | \(-0.304086\pi\) | ||||
0.577351 | + | 0.816496i | \(0.304086\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.90091 | 0.894931 | 0.447465 | − | 0.894301i | \(-0.352327\pi\) | ||||
0.447465 | + | 0.894301i | \(0.352327\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.25272 | 1.72081 | 0.860405 | − | 0.509610i | \(-0.170210\pi\) | ||||
0.860405 | + | 0.509610i | \(0.170210\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.372345 | −0.0744690 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.25168 | −1.01069 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.0576440 | 0.0107042 | 0.00535211 | − | 0.999986i | \(-0.498296\pi\) | ||||
0.00535211 | + | 0.999986i | \(0.498296\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.30049 | −0.772391 | −0.386196 | − | 0.922417i | \(-0.626211\pi\) | ||||
−0.386196 | + | 0.922417i | \(0.626211\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.18615 | −0.902793 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.475316 | 0.0781414 | 0.0390707 | − | 0.999236i | \(-0.487560\pi\) | ||||
0.0390707 | + | 0.999236i | \(0.487560\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.45321 | −0.232700 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.82667 | 0.431063 | 0.215531 | − | 0.976497i | \(-0.430852\pi\) | ||||
0.215531 | + | 0.976497i | \(0.430852\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.141861 | 0.0211474 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.71976 | −0.980178 | −0.490089 | − | 0.871673i | \(-0.663036\pi\) | ||||
−0.490089 | + | 0.871673i | \(0.663036\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.15508 | 1.14194 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.42941 | −0.471065 | −0.235533 | − | 0.971866i | \(-0.575683\pi\) | ||||
−0.235533 | + | 0.971866i | \(0.575683\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.51316 | 0.878234 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.68191 | 0.885040 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.72894 | −0.745844 | −0.372922 | − | 0.927863i | \(-0.621644\pi\) | ||||
−0.372922 | + | 0.927863i | \(0.621644\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.96715 | −0.764015 | −0.382007 | − | 0.924159i | \(-0.624767\pi\) | ||||
−0.382007 | + | 0.924159i | \(0.624767\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.82505 | 0.226369 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.53549 | −1.16495 | −0.582473 | − | 0.812850i | \(-0.697915\pi\) | ||||
−0.582473 | + | 0.812850i | \(0.697915\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 14.1362 | 1.70179 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.84489 | −0.218948 | −0.109474 | − | 0.993990i | \(-0.534917\pi\) | ||||
−0.109474 | + | 0.993990i | \(0.534917\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.89877 | −0.456317 | −0.228158 | − | 0.973624i | \(-0.573270\pi\) | ||||
−0.228158 | + | 0.973624i | \(0.573270\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.637793 | −0.0736460 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.11742 | 0.575755 | 0.287877 | − | 0.957667i | \(-0.407050\pi\) | ||||
0.287877 | + | 0.957667i | \(0.407050\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.79782 | −0.977535 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.41218 | 0.813592 | 0.406796 | − | 0.913519i | \(-0.366646\pi\) | ||||
0.406796 | + | 0.913519i | \(0.366646\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.2418 | −1.11088 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.0987388 | 0.0105859 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.305139 | 0.0323447 | 0.0161723 | − | 0.999869i | \(-0.494852\pi\) | ||||
0.0161723 | + | 0.999869i | \(0.494852\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.36635 | −0.763855 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.39164 | −0.860964 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.7545 | 1.19349 | 0.596743 | − | 0.802433i | \(-0.296461\pi\) | ||||
0.596743 | + | 0.802433i | \(0.296461\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.199662 | 0.0200668 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.12301 | −0.211247 | −0.105623 | − | 0.994406i | \(-0.533684\pi\) | ||||
−0.105623 | + | 0.994406i | \(0.533684\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.52336 | 0.741299 | 0.370650 | − | 0.928773i | \(-0.379135\pi\) | ||||
0.370650 | + | 0.928773i | \(0.379135\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.9029 | −1.24737 | −0.623684 | − | 0.781677i | \(-0.714365\pi\) | ||||
−0.623684 | + | 0.781677i | \(0.714365\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.587473 | 0.0562697 | 0.0281349 | − | 0.999604i | \(-0.491043\pi\) | ||||
0.0281349 | + | 0.999604i | \(0.491043\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.814172 | 0.0772778 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.87770 | −0.176639 | −0.0883197 | − | 0.996092i | \(-0.528150\pi\) | ||||
−0.0883197 | + | 0.996092i | \(0.528150\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −17.7532 | −1.65550 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.0559471 | 0.00517231 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.83310 | −0.166646 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.71291 | −0.154448 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.5570 | 1.03369 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.9240 | 1.05808 | 0.529040 | − | 0.848597i | \(-0.322552\pi\) | ||||
0.529040 | + | 0.848597i | \(0.322552\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.84182 | 0.426299 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.1882 | 1.67648 | 0.838239 | − | 0.545303i | \(-0.183585\pi\) | ||||
0.838239 | + | 0.545303i | \(0.183585\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.2974 | 0.972326 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.01114 | −0.684438 | −0.342219 | − | 0.939620i | \(-0.611178\pi\) | ||||
−0.342219 | + | 0.939620i | \(0.611178\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.3407 | −1.72528 | −0.862639 | − | 0.505821i | \(-0.831190\pi\) | ||||
−0.862639 | + | 0.505821i | \(0.831190\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.5103 | −0.969345 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.56865 | 0.214801 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.124004 | −0.0102979 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.5821 | −0.866923 | −0.433462 | − | 0.901172i | \(-0.642708\pi\) | ||||
−0.433462 | + | 0.901172i | \(0.642708\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.5202 | −0.937501 | −0.468750 | − | 0.883331i | \(-0.655296\pi\) | ||||
−0.468750 | + | 0.883331i | \(0.655296\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.313963 | −0.0253824 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.25121 | 0.743075 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.02606 | −0.321315 | −0.160657 | − | 0.987010i | \(-0.551361\pi\) | ||||
−0.160657 | + | 0.987010i | \(0.551361\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.87426 | −0.465859 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.0562 | −1.49259 | −0.746296 | − | 0.665614i | \(-0.768170\pi\) | ||||
−0.746296 | + | 0.665614i | \(0.768170\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 11.1564 | 0.868528 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.7372 | −0.908252 | −0.454126 | − | 0.890937i | \(-0.650048\pi\) | ||||
−0.454126 | + | 0.890937i | \(0.650048\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.2802 | −0.944634 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.257247 | −0.0196722 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.51029 | 0.114825 | 0.0574126 | − | 0.998351i | \(-0.481715\pi\) | ||||
0.0574126 | + | 0.998351i | \(0.481715\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.81315 | −0.737601 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.38268 | −0.103346 | −0.0516731 | − | 0.998664i | \(-0.516455\pi\) | ||||
−0.0516731 | + | 0.998664i | \(0.516455\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.21399 | 0.238894 | 0.119447 | − | 0.992841i | \(-0.461888\pi\) | ||||
0.119447 | + | 0.992841i | \(0.461888\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.2212 | −0.755571 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.02250 | −0.0751756 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.4147 | −1.05411 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.31469 | −0.456915 | −0.228457 | − | 0.973554i | \(-0.573368\pi\) | ||||
−0.228457 | + | 0.973554i | \(0.573368\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.1817 | −1.09281 | −0.546403 | − | 0.837523i | \(-0.684003\pi\) | ||||
−0.546403 | + | 0.837523i | \(0.684003\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.12614 | 0.223868 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.9461 | −1.27861 | −0.639304 | − | 0.768954i | \(-0.720778\pi\) | ||||
−0.639304 | + | 0.768954i | \(0.720778\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.82193 | −0.554482 | −0.277241 | − | 0.960800i | \(-0.589420\pi\) | ||||
−0.277241 | + | 0.960800i | \(0.589420\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.3334 | −1.15207 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.15120 | 0.150246 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.544228 | −0.0378264 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.8108 | −0.816967 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.30039 | −0.158366 | −0.0791828 | − | 0.996860i | \(-0.525231\pi\) | ||||
−0.0791828 | + | 0.996860i | \(0.525231\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.16012 | −0.216528 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.08072 | −0.414702 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.67824 | −0.451274 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.03913 | −0.271702 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.01186 | 0.402584 | 0.201292 | − | 0.979531i | \(-0.435486\pi\) | ||||
0.201292 | + | 0.979531i | \(0.435486\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.0245544 | 0.00163696 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −24.8633 | −1.65023 | −0.825117 | − | 0.564961i | \(-0.808891\pi\) | ||||
−0.825117 | + | 0.564961i | \(0.808891\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.0310 | 1.58801 | 0.794007 | − | 0.607908i | \(-0.207991\pi\) | ||||
0.794007 | + | 0.607908i | \(0.207991\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.77524 | −0.509373 | −0.254686 | − | 0.967024i | \(-0.581972\pi\) | ||||
−0.254686 | + | 0.967024i | \(0.581972\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.4555 | 0.942975 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.76567 | 0.569391 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.2557 | 1.24555 | 0.622774 | − | 0.782402i | \(-0.286006\pi\) | ||||
0.622774 | + | 0.782402i | \(0.286006\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.91887 | −0.381268 | −0.190634 | − | 0.981661i | \(-0.561054\pi\) | ||||
−0.190634 | + | 0.981661i | \(0.561054\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.685198 | 0.0439555 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.30948 | −0.210577 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.6964 | 0.804601 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −28.1909 | −1.77939 | −0.889697 | − | 0.456551i | \(-0.849084\pi\) | ||||
−0.889697 | + | 0.456551i | \(0.849084\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24.9867 | −1.57090 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −17.5432 | −1.09860 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.27874 | −0.266900 | −0.133450 | − | 0.991056i | \(-0.542606\pi\) | ||||
−0.133450 | + | 0.991056i | \(0.542606\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.00380135 | −0.000235297 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.43795 | −0.335318 | −0.167659 | − | 0.985845i | \(-0.553621\pi\) | ||||
−0.167659 | + | 0.985845i | \(0.553621\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.37733 | 0.453186 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.522675 | 0.0319872 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.8682 | −0.845561 | −0.422780 | − | 0.906232i | \(-0.638946\pi\) | ||||
−0.422780 | + | 0.906232i | \(0.638946\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.7110 | −0.832884 | −0.416442 | − | 0.909162i | \(-0.636723\pi\) | ||||
−0.416442 | + | 0.909162i | \(0.636723\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.12734 | 0.0679814 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.62629 | −0.458219 | −0.229110 | − | 0.973401i | \(-0.573581\pi\) | ||||
−0.229110 | + | 0.973401i | \(0.573581\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.283597 | 0.0169785 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.0467 | −1.55382 | −0.776908 | − | 0.629614i | \(-0.783213\pi\) | ||||
−0.776908 | + | 0.629614i | \(0.783213\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.46133 | −0.205755 | −0.102877 | − | 0.994694i | \(-0.532805\pi\) | ||||
−0.102877 | + | 0.994694i | \(0.532805\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −14.3741 | −0.851449 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.66671 | 0.333336 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 20.1343 | 1.18030 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.2067 | 0.654705 | 0.327352 | − | 0.944902i | \(-0.393844\pi\) | ||||
0.327352 | + | 0.944902i | \(0.393844\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.3241 | 0.717536 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 15.9005 | 0.922638 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.00150 | −0.404907 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.63651 | −0.208912 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.8365 | 0.735017 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.582689 | 0.0332558 | 0.0166279 | − | 0.999862i | \(-0.494707\pi\) | ||||
0.0166279 | + | 0.999862i | \(0.494707\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.8868 | 0.733106 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.24581 | −0.354167 | −0.177084 | − | 0.984196i | \(-0.556666\pi\) | ||||
−0.177084 | + | 0.984196i | \(0.556666\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.7415 | 1.00281 | 0.501405 | − | 0.865213i | \(-0.332817\pi\) | ||||
0.501405 | + | 0.865213i | \(0.332817\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.9364 | 0.726583 | 0.363291 | − | 0.931676i | \(-0.381653\pi\) | ||||
0.363291 | + | 0.931676i | \(0.381653\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.174528 | −0.00977169 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −22.1014 | −1.23358 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.5721 | 1.03338 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.315893 | 0.0175226 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.00629 | 0.0556478 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.9270 | −1.04032 | −0.520161 | − | 0.854068i | \(-0.674128\pi\) | ||||
−0.520161 | + | 0.854068i | \(0.674128\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.0313448 | −0.00171768 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 20.5127 | 1.12073 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.2630 | 0.885903 | 0.442951 | − | 0.896546i | \(-0.353931\pi\) | ||||
0.442951 | + | 0.896546i | \(0.353931\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.21633 | −0.174687 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.0205 | 0.705102 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −30.4097 | −1.63720 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.71825 | 0.145923 | 0.0729615 | − | 0.997335i | \(-0.476755\pi\) | ||||
0.0729615 | + | 0.997335i | \(0.476755\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.9033 | 1.11893 | 0.559464 | − | 0.828855i | \(-0.311007\pi\) | ||||
0.559464 | + | 0.828855i | \(0.311007\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.45546 | 0.237815 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.0242 | −0.533533 | −0.266766 | − | 0.963761i | \(-0.585955\pi\) | ||||
−0.266766 | + | 0.963761i | \(0.585955\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.96872 | 0.210638 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −33.9417 | −1.79137 | −0.895686 | − | 0.444686i | \(-0.853315\pi\) | ||||
−0.895686 | + | 0.444686i | \(0.853315\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.78287 | −0.199099 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.13994 | −0.164804 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.38704 | 0.438998 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.3396 | −1.47931 | −0.739656 | − | 0.672985i | \(-0.765012\pi\) | ||||
−0.739656 | + | 0.672985i | \(0.765012\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.0659453 | 0.00343297 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −31.3865 | −1.62513 | −0.812565 | − | 0.582871i | \(-0.801929\pi\) | ||||
−0.812565 | + | 0.582871i | \(0.801929\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 19.7960 | 1.02226 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.0489044 | −0.00251870 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.85269 | −0.351999 | −0.176000 | − | 0.984390i | \(-0.556316\pi\) | ||||
−0.176000 | + | 0.984390i | \(0.556316\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.4246 | 1.04639 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 37.9314 | 1.93820 | 0.969102 | − | 0.246659i | \(-0.0793326\pi\) | ||||
0.969102 | + | 0.246659i | \(0.0793326\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.186405 | −0.00947551 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.7304 | 0.949668 | 0.474834 | − | 0.880075i | \(-0.342508\pi\) | ||||
0.474834 | + | 0.880075i | \(0.342508\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 39.2908 | 1.98702 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 32.8676 | 1.65795 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.0086 | −0.553902 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.6693 | −1.03736 | −0.518681 | − | 0.854968i | \(-0.673577\pi\) | ||||
−0.518681 | + | 0.854968i | \(0.673577\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 36.6913 | 1.83227 | 0.916137 | − | 0.400866i | \(-0.131291\pi\) | ||||
0.916137 | + | 0.400866i | \(0.131291\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.64848 | 0.181744 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.9258 | 0.940433 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.43911 | −0.0713339 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.8678 | 1.32853 | 0.664264 | − | 0.747498i | \(-0.268745\pi\) | ||||
0.664264 | + | 0.747498i | \(0.268745\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.7223 | −0.676873 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.9451 | −0.782713 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −34.8418 | −1.70621 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.5057 | 1.58801 | 0.794004 | − | 0.607913i | \(-0.207993\pi\) | ||||
0.794004 | + | 0.607913i | \(0.207993\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −39.9668 | −1.94786 | −0.973931 | − | 0.226844i | \(-0.927159\pi\) | ||||
−0.973931 | + | 0.226844i | \(0.927159\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.443136 | 0.0215460 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.77272 | −0.0859895 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.39986 | 0.212427 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 34.2574 | 1.65012 | 0.825061 | − | 0.565043i | \(-0.191141\pi\) | ||||
0.825061 | + | 0.565043i | \(0.191141\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.9293 | 0.525229 | 0.262615 | − | 0.964901i | \(-0.415415\pi\) | ||||
0.262615 | + | 0.964901i | \(0.415415\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.212407 | −0.0101841 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 32.1931 | 1.54001 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −36.0170 | −1.71900 | −0.859499 | − | 0.511137i | \(-0.829225\pi\) | ||||
−0.859499 | + | 0.511137i | \(0.829225\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.2933 | −0.726609 | −0.363304 | − | 0.931670i | \(-0.618352\pi\) | ||||
−0.363304 | + | 0.931670i | \(0.618352\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.656415 | −0.0311171 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −18.1263 | −0.857342 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.7342 | −1.07289 | −0.536447 | − | 0.843934i | \(-0.680234\pi\) | ||||
−0.536447 | + | 0.843934i | \(0.680234\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.02769 | 0.142568 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −19.7330 | −0.927139 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.18370 | −0.242483 | −0.121242 | − | 0.992623i | \(-0.538688\pi\) | ||||
−0.121242 | + | 0.992623i | \(0.538688\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −25.0030 | −1.16704 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.9517 | 0.742946 | 0.371473 | − | 0.928444i | \(-0.378853\pi\) | ||||
0.371473 | + | 0.928444i | \(0.378853\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.8765 | −1.10964 | −0.554818 | − | 0.831972i | \(-0.687212\pi\) | ||||
−0.554818 | + | 0.831972i | \(0.687212\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 15.8465 | 0.734863 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.3183 | −0.801395 | −0.400697 | − | 0.916211i | \(-0.631232\pi\) | ||||
−0.400697 | + | 0.916211i | \(0.631232\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.89627 | −0.317764 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.55827 | −0.393510 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.45249 | −0.0666446 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.226153 | 0.0103548 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 35.3931 | 1.61715 | 0.808575 | − | 0.588393i | \(-0.200239\pi\) | ||||
0.808575 | + | 0.588393i | \(0.200239\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.403252 | −0.0183867 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −25.2862 | −1.14819 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −35.2364 | −1.59671 | −0.798357 | − | 0.602185i | \(-0.794297\pi\) | ||||
−0.798357 | + | 0.602185i | \(0.794297\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −32.6414 | −1.47610 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.56552 | 0.386556 | 0.193278 | − | 0.981144i | \(-0.438088\pi\) | ||||
0.193278 | + | 0.981144i | \(0.438088\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.274440 | 0.0123602 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.429512 | −0.0193051 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.6719 | 0.612040 | 0.306020 | − | 0.952025i | \(-0.401003\pi\) | ||||
0.306020 | + | 0.952025i | \(0.401003\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.1048 | −0.898214 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.0857 | 0.940167 | 0.470084 | − | 0.882622i | \(-0.344224\pi\) | ||||
0.470084 | + | 0.882622i | \(0.344224\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.56701 | 0.203229 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −21.0349 | −0.934194 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.6892 | 1.18298 | 0.591489 | − | 0.806313i | \(-0.298540\pi\) | ||||
0.591489 | + | 0.806313i | \(0.298540\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −20.4864 | −0.904495 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.1843 | −0.713163 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.3453 | 0.894787 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.58699 | 0.113556 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.4396 | 0.764041 | 0.382020 | − | 0.924154i | \(-0.375228\pi\) | ||||
0.382020 | + | 0.924154i | \(0.375228\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −38.3651 | −1.67759 | −0.838795 | − | 0.544448i | \(-0.816739\pi\) | ||||
−0.838795 | + | 0.544448i | \(0.816739\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.4745 | −0.891881 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 45.1074 | 1.96119 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.377796 | 0.0163950 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.848387 | 0.0367477 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 27.7566 | 1.20002 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.36840 | −0.102204 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.86191 | −0.0800497 | −0.0400249 | − | 0.999199i | \(-0.512744\pi\) | ||||
−0.0400249 | + | 0.999199i | \(0.512744\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.50527 | 0.236254 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.26377 | −0.0541340 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.7545 | 1.40048 | 0.700240 | − | 0.713908i | \(-0.253076\pi\) | ||||
0.700240 | + | 0.713908i | \(0.253076\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.393505 | 0.0167944 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.224864 | 0.00957953 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.75145 | −0.0743447 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −33.9771 | −1.43966 | −0.719828 | − | 0.694152i | \(-0.755779\pi\) | ||||
−0.719828 | + | 0.694152i | \(0.755779\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.39811 | −0.101429 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.6910 | −1.04246 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 33.7187 | 1.42107 | 0.710536 | − | 0.703661i | \(-0.248452\pi\) | ||||
0.710536 | + | 0.703661i | \(0.248452\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.03931 | 0.169935 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.8428 | 0.664166 | 0.332083 | − | 0.943250i | \(-0.392249\pi\) | ||||
0.332083 | + | 0.943250i | \(0.392249\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −42.5373 | −1.78013 | −0.890065 | − | 0.455833i | \(-0.849341\pi\) | ||||
−0.890065 | + | 0.455833i | \(0.849341\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.8165 | −0.451865 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.07286 | −0.128147 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.79836 | 0.199758 | 0.0998791 | − | 0.995000i | \(-0.468154\pi\) | ||||
0.0998791 | + | 0.995000i | \(0.468154\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −26.0049 | −1.08073 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.3832 | 0.430027 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.120353 | −0.00497600 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.292839 | −0.0120868 | −0.00604339 | − | 0.999982i | \(-0.501924\pi\) | ||||
−0.00604339 | + | 0.999982i | \(0.501924\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.7758 | −0.691237 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −30.7401 | −1.26448 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.67878 | −0.110004 | −0.0550022 | − | 0.998486i | \(-0.517517\pi\) | ||||
−0.0550022 | + | 0.998486i | \(0.517517\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.3982 | −0.548354 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.9623 | −0.652204 | −0.326102 | − | 0.945335i | \(-0.605735\pi\) | ||||
−0.326102 | + | 0.945335i | \(0.605735\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.88205 | −0.321516 | −0.160758 | − | 0.986994i | \(-0.551394\pi\) | ||||
−0.160758 | + | 0.986994i | \(0.551394\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.628821 | 0.0256076 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.94337 | 0.160321 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.5100 | 1.36013 | 0.680064 | − | 0.733153i | \(-0.261952\pi\) | ||||
0.680064 | + | 0.733153i | \(0.261952\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.70096 | 0.230636 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.5090 | 1.35342 | 0.676708 | − | 0.736251i | \(-0.263406\pi\) | ||||
0.676708 | + | 0.736251i | \(0.263406\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.68481 | 0.148586 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 45.8922 | 1.84755 | 0.923775 | − | 0.382935i | \(-0.125087\pi\) | ||||
0.923775 | + | 0.382935i | \(0.125087\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.8762 | −1.20082 | −0.600412 | − | 0.799691i | \(-0.704997\pi\) | ||||
−0.600412 | + | 0.799691i | \(0.704997\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −43.3407 | −1.73920 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.9996 | −0.919985 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −20.2307 | −0.807938 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.26296 | 0.0902300 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.54997 | 0.220941 | 0.110470 | − | 0.993879i | \(-0.464764\pi\) | ||||
0.110470 | + | 0.993879i | \(0.464764\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.94036 | −0.156615 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −25.6508 | −1.01792 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.121662 | 0.00481286 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.0010 | 1.02698 | 0.513489 | − | 0.858096i | \(-0.328353\pi\) | ||||
0.513489 | + | 0.858096i | \(0.328353\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.0891 | −0.989419 | −0.494709 | − | 0.869058i | \(-0.664725\pi\) | ||||
−0.494709 | + | 0.869058i | \(0.664725\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.4157 | −0.410119 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.2904 | 0.679757 | 0.339878 | − | 0.940469i | \(-0.389614\pi\) | ||||
0.339878 | + | 0.940469i | \(0.389614\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.3454 | 0.680868 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.29684 | 0.363814 | 0.181907 | − | 0.983316i | \(-0.441773\pi\) | ||||
0.181907 | + | 0.983316i | \(0.441773\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −41.2776 | −1.61285 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.257106 | 0.0100306 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.40667 | 0.210614 | 0.105307 | − | 0.994440i | \(-0.466417\pi\) | ||||
0.105307 | + | 0.994440i | \(0.466417\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.7223 | −0.961584 | −0.480792 | − | 0.876835i | \(-0.659651\pi\) | ||||
−0.480792 | + | 0.876835i | \(0.659651\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.91867 | −0.268699 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.475719 | 0.0184199 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.2978 | 0.398134 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.0667 | 0.697456 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.7190 | −0.760110 | −0.380055 | − | 0.924964i | \(-0.624095\pi\) | ||||
−0.380055 | + | 0.924964i | \(0.624095\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.95544 | 0.0752648 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.6496 | 0.678330 | 0.339165 | − | 0.940727i | \(-0.389856\pi\) | ||||
0.339165 | + | 0.940727i | \(0.389856\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −42.5885 | −1.63200 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −45.9083 | −1.75663 | −0.878317 | − | 0.478080i | \(-0.841333\pi\) | ||||
−0.878317 | + | 0.478080i | \(0.841333\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.2336 | 0.658460 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 41.1629 | 1.57046 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.90946 | 0.110842 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 38.9277 | 1.48088 | 0.740439 | − | 0.672124i | \(-0.234618\pi\) | ||||
0.740439 | + | 0.672124i | \(0.234618\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 43.7569 | 1.65979 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.76096 | −0.180334 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.3183 | −0.503743 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.2696 | 0.727803 | 0.363902 | − | 0.931437i | \(-0.381444\pi\) | ||||
0.363902 | + | 0.931437i | \(0.381444\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.85417 | 0.0699312 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 24.7610 | 0.932553 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.2495 | −0.910709 | −0.455355 | − | 0.890310i | \(-0.650488\pi\) | ||||
−0.455355 | + | 0.890310i | \(0.650488\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.337470 | −0.0126561 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −35.4908 | −1.32914 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.52568 | −0.206649 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 32.9832 | 1.23178 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.4335 | 0.612867 | 0.306434 | − | 0.951892i | \(-0.400864\pi\) | ||||
0.306434 | + | 0.951892i | \(0.400864\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.1385 | −0.377054 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.0214634 | −0.000797132 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 47.2145 | 1.75109 | 0.875545 | − | 0.483136i | \(-0.160503\pi\) | ||||
0.875545 | + | 0.483136i | \(0.160503\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.5671 | 1.02100 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.4576 | 0.497749 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.860012 | 0.0317653 | 0.0158826 | − | 0.999874i | \(-0.494944\pi\) | ||||
0.0158826 | + | 0.999874i | \(0.494944\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 28.8705 | 1.06346 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.8084 | 0.655094 | 0.327547 | − | 0.944835i | \(-0.393778\pi\) | ||||
0.327547 | + | 0.944835i | \(0.393778\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.66884 | −0.208250 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.23502 | −0.0819950 | −0.0409975 | − | 0.999159i | \(-0.513054\pi\) | ||||
−0.0409975 | + | 0.999159i | \(0.513054\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 22.7643 | 0.834020 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.488798 | −0.0178842 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 52.0736 | 1.90019 | 0.950097 | − | 0.311955i | \(-0.100984\pi\) | ||||
0.950097 | + | 0.311955i | \(0.100984\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −48.2884 | −1.75973 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.7822 | 0.901918 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.36576 | 0.122331 | 0.0611653 | − | 0.998128i | \(-0.480518\pi\) | ||||
0.0611653 | + | 0.998128i | \(0.480518\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −42.7999 | −1.55354 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.18908 | −0.260604 | −0.130302 | − | 0.991474i | \(-0.541595\pi\) | ||||
−0.130302 | + | 0.991474i | \(0.541595\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.675396 | 0.0244190 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.86036 | 0.175497 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.07410 | −0.110855 | −0.0554275 | − | 0.998463i | \(-0.517652\pi\) | ||||
−0.0554275 | + | 0.998463i | \(0.517652\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.32908 | −0.263951 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.7338 | 0.673808 | 0.336904 | − | 0.941539i | \(-0.390620\pi\) | ||||
0.336904 | + | 0.941539i | \(0.390620\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.60127 | 0.0575192 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.90091 | −0.139765 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.58574 | 0.199874 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.302728 | −0.0108186 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.66086 | 0.309119 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37.5567 | −1.33875 | −0.669377 | − | 0.742923i | \(-0.733439\pi\) | ||||
−0.669377 | + | 0.742923i | \(0.733439\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.31471 | −0.331612 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.06245 | 0.179773 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12.6367 | 0.448177 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.5950 | 0.481559 | 0.240779 | − | 0.970580i | \(-0.422597\pi\) | ||||
0.240779 | + | 0.970580i | \(0.422597\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −31.9925 | −1.13181 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.0201225 | −0.000710993 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.8043 | 0.416564 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −23.7550 | −0.836216 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.6190 | 0.795242 | 0.397621 | − | 0.917550i | \(-0.369836\pi\) | ||||
0.397621 | + | 0.917550i | \(0.369836\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.5762 | 1.28437 | 0.642183 | − | 0.766552i | \(-0.278029\pi\) | ||||
0.642183 | + | 0.766552i | \(0.278029\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −23.4857 | −0.823679 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 40.9936 | 1.43594 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.0266 | 0.385771 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 43.8441 | 1.53017 | 0.765084 | − | 0.643930i | \(-0.222697\pi\) | ||||
0.765084 | + | 0.643930i | \(0.222697\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.8684 | 0.866859 | 0.433429 | − | 0.901188i | \(-0.357303\pi\) | ||||
0.433429 | + | 0.901188i | \(0.357303\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.93104 | 0.0672301 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19.4951 | −0.677911 | −0.338956 | − | 0.940802i | \(-0.610074\pi\) | ||||
−0.338956 | + | 0.940802i | \(0.610074\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.46834 | 0.259386 | 0.129693 | − | 0.991554i | \(-0.458601\pi\) | ||||
0.129693 | + | 0.991554i | \(0.458601\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.0631 | −0.453155 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 25.2491 | 0.873780 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 22.5848 | 0.780646 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.549539 | 0.0189722 | 0.00948610 | − | 0.999955i | \(-0.496980\pi\) | ||||
0.00948610 | + | 0.999955i | \(0.496980\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9967 | −0.999885 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −44.6156 | −1.53664 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 26.4172 | 0.908780 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.92894 | −0.203481 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.92265 | 0.134467 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.6543 | −0.467516 | −0.233758 | − | 0.972295i | \(-0.575102\pi\) | ||||
−0.233758 | + | 0.972295i | \(0.575102\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.553389 | 0.0189255 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −33.9066 | −1.15823 | −0.579115 | − | 0.815246i | \(-0.696602\pi\) | ||||
−0.579115 | + | 0.815246i | \(0.696602\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.8208 | 1.22219 | 0.611095 | − | 0.791557i | \(-0.290729\pi\) | ||||
0.611095 | + | 0.791557i | \(0.290729\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34.4639 | 1.17316 | 0.586582 | − | 0.809890i | \(-0.300473\pi\) | ||||
0.586582 | + | 0.809890i | \(0.300473\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.24893 | −0.110467 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.70656 | 0.329652 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.4939 | −0.525596 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.08979 | 0.274112 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.775151 | −0.0262349 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −49.3159 | −1.66528 | −0.832640 | − | 0.553815i | \(-0.813172\pi\) | ||||
−0.832640 | + | 0.553815i | \(0.813172\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.1961 | 0.647469 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 52.6993 | 1.77548 | 0.887742 | − | 0.460342i | \(-0.152273\pi\) | ||||
0.887742 | + | 0.460342i | \(0.152273\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47.2828 | 1.59119 | 0.795597 | − | 0.605827i | \(-0.207157\pi\) | ||||
0.795597 | + | 0.605827i | \(0.207157\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 21.1100 | 0.709606 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.0043 | −0.369487 | −0.184744 | − | 0.982787i | \(-0.559145\pi\) | ||||
−0.184744 | + | 0.982787i | \(0.559145\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 26.6370 | 0.892374 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −26.2132 | −0.877191 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.97441 | 0.0994237 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −11.9929 | −0.400432 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.247897 | −0.00826784 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.3273 | −0.543940 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.91393 | −0.229827 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −50.3611 | −1.67221 | −0.836106 | − | 0.548568i | \(-0.815173\pi\) | ||||
−0.836106 | + | 0.548568i | \(0.815173\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.140002 | 0.00464358 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.11340 | 0.301940 | 0.150970 | − | 0.988538i | \(-0.451760\pi\) | ||||
0.150970 | + | 0.988538i | \(0.451760\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22.4418 | −0.742714 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 21.9878 | 0.726893 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.7583 | 0.783714 | 0.391857 | − | 0.920026i | \(-0.371833\pi\) | ||||
0.391857 | + | 0.920026i | \(0.371833\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.998093 | 0.0328883 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.56518 | 0.0515185 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.176981 | −0.00581911 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.496130 | −0.0162951 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.179643 | −0.00589390 | −0.00294695 | − | 0.999996i | \(-0.500938\pi\) | ||||
−0.00294695 | + | 0.999996i | \(0.500938\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10.6985 | −0.350253 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 31.0089 | 1.01410 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25.1739 | −0.822396 | −0.411198 | − | 0.911546i | \(-0.634890\pi\) | ||||
−0.411198 | + | 0.911546i | \(0.634890\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 30.3896 | 0.991727 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.0109 | 0.358947 | 0.179473 | − | 0.983763i | \(-0.442561\pi\) | ||||
0.179473 | + | 0.983763i | \(0.442561\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.25272 | −0.268746 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.27919 | −0.301533 | −0.150767 | − | 0.988569i | \(-0.548174\pi\) | ||||
−0.150767 | + | 0.988569i | \(0.548174\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.30767 | 0.107371 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.1589 | 0.718553 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.8414 | 0.804691 | 0.402345 | − | 0.915488i | \(-0.368195\pi\) | ||||
0.402345 | + | 0.915488i | \(0.368195\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.5842 | 0.439573 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.298950 | −0.00966369 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.5058 | −0.403412 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.850883 | 0.0274193 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 32.6589 | 1.05133 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.4773 | −0.787138 | −0.393569 | − | 0.919295i | \(-0.628760\pi\) | ||||
−0.393569 | + | 0.919295i | \(0.628760\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 31.8123 | 1.02196 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.3746 | 0.557576 | 0.278788 | − | 0.960353i | \(-0.410067\pi\) | ||||
0.278788 | + | 0.960353i | \(0.410067\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.541095 | 0.0173289 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 41.1045 | 1.31505 | 0.657525 | − | 0.753432i | \(-0.271603\pi\) | ||||
0.657525 | + | 0.753432i | \(0.271603\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.923866 | −0.0295269 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.0387411 | −0.00123691 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.1694 | 0.962255 | 0.481127 | − | 0.876651i | \(-0.340227\pi\) | ||||
0.481127 | + | 0.876651i | \(0.340227\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 38.6057 | 1.23008 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23.3277 | 0.741777 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.95738 | 0.284540 | 0.142270 | − | 0.989828i | \(-0.454560\pi\) | ||||
0.142270 | + | 0.989828i | \(0.454560\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −32.4202 | −1.02882 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.8265 | 0.533436 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40.8257 | −1.29296 | −0.646482 | − | 0.762930i | \(-0.723760\pi\) | ||||
−0.646482 | + | 0.762930i | \(0.723760\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.49621 | −0.0789765 |
(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 | 8036.2.a.n.1.6 | 8 | ||
7.3 | odd | 6 | 1148.2.i.d.821.6 | yes | 16 | ||
7.5 | odd | 6 | 1148.2.i.d.165.6 | ✓ | 16 | ||
7.6 | odd | 2 | 8036.2.a.m.1.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.i.d.165.6 | ✓ | 16 | 7.5 | odd | 6 | ||
1148.2.i.d.821.6 | yes | 16 | 7.3 | odd | 6 | ||
8036.2.a.m.1.3 | 8 | 7.6 | odd | 2 | |||
8036.2.a.n.1.6 | 8 | 1.1 | even | 1 | trivial |