Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2535,2,Mod(1,2535)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2535, 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("2535.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2535 = 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2535.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: | \(20.2420769124\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.13824.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} + 6 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 195) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.12603\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2535.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.12603 | −0.796225 | −0.398113 | − | 0.917337i | \(-0.630335\pi\) | ||||
−0.398113 | + | 0.917337i | \(0.630335\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.732051 | −0.366025 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.12603 | 0.459701 | ||||||||
\(7\) | −0.606018 | −0.229053 | −0.114527 | − | 0.993420i | \(-0.536535\pi\) | ||||
−0.114527 | + | 0.993420i | \(0.536535\pi\) | |||||||
\(8\) | 3.07638 | 1.08766 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.12603 | 0.356083 | ||||||||
\(11\) | 3.07638 | 0.927563 | 0.463781 | − | 0.885950i | \(-0.346492\pi\) | ||||
0.463781 | + | 0.885950i | \(0.346492\pi\) | |||||||
\(12\) | 0.732051 | 0.211325 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.682396 | 0.182378 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −2.00000 | −0.500000 | ||||||||
\(17\) | 1.95035 | 0.473028 | 0.236514 | − | 0.971628i | \(-0.423995\pi\) | ||||
0.236514 | + | 0.971628i | \(0.423995\pi\) | |||||||
\(18\) | −1.12603 | −0.265408 | ||||||||
\(19\) | −4.88481 | −1.12065 | −0.560326 | − | 0.828272i | \(-0.689324\pi\) | ||||
−0.560326 | + | 0.828272i | \(0.689324\pi\) | |||||||
\(20\) | 0.732051 | 0.163692 | ||||||||
\(21\) | 0.606018 | 0.132244 | ||||||||
\(22\) | −3.46410 | −0.738549 | ||||||||
\(23\) | 1.86434 | 0.388742 | 0.194371 | − | 0.980928i | \(-0.437733\pi\) | ||||
0.194371 | + | 0.980928i | \(0.437733\pi\) | |||||||
\(24\) | −3.07638 | −0.627963 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.443636 | 0.0838394 | ||||||||
\(29\) | −2.78171 | −0.516550 | −0.258275 | − | 0.966071i | \(-0.583154\pi\) | ||||
−0.258275 | + | 0.966071i | \(0.583154\pi\) | |||||||
\(30\) | −1.12603 | −0.205584 | ||||||||
\(31\) | 9.15276 | 1.64388 | 0.821942 | − | 0.569572i | \(-0.192891\pi\) | ||||
0.821942 | + | 0.569572i | \(0.192891\pi\) | |||||||
\(32\) | −3.90069 | −0.689551 | ||||||||
\(33\) | −3.07638 | −0.535529 | ||||||||
\(34\) | −2.19615 | −0.376637 | ||||||||
\(35\) | 0.606018 | 0.102436 | ||||||||
\(36\) | −0.732051 | −0.122008 | ||||||||
\(37\) | 3.74793 | 0.616157 | 0.308078 | − | 0.951361i | \(-0.400314\pi\) | ||||
0.308078 | + | 0.951361i | \(0.400314\pi\) | |||||||
\(38\) | 5.50045 | 0.892291 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.07638 | −0.486418 | ||||||||
\(41\) | −1.07012 | −0.167125 | −0.0835623 | − | 0.996503i | \(-0.526630\pi\) | ||||
−0.0835623 | + | 0.996503i | \(0.526630\pi\) | |||||||
\(42\) | −0.682396 | −0.105296 | ||||||||
\(43\) | −5.01084 | −0.764146 | −0.382073 | − | 0.924132i | \(-0.624790\pi\) | ||||
−0.382073 | + | 0.924132i | \(0.624790\pi\) | |||||||
\(44\) | −2.25207 | −0.339512 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −2.09931 | −0.309526 | ||||||||
\(47\) | 10.2024 | 1.48817 | 0.744087 | − | 0.668082i | \(-0.232885\pi\) | ||||
0.744087 | + | 0.668082i | \(0.232885\pi\) | |||||||
\(48\) | 2.00000 | 0.288675 | ||||||||
\(49\) | −6.63274 | −0.947535 | ||||||||
\(50\) | −1.12603 | −0.159245 | ||||||||
\(51\) | −1.95035 | −0.273103 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.6569 | −1.46384 | −0.731918 | − | 0.681393i | \(-0.761375\pi\) | ||||
−0.731918 | + | 0.681393i | \(0.761375\pi\) | |||||||
\(54\) | 1.12603 | 0.153234 | ||||||||
\(55\) | −3.07638 | −0.414819 | ||||||||
\(56\) | −1.86434 | −0.249133 | ||||||||
\(57\) | 4.88481 | 0.647008 | ||||||||
\(58\) | 3.13229 | 0.411290 | ||||||||
\(59\) | −11.5742 | −1.50684 | −0.753419 | − | 0.657540i | \(-0.771597\pi\) | ||||
−0.753419 | + | 0.657540i | \(0.771597\pi\) | |||||||
\(60\) | −0.732051 | −0.0945074 | ||||||||
\(61\) | −6.26795 | −0.802529 | −0.401264 | − | 0.915962i | \(-0.631429\pi\) | ||||
−0.401264 | + | 0.915962i | \(0.631429\pi\) | |||||||
\(62\) | −10.3063 | −1.30890 | ||||||||
\(63\) | −0.606018 | −0.0763511 | ||||||||
\(64\) | 8.39230 | 1.04904 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.46410 | 0.426401 | ||||||||
\(67\) | 1.97786 | 0.241634 | 0.120817 | − | 0.992675i | \(-0.461449\pi\) | ||||
0.120817 | + | 0.992675i | \(0.461449\pi\) | |||||||
\(68\) | −1.42775 | −0.173140 | ||||||||
\(69\) | −1.86434 | −0.224440 | ||||||||
\(70\) | −0.682396 | −0.0815620 | ||||||||
\(71\) | −5.90695 | −0.701026 | −0.350513 | − | 0.936558i | \(-0.613993\pi\) | ||||
−0.350513 | + | 0.936558i | \(0.613993\pi\) | |||||||
\(72\) | 3.07638 | 0.362555 | ||||||||
\(73\) | 4.35395 | 0.509592 | 0.254796 | − | 0.966995i | \(-0.417992\pi\) | ||||
0.254796 | + | 0.966995i | \(0.417992\pi\) | |||||||
\(74\) | −4.22030 | −0.490600 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 3.57593 | 0.410187 | ||||||||
\(77\) | −1.86434 | −0.212461 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.29546 | −0.370768 | −0.185384 | − | 0.982666i | \(-0.559353\pi\) | ||||
−0.185384 | + | 0.982666i | \(0.559353\pi\) | |||||||
\(80\) | 2.00000 | 0.223607 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.20499 | 0.133069 | ||||||||
\(83\) | −6.97707 | −0.765833 | −0.382916 | − | 0.923783i | \(-0.625080\pi\) | ||||
−0.382916 | + | 0.923783i | \(0.625080\pi\) | |||||||
\(84\) | −0.443636 | −0.0484047 | ||||||||
\(85\) | −1.95035 | −0.211545 | ||||||||
\(86\) | 5.64237 | 0.608432 | ||||||||
\(87\) | 2.78171 | 0.298230 | ||||||||
\(88\) | 9.46410 | 1.00888 | ||||||||
\(89\) | 16.2993 | 1.72772 | 0.863859 | − | 0.503734i | \(-0.168041\pi\) | ||||
0.863859 | + | 0.503734i | \(0.168041\pi\) | |||||||
\(90\) | 1.12603 | 0.118694 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.36479 | −0.142289 | ||||||||
\(93\) | −9.15276 | −0.949097 | ||||||||
\(94\) | −11.4882 | −1.18492 | ||||||||
\(95\) | 4.88481 | 0.501171 | ||||||||
\(96\) | 3.90069 | 0.398113 | ||||||||
\(97\) | 13.2024 | 1.34050 | 0.670251 | − | 0.742135i | \(-0.266187\pi\) | ||||
0.670251 | + | 0.742135i | \(0.266187\pi\) | |||||||
\(98\) | 7.46868 | 0.754451 | ||||||||
\(99\) | 3.07638 | 0.309188 | ||||||||
\(100\) | −0.732051 | −0.0732051 | ||||||||
\(101\) | −7.86434 | −0.782531 | −0.391266 | − | 0.920278i | \(-0.627963\pi\) | ||||
−0.391266 | + | 0.920278i | \(0.627963\pi\) | |||||||
\(102\) | 2.19615 | 0.217451 | ||||||||
\(103\) | 15.1101 | 1.48885 | 0.744424 | − | 0.667708i | \(-0.232724\pi\) | ||||
0.744424 | + | 0.667708i | \(0.232724\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.606018 | −0.0591413 | ||||||||
\(106\) | 12.0000 | 1.16554 | ||||||||
\(107\) | −8.20699 | −0.793400 | −0.396700 | − | 0.917948i | \(-0.629845\pi\) | ||||
−0.396700 | + | 0.917948i | \(0.629845\pi\) | |||||||
\(108\) | 0.732051 | 0.0704416 | ||||||||
\(109\) | 10.5927 | 1.01460 | 0.507299 | − | 0.861770i | \(-0.330644\pi\) | ||||
0.507299 | + | 0.861770i | \(0.330644\pi\) | |||||||
\(110\) | 3.46410 | 0.330289 | ||||||||
\(111\) | −3.74793 | −0.355738 | ||||||||
\(112\) | 1.21204 | 0.114527 | ||||||||
\(113\) | 3.46410 | 0.325875 | 0.162938 | − | 0.986636i | \(-0.447903\pi\) | ||||
0.162938 | + | 0.986636i | \(0.447903\pi\) | |||||||
\(114\) | −5.50045 | −0.515164 | ||||||||
\(115\) | −1.86434 | −0.173851 | ||||||||
\(116\) | 2.03635 | 0.189070 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 13.0330 | 1.19978 | ||||||||
\(119\) | −1.18195 | −0.108349 | ||||||||
\(120\) | 3.07638 | 0.280834 | ||||||||
\(121\) | −1.53590 | −0.139627 | ||||||||
\(122\) | 7.05791 | 0.638994 | ||||||||
\(123\) | 1.07012 | 0.0964895 | ||||||||
\(124\) | −6.70028 | −0.601703 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0.682396 | 0.0607927 | ||||||||
\(127\) | 18.0438 | 1.60113 | 0.800565 | − | 0.599246i | \(-0.204533\pi\) | ||||
0.800565 | + | 0.599246i | \(0.204533\pi\) | |||||||
\(128\) | −1.64863 | −0.145719 | ||||||||
\(129\) | 5.01084 | 0.441180 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.11899 | 0.0977662 | 0.0488831 | − | 0.998805i | \(-0.484434\pi\) | ||||
0.0488831 | + | 0.998805i | \(0.484434\pi\) | |||||||
\(132\) | 2.25207 | 0.196017 | ||||||||
\(133\) | 2.96028 | 0.256689 | ||||||||
\(134\) | −2.22713 | −0.192395 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 6.00000 | 0.514496 | ||||||||
\(137\) | 8.70654 | 0.743850 | 0.371925 | − | 0.928263i | \(-0.378698\pi\) | ||||
0.371925 | + | 0.928263i | \(0.378698\pi\) | |||||||
\(138\) | 2.09931 | 0.178705 | ||||||||
\(139\) | 9.65689 | 0.819086 | 0.409543 | − | 0.912291i | \(-0.365688\pi\) | ||||
0.409543 | + | 0.912291i | \(0.365688\pi\) | |||||||
\(140\) | −0.443636 | −0.0374941 | ||||||||
\(141\) | −10.2024 | −0.859198 | ||||||||
\(142\) | 6.65142 | 0.558174 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.00000 | −0.166667 | ||||||||
\(145\) | 2.78171 | 0.231008 | ||||||||
\(146\) | −4.90269 | −0.405750 | ||||||||
\(147\) | 6.63274 | 0.547059 | ||||||||
\(148\) | −2.74368 | −0.225529 | ||||||||
\(149\) | 5.17569 | 0.424009 | 0.212004 | − | 0.977269i | \(-0.432001\pi\) | ||||
0.212004 | + | 0.977269i | \(0.432001\pi\) | |||||||
\(150\) | 1.12603 | 0.0919402 | ||||||||
\(151\) | 22.1451 | 1.80215 | 0.901073 | − | 0.433668i | \(-0.142781\pi\) | ||||
0.901073 | + | 0.433668i | \(0.142781\pi\) | |||||||
\(152\) | −15.0275 | −1.21889 | ||||||||
\(153\) | 1.95035 | 0.157676 | ||||||||
\(154\) | 2.09931 | 0.169167 | ||||||||
\(155\) | −9.15276 | −0.735167 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.3756 | −1.14730 | −0.573650 | − | 0.819100i | \(-0.694473\pi\) | ||||
−0.573650 | + | 0.819100i | \(0.694473\pi\) | |||||||
\(158\) | 3.71080 | 0.295215 | ||||||||
\(159\) | 10.6569 | 0.845146 | ||||||||
\(160\) | 3.90069 | 0.308377 | ||||||||
\(161\) | −1.12983 | −0.0890427 | ||||||||
\(162\) | −1.12603 | −0.0884695 | ||||||||
\(163\) | 10.0701 | 0.788753 | 0.394376 | − | 0.918949i | \(-0.370961\pi\) | ||||
0.394376 | + | 0.918949i | \(0.370961\pi\) | |||||||
\(164\) | 0.783382 | 0.0611719 | ||||||||
\(165\) | 3.07638 | 0.239496 | ||||||||
\(166\) | 7.85641 | 0.609775 | ||||||||
\(167\) | −10.8430 | −0.839056 | −0.419528 | − | 0.907742i | \(-0.637804\pi\) | ||||
−0.419528 | + | 0.907742i | \(0.637804\pi\) | |||||||
\(168\) | 1.86434 | 0.143837 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 2.19615 | 0.168437 | ||||||||
\(171\) | −4.88481 | −0.373551 | ||||||||
\(172\) | 3.66819 | 0.279697 | ||||||||
\(173\) | 24.6623 | 1.87504 | 0.937518 | − | 0.347936i | \(-0.113117\pi\) | ||||
0.937518 | + | 0.347936i | \(0.113117\pi\) | |||||||
\(174\) | −3.13229 | −0.237458 | ||||||||
\(175\) | −0.606018 | −0.0458107 | ||||||||
\(176\) | −6.15276 | −0.463781 | ||||||||
\(177\) | 11.5742 | 0.869974 | ||||||||
\(178\) | −18.3535 | −1.37565 | ||||||||
\(179\) | −22.8397 | −1.70712 | −0.853561 | − | 0.520993i | \(-0.825562\pi\) | ||||
−0.853561 | + | 0.520993i | \(0.825562\pi\) | |||||||
\(180\) | 0.732051 | 0.0545638 | ||||||||
\(181\) | 17.4616 | 1.29791 | 0.648957 | − | 0.760825i | \(-0.275206\pi\) | ||||
0.648957 | + | 0.760825i | \(0.275206\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.26795 | 0.463340 | ||||||||
\(184\) | 5.73542 | 0.422821 | ||||||||
\(185\) | −3.74793 | −0.275554 | ||||||||
\(186\) | 10.3063 | 0.755695 | ||||||||
\(187\) | 6.00000 | 0.438763 | ||||||||
\(188\) | −7.46868 | −0.544710 | ||||||||
\(189\) | 0.606018 | 0.0440813 | ||||||||
\(190\) | −5.50045 | −0.399045 | ||||||||
\(191\) | 7.67356 | 0.555239 | 0.277620 | − | 0.960691i | \(-0.410455\pi\) | ||||
0.277620 | + | 0.960691i | \(0.410455\pi\) | |||||||
\(192\) | −8.39230 | −0.605662 | ||||||||
\(193\) | 21.0108 | 1.51239 | 0.756197 | − | 0.654344i | \(-0.227055\pi\) | ||||
0.756197 | + | 0.654344i | \(0.227055\pi\) | |||||||
\(194\) | −14.8663 | −1.06734 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.85550 | 0.346822 | ||||||||
\(197\) | 20.3776 | 1.45185 | 0.725923 | − | 0.687776i | \(-0.241413\pi\) | ||||
0.725923 | + | 0.687776i | \(0.241413\pi\) | |||||||
\(198\) | −3.46410 | −0.246183 | ||||||||
\(199\) | −14.8014 | −1.04924 | −0.524621 | − | 0.851336i | \(-0.675793\pi\) | ||||
−0.524621 | + | 0.851336i | \(0.675793\pi\) | |||||||
\(200\) | 3.07638 | 0.217533 | ||||||||
\(201\) | −1.97786 | −0.139507 | ||||||||
\(202\) | 8.85550 | 0.623071 | ||||||||
\(203\) | 1.68576 | 0.118317 | ||||||||
\(204\) | 1.42775 | 0.0999626 | ||||||||
\(205\) | 1.07012 | 0.0747404 | ||||||||
\(206\) | −17.0145 | −1.18546 | ||||||||
\(207\) | 1.86434 | 0.129581 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15.0275 | −1.03947 | ||||||||
\(210\) | 0.682396 | 0.0470898 | ||||||||
\(211\) | 5.22030 | 0.359380 | 0.179690 | − | 0.983723i | \(-0.442491\pi\) | ||||
0.179690 | + | 0.983723i | \(0.442491\pi\) | |||||||
\(212\) | 7.80138 | 0.535801 | ||||||||
\(213\) | 5.90695 | 0.404737 | ||||||||
\(214\) | 9.24134 | 0.631725 | ||||||||
\(215\) | 5.01084 | 0.341736 | ||||||||
\(216\) | −3.07638 | −0.209321 | ||||||||
\(217\) | −5.54674 | −0.376537 | ||||||||
\(218\) | −11.9277 | −0.807848 | ||||||||
\(219\) | −4.35395 | −0.294213 | ||||||||
\(220\) | 2.25207 | 0.151834 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 4.22030 | 0.283248 | ||||||||
\(223\) | −6.16685 | −0.412963 | −0.206481 | − | 0.978451i | \(-0.566201\pi\) | ||||
−0.206481 | + | 0.978451i | \(0.566201\pi\) | |||||||
\(224\) | 2.36389 | 0.157944 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −3.90069 | −0.259470 | ||||||||
\(227\) | 17.1114 | 1.13572 | 0.567860 | − | 0.823125i | \(-0.307771\pi\) | ||||
0.567860 | + | 0.823125i | \(0.307771\pi\) | |||||||
\(228\) | −3.57593 | −0.236822 | ||||||||
\(229\) | −28.9206 | −1.91113 | −0.955563 | − | 0.294788i | \(-0.904751\pi\) | ||||
−0.955563 | + | 0.294788i | \(0.904751\pi\) | |||||||
\(230\) | 2.09931 | 0.138424 | ||||||||
\(231\) | 1.86434 | 0.122665 | ||||||||
\(232\) | −8.55758 | −0.561832 | ||||||||
\(233\) | 11.3284 | 0.742151 | 0.371075 | − | 0.928603i | \(-0.378989\pi\) | ||||
0.371075 | + | 0.928603i | \(0.378989\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.2024 | −0.665532 | ||||||||
\(236\) | 8.47294 | 0.551541 | ||||||||
\(237\) | 3.29546 | 0.214063 | ||||||||
\(238\) | 1.33091 | 0.0862700 | ||||||||
\(239\) | −19.1298 | −1.23741 | −0.618703 | − | 0.785625i | \(-0.712341\pi\) | ||||
−0.618703 | + | 0.785625i | \(0.712341\pi\) | |||||||
\(240\) | −2.00000 | −0.129099 | ||||||||
\(241\) | −5.47415 | −0.352621 | −0.176311 | − | 0.984335i | \(-0.556416\pi\) | ||||
−0.176311 | + | 0.984335i | \(0.556416\pi\) | |||||||
\(242\) | 1.72947 | 0.111175 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 4.58846 | 0.293746 | ||||||||
\(245\) | 6.63274 | 0.423750 | ||||||||
\(246\) | −1.20499 | −0.0768273 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 28.1573 | 1.78799 | ||||||||
\(249\) | 6.97707 | 0.442154 | ||||||||
\(250\) | 1.12603 | 0.0712165 | ||||||||
\(251\) | 4.71985 | 0.297914 | 0.148957 | − | 0.988844i | \(-0.452408\pi\) | ||||
0.148957 | + | 0.988844i | \(0.452408\pi\) | |||||||
\(252\) | 0.443636 | 0.0279465 | ||||||||
\(253\) | 5.73542 | 0.360583 | ||||||||
\(254\) | −20.3179 | −1.27486 | ||||||||
\(255\) | 1.95035 | 0.122135 | ||||||||
\(256\) | −14.9282 | −0.933013 | ||||||||
\(257\) | 7.27879 | 0.454038 | 0.227019 | − | 0.973890i | \(-0.427102\pi\) | ||||
0.227019 | + | 0.973890i | \(0.427102\pi\) | |||||||
\(258\) | −5.64237 | −0.351278 | ||||||||
\(259\) | −2.27132 | −0.141133 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.78171 | −0.172183 | ||||||||
\(262\) | −1.26001 | −0.0778439 | ||||||||
\(263\) | −1.28672 | −0.0793428 | −0.0396714 | − | 0.999213i | \(-0.512631\pi\) | ||||
−0.0396714 | + | 0.999213i | \(0.512631\pi\) | |||||||
\(264\) | −9.46410 | −0.582475 | ||||||||
\(265\) | 10.6569 | 0.654647 | ||||||||
\(266\) | −3.33337 | −0.204382 | ||||||||
\(267\) | −16.2993 | −0.997498 | ||||||||
\(268\) | −1.44789 | −0.0884441 | ||||||||
\(269\) | 18.9390 | 1.15473 | 0.577367 | − | 0.816485i | \(-0.304080\pi\) | ||||
0.577367 | + | 0.816485i | \(0.304080\pi\) | |||||||
\(270\) | −1.12603 | −0.0685282 | ||||||||
\(271\) | 11.0241 | 0.669669 | 0.334835 | − | 0.942277i | \(-0.391320\pi\) | ||||
0.334835 | + | 0.942277i | \(0.391320\pi\) | |||||||
\(272\) | −3.90069 | −0.236514 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.80385 | −0.592272 | ||||||||
\(275\) | 3.07638 | 0.185513 | ||||||||
\(276\) | 1.36479 | 0.0821509 | ||||||||
\(277\) | 20.9215 | 1.25705 | 0.628525 | − | 0.777790i | \(-0.283659\pi\) | ||||
0.628525 | + | 0.777790i | \(0.283659\pi\) | |||||||
\(278\) | −10.8740 | −0.652177 | ||||||||
\(279\) | 9.15276 | 0.547961 | ||||||||
\(280\) | 1.86434 | 0.111416 | ||||||||
\(281\) | 10.6653 | 0.636238 | 0.318119 | − | 0.948051i | \(-0.396949\pi\) | ||||
0.318119 | + | 0.948051i | \(0.396949\pi\) | |||||||
\(282\) | 11.4882 | 0.684115 | ||||||||
\(283\) | 2.78507 | 0.165555 | 0.0827777 | − | 0.996568i | \(-0.473621\pi\) | ||||
0.0827777 | + | 0.996568i | \(0.473621\pi\) | |||||||
\(284\) | 4.32419 | 0.256593 | ||||||||
\(285\) | −4.88481 | −0.289351 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.648512 | 0.0382805 | ||||||||
\(288\) | −3.90069 | −0.229850 | ||||||||
\(289\) | −13.1962 | −0.776244 | ||||||||
\(290\) | −3.13229 | −0.183934 | ||||||||
\(291\) | −13.2024 | −0.773939 | ||||||||
\(292\) | −3.18732 | −0.186524 | ||||||||
\(293\) | −4.95861 | −0.289685 | −0.144842 | − | 0.989455i | \(-0.546268\pi\) | ||||
−0.144842 | + | 0.989455i | \(0.546268\pi\) | |||||||
\(294\) | −7.46868 | −0.435582 | ||||||||
\(295\) | 11.5742 | 0.673879 | ||||||||
\(296\) | 11.5301 | 0.670171 | ||||||||
\(297\) | −3.07638 | −0.178510 | ||||||||
\(298\) | −5.82799 | −0.337606 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.732051 | 0.0422650 | ||||||||
\(301\) | 3.03666 | 0.175030 | ||||||||
\(302\) | −24.9361 | −1.43491 | ||||||||
\(303\) | 7.86434 | 0.451795 | ||||||||
\(304\) | 9.76961 | 0.560326 | ||||||||
\(305\) | 6.26795 | 0.358902 | ||||||||
\(306\) | −2.19615 | −0.125546 | ||||||||
\(307\) | −9.60723 | −0.548314 | −0.274157 | − | 0.961685i | \(-0.588399\pi\) | ||||
−0.274157 | + | 0.961685i | \(0.588399\pi\) | |||||||
\(308\) | 1.36479 | 0.0777663 | ||||||||
\(309\) | −15.1101 | −0.859586 | ||||||||
\(310\) | 10.3063 | 0.585359 | ||||||||
\(311\) | −26.0393 | −1.47655 | −0.738275 | − | 0.674499i | \(-0.764359\pi\) | ||||
−0.738275 | + | 0.674499i | \(0.764359\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.2311 | 1.65224 | 0.826121 | − | 0.563493i | \(-0.190543\pi\) | ||||
0.826121 | + | 0.563493i | \(0.190543\pi\) | |||||||
\(314\) | 16.1874 | 0.913509 | ||||||||
\(315\) | 0.606018 | 0.0341453 | ||||||||
\(316\) | 2.41245 | 0.135711 | ||||||||
\(317\) | −8.62570 | −0.484467 | −0.242234 | − | 0.970218i | \(-0.577880\pi\) | ||||
−0.242234 | + | 0.970218i | \(0.577880\pi\) | |||||||
\(318\) | −12.0000 | −0.672927 | ||||||||
\(319\) | −8.55758 | −0.479132 | ||||||||
\(320\) | −8.39230 | −0.469144 | ||||||||
\(321\) | 8.20699 | 0.458070 | ||||||||
\(322\) | 1.27222 | 0.0708980 | ||||||||
\(323\) | −9.52706 | −0.530100 | ||||||||
\(324\) | −0.732051 | −0.0406695 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −11.3393 | −0.628025 | ||||||||
\(327\) | −10.5927 | −0.585778 | ||||||||
\(328\) | −3.29209 | −0.181775 | ||||||||
\(329\) | −6.18285 | −0.340871 | ||||||||
\(330\) | −3.46410 | −0.190693 | ||||||||
\(331\) | 20.3021 | 1.11591 | 0.557953 | − | 0.829872i | \(-0.311587\pi\) | ||||
0.557953 | + | 0.829872i | \(0.311587\pi\) | |||||||
\(332\) | 5.10757 | 0.280314 | ||||||||
\(333\) | 3.74793 | 0.205386 | ||||||||
\(334\) | 12.2096 | 0.668077 | ||||||||
\(335\) | −1.97786 | −0.108062 | ||||||||
\(336\) | −1.21204 | −0.0661220 | ||||||||
\(337\) | −17.7847 | −0.968795 | −0.484397 | − | 0.874848i | \(-0.660961\pi\) | ||||
−0.484397 | + | 0.874848i | \(0.660961\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.46410 | −0.188144 | ||||||||
\(340\) | 1.42775 | 0.0774307 | ||||||||
\(341\) | 28.1573 | 1.52481 | ||||||||
\(342\) | 5.50045 | 0.297430 | ||||||||
\(343\) | 8.26169 | 0.446089 | ||||||||
\(344\) | −15.4152 | −0.831134 | ||||||||
\(345\) | 1.86434 | 0.100373 | ||||||||
\(346\) | −27.7705 | −1.49295 | ||||||||
\(347\) | 8.59092 | 0.461185 | 0.230592 | − | 0.973050i | \(-0.425934\pi\) | ||||
0.230592 | + | 0.973050i | \(0.425934\pi\) | |||||||
\(348\) | −2.03635 | −0.109160 | ||||||||
\(349\) | 30.1803 | 1.61551 | 0.807756 | − | 0.589516i | \(-0.200682\pi\) | ||||
0.807756 | + | 0.589516i | \(0.200682\pi\) | |||||||
\(350\) | 0.682396 | 0.0364756 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −12.0000 | −0.639602 | ||||||||
\(353\) | −28.6297 | −1.52381 | −0.761903 | − | 0.647692i | \(-0.775735\pi\) | ||||
−0.761903 | + | 0.647692i | \(0.775735\pi\) | |||||||
\(354\) | −13.0330 | −0.692695 | ||||||||
\(355\) | 5.90695 | 0.313508 | ||||||||
\(356\) | −11.9319 | −0.632388 | ||||||||
\(357\) | 1.18195 | 0.0625552 | ||||||||
\(358\) | 25.7183 | 1.35925 | ||||||||
\(359\) | −17.4624 | −0.921632 | −0.460816 | − | 0.887496i | \(-0.652443\pi\) | ||||
−0.460816 | + | 0.887496i | \(0.652443\pi\) | |||||||
\(360\) | −3.07638 | −0.162139 | ||||||||
\(361\) | 4.86134 | 0.255860 | ||||||||
\(362\) | −19.6624 | −1.03343 | ||||||||
\(363\) | 1.53590 | 0.0806138 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.35395 | −0.227896 | ||||||||
\(366\) | −7.05791 | −0.368923 | ||||||||
\(367\) | 32.4966 | 1.69631 | 0.848155 | − | 0.529748i | \(-0.177714\pi\) | ||||
0.848155 | + | 0.529748i | \(0.177714\pi\) | |||||||
\(368\) | −3.72868 | −0.194371 | ||||||||
\(369\) | −1.07012 | −0.0557082 | ||||||||
\(370\) | 4.22030 | 0.219403 | ||||||||
\(371\) | 6.45827 | 0.335297 | ||||||||
\(372\) | 6.70028 | 0.347393 | ||||||||
\(373\) | 10.7517 | 0.556703 | 0.278352 | − | 0.960479i | \(-0.410212\pi\) | ||||
0.278352 | + | 0.960479i | \(0.410212\pi\) | |||||||
\(374\) | −6.75620 | −0.349355 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 31.3865 | 1.61863 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.682396 | −0.0350987 | ||||||||
\(379\) | −5.84141 | −0.300053 | −0.150027 | − | 0.988682i | \(-0.547936\pi\) | ||||
−0.150027 | + | 0.988682i | \(0.547936\pi\) | |||||||
\(380\) | −3.57593 | −0.183441 | ||||||||
\(381\) | −18.0438 | −0.924413 | ||||||||
\(382\) | −8.64068 | −0.442095 | ||||||||
\(383\) | −23.6439 | −1.20815 | −0.604074 | − | 0.796929i | \(-0.706457\pi\) | ||||
−0.604074 | + | 0.796929i | \(0.706457\pi\) | |||||||
\(384\) | 1.64863 | 0.0841311 | ||||||||
\(385\) | 1.86434 | 0.0950156 | ||||||||
\(386\) | −23.6589 | −1.20421 | ||||||||
\(387\) | −5.01084 | −0.254715 | ||||||||
\(388\) | −9.66484 | −0.490658 | ||||||||
\(389\) | 16.5939 | 0.841345 | 0.420673 | − | 0.907212i | \(-0.361794\pi\) | ||||
0.420673 | + | 0.907212i | \(0.361794\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.63611 | 0.183886 | ||||||||
\(392\) | −20.4048 | −1.03060 | ||||||||
\(393\) | −1.11899 | −0.0564454 | ||||||||
\(394\) | −22.9459 | −1.15600 | ||||||||
\(395\) | 3.29546 | 0.165813 | ||||||||
\(396\) | −2.25207 | −0.113171 | ||||||||
\(397\) | 23.4035 | 1.17459 | 0.587293 | − | 0.809375i | \(-0.300194\pi\) | ||||
0.587293 | + | 0.809375i | \(0.300194\pi\) | |||||||
\(398\) | 16.6668 | 0.835433 | ||||||||
\(399\) | −2.96028 | −0.148199 | ||||||||
\(400\) | −2.00000 | −0.100000 | ||||||||
\(401\) | 0.111825 | 0.00558428 | 0.00279214 | − | 0.999996i | \(-0.499111\pi\) | ||||
0.00279214 | + | 0.999996i | \(0.499111\pi\) | |||||||
\(402\) | 2.22713 | 0.111079 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 5.75710 | 0.286426 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | −1.89823 | −0.0942073 | ||||||||
\(407\) | 11.5301 | 0.571524 | ||||||||
\(408\) | −6.00000 | −0.297044 | ||||||||
\(409\) | 19.2805 | 0.953358 | 0.476679 | − | 0.879077i | \(-0.341840\pi\) | ||||
0.476679 | + | 0.879077i | \(0.341840\pi\) | |||||||
\(410\) | −1.20499 | −0.0595102 | ||||||||
\(411\) | −8.70654 | −0.429462 | ||||||||
\(412\) | −11.0614 | −0.544956 | ||||||||
\(413\) | 7.01421 | 0.345147 | ||||||||
\(414\) | −2.09931 | −0.103175 | ||||||||
\(415\) | 6.97707 | 0.342491 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.65689 | −0.472900 | ||||||||
\(418\) | 16.9215 | 0.827656 | ||||||||
\(419\) | 22.1386 | 1.08154 | 0.540770 | − | 0.841171i | \(-0.318133\pi\) | ||||
0.540770 | + | 0.841171i | \(0.318133\pi\) | |||||||
\(420\) | 0.443636 | 0.0216472 | ||||||||
\(421\) | 0.914785 | 0.0445839 | 0.0222919 | − | 0.999752i | \(-0.492904\pi\) | ||||
0.0222919 | + | 0.999752i | \(0.492904\pi\) | |||||||
\(422\) | −5.87822 | −0.286147 | ||||||||
\(423\) | 10.2024 | 0.496058 | ||||||||
\(424\) | −32.7846 | −1.59216 | ||||||||
\(425\) | 1.95035 | 0.0946057 | ||||||||
\(426\) | −6.65142 | −0.322262 | ||||||||
\(427\) | 3.79849 | 0.183822 | ||||||||
\(428\) | 6.00793 | 0.290404 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.64237 | −0.272099 | ||||||||
\(431\) | −36.9771 | −1.78112 | −0.890561 | − | 0.454863i | \(-0.849688\pi\) | ||||
−0.890561 | + | 0.454863i | \(0.849688\pi\) | |||||||
\(432\) | 2.00000 | 0.0962250 | ||||||||
\(433\) | −28.6898 | −1.37874 | −0.689371 | − | 0.724408i | \(-0.742113\pi\) | ||||
−0.689371 | + | 0.724408i | \(0.742113\pi\) | |||||||
\(434\) | 6.24581 | 0.299808 | ||||||||
\(435\) | −2.78171 | −0.133373 | ||||||||
\(436\) | −7.75440 | −0.371369 | ||||||||
\(437\) | −9.10695 | −0.435644 | ||||||||
\(438\) | 4.90269 | 0.234260 | ||||||||
\(439\) | 5.26212 | 0.251147 | 0.125574 | − | 0.992084i | \(-0.459923\pi\) | ||||
0.125574 | + | 0.992084i | \(0.459923\pi\) | |||||||
\(440\) | −9.46410 | −0.451183 | ||||||||
\(441\) | −6.63274 | −0.315845 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.8275 | 1.36964 | 0.684819 | − | 0.728714i | \(-0.259881\pi\) | ||||
0.684819 | + | 0.728714i | \(0.259881\pi\) | |||||||
\(444\) | 2.74368 | 0.130209 | ||||||||
\(445\) | −16.2993 | −0.772659 | ||||||||
\(446\) | 6.94407 | 0.328811 | ||||||||
\(447\) | −5.17569 | −0.244802 | ||||||||
\(448\) | −5.08589 | −0.240286 | ||||||||
\(449\) | −3.00826 | −0.141969 | −0.0709843 | − | 0.997477i | \(-0.522614\pi\) | ||||
−0.0709843 | + | 0.997477i | \(0.522614\pi\) | |||||||
\(450\) | −1.12603 | −0.0530817 | ||||||||
\(451\) | −3.29209 | −0.155019 | ||||||||
\(452\) | −2.53590 | −0.119279 | ||||||||
\(453\) | −22.1451 | −1.04047 | ||||||||
\(454\) | −19.2679 | −0.904290 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 15.0275 | 0.703728 | ||||||||
\(457\) | −8.88681 | −0.415707 | −0.207854 | − | 0.978160i | \(-0.566648\pi\) | ||||
−0.207854 | + | 0.978160i | \(0.566648\pi\) | |||||||
\(458\) | 32.5655 | 1.52169 | ||||||||
\(459\) | −1.95035 | −0.0910343 | ||||||||
\(460\) | 1.36479 | 0.0636338 | ||||||||
\(461\) | −21.1089 | −0.983139 | −0.491570 | − | 0.870838i | \(-0.663577\pi\) | ||||
−0.491570 | + | 0.870838i | \(0.663577\pi\) | |||||||
\(462\) | −2.09931 | −0.0976687 | ||||||||
\(463\) | 24.4679 | 1.13712 | 0.568560 | − | 0.822642i | \(-0.307501\pi\) | ||||
0.568560 | + | 0.822642i | \(0.307501\pi\) | |||||||
\(464\) | 5.56341 | 0.258275 | ||||||||
\(465\) | 9.15276 | 0.424449 | ||||||||
\(466\) | −12.7562 | −0.590919 | ||||||||
\(467\) | −19.5058 | −0.902622 | −0.451311 | − | 0.892367i | \(-0.649043\pi\) | ||||
−0.451311 | + | 0.892367i | \(0.649043\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.19862 | −0.0553470 | ||||||||
\(470\) | 11.4882 | 0.529913 | ||||||||
\(471\) | 14.3756 | 0.662394 | ||||||||
\(472\) | −35.6068 | −1.63893 | ||||||||
\(473\) | −15.4152 | −0.708793 | ||||||||
\(474\) | −3.71080 | −0.170443 | ||||||||
\(475\) | −4.88481 | −0.224130 | ||||||||
\(476\) | 0.865244 | 0.0396584 | ||||||||
\(477\) | −10.6569 | −0.487945 | ||||||||
\(478\) | 21.5408 | 0.985253 | ||||||||
\(479\) | 27.0304 | 1.23505 | 0.617526 | − | 0.786551i | \(-0.288135\pi\) | ||||
0.617526 | + | 0.786551i | \(0.288135\pi\) | |||||||
\(480\) | −3.90069 | −0.178041 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 6.16407 | 0.280766 | ||||||||
\(483\) | 1.12983 | 0.0514088 | ||||||||
\(484\) | 1.12436 | 0.0511071 | ||||||||
\(485\) | −13.2024 | −0.599491 | ||||||||
\(486\) | 1.12603 | 0.0510779 | ||||||||
\(487\) | −5.21751 | −0.236428 | −0.118214 | − | 0.992988i | \(-0.537717\pi\) | ||||
−0.118214 | + | 0.992988i | \(0.537717\pi\) | |||||||
\(488\) | −19.2826 | −0.872881 | ||||||||
\(489\) | −10.0701 | −0.455387 | ||||||||
\(490\) | −7.46868 | −0.337401 | ||||||||
\(491\) | 14.7817 | 0.667089 | 0.333545 | − | 0.942734i | \(-0.391755\pi\) | ||||
0.333545 | + | 0.942734i | \(0.391755\pi\) | |||||||
\(492\) | −0.783382 | −0.0353176 | ||||||||
\(493\) | −5.42529 | −0.244343 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.07638 | −0.138273 | ||||||||
\(496\) | −18.3055 | −0.821942 | ||||||||
\(497\) | 3.57972 | 0.160572 | ||||||||
\(498\) | −7.85641 | −0.352054 | ||||||||
\(499\) | −10.3171 | −0.461859 | −0.230929 | − | 0.972971i | \(-0.574177\pi\) | ||||
−0.230929 | + | 0.972971i | \(0.574177\pi\) | |||||||
\(500\) | 0.732051 | 0.0327383 | ||||||||
\(501\) | 10.8430 | 0.484429 | ||||||||
\(502\) | −5.31470 | −0.237207 | ||||||||
\(503\) | 26.6343 | 1.18756 | 0.593782 | − | 0.804626i | \(-0.297634\pi\) | ||||
0.593782 | + | 0.804626i | \(0.297634\pi\) | |||||||
\(504\) | −1.86434 | −0.0830444 | ||||||||
\(505\) | 7.86434 | 0.349959 | ||||||||
\(506\) | −6.45827 | −0.287105 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −13.2090 | −0.586054 | ||||||||
\(509\) | 1.42775 | 0.0632840 | 0.0316420 | − | 0.999499i | \(-0.489926\pi\) | ||||
0.0316420 | + | 0.999499i | \(0.489926\pi\) | |||||||
\(510\) | −2.19615 | −0.0972473 | ||||||||
\(511\) | −2.63858 | −0.116724 | ||||||||
\(512\) | 20.1069 | 0.888608 | ||||||||
\(513\) | 4.88481 | 0.215669 | ||||||||
\(514\) | −8.19615 | −0.361517 | ||||||||
\(515\) | −15.1101 | −0.665833 | ||||||||
\(516\) | −3.66819 | −0.161483 | ||||||||
\(517\) | 31.3865 | 1.38038 | ||||||||
\(518\) | 2.55758 | 0.112373 | ||||||||
\(519\) | −24.6623 | −1.08255 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.8623 | 0.563509 | 0.281755 | − | 0.959486i | \(-0.409084\pi\) | ||||
0.281755 | + | 0.959486i | \(0.409084\pi\) | |||||||
\(522\) | 3.13229 | 0.137097 | ||||||||
\(523\) | 15.1002 | 0.660286 | 0.330143 | − | 0.943931i | \(-0.392903\pi\) | ||||
0.330143 | + | 0.943931i | \(0.392903\pi\) | |||||||
\(524\) | −0.819154 | −0.0357849 | ||||||||
\(525\) | 0.606018 | 0.0264488 | ||||||||
\(526\) | 1.44889 | 0.0631747 | ||||||||
\(527\) | 17.8510 | 0.777603 | ||||||||
\(528\) | 6.15276 | 0.267764 | ||||||||
\(529\) | −19.5242 | −0.848880 | ||||||||
\(530\) | −12.0000 | −0.521247 | ||||||||
\(531\) | −11.5742 | −0.502280 | ||||||||
\(532\) | −2.16708 | −0.0939547 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 18.3535 | 0.794233 | ||||||||
\(535\) | 8.20699 | 0.354819 | ||||||||
\(536\) | 6.08464 | 0.262816 | ||||||||
\(537\) | 22.8397 | 0.985607 | ||||||||
\(538\) | −21.3260 | −0.919428 | ||||||||
\(539\) | −20.4048 | −0.878898 | ||||||||
\(540\) | −0.732051 | −0.0315025 | ||||||||
\(541\) | 41.1084 | 1.76739 | 0.883695 | − | 0.468064i | \(-0.155048\pi\) | ||||
0.883695 | + | 0.468064i | \(0.155048\pi\) | |||||||
\(542\) | −12.4135 | −0.533207 | ||||||||
\(543\) | −17.4616 | −0.749351 | ||||||||
\(544\) | −7.60770 | −0.326177 | ||||||||
\(545\) | −10.5927 | −0.453742 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.1327 | 1.28838 | 0.644191 | − | 0.764864i | \(-0.277194\pi\) | ||||
0.644191 | + | 0.764864i | \(0.277194\pi\) | |||||||
\(548\) | −6.37363 | −0.272268 | ||||||||
\(549\) | −6.26795 | −0.267510 | ||||||||
\(550\) | −3.46410 | −0.147710 | ||||||||
\(551\) | 13.5881 | 0.578872 | ||||||||
\(552\) | −5.73542 | −0.244116 | ||||||||
\(553\) | 1.99711 | 0.0849258 | ||||||||
\(554\) | −23.5583 | −1.00089 | ||||||||
\(555\) | 3.74793 | 0.159091 | ||||||||
\(556\) | −7.06933 | −0.299806 | ||||||||
\(557\) | −25.2041 | −1.06793 | −0.533966 | − | 0.845506i | \(-0.679299\pi\) | ||||
−0.533966 | + | 0.845506i | \(0.679299\pi\) | |||||||
\(558\) | −10.3063 | −0.436301 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.21204 | −0.0512179 | ||||||||
\(561\) | −6.00000 | −0.253320 | ||||||||
\(562\) | −12.0095 | −0.506589 | ||||||||
\(563\) | −7.19278 | −0.303140 | −0.151570 | − | 0.988447i | \(-0.548433\pi\) | ||||
−0.151570 | + | 0.988447i | \(0.548433\pi\) | |||||||
\(564\) | 7.46868 | 0.314488 | ||||||||
\(565\) | −3.46410 | −0.145736 | ||||||||
\(566\) | −3.13608 | −0.131819 | ||||||||
\(567\) | −0.606018 | −0.0254504 | ||||||||
\(568\) | −18.1720 | −0.762481 | ||||||||
\(569\) | 18.3521 | 0.769361 | 0.384681 | − | 0.923050i | \(-0.374312\pi\) | ||||
0.384681 | + | 0.923050i | \(0.374312\pi\) | |||||||
\(570\) | 5.50045 | 0.230389 | ||||||||
\(571\) | −27.5433 | −1.15265 | −0.576325 | − | 0.817221i | \(-0.695514\pi\) | ||||
−0.576325 | + | 0.817221i | \(0.695514\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.67356 | −0.320568 | ||||||||
\(574\) | −0.730246 | −0.0304799 | ||||||||
\(575\) | 1.86434 | 0.0777484 | ||||||||
\(576\) | 8.39230 | 0.349679 | ||||||||
\(577\) | 19.1378 | 0.796715 | 0.398358 | − | 0.917230i | \(-0.369580\pi\) | ||||
0.398358 | + | 0.917230i | \(0.369580\pi\) | |||||||
\(578\) | 14.8593 | 0.618065 | ||||||||
\(579\) | −21.0108 | −0.873181 | ||||||||
\(580\) | −2.03635 | −0.0845548 | ||||||||
\(581\) | 4.22823 | 0.175417 | ||||||||
\(582\) | 14.8663 | 0.616230 | ||||||||
\(583\) | −32.7846 | −1.35780 | ||||||||
\(584\) | 13.3944 | 0.554264 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.58355 | 0.230654 | ||||||||
\(587\) | 17.5620 | 0.724863 | 0.362432 | − | 0.932010i | \(-0.381947\pi\) | ||||
0.362432 | + | 0.932010i | \(0.381947\pi\) | |||||||
\(588\) | −4.85550 | −0.200238 | ||||||||
\(589\) | −44.7094 | −1.84222 | ||||||||
\(590\) | −13.0330 | −0.536559 | ||||||||
\(591\) | −20.3776 | −0.838224 | ||||||||
\(592\) | −7.49587 | −0.308078 | ||||||||
\(593\) | 28.9248 | 1.18780 | 0.593901 | − | 0.804538i | \(-0.297587\pi\) | ||||
0.593901 | + | 0.804538i | \(0.297587\pi\) | |||||||
\(594\) | 3.46410 | 0.142134 | ||||||||
\(595\) | 1.18195 | 0.0484550 | ||||||||
\(596\) | −3.78887 | −0.155198 | ||||||||
\(597\) | 14.8014 | 0.605780 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −46.1052 | −1.88381 | −0.941904 | − | 0.335882i | \(-0.890966\pi\) | ||||
−0.941904 | + | 0.335882i | \(0.890966\pi\) | |||||||
\(600\) | −3.07638 | −0.125593 | ||||||||
\(601\) | −19.5099 | −0.795826 | −0.397913 | − | 0.917423i | \(-0.630265\pi\) | ||||
−0.397913 | + | 0.917423i | \(0.630265\pi\) | |||||||
\(602\) | −3.41938 | −0.139363 | ||||||||
\(603\) | 1.97786 | 0.0805446 | ||||||||
\(604\) | −16.2114 | −0.659631 | ||||||||
\(605\) | 1.53590 | 0.0624431 | ||||||||
\(606\) | −8.85550 | −0.359730 | ||||||||
\(607\) | 25.4253 | 1.03198 | 0.515990 | − | 0.856594i | \(-0.327424\pi\) | ||||
0.515990 | + | 0.856594i | \(0.327424\pi\) | |||||||
\(608\) | 19.0541 | 0.772747 | ||||||||
\(609\) | −1.68576 | −0.0683106 | ||||||||
\(610\) | −7.05791 | −0.285767 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −1.42775 | −0.0577135 | ||||||||
\(613\) | −33.4569 | −1.35131 | −0.675656 | − | 0.737217i | \(-0.736139\pi\) | ||||
−0.675656 | + | 0.737217i | \(0.736139\pi\) | |||||||
\(614\) | 10.8181 | 0.436581 | ||||||||
\(615\) | −1.07012 | −0.0431514 | ||||||||
\(616\) | −5.73542 | −0.231087 | ||||||||
\(617\) | 13.9603 | 0.562020 | 0.281010 | − | 0.959705i | \(-0.409331\pi\) | ||||
0.281010 | + | 0.959705i | \(0.409331\pi\) | |||||||
\(618\) | 17.0145 | 0.684424 | ||||||||
\(619\) | −42.1677 | −1.69486 | −0.847432 | − | 0.530904i | \(-0.821852\pi\) | ||||
−0.847432 | + | 0.530904i | \(0.821852\pi\) | |||||||
\(620\) | 6.70028 | 0.269090 | ||||||||
\(621\) | −1.86434 | −0.0748134 | ||||||||
\(622\) | 29.3210 | 1.17567 | ||||||||
\(623\) | −9.87765 | −0.395740 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −32.9152 | −1.31556 | ||||||||
\(627\) | 15.0275 | 0.600141 | ||||||||
\(628\) | 10.5237 | 0.419941 | ||||||||
\(629\) | 7.30977 | 0.291460 | ||||||||
\(630\) | −0.682396 | −0.0271873 | ||||||||
\(631\) | 39.9691 | 1.59115 | 0.795573 | − | 0.605858i | \(-0.207170\pi\) | ||||
0.795573 | + | 0.605858i | \(0.207170\pi\) | |||||||
\(632\) | −10.1381 | −0.403271 | ||||||||
\(633\) | −5.22030 | −0.207488 | ||||||||
\(634\) | 9.71281 | 0.385745 | ||||||||
\(635\) | −18.0438 | −0.716047 | ||||||||
\(636\) | −7.80138 | −0.309345 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 9.63611 | 0.381497 | ||||||||
\(639\) | −5.90695 | −0.233675 | ||||||||
\(640\) | 1.64863 | 0.0651677 | ||||||||
\(641\) | −26.6422 | −1.05230 | −0.526152 | − | 0.850390i | \(-0.676366\pi\) | ||||
−0.526152 | + | 0.850390i | \(0.676366\pi\) | |||||||
\(642\) | −9.24134 | −0.364727 | ||||||||
\(643\) | −16.6185 | −0.655371 | −0.327686 | − | 0.944787i | \(-0.606269\pi\) | ||||
−0.327686 | + | 0.944787i | \(0.606269\pi\) | |||||||
\(644\) | 0.827089 | 0.0325919 | ||||||||
\(645\) | −5.01084 | −0.197302 | ||||||||
\(646\) | 10.7278 | 0.422079 | ||||||||
\(647\) | −20.4729 | −0.804874 | −0.402437 | − | 0.915448i | \(-0.631837\pi\) | ||||
−0.402437 | + | 0.915448i | \(0.631837\pi\) | |||||||
\(648\) | 3.07638 | 0.120852 | ||||||||
\(649\) | −35.6068 | −1.39769 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.54674 | 0.217394 | ||||||||
\(652\) | −7.37184 | −0.288704 | ||||||||
\(653\) | 5.76740 | 0.225696 | 0.112848 | − | 0.993612i | \(-0.464003\pi\) | ||||
0.112848 | + | 0.993612i | \(0.464003\pi\) | |||||||
\(654\) | 11.9277 | 0.466412 | ||||||||
\(655\) | −1.11899 | −0.0437224 | ||||||||
\(656\) | 2.14024 | 0.0835623 | ||||||||
\(657\) | 4.35395 | 0.169864 | ||||||||
\(658\) | 6.96209 | 0.271410 | ||||||||
\(659\) | 30.9499 | 1.20564 | 0.602818 | − | 0.797879i | \(-0.294044\pi\) | ||||
0.602818 | + | 0.797879i | \(0.294044\pi\) | |||||||
\(660\) | −2.25207 | −0.0876615 | ||||||||
\(661\) | 30.8806 | 1.20111 | 0.600557 | − | 0.799582i | \(-0.294946\pi\) | ||||
0.600557 | + | 0.799582i | \(0.294946\pi\) | |||||||
\(662\) | −22.8609 | −0.888513 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −21.4641 | −0.832969 | ||||||||
\(665\) | −2.96028 | −0.114795 | ||||||||
\(666\) | −4.22030 | −0.163533 | ||||||||
\(667\) | −5.18605 | −0.200805 | ||||||||
\(668\) | 7.93762 | 0.307116 | ||||||||
\(669\) | 6.16685 | 0.238424 | ||||||||
\(670\) | 2.22713 | 0.0860416 | ||||||||
\(671\) | −19.2826 | −0.744396 | ||||||||
\(672\) | −2.36389 | −0.0911890 | ||||||||
\(673\) | 23.5079 | 0.906164 | 0.453082 | − | 0.891469i | \(-0.350325\pi\) | ||||
0.453082 | + | 0.891469i | \(0.350325\pi\) | |||||||
\(674\) | 20.0262 | 0.771379 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.52213 | −0.212233 | −0.106116 | − | 0.994354i | \(-0.533842\pi\) | ||||
−0.106116 | + | 0.994354i | \(0.533842\pi\) | |||||||
\(678\) | 3.90069 | 0.149805 | ||||||||
\(679\) | −8.00090 | −0.307046 | ||||||||
\(680\) | −6.00000 | −0.230089 | ||||||||
\(681\) | −17.1114 | −0.655709 | ||||||||
\(682\) | −31.7061 | −1.21409 | ||||||||
\(683\) | 13.4725 | 0.515510 | 0.257755 | − | 0.966210i | \(-0.417017\pi\) | ||||
0.257755 | + | 0.966210i | \(0.417017\pi\) | |||||||
\(684\) | 3.57593 | 0.136729 | ||||||||
\(685\) | −8.70654 | −0.332660 | ||||||||
\(686\) | −9.30293 | −0.355188 | ||||||||
\(687\) | 28.9206 | 1.10339 | ||||||||
\(688\) | 10.0217 | 0.382073 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −2.09931 | −0.0799193 | ||||||||
\(691\) | 42.5023 | 1.61686 | 0.808432 | − | 0.588590i | \(-0.200317\pi\) | ||||
0.808432 | + | 0.588590i | \(0.200317\pi\) | |||||||
\(692\) | −18.0540 | −0.686311 | ||||||||
\(693\) | −1.86434 | −0.0708205 | ||||||||
\(694\) | −9.67366 | −0.367207 | ||||||||
\(695\) | −9.65689 | −0.366307 | ||||||||
\(696\) | 8.55758 | 0.324374 | ||||||||
\(697\) | −2.08710 | −0.0790547 | ||||||||
\(698\) | −33.9840 | −1.28631 | ||||||||
\(699\) | −11.3284 | −0.428481 | ||||||||
\(700\) | 0.443636 | 0.0167679 | ||||||||
\(701\) | −0.553573 | −0.0209082 | −0.0104541 | − | 0.999945i | \(-0.503328\pi\) | ||||
−0.0104541 | + | 0.999945i | \(0.503328\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.3079 | −0.690497 | ||||||||
\(704\) | 25.8179 | 0.973049 | ||||||||
\(705\) | 10.2024 | 0.384245 | ||||||||
\(706\) | 32.2380 | 1.21329 | ||||||||
\(707\) | 4.76593 | 0.179241 | ||||||||
\(708\) | −8.47294 | −0.318433 | ||||||||
\(709\) | 12.9783 | 0.487410 | 0.243705 | − | 0.969849i | \(-0.421637\pi\) | ||||
0.243705 | + | 0.969849i | \(0.421637\pi\) | |||||||
\(710\) | −6.65142 | −0.249623 | ||||||||
\(711\) | −3.29546 | −0.123589 | ||||||||
\(712\) | 50.1427 | 1.87918 | ||||||||
\(713\) | 17.0639 | 0.639047 | ||||||||
\(714\) | −1.33091 | −0.0498080 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.7198 | 0.624850 | ||||||||
\(717\) | 19.1298 | 0.714416 | ||||||||
\(718\) | 19.6633 | 0.733826 | ||||||||
\(719\) | −22.4328 | −0.836601 | −0.418300 | − | 0.908309i | \(-0.637374\pi\) | ||||
−0.418300 | + | 0.908309i | \(0.637374\pi\) | |||||||
\(720\) | 2.00000 | 0.0745356 | ||||||||
\(721\) | −9.15703 | −0.341025 | ||||||||
\(722\) | −5.47402 | −0.203722 | ||||||||
\(723\) | 5.47415 | 0.203586 | ||||||||
\(724\) | −12.7828 | −0.475069 | ||||||||
\(725\) | −2.78171 | −0.103310 | ||||||||
\(726\) | −1.72947 | −0.0641867 | ||||||||
\(727\) | −48.3530 | −1.79331 | −0.896657 | − | 0.442725i | \(-0.854012\pi\) | ||||
−0.896657 | + | 0.442725i | \(0.854012\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 4.90269 | 0.181457 | ||||||||
\(731\) | −9.77287 | −0.361463 | ||||||||
\(732\) | −4.58846 | −0.169594 | ||||||||
\(733\) | 5.72579 | 0.211487 | 0.105743 | − | 0.994393i | \(-0.466278\pi\) | ||||
0.105743 | + | 0.994393i | \(0.466278\pi\) | |||||||
\(734\) | −36.5922 | −1.35064 | ||||||||
\(735\) | −6.63274 | −0.244652 | ||||||||
\(736\) | −7.27222 | −0.268058 | ||||||||
\(737\) | 6.08464 | 0.224131 | ||||||||
\(738\) | 1.20499 | 0.0443563 | ||||||||
\(739\) | −20.8964 | −0.768688 | −0.384344 | − | 0.923190i | \(-0.625572\pi\) | ||||
−0.384344 | + | 0.923190i | \(0.625572\pi\) | |||||||
\(740\) | 2.74368 | 0.100860 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.27222 | −0.266972 | ||||||||
\(743\) | −29.5593 | −1.08442 | −0.542212 | − | 0.840242i | \(-0.682413\pi\) | ||||
−0.542212 | + | 0.840242i | \(0.682413\pi\) | |||||||
\(744\) | −28.1573 | −1.03230 | ||||||||
\(745\) | −5.17569 | −0.189622 | ||||||||
\(746\) | −12.1068 | −0.443261 | ||||||||
\(747\) | −6.97707 | −0.255278 | ||||||||
\(748\) | −4.39230 | −0.160599 | ||||||||
\(749\) | 4.97359 | 0.181731 | ||||||||
\(750\) | −1.12603 | −0.0411169 | ||||||||
\(751\) | −21.0467 | −0.768006 | −0.384003 | − | 0.923332i | \(-0.625455\pi\) | ||||
−0.384003 | + | 0.923332i | \(0.625455\pi\) | |||||||
\(752\) | −20.4048 | −0.744087 | ||||||||
\(753\) | −4.71985 | −0.172001 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22.1451 | −0.805944 | ||||||||
\(756\) | −0.443636 | −0.0161349 | ||||||||
\(757\) | 14.0849 | 0.511925 | 0.255962 | − | 0.966687i | \(-0.417608\pi\) | ||||
0.255962 | + | 0.966687i | \(0.417608\pi\) | |||||||
\(758\) | 6.57762 | 0.238910 | ||||||||
\(759\) | −5.73542 | −0.208183 | ||||||||
\(760\) | 15.0275 | 0.545105 | ||||||||
\(761\) | 45.3819 | 1.64509 | 0.822546 | − | 0.568698i | \(-0.192553\pi\) | ||||
0.822546 | + | 0.568698i | \(0.192553\pi\) | |||||||
\(762\) | 20.3179 | 0.736041 | ||||||||
\(763\) | −6.41938 | −0.232397 | ||||||||
\(764\) | −5.61744 | −0.203232 | ||||||||
\(765\) | −1.95035 | −0.0705149 | ||||||||
\(766\) | 26.6238 | 0.961957 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 14.9282 | 0.538675 | ||||||||
\(769\) | 44.1769 | 1.59306 | 0.796530 | − | 0.604599i | \(-0.206667\pi\) | ||||
0.796530 | + | 0.604599i | \(0.206667\pi\) | |||||||
\(770\) | −2.09931 | −0.0756538 | ||||||||
\(771\) | −7.27879 | −0.262139 | ||||||||
\(772\) | −15.3810 | −0.553574 | ||||||||
\(773\) | 35.7458 | 1.28569 | 0.642843 | − | 0.765998i | \(-0.277755\pi\) | ||||
0.642843 | + | 0.765998i | \(0.277755\pi\) | |||||||
\(774\) | 5.64237 | 0.202811 | ||||||||
\(775\) | 9.15276 | 0.328777 | ||||||||
\(776\) | 40.6156 | 1.45802 | ||||||||
\(777\) | 2.27132 | 0.0814831 | ||||||||
\(778\) | −18.6853 | −0.669900 | ||||||||
\(779\) | 5.22733 | 0.187289 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.1720 | −0.650246 | ||||||||
\(782\) | −4.09438 | −0.146415 | ||||||||
\(783\) | 2.78171 | 0.0994100 | ||||||||
\(784\) | 13.2655 | 0.473767 | ||||||||
\(785\) | 14.3756 | 0.513088 | ||||||||
\(786\) | 1.26001 | 0.0449432 | ||||||||
\(787\) | 10.1819 | 0.362947 | 0.181474 | − | 0.983396i | \(-0.441913\pi\) | ||||
0.181474 | + | 0.983396i | \(0.441913\pi\) | |||||||
\(788\) | −14.9175 | −0.531413 | ||||||||
\(789\) | 1.28672 | 0.0458086 | ||||||||
\(790\) | −3.71080 | −0.132024 | ||||||||
\(791\) | −2.09931 | −0.0746428 | ||||||||
\(792\) | 9.46410 | 0.336292 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −26.3531 | −0.935235 | ||||||||
\(795\) | −10.6569 | −0.377961 | ||||||||
\(796\) | 10.8354 | 0.384049 | ||||||||
\(797\) | −36.8856 | −1.30655 | −0.653277 | − | 0.757119i | \(-0.726606\pi\) | ||||
−0.653277 | + | 0.757119i | \(0.726606\pi\) | |||||||
\(798\) | 3.33337 | 0.118000 | ||||||||
\(799\) | 19.8982 | 0.703949 | ||||||||
\(800\) | −3.90069 | −0.137910 | ||||||||
\(801\) | 16.2993 | 0.575906 | ||||||||
\(802\) | −0.125919 | −0.00444635 | ||||||||
\(803\) | 13.3944 | 0.472678 | ||||||||
\(804\) | 1.44789 | 0.0510632 | ||||||||
\(805\) | 1.12983 | 0.0398211 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.9390 | −0.666686 | ||||||||
\(808\) | −24.1937 | −0.851131 | ||||||||
\(809\) | −12.1693 | −0.427849 | −0.213924 | − | 0.976850i | \(-0.568625\pi\) | ||||
−0.213924 | + | 0.976850i | \(0.568625\pi\) | |||||||
\(810\) | 1.12603 | 0.0395647 | ||||||||
\(811\) | 26.2312 | 0.921104 | 0.460552 | − | 0.887633i | \(-0.347652\pi\) | ||||
0.460552 | + | 0.887633i | \(0.347652\pi\) | |||||||
\(812\) | −1.23407 | −0.0433072 | ||||||||
\(813\) | −11.0241 | −0.386634 | ||||||||
\(814\) | −12.9832 | −0.455062 | ||||||||
\(815\) | −10.0701 | −0.352741 | ||||||||
\(816\) | 3.90069 | 0.136551 | ||||||||
\(817\) | 24.4770 | 0.856341 | ||||||||
\(818\) | −21.7104 | −0.759088 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.783382 | −0.0273569 | ||||||||
\(821\) | −16.5451 | −0.577427 | −0.288713 | − | 0.957416i | \(-0.593227\pi\) | ||||
−0.288713 | + | 0.957416i | \(0.593227\pi\) | |||||||
\(822\) | 9.80385 | 0.341948 | ||||||||
\(823\) | 27.9291 | 0.973547 | 0.486774 | − | 0.873528i | \(-0.338174\pi\) | ||||
0.486774 | + | 0.873528i | \(0.338174\pi\) | |||||||
\(824\) | 46.4845 | 1.61937 | ||||||||
\(825\) | −3.07638 | −0.107106 | ||||||||
\(826\) | −7.89823 | −0.274814 | ||||||||
\(827\) | 1.83852 | 0.0639316 | 0.0319658 | − | 0.999489i | \(-0.489823\pi\) | ||||
0.0319658 | + | 0.999489i | \(0.489823\pi\) | |||||||
\(828\) | −1.36479 | −0.0474298 | ||||||||
\(829\) | −34.9731 | −1.21467 | −0.607333 | − | 0.794447i | \(-0.707761\pi\) | ||||
−0.607333 | + | 0.794447i | \(0.707761\pi\) | |||||||
\(830\) | −7.85641 | −0.272700 | ||||||||
\(831\) | −20.9215 | −0.725758 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12.9361 | −0.448211 | ||||||||
\(834\) | 10.8740 | 0.376535 | ||||||||
\(835\) | 10.8430 | 0.375237 | ||||||||
\(836\) | 11.0009 | 0.380474 | ||||||||
\(837\) | −9.15276 | −0.316366 | ||||||||
\(838\) | −24.9287 | −0.861149 | ||||||||
\(839\) | −12.7125 | −0.438884 | −0.219442 | − | 0.975626i | \(-0.570424\pi\) | ||||
−0.219442 | + | 0.975626i | \(0.570424\pi\) | |||||||
\(840\) | −1.86434 | −0.0643259 | ||||||||
\(841\) | −21.2621 | −0.733176 | ||||||||
\(842\) | −1.03008 | −0.0354988 | ||||||||
\(843\) | −10.6653 | −0.367332 | ||||||||
\(844\) | −3.82152 | −0.131542 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −11.4882 | −0.394974 | ||||||||
\(847\) | 0.930783 | 0.0319821 | ||||||||
\(848\) | 21.3138 | 0.731918 | ||||||||
\(849\) | −2.78507 | −0.0955835 | ||||||||
\(850\) | −2.19615 | −0.0753274 | ||||||||
\(851\) | 6.98743 | 0.239526 | ||||||||
\(852\) | −4.32419 | −0.148144 | ||||||||
\(853\) | −20.2430 | −0.693106 | −0.346553 | − | 0.938030i | \(-0.612648\pi\) | ||||
−0.346553 | + | 0.938030i | \(0.612648\pi\) | |||||||
\(854\) | −4.27723 | −0.146364 | ||||||||
\(855\) | 4.88481 | 0.167057 | ||||||||
\(856\) | −25.2478 | −0.862952 | ||||||||
\(857\) | 53.5208 | 1.82823 | 0.914117 | − | 0.405450i | \(-0.132885\pi\) | ||||
0.914117 | + | 0.405450i | \(0.132885\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.969120 | −0.0330659 | −0.0165330 | − | 0.999863i | \(-0.505263\pi\) | ||||
−0.0165330 | + | 0.999863i | \(0.505263\pi\) | |||||||
\(860\) | −3.66819 | −0.125084 | ||||||||
\(861\) | −0.648512 | −0.0221012 | ||||||||
\(862\) | 41.6374 | 1.41817 | ||||||||
\(863\) | 5.67766 | 0.193270 | 0.0966349 | − | 0.995320i | \(-0.469192\pi\) | ||||
0.0966349 | + | 0.995320i | \(0.469192\pi\) | |||||||
\(864\) | 3.90069 | 0.132704 | ||||||||
\(865\) | −24.6623 | −0.838542 | ||||||||
\(866\) | 32.3056 | 1.09779 | ||||||||
\(867\) | 13.1962 | 0.448165 | ||||||||
\(868\) | 4.06049 | 0.137822 | ||||||||
\(869\) | −10.1381 | −0.343911 | ||||||||
\(870\) | 3.13229 | 0.106195 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 32.5872 | 1.10354 | ||||||||
\(873\) | 13.2024 | 0.446834 | ||||||||
\(874\) | 10.2547 | 0.346871 | ||||||||
\(875\) | 0.606018 | 0.0204872 | ||||||||
\(876\) | 3.18732 | 0.107689 | ||||||||
\(877\) | −32.2169 | −1.08789 | −0.543944 | − | 0.839121i | \(-0.683070\pi\) | ||||
−0.543944 | + | 0.839121i | \(0.683070\pi\) | |||||||
\(878\) | −5.92531 | −0.199970 | ||||||||
\(879\) | 4.95861 | 0.167250 | ||||||||
\(880\) | 6.15276 | 0.207409 | ||||||||
\(881\) | 41.1152 | 1.38520 | 0.692602 | − | 0.721320i | \(-0.256464\pi\) | ||||
0.692602 | + | 0.721320i | \(0.256464\pi\) | |||||||
\(882\) | 7.46868 | 0.251484 | ||||||||
\(883\) | −14.6027 | −0.491419 | −0.245709 | − | 0.969344i | \(-0.579021\pi\) | ||||
−0.245709 | + | 0.969344i | \(0.579021\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −11.5742 | −0.389064 | ||||||||
\(886\) | −32.4607 | −1.09054 | ||||||||
\(887\) | 9.10558 | 0.305736 | 0.152868 | − | 0.988247i | \(-0.451149\pi\) | ||||
0.152868 | + | 0.988247i | \(0.451149\pi\) | |||||||
\(888\) | −11.5301 | −0.386924 | ||||||||
\(889\) | −10.9349 | −0.366744 | ||||||||
\(890\) | 18.3535 | 0.615210 | ||||||||
\(891\) | 3.07638 | 0.103063 | ||||||||
\(892\) | 4.51445 | 0.151155 | ||||||||
\(893\) | −49.8368 | −1.66773 | ||||||||
\(894\) | 5.82799 | 0.194917 | ||||||||
\(895\) | 22.8397 | 0.763448 | ||||||||
\(896\) | 0.999098 | 0.0333775 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.38740 | 0.113039 | ||||||||
\(899\) | −25.4603 | −0.849148 | ||||||||
\(900\) | −0.732051 | −0.0244017 | ||||||||
\(901\) | −20.7846 | −0.692436 | ||||||||
\(902\) | 3.70700 | 0.123430 | ||||||||
\(903\) | −3.03666 | −0.101054 | ||||||||
\(904\) | 10.6569 | 0.354443 | ||||||||
\(905\) | −17.4616 | −0.580444 | ||||||||
\(906\) | 24.9361 | 0.828448 | ||||||||
\(907\) | −50.5160 | −1.67736 | −0.838679 | − | 0.544627i | \(-0.816671\pi\) | ||||
−0.838679 | + | 0.544627i | \(0.816671\pi\) | |||||||
\(908\) | −12.5264 | −0.415703 | ||||||||
\(909\) | −7.86434 | −0.260844 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.3571 | 1.50275 | 0.751374 | − | 0.659876i | \(-0.229391\pi\) | ||||
0.751374 | + | 0.659876i | \(0.229391\pi\) | |||||||
\(912\) | −9.76961 | −0.323504 | ||||||||
\(913\) | −21.4641 | −0.710358 | ||||||||
\(914\) | 10.0068 | 0.330997 | ||||||||
\(915\) | −6.26795 | −0.207212 | ||||||||
\(916\) | 21.1713 | 0.699521 | ||||||||
\(917\) | −0.678126 | −0.0223937 | ||||||||
\(918\) | 2.19615 | 0.0724838 | ||||||||
\(919\) | 4.30220 | 0.141916 | 0.0709582 | − | 0.997479i | \(-0.477394\pi\) | ||||
0.0709582 | + | 0.997479i | \(0.477394\pi\) | |||||||
\(920\) | −5.73542 | −0.189091 | ||||||||
\(921\) | 9.60723 | 0.316569 | ||||||||
\(922\) | 23.7693 | 0.782800 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −1.36479 | −0.0448984 | ||||||||
\(925\) | 3.74793 | 0.123231 | ||||||||
\(926\) | −27.5516 | −0.905403 | ||||||||
\(927\) | 15.1101 | 0.496282 | ||||||||
\(928\) | 10.8506 | 0.356188 | ||||||||
\(929\) | 48.3874 | 1.58754 | 0.793769 | − | 0.608219i | \(-0.208116\pi\) | ||||
0.793769 | + | 0.608219i | \(0.208116\pi\) | |||||||
\(930\) | −10.3063 | −0.337957 | ||||||||
\(931\) | 32.3997 | 1.06186 | ||||||||
\(932\) | −8.29300 | −0.271646 | ||||||||
\(933\) | 26.0393 | 0.852487 | ||||||||
\(934\) | 21.9642 | 0.718690 | ||||||||
\(935\) | −6.00000 | −0.196221 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.9291 | 1.10842 | 0.554208 | − | 0.832378i | \(-0.313021\pi\) | ||||
0.554208 | + | 0.832378i | \(0.313021\pi\) | |||||||
\(938\) | 1.34968 | 0.0440687 | ||||||||
\(939\) | −29.2311 | −0.953922 | ||||||||
\(940\) | 7.46868 | 0.243602 | ||||||||
\(941\) | −8.20272 | −0.267401 | −0.133701 | − | 0.991022i | \(-0.542686\pi\) | ||||
−0.133701 | + | 0.991022i | \(0.542686\pi\) | |||||||
\(942\) | −16.1874 | −0.527415 | ||||||||
\(943\) | −1.99507 | −0.0649684 | ||||||||
\(944\) | 23.1485 | 0.753419 | ||||||||
\(945\) | −0.606018 | −0.0197138 | ||||||||
\(946\) | 17.3581 | 0.564359 | ||||||||
\(947\) | −45.0093 | −1.46260 | −0.731302 | − | 0.682053i | \(-0.761087\pi\) | ||||
−0.731302 | + | 0.682053i | \(0.761087\pi\) | |||||||
\(948\) | −2.41245 | −0.0783526 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 5.50045 | 0.178458 | ||||||||
\(951\) | 8.62570 | 0.279707 | ||||||||
\(952\) | −3.63611 | −0.117847 | ||||||||
\(953\) | 53.0188 | 1.71745 | 0.858724 | − | 0.512438i | \(-0.171257\pi\) | ||||
0.858724 | + | 0.512438i | \(0.171257\pi\) | |||||||
\(954\) | 12.0000 | 0.388514 | ||||||||
\(955\) | −7.67356 | −0.248311 | ||||||||
\(956\) | 14.0040 | 0.452922 | ||||||||
\(957\) | 8.55758 | 0.276627 | ||||||||
\(958\) | −30.4371 | −0.983379 | ||||||||
\(959\) | −5.27632 | −0.170381 | ||||||||
\(960\) | 8.39230 | 0.270860 | ||||||||
\(961\) | 52.7729 | 1.70235 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.20699 | −0.264467 | ||||||||
\(964\) | 4.00736 | 0.129068 | ||||||||
\(965\) | −21.0108 | −0.676363 | ||||||||
\(966\) | −1.27222 | −0.0409330 | ||||||||
\(967\) | −31.7061 | −1.01960 | −0.509799 | − | 0.860293i | \(-0.670280\pi\) | ||||
−0.509799 | + | 0.860293i | \(0.670280\pi\) | |||||||
\(968\) | −4.72500 | −0.151867 | ||||||||
\(969\) | 9.52706 | 0.306053 | ||||||||
\(970\) | 14.8663 | 0.477330 | ||||||||
\(971\) | −29.6147 | −0.950381 | −0.475191 | − | 0.879883i | \(-0.657621\pi\) | ||||
−0.475191 | + | 0.879883i | \(0.657621\pi\) | |||||||
\(972\) | 0.732051 | 0.0234805 | ||||||||
\(973\) | −5.85225 | −0.187615 | ||||||||
\(974\) | 5.87508 | 0.188250 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.5359 | 0.401264 | ||||||||
\(977\) | 1.23129 | 0.0393924 | 0.0196962 | − | 0.999806i | \(-0.493730\pi\) | ||||
0.0196962 | + | 0.999806i | \(0.493730\pi\) | |||||||
\(978\) | 11.3393 | 0.362590 | ||||||||
\(979\) | 50.1427 | 1.60257 | ||||||||
\(980\) | −4.85550 | −0.155103 | ||||||||
\(981\) | 10.5927 | 0.338199 | ||||||||
\(982\) | −16.6447 | −0.531153 | ||||||||
\(983\) | 25.1632 | 0.802581 | 0.401290 | − | 0.915951i | \(-0.368562\pi\) | ||||
0.401290 | + | 0.915951i | \(0.368562\pi\) | |||||||
\(984\) | 3.29209 | 0.104948 | ||||||||
\(985\) | −20.3776 | −0.649285 | ||||||||
\(986\) | 6.10905 | 0.194552 | ||||||||
\(987\) | 6.18285 | 0.196802 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.34192 | −0.297056 | ||||||||
\(990\) | 3.46410 | 0.110096 | ||||||||
\(991\) | −59.4589 | −1.88877 | −0.944387 | − | 0.328836i | \(-0.893344\pi\) | ||||
−0.944387 | + | 0.328836i | \(0.893344\pi\) | |||||||
\(992\) | −35.7021 | −1.13354 | ||||||||
\(993\) | −20.3021 | −0.644269 | ||||||||
\(994\) | −4.03088 | −0.127852 | ||||||||
\(995\) | 14.8014 | 0.469235 | ||||||||
\(996\) | −5.10757 | −0.161840 | ||||||||
\(997\) | 37.9219 | 1.20100 | 0.600499 | − | 0.799625i | \(-0.294968\pi\) | ||||
0.600499 | + | 0.799625i | \(0.294968\pi\) | |||||||
\(998\) | 11.6174 | 0.367743 | ||||||||
\(999\) | −3.74793 | −0.118579 |
(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 | 2535.2.a.bj.1.2 | 4 | ||
3.2 | odd | 2 | 7605.2.a.ci.1.3 | 4 | |||
13.6 | odd | 12 | 195.2.bb.b.166.3 | yes | 8 | ||
13.11 | odd | 12 | 195.2.bb.b.121.3 | ✓ | 8 | ||
13.12 | even | 2 | 2535.2.a.bk.1.3 | 4 | |||
39.11 | even | 12 | 585.2.bu.d.316.2 | 8 | |||
39.32 | even | 12 | 585.2.bu.d.361.2 | 8 | |||
39.38 | odd | 2 | 7605.2.a.ch.1.2 | 4 | |||
65.19 | odd | 12 | 975.2.bc.j.751.2 | 8 | |||
65.24 | odd | 12 | 975.2.bc.j.901.2 | 8 | |||
65.32 | even | 12 | 975.2.w.h.49.3 | 8 | |||
65.37 | even | 12 | 975.2.w.i.199.2 | 8 | |||
65.58 | even | 12 | 975.2.w.i.49.2 | 8 | |||
65.63 | even | 12 | 975.2.w.h.199.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
195.2.bb.b.121.3 | ✓ | 8 | 13.11 | odd | 12 | ||
195.2.bb.b.166.3 | yes | 8 | 13.6 | odd | 12 | ||
585.2.bu.d.316.2 | 8 | 39.11 | even | 12 | |||
585.2.bu.d.361.2 | 8 | 39.32 | even | 12 | |||
975.2.w.h.49.3 | 8 | 65.32 | even | 12 | |||
975.2.w.h.199.3 | 8 | 65.63 | even | 12 | |||
975.2.w.i.49.2 | 8 | 65.58 | even | 12 | |||
975.2.w.i.199.2 | 8 | 65.37 | even | 12 | |||
975.2.bc.j.751.2 | 8 | 65.19 | odd | 12 | |||
975.2.bc.j.901.2 | 8 | 65.24 | odd | 12 | |||
2535.2.a.bj.1.2 | 4 | 1.1 | even | 1 | trivial | ||
2535.2.a.bk.1.3 | 4 | 13.12 | even | 2 | |||
7605.2.a.ch.1.2 | 4 | 39.38 | odd | 2 | |||
7605.2.a.ci.1.3 | 4 | 3.2 | odd | 2 |