Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1351,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5070.1351");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(40.4841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.153664.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 5x^{4} + 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1351.6 | ||
Root | \(1.24698i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1351 |
Dual form | 5070.2.b.u.1351.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5070\mathbb{Z}\right)^\times\).
\(n\) | \(1691\) | \(1861\) | \(4057\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − 1.00000i | − 0.447214i | ||||||||
\(6\) | − 1.00000i | − 0.408248i | ||||||||
\(7\) | 4.24698i | 1.60521i | 0.596513 | + | 0.802604i | \(0.296553\pi\) | ||||
−0.596513 | + | 0.802604i | \(0.703447\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | − 0.801938i | − 0.241793i | −0.992665 | − | 0.120897i | \(-0.961423\pi\) | ||||
0.992665 | − | 0.120897i | \(-0.0385770\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −4.24698 | −1.13505 | ||||||||
\(15\) | 1.00000i | 0.258199i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.43296 | −1.80276 | −0.901379 | − | 0.433031i | \(-0.857444\pi\) | ||||
−0.901379 | + | 0.433031i | \(0.857444\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | − 3.74094i | − 0.858230i | −0.903250 | − | 0.429115i | \(-0.858825\pi\) | ||||
0.903250 | − | 0.429115i | \(-0.141175\pi\) | |||||||
\(20\) | 1.00000i | 0.223607i | ||||||||
\(21\) | − 4.24698i | − 0.926767i | ||||||||
\(22\) | 0.801938 | 0.170974 | ||||||||
\(23\) | 2.54288 | 0.530226 | 0.265113 | − | 0.964217i | \(-0.414591\pi\) | ||||
0.265113 | + | 0.964217i | \(0.414591\pi\) | |||||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | − 4.24698i | − 0.802604i | ||||||||
\(29\) | 5.63102 | 1.04565 | 0.522827 | − | 0.852439i | \(-0.324877\pi\) | ||||
0.522827 | + | 0.852439i | \(0.324877\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | 1.69202i | 0.303896i | 0.988388 | + | 0.151948i | \(0.0485546\pi\) | ||||
−0.988388 | + | 0.151948i | \(0.951445\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0.801938i | 0.139599i | ||||||||
\(34\) | − 7.43296i | − 1.27474i | ||||||||
\(35\) | 4.24698 | 0.717871 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | − 9.67456i | − 1.59049i | −0.606289 | − | 0.795244i | \(-0.707343\pi\) | ||||
0.606289 | − | 0.795244i | \(-0.292657\pi\) | |||||||
\(38\) | 3.74094 | 0.606860 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | − 8.85086i | − 1.38227i | −0.722725 | − | 0.691136i | \(-0.757111\pi\) | ||||
0.722725 | − | 0.691136i | \(-0.242889\pi\) | |||||||
\(42\) | 4.24698 | 0.655323 | ||||||||
\(43\) | 6.29590 | 0.960115 | 0.480058 | − | 0.877237i | \(-0.340616\pi\) | ||||
0.480058 | + | 0.877237i | \(0.340616\pi\) | |||||||
\(44\) | 0.801938i | 0.120897i | ||||||||
\(45\) | − 1.00000i | − 0.149071i | ||||||||
\(46\) | 2.54288i | 0.374927i | ||||||||
\(47\) | 7.53750i | 1.09946i | 0.835343 | + | 0.549729i | \(0.185269\pi\) | ||||
−0.835343 | + | 0.549729i | \(0.814731\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −11.0368 | −1.57669 | ||||||||
\(50\) | − 1.00000i | − 0.141421i | ||||||||
\(51\) | 7.43296 | 1.04082 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.5646 | 1.86325 | 0.931624 | − | 0.363424i | \(-0.118392\pi\) | ||||
0.931624 | + | 0.363424i | \(0.118392\pi\) | |||||||
\(54\) | − 1.00000i | − 0.136083i | ||||||||
\(55\) | −0.801938 | −0.108133 | ||||||||
\(56\) | 4.24698 | 0.567527 | ||||||||
\(57\) | 3.74094i | 0.495499i | ||||||||
\(58\) | 5.63102i | 0.739389i | ||||||||
\(59\) | 9.58211i | 1.24748i | 0.781630 | + | 0.623742i | \(0.214388\pi\) | ||||
−0.781630 | + | 0.623742i | \(0.785612\pi\) | |||||||
\(60\) | − 1.00000i | − 0.129099i | ||||||||
\(61\) | −10.7899 | −1.38150 | −0.690750 | − | 0.723094i | \(-0.742719\pi\) | ||||
−0.690750 | + | 0.723094i | \(0.742719\pi\) | |||||||
\(62\) | −1.69202 | −0.214887 | ||||||||
\(63\) | 4.24698i | 0.535069i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.801938 | −0.0987117 | ||||||||
\(67\) | − 7.82908i | − 0.956475i | −0.878231 | − | 0.478237i | \(-0.841276\pi\) | ||||
0.878231 | − | 0.478237i | \(-0.158724\pi\) | |||||||
\(68\) | 7.43296 | 0.901379 | ||||||||
\(69\) | −2.54288 | −0.306126 | ||||||||
\(70\) | 4.24698i | 0.507611i | ||||||||
\(71\) | 2.04892i | 0.243162i | 0.992582 | + | 0.121581i | \(0.0387964\pi\) | ||||
−0.992582 | + | 0.121581i | \(0.961204\pi\) | |||||||
\(72\) | − 1.00000i | − 0.117851i | ||||||||
\(73\) | 2.17092i | 0.254086i | 0.991897 | + | 0.127043i | \(0.0405487\pi\) | ||||
−0.991897 | + | 0.127043i | \(0.959451\pi\) | |||||||
\(74\) | 9.67456 | 1.12465 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 3.74094i | 0.429115i | ||||||||
\(77\) | 3.40581 | 0.388128 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.2349 | −1.82657 | −0.913284 | − | 0.407323i | \(-0.866462\pi\) | ||||
−0.913284 | + | 0.407323i | \(0.866462\pi\) | |||||||
\(80\) | − 1.00000i | − 0.111803i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 8.85086 | 0.977413 | ||||||||
\(83\) | 3.61356i | 0.396640i | 0.980137 | + | 0.198320i | \(0.0635486\pi\) | ||||
−0.980137 | + | 0.198320i | \(0.936451\pi\) | |||||||
\(84\) | 4.24698i | 0.463383i | ||||||||
\(85\) | 7.43296i | 0.806218i | ||||||||
\(86\) | 6.29590i | 0.678904i | ||||||||
\(87\) | −5.63102 | −0.603709 | ||||||||
\(88\) | −0.801938 | −0.0854868 | ||||||||
\(89\) | − 8.24459i | − 0.873924i | −0.899480 | − | 0.436962i | \(-0.856054\pi\) | ||||
0.899480 | − | 0.436962i | \(-0.143946\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.54288 | −0.265113 | ||||||||
\(93\) | − 1.69202i | − 0.175454i | ||||||||
\(94\) | −7.53750 | −0.777434 | ||||||||
\(95\) | −3.74094 | −0.383812 | ||||||||
\(96\) | − 1.00000i | − 0.102062i | ||||||||
\(97\) | − 6.07069i | − 0.616385i | −0.951324 | − | 0.308192i | \(-0.900276\pi\) | ||||
0.951324 | − | 0.308192i | \(-0.0997241\pi\) | |||||||
\(98\) | − 11.0368i | − 1.11489i | ||||||||
\(99\) | − 0.801938i | − 0.0805978i | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 5.38404 | 0.535732 | 0.267866 | − | 0.963456i | \(-0.413682\pi\) | ||||
0.267866 | + | 0.963456i | \(0.413682\pi\) | |||||||
\(102\) | 7.43296i | 0.735973i | ||||||||
\(103\) | 8.92154 | 0.879066 | 0.439533 | − | 0.898227i | \(-0.355144\pi\) | ||||
0.439533 | + | 0.898227i | \(0.355144\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.24698 | −0.414463 | ||||||||
\(106\) | 13.5646i | 1.31751i | ||||||||
\(107\) | 13.9976 | 1.35320 | 0.676600 | − | 0.736351i | \(-0.263453\pi\) | ||||
0.676600 | + | 0.736351i | \(0.263453\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | − 13.8605i | − 1.32760i | −0.747910 | − | 0.663800i | \(-0.768943\pi\) | ||||
0.747910 | − | 0.663800i | \(-0.231057\pi\) | |||||||
\(110\) | − 0.801938i | − 0.0764618i | ||||||||
\(111\) | 9.67456i | 0.918269i | ||||||||
\(112\) | 4.24698i | 0.401302i | ||||||||
\(113\) | 2.19806 | 0.206776 | 0.103388 | − | 0.994641i | \(-0.467032\pi\) | ||||
0.103388 | + | 0.994641i | \(0.467032\pi\) | |||||||
\(114\) | −3.74094 | −0.350371 | ||||||||
\(115\) | − 2.54288i | − 0.237124i | ||||||||
\(116\) | −5.63102 | −0.522827 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −9.58211 | −0.882104 | ||||||||
\(119\) | − 31.5676i | − 2.89380i | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | 10.3569 | 0.941536 | ||||||||
\(122\) | − 10.7899i | − 0.976868i | ||||||||
\(123\) | 8.85086i | 0.798055i | ||||||||
\(124\) | − 1.69202i | − 0.151948i | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −4.24698 | −0.378351 | ||||||||
\(127\) | 4.19136 | 0.371923 | 0.185961 | − | 0.982557i | \(-0.440460\pi\) | ||||
0.185961 | + | 0.982557i | \(0.440460\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | −6.29590 | −0.554323 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.8140 | −0.944825 | −0.472413 | − | 0.881378i | \(-0.656617\pi\) | ||||
−0.472413 | + | 0.881378i | \(0.656617\pi\) | |||||||
\(132\) | − 0.801938i | − 0.0697997i | ||||||||
\(133\) | 15.8877 | 1.37764 | ||||||||
\(134\) | 7.82908 | 0.676330 | ||||||||
\(135\) | 1.00000i | 0.0860663i | ||||||||
\(136\) | 7.43296i | 0.637371i | ||||||||
\(137\) | 12.8509i | 1.09792i | 0.835848 | + | 0.548961i | \(0.184977\pi\) | ||||
−0.835848 | + | 0.548961i | \(0.815023\pi\) | |||||||
\(138\) | − 2.54288i | − 0.216464i | ||||||||
\(139\) | 16.6233 | 1.40997 | 0.704983 | − | 0.709224i | \(-0.250955\pi\) | ||||
0.704983 | + | 0.709224i | \(0.250955\pi\) | |||||||
\(140\) | −4.24698 | −0.358935 | ||||||||
\(141\) | − 7.53750i | − 0.634772i | ||||||||
\(142\) | −2.04892 | −0.171941 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | − 5.63102i | − 0.467631i | ||||||||
\(146\) | −2.17092 | −0.179666 | ||||||||
\(147\) | 11.0368 | 0.910303 | ||||||||
\(148\) | 9.67456i | 0.795244i | ||||||||
\(149\) | 1.74094i | 0.142623i | 0.997454 | + | 0.0713116i | \(0.0227185\pi\) | ||||
−0.997454 | + | 0.0713116i | \(0.977282\pi\) | |||||||
\(150\) | 1.00000i | 0.0816497i | ||||||||
\(151\) | − 1.75840i | − 0.143096i | −0.997437 | − | 0.0715482i | \(-0.977206\pi\) | ||||
0.997437 | − | 0.0715482i | \(-0.0227940\pi\) | |||||||
\(152\) | −3.74094 | −0.303430 | ||||||||
\(153\) | −7.43296 | −0.600919 | ||||||||
\(154\) | 3.40581i | 0.274448i | ||||||||
\(155\) | 1.69202 | 0.135906 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.9825 | −1.27555 | −0.637773 | − | 0.770225i | \(-0.720144\pi\) | ||||
−0.637773 | + | 0.770225i | \(0.720144\pi\) | |||||||
\(158\) | − 16.2349i | − 1.29158i | ||||||||
\(159\) | −13.5646 | −1.07575 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 10.7995i | 0.851123i | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | − 5.18598i | − 0.406197i | −0.979158 | − | 0.203099i | \(-0.934899\pi\) | ||||
0.979158 | − | 0.203099i | \(-0.0651012\pi\) | |||||||
\(164\) | 8.85086i | 0.691136i | ||||||||
\(165\) | 0.801938 | 0.0624308 | ||||||||
\(166\) | −3.61356 | −0.280467 | ||||||||
\(167\) | − 5.29590i | − 0.409809i | −0.978782 | − | 0.204904i | \(-0.934312\pi\) | ||||
0.978782 | − | 0.204904i | \(-0.0656884\pi\) | |||||||
\(168\) | −4.24698 | −0.327662 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −7.43296 | −0.570082 | ||||||||
\(171\) | − 3.74094i | − 0.286077i | ||||||||
\(172\) | −6.29590 | −0.480058 | ||||||||
\(173\) | 19.6558 | 1.49440 | 0.747201 | − | 0.664599i | \(-0.231397\pi\) | ||||
0.747201 | + | 0.664599i | \(0.231397\pi\) | |||||||
\(174\) | − 5.63102i | − 0.426887i | ||||||||
\(175\) | − 4.24698i | − 0.321041i | ||||||||
\(176\) | − 0.801938i | − 0.0604483i | ||||||||
\(177\) | − 9.58211i | − 0.720235i | ||||||||
\(178\) | 8.24459 | 0.617958 | ||||||||
\(179\) | 17.9095 | 1.33862 | 0.669308 | − | 0.742985i | \(-0.266591\pi\) | ||||
0.669308 | + | 0.742985i | \(0.266591\pi\) | |||||||
\(180\) | 1.00000i | 0.0745356i | ||||||||
\(181\) | 8.74094 | 0.649709 | 0.324854 | − | 0.945764i | \(-0.394685\pi\) | ||||
0.324854 | + | 0.945764i | \(0.394685\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.7899 | 0.797609 | ||||||||
\(184\) | − 2.54288i | − 0.187463i | ||||||||
\(185\) | −9.67456 | −0.711288 | ||||||||
\(186\) | 1.69202 | 0.124065 | ||||||||
\(187\) | 5.96077i | 0.435895i | ||||||||
\(188\) | − 7.53750i | − 0.549729i | ||||||||
\(189\) | − 4.24698i | − 0.308922i | ||||||||
\(190\) | − 3.74094i | − 0.271396i | ||||||||
\(191\) | −3.76510 | −0.272433 | −0.136217 | − | 0.990679i | \(-0.543494\pi\) | ||||
−0.136217 | + | 0.990679i | \(0.543494\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 21.9584i | 1.58060i | 0.612721 | + | 0.790299i | \(0.290075\pi\) | ||||
−0.612721 | + | 0.790299i | \(0.709925\pi\) | |||||||
\(194\) | 6.07069 | 0.435850 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.0368 | 0.788345 | ||||||||
\(197\) | 18.2446i | 1.29987i | 0.759989 | + | 0.649936i | \(0.225205\pi\) | ||||
−0.759989 | + | 0.649936i | \(0.774795\pi\) | |||||||
\(198\) | 0.801938 | 0.0569912 | ||||||||
\(199\) | 1.77479 | 0.125812 | 0.0629058 | − | 0.998019i | \(-0.479963\pi\) | ||||
0.0629058 | + | 0.998019i | \(0.479963\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | 7.82908i | 0.552221i | ||||||||
\(202\) | 5.38404i | 0.378820i | ||||||||
\(203\) | 23.9148i | 1.67849i | ||||||||
\(204\) | −7.43296 | −0.520411 | ||||||||
\(205\) | −8.85086 | −0.618171 | ||||||||
\(206\) | 8.92154i | 0.621593i | ||||||||
\(207\) | 2.54288 | 0.176742 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.00000 | −0.207514 | ||||||||
\(210\) | − 4.24698i | − 0.293069i | ||||||||
\(211\) | 0.0978347 | 0.00673522 | 0.00336761 | − | 0.999994i | \(-0.498928\pi\) | ||||
0.00336761 | + | 0.999994i | \(0.498928\pi\) | |||||||
\(212\) | −13.5646 | −0.931624 | ||||||||
\(213\) | − 2.04892i | − 0.140390i | ||||||||
\(214\) | 13.9976i | 0.956857i | ||||||||
\(215\) | − 6.29590i | − 0.429377i | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | −7.18598 | −0.487816 | ||||||||
\(218\) | 13.8605 | 0.938754 | ||||||||
\(219\) | − 2.17092i | − 0.146697i | ||||||||
\(220\) | 0.801938 | 0.0540666 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −9.67456 | −0.649314 | ||||||||
\(223\) | 19.5080i | 1.30635i | 0.757207 | + | 0.653175i | \(0.226563\pi\) | ||||
−0.757207 | + | 0.653175i | \(0.773437\pi\) | |||||||
\(224\) | −4.24698 | −0.283763 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 2.19806i | 0.146213i | ||||||||
\(227\) | − 3.23059i | − 0.214422i | −0.994236 | − | 0.107211i | \(-0.965808\pi\) | ||||
0.994236 | − | 0.107211i | \(-0.0341920\pi\) | |||||||
\(228\) | − 3.74094i | − 0.247750i | ||||||||
\(229\) | − 4.58748i | − 0.303149i | −0.988446 | − | 0.151575i | \(-0.951566\pi\) | ||||
0.988446 | − | 0.151575i | \(-0.0484344\pi\) | |||||||
\(230\) | 2.54288 | 0.167672 | ||||||||
\(231\) | −3.40581 | −0.224086 | ||||||||
\(232\) | − 5.63102i | − 0.369695i | ||||||||
\(233\) | 6.18359 | 0.405100 | 0.202550 | − | 0.979272i | \(-0.435077\pi\) | ||||
0.202550 | + | 0.979272i | \(0.435077\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.53750 | 0.491692 | ||||||||
\(236\) | − 9.58211i | − 0.623742i | ||||||||
\(237\) | 16.2349 | 1.05457 | ||||||||
\(238\) | 31.5676 | 2.04623 | ||||||||
\(239\) | − 8.42998i | − 0.545290i | −0.962115 | − | 0.272645i | \(-0.912102\pi\) | ||||
0.962115 | − | 0.272645i | \(-0.0878984\pi\) | |||||||
\(240\) | 1.00000i | 0.0645497i | ||||||||
\(241\) | 20.8485i | 1.34297i | 0.741019 | + | 0.671484i | \(0.234343\pi\) | ||||
−0.741019 | + | 0.671484i | \(0.765657\pi\) | |||||||
\(242\) | 10.3569i | 0.665766i | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 10.7899 | 0.690750 | ||||||||
\(245\) | 11.0368i | 0.705118i | ||||||||
\(246\) | −8.85086 | −0.564310 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.69202 | 0.107443 | ||||||||
\(249\) | − 3.61356i | − 0.229000i | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 6.39075 | 0.403380 | 0.201690 | − | 0.979449i | \(-0.435357\pi\) | ||||
0.201690 | + | 0.979449i | \(0.435357\pi\) | |||||||
\(252\) | − 4.24698i | − 0.267535i | ||||||||
\(253\) | − 2.03923i | − 0.128205i | ||||||||
\(254\) | 4.19136i | 0.262989i | ||||||||
\(255\) | − 7.43296i | − 0.465470i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.78687 | −0.610488 | −0.305244 | − | 0.952274i | \(-0.598738\pi\) | ||||
−0.305244 | + | 0.952274i | \(0.598738\pi\) | |||||||
\(258\) | − 6.29590i | − 0.391965i | ||||||||
\(259\) | 41.0877 | 2.55306 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.63102 | 0.348552 | ||||||||
\(262\) | − 10.8140i | − 0.668092i | ||||||||
\(263\) | 14.0465 | 0.866146 | 0.433073 | − | 0.901359i | \(-0.357429\pi\) | ||||
0.433073 | + | 0.901359i | \(0.357429\pi\) | |||||||
\(264\) | 0.801938 | 0.0493559 | ||||||||
\(265\) | − 13.5646i | − 0.833270i | ||||||||
\(266\) | 15.8877i | 0.974137i | ||||||||
\(267\) | 8.24459i | 0.504561i | ||||||||
\(268\) | 7.82908i | 0.478237i | ||||||||
\(269\) | −17.2597 | −1.05234 | −0.526170 | − | 0.850380i | \(-0.676372\pi\) | ||||
−0.526170 | + | 0.850380i | \(0.676372\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | − 17.1782i | − 1.04350i | −0.853098 | − | 0.521751i | \(-0.825279\pi\) | ||||
0.853098 | − | 0.521751i | \(-0.174721\pi\) | |||||||
\(272\) | −7.43296 | −0.450689 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.8509 | −0.776349 | ||||||||
\(275\) | 0.801938i | 0.0483587i | ||||||||
\(276\) | 2.54288 | 0.153063 | ||||||||
\(277\) | 21.1444 | 1.27044 | 0.635221 | − | 0.772331i | \(-0.280909\pi\) | ||||
0.635221 | + | 0.772331i | \(0.280909\pi\) | |||||||
\(278\) | 16.6233i | 0.996996i | ||||||||
\(279\) | 1.69202i | 0.101299i | ||||||||
\(280\) | − 4.24698i | − 0.253806i | ||||||||
\(281\) | 4.09246i | 0.244136i | 0.992522 | + | 0.122068i | \(0.0389525\pi\) | ||||
−0.992522 | + | 0.122068i | \(0.961047\pi\) | |||||||
\(282\) | 7.53750 | 0.448852 | ||||||||
\(283\) | −12.1468 | −0.722049 | −0.361025 | − | 0.932556i | \(-0.617573\pi\) | ||||
−0.361025 | + | 0.932556i | \(0.617573\pi\) | |||||||
\(284\) | − 2.04892i | − 0.121581i | ||||||||
\(285\) | 3.74094 | 0.221594 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 37.5894 | 2.21883 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 38.2489 | 2.24994 | ||||||||
\(290\) | 5.63102 | 0.330665 | ||||||||
\(291\) | 6.07069i | 0.355870i | ||||||||
\(292\) | − 2.17092i | − 0.127043i | ||||||||
\(293\) | 20.6789i | 1.20807i | 0.796957 | + | 0.604036i | \(0.206442\pi\) | ||||
−0.796957 | + | 0.604036i | \(0.793558\pi\) | |||||||
\(294\) | 11.0368i | 0.643681i | ||||||||
\(295\) | 9.58211 | 0.557892 | ||||||||
\(296\) | −9.67456 | −0.562323 | ||||||||
\(297\) | 0.801938i | 0.0465331i | ||||||||
\(298\) | −1.74094 | −0.100850 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 26.7385i | 1.54118i | ||||||||
\(302\) | 1.75840 | 0.101184 | ||||||||
\(303\) | −5.38404 | −0.309305 | ||||||||
\(304\) | − 3.74094i | − 0.214558i | ||||||||
\(305\) | 10.7899i | 0.617825i | ||||||||
\(306\) | − 7.43296i | − 0.424914i | ||||||||
\(307\) | 11.3123i | 0.645627i | 0.946463 | + | 0.322813i | \(0.104629\pi\) | ||||
−0.946463 | + | 0.322813i | \(0.895371\pi\) | |||||||
\(308\) | −3.40581 | −0.194064 | ||||||||
\(309\) | −8.92154 | −0.507529 | ||||||||
\(310\) | 1.69202i | 0.0961004i | ||||||||
\(311\) | 26.2282 | 1.48726 | 0.743632 | − | 0.668589i | \(-0.233101\pi\) | ||||
0.743632 | + | 0.668589i | \(0.233101\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.5023 | 1.66757 | 0.833785 | − | 0.552089i | \(-0.186169\pi\) | ||||
0.833785 | + | 0.552089i | \(0.186169\pi\) | |||||||
\(314\) | − 15.9825i | − 0.901947i | ||||||||
\(315\) | 4.24698 | 0.239290 | ||||||||
\(316\) | 16.2349 | 0.913284 | ||||||||
\(317\) | 7.06398i | 0.396753i | 0.980126 | + | 0.198376i | \(0.0635668\pi\) | ||||
−0.980126 | + | 0.198376i | \(0.936433\pi\) | |||||||
\(318\) | − 13.5646i | − 0.760668i | ||||||||
\(319\) | − 4.51573i | − 0.252832i | ||||||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | −13.9976 | −0.781270 | ||||||||
\(322\) | −10.7995 | −0.601835 | ||||||||
\(323\) | 27.8062i | 1.54718i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.18598 | 0.287225 | ||||||||
\(327\) | 13.8605i | 0.766490i | ||||||||
\(328\) | −8.85086 | −0.488707 | ||||||||
\(329\) | −32.0116 | −1.76486 | ||||||||
\(330\) | 0.801938i | 0.0441452i | ||||||||
\(331\) | − 10.3134i | − 0.566873i | −0.958991 | − | 0.283437i | \(-0.908525\pi\) | ||||
0.958991 | − | 0.283437i | \(-0.0914746\pi\) | |||||||
\(332\) | − 3.61356i | − 0.198320i | ||||||||
\(333\) | − 9.67456i | − 0.530163i | ||||||||
\(334\) | 5.29590 | 0.289779 | ||||||||
\(335\) | −7.82908 | −0.427749 | ||||||||
\(336\) | − 4.24698i | − 0.231692i | ||||||||
\(337\) | −30.3163 | −1.65144 | −0.825718 | − | 0.564083i | \(-0.809230\pi\) | ||||
−0.825718 | + | 0.564083i | \(0.809230\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.19806 | −0.119382 | ||||||||
\(340\) | − 7.43296i | − 0.403109i | ||||||||
\(341\) | 1.35690 | 0.0734800 | ||||||||
\(342\) | 3.74094 | 0.202287 | ||||||||
\(343\) | − 17.1444i | − 0.925708i | ||||||||
\(344\) | − 6.29590i | − 0.339452i | ||||||||
\(345\) | 2.54288i | 0.136904i | ||||||||
\(346\) | 19.6558i | 1.05670i | ||||||||
\(347\) | 28.8592 | 1.54924 | 0.774622 | − | 0.632425i | \(-0.217940\pi\) | ||||
0.774622 | + | 0.632425i | \(0.217940\pi\) | |||||||
\(348\) | 5.63102 | 0.301854 | ||||||||
\(349\) | − 27.4566i | − 1.46972i | −0.678218 | − | 0.734860i | \(-0.737248\pi\) | ||||
0.678218 | − | 0.734860i | \(-0.262752\pi\) | |||||||
\(350\) | 4.24698 | 0.227011 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.801938 | 0.0427434 | ||||||||
\(353\) | − 0.885772i | − 0.0471449i | −0.999722 | − | 0.0235724i | \(-0.992496\pi\) | ||||
0.999722 | − | 0.0235724i | \(-0.00750404\pi\) | |||||||
\(354\) | 9.58211 | 0.509283 | ||||||||
\(355\) | 2.04892 | 0.108745 | ||||||||
\(356\) | 8.24459i | 0.436962i | ||||||||
\(357\) | 31.5676i | 1.67074i | ||||||||
\(358\) | 17.9095i | 0.946544i | ||||||||
\(359\) | 7.07069i | 0.373177i | 0.982438 | + | 0.186588i | \(0.0597430\pi\) | ||||
−0.982438 | + | 0.186588i | \(0.940257\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | 5.00538 | 0.263441 | ||||||||
\(362\) | 8.74094i | 0.459414i | ||||||||
\(363\) | −10.3569 | −0.543596 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.17092 | 0.113631 | ||||||||
\(366\) | 10.7899i | 0.563995i | ||||||||
\(367\) | 27.3588 | 1.42812 | 0.714059 | − | 0.700085i | \(-0.246855\pi\) | ||||
0.714059 | + | 0.700085i | \(0.246855\pi\) | |||||||
\(368\) | 2.54288 | 0.132557 | ||||||||
\(369\) | − 8.85086i | − 0.460757i | ||||||||
\(370\) | − 9.67456i | − 0.502957i | ||||||||
\(371\) | 57.6088i | 2.99090i | ||||||||
\(372\) | 1.69202i | 0.0877272i | ||||||||
\(373\) | 18.3370 | 0.949456 | 0.474728 | − | 0.880133i | \(-0.342546\pi\) | ||||
0.474728 | + | 0.880133i | \(0.342546\pi\) | |||||||
\(374\) | −5.96077 | −0.308224 | ||||||||
\(375\) | − 1.00000i | − 0.0516398i | ||||||||
\(376\) | 7.53750 | 0.388717 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 4.24698 | 0.218441 | ||||||||
\(379\) | 14.3690i | 0.738085i | 0.929413 | + | 0.369042i | \(0.120314\pi\) | ||||
−0.929413 | + | 0.369042i | \(0.879686\pi\) | |||||||
\(380\) | 3.74094 | 0.191906 | ||||||||
\(381\) | −4.19136 | −0.214730 | ||||||||
\(382\) | − 3.76510i | − 0.192639i | ||||||||
\(383\) | − 34.6920i | − 1.77268i | −0.463035 | − | 0.886340i | \(-0.653240\pi\) | ||||
0.463035 | − | 0.886340i | \(-0.346760\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | − 3.40581i | − 0.173576i | ||||||||
\(386\) | −21.9584 | −1.11765 | ||||||||
\(387\) | 6.29590 | 0.320038 | ||||||||
\(388\) | 6.07069i | 0.308192i | ||||||||
\(389\) | 32.6872 | 1.65731 | 0.828654 | − | 0.559761i | \(-0.189107\pi\) | ||||
0.828654 | + | 0.559761i | \(0.189107\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.9011 | −0.955870 | ||||||||
\(392\) | 11.0368i | 0.557444i | ||||||||
\(393\) | 10.8140 | 0.545495 | ||||||||
\(394\) | −18.2446 | −0.919149 | ||||||||
\(395\) | 16.2349i | 0.816866i | ||||||||
\(396\) | 0.801938i | 0.0402989i | ||||||||
\(397\) | 12.3080i | 0.617720i | 0.951108 | + | 0.308860i | \(0.0999474\pi\) | ||||
−0.951108 | + | 0.308860i | \(0.900053\pi\) | |||||||
\(398\) | 1.77479i | 0.0889622i | ||||||||
\(399\) | −15.8877 | −0.795379 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 19.2524i | 0.961417i | 0.876881 | + | 0.480708i | \(0.159620\pi\) | ||||
−0.876881 | + | 0.480708i | \(0.840380\pi\) | |||||||
\(402\) | −7.82908 | −0.390479 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −5.38404 | −0.267866 | ||||||||
\(405\) | − 1.00000i | − 0.0496904i | ||||||||
\(406\) | −23.9148 | −1.18687 | ||||||||
\(407\) | −7.75840 | −0.384569 | ||||||||
\(408\) | − 7.43296i | − 0.367986i | ||||||||
\(409\) | 22.8672i | 1.13071i | 0.824847 | + | 0.565356i | \(0.191261\pi\) | ||||
−0.824847 | + | 0.565356i | \(0.808739\pi\) | |||||||
\(410\) | − 8.85086i | − 0.437113i | ||||||||
\(411\) | − 12.8509i | − 0.633886i | ||||||||
\(412\) | −8.92154 | −0.439533 | ||||||||
\(413\) | −40.6950 | −2.00247 | ||||||||
\(414\) | 2.54288i | 0.124976i | ||||||||
\(415\) | 3.61356 | 0.177383 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.6233 | −0.814044 | ||||||||
\(418\) | − 3.00000i | − 0.146735i | ||||||||
\(419\) | −17.1806 | −0.839327 | −0.419664 | − | 0.907680i | \(-0.637852\pi\) | ||||
−0.419664 | + | 0.907680i | \(0.637852\pi\) | |||||||
\(420\) | 4.24698 | 0.207231 | ||||||||
\(421\) | − 36.9922i | − 1.80289i | −0.432893 | − | 0.901445i | \(-0.642507\pi\) | ||||
0.432893 | − | 0.901445i | \(-0.357493\pi\) | |||||||
\(422\) | 0.0978347i | 0.00476252i | ||||||||
\(423\) | 7.53750i | 0.366486i | ||||||||
\(424\) | − 13.5646i | − 0.658757i | ||||||||
\(425\) | 7.43296 | 0.360552 | ||||||||
\(426\) | 2.04892 | 0.0992704 | ||||||||
\(427\) | − 45.8243i | − 2.21759i | ||||||||
\(428\) | −13.9976 | −0.676600 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.29590 | 0.303615 | ||||||||
\(431\) | 19.0834i | 0.919213i | 0.888123 | + | 0.459607i | \(0.152010\pi\) | ||||
−0.888123 | + | 0.459607i | \(0.847990\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −11.5084 | −0.553060 | −0.276530 | − | 0.961005i | \(-0.589185\pi\) | ||||
−0.276530 | + | 0.961005i | \(0.589185\pi\) | |||||||
\(434\) | − 7.18598i | − 0.344938i | ||||||||
\(435\) | 5.63102i | 0.269987i | ||||||||
\(436\) | 13.8605i | 0.663800i | ||||||||
\(437\) | − 9.51275i | − 0.455056i | ||||||||
\(438\) | 2.17092 | 0.103730 | ||||||||
\(439\) | −8.87502 | −0.423582 | −0.211791 | − | 0.977315i | \(-0.567930\pi\) | ||||
−0.211791 | + | 0.977315i | \(0.567930\pi\) | |||||||
\(440\) | 0.801938i | 0.0382309i | ||||||||
\(441\) | −11.0368 | −0.525564 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.4838 | 1.16326 | 0.581630 | − | 0.813453i | \(-0.302415\pi\) | ||||
0.581630 | + | 0.813453i | \(0.302415\pi\) | |||||||
\(444\) | − 9.67456i | − 0.459134i | ||||||||
\(445\) | −8.24459 | −0.390831 | ||||||||
\(446\) | −19.5080 | −0.923729 | ||||||||
\(447\) | − 1.74094i | − 0.0823436i | ||||||||
\(448\) | − 4.24698i | − 0.200651i | ||||||||
\(449\) | 10.2567i | 0.484042i | 0.970271 | + | 0.242021i | \(0.0778103\pi\) | ||||
−0.970271 | + | 0.242021i | \(0.922190\pi\) | |||||||
\(450\) | − 1.00000i | − 0.0471405i | ||||||||
\(451\) | −7.09783 | −0.334224 | ||||||||
\(452\) | −2.19806 | −0.103388 | ||||||||
\(453\) | 1.75840i | 0.0826167i | ||||||||
\(454\) | 3.23059 | 0.151619 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.74094 | 0.175186 | ||||||||
\(457\) | − 38.6359i | − 1.80731i | −0.428259 | − | 0.903656i | \(-0.640873\pi\) | ||||
0.428259 | − | 0.903656i | \(-0.359127\pi\) | |||||||
\(458\) | 4.58748 | 0.214359 | ||||||||
\(459\) | 7.43296 | 0.346941 | ||||||||
\(460\) | 2.54288i | 0.118562i | ||||||||
\(461\) | − 24.8073i | − 1.15539i | −0.816252 | − | 0.577696i | \(-0.803952\pi\) | ||||
0.816252 | − | 0.577696i | \(-0.196048\pi\) | |||||||
\(462\) | − 3.40581i | − 0.158453i | ||||||||
\(463\) | − 18.0713i | − 0.839844i | −0.907560 | − | 0.419922i | \(-0.862058\pi\) | ||||
0.907560 | − | 0.419922i | \(-0.137942\pi\) | |||||||
\(464\) | 5.63102 | 0.261414 | ||||||||
\(465\) | −1.69202 | −0.0784656 | ||||||||
\(466\) | 6.18359i | 0.286449i | ||||||||
\(467\) | 16.8834 | 0.781270 | 0.390635 | − | 0.920546i | \(-0.372256\pi\) | ||||
0.390635 | + | 0.920546i | \(0.372256\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 33.2500 | 1.53534 | ||||||||
\(470\) | 7.53750i | 0.347679i | ||||||||
\(471\) | 15.9825 | 0.736437 | ||||||||
\(472\) | 9.58211 | 0.441052 | ||||||||
\(473\) | − 5.04892i | − 0.232149i | ||||||||
\(474\) | 16.2349i | 0.745694i | ||||||||
\(475\) | 3.74094i | 0.171646i | ||||||||
\(476\) | 31.5676i | 1.44690i | ||||||||
\(477\) | 13.5646 | 0.621083 | ||||||||
\(478\) | 8.42998 | 0.385578 | ||||||||
\(479\) | 13.9879i | 0.639124i | 0.947565 | + | 0.319562i | \(0.103536\pi\) | ||||
−0.947565 | + | 0.319562i | \(0.896464\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −20.8485 | −0.949621 | ||||||||
\(483\) | − 10.7995i | − 0.491396i | ||||||||
\(484\) | −10.3569 | −0.470768 | ||||||||
\(485\) | −6.07069 | −0.275656 | ||||||||
\(486\) | − 1.00000i | − 0.0453609i | ||||||||
\(487\) | − 23.2760i | − 1.05474i | −0.849636 | − | 0.527369i | \(-0.823178\pi\) | ||||
0.849636 | − | 0.527369i | \(-0.176822\pi\) | |||||||
\(488\) | 10.7899i | 0.488434i | ||||||||
\(489\) | 5.18598i | 0.234518i | ||||||||
\(490\) | −11.0368 | −0.498593 | ||||||||
\(491\) | 32.5918 | 1.47085 | 0.735424 | − | 0.677608i | \(-0.236983\pi\) | ||||
0.735424 | + | 0.677608i | \(0.236983\pi\) | |||||||
\(492\) | − 8.85086i | − 0.399027i | ||||||||
\(493\) | −41.8552 | −1.88506 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.801938 | −0.0360444 | ||||||||
\(496\) | 1.69202i | 0.0759740i | ||||||||
\(497\) | −8.70171 | −0.390325 | ||||||||
\(498\) | 3.61356 | 0.161928 | ||||||||
\(499\) | 1.48666i | 0.0665522i | 0.999446 | + | 0.0332761i | \(0.0105941\pi\) | ||||
−0.999446 | + | 0.0332761i | \(0.989406\pi\) | |||||||
\(500\) | − 1.00000i | − 0.0447214i | ||||||||
\(501\) | 5.29590i | 0.236603i | ||||||||
\(502\) | 6.39075i | 0.285233i | ||||||||
\(503\) | 38.3629 | 1.71052 | 0.855258 | − | 0.518203i | \(-0.173399\pi\) | ||||
0.855258 | + | 0.518203i | \(0.173399\pi\) | |||||||
\(504\) | 4.24698 | 0.189176 | ||||||||
\(505\) | − 5.38404i | − 0.239587i | ||||||||
\(506\) | 2.03923 | 0.0906548 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.19136 | −0.185961 | ||||||||
\(509\) | − 0.770479i | − 0.0341509i | −0.999854 | − | 0.0170754i | \(-0.994564\pi\) | ||||
0.999854 | − | 0.0170754i | \(-0.00543554\pi\) | |||||||
\(510\) | 7.43296 | 0.329137 | ||||||||
\(511\) | −9.21983 | −0.407861 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 3.74094i | 0.165166i | ||||||||
\(514\) | − 9.78687i | − 0.431680i | ||||||||
\(515\) | − 8.92154i | − 0.393130i | ||||||||
\(516\) | 6.29590 | 0.277161 | ||||||||
\(517\) | 6.04461 | 0.265841 | ||||||||
\(518\) | 41.0877i | 1.80529i | ||||||||
\(519\) | −19.6558 | −0.862793 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.7657 | −0.603086 | −0.301543 | − | 0.953453i | \(-0.597502\pi\) | ||||
−0.301543 | + | 0.953453i | \(0.597502\pi\) | |||||||
\(522\) | 5.63102i | 0.246463i | ||||||||
\(523\) | −17.5991 | −0.769554 | −0.384777 | − | 0.923009i | \(-0.625722\pi\) | ||||
−0.384777 | + | 0.923009i | \(0.625722\pi\) | |||||||
\(524\) | 10.8140 | 0.472413 | ||||||||
\(525\) | 4.24698i | 0.185353i | ||||||||
\(526\) | 14.0465i | 0.612458i | ||||||||
\(527\) | − 12.5767i | − 0.547851i | ||||||||
\(528\) | 0.801938i | 0.0348999i | ||||||||
\(529\) | −16.5338 | −0.718860 | ||||||||
\(530\) | 13.5646 | 0.589211 | ||||||||
\(531\) | 9.58211i | 0.415828i | ||||||||
\(532\) | −15.8877 | −0.688819 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −8.24459 | −0.356778 | ||||||||
\(535\) | − 13.9976i | − 0.605169i | ||||||||
\(536\) | −7.82908 | −0.338165 | ||||||||
\(537\) | −17.9095 | −0.772850 | ||||||||
\(538\) | − 17.2597i | − 0.744116i | ||||||||
\(539\) | 8.85086i | 0.381233i | ||||||||
\(540\) | − 1.00000i | − 0.0430331i | ||||||||
\(541\) | − 20.9259i | − 0.899673i | −0.893111 | − | 0.449836i | \(-0.851482\pi\) | ||||
0.893111 | − | 0.449836i | \(-0.148518\pi\) | |||||||
\(542\) | 17.1782 | 0.737867 | ||||||||
\(543\) | −8.74094 | −0.375110 | ||||||||
\(544\) | − 7.43296i | − 0.318686i | ||||||||
\(545\) | −13.8605 | −0.593720 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 42.5599 | 1.81973 | 0.909864 | − | 0.414906i | \(-0.136186\pi\) | ||||
0.909864 | + | 0.414906i | \(0.136186\pi\) | |||||||
\(548\) | − 12.8509i | − 0.548961i | ||||||||
\(549\) | −10.7899 | −0.460500 | ||||||||
\(550\) | −0.801938 | −0.0341947 | ||||||||
\(551\) | − 21.0653i | − 0.897412i | ||||||||
\(552\) | 2.54288i | 0.108232i | ||||||||
\(553\) | − 68.9493i | − 2.93202i | ||||||||
\(554\) | 21.1444i | 0.898338i | ||||||||
\(555\) | 9.67456 | 0.410662 | ||||||||
\(556\) | −16.6233 | −0.704983 | ||||||||
\(557\) | 33.1637i | 1.40519i | 0.711589 | + | 0.702596i | \(0.247976\pi\) | ||||
−0.711589 | + | 0.702596i | \(0.752024\pi\) | |||||||
\(558\) | −1.69202 | −0.0716290 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 4.24698 | 0.179468 | ||||||||
\(561\) | − 5.96077i | − 0.251664i | ||||||||
\(562\) | −4.09246 | −0.172630 | ||||||||
\(563\) | 7.27173 | 0.306467 | 0.153234 | − | 0.988190i | \(-0.451031\pi\) | ||||
0.153234 | + | 0.988190i | \(0.451031\pi\) | |||||||
\(564\) | 7.53750i | 0.317386i | ||||||||
\(565\) | − 2.19806i | − 0.0924732i | ||||||||
\(566\) | − 12.1468i | − 0.510566i | ||||||||
\(567\) | 4.24698i | 0.178356i | ||||||||
\(568\) | 2.04892 | 0.0859707 | ||||||||
\(569\) | −38.9269 | −1.63190 | −0.815951 | − | 0.578122i | \(-0.803786\pi\) | ||||
−0.815951 | + | 0.578122i | \(0.803786\pi\) | |||||||
\(570\) | 3.74094i | 0.156691i | ||||||||
\(571\) | −38.6045 | −1.61555 | −0.807773 | − | 0.589493i | \(-0.799327\pi\) | ||||
−0.807773 | + | 0.589493i | \(0.799327\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.76510 | 0.157289 | ||||||||
\(574\) | 37.5894i | 1.56895i | ||||||||
\(575\) | −2.54288 | −0.106045 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | − 27.8646i | − 1.16002i | −0.814610 | − | 0.580009i | \(-0.803049\pi\) | ||||
0.814610 | − | 0.580009i | \(-0.196951\pi\) | |||||||
\(578\) | 38.2489i | 1.59094i | ||||||||
\(579\) | − 21.9584i | − 0.912559i | ||||||||
\(580\) | 5.63102i | 0.233815i | ||||||||
\(581\) | −15.3467 | −0.636690 | ||||||||
\(582\) | −6.07069 | −0.251638 | ||||||||
\(583\) | − 10.8780i | − 0.450521i | ||||||||
\(584\) | 2.17092 | 0.0898331 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −20.6789 | −0.854236 | ||||||||
\(587\) | 26.1648i | 1.07994i | 0.841685 | + | 0.539968i | \(0.181564\pi\) | ||||
−0.841685 | + | 0.539968i | \(0.818436\pi\) | |||||||
\(588\) | −11.0368 | −0.455151 | ||||||||
\(589\) | 6.32975 | 0.260813 | ||||||||
\(590\) | 9.58211i | 0.394489i | ||||||||
\(591\) | − 18.2446i | − 0.750482i | ||||||||
\(592\) | − 9.67456i | − 0.397622i | ||||||||
\(593\) | − 8.61117i | − 0.353618i | −0.984245 | − | 0.176809i | \(-0.943422\pi\) | ||||
0.984245 | − | 0.176809i | \(-0.0565776\pi\) | |||||||
\(594\) | −0.801938 | −0.0329039 | ||||||||
\(595\) | −31.5676 | −1.29415 | ||||||||
\(596\) | − 1.74094i | − 0.0713116i | ||||||||
\(597\) | −1.77479 | −0.0726373 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.1709 | 0.456431 | 0.228216 | − | 0.973611i | \(-0.426711\pi\) | ||||
0.228216 | + | 0.973611i | \(0.426711\pi\) | |||||||
\(600\) | − 1.00000i | − 0.0408248i | ||||||||
\(601\) | 8.91856 | 0.363796 | 0.181898 | − | 0.983317i | \(-0.441776\pi\) | ||||
0.181898 | + | 0.983317i | \(0.441776\pi\) | |||||||
\(602\) | −26.7385 | −1.08978 | ||||||||
\(603\) | − 7.82908i | − 0.318825i | ||||||||
\(604\) | 1.75840i | 0.0715482i | ||||||||
\(605\) | − 10.3569i | − 0.421068i | ||||||||
\(606\) | − 5.38404i | − 0.218712i | ||||||||
\(607\) | −28.0277 | −1.13761 | −0.568805 | − | 0.822472i | \(-0.692594\pi\) | ||||
−0.568805 | + | 0.822472i | \(0.692594\pi\) | |||||||
\(608\) | 3.74094 | 0.151715 | ||||||||
\(609\) | − 23.9148i | − 0.969078i | ||||||||
\(610\) | −10.7899 | −0.436869 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 7.43296 | 0.300460 | ||||||||
\(613\) | − 1.10885i | − 0.0447861i | −0.999749 | − | 0.0223930i | \(-0.992871\pi\) | ||||
0.999749 | − | 0.0223930i | \(-0.00712852\pi\) | |||||||
\(614\) | −11.3123 | −0.456527 | ||||||||
\(615\) | 8.85086 | 0.356901 | ||||||||
\(616\) | − 3.40581i | − 0.137224i | ||||||||
\(617\) | 16.2905i | 0.655832i | 0.944707 | + | 0.327916i | \(0.106346\pi\) | ||||
−0.944707 | + | 0.327916i | \(0.893654\pi\) | |||||||
\(618\) | − 8.92154i | − 0.358877i | ||||||||
\(619\) | − 23.2252i | − 0.933500i | −0.884389 | − | 0.466750i | \(-0.845425\pi\) | ||||
0.884389 | − | 0.466750i | \(-0.154575\pi\) | |||||||
\(620\) | −1.69202 | −0.0679532 | ||||||||
\(621\) | −2.54288 | −0.102042 | ||||||||
\(622\) | 26.2282i | 1.05165i | ||||||||
\(623\) | 35.0146 | 1.40283 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 29.5023i | 1.17915i | ||||||||
\(627\) | 3.00000 | 0.119808 | ||||||||
\(628\) | 15.9825 | 0.637773 | ||||||||
\(629\) | 71.9106i | 2.86727i | ||||||||
\(630\) | 4.24698i | 0.169204i | ||||||||
\(631\) | 0.357961i | 0.0142502i | 0.999975 | + | 0.00712510i | \(0.00226801\pi\) | ||||
−0.999975 | + | 0.00712510i | \(0.997732\pi\) | |||||||
\(632\) | 16.2349i | 0.645790i | ||||||||
\(633\) | −0.0978347 | −0.00388858 | ||||||||
\(634\) | −7.06398 | −0.280547 | ||||||||
\(635\) | − 4.19136i | − 0.166329i | ||||||||
\(636\) | 13.5646 | 0.537873 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.51573 | 0.178779 | ||||||||
\(639\) | 2.04892i | 0.0810539i | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −33.2814 | −1.31454 | −0.657269 | − | 0.753656i | \(-0.728288\pi\) | ||||
−0.657269 | + | 0.753656i | \(0.728288\pi\) | |||||||
\(642\) | − 13.9976i | − 0.552441i | ||||||||
\(643\) | 48.4172i | 1.90939i | 0.297592 | + | 0.954693i | \(0.403817\pi\) | ||||
−0.297592 | + | 0.954693i | \(0.596183\pi\) | |||||||
\(644\) | − 10.7995i | − 0.425562i | ||||||||
\(645\) | 6.29590i | 0.247901i | ||||||||
\(646\) | −27.8062 | −1.09402 | ||||||||
\(647\) | 47.4814 | 1.86669 | 0.933343 | − | 0.358985i | \(-0.116877\pi\) | ||||
0.933343 | + | 0.358985i | \(0.116877\pi\) | |||||||
\(648\) | − 1.00000i | − 0.0392837i | ||||||||
\(649\) | 7.68425 | 0.301633 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.18598 | 0.281641 | ||||||||
\(652\) | 5.18598i | 0.203099i | ||||||||
\(653\) | −25.4336 | −0.995292 | −0.497646 | − | 0.867380i | \(-0.665802\pi\) | ||||
−0.497646 | + | 0.867380i | \(0.665802\pi\) | |||||||
\(654\) | −13.8605 | −0.541990 | ||||||||
\(655\) | 10.8140i | 0.422539i | ||||||||
\(656\) | − 8.85086i | − 0.345568i | ||||||||
\(657\) | 2.17092i | 0.0846955i | ||||||||
\(658\) | − 32.0116i | − 1.24794i | ||||||||
\(659\) | −2.55496 | −0.0995270 | −0.0497635 | − | 0.998761i | \(-0.515847\pi\) | ||||
−0.0497635 | + | 0.998761i | \(0.515847\pi\) | |||||||
\(660\) | −0.801938 | −0.0312154 | ||||||||
\(661\) | 26.3394i | 1.02449i | 0.858841 | + | 0.512243i | \(0.171185\pi\) | ||||
−0.858841 | + | 0.512243i | \(0.828815\pi\) | |||||||
\(662\) | 10.3134 | 0.400840 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.61356 | 0.140233 | ||||||||
\(665\) | − 15.8877i | − 0.616098i | ||||||||
\(666\) | 9.67456 | 0.374882 | ||||||||
\(667\) | 14.3190 | 0.554434 | ||||||||
\(668\) | 5.29590i | 0.204904i | ||||||||
\(669\) | − 19.5080i | − 0.754221i | ||||||||
\(670\) | − 7.82908i | − 0.302464i | ||||||||
\(671\) | 8.65279i | 0.334037i | ||||||||
\(672\) | 4.24698 | 0.163831 | ||||||||
\(673\) | 23.7767 | 0.916525 | 0.458262 | − | 0.888817i | \(-0.348472\pi\) | ||||
0.458262 | + | 0.888817i | \(0.348472\pi\) | |||||||
\(674\) | − 30.3163i | − 1.16774i | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −40.3250 | −1.54981 | −0.774907 | − | 0.632075i | \(-0.782203\pi\) | ||||
−0.774907 | + | 0.632075i | \(0.782203\pi\) | |||||||
\(678\) | − 2.19806i | − 0.0844161i | ||||||||
\(679\) | 25.7821 | 0.989426 | ||||||||
\(680\) | 7.43296 | 0.285041 | ||||||||
\(681\) | 3.23059i | 0.123796i | ||||||||
\(682\) | 1.35690i | 0.0519582i | ||||||||
\(683\) | − 4.51573i | − 0.172790i | −0.996261 | − | 0.0863948i | \(-0.972465\pi\) | ||||
0.996261 | − | 0.0863948i | \(-0.0275346\pi\) | |||||||
\(684\) | 3.74094i | 0.143038i | ||||||||
\(685\) | 12.8509 | 0.491006 | ||||||||
\(686\) | 17.1444 | 0.654575 | ||||||||
\(687\) | 4.58748i | 0.175023i | ||||||||
\(688\) | 6.29590 | 0.240029 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −2.54288 | −0.0968057 | ||||||||
\(691\) | − 5.44398i | − 0.207099i | −0.994624 | − | 0.103549i | \(-0.966980\pi\) | ||||
0.994624 | − | 0.103549i | \(-0.0330200\pi\) | |||||||
\(692\) | −19.6558 | −0.747201 | ||||||||
\(693\) | 3.40581 | 0.129376 | ||||||||
\(694\) | 28.8592i | 1.09548i | ||||||||
\(695\) | − 16.6233i | − 0.630556i | ||||||||
\(696\) | 5.63102i | 0.213443i | ||||||||
\(697\) | 65.7881i | 2.49190i | ||||||||
\(698\) | 27.4566 | 1.03925 | ||||||||
\(699\) | −6.18359 | −0.233885 | ||||||||
\(700\) | 4.24698i | 0.160521i | ||||||||
\(701\) | 19.8670 | 0.750366 | 0.375183 | − | 0.926951i | \(-0.377580\pi\) | ||||
0.375183 | + | 0.926951i | \(0.377580\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −36.1919 | −1.36501 | ||||||||
\(704\) | 0.801938i | 0.0302242i | ||||||||
\(705\) | −7.53750 | −0.283879 | ||||||||
\(706\) | 0.885772 | 0.0333365 | ||||||||
\(707\) | 22.8659i | 0.859961i | ||||||||
\(708\) | 9.58211i | 0.360118i | ||||||||
\(709\) | 5.64204i | 0.211891i | 0.994372 | + | 0.105946i | \(0.0337869\pi\) | ||||
−0.994372 | + | 0.105946i | \(0.966213\pi\) | |||||||
\(710\) | 2.04892i | 0.0768945i | ||||||||
\(711\) | −16.2349 | −0.608856 | ||||||||
\(712\) | −8.24459 | −0.308979 | ||||||||
\(713\) | 4.30260i | 0.161134i | ||||||||
\(714\) | −31.5676 | −1.18139 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −17.9095 | −0.669308 | ||||||||
\(717\) | 8.42998i | 0.314823i | ||||||||
\(718\) | −7.07069 | −0.263876 | ||||||||
\(719\) | −9.49289 | −0.354025 | −0.177013 | − | 0.984209i | \(-0.556643\pi\) | ||||
−0.177013 | + | 0.984209i | \(0.556643\pi\) | |||||||
\(720\) | − 1.00000i | − 0.0372678i | ||||||||
\(721\) | 37.8896i | 1.41108i | ||||||||
\(722\) | 5.00538i | 0.186281i | ||||||||
\(723\) | − 20.8485i | − 0.775363i | ||||||||
\(724\) | −8.74094 | −0.324854 | ||||||||
\(725\) | −5.63102 | −0.209131 | ||||||||
\(726\) | − 10.3569i | − 0.384380i | ||||||||
\(727\) | 18.2338 | 0.676255 | 0.338128 | − | 0.941100i | \(-0.390206\pi\) | ||||
0.338128 | + | 0.941100i | \(0.390206\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.17092i | 0.0803492i | ||||||||
\(731\) | −46.7972 | −1.73086 | ||||||||
\(732\) | −10.7899 | −0.398805 | ||||||||
\(733\) | − 36.4172i | − 1.34510i | −0.740052 | − | 0.672549i | \(-0.765199\pi\) | ||||
0.740052 | − | 0.672549i | \(-0.234801\pi\) | |||||||
\(734\) | 27.3588i | 1.00983i | ||||||||
\(735\) | − 11.0368i | − 0.407100i | ||||||||
\(736\) | 2.54288i | 0.0937317i | ||||||||
\(737\) | −6.27844 | −0.231269 | ||||||||
\(738\) | 8.85086 | 0.325804 | ||||||||
\(739\) | − 48.2312i | − 1.77421i | −0.461565 | − | 0.887106i | \(-0.652712\pi\) | ||||
0.461565 | − | 0.887106i | \(-0.347288\pi\) | |||||||
\(740\) | 9.67456 | 0.355644 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −57.6088 | −2.11488 | ||||||||
\(743\) | − 41.6859i | − 1.52931i | −0.644441 | − | 0.764654i | \(-0.722910\pi\) | ||||
0.644441 | − | 0.764654i | \(-0.277090\pi\) | |||||||
\(744\) | −1.69202 | −0.0620325 | ||||||||
\(745\) | 1.74094 | 0.0637831 | ||||||||
\(746\) | 18.3370i | 0.671367i | ||||||||
\(747\) | 3.61356i | 0.132213i | ||||||||
\(748\) | − 5.96077i | − 0.217947i | ||||||||
\(749\) | 59.4476i | 2.17217i | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | 0.486663 | 0.0177586 | 0.00887930 | − | 0.999961i | \(-0.497174\pi\) | ||||
0.00887930 | + | 0.999961i | \(0.497174\pi\) | |||||||
\(752\) | 7.53750i | 0.274864i | ||||||||
\(753\) | −6.39075 | −0.232892 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.75840 | −0.0639946 | ||||||||
\(756\) | 4.24698i | 0.154461i | ||||||||
\(757\) | −46.2784 | −1.68202 | −0.841009 | − | 0.541021i | \(-0.818038\pi\) | ||||
−0.841009 | + | 0.541021i | \(0.818038\pi\) | |||||||
\(758\) | −14.3690 | −0.521905 | ||||||||
\(759\) | 2.03923i | 0.0740193i | ||||||||
\(760\) | 3.74094i | 0.135698i | ||||||||
\(761\) | 9.76915i | 0.354131i | 0.984199 | + | 0.177066i | \(0.0566605\pi\) | ||||
−0.984199 | + | 0.177066i | \(0.943339\pi\) | |||||||
\(762\) | − 4.19136i | − 0.151837i | ||||||||
\(763\) | 58.8654 | 2.13107 | ||||||||
\(764\) | 3.76510 | 0.136217 | ||||||||
\(765\) | 7.43296i | 0.268739i | ||||||||
\(766\) | 34.6920 | 1.25347 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 18.5888i | 0.670330i | 0.942160 | + | 0.335165i | \(0.108792\pi\) | ||||
−0.942160 | + | 0.335165i | \(0.891208\pi\) | |||||||
\(770\) | 3.40581 | 0.122737 | ||||||||
\(771\) | 9.78687 | 0.352466 | ||||||||
\(772\) | − 21.9584i | − 0.790299i | ||||||||
\(773\) | − 23.4480i | − 0.843367i | −0.906743 | − | 0.421683i | \(-0.861439\pi\) | ||||
0.906743 | − | 0.421683i | \(-0.138561\pi\) | |||||||
\(774\) | 6.29590i | 0.226301i | ||||||||
\(775\) | − 1.69202i | − 0.0607792i | ||||||||
\(776\) | −6.07069 | −0.217925 | ||||||||
\(777\) | −41.0877 | −1.47401 | ||||||||
\(778\) | 32.6872i | 1.17189i | ||||||||
\(779\) | −33.1105 | −1.18631 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.64310 | 0.0587949 | ||||||||
\(782\) | − 18.9011i | − 0.675902i | ||||||||
\(783\) | −5.63102 | −0.201236 | ||||||||
\(784\) | −11.0368 | −0.394173 | ||||||||
\(785\) | 15.9825i | 0.570441i | ||||||||
\(786\) | 10.8140i | 0.385723i | ||||||||
\(787\) | 28.0030i | 0.998199i | 0.866545 | + | 0.499099i | \(0.166336\pi\) | ||||
−0.866545 | + | 0.499099i | \(0.833664\pi\) | |||||||
\(788\) | − 18.2446i | − 0.649936i | ||||||||
\(789\) | −14.0465 | −0.500070 | ||||||||
\(790\) | −16.2349 | −0.577612 | ||||||||
\(791\) | 9.33513i | 0.331919i | ||||||||
\(792\) | −0.801938 | −0.0284956 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −12.3080 | −0.436794 | ||||||||
\(795\) | 13.5646i | 0.481088i | ||||||||
\(796\) | −1.77479 | −0.0629058 | ||||||||
\(797\) | −42.9452 | −1.52120 | −0.760599 | − | 0.649222i | \(-0.775095\pi\) | ||||
−0.760599 | + | 0.649222i | \(0.775095\pi\) | |||||||
\(798\) | − 15.8877i | − 0.562418i | ||||||||
\(799\) | − 56.0259i | − 1.98206i | ||||||||
\(800\) | − 1.00000i | − 0.0353553i | ||||||||
\(801\) | − 8.24459i | − 0.291308i | ||||||||
\(802\) | −19.2524 | −0.679824 | ||||||||
\(803\) | 1.74094 | 0.0614364 | ||||||||
\(804\) | − 7.82908i | − 0.276111i | ||||||||
\(805\) | 10.7995 | 0.380634 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17.2597 | 0.607569 | ||||||||
\(808\) | − 5.38404i | − 0.189410i | ||||||||
\(809\) | 36.8622 | 1.29601 | 0.648003 | − | 0.761638i | \(-0.275604\pi\) | ||||
0.648003 | + | 0.761638i | \(0.275604\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | − 27.9952i | − 0.983045i | −0.870865 | − | 0.491522i | \(-0.836441\pi\) | ||||
0.870865 | − | 0.491522i | \(-0.163559\pi\) | |||||||
\(812\) | − 23.9148i | − 0.839246i | ||||||||
\(813\) | 17.1782i | 0.602466i | ||||||||
\(814\) | − 7.75840i | − 0.271932i | ||||||||
\(815\) | −5.18598 | −0.181657 | ||||||||
\(816\) | 7.43296 | 0.260206 | ||||||||
\(817\) | − 23.5526i | − 0.824000i | ||||||||
\(818\) | −22.8672 | −0.799535 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.85086 | 0.309085 | ||||||||
\(821\) | − 18.5593i | − 0.647723i | −0.946105 | − | 0.323861i | \(-0.895019\pi\) | ||||
0.946105 | − | 0.323861i | \(-0.104981\pi\) | |||||||
\(822\) | 12.8509 | 0.448225 | ||||||||
\(823\) | 43.2234 | 1.50667 | 0.753337 | − | 0.657635i | \(-0.228443\pi\) | ||||
0.753337 | + | 0.657635i | \(0.228443\pi\) | |||||||
\(824\) | − 8.92154i | − 0.310797i | ||||||||
\(825\) | − 0.801938i | − 0.0279199i | ||||||||
\(826\) | − 40.6950i | − 1.41596i | ||||||||
\(827\) | − 16.7162i | − 0.581279i | −0.956833 | − | 0.290639i | \(-0.906132\pi\) | ||||
0.956833 | − | 0.290639i | \(-0.0938680\pi\) | |||||||
\(828\) | −2.54288 | −0.0883711 | ||||||||
\(829\) | 10.6735 | 0.370706 | 0.185353 | − | 0.982672i | \(-0.440657\pi\) | ||||
0.185353 | + | 0.982672i | \(0.440657\pi\) | |||||||
\(830\) | 3.61356i | 0.125429i | ||||||||
\(831\) | −21.1444 | −0.733490 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 82.0364 | 2.84239 | ||||||||
\(834\) | − 16.6233i | − 0.575616i | ||||||||
\(835\) | −5.29590 | −0.183272 | ||||||||
\(836\) | 3.00000 | 0.103757 | ||||||||
\(837\) | − 1.69202i | − 0.0584848i | ||||||||
\(838\) | − 17.1806i | − 0.593494i | ||||||||
\(839\) | − 44.2465i | − 1.52756i | −0.645477 | − | 0.763780i | \(-0.723341\pi\) | ||||
0.645477 | − | 0.763780i | \(-0.276659\pi\) | |||||||
\(840\) | 4.24698i | 0.146535i | ||||||||
\(841\) | 2.70841 | 0.0933936 | ||||||||
\(842\) | 36.9922 | 1.27484 | ||||||||
\(843\) | − 4.09246i | − 0.140952i | ||||||||
\(844\) | −0.0978347 | −0.00336761 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.53750 | −0.259145 | ||||||||
\(847\) | 43.9855i | 1.51136i | ||||||||
\(848\) | 13.5646 | 0.465812 | ||||||||
\(849\) | 12.1468 | 0.416875 | ||||||||
\(850\) | 7.43296i | 0.254948i | ||||||||
\(851\) | − 24.6012i | − 0.843319i | ||||||||
\(852\) | 2.04892i | 0.0701948i | ||||||||
\(853\) | − 42.5437i | − 1.45667i | −0.685221 | − | 0.728335i | \(-0.740295\pi\) | ||||
0.685221 | − | 0.728335i | \(-0.259705\pi\) | |||||||
\(854\) | 45.8243 | 1.56808 | ||||||||
\(855\) | −3.74094 | −0.127937 | ||||||||
\(856\) | − 13.9976i | − 0.478428i | ||||||||
\(857\) | −8.95061 | −0.305747 | −0.152873 | − | 0.988246i | \(-0.548853\pi\) | ||||
−0.152873 | + | 0.988246i | \(0.548853\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.8810 | −0.848928 | −0.424464 | − | 0.905445i | \(-0.639538\pi\) | ||||
−0.424464 | + | 0.905445i | \(0.639538\pi\) | |||||||
\(860\) | 6.29590i | 0.214688i | ||||||||
\(861\) | −37.5894 | −1.28104 | ||||||||
\(862\) | −19.0834 | −0.649982 | ||||||||
\(863\) | − 53.7531i | − 1.82978i | −0.403705 | − | 0.914889i | \(-0.632278\pi\) | ||||
0.403705 | − | 0.914889i | \(-0.367722\pi\) | |||||||
\(864\) | − 1.00000i | − 0.0340207i | ||||||||
\(865\) | − 19.6558i | − 0.668316i | ||||||||
\(866\) | − 11.5084i | − 0.391072i | ||||||||
\(867\) | −38.2489 | −1.29900 | ||||||||
\(868\) | 7.18598 | 0.243908 | ||||||||
\(869\) | 13.0194i | 0.441652i | ||||||||
\(870\) | −5.63102 | −0.190910 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −13.8605 | −0.469377 | ||||||||
\(873\) | − 6.07069i | − 0.205462i | ||||||||
\(874\) | 9.51275 | 0.321773 | ||||||||
\(875\) | −4.24698 | −0.143574 | ||||||||
\(876\) | 2.17092i | 0.0733484i | ||||||||
\(877\) | 36.1782i | 1.22165i | 0.791765 | + | 0.610826i | \(0.209162\pi\) | ||||
−0.791765 | + | 0.610826i | \(0.790838\pi\) | |||||||
\(878\) | − 8.87502i | − 0.299517i | ||||||||
\(879\) | − 20.6789i | − 0.697481i | ||||||||
\(880\) | −0.801938 | −0.0270333 | ||||||||
\(881\) | 24.3075 | 0.818941 | 0.409470 | − | 0.912323i | \(-0.365714\pi\) | ||||
0.409470 | + | 0.912323i | \(0.365714\pi\) | |||||||
\(882\) | − 11.0368i | − 0.371630i | ||||||||
\(883\) | −33.9764 | −1.14340 | −0.571699 | − | 0.820463i | \(-0.693715\pi\) | ||||
−0.571699 | + | 0.820463i | \(0.693715\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.58211 | −0.322099 | ||||||||
\(886\) | 24.4838i | 0.822549i | ||||||||
\(887\) | −4.97929 | −0.167188 | −0.0835942 | − | 0.996500i | \(-0.526640\pi\) | ||||
−0.0835942 | + | 0.996500i | \(0.526640\pi\) | |||||||
\(888\) | 9.67456 | 0.324657 | ||||||||
\(889\) | 17.8006i | 0.597013i | ||||||||
\(890\) | − 8.24459i | − 0.276359i | ||||||||
\(891\) | − 0.801938i | − 0.0268659i | ||||||||
\(892\) | − 19.5080i | − 0.653175i | ||||||||
\(893\) | 28.1973 | 0.943588 | ||||||||
\(894\) | 1.74094 | 0.0582257 | ||||||||
\(895\) | − 17.9095i | − 0.598647i | ||||||||
\(896\) | 4.24698 | 0.141882 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −10.2567 | −0.342269 | ||||||||
\(899\) | 9.52781i | 0.317770i | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −100.825 | −3.35898 | ||||||||
\(902\) | − 7.09783i | − 0.236332i | ||||||||
\(903\) | − 26.7385i | − 0.889803i | ||||||||
\(904\) | − 2.19806i | − 0.0731065i | ||||||||
\(905\) | − 8.74094i | − 0.290559i | ||||||||
\(906\) | −1.75840 | −0.0584188 | ||||||||
\(907\) | 24.1919 | 0.803280 | 0.401640 | − | 0.915798i | \(-0.368440\pi\) | ||||
0.401640 | + | 0.915798i | \(0.368440\pi\) | |||||||
\(908\) | 3.23059i | 0.107211i | ||||||||
\(909\) | 5.38404 | 0.178577 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.3284 | −0.839168 | −0.419584 | − | 0.907717i | \(-0.637824\pi\) | ||||
−0.419584 | + | 0.907717i | \(0.637824\pi\) | |||||||
\(912\) | 3.74094i | 0.123875i | ||||||||
\(913\) | 2.89785 | 0.0959050 | ||||||||
\(914\) | 38.6359 | 1.27796 | ||||||||
\(915\) | − 10.7899i | − 0.356702i | ||||||||
\(916\) | 4.58748i | 0.151575i | ||||||||
\(917\) | − 45.9269i | − 1.51664i | ||||||||
\(918\) | 7.43296i | 0.245324i | ||||||||
\(919\) | 24.4316 | 0.805925 | 0.402963 | − | 0.915216i | \(-0.367980\pi\) | ||||
0.402963 | + | 0.915216i | \(0.367980\pi\) | |||||||
\(920\) | −2.54288 | −0.0838362 | ||||||||
\(921\) | − 11.3123i | − 0.372753i | ||||||||
\(922\) | 24.8073 | 0.816985 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 3.40581 | 0.112043 | ||||||||
\(925\) | 9.67456i | 0.318098i | ||||||||
\(926\) | 18.0713 | 0.593859 | ||||||||
\(927\) | 8.92154 | 0.293022 | ||||||||
\(928\) | 5.63102i | 0.184847i | ||||||||
\(929\) | − 1.78448i | − 0.0585469i | −0.999571 | − | 0.0292734i | \(-0.990681\pi\) | ||||
0.999571 | − | 0.0292734i | \(-0.00931935\pi\) | |||||||
\(930\) | − 1.69202i | − 0.0554836i | ||||||||
\(931\) | 41.2881i | 1.35316i | ||||||||
\(932\) | −6.18359 | −0.202550 | ||||||||
\(933\) | −26.2282 | −0.858672 | ||||||||
\(934\) | 16.8834i | 0.552441i | ||||||||
\(935\) | 5.96077 | 0.194938 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.9463 | 1.53367 | 0.766834 | − | 0.641845i | \(-0.221831\pi\) | ||||
0.766834 | + | 0.641845i | \(0.221831\pi\) | |||||||
\(938\) | 33.2500i | 1.08565i | ||||||||
\(939\) | −29.5023 | −0.962772 | ||||||||
\(940\) | −7.53750 | −0.245846 | ||||||||
\(941\) | − 27.4047i | − 0.893369i | −0.894691 | − | 0.446685i | \(-0.852605\pi\) | ||||
0.894691 | − | 0.446685i | \(-0.147395\pi\) | |||||||
\(942\) | 15.9825i | 0.520739i | ||||||||
\(943\) | − 22.5066i | − 0.732917i | ||||||||
\(944\) | 9.58211i | 0.311871i | ||||||||
\(945\) | −4.24698 | −0.138154 | ||||||||
\(946\) | 5.04892 | 0.164154 | ||||||||
\(947\) | − 34.6055i | − 1.12453i | −0.826958 | − | 0.562264i | \(-0.809930\pi\) | ||||
0.826958 | − | 0.562264i | \(-0.190070\pi\) | |||||||
\(948\) | −16.2349 | −0.527285 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −3.74094 | −0.121372 | ||||||||
\(951\) | − 7.06398i | − 0.229065i | ||||||||
\(952\) | −31.5676 | −1.02311 | ||||||||
\(953\) | −42.3435 | −1.37164 | −0.685820 | − | 0.727771i | \(-0.740556\pi\) | ||||
−0.685820 | + | 0.727771i | \(0.740556\pi\) | |||||||
\(954\) | 13.5646i | 0.439172i | ||||||||
\(955\) | 3.76510i | 0.121836i | ||||||||
\(956\) | 8.42998i | 0.272645i | ||||||||
\(957\) | 4.51573i | 0.145973i | ||||||||
\(958\) | −13.9879 | −0.451929 | ||||||||
\(959\) | −54.5773 | −1.76239 | ||||||||
\(960\) | − 1.00000i | − 0.0322749i | ||||||||
\(961\) | 28.1371 | 0.907647 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.9976 | 0.451067 | ||||||||
\(964\) | − 20.8485i | − 0.671484i | ||||||||
\(965\) | 21.9584 | 0.706865 | ||||||||
\(966\) | 10.7995 | 0.347470 | ||||||||
\(967\) | 31.6437i | 1.01759i | 0.860887 | + | 0.508796i | \(0.169909\pi\) | ||||
−0.860887 | + | 0.508796i | \(0.830091\pi\) | |||||||
\(968\) | − 10.3569i | − 0.332883i | ||||||||
\(969\) | − 27.8062i | − 0.893265i | ||||||||
\(970\) | − 6.07069i | − 0.194918i | ||||||||
\(971\) | 8.41849 | 0.270162 | 0.135081 | − | 0.990835i | \(-0.456871\pi\) | ||||
0.135081 | + | 0.990835i | \(0.456871\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 70.5986i | 2.26329i | ||||||||
\(974\) | 23.2760 | 0.745813 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.7899 | −0.345375 | ||||||||
\(977\) | 22.0814i | 0.706448i | 0.935539 | + | 0.353224i | \(0.114915\pi\) | ||||
−0.935539 | + | 0.353224i | \(0.885085\pi\) | |||||||
\(978\) | −5.18598 | −0.165829 | ||||||||
\(979\) | −6.61165 | −0.211309 | ||||||||
\(980\) | − 11.0368i | − 0.352559i | ||||||||
\(981\) | − 13.8605i | − 0.442533i | ||||||||
\(982\) | 32.5918i | 1.04005i | ||||||||
\(983\) | − 32.7217i | − 1.04366i | −0.853050 | − | 0.521830i | \(-0.825250\pi\) | ||||
0.853050 | − | 0.521830i | \(-0.174750\pi\) | |||||||
\(984\) | 8.85086 | 0.282155 | ||||||||
\(985\) | 18.2446 | 0.581321 | ||||||||
\(986\) | − 41.8552i | − 1.33294i | ||||||||
\(987\) | 32.0116 | 1.01894 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.0097 | 0.509078 | ||||||||
\(990\) | − 0.801938i | − 0.0254873i | ||||||||
\(991\) | −52.9329 | −1.68147 | −0.840734 | − | 0.541448i | \(-0.817876\pi\) | ||||
−0.840734 | + | 0.541448i | \(0.817876\pi\) | |||||||
\(992\) | −1.69202 | −0.0537217 | ||||||||
\(993\) | 10.3134i | 0.327284i | ||||||||
\(994\) | − 8.70171i | − 0.276001i | ||||||||
\(995\) | − 1.77479i | − 0.0562646i | ||||||||
\(996\) | 3.61356i | 0.114500i | ||||||||
\(997\) | −10.8823 | −0.344646 | −0.172323 | − | 0.985040i | \(-0.555127\pi\) | ||||
−0.172323 | + | 0.985040i | \(0.555127\pi\) | |||||||
\(998\) | −1.48666 | −0.0470595 | ||||||||
\(999\) | 9.67456i | 0.306090i |
(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 | 5070.2.b.u.1351.6 | 6 | ||
13.5 | odd | 4 | 5070.2.a.br.1.1 | yes | 3 | ||
13.8 | odd | 4 | 5070.2.a.bm.1.3 | ✓ | 3 | ||
13.12 | even | 2 | inner | 5070.2.b.u.1351.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5070.2.a.bm.1.3 | ✓ | 3 | 13.8 | odd | 4 | ||
5070.2.a.br.1.1 | yes | 3 | 13.5 | odd | 4 | ||
5070.2.b.u.1351.1 | 6 | 13.12 | even | 2 | inner | ||
5070.2.b.u.1351.6 | 6 | 1.1 | even | 1 | trivial |