Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(449,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.g (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: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 20x^{10} + 148x^{8} + 494x^{6} + 708x^{4} + 304x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 1120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.4 | ||
Root | \(2.36682i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.449 |
Dual form | 2240.2.g.p.449.9 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 2.17741i | − | 1.25713i | −0.777758 | − | 0.628564i | \(-0.783643\pi\) | ||
0.777758 | − | 0.628564i | \(-0.216357\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.45926 | + | 1.69427i | 0.652601 | + | 0.757701i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.74111 | −0.580371 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.13290 | −0.643093 | −0.321546 | − | 0.946894i | \(-0.604203\pi\) | ||||
−0.321546 | + | 0.946894i | \(0.604203\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.52144i | − | 1.53137i | −0.643215 | − | 0.765686i | \(-0.722400\pi\) | ||
0.643215 | − | 0.765686i | \(-0.277600\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.68912 | − | 3.17741i | 0.952528 | − | 0.820404i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 5.24535i | − | 1.27218i | −0.771613 | − | 0.636092i | \(-0.780550\pi\) | ||
0.771613 | − | 0.636092i | \(-0.219450\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.50100 | −1.49143 | −0.745715 | − | 0.666265i | \(-0.767892\pi\) | ||||
−0.745715 | + | 0.666265i | \(0.767892\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.17741 | 0.475150 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.35482i | 1.32507i | 0.749030 | + | 0.662536i | \(0.230520\pi\) | ||||
−0.749030 | + | 0.662536i | \(0.769480\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.741113 | + | 4.94477i | −0.148223 | + | 0.988954i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 2.74111i | − | 0.527527i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.09593 | 1.68907 | 0.844536 | − | 0.535499i | \(-0.179876\pi\) | ||||
0.844536 | + | 0.535499i | \(0.179876\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.77709 | −1.21720 | −0.608600 | − | 0.793477i | \(-0.708269\pi\) | ||||
−0.608600 | + | 0.793477i | \(0.708269\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.64419i | 0.808450i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.69427 | + | 1.45926i | −0.286384 | + | 0.246660i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 9.88954i | − | 1.62583i | −0.582382 | − | 0.812915i | \(-0.697879\pi\) | ||
0.582382 | − | 0.812915i | \(-0.302121\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −12.0224 | −1.92513 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.35482 | −0.367761 | −0.183880 | − | 0.982949i | \(-0.558866\pi\) | ||||
−0.183880 | + | 0.982949i | \(0.558866\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 0.354819i | − | 0.0541094i | −0.999634 | − | 0.0270547i | \(-0.991387\pi\) | ||
0.999634 | − | 0.0270547i | \(-0.00861284\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.54074 | − | 2.94992i | −0.378751 | − | 0.439748i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 8.57816i | − | 1.25125i | −0.780123 | − | 0.625626i | \(-0.784843\pi\) | ||
0.780123 | − | 0.625626i | \(-0.215157\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.4213 | −1.59930 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 7.37825i | − | 1.01348i | −0.862099 | − | 0.506740i | \(-0.830850\pi\) | ||
0.862099 | − | 0.506740i | \(-0.169150\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.11245 | − | 3.61371i | −0.419683 | − | 0.487272i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 14.1553i | 1.87492i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.50100 | 0.846358 | 0.423179 | − | 0.906046i | \(-0.360914\pi\) | ||||
0.423179 | + | 0.906046i | \(0.360914\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.43630 | −0.696046 | −0.348023 | − | 0.937486i | \(-0.613147\pi\) | ||||
−0.348023 | + | 0.937486i | \(0.613147\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 1.74111i | − | 0.219360i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.35482 | − | 8.05722i | 1.16032 | − | 0.999376i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 5.48223i | − | 0.669760i | −0.942261 | − | 0.334880i | \(-0.891304\pi\) | ||
0.942261 | − | 0.334880i | \(-0.108696\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13.8370 | 1.66578 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.11245 | 0.369380 | 0.184690 | − | 0.982797i | \(-0.440872\pi\) | ||||
0.184690 | + | 0.982797i | \(0.440872\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 7.37825i | − | 0.863558i | −0.901979 | − | 0.431779i | \(-0.857886\pi\) | ||
0.901979 | − | 0.431779i | \(-0.142114\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10.7668 | + | 1.61371i | 1.24324 | + | 0.186335i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 2.13290i | − | 0.243066i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.0224 | 1.35263 | 0.676315 | − | 0.736613i | \(-0.263576\pi\) | ||||
0.676315 | + | 0.736613i | \(0.263576\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.1919 | −1.24354 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 11.1104i | − | 1.21952i | −0.792585 | − | 0.609762i | \(-0.791265\pi\) | ||
0.792585 | − | 0.609762i | \(-0.208735\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.88705 | − | 7.65434i | 0.963936 | − | 0.830229i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 19.8056i | − | 2.12338i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.52144 | 0.578804 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 14.7565i | 1.53018i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.48665 | − | 11.0145i | −0.973310 | − | 1.13006i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.979557i | 0.0994589i | 0.998763 | + | 0.0497295i | \(0.0158359\pi\) | ||||
−0.998763 | + | 0.0497295i | \(0.984164\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.71361 | 0.373232 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.1459 | −1.40757 | −0.703787 | − | 0.710411i | \(-0.748509\pi\) | ||||
−0.703787 | + | 0.710411i | \(0.748509\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.61371i | 0.947267i | 0.880722 | + | 0.473633i | \(0.157058\pi\) | ||||
−0.880722 | + | 0.473633i | \(0.842942\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.17741 | + | 3.68912i | 0.310083 | + | 0.360022i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 2.96445i | − | 0.286584i | −0.989680 | − | 0.143292i | \(-0.954231\pi\) | ||
0.989680 | − | 0.143292i | \(-0.0457689\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.6137 | 1.11239 | 0.556196 | − | 0.831051i | \(-0.312261\pi\) | ||||
0.556196 | + | 0.831051i | \(0.312261\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −21.5336 | −2.04388 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 3.66463i | − | 0.344740i | −0.985032 | − | 0.172370i | \(-0.944858\pi\) | ||
0.985032 | − | 0.172370i | \(-0.0551424\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.7668 | + | 9.27334i | −1.00401 | + | 0.864744i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.61345i | 0.888764i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.24535 | 0.480840 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.45075 | −0.586432 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.12741i | 0.462323i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.45926 | + | 5.96007i | −0.846062 | + | 0.533084i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.87259i | 0.432373i | 0.976352 | + | 0.216186i | \(0.0693619\pi\) | ||||
−0.976352 | + | 0.216186i | \(0.930638\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.772587 | −0.0680225 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.23520 | 0.195291 | 0.0976453 | − | 0.995221i | \(-0.468869\pi\) | ||||
0.0976453 | + | 0.995221i | \(0.468869\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 6.50100i | − | 0.563708i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.64419 | − | 4.00000i | 0.399708 | − | 0.344265i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.26579i | 0.364451i | 0.983257 | + | 0.182226i | \(0.0583301\pi\) | ||||
−0.983257 | + | 0.182226i | \(0.941670\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.0326 | −1.27505 | −0.637524 | − | 0.770431i | \(-0.720041\pi\) | ||||
−0.637524 | + | 0.770431i | \(0.720041\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18.6782 | −1.57299 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.7767i | 0.984814i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.2733 | + | 15.4110i | 1.10229 | + | 1.27981i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.17741i | 0.179590i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.67409 | −0.464840 | −0.232420 | − | 0.972616i | \(-0.574664\pi\) | ||||
−0.232420 | + | 0.972616i | \(0.574664\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.1758 | 1.07223 | 0.536115 | − | 0.844145i | \(-0.319891\pi\) | ||||
0.536115 | + | 0.844145i | \(0.319891\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.13275i | 0.738339i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.88954 | − | 11.4822i | −0.794347 | − | 0.922275i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.1450i | 1.44813i | 0.689731 | + | 0.724066i | \(0.257729\pi\) | ||||
−0.689731 | + | 0.724066i | \(0.742271\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −16.0655 | −1.27407 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.35482 | −0.500830 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 12.0289i | − | 0.942177i | −0.882086 | − | 0.471088i | \(-0.843861\pi\) | ||
0.882086 | − | 0.471088i | \(-0.156139\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.86852 | + | 6.77709i | −0.612563 | + | 0.527595i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 0.904068i | − | 0.0699589i | −0.999388 | − | 0.0349794i | \(-0.988863\pi\) | ||
0.999388 | − | 0.0349794i | \(-0.0111366\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −17.4863 | −1.34510 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.3190 | 0.865583 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.0756i | 1.45029i | 0.688595 | + | 0.725146i | \(0.258228\pi\) | ||||
−0.688595 | + | 0.725146i | \(0.741772\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.94477 | − | 0.741113i | −0.373789 | − | 0.0560229i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 14.1553i | − | 1.06398i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.22491 | −0.465271 | −0.232636 | − | 0.972564i | \(-0.574735\pi\) | ||||
−0.232636 | + | 0.972564i | \(0.574735\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.27334 | 0.540623 | 0.270312 | − | 0.962773i | \(-0.412873\pi\) | ||||
0.270312 | + | 0.962773i | \(0.412873\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.8370i | 0.875020i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 16.7556 | − | 14.4314i | 1.23189 | − | 1.06102i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.1878i | 0.818132i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.74111 | 0.199387 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.5540 | 1.48724 | 0.743618 | − | 0.668604i | \(-0.233108\pi\) | ||||
0.743618 | + | 0.668604i | \(0.233108\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.93043i | 0.570845i | 0.958402 | + | 0.285422i | \(0.0921338\pi\) | ||||
−0.958402 | + | 0.285422i | \(0.907866\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −17.5439 | − | 20.3693i | −1.25634 | − | 1.45867i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.4417i | 0.743942i | 0.928244 | + | 0.371971i | \(0.121318\pi\) | ||||
−0.928244 | + | 0.371971i | \(0.878682\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.0429 | −0.782809 | −0.391405 | − | 0.920219i | \(-0.628011\pi\) | ||||
−0.391405 | + | 0.920219i | \(0.628011\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.9371 | −0.841975 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.09593i | 0.638409i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.43630 | − | 3.98970i | −0.240001 | − | 0.278653i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 11.0645i | − | 0.769033i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.8660 | 0.959128 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.64419 | −0.319719 | −0.159860 | − | 0.987140i | \(-0.551104\pi\) | ||||
−0.159860 | + | 0.987140i | \(0.551104\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 6.77709i | − | 0.464358i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.601160 | − | 0.517774i | 0.0409988 | − | 0.0353119i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 6.77709i | − | 0.460059i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −16.0655 | −1.08560 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −28.9619 | −1.94819 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 9.96853i | − | 0.667542i | −0.942654 | − | 0.333771i | \(-0.891679\pi\) | ||
0.942654 | − | 0.333771i | \(-0.108321\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.29036 | − | 8.60940i | 0.0860241 | − | 0.573960i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 23.2419i | − | 1.54262i | −0.636461 | − | 0.771308i | \(-0.719603\pi\) | ||
0.636461 | − | 0.771308i | \(-0.280397\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.371839 | 0.0245718 | 0.0122859 | − | 0.999925i | \(-0.496089\pi\) | ||||
0.0122859 | + | 0.999925i | \(0.496089\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.64419 | −0.305565 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.22491i | 0.407807i | 0.978991 | + | 0.203904i | \(0.0653629\pi\) | ||||
−0.978991 | + | 0.203904i | \(0.934637\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.5337 | − | 12.5178i | 0.948076 | − | 0.816570i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 26.1778i | − | 1.70043i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.90998 | 0.576339 | 0.288169 | − | 0.957579i | \(-0.406953\pi\) | ||||
0.288169 | + | 0.957579i | \(0.406953\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 30.0289 | 1.93433 | 0.967166 | − | 0.254145i | \(-0.0817941\pi\) | ||||
0.967166 | + | 0.254145i | \(0.0817941\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.1459i | 1.03576i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.45926 | − | 1.69427i | −0.0932288 | − | 0.108243i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 35.8949i | 2.28394i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −24.1919 | −1.53310 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −28.0346 | −1.76953 | −0.884763 | − | 0.466040i | \(-0.845680\pi\) | ||||
−0.884763 | + | 0.466040i | \(0.845680\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 13.5542i | − | 0.852144i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −16.6666 | − | 19.3507i | −1.04370 | − | 1.21179i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1.15334i | − | 0.0719434i | −0.999353 | − | 0.0359717i | \(-0.988547\pi\) | ||
0.999353 | − | 0.0359717i | \(-0.0114526\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.88954 | 0.614506 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −15.8370 | −0.980288 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 11.6741i | − | 0.719855i | −0.932980 | − | 0.359928i | \(-0.882801\pi\) | ||
0.932980 | − | 0.359928i | \(-0.117199\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.5008 | − | 10.7668i | 0.767915 | − | 0.661399i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.0645i | 0.799532i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.1815 | 0.925631 | 0.462816 | − | 0.886455i | \(-0.346839\pi\) | ||||
0.462816 | + | 0.886455i | \(0.346839\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.95911 | 0.119008 | 0.0595038 | − | 0.998228i | \(-0.481048\pi\) | ||||
0.0595038 | + | 0.998228i | \(0.481048\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 12.0224i | − | 0.727631i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.58072 | − | 10.5467i | 0.0953208 | − | 0.635989i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.7075i | 0.883689i | 0.897092 | + | 0.441844i | \(0.145676\pi\) | ||||
−0.897092 | + | 0.441844i | \(0.854324\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.7997 | 0.706428 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.3523 | 1.45273 | 0.726367 | − | 0.687307i | \(-0.241207\pi\) | ||||
0.726367 | + | 0.687307i | \(0.241207\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.3982i | 1.45032i | 0.688580 | + | 0.725161i | \(0.258235\pi\) | ||||
−0.688580 | + | 0.725161i | \(0.741765\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −23.9830 | + | 20.6563i | −1.42063 | + | 1.22358i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 2.35482i | − | 0.139001i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.5137 | −0.618453 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.13290 | 0.125033 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.5234i | 1.08215i | 0.840974 | + | 0.541075i | \(0.181983\pi\) | ||||
−0.840974 | + | 0.541075i | \(0.818017\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.48665 | + | 11.0145i | 0.552334 | + | 0.641286i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.84651i | 0.339249i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 35.0878 | 2.02918 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.354819 | 0.0204514 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 30.8015i | 1.76950i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.93298 | − | 9.21056i | −0.454241 | − | 0.527395i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 9.05000i | − | 0.516511i | −0.966077 | − | 0.258255i | \(-0.916852\pi\) | ||
0.966077 | − | 0.258255i | \(-0.0831476\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20.9330 | 1.19084 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.4907 | −0.594873 | −0.297437 | − | 0.954742i | \(-0.596132\pi\) | ||||
−0.297437 | + | 0.954742i | \(0.596132\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 5.24535i | − | 0.296485i | −0.988951 | − | 0.148242i | \(-0.952638\pi\) | ||
0.988951 | − | 0.148242i | \(-0.0473616\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.94992 | − | 2.54074i | 0.166209 | − | 0.143154i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.13504i | 0.456909i | 0.973555 | + | 0.228455i | \(0.0733673\pi\) | ||||
−0.973555 | + | 0.228455i | \(0.926633\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −19.4007 | −1.08623 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.45483 | −0.360273 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 34.1000i | 1.89738i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 27.3023 | + | 4.09201i | 1.51446 | + | 0.226984i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 25.2878i | − | 1.39842i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.57816 | 0.472929 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.7585 | 1.52574 | 0.762872 | − | 0.646549i | \(-0.223789\pi\) | ||||
0.762872 | + | 0.646549i | \(0.223789\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 17.2188i | 0.943585i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.28838 | − | 8.00000i | 0.507478 | − | 0.437087i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 11.8487i | − | 0.645437i | −0.946495 | − | 0.322719i | \(-0.895403\pi\) | ||
0.946495 | − | 0.322719i | \(-0.104597\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.97941 | −0.433382 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.4548 | 0.782773 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 20.1919 | + | 23.4437i | 1.08709 | + | 1.26217i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 3.90814i | − | 0.209800i | −0.994483 | − | 0.104900i | \(-0.966548\pi\) | ||
0.994483 | − | 0.104900i | \(-0.0334523\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.40075 | 0.235567 | 0.117783 | − | 0.993039i | \(-0.462421\pi\) | ||||
0.117783 | + | 0.993039i | \(0.462421\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.1349 | −0.807841 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 21.3108i | − | 1.13426i | −0.823628 | − | 0.567130i | \(-0.808054\pi\) | ||
0.823628 | − | 0.567130i | \(-0.191946\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.54188 | + | 5.27334i | 0.241058 | + | 0.279880i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 11.4213i | − | 0.604478i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.32927 | 0.386824 | 0.193412 | − | 0.981118i | \(-0.438045\pi\) | ||||
0.193412 | + | 0.981118i | \(0.438045\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 23.2630 | 1.22437 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 14.0459i | 0.737220i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.5008 | − | 10.7668i | 0.654319 | − | 0.563560i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 11.4508i | − | 0.597724i | −0.954296 | − | 0.298862i | \(-0.903393\pi\) | ||
0.954296 | − | 0.298862i | \(-0.0966071\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.10001 | 0.213438 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.37825 | 0.383059 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.17593i | 0.319777i | 0.987135 | + | 0.159889i | \(0.0511135\pi\) | ||||
−0.987135 | + | 0.159889i | \(0.948886\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.9775 | + | 20.5967i | 0.670155 | + | 1.06361i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 50.2226i | − | 2.58660i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.1064 | 0.724595 | 0.362297 | − | 0.932063i | \(-0.381992\pi\) | ||||
0.362297 | + | 0.932063i | \(0.381992\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.6096 | 0.543548 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 7.25632i | − | 0.370781i | −0.982665 | − | 0.185390i | \(-0.940645\pi\) | ||
0.982665 | − | 0.185390i | \(-0.0593550\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.61371 | − | 3.11245i | 0.184172 | − | 0.158625i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.617781i | 0.0314036i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.5152 | −0.735950 | −0.367975 | − | 0.929836i | \(-0.619949\pi\) | ||||
−0.367975 | + | 0.929836i | \(0.619949\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 33.3333 | 1.68574 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 4.86695i | − | 0.245505i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 17.5439 | + | 20.3693i | 0.882728 | + | 1.02489i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 26.5028i | − | 1.33014i | −0.746781 | − | 0.665070i | \(-0.768402\pi\) | ||
0.746781 | − | 0.665070i | \(-0.231598\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −14.1553 | −0.708653 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.4863 | −0.623536 | −0.311768 | − | 0.950158i | \(-0.600921\pi\) | ||||
−0.311768 | + | 0.950158i | \(0.600921\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 37.4193i | 1.86399i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −16.3319 | − | 18.9621i | −0.811536 | − | 0.942232i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.0934i | 1.04556i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.0645 | −1.14046 | −0.570232 | − | 0.821484i | \(-0.693147\pi\) | ||||
−0.570232 | + | 0.821484i | \(0.693147\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.28838 | 0.458162 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.50100i | 0.319893i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.8240 | − | 16.2130i | 0.924035 | − | 0.795863i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 32.7321i | 1.60290i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.47841 | 0.0722251 | 0.0361125 | − | 0.999348i | \(-0.488503\pi\) | ||||
0.0361125 | + | 0.999348i | \(0.488503\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −38.1604 | −1.85982 | −0.929912 | − | 0.367783i | \(-0.880117\pi\) | ||||
−0.929912 | + | 0.367783i | \(0.880117\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 14.9355i | 0.726191i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 25.9371 | + | 3.88740i | 1.25813 | + | 0.188566i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 5.43630i | − | 0.263081i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 25.6426 | 1.23804 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.7300 | −1.28754 | −0.643768 | − | 0.765221i | \(-0.722630\pi\) | ||||
−0.643768 | + | 0.765221i | \(0.722630\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2.90784i | − | 0.139742i | −0.997556 | − | 0.0698709i | \(-0.977741\pi\) | ||
0.997556 | − | 0.0698709i | \(-0.0222587\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 33.5560 | − | 28.9015i | 1.60889 | − | 1.38572i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 41.3127i | − | 1.97625i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.3741 | 1.49741 | 0.748703 | − | 0.662906i | \(-0.230677\pi\) | ||||
0.748703 | + | 0.662906i | \(0.230677\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.74111 | 0.0829101 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.2274i | 0.533430i | 0.963775 | + | 0.266715i | \(0.0859383\pi\) | ||||
−0.963775 | + | 0.266715i | \(0.914062\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.75557 | − | 10.1656i | −0.415054 | − | 0.481897i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.3548i | 0.584363i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.4152 | 1.15222 | 0.576112 | − | 0.817371i | \(-0.304569\pi\) | ||||
0.576112 | + | 0.817371i | \(0.304569\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.02259 | 0.236504 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 28.6891i | − | 1.34793i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.05722 | + | 9.35482i | 0.377728 | + | 0.438561i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.2188i | 0.805462i | 0.915318 | + | 0.402731i | \(0.131939\pi\) | ||||
−0.915318 | + | 0.402731i | \(0.868061\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −14.3781 | −0.671112 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 38.1748 | 1.77798 | 0.888990 | − | 0.457927i | \(-0.151408\pi\) | ||||
0.888990 | + | 0.457927i | \(0.151408\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 10.5178i | − | 0.488802i | −0.969674 | − | 0.244401i | \(-0.921409\pi\) | ||
0.969674 | − | 0.244401i | \(-0.0785914\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −25.0015 | + | 21.5336i | −1.15942 | + | 0.998596i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 26.8870i | − | 1.24418i | −0.782944 | − | 0.622092i | \(-0.786283\pi\) | ||
0.782944 | − | 0.622092i | \(-0.213717\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.48223 | 0.253146 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 39.5092 | 1.82049 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.756793i | 0.0347974i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.81797 | − | 32.1459i | 0.221064 | − | 1.47496i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.8464i | 0.588194i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.97941 | 0.364588 | 0.182294 | − | 0.983244i | \(-0.441648\pi\) | ||||
0.182294 | + | 0.983244i | \(0.441648\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −54.6045 | −2.48975 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13.8370i | 0.629607i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.65964 | + | 1.42943i | −0.0753602 | + | 0.0649070i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.83705i | 0.173873i | 0.996214 | + | 0.0869366i | \(0.0277077\pi\) | ||||
−0.996214 | + | 0.0869366i | \(0.972292\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −26.1919 | −1.18444 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.60330 | 0.298003 | 0.149001 | − | 0.988837i | \(-0.452394\pi\) | ||||
0.149001 | + | 0.988837i | \(0.452394\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 47.7114i | − | 2.14881i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.41913 | + | 6.29187i | 0.243572 | + | 0.282799i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.11245i | 0.139613i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.95087 | −0.311164 | −0.155582 | − | 0.987823i | \(-0.549725\pi\) | ||||
−0.155582 | + | 0.987823i | \(0.549725\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.96853 | −0.0879472 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.8974i | 1.06553i | 0.846262 | + | 0.532767i | \(0.178848\pi\) | ||||
−0.846262 | + | 0.532767i | \(0.821152\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −20.6426 | − | 23.9671i | −0.918584 | − | 1.06652i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 38.0748i | 1.69096i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.36520 | −0.326457 | −0.163228 | − | 0.986588i | \(-0.552191\pi\) | ||||
−0.163228 | + | 0.986588i | \(0.552191\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.37825 | 0.326394 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 17.8200i | 0.786771i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.2882 | + | 14.0289i | −0.717745 | + | 0.618188i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.2963i | 0.804671i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 41.5354 | 1.82320 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.2563 | 0.580770 | 0.290385 | − | 0.956910i | \(-0.406217\pi\) | ||||
0.290385 | + | 0.956910i | \(0.406217\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.7845i | 0.996296i | 0.867092 | + | 0.498148i | \(0.165986\pi\) | ||||
−0.867092 | + | 0.498148i | \(0.834014\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.61371 | + | 10.7668i | −0.0704279 | + | 0.469901i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 35.5482i | 1.54850i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.3837 | −0.755814 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.3190 | −0.491201 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.0020i | 0.563179i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.02259 | − | 4.32591i | 0.217145 | − | 0.187025i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.5542i | 0.584906i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.13290 | 0.0918704 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.8345 | 0.766764 | 0.383382 | − | 0.923590i | \(-0.374759\pi\) | ||||
0.383382 | + | 0.923590i | \(0.374759\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 15.8370i | − | 0.679633i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.9474 | + | 19.6768i | 0.725948 | + | 0.842860i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 24.3548i | − | 1.04134i | −0.853759 | − | 0.520668i | \(-0.825683\pi\) | ||
0.853759 | − | 0.520668i | \(-0.174317\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.46521 | 0.403965 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −59.1326 | −2.51913 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.0224i | 0.511246i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −31.4231 | − | 36.4837i | −1.33384 | − | 1.54865i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 36.4457i | 1.54425i | 0.635468 | + | 0.772127i | \(0.280807\pi\) | ||||
−0.635468 | + | 0.772127i | \(0.719193\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.95911 | −0.0828617 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.3604 | 1.02850 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 23.4363i | − | 0.987722i | −0.869541 | − | 0.493861i | \(-0.835585\pi\) | ||
0.869541 | − | 0.493861i | \(-0.164415\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.20888 | − | 5.34766i | 0.261210 | − | 0.224978i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 11.1919i | − | 0.470014i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.9015 | −0.457015 | −0.228507 | − | 0.973542i | \(-0.573385\pi\) | ||||
−0.228507 | + | 0.973542i | \(0.573385\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.6379 | 0.947368 | 0.473684 | − | 0.880695i | \(-0.342924\pi\) | ||||
0.473684 | + | 0.880695i | \(0.342924\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 44.7545i | − | 1.86965i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −31.4231 | − | 4.70964i | −1.31043 | − | 0.196406i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.7789i | 1.11482i | 0.830237 | + | 0.557411i | \(0.188205\pi\) | ||||
−0.830237 | + | 0.557411i | \(0.811795\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 17.2678 | 0.717625 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.1104 | 0.460937 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.7370i | 0.651762i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −16.2878 | + | 14.0285i | −0.673418 | + | 0.580009i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 11.5282i | − | 0.475818i | −0.971287 | − | 0.237909i | \(-0.923538\pi\) | ||
0.971287 | − | 0.237909i | \(-0.0764620\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 44.0578 | 1.81537 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.7359 | 0.935230 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.5949i | 0.763601i | 0.924245 | + | 0.381801i | \(0.124696\pi\) | ||||
−0.924245 | + | 0.381801i | \(0.875304\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.65434 | + | 8.88705i | 0.313797 | + | 0.364333i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 24.0449i | 0.984091i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.5131 | 0.919862 | 0.459931 | − | 0.887955i | \(-0.347874\pi\) | ||||
0.459931 | + | 0.887955i | \(0.347874\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.2274 | 1.68170 | 0.840851 | − | 0.541267i | \(-0.182055\pi\) | ||||
0.840851 | + | 0.541267i | \(0.182055\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.54517i | 0.388710i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.41333 | − | 10.9293i | −0.382706 | − | 0.444340i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.74111i | 0.273613i | 0.990598 | + | 0.136807i | \(0.0436839\pi\) | ||||
−0.990598 | + | 0.136807i | \(0.956316\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 19.8056 | 0.802562 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −47.3638 | −1.91613 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 37.0958i | 1.49829i | 0.662408 | + | 0.749144i | \(0.269535\pi\) | ||||
−0.662408 | + | 0.749144i | \(0.730465\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.68722 | + | 7.48223i | −0.350302 | + | 0.301712i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.8487i | 0.477009i | 0.971141 | + | 0.238504i | \(0.0766572\pi\) | ||||
−0.971141 | + | 0.238504i | \(0.923343\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 46.4067 | 1.86524 | 0.932622 | − | 0.360855i | \(-0.117515\pi\) | ||||
0.932622 | + | 0.360855i | \(0.117515\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 17.4193 | 0.699012 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 6.00000i | − | 0.240385i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.9015 | − | 7.32927i | −0.956060 | − | 0.293171i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 30.1919i | − | 1.20575i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −51.8741 | −2.06836 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 39.1308 | 1.55777 | 0.778886 | − | 0.627166i | \(-0.215785\pi\) | ||||
0.778886 | + | 0.627166i | \(0.215785\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.1123i | 0.401928i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.25550 | + | 7.11039i | −0.327609 | + | 0.282167i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.52144i | 0.218767i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.41913 | −0.214378 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.48223 | −0.0585444 | −0.0292722 | − | 0.999571i | \(-0.509319\pi\) | ||||
−0.0292722 | + | 0.999571i | \(0.509319\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.5322i | 1.51956i | 0.650179 | + | 0.759781i | \(0.274694\pi\) | ||||
−0.650179 | + | 0.759781i | \(0.725306\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.12741 | − | 1.30897i | −0.0443916 | − | 0.0515407i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 46.5467i | − | 1.82994i | −0.403523 | − | 0.914969i | \(-0.632214\pi\) | ||
0.403523 | − | 0.914969i | \(-0.367786\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.8660 | −0.544286 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.7565 | −0.578353 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 42.4660i | − | 1.66182i | −0.556405 | − | 0.830912i | \(-0.687820\pi\) | ||
0.556405 | − | 0.830912i | \(-0.312180\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.26175 | + | 3.78704i | 0.127447 | + | 0.147972i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.8464i | 0.501184i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −39.7319 | −1.54774 | −0.773868 | − | 0.633346i | \(-0.781681\pi\) | ||||
−0.773868 | + | 0.633346i | \(0.781681\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.2667 | 1.02166 | 0.510828 | − | 0.859683i | \(-0.329339\pi\) | ||||
0.510828 | + | 0.859683i | \(0.329339\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 63.0619i | 2.44912i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.0145 | − | 9.48665i | 0.427122 | − | 0.367877i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 57.8030i | 2.23814i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −21.7056 | −0.839186 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.5951 | 0.447622 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 22.8426i | − | 0.880516i | −0.897871 | − | 0.440258i | \(-0.854887\pi\) | ||
0.897871 | − | 0.440258i | \(-0.145113\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 13.5542 | + | 2.03147i | 0.521700 | + | 0.0781915i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.27594i | 0.279637i | 0.990177 | + | 0.139819i | \(0.0446519\pi\) | ||||
−0.990177 | + | 0.139819i | \(0.955348\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.979557 | −0.0375919 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −50.6071 | −1.93927 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.9015i | 1.48852i | 0.667887 | + | 0.744262i | \(0.267199\pi\) | ||||
−0.667887 | + | 0.744262i | \(0.732801\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.22741 | + | 6.22491i | −0.276145 | + | 0.237841i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 0.809645i | − | 0.0308899i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −40.7385 | −1.55202 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.2146 | −0.388582 | −0.194291 | − | 0.980944i | \(-0.562241\pi\) | ||||
−0.194291 | + | 0.980944i | \(0.562241\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.71361i | 0.141069i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −21.9365 | − | 25.4693i | −0.832098 | − | 0.966105i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.3519i | 0.467860i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.5542 | 0.512666 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.5508 | −0.889500 | −0.444750 | − | 0.895655i | \(-0.646707\pi\) | ||||
−0.444750 | + | 0.895655i | \(0.646707\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 64.2919i | 2.42481i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −27.2563 | − | 31.6459i | −1.02653 | − | 1.19185i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 14.1459i | − | 0.532013i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.6715 | −1.33967 | −0.669836 | − | 0.742509i | \(-0.733636\pi\) | ||||
−0.669836 | + | 0.742509i | \(0.733636\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.9324 | −0.785027 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 43.0672i | − | 1.61288i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19.9529 | + | 17.1852i | −0.746195 | + | 0.642691i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 19.4007i | − | 0.724532i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.3087 | −0.570917 | −0.285459 | − | 0.958391i | \(-0.592146\pi\) | ||||
−0.285459 | + | 0.958391i | \(0.592146\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.61371 | −0.358033 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 65.3852i | − | 2.43170i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.74111 | + | 44.9773i | −0.250359 | + | 1.67041i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.9304i | 0.850442i | 0.905090 | + | 0.425221i | \(0.139804\pi\) | ||||
−0.905090 | + | 0.425221i | \(0.860196\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.58072 | 0.0585453 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.86115 | −0.0688372 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.8118i | 1.02725i | 0.858014 | + | 0.513626i | \(0.171698\pi\) | ||||
−0.858014 | + | 0.513626i | \(0.828302\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.68912 | + | 3.17741i | −0.136075 | + | 0.117201i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.6930i | 0.430718i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.3392 | 1.07926 | 0.539630 | − | 0.841902i | \(-0.318564\pi\) | ||||
0.539630 | + | 0.841902i | \(0.318564\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 78.1578 | 2.87120 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 20.5467i | − | 0.753785i | −0.926257 | − | 0.376892i | \(-0.876993\pi\) | ||
0.926257 | − | 0.376892i | \(-0.123007\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.27998 | − | 9.61345i | −0.303355 | − | 0.352210i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 19.3444i | 0.707776i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.96445 | 0.108319 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.3598 | −0.779430 | −0.389715 | − | 0.920935i | \(-0.627426\pi\) | ||||
−0.389715 | + | 0.920935i | \(0.627426\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 61.0428i | 2.22452i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 19.2269 | + | 22.3233i | 0.699739 | + | 0.812430i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 51.7544i | − | 1.88104i | −0.339731 | − | 0.940522i | \(-0.610336\pi\) | ||
0.339731 | − | 0.940522i | \(-0.389664\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −29.5130 | −1.07125 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.02891 | 0.218548 | 0.109274 | − | 0.994012i | \(-0.465147\pi\) | ||||
0.109274 | + | 0.994012i | \(0.465147\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.6137i | 0.420444i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −15.4734 | + | 13.3271i | −0.559440 | + | 0.481841i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 35.8949i | − | 1.29609i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.7385 | 0.964217 | 0.482108 | − | 0.876112i | \(-0.339871\pi\) | ||||
0.482108 | + | 0.876112i | \(0.339871\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.51129 | −0.0904420 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.5437i | 0.882777i | 0.897316 | + | 0.441388i | \(0.145514\pi\) | ||||
−0.897316 | + | 0.441388i | \(0.854486\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.02259 | − | 33.5111i | 0.180417 | − | 1.20376i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 21.5336i | − | 0.772513i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15.3087 | 0.548490 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.63854 | −0.237546 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 24.9330i | − | 0.891032i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −30.7426 | + | 26.4784i | −1.09725 | + | 0.945053i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.59518i | 0.0925081i | 0.998930 | + | 0.0462540i | \(0.0147284\pi\) | ||||
−0.998930 | + | 0.0462540i | \(0.985272\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −25.4193 | −0.904950 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.66463 | 0.130299 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 30.0162i | 1.06591i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −23.4437 | − | 27.2193i | −0.831463 | − | 0.965368i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 29.7709i | − | 1.05454i | −0.849698 | − | 0.527270i | \(-0.823216\pi\) | ||
0.849698 | − | 0.527270i | \(-0.176784\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −44.9954 | −1.59182 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.4467 | 0.369115 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.7370i | 0.555348i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.27334 | − | 10.7668i | −0.326842 | − | 0.379479i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 33.0563i | − | 1.16364i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.32184 | 0.0464733 | 0.0232366 | − | 0.999730i | \(-0.492603\pi\) | ||||
0.0232366 | + | 0.999730i | \(0.492603\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 54.5907 | 1.91694 | 0.958470 | − | 0.285193i | \(-0.0920576\pi\) | ||||
0.958470 | + | 0.285193i | \(0.0920576\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 4.26579i | − | 0.149608i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20.3802 | − | 17.5533i | 0.713889 | − | 0.614866i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.30668i | 0.0807005i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.61345 | −0.335921 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.7137 | 0.618213 | 0.309106 | − | 0.951027i | \(-0.399970\pi\) | ||||
0.309106 | + | 0.951027i | \(0.399970\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 43.7319i | 1.52440i | 0.647342 | + | 0.762199i | \(0.275880\pi\) | ||||
−0.647342 | + | 0.762199i | \(0.724120\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −22.9645 | − | 3.44187i | −0.799520 | − | 0.119831i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 34.9015i | − | 1.21364i | −0.794838 | − | 0.606822i | \(-0.792444\pi\) | ||
0.794838 | − | 0.606822i | \(-0.207556\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.11703 | −0.0735273 | −0.0367637 | − | 0.999324i | \(-0.511705\pi\) | ||||
−0.0367637 | + | 0.999324i | \(0.511705\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 32.0243 | 1.11091 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.24535i | 0.181741i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.53174 | − | 1.31927i | 0.0530079 | − | 0.0456553i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 18.5768i | 0.642107i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −40.1103 | −1.38476 | −0.692381 | − | 0.721532i | \(-0.743438\pi\) | ||||
−0.692381 | + | 0.721532i | \(0.743438\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 53.7360 | 1.85296 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 53.0248i | − | 1.82627i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −25.5171 | − | 29.6265i | −0.877814 | − | 1.01918i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 6.45075i | − | 0.221650i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 53.1248 | 1.82324 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 62.8462 | 2.15434 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.0039i | 0.719160i | 0.933114 | + | 0.359580i | \(0.117080\pi\) | ||||
−0.933114 | + | 0.359580i | \(0.882920\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 16.5173 | + | 19.1774i | 0.564881 | + | 0.655854i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 47.4886i | − | 1.62218i | −0.584922 | − | 0.811090i | \(-0.698875\pi\) | ||
0.584922 | − | 0.811090i | \(-0.301125\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −45.8545 | −1.56454 | −0.782268 | − | 0.622941i | \(-0.785937\pi\) | ||||
−0.782268 | + | 0.622941i | \(0.785937\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.12741 | −0.174742 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.36146i | 0.0463446i | 0.999731 | + | 0.0231723i | \(0.00737663\pi\) | ||||
−0.999731 | + | 0.0231723i | \(0.992623\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −32.3193 | + | 27.8363i | −1.09889 | + | 0.946463i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 22.8926i | 0.777475i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −25.6426 | −0.869866 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.2698 | −1.02565 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 1.70552i | − | 0.0577231i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.96007 | − | 9.45926i | −0.201487 | − | 0.319781i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 25.4028i | − | 0.857793i | −0.903354 | − | 0.428896i | \(-0.858903\pi\) | ||
0.903354 | − | 0.428896i | \(-0.141097\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 40.3331 | 1.36040 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.5756 | 1.23226 | 0.616132 | − | 0.787643i | \(-0.288699\pi\) | ||||
0.616132 | + | 0.787643i | \(0.288699\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.1919i | 1.01604i | 0.861346 | + | 0.508019i | \(0.169622\pi\) | ||||
−0.861346 | + | 0.508019i | \(0.830378\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 23.9830 | − | 20.6563i | 0.806179 | − | 0.694355i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 58.7467i | − | 1.97252i | −0.165197 | − | 0.986261i | \(-0.552826\pi\) | ||
0.165197 | − | 0.986261i | \(-0.447174\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.87259 | −0.163422 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23.8711 | 0.799712 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 55.7666i | 1.86616i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.08377 | − | 10.5467i | −0.303637 | − | 0.352537i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 76.4004i | − | 2.55094i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −61.6439 | −2.05594 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −38.7015 | −1.28933 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 0.772587i | − | 0.0257101i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.6137 | + | 12.3230i | 0.352812 | + | 0.409631i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 18.1289i | − | 0.601961i | −0.953630 | − | 0.300980i | \(-0.902686\pi\) | ||
0.953630 | − | 0.300980i | \(-0.0973139\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 24.6297 | 0.816915 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.2475 | 0.372646 | 0.186323 | − | 0.982489i | \(-0.440343\pi\) | ||||
0.186323 | + | 0.982489i | \(0.440343\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23.6973i | 0.784266i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −20.0552 | + | 17.2733i | −0.663003 | + | 0.571039i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.23520i | 0.0738129i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.1082 | 1.12513 | 0.562563 | − | 0.826755i | \(-0.309815\pi\) | ||||
0.562563 | + | 0.826755i | \(0.309815\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19.7056 | −0.649320 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 17.1852i | − | 0.565659i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 48.9015 | + | 7.32927i | 1.60787 | + | 0.240985i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 16.7385i | − | 0.549766i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.546684 | −0.0179361 | −0.00896806 | − | 0.999960i | \(-0.502855\pi\) | ||||
−0.00896806 | + | 0.999960i | \(0.502855\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.50100 | 0.213062 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 22.8426i | 0.747832i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −18.9552 | + | 16.3259i | −0.619900 | + | 0.533914i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.8424i | 0.974909i | 0.873148 | + | 0.487454i | \(0.162074\pi\) | ||||
−0.873148 | + | 0.487454i | \(0.837926\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.4213 | −0.372719 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.20225 | −0.299985 | −0.149992 | − | 0.988687i | \(-0.547925\pi\) | ||||
−0.149992 | + | 0.988687i | \(0.547925\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 14.9645i | − | 0.487310i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.00000 | + | 4.64419i | 0.130120 | + | 0.151076i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.9304i | 1.00510i | 0.864547 | + | 0.502552i | \(0.167605\pi\) | ||||
−0.864547 | + | 0.502552i | \(0.832395\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −40.7385 | −1.32243 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17.7133 | 0.574394 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.8383i | 0.351086i | 0.984472 | + | 0.175543i | \(0.0561681\pi\) | ||||
−0.984472 | + | 0.175543i | \(0.943832\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 29.9937 | + | 34.8241i | 0.970573 | + | 1.12688i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 42.2432i | 1.36553i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.26579 | −0.137750 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.9289 | 0.481578 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.16145i | 0.166325i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13.4363 | + | 11.5726i | −0.432530 | + | 0.372534i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1.31927i | − | 0.0424249i | −0.999775 | − | 0.0212124i | \(-0.993247\pi\) | ||
0.999775 | − | 0.0212124i | \(-0.00675264\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 74.2497 | 2.38524 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.25779 | −0.232914 | −0.116457 | − | 0.993196i | \(-0.537154\pi\) | ||||
−0.116457 | + | 0.993196i | \(0.537154\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 15.0326i | − | 0.481923i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.90998 | − | 59.4482i | 0.285348 | − | 1.90387i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.26579i | 0.136475i | 0.997669 | + | 0.0682374i | \(0.0217375\pi\) | ||||
−0.997669 | + | 0.0682374i | \(0.978262\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.7974 | 0.409006 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −20.2208 | −0.645600 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 34.3863i | 1.09675i | 0.836232 | + | 0.548376i | \(0.184754\pi\) | ||||
−0.836232 | + | 0.548376i | \(0.815246\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.6911 | + | 15.2372i | −0.563686 | + | 0.485497i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 18.6782i | − | 0.594533i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.25481 | 0.0716989 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.4417 | 0.331692 | 0.165846 | − | 0.986152i | \(-0.446965\pi\) | ||||
0.165846 | + | 0.986152i | \(0.446965\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 60.4416i | − | 1.91806i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.1144 | − | 18.7096i | −0.510862 | − | 0.593135i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.7075i | 0.845834i | 0.906169 | + | 0.422917i | \(0.138994\pi\) | ||||
−0.906169 | + | 0.422917i | \(0.861006\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −27.1083 | −0.857670 |
(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 | 2240.2.g.p.449.4 | 12 | ||
4.3 | odd | 2 | inner | 2240.2.g.p.449.10 | 12 | ||
5.4 | even | 2 | inner | 2240.2.g.p.449.9 | 12 | ||
8.3 | odd | 2 | 1120.2.g.d.449.3 | ✓ | 12 | ||
8.5 | even | 2 | 1120.2.g.d.449.9 | yes | 12 | ||
20.19 | odd | 2 | inner | 2240.2.g.p.449.3 | 12 | ||
40.3 | even | 4 | 5600.2.a.by.1.5 | 6 | |||
40.13 | odd | 4 | 5600.2.a.bz.1.2 | 6 | |||
40.19 | odd | 2 | 1120.2.g.d.449.10 | yes | 12 | ||
40.27 | even | 4 | 5600.2.a.bz.1.1 | 6 | |||
40.29 | even | 2 | 1120.2.g.d.449.4 | yes | 12 | ||
40.37 | odd | 4 | 5600.2.a.by.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1120.2.g.d.449.3 | ✓ | 12 | 8.3 | odd | 2 | ||
1120.2.g.d.449.4 | yes | 12 | 40.29 | even | 2 | ||
1120.2.g.d.449.9 | yes | 12 | 8.5 | even | 2 | ||
1120.2.g.d.449.10 | yes | 12 | 40.19 | odd | 2 | ||
2240.2.g.p.449.3 | 12 | 20.19 | odd | 2 | inner | ||
2240.2.g.p.449.4 | 12 | 1.1 | even | 1 | trivial | ||
2240.2.g.p.449.9 | 12 | 5.4 | even | 2 | inner | ||
2240.2.g.p.449.10 | 12 | 4.3 | odd | 2 | inner | ||
5600.2.a.by.1.5 | 6 | 40.3 | even | 4 | |||
5600.2.a.by.1.6 | 6 | 40.37 | odd | 4 | |||
5600.2.a.bz.1.1 | 6 | 40.27 | even | 4 | |||
5600.2.a.bz.1.2 | 6 | 40.13 | odd | 4 |