Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3675,2,Mod(1,3675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3675, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3675.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3675 = 3 \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3675.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(29.3450227428\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.88404.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 7x^{2} + 5x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 525) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.22868\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3675.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22868 | −0.868807 | −0.434404 | − | 0.900718i | \(-0.643041\pi\) | ||||
−0.434404 | + | 0.900718i | \(0.643041\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.490347 | −0.245174 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.22868 | −0.501606 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.05984 | 1.08182 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.74588 | −1.43094 | −0.715468 | − | 0.698646i | \(-0.753786\pi\) | ||||
−0.715468 | + | 0.698646i | \(0.753786\pi\) | |||||||
\(12\) | −0.490347 | −0.141551 | ||||||||
\(13\) | 6.25553 | 1.73497 | 0.867486 | − | 0.497462i | \(-0.165735\pi\) | ||||
0.867486 | + | 0.497462i | \(0.165735\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.77886 | −0.694716 | ||||||||
\(17\) | 6.28852 | 1.52519 | 0.762595 | − | 0.646877i | \(-0.223925\pi\) | ||||
0.762595 | + | 0.646877i | \(0.223925\pi\) | |||||||
\(18\) | −1.22868 | −0.289602 | ||||||||
\(19\) | 4.94771 | 1.13508 | 0.567541 | − | 0.823345i | \(-0.307895\pi\) | ||||
0.567541 | + | 0.823345i | \(0.307895\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.83116 | 1.24321 | ||||||||
\(23\) | −4.98069 | −1.03855 | −0.519273 | − | 0.854608i | \(-0.673797\pi\) | ||||
−0.519273 | + | 0.854608i | \(0.673797\pi\) | |||||||
\(24\) | 3.05984 | 0.624587 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −7.68604 | −1.50736 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.00000 | 0.742781 | 0.371391 | − | 0.928477i | \(-0.378881\pi\) | ||||
0.371391 | + | 0.928477i | \(0.378881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.65919 | 0.297999 | 0.149000 | − | 0.988837i | \(-0.452395\pi\) | ||||
0.149000 | + | 0.988837i | \(0.452395\pi\) | |||||||
\(32\) | −2.70534 | −0.478242 | ||||||||
\(33\) | −4.74588 | −0.826151 | ||||||||
\(34\) | −7.72657 | −1.32510 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.490347 | −0.0817246 | ||||||||
\(37\) | 4.43805 | 0.729611 | 0.364806 | − | 0.931084i | \(-0.381135\pi\) | ||||
0.364806 | + | 0.931084i | \(0.381135\pi\) | |||||||
\(38\) | −6.07914 | −0.986167 | ||||||||
\(39\) | 6.25553 | 1.00169 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.30782 | 0.204248 | 0.102124 | − | 0.994772i | \(-0.467436\pi\) | ||||
0.102124 | + | 0.994772i | \(0.467436\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.2362 | −1.56101 | −0.780505 | − | 0.625150i | \(-0.785038\pi\) | ||||
−0.780505 | + | 0.625150i | \(0.785038\pi\) | |||||||
\(44\) | 2.32713 | 0.350828 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.11968 | 0.902297 | ||||||||
\(47\) | −3.76518 | −0.549208 | −0.274604 | − | 0.961557i | \(-0.588547\pi\) | ||||
−0.274604 | + | 0.961557i | \(0.588547\pi\) | |||||||
\(48\) | −2.77886 | −0.401095 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.28852 | 0.880569 | ||||||||
\(52\) | −3.06738 | −0.425369 | ||||||||
\(53\) | −7.20323 | −0.989440 | −0.494720 | − | 0.869052i | \(-0.664729\pi\) | ||||
−0.494720 | + | 0.869052i | \(0.664729\pi\) | |||||||
\(54\) | −1.22868 | −0.167202 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.94771 | 0.655340 | ||||||||
\(58\) | −4.91472 | −0.645334 | ||||||||
\(59\) | 0.234819 | 0.0305708 | 0.0152854 | − | 0.999883i | \(-0.495134\pi\) | ||||
0.0152854 | + | 0.999883i | \(0.495134\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.00000 | −0.640184 | −0.320092 | − | 0.947386i | \(-0.603714\pi\) | ||||
−0.320092 | + | 0.947386i | \(0.603714\pi\) | |||||||
\(62\) | −2.03861 | −0.258904 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.88173 | 1.11022 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.83116 | 0.717766 | ||||||||
\(67\) | −2.49035 | −0.304244 | −0.152122 | − | 0.988362i | \(-0.548611\pi\) | ||||
−0.152122 | + | 0.988362i | \(0.548611\pi\) | |||||||
\(68\) | −3.08356 | −0.373936 | ||||||||
\(69\) | −4.98069 | −0.599605 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.06598 | 0.719899 | 0.359950 | − | 0.932972i | \(-0.382794\pi\) | ||||
0.359950 | + | 0.932972i | \(0.382794\pi\) | |||||||
\(72\) | 3.05984 | 0.360605 | ||||||||
\(73\) | 12.4918 | 1.46205 | 0.731024 | − | 0.682351i | \(-0.239043\pi\) | ||||
0.731024 | + | 0.682351i | \(0.239043\pi\) | |||||||
\(74\) | −5.45294 | −0.633892 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.42609 | −0.278292 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −7.68604 | −0.870272 | ||||||||
\(79\) | −0.831159 | −0.0935127 | −0.0467563 | − | 0.998906i | \(-0.514888\pi\) | ||||
−0.0467563 | + | 0.998906i | \(0.514888\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.60689 | −0.177452 | ||||||||
\(83\) | 1.14954 | 0.126178 | 0.0630890 | − | 0.998008i | \(-0.479905\pi\) | ||||
0.0630890 | + | 0.998008i | \(0.479905\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 12.5770 | 1.35622 | ||||||||
\(87\) | 4.00000 | 0.428845 | ||||||||
\(88\) | −14.5216 | −1.54801 | ||||||||
\(89\) | 2.28852 | 0.242582 | 0.121291 | − | 0.992617i | \(-0.461297\pi\) | ||||
0.121291 | + | 0.992617i | \(0.461297\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.44227 | 0.254624 | ||||||||
\(93\) | 1.65919 | 0.172050 | ||||||||
\(94\) | 4.62620 | 0.477156 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.70534 | −0.276113 | ||||||||
\(97\) | 0.476664 | 0.0483979 | 0.0241989 | − | 0.999707i | \(-0.492296\pi\) | ||||
0.0241989 | + | 0.999707i | \(0.492296\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.74588 | −0.476978 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.28852 | 0.824738 | 0.412369 | − | 0.911017i | \(-0.364701\pi\) | ||||
0.412369 | + | 0.911017i | \(0.364701\pi\) | |||||||
\(102\) | −7.72657 | −0.765044 | ||||||||
\(103\) | 14.2692 | 1.40599 | 0.702994 | − | 0.711196i | \(-0.251846\pi\) | ||||
0.702994 | + | 0.711196i | \(0.251846\pi\) | |||||||
\(104\) | 19.1409 | 1.87692 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.85046 | 0.859633 | ||||||||
\(107\) | 2.16884 | 0.209670 | 0.104835 | − | 0.994490i | \(-0.466569\pi\) | ||||
0.104835 | + | 0.994490i | \(0.466569\pi\) | |||||||
\(108\) | −0.490347 | −0.0471837 | ||||||||
\(109\) | 7.79817 | 0.746929 | 0.373465 | − | 0.927644i | \(-0.378170\pi\) | ||||
0.373465 | + | 0.927644i | \(0.378170\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.43805 | 0.421241 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.4918 | −1.45734 | −0.728671 | − | 0.684864i | \(-0.759861\pi\) | ||||
−0.728671 | + | 0.684864i | \(0.759861\pi\) | |||||||
\(114\) | −6.07914 | −0.569364 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.96139 | −0.182110 | ||||||||
\(117\) | 6.25553 | 0.578324 | ||||||||
\(118\) | −0.288517 | −0.0265602 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.5233 | 1.04758 | ||||||||
\(122\) | 6.14340 | 0.556197 | ||||||||
\(123\) | 1.30782 | 0.117922 | ||||||||
\(124\) | −0.813579 | −0.0730615 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.7996 | −1.04704 | −0.523521 | − | 0.852013i | \(-0.675382\pi\) | ||||
−0.523521 | + | 0.852013i | \(0.675382\pi\) | |||||||
\(128\) | −5.50211 | −0.486322 | ||||||||
\(129\) | −10.2362 | −0.901249 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.96139 | −0.346108 | −0.173054 | − | 0.984912i | \(-0.555364\pi\) | ||||
−0.173054 | + | 0.984912i | \(0.555364\pi\) | |||||||
\(132\) | 2.32713 | 0.202550 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.05984 | 0.264330 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 19.2418 | 1.64997 | ||||||||
\(137\) | 18.4724 | 1.57821 | 0.789104 | − | 0.614260i | \(-0.210545\pi\) | ||||
0.789104 | + | 0.614260i | \(0.210545\pi\) | |||||||
\(138\) | 6.11968 | 0.520941 | ||||||||
\(139\) | 2.66059 | 0.225669 | 0.112834 | − | 0.993614i | \(-0.464007\pi\) | ||||
0.112834 | + | 0.993614i | \(0.464007\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.76518 | −0.317085 | ||||||||
\(142\) | −7.45314 | −0.625454 | ||||||||
\(143\) | −29.6880 | −2.48263 | ||||||||
\(144\) | −2.77886 | −0.231572 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −15.3484 | −1.27024 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.17619 | −0.178882 | ||||||||
\(149\) | 14.5876 | 1.19506 | 0.597531 | − | 0.801846i | \(-0.296149\pi\) | ||||
0.597531 | + | 0.801846i | \(0.296149\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.2569 | −1.16021 | −0.580106 | − | 0.814541i | \(-0.696989\pi\) | ||||
−0.580106 | + | 0.814541i | \(0.696989\pi\) | |||||||
\(152\) | 15.1392 | 1.22795 | ||||||||
\(153\) | 6.28852 | 0.508396 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.06738 | −0.245587 | ||||||||
\(157\) | 12.1004 | 0.965715 | 0.482857 | − | 0.875699i | \(-0.339599\pi\) | ||||
0.482857 | + | 0.875699i | \(0.339599\pi\) | |||||||
\(158\) | 1.02123 | 0.0812445 | ||||||||
\(159\) | −7.20323 | −0.571254 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.22868 | −0.0965342 | ||||||||
\(163\) | 6.72657 | 0.526866 | 0.263433 | − | 0.964678i | \(-0.415145\pi\) | ||||
0.263433 | + | 0.964678i | \(0.415145\pi\) | |||||||
\(164\) | −0.641287 | −0.0500761 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.41241 | −0.109624 | ||||||||
\(167\) | −0.916442 | −0.0709164 | −0.0354582 | − | 0.999371i | \(-0.511289\pi\) | ||||
−0.0354582 | + | 0.999371i | \(0.511289\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 26.1316 | 2.01013 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.94771 | 0.378361 | ||||||||
\(172\) | 5.01931 | 0.382718 | ||||||||
\(173\) | −7.49175 | −0.569587 | −0.284794 | − | 0.958589i | \(-0.591925\pi\) | ||||
−0.284794 | + | 0.958589i | \(0.591925\pi\) | |||||||
\(174\) | −4.91472 | −0.372584 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 13.1881 | 0.994094 | ||||||||
\(177\) | 0.234819 | 0.0176501 | ||||||||
\(178\) | −2.81185 | −0.210757 | ||||||||
\(179\) | 14.8761 | 1.11189 | 0.555946 | − | 0.831218i | \(-0.312356\pi\) | ||||
0.555946 | + | 0.831218i | \(0.312356\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.62760 | −0.492626 | −0.246313 | − | 0.969190i | \(-0.579219\pi\) | ||||
−0.246313 | + | 0.969190i | \(0.579219\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.00000 | −0.369611 | ||||||||
\(184\) | −15.2401 | −1.12352 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.03861 | −0.149478 | ||||||||
\(187\) | −29.8445 | −2.18245 | ||||||||
\(188\) | 1.84625 | 0.134651 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.2569 | −1.68281 | −0.841406 | − | 0.540403i | \(-0.818272\pi\) | ||||
−0.841406 | + | 0.540403i | \(0.818272\pi\) | |||||||
\(192\) | 8.88173 | 0.640983 | ||||||||
\(193\) | 7.20183 | 0.518399 | 0.259200 | − | 0.965824i | \(-0.416541\pi\) | ||||
0.259200 | + | 0.965824i | \(0.416541\pi\) | |||||||
\(194\) | −0.585667 | −0.0420484 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.0881 | 1.35997 | 0.679985 | − | 0.733226i | \(-0.261986\pi\) | ||||
0.679985 | + | 0.733226i | \(0.261986\pi\) | |||||||
\(198\) | 5.83116 | 0.414402 | ||||||||
\(199\) | 20.8340 | 1.47688 | 0.738440 | − | 0.674319i | \(-0.235563\pi\) | ||||
0.738440 | + | 0.674319i | \(0.235563\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.49035 | −0.175656 | ||||||||
\(202\) | −10.1839 | −0.716539 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3.08356 | −0.215892 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −17.5323 | −1.22153 | ||||||||
\(207\) | −4.98069 | −0.346182 | ||||||||
\(208\) | −17.3833 | −1.20531 | ||||||||
\(209\) | −23.4812 | −1.62423 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.5876 | 1.07309 | 0.536547 | − | 0.843870i | \(-0.319728\pi\) | ||||
0.536547 | + | 0.843870i | \(0.319728\pi\) | |||||||
\(212\) | 3.53209 | 0.242585 | ||||||||
\(213\) | 6.06598 | 0.415634 | ||||||||
\(214\) | −2.66481 | −0.182163 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.05984 | 0.208196 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −9.58145 | −0.648938 | ||||||||
\(219\) | 12.4918 | 0.844114 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 39.3380 | 2.64616 | ||||||||
\(222\) | −5.45294 | −0.365978 | ||||||||
\(223\) | 3.57250 | 0.239232 | 0.119616 | − | 0.992820i | \(-0.461834\pi\) | ||||
0.119616 | + | 0.992820i | \(0.461834\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 19.0344 | 1.26615 | ||||||||
\(227\) | −15.4258 | −1.02384 | −0.511922 | − | 0.859032i | \(-0.671066\pi\) | ||||
−0.511922 | + | 0.859032i | \(0.671066\pi\) | |||||||
\(228\) | −2.42609 | −0.160672 | ||||||||
\(229\) | 15.3285 | 1.01294 | 0.506469 | − | 0.862258i | \(-0.330950\pi\) | ||||
0.506469 | + | 0.862258i | \(0.330950\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12.2394 | 0.803553 | ||||||||
\(233\) | −20.2885 | −1.32914 | −0.664572 | − | 0.747224i | \(-0.731386\pi\) | ||||
−0.664572 | + | 0.747224i | \(0.731386\pi\) | |||||||
\(234\) | −7.68604 | −0.502452 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.115143 | −0.00749516 | ||||||||
\(237\) | −0.831159 | −0.0539896 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.8954 | −0.769450 | −0.384725 | − | 0.923031i | \(-0.625704\pi\) | ||||
−0.384725 | + | 0.923031i | \(0.625704\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.4847 | 1.12629 | 0.563145 | − | 0.826358i | \(-0.309591\pi\) | ||||
0.563145 | + | 0.826358i | \(0.309591\pi\) | |||||||
\(242\) | −14.1585 | −0.910142 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 2.45174 | 0.156956 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.60689 | −0.102452 | ||||||||
\(247\) | 30.9505 | 1.96933 | ||||||||
\(248\) | 5.07685 | 0.322380 | ||||||||
\(249\) | 1.14954 | 0.0728489 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.2348 | −0.646016 | −0.323008 | − | 0.946396i | \(-0.604694\pi\) | ||||
−0.323008 | + | 0.946396i | \(0.604694\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 23.6378 | 1.48609 | ||||||||
\(254\) | 14.4979 | 0.909679 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.0031 | −0.687696 | ||||||||
\(257\) | −22.3545 | −1.39444 | −0.697218 | − | 0.716860i | \(-0.745579\pi\) | ||||
−0.697218 | + | 0.716860i | \(0.745579\pi\) | |||||||
\(258\) | 12.5770 | 0.783012 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.00000 | 0.247594 | ||||||||
\(262\) | 4.86728 | 0.300701 | ||||||||
\(263\) | 24.8101 | 1.52986 | 0.764929 | − | 0.644115i | \(-0.222774\pi\) | ||||
0.764929 | + | 0.644115i | \(0.222774\pi\) | |||||||
\(264\) | −14.5216 | −0.893743 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.28852 | 0.140055 | ||||||||
\(268\) | 1.22114 | 0.0745927 | ||||||||
\(269\) | 17.7803 | 1.08408 | 0.542041 | − | 0.840352i | \(-0.317652\pi\) | ||||
0.542041 | + | 0.840352i | \(0.317652\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.1390 | 1.04112 | 0.520559 | − | 0.853825i | \(-0.325723\pi\) | ||||
0.520559 | + | 0.853825i | \(0.325723\pi\) | |||||||
\(272\) | −17.4749 | −1.05957 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −22.6967 | −1.37116 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.44227 | 0.147007 | ||||||||
\(277\) | −2.88345 | −0.173250 | −0.0866250 | − | 0.996241i | \(-0.527608\pi\) | ||||
−0.0866250 | + | 0.996241i | \(0.527608\pi\) | |||||||
\(278\) | −3.26901 | −0.196062 | ||||||||
\(279\) | 1.65919 | 0.0993330 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.7803 | 1.65723 | 0.828616 | − | 0.559817i | \(-0.189129\pi\) | ||||
0.828616 | + | 0.559817i | \(0.189129\pi\) | |||||||
\(282\) | 4.62620 | 0.275486 | ||||||||
\(283\) | −8.70233 | −0.517300 | −0.258650 | − | 0.965971i | \(-0.583278\pi\) | ||||
−0.258650 | + | 0.965971i | \(0.583278\pi\) | |||||||
\(284\) | −2.97444 | −0.176500 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 36.4770 | 2.15693 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.70534 | −0.159414 | ||||||||
\(289\) | 22.5454 | 1.32620 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.476664 | 0.0279425 | ||||||||
\(292\) | −6.12530 | −0.358456 | ||||||||
\(293\) | −19.8954 | −1.16230 | −0.581151 | − | 0.813796i | \(-0.697398\pi\) | ||||
−0.581151 | + | 0.813796i | \(0.697398\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 13.5797 | 0.789305 | ||||||||
\(297\) | −4.74588 | −0.275384 | ||||||||
\(298\) | −17.9235 | −1.03828 | ||||||||
\(299\) | −31.1569 | −1.80185 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 17.5172 | 1.00800 | ||||||||
\(303\) | 8.28852 | 0.476163 | ||||||||
\(304\) | −13.7490 | −0.788560 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −7.72657 | −0.441699 | ||||||||
\(307\) | 5.32151 | 0.303714 | 0.151857 | − | 0.988402i | \(-0.451475\pi\) | ||||
0.151857 | + | 0.988402i | \(0.451475\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.2692 | 0.811747 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.89541 | 0.107479 | 0.0537395 | − | 0.998555i | \(-0.482886\pi\) | ||||
0.0537395 | + | 0.998555i | \(0.482886\pi\) | |||||||
\(312\) | 19.1409 | 1.08364 | ||||||||
\(313\) | 26.5230 | 1.49917 | 0.749585 | − | 0.661908i | \(-0.230253\pi\) | ||||
0.749585 | + | 0.661908i | \(0.230253\pi\) | |||||||
\(314\) | −14.8675 | −0.839020 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.407557 | 0.0229268 | ||||||||
\(317\) | −15.6237 | −0.877515 | −0.438757 | − | 0.898606i | \(-0.644581\pi\) | ||||
−0.438757 | + | 0.898606i | \(0.644581\pi\) | |||||||
\(318\) | 8.85046 | 0.496309 | ||||||||
\(319\) | −18.9835 | −1.06287 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.16884 | 0.121053 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 31.1137 | 1.73121 | ||||||||
\(324\) | −0.490347 | −0.0272415 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.26480 | −0.457745 | ||||||||
\(327\) | 7.79817 | 0.431240 | ||||||||
\(328\) | 4.00173 | 0.220958 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.02986 | −0.221501 | −0.110751 | − | 0.993848i | \(-0.535325\pi\) | ||||
−0.110751 | + | 0.993848i | \(0.535325\pi\) | |||||||
\(332\) | −0.563672 | −0.0309355 | ||||||||
\(333\) | 4.43805 | 0.243204 | ||||||||
\(334\) | 1.12601 | 0.0616127 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.86415 | −0.156020 | −0.0780100 | − | 0.996953i | \(-0.524857\pi\) | ||||
−0.0780100 | + | 0.996953i | \(0.524857\pi\) | |||||||
\(338\) | −32.1074 | −1.74641 | ||||||||
\(339\) | −15.4918 | −0.841396 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.87430 | −0.426417 | ||||||||
\(342\) | −6.07914 | −0.328722 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −31.3212 | −1.68873 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.20496 | 0.494862 | ||||||||
\(347\) | −2.51278 | −0.134893 | −0.0674466 | − | 0.997723i | \(-0.521485\pi\) | ||||
−0.0674466 | + | 0.997723i | \(0.521485\pi\) | |||||||
\(348\) | −1.96139 | −0.105142 | ||||||||
\(349\) | 12.6307 | 0.676108 | 0.338054 | − | 0.941127i | \(-0.390231\pi\) | ||||
0.338054 | + | 0.941127i | \(0.390231\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.25553 | 0.333895 | ||||||||
\(352\) | 12.8392 | 0.684333 | ||||||||
\(353\) | −22.5876 | −1.20222 | −0.601108 | − | 0.799168i | \(-0.705274\pi\) | ||||
−0.601108 | + | 0.799168i | \(0.705274\pi\) | |||||||
\(354\) | −0.288517 | −0.0153345 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.12217 | −0.0594748 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −18.2780 | −0.966020 | ||||||||
\(359\) | −0.342216 | −0.0180614 | −0.00903072 | − | 0.999959i | \(-0.502875\pi\) | ||||
−0.00903072 | + | 0.999959i | \(0.502875\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.47979 | 0.288410 | ||||||||
\(362\) | 8.14320 | 0.427997 | ||||||||
\(363\) | 11.5233 | 0.604818 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6.14340 | 0.321120 | ||||||||
\(367\) | −3.27062 | −0.170725 | −0.0853624 | − | 0.996350i | \(-0.527205\pi\) | ||||
−0.0853624 | + | 0.996350i | \(0.527205\pi\) | |||||||
\(368\) | 13.8407 | 0.721495 | ||||||||
\(369\) | 1.30782 | 0.0680825 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.813579 | −0.0421821 | ||||||||
\(373\) | −13.3559 | −0.691542 | −0.345771 | − | 0.938319i | \(-0.612383\pi\) | ||||
−0.345771 | + | 0.938319i | \(0.612383\pi\) | |||||||
\(374\) | 36.6693 | 1.89613 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11.5208 | −0.594142 | ||||||||
\(377\) | 25.0221 | 1.28870 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.8968 | 1.48433 | 0.742165 | − | 0.670217i | \(-0.233799\pi\) | ||||
0.742165 | + | 0.670217i | \(0.233799\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.7996 | −0.604510 | ||||||||
\(382\) | 28.5753 | 1.46204 | ||||||||
\(383\) | 20.7504 | 1.06030 | 0.530148 | − | 0.847905i | \(-0.322136\pi\) | ||||
0.530148 | + | 0.847905i | \(0.322136\pi\) | |||||||
\(384\) | −5.50211 | −0.280778 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.84874 | −0.450389 | ||||||||
\(387\) | −10.2362 | −0.520336 | ||||||||
\(388\) | −0.233731 | −0.0118659 | ||||||||
\(389\) | 8.26115 | 0.418857 | 0.209428 | − | 0.977824i | \(-0.432840\pi\) | ||||
0.209428 | + | 0.977824i | \(0.432840\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −31.3212 | −1.58398 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.96139 | −0.199826 | ||||||||
\(394\) | −23.4531 | −1.18155 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.32713 | 0.116943 | ||||||||
\(397\) | 24.9329 | 1.25135 | 0.625674 | − | 0.780085i | \(-0.284824\pi\) | ||||
0.625674 | + | 0.780085i | \(0.284824\pi\) | |||||||
\(398\) | −25.5983 | −1.28312 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.26921 | −0.363007 | −0.181504 | − | 0.983390i | \(-0.558096\pi\) | ||||
−0.181504 | + | 0.983390i | \(0.558096\pi\) | |||||||
\(402\) | 3.05984 | 0.152611 | ||||||||
\(403\) | 10.3791 | 0.517020 | ||||||||
\(404\) | −4.06425 | −0.202204 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.0624 | −1.04403 | ||||||||
\(408\) | 19.2418 | 0.952613 | ||||||||
\(409\) | −35.4096 | −1.75089 | −0.875446 | − | 0.483316i | \(-0.839432\pi\) | ||||
−0.875446 | + | 0.483316i | \(0.839432\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.4724 | 0.911179 | ||||||||
\(412\) | −6.99687 | −0.344711 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 6.11968 | 0.300766 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −16.9233 | −0.829735 | ||||||||
\(417\) | 2.66059 | 0.130290 | ||||||||
\(418\) | 28.8509 | 1.41114 | ||||||||
\(419\) | 38.1119 | 1.86189 | 0.930945 | − | 0.365160i | \(-0.118986\pi\) | ||||
0.930945 | + | 0.365160i | \(0.118986\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.5454 | 0.611428 | 0.305714 | − | 0.952123i | \(-0.401105\pi\) | ||||
0.305714 | + | 0.952123i | \(0.401105\pi\) | |||||||
\(422\) | −19.1521 | −0.932312 | ||||||||
\(423\) | −3.76518 | −0.183069 | ||||||||
\(424\) | −22.0407 | −1.07039 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −7.45314 | −0.361106 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.06349 | −0.0514055 | ||||||||
\(429\) | −29.6880 | −1.43335 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.51106 | −0.409963 | −0.204982 | − | 0.978766i | \(-0.565713\pi\) | ||||
−0.204982 | + | 0.978766i | \(0.565713\pi\) | |||||||
\(432\) | −2.77886 | −0.133698 | ||||||||
\(433\) | 20.8010 | 0.999631 | 0.499816 | − | 0.866132i | \(-0.333401\pi\) | ||||
0.499816 | + | 0.866132i | \(0.333401\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.82381 | −0.183127 | ||||||||
\(437\) | −24.6430 | −1.17884 | ||||||||
\(438\) | −15.3484 | −0.733373 | ||||||||
\(439\) | 10.9508 | 0.522655 | 0.261327 | − | 0.965250i | \(-0.415840\pi\) | ||||
0.261327 | + | 0.965250i | \(0.415840\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −48.3338 | −2.29900 | ||||||||
\(443\) | 38.5525 | 1.83168 | 0.915842 | − | 0.401540i | \(-0.131525\pi\) | ||||
0.915842 | + | 0.401540i | \(0.131525\pi\) | |||||||
\(444\) | −2.17619 | −0.103277 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.38946 | −0.207847 | ||||||||
\(447\) | 14.5876 | 0.689969 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.8462 | −1.03099 | −0.515494 | − | 0.856893i | \(-0.672392\pi\) | ||||
−0.515494 | + | 0.856893i | \(0.672392\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.20676 | −0.292265 | ||||||||
\(452\) | 7.59634 | 0.357302 | ||||||||
\(453\) | −14.2569 | −0.669849 | ||||||||
\(454\) | 18.9533 | 0.889524 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 15.1392 | 0.708957 | ||||||||
\(457\) | 3.69045 | 0.172632 | 0.0863160 | − | 0.996268i | \(-0.472491\pi\) | ||||
0.0863160 | + | 0.996268i | \(0.472491\pi\) | |||||||
\(458\) | −18.8338 | −0.880048 | ||||||||
\(459\) | 6.28852 | 0.293523 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.9449 | −1.44125 | −0.720624 | − | 0.693326i | \(-0.756144\pi\) | ||||
−0.720624 | + | 0.693326i | \(0.756144\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.97717 | −0.231309 | −0.115654 | − | 0.993290i | \(-0.536896\pi\) | ||||
−0.115654 | + | 0.993290i | \(0.536896\pi\) | |||||||
\(464\) | −11.1155 | −0.516022 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 24.9281 | 1.15477 | ||||||||
\(467\) | 7.02211 | 0.324945 | 0.162472 | − | 0.986713i | \(-0.448053\pi\) | ||||
0.162472 | + | 0.986713i | \(0.448053\pi\) | |||||||
\(468\) | −3.06738 | −0.141790 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.1004 | 0.557556 | ||||||||
\(472\) | 0.718508 | 0.0330720 | ||||||||
\(473\) | 48.5798 | 2.23370 | ||||||||
\(474\) | 1.02123 | 0.0469065 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.20323 | −0.329813 | ||||||||
\(478\) | 14.6156 | 0.668504 | ||||||||
\(479\) | −9.22956 | −0.421710 | −0.210855 | − | 0.977517i | \(-0.567625\pi\) | ||||
−0.210855 | + | 0.977517i | \(0.567625\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.7624 | 1.26586 | ||||||||
\(482\) | −21.4831 | −0.978529 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.65044 | −0.256838 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.22868 | −0.0557340 | ||||||||
\(487\) | −13.7638 | −0.623696 | −0.311848 | − | 0.950132i | \(-0.600948\pi\) | ||||
−0.311848 | + | 0.950132i | \(0.600948\pi\) | |||||||
\(488\) | −15.2992 | −0.692562 | ||||||||
\(489\) | 6.72657 | 0.304186 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −31.0495 | −1.40124 | −0.700622 | − | 0.713533i | \(-0.747094\pi\) | ||||
−0.700622 | + | 0.713533i | \(0.747094\pi\) | |||||||
\(492\) | −0.641287 | −0.0289115 | ||||||||
\(493\) | 25.1541 | 1.13288 | ||||||||
\(494\) | −38.0283 | −1.71097 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.61066 | −0.207025 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.41241 | −0.0632916 | ||||||||
\(499\) | −21.5907 | −0.966533 | −0.483267 | − | 0.875473i | \(-0.660550\pi\) | ||||
−0.483267 | + | 0.875473i | \(0.660550\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.916442 | −0.0409436 | ||||||||
\(502\) | 12.5753 | 0.561264 | ||||||||
\(503\) | −33.2826 | −1.48400 | −0.741998 | − | 0.670402i | \(-0.766122\pi\) | ||||
−0.741998 | + | 0.670402i | \(0.766122\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −29.0432 | −1.29113 | ||||||||
\(507\) | 26.1316 | 1.16055 | ||||||||
\(508\) | 5.78589 | 0.256707 | ||||||||
\(509\) | 19.2200 | 0.851914 | 0.425957 | − | 0.904744i | \(-0.359938\pi\) | ||||
0.425957 | + | 0.904744i | \(0.359938\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 24.5235 | 1.08380 | ||||||||
\(513\) | 4.94771 | 0.218447 | ||||||||
\(514\) | 27.4665 | 1.21150 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.01931 | 0.220963 | ||||||||
\(517\) | 17.8691 | 0.785881 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.49175 | −0.328851 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.483689 | 0.0211908 | 0.0105954 | − | 0.999944i | \(-0.496627\pi\) | ||||
0.0105954 | + | 0.999944i | \(0.496627\pi\) | |||||||
\(522\) | −4.91472 | −0.215111 | ||||||||
\(523\) | 6.31344 | 0.276068 | 0.138034 | − | 0.990428i | \(-0.455922\pi\) | ||||
0.138034 | + | 0.990428i | \(0.455922\pi\) | |||||||
\(524\) | 1.94246 | 0.0848566 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −30.4837 | −1.32915 | ||||||||
\(527\) | 10.4338 | 0.454505 | ||||||||
\(528\) | 13.1881 | 0.573940 | ||||||||
\(529\) | 1.80732 | 0.0785791 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.234819 | 0.0101903 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.18112 | 0.354364 | ||||||||
\(534\) | −2.81185 | −0.121681 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.62006 | −0.329136 | ||||||||
\(537\) | 14.8761 | 0.641951 | ||||||||
\(538\) | −21.8462 | −0.941859 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.0435 | 0.689766 | 0.344883 | − | 0.938646i | \(-0.387919\pi\) | ||||
0.344883 | + | 0.938646i | \(0.387919\pi\) | |||||||
\(542\) | −21.0583 | −0.904532 | ||||||||
\(543\) | −6.62760 | −0.284418 | ||||||||
\(544\) | −17.0126 | −0.729409 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.2078 | 1.16332 | 0.581660 | − | 0.813432i | \(-0.302403\pi\) | ||||
0.581660 | + | 0.813432i | \(0.302403\pi\) | |||||||
\(548\) | −9.05792 | −0.386935 | ||||||||
\(549\) | −5.00000 | −0.213395 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.7908 | 0.843117 | ||||||||
\(552\) | −15.2401 | −0.648663 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.54284 | 0.150521 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.30461 | −0.0553280 | ||||||||
\(557\) | −12.4724 | −0.528475 | −0.264237 | − | 0.964458i | \(-0.585120\pi\) | ||||
−0.264237 | + | 0.964458i | \(0.585120\pi\) | |||||||
\(558\) | −2.03861 | −0.0863013 | ||||||||
\(559\) | −64.0330 | −2.70831 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −29.8445 | −1.26004 | ||||||||
\(562\) | −34.1330 | −1.43982 | ||||||||
\(563\) | −15.8312 | −0.667204 | −0.333602 | − | 0.942714i | \(-0.608264\pi\) | ||||
−0.333602 | + | 0.942714i | \(0.608264\pi\) | |||||||
\(564\) | 1.84625 | 0.0777410 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 10.6924 | 0.449434 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 18.5609 | 0.778798 | ||||||||
\(569\) | 22.5665 | 0.946036 | 0.473018 | − | 0.881053i | \(-0.343165\pi\) | ||||
0.473018 | + | 0.881053i | \(0.343165\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.3180 | 0.473643 | 0.236821 | − | 0.971553i | \(-0.423894\pi\) | ||||
0.236821 | + | 0.971553i | \(0.423894\pi\) | |||||||
\(572\) | 14.5574 | 0.608676 | ||||||||
\(573\) | −23.2569 | −0.971572 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 8.88173 | 0.370072 | ||||||||
\(577\) | −24.8133 | −1.03299 | −0.516495 | − | 0.856290i | \(-0.672763\pi\) | ||||
−0.516495 | + | 0.856290i | \(0.672763\pi\) | |||||||
\(578\) | −27.7011 | −1.15221 | ||||||||
\(579\) | 7.20183 | 0.299298 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −0.585667 | −0.0242767 | ||||||||
\(583\) | 34.1857 | 1.41583 | ||||||||
\(584\) | 38.2227 | 1.58167 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.4451 | 1.00982 | ||||||||
\(587\) | −3.96139 | −0.163504 | −0.0817520 | − | 0.996653i | \(-0.526052\pi\) | ||||
−0.0817520 | + | 0.996653i | \(0.526052\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.20918 | 0.338253 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19.0881 | 0.785179 | ||||||||
\(592\) | −12.3327 | −0.506873 | ||||||||
\(593\) | 6.10459 | 0.250685 | 0.125343 | − | 0.992114i | \(-0.459997\pi\) | ||||
0.125343 | + | 0.992114i | \(0.459997\pi\) | |||||||
\(594\) | 5.83116 | 0.239255 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.15299 | −0.292998 | ||||||||
\(597\) | 20.8340 | 0.852678 | ||||||||
\(598\) | 38.2818 | 1.56546 | ||||||||
\(599\) | 24.7845 | 1.01267 | 0.506333 | − | 0.862338i | \(-0.331001\pi\) | ||||
0.506333 | + | 0.862338i | \(0.331001\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 43.9866 | 1.79425 | 0.897126 | − | 0.441775i | \(-0.145651\pi\) | ||||
0.897126 | + | 0.441775i | \(0.145651\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.49035 | −0.101415 | ||||||||
\(604\) | 6.99085 | 0.284454 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −10.1839 | −0.413694 | ||||||||
\(607\) | 17.3008 | 0.702218 | 0.351109 | − | 0.936335i | \(-0.385805\pi\) | ||||
0.351109 | + | 0.936335i | \(0.385805\pi\) | |||||||
\(608\) | −13.3852 | −0.542843 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −23.5532 | −0.952860 | ||||||||
\(612\) | −3.08356 | −0.124645 | ||||||||
\(613\) | 15.3994 | 0.621978 | 0.310989 | − | 0.950414i | \(-0.399340\pi\) | ||||
0.310989 | + | 0.950414i | \(0.399340\pi\) | |||||||
\(614\) | −6.53842 | −0.263869 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.70273 | −0.350359 | −0.175179 | − | 0.984537i | \(-0.556051\pi\) | ||||
−0.175179 | + | 0.984537i | \(0.556051\pi\) | |||||||
\(618\) | −17.5323 | −0.705252 | ||||||||
\(619\) | −7.15094 | −0.287421 | −0.143710 | − | 0.989620i | \(-0.545903\pi\) | ||||
−0.143710 | + | 0.989620i | \(0.545903\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.98069 | −0.199868 | ||||||||
\(622\) | −2.32885 | −0.0933785 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −17.3833 | −0.695888 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −32.5883 | −1.30249 | ||||||||
\(627\) | −23.4812 | −0.937749 | ||||||||
\(628\) | −5.93339 | −0.236768 | ||||||||
\(629\) | 27.9088 | 1.11280 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.1797 | −1.59953 | −0.799765 | − | 0.600314i | \(-0.795042\pi\) | ||||
−0.799765 | + | 0.600314i | \(0.795042\pi\) | |||||||
\(632\) | −2.54321 | −0.101164 | ||||||||
\(633\) | 15.5876 | 0.619551 | ||||||||
\(634\) | 19.1965 | 0.762391 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.53209 | 0.140056 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 23.3246 | 0.923431 | ||||||||
\(639\) | 6.06598 | 0.239966 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.1478 | 0.835288 | 0.417644 | − | 0.908611i | \(-0.362856\pi\) | ||||
0.417644 | + | 0.908611i | \(0.362856\pi\) | |||||||
\(642\) | −2.66481 | −0.105172 | ||||||||
\(643\) | 29.4981 | 1.16329 | 0.581646 | − | 0.813442i | \(-0.302409\pi\) | ||||
0.581646 | + | 0.813442i | \(0.302409\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −38.2288 | −1.50409 | ||||||||
\(647\) | 28.3836 | 1.11588 | 0.557938 | − | 0.829883i | \(-0.311593\pi\) | ||||
0.557938 | + | 0.829883i | \(0.311593\pi\) | |||||||
\(648\) | 3.05984 | 0.120202 | ||||||||
\(649\) | −1.11442 | −0.0437449 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.29836 | −0.129174 | ||||||||
\(653\) | −23.2692 | −0.910595 | −0.455297 | − | 0.890339i | \(-0.650467\pi\) | ||||
−0.455297 | + | 0.890339i | \(0.650467\pi\) | |||||||
\(654\) | −9.58145 | −0.374664 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.63426 | −0.141894 | ||||||||
\(657\) | 12.4918 | 0.487350 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.9852 | 0.817468 | 0.408734 | − | 0.912653i | \(-0.365970\pi\) | ||||
0.408734 | + | 0.912653i | \(0.365970\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.7160 | −1.35030 | −0.675148 | − | 0.737682i | \(-0.735920\pi\) | ||||
−0.675148 | + | 0.737682i | \(0.735920\pi\) | |||||||
\(662\) | 4.95140 | 0.192442 | ||||||||
\(663\) | 39.3380 | 1.52776 | ||||||||
\(664\) | 3.51739 | 0.136501 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.45294 | −0.211297 | ||||||||
\(667\) | −19.9228 | −0.771413 | ||||||||
\(668\) | 0.449375 | 0.0173868 | ||||||||
\(669\) | 3.57250 | 0.138121 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 23.7294 | 0.916063 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.4998 | 0.828757 | 0.414378 | − | 0.910105i | \(-0.363999\pi\) | ||||
0.414378 | + | 0.910105i | \(0.363999\pi\) | |||||||
\(674\) | 3.51912 | 0.135551 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.8136 | −0.492830 | ||||||||
\(677\) | −49.7936 | −1.91372 | −0.956862 | − | 0.290542i | \(-0.906165\pi\) | ||||
−0.956862 | + | 0.290542i | \(0.906165\pi\) | |||||||
\(678\) | 19.0344 | 0.731011 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.4258 | −0.591117 | ||||||||
\(682\) | 9.67499 | 0.370475 | ||||||||
\(683\) | −31.2597 | −1.19612 | −0.598060 | − | 0.801451i | \(-0.704062\pi\) | ||||
−0.598060 | + | 0.801451i | \(0.704062\pi\) | |||||||
\(684\) | −2.42609 | −0.0927640 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.3285 | 0.584820 | ||||||||
\(688\) | 28.4451 | 1.08446 | ||||||||
\(689\) | −45.0600 | −1.71665 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.1594 | −0.957108 | −0.478554 | − | 0.878058i | \(-0.658839\pi\) | ||||
−0.478554 | + | 0.878058i | \(0.658839\pi\) | |||||||
\(692\) | 3.67356 | 0.139648 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.08740 | 0.117196 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 12.2394 | 0.463931 | ||||||||
\(697\) | 8.22426 | 0.311516 | ||||||||
\(698\) | −15.5191 | −0.587407 | ||||||||
\(699\) | −20.2885 | −0.767382 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.21130 | −0.234597 | −0.117299 | − | 0.993097i | \(-0.537423\pi\) | ||||
−0.117299 | + | 0.993097i | \(0.537423\pi\) | |||||||
\(702\) | −7.68604 | −0.290091 | ||||||||
\(703\) | 21.9582 | 0.828169 | ||||||||
\(704\) | −42.1516 | −1.58865 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 27.7529 | 1.04449 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.115143 | −0.00432734 | ||||||||
\(709\) | −14.8831 | −0.558948 | −0.279474 | − | 0.960153i | \(-0.590160\pi\) | ||||
−0.279474 | + | 0.960153i | \(0.590160\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.831159 | −0.0311709 | ||||||||
\(712\) | 7.00249 | 0.262429 | ||||||||
\(713\) | −8.26391 | −0.309486 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.29446 | −0.272607 | ||||||||
\(717\) | −11.8954 | −0.444242 | ||||||||
\(718\) | 0.420473 | 0.0156919 | ||||||||
\(719\) | 36.6167 | 1.36557 | 0.682787 | − | 0.730618i | \(-0.260768\pi\) | ||||
0.682787 | + | 0.730618i | \(0.260768\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −6.73291 | −0.250573 | ||||||||
\(723\) | 17.4847 | 0.650264 | ||||||||
\(724\) | 3.24983 | 0.120779 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −14.1585 | −0.525471 | ||||||||
\(727\) | 13.8624 | 0.514129 | 0.257064 | − | 0.966394i | \(-0.417245\pi\) | ||||
0.257064 | + | 0.966394i | \(0.417245\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −64.3707 | −2.38084 | ||||||||
\(732\) | 2.45174 | 0.0906188 | ||||||||
\(733\) | −32.7697 | −1.21038 | −0.605189 | − | 0.796082i | \(-0.706902\pi\) | ||||
−0.605189 | + | 0.796082i | \(0.706902\pi\) | |||||||
\(734\) | 4.01854 | 0.148327 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.4745 | 0.496676 | ||||||||
\(737\) | 11.8189 | 0.435354 | ||||||||
\(738\) | −1.60689 | −0.0591506 | ||||||||
\(739\) | 29.8684 | 1.09873 | 0.549363 | − | 0.835584i | \(-0.314871\pi\) | ||||
0.549363 | + | 0.835584i | \(0.314871\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 30.9505 | 1.13700 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 49.5577 | 1.81810 | 0.909048 | − | 0.416691i | \(-0.136810\pi\) | ||||
0.909048 | + | 0.416691i | \(0.136810\pi\) | |||||||
\(744\) | 5.07685 | 0.186126 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 16.4101 | 0.600817 | ||||||||
\(747\) | 1.14954 | 0.0420593 | ||||||||
\(748\) | 14.6342 | 0.535079 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.61034 | −0.241215 | −0.120607 | − | 0.992700i | \(-0.538484\pi\) | ||||
−0.120607 | + | 0.992700i | \(0.538484\pi\) | |||||||
\(752\) | 10.4629 | 0.381544 | ||||||||
\(753\) | −10.2348 | −0.372978 | ||||||||
\(754\) | −30.7442 | −1.11964 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.01509 | 0.254968 | 0.127484 | − | 0.991841i | \(-0.459310\pi\) | ||||
0.127484 | + | 0.991841i | \(0.459310\pi\) | |||||||
\(758\) | −35.5049 | −1.28960 | ||||||||
\(759\) | 23.6378 | 0.857996 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.0088 | 0.471567 | 0.235783 | − | 0.971806i | \(-0.424234\pi\) | ||||
0.235783 | + | 0.971806i | \(0.424234\pi\) | |||||||
\(762\) | 14.4979 | 0.525203 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 11.4040 | 0.412581 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25.4956 | −0.921193 | ||||||||
\(767\) | 1.46892 | 0.0530395 | ||||||||
\(768\) | −11.0031 | −0.397041 | ||||||||
\(769\) | 0.822729 | 0.0296684 | 0.0148342 | − | 0.999890i | \(-0.495278\pi\) | ||||
0.0148342 | + | 0.999890i | \(0.495278\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.3545 | −0.805077 | ||||||||
\(772\) | −3.53140 | −0.127098 | ||||||||
\(773\) | −24.6844 | −0.887837 | −0.443919 | − | 0.896067i | \(-0.646412\pi\) | ||||
−0.443919 | + | 0.896067i | \(0.646412\pi\) | |||||||
\(774\) | 12.5770 | 0.452072 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.45851 | 0.0523576 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10.1503 | −0.363906 | ||||||||
\(779\) | 6.47072 | 0.231838 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.7884 | −1.03013 | ||||||||
\(782\) | 38.4837 | 1.37617 | ||||||||
\(783\) | 4.00000 | 0.142948 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4.86728 | 0.173610 | ||||||||
\(787\) | 15.7582 | 0.561718 | 0.280859 | − | 0.959749i | \(-0.409381\pi\) | ||||
0.280859 | + | 0.959749i | \(0.409381\pi\) | |||||||
\(788\) | −9.35980 | −0.333429 | ||||||||
\(789\) | 24.8101 | 0.883264 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −14.5216 | −0.516003 | ||||||||
\(793\) | −31.2776 | −1.11070 | ||||||||
\(794\) | −30.6346 | −1.08718 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.2159 | −0.362092 | ||||||||
\(797\) | −15.8568 | −0.561677 | −0.280838 | − | 0.959755i | \(-0.590612\pi\) | ||||
−0.280838 | + | 0.959755i | \(0.590612\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23.6774 | −0.837646 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.28852 | 0.0808608 | ||||||||
\(802\) | 8.93153 | 0.315383 | ||||||||
\(803\) | −59.2843 | −2.09210 | ||||||||
\(804\) | 1.22114 | 0.0430661 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12.7526 | −0.449191 | ||||||||
\(807\) | 17.7803 | 0.625895 | ||||||||
\(808\) | 25.3615 | 0.892215 | ||||||||
\(809\) | −7.85680 | −0.276230 | −0.138115 | − | 0.990416i | \(-0.544104\pi\) | ||||
−0.138115 | + | 0.990416i | \(0.544104\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −55.8410 | −1.96084 | −0.980421 | − | 0.196912i | \(-0.936909\pi\) | ||||
−0.980421 | + | 0.196912i | \(0.936909\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.1390 | 0.601090 | ||||||||
\(814\) | 25.8790 | 0.907058 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −17.4749 | −0.611745 | ||||||||
\(817\) | −50.6458 | −1.77187 | ||||||||
\(818\) | 43.5070 | 1.52119 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.02806 | 0.280181 | 0.140091 | − | 0.990139i | \(-0.455261\pi\) | ||||
0.140091 | + | 0.990139i | \(0.455261\pi\) | |||||||
\(822\) | −22.6967 | −0.791639 | ||||||||
\(823\) | −22.2720 | −0.776354 | −0.388177 | − | 0.921585i | \(-0.626895\pi\) | ||||
−0.388177 | + | 0.921585i | \(0.626895\pi\) | |||||||
\(824\) | 43.6615 | 1.52102 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −53.3872 | −1.85645 | −0.928227 | − | 0.372015i | \(-0.878667\pi\) | ||||
−0.928227 | + | 0.372015i | \(0.878667\pi\) | |||||||
\(828\) | 2.44227 | 0.0848748 | ||||||||
\(829\) | −28.8445 | −1.00181 | −0.500906 | − | 0.865502i | \(-0.667000\pi\) | ||||
−0.500906 | + | 0.865502i | \(0.667000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.88345 | −0.100026 | ||||||||
\(832\) | 55.5599 | 1.92619 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −3.26901 | −0.113197 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 11.5139 | 0.398218 | ||||||||
\(837\) | 1.65919 | 0.0573499 | ||||||||
\(838\) | −46.8273 | −1.61762 | ||||||||
\(839\) | 3.38435 | 0.116841 | 0.0584205 | − | 0.998292i | \(-0.481394\pi\) | ||||
0.0584205 | + | 0.998292i | \(0.481394\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | −15.4143 | −0.531213 | ||||||||
\(843\) | 27.7803 | 0.956803 | ||||||||
\(844\) | −7.64333 | −0.263094 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.62620 | 0.159052 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 20.0168 | 0.687380 | ||||||||
\(849\) | −8.70233 | −0.298663 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22.1046 | −0.757736 | ||||||||
\(852\) | −2.97444 | −0.101903 | ||||||||
\(853\) | −32.8905 | −1.12615 | −0.563074 | − | 0.826406i | \(-0.690382\pi\) | ||||
−0.563074 | + | 0.826406i | \(0.690382\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.63630 | 0.226824 | ||||||||
\(857\) | −27.0193 | −0.922962 | −0.461481 | − | 0.887150i | \(-0.652682\pi\) | ||||
−0.461481 | + | 0.887150i | \(0.652682\pi\) | |||||||
\(858\) | 36.4770 | 1.24530 | ||||||||
\(859\) | 48.1074 | 1.64140 | 0.820702 | − | 0.571357i | \(-0.193583\pi\) | ||||
0.820702 | + | 0.571357i | \(0.193583\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10.4574 | 0.356179 | ||||||||
\(863\) | −10.1716 | −0.346247 | −0.173123 | − | 0.984900i | \(-0.555386\pi\) | ||||
−0.173123 | + | 0.984900i | \(0.555386\pi\) | |||||||
\(864\) | −2.70534 | −0.0920376 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −25.5577 | −0.868487 | ||||||||
\(867\) | 22.5454 | 0.765684 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.94458 | 0.133811 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.5784 | −0.527855 | ||||||||
\(872\) | 23.8611 | 0.808040 | ||||||||
\(873\) | 0.476664 | 0.0161326 | ||||||||
\(874\) | 30.2784 | 1.02418 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.12530 | −0.206955 | ||||||||
\(877\) | −36.8596 | −1.24466 | −0.622330 | − | 0.782755i | \(-0.713814\pi\) | ||||
−0.622330 | + | 0.782755i | \(0.713814\pi\) | |||||||
\(878\) | −13.4551 | −0.454086 | ||||||||
\(879\) | −19.8954 | −0.671056 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.1945 | 1.42157 | 0.710784 | − | 0.703410i | \(-0.248340\pi\) | ||||
0.710784 | + | 0.703410i | \(0.248340\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.7880 | −1.20436 | −0.602181 | − | 0.798359i | \(-0.705702\pi\) | ||||
−0.602181 | + | 0.798359i | \(0.705702\pi\) | |||||||
\(884\) | −19.2893 | −0.648769 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −47.3686 | −1.59138 | ||||||||
\(887\) | 42.3980 | 1.42359 | 0.711793 | − | 0.702389i | \(-0.247883\pi\) | ||||
0.711793 | + | 0.702389i | \(0.247883\pi\) | |||||||
\(888\) | 13.5797 | 0.455706 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.74588 | −0.158993 | ||||||||
\(892\) | −1.75177 | −0.0586535 | ||||||||
\(893\) | −18.6290 | −0.623396 | ||||||||
\(894\) | −17.9235 | −0.599450 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −31.1569 | −1.04030 | ||||||||
\(898\) | 26.8420 | 0.895730 | ||||||||
\(899\) | 6.63675 | 0.221348 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −45.2977 | −1.50908 | ||||||||
\(902\) | 7.62612 | 0.253922 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −47.4023 | −1.57658 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 17.5172 | 0.581970 | ||||||||
\(907\) | −52.5437 | −1.74469 | −0.872343 | − | 0.488895i | \(-0.837400\pi\) | ||||
−0.872343 | + | 0.488895i | \(0.837400\pi\) | |||||||
\(908\) | 7.56399 | 0.251020 | ||||||||
\(909\) | 8.28852 | 0.274913 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.7118 | 1.28258 | 0.641290 | − | 0.767299i | \(-0.278400\pi\) | ||||
0.641290 | + | 0.767299i | \(0.278400\pi\) | |||||||
\(912\) | −13.7490 | −0.455275 | ||||||||
\(913\) | −5.45555 | −0.180553 | ||||||||
\(914\) | −4.53438 | −0.149984 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.51631 | −0.248346 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −7.72657 | −0.255015 | ||||||||
\(919\) | −25.8740 | −0.853504 | −0.426752 | − | 0.904369i | \(-0.640342\pi\) | ||||
−0.426752 | + | 0.904369i | \(0.640342\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.32151 | 0.175350 | ||||||||
\(922\) | 38.0213 | 1.25217 | ||||||||
\(923\) | 37.9459 | 1.24900 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6.11534 | 0.200963 | ||||||||
\(927\) | 14.2692 | 0.468662 | ||||||||
\(928\) | −10.8214 | −0.355229 | ||||||||
\(929\) | −1.77746 | −0.0583166 | −0.0291583 | − | 0.999575i | \(-0.509283\pi\) | ||||
−0.0291583 | + | 0.999575i | \(0.509283\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 9.94842 | 0.325871 | ||||||||
\(933\) | 1.89541 | 0.0620530 | ||||||||
\(934\) | −8.62792 | −0.282314 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 19.1409 | 0.625640 | ||||||||
\(937\) | −58.4486 | −1.90943 | −0.954716 | − | 0.297518i | \(-0.903841\pi\) | ||||
−0.954716 | + | 0.297518i | \(0.903841\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.5230 | 0.865546 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.80832 | 0.124148 | 0.0620739 | − | 0.998072i | \(-0.480229\pi\) | ||||
0.0620739 | + | 0.998072i | \(0.480229\pi\) | |||||||
\(942\) | −14.8675 | −0.484408 | ||||||||
\(943\) | −6.51386 | −0.212121 | ||||||||
\(944\) | −0.652530 | −0.0212381 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −59.6890 | −1.94066 | ||||||||
\(947\) | −54.8431 | −1.78216 | −0.891081 | − | 0.453845i | \(-0.850052\pi\) | ||||
−0.891081 | + | 0.453845i | \(0.850052\pi\) | |||||||
\(948\) | 0.407557 | 0.0132368 | ||||||||
\(949\) | 78.1425 | 2.53661 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.6237 | −0.506633 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −37.4426 | −1.21288 | −0.606442 | − | 0.795128i | \(-0.707404\pi\) | ||||
−0.606442 | + | 0.795128i | \(0.707404\pi\) | |||||||
\(954\) | 8.85046 | 0.286544 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.83288 | 0.188649 | ||||||||
\(957\) | −18.9835 | −0.613649 | ||||||||
\(958\) | 11.3402 | 0.366384 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.2471 | −0.911197 | ||||||||
\(962\) | −34.1110 | −1.09978 | ||||||||
\(963\) | 2.16884 | 0.0698899 | ||||||||
\(964\) | −8.57359 | −0.276137 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.0098 | −1.02937 | −0.514683 | − | 0.857381i | \(-0.672090\pi\) | ||||
−0.514683 | + | 0.857381i | \(0.672090\pi\) | |||||||
\(968\) | 35.2595 | 1.13328 | ||||||||
\(969\) | 31.1137 | 0.999517 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 51.4963 | 1.65259 | 0.826297 | − | 0.563234i | \(-0.190443\pi\) | ||||
0.826297 | + | 0.563234i | \(0.190443\pi\) | |||||||
\(972\) | −0.490347 | −0.0157279 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 16.9113 | 0.541872 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.8943 | 0.444746 | ||||||||
\(977\) | 3.13445 | 0.100280 | 0.0501399 | − | 0.998742i | \(-0.484033\pi\) | ||||
0.0501399 | + | 0.998742i | \(0.484033\pi\) | |||||||
\(978\) | −8.26480 | −0.264279 | ||||||||
\(979\) | −10.8610 | −0.347120 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.79817 | 0.248976 | ||||||||
\(982\) | 38.1499 | 1.21741 | ||||||||
\(983\) | 43.1165 | 1.37520 | 0.687602 | − | 0.726088i | \(-0.258663\pi\) | ||||
0.687602 | + | 0.726088i | \(0.258663\pi\) | |||||||
\(984\) | 4.00173 | 0.127570 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −30.9063 | −0.984257 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −15.1765 | −0.482829 | ||||||||
\(989\) | 50.9835 | 1.62118 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.1552 | −0.386121 | −0.193061 | − | 0.981187i | \(-0.561841\pi\) | ||||
−0.193061 | + | 0.981187i | \(0.561841\pi\) | |||||||
\(992\) | −4.48867 | −0.142516 | ||||||||
\(993\) | −4.02986 | −0.127884 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.563672 | −0.0178606 | ||||||||
\(997\) | −22.7757 | −0.721315 | −0.360657 | − | 0.932698i | \(-0.617448\pi\) | ||||
−0.360657 | + | 0.932698i | \(0.617448\pi\) | |||||||
\(998\) | 26.5281 | 0.839731 | ||||||||
\(999\) | 4.43805 | 0.140414 |
(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 | 3675.2.a.br.1.2 | 4 | ||
5.4 | even | 2 | 3675.2.a.bw.1.3 | 4 | |||
7.2 | even | 3 | 525.2.i.j.151.3 | yes | 8 | ||
7.4 | even | 3 | 525.2.i.j.226.3 | yes | 8 | ||
7.6 | odd | 2 | 3675.2.a.bq.1.2 | 4 | |||
35.2 | odd | 12 | 525.2.r.h.424.3 | 16 | |||
35.4 | even | 6 | 525.2.i.i.226.2 | yes | 8 | ||
35.9 | even | 6 | 525.2.i.i.151.2 | ✓ | 8 | ||
35.18 | odd | 12 | 525.2.r.h.499.3 | 16 | |||
35.23 | odd | 12 | 525.2.r.h.424.6 | 16 | |||
35.32 | odd | 12 | 525.2.r.h.499.6 | 16 | |||
35.34 | odd | 2 | 3675.2.a.bx.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.i.i.151.2 | ✓ | 8 | 35.9 | even | 6 | ||
525.2.i.i.226.2 | yes | 8 | 35.4 | even | 6 | ||
525.2.i.j.151.3 | yes | 8 | 7.2 | even | 3 | ||
525.2.i.j.226.3 | yes | 8 | 7.4 | even | 3 | ||
525.2.r.h.424.3 | 16 | 35.2 | odd | 12 | |||
525.2.r.h.424.6 | 16 | 35.23 | odd | 12 | |||
525.2.r.h.499.3 | 16 | 35.18 | odd | 12 | |||
525.2.r.h.499.6 | 16 | 35.32 | odd | 12 | |||
3675.2.a.bq.1.2 | 4 | 7.6 | odd | 2 | |||
3675.2.a.br.1.2 | 4 | 1.1 | even | 1 | trivial | ||
3675.2.a.bw.1.3 | 4 | 5.4 | even | 2 | |||
3675.2.a.bx.1.3 | 4 | 35.34 | odd | 2 |