Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4005,2,Mod(1,4005)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4005, 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("4005.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4005 = 3^{2} \cdot 5 \cdot 89 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4005.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: | \(31.9800860095\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1335) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.80194\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4005.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.801938 | −0.567056 | −0.283528 | − | 0.958964i | \(-0.591505\pi\) | ||||
−0.283528 | + | 0.958964i | \(0.591505\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.35690 | −0.678448 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.24698 | −1.22724 | −0.613621 | − | 0.789600i | \(-0.710288\pi\) | ||||
−0.613621 | + | 0.789600i | \(0.710288\pi\) | |||||||
\(8\) | 2.69202 | 0.951773 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.801938 | 0.253595 | ||||||||
\(11\) | −2.49396 | −0.751957 | −0.375978 | − | 0.926628i | \(-0.622693\pi\) | ||||
−0.375978 | + | 0.926628i | \(0.622693\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.55496 | −0.431268 | −0.215634 | − | 0.976474i | \(-0.569182\pi\) | ||||
−0.215634 | + | 0.976474i | \(0.569182\pi\) | |||||||
\(14\) | 2.60388 | 0.695915 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.554958 | 0.138740 | ||||||||
\(17\) | 6.29590 | 1.52698 | 0.763490 | − | 0.645820i | \(-0.223484\pi\) | ||||
0.763490 | + | 0.645820i | \(0.223484\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.89008 | −1.12186 | −0.560931 | − | 0.827863i | \(-0.689557\pi\) | ||||
−0.560931 | + | 0.827863i | \(0.689557\pi\) | |||||||
\(20\) | 1.35690 | 0.303411 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.00000 | 0.426401 | ||||||||
\(23\) | 1.10992 | 0.231434 | 0.115717 | − | 0.993282i | \(-0.463084\pi\) | ||||
0.115717 | + | 0.993282i | \(0.463084\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.24698 | 0.244553 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.40581 | 0.832620 | ||||||||
\(29\) | 9.40581 | 1.74662 | 0.873308 | − | 0.487169i | \(-0.161970\pi\) | ||||
0.873308 | + | 0.487169i | \(0.161970\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.713792 | 0.128201 | 0.0641004 | − | 0.997943i | \(-0.479582\pi\) | ||||
0.0641004 | + | 0.997943i | \(0.479582\pi\) | |||||||
\(32\) | −5.82908 | −1.03045 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.04892 | −0.865882 | ||||||||
\(35\) | 3.24698 | 0.548840 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.29590 | 1.03504 | 0.517520 | − | 0.855671i | \(-0.326855\pi\) | ||||
0.517520 | + | 0.855671i | \(0.326855\pi\) | |||||||
\(38\) | 3.92154 | 0.636158 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.69202 | −0.425646 | ||||||||
\(41\) | 4.53319 | 0.707965 | 0.353983 | − | 0.935252i | \(-0.384827\pi\) | ||||
0.353983 | + | 0.935252i | \(0.384827\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.19806 | −0.335201 | −0.167601 | − | 0.985855i | \(-0.553602\pi\) | ||||
−0.167601 | + | 0.985855i | \(0.553602\pi\) | |||||||
\(44\) | 3.38404 | 0.510164 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.890084 | −0.131236 | ||||||||
\(47\) | −2.53319 | −0.369503 | −0.184752 | − | 0.982785i | \(-0.559148\pi\) | ||||
−0.184752 | + | 0.982785i | \(0.559148\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.54288 | 0.506125 | ||||||||
\(50\) | −0.801938 | −0.113411 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.10992 | 0.292593 | ||||||||
\(53\) | −3.56465 | −0.489642 | −0.244821 | − | 0.969568i | \(-0.578729\pi\) | ||||
−0.244821 | + | 0.969568i | \(0.578729\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.49396 | 0.336285 | ||||||||
\(56\) | −8.74094 | −1.16806 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.54288 | −0.990428 | ||||||||
\(59\) | 14.2446 | 1.85449 | 0.927244 | − | 0.374459i | \(-0.122171\pi\) | ||||
0.927244 | + | 0.374459i | \(0.122171\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.49396 | −1.08754 | −0.543770 | − | 0.839234i | \(-0.683004\pi\) | ||||
−0.543770 | + | 0.839234i | \(0.683004\pi\) | |||||||
\(62\) | −0.572417 | −0.0726970 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.56465 | 0.445581 | ||||||||
\(65\) | 1.55496 | 0.192869 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.09783 | −0.500630 | −0.250315 | − | 0.968164i | \(-0.580534\pi\) | ||||
−0.250315 | + | 0.968164i | \(0.580534\pi\) | |||||||
\(68\) | −8.54288 | −1.03598 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.60388 | −0.311223 | ||||||||
\(71\) | 9.08575 | 1.07828 | 0.539140 | − | 0.842216i | \(-0.318749\pi\) | ||||
0.539140 | + | 0.842216i | \(0.318749\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.72587 | −0.201998 | −0.100999 | − | 0.994887i | \(-0.532204\pi\) | ||||
−0.100999 | + | 0.994887i | \(0.532204\pi\) | |||||||
\(74\) | −5.04892 | −0.586925 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.63533 | 0.761125 | ||||||||
\(77\) | 8.09783 | 0.922834 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.79656 | −0.314638 | −0.157319 | − | 0.987548i | \(-0.550285\pi\) | ||||
−0.157319 | + | 0.987548i | \(0.550285\pi\) | |||||||
\(80\) | −0.554958 | −0.0620462 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.63533 | −0.401456 | ||||||||
\(83\) | −17.7560 | −1.94897 | −0.974487 | − | 0.224442i | \(-0.927944\pi\) | ||||
−0.974487 | + | 0.224442i | \(0.927944\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.29590 | −0.682886 | ||||||||
\(86\) | 1.76271 | 0.190078 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.71379 | −0.715693 | ||||||||
\(89\) | 1.00000 | 0.106000 | ||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.04892 | 0.529270 | ||||||||
\(92\) | −1.50604 | −0.157016 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.03146 | 0.209529 | ||||||||
\(95\) | 4.89008 | 0.501712 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.9758 | 1.41903 | 0.709516 | − | 0.704690i | \(-0.248914\pi\) | ||||
0.709516 | + | 0.704690i | \(0.248914\pi\) | |||||||
\(98\) | −2.84117 | −0.287001 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.35690 | −0.135690 | ||||||||
\(101\) | −9.97046 | −0.992098 | −0.496049 | − | 0.868295i | \(-0.665216\pi\) | ||||
−0.496049 | + | 0.868295i | \(0.665216\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.58642 | 0.846045 | 0.423022 | − | 0.906119i | \(-0.360969\pi\) | ||||
0.423022 | + | 0.906119i | \(0.360969\pi\) | |||||||
\(104\) | −4.18598 | −0.410469 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.85862 | 0.277654 | ||||||||
\(107\) | −3.58211 | −0.346295 | −0.173148 | − | 0.984896i | \(-0.555394\pi\) | ||||
−0.173148 | + | 0.984896i | \(0.555394\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.4209 | 0.998139 | 0.499070 | − | 0.866562i | \(-0.333675\pi\) | ||||
0.499070 | + | 0.866562i | \(0.333675\pi\) | |||||||
\(110\) | −2.00000 | −0.190693 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.80194 | −0.170267 | ||||||||
\(113\) | 2.67025 | 0.251196 | 0.125598 | − | 0.992081i | \(-0.459915\pi\) | ||||
0.125598 | + | 0.992081i | \(0.459915\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.10992 | −0.103500 | ||||||||
\(116\) | −12.7627 | −1.18499 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.4233 | −1.05160 | ||||||||
\(119\) | −20.4426 | −1.87397 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.78017 | −0.434561 | ||||||||
\(122\) | 6.81163 | 0.616696 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.968541 | −0.0869776 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.7463 | −0.953581 | −0.476791 | − | 0.879017i | \(-0.658200\pi\) | ||||
−0.476791 | + | 0.879017i | \(0.658200\pi\) | |||||||
\(128\) | 8.79954 | 0.777777 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.24698 | −0.109367 | ||||||||
\(131\) | −19.7995 | −1.72989 | −0.864947 | − | 0.501863i | \(-0.832648\pi\) | ||||
−0.864947 | + | 0.501863i | \(0.832648\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.8780 | 1.37680 | ||||||||
\(134\) | 3.28621 | 0.283885 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 16.9487 | 1.45334 | ||||||||
\(137\) | 15.7453 | 1.34521 | 0.672604 | − | 0.740003i | \(-0.265176\pi\) | ||||
0.672604 | + | 0.740003i | \(0.265176\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.4765 | −1.31270 | −0.656350 | − | 0.754457i | \(-0.727900\pi\) | ||||
−0.656350 | + | 0.754457i | \(0.727900\pi\) | |||||||
\(140\) | −4.40581 | −0.372359 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.28621 | −0.611445 | ||||||||
\(143\) | 3.87800 | 0.324295 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.40581 | −0.781110 | ||||||||
\(146\) | 1.38404 | 0.114544 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.54288 | −0.702220 | ||||||||
\(149\) | −4.41550 | −0.361732 | −0.180866 | − | 0.983508i | \(-0.557890\pi\) | ||||
−0.180866 | + | 0.983508i | \(0.557890\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.5918 | −1.02471 | −0.512353 | − | 0.858775i | \(-0.671226\pi\) | ||||
−0.512353 | + | 0.858775i | \(0.671226\pi\) | |||||||
\(152\) | −13.1642 | −1.06776 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.49396 | −0.523298 | ||||||||
\(155\) | −0.713792 | −0.0573331 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.9095 | 1.82837 | 0.914187 | − | 0.405293i | \(-0.132830\pi\) | ||||
0.914187 | + | 0.405293i | \(0.132830\pi\) | |||||||
\(158\) | 2.24267 | 0.178417 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.82908 | 0.460830 | ||||||||
\(161\) | −3.60388 | −0.284025 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.0489 | 0.943744 | 0.471872 | − | 0.881667i | \(-0.343578\pi\) | ||||
0.471872 | + | 0.881667i | \(0.343578\pi\) | |||||||
\(164\) | −6.15106 | −0.480317 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.2392 | 1.10518 | ||||||||
\(167\) | −1.37867 | −0.106684 | −0.0533422 | − | 0.998576i | \(-0.516987\pi\) | ||||
−0.0533422 | + | 0.998576i | \(0.516987\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.5821 | −0.814008 | ||||||||
\(170\) | 5.04892 | 0.387234 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.98254 | 0.227417 | ||||||||
\(173\) | −6.88471 | −0.523435 | −0.261717 | − | 0.965145i | \(-0.584289\pi\) | ||||
−0.261717 | + | 0.965145i | \(0.584289\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.24698 | −0.245449 | ||||||||
\(176\) | −1.38404 | −0.104326 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.801938 | −0.0601078 | ||||||||
\(179\) | 9.04221 | 0.675847 | 0.337923 | − | 0.941174i | \(-0.390276\pi\) | ||||
0.337923 | + | 0.941174i | \(0.390276\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −26.4698 | −1.96748 | −0.983742 | − | 0.179586i | \(-0.942524\pi\) | ||||
−0.983742 | + | 0.179586i | \(0.942524\pi\) | |||||||
\(182\) | −4.04892 | −0.300126 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.98792 | 0.220272 | ||||||||
\(185\) | −6.29590 | −0.462884 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.7017 | −1.14822 | ||||||||
\(188\) | 3.43727 | 0.250689 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.92154 | −0.284499 | ||||||||
\(191\) | −19.0368 | −1.37746 | −0.688729 | − | 0.725019i | \(-0.741831\pi\) | ||||
−0.688729 | + | 0.725019i | \(0.741831\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.5646 | −0.832441 | −0.416221 | − | 0.909264i | \(-0.636646\pi\) | ||||
−0.416221 | + | 0.909264i | \(0.636646\pi\) | |||||||
\(194\) | −11.2078 | −0.804670 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.80731 | −0.343380 | ||||||||
\(197\) | 17.8538 | 1.27203 | 0.636017 | − | 0.771675i | \(-0.280581\pi\) | ||||
0.636017 | + | 0.771675i | \(0.280581\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.6993 | 1.53822 | 0.769112 | − | 0.639114i | \(-0.220699\pi\) | ||||
0.769112 | + | 0.639114i | \(0.220699\pi\) | |||||||
\(200\) | 2.69202 | 0.190355 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.99569 | 0.562575 | ||||||||
\(203\) | −30.5405 | −2.14352 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.53319 | −0.316612 | ||||||||
\(206\) | −6.88577 | −0.479754 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.862937 | −0.0598339 | ||||||||
\(209\) | 12.1957 | 0.843592 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.70171 | 0.667893 | 0.333947 | − | 0.942592i | \(-0.391619\pi\) | ||||
0.333947 | + | 0.942592i | \(0.391619\pi\) | |||||||
\(212\) | 4.83685 | 0.332197 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.87263 | 0.196369 | ||||||||
\(215\) | 2.19806 | 0.149907 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.31767 | −0.157334 | ||||||||
\(218\) | −8.35690 | −0.566000 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.38404 | −0.228152 | ||||||||
\(221\) | −9.78986 | −0.658537 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.53750 | −0.169924 | −0.0849618 | − | 0.996384i | \(-0.527077\pi\) | ||||
−0.0849618 | + | 0.996384i | \(0.527077\pi\) | |||||||
\(224\) | 18.9269 | 1.26461 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.14138 | −0.142442 | ||||||||
\(227\) | −13.4668 | −0.893824 | −0.446912 | − | 0.894578i | \(-0.647476\pi\) | ||||
−0.446912 | + | 0.894578i | \(0.647476\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.2513 | −0.875670 | −0.437835 | − | 0.899055i | \(-0.644255\pi\) | ||||
−0.437835 | + | 0.899055i | \(0.644255\pi\) | |||||||
\(230\) | 0.890084 | 0.0586904 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 25.3207 | 1.66238 | ||||||||
\(233\) | −6.98254 | −0.457442 | −0.228721 | − | 0.973492i | \(-0.573454\pi\) | ||||
−0.228721 | + | 0.973492i | \(0.573454\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.53319 | 0.165247 | ||||||||
\(236\) | −19.3284 | −1.25817 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 16.3937 | 1.06265 | ||||||||
\(239\) | −18.1129 | −1.17163 | −0.585813 | − | 0.810446i | \(-0.699225\pi\) | ||||
−0.585813 | + | 0.810446i | \(0.699225\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.70171 | 0.238448 | 0.119224 | − | 0.992867i | \(-0.461959\pi\) | ||||
0.119224 | + | 0.992867i | \(0.461959\pi\) | |||||||
\(242\) | 3.83340 | 0.246420 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.5254 | 0.737839 | ||||||||
\(245\) | −3.54288 | −0.226346 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.60388 | 0.483823 | ||||||||
\(248\) | 1.92154 | 0.122018 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.801938 | 0.0507190 | ||||||||
\(251\) | 1.42758 | 0.0901083 | 0.0450541 | − | 0.998985i | \(-0.485654\pi\) | ||||
0.0450541 | + | 0.998985i | \(0.485654\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.76809 | −0.174028 | ||||||||
\(254\) | 8.61788 | 0.540734 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.1860 | −0.886624 | ||||||||
\(257\) | −7.12498 | −0.444444 | −0.222222 | − | 0.974996i | \(-0.571331\pi\) | ||||
−0.222222 | + | 0.974996i | \(0.571331\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −20.4426 | −1.27024 | ||||||||
\(260\) | −2.10992 | −0.130851 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 15.8780 | 0.980946 | ||||||||
\(263\) | −27.6209 | −1.70318 | −0.851588 | − | 0.524212i | \(-0.824360\pi\) | ||||
−0.851588 | + | 0.524212i | \(0.824360\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.56465 | 0.218975 | ||||||||
\(266\) | −12.7332 | −0.780721 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.56033 | 0.339652 | ||||||||
\(269\) | 21.9952 | 1.34107 | 0.670536 | − | 0.741877i | \(-0.266064\pi\) | ||||
0.670536 | + | 0.741877i | \(0.266064\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.00431 | −0.121753 | −0.0608766 | − | 0.998145i | \(-0.519390\pi\) | ||||
−0.0608766 | + | 0.998145i | \(0.519390\pi\) | |||||||
\(272\) | 3.49396 | 0.211852 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.6267 | −0.762807 | ||||||||
\(275\) | −2.49396 | −0.150391 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.2935 | −0.978982 | −0.489491 | − | 0.872008i | \(-0.662817\pi\) | ||||
−0.489491 | + | 0.872008i | \(0.662817\pi\) | |||||||
\(278\) | 12.4112 | 0.744374 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8.74094 | 0.522371 | ||||||||
\(281\) | 3.93469 | 0.234724 | 0.117362 | − | 0.993089i | \(-0.462556\pi\) | ||||
0.117362 | + | 0.993089i | \(0.462556\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.04221 | −0.537504 | −0.268752 | − | 0.963209i | \(-0.586611\pi\) | ||||
−0.268752 | + | 0.963209i | \(0.586611\pi\) | |||||||
\(284\) | −12.3284 | −0.731557 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.10992 | −0.183893 | ||||||||
\(287\) | −14.7192 | −0.868845 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 22.6383 | 1.33167 | ||||||||
\(290\) | 7.54288 | 0.442933 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.34183 | 0.137045 | ||||||||
\(293\) | −14.0000 | −0.817889 | −0.408944 | − | 0.912559i | \(-0.634103\pi\) | ||||
−0.408944 | + | 0.912559i | \(0.634103\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.2446 | −0.829352 | ||||||||
\(296\) | 16.9487 | 0.985123 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.54096 | 0.205122 | ||||||||
\(299\) | −1.72587 | −0.0998098 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.13706 | 0.411373 | ||||||||
\(302\) | 10.0978 | 0.581065 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.71379 | −0.155647 | ||||||||
\(305\) | 8.49396 | 0.486363 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.5676 | −0.831419 | −0.415709 | − | 0.909498i | \(-0.636467\pi\) | ||||
−0.415709 | + | 0.909498i | \(0.636467\pi\) | |||||||
\(308\) | −10.9879 | −0.626095 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.572417 | 0.0325111 | ||||||||
\(311\) | −17.8237 | −1.01069 | −0.505345 | − | 0.862917i | \(-0.668635\pi\) | ||||
−0.505345 | + | 0.862917i | \(0.668635\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.77910 | −0.157084 | −0.0785421 | − | 0.996911i | \(-0.525026\pi\) | ||||
−0.0785421 | + | 0.996911i | \(0.525026\pi\) | |||||||
\(314\) | −18.3720 | −1.03679 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.79464 | 0.213465 | ||||||||
\(317\) | 30.2476 | 1.69887 | 0.849436 | − | 0.527691i | \(-0.176942\pi\) | ||||
0.849436 | + | 0.527691i | \(0.176942\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −23.4577 | −1.31338 | ||||||||
\(320\) | −3.56465 | −0.199270 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.89008 | 0.161058 | ||||||||
\(323\) | −30.7875 | −1.71306 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.55496 | −0.0862536 | ||||||||
\(326\) | −9.66248 | −0.535155 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 12.2034 | 0.673822 | ||||||||
\(329\) | 8.22521 | 0.453470 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.2325 | −1.05711 | −0.528557 | − | 0.848898i | \(-0.677267\pi\) | ||||
−0.528557 | + | 0.848898i | \(0.677267\pi\) | |||||||
\(332\) | 24.0930 | 1.32228 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.10560 | 0.0604960 | ||||||||
\(335\) | 4.09783 | 0.223889 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.7060 | 0.746615 | 0.373307 | − | 0.927708i | \(-0.378224\pi\) | ||||
0.373307 | + | 0.927708i | \(0.378224\pi\) | |||||||
\(338\) | 8.48619 | 0.461588 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 8.54288 | 0.463303 | ||||||||
\(341\) | −1.78017 | −0.0964015 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.2252 | 0.606104 | ||||||||
\(344\) | −5.91723 | −0.319036 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.52111 | 0.296817 | ||||||||
\(347\) | 19.7560 | 1.06056 | 0.530279 | − | 0.847823i | \(-0.322087\pi\) | ||||
0.530279 | + | 0.847823i | \(0.322087\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.7560 | −0.950457 | −0.475229 | − | 0.879862i | \(-0.657635\pi\) | ||||
−0.475229 | + | 0.879862i | \(0.657635\pi\) | |||||||
\(350\) | 2.60388 | 0.139183 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 14.5375 | 0.774851 | ||||||||
\(353\) | 3.43834 | 0.183004 | 0.0915021 | − | 0.995805i | \(-0.470833\pi\) | ||||
0.0915021 | + | 0.995805i | \(0.470833\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.08575 | −0.482222 | ||||||||
\(356\) | −1.35690 | −0.0719153 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.25129 | −0.383243 | ||||||||
\(359\) | 1.56465 | 0.0825789 | 0.0412895 | − | 0.999147i | \(-0.486853\pi\) | ||||
0.0412895 | + | 0.999147i | \(0.486853\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.91292 | 0.258575 | ||||||||
\(362\) | 21.2271 | 1.11567 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.85086 | −0.359082 | ||||||||
\(365\) | 1.72587 | 0.0903363 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.3526 | 0.540400 | 0.270200 | − | 0.962804i | \(-0.412910\pi\) | ||||
0.270200 | + | 0.962804i | \(0.412910\pi\) | |||||||
\(368\) | 0.615957 | 0.0321090 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.04892 | 0.262481 | ||||||||
\(371\) | 11.5743 | 0.600910 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.1051 | −0.885670 | −0.442835 | − | 0.896603i | \(-0.646027\pi\) | ||||
−0.442835 | + | 0.896603i | \(0.646027\pi\) | |||||||
\(374\) | 12.5918 | 0.651106 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.81940 | −0.351684 | ||||||||
\(377\) | −14.6256 | −0.753259 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.3163 | −0.581281 | −0.290641 | − | 0.956832i | \(-0.593868\pi\) | ||||
−0.290641 | + | 0.956832i | \(0.593868\pi\) | |||||||
\(380\) | −6.63533 | −0.340385 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 15.2664 | 0.781095 | ||||||||
\(383\) | 16.4940 | 0.842802 | 0.421401 | − | 0.906874i | \(-0.361539\pi\) | ||||
0.421401 | + | 0.906874i | \(0.361539\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.09783 | −0.412704 | ||||||||
\(386\) | 9.27413 | 0.472041 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −18.9638 | −0.962739 | ||||||||
\(389\) | −3.57540 | −0.181280 | −0.0906400 | − | 0.995884i | \(-0.528891\pi\) | ||||
−0.0906400 | + | 0.995884i | \(0.528891\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.98792 | 0.353394 | ||||||||
\(392\) | 9.53750 | 0.481716 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −14.3177 | −0.721314 | ||||||||
\(395\) | 2.79656 | 0.140710 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.54048 | 0.478823 | 0.239412 | − | 0.970918i | \(-0.423045\pi\) | ||||
0.239412 | + | 0.970918i | \(0.423045\pi\) | |||||||
\(398\) | −17.4015 | −0.872258 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.554958 | 0.0277479 | ||||||||
\(401\) | 10.9772 | 0.548173 | 0.274087 | − | 0.961705i | \(-0.411624\pi\) | ||||
0.274087 | + | 0.961705i | \(0.411624\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.10992 | −0.0552889 | ||||||||
\(404\) | 13.5289 | 0.673087 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 24.4916 | 1.21550 | ||||||||
\(407\) | −15.7017 | −0.778305 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.4426 | −0.664696 | −0.332348 | − | 0.943157i | \(-0.607841\pi\) | ||||
−0.332348 | + | 0.943157i | \(0.607841\pi\) | |||||||
\(410\) | 3.63533 | 0.179536 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −11.6509 | −0.573997 | ||||||||
\(413\) | −46.2519 | −2.27591 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.7560 | 0.871608 | ||||||||
\(416\) | 9.06398 | 0.444398 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −9.78017 | −0.478364 | ||||||||
\(419\) | −28.7114 | −1.40264 | −0.701322 | − | 0.712845i | \(-0.747406\pi\) | ||||
−0.701322 | + | 0.712845i | \(0.747406\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.7754 | −1.74359 | −0.871793 | − | 0.489875i | \(-0.837042\pi\) | ||||
−0.871793 | + | 0.489875i | \(0.837042\pi\) | |||||||
\(422\) | −7.78017 | −0.378733 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.59611 | −0.466028 | ||||||||
\(425\) | 6.29590 | 0.305396 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 27.5797 | 1.33468 | ||||||||
\(428\) | 4.86054 | 0.234943 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.76271 | −0.0850054 | ||||||||
\(431\) | 8.67264 | 0.417747 | 0.208873 | − | 0.977943i | \(-0.433020\pi\) | ||||
0.208873 | + | 0.977943i | \(0.433020\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.1890 | −1.11439 | −0.557195 | − | 0.830382i | \(-0.688123\pi\) | ||||
−0.557195 | + | 0.830382i | \(0.688123\pi\) | |||||||
\(434\) | 1.85862 | 0.0892168 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14.1400 | −0.677185 | ||||||||
\(437\) | −5.42758 | −0.259637 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.12067 | 0.244396 | 0.122198 | − | 0.992506i | \(-0.461006\pi\) | ||||
0.122198 | + | 0.992506i | \(0.461006\pi\) | |||||||
\(440\) | 6.71379 | 0.320067 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.85086 | 0.373427 | ||||||||
\(443\) | 17.5743 | 0.834982 | 0.417491 | − | 0.908681i | \(-0.362910\pi\) | ||||
0.417491 | + | 0.908681i | \(0.362910\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.00000 | −0.0474045 | ||||||||
\(446\) | 2.03492 | 0.0963561 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −11.5743 | −0.546836 | ||||||||
\(449\) | −30.5676 | −1.44258 | −0.721288 | − | 0.692635i | \(-0.756449\pi\) | ||||
−0.721288 | + | 0.692635i | \(0.756449\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.3056 | −0.532359 | ||||||||
\(452\) | −3.62325 | −0.170423 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10.7995 | 0.506848 | ||||||||
\(455\) | −5.04892 | −0.236697 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −35.8189 | −1.67554 | −0.837769 | − | 0.546024i | \(-0.816141\pi\) | ||||
−0.837769 | + | 0.546024i | \(0.816141\pi\) | |||||||
\(458\) | 10.6267 | 0.496554 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.50604 | 0.0702195 | ||||||||
\(461\) | 4.23921 | 0.197440 | 0.0987198 | − | 0.995115i | \(-0.468525\pi\) | ||||
0.0987198 | + | 0.995115i | \(0.468525\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 41.3793 | 1.92306 | 0.961529 | − | 0.274705i | \(-0.0885802\pi\) | ||||
0.961529 | + | 0.274705i | \(0.0885802\pi\) | |||||||
\(464\) | 5.21983 | 0.242325 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.59956 | 0.259395 | ||||||||
\(467\) | −8.93900 | −0.413648 | −0.206824 | − | 0.978378i | \(-0.566313\pi\) | ||||
−0.206824 | + | 0.978378i | \(0.566313\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.3056 | 0.614395 | ||||||||
\(470\) | −2.03146 | −0.0937042 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 38.3467 | 1.76505 | ||||||||
\(473\) | 5.48188 | 0.252057 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.89008 | −0.224372 | ||||||||
\(476\) | 27.7385 | 1.27139 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 14.5254 | 0.664377 | ||||||||
\(479\) | 38.1608 | 1.74361 | 0.871805 | − | 0.489854i | \(-0.162950\pi\) | ||||
0.871805 | + | 0.489854i | \(0.162950\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.78986 | −0.446379 | ||||||||
\(482\) | −2.96854 | −0.135213 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.48619 | 0.294827 | ||||||||
\(485\) | −13.9758 | −0.634610 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.2741 | 1.28122 | 0.640611 | − | 0.767865i | \(-0.278681\pi\) | ||||
0.640611 | + | 0.767865i | \(0.278681\pi\) | |||||||
\(488\) | −22.8659 | −1.03509 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.84117 | 0.128351 | ||||||||
\(491\) | 27.4034 | 1.23670 | 0.618350 | − | 0.785903i | \(-0.287802\pi\) | ||||
0.618350 | + | 0.785903i | \(0.287802\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 59.2180 | 2.66705 | ||||||||
\(494\) | −6.09783 | −0.274355 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.396125 | 0.0177865 | ||||||||
\(497\) | −29.5013 | −1.32331 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.3284 | −0.910025 | −0.455013 | − | 0.890485i | \(-0.650365\pi\) | ||||
−0.455013 | + | 0.890485i | \(0.650365\pi\) | |||||||
\(500\) | 1.35690 | 0.0606822 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.14483 | −0.0510964 | ||||||||
\(503\) | 21.7995 | 0.971994 | 0.485997 | − | 0.873961i | \(-0.338457\pi\) | ||||
0.485997 | + | 0.873961i | \(0.338457\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.97046 | 0.443680 | ||||||||
\(506\) | 2.21983 | 0.0986836 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14.5816 | 0.646955 | ||||||||
\(509\) | −42.7875 | −1.89652 | −0.948260 | − | 0.317493i | \(-0.897159\pi\) | ||||
−0.948260 | + | 0.317493i | \(0.897159\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.60388 | 0.247901 | ||||||||
\(512\) | −6.22282 | −0.275012 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.71379 | 0.252025 | ||||||||
\(515\) | −8.58642 | −0.378363 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.31767 | 0.277851 | ||||||||
\(518\) | 16.3937 | 0.720299 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.18598 | 0.183567 | ||||||||
\(521\) | −27.6142 | −1.20980 | −0.604899 | − | 0.796302i | \(-0.706787\pi\) | ||||
−0.604899 | + | 0.796302i | \(0.706787\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.2198 | −0.796698 | −0.398349 | − | 0.917234i | \(-0.630417\pi\) | ||||
−0.398349 | + | 0.917234i | \(0.630417\pi\) | |||||||
\(524\) | 26.8659 | 1.17364 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.1502 | 0.965795 | ||||||||
\(527\) | 4.49396 | 0.195760 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.7681 | −0.946439 | ||||||||
\(530\) | −2.85862 | −0.124171 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −21.5448 | −0.934085 | ||||||||
\(533\) | −7.04892 | −0.305323 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.58211 | 0.154868 | ||||||||
\(536\) | −11.0315 | −0.476486 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −17.6388 | −0.760462 | ||||||||
\(539\) | −8.83579 | −0.380584 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.7560 | 0.849377 | 0.424688 | − | 0.905340i | \(-0.360384\pi\) | ||||
0.424688 | + | 0.905340i | \(0.360384\pi\) | |||||||
\(542\) | 1.60733 | 0.0690409 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −36.6993 | −1.57347 | ||||||||
\(545\) | −10.4209 | −0.446381 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.4403 | 0.702935 | 0.351467 | − | 0.936200i | \(-0.385683\pi\) | ||||
0.351467 | + | 0.936200i | \(0.385683\pi\) | |||||||
\(548\) | −21.3647 | −0.912653 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.00000 | 0.0852803 | ||||||||
\(551\) | −45.9952 | −1.95946 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.08038 | 0.386137 | ||||||||
\(554\) | 13.0664 | 0.555137 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 21.0000 | 0.890598 | ||||||||
\(557\) | 1.10992 | 0.0470287 | 0.0235143 | − | 0.999723i | \(-0.492514\pi\) | ||||
0.0235143 | + | 0.999723i | \(0.492514\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.41789 | 0.144562 | ||||||||
\(560\) | 1.80194 | 0.0761458 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.15538 | −0.133101 | ||||||||
\(563\) | 15.2078 | 0.640930 | 0.320465 | − | 0.947260i | \(-0.396161\pi\) | ||||
0.320465 | + | 0.947260i | \(0.396161\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.67025 | −0.112338 | ||||||||
\(566\) | 7.25129 | 0.304795 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 24.4590 | 1.02628 | ||||||||
\(569\) | 40.1312 | 1.68239 | 0.841194 | − | 0.540733i | \(-0.181853\pi\) | ||||
0.841194 | + | 0.540733i | \(0.181853\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.84787 | −0.161028 | −0.0805142 | − | 0.996753i | \(-0.525656\pi\) | ||||
−0.0805142 | + | 0.996753i | \(0.525656\pi\) | |||||||
\(572\) | −5.26205 | −0.220017 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 11.8039 | 0.492683 | ||||||||
\(575\) | 1.10992 | 0.0462867 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.60089 | 0.191538 | 0.0957688 | − | 0.995404i | \(-0.469469\pi\) | ||||
0.0957688 | + | 0.995404i | \(0.469469\pi\) | |||||||
\(578\) | −18.1545 | −0.755129 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 12.7627 | 0.529943 | ||||||||
\(581\) | 57.6534 | 2.39187 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.89008 | 0.368190 | ||||||||
\(584\) | −4.64609 | −0.192256 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.2271 | 0.463788 | ||||||||
\(587\) | 1.58450 | 0.0653992 | 0.0326996 | − | 0.999465i | \(-0.489590\pi\) | ||||
0.0326996 | + | 0.999465i | \(0.489590\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.49050 | −0.143824 | ||||||||
\(590\) | 11.4233 | 0.470289 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.49396 | 0.143601 | ||||||||
\(593\) | 23.7211 | 0.974108 | 0.487054 | − | 0.873372i | \(-0.338071\pi\) | ||||
0.487054 | + | 0.873372i | \(0.338071\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.4426 | 0.838067 | ||||||||
\(596\) | 5.99138 | 0.245416 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.38404 | 0.0565977 | ||||||||
\(599\) | −25.5646 | −1.04454 | −0.522272 | − | 0.852779i | \(-0.674915\pi\) | ||||
−0.522272 | + | 0.852779i | \(0.674915\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.1739 | −1.14924 | −0.574619 | − | 0.818421i | \(-0.694850\pi\) | ||||
−0.574619 | + | 0.818421i | \(0.694850\pi\) | |||||||
\(602\) | −5.72348 | −0.233272 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 17.0858 | 0.695209 | ||||||||
\(605\) | 4.78017 | 0.194341 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −33.1836 | −1.34688 | −0.673440 | − | 0.739242i | \(-0.735184\pi\) | ||||
−0.673440 | + | 0.739242i | \(0.735184\pi\) | |||||||
\(608\) | 28.5047 | 1.15602 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.81163 | −0.275795 | ||||||||
\(611\) | 3.93900 | 0.159355 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.42758 | −0.138439 | −0.0692194 | − | 0.997601i | \(-0.522051\pi\) | ||||
−0.0692194 | + | 0.997601i | \(0.522051\pi\) | |||||||
\(614\) | 11.6823 | 0.471461 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 21.7995 | 0.878329 | ||||||||
\(617\) | 19.5496 | 0.787037 | 0.393518 | − | 0.919317i | \(-0.371258\pi\) | ||||
0.393518 | + | 0.919317i | \(0.371258\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.3811 | −0.819184 | −0.409592 | − | 0.912269i | \(-0.634329\pi\) | ||||
−0.409592 | + | 0.912269i | \(0.634329\pi\) | |||||||
\(620\) | 0.968541 | 0.0388975 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 14.2935 | 0.573117 | ||||||||
\(623\) | −3.24698 | −0.130087 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 2.22867 | 0.0890755 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −31.0858 | −1.24046 | ||||||||
\(629\) | 39.6383 | 1.58048 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.7713 | 1.06575 | 0.532875 | − | 0.846194i | \(-0.321112\pi\) | ||||
0.532875 | + | 0.846194i | \(0.321112\pi\) | |||||||
\(632\) | −7.52840 | −0.299464 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −24.2567 | −0.963355 | ||||||||
\(635\) | 10.7463 | 0.426455 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.50902 | −0.218276 | ||||||||
\(638\) | 18.8116 | 0.744759 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8.79954 | −0.347833 | ||||||||
\(641\) | 30.0737 | 1.18784 | 0.593919 | − | 0.804525i | \(-0.297580\pi\) | ||||
0.593919 | + | 0.804525i | \(0.297580\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.4470 | −1.08240 | −0.541201 | − | 0.840893i | \(-0.682030\pi\) | ||||
−0.541201 | + | 0.840893i | \(0.682030\pi\) | |||||||
\(644\) | 4.89008 | 0.192696 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 24.6896 | 0.971400 | ||||||||
\(647\) | −18.5483 | −0.729207 | −0.364604 | − | 0.931163i | \(-0.618795\pi\) | ||||
−0.364604 | + | 0.931163i | \(0.618795\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −35.5254 | −1.39449 | ||||||||
\(650\) | 1.24698 | 0.0489106 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −16.3491 | −0.640281 | ||||||||
\(653\) | −21.6582 | −0.847550 | −0.423775 | − | 0.905768i | \(-0.639295\pi\) | ||||
−0.423775 | + | 0.905768i | \(0.639295\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.7995 | 0.773632 | ||||||||
\(656\) | 2.51573 | 0.0982227 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.59611 | −0.257143 | ||||||||
\(659\) | −6.90084 | −0.268818 | −0.134409 | − | 0.990926i | \(-0.542914\pi\) | ||||
−0.134409 | + | 0.990926i | \(0.542914\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.03624 | −0.118096 | −0.0590481 | − | 0.998255i | \(-0.518807\pi\) | ||||
−0.0590481 | + | 0.998255i | \(0.518807\pi\) | |||||||
\(662\) | 15.4233 | 0.599442 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −47.7995 | −1.85498 | ||||||||
\(665\) | −15.8780 | −0.615723 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.4397 | 0.404225 | ||||||||
\(668\) | 1.87071 | 0.0723798 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.28621 | −0.126957 | ||||||||
\(671\) | 21.1836 | 0.817783 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.0844 | −1.54514 | −0.772571 | − | 0.634929i | \(-0.781029\pi\) | ||||
−0.772571 | + | 0.634929i | \(0.781029\pi\) | |||||||
\(674\) | −10.9914 | −0.423372 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 14.3588 | 0.552262 | ||||||||
\(677\) | 32.9181 | 1.26514 | 0.632572 | − | 0.774501i | \(-0.281999\pi\) | ||||
0.632572 | + | 0.774501i | \(0.281999\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −45.3793 | −1.74150 | ||||||||
\(680\) | −16.9487 | −0.649953 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.42758 | 0.0546650 | ||||||||
\(683\) | 47.6883 | 1.82474 | 0.912371 | − | 0.409364i | \(-0.134249\pi\) | ||||
0.912371 | + | 0.409364i | \(0.134249\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.7453 | −0.601595 | ||||||||
\(686\) | −9.00192 | −0.343695 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.21983 | −0.0465057 | ||||||||
\(689\) | 5.54288 | 0.211167 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.7192 | 0.636027 | 0.318014 | − | 0.948086i | \(-0.396984\pi\) | ||||
0.318014 | + | 0.948086i | \(0.396984\pi\) | |||||||
\(692\) | 9.34183 | 0.355123 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −15.8431 | −0.601395 | ||||||||
\(695\) | 15.4765 | 0.587057 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 28.5405 | 1.08105 | ||||||||
\(698\) | 14.2392 | 0.538962 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.40581 | 0.166524 | ||||||||
\(701\) | −26.1957 | −0.989397 | −0.494698 | − | 0.869065i | \(-0.664721\pi\) | ||||
−0.494698 | + | 0.869065i | \(0.664721\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −30.7875 | −1.16117 | ||||||||
\(704\) | −8.89008 | −0.335058 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.75733 | −0.103774 | ||||||||
\(707\) | 32.3739 | 1.21755 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −47.2900 | −1.77601 | −0.888007 | − | 0.459829i | \(-0.847911\pi\) | ||||
−0.888007 | + | 0.459829i | \(0.847911\pi\) | |||||||
\(710\) | 7.28621 | 0.273447 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.69202 | 0.100888 | ||||||||
\(713\) | 0.792249 | 0.0296700 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.87800 | −0.145029 | ||||||||
\(716\) | −12.2693 | −0.458527 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.25475 | −0.0468268 | ||||||||
\(719\) | −47.2403 | −1.76176 | −0.880882 | − | 0.473335i | \(-0.843050\pi\) | ||||
−0.880882 | + | 0.473335i | \(0.843050\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −27.8799 | −1.03830 | ||||||||
\(722\) | −3.93986 | −0.146626 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 35.9168 | 1.33484 | ||||||||
\(725\) | 9.40581 | 0.349323 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.5894 | 0.541091 | 0.270545 | − | 0.962707i | \(-0.412796\pi\) | ||||
0.270545 | + | 0.962707i | \(0.412796\pi\) | |||||||
\(728\) | 13.5918 | 0.503745 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.38404 | −0.0512257 | ||||||||
\(731\) | −13.8388 | −0.511846 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.04354 | 0.297095 | 0.148547 | − | 0.988905i | \(-0.452540\pi\) | ||||
0.148547 | + | 0.988905i | \(0.452540\pi\) | |||||||
\(734\) | −8.30213 | −0.306437 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.46980 | −0.238480 | ||||||||
\(737\) | 10.2198 | 0.376452 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −42.7633 | −1.57307 | −0.786537 | − | 0.617544i | \(-0.788128\pi\) | ||||
−0.786537 | + | 0.617544i | \(0.788128\pi\) | |||||||
\(740\) | 8.54288 | 0.314042 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.28190 | −0.340749 | ||||||||
\(743\) | −6.06292 | −0.222427 | −0.111213 | − | 0.993797i | \(-0.535474\pi\) | ||||
−0.111213 | + | 0.993797i | \(0.535474\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.41550 | 0.161771 | ||||||||
\(746\) | 13.7172 | 0.502224 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 21.3056 | 0.779009 | ||||||||
\(749\) | 11.6310 | 0.424988 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −33.4553 | −1.22080 | −0.610401 | − | 0.792093i | \(-0.708992\pi\) | ||||
−0.610401 | + | 0.792093i | \(0.708992\pi\) | |||||||
\(752\) | −1.40581 | −0.0512647 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 11.7289 | 0.427140 | ||||||||
\(755\) | 12.5918 | 0.458262 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.4926 | −1.14462 | −0.572310 | − | 0.820038i | \(-0.693952\pi\) | ||||
−0.572310 | + | 0.820038i | \(0.693952\pi\) | |||||||
\(758\) | 9.07500 | 0.329619 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 13.1642 | 0.477516 | ||||||||
\(761\) | 30.9336 | 1.12134 | 0.560672 | − | 0.828038i | \(-0.310543\pi\) | ||||
0.560672 | + | 0.828038i | \(0.310543\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −33.8364 | −1.22496 | ||||||||
\(764\) | 25.8310 | 0.934533 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −13.2271 | −0.477916 | ||||||||
\(767\) | −22.1497 | −0.799781 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.8092 | 1.32737 | 0.663687 | − | 0.748010i | \(-0.268991\pi\) | ||||
0.663687 | + | 0.748010i | \(0.268991\pi\) | |||||||
\(770\) | 6.49396 | 0.234026 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 15.6920 | 0.564768 | ||||||||
\(773\) | −40.1280 | −1.44330 | −0.721651 | − | 0.692257i | \(-0.756617\pi\) | ||||
−0.721651 | + | 0.692257i | \(0.756617\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.713792 | 0.0256402 | ||||||||
\(776\) | 37.6233 | 1.35060 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.86725 | 0.102796 | ||||||||
\(779\) | −22.1677 | −0.794239 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.6595 | −0.810821 | ||||||||
\(782\) | −5.60388 | −0.200394 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.96615 | 0.0702196 | ||||||||
\(785\) | −22.9095 | −0.817674 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.4547 | −0.943009 | −0.471505 | − | 0.881864i | \(-0.656289\pi\) | ||||
−0.471505 | + | 0.881864i | \(0.656289\pi\) | |||||||
\(788\) | −24.2258 | −0.863008 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.24267 | −0.0797905 | ||||||||
\(791\) | −8.67025 | −0.308279 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.2078 | 0.469021 | ||||||||
\(794\) | −7.65087 | −0.271519 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −29.4437 | −1.04360 | ||||||||
\(797\) | 18.8847 | 0.668931 | 0.334465 | − | 0.942408i | \(-0.391444\pi\) | ||||
0.334465 | + | 0.942408i | \(0.391444\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.9487 | −0.564224 | ||||||||
\(800\) | −5.82908 | −0.206089 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.80300 | −0.310845 | ||||||||
\(803\) | 4.30426 | 0.151894 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.60388 | 0.127020 | ||||||||
\(806\) | 0.890084 | 0.0313519 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −26.8407 | −0.944252 | ||||||||
\(809\) | −21.8974 | −0.769871 | −0.384935 | − | 0.922944i | \(-0.625776\pi\) | ||||
−0.384935 | + | 0.922944i | \(0.625776\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.4118 | 0.892328 | 0.446164 | − | 0.894951i | \(-0.352790\pi\) | ||||
0.446164 | + | 0.894951i | \(0.352790\pi\) | |||||||
\(812\) | 41.4403 | 1.45427 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 12.5918 | 0.441342 | ||||||||
\(815\) | −12.0489 | −0.422055 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.7487 | 0.376050 | ||||||||
\(818\) | 10.7802 | 0.376920 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.15106 | 0.214804 | ||||||||
\(821\) | −15.4228 | −0.538259 | −0.269130 | − | 0.963104i | \(-0.586736\pi\) | ||||
−0.269130 | + | 0.963104i | \(0.586736\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.63533 | 0.231293 | 0.115647 | − | 0.993290i | \(-0.463106\pi\) | ||||
0.115647 | + | 0.993290i | \(0.463106\pi\) | |||||||
\(824\) | 23.1148 | 0.805243 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 37.0911 | 1.29057 | ||||||||
\(827\) | −8.22462 | −0.285998 | −0.142999 | − | 0.989723i | \(-0.545675\pi\) | ||||
−0.142999 | + | 0.989723i | \(0.545675\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.0315 | −0.452601 | −0.226301 | − | 0.974058i | \(-0.572663\pi\) | ||||
−0.226301 | + | 0.974058i | \(0.572663\pi\) | |||||||
\(830\) | −14.2392 | −0.494250 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.54288 | −0.192165 | ||||||||
\(833\) | 22.3056 | 0.772843 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.37867 | 0.0477107 | ||||||||
\(836\) | −16.5483 | −0.572333 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 23.0248 | 0.795377 | ||||||||
\(839\) | 33.9861 | 1.17333 | 0.586666 | − | 0.809829i | \(-0.300440\pi\) | ||||
0.586666 | + | 0.809829i | \(0.300440\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 59.4693 | 2.05067 | ||||||||
\(842\) | 28.6896 | 0.988710 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13.1642 | −0.453131 | ||||||||
\(845\) | 10.5821 | 0.364035 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.5211 | 0.533312 | ||||||||
\(848\) | −1.97823 | −0.0679327 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.04892 | −0.173176 | ||||||||
\(851\) | 6.98792 | 0.239543 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.0398 | 0.377996 | 0.188998 | − | 0.981977i | \(-0.439476\pi\) | ||||
0.188998 | + | 0.981977i | \(0.439476\pi\) | |||||||
\(854\) | −22.1172 | −0.756835 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.64310 | −0.329595 | ||||||||
\(857\) | −38.3672 | −1.31060 | −0.655299 | − | 0.755370i | \(-0.727457\pi\) | ||||
−0.655299 | + | 0.755370i | \(0.727457\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.4215 | 1.03797 | 0.518984 | − | 0.854784i | \(-0.326311\pi\) | ||||
0.518984 | + | 0.854784i | \(0.326311\pi\) | |||||||
\(860\) | −2.98254 | −0.101704 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.95492 | −0.236886 | ||||||||
\(863\) | 23.9892 | 0.816603 | 0.408302 | − | 0.912847i | \(-0.366121\pi\) | ||||
0.408302 | + | 0.912847i | \(0.366121\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.88471 | 0.234087 | ||||||||
\(866\) | 18.5961 | 0.631921 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.14483 | 0.106743 | ||||||||
\(869\) | 6.97451 | 0.236594 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.37196 | 0.215906 | ||||||||
\(872\) | 28.0532 | 0.950002 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.35258 | 0.147228 | ||||||||
\(875\) | 3.24698 | 0.109768 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.9396 | 1.31490 | 0.657448 | − | 0.753500i | \(-0.271636\pi\) | ||||
0.657448 | + | 0.753500i | \(0.271636\pi\) | |||||||
\(878\) | −4.10646 | −0.138586 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.38404 | 0.0466561 | ||||||||
\(881\) | −19.3104 | −0.650583 | −0.325291 | − | 0.945614i | \(-0.605462\pi\) | ||||
−0.325291 | + | 0.945614i | \(0.605462\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.28322 | −0.144142 | −0.0720710 | − | 0.997400i | \(-0.522961\pi\) | ||||
−0.0720710 | + | 0.997400i | \(0.522961\pi\) | |||||||
\(884\) | 13.2838 | 0.446783 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14.0935 | −0.473481 | ||||||||
\(887\) | −12.3720 | −0.415410 | −0.207705 | − | 0.978192i | \(-0.566599\pi\) | ||||
−0.207705 | + | 0.978192i | \(0.566599\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 34.8931 | 1.17028 | ||||||||
\(890\) | 0.801938 | 0.0268810 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.44312 | 0.115284 | ||||||||
\(893\) | 12.3875 | 0.414532 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.04221 | −0.302248 | ||||||||
\(896\) | −28.5719 | −0.954522 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 24.5133 | 0.818021 | ||||||||
\(899\) | 6.71379 | 0.223917 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.4426 | −0.747673 | ||||||||
\(902\) | 9.06638 | 0.301877 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.18837 | 0.239082 | ||||||||
\(905\) | 26.4698 | 0.879886 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.4276 | 1.17635 | 0.588177 | − | 0.808732i | \(-0.299846\pi\) | ||||
0.588177 | + | 0.808732i | \(0.299846\pi\) | |||||||
\(908\) | 18.2731 | 0.606413 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4.04892 | 0.134220 | ||||||||
\(911\) | −0.792249 | −0.0262484 | −0.0131242 | − | 0.999914i | \(-0.504178\pi\) | ||||
−0.0131242 | + | 0.999914i | \(0.504178\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 44.2828 | 1.46555 | ||||||||
\(914\) | 28.7245 | 0.950124 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17.9806 | 0.594096 | ||||||||
\(917\) | 64.2887 | 2.12300 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.1099 | 0.894274 | 0.447137 | − | 0.894466i | \(-0.352444\pi\) | ||||
0.447137 | + | 0.894466i | \(0.352444\pi\) | |||||||
\(920\) | −2.98792 | −0.0985088 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.39958 | −0.111959 | ||||||||
\(923\) | −14.1280 | −0.465028 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.29590 | 0.207008 | ||||||||
\(926\) | −33.1836 | −1.09048 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −54.8273 | −1.79979 | ||||||||
\(929\) | 13.5013 | 0.442962 | 0.221481 | − | 0.975165i | \(-0.428911\pi\) | ||||
0.221481 | + | 0.975165i | \(0.428911\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.3250 | −0.567803 | ||||||||
\(932\) | 9.47458 | 0.310350 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.16852 | 0.234561 | ||||||||
\(935\) | 15.7017 | 0.513501 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.5582 | −0.769613 | −0.384807 | − | 0.922997i | \(-0.625732\pi\) | ||||
−0.384807 | + | 0.922997i | \(0.625732\pi\) | |||||||
\(938\) | −10.6703 | −0.348396 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.43727 | −0.112111 | ||||||||
\(941\) | 17.5579 | 0.572373 | 0.286186 | − | 0.958174i | \(-0.407612\pi\) | ||||
0.286186 | + | 0.958174i | \(0.407612\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.03146 | 0.163847 | ||||||||
\(944\) | 7.90515 | 0.257291 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.39612 | −0.142930 | ||||||||
\(947\) | 32.4510 | 1.05452 | 0.527258 | − | 0.849705i | \(-0.323220\pi\) | ||||
0.527258 | + | 0.849705i | \(0.323220\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.68366 | 0.0871153 | ||||||||
\(950\) | 3.92154 | 0.127232 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −55.0320 | −1.78360 | ||||||||
\(953\) | 49.0025 | 1.58735 | 0.793673 | − | 0.608344i | \(-0.208166\pi\) | ||||
0.793673 | + | 0.608344i | \(0.208166\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.0368 | 0.616018 | ||||||||
\(956\) | 24.5773 | 0.794887 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −30.6025 | −0.988723 | ||||||||
\(959\) | −51.1245 | −1.65090 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.4905 | −0.983565 | ||||||||
\(962\) | 7.85086 | 0.253122 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.02284 | −0.161775 | ||||||||
\(965\) | 11.5646 | 0.372279 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.4510 | 1.55808 | 0.779040 | − | 0.626975i | \(-0.215707\pi\) | ||||
0.779040 | + | 0.626975i | \(0.215707\pi\) | |||||||
\(968\) | −12.8683 | −0.413603 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 11.2078 | 0.359859 | ||||||||
\(971\) | −30.6305 | −0.982981 | −0.491491 | − | 0.870883i | \(-0.663548\pi\) | ||||
−0.491491 | + | 0.870883i | \(0.663548\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 50.2519 | 1.61100 | ||||||||
\(974\) | −22.6741 | −0.726525 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.71379 | −0.150885 | ||||||||
\(977\) | −42.2629 | −1.35211 | −0.676055 | − | 0.736851i | \(-0.736312\pi\) | ||||
−0.676055 | + | 0.736851i | \(0.736312\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.49396 | −0.0797073 | ||||||||
\(980\) | 4.80731 | 0.153564 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −21.9758 | −0.701277 | ||||||||
\(983\) | 57.1355 | 1.82234 | 0.911170 | − | 0.412030i | \(-0.135180\pi\) | ||||
0.911170 | + | 0.412030i | \(0.135180\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.8538 | −0.568871 | ||||||||
\(986\) | −47.4892 | −1.51236 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −10.3177 | −0.328249 | ||||||||
\(989\) | −2.43967 | −0.0775768 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.8418 | 0.852657 | 0.426328 | − | 0.904569i | \(-0.359807\pi\) | ||||
0.426328 | + | 0.904569i | \(0.359807\pi\) | |||||||
\(992\) | −4.16075 | −0.132104 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 23.6582 | 0.750392 | ||||||||
\(995\) | −21.6993 | −0.687915 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.6595 | 0.400930 | 0.200465 | − | 0.979701i | \(-0.435755\pi\) | ||||
0.200465 | + | 0.979701i | \(0.435755\pi\) | |||||||
\(998\) | 16.3021 | 0.516035 | ||||||||
\(999\) | 0 | 0 |
(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 | 4005.2.a.j.1.1 | 3 | ||
3.2 | odd | 2 | 1335.2.a.d.1.3 | ✓ | 3 | ||
15.14 | odd | 2 | 6675.2.a.o.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1335.2.a.d.1.3 | ✓ | 3 | 3.2 | odd | 2 | ||
4005.2.a.j.1.1 | 3 | 1.1 | even | 1 | trivial | ||
6675.2.a.o.1.1 | 3 | 15.14 | odd | 2 |