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: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 11x^{6} + 9x^{5} + 34x^{4} - 19x^{3} - 27x^{2} + 11x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 445) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-2.50065\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.50065 | 1.76823 | 0.884114 | − | 0.467272i | \(-0.154763\pi\) | ||||
0.884114 | + | 0.467272i | \(0.154763\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.25326 | 2.12663 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.89614 | −1.85057 | −0.925284 | − | 0.379275i | \(-0.876173\pi\) | ||||
−0.925284 | + | 0.379275i | \(0.876173\pi\) | |||||||
\(8\) | 5.63461 | 1.99214 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.50065 | 0.790775 | ||||||||
\(11\) | −5.13396 | −1.54795 | −0.773974 | − | 0.633218i | \(-0.781734\pi\) | ||||
−0.773974 | + | 0.633218i | \(0.781734\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.293733 | 0.0814670 | 0.0407335 | − | 0.999170i | \(-0.487031\pi\) | ||||
0.0407335 | + | 0.999170i | \(0.487031\pi\) | |||||||
\(14\) | −12.2435 | −3.27223 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.58369 | 1.39592 | ||||||||
\(17\) | −4.78896 | −1.16149 | −0.580747 | − | 0.814084i | \(-0.697240\pi\) | ||||
−0.580747 | + | 0.814084i | \(0.697240\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.79227 | 1.09942 | 0.549711 | − | 0.835355i | \(-0.314738\pi\) | ||||
0.549711 | + | 0.835355i | \(0.314738\pi\) | |||||||
\(20\) | 4.25326 | 0.951057 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −12.8382 | −2.73712 | ||||||||
\(23\) | −5.18988 | −1.08216 | −0.541082 | − | 0.840970i | \(-0.681985\pi\) | ||||
−0.541082 | + | 0.840970i | \(0.681985\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.734525 | 0.144052 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −20.8246 | −3.93547 | ||||||||
\(29\) | −8.87657 | −1.64834 | −0.824169 | − | 0.566344i | \(-0.808357\pi\) | ||||
−0.824169 | + | 0.566344i | \(0.808357\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.58148 | −1.18207 | −0.591034 | − | 0.806646i | \(-0.701280\pi\) | ||||
−0.591034 | + | 0.806646i | \(0.701280\pi\) | |||||||
\(32\) | 2.69363 | 0.476171 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −11.9755 | −2.05379 | ||||||||
\(35\) | −4.89614 | −0.827599 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.840228 | 0.138133 | 0.0690663 | − | 0.997612i | \(-0.477998\pi\) | ||||
0.0690663 | + | 0.997612i | \(0.477998\pi\) | |||||||
\(38\) | 11.9838 | 1.94403 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.63461 | 0.890910 | ||||||||
\(41\) | 2.51195 | 0.392301 | 0.196150 | − | 0.980574i | \(-0.437156\pi\) | ||||
0.196150 | + | 0.980574i | \(0.437156\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.39183 | 1.43224 | 0.716120 | − | 0.697977i | \(-0.245916\pi\) | ||||
0.716120 | + | 0.697977i | \(0.245916\pi\) | |||||||
\(44\) | −21.8361 | −3.29191 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12.9781 | −1.91351 | ||||||||
\(47\) | −8.06738 | −1.17675 | −0.588374 | − | 0.808589i | \(-0.700232\pi\) | ||||
−0.588374 | + | 0.808589i | \(0.700232\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16.9722 | 2.42460 | ||||||||
\(50\) | 2.50065 | 0.353646 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.24932 | 0.173250 | ||||||||
\(53\) | 11.4348 | 1.57070 | 0.785348 | − | 0.619055i | \(-0.212484\pi\) | ||||
0.785348 | + | 0.619055i | \(0.212484\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.13396 | −0.692263 | ||||||||
\(56\) | −27.5879 | −3.68658 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −22.1972 | −2.91464 | ||||||||
\(59\) | −1.04378 | −0.135888 | −0.0679441 | − | 0.997689i | \(-0.521644\pi\) | ||||
−0.0679441 | + | 0.997689i | \(0.521644\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.77868 | 0.867921 | 0.433961 | − | 0.900932i | \(-0.357116\pi\) | ||||
0.433961 | + | 0.900932i | \(0.357116\pi\) | |||||||
\(62\) | −16.4580 | −2.09017 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.43155 | −0.553943 | ||||||||
\(65\) | 0.293733 | 0.0364331 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.0551 | −1.71710 | −0.858551 | − | 0.512727i | \(-0.828635\pi\) | ||||
−0.858551 | + | 0.512727i | \(0.828635\pi\) | |||||||
\(68\) | −20.3687 | −2.47007 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −12.2435 | −1.46338 | ||||||||
\(71\) | −2.08800 | −0.247800 | −0.123900 | − | 0.992295i | \(-0.539540\pi\) | ||||
−0.123900 | + | 0.992295i | \(0.539540\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.37951 | 0.746665 | 0.373332 | − | 0.927698i | \(-0.378215\pi\) | ||||
0.373332 | + | 0.927698i | \(0.378215\pi\) | |||||||
\(74\) | 2.10112 | 0.244250 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 20.3827 | 2.33806 | ||||||||
\(77\) | 25.1366 | 2.86458 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.566895 | 0.0637807 | 0.0318903 | − | 0.999491i | \(-0.489847\pi\) | ||||
0.0318903 | + | 0.999491i | \(0.489847\pi\) | |||||||
\(80\) | 5.58369 | 0.624275 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.28152 | 0.693677 | ||||||||
\(83\) | −6.12572 | −0.672385 | −0.336192 | − | 0.941793i | \(-0.609139\pi\) | ||||
−0.336192 | + | 0.941793i | \(0.609139\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.78896 | −0.519436 | ||||||||
\(86\) | 23.4857 | 2.53253 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −28.9279 | −3.08372 | ||||||||
\(89\) | −1.00000 | −0.106000 | ||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.43816 | −0.150760 | ||||||||
\(92\) | −22.0739 | −2.30136 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −20.1737 | −2.08076 | ||||||||
\(95\) | 4.79227 | 0.491676 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.68712 | −0.374370 | −0.187185 | − | 0.982325i | \(-0.559936\pi\) | ||||
−0.187185 | + | 0.982325i | \(0.559936\pi\) | |||||||
\(98\) | 42.4416 | 4.28725 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.25326 | 0.425326 | ||||||||
\(101\) | 6.79147 | 0.675777 | 0.337888 | − | 0.941186i | \(-0.390287\pi\) | ||||
0.337888 | + | 0.941186i | \(0.390287\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.1620 | 1.00129 | 0.500646 | − | 0.865652i | \(-0.333096\pi\) | ||||
0.500646 | + | 0.865652i | \(0.333096\pi\) | |||||||
\(104\) | 1.65507 | 0.162293 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 28.5945 | 2.77735 | ||||||||
\(107\) | −7.95873 | −0.769399 | −0.384700 | − | 0.923042i | \(-0.625695\pi\) | ||||
−0.384700 | + | 0.923042i | \(0.625695\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.91220 | −0.374721 | −0.187360 | − | 0.982291i | \(-0.559993\pi\) | ||||
−0.187360 | + | 0.982291i | \(0.559993\pi\) | |||||||
\(110\) | −12.8382 | −1.22408 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −27.3385 | −2.58325 | ||||||||
\(113\) | 8.18970 | 0.770423 | 0.385211 | − | 0.922828i | \(-0.374129\pi\) | ||||
0.385211 | + | 0.922828i | \(0.374129\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.18988 | −0.483958 | ||||||||
\(116\) | −37.7543 | −3.50540 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.61012 | −0.240281 | ||||||||
\(119\) | 23.4475 | 2.14942 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.3576 | 1.39614 | ||||||||
\(122\) | 16.9511 | 1.53468 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −27.9927 | −2.51382 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.03100 | −0.180222 | −0.0901110 | − | 0.995932i | \(-0.528722\pi\) | ||||
−0.0901110 | + | 0.995932i | \(0.528722\pi\) | |||||||
\(128\) | −16.4690 | −1.45567 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.734525 | 0.0644221 | ||||||||
\(131\) | −9.71902 | −0.849155 | −0.424578 | − | 0.905392i | \(-0.639577\pi\) | ||||
−0.424578 | + | 0.905392i | \(0.639577\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −23.4636 | −2.03455 | ||||||||
\(134\) | −35.1469 | −3.03623 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −26.9840 | −2.31386 | ||||||||
\(137\) | −21.4520 | −1.83277 | −0.916386 | − | 0.400296i | \(-0.868907\pi\) | ||||
−0.916386 | + | 0.400296i | \(0.868907\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.595475 | −0.0505075 | −0.0252538 | − | 0.999681i | \(-0.508039\pi\) | ||||
−0.0252538 | + | 0.999681i | \(0.508039\pi\) | |||||||
\(140\) | −20.8246 | −1.76000 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.22136 | −0.438166 | ||||||||
\(143\) | −1.50802 | −0.126107 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.87657 | −0.737159 | ||||||||
\(146\) | 15.9529 | 1.32027 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.57371 | 0.293757 | ||||||||
\(149\) | 16.4598 | 1.34844 | 0.674220 | − | 0.738531i | \(-0.264480\pi\) | ||||
0.674220 | + | 0.738531i | \(0.264480\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.01236 | 0.0823849 | 0.0411924 | − | 0.999151i | \(-0.486884\pi\) | ||||
0.0411924 | + | 0.999151i | \(0.486884\pi\) | |||||||
\(152\) | 27.0026 | 2.19020 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 62.8579 | 5.06523 | ||||||||
\(155\) | −6.58148 | −0.528637 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.66401 | −0.292420 | −0.146210 | − | 0.989254i | \(-0.546707\pi\) | ||||
−0.146210 | + | 0.989254i | \(0.546707\pi\) | |||||||
\(158\) | 1.41761 | 0.112779 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.69363 | 0.212950 | ||||||||
\(161\) | 25.4104 | 2.00262 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.396340 | −0.0310437 | −0.0155219 | − | 0.999880i | \(-0.504941\pi\) | ||||
−0.0155219 | + | 0.999880i | \(0.504941\pi\) | |||||||
\(164\) | 10.6840 | 0.834279 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.3183 | −1.18893 | ||||||||
\(167\) | 8.91272 | 0.689687 | 0.344843 | − | 0.938660i | \(-0.387932\pi\) | ||||
0.344843 | + | 0.938660i | \(0.387932\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9137 | −0.993363 | ||||||||
\(170\) | −11.9755 | −0.918481 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 39.9459 | 3.04584 | ||||||||
\(173\) | −20.4096 | −1.55171 | −0.775855 | − | 0.630911i | \(-0.782681\pi\) | ||||
−0.775855 | + | 0.630911i | \(0.782681\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.89614 | −0.370114 | ||||||||
\(176\) | −28.6664 | −2.16081 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.50065 | −0.187432 | ||||||||
\(179\) | 3.85954 | 0.288476 | 0.144238 | − | 0.989543i | \(-0.453927\pi\) | ||||
0.144238 | + | 0.989543i | \(0.453927\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.85674 | −0.360998 | −0.180499 | − | 0.983575i | \(-0.557771\pi\) | ||||
−0.180499 | + | 0.983575i | \(0.557771\pi\) | |||||||
\(182\) | −3.59634 | −0.266578 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −29.2429 | −2.15582 | ||||||||
\(185\) | 0.840228 | 0.0617748 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24.5864 | 1.79793 | ||||||||
\(188\) | −34.3126 | −2.50251 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 11.9838 | 0.869395 | ||||||||
\(191\) | −7.44680 | −0.538831 | −0.269416 | − | 0.963024i | \(-0.586831\pi\) | ||||
−0.269416 | + | 0.963024i | \(0.586831\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.68593 | −0.553245 | −0.276623 | − | 0.960979i | \(-0.589215\pi\) | ||||
−0.276623 | + | 0.960979i | \(0.589215\pi\) | |||||||
\(194\) | −9.22021 | −0.661972 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 72.1872 | 5.15623 | ||||||||
\(197\) | 26.9802 | 1.92226 | 0.961131 | − | 0.276092i | \(-0.0890395\pi\) | ||||
0.961131 | + | 0.276092i | \(0.0890395\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.24242 | 0.371625 | 0.185813 | − | 0.982585i | \(-0.440508\pi\) | ||||
0.185813 | + | 0.982585i | \(0.440508\pi\) | |||||||
\(200\) | 5.63461 | 0.398427 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 16.9831 | 1.19493 | ||||||||
\(203\) | 43.4609 | 3.05036 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.51195 | 0.175442 | ||||||||
\(206\) | 25.4116 | 1.77051 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.64012 | 0.113722 | ||||||||
\(209\) | −24.6033 | −1.70185 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.509470 | −0.0350734 | −0.0175367 | − | 0.999846i | \(-0.505582\pi\) | ||||
−0.0175367 | + | 0.999846i | \(0.505582\pi\) | |||||||
\(212\) | 48.6353 | 3.34029 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −19.9020 | −1.36047 | ||||||||
\(215\) | 9.39183 | 0.640518 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 32.2239 | 2.18750 | ||||||||
\(218\) | −9.78305 | −0.662592 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −21.8361 | −1.47219 | ||||||||
\(221\) | −1.40668 | −0.0946235 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.1310 | 0.745384 | 0.372692 | − | 0.927955i | \(-0.378435\pi\) | ||||
0.372692 | + | 0.927955i | \(0.378435\pi\) | |||||||
\(224\) | −13.1884 | −0.881186 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 20.4796 | 1.36228 | ||||||||
\(227\) | 1.50278 | 0.0997427 | 0.0498713 | − | 0.998756i | \(-0.484119\pi\) | ||||
0.0498713 | + | 0.998756i | \(0.484119\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.07817 | −0.533820 | −0.266910 | − | 0.963721i | \(-0.586003\pi\) | ||||
−0.266910 | + | 0.963721i | \(0.586003\pi\) | |||||||
\(230\) | −12.9781 | −0.855749 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −50.0160 | −3.28371 | ||||||||
\(233\) | −9.45410 | −0.619359 | −0.309679 | − | 0.950841i | \(-0.600222\pi\) | ||||
−0.309679 | + | 0.950841i | \(0.600222\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.06738 | −0.526258 | ||||||||
\(236\) | −4.43945 | −0.288984 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 58.6339 | 3.80067 | ||||||||
\(239\) | 9.38903 | 0.607326 | 0.303663 | − | 0.952780i | \(-0.401790\pi\) | ||||
0.303663 | + | 0.952780i | \(0.401790\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.14337 | −0.0736510 | −0.0368255 | − | 0.999322i | \(-0.511725\pi\) | ||||
−0.0368255 | + | 0.999322i | \(0.511725\pi\) | |||||||
\(242\) | 38.4039 | 2.46870 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 28.8315 | 1.84575 | ||||||||
\(245\) | 16.9722 | 1.08431 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.40765 | 0.0895665 | ||||||||
\(248\) | −37.0841 | −2.35484 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.50065 | 0.158155 | ||||||||
\(251\) | 16.7613 | 1.05796 | 0.528981 | − | 0.848634i | \(-0.322574\pi\) | ||||
0.528981 | + | 0.848634i | \(0.322574\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 26.6446 | 1.67513 | ||||||||
\(254\) | −5.07882 | −0.318674 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −32.3202 | −2.02001 | ||||||||
\(257\) | −17.2697 | −1.07725 | −0.538626 | − | 0.842545i | \(-0.681056\pi\) | ||||
−0.538626 | + | 0.842545i | \(0.681056\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.11387 | −0.255624 | ||||||||
\(260\) | 1.24932 | 0.0774798 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −24.3039 | −1.50150 | ||||||||
\(263\) | −27.3161 | −1.68438 | −0.842192 | − | 0.539177i | \(-0.818735\pi\) | ||||
−0.842192 | + | 0.539177i | \(0.818735\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.4348 | 0.702437 | ||||||||
\(266\) | −58.6743 | −3.59755 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −59.7799 | −3.65164 | ||||||||
\(269\) | 8.56066 | 0.521953 | 0.260976 | − | 0.965345i | \(-0.415956\pi\) | ||||
0.260976 | + | 0.965345i | \(0.415956\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.04443 | −0.367173 | −0.183587 | − | 0.983004i | \(-0.558771\pi\) | ||||
−0.183587 | + | 0.983004i | \(0.558771\pi\) | |||||||
\(272\) | −26.7401 | −1.62136 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −53.6441 | −3.24076 | ||||||||
\(275\) | −5.13396 | −0.309590 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.06300 | 0.0638694 | 0.0319347 | − | 0.999490i | \(-0.489833\pi\) | ||||
0.0319347 | + | 0.999490i | \(0.489833\pi\) | |||||||
\(278\) | −1.48908 | −0.0893088 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −27.5879 | −1.64869 | ||||||||
\(281\) | 0.545199 | 0.0325239 | 0.0162619 | − | 0.999868i | \(-0.494823\pi\) | ||||
0.0162619 | + | 0.999868i | \(0.494823\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.1051 | 0.838461 | 0.419230 | − | 0.907880i | \(-0.362300\pi\) | ||||
0.419230 | + | 0.907880i | \(0.362300\pi\) | |||||||
\(284\) | −8.88079 | −0.526978 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.77102 | −0.222985 | ||||||||
\(287\) | −12.2989 | −0.725980 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.93418 | 0.349069 | ||||||||
\(290\) | −22.1972 | −1.30346 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 27.1337 | 1.58788 | ||||||||
\(293\) | 17.0930 | 0.998586 | 0.499293 | − | 0.866433i | \(-0.333593\pi\) | ||||
0.499293 | + | 0.866433i | \(0.333593\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.04378 | −0.0607711 | ||||||||
\(296\) | 4.73436 | 0.275179 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 41.1602 | 2.38435 | ||||||||
\(299\) | −1.52444 | −0.0881606 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −45.9837 | −2.65046 | ||||||||
\(302\) | 2.53157 | 0.145675 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 26.7585 | 1.53471 | ||||||||
\(305\) | 6.77868 | 0.388146 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.280920 | −0.0160329 | −0.00801646 | − | 0.999968i | \(-0.502552\pi\) | ||||
−0.00801646 | + | 0.999968i | \(0.502552\pi\) | |||||||
\(308\) | 106.912 | 6.09190 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −16.4580 | −0.934751 | ||||||||
\(311\) | 12.9003 | 0.731507 | 0.365753 | − | 0.930712i | \(-0.380811\pi\) | ||||
0.365753 | + | 0.930712i | \(0.380811\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.04911 | −0.172346 | −0.0861729 | − | 0.996280i | \(-0.527464\pi\) | ||||
−0.0861729 | + | 0.996280i | \(0.527464\pi\) | |||||||
\(314\) | −9.16241 | −0.517065 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.41115 | 0.135638 | ||||||||
\(317\) | −1.96859 | −0.110567 | −0.0552835 | − | 0.998471i | \(-0.517606\pi\) | ||||
−0.0552835 | + | 0.998471i | \(0.517606\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 45.5720 | 2.55154 | ||||||||
\(320\) | −4.43155 | −0.247731 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 63.5425 | 3.54108 | ||||||||
\(323\) | −22.9500 | −1.27697 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.293733 | 0.0162934 | ||||||||
\(326\) | −0.991107 | −0.0548923 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 14.1539 | 0.781517 | ||||||||
\(329\) | 39.4990 | 2.17765 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.6542 | 1.08029 | 0.540147 | − | 0.841571i | \(-0.318369\pi\) | ||||
0.540147 | + | 0.841571i | \(0.318369\pi\) | |||||||
\(332\) | −26.0543 | −1.42991 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 22.2876 | 1.21952 | ||||||||
\(335\) | −14.0551 | −0.767912 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.5743 | −1.06628 | −0.533140 | − | 0.846027i | \(-0.678988\pi\) | ||||
−0.533140 | + | 0.846027i | \(0.678988\pi\) | |||||||
\(338\) | −32.2927 | −1.75649 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −20.3687 | −1.10465 | ||||||||
\(341\) | 33.7891 | 1.82978 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −48.8254 | −2.63632 | ||||||||
\(344\) | 52.9193 | 2.85322 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −51.0372 | −2.74378 | ||||||||
\(347\) | −13.2711 | −0.712431 | −0.356215 | − | 0.934404i | \(-0.615933\pi\) | ||||
−0.356215 | + | 0.934404i | \(0.615933\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.7299 | 1.37729 | 0.688646 | − | 0.725097i | \(-0.258205\pi\) | ||||
0.688646 | + | 0.725097i | \(0.258205\pi\) | |||||||
\(350\) | −12.2435 | −0.654445 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −13.8290 | −0.737088 | ||||||||
\(353\) | −33.4472 | −1.78022 | −0.890108 | − | 0.455750i | \(-0.849371\pi\) | ||||
−0.890108 | + | 0.455750i | \(0.849371\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.08800 | −0.110819 | ||||||||
\(356\) | −4.25326 | −0.225422 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.65137 | 0.510091 | ||||||||
\(359\) | −2.49760 | −0.131818 | −0.0659090 | − | 0.997826i | \(-0.520995\pi\) | ||||
−0.0659090 | + | 0.997826i | \(0.520995\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.96581 | 0.208727 | ||||||||
\(362\) | −12.1450 | −0.638327 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.11687 | −0.320611 | ||||||||
\(365\) | 6.37951 | 0.333919 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.2573 | −1.63162 | −0.815810 | − | 0.578320i | \(-0.803708\pi\) | ||||
−0.815810 | + | 0.578320i | \(0.803708\pi\) | |||||||
\(368\) | −28.9786 | −1.51062 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.10112 | 0.109232 | ||||||||
\(371\) | −55.9866 | −2.90668 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −35.2179 | −1.82351 | −0.911757 | − | 0.410730i | \(-0.865274\pi\) | ||||
−0.911757 | + | 0.410730i | \(0.865274\pi\) | |||||||
\(374\) | 61.4819 | 3.17915 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −45.4566 | −2.34424 | ||||||||
\(377\) | −2.60735 | −0.134285 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.50658 | −0.180121 | −0.0900605 | − | 0.995936i | \(-0.528706\pi\) | ||||
−0.0900605 | + | 0.995936i | \(0.528706\pi\) | |||||||
\(380\) | 20.3827 | 1.04561 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −18.6218 | −0.952776 | ||||||||
\(383\) | −21.9576 | −1.12198 | −0.560991 | − | 0.827822i | \(-0.689580\pi\) | ||||
−0.560991 | + | 0.827822i | \(0.689580\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 25.1366 | 1.28108 | ||||||||
\(386\) | −19.2198 | −0.978263 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −15.6823 | −0.796147 | ||||||||
\(389\) | 13.3115 | 0.674918 | 0.337459 | − | 0.941340i | \(-0.390433\pi\) | ||||
0.337459 | + | 0.941340i | \(0.390433\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.8541 | 1.25693 | ||||||||
\(392\) | 95.6318 | 4.83014 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 67.4682 | 3.39900 | ||||||||
\(395\) | 0.566895 | 0.0285236 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.8358 | 0.895155 | 0.447578 | − | 0.894245i | \(-0.352287\pi\) | ||||
0.447578 | + | 0.894245i | \(0.352287\pi\) | |||||||
\(398\) | 13.1095 | 0.657118 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.58369 | 0.279184 | ||||||||
\(401\) | 3.19387 | 0.159494 | 0.0797471 | − | 0.996815i | \(-0.474589\pi\) | ||||
0.0797471 | + | 0.996815i | \(0.474589\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.93320 | −0.0962996 | ||||||||
\(404\) | 28.8859 | 1.43713 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 108.681 | 5.39373 | ||||||||
\(407\) | −4.31370 | −0.213822 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.5244 | −1.21266 | −0.606328 | − | 0.795215i | \(-0.707358\pi\) | ||||
−0.606328 | + | 0.795215i | \(0.707358\pi\) | |||||||
\(410\) | 6.28152 | 0.310222 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 43.2216 | 2.12938 | ||||||||
\(413\) | 5.11048 | 0.251470 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.12572 | −0.300700 | ||||||||
\(416\) | 0.791209 | 0.0387922 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −61.5243 | −3.00925 | ||||||||
\(419\) | −4.89589 | −0.239180 | −0.119590 | − | 0.992823i | \(-0.538158\pi\) | ||||
−0.119590 | + | 0.992823i | \(0.538158\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.48965 | 0.218812 | 0.109406 | − | 0.993997i | \(-0.465105\pi\) | ||||
0.109406 | + | 0.993997i | \(0.465105\pi\) | |||||||
\(422\) | −1.27401 | −0.0620177 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 64.4309 | 3.12904 | ||||||||
\(425\) | −4.78896 | −0.232299 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −33.1894 | −1.60615 | ||||||||
\(428\) | −33.8505 | −1.63623 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 23.4857 | 1.13258 | ||||||||
\(431\) | −35.8073 | −1.72477 | −0.862387 | − | 0.506249i | \(-0.831032\pi\) | ||||
−0.862387 | + | 0.506249i | \(0.831032\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.7569 | −0.901399 | −0.450700 | − | 0.892676i | \(-0.648825\pi\) | ||||
−0.450700 | + | 0.892676i | \(0.648825\pi\) | |||||||
\(434\) | 80.5807 | 3.86800 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −16.6396 | −0.796892 | ||||||||
\(437\) | −24.8713 | −1.18975 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.4002 | 1.49865 | 0.749325 | − | 0.662202i | \(-0.230378\pi\) | ||||
0.749325 | + | 0.662202i | \(0.230378\pi\) | |||||||
\(440\) | −28.9279 | −1.37908 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.51761 | −0.167316 | ||||||||
\(443\) | 25.6079 | 1.21667 | 0.608334 | − | 0.793681i | \(-0.291838\pi\) | ||||
0.608334 | + | 0.793681i | \(0.291838\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.00000 | −0.0474045 | ||||||||
\(446\) | 27.8347 | 1.31801 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 21.6975 | 1.02511 | ||||||||
\(449\) | 21.3542 | 1.00777 | 0.503883 | − | 0.863772i | \(-0.331904\pi\) | ||||
0.503883 | + | 0.863772i | \(0.331904\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.8963 | −0.607261 | ||||||||
\(452\) | 34.8329 | 1.63840 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.75792 | 0.176368 | ||||||||
\(455\) | −1.43816 | −0.0674220 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.2671 | −1.27550 | −0.637750 | − | 0.770243i | \(-0.720135\pi\) | ||||
−0.637750 | + | 0.770243i | \(0.720135\pi\) | |||||||
\(458\) | −20.2007 | −0.943916 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −22.0739 | −1.02920 | ||||||||
\(461\) | 18.9331 | 0.881801 | 0.440900 | − | 0.897556i | \(-0.354659\pi\) | ||||
0.440900 | + | 0.897556i | \(0.354659\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.1659 | 1.40193 | 0.700965 | − | 0.713196i | \(-0.252753\pi\) | ||||
0.700965 | + | 0.713196i | \(0.252753\pi\) | |||||||
\(464\) | −49.5640 | −2.30095 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −23.6414 | −1.09517 | ||||||||
\(467\) | −34.1721 | −1.58130 | −0.790649 | − | 0.612270i | \(-0.790257\pi\) | ||||
−0.790649 | + | 0.612270i | \(0.790257\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 68.8157 | 3.17762 | ||||||||
\(470\) | −20.1737 | −0.930544 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.88128 | −0.270708 | ||||||||
\(473\) | −48.2173 | −2.21703 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.79227 | 0.219884 | ||||||||
\(476\) | 99.7281 | 4.57103 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 23.4787 | 1.07389 | ||||||||
\(479\) | −19.0555 | −0.870666 | −0.435333 | − | 0.900269i | \(-0.643369\pi\) | ||||
−0.435333 | + | 0.900269i | \(0.643369\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.246803 | 0.0112532 | ||||||||
\(482\) | −2.85917 | −0.130232 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 65.3196 | 2.96907 | ||||||||
\(485\) | −3.68712 | −0.167424 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.7093 | 1.16500 | 0.582501 | − | 0.812830i | \(-0.302074\pi\) | ||||
0.582501 | + | 0.812830i | \(0.302074\pi\) | |||||||
\(488\) | 38.1952 | 1.72902 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 42.4416 | 1.91732 | ||||||||
\(491\) | −21.1649 | −0.955158 | −0.477579 | − | 0.878589i | \(-0.658486\pi\) | ||||
−0.477579 | + | 0.878589i | \(0.658486\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 42.5096 | 1.91454 | ||||||||
\(494\) | 3.52004 | 0.158374 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −36.7489 | −1.65008 | ||||||||
\(497\) | 10.2231 | 0.458570 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.0315 | 1.12056 | 0.560281 | − | 0.828302i | \(-0.310693\pi\) | ||||
0.560281 | + | 0.828302i | \(0.310693\pi\) | |||||||
\(500\) | 4.25326 | 0.190211 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 41.9141 | 1.87072 | ||||||||
\(503\) | −5.82665 | −0.259797 | −0.129899 | − | 0.991527i | \(-0.541465\pi\) | ||||
−0.129899 | + | 0.991527i | \(0.541465\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.79147 | 0.302217 | ||||||||
\(506\) | 66.6289 | 2.96202 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.63836 | −0.383265 | ||||||||
\(509\) | 13.7961 | 0.611503 | 0.305752 | − | 0.952111i | \(-0.401092\pi\) | ||||
0.305752 | + | 0.952111i | \(0.401092\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −31.2350 | −1.38175 | ||||||||
\(512\) | −47.8834 | −2.11617 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −43.1854 | −1.90483 | ||||||||
\(515\) | 10.1620 | 0.447792 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 41.4176 | 1.82154 | ||||||||
\(518\) | −10.2874 | −0.452001 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.65507 | 0.0725798 | ||||||||
\(521\) | −34.4027 | −1.50721 | −0.753604 | − | 0.657329i | \(-0.771686\pi\) | ||||
−0.753604 | + | 0.657329i | \(0.771686\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.0955 | −1.09735 | −0.548674 | − | 0.836036i | \(-0.684867\pi\) | ||||
−0.548674 | + | 0.836036i | \(0.684867\pi\) | |||||||
\(524\) | −41.3375 | −1.80584 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −68.3081 | −2.97838 | ||||||||
\(527\) | 31.5185 | 1.37297 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.93481 | 0.171079 | ||||||||
\(530\) | 28.5945 | 1.24207 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −99.7968 | −4.32674 | ||||||||
\(533\) | 0.737844 | 0.0319596 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.95873 | −0.344086 | ||||||||
\(536\) | −79.1950 | −3.42070 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 21.4072 | 0.922931 | ||||||||
\(539\) | −87.1347 | −3.75316 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.2525 | 0.698750 | 0.349375 | − | 0.936983i | \(-0.386394\pi\) | ||||
0.349375 | + | 0.936983i | \(0.386394\pi\) | |||||||
\(542\) | −15.1150 | −0.649246 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −12.8997 | −0.553070 | ||||||||
\(545\) | −3.91220 | −0.167580 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.3751 | 0.742905 | 0.371452 | − | 0.928452i | \(-0.378860\pi\) | ||||
0.371452 | + | 0.928452i | \(0.378860\pi\) | |||||||
\(548\) | −91.2411 | −3.89762 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −12.8382 | −0.547425 | ||||||||
\(551\) | −42.5389 | −1.81222 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.77560 | −0.118030 | ||||||||
\(554\) | 2.65819 | 0.112936 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.53271 | −0.107411 | ||||||||
\(557\) | 43.3855 | 1.83830 | 0.919152 | − | 0.393904i | \(-0.128876\pi\) | ||||
0.919152 | + | 0.393904i | \(0.128876\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.75869 | 0.116680 | ||||||||
\(560\) | −27.3385 | −1.15526 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.36335 | 0.0575096 | ||||||||
\(563\) | −14.5950 | −0.615108 | −0.307554 | − | 0.951531i | \(-0.599510\pi\) | ||||
−0.307554 | + | 0.951531i | \(0.599510\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.18970 | 0.344543 | ||||||||
\(566\) | 35.2719 | 1.48259 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.7651 | −0.493651 | ||||||||
\(569\) | 25.4644 | 1.06752 | 0.533762 | − | 0.845635i | \(-0.320778\pi\) | ||||
0.533762 | + | 0.845635i | \(0.320778\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.34046 | 0.139794 | 0.0698969 | − | 0.997554i | \(-0.477733\pi\) | ||||
0.0698969 | + | 0.997554i | \(0.477733\pi\) | |||||||
\(572\) | −6.41398 | −0.268182 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −30.7552 | −1.28370 | ||||||||
\(575\) | −5.18988 | −0.216433 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.9214 | −1.20401 | −0.602007 | − | 0.798491i | \(-0.705632\pi\) | ||||
−0.602007 | + | 0.798491i | \(0.705632\pi\) | |||||||
\(578\) | 14.8393 | 0.617234 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −37.7543 | −1.56766 | ||||||||
\(581\) | 29.9924 | 1.24429 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −58.7060 | −2.43135 | ||||||||
\(584\) | 35.9460 | 1.48746 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 42.7437 | 1.76573 | ||||||||
\(587\) | −16.5407 | −0.682706 | −0.341353 | − | 0.939935i | \(-0.610885\pi\) | ||||
−0.341353 | + | 0.939935i | \(0.610885\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −31.5402 | −1.29959 | ||||||||
\(590\) | −2.61012 | −0.107457 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.69157 | 0.192822 | ||||||||
\(593\) | 27.0667 | 1.11150 | 0.555748 | − | 0.831351i | \(-0.312432\pi\) | ||||
0.555748 | + | 0.831351i | \(0.312432\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 23.4475 | 0.961252 | ||||||||
\(596\) | 70.0078 | 2.86763 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.81209 | −0.155888 | ||||||||
\(599\) | −7.11352 | −0.290651 | −0.145325 | − | 0.989384i | \(-0.546423\pi\) | ||||
−0.145325 | + | 0.989384i | \(0.546423\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −42.8950 | −1.74972 | −0.874861 | − | 0.484374i | \(-0.839047\pi\) | ||||
−0.874861 | + | 0.484374i | \(0.839047\pi\) | |||||||
\(602\) | −114.989 | −4.68661 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.30584 | 0.175202 | ||||||||
\(605\) | 15.3576 | 0.624373 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.9087 | −1.13278 | −0.566390 | − | 0.824137i | \(-0.691660\pi\) | ||||
−0.566390 | + | 0.824137i | \(0.691660\pi\) | |||||||
\(608\) | 12.9086 | 0.523512 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 16.9511 | 0.686331 | ||||||||
\(611\) | −2.36966 | −0.0958662 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.2291 | 0.453538 | 0.226769 | − | 0.973949i | \(-0.427184\pi\) | ||||
0.226769 | + | 0.973949i | \(0.427184\pi\) | |||||||
\(614\) | −0.702482 | −0.0283499 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 141.635 | 5.70664 | ||||||||
\(617\) | 29.7394 | 1.19726 | 0.598631 | − | 0.801025i | \(-0.295712\pi\) | ||||
0.598631 | + | 0.801025i | \(0.295712\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −47.0184 | −1.88983 | −0.944915 | − | 0.327315i | \(-0.893856\pi\) | ||||
−0.944915 | + | 0.327315i | \(0.893856\pi\) | |||||||
\(620\) | −27.9927 | −1.12422 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 32.2591 | 1.29347 | ||||||||
\(623\) | 4.89614 | 0.196160 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −7.62476 | −0.304747 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −15.5840 | −0.621869 | ||||||||
\(629\) | −4.02382 | −0.160440 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.61993 | −0.183917 | −0.0919583 | − | 0.995763i | \(-0.529313\pi\) | ||||
−0.0919583 | + | 0.995763i | \(0.529313\pi\) | |||||||
\(632\) | 3.19423 | 0.127060 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.92276 | −0.195508 | ||||||||
\(635\) | −2.03100 | −0.0805978 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.98531 | 0.197525 | ||||||||
\(638\) | 113.960 | 4.51170 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −16.4690 | −0.650995 | ||||||||
\(641\) | 0.763355 | 0.0301507 | 0.0150754 | − | 0.999886i | \(-0.495201\pi\) | ||||
0.0150754 | + | 0.999886i | \(0.495201\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.5483 | −0.968091 | −0.484046 | − | 0.875043i | \(-0.660833\pi\) | ||||
−0.484046 | + | 0.875043i | \(0.660833\pi\) | |||||||
\(644\) | 108.077 | 4.25882 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −57.3899 | −2.25798 | ||||||||
\(647\) | 20.9739 | 0.824567 | 0.412284 | − | 0.911056i | \(-0.364731\pi\) | ||||
0.412284 | + | 0.911056i | \(0.364731\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.35871 | 0.210348 | ||||||||
\(650\) | 0.734525 | 0.0288104 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.68573 | −0.0660185 | ||||||||
\(653\) | 0.521815 | 0.0204202 | 0.0102101 | − | 0.999948i | \(-0.496750\pi\) | ||||
0.0102101 | + | 0.999948i | \(0.496750\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.71902 | −0.379754 | ||||||||
\(656\) | 14.0260 | 0.547621 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 98.7733 | 3.85059 | ||||||||
\(659\) | −1.63679 | −0.0637603 | −0.0318802 | − | 0.999492i | \(-0.510149\pi\) | ||||
−0.0318802 | + | 0.999492i | \(0.510149\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.0711 | 0.975151 | 0.487576 | − | 0.873081i | \(-0.337881\pi\) | ||||
0.487576 | + | 0.873081i | \(0.337881\pi\) | |||||||
\(662\) | 49.1484 | 1.91021 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −34.5161 | −1.33948 | ||||||||
\(665\) | −23.4636 | −0.909880 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 46.0683 | 1.78377 | ||||||||
\(668\) | 37.9081 | 1.46671 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −35.1469 | −1.35784 | ||||||||
\(671\) | −34.8015 | −1.34350 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −33.2875 | −1.28314 | −0.641569 | − | 0.767065i | \(-0.721716\pi\) | ||||
−0.641569 | + | 0.767065i | \(0.721716\pi\) | |||||||
\(674\) | −48.9485 | −1.88542 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −54.9254 | −2.11251 | ||||||||
\(677\) | −17.5066 | −0.672834 | −0.336417 | − | 0.941713i | \(-0.609215\pi\) | ||||
−0.336417 | + | 0.941713i | \(0.609215\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.0527 | 0.692798 | ||||||||
\(680\) | −26.9840 | −1.03479 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 84.4947 | 3.23547 | ||||||||
\(683\) | 46.2972 | 1.77151 | 0.885757 | − | 0.464150i | \(-0.153640\pi\) | ||||
0.885757 | + | 0.464150i | \(0.153640\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.4520 | −0.819640 | ||||||||
\(686\) | −122.095 | −4.66162 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 52.4410 | 1.99930 | ||||||||
\(689\) | 3.35879 | 0.127960 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.46210 | 0.169746 | 0.0848732 | − | 0.996392i | \(-0.472951\pi\) | ||||
0.0848732 | + | 0.996392i | \(0.472951\pi\) | |||||||
\(692\) | −86.8071 | −3.29991 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −33.1864 | −1.25974 | ||||||||
\(695\) | −0.595475 | −0.0225877 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.0296 | −0.455655 | ||||||||
\(698\) | 64.3416 | 2.43537 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −20.8246 | −0.787094 | ||||||||
\(701\) | 5.13544 | 0.193963 | 0.0969815 | − | 0.995286i | \(-0.469081\pi\) | ||||
0.0969815 | + | 0.995286i | \(0.469081\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.02659 | 0.151866 | ||||||||
\(704\) | 22.7514 | 0.857475 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −83.6398 | −3.14783 | ||||||||
\(707\) | −33.2520 | −1.25057 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.95502 | 0.186090 | 0.0930449 | − | 0.995662i | \(-0.470340\pi\) | ||||
0.0930449 | + | 0.995662i | \(0.470340\pi\) | |||||||
\(710\) | −5.22136 | −0.195954 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.63461 | −0.211166 | ||||||||
\(713\) | 34.1571 | 1.27919 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.50802 | −0.0563966 | ||||||||
\(716\) | 16.4156 | 0.613481 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.24562 | −0.233084 | ||||||||
\(719\) | 32.2241 | 1.20176 | 0.600878 | − | 0.799341i | \(-0.294818\pi\) | ||||
0.600878 | + | 0.799341i | \(0.294818\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −49.7546 | −1.85296 | ||||||||
\(722\) | 9.91712 | 0.369077 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −20.6570 | −0.767710 | ||||||||
\(725\) | −8.87657 | −0.329668 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31.3167 | −1.16147 | −0.580735 | − | 0.814093i | \(-0.697235\pi\) | ||||
−0.580735 | + | 0.814093i | \(0.697235\pi\) | |||||||
\(728\) | −8.10348 | −0.300335 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 15.9529 | 0.590444 | ||||||||
\(731\) | −44.9771 | −1.66354 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.84406 | −0.0681118 | −0.0340559 | − | 0.999420i | \(-0.510842\pi\) | ||||
−0.0340559 | + | 0.999420i | \(0.510842\pi\) | |||||||
\(734\) | −78.1637 | −2.88508 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −13.9796 | −0.515295 | ||||||||
\(737\) | 72.1583 | 2.65799 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.1432 | 0.851338 | 0.425669 | − | 0.904879i | \(-0.360039\pi\) | ||||
0.425669 | + | 0.904879i | \(0.360039\pi\) | |||||||
\(740\) | 3.57371 | 0.131372 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −140.003 | −5.13967 | ||||||||
\(743\) | 2.13174 | 0.0782059 | 0.0391029 | − | 0.999235i | \(-0.487550\pi\) | ||||
0.0391029 | + | 0.999235i | \(0.487550\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.4598 | 0.603041 | ||||||||
\(746\) | −88.0677 | −3.22439 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 104.572 | 3.82354 | ||||||||
\(749\) | 38.9671 | 1.42383 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.83764 | 0.358981 | 0.179490 | − | 0.983760i | \(-0.442555\pi\) | ||||
0.179490 | + | 0.983760i | \(0.442555\pi\) | |||||||
\(752\) | −45.0457 | −1.64265 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.52006 | −0.237447 | ||||||||
\(755\) | 1.01236 | 0.0368436 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.2109 | −1.38880 | −0.694400 | − | 0.719590i | \(-0.744330\pi\) | ||||
−0.694400 | + | 0.719590i | \(0.744330\pi\) | |||||||
\(758\) | −8.76874 | −0.318495 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 27.0026 | 0.979486 | ||||||||
\(761\) | 5.67543 | 0.205734 | 0.102867 | − | 0.994695i | \(-0.467198\pi\) | ||||
0.102867 | + | 0.994695i | \(0.467198\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.1547 | 0.693446 | ||||||||
\(764\) | −31.6731 | −1.14589 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −54.9083 | −1.98392 | ||||||||
\(767\) | −0.306592 | −0.0110704 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.1784 | 0.691590 | 0.345795 | − | 0.938310i | \(-0.387609\pi\) | ||||
0.345795 | + | 0.938310i | \(0.387609\pi\) | |||||||
\(770\) | 62.8579 | 2.26524 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −32.6902 | −1.17655 | ||||||||
\(773\) | −26.8742 | −0.966598 | −0.483299 | − | 0.875455i | \(-0.660562\pi\) | ||||
−0.483299 | + | 0.875455i | \(0.660562\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.58148 | −0.236414 | ||||||||
\(776\) | −20.7755 | −0.745797 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 33.2873 | 1.19341 | ||||||||
\(779\) | 12.0379 | 0.431304 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.7197 | 0.383581 | ||||||||
\(782\) | 62.1515 | 2.22253 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 94.7675 | 3.38455 | ||||||||
\(785\) | −3.66401 | −0.130774 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.4331 | 0.407546 | 0.203773 | − | 0.979018i | \(-0.434680\pi\) | ||||
0.203773 | + | 0.979018i | \(0.434680\pi\) | |||||||
\(788\) | 114.754 | 4.08794 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.41761 | 0.0504362 | ||||||||
\(791\) | −40.0980 | −1.42572 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.99113 | 0.0707069 | ||||||||
\(794\) | 44.6012 | 1.58284 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 22.2974 | 0.790309 | ||||||||
\(797\) | 38.2874 | 1.35621 | 0.678105 | − | 0.734965i | \(-0.262801\pi\) | ||||
0.678105 | + | 0.734965i | \(0.262801\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 38.6344 | 1.36679 | ||||||||
\(800\) | 2.69363 | 0.0952342 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.98676 | 0.282022 | ||||||||
\(803\) | −32.7521 | −1.15580 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 25.4104 | 0.895598 | ||||||||
\(806\) | −4.83426 | −0.170280 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 38.2673 | 1.34624 | ||||||||
\(809\) | 4.98203 | 0.175159 | 0.0875794 | − | 0.996158i | \(-0.472087\pi\) | ||||
0.0875794 | + | 0.996158i | \(0.472087\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.56566 | 0.0900924 | 0.0450462 | − | 0.998985i | \(-0.485656\pi\) | ||||
0.0450462 | + | 0.998985i | \(0.485656\pi\) | |||||||
\(812\) | 184.851 | 6.48699 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −10.7871 | −0.378086 | ||||||||
\(815\) | −0.396340 | −0.0138832 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 45.0082 | 1.57464 | ||||||||
\(818\) | −61.3271 | −2.14425 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.6840 | 0.373101 | ||||||||
\(821\) | −7.39548 | −0.258104 | −0.129052 | − | 0.991638i | \(-0.541193\pi\) | ||||
−0.129052 | + | 0.991638i | \(0.541193\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.2404 | 0.496389 | 0.248195 | − | 0.968710i | \(-0.420163\pi\) | ||||
0.248195 | + | 0.968710i | \(0.420163\pi\) | |||||||
\(824\) | 57.2590 | 1.99471 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.7795 | 0.444657 | ||||||||
\(827\) | 22.1225 | 0.769273 | 0.384637 | − | 0.923068i | \(-0.374327\pi\) | ||||
0.384637 | + | 0.923068i | \(0.374327\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 43.2604 | 1.50250 | 0.751248 | − | 0.660021i | \(-0.229452\pi\) | ||||
0.751248 | + | 0.660021i | \(0.229452\pi\) | |||||||
\(830\) | −15.3183 | −0.531706 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.30169 | −0.0451281 | ||||||||
\(833\) | −81.2793 | −2.81616 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.91272 | 0.308437 | ||||||||
\(836\) | −104.644 | −3.61920 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −12.2429 | −0.422925 | ||||||||
\(839\) | 6.71522 | 0.231835 | 0.115917 | − | 0.993259i | \(-0.463019\pi\) | ||||
0.115917 | + | 0.993259i | \(0.463019\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 49.7935 | 1.71702 | ||||||||
\(842\) | 11.2271 | 0.386910 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.16691 | −0.0745880 | ||||||||
\(845\) | −12.9137 | −0.444245 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −75.1928 | −2.58365 | ||||||||
\(848\) | 63.8486 | 2.19257 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −11.9755 | −0.410757 | ||||||||
\(851\) | −4.36068 | −0.149482 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.93209 | −0.134632 | −0.0673160 | − | 0.997732i | \(-0.521444\pi\) | ||||
−0.0673160 | + | 0.997732i | \(0.521444\pi\) | |||||||
\(854\) | −82.9951 | −2.84003 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −44.8443 | −1.53275 | ||||||||
\(857\) | 4.62748 | 0.158072 | 0.0790358 | − | 0.996872i | \(-0.474816\pi\) | ||||
0.0790358 | + | 0.996872i | \(0.474816\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.7777 | −0.674805 | −0.337403 | − | 0.941360i | \(-0.609548\pi\) | ||||
−0.337403 | + | 0.941360i | \(0.609548\pi\) | |||||||
\(860\) | 39.9459 | 1.36214 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −89.5415 | −3.04979 | ||||||||
\(863\) | −8.03916 | −0.273656 | −0.136828 | − | 0.990595i | \(-0.543691\pi\) | ||||
−0.136828 | + | 0.990595i | \(0.543691\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.4096 | −0.693946 | ||||||||
\(866\) | −46.9045 | −1.59388 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 137.056 | 4.65200 | ||||||||
\(869\) | −2.91042 | −0.0987292 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.12845 | −0.139887 | ||||||||
\(872\) | −22.0437 | −0.746495 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −62.1944 | −2.10376 | ||||||||
\(875\) | −4.89614 | −0.165520 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 55.5811 | 1.87684 | 0.938420 | − | 0.345496i | \(-0.112289\pi\) | ||||
0.938420 | + | 0.345496i | \(0.112289\pi\) | |||||||
\(878\) | 78.5210 | 2.64996 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −28.6664 | −0.966345 | ||||||||
\(881\) | −44.8890 | −1.51235 | −0.756174 | − | 0.654370i | \(-0.772934\pi\) | ||||
−0.756174 | + | 0.654370i | \(0.772934\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.5457 | −0.455848 | −0.227924 | − | 0.973679i | \(-0.573194\pi\) | ||||
−0.227924 | + | 0.973679i | \(0.573194\pi\) | |||||||
\(884\) | −5.98297 | −0.201229 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 64.0364 | 2.15135 | ||||||||
\(887\) | −36.1333 | −1.21324 | −0.606619 | − | 0.794992i | \(-0.707475\pi\) | ||||
−0.606619 | + | 0.794992i | \(0.707475\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.94406 | 0.333513 | ||||||||
\(890\) | −2.50065 | −0.0838220 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 47.3429 | 1.58516 | ||||||||
\(893\) | −38.6610 | −1.29374 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.85954 | 0.129010 | ||||||||
\(896\) | 80.6346 | 2.69381 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 53.3994 | 1.78196 | ||||||||
\(899\) | 58.4210 | 1.94845 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −54.7610 | −1.82435 | ||||||||
\(902\) | −32.2491 | −1.07378 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 46.1458 | 1.53479 | ||||||||
\(905\) | −4.85674 | −0.161443 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41.6649 | −1.38346 | −0.691730 | − | 0.722156i | \(-0.743151\pi\) | ||||
−0.691730 | + | 0.722156i | \(0.743151\pi\) | |||||||
\(908\) | 6.39169 | 0.212116 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.59634 | −0.119217 | ||||||||
\(911\) | 55.3548 | 1.83399 | 0.916993 | − | 0.398903i | \(-0.130609\pi\) | ||||
0.916993 | + | 0.398903i | \(0.130609\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31.4492 | 1.04082 | ||||||||
\(914\) | −68.1855 | −2.25537 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −34.3585 | −1.13524 | ||||||||
\(917\) | 47.5857 | 1.57142 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.44714 | 0.311633 | 0.155816 | − | 0.987786i | \(-0.450199\pi\) | ||||
0.155816 | + | 0.987786i | \(0.450199\pi\) | |||||||
\(920\) | −29.2429 | −0.964111 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 47.3450 | 1.55922 | ||||||||
\(923\) | −0.613315 | −0.0201875 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.840228 | 0.0276265 | ||||||||
\(926\) | 75.4345 | 2.47893 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −23.9102 | −0.784890 | ||||||||
\(929\) | 23.0801 | 0.757234 | 0.378617 | − | 0.925553i | \(-0.376400\pi\) | ||||
0.378617 | + | 0.925553i | \(0.376400\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 81.3353 | 2.66566 | ||||||||
\(932\) | −40.2107 | −1.31715 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −85.4526 | −2.79609 | ||||||||
\(935\) | 24.5864 | 0.804060 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.4855 | 1.02859 | 0.514293 | − | 0.857615i | \(-0.328054\pi\) | ||||
0.514293 | + | 0.857615i | \(0.328054\pi\) | |||||||
\(938\) | 172.084 | 5.61875 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −34.3126 | −1.11916 | ||||||||
\(941\) | −16.7640 | −0.546492 | −0.273246 | − | 0.961944i | \(-0.588097\pi\) | ||||
−0.273246 | + | 0.961944i | \(0.588097\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.0367 | −0.424534 | ||||||||
\(944\) | −5.82812 | −0.189689 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −120.575 | −3.92022 | ||||||||
\(947\) | 59.7924 | 1.94299 | 0.971497 | − | 0.237053i | \(-0.0761816\pi\) | ||||
0.971497 | + | 0.237053i | \(0.0761816\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.87387 | 0.0608285 | ||||||||
\(950\) | 11.9838 | 0.388805 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 132.117 | 4.28195 | ||||||||
\(953\) | −17.8565 | −0.578428 | −0.289214 | − | 0.957264i | \(-0.593394\pi\) | ||||
−0.289214 | + | 0.957264i | \(0.593394\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.44680 | −0.240973 | ||||||||
\(956\) | 39.9340 | 1.29156 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −47.6511 | −1.53954 | ||||||||
\(959\) | 105.032 | 3.39167 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.3159 | 0.397287 | ||||||||
\(962\) | 0.617168 | 0.0198983 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.86305 | −0.156628 | ||||||||
\(965\) | −7.68593 | −0.247419 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.9918 | −1.02879 | −0.514393 | − | 0.857554i | \(-0.671983\pi\) | ||||
−0.514393 | + | 0.857554i | \(0.671983\pi\) | |||||||
\(968\) | 86.5339 | 2.78130 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9.22021 | −0.296043 | ||||||||
\(971\) | −13.8839 | −0.445555 | −0.222778 | − | 0.974869i | \(-0.571512\pi\) | ||||
−0.222778 | + | 0.974869i | \(0.571512\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.91553 | 0.0934676 | ||||||||
\(974\) | 64.2901 | 2.05999 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 37.8500 | 1.21155 | ||||||||
\(977\) | −5.04704 | −0.161469 | −0.0807346 | − | 0.996736i | \(-0.525727\pi\) | ||||
−0.0807346 | + | 0.996736i | \(0.525727\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.13396 | 0.164082 | ||||||||
\(980\) | 72.1872 | 2.30593 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −52.9260 | −1.68894 | ||||||||
\(983\) | 26.6803 | 0.850971 | 0.425485 | − | 0.904965i | \(-0.360103\pi\) | ||||
0.425485 | + | 0.904965i | \(0.360103\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26.9802 | 0.859662 | ||||||||
\(986\) | 106.302 | 3.38533 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.98709 | 0.190475 | ||||||||
\(989\) | −48.7424 | −1.54992 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.2339 | −1.18277 | −0.591386 | − | 0.806388i | \(-0.701419\pi\) | ||||
−0.591386 | + | 0.806388i | \(0.701419\pi\) | |||||||
\(992\) | −17.7281 | −0.562867 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 25.5645 | 0.810857 | ||||||||
\(995\) | 5.24242 | 0.166196 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.6534 | −0.495748 | −0.247874 | − | 0.968792i | \(-0.579732\pi\) | ||||
−0.247874 | + | 0.968792i | \(0.579732\pi\) | |||||||
\(998\) | 62.5950 | 1.98141 | ||||||||
\(999\) | 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.p.1.8 | 8 | ||
3.2 | odd | 2 | 445.2.a.g.1.1 | ✓ | 8 | ||
12.11 | even | 2 | 7120.2.a.bk.1.4 | 8 | |||
15.14 | odd | 2 | 2225.2.a.l.1.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
445.2.a.g.1.1 | ✓ | 8 | 3.2 | odd | 2 | ||
2225.2.a.l.1.8 | 8 | 15.14 | odd | 2 | |||
4005.2.a.p.1.8 | 8 | 1.1 | even | 1 | trivial | ||
7120.2.a.bk.1.4 | 8 | 12.11 | even | 2 |