Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4004,2,Mod(1,4004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4004.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: | \(31.9721009693\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 18x^{8} + 32x^{7} + 93x^{6} - 119x^{5} - 174x^{4} + 107x^{3} + 51x^{2} - 17x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-1.59443\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4004.1 |
$q$-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 | 0 | ||||||||
\(3\) | 1.59443 | 0.920546 | 0.460273 | − | 0.887777i | \(-0.347751\pi\) | ||||
0.460273 | + | 0.887777i | \(0.347751\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.37026 | 1.95444 | 0.977221 | − | 0.212226i | \(-0.0680712\pi\) | ||||
0.977221 | + | 0.212226i | \(0.0680712\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.457782 | −0.152594 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.96809 | 1.79915 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.00996 | 1.21509 | 0.607547 | − | 0.794284i | \(-0.292154\pi\) | ||||
0.607547 | + | 0.794284i | \(0.292154\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.82903 | 1.33727 | 0.668635 | − | 0.743591i | \(-0.266879\pi\) | ||||
0.668635 | + | 0.743591i | \(0.266879\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.59443 | −0.347934 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.91986 | 1.02586 | 0.512931 | − | 0.858430i | \(-0.328560\pi\) | ||||
0.512931 | + | 0.858430i | \(0.328560\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 14.0992 | 2.81984 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.51320 | −1.06102 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.0873354 | −0.0162178 | −0.00810889 | − | 0.999967i | \(-0.502581\pi\) | ||||
−0.00810889 | + | 0.999967i | \(0.502581\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.3085 | −1.85146 | −0.925732 | − | 0.378181i | \(-0.876550\pi\) | ||||
−0.925732 | + | 0.378181i | \(0.876550\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.59443 | −0.277555 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.37026 | −0.738709 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.36576 | −0.717727 | −0.358863 | − | 0.933390i | \(-0.616836\pi\) | ||||
−0.358863 | + | 0.933390i | \(0.616836\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.59443 | −0.255314 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.46920 | 0.541797 | 0.270899 | − | 0.962608i | \(-0.412679\pi\) | ||||
0.270899 | + | 0.962608i | \(0.412679\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.3014 | 1.57094 | 0.785471 | − | 0.618899i | \(-0.212421\pi\) | ||||
0.785471 | + | 0.618899i | \(0.212421\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.00063 | −0.298236 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.16163 | 0.752901 | 0.376451 | − | 0.926437i | \(-0.377144\pi\) | ||||
0.376451 | + | 0.926437i | \(0.377144\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.98805 | 1.11855 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.50483 | 1.30559 | 0.652794 | − | 0.757535i | \(-0.273597\pi\) | ||||
0.652794 | + | 0.757535i | \(0.273597\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.37026 | −0.589286 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.29399 | 1.23102 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.3958 | −1.61380 | −0.806901 | − | 0.590687i | \(-0.798857\pi\) | ||||
−0.806901 | + | 0.590687i | \(0.798857\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.50512 | −0.960932 | −0.480466 | − | 0.877013i | \(-0.659533\pi\) | ||||
−0.480466 | + | 0.877013i | \(0.659533\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.457782 | 0.0576752 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.37026 | −0.542065 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.26781 | −0.643565 | −0.321783 | − | 0.946814i | \(-0.604282\pi\) | ||||
−0.321783 | + | 0.946814i | \(0.604282\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.84439 | 0.944353 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.1711 | −1.80048 | −0.900242 | − | 0.435391i | \(-0.856610\pi\) | ||||
−0.900242 | + | 0.435391i | \(0.856610\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.63392 | 0.308277 | 0.154139 | − | 0.988049i | \(-0.450740\pi\) | ||||
0.154139 | + | 0.988049i | \(0.450740\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 22.4802 | 2.59579 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.66388 | −0.524727 | −0.262364 | − | 0.964969i | \(-0.584502\pi\) | ||||
−0.262364 | + | 0.964969i | \(0.584502\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.41709 | −0.824121 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 18.1210 | 1.98904 | 0.994521 | − | 0.104533i | \(-0.0333346\pi\) | ||||
0.994521 | + | 0.104533i | \(0.0333346\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 21.8948 | 2.37483 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.139250 | −0.0149292 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.350510 | 0.0371540 | 0.0185770 | − | 0.999827i | \(-0.494086\pi\) | ||||
0.0185770 | + | 0.999827i | \(0.494086\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −16.4362 | −1.70436 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 25.4744 | 2.61362 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.42082 | 0.651935 | 0.325968 | − | 0.945381i | \(-0.394310\pi\) | ||||
0.325968 | + | 0.945381i | \(0.394310\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.457782 | 0.0460089 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.32677 | −0.729041 | −0.364521 | − | 0.931195i | \(-0.618767\pi\) | ||||
−0.364521 | + | 0.931195i | \(0.618767\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.18643 | 0.806633 | 0.403317 | − | 0.915061i | \(-0.367857\pi\) | ||||
0.403317 | + | 0.915061i | \(0.367857\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.96809 | −0.680016 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.9848 | 1.54531 | 0.772654 | − | 0.634827i | \(-0.218929\pi\) | ||||
0.772654 | + | 0.634827i | \(0.218929\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.10632 | −0.105967 | −0.0529833 | − | 0.998595i | \(-0.516873\pi\) | ||||
−0.0529833 | + | 0.998595i | \(0.516873\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.96092 | −0.660701 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.18127 | −0.111124 | −0.0555621 | − | 0.998455i | \(-0.517695\pi\) | ||||
−0.0555621 | + | 0.998455i | \(0.517695\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 21.5011 | 2.00499 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.457782 | 0.0423220 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.00996 | −0.459262 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.53140 | 0.498750 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 39.7659 | 3.55677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.32576 | −0.295114 | −0.147557 | − | 0.989054i | \(-0.547141\pi\) | ||||
−0.147557 | + | 0.989054i | \(0.547141\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 16.4248 | 1.44612 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.00776 | 0.175419 | 0.0877093 | − | 0.996146i | \(-0.472045\pi\) | ||||
0.0877093 | + | 0.996146i | \(0.472045\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.82903 | −0.505441 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −24.0942 | −2.07369 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.6995 | 1.42674 | 0.713368 | − | 0.700790i | \(-0.247169\pi\) | ||||
0.713368 | + | 0.700790i | \(0.247169\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.13299 | 0.0960989 | 0.0480494 | − | 0.998845i | \(-0.484699\pi\) | ||||
0.0480494 | + | 0.998845i | \(0.484699\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.22987 | 0.693080 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.381679 | −0.0316967 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.59443 | 0.131507 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.7438 | 1.04401 | 0.522007 | − | 0.852941i | \(-0.325183\pi\) | ||||
0.522007 | + | 0.852941i | \(0.325183\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.79298 | −0.471426 | −0.235713 | − | 0.971823i | \(-0.575742\pi\) | ||||
−0.235713 | + | 0.971823i | \(0.575742\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.29347 | −0.185416 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −45.0509 | −3.61858 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.48499 | −0.118515 | −0.0592576 | − | 0.998243i | \(-0.518873\pi\) | ||||
−0.0592576 | + | 0.998243i | \(0.518873\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15.1548 | 1.20186 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.91986 | −0.387739 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.0134 | −1.25427 | −0.627134 | − | 0.778911i | \(-0.715772\pi\) | ||||
−0.627134 | + | 0.778911i | \(0.715772\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.96809 | −0.542465 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.51840 | −0.117497 | −0.0587486 | − | 0.998273i | \(-0.518711\pi\) | ||||
−0.0587486 | + | 0.998273i | \(0.518711\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.66843 | −0.204060 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.2659 | 1.23668 | 0.618339 | − | 0.785912i | \(-0.287806\pi\) | ||||
0.618339 | + | 0.785912i | \(0.287806\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.0992 | −1.06580 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −19.7644 | −1.48558 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.1877 | −1.50890 | −0.754449 | − | 0.656358i | \(-0.772096\pi\) | ||||
−0.754449 | + | 0.656358i | \(0.772096\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.44988 | −0.628075 | −0.314037 | − | 0.949411i | \(-0.601682\pi\) | ||||
−0.314037 | + | 0.949411i | \(0.601682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.9664 | −0.884583 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −19.0795 | −1.40276 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.00996 | −0.366365 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.51320 | 0.401027 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.2739 | −0.960465 | −0.480233 | − | 0.877141i | \(-0.659448\pi\) | ||||
−0.480233 | + | 0.877141i | \(0.659448\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −26.5622 | −1.91199 | −0.955995 | − | 0.293384i | \(-0.905219\pi\) | ||||
−0.955995 | + | 0.293384i | \(0.905219\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.96809 | −0.498996 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.65367 | 0.189066 | 0.0945332 | − | 0.995522i | \(-0.469864\pi\) | ||||
0.0945332 | + | 0.995522i | \(0.469864\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.5382 | −1.73947 | −0.869734 | − | 0.493521i | \(-0.835710\pi\) | ||||
−0.869734 | + | 0.493521i | \(0.835710\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.39917 | −0.592432 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.0873354 | 0.00612974 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.1613 | 1.05891 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.25222 | −0.156540 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.82903 | −0.403202 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.83448 | 0.195134 | 0.0975669 | − | 0.995229i | \(-0.468894\pi\) | ||||
0.0975669 | + | 0.995229i | \(0.468894\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −24.1894 | −1.65743 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 45.0196 | 3.07031 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.3085 | 0.699787 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.19961 | 0.283784 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.00996 | −0.337006 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.13256 | −0.0758420 | −0.0379210 | − | 0.999281i | \(-0.512074\pi\) | ||||
−0.0379210 | + | 0.999281i | \(0.512074\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.45437 | −0.430291 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.6316 | −0.904763 | −0.452381 | − | 0.891825i | \(-0.649425\pi\) | ||||
−0.452381 | + | 0.891825i | \(0.649425\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.15726 | 0.340801 | 0.170401 | − | 0.985375i | \(-0.445494\pi\) | ||||
0.170401 | + | 0.985375i | \(0.445494\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.59443 | 0.104906 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.22082 | 0.604076 | 0.302038 | − | 0.953296i | \(-0.402333\pi\) | ||||
0.302038 | + | 0.953296i | \(0.402333\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 22.5577 | 1.47150 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.43624 | −0.483036 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.08098 | −0.134607 | −0.0673037 | − | 0.997733i | \(-0.521440\pi\) | ||||
−0.0673037 | + | 0.997733i | \(0.521440\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.84967 | 0.441226 | 0.220613 | − | 0.975361i | \(-0.429194\pi\) | ||||
0.220613 | + | 0.975361i | \(0.429194\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.71356 | 0.302375 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.37026 | 0.279206 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.82903 | −0.370892 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 28.8928 | 1.83101 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.53518 | 0.286258 | 0.143129 | − | 0.989704i | \(-0.454284\pi\) | ||||
0.143129 | + | 0.989704i | \(0.454284\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.91986 | −0.309309 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 34.9099 | 2.18614 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.4454 | −1.33773 | −0.668863 | − | 0.743385i | \(-0.733219\pi\) | ||||
−0.668863 | + | 0.743385i | \(0.733219\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.36576 | 0.271275 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.0399806 | 0.00247474 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.32971 | −0.328644 | −0.164322 | − | 0.986407i | \(-0.552544\pi\) | ||||
−0.164322 | + | 0.986407i | \(0.552544\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 41.5386 | 2.55170 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.558865 | 0.0342020 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.08626 | 0.493028 | 0.246514 | − | 0.969139i | \(-0.420715\pi\) | ||||
0.246514 | + | 0.969139i | \(0.420715\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.76102 | 0.410703 | 0.205351 | − | 0.978688i | \(-0.434166\pi\) | ||||
0.205351 | + | 0.978688i | \(0.434166\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.59443 | 0.0964995 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.0992 | −0.850214 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −27.4920 | −1.65184 | −0.825918 | − | 0.563790i | \(-0.809343\pi\) | ||||
−0.825918 | + | 0.563790i | \(0.809343\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.71906 | 0.282523 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.0366 | −0.956661 | −0.478330 | − | 0.878180i | \(-0.658758\pi\) | ||||
−0.478330 | + | 0.878180i | \(0.658758\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.9216 | −0.946440 | −0.473220 | − | 0.880944i | \(-0.656908\pi\) | ||||
−0.473220 | + | 0.880944i | \(0.656908\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 40.6172 | 2.40596 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.46920 | −0.204780 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.09970 | 0.476453 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.2376 | 0.600137 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.9566 | 1.16588 | 0.582939 | − | 0.812516i | \(-0.301902\pi\) | ||||
0.582939 | + | 0.812516i | \(0.301902\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −54.1731 | −3.15408 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.51320 | 0.319909 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.91986 | −0.284523 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.3014 | −0.593760 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.6820 | −0.671116 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −32.7994 | −1.87809 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.0950 | −1.54639 | −0.773196 | − | 0.634168i | \(-0.781343\pi\) | ||||
−0.773196 | + | 0.634168i | \(0.781343\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.0527 | 0.742543 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.8123 | 1.35027 | 0.675137 | − | 0.737693i | \(-0.264085\pi\) | ||||
0.675137 | + | 0.737693i | \(0.264085\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.18696 | −0.180138 | −0.0900689 | − | 0.995936i | \(-0.528709\pi\) | ||||
−0.0900689 | + | 0.995936i | \(0.528709\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.00063 | 0.112723 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.79545 | 0.325505 | 0.162752 | − | 0.986667i | \(-0.447963\pi\) | ||||
0.162752 | + | 0.986667i | \(0.447963\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.0873354 | 0.00488984 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 25.4867 | 1.42253 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 29.2032 | 1.62491 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.0992 | −0.782083 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.76396 | −0.0975472 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.16163 | −0.284570 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.58775 | −0.0872707 | −0.0436354 | − | 0.999048i | \(-0.513894\pi\) | ||||
−0.0436354 | + | 0.999048i | \(0.513894\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.99857 | 0.109521 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −23.0217 | −1.25781 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.1356 | 1.85948 | 0.929741 | − | 0.368214i | \(-0.120030\pi\) | ||||
0.929741 | + | 0.368214i | \(0.120030\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.88345 | −0.102295 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.3085 | 0.558237 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 34.2820 | 1.84568 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.2636 | 0.819393 | 0.409696 | − | 0.912222i | \(-0.365635\pi\) | ||||
0.409696 | + | 0.912222i | \(0.365635\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.6193 | −0.836080 | −0.418040 | − | 0.908429i | \(-0.637283\pi\) | ||||
−0.418040 | + | 0.908429i | \(0.637283\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.51320 | 0.294273 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.4801 | 1.19649 | 0.598247 | − | 0.801312i | \(-0.295864\pi\) | ||||
0.598247 | + | 0.801312i | \(0.295864\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −66.3019 | −3.51894 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.98805 | −0.422772 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.3773 | −1.60325 | −0.801626 | − | 0.597826i | \(-0.796031\pi\) | ||||
−0.801626 | + | 0.597826i | \(0.796031\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.9775 | 0.788292 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.59443 | 0.0836860 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.5109 | 0.602510 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.5608 | −0.603468 | −0.301734 | − | 0.953392i | \(-0.597565\pi\) | ||||
−0.301734 | + | 0.953392i | \(0.597565\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.58814 | −0.0826751 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.50483 | −0.493466 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.41012 | 0.487238 | 0.243619 | − | 0.969871i | \(-0.421665\pi\) | ||||
0.243619 | + | 0.969871i | \(0.421665\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 63.4041 | 3.27417 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.0873354 | 0.00449800 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.39466 | −0.277105 | −0.138553 | − | 0.990355i | \(-0.544245\pi\) | ||||
−0.138553 | + | 0.990355i | \(0.544245\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.30271 | −0.271666 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.86021 | 0.350540 | 0.175270 | − | 0.984520i | \(-0.443920\pi\) | ||||
0.175270 | + | 0.984520i | \(0.443920\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.37026 | 0.222729 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.71578 | −0.239717 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.84071 | 0.0933279 | 0.0466639 | − | 0.998911i | \(-0.485141\pi\) | ||||
0.0466639 | + | 0.998911i | \(0.485141\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.6483 | 1.24652 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.20124 | 0.161481 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −20.3824 | −1.02555 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.5268 | −0.980024 | −0.490012 | − | 0.871716i | \(-0.663008\pi\) | ||||
−0.490012 | + | 0.871716i | \(0.663008\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.29399 | −0.465282 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.6866 | −0.533663 | −0.266831 | − | 0.963743i | \(-0.585977\pi\) | ||||
−0.266831 | + | 0.963743i | \(0.585977\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.3085 | 0.513504 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −32.4146 | −1.61070 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.36576 | 0.216403 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.2901 | 0.508810 | 0.254405 | − | 0.967098i | \(-0.418120\pi\) | ||||
0.254405 | + | 0.967098i | \(0.418120\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 26.6263 | 1.31338 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.3958 | 0.609960 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 79.1937 | 3.88747 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.80648 | 0.0884635 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.6990 | −0.669238 | −0.334619 | − | 0.942354i | \(-0.608608\pi\) | ||||
−0.334619 | + | 0.942354i | \(0.608608\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.9608 | −0.631669 | −0.315834 | − | 0.948814i | \(-0.602284\pi\) | ||||
−0.315834 | + | 0.948814i | \(0.602284\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.36290 | −0.114888 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 70.6365 | 3.42637 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.50512 | 0.363198 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.59443 | 0.0769800 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.5057 | −0.843221 | −0.421611 | − | 0.906777i | \(-0.638535\pi\) | ||||
−0.421611 | + | 0.906777i | \(0.638535\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.3398 | −1.65027 | −0.825134 | − | 0.564938i | \(-0.808900\pi\) | ||||
−0.825134 | + | 0.564938i | \(0.808900\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.608561 | −0.0291783 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 28.6780 | 1.37185 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.99675 | 0.477119 | 0.238559 | − | 0.971128i | \(-0.423325\pi\) | ||||
0.238559 | + | 0.971128i | \(0.423325\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.457782 | −0.0217992 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −32.9060 | −1.56341 | −0.781705 | − | 0.623649i | \(-0.785650\pi\) | ||||
−0.781705 | + | 0.623649i | \(0.785650\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.53182 | 0.0726153 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 20.3192 | 0.961064 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 32.5993 | 1.53846 | 0.769228 | − | 0.638974i | \(-0.220641\pi\) | ||||
0.769228 | + | 0.638974i | \(0.220641\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.46920 | −0.163358 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.23651 | −0.433969 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.37026 | 0.204881 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.6730 | −1.48160 | −0.740801 | − | 0.671724i | \(-0.765554\pi\) | ||||
−0.740801 | + | 0.671724i | \(0.765554\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −27.6209 | −1.28923 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.2165 | −1.31418 | −0.657088 | − | 0.753814i | \(-0.728212\pi\) | ||||
−0.657088 | + | 0.753814i | \(0.728212\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.5157 | 1.37171 | 0.685855 | − | 0.727738i | \(-0.259428\pi\) | ||||
0.685855 | + | 0.727738i | \(0.259428\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −71.8307 | −3.33107 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 36.3702 | 1.68301 | 0.841505 | − | 0.540249i | \(-0.181670\pi\) | ||||
0.841505 | + | 0.540249i | \(0.181670\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.26781 | 0.243245 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.36772 | −0.109099 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.3014 | −0.473657 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 82.1846 | 3.77089 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.35114 | −0.199225 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.6354 | 1.26269 | 0.631346 | − | 0.775501i | \(-0.282503\pi\) | ||||
0.631346 | + | 0.775501i | \(0.282503\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.36576 | 0.199062 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.84439 | −0.356932 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 28.0607 | 1.27417 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.6605 | −0.890902 | −0.445451 | − | 0.895306i | \(-0.646957\pi\) | ||||
−0.445451 | + | 0.895306i | \(0.646957\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −25.5323 | −1.15461 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.4977 | −1.01531 | −0.507653 | − | 0.861562i | \(-0.669487\pi\) | ||||
−0.507653 | + | 0.861562i | \(0.669487\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.437547 | −0.0197061 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.00063 | 0.0899216 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.1711 | 0.680519 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.58842 | 0.294938 | 0.147469 | − | 0.989067i | \(-0.452887\pi\) | ||||
0.147469 | + | 0.989067i | \(0.452887\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.42098 | −0.108162 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.9999 | 1.15928 | 0.579639 | − | 0.814873i | \(-0.303193\pi\) | ||||
0.579639 | + | 0.814873i | \(0.303193\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −32.0199 | −1.42487 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.59443 | 0.0708113 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.198995 | 0.00882032 | 0.00441016 | − | 0.999990i | \(-0.498596\pi\) | ||||
0.00441016 | + | 0.999990i | \(0.498596\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.63392 | −0.116518 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −32.1366 | −1.41887 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 35.7769 | 1.57652 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.16163 | −0.227008 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 25.9350 | 1.13842 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.8049 | 1.08672 | 0.543361 | − | 0.839499i | \(-0.317152\pi\) | ||||
0.543361 | + | 0.839499i | \(0.317152\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.3707 | −1.02193 | −0.510964 | − | 0.859602i | \(-0.670711\pi\) | ||||
−0.510964 | + | 0.859602i | \(0.670711\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −22.4802 | −0.981118 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −51.6452 | −2.24970 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.20500 | 0.0523913 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.67460 | 0.246257 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.46920 | −0.150268 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 69.8578 | 3.02022 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −32.1879 | −1.38901 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.66279 | 0.286456 | 0.143228 | − | 0.989690i | \(-0.454252\pi\) | ||||
0.143228 | + | 0.989690i | \(0.454252\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.4728 | −0.578172 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.83493 | −0.207105 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.9208 | 1.57862 | 0.789311 | − | 0.613994i | \(-0.210438\pi\) | ||||
0.789311 | + | 0.613994i | \(0.210438\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.43571 | 0.146633 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.509080 | −0.0216876 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.66388 | 0.198328 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −30.4210 | −1.29130 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.99870 | −0.254173 | −0.127086 | − | 0.991892i | \(-0.540563\pi\) | ||||
−0.127086 | + | 0.991892i | \(0.540563\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.3014 | −0.435701 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.98805 | −0.337256 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.3954 | −0.817418 | −0.408709 | − | 0.912665i | \(-0.634021\pi\) | ||||
−0.408709 | + | 0.912665i | \(0.634021\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.16244 | −0.217186 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.41709 | 0.311488 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.7023 | 0.742118 | 0.371059 | − | 0.928609i | \(-0.378995\pi\) | ||||
0.371059 | + | 0.928609i | \(0.378995\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.84498 | 0.0772100 | 0.0386050 | − | 0.999255i | \(-0.487709\pi\) | ||||
0.0386050 | + | 0.999255i | \(0.487709\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21.1643 | −0.884153 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 69.3661 | 2.89277 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.26948 | 0.219371 | 0.109686 | − | 0.993966i | \(-0.465016\pi\) | ||||
0.109686 | + | 0.993966i | \(0.465016\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −42.3517 | −1.76008 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.1210 | −0.751788 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.50483 | −0.393650 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.00063 | 0.0827159 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.4801 | −0.762757 | −0.381379 | − | 0.924419i | \(-0.624551\pi\) | ||||
−0.381379 | + | 0.924419i | \(0.624551\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −60.0886 | −2.47591 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.23111 | 0.174044 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.7446 | 0.687618 | 0.343809 | − | 0.939040i | \(-0.388283\pi\) | ||||
0.343809 | + | 0.939040i | \(0.388283\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −21.8948 | −0.897601 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −39.1245 | −1.60126 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.670307 | −0.0273880 | −0.0136940 | − | 0.999906i | \(-0.504359\pi\) | ||||
−0.0136940 | + | 0.999906i | \(0.504359\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.2148 | −0.620623 | −0.310311 | − | 0.950635i | \(-0.600433\pi\) | ||||
−0.310311 | + | 0.950635i | \(0.600433\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.41151 | 0.0982043 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.37026 | 0.177676 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.0891 | −0.531268 | −0.265634 | − | 0.964074i | \(-0.585581\pi\) | ||||
−0.265634 | + | 0.964074i | \(0.585581\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.139250 | 0.00564271 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.16163 | −0.208817 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.8134 | 1.16376 | 0.581881 | − | 0.813274i | \(-0.302317\pi\) | ||||
0.581881 | + | 0.813274i | \(0.302317\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 24.1737 | 0.974777 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.7648 | −0.956733 | −0.478367 | − | 0.878160i | \(-0.658771\pi\) | ||||
−0.478367 | + | 0.878160i | \(0.658771\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.1544 | −1.09143 | −0.545714 | − | 0.837971i | \(-0.683742\pi\) | ||||
−0.545714 | + | 0.837971i | \(0.683742\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −27.1242 | −1.08846 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.350510 | −0.0140429 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 103.292 | 4.13166 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.29399 | −0.371166 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.8723 | −0.872106 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.5102 | −0.935927 | −0.467964 | − | 0.883748i | \(-0.655012\pi\) | ||||
−0.467964 | + | 0.883748i | \(0.655012\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.51939 | 0.179630 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.5345 | −0.576783 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.94508 | 0.274743 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.5626 | −0.930668 | −0.465334 | − | 0.885135i | \(-0.654066\pi\) | ||||
−0.465334 | + | 0.885135i | \(0.654066\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.51124 | −0.217342 | −0.108671 | − | 0.994078i | \(-0.534659\pi\) | ||||
−0.108671 | + | 0.994078i | \(0.534659\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 71.7808 | 2.82637 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.6951 | −0.852922 | −0.426461 | − | 0.904506i | \(-0.640240\pi\) | ||||
−0.426461 | + | 0.904506i | \(0.640240\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.3958 | 0.486580 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.4362 | 0.644187 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −32.3455 | −1.26578 | −0.632889 | − | 0.774243i | \(-0.718131\pi\) | ||||
−0.632889 | + | 0.774243i | \(0.718131\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.77443 | 0.342846 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.20576 | −0.0470413 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −44.8397 | −1.74671 | −0.873353 | − | 0.487087i | \(-0.838059\pi\) | ||||
−0.873353 | + | 0.487087i | \(0.838059\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.4043 | −1.45486 | −0.727430 | − | 0.686182i | \(-0.759285\pi\) | ||||
−0.727430 | + | 0.686182i | \(0.759285\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.98805 | −0.310230 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −25.4744 | −0.987854 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.429678 | −0.0166372 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.80580 | −0.0698161 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.50512 | 0.289732 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.0085 | −0.501442 | −0.250721 | − | 0.968059i | \(-0.580668\pi\) | ||||
−0.250721 | + | 0.968059i | \(0.580668\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −77.7318 | −2.99190 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −29.3502 | −1.12802 | −0.564009 | − | 0.825769i | \(-0.690742\pi\) | ||||
−0.564009 | + | 0.825769i | \(0.690742\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.42082 | −0.246408 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21.7347 | −0.832876 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.4697 | 0.974573 | 0.487286 | − | 0.873242i | \(-0.337987\pi\) | ||||
0.487286 | + | 0.873242i | \(0.337987\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 72.9813 | 2.78847 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.22290 | 0.313723 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.50483 | −0.362105 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.60340 | −0.175121 | −0.0875607 | − | 0.996159i | \(-0.527907\pi\) | ||||
−0.0875607 | + | 0.996159i | \(0.527907\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.457782 | −0.0173897 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.95146 | 0.187820 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.3805 | 0.658335 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14.7020 | 0.556080 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.0383 | −0.681299 | −0.340649 | − | 0.940190i | \(-0.610647\pi\) | ||||
−0.340649 | + | 0.940190i | \(0.610647\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.4481 | −0.959795 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 35.9667 | 1.35459 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.32677 | 0.275552 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.0735 | −1.09188 | −0.545940 | − | 0.837824i | \(-0.683827\pi\) | ||||
−0.545940 | + | 0.837824i | \(0.683827\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.13504 | 0.0800703 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −50.7164 | −1.89934 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.37026 | 0.163439 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.31799 | −0.123912 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.49859 | 0.316944 | 0.158472 | − | 0.987363i | \(-0.449343\pi\) | ||||
0.158472 | + | 0.987363i | \(0.449343\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.18643 | −0.304879 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.9213 | 0.406169 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.23136 | −0.0457316 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.4840 | 1.42729 | 0.713647 | − | 0.700506i | \(-0.247042\pi\) | ||||
0.713647 | + | 0.700506i | \(0.247042\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.7667 | 1.10247 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 51.6094 | 1.90884 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.2314 | 1.15356 | 0.576779 | − | 0.816900i | \(-0.304309\pi\) | ||||
0.576779 | + | 0.816900i | \(0.304309\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.96809 | 0.257022 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.26781 | 0.194042 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.926502 | 0.0340819 | 0.0170410 | − | 0.999855i | \(-0.494575\pi\) | ||||
0.0170410 | + | 0.999855i | \(0.494575\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.29399 | −0.341423 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −46.6500 | −1.71142 | −0.855711 | − | 0.517454i | \(-0.826880\pi\) | ||||
−0.855711 | + | 0.517454i | \(0.826880\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 55.6939 | 2.04047 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.29550 | −0.303516 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.9848 | −0.584072 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 52.6417 | 1.92092 | 0.960461 | − | 0.278414i | \(-0.0898088\pi\) | ||||
0.960461 | + | 0.278414i | \(0.0898088\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.23104 | 0.263514 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −25.3168 | −0.921374 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.9426 | 1.01559 | 0.507796 | − | 0.861477i | \(-0.330460\pi\) | ||||
0.507796 | + | 0.861477i | \(0.330460\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.84439 | −0.284733 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.15873 | 0.114504 | 0.0572520 | − | 0.998360i | \(-0.481766\pi\) | ||||
0.0572520 | + | 0.998360i | \(0.481766\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.10632 | 0.0400516 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10.0231 | −0.362385 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.3958 | 0.447588 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.2104 | −1.26972 | −0.634859 | − | 0.772628i | \(-0.718942\pi\) | ||||
−0.634859 | + | 0.772628i | \(0.718942\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −34.1932 | −1.23144 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.25876 | −0.153177 | −0.0765885 | − | 0.997063i | \(-0.524403\pi\) | ||||
−0.0765885 | + | 0.997063i | \(0.524403\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −145.342 | −5.22083 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.96092 | 0.249722 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.2220 | 0.724530 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.1711 | 0.542866 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.481498 | 0.0172073 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.48981 | −0.231631 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.1650 | 0.504926 | 0.252463 | − | 0.967607i | \(-0.418759\pi\) | ||||
0.252463 | + | 0.967607i | \(0.418759\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.49787 | −0.302532 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.18127 | 0.0420010 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.50512 | 0.266515 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 66.2306 | 2.34896 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34.9117 | 1.23663 | 0.618317 | − | 0.785929i | \(-0.287815\pi\) | ||||
0.618317 | + | 0.785929i | \(0.287815\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.8596 | 0.914845 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.160457 | −0.00566948 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.63392 | −0.0929491 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −21.5011 | −0.757813 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.8930 | 0.453855 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 48.4361 | 1.70292 | 0.851461 | − | 0.524418i | \(-0.175717\pi\) | ||||
0.851461 | + | 0.524418i | \(0.175717\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.9726 | 0.420417 | 0.210208 | − | 0.977657i | \(-0.432586\pi\) | ||||
0.210208 | + | 0.977657i | \(0.432586\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.7800 | 0.378071 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −69.9829 | −2.45139 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 60.0469 | 2.10077 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.457782 | −0.0159962 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.06847 | 0.107090 | 0.0535451 | − | 0.998565i | \(-0.482948\pi\) | ||||
0.0535451 | + | 0.998565i | \(0.482948\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.3991 | −1.40823 | −0.704113 | − | 0.710088i | \(-0.748655\pi\) | ||||
−0.704113 | + | 0.710088i | \(0.748655\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −22.4802 | −0.782662 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −42.8546 | −1.49020 | −0.745101 | − | 0.666952i | \(-0.767599\pi\) | ||||
−0.745101 | + | 0.666952i | \(0.767599\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −39.6855 | −1.37833 | −0.689167 | − | 0.724603i | \(-0.742023\pi\) | ||||
−0.689167 | + | 0.724603i | \(0.742023\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −43.8342 | −1.52059 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.00996 | 0.173585 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.63580 | −0.229641 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 56.8329 | 1.96443 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27.1774 | −0.938270 | −0.469135 | − | 0.883127i | \(-0.655434\pi\) | ||||
−0.469135 | + | 0.883127i | \(0.655434\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9924 | −0.999737 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −25.5692 | −0.880651 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.37026 | 0.150342 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −25.3859 | −0.871242 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.4789 | −0.736288 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.87863 | 0.0643230 | 0.0321615 | − | 0.999483i | \(-0.489761\pi\) | ||||
0.0321615 | + | 0.999483i | \(0.489761\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −11.6617 | −0.398823 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 45.9573 | 1.56987 | 0.784936 | − | 0.619577i | \(-0.212696\pi\) | ||||
0.784936 | + | 0.619577i | \(0.212696\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.6428 | −0.670204 | −0.335102 | − | 0.942182i | \(-0.608771\pi\) | ||||
−0.335102 | + | 0.942182i | \(0.608771\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.53140 | −0.188510 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.4940 | −0.391260 | −0.195630 | − | 0.980678i | \(-0.562675\pi\) | ||||
−0.195630 | + | 0.980678i | \(0.562675\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 71.0865 | 2.41701 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12.9144 | 0.438597 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.66388 | 0.158211 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.26781 | 0.178493 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.93934 | −0.0994815 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −39.7659 | −1.34433 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −35.5381 | −1.20004 | −0.600018 | − | 0.799986i | \(-0.704840\pi\) | ||||
−0.600018 | + | 0.799986i | \(0.704840\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 31.8195 | 1.07325 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.88715 | −0.0635797 | −0.0317899 | − | 0.999495i | \(-0.510121\pi\) | ||||
−0.0317899 | + | 0.999495i | \(0.510121\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.4260 | 0.552777 | 0.276389 | − | 0.961046i | \(-0.410862\pi\) | ||||
0.276389 | + | 0.961046i | \(0.410862\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −86.3754 | −2.90348 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 53.1774 | 1.78552 | 0.892761 | − | 0.450530i | \(-0.148765\pi\) | ||||
0.892761 | + | 0.450530i | \(0.148765\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.32576 | 0.111543 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.41709 | 0.248482 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 30.0873 | 1.00683 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −88.2255 | −2.94905 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.84439 | −0.261916 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.900298 | 0.0300266 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 47.6188 | 1.58641 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −16.4248 | −0.546584 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −36.9282 | −1.22754 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 49.4232 | 1.64107 | 0.820536 | − | 0.571595i | \(-0.193675\pi\) | ||||
0.820536 | + | 0.571595i | \(0.193675\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.35407 | 0.111247 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.65862 | −0.320004 | −0.160002 | − | 0.987117i | \(-0.551150\pi\) | ||||
−0.160002 | + | 0.987117i | \(0.551150\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.1210 | −0.599719 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −52.2964 | −1.72887 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.00776 | −0.0663020 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.92694 | −0.162525 | −0.0812624 | − | 0.996693i | \(-0.525895\pi\) | ||||
−0.0812624 | + | 0.996693i | \(0.525895\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −43.2011 | −1.42353 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15.1711 | 0.499364 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −61.5538 | −2.02388 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.74761 | −0.123088 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.9980 | 0.754540 | 0.377270 | − | 0.926103i | \(-0.376863\pi\) | ||||
0.377270 | + | 0.926103i | \(0.376863\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.82903 | 0.191039 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 37.9672 | 1.24299 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −21.8948 | −0.716038 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.47482 | 0.309529 | 0.154764 | − | 0.987951i | \(-0.450538\pi\) | ||||
0.154764 | + | 0.987951i | \(0.450538\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.08140 | −0.165825 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.8949 | −0.681154 | −0.340577 | − | 0.940217i | \(-0.610622\pi\) | ||||
−0.340577 | + | 0.940217i | \(0.610622\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.0680 | 0.555809 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 24.0942 | 0.783783 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −40.8100 | −1.32615 | −0.663074 | − | 0.748554i | \(-0.730749\pi\) | ||||
−0.663074 | + | 0.748554i | \(0.730749\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.63392 | −0.0855007 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.24046 | 0.299642 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27.9634 | −0.905824 | −0.452912 | − | 0.891555i | \(-0.649615\pi\) | ||||
−0.452912 | + | 0.891555i | \(0.649615\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −58.0104 | −1.87717 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.139250 | 0.00450133 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16.6995 | −0.539255 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 75.2654 | 2.42792 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.31756 | −0.235805 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −116.084 | −3.73687 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.7327 | −0.473772 | −0.236886 | − | 0.971538i | \(-0.576127\pi\) | ||||
−0.236886 | + | 0.971538i | \(0.576127\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 46.5625 | 1.49580 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −37.5031 | −1.20353 | −0.601766 | − | 0.798672i | \(-0.705536\pi\) | ||||
−0.601766 | + | 0.798672i | \(0.705536\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.13299 | −0.0363220 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −22.4802 | −0.719944 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.71190 | −0.150747 | −0.0753735 | − | 0.997155i | \(-0.524015\pi\) | ||||
−0.0753735 | + | 0.997155i | \(0.524015\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.350510 | −0.0112023 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.506456 | 0.0161699 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −50.9941 | −1.62646 | −0.813229 | − | 0.581944i | \(-0.802292\pi\) | ||||
−0.813229 | + | 0.581944i | \(0.802292\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.5973 | 0.369519 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.22987 | −0.261960 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 50.6812 | 1.61157 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.9246 | 0.982354 | 0.491177 | − | 0.871060i | \(-0.336567\pi\) | ||||
0.491177 | + | 0.871060i | \(0.336567\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.53156 | −0.0803368 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −107.238 | −3.39969 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.29052 | 0.0408711 | 0.0204356 | − | 0.999791i | \(-0.493495\pi\) | ||||
0.0204356 | + | 0.999791i | \(0.493495\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 24.0693 | 0.761520 |
(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 | 4004.2.a.j.1.8 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4004.2.a.j.1.8 | ✓ | 10 | 1.1 | even | 1 | trivial |