Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1336,2,Mod(1,1336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1336, 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("1336.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1336 = 2^{3} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1336.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: | \(10.6680137100\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5 x^{11} - 15 x^{10} + 100 x^{9} + 36 x^{8} - 641 x^{7} + 129 x^{6} + 1804 x^{5} - 433 x^{4} + \cdots + 224 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.26807\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1336.1 |
$q$-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 | ||||||||
\(3\) | −1.26807 | −0.732122 | −0.366061 | − | 0.930591i | \(-0.619294\pi\) | ||||
−0.366061 | + | 0.930591i | \(0.619294\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.339536 | −0.151845 | −0.0759226 | − | 0.997114i | \(-0.524190\pi\) | ||||
−0.0759226 | + | 0.997114i | \(0.524190\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.08348 | −1.54341 | −0.771705 | − | 0.635981i | \(-0.780596\pi\) | ||||
−0.771705 | + | 0.635981i | \(0.780596\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.39199 | −0.463997 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.81132 | 0.847646 | 0.423823 | − | 0.905745i | \(-0.360688\pi\) | ||||
0.423823 | + | 0.905745i | \(0.360688\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.28108 | −0.910008 | −0.455004 | − | 0.890489i | \(-0.650362\pi\) | ||||
−0.455004 | + | 0.890489i | \(0.650362\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.430557 | 0.111169 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.05307 | −0.740479 | −0.370240 | − | 0.928936i | \(-0.620724\pi\) | ||||
−0.370240 | + | 0.928936i | \(0.620724\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.09371 | 1.39799 | 0.698997 | − | 0.715125i | \(-0.253630\pi\) | ||||
0.698997 | + | 0.715125i | \(0.253630\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.17815 | 1.12997 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.204048 | 0.0425470 | 0.0212735 | − | 0.999774i | \(-0.493228\pi\) | ||||
0.0212735 | + | 0.999774i | \(0.493228\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.88472 | −0.976943 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.56937 | 1.07182 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.58414 | −0.479864 | −0.239932 | − | 0.970790i | \(-0.577125\pi\) | ||||
−0.239932 | + | 0.970790i | \(0.577125\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.00151 | 1.25751 | 0.628754 | − | 0.777604i | \(-0.283565\pi\) | ||||
0.628754 | + | 0.777604i | \(0.283565\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.56496 | −0.620580 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.38649 | 0.234360 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.47670 | 0.407166 | 0.203583 | − | 0.979058i | \(-0.434741\pi\) | ||||
0.203583 | + | 0.979058i | \(0.434741\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.16065 | 0.666237 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.44665 | 0.694450 | 0.347225 | − | 0.937782i | \(-0.387124\pi\) | ||||
0.347225 | + | 0.937782i | \(0.387124\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.73921 | 1.33272 | 0.666359 | − | 0.745631i | \(-0.267852\pi\) | ||||
0.666359 | + | 0.745631i | \(0.267852\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.472631 | 0.0704557 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.38631 | −0.348079 | −0.174039 | − | 0.984739i | \(-0.555682\pi\) | ||||
−0.174039 | + | 0.984739i | \(0.555682\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.67481 | 1.38212 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.87152 | 0.542121 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.43102 | 0.196566 | 0.0982831 | − | 0.995158i | \(-0.468665\pi\) | ||||
0.0982831 | + | 0.995158i | \(0.468665\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.954546 | −0.128711 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.72727 | −1.02350 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.48037 | 0.713483 | 0.356742 | − | 0.934203i | \(-0.383888\pi\) | ||||
0.356742 | + | 0.934203i | \(0.383888\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.24427 | −0.671459 | −0.335730 | − | 0.941958i | \(-0.608983\pi\) | ||||
−0.335730 | + | 0.941958i | \(0.608983\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.68416 | 0.716137 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.11405 | 0.138180 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.65639 | −1.17972 | −0.589858 | − | 0.807507i | \(-0.700816\pi\) | ||||
−0.589858 | + | 0.807507i | \(0.700816\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.258748 | −0.0311496 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.65390 | −0.196282 | −0.0981408 | − | 0.995173i | \(-0.531290\pi\) | ||||
−0.0981408 | + | 0.995173i | \(0.531290\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.8129 | 1.61668 | 0.808339 | − | 0.588717i | \(-0.200367\pi\) | ||||
0.808339 | + | 0.588717i | \(0.200367\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.19418 | 0.715242 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −11.4800 | −1.30827 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.14569 | 0.691445 | 0.345722 | − | 0.938337i | \(-0.387634\pi\) | ||||
0.345722 | + | 0.938337i | \(0.387634\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.88639 | −0.320710 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.56244 | 0.171500 | 0.0857502 | − | 0.996317i | \(-0.472671\pi\) | ||||
0.0857502 | + | 0.996317i | \(0.472671\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.03663 | 0.112438 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.27689 | 0.351319 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.8018 | 1.67499 | 0.837494 | − | 0.546446i | \(-0.184020\pi\) | ||||
0.837494 | + | 0.546446i | \(0.184020\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.3982 | 1.40452 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.87842 | −0.920650 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.06904 | −0.212279 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.47842 | 0.251646 | 0.125823 | − | 0.992053i | \(-0.459843\pi\) | ||||
0.125823 | + | 0.992053i | \(0.459843\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.91333 | −0.393305 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.74698 | −0.372838 | −0.186419 | − | 0.982470i | \(-0.559688\pi\) | ||||
−0.186419 | + | 0.982470i | \(0.559688\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.95200 | −0.389402 | −0.194701 | − | 0.980863i | \(-0.562374\pi\) | ||||
−0.194701 | + | 0.980863i | \(0.562374\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.75817 | −0.171580 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.73495 | −0.941113 | −0.470557 | − | 0.882370i | \(-0.655947\pi\) | ||||
−0.470557 | + | 0.882370i | \(0.655947\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.7376 | 1.02847 | 0.514236 | − | 0.857649i | \(-0.328076\pi\) | ||||
0.514236 | + | 0.857649i | \(0.328076\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.14063 | −0.298096 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.80794 | 0.358221 | 0.179110 | − | 0.983829i | \(-0.442678\pi\) | ||||
0.179110 | + | 0.983829i | \(0.442678\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.0692818 | −0.00646056 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.56723 | 0.422241 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.4672 | 1.14286 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.09646 | −0.281497 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.63868 | −0.508423 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.35622 | 0.300189 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.16000 | 0.369140 | 0.184570 | − | 0.982819i | \(-0.440911\pi\) | ||||
0.184570 | + | 0.982819i | \(0.440911\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.0820 | −0.975712 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.25324 | −0.721089 | −0.360545 | − | 0.932742i | \(-0.617409\pi\) | ||||
−0.360545 | + | 0.932742i | \(0.617409\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −24.8836 | −2.15768 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.89100 | −0.162752 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.5104 | 0.897966 | 0.448983 | − | 0.893540i | \(-0.351786\pi\) | ||||
0.448983 | + | 0.893540i | \(0.351786\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.53230 | 0.554063 | 0.277031 | − | 0.960861i | \(-0.410649\pi\) | ||||
0.277031 | + | 0.960861i | \(0.410649\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.02601 | 0.254836 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.22417 | −0.771364 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.877411 | 0.0728650 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.2684 | −1.01188 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.3752 | 1.50535 | 0.752677 | − | 0.658390i | \(-0.228762\pi\) | ||||
0.752677 | + | 0.658390i | \(0.228762\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.09651 | 0.740263 | 0.370132 | − | 0.928979i | \(-0.379313\pi\) | ||||
0.370132 | + | 0.928979i | \(0.379313\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.24985 | 0.343580 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.37727 | −0.190947 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.6017 | −0.925914 | −0.462957 | − | 0.886381i | \(-0.653212\pi\) | ||||
−0.462957 | + | 0.886381i | \(0.653212\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.81464 | −0.143911 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.833227 | −0.0656675 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.1954 | 1.19019 | 0.595097 | − | 0.803654i | \(-0.297114\pi\) | ||||
0.595097 | + | 0.803654i | \(0.297114\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.21043 | 0.0942322 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.23452 | −0.171886 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.48239 | −0.648664 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.63510 | −0.732543 | −0.366271 | − | 0.930508i | \(-0.619366\pi\) | ||||
−0.366271 | + | 0.930508i | \(0.619366\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 19.9466 | 1.50782 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.94951 | −0.522357 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.4061 | 1.00202 | 0.501008 | − | 0.865443i | \(-0.332963\pi\) | ||||
0.501008 | + | 0.865443i | \(0.332963\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.1645 | −1.42448 | −0.712242 | − | 0.701934i | \(-0.752320\pi\) | ||||
−0.712242 | + | 0.701934i | \(0.752320\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.65011 | 0.491591 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.840929 | −0.0618263 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.58318 | −0.627664 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −22.7424 | −1.65427 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.0857 | 1.74278 | 0.871389 | − | 0.490593i | \(-0.163220\pi\) | ||||
0.871389 | + | 0.490593i | \(0.163220\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.00801 | −0.504447 | −0.252224 | − | 0.967669i | \(-0.581162\pi\) | ||||
−0.252224 | + | 0.967669i | \(0.581162\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.41269 | −0.101165 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.4779 | 1.17400 | 0.587002 | − | 0.809585i | \(-0.300308\pi\) | ||||
0.587002 | + | 0.809585i | \(0.300308\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.86255 | −0.132032 | −0.0660162 | − | 0.997819i | \(-0.521029\pi\) | ||||
−0.0660162 | + | 0.997819i | \(0.521029\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.2450 | 0.863697 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.5523 | 0.740626 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.50980 | −0.105449 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.284033 | −0.0197417 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 17.1314 | 1.18500 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.154370 | 0.0106273 | 0.00531363 | − | 0.999986i | \(-0.498309\pi\) | ||||
0.00531363 | + | 0.999986i | \(0.498309\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.09726 | 0.143702 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.96728 | −0.202367 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −28.5905 | −1.94085 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −17.5158 | −1.18361 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.0174 | 0.673842 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.14304 | −0.277438 | −0.138719 | − | 0.990332i | \(-0.544299\pi\) | ||||
−0.138719 | + | 0.990332i | \(0.544299\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.79948 | 0.453298 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.3859 | −1.48580 | −0.742901 | − | 0.669401i | \(-0.766551\pi\) | ||||
−0.742901 | + | 0.669401i | \(0.766551\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.7127 | −1.03832 | −0.519161 | − | 0.854676i | \(-0.673756\pi\) | ||||
−0.519161 | + | 0.854676i | \(0.673756\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.5575 | 0.957810 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.58198 | −0.562224 | −0.281112 | − | 0.959675i | \(-0.590703\pi\) | ||||
−0.281112 | + | 0.959675i | \(0.590703\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.810238 | 0.0528541 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.79319 | −0.506222 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.3840 | −1.31853 | −0.659267 | − | 0.751909i | \(-0.729133\pi\) | ||||
−0.659267 | + | 0.751909i | \(0.729133\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.91994 | −0.510168 | −0.255084 | − | 0.966919i | \(-0.582103\pi\) | ||||
−0.255084 | + | 0.966919i | \(0.582103\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.0479 | −0.837026 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.28495 | −0.209868 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −19.9940 | −1.27218 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.98129 | −0.125559 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.5810 | 0.794108 | 0.397054 | − | 0.917795i | \(-0.370033\pi\) | ||||
0.397054 | + | 0.917795i | \(0.370033\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.573646 | 0.0360648 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.31452 | −0.0823185 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.89101 | −0.492228 | −0.246114 | − | 0.969241i | \(-0.579154\pi\) | ||||
−0.246114 | + | 0.969241i | \(0.579154\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.1135 | −0.628425 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.59710 | 0.222655 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.6589 | 1.39720 | 0.698602 | − | 0.715510i | \(-0.253806\pi\) | ||||
0.698602 | + | 0.715510i | \(0.253806\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.485884 | −0.0298476 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −20.0379 | −1.22630 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −21.6950 | −1.32277 | −0.661384 | − | 0.750047i | \(-0.730031\pi\) | ||||
−0.661384 | + | 0.750047i | \(0.730031\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.65542 | −0.161305 | −0.0806526 | − | 0.996742i | \(-0.525700\pi\) | ||||
−0.0806526 | + | 0.996742i | \(0.525700\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −16.9899 | −1.02828 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −13.7325 | −0.828102 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.04397 | −0.0627262 | −0.0313631 | − | 0.999508i | \(-0.509985\pi\) | ||||
−0.0313631 | + | 0.999508i | \(0.509985\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.74603 | −0.583479 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.63761 | −0.455622 | −0.227811 | − | 0.973705i | \(-0.573157\pi\) | ||||
−0.227811 | + | 0.973705i | \(0.573157\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −31.6025 | −1.87857 | −0.939287 | − | 0.343134i | \(-0.888512\pi\) | ||||
−0.939287 | + | 0.343134i | \(0.888512\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.62369 | 0.155414 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −18.1578 | −1.07182 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.67874 | −0.451691 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.14282 | −0.184235 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.2276 | 0.948025 | 0.474012 | − | 0.880518i | \(-0.342805\pi\) | ||||
0.474012 | + | 0.880518i | \(0.342805\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.86078 | −0.108339 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 15.6573 | 0.908528 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.669499 | −0.0387181 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −35.6864 | −2.05693 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.75144 | 0.272963 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.78062 | 0.101958 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.0897 | 1.43195 | 0.715974 | − | 0.698127i | \(-0.245983\pi\) | ||||
0.715974 | + | 0.698127i | \(0.245983\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.01142 | 0.285090 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.15439 | −0.235574 | −0.117787 | − | 0.993039i | \(-0.537580\pi\) | ||||
−0.117787 | + | 0.993039i | \(0.537580\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.01625 | 0.113965 | 0.0569827 | − | 0.998375i | \(-0.481852\pi\) | ||||
0.0569827 | + | 0.998375i | \(0.481852\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.92998 | −0.108742 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.92051 | 0.164032 | 0.0820162 | − | 0.996631i | \(-0.473864\pi\) | ||||
0.0820162 | + | 0.996631i | \(0.473864\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.26487 | −0.406754 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.3446 | 0.689010 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18.6046 | −1.03518 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.0271 | 0.889026 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −13.6160 | −0.752967 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.74444 | 0.537228 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.9210 | 1.14992 | 0.574962 | − | 0.818180i | \(-0.305017\pi\) | ||||
0.574962 | + | 0.818180i | \(0.305017\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.44754 | −0.188924 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.27870 | 0.179134 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.9760 | 0.706848 | 0.353424 | − | 0.935463i | \(-0.385017\pi\) | ||||
0.353424 | + | 0.935463i | \(0.385017\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.82874 | −0.262261 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.6835 | 1.06592 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.9225 | −0.589760 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.0878544 | 0.00472992 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 34.3198 | 1.84239 | 0.921193 | − | 0.389106i | \(-0.127216\pi\) | ||||
0.921193 | + | 0.389106i | \(0.127216\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.9679 | −0.908269 | −0.454135 | − | 0.890933i | \(-0.650051\pi\) | ||||
−0.454135 | + | 0.890933i | \(0.650051\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18.2735 | −0.975369 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 30.7542 | 1.63688 | 0.818440 | − | 0.574592i | \(-0.194839\pi\) | ||||
0.818440 | + | 0.574592i | \(0.194839\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.561558 | 0.0298044 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −15.8093 | −0.836716 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 34.1313 | 1.80138 | 0.900689 | − | 0.434463i | \(-0.143062\pi\) | ||||
0.900689 | + | 0.434463i | \(0.143062\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.1333 | 0.954386 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.92654 | 0.206090 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.68998 | −0.245485 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −33.6092 | −1.75438 | −0.877192 | − | 0.480140i | \(-0.840586\pi\) | ||||
−0.877192 | + | 0.480140i | \(0.840586\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.18969 | −0.322223 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.84356 | −0.303382 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.5963 | −0.652213 | −0.326106 | − | 0.945333i | \(-0.605737\pi\) | ||||
−0.326106 | + | 0.945333i | \(0.605737\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.25593 | −0.219775 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.47878 | 0.436680 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.87913 | −0.301991 | −0.150995 | − | 0.988534i | \(-0.548248\pi\) | ||||
−0.150995 | + | 0.988534i | \(0.548248\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.27518 | −0.270256 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.9190 | 1.47769 | 0.738847 | − | 0.673873i | \(-0.235371\pi\) | ||||
0.738847 | + | 0.673873i | \(0.235371\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.89787 | 0.198654 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −12.1649 | −0.618376 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.6655 | 0.743569 | 0.371784 | − | 0.928319i | \(-0.378746\pi\) | ||||
0.371784 | + | 0.928319i | \(0.378746\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.622974 | −0.0315052 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.4657 | 0.527925 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.08669 | −0.104993 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.77443 | −0.339999 | −0.169999 | − | 0.985444i | \(-0.554377\pi\) | ||||
−0.169999 | + | 0.985444i | \(0.554377\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 31.5542 | 1.57968 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.12061 | 0.255711 | 0.127855 | − | 0.991793i | \(-0.459191\pi\) | ||||
0.127855 | + | 0.991793i | \(0.459191\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.9725 | −1.14434 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.980035 | 0.0486983 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.96280 | 0.345133 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.30937 | −0.163638 | −0.0818189 | − | 0.996647i | \(-0.526073\pi\) | ||||
−0.0818189 | + | 0.996647i | \(0.526073\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.3280 | −0.657421 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −22.3790 | −1.10120 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.530506 | −0.0260415 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.28344 | −0.405642 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.8735 | 0.531203 | 0.265601 | − | 0.964083i | \(-0.414429\pi\) | ||||
0.265601 | + | 0.964083i | \(0.414429\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.8911 | −1.70049 | −0.850243 | − | 0.526390i | \(-0.823545\pi\) | ||||
−0.850243 | + | 0.526390i | \(0.823545\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.32172 | 0.161507 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.9134 | 0.723406 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 21.4149 | 1.03634 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.6969 | 0.564733 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.9942 | −0.577741 | −0.288871 | − | 0.957368i | \(-0.593280\pi\) | ||||
−0.288871 | + | 0.957368i | \(0.593280\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.3972 | 1.74914 | 0.874570 | − | 0.484899i | \(-0.161144\pi\) | ||||
0.874570 | + | 0.484899i | \(0.161144\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.11262 | −0.0533461 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.24341 | 0.0594805 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.2543 | 0.489409 | 0.244705 | − | 0.969598i | \(-0.421309\pi\) | ||||
0.244705 | + | 0.969598i | \(0.421309\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.4672 | −0.641297 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.0018 | −0.997825 | −0.498912 | − | 0.866652i | \(-0.666267\pi\) | ||||
−0.498912 | + | 0.866652i | \(0.666267\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.36529 | −0.254339 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −23.3011 | −1.10210 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.8067 | 0.840349 | 0.420174 | − | 0.907443i | \(-0.361969\pi\) | ||||
0.420174 | + | 0.907443i | \(0.361969\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.5010 | 0.588648 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11.5350 | −0.541963 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.54918 | −0.213269 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.5032 | 0.818767 | 0.409384 | − | 0.912362i | \(-0.365744\pi\) | ||||
0.409384 | + | 0.912362i | \(0.365744\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −17.0037 | −0.793664 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 36.9332 | 1.72015 | 0.860076 | − | 0.510166i | \(-0.170416\pi\) | ||||
0.860076 | + | 0.510166i | \(0.170416\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.67663 | −0.403237 | −0.201619 | − | 0.979464i | \(-0.564620\pi\) | ||||
−0.201619 | + | 0.979464i | \(0.564620\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.01455 | 0.139796 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.4427 | −1.03852 | −0.519261 | − | 0.854616i | \(-0.673793\pi\) | ||||
−0.519261 | + | 0.854616i | \(0.673793\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 39.4317 | 1.82079 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.7118 | 0.677882 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 24.5687 | 1.12967 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −29.7661 | −1.36576 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.99197 | −0.0912061 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.1267 | 0.736849 | 0.368425 | − | 0.929658i | \(-0.379897\pi\) | ||||
0.368425 | + | 0.929658i | \(0.379897\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.12624 | −0.370525 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.05659 | 0.0480766 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.841515 | −0.0382112 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.4310 | 1.46959 | 0.734795 | − | 0.678289i | \(-0.237278\pi\) | ||||
0.734795 | + | 0.678289i | \(0.237278\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −19.2689 | −0.871368 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.2092 | 0.505863 | 0.252932 | − | 0.967484i | \(-0.418605\pi\) | ||||
0.252932 | + | 0.967484i | \(0.418605\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.88958 | 0.355329 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.32872 | 0.0597215 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.75366 | 0.302943 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.3022 | 1.13268 | 0.566341 | − | 0.824171i | \(-0.308358\pi\) | ||||
0.566341 | + | 0.824171i | \(0.308358\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.26807 | −0.0566533 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 35.4969 | 1.58273 | 0.791364 | − | 0.611345i | \(-0.209371\pi\) | ||||
0.791364 | + | 0.611345i | \(0.209371\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.27224 | 0.0566137 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.83354 | 0.125842 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.85286 | −0.215099 | −0.107550 | − | 0.994200i | \(-0.534300\pi\) | ||||
−0.107550 | + | 0.994200i | \(0.534300\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −56.4047 | −2.49520 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 33.9381 | 1.49840 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.34185 | 0.0591288 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.70868 | −0.295047 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.2180 | 0.536311 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.2582 | −1.54469 | −0.772346 | − | 0.635202i | \(-0.780917\pi\) | ||||
−0.772346 | + | 0.635202i | \(0.780917\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.3986 | −0.542151 | −0.271076 | − | 0.962558i | \(-0.587379\pi\) | ||||
−0.271076 | + | 0.962558i | \(0.587379\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −25.2938 | −1.10391 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.3761 | −0.931158 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9584 | −0.998190 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.62862 | −0.331054 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.5898 | −0.631955 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.30537 | 0.142904 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.9999 | −0.733598 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 27.1990 | 1.17154 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.2209 | −0.525417 | −0.262708 | − | 0.964875i | \(-0.584616\pi\) | ||||
−0.262708 | + | 0.964875i | \(0.584616\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 24.3020 | 1.04290 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.64579 | −0.156169 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.1595 | 0.947473 | 0.473737 | − | 0.880667i | \(-0.342905\pi\) | ||||
0.473737 | + | 0.880667i | \(0.342905\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.29997 | 0.311555 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.7470 | −0.670846 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −25.0958 | −1.06718 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.06636 | 0.0452644 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −28.1364 | −1.19218 | −0.596089 | − | 0.802918i | \(-0.703280\pi\) | ||||
−0.596089 | + | 0.802918i | \(0.703280\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −28.6740 | −1.21278 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.8841 | 0.459527 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.73478 | 0.368127 | 0.184064 | − | 0.982914i | \(-0.441075\pi\) | ||||
0.184064 | + | 0.982914i | \(0.441075\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.29293 | −0.0543941 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 11.7865 | 0.494988 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.1529 | 0.467553 | 0.233776 | − | 0.972290i | \(-0.424892\pi\) | ||||
0.233776 | + | 0.972290i | \(0.424892\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.0009 | 1.54844 | 0.774220 | − | 0.632917i | \(-0.218143\pi\) | ||||
0.774220 | + | 0.632917i | \(0.218143\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −30.5424 | −1.27593 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.996718 | −0.0415660 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 47.3480 | 1.97112 | 0.985561 | − | 0.169323i | \(-0.0541580\pi\) | ||||
0.985561 | + | 0.169323i | \(0.0541580\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.88667 | 0.369317 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.38021 | −0.264696 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.02307 | 0.166619 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.55074 | −0.0641152 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.16219 | −0.336890 | −0.168445 | − | 0.985711i | \(-0.553874\pi\) | ||||
−0.168445 | + | 0.985711i | \(0.553874\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 42.6652 | 1.75799 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.8952 | −0.859515 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.4939 | −0.471999 | −0.236000 | − | 0.971753i | \(-0.575836\pi\) | ||||
−0.236000 | + | 0.971753i | \(0.575836\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.23305 | −0.173538 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.36185 | 0.0966639 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.7338 | 0.765440 | 0.382720 | − | 0.923864i | \(-0.374987\pi\) | ||||
0.382720 | + | 0.923864i | \(0.374987\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.66239 | −0.353346 | −0.176673 | − | 0.984270i | \(-0.556534\pi\) | ||||
−0.176673 | + | 0.984270i | \(0.556534\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.4416 | 0.547384 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.05136 | 0.0427439 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.3746 | 0.705214 | 0.352607 | − | 0.935772i | \(-0.385295\pi\) | ||||
0.352607 | + | 0.935772i | \(0.385295\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.3811 | −0.542229 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.82966 | 0.316754 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.03241 | 0.243647 | 0.121823 | − | 0.992552i | \(-0.461126\pi\) | ||||
0.121823 | + | 0.992552i | \(0.461126\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.91454 | 0.0772016 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 47.4933 | 1.91201 | 0.956004 | − | 0.293353i | \(-0.0947711\pi\) | ||||
0.956004 | + | 0.293353i | \(0.0947711\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.05320 | −0.363879 | −0.181939 | − | 0.983310i | \(-0.558237\pi\) | ||||
−0.181939 | + | 0.983310i | \(0.558237\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.13642 | 0.0456029 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −64.5264 | −2.58519 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.2840 | 0.931361 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −21.7239 | −0.867568 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.56154 | −0.301498 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.3038 | 0.529616 | 0.264808 | − | 0.964301i | \(-0.414691\pi\) | ||||
0.264808 | + | 0.964301i | \(0.414691\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.195752 | −0.00778045 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.41247 | −0.0560522 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −31.7438 | −1.25774 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.30221 | 0.0910740 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.50825 | −0.257060 | −0.128530 | − | 0.991706i | \(-0.541026\pi\) | ||||
−0.128530 | + | 0.991706i | \(0.541026\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 41.5717 | 1.63943 | 0.819713 | − | 0.572774i | \(-0.194133\pi\) | ||||
0.819713 | + | 0.572774i | \(0.194133\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.76273 | 0.148157 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −47.0603 | −1.85013 | −0.925066 | − | 0.379807i | \(-0.875990\pi\) | ||||
−0.925066 | + | 0.379807i | \(0.875990\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.4071 | 0.604781 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 36.2549 | 1.42094 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 48.4752 | 1.89698 | 0.948490 | − | 0.316808i | \(-0.102611\pi\) | ||||
0.948490 | + | 0.316808i | \(0.102611\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.80227 | 0.109494 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −19.2274 | −0.750133 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.2186 | −0.670740 | −0.335370 | − | 0.942087i | \(-0.608861\pi\) | ||||
−0.335370 | + | 0.942087i | \(0.608861\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.04694 | 0.312990 | 0.156495 | − | 0.987679i | \(-0.449981\pi\) | ||||
0.156495 | + | 0.987679i | \(0.449981\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.7028 | −0.493335 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.44887 | 0.327633 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.527290 | −0.0204168 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.25367 | 0.203119 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.7433 | −0.569160 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.9163 | 0.729171 | 0.364585 | − | 0.931170i | \(-0.381211\pi\) | ||||
0.364585 | + | 0.931170i | \(0.381211\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −27.2048 | −1.04711 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.8057 | 1.06866 | 0.534330 | − | 0.845276i | \(-0.320564\pi\) | ||||
0.534330 | + | 0.845276i | \(0.320564\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.1206 | −0.388393 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 28.3869 | 1.08779 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.4005 | 1.35456 | 0.677280 | − | 0.735725i | \(-0.263158\pi\) | ||||
0.677280 | + | 0.735725i | \(0.263158\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.56867 | −0.136352 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.9248 | 0.760179 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.69530 | −0.178877 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.9001 | 0.947244 | 0.473622 | − | 0.880728i | \(-0.342946\pi\) | ||||
0.473622 | + | 0.880728i | \(0.342946\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 15.9800 | 0.607031 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.21795 | −0.0841318 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.5760 | −0.514226 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.8826 | 0.411617 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.7962 | −0.483306 | −0.241653 | − | 0.970363i | \(-0.577690\pi\) | ||||
−0.241653 | + | 0.970363i | \(0.577690\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.0923 | 0.569216 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.02744 | −0.0386957 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.3007 | 0.575443 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.8228 | −0.594236 | −0.297118 | − | 0.954841i | \(-0.596025\pi\) | ||||
−0.297118 | + | 0.954841i | \(0.596025\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.55475 | −0.320828 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.42865 | 0.0535032 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.13194 | 0.117128 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 25.8485 | 0.965329 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 43.5601 | 1.62452 | 0.812259 | − | 0.583298i | \(-0.198238\pi\) | ||||
0.812259 | + | 0.583298i | \(0.198238\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.1379 | 0.601007 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.0431 | 0.373506 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.6228 | 0.468799 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −48.8752 | −1.81268 | −0.906340 | − | 0.422549i | \(-0.861135\pi\) | ||||
−0.906340 | + | 0.422549i | \(0.861135\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.2049 | 0.933516 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −26.6815 | −0.986849 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.61109 | 0.207250 | 0.103625 | − | 0.994616i | \(-0.466956\pi\) | ||||
0.103625 | + | 0.994616i | \(0.466956\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.16555 | 0.153649 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −27.1472 | −0.999981 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.778753 | 0.0286469 | 0.0143235 | − | 0.999897i | \(-0.495441\pi\) | ||||
0.0143235 | + | 0.999897i | \(0.495441\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 25.3538 | 0.931395 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.2378 | −0.962571 | −0.481285 | − | 0.876564i | \(-0.659830\pi\) | ||||
−0.481285 | + | 0.876564i | \(0.659830\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.23904 | −0.228581 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.17491 | −0.0795756 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 39.7525 | 1.45252 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −45.6386 | −1.66538 | −0.832688 | − | 0.553742i | \(-0.813200\pi\) | ||||
−0.832688 | + | 0.553742i | \(0.813200\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.9537 | −0.581385 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.08859 | −0.112405 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.3332 | 1.02979 | 0.514893 | − | 0.857254i | \(-0.327832\pi\) | ||||
0.514893 | + | 0.857254i | \(0.327832\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.727425 | −0.0264038 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.80438 | 0.355408 | 0.177704 | − | 0.984084i | \(-0.443133\pi\) | ||||
0.177704 | + | 0.984084i | \(0.443133\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −43.8466 | −1.58735 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.44298 | −0.0521710 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17.9815 | −0.649275 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.2777 | 1.16396 | 0.581981 | − | 0.813202i | \(-0.302278\pi\) | ||||
0.581981 | + | 0.813202i | \(0.302278\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.0064 | 0.360371 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −28.9014 | −1.03951 | −0.519755 | − | 0.854315i | \(-0.673977\pi\) | ||||
−0.519755 | + | 0.854315i | \(0.673977\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −34.2004 | −1.22851 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12.8247 | 0.460084 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 27.0966 | 0.970837 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.64964 | −0.166377 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −14.3920 | −0.514330 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.93919 | 0.140596 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37.9186 | −1.35165 | −0.675827 | − | 0.737060i | \(-0.736213\pi\) | ||||
−0.675827 | + | 0.737060i | \(0.736213\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −28.7331 | −1.02292 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.5496 | −0.552881 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.2069 | 0.611033 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.616137 | 0.0218521 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.20227 | −0.113430 | −0.0567150 | − | 0.998390i | \(-0.518063\pi\) | ||||
−0.0567150 | + | 0.998390i | \(0.518063\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.28557 | 0.257745 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −21.9960 | −0.777189 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 38.8325 | 1.37037 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.282911 | 0.00997130 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 27.5109 | 0.968428 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.1070 | 0.460819 | 0.230410 | − | 0.973094i | \(-0.425993\pi\) | ||||
0.230410 | + | 0.973094i | \(0.425993\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.81554 | −0.169097 | −0.0845483 | − | 0.996419i | \(-0.526945\pi\) | ||||
−0.0845483 | + | 0.996419i | \(0.526945\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.36727 | 0.118095 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.15938 | −0.180725 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 53.2542 | 1.86313 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −18.6502 | −0.651690 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.5024 | 0.506139 | 0.253069 | − | 0.967448i | \(-0.418560\pi\) | ||||
0.253069 | + | 0.967448i | \(0.418560\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −41.2620 | −1.43830 | −0.719152 | − | 0.694853i | \(-0.755469\pi\) | ||||
−0.719152 | + | 0.694853i | \(0.755469\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 17.4138 | 0.606272 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.5334 | 1.20084 | 0.600422 | − | 0.799684i | \(-0.294999\pi\) | ||||
0.600422 | + | 0.799684i | \(0.294999\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −39.6825 | −1.37823 | −0.689115 | − | 0.724652i | \(-0.742001\pi\) | ||||
−0.689115 | + | 0.724652i | \(0.742001\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.32383 | 0.0459232 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −29.5379 | −1.02343 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.339536 | −0.0117501 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 38.9939 | 1.34783 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.33133 | 0.184058 | 0.0920290 | − | 0.995756i | \(-0.470665\pi\) | ||||
0.0920290 | + | 0.995756i | \(0.470665\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.3222 | −0.769731 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.68505 | 0.333571 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.758701 | 0.0261001 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.6443 | 0.434465 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 40.0743 | 1.37535 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.505366 | 0.0173237 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.06747 | 0.241986 | 0.120993 | − | 0.992653i | \(-0.461392\pi\) | ||||
0.120993 | + | 0.992653i | \(0.461392\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.88008 | 0.0984966 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −57.2790 | −1.95661 | −0.978307 | − | 0.207162i | \(-0.933577\pi\) | ||||
−0.978307 | + | 0.207162i | \(0.933577\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.80660 | −0.266358 | −0.133179 | − | 0.991092i | \(-0.542518\pi\) | ||||
−0.133179 | + | 0.991092i | \(0.542518\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 23.0254 | 0.784705 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41.5422 | 1.41411 | 0.707057 | − | 0.707157i | \(-0.250022\pi\) | ||||
0.707057 | + | 0.707157i | \(0.250022\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.27147 | 0.111233 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.73721 | 0.330693 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.2775 | 0.586100 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.6834 | 1.07355 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.44994 | −0.116763 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.7051 | −0.463315 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.0074 | 0.878207 | 0.439103 | − | 0.898437i | \(-0.355296\pi\) | ||||
0.439103 | + | 0.898437i | \(0.355296\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −20.5778 | −0.694070 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.5891 | 1.03057 | 0.515286 | − | 0.857018i | \(-0.327686\pi\) | ||||
0.515286 | + | 0.857018i | \(0.327686\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.4371 | −1.05794 | −0.528971 | − | 0.848640i | \(-0.677422\pi\) | ||||
−0.528971 | + | 0.848640i | \(0.677422\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.35961 | 0.0793174 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.6686 | −0.929020 | −0.464510 | − | 0.885568i | \(-0.653770\pi\) | ||||
−0.464510 | + | 0.885568i | \(0.653770\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.9873 | −0.569735 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.11458 | −0.271849 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14.5415 | −0.486612 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.55184 | −0.152151 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.848973 | 0.0283464 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −18.0929 | −0.603432 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.36902 | −0.145553 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 45.2530 | 1.50592 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.50703 | 0.216301 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.7131 | 1.61749 | 0.808746 | − | 0.588159i | \(-0.200147\pi\) | ||||
0.808746 | + | 0.588159i | \(0.200147\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.21576 | 0.172996 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.6411 | −0.717002 | −0.358501 | − | 0.933529i | \(-0.616712\pi\) | ||||
−0.358501 | + | 0.933529i | \(0.616712\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.39253 | 0.145372 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.25796 | −0.0746457 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 33.7019 | 1.11294 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.0283 | 0.759634 | 0.379817 | − | 0.925062i | \(-0.375987\pi\) | ||||
0.379817 | + | 0.925062i | \(0.375987\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −31.8156 | −1.04836 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.42657 | 0.178618 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.0980 | −0.397778 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.50114 | 0.180681 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.5264 | 0.771877 | 0.385939 | − | 0.922524i | \(-0.373878\pi\) | ||||
0.385939 | + | 0.922524i | \(0.373878\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 58.9555 | 1.93219 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.26807 | 0.172469 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.91430 | 0.0953078 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.6086 | −1.32662 | −0.663312 | − | 0.748343i | \(-0.730850\pi\) | ||||
−0.663312 | + | 0.748343i | \(0.730850\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.55676 | −0.0834366 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.6490 | 1.06433 | 0.532164 | − | 0.846641i | \(-0.321379\pi\) | ||||
0.532164 | + | 0.846641i | \(0.321379\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.907332 | 0.0295468 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.72187 | 0.251192 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34.3652 | −1.11672 | −0.558359 | − | 0.829599i | \(-0.688569\pi\) | ||||
−0.558359 | + | 0.829599i | \(0.688569\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −45.3212 | −1.47119 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.70342 | −0.120092 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.47688 | −0.177413 | −0.0887067 | − | 0.996058i | \(-0.528273\pi\) | ||||
−0.0887067 | + | 0.996058i | \(0.528273\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.17796 | −0.264633 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.21238 | 0.297794 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −42.9191 | −1.38593 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.0211 | 0.581325 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.5510 | 0.436673 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.37947 | 0.0765979 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.38197 | 0.0444413 | 0.0222206 | − | 0.999753i | \(-0.492926\pi\) | ||||
0.0222206 | + | 0.999753i | \(0.492926\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 23.5919 | 0.757882 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.5046 | 0.850573 | 0.425286 | − | 0.905059i | \(-0.360173\pi\) | ||||
0.425286 | + | 0.905059i | \(0.360173\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −26.6745 | −0.855146 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −20.3236 | −0.650876 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −61.3580 | −1.96302 | −0.981508 | − | 0.191420i | \(-0.938691\pi\) | ||||
−0.981508 | + | 0.191420i | \(0.938691\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 44.4240 | 1.41980 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.9466 | −0.477208 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17.6436 | 0.562743 | 0.281371 | − | 0.959599i | \(-0.409211\pi\) | ||||
0.281371 | + | 0.959599i | \(0.409211\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.59486 | −0.178267 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.3567 | −0.393317 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.78322 | 0.0567031 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.48199 | 0.301205 | 0.150603 | − | 0.988594i | \(-0.451879\pi\) | ||||
0.150603 | + | 0.988594i | \(0.451879\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −26.5294 | −0.841885 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.632402 | 0.0200485 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.0000 | −1.23514 | −0.617571 | − | 0.786515i | \(-0.711883\pi\) | ||||
−0.617571 | + | 0.786515i | \(0.711883\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 13.7936 | 0.436411 |
(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 | 1336.2.a.e.1.3 | ✓ | 12 | |
4.3 | odd | 2 | 2672.2.a.n.1.10 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1336.2.a.e.1.3 | ✓ | 12 | 1.1 | even | 1 | trivial | |
2672.2.a.n.1.10 | 12 | 4.3 | odd | 2 |