Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7623,2,Mod(1,7623)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7623, 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("7623.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7623.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: | \(60.8699614608\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.7488.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4x^{2} + 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2541) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.326909\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7623.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.05896 | −1.45590 | −0.727952 | − | 0.685628i | \(-0.759528\pi\) | ||||
−0.727952 | + | 0.685628i | \(0.759528\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.23931 | 1.11966 | ||||||||
\(5\) | 3.05896 | 1.36801 | 0.684004 | − | 0.729478i | \(-0.260237\pi\) | ||||
0.684004 | + | 0.729478i | \(0.260237\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −0.492737 | −0.174209 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −6.29827 | −1.99169 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.32691 | −0.922718 | −0.461359 | − | 0.887213i | \(-0.652638\pi\) | ||||
−0.461359 | + | 0.887213i | \(0.652638\pi\) | |||||||
\(14\) | −2.05896 | −0.550280 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.46410 | −0.866025 | ||||||||
\(17\) | 5.37651 | 1.30399 | 0.651997 | − | 0.758221i | \(-0.273931\pi\) | ||||
0.651997 | + | 0.758221i | \(0.273931\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.29827 | −1.90375 | −0.951877 | − | 0.306480i | \(-0.900849\pi\) | ||||
−0.951877 | + | 0.306480i | \(0.900849\pi\) | |||||||
\(20\) | 6.84997 | 1.53170 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.74141 | 0.363110 | 0.181555 | − | 0.983381i | \(-0.441887\pi\) | ||||
0.181555 | + | 0.983381i | \(0.441887\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.35723 | 0.871446 | ||||||||
\(26\) | 6.84997 | 1.34339 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.23931 | 0.423191 | ||||||||
\(29\) | −8.16277 | −1.51579 | −0.757894 | − | 0.652378i | \(-0.773772\pi\) | ||||
−0.757894 | + | 0.652378i | \(0.773772\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.44999 | −0.978847 | −0.489424 | − | 0.872046i | \(-0.662793\pi\) | ||||
−0.489424 | + | 0.872046i | \(0.662793\pi\) | |||||||
\(32\) | 8.11792 | 1.43506 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −11.0700 | −1.89849 | ||||||||
\(35\) | 3.05896 | 0.517059 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.53242 | 0.745126 | 0.372563 | − | 0.928007i | \(-0.378479\pi\) | ||||
0.372563 | + | 0.928007i | \(0.378479\pi\) | |||||||
\(38\) | 17.0858 | 2.77168 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.50726 | −0.238319 | ||||||||
\(41\) | −6.84997 | −1.06979 | −0.534893 | − | 0.844920i | \(-0.679648\pi\) | ||||
−0.534893 | + | 0.844920i | \(0.679648\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.84997 | 0.282118 | 0.141059 | − | 0.990001i | \(-0.454949\pi\) | ||||
0.141059 | + | 0.990001i | \(0.454949\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.58550 | −0.528653 | ||||||||
\(47\) | 7.28416 | 1.06250 | 0.531252 | − | 0.847214i | \(-0.321722\pi\) | ||||
0.531252 | + | 0.847214i | \(0.321722\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −8.97136 | −1.26874 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.44999 | −1.03313 | ||||||||
\(53\) | 0.985474 | 0.135365 | 0.0676827 | − | 0.997707i | \(-0.478439\pi\) | ||||
0.0676827 | + | 0.997707i | \(0.478439\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.492737 | −0.0658448 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 16.8068 | 2.20684 | ||||||||
\(59\) | −4.52306 | −0.588852 | −0.294426 | − | 0.955674i | \(-0.595129\pi\) | ||||
−0.294426 | + | 0.955674i | \(0.595129\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.0845 | 1.54727 | 0.773633 | − | 0.633634i | \(-0.218437\pi\) | ||||
0.773633 | + | 0.633634i | \(0.218437\pi\) | |||||||
\(62\) | 11.2213 | 1.42511 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.78626 | −1.22328 | ||||||||
\(65\) | −10.1769 | −1.26229 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.170993 | 0.0208901 | 0.0104451 | − | 0.999945i | \(-0.496675\pi\) | ||||
0.0104451 | + | 0.999945i | \(0.496675\pi\) | |||||||
\(68\) | 12.0397 | 1.46003 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.29827 | −0.752788 | ||||||||
\(71\) | 10.0017 | 1.18698 | 0.593491 | − | 0.804841i | \(-0.297749\pi\) | ||||
0.593491 | + | 0.804841i | \(0.297749\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.7910 | −1.49707 | −0.748537 | − | 0.663093i | \(-0.769243\pi\) | ||||
−0.748537 | + | 0.663093i | \(0.769243\pi\) | |||||||
\(74\) | −9.33207 | −1.08483 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −18.5824 | −2.13155 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.6794 | −1.65156 | −0.825780 | − | 0.563992i | \(-0.809265\pi\) | ||||
−0.825780 | + | 0.563992i | \(0.809265\pi\) | |||||||
\(80\) | −10.5965 | −1.18473 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 14.1038 | 1.55751 | ||||||||
\(83\) | −1.62993 | −0.178908 | −0.0894540 | − | 0.995991i | \(-0.528512\pi\) | ||||
−0.0894540 | + | 0.995991i | \(0.528512\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.4465 | 1.78388 | ||||||||
\(86\) | −3.80901 | −0.410736 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.9872 | −1.48264 | −0.741318 | − | 0.671154i | \(-0.765799\pi\) | ||||
−0.741318 | + | 0.671154i | \(0.765799\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.32691 | −0.348755 | ||||||||
\(92\) | 3.89957 | 0.406558 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −14.9978 | −1.54690 | ||||||||
\(95\) | −25.3841 | −2.60435 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.44483 | 0.349769 | 0.174885 | − | 0.984589i | \(-0.444045\pi\) | ||||
0.174885 | + | 0.984589i | \(0.444045\pi\) | |||||||
\(98\) | −2.05896 | −0.207986 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.75721 | 0.975721 | ||||||||
\(101\) | 9.35554 | 0.930911 | 0.465456 | − | 0.885071i | \(-0.345890\pi\) | ||||
0.465456 | + | 0.885071i | \(0.345890\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.6952 | 1.25089 | 0.625447 | − | 0.780267i | \(-0.284917\pi\) | ||||
0.625447 | + | 0.780267i | \(0.284917\pi\) | |||||||
\(104\) | 1.63929 | 0.160746 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.02905 | −0.197079 | ||||||||
\(107\) | 11.7589 | 1.13678 | 0.568388 | − | 0.822761i | \(-0.307567\pi\) | ||||
0.568388 | + | 0.822761i | \(0.307567\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.9038 | −1.52330 | −0.761652 | − | 0.647986i | \(-0.775611\pi\) | ||||
−0.761652 | + | 0.647986i | \(0.775611\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.46410 | −0.327327 | ||||||||
\(113\) | −7.30763 | −0.687444 | −0.343722 | − | 0.939071i | \(-0.611688\pi\) | ||||
−0.343722 | + | 0.939071i | \(0.611688\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.32691 | 0.496737 | ||||||||
\(116\) | −18.2790 | −1.69716 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.31280 | 0.857313 | ||||||||
\(119\) | 5.37651 | 0.492864 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −24.8816 | −2.25267 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −12.2042 | −1.09597 | ||||||||
\(125\) | −1.96620 | −0.175862 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.32860 | 0.384101 | 0.192050 | − | 0.981385i | \(-0.438486\pi\) | ||||
0.192050 | + | 0.981385i | \(0.438486\pi\) | |||||||
\(128\) | 3.91368 | 0.345923 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 20.9538 | 1.83777 | ||||||||
\(131\) | 8.71236 | 0.761202 | 0.380601 | − | 0.924739i | \(-0.375717\pi\) | ||||
0.380601 | + | 0.924739i | \(0.375717\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.29827 | −0.719552 | ||||||||
\(134\) | −0.352068 | −0.0304140 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.64920 | −0.227167 | ||||||||
\(137\) | 0.234149 | 0.0200047 | 0.0100024 | − | 0.999950i | \(-0.496816\pi\) | ||||
0.0100024 | + | 0.999950i | \(0.496816\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.3200 | −1.63870 | −0.819349 | − | 0.573296i | \(-0.805665\pi\) | ||||
−0.819349 | + | 0.573296i | \(0.805665\pi\) | |||||||
\(140\) | 6.84997 | 0.578928 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −20.5931 | −1.72813 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −24.9696 | −2.07361 | ||||||||
\(146\) | 26.3362 | 2.17960 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.1495 | 0.834285 | ||||||||
\(149\) | −5.20090 | −0.426074 | −0.213037 | − | 0.977044i | \(-0.568336\pi\) | ||||
−0.213037 | + | 0.977044i | \(0.568336\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.35682 | −0.517310 | −0.258655 | − | 0.965970i | \(-0.583279\pi\) | ||||
−0.258655 | + | 0.965970i | \(0.583279\pi\) | |||||||
\(152\) | 4.08887 | 0.331651 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.6713 | −1.33907 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0141 | −0.799213 | −0.399606 | − | 0.916687i | \(-0.630853\pi\) | ||||
−0.399606 | + | 0.916687i | \(0.630853\pi\) | |||||||
\(158\) | 30.2243 | 2.40451 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 24.8324 | 1.96317 | ||||||||
\(161\) | 1.74141 | 0.137242 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.50337 | −0.666035 | −0.333018 | − | 0.942921i | \(-0.608067\pi\) | ||||
−0.333018 | + | 0.942921i | \(0.608067\pi\) | |||||||
\(164\) | −15.3392 | −1.19779 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.35596 | 0.260473 | ||||||||
\(167\) | 2.93756 | 0.227316 | 0.113658 | − | 0.993520i | \(-0.463743\pi\) | ||||
0.113658 | + | 0.993520i | \(0.463743\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.93168 | −0.148591 | ||||||||
\(170\) | −33.8627 | −2.59715 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.14266 | 0.315875 | ||||||||
\(173\) | −20.6841 | −1.57259 | −0.786293 | − | 0.617854i | \(-0.788002\pi\) | ||||
−0.786293 | + | 0.617854i | \(0.788002\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.35723 | 0.329376 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 28.7990 | 2.15858 | ||||||||
\(179\) | −6.14697 | −0.459446 | −0.229723 | − | 0.973256i | \(-0.573782\pi\) | ||||
−0.229723 | + | 0.973256i | \(0.573782\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.2458 | −1.43053 | −0.715263 | − | 0.698856i | \(-0.753693\pi\) | ||||
−0.715263 | + | 0.698856i | \(0.753693\pi\) | |||||||
\(182\) | 6.84997 | 0.507754 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.858058 | −0.0632569 | ||||||||
\(185\) | 13.8645 | 1.01934 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 16.3115 | 1.18964 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 52.2648 | 3.79169 | ||||||||
\(191\) | −25.5978 | −1.85219 | −0.926097 | − | 0.377287i | \(-0.876857\pi\) | ||||
−0.926097 | + | 0.377287i | \(0.876857\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.1962 | −0.805917 | −0.402958 | − | 0.915218i | \(-0.632018\pi\) | ||||
−0.402958 | + | 0.915218i | \(0.632018\pi\) | |||||||
\(194\) | −7.09276 | −0.509230 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.23931 | 0.159951 | ||||||||
\(197\) | −17.4687 | −1.24459 | −0.622297 | − | 0.782781i | \(-0.713800\pi\) | ||||
−0.622297 | + | 0.782781i | \(0.713800\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.71963 | −0.476342 | −0.238171 | − | 0.971223i | \(-0.576548\pi\) | ||||
−0.238171 | + | 0.971223i | \(0.576548\pi\) | |||||||
\(200\) | −2.14697 | −0.151814 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −19.2627 | −1.35532 | ||||||||
\(203\) | −8.16277 | −0.572914 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −20.9538 | −1.46348 | ||||||||
\(206\) | −26.1389 | −1.82118 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 11.5247 | 0.799098 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.2293 | 1.39264 | 0.696321 | − | 0.717730i | \(-0.254819\pi\) | ||||
0.696321 | + | 0.717730i | \(0.254819\pi\) | |||||||
\(212\) | 2.20679 | 0.151563 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −24.2111 | −1.65504 | ||||||||
\(215\) | 5.65898 | 0.385939 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.44999 | −0.369970 | ||||||||
\(218\) | 32.7452 | 2.21779 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.8871 | −1.20322 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.8705 | 0.794909 | 0.397454 | − | 0.917622i | \(-0.369894\pi\) | ||||
0.397454 | + | 0.917622i | \(0.369894\pi\) | |||||||
\(224\) | 8.11792 | 0.542401 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.0461 | 1.00085 | ||||||||
\(227\) | 13.9521 | 0.926033 | 0.463016 | − | 0.886350i | \(-0.346767\pi\) | ||||
0.463016 | + | 0.886350i | \(0.346767\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.8324 | 1.64097 | 0.820485 | − | 0.571668i | \(-0.193703\pi\) | ||||
0.820485 | + | 0.571668i | \(0.193703\pi\) | |||||||
\(230\) | −10.9679 | −0.723201 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.02210 | 0.264064 | ||||||||
\(233\) | −11.8265 | −0.774780 | −0.387390 | − | 0.921916i | \(-0.626623\pi\) | ||||
−0.387390 | + | 0.921916i | \(0.626623\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 22.2820 | 1.45351 | ||||||||
\(236\) | −10.1286 | −0.659313 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −11.0700 | −0.717562 | ||||||||
\(239\) | −8.86522 | −0.573443 | −0.286722 | − | 0.958014i | \(-0.592565\pi\) | ||||
−0.286722 | + | 0.958014i | \(0.592565\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.3922 | −0.733834 | −0.366917 | − | 0.930254i | \(-0.619587\pi\) | ||||
−0.366917 | + | 0.930254i | \(0.619587\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 27.0611 | 1.73241 | ||||||||
\(245\) | 3.05896 | 0.195430 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 27.6076 | 1.75663 | ||||||||
\(248\) | 2.68541 | 0.170524 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.04833 | 0.256039 | ||||||||
\(251\) | −9.71866 | −0.613436 | −0.306718 | − | 0.951800i | \(-0.599231\pi\) | ||||
−0.306718 | + | 0.951800i | \(0.599231\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −8.91241 | −0.559214 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.5144 | 0.719651 | ||||||||
\(257\) | 20.0456 | 1.25041 | 0.625204 | − | 0.780461i | \(-0.285016\pi\) | ||||
0.625204 | + | 0.780461i | \(0.285016\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.53242 | 0.281631 | ||||||||
\(260\) | −22.7892 | −1.41333 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −17.9384 | −1.10824 | ||||||||
\(263\) | 12.9345 | 0.797576 | 0.398788 | − | 0.917043i | \(-0.369431\pi\) | ||||
0.398788 | + | 0.917043i | \(0.369431\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.01453 | 0.185181 | ||||||||
\(266\) | 17.0858 | 1.04760 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.382907 | 0.0233898 | ||||||||
\(269\) | −4.44958 | −0.271295 | −0.135648 | − | 0.990757i | \(-0.543312\pi\) | ||||
−0.135648 | + | 0.990757i | \(0.543312\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.59696 | −0.582974 | −0.291487 | − | 0.956575i | \(-0.594150\pi\) | ||||
−0.291487 | + | 0.956575i | \(0.594150\pi\) | |||||||
\(272\) | −18.6248 | −1.12929 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.482104 | −0.0291249 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.80037 | 0.168258 | 0.0841290 | − | 0.996455i | \(-0.473189\pi\) | ||||
0.0841290 | + | 0.996455i | \(0.473189\pi\) | |||||||
\(278\) | 39.7790 | 2.38579 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.50726 | −0.0900762 | ||||||||
\(281\) | 15.4721 | 0.922988 | 0.461494 | − | 0.887143i | \(-0.347314\pi\) | ||||
0.461494 | + | 0.887143i | \(0.347314\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.9076 | 1.54004 | 0.770022 | − | 0.638017i | \(-0.220245\pi\) | ||||
0.770022 | + | 0.638017i | \(0.220245\pi\) | |||||||
\(284\) | 22.3969 | 1.32901 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.84997 | −0.404341 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.9068 | 0.700401 | ||||||||
\(290\) | 51.4113 | 3.01898 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −28.6431 | −1.67621 | ||||||||
\(293\) | 23.3799 | 1.36587 | 0.682934 | − | 0.730480i | \(-0.260704\pi\) | ||||
0.682934 | + | 0.730480i | \(0.260704\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.8359 | −0.805555 | ||||||||
\(296\) | −2.23329 | −0.129808 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.7084 | 0.620323 | ||||||||
\(299\) | −5.79352 | −0.335048 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.84997 | 0.106630 | ||||||||
\(302\) | 13.0884 | 0.753154 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 28.7461 | 1.64870 | ||||||||
\(305\) | 36.9661 | 2.11667 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.0742 | 0.574965 | 0.287483 | − | 0.957786i | \(-0.407182\pi\) | ||||
0.287483 | + | 0.957786i | \(0.407182\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 34.3255 | 1.94956 | ||||||||
\(311\) | −8.26014 | −0.468390 | −0.234195 | − | 0.972190i | \(-0.575245\pi\) | ||||
−0.234195 | + | 0.972190i | \(0.575245\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.39189 | −0.417814 | −0.208907 | − | 0.977935i | \(-0.566991\pi\) | ||||
−0.208907 | + | 0.977935i | \(0.566991\pi\) | |||||||
\(314\) | 20.6186 | 1.16358 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −32.8718 | −1.84918 | ||||||||
\(317\) | −31.1600 | −1.75012 | −0.875060 | − | 0.484014i | \(-0.839178\pi\) | ||||
−0.875060 | + | 0.484014i | \(0.839178\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −29.9358 | −1.67346 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.58550 | −0.199812 | ||||||||
\(323\) | −44.6157 | −2.48249 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.4961 | −0.804100 | ||||||||
\(326\) | 17.5081 | 0.969684 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.37523 | 0.186366 | ||||||||
\(329\) | 7.28416 | 0.401589 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.0110 | −1.09991 | −0.549953 | − | 0.835195i | \(-0.685355\pi\) | ||||
−0.549953 | + | 0.835195i | \(0.685355\pi\) | |||||||
\(332\) | −3.64992 | −0.200316 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.04833 | −0.330950 | ||||||||
\(335\) | 0.523061 | 0.0285779 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.4973 | 1.11656 | 0.558278 | − | 0.829654i | \(-0.311462\pi\) | ||||
0.558278 | + | 0.829654i | \(0.311462\pi\) | |||||||
\(338\) | 3.97725 | 0.216334 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 36.8289 | 1.99733 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −0.911549 | −0.0491474 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 42.5878 | 2.28953 | ||||||||
\(347\) | 33.7959 | 1.81426 | 0.907131 | − | 0.420849i | \(-0.138268\pi\) | ||||
0.907131 | + | 0.420849i | \(0.138268\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −33.0030 | −1.76661 | −0.883304 | − | 0.468801i | \(-0.844686\pi\) | ||||
−0.883304 | + | 0.468801i | \(0.844686\pi\) | |||||||
\(350\) | −8.97136 | −0.479540 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.49315 | −0.505270 | −0.252635 | − | 0.967562i | \(-0.581297\pi\) | ||||
−0.252635 | + | 0.967562i | \(0.581297\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 30.5948 | 1.62380 | ||||||||
\(356\) | −31.3216 | −1.66004 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.6564 | 0.668910 | ||||||||
\(359\) | −13.0490 | −0.688702 | −0.344351 | − | 0.938841i | \(-0.611901\pi\) | ||||
−0.344351 | + | 0.938841i | \(0.611901\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 49.8613 | 2.62428 | ||||||||
\(362\) | 39.6262 | 2.08271 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.44999 | −0.390486 | ||||||||
\(365\) | −39.1272 | −2.04801 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.93419 | −0.100964 | −0.0504819 | − | 0.998725i | \(-0.516076\pi\) | ||||
−0.0504819 | + | 0.998725i | \(0.516076\pi\) | |||||||
\(368\) | −6.03243 | −0.314462 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −28.5464 | −1.48406 | ||||||||
\(371\) | 0.985474 | 0.0511633 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.8816 | −1.23654 | −0.618270 | − | 0.785966i | \(-0.712166\pi\) | ||||
−0.618270 | + | 0.785966i | \(0.712166\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.58918 | −0.185098 | ||||||||
\(377\) | 27.1568 | 1.39865 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −38.0262 | −1.95327 | −0.976637 | − | 0.214895i | \(-0.931059\pi\) | ||||
−0.976637 | + | 0.214895i | \(0.931059\pi\) | |||||||
\(380\) | −56.8429 | −2.91598 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 52.7049 | 2.69662 | ||||||||
\(383\) | −31.5678 | −1.61304 | −0.806519 | − | 0.591208i | \(-0.798651\pi\) | ||||
−0.806519 | + | 0.591208i | \(0.798651\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 23.0524 | 1.17334 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.71405 | 0.391621 | ||||||||
\(389\) | −10.1308 | −0.513652 | −0.256826 | − | 0.966458i | \(-0.582677\pi\) | ||||
−0.256826 | + | 0.966458i | \(0.582677\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.36271 | 0.473493 | ||||||||
\(392\) | −0.492737 | −0.0248870 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 35.9674 | 1.81201 | ||||||||
\(395\) | −44.9037 | −2.25935 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.51188 | −0.377010 | −0.188505 | − | 0.982072i | \(-0.560364\pi\) | ||||
−0.188505 | + | 0.982072i | \(0.560364\pi\) | |||||||
\(398\) | 13.8354 | 0.693508 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −15.0939 | −0.754695 | ||||||||
\(401\) | −19.2645 | −0.962022 | −0.481011 | − | 0.876715i | \(-0.659730\pi\) | ||||
−0.481011 | + | 0.876715i | \(0.659730\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.1316 | 0.903201 | ||||||||
\(404\) | 20.9500 | 1.04230 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 16.8068 | 0.834108 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.0605 | −0.645801 | −0.322900 | − | 0.946433i | \(-0.604658\pi\) | ||||
−0.322900 | + | 0.946433i | \(0.604658\pi\) | |||||||
\(410\) | 43.1430 | 2.13068 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 28.4285 | 1.40057 | ||||||||
\(413\) | −4.52306 | −0.222565 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.98589 | −0.244748 | ||||||||
\(416\) | −27.0076 | −1.32416 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.7589 | 1.50267 | 0.751335 | − | 0.659921i | \(-0.229410\pi\) | ||||
0.751335 | + | 0.659921i | \(0.229410\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.0657 | 0.782993 | 0.391497 | − | 0.920180i | \(-0.371957\pi\) | ||||
0.391497 | + | 0.920180i | \(0.371957\pi\) | |||||||
\(422\) | −41.6513 | −2.02755 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.485580 | −0.0235818 | ||||||||
\(425\) | 23.4267 | 1.13636 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.0845 | 0.584812 | ||||||||
\(428\) | 26.3319 | 1.27280 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.6516 | −0.561891 | ||||||||
\(431\) | 13.0752 | 0.629809 | 0.314904 | − | 0.949123i | \(-0.398028\pi\) | ||||
0.314904 | + | 0.949123i | \(0.398028\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.9757 | 0.623572 | 0.311786 | − | 0.950152i | \(-0.399073\pi\) | ||||
0.311786 | + | 0.950152i | \(0.399073\pi\) | |||||||
\(434\) | 11.2213 | 0.538640 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −35.6135 | −1.70558 | ||||||||
\(437\) | −14.4507 | −0.691271 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.9709 | 0.762252 | 0.381126 | − | 0.924523i | \(-0.375536\pi\) | ||||
0.381126 | + | 0.924523i | \(0.375536\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 36.8289 | 1.75177 | ||||||||
\(443\) | 21.2695 | 1.01055 | 0.505273 | − | 0.862959i | \(-0.331392\pi\) | ||||
0.505273 | + | 0.862959i | \(0.331392\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −42.7862 | −2.02826 | ||||||||
\(446\) | −24.4409 | −1.15731 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −9.78626 | −0.462357 | ||||||||
\(449\) | 6.63021 | 0.312899 | 0.156449 | − | 0.987686i | \(-0.449995\pi\) | ||||
0.156449 | + | 0.987686i | \(0.449995\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −16.3641 | −0.769702 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −28.7268 | −1.34821 | ||||||||
\(455\) | −10.1769 | −0.477099 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.1191 | −0.800796 | −0.400398 | − | 0.916341i | \(-0.631128\pi\) | ||||
−0.400398 | + | 0.916341i | \(0.631128\pi\) | |||||||
\(458\) | −51.1289 | −2.38910 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 11.9286 | 0.556175 | ||||||||
\(461\) | 19.1173 | 0.890380 | 0.445190 | − | 0.895436i | \(-0.353136\pi\) | ||||
0.445190 | + | 0.895436i | \(0.353136\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.0828 | 0.747433 | 0.373717 | − | 0.927543i | \(-0.378083\pi\) | ||||
0.373717 | + | 0.927543i | \(0.378083\pi\) | |||||||
\(464\) | 28.2767 | 1.31271 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 24.3503 | 1.12800 | ||||||||
\(467\) | 13.4920 | 0.624336 | 0.312168 | − | 0.950027i | \(-0.398945\pi\) | ||||
0.312168 | + | 0.950027i | \(0.398945\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.170993 | 0.00789573 | ||||||||
\(470\) | −45.8776 | −2.11618 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.22868 | 0.102583 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −36.1575 | −1.65902 | ||||||||
\(476\) | 12.0397 | 0.551838 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.2531 | 0.834878 | ||||||||
\(479\) | 25.0471 | 1.14443 | 0.572215 | − | 0.820103i | \(-0.306084\pi\) | ||||
0.572215 | + | 0.820103i | \(0.306084\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.0790 | −0.687541 | ||||||||
\(482\) | 23.4560 | 1.06839 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.5376 | 0.478487 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.7888 | −1.39517 | −0.697587 | − | 0.716500i | \(-0.745743\pi\) | ||||
−0.697587 | + | 0.716500i | \(0.745743\pi\) | |||||||
\(488\) | −5.95450 | −0.269548 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.29827 | −0.284527 | ||||||||
\(491\) | 39.1200 | 1.76546 | 0.882731 | − | 0.469879i | \(-0.155702\pi\) | ||||
0.882731 | + | 0.469879i | \(0.155702\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −43.8872 | −1.97658 | ||||||||
\(494\) | −56.8429 | −2.55748 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 18.8793 | 0.847707 | ||||||||
\(497\) | 10.0017 | 0.448637 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.5522 | 0.606682 | 0.303341 | − | 0.952882i | \(-0.401898\pi\) | ||||
0.303341 | + | 0.952882i | \(0.401898\pi\) | |||||||
\(500\) | −4.40294 | −0.196905 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 20.0103 | 0.893105 | ||||||||
\(503\) | −18.1214 | −0.807995 | −0.403997 | − | 0.914760i | \(-0.632380\pi\) | ||||
−0.403997 | + | 0.914760i | \(0.632380\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 28.6182 | 1.27349 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.69309 | 0.430061 | ||||||||
\(509\) | 40.4192 | 1.79155 | 0.895774 | − | 0.444510i | \(-0.146622\pi\) | ||||
0.895774 | + | 0.444510i | \(0.146622\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.7910 | −0.565841 | ||||||||
\(512\) | −31.5351 | −1.39367 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −41.2730 | −1.82047 | ||||||||
\(515\) | 38.8341 | 1.71123 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −9.33207 | −0.410028 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.01453 | 0.219902 | ||||||||
\(521\) | 7.74795 | 0.339444 | 0.169722 | − | 0.985492i | \(-0.445713\pi\) | ||||
0.169722 | + | 0.985492i | \(0.445713\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.6047 | −0.944706 | −0.472353 | − | 0.881409i | \(-0.656595\pi\) | ||||
−0.472353 | + | 0.881409i | \(0.656595\pi\) | |||||||
\(524\) | 19.5097 | 0.852286 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −26.6316 | −1.16119 | ||||||||
\(527\) | −29.3019 | −1.27641 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.9675 | −0.868151 | ||||||||
\(530\) | −6.20679 | −0.269606 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −18.5824 | −0.805651 | ||||||||
\(533\) | 22.7892 | 0.987111 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 35.9700 | 1.55512 | ||||||||
\(536\) | −0.0842547 | −0.00363925 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9.16150 | 0.394980 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −35.2507 | −1.51555 | −0.757773 | − | 0.652519i | \(-0.773712\pi\) | ||||
−0.757773 | + | 0.652519i | \(0.773712\pi\) | |||||||
\(542\) | 19.7598 | 0.848754 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 43.6460 | 1.87131 | ||||||||
\(545\) | −48.6490 | −2.08389 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.44775 | −0.232929 | −0.116465 | − | 0.993195i | \(-0.537156\pi\) | ||||
−0.116465 | + | 0.993195i | \(0.537156\pi\) | |||||||
\(548\) | 0.524333 | 0.0223984 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 67.7369 | 2.88569 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.6794 | −0.624231 | ||||||||
\(554\) | −5.76585 | −0.244968 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −43.2634 | −1.83478 | ||||||||
\(557\) | 8.73429 | 0.370084 | 0.185042 | − | 0.982731i | \(-0.440758\pi\) | ||||
0.185042 | + | 0.982731i | \(0.440758\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.15468 | −0.260315 | ||||||||
\(560\) | −10.5965 | −0.447786 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −31.8564 | −1.34378 | ||||||||
\(563\) | −15.2200 | −0.641448 | −0.320724 | − | 0.947173i | \(-0.603926\pi\) | ||||
−0.320724 | + | 0.947173i | \(0.603926\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.3538 | −0.940430 | ||||||||
\(566\) | −53.3426 | −2.24216 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.92820 | −0.206783 | ||||||||
\(569\) | −0.0166300 | −0.000697167 0 | −0.000348583 | − | 1.00000i | \(-0.500111\pi\) | ||||
−0.000348583 | 1.00000i | \(0.500111\pi\) | ||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.08632 | −0.254705 | −0.127352 | − | 0.991858i | \(-0.540648\pi\) | ||||
−0.127352 | + | 0.991858i | \(0.540648\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 14.1038 | 0.588682 | ||||||||
\(575\) | 7.58774 | 0.316430 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.6359 | −1.52517 | −0.762585 | − | 0.646888i | \(-0.776070\pi\) | ||||
−0.762585 | + | 0.646888i | \(0.776070\pi\) | |||||||
\(578\) | −24.5157 | −1.01972 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −55.9147 | −2.32173 | ||||||||
\(581\) | −1.62993 | −0.0676209 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 6.30261 | 0.260804 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −48.1382 | −1.98857 | ||||||||
\(587\) | −5.52836 | −0.228180 | −0.114090 | − | 0.993470i | \(-0.536395\pi\) | ||||
−0.114090 | + | 0.993470i | \(0.536395\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 45.2255 | 1.86349 | ||||||||
\(590\) | 28.4875 | 1.17281 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −15.7008 | −0.645298 | ||||||||
\(593\) | −33.1440 | −1.36106 | −0.680531 | − | 0.732719i | \(-0.738251\pi\) | ||||
−0.680531 | + | 0.732719i | \(0.738251\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.4465 | 0.674241 | ||||||||
\(596\) | −11.6464 | −0.477057 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 11.9286 | 0.487798 | ||||||||
\(599\) | −18.8290 | −0.769332 | −0.384666 | − | 0.923056i | \(-0.625683\pi\) | ||||
−0.384666 | + | 0.923056i | \(0.625683\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.88491 | 0.321632 | 0.160816 | − | 0.986984i | \(-0.448587\pi\) | ||||
0.160816 | + | 0.986984i | \(0.448587\pi\) | |||||||
\(602\) | −3.80901 | −0.155244 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −14.2349 | −0.579210 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.34563 | −0.0546175 | −0.0273087 | − | 0.999627i | \(-0.508694\pi\) | ||||
−0.0273087 | + | 0.999627i | \(0.508694\pi\) | |||||||
\(608\) | −67.3647 | −2.73200 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −76.1117 | −3.08167 | ||||||||
\(611\) | −24.2337 | −0.980392 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.8217 | −0.881372 | −0.440686 | − | 0.897661i | \(-0.645265\pi\) | ||||
−0.440686 | + | 0.897661i | \(0.645265\pi\) | |||||||
\(614\) | −20.7424 | −0.837094 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.1973 | −1.21570 | −0.607849 | − | 0.794053i | \(-0.707967\pi\) | ||||
−0.607849 | + | 0.794053i | \(0.707967\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −39.2011 | −1.57562 | −0.787812 | − | 0.615915i | \(-0.788786\pi\) | ||||
−0.787812 | + | 0.615915i | \(0.788786\pi\) | |||||||
\(620\) | −37.3323 | −1.49930 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17.0073 | 0.681930 | ||||||||
\(623\) | −13.9872 | −0.560384 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.8007 | −1.11203 | ||||||||
\(626\) | 15.2196 | 0.608298 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −22.4247 | −0.894844 | ||||||||
\(629\) | 24.3686 | 0.971640 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.44272 | 0.216671 | 0.108336 | − | 0.994114i | \(-0.465448\pi\) | ||||
0.108336 | + | 0.994114i | \(0.465448\pi\) | |||||||
\(632\) | 7.23308 | 0.287717 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 64.1572 | 2.54801 | ||||||||
\(635\) | 13.2410 | 0.525453 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.32691 | −0.131817 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 11.9718 | 0.473226 | ||||||||
\(641\) | −45.6066 | −1.80135 | −0.900677 | − | 0.434489i | \(-0.856929\pi\) | ||||
−0.900677 | + | 0.434489i | \(0.856929\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.2599 | 0.838407 | 0.419204 | − | 0.907892i | \(-0.362309\pi\) | ||||
0.419204 | + | 0.907892i | \(0.362309\pi\) | |||||||
\(644\) | 3.89957 | 0.153664 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 91.8620 | 3.61426 | ||||||||
\(647\) | 18.5756 | 0.730283 | 0.365141 | − | 0.930952i | \(-0.381021\pi\) | ||||
0.365141 | + | 0.930952i | \(0.381021\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 29.8469 | 1.17069 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −19.0417 | −0.745731 | ||||||||
\(653\) | 32.1882 | 1.25962 | 0.629812 | − | 0.776748i | \(-0.283132\pi\) | ||||
0.629812 | + | 0.776748i | \(0.283132\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26.6508 | 1.04133 | ||||||||
\(656\) | 23.7290 | 0.926461 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −14.9978 | −0.584675 | ||||||||
\(659\) | 40.6203 | 1.58234 | 0.791172 | − | 0.611594i | \(-0.209471\pi\) | ||||
0.791172 | + | 0.611594i | \(0.209471\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.69278 | 0.299215 | 0.149607 | − | 0.988746i | \(-0.452199\pi\) | ||||
0.149607 | + | 0.988746i | \(0.452199\pi\) | |||||||
\(662\) | 41.2019 | 1.60136 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.803127 | 0.0311674 | ||||||||
\(665\) | −25.3841 | −0.984352 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.2147 | −0.550397 | ||||||||
\(668\) | 6.57813 | 0.254515 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.07696 | −0.0416066 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.24740 | −0.279367 | −0.139683 | − | 0.990196i | \(-0.544608\pi\) | ||||
−0.139683 | + | 0.990196i | \(0.544608\pi\) | |||||||
\(674\) | −42.2030 | −1.62560 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.32564 | −0.166371 | ||||||||
\(677\) | 6.52296 | 0.250698 | 0.125349 | − | 0.992113i | \(-0.459995\pi\) | ||||
0.125349 | + | 0.992113i | \(0.459995\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.44483 | 0.132200 | ||||||||
\(680\) | −8.10381 | −0.310767 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.12170 | −0.0811846 | −0.0405923 | − | 0.999176i | \(-0.512924\pi\) | ||||
−0.0405923 | + | 0.999176i | \(0.512924\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.716253 | 0.0273666 | ||||||||
\(686\) | −2.05896 | −0.0786114 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.40848 | −0.244321 | ||||||||
\(689\) | −3.27858 | −0.124904 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.66834 | −0.215634 | −0.107817 | − | 0.994171i | \(-0.534386\pi\) | ||||
−0.107817 | + | 0.994171i | \(0.534386\pi\) | |||||||
\(692\) | −46.3183 | −1.76076 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −69.5845 | −2.64139 | ||||||||
\(695\) | −59.0990 | −2.24175 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −36.8289 | −1.39499 | ||||||||
\(698\) | 67.9518 | 2.57201 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 9.75721 | 0.368788 | ||||||||
\(701\) | 8.22087 | 0.310498 | 0.155249 | − | 0.987875i | \(-0.450382\pi\) | ||||
0.155249 | + | 0.987875i | \(0.450382\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −37.6113 | −1.41854 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 19.5460 | 0.735624 | ||||||||
\(707\) | 9.35554 | 0.351851 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.38116 | −0.239649 | −0.119825 | − | 0.992795i | \(-0.538233\pi\) | ||||
−0.119825 | + | 0.992795i | \(0.538233\pi\) | |||||||
\(710\) | −62.9934 | −2.36410 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.89199 | 0.258288 | ||||||||
\(713\) | −9.49068 | −0.355429 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −13.7650 | −0.514422 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 26.8675 | 1.00268 | ||||||||
\(719\) | −22.6376 | −0.844241 | −0.422121 | − | 0.906540i | \(-0.638714\pi\) | ||||
−0.422121 | + | 0.906540i | \(0.638714\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.6952 | 0.472794 | ||||||||
\(722\) | −102.662 | −3.82070 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −43.0973 | −1.60170 | ||||||||
\(725\) | −35.5671 | −1.32093 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.6482 | 0.914153 | 0.457076 | − | 0.889427i | \(-0.348897\pi\) | ||||
0.457076 | + | 0.889427i | \(0.348897\pi\) | |||||||
\(728\) | 1.63929 | 0.0607562 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 80.5613 | 2.98171 | ||||||||
\(731\) | 9.94637 | 0.367880 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 42.4229 | 1.56693 | 0.783464 | − | 0.621438i | \(-0.213451\pi\) | ||||
0.783464 | + | 0.621438i | \(0.213451\pi\) | |||||||
\(734\) | 3.98241 | 0.146994 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 14.1366 | 0.521084 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.2443 | −0.634343 | −0.317172 | − | 0.948368i | \(-0.602733\pi\) | ||||
−0.317172 | + | 0.948368i | \(0.602733\pi\) | |||||||
\(740\) | 31.0470 | 1.14131 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.02905 | −0.0744888 | ||||||||
\(743\) | 31.2944 | 1.14808 | 0.574040 | − | 0.818827i | \(-0.305375\pi\) | ||||
0.574040 | + | 0.818827i | \(0.305375\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.9093 | −0.582873 | ||||||||
\(746\) | 49.1712 | 1.80028 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.7589 | 0.429661 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.4340 | −1.14704 | −0.573521 | − | 0.819191i | \(-0.694423\pi\) | ||||
−0.573521 | + | 0.819191i | \(0.694423\pi\) | |||||||
\(752\) | −25.2331 | −0.920156 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −55.9147 | −2.03629 | ||||||||
\(755\) | −19.4452 | −0.707685 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.3641 | 0.921873 | 0.460937 | − | 0.887433i | \(-0.347514\pi\) | ||||
0.460937 | + | 0.887433i | \(0.347514\pi\) | |||||||
\(758\) | 78.2944 | 2.84378 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 12.5077 | 0.453701 | ||||||||
\(761\) | 10.0619 | 0.364744 | 0.182372 | − | 0.983230i | \(-0.441622\pi\) | ||||
0.182372 | + | 0.983230i | \(0.441622\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.9038 | −0.575755 | ||||||||
\(764\) | −57.3215 | −2.07382 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 64.9968 | 2.34843 | ||||||||
\(767\) | 15.0478 | 0.543345 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.408482 | 0.0147303 | 0.00736513 | − | 0.999973i | \(-0.497656\pi\) | ||||
0.00736513 | + | 0.999973i | \(0.497656\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −25.0717 | −0.902350 | ||||||||
\(773\) | −11.9310 | −0.429129 | −0.214565 | − | 0.976710i | \(-0.568833\pi\) | ||||
−0.214565 | + | 0.976710i | \(0.568833\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −23.7469 | −0.853013 | ||||||||
\(776\) | −1.69739 | −0.0609329 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20.8589 | 0.747827 | ||||||||
\(779\) | 56.8429 | 2.03661 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −19.2774 | −0.689360 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.46410 | −0.123718 | ||||||||
\(785\) | −30.6328 | −1.09333 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.3396 | −0.725030 | −0.362515 | − | 0.931978i | \(-0.618082\pi\) | ||||
−0.362515 | + | 0.931978i | \(0.618082\pi\) | |||||||
\(788\) | −39.1179 | −1.39352 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 92.4548 | 3.28939 | ||||||||
\(791\) | −7.30763 | −0.259830 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −40.2041 | −1.42769 | ||||||||
\(794\) | 15.4666 | 0.548891 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −15.0474 | −0.533339 | ||||||||
\(797\) | −6.82763 | −0.241847 | −0.120924 | − | 0.992662i | \(-0.538586\pi\) | ||||
−0.120924 | + | 0.992662i | \(0.538586\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 39.1634 | 1.38550 | ||||||||
\(800\) | 35.3717 | 1.25058 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 39.6648 | 1.40061 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.32691 | 0.187749 | ||||||||
\(806\) | −37.3323 | −1.31497 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.60982 | −0.162173 | ||||||||
\(809\) | 15.3890 | 0.541047 | 0.270524 | − | 0.962713i | \(-0.412803\pi\) | ||||
0.270524 | + | 0.962713i | \(0.412803\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.42694 | −0.331025 | −0.165512 | − | 0.986208i | \(-0.552928\pi\) | ||||
−0.165512 | + | 0.986208i | \(0.552928\pi\) | |||||||
\(812\) | −18.2790 | −0.641467 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −26.0115 | −0.911142 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.3516 | −0.537083 | ||||||||
\(818\) | 26.8911 | 0.940224 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −46.9221 | −1.63859 | ||||||||
\(821\) | 32.3301 | 1.12833 | 0.564165 | − | 0.825662i | \(-0.309198\pi\) | ||||
0.564165 | + | 0.825662i | \(0.309198\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.3223 | −0.638676 | −0.319338 | − | 0.947641i | \(-0.603461\pi\) | ||||
−0.319338 | + | 0.947641i | \(0.603461\pi\) | |||||||
\(824\) | −6.25539 | −0.217917 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.31280 | 0.324034 | ||||||||
\(827\) | −6.37527 | −0.221690 | −0.110845 | − | 0.993838i | \(-0.535356\pi\) | ||||
−0.110845 | + | 0.993838i | \(0.535356\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.949545 | 0.0329791 | 0.0164895 | − | 0.999864i | \(-0.494751\pi\) | ||||
0.0164895 | + | 0.999864i | \(0.494751\pi\) | |||||||
\(830\) | 10.2657 | 0.356329 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 32.5580 | 1.12875 | ||||||||
\(833\) | 5.37651 | 0.186285 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.98589 | 0.310970 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −63.3313 | −2.18774 | ||||||||
\(839\) | −14.3937 | −0.496925 | −0.248462 | − | 0.968642i | \(-0.579925\pi\) | ||||
−0.248462 | + | 0.968642i | \(0.579925\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 37.6308 | 1.29761 | ||||||||
\(842\) | −33.0786 | −1.13996 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 45.2998 | 1.55928 | ||||||||
\(845\) | −5.90893 | −0.203273 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.41378 | −0.117230 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −48.2346 | −1.65443 | ||||||||
\(851\) | 7.89281 | 0.270562 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39.9349 | 1.36735 | 0.683673 | − | 0.729788i | \(-0.260381\pi\) | ||||
0.683673 | + | 0.729788i | \(0.260381\pi\) | |||||||
\(854\) | −24.8816 | −0.851430 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.79405 | −0.198036 | ||||||||
\(857\) | −52.2332 | −1.78425 | −0.892127 | − | 0.451786i | \(-0.850787\pi\) | ||||
−0.892127 | + | 0.451786i | \(0.850787\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.1209 | −1.26655 | −0.633274 | − | 0.773928i | \(-0.718289\pi\) | ||||
−0.633274 | + | 0.773928i | \(0.718289\pi\) | |||||||
\(860\) | 12.6722 | 0.432120 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −26.9213 | −0.916941 | ||||||||
\(863\) | 34.0072 | 1.15762 | 0.578809 | − | 0.815463i | \(-0.303518\pi\) | ||||
0.578809 | + | 0.815463i | \(0.303518\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −63.2719 | −2.15131 | ||||||||
\(866\) | −26.7164 | −0.907861 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −12.2042 | −0.414239 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.568878 | −0.0192757 | ||||||||
\(872\) | 7.83638 | 0.265373 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 29.7534 | 1.00642 | ||||||||
\(875\) | −1.96620 | −0.0664697 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.3869 | −1.53261 | −0.766303 | − | 0.642479i | \(-0.777906\pi\) | ||||
−0.766303 | + | 0.642479i | \(0.777906\pi\) | |||||||
\(878\) | −32.8835 | −1.10977 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.0836 | −0.609251 | −0.304626 | − | 0.952472i | \(-0.598531\pi\) | ||||
−0.304626 | + | 0.952472i | \(0.598531\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.8564 | 0.499958 | 0.249979 | − | 0.968251i | \(-0.419576\pi\) | ||||
0.249979 | + | 0.968251i | \(0.419576\pi\) | |||||||
\(884\) | −40.0549 | −1.34719 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −43.7931 | −1.47126 | ||||||||
\(887\) | −29.3108 | −0.984162 | −0.492081 | − | 0.870549i | \(-0.663764\pi\) | ||||
−0.492081 | + | 0.870549i | \(0.663764\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.32860 | 0.145176 | ||||||||
\(890\) | 88.0950 | 2.95295 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 26.5818 | 0.890025 | ||||||||
\(893\) | −60.4460 | −2.02275 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18.8033 | −0.628526 | ||||||||
\(896\) | 3.91368 | 0.130747 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −13.6513 | −0.455551 | ||||||||
\(899\) | 44.4870 | 1.48373 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.29841 | 0.176516 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.60074 | 0.119759 | ||||||||
\(905\) | −58.8720 | −1.95697 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.784709 | 0.0260558 | 0.0130279 | − | 0.999915i | \(-0.495853\pi\) | ||||
0.0130279 | + | 0.999915i | \(0.495853\pi\) | |||||||
\(908\) | 31.2431 | 1.03684 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 20.9538 | 0.694611 | ||||||||
\(911\) | −49.3824 | −1.63611 | −0.818056 | − | 0.575139i | \(-0.804948\pi\) | ||||
−0.818056 | + | 0.575139i | \(0.804948\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 35.2474 | 1.16588 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 55.6075 | 1.83732 | ||||||||
\(917\) | 8.71236 | 0.287707 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.20242 | −0.0396641 | −0.0198320 | − | 0.999803i | \(-0.506313\pi\) | ||||
−0.0198320 | + | 0.999803i | \(0.506313\pi\) | |||||||
\(920\) | −2.62477 | −0.0865360 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −39.3617 | −1.29631 | ||||||||
\(923\) | −33.2747 | −1.09525 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.7488 | 0.649337 | ||||||||
\(926\) | −33.1139 | −1.08819 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −66.2647 | −2.17525 | ||||||||
\(929\) | 16.9944 | 0.557569 | 0.278785 | − | 0.960354i | \(-0.410068\pi\) | ||||
0.278785 | + | 0.960354i | \(0.410068\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.29827 | −0.271965 | ||||||||
\(932\) | −26.4832 | −0.867487 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −27.7795 | −0.908973 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.4196 | 0.928427 | 0.464213 | − | 0.885723i | \(-0.346337\pi\) | ||||
0.464213 | + | 0.885723i | \(0.346337\pi\) | |||||||
\(938\) | −0.352068 | −0.0114954 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 49.8963 | 1.62744 | ||||||||
\(941\) | −27.9160 | −0.910034 | −0.455017 | − | 0.890483i | \(-0.650367\pi\) | ||||
−0.455017 | + | 0.890483i | \(0.650367\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.9286 | −0.388449 | ||||||||
\(944\) | 15.6683 | 0.509961 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34.5418 | −1.12246 | −0.561229 | − | 0.827660i | \(-0.689671\pi\) | ||||
−0.561229 | + | 0.827660i | \(0.689671\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42.5545 | 1.38138 | ||||||||
\(950\) | 74.4468 | 2.41537 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.64920 | −0.0858612 | ||||||||
\(953\) | −13.8398 | −0.448314 | −0.224157 | − | 0.974553i | \(-0.571963\pi\) | ||||
−0.224157 | + | 0.974553i | \(0.571963\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −78.3027 | −2.53382 | ||||||||
\(956\) | −19.8520 | −0.642060 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −51.5709 | −1.66618 | ||||||||
\(959\) | 0.234149 | 0.00756107 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.29759 | −0.0418577 | ||||||||
\(962\) | 31.0470 | 1.00099 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −25.5106 | −0.821642 | ||||||||
\(965\) | −34.2486 | −1.10250 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.67468 | 0.246801 | 0.123401 | − | 0.992357i | \(-0.460620\pi\) | ||||
0.123401 | + | 0.992357i | \(0.460620\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −21.6965 | −0.696631 | ||||||||
\(971\) | −6.99587 | −0.224508 | −0.112254 | − | 0.993680i | \(-0.535807\pi\) | ||||
−0.112254 | + | 0.993680i | \(0.535807\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.3200 | −0.619369 | ||||||||
\(974\) | 63.3929 | 2.03124 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −41.8621 | −1.33997 | ||||||||
\(977\) | 11.0312 | 0.352918 | 0.176459 | − | 0.984308i | \(-0.443536\pi\) | ||||
0.176459 | + | 0.984308i | \(0.443536\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 6.84997 | 0.218814 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −80.5465 | −2.57034 | ||||||||
\(983\) | −13.4873 | −0.430178 | −0.215089 | − | 0.976594i | \(-0.569004\pi\) | ||||
−0.215089 | + | 0.976594i | \(0.569004\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −53.4361 | −1.70262 | ||||||||
\(986\) | 90.3619 | 2.87771 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 61.8221 | 1.96682 | ||||||||
\(989\) | 3.22156 | 0.102440 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.759034 | 0.0241115 | 0.0120558 | − | 0.999927i | \(-0.496162\pi\) | ||||
0.0120558 | + | 0.999927i | \(0.496162\pi\) | |||||||
\(992\) | −44.2426 | −1.40470 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −20.5931 | −0.653173 | ||||||||
\(995\) | −20.5551 | −0.651640 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −47.7793 | −1.51319 | −0.756593 | − | 0.653886i | \(-0.773138\pi\) | ||||
−0.756593 | + | 0.653886i | \(0.773138\pi\) | |||||||
\(998\) | −27.9035 | −0.883271 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 7623.2.a.cn.1.1 | 4 | ||
3.2 | odd | 2 | 2541.2.a.bl.1.4 | ✓ | 4 | ||
11.10 | odd | 2 | 7623.2.a.cg.1.4 | 4 | |||
33.32 | even | 2 | 2541.2.a.bp.1.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2541.2.a.bl.1.4 | ✓ | 4 | 3.2 | odd | 2 | ||
2541.2.a.bp.1.1 | yes | 4 | 33.32 | even | 2 | ||
7623.2.a.cg.1.4 | 4 | 11.10 | odd | 2 | |||
7623.2.a.cn.1.1 | 4 | 1.1 | even | 1 | trivial |