Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6042,2,Mod(1,6042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6042, 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("6042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6042.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: | \(48.2456129013\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 4x^{8} - 11x^{7} + 51x^{6} + 25x^{5} - 180x^{4} + 29x^{3} + 119x^{2} - 8x - 14 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.407650\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6042.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.186875 | −0.0835732 | −0.0417866 | − | 0.999127i | \(-0.513305\pi\) | ||||
−0.0417866 | + | 0.999127i | \(0.513305\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −2.28090 | −0.862099 | −0.431049 | − | 0.902328i | \(-0.641857\pi\) | ||||
−0.431049 | + | 0.902328i | \(0.641857\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.186875 | 0.0590952 | ||||||||
\(11\) | −2.54682 | −0.767896 | −0.383948 | − | 0.923355i | \(-0.625436\pi\) | ||||
−0.383948 | + | 0.923355i | \(0.625436\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −3.08013 | −0.854273 | −0.427137 | − | 0.904187i | \(-0.640478\pi\) | ||||
−0.427137 | + | 0.904187i | \(0.640478\pi\) | |||||||
\(14\) | 2.28090 | 0.609596 | ||||||||
\(15\) | 0.186875 | 0.0482510 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.350064 | 0.0849030 | 0.0424515 | − | 0.999099i | \(-0.486483\pi\) | ||||
0.0424515 | + | 0.999099i | \(0.486483\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −0.186875 | −0.0417866 | ||||||||
\(21\) | 2.28090 | 0.497733 | ||||||||
\(22\) | 2.54682 | 0.542985 | ||||||||
\(23\) | 3.42727 | 0.714635 | 0.357318 | − | 0.933983i | \(-0.383691\pi\) | ||||
0.357318 | + | 0.933983i | \(0.383691\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.96508 | −0.993016 | ||||||||
\(26\) | 3.08013 | 0.604063 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −2.28090 | −0.431049 | ||||||||
\(29\) | −3.84729 | −0.714423 | −0.357212 | − | 0.934023i | \(-0.616273\pi\) | ||||
−0.357212 | + | 0.934023i | \(0.616273\pi\) | |||||||
\(30\) | −0.186875 | −0.0341186 | ||||||||
\(31\) | 0.257212 | 0.0461967 | 0.0230983 | − | 0.999733i | \(-0.492647\pi\) | ||||
0.0230983 | + | 0.999733i | \(0.492647\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.54682 | 0.443345 | ||||||||
\(34\) | −0.350064 | −0.0600355 | ||||||||
\(35\) | 0.426244 | 0.0720484 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −0.640362 | −0.105275 | −0.0526375 | − | 0.998614i | \(-0.516763\pi\) | ||||
−0.0526375 | + | 0.998614i | \(0.516763\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 3.08013 | 0.493215 | ||||||||
\(40\) | 0.186875 | 0.0295476 | ||||||||
\(41\) | −5.74256 | −0.896837 | −0.448418 | − | 0.893824i | \(-0.648013\pi\) | ||||
−0.448418 | + | 0.893824i | \(0.648013\pi\) | |||||||
\(42\) | −2.28090 | −0.351950 | ||||||||
\(43\) | 6.19735 | 0.945087 | 0.472544 | − | 0.881307i | \(-0.343336\pi\) | ||||
0.472544 | + | 0.881307i | \(0.343336\pi\) | |||||||
\(44\) | −2.54682 | −0.383948 | ||||||||
\(45\) | −0.186875 | −0.0278577 | ||||||||
\(46\) | −3.42727 | −0.505323 | ||||||||
\(47\) | −6.20583 | −0.905214 | −0.452607 | − | 0.891710i | \(-0.649506\pi\) | ||||
−0.452607 | + | 0.891710i | \(0.649506\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −1.79750 | −0.256786 | ||||||||
\(50\) | 4.96508 | 0.702168 | ||||||||
\(51\) | −0.350064 | −0.0490188 | ||||||||
\(52\) | −3.08013 | −0.427137 | ||||||||
\(53\) | 1.00000 | 0.137361 | ||||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0.475939 | 0.0641756 | ||||||||
\(56\) | 2.28090 | 0.304798 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | 3.84729 | 0.505174 | ||||||||
\(59\) | −12.5274 | −1.63093 | −0.815466 | − | 0.578805i | \(-0.803519\pi\) | ||||
−0.815466 | + | 0.578805i | \(0.803519\pi\) | |||||||
\(60\) | 0.186875 | 0.0241255 | ||||||||
\(61\) | 3.02205 | 0.386934 | 0.193467 | − | 0.981107i | \(-0.438027\pi\) | ||||
0.193467 | + | 0.981107i | \(0.438027\pi\) | |||||||
\(62\) | −0.257212 | −0.0326660 | ||||||||
\(63\) | −2.28090 | −0.287366 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.575600 | 0.0713944 | ||||||||
\(66\) | −2.54682 | −0.313492 | ||||||||
\(67\) | −0.411602 | −0.0502852 | −0.0251426 | − | 0.999684i | \(-0.508004\pi\) | ||||
−0.0251426 | + | 0.999684i | \(0.508004\pi\) | |||||||
\(68\) | 0.350064 | 0.0424515 | ||||||||
\(69\) | −3.42727 | −0.412595 | ||||||||
\(70\) | −0.426244 | −0.0509459 | ||||||||
\(71\) | 4.85454 | 0.576128 | 0.288064 | − | 0.957611i | \(-0.406988\pi\) | ||||
0.288064 | + | 0.957611i | \(0.406988\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −7.21818 | −0.844824 | −0.422412 | − | 0.906404i | \(-0.638816\pi\) | ||||
−0.422412 | + | 0.906404i | \(0.638816\pi\) | |||||||
\(74\) | 0.640362 | 0.0744406 | ||||||||
\(75\) | 4.96508 | 0.573318 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 5.80905 | 0.662002 | ||||||||
\(78\) | −3.08013 | −0.348756 | ||||||||
\(79\) | −1.68110 | −0.189139 | −0.0945695 | − | 0.995518i | \(-0.530147\pi\) | ||||
−0.0945695 | + | 0.995518i | \(0.530147\pi\) | |||||||
\(80\) | −0.186875 | −0.0208933 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.74256 | 0.634159 | ||||||||
\(83\) | −7.08712 | −0.777912 | −0.388956 | − | 0.921256i | \(-0.627164\pi\) | ||||
−0.388956 | + | 0.921256i | \(0.627164\pi\) | |||||||
\(84\) | 2.28090 | 0.248866 | ||||||||
\(85\) | −0.0654184 | −0.00709562 | ||||||||
\(86\) | −6.19735 | −0.668278 | ||||||||
\(87\) | 3.84729 | 0.412472 | ||||||||
\(88\) | 2.54682 | 0.271492 | ||||||||
\(89\) | 1.55305 | 0.164623 | 0.0823114 | − | 0.996607i | \(-0.473770\pi\) | ||||
0.0823114 | + | 0.996607i | \(0.473770\pi\) | |||||||
\(90\) | 0.186875 | 0.0196984 | ||||||||
\(91\) | 7.02546 | 0.736468 | ||||||||
\(92\) | 3.42727 | 0.357318 | ||||||||
\(93\) | −0.257212 | −0.0266717 | ||||||||
\(94\) | 6.20583 | 0.640083 | ||||||||
\(95\) | 0.186875 | 0.0191730 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −5.00597 | −0.508279 | −0.254139 | − | 0.967168i | \(-0.581792\pi\) | ||||
−0.254139 | + | 0.967168i | \(0.581792\pi\) | |||||||
\(98\) | 1.79750 | 0.181575 | ||||||||
\(99\) | −2.54682 | −0.255965 | ||||||||
\(100\) | −4.96508 | −0.496508 | ||||||||
\(101\) | 19.0875 | 1.89928 | 0.949640 | − | 0.313343i | \(-0.101449\pi\) | ||||
0.949640 | + | 0.313343i | \(0.101449\pi\) | |||||||
\(102\) | 0.350064 | 0.0346615 | ||||||||
\(103\) | −0.920029 | −0.0906532 | −0.0453266 | − | 0.998972i | \(-0.514433\pi\) | ||||
−0.0453266 | + | 0.998972i | \(0.514433\pi\) | |||||||
\(104\) | 3.08013 | 0.302031 | ||||||||
\(105\) | −0.426244 | −0.0415972 | ||||||||
\(106\) | −1.00000 | −0.0971286 | ||||||||
\(107\) | −7.42877 | −0.718166 | −0.359083 | − | 0.933306i | \(-0.616911\pi\) | ||||
−0.359083 | + | 0.933306i | \(0.616911\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −7.59367 | −0.727342 | −0.363671 | − | 0.931528i | \(-0.618477\pi\) | ||||
−0.363671 | + | 0.931528i | \(0.618477\pi\) | |||||||
\(110\) | −0.475939 | −0.0453790 | ||||||||
\(111\) | 0.640362 | 0.0607805 | ||||||||
\(112\) | −2.28090 | −0.215525 | ||||||||
\(113\) | 6.98697 | 0.657279 | 0.328639 | − | 0.944455i | \(-0.393410\pi\) | ||||
0.328639 | + | 0.944455i | \(0.393410\pi\) | |||||||
\(114\) | −1.00000 | −0.0936586 | ||||||||
\(115\) | −0.640473 | −0.0597244 | ||||||||
\(116\) | −3.84729 | −0.357212 | ||||||||
\(117\) | −3.08013 | −0.284758 | ||||||||
\(118\) | 12.5274 | 1.15324 | ||||||||
\(119\) | −0.798461 | −0.0731948 | ||||||||
\(120\) | −0.186875 | −0.0170593 | ||||||||
\(121\) | −4.51369 | −0.410335 | ||||||||
\(122\) | −3.02205 | −0.273604 | ||||||||
\(123\) | 5.74256 | 0.517789 | ||||||||
\(124\) | 0.257212 | 0.0230983 | ||||||||
\(125\) | 1.86223 | 0.166563 | ||||||||
\(126\) | 2.28090 | 0.203199 | ||||||||
\(127\) | 8.58689 | 0.761964 | 0.380982 | − | 0.924583i | \(-0.375586\pi\) | ||||
0.380982 | + | 0.924583i | \(0.375586\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −6.19735 | −0.545646 | ||||||||
\(130\) | −0.575600 | −0.0504835 | ||||||||
\(131\) | 16.2550 | 1.42021 | 0.710103 | − | 0.704098i | \(-0.248649\pi\) | ||||
0.710103 | + | 0.704098i | \(0.248649\pi\) | |||||||
\(132\) | 2.54682 | 0.221673 | ||||||||
\(133\) | 2.28090 | 0.197779 | ||||||||
\(134\) | 0.411602 | 0.0355570 | ||||||||
\(135\) | 0.186875 | 0.0160837 | ||||||||
\(136\) | −0.350064 | −0.0300178 | ||||||||
\(137\) | 13.6345 | 1.16487 | 0.582435 | − | 0.812877i | \(-0.302100\pi\) | ||||
0.582435 | + | 0.812877i | \(0.302100\pi\) | |||||||
\(138\) | 3.42727 | 0.291749 | ||||||||
\(139\) | −10.8327 | −0.918818 | −0.459409 | − | 0.888225i | \(-0.651939\pi\) | ||||
−0.459409 | + | 0.888225i | \(0.651939\pi\) | |||||||
\(140\) | 0.426244 | 0.0360242 | ||||||||
\(141\) | 6.20583 | 0.522626 | ||||||||
\(142\) | −4.85454 | −0.407384 | ||||||||
\(143\) | 7.84454 | 0.655993 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0.718963 | 0.0597067 | ||||||||
\(146\) | 7.21818 | 0.597381 | ||||||||
\(147\) | 1.79750 | 0.148255 | ||||||||
\(148\) | −0.640362 | −0.0526375 | ||||||||
\(149\) | −10.5372 | −0.863244 | −0.431622 | − | 0.902055i | \(-0.642059\pi\) | ||||
−0.431622 | + | 0.902055i | \(0.642059\pi\) | |||||||
\(150\) | −4.96508 | −0.405397 | ||||||||
\(151\) | −21.7766 | −1.77215 | −0.886076 | − | 0.463541i | \(-0.846579\pi\) | ||||
−0.886076 | + | 0.463541i | \(0.846579\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 0.350064 | 0.0283010 | ||||||||
\(154\) | −5.80905 | −0.468106 | ||||||||
\(155\) | −0.0480666 | −0.00386081 | ||||||||
\(156\) | 3.08013 | 0.246608 | ||||||||
\(157\) | 11.0450 | 0.881488 | 0.440744 | − | 0.897633i | \(-0.354715\pi\) | ||||
0.440744 | + | 0.897633i | \(0.354715\pi\) | |||||||
\(158\) | 1.68110 | 0.133741 | ||||||||
\(159\) | −1.00000 | −0.0793052 | ||||||||
\(160\) | 0.186875 | 0.0147738 | ||||||||
\(161\) | −7.81726 | −0.616086 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −5.74171 | −0.449725 | −0.224863 | − | 0.974390i | \(-0.572193\pi\) | ||||
−0.224863 | + | 0.974390i | \(0.572193\pi\) | |||||||
\(164\) | −5.74256 | −0.448418 | ||||||||
\(165\) | −0.475939 | −0.0370518 | ||||||||
\(166\) | 7.08712 | 0.550067 | ||||||||
\(167\) | 25.5126 | 1.97423 | 0.987113 | − | 0.160026i | \(-0.0511578\pi\) | ||||
0.987113 | + | 0.160026i | \(0.0511578\pi\) | |||||||
\(168\) | −2.28090 | −0.175975 | ||||||||
\(169\) | −3.51282 | −0.270217 | ||||||||
\(170\) | 0.0654184 | 0.00501736 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 6.19735 | 0.472544 | ||||||||
\(173\) | 8.86507 | 0.673999 | 0.337000 | − | 0.941505i | \(-0.390588\pi\) | ||||
0.337000 | + | 0.941505i | \(0.390588\pi\) | |||||||
\(174\) | −3.84729 | −0.291662 | ||||||||
\(175\) | 11.3248 | 0.856077 | ||||||||
\(176\) | −2.54682 | −0.191974 | ||||||||
\(177\) | 12.5274 | 0.941619 | ||||||||
\(178\) | −1.55305 | −0.116406 | ||||||||
\(179\) | 9.11968 | 0.681637 | 0.340819 | − | 0.940129i | \(-0.389296\pi\) | ||||
0.340819 | + | 0.940129i | \(0.389296\pi\) | |||||||
\(180\) | −0.186875 | −0.0139289 | ||||||||
\(181\) | −3.03839 | −0.225842 | −0.112921 | − | 0.993604i | \(-0.536021\pi\) | ||||
−0.112921 | + | 0.993604i | \(0.536021\pi\) | |||||||
\(182\) | −7.02546 | −0.520762 | ||||||||
\(183\) | −3.02205 | −0.223396 | ||||||||
\(184\) | −3.42727 | −0.252662 | ||||||||
\(185\) | 0.119668 | 0.00879817 | ||||||||
\(186\) | 0.257212 | 0.0188597 | ||||||||
\(187\) | −0.891552 | −0.0651967 | ||||||||
\(188\) | −6.20583 | −0.452607 | ||||||||
\(189\) | 2.28090 | 0.165911 | ||||||||
\(190\) | −0.186875 | −0.0135574 | ||||||||
\(191\) | 4.96532 | 0.359278 | 0.179639 | − | 0.983733i | \(-0.442507\pi\) | ||||
0.179639 | + | 0.983733i | \(0.442507\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −18.9514 | −1.36415 | −0.682074 | − | 0.731283i | \(-0.738922\pi\) | ||||
−0.682074 | + | 0.731283i | \(0.738922\pi\) | |||||||
\(194\) | 5.00597 | 0.359407 | ||||||||
\(195\) | −0.575600 | −0.0412196 | ||||||||
\(196\) | −1.79750 | −0.128393 | ||||||||
\(197\) | 0.325789 | 0.0232115 | 0.0116058 | − | 0.999933i | \(-0.496306\pi\) | ||||
0.0116058 | + | 0.999933i | \(0.496306\pi\) | |||||||
\(198\) | 2.54682 | 0.180995 | ||||||||
\(199\) | 5.06882 | 0.359319 | 0.179660 | − | 0.983729i | \(-0.442500\pi\) | ||||
0.179660 | + | 0.983729i | \(0.442500\pi\) | |||||||
\(200\) | 4.96508 | 0.351084 | ||||||||
\(201\) | 0.411602 | 0.0290322 | ||||||||
\(202\) | −19.0875 | −1.34299 | ||||||||
\(203\) | 8.77527 | 0.615903 | ||||||||
\(204\) | −0.350064 | −0.0245094 | ||||||||
\(205\) | 1.07314 | 0.0749516 | ||||||||
\(206\) | 0.920029 | 0.0641015 | ||||||||
\(207\) | 3.42727 | 0.238212 | ||||||||
\(208\) | −3.08013 | −0.213568 | ||||||||
\(209\) | 2.54682 | 0.176168 | ||||||||
\(210\) | 0.426244 | 0.0294136 | ||||||||
\(211\) | 15.3166 | 1.05444 | 0.527218 | − | 0.849730i | \(-0.323235\pi\) | ||||
0.527218 | + | 0.849730i | \(0.323235\pi\) | |||||||
\(212\) | 1.00000 | 0.0686803 | ||||||||
\(213\) | −4.85454 | −0.332628 | ||||||||
\(214\) | 7.42877 | 0.507820 | ||||||||
\(215\) | −1.15813 | −0.0789840 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −0.586675 | −0.0398261 | ||||||||
\(218\) | 7.59367 | 0.514308 | ||||||||
\(219\) | 7.21818 | 0.487759 | ||||||||
\(220\) | 0.475939 | 0.0320878 | ||||||||
\(221\) | −1.07824 | −0.0725304 | ||||||||
\(222\) | −0.640362 | −0.0429783 | ||||||||
\(223\) | 0.00422436 | 0.000282884 0 | 0.000141442 | − | 1.00000i | \(-0.499955\pi\) | ||||
0.000141442 | 1.00000i | \(0.499955\pi\) | ||||||||
\(224\) | 2.28090 | 0.152399 | ||||||||
\(225\) | −4.96508 | −0.331005 | ||||||||
\(226\) | −6.98697 | −0.464766 | ||||||||
\(227\) | 8.50529 | 0.564516 | 0.282258 | − | 0.959339i | \(-0.408917\pi\) | ||||
0.282258 | + | 0.959339i | \(0.408917\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | −17.5801 | −1.16173 | −0.580864 | − | 0.814001i | \(-0.697285\pi\) | ||||
−0.580864 | + | 0.814001i | \(0.697285\pi\) | |||||||
\(230\) | 0.640473 | 0.0422315 | ||||||||
\(231\) | −5.80905 | −0.382207 | ||||||||
\(232\) | 3.84729 | 0.252587 | ||||||||
\(233\) | −12.6432 | −0.828285 | −0.414143 | − | 0.910212i | \(-0.635919\pi\) | ||||
−0.414143 | + | 0.910212i | \(0.635919\pi\) | |||||||
\(234\) | 3.08013 | 0.201354 | ||||||||
\(235\) | 1.15972 | 0.0756517 | ||||||||
\(236\) | −12.5274 | −0.815466 | ||||||||
\(237\) | 1.68110 | 0.109199 | ||||||||
\(238\) | 0.798461 | 0.0517565 | ||||||||
\(239\) | 29.8548 | 1.93115 | 0.965574 | − | 0.260128i | \(-0.0837646\pi\) | ||||
0.965574 | + | 0.260128i | \(0.0837646\pi\) | |||||||
\(240\) | 0.186875 | 0.0120628 | ||||||||
\(241\) | 6.92064 | 0.445798 | 0.222899 | − | 0.974842i | \(-0.428448\pi\) | ||||
0.222899 | + | 0.974842i | \(0.428448\pi\) | |||||||
\(242\) | 4.51369 | 0.290151 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 3.02205 | 0.193467 | ||||||||
\(245\) | 0.335909 | 0.0214604 | ||||||||
\(246\) | −5.74256 | −0.366132 | ||||||||
\(247\) | 3.08013 | 0.195984 | ||||||||
\(248\) | −0.257212 | −0.0163330 | ||||||||
\(249\) | 7.08712 | 0.449128 | ||||||||
\(250\) | −1.86223 | −0.117778 | ||||||||
\(251\) | −12.9677 | −0.818514 | −0.409257 | − | 0.912419i | \(-0.634212\pi\) | ||||
−0.409257 | + | 0.912419i | \(0.634212\pi\) | |||||||
\(252\) | −2.28090 | −0.143683 | ||||||||
\(253\) | −8.72865 | −0.548766 | ||||||||
\(254\) | −8.58689 | −0.538790 | ||||||||
\(255\) | 0.0654184 | 0.00409666 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.5969 | 0.848151 | 0.424076 | − | 0.905627i | \(-0.360599\pi\) | ||||
0.424076 | + | 0.905627i | \(0.360599\pi\) | |||||||
\(258\) | 6.19735 | 0.385830 | ||||||||
\(259\) | 1.46060 | 0.0907574 | ||||||||
\(260\) | 0.575600 | 0.0356972 | ||||||||
\(261\) | −3.84729 | −0.238141 | ||||||||
\(262\) | −16.2550 | −1.00424 | ||||||||
\(263\) | −15.4410 | −0.952133 | −0.476066 | − | 0.879409i | \(-0.657938\pi\) | ||||
−0.476066 | + | 0.879409i | \(0.657938\pi\) | |||||||
\(264\) | −2.54682 | −0.156746 | ||||||||
\(265\) | −0.186875 | −0.0114797 | ||||||||
\(266\) | −2.28090 | −0.139851 | ||||||||
\(267\) | −1.55305 | −0.0950451 | ||||||||
\(268\) | −0.411602 | −0.0251426 | ||||||||
\(269\) | 21.3228 | 1.30008 | 0.650038 | − | 0.759902i | \(-0.274753\pi\) | ||||
0.650038 | + | 0.759902i | \(0.274753\pi\) | |||||||
\(270\) | −0.186875 | −0.0113729 | ||||||||
\(271\) | −13.3895 | −0.813355 | −0.406677 | − | 0.913572i | \(-0.633313\pi\) | ||||
−0.406677 | + | 0.913572i | \(0.633313\pi\) | |||||||
\(272\) | 0.350064 | 0.0212258 | ||||||||
\(273\) | −7.02546 | −0.425200 | ||||||||
\(274\) | −13.6345 | −0.823688 | ||||||||
\(275\) | 12.6452 | 0.762533 | ||||||||
\(276\) | −3.42727 | −0.206297 | ||||||||
\(277\) | −6.96535 | −0.418508 | −0.209254 | − | 0.977861i | \(-0.567103\pi\) | ||||
−0.209254 | + | 0.977861i | \(0.567103\pi\) | |||||||
\(278\) | 10.8327 | 0.649703 | ||||||||
\(279\) | 0.257212 | 0.0153989 | ||||||||
\(280\) | −0.426244 | −0.0254729 | ||||||||
\(281\) | −3.57358 | −0.213182 | −0.106591 | − | 0.994303i | \(-0.533994\pi\) | ||||
−0.106591 | + | 0.994303i | \(0.533994\pi\) | |||||||
\(282\) | −6.20583 | −0.369552 | ||||||||
\(283\) | 27.0801 | 1.60975 | 0.804873 | − | 0.593447i | \(-0.202233\pi\) | ||||
0.804873 | + | 0.593447i | \(0.202233\pi\) | |||||||
\(284\) | 4.85454 | 0.288064 | ||||||||
\(285\) | −0.186875 | −0.0110695 | ||||||||
\(286\) | −7.84454 | −0.463857 | ||||||||
\(287\) | 13.0982 | 0.773162 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −16.8775 | −0.992791 | ||||||||
\(290\) | −0.718963 | −0.0422190 | ||||||||
\(291\) | 5.00597 | 0.293455 | ||||||||
\(292\) | −7.21818 | −0.422412 | ||||||||
\(293\) | −5.34975 | −0.312536 | −0.156268 | − | 0.987715i | \(-0.549946\pi\) | ||||
−0.156268 | + | 0.987715i | \(0.549946\pi\) | |||||||
\(294\) | −1.79750 | −0.104832 | ||||||||
\(295\) | 2.34107 | 0.136302 | ||||||||
\(296\) | 0.640362 | 0.0372203 | ||||||||
\(297\) | 2.54682 | 0.147782 | ||||||||
\(298\) | 10.5372 | 0.610406 | ||||||||
\(299\) | −10.5564 | −0.610494 | ||||||||
\(300\) | 4.96508 | 0.286659 | ||||||||
\(301\) | −14.1355 | −0.814758 | ||||||||
\(302\) | 21.7766 | 1.25310 | ||||||||
\(303\) | −19.0875 | −1.09655 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −0.564747 | −0.0323373 | ||||||||
\(306\) | −0.350064 | −0.0200118 | ||||||||
\(307\) | 21.4945 | 1.22676 | 0.613378 | − | 0.789789i | \(-0.289810\pi\) | ||||
0.613378 | + | 0.789789i | \(0.289810\pi\) | |||||||
\(308\) | 5.80905 | 0.331001 | ||||||||
\(309\) | 0.920029 | 0.0523386 | ||||||||
\(310\) | 0.0480666 | 0.00273000 | ||||||||
\(311\) | −3.36641 | −0.190891 | −0.0954457 | − | 0.995435i | \(-0.530428\pi\) | ||||
−0.0954457 | + | 0.995435i | \(0.530428\pi\) | |||||||
\(312\) | −3.08013 | −0.174378 | ||||||||
\(313\) | −1.09924 | −0.0621325 | −0.0310663 | − | 0.999517i | \(-0.509890\pi\) | ||||
−0.0310663 | + | 0.999517i | \(0.509890\pi\) | |||||||
\(314\) | −11.0450 | −0.623306 | ||||||||
\(315\) | 0.426244 | 0.0240161 | ||||||||
\(316\) | −1.68110 | −0.0945695 | ||||||||
\(317\) | −29.9903 | −1.68442 | −0.842210 | − | 0.539149i | \(-0.818746\pi\) | ||||
−0.842210 | + | 0.539149i | \(0.818746\pi\) | |||||||
\(318\) | 1.00000 | 0.0560772 | ||||||||
\(319\) | 9.79836 | 0.548603 | ||||||||
\(320\) | −0.186875 | −0.0104467 | ||||||||
\(321\) | 7.42877 | 0.414633 | ||||||||
\(322\) | 7.81726 | 0.435639 | ||||||||
\(323\) | −0.350064 | −0.0194781 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 15.2931 | 0.848307 | ||||||||
\(326\) | 5.74171 | 0.318004 | ||||||||
\(327\) | 7.59367 | 0.419931 | ||||||||
\(328\) | 5.74256 | 0.317080 | ||||||||
\(329\) | 14.1549 | 0.780384 | ||||||||
\(330\) | 0.475939 | 0.0261996 | ||||||||
\(331\) | −23.7133 | −1.30340 | −0.651700 | − | 0.758477i | \(-0.725944\pi\) | ||||
−0.651700 | + | 0.758477i | \(0.725944\pi\) | |||||||
\(332\) | −7.08712 | −0.388956 | ||||||||
\(333\) | −0.640362 | −0.0350916 | ||||||||
\(334\) | −25.5126 | −1.39599 | ||||||||
\(335\) | 0.0769183 | 0.00420250 | ||||||||
\(336\) | 2.28090 | 0.124433 | ||||||||
\(337\) | 0.472626 | 0.0257456 | 0.0128728 | − | 0.999917i | \(-0.495902\pi\) | ||||
0.0128728 | + | 0.999917i | \(0.495902\pi\) | |||||||
\(338\) | 3.51282 | 0.191072 | ||||||||
\(339\) | −6.98697 | −0.379480 | ||||||||
\(340\) | −0.0654184 | −0.00354781 | ||||||||
\(341\) | −0.655074 | −0.0354743 | ||||||||
\(342\) | 1.00000 | 0.0540738 | ||||||||
\(343\) | 20.0662 | 1.08347 | ||||||||
\(344\) | −6.19735 | −0.334139 | ||||||||
\(345\) | 0.640473 | 0.0344819 | ||||||||
\(346\) | −8.86507 | −0.476589 | ||||||||
\(347\) | 35.4792 | 1.90462 | 0.952311 | − | 0.305128i | \(-0.0986993\pi\) | ||||
0.952311 | + | 0.305128i | \(0.0986993\pi\) | |||||||
\(348\) | 3.84729 | 0.206236 | ||||||||
\(349\) | 26.7603 | 1.43245 | 0.716223 | − | 0.697872i | \(-0.245869\pi\) | ||||
0.716223 | + | 0.697872i | \(0.245869\pi\) | |||||||
\(350\) | −11.3248 | −0.605338 | ||||||||
\(351\) | 3.08013 | 0.164405 | ||||||||
\(352\) | 2.54682 | 0.135746 | ||||||||
\(353\) | −7.69557 | −0.409594 | −0.204797 | − | 0.978804i | \(-0.565653\pi\) | ||||
−0.204797 | + | 0.978804i | \(0.565653\pi\) | |||||||
\(354\) | −12.5274 | −0.665825 | ||||||||
\(355\) | −0.907194 | −0.0481489 | ||||||||
\(356\) | 1.55305 | 0.0823114 | ||||||||
\(357\) | 0.798461 | 0.0422590 | ||||||||
\(358\) | −9.11968 | −0.481990 | ||||||||
\(359\) | 21.8889 | 1.15525 | 0.577626 | − | 0.816301i | \(-0.303979\pi\) | ||||
0.577626 | + | 0.816301i | \(0.303979\pi\) | |||||||
\(360\) | 0.186875 | 0.00984920 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 3.03839 | 0.159694 | ||||||||
\(363\) | 4.51369 | 0.236907 | ||||||||
\(364\) | 7.02546 | 0.368234 | ||||||||
\(365\) | 1.34890 | 0.0706046 | ||||||||
\(366\) | 3.02205 | 0.157965 | ||||||||
\(367\) | −24.8872 | −1.29910 | −0.649551 | − | 0.760318i | \(-0.725043\pi\) | ||||
−0.649551 | + | 0.760318i | \(0.725043\pi\) | |||||||
\(368\) | 3.42727 | 0.178659 | ||||||||
\(369\) | −5.74256 | −0.298946 | ||||||||
\(370\) | −0.119668 | −0.00622124 | ||||||||
\(371\) | −2.28090 | −0.118418 | ||||||||
\(372\) | −0.257212 | −0.0133358 | ||||||||
\(373\) | 15.2669 | 0.790490 | 0.395245 | − | 0.918576i | \(-0.370660\pi\) | ||||
0.395245 | + | 0.918576i | \(0.370660\pi\) | |||||||
\(374\) | 0.891552 | 0.0461010 | ||||||||
\(375\) | −1.86223 | −0.0961650 | ||||||||
\(376\) | 6.20583 | 0.320041 | ||||||||
\(377\) | 11.8501 | 0.610313 | ||||||||
\(378\) | −2.28090 | −0.117317 | ||||||||
\(379\) | 27.7711 | 1.42651 | 0.713253 | − | 0.700906i | \(-0.247221\pi\) | ||||
0.713253 | + | 0.700906i | \(0.247221\pi\) | |||||||
\(380\) | 0.186875 | 0.00958651 | ||||||||
\(381\) | −8.58689 | −0.439920 | ||||||||
\(382\) | −4.96532 | −0.254048 | ||||||||
\(383\) | 19.3058 | 0.986481 | 0.493241 | − | 0.869893i | \(-0.335812\pi\) | ||||
0.493241 | + | 0.869893i | \(0.335812\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −1.08557 | −0.0553257 | ||||||||
\(386\) | 18.9514 | 0.964599 | ||||||||
\(387\) | 6.19735 | 0.315029 | ||||||||
\(388\) | −5.00597 | −0.254139 | ||||||||
\(389\) | −29.2133 | −1.48118 | −0.740588 | − | 0.671960i | \(-0.765453\pi\) | ||||
−0.740588 | + | 0.671960i | \(0.765453\pi\) | |||||||
\(390\) | 0.575600 | 0.0291466 | ||||||||
\(391\) | 1.19976 | 0.0606747 | ||||||||
\(392\) | 1.79750 | 0.0907875 | ||||||||
\(393\) | −16.2550 | −0.819956 | ||||||||
\(394\) | −0.325789 | −0.0164130 | ||||||||
\(395\) | 0.314157 | 0.0158070 | ||||||||
\(396\) | −2.54682 | −0.127983 | ||||||||
\(397\) | 11.1577 | 0.559987 | 0.279993 | − | 0.960002i | \(-0.409668\pi\) | ||||
0.279993 | + | 0.960002i | \(0.409668\pi\) | |||||||
\(398\) | −5.06882 | −0.254077 | ||||||||
\(399\) | −2.28090 | −0.114188 | ||||||||
\(400\) | −4.96508 | −0.248254 | ||||||||
\(401\) | −36.3134 | −1.81341 | −0.906703 | − | 0.421770i | \(-0.861409\pi\) | ||||
−0.906703 | + | 0.421770i | \(0.861409\pi\) | |||||||
\(402\) | −0.411602 | −0.0205288 | ||||||||
\(403\) | −0.792246 | −0.0394646 | ||||||||
\(404\) | 19.0875 | 0.949640 | ||||||||
\(405\) | −0.186875 | −0.00928591 | ||||||||
\(406\) | −8.77527 | −0.435509 | ||||||||
\(407\) | 1.63089 | 0.0808402 | ||||||||
\(408\) | 0.350064 | 0.0173308 | ||||||||
\(409\) | −17.9524 | −0.887691 | −0.443846 | − | 0.896103i | \(-0.646386\pi\) | ||||
−0.443846 | + | 0.896103i | \(0.646386\pi\) | |||||||
\(410\) | −1.07314 | −0.0529988 | ||||||||
\(411\) | −13.6345 | −0.672539 | ||||||||
\(412\) | −0.920029 | −0.0453266 | ||||||||
\(413\) | 28.5738 | 1.40602 | ||||||||
\(414\) | −3.42727 | −0.168441 | ||||||||
\(415\) | 1.32441 | 0.0650126 | ||||||||
\(416\) | 3.08013 | 0.151016 | ||||||||
\(417\) | 10.8327 | 0.530480 | ||||||||
\(418\) | −2.54682 | −0.124569 | ||||||||
\(419\) | 8.65145 | 0.422651 | 0.211326 | − | 0.977416i | \(-0.432222\pi\) | ||||
0.211326 | + | 0.977416i | \(0.432222\pi\) | |||||||
\(420\) | −0.426244 | −0.0207986 | ||||||||
\(421\) | −5.56253 | −0.271101 | −0.135551 | − | 0.990770i | \(-0.543280\pi\) | ||||
−0.135551 | + | 0.990770i | \(0.543280\pi\) | |||||||
\(422\) | −15.3166 | −0.745599 | ||||||||
\(423\) | −6.20583 | −0.301738 | ||||||||
\(424\) | −1.00000 | −0.0485643 | ||||||||
\(425\) | −1.73810 | −0.0843100 | ||||||||
\(426\) | 4.85454 | 0.235203 | ||||||||
\(427\) | −6.89299 | −0.333575 | ||||||||
\(428\) | −7.42877 | −0.359083 | ||||||||
\(429\) | −7.84454 | −0.378738 | ||||||||
\(430\) | 1.15813 | 0.0558501 | ||||||||
\(431\) | 10.9227 | 0.526126 | 0.263063 | − | 0.964779i | \(-0.415267\pi\) | ||||
0.263063 | + | 0.964779i | \(0.415267\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 29.1082 | 1.39885 | 0.699425 | − | 0.714706i | \(-0.253440\pi\) | ||||
0.699425 | + | 0.714706i | \(0.253440\pi\) | |||||||
\(434\) | 0.586675 | 0.0281613 | ||||||||
\(435\) | −0.718963 | −0.0344717 | ||||||||
\(436\) | −7.59367 | −0.363671 | ||||||||
\(437\) | −3.42727 | −0.163949 | ||||||||
\(438\) | −7.21818 | −0.344898 | ||||||||
\(439\) | −6.83597 | −0.326263 | −0.163131 | − | 0.986604i | \(-0.552159\pi\) | ||||
−0.163131 | + | 0.986604i | \(0.552159\pi\) | |||||||
\(440\) | −0.475939 | −0.0226895 | ||||||||
\(441\) | −1.79750 | −0.0855952 | ||||||||
\(442\) | 1.07824 | 0.0512867 | ||||||||
\(443\) | 29.3517 | 1.39454 | 0.697270 | − | 0.716809i | \(-0.254398\pi\) | ||||
0.697270 | + | 0.716809i | \(0.254398\pi\) | |||||||
\(444\) | 0.640362 | 0.0303903 | ||||||||
\(445\) | −0.290227 | −0.0137581 | ||||||||
\(446\) | −0.00422436 | −0.000200029 0 | ||||||||
\(447\) | 10.5372 | 0.498394 | ||||||||
\(448\) | −2.28090 | −0.107762 | ||||||||
\(449\) | −10.6310 | −0.501709 | −0.250855 | − | 0.968025i | \(-0.580712\pi\) | ||||
−0.250855 | + | 0.968025i | \(0.580712\pi\) | |||||||
\(450\) | 4.96508 | 0.234056 | ||||||||
\(451\) | 14.6253 | 0.688678 | ||||||||
\(452\) | 6.98697 | 0.328639 | ||||||||
\(453\) | 21.7766 | 1.02315 | ||||||||
\(454\) | −8.50529 | −0.399173 | ||||||||
\(455\) | −1.31289 | −0.0615490 | ||||||||
\(456\) | −1.00000 | −0.0468293 | ||||||||
\(457\) | 37.5623 | 1.75709 | 0.878546 | − | 0.477659i | \(-0.158514\pi\) | ||||
0.878546 | + | 0.477659i | \(0.158514\pi\) | |||||||
\(458\) | 17.5801 | 0.821465 | ||||||||
\(459\) | −0.350064 | −0.0163396 | ||||||||
\(460\) | −0.640473 | −0.0298622 | ||||||||
\(461\) | 18.1122 | 0.843568 | 0.421784 | − | 0.906696i | \(-0.361404\pi\) | ||||
0.421784 | + | 0.906696i | \(0.361404\pi\) | |||||||
\(462\) | 5.80905 | 0.270261 | ||||||||
\(463\) | 19.6837 | 0.914777 | 0.457389 | − | 0.889267i | \(-0.348785\pi\) | ||||
0.457389 | + | 0.889267i | \(0.348785\pi\) | |||||||
\(464\) | −3.84729 | −0.178606 | ||||||||
\(465\) | 0.0480666 | 0.00222904 | ||||||||
\(466\) | 12.6432 | 0.585686 | ||||||||
\(467\) | 24.5957 | 1.13815 | 0.569076 | − | 0.822285i | \(-0.307301\pi\) | ||||
0.569076 | + | 0.822285i | \(0.307301\pi\) | |||||||
\(468\) | −3.08013 | −0.142379 | ||||||||
\(469\) | 0.938822 | 0.0433508 | ||||||||
\(470\) | −1.15972 | −0.0534938 | ||||||||
\(471\) | −11.0450 | −0.508927 | ||||||||
\(472\) | 12.5274 | 0.576621 | ||||||||
\(473\) | −15.7836 | −0.725729 | ||||||||
\(474\) | −1.68110 | −0.0772156 | ||||||||
\(475\) | 4.96508 | 0.227813 | ||||||||
\(476\) | −0.798461 | −0.0365974 | ||||||||
\(477\) | 1.00000 | 0.0457869 | ||||||||
\(478\) | −29.8548 | −1.36553 | ||||||||
\(479\) | 27.7898 | 1.26975 | 0.634874 | − | 0.772616i | \(-0.281052\pi\) | ||||
0.634874 | + | 0.772616i | \(0.281052\pi\) | |||||||
\(480\) | −0.186875 | −0.00852966 | ||||||||
\(481\) | 1.97240 | 0.0899336 | ||||||||
\(482\) | −6.92064 | −0.315227 | ||||||||
\(483\) | 7.81726 | 0.355697 | ||||||||
\(484\) | −4.51369 | −0.205168 | ||||||||
\(485\) | 0.935492 | 0.0424785 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −16.3624 | −0.741450 | −0.370725 | − | 0.928743i | \(-0.620891\pi\) | ||||
−0.370725 | + | 0.928743i | \(0.620891\pi\) | |||||||
\(488\) | −3.02205 | −0.136802 | ||||||||
\(489\) | 5.74171 | 0.259649 | ||||||||
\(490\) | −0.335909 | −0.0151748 | ||||||||
\(491\) | 35.6365 | 1.60825 | 0.804127 | − | 0.594458i | \(-0.202633\pi\) | ||||
0.804127 | + | 0.594458i | \(0.202633\pi\) | |||||||
\(492\) | 5.74256 | 0.258895 | ||||||||
\(493\) | −1.34680 | −0.0606567 | ||||||||
\(494\) | −3.08013 | −0.138581 | ||||||||
\(495\) | 0.475939 | 0.0213919 | ||||||||
\(496\) | 0.257212 | 0.0115492 | ||||||||
\(497\) | −11.0727 | −0.496679 | ||||||||
\(498\) | −7.08712 | −0.317581 | ||||||||
\(499\) | 27.6074 | 1.23588 | 0.617938 | − | 0.786227i | \(-0.287968\pi\) | ||||
0.617938 | + | 0.786227i | \(0.287968\pi\) | |||||||
\(500\) | 1.86223 | 0.0832814 | ||||||||
\(501\) | −25.5126 | −1.13982 | ||||||||
\(502\) | 12.9677 | 0.578777 | ||||||||
\(503\) | −1.20332 | −0.0536532 | −0.0268266 | − | 0.999640i | \(-0.508540\pi\) | ||||
−0.0268266 | + | 0.999640i | \(0.508540\pi\) | |||||||
\(504\) | 2.28090 | 0.101599 | ||||||||
\(505\) | −3.56699 | −0.158729 | ||||||||
\(506\) | 8.72865 | 0.388036 | ||||||||
\(507\) | 3.51282 | 0.156010 | ||||||||
\(508\) | 8.58689 | 0.380982 | ||||||||
\(509\) | 10.1426 | 0.449562 | 0.224781 | − | 0.974409i | \(-0.427833\pi\) | ||||
0.224781 | + | 0.974409i | \(0.427833\pi\) | |||||||
\(510\) | −0.0654184 | −0.00289678 | ||||||||
\(511\) | 16.4639 | 0.728321 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | −13.5969 | −0.599734 | ||||||||
\(515\) | 0.171931 | 0.00757618 | ||||||||
\(516\) | −6.19735 | −0.272823 | ||||||||
\(517\) | 15.8052 | 0.695110 | ||||||||
\(518\) | −1.46060 | −0.0641752 | ||||||||
\(519\) | −8.86507 | −0.389134 | ||||||||
\(520\) | −0.575600 | −0.0252417 | ||||||||
\(521\) | 33.7856 | 1.48017 | 0.740086 | − | 0.672512i | \(-0.234785\pi\) | ||||
0.740086 | + | 0.672512i | \(0.234785\pi\) | |||||||
\(522\) | 3.84729 | 0.168391 | ||||||||
\(523\) | 35.7142 | 1.56167 | 0.780837 | − | 0.624735i | \(-0.214793\pi\) | ||||
0.780837 | + | 0.624735i | \(0.214793\pi\) | |||||||
\(524\) | 16.2550 | 0.710103 | ||||||||
\(525\) | −11.3248 | −0.494257 | ||||||||
\(526\) | 15.4410 | 0.673260 | ||||||||
\(527\) | 0.0900408 | 0.00392224 | ||||||||
\(528\) | 2.54682 | 0.110836 | ||||||||
\(529\) | −11.2538 | −0.489297 | ||||||||
\(530\) | 0.186875 | 0.00811735 | ||||||||
\(531\) | −12.5274 | −0.543644 | ||||||||
\(532\) | 2.28090 | 0.0988895 | ||||||||
\(533\) | 17.6878 | 0.766144 | ||||||||
\(534\) | 1.55305 | 0.0672070 | ||||||||
\(535\) | 1.38825 | 0.0600195 | ||||||||
\(536\) | 0.411602 | 0.0177785 | ||||||||
\(537\) | −9.11968 | −0.393543 | ||||||||
\(538\) | −21.3228 | −0.919293 | ||||||||
\(539\) | 4.57792 | 0.197185 | ||||||||
\(540\) | 0.186875 | 0.00804184 | ||||||||
\(541\) | −16.5988 | −0.713640 | −0.356820 | − | 0.934173i | \(-0.616139\pi\) | ||||
−0.356820 | + | 0.934173i | \(0.616139\pi\) | |||||||
\(542\) | 13.3895 | 0.575129 | ||||||||
\(543\) | 3.03839 | 0.130390 | ||||||||
\(544\) | −0.350064 | −0.0150089 | ||||||||
\(545\) | 1.41907 | 0.0607863 | ||||||||
\(546\) | 7.02546 | 0.300662 | ||||||||
\(547\) | −32.3716 | −1.38411 | −0.692055 | − | 0.721845i | \(-0.743294\pi\) | ||||
−0.692055 | + | 0.721845i | \(0.743294\pi\) | |||||||
\(548\) | 13.6345 | 0.582435 | ||||||||
\(549\) | 3.02205 | 0.128978 | ||||||||
\(550\) | −12.6452 | −0.539192 | ||||||||
\(551\) | 3.84729 | 0.163900 | ||||||||
\(552\) | 3.42727 | 0.145874 | ||||||||
\(553\) | 3.83443 | 0.163056 | ||||||||
\(554\) | 6.96535 | 0.295930 | ||||||||
\(555\) | −0.119668 | −0.00507962 | ||||||||
\(556\) | −10.8327 | −0.459409 | ||||||||
\(557\) | −42.3738 | −1.79544 | −0.897718 | − | 0.440570i | \(-0.854776\pi\) | ||||
−0.897718 | + | 0.440570i | \(0.854776\pi\) | |||||||
\(558\) | −0.257212 | −0.0108887 | ||||||||
\(559\) | −19.0886 | −0.807363 | ||||||||
\(560\) | 0.426244 | 0.0180121 | ||||||||
\(561\) | 0.891552 | 0.0376413 | ||||||||
\(562\) | 3.57358 | 0.150742 | ||||||||
\(563\) | −32.3856 | −1.36489 | −0.682444 | − | 0.730938i | \(-0.739083\pi\) | ||||
−0.682444 | + | 0.730938i | \(0.739083\pi\) | |||||||
\(564\) | 6.20583 | 0.261313 | ||||||||
\(565\) | −1.30569 | −0.0549309 | ||||||||
\(566\) | −27.0801 | −1.13826 | ||||||||
\(567\) | −2.28090 | −0.0957888 | ||||||||
\(568\) | −4.85454 | −0.203692 | ||||||||
\(569\) | −12.8053 | −0.536824 | −0.268412 | − | 0.963304i | \(-0.586499\pi\) | ||||
−0.268412 | + | 0.963304i | \(0.586499\pi\) | |||||||
\(570\) | 0.186875 | 0.00782735 | ||||||||
\(571\) | 20.0575 | 0.839382 | 0.419691 | − | 0.907667i | \(-0.362138\pi\) | ||||
0.419691 | + | 0.907667i | \(0.362138\pi\) | |||||||
\(572\) | 7.84454 | 0.327997 | ||||||||
\(573\) | −4.96532 | −0.207429 | ||||||||
\(574\) | −13.0982 | −0.546708 | ||||||||
\(575\) | −17.0167 | −0.709644 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −30.2183 | −1.25800 | −0.629002 | − | 0.777404i | \(-0.716536\pi\) | ||||
−0.629002 | + | 0.777404i | \(0.716536\pi\) | |||||||
\(578\) | 16.8775 | 0.702010 | ||||||||
\(579\) | 18.9514 | 0.787591 | ||||||||
\(580\) | 0.718963 | 0.0298533 | ||||||||
\(581\) | 16.1650 | 0.670637 | ||||||||
\(582\) | −5.00597 | −0.207504 | ||||||||
\(583\) | −2.54682 | −0.105479 | ||||||||
\(584\) | 7.21818 | 0.298690 | ||||||||
\(585\) | 0.575600 | 0.0237981 | ||||||||
\(586\) | 5.34975 | 0.220996 | ||||||||
\(587\) | 22.2165 | 0.916973 | 0.458486 | − | 0.888701i | \(-0.348392\pi\) | ||||
0.458486 | + | 0.888701i | \(0.348392\pi\) | |||||||
\(588\) | 1.79750 | 0.0741277 | ||||||||
\(589\) | −0.257212 | −0.0105982 | ||||||||
\(590\) | −2.34107 | −0.0963802 | ||||||||
\(591\) | −0.325789 | −0.0134012 | ||||||||
\(592\) | −0.640362 | −0.0263187 | ||||||||
\(593\) | 20.5845 | 0.845306 | 0.422653 | − | 0.906292i | \(-0.361099\pi\) | ||||
0.422653 | + | 0.906292i | \(0.361099\pi\) | |||||||
\(594\) | −2.54682 | −0.104497 | ||||||||
\(595\) | 0.149213 | 0.00611713 | ||||||||
\(596\) | −10.5372 | −0.431622 | ||||||||
\(597\) | −5.06882 | −0.207453 | ||||||||
\(598\) | 10.5564 | 0.431684 | ||||||||
\(599\) | 40.7510 | 1.66504 | 0.832521 | − | 0.553994i | \(-0.186897\pi\) | ||||
0.832521 | + | 0.553994i | \(0.186897\pi\) | |||||||
\(600\) | −4.96508 | −0.202698 | ||||||||
\(601\) | 21.8974 | 0.893215 | 0.446608 | − | 0.894730i | \(-0.352632\pi\) | ||||
0.446608 | + | 0.894730i | \(0.352632\pi\) | |||||||
\(602\) | 14.1355 | 0.576121 | ||||||||
\(603\) | −0.411602 | −0.0167617 | ||||||||
\(604\) | −21.7766 | −0.886076 | ||||||||
\(605\) | 0.843497 | 0.0342930 | ||||||||
\(606\) | 19.0875 | 0.775378 | ||||||||
\(607\) | −21.4337 | −0.869969 | −0.434985 | − | 0.900438i | \(-0.643246\pi\) | ||||
−0.434985 | + | 0.900438i | \(0.643246\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | −8.77527 | −0.355592 | ||||||||
\(610\) | 0.564747 | 0.0228659 | ||||||||
\(611\) | 19.1148 | 0.773300 | ||||||||
\(612\) | 0.350064 | 0.0141505 | ||||||||
\(613\) | 15.1858 | 0.613348 | 0.306674 | − | 0.951815i | \(-0.400784\pi\) | ||||
0.306674 | + | 0.951815i | \(0.400784\pi\) | |||||||
\(614\) | −21.4945 | −0.867448 | ||||||||
\(615\) | −1.07314 | −0.0432733 | ||||||||
\(616\) | −5.80905 | −0.234053 | ||||||||
\(617\) | 14.2684 | 0.574423 | 0.287211 | − | 0.957867i | \(-0.407272\pi\) | ||||
0.287211 | + | 0.957867i | \(0.407272\pi\) | |||||||
\(618\) | −0.920029 | −0.0370090 | ||||||||
\(619\) | −20.6384 | −0.829527 | −0.414763 | − | 0.909929i | \(-0.636136\pi\) | ||||
−0.414763 | + | 0.909929i | \(0.636136\pi\) | |||||||
\(620\) | −0.0480666 | −0.00193040 | ||||||||
\(621\) | −3.42727 | −0.137532 | ||||||||
\(622\) | 3.36641 | 0.134981 | ||||||||
\(623\) | −3.54235 | −0.141921 | ||||||||
\(624\) | 3.08013 | 0.123304 | ||||||||
\(625\) | 24.4774 | 0.979095 | ||||||||
\(626\) | 1.09924 | 0.0439343 | ||||||||
\(627\) | −2.54682 | −0.101710 | ||||||||
\(628\) | 11.0450 | 0.440744 | ||||||||
\(629\) | −0.224168 | −0.00893816 | ||||||||
\(630\) | −0.426244 | −0.0169820 | ||||||||
\(631\) | −37.1256 | −1.47795 | −0.738973 | − | 0.673735i | \(-0.764689\pi\) | ||||
−0.738973 | + | 0.673735i | \(0.764689\pi\) | |||||||
\(632\) | 1.68110 | 0.0668707 | ||||||||
\(633\) | −15.3166 | −0.608779 | ||||||||
\(634\) | 29.9903 | 1.19107 | ||||||||
\(635\) | −1.60468 | −0.0636798 | ||||||||
\(636\) | −1.00000 | −0.0396526 | ||||||||
\(637\) | 5.53653 | 0.219365 | ||||||||
\(638\) | −9.79836 | −0.387921 | ||||||||
\(639\) | 4.85454 | 0.192043 | ||||||||
\(640\) | 0.186875 | 0.00738690 | ||||||||
\(641\) | −21.4907 | −0.848830 | −0.424415 | − | 0.905468i | \(-0.639520\pi\) | ||||
−0.424415 | + | 0.905468i | \(0.639520\pi\) | |||||||
\(642\) | −7.42877 | −0.293190 | ||||||||
\(643\) | 4.80565 | 0.189516 | 0.0947581 | − | 0.995500i | \(-0.469792\pi\) | ||||
0.0947581 | + | 0.995500i | \(0.469792\pi\) | |||||||
\(644\) | −7.81726 | −0.308043 | ||||||||
\(645\) | 1.15813 | 0.0456014 | ||||||||
\(646\) | 0.350064 | 0.0137731 | ||||||||
\(647\) | 40.3109 | 1.58478 | 0.792392 | − | 0.610013i | \(-0.208836\pi\) | ||||
0.792392 | + | 0.610013i | \(0.208836\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 31.9051 | 1.25239 | ||||||||
\(650\) | −15.2931 | −0.599843 | ||||||||
\(651\) | 0.586675 | 0.0229936 | ||||||||
\(652\) | −5.74171 | −0.224863 | ||||||||
\(653\) | 26.0036 | 1.01760 | 0.508801 | − | 0.860884i | \(-0.330089\pi\) | ||||
0.508801 | + | 0.860884i | \(0.330089\pi\) | |||||||
\(654\) | −7.59367 | −0.296936 | ||||||||
\(655\) | −3.03766 | −0.118691 | ||||||||
\(656\) | −5.74256 | −0.224209 | ||||||||
\(657\) | −7.21818 | −0.281608 | ||||||||
\(658\) | −14.1549 | −0.551815 | ||||||||
\(659\) | −33.6329 | −1.31015 | −0.655076 | − | 0.755563i | \(-0.727363\pi\) | ||||
−0.655076 | + | 0.755563i | \(0.727363\pi\) | |||||||
\(660\) | −0.475939 | −0.0185259 | ||||||||
\(661\) | −4.53814 | −0.176513 | −0.0882567 | − | 0.996098i | \(-0.528130\pi\) | ||||
−0.0882567 | + | 0.996098i | \(0.528130\pi\) | |||||||
\(662\) | 23.7133 | 0.921642 | ||||||||
\(663\) | 1.07824 | 0.0418754 | ||||||||
\(664\) | 7.08712 | 0.275034 | ||||||||
\(665\) | −0.426244 | −0.0165290 | ||||||||
\(666\) | 0.640362 | 0.0248135 | ||||||||
\(667\) | −13.1857 | −0.510552 | ||||||||
\(668\) | 25.5126 | 0.987113 | ||||||||
\(669\) | −0.00422436 | −0.000163323 0 | ||||||||
\(670\) | −0.0769183 | −0.00297161 | ||||||||
\(671\) | −7.69663 | −0.297125 | ||||||||
\(672\) | −2.28090 | −0.0879876 | ||||||||
\(673\) | −25.5314 | −0.984164 | −0.492082 | − | 0.870549i | \(-0.663764\pi\) | ||||
−0.492082 | + | 0.870549i | \(0.663764\pi\) | |||||||
\(674\) | −0.472626 | −0.0182049 | ||||||||
\(675\) | 4.96508 | 0.191106 | ||||||||
\(676\) | −3.51282 | −0.135108 | ||||||||
\(677\) | −8.22629 | −0.316162 | −0.158081 | − | 0.987426i | \(-0.550531\pi\) | ||||
−0.158081 | + | 0.987426i | \(0.550531\pi\) | |||||||
\(678\) | 6.98697 | 0.268333 | ||||||||
\(679\) | 11.4181 | 0.438187 | ||||||||
\(680\) | 0.0654184 | 0.00250868 | ||||||||
\(681\) | −8.50529 | −0.325924 | ||||||||
\(682\) | 0.655074 | 0.0250841 | ||||||||
\(683\) | 41.8460 | 1.60119 | 0.800597 | − | 0.599204i | \(-0.204516\pi\) | ||||
0.800597 | + | 0.599204i | \(0.204516\pi\) | |||||||
\(684\) | −1.00000 | −0.0382360 | ||||||||
\(685\) | −2.54795 | −0.0973520 | ||||||||
\(686\) | −20.0662 | −0.766131 | ||||||||
\(687\) | 17.5801 | 0.670723 | ||||||||
\(688\) | 6.19735 | 0.236272 | ||||||||
\(689\) | −3.08013 | −0.117343 | ||||||||
\(690\) | −0.640473 | −0.0243824 | ||||||||
\(691\) | 7.33820 | 0.279158 | 0.139579 | − | 0.990211i | \(-0.455425\pi\) | ||||
0.139579 | + | 0.990211i | \(0.455425\pi\) | |||||||
\(692\) | 8.86507 | 0.337000 | ||||||||
\(693\) | 5.80905 | 0.220667 | ||||||||
\(694\) | −35.4792 | −1.34677 | ||||||||
\(695\) | 2.02437 | 0.0767886 | ||||||||
\(696\) | −3.84729 | −0.145831 | ||||||||
\(697\) | −2.01026 | −0.0761442 | ||||||||
\(698\) | −26.7603 | −1.01289 | ||||||||
\(699\) | 12.6432 | 0.478211 | ||||||||
\(700\) | 11.3248 | 0.428039 | ||||||||
\(701\) | 18.1805 | 0.686670 | 0.343335 | − | 0.939213i | \(-0.388443\pi\) | ||||
0.343335 | + | 0.939213i | \(0.388443\pi\) | |||||||
\(702\) | −3.08013 | −0.116252 | ||||||||
\(703\) | 0.640362 | 0.0241517 | ||||||||
\(704\) | −2.54682 | −0.0959870 | ||||||||
\(705\) | −1.15972 | −0.0436775 | ||||||||
\(706\) | 7.69557 | 0.289627 | ||||||||
\(707\) | −43.5367 | −1.63737 | ||||||||
\(708\) | 12.5274 | 0.470809 | ||||||||
\(709\) | −4.92445 | −0.184942 | −0.0924708 | − | 0.995715i | \(-0.529476\pi\) | ||||
−0.0924708 | + | 0.995715i | \(0.529476\pi\) | |||||||
\(710\) | 0.907194 | 0.0340464 | ||||||||
\(711\) | −1.68110 | −0.0630463 | ||||||||
\(712\) | −1.55305 | −0.0582030 | ||||||||
\(713\) | 0.881536 | 0.0330138 | ||||||||
\(714\) | −0.798461 | −0.0298817 | ||||||||
\(715\) | −1.46595 | −0.0548235 | ||||||||
\(716\) | 9.11968 | 0.340819 | ||||||||
\(717\) | −29.8548 | −1.11495 | ||||||||
\(718\) | −21.8889 | −0.816887 | ||||||||
\(719\) | −23.5130 | −0.876889 | −0.438444 | − | 0.898758i | \(-0.644470\pi\) | ||||
−0.438444 | + | 0.898758i | \(0.644470\pi\) | |||||||
\(720\) | −0.186875 | −0.00696444 | ||||||||
\(721\) | 2.09849 | 0.0781520 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −6.92064 | −0.257381 | ||||||||
\(724\) | −3.03839 | −0.112921 | ||||||||
\(725\) | 19.1021 | 0.709433 | ||||||||
\(726\) | −4.51369 | −0.167519 | ||||||||
\(727\) | 31.1464 | 1.15515 | 0.577577 | − | 0.816336i | \(-0.303998\pi\) | ||||
0.577577 | + | 0.816336i | \(0.303998\pi\) | |||||||
\(728\) | −7.02546 | −0.260381 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.34890 | −0.0499250 | ||||||||
\(731\) | 2.16947 | 0.0802408 | ||||||||
\(732\) | −3.02205 | −0.111698 | ||||||||
\(733\) | −20.4692 | −0.756047 | −0.378024 | − | 0.925796i | \(-0.623396\pi\) | ||||
−0.378024 | + | 0.925796i | \(0.623396\pi\) | |||||||
\(734\) | 24.8872 | 0.918604 | ||||||||
\(735\) | −0.335909 | −0.0123902 | ||||||||
\(736\) | −3.42727 | −0.126331 | ||||||||
\(737\) | 1.04828 | 0.0386138 | ||||||||
\(738\) | 5.74256 | 0.211386 | ||||||||
\(739\) | −39.1859 | −1.44148 | −0.720739 | − | 0.693207i | \(-0.756197\pi\) | ||||
−0.720739 | + | 0.693207i | \(0.756197\pi\) | |||||||
\(740\) | 0.119668 | 0.00439908 | ||||||||
\(741\) | −3.08013 | −0.113151 | ||||||||
\(742\) | 2.28090 | 0.0837344 | ||||||||
\(743\) | −28.1211 | −1.03166 | −0.515832 | − | 0.856690i | \(-0.672517\pi\) | ||||
−0.515832 | + | 0.856690i | \(0.672517\pi\) | |||||||
\(744\) | 0.257212 | 0.00942986 | ||||||||
\(745\) | 1.96915 | 0.0721441 | ||||||||
\(746\) | −15.2669 | −0.558961 | ||||||||
\(747\) | −7.08712 | −0.259304 | ||||||||
\(748\) | −0.891552 | −0.0325984 | ||||||||
\(749\) | 16.9443 | 0.619130 | ||||||||
\(750\) | 1.86223 | 0.0679990 | ||||||||
\(751\) | −17.6260 | −0.643181 | −0.321591 | − | 0.946879i | \(-0.604217\pi\) | ||||
−0.321591 | + | 0.946879i | \(0.604217\pi\) | |||||||
\(752\) | −6.20583 | −0.226303 | ||||||||
\(753\) | 12.9677 | 0.472569 | ||||||||
\(754\) | −11.8501 | −0.431556 | ||||||||
\(755\) | 4.06950 | 0.148104 | ||||||||
\(756\) | 2.28090 | 0.0829555 | ||||||||
\(757\) | 43.5877 | 1.58422 | 0.792112 | − | 0.610376i | \(-0.208982\pi\) | ||||
0.792112 | + | 0.610376i | \(0.208982\pi\) | |||||||
\(758\) | −27.7711 | −1.00869 | ||||||||
\(759\) | 8.72865 | 0.316830 | ||||||||
\(760\) | −0.186875 | −0.00677868 | ||||||||
\(761\) | 49.3926 | 1.79048 | 0.895240 | − | 0.445584i | \(-0.147004\pi\) | ||||
0.895240 | + | 0.445584i | \(0.147004\pi\) | |||||||
\(762\) | 8.58689 | 0.311070 | ||||||||
\(763\) | 17.3204 | 0.627040 | ||||||||
\(764\) | 4.96532 | 0.179639 | ||||||||
\(765\) | −0.0654184 | −0.00236521 | ||||||||
\(766\) | −19.3058 | −0.697548 | ||||||||
\(767\) | 38.5861 | 1.39326 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −36.4836 | −1.31563 | −0.657817 | − | 0.753178i | \(-0.728520\pi\) | ||||
−0.657817 | + | 0.753178i | \(0.728520\pi\) | |||||||
\(770\) | 1.08557 | 0.0391212 | ||||||||
\(771\) | −13.5969 | −0.489680 | ||||||||
\(772\) | −18.9514 | −0.682074 | ||||||||
\(773\) | 13.8819 | 0.499299 | 0.249649 | − | 0.968336i | \(-0.419685\pi\) | ||||
0.249649 | + | 0.968336i | \(0.419685\pi\) | |||||||
\(774\) | −6.19735 | −0.222759 | ||||||||
\(775\) | −1.27708 | −0.0458740 | ||||||||
\(776\) | 5.00597 | 0.179704 | ||||||||
\(777\) | −1.46060 | −0.0523988 | ||||||||
\(778\) | 29.2133 | 1.04735 | ||||||||
\(779\) | 5.74256 | 0.205748 | ||||||||
\(780\) | −0.575600 | −0.0206098 | ||||||||
\(781\) | −12.3637 | −0.442406 | ||||||||
\(782\) | −1.19976 | −0.0429035 | ||||||||
\(783\) | 3.84729 | 0.137491 | ||||||||
\(784\) | −1.79750 | −0.0641964 | ||||||||
\(785\) | −2.06404 | −0.0736688 | ||||||||
\(786\) | 16.2550 | 0.579796 | ||||||||
\(787\) | 51.7741 | 1.84555 | 0.922773 | − | 0.385344i | \(-0.125917\pi\) | ||||
0.922773 | + | 0.385344i | \(0.125917\pi\) | |||||||
\(788\) | 0.325789 | 0.0116058 | ||||||||
\(789\) | 15.4410 | 0.549714 | ||||||||
\(790\) | −0.314157 | −0.0111772 | ||||||||
\(791\) | −15.9366 | −0.566639 | ||||||||
\(792\) | 2.54682 | 0.0904975 | ||||||||
\(793\) | −9.30830 | −0.330547 | ||||||||
\(794\) | −11.1577 | −0.395970 | ||||||||
\(795\) | 0.186875 | 0.00662779 | ||||||||
\(796\) | 5.06882 | 0.179660 | ||||||||
\(797\) | 53.1651 | 1.88320 | 0.941602 | − | 0.336729i | \(-0.109321\pi\) | ||||
0.941602 | + | 0.336729i | \(0.109321\pi\) | |||||||
\(798\) | 2.28090 | 0.0807429 | ||||||||
\(799\) | −2.17244 | −0.0768554 | ||||||||
\(800\) | 4.96508 | 0.175542 | ||||||||
\(801\) | 1.55305 | 0.0548743 | ||||||||
\(802\) | 36.3134 | 1.28227 | ||||||||
\(803\) | 18.3834 | 0.648737 | ||||||||
\(804\) | 0.411602 | 0.0145161 | ||||||||
\(805\) | 1.46085 | 0.0514883 | ||||||||
\(806\) | 0.792246 | 0.0279057 | ||||||||
\(807\) | −21.3228 | −0.750599 | ||||||||
\(808\) | −19.0875 | −0.671497 | ||||||||
\(809\) | 43.3216 | 1.52311 | 0.761553 | − | 0.648102i | \(-0.224437\pi\) | ||||
0.761553 | + | 0.648102i | \(0.224437\pi\) | |||||||
\(810\) | 0.186875 | 0.00656613 | ||||||||
\(811\) | 4.84566 | 0.170154 | 0.0850770 | − | 0.996374i | \(-0.472886\pi\) | ||||
0.0850770 | + | 0.996374i | \(0.472886\pi\) | |||||||
\(812\) | 8.77527 | 0.307952 | ||||||||
\(813\) | 13.3895 | 0.469591 | ||||||||
\(814\) | −1.63089 | −0.0571627 | ||||||||
\(815\) | 1.07298 | 0.0375850 | ||||||||
\(816\) | −0.350064 | −0.0122547 | ||||||||
\(817\) | −6.19735 | −0.216818 | ||||||||
\(818\) | 17.9524 | 0.627692 | ||||||||
\(819\) | 7.02546 | 0.245489 | ||||||||
\(820\) | 1.07314 | 0.0374758 | ||||||||
\(821\) | −17.3850 | −0.606740 | −0.303370 | − | 0.952873i | \(-0.598112\pi\) | ||||
−0.303370 | + | 0.952873i | \(0.598112\pi\) | |||||||
\(822\) | 13.6345 | 0.475557 | ||||||||
\(823\) | 18.7552 | 0.653766 | 0.326883 | − | 0.945065i | \(-0.394002\pi\) | ||||
0.326883 | + | 0.945065i | \(0.394002\pi\) | |||||||
\(824\) | 0.920029 | 0.0320507 | ||||||||
\(825\) | −12.6452 | −0.440249 | ||||||||
\(826\) | −28.5738 | −0.994209 | ||||||||
\(827\) | −23.1480 | −0.804936 | −0.402468 | − | 0.915434i | \(-0.631848\pi\) | ||||
−0.402468 | + | 0.915434i | \(0.631848\pi\) | |||||||
\(828\) | 3.42727 | 0.119106 | ||||||||
\(829\) | −45.2091 | −1.57018 | −0.785089 | − | 0.619383i | \(-0.787383\pi\) | ||||
−0.785089 | + | 0.619383i | \(0.787383\pi\) | |||||||
\(830\) | −1.32441 | −0.0459709 | ||||||||
\(831\) | 6.96535 | 0.241625 | ||||||||
\(832\) | −3.08013 | −0.106784 | ||||||||
\(833\) | −0.629240 | −0.0218019 | ||||||||
\(834\) | −10.8327 | −0.375106 | ||||||||
\(835\) | −4.76768 | −0.164992 | ||||||||
\(836\) | 2.54682 | 0.0880838 | ||||||||
\(837\) | −0.257212 | −0.00889056 | ||||||||
\(838\) | −8.65145 | −0.298859 | ||||||||
\(839\) | −34.4667 | −1.18992 | −0.594962 | − | 0.803754i | \(-0.702833\pi\) | ||||
−0.594962 | + | 0.803754i | \(0.702833\pi\) | |||||||
\(840\) | 0.426244 | 0.0147068 | ||||||||
\(841\) | −14.1984 | −0.489599 | ||||||||
\(842\) | 5.56253 | 0.191697 | ||||||||
\(843\) | 3.57358 | 0.123081 | ||||||||
\(844\) | 15.3166 | 0.527218 | ||||||||
\(845\) | 0.656460 | 0.0225829 | ||||||||
\(846\) | 6.20583 | 0.213361 | ||||||||
\(847\) | 10.2953 | 0.353749 | ||||||||
\(848\) | 1.00000 | 0.0343401 | ||||||||
\(849\) | −27.0801 | −0.929387 | ||||||||
\(850\) | 1.73810 | 0.0596162 | ||||||||
\(851\) | −2.19469 | −0.0752332 | ||||||||
\(852\) | −4.85454 | −0.166314 | ||||||||
\(853\) | 25.0417 | 0.857411 | 0.428706 | − | 0.903444i | \(-0.358970\pi\) | ||||
0.428706 | + | 0.903444i | \(0.358970\pi\) | |||||||
\(854\) | 6.89299 | 0.235873 | ||||||||
\(855\) | 0.186875 | 0.00639100 | ||||||||
\(856\) | 7.42877 | 0.253910 | ||||||||
\(857\) | −5.97200 | −0.204000 | −0.102000 | − | 0.994784i | \(-0.532524\pi\) | ||||
−0.102000 | + | 0.994784i | \(0.532524\pi\) | |||||||
\(858\) | 7.84454 | 0.267808 | ||||||||
\(859\) | 44.4146 | 1.51541 | 0.757703 | − | 0.652600i | \(-0.226322\pi\) | ||||
0.757703 | + | 0.652600i | \(0.226322\pi\) | |||||||
\(860\) | −1.15813 | −0.0394920 | ||||||||
\(861\) | −13.0982 | −0.446385 | ||||||||
\(862\) | −10.9227 | −0.372028 | ||||||||
\(863\) | 25.3919 | 0.864349 | 0.432175 | − | 0.901790i | \(-0.357746\pi\) | ||||
0.432175 | + | 0.901790i | \(0.357746\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −1.65666 | −0.0563283 | ||||||||
\(866\) | −29.1082 | −0.989136 | ||||||||
\(867\) | 16.8775 | 0.573188 | ||||||||
\(868\) | −0.586675 | −0.0199131 | ||||||||
\(869\) | 4.28147 | 0.145239 | ||||||||
\(870\) | 0.718963 | 0.0243751 | ||||||||
\(871\) | 1.26779 | 0.0429573 | ||||||||
\(872\) | 7.59367 | 0.257154 | ||||||||
\(873\) | −5.00597 | −0.169426 | ||||||||
\(874\) | 3.42727 | 0.115929 | ||||||||
\(875\) | −4.24755 | −0.143594 | ||||||||
\(876\) | 7.21818 | 0.243880 | ||||||||
\(877\) | −11.4426 | −0.386390 | −0.193195 | − | 0.981160i | \(-0.561885\pi\) | ||||
−0.193195 | + | 0.981160i | \(0.561885\pi\) | |||||||
\(878\) | 6.83597 | 0.230703 | ||||||||
\(879\) | 5.34975 | 0.180443 | ||||||||
\(880\) | 0.475939 | 0.0160439 | ||||||||
\(881\) | −38.2947 | −1.29018 | −0.645091 | − | 0.764106i | \(-0.723181\pi\) | ||||
−0.645091 | + | 0.764106i | \(0.723181\pi\) | |||||||
\(882\) | 1.79750 | 0.0605250 | ||||||||
\(883\) | 9.91817 | 0.333773 | 0.166886 | − | 0.985976i | \(-0.446629\pi\) | ||||
0.166886 | + | 0.985976i | \(0.446629\pi\) | |||||||
\(884\) | −1.07824 | −0.0362652 | ||||||||
\(885\) | −2.34107 | −0.0786941 | ||||||||
\(886\) | −29.3517 | −0.986088 | ||||||||
\(887\) | −6.10910 | −0.205124 | −0.102562 | − | 0.994727i | \(-0.532704\pi\) | ||||
−0.102562 | + | 0.994727i | \(0.532704\pi\) | |||||||
\(888\) | −0.640362 | −0.0214892 | ||||||||
\(889\) | −19.5858 | −0.656888 | ||||||||
\(890\) | 0.290227 | 0.00972842 | ||||||||
\(891\) | −2.54682 | −0.0853218 | ||||||||
\(892\) | 0.00422436 | 0.000141442 0 | ||||||||
\(893\) | 6.20583 | 0.207670 | ||||||||
\(894\) | −10.5372 | −0.352418 | ||||||||
\(895\) | −1.70424 | −0.0569666 | ||||||||
\(896\) | 2.28090 | 0.0761995 | ||||||||
\(897\) | 10.5564 | 0.352469 | ||||||||
\(898\) | 10.6310 | 0.354762 | ||||||||
\(899\) | −0.989569 | −0.0330040 | ||||||||
\(900\) | −4.96508 | −0.165503 | ||||||||
\(901\) | 0.350064 | 0.0116623 | ||||||||
\(902\) | −14.6253 | −0.486969 | ||||||||
\(903\) | 14.1355 | 0.470401 | ||||||||
\(904\) | −6.98697 | −0.232383 | ||||||||
\(905\) | 0.567800 | 0.0188743 | ||||||||
\(906\) | −21.7766 | −0.723478 | ||||||||
\(907\) | 35.1244 | 1.16629 | 0.583144 | − | 0.812369i | \(-0.301822\pi\) | ||||
0.583144 | + | 0.812369i | \(0.301822\pi\) | |||||||
\(908\) | 8.50529 | 0.282258 | ||||||||
\(909\) | 19.0875 | 0.633093 | ||||||||
\(910\) | 1.31289 | 0.0435217 | ||||||||
\(911\) | −13.3495 | −0.442289 | −0.221145 | − | 0.975241i | \(-0.570979\pi\) | ||||
−0.221145 | + | 0.975241i | \(0.570979\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | 18.0496 | 0.597356 | ||||||||
\(914\) | −37.5623 | −1.24245 | ||||||||
\(915\) | 0.564747 | 0.0186700 | ||||||||
\(916\) | −17.5801 | −0.580864 | ||||||||
\(917\) | −37.0760 | −1.22436 | ||||||||
\(918\) | 0.350064 | 0.0115538 | ||||||||
\(919\) | −7.67588 | −0.253204 | −0.126602 | − | 0.991954i | \(-0.540407\pi\) | ||||
−0.126602 | + | 0.991954i | \(0.540407\pi\) | |||||||
\(920\) | 0.640473 | 0.0211158 | ||||||||
\(921\) | −21.4945 | −0.708268 | ||||||||
\(922\) | −18.1122 | −0.596493 | ||||||||
\(923\) | −14.9526 | −0.492171 | ||||||||
\(924\) | −5.80905 | −0.191104 | ||||||||
\(925\) | 3.17945 | 0.104540 | ||||||||
\(926\) | −19.6837 | −0.646845 | ||||||||
\(927\) | −0.920029 | −0.0302177 | ||||||||
\(928\) | 3.84729 | 0.126293 | ||||||||
\(929\) | 15.8292 | 0.519340 | 0.259670 | − | 0.965697i | \(-0.416386\pi\) | ||||
0.259670 | + | 0.965697i | \(0.416386\pi\) | |||||||
\(930\) | −0.0480666 | −0.00157617 | ||||||||
\(931\) | 1.79750 | 0.0589107 | ||||||||
\(932\) | −12.6432 | −0.414143 | ||||||||
\(933\) | 3.36641 | 0.110211 | ||||||||
\(934\) | −24.5957 | −0.804795 | ||||||||
\(935\) | 0.166609 | 0.00544870 | ||||||||
\(936\) | 3.08013 | 0.100677 | ||||||||
\(937\) | 30.7700 | 1.00521 | 0.502606 | − | 0.864515i | \(-0.332375\pi\) | ||||
0.502606 | + | 0.864515i | \(0.332375\pi\) | |||||||
\(938\) | −0.938822 | −0.0306536 | ||||||||
\(939\) | 1.09924 | 0.0358722 | ||||||||
\(940\) | 1.15972 | 0.0378258 | ||||||||
\(941\) | 6.64704 | 0.216687 | 0.108344 | − | 0.994113i | \(-0.465445\pi\) | ||||
0.108344 | + | 0.994113i | \(0.465445\pi\) | |||||||
\(942\) | 11.0450 | 0.359866 | ||||||||
\(943\) | −19.6813 | −0.640911 | ||||||||
\(944\) | −12.5274 | −0.407733 | ||||||||
\(945\) | −0.426244 | −0.0138657 | ||||||||
\(946\) | 15.7836 | 0.513168 | ||||||||
\(947\) | −4.83921 | −0.157253 | −0.0786267 | − | 0.996904i | \(-0.525054\pi\) | ||||
−0.0786267 | + | 0.996904i | \(0.525054\pi\) | |||||||
\(948\) | 1.68110 | 0.0545997 | ||||||||
\(949\) | 22.2329 | 0.721710 | ||||||||
\(950\) | −4.96508 | −0.161088 | ||||||||
\(951\) | 29.9903 | 0.972501 | ||||||||
\(952\) | 0.798461 | 0.0258783 | ||||||||
\(953\) | 55.7707 | 1.80659 | 0.903295 | − | 0.429019i | \(-0.141141\pi\) | ||||
0.903295 | + | 0.429019i | \(0.141141\pi\) | |||||||
\(954\) | −1.00000 | −0.0323762 | ||||||||
\(955\) | −0.927896 | −0.0300260 | ||||||||
\(956\) | 29.8548 | 0.965574 | ||||||||
\(957\) | −9.79836 | −0.316736 | ||||||||
\(958\) | −27.7898 | −0.897847 | ||||||||
\(959\) | −31.0988 | −1.00423 | ||||||||
\(960\) | 0.186875 | 0.00603138 | ||||||||
\(961\) | −30.9338 | −0.997866 | ||||||||
\(962\) | −1.97240 | −0.0635926 | ||||||||
\(963\) | −7.42877 | −0.239389 | ||||||||
\(964\) | 6.92064 | 0.222899 | ||||||||
\(965\) | 3.54154 | 0.114006 | ||||||||
\(966\) | −7.81726 | −0.251516 | ||||||||
\(967\) | 17.6940 | 0.569002 | 0.284501 | − | 0.958676i | \(-0.408172\pi\) | ||||
0.284501 | + | 0.958676i | \(0.408172\pi\) | |||||||
\(968\) | 4.51369 | 0.145075 | ||||||||
\(969\) | 0.350064 | 0.0112457 | ||||||||
\(970\) | −0.935492 | −0.0300368 | ||||||||
\(971\) | 2.83821 | 0.0910825 | 0.0455412 | − | 0.998962i | \(-0.485499\pi\) | ||||
0.0455412 | + | 0.998962i | \(0.485499\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 24.7083 | 0.792112 | ||||||||
\(974\) | 16.3624 | 0.524284 | ||||||||
\(975\) | −15.2931 | −0.489770 | ||||||||
\(976\) | 3.02205 | 0.0967335 | ||||||||
\(977\) | −33.3946 | −1.06839 | −0.534194 | − | 0.845362i | \(-0.679385\pi\) | ||||
−0.534194 | + | 0.845362i | \(0.679385\pi\) | |||||||
\(978\) | −5.74171 | −0.183600 | ||||||||
\(979\) | −3.95534 | −0.126413 | ||||||||
\(980\) | 0.335909 | 0.0107302 | ||||||||
\(981\) | −7.59367 | −0.242447 | ||||||||
\(982\) | −35.6365 | −1.13721 | ||||||||
\(983\) | −12.1833 | −0.388587 | −0.194293 | − | 0.980943i | \(-0.562241\pi\) | ||||
−0.194293 | + | 0.980943i | \(0.562241\pi\) | |||||||
\(984\) | −5.74256 | −0.183066 | ||||||||
\(985\) | −0.0608820 | −0.00193986 | ||||||||
\(986\) | 1.34680 | 0.0428908 | ||||||||
\(987\) | −14.1549 | −0.450555 | ||||||||
\(988\) | 3.08013 | 0.0979919 | ||||||||
\(989\) | 21.2400 | 0.675393 | ||||||||
\(990\) | −0.475939 | −0.0151263 | ||||||||
\(991\) | −19.0453 | −0.604994 | −0.302497 | − | 0.953150i | \(-0.597820\pi\) | ||||
−0.302497 | + | 0.953150i | \(0.597820\pi\) | |||||||
\(992\) | −0.257212 | −0.00816650 | ||||||||
\(993\) | 23.7133 | 0.752518 | ||||||||
\(994\) | 11.0727 | 0.351205 | ||||||||
\(995\) | −0.947238 | −0.0300295 | ||||||||
\(996\) | 7.08712 | 0.224564 | ||||||||
\(997\) | −4.77757 | −0.151307 | −0.0756535 | − | 0.997134i | \(-0.524104\pi\) | ||||
−0.0756535 | + | 0.997134i | \(0.524104\pi\) | |||||||
\(998\) | −27.6074 | −0.873896 | ||||||||
\(999\) | 0.640362 | 0.0202602 |
(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 | 6042.2.a.z.1.5 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6042.2.a.z.1.5 | ✓ | 9 | 1.1 | even | 1 | trivial |