Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1850,2,Mod(149,1850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1850, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1850.149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1850 = 2 \cdot 5^{2} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1850.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(14.7723243739\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.3182656.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{3} + 25x^{2} - 10x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 370) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 149.3 | ||
Root | \(1.46962 - 1.46962i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1850.149 |
Dual form | 1850.2.b.o.149.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1850\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1777\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | 2.93923i | 1.69697i | 0.529221 | + | 0.848484i | \(0.322484\pi\) | ||||
−0.529221 | + | 0.848484i | \(0.677516\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.93923 | 1.19994 | ||||||||
\(7\) | 1.31955i | 0.498743i | 0.968408 | + | 0.249372i | \(0.0802241\pi\) | ||||
−0.968408 | + | 0.249372i | \(0.919776\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −5.63910 | −1.87970 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.258786 | −0.0780268 | −0.0390134 | − | 0.999239i | \(-0.512422\pi\) | ||||
−0.0390134 | + | 0.999239i | \(0.512422\pi\) | |||||||
\(12\) | − 2.93923i | − 0.848484i | ||||||||
\(13\) | − 5.87847i | − 1.63039i | −0.579184 | − | 0.815197i | \(-0.696629\pi\) | ||||
0.579184 | − | 0.815197i | \(-0.303371\pi\) | |||||||
\(14\) | 1.31955 | 0.352665 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − 4.25879i | − 1.03291i | −0.856315 | − | 0.516454i | \(-0.827252\pi\) | ||||
0.856315 | − | 0.516454i | \(-0.172748\pi\) | |||||||
\(18\) | 5.63910i | 1.32915i | ||||||||
\(19\) | −2.93923 | −0.674307 | −0.337153 | − | 0.941450i | \(-0.609464\pi\) | ||||
−0.337153 | + | 0.941450i | \(0.609464\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.87847 | −0.846351 | ||||||||
\(22\) | 0.258786i | 0.0551733i | ||||||||
\(23\) | − 8.51757i | − 1.77604i | −0.459808 | − | 0.888018i | \(-0.652082\pi\) | ||||
0.459808 | − | 0.888018i | \(-0.347918\pi\) | |||||||
\(24\) | −2.93923 | −0.599969 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.87847 | −1.15286 | ||||||||
\(27\) | − 7.75694i | − 1.49282i | ||||||||
\(28\) | − 1.31955i | − 0.249372i | ||||||||
\(29\) | 3.61968 | 0.672158 | 0.336079 | − | 0.941834i | \(-0.390899\pi\) | ||||
0.336079 | + | 0.941834i | \(0.390899\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.95865 | 0.710995 | 0.355497 | − | 0.934677i | \(-0.384311\pi\) | ||||
0.355497 | + | 0.934677i | \(0.384311\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | − 0.760632i | − 0.132409i | ||||||||
\(34\) | −4.25879 | −0.730376 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.63910 | 0.939850 | ||||||||
\(37\) | 1.00000i | 0.164399i | ||||||||
\(38\) | 2.93923i | 0.476807i | ||||||||
\(39\) | 17.2782 | 2.76673 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.89789 | −1.38962 | −0.694808 | − | 0.719195i | \(-0.744511\pi\) | ||||
−0.694808 | + | 0.719195i | \(0.744511\pi\) | |||||||
\(42\) | 3.87847i | 0.598461i | ||||||||
\(43\) | − 5.61968i | − 0.856994i | −0.903543 | − | 0.428497i | \(-0.859043\pi\) | ||||
0.903543 | − | 0.428497i | \(-0.140957\pi\) | |||||||
\(44\) | 0.258786 | 0.0390134 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.51757 | −1.25585 | ||||||||
\(47\) | − 5.57834i | − 0.813684i | −0.913499 | − | 0.406842i | \(-0.866630\pi\) | ||||
0.913499 | − | 0.406842i | \(-0.133370\pi\) | |||||||
\(48\) | 2.93923i | 0.424242i | ||||||||
\(49\) | 5.25879 | 0.751255 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.5176 | 1.75281 | ||||||||
\(52\) | 5.87847i | 0.815197i | ||||||||
\(53\) | 12.8979i | 1.77166i | 0.464009 | + | 0.885831i | \(0.346411\pi\) | ||||
−0.464009 | + | 0.885831i | \(0.653589\pi\) | |||||||
\(54\) | −7.75694 | −1.05559 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.31955 | −0.176332 | ||||||||
\(57\) | − 8.63910i | − 1.14428i | ||||||||
\(58\) | − 3.61968i | − 0.475288i | ||||||||
\(59\) | −9.57834 | −1.24699 | −0.623497 | − | 0.781826i | \(-0.714288\pi\) | ||||
−0.623497 | + | 0.781826i | \(0.714288\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.380316 | 0.0486945 | 0.0243472 | − | 0.999704i | \(-0.492249\pi\) | ||||
0.0243472 | + | 0.999704i | \(0.492249\pi\) | |||||||
\(62\) | − 3.95865i | − 0.502749i | ||||||||
\(63\) | − 7.44108i | − 0.937488i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.760632 | −0.0936273 | ||||||||
\(67\) | − 5.57834i | − 0.681502i | −0.940154 | − | 0.340751i | \(-0.889319\pi\) | ||||
0.940154 | − | 0.340751i | \(-0.110681\pi\) | |||||||
\(68\) | 4.25879i | 0.516454i | ||||||||
\(69\) | 25.0351 | 3.01388 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.2394 | 1.33387 | 0.666934 | − | 0.745117i | \(-0.267606\pi\) | ||||
0.666934 | + | 0.745117i | \(0.267606\pi\) | |||||||
\(72\) | − 5.63910i | − 0.664574i | ||||||||
\(73\) | 2.51757i | 0.294659i | 0.989087 | + | 0.147330i | \(0.0470678\pi\) | ||||
−0.989087 | + | 0.147330i | \(0.952932\pi\) | |||||||
\(74\) | 1.00000 | 0.116248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.93923 | 0.337153 | ||||||||
\(77\) | − 0.341481i | − 0.0389154i | ||||||||
\(78\) | − 17.2782i | − 1.95637i | ||||||||
\(79\) | 7.69987 | 0.866303 | 0.433151 | − | 0.901321i | \(-0.357402\pi\) | ||||
0.433151 | + | 0.901321i | \(0.357402\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.88216 | 0.653574 | ||||||||
\(82\) | 8.89789i | 0.982607i | ||||||||
\(83\) | − 6.17860i | − 0.678190i | −0.940752 | − | 0.339095i | \(-0.889879\pi\) | ||||
0.940752 | − | 0.339095i | \(-0.110121\pi\) | |||||||
\(84\) | 3.87847 | 0.423176 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.61968 | −0.605986 | ||||||||
\(87\) | 10.6391i | 1.14063i | ||||||||
\(88\) | − 0.258786i | − 0.0275866i | ||||||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.75694 | 0.813148 | ||||||||
\(92\) | 8.51757i | 0.888018i | ||||||||
\(93\) | 11.6354i | 1.20654i | ||||||||
\(94\) | −5.57834 | −0.575361 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.93923 | 0.299984 | ||||||||
\(97\) | 12.8979i | 1.30958i | 0.755810 | + | 0.654791i | \(0.227243\pi\) | ||||
−0.755810 | + | 0.654791i | \(0.772757\pi\) | |||||||
\(98\) | − 5.25879i | − 0.531218i | ||||||||
\(99\) | 1.45932 | 0.146667 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.3960 | 1.03444 | 0.517222 | − | 0.855851i | \(-0.326966\pi\) | ||||
0.517222 | + | 0.855851i | \(0.326966\pi\) | |||||||
\(102\) | − 12.5176i | − 1.23942i | ||||||||
\(103\) | − 13.8785i | − 1.36749i | −0.729723 | − | 0.683743i | \(-0.760351\pi\) | ||||
0.729723 | − | 0.683743i | \(-0.239649\pi\) | |||||||
\(104\) | 5.87847 | 0.576431 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.8979 | 1.25275 | ||||||||
\(107\) | 4.21744i | 0.407715i | 0.979001 | + | 0.203858i | \(0.0653479\pi\) | ||||
−0.979001 | + | 0.203858i | \(0.934652\pi\) | |||||||
\(108\) | 7.75694i | 0.746412i | ||||||||
\(109\) | −16.1373 | −1.54567 | −0.772834 | − | 0.634608i | \(-0.781162\pi\) | ||||
−0.772834 | + | 0.634608i | \(0.781162\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.93923 | −0.278980 | ||||||||
\(112\) | 1.31955i | 0.124686i | ||||||||
\(113\) | 1.01942i | 0.0958987i | 0.998850 | + | 0.0479494i | \(0.0152686\pi\) | ||||
−0.998850 | + | 0.0479494i | \(0.984731\pi\) | |||||||
\(114\) | −8.63910 | −0.809126 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.61968 | −0.336079 | ||||||||
\(117\) | 33.1493i | 3.06465i | ||||||||
\(118\) | 9.57834i | 0.881757i | ||||||||
\(119\) | 5.61968 | 0.515156 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9330 | −0.993912 | ||||||||
\(122\) | − 0.380316i | − 0.0344322i | ||||||||
\(123\) | − 26.1530i | − 2.35813i | ||||||||
\(124\) | −3.95865 | −0.355497 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −7.44108 | −0.662904 | ||||||||
\(127\) | − 7.45681i | − 0.661685i | −0.943686 | − | 0.330842i | \(-0.892667\pi\) | ||||
0.943686 | − | 0.330842i | \(-0.107333\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 16.5176 | 1.45429 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.42166 | 0.211582 | 0.105791 | − | 0.994388i | \(-0.466263\pi\) | ||||
0.105791 | + | 0.994388i | \(0.466263\pi\) | |||||||
\(132\) | 0.760632i | 0.0662045i | ||||||||
\(133\) | − 3.87847i | − 0.336306i | ||||||||
\(134\) | −5.57834 | −0.481895 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.25879 | 0.365188 | ||||||||
\(137\) | − 15.7958i | − 1.34952i | −0.738035 | − | 0.674762i | \(-0.764246\pi\) | ||||
0.738035 | − | 0.674762i | \(-0.235754\pi\) | |||||||
\(138\) | − 25.0351i | − 2.13113i | ||||||||
\(139\) | 11.4155 | 0.968247 | 0.484123 | − | 0.875000i | \(-0.339139\pi\) | ||||
0.484123 | + | 0.875000i | \(0.339139\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.3960 | 1.38080 | ||||||||
\(142\) | − 11.2394i | − 0.943187i | ||||||||
\(143\) | 1.52126i | 0.127214i | ||||||||
\(144\) | −5.63910 | −0.469925 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.51757 | 0.208356 | ||||||||
\(147\) | 15.4568i | 1.27486i | ||||||||
\(148\) | − 1.00000i | − 0.0821995i | ||||||||
\(149\) | −18.3960 | −1.50706 | −0.753531 | − | 0.657412i | \(-0.771651\pi\) | ||||
−0.753531 | + | 0.657412i | \(0.771651\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.87847 | 0.478383 | 0.239192 | − | 0.970972i | \(-0.423118\pi\) | ||||
0.239192 | + | 0.970972i | \(0.423118\pi\) | |||||||
\(152\) | − 2.93923i | − 0.238403i | ||||||||
\(153\) | 24.0157i | 1.94156i | ||||||||
\(154\) | −0.341481 | −0.0275173 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −17.2782 | −1.38336 | ||||||||
\(157\) | − 3.61968i | − 0.288882i | −0.989513 | − | 0.144441i | \(-0.953862\pi\) | ||||
0.989513 | − | 0.144441i | \(-0.0461384\pi\) | |||||||
\(158\) | − 7.69987i | − 0.612569i | ||||||||
\(159\) | −37.9099 | −3.00645 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.2394 | 0.885786 | ||||||||
\(162\) | − 5.88216i | − 0.462146i | ||||||||
\(163\) | − 22.0546i | − 1.72745i | −0.503966 | − | 0.863723i | \(-0.668126\pi\) | ||||
0.503966 | − | 0.863723i | \(-0.331874\pi\) | |||||||
\(164\) | 8.89789 | 0.694808 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.17860 | −0.479553 | ||||||||
\(167\) | 0.600267i | 0.0464500i | 0.999730 | + | 0.0232250i | \(0.00739341\pi\) | ||||
−0.999730 | + | 0.0232250i | \(0.992607\pi\) | |||||||
\(168\) | − 3.87847i | − 0.299230i | ||||||||
\(169\) | −21.5564 | −1.65819 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 16.5746 | 1.26749 | ||||||||
\(172\) | 5.61968i | 0.428497i | ||||||||
\(173\) | − 22.6937i | − 1.72537i | −0.505744 | − | 0.862684i | \(-0.668782\pi\) | ||||
0.505744 | − | 0.862684i | \(-0.331218\pi\) | |||||||
\(174\) | 10.6391 | 0.806548 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.258786 | −0.0195067 | ||||||||
\(177\) | − 28.1530i | − 2.11611i | ||||||||
\(178\) | 6.00000i | 0.449719i | ||||||||
\(179\) | 8.73501 | 0.652885 | 0.326443 | − | 0.945217i | \(-0.394150\pi\) | ||||
0.326443 | + | 0.945217i | \(0.394150\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.6391 | 0.790798 | 0.395399 | − | 0.918509i | \(-0.370606\pi\) | ||||
0.395399 | + | 0.918509i | \(0.370606\pi\) | |||||||
\(182\) | − 7.75694i | − 0.574983i | ||||||||
\(183\) | 1.11784i | 0.0826330i | ||||||||
\(184\) | 8.51757 | 0.627924 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 11.6354 | 0.853150 | ||||||||
\(187\) | 1.10211i | 0.0805945i | ||||||||
\(188\) | 5.57834i | 0.406842i | ||||||||
\(189\) | 10.2357 | 0.744536 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.1116 | 1.59994 | 0.799971 | − | 0.600039i | \(-0.204848\pi\) | ||||
0.799971 | + | 0.600039i | \(0.204848\pi\) | |||||||
\(192\) | − 2.93923i | − 0.212121i | ||||||||
\(193\) | 7.03514i | 0.506401i | 0.967414 | + | 0.253200i | \(0.0814832\pi\) | ||||
−0.967414 | + | 0.253200i | \(0.918517\pi\) | |||||||
\(194\) | 12.8979 | 0.926014 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.25879 | −0.375628 | ||||||||
\(197\) | − 25.7569i | − 1.83511i | −0.397614 | − | 0.917553i | \(-0.630162\pi\) | ||||
0.397614 | − | 0.917553i | \(-0.369838\pi\) | |||||||
\(198\) | − 1.45932i | − 0.103709i | ||||||||
\(199\) | 12.7350 | 0.902761 | 0.451380 | − | 0.892332i | \(-0.350932\pi\) | ||||
0.451380 | + | 0.892332i | \(0.350932\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 16.3960 | 1.15649 | ||||||||
\(202\) | − 10.3960i | − 0.731463i | ||||||||
\(203\) | 4.77636i | 0.335235i | ||||||||
\(204\) | −12.5176 | −0.876405 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −13.8785 | −0.966959 | ||||||||
\(207\) | 48.0315i | 3.33842i | ||||||||
\(208\) | − 5.87847i | − 0.407599i | ||||||||
\(209\) | 0.760632 | 0.0526140 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.65483 | −0.458137 | −0.229069 | − | 0.973410i | \(-0.573568\pi\) | ||||
−0.229069 | + | 0.973410i | \(0.573568\pi\) | |||||||
\(212\) | − 12.8979i | − 0.885831i | ||||||||
\(213\) | 33.0351i | 2.26353i | ||||||||
\(214\) | 4.21744 | 0.288298 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 7.75694 | 0.527793 | ||||||||
\(217\) | 5.22364i | 0.354604i | ||||||||
\(218\) | 16.1373i | 1.09295i | ||||||||
\(219\) | −7.39973 | −0.500028 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −25.0351 | −1.68405 | ||||||||
\(222\) | 2.93923i | 0.197269i | ||||||||
\(223\) | − 16.5589i | − 1.10887i | −0.832228 | − | 0.554434i | \(-0.812935\pi\) | ||||
0.832228 | − | 0.554434i | \(-0.187065\pi\) | |||||||
\(224\) | 1.31955 | 0.0881662 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.01942 | 0.0678106 | ||||||||
\(227\) | 4.01573i | 0.266533i | 0.991080 | + | 0.133267i | \(0.0425466\pi\) | ||||
−0.991080 | + | 0.133267i | \(0.957453\pi\) | |||||||
\(228\) | 8.63910i | 0.572138i | ||||||||
\(229\) | −25.5139 | −1.68600 | −0.843002 | − | 0.537910i | \(-0.819214\pi\) | ||||
−0.843002 | + | 0.537910i | \(0.819214\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.00369 | 0.0660381 | ||||||||
\(232\) | 3.61968i | 0.237644i | ||||||||
\(233\) | 7.96116i | 0.521553i | 0.965399 | + | 0.260777i | \(0.0839786\pi\) | ||||
−0.965399 | + | 0.260777i | \(0.916021\pi\) | |||||||
\(234\) | 33.1493 | 2.16704 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.57834 | 0.623497 | ||||||||
\(237\) | 22.6317i | 1.47009i | ||||||||
\(238\) | − 5.61968i | − 0.364270i | ||||||||
\(239\) | −11.7983 | −0.763168 | −0.381584 | − | 0.924334i | \(-0.624621\pi\) | ||||
−0.381584 | + | 0.924334i | \(0.624621\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.9963 | 1.61015 | 0.805077 | − | 0.593171i | \(-0.202124\pi\) | ||||
0.805077 | + | 0.593171i | \(0.202124\pi\) | |||||||
\(242\) | 10.9330i | 0.702802i | ||||||||
\(243\) | − 5.98176i | − 0.383730i | ||||||||
\(244\) | −0.380316 | −0.0243472 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −26.1530 | −1.66745 | ||||||||
\(247\) | 17.2782i | 1.09939i | ||||||||
\(248\) | 3.95865i | 0.251375i | ||||||||
\(249\) | 18.1604 | 1.15087 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.81770 | −0.556569 | −0.278284 | − | 0.960499i | \(-0.589766\pi\) | ||||
−0.278284 | + | 0.960499i | \(0.589766\pi\) | |||||||
\(252\) | 7.44108i | 0.468744i | ||||||||
\(253\) | 2.20423i | 0.138578i | ||||||||
\(254\) | −7.45681 | −0.467882 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − 11.8396i | − 0.738536i | −0.929323 | − | 0.369268i | \(-0.879608\pi\) | ||||
0.929323 | − | 0.369268i | \(-0.120392\pi\) | |||||||
\(258\) | − 16.5176i | − 1.02834i | ||||||||
\(259\) | −1.31955 | −0.0819929 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −20.4118 | −1.26346 | ||||||||
\(262\) | − 2.42166i | − 0.149611i | ||||||||
\(263\) | − 9.15919i | − 0.564780i | −0.959300 | − | 0.282390i | \(-0.908873\pi\) | ||||
0.959300 | − | 0.282390i | \(-0.0911271\pi\) | |||||||
\(264\) | 0.760632 | 0.0468137 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.87847 | −0.237804 | ||||||||
\(267\) | − 17.6354i | − 1.07927i | ||||||||
\(268\) | 5.57834i | 0.340751i | ||||||||
\(269\) | −18.3960 | −1.12163 | −0.560813 | − | 0.827942i | \(-0.689511\pi\) | ||||
−0.560813 | + | 0.827942i | \(0.689511\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.2394 | −1.65467 | −0.827337 | − | 0.561706i | \(-0.810145\pi\) | ||||
−0.827337 | + | 0.561706i | \(0.810145\pi\) | |||||||
\(272\) | − 4.25879i | − 0.258227i | ||||||||
\(273\) | 22.7995i | 1.37989i | ||||||||
\(274\) | −15.7958 | −0.954258 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −25.0351 | −1.50694 | ||||||||
\(277\) | 21.8785i | 1.31455i | 0.753651 | + | 0.657275i | \(0.228291\pi\) | ||||
−0.753651 | + | 0.657275i | \(0.771709\pi\) | |||||||
\(278\) | − 11.4155i | − 0.684654i | ||||||||
\(279\) | −22.3232 | −1.33646 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.9963 | −1.25253 | −0.626267 | − | 0.779608i | \(-0.715418\pi\) | ||||
−0.626267 | + | 0.779608i | \(0.715418\pi\) | |||||||
\(282\) | − 16.3960i | − 0.976370i | ||||||||
\(283\) | 18.9136i | 1.12430i | 0.827036 | + | 0.562149i | \(0.190025\pi\) | ||||
−0.827036 | + | 0.562149i | \(0.809975\pi\) | |||||||
\(284\) | −11.2394 | −0.666934 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.52126 | 0.0899542 | ||||||||
\(287\) | − 11.7412i | − 0.693062i | ||||||||
\(288\) | 5.63910i | 0.332287i | ||||||||
\(289\) | −1.13726 | −0.0668974 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −37.9099 | −2.22232 | ||||||||
\(292\) | − 2.51757i | − 0.147330i | ||||||||
\(293\) | − 12.8979i | − 0.753503i | −0.926314 | − | 0.376751i | \(-0.877041\pi\) | ||||
0.926314 | − | 0.376751i | \(-0.122959\pi\) | |||||||
\(294\) | 15.4568 | 0.901459 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.00000 | −0.0581238 | ||||||||
\(297\) | 2.00738i | 0.116480i | ||||||||
\(298\) | 18.3960i | 1.06565i | ||||||||
\(299\) | −50.0703 | −2.89564 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.41546 | 0.427420 | ||||||||
\(302\) | − 5.87847i | − 0.338268i | ||||||||
\(303\) | 30.5564i | 1.75542i | ||||||||
\(304\) | −2.93923 | −0.168577 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 24.0157 | 1.37289 | ||||||||
\(307\) | 3.78256i | 0.215882i | 0.994157 | + | 0.107941i | \(0.0344258\pi\) | ||||
−0.994157 | + | 0.107941i | \(0.965574\pi\) | |||||||
\(308\) | 0.341481i | 0.0194577i | ||||||||
\(309\) | 40.7921 | 2.32058 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.2807 | −0.866490 | −0.433245 | − | 0.901276i | \(-0.642631\pi\) | ||||
−0.433245 | + | 0.901276i | \(0.642631\pi\) | |||||||
\(312\) | 17.2782i | 0.978186i | ||||||||
\(313\) | 19.0351i | 1.07593i | 0.842967 | + | 0.537965i | \(0.180807\pi\) | ||||
−0.842967 | + | 0.537965i | \(0.819193\pi\) | |||||||
\(314\) | −3.61968 | −0.204271 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.69987 | −0.433151 | ||||||||
\(317\) | 24.1373i | 1.35568i | 0.735208 | + | 0.677842i | \(0.237085\pi\) | ||||
−0.735208 | + | 0.677842i | \(0.762915\pi\) | |||||||
\(318\) | 37.9099i | 2.12588i | ||||||||
\(319\) | −0.936722 | −0.0524464 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.3960 | −0.691880 | ||||||||
\(322\) | − 11.2394i | − 0.626345i | ||||||||
\(323\) | 12.5176i | 0.696496i | ||||||||
\(324\) | −5.88216 | −0.326787 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −22.0546 | −1.22149 | ||||||||
\(327\) | − 47.4312i | − 2.62295i | ||||||||
\(328\) | − 8.89789i | − 0.491304i | ||||||||
\(329\) | 7.36090 | 0.405819 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.817705 | 0.0449451 | 0.0224726 | − | 0.999747i | \(-0.492846\pi\) | ||||
0.0224726 | + | 0.999747i | \(0.492846\pi\) | |||||||
\(332\) | 6.17860i | 0.339095i | ||||||||
\(333\) | − 5.63910i | − 0.309021i | ||||||||
\(334\) | 0.600267 | 0.0328451 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.87847 | −0.211588 | ||||||||
\(337\) | 19.7958i | 1.07834i | 0.842195 | + | 0.539172i | \(0.181263\pi\) | ||||
−0.842195 | + | 0.539172i | \(0.818737\pi\) | |||||||
\(338\) | 21.5564i | 1.17251i | ||||||||
\(339\) | −2.99631 | −0.162737 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.02444 | −0.0554767 | ||||||||
\(342\) | − 16.5746i | − 0.896254i | ||||||||
\(343\) | 16.1761i | 0.873427i | ||||||||
\(344\) | 5.61968 | 0.302993 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −22.6937 | −1.22002 | ||||||||
\(347\) | − 15.7569i | − 0.845877i | −0.906158 | − | 0.422938i | \(-0.860999\pi\) | ||||
0.906158 | − | 0.422938i | \(-0.139001\pi\) | |||||||
\(348\) | − 10.6391i | − 0.570316i | ||||||||
\(349\) | 0.160365 | 0.00858416 | 0.00429208 | − | 0.999991i | \(-0.498634\pi\) | ||||
0.00429208 | + | 0.999991i | \(0.498634\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −45.5989 | −2.43389 | ||||||||
\(352\) | 0.258786i | 0.0137933i | ||||||||
\(353\) | − 30.2075i | − 1.60779i | −0.594775 | − | 0.803893i | \(-0.702759\pi\) | ||||
0.594775 | − | 0.803893i | \(-0.297241\pi\) | |||||||
\(354\) | −28.1530 | −1.49631 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | 16.5176i | 0.874203i | ||||||||
\(358\) | − 8.73501i | − 0.461660i | ||||||||
\(359\) | 7.39973 | 0.390543 | 0.195271 | − | 0.980749i | \(-0.437441\pi\) | ||||
0.195271 | + | 0.980749i | \(0.437441\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.3609 | −0.545310 | ||||||||
\(362\) | − 10.6391i | − 0.559179i | ||||||||
\(363\) | − 32.1347i | − 1.68664i | ||||||||
\(364\) | −7.75694 | −0.406574 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.11784 | 0.0584303 | ||||||||
\(367\) | 13.9198i | 0.726609i | 0.931671 | + | 0.363304i | \(0.118351\pi\) | ||||
−0.931671 | + | 0.363304i | \(0.881649\pi\) | |||||||
\(368\) | − 8.51757i | − 0.444009i | ||||||||
\(369\) | 50.1761 | 2.61206 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.0194 | −0.883604 | ||||||||
\(372\) | − 11.6354i | − 0.603268i | ||||||||
\(373\) | 20.2357i | 1.04776i | 0.851791 | + | 0.523882i | \(0.175517\pi\) | ||||
−0.851791 | + | 0.523882i | \(0.824483\pi\) | |||||||
\(374\) | 1.10211 | 0.0569889 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.57834 | 0.287681 | ||||||||
\(377\) | − 21.2782i | − 1.09588i | ||||||||
\(378\) | − 10.2357i | − 0.526466i | ||||||||
\(379\) | 27.9488 | 1.43563 | 0.717816 | − | 0.696233i | \(-0.245142\pi\) | ||||
0.717816 | + | 0.696233i | \(0.245142\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 21.9173 | 1.12286 | ||||||||
\(382\) | − 22.1116i | − 1.13133i | ||||||||
\(383\) | 11.7569i | 0.600752i | 0.953821 | + | 0.300376i | \(0.0971121\pi\) | ||||
−0.953821 | + | 0.300376i | \(0.902888\pi\) | |||||||
\(384\) | −2.93923 | −0.149992 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.03514 | 0.358079 | ||||||||
\(387\) | 31.6900i | 1.61089i | ||||||||
\(388\) | − 12.8979i | − 0.654791i | ||||||||
\(389\) | 9.58085 | 0.485768 | 0.242884 | − | 0.970055i | \(-0.421907\pi\) | ||||
0.242884 | + | 0.970055i | \(0.421907\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −36.2745 | −1.83448 | ||||||||
\(392\) | 5.25879i | 0.265609i | ||||||||
\(393\) | 7.11784i | 0.359047i | ||||||||
\(394\) | −25.7569 | −1.29762 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.45932 | −0.0733335 | ||||||||
\(397\) | 32.4787i | 1.63006i | 0.579418 | + | 0.815031i | \(0.303280\pi\) | ||||
−0.579418 | + | 0.815031i | \(0.696720\pi\) | |||||||
\(398\) | − 12.7350i | − 0.638348i | ||||||||
\(399\) | 11.3997 | 0.570700 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.27820 | 0.363456 | 0.181728 | − | 0.983349i | \(-0.441831\pi\) | ||||
0.181728 | + | 0.983349i | \(0.441831\pi\) | |||||||
\(402\) | − 16.3960i | − 0.817760i | ||||||||
\(403\) | − 23.2708i | − 1.15920i | ||||||||
\(404\) | −10.3960 | −0.517222 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.77636 | 0.237047 | ||||||||
\(407\) | − 0.258786i | − 0.0128275i | ||||||||
\(408\) | 12.5176i | 0.619712i | ||||||||
\(409\) | 32.9963 | 1.63156 | 0.815781 | − | 0.578361i | \(-0.196307\pi\) | ||||
0.815781 | + | 0.578361i | \(0.196307\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 46.4275 | 2.29010 | ||||||||
\(412\) | 13.8785i | 0.683743i | ||||||||
\(413\) | − 12.6391i | − 0.621930i | ||||||||
\(414\) | 48.0315 | 2.36062 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.87847 | −0.288216 | ||||||||
\(417\) | 33.5527i | 1.64308i | ||||||||
\(418\) | − 0.760632i | − 0.0372037i | ||||||||
\(419\) | −25.7131 | −1.25617 | −0.628083 | − | 0.778146i | \(-0.716160\pi\) | ||||
−0.628083 | + | 0.778146i | \(0.716160\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.0000 | 1.07221 | 0.536107 | − | 0.844150i | \(-0.319894\pi\) | ||||
0.536107 | + | 0.844150i | \(0.319894\pi\) | |||||||
\(422\) | 6.65483i | 0.323952i | ||||||||
\(423\) | 31.4568i | 1.52948i | ||||||||
\(424\) | −12.8979 | −0.626377 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 33.0351 | 1.60056 | ||||||||
\(427\) | 0.501846i | 0.0242860i | ||||||||
\(428\) | − 4.21744i | − 0.203858i | ||||||||
\(429\) | −4.47135 | −0.215879 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.9198 | 0.863167 | 0.431584 | − | 0.902073i | \(-0.357955\pi\) | ||||
0.431584 | + | 0.902073i | \(0.357955\pi\) | |||||||
\(432\) | − 7.75694i | − 0.373206i | ||||||||
\(433\) | 4.96486i | 0.238596i | 0.992859 | + | 0.119298i | \(0.0380644\pi\) | ||||
−0.992859 | + | 0.119298i | \(0.961936\pi\) | |||||||
\(434\) | 5.22364 | 0.250743 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 16.1373 | 0.772834 | ||||||||
\(437\) | 25.0351i | 1.19759i | ||||||||
\(438\) | 7.39973i | 0.353573i | ||||||||
\(439\) | 13.8371 | 0.660410 | 0.330205 | − | 0.943909i | \(-0.392882\pi\) | ||||
0.330205 | + | 0.943909i | \(0.392882\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −29.6548 | −1.41213 | ||||||||
\(442\) | 25.0351i | 1.19080i | ||||||||
\(443\) | 14.3390i | 0.681265i | 0.940197 | + | 0.340632i | \(0.110641\pi\) | ||||
−0.940197 | + | 0.340632i | \(0.889359\pi\) | |||||||
\(444\) | 2.93923 | 0.139490 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −16.5589 | −0.784088 | ||||||||
\(447\) | − 54.0703i | − 2.55744i | ||||||||
\(448\) | − 1.31955i | − 0.0623429i | ||||||||
\(449\) | −12.4787 | −0.588908 | −0.294454 | − | 0.955666i | \(-0.595138\pi\) | ||||
−0.294454 | + | 0.955666i | \(0.595138\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.30265 | 0.108427 | ||||||||
\(452\) | − 1.01942i | − 0.0479494i | ||||||||
\(453\) | 17.2782i | 0.811801i | ||||||||
\(454\) | 4.01573 | 0.188467 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.63910 | 0.404563 | ||||||||
\(457\) | − 21.6585i | − 1.01314i | −0.862198 | − | 0.506571i | \(-0.830913\pi\) | ||||
0.862198 | − | 0.506571i | \(-0.169087\pi\) | |||||||
\(458\) | 25.5139i | 1.19219i | ||||||||
\(459\) | −33.0351 | −1.54195 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −29.4155 | −1.37001 | −0.685007 | − | 0.728536i | \(-0.740201\pi\) | ||||
−0.685007 | + | 0.728536i | \(0.740201\pi\) | |||||||
\(462\) | − 1.00369i | − 0.0466960i | ||||||||
\(463\) | − 9.03514i | − 0.419899i | −0.977712 | − | 0.209949i | \(-0.932670\pi\) | ||||
0.977712 | − | 0.209949i | \(-0.0673299\pi\) | |||||||
\(464\) | 3.61968 | 0.168040 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.96116 | 0.368794 | ||||||||
\(467\) | − 7.05825i | − 0.326617i | −0.986575 | − | 0.163308i | \(-0.947783\pi\) | ||||
0.986575 | − | 0.163308i | \(-0.0522166\pi\) | |||||||
\(468\) | − 33.1493i | − 1.53233i | ||||||||
\(469\) | 7.36090 | 0.339895 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.6391 | 0.490224 | ||||||||
\(472\) | − 9.57834i | − 0.440879i | ||||||||
\(473\) | 1.45429i | 0.0668685i | ||||||||
\(474\) | 22.6317 | 1.03951 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −5.61968 | −0.257578 | ||||||||
\(477\) | − 72.7325i | − 3.33019i | ||||||||
\(478\) | 11.7983i | 0.539641i | ||||||||
\(479\) | 29.3353 | 1.34036 | 0.670181 | − | 0.742197i | \(-0.266216\pi\) | ||||
0.670181 | + | 0.742197i | \(0.266216\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.87847 | 0.268035 | ||||||||
\(482\) | − 24.9963i | − 1.13855i | ||||||||
\(483\) | 33.0351i | 1.50315i | ||||||||
\(484\) | 10.9330 | 0.496956 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −5.98176 | −0.271338 | ||||||||
\(487\) | 37.9099i | 1.71786i | 0.512091 | + | 0.858931i | \(0.328871\pi\) | ||||
−0.512091 | + | 0.858931i | \(0.671129\pi\) | |||||||
\(488\) | 0.380316i | 0.0172161i | ||||||||
\(489\) | 64.8235 | 2.93142 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.5564 | −0.656921 | −0.328461 | − | 0.944518i | \(-0.606530\pi\) | ||||
−0.328461 | + | 0.944518i | \(0.606530\pi\) | |||||||
\(492\) | 26.1530i | 1.17907i | ||||||||
\(493\) | − 15.4155i | − 0.694277i | ||||||||
\(494\) | 17.2782 | 0.777383 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.95865 | 0.177749 | ||||||||
\(497\) | 14.8309i | 0.665258i | ||||||||
\(498\) | − 18.1604i | − 0.813785i | ||||||||
\(499\) | −23.9744 | −1.07324 | −0.536620 | − | 0.843824i | \(-0.680299\pi\) | ||||
−0.536620 | + | 0.843824i | \(0.680299\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.76432 | −0.0788242 | ||||||||
\(502\) | 8.81770i | 0.393553i | ||||||||
\(503\) | − 43.7569i | − 1.95103i | −0.219943 | − | 0.975513i | \(-0.570587\pi\) | ||||
0.219943 | − | 0.975513i | \(-0.429413\pi\) | |||||||
\(504\) | 7.44108 | 0.331452 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.20423 | 0.0979898 | ||||||||
\(507\) | − 63.3593i | − 2.81389i | ||||||||
\(508\) | 7.45681i | 0.330842i | ||||||||
\(509\) | −11.7958 | −0.522839 | −0.261419 | − | 0.965225i | \(-0.584191\pi\) | ||||
−0.261419 | + | 0.965225i | \(0.584191\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.32206 | −0.146959 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | 22.7995i | 1.00662i | ||||||||
\(514\) | −11.8396 | −0.522224 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −16.5176 | −0.727146 | ||||||||
\(517\) | 1.44359i | 0.0634892i | ||||||||
\(518\) | 1.31955i | 0.0579777i | ||||||||
\(519\) | 66.7020 | 2.92789 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.9806 | 0.656311 | 0.328156 | − | 0.944624i | \(-0.393573\pi\) | ||||
0.328156 | + | 0.944624i | \(0.393573\pi\) | |||||||
\(522\) | 20.4118i | 0.893399i | ||||||||
\(523\) | − 27.5139i | − 1.20310i | −0.798836 | − | 0.601549i | \(-0.794550\pi\) | ||||
0.798836 | − | 0.601549i | \(-0.205450\pi\) | |||||||
\(524\) | −2.42166 | −0.105791 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.15919 | −0.399359 | ||||||||
\(527\) | − 16.8591i | − 0.734392i | ||||||||
\(528\) | − 0.760632i | − 0.0331023i | ||||||||
\(529\) | −49.5490 | −2.15431 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 54.0132 | 2.34397 | ||||||||
\(532\) | 3.87847i | 0.168153i | ||||||||
\(533\) | 52.3060i | 2.26562i | ||||||||
\(534\) | −17.6354 | −0.763159 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.57834 | 0.240947 | ||||||||
\(537\) | 25.6742i | 1.10793i | ||||||||
\(538\) | 18.3960i | 0.793110i | ||||||||
\(539\) | −1.36090 | −0.0586180 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.0351 | −0.474438 | −0.237219 | − | 0.971456i | \(-0.576236\pi\) | ||||
−0.237219 | + | 0.971456i | \(0.576236\pi\) | |||||||
\(542\) | 27.2394i | 1.17003i | ||||||||
\(543\) | 31.2708i | 1.34196i | ||||||||
\(544\) | −4.25879 | −0.182594 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 22.7995 | 0.975727 | ||||||||
\(547\) | 16.1761i | 0.691640i | 0.938301 | + | 0.345820i | \(0.112399\pi\) | ||||
−0.938301 | + | 0.345820i | \(0.887601\pi\) | |||||||
\(548\) | 15.7958i | 0.674762i | ||||||||
\(549\) | −2.14464 | −0.0915310 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.6391 | −0.453241 | ||||||||
\(552\) | 25.0351i | 1.06557i | ||||||||
\(553\) | 10.1604i | 0.432063i | ||||||||
\(554\) | 21.8785 | 0.929527 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.4155 | −0.484123 | ||||||||
\(557\) | − 11.1567i | − 0.472723i | −0.971665 | − | 0.236362i | \(-0.924045\pi\) | ||||
0.971665 | − | 0.236362i | \(-0.0759550\pi\) | |||||||
\(558\) | 22.3232i | 0.945018i | ||||||||
\(559\) | −33.0351 | −1.39724 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.23937 | −0.136766 | ||||||||
\(562\) | 20.9963i | 0.885676i | ||||||||
\(563\) | − 41.7288i | − 1.75866i | −0.476213 | − | 0.879330i | \(-0.657991\pi\) | ||||
0.476213 | − | 0.879330i | \(-0.342009\pi\) | |||||||
\(564\) | −16.3960 | −0.690398 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 18.9136 | 0.794998 | ||||||||
\(567\) | 7.76181i | 0.325965i | ||||||||
\(568\) | 11.2394i | 0.471593i | ||||||||
\(569\) | 24.0703 | 1.00908 | 0.504539 | − | 0.863389i | \(-0.331662\pi\) | ||||
0.504539 | + | 0.863389i | \(0.331662\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.6511 | 1.57565 | 0.787825 | − | 0.615899i | \(-0.211207\pi\) | ||||
0.787825 | + | 0.615899i | \(0.211207\pi\) | |||||||
\(572\) | − 1.52126i | − 0.0636072i | ||||||||
\(573\) | 64.9913i | 2.71505i | ||||||||
\(574\) | −11.7412 | −0.490069 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 5.63910 | 0.234963 | ||||||||
\(577\) | − 23.4312i | − 0.975453i | −0.872996 | − | 0.487726i | \(-0.837826\pi\) | ||||
0.872996 | − | 0.487726i | \(-0.162174\pi\) | |||||||
\(578\) | 1.13726i | 0.0473036i | ||||||||
\(579\) | −20.6779 | −0.859346 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.15298 | 0.338243 | ||||||||
\(582\) | 37.9099i | 1.57142i | ||||||||
\(583\) | − 3.33779i | − 0.138237i | ||||||||
\(584\) | −2.51757 | −0.104178 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.8979 | −0.532807 | ||||||||
\(587\) | − 6.30265i | − 0.260138i | −0.991505 | − | 0.130069i | \(-0.958480\pi\) | ||||
0.991505 | − | 0.130069i | \(-0.0415199\pi\) | |||||||
\(588\) | − 15.4568i | − 0.637428i | ||||||||
\(589\) | −11.6354 | −0.479429 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 75.7057 | 3.11412 | ||||||||
\(592\) | 1.00000i | 0.0410997i | ||||||||
\(593\) | − 34.0315i | − 1.39750i | −0.715364 | − | 0.698752i | \(-0.753739\pi\) | ||||
0.715364 | − | 0.698752i | \(-0.246261\pi\) | |||||||
\(594\) | 2.00738 | 0.0823640 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 18.3960 | 0.753531 | ||||||||
\(597\) | 37.4312i | 1.53196i | ||||||||
\(598\) | 50.0703i | 2.04753i | ||||||||
\(599\) | −34.8359 | −1.42336 | −0.711679 | − | 0.702505i | \(-0.752065\pi\) | ||||
−0.711679 | + | 0.702505i | \(0.752065\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.2236 | 0.620985 | 0.310493 | − | 0.950576i | \(-0.399506\pi\) | ||||
0.310493 | + | 0.950576i | \(0.399506\pi\) | |||||||
\(602\) | − 7.41546i | − 0.302232i | ||||||||
\(603\) | 31.4568i | 1.28102i | ||||||||
\(604\) | −5.87847 | −0.239192 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 30.5564 | 1.24127 | ||||||||
\(607\) | 30.8309i | 1.25139i | 0.780068 | + | 0.625694i | \(0.215184\pi\) | ||||
−0.780068 | + | 0.625694i | \(0.784816\pi\) | |||||||
\(608\) | 2.93923i | 0.119202i | ||||||||
\(609\) | −14.0388 | −0.568882 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −32.7921 | −1.32663 | ||||||||
\(612\) | − 24.0157i | − 0.970778i | ||||||||
\(613\) | − 11.2112i | − 0.452817i | −0.974032 | − | 0.226409i | \(-0.927302\pi\) | ||||
0.974032 | − | 0.226409i | \(-0.0726985\pi\) | |||||||
\(614\) | 3.78256 | 0.152652 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.341481 | 0.0137587 | ||||||||
\(617\) | − 26.5176i | − 1.06756i | −0.845624 | − | 0.533779i | \(-0.820772\pi\) | ||||
0.845624 | − | 0.533779i | \(-0.179228\pi\) | |||||||
\(618\) | − 40.7921i | − 1.64090i | ||||||||
\(619\) | 3.41546 | 0.137279 | 0.0686394 | − | 0.997642i | \(-0.478134\pi\) | ||||
0.0686394 | + | 0.997642i | \(0.478134\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −66.0703 | −2.65131 | ||||||||
\(622\) | 15.2807i | 0.612701i | ||||||||
\(623\) | − 7.91730i | − 0.317200i | ||||||||
\(624\) | 17.2782 | 0.691682 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 19.0351 | 0.760797 | ||||||||
\(627\) | 2.23568i | 0.0892843i | ||||||||
\(628\) | 3.61968i | 0.144441i | ||||||||
\(629\) | 4.25879 | 0.169809 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.11533 | 0.124019 | 0.0620096 | − | 0.998076i | \(-0.480249\pi\) | ||||
0.0620096 | + | 0.998076i | \(0.480249\pi\) | |||||||
\(632\) | 7.69987i | 0.306284i | ||||||||
\(633\) | − 19.5601i | − 0.777444i | ||||||||
\(634\) | 24.1373 | 0.958613 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 37.9099 | 1.50323 | ||||||||
\(637\) | − 30.9136i | − 1.22484i | ||||||||
\(638\) | 0.936722i | 0.0370852i | ||||||||
\(639\) | −63.3799 | −2.50727 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.5018 | −0.809774 | −0.404887 | − | 0.914367i | \(-0.632689\pi\) | ||||
−0.404887 | + | 0.914367i | \(0.632689\pi\) | |||||||
\(642\) | 12.3960i | 0.489233i | ||||||||
\(643\) | 5.70238i | 0.224880i | 0.993659 | + | 0.112440i | \(0.0358666\pi\) | ||||
−0.993659 | + | 0.112440i | \(0.964133\pi\) | |||||||
\(644\) | −11.2394 | −0.442893 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.5176 | 0.492497 | ||||||||
\(647\) | 41.0351i | 1.61326i | 0.591058 | + | 0.806629i | \(0.298710\pi\) | ||||
−0.591058 | + | 0.806629i | \(0.701290\pi\) | |||||||
\(648\) | 5.88216i | 0.231073i | ||||||||
\(649\) | 2.47874 | 0.0972989 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.3535 | −0.601752 | ||||||||
\(652\) | 22.0546i | 0.863723i | ||||||||
\(653\) | 14.9575i | 0.585331i | 0.956215 | + | 0.292666i | \(0.0945423\pi\) | ||||
−0.956215 | + | 0.292666i | \(0.905458\pi\) | |||||||
\(654\) | −47.4312 | −1.85471 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −8.89789 | −0.347404 | ||||||||
\(657\) | − 14.1968i | − 0.553872i | ||||||||
\(658\) | − 7.36090i | − 0.286958i | ||||||||
\(659\) | 15.7569 | 0.613803 | 0.306902 | − | 0.951741i | \(-0.400708\pi\) | ||||
0.306902 | + | 0.951741i | \(0.400708\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.6197 | 0.451953 | 0.225977 | − | 0.974133i | \(-0.427443\pi\) | ||||
0.225977 | + | 0.974133i | \(0.427443\pi\) | |||||||
\(662\) | − 0.817705i | − 0.0317810i | ||||||||
\(663\) | − 73.5842i | − 2.85777i | ||||||||
\(664\) | 6.17860 | 0.239776 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.63910 | −0.218511 | ||||||||
\(667\) | − 30.8309i | − 1.19378i | ||||||||
\(668\) | − 0.600267i | − 0.0232250i | ||||||||
\(669\) | 48.6706 | 1.88171 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.0984203 | −0.00379947 | ||||||||
\(672\) | 3.87847i | 0.149615i | ||||||||
\(673\) | 12.7218i | 0.490389i | 0.969474 | + | 0.245195i | \(0.0788519\pi\) | ||||
−0.969474 | + | 0.245195i | \(0.921148\pi\) | |||||||
\(674\) | 19.7958 | 0.762505 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 21.5564 | 0.829093 | ||||||||
\(677\) | 21.5139i | 0.826846i | 0.910539 | + | 0.413423i | \(0.135667\pi\) | ||||
−0.910539 | + | 0.413423i | \(0.864333\pi\) | |||||||
\(678\) | 2.99631i | 0.115073i | ||||||||
\(679\) | −17.0194 | −0.653145 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.8032 | −0.452298 | ||||||||
\(682\) | 1.02444i | 0.0392279i | ||||||||
\(683\) | 47.6900i | 1.82481i | 0.409293 | + | 0.912403i | \(0.365775\pi\) | ||||
−0.409293 | + | 0.912403i | \(0.634225\pi\) | |||||||
\(684\) | −16.5746 | −0.633747 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 16.1761 | 0.617606 | ||||||||
\(687\) | − 74.9913i | − 2.86110i | ||||||||
\(688\) | − 5.61968i | − 0.214248i | ||||||||
\(689\) | 75.8198 | 2.88851 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.5721 | 1.16302 | 0.581509 | − | 0.813540i | \(-0.302462\pi\) | ||||
0.581509 | + | 0.813540i | \(0.302462\pi\) | |||||||
\(692\) | 22.6937i | 0.862684i | ||||||||
\(693\) | 1.92565i | 0.0731492i | ||||||||
\(694\) | −15.7569 | −0.598125 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −10.6391 | −0.403274 | ||||||||
\(697\) | 37.8942i | 1.43534i | ||||||||
\(698\) | − 0.160365i | − 0.00606992i | ||||||||
\(699\) | −23.3997 | −0.885059 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.0703 | 1.21128 | 0.605639 | − | 0.795740i | \(-0.292918\pi\) | ||||
0.605639 | + | 0.795740i | \(0.292918\pi\) | |||||||
\(702\) | 45.5989i | 1.72102i | ||||||||
\(703\) | − 2.93923i | − 0.110855i | ||||||||
\(704\) | 0.258786 | 0.00975335 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −30.2075 | −1.13688 | ||||||||
\(707\) | 13.7181i | 0.515922i | ||||||||
\(708\) | 28.1530i | 1.05805i | ||||||||
\(709\) | −10.6160 | −0.398692 | −0.199346 | − | 0.979929i | \(-0.563882\pi\) | ||||
−0.199346 | + | 0.979929i | \(0.563882\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −43.4203 | −1.62839 | ||||||||
\(712\) | − 6.00000i | − 0.224860i | ||||||||
\(713\) | − 33.7181i | − 1.26275i | ||||||||
\(714\) | 16.5176 | 0.618155 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.73501 | −0.326443 | ||||||||
\(717\) | − 34.6779i | − 1.29507i | ||||||||
\(718\) | − 7.39973i | − 0.276156i | ||||||||
\(719\) | 32.4663 | 1.21079 | 0.605395 | − | 0.795925i | \(-0.293015\pi\) | ||||
0.605395 | + | 0.795925i | \(0.293015\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.3133 | 0.682025 | ||||||||
\(722\) | 10.3609i | 0.385593i | ||||||||
\(723\) | 73.4700i | 2.73238i | ||||||||
\(724\) | −10.6391 | −0.395399 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −32.1347 | −1.19263 | ||||||||
\(727\) | − 31.5139i | − 1.16879i | −0.811471 | − | 0.584393i | \(-0.801333\pi\) | ||||
0.811471 | − | 0.584393i | \(-0.198667\pi\) | |||||||
\(728\) | 7.75694i | 0.287491i | ||||||||
\(729\) | 35.2283 | 1.30475 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −23.9330 | −0.885195 | ||||||||
\(732\) | − 1.11784i | − 0.0413165i | ||||||||
\(733\) | − 16.8202i | − 0.621269i | −0.950529 | − | 0.310634i | \(-0.899459\pi\) | ||||
0.950529 | − | 0.310634i | \(-0.100541\pi\) | |||||||
\(734\) | 13.9198 | 0.513790 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.51757 | −0.313962 | ||||||||
\(737\) | 1.44359i | 0.0531755i | ||||||||
\(738\) | − 50.1761i | − 1.84701i | ||||||||
\(739\) | −9.69735 | −0.356723 | −0.178361 | − | 0.983965i | \(-0.557080\pi\) | ||||
−0.178361 | + | 0.983965i | \(0.557080\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −50.7847 | −1.86562 | ||||||||
\(742\) | 17.0194i | 0.624802i | ||||||||
\(743\) | − 39.1153i | − 1.43500i | −0.696557 | − | 0.717501i | \(-0.745286\pi\) | ||||
0.696557 | − | 0.717501i | \(-0.254714\pi\) | |||||||
\(744\) | −11.6354 | −0.426575 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 20.2357 | 0.740881 | ||||||||
\(747\) | 34.8418i | 1.27479i | ||||||||
\(748\) | − 1.10211i | − 0.0402972i | ||||||||
\(749\) | −5.56512 | −0.203345 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.1530 | −0.954336 | −0.477168 | − | 0.878812i | \(-0.658337\pi\) | ||||
−0.477168 | + | 0.878812i | \(0.658337\pi\) | |||||||
\(752\) | − 5.57834i | − 0.203421i | ||||||||
\(753\) | − 25.9173i | − 0.944479i | ||||||||
\(754\) | −21.2782 | −0.774906 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −10.2357 | −0.372268 | ||||||||
\(757\) | 33.5915i | 1.22091i | 0.792053 | + | 0.610453i | \(0.209013\pi\) | ||||
−0.792053 | + | 0.610453i | \(0.790987\pi\) | |||||||
\(758\) | − 27.9488i | − 1.01514i | ||||||||
\(759\) | −6.47874 | −0.235163 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −51.3766 | −1.86240 | −0.931201 | − | 0.364507i | \(-0.881237\pi\) | ||||
−0.931201 | + | 0.364507i | \(0.881237\pi\) | |||||||
\(762\) | − 21.9173i | − 0.793980i | ||||||||
\(763\) | − 21.2939i | − 0.770892i | ||||||||
\(764\) | −22.1116 | −0.799971 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11.7569 | 0.424795 | ||||||||
\(767\) | 56.3060i | 2.03309i | ||||||||
\(768\) | 2.93923i | 0.106061i | ||||||||
\(769\) | −27.5527 | −0.993576 | −0.496788 | − | 0.867872i | \(-0.665487\pi\) | ||||
−0.496788 | + | 0.867872i | \(0.665487\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 34.7995 | 1.25327 | ||||||||
\(772\) | − 7.03514i | − 0.253200i | ||||||||
\(773\) | 13.4155i | 0.482521i | 0.970460 | + | 0.241260i | \(0.0775607\pi\) | ||||
−0.970460 | + | 0.241260i | \(0.922439\pi\) | |||||||
\(774\) | 31.6900 | 1.13907 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −12.8979 | −0.463007 | ||||||||
\(777\) | − 3.87847i | − 0.139139i | ||||||||
\(778\) | − 9.58085i | − 0.343490i | ||||||||
\(779\) | 26.1530 | 0.937028 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.90859 | −0.104077 | ||||||||
\(782\) | 36.2745i | 1.29717i | ||||||||
\(783\) | − 28.0777i | − 1.00341i | ||||||||
\(784\) | 5.25879 | 0.187814 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 7.11784 | 0.253885 | ||||||||
\(787\) | 25.4956i | 0.908821i | 0.890792 | + | 0.454411i | \(0.150150\pi\) | ||||
−0.890792 | + | 0.454411i | \(0.849850\pi\) | |||||||
\(788\) | 25.7569i | 0.917553i | ||||||||
\(789\) | 26.9210 | 0.958413 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.34517 | −0.0478289 | ||||||||
\(792\) | 1.45932i | 0.0518546i | ||||||||
\(793\) | − 2.23568i | − 0.0793912i | ||||||||
\(794\) | 32.4787 | 1.15263 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −12.7350 | −0.451380 | ||||||||
\(797\) | − 48.4663i | − 1.71677i | −0.513010 | − | 0.858383i | \(-0.671470\pi\) | ||||
0.513010 | − | 0.858383i | \(-0.328530\pi\) | |||||||
\(798\) | − 11.3997i | − 0.403546i | ||||||||
\(799\) | −23.7569 | −0.840460 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 33.8346 | 1.19549 | ||||||||
\(802\) | − 7.27820i | − 0.257002i | ||||||||
\(803\) | − 0.651511i | − 0.0229913i | ||||||||
\(804\) | −16.3960 | −0.578244 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −23.2708 | −0.819680 | ||||||||
\(807\) | − 54.0703i | − 1.90336i | ||||||||
\(808\) | 10.3960i | 0.365731i | ||||||||
\(809\) | 12.9649 | 0.455820 | 0.227910 | − | 0.973682i | \(-0.426811\pi\) | ||||
0.227910 | + | 0.973682i | \(0.426811\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.0776702 | 0.00272737 | 0.00136368 | − | 0.999999i | \(-0.499566\pi\) | ||||
0.00136368 | + | 0.999999i | \(0.499566\pi\) | |||||||
\(812\) | − 4.77636i | − 0.167617i | ||||||||
\(813\) | − 80.0629i | − 2.80793i | ||||||||
\(814\) | −0.258786 | −0.00907043 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 12.5176 | 0.438203 | ||||||||
\(817\) | 16.5176i | 0.577877i | ||||||||
\(818\) | − 32.9963i | − 1.15369i | ||||||||
\(819\) | −43.7422 | −1.52848 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.3448 | 1.26844 | 0.634221 | − | 0.773152i | \(-0.281321\pi\) | ||||
0.634221 | + | 0.773152i | \(0.281321\pi\) | |||||||
\(822\) | − 46.4275i | − 1.61934i | ||||||||
\(823\) | − 23.0996i | − 0.805201i | −0.915376 | − | 0.402601i | \(-0.868106\pi\) | ||||
0.915376 | − | 0.402601i | \(-0.131894\pi\) | |||||||
\(824\) | 13.8785 | 0.483479 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12.6391 | −0.439771 | ||||||||
\(827\) | − 15.2551i | − 0.530472i | −0.964184 | − | 0.265236i | \(-0.914550\pi\) | ||||
0.964184 | − | 0.265236i | \(-0.0854498\pi\) | |||||||
\(828\) | − 48.0315i | − 1.66921i | ||||||||
\(829\) | −28.1373 | −0.977247 | −0.488624 | − | 0.872495i | \(-0.662501\pi\) | ||||
−0.488624 | + | 0.872495i | \(0.662501\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −64.3060 | −2.23075 | ||||||||
\(832\) | 5.87847i | 0.203799i | ||||||||
\(833\) | − 22.3960i | − 0.775977i | ||||||||
\(834\) | 33.5527 | 1.16184 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.760632 | −0.0263070 | ||||||||
\(837\) | − 30.7070i | − 1.06139i | ||||||||
\(838\) | 25.7131i | 0.888244i | ||||||||
\(839\) | −4.24306 | −0.146487 | −0.0732434 | − | 0.997314i | \(-0.523335\pi\) | ||||
−0.0732434 | + | 0.997314i | \(0.523335\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.8979 | −0.548203 | ||||||||
\(842\) | − 22.0000i | − 0.758170i | ||||||||
\(843\) | − 61.7131i | − 2.12551i | ||||||||
\(844\) | 6.65483 | 0.229069 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 31.4568 | 1.08151 | ||||||||
\(847\) | − 14.4267i | − 0.495707i | ||||||||
\(848\) | 12.8979i | 0.442915i | ||||||||
\(849\) | −55.5915 | −1.90790 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.51757 | 0.291979 | ||||||||
\(852\) | − 33.0351i | − 1.13177i | ||||||||
\(853\) | 36.4787i | 1.24901i | 0.781022 | + | 0.624504i | \(0.214699\pi\) | ||||
−0.781022 | + | 0.624504i | \(0.785301\pi\) | |||||||
\(854\) | 0.501846 | 0.0171728 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.21744 | −0.144149 | ||||||||
\(857\) | − 23.7288i | − 0.810561i | −0.914192 | − | 0.405280i | \(-0.867174\pi\) | ||||
0.914192 | − | 0.405280i | \(-0.132826\pi\) | |||||||
\(858\) | 4.47135i | 0.152649i | ||||||||
\(859\) | −2.77887 | −0.0948138 | −0.0474069 | − | 0.998876i | \(-0.515096\pi\) | ||||
−0.0474069 | + | 0.998876i | \(0.515096\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 34.5102 | 1.17610 | ||||||||
\(862\) | − 17.9198i | − 0.610351i | ||||||||
\(863\) | 10.5151i | 0.357937i | 0.983855 | + | 0.178968i | \(0.0572760\pi\) | ||||
−0.983855 | + | 0.178968i | \(0.942724\pi\) | |||||||
\(864\) | −7.75694 | −0.263896 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.96486 | 0.168713 | ||||||||
\(867\) | − 3.34266i | − 0.113523i | ||||||||
\(868\) | − 5.22364i | − 0.177302i | ||||||||
\(869\) | −1.99262 | −0.0675948 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −32.7921 | −1.11112 | ||||||||
\(872\) | − 16.1373i | − 0.546476i | ||||||||
\(873\) | − 72.7325i | − 2.46162i | ||||||||
\(874\) | 25.0351 | 0.846826 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.39973 | 0.250014 | ||||||||
\(877\) | − 27.6197i | − 0.932650i | −0.884613 | − | 0.466325i | \(-0.845578\pi\) | ||||
0.884613 | − | 0.466325i | \(-0.154422\pi\) | |||||||
\(878\) | − 13.8371i | − 0.466980i | ||||||||
\(879\) | 37.9099 | 1.27867 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.2200 | 0.344319 | 0.172159 | − | 0.985069i | \(-0.444926\pi\) | ||||
0.172159 | + | 0.985069i | \(0.444926\pi\) | |||||||
\(882\) | 29.6548i | 0.998530i | ||||||||
\(883\) | 53.5684i | 1.80272i | 0.433069 | + | 0.901361i | \(0.357431\pi\) | ||||
−0.433069 | + | 0.901361i | \(0.642569\pi\) | |||||||
\(884\) | 25.0351 | 0.842023 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14.3390 | 0.481727 | ||||||||
\(887\) | − 36.5904i | − 1.22858i | −0.789079 | − | 0.614292i | \(-0.789442\pi\) | ||||
0.789079 | − | 0.614292i | \(-0.210558\pi\) | |||||||
\(888\) | − 2.93923i | − 0.0986343i | ||||||||
\(889\) | 9.83963 | 0.330011 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.52222 | −0.0509963 | ||||||||
\(892\) | 16.5589i | 0.554434i | ||||||||
\(893\) | 16.3960i | 0.548673i | ||||||||
\(894\) | −54.0703 | −1.80838 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.31955 | −0.0440831 | ||||||||
\(897\) | − 147.168i | − 4.91381i | ||||||||
\(898\) | 12.4787i | 0.416421i | ||||||||
\(899\) | 14.3291 | 0.477901 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 54.9293 | 1.82996 | ||||||||
\(902\) | − 2.30265i | − 0.0766697i | ||||||||
\(903\) | 21.7958i | 0.725318i | ||||||||
\(904\) | −1.01942 | −0.0339053 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 17.2782 | 0.574030 | ||||||||
\(907\) | − 7.64279i | − 0.253775i | −0.991917 | − | 0.126887i | \(-0.959501\pi\) | ||||
0.991917 | − | 0.126887i | \(-0.0404987\pi\) | |||||||
\(908\) | − 4.01573i | − 0.133267i | ||||||||
\(909\) | −58.6243 | −1.94445 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.0132 | 0.729330 | 0.364665 | − | 0.931139i | \(-0.381183\pi\) | ||||
0.364665 | + | 0.931139i | \(0.381183\pi\) | |||||||
\(912\) | − 8.63910i | − 0.286069i | ||||||||
\(913\) | 1.59893i | 0.0529170i | ||||||||
\(914\) | −21.6585 | −0.716400 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 25.5139 | 0.843002 | ||||||||
\(917\) | 3.19551i | 0.105525i | ||||||||
\(918\) | 33.0351i | 1.09032i | ||||||||
\(919\) | −23.6999 | −0.781786 | −0.390893 | − | 0.920436i | \(-0.627834\pi\) | ||||
−0.390893 | + | 0.920436i | \(0.627834\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.1178 | −0.366345 | ||||||||
\(922\) | 29.4155i | 0.968747i | ||||||||
\(923\) | − 66.0703i | − 2.17473i | ||||||||
\(924\) | −1.00369 | −0.0330191 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −9.03514 | −0.296913 | ||||||||
\(927\) | 78.2621i | 2.57046i | ||||||||
\(928\) | − 3.61968i | − 0.118822i | ||||||||
\(929\) | −8.82022 | −0.289382 | −0.144691 | − | 0.989477i | \(-0.546219\pi\) | ||||
−0.144691 | + | 0.989477i | \(0.546219\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.4568 | −0.506576 | ||||||||
\(932\) | − 7.96116i | − 0.260777i | ||||||||
\(933\) | − 44.9136i | − 1.47041i | ||||||||
\(934\) | −7.05825 | −0.230953 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −33.1493 | −1.08352 | ||||||||
\(937\) | − 40.0703i | − 1.30904i | −0.756045 | − | 0.654520i | \(-0.772871\pi\) | ||||
0.756045 | − | 0.654520i | \(-0.227129\pi\) | |||||||
\(938\) | − 7.36090i | − 0.240342i | ||||||||
\(939\) | −55.9488 | −1.82582 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31.4312 | −1.02463 | −0.512314 | − | 0.858798i | \(-0.671211\pi\) | ||||
−0.512314 | + | 0.858798i | \(0.671211\pi\) | |||||||
\(942\) | − 10.6391i | − 0.346641i | ||||||||
\(943\) | 75.7884i | 2.46801i | ||||||||
\(944\) | −9.57834 | −0.311748 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.45429 | 0.0472832 | ||||||||
\(947\) | 53.5370i | 1.73972i | 0.493300 | + | 0.869859i | \(0.335790\pi\) | ||||
−0.493300 | + | 0.869859i | \(0.664210\pi\) | |||||||
\(948\) | − 22.6317i | − 0.735044i | ||||||||
\(949\) | 14.7995 | 0.480411 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −70.9451 | −2.30055 | ||||||||
\(952\) | 5.61968i | 0.182135i | ||||||||
\(953\) | 5.23937i | 0.169720i | 0.996393 | + | 0.0848599i | \(0.0270443\pi\) | ||||
−0.996393 | + | 0.0848599i | \(0.972956\pi\) | |||||||
\(954\) | −72.7325 | −2.35480 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 11.7983 | 0.381584 | ||||||||
\(957\) | − 2.75325i | − 0.0889998i | ||||||||
\(958\) | − 29.3353i | − 0.947780i | ||||||||
\(959\) | 20.8433 | 0.673066 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.3291 | −0.494486 | ||||||||
\(962\) | − 5.87847i | − 0.189529i | ||||||||
\(963\) | − 23.7826i | − 0.766382i | ||||||||
\(964\) | −24.9963 | −0.805077 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 33.0351 | 1.06289 | ||||||||
\(967\) | 46.5929i | 1.49833i | 0.662386 | + | 0.749163i | \(0.269544\pi\) | ||||
−0.662386 | + | 0.749163i | \(0.730456\pi\) | |||||||
\(968\) | − 10.9330i | − 0.351401i | ||||||||
\(969\) | −36.7921 | −1.18193 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.1373 | 1.22388 | 0.611941 | − | 0.790903i | \(-0.290389\pi\) | ||||
0.611941 | + | 0.790903i | \(0.290389\pi\) | |||||||
\(972\) | 5.98176i | 0.191865i | ||||||||
\(973\) | 15.0633i | 0.482907i | ||||||||
\(974\) | 37.9099 | 1.21471 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.380316 | 0.0121736 | ||||||||
\(977\) | − 40.8979i | − 1.30844i | −0.756305 | − | 0.654220i | \(-0.772997\pi\) | ||||
0.756305 | − | 0.654220i | \(-0.227003\pi\) | |||||||
\(978\) | − 64.8235i | − 2.07283i | ||||||||
\(979\) | 1.55271 | 0.0496250 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 90.9996 | 2.90539 | ||||||||
\(982\) | 14.5564i | 0.464514i | ||||||||
\(983\) | 50.4638i | 1.60955i | 0.593583 | + | 0.804773i | \(0.297713\pi\) | ||||
−0.593583 | + | 0.804773i | \(0.702287\pi\) | |||||||
\(984\) | 26.1530 | 0.833727 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −15.4155 | −0.490928 | ||||||||
\(987\) | 21.6354i | 0.688663i | ||||||||
\(988\) | − 17.2782i | − 0.549693i | ||||||||
\(989\) | −47.8661 | −1.52205 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.9587 | −0.506943 | −0.253472 | − | 0.967343i | \(-0.581572\pi\) | ||||
−0.253472 | + | 0.967343i | \(0.581572\pi\) | |||||||
\(992\) | − 3.95865i | − 0.125687i | ||||||||
\(993\) | 2.40343i | 0.0762704i | ||||||||
\(994\) | 14.8309 | 0.470408 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −18.1604 | −0.575433 | ||||||||
\(997\) | 9.23937i | 0.292614i | 0.989239 | + | 0.146307i | \(0.0467387\pi\) | ||||
−0.989239 | + | 0.146307i | \(0.953261\pi\) | |||||||
\(998\) | 23.9744i | 0.758896i | ||||||||
\(999\) | 7.75694 | 0.245419 |
(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 | 1850.2.b.o.149.3 | 6 | ||
5.2 | odd | 4 | 370.2.a.g.1.3 | ✓ | 3 | ||
5.3 | odd | 4 | 1850.2.a.z.1.1 | 3 | |||
5.4 | even | 2 | inner | 1850.2.b.o.149.4 | 6 | ||
15.2 | even | 4 | 3330.2.a.bg.1.2 | 3 | |||
20.7 | even | 4 | 2960.2.a.u.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.a.g.1.3 | ✓ | 3 | 5.2 | odd | 4 | ||
1850.2.a.z.1.1 | 3 | 5.3 | odd | 4 | |||
1850.2.b.o.149.3 | 6 | 1.1 | even | 1 | trivial | ||
1850.2.b.o.149.4 | 6 | 5.4 | even | 2 | inner | ||
2960.2.a.u.1.1 | 3 | 20.7 | even | 4 | |||
3330.2.a.bg.1.2 | 3 | 15.2 | even | 4 |