Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(341,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.341");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.f (of order \(2\), degree \(1\), 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: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.7278137344.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + x^{6} + 6x^{5} - 20x^{4} + 18x^{3} + 9x^{2} - 54x + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 341.2 | ||
Root | \(-1.71731 + 0.225499i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.341 |
Dual form | 570.2.f.c.341.1 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.71731 | + | 0.225499i | −0.991489 | + | 0.130192i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 1.71731 | − | 0.225499i | 0.701088 | − | 0.0920594i | ||||
\(7\) | −0.631989 | −0.238869 | −0.119435 | − | 0.992842i | \(-0.538108\pi\) | ||||
−0.119435 | + | 0.992842i | \(0.538108\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.89830 | − | 0.774501i | 0.966100 | − | 0.258167i | ||||
\(10\) | 1.00000i | 0.316228i | ||||||||
\(11\) | − | 2.00000i | − | 0.603023i | −0.953463 | − | 0.301511i | \(-0.902509\pi\) | ||
0.953463 | − | 0.301511i | \(-0.0974911\pi\) | |||||||
\(12\) | −1.71731 | + | 0.225499i | −0.495744 | + | 0.0650958i | ||||
\(13\) | 2.45100i | 0.679784i | 0.940464 | + | 0.339892i | \(0.110391\pi\) | ||||
−0.940464 | + | 0.339892i | \(0.889609\pi\) | |||||||
\(14\) | 0.631989 | 0.168906 | ||||||||
\(15\) | 0.225499 | + | 1.71731i | 0.0582235 | + | 0.443407i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.25363i | 0.789120i | 0.918870 | + | 0.394560i | \(0.129103\pi\) | ||||
−0.918870 | + | 0.394560i | \(0.870897\pi\) | |||||||
\(18\) | −2.89830 | + | 0.774501i | −0.683136 | + | 0.182552i | ||||
\(19\) | −2.43462 | − | 3.61561i | −0.558540 | − | 0.829478i | ||||
\(20\) | − | 1.00000i | − | 0.223607i | ||||||
\(21\) | 1.08532 | − | 0.142513i | 0.236836 | − | 0.0310988i | ||||
\(22\) | 2.00000i | 0.426401i | ||||||||
\(23\) | − | 0.812981i | − | 0.169518i | −0.996401 | − | 0.0847591i | \(-0.972988\pi\) | ||
0.996401 | − | 0.0847591i | \(-0.0270121\pi\) | |||||||
\(24\) | 1.71731 | − | 0.225499i | 0.350544 | − | 0.0460297i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | − | 2.45100i | − | 0.480680i | ||||||
\(27\) | −4.80263 | + | 1.98362i | −0.924266 | + | 0.381748i | ||||
\(28\) | −0.631989 | −0.119435 | ||||||||
\(29\) | −3.43462 | −0.637793 | −0.318896 | − | 0.947790i | \(-0.603312\pi\) | ||||
−0.318896 | + | 0.947790i | \(0.603312\pi\) | |||||||
\(30\) | −0.225499 | − | 1.71731i | −0.0411702 | − | 0.313536i | ||||
\(31\) | − | 7.16461i | − | 1.28680i | −0.765529 | − | 0.643401i | \(-0.777523\pi\) | ||
0.765529 | − | 0.643401i | \(-0.222477\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.450997 | + | 3.43462i | 0.0785085 | + | 0.597890i | ||||
\(34\) | − | 3.25363i | − | 0.557992i | ||||||
\(35\) | 0.631989i | 0.106826i | ||||||||
\(36\) | 2.89830 | − | 0.774501i | 0.483050 | − | 0.129084i | ||||
\(37\) | − | 5.60526i | − | 0.921499i | −0.887530 | − | 0.460749i | \(-0.847581\pi\) | ||
0.887530 | − | 0.460749i | \(-0.152419\pi\) | |||||||
\(38\) | 2.43462 | + | 3.61561i | 0.394947 | + | 0.586529i | ||||
\(39\) | −0.552696 | − | 4.20912i | −0.0885022 | − | 0.673999i | ||||
\(40\) | 1.00000i | 0.158114i | ||||||||
\(41\) | 0.802629 | 0.125350 | 0.0626748 | − | 0.998034i | \(-0.480037\pi\) | ||||
0.0626748 | + | 0.998034i | \(0.480037\pi\) | |||||||
\(42\) | −1.08532 | + | 0.142513i | −0.167469 | + | 0.0219902i | ||||
\(43\) | −11.9672 | −1.82499 | −0.912494 | − | 0.409091i | \(-0.865846\pi\) | ||||
−0.912494 | + | 0.409091i | \(0.865846\pi\) | |||||||
\(44\) | − | 2.00000i | − | 0.301511i | ||||||
\(45\) | −0.774501 | − | 2.89830i | −0.115456 | − | 0.432053i | ||||
\(46\) | 0.812981i | 0.119867i | ||||||||
\(47\) | − | 7.96724i | − | 1.16214i | −0.813853 | − | 0.581071i | \(-0.802634\pi\) | ||
0.813853 | − | 0.581071i | \(-0.197366\pi\) | |||||||
\(48\) | −1.71731 | + | 0.225499i | −0.247872 | + | 0.0325479i | ||||
\(49\) | −6.60059 | −0.942941 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −0.733688 | − | 5.58748i | −0.102737 | − | 0.782404i | ||||
\(52\) | 2.45100i | 0.339892i | ||||||||
\(53\) | −6.53262 | −0.897325 | −0.448662 | − | 0.893701i | \(-0.648099\pi\) | ||||
−0.448662 | + | 0.893701i | \(0.648099\pi\) | |||||||
\(54\) | 4.80263 | − | 1.98362i | 0.653555 | − | 0.269937i | ||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | 0.631989 | 0.0844531 | ||||||||
\(57\) | 4.99631 | + | 5.66012i | 0.661777 | + | 0.749701i | ||||
\(58\) | 3.43462 | 0.450987 | ||||||||
\(59\) | 2.09198 | 0.272352 | 0.136176 | − | 0.990685i | \(-0.456519\pi\) | ||||
0.136176 | + | 0.990685i | \(0.456519\pi\) | |||||||
\(60\) | 0.225499 | + | 1.71731i | 0.0291117 | + | 0.221704i | ||||
\(61\) | −2.70326 | −0.346118 | −0.173059 | − | 0.984912i | \(-0.555365\pi\) | ||||
−0.173059 | + | 0.984912i | \(0.555365\pi\) | |||||||
\(62\) | 7.16461i | 0.909907i | ||||||||
\(63\) | −1.83169 | + | 0.489476i | −0.230772 | + | 0.0616682i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.45100 | 0.304009 | ||||||||
\(66\) | −0.450997 | − | 3.43462i | −0.0555139 | − | 0.422772i | ||||
\(67\) | − | 14.9462i | − | 1.82597i | −0.407995 | − | 0.912984i | \(-0.633772\pi\) | ||
0.407995 | − | 0.912984i | \(-0.366228\pi\) | |||||||
\(68\) | 3.25363i | 0.394560i | ||||||||
\(69\) | 0.183326 | + | 1.39614i | 0.0220699 | + | 0.168075i | ||||
\(70\) | − | 0.631989i | − | 0.0755371i | ||||||
\(71\) | −6.16597 | −0.731766 | −0.365883 | − | 0.930661i | \(-0.619233\pi\) | ||||
−0.365883 | + | 0.930661i | \(0.619233\pi\) | |||||||
\(72\) | −2.89830 | + | 0.774501i | −0.341568 | + | 0.0912759i | ||||
\(73\) | −4.89461 | −0.572870 | −0.286435 | − | 0.958100i | \(-0.592470\pi\) | ||||
−0.286435 | + | 0.958100i | \(0.592470\pi\) | |||||||
\(74\) | 5.60526i | 0.651598i | ||||||||
\(75\) | 1.71731 | − | 0.225499i | 0.198298 | − | 0.0260383i | ||||
\(76\) | −2.43462 | − | 3.61561i | −0.279270 | − | 0.414739i | ||||
\(77\) | 1.26398i | 0.144044i | ||||||||
\(78\) | 0.552696 | + | 4.20912i | 0.0625805 | + | 0.476589i | ||||
\(79\) | 4.42859i | 0.498255i | 0.968471 | + | 0.249128i | \(0.0801439\pi\) | ||||
−0.968471 | + | 0.249128i | \(0.919856\pi\) | |||||||
\(80\) | − | 1.00000i | − | 0.111803i | ||||||
\(81\) | 7.80030 | − | 4.48948i | 0.866699 | − | 0.498831i | ||||
\(82\) | −0.802629 | −0.0886356 | ||||||||
\(83\) | − | 5.86788i | − | 0.644083i | −0.946726 | − | 0.322042i | \(-0.895631\pi\) | ||
0.946726 | − | 0.322042i | \(-0.104369\pi\) | |||||||
\(84\) | 1.08532 | − | 0.142513i | 0.118418 | − | 0.0155494i | ||||
\(85\) | 3.25363 | 0.352905 | ||||||||
\(86\) | 11.9672 | 1.29046 | ||||||||
\(87\) | 5.89830 | − | 0.774501i | 0.632364 | − | 0.0830353i | ||||
\(88\) | 2.00000i | 0.213201i | ||||||||
\(89\) | 5.93339 | 0.628938 | 0.314469 | − | 0.949268i | \(-0.398173\pi\) | ||||
0.314469 | + | 0.949268i | \(0.398173\pi\) | |||||||
\(90\) | 0.774501 | + | 2.89830i | 0.0816396 | + | 0.305508i | ||||
\(91\) | − | 1.54900i | − | 0.162380i | ||||||
\(92\) | − | 0.812981i | − | 0.0847591i | ||||||
\(93\) | 1.61561 | + | 12.3039i | 0.167531 | + | 1.27585i | ||||
\(94\) | 7.96724i | 0.821758i | ||||||||
\(95\) | −3.61561 | + | 2.43462i | −0.370954 | + | 0.249787i | ||||
\(96\) | 1.71731 | − | 0.225499i | 0.175272 | − | 0.0230149i | ||||
\(97\) | − | 3.26398i | − | 0.331407i | −0.986176 | − | 0.165703i | \(-0.947011\pi\) | ||
0.986176 | − | 0.165703i | \(-0.0529894\pi\) | |||||||
\(98\) | 6.60059 | 0.666760 | ||||||||
\(99\) | −1.54900 | − | 5.79660i | −0.155681 | − | 0.582580i | ||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | 7.45999i | 0.742297i | 0.928574 | + | 0.371148i | \(0.121036\pi\) | ||||
−0.928574 | + | 0.371148i | \(0.878964\pi\) | |||||||
\(102\) | 0.733688 | + | 5.58748i | 0.0726459 | + | 0.553243i | ||||
\(103\) | 17.9345i | 1.76714i | 0.468302 | + | 0.883569i | \(0.344866\pi\) | ||||
−0.468302 | + | 0.883569i | \(0.655134\pi\) | |||||||
\(104\) | − | 2.45100i | − | 0.240340i | ||||||
\(105\) | −0.142513 | − | 1.08532i | −0.0139078 | − | 0.105916i | ||||
\(106\) | 6.53262 | 0.634505 | ||||||||
\(107\) | 5.63063 | 0.544334 | 0.272167 | − | 0.962250i | \(-0.412260\pi\) | ||||
0.272167 | + | 0.962250i | \(0.412260\pi\) | |||||||
\(108\) | −4.80263 | + | 1.98362i | −0.462133 | + | 0.190874i | ||||
\(109\) | 8.71362i | 0.834613i | 0.908766 | + | 0.417307i | \(0.137026\pi\) | ||||
−0.908766 | + | 0.417307i | \(0.862974\pi\) | |||||||
\(110\) | 2.00000 | 0.190693 | ||||||||
\(111\) | 1.26398 | + | 9.62596i | 0.119971 | + | 0.913656i | ||||
\(112\) | −0.631989 | −0.0597173 | ||||||||
\(113\) | 0.705983 | 0.0664133 | 0.0332066 | − | 0.999449i | \(-0.489428\pi\) | ||||
0.0332066 | + | 0.999449i | \(0.489428\pi\) | |||||||
\(114\) | −4.99631 | − | 5.66012i | −0.467947 | − | 0.530118i | ||||
\(115\) | −0.812981 | −0.0758108 | ||||||||
\(116\) | −3.43462 | −0.318896 | ||||||||
\(117\) | 1.89830 | + | 7.10373i | 0.175498 | + | 0.656740i | ||||
\(118\) | −2.09198 | −0.192582 | ||||||||
\(119\) | − | 2.05626i | − | 0.188497i | ||||||
\(120\) | −0.225499 | − | 1.71731i | −0.0205851 | − | 0.156768i | ||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 2.70326 | 0.244742 | ||||||||
\(123\) | −1.37836 | + | 0.180992i | −0.124283 | + | 0.0163195i | ||||
\(124\) | − | 7.16461i | − | 0.643401i | ||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 1.83169 | − | 0.489476i | 0.163180 | − | 0.0436060i | ||||
\(127\) | − | 4.86924i | − | 0.432075i | −0.976385 | − | 0.216037i | \(-0.930687\pi\) | ||
0.976385 | − | 0.216037i | \(-0.0693133\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 20.5515 | − | 2.69860i | 1.80945 | − | 0.237598i | ||||
\(130\) | −2.45100 | −0.214967 | ||||||||
\(131\) | 20.1005i | 1.75618i | 0.478491 | + | 0.878092i | \(0.341184\pi\) | ||||
−0.478491 | + | 0.878092i | \(0.658816\pi\) | |||||||
\(132\) | 0.450997 | + | 3.43462i | 0.0392543 | + | 0.298945i | ||||
\(133\) | 1.53865 | + | 2.28503i | 0.133418 | + | 0.198137i | ||||
\(134\) | 14.9462i | 1.29115i | ||||||||
\(135\) | 1.98362 | + | 4.80263i | 0.170723 | + | 0.413345i | ||||
\(136\) | − | 3.25363i | − | 0.278996i | ||||||
\(137\) | − | 8.28883i | − | 0.708163i | −0.935215 | − | 0.354081i | \(-0.884794\pi\) | ||
0.935215 | − | 0.354081i | \(-0.115206\pi\) | |||||||
\(138\) | −0.183326 | − | 1.39614i | −0.0156057 | − | 0.118847i | ||||
\(139\) | −0.196012 | −0.0166255 | −0.00831274 | − | 0.999965i | \(-0.502646\pi\) | ||||
−0.00831274 | + | 0.999965i | \(0.502646\pi\) | |||||||
\(140\) | 0.631989i | 0.0534128i | ||||||||
\(141\) | 1.79660 | + | 13.6822i | 0.151301 | + | 1.15225i | ||||
\(142\) | 6.16597 | 0.517437 | ||||||||
\(143\) | 4.90199 | 0.409925 | ||||||||
\(144\) | 2.89830 | − | 0.774501i | 0.241525 | − | 0.0645418i | ||||
\(145\) | 3.43462i | 0.285230i | ||||||||
\(146\) | 4.89461 | 0.405081 | ||||||||
\(147\) | 11.3353 | − | 1.48842i | 0.934916 | − | 0.122763i | ||||
\(148\) | − | 5.60526i | − | 0.460749i | ||||||
\(149\) | − | 11.4092i | − | 0.934682i | −0.884077 | − | 0.467341i | \(-0.845212\pi\) | ||
0.884077 | − | 0.467341i | \(-0.154788\pi\) | |||||||
\(150\) | −1.71731 | + | 0.225499i | −0.140218 | + | 0.0184119i | ||||
\(151\) | − | 10.2119i | − | 0.831031i | −0.909586 | − | 0.415515i | \(-0.863601\pi\) | ||
0.909586 | − | 0.415515i | \(-0.136399\pi\) | |||||||
\(152\) | 2.43462 | + | 3.61561i | 0.197474 | + | 0.293265i | ||||
\(153\) | 2.51994 | + | 9.42999i | 0.203725 | + | 0.762369i | ||||
\(154\) | − | 1.26398i | − | 0.101854i | ||||||
\(155\) | −7.16461 | −0.575476 | ||||||||
\(156\) | −0.552696 | − | 4.20912i | −0.0442511 | − | 0.336999i | ||||
\(157\) | 14.0338 | 1.12002 | 0.560012 | − | 0.828485i | \(-0.310797\pi\) | ||||
0.560012 | + | 0.828485i | \(0.310797\pi\) | |||||||
\(158\) | − | 4.42859i | − | 0.352320i | ||||||
\(159\) | 11.2185 | − | 1.47310i | 0.889688 | − | 0.116824i | ||||
\(160\) | 1.00000i | 0.0790569i | ||||||||
\(161\) | 0.513795i | 0.0404927i | ||||||||
\(162\) | −7.80030 | + | 4.48948i | −0.612849 | + | 0.352727i | ||||
\(163\) | −19.3765 | −1.51768 | −0.758842 | − | 0.651275i | \(-0.774234\pi\) | ||||
−0.758842 | + | 0.651275i | \(0.774234\pi\) | |||||||
\(164\) | 0.802629 | 0.0626748 | ||||||||
\(165\) | 3.43462 | − | 0.450997i | 0.267385 | − | 0.0351101i | ||||
\(166\) | 5.86788i | 0.455436i | ||||||||
\(167\) | 9.23122 | 0.714333 | 0.357167 | − | 0.934041i | \(-0.383743\pi\) | ||||
0.357167 | + | 0.934041i | \(0.383743\pi\) | |||||||
\(168\) | −1.08532 | + | 0.142513i | −0.0837343 | + | 0.0109951i | ||||
\(169\) | 6.99261 | 0.537893 | ||||||||
\(170\) | −3.25363 | −0.249542 | ||||||||
\(171\) | −9.85655 | − | 8.59351i | −0.753749 | − | 0.657162i | ||||
\(172\) | −11.9672 | −0.912494 | ||||||||
\(173\) | −1.98794 | −0.151141 | −0.0755703 | − | 0.997140i | \(-0.524078\pi\) | ||||
−0.0755703 | + | 0.997140i | \(0.524078\pi\) | |||||||
\(174\) | −5.89830 | + | 0.774501i | −0.447149 | + | 0.0587148i | ||||
\(175\) | 0.631989 | 0.0477739 | ||||||||
\(176\) | − | 2.00000i | − | 0.150756i | ||||||
\(177\) | −3.59257 | + | 0.471738i | −0.270034 | + | 0.0354580i | ||||
\(178\) | −5.93339 | −0.444727 | ||||||||
\(179\) | −11.4938 | −0.859090 | −0.429545 | − | 0.903046i | \(-0.641326\pi\) | ||||
−0.429545 | + | 0.903046i | \(0.641326\pi\) | |||||||
\(180\) | −0.774501 | − | 2.89830i | −0.0577279 | − | 0.216027i | ||||
\(181\) | − | 18.1671i | − | 1.35035i | −0.737659 | − | 0.675174i | \(-0.764069\pi\) | ||
0.737659 | − | 0.675174i | \(-0.235931\pi\) | |||||||
\(182\) | 1.54900i | 0.114820i | ||||||||
\(183\) | 4.64234 | − | 0.609582i | 0.343172 | − | 0.0450616i | ||||
\(184\) | 0.812981i | 0.0599337i | ||||||||
\(185\) | −5.60526 | −0.412107 | ||||||||
\(186\) | −1.61561 | − | 12.3039i | −0.118462 | − | 0.902162i | ||||
\(187\) | 6.50725 | 0.475857 | ||||||||
\(188\) | − | 7.96724i | − | 0.581071i | ||||||
\(189\) | 3.03521 | − | 1.25363i | 0.220779 | − | 0.0911879i | ||||
\(190\) | 3.61561 | − | 2.43462i | 0.262304 | − | 0.176626i | ||||
\(191\) | − | 2.80093i | − | 0.202668i | −0.994852 | − | 0.101334i | \(-0.967689\pi\) | ||
0.994852 | − | 0.101334i | \(-0.0323110\pi\) | |||||||
\(192\) | −1.71731 | + | 0.225499i | −0.123936 | + | 0.0162740i | ||||
\(193\) | 15.9552i | 1.14848i | 0.818687 | + | 0.574240i | \(0.194702\pi\) | ||||
−0.818687 | + | 0.574240i | \(0.805298\pi\) | |||||||
\(194\) | 3.26398i | 0.234340i | ||||||||
\(195\) | −4.20912 | + | 0.552696i | −0.301421 | + | 0.0395794i | ||||
\(196\) | −6.60059 | −0.471471 | ||||||||
\(197\) | − | 19.0352i | − | 1.35620i | −0.734969 | − | 0.678101i | \(-0.762803\pi\) | ||
0.734969 | − | 0.678101i | \(-0.237197\pi\) | |||||||
\(198\) | 1.54900 | + | 5.79660i | 0.110083 | + | 0.411947i | ||||
\(199\) | −15.3691 | −1.08949 | −0.544743 | − | 0.838603i | \(-0.683373\pi\) | ||||
−0.544743 | + | 0.838603i | \(0.683373\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 3.37035 | + | 25.6672i | 0.237726 | + | 1.81043i | ||||
\(202\) | − | 7.45999i | − | 0.524883i | ||||||
\(203\) | 2.17064 | 0.152349 | ||||||||
\(204\) | −0.733688 | − | 5.58748i | −0.0513684 | − | 0.391202i | ||||
\(205\) | − | 0.802629i | − | 0.0560581i | ||||||
\(206\) | − | 17.9345i | − | 1.24955i | ||||||
\(207\) | −0.629655 | − | 2.35626i | −0.0437640 | − | 0.163772i | ||||
\(208\) | 2.45100i | 0.169946i | ||||||||
\(209\) | −7.23122 | + | 4.86924i | −0.500194 | + | 0.336812i | ||||
\(210\) | 0.142513 | + | 1.08532i | 0.00983430 | + | 0.0748942i | ||||
\(211\) | − | 2.13976i | − | 0.147307i | −0.997284 | − | 0.0736534i | \(-0.976534\pi\) | ||
0.997284 | − | 0.0736534i | \(-0.0234659\pi\) | |||||||
\(212\) | −6.53262 | −0.448662 | ||||||||
\(213\) | 10.5889 | − | 1.39042i | 0.725538 | − | 0.0952699i | ||||
\(214\) | −5.63063 | −0.384902 | ||||||||
\(215\) | 11.9672i | 0.816159i | ||||||||
\(216\) | 4.80263 | − | 1.98362i | 0.326778 | − | 0.134968i | ||||
\(217\) | 4.52796i | 0.307378i | ||||||||
\(218\) | − | 8.71362i | − | 0.590161i | ||||||
\(219\) | 8.40555 | − | 1.10373i | 0.567995 | − | 0.0745830i | ||||
\(220\) | −2.00000 | −0.134840 | ||||||||
\(221\) | −7.97463 | −0.536432 | ||||||||
\(222\) | −1.26398 | − | 9.62596i | −0.0848326 | − | 0.646052i | ||||
\(223\) | 17.9044i | 1.19897i | 0.800386 | + | 0.599485i | \(0.204628\pi\) | ||||
−0.800386 | + | 0.599485i | \(0.795372\pi\) | |||||||
\(224\) | 0.631989 | 0.0422265 | ||||||||
\(225\) | −2.89830 | + | 0.774501i | −0.193220 | + | 0.0516334i | ||||
\(226\) | −0.705983 | −0.0469613 | ||||||||
\(227\) | 3.97463 | 0.263805 | 0.131903 | − | 0.991263i | \(-0.457891\pi\) | ||||
0.131903 | + | 0.991263i | \(0.457891\pi\) | |||||||
\(228\) | 4.99631 | + | 5.66012i | 0.330888 | + | 0.374850i | ||||
\(229\) | 13.5932 | 0.898264 | 0.449132 | − | 0.893465i | \(-0.351733\pi\) | ||||
0.449132 | + | 0.893465i | \(0.351733\pi\) | |||||||
\(230\) | 0.812981 | 0.0536064 | ||||||||
\(231\) | −0.285025 | − | 2.17064i | −0.0187533 | − | 0.142818i | ||||
\(232\) | 3.43462 | 0.225494 | ||||||||
\(233\) | − | 21.2323i | − | 1.39097i | −0.718538 | − | 0.695487i | \(-0.755188\pi\) | ||
0.718538 | − | 0.695487i | \(-0.244812\pi\) | |||||||
\(234\) | −1.89830 | − | 7.10373i | −0.124096 | − | 0.464385i | ||||
\(235\) | −7.96724 | −0.519726 | ||||||||
\(236\) | 2.09198 | 0.136176 | ||||||||
\(237\) | −0.998641 | − | 7.60526i | −0.0648687 | − | 0.494015i | ||||
\(238\) | 2.05626i | 0.133287i | ||||||||
\(239\) | 22.2899i | 1.44182i | 0.693031 | + | 0.720908i | \(0.256275\pi\) | ||||
−0.693031 | + | 0.720908i | \(0.743725\pi\) | |||||||
\(240\) | 0.225499 | + | 1.71731i | 0.0145559 | + | 0.110852i | ||||
\(241\) | 4.19873i | 0.270464i | 0.990814 | + | 0.135232i | \(0.0431780\pi\) | ||||
−0.990814 | + | 0.135232i | \(0.956822\pi\) | |||||||
\(242\) | −7.00000 | −0.449977 | ||||||||
\(243\) | −12.3831 | + | 9.46877i | −0.794379 | + | 0.607422i | ||||
\(244\) | −2.70326 | −0.173059 | ||||||||
\(245\) | 6.60059i | 0.421696i | ||||||||
\(246\) | 1.37836 | − | 0.180992i | 0.0878812 | − | 0.0115396i | ||||
\(247\) | 8.86185 | − | 5.96724i | 0.563866 | − | 0.379687i | ||||
\(248\) | 7.16461i | 0.454953i | ||||||||
\(249\) | 1.32320 | + | 10.0770i | 0.0838543 | + | 0.638601i | ||||
\(250\) | − | 1.00000i | − | 0.0632456i | ||||||
\(251\) | − | 18.6377i | − | 1.17640i | −0.808714 | − | 0.588202i | \(-0.799836\pi\) | ||
0.808714 | − | 0.588202i | \(-0.200164\pi\) | |||||||
\(252\) | −1.83169 | + | 0.489476i | −0.115386 | + | 0.0308341i | ||||
\(253\) | −1.62596 | −0.102223 | ||||||||
\(254\) | 4.86924i | 0.305523i | ||||||||
\(255\) | −5.58748 | + | 0.733688i | −0.349902 | + | 0.0459453i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.63802 | 0.351690 | 0.175845 | − | 0.984418i | \(-0.443734\pi\) | ||||
0.175845 | + | 0.984418i | \(0.443734\pi\) | |||||||
\(258\) | −20.5515 | + | 2.69860i | −1.27948 | + | 0.168007i | ||||
\(259\) | 3.54246i | 0.220118i | ||||||||
\(260\) | 2.45100 | 0.152004 | ||||||||
\(261\) | −9.95456 | + | 2.66012i | −0.616172 | + | 0.164657i | ||||
\(262\) | − | 20.1005i | − | 1.24181i | ||||||
\(263\) | − | 25.9044i | − | 1.59734i | −0.601772 | − | 0.798668i | \(-0.705538\pi\) | ||
0.601772 | − | 0.798668i | \(-0.294462\pi\) | |||||||
\(264\) | −0.450997 | − | 3.43462i | −0.0277570 | − | 0.211386i | ||||
\(265\) | 6.53262i | 0.401296i | ||||||||
\(266\) | −1.53865 | − | 2.28503i | −0.0943408 | − | 0.140104i | ||||
\(267\) | −10.1895 | + | 1.33797i | −0.623585 | + | 0.0818825i | ||||
\(268\) | − | 14.9462i | − | 0.912984i | ||||||
\(269\) | −25.3317 | −1.54450 | −0.772250 | − | 0.635319i | \(-0.780869\pi\) | ||||
−0.772250 | + | 0.635319i | \(0.780869\pi\) | |||||||
\(270\) | −1.98362 | − | 4.80263i | −0.120719 | − | 0.292279i | ||||
\(271\) | 17.5799 | 1.06790 | 0.533951 | − | 0.845515i | \(-0.320707\pi\) | ||||
0.533951 | + | 0.845515i | \(0.320707\pi\) | |||||||
\(272\) | 3.25363i | 0.197280i | ||||||||
\(273\) | 0.349298 | + | 2.66012i | 0.0211405 | + | 0.160998i | ||||
\(274\) | 8.28883i | 0.500747i | ||||||||
\(275\) | 2.00000i | 0.120605i | ||||||||
\(276\) | 0.183326 | + | 1.39614i | 0.0110349 | + | 0.0840377i | ||||
\(277\) | 21.6271 | 1.29944 | 0.649722 | − | 0.760172i | \(-0.274885\pi\) | ||||
0.649722 | + | 0.760172i | \(0.274885\pi\) | |||||||
\(278\) | 0.196012 | 0.0117560 | ||||||||
\(279\) | −5.54900 | − | 20.7652i | −0.332210 | − | 1.24318i | ||||
\(280\) | − | 0.631989i | − | 0.0377686i | ||||||
\(281\) | −21.6598 | −1.29212 | −0.646058 | − | 0.763288i | \(-0.723584\pi\) | ||||
−0.646058 | + | 0.763288i | \(0.723584\pi\) | |||||||
\(282\) | −1.79660 | − | 13.6822i | −0.106986 | − | 0.814764i | ||||
\(283\) | −15.2132 | −0.904333 | −0.452166 | − | 0.891934i | \(-0.649349\pi\) | ||||
−0.452166 | + | 0.891934i | \(0.649349\pi\) | |||||||
\(284\) | −6.16597 | −0.365883 | ||||||||
\(285\) | 5.66012 | − | 4.99631i | 0.335276 | − | 0.295956i | ||||
\(286\) | −4.90199 | −0.289861 | ||||||||
\(287\) | −0.507253 | −0.0299422 | ||||||||
\(288\) | −2.89830 | + | 0.774501i | −0.170784 | + | 0.0456379i | ||||
\(289\) | 6.41392 | 0.377289 | ||||||||
\(290\) | − | 3.43462i | − | 0.201688i | ||||||
\(291\) | 0.736022 | + | 5.60526i | 0.0431464 | + | 0.328586i | ||||
\(292\) | −4.89461 | −0.286435 | ||||||||
\(293\) | 5.38980 | 0.314876 | 0.157438 | − | 0.987529i | \(-0.449677\pi\) | ||||
0.157438 | + | 0.987529i | \(0.449677\pi\) | |||||||
\(294\) | −11.3353 | + | 1.48842i | −0.661085 | + | 0.0868066i | ||||
\(295\) | − | 2.09198i | − | 0.121800i | ||||||
\(296\) | 5.60526i | 0.325799i | ||||||||
\(297\) | 3.96724 | + | 9.60526i | 0.230203 | + | 0.557354i | ||||
\(298\) | 11.4092i | 0.660920i | ||||||||
\(299\) | 1.99261 | 0.115236 | ||||||||
\(300\) | 1.71731 | − | 0.225499i | 0.0991489 | − | 0.0130192i | ||||
\(301\) | 7.56316 | 0.435934 | ||||||||
\(302\) | 10.2119i | 0.587627i | ||||||||
\(303\) | −1.68222 | − | 12.8111i | −0.0966408 | − | 0.735979i | ||||
\(304\) | −2.43462 | − | 3.61561i | −0.139635 | − | 0.207369i | ||||
\(305\) | 2.70326i | 0.154788i | ||||||||
\(306\) | −2.51994 | − | 9.42999i | −0.144055 | − | 0.539077i | ||||
\(307\) | 0.570050i | 0.0325345i | 0.999868 | + | 0.0162672i | \(0.00517825\pi\) | ||||
−0.999868 | + | 0.0162672i | \(0.994822\pi\) | |||||||
\(308\) | 1.26398i | 0.0720218i | ||||||||
\(309\) | −4.04420 | − | 30.7991i | −0.230067 | − | 1.75210i | ||||
\(310\) | 7.16461 | 0.406923 | ||||||||
\(311\) | 8.38548i | 0.475497i | 0.971327 | + | 0.237749i | \(0.0764094\pi\) | ||||
−0.971327 | + | 0.237749i | \(0.923591\pi\) | |||||||
\(312\) | 0.552696 | + | 4.20912i | 0.0312903 | + | 0.238294i | ||||
\(313\) | 24.6358 | 1.39250 | 0.696249 | − | 0.717801i | \(-0.254851\pi\) | ||||
0.696249 | + | 0.717801i | \(0.254851\pi\) | |||||||
\(314\) | −14.0338 | −0.791976 | ||||||||
\(315\) | 0.489476 | + | 1.83169i | 0.0275789 | + | 0.103204i | ||||
\(316\) | 4.42859i | 0.249128i | ||||||||
\(317\) | −17.0071 | −0.955215 | −0.477607 | − | 0.878573i | \(-0.658496\pi\) | ||||
−0.477607 | + | 0.878573i | \(0.658496\pi\) | |||||||
\(318\) | −11.2185 | + | 1.47310i | −0.629104 | + | 0.0826072i | ||||
\(319\) | 6.86924i | 0.384603i | ||||||||
\(320\) | − | 1.00000i | − | 0.0559017i | ||||||
\(321\) | −9.66953 | + | 1.26970i | −0.539701 | + | 0.0708677i | ||||
\(322\) | − | 0.513795i | − | 0.0286327i | ||||||
\(323\) | 11.7638 | − | 7.92134i | 0.654558 | − | 0.440755i | ||||
\(324\) | 7.80030 | − | 4.48948i | 0.433350 | − | 0.249415i | ||||
\(325\) | − | 2.45100i | − | 0.135957i | ||||||
\(326\) | 19.3765 | 1.07316 | ||||||||
\(327\) | −1.96491 | − | 14.9640i | −0.108660 | − | 0.827509i | ||||
\(328\) | −0.802629 | −0.0443178 | ||||||||
\(329\) | 5.03521i | 0.277600i | ||||||||
\(330\) | −3.43462 | + | 0.450997i | −0.189070 | + | 0.0248266i | ||||
\(331\) | − | 9.74773i | − | 0.535784i | −0.963449 | − | 0.267892i | \(-0.913673\pi\) | ||
0.963449 | − | 0.267892i | \(-0.0863270\pi\) | |||||||
\(332\) | − | 5.86788i | − | 0.322042i | ||||||
\(333\) | −4.34128 | − | 16.2457i | −0.237901 | − | 0.890260i | ||||
\(334\) | −9.23122 | −0.505110 | ||||||||
\(335\) | −14.9462 | −0.816598 | ||||||||
\(336\) | 1.08532 | − | 0.142513i | 0.0592091 | − | 0.00777470i | ||||
\(337\) | 23.7505i | 1.29377i | 0.762586 | + | 0.646887i | \(0.223929\pi\) | ||||
−0.762586 | + | 0.646887i | \(0.776071\pi\) | |||||||
\(338\) | −6.99261 | −0.380348 | ||||||||
\(339\) | −1.21239 | + | 0.159198i | −0.0658480 | + | 0.00864645i | ||||
\(340\) | 3.25363 | 0.176453 | ||||||||
\(341\) | −14.3292 | −0.775971 | ||||||||
\(342\) | 9.85655 | + | 8.59351i | 0.532981 | + | 0.464684i | ||||
\(343\) | 8.59542 | 0.464109 | ||||||||
\(344\) | 11.9672 | 0.645230 | ||||||||
\(345\) | 1.39614 | − | 0.183326i | 0.0751656 | − | 0.00986994i | ||||
\(346\) | 1.98794 | 0.106873 | ||||||||
\(347\) | − | 22.9031i | − | 1.22950i | −0.788721 | − | 0.614751i | \(-0.789256\pi\) | ||
0.788721 | − | 0.614751i | \(-0.210744\pi\) | |||||||
\(348\) | 5.89830 | − | 0.774501i | 0.316182 | − | 0.0415176i | ||||
\(349\) | 11.1985 | 0.599440 | 0.299720 | − | 0.954027i | \(-0.403107\pi\) | ||||
0.299720 | + | 0.954027i | \(0.403107\pi\) | |||||||
\(350\) | −0.631989 | −0.0337812 | ||||||||
\(351\) | −4.86185 | − | 11.7712i | −0.259506 | − | 0.628302i | ||||
\(352\) | 2.00000i | 0.106600i | ||||||||
\(353\) | − | 1.64837i | − | 0.0877338i | −0.999037 | − | 0.0438669i | \(-0.986032\pi\) | ||
0.999037 | − | 0.0438669i | \(-0.0139677\pi\) | |||||||
\(354\) | 3.59257 | − | 0.471738i | 0.190943 | − | 0.0250726i | ||||
\(355\) | 6.16597i | 0.327256i | ||||||||
\(356\) | 5.93339 | 0.314469 | ||||||||
\(357\) | 0.463683 | + | 3.53123i | 0.0245407 | + | 0.186892i | ||||
\(358\) | 11.4938 | 0.607468 | ||||||||
\(359\) | 32.3079i | 1.70515i | 0.522608 | + | 0.852573i | \(0.324959\pi\) | ||||
−0.522608 | + | 0.852573i | \(0.675041\pi\) | |||||||
\(360\) | 0.774501 | + | 2.89830i | 0.0408198 | + | 0.152754i | ||||
\(361\) | −7.14527 | + | 17.6053i | −0.376067 | + | 0.926593i | ||||
\(362\) | 18.1671i | 0.954840i | ||||||||
\(363\) | −12.0212 | + | 1.57849i | −0.630947 | + | 0.0828492i | ||||
\(364\) | − | 1.54900i | − | 0.0811898i | ||||||
\(365\) | 4.89461i | 0.256195i | ||||||||
\(366\) | −4.64234 | + | 0.609582i | −0.242659 | + | 0.0318634i | ||||
\(367\) | −4.78465 | −0.249756 | −0.124878 | − | 0.992172i | \(-0.539854\pi\) | ||||
−0.124878 | + | 0.992172i | \(0.539854\pi\) | |||||||
\(368\) | − | 0.812981i | − | 0.0423795i | ||||||
\(369\) | 2.32626 | − | 0.621638i | 0.121100 | − | 0.0323612i | ||||
\(370\) | 5.60526 | 0.291404 | ||||||||
\(371\) | 4.12855 | 0.214343 | ||||||||
\(372\) | 1.61561 | + | 12.3039i | 0.0837655 | + | 0.637925i | ||||
\(373\) | − | 3.21978i | − | 0.166714i | −0.996520 | − | 0.0833569i | \(-0.973436\pi\) | ||
0.996520 | − | 0.0833569i | \(-0.0265641\pi\) | |||||||
\(374\) | −6.50725 | −0.336482 | ||||||||
\(375\) | −0.225499 | − | 1.71731i | −0.0116447 | − | 0.0886815i | ||||
\(376\) | 7.96724i | 0.410879i | ||||||||
\(377\) | − | 8.41824i | − | 0.433561i | ||||||
\(378\) | −3.03521 | + | 1.25363i | −0.156114 | + | 0.0644796i | ||||
\(379\) | − | 23.0887i | − | 1.18599i | −0.805206 | − | 0.592995i | \(-0.797946\pi\) | ||
0.805206 | − | 0.592995i | \(-0.202054\pi\) | |||||||
\(380\) | −3.61561 | + | 2.43462i | −0.185477 | + | 0.124893i | ||||
\(381\) | 1.09801 | + | 8.36198i | 0.0562525 | + | 0.428397i | ||||
\(382\) | 2.80093i | 0.143308i | ||||||||
\(383\) | 28.8124 | 1.47224 | 0.736122 | − | 0.676849i | \(-0.236655\pi\) | ||||
0.736122 | + | 0.676849i | \(0.236655\pi\) | |||||||
\(384\) | 1.71731 | − | 0.225499i | 0.0876361 | − | 0.0115074i | ||||
\(385\) | 1.26398 | 0.0644183 | ||||||||
\(386\) | − | 15.9552i | − | 0.812098i | ||||||
\(387\) | −34.6847 | + | 9.26865i | −1.76312 | + | 0.471152i | ||||
\(388\) | − | 3.26398i | − | 0.165703i | ||||||
\(389\) | − | 13.5545i | − | 0.687241i | −0.939109 | − | 0.343621i | \(-0.888347\pi\) | ||
0.939109 | − | 0.343621i | \(-0.111653\pi\) | |||||||
\(390\) | 4.20912 | − | 0.552696i | 0.213137 | − | 0.0279869i | ||||
\(391\) | 2.64514 | 0.133770 | ||||||||
\(392\) | 6.60059 | 0.333380 | ||||||||
\(393\) | −4.53262 | − | 34.5187i | −0.228641 | − | 1.74124i | ||||
\(394\) | 19.0352i | 0.958980i | ||||||||
\(395\) | 4.42859 | 0.222827 | ||||||||
\(396\) | −1.54900 | − | 5.79660i | −0.0778403 | − | 0.291290i | ||||
\(397\) | 1.51795 | 0.0761837 | 0.0380918 | − | 0.999274i | \(-0.487872\pi\) | ||||
0.0380918 | + | 0.999274i | \(0.487872\pi\) | |||||||
\(398\) | 15.3691 | 0.770383 | ||||||||
\(399\) | −3.15761 | − | 3.57713i | −0.158078 | − | 0.179081i | ||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 9.81713 | 0.490244 | 0.245122 | − | 0.969492i | \(-0.421172\pi\) | ||||
0.245122 | + | 0.969492i | \(0.421172\pi\) | |||||||
\(402\) | −3.37035 | − | 25.6672i | −0.168098 | − | 1.28017i | ||||
\(403\) | 17.5604 | 0.874748 | ||||||||
\(404\) | 7.45999i | 0.371148i | ||||||||
\(405\) | −4.48948 | − | 7.80030i | −0.223084 | − | 0.387600i | ||||
\(406\) | −2.17064 | −0.107727 | ||||||||
\(407\) | −11.2105 | −0.555685 | ||||||||
\(408\) | 0.733688 | + | 5.58748i | 0.0363230 | + | 0.276622i | ||||
\(409\) | − | 18.1453i | − | 0.897226i | −0.893726 | − | 0.448613i | \(-0.851918\pi\) | ||
0.893726 | − | 0.448613i | \(-0.148082\pi\) | |||||||
\(410\) | 0.802629i | 0.0396390i | ||||||||
\(411\) | 1.86912 | + | 14.2345i | 0.0921969 | + | 0.702136i | ||||
\(412\) | 17.9345i | 0.883569i | ||||||||
\(413\) | −1.32211 | −0.0650566 | ||||||||
\(414\) | 0.629655 | + | 2.35626i | 0.0309458 | + | 0.115804i | ||||
\(415\) | −5.86788 | −0.288043 | ||||||||
\(416\) | − | 2.45100i | − | 0.120170i | ||||||
\(417\) | 0.336612 | − | 0.0442003i | 0.0164840 | − | 0.00216450i | ||||
\(418\) | 7.23122 | − | 4.86924i | 0.353691 | − | 0.238162i | ||||
\(419\) | 15.0145i | 0.733507i | 0.930318 | + | 0.366753i | \(0.119531\pi\) | ||||
−0.930318 | + | 0.366753i | \(0.880469\pi\) | |||||||
\(420\) | −0.142513 | − | 1.08532i | −0.00695390 | − | 0.0529582i | ||||
\(421\) | 24.4341i | 1.19085i | 0.803413 | + | 0.595423i | \(0.203015\pi\) | ||||
−0.803413 | + | 0.595423i | \(0.796985\pi\) | |||||||
\(422\) | 2.13976i | 0.104162i | ||||||||
\(423\) | −6.17064 | − | 23.0915i | −0.300027 | − | 1.12275i | ||||
\(424\) | 6.53262 | 0.317252 | ||||||||
\(425\) | − | 3.25363i | − | 0.157824i | ||||||
\(426\) | −10.5889 | + | 1.39042i | −0.513033 | + | 0.0673660i | ||||
\(427\) | 1.70843 | 0.0826769 | ||||||||
\(428\) | 5.63063 | 0.272167 | ||||||||
\(429\) | −8.41824 | + | 1.10539i | −0.406436 | + | 0.0533689i | ||||
\(430\) | − | 11.9672i | − | 0.577112i | ||||||
\(431\) | 41.0522 | 1.97741 | 0.988707 | − | 0.149864i | \(-0.0478837\pi\) | ||||
0.988707 | + | 0.149864i | \(0.0478837\pi\) | |||||||
\(432\) | −4.80263 | + | 1.98362i | −0.231067 | + | 0.0954370i | ||||
\(433\) | − | 18.0121i | − | 0.865604i | −0.901489 | − | 0.432802i | \(-0.857525\pi\) | ||
0.901489 | − | 0.432802i | \(-0.142475\pi\) | |||||||
\(434\) | − | 4.52796i | − | 0.217349i | ||||||
\(435\) | −0.774501 | − | 5.89830i | −0.0371345 | − | 0.282802i | ||||
\(436\) | 8.71362i | 0.417307i | ||||||||
\(437\) | −2.93942 | + | 1.97930i | −0.140612 | + | 0.0946826i | ||||
\(438\) | −8.40555 | + | 1.10373i | −0.401633 | + | 0.0527381i | ||||
\(439\) | 27.8024i | 1.32693i | 0.748205 | + | 0.663467i | \(0.230916\pi\) | ||||
−0.748205 | + | 0.663467i | \(0.769084\pi\) | |||||||
\(440\) | 2.00000 | 0.0953463 | ||||||||
\(441\) | −19.1305 | + | 5.11217i | −0.910976 | + | 0.243437i | ||||
\(442\) | 7.97463 | 0.379314 | ||||||||
\(443\) | 10.0366i | 0.476852i | 0.971161 | + | 0.238426i | \(0.0766314\pi\) | ||||
−0.971161 | + | 0.238426i | \(0.923369\pi\) | |||||||
\(444\) | 1.26398 | + | 9.62596i | 0.0599857 | + | 0.456828i | ||||
\(445\) | − | 5.93339i | − | 0.281270i | ||||||
\(446\) | − | 17.9044i | − | 0.847800i | ||||||
\(447\) | 2.57277 | + | 19.5932i | 0.121688 | + | 0.926727i | ||||
\(448\) | −0.631989 | −0.0298587 | ||||||||
\(449\) | −33.9055 | −1.60010 | −0.800051 | − | 0.599933i | \(-0.795194\pi\) | ||||
−0.800051 | + | 0.599933i | \(0.795194\pi\) | |||||||
\(450\) | 2.89830 | − | 0.774501i | 0.136627 | − | 0.0365103i | ||||
\(451\) | − | 1.60526i | − | 0.0755887i | ||||||
\(452\) | 0.705983 | 0.0332066 | ||||||||
\(453\) | 2.30276 | + | 17.5369i | 0.108193 | + | 0.823958i | ||||
\(454\) | −3.97463 | −0.186539 | ||||||||
\(455\) | −1.54900 | −0.0726184 | ||||||||
\(456\) | −4.99631 | − | 5.66012i | −0.233973 | − | 0.265059i | ||||
\(457\) | −31.7131 | −1.48348 | −0.741738 | − | 0.670690i | \(-0.765998\pi\) | ||||
−0.741738 | + | 0.670690i | \(0.765998\pi\) | |||||||
\(458\) | −13.5932 | −0.635169 | ||||||||
\(459\) | −6.45396 | − | 15.6260i | −0.301245 | − | 0.729357i | ||||
\(460\) | −0.812981 | −0.0379054 | ||||||||
\(461\) | − | 23.1029i | − | 1.07601i | −0.842942 | − | 0.538005i | \(-0.819178\pi\) | ||
0.842942 | − | 0.538005i | \(-0.180822\pi\) | |||||||
\(462\) | 0.285025 | + | 2.17064i | 0.0132606 | + | 0.100987i | ||||
\(463\) | 32.6950 | 1.51947 | 0.759733 | − | 0.650235i | \(-0.225330\pi\) | ||||
0.759733 | + | 0.650235i | \(0.225330\pi\) | |||||||
\(464\) | −3.43462 | −0.159448 | ||||||||
\(465\) | 12.3039 | − | 1.61561i | 0.570578 | − | 0.0749221i | ||||
\(466\) | 21.2323i | 0.983568i | ||||||||
\(467\) | 29.2023i | 1.35132i | 0.737213 | + | 0.675660i | \(0.236141\pi\) | ||||
−0.737213 | + | 0.675660i | \(0.763859\pi\) | |||||||
\(468\) | 1.89830 | + | 7.10373i | 0.0877490 | + | 0.328370i | ||||
\(469\) | 9.44583i | 0.436168i | ||||||||
\(470\) | 7.96724 | 0.367501 | ||||||||
\(471\) | −24.1005 | + | 3.16461i | −1.11049 | + | 0.145818i | ||||
\(472\) | −2.09198 | −0.0962911 | ||||||||
\(473\) | 23.9345i | 1.10051i | ||||||||
\(474\) | 0.998641 | + | 7.60526i | 0.0458691 | + | 0.349321i | ||||
\(475\) | 2.43462 | + | 3.61561i | 0.111708 | + | 0.165896i | ||||
\(476\) | − | 2.05626i | − | 0.0942483i | ||||||
\(477\) | −18.9335 | + | 5.05953i | −0.866906 | + | 0.231660i | ||||
\(478\) | − | 22.2899i | − | 1.01952i | ||||||
\(479\) | 17.7712i | 0.811988i | 0.913876 | + | 0.405994i | \(0.133075\pi\) | ||||
−0.913876 | + | 0.405994i | \(0.866925\pi\) | |||||||
\(480\) | −0.225499 | − | 1.71731i | −0.0102926 | − | 0.0783841i | ||||
\(481\) | 13.7385 | 0.626420 | ||||||||
\(482\) | − | 4.19873i | − | 0.191247i | ||||||
\(483\) | −0.115860 | − | 0.882344i | −0.00527181 | − | 0.0401481i | ||||
\(484\) | 7.00000 | 0.318182 | ||||||||
\(485\) | −3.26398 | −0.148210 | ||||||||
\(486\) | 12.3831 | − | 9.46877i | 0.561711 | − | 0.429512i | ||||
\(487\) | 10.3620i | 0.469546i | 0.972050 | + | 0.234773i | \(0.0754347\pi\) | ||||
−0.972050 | + | 0.234773i | \(0.924565\pi\) | |||||||
\(488\) | 2.70326 | 0.122371 | ||||||||
\(489\) | 33.2754 | − | 4.36937i | 1.50477 | − | 0.197590i | ||||
\(490\) | − | 6.60059i | − | 0.298184i | ||||||
\(491\) | − | 16.8993i | − | 0.762654i | −0.924440 | − | 0.381327i | \(-0.875467\pi\) | ||
0.924440 | − | 0.381327i | \(-0.124533\pi\) | |||||||
\(492\) | −1.37836 | + | 0.180992i | −0.0621414 | + | 0.00815974i | ||||
\(493\) | − | 11.1750i | − | 0.503295i | ||||||
\(494\) | −8.86185 | + | 5.96724i | −0.398713 | + | 0.268479i | ||||
\(495\) | −5.79660 | + | 1.54900i | −0.260538 | + | 0.0696225i | ||||
\(496\) | − | 7.16461i | − | 0.321701i | ||||||
\(497\) | 3.89683 | 0.174797 | ||||||||
\(498\) | −1.32320 | − | 10.0770i | −0.0592939 | − | 0.451559i | ||||
\(499\) | 0.364702 | 0.0163263 | 0.00816315 | − | 0.999967i | \(-0.497402\pi\) | ||||
0.00816315 | + | 0.999967i | \(0.497402\pi\) | |||||||
\(500\) | 1.00000i | 0.0447214i | ||||||||
\(501\) | −15.8529 | + | 2.08163i | −0.708253 | + | 0.0930002i | ||||
\(502\) | 18.6377i | 0.831843i | ||||||||
\(503\) | − | 30.0939i | − | 1.34182i | −0.741538 | − | 0.670911i | \(-0.765903\pi\) | ||
0.741538 | − | 0.670911i | \(-0.234097\pi\) | |||||||
\(504\) | 1.83169 | − | 0.489476i | 0.0815901 | − | 0.0218030i | ||||
\(505\) | 7.45999 | 0.331965 | ||||||||
\(506\) | 1.62596 | 0.0722828 | ||||||||
\(507\) | −12.0085 | + | 1.57682i | −0.533315 | + | 0.0700292i | ||||
\(508\) | − | 4.86924i | − | 0.216037i | ||||||
\(509\) | 44.3849 | 1.96732 | 0.983662 | − | 0.180023i | \(-0.0576173\pi\) | ||||
0.983662 | + | 0.180023i | \(0.0576173\pi\) | |||||||
\(510\) | 5.58748 | − | 0.733688i | 0.247418 | − | 0.0324883i | ||||
\(511\) | 3.09334 | 0.136841 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 18.8646 | + | 12.5351i | 0.832891 | + | 0.553437i | ||||
\(514\) | −5.63802 | −0.248682 | ||||||||
\(515\) | 17.9345 | 0.790288 | ||||||||
\(516\) | 20.5515 | − | 2.69860i | 0.904727 | − | 0.118799i | ||||
\(517\) | −15.9345 | −0.700798 | ||||||||
\(518\) | − | 3.54246i | − | 0.155647i | ||||||
\(519\) | 3.41392 | − | 0.448279i | 0.149854 | − | 0.0196772i | ||||
\(520\) | −2.45100 | −0.107483 | ||||||||
\(521\) | 17.8472 | 0.781899 | 0.390949 | − | 0.920412i | \(-0.372147\pi\) | ||||
0.390949 | + | 0.920412i | \(0.372147\pi\) | |||||||
\(522\) | 9.95456 | − | 2.66012i | 0.435699 | − | 0.116430i | ||||
\(523\) | − | 14.2222i | − | 0.621895i | −0.950427 | − | 0.310947i | \(-0.899354\pi\) | ||
0.950427 | − | 0.310947i | \(-0.100646\pi\) | |||||||
\(524\) | 20.1005i | 0.878092i | ||||||||
\(525\) | −1.08532 | + | 0.142513i | −0.0473673 | + | 0.00621976i | ||||
\(526\) | 25.9044i | 1.12949i | ||||||||
\(527\) | 23.3110 | 1.01544 | ||||||||
\(528\) | 0.450997 | + | 3.43462i | 0.0196271 | + | 0.149473i | ||||
\(529\) | 22.3391 | 0.971264 | ||||||||
\(530\) | − | 6.53262i | − | 0.283759i | ||||||
\(531\) | 6.06318 | − | 1.62024i | 0.263120 | − | 0.0703124i | ||||
\(532\) | 1.53865 | + | 2.28503i | 0.0667090 | + | 0.0990684i | ||||
\(533\) | 1.96724i | 0.0852107i | ||||||||
\(534\) | 10.1895 | − | 1.33797i | 0.440941 | − | 0.0578997i | ||||
\(535\) | − | 5.63063i | − | 0.243433i | ||||||
\(536\) | 14.9462i | 0.645577i | ||||||||
\(537\) | 19.7385 | − | 2.59184i | 0.851778 | − | 0.111846i | ||||
\(538\) | 25.3317 | 1.09213 | ||||||||
\(539\) | 13.2012i | 0.568615i | ||||||||
\(540\) | 1.98362 | + | 4.80263i | 0.0853615 | + | 0.206672i | ||||
\(541\) | −37.2164 | −1.60006 | −0.800030 | − | 0.599960i | \(-0.795183\pi\) | ||||
−0.800030 | + | 0.599960i | \(0.795183\pi\) | |||||||
\(542\) | −17.5799 | −0.755121 | ||||||||
\(543\) | 4.09665 | + | 31.1985i | 0.175804 | + | 1.33885i | ||||
\(544\) | − | 3.25363i | − | 0.139498i | ||||||
\(545\) | 8.71362 | 0.373250 | ||||||||
\(546\) | −0.349298 | − | 2.66012i | −0.0149486 | − | 0.113842i | ||||
\(547\) | 16.3789i | 0.700313i | 0.936691 | + | 0.350156i | \(0.113872\pi\) | ||||
−0.936691 | + | 0.350156i | \(0.886128\pi\) | |||||||
\(548\) | − | 8.28883i | − | 0.354081i | ||||||
\(549\) | −7.83487 | + | 2.09368i | −0.334384 | + | 0.0893562i | ||||
\(550\) | − | 2.00000i | − | 0.0852803i | ||||||
\(551\) | 8.36198 | + | 12.4182i | 0.356232 | + | 0.529035i | ||||
\(552\) | −0.183326 | − | 1.39614i | −0.00780287 | − | 0.0594236i | ||||
\(553\) | − | 2.79882i | − | 0.119018i | ||||||
\(554\) | −21.6271 | −0.918845 | ||||||||
\(555\) | 9.62596 | − | 1.26398i | 0.408599 | − | 0.0536529i | ||||
\(556\) | −0.196012 | −0.00831274 | ||||||||
\(557\) | 36.8244i | 1.56030i | 0.625592 | + | 0.780150i | \(0.284858\pi\) | ||||
−0.625592 | + | 0.780150i | \(0.715142\pi\) | |||||||
\(558\) | 5.54900 | + | 20.7652i | 0.234908 | + | 0.879061i | ||||
\(559\) | − | 29.3317i | − | 1.24060i | ||||||
\(560\) | 0.631989i | 0.0267064i | ||||||||
\(561\) | −11.1750 | + | 1.46738i | −0.471807 | + | 0.0619527i | ||||
\(562\) | 21.6598 | 0.913664 | ||||||||
\(563\) | 40.0022 | 1.68589 | 0.842945 | − | 0.537999i | \(-0.180820\pi\) | ||||
0.842945 | + | 0.537999i | \(0.180820\pi\) | |||||||
\(564\) | 1.79660 | + | 13.6822i | 0.0756506 | + | 0.576125i | ||||
\(565\) | − | 0.705983i | − | 0.0297009i | ||||||
\(566\) | 15.2132 | 0.639460 | ||||||||
\(567\) | −4.92970 | + | 2.83730i | −0.207028 | + | 0.119155i | ||||
\(568\) | 6.16597 | 0.258718 | ||||||||
\(569\) | 21.6953 | 0.909514 | 0.454757 | − | 0.890616i | \(-0.349726\pi\) | ||||
0.454757 | + | 0.890616i | \(0.349726\pi\) | |||||||
\(570\) | −5.66012 | + | 4.99631i | −0.237076 | + | 0.209272i | ||||
\(571\) | 3.37377 | 0.141188 | 0.0705940 | − | 0.997505i | \(-0.477511\pi\) | ||||
0.0705940 | + | 0.997505i | \(0.477511\pi\) | |||||||
\(572\) | 4.90199 | 0.204963 | ||||||||
\(573\) | 0.631605 | + | 4.81005i | 0.0263857 | + | 0.200943i | ||||
\(574\) | 0.507253 | 0.0211723 | ||||||||
\(575\) | 0.812981i | 0.0339036i | ||||||||
\(576\) | 2.89830 | − | 0.774501i | 0.120763 | − | 0.0322709i | ||||
\(577\) | −31.3740 | −1.30612 | −0.653058 | − | 0.757308i | \(-0.726514\pi\) | ||||
−0.653058 | + | 0.757308i | \(0.726514\pi\) | |||||||
\(578\) | −6.41392 | −0.266784 | ||||||||
\(579\) | −3.59787 | − | 27.4000i | −0.149522 | − | 1.13870i | ||||
\(580\) | 3.43462i | 0.142615i | ||||||||
\(581\) | 3.70843i | 0.153852i | ||||||||
\(582\) | −0.736022 | − | 5.60526i | −0.0305091 | − | 0.232345i | ||||
\(583\) | 13.0652i | 0.541107i | ||||||||
\(584\) | 4.89461 | 0.202540 | ||||||||
\(585\) | 7.10373 | − | 1.89830i | 0.293703 | − | 0.0784851i | ||||
\(586\) | −5.38980 | −0.222651 | ||||||||
\(587\) | 39.0718i | 1.61266i | 0.591463 | + | 0.806332i | \(0.298551\pi\) | ||||
−0.591463 | + | 0.806332i | \(0.701449\pi\) | |||||||
\(588\) | 11.3353 | − | 1.48842i | 0.467458 | − | 0.0613816i | ||||
\(589\) | −25.9044 | + | 17.4431i | −1.06737 | + | 0.718730i | ||||
\(590\) | 2.09198i | 0.0861254i | ||||||||
\(591\) | 4.29241 | + | 32.6893i | 0.176566 | + | 1.34466i | ||||
\(592\) | − | 5.60526i | − | 0.230375i | ||||||
\(593\) | 26.6367i | 1.09384i | 0.837186 | + | 0.546918i | \(0.184199\pi\) | ||||
−0.837186 | + | 0.546918i | \(0.815801\pi\) | |||||||
\(594\) | −3.96724 | − | 9.60526i | −0.162778 | − | 0.394109i | ||||
\(595\) | −2.05626 | −0.0842983 | ||||||||
\(596\) | − | 11.4092i | − | 0.467341i | ||||||
\(597\) | 26.3935 | − | 3.46571i | 1.08021 | − | 0.141842i | ||||
\(598\) | −1.99261 | −0.0814840 | ||||||||
\(599\) | −0.952736 | −0.0389278 | −0.0194639 | − | 0.999811i | \(-0.506196\pi\) | ||||
−0.0194639 | + | 0.999811i | \(0.506196\pi\) | |||||||
\(600\) | −1.71731 | + | 0.225499i | −0.0701088 | + | 0.00920594i | ||||
\(601\) | 14.6050i | 0.595750i | 0.954605 | + | 0.297875i | \(0.0962779\pi\) | ||||
−0.954605 | + | 0.297875i | \(0.903722\pi\) | |||||||
\(602\) | −7.56316 | −0.308252 | ||||||||
\(603\) | −11.5758 | − | 43.3186i | −0.471405 | − | 1.76407i | ||||
\(604\) | − | 10.2119i | − | 0.415515i | ||||||
\(605\) | − | 7.00000i | − | 0.284590i | ||||||
\(606\) | 1.68222 | + | 12.8111i | 0.0683354 | + | 0.520416i | ||||
\(607\) | − | 11.5304i | − | 0.468005i | −0.972236 | − | 0.234002i | \(-0.924818\pi\) | ||
0.972236 | − | 0.234002i | \(-0.0751823\pi\) | |||||||
\(608\) | 2.43462 | + | 3.61561i | 0.0987368 | + | 0.146632i | ||||
\(609\) | −3.72766 | + | 0.489476i | −0.151052 | + | 0.0198346i | ||||
\(610\) | − | 2.70326i | − | 0.109452i | ||||||
\(611\) | 19.5277 | 0.790006 | ||||||||
\(612\) | 2.51994 | + | 9.42999i | 0.101862 | + | 0.381185i | ||||
\(613\) | −25.1996 | −1.01780 | −0.508900 | − | 0.860826i | \(-0.669948\pi\) | ||||
−0.508900 | + | 0.860826i | \(0.669948\pi\) | |||||||
\(614\) | − | 0.570050i | − | 0.0230054i | ||||||
\(615\) | 0.180992 | + | 1.37836i | 0.00729829 | + | 0.0555809i | ||||
\(616\) | − | 1.26398i | − | 0.0509271i | ||||||
\(617\) | − | 18.3724i | − | 0.739645i | −0.929102 | − | 0.369823i | \(-0.879418\pi\) | ||
0.929102 | − | 0.369823i | \(-0.120582\pi\) | |||||||
\(618\) | 4.04420 | + | 30.7991i | 0.162682 | + | 1.23892i | ||||
\(619\) | −16.4952 | −0.662998 | −0.331499 | − | 0.943456i | \(-0.607554\pi\) | ||||
−0.331499 | + | 0.943456i | \(0.607554\pi\) | |||||||
\(620\) | −7.16461 | −0.287738 | ||||||||
\(621\) | 1.61265 | + | 3.90444i | 0.0647132 | + | 0.156680i | ||||
\(622\) | − | 8.38548i | − | 0.336227i | ||||||
\(623\) | −3.74984 | −0.150234 | ||||||||
\(624\) | −0.552696 | − | 4.20912i | −0.0221256 | − | 0.168500i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −24.6358 | −0.984645 | ||||||||
\(627\) | 11.3202 | − | 9.99261i | 0.452087 | − | 0.399067i | ||||
\(628\) | 14.0338 | 0.560012 | ||||||||
\(629\) | 18.2374 | 0.727173 | ||||||||
\(630\) | −0.489476 | − | 1.83169i | −0.0195012 | − | 0.0729764i | ||||
\(631\) | −11.0532 | −0.440021 | −0.220010 | − | 0.975498i | \(-0.570609\pi\) | ||||
−0.220010 | + | 0.975498i | \(0.570609\pi\) | |||||||
\(632\) | − | 4.42859i | − | 0.176160i | ||||||
\(633\) | 0.482512 | + | 3.67462i | 0.0191781 | + | 0.146053i | ||||
\(634\) | 17.0071 | 0.675439 | ||||||||
\(635\) | −4.86924 | −0.193230 | ||||||||
\(636\) | 11.2185 | − | 1.47310i | 0.444844 | − | 0.0584121i | ||||
\(637\) | − | 16.1780i | − | 0.640997i | ||||||
\(638\) | − | 6.86924i | − | 0.271956i | ||||||
\(639\) | −17.8708 | + | 4.77555i | −0.706960 | + | 0.188918i | ||||
\(640\) | 1.00000i | 0.0395285i | ||||||||
\(641\) | −33.7368 | −1.33253 | −0.666263 | − | 0.745717i | \(-0.732107\pi\) | ||||
−0.666263 | + | 0.745717i | \(0.732107\pi\) | |||||||
\(642\) | 9.66953 | − | 1.26970i | 0.381626 | − | 0.0501110i | ||||
\(643\) | −28.9369 | −1.14116 | −0.570581 | − | 0.821242i | \(-0.693282\pi\) | ||||
−0.570581 | + | 0.821242i | \(0.693282\pi\) | |||||||
\(644\) | 0.513795i | 0.0202463i | ||||||||
\(645\) | −2.69860 | − | 20.5515i | −0.106257 | − | 0.809213i | ||||
\(646\) | −11.7638 | + | 7.92134i | −0.462842 | + | 0.311661i | ||||
\(647\) | − | 35.3409i | − | 1.38940i | −0.719302 | − | 0.694698i | \(-0.755538\pi\) | ||
0.719302 | − | 0.694698i | \(-0.244462\pi\) | |||||||
\(648\) | −7.80030 | + | 4.48948i | −0.306425 | + | 0.176363i | ||||
\(649\) | − | 4.18396i | − | 0.164235i | ||||||
\(650\) | 2.45100i | 0.0961360i | ||||||||
\(651\) | −1.02105 | − | 7.77590i | −0.0400180 | − | 0.304762i | ||||
\(652\) | −19.3765 | −0.758842 | ||||||||
\(653\) | − | 5.41518i | − | 0.211912i | −0.994371 | − | 0.105956i | \(-0.966210\pi\) | ||
0.994371 | − | 0.105956i | \(-0.0337903\pi\) | |||||||
\(654\) | 1.96491 | + | 14.9640i | 0.0768340 | + | 0.585138i | ||||
\(655\) | 20.1005 | 0.785390 | ||||||||
\(656\) | 0.802629 | 0.0313374 | ||||||||
\(657\) | −14.1860 | + | 3.79088i | −0.553450 | + | 0.147896i | ||||
\(658\) | − | 5.03521i | − | 0.196293i | ||||||
\(659\) | −23.8546 | −0.929242 | −0.464621 | − | 0.885510i | \(-0.653809\pi\) | ||||
−0.464621 | + | 0.885510i | \(0.653809\pi\) | |||||||
\(660\) | 3.43462 | − | 0.450997i | 0.133692 | − | 0.0175550i | ||||
\(661\) | − | 14.3396i | − | 0.557745i | −0.960328 | − | 0.278872i | \(-0.910039\pi\) | ||
0.960328 | − | 0.278872i | \(-0.0899607\pi\) | |||||||
\(662\) | 9.74773i | 0.378856i | ||||||||
\(663\) | 13.6949 | − | 1.79827i | 0.531866 | − | 0.0698389i | ||||
\(664\) | 5.86788i | 0.227718i | ||||||||
\(665\) | 2.28503 | − | 1.53865i | 0.0886095 | − | 0.0596663i | ||||
\(666\) | 4.34128 | + | 16.2457i | 0.168221 | + | 0.629509i | ||||
\(667\) | 2.79228i | 0.108117i | ||||||||
\(668\) | 9.23122 | 0.357167 | ||||||||
\(669\) | −4.03743 | − | 30.7475i | −0.156096 | − | 1.18877i | ||||
\(670\) | 14.9462 | 0.577422 | ||||||||
\(671\) | 5.40653i | 0.208717i | ||||||||
\(672\) | −1.08532 | + | 0.142513i | −0.0418671 | + | 0.00549754i | ||||
\(673\) | − | 49.3290i | − | 1.90149i | −0.309972 | − | 0.950746i | \(-0.600320\pi\) | ||
0.309972 | − | 0.950746i | \(-0.399680\pi\) | |||||||
\(674\) | − | 23.7505i | − | 0.914836i | ||||||
\(675\) | 4.80263 | − | 1.98362i | 0.184853 | − | 0.0763496i | ||||
\(676\) | 6.99261 | 0.268947 | ||||||||
\(677\) | 23.1431 | 0.889460 | 0.444730 | − | 0.895665i | \(-0.353300\pi\) | ||||
0.444730 | + | 0.895665i | \(0.353300\pi\) | |||||||
\(678\) | 1.21239 | − | 0.159198i | 0.0465616 | − | 0.00611397i | ||||
\(679\) | 2.06280i | 0.0791629i | ||||||||
\(680\) | −3.25363 | −0.124771 | ||||||||
\(681\) | −6.82567 | + | 0.896273i | −0.261560 | + | 0.0343453i | ||||
\(682\) | 14.3292 | 0.548694 | ||||||||
\(683\) | −20.2905 | −0.776396 | −0.388198 | − | 0.921576i | \(-0.626902\pi\) | ||||
−0.388198 | + | 0.921576i | \(0.626902\pi\) | |||||||
\(684\) | −9.85655 | − | 8.59351i | −0.376875 | − | 0.328581i | ||||
\(685\) | −8.28883 | −0.316700 | ||||||||
\(686\) | −8.59542 | −0.328175 | ||||||||
\(687\) | −23.3437 | + | 3.06525i | −0.890619 | + | 0.116946i | ||||
\(688\) | −11.9672 | −0.456247 | ||||||||
\(689\) | − | 16.0114i | − | 0.609987i | ||||||
\(690\) | −1.39614 | + | 0.183326i | −0.0531501 | + | 0.00697910i | ||||
\(691\) | −18.5280 | −0.704837 | −0.352418 | − | 0.935843i | \(-0.614641\pi\) | ||||
−0.352418 | + | 0.935843i | \(0.614641\pi\) | |||||||
\(692\) | −1.98794 | −0.0755703 | ||||||||
\(693\) | 0.978953 | + | 3.66339i | 0.0371873 | + | 0.139161i | ||||
\(694\) | 22.9031i | 0.869389i | ||||||||
\(695\) | 0.196012i | 0.00743514i | ||||||||
\(696\) | −5.89830 | + | 0.774501i | −0.223575 | + | 0.0293574i | ||||
\(697\) | 2.61146i | 0.0989159i | ||||||||
\(698\) | −11.1985 | −0.423868 | ||||||||
\(699\) | 4.78786 | + | 36.4624i | 0.181093 | + | 1.37914i | ||||
\(700\) | 0.631989 | 0.0238869 | ||||||||
\(701\) | 3.42130i | 0.129221i | 0.997911 | + | 0.0646104i | \(0.0205805\pi\) | ||||
−0.997911 | + | 0.0646104i | \(0.979420\pi\) | |||||||
\(702\) | 4.86185 | + | 11.7712i | 0.183499 | + | 0.444276i | ||||
\(703\) | −20.2664 | + | 13.6467i | −0.764363 | + | 0.514694i | ||||
\(704\) | − | 2.00000i | − | 0.0753778i | ||||||
\(705\) | 13.6822 | − | 1.79660i | 0.515302 | − | 0.0676639i | ||||
\(706\) | 1.64837i | 0.0620371i | ||||||||
\(707\) | − | 4.71463i | − | 0.177312i | ||||||
\(708\) | −3.59257 | + | 0.471738i | −0.135017 | + | 0.0177290i | ||||
\(709\) | 15.1329 | 0.568330 | 0.284165 | − | 0.958775i | \(-0.408284\pi\) | ||||
0.284165 | + | 0.958775i | \(0.408284\pi\) | |||||||
\(710\) | − | 6.16597i | − | 0.231405i | ||||||
\(711\) | 3.42995 | + | 12.8354i | 0.128633 | + | 0.481365i | ||||
\(712\) | −5.93339 | −0.222363 | ||||||||
\(713\) | −5.82469 | −0.218136 | ||||||||
\(714\) | −0.463683 | − | 3.53123i | −0.0173529 | − | 0.132153i | ||||
\(715\) | − | 4.90199i | − | 0.183324i | ||||||
\(716\) | −11.4938 | −0.429545 | ||||||||
\(717\) | −5.02635 | − | 38.2787i | −0.187712 | − | 1.42954i | ||||
\(718\) | − | 32.3079i | − | 1.20572i | ||||||
\(719\) | 4.37343i | 0.163101i | 0.996669 | + | 0.0815506i | \(0.0259872\pi\) | ||||
−0.996669 | + | 0.0815506i | \(0.974013\pi\) | |||||||
\(720\) | −0.774501 | − | 2.89830i | −0.0288640 | − | 0.108013i | ||||
\(721\) | − | 11.3344i | − | 0.422115i | ||||||
\(722\) | 7.14527 | − | 17.6053i | 0.265919 | − | 0.655200i | ||||
\(723\) | −0.946808 | − | 7.21052i | −0.0352122 | − | 0.268162i | ||||
\(724\) | − | 18.1671i | − | 0.675174i | ||||||
\(725\) | 3.43462 | 0.127559 | ||||||||
\(726\) | 12.0212 | − | 1.57849i | 0.446147 | − | 0.0585833i | ||||
\(727\) | 26.6517 | 0.988455 | 0.494228 | − | 0.869332i | \(-0.335451\pi\) | ||||
0.494228 | + | 0.869332i | \(0.335451\pi\) | |||||||
\(728\) | 1.54900i | 0.0574099i | ||||||||
\(729\) | 19.1305 | − | 19.0532i | 0.708537 | − | 0.705674i | ||||
\(730\) | − | 4.89461i | − | 0.181158i | ||||||
\(731\) | − | 38.9369i | − | 1.44013i | ||||||
\(732\) | 4.64234 | − | 0.609582i | 0.171586 | − | 0.0225308i | ||||
\(733\) | 14.1501 | 0.522646 | 0.261323 | − | 0.965251i | \(-0.415841\pi\) | ||||
0.261323 | + | 0.965251i | \(0.415841\pi\) | |||||||
\(734\) | 4.78465 | 0.176604 | ||||||||
\(735\) | −1.48842 | − | 11.3353i | −0.0549013 | − | 0.418107i | ||||
\(736\) | 0.812981i | 0.0299669i | ||||||||
\(737\) | −29.8924 | −1.10110 | ||||||||
\(738\) | −2.32626 | + | 0.621638i | −0.0856309 | + | 0.0228828i | ||||
\(739\) | −47.9721 | −1.76468 | −0.882342 | − | 0.470609i | \(-0.844034\pi\) | ||||
−0.882342 | + | 0.470609i | \(0.844034\pi\) | |||||||
\(740\) | −5.60526 | −0.206053 | ||||||||
\(741\) | −13.8729 | + | 12.2459i | −0.509635 | + | 0.449866i | ||||
\(742\) | −4.12855 | −0.151564 | ||||||||
\(743\) | −43.3765 | −1.59133 | −0.795665 | − | 0.605738i | \(-0.792878\pi\) | ||||
−0.795665 | + | 0.605738i | \(0.792878\pi\) | |||||||
\(744\) | −1.61561 | − | 12.3039i | −0.0592311 | − | 0.451081i | ||||
\(745\) | −11.4092 | −0.418002 | ||||||||
\(746\) | 3.21978i | 0.117884i | ||||||||
\(747\) | −4.54468 | − | 17.0069i | −0.166281 | − | 0.622249i | ||||
\(748\) | 6.50725 | 0.237929 | ||||||||
\(749\) | −3.55850 | −0.130025 | ||||||||
\(750\) | 0.225499 | + | 1.71731i | 0.00823404 | + | 0.0627073i | ||||
\(751\) | 3.58278i | 0.130737i | 0.997861 | + | 0.0653687i | \(0.0208223\pi\) | ||||
−0.997861 | + | 0.0653687i | \(0.979178\pi\) | |||||||
\(752\) | − | 7.96724i | − | 0.290535i | ||||||
\(753\) | 4.20279 | + | 32.0068i | 0.153158 | + | 1.16639i | ||||
\(754\) | 8.41824i | 0.306574i | ||||||||
\(755\) | −10.2119 | −0.371648 | ||||||||
\(756\) | 3.03521 | − | 1.25363i | 0.110389 | − | 0.0455940i | ||||
\(757\) | −16.5618 | −0.601949 | −0.300975 | − | 0.953632i | \(-0.597312\pi\) | ||||
−0.300975 | + | 0.953632i | \(0.597312\pi\) | |||||||
\(758\) | 23.0887i | 0.838621i | ||||||||
\(759\) | 2.79228 | − | 0.366652i | 0.101353 | − | 0.0133086i | ||||
\(760\) | 3.61561 | − | 2.43462i | 0.131152 | − | 0.0883129i | ||||
\(761\) | 34.6726i | 1.25688i | 0.777858 | + | 0.628441i | \(0.216306\pi\) | ||||
−0.777858 | + | 0.628441i | \(0.783694\pi\) | |||||||
\(762\) | −1.09801 | − | 8.36198i | −0.0397766 | − | 0.302923i | ||||
\(763\) | − | 5.50691i | − | 0.199363i | ||||||
\(764\) | − | 2.80093i | − | 0.101334i | ||||||
\(765\) | 9.42999 | − | 2.51994i | 0.340942 | − | 0.0911086i | ||||
\(766\) | −28.8124 | −1.04103 | ||||||||
\(767\) | 5.12743i | 0.185141i | ||||||||
\(768\) | −1.71731 | + | 0.225499i | −0.0619681 | + | 0.00813698i | ||||
\(769\) | −20.4698 | −0.738161 | −0.369080 | − | 0.929397i | \(-0.620327\pi\) | ||||
−0.369080 | + | 0.929397i | \(0.620327\pi\) | |||||||
\(770\) | −1.26398 | −0.0455506 | ||||||||
\(771\) | −9.68222 | + | 1.27136i | −0.348697 | + | 0.0457871i | ||||
\(772\) | 15.9552i | 0.574240i | ||||||||
\(773\) | −27.5738 | −0.991759 | −0.495880 | − | 0.868391i | \(-0.665154\pi\) | ||||
−0.495880 | + | 0.868391i | \(0.665154\pi\) | |||||||
\(774\) | 34.6847 | − | 9.26865i | 1.24671 | − | 0.333155i | ||||
\(775\) | 7.16461i | 0.257360i | ||||||||
\(776\) | 3.26398i | 0.117170i | ||||||||
\(777\) | −0.798820 | − | 6.08350i | −0.0286575 | − | 0.218244i | ||||
\(778\) | 13.5545i | 0.485953i | ||||||||
\(779\) | −1.95410 | − | 2.90199i | −0.0700127 | − | 0.103975i | ||||
\(780\) | −4.20912 | + | 0.552696i | −0.150711 | + | 0.0197897i | ||||
\(781\) | 12.3319i | 0.441272i | ||||||||
\(782\) | −2.64514 | −0.0945898 | ||||||||
\(783\) | 16.4952 | − | 6.81298i | 0.589490 | − | 0.243476i | ||||
\(784\) | −6.60059 | −0.235735 | ||||||||
\(785\) | − | 14.0338i | − | 0.500890i | ||||||
\(786\) | 4.53262 | + | 34.5187i | 0.161673 | + | 1.23124i | ||||
\(787\) | − | 54.0584i | − | 1.92698i | −0.267753 | − | 0.963488i | \(-0.586281\pi\) | ||
0.267753 | − | 0.963488i | \(-0.413719\pi\) | |||||||
\(788\) | − | 19.0352i | − | 0.678101i | ||||||
\(789\) | 5.84141 | + | 44.4859i | 0.207960 | + | 1.58374i | ||||
\(790\) | −4.42859 | −0.157562 | ||||||||
\(791\) | −0.446173 | −0.0158641 | ||||||||
\(792\) | 1.54900 | + | 5.79660i | 0.0550414 | + | 0.205973i | ||||
\(793\) | − | 6.62569i | − | 0.235285i | ||||||
\(794\) | −1.51795 | −0.0538700 | ||||||||
\(795\) | −1.47310 | − | 11.2185i | −0.0522454 | − | 0.397880i | ||||
\(796\) | −15.3691 | −0.544743 | ||||||||
\(797\) | 41.6148 | 1.47407 | 0.737036 | − | 0.675853i | \(-0.236225\pi\) | ||||
0.737036 | + | 0.675853i | \(0.236225\pi\) | |||||||
\(798\) | 3.15761 | + | 3.57713i | 0.111778 | + | 0.126629i | ||||
\(799\) | 25.9224 | 0.917070 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 17.1968 | − | 4.59542i | 0.607618 | − | 0.162371i | ||||
\(802\) | −9.81713 | −0.346655 | ||||||||
\(803\) | 9.78921i | 0.345454i | ||||||||
\(804\) | 3.37035 | + | 25.6672i | 0.118863 | + | 0.905214i | ||||
\(805\) | 0.513795 | 0.0181089 | ||||||||
\(806\) | −17.5604 | −0.618540 | ||||||||
\(807\) | 43.5023 | − | 5.71226i | 1.53135 | − | 0.201081i | ||||
\(808\) | − | 7.45999i | − | 0.262442i | ||||||
\(809\) | − | 50.5187i | − | 1.77614i | −0.459706 | − | 0.888071i | \(-0.652045\pi\) | ||
0.459706 | − | 0.888071i | \(-0.347955\pi\) | |||||||
\(810\) | 4.48948 | + | 7.80030i | 0.157744 | + | 0.274074i | ||||
\(811\) | − | 16.1447i | − | 0.566916i | −0.958985 | − | 0.283458i | \(-0.908518\pi\) | ||
0.958985 | − | 0.283458i | \(-0.0914816\pi\) | |||||||
\(812\) | 2.17064 | 0.0761745 | ||||||||
\(813\) | −30.1901 | + | 3.96424i | −1.05881 | + | 0.139032i | ||||
\(814\) | 11.2105 | 0.392928 | ||||||||
\(815\) | 19.3765i | 0.678729i | ||||||||
\(816\) | −0.733688 | − | 5.58748i | −0.0256842 | − | 0.195601i | ||||
\(817\) | 29.1357 | + | 43.2689i | 1.01933 | + | 1.51379i | ||||
\(818\) | 18.1453i | 0.634434i | ||||||||
\(819\) | −1.19970 | − | 4.48948i | −0.0419211 | − | 0.156875i | ||||
\(820\) | − | 0.802629i | − | 0.0280290i | ||||||
\(821\) | 11.9793i | 0.418080i | 0.977907 | + | 0.209040i | \(0.0670339\pi\) | ||||
−0.977907 | + | 0.209040i | \(0.932966\pi\) | |||||||
\(822\) | −1.86912 | − | 14.2345i | −0.0651931 | − | 0.496485i | ||||
\(823\) | 8.11609 | 0.282909 | 0.141455 | − | 0.989945i | \(-0.454822\pi\) | ||||
0.141455 | + | 0.989945i | \(0.454822\pi\) | |||||||
\(824\) | − | 17.9345i | − | 0.624777i | ||||||
\(825\) | −0.450997 | − | 3.43462i | −0.0157017 | − | 0.119578i | ||||
\(826\) | 1.32211 | 0.0460020 | ||||||||
\(827\) | −5.83870 | −0.203031 | −0.101516 | − | 0.994834i | \(-0.532369\pi\) | ||||
−0.101516 | + | 0.994834i | \(0.532369\pi\) | |||||||
\(828\) | −0.629655 | − | 2.35626i | −0.0218820 | − | 0.0818858i | ||||
\(829\) | − | 15.7254i | − | 0.546166i | −0.961991 | − | 0.273083i | \(-0.911957\pi\) | ||
0.961991 | − | 0.273083i | \(-0.0880433\pi\) | |||||||
\(830\) | 5.86788 | 0.203677 | ||||||||
\(831\) | −37.1403 | + | 4.87687i | −1.28838 | + | 0.169177i | ||||
\(832\) | 2.45100i | 0.0849730i | ||||||||
\(833\) | − | 21.4759i | − | 0.744094i | ||||||
\(834\) | −0.336612 | + | 0.0442003i | −0.0116559 | + | 0.00153053i | ||||
\(835\) | − | 9.23122i | − | 0.319460i | ||||||
\(836\) | −7.23122 | + | 4.86924i | −0.250097 | + | 0.168406i | ||||
\(837\) | 14.2119 | + | 34.4090i | 0.491234 | + | 1.18935i | ||||
\(838\) | − | 15.0145i | − | 0.518667i | ||||||
\(839\) | −34.7796 | −1.20073 | −0.600363 | − | 0.799728i | \(-0.704977\pi\) | ||||
−0.600363 | + | 0.799728i | \(0.704977\pi\) | |||||||
\(840\) | 0.142513 | + | 1.08532i | 0.00491715 | + | 0.0374471i | ||||
\(841\) | −17.2034 | −0.593221 | ||||||||
\(842\) | − | 24.4341i | − | 0.842055i | ||||||
\(843\) | 37.1966 | − | 4.88426i | 1.28112 | − | 0.168223i | ||||
\(844\) | − | 2.13976i | − | 0.0736534i | ||||||
\(845\) | − | 6.99261i | − | 0.240553i | ||||||
\(846\) | 6.17064 | + | 23.0915i | 0.212151 | + | 0.793901i | ||||
\(847\) | −4.42392 | −0.152008 | ||||||||
\(848\) | −6.53262 | −0.224331 | ||||||||
\(849\) | 26.1258 | − | 3.43056i | 0.896636 | − | 0.117737i | ||||
\(850\) | 3.25363i | 0.111598i | ||||||||
\(851\) | −4.55697 | −0.156211 | ||||||||
\(852\) | 10.5889 | − | 1.39042i | 0.362769 | − | 0.0476349i | ||||
\(853\) | 1.55935 | 0.0533913 | 0.0266956 | − | 0.999644i | \(-0.491502\pi\) | ||||
0.0266956 | + | 0.999644i | \(0.491502\pi\) | |||||||
\(854\) | −1.70843 | −0.0584614 | ||||||||
\(855\) | −8.59351 | + | 9.85655i | −0.293892 | + | 0.337087i | ||||
\(856\) | −5.63063 | −0.192451 | ||||||||
\(857\) | −31.4649 | −1.07482 | −0.537410 | − | 0.843321i | \(-0.680597\pi\) | ||||
−0.537410 | + | 0.843321i | \(0.680597\pi\) | |||||||
\(858\) | 8.41824 | − | 1.10539i | 0.287394 | − | 0.0377375i | ||||
\(859\) | 36.4445 | 1.24347 | 0.621734 | − | 0.783228i | \(-0.286428\pi\) | ||||
0.621734 | + | 0.783228i | \(0.286428\pi\) | |||||||
\(860\) | 11.9672i | 0.408080i | ||||||||
\(861\) | 0.871110 | − | 0.114385i | 0.0296873 | − | 0.00389822i | ||||
\(862\) | −41.0522 | −1.39824 | ||||||||
\(863\) | 52.3041 | 1.78045 | 0.890226 | − | 0.455519i | \(-0.150546\pi\) | ||||
0.890226 | + | 0.455519i | \(0.150546\pi\) | |||||||
\(864\) | 4.80263 | − | 1.98362i | 0.163389 | − | 0.0674842i | ||||
\(865\) | 1.98794i | 0.0675921i | ||||||||
\(866\) | 18.0121i | 0.612075i | ||||||||
\(867\) | −11.0147 | + | 1.44633i | −0.374078 | + | 0.0491199i | ||||
\(868\) | 4.52796i | 0.153689i | ||||||||
\(869\) | 8.85718 | 0.300459 | ||||||||
\(870\) | 0.774501 | + | 5.89830i | 0.0262581 | + | 0.199971i | ||||
\(871\) | 36.6331 | 1.24126 | ||||||||
\(872\) | − | 8.71362i | − | 0.295080i | ||||||
\(873\) | −2.52796 | − | 9.45999i | −0.0855583 | − | 0.320172i | ||||
\(874\) | 2.93942 | − | 1.97930i | 0.0994274 | − | 0.0669507i | ||||
\(875\) | − | 0.631989i | − | 0.0213651i | ||||||
\(876\) | 8.40555 | − | 1.10373i | 0.283997 | − | 0.0372915i | ||||
\(877\) | 25.0259i | 0.845066i | 0.906347 | + | 0.422533i | \(0.138859\pi\) | ||||
−0.906347 | + | 0.422533i | \(0.861141\pi\) | |||||||
\(878\) | − | 27.8024i | − | 0.938284i | ||||||
\(879\) | −9.25596 | + | 1.21539i | −0.312196 | + | 0.0409942i | ||||
\(880\) | −2.00000 | −0.0674200 | ||||||||
\(881\) | − | 12.4597i | − | 0.419779i | −0.977725 | − | 0.209889i | \(-0.932690\pi\) | ||
0.977725 | − | 0.209889i | \(-0.0673104\pi\) | |||||||
\(882\) | 19.1305 | − | 5.11217i | 0.644157 | − | 0.172136i | ||||
\(883\) | 3.72152 | 0.125239 | 0.0626195 | − | 0.998037i | \(-0.480055\pi\) | ||||
0.0626195 | + | 0.998037i | \(0.480055\pi\) | |||||||
\(884\) | −7.97463 | −0.268216 | ||||||||
\(885\) | 0.471738 | + | 3.59257i | 0.0158573 | + | 0.120763i | ||||
\(886\) | − | 10.0366i | − | 0.337185i | ||||||
\(887\) | −8.17531 | −0.274500 | −0.137250 | − | 0.990536i | \(-0.543826\pi\) | ||||
−0.137250 | + | 0.990536i | \(0.543826\pi\) | |||||||
\(888\) | −1.26398 | − | 9.62596i | −0.0424163 | − | 0.323026i | ||||
\(889\) | 3.07730i | 0.103209i | ||||||||
\(890\) | 5.93339i | 0.198888i | ||||||||
\(891\) | −8.97895 | − | 15.6006i | −0.300806 | − | 0.522639i | ||||
\(892\) | 17.9044i | 0.599485i | ||||||||
\(893\) | −28.8064 | + | 19.3972i | −0.963971 | + | 0.649102i | ||||
\(894\) | −2.57277 | − | 19.5932i | −0.0860463 | − | 0.655295i | ||||
\(895\) | 11.4938i | 0.384197i | ||||||||
\(896\) | 0.631989 | 0.0211133 | ||||||||
\(897\) | −3.42193 | + | 0.449331i | −0.114255 | + | 0.0150027i | ||||
\(898\) | 33.9055 | 1.13144 | ||||||||
\(899\) | 24.6077i | 0.820713i | ||||||||
\(900\) | −2.89830 | + | 0.774501i | −0.0966100 | + | 0.0258167i | ||||
\(901\) | − | 21.2547i | − | 0.708097i | ||||||
\(902\) | 1.60526i | 0.0534493i | ||||||||
\(903\) | −12.9883 | + | 1.70548i | −0.432223 | + | 0.0567549i | ||||
\(904\) | −0.705983 | −0.0234806 | ||||||||
\(905\) | −18.1671 | −0.603894 | ||||||||
\(906\) | −2.30276 | − | 17.5369i | −0.0765042 | − | 0.582626i | ||||
\(907\) | 13.5724i | 0.450665i | 0.974282 | + | 0.225332i | \(0.0723468\pi\) | ||||
−0.974282 | + | 0.225332i | \(0.927653\pi\) | |||||||
\(908\) | 3.97463 | 0.131903 | ||||||||
\(909\) | 5.77777 | + | 21.6213i | 0.191637 | + | 0.717133i | ||||
\(910\) | 1.54900 | 0.0513489 | ||||||||
\(911\) | −41.6636 | −1.38038 | −0.690189 | − | 0.723629i | \(-0.742472\pi\) | ||||
−0.690189 | + | 0.723629i | \(0.742472\pi\) | |||||||
\(912\) | 4.99631 | + | 5.66012i | 0.165444 | + | 0.187425i | ||||
\(913\) | −11.7358 | −0.388397 | ||||||||
\(914\) | 31.7131 | 1.04898 | ||||||||
\(915\) | −0.609582 | − | 4.64234i | −0.0201522 | − | 0.153471i | ||||
\(916\) | 13.5932 | 0.449132 | ||||||||
\(917\) | − | 12.7033i | − | 0.419499i | ||||||
\(918\) | 6.45396 | + | 15.6260i | 0.213012 | + | 0.515734i | ||||
\(919\) | 27.9916 | 0.923357 | 0.461679 | − | 0.887047i | \(-0.347247\pi\) | ||||
0.461679 | + | 0.887047i | \(0.347247\pi\) | |||||||
\(920\) | 0.812981 | 0.0268032 | ||||||||
\(921\) | −0.128546 | − | 0.978953i | −0.00423572 | − | 0.0322576i | ||||
\(922\) | 23.1029i | 0.760854i | ||||||||
\(923\) | − | 15.1128i | − | 0.497443i | ||||||
\(924\) | −0.285025 | − | 2.17064i | −0.00937664 | − | 0.0714088i | ||||
\(925\) | 5.60526i | 0.184300i | ||||||||
\(926\) | −32.6950 | −1.07442 | ||||||||
\(927\) | 13.8903 | + | 51.9795i | 0.456217 | + | 1.70723i | ||||
\(928\) | 3.43462 | 0.112747 | ||||||||
\(929\) | − | 15.0942i | − | 0.495224i | −0.968859 | − | 0.247612i | \(-0.920354\pi\) | ||
0.968859 | − | 0.247612i | \(-0.0796458\pi\) | |||||||
\(930\) | −12.3039 | + | 1.61561i | −0.403459 | + | 0.0529779i | ||||
\(931\) | 16.0699 | + | 23.8652i | 0.526670 | + | 0.782149i | ||||
\(932\) | − | 21.2323i | − | 0.695487i | ||||||
\(933\) | −1.89091 | − | 14.4005i | −0.0619057 | − | 0.471450i | ||||
\(934\) | − | 29.2023i | − | 0.955527i | ||||||
\(935\) | − | 6.50725i | − | 0.212810i | ||||||
\(936\) | −1.89830 | − | 7.10373i | −0.0620479 | − | 0.232193i | ||||
\(937\) | −53.5045 | −1.74792 | −0.873958 | − | 0.486002i | \(-0.838455\pi\) | ||||
−0.873958 | + | 0.486002i | \(0.838455\pi\) | |||||||
\(938\) | − | 9.44583i | − | 0.308417i | ||||||
\(939\) | −42.3073 | + | 5.55534i | −1.38065 | + | 0.181292i | ||||
\(940\) | −7.96724 | −0.259863 | ||||||||
\(941\) | 2.22682 | 0.0725922 | 0.0362961 | − | 0.999341i | \(-0.488444\pi\) | ||||
0.0362961 | + | 0.999341i | \(0.488444\pi\) | |||||||
\(942\) | 24.1005 | − | 3.16461i | 0.785235 | − | 0.103109i | ||||
\(943\) | − | 0.652522i | − | 0.0212490i | ||||||
\(944\) | 2.09198 | 0.0680881 | ||||||||
\(945\) | −1.25363 | − | 3.03521i | −0.0407805 | − | 0.0987353i | ||||
\(946\) | − | 23.9345i | − | 0.778177i | ||||||
\(947\) | − | 41.4103i | − | 1.34566i | −0.739799 | − | 0.672828i | \(-0.765080\pi\) | ||
0.739799 | − | 0.672828i | \(-0.234920\pi\) | |||||||
\(948\) | −0.998641 | − | 7.60526i | −0.0324343 | − | 0.247007i | ||||
\(949\) | − | 11.9967i | − | 0.389428i | ||||||
\(950\) | −2.43462 | − | 3.61561i | −0.0789894 | − | 0.117306i | ||||
\(951\) | 29.2065 | − | 3.83508i | 0.947085 | − | 0.124361i | ||||
\(952\) | 2.05626i | 0.0666436i | ||||||||
\(953\) | 23.7444 | 0.769157 | 0.384578 | − | 0.923092i | \(-0.374347\pi\) | ||||
0.384578 | + | 0.923092i | \(0.374347\pi\) | |||||||
\(954\) | 18.9335 | − | 5.05953i | 0.612995 | − | 0.163808i | ||||
\(955\) | −2.80093 | −0.0906358 | ||||||||
\(956\) | 22.2899i | 0.720908i | ||||||||
\(957\) | −1.54900 | − | 11.7966i | −0.0500722 | − | 0.381330i | ||||
\(958\) | − | 17.7712i | − | 0.574162i | ||||||
\(959\) | 5.23845i | 0.169158i | ||||||||
\(960\) | 0.225499 | + | 1.71731i | 0.00727793 | + | 0.0554259i | ||||
\(961\) | −20.3317 | −0.655861 | ||||||||
\(962\) | −13.7385 | −0.442946 | ||||||||
\(963\) | 16.3193 | − | 4.36093i | 0.525881 | − | 0.140529i | ||||
\(964\) | 4.19873i | 0.135232i | ||||||||
\(965\) | 15.9552 | 0.513616 | ||||||||
\(966\) | 0.115860 | + | 0.882344i | 0.00372773 | + | 0.0283890i | ||||
\(967\) | 39.8400 | 1.28117 | 0.640584 | − | 0.767888i | \(-0.278692\pi\) | ||||
0.640584 | + | 0.767888i | \(0.278692\pi\) | |||||||
\(968\) | −7.00000 | −0.224989 | ||||||||
\(969\) | −18.4159 | + | 16.2561i | −0.591604 | + | 0.522222i | ||||
\(970\) | 3.26398 | 0.104800 | ||||||||
\(971\) | −4.70489 | −0.150987 | −0.0754936 | − | 0.997146i | \(-0.524053\pi\) | ||||
−0.0754936 | + | 0.997146i | \(0.524053\pi\) | |||||||
\(972\) | −12.3831 | + | 9.46877i | −0.397190 | + | 0.303711i | ||||
\(973\) | 0.123877 | 0.00397132 | ||||||||
\(974\) | − | 10.3620i | − | 0.332019i | ||||||
\(975\) | 0.552696 | + | 4.20912i | 0.0177004 | + | 0.134800i | ||||
\(976\) | −2.70326 | −0.0865294 | ||||||||
\(977\) | −38.3620 | −1.22731 | −0.613654 | − | 0.789575i | \(-0.710301\pi\) | ||||
−0.613654 | + | 0.789575i | \(0.710301\pi\) | |||||||
\(978\) | −33.2754 | + | 4.36937i | −1.06403 | + | 0.139717i | ||||
\(979\) | − | 11.8668i | − | 0.379264i | ||||||
\(980\) | 6.60059i | 0.210848i | ||||||||
\(981\) | 6.74871 | + | 25.2547i | 0.215470 | + | 0.806320i | ||||
\(982\) | 16.8993i | 0.539278i | ||||||||
\(983\) | 26.8720 | 0.857082 | 0.428541 | − | 0.903522i | \(-0.359028\pi\) | ||||
0.428541 | + | 0.903522i | \(0.359028\pi\) | |||||||
\(984\) | 1.37836 | − | 0.180992i | 0.0439406 | − | 0.00576981i | ||||
\(985\) | −19.0352 | −0.606512 | ||||||||
\(986\) | 11.1750i | 0.355883i | ||||||||
\(987\) | −1.13543 | − | 8.64701i | −0.0361412 | − | 0.275237i | ||||
\(988\) | 8.86185 | − | 5.96724i | 0.281933 | − | 0.189843i | ||||
\(989\) | 9.72914i | 0.309369i | ||||||||
\(990\) | 5.79660 | − | 1.54900i | 0.184228 | − | 0.0492305i | ||||
\(991\) | 19.9782i | 0.634629i | 0.948320 | + | 0.317314i | \(0.102781\pi\) | ||||
−0.948320 | + | 0.317314i | \(0.897219\pi\) | |||||||
\(992\) | 7.16461i | 0.227477i | ||||||||
\(993\) | 2.19810 | + | 16.7399i | 0.0697546 | + | 0.531224i | ||||
\(994\) | −3.89683 | −0.123600 | ||||||||
\(995\) | 15.3691i | 0.487233i | ||||||||
\(996\) | 1.32320 | + | 10.0770i | 0.0419271 | + | 0.319301i | ||||
\(997\) | 36.8316 | 1.16647 | 0.583235 | − | 0.812304i | \(-0.301787\pi\) | ||||
0.583235 | + | 0.812304i | \(0.301787\pi\) | |||||||
\(998\) | −0.364702 | −0.0115444 | ||||||||
\(999\) | 11.1187 | + | 26.9200i | 0.351780 | + | 0.851710i |
(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 | 570.2.f.c.341.2 | yes | 8 | |
3.2 | odd | 2 | 570.2.f.d.341.8 | yes | 8 | ||
19.18 | odd | 2 | 570.2.f.d.341.7 | yes | 8 | ||
57.56 | even | 2 | inner | 570.2.f.c.341.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.f.c.341.1 | ✓ | 8 | 57.56 | even | 2 | inner | |
570.2.f.c.341.2 | yes | 8 | 1.1 | even | 1 | trivial | |
570.2.f.d.341.7 | yes | 8 | 19.18 | odd | 2 | ||
570.2.f.d.341.8 | yes | 8 | 3.2 | odd | 2 |