Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1710,2,Mod(647,1710)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1710, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 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("1710.647");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1710.n (of order \(4\), degree \(2\), 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: | \(13.6544187456\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 2 x^{14} + 24 x^{13} + 2 x^{12} - 48 x^{11} + 88 x^{10} - 72 x^{9} + 18 x^{8} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1673.2 | ||
Root | \(-1.97269 - 0.817117i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1710.1673 |
Dual form | 1710.2.n.h.647.2 |
$q$-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 \(\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(1027\) | \(1351\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | −0.379071 | + | 2.20370i | −0.169526 | + | 0.985526i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.44579 | − | 2.44579i | 0.924421 | − | 0.924421i | −0.0729174 | − | 0.997338i | \(-0.523231\pi\) |
0.997338 | + | 0.0729174i | \(0.0232309\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.82630 | − | 1.29021i | 0.577526 | − | 0.408000i | ||||
\(11\) | − | 1.85425i | − | 0.559078i | −0.960134 | − | 0.279539i | \(-0.909818\pi\) | ||
0.960134 | − | 0.279539i | \(-0.0901817\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.11651 | − | 2.11651i | −0.587013 | − | 0.587013i | 0.349808 | − | 0.936821i | \(-0.386247\pi\) |
−0.936821 | + | 0.349808i | \(0.886247\pi\) | |||||||
\(14\) | −3.45887 | −0.924421 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −2.29031 | − | 2.29031i | −0.555481 | − | 0.555481i | 0.372537 | − | 0.928017i | \(-0.378488\pi\) |
−0.928017 | + | 0.372537i | \(0.878488\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.00000i | − | 0.229416i | ||||||
\(20\) | −2.20370 | − | 0.379071i | −0.492763 | − | 0.0847628i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.31116 | + | 1.31116i | −0.279539 | + | 0.279539i | ||||
\(23\) | −2.39238 | + | 2.39238i | −0.498845 | + | 0.498845i | −0.911078 | − | 0.412233i | \(-0.864749\pi\) |
0.412233 | + | 0.911078i | \(0.364749\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.71261 | − | 1.67072i | −0.942522 | − | 0.334144i | ||||
\(26\) | 2.99319i | 0.587013i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.44579 | + | 2.44579i | 0.462210 | + | 0.462210i | ||||
\(29\) | −6.09689 | −1.13216 | −0.566082 | − | 0.824349i | \(-0.691542\pi\) | ||||
−0.566082 | + | 0.824349i | \(0.691542\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.81940 | 0.326774 | 0.163387 | − | 0.986562i | \(-0.447758\pi\) | ||||
0.163387 | + | 0.986562i | \(0.447758\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.23898i | 0.555481i | ||||||||
\(35\) | 4.46266 | + | 6.31691i | 0.754327 | + | 1.06775i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.38577 | − | 4.38577i | 0.721016 | − | 0.721016i | −0.247796 | − | 0.968812i | \(-0.579706\pi\) |
0.968812 | + | 0.247796i | \(0.0797063\pi\) | |||||||
\(38\) | −0.707107 | + | 0.707107i | −0.114708 | + | 0.114708i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.29021 | + | 1.82630i | 0.204000 | + | 0.288763i | ||||
\(41\) | 4.05224i | 0.632854i | 0.948617 | + | 0.316427i | \(0.102483\pi\) | ||||
−0.948617 | + | 0.316427i | \(0.897517\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.27490 | − | 7.27490i | −1.10941 | − | 1.10941i | −0.993228 | − | 0.116185i | \(-0.962934\pi\) |
−0.116185 | − | 0.993228i | \(-0.537066\pi\) | |||||||
\(44\) | 1.85425 | 0.279539 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.38333 | 0.498845 | ||||||||
\(47\) | 1.44384 | + | 1.44384i | 0.210605 | + | 0.210605i | 0.804524 | − | 0.593919i | \(-0.202420\pi\) |
−0.593919 | + | 0.804524i | \(0.702420\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 4.96375i | − | 0.709107i | ||||||
\(50\) | 2.15094 | + | 4.51370i | 0.304189 | + | 0.638333i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.11651 | − | 2.11651i | 0.293507 | − | 0.293507i | ||||
\(53\) | 1.03342 | − | 1.03342i | 0.141951 | − | 0.141951i | −0.632560 | − | 0.774511i | \(-0.717996\pi\) |
0.774511 | + | 0.632560i | \(0.217996\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.08622 | + | 0.702894i | 0.550986 | + | 0.0947781i | ||||
\(56\) | − | 3.45887i | − | 0.462210i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.31116 | + | 4.31116i | 0.566082 | + | 0.566082i | ||||
\(59\) | −3.94173 | −0.513170 | −0.256585 | − | 0.966522i | \(-0.582597\pi\) | ||||
−0.256585 | + | 0.966522i | \(0.582597\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.18060 | −0.279197 | −0.139599 | − | 0.990208i | \(-0.544581\pi\) | ||||
−0.139599 | + | 0.990208i | \(0.544581\pi\) | |||||||
\(62\) | −1.28651 | − | 1.28651i | −0.163387 | − | 0.163387i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 5.46646 | − | 3.86184i | 0.678030 | − | 0.479003i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.80291 | − | 4.80291i | 0.586769 | − | 0.586769i | −0.349986 | − | 0.936755i | \(-0.613814\pi\) |
0.936755 | + | 0.349986i | \(0.113814\pi\) | |||||||
\(68\) | 2.29031 | − | 2.29031i | 0.277740 | − | 0.277740i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.31116 | − | 7.62231i | 0.156713 | − | 0.911040i | ||||
\(71\) | 2.06683i | 0.245288i | 0.992451 | + | 0.122644i | \(0.0391373\pi\) | ||||
−0.992451 | + | 0.122644i | \(0.960863\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.58606 | − | 9.58606i | −1.12196 | − | 1.12196i | −0.991446 | − | 0.130517i | \(-0.958336\pi\) |
−0.130517 | − | 0.991446i | \(-0.541664\pi\) | |||||||
\(74\) | −6.20242 | −0.721016 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −4.53511 | − | 4.53511i | −0.516824 | − | 0.516824i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1.43010i | − | 0.160899i | −0.996759 | − | 0.0804495i | \(-0.974364\pi\) | ||
0.996759 | − | 0.0804495i | \(-0.0256356\pi\) | |||||||
\(80\) | 0.379071 | − | 2.20370i | 0.0423814 | − | 0.246381i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.86537 | − | 2.86537i | 0.316427 | − | 0.316427i | ||||
\(83\) | 2.48070 | − | 2.48070i | 0.272293 | − | 0.272293i | −0.557730 | − | 0.830022i | \(-0.688328\pi\) |
0.830022 | + | 0.557730i | \(0.188328\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.91534 | − | 4.17896i | 0.641609 | − | 0.453272i | ||||
\(86\) | 10.2883i | 1.10941i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.31116 | − | 1.31116i | −0.139770 | − | 0.139770i | ||||
\(89\) | −13.4176 | −1.42226 | −0.711132 | − | 0.703059i | \(-0.751817\pi\) | ||||
−0.711132 | + | 0.703059i | \(0.751817\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.3530 | −1.08529 | ||||||||
\(92\) | −2.39238 | − | 2.39238i | −0.249422 | − | 0.249422i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 2.04189i | − | 0.210605i | ||||||
\(95\) | 2.20370 | + | 0.379071i | 0.226095 | + | 0.0388919i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.00000 | − | 4.00000i | 0.406138 | − | 0.406138i | −0.474251 | − | 0.880390i | \(-0.657281\pi\) |
0.880390 | + | 0.474251i | \(0.157281\pi\) | |||||||
\(98\) | −3.50990 | + | 3.50990i | −0.354553 | + | 0.354553i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.67072 | − | 4.71261i | 0.167072 | − | 0.471261i | ||||
\(101\) | − | 19.4889i | − | 1.93921i | −0.244667 | − | 0.969607i | \(-0.578679\pi\) | ||
0.244667 | − | 0.969607i | \(-0.421321\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.23654 | + | 4.23654i | 0.417439 | + | 0.417439i | 0.884320 | − | 0.466881i | \(-0.154622\pi\) |
−0.466881 | + | 0.884320i | \(0.654622\pi\) | |||||||
\(104\) | −2.99319 | −0.293507 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.46147 | −0.141951 | ||||||||
\(107\) | −1.11330 | − | 1.11330i | −0.107627 | − | 0.107627i | 0.651242 | − | 0.758870i | \(-0.274248\pi\) |
−0.758870 | + | 0.651242i | \(0.774248\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.40579i | 0.326215i | 0.986608 | + | 0.163108i | \(0.0521518\pi\) | ||||
−0.986608 | + | 0.163108i | \(0.947848\pi\) | |||||||
\(110\) | −2.39238 | − | 3.38642i | −0.228104 | − | 0.322882i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.44579 | + | 2.44579i | −0.231105 | + | 0.231105i | ||||
\(113\) | 1.01123 | − | 1.01123i | 0.0951289 | − | 0.0951289i | −0.657941 | − | 0.753070i | \(-0.728572\pi\) |
0.753070 | + | 0.657941i | \(0.228572\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.36520 | − | 6.17896i | −0.407057 | − | 0.576191i | ||||
\(116\) | − | 6.09689i | − | 0.566082i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.78723 | + | 2.78723i | 0.256585 | + | 0.256585i | ||||
\(119\) | −11.2032 | −1.02700 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.56174 | 0.687431 | ||||||||
\(122\) | 1.54192 | + | 1.54192i | 0.139599 | + | 0.139599i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.81940i | 0.163387i | ||||||||
\(125\) | 5.46818 | − | 9.75187i | 0.489089 | − | 0.872234i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.919417 | + | 0.919417i | −0.0815850 | + | 0.0815850i | −0.746722 | − | 0.665137i | \(-0.768373\pi\) |
0.665137 | + | 0.746722i | \(0.268373\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.59610 | − | 1.13463i | −0.578517 | − | 0.0995138i | ||||
\(131\) | − | 4.24264i | − | 0.370681i | −0.982674 | − | 0.185341i | \(-0.940661\pi\) | ||
0.982674 | − | 0.185341i | \(-0.0593388\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.44579 | − | 2.44579i | −0.212077 | − | 0.212077i | ||||
\(134\) | −6.79234 | −0.586769 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.23898 | −0.277740 | ||||||||
\(137\) | −8.15130 | − | 8.15130i | −0.696413 | − | 0.696413i | 0.267222 | − | 0.963635i | \(-0.413894\pi\) |
−0.963635 | + | 0.267222i | \(0.913894\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.18060i | 0.524232i | 0.965036 | + | 0.262116i | \(0.0844203\pi\) | ||||
−0.965036 | + | 0.262116i | \(0.915580\pi\) | |||||||
\(140\) | −6.31691 | + | 4.46266i | −0.533877 | + | 0.377164i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.46147 | − | 1.46147i | 0.122644 | − | 0.122644i | ||||
\(143\) | −3.92454 | + | 3.92454i | −0.328186 | + | 0.328186i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.31116 | − | 13.4357i | 0.191931 | − | 1.11578i | ||||
\(146\) | 13.5567i | 1.12196i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.38577 | + | 4.38577i | 0.360508 | + | 0.360508i | ||||
\(149\) | −5.71955 | −0.468564 | −0.234282 | − | 0.972169i | \(-0.575274\pi\) | ||||
−0.234282 | + | 0.972169i | \(0.575274\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.8191 | −1.36872 | −0.684358 | − | 0.729146i | \(-0.739918\pi\) | ||||
−0.684358 | + | 0.729146i | \(0.739918\pi\) | |||||||
\(152\) | −0.707107 | − | 0.707107i | −0.0573539 | − | 0.0573539i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.41361i | 0.516824i | ||||||||
\(155\) | −0.689681 | + | 4.00942i | −0.0553965 | + | 0.322044i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.82912 | + | 1.82912i | −0.145979 | + | 0.145979i | −0.776319 | − | 0.630340i | \(-0.782916\pi\) |
0.630340 | + | 0.776319i | \(0.282916\pi\) | |||||||
\(158\) | −1.01123 | + | 1.01123i | −0.0804495 | + | 0.0804495i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.82630 | + | 1.29021i | −0.144381 | + | 0.102000i | ||||
\(161\) | 11.7025i | 0.922285i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.5861 | + | 15.5861i | 1.22079 | + | 1.22079i | 0.967350 | + | 0.253444i | \(0.0815635\pi\) |
0.253444 | + | 0.967350i | \(0.418437\pi\) | |||||||
\(164\) | −4.05224 | −0.316427 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.50824 | −0.272293 | ||||||||
\(167\) | −12.1544 | − | 12.1544i | −0.940537 | − | 0.940537i | 0.0577920 | − | 0.998329i | \(-0.481594\pi\) |
−0.998329 | + | 0.0577920i | \(0.981594\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 4.04080i | − | 0.310831i | ||||||
\(170\) | −7.13775 | − | 1.22780i | −0.547440 | − | 0.0941682i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.27490 | − | 7.27490i | 0.554706 | − | 0.554706i | ||||
\(173\) | 11.9151 | − | 11.9151i | 0.905885 | − | 0.905885i | −0.0900517 | − | 0.995937i | \(-0.528703\pi\) |
0.995937 | + | 0.0900517i | \(0.0287032\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15.6123 | + | 7.43982i | −1.18018 | + | 0.562397i | ||||
\(176\) | 1.85425i | 0.139770i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 9.48768 | + | 9.48768i | 0.711132 | + | 0.711132i | ||||
\(179\) | 15.8288 | 1.18310 | 0.591552 | − | 0.806267i | \(-0.298516\pi\) | ||||
0.591552 | + | 0.806267i | \(0.298516\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.63425 | −0.195802 | −0.0979010 | − | 0.995196i | \(-0.531213\pi\) | ||||
−0.0979010 | + | 0.995196i | \(0.531213\pi\) | |||||||
\(182\) | 7.32071 | + | 7.32071i | 0.542647 | + | 0.542647i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.38333i | 0.249422i | ||||||||
\(185\) | 8.00241 | + | 11.3275i | 0.588349 | + | 0.832811i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.24681 | + | 4.24681i | −0.310557 | + | 0.310557i | ||||
\(188\) | −1.44384 | + | 1.44384i | −0.105303 | + | 0.105303i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.29021 | − | 1.82630i | −0.0936016 | − | 0.132493i | ||||
\(191\) | − | 16.9820i | − | 1.22877i | −0.789005 | − | 0.614387i | \(-0.789403\pi\) | ||
0.789005 | − | 0.614387i | \(-0.210597\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.1246 | + | 15.1246i | 1.08869 | + | 1.08869i | 0.995663 | + | 0.0930281i | \(0.0296546\pi\) |
0.0930281 | + | 0.995663i | \(0.470345\pi\) | |||||||
\(194\) | −5.65685 | −0.406138 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.96375 | 0.354553 | ||||||||
\(197\) | 10.3726 | + | 10.3726i | 0.739018 | + | 0.739018i | 0.972388 | − | 0.233370i | \(-0.0749754\pi\) |
−0.233370 | + | 0.972388i | \(0.574975\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.3411i | 1.58372i | 0.610703 | + | 0.791860i | \(0.290887\pi\) | ||||
−0.610703 | + | 0.791860i | \(0.709113\pi\) | |||||||
\(200\) | −4.51370 | + | 2.15094i | −0.319166 | + | 0.152095i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −13.7807 | + | 13.7807i | −0.969607 | + | 0.969607i | ||||
\(203\) | −14.9117 | + | 14.9117i | −1.04660 | + | 1.04660i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.92994 | − | 1.53609i | −0.623694 | − | 0.107285i | ||||
\(206\) | − | 5.99137i | − | 0.417439i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.11651 | + | 2.11651i | 0.146753 | + | 0.146753i | ||||
\(209\) | −1.85425 | −0.128261 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.6747 | −1.42331 | −0.711653 | − | 0.702531i | \(-0.752053\pi\) | ||||
−0.711653 | + | 0.702531i | \(0.752053\pi\) | |||||||
\(212\) | 1.03342 | + | 1.03342i | 0.0709754 | + | 0.0709754i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.57445i | 0.107627i | ||||||||
\(215\) | 18.7894 | − | 13.2740i | 1.28143 | − | 0.905281i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.44986 | − | 4.44986i | 0.302076 | − | 0.302076i | ||||
\(218\) | 2.40826 | − | 2.40826i | 0.163108 | − | 0.163108i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.702894 | + | 4.08622i | −0.0473891 | + | 0.275493i | ||||
\(221\) | 9.69489i | 0.652149i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.03945 | + | 7.03945i | 0.471397 | + | 0.471397i | 0.902366 | − | 0.430970i | \(-0.141828\pi\) |
−0.430970 | + | 0.902366i | \(0.641828\pi\) | |||||||
\(224\) | 3.45887 | 0.231105 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.43010 | −0.0951289 | ||||||||
\(227\) | 12.2308 | + | 12.2308i | 0.811790 | + | 0.811790i | 0.984902 | − | 0.173112i | \(-0.0553823\pi\) |
−0.173112 | + | 0.984902i | \(0.555382\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 22.0162i | − | 1.45487i | −0.686177 | − | 0.727434i | \(-0.740713\pi\) | ||
0.686177 | − | 0.727434i | \(-0.259287\pi\) | |||||||
\(230\) | −1.28252 | + | 7.45585i | −0.0845670 | + | 0.491624i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.31116 | + | 4.31116i | −0.283041 | + | 0.283041i | ||||
\(233\) | −10.0056 | + | 10.0056i | −0.655486 | + | 0.655486i | −0.954309 | − | 0.298823i | \(-0.903406\pi\) |
0.298823 | + | 0.954309i | \(0.403406\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.72910 | + | 2.63447i | −0.243260 | + | 0.171854i | ||||
\(236\) | − | 3.94173i | − | 0.256585i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.92186 | + | 7.92186i | 0.513498 | + | 0.513498i | ||||
\(239\) | −6.74453 | −0.436267 | −0.218134 | − | 0.975919i | \(-0.569997\pi\) | ||||
−0.218134 | + | 0.975919i | \(0.569997\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.7353 | −1.59334 | −0.796670 | − | 0.604415i | \(-0.793407\pi\) | ||||
−0.796670 | + | 0.604415i | \(0.793407\pi\) | |||||||
\(242\) | −5.34696 | − | 5.34696i | −0.343716 | − | 0.343716i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 2.18060i | − | 0.139599i | ||||||
\(245\) | 10.9386 | + | 1.88161i | 0.698843 | + | 0.120212i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.11651 | + | 2.11651i | −0.134670 | + | 0.134670i | ||||
\(248\) | 1.28651 | − | 1.28651i | 0.0816935 | − | 0.0816935i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −10.7622 | + | 3.02903i | −0.680661 | + | 0.191572i | ||||
\(251\) | − | 26.1657i | − | 1.65156i | −0.563989 | − | 0.825782i | \(-0.690734\pi\) | ||
0.563989 | − | 0.825782i | \(-0.309266\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.43607 | + | 4.43607i | 0.278893 | + | 0.278893i | ||||
\(254\) | 1.30025 | 0.0815850 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.39021 | − | 4.39021i | −0.273854 | − | 0.273854i | 0.556796 | − | 0.830650i | \(-0.312031\pi\) |
−0.830650 | + | 0.556796i | \(0.812031\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 21.4533i | − | 1.33304i | ||||||
\(260\) | 3.86184 | + | 5.46646i | 0.239501 | + | 0.339015i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.00000 | + | 3.00000i | −0.185341 | + | 0.185341i | ||||
\(263\) | 9.13690 | − | 9.13690i | 0.563405 | − | 0.563405i | −0.366868 | − | 0.930273i | \(-0.619570\pi\) |
0.930273 | + | 0.366868i | \(0.119570\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.88561 | + | 2.66908i | 0.115832 | + | 0.163960i | ||||
\(266\) | 3.45887i | 0.212077i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.80291 | + | 4.80291i | 0.293384 | + | 0.293384i | ||||
\(269\) | 12.9121 | 0.787264 | 0.393632 | − | 0.919268i | \(-0.371218\pi\) | ||||
0.393632 | + | 0.919268i | \(0.371218\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.8032 | −0.716996 | −0.358498 | − | 0.933531i | \(-0.616711\pi\) | ||||
−0.358498 | + | 0.933531i | \(0.616711\pi\) | |||||||
\(272\) | 2.29031 | + | 2.29031i | 0.138870 | + | 0.138870i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.5277i | 0.696413i | ||||||||
\(275\) | −3.09794 | + | 8.73837i | −0.186813 | + | 0.526944i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.2184 | − | 10.2184i | 0.613965 | − | 0.613965i | −0.330012 | − | 0.943977i | \(-0.607053\pi\) |
0.943977 | + | 0.330012i | \(0.107053\pi\) | |||||||
\(278\) | 4.37034 | − | 4.37034i | 0.262116 | − | 0.262116i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7.62231 | + | 1.31116i | 0.455520 | + | 0.0783565i | ||||
\(281\) | 19.0301i | 1.13524i | 0.823291 | + | 0.567620i | \(0.192136\pi\) | ||||
−0.823291 | + | 0.567620i | \(0.807864\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.7166 | − | 17.7166i | −1.05314 | − | 1.05314i | −0.998506 | − | 0.0546371i | \(-0.982600\pi\) |
−0.0546371 | − | 0.998506i | \(-0.517400\pi\) | |||||||
\(284\) | −2.06683 | −0.122644 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.55014 | 0.328186 | ||||||||
\(287\) | 9.91092 | + | 9.91092i | 0.585023 | + | 0.585023i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 6.50900i | − | 0.382883i | ||||||
\(290\) | −11.1347 | + | 7.86627i | −0.653854 | + | 0.461923i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 9.58606 | − | 9.58606i | 0.560982 | − | 0.560982i | ||||
\(293\) | 11.0892 | − | 11.0892i | 0.647840 | − | 0.647840i | −0.304631 | − | 0.952471i | \(-0.598533\pi\) |
0.952471 | + | 0.304631i | \(0.0985330\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.49420 | − | 8.68640i | 0.0869954 | − | 0.505742i | ||||
\(296\) | − | 6.20242i | − | 0.360508i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.04433 | + | 4.04433i | 0.234282 | + | 0.234282i | ||||
\(299\) | 10.1270 | 0.585657 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −35.5857 | −2.05113 | ||||||||
\(302\) | 11.8929 | + | 11.8929i | 0.684358 | + | 0.684358i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.00000i | 0.0573539i | ||||||||
\(305\) | 0.826602 | − | 4.80539i | 0.0473311 | − | 0.275156i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.7304 | − | 16.7304i | 0.954855 | − | 0.954855i | −0.0441693 | − | 0.999024i | \(-0.514064\pi\) |
0.999024 | + | 0.0441693i | \(0.0140641\pi\) | |||||||
\(308\) | 4.53511 | − | 4.53511i | 0.258412 | − | 0.258412i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.32276 | − | 2.34741i | 0.188720 | − | 0.133324i | ||||
\(311\) | − | 11.1802i | − | 0.633973i | −0.948430 | − | 0.316987i | \(-0.897329\pi\) | ||
0.948430 | − | 0.316987i | \(-0.102671\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.6888 | + | 10.6888i | 0.604169 | + | 0.604169i | 0.941416 | − | 0.337247i | \(-0.109496\pi\) |
−0.337247 | + | 0.941416i | \(0.609496\pi\) | |||||||
\(314\) | 2.58676 | 0.145979 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.43010 | 0.0804495 | ||||||||
\(317\) | 16.9307 | + | 16.9307i | 0.950924 | + | 0.950924i | 0.998851 | − | 0.0479267i | \(-0.0152614\pi\) |
−0.0479267 | + | 0.998851i | \(0.515261\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.3052i | 0.632969i | ||||||||
\(320\) | 2.20370 | + | 0.379071i | 0.123191 | + | 0.0211907i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.27490 | − | 8.27490i | 0.461142 | − | 0.461142i | ||||
\(323\) | −2.29031 | + | 2.29031i | −0.127436 | + | 0.127436i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.43818 | + | 13.5104i | 0.357126 | + | 0.749420i | ||||
\(326\) | − | 22.0420i | − | 1.22079i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.86537 | + | 2.86537i | 0.158213 | + | 0.158213i | ||||
\(329\) | 7.06263 | 0.389375 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.54526 | 0.194865 | 0.0974324 | − | 0.995242i | \(-0.468937\pi\) | ||||
0.0974324 | + | 0.995242i | \(0.468937\pi\) | |||||||
\(332\) | 2.48070 | + | 2.48070i | 0.136146 | + | 0.136146i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 17.1889i | 0.940537i | ||||||||
\(335\) | 8.76354 | + | 12.4048i | 0.478804 | + | 0.677748i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.5139 | − | 21.5139i | 1.17194 | − | 1.17194i | 0.190188 | − | 0.981748i | \(-0.439090\pi\) |
0.981748 | − | 0.190188i | \(-0.0609099\pi\) | |||||||
\(338\) | −2.85728 | + | 2.85728i | −0.155416 | + | 0.155416i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.17896 | + | 5.91534i | 0.226636 | + | 0.320804i | ||||
\(341\) | − | 3.37363i | − | 0.182692i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.98024 | + | 4.98024i | 0.268908 | + | 0.268908i | ||||
\(344\) | −10.2883 | −0.554706 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −16.8504 | −0.905885 | ||||||||
\(347\) | −19.8400 | − | 19.8400i | −1.06507 | − | 1.06507i | −0.997730 | − | 0.0673389i | \(-0.978549\pi\) |
−0.0673389 | − | 0.997730i | \(-0.521451\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.3808i | 1.35860i | 0.733859 | + | 0.679302i | \(0.237717\pi\) | ||||
−0.733859 | + | 0.679302i | \(0.762283\pi\) | |||||||
\(350\) | 16.3003 | + | 5.77879i | 0.871287 | + | 0.308889i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.31116 | − | 1.31116i | 0.0698848 | − | 0.0698848i | ||||
\(353\) | 12.0280 | − | 12.0280i | 0.640187 | − | 0.640187i | −0.310414 | − | 0.950601i | \(-0.600468\pi\) |
0.950601 | + | 0.310414i | \(0.100468\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.55469 | − | 0.783477i | −0.241738 | − | 0.0415826i | ||||
\(356\) | − | 13.4176i | − | 0.711132i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.1927 | − | 11.1927i | −0.591552 | − | 0.591552i | ||||
\(359\) | −4.14510 | −0.218770 | −0.109385 | − | 0.993999i | \(-0.534888\pi\) | ||||
−0.109385 | + | 0.993999i | \(0.534888\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 1.86269 | + | 1.86269i | 0.0979010 | + | 0.0979010i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 10.3530i | − | 0.542647i | ||||||
\(365\) | 24.7586 | − | 17.4910i | 1.29593 | − | 0.915522i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.5236 | + | 17.5236i | −0.914725 | + | 0.914725i | −0.996639 | − | 0.0819148i | \(-0.973896\pi\) |
0.0819148 | + | 0.996639i | \(0.473896\pi\) | |||||||
\(368\) | 2.39238 | − | 2.39238i | 0.124711 | − | 0.124711i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.35116 | − | 13.6683i | 0.122231 | − | 0.710580i | ||||
\(371\) | − | 5.05504i | − | 0.262444i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.4452 | + | 14.4452i | 0.747946 | + | 0.747946i | 0.974093 | − | 0.226147i | \(-0.0726130\pi\) |
−0.226147 | + | 0.974093i | \(0.572613\pi\) | |||||||
\(374\) | 6.00589 | 0.310557 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.04189 | 0.105303 | ||||||||
\(377\) | 12.9041 | + | 12.9041i | 0.664596 | + | 0.664596i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.12491i | 0.417349i | 0.977985 | + | 0.208674i | \(0.0669149\pi\) | ||||
−0.977985 | + | 0.208674i | \(0.933085\pi\) | |||||||
\(380\) | −0.379071 | + | 2.20370i | −0.0194459 | + | 0.113048i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −12.0081 | + | 12.0081i | −0.614387 | + | 0.614387i | ||||
\(383\) | −23.6409 | + | 23.6409i | −1.20799 | + | 1.20799i | −0.236315 | + | 0.971676i | \(0.575940\pi\) |
−0.971676 | + | 0.236315i | \(0.924060\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.7132 | − | 8.27490i | 0.596958 | − | 0.421728i | ||||
\(386\) | − | 21.3894i | − | 1.08869i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.00000 | + | 4.00000i | 0.203069 | + | 0.203069i | ||||
\(389\) | 8.51622 | 0.431789 | 0.215895 | − | 0.976417i | \(-0.430733\pi\) | ||||
0.215895 | + | 0.976417i | \(0.430733\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.9585 | 0.554197 | ||||||||
\(392\) | −3.50990 | − | 3.50990i | −0.177277 | − | 0.177277i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 14.6691i | − | 0.739018i | ||||||
\(395\) | 3.15152 | + | 0.542110i | 0.158570 | + | 0.0272765i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.7675 | − | 18.7675i | 0.941912 | − | 0.941912i | −0.0564911 | − | 0.998403i | \(-0.517991\pi\) |
0.998403 | + | 0.0564911i | \(0.0179913\pi\) | |||||||
\(398\) | 15.7976 | − | 15.7976i | 0.791860 | − | 0.791860i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.71261 | + | 1.67072i | 0.235631 | + | 0.0835360i | ||||
\(401\) | 34.6647i | 1.73107i | 0.500845 | + | 0.865537i | \(0.333023\pi\) | ||||
−0.500845 | + | 0.865537i | \(0.666977\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.85077 | − | 3.85077i | −0.191821 | − | 0.191821i | ||||
\(404\) | 19.4889 | 0.969607 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 21.0883 | 1.04660 | ||||||||
\(407\) | −8.13233 | − | 8.13233i | −0.403105 | − | 0.403105i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.4825i | 0.864455i | 0.901765 | + | 0.432227i | \(0.142272\pi\) | ||||
−0.901765 | + | 0.432227i | \(0.857728\pi\) | |||||||
\(410\) | 5.22824 | + | 7.40060i | 0.258204 | + | 0.365489i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.23654 | + | 4.23654i | −0.208719 | + | 0.208719i | ||||
\(413\) | −9.64064 | + | 9.64064i | −0.474385 | + | 0.474385i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.52637 | + | 6.40710i | 0.222191 | + | 0.314512i | ||||
\(416\) | − | 2.99319i | − | 0.146753i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.31116 | + | 1.31116i | 0.0641307 | + | 0.0641307i | ||||
\(419\) | 28.3156 | 1.38331 | 0.691653 | − | 0.722230i | \(-0.256883\pi\) | ||||
0.691653 | + | 0.722230i | \(0.256883\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.8666 | 1.01698 | 0.508488 | − | 0.861069i | \(-0.330205\pi\) | ||||
0.508488 | + | 0.861069i | \(0.330205\pi\) | |||||||
\(422\) | 14.6192 | + | 14.6192i | 0.711653 | + | 0.711653i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 1.46147i | − | 0.0709754i | ||||||
\(425\) | 6.96686 | + | 14.6198i | 0.337942 | + | 0.709163i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.33328 | + | 5.33328i | −0.258096 | + | 0.258096i | ||||
\(428\) | 1.11330 | − | 1.11330i | 0.0538136 | − | 0.0538136i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −22.6723 | − | 3.89998i | −1.09335 | − | 0.188074i | ||||
\(431\) | − | 16.8849i | − | 0.813317i | −0.913580 | − | 0.406659i | \(-0.866694\pi\) | ||
0.913580 | − | 0.406659i | \(-0.133306\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.3819 | + | 19.3819i | 0.931435 | + | 0.931435i | 0.997796 | − | 0.0663604i | \(-0.0211387\pi\) |
−0.0663604 | + | 0.997796i | \(0.521139\pi\) | |||||||
\(434\) | −6.29306 | −0.302076 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.40579 | −0.163108 | ||||||||
\(437\) | 2.39238 | + | 2.39238i | 0.114443 | + | 0.114443i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.6631i | 1.03392i | 0.856008 | + | 0.516962i | \(0.172937\pi\) | ||||
−0.856008 | + | 0.516962i | \(0.827063\pi\) | |||||||
\(440\) | 3.38642 | − | 2.39238i | 0.161441 | − | 0.114052i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.85532 | − | 6.85532i | 0.326074 | − | 0.326074i | ||||
\(443\) | 1.39602 | − | 1.39602i | 0.0663269 | − | 0.0663269i | −0.673165 | − | 0.739492i | \(-0.735066\pi\) |
0.739492 | + | 0.673165i | \(0.235066\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.08622 | − | 29.5684i | 0.241110 | − | 1.40168i | ||||
\(446\) | − | 9.95529i | − | 0.471397i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.44579 | − | 2.44579i | −0.115553 | − | 0.115553i | ||||
\(449\) | −27.2531 | −1.28615 | −0.643076 | − | 0.765803i | \(-0.722342\pi\) | ||||
−0.643076 | + | 0.765803i | \(0.722342\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.51388 | 0.353815 | ||||||||
\(452\) | 1.01123 | + | 1.01123i | 0.0475645 | + | 0.0475645i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 17.2970i | − | 0.811790i | ||||||
\(455\) | 3.92454 | − | 22.8150i | 0.183985 | − | 1.06959i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.83134 | + | 2.83134i | −0.132444 | + | 0.132444i | −0.770221 | − | 0.637777i | \(-0.779854\pi\) |
0.637777 | + | 0.770221i | \(0.279854\pi\) | |||||||
\(458\) | −15.5678 | + | 15.5678i | −0.727434 | + | 0.727434i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.17896 | − | 4.36520i | 0.288096 | − | 0.203529i | ||||
\(461\) | 11.3251i | 0.527464i | 0.964596 | + | 0.263732i | \(0.0849535\pi\) | ||||
−0.964596 | + | 0.263732i | \(0.915047\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.1265 | − | 12.1265i | −0.563565 | − | 0.563565i | 0.366753 | − | 0.930318i | \(-0.380469\pi\) |
−0.930318 | + | 0.366753i | \(0.880469\pi\) | |||||||
\(464\) | 6.09689 | 0.283041 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.1500 | 0.655486 | ||||||||
\(467\) | −23.4660 | − | 23.4660i | −1.08588 | − | 1.08588i | −0.995948 | − | 0.0899279i | \(-0.971336\pi\) |
−0.0899279 | − | 0.995948i | \(-0.528664\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 23.4938i | − | 1.08484i | ||||||
\(470\) | 4.49972 | + | 0.774022i | 0.207557 | + | 0.0357030i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.78723 | + | 2.78723i | −0.128292 | + | 0.128292i | ||||
\(473\) | −13.4895 | + | 13.4895i | −0.620249 | + | 0.620249i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.67072 | + | 4.71261i | −0.0766578 | + | 0.216229i | ||||
\(476\) | − | 11.2032i | − | 0.513498i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.76910 | + | 4.76910i | 0.218134 | + | 0.218134i | ||||
\(479\) | 5.29439 | 0.241907 | 0.120953 | − | 0.992658i | \(-0.461405\pi\) | ||||
0.120953 | + | 0.992658i | \(0.461405\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.5650 | −0.846492 | ||||||||
\(482\) | 17.4905 | + | 17.4905i | 0.796670 | + | 0.796670i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.56174i | 0.343716i | ||||||||
\(485\) | 7.29853 | + | 10.3311i | 0.331409 | + | 0.469111i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.8077 | + | 15.8077i | −0.716316 | + | 0.716316i | −0.967849 | − | 0.251533i | \(-0.919065\pi\) |
0.251533 | + | 0.967849i | \(0.419065\pi\) | |||||||
\(488\) | −1.54192 | + | 1.54192i | −0.0697993 | + | 0.0697993i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.40428 | − | 9.06528i | −0.289316 | − | 0.409527i | ||||
\(491\) | − | 11.1535i | − | 0.503349i | −0.967812 | − | 0.251675i | \(-0.919019\pi\) | ||
0.967812 | − | 0.251675i | \(-0.0809812\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.9637 | + | 13.9637i | 0.628896 | + | 0.628896i | ||||
\(494\) | 2.99319 | 0.134670 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.81940 | −0.0816935 | ||||||||
\(497\) | 5.05504 | + | 5.05504i | 0.226749 | + | 0.226749i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.8109i | 1.20022i | 0.799917 | + | 0.600111i | \(0.204877\pi\) | ||||
−0.799917 | + | 0.600111i | \(0.795123\pi\) | |||||||
\(500\) | 9.75187 | + | 5.46818i | 0.436117 | + | 0.244545i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −18.5019 | + | 18.5019i | −0.825782 | + | 0.825782i | ||||
\(503\) | 2.38661 | − | 2.38661i | 0.106414 | − | 0.106414i | −0.651895 | − | 0.758309i | \(-0.726026\pi\) |
0.758309 | + | 0.651895i | \(0.226026\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 42.9477 | + | 7.38766i | 1.91115 | + | 0.328747i | ||||
\(506\) | − | 6.27355i | − | 0.278893i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.919417 | − | 0.919417i | −0.0407925 | − | 0.0407925i | ||||
\(509\) | 34.5225 | 1.53018 | 0.765092 | − | 0.643921i | \(-0.222694\pi\) | ||||
0.765092 | + | 0.643921i | \(0.222694\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −46.8909 | −2.07433 | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.20870i | 0.273854i | ||||||||
\(515\) | −10.9420 | + | 7.73013i | −0.482163 | + | 0.340630i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.67724 | − | 2.67724i | 0.117745 | − | 0.117745i | ||||
\(518\) | −15.1698 | + | 15.1698i | −0.666522 | + | 0.666522i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.13463 | − | 6.59610i | 0.0497569 | − | 0.289258i | ||||
\(521\) | 37.3357i | 1.63570i | 0.575428 | + | 0.817852i | \(0.304835\pi\) | ||||
−0.575428 | + | 0.817852i | \(0.695165\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.0356 | + | 22.0356i | 0.963549 | + | 0.963549i | 0.999359 | − | 0.0358094i | \(-0.0114009\pi\) |
−0.0358094 | + | 0.999359i | \(0.511401\pi\) | |||||||
\(524\) | 4.24264 | 0.185341 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.9215 | −0.563405 | ||||||||
\(527\) | −4.16698 | − | 4.16698i | −0.181517 | − | 0.181517i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.5531i | 0.502308i | ||||||||
\(530\) | 0.554002 | − | 3.22065i | 0.0240643 | − | 0.139896i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.44579 | − | 2.44579i | 0.106038 | − | 0.106038i | ||||
\(533\) | 8.57660 | − | 8.57660i | 0.371494 | − | 0.371494i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.87541 | − | 2.03137i | 0.124315 | − | 0.0878238i | ||||
\(536\) | − | 6.79234i | − | 0.293384i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −9.13023 | − | 9.13023i | −0.393632 | − | 0.393632i | ||||
\(539\) | −9.20405 | −0.396446 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.8429 | −0.466175 | −0.233087 | − | 0.972456i | \(-0.574883\pi\) | ||||
−0.233087 | + | 0.972456i | \(0.574883\pi\) | |||||||
\(542\) | 8.34615 | + | 8.34615i | 0.358498 | + | 0.358498i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 3.23898i | − | 0.138870i | ||||||
\(545\) | −7.50534 | − | 1.29103i | −0.321494 | − | 0.0553019i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.13652 | − | 1.13652i | 0.0485942 | − | 0.0485942i | −0.682392 | − | 0.730986i | \(-0.739060\pi\) |
0.730986 | + | 0.682392i | \(0.239060\pi\) | |||||||
\(548\) | 8.15130 | − | 8.15130i | 0.348206 | − | 0.348206i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 8.36954 | − | 3.98839i | 0.356878 | − | 0.170066i | ||||
\(551\) | 6.09689i | 0.259736i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.49772 | − | 3.49772i | −0.148738 | − | 0.148738i | ||||
\(554\) | −14.4510 | −0.613965 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.18060 | −0.262116 | ||||||||
\(557\) | 5.70866 | + | 5.70866i | 0.241884 | + | 0.241884i | 0.817629 | − | 0.575745i | \(-0.195288\pi\) |
−0.575745 | + | 0.817629i | \(0.695288\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 30.7948i | 1.30248i | ||||||||
\(560\) | −4.46266 | − | 6.31691i | −0.188582 | − | 0.266938i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13.4563 | − | 13.4563i | 0.567620 | − | 0.567620i | ||||
\(563\) | −9.42883 | + | 9.42883i | −0.397378 | + | 0.397378i | −0.877307 | − | 0.479929i | \(-0.840662\pi\) |
0.479929 | + | 0.877307i | \(0.340662\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.84513 | + | 2.61179i | 0.0776252 | + | 0.109879i | ||||
\(566\) | 25.0551i | 1.05314i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.46147 | + | 1.46147i | 0.0613220 | + | 0.0613220i | ||||
\(569\) | −14.8826 | −0.623912 | −0.311956 | − | 0.950097i | \(-0.600984\pi\) | ||||
−0.311956 | + | 0.950097i | \(0.600984\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.0430 | −0.629529 | −0.314765 | − | 0.949170i | \(-0.601926\pi\) | ||||
−0.314765 | + | 0.949170i | \(0.601926\pi\) | |||||||
\(572\) | −3.92454 | − | 3.92454i | −0.164093 | − | 0.164093i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 14.0162i | − | 0.585023i | ||||||
\(575\) | 15.2713 | − | 7.27735i | 0.636858 | − | 0.303486i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.9500 | + | 16.9500i | −0.705636 | + | 0.705636i | −0.965614 | − | 0.259979i | \(-0.916285\pi\) |
0.259979 | + | 0.965614i | \(0.416285\pi\) | |||||||
\(578\) | −4.60256 | + | 4.60256i | −0.191441 | + | 0.191441i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 13.4357 | + | 2.31116i | 0.557889 | + | 0.0959655i | ||||
\(581\) | − | 12.1345i | − | 0.503426i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.91622 | − | 1.91622i | −0.0793616 | − | 0.0793616i | ||||
\(584\) | −13.5567 | −0.560982 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.6825 | −0.647840 | ||||||||
\(587\) | 17.9345 | + | 17.9345i | 0.740237 | + | 0.740237i | 0.972623 | − | 0.232387i | \(-0.0746535\pi\) |
−0.232387 | + | 0.972623i | \(0.574653\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1.81940i | − | 0.0749671i | ||||||
\(590\) | −7.19877 | + | 5.08566i | −0.296369 | + | 0.209373i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.38577 | + | 4.38577i | −0.180254 | + | 0.180254i | ||||
\(593\) | 19.6576 | − | 19.6576i | 0.807242 | − | 0.807242i | −0.176974 | − | 0.984216i | \(-0.556631\pi\) |
0.984216 | + | 0.176974i | \(0.0566308\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.24681 | − | 24.6885i | 0.174102 | − | 1.01213i | ||||
\(596\) | − | 5.71955i | − | 0.234282i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7.16084 | − | 7.16084i | −0.292828 | − | 0.292828i | ||||
\(599\) | 2.58990 | 0.105820 | 0.0529102 | − | 0.998599i | \(-0.483150\pi\) | ||||
0.0529102 | + | 0.998599i | \(0.483150\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.9918 | 0.652321 | 0.326160 | − | 0.945314i | \(-0.394245\pi\) | ||||
0.326160 | + | 0.945314i | \(0.394245\pi\) | |||||||
\(602\) | 25.1629 | + | 25.1629i | 1.02556 | + | 1.02556i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 16.8191i | − | 0.684358i | ||||||
\(605\) | −2.86644 | + | 16.6638i | −0.116537 | + | 0.677481i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.09219 | − | 8.09219i | 0.328452 | − | 0.328452i | −0.523546 | − | 0.851998i | \(-0.675391\pi\) |
0.851998 | + | 0.523546i | \(0.175391\pi\) | |||||||
\(608\) | 0.707107 | − | 0.707107i | 0.0286770 | − | 0.0286770i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.98242 | + | 2.81343i | −0.161244 | + | 0.113912i | ||||
\(611\) | − | 6.11177i | − | 0.247256i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.5239 | + | 16.5239i | 0.667395 | + | 0.667395i | 0.957112 | − | 0.289717i | \(-0.0935612\pi\) |
−0.289717 | + | 0.957112i | \(0.593561\pi\) | |||||||
\(614\) | −23.6604 | −0.954855 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.41361 | −0.258412 | ||||||||
\(617\) | 5.82216 | + | 5.82216i | 0.234391 | + | 0.234391i | 0.814523 | − | 0.580132i | \(-0.196999\pi\) |
−0.580132 | + | 0.814523i | \(0.696999\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.4343i | 1.02229i | 0.859494 | + | 0.511146i | \(0.170779\pi\) | ||||
−0.859494 | + | 0.511146i | \(0.829221\pi\) | |||||||
\(620\) | −4.00942 | − | 0.689681i | −0.161022 | − | 0.0276983i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7.90562 | + | 7.90562i | −0.316987 | + | 0.316987i | ||||
\(623\) | −32.8166 | + | 32.8166i | −1.31477 | + | 1.31477i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.4174 | + | 15.7469i | 0.776696 | + | 0.629876i | ||||
\(626\) | − | 15.1163i | − | 0.604169i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.82912 | − | 1.82912i | −0.0729897 | − | 0.0729897i | ||||
\(629\) | −20.0895 | −0.801021 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 45.9025 | 1.82735 | 0.913675 | − | 0.406445i | \(-0.133232\pi\) | ||||
0.913675 | + | 0.406445i | \(0.133232\pi\) | |||||||
\(632\) | −1.01123 | − | 1.01123i | −0.0402248 | − | 0.0402248i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 23.9437i | − | 0.950924i | ||||||
\(635\) | −1.67760 | − | 2.37465i | −0.0665734 | − | 0.0942349i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.5058 | + | 10.5058i | −0.416255 | + | 0.416255i | ||||
\(638\) | 7.99397 | − | 7.99397i | 0.316484 | − | 0.316484i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.29021 | − | 1.82630i | −0.0510000 | − | 0.0721907i | ||||
\(641\) | 36.1191i | 1.42662i | 0.700848 | + | 0.713310i | \(0.252805\pi\) | ||||
−0.700848 | + | 0.713310i | \(0.747195\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.8180 | − | 24.8180i | −0.978726 | − | 0.978726i | 0.0210526 | − | 0.999778i | \(-0.493298\pi\) |
−0.999778 | + | 0.0210526i | \(0.993298\pi\) | |||||||
\(644\) | −11.7025 | −0.461142 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.23898 | 0.127436 | ||||||||
\(647\) | −29.5857 | − | 29.5857i | −1.16314 | − | 1.16314i | −0.983785 | − | 0.179350i | \(-0.942601\pi\) |
−0.179350 | − | 0.983785i | \(-0.557399\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.30897i | 0.286902i | ||||||||
\(650\) | 5.00078 | − | 14.1057i | 0.196147 | − | 0.553273i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −15.5861 | + | 15.5861i | −0.610397 | + | 0.610397i | ||||
\(653\) | −7.70050 | + | 7.70050i | −0.301344 | + | 0.301344i | −0.841540 | − | 0.540196i | \(-0.818350\pi\) |
0.540196 | + | 0.841540i | \(0.318350\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.34952 | + | 1.60826i | 0.365316 | + | 0.0628400i | ||||
\(656\) | − | 4.05224i | − | 0.158213i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.99403 | − | 4.99403i | −0.194688 | − | 0.194688i | ||||
\(659\) | 21.6601 | 0.843757 | 0.421879 | − | 0.906652i | \(-0.361371\pi\) | ||||
0.421879 | + | 0.906652i | \(0.361371\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.4825 | −0.913364 | −0.456682 | − | 0.889630i | \(-0.650962\pi\) | ||||
−0.456682 | + | 0.889630i | \(0.650962\pi\) | |||||||
\(662\) | −2.50687 | − | 2.50687i | −0.0974324 | − | 0.0974324i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 3.50824i | − | 0.136146i | ||||||
\(665\) | 6.31691 | − | 4.46266i | 0.244959 | − | 0.173055i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.5861 | − | 14.5861i | 0.564774 | − | 0.564774i | ||||
\(668\) | 12.1544 | − | 12.1544i | 0.470268 | − | 0.470268i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.57478 | − | 14.9683i | 0.0994724 | − | 0.578276i | ||||
\(671\) | 4.04339i | 0.156093i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.4974 | − | 28.4974i | −1.09849 | − | 1.09849i | −0.994587 | − | 0.103907i | \(-0.966866\pi\) |
−0.103907 | − | 0.994587i | \(-0.533134\pi\) | |||||||
\(674\) | −30.4252 | −1.17194 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.04080 | 0.155416 | ||||||||
\(677\) | −15.1954 | − | 15.1954i | −0.584007 | − | 0.584007i | 0.351995 | − | 0.936002i | \(-0.385504\pi\) |
−0.936002 | + | 0.351995i | \(0.885504\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 19.5663i | − | 0.750886i | ||||||
\(680\) | 1.22780 | − | 7.13775i | 0.0470841 | − | 0.273720i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.38552 | + | 2.38552i | −0.0913461 | + | 0.0913461i | ||||
\(683\) | 34.6257 | − | 34.6257i | 1.32492 | − | 1.32492i | 0.415174 | − | 0.909742i | \(-0.363721\pi\) |
0.909742 | − | 0.415174i | \(-0.136279\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.0530 | − | 14.8731i | 0.804392 | − | 0.568273i | ||||
\(686\) | − | 7.04312i | − | 0.268908i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.27490 | + | 7.27490i | 0.277353 | + | 0.277353i | ||||
\(689\) | −4.37447 | −0.166654 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.0799 | −1.37254 | −0.686271 | − | 0.727346i | \(-0.740754\pi\) | ||||
−0.686271 | + | 0.727346i | \(0.740754\pi\) | |||||||
\(692\) | 11.9151 | + | 11.9151i | 0.452943 | + | 0.452943i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 28.0581i | 1.06507i | ||||||||
\(695\) | −13.6202 | − | 2.34289i | −0.516644 | − | 0.0888707i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.28087 | − | 9.28087i | 0.351538 | − | 0.351538i | ||||
\(698\) | 17.9469 | − | 17.9469i | 0.679302 | − | 0.679302i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −7.43982 | − | 15.6123i | −0.281199 | − | 0.590088i | ||||
\(701\) | − | 28.8611i | − | 1.09007i | −0.838413 | − | 0.545035i | \(-0.816516\pi\) | ||
0.838413 | − | 0.545035i | \(-0.183484\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.38577 | − | 4.38577i | −0.165412 | − | 0.165412i | ||||
\(704\) | −1.85425 | −0.0698848 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17.0102 | −0.640187 | ||||||||
\(707\) | −47.6656 | − | 47.6656i | −1.79265 | − | 1.79265i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.25277i | 0.122161i | 0.998133 | + | 0.0610803i | \(0.0194546\pi\) | ||||
−0.998133 | + | 0.0610803i | \(0.980545\pi\) | |||||||
\(710\) | 2.66665 | + | 3.77465i | 0.100078 | + | 0.141660i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.48768 | + | 9.48768i | −0.355566 | + | 0.355566i | ||||
\(713\) | −4.35269 | + | 4.35269i | −0.163009 | + | 0.163009i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.16084 | − | 10.1362i | −0.267800 | − | 0.379072i | ||||
\(716\) | 15.8288i | 0.591552i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.93103 | + | 2.93103i | 0.109385 | + | 0.109385i | ||||
\(719\) | 11.0628 | 0.412574 | 0.206287 | − | 0.978492i | \(-0.433862\pi\) | ||||
0.206287 | + | 0.978492i | \(0.433862\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.7234 | 0.771778 | ||||||||
\(722\) | 0.707107 | + | 0.707107i | 0.0263158 | + | 0.0263158i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 2.63425i | − | 0.0979010i | ||||||
\(725\) | 28.7323 | + | 10.1862i | 1.06709 | + | 0.378306i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.4444 | + | 24.4444i | −0.906592 | + | 0.906592i | −0.995995 | − | 0.0894039i | \(-0.971504\pi\) |
0.0894039 | + | 0.995995i | \(0.471504\pi\) | |||||||
\(728\) | −7.32071 | + | 7.32071i | −0.271324 | + | 0.271324i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −29.8750 | − | 5.13896i | −1.10572 | − | 0.190202i | ||||
\(731\) | 33.3235i | 1.23251i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.8872 | − | 19.8872i | −0.734549 | − | 0.734549i | 0.236968 | − | 0.971517i | \(-0.423846\pi\) |
−0.971517 | + | 0.236968i | \(0.923846\pi\) | |||||||
\(734\) | 24.7821 | 0.914725 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.38333 | −0.124711 | ||||||||
\(737\) | −8.90581 | − | 8.90581i | −0.328050 | − | 0.328050i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 9.06729i | − | 0.333546i | −0.985995 | − | 0.166773i | \(-0.946665\pi\) | ||
0.985995 | − | 0.166773i | \(-0.0533347\pi\) | |||||||
\(740\) | −11.3275 | + | 8.00241i | −0.416405 | + | 0.294175i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.57445 | + | 3.57445i | −0.131222 | + | 0.131222i | ||||
\(743\) | −25.6087 | + | 25.6087i | −0.939493 | + | 0.939493i | −0.998271 | − | 0.0587784i | \(-0.981279\pi\) |
0.0587784 | + | 0.998271i | \(0.481279\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.16811 | − | 12.6042i | 0.0794336 | − | 0.461782i | ||||
\(746\) | − | 20.4287i | − | 0.747946i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.24681 | − | 4.24681i | −0.155279 | − | 0.155279i | ||||
\(749\) | −5.44581 | −0.198986 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 51.1239 | 1.86554 | 0.932769 | − | 0.360474i | \(-0.117385\pi\) | ||||
0.932769 | + | 0.360474i | \(0.117385\pi\) | |||||||
\(752\) | −1.44384 | − | 1.44384i | −0.0526513 | − | 0.0526513i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 18.2492i | − | 0.664596i | ||||||
\(755\) | 6.37562 | − | 37.0642i | 0.232033 | − | 1.34891i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.1378 | − | 32.1378i | 1.16807 | − | 1.16807i | 0.185404 | − | 0.982662i | \(-0.440641\pi\) |
0.982662 | − | 0.185404i | \(-0.0593595\pi\) | |||||||
\(758\) | 5.74518 | − | 5.74518i | 0.208674 | − | 0.208674i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.82630 | − | 1.29021i | 0.0662467 | − | 0.0468008i | ||||
\(761\) | − | 17.3658i | − | 0.629509i | −0.949173 | − | 0.314754i | \(-0.898078\pi\) | ||
0.949173 | − | 0.314754i | \(-0.101922\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.32983 | + | 8.32983i | 0.301560 | + | 0.301560i | ||||
\(764\) | 16.9820 | 0.614387 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 33.4332 | 1.20799 | ||||||||
\(767\) | 8.34270 | + | 8.34270i | 0.301237 | + | 0.301237i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 0.768835i | − | 0.0277249i | −0.999904 | − | 0.0138624i | \(-0.995587\pi\) | ||
0.999904 | − | 0.0138624i | \(-0.00441270\pi\) | |||||||
\(770\) | −14.1337 | − | 2.43121i | −0.509343 | − | 0.0876149i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −15.1246 | + | 15.1246i | −0.544346 | + | 0.544346i | ||||
\(773\) | −23.4941 | + | 23.4941i | −0.845023 | + | 0.845023i | −0.989507 | − | 0.144484i | \(-0.953848\pi\) |
0.144484 | + | 0.989507i | \(0.453848\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.57412 | − | 3.03971i | −0.307992 | − | 0.109189i | ||||
\(776\) | − | 5.65685i | − | 0.203069i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.02187 | − | 6.02187i | −0.215895 | − | 0.215895i | ||||
\(779\) | 4.05224 | 0.145187 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.83243 | 0.137135 | ||||||||
\(782\) | −7.74886 | − | 7.74886i | −0.277099 | − | 0.277099i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.96375i | 0.177277i | ||||||||
\(785\) | −3.33746 | − | 4.72419i | −0.119119 | − | 0.168614i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.8310 | − | 20.8310i | 0.742545 | − | 0.742545i | −0.230522 | − | 0.973067i | \(-0.574043\pi\) |
0.973067 | + | 0.230522i | \(0.0740433\pi\) | |||||||
\(788\) | −10.3726 | + | 10.3726i | −0.369509 | + | 0.369509i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.84513 | − | 2.61179i | −0.0656468 | − | 0.0929233i | ||||
\(791\) | − | 4.94653i | − | 0.175878i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.61525 | + | 4.61525i | 0.163892 | + | 0.163892i | ||||
\(794\) | −26.5412 | −0.941912 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −22.3411 | −0.791860 | ||||||||
\(797\) | −22.4652 | − | 22.4652i | −0.795757 | − | 0.795757i | 0.186666 | − | 0.982423i | \(-0.440232\pi\) |
−0.982423 | + | 0.186666i | \(0.940232\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 6.61365i | − | 0.233974i | ||||||
\(800\) | −2.15094 | − | 4.51370i | −0.0760473 | − | 0.159583i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 24.5117 | − | 24.5117i | 0.865537 | − | 0.865537i | ||||
\(803\) | −17.7750 | + | 17.7750i | −0.627266 | + | 0.627266i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −25.7888 | − | 4.43607i | −0.908935 | − | 0.156351i | ||||
\(806\) | 5.44581i | 0.191821i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −13.7807 | − | 13.7807i | −0.484804 | − | 0.484804i | ||||
\(809\) | −52.9692 | −1.86230 | −0.931148 | − | 0.364641i | \(-0.881192\pi\) | ||||
−0.931148 | + | 0.364641i | \(0.881192\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.4459 | −1.27979 | −0.639895 | − | 0.768462i | \(-0.721022\pi\) | ||||
−0.639895 | + | 0.768462i | \(0.721022\pi\) | |||||||
\(812\) | −14.9117 | − | 14.9117i | −0.523298 | − | 0.523298i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 11.5008i | 0.403105i | ||||||||
\(815\) | −40.2553 | + | 28.4388i | −1.41008 | + | 0.996168i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.27490 | + | 7.27490i | −0.254517 | + | 0.254517i | ||||
\(818\) | 12.3620 | − | 12.3620i | 0.432227 | − | 0.432227i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.53609 | − | 8.92994i | 0.0536425 | − | 0.311847i | ||||
\(821\) | − | 9.58783i | − | 0.334618i | −0.985905 | − | 0.167309i | \(-0.946492\pi\) | ||
0.985905 | − | 0.167309i | \(-0.0535077\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.9600 | − | 14.9600i | −0.521473 | − | 0.521473i | 0.396543 | − | 0.918016i | \(-0.370210\pi\) |
−0.918016 | + | 0.396543i | \(0.870210\pi\) | |||||||
\(824\) | 5.99137 | 0.208719 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.6339 | 0.474385 | ||||||||
\(827\) | −0.562754 | − | 0.562754i | −0.0195689 | − | 0.0195689i | 0.697255 | − | 0.716824i | \(-0.254405\pi\) |
−0.716824 | + | 0.697255i | \(0.754405\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 19.0932i | − | 0.663135i | −0.943432 | − | 0.331567i | \(-0.892423\pi\) | ||
0.943432 | − | 0.331567i | \(-0.107577\pi\) | |||||||
\(830\) | 1.32987 | − | 7.73113i | 0.0461606 | − | 0.268351i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.11651 | + | 2.11651i | −0.0733766 | + | 0.0733766i | ||||
\(833\) | −11.3685 | + | 11.3685i | −0.393895 | + | 0.393895i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 31.3921 | − | 22.1773i | 1.08637 | − | 0.767478i | ||||
\(836\) | − | 1.85425i | − | 0.0641307i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −20.0221 | − | 20.0221i | −0.691653 | − | 0.691653i | ||||
\(839\) | −6.82673 | −0.235685 | −0.117842 | − | 0.993032i | \(-0.537598\pi\) | ||||
−0.117842 | + | 0.993032i | \(0.537598\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.17212 | 0.281797 | ||||||||
\(842\) | −14.7549 | − | 14.7549i | −0.508488 | − | 0.508488i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 20.6747i | − | 0.711653i | ||||||
\(845\) | 8.90473 | + | 1.53175i | 0.306332 | + | 0.0526938i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.4944 | − | 18.4944i | 0.635476 | − | 0.635476i | ||||
\(848\) | −1.03342 | + | 1.03342i | −0.0354877 | + | 0.0354877i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5.41143 | − | 15.2641i | 0.185610 | − | 0.523553i | ||||
\(851\) | 20.9848i | 0.719350i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.1332 | − | 10.1332i | −0.346955 | − | 0.346955i | 0.512019 | − | 0.858974i | \(-0.328898\pi\) |
−0.858974 | + | 0.512019i | \(0.828898\pi\) | |||||||
\(854\) | 7.54240 | 0.258096 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.57445 | −0.0538136 | ||||||||
\(857\) | 30.6067 | + | 30.6067i | 1.04551 | + | 1.04551i | 0.998914 | + | 0.0465916i | \(0.0148359\pi\) |
0.0465916 | + | 0.998914i | \(0.485164\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.5487i | 1.72470i | 0.506313 | + | 0.862350i | \(0.331008\pi\) | ||||
−0.506313 | + | 0.862350i | \(0.668992\pi\) | |||||||
\(860\) | 13.2740 | + | 18.7894i | 0.452640 | + | 0.640714i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.9394 | + | 11.9394i | −0.406659 | + | 0.406659i | ||||
\(863\) | −32.9784 | + | 32.9784i | −1.12260 | + | 1.12260i | −0.131247 | + | 0.991350i | \(0.541898\pi\) |
−0.991350 | + | 0.131247i | \(0.958102\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.7406 | + | 30.7739i | 0.739203 | + | 1.04634i | ||||
\(866\) | − | 27.4102i | − | 0.931435i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.44986 | + | 4.44986i | 0.151038 | + | 0.151038i | ||||
\(869\) | −2.65177 | −0.0899552 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.3308 | −0.688882 | ||||||||
\(872\) | 2.40826 | + | 2.40826i | 0.0815538 | + | 0.0815538i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 3.38333i | − | 0.114443i | ||||||
\(875\) | −10.4770 | − | 37.2250i | −0.354187 | − | 1.25843i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.8518 | − | 16.8518i | 0.569045 | − | 0.569045i | −0.362816 | − | 0.931861i | \(-0.618185\pi\) |
0.931861 | + | 0.362816i | \(0.118185\pi\) | |||||||
\(878\) | 15.3181 | − | 15.3181i | 0.516962 | − | 0.516962i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.08622 | − | 0.702894i | −0.137747 | − | 0.0236945i | ||||
\(881\) | − | 26.9178i | − | 0.906883i | −0.891286 | − | 0.453441i | \(-0.850196\pi\) | ||
0.891286 | − | 0.453441i | \(-0.149804\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.1164 | + | 16.1164i | 0.542361 | + | 0.542361i | 0.924220 | − | 0.381859i | \(-0.124716\pi\) |
−0.381859 | + | 0.924220i | \(0.624716\pi\) | |||||||
\(884\) | −9.69489 | −0.326074 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.97427 | −0.0663269 | ||||||||
\(887\) | −7.24427 | − | 7.24427i | −0.243239 | − | 0.243239i | 0.574950 | − | 0.818189i | \(-0.305022\pi\) |
−0.818189 | + | 0.574950i | \(0.805022\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.49740i | 0.150838i | ||||||||
\(890\) | −24.5045 | + | 17.3115i | −0.821394 | + | 0.580283i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.03945 | + | 7.03945i | −0.235698 | + | 0.235698i | ||||
\(893\) | 1.44384 | − | 1.44384i | 0.0483161 | − | 0.0483161i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.00025 | + | 34.8821i | −0.200566 | + | 1.16598i | ||||
\(896\) | 3.45887i | 0.115553i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 19.2708 | + | 19.2708i | 0.643076 | + | 0.643076i | ||||
\(899\) | −11.0927 | −0.369962 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.73368 | −0.157702 | ||||||||
\(902\) | −5.31312 | − | 5.31312i | −0.176907 | − | 0.176907i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 1.43010i | − | 0.0475645i | ||||||
\(905\) | 0.998566 | − | 5.80510i | 0.0331935 | − | 0.192968i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.9997 | + | 34.9997i | −1.16215 | + | 1.16215i | −0.178140 | + | 0.984005i | \(0.557008\pi\) |
−0.984005 | + | 0.178140i | \(0.942992\pi\) | |||||||
\(908\) | −12.2308 | + | 12.2308i | −0.405895 | + | 0.405895i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −18.9077 | + | 13.3576i | −0.626785 | + | 0.442800i | ||||
\(911\) | − | 24.7981i | − | 0.821599i | −0.911726 | − | 0.410799i | \(-0.865250\pi\) | ||
0.911726 | − | 0.410799i | \(-0.134750\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.59985 | − | 4.59985i | −0.152233 | − | 0.152233i | ||||
\(914\) | 4.00411 | 0.132444 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 22.0162 | 0.727434 | ||||||||
\(917\) | −10.3766 | − | 10.3766i | −0.342665 | − | 0.342665i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.0962i | 0.464989i | 0.972598 | + | 0.232495i | \(0.0746888\pi\) | ||||
−0.972598 | + | 0.232495i | \(0.925311\pi\) | |||||||
\(920\) | −7.45585 | − | 1.28252i | −0.245812 | − | 0.0422835i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8.00808 | − | 8.00808i | 0.263732 | − | 0.263732i | ||||
\(923\) | 4.37447 | − | 4.37447i | 0.143987 | − | 0.143987i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −27.9958 | + | 13.3410i | −0.920497 | + | 0.438651i | ||||
\(926\) | 17.1494i | 0.563565i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.31116 | − | 4.31116i | −0.141521 | − | 0.141521i | ||||
\(929\) | 35.0100 | 1.14864 | 0.574320 | − | 0.818631i | \(-0.305266\pi\) | ||||
0.574320 | + | 0.818631i | \(0.305266\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.96375 | −0.162680 | ||||||||
\(932\) | −10.0056 | − | 10.0056i | −0.327743 | − | 0.327743i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 33.1859i | 1.08588i | ||||||||
\(935\) | −7.74886 | − | 10.9685i | −0.253415 | − | 0.358710i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.4974 | − | 21.4974i | 0.702289 | − | 0.702289i | −0.262612 | − | 0.964901i | \(-0.584584\pi\) |
0.964901 | + | 0.262612i | \(0.0845840\pi\) | |||||||
\(938\) | −16.6126 | + | 16.6126i | −0.542421 | + | 0.542421i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.63447 | − | 3.72910i | −0.0859269 | − | 0.121630i | ||||
\(941\) | − | 58.7403i | − | 1.91488i | −0.288632 | − | 0.957440i | \(-0.593201\pi\) | ||
0.288632 | − | 0.957440i | \(-0.406799\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.69448 | − | 9.69448i | −0.315696 | − | 0.315696i | ||||
\(944\) | 3.94173 | 0.128292 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 19.0771 | 0.620249 | ||||||||
\(947\) | 26.0670 | + | 26.0670i | 0.847062 | + | 0.847062i | 0.989765 | − | 0.142703i | \(-0.0455795\pi\) |
−0.142703 | + | 0.989765i | \(0.545580\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 40.5779i | 1.31721i | ||||||||
\(950\) | 4.51370 | − | 2.15094i | 0.146444 | − | 0.0697858i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.92186 | + | 7.92186i | −0.256749 | + | 0.256749i | ||||
\(953\) | 10.5093 | − | 10.5093i | 0.340429 | − | 0.340429i | −0.516099 | − | 0.856529i | \(-0.672617\pi\) |
0.856529 | + | 0.516099i | \(0.172617\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 37.4233 | + | 6.43738i | 1.21099 | + | 0.208309i | ||||
\(956\) | − | 6.74453i | − | 0.218134i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.74370 | − | 3.74370i | −0.120953 | − | 0.120953i | ||||
\(959\) | −39.8727 | −1.28756 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.6898 | −0.893219 | ||||||||
\(962\) | 13.1274 | + | 13.1274i | 0.423246 | + | 0.423246i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 24.7353i | − | 0.796670i | ||||||
\(965\) | −39.0634 | + | 27.5968i | −1.25749 | + | 0.888372i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.3338 | − | 18.3338i | 0.589574 | − | 0.589574i | −0.347942 | − | 0.937516i | \(-0.613119\pi\) |
0.937516 | + | 0.347942i | \(0.113119\pi\) | |||||||
\(968\) | 5.34696 | − | 5.34696i | 0.171858 | − | 0.171858i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.14435 | − | 12.4660i | 0.0688509 | − | 0.400260i | ||||
\(971\) | 53.9006i | 1.72975i | 0.501986 | + | 0.864876i | \(0.332603\pi\) | ||||
−0.501986 | + | 0.864876i | \(0.667397\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.1164 | + | 15.1164i | 0.484611 | + | 0.484611i | ||||
\(974\) | 22.3555 | 0.716316 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.18060 | 0.0697993 | ||||||||
\(977\) | −6.88644 | − | 6.88644i | −0.220317 | − | 0.220317i | 0.588315 | − | 0.808632i | \(-0.299791\pi\) |
−0.808632 | + | 0.588315i | \(0.799791\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.8796i | 0.795157i | ||||||||
\(980\) | −1.88161 | + | 10.9386i | −0.0601059 | + | 0.349422i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.88669 | + | 7.88669i | −0.251675 | + | 0.251675i | ||||
\(983\) | −16.7893 | + | 16.7893i | −0.535495 | + | 0.535495i | −0.922202 | − | 0.386708i | \(-0.873612\pi\) |
0.386708 | + | 0.922202i | \(0.373612\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −26.7901 | + | 18.9262i | −0.853603 | + | 0.603039i | ||||
\(986\) | − | 19.7477i | − | 0.628896i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.11651 | − | 2.11651i | −0.0673350 | − | 0.0673350i | ||||
\(989\) | 34.8086 | 1.10685 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.7844 | 0.660239 | 0.330120 | − | 0.943939i | \(-0.392911\pi\) | ||||
0.330120 | + | 0.943939i | \(0.392911\pi\) | |||||||
\(992\) | 1.28651 | + | 1.28651i | 0.0408467 | + | 0.0408467i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 7.14890i | − | 0.226749i | ||||||
\(995\) | −49.2332 | − | 8.46886i | −1.56080 | − | 0.268481i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.0505 | − | 17.0505i | 0.539995 | − | 0.539995i | −0.383532 | − | 0.923528i | \(-0.625292\pi\) |
0.923528 | + | 0.383532i | \(0.125292\pi\) | |||||||
\(998\) | 18.9582 | − | 18.9582i | 0.600111 | − | 0.600111i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1710.2.n.h.1673.2 | yes | 16 | |
3.2 | odd | 2 | inner | 1710.2.n.h.1673.7 | yes | 16 | |
5.2 | odd | 4 | inner | 1710.2.n.h.647.7 | yes | 16 | |
15.2 | even | 4 | inner | 1710.2.n.h.647.2 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1710.2.n.h.647.2 | ✓ | 16 | 15.2 | even | 4 | inner | |
1710.2.n.h.647.7 | yes | 16 | 5.2 | odd | 4 | inner | |
1710.2.n.h.1673.2 | yes | 16 | 1.1 | even | 1 | trivial | |
1710.2.n.h.1673.7 | yes | 16 | 3.2 | odd | 2 | inner |