Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,2,Mod(449,1792)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 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("1792.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.m (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: | \(14.3091920422\) |
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: | \( x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1345.5 | ||
Root | \(-0.424637 - 3.22544i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.1345 |
Dual form | 1792.2.m.h.449.5 |
$q$-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 \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | 0 | ||||||||
\(3\) | 0.171192 | + | 0.171192i | 0.0988380 | + | 0.0988380i | 0.754797 | − | 0.655959i | \(-0.227735\pi\) |
−0.655959 | + | 0.754797i | \(0.727735\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.268425 | + | 0.268425i | −0.120043 | + | 0.120043i | −0.764576 | − | 0.644533i | \(-0.777052\pi\) |
0.644533 | + | 0.764576i | \(0.277052\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 2.94139i | − | 0.980462i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.84927 | + | 1.84927i | −0.557577 | + | 0.557577i | −0.928617 | − | 0.371040i | \(-0.879001\pi\) |
0.371040 | + | 0.928617i | \(0.379001\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.63574 | + | 1.63574i | 0.453672 | + | 0.453672i | 0.896571 | − | 0.442899i | \(-0.146050\pi\) |
−0.442899 | + | 0.896571i | \(0.646050\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.0919045 | −0.0237296 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.37134 | −1.78781 | −0.893906 | − | 0.448255i | \(-0.852046\pi\) | ||||
−0.893906 | + | 0.448255i | \(0.852046\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.84975 | + | 3.84975i | 0.883193 | + | 0.883193i | 0.993858 | − | 0.110665i | \(-0.0352979\pi\) |
−0.110665 | + | 0.993858i | \(0.535298\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.171192 | − | 0.171192i | 0.0373573 | − | 0.0373573i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.44892i | 1.34469i | 0.740236 | + | 0.672347i | \(0.234714\pi\) | ||||
−0.740236 | + | 0.672347i | \(0.765286\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.85590i | 0.971179i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.01712 | − | 1.01712i | 0.195745 | − | 0.195745i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.58700 | + | 3.58700i | 0.666089 | + | 0.666089i | 0.956808 | − | 0.290720i | \(-0.0938947\pi\) |
−0.290720 | + | 0.956808i | \(0.593895\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.10161 | 1.09588 | 0.547941 | − | 0.836517i | \(-0.315412\pi\) | ||||
0.547941 | + | 0.836517i | \(0.315412\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.633164 | −0.110220 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.268425 | + | 0.268425i | 0.0453720 | + | 0.0453720i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.41852 | − | 7.41852i | 1.21960 | − | 1.21960i | 0.251825 | − | 0.967773i | \(-0.418969\pi\) |
0.967773 | − | 0.251825i | \(-0.0810307\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.560052i | 0.0896801i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 0.836588i | − | 0.130653i | −0.997864 | − | 0.0653265i | \(-0.979191\pi\) | ||
0.997864 | − | 0.0653265i | \(-0.0208089\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.88949 | − | 3.88949i | 0.593141 | − | 0.593141i | −0.345337 | − | 0.938479i | \(-0.612236\pi\) |
0.938479 | + | 0.345337i | \(0.112236\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.789540 | + | 0.789540i | 0.117698 | + | 0.117698i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.02070 | 0.878209 | 0.439104 | − | 0.898436i | \(-0.355296\pi\) | ||||
0.439104 | + | 0.898436i | \(0.355296\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.26192 | − | 1.26192i | −0.176704 | − | 0.176704i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.575460 | − | 0.575460i | 0.0790455 | − | 0.0790455i | −0.666479 | − | 0.745524i | \(-0.732199\pi\) |
0.745524 | + | 0.666479i | \(0.232199\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.992782i | − | 0.133867i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.31810i | 0.174586i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.33013 | + | 5.33013i | −0.693924 | + | 0.693924i | −0.963093 | − | 0.269169i | \(-0.913251\pi\) |
0.269169 | + | 0.963093i | \(0.413251\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.929862 | + | 0.929862i | 0.119057 | + | 0.119057i | 0.764125 | − | 0.645068i | \(-0.223171\pi\) |
−0.645068 | + | 0.764125i | \(0.723171\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.94139 | −0.370580 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.878144 | −0.108920 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.21819 | + | 6.21819i | 0.759672 | + | 0.759672i | 0.976263 | − | 0.216590i | \(-0.0694935\pi\) |
−0.216590 | + | 0.976263i | \(0.569494\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.10401 | + | 1.10401i | −0.132907 | + | 0.132907i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.4285i | 1.35631i | 0.734919 | + | 0.678155i | \(0.237220\pi\) | ||||
−0.734919 | + | 0.678155i | \(0.762780\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 3.68616i | − | 0.431433i | −0.976456 | − | 0.215716i | \(-0.930791\pi\) | ||
0.976456 | − | 0.215716i | \(-0.0692087\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.831293 | + | 0.831293i | −0.0959895 | + | 0.0959895i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.84927 | + | 1.84927i | 0.210744 | + | 0.210744i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.21672 | 0.474418 | 0.237209 | − | 0.971459i | \(-0.423767\pi\) | ||||
0.237209 | + | 0.971459i | \(0.423767\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.47591 | −0.941768 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0147 | + | 12.0147i | 1.31878 | + | 1.31878i | 0.914742 | + | 0.404038i | \(0.132393\pi\) |
0.404038 | + | 0.914742i | \(0.367607\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.97865 | − | 1.97865i | 0.214614 | − | 0.214614i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.22813i | 0.131670i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 9.32780i | − | 0.988745i | −0.869250 | − | 0.494373i | \(-0.835398\pi\) | ||
0.869250 | − | 0.494373i | \(-0.164602\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.63574 | − | 1.63574i | 0.171472 | − | 0.171472i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.04455 | + | 1.04455i | 0.108315 | + | 0.108315i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.06673 | −0.212043 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.9032 | −1.41166 | −0.705828 | − | 0.708384i | \(-0.749425\pi\) | ||||
−0.705828 | + | 0.708384i | \(0.749425\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.43943 | + | 5.43943i | 0.546683 | + | 0.546683i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.813911 | − | 0.813911i | 0.0809872 | − | 0.0809872i | −0.665453 | − | 0.746440i | \(-0.731762\pi\) |
0.746440 | + | 0.665453i | \(0.231762\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.39975i | 0.827652i | 0.910356 | + | 0.413826i | \(0.135808\pi\) | ||||
−0.910356 | + | 0.413826i | \(0.864192\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.0919045i | 0.00896896i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.705176 | − | 0.705176i | 0.0681719 | − | 0.0681719i | −0.672199 | − | 0.740371i | \(-0.734650\pi\) |
0.740371 | + | 0.672199i | \(0.234650\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.1263 | + | 12.1263i | 1.16149 | + | 1.16149i | 0.984150 | + | 0.177337i | \(0.0567481\pi\) |
0.177337 | + | 0.984150i | \(0.443252\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.53999 | 0.241085 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.51705 | −0.330856 | −0.165428 | − | 0.986222i | \(-0.552901\pi\) | ||||
−0.165428 | + | 0.986222i | \(0.552901\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.73105 | − | 1.73105i | −0.161421 | − | 0.161421i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.81133 | − | 4.81133i | 0.444808 | − | 0.444808i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.37134i | 0.675729i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.16036i | 0.378215i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.143218 | − | 0.143218i | 0.0129135 | − | 0.0129135i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.64556 | − | 2.64556i | −0.236626 | − | 0.236626i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.86352 | 0.520303 | 0.260152 | − | 0.965568i | \(-0.416227\pi\) | ||||
0.260152 | + | 0.965568i | \(0.416227\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.33170 | 0.117250 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.79029 | − | 7.79029i | −0.680641 | − | 0.680641i | 0.279504 | − | 0.960145i | \(-0.409830\pi\) |
−0.960145 | + | 0.279504i | \(0.909830\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.84975 | − | 3.84975i | 0.333816 | − | 0.333816i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.546040i | 0.0469957i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 6.34879i | − | 0.542414i | −0.962521 | − | 0.271207i | \(-0.912577\pi\) | ||
0.962521 | − | 0.271207i | \(-0.0874228\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.1119 | + | 14.1119i | −1.19696 | + | 1.19696i | −0.221885 | + | 0.975073i | \(0.571221\pi\) |
−0.975073 | + | 0.221885i | \(0.928779\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.03070 | + | 1.03070i | 0.0868004 | + | 0.0868004i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.04986 | −0.505914 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.92568 | −0.159919 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.171192 | − | 0.171192i | −0.0141197 | − | 0.0141197i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.08686 | + | 7.08686i | −0.580578 | + | 0.580578i | −0.935062 | − | 0.354484i | \(-0.884657\pi\) |
0.354484 | + | 0.935062i | \(0.384657\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 8.28521i | − | 0.674241i | −0.941462 | − | 0.337120i | \(-0.890547\pi\) | ||
0.941462 | − | 0.337120i | \(-0.109453\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 21.6819i | 1.75288i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.63782 | + | 1.63782i | −0.131553 | + | 0.131553i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.68999 | − | 7.68999i | −0.613728 | − | 0.613728i | 0.330188 | − | 0.943915i | \(-0.392888\pi\) |
−0.943915 | + | 0.330188i | \(0.892888\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.197029 | 0.0156254 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.44892 | 0.508246 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.46953 | + | 4.46953i | 0.350081 | + | 0.350081i | 0.860140 | − | 0.510059i | \(-0.170376\pi\) |
−0.510059 | + | 0.860140i | \(0.670376\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.169957 | − | 0.169957i | 0.0132311 | − | 0.0132311i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 12.8905i | − | 0.997493i | −0.866748 | − | 0.498747i | \(-0.833794\pi\) | ||
0.866748 | − | 0.498747i | \(-0.166206\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 7.64873i | − | 0.588364i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.3236 | − | 11.3236i | 0.865938 | − | 0.865938i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.21257 | + | 6.21257i | 0.472333 | + | 0.472333i | 0.902669 | − | 0.430336i | \(-0.141605\pi\) |
−0.430336 | + | 0.902669i | \(0.641605\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.85590 | 0.367071 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.82496 | −0.137172 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.03654 | − | 2.03654i | −0.152218 | − | 0.152218i | 0.626890 | − | 0.779108i | \(-0.284328\pi\) |
−0.779108 | + | 0.626890i | \(0.784328\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.7116 | + | 16.7116i | −1.24217 | + | 1.24217i | −0.283064 | + | 0.959101i | \(0.591351\pi\) |
−0.959101 | + | 0.283064i | \(0.908649\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.318371i | 0.0235346i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.98263i | 0.292809i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.6316 | − | 13.6316i | 0.996843 | − | 0.996843i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.01712 | − | 1.01712i | −0.0739846 | − | 0.0739846i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.11015 | −0.369758 | −0.184879 | − | 0.982761i | \(-0.559189\pi\) | ||||
−0.184879 | + | 0.982761i | \(0.559189\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.676235 | 0.0486765 | 0.0243382 | − | 0.999704i | \(-0.492252\pi\) | ||||
0.0243382 | + | 0.999704i | \(0.492252\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.150332 | − | 0.150332i | −0.0107655 | − | 0.0107655i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.3449 | − | 14.3449i | 1.02203 | − | 1.02203i | 0.0222782 | − | 0.999752i | \(-0.492908\pi\) |
0.999752 | − | 0.0222782i | \(-0.00709197\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.94660i | 0.350655i | 0.984510 | + | 0.175328i | \(0.0560984\pi\) | ||||
−0.984510 | + | 0.175328i | \(0.943902\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.12901i | 0.150169i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.58700 | − | 3.58700i | 0.251758 | − | 0.251758i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.224561 | + | 0.224561i | 0.0156840 | + | 0.0156840i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 18.9688 | 1.31842 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −14.2385 | −0.984897 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.67810 | − | 4.67810i | −0.322054 | − | 0.322054i | 0.527501 | − | 0.849555i | \(-0.323129\pi\) |
−0.849555 | + | 0.527501i | \(0.823129\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.95647 | + | 1.95647i | −0.134055 | + | 0.134055i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.08807i | 0.142405i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 6.10161i | − | 0.414204i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.631044 | − | 0.631044i | 0.0426420 | − | 0.0426420i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.0576 | − | 12.0576i | −0.811080 | − | 0.811080i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.16691 | 0.279037 | 0.139518 | − | 0.990219i | \(-0.455445\pi\) | ||||
0.139518 | + | 0.990219i | \(0.455445\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.2831 | 0.952204 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.1022 | + | 12.1022i | 0.803248 | + | 0.803248i | 0.983602 | − | 0.180353i | \(-0.0577241\pi\) |
−0.180353 | + | 0.983602i | \(0.557724\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.5287 | − | 13.5287i | 0.893999 | − | 0.893999i | −0.100898 | − | 0.994897i | \(-0.532171\pi\) |
0.994897 | + | 0.100898i | \(0.0321714\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.633164i | 0.0416591i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 13.3857i | − | 0.876924i | −0.898750 | − | 0.438462i | \(-0.855523\pi\) | ||
0.898750 | − | 0.438462i | \(-0.144477\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.61610 | + | 1.61610i | −0.105423 | + | 0.105423i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.721871 | + | 0.721871i | 0.0468905 | + | 0.0468905i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.6475 | −1.33558 | −0.667788 | − | 0.744352i | \(-0.732759\pi\) | ||||
−0.667788 | + | 0.744352i | \(0.732759\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.401861 | −0.0258861 | −0.0129431 | − | 0.999916i | \(-0.504120\pi\) | ||||
−0.0129431 | + | 0.999916i | \(0.504120\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.50237 | − | 4.50237i | −0.288827 | − | 0.288827i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.268425 | − | 0.268425i | 0.0171490 | − | 0.0171490i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.5944i | 0.801360i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.11364i | 0.260691i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.25468 | + | 9.25468i | −0.584150 | + | 0.584150i | −0.936041 | − | 0.351891i | \(-0.885539\pi\) |
0.351891 | + | 0.936041i | \(0.385539\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.9258 | − | 11.9258i | −0.749771 | − | 0.749771i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.677459 | 0.0424241 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.3273 | 1.01847 | 0.509234 | − | 0.860628i | \(-0.329929\pi\) | ||||
0.509234 | + | 0.860628i | \(0.329929\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.41852 | − | 7.41852i | −0.460965 | − | 0.460965i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.5507 | − | 10.5507i | 0.653075 | − | 0.653075i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 13.3352i | − | 0.822284i | −0.911571 | − | 0.411142i | \(-0.865130\pi\) | ||
0.911571 | − | 0.411142i | \(-0.134870\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.308935i | 0.0189777i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.59685 | − | 1.59685i | 0.0977256 | − | 0.0977256i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.3277 | + | 19.3277i | 1.17843 | + | 1.17843i | 0.980145 | + | 0.198284i | \(0.0635367\pi\) |
0.198284 | + | 0.980145i | \(0.436463\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.5968 | −1.49415 | −0.747074 | − | 0.664741i | \(-0.768542\pi\) | ||||
−0.747074 | + | 0.664741i | \(0.768542\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.560052 | 0.0338959 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.97989 | − | 8.97989i | −0.541508 | − | 0.541508i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.9974 | + | 17.9974i | −1.08136 | + | 1.08136i | −0.0849786 | + | 0.996383i | \(0.527082\pi\) |
−0.996383 | + | 0.0849786i | \(0.972918\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 17.9472i | − | 1.07447i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 13.7357i | − | 0.819404i | −0.912219 | − | 0.409702i | \(-0.865633\pi\) | ||
0.912219 | − | 0.409702i | \(-0.134367\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.0342 | + | 10.0342i | −0.596473 | + | 0.596473i | −0.939372 | − | 0.342900i | \(-0.888591\pi\) |
0.342900 | + | 0.939372i | \(0.388591\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.353810 | − | 0.353810i | −0.0209579 | − | 0.0209579i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.836588 | −0.0493822 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 37.3366 | 2.19627 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.38012 | − | 2.38012i | −0.139525 | − | 0.139525i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.7376 | + | 19.7376i | −1.15308 | + | 1.15308i | −0.167151 | + | 0.985931i | \(0.553457\pi\) |
−0.985931 | + | 0.167151i | \(0.946543\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 2.86148i | − | 0.166602i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.76187i | 0.218286i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.5487 | + | 10.5487i | −0.610050 | + | 0.610050i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.88949 | − | 3.88949i | −0.224186 | − | 0.224186i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.278671 | 0.0160092 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.499195 | −0.0285838 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.14804 | − | 3.14804i | −0.179668 | − | 0.179668i | 0.611543 | − | 0.791211i | \(-0.290549\pi\) |
−0.791211 | + | 0.611543i | \(0.790549\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.43797 | + | 1.43797i | −0.0818035 | + | 0.0818035i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 32.2711i | − | 1.82993i | −0.403535 | − | 0.914964i | \(-0.632219\pi\) | ||
0.403535 | − | 0.914964i | \(-0.367781\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.3372i | 1.26257i | 0.775550 | + | 0.631286i | \(0.217473\pi\) | ||||
−0.775550 | + | 0.631286i | \(0.782527\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.789540 | − | 0.789540i | 0.0444856 | − | 0.0444856i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.148346 | + | 0.148346i | 0.00833196 | + | 0.00833196i | 0.711260 | − | 0.702929i | \(-0.248125\pi\) |
−0.702929 | + | 0.711260i | \(0.748125\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.2667 | −0.742792 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.241442 | 0.0134760 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −28.3778 | − | 28.3778i | −1.57898 | − | 1.57898i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.94297 | + | 7.94297i | −0.440597 | + | 0.440597i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.15186i | 0.229598i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 6.02070i | − | 0.331932i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.1427 | − | 20.1427i | 1.10714 | − | 1.10714i | 0.113618 | − | 0.993525i | \(-0.463756\pi\) |
0.993525 | − | 0.113618i | \(-0.0362440\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −21.8207 | − | 21.8207i | −1.19577 | − | 1.19577i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.33823 | −0.182387 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.83335 | 0.372236 | 0.186118 | − | 0.982527i | \(-0.440409\pi\) | ||||
0.186118 | + | 0.982527i | \(0.440409\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.602092 | − | 0.602092i | −0.0327012 | − | 0.0327012i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.2836 | + | 11.2836i | −0.611039 | + | 0.611039i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 0.592685i | − | 0.0319091i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.8489 | + | 19.8489i | −1.06554 | + | 1.06554i | −0.0678488 | + | 0.997696i | \(0.521614\pi\) |
−0.997696 | + | 0.0678488i | \(0.978386\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.6099 | − | 16.6099i | −0.889105 | − | 0.889105i | 0.105332 | − | 0.994437i | \(-0.466409\pi\) |
−0.994437 | + | 0.105332i | \(0.966409\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.32748 | 0.177608 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.41293 | 0.288101 | 0.144051 | − | 0.989570i | \(-0.453987\pi\) | ||||
0.144051 | + | 0.989570i | \(0.453987\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.06768 | − | 3.06768i | −0.162816 | − | 0.162816i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.26192 | + | 1.26192i | −0.0667878 | + | 0.0667878i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.1561i | 1.53880i | 0.638768 | + | 0.769399i | \(0.279444\pi\) | ||||
−0.638768 | + | 0.769399i | \(0.720556\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.6412i | 0.560061i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.712223 | + | 0.712223i | −0.0373820 | + | 0.0373820i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.989457 | + | 0.989457i | 0.0517906 | + | 0.0517906i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.14461 | −0.320746 | −0.160373 | − | 0.987056i | \(-0.551270\pi\) | ||||
−0.160373 | + | 0.987056i | \(0.551270\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.46073 | −0.128100 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.575460 | − | 0.575460i | −0.0298764 | − | 0.0298764i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.9348 | − | 20.9348i | 1.08396 | − | 1.08396i | 0.0878283 | − | 0.996136i | \(-0.472007\pi\) |
0.996136 | − | 0.0878283i | \(-0.0279927\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 0.905802i | − | 0.0467754i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.7348i | 0.604371i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.6398 | − | 23.6398i | 1.21429 | − | 1.21429i | 0.244693 | − | 0.969601i | \(-0.421313\pi\) |
0.969601 | − | 0.244693i | \(-0.0786872\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.00379 | + | 1.00379i | 0.0514257 | + | 0.0514257i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.99982 | 0.357674 | 0.178837 | − | 0.983879i | \(-0.442767\pi\) | ||||
0.178837 | + | 0.983879i | \(0.442767\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.992782 | −0.0505968 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.4405 | − | 11.4405i | −0.581552 | − | 0.581552i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.4838 | + | 15.4838i | −0.785060 | + | 0.785060i | −0.980680 | − | 0.195620i | \(-0.937328\pi\) |
0.195620 | + | 0.980680i | \(0.437328\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 47.5372i | − | 2.40406i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 2.66728i | − | 0.134546i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.13187 | + | 1.13187i | −0.0569506 | + | 0.0569506i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.65923 | − | 5.65923i | −0.284029 | − | 0.284029i | 0.550685 | − | 0.834713i | \(-0.314367\pi\) |
−0.834713 | + | 0.550685i | \(0.814367\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.31810 | 0.0659874 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.7191 | 1.33429 | 0.667144 | − | 0.744929i | \(-0.267517\pi\) | ||||
0.667144 | + | 0.744929i | \(0.267517\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.98063 | + | 9.98063i | 0.497171 | + | 0.497171i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.27514 | − | 2.27514i | 0.113053 | − | 0.113053i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 27.4378i | 1.36004i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.7456i | 1.02581i | 0.858447 | + | 0.512903i | \(0.171430\pi\) | ||||
−0.858447 | + | 0.512903i | \(0.828570\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.08687 | − | 1.08687i | 0.0536111 | − | 0.0536111i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.33013 | + | 5.33013i | 0.262279 | + | 0.262279i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.45006 | −0.316621 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.83171 | −0.236610 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.11779 | + | 6.11779i | 0.298874 | + | 0.298874i | 0.840573 | − | 0.541699i | \(-0.182219\pi\) |
−0.541699 | + | 0.840573i | \(0.682219\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.03252 | − | 9.03252i | 0.440218 | − | 0.440218i | −0.451867 | − | 0.892085i | \(-0.649242\pi\) |
0.892085 | + | 0.451867i | \(0.149242\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 17.7092i | − | 0.861050i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 35.7945i | − | 1.73629i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.929862 | − | 0.929862i | 0.0449992 | − | 0.0449992i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.03569 | − | 1.03569i | −0.0500036 | − | 0.0500036i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.81338 | −0.135516 | −0.0677579 | − | 0.997702i | \(-0.521585\pi\) | ||||
−0.0677579 | + | 0.997702i | \(0.521585\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.6954 | −0.994558 | −0.497279 | − | 0.867591i | \(-0.665667\pi\) | ||||
−0.497279 | + | 0.867591i | \(0.665667\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.329661 | − | 0.329661i | −0.0158060 | − | 0.0158060i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −24.8267 | + | 24.8267i | −1.18762 | + | 1.18762i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 15.6336i | − | 0.746151i | −0.927801 | − | 0.373075i | \(-0.878303\pi\) | ||
0.927801 | − | 0.373075i | \(-0.121697\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.94139i | 0.140066i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.6608 | − | 18.6608i | 0.886603 | − | 0.886603i | −0.107592 | − | 0.994195i | \(-0.534314\pi\) |
0.994195 | + | 0.107592i | \(0.0343141\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.50381 | + | 2.50381i | 0.118692 | + | 0.118692i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.42643 | −0.114766 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.8536 | 1.26730 | 0.633650 | − | 0.773620i | \(-0.281556\pi\) | ||||
0.633650 | + | 0.773620i | \(0.281556\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.54708 | + | 1.54708i | 0.0728492 | + | 0.0728492i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.41837 | − | 1.41837i | 0.0666406 | − | 0.0666406i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.878144i | 0.0411680i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.385896i | 0.0180514i | 0.999959 | + | 0.00902572i | \(0.00287302\pi\) | ||||
−0.999959 | + | 0.00902572i | \(0.997127\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.49754 | + | 7.49754i | −0.349955 | + | 0.349955i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.13650 | + | 2.13650i | 0.0995065 | + | 0.0995065i | 0.755108 | − | 0.655601i | \(-0.227585\pi\) |
−0.655601 | + | 0.755108i | \(0.727585\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.5560 | 1.51301 | 0.756503 | − | 0.653991i | \(-0.226906\pi\) | ||||
0.756503 | + | 0.653991i | \(0.226906\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.560766 | −0.0260049 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.00295 | − | 8.00295i | −0.370332 | − | 0.370332i | 0.497266 | − | 0.867598i | \(-0.334337\pi\) |
−0.867598 | + | 0.497266i | \(0.834337\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.21819 | − | 6.21819i | 0.287129 | − | 0.287129i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 2.63294i | − | 0.121319i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14.3855i | 0.661444i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.6940 | + | 18.6940i | −0.857739 | + | 0.857739i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.69265 | − | 1.69265i | −0.0775012 | − | 0.0775012i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −20.2388 | −0.924735 | −0.462368 | − | 0.886688i | \(-0.653000\pi\) | ||||
−0.462368 | + | 0.886688i | \(0.653000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.2695 | 1.10659 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.10401 | + | 1.10401i | 0.0502341 | + | 0.0502341i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.73196 | − | 3.73196i | 0.169459 | − | 0.169459i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 36.6988i | − | 1.66298i | −0.555537 | − | 0.831492i | \(-0.687487\pi\) | ||
0.555537 | − | 0.831492i | \(-0.312513\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.53030i | 0.0692026i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.6015 | + | 13.6015i | −0.613829 | + | 0.613829i | −0.943942 | − | 0.330113i | \(-0.892913\pi\) |
0.330113 | + | 0.943942i | \(0.392913\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −26.4410 | − | 26.4410i | −1.19084 | − | 1.19084i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.92015 | −0.131251 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.4285 | 0.512637 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.1970 | − | 24.1970i | −1.08321 | − | 1.08321i | −0.996209 | − | 0.0869972i | \(-0.972273\pi\) |
−0.0869972 | − | 0.996209i | \(-0.527727\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.20675 | − | 2.20675i | 0.0985903 | − | 0.0985903i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 13.4123i | − | 0.598026i | −0.954249 | − | 0.299013i | \(-0.903343\pi\) | ||
0.954249 | − | 0.299013i | \(-0.0966574\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.436947i | 0.0194439i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.30940 | − | 1.30940i | 0.0581527 | − | 0.0581527i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.9792 | − | 18.9792i | −0.841240 | − | 0.841240i | 0.147781 | − | 0.989020i | \(-0.452787\pi\) |
−0.989020 | + | 0.147781i | \(0.952787\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.68616 | −0.163066 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.83132 | 0.345761 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.25470 | − | 2.25470i | −0.0993540 | − | 0.0993540i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.1339 | + | 11.1339i | −0.489669 | + | 0.489669i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.12709i | 0.0933689i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 0.00960703i | − | 0.000420892i | −1.00000 | 0.000210446i | \(-0.999933\pi\) | |||
1.00000 | 0.000210446i | \(-6.69870e-5\pi\) | ||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.5829 | − | 23.5829i | 1.03121 | − | 1.03121i | 0.0317098 | − | 0.999497i | \(-0.489905\pi\) |
0.999497 | − | 0.0317098i | \(-0.0100952\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.831293 | + | 0.831293i | 0.0362806 | + | 0.0362806i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −44.9770 | −1.95923 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.5886 | −0.808201 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.6780 | + | 15.6780i | 0.680366 | + | 0.680366i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.36844 | − | 1.36844i | 0.0592736 | − | 0.0592736i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.378573i | 0.0163671i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 0.697281i | − | 0.0300899i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.84927 | − | 1.84927i | 0.0796539 | − | 0.0796539i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.6478 | − | 11.6478i | −0.500776 | − | 0.500776i | 0.410903 | − | 0.911679i | \(-0.365214\pi\) |
−0.911679 | + | 0.410903i | \(0.865214\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.72181 | −0.245546 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.50998 | −0.278857 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.0041 | − | 14.0041i | −0.598773 | − | 0.598773i | 0.341213 | − | 0.939986i | \(-0.389162\pi\) |
−0.939986 | + | 0.341213i | \(0.889162\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.73508 | − | 2.73508i | 0.116730 | − | 0.116730i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27.6181i | 1.17657i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 4.21672i | − | 0.179313i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.681796 | + | 0.681796i | −0.0289406 | + | 0.0289406i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.3807 | + | 24.3807i | 1.03305 | + | 1.03305i | 0.999435 | + | 0.0336103i | \(0.0107005\pi\) |
0.0336103 | + | 0.999435i | \(0.489299\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.7244 | 0.538183 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.66727 | 0.197052 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −26.2789 | − | 26.2789i | −1.10752 | − | 1.10752i | −0.993475 | − | 0.114046i | \(-0.963619\pi\) |
−0.114046 | − | 0.993475i | \(-0.536381\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.944062 | − | 0.944062i | 0.0397170 | − | 0.0397170i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.47591i | 0.355955i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 36.8053i | − | 1.54296i | −0.636255 | − | 0.771479i | \(-0.719517\pi\) | ||
0.636255 | − | 0.771479i | \(-0.280483\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.0536 | − | 23.0536i | 0.964762 | − | 0.964762i | −0.0346376 | − | 0.999400i | \(-0.511028\pi\) |
0.999400 | + | 0.0346376i | \(0.0110277\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.874820 | − | 0.874820i | −0.0365461 | − | 0.0365461i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −31.3153 | −1.30594 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.51057 | −0.146147 | −0.0730735 | − | 0.997327i | \(-0.523281\pi\) | ||||
−0.0730735 | + | 0.997327i | \(0.523281\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.115766 | + | 0.115766i | 0.00481109 | + | 0.00481109i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.0147 | − | 12.0147i | 0.498452 | − | 0.498452i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.12837i | 0.0881480i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.58296i | 0.106792i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.0315 | + | 28.0315i | −1.15699 | + | 1.15699i | −0.171865 | + | 0.985120i | \(0.554979\pi\) |
−0.985120 | + | 0.171865i | \(0.945021\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.4897 | + | 23.4897i | 0.967876 | + | 0.967876i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.91147 | 0.202031 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.27767 | 0.257793 | 0.128896 | − | 0.991658i | \(-0.458857\pi\) | ||||
0.128896 | + | 0.991658i | \(0.458857\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.97865 | − | 1.97865i | −0.0811167 | − | 0.0811167i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.846821 | + | 0.846821i | −0.0346581 | + | 0.0346581i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.3600i | 0.423300i | 0.977346 | + | 0.211650i | \(0.0678836\pi\) | ||||
−0.977346 | + | 0.211650i | \(0.932116\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.9656i | 0.977576i | 0.872403 | + | 0.488788i | \(0.162561\pi\) | ||||
−0.872403 | + | 0.488788i | \(0.837439\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 18.2901 | − | 18.2901i | 0.744830 | − | 0.744830i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.11674 | − | 1.11674i | −0.0454021 | − | 0.0454021i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.4285 | 0.585633 | 0.292817 | − | 0.956169i | \(-0.405407\pi\) | ||||
0.292817 | + | 0.956169i | \(0.405407\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.22813 | 0.0497665 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.84828 | + | 9.84828i | 0.398419 | + | 0.398419i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.13825 | − | 3.13825i | 0.126753 | − | 0.126753i | −0.640885 | − | 0.767637i | \(-0.721432\pi\) |
0.767637 | + | 0.640885i | \(0.221432\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.0768862i | 0.00310035i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 15.7644i | − | 0.634651i | −0.948317 | − | 0.317325i | \(-0.897215\pi\) | ||
0.948317 | − | 0.317325i | \(-0.102785\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.16647 | + | 6.16647i | −0.247851 | + | 0.247851i | −0.820088 | − | 0.572237i | \(-0.806076\pi\) |
0.572237 | + | 0.820088i | \(0.306076\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.55934 | + | 6.55934i | 0.263217 | + | 0.263217i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.32780 | −0.373711 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.8592 | −0.914369 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.43752 | − | 2.43752i | −0.0973453 | − | 0.0973453i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −54.6844 | + | 54.6844i | −2.18041 | + | 2.18041i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.5796i | 1.21736i | 0.793417 | + | 0.608678i | \(0.208300\pi\) | ||||
−0.793417 | + | 0.608678i | \(0.791700\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 1.60171i | − | 0.0636623i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.57391 | + | 1.57391i | −0.0624588 | + | 0.0624588i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.63574 | − | 1.63574i | −0.0648103 | − | 0.0648103i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 33.6155 | 1.32981 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.6228 | −0.735556 | −0.367778 | − | 0.929914i | \(-0.619881\pi\) | ||||
−0.367778 | + | 0.929914i | \(0.619881\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.8340 | + | 27.8340i | 1.09766 | + | 1.09766i | 0.994683 | + | 0.102981i | \(0.0328381\pi\) |
0.102981 | + | 0.994683i | \(0.467162\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.357461 | + | 0.357461i | −0.0140750 | + | 0.0140750i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.2607i | 1.15036i | 0.818029 | + | 0.575178i | \(0.195067\pi\) | ||||
−0.818029 | + | 0.575178i | \(0.804933\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 19.7138i | − | 0.773833i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.04455 | − | 1.04455i | 0.0409392 | − | 0.0409392i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.3825 | + | 17.3825i | 0.680229 | + | 0.680229i | 0.960052 | − | 0.279822i | \(-0.0902756\pi\) |
−0.279822 | + | 0.960052i | \(0.590276\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.18221 | 0.163413 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.8424 | −0.423004 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.7030 | + | 27.7030i | 1.07916 | + | 1.07916i | 0.996585 | + | 0.0825717i | \(0.0263134\pi\) |
0.0825717 | + | 0.996585i | \(0.473687\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.7539 | − | 18.7539i | 0.729443 | − | 0.729443i | −0.241066 | − | 0.970509i | \(-0.577497\pi\) |
0.970509 | + | 0.241066i | \(0.0774970\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 4.12833i | − | 0.160331i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.06673i | 0.0801445i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23.1323 | + | 23.1323i | −0.895685 | + | 0.895685i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.713343 | + | 0.713343i | 0.0275794 | + | 0.0275794i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.43914 | −0.132767 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.89179 | 0.342753 | 0.171377 | − | 0.985206i | \(-0.445179\pi\) | ||||
0.171377 | + | 0.985206i | \(0.445179\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.93903 | + | 4.93903i | 0.190103 | + | 0.190103i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.0023 | − | 23.0023i | 0.884049 | − | 0.884049i | −0.109895 | − | 0.993943i | \(-0.535051\pi\) |
0.993943 | + | 0.109895i | \(0.0350514\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.9032i | 0.533556i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.14360i | 0.158783i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.13050 | + | 8.13050i | −0.311105 | + | 0.311105i | −0.845337 | − | 0.534233i | \(-0.820601\pi\) |
0.534233 | + | 0.845337i | \(0.320601\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.70417 | + | 1.70417i | 0.0651131 | + | 0.0651131i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.63201 | 0.176722 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.88260 | 0.0717215 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.09420 | + | 1.09420i | 0.0416253 | + | 0.0416253i | 0.727613 | − | 0.685988i | \(-0.240630\pi\) |
−0.685988 | + | 0.727613i | \(0.740630\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.43943 | − | 5.43943i | 0.206627 | − | 0.206627i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 7.57597i | − | 0.287373i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.16677i | 0.233583i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.29152 | − | 2.29152i | 0.0866734 | − | 0.0866734i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.5656 | − | 11.5656i | −0.436825 | − | 0.436825i | 0.454117 | − | 0.890942i | \(-0.349955\pi\) |
−0.890942 | + | 0.454117i | \(0.849955\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 57.1189 | 2.15428 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.553329 | −0.0208396 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.813911 | − | 0.813911i | −0.0306103 | − | 0.0306103i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.69651 | − | 2.69651i | 0.101270 | − | 0.101270i | −0.654657 | − | 0.755926i | \(-0.727187\pi\) |
0.755926 | + | 0.654657i | \(0.227187\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 12.4030i | − | 0.465149i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 39.3488i | 1.47363i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.62393 | − | 1.62393i | 0.0607315 | − | 0.0607315i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.53470 | − | 3.53470i | −0.132006 | − | 0.132006i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.08527 | 0.226942 | 0.113471 | − | 0.993541i | \(-0.463803\pi\) | ||||
0.113471 | + | 0.993541i | \(0.463803\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.39975 | 0.312823 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.0687956 | − | 0.0687956i | −0.00255854 | − | 0.00255854i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −17.4181 | + | 17.4181i | −0.646891 | + | 0.646891i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 41.6162i | − | 1.54346i | −0.635951 | − | 0.771729i | \(-0.719392\pi\) | ||
0.635951 | − | 0.771729i | \(-0.280608\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.8862i | 0.884674i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −28.6707 | + | 28.6707i | −1.06042 | + | 1.06042i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.5929 | + | 23.5929i | 0.871422 | + | 0.871422i | 0.992627 | − | 0.121206i | \(-0.0386760\pi\) |
−0.121206 | + | 0.992627i | \(0.538676\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.0919045 | 0.00338995 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22.9983 | −0.847152 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.53135 | − | 7.53135i | −0.277045 | − | 0.277045i | 0.554883 | − | 0.831928i | \(-0.312763\pi\) |
−0.831928 | + | 0.554883i | \(0.812763\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.15606 | + | 2.15606i | −0.0792048 | + | 0.0792048i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 14.4179i | − | 0.528943i | −0.964393 | − | 0.264472i | \(-0.914802\pi\) | ||
0.964393 | − | 0.264472i | \(-0.0851975\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 3.80457i | − | 0.139389i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 35.3397 | − | 35.3397i | 1.29301 | − | 1.29301i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.705176 | − | 0.705176i | −0.0257666 | − | 0.0257666i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.6760 | 0.645008 | 0.322504 | − | 0.946568i | \(-0.395475\pi\) | ||||
0.322504 | + | 0.946568i | \(0.395475\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.16866 | −0.115472 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.22395 | + | 2.22395i | 0.0809379 | + | 0.0809379i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.3351 | − | 21.3351i | 0.775437 | − | 0.775437i | −0.203614 | − | 0.979051i | \(-0.565269\pi\) |
0.979051 | + | 0.203614i | \(0.0652687\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 4.08323i | − | 0.148212i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 22.2510i | − | 0.806597i | −0.915068 | − | 0.403299i | \(-0.867864\pi\) | ||
0.915068 | − | 0.403299i | \(-0.132136\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.1263 | − | 12.1263i | 0.439001 | − | 0.439001i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.81997 | − | 5.81997i | −0.210421 | − | 0.210421i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17.4374 | −0.629628 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.5537 | −1.10179 | −0.550897 | − | 0.834573i | \(-0.685714\pi\) | ||||
−0.550897 | + | 0.834573i | \(0.685714\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.79511 | + | 2.79511i | 0.100663 | + | 0.100663i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.1590 | − | 19.1590i | 0.689100 | − | 0.689100i | −0.272933 | − | 0.962033i | \(-0.587994\pi\) |
0.962033 | + | 0.272933i | \(0.0879938\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.6288i | 1.06430i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 2.53999i | − | 0.0911217i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.22065 | − | 3.22065i | 0.115392 | − | 0.115392i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.1344 | − | 21.1344i | −0.756247 | − | 0.756247i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.29682 | 0.260767 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.12836 | 0.147348 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.8172 | + | 13.8172i | 0.492528 | + | 0.492528i | 0.909102 | − | 0.416574i | \(-0.136769\pi\) |
−0.416574 | + | 0.909102i | \(0.636769\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.28289 | − | 2.28289i | 0.0812729 | − | 0.0812729i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.51705i | 0.125052i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.04202i | 0.108025i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.0528874 | + | 0.0528874i | −0.00187572 | + | 0.00187572i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.78511 | + | 8.78511i | 0.311185 | + | 0.311185i | 0.845368 | − | 0.534184i | \(-0.179381\pi\) |
−0.534184 | + | 0.845368i | \(0.679381\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −44.3806 | −1.57007 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −27.4367 | −0.969427 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.81673 | + | 6.81673i | 0.240557 | + | 0.240557i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.73105 | + | 1.73105i | −0.0610115 | + | 0.0610115i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.61750i | 0.232947i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 2.11808i | − | 0.0744676i | −0.999307 | − | 0.0372338i | \(-0.988145\pi\) | ||
0.999307 | − | 0.0372338i | \(-0.0118546\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.203189 | − | 0.203189i | 0.00713494 | − | 0.00713494i | −0.703530 | − | 0.710665i | \(-0.748394\pi\) |
0.710665 | + | 0.703530i | \(0.248394\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.21078 | − | 4.21078i | −0.147679 | − | 0.147679i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.39946 | −0.0840496 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.9471 | 1.04772 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.81133 | − | 4.81133i | −0.168122 | − | 0.168122i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.7943 | − | 20.7943i | 0.725726 | − | 0.725726i | −0.244039 | − | 0.969765i | \(-0.578473\pi\) |
0.969765 | + | 0.244039i | \(0.0784726\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.1430i | 0.353563i | 0.984250 | + | 0.176782i | \(0.0565686\pi\) | ||||
−0.984250 | + | 0.176782i | \(0.943431\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 3.07458i | − | 0.107043i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.6137 | − | 19.6137i | 0.682035 | − | 0.682035i | −0.278424 | − | 0.960458i | \(-0.589812\pi\) |
0.960458 | + | 0.278424i | \(0.0898120\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.25634 | + | 9.25634i | 0.321486 | + | 0.321486i | 0.849337 | − | 0.527851i | \(-0.177002\pi\) |
−0.527851 | + | 0.849337i | \(0.677002\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.16205 | −0.213759 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.37134 | 0.255402 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.46011 | + | 3.46011i | 0.119742 | + | 0.119742i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.20608 | − | 6.20608i | 0.214513 | − | 0.214513i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 9.57102i | − | 0.330428i | −0.986258 | − | 0.165214i | \(-0.947168\pi\) | ||
0.986258 | − | 0.165214i | \(-0.0528315\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 3.26691i | − | 0.112652i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.35145 | − | 2.35145i | 0.0809882 | − | 0.0809882i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.05311 | + | 2.05311i | 0.0706290 | + | 0.0706290i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.16036 | 0.142952 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.43557 | −0.117908 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 47.8415 | + | 47.8415i | 1.63999 | + | 1.63999i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.2865 | − | 14.2865i | 0.489162 | − | 0.489162i | −0.418880 | − | 0.908042i | \(-0.637577\pi\) |
0.908042 | + | 0.418880i | \(0.137577\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.07907i | 0.207900i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 37.1981i | − | 1.27066i | −0.772239 | − | 0.635332i | \(-0.780863\pi\) | ||
0.772239 | − | 0.635332i | \(-0.219137\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.1537 | + | 36.1537i | −1.23355 | + | 1.23355i | −0.270959 | + | 0.962591i | \(0.587341\pi\) |
−0.962591 | + | 0.270959i | \(0.912659\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.143218 | − | 0.143218i | −0.00488084 | − | 0.00488084i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27.6826 | 0.942325 | 0.471163 | − | 0.882046i | \(-0.343835\pi\) | ||||
0.471163 | + | 0.882046i | \(0.343835\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.33521 | −0.113401 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.39175 | + | 6.39175i | 0.217075 | + | 0.217075i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.79787 | + | 7.79787i | −0.264525 | + | 0.264525i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.3426i | 0.689284i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 40.8947i | 1.38407i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.64556 | + | 2.64556i | −0.0894364 | + | 0.0894364i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.17870 | + | 2.17870i | 0.0735694 | + | 0.0735694i | 0.742934 | − | 0.669365i | \(-0.233434\pi\) |
−0.669365 | + | 0.742934i | \(0.733434\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.75785 | −0.227937 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.9678 | −1.34655 | −0.673276 | − | 0.739392i | \(-0.735113\pi\) | ||||
−0.673276 | + | 0.739392i | \(0.735113\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.53035 | − | 5.53035i | −0.186111 | − | 0.186111i | 0.607901 | − | 0.794013i | \(-0.292012\pi\) |
−0.794013 | + | 0.607901i | \(0.792012\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.489863 | − | 0.489863i | 0.0164666 | − | 0.0164666i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 47.8800i | 1.60765i | 0.594865 | + | 0.803826i | \(0.297206\pi\) | ||||
−0.594865 | + | 0.803826i | \(0.702794\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 5.86352i | − | 0.196656i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.6743 | − | 15.6743i | 0.525109 | − | 0.525109i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 23.1782 | + | 23.1782i | 0.775628 | + | 0.775628i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.09332 | 0.0365455 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.61173 | −0.120592 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 21.8865 | + | 21.8865i | 0.729954 | + | 0.729954i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.24191 | + | 4.24191i | −0.141319 | + | 0.141319i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 1.33170i | − | 0.0443163i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 8.97162i | − | 0.298227i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.4221 | + | 28.4221i | −0.943740 | + | 0.943740i | −0.998500 | − | 0.0547595i | \(-0.982561\pi\) |
0.0547595 | + | 0.998500i | \(0.482561\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.39403 | − | 2.39403i | −0.0794048 | − | 0.0794048i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 50.4192 | 1.67046 | 0.835231 | − | 0.549899i | \(-0.185334\pi\) | ||||
0.835231 | + | 0.549899i | \(0.185334\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −44.4368 | −1.47064 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.0854585 | − | 0.0854585i | −0.00282517 | − | 0.00282517i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.79029 | + | 7.79029i | −0.257258 | + | 0.257258i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41.1782i | 1.35834i | 0.733980 | + | 0.679171i | \(0.237661\pi\) | ||||
−0.733980 | + | 0.679171i | \(0.762339\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 1.07784i | − | 0.0355161i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −18.6940 | + | 18.6940i | −0.615319 | + | 0.615319i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 36.0236 | + | 36.0236i | 1.18445 | + | 1.18445i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 24.7069 | 0.811482 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −57.2128 | −1.87709 | −0.938546 | − | 0.345155i | \(-0.887826\pi\) | ||||
−0.938546 | + | 0.345155i | \(0.887826\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.84975 | − | 3.84975i | −0.126170 | − | 0.126170i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.52458 | − | 5.52458i | 0.180866 | − | 0.180866i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.31813i | 0.239328i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.3565i | 0.730353i | 0.930938 | + | 0.365177i | \(0.118991\pi\) | ||||
−0.930938 | + | 0.365177i | \(0.881009\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.82396 | + | 3.82396i | −0.124790 | + | 0.124790i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.0080 | + | 15.0080i | 0.489246 | + | 0.489246i | 0.908068 | − | 0.418822i | \(-0.137557\pi\) |
−0.418822 | + | 0.908068i | \(0.637557\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.39509 | 0.175688 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.546040 | 0.0177627 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.21317 | − | 7.21317i | −0.234396 | − | 0.234396i | 0.580129 | − | 0.814525i | \(-0.303002\pi\) |
−0.814525 | + | 0.580129i | \(0.803002\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.02960 | − | 6.02960i | 0.195729 | − | 0.195729i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.0507915i | 0.00164703i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 49.0686i | − | 1.58949i | −0.606944 | − | 0.794744i | \(-0.707605\pi\) | ||
0.606944 | − | 0.794744i | \(-0.292395\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.37169 | − | 1.37169i | 0.0443869 | − | 0.0443869i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.27116 | − | 2.27116i | −0.0734161 | − | 0.0734161i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.34879 | −0.205013 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.22968 | 0.200957 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.07420 | − | 2.07420i | −0.0668400 | − | 0.0668400i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.181518 | + | 0.181518i | −0.00584327 | + | 0.00584327i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 3.07877i | − | 0.0990064i | −0.998774 | − | 0.0495032i | \(-0.984236\pi\) | ||
0.998774 | − | 0.0495032i | \(-0.0157638\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 9.71614i | − | 0.312127i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.0104 | + | 16.0104i | −0.513797 | + | 0.513797i | −0.915688 | − | 0.401890i | \(-0.868353\pi\) |
0.401890 | + | 0.915688i | \(0.368353\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.1119 | + | 14.1119i | 0.452408 | + | 0.452408i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.71955 | −0.0870954 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.9770 | 0.351185 | 0.175592 | − | 0.984463i | \(-0.443816\pi\) | ||||
0.175592 | + | 0.984463i | \(0.443816\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.2497 | + | 17.2497i | 0.551302 | + | 0.551302i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 35.6681 | − | 35.6681i | 1.13879 | − | 1.13879i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 15.7349i | − | 0.501864i | −0.968005 | − | 0.250932i | \(-0.919263\pi\) | ||
0.968005 | − | 0.250932i | \(-0.0807371\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.70103i | 0.245375i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.03070 | − | 1.03070i | 0.0328075 | − | 0.0328075i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25.0830 | + | 25.0830i | 0.797593 | + | 0.797593i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.7969 | 1.48655 | 0.743276 | − | 0.668984i | \(-0.233271\pi\) | ||||
0.743276 | + | 0.668984i | \(0.233271\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.89656 | 0.218856 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.32779 | − | 1.32779i | −0.0420937 | − | 0.0420937i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.1536 | + | 29.1536i | −0.923305 | + | 0.923305i | −0.997261 | − | 0.0739568i | \(-0.976437\pi\) |
0.0739568 | + | 0.997261i | \(0.476437\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 15.0911i | − | 0.477460i |
(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 | 1792.2.m.h.1345.5 | yes | 16 | |
4.3 | odd | 2 | 1792.2.m.f.1345.4 | yes | 16 | ||
8.3 | odd | 2 | 1792.2.m.g.1345.5 | yes | 16 | ||
8.5 | even | 2 | 1792.2.m.e.1345.4 | yes | 16 | ||
16.3 | odd | 4 | 1792.2.m.g.449.5 | yes | 16 | ||
16.5 | even | 4 | inner | 1792.2.m.h.449.5 | yes | 16 | |
16.11 | odd | 4 | 1792.2.m.f.449.4 | yes | 16 | ||
16.13 | even | 4 | 1792.2.m.e.449.4 | ✓ | 16 | ||
32.5 | even | 8 | 7168.2.a.bf.1.4 | 8 | |||
32.11 | odd | 8 | 7168.2.a.ba.1.4 | 8 | |||
32.21 | even | 8 | 7168.2.a.bb.1.5 | 8 | |||
32.27 | odd | 8 | 7168.2.a.be.1.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1792.2.m.e.449.4 | ✓ | 16 | 16.13 | even | 4 | ||
1792.2.m.e.1345.4 | yes | 16 | 8.5 | even | 2 | ||
1792.2.m.f.449.4 | yes | 16 | 16.11 | odd | 4 | ||
1792.2.m.f.1345.4 | yes | 16 | 4.3 | odd | 2 | ||
1792.2.m.g.449.5 | yes | 16 | 16.3 | odd | 4 | ||
1792.2.m.g.1345.5 | yes | 16 | 8.3 | odd | 2 | ||
1792.2.m.h.449.5 | yes | 16 | 16.5 | even | 4 | inner | |
1792.2.m.h.1345.5 | yes | 16 | 1.1 | even | 1 | trivial | |
7168.2.a.ba.1.4 | 8 | 32.11 | odd | 8 | |||
7168.2.a.bb.1.5 | 8 | 32.21 | even | 8 | |||
7168.2.a.be.1.5 | 8 | 32.27 | odd | 8 | |||
7168.2.a.bf.1.4 | 8 | 32.5 | even | 8 |