Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1357,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.1357");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.x (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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1357.3 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1357 |
Dual form | 2100.2.x.a.1693.3 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.63896 | + | 0.189469i | −0.997433 | + | 0.0716124i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | −0.904534 | −0.452267 | − | 0.891883i | \(-0.649385\pi\) | ||||
−0.452267 | + | 0.891883i | \(0.649385\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.41421 | − | 1.41421i | −0.392232 | − | 0.392232i | 0.483250 | − | 0.875482i | \(-0.339456\pi\) |
−0.875482 | + | 0.483250i | \(0.839456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.24264 | − | 4.24264i | 1.02899 | − | 1.02899i | 0.0294245 | − | 0.999567i | \(-0.490633\pi\) |
0.999567 | − | 0.0294245i | \(-0.00936746\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.46410 | 0.794719 | 0.397360 | − | 0.917663i | \(-0.369927\pi\) | ||||
0.397360 | + | 0.917663i | \(0.369927\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.00000 | − | 1.73205i | −0.436436 | − | 0.377964i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.67423 | − | 3.67423i | 0.766131 | − | 0.766131i | −0.211292 | − | 0.977423i | \(-0.567767\pi\) |
0.977423 | + | 0.211292i | \(0.0677671\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.00000i | 1.67126i | 0.549294 | + | 0.835629i | \(0.314897\pi\) | ||||
−0.549294 | + | 0.835629i | \(0.685103\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.92820i | − | 1.24434i | −0.782881 | − | 0.622171i | \(-0.786251\pi\) | ||
0.782881 | − | 0.622171i | \(-0.213749\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.12132 | − | 2.12132i | −0.369274 | − | 0.369274i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.67423 | + | 3.67423i | 0.604040 | + | 0.604040i | 0.941382 | − | 0.337342i | \(-0.109528\pi\) |
−0.337342 | + | 0.941382i | \(0.609528\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 2.00000i | − | 0.320256i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.57321 | − | 8.57321i | 1.30740 | − | 1.30740i | 0.384120 | − | 0.923283i | \(-0.374505\pi\) |
0.923283 | − | 0.384120i | \(-0.125495\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.24264 | − | 4.24264i | 0.618853 | − | 0.618853i | −0.326384 | − | 0.945237i | \(-0.605830\pi\) |
0.945237 | + | 0.326384i | \(0.105830\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.92820 | − | 1.00000i | 0.989743 | − | 0.142857i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.00000 | 0.840168 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.44949 | + | 2.44949i | 0.324443 | + | 0.324443i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.3923 | 1.35296 | 0.676481 | − | 0.736460i | \(-0.263504\pi\) | ||||
0.676481 | + | 0.736460i | \(0.263504\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.92820i | 0.887066i | 0.896258 | + | 0.443533i | \(0.146275\pi\) | ||||
−0.896258 | + | 0.443533i | \(0.853725\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.189469 | − | 2.63896i | −0.0238708 | − | 0.332478i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.57321 | + | 8.57321i | 1.04738 | + | 1.04738i | 0.998820 | + | 0.0485648i | \(0.0154647\pi\) |
0.0485648 | + | 0.998820i | \(0.484535\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.19615 | 0.625543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.00000 | 0.356034 | 0.178017 | − | 0.984027i | \(-0.443032\pi\) | ||||
0.178017 | + | 0.984027i | \(0.443032\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.41421 | + | 1.41421i | 0.165521 | + | 0.165521i | 0.785007 | − | 0.619486i | \(-0.212659\pi\) |
−0.619486 | + | 0.785007i | \(0.712659\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.91688 | − | 0.568406i | 0.902212 | − | 0.0647759i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.00000i | 0.112509i | 0.998416 | + | 0.0562544i | \(0.0179158\pi\) | ||||
−0.998416 | + | 0.0562544i | \(0.982084\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.48528 | − | 8.48528i | −0.931381 | − | 0.931381i | 0.0664117 | − | 0.997792i | \(-0.478845\pi\) |
−0.997792 | + | 0.0664117i | \(0.978845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.36396 | + | 6.36396i | −0.682288 | + | 0.682288i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.3923 | −1.10158 | −0.550791 | − | 0.834643i | \(-0.685674\pi\) | ||||
−0.550791 | + | 0.834643i | \(0.685674\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000 | + | 3.46410i | 0.419314 | + | 0.363137i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.89898 | − | 4.89898i | 0.508001 | − | 0.508001i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.82843 | − | 2.82843i | 0.287183 | − | 0.287183i | −0.548782 | − | 0.835965i | \(-0.684908\pi\) |
0.835965 | + | 0.548782i | \(0.184908\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 3.00000i | − | 0.301511i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 10.3923i | − | 1.03407i | −0.855963 | − | 0.517036i | \(-0.827035\pi\) | ||
0.855963 | − | 0.517036i | \(-0.172965\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.89949 | − | 9.89949i | −0.975426 | − | 0.975426i | 0.0242790 | − | 0.999705i | \(-0.492271\pi\) |
−0.999705 | + | 0.0242790i | \(0.992271\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.34847 | − | 7.34847i | −0.710403 | − | 0.710403i | 0.256216 | − | 0.966620i | \(-0.417524\pi\) |
−0.966620 | + | 0.256216i | \(0.917524\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.0000i | 1.62830i | 0.580651 | + | 0.814152i | \(0.302798\pi\) | ||||
−0.580651 | + | 0.814152i | \(0.697202\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.19615i | 0.493197i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.67423 | − | 3.67423i | 0.345643 | − | 0.345643i | −0.512841 | − | 0.858484i | \(-0.671407\pi\) |
0.858484 | + | 0.512841i | \(0.171407\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.41421 | − | 1.41421i | 0.130744 | − | 0.130744i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.3923 | + | 12.0000i | −0.952661 | + | 1.10004i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.67423 | − | 3.67423i | −0.326036 | − | 0.326036i | 0.525041 | − | 0.851077i | \(-0.324050\pi\) |
−0.851077 | + | 0.525041i | \(0.824050\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.1244 | 1.06749 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 10.3923i | − | 0.907980i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||
0.891007 | − | 0.453990i | \(-0.150000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.14162 | + | 0.656339i | −0.792679 | + | 0.0569118i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.3923 | 0.881464 | 0.440732 | − | 0.897639i | \(-0.354719\pi\) | ||||
0.440732 | + | 0.897639i | \(0.354719\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | 0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.24264 | + | 4.24264i | 0.354787 | + | 0.354787i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.60609 | + | 4.19187i | 0.462382 | + | 0.345740i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.0000i | 1.22885i | 0.788976 | + | 0.614424i | \(0.210612\pi\) | ||||
−0.788976 | + | 0.614424i | \(0.789388\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.00000 | 0.406894 | 0.203447 | − | 0.979086i | \(-0.434786\pi\) | ||||
0.203447 | + | 0.979086i | \(0.434786\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.24264 | + | 4.24264i | 0.342997 | + | 0.342997i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.3137 | − | 11.3137i | 0.902932 | − | 0.902932i | −0.0927566 | − | 0.995689i | \(-0.529568\pi\) |
0.995689 | + | 0.0927566i | \(0.0295678\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.00000 | + | 10.3923i | −0.709299 | + | 0.819028i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.44949 | − | 2.44949i | 0.191859 | − | 0.191859i | −0.604640 | − | 0.796499i | \(-0.706683\pi\) |
0.796499 | + | 0.604640i | \(0.206683\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.24264 | − | 4.24264i | 0.328305 | − | 0.328305i | −0.523636 | − | 0.851942i | \(-0.675425\pi\) |
0.851942 | + | 0.523636i | \(0.175425\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 9.00000i | − | 0.692308i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.46410i | 0.264906i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.7279 | − | 12.7279i | −0.967686 | − | 0.967686i | 0.0318080 | − | 0.999494i | \(-0.489873\pi\) |
−0.999494 | + | 0.0318080i | \(0.989873\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.34847 | + | 7.34847i | 0.552345 | + | 0.552345i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0000i | 0.896922i | 0.893802 | + | 0.448461i | \(0.148028\pi\) | ||||
−0.893802 | + | 0.448461i | \(0.851972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.46410i | 0.257485i | 0.991678 | + | 0.128742i | \(0.0410940\pi\) | ||||
−0.991678 | + | 0.128742i | \(0.958906\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.89898 | + | 4.89898i | −0.362143 | + | 0.362143i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.7279 | + | 12.7279i | −0.930758 | + | 0.930758i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.73205 | − | 2.00000i | 0.125988 | − | 0.145479i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.4722 | − | 13.4722i | 0.969750 | − | 0.969750i | −0.0298060 | − | 0.999556i | \(-0.509489\pi\) |
0.999556 | + | 0.0298060i | \(0.00948895\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.0227 | − | 11.0227i | −0.785335 | − | 0.785335i | 0.195390 | − | 0.980726i | \(-0.437403\pi\) |
−0.980726 | + | 0.195390i | \(0.937403\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.92820 | 0.491127 | 0.245564 | − | 0.969380i | \(-0.421027\pi\) | ||||
0.245564 | + | 0.969380i | \(0.421027\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.1244i | 0.855186i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.70522 | − | 23.7506i | −0.119683 | − | 1.66697i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.67423 | + | 3.67423i | 0.255377 | + | 0.255377i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.3923 | −0.718851 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.0000 | 1.10149 | 0.550743 | − | 0.834675i | \(-0.314345\pi\) | ||||
0.550743 | + | 0.834675i | \(0.314345\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.12132 | + | 2.12132i | 0.145350 | + | 0.145350i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.31268 | + | 18.2832i | 0.0891104 | + | 1.24115i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.00000i | 0.135147i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.0000 | −0.807207 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.89949 | + | 9.89949i | 0.662919 | + | 0.662919i | 0.956067 | − | 0.293148i | \(-0.0947028\pi\) |
−0.293148 | + | 0.956067i | \(0.594703\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.24264 | − | 4.24264i | 0.281594 | − | 0.281594i | −0.552151 | − | 0.833744i | \(-0.686193\pi\) |
0.833744 | + | 0.552151i | \(0.186193\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.92820 | 0.457829 | 0.228914 | − | 0.973447i | \(-0.426482\pi\) | ||||
0.228914 | + | 0.973447i | \(0.426482\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.00000 | + | 5.19615i | 0.394771 | + | 0.341882i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.3712 | + | 18.3712i | −1.20354 | + | 1.20354i | −0.230452 | + | 0.973084i | \(0.574020\pi\) |
−0.973084 | + | 0.230452i | \(0.925980\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.707107 | + | 0.707107i | −0.0459315 | + | 0.0459315i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 17.3205i | − | 1.11571i | −0.829938 | − | 0.557856i | \(-0.811624\pi\) | ||
0.829938 | − | 0.557856i | \(-0.188376\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.89898 | − | 4.89898i | −0.311715 | − | 0.311715i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 12.0000i | − | 0.760469i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 31.1769i | − | 1.96787i | −0.178529 | − | 0.983935i | \(-0.557134\pi\) | ||
0.178529 | − | 0.983935i | \(-0.442866\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.0227 | + | 11.0227i | −0.692991 | + | 0.692991i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.48528 | − | 8.48528i | 0.529297 | − | 0.529297i | −0.391066 | − | 0.920363i | \(-0.627893\pi\) |
0.920363 | + | 0.391066i | \(0.127893\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.3923 | − | 9.00000i | −0.645746 | − | 0.559233i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.00000 | −0.557086 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.0227 | + | 11.0227i | −0.679689 | + | 0.679689i | −0.959930 | − | 0.280241i | \(-0.909586\pi\) |
0.280241 | + | 0.959930i | \(0.409586\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.34847 | − | 7.34847i | −0.449719 | − | 0.449719i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −20.7846 | −1.26726 | −0.633630 | − | 0.773636i | \(-0.718436\pi\) | ||||
−0.633630 | + | 0.773636i | \(0.718436\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.1769i | 1.89386i | 0.321436 | + | 0.946931i | \(0.395835\pi\) | ||||
−0.321436 | + | 0.946931i | \(0.604165\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.378937 | + | 5.27792i | 0.0229343 | + | 0.319434i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.79796 | + | 9.79796i | 0.588702 | + | 0.588702i | 0.937280 | − | 0.348578i | \(-0.113335\pi\) |
−0.348578 | + | 0.937280i | \(0.613335\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.92820 | 0.414781 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.00000 | 0.178965 | 0.0894825 | − | 0.995988i | \(-0.471479\pi\) | ||||
0.0894825 | + | 0.995988i | \(0.471479\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.3137 | + | 11.3137i | 0.672530 | + | 0.672530i | 0.958299 | − | 0.285769i | \(-0.0922488\pi\) |
−0.285769 | + | 0.958299i | \(0.592249\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 19.0000i | − | 1.11765i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.00000 | 0.234484 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.7279 | + | 12.7279i | 0.743573 | + | 0.743573i | 0.973264 | − | 0.229691i | \(-0.0737714\pi\) |
−0.229691 | + | 0.973264i | \(0.573771\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.12132 | − | 2.12132i | 0.123091 | − | 0.123091i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.3923 | −0.601003 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.0000 | + | 24.2487i | −1.21042 | + | 1.39767i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.34847 | − | 7.34847i | 0.422159 | − | 0.422159i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.07107 | + | 7.07107i | −0.403567 | + | 0.403567i | −0.879488 | − | 0.475921i | \(-0.842115\pi\) |
0.475921 | + | 0.879488i | \(0.342115\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 14.0000i | − | 0.796432i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 31.1769i | − | 1.76788i | −0.467600 | − | 0.883940i | \(-0.654881\pi\) | ||
0.467600 | − | 0.883940i | \(-0.345119\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.89949 | + | 9.89949i | 0.559553 | + | 0.559553i | 0.929180 | − | 0.369627i | \(-0.120515\pi\) |
−0.369627 | + | 0.929180i | \(0.620515\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.67423 | − | 3.67423i | −0.206366 | − | 0.206366i | 0.596355 | − | 0.802721i | \(-0.296615\pi\) |
−0.802721 | + | 0.596355i | \(0.796615\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 27.0000i | − | 1.51171i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 10.3923i | − | 0.580042i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.6969 | − | 14.6969i | 0.817760 | − | 0.817760i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.0208 | + | 12.0208i | −0.664753 | + | 0.664753i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.3923 | + | 12.0000i | −0.572946 | + | 0.661581i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.0000 | 1.04433 | 0.522167 | − | 0.852843i | \(-0.325124\pi\) | ||||
0.522167 | + | 0.852843i | \(0.325124\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.67423 | + | 3.67423i | −0.201347 | + | 0.201347i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.89898 | + | 4.89898i | 0.266864 | + | 0.266864i | 0.827835 | − | 0.560971i | \(-0.189572\pi\) |
−0.560971 | + | 0.827835i | \(0.689572\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.19615 | 0.282216 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.7846i | 1.12555i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.0938 | + | 3.95164i | −0.976972 | + | 0.213368i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.7196 | − | 25.7196i | −1.38070 | − | 1.38070i | −0.843371 | − | 0.537332i | \(-0.819432\pi\) |
−0.537332 | − | 0.843371i | \(-0.680568\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.3923 | 0.556287 | 0.278144 | − | 0.960539i | \(-0.410281\pi\) | ||||
0.278144 | + | 0.960539i | \(0.410281\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.00000 | 0.106752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.4558 | + | 25.4558i | 1.35488 | + | 1.35488i | 0.880112 | + | 0.474766i | \(0.157467\pi\) |
0.474766 | + | 0.880112i | \(0.342533\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −15.8338 | + | 1.13681i | −0.838011 | + | 0.0601665i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 27.0000i | − | 1.42501i | −0.701669 | − | 0.712503i | \(-0.747562\pi\) | ||
0.701669 | − | 0.712503i | \(-0.252438\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.00000 | −0.368421 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.41421 | − | 1.41421i | −0.0742270 | − | 0.0742270i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.6274 | + | 22.6274i | −1.18114 | + | 1.18114i | −0.201693 | + | 0.979449i | \(0.564644\pi\) |
−0.979449 | + | 0.201693i | \(0.935356\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.12372 | − | 6.12372i | 0.317074 | − | 0.317074i | −0.530568 | − | 0.847642i | \(-0.678021\pi\) |
0.847642 | + | 0.530568i | \(0.178021\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.7279 | − | 12.7279i | 0.655521 | − | 0.655521i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.00000i | 0.0513665i | 0.999670 | + | 0.0256833i | \(0.00817614\pi\) | ||||
−0.999670 | + | 0.0256833i | \(0.991824\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 5.19615i | − | 0.266207i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.24264 | + | 4.24264i | 0.216789 | + | 0.216789i | 0.807144 | − | 0.590355i | \(-0.201012\pi\) |
−0.590355 | + | 0.807144i | \(0.701012\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.57321 | + | 8.57321i | 0.435801 | + | 0.435801i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 3.00000i | − | 0.152106i | −0.997104 | − | 0.0760530i | \(-0.975768\pi\) | ||
0.997104 | − | 0.0760530i | \(-0.0242318\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 31.1769i | − | 1.57668i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.34847 | − | 7.34847i | 0.370681 | − | 0.370681i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.65685 | − | 5.65685i | 0.283909 | − | 0.283909i | −0.550757 | − | 0.834666i | \(-0.685661\pi\) |
0.834666 | + | 0.550757i | \(0.185661\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.92820 | − | 6.00000i | −0.346844 | − | 0.300376i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.0000 | −1.34832 | −0.674158 | − | 0.738587i | \(-0.735493\pi\) | ||||
−0.674158 | + | 0.738587i | \(0.735493\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.79796 | + | 9.79796i | −0.488071 | + | 0.488071i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.0227 | − | 11.0227i | −0.546375 | − | 0.546375i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 38.1051 | 1.88418 | 0.942088 | − | 0.335365i | \(-0.108860\pi\) | ||||
0.942088 | + | 0.335365i | \(0.108860\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −27.4249 | + | 1.96902i | −1.34949 | + | 0.0968890i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.34847 | + | 7.34847i | 0.359856 | + | 0.359856i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.7846 | −1.01539 | −0.507697 | − | 0.861536i | \(-0.669503\pi\) | ||||
−0.507697 | + | 0.861536i | \(0.669503\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.0000 | −0.828529 | −0.414265 | − | 0.910156i | \(-0.635961\pi\) | ||||
−0.414265 | + | 0.910156i | \(0.635961\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.24264 | + | 4.24264i | 0.206284 | + | 0.206284i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.31268 | − | 18.2832i | −0.0635249 | − | 0.884788i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.00000i | 0.289683i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.0000 | −0.578020 | −0.289010 | − | 0.957326i | \(-0.593326\pi\) | ||||
−0.289010 | + | 0.957326i | \(0.593326\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.65685 | + | 5.65685i | 0.271851 | + | 0.271851i | 0.829845 | − | 0.557994i | \(-0.188429\pi\) |
−0.557994 | + | 0.829845i | \(0.688429\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.7279 | − | 12.7279i | 0.608859 | − | 0.608859i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −38.1051 | −1.81866 | −0.909329 | − | 0.416078i | \(-0.863404\pi\) | ||||
−0.909329 | + | 0.416078i | \(0.863404\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | + | 6.92820i | 0.0476190 | + | 0.329914i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.34847 | + | 7.34847i | −0.349136 | + | 0.349136i | −0.859788 | − | 0.510651i | \(-0.829404\pi\) |
0.510651 | + | 0.859788i | \(0.329404\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.6066 | + | 10.6066i | −0.501675 | + | 0.501675i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.0000i | 1.27421i | 0.770778 | + | 0.637104i | \(0.219868\pi\) | ||||
−0.770778 | + | 0.637104i | \(0.780132\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.53553 | + | 3.53553i | 0.166114 | + | 0.166114i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.67423 | − | 3.67423i | −0.171873 | − | 0.171873i | 0.615929 | − | 0.787802i | \(-0.288781\pi\) |
−0.787802 | + | 0.615929i | \(0.788781\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.00000i | 0.280056i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.1769i | 1.45205i | 0.687666 | + | 0.726027i | \(0.258635\pi\) | ||||
−0.687666 | + | 0.726027i | \(0.741365\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.34847 | + | 7.34847i | −0.341512 | + | 0.341512i | −0.856936 | − | 0.515423i | \(-0.827635\pi\) |
0.515423 | + | 0.856936i | \(0.327635\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.48528 | + | 8.48528i | −0.392652 | + | 0.392652i | −0.875632 | − | 0.482980i | \(-0.839555\pi\) |
0.482980 | + | 0.875632i | \(0.339555\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −24.2487 | − | 21.0000i | −1.11970 | − | 0.969690i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.0000 | 0.737241 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −25.7196 | + | 25.7196i | −1.18259 | + | 1.18259i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.3923 | 0.474837 | 0.237418 | − | 0.971408i | \(-0.423699\pi\) | ||||
0.237418 | + | 0.971408i | \(0.423699\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 10.3923i | − | 0.473848i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −13.7124 | + | 0.984508i | −0.623937 | + | 0.0447967i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.9217 | − | 15.9217i | −0.721480 | − | 0.721480i | 0.247426 | − | 0.968907i | \(-0.420415\pi\) |
−0.968907 | + | 0.247426i | \(0.920415\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.46410 | 0.156652 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.0000 | −0.676941 | −0.338470 | − | 0.940977i | \(-0.609909\pi\) | ||||
−0.338470 | + | 0.940977i | \(0.609909\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 38.1838 | + | 38.1838i | 1.71971 | + | 1.71971i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.91688 | + | 0.568406i | −0.355120 | + | 0.0254965i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.0000i | 0.895323i | 0.894203 | + | 0.447661i | \(0.147743\pi\) | ||||
−0.894203 | + | 0.447661i | \(0.852257\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.00000 | 0.268060 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.4558 | + | 25.4558i | 1.13502 | + | 1.13502i | 0.989330 | + | 0.145690i | \(0.0465401\pi\) |
0.145690 | + | 0.989330i | \(0.453460\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.36396 | − | 6.36396i | 0.282633 | − | 0.282633i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −31.1769 | −1.38189 | −0.690946 | − | 0.722906i | \(-0.742806\pi\) | ||||
−0.690946 | + | 0.722906i | \(0.742806\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.00000 | − | 3.46410i | −0.176950 | − | 0.153243i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.44949 | + | 2.44949i | −0.108148 | + | 0.108148i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.7279 | + | 12.7279i | −0.559773 | + | 0.559773i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 18.0000i | − | 0.790112i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 20.7846i | − | 0.910590i | −0.890341 | − | 0.455295i | \(-0.849534\pi\) | ||
0.890341 | − | 0.455295i | \(-0.150466\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.1127 | − | 31.1127i | −1.36046 | − | 1.36046i | −0.873325 | − | 0.487139i | \(-0.838041\pi\) |
−0.487139 | − | 0.873325i | \(-0.661959\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −29.3939 | − | 29.3939i | −1.28042 | − | 1.28042i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 4.00000i | − | 0.173913i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.3923i | 0.450988i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.48528 | + | 8.48528i | −0.366167 | + | 0.366167i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20.7846 | + | 3.00000i | −0.895257 | + | 0.129219i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.0000 | 0.730887 | 0.365444 | − | 0.930834i | \(-0.380917\pi\) | ||||
0.365444 | + | 0.930834i | \(0.380917\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.44949 | + | 2.44949i | −0.105118 | + | 0.105118i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.0227 | − | 11.0227i | −0.471297 | − | 0.471297i | 0.431037 | − | 0.902334i | \(-0.358148\pi\) |
−0.902334 | + | 0.431037i | \(0.858148\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.92820 | −0.295689 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 31.1769i | 1.32818i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.189469 | − | 2.63896i | −0.00805703 | − | 0.112220i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.7196 | + | 25.7196i | 1.08978 | + | 1.08978i | 0.995551 | + | 0.0942253i | \(0.0300374\pi\) |
0.0942253 | + | 0.995551i | \(0.469963\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −24.2487 | −1.02561 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.0000 | −0.759961 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.9706 | + | 16.9706i | 0.715224 | + | 0.715224i | 0.967623 | − | 0.252399i | \(-0.0812196\pi\) |
−0.252399 | + | 0.967623i | \(0.581220\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.63896 | − | 0.189469i | 0.110826 | − | 0.00795694i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 39.0000i | − | 1.63497i | −0.575953 | − | 0.817483i | \(-0.695369\pi\) | ||
0.575953 | − | 0.817483i | \(-0.304631\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.00000 | −0.292941 | −0.146470 | − | 0.989215i | \(-0.546791\pi\) | ||||
−0.146470 | + | 0.989215i | \(0.546791\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.07107 | + | 7.07107i | −0.294372 | + | 0.294372i | −0.838805 | − | 0.544432i | \(-0.816745\pi\) |
0.544432 | + | 0.838805i | \(0.316745\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.0526 | 0.791797 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24.0000 | + | 20.7846i | 0.995688 | + | 0.862291i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.7279 | − | 12.7279i | 0.525338 | − | 0.525338i | −0.393841 | − | 0.919179i | \(-0.628854\pi\) |
0.919179 | + | 0.393841i | \(0.128854\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 24.0000i | − | 0.988903i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 15.5885i | − | 0.641223i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −25.4558 | − | 25.4558i | −1.04535 | − | 1.04535i | −0.998922 | − | 0.0464244i | \(-0.985217\pi\) |
−0.0464244 | − | 0.998922i | \(-0.514783\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.89898 | + | 4.89898i | 0.200502 | + | 0.200502i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 39.0000i | − | 1.59350i | −0.604311 | − | 0.796748i | \(-0.706552\pi\) | ||
0.604311 | − | 0.796748i | \(-0.293448\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.7128i | 1.13043i | 0.824944 | + | 0.565215i | \(0.191207\pi\) | ||||
−0.824944 | + | 0.565215i | \(0.808793\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.57321 | + | 8.57321i | −0.349128 | + | 0.349128i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.5563 | + | 15.5563i | −0.631413 | + | 0.631413i | −0.948422 | − | 0.317010i | \(-0.897321\pi\) |
0.317010 | + | 0.948422i | \(0.397321\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 15.5885 | − | 18.0000i | 0.631676 | − | 0.729397i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.0000 | −0.485468 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.0227 | + | 11.0227i | −0.445203 | + | 0.445203i | −0.893756 | − | 0.448553i | \(-0.851939\pi\) |
0.448553 | + | 0.893756i | \(0.351939\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.7196 | + | 25.7196i | 1.03543 | + | 1.03543i | 0.999349 | + | 0.0360851i | \(0.0114887\pi\) |
0.0360851 | + | 0.999349i | \(0.488511\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.2487 | 0.974638 | 0.487319 | − | 0.873224i | \(-0.337975\pi\) | ||||
0.487319 | + | 0.873224i | \(0.337975\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.19615i | 0.208514i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 27.4249 | − | 1.96902i | 1.09875 | − | 0.0788870i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.34847 | − | 7.34847i | −0.293470 | − | 0.293470i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 31.1769 | 1.24310 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.0000 | 1.39333 | 0.696664 | − | 0.717398i | \(-0.254667\pi\) | ||||
0.696664 | + | 0.717398i | \(0.254667\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.3137 | + | 11.3137i | 0.449680 | + | 0.449680i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.2122 | − | 8.38375i | −0.444242 | − | 0.332176i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.00000i | 0.118678i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.00000 | 0.355479 | 0.177739 | − | 0.984078i | \(-0.443122\pi\) | ||||
0.177739 | + | 0.984078i | \(0.443122\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.82843 | − | 2.82843i | −0.111542 | − | 0.111542i | 0.649133 | − | 0.760675i | \(-0.275132\pi\) |
−0.760675 | + | 0.649133i | \(0.775132\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −31.1769 | −1.22380 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.0000 | + | 13.8564i | −0.470317 | + | 0.543075i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −29.3939 | + | 29.3939i | −1.15027 | + | 1.15027i | −0.163773 | + | 0.986498i | \(0.552367\pi\) |
−0.986498 | + | 0.163773i | \(0.947633\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.41421 | + | 1.41421i | −0.0551737 | + | 0.0551737i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.0000i | 0.934907i | 0.884018 | + | 0.467454i | \(0.154829\pi\) | ||||
−0.884018 | + | 0.467454i | \(0.845171\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 31.1769i | − | 1.21264i | −0.795220 | − | 0.606321i | \(-0.792645\pi\) | ||
0.795220 | − | 0.606321i | \(-0.207355\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.48528 | − | 8.48528i | −0.329541 | − | 0.329541i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 33.0681 | + | 33.0681i | 1.28040 | + | 1.28040i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.0000i | 0.541271i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 20.7846i | − | 0.802381i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.6969 | + | 14.6969i | −0.566525 | + | 0.566525i | −0.931153 | − | 0.364628i | \(-0.881196\pi\) |
0.364628 | + | 0.931153i | \(0.381196\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.48528 | + | 8.48528i | −0.326116 | + | 0.326116i | −0.851107 | − | 0.524992i | \(-0.824068\pi\) |
0.524992 | + | 0.851107i | \(0.324068\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.92820 | + | 8.00000i | −0.265880 | + | 0.307012i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.00000 | 0.229920 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.7196 | − | 25.7196i | 0.984135 | − | 0.984135i | −0.0157413 | − | 0.999876i | \(-0.505011\pi\) |
0.999876 | + | 0.0157413i | \(0.00501083\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.89898 | + | 4.89898i | 0.186908 | + | 0.186908i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.7846i | 0.790684i | 0.918534 | + | 0.395342i | \(0.129374\pi\) | ||||
−0.918534 | + | 0.395342i | \(0.870626\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.568406 | + | 7.91688i | 0.0215920 | + | 0.300737i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −25.9808 | −0.982683 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.0000 | 1.13308 | 0.566542 | − | 0.824033i | \(-0.308281\pi\) | ||||
0.566542 | + | 0.824033i | \(0.308281\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.7279 | + | 12.7279i | 0.480043 | + | 0.480043i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.96902 | + | 27.4249i | 0.0740525 | + | 1.03142i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.0000i | 0.826227i | 0.910679 | + | 0.413114i | \(0.135559\pi\) | ||||
−0.910679 | + | 0.413114i | \(0.864441\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.00000 | −0.0375029 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −25.4558 | − | 25.4558i | −0.953329 | − | 0.953329i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28.0000 | + | 24.2487i | 1.04277 | + | 0.903069i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.2474 | − | 12.2474i | 0.455488 | − | 0.455488i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.89949 | − | 9.89949i | 0.367152 | − | 0.367152i | −0.499286 | − | 0.866437i | \(-0.666404\pi\) |
0.866437 | + | 0.499286i | \(0.166404\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 72.7461i | − | 2.69061i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.82843 | − | 2.82843i | −0.104470 | − | 0.104470i | 0.652940 | − | 0.757410i | \(-0.273536\pi\) |
−0.757410 | + | 0.652940i | \(0.773536\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −25.7196 | − | 25.7196i | −0.947395 | − | 0.947395i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.0000i | 0.404642i | 0.979319 | + | 0.202321i | \(0.0648484\pi\) | ||||
−0.979319 | + | 0.202321i | \(0.935152\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 6.92820i | − | 0.254514i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.34847 | + | 7.34847i | −0.269589 | + | 0.269589i | −0.828935 | − | 0.559345i | \(-0.811053\pi\) |
0.559345 | + | 0.828935i | \(0.311053\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.48528 | − | 8.48528i | 0.310460 | − | 0.310460i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 20.7846 | + | 18.0000i | 0.759453 | + | 0.657706i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.0000 | −1.45962 | −0.729810 | − | 0.683650i | \(-0.760392\pi\) | ||||
−0.729810 | + | 0.683650i | \(0.760392\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 22.0454 | − | 22.0454i | 0.803379 | − | 0.803379i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.22474 | + | 1.22474i | 0.0445141 | + | 0.0445141i | 0.729013 | − | 0.684499i | \(-0.239979\pi\) |
−0.684499 | + | 0.729013i | \(0.739979\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −15.5885 | −0.565825 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 41.5692i | 1.50688i | 0.657515 | + | 0.753442i | \(0.271608\pi\) | ||||
−0.657515 | + | 0.753442i | \(0.728392\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.22097 | − | 44.8623i | −0.116607 | − | 1.62412i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.6969 | − | 14.6969i | −0.530676 | − | 0.530676i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.8564 | 0.499675 | 0.249837 | − | 0.968288i | \(-0.419623\pi\) | ||||
0.249837 | + | 0.968288i | \(0.419623\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.0000 | 0.432169 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.9706 | − | 16.9706i | −0.610389 | − | 0.610389i | 0.332659 | − | 0.943047i | \(-0.392054\pi\) |
−0.943047 | + | 0.332659i | \(0.892054\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.984508 | − | 13.7124i | −0.0353190 | − | 0.491931i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.00000 | −0.322045 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.36396 | − | 6.36396i | −0.227429 | − | 0.227429i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.8701 | − | 26.8701i | 0.957814 | − | 0.957814i | −0.0413314 | − | 0.999145i | \(-0.513160\pi\) |
0.999145 | + | 0.0413314i | \(0.0131599\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.5885 | −0.554964 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.00000 | + | 10.3923i | −0.320003 | + | 0.369508i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.79796 | − | 9.79796i | 0.347936 | − | 0.347936i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.2132 | + | 21.2132i | −0.751410 | + | 0.751410i | −0.974742 | − | 0.223332i | \(-0.928307\pi\) |
0.223332 | + | 0.974742i | \(0.428307\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 36.0000i | − | 1.27359i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 10.3923i | − | 0.367194i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.24264 | − | 4.24264i | −0.149720 | − | 0.149720i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.6969 | − | 14.6969i | −0.517357 | − | 0.517357i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 51.0000i | 1.79306i | 0.442978 | + | 0.896532i | \(0.353922\pi\) | ||||
−0.442978 | + | 0.896532i | \(0.646078\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.7128i | 0.973128i | 0.873645 | + | 0.486564i | \(0.161750\pi\) | ||||
−0.873645 | + | 0.486564i | \(0.838250\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −22.0454 | + | 22.0454i | −0.773166 | + | 0.773166i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.6985 | − | 29.6985i | 1.03902 | − | 1.03902i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.46410 | + | 4.00000i | −0.121046 | + | 0.139771i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.0000 | 1.04701 | 0.523504 | − | 0.852023i | \(-0.324625\pi\) | ||||
0.523504 | + | 0.852023i | \(0.324625\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.22474 | + | 1.22474i | −0.0426919 | + | 0.0426919i | −0.728130 | − | 0.685439i | \(-0.759611\pi\) |
0.685439 | + | 0.728130i | \(0.259611\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.3712 | + | 18.3712i | 0.638828 | + | 0.638828i | 0.950266 | − | 0.311438i | \(-0.100811\pi\) |
−0.311438 | + | 0.950266i | \(0.600811\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.3923 | 0.360940 | 0.180470 | − | 0.983581i | \(-0.442238\pi\) | ||||
0.180470 | + | 0.983581i | \(0.442238\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.8564i | 0.480673i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 25.1512 | − | 33.6365i | 0.871439 | − | 1.16544i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.89898 | + | 4.89898i | 0.169334 | + | 0.169334i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.3923 | −0.358782 | −0.179391 | − | 0.983778i | \(-0.557413\pi\) | ||||
−0.179391 | + | 0.983778i | \(0.557413\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −52.0000 | −1.79310 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.12132 | + | 2.12132i | 0.0730622 | + | 0.0730622i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.27792 | − | 0.378937i | 0.181351 | − | 0.0130204i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.0000i | 0.549119i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 27.0000 | 0.925548 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.82843 | + | 2.82843i | 0.0968435 | + | 0.0968435i | 0.753869 | − | 0.657025i | \(-0.228185\pi\) |
−0.657025 | + | 0.753869i | \(0.728185\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.48528 | − | 8.48528i | 0.289852 | − | 0.289852i | −0.547170 | − | 0.837022i | \(-0.684295\pi\) |
0.837022 | + | 0.547170i | \(0.184295\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.5692 | 1.41832 | 0.709162 | − | 0.705046i | \(-0.249074\pi\) | ||||
0.709162 | + | 0.705046i | \(0.249074\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.3712 | + | 18.3712i | −0.625362 | + | 0.625362i | −0.946898 | − | 0.321536i | \(-0.895801\pi\) |
0.321536 | + | 0.946898i | \(0.395801\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.4350 | − | 13.4350i | 0.456278 | − | 0.456278i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 3.00000i | − | 0.101768i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 24.2487i | − | 0.821636i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.82843 | + | 2.82843i | 0.0957278 | + | 0.0957278i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.79796 | + | 9.79796i | 0.330854 | + | 0.330854i | 0.852911 | − | 0.522057i | \(-0.174835\pi\) |
−0.522057 | + | 0.852911i | \(0.674835\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18.0000i | 0.607125i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 20.7846i | − | 0.700251i | −0.936703 | − | 0.350126i | \(-0.886139\pi\) | ||
0.936703 | − | 0.350126i | \(-0.113861\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.4722 | + | 13.4722i | −0.453375 | + | 0.453375i | −0.896473 | − | 0.443098i | \(-0.853879\pi\) |
0.443098 | + | 0.896473i | \(0.353879\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25.4558 | + | 25.4558i | −0.854724 | + | 0.854724i | −0.990711 | − | 0.135987i | \(-0.956579\pi\) |
0.135987 | + | 0.990711i | \(0.456579\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.3923 | + | 9.00000i | 0.348547 | + | 0.301850i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.00000 | 0.100504 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14.6969 | − | 14.6969i | 0.491814 | − | 0.491814i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.34847 | − | 7.34847i | −0.245358 | − | 0.245358i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 62.3538 | 2.07962 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −31.9957 | + | 2.29719i | −1.06475 | + | 0.0764456i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.34847 | + | 7.34847i | 0.244002 | + | 0.244002i | 0.818503 | − | 0.574502i | \(-0.194804\pi\) |
−0.574502 | + | 0.818503i | \(0.694804\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.3923 | 0.344691 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.0000 | −1.68971 | −0.844853 | − | 0.534999i | \(-0.820312\pi\) | ||||
−0.844853 | + | 0.534999i | \(0.820312\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.4558 | + | 25.4558i | 0.842465 | + | 0.842465i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.96902 | + | 27.4249i | 0.0650226 | + | 0.905649i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 55.0000i | 1.81428i | 0.420826 | + | 0.907141i | \(0.361740\pi\) | ||||
−0.420826 | + | 0.907141i | \(0.638260\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.0000 | −0.329511 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.24264 | − | 4.24264i | −0.139648 | − | 0.139648i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.89949 | − | 9.89949i | 0.325142 | − | 0.325142i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31.1769 | −1.02288 | −0.511441 | − | 0.859319i | \(-0.670888\pi\) | ||||
−0.511441 | + | 0.859319i | \(0.670888\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.0000 | − | 3.46410i | 0.786568 | − | 0.113531i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 22.0454 | − | 22.0454i | 0.721734 | − | 0.721734i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.65685 | + | 5.65685i | −0.184801 | + | 0.184801i | −0.793444 | − | 0.608643i | \(-0.791714\pi\) |
0.608643 | + | 0.793444i | \(0.291714\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.0000i | 0.456873i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.7846i | 0.677559i | 0.940866 | + | 0.338779i | \(0.110014\pi\) | ||||
−0.940866 | + | 0.338779i | \(0.889986\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.0454 | + | 22.0454i | 0.716379 | + | 0.716379i | 0.967862 | − | 0.251482i | \(-0.0809181\pi\) |
−0.251482 | + | 0.967862i | \(0.580918\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 4.00000i | − | 0.129845i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 5.19615i | − | 0.168497i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.4166 | − | 40.4166i | 1.30922 | − | 1.30922i | 0.387244 | − | 0.921977i | \(-0.373427\pi\) |
0.921977 | − | 0.387244i | \(-0.126573\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 19.0919 | − | 19.0919i | 0.617153 | − | 0.617153i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.0000 | −0.548387 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.34847 | − | 7.34847i | 0.236801 | − | 0.236801i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.0454 | − | 22.0454i | −0.708933 | − | 0.708933i | 0.257378 | − | 0.966311i | \(-0.417141\pi\) |
−0.966311 | + | 0.257378i | \(0.917141\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 20.7846 | 0.667698 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 10.3923i | − | 0.333505i | −0.985999 | − | 0.166752i | \(-0.946672\pi\) | ||
0.985999 | − | 0.166752i | \(-0.0533281\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −27.4249 | + | 1.96902i | −0.879201 | + | 0.0631238i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.0227 | − | 11.0227i | −0.352648 | − | 0.352648i | 0.508446 | − | 0.861094i | \(-0.330220\pi\) |
−0.861094 | + | 0.508446i | \(0.830220\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 31.1769 | 0.996419 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.0000 | −0.542768 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33.9411 | + | 33.9411i | 1.08255 | + | 1.08255i | 0.996271 | + | 0.0862831i | \(0.0274990\pi\) |
0.0862831 | + | 0.996271i | \(0.472501\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −15.8338 | + | 1.13681i | −0.503994 | + | 0.0361851i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 63.0000i | − | 2.00328i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 55.0000 | 1.74713 | 0.873566 | − | 0.486705i | \(-0.161801\pi\) | ||||
0.873566 | + | 0.486705i | \(0.161801\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.4350 | + | 13.4350i | 0.426348 | + | 0.426348i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.07107 | − | 7.07107i | 0.223943 | − | 0.223943i | −0.586214 | − | 0.810157i | \(-0.699382\pi\) |
0.810157 | + | 0.586214i | \(0.199382\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.19615 | −0.164399 |
(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 | 2100.2.x.a.1357.3 | yes | 8 | |
5.2 | odd | 4 | inner | 2100.2.x.a.1693.4 | yes | 8 | |
5.3 | odd | 4 | inner | 2100.2.x.a.1693.1 | yes | 8 | |
5.4 | even | 2 | inner | 2100.2.x.a.1357.2 | yes | 8 | |
7.6 | odd | 2 | inner | 2100.2.x.a.1357.1 | ✓ | 8 | |
35.13 | even | 4 | inner | 2100.2.x.a.1693.3 | yes | 8 | |
35.27 | even | 4 | inner | 2100.2.x.a.1693.2 | yes | 8 | |
35.34 | odd | 2 | inner | 2100.2.x.a.1357.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.2.x.a.1357.1 | ✓ | 8 | 7.6 | odd | 2 | inner | |
2100.2.x.a.1357.2 | yes | 8 | 5.4 | even | 2 | inner | |
2100.2.x.a.1357.3 | yes | 8 | 1.1 | even | 1 | trivial | |
2100.2.x.a.1357.4 | yes | 8 | 35.34 | odd | 2 | inner | |
2100.2.x.a.1693.1 | yes | 8 | 5.3 | odd | 4 | inner | |
2100.2.x.a.1693.2 | yes | 8 | 35.27 | even | 4 | inner | |
2100.2.x.a.1693.3 | yes | 8 | 35.13 | even | 4 | inner | |
2100.2.x.a.1693.4 | yes | 8 | 5.2 | odd | 4 | inner |