Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,3,Mod(82,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.82");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.g (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: | \(6.13080594811\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} + 9 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 118.1 | ||
Root | \(-1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.118 |
Dual form | 225.3.g.b.82.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.44949 | + | 2.44949i | −1.22474 | + | 1.22474i | −0.258819 | + | 0.965926i | \(0.583333\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 8.00000i | − | 2.00000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.12372 | + | 6.12372i | −0.874818 | + | 0.874818i | −0.992993 | − | 0.118175i | \(-0.962296\pi\) |
0.118175 | + | 0.992993i | \(0.462296\pi\) | |||||||
\(8\) | 9.79796 | + | 9.79796i | 1.22474 | + | 1.22474i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.00000 | −0.545455 | −0.272727 | − | 0.962091i | \(-0.587926\pi\) | ||||
−0.272727 | + | 0.962091i | \(0.587926\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.67423 | − | 3.67423i | −0.282633 | − | 0.282633i | 0.551525 | − | 0.834158i | \(-0.314046\pi\) |
−0.834158 | + | 0.551525i | \(0.814046\pi\) | |||||||
\(14\) | − | 30.0000i | − | 2.14286i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −16.0000 | −1.00000 | ||||||||
\(17\) | 17.1464 | − | 17.1464i | 1.00861 | − | 1.00861i | 0.00865084 | − | 0.999963i | \(-0.497246\pi\) |
0.999963 | − | 0.00865084i | \(-0.00275368\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 23.0000i | − | 1.21053i | −0.796025 | − | 0.605263i | \(-0.793068\pi\) | ||
0.796025 | − | 0.605263i | \(-0.206932\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 14.6969 | − | 14.6969i | 0.668043 | − | 0.668043i | ||||
\(23\) | −12.2474 | − | 12.2474i | −0.532498 | − | 0.532498i | 0.388817 | − | 0.921315i | \(-0.372884\pi\) |
−0.921315 | + | 0.388817i | \(0.872884\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 18.0000 | 0.692308 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 48.9898 | + | 48.9898i | 1.74964 | + | 1.74964i | ||||
\(29\) | 6.00000i | 0.206897i | 0.994635 | + | 0.103448i | \(0.0329876\pi\) | ||||
−0.994635 | + | 0.103448i | \(0.967012\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 25.0000 | 0.806452 | 0.403226 | − | 0.915101i | \(-0.367889\pi\) | ||||
0.403226 | + | 0.915101i | \(0.367889\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 84.0000i | 2.47059i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 24.4949 | − | 24.4949i | 0.662024 | − | 0.662024i | −0.293833 | − | 0.955857i | \(-0.594931\pi\) |
0.955857 | + | 0.293833i | \(0.0949308\pi\) | |||||||
\(38\) | 56.3383 | + | 56.3383i | 1.48259 | + | 1.48259i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 60.0000 | 1.46341 | 0.731707 | − | 0.681619i | \(-0.238724\pi\) | ||||
0.731707 | + | 0.681619i | \(0.238724\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −60.0125 | − | 60.0125i | −1.39564 | − | 1.39564i | −0.812046 | − | 0.583594i | \(-0.801646\pi\) |
−0.583594 | − | 0.812046i | \(-0.698354\pi\) | |||||||
\(44\) | 48.0000i | 1.09091i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 60.0000 | 1.30435 | ||||||||
\(47\) | 7.34847 | − | 7.34847i | 0.156350 | − | 0.156350i | −0.624597 | − | 0.780947i | \(-0.714737\pi\) |
0.780947 | + | 0.624597i | \(0.214737\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 26.0000i | − | 0.530612i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −29.3939 | + | 29.3939i | −0.565267 | + | 0.565267i | ||||
\(53\) | −24.4949 | − | 24.4949i | −0.462168 | − | 0.462168i | 0.437198 | − | 0.899365i | \(-0.355971\pi\) |
−0.899365 | + | 0.437198i | \(0.855971\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −120.000 | −2.14286 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −14.6969 | − | 14.6969i | −0.253395 | − | 0.253395i | ||||
\(59\) | − | 18.0000i | − | 0.305085i | −0.988297 | − | 0.152542i | \(-0.951254\pi\) | ||
0.988297 | − | 0.152542i | \(-0.0487461\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −37.0000 | −0.606557 | −0.303279 | − | 0.952902i | \(-0.598081\pi\) | ||||
−0.303279 | + | 0.952902i | \(0.598081\pi\) | |||||||
\(62\) | −61.2372 | + | 61.2372i | −0.987697 | + | 0.987697i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 64.0000i | − | 1.00000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 25.7196 | − | 25.7196i | 0.383875 | − | 0.383875i | −0.488621 | − | 0.872496i | \(-0.662500\pi\) |
0.872496 | + | 0.488621i | \(0.162500\pi\) | |||||||
\(68\) | −137.171 | − | 137.171i | −2.01723 | − | 2.01723i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −132.000 | −1.85915 | −0.929577 | − | 0.368627i | \(-0.879828\pi\) | ||||
−0.929577 | + | 0.368627i | \(0.879828\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 24.4949 | + | 24.4949i | 0.335547 | + | 0.335547i | 0.854688 | − | 0.519142i | \(-0.173748\pi\) |
−0.519142 | + | 0.854688i | \(0.673748\pi\) | |||||||
\(74\) | 120.000i | 1.62162i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −184.000 | −2.42105 | ||||||||
\(77\) | 36.7423 | − | 36.7423i | 0.477173 | − | 0.477173i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 10.0000i | − | 0.126582i | −0.997995 | − | 0.0632911i | \(-0.979840\pi\) | ||
0.997995 | − | 0.0632911i | \(-0.0201597\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −146.969 | + | 146.969i | −1.79231 | + | 1.79231i | ||||
\(83\) | 2.44949 | + | 2.44949i | 0.0295119 | + | 0.0295119i | 0.721709 | − | 0.692197i | \(-0.243357\pi\) |
−0.692197 | + | 0.721709i | \(0.743357\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 294.000 | 3.41860 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −58.7878 | − | 58.7878i | −0.668043 | − | 0.668043i | ||||
\(89\) | − | 132.000i | − | 1.48315i | −0.670872 | − | 0.741573i | \(-0.734080\pi\) | ||
0.670872 | − | 0.741573i | \(-0.265920\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 45.0000 | 0.494505 | ||||||||
\(92\) | −97.9796 | + | 97.9796i | −1.06500 | + | 1.06500i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 36.0000i | 0.382979i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −23.2702 | + | 23.2702i | −0.239898 | + | 0.239898i | −0.816808 | − | 0.576910i | \(-0.804259\pi\) |
0.576910 | + | 0.816808i | \(0.304259\pi\) | |||||||
\(98\) | 63.6867 | + | 63.6867i | 0.649865 | + | 0.649865i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −96.0000 | −0.950495 | −0.475248 | − | 0.879852i | \(-0.657641\pi\) | ||||
−0.475248 | + | 0.879852i | \(0.657641\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.5959 | + | 19.5959i | 0.190252 | + | 0.190252i | 0.795805 | − | 0.605553i | \(-0.207048\pi\) |
−0.605553 | + | 0.795805i | \(0.707048\pi\) | |||||||
\(104\) | − | 72.0000i | − | 0.692308i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 120.000 | 1.13208 | ||||||||
\(107\) | −29.3939 | + | 29.3939i | −0.274709 | + | 0.274709i | −0.830993 | − | 0.556283i | \(-0.812227\pi\) |
0.556283 | + | 0.830993i | \(0.312227\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 167.000i | 1.53211i | 0.642775 | + | 0.766055i | \(0.277783\pi\) | ||||
−0.642775 | + | 0.766055i | \(0.722217\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 97.9796 | − | 97.9796i | 0.874818 | − | 0.874818i | ||||
\(113\) | −58.7878 | − | 58.7878i | −0.520246 | − | 0.520246i | 0.397400 | − | 0.917646i | \(-0.369913\pi\) |
−0.917646 | + | 0.397400i | \(0.869913\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 48.0000 | 0.413793 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 44.0908 | + | 44.0908i | 0.373651 | + | 0.373651i | ||||
\(119\) | 210.000i | 1.76471i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −85.0000 | −0.702479 | ||||||||
\(122\) | 90.6311 | − | 90.6311i | 0.742878 | − | 0.742878i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 200.000i | − | 1.61290i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 44.0908 | − | 44.0908i | 0.347172 | − | 0.347172i | −0.511883 | − | 0.859055i | \(-0.671052\pi\) |
0.859055 | + | 0.511883i | \(0.171052\pi\) | |||||||
\(128\) | 156.767 | + | 156.767i | 1.22474 | + | 1.22474i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −108.000 | −0.824427 | −0.412214 | − | 0.911087i | \(-0.635244\pi\) | ||||
−0.412214 | + | 0.911087i | \(0.635244\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 140.846 | + | 140.846i | 1.05899 | + | 1.05899i | ||||
\(134\) | 126.000i | 0.940299i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 336.000 | 2.47059 | ||||||||
\(137\) | 120.025 | − | 120.025i | 0.876095 | − | 0.876095i | −0.117033 | − | 0.993128i | \(-0.537338\pi\) |
0.993128 | + | 0.117033i | \(0.0373384\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 58.0000i | 0.417266i | 0.977994 | + | 0.208633i | \(0.0669014\pi\) | ||||
−0.977994 | + | 0.208633i | \(0.933099\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 323.333 | − | 323.333i | 2.27699 | − | 2.27699i | ||||
\(143\) | 22.0454 | + | 22.0454i | 0.154164 | + | 0.154164i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −120.000 | −0.821918 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −195.959 | − | 195.959i | −1.32405 | − | 1.32405i | ||||
\(149\) | − | 186.000i | − | 1.24832i | −0.781296 | − | 0.624161i | \(-0.785441\pi\) | ||
0.781296 | − | 0.624161i | \(-0.214559\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −83.0000 | −0.549669 | −0.274834 | − | 0.961492i | \(-0.588623\pi\) | ||||
−0.274834 | + | 0.961492i | \(0.588623\pi\) | |||||||
\(152\) | 225.353 | − | 225.353i | 1.48259 | − | 1.48259i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 180.000i | 1.16883i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 45.3156 | − | 45.3156i | 0.288634 | − | 0.288634i | −0.547906 | − | 0.836540i | \(-0.684575\pi\) |
0.836540 | + | 0.547906i | \(0.184575\pi\) | |||||||
\(158\) | 24.4949 | + | 24.4949i | 0.155031 | + | 0.155031i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 150.000 | 0.931677 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −99.2043 | − | 99.2043i | −0.608616 | − | 0.608616i | 0.333969 | − | 0.942584i | \(-0.391612\pi\) |
−0.942584 | + | 0.333969i | \(0.891612\pi\) | |||||||
\(164\) | − | 480.000i | − | 2.92683i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.0000 | −0.0722892 | ||||||||
\(167\) | −97.9796 | + | 97.9796i | −0.586704 | + | 0.586704i | −0.936737 | − | 0.350033i | \(-0.886170\pi\) |
0.350033 | + | 0.936737i | \(0.386170\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 142.000i | − | 0.840237i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −480.100 | + | 480.100i | −2.79128 | + | 2.79128i | ||||
\(173\) | 173.914 | + | 173.914i | 1.00528 | + | 1.00528i | 0.999986 | + | 0.00529594i | \(0.00168576\pi\) |
0.00529594 | + | 0.999986i | \(0.498314\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 96.0000 | 0.545455 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 323.333 | + | 323.333i | 1.81648 | + | 1.81648i | ||||
\(179\) | 150.000i | 0.837989i | 0.907989 | + | 0.418994i | \(0.137617\pi\) | ||||
−0.907989 | + | 0.418994i | \(0.862383\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −215.000 | −1.18785 | −0.593923 | − | 0.804522i | \(-0.702421\pi\) | ||||
−0.593923 | + | 0.804522i | \(0.702421\pi\) | |||||||
\(182\) | −110.227 | + | 110.227i | −0.605643 | + | 0.605643i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 240.000i | − | 1.30435i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −102.879 | + | 102.879i | −0.550153 | + | 0.550153i | ||||
\(188\) | −58.7878 | − | 58.7878i | −0.312701 | − | 0.312701i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 234.000 | 1.22513 | 0.612565 | − | 0.790420i | \(-0.290138\pi\) | ||||
0.612565 | + | 0.790420i | \(0.290138\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 64.9115 | + | 64.9115i | 0.336329 | + | 0.336329i | 0.854984 | − | 0.518655i | \(-0.173567\pi\) |
−0.518655 | + | 0.854984i | \(0.673567\pi\) | |||||||
\(194\) | − | 114.000i | − | 0.587629i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −208.000 | −1.06122 | ||||||||
\(197\) | −193.510 | + | 193.510i | −0.982283 | + | 0.982283i | −0.999846 | − | 0.0175631i | \(-0.994409\pi\) |
0.0175631 | + | 0.999846i | \(0.494409\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.0000i | 0.0552764i | 0.999618 | + | 0.0276382i | \(0.00879863\pi\) | ||||
−0.999618 | + | 0.0276382i | \(0.991201\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 235.151 | − | 235.151i | 1.16411 | − | 1.16411i | ||||
\(203\) | −36.7423 | − | 36.7423i | −0.180997 | − | 0.180997i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −96.0000 | −0.466019 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 58.7878 | + | 58.7878i | 0.282633 | + | 0.282633i | ||||
\(209\) | 138.000i | 0.660287i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −85.0000 | −0.402844 | −0.201422 | − | 0.979505i | \(-0.564556\pi\) | ||||
−0.201422 | + | 0.979505i | \(0.564556\pi\) | |||||||
\(212\) | −195.959 | + | 195.959i | −0.924336 | + | 0.924336i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 144.000i | − | 0.672897i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −153.093 | + | 153.093i | −0.705498 | + | 0.705498i | ||||
\(218\) | −409.065 | − | 409.065i | −1.87644 | − | 1.87644i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −126.000 | −0.570136 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −101.654 | − | 101.654i | −0.455847 | − | 0.455847i | 0.441443 | − | 0.897289i | \(-0.354467\pi\) |
−0.897289 | + | 0.441443i | \(0.854467\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 288.000 | 1.27434 | ||||||||
\(227\) | 195.959 | − | 195.959i | 0.863256 | − | 0.863256i | −0.128459 | − | 0.991715i | \(-0.541003\pi\) |
0.991715 | + | 0.128459i | \(0.0410029\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 227.000i | − | 0.991266i | −0.868532 | − | 0.495633i | \(-0.834936\pi\) | ||
0.868532 | − | 0.495633i | \(-0.165064\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −58.7878 | + | 58.7878i | −0.253395 | + | 0.253395i | ||||
\(233\) | 102.879 | + | 102.879i | 0.441539 | + | 0.441539i | 0.892529 | − | 0.450990i | \(-0.148929\pi\) |
−0.450990 | + | 0.892529i | \(0.648929\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −144.000 | −0.610169 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −514.393 | − | 514.393i | −2.16131 | − | 2.16131i | ||||
\(239\) | 228.000i | 0.953975i | 0.878910 | + | 0.476987i | \(0.158271\pi\) | ||||
−0.878910 | + | 0.476987i | \(0.841729\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 191.000 | 0.792531 | 0.396266 | − | 0.918136i | \(-0.370306\pi\) | ||||
0.396266 | + | 0.918136i | \(0.370306\pi\) | |||||||
\(242\) | 208.207 | − | 208.207i | 0.860358 | − | 0.860358i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 296.000i | 1.21311i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −84.5074 | + | 84.5074i | −0.342135 | + | 0.342135i | ||||
\(248\) | 244.949 | + | 244.949i | 0.987697 | + | 0.987697i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −192.000 | −0.764940 | −0.382470 | − | 0.923968i | \(-0.624927\pi\) | ||||
−0.382470 | + | 0.923968i | \(0.624927\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 73.4847 | + | 73.4847i | 0.290453 | + | 0.290453i | ||||
\(254\) | 216.000i | 0.850394i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −512.000 | −2.00000 | ||||||||
\(257\) | 142.070 | − | 142.070i | 0.552803 | − | 0.552803i | −0.374446 | − | 0.927249i | \(-0.622167\pi\) |
0.927249 | + | 0.374446i | \(0.122167\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 300.000i | 1.15830i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 264.545 | − | 264.545i | 1.00971 | − | 1.00971i | ||||
\(263\) | −249.848 | − | 249.848i | −0.949992 | − | 0.949992i | 0.0488156 | − | 0.998808i | \(-0.484455\pi\) |
−0.998808 | + | 0.0488156i | \(0.984455\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −690.000 | −2.59398 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −205.757 | − | 205.757i | −0.767751 | − | 0.767751i | ||||
\(269\) | − | 462.000i | − | 1.71747i | −0.512418 | − | 0.858736i | \(-0.671250\pi\) | ||
0.512418 | − | 0.858736i | \(-0.328750\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 446.000 | 1.64576 | 0.822878 | − | 0.568218i | \(-0.192367\pi\) | ||||
0.822878 | + | 0.568218i | \(0.192367\pi\) | |||||||
\(272\) | −274.343 | + | 274.343i | −1.00861 | + | 1.00861i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 588.000i | 2.14599i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 175.139 | − | 175.139i | 0.632269 | − | 0.632269i | −0.316368 | − | 0.948637i | \(-0.602463\pi\) |
0.948637 | + | 0.316368i | \(0.102463\pi\) | |||||||
\(278\) | −142.070 | − | 142.070i | −0.511045 | − | 0.511045i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 546.000 | 1.94306 | 0.971530 | − | 0.236916i | \(-0.0761365\pi\) | ||||
0.971530 | + | 0.236916i | \(0.0761365\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 192.285 | + | 192.285i | 0.679452 | + | 0.679452i | 0.959876 | − | 0.280424i | \(-0.0904751\pi\) |
−0.280424 | + | 0.959876i | \(0.590475\pi\) | |||||||
\(284\) | 1056.00i | 3.71831i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −108.000 | −0.377622 | ||||||||
\(287\) | −367.423 | + | 367.423i | −1.28022 | + | 1.28022i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 299.000i | − | 1.03460i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 195.959 | − | 195.959i | 0.671093 | − | 0.671093i | ||||
\(293\) | 276.792 | + | 276.792i | 0.944684 | + | 0.944684i | 0.998548 | − | 0.0538645i | \(-0.0171539\pi\) |
−0.0538645 | + | 0.998548i | \(0.517154\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 480.000 | 1.62162 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 455.605 | + | 455.605i | 1.52888 | + | 1.52888i | ||||
\(299\) | 90.0000i | 0.301003i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 735.000 | 2.44186 | ||||||||
\(302\) | 203.308 | − | 203.308i | 0.673204 | − | 0.673204i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 368.000i | 1.21053i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −86.9569 | + | 86.9569i | −0.283247 | + | 0.283247i | −0.834403 | − | 0.551155i | \(-0.814187\pi\) |
0.551155 | + | 0.834403i | \(0.314187\pi\) | |||||||
\(308\) | −293.939 | − | 293.939i | −0.954347 | − | 0.954347i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 294.000 | 0.945338 | 0.472669 | − | 0.881240i | \(-0.343291\pi\) | ||||
0.472669 | + | 0.881240i | \(0.343291\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −393.143 | − | 393.143i | −1.25605 | − | 1.25605i | −0.952964 | − | 0.303085i | \(-0.901984\pi\) |
−0.303085 | − | 0.952964i | \(-0.598016\pi\) | |||||||
\(314\) | 222.000i | 0.707006i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −80.0000 | −0.253165 | ||||||||
\(317\) | 93.0806 | − | 93.0806i | 0.293630 | − | 0.293630i | −0.544883 | − | 0.838512i | \(-0.683426\pi\) |
0.838512 | + | 0.544883i | \(0.183426\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 36.0000i | − | 0.112853i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −367.423 | + | 367.423i | −1.14107 | + | 1.14107i | ||||
\(323\) | −394.368 | − | 394.368i | −1.22095 | − | 1.22095i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 486.000 | 1.49080 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 587.878 | + | 587.878i | 1.79231 | + | 1.79231i | ||||
\(329\) | 90.0000i | 0.273556i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −178.000 | −0.537764 | −0.268882 | − | 0.963173i | \(-0.586654\pi\) | ||||
−0.268882 | + | 0.963173i | \(0.586654\pi\) | |||||||
\(332\) | 19.5959 | − | 19.5959i | 0.0590238 | − | 0.0590238i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 480.000i | − | 1.43713i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 150.644 | − | 150.644i | 0.447014 | − | 0.447014i | −0.447347 | − | 0.894361i | \(-0.647631\pi\) |
0.894361 | + | 0.447347i | \(0.147631\pi\) | |||||||
\(338\) | 347.828 | + | 347.828i | 1.02908 | + | 1.02908i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −150.000 | −0.439883 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −140.846 | − | 140.846i | −0.410629 | − | 0.410629i | ||||
\(344\) | − | 1176.00i | − | 3.41860i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −852.000 | −2.46243 | ||||||||
\(347\) | −374.772 | + | 374.772i | −1.08003 | + | 1.08003i | −0.0835290 | + | 0.996505i | \(0.526619\pi\) |
−0.996505 | + | 0.0835290i | \(0.973381\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 514.000i | 1.47278i | 0.676558 | + | 0.736390i | \(0.263471\pi\) | ||||
−0.676558 | + | 0.736390i | \(0.736529\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 242.499 | + | 242.499i | 0.686967 | + | 0.686967i | 0.961561 | − | 0.274593i | \(-0.0885432\pi\) |
−0.274593 | + | 0.961561i | \(0.588543\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1056.00 | −2.96629 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −367.423 | − | 367.423i | −1.02632 | − | 1.02632i | ||||
\(359\) | − | 648.000i | − | 1.80501i | −0.430675 | − | 0.902507i | \(-0.641725\pi\) | ||
0.430675 | − | 0.902507i | \(-0.358275\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −168.000 | −0.465374 | ||||||||
\(362\) | 526.640 | − | 526.640i | 1.45481 | − | 1.45481i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 360.000i | − | 0.989011i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −143.295 | + | 143.295i | −0.390450 | + | 0.390450i | −0.874848 | − | 0.484398i | \(-0.839039\pi\) |
0.484398 | + | 0.874848i | \(0.339039\pi\) | |||||||
\(368\) | 195.959 | + | 195.959i | 0.532498 | + | 0.532498i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 300.000 | 0.808625 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −35.5176 | − | 35.5176i | −0.0952215 | − | 0.0952215i | 0.657891 | − | 0.753113i | \(-0.271449\pi\) |
−0.753113 | + | 0.657891i | \(0.771449\pi\) | |||||||
\(374\) | − | 504.000i | − | 1.34759i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 144.000 | 0.382979 | ||||||||
\(377\) | 22.0454 | − | 22.0454i | 0.0584759 | − | 0.0584759i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 215.000i | − | 0.567282i | −0.958930 | − | 0.283641i | \(-0.908458\pi\) | ||
0.958930 | − | 0.283641i | \(-0.0915425\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −573.181 | + | 573.181i | −1.50047 | + | 1.50047i | ||||
\(383\) | 19.5959 | + | 19.5959i | 0.0511643 | + | 0.0511643i | 0.732226 | − | 0.681062i | \(-0.238481\pi\) |
−0.681062 | + | 0.732226i | \(0.738481\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −318.000 | −0.823834 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 186.161 | + | 186.161i | 0.479797 | + | 0.479797i | ||||
\(389\) | 192.000i | 0.493573i | 0.969070 | + | 0.246787i | \(0.0793747\pi\) | ||||
−0.969070 | + | 0.246787i | \(0.920625\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −420.000 | −1.07417 | ||||||||
\(392\) | 254.747 | − | 254.747i | 0.649865 | − | 0.649865i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 948.000i | − | 2.40609i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 366.199 | − | 366.199i | 0.922415 | − | 0.922415i | −0.0747848 | − | 0.997200i | \(-0.523827\pi\) |
0.997200 | + | 0.0747848i | \(0.0238270\pi\) | |||||||
\(398\) | −26.9444 | − | 26.9444i | −0.0676995 | − | 0.0676995i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −228.000 | −0.568579 | −0.284289 | − | 0.958739i | \(-0.591758\pi\) | ||||
−0.284289 | + | 0.958739i | \(0.591758\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −91.8559 | − | 91.8559i | −0.227930 | − | 0.227930i | ||||
\(404\) | 768.000i | 1.90099i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 180.000 | 0.443350 | ||||||||
\(407\) | −146.969 | + | 146.969i | −0.361104 | + | 0.361104i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 707.000i | − | 1.72861i | −0.502971 | − | 0.864303i | \(-0.667760\pi\) | ||
0.502971 | − | 0.864303i | \(-0.332240\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 156.767 | − | 156.767i | 0.380503 | − | 0.380503i | ||||
\(413\) | 110.227 | + | 110.227i | 0.266894 | + | 0.266894i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −338.030 | − | 338.030i | −0.808683 | − | 0.808683i | ||||
\(419\) | 48.0000i | 0.114558i | 0.998358 | + | 0.0572792i | \(0.0182425\pi\) | ||||
−0.998358 | + | 0.0572792i | \(0.981757\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 514.000 | 1.22090 | 0.610451 | − | 0.792054i | \(-0.290988\pi\) | ||||
0.610451 | + | 0.792054i | \(0.290988\pi\) | |||||||
\(422\) | 208.207 | − | 208.207i | 0.493381 | − | 0.493381i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 480.000i | − | 1.13208i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 226.578 | − | 226.578i | 0.530627 | − | 0.530627i | ||||
\(428\) | 235.151 | + | 235.151i | 0.549418 | + | 0.549418i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −30.0000 | −0.0696056 | −0.0348028 | − | 0.999394i | \(-0.511080\pi\) | ||||
−0.0348028 | + | 0.999394i | \(0.511080\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 353.951 | + | 353.951i | 0.817439 | + | 0.817439i | 0.985736 | − | 0.168297i | \(-0.0538267\pi\) |
−0.168297 | + | 0.985736i | \(0.553827\pi\) | |||||||
\(434\) | − | 750.000i | − | 1.72811i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1336.00 | 3.06422 | ||||||||
\(437\) | −281.691 | + | 281.691i | −0.644603 | + | 0.644603i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 575.000i | 1.30979i | 0.755718 | + | 0.654897i | \(0.227288\pi\) | ||||
−0.755718 | + | 0.654897i | \(0.772712\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 308.636 | − | 308.636i | 0.698271 | − | 0.698271i | ||||
\(443\) | −112.677 | − | 112.677i | −0.254349 | − | 0.254349i | 0.568402 | − | 0.822751i | \(-0.307562\pi\) |
−0.822751 | + | 0.568402i | \(0.807562\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 498.000 | 1.11659 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 391.918 | + | 391.918i | 0.874818 | + | 0.874818i | ||||
\(449\) | 204.000i | 0.454343i | 0.973855 | + | 0.227171i | \(0.0729478\pi\) | ||||
−0.973855 | + | 0.227171i | \(0.927052\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −360.000 | −0.798226 | ||||||||
\(452\) | −470.302 | + | 470.302i | −1.04049 | + | 1.04049i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 960.000i | 2.11454i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −440.908 | + | 440.908i | −0.964788 | + | 0.964788i | −0.999401 | − | 0.0346127i | \(-0.988980\pi\) |
0.0346127 | + | 0.999401i | \(0.488980\pi\) | |||||||
\(458\) | 556.034 | + | 556.034i | 1.21405 | + | 1.21405i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −132.000 | −0.286334 | −0.143167 | − | 0.989699i | \(-0.545729\pi\) | ||||
−0.143167 | + | 0.989699i | \(0.545729\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 436.009 | + | 436.009i | 0.941704 | + | 0.941704i | 0.998392 | − | 0.0566875i | \(-0.0180539\pi\) |
−0.0566875 | + | 0.998392i | \(0.518054\pi\) | |||||||
\(464\) | − | 96.0000i | − | 0.206897i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −504.000 | −1.08155 | ||||||||
\(467\) | 276.792 | − | 276.792i | 0.592703 | − | 0.592703i | −0.345658 | − | 0.938361i | \(-0.612344\pi\) |
0.938361 | + | 0.345658i | \(0.112344\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 315.000i | 0.671642i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 176.363 | − | 176.363i | 0.373651 | − | 0.373651i | ||||
\(473\) | 360.075 | + | 360.075i | 0.761258 | + | 0.761258i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1680.00 | 3.52941 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −558.484 | − | 558.484i | −1.16838 | − | 1.16838i | ||||
\(479\) | 810.000i | 1.69102i | 0.533957 | + | 0.845511i | \(0.320704\pi\) | ||||
−0.533957 | + | 0.845511i | \(0.679296\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −180.000 | −0.374220 | ||||||||
\(482\) | −467.853 | + | 467.853i | −0.970648 | + | 0.970648i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 680.000i | 1.40496i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −488.673 | + | 488.673i | −1.00344 | + | 1.00344i | −0.00344166 | + | 0.999994i | \(0.501096\pi\) |
−0.999994 | + | 0.00344166i | \(0.998904\pi\) | |||||||
\(488\) | −362.524 | − | 362.524i | −0.742878 | − | 0.742878i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −348.000 | −0.708758 | −0.354379 | − | 0.935102i | \(-0.615308\pi\) | ||||
−0.354379 | + | 0.935102i | \(0.615308\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 102.879 | + | 102.879i | 0.208679 | + | 0.208679i | ||||
\(494\) | − | 414.000i | − | 0.838057i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −400.000 | −0.806452 | ||||||||
\(497\) | 808.332 | − | 808.332i | 1.62642 | − | 1.62642i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 227.000i | 0.454910i | 0.973789 | + | 0.227455i | \(0.0730404\pi\) | ||||
−0.973789 | + | 0.227455i | \(0.926960\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 470.302 | − | 470.302i | 0.936857 | − | 0.936857i | ||||
\(503\) | −137.171 | − | 137.171i | −0.272707 | − | 0.272707i | 0.557482 | − | 0.830189i | \(-0.311767\pi\) |
−0.830189 | + | 0.557482i | \(0.811767\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −360.000 | −0.711462 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −352.727 | − | 352.727i | −0.694344 | − | 0.694344i | ||||
\(509\) | − | 618.000i | − | 1.21415i | −0.794646 | − | 0.607073i | \(-0.792344\pi\) | ||
0.794646 | − | 0.607073i | \(-0.207656\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −300.000 | −0.587084 | ||||||||
\(512\) | 627.069 | − | 627.069i | 1.22474 | − | 1.22474i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 696.000i | 1.35409i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −44.0908 | + | 44.0908i | −0.0852820 | + | 0.0852820i | ||||
\(518\) | −734.847 | − | 734.847i | −1.41862 | − | 1.41862i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −690.000 | −1.32438 | −0.662188 | − | 0.749338i | \(-0.730372\pi\) | ||||
−0.662188 | + | 0.749338i | \(0.730372\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −255.972 | − | 255.972i | −0.489430 | − | 0.489430i | 0.418697 | − | 0.908126i | \(-0.362487\pi\) |
−0.908126 | + | 0.418697i | \(0.862487\pi\) | |||||||
\(524\) | 864.000i | 1.64885i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1224.00 | 2.32700 | ||||||||
\(527\) | 428.661 | − | 428.661i | 0.813398 | − | 0.813398i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 229.000i | − | 0.432892i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1126.77 | − | 1126.77i | 2.11798 | − | 2.11798i | ||||
\(533\) | −220.454 | − | 220.454i | −0.413610 | − | 0.413610i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 504.000 | 0.940299 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1131.66 | + | 1131.66i | 2.10347 | + | 2.10347i | ||||
\(539\) | 156.000i | 0.289425i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −325.000 | −0.600739 | −0.300370 | − | 0.953823i | \(-0.597110\pi\) | ||||
−0.300370 | + | 0.953823i | \(0.597110\pi\) | |||||||
\(542\) | −1092.47 | + | 1092.47i | −2.01563 | + | 2.01563i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 489.898 | − | 489.898i | 0.895609 | − | 0.895609i | −0.0994353 | − | 0.995044i | \(-0.531704\pi\) |
0.995044 | + | 0.0994353i | \(0.0317036\pi\) | |||||||
\(548\) | −960.200 | − | 960.200i | −1.75219 | − | 1.75219i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 138.000 | 0.250454 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 61.2372 | + | 61.2372i | 0.110736 | + | 0.110736i | ||||
\(554\) | 858.000i | 1.54874i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 464.000 | 0.834532 | ||||||||
\(557\) | −154.318 | + | 154.318i | −0.277052 | + | 0.277052i | −0.831931 | − | 0.554879i | \(-0.812764\pi\) |
0.554879 | + | 0.831931i | \(0.312764\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 441.000i | 0.788909i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1337.42 | + | 1337.42i | −2.37975 | + | 2.37975i | ||||
\(563\) | −609.923 | − | 609.923i | −1.08334 | − | 1.08334i | −0.996195 | − | 0.0871492i | \(-0.972224\pi\) |
−0.0871492 | − | 0.996195i | \(-0.527776\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −942.000 | −1.66431 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1293.33 | − | 1293.33i | −2.27699 | − | 2.27699i | ||||
\(569\) | 198.000i | 0.347979i | 0.984748 | + | 0.173989i | \(0.0556659\pi\) | ||||
−0.984748 | + | 0.173989i | \(0.944334\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −169.000 | −0.295972 | −0.147986 | − | 0.988989i | \(-0.547279\pi\) | ||||
−0.147986 | + | 0.988989i | \(0.547279\pi\) | |||||||
\(572\) | 176.363 | − | 176.363i | 0.308327 | − | 0.308327i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 1800.00i | − | 3.13589i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −243.724 | + | 243.724i | −0.422399 | + | 0.422399i | −0.886029 | − | 0.463630i | \(-0.846547\pi\) |
0.463630 | + | 0.886029i | \(0.346547\pi\) | |||||||
\(578\) | 732.397 | + | 732.397i | 1.26712 | + | 1.26712i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −30.0000 | −0.0516351 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 146.969 | + | 146.969i | 0.252092 | + | 0.252092i | ||||
\(584\) | 480.000i | 0.821918i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1356.00 | −2.31399 | ||||||||
\(587\) | 289.040 | − | 289.040i | 0.492402 | − | 0.492402i | −0.416660 | − | 0.909062i | \(-0.636800\pi\) |
0.909062 | + | 0.416660i | \(0.136800\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 575.000i | − | 0.976231i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −391.918 | + | 391.918i | −0.662024 | + | 0.662024i | ||||
\(593\) | 421.312 | + | 421.312i | 0.710476 | + | 0.710476i | 0.966635 | − | 0.256159i | \(-0.0824570\pi\) |
−0.256159 | + | 0.966635i | \(0.582457\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1488.00 | −2.49664 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −220.454 | − | 220.454i | −0.368652 | − | 0.368652i | ||||
\(599\) | 144.000i | 0.240401i | 0.992750 | + | 0.120200i | \(0.0383537\pi\) | ||||
−0.992750 | + | 0.120200i | \(0.961646\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −899.000 | −1.49584 | −0.747920 | − | 0.663789i | \(-0.768947\pi\) | ||||
−0.747920 | + | 0.663789i | \(0.768947\pi\) | |||||||
\(602\) | −1800.37 | + | 1800.37i | −2.99066 | + | 2.99066i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 664.000i | 1.09934i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.89898 | + | 4.89898i | −0.00807081 | + | 0.00807081i | −0.711131 | − | 0.703060i | \(-0.751817\pi\) |
0.703060 | + | 0.711131i | \(0.251817\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −54.0000 | −0.0883797 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −259.646 | − | 259.646i | −0.423566 | − | 0.423566i | 0.462864 | − | 0.886430i | \(-0.346822\pi\) |
−0.886430 | + | 0.462864i | \(0.846822\pi\) | |||||||
\(614\) | − | 426.000i | − | 0.693811i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 720.000 | 1.16883 | ||||||||
\(617\) | 9.79796 | − | 9.79796i | 0.0158800 | − | 0.0158800i | −0.699122 | − | 0.715002i | \(-0.746426\pi\) |
0.715002 | + | 0.699122i | \(0.246426\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 637.000i | − | 1.02908i | −0.857467 | − | 0.514540i | \(-0.827963\pi\) | ||
0.857467 | − | 0.514540i | \(-0.172037\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −720.150 | + | 720.150i | −1.15780 | + | 1.15780i | ||||
\(623\) | 808.332 | + | 808.332i | 1.29748 | + | 1.29748i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1926.00 | 3.07668 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −362.524 | − | 362.524i | −0.577268 | − | 0.577268i | ||||
\(629\) | − | 840.000i | − | 1.33545i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 287.000 | 0.454834 | 0.227417 | − | 0.973798i | \(-0.426972\pi\) | ||||
0.227417 | + | 0.973798i | \(0.426972\pi\) | |||||||
\(632\) | 97.9796 | − | 97.9796i | 0.155031 | − | 0.155031i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 456.000i | 0.719243i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −95.5301 | + | 95.5301i | −0.149969 | + | 0.149969i | ||||
\(638\) | 88.1816 | + | 88.1816i | 0.138216 | + | 0.138216i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 60.0000 | 0.0936037 | 0.0468019 | − | 0.998904i | \(-0.485097\pi\) | ||||
0.0468019 | + | 0.998904i | \(0.485097\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 191.060 | + | 191.060i | 0.297139 | + | 0.297139i | 0.839892 | − | 0.542753i | \(-0.182618\pi\) |
−0.542753 | + | 0.839892i | \(0.682618\pi\) | |||||||
\(644\) | − | 1200.00i | − | 1.86335i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1932.00 | 2.99071 | ||||||||
\(647\) | −656.463 | + | 656.463i | −1.01463 | + | 1.01463i | −0.0147349 | + | 0.999891i | \(0.504690\pi\) |
−0.999891 | + | 0.0147349i | \(0.995310\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 108.000i | 0.166410i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −793.635 | + | 793.635i | −1.21723 | + | 1.21723i | ||||
\(653\) | −751.993 | − | 751.993i | −1.15160 | − | 1.15160i | −0.986232 | − | 0.165365i | \(-0.947120\pi\) |
−0.165365 | − | 0.986232i | \(-0.552880\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −960.000 | −1.46341 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −220.454 | − | 220.454i | −0.335037 | − | 0.335037i | ||||
\(659\) | 420.000i | 0.637329i | 0.947868 | + | 0.318665i | \(0.103234\pi\) | ||||
−0.947868 | + | 0.318665i | \(0.896766\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −158.000 | −0.239032 | −0.119516 | − | 0.992832i | \(-0.538134\pi\) | ||||
−0.119516 | + | 0.992832i | \(0.538134\pi\) | |||||||
\(662\) | 436.009 | − | 436.009i | 0.658624 | − | 0.658624i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 48.0000i | 0.0722892i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 73.4847 | − | 73.4847i | 0.110172 | − | 0.110172i | ||||
\(668\) | 783.837 | + | 783.837i | 1.17341 | + | 1.17341i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 222.000 | 0.330849 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −122.474 | − | 122.474i | −0.181983 | − | 0.181983i | 0.610236 | − | 0.792219i | \(-0.291074\pi\) |
−0.792219 | + | 0.610236i | \(0.791074\pi\) | |||||||
\(674\) | 738.000i | 1.09496i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1136.00 | −1.68047 | ||||||||
\(677\) | −242.499 | + | 242.499i | −0.358197 | + | 0.358197i | −0.863148 | − | 0.504951i | \(-0.831511\pi\) |
0.504951 | + | 0.863148i | \(0.331511\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 285.000i | − | 0.419735i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 367.423 | − | 367.423i | 0.538744 | − | 0.538744i | ||||
\(683\) | 19.5959 | + | 19.5959i | 0.0286909 | + | 0.0286909i | 0.721307 | − | 0.692616i | \(-0.243542\pi\) |
−0.692616 | + | 0.721307i | \(0.743542\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 690.000 | 1.00583 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 960.200 | + | 960.200i | 1.39564 | + | 1.39564i | ||||
\(689\) | 180.000i | 0.261248i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −74.0000 | −0.107091 | −0.0535456 | − | 0.998565i | \(-0.517052\pi\) | ||||
−0.0535456 | + | 0.998565i | \(0.517052\pi\) | |||||||
\(692\) | 1391.31 | − | 1391.31i | 2.01056 | − | 2.01056i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 1836.00i | − | 2.64553i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1028.79 | − | 1028.79i | 1.47602 | − | 1.47602i | ||||
\(698\) | −1259.04 | − | 1259.04i | −1.80378 | − | 1.80378i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 102.000 | 0.145506 | 0.0727532 | − | 0.997350i | \(-0.476821\pi\) | ||||
0.0727532 | + | 0.997350i | \(0.476821\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −563.383 | − | 563.383i | −0.801398 | − | 0.801398i | ||||
\(704\) | 384.000i | 0.545455i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1188.00 | −1.68272 | ||||||||
\(707\) | 587.878 | − | 587.878i | 0.831510 | − | 0.831510i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 817.000i | 1.15233i | 0.817334 | + | 0.576164i | \(0.195451\pi\) | ||||
−0.817334 | + | 0.576164i | \(0.804549\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1293.33 | − | 1293.33i | 1.81648 | − | 1.81648i | ||||
\(713\) | −306.186 | − | 306.186i | −0.429434 | − | 0.429434i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1200.00 | 1.67598 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1587.27 | + | 1587.27i | 2.21068 | + | 2.21068i | ||||
\(719\) | − | 6.00000i | − | 0.00834492i | −0.999991 | − | 0.00417246i | \(-0.998672\pi\) | ||
0.999991 | − | 0.00417246i | \(-0.00132814\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −240.000 | −0.332871 | ||||||||
\(722\) | 411.514 | − | 411.514i | 0.569964 | − | 0.569964i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1720.00i | 2.37569i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 45.3156 | − | 45.3156i | 0.0623323 | − | 0.0623323i | −0.675253 | − | 0.737586i | \(-0.735966\pi\) |
0.737586 | + | 0.675253i | \(0.235966\pi\) | |||||||
\(728\) | 440.908 | + | 440.908i | 0.605643 | + | 0.605643i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2058.00 | −2.81532 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 484.999 | + | 484.999i | 0.661663 | + | 0.661663i | 0.955772 | − | 0.294109i | \(-0.0950228\pi\) |
−0.294109 | + | 0.955772i | \(0.595023\pi\) | |||||||
\(734\) | − | 702.000i | − | 0.956403i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −154.318 | + | 154.318i | −0.209387 | + | 0.209387i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 298.000i | 0.403248i | 0.979463 | + | 0.201624i | \(0.0646218\pi\) | ||||
−0.979463 | + | 0.201624i | \(0.935378\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −734.847 | + | 734.847i | −0.990360 | + | 0.990360i | ||||
\(743\) | 249.848 | + | 249.848i | 0.336269 | + | 0.336269i | 0.854961 | − | 0.518692i | \(-0.173581\pi\) |
−0.518692 | + | 0.854961i | \(0.673581\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 174.000 | 0.233244 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 823.029 | + | 823.029i | 1.10031 | + | 1.10031i | ||||
\(749\) | − | 360.000i | − | 0.480641i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1186.00 | 1.57923 | 0.789614 | − | 0.613604i | \(-0.210281\pi\) | ||||
0.789614 | + | 0.613604i | \(0.210281\pi\) | |||||||
\(752\) | −117.576 | + | 117.576i | −0.156350 | + | 0.156350i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 108.000i | 0.143236i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 743.420 | − | 743.420i | 0.982061 | − | 0.982061i | −0.0177810 | − | 0.999842i | \(-0.505660\pi\) |
0.999842 | + | 0.0177810i | \(0.00566015\pi\) | |||||||
\(758\) | 526.640 | + | 526.640i | 0.694776 | + | 0.694776i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 576.000 | 0.756899 | 0.378449 | − | 0.925622i | \(-0.376457\pi\) | ||||
0.378449 | + | 0.925622i | \(0.376457\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1022.66 | − | 1022.66i | −1.34032 | − | 1.34032i | ||||
\(764\) | − | 1872.00i | − | 2.45026i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −96.0000 | −0.125326 | ||||||||
\(767\) | −66.1362 | + | 66.1362i | −0.0862271 | + | 0.0862271i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 491.000i | 0.638492i | 0.947672 | + | 0.319246i | \(0.103430\pi\) | ||||
−0.947672 | + | 0.319246i | \(0.896570\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 519.292 | − | 519.292i | 0.672658 | − | 0.672658i | ||||
\(773\) | −519.292 | − | 519.292i | −0.671788 | − | 0.671788i | 0.286340 | − | 0.958128i | \(-0.407561\pi\) |
−0.958128 | + | 0.286340i | \(0.907561\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −456.000 | −0.587629 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −470.302 | − | 470.302i | −0.604501 | − | 0.604501i | ||||
\(779\) | − | 1380.00i | − | 1.77150i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 792.000 | 1.01408 | ||||||||
\(782\) | 1028.79 | − | 1028.79i | 1.31558 | − | 1.31558i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 416.000i | 0.530612i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −123.699 | + | 123.699i | −0.157178 | + | 0.157178i | −0.781315 | − | 0.624137i | \(-0.785451\pi\) |
0.624137 | + | 0.781315i | \(0.285451\pi\) | |||||||
\(788\) | 1548.08 | + | 1548.08i | 1.96457 | + | 1.96457i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 720.000 | 0.910240 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 135.947 | + | 135.947i | 0.171433 | + | 0.171433i | ||||
\(794\) | 1794.00i | 2.25945i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 88.0000 | 0.110553 | ||||||||
\(797\) | 460.504 | − | 460.504i | 0.577797 | − | 0.577797i | −0.356499 | − | 0.934296i | \(-0.616030\pi\) |
0.934296 | + | 0.356499i | \(0.116030\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 252.000i | − | 0.315394i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 558.484 | − | 558.484i | 0.696364 | − | 0.696364i | ||||
\(803\) | −146.969 | − | 146.969i | −0.183025 | − | 0.183025i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 450.000 | 0.558313 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −940.604 | − | 940.604i | −1.16411 | − | 1.16411i | ||||
\(809\) | 900.000i | 1.11248i | 0.831020 | + | 0.556242i | \(0.187757\pi\) | ||||
−0.831020 | + | 0.556242i | \(0.812243\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1477.00 | 1.82121 | 0.910604 | − | 0.413280i | \(-0.135617\pi\) | ||||
0.910604 | + | 0.413280i | \(0.135617\pi\) | |||||||
\(812\) | −293.939 | + | 293.939i | −0.361994 | + | 0.361994i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 720.000i | − | 0.884521i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1380.29 | + | 1380.29i | −1.68946 | + | 1.68946i | ||||
\(818\) | 1731.79 | + | 1731.79i | 2.11710 | + | 2.11710i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 786.000 | 0.957369 | 0.478685 | − | 0.877987i | \(-0.341114\pi\) | ||||
0.478685 | + | 0.877987i | \(0.341114\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 371.098 | + | 371.098i | 0.450909 | + | 0.450909i | 0.895656 | − | 0.444747i | \(-0.146707\pi\) |
−0.444747 | + | 0.895656i | \(0.646707\pi\) | |||||||
\(824\) | 384.000i | 0.466019i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −540.000 | −0.653753 | ||||||||
\(827\) | 788.736 | − | 788.736i | 0.953731 | − | 0.953731i | −0.0452447 | − | 0.998976i | \(-0.514407\pi\) |
0.998976 | + | 0.0452447i | \(0.0144068\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 170.000i | − | 0.205066i | −0.994730 | − | 0.102533i | \(-0.967305\pi\) | ||
0.994730 | − | 0.102533i | \(-0.0326948\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −235.151 | + | 235.151i | −0.282633 | + | 0.282633i | ||||
\(833\) | −445.807 | − | 445.807i | −0.535183 | − | 0.535183i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1104.00 | 1.32057 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −117.576 | − | 117.576i | −0.140305 | − | 0.140305i | ||||
\(839\) | − | 990.000i | − | 1.17998i | −0.807412 | − | 0.589988i | \(-0.799132\pi\) | ||
0.807412 | − | 0.589988i | \(-0.200868\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 805.000 | 0.957194 | ||||||||
\(842\) | −1259.04 | + | 1259.04i | −1.49529 | + | 1.49529i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 680.000i | 0.805687i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 520.517 | − | 520.517i | 0.614541 | − | 0.614541i | ||||
\(848\) | 391.918 | + | 391.918i | 0.462168 | + | 0.462168i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −600.000 | −0.705053 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −723.824 | − | 723.824i | −0.848563 | − | 0.848563i | 0.141391 | − | 0.989954i | \(-0.454843\pi\) |
−0.989954 | + | 0.141391i | \(0.954843\pi\) | |||||||
\(854\) | 1110.00i | 1.29977i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −576.000 | −0.672897 | ||||||||
\(857\) | −739.746 | + | 739.746i | −0.863181 | + | 0.863181i | −0.991706 | − | 0.128525i | \(-0.958976\pi\) |
0.128525 | + | 0.991706i | \(0.458976\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1510.00i | − | 1.75786i | −0.476953 | − | 0.878929i | \(-0.658259\pi\) | ||
0.476953 | − | 0.878929i | \(-0.341741\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 73.4847 | − | 73.4847i | 0.0852491 | − | 0.0852491i | ||||
\(863\) | 372.322 | + | 372.322i | 0.431428 | + | 0.431428i | 0.889114 | − | 0.457686i | \(-0.151322\pi\) |
−0.457686 | + | 0.889114i | \(0.651322\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1734.00 | −2.00231 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1224.74 | + | 1224.74i | 1.41100 | + | 1.41100i | ||||
\(869\) | 60.0000i | 0.0690449i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −189.000 | −0.216992 | ||||||||
\(872\) | −1636.26 | + | 1636.26i | −1.87644 | + | 1.87644i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 1380.00i | − | 1.57895i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −300.062 | + | 300.062i | −0.342147 | + | 0.342147i | −0.857174 | − | 0.515027i | \(-0.827782\pi\) |
0.515027 | + | 0.857174i | \(0.327782\pi\) | |||||||
\(878\) | −1408.46 | − | 1408.46i | −1.60416 | − | 1.60416i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 216.000 | 0.245176 | 0.122588 | − | 0.992458i | \(-0.460881\pi\) | ||||
0.122588 | + | 0.992458i | \(0.460881\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 846.299 | + | 846.299i | 0.958436 | + | 0.958436i | 0.999170 | − | 0.0407343i | \(-0.0129697\pi\) |
−0.0407343 | + | 0.999170i | \(0.512970\pi\) | |||||||
\(884\) | 1008.00i | 1.14027i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 552.000 | 0.623025 | ||||||||
\(887\) | −996.942 | + | 996.942i | −1.12395 | + | 1.12395i | −0.132807 | + | 0.991142i | \(0.542399\pi\) |
−0.991142 | + | 0.132807i | \(0.957601\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 540.000i | 0.607424i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −813.231 | + | 813.231i | −0.911693 | + | 0.911693i | ||||
\(893\) | −169.015 | − | 169.015i | −0.189266 | − | 0.189266i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1920.00 | −2.14286 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −499.696 | − | 499.696i | −0.556454 | − | 0.556454i | ||||
\(899\) | 150.000i | 0.166852i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −840.000 | −0.932297 | ||||||||
\(902\) | 881.816 | − | 881.816i | 0.977623 | − | 0.977623i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 1152.00i | − | 1.27434i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 53.8888 | − | 53.8888i | 0.0594143 | − | 0.0594143i | −0.676775 | − | 0.736190i | \(-0.736623\pi\) |
0.736190 | + | 0.676775i | \(0.236623\pi\) | |||||||
\(908\) | −1567.67 | − | 1567.67i | −1.72651 | − | 1.72651i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 558.000 | 0.612514 | 0.306257 | − | 0.951949i | \(-0.400923\pi\) | ||||
0.306257 | + | 0.951949i | \(0.400923\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.6969 | − | 14.6969i | −0.0160974 | − | 0.0160974i | ||||
\(914\) | − | 2160.00i | − | 2.36324i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1816.00 | −1.98253 | ||||||||
\(917\) | 661.362 | − | 661.362i | 0.721224 | − | 0.721224i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 755.000i | − | 0.821545i | −0.911738 | − | 0.410773i | \(-0.865259\pi\) | ||
0.911738 | − | 0.410773i | \(-0.134741\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 323.333 | − | 323.333i | 0.350686 | − | 0.350686i | ||||
\(923\) | 484.999 | + | 484.999i | 0.525459 | + | 0.525459i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2136.00 | −2.30670 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 762.000i | − | 0.820237i | −0.912032 | − | 0.410118i | \(-0.865487\pi\) | ||
0.912032 | − | 0.410118i | \(-0.134513\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −598.000 | −0.642320 | ||||||||
\(932\) | 823.029 | − | 823.029i | 0.883078 | − | 0.883078i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1356.00i | 1.45182i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −388.244 | + | 388.244i | −0.414348 | + | 0.414348i | −0.883250 | − | 0.468902i | \(-0.844650\pi\) |
0.468902 | + | 0.883250i | \(0.344650\pi\) | |||||||
\(938\) | −771.589 | − | 771.589i | −0.822590 | − | 0.822590i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 690.000 | 0.733262 | 0.366631 | − | 0.930366i | \(-0.380511\pi\) | ||||
0.366631 | + | 0.930366i | \(0.380511\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −734.847 | − | 734.847i | −0.779265 | − | 0.779265i | ||||
\(944\) | 288.000i | 0.305085i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1764.00 | −1.86469 | ||||||||
\(947\) | −100.429 | + | 100.429i | −0.106050 | + | 0.106050i | −0.758141 | − | 0.652091i | \(-0.773892\pi\) |
0.652091 | + | 0.758141i | \(0.273892\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 180.000i | − | 0.189673i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2057.57 | + | 2057.57i | −2.16131 | + | 2.16131i | ||||
\(953\) | −749.544 | − | 749.544i | −0.786510 | − | 0.786510i | 0.194410 | − | 0.980920i | \(-0.437721\pi\) |
−0.980920 | + | 0.194410i | \(0.937721\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1824.00 | 1.90795 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1984.09 | − | 1984.09i | −2.07107 | − | 2.07107i | ||||
\(959\) | 1470.00i | 1.53285i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −336.000 | −0.349636 | ||||||||
\(962\) | 440.908 | − | 440.908i | 0.458324 | − | 0.458324i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 1528.00i | − | 1.58506i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.89898 | + | 4.89898i | −0.00506616 | + | 0.00506616i | −0.709635 | − | 0.704569i | \(-0.751140\pi\) |
0.704569 | + | 0.709635i | \(0.251140\pi\) | |||||||
\(968\) | −832.827 | − | 832.827i | −0.860358 | − | 0.860358i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −90.0000 | −0.0926880 | −0.0463440 | − | 0.998926i | \(-0.514757\pi\) | ||||
−0.0463440 | + | 0.998926i | \(0.514757\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −355.176 | − | 355.176i | −0.365032 | − | 0.365032i | ||||
\(974\) | − | 2394.00i | − | 2.45791i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 592.000 | 0.606557 | ||||||||
\(977\) | −301.287 | + | 301.287i | −0.308380 | + | 0.308380i | −0.844281 | − | 0.535901i | \(-0.819972\pi\) |
0.535901 | + | 0.844281i | \(0.319972\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 792.000i | 0.808989i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 852.422 | − | 852.422i | 0.868047 | − | 0.868047i | ||||
\(983\) | 465.403 | + | 465.403i | 0.473452 | + | 0.473452i | 0.903030 | − | 0.429578i | \(-0.141338\pi\) |
−0.429578 | + | 0.903030i | \(0.641338\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −504.000 | −0.511156 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 676.059 | + | 676.059i | 0.684270 | + | 0.684270i | ||||
\(989\) | 1470.00i | 1.48635i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1067.00 | 1.07669 | 0.538345 | − | 0.842724i | \(-0.319050\pi\) | ||||
0.538345 | + | 0.842724i | \(0.319050\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3960.00i | 3.98390i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −279.242 | + | 279.242i | −0.280082 | + | 0.280082i | −0.833142 | − | 0.553060i | \(-0.813460\pi\) |
0.553060 | + | 0.833142i | \(0.313460\pi\) | |||||||
\(998\) | −556.034 | − | 556.034i | −0.557148 | − | 0.557148i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 225.3.g.b.118.1 | 4 | ||
3.2 | odd | 2 | 75.3.f.b.43.2 | yes | 4 | ||
5.2 | odd | 4 | inner | 225.3.g.b.82.1 | 4 | ||
5.3 | odd | 4 | inner | 225.3.g.b.82.2 | 4 | ||
5.4 | even | 2 | inner | 225.3.g.b.118.2 | 4 | ||
12.11 | even | 2 | 1200.3.bg.g.193.1 | 4 | |||
15.2 | even | 4 | 75.3.f.b.7.2 | yes | 4 | ||
15.8 | even | 4 | 75.3.f.b.7.1 | ✓ | 4 | ||
15.14 | odd | 2 | 75.3.f.b.43.1 | yes | 4 | ||
60.23 | odd | 4 | 1200.3.bg.g.1057.2 | 4 | |||
60.47 | odd | 4 | 1200.3.bg.g.1057.1 | 4 | |||
60.59 | even | 2 | 1200.3.bg.g.193.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.3.f.b.7.1 | ✓ | 4 | 15.8 | even | 4 | ||
75.3.f.b.7.2 | yes | 4 | 15.2 | even | 4 | ||
75.3.f.b.43.1 | yes | 4 | 15.14 | odd | 2 | ||
75.3.f.b.43.2 | yes | 4 | 3.2 | odd | 2 | ||
225.3.g.b.82.1 | 4 | 5.2 | odd | 4 | inner | ||
225.3.g.b.82.2 | 4 | 5.3 | odd | 4 | inner | ||
225.3.g.b.118.1 | 4 | 1.1 | even | 1 | trivial | ||
225.3.g.b.118.2 | 4 | 5.4 | even | 2 | inner | ||
1200.3.bg.g.193.1 | 4 | 12.11 | even | 2 | |||
1200.3.bg.g.193.2 | 4 | 60.59 | even | 2 | |||
1200.3.bg.g.1057.1 | 4 | 60.47 | odd | 4 | |||
1200.3.bg.g.1057.2 | 4 | 60.23 | odd | 4 |