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 | 118.2 | ||
Root | \(1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.118 |
Dual form | 225.3.g.b.82.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | \(-0.416667\pi\) |
0.965926 | − | 0.258819i | \(-0.0833333\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 8.00000i | − | 2.00000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.12372 | − | 6.12372i | 0.874818 | − | 0.874818i | −0.118175 | − | 0.992993i | \(-0.537704\pi\) |
0.992993 | + | 0.118175i | \(0.0377044\pi\) | |||||||
\(8\) | −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 | 0.834158 | − | 0.551525i | \(-0.185954\pi\) |
−0.551525 | + | 0.834158i | \(0.685954\pi\) | |||||||
\(14\) | − | 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 | \(0.502754\pi\) |
−0.999963 | + | 0.00865084i | \(0.997246\pi\) | |||||||
\(18\) | 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 | 0.921315 | − | 0.388817i | \(-0.127116\pi\) |
−0.388817 | + | 0.921315i | \(0.627116\pi\) | |||||||
\(24\) | 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 | −0.955857 | − | 0.293833i | \(-0.905069\pi\) |
0.293833 | + | 0.955857i | \(0.405069\pi\) | |||||||
\(38\) | −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 | \(0.198354\pi\) |
0.583594 | + | 0.812046i | \(0.301646\pi\) | |||||||
\(44\) | 48.0000i | 1.09091i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 60.0000 | 1.30435 | ||||||||
\(47\) | −7.34847 | + | 7.34847i | −0.156350 | + | 0.156350i | −0.780947 | − | 0.624597i | \(-0.785263\pi\) |
0.624597 | + | 0.780947i | \(0.285263\pi\) | |||||||
\(48\) | 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 | 0.899365 | − | 0.437198i | \(-0.144029\pi\) |
−0.437198 | + | 0.899365i | \(0.644029\pi\) | |||||||
\(54\) | 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 | −0.872496 | − | 0.488621i | \(-0.837500\pi\) |
0.488621 | + | 0.872496i | \(0.337500\pi\) | |||||||
\(68\) | 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 | 0.519142 | − | 0.854688i | \(-0.326252\pi\) |
−0.854688 | + | 0.519142i | \(0.826252\pi\) | |||||||
\(74\) | 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 | 0.692197 | − | 0.721709i | \(-0.256643\pi\) |
−0.721709 | + | 0.692197i | \(0.756643\pi\) | |||||||
\(84\) | 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 | −0.576910 | − | 0.816808i | \(-0.695741\pi\) |
0.816808 | + | 0.576910i | \(0.195741\pi\) | |||||||
\(98\) | −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 | 0.605553 | − | 0.795805i | \(-0.292952\pi\) |
−0.795805 | + | 0.605553i | \(0.792952\pi\) | |||||||
\(104\) | − | 72.0000i | − | 0.692308i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 120.000 | 1.13208 | ||||||||
\(107\) | 29.3939 | − | 29.3939i | 0.274709 | − | 0.274709i | −0.556283 | − | 0.830993i | \(-0.687773\pi\) |
0.830993 | + | 0.556283i | \(0.187773\pi\) | |||||||
\(108\) | 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 | 0.917646 | − | 0.397400i | \(-0.130087\pi\) |
−0.397400 | + | 0.917646i | \(0.630087\pi\) | |||||||
\(114\) | 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 | −0.859055 | − | 0.511883i | \(-0.828948\pi\) |
0.511883 | + | 0.859055i | \(0.328948\pi\) | |||||||
\(128\) | −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 | −0.993128 | − | 0.117033i | \(-0.962662\pi\) |
0.117033 | + | 0.993128i | \(0.462662\pi\) | |||||||
\(138\) | 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 | −0.836540 | − | 0.547906i | \(-0.815425\pi\) |
0.547906 | + | 0.836540i | \(0.315425\pi\) | |||||||
\(158\) | −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 | 0.942584 | − | 0.333969i | \(-0.108388\pi\) |
−0.333969 | + | 0.942584i | \(0.608388\pi\) | |||||||
\(164\) | − | 480.000i | − | 2.92683i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.0000 | −0.0722892 | ||||||||
\(167\) | 97.9796 | − | 97.9796i | 0.586704 | − | 0.586704i | −0.350033 | − | 0.936737i | \(-0.613830\pi\) |
0.936737 | + | 0.350033i | \(0.113830\pi\) | |||||||
\(168\) | 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 | \(-0.998314\pi\) |
−0.00529594 | − | 0.999986i | \(-0.501686\pi\) | |||||||
\(174\) | 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 | 0.518655 | − | 0.854984i | \(-0.326433\pi\) |
−0.854984 | + | 0.518655i | \(0.826433\pi\) | |||||||
\(194\) | − | 114.000i | − | 0.587629i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −208.000 | −1.06122 | ||||||||
\(197\) | 193.510 | − | 193.510i | 0.982283 | − | 0.982283i | −0.0175631 | − | 0.999846i | \(-0.505591\pi\) |
0.999846 | + | 0.0175631i | \(0.00559079\pi\) | |||||||
\(198\) | 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 | 0.897289 | − | 0.441443i | \(-0.145533\pi\) |
−0.441443 | + | 0.897289i | \(0.645533\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 288.000 | 1.27434 | ||||||||
\(227\) | −195.959 | + | 195.959i | −0.863256 | + | 0.863256i | −0.991715 | − | 0.128459i | \(-0.958997\pi\) |
0.128459 | + | 0.991715i | \(0.458997\pi\) | |||||||
\(228\) | 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 | 0.450990 | − | 0.892529i | \(-0.351071\pi\) |
−0.892529 | + | 0.450990i | \(0.851071\pi\) | |||||||
\(234\) | 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 | −0.927249 | − | 0.374446i | \(-0.877833\pi\) |
0.374446 | + | 0.927249i | \(0.377833\pi\) | |||||||
\(258\) | 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 | 0.998808 | − | 0.0488156i | \(-0.0155447\pi\) |
−0.0488156 | + | 0.998808i | \(0.515545\pi\) | |||||||
\(264\) | 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 | −0.948637 | − | 0.316368i | \(-0.897537\pi\) |
0.316368 | + | 0.948637i | \(0.397537\pi\) | |||||||
\(278\) | 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 | 0.280424 | − | 0.959876i | \(-0.409525\pi\) |
−0.959876 | + | 0.280424i | \(0.909525\pi\) | |||||||
\(284\) | 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 | 0.0538645 | − | 0.998548i | \(-0.482846\pi\) |
−0.998548 | + | 0.0538645i | \(0.982846\pi\) | |||||||
\(294\) | 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 | −0.551155 | − | 0.834403i | \(-0.685813\pi\) |
0.834403 | + | 0.551155i | \(0.185813\pi\) | |||||||
\(308\) | 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 | \(0.0980165\pi\) |
0.303085 | + | 0.952964i | \(0.401984\pi\) | |||||||
\(314\) | 222.000i | 0.707006i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −80.0000 | −0.253165 | ||||||||
\(317\) | −93.0806 | + | 93.0806i | −0.293630 | + | 0.293630i | −0.838512 | − | 0.544883i | \(-0.816574\pi\) |
0.544883 | + | 0.838512i | \(0.316574\pi\) | |||||||
\(318\) | 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 | −0.894361 | − | 0.447347i | \(-0.852369\pi\) |
0.447347 | + | 0.894361i | \(0.352369\pi\) | |||||||
\(338\) | −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 | \(-0.473381\pi\) |
0.996505 | − | 0.0835290i | \(-0.0266191\pi\) | |||||||
\(348\) | 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 | 0.274593 | − | 0.961561i | \(-0.411457\pi\) |
−0.961561 | + | 0.274593i | \(0.911457\pi\) | |||||||
\(354\) | 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 | −0.484398 | − | 0.874848i | \(-0.660961\pi\) |
0.874848 | + | 0.484398i | \(0.160961\pi\) | |||||||
\(368\) | −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 | 0.753113 | − | 0.657891i | \(-0.228551\pi\) |
−0.657891 | + | 0.753113i | \(0.728551\pi\) | |||||||
\(374\) | − | 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 | 0.681062 | − | 0.732226i | \(-0.261519\pi\) |
−0.732226 | + | 0.681062i | \(0.761519\pi\) | |||||||
\(384\) | 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 | −0.997200 | − | 0.0747848i | \(-0.976173\pi\) |
0.0747848 | + | 0.997200i | \(0.476173\pi\) | |||||||
\(398\) | 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 | 0.168297 | − | 0.985736i | \(-0.446173\pi\) |
−0.985736 | + | 0.168297i | \(0.946173\pi\) | |||||||
\(434\) | − | 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 | 0.822751 | − | 0.568402i | \(-0.192438\pi\) |
−0.568402 | + | 0.822751i | \(0.692438\pi\) | |||||||
\(444\) | 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 | −0.0346127 | − | 0.999401i | \(-0.511020\pi\) |
0.999401 | + | 0.0346127i | \(0.0110198\pi\) | |||||||
\(458\) | −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 | 0.0566875 | − | 0.998392i | \(-0.481946\pi\) |
−0.998392 | + | 0.0566875i | \(0.981946\pi\) | |||||||
\(464\) | − | 96.0000i | − | 0.206897i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −504.000 | −1.08155 | ||||||||
\(467\) | −276.792 | + | 276.792i | −0.592703 | + | 0.592703i | −0.938361 | − | 0.345658i | \(-0.887656\pi\) |
0.345658 | + | 0.938361i | \(0.387656\pi\) | |||||||
\(468\) | 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 | \(-0.498904\pi\) |
0.999994 | − | 0.00344166i | \(-0.00109552\pi\) | |||||||
\(488\) | 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 | 0.830189 | − | 0.557482i | \(-0.188233\pi\) |
−0.557482 | + | 0.830189i | \(0.688233\pi\) | |||||||
\(504\) | 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 | 0.908126 | − | 0.418697i | \(-0.137513\pi\) |
−0.418697 | + | 0.908126i | \(0.637513\pi\) | |||||||
\(524\) | 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 | −0.995044 | − | 0.0994353i | \(-0.968296\pi\) |
0.0994353 | + | 0.995044i | \(0.468296\pi\) | |||||||
\(548\) | 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 | −0.554879 | − | 0.831931i | \(-0.687236\pi\) |
0.831931 | + | 0.554879i | \(0.187236\pi\) | |||||||
\(558\) | 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 | \(0.0277757\pi\) |
0.0871492 | + | 0.996195i | \(0.472224\pi\) | |||||||
\(564\) | 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 | −0.463630 | − | 0.886029i | \(-0.653453\pi\) |
0.886029 | + | 0.463630i | \(0.153453\pi\) | |||||||
\(578\) | −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 | −0.909062 | − | 0.416660i | \(-0.863200\pi\) |
0.416660 | + | 0.909062i | \(0.363200\pi\) | |||||||
\(588\) | 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 | 0.256159 | − | 0.966635i | \(-0.417543\pi\) |
−0.966635 | + | 0.256159i | \(0.917543\pi\) | |||||||
\(594\) | 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 | −0.703060 | − | 0.711131i | \(-0.748183\pi\) |
0.711131 | + | 0.703060i | \(0.248183\pi\) | |||||||
\(608\) | 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 | 0.886430 | − | 0.462864i | \(-0.153178\pi\) |
−0.462864 | + | 0.886430i | \(0.653178\pi\) | |||||||
\(614\) | − | 426.000i | − | 0.693811i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 720.000 | 1.16883 | ||||||||
\(617\) | −9.79796 | + | 9.79796i | −0.0158800 | + | 0.0158800i | −0.715002 | − | 0.699122i | \(-0.753574\pi\) |
0.699122 | + | 0.715002i | \(0.253574\pi\) | |||||||
\(618\) | 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 | 0.542753 | − | 0.839892i | \(-0.317382\pi\) |
−0.839892 | + | 0.542753i | \(0.817382\pi\) | |||||||
\(644\) | − | 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 | \(-0.495310\pi\) |
0.999891 | − | 0.0147349i | \(-0.00469044\pi\) | |||||||
\(648\) | 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 | \(0.0528803\pi\) |
0.165365 | + | 0.986232i | \(0.447120\pi\) | |||||||
\(654\) | 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 | 0.792219 | − | 0.610236i | \(-0.208926\pi\) |
−0.610236 | + | 0.792219i | \(0.708926\pi\) | |||||||
\(674\) | 738.000i | 1.09496i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1136.00 | −1.68047 | ||||||||
\(677\) | 242.499 | − | 242.499i | 0.358197 | − | 0.358197i | −0.504951 | − | 0.863148i | \(-0.668489\pi\) |
0.863148 | + | 0.504951i | \(0.168489\pi\) | |||||||
\(678\) | 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 | 0.692616 | − | 0.721307i | \(-0.256458\pi\) |
−0.721307 | + | 0.692616i | \(0.756458\pi\) | |||||||
\(684\) | 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 | −0.737586 | − | 0.675253i | \(-0.764034\pi\) |
0.675253 | + | 0.737586i | \(0.264034\pi\) | |||||||
\(728\) | −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 | 0.294109 | − | 0.955772i | \(-0.404977\pi\) |
−0.955772 | + | 0.294109i | \(0.904977\pi\) | |||||||
\(734\) | − | 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 | 0.518692 | − | 0.854961i | \(-0.326419\pi\) |
−0.854961 | + | 0.518692i | \(0.826419\pi\) | |||||||
\(744\) | 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 | −0.999842 | − | 0.0177810i | \(-0.994340\pi\) |
0.0177810 | + | 0.999842i | \(0.494340\pi\) | |||||||
\(758\) | −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 | 0.958128 | − | 0.286340i | \(-0.0924388\pi\) |
−0.286340 | + | 0.958128i | \(0.592439\pi\) | |||||||
\(774\) | 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 | −0.624137 | − | 0.781315i | \(-0.714549\pi\) |
0.781315 | + | 0.624137i | \(0.214549\pi\) | |||||||
\(788\) | −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 | −0.934296 | − | 0.356499i | \(-0.883970\pi\) |
0.356499 | + | 0.934296i | \(0.383970\pi\) | |||||||
\(798\) | 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 | 0.444747 | − | 0.895656i | \(-0.353293\pi\) |
−0.895656 | + | 0.444747i | \(0.853293\pi\) | |||||||
\(824\) | 384.000i | 0.466019i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −540.000 | −0.653753 | ||||||||
\(827\) | −788.736 | + | 788.736i | −0.953731 | + | 0.953731i | −0.998976 | − | 0.0452447i | \(-0.985593\pi\) |
0.0452447 | + | 0.998976i | \(0.485593\pi\) | |||||||
\(828\) | 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 | 0.989954 | − | 0.141391i | \(-0.0451574\pi\) |
−0.141391 | + | 0.989954i | \(0.545157\pi\) | |||||||
\(854\) | 1110.00i | 1.29977i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −576.000 | −0.672897 | ||||||||
\(857\) | 739.746 | − | 739.746i | 0.863181 | − | 0.863181i | −0.128525 | − | 0.991706i | \(-0.541024\pi\) |
0.991706 | + | 0.128525i | \(0.0410244\pi\) | |||||||
\(858\) | 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 | 0.457686 | − | 0.889114i | \(-0.348678\pi\) |
−0.889114 | + | 0.457686i | \(0.848678\pi\) | |||||||
\(864\) | 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 | −0.515027 | − | 0.857174i | \(-0.672218\pi\) |
0.857174 | + | 0.515027i | \(0.172218\pi\) | |||||||
\(878\) | 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 | 0.0407343 | − | 0.999170i | \(-0.487030\pi\) |
−0.999170 | + | 0.0407343i | \(0.987030\pi\) | |||||||
\(884\) | 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 | \(-0.457601\pi\) |
0.991142 | − | 0.132807i | \(-0.0423989\pi\) | |||||||
\(888\) | 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 | −0.736190 | − | 0.676775i | \(-0.763377\pi\) |
0.676775 | + | 0.736190i | \(0.263377\pi\) | |||||||
\(908\) | 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 | −0.468902 | − | 0.883250i | \(-0.655350\pi\) |
0.883250 | + | 0.468902i | \(0.155350\pi\) | |||||||
\(938\) | 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 | −0.652091 | − | 0.758141i | \(-0.726108\pi\) |
0.758141 | + | 0.652091i | \(0.226108\pi\) | |||||||
\(948\) | 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 | 0.980920 | − | 0.194410i | \(-0.0622794\pi\) |
−0.194410 | + | 0.980920i | \(0.562279\pi\) | |||||||
\(954\) | 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 | −0.704569 | − | 0.709635i | \(-0.748860\pi\) |
0.709635 | + | 0.704569i | \(0.248860\pi\) | |||||||
\(968\) | 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 | −0.535901 | − | 0.844281i | \(-0.680028\pi\) |
0.844281 | + | 0.535901i | \(0.180028\pi\) | |||||||
\(978\) | 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 | 0.429578 | − | 0.903030i | \(-0.358662\pi\) |
−0.903030 | + | 0.429578i | \(0.858662\pi\) | |||||||
\(984\) | 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 | −0.553060 | − | 0.833142i | \(-0.686540\pi\) |
0.833142 | + | 0.553060i | \(0.186540\pi\) | |||||||
\(998\) | 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.118.2 | 4 | ||
3.2 | odd | 2 | 75.3.f.b.43.1 | yes | 4 | ||
5.2 | odd | 4 | inner | 225.3.g.b.82.2 | 4 | ||
5.3 | odd | 4 | inner | 225.3.g.b.82.1 | 4 | ||
5.4 | even | 2 | inner | 225.3.g.b.118.1 | 4 | ||
12.11 | even | 2 | 1200.3.bg.g.193.2 | 4 | |||
15.2 | even | 4 | 75.3.f.b.7.1 | ✓ | 4 | ||
15.8 | even | 4 | 75.3.f.b.7.2 | yes | 4 | ||
15.14 | odd | 2 | 75.3.f.b.43.2 | yes | 4 | ||
60.23 | odd | 4 | 1200.3.bg.g.1057.1 | 4 | |||
60.47 | odd | 4 | 1200.3.bg.g.1057.2 | 4 | |||
60.59 | even | 2 | 1200.3.bg.g.193.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.3.f.b.7.1 | ✓ | 4 | 15.2 | even | 4 | ||
75.3.f.b.7.2 | yes | 4 | 15.8 | even | 4 | ||
75.3.f.b.43.1 | yes | 4 | 3.2 | odd | 2 | ||
75.3.f.b.43.2 | yes | 4 | 15.14 | odd | 2 | ||
225.3.g.b.82.1 | 4 | 5.3 | odd | 4 | inner | ||
225.3.g.b.82.2 | 4 | 5.2 | odd | 4 | inner | ||
225.3.g.b.118.1 | 4 | 5.4 | even | 2 | inner | ||
225.3.g.b.118.2 | 4 | 1.1 | even | 1 | trivial | ||
1200.3.bg.g.193.1 | 4 | 60.59 | even | 2 | |||
1200.3.bg.g.193.2 | 4 | 12.11 | even | 2 | |||
1200.3.bg.g.1057.1 | 4 | 60.23 | odd | 4 | |||
1200.3.bg.g.1057.2 | 4 | 60.47 | odd | 4 |