Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1357,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.1357");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.x (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8x^{14} + 8x^{12} - 8x^{10} + 212x^{8} + 248x^{6} + 368x^{4} + 32x^{2} + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1693.8 | ||
Root | \(0.522506 - 1.01508i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1693 |
Dual form | 2100.2.x.d.1357.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.707107 | − | 0.707107i | 0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.63522 | − | 0.235858i | 0.996019 | − | 0.0891461i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.99261 | 1.50533 | 0.752665 | − | 0.658404i | \(-0.228768\pi\) | ||||
0.752665 | + | 0.658404i | \(0.228768\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.63111 | + | 2.63111i | −0.729738 | + | 0.729738i | −0.970567 | − | 0.240830i | \(-0.922580\pi\) |
0.240830 | + | 0.970567i | \(0.422580\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.14626 | + | 4.14626i | 1.00561 | + | 1.00561i | 0.999984 | + | 0.00563041i | \(0.00179222\pi\) |
0.00563041 | + | 0.999984i | \(0.498208\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.66126 | 1.06937 | 0.534684 | − | 0.845052i | \(-0.320431\pi\) | ||||
0.534684 | + | 0.845052i | \(0.320431\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.69660 | − | 2.03016i | 0.370229 | − | 0.443017i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.41755 | − | 4.41755i | −0.921123 | − | 0.921123i | 0.0759861 | − | 0.997109i | \(-0.475790\pi\) |
−0.997109 | + | 0.0759861i | \(0.975790\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.34895i | 0.436188i | 0.975928 | + | 0.218094i | \(0.0699840\pi\) | ||||
−0.975928 | + | 0.218094i | \(0.930016\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.57124i | − | 0.461808i | −0.972976 | − | 0.230904i | \(-0.925832\pi\) | ||
0.972976 | − | 0.230904i | \(-0.0741684\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.53031 | − | 3.53031i | 0.614548 | − | 0.614548i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.06989 | + | 7.06989i | −1.16228 | + | 1.16228i | −0.178309 | + | 0.983975i | \(0.557063\pi\) |
−0.983975 | + | 0.178309i | \(0.942937\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.72095i | 0.595828i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.87389i | 1.22969i | 0.788646 | + | 0.614847i | \(0.210782\pi\) | ||||
−0.788646 | + | 0.614847i | \(0.789218\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.59202 | + | 2.59202i | 0.395280 | + | 0.395280i | 0.876564 | − | 0.481285i | \(-0.159830\pi\) |
−0.481285 | + | 0.876564i | \(0.659830\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.813264 | + | 0.813264i | 0.118627 | + | 0.118627i | 0.763928 | − | 0.645301i | \(-0.223268\pi\) |
−0.645301 | + | 0.763928i | \(0.723268\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.88874 | − | 1.24308i | 0.984106 | − | 0.177582i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.86369 | 0.821081 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.0317294 | + | 0.0317294i | 0.00435837 | + | 0.00435837i | 0.709283 | − | 0.704924i | \(-0.249019\pi\) |
−0.704924 | + | 0.709283i | \(0.749019\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.29601 | − | 3.29601i | 0.436567 | − | 0.436567i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.858136 | −0.111720 | −0.0558599 | − | 0.998439i | \(-0.517790\pi\) | ||||
−0.0558599 | + | 0.998439i | \(0.517790\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 1.59654i | − | 0.204416i | −0.994763 | − | 0.102208i | \(-0.967409\pi\) | ||
0.994763 | − | 0.102208i | \(-0.0325907\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.235858 | − | 2.63522i | −0.0297154 | − | 0.332006i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.5074 | − | 10.5074i | 1.28368 | − | 1.28368i | 0.345119 | − | 0.938559i | \(-0.387838\pi\) |
0.938559 | − | 0.345119i | \(-0.112162\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.24736 | −0.752094 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.5404 | −1.48827 | −0.744134 | − | 0.668030i | \(-0.767138\pi\) | ||||
−0.744134 | + | 0.668030i | \(0.767138\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.92331 | − | 7.92331i | 0.927353 | − | 0.927353i | −0.0701812 | − | 0.997534i | \(-0.522358\pi\) |
0.997534 | + | 0.0701812i | \(0.0223577\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.1566 | − | 1.17755i | 1.49934 | − | 0.134194i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 8.69789i | − | 0.978589i | −0.872119 | − | 0.489295i | \(-0.837254\pi\) | ||
0.872119 | − | 0.489295i | \(-0.162746\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.50896 | − | 5.50896i | 0.604686 | − | 0.604686i | −0.336866 | − | 0.941553i | \(-0.609367\pi\) |
0.941553 | + | 0.336866i | \(0.109367\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.66096 | + | 1.66096i | 0.178073 | + | 0.178073i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.62052 | −0.171775 | −0.0858875 | − | 0.996305i | \(-0.527373\pi\) | ||||
−0.0858875 | + | 0.996305i | \(0.527373\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.31297 | + | 7.55411i | −0.661779 | + | 0.791886i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.81814 | − | 1.81814i | −0.188532 | − | 0.188532i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.51923 | + | 3.51923i | 0.357324 | + | 0.357324i | 0.862826 | − | 0.505502i | \(-0.168693\pi\) |
−0.505502 | + | 0.862826i | \(0.668693\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 4.99261i | − | 0.501777i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.6729i | 1.55951i | 0.626083 | + | 0.779757i | \(0.284657\pi\) | ||||
−0.626083 | + | 0.779757i | \(0.715343\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.83284 | + | 1.83284i | −0.180595 | + | 0.180595i | −0.791615 | − | 0.611020i | \(-0.790759\pi\) |
0.611020 | + | 0.791615i | \(0.290759\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.869787 | − | 0.869787i | 0.0840855 | − | 0.0840855i | −0.663813 | − | 0.747899i | \(-0.731063\pi\) |
0.747899 | + | 0.663813i | \(0.231063\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 11.7274i | − | 1.12328i | −0.827382 | − | 0.561640i | \(-0.810171\pi\) | ||
0.827382 | − | 0.561640i | \(-0.189829\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.99834i | 0.949000i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.3172 | − | 10.3172i | −0.970562 | − | 0.970562i | 0.0290168 | − | 0.999579i | \(-0.490762\pi\) |
−0.999579 | + | 0.0290168i | \(0.990762\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.63111 | + | 2.63111i | 0.243246 | + | 0.243246i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.9042 | + | 9.94835i | 1.09126 | + | 0.911964i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.9262 | 1.26602 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.56768 | + | 5.56768i | 0.502021 | + | 0.502021i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.4843 | − | 11.4843i | 1.01907 | − | 1.01907i | 0.0192525 | − | 0.999815i | \(-0.493871\pi\) |
0.999815 | − | 0.0192525i | \(-0.00612864\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.66567 | 0.322745 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.2928i | 0.986658i | 0.869843 | + | 0.493329i | \(0.164220\pi\) | ||||
−0.869843 | + | 0.493329i | \(0.835780\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.2834 | − | 1.09940i | 1.06511 | − | 0.0953299i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.75911 | + | 9.75911i | −0.833777 | + | 0.833777i | −0.988031 | − | 0.154254i | \(-0.950703\pi\) |
0.154254 | + | 0.988031i | \(0.450703\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.88433 | −0.668740 | −0.334370 | − | 0.942442i | \(-0.608524\pi\) | ||||
−0.334370 | + | 0.942442i | \(0.608524\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.15013 | 0.0968584 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.1361 | + | 13.1361i | −1.09850 | + | 1.09850i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.99209 | − | 5.75006i | 0.329262 | − | 0.474257i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 11.4991i | − | 0.942041i | −0.882122 | − | 0.471020i | \(-0.843886\pi\) | ||
0.882122 | − | 0.471020i | \(-0.156114\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.7274 | 1.60539 | 0.802696 | − | 0.596389i | \(-0.203398\pi\) | ||||
0.802696 | + | 0.596389i | \(0.203398\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.14626 | − | 4.14626i | 0.335205 | − | 0.335205i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.1764 | − | 12.1764i | −0.971782 | − | 0.971782i | 0.0278306 | − | 0.999613i | \(-0.491140\pi\) |
−0.999613 | + | 0.0278306i | \(0.991140\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.0448722 | 0.00355859 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.6831 | − | 10.5993i | −0.999570 | − | 0.835341i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.75692 | + | 1.75692i | 0.137613 | + | 0.137613i | 0.772558 | − | 0.634945i | \(-0.218977\pi\) |
−0.634945 | + | 0.772558i | \(0.718977\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.14217 | + | 2.14217i | 0.165766 | + | 0.165766i | 0.785116 | − | 0.619349i | \(-0.212604\pi\) |
−0.619349 | + | 0.785116i | \(0.712604\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 0.845444i | − | 0.0650341i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 4.66126i | − | 0.356456i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.06440 | − | 6.06440i | 0.461068 | − | 0.461068i | −0.437938 | − | 0.899005i | \(-0.644291\pi\) |
0.899005 | + | 0.437938i | \(0.144291\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.606794 | + | 0.606794i | −0.0456094 | + | 0.0456094i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.1280i | 0.906487i | 0.891387 | + | 0.453244i | \(0.149733\pi\) | ||||
−0.891387 | + | 0.453244i | \(0.850267\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 17.9366i | − | 1.33322i | −0.745407 | − | 0.666610i | \(-0.767745\pi\) | ||
0.745407 | − | 0.666610i | \(-0.232255\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.12892 | − | 1.12892i | −0.0834525 | − | 0.0834525i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.7007 | + | 20.7007i | 1.51378 | + | 1.51378i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.03016 | − | 1.69660i | −0.147672 | − | 0.123410i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.8764 | 1.43821 | 0.719103 | − | 0.694904i | \(-0.244553\pi\) | ||||
0.719103 | + | 0.694904i | \(0.244553\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.35723 | − | 4.35723i | −0.313640 | − | 0.313640i | 0.532678 | − | 0.846318i | \(-0.321186\pi\) |
−0.846318 | + | 0.532678i | \(0.821186\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.75911 | − | 1.75911i | 0.125331 | − | 0.125331i | −0.641659 | − | 0.766990i | \(-0.721753\pi\) |
0.766990 | + | 0.641659i | \(0.221753\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.9162 | −1.83715 | −0.918574 | − | 0.395248i | \(-0.870659\pi\) | ||||
−0.918574 | + | 0.395248i | \(0.870659\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 14.8596i | − | 1.04812i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.554019 | + | 6.18998i | 0.0388845 | + | 0.434452i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.41755 | + | 4.41755i | −0.307041 | + | 0.307041i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 23.2719 | 1.60975 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.412405 | −0.0283911 | −0.0141956 | − | 0.999899i | \(-0.504519\pi\) | ||||
−0.0141956 | + | 0.999899i | \(0.504519\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.86739 | + | 8.86739i | −0.607583 | + | 0.607583i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.606449 | − | 6.77578i | −0.0411684 | − | 0.459970i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 11.2053i | − | 0.757181i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.8185 | −1.46767 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.0779 | + | 12.0779i | −0.808797 | + | 0.808797i | −0.984452 | − | 0.175655i | \(-0.943796\pi\) |
0.175655 | + | 0.984452i | \(0.443796\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.84390 | − | 7.84390i | −0.520618 | − | 0.520618i | 0.397140 | − | 0.917758i | \(-0.370003\pi\) |
−0.917758 | + | 0.397140i | \(0.870003\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.7475 | 0.908460 | 0.454230 | − | 0.890884i | \(-0.349914\pi\) | ||||
0.454230 | + | 0.890884i | \(0.349914\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.47048 | − | 10.1358i | 0.557317 | − | 0.666886i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.7104 | − | 13.7104i | −0.898200 | − | 0.898200i | 0.0970772 | − | 0.995277i | \(-0.469051\pi\) |
−0.995277 | + | 0.0970772i | \(0.969051\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.15034 | − | 6.15034i | −0.399507 | − | 0.399507i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 2.69236i | − | 0.174154i | −0.996202 | − | 0.0870770i | \(-0.972247\pi\) | ||
0.996202 | − | 0.0870770i | \(-0.0277526\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.2501i | 1.75533i | 0.479273 | + | 0.877666i | \(0.340900\pi\) | ||||
−0.479273 | + | 0.877666i | \(0.659100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.707107 | + | 0.707107i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.2643 | + | 12.2643i | −0.780358 | + | 0.780358i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 7.79084i | − | 0.493724i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.91873i | 0.436706i | 0.975870 | + | 0.218353i | \(0.0700685\pi\) | ||||
−0.975870 | + | 0.218353i | \(0.929932\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −22.0551 | − | 22.0551i | −1.38659 | − | 1.38659i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.405721 | + | 0.405721i | 0.0253082 | + | 0.0253082i | 0.719648 | − | 0.694339i | \(-0.244303\pi\) |
−0.694339 | + | 0.719648i | \(0.744303\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.9632 | + | 20.2982i | −1.05404 | + | 1.26127i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.34895 | 0.145396 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.57949 | − | 5.57949i | −0.344046 | − | 0.344046i | 0.513840 | − | 0.857886i | \(-0.328223\pi\) |
−0.857886 | + | 0.513840i | \(0.828223\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.14588 | + | 1.14588i | −0.0701268 | + | 0.0701268i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.43131 | −0.514066 | −0.257033 | − | 0.966403i | \(-0.582745\pi\) | ||||
−0.257033 | + | 0.966403i | \(0.582745\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 15.2157i | − | 0.924287i | −0.886805 | − | 0.462143i | \(-0.847081\pi\) | ||
0.886805 | − | 0.462143i | \(-0.152919\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.877617 | + | 9.80550i | 0.0531158 | + | 0.593456i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.76521 | + | 1.76521i | −0.106061 | + | 0.106061i | −0.758146 | − | 0.652085i | \(-0.773895\pi\) |
0.652085 | + | 0.758146i | \(0.273895\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.57124 | −0.153936 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.7230 | −0.997608 | −0.498804 | − | 0.866715i | \(-0.666227\pi\) | ||||
−0.498804 | + | 0.866715i | \(0.666227\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.00974 | − | 7.00974i | 0.416686 | − | 0.416686i | −0.467374 | − | 0.884060i | \(-0.654800\pi\) |
0.884060 | + | 0.467374i | \(0.154800\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.85712 | + | 20.7494i | 0.109622 | + | 1.22480i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.3829i | 1.02252i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.97694 | 0.291754 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.405721 | + | 0.405721i | −0.0237025 | + | 0.0237025i | −0.718859 | − | 0.695156i | \(-0.755335\pi\) |
0.695156 | + | 0.718859i | \(0.255335\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.53031 | − | 3.53031i | −0.204849 | − | 0.204849i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 23.2461 | 1.34436 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.44189 | + | 6.21919i | 0.428944 | + | 0.358468i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.0824 | + | 11.0824i | 0.636669 | + | 0.636669i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.01258 | + | 3.01258i | 0.171937 | + | 0.171937i | 0.787830 | − | 0.615893i | \(-0.211205\pi\) |
−0.615893 | + | 0.787830i | \(0.711205\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.59202i | 0.147455i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.49770i | 0.0849266i | 0.999098 | + | 0.0424633i | \(0.0135206\pi\) | ||||
−0.999098 | + | 0.0424633i | \(0.986479\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.0870 | − | 16.0870i | 0.909290 | − | 0.909290i | −0.0869246 | − | 0.996215i | \(-0.527704\pi\) |
0.996215 | + | 0.0869246i | \(0.0277039\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.95350 | + | 1.95350i | −0.109719 | + | 0.109719i | −0.759835 | − | 0.650116i | \(-0.774720\pi\) |
0.650116 | + | 0.759835i | \(0.274720\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.7274i | 0.656607i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 1.23006i | − | 0.0686555i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.3268 | + | 19.3268i | 1.07537 | + | 1.07537i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.29251 | − | 8.29251i | −0.458577 | − | 0.458577i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.33494 | + | 1.95131i | 0.128730 | + | 0.107579i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.4271 | −1.39760 | −0.698801 | − | 0.715317i | \(-0.746282\pi\) | ||||
−0.698801 | + | 0.715317i | \(0.746282\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.06989 | + | 7.06989i | 0.387428 | + | 0.387428i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.43562 | + | 8.43562i | −0.459517 | + | 0.459517i | −0.898497 | − | 0.438980i | \(-0.855340\pi\) |
0.438980 | + | 0.898497i | \(0.355340\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.5907 | −0.792461 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 12.8372i | − | 0.695174i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.8601 | − | 4.90055i | 0.964357 | − | 0.264605i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.66801 | − | 7.66801i | 0.411640 | − | 0.411640i | −0.470669 | − | 0.882310i | \(-0.655987\pi\) |
0.882310 | + | 0.470669i | \(0.155987\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.2122 | 0.707234 | 0.353617 | − | 0.935390i | \(-0.384952\pi\) | ||||
0.353617 | + | 0.935390i | \(0.384952\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.72095 | 0.198609 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.4154 | + | 18.4154i | −0.980153 | + | 0.980153i | −0.999807 | − | 0.0196540i | \(-0.993744\pi\) |
0.0196540 | + | 0.999807i | \(0.493744\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 15.4521 | − | 1.38300i | 0.817812 | − | 0.0731962i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.5636i | 0.926971i | 0.886105 | + | 0.463485i | \(0.153401\pi\) | ||||
−0.886105 | + | 0.463485i | \(0.846599\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.72738 | 0.143546 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.84731 | − | 9.84731i | 0.516850 | − | 0.516850i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.5241 | − | 18.5241i | −0.966948 | − | 0.966948i | 0.0325233 | − | 0.999471i | \(-0.489646\pi\) |
−0.999471 | + | 0.0325233i | \(0.989646\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.87389 | 0.409898 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.0910975 | + | 0.0761302i | 0.00472955 | + | 0.00395249i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.7274 | + | 14.7274i | 0.762555 | + | 0.762555i | 0.976784 | − | 0.214229i | \(-0.0687238\pi\) |
−0.214229 | + | 0.976784i | \(0.568724\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.18033 | − | 6.18033i | −0.318303 | − | 0.318303i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 22.2943i | − | 1.14518i | −0.819841 | − | 0.572592i | \(-0.805938\pi\) | ||
0.819841 | − | 0.572592i | \(-0.194062\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 16.2413i | − | 0.832065i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.8978 | + | 18.8978i | −0.965633 | + | 0.965633i | −0.999429 | − | 0.0337961i | \(-0.989240\pi\) |
0.0337961 | + | 0.999429i | \(0.489240\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.59202 | − | 2.59202i | 0.131760 | − | 0.131760i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 2.77164i | − | 0.140528i | −0.997528 | − | 0.0702639i | \(-0.977616\pi\) | ||
0.997528 | − | 0.0702639i | \(-0.0223841\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 36.6326i | − | 1.85259i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.98523 | + | 7.98523i | 0.402801 | + | 0.402801i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.6199 | − | 20.6199i | −1.03488 | − | 1.03488i | −0.999369 | − | 0.0355137i | \(-0.988693\pi\) |
−0.0355137 | − | 0.999369i | \(-0.511307\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.90831 | − | 9.46310i | 0.395911 | − | 0.473747i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −28.3385 | −1.41516 | −0.707580 | − | 0.706633i | \(-0.750213\pi\) | ||||
−0.707580 | + | 0.706633i | \(0.750213\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.76521 | + | 6.76521i | 0.336999 | + | 0.336999i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −35.2972 | + | 35.2972i | −1.74962 | + | 1.74962i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −38.1691 | −1.88734 | −0.943671 | − | 0.330885i | \(-0.892653\pi\) | ||||
−0.943671 | + | 0.330885i | \(0.892653\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.8015i | 0.680776i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.26138 | + | 0.202399i | −0.111275 | + | 0.00995939i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.57506 | + | 5.57506i | −0.273012 | + | 0.273012i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −33.3495 | −1.62923 | −0.814616 | − | 0.580001i | \(-0.803052\pi\) | ||||
−0.814616 | + | 0.580001i | \(0.803052\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.41055 | 0.361168 | 0.180584 | − | 0.983560i | \(-0.442201\pi\) | ||||
0.180584 | + | 0.983560i | \(0.442201\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.813264 | − | 0.813264i | 0.0395423 | − | 0.0395423i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.376557 | − | 4.20723i | −0.0182229 | − | 0.203602i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 18.5773i | 0.896918i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.4005 | −0.741818 | −0.370909 | − | 0.928669i | \(-0.620954\pi\) | ||||
−0.370909 | + | 0.928669i | \(0.620954\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.12490 | + | 6.12490i | −0.294344 | + | 0.294344i | −0.838794 | − | 0.544450i | \(-0.816739\pi\) |
0.544450 | + | 0.838794i | \(0.316739\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −20.5914 | − | 20.5914i | −0.985019 | − | 0.985019i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.18867 | 0.199914 | 0.0999572 | − | 0.994992i | \(-0.468129\pi\) | ||||
0.0999572 | + | 0.994992i | \(0.468129\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.24308 | − | 6.88874i | −0.0591941 | − | 0.328035i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.45442 | + | 2.45442i | 0.116613 | + | 0.116613i | 0.763005 | − | 0.646392i | \(-0.223723\pi\) |
−0.646392 | + | 0.763005i | \(0.723723\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.13107 | − | 8.13107i | −0.384587 | − | 0.384587i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.6407i | 1.49321i | 0.665265 | + | 0.746607i | \(0.268319\pi\) | ||||
−0.665265 | + | 0.746607i | \(0.731681\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 39.3113i | 1.85110i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.9494 | − | 13.9494i | 0.655398 | − | 0.655398i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.4887 | − | 11.4887i | 0.537420 | − | 0.537420i | −0.385350 | − | 0.922770i | \(-0.625919\pi\) |
0.922770 | + | 0.385350i | \(0.125919\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 5.86369i | − | 0.273694i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 37.4080i | 1.74227i | 0.491048 | + | 0.871133i | \(0.336614\pi\) | ||||
−0.491048 | + | 0.871133i | \(0.663386\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.4695 | + | 21.4695i | 0.997774 | + | 0.997774i | 0.999998 | − | 0.00222376i | \(-0.000707846\pi\) |
−0.00222376 | + | 0.999998i | \(0.500708\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.1279 | + | 21.1279i | 0.977683 | + | 0.977683i | 0.999756 | − | 0.0220738i | \(-0.00702689\pi\) |
−0.0220738 | + | 0.999756i | \(0.507027\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 25.2109 | − | 30.1674i | 1.16413 | − | 1.39300i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.2200 | −0.793457 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.9410 | + | 12.9410i | 0.595026 | + | 0.595026i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.0317294 | − | 0.0317294i | 0.00145279 | − | 0.00145279i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −36.6835 | −1.67611 | −0.838055 | − | 0.545586i | \(-0.816307\pi\) | ||||
−0.838055 | + | 0.545586i | \(0.816307\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 37.2033i | − | 1.69632i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −16.4631 | + | 1.47349i | −0.749099 | + | 0.0670462i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.19439 | + | 2.19439i | −0.0994373 | + | 0.0994373i | −0.755075 | − | 0.655638i | \(-0.772400\pi\) |
0.655638 | + | 0.755075i | \(0.272400\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.48466 | 0.112360 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.6566 | −0.616313 | −0.308157 | − | 0.951336i | \(-0.599712\pi\) | ||||
−0.308157 | + | 0.951336i | \(0.599712\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.73933 | + | 9.73933i | −0.438637 | + | 0.438637i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −33.0466 | + | 2.95775i | −1.48234 | + | 0.132673i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.27077i | 0.146420i | 0.997317 | + | 0.0732099i | \(0.0233243\pi\) | ||||
−0.997317 | + | 0.0732099i | \(0.976676\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.02949 | 0.135348 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.91904 | + | 9.91904i | −0.442268 | + | 0.442268i | −0.892774 | − | 0.450506i | \(-0.851244\pi\) |
0.450506 | + | 0.892774i | \(0.351244\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.597819 | − | 0.597819i | −0.0265501 | − | 0.0265501i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.6081 | 0.913437 | 0.456718 | − | 0.889611i | \(-0.349025\pi\) | ||||
0.456718 | + | 0.889611i | \(0.349025\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.0109 | − | 22.7484i | 0.840991 | − | 1.00633i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.29601 | − | 3.29601i | −0.145522 | − | 0.145522i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.06031 | + | 4.06031i | 0.178572 | + | 0.178572i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 8.57635i | − | 0.376460i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 14.3938i | − | 0.630603i | −0.948991 | − | 0.315302i | \(-0.897894\pi\) | ||
0.948991 | − | 0.315302i | \(-0.102106\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.7222 | + | 14.7222i | −0.643757 | + | 0.643757i | −0.951477 | − | 0.307720i | \(-0.900434\pi\) |
0.307720 | + | 0.951477i | \(0.400434\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.6610 | − | 10.6610i | 0.464401 | − | 0.464401i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.0295i | 0.696934i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.858136i | 0.0372399i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −20.7170 | − | 20.7170i | −0.897354 | − | 0.897354i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.57577 | + | 8.57577i | 0.370072 | + | 0.370072i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 34.3928 | − | 6.20620i | 1.48140 | − | 0.267320i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.5138 | −0.538010 | −0.269005 | − | 0.963139i | \(-0.586695\pi\) | ||||
−0.269005 | + | 0.963139i | \(0.586695\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.6831 | − | 12.6831i | −0.544285 | − | 0.544285i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.66191 | + | 4.66191i | −0.199329 | + | 0.199329i | −0.799712 | − | 0.600383i | \(-0.795015\pi\) |
0.600383 | + | 0.799712i | \(0.295015\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.59654 | −0.0681387 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.9491i | 0.466445i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.05147 | − | 22.9208i | −0.0872374 | − | 0.974693i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.2626 | − | 18.2626i | 0.773812 | − | 0.773812i | −0.204959 | − | 0.978771i | \(-0.565706\pi\) |
0.978771 | + | 0.204959i | \(0.0657061\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.6398 | −0.576901 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 29.2751 | 1.23600 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.858136 | + | 0.858136i | −0.0361661 | + | 0.0361661i | −0.724959 | − | 0.688792i | \(-0.758141\pi\) |
0.688792 | + | 0.724959i | \(0.258141\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.63522 | + | 0.235858i | −0.110669 | + | 0.00990512i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 24.5451i | − | 1.02899i | −0.857495 | − | 0.514493i | \(-0.827980\pi\) | ||
0.857495 | − | 0.514493i | \(-0.172020\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.528564 | −0.0221197 | −0.0110599 | − | 0.999939i | \(-0.503521\pi\) | ||||
−0.0110599 | + | 0.999939i | \(0.503521\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.0547 | − | 14.0547i | 0.587145 | − | 0.587145i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.90536 | − | 8.90536i | −0.370735 | − | 0.370735i | 0.497010 | − | 0.867745i | \(-0.334431\pi\) |
−0.867745 | + | 0.497010i | \(0.834431\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.16205 | −0.256086 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.2180 | − | 15.8166i | 0.548373 | − | 0.656184i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.158413 | + | 0.158413i | 0.00656078 | + | 0.00656078i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17.0394 | − | 17.0394i | −0.703292 | − | 0.703292i | 0.261824 | − | 0.965116i | \(-0.415676\pi\) |
−0.965116 | + | 0.261824i | \(0.915676\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 11.9852i | − | 0.493843i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 2.48776i | − | 0.102333i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.25748 | − | 9.25748i | 0.380159 | − | 0.380159i | −0.491000 | − | 0.871159i | \(-0.663369\pi\) |
0.871159 | + | 0.491000i | \(0.163369\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.3255 | + | 18.3255i | −0.750013 | + | 0.750013i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.6462i | 1.12959i | 0.825230 | + | 0.564796i | \(0.191045\pi\) | ||||
−0.825230 | + | 0.564796i | \(0.808955\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 20.7142i | − | 0.844949i | −0.906375 | − | 0.422475i | \(-0.861162\pi\) | ||
0.906375 | − | 0.422475i | \(-0.138838\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.5074 | − | 10.5074i | −0.427893 | − | 0.427893i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.59685 | + | 4.59685i | 0.186580 | + | 0.186580i | 0.794216 | − | 0.607636i | \(-0.207882\pi\) |
−0.607636 | + | 0.794216i | \(0.707882\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.76873 | + | 3.98523i | 0.193239 | + | 0.161490i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.27957 | −0.173133 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.5964 | + | 29.5964i | 1.19539 | + | 1.19539i | 0.975533 | + | 0.219854i | \(0.0705582\pi\) |
0.219854 | + | 0.975533i | \(0.429442\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.2730 | + | 23.2730i | −0.936934 | + | 0.936934i | −0.998126 | − | 0.0611921i | \(-0.980510\pi\) |
0.0611921 | + | 0.998126i | \(0.480510\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.8683 | 0.798575 | 0.399288 | − | 0.916826i | \(-0.369257\pi\) | ||||
0.399288 | + | 0.916826i | \(0.369257\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.24736i | 0.250698i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.27043 | + | 0.382214i | −0.171091 | + | 0.0153131i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 16.4557 | − | 16.4557i | 0.657178 | − | 0.657178i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −58.6272 | −2.33762 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.05496 | 0.320663 | 0.160332 | − | 0.987063i | \(-0.448744\pi\) | ||||
0.160332 | + | 0.987063i | \(0.448744\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.291614 | + | 0.291614i | −0.0115906 | + | 0.0115906i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.8543 | + | 21.3957i | −0.588551 | + | 0.847728i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.5404i | 0.496090i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.5201 | 0.415518 | 0.207759 | − | 0.978180i | \(-0.433383\pi\) | ||||
0.207759 | + | 0.978180i | \(0.433383\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.2466 | + | 24.2466i | −0.956192 | + | 0.956192i | −0.999080 | − | 0.0428876i | \(-0.986344\pi\) |
0.0428876 | + | 0.999080i | \(0.486344\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.1304 | + | 15.1304i | 0.594836 | + | 0.594836i | 0.938934 | − | 0.344098i | \(-0.111815\pi\) |
−0.344098 | + | 0.938934i | \(0.611815\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.28434 | −0.168175 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.22002 | − | 4.36237i | −0.204589 | − | 0.170975i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −27.7591 | − | 27.7591i | −1.08630 | − | 1.08630i | −0.995906 | − | 0.0903916i | \(-0.971188\pi\) |
−0.0903916 | − | 0.995906i | \(-0.528812\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.92331 | − | 7.92331i | −0.309118 | − | 0.309118i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.15936i | 0.200980i | 0.994938 | + | 0.100490i | \(0.0320411\pi\) | ||||
−0.994938 | + | 0.100490i | \(0.967959\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 8.62844i | − | 0.335608i | −0.985820 | − | 0.167804i | \(-0.946332\pi\) | ||
0.985820 | − | 0.167804i | \(-0.0536675\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −15.4280 | + | 15.4280i | −0.599174 | + | 0.599174i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.3766 | − | 10.3766i | 0.401783 | − | 0.401783i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17.0808i | 0.660380i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 7.97091i | − | 0.307713i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.88585 | + | 1.88585i | 0.0726941 | + | 0.0726941i | 0.742519 | − | 0.669825i | \(-0.233631\pi\) |
−0.669825 | + | 0.742519i | \(0.733631\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.56673 | + | 5.56673i | 0.213947 | + | 0.213947i | 0.805942 | − | 0.591995i | \(-0.201659\pi\) |
−0.591995 | + | 0.805942i | \(0.701659\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.1040 | + | 8.44390i | 0.387755 | + | 0.324047i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.0929 | −0.425083 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.4526 | − | 25.4526i | −0.973916 | − | 0.973916i | 0.0257527 | − | 0.999668i | \(-0.491802\pi\) |
−0.999668 | + | 0.0257527i | \(0.991802\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.72095 | − | 9.72095i | 0.370877 | − | 0.370877i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.166967 | −0.00636093 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 15.5594i | − | 0.591909i | −0.955202 | − | 0.295955i | \(-0.904362\pi\) | ||
0.955202 | − | 0.295955i | \(-0.0956377\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.17755 | − | 13.1566i | −0.0447314 | − | 0.499779i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −32.6471 | + | 32.6471i | −1.23660 | + | 1.23660i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19.3895 | −0.733377 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.61966 | 0.325560 | 0.162780 | − | 0.986662i | \(-0.447954\pi\) | ||||
0.162780 | + | 0.986662i | \(0.447954\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −32.9546 | + | 32.9546i | −1.24291 | + | 1.24291i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.69659 | + | 41.3015i | 0.139025 | + | 1.55330i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 8.58353i | − | 0.322361i | −0.986925 | − | 0.161181i | \(-0.948470\pi\) | ||
0.986925 | − | 0.161181i | \(-0.0515302\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.69789 | −0.326196 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11.3586 | + | 11.3586i | −0.425382 | + | 0.425382i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.90378 | − | 1.90378i | −0.0710981 | − | 0.0710981i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.8287 | 0.664898 | 0.332449 | − | 0.943121i | \(-0.392125\pi\) | ||||
0.332449 | + | 0.943121i | \(0.392125\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.39763 | + | 5.26221i | −0.163776 | + | 0.195975i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 19.2687 | + | 19.2687i | 0.716611 | + | 0.716611i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.5253 | − | 18.5253i | −0.687066 | − | 0.687066i | 0.274516 | − | 0.961582i | \(-0.411482\pi\) |
−0.961582 | + | 0.274516i | \(0.911482\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.4944i | 0.794998i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.8206 | + | 10.8206i | −0.399668 | + | 0.399668i | −0.878116 | − | 0.478448i | \(-0.841199\pi\) |
0.478448 | + | 0.878116i | \(0.341199\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 52.4592 | − | 52.4592i | 1.93236 | − | 1.93236i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 26.7993i | − | 0.985827i | −0.870078 | − | 0.492914i | \(-0.835932\pi\) | ||
0.870078 | − | 0.492914i | \(-0.164068\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17.3443i | 0.637159i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.5456 | + | 13.5456i | 0.496939 | + | 0.496939i | 0.910484 | − | 0.413545i | \(-0.135709\pi\) |
−0.413545 | + | 0.910484i | \(0.635709\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.50896 | − | 5.50896i | −0.201562 | − | 0.201562i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.08693 | − | 2.49723i | 0.0762548 | − | 0.0912466i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.3386 | −0.997600 | −0.498800 | − | 0.866717i | \(-0.666226\pi\) | ||||
−0.498800 | + | 0.866717i | \(0.666226\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.89228 | + | 4.89228i | 0.178285 | + | 0.178285i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.47988 | − | 9.47988i | 0.344552 | − | 0.344552i | −0.513524 | − | 0.858076i | \(-0.671660\pi\) |
0.858076 | + | 0.513524i | \(0.171660\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −31.1907 | −1.13215 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 21.2685i | − | 0.770983i | −0.922711 | − | 0.385492i | \(-0.874032\pi\) | ||
0.922711 | − | 0.385492i | \(-0.125968\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.76600 | − | 30.9042i | −0.100136 | − | 1.11881i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.25785 | − | 2.25785i | 0.0815262 | − | 0.0815262i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.1127 | 0.653161 | 0.326580 | − | 0.945169i | \(-0.394104\pi\) | ||||
0.326580 | + | 0.945169i | \(0.394104\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.573776 | 0.0206640 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.5967 | − | 22.5967i | 0.812747 | − | 0.812747i | −0.172298 | − | 0.985045i | \(-0.555119\pi\) |
0.985045 | + | 0.172298i | \(0.0551191\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.35819 | + | 26.3478i | 0.0845997 | + | 0.945222i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 36.7023i | 1.31500i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −62.6093 | −2.24034 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.66096 | − | 1.66096i | 0.0593577 | − | 0.0593577i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.4776 | − | 18.4776i | −0.658656 | − | 0.658656i | 0.296406 | − | 0.955062i | \(-0.404212\pi\) |
−0.955062 | + | 0.296406i | \(0.904212\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.89059 | −0.280913 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −29.6215 | − | 24.7547i | −1.05322 | − | 0.880176i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.20067 | + | 4.20067i | 0.149170 | + | 0.149170i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.01770 | − | 6.01770i | −0.213158 | − | 0.213158i | 0.592450 | − | 0.805608i | \(-0.298161\pi\) |
−0.805608 | + | 0.592450i | \(0.798161\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.74400i | 0.238586i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.62052i | 0.0572583i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 39.5580 | − | 39.5580i | 1.39597 | − | 1.39597i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.96184 | + | 5.96184i | −0.209867 | + | 0.209867i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 55.4002i | − | 1.94777i | −0.227051 | − | 0.973883i | \(-0.572908\pi\) | ||
0.227051 | − | 0.973883i | \(-0.427092\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 54.3175i | 1.90734i | 0.300847 | + | 0.953672i | \(0.402731\pi\) | ||||
−0.300847 | + | 0.953672i | \(0.597269\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.7591 | − | 10.7591i | −0.377338 | − | 0.377338i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.0821 | + | 12.0821i | 0.422699 | + | 0.422699i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.55411 | + | 6.31297i | 0.263962 | + | 0.220593i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33.2327 | 1.15983 | 0.579915 | − | 0.814677i | \(-0.303086\pi\) | ||||
0.579915 | + | 0.814677i | \(0.303086\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.3976 | − | 14.3976i | −0.501870 | − | 0.501870i | 0.410149 | − | 0.912019i | \(-0.365477\pi\) |
−0.912019 | + | 0.410149i | \(0.865477\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.5824 | − | 18.5824i | 0.646173 | − | 0.646173i | −0.305893 | − | 0.952066i | \(-0.598955\pi\) |
0.952066 | + | 0.305893i | \(0.0989549\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −36.0402 | −1.25173 | −0.625865 | − | 0.779932i | \(-0.715254\pi\) | ||||
−0.625865 | + | 0.779932i | \(0.715254\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.49638i | 0.0865984i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 33.7166 | + | 23.4084i | 1.16821 | + | 0.811052i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.81814 | + | 1.81814i | −0.0628442 | + | 0.0628442i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 37.2603 | 1.28637 | 0.643185 | − | 0.765711i | \(-0.277613\pi\) | ||||
0.643185 | + | 0.765711i | \(0.277613\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.4825 | 0.809740 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.8249 | + | 11.8249i | −0.407272 | + | 0.407272i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 36.6986 | − | 3.28461i | 1.26098 | − | 0.112861i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 9.91328i | − | 0.340223i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 62.4632 | 2.14121 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.65231 | + | 5.65231i | −0.193531 | + | 0.193531i | −0.797220 | − | 0.603689i | \(-0.793697\pi\) |
0.603689 | + | 0.797220i | \(0.293697\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −31.5964 | − | 31.5964i | −1.07931 | − | 1.07931i | −0.996571 | − | 0.0827404i | \(-0.973633\pi\) |
−0.0827404 | − | 0.996571i | \(-0.526367\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.7273 | 0.809565 | 0.404783 | − | 0.914413i | \(-0.367347\pi\) | ||||
0.404783 | + | 0.914413i | \(0.367347\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.9852 | + | 13.3589i | 0.544775 | + | 0.455269i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 36.0121 | + | 36.0121i | 1.22587 | + | 1.22587i | 0.965514 | + | 0.260352i | \(0.0838387\pi\) |
0.260352 | + | 0.965514i | \(0.416161\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12.2915 | + | 12.2915i | 0.417443 | + | 0.417443i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 43.4252i | − | 1.47310i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 55.2920i | 1.87350i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.51923 | − | 3.51923i | 0.119108 | − | 0.119108i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.97231 | − | 9.97231i | 0.336741 | − | 0.336741i | −0.518398 | − | 0.855139i | \(-0.673472\pi\) |
0.855139 | + | 0.518398i | \(0.173472\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.573776i | 0.0193530i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35.5199i | 1.19669i | 0.801237 | + | 0.598347i | \(0.204176\pi\) | ||||
−0.801237 | + | 0.598347i | \(0.795824\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.9006 | − | 15.9006i | −0.535097 | − | 0.535097i | 0.386988 | − | 0.922085i | \(-0.373515\pi\) |
−0.922085 | + | 0.386988i | \(0.873515\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.98186 | − | 8.98186i | −0.301581 | − | 0.301581i | 0.540051 | − | 0.841632i | \(-0.318405\pi\) |
−0.841632 | + | 0.540051i | \(0.818405\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 27.5550 | − | 32.9723i | 0.924164 | − | 1.10586i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.99261 | −0.167259 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.79084 | + | 3.79084i | 0.126856 | + | 0.126856i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.4375 | − | 16.4375i | 0.548831 | − | 0.548831i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.03970 | 0.201435 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.263116i | 0.00876568i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.65985 | − | 0.864580i | 0.321460 | − | 0.0287714i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.91534 | − | 9.91534i | 0.329233 | − | 0.329233i | −0.523062 | − | 0.852295i | \(-0.675210\pi\) |
0.852295 | + | 0.523062i | \(0.175210\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.6729 | 0.519838 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.7476 | 0.886189 | 0.443094 | − | 0.896475i | \(-0.353881\pi\) | ||||
0.443094 | + | 0.896475i | \(0.353881\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27.5041 | − | 27.5041i | 0.910252 | − | 0.910252i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.66351 | + | 29.7590i | 0.0879567 | + | 0.982730i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 4.81405i | − | 0.158801i | −0.996843 | − | 0.0794004i | \(-0.974699\pi\) | ||
0.996843 | − | 0.0794004i | \(-0.0253006\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.26043 | 0.140386 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 32.9951 | − | 32.9951i | 1.08605 | − | 1.08605i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.83284 | + | 1.83284i | 0.0601983 | + | 0.0601983i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.1224 | −0.627385 | −0.313693 | − | 0.949525i | \(-0.601566\pi\) | ||||
−0.313693 | + | 0.949525i | \(0.601566\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 32.1102 | − | 5.79431i | 1.05237 | − | 0.189901i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.05903 | + | 1.05903i | 0.0346711 | + | 0.0346711i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.2759 | + | 18.2759i | 0.597046 | + | 0.597046i | 0.939525 | − | 0.342479i | \(-0.111267\pi\) |
−0.342479 | + | 0.939525i | \(0.611267\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 22.7504i | − | 0.742432i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 3.37097i | − | 0.109890i | −0.998489 | − | 0.0549452i | \(-0.982502\pi\) | ||
0.998489 | − | 0.0549452i | \(-0.0174984\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 34.7833 | − | 34.7833i | 1.13270 | − | 1.13270i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 35.6046 | − | 35.6046i | 1.15699 | − | 1.15699i | 0.171873 | − | 0.985119i | \(-0.445018\pi\) |
0.985119 | − | 0.171873i | \(-0.0549820\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 41.6941i | 1.35345i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.76266i | 0.0895855i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.2600 | + | 24.2600i | 0.785860 | + | 0.785860i | 0.980813 | − | 0.194953i | \(-0.0624554\pi\) |
−0.194953 | + | 0.980813i | \(0.562455\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.29251 | + | 8.29251i | 0.268059 | + | 0.268059i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −23.4156 | + | 28.0191i | −0.756129 | + | 0.904785i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.3887 | 0.786733 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.869787 | − | 0.869787i | −0.0280285 | − | 0.0280285i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.00833799 | − | 0.00833799i | 0.000268132 | − | 0.000268132i | −0.706973 | − | 0.707241i | \(-0.749940\pi\) |
0.707241 | + | 0.706973i | \(0.249940\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 27.3322 | 0.878037 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 23.9127i | − | 0.767396i | −0.923459 | − | 0.383698i | \(-0.874650\pi\) | ||
0.923459 | − | 0.383698i | \(-0.125350\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.7769 | + | 1.85959i | −0.666078 | + | 0.0596156i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.23497 | + | 4.23497i | −0.135489 | + | 0.135489i | −0.771599 | − | 0.636110i | \(-0.780543\pi\) |
0.636110 | + | 0.771599i | \(0.280543\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.09064 | −0.258578 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.7274 | −0.374426 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.01578 | + | 8.01578i | −0.255664 | + | 0.255664i | −0.823288 | − | 0.567624i | \(-0.807863\pi\) |
0.567624 | + | 0.823288i | \(0.307863\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.03084 | − | 0.271268i | 0.0964727 | − | 0.00863455i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 22.9008i | − | 0.728202i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −55.1397 | −1.75157 | −0.875786 | − | 0.482700i | \(-0.839656\pi\) | ||||
−0.875786 | + | 0.482700i | \(0.839656\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −17.9797 | + | 17.9797i | −0.570568 | + | 0.570568i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37.6893 | + | 37.6893i | 1.19363 | + | 1.19363i | 0.976040 | + | 0.217592i | \(0.0698203\pi\) |
0.217592 | + | 0.976040i | \(0.430180\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.99834 | 0.316333 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2100.2.x.d.1693.8 | 16 | ||
5.2 | odd | 4 | inner | 2100.2.x.d.1357.3 | 16 | ||
5.3 | odd | 4 | 420.2.x.a.97.6 | yes | 16 | ||
5.4 | even | 2 | 420.2.x.a.13.3 | ✓ | 16 | ||
7.6 | odd | 2 | inner | 2100.2.x.d.1693.3 | 16 | ||
15.8 | even | 4 | 1260.2.ba.b.937.6 | 16 | |||
15.14 | odd | 2 | 1260.2.ba.b.433.3 | 16 | |||
20.3 | even | 4 | 1680.2.cz.c.97.2 | 16 | |||
20.19 | odd | 2 | 1680.2.cz.c.433.7 | 16 | |||
35.13 | even | 4 | 420.2.x.a.97.3 | yes | 16 | ||
35.27 | even | 4 | inner | 2100.2.x.d.1357.8 | 16 | ||
35.34 | odd | 2 | 420.2.x.a.13.6 | yes | 16 | ||
105.83 | odd | 4 | 1260.2.ba.b.937.3 | 16 | |||
105.104 | even | 2 | 1260.2.ba.b.433.6 | 16 | |||
140.83 | odd | 4 | 1680.2.cz.c.97.7 | 16 | |||
140.139 | even | 2 | 1680.2.cz.c.433.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.x.a.13.3 | ✓ | 16 | 5.4 | even | 2 | ||
420.2.x.a.13.6 | yes | 16 | 35.34 | odd | 2 | ||
420.2.x.a.97.3 | yes | 16 | 35.13 | even | 4 | ||
420.2.x.a.97.6 | yes | 16 | 5.3 | odd | 4 | ||
1260.2.ba.b.433.3 | 16 | 15.14 | odd | 2 | |||
1260.2.ba.b.433.6 | 16 | 105.104 | even | 2 | |||
1260.2.ba.b.937.3 | 16 | 105.83 | odd | 4 | |||
1260.2.ba.b.937.6 | 16 | 15.8 | even | 4 | |||
1680.2.cz.c.97.2 | 16 | 20.3 | even | 4 | |||
1680.2.cz.c.97.7 | 16 | 140.83 | odd | 4 | |||
1680.2.cz.c.433.2 | 16 | 140.139 | even | 2 | |||
1680.2.cz.c.433.7 | 16 | 20.19 | odd | 2 | |||
2100.2.x.d.1357.3 | 16 | 5.2 | odd | 4 | inner | ||
2100.2.x.d.1357.8 | 16 | 35.27 | even | 4 | inner | ||
2100.2.x.d.1693.3 | 16 | 7.6 | odd | 2 | inner | ||
2100.2.x.d.1693.8 | 16 | 1.1 | even | 1 | trivial |