Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9200,2,Mod(1,9200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9200.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9200.a (trivial) |
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: | yes |
Analytic conductor: | \(73.4623698596\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 7x^{5} + 24x^{4} + x^{3} - 35x^{2} + 17x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 920) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.189375\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9200.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −0.189375 | −0.109336 | −0.0546680 | − | 0.998505i | \(-0.517410\pi\) | ||||
−0.0546680 | + | 0.998505i | \(0.517410\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.65661 | 0.626139 | 0.313070 | − | 0.949730i | \(-0.398643\pi\) | ||||
0.313070 | + | 0.949730i | \(0.398643\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.96414 | −0.988046 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.0759321 | −0.0228944 | −0.0114472 | − | 0.999934i | \(-0.503644\pi\) | ||||
−0.0114472 | + | 0.999934i | \(0.503644\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.24146 | −0.344319 | −0.172159 | − | 0.985069i | \(-0.555074\pi\) | ||||
−0.172159 | + | 0.985069i | \(0.555074\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.17593 | 1.25535 | 0.627673 | − | 0.778477i | \(-0.284007\pi\) | ||||
0.627673 | + | 0.778477i | \(0.284007\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.792262 | −0.181757 | −0.0908787 | − | 0.995862i | \(-0.528968\pi\) | ||||
−0.0908787 | + | 0.995862i | \(0.528968\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.313721 | −0.0684595 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.12946 | 0.217365 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.85401 | −0.529976 | −0.264988 | − | 0.964252i | \(-0.585368\pi\) | ||||
−0.264988 | + | 0.964252i | \(0.585368\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.90112 | −1.59869 | −0.799345 | − | 0.600873i | \(-0.794820\pi\) | ||||
−0.799345 | + | 0.600873i | \(0.794820\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.0143797 | 0.00250318 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.92065 | 1.13775 | 0.568874 | − | 0.822425i | \(-0.307379\pi\) | ||||
0.568874 | + | 0.822425i | \(0.307379\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.235102 | 0.0376464 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.64279 | 0.725082 | 0.362541 | − | 0.931968i | \(-0.381909\pi\) | ||||
0.362541 | + | 0.931968i | \(0.381909\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.75255 | 0.267262 | 0.133631 | − | 0.991031i | \(-0.457336\pi\) | ||||
0.133631 | + | 0.991031i | \(0.457336\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.0033 | −1.45913 | −0.729563 | − | 0.683914i | \(-0.760276\pi\) | ||||
−0.729563 | + | 0.683914i | \(0.760276\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.25565 | −0.607950 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.980193 | −0.137254 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.1284 | −1.52860 | −0.764301 | − | 0.644859i | \(-0.776916\pi\) | ||||
−0.764301 | + | 0.644859i | \(0.776916\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.150035 | 0.0198726 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.4581 | 1.62191 | 0.810955 | − | 0.585108i | \(-0.198948\pi\) | ||||
0.810955 | + | 0.585108i | \(0.198948\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.0098 | −1.53770 | −0.768849 | − | 0.639430i | \(-0.779170\pi\) | ||||
−0.768849 | + | 0.639430i | \(0.779170\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.91041 | −0.618654 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.96067 | 0.850381 | 0.425191 | − | 0.905104i | \(-0.360207\pi\) | ||||
0.425191 | + | 0.905104i | \(0.360207\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.189375 | −0.0227981 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.71650 | 0.915779 | 0.457890 | − | 0.889009i | \(-0.348605\pi\) | ||||
0.457890 | + | 0.889009i | \(0.348605\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.49476 | −0.877196 | −0.438598 | − | 0.898683i | \(-0.644525\pi\) | ||||
−0.438598 | + | 0.898683i | \(0.644525\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.125790 | −0.0143351 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.6615 | 1.76206 | 0.881029 | − | 0.473063i | \(-0.156852\pi\) | ||||
0.881029 | + | 0.473063i | \(0.156852\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.67852 | 0.964280 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.68518 | −0.733793 | −0.366897 | − | 0.930262i | \(-0.619580\pi\) | ||||
−0.366897 | + | 0.930262i | \(0.619580\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.540478 | 0.0579454 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.03333 | −0.321532 | −0.160766 | − | 0.986993i | \(-0.551396\pi\) | ||||
−0.160766 | + | 0.986993i | \(0.551396\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.05661 | −0.215592 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.68565 | 0.174794 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.21747 | −0.326684 | −0.163342 | − | 0.986569i | \(-0.552227\pi\) | ||||
−0.163342 | + | 0.986569i | \(0.552227\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.225073 | 0.0226207 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.6059 | −1.65235 | −0.826173 | − | 0.563417i | \(-0.809486\pi\) | ||||
−0.826173 | + | 0.563417i | \(0.809486\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.30241 | −0.719528 | −0.359764 | − | 0.933043i | \(-0.617143\pi\) | ||||
−0.359764 | + | 0.933043i | \(0.617143\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.356936 | −0.0345063 | −0.0172532 | − | 0.999851i | \(-0.505492\pi\) | ||||
−0.0172532 | + | 0.999851i | \(0.505492\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.0359 | 1.34440 | 0.672198 | − | 0.740371i | \(-0.265350\pi\) | ||||
0.672198 | + | 0.740371i | \(0.265350\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.31060 | −0.124397 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.17924 | 0.110933 | 0.0554667 | − | 0.998461i | \(-0.482335\pi\) | ||||
0.0554667 | + | 0.998461i | \(0.482335\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.67986 | 0.340203 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.57448 | 0.786022 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9942 | −0.999476 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.879230 | −0.0792775 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.0097 | 1.68684 | 0.843420 | − | 0.537255i | \(-0.180539\pi\) | ||||
0.843420 | + | 0.537255i | \(0.180539\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.331890 | −0.0292213 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.29043 | −0.374857 | −0.187428 | − | 0.982278i | \(-0.560015\pi\) | ||||
−0.187428 | + | 0.982278i | \(0.560015\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.31247 | −0.113805 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.2499 | −1.04658 | −0.523290 | − | 0.852155i | \(-0.675296\pi\) | ||||
−0.523290 | + | 0.852155i | \(0.675296\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.61437 | −0.221748 | −0.110874 | − | 0.993834i | \(-0.535365\pi\) | ||||
−0.110874 | + | 0.993834i | \(0.535365\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.89437 | 0.159535 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.0942666 | 0.00788297 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.805915 | 0.0664707 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.0404 | −1.55985 | −0.779927 | − | 0.625870i | \(-0.784744\pi\) | ||||
−0.779927 | + | 0.625870i | \(0.784744\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.3252 | 1.49128 | 0.745640 | − | 0.666349i | \(-0.232144\pi\) | ||||
0.745640 | + | 0.666349i | \(0.232144\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −15.3422 | −1.24034 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.37467 | −0.349137 | −0.174569 | − | 0.984645i | \(-0.555853\pi\) | ||||
−0.174569 | + | 0.984645i | \(0.555853\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.10744 | 0.167131 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.65661 | 0.130559 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.8050 | −0.924639 | −0.462319 | − | 0.886714i | \(-0.652983\pi\) | ||||
−0.462319 | + | 0.886714i | \(0.652983\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.19760 | −0.402202 | −0.201101 | − | 0.979570i | \(-0.564452\pi\) | ||||
−0.201101 | + | 0.979570i | \(0.564452\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.4588 | −0.881444 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.34837 | 0.179585 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.61834 | −0.199069 | −0.0995345 | − | 0.995034i | \(-0.531735\pi\) | ||||
−0.0995345 | + | 0.995034i | \(0.531735\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.35926 | −0.177333 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.627563 | −0.0469062 | −0.0234531 | − | 0.999725i | \(-0.507466\pi\) | ||||
−0.0234531 | + | 0.999725i | \(0.507466\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.15848 | −0.457756 | −0.228878 | − | 0.973455i | \(-0.573506\pi\) | ||||
−0.228878 | + | 0.973455i | \(0.573506\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.27436 | 0.168126 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.393019 | −0.0287404 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.87107 | 0.136101 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.1343 | 1.38451 | 0.692254 | − | 0.721654i | \(-0.256618\pi\) | ||||
0.692254 | + | 0.721654i | \(0.256618\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.810900 | −0.0583698 | −0.0291849 | − | 0.999574i | \(-0.509291\pi\) | ||||
−0.0291849 | + | 0.999574i | \(0.509291\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.15110 | −0.438248 | −0.219124 | − | 0.975697i | \(-0.570320\pi\) | ||||
−0.219124 | + | 0.975697i | \(0.570320\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.03061 | −0.498387 | −0.249193 | − | 0.968454i | \(-0.580166\pi\) | ||||
−0.249193 | + | 0.968454i | \(0.580166\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.31818 | −0.0929772 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.72797 | −0.331838 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.96414 | −0.206022 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.0601581 | 0.00416122 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.12120 | −0.559086 | −0.279543 | − | 0.960133i | \(-0.590183\pi\) | ||||
−0.279543 | + | 0.960133i | \(0.590183\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.46131 | −0.100128 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14.7457 | −1.00100 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.41932 | 0.0959090 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.42570 | −0.432240 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.86268 | −0.191699 | −0.0958495 | − | 0.995396i | \(-0.530557\pi\) | ||||
−0.0958495 | + | 0.995396i | \(0.530557\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −27.4500 | −1.82192 | −0.910960 | − | 0.412496i | \(-0.864657\pi\) | ||||
−0.910960 | + | 0.412496i | \(0.864657\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.11319 | 0.0735613 | 0.0367807 | − | 0.999323i | \(-0.488290\pi\) | ||||
0.0367807 | + | 0.999323i | \(0.488290\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.0238215 | 0.00156734 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 21.2957 | 1.39513 | 0.697564 | − | 0.716523i | \(-0.254267\pi\) | ||||
0.697564 | + | 0.716523i | \(0.254267\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.96590 | −0.192656 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.68036 | −0.496801 | −0.248401 | − | 0.968657i | \(-0.579905\pi\) | ||||
−0.248401 | + | 0.968657i | \(0.579905\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.42476 | 0.542687 | 0.271343 | − | 0.962483i | \(-0.412532\pi\) | ||||
0.271343 | + | 0.962483i | \(0.412532\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.03188 | −0.322795 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.983561 | 0.0625825 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.26601 | 0.0802300 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.56210 | 0.161718 | 0.0808590 | − | 0.996726i | \(-0.474234\pi\) | ||||
0.0808590 | + | 0.996726i | \(0.474234\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.0759321 | −0.00477381 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.39999 | 0.274464 | 0.137232 | − | 0.990539i | \(-0.456179\pi\) | ||||
0.137232 | + | 0.990539i | \(0.456179\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.4648 | 0.712388 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.45966 | 0.523640 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −24.8510 | −1.53238 | −0.766191 | − | 0.642613i | \(-0.777850\pi\) | ||||
−0.766191 | + | 0.642613i | \(0.777850\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.574437 | 0.0351550 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.8742 | −0.663012 | −0.331506 | − | 0.943453i | \(-0.607557\pi\) | ||||
−0.331506 | + | 0.943453i | \(0.607557\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.60290 | 0.158115 | 0.0790575 | − | 0.996870i | \(-0.474809\pi\) | ||||
0.0790575 | + | 0.996870i | \(0.474809\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.389472 | 0.0235719 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.1918 | −0.732537 | −0.366269 | − | 0.930509i | \(-0.619365\pi\) | ||||
−0.366269 | + | 0.930509i | \(0.619365\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 26.3842 | 1.57958 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.85068 | 0.349022 | 0.174511 | − | 0.984655i | \(-0.444165\pi\) | ||||
0.174511 | + | 0.984655i | \(0.444165\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.7223 | −0.637375 | −0.318688 | − | 0.947860i | \(-0.603242\pi\) | ||||
−0.318688 | + | 0.947860i | \(0.603242\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.69129 | 0.454002 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.79021 | 0.575895 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.609309 | 0.0357183 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.72596 | −0.159252 | −0.0796261 | − | 0.996825i | \(-0.525373\pi\) | ||||
−0.0796261 | + | 0.996825i | \(0.525373\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.0857623 | −0.00497643 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.24146 | −0.0717955 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.90329 | 0.167343 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.14474 | 0.180661 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.4979 | −1.28402 | −0.642012 | − | 0.766695i | \(-0.721900\pi\) | ||||
−0.642012 | + | 0.766695i | \(0.721900\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.38290 | 0.0786703 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.9597 | −1.01840 | −0.509200 | − | 0.860648i | \(-0.670058\pi\) | ||||
−0.509200 | + | 0.860648i | \(0.670058\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.4728 | −0.818052 | −0.409026 | − | 0.912523i | \(-0.634131\pi\) | ||||
−0.409026 | + | 0.912523i | \(0.634131\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.47689 | 0.419944 | 0.209972 | − | 0.977707i | \(-0.432663\pi\) | ||||
0.209972 | + | 0.977707i | \(0.432663\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.216711 | 0.0121335 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.0675949 | 0.00377278 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.10069 | −0.228168 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.65806 | −0.146991 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.5715 | −0.913616 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.3565 | 1.50365 | 0.751826 | − | 0.659362i | \(-0.229173\pi\) | ||||
0.751826 | + | 0.659362i | \(0.229173\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −20.5137 | −1.12415 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.65271 | −0.307923 | −0.153961 | − | 0.988077i | \(-0.549203\pi\) | ||||
−0.153961 | + | 0.988077i | \(0.549203\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.223319 | −0.0121290 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.675881 | 0.0366010 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.6462 | −1.00680 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.5293 | 0.833658 | 0.416829 | − | 0.908985i | \(-0.363141\pi\) | ||||
0.416829 | + | 0.908985i | \(0.363141\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.0559 | 0.591810 | 0.295905 | − | 0.955217i | \(-0.404379\pi\) | ||||
0.295905 | + | 0.955217i | \(0.404379\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.40218 | −0.0748428 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.85381 | −0.364792 | −0.182396 | − | 0.983225i | \(-0.558385\pi\) | ||||
−0.182396 | + | 0.983225i | \(0.558385\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.62380 | −0.0859404 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.3104 | −0.860832 | −0.430416 | − | 0.902631i | \(-0.641633\pi\) | ||||
−0.430416 | + | 0.902631i | \(0.641633\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.3723 | −0.966964 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.08204 | 0.109279 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.6200 | −1.65055 | −0.825275 | − | 0.564731i | \(-0.808980\pi\) | ||||
−0.825275 | + | 0.564731i | \(0.808980\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −13.7619 | −0.716414 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.4354 | −0.957118 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.2458 | −1.46251 | −0.731256 | − | 0.682104i | \(-0.761065\pi\) | ||||
−0.731256 | + | 0.682104i | \(0.761065\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.54313 | 0.182481 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.98772 | −0.153469 | −0.0767345 | − | 0.997052i | \(-0.524449\pi\) | ||||
−0.0767345 | + | 0.997052i | \(0.524449\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.59997 | −0.184432 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.5176 | 0.639621 | 0.319810 | − | 0.947482i | \(-0.396381\pi\) | ||||
0.319810 | + | 0.947482i | \(0.396381\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.19480 | −0.264067 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.4861 | −0.987982 | −0.493991 | − | 0.869467i | \(-0.664462\pi\) | ||||
−0.493991 | + | 0.869467i | \(0.664462\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.17593 | 0.261758 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.812503 | 0.0409853 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.3203 | −0.869281 | −0.434640 | − | 0.900604i | \(-0.643124\pi\) | ||||
−0.434640 | + | 0.900604i | \(0.643124\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.248549 | 0.0124430 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.3727 | 0.867553 | 0.433777 | − | 0.901020i | \(-0.357181\pi\) | ||||
0.433777 | + | 0.901020i | \(0.357181\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.0504 | 0.550459 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.525499 | −0.0260480 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.6874 | −0.627350 | −0.313675 | − | 0.949530i | \(-0.601560\pi\) | ||||
−0.313675 | + | 0.949530i | \(0.601560\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.31983 | 0.114429 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 20.6383 | 1.01554 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.495098 | 0.0242450 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.23468 | 0.206878 | 0.103439 | − | 0.994636i | \(-0.467015\pi\) | ||||
0.103439 | + | 0.994636i | \(0.467015\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.17837 | 0.203641 | 0.101821 | − | 0.994803i | \(-0.467533\pi\) | ||||
0.101821 | + | 0.994803i | \(0.467533\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 29.6510 | 1.44168 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.8956 | −0.962813 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.0178518 | −0.000861892 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.9197 | 1.05583 | 0.527917 | − | 0.849296i | \(-0.322973\pi\) | ||||
0.527917 | + | 0.849296i | \(0.322973\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.2195 | 0.971688 | 0.485844 | − | 0.874046i | \(-0.338512\pi\) | ||||
0.485844 | + | 0.874046i | \(0.338512\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.792262 | −0.0378990 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.3149 | 0.778666 | 0.389333 | − | 0.921097i | \(-0.372706\pi\) | ||||
0.389333 | + | 0.921097i | \(0.372706\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.6143 | 0.600682 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.0868 | 1.33444 | 0.667222 | − | 0.744859i | \(-0.267483\pi\) | ||||
0.667222 | + | 0.744859i | \(0.267483\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.60579 | 0.170548 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.5071 | −1.15656 | −0.578282 | − | 0.815837i | \(-0.696277\pi\) | ||||
−0.578282 | + | 0.815837i | \(0.696277\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.352537 | −0.0166003 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.47033 | −0.163050 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.87128 | 0.134313 | 0.0671564 | − | 0.997742i | \(-0.478607\pi\) | ||||
0.0671564 | + | 0.997742i | \(0.478607\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.84601 | 0.272868 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.2264 | 0.709162 | 0.354581 | − | 0.935025i | \(-0.384623\pi\) | ||||
0.354581 | + | 0.935025i | \(0.384623\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.6480 | −1.70318 | −0.851588 | − | 0.524212i | \(-0.824360\pi\) | ||||
−0.851588 | + | 0.524212i | \(0.824360\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.9765 | 0.693031 | 0.346516 | − | 0.938044i | \(-0.387365\pi\) | ||||
0.346516 | + | 0.938044i | \(0.387365\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.5311 | 0.532457 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.828456 | 0.0381732 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.133075 | −0.00611879 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 32.9861 | 1.51033 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.03398 | −0.184317 | −0.0921587 | − | 0.995744i | \(-0.529377\pi\) | ||||
−0.0921587 | + | 0.995744i | \(0.529377\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.59171 | −0.391748 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.313721 | −0.0142748 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.28846 | 0.194329 | 0.0971643 | − | 0.995268i | \(-0.469023\pi\) | ||||
0.0971643 | + | 0.995268i | \(0.469023\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.23558 | 0.101096 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.8754 | 1.66416 | 0.832081 | − | 0.554654i | \(-0.187149\pi\) | ||||
0.832081 | + | 0.554654i | \(0.187149\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.7721 | −0.665303 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.7832 | 0.573405 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.74707 | 0.257274 | 0.128637 | − | 0.991692i | \(-0.458940\pi\) | ||||
0.128637 | + | 0.991692i | \(0.458940\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.984298 | 0.0439752 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.7850 | 0.837583 | 0.418792 | − | 0.908082i | \(-0.362454\pi\) | ||||
0.418792 | + | 0.908082i | \(0.362454\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.17001 | 0.0963735 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.2669 | −0.898313 | −0.449157 | − | 0.893453i | \(-0.648275\pi\) | ||||
−0.449157 | + | 0.893453i | \(0.648275\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.4159 | −0.549247 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.894829 | −0.0395077 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.759568 | 0.0334058 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.495850 | 0.0217654 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.47593 | 0.283716 | 0.141858 | − | 0.989887i | \(-0.454692\pi\) | ||||
0.141858 | + | 0.989887i | \(0.454692\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.414671 | 0.0181323 | 0.00906615 | − | 0.999959i | \(-0.497114\pi\) | ||||
0.00906615 | + | 0.999959i | \(0.497114\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −46.0716 | −2.00691 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −36.9276 | −1.60252 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.76384 | −0.249659 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.118845 | 0.00512854 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.323140 | 0.0139186 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.5708 | 1.22835 | 0.614177 | − | 0.789169i | \(-0.289488\pi\) | ||||
0.614177 | + | 0.789169i | \(0.289488\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.16626 | 0.0500492 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.0974 | 1.67168 | 0.835841 | − | 0.548971i | \(-0.184980\pi\) | ||||
0.835841 | + | 0.548971i | \(0.184980\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 35.5987 | 1.51932 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.26112 | 0.0963270 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 25.9450 | 1.10329 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −33.9136 | −1.43696 | −0.718482 | − | 0.695546i | \(-0.755163\pi\) | ||||
−0.718482 | + | 0.695546i | \(0.755163\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.17572 | −0.0920232 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.0744281 | 0.00314236 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −25.6390 | −1.08056 | −0.540278 | − | 0.841486i | \(-0.681681\pi\) | ||||
−0.540278 | + | 0.841486i | \(0.681681\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 14.3769 | 0.603773 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.6257 | −0.571218 | −0.285609 | − | 0.958346i | \(-0.592196\pi\) | ||||
−0.285609 | + | 0.958346i | \(0.592196\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.354294 | −0.0148267 | −0.00741337 | − | 0.999973i | \(-0.502360\pi\) | ||||
−0.00741337 | + | 0.999973i | \(0.502360\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.62356 | −0.151376 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.5870 | −0.773788 | −0.386894 | − | 0.922124i | \(-0.626452\pi\) | ||||
−0.386894 | + | 0.922124i | \(0.626452\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.153564 | 0.00638192 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.0747 | −0.459457 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.845002 | 0.0349964 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.75193 | −0.319956 | −0.159978 | − | 0.987121i | \(-0.551142\pi\) | ||||
−0.159978 | + | 0.987121i | \(0.551142\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.05202 | 0.290573 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.16487 | 0.0479162 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −23.3828 | −0.960215 | −0.480107 | − | 0.877210i | \(-0.659402\pi\) | ||||
−0.480107 | + | 0.877210i | \(0.659402\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.33142 | 0.0544916 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.6075 | 1.04629 | 0.523146 | − | 0.852243i | \(-0.324758\pi\) | ||||
0.523146 | + | 0.852243i | \(0.324758\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.03750 | 0.164693 | 0.0823466 | − | 0.996604i | \(-0.473759\pi\) | ||||
0.0823466 | + | 0.996604i | \(0.473759\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −20.6324 | −0.840215 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −45.8176 | −1.85968 | −0.929839 | − | 0.367967i | \(-0.880054\pi\) | ||||
−0.929839 | + | 0.367967i | \(0.880054\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.895361 | 0.0362819 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.4186 | 0.502405 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.1714 | −1.17822 | −0.589112 | − | 0.808052i | \(-0.700522\pi\) | ||||
−0.589112 | + | 0.808052i | \(0.700522\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.0562 | 0.686659 | 0.343329 | − | 0.939215i | \(-0.388445\pi\) | ||||
0.343329 | + | 0.939215i | \(0.388445\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −36.0620 | −1.44946 | −0.724728 | − | 0.689035i | \(-0.758034\pi\) | ||||
−0.724728 | + | 0.689035i | \(0.758034\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.12946 | 0.0453237 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.02503 | −0.201324 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.0113925 | −0.000454971 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 35.8208 | 1.42827 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.4958 | −0.696496 | −0.348248 | − | 0.937402i | \(-0.613223\pi\) | ||||
−0.348248 | + | 0.937402i | \(0.613223\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.53795 | 0.0611282 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.28322 | 0.209329 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −22.8727 | −0.904832 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −39.9200 | −1.57675 | −0.788373 | − | 0.615197i | \(-0.789076\pi\) | ||||
−0.788373 | + | 0.615197i | \(0.789076\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −41.8187 | −1.64917 | −0.824584 | − | 0.565740i | \(-0.808591\pi\) | ||||
−0.824584 | + | 0.565740i | \(0.808591\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 38.8026 | 1.52549 | 0.762743 | − | 0.646702i | \(-0.223852\pi\) | ||||
0.762743 | + | 0.646702i | \(0.223852\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.945972 | −0.0371327 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.79247 | 0.109445 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −39.8995 | −1.56139 | −0.780694 | − | 0.624914i | \(-0.785134\pi\) | ||||
−0.780694 | + | 0.624914i | \(0.785134\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 22.2155 | 0.866709 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.9449 | −0.893808 | −0.446904 | − | 0.894582i | \(-0.647473\pi\) | ||||
−0.446904 | + | 0.894582i | \(0.647473\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.2759 | 0.749745 | 0.374873 | − | 0.927076i | \(-0.377686\pi\) | ||||
0.374873 | + | 0.927076i | \(0.377686\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.21687 | 0.0472593 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.85401 | −0.110508 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.542121 | 0.0209596 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.911930 | 0.0352047 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 38.0041 | 1.46495 | 0.732476 | − | 0.680793i | \(-0.238365\pi\) | ||||
0.732476 | + | 0.680793i | \(0.238365\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −41.0387 | −1.57725 | −0.788623 | − | 0.614878i | \(-0.789205\pi\) | ||||
−0.788623 | + | 0.614878i | \(0.789205\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.33008 | −0.204550 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.19835 | 0.199201 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27.6705 | 1.05878 | 0.529390 | − | 0.848378i | \(-0.322421\pi\) | ||||
0.529390 | + | 0.848378i | \(0.322421\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.210810 | −0.00804290 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.8155 | 0.526327 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.8078 | −1.28611 | −0.643056 | − | 0.765820i | \(-0.722334\pi\) | ||||
−0.643056 | + | 0.765820i | \(0.722334\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.372858 | 0.0141637 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.0307 | 0.910229 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.03288 | −0.152538 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −46.4878 | −1.75582 | −0.877909 | − | 0.478827i | \(-0.841062\pi\) | ||||
−0.877909 | + | 0.478827i | \(0.841062\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.48297 | −0.206794 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −27.5094 | −1.03460 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.5298 | −0.508122 | −0.254061 | − | 0.967188i | \(-0.581766\pi\) | ||||
−0.254061 | + | 0.967188i | \(0.581766\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −46.4229 | −1.74099 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.90112 | −0.333350 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.45447 | 0.0543182 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.64955 | 0.0988115 | 0.0494057 | − | 0.998779i | \(-0.484267\pi\) | ||||
0.0494057 | + | 0.998779i | \(0.484267\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.0972 | −0.450525 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.59544 | −0.0593351 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 46.8796 | 1.73867 | 0.869334 | − | 0.494226i | \(-0.164548\pi\) | ||||
0.869334 | + | 0.494226i | \(0.164548\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.0826 | −0.928987 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.07108 | 0.335506 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36.1389 | −1.33482 | −0.667410 | − | 0.744691i | \(-0.732597\pi\) | ||||
−0.667410 | + | 0.744691i | \(0.732597\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.528538 | −0.0194690 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.6473 | −0.833095 | −0.416547 | − | 0.909114i | \(-0.636760\pi\) | ||||
−0.416547 | + | 0.909114i | \(0.636760\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.186262 | −0.00684252 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.04015 | 0.258278 | 0.129139 | − | 0.991627i | \(-0.458779\pi\) | ||||
0.129139 | + | 0.991627i | \(0.458779\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 19.8158 | 0.725021 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.591304 | −0.0216058 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.94539 | 0.216950 | 0.108475 | − | 0.994099i | \(-0.465403\pi\) | ||||
0.108475 | + | 0.994099i | \(0.465403\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.485198 | −0.0176816 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −43.9519 | −1.59746 | −0.798729 | − | 0.601691i | \(-0.794494\pi\) | ||||
−0.798729 | + | 0.601691i | \(0.794494\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.0143797 | 0.000521949 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.0290 | 0.798549 | 0.399274 | − | 0.916831i | \(-0.369262\pi\) | ||||
0.399274 | + | 0.916831i | \(0.369262\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23.2520 | 0.841779 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.4663 | −0.558455 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.6958 | −0.638128 | −0.319064 | − | 0.947733i | \(-0.603368\pi\) | ||||
−0.319064 | + | 0.947733i | \(0.603368\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.833250 | −0.0300088 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.63758 | −0.0588997 | −0.0294498 | − | 0.999566i | \(-0.509376\pi\) | ||||
−0.0294498 | + | 0.999566i | \(0.509376\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.17115 | −0.0778896 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.67831 | −0.131789 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.585930 | −0.0209662 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.22349 | −0.115198 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.6760 | 0.986543 | 0.493272 | − | 0.869875i | \(-0.335801\pi\) | ||||
0.493272 | + | 0.869875i | \(0.335801\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.70618 | 0.167544 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.95354 | 0.0694598 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.9097 | 0.529459 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.29831 | 0.329363 | 0.164681 | − | 0.986347i | \(-0.447340\pi\) | ||||
0.164681 | + | 0.986347i | \(0.447340\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −51.7761 | −1.83171 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.99119 | 0.317688 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.569093 | 0.0200829 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.05931 | 0.0724911 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 48.8800 | 1.71853 | 0.859264 | − | 0.511532i | \(-0.170922\pi\) | ||||
0.859264 | + | 0.511532i | \(0.170922\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −44.0615 | −1.54721 | −0.773604 | − | 0.633669i | \(-0.781548\pi\) | ||||
−0.773604 | + | 0.633669i | \(0.781548\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.492926 | −0.0172877 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.38848 | −0.0485768 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.09608 | 0.213014 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.1832 | 1.05340 | 0.526700 | − | 0.850051i | \(-0.323429\pi\) | ||||
0.526700 | + | 0.850051i | \(0.323429\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32.0171 | −1.11605 | −0.558023 | − | 0.829826i | \(-0.688440\pi\) | ||||
−0.558023 | + | 0.829826i | \(0.688440\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.5192 | −0.713523 | −0.356761 | − | 0.934196i | \(-0.616119\pi\) | ||||
−0.356761 | + | 0.934196i | \(0.616119\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.0551 | 1.32171 | 0.660854 | − | 0.750515i | \(-0.270194\pi\) | ||||
0.660854 | + | 0.750515i | \(0.270194\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.30884 | 0.0800926 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −22.0269 | −0.763188 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.0535 | −0.347499 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.6946 | −0.852553 | −0.426277 | − | 0.904593i | \(-0.640175\pi\) | ||||
−0.426277 | + | 0.904593i | \(0.640175\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.8547 | −0.719126 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.10797 | −0.0381607 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.2131 | −0.625811 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.03054 | 0.0696880 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.92065 | 0.237237 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.4770 | 0.803837 | 0.401919 | − | 0.915675i | \(-0.368343\pi\) | ||||
0.401919 | + | 0.915675i | \(0.368343\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.9632 | 0.716090 | 0.358045 | − | 0.933704i | \(-0.383443\pi\) | ||||
0.358045 | + | 0.933704i | \(0.383443\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.7273 | −1.21900 | −0.609500 | − | 0.792786i | \(-0.708630\pi\) | ||||
−0.609500 | + | 0.792786i | \(0.708630\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.45654 | −0.0496388 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.5880 | −0.666784 | −0.333392 | − | 0.942788i | \(-0.608193\pi\) | ||||
−0.333392 | + | 0.942788i | \(0.608193\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.85403 | −0.0629660 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.18921 | −0.0403412 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.64139 | −0.292802 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.53702 | 0.322779 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −49.5791 | −1.67417 | −0.837084 | − | 0.547074i | \(-0.815741\pi\) | ||||
−0.837084 | + | 0.547074i | \(0.815741\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.516230 | 0.0174120 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.4406 | 0.722353 | 0.361177 | − | 0.932497i | \(-0.382375\pi\) | ||||
0.361177 | + | 0.932497i | \(0.382375\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −52.7646 | −1.77567 | −0.887836 | − | 0.460161i | \(-0.847792\pi\) | ||||
−0.887836 | + | 0.460161i | \(0.847792\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30.1462 | 1.01221 | 0.506105 | − | 0.862472i | \(-0.331085\pi\) | ||||
0.506105 | + | 0.862472i | \(0.331085\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 31.4917 | 1.05620 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.658978 | −0.0220766 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.92520 | 0.265207 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.235102 | 0.00784982 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 25.4039 | 0.847266 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −57.5998 | −1.91893 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.549812 | −0.0182966 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.3987 | 0.677329 | 0.338665 | − | 0.940907i | \(-0.390025\pi\) | ||||
0.338665 | + | 0.940907i | \(0.390025\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 49.2221 | 1.63259 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 57.7921 | 1.91474 | 0.957369 | − | 0.288869i | \(-0.0932792\pi\) | ||||
0.957369 | + | 0.288869i | \(0.0932792\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.507619 | 0.0167998 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.10757 | −0.234713 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.0255 | 0.858502 | 0.429251 | − | 0.903185i | \(-0.358778\pi\) | ||||
0.429251 | + | 0.903185i | \(0.358778\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.26055 | 0.140390 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.57972 | −0.315320 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 21.6454 | 0.710927 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26.9839 | 0.885313 | 0.442656 | − | 0.896691i | \(-0.354036\pi\) | ||||
0.442656 | + | 0.896691i | \(0.354036\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.37159 | 0.110499 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.40112 | 0.111348 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.8201 | 1.17019 | 0.585096 | − | 0.810964i | \(-0.301057\pi\) | ||||
0.585096 | + | 0.810964i | \(0.301057\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.74079 | 0.0894424 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32.0416 | −1.04453 | −0.522263 | − | 0.852785i | \(-0.674912\pi\) | ||||
−0.522263 | + | 0.852785i | \(0.674912\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.64279 | 0.151190 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.53256 | 0.277271 | 0.138635 | − | 0.990343i | \(-0.455728\pi\) | ||||
0.138635 | + | 0.990343i | \(0.455728\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.30445 | 0.302035 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.41594 | −0.0459150 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42.4054 | 1.37365 | 0.686823 | − | 0.726825i | \(-0.259005\pi\) | ||||
0.686823 | + | 0.726825i | \(0.259005\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.0410397 | −0.00132662 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.2933 | −0.655305 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 48.2300 | 1.55581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.05801 | 0.0340938 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.0988 | −0.324755 | −0.162377 | − | 0.986729i | \(-0.551916\pi\) | ||||
−0.162377 | + | 0.986729i | \(0.551916\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.776570 | 0.0249470 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.7943 | 0.506863 | 0.253431 | − | 0.967353i | \(-0.418441\pi\) | ||||
0.253431 | + | 0.967353i | \(0.418441\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.33099 | −0.138845 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.0055 | 0.863984 | 0.431992 | − | 0.901877i | \(-0.357811\pi\) | ||||
0.431992 | + | 0.901877i | \(0.357811\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.230327 | 0.00736128 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −41.6043 | −1.32832 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.0647 | −0.512384 | −0.256192 | − | 0.966626i | \(-0.582468\pi\) | ||||
−0.256192 | + | 0.966626i | \(0.582468\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.13823 | 0.0998910 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.75255 | 0.0557279 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −51.4433 | −1.63415 | −0.817075 | − | 0.576532i | \(-0.804406\pi\) | ||||
−0.817075 | + | 0.576532i | \(0.804406\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.18066 | −0.164403 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.2639 | 1.24350 | 0.621751 | − | 0.783215i | \(-0.286422\pi\) | ||||
0.621751 | + | 0.783215i | \(0.286422\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.81660 | 0.247306 |
(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 | 9200.2.a.cz.1.5 | 7 | ||
4.3 | odd | 2 | 4600.2.a.bi.1.3 | 7 | |||
5.2 | odd | 4 | 1840.2.e.g.369.8 | 14 | |||
5.3 | odd | 4 | 1840.2.e.g.369.7 | 14 | |||
5.4 | even | 2 | 9200.2.a.dc.1.3 | 7 | |||
20.3 | even | 4 | 920.2.e.b.369.8 | yes | 14 | ||
20.7 | even | 4 | 920.2.e.b.369.7 | ✓ | 14 | ||
20.19 | odd | 2 | 4600.2.a.bh.1.5 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.e.b.369.7 | ✓ | 14 | 20.7 | even | 4 | ||
920.2.e.b.369.8 | yes | 14 | 20.3 | even | 4 | ||
1840.2.e.g.369.7 | 14 | 5.3 | odd | 4 | |||
1840.2.e.g.369.8 | 14 | 5.2 | odd | 4 | |||
4600.2.a.bh.1.5 | 7 | 20.19 | odd | 2 | |||
4600.2.a.bi.1.3 | 7 | 4.3 | odd | 2 | |||
9200.2.a.cz.1.5 | 7 | 1.1 | even | 1 | trivial | ||
9200.2.a.dc.1.3 | 7 | 5.4 | even | 2 |