Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(593,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.593");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.bl (of order \(6\), 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: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 16.0.81094542259068665856.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{14} + 9x^{12} - 8x^{10} + 44x^{8} - 32x^{6} + 144x^{4} - 64x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{16} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1025.4 | ||
Root | \(-1.12988 - 0.850516i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1512.1025 |
Dual form | 1512.2.bl.d.593.4 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.310225 | − | 0.537326i | −0.138737 | − | 0.240299i | 0.788282 | − | 0.615314i | \(-0.210971\pi\) |
−0.927019 | + | 0.375015i | \(0.877638\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.44109 | + | 2.21884i | −0.544679 | + | 0.838644i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.91649 | − | 1.10649i | −0.577845 | − | 0.333619i | 0.182432 | − | 0.983219i | \(-0.441603\pi\) |
−0.760276 | + | 0.649600i | \(0.774936\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 0.963711i | − | 0.267285i | −0.991030 | − | 0.133643i | \(-0.957333\pi\) | ||
0.991030 | − | 0.133643i | \(-0.0426674\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.653486 | − | 1.13187i | 0.158494 | − | 0.274519i | −0.775832 | − | 0.630939i | \(-0.782670\pi\) |
0.934326 | + | 0.356421i | \(0.116003\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.57941 | + | 0.911873i | −0.362342 | + | 0.209198i | −0.670107 | − | 0.742264i | \(-0.733752\pi\) |
0.307766 | + | 0.951462i | \(0.400419\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.27562 | − | 3.04588i | 1.10004 | − | 0.635110i | 0.163810 | − | 0.986492i | \(-0.447622\pi\) |
0.936232 | + | 0.351382i | \(0.114288\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.30752 | − | 3.99674i | 0.461504 | − | 0.799349i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 6.68969i | − | 1.24224i | −0.783714 | − | 0.621122i | \(-0.786677\pi\) | ||
0.783714 | − | 0.621122i | \(-0.213323\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.48866 | + | 2.01418i | 0.626582 | + | 0.361757i | 0.779427 | − | 0.626493i | \(-0.215510\pi\) |
−0.152845 | + | 0.988250i | \(0.548844\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.63930 | + | 0.0859913i | 0.277093 | + | 0.0145352i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.165402 | + | 0.286485i | 0.0271919 | + | 0.0470978i | 0.879301 | − | 0.476266i | \(-0.158010\pi\) |
−0.852109 | + | 0.523364i | \(0.824677\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.7190 | 1.83020 | 0.915102 | − | 0.403221i | \(-0.132110\pi\) | ||||
0.915102 | + | 0.403221i | \(0.132110\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.18909 | −0.333833 | −0.166916 | − | 0.985971i | \(-0.553381\pi\) | ||||
−0.166916 | + | 0.985971i | \(0.553381\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.27394 | − | 2.20652i | −0.185823 | − | 0.321854i | 0.758031 | − | 0.652219i | \(-0.226162\pi\) |
−0.943853 | + | 0.330364i | \(0.892828\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.84654 | − | 6.39509i | −0.406649 | − | 0.913585i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.985818 | + | 0.569162i | 0.135413 | + | 0.0781804i | 0.566176 | − | 0.824284i | \(-0.308422\pi\) |
−0.430763 | + | 0.902465i | \(0.641756\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.37304i | 0.185141i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.20629 | − | 10.7496i | 0.807991 | − | 1.39948i | −0.106263 | − | 0.994338i | \(-0.533889\pi\) |
0.914254 | − | 0.405143i | \(-0.132778\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.603098 | − | 0.348199i | 0.0772188 | − | 0.0445823i | −0.460893 | − | 0.887455i | \(-0.652471\pi\) |
0.538112 | + | 0.842873i | \(0.319138\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.517827 | + | 0.298967i | −0.0642285 | + | 0.0370823i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.61028 | + | 6.25319i | −0.441066 | + | 0.763949i | −0.997769 | − | 0.0667628i | \(-0.978733\pi\) |
0.556703 | + | 0.830712i | \(0.312066\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.40207i | − | 0.878464i | −0.898374 | − | 0.439232i | \(-0.855251\pi\) | ||
0.898374 | − | 0.439232i | \(-0.144749\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.17396 | − | 1.25513i | −0.254442 | − | 0.146902i | 0.367354 | − | 0.930081i | \(-0.380264\pi\) |
−0.621797 | + | 0.783179i | \(0.713597\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.21696 | − | 2.65786i | 0.594527 | − | 0.302891i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.52429 | + | 7.83630i | 0.509023 | + | 0.881653i | 0.999945 | + | 0.0104498i | \(0.00332634\pi\) |
−0.490923 | + | 0.871203i | \(0.663340\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.85562 | 0.972031 | 0.486016 | − | 0.873950i | \(-0.338450\pi\) | ||||
0.486016 | + | 0.873950i | \(0.338450\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.810911 | −0.0879556 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.20928 | − | 7.29069i | −0.446183 | − | 0.772812i | 0.551951 | − | 0.833877i | \(-0.313884\pi\) |
−0.998134 | + | 0.0610650i | \(0.980550\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.13832 | + | 1.38879i | 0.224157 | + | 0.145585i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.979946 | + | 0.565772i | 0.100540 | + | 0.0580470i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 12.4027i | − | 1.25930i | −0.776877 | − | 0.629652i | \(-0.783197\pi\) | ||
0.776877 | − | 0.629652i | \(-0.216803\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.82480 | + | 3.16064i | −0.181574 | + | 0.314496i | −0.942417 | − | 0.334441i | \(-0.891453\pi\) |
0.760843 | + | 0.648936i | \(0.224786\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.12562 | − | 1.80458i | 0.307976 | − | 0.177810i | −0.338044 | − | 0.941130i | \(-0.609765\pi\) |
0.646020 | + | 0.763320i | \(0.276432\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.1599 | + | 7.02050i | −1.17554 | + | 0.678697i | −0.954978 | − | 0.296676i | \(-0.904122\pi\) |
−0.220560 | + | 0.975373i | \(0.570788\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.681140 | + | 1.17977i | −0.0652413 | + | 0.113001i | −0.896801 | − | 0.442434i | \(-0.854115\pi\) |
0.831560 | + | 0.555435i | \(0.187448\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 16.1266i | − | 1.51707i | −0.651635 | − | 0.758533i | \(-0.725917\pi\) | ||
0.651635 | − | 0.758533i | \(-0.274083\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.27326 | − | 1.88982i | −0.305233 | − | 0.176226i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.56972 | + | 3.08111i | 0.143896 | + | 0.282444i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.05137 | − | 5.28513i | −0.277397 | − | 0.480466i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.96566 | −0.533585 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.16641 | 0.724652 | 0.362326 | − | 0.932051i | \(-0.381983\pi\) | ||||
0.362326 | + | 0.932051i | \(0.381983\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.50391 | − | 4.33690i | −0.218768 | − | 0.378916i | 0.735664 | − | 0.677347i | \(-0.236870\pi\) |
−0.954431 | + | 0.298430i | \(0.903537\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.252762 | − | 4.81855i | 0.0219172 | − | 0.417822i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.08103 | − | 2.35619i | −0.348666 | − | 0.201303i | 0.315431 | − | 0.948948i | \(-0.397851\pi\) |
−0.664098 | + | 0.747646i | \(0.731184\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.3716i | 0.879709i | 0.898069 | + | 0.439854i | \(0.144970\pi\) | ||||
−0.898069 | + | 0.439854i | \(0.855030\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.06633 | + | 1.84695i | −0.0891714 | + | 0.154449i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.59454 | + | 2.07531i | −0.298511 | + | 0.172345i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.01781 | − | 4.62908i | 0.656844 | − | 0.379229i | −0.134229 | − | 0.990950i | \(-0.542856\pi\) |
0.791074 | + | 0.611721i | \(0.209522\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.62359 | + | 14.9365i | −0.701778 | + | 1.21552i | 0.266064 | + | 0.963955i | \(0.414277\pi\) |
−0.967842 | + | 0.251560i | \(0.919056\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 2.49940i | − | 0.200756i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.59454 | + | 2.07531i | 0.286876 | + | 0.165628i | 0.636532 | − | 0.771250i | \(-0.280368\pi\) |
−0.349656 | + | 0.936878i | \(0.613702\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.844287 | + | 16.0951i | −0.0665391 | + | 1.26848i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.38217 | − | 11.0542i | −0.499890 | − | 0.865835i | 0.500110 | − | 0.865962i | \(-0.333293\pi\) |
−1.00000 | 0.000126653i | \(0.999960\pi\) | ||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.5086 | 1.58700 | 0.793501 | − | 0.608569i | \(-0.208256\pi\) | ||||
0.793501 | + | 0.608569i | \(0.208256\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0713 | 0.928559 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.81088 | + | 6.60064i | 0.289736 | + | 0.501837i | 0.973747 | − | 0.227635i | \(-0.0730992\pi\) |
−0.684011 | + | 0.729472i | \(0.739766\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.54282 | + | 10.8797i | 0.418997 | + | 0.822427i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.78757 | − | 3.34146i | −0.432583 | − | 0.249752i | 0.267863 | − | 0.963457i | \(-0.413682\pi\) |
−0.700447 | + | 0.713705i | \(0.747016\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 5.28785i | − | 0.393043i | −0.980500 | − | 0.196521i | \(-0.937036\pi\) | ||
0.980500 | − | 0.196521i | \(-0.0629645\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.102624 | − | 0.177749i | 0.00754504 | − | 0.0130684i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.50480 | + | 1.44615i | −0.183169 | + | 0.105753i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.45434 | + | 3.72641i | −0.467020 | + | 0.269634i | −0.714991 | − | 0.699133i | \(-0.753569\pi\) |
0.247972 | + | 0.968767i | \(0.420236\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.74522 | − | 16.8792i | 0.701476 | − | 1.21499i | −0.266472 | − | 0.963843i | \(-0.585858\pi\) |
0.967948 | − | 0.251150i | \(-0.0808086\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2.62061i | − | 0.186711i | −0.995633 | − | 0.0933555i | \(-0.970241\pi\) | ||
0.995633 | − | 0.0933555i | \(-0.0297593\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.10031 | + | 4.09937i | 0.503328 | + | 0.290596i | 0.730087 | − | 0.683355i | \(-0.239480\pi\) |
−0.226759 | + | 0.973951i | \(0.572813\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.8434 | + | 9.64042i | 1.04180 | + | 0.676625i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.63554 | − | 6.29694i | −0.253917 | − | 0.439797i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.03591 | 0.279170 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.6095 | −1.34997 | −0.674986 | − | 0.737831i | \(-0.735850\pi\) | ||||
−0.674986 | + | 0.737831i | \(0.735850\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.679111 | + | 1.17625i | 0.0463150 | + | 0.0802199i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.49661 | + | 4.83819i | −0.644672 | + | 0.328438i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.09080 | − | 0.629771i | −0.0733749 | − | 0.0423630i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.9924i | 1.60665i | 0.595539 | + | 0.803326i | \(0.296938\pi\) | ||||
−0.595539 | + | 0.803326i | \(0.703062\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.8243 | + | 22.2123i | −0.851177 | + | 1.47428i | 0.0289703 | + | 0.999580i | \(0.490777\pi\) |
−0.880147 | + | 0.474701i | \(0.842556\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.65507 | − | 4.99701i | 0.571943 | − | 0.330212i | −0.185982 | − | 0.982553i | \(-0.559547\pi\) |
0.757925 | + | 0.652342i | \(0.226213\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22.4800 | + | 12.9788i | −1.47271 | + | 0.850271i | −0.999529 | − | 0.0306937i | \(-0.990228\pi\) |
−0.473183 | + | 0.880964i | \(0.656895\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.790414 | + | 1.36904i | −0.0515609 | + | 0.0893062i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 18.1554i | − | 1.17438i | −0.809450 | − | 0.587189i | \(-0.800235\pi\) | ||
0.809450 | − | 0.587189i | \(-0.199765\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.44245 | + | 1.98750i | 0.221748 | + | 0.128026i | 0.606759 | − | 0.794886i | \(-0.292469\pi\) |
−0.385011 | + | 0.922912i | \(0.625802\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.55318 | + | 3.51344i | −0.163117 | + | 0.224465i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.878782 | + | 1.52210i | 0.0559156 | + | 0.0968486i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.403459 | −0.0254661 | −0.0127331 | − | 0.999919i | \(-0.504053\pi\) | ||||
−0.0127331 | + | 0.999919i | \(0.504053\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.4809 | −0.847538 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.22515 | + | 12.5143i | 0.450692 | + | 0.780622i | 0.998429 | − | 0.0560288i | \(-0.0178439\pi\) |
−0.547737 | + | 0.836651i | \(0.684511\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.874023 | − | 0.0458477i | −0.0543091 | − | 0.00284884i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.3400 | − | 9.43390i | −1.00757 | − | 0.581719i | −0.0970889 | − | 0.995276i | \(-0.530953\pi\) |
−0.910478 | + | 0.413556i | \(0.864286\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.706274i | − | 0.0433861i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.65868 | + | 8.06908i | −0.284045 | + | 0.491980i | −0.972377 | − | 0.233415i | \(-0.925010\pi\) |
0.688332 | + | 0.725396i | \(0.258343\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.0776 | − | 13.3239i | 1.40187 | − | 0.809368i | 0.407282 | − | 0.913302i | \(-0.366477\pi\) |
0.994584 | + | 0.103934i | \(0.0331432\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.84470 | + | 5.10649i | −0.533355 | + | 0.307933i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.63457 | − | 16.6876i | 0.578885 | − | 1.00266i | −0.416722 | − | 0.909034i | \(-0.636821\pi\) |
0.995608 | − | 0.0936250i | \(-0.0298455\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.20740i | 0.0720276i | 0.999351 | + | 0.0360138i | \(0.0114660\pi\) | ||||
−0.999351 | + | 0.0360138i | \(0.988534\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.2610 | − | 7.65622i | −0.788282 | − | 0.455115i | 0.0510754 | − | 0.998695i | \(-0.483735\pi\) |
−0.839357 | + | 0.543580i | \(0.817068\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −16.8881 | + | 26.0027i | −0.996875 | + | 1.53489i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.64591 | + | 13.2431i | 0.449760 | + | 0.779006i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.9303 | 1.10592 | 0.552960 | − | 0.833208i | \(-0.313498\pi\) | ||||
0.552960 | + | 0.833208i | \(0.313498\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.70139 | −0.448392 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.93535 | − | 5.08417i | −0.169755 | − | 0.294025i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.15467 | − | 4.85725i | 0.181832 | − | 0.279967i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.374192 | − | 0.216040i | −0.0214262 | − | 0.0123704i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 19.4828i | − | 1.11194i | −0.831202 | − | 0.555971i | \(-0.812346\pi\) | ||
0.831202 | − | 0.555971i | \(-0.187654\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.06853 | + | 15.7072i | −0.514229 | + | 0.890671i | 0.485634 | + | 0.874162i | \(0.338589\pi\) |
−0.999864 | + | 0.0165093i | \(0.994745\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.2088 | + | 9.35817i | −0.916177 | + | 0.528955i | −0.882413 | − | 0.470475i | \(-0.844083\pi\) |
−0.0337634 | + | 0.999430i | \(0.510749\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −29.4904 | + | 17.0263i | −1.65634 | + | 0.956290i | −0.681962 | + | 0.731388i | \(0.738873\pi\) |
−0.974381 | + | 0.224903i | \(0.927794\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.40207 | + | 12.8208i | −0.414436 | + | 0.717824i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.38358i | 0.132626i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.85170 | − | 2.22378i | −0.213654 | − | 0.123353i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.73178 | + | 0.353122i | 0.371135 | + | 0.0194683i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.76511 | − | 15.1816i | −0.481774 | − | 0.834457i | 0.518007 | − | 0.855376i | \(-0.326674\pi\) |
−0.999781 | + | 0.0209192i | \(0.993341\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.48000 | 0.244769 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.53700 | 0.519513 | 0.259757 | − | 0.965674i | \(-0.416358\pi\) | ||||
0.259757 | + | 0.965674i | \(0.416358\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.45733 | − | 7.72032i | −0.241378 | − | 0.418079i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.2918 | + | 2.89985i | 0.987666 | + | 0.156577i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.58768 | − | 2.64870i | −0.246280 | − | 0.142190i | 0.371780 | − | 0.928321i | \(-0.378748\pi\) |
−0.618060 | + | 0.786131i | \(0.712081\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 20.7945i | − | 1.11310i | −0.830813 | − | 0.556552i | \(-0.812124\pi\) | ||
0.830813 | − | 0.556552i | \(-0.187876\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.79161 | + | 16.9596i | −0.521155 | + | 0.902666i | 0.478543 | + | 0.878064i | \(0.341165\pi\) |
−0.999697 | + | 0.0246021i | \(0.992168\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.97732 | + | 2.29631i | −0.211094 | + | 0.121875i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.1760 | + | 11.0713i | −1.01207 | + | 0.584319i | −0.911797 | − | 0.410641i | \(-0.865305\pi\) |
−0.100273 | + | 0.994960i | \(0.531972\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.83697 | + | 13.5740i | −0.412472 | + | 0.714423i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.55750i | 0.0815231i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.1684 | + | 10.4895i | 0.948382 | + | 0.547549i | 0.892578 | − | 0.450893i | \(-0.148894\pi\) |
0.0558039 | + | 0.998442i | \(0.482228\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.68353 | + | 1.36716i | −0.139322 | + | 0.0709797i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.6507 | + | 23.6437i | 0.706805 | + | 1.22422i | 0.966036 | + | 0.258407i | \(0.0831975\pi\) |
−0.259231 | + | 0.965815i | \(0.583469\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.44693 | −0.332034 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.96174 | 0.100768 | 0.0503840 | − | 0.998730i | \(-0.483955\pi\) | ||||
0.0503840 | + | 0.998730i | \(0.483955\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.10367 | + | 10.5719i | 0.311883 | + | 0.540197i | 0.978770 | − | 0.204962i | \(-0.0657070\pi\) |
−0.666887 | + | 0.745159i | \(0.732374\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.04657 | − | 1.97867i | −0.155267 | − | 0.100842i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.8845 | − | 13.7897i | −1.21099 | − | 0.699167i | −0.248017 | − | 0.968756i | \(-0.579779\pi\) |
−0.962976 | + | 0.269589i | \(0.913112\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 7.96175i | − | 0.402643i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.80710 | − | 4.86204i | 0.141240 | − | 0.244636i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.7563 | + | 16.6025i | −1.44324 | + | 0.833255i | −0.998064 | − | 0.0621887i | \(-0.980192\pi\) |
−0.445175 | + | 0.895443i | \(0.646859\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.1061 | + | 8.72153i | −0.754364 | + | 0.435532i | −0.827269 | − | 0.561807i | \(-0.810107\pi\) |
0.0729044 | + | 0.997339i | \(0.476773\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.94109 | − | 3.36206i | 0.0966924 | − | 0.167476i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 0.732061i | − | 0.0362869i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.3281 | − | 8.27231i | −0.708477 | − | 0.409039i | 0.102020 | − | 0.994782i | \(-0.467469\pi\) |
−0.810497 | + | 0.585743i | \(0.800803\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.9079 | + | 29.2619i | 0.733571 | + | 1.43988i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.74724 | − | 4.75836i | −0.134857 | − | 0.233578i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.7781 | 1.11278 | 0.556392 | − | 0.830920i | \(-0.312185\pi\) | ||||
0.556392 | + | 0.830920i | \(0.312185\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.6863 | 0.764504 | 0.382252 | − | 0.924058i | \(-0.375149\pi\) | ||||
0.382252 | + | 0.924058i | \(0.375149\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.01586 | − | 5.22363i | −0.146291 | − | 0.253383i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.0965172 | + | 1.83996i | −0.00467079 | + | 0.0890421i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.9241 | + | 12.6579i | 1.05604 | + | 0.609707i | 0.924335 | − | 0.381581i | \(-0.124620\pi\) |
0.131709 | + | 0.991288i | \(0.457954\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.9831i | 1.82535i | 0.408686 | + | 0.912675i | \(0.365987\pi\) | ||||
−0.408686 | + | 0.912675i | \(0.634013\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.55491 | + | 9.62139i | −0.265727 | + | 0.460253i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.42813 | − | 4.28864i | 0.354526 | − | 0.204685i | −0.312151 | − | 0.950032i | \(-0.601050\pi\) |
0.666677 | + | 0.745347i | \(0.267716\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.94380 | + | 5.16371i | −0.424933 | + | 0.245335i | −0.697186 | − | 0.716891i | \(-0.745565\pi\) |
0.272253 | + | 0.962226i | \(0.412231\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.61165 | + | 4.52351i | −0.123804 | + | 0.214435i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 20.5336i | − | 0.969041i | −0.874780 | − | 0.484520i | \(-0.838994\pi\) | ||
0.874780 | − | 0.484520i | \(-0.161006\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.4594 | − | 12.9670i | −1.05757 | − | 0.610591i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.0828707 | − | 1.57981i | 0.00388504 | − | 0.0740629i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.4978 | + | 21.6469i | 0.584623 | + | 1.01260i | 0.994922 | + | 0.100646i | \(0.0320910\pi\) |
−0.410299 | + | 0.911951i | \(0.634576\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 42.6072 | 1.98442 | 0.992208 | − | 0.124596i | \(-0.0397634\pi\) | ||||
0.992208 | + | 0.124596i | \(0.0397634\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.1942 | 1.40325 | 0.701623 | − | 0.712549i | \(-0.252459\pi\) | ||||
0.701623 | + | 0.712549i | \(0.252459\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.90935 | − | 10.2353i | −0.273452 | − | 0.473633i | 0.696291 | − | 0.717759i | \(-0.254832\pi\) |
−0.969743 | + | 0.244126i | \(0.921499\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.67213 | − | 17.0220i | −0.400442 | − | 0.786005i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.19538 | + | 2.42220i | 0.192904 | + | 0.111373i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.41666i | 0.386183i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.12346 | + | 7.14204i | −0.188406 | + | 0.326328i | −0.944719 | − | 0.327882i | \(-0.893665\pi\) |
0.756313 | + | 0.654210i | \(0.226999\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.276088 | − | 0.159400i | 0.0125885 | − | 0.00726800i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.66430 | + | 3.84763i | −0.302610 | + | 0.174712i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.5643 | − | 21.7620i | 0.569344 | − | 0.986132i | −0.427287 | − | 0.904116i | \(-0.640531\pi\) |
0.996631 | − | 0.0820163i | \(-0.0261359\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 7.80970i | − | 0.352447i | −0.984350 | − | 0.176223i | \(-0.943612\pi\) | ||
0.984350 | − | 0.176223i | \(-0.0563881\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.57187 | − | 4.37162i | −0.341020 | − | 0.196888i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16.4240 | + | 10.6670i | 0.736718 | + | 0.478481i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.6425 | − | 25.3616i | −0.655489 | − | 1.13534i | −0.981771 | − | 0.190068i | \(-0.939129\pi\) |
0.326282 | − | 0.945273i | \(-0.394204\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.32335 | −0.237356 | −0.118678 | − | 0.992933i | \(-0.537866\pi\) | ||||
−0.118678 | + | 0.992933i | \(0.537866\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.26439 | 0.100764 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.7275 | − | 25.5087i | −0.652784 | − | 1.13066i | −0.982444 | − | 0.186556i | \(-0.940268\pi\) |
0.329660 | − | 0.944100i | \(-0.393066\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.91780 | − | 3.01491i | 0.261788 | − | 0.133372i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.93929 | − | 1.11965i | −0.0854553 | − | 0.0493376i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.63838i | 0.247976i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.43563 | − | 16.3430i | 0.413382 | − | 0.715999i | −0.581875 | − | 0.813278i | \(-0.697681\pi\) |
0.995257 | + | 0.0972791i | \(0.0310139\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.1439 | − | 12.7848i | 0.968285 | − | 0.559039i | 0.0695719 | − | 0.997577i | \(-0.477837\pi\) |
0.898713 | + | 0.438537i | \(0.144503\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.55958 | − | 2.63247i | 0.198618 | − | 0.114672i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.05476 | − | 12.2192i | 0.306729 | − | 0.531270i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 11.2938i | − | 0.489187i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.54459 | + | 4.35587i | 0.326181 | + | 0.188321i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.62071 | + | 15.4058i | −0.0698091 | + | 0.663575i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.3471 | + | 28.3141i | 0.702819 | + | 1.21732i | 0.967473 | + | 0.252974i | \(0.0814088\pi\) |
−0.264654 | + | 0.964343i | \(0.585258\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.845227 | 0.0362055 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −41.0972 | −1.75719 | −0.878594 | − | 0.477570i | \(-0.841518\pi\) | ||||
−0.878594 | + | 0.477570i | \(0.841518\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.10015 | + | 10.5658i | 0.259875 | + | 0.450117i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −23.9074 | − | 1.25409i | −1.01665 | − | 0.0533292i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.412224 | − | 0.237997i | −0.0174665 | − | 0.0100843i | 0.491241 | − | 0.871024i | \(-0.336543\pi\) |
−0.508708 | + | 0.860939i | \(0.669877\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.10965i | 0.0892286i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.43275 | + | 12.8739i | −0.313253 | + | 0.542570i | −0.979065 | − | 0.203550i | \(-0.934752\pi\) |
0.665812 | + | 0.746120i | \(0.268085\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.66525 | + | 5.00288i | −0.364550 | + | 0.210473i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.0050 | − | 6.93112i | 0.503278 | − | 0.290567i | −0.226788 | − | 0.973944i | \(-0.572823\pi\) |
0.730066 | + | 0.683377i | \(0.239489\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.96776 | + | 3.40826i | −0.0823482 | + | 0.142631i | −0.904258 | − | 0.426986i | \(-0.859575\pi\) |
0.821910 | + | 0.569617i | \(0.192909\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 28.1137i | − | 1.17242i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.6457 | + | 15.3839i | 1.10928 | + | 0.640440i | 0.938642 | − | 0.344894i | \(-0.112085\pi\) |
0.170634 | + | 0.985335i | \(0.445419\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.7617 | + | 19.6493i | −0.529445 | + | 0.815188i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.25954 | − | 2.18159i | −0.0521649 | − | 0.0903523i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.7214 | 1.10291 | 0.551455 | − | 0.834205i | \(-0.314073\pi\) | ||||
0.551455 | + | 0.834205i | \(0.314073\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.34670 | −0.302716 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.21759 | + | 5.57303i | 0.132131 | + | 0.228857i | 0.924498 | − | 0.381188i | \(-0.124485\pi\) |
−0.792367 | + | 0.610045i | \(0.791151\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.16859 | − | 1.79929i | 0.0479076 | − | 0.0737635i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −39.0065 | − | 22.5204i | −1.59376 | − | 0.920159i | −0.992653 | − | 0.120992i | \(-0.961392\pi\) |
−0.601109 | − | 0.799167i | \(-0.705274\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.29317i | 0.256704i | 0.991729 | + | 0.128352i | \(0.0409687\pi\) | ||||
−0.991729 | + | 0.128352i | \(0.959031\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.89322 | + | 3.27916i | −0.0769704 | + | 0.133317i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.21834 | + | 1.28076i | −0.0900396 | + | 0.0519844i | −0.544344 | − | 0.838862i | \(-0.683221\pi\) |
0.454304 | + | 0.890847i | \(0.349888\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.12645 | + | 1.22771i | −0.0860269 | + | 0.0496677i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.95779 | − | 10.3192i | 0.240633 | − | 0.416788i | −0.720262 | − | 0.693702i | \(-0.755978\pi\) |
0.960895 | + | 0.276914i | \(0.0893117\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 17.0171i | − | 0.685083i | −0.939503 | − | 0.342541i | \(-0.888712\pi\) | ||
0.939503 | − | 0.342541i | \(-0.111288\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.8253 | − | 15.4876i | −1.07820 | − | 0.622498i | −0.147789 | − | 0.989019i | \(-0.547216\pi\) |
−0.930410 | + | 0.366521i | \(0.880549\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 22.2428 | + | 1.16677i | 0.891141 | + | 0.0467457i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.68691 | − | 16.7782i | −0.387476 | − | 0.671129i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.432351 | 0.0172390 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.21976 | −0.207795 | −0.103898 | − | 0.994588i | \(-0.533131\pi\) | ||||
−0.103898 | + | 0.994588i | \(0.533131\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.53343 | − | 4.38802i | −0.100536 | − | 0.174133i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.16302 | + | 2.74324i | −0.244188 | + | 0.108691i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.0187 | − | 11.5578i | −0.790693 | − | 0.456507i | 0.0495138 | − | 0.998773i | \(-0.484233\pi\) |
−0.840206 | + | 0.542267i | \(0.817566\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 23.2939i | − | 0.918623i | −0.888275 | − | 0.459312i | \(-0.848096\pi\) | ||
0.888275 | − | 0.459312i | \(-0.151904\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.2570 | − | 35.0862i | 0.796386 | − | 1.37938i | −0.125570 | − | 0.992085i | \(-0.540076\pi\) |
0.921956 | − | 0.387296i | \(-0.126591\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −23.7886 | + | 13.7344i | −0.933786 | + | 0.539121i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10.3425 | + | 5.97123i | −0.404732 | + | 0.233672i | −0.688524 | − | 0.725214i | \(-0.741741\pi\) |
0.283792 | + | 0.958886i | \(0.408408\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.55355 | + | 2.69083i | −0.0607023 | + | 0.105139i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 43.4636i | − | 1.69310i | −0.532307 | − | 0.846552i | \(-0.678675\pi\) | ||
0.532307 | − | 0.846552i | \(-0.321325\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.1033 | + | 24.8857i | 1.67653 | + | 0.967942i | 0.963849 | + | 0.266450i | \(0.0858506\pi\) |
0.712677 | + | 0.701493i | \(0.247483\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.66755 | + | 1.35902i | −0.103443 | + | 0.0527006i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.3760 | − | 35.2923i | −0.788962 | − | 1.36652i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.54111 | −0.0594939 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.8822 | 1.26751 | 0.633757 | − | 0.773532i | \(-0.281512\pi\) | ||||
0.633757 | + | 0.773532i | \(0.281512\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.7744 | + | 22.1260i | 0.490961 | + | 0.850370i | 0.999946 | − | 0.0104056i | \(-0.00331226\pi\) |
−0.508984 | + | 0.860776i | \(0.669979\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.5197 | + | 17.8734i | 1.05611 | + | 0.685917i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 37.4260 | + | 21.6079i | 1.43207 | + | 0.826803i | 0.997278 | − | 0.0737300i | \(-0.0234903\pi\) |
0.434787 | + | 0.900533i | \(0.356824\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.92379i | 0.111712i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.548508 | − | 0.950043i | 0.0208965 | − | 0.0361938i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.2836 | − | 10.5561i | 0.695542 | − | 0.401571i | −0.110143 | − | 0.993916i | \(-0.535131\pi\) |
0.805685 | + | 0.592344i | \(0.201797\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.57293 | − | 3.21754i | 0.211393 | − | 0.122048i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.65822 | − | 13.2644i | 0.290076 | − | 0.502426i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 33.7546i | − | 1.27489i | −0.770495 | − | 0.637446i | \(-0.779991\pi\) | ||
0.770495 | − | 0.637446i | \(-0.220009\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.522475 | − | 0.301651i | −0.0197055 | − | 0.0113770i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.38328 | − | 8.60370i | −0.164850 | − | 0.323576i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.5489 | + | 28.6636i | 0.621509 | + | 1.07648i | 0.989205 | + | 0.146539i | \(0.0468132\pi\) |
−0.367696 | + | 0.929946i | \(0.619853\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.5398 | 0.919022 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.32322 | 0.0494854 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.6731 | − | 34.0748i | −0.733684 | − | 1.27078i | −0.955298 | − | 0.295643i | \(-0.904466\pi\) |
0.221615 | − | 0.975134i | \(-0.428867\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.500210 | + | 9.53580i | −0.0186288 | + | 0.355132i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −26.7370 | − | 15.4366i | −0.992987 | − | 0.573301i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.7164i | 0.545803i | 0.962042 | + | 0.272901i | \(0.0879832\pi\) | ||||
−0.962042 | + | 0.272901i | \(0.912017\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.43054 | + | 2.47777i | −0.0529104 | + | 0.0916435i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −39.3009 | + | 22.6904i | −1.45161 | + | 0.838089i | −0.998573 | − | 0.0534010i | \(-0.982994\pi\) |
−0.453040 | + | 0.891490i | \(0.649661\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.8382 | − | 7.98947i | 0.509735 | − | 0.294296i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.90885 | + | 8.50237i | −0.180575 | + | 0.312765i | −0.942076 | − | 0.335398i | \(-0.891129\pi\) |
0.761502 | + | 0.648163i | \(0.224462\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.2980i | 0.744660i | 0.928100 | + | 0.372330i | \(0.121441\pi\) | ||||
−0.928100 | + | 0.372330i | \(0.878559\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.97465 | − | 2.87212i | −0.182257 | − | 0.105226i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.94601 | − | 37.0980i | 0.0711057 | − | 1.35553i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.84315 | − | 15.3168i | −0.322691 | − | 0.558918i | 0.658351 | − | 0.752711i | \(-0.271254\pi\) |
−0.981042 | + | 0.193793i | \(0.937921\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.7010 | 0.389450 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.2142 | −0.880079 | −0.440040 | − | 0.897978i | \(-0.645036\pi\) | ||||
−0.440040 | + | 0.897978i | \(0.645036\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.664665 | + | 1.15123i | 0.0240941 | + | 0.0417322i | 0.877821 | − | 0.478989i | \(-0.158997\pi\) |
−0.853727 | + | 0.520721i | \(0.825663\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.63614 | − | 3.21149i | −0.0592323 | − | 0.116264i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.3595 | − | 5.98107i | −0.374061 | − | 0.215964i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 9.99518i | − | 0.360435i | −0.983627 | − | 0.180218i | \(-0.942320\pi\) | ||
0.983627 | − | 0.180218i | \(-0.0576802\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.3473 | − | 35.2426i | 0.731841 | − | 1.26759i | −0.224254 | − | 0.974531i | \(-0.571994\pi\) |
0.956095 | − | 0.293056i | \(-0.0946722\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16.1003 | − | 9.29552i | 0.578340 | − | 0.333905i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18.5092 | + | 10.6863i | −0.663159 | + | 0.382875i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.19030 | + | 14.1860i | −0.293072 | + | 0.507615i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 2.57526i | − | 0.0919148i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.0048 | − | 9.24038i | −0.570510 | − | 0.329384i | 0.186843 | − | 0.982390i | \(-0.440174\pi\) |
−0.757353 | + | 0.653006i | \(0.773508\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 35.7825 | + | 23.2399i | 1.27228 | + | 0.826314i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.335563 | − | 0.581212i | −0.0119162 | − | 0.0206394i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.8741 | 1.27073 | 0.635363 | − | 0.772213i | \(-0.280850\pi\) | ||||
0.635363 | + | 0.772213i | \(0.280850\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.33000 | −0.117807 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.77758 | + | 4.81091i | 0.0980187 | + | 0.169773i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.91026 | − | 4.53946i | 0.314045 | − | 0.159995i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36.3089 | + | 20.9630i | 1.27655 | + | 0.737018i | 0.976213 | − | 0.216814i | \(-0.0695665\pi\) |
0.300340 | + | 0.953832i | \(0.402900\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 34.1402i | − | 1.19883i | −0.800440 | − | 0.599413i | \(-0.795401\pi\) | ||
0.800440 | − | 0.599413i | \(-0.204599\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.95982 | + | 6.85861i | −0.138706 | + | 0.240247i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.45747 | − | 1.99617i | 0.120962 | − | 0.0698372i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.2818 | − | 15.7512i | 0.952143 | − | 0.549720i | 0.0583971 | − | 0.998293i | \(-0.481401\pi\) |
0.893746 | + | 0.448573i | \(0.148068\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.47768 | + | 14.6838i | −0.295513 | + | 0.511844i | −0.975104 | − | 0.221747i | \(-0.928824\pi\) |
0.679591 | + | 0.733591i | \(0.262157\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 43.7684i | − | 1.52198i | −0.648766 | − | 0.760988i | \(-0.724715\pi\) | ||
0.648766 | − | 0.760988i | \(-0.275285\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.86284 | + | 2.80756i | 0.168893 | + | 0.0975107i | 0.582064 | − | 0.813143i | \(-0.302245\pi\) |
−0.413171 | + | 0.910654i | \(0.635579\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.09859 | − | 0.957185i | −0.315247 | − | 0.0331645i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.36228 | − | 11.0198i | −0.220176 | − | 0.381356i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 36.7401 | 1.26841 | 0.634204 | − | 0.773166i | \(-0.281328\pi\) | ||||
0.634204 | + | 0.773166i | \(0.281328\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.7520 | −0.543172 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.74481 | − | 6.48620i | −0.128825 | − | 0.223132i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.1242 | + | 0.845809i | 0.554033 | + | 0.0290623i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.74519 | + | 1.00759i | 0.0598245 | + | 0.0345397i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 35.6583i | − | 1.22092i | −0.792048 | − | 0.610459i | \(-0.790985\pi\) | ||
0.792048 | − | 0.610459i | \(-0.209015\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.444720 | + | 0.770278i | −0.0151914 | + | 0.0263122i | −0.873521 | − | 0.486786i | \(-0.838169\pi\) |
0.858330 | + | 0.513098i | \(0.171502\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.1560 | − | 11.6371i | 0.687715 | − | 0.397052i | −0.115040 | − | 0.993361i | \(-0.536700\pi\) |
0.802755 | + | 0.596308i | \(0.203366\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.72738 | − | 2.15201i | 0.126882 | − | 0.0732551i | −0.435216 | − | 0.900326i | \(-0.643328\pi\) |
0.562097 | + | 0.827071i | \(0.309995\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.36446 | − | 4.09537i | 0.0803941 | − | 0.139247i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 20.0243i | − | 0.679278i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.02627 | + | 3.47927i | 0.204192 | + | 0.117891i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.59702 | − | 13.2369i | 0.290632 | − | 0.447488i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.1826 | + | 50.5457i | 0.985425 | + | 1.70681i | 0.640034 | + | 0.768347i | \(0.278920\pi\) |
0.345391 | + | 0.938459i | \(0.387746\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.9914 | 0.471381 | 0.235691 | − | 0.971828i | \(-0.424265\pi\) | ||||
0.235691 | + | 0.971828i | \(0.424265\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.64531 | −0.0553691 | −0.0276845 | − | 0.999617i | \(-0.508813\pi\) | ||||
−0.0276845 | + | 0.999617i | \(0.508813\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.976428 | − | 1.69122i | −0.0327852 | − | 0.0567857i | 0.849167 | − | 0.528124i | \(-0.177104\pi\) |
−0.881952 | + | 0.471338i | \(0.843771\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.7685 | + | 18.1200i | −0.394703 | + | 0.607725i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.02414 | + | 2.32334i | 0.134663 | + | 0.0777475i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.14642i | 0.138599i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.4742 | − | 23.3381i | 0.449391 | − | 0.778368i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.28844 | − | 0.743879i | 0.0429240 | − | 0.0247822i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.84130 | + | 1.64042i | −0.0944479 | + | 0.0545295i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.98547 | + | 12.0992i | −0.231949 | + | 0.401747i | −0.958382 | − | 0.285491i | \(-0.907843\pi\) |
0.726433 | + | 0.687237i | \(0.241177\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 6.79122i | − | 0.225003i | −0.993652 | − | 0.112502i | \(-0.964114\pi\) | ||
0.993652 | − | 0.112502i | \(-0.0358863\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.9717 | − | 9.79864i | −0.561683 | − | 0.324288i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.2312 | + | 0.694058i | 0.436934 | + | 0.0229198i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.292791 | + | 0.507128i | 0.00965828 | + | 0.0167286i | 0.870814 | − | 0.491612i | \(-0.163592\pi\) |
−0.861156 | + | 0.508341i | \(0.830259\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.13345 | −0.234800 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.52667 | 0.0501967 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18.4832 | − | 32.0139i | −0.606415 | − | 1.05034i | −0.991826 | − | 0.127596i | \(-0.959274\pi\) |
0.385411 | − | 0.922745i | \(-0.374060\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.3274 | + | 7.50479i | 0.338466 | + | 0.245960i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.55411 | + | 0.897263i | 0.0508247 | + | 0.0293436i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.9658i | 1.10961i | 0.831979 | + | 0.554807i | \(0.187208\pi\) | ||||
−0.831979 | + | 0.554807i | \(0.812792\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23.0968 | + | 40.0048i | −0.752933 | + | 1.30412i | 0.193462 | + | 0.981108i | \(0.438028\pi\) |
−0.946395 | + | 0.323011i | \(0.895305\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 61.8251 | − | 35.6947i | 2.01330 | − | 1.16238i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.9927 | − | 12.1202i | 0.682173 | − | 0.393853i | −0.118500 | − | 0.992954i | \(-0.537809\pi\) |
0.800673 | + | 0.599101i | \(0.204475\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.20959 | + | 2.09506i | −0.0392648 | + | 0.0680087i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.7820i | 0.899947i | 0.893042 | + | 0.449974i | \(0.148567\pi\) | ||||
−0.893042 | + | 0.449974i | \(0.851433\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.00460 | + | 2.31206i | 0.129586 | + | 0.0748164i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.1091 | − | 5.65971i | 0.358733 | − | 0.182762i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.38617 | − | 12.7932i | −0.238263 | − | 0.412684i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.0928 | −0.389283 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.92003 | 0.254691 | 0.127345 | − | 0.991858i | \(-0.459354\pi\) | ||||
0.127345 | + | 0.991858i | \(0.459354\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.806196 | − | 1.39637i | −0.0258720 | − | 0.0448117i | 0.852799 | − | 0.522238i | \(-0.174903\pi\) |
−0.878672 | + | 0.477427i | \(0.841570\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −23.0130 | − | 14.9464i | −0.737763 | − | 0.479159i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.4103 | − | 6.58776i | −0.365049 | − | 0.210761i | 0.306244 | − | 0.951953i | \(-0.400928\pi\) |
−0.671293 | + | 0.741192i | \(0.734261\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.6301i | 0.595420i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.52198 | + | 2.63615i | −0.0485437 | + | 0.0840802i | −0.889276 | − | 0.457370i | \(-0.848791\pi\) |
0.840733 | + | 0.541451i | \(0.182125\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.40812 | + | 0.812981i | −0.0448665 | + | 0.0259037i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11.5488 | + | 6.66770i | −0.367230 | + | 0.212021i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.7482 | + | 22.0806i | −0.404961 | + | 0.701414i | −0.994317 | − | 0.106460i | \(-0.966048\pi\) |
0.589356 | + | 0.807874i | \(0.299382\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 5.08691i | − | 0.161266i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.34395 | − | 3.08533i | −0.169245 | − | 0.0977135i | 0.412985 | − | 0.910738i | \(-0.364486\pi\) |
−0.582230 | + | 0.813024i | \(0.697820\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1512.2.bl.d.1025.4 | yes | 16 | |
3.2 | odd | 2 | inner | 1512.2.bl.d.1025.5 | yes | 16 | |
7.5 | odd | 6 | inner | 1512.2.bl.d.593.5 | yes | 16 | |
21.5 | even | 6 | inner | 1512.2.bl.d.593.4 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.bl.d.593.4 | ✓ | 16 | 21.5 | even | 6 | inner | |
1512.2.bl.d.593.5 | yes | 16 | 7.5 | odd | 6 | inner | |
1512.2.bl.d.1025.4 | yes | 16 | 1.1 | even | 1 | trivial | |
1512.2.bl.d.1025.5 | yes | 16 | 3.2 | odd | 2 | inner |