Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1856,2,Mod(1,1856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1856, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1856.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.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: | \(14.8202346151\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 928) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1856.1 |
$q$-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 | ||||||||
\(3\) | 0.414214 | 0.239146 | 0.119573 | − | 0.992825i | \(-0.461847\pi\) | ||||
0.119573 | + | 0.992825i | \(0.461847\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | −0.223607 | − | 0.974679i | \(-0.571783\pi\) | ||||
−0.223607 | + | 0.974679i | \(0.571783\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | 0.755929 | 0.377964 | − | 0.925820i | \(-0.376624\pi\) | ||||
0.377964 | + | 0.925820i | \(0.376624\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.82843 | −0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.41421 | −0.727913 | −0.363956 | − | 0.931416i | \(-0.618574\pi\) | ||||
−0.363956 | + | 0.931416i | \(0.618574\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.82843 | 0.507114 | 0.253557 | − | 0.967320i | \(-0.418399\pi\) | ||||
0.253557 | + | 0.967320i | \(0.418399\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.414214 | −0.106949 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.82843 | 0.685994 | 0.342997 | − | 0.939336i | \(-0.388558\pi\) | ||||
0.342997 | + | 0.939336i | \(0.388558\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.65685 | −1.75660 | −0.878301 | − | 0.478107i | \(-0.841323\pi\) | ||||
−0.878301 | + | 0.478107i | \(0.841323\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.828427 | 0.180778 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.17157 | 0.244290 | 0.122145 | − | 0.992512i | \(-0.461023\pi\) | ||||
0.122145 | + | 0.992512i | \(0.461023\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.41421 | −0.464616 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.41421 | 0.433606 | 0.216803 | − | 0.976215i | \(-0.430437\pi\) | ||||
0.216803 | + | 0.976215i | \(0.430437\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00000 | −0.338062 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.65685 | −0.929981 | −0.464991 | − | 0.885316i | \(-0.653942\pi\) | ||||
−0.464991 | + | 0.885316i | \(0.653942\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.757359 | 0.121275 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.82843 | −0.754074 | −0.377037 | − | 0.926198i | \(-0.623057\pi\) | ||||
−0.377037 | + | 0.926198i | \(0.623057\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.24264 | 0.494498 | 0.247249 | − | 0.968952i | \(-0.420473\pi\) | ||||
0.247249 | + | 0.968952i | \(0.420473\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.82843 | 0.421637 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.41421 | 0.643879 | 0.321940 | − | 0.946760i | \(-0.395665\pi\) | ||||
0.321940 | + | 0.946760i | \(0.395665\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.17157 | 0.164053 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.4853 | −1.57762 | −0.788812 | − | 0.614634i | \(-0.789304\pi\) | ||||
−0.788812 | + | 0.614634i | \(0.789304\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.41421 | 0.325532 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.17157 | −0.420085 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.48528 | 0.583934 | 0.291967 | − | 0.956428i | \(-0.405690\pi\) | ||||
0.291967 | + | 0.956428i | \(0.405690\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.4853 | −1.59858 | −0.799288 | − | 0.600948i | \(-0.794790\pi\) | ||||
−0.799288 | + | 0.600948i | \(0.794790\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.65685 | −0.712697 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.82843 | −0.226788 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.485281 | 0.0584210 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.82843 | 1.04774 | 0.523871 | − | 0.851798i | \(-0.324487\pi\) | ||||
0.523871 | + | 0.851798i | \(0.324487\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.00000 | −0.936329 | −0.468165 | − | 0.883641i | \(-0.655085\pi\) | ||||
−0.468165 | + | 0.883641i | \(0.655085\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.65685 | −0.191317 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.82843 | −0.550250 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.8995 | 1.22629 | 0.613144 | − | 0.789971i | \(-0.289904\pi\) | ||||
0.613144 | + | 0.789971i | \(0.289904\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.48528 | 0.831698 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.4853 | −1.37044 | −0.685219 | − | 0.728337i | \(-0.740293\pi\) | ||||
−0.685219 | + | 0.728337i | \(0.740293\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.82843 | −0.306786 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.414214 | −0.0444084 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.17157 | −0.336186 | −0.168093 | − | 0.985771i | \(-0.553761\pi\) | ||||
−0.168093 | + | 0.985771i | \(0.553761\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.65685 | 0.383342 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.00000 | 0.103695 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.65685 | 0.785577 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.17157 | −0.322024 | −0.161012 | − | 0.986952i | \(-0.551476\pi\) | ||||
−0.161012 | + | 0.986952i | \(0.551476\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.82843 | 0.686283 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.3137 | 1.12576 | 0.562878 | − | 0.826540i | \(-0.309694\pi\) | ||||
0.562878 | + | 0.826540i | \(0.309694\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −20.1421 | −1.98466 | −0.992332 | − | 0.123603i | \(-0.960555\pi\) | ||||
−0.992332 | + | 0.123603i | \(0.960555\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.828427 | −0.0808462 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.00000 | −0.580042 | −0.290021 | − | 0.957020i | \(-0.593662\pi\) | ||||
−0.290021 | + | 0.957020i | \(0.593662\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.656854 | 0.0629152 | 0.0314576 | − | 0.999505i | \(-0.489985\pi\) | ||||
0.0314576 | + | 0.999505i | \(0.489985\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.34315 | −0.222402 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.65685 | −0.344008 | −0.172004 | − | 0.985096i | \(-0.555024\pi\) | ||||
−0.172004 | + | 0.985096i | \(0.555024\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.17157 | −0.109250 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.17157 | −0.478112 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.65685 | 0.518563 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.17157 | −0.470143 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.00000 | −0.180334 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.34315 | −0.740334 | −0.370167 | − | 0.928965i | \(-0.620700\pi\) | ||||
−0.370167 | + | 0.928965i | \(0.620700\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.34315 | 0.118257 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.3137 | 1.51271 | 0.756353 | − | 0.654164i | \(-0.226979\pi\) | ||||
0.756353 | + | 0.654164i | \(0.226979\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −15.3137 | −1.32787 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.41421 | 0.207782 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.31371 | 0.624852 | 0.312426 | − | 0.949942i | \(-0.398858\pi\) | ||||
0.312426 | + | 0.949942i | \(0.398858\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.48528 | 0.380437 | 0.190218 | − | 0.981742i | \(-0.439080\pi\) | ||||
0.190218 | + | 0.981742i | \(0.439080\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.82843 | 0.153981 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.41421 | −0.369135 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.00000 | 0.0830455 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.24264 | −0.102491 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.17157 | −0.505595 | −0.252797 | − | 0.967519i | \(-0.581351\pi\) | ||||
−0.252797 | + | 0.967519i | \(0.581351\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.6569 | −0.948621 | −0.474311 | − | 0.880358i | \(-0.657303\pi\) | ||||
−0.474311 | + | 0.880358i | \(0.657303\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.00000 | −0.646762 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.41421 | −0.193914 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.48528 | 0.517582 | 0.258791 | − | 0.965933i | \(-0.416676\pi\) | ||||
0.258791 | + | 0.965933i | \(0.416676\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.75736 | −0.377283 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.34315 | 0.184666 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.58579 | 0.594165 | 0.297082 | − | 0.954852i | \(-0.403986\pi\) | ||||
0.297082 | + | 0.954852i | \(0.403986\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.00000 | 0.0778499 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.48528 | 0.501846 | 0.250923 | − | 0.968007i | \(-0.419266\pi\) | ||||
0.250923 | + | 0.968007i | \(0.419266\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.65685 | −0.742835 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 21.6569 | 1.65614 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.34315 | 0.330203 | 0.165102 | − | 0.986277i | \(-0.447205\pi\) | ||||
0.165102 | + | 0.986277i | \(0.447205\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.00000 | −0.604743 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.85786 | 0.139646 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.48528 | −0.185759 | −0.0928793 | − | 0.995677i | \(-0.529607\pi\) | ||||
−0.0928793 | + | 0.995677i | \(0.529607\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.68629 | −0.274000 | −0.137000 | − | 0.990571i | \(-0.543746\pi\) | ||||
−0.137000 | + | 0.990571i | \(0.543746\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.17157 | −0.382294 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.65685 | 0.415900 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.82843 | −0.499344 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.82843 | −0.351216 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.3137 | −1.25278 | −0.626388 | − | 0.779511i | \(-0.715467\pi\) | ||||
−0.626388 | + | 0.779511i | \(0.715467\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −27.4558 | −1.97631 | −0.988157 | − | 0.153443i | \(-0.950964\pi\) | ||||
−0.988157 | + | 0.153443i | \(0.950964\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.757359 | −0.0542356 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.31371 | −0.378586 | −0.189293 | − | 0.981921i | \(-0.560620\pi\) | ||||
−0.189293 | + | 0.981921i | \(0.560620\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.34315 | −0.307877 | −0.153939 | − | 0.988080i | \(-0.549196\pi\) | ||||
−0.153939 | + | 0.988080i | \(0.549196\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.65685 | −0.116865 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.00000 | −0.140372 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.82843 | 0.337232 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.31371 | −0.230319 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 18.4853 | 1.27865 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.5858 | 1.34834 | 0.674171 | − | 0.738576i | \(-0.264501\pi\) | ||||
0.674171 | + | 0.738576i | \(0.264501\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.65685 | 0.250564 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.24264 | −0.221146 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.82843 | 0.327775 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.31371 | −0.223920 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.17157 | 0.347878 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.82843 | 0.323335 | 0.161668 | − | 0.986845i | \(-0.448313\pi\) | ||||
0.161668 | + | 0.986845i | \(0.448313\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.3137 | 0.754247 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.7990 | 0.915871 | 0.457936 | − | 0.888985i | \(-0.348589\pi\) | ||||
0.457936 | + | 0.888985i | \(0.348589\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.4853 | −0.692887 | −0.346443 | − | 0.938071i | \(-0.612611\pi\) | ||||
−0.346443 | + | 0.938071i | \(0.612611\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.00000 | −0.131590 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.31371 | −0.282600 | −0.141300 | − | 0.989967i | \(-0.545128\pi\) | ||||
−0.141300 | + | 0.989967i | \(0.545128\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.41421 | −0.287952 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.51472 | 0.293262 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.8284 | 1.21791 | 0.608955 | − | 0.793205i | \(-0.291589\pi\) | ||||
0.608955 | + | 0.793205i | \(0.291589\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.6274 | 1.52198 | 0.760988 | − | 0.648766i | \(-0.224715\pi\) | ||||
0.760988 | + | 0.648766i | \(0.224715\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.3431 | 0.663513 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.00000 | 0.191663 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.0000 | −0.890799 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.17157 | −0.327735 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.24264 | −0.583390 | −0.291695 | − | 0.956511i | \(-0.594219\pi\) | ||||
−0.291695 | + | 0.956511i | \(0.594219\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.82843 | −0.177822 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.17157 | −0.0733667 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.7990 | 0.923136 | 0.461568 | − | 0.887105i | \(-0.347287\pi\) | ||||
0.461568 | + | 0.887105i | \(0.347287\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.3137 | −0.703000 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.82843 | 0.175075 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 25.7279 | 1.58645 | 0.793226 | − | 0.608928i | \(-0.208400\pi\) | ||||
0.793226 | + | 0.608928i | \(0.208400\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.4853 | 0.705535 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.31371 | −0.0803977 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.5147 | 0.702065 | 0.351032 | − | 0.936363i | \(-0.385831\pi\) | ||||
0.351032 | + | 0.936363i | \(0.385831\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.24264 | 0.196976 | 0.0984882 | − | 0.995138i | \(-0.468599\pi\) | ||||
0.0984882 | + | 0.995138i | \(0.468599\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.51472 | 0.0916749 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.65685 | 0.582330 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.00000 | 0.360505 | 0.180253 | − | 0.983620i | \(-0.442309\pi\) | ||||
0.180253 | + | 0.983620i | \(0.442309\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.82843 | −0.408807 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.9706 | −1.31065 | −0.655327 | − | 0.755345i | \(-0.727469\pi\) | ||||
−0.655327 | + | 0.755345i | \(0.727469\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.4853 | 1.21772 | 0.608862 | − | 0.793276i | \(-0.291626\pi\) | ||||
0.608862 | + | 0.793276i | \(0.291626\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.17157 | 0.187868 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.65685 | −0.570026 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.00000 | −0.529412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.31371 | −0.0770110 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.31371 | 0.544113 | 0.272056 | − | 0.962281i | \(-0.412296\pi\) | ||||
0.272056 | + | 0.962281i | \(0.412296\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.48528 | −0.261143 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.82843 | 0.338200 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.14214 | 0.123883 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.48528 | 0.373805 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.68629 | 0.269220 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.4853 | 0.714905 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.92893 | 0.224236 | 0.112118 | − | 0.993695i | \(-0.464237\pi\) | ||||
0.112118 | + | 0.993695i | \(0.464237\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.34315 | −0.474625 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.68629 | 0.379145 | 0.189572 | − | 0.981867i | \(-0.439290\pi\) | ||||
0.189572 | + | 0.981867i | \(0.439290\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.5147 | −0.933467 | −0.466734 | − | 0.884398i | \(-0.654569\pi\) | ||||
−0.466734 | + | 0.884398i | \(0.654569\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.65685 | 0.318728 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.8284 | 1.28217 | 0.641086 | − | 0.767469i | \(-0.278484\pi\) | ||||
0.641086 | + | 0.767469i | \(0.278484\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.41421 | 0.135170 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.48528 | −0.138715 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.6569 | −1.20502 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.31371 | −0.405692 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.272078 | 0.0150459 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.82843 | 0.486727 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.5858 | 0.856672 | 0.428336 | − | 0.903619i | \(-0.359100\pi\) | ||||
0.428336 | + | 0.903619i | \(0.359100\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 16.0000 | 0.876795 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.00000 | 0.218543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.4853 | 0.680117 | 0.340058 | − | 0.940404i | \(-0.389553\pi\) | ||||
0.340058 | + | 0.940404i | \(0.389553\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.51472 | −0.0822682 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.82843 | −0.315627 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.485281 | −0.0261267 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −32.8284 | −1.76232 | −0.881161 | − | 0.472816i | \(-0.843238\pi\) | ||||
−0.881161 | + | 0.472816i | \(0.843238\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.14214 | 0.382310 | 0.191155 | − | 0.981560i | \(-0.438777\pi\) | ||||
0.191155 | + | 0.981560i | \(0.438777\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.41421 | −0.235613 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.65685 | 0.407533 | 0.203767 | − | 0.979019i | \(-0.434682\pi\) | ||||
0.203767 | + | 0.979019i | \(0.434682\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.82843 | −0.468564 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.34315 | 0.124012 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −27.7279 | −1.46342 | −0.731712 | − | 0.681614i | \(-0.761278\pi\) | ||||
−0.731712 | + | 0.681614i | \(0.761278\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 39.6274 | 2.08565 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.14214 | −0.112433 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.00000 | 0.418739 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.02944 | 0.0537362 | 0.0268681 | − | 0.999639i | \(-0.491447\pi\) | ||||
0.0268681 | + | 0.999639i | \(0.491447\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.6569 | 0.710947 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −22.9706 | −1.19257 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.0000 | −0.569558 | −0.284779 | − | 0.958593i | \(-0.591920\pi\) | ||||
−0.284779 | + | 0.958593i | \(0.591920\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.72792 | 0.192509 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.82843 | −0.0941688 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.6274 | 0.854093 | 0.427047 | − | 0.904230i | \(-0.359554\pi\) | ||||
0.427047 | + | 0.904230i | \(0.359554\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.45584 | −0.177048 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.9706 | 1.37813 | 0.689066 | − | 0.724699i | \(-0.258021\pi\) | ||||
0.689066 | + | 0.724699i | \(0.258021\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.82843 | 0.246079 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.17157 | −0.466217 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.970563 | 0.0492095 | 0.0246047 | − | 0.999697i | \(-0.492167\pi\) | ||||
0.0246047 | + | 0.999697i | \(0.492167\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.31371 | 0.167581 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.17157 | 0.361758 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.8995 | −0.548413 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.65685 | −0.233721 | −0.116860 | − | 0.993148i | \(-0.537283\pi\) | ||||
−0.116860 | + | 0.993148i | \(0.537283\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.34315 | −0.317554 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.9706 | −0.697657 | −0.348828 | − | 0.937187i | \(-0.613420\pi\) | ||||
−0.348828 | + | 0.937187i | \(0.613420\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.41421 | 0.219888 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.48528 | −0.371947 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.6569 | 0.676945 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.6274 | −1.41553 | −0.707767 | − | 0.706446i | \(-0.750297\pi\) | ||||
−0.707767 | + | 0.706446i | \(0.750297\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.02944 | 0.149431 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.97056 | 0.441413 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.4853 | 0.612878 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.85786 | 0.0909800 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −36.8284 | −1.79919 | −0.899593 | − | 0.436729i | \(-0.856137\pi\) | ||||
−0.899593 | + | 0.436729i | \(0.856137\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.1421 | 0.494297 | 0.247149 | − | 0.968978i | \(-0.420506\pi\) | ||||
0.247149 | + | 0.968978i | \(0.420506\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.4853 | −0.607055 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.3137 | −0.548795 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −24.9706 | −1.20841 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.82843 | −0.0882773 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.7990 | −0.761011 | −0.380505 | − | 0.924779i | \(-0.624250\pi\) | ||||
−0.380505 | + | 0.924779i | \(0.624250\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.0000 | 1.34559 | 0.672797 | − | 0.739827i | \(-0.265093\pi\) | ||||
0.672797 | + | 0.739827i | \(0.265093\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.414214 | 0.0198600 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.97056 | −0.429120 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.1421 | 1.24770 | 0.623848 | − | 0.781546i | \(-0.285568\pi\) | ||||
0.623848 | + | 0.781546i | \(0.285568\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.48528 | 0.404061 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.6569 | −0.743880 | −0.371940 | − | 0.928257i | \(-0.621307\pi\) | ||||
−0.371940 | + | 0.928257i | \(0.621307\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.17157 | 0.150347 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.55635 | −0.120911 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.6863 | 0.693089 | 0.346544 | − | 0.938034i | \(-0.387355\pi\) | ||||
0.346544 | + | 0.938034i | \(0.387355\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.6569 | 0.548900 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.82843 | −0.226859 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.65685 | −0.171436 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.2843 | −1.22953 | −0.614763 | − | 0.788712i | \(-0.710748\pi\) | ||||
−0.614763 | + | 0.788712i | \(0.710748\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.82843 | −0.318724 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.3137 | 0.806380 | 0.403190 | − | 0.915116i | \(-0.367901\pi\) | ||||
0.403190 | + | 0.915116i | \(0.367901\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.7990 | 1.10603 | 0.553016 | − | 0.833170i | \(-0.313477\pi\) | ||||
0.553016 | + | 0.833170i | \(0.313477\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.00000 | −0.0463739 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.7574 | −0.960536 | −0.480268 | − | 0.877122i | \(-0.659461\pi\) | ||||
−0.480268 | + | 0.877122i | \(0.659461\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.00000 | −0.369406 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.68629 | 0.123778 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.82843 | −0.359951 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 30.6274 | 1.40528 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 32.4853 | 1.48740 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.5563 | 0.665097 | 0.332548 | − | 0.943086i | \(-0.392092\pi\) | ||||
0.332548 | + | 0.943086i | \(0.392092\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.3431 | −0.471607 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.970563 | 0.0441621 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.17157 | 0.144014 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 37.3137 | 1.69085 | 0.845423 | − | 0.534098i | \(-0.179349\pi\) | ||||
0.845423 | + | 0.534098i | \(0.179349\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.14214 | 0.142092 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.7279 | 1.16108 | 0.580542 | − | 0.814230i | \(-0.302841\pi\) | ||||
0.580542 | + | 0.814230i | \(0.302841\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.82843 | −0.127386 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.82843 | −0.306915 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.6569 | 0.792018 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 39.1127 | 1.75092 | 0.875462 | − | 0.483286i | \(-0.160557\pi\) | ||||
0.875462 | + | 0.483286i | \(0.160557\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.68629 | 0.120015 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.9289 | 0.710236 | 0.355118 | − | 0.934821i | \(-0.384441\pi\) | ||||
0.355118 | + | 0.934821i | \(0.384441\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.3137 | −0.503453 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.00000 | −0.177646 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.4558 | 0.818041 | 0.409020 | − | 0.912525i | \(-0.365870\pi\) | ||||
0.409020 | + | 0.912525i | \(0.365870\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.0000 | −0.707798 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 18.4853 | 0.816145 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 20.1421 | 0.887569 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.6569 | −0.468688 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.79899 | 0.0789669 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.1421 | 1.18912 | 0.594559 | − | 0.804052i | \(-0.297327\pi\) | ||||
0.594559 | + | 0.804052i | \(0.297327\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.9706 | −1.26679 | −0.633397 | − | 0.773827i | \(-0.718340\pi\) | ||||
−0.633397 | + | 0.773827i | \(0.718340\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.31371 | −0.144622 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.82843 | 0.297451 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.6274 | −0.940322 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.6863 | −0.550538 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.82843 | −0.382402 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.00000 | 0.259403 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.02944 | −0.0444235 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.24264 | 0.311963 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.62742 | 0.112961 | 0.0564807 | − | 0.998404i | \(-0.482012\pi\) | ||||
0.0564807 | + | 0.998404i | \(0.482012\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.52691 | −0.0655261 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.656854 | −0.0281365 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.31371 | 0.0561701 | 0.0280851 | − | 0.999606i | \(-0.491059\pi\) | ||||
0.0280851 | + | 0.999606i | \(0.491059\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 35.3137 | 1.50715 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.65685 | 0.326193 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 21.7990 | 0.926987 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.34315 | 0.0994610 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 45.3137 | 1.92000 | 0.960002 | − | 0.279994i | \(-0.0903325\pi\) | ||||
0.960002 | + | 0.279994i | \(0.0903325\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.92893 | 0.250767 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.82843 | −0.119416 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16.6985 | −0.703757 | −0.351879 | − | 0.936046i | \(-0.614457\pi\) | ||||
−0.351879 | + | 0.936046i | \(0.614457\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.65685 | 0.153845 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 14.9706 | 0.628705 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.65685 | −0.153303 | −0.0766517 | − | 0.997058i | \(-0.524423\pi\) | ||||
−0.0766517 | + | 0.997058i | \(0.524423\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.2843 | −0.848870 | −0.424435 | − | 0.905458i | \(-0.639527\pi\) | ||||
−0.424435 | + | 0.905458i | \(0.639527\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.17157 | −0.299597 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.68629 | −0.195432 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.4558 | 0.726696 | 0.363348 | − | 0.931653i | \(-0.381634\pi\) | ||||
0.363348 | + | 0.931653i | \(0.381634\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.3726 | −0.472628 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.9706 | −1.03595 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 27.7279 | 1.14837 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.17157 | 0.213818 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −34.8284 | −1.43752 | −0.718762 | − | 0.695257i | \(-0.755291\pi\) | ||||
−0.718762 | + | 0.695257i | \(0.755291\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.4853 | −0.761673 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.20101 | −0.0905375 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.45584 | −0.347240 | −0.173620 | − | 0.984813i | \(-0.555546\pi\) | ||||
−0.173620 | + | 0.984813i | \(0.555546\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.65685 | −0.231908 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.79899 | −0.0736278 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 38.8995 | 1.58939 | 0.794695 | − | 0.607009i | \(-0.207631\pi\) | ||||
0.794695 | + | 0.607009i | \(0.207631\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −44.1421 | −1.80060 | −0.900298 | − | 0.435275i | \(-0.856651\pi\) | ||||
−0.900298 | + | 0.435275i | \(0.856651\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.3137 | 0.460730 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.17157 | 0.210254 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −42.0122 | −1.70522 | −0.852611 | − | 0.522546i | \(-0.824982\pi\) | ||||
−0.852611 | + | 0.522546i | \(0.824982\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.828427 | −0.0335696 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.07107 | 0.326520 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.6274 | 1.19664 | 0.598320 | − | 0.801257i | \(-0.295835\pi\) | ||||
0.598320 | + | 0.801257i | \(0.295835\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.00000 | 0.0806478 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.3137 | 1.26064 | 0.630321 | − | 0.776334i | \(-0.282923\pi\) | ||||
0.630321 | + | 0.776334i | \(0.282923\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.7279 | −0.632159 | −0.316079 | − | 0.948733i | \(-0.602367\pi\) | ||||
−0.316079 | + | 0.948733i | \(0.602367\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.82843 | −0.113501 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.34315 | −0.254133 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.65685 | 0.305785 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −16.0000 | −0.637962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −44.8284 | −1.78459 | −0.892296 | − | 0.451451i | \(-0.850906\pi\) | ||||
−0.892296 | + | 0.451451i | \(0.850906\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.11270 | 0.322451 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.34315 | 0.331088 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.48528 | −0.217335 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −24.9706 | −0.987820 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.7696 | 1.29432 | 0.647160 | − | 0.762354i | \(-0.275957\pi\) | ||||
0.647160 | + | 0.762354i | \(0.275957\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.6569 | 0.775191 | 0.387595 | − | 0.921830i | \(-0.373306\pi\) | ||||
0.387595 | + | 0.921830i | \(0.373306\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.34315 | −0.0528863 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 38.4264 | 1.51070 | 0.755349 | − | 0.655323i | \(-0.227467\pi\) | ||||
0.755349 | + | 0.655323i | \(0.227467\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.8284 | −0.425053 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.00000 | 0.0783862 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −26.4853 | −1.03645 | −0.518225 | − | 0.855245i | \(-0.673407\pi\) | ||||
−0.518225 | + | 0.855245i | \(0.673407\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.3137 | −0.676503 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 22.6274 | 0.882780 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29.2426 | −1.13913 | −0.569566 | − | 0.821946i | \(-0.692889\pi\) | ||||
−0.569566 | + | 0.821946i | \(0.692889\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.0000 | −0.388955 | −0.194477 | − | 0.980907i | \(-0.562301\pi\) | ||||
−0.194477 | + | 0.980907i | \(0.562301\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.14214 | 0.0831937 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.3137 | 0.593840 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.17157 | −0.0453635 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.00000 | 0.0773245 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 30.1421 | 1.16362 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.68629 | −0.142096 | −0.0710480 | − | 0.997473i | \(-0.522634\pi\) | ||||
−0.0710480 | + | 0.997473i | \(0.522634\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.65685 | 0.371692 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.00000 | −0.230599 | −0.115299 | − | 0.993331i | \(-0.536783\pi\) | ||||
−0.115299 | + | 0.993331i | \(0.536783\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.34315 | −0.243428 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.71573 | 0.219027 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.97056 | −0.343249 | −0.171625 | − | 0.985162i | \(-0.554902\pi\) | ||||
−0.171625 | + | 0.985162i | \(0.554902\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.31371 | −0.279442 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.34315 | −0.165701 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −21.0000 | −0.800036 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.3431 | 1.30647 | 0.653237 | − | 0.757153i | \(-0.273410\pi\) | ||||
0.653237 | + | 0.757153i | \(0.273410\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 13.6569 | 0.518781 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.48528 | −0.170136 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.6569 | −0.517290 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.78680 | −0.0675829 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33.7696 | −1.27546 | −0.637729 | − | 0.770261i | \(-0.720126\pi\) | ||||
−0.637729 | + | 0.770261i | \(0.720126\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 43.3137 | 1.63361 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.82843 | −0.0688625 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 22.6274 | 0.850992 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.17157 | 0.156667 | 0.0783334 | − | 0.996927i | \(-0.475040\pi\) | ||||
0.0783334 | + | 0.996927i | \(0.475040\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −30.8284 | −1.15616 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.82843 | 0.105925 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.41421 | 0.165082 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.79899 | 0.291259 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.1421 | −0.900350 | −0.450175 | − | 0.892940i | \(-0.648638\pi\) | ||||
−0.450175 | + | 0.892940i | \(0.648638\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −40.2843 | −1.50026 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.78680 | 0.363975 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.00000 | 0.148556 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.31371 | −0.0487228 | −0.0243614 | − | 0.999703i | \(-0.507755\pi\) | ||||
−0.0243614 | + | 0.999703i | \(0.507755\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.1716 | −0.673021 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.17157 | 0.339223 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32.9706 | −1.21780 | −0.608898 | − | 0.793249i | \(-0.708388\pi\) | ||||
−0.608898 | + | 0.793249i | \(0.708388\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.24264 | 0.0458355 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.65685 | 0.355715 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.92893 | −0.218099 | −0.109050 | − | 0.994036i | \(-0.534781\pi\) | ||||
−0.109050 | + | 0.994036i | \(0.534781\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.79899 | −0.213031 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −51.2548 | −1.88036 | −0.940179 | − | 0.340682i | \(-0.889342\pi\) | ||||
−0.940179 | + | 0.340682i | \(0.889342\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.17157 | 0.226109 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 35.3137 | 1.29206 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.0000 | −0.438470 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.3431 | −0.742332 | −0.371166 | − | 0.928567i | \(-0.621042\pi\) | ||||
−0.371166 | + | 0.928567i | \(0.621042\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.82843 | −0.139516 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.6569 | 0.424236 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.7990 | 1.15575 | 0.577877 | − | 0.816124i | \(-0.303881\pi\) | ||||
0.577877 | + | 0.816124i | \(0.303881\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.17157 | −0.0425254 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −42.9706 | −1.55768 | −0.778841 | − | 0.627222i | \(-0.784192\pi\) | ||||
−0.778841 | + | 0.627222i | \(0.784192\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.31371 | 0.0475594 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.00000 | 0.289241 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.20101 | 0.296121 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −45.4558 | −1.63918 | −0.819590 | − | 0.572951i | \(-0.805799\pi\) | ||||
−0.819590 | + | 0.572951i | \(0.805799\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.12994 | 0.220764 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −44.8284 | −1.61237 | −0.806183 | − | 0.591666i | \(-0.798470\pi\) | ||||
−0.806183 | + | 0.591666i | \(0.798470\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.65685 | −0.346884 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.68629 | −0.168120 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 36.9706 | 1.32461 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.3137 | −0.762664 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.41421 | 0.0862770 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.48528 | −0.231470 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −41.7990 | −1.48997 | −0.744987 | − | 0.667079i | \(-0.767544\pi\) | ||||
−0.744987 | + | 0.667079i | \(0.767544\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.6569 | 0.379394 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.31371 | −0.260046 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22.8284 | −0.810661 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.75736 | 0.168726 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.1421 | 0.642627 | 0.321314 | − | 0.946973i | \(-0.395876\pi\) | ||||
0.321314 | + | 0.946973i | \(0.395876\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.4853 | 0.441698 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.97056 | 0.316959 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.3137 | 0.681566 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.34315 | −0.0825850 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.76955 | 0.167896 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.3137 | 0.679034 | 0.339517 | − | 0.940600i | \(-0.389736\pi\) | ||||
0.339517 | + | 0.940600i | \(0.389736\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.3431 | −0.854803 | −0.427402 | − | 0.904062i | \(-0.640571\pi\) | ||||
−0.427402 | + | 0.904062i | \(0.640571\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.34315 | 0.0471062 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.58579 | −0.265719 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.8284 | −0.868637 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −10.3431 | −0.361419 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34.7990 | 1.21449 | 0.607247 | − | 0.794513i | \(-0.292274\pi\) | ||||
0.607247 | + | 0.794513i | \(0.292274\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35.6569 | −1.24292 | −0.621460 | − | 0.783446i | \(-0.713460\pi\) | ||||
−0.621460 | + | 0.783446i | \(0.713460\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.00000 | 0.139262 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.2426 | 0.877773 | 0.438886 | − | 0.898543i | \(-0.355373\pi\) | ||||
0.438886 | + | 0.898543i | \(0.355373\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28.4853 | −0.989335 | −0.494667 | − | 0.869082i | \(-0.664710\pi\) | ||||
−0.494667 | + | 0.869082i | \(0.664710\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.48528 | 0.0862135 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.48528 | −0.293998 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.48528 | −0.224432 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.82843 | −0.201460 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −34.2132 | −1.18117 | −0.590585 | − | 0.806975i | \(-0.701103\pi\) | ||||
−0.590585 | + | 0.806975i | \(0.701103\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.10051 | −0.313438 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.65685 | 0.332206 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.3431 | −0.355395 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.48528 | 0.291214 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.62742 | −0.227185 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.0000 | −0.753266 | −0.376633 | − | 0.926363i | \(-0.622918\pi\) | ||||
−0.376633 | + | 0.926363i | \(0.622918\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −21.6569 | −0.740649 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.4558 | −0.767077 | −0.383539 | − | 0.923525i | \(-0.625295\pi\) | ||||
−0.383539 | + | 0.923525i | \(0.625295\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.4437 | 0.731648 | 0.365824 | − | 0.930684i | \(-0.380787\pi\) | ||||
0.365824 | + | 0.930684i | \(0.380787\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.00000 | −0.136320 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −34.4853 | −1.17389 | −0.586946 | − | 0.809626i | \(-0.699670\pi\) | ||||
−0.586946 | + | 0.809626i | \(0.699670\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.34315 | −0.147671 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.72792 | −0.126607 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −26.3137 | −0.892631 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.31371 | −0.247816 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.97056 | 0.303608 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 18.0000 | 0.608511 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −35.4853 | −1.19825 | −0.599126 | − | 0.800654i | \(-0.704485\pi\) | ||||
−0.599126 | + | 0.800654i | \(0.704485\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.85786 | 0.130123 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.2843 | −1.02030 | −0.510152 | − | 0.860085i | \(-0.670411\pi\) | ||||
−0.510152 | + | 0.860085i | \(0.670411\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.6274 | −0.424946 | −0.212473 | − | 0.977167i | \(-0.568152\pi\) | ||||
−0.212473 | + | 0.977167i | \(0.568152\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.85786 | −0.0624514 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 37.0416 | 1.24374 | 0.621868 | − | 0.783122i | \(-0.286374\pi\) | ||||
0.621868 | + | 0.783122i | \(0.286374\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.6863 | −0.559640 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.0711 | −0.605404 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −33.7990 | −1.13104 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.48528 | 0.0830738 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.887302 | 0.0296261 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.41421 | −0.0805185 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32.4853 | −1.08224 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.68629 | 0.0893942 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.68629 | 0.122536 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −46.2843 | −1.53684 | −0.768422 | − | 0.639943i | \(-0.778958\pi\) | ||||
−0.768422 | + | 0.639943i | \(0.778958\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −32.0000 | −1.06137 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.0711 | −1.06256 | −0.531281 | − | 0.847196i | \(-0.678289\pi\) | ||||
−0.531281 | + | 0.847196i | \(0.678289\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30.1421 | 0.997559 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.17157 | 0.170967 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 34.6274 | 1.14350 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.2010 | 0.468448 | 0.234224 | − | 0.972183i | \(-0.424745\pi\) | ||||
0.234224 | + | 0.972183i | \(0.424745\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.62742 | 0.0536252 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.1421 | 0.531325 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22.6274 | 0.743985 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 56.9706 | 1.87116 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −34.0000 | −1.11550 | −0.557752 | − | 0.830008i | \(-0.688336\pi\) | ||||
−0.557752 | + | 0.830008i | \(0.688336\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.9706 | 0.752830 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.76955 | 0.0906711 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.82843 | 0.223313 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.6863 | 1.00248 | 0.501239 | − | 0.865309i | \(-0.332878\pi\) | ||||
0.501239 | + | 0.865309i | \(0.332878\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.84062 | −0.223235 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.6569 | 0.803790 | 0.401895 | − | 0.915686i | \(-0.368352\pi\) | ||||
0.401895 | + | 0.915686i | \(0.368352\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.65685 | −0.184213 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.82843 | 0.157069 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.07107 | −0.132292 | −0.0661460 | − | 0.997810i | \(-0.521070\pi\) | ||||
−0.0661460 | + | 0.997810i | \(0.521070\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.6274 | −0.474826 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.45584 | 0.306627 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28.3137 | −0.917171 | −0.458585 | − | 0.888650i | \(-0.651644\pi\) | ||||
−0.458585 | + | 0.888650i | \(0.651644\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.3137 | 0.560258 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.00000 | 0.0323254 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.6274 | 0.472344 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.1716 | −0.811986 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.9706 | 0.546869 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 27.4558 | 0.883835 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.5269 | −0.949521 | −0.474761 | − | 0.880115i | \(-0.657465\pi\) | ||||
−0.474761 | + | 0.880115i | \(0.657465\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.97056 | −0.288176 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.9706 | 1.37899 | 0.689495 | − | 0.724290i | \(-0.257832\pi\) | ||||
0.689495 | + | 0.724290i | \(0.257832\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.97056 | 0.287583 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.02944 | −0.0970196 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 36.4558 | 1.16633 | 0.583163 | − | 0.812355i | \(-0.301815\pi\) | ||||
0.583163 | + | 0.812355i | \(0.301815\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.65685 | 0.244714 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.85786 | −0.0593170 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −38.2132 | −1.21881 | −0.609406 | − | 0.792858i | \(-0.708592\pi\) | ||||
−0.609406 | + | 0.792858i | \(0.708592\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.31371 | 0.169309 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.65685 | 0.116399 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.79899 | 0.120801 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.7696 | −0.596234 | −0.298117 | − | 0.954529i | \(-0.596359\pi\) | ||||
−0.298117 | + | 0.954529i | \(0.596359\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.45584 | 0.204870 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.34315 | 0.137687 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.686292 | 0.0217351 | 0.0108675 | − | 0.999941i | \(-0.496541\pi\) | ||||
0.0108675 | + | 0.999941i | \(0.496541\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 13.6569 | 0.432084 |
(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 | 1856.2.a.q.1.2 | 2 | ||
4.3 | odd | 2 | 1856.2.a.u.1.1 | 2 | |||
8.3 | odd | 2 | 928.2.a.c.1.2 | ✓ | 2 | ||
8.5 | even | 2 | 928.2.a.e.1.1 | yes | 2 | ||
24.5 | odd | 2 | 8352.2.a.o.1.1 | 2 | |||
24.11 | even | 2 | 8352.2.a.l.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
928.2.a.c.1.2 | ✓ | 2 | 8.3 | odd | 2 | ||
928.2.a.e.1.1 | yes | 2 | 8.5 | even | 2 | ||
1856.2.a.q.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1856.2.a.u.1.1 | 2 | 4.3 | odd | 2 | |||
8352.2.a.l.1.2 | 2 | 24.11 | even | 2 | |||
8352.2.a.o.1.1 | 2 | 24.5 | odd | 2 |