Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [729,2,Mod(1,729)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(729, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("729.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 729 = 3^{6} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 729.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: | \(5.82109430735\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.7459857.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 3x^{5} - 6x^{4} + 13x^{3} + 12x^{2} - 12x - 8 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.17298\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 729.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.70506 | −1.91277 | −0.956385 | − | 0.292110i | \(-0.905643\pi\) | ||||
−0.956385 | + | 0.292110i | \(0.905643\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.31738 | 2.65869 | ||||||||
\(5\) | 1.67238 | 0.747913 | 0.373957 | − | 0.927446i | \(-0.378001\pi\) | ||||
0.373957 | + | 0.927446i | \(0.378001\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500591 | 0.189206 | 0.0946028 | − | 0.995515i | \(-0.469842\pi\) | ||||
0.0946028 | + | 0.995515i | \(0.469842\pi\) | |||||||
\(8\) | −8.97372 | −3.17269 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.52391 | −1.43059 | ||||||||
\(11\) | 1.91772 | 0.578214 | 0.289107 | − | 0.957297i | \(-0.406642\pi\) | ||||
0.289107 | + | 0.957297i | \(0.406642\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.11244 | 0.863234 | 0.431617 | − | 0.902057i | \(-0.357943\pi\) | ||||
0.431617 | + | 0.902057i | \(0.357943\pi\) | |||||||
\(14\) | −1.35413 | −0.361907 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 13.6397 | 3.40993 | ||||||||
\(17\) | −2.66467 | −0.646278 | −0.323139 | − | 0.946352i | \(-0.604738\pi\) | ||||
−0.323139 | + | 0.946352i | \(0.604738\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.79664 | 1.32984 | 0.664920 | − | 0.746915i | \(-0.268466\pi\) | ||||
0.664920 | + | 0.746915i | \(0.268466\pi\) | |||||||
\(20\) | 8.89270 | 1.98847 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.18755 | −1.10599 | ||||||||
\(23\) | 4.64587 | 0.968731 | 0.484365 | − | 0.874866i | \(-0.339051\pi\) | ||||
0.484365 | + | 0.874866i | \(0.339051\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.20313 | −0.440626 | ||||||||
\(26\) | −8.41934 | −1.65117 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.66183 | 0.503039 | ||||||||
\(29\) | 2.61507 | 0.485606 | 0.242803 | − | 0.970076i | \(-0.421933\pi\) | ||||
0.242803 | + | 0.970076i | \(0.421933\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.61460 | −0.828807 | −0.414404 | − | 0.910093i | \(-0.636010\pi\) | ||||
−0.414404 | + | 0.910093i | \(0.636010\pi\) | |||||||
\(32\) | −18.9489 | −3.34973 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.20811 | 1.23618 | ||||||||
\(35\) | 0.837181 | 0.141509 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.85867 | −0.798761 | −0.399381 | − | 0.916785i | \(-0.630775\pi\) | ||||
−0.399381 | + | 0.916785i | \(0.630775\pi\) | |||||||
\(38\) | −15.6803 | −2.54368 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −15.0075 | −2.37290 | ||||||||
\(41\) | 11.5482 | 1.80352 | 0.901760 | − | 0.432237i | \(-0.142276\pi\) | ||||
0.901760 | + | 0.432237i | \(0.142276\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.00434 | −1.37315 | −0.686574 | − | 0.727060i | \(-0.740886\pi\) | ||||
−0.686574 | + | 0.727060i | \(0.740886\pi\) | |||||||
\(44\) | 10.1972 | 1.53729 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12.5674 | −1.85296 | ||||||||
\(47\) | −6.83224 | −0.996584 | −0.498292 | − | 0.867009i | \(-0.666039\pi\) | ||||
−0.498292 | + | 0.867009i | \(0.666039\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.74941 | −0.964201 | ||||||||
\(50\) | 5.95961 | 0.842816 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 16.5500 | 2.29507 | ||||||||
\(53\) | 5.43322 | 0.746309 | 0.373155 | − | 0.927769i | \(-0.378276\pi\) | ||||
0.373155 | + | 0.927769i | \(0.378276\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.20716 | 0.432454 | ||||||||
\(56\) | −4.49216 | −0.600291 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.07393 | −0.928853 | ||||||||
\(59\) | 2.19131 | 0.285285 | 0.142642 | − | 0.989774i | \(-0.454440\pi\) | ||||
0.142642 | + | 0.989774i | \(0.454440\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.84034 | 0.875815 | 0.437908 | − | 0.899020i | \(-0.355720\pi\) | ||||
0.437908 | + | 0.899020i | \(0.355720\pi\) | |||||||
\(62\) | 12.4828 | 1.58532 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 23.9786 | 2.99733 | ||||||||
\(65\) | 5.20519 | 0.645624 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.4836 | 1.52511 | 0.762557 | − | 0.646921i | \(-0.223944\pi\) | ||||
0.762557 | + | 0.646921i | \(0.223944\pi\) | |||||||
\(68\) | −14.1691 | −1.71825 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.26463 | −0.270675 | ||||||||
\(71\) | 2.83568 | 0.336534 | 0.168267 | − | 0.985741i | \(-0.446183\pi\) | ||||
0.168267 | + | 0.985741i | \(0.446183\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.93497 | 1.16280 | 0.581400 | − | 0.813618i | \(-0.302505\pi\) | ||||
0.581400 | + | 0.813618i | \(0.302505\pi\) | |||||||
\(74\) | 13.1430 | 1.52785 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 30.8229 | 3.53563 | ||||||||
\(77\) | 0.959993 | 0.109401 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.31121 | 0.597558 | 0.298779 | − | 0.954322i | \(-0.403421\pi\) | ||||
0.298779 | + | 0.954322i | \(0.403421\pi\) | |||||||
\(80\) | 22.8109 | 2.55033 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −31.2385 | −3.44972 | ||||||||
\(83\) | 2.72815 | 0.299453 | 0.149727 | − | 0.988727i | \(-0.452161\pi\) | ||||
0.149727 | + | 0.988727i | \(0.452161\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.45636 | −0.483360 | ||||||||
\(86\) | 24.3573 | 2.62652 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −17.2091 | −1.83449 | ||||||||
\(89\) | −11.2189 | −1.18920 | −0.594600 | − | 0.804021i | \(-0.702690\pi\) | ||||
−0.594600 | + | 0.804021i | \(0.702690\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.55806 | 0.163329 | ||||||||
\(92\) | 24.7038 | 2.57555 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 18.4816 | 1.90624 | ||||||||
\(95\) | 9.69421 | 0.994605 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.88914 | −0.699486 | −0.349743 | − | 0.936846i | \(-0.613731\pi\) | ||||
−0.349743 | + | 0.936846i | \(0.613731\pi\) | |||||||
\(98\) | 18.2576 | 1.84429 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −11.7149 | −1.17149 | ||||||||
\(101\) | −3.72965 | −0.371114 | −0.185557 | − | 0.982634i | \(-0.559409\pi\) | ||||
−0.185557 | + | 0.982634i | \(0.559409\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.68080 | 0.756811 | 0.378406 | − | 0.925640i | \(-0.376472\pi\) | ||||
0.378406 | + | 0.925640i | \(0.376472\pi\) | |||||||
\(104\) | −27.9301 | −2.73877 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14.6972 | −1.42752 | ||||||||
\(107\) | 10.7658 | 1.04077 | 0.520383 | − | 0.853933i | \(-0.325789\pi\) | ||||
0.520383 | + | 0.853933i | \(0.325789\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.2298 | 1.17141 | 0.585703 | − | 0.810526i | \(-0.300819\pi\) | ||||
0.585703 | + | 0.810526i | \(0.300819\pi\) | |||||||
\(110\) | −8.67558 | −0.827184 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 6.82793 | 0.645179 | ||||||||
\(113\) | 1.94395 | 0.182871 | 0.0914357 | − | 0.995811i | \(-0.470854\pi\) | ||||
0.0914357 | + | 0.995811i | \(0.470854\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.76968 | 0.724526 | ||||||||
\(116\) | 13.9053 | 1.29108 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.92764 | −0.545684 | ||||||||
\(119\) | −1.33391 | −0.122279 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.32236 | −0.665669 | ||||||||
\(122\) | −18.5036 | −1.67523 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −24.5376 | −2.20354 | ||||||||
\(125\) | −12.0464 | −1.07746 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.34433 | 0.208026 | 0.104013 | − | 0.994576i | \(-0.466832\pi\) | ||||
0.104013 | + | 0.994576i | \(0.466832\pi\) | |||||||
\(128\) | −26.9659 | −2.38347 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −14.0804 | −1.23493 | ||||||||
\(131\) | 17.1024 | 1.49424 | 0.747121 | − | 0.664688i | \(-0.231435\pi\) | ||||
0.747121 | + | 0.664688i | \(0.231435\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.90174 | 0.251613 | ||||||||
\(134\) | −33.7689 | −2.91719 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 23.9120 | 2.05044 | ||||||||
\(137\) | −13.9272 | −1.18988 | −0.594939 | − | 0.803771i | \(-0.702824\pi\) | ||||
−0.594939 | + | 0.803771i | \(0.702824\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.91664 | 0.671480 | 0.335740 | − | 0.941955i | \(-0.391014\pi\) | ||||
0.335740 | + | 0.941955i | \(0.391014\pi\) | |||||||
\(140\) | 4.45161 | 0.376229 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.67071 | −0.643712 | ||||||||
\(143\) | 5.96877 | 0.499134 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.37340 | 0.363191 | ||||||||
\(146\) | −26.8747 | −2.22417 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −25.8354 | −2.12366 | ||||||||
\(149\) | −0.728134 | −0.0596511 | −0.0298255 | − | 0.999555i | \(-0.509495\pi\) | ||||
−0.0298255 | + | 0.999555i | \(0.509495\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.34209 | 0.353354 | 0.176677 | − | 0.984269i | \(-0.443465\pi\) | ||||
0.176677 | + | 0.984269i | \(0.443465\pi\) | |||||||
\(152\) | −52.0174 | −4.21917 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.59684 | −0.209260 | ||||||||
\(155\) | −7.71739 | −0.619876 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.5233 | −1.23889 | −0.619446 | − | 0.785040i | \(-0.712643\pi\) | ||||
−0.619446 | + | 0.785040i | \(0.712643\pi\) | |||||||
\(158\) | −14.3672 | −1.14299 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −31.6899 | −2.50531 | ||||||||
\(161\) | 2.32568 | 0.183289 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.49738 | 0.665566 | 0.332783 | − | 0.943003i | \(-0.392012\pi\) | ||||
0.332783 | + | 0.943003i | \(0.392012\pi\) | |||||||
\(164\) | 61.4059 | 4.79500 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.37982 | −0.572785 | ||||||||
\(167\) | −23.1419 | −1.79078 | −0.895389 | − | 0.445285i | \(-0.853102\pi\) | ||||
−0.895389 | + | 0.445285i | \(0.853102\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.31275 | −0.254827 | ||||||||
\(170\) | 12.0547 | 0.924556 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −47.8794 | −3.65077 | ||||||||
\(173\) | 2.57848 | 0.196038 | 0.0980190 | − | 0.995185i | \(-0.468749\pi\) | ||||
0.0980190 | + | 0.995185i | \(0.468749\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.10287 | −0.0833689 | ||||||||
\(176\) | 26.1572 | 1.97167 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 30.3478 | 2.27467 | ||||||||
\(179\) | 8.89613 | 0.664928 | 0.332464 | − | 0.943116i | \(-0.392120\pi\) | ||||
0.332464 | + | 0.943116i | \(0.392120\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.91183 | 0.588082 | 0.294041 | − | 0.955793i | \(-0.405000\pi\) | ||||
0.294041 | + | 0.955793i | \(0.405000\pi\) | |||||||
\(182\) | −4.21465 | −0.312410 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −41.6907 | −3.07348 | ||||||||
\(185\) | −8.12557 | −0.597404 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.11009 | −0.373687 | ||||||||
\(188\) | −36.3296 | −2.64961 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −26.2235 | −1.90245 | ||||||||
\(191\) | 15.8973 | 1.15029 | 0.575146 | − | 0.818051i | \(-0.304945\pi\) | ||||
0.575146 | + | 0.818051i | \(0.304945\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.58478 | −0.330020 | −0.165010 | − | 0.986292i | \(-0.552766\pi\) | ||||
−0.165010 | + | 0.986292i | \(0.552766\pi\) | |||||||
\(194\) | 18.6356 | 1.33796 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −35.8891 | −2.56351 | ||||||||
\(197\) | −2.99417 | −0.213326 | −0.106663 | − | 0.994295i | \(-0.534017\pi\) | ||||
−0.106663 | + | 0.994295i | \(0.534017\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.8885 | 1.05542 | 0.527709 | − | 0.849425i | \(-0.323051\pi\) | ||||
0.527709 | + | 0.849425i | \(0.323051\pi\) | |||||||
\(200\) | 19.7703 | 1.39797 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.0889 | 0.709855 | ||||||||
\(203\) | 1.30908 | 0.0918795 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.3130 | 1.34888 | ||||||||
\(206\) | −20.7771 | −1.44761 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 42.4528 | 2.94357 | ||||||||
\(209\) | 11.1163 | 0.768932 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.8790 | 0.955467 | 0.477733 | − | 0.878505i | \(-0.341458\pi\) | ||||
0.477733 | + | 0.878505i | \(0.341458\pi\) | |||||||
\(212\) | 28.8904 | 1.98420 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −29.1221 | −1.99074 | ||||||||
\(215\) | −15.0587 | −1.02700 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.31003 | −0.156815 | ||||||||
\(218\) | −33.0825 | −2.24063 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 17.0537 | 1.14976 | ||||||||
\(221\) | −8.29362 | −0.557889 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.81198 | −0.456164 | −0.228082 | − | 0.973642i | \(-0.573245\pi\) | ||||
−0.228082 | + | 0.973642i | \(0.573245\pi\) | |||||||
\(224\) | −9.48567 | −0.633788 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.25851 | −0.349791 | ||||||||
\(227\) | 9.74084 | 0.646522 | 0.323261 | − | 0.946310i | \(-0.395221\pi\) | ||||
0.323261 | + | 0.946310i | \(0.395221\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.0448 | −0.928109 | −0.464055 | − | 0.885807i | \(-0.653606\pi\) | ||||
−0.464055 | + | 0.885807i | \(0.653606\pi\) | |||||||
\(230\) | −21.0175 | −1.38585 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −23.4669 | −1.54068 | ||||||||
\(233\) | −5.32333 | −0.348743 | −0.174372 | − | 0.984680i | \(-0.555789\pi\) | ||||
−0.174372 | + | 0.984680i | \(0.555789\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.4261 | −0.745359 | ||||||||
\(236\) | 11.6520 | 0.758483 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.60832 | 0.233892 | ||||||||
\(239\) | −17.7735 | −1.14967 | −0.574836 | − | 0.818268i | \(-0.694934\pi\) | ||||
−0.574836 | + | 0.818268i | \(0.694934\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.00679 | −0.129269 | −0.0646344 | − | 0.997909i | \(-0.520588\pi\) | ||||
−0.0646344 | + | 0.997909i | \(0.520588\pi\) | |||||||
\(242\) | 19.8075 | 1.27327 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 36.3726 | 2.32852 | ||||||||
\(245\) | −11.2876 | −0.721139 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.0417 | 1.14796 | ||||||||
\(248\) | 41.4101 | 2.62955 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 32.5863 | 2.06094 | ||||||||
\(251\) | −23.5643 | −1.48737 | −0.743683 | − | 0.668533i | \(-0.766923\pi\) | ||||
−0.743683 | + | 0.668533i | \(0.766923\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.90947 | 0.560133 | ||||||||
\(254\) | −6.34157 | −0.397906 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 24.9871 | 1.56170 | ||||||||
\(257\) | −5.87457 | −0.366445 | −0.183223 | − | 0.983071i | \(-0.558653\pi\) | ||||
−0.183223 | + | 0.983071i | \(0.558653\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.43221 | −0.151130 | ||||||||
\(260\) | 27.6779 | 1.71651 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −46.2631 | −2.85814 | ||||||||
\(263\) | −21.9781 | −1.35523 | −0.677615 | − | 0.735417i | \(-0.736986\pi\) | ||||
−0.677615 | + | 0.735417i | \(0.736986\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.08643 | 0.558175 | ||||||||
\(266\) | −7.84941 | −0.481278 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 66.3800 | 4.05480 | ||||||||
\(269\) | 30.6026 | 1.86587 | 0.932937 | − | 0.360041i | \(-0.117237\pi\) | ||||
0.932937 | + | 0.360041i | \(0.117237\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.0823 | −0.976928 | −0.488464 | − | 0.872584i | \(-0.662443\pi\) | ||||
−0.488464 | + | 0.872584i | \(0.662443\pi\) | |||||||
\(272\) | −36.3454 | −2.20376 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 37.6739 | 2.27596 | ||||||||
\(275\) | −4.22498 | −0.254776 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.8136 | −1.25057 | −0.625283 | − | 0.780398i | \(-0.715017\pi\) | ||||
−0.625283 | + | 0.780398i | \(0.715017\pi\) | |||||||
\(278\) | −21.4150 | −1.28439 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7.51263 | −0.448965 | ||||||||
\(281\) | −12.2603 | −0.731387 | −0.365693 | − | 0.930735i | \(-0.619168\pi\) | ||||
−0.365693 | + | 0.930735i | \(0.619168\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.57258 | 0.271812 | 0.135906 | − | 0.990722i | \(-0.456606\pi\) | ||||
0.135906 | + | 0.990722i | \(0.456606\pi\) | |||||||
\(284\) | 15.0784 | 0.894738 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −16.1459 | −0.954728 | ||||||||
\(287\) | 5.78091 | 0.341236 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.89952 | −0.582325 | ||||||||
\(290\) | −11.8303 | −0.694702 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 52.8280 | 3.09152 | ||||||||
\(293\) | −26.1234 | −1.52615 | −0.763073 | − | 0.646312i | \(-0.776310\pi\) | ||||
−0.763073 | + | 0.646312i | \(0.776310\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.66472 | 0.213368 | ||||||||
\(296\) | 43.6004 | 2.53422 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.96965 | 0.114099 | ||||||||
\(299\) | 14.4600 | 0.836241 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.50749 | −0.259807 | ||||||||
\(302\) | −11.7456 | −0.675885 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 79.0646 | 4.53466 | ||||||||
\(305\) | 11.4397 | 0.655034 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.29277 | 0.187928 | 0.0939641 | − | 0.995576i | \(-0.470046\pi\) | ||||
0.0939641 | + | 0.995576i | \(0.470046\pi\) | |||||||
\(308\) | 5.10464 | 0.290864 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 20.8760 | 1.18568 | ||||||||
\(311\) | −34.7926 | −1.97291 | −0.986455 | − | 0.164034i | \(-0.947549\pi\) | ||||
−0.986455 | + | 0.164034i | \(0.947549\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.6278 | 0.600721 | 0.300360 | − | 0.953826i | \(-0.402893\pi\) | ||||
0.300360 | + | 0.953826i | \(0.402893\pi\) | |||||||
\(314\) | 41.9914 | 2.36971 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 28.2417 | 1.58872 | ||||||||
\(317\) | 15.5002 | 0.870579 | 0.435290 | − | 0.900290i | \(-0.356646\pi\) | ||||
0.435290 | + | 0.900290i | \(0.356646\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.01497 | 0.280784 | ||||||||
\(320\) | 40.1015 | 2.24174 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.29112 | −0.350590 | ||||||||
\(323\) | −15.4461 | −0.859446 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.85710 | −0.380363 | ||||||||
\(326\) | −22.9860 | −1.27308 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −103.630 | −5.72201 | ||||||||
\(329\) | −3.42016 | −0.188559 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.5703 | −0.800855 | −0.400427 | − | 0.916328i | \(-0.631138\pi\) | ||||
−0.400427 | + | 0.916328i | \(0.631138\pi\) | |||||||
\(332\) | 14.5066 | 0.796153 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 62.6005 | 3.42534 | ||||||||
\(335\) | 20.8774 | 1.14065 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.6148 | −1.12296 | −0.561479 | − | 0.827491i | \(-0.689768\pi\) | ||||
−0.561479 | + | 0.827491i | \(0.689768\pi\) | |||||||
\(338\) | 8.96120 | 0.487425 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −23.6961 | −1.28510 | ||||||||
\(341\) | −8.84951 | −0.479228 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.88283 | −0.371638 | ||||||||
\(344\) | 80.8024 | 4.35657 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.97495 | −0.374976 | ||||||||
\(347\) | 21.1835 | 1.13719 | 0.568596 | − | 0.822617i | \(-0.307487\pi\) | ||||
0.568596 | + | 0.822617i | \(0.307487\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.62597 | −0.247623 | −0.123811 | − | 0.992306i | \(-0.539512\pi\) | ||||
−0.123811 | + | 0.992306i | \(0.539512\pi\) | |||||||
\(350\) | 2.98333 | 0.159466 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −36.3387 | −1.93686 | ||||||||
\(353\) | 13.6434 | 0.726165 | 0.363083 | − | 0.931757i | \(-0.381724\pi\) | ||||
0.363083 | + | 0.931757i | \(0.381724\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.74236 | 0.251698 | ||||||||
\(356\) | −59.6551 | −3.16171 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −24.0646 | −1.27185 | ||||||||
\(359\) | 28.2447 | 1.49070 | 0.745349 | − | 0.666675i | \(-0.232283\pi\) | ||||
0.745349 | + | 0.666675i | \(0.232283\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.6010 | 0.768473 | ||||||||
\(362\) | −21.4020 | −1.12486 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.28478 | 0.434240 | ||||||||
\(365\) | 16.6151 | 0.869674 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.8802 | 1.82073 | 0.910366 | − | 0.413804i | \(-0.135800\pi\) | ||||
0.910366 | + | 0.413804i | \(0.135800\pi\) | |||||||
\(368\) | 63.3684 | 3.30331 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 21.9802 | 1.14270 | ||||||||
\(371\) | 2.71982 | 0.141206 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.05944 | 0.158412 | 0.0792059 | − | 0.996858i | \(-0.474762\pi\) | ||||
0.0792059 | + | 0.996858i | \(0.474762\pi\) | |||||||
\(374\) | 13.8231 | 0.714777 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 61.3106 | 3.16185 | ||||||||
\(377\) | 8.13924 | 0.419192 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.67705 | −0.394344 | −0.197172 | − | 0.980369i | \(-0.563176\pi\) | ||||
−0.197172 | + | 0.980369i | \(0.563176\pi\) | |||||||
\(380\) | 51.5477 | 2.64434 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −43.0034 | −2.20024 | ||||||||
\(383\) | −10.3619 | −0.529470 | −0.264735 | − | 0.964321i | \(-0.585285\pi\) | ||||
−0.264735 | + | 0.964321i | \(0.585285\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.60548 | 0.0818227 | ||||||||
\(386\) | 12.4021 | 0.631252 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −36.6322 | −1.85972 | ||||||||
\(389\) | 0.426951 | 0.0216473 | 0.0108236 | − | 0.999941i | \(-0.496555\pi\) | ||||
0.0108236 | + | 0.999941i | \(0.496555\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.3797 | −0.626069 | ||||||||
\(392\) | 60.5673 | 3.05911 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.09942 | 0.408043 | ||||||||
\(395\) | 8.88239 | 0.446922 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.0891 | −1.35956 | −0.679781 | − | 0.733416i | \(-0.737925\pi\) | ||||
−0.679781 | + | 0.733416i | \(0.737925\pi\) | |||||||
\(398\) | −40.2743 | −2.01877 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −30.0501 | −1.50250 | ||||||||
\(401\) | −29.3605 | −1.46619 | −0.733096 | − | 0.680125i | \(-0.761925\pi\) | ||||
−0.733096 | + | 0.680125i | \(0.761925\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.3627 | −0.715455 | ||||||||
\(404\) | −19.8319 | −0.986675 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.54115 | −0.175744 | ||||||||
\(407\) | −9.31757 | −0.461855 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.1839 | −0.998031 | −0.499015 | − | 0.866593i | \(-0.666305\pi\) | ||||
−0.499015 | + | 0.866593i | \(0.666305\pi\) | |||||||
\(410\) | −52.2428 | −2.58009 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 40.8417 | 2.01213 | ||||||||
\(413\) | 1.09695 | 0.0539775 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.56252 | 0.223965 | ||||||||
\(416\) | −58.9773 | −2.89160 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −30.0704 | −1.47079 | ||||||||
\(419\) | −24.3703 | −1.19057 | −0.595284 | − | 0.803515i | \(-0.702960\pi\) | ||||
−0.595284 | + | 0.803515i | \(0.702960\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.1745 | −1.27567 | −0.637835 | − | 0.770173i | \(-0.720170\pi\) | ||||
−0.637835 | + | 0.770173i | \(0.720170\pi\) | |||||||
\(422\) | −37.5435 | −1.82759 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −48.7561 | −2.36781 | ||||||||
\(425\) | 5.87062 | 0.284767 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.42421 | 0.165709 | ||||||||
\(428\) | 57.2456 | 2.76707 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 40.7348 | 1.96441 | ||||||||
\(431\) | −31.9185 | −1.53746 | −0.768731 | − | 0.639572i | \(-0.779111\pi\) | ||||
−0.768731 | + | 0.639572i | \(0.779111\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.0123080 | 0.000591484 0 | 0.000295742 | − | 1.00000i | \(-0.499906\pi\) | ||||
0.000295742 | 1.00000i | \(0.499906\pi\) | ||||||||
\(434\) | 6.24878 | 0.299951 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 65.0306 | 3.11440 | ||||||||
\(437\) | 26.9304 | 1.28826 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.30480 | 0.253185 | 0.126592 | − | 0.991955i | \(-0.459596\pi\) | ||||
0.126592 | + | 0.991955i | \(0.459596\pi\) | |||||||
\(440\) | −28.7802 | −1.37204 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 22.4348 | 1.06711 | ||||||||
\(443\) | −40.6963 | −1.93354 | −0.966771 | − | 0.255645i | \(-0.917712\pi\) | ||||
−0.966771 | + | 0.255645i | \(0.917712\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.7623 | −0.889419 | ||||||||
\(446\) | 18.4268 | 0.872536 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 12.0035 | 0.567111 | ||||||||
\(449\) | −15.4280 | −0.728093 | −0.364047 | − | 0.931381i | \(-0.618605\pi\) | ||||
−0.364047 | + | 0.931381i | \(0.618605\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.1461 | 1.04282 | ||||||||
\(452\) | 10.3367 | 0.486198 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −26.3496 | −1.23665 | ||||||||
\(455\) | 2.60567 | 0.122156 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.38875 | 0.111741 | 0.0558704 | − | 0.998438i | \(-0.482207\pi\) | ||||
0.0558704 | + | 0.998438i | \(0.482207\pi\) | |||||||
\(458\) | 37.9922 | 1.77526 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 41.3143 | 1.92629 | ||||||||
\(461\) | −32.4839 | −1.51292 | −0.756462 | − | 0.654037i | \(-0.773074\pi\) | ||||
−0.756462 | + | 0.654037i | \(0.773074\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 33.8785 | 1.57447 | 0.787234 | − | 0.616654i | \(-0.211512\pi\) | ||||
0.787234 | + | 0.616654i | \(0.211512\pi\) | |||||||
\(464\) | 35.6689 | 1.65589 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.4000 | 0.667065 | ||||||||
\(467\) | 13.8027 | 0.638711 | 0.319356 | − | 0.947635i | \(-0.396534\pi\) | ||||
0.319356 | + | 0.947635i | \(0.396534\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.24918 | 0.288560 | ||||||||
\(470\) | 30.9084 | 1.42570 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −19.6642 | −0.905119 | ||||||||
\(473\) | −17.2678 | −0.793973 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.7707 | −0.585962 | ||||||||
\(476\) | −7.09291 | −0.325103 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 48.0785 | 2.19906 | ||||||||
\(479\) | −5.89112 | −0.269172 | −0.134586 | − | 0.990902i | \(-0.542970\pi\) | ||||
−0.134586 | + | 0.990902i | \(0.542970\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.1223 | −0.689518 | ||||||||
\(482\) | 5.42850 | 0.247262 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −38.9357 | −1.76981 | ||||||||
\(485\) | −11.5213 | −0.523155 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.0299 | 1.31547 | 0.657736 | − | 0.753249i | \(-0.271514\pi\) | ||||
0.657736 | + | 0.753249i | \(0.271514\pi\) | |||||||
\(488\) | −61.3832 | −2.77869 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 30.5337 | 1.37937 | ||||||||
\(491\) | −4.38351 | −0.197825 | −0.0989125 | − | 0.995096i | \(-0.531536\pi\) | ||||
−0.0989125 | + | 0.995096i | \(0.531536\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.96830 | −0.313837 | ||||||||
\(494\) | −48.8038 | −2.19579 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −62.9420 | −2.82618 | ||||||||
\(497\) | 1.41952 | 0.0636741 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 35.3435 | 1.58219 | 0.791096 | − | 0.611691i | \(-0.209511\pi\) | ||||
0.791096 | + | 0.611691i | \(0.209511\pi\) | |||||||
\(500\) | −64.0553 | −2.86464 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 63.7430 | 2.84499 | ||||||||
\(503\) | 8.37659 | 0.373494 | 0.186747 | − | 0.982408i | \(-0.440206\pi\) | ||||
0.186747 | + | 0.982408i | \(0.440206\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.23740 | −0.277561 | ||||||||
\(506\) | −24.1007 | −1.07141 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12.4657 | 0.553076 | ||||||||
\(509\) | 3.84297 | 0.170337 | 0.0851683 | − | 0.996367i | \(-0.472857\pi\) | ||||
0.0851683 | + | 0.996367i | \(0.472857\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.97336 | 0.220008 | ||||||||
\(512\) | −13.6601 | −0.603699 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.8911 | 0.700925 | ||||||||
\(515\) | 12.8452 | 0.566029 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.1023 | −0.576239 | ||||||||
\(518\) | 6.57928 | 0.289077 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −46.7099 | −2.04836 | ||||||||
\(521\) | −19.6523 | −0.860983 | −0.430491 | − | 0.902595i | \(-0.641660\pi\) | ||||
−0.430491 | + | 0.902595i | \(0.641660\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −39.6103 | −1.73204 | −0.866018 | − | 0.500012i | \(-0.833329\pi\) | ||||
−0.866018 | + | 0.500012i | \(0.833329\pi\) | |||||||
\(524\) | 90.9398 | 3.97272 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 59.4523 | 2.59224 | ||||||||
\(527\) | 12.2964 | 0.535640 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.41591 | −0.0615611 | ||||||||
\(530\) | −24.5794 | −1.06766 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 15.4297 | 0.668961 | ||||||||
\(533\) | 35.9429 | 1.55686 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.0045 | 0.778402 | ||||||||
\(536\) | −112.024 | −4.83871 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −82.7820 | −3.56899 | ||||||||
\(539\) | −12.9435 | −0.557514 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −41.8257 | −1.79823 | −0.899115 | − | 0.437713i | \(-0.855788\pi\) | ||||
−0.899115 | + | 0.437713i | \(0.855788\pi\) | |||||||
\(542\) | 43.5036 | 1.86864 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 50.4927 | 2.16486 | ||||||||
\(545\) | 20.4530 | 0.876110 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.0343 | −0.728335 | −0.364168 | − | 0.931333i | \(-0.618646\pi\) | ||||
−0.364168 | + | 0.931333i | \(0.618646\pi\) | |||||||
\(548\) | −74.0559 | −3.16351 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 11.4288 | 0.487328 | ||||||||
\(551\) | 15.1586 | 0.645779 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.65875 | 0.113061 | ||||||||
\(554\) | 56.3021 | 2.39205 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 42.0957 | 1.78526 | ||||||||
\(557\) | 33.7680 | 1.43080 | 0.715398 | − | 0.698717i | \(-0.246245\pi\) | ||||
0.715398 | + | 0.698717i | \(0.246245\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −28.0254 | −1.18535 | ||||||||
\(560\) | 11.4189 | 0.482538 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 33.1648 | 1.39897 | ||||||||
\(563\) | 22.7113 | 0.957166 | 0.478583 | − | 0.878042i | \(-0.341151\pi\) | ||||
0.478583 | + | 0.878042i | \(0.341151\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.25103 | 0.136772 | ||||||||
\(566\) | −12.3691 | −0.519913 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −25.4466 | −1.06772 | ||||||||
\(569\) | −10.8714 | −0.455755 | −0.227877 | − | 0.973690i | \(-0.573179\pi\) | ||||
−0.227877 | + | 0.973690i | \(0.573179\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.8837 | 0.622864 | 0.311432 | − | 0.950268i | \(-0.399191\pi\) | ||||
0.311432 | + | 0.950268i | \(0.399191\pi\) | |||||||
\(572\) | 31.7382 | 1.32704 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −15.6377 | −0.652706 | ||||||||
\(575\) | −10.2354 | −0.426848 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.1163 | −1.54517 | −0.772586 | − | 0.634910i | \(-0.781037\pi\) | ||||
−0.772586 | + | 0.634910i | \(0.781037\pi\) | |||||||
\(578\) | 26.7789 | 1.11385 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 23.2550 | 0.965613 | ||||||||
\(581\) | 1.36569 | 0.0566583 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.4194 | 0.431526 | ||||||||
\(584\) | −89.1536 | −3.68920 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 70.6655 | 2.91917 | ||||||||
\(587\) | −14.6432 | −0.604390 | −0.302195 | − | 0.953246i | \(-0.597719\pi\) | ||||
−0.302195 | + | 0.953246i | \(0.597719\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.7492 | −1.10218 | ||||||||
\(590\) | −9.91330 | −0.408124 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −66.2710 | −2.72372 | ||||||||
\(593\) | 36.4392 | 1.49638 | 0.748189 | − | 0.663485i | \(-0.230924\pi\) | ||||
0.748189 | + | 0.663485i | \(0.230924\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.23081 | −0.0914544 | ||||||||
\(596\) | −3.87176 | −0.158594 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −39.1151 | −1.59954 | ||||||||
\(599\) | 27.4949 | 1.12341 | 0.561705 | − | 0.827337i | \(-0.310145\pi\) | ||||
0.561705 | + | 0.827337i | \(0.310145\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 45.1770 | 1.84281 | 0.921404 | − | 0.388606i | \(-0.127043\pi\) | ||||
0.921404 | + | 0.388606i | \(0.127043\pi\) | |||||||
\(602\) | 12.1931 | 0.496952 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 23.0885 | 0.939459 | ||||||||
\(605\) | −12.2458 | −0.497863 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.1372 | 0.695576 | 0.347788 | − | 0.937573i | \(-0.386933\pi\) | ||||
0.347788 | + | 0.937573i | \(0.386933\pi\) | |||||||
\(608\) | −109.840 | −4.45460 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −30.9451 | −1.25293 | ||||||||
\(611\) | −21.2649 | −0.860286 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.468761 | −0.0189331 | −0.00946653 | − | 0.999955i | \(-0.503013\pi\) | ||||
−0.00946653 | + | 0.999955i | \(0.503013\pi\) | |||||||
\(614\) | −8.90715 | −0.359463 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.61470 | −0.347096 | ||||||||
\(617\) | −2.13485 | −0.0859458 | −0.0429729 | − | 0.999076i | \(-0.513683\pi\) | ||||
−0.0429729 | + | 0.999076i | \(0.513683\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.53760 | 0.343155 | 0.171578 | − | 0.985171i | \(-0.445114\pi\) | ||||
0.171578 | + | 0.985171i | \(0.445114\pi\) | |||||||
\(620\) | −41.0363 | −1.64806 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 94.1163 | 3.77372 | ||||||||
\(623\) | −5.61608 | −0.225004 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.13058 | −0.365223 | ||||||||
\(626\) | −28.7490 | −1.14904 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −82.5430 | −3.29383 | ||||||||
\(629\) | 12.9468 | 0.516222 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.8708 | −0.472569 | −0.236284 | − | 0.971684i | \(-0.575930\pi\) | ||||
−0.236284 | + | 0.971684i | \(0.575930\pi\) | |||||||
\(632\) | −47.6613 | −1.89587 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −41.9291 | −1.66522 | ||||||||
\(635\) | 3.92063 | 0.155585 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −21.0071 | −0.832331 | ||||||||
\(638\) | −13.5658 | −0.537076 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −45.0973 | −1.78263 | ||||||||
\(641\) | 5.30366 | 0.209482 | 0.104741 | − | 0.994500i | \(-0.466599\pi\) | ||||
0.104741 | + | 0.994500i | \(0.466599\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.823869 | −0.0324902 | −0.0162451 | − | 0.999868i | \(-0.505171\pi\) | ||||
−0.0162451 | + | 0.999868i | \(0.505171\pi\) | |||||||
\(644\) | 12.3665 | 0.487309 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 41.7828 | 1.64392 | ||||||||
\(647\) | −40.8373 | −1.60548 | −0.802740 | − | 0.596329i | \(-0.796626\pi\) | ||||
−0.802740 | + | 0.596329i | \(0.796626\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.20232 | 0.164955 | ||||||||
\(650\) | 18.5489 | 0.727547 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 45.1838 | 1.76953 | ||||||||
\(653\) | 1.06936 | 0.0418472 | 0.0209236 | − | 0.999781i | \(-0.493339\pi\) | ||||
0.0209236 | + | 0.999781i | \(0.493339\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 28.6018 | 1.11756 | ||||||||
\(656\) | 157.514 | 6.14988 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9.25175 | 0.360671 | ||||||||
\(659\) | −28.6643 | −1.11660 | −0.558301 | − | 0.829638i | \(-0.688547\pi\) | ||||
−0.558301 | + | 0.829638i | \(0.688547\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.49572 | −0.174863 | −0.0874316 | − | 0.996171i | \(-0.527866\pi\) | ||||
−0.0874316 | + | 0.996171i | \(0.527866\pi\) | |||||||
\(662\) | 39.4135 | 1.53185 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −24.4816 | −0.950072 | ||||||||
\(665\) | 4.85283 | 0.188185 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.1493 | 0.470422 | ||||||||
\(668\) | −123.054 | −4.76112 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −56.4747 | −2.18181 | ||||||||
\(671\) | 13.1178 | 0.506409 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.0586 | 0.696107 | 0.348054 | − | 0.937475i | \(-0.386843\pi\) | ||||
0.348054 | + | 0.937475i | \(0.386843\pi\) | |||||||
\(674\) | 55.7643 | 2.14796 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −17.6151 | −0.677505 | ||||||||
\(677\) | 15.7392 | 0.604906 | 0.302453 | − | 0.953164i | \(-0.402195\pi\) | ||||
0.302453 | + | 0.953164i | \(0.402195\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.44864 | −0.132347 | ||||||||
\(680\) | 39.9901 | 1.53355 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 23.9385 | 0.916652 | ||||||||
\(683\) | −2.76118 | −0.105654 | −0.0528268 | − | 0.998604i | \(-0.516823\pi\) | ||||
−0.0528268 | + | 0.998604i | \(0.516823\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −23.2916 | −0.889925 | ||||||||
\(686\) | 18.6185 | 0.710858 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −122.817 | −4.68234 | ||||||||
\(689\) | 16.9105 | 0.644240 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.5255 | −1.31341 | −0.656707 | − | 0.754146i | \(-0.728051\pi\) | ||||
−0.656707 | + | 0.754146i | \(0.728051\pi\) | |||||||
\(692\) | 13.7107 | 0.521204 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −57.3029 | −2.17519 | ||||||||
\(695\) | 13.2397 | 0.502209 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30.7721 | −1.16557 | ||||||||
\(698\) | 12.5136 | 0.473645 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.86436 | −0.221652 | ||||||||
\(701\) | −20.7410 | −0.783378 | −0.391689 | − | 0.920098i | \(-0.628109\pi\) | ||||
−0.391689 | + | 0.920098i | \(0.628109\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −28.1640 | −1.06222 | ||||||||
\(704\) | 45.9842 | 1.73310 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −36.9063 | −1.38899 | ||||||||
\(707\) | −1.86703 | −0.0702168 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.7071 | 1.04056 | 0.520281 | − | 0.853995i | \(-0.325827\pi\) | ||||
0.520281 | + | 0.853995i | \(0.325827\pi\) | |||||||
\(710\) | −12.8284 | −0.481441 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 100.675 | 3.77296 | ||||||||
\(713\) | −21.4388 | −0.802891 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.98209 | 0.373309 | ||||||||
\(716\) | 47.3041 | 1.76784 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −76.4037 | −2.85136 | ||||||||
\(719\) | 33.1314 | 1.23559 | 0.617797 | − | 0.786337i | \(-0.288025\pi\) | ||||
0.617797 | + | 0.786337i | \(0.288025\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.84494 | 0.143193 | ||||||||
\(722\) | −39.4966 | −1.46991 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 42.0702 | 1.56353 | ||||||||
\(725\) | −5.76134 | −0.213971 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.0826055 | −0.00306367 | −0.00153183 | − | 0.999999i | \(-0.500488\pi\) | ||||
−0.00153183 | + | 0.999999i | \(0.500488\pi\) | |||||||
\(728\) | −13.9816 | −0.518191 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −44.9449 | −1.66349 | ||||||||
\(731\) | 23.9936 | 0.887435 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.9175 | −1.17890 | −0.589450 | − | 0.807805i | \(-0.700655\pi\) | ||||
−0.589450 | + | 0.807805i | \(0.700655\pi\) | |||||||
\(734\) | −94.3532 | −3.48264 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −88.0342 | −3.24498 | ||||||||
\(737\) | 23.9400 | 0.881842 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.7919 | −1.31663 | −0.658314 | − | 0.752744i | \(-0.728730\pi\) | ||||
−0.658314 | + | 0.752744i | \(0.728730\pi\) | |||||||
\(740\) | −43.2067 | −1.58831 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.35729 | −0.270095 | ||||||||
\(743\) | 19.7789 | 0.725616 | 0.362808 | − | 0.931864i | \(-0.381818\pi\) | ||||
0.362808 | + | 0.931864i | \(0.381818\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.21772 | −0.0446138 | ||||||||
\(746\) | −8.27598 | −0.303005 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −27.1723 | −0.993517 | ||||||||
\(749\) | 5.38924 | 0.196919 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.5806 | 1.11590 | 0.557950 | − | 0.829874i | \(-0.311588\pi\) | ||||
0.557950 | + | 0.829874i | \(0.311588\pi\) | |||||||
\(752\) | −93.1899 | −3.39829 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −22.0172 | −0.801818 | ||||||||
\(755\) | 7.26165 | 0.264278 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.4129 | 0.923647 | 0.461824 | − | 0.886972i | \(-0.347195\pi\) | ||||
0.461824 | + | 0.886972i | \(0.347195\pi\) | |||||||
\(758\) | 20.7669 | 0.754289 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −86.9931 | −3.15557 | ||||||||
\(761\) | 46.8180 | 1.69715 | 0.848575 | − | 0.529075i | \(-0.177461\pi\) | ||||
0.848575 | + | 0.529075i | \(0.177461\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.12215 | 0.221637 | ||||||||
\(764\) | 84.5322 | 3.05827 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 28.0297 | 1.01275 | ||||||||
\(767\) | 6.82032 | 0.246267 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.5654 | 0.525243 | 0.262621 | − | 0.964899i | \(-0.415413\pi\) | ||||
0.262621 | + | 0.964899i | \(0.415413\pi\) | |||||||
\(770\) | −4.34292 | −0.156508 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −24.3790 | −0.877419 | ||||||||
\(773\) | −24.3533 | −0.875929 | −0.437964 | − | 0.898992i | \(-0.644300\pi\) | ||||
−0.437964 | + | 0.898992i | \(0.644300\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.1666 | 0.365194 | ||||||||
\(776\) | 61.8212 | 2.21925 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.15493 | −0.0414063 | ||||||||
\(779\) | 66.9405 | 2.39839 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.43804 | 0.194589 | ||||||||
\(782\) | 33.4879 | 1.19753 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −92.0601 | −3.28786 | ||||||||
\(785\) | −25.9609 | −0.926583 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27.5672 | −0.982664 | −0.491332 | − | 0.870972i | \(-0.663490\pi\) | ||||
−0.491332 | + | 0.870972i | \(0.663490\pi\) | |||||||
\(788\) | −15.9211 | −0.567166 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −24.0274 | −0.854858 | ||||||||
\(791\) | 0.973124 | 0.0346003 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.2901 | 0.756034 | ||||||||
\(794\) | 73.2777 | 2.60053 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 79.1677 | 2.80603 | ||||||||
\(797\) | 6.61692 | 0.234383 | 0.117192 | − | 0.993109i | \(-0.462611\pi\) | ||||
0.117192 | + | 0.993109i | \(0.462611\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.2057 | 0.644070 | ||||||||
\(800\) | 41.7469 | 1.47598 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 79.4220 | 2.80449 | ||||||||
\(803\) | 19.0525 | 0.672347 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.88943 | 0.137084 | ||||||||
\(806\) | 38.8519 | 1.36850 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 33.4688 | 1.17743 | ||||||||
\(809\) | 8.61362 | 0.302839 | 0.151419 | − | 0.988470i | \(-0.451616\pi\) | ||||
0.151419 | + | 0.988470i | \(0.451616\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.58716 | −0.336651 | −0.168325 | − | 0.985732i | \(-0.553836\pi\) | ||||
−0.168325 | + | 0.985732i | \(0.553836\pi\) | |||||||
\(812\) | 6.96088 | 0.244279 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 25.2046 | 0.883422 | ||||||||
\(815\) | 14.2109 | 0.497786 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −52.1949 | −1.82607 | ||||||||
\(818\) | 54.5988 | 1.90900 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 102.694 | 3.58624 | ||||||||
\(821\) | 13.8635 | 0.483838 | 0.241919 | − | 0.970296i | \(-0.422223\pi\) | ||||
0.241919 | + | 0.970296i | \(0.422223\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 47.8257 | 1.66710 | 0.833550 | − | 0.552444i | \(-0.186305\pi\) | ||||
0.833550 | + | 0.552444i | \(0.186305\pi\) | |||||||
\(824\) | −68.9253 | −2.40113 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.96733 | −0.103246 | ||||||||
\(827\) | 42.4417 | 1.47584 | 0.737921 | − | 0.674887i | \(-0.235808\pi\) | ||||
0.737921 | + | 0.674887i | \(0.235808\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.0037 | 0.903146 | 0.451573 | − | 0.892234i | \(-0.350863\pi\) | ||||
0.451573 | + | 0.892234i | \(0.350863\pi\) | |||||||
\(830\) | −12.3419 | −0.428394 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 74.6319 | 2.58740 | ||||||||
\(833\) | 17.9850 | 0.623142 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −38.7022 | −1.33935 | ||||||||
\(836\) | 59.1096 | 2.04435 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 65.9233 | 2.27728 | ||||||||
\(839\) | −1.25628 | −0.0433715 | −0.0216857 | − | 0.999765i | \(-0.506903\pi\) | ||||
−0.0216857 | + | 0.999765i | \(0.506903\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.1614 | −0.764186 | ||||||||
\(842\) | 70.8038 | 2.44006 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 73.7996 | 2.54029 | ||||||||
\(845\) | −5.54019 | −0.190588 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.66551 | −0.125948 | ||||||||
\(848\) | 74.1076 | 2.54487 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −15.8804 | −0.544693 | ||||||||
\(851\) | −22.5728 | −0.773784 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.45435 | 0.0497959 | 0.0248979 | − | 0.999690i | \(-0.492074\pi\) | ||||
0.0248979 | + | 0.999690i | \(0.492074\pi\) | |||||||
\(854\) | −9.26272 | −0.316964 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −96.6089 | −3.30202 | ||||||||
\(857\) | 52.3097 | 1.78686 | 0.893432 | − | 0.449198i | \(-0.148290\pi\) | ||||
0.893432 | + | 0.449198i | \(0.148290\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.0043 | −0.716659 | −0.358329 | − | 0.933595i | \(-0.616654\pi\) | ||||
−0.358329 | + | 0.933595i | \(0.616654\pi\) | |||||||
\(860\) | −80.0728 | −2.73046 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 86.3417 | 2.94081 | ||||||||
\(863\) | −12.9813 | −0.441890 | −0.220945 | − | 0.975286i | \(-0.570914\pi\) | ||||
−0.220945 | + | 0.975286i | \(0.570914\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.31221 | 0.146619 | ||||||||
\(866\) | −0.0332939 | −0.00113137 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −12.2833 | −0.416922 | ||||||||
\(869\) | 10.1854 | 0.345516 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.8544 | 1.31653 | ||||||||
\(872\) | −109.747 | −3.71650 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −72.8485 | −2.46414 | ||||||||
\(875\) | −6.03032 | −0.203862 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.0457 | 1.04834 | 0.524169 | − | 0.851614i | \(-0.324376\pi\) | ||||
0.524169 | + | 0.851614i | \(0.324376\pi\) | |||||||
\(878\) | −14.3498 | −0.484284 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 43.7448 | 1.47464 | ||||||||
\(881\) | −19.2957 | −0.650087 | −0.325044 | − | 0.945699i | \(-0.605379\pi\) | ||||
−0.325044 | + | 0.945699i | \(0.605379\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.82388 | −0.330600 | −0.165300 | − | 0.986243i | \(-0.552859\pi\) | ||||
−0.165300 | + | 0.986243i | \(0.552859\pi\) | |||||||
\(884\) | −44.1003 | −1.48325 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 110.086 | 3.69842 | ||||||||
\(887\) | −44.1133 | −1.48118 | −0.740590 | − | 0.671958i | \(-0.765454\pi\) | ||||
−0.740590 | + | 0.671958i | \(0.765454\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.17355 | 0.0393597 | ||||||||
\(890\) | 50.7533 | 1.70125 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −36.2219 | −1.21280 | ||||||||
\(893\) | −39.6040 | −1.32530 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.8778 | 0.497308 | ||||||||
\(896\) | −13.4989 | −0.450965 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 41.7338 | 1.39268 | ||||||||
\(899\) | −12.0675 | −0.402474 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.4777 | −0.482323 | ||||||||
\(902\) | −59.9067 | −1.99467 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −17.4444 | −0.580194 | ||||||||
\(905\) | 13.2316 | 0.439834 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42.4124 | −1.40828 | −0.704140 | − | 0.710061i | \(-0.748667\pi\) | ||||
−0.704140 | + | 0.710061i | \(0.748667\pi\) | |||||||
\(908\) | 51.7957 | 1.71890 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7.04851 | −0.233656 | ||||||||
\(911\) | −36.7104 | −1.21627 | −0.608134 | − | 0.793834i | \(-0.708082\pi\) | ||||
−0.608134 | + | 0.793834i | \(0.708082\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.23182 | 0.173148 | ||||||||
\(914\) | −6.46171 | −0.213735 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −74.6817 | −2.46755 | ||||||||
\(917\) | 8.56130 | 0.282719 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.0589 | −0.463761 | −0.231881 | − | 0.972744i | \(-0.574488\pi\) | ||||
−0.231881 | + | 0.972744i | \(0.574488\pi\) | |||||||
\(920\) | −69.7229 | −2.29870 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 87.8710 | 2.89388 | ||||||||
\(923\) | 8.82588 | 0.290508 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.7043 | 0.351955 | ||||||||
\(926\) | −91.6436 | −3.01160 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −49.5528 | −1.62665 | ||||||||
\(929\) | 18.5175 | 0.607539 | 0.303770 | − | 0.952746i | \(-0.401755\pi\) | ||||
0.303770 | + | 0.952746i | \(0.401755\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −39.1239 | −1.28223 | ||||||||
\(932\) | −28.3062 | −0.927199 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −37.3371 | −1.22171 | ||||||||
\(935\) | −8.54604 | −0.279485 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.46818 | 0.145969 | 0.0729845 | − | 0.997333i | \(-0.476748\pi\) | ||||
0.0729845 | + | 0.997333i | \(0.476748\pi\) | |||||||
\(938\) | −16.9044 | −0.551949 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −60.7570 | −1.98168 | ||||||||
\(941\) | 2.00386 | 0.0653239 | 0.0326620 | − | 0.999466i | \(-0.489602\pi\) | ||||
0.0326620 | + | 0.999466i | \(0.489602\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 53.6512 | 1.74712 | ||||||||
\(944\) | 29.8889 | 0.972801 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 46.7105 | 1.51869 | ||||||||
\(947\) | 12.5838 | 0.408919 | 0.204460 | − | 0.978875i | \(-0.434456\pi\) | ||||
0.204460 | + | 0.978875i | \(0.434456\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30.9220 | 1.00377 | ||||||||
\(950\) | 34.5457 | 1.12081 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 11.9701 | 0.387955 | ||||||||
\(953\) | 19.9641 | 0.646700 | 0.323350 | − | 0.946279i | \(-0.395191\pi\) | ||||
0.323350 | + | 0.946279i | \(0.395191\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 26.5865 | 0.860318 | ||||||||
\(956\) | −94.5084 | −3.05662 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 15.9359 | 0.514864 | ||||||||
\(959\) | −6.97181 | −0.225132 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.70544 | −0.313079 | ||||||||
\(962\) | 40.9068 | 1.31889 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.6709 | −0.343686 | ||||||||
\(965\) | −7.66752 | −0.246826 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.2086 | −1.03576 | −0.517879 | − | 0.855454i | \(-0.673278\pi\) | ||||
−0.517879 | + | 0.855454i | \(0.673278\pi\) | |||||||
\(968\) | 65.7088 | 2.11196 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 31.1659 | 1.00068 | ||||||||
\(971\) | 6.62934 | 0.212746 | 0.106373 | − | 0.994326i | \(-0.466076\pi\) | ||||
0.106373 | + | 0.994326i | \(0.466076\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.96300 | 0.127048 | ||||||||
\(974\) | −78.5278 | −2.51619 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 93.3004 | 2.98647 | ||||||||
\(977\) | −11.8566 | −0.379328 | −0.189664 | − | 0.981849i | \(-0.560740\pi\) | ||||
−0.189664 | + | 0.981849i | \(0.560740\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −21.5147 | −0.687612 | ||||||||
\(980\) | −60.0205 | −1.91728 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 11.8577 | 0.378394 | ||||||||
\(983\) | 52.0650 | 1.66062 | 0.830308 | − | 0.557305i | \(-0.188165\pi\) | ||||
0.830308 | + | 0.557305i | \(0.188165\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.00740 | −0.159549 | ||||||||
\(986\) | 18.8497 | 0.600297 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 95.9343 | 3.05208 | ||||||||
\(989\) | −41.8330 | −1.33021 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.47115 | 0.0467326 | 0.0233663 | − | 0.999727i | \(-0.492562\pi\) | ||||
0.0233663 | + | 0.999727i | \(0.492562\pi\) | |||||||
\(992\) | 87.4418 | 2.77628 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.83989 | −0.121794 | ||||||||
\(995\) | 24.8993 | 0.789361 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.4213 | −0.836771 | −0.418385 | − | 0.908270i | \(-0.637404\pi\) | ||||
−0.418385 | + | 0.908270i | \(0.637404\pi\) | |||||||
\(998\) | −95.6065 | −3.02637 | ||||||||
\(999\) | 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 | 729.2.a.b.1.1 | ✓ | 6 | |
3.2 | odd | 2 | 729.2.a.e.1.6 | yes | 6 | ||
9.2 | odd | 6 | 729.2.c.a.244.1 | 12 | |||
9.4 | even | 3 | 729.2.c.d.487.6 | 12 | |||
9.5 | odd | 6 | 729.2.c.a.487.1 | 12 | |||
9.7 | even | 3 | 729.2.c.d.244.6 | 12 | |||
27.2 | odd | 18 | 729.2.e.k.568.1 | 12 | |||
27.4 | even | 9 | 729.2.e.j.406.1 | 12 | |||
27.5 | odd | 18 | 729.2.e.l.649.2 | 12 | |||
27.7 | even | 9 | 729.2.e.j.325.1 | 12 | |||
27.11 | odd | 18 | 729.2.e.l.82.2 | 12 | |||
27.13 | even | 9 | 729.2.e.t.163.2 | 12 | |||
27.14 | odd | 18 | 729.2.e.k.163.1 | 12 | |||
27.16 | even | 9 | 729.2.e.s.82.1 | 12 | |||
27.20 | odd | 18 | 729.2.e.u.325.2 | 12 | |||
27.22 | even | 9 | 729.2.e.s.649.1 | 12 | |||
27.23 | odd | 18 | 729.2.e.u.406.2 | 12 | |||
27.25 | even | 9 | 729.2.e.t.568.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
729.2.a.b.1.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
729.2.a.e.1.6 | yes | 6 | 3.2 | odd | 2 | ||
729.2.c.a.244.1 | 12 | 9.2 | odd | 6 | |||
729.2.c.a.487.1 | 12 | 9.5 | odd | 6 | |||
729.2.c.d.244.6 | 12 | 9.7 | even | 3 | |||
729.2.c.d.487.6 | 12 | 9.4 | even | 3 | |||
729.2.e.j.325.1 | 12 | 27.7 | even | 9 | |||
729.2.e.j.406.1 | 12 | 27.4 | even | 9 | |||
729.2.e.k.163.1 | 12 | 27.14 | odd | 18 | |||
729.2.e.k.568.1 | 12 | 27.2 | odd | 18 | |||
729.2.e.l.82.2 | 12 | 27.11 | odd | 18 | |||
729.2.e.l.649.2 | 12 | 27.5 | odd | 18 | |||
729.2.e.s.82.1 | 12 | 27.16 | even | 9 | |||
729.2.e.s.649.1 | 12 | 27.22 | even | 9 | |||
729.2.e.t.163.2 | 12 | 27.13 | even | 9 | |||
729.2.e.t.568.2 | 12 | 27.25 | even | 9 | |||
729.2.e.u.325.2 | 12 | 27.20 | odd | 18 | |||
729.2.e.u.406.2 | 12 | 27.23 | odd | 18 |