Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9036,2,Mod(1,9036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9036, 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("9036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9036 = 2^{2} \cdot 3^{2} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9036.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: | \(72.1528232664\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 6x^{5} + 18x^{4} + 8x^{3} - 17x^{2} - 9x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1004) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(2.29157\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9036.1 |
$q$-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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.78468 | 0.798133 | 0.399067 | − | 0.916922i | \(-0.369334\pi\) | ||||
0.399067 | + | 0.916922i | \(0.369334\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.671050 | 0.253633 | 0.126817 | − | 0.991926i | \(-0.459524\pi\) | ||||
0.126817 | + | 0.991926i | \(0.459524\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.23015 | −0.672416 | −0.336208 | − | 0.941788i | \(-0.609145\pi\) | ||||
−0.336208 | + | 0.941788i | \(0.609145\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.0525243 | 0.0145676 | 0.00728381 | − | 0.999973i | \(-0.497681\pi\) | ||||
0.00728381 | + | 0.999973i | \(0.497681\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.52610 | −1.34028 | −0.670138 | − | 0.742236i | \(-0.733765\pi\) | ||||
−0.670138 | + | 0.742236i | \(0.733765\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.49944 | 0.343995 | 0.171997 | − | 0.985097i | \(-0.444978\pi\) | ||||
0.171997 | + | 0.985097i | \(0.444978\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.13437 | 1.48762 | 0.743810 | − | 0.668391i | \(-0.233017\pi\) | ||||
0.743810 | + | 0.668391i | \(0.233017\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.81492 | −0.362984 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.08515 | −0.387202 | −0.193601 | − | 0.981080i | \(-0.562017\pi\) | ||||
−0.193601 | + | 0.981080i | \(0.562017\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.61596 | −1.72708 | −0.863539 | − | 0.504282i | \(-0.831757\pi\) | ||||
−0.863539 | + | 0.504282i | \(0.831757\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.19761 | 0.202433 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.33025 | 0.876288 | 0.438144 | − | 0.898905i | \(-0.355636\pi\) | ||||
0.438144 | + | 0.898905i | \(0.355636\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.8708 | 1.85391 | 0.926956 | − | 0.375170i | \(-0.122416\pi\) | ||||
0.926956 | + | 0.375170i | \(0.122416\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.09066 | −1.38631 | −0.693157 | − | 0.720787i | \(-0.743781\pi\) | ||||
−0.693157 | + | 0.720787i | \(0.743781\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.21388 | −0.760523 | −0.380261 | − | 0.924879i | \(-0.624166\pi\) | ||||
−0.380261 | + | 0.924879i | \(0.624166\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.54969 | −0.935670 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.27480 | −0.587189 | −0.293595 | − | 0.955930i | \(-0.594852\pi\) | ||||
−0.293595 | + | 0.955930i | \(0.594852\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.98011 | −0.536678 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.163804 | 0.0213254 | 0.0106627 | − | 0.999943i | \(-0.496606\pi\) | ||||
0.0106627 | + | 0.999943i | \(0.496606\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.4800 | 1.46987 | 0.734934 | − | 0.678138i | \(-0.237213\pi\) | ||||
0.734934 | + | 0.678138i | \(0.237213\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.0937391 | 0.0116269 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.6984 | −1.30702 | −0.653509 | − | 0.756918i | \(-0.726704\pi\) | ||||
−0.653509 | + | 0.756918i | \(0.726704\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.24538 | 0.978546 | 0.489273 | − | 0.872131i | \(-0.337262\pi\) | ||||
0.489273 | + | 0.872131i | \(0.337262\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.8635 | −1.50556 | −0.752779 | − | 0.658273i | \(-0.771287\pi\) | ||||
−0.752779 | + | 0.658273i | \(0.771287\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.49654 | −0.170547 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.86983 | −0.885425 | −0.442712 | − | 0.896664i | \(-0.645984\pi\) | ||||
−0.442712 | + | 0.896664i | \(0.645984\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.22811 | 0.573860 | 0.286930 | − | 0.957952i | \(-0.407365\pi\) | ||||
0.286930 | + | 0.957952i | \(0.407365\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.86233 | −1.06972 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.70075 | 0.286279 | 0.143140 | − | 0.989703i | \(-0.454280\pi\) | ||||
0.143140 | + | 0.989703i | \(0.454280\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0352465 | 0.00369483 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.67602 | 0.274554 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.2733 | 1.65230 | 0.826150 | − | 0.563450i | \(-0.190526\pi\) | ||||
0.826150 | + | 0.563450i | \(0.190526\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.31471 | −0.727841 | −0.363920 | − | 0.931430i | \(-0.618562\pi\) | ||||
−0.363920 | + | 0.931430i | \(0.618562\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.43476 | −0.831102 | −0.415551 | − | 0.909570i | \(-0.636411\pi\) | ||||
−0.415551 | + | 0.909570i | \(0.636411\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.4235 | 1.29770 | 0.648851 | − | 0.760915i | \(-0.275250\pi\) | ||||
0.648851 | + | 0.760915i | \(0.275250\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.8033 | −1.03477 | −0.517386 | − | 0.855752i | \(-0.673095\pi\) | ||||
−0.517386 | + | 0.855752i | \(0.673095\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.62110 | −0.622861 | −0.311431 | − | 0.950269i | \(-0.600808\pi\) | ||||
−0.311431 | + | 0.950269i | \(0.600808\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.7326 | 1.18732 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.70829 | −0.339939 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.02642 | −0.547856 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.1624 | −1.08784 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.34857 | −0.119666 | −0.0598329 | − | 0.998208i | \(-0.519057\pi\) | ||||
−0.0598329 | + | 0.998208i | \(0.519057\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.5213 | −1.26873 | −0.634365 | − | 0.773034i | \(-0.718738\pi\) | ||||
−0.634365 | + | 0.773034i | \(0.718738\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.00620 | 0.0872484 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.81237 | −0.411148 | −0.205574 | − | 0.978642i | \(-0.565906\pi\) | ||||
−0.205574 | + | 0.978642i | \(0.565906\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.6736 | −1.49905 | −0.749527 | − | 0.661974i | \(-0.769719\pi\) | ||||
−0.749527 | + | 0.661974i | \(0.769719\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.117137 | −0.00979551 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.72132 | −0.309039 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.49560 | −0.286371 | −0.143185 | − | 0.989696i | \(-0.545735\pi\) | ||||
−0.143185 | + | 0.989696i | \(0.545735\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.05261 | −0.248418 | −0.124209 | − | 0.992256i | \(-0.539639\pi\) | ||||
−0.124209 | + | 0.992256i | \(0.539639\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −17.1614 | −1.37844 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.92795 | −0.233676 | −0.116838 | − | 0.993151i | \(-0.537276\pi\) | ||||
−0.116838 | + | 0.993151i | \(0.537276\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.78752 | 0.377310 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.1100 | 0.870200 | 0.435100 | − | 0.900382i | \(-0.356713\pi\) | ||||
0.435100 | + | 0.900382i | \(0.356713\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.79223 | −0.525599 | −0.262799 | − | 0.964851i | \(-0.584646\pi\) | ||||
−0.262799 | + | 0.964851i | \(0.584646\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9972 | −0.999788 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.7703 | −1.50311 | −0.751553 | − | 0.659673i | \(-0.770695\pi\) | ||||
−0.751553 | + | 0.659673i | \(0.770695\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.21790 | −0.0920646 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.5575 | 1.31231 | 0.656154 | − | 0.754627i | \(-0.272182\pi\) | ||||
0.656154 | + | 0.754627i | \(0.272182\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.21551 | −0.239007 | −0.119503 | − | 0.992834i | \(-0.538130\pi\) | ||||
−0.119503 | + | 0.992834i | \(0.538130\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.51280 | 0.699395 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.3241 | 0.901224 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.1389 | 0.878342 | 0.439171 | − | 0.898404i | \(-0.355272\pi\) | ||||
0.439171 | + | 0.898404i | \(0.355272\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.5502 | 0.831399 | 0.415700 | − | 0.909502i | \(-0.363537\pi\) | ||||
0.415700 | + | 0.909502i | \(0.363537\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.556439 | 0.0396447 | 0.0198223 | − | 0.999804i | \(-0.493690\pi\) | ||||
0.0198223 | + | 0.999804i | \(0.493690\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.8849 | 1.12605 | 0.563025 | − | 0.826440i | \(-0.309637\pi\) | ||||
0.563025 | + | 0.826440i | \(0.309637\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.39924 | −0.0982072 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 21.1856 | 1.47967 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.34398 | −0.231308 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.8560 | −1.64231 | −0.821156 | − | 0.570703i | \(-0.806671\pi\) | ||||
−0.821156 | + | 0.570703i | \(0.806671\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16.2239 | −1.10646 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.45279 | −0.438044 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.290255 | −0.0195247 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.27008 | 0.419876 | 0.209938 | − | 0.977715i | \(-0.432674\pi\) | ||||
0.209938 | + | 0.977715i | \(0.432674\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.69103 | −0.377727 | −0.188863 | − | 0.982003i | \(-0.560480\pi\) | ||||
−0.188863 | + | 0.982003i | \(0.560480\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.9135 | −1.44808 | −0.724042 | − | 0.689756i | \(-0.757718\pi\) | ||||
−0.724042 | + | 0.689756i | \(0.757718\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.6290 | −0.761841 | −0.380921 | − | 0.924608i | \(-0.624393\pi\) | ||||
−0.380921 | + | 0.924608i | \(0.624393\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.30511 | −0.606999 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.3971 | −1.12533 | −0.562664 | − | 0.826686i | \(-0.690223\pi\) | ||||
−0.562664 | + | 0.826686i | \(0.690223\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.35929 | −0.151975 | −0.0759875 | − | 0.997109i | \(-0.524211\pi\) | ||||
−0.0759875 | + | 0.997109i | \(0.524211\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.6891 | −0.746789 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.0787570 | 0.00501119 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.00000 | −0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.9107 | −1.00030 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.2850 | 1.14059 | 0.570293 | − | 0.821442i | \(-0.306830\pi\) | ||||
0.570293 | + | 0.821442i | \(0.306830\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.57687 | 0.222256 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.62067 | 0.0999350 | 0.0499675 | − | 0.998751i | \(-0.484088\pi\) | ||||
0.0499675 | + | 0.998751i | \(0.484088\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.62916 | −0.468655 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.9395 | 1.64253 | 0.821265 | − | 0.570547i | \(-0.193269\pi\) | ||||
0.821265 | + | 0.570547i | \(0.193269\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.70433 | 0.103531 | 0.0517653 | − | 0.998659i | \(-0.483515\pi\) | ||||
0.0517653 | + | 0.998659i | \(0.483515\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.04754 | 0.244076 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.720069 | 0.0432648 | 0.0216324 | − | 0.999766i | \(-0.493114\pi\) | ||||
0.0216324 | + | 0.999766i | \(0.493114\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.07112 | 0.541138 | 0.270569 | − | 0.962701i | \(-0.412788\pi\) | ||||
0.270569 | + | 0.962701i | \(0.412788\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.0455 | −0.597140 | −0.298570 | − | 0.954388i | \(-0.596510\pi\) | ||||
−0.298570 | + | 0.954388i | \(0.596510\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.96592 | 0.470213 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.5378 | 0.796342 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.10277 | 0.531790 | 0.265895 | − | 0.964002i | \(-0.414333\pi\) | ||||
0.265895 | + | 0.964002i | \(0.414333\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.292337 | 0.0170205 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.374728 | 0.0216711 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.10029 | −0.351615 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 20.4882 | 1.17315 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.11554 | −0.520251 | −0.260126 | − | 0.965575i | \(-0.583764\pi\) | ||||
−0.260126 | + | 0.965575i | \(0.583764\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.5389 | −1.67500 | −0.837498 | − | 0.546440i | \(-0.815982\pi\) | ||||
−0.837498 | + | 0.546440i | \(0.815982\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.02555 | −0.0579676 | −0.0289838 | − | 0.999580i | \(-0.509227\pi\) | ||||
−0.0289838 | + | 0.999580i | \(0.509227\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.25854 | 0.183018 | 0.0915089 | − | 0.995804i | \(-0.470831\pi\) | ||||
0.0915089 | + | 0.995804i | \(0.470831\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.65019 | 0.260361 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.28605 | −0.461048 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.0953273 | −0.00528781 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.49878 | −0.192894 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.22129 | 0.0671281 | 0.0335640 | − | 0.999437i | \(-0.489314\pi\) | ||||
0.0335640 | + | 0.999437i | \(0.489314\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −19.0932 | −1.04318 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.7954 | 1.56859 | 0.784293 | − | 0.620391i | \(-0.213026\pi\) | ||||
0.784293 | + | 0.620391i | \(0.213026\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.4451 | 1.16132 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.09252 | −0.490950 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.0949 | 0.702970 | 0.351485 | − | 0.936194i | \(-0.385677\pi\) | ||||
0.351485 | + | 0.936194i | \(0.385677\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.8887 | −0.796974 | −0.398487 | − | 0.917174i | \(-0.630465\pi\) | ||||
−0.398487 | + | 0.917174i | \(0.630465\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 29.2068 | 1.55452 | 0.777260 | − | 0.629179i | \(-0.216609\pi\) | ||||
0.777260 | + | 0.629179i | \(0.216609\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.7154 | 0.781010 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −27.4180 | −1.44707 | −0.723534 | − | 0.690288i | \(-0.757484\pi\) | ||||
−0.723534 | + | 0.690288i | \(0.757484\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.7517 | −0.881668 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −22.9572 | −1.20164 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.9200 | −1.66621 | −0.833105 | − | 0.553115i | \(-0.813439\pi\) | ||||
−0.833105 | + | 0.553115i | \(0.813439\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.86861 | −0.148931 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.2376 | 0.840753 | 0.420376 | − | 0.907350i | \(-0.361898\pi\) | ||||
0.420376 | + | 0.907350i | \(0.361898\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.109521 | −0.00564061 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.8277 | 1.12121 | 0.560607 | − | 0.828082i | \(-0.310568\pi\) | ||||
0.560607 | + | 0.828082i | \(0.310568\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.38270 | −0.275043 | −0.137521 | − | 0.990499i | \(-0.543914\pi\) | ||||
−0.137521 | + | 0.990499i | \(0.543914\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.67085 | −0.136119 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.3894 | 1.54080 | 0.770401 | − | 0.637560i | \(-0.220056\pi\) | ||||
0.770401 | + | 0.637560i | \(0.220056\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −39.4253 | −1.99382 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.0451 | −0.706687 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.3900 | 0.672023 | 0.336011 | − | 0.941858i | \(-0.390922\pi\) | ||||
0.336011 | + | 0.941858i | \(0.390922\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 34.2511 | 1.71042 | 0.855209 | − | 0.518284i | \(-0.173429\pi\) | ||||
0.855209 | + | 0.518284i | \(0.173429\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.505072 | −0.0251594 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.8873 | −0.589231 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.3152 | 0.658394 | 0.329197 | − | 0.944261i | \(-0.393222\pi\) | ||||
0.329197 | + | 0.944261i | \(0.393222\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.109920 | 0.00540883 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.33050 | 0.458016 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.62652 | −0.177167 | −0.0885836 | − | 0.996069i | \(-0.528234\pi\) | ||||
−0.0885836 | + | 0.996069i | \(0.528234\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.05916 | −0.441516 | −0.220758 | − | 0.975329i | \(-0.570853\pi\) | ||||
−0.220758 | + | 0.975329i | \(0.570853\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.0294 | 0.486498 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.70368 | 0.372807 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.80929 | −0.0871506 | −0.0435753 | − | 0.999050i | \(-0.513875\pi\) | ||||
−0.0435753 | + | 0.999050i | \(0.513875\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.34504 | 0.304923 | 0.152462 | − | 0.988309i | \(-0.451280\pi\) | ||||
0.152462 | + | 0.988309i | \(0.451280\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.6975 | 0.511733 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.1384 | 1.43843 | 0.719214 | − | 0.694788i | \(-0.244502\pi\) | ||||
0.719214 | + | 0.694788i | \(0.244502\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.1274 | 0.528679 | 0.264339 | − | 0.964430i | \(-0.414846\pi\) | ||||
0.264339 | + | 0.964430i | \(0.414846\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.81998 | 0.228489 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −35.6616 | −1.68297 | −0.841487 | − | 0.540277i | \(-0.818320\pi\) | ||||
−0.841487 | + | 0.540277i | \(0.818320\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −26.4738 | −1.24660 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.0629036 | 0.00294897 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.2226 | −1.46053 | −0.730266 | − | 0.683163i | \(-0.760604\pi\) | ||||
−0.730266 | + | 0.683163i | \(0.760604\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.3296 | −0.481097 | −0.240549 | − | 0.970637i | \(-0.577327\pi\) | ||||
−0.240549 | + | 0.970637i | \(0.577327\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.1578 | −1.12271 | −0.561355 | − | 0.827575i | \(-0.689720\pi\) | ||||
−0.561355 | + | 0.827575i | \(0.689720\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −35.6761 | −1.65089 | −0.825447 | − | 0.564479i | \(-0.809077\pi\) | ||||
−0.825447 | + | 0.564479i | \(0.809077\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.17917 | −0.331503 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20.2736 | 0.932180 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.72136 | −0.124864 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.37843 | 0.200055 | 0.100028 | − | 0.994985i | \(-0.468107\pi\) | ||||
0.100028 | + | 0.994985i | \(0.468107\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.279968 | 0.0127654 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 29.0426 | 1.31876 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.4930 | −1.47240 | −0.736198 | − | 0.676766i | \(-0.763381\pi\) | ||||
−0.736198 | + | 0.676766i | \(0.763381\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.9926 | −0.586348 | −0.293174 | − | 0.956059i | \(-0.594711\pi\) | ||||
−0.293174 | + | 0.956059i | \(0.594711\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.5227 | 0.518958 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.53306 | 0.248192 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.12523 | 0.0951383 | 0.0475691 | − | 0.998868i | \(-0.484853\pi\) | ||||
0.0475691 | + | 0.998868i | \(0.484853\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −28.1675 | −1.25593 | −0.627964 | − | 0.778243i | \(-0.716111\pi\) | ||||
−0.627964 | + | 0.778243i | \(0.716111\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.0544 | −0.580914 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.65358 | 0.161942 | 0.0809710 | − | 0.996716i | \(-0.474198\pi\) | ||||
0.0809710 | + | 0.996716i | \(0.474198\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.63205 | −0.381859 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −15.0533 | −0.663330 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.6278 | 0.511388 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.7443 | 1.34693 | 0.673465 | − | 0.739219i | \(-0.264805\pi\) | ||||
0.673465 | + | 0.739219i | \(0.264805\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.0146 | 1.09381 | 0.546906 | − | 0.837194i | \(-0.315806\pi\) | ||||
0.546906 | + | 0.837194i | \(0.315806\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 53.1388 | 2.31476 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.8993 | 1.21301 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.623507 | 0.0270071 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.9567 | 1.03574 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 14.6068 | 0.629160 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.3510 | 0.831964 | 0.415982 | − | 0.909373i | \(-0.363438\pi\) | ||||
0.415982 | + | 0.909373i | \(0.363438\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −19.2805 | −0.825886 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.14537 | −0.0917294 | −0.0458647 | − | 0.998948i | \(-0.514604\pi\) | ||||
−0.0458647 | + | 0.998948i | \(0.514604\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.12655 | −0.133195 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.28105 | −0.224573 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −42.7554 | −1.81160 | −0.905802 | − | 0.423702i | \(-0.860730\pi\) | ||||
−0.905802 | + | 0.423702i | \(0.860730\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.477481 | −0.0201953 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.4443 | −0.735191 | −0.367596 | − | 0.929986i | \(-0.619819\pi\) | ||||
−0.367596 | + | 0.929986i | \(0.619819\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.8166 | −0.497126 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 36.4900 | 1.52974 | 0.764871 | − | 0.644184i | \(-0.222803\pi\) | ||||
0.764871 | + | 0.644184i | \(0.222803\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −41.9707 | −1.75642 | −0.878210 | − | 0.478275i | \(-0.841262\pi\) | ||||
−0.878210 | + | 0.478275i | \(0.841262\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.9483 | −0.539981 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.3140 | 0.512639 | 0.256320 | − | 0.966592i | \(-0.417490\pi\) | ||||
0.256320 | + | 0.966592i | \(0.417490\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.50832 | 0.145550 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.53347 | 0.394836 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.8231 | −0.570540 | −0.285270 | − | 0.958447i | \(-0.592083\pi\) | ||||
−0.285270 | + | 0.958447i | \(0.592083\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.4185 | −0.594105 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.5625 | −0.639075 | −0.319538 | − | 0.947574i | \(-0.603528\pi\) | ||||
−0.319538 | + | 0.947574i | \(0.603528\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.61811 | −0.271316 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.86070 | −0.280321 | −0.140160 | − | 0.990129i | \(-0.544762\pi\) | ||||
−0.140160 | + | 0.990129i | \(0.544762\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.73347 | 0.152292 | 0.0761458 | − | 0.997097i | \(-0.475739\pi\) | ||||
0.0761458 | + | 0.997097i | \(0.475739\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.7552 | −0.437262 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 40.4537 | 1.64197 | 0.820983 | − | 0.570953i | \(-0.193426\pi\) | ||||
0.820983 | + | 0.570953i | \(0.193426\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.273856 | −0.0110790 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.2453 | −0.736921 | −0.368460 | − | 0.929643i | \(-0.620115\pi\) | ||||
−0.368460 | + | 0.929643i | \(0.620115\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.5886 | −0.828864 | −0.414432 | − | 0.910080i | \(-0.636020\pi\) | ||||
−0.414432 | + | 0.910080i | \(0.636020\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.8400 | −0.475890 | −0.237945 | − | 0.971279i | \(-0.576474\pi\) | ||||
−0.237945 | + | 0.971279i | \(0.576474\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.81234 | 0.0726098 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.6315 | −0.505259 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −29.4555 | −1.17447 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.3224 | −0.968258 | −0.484129 | − | 0.874997i | \(-0.660863\pi\) | ||||
−0.484129 | + | 0.874997i | \(0.660863\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.40676 | −0.0955093 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.344018 | −0.0136305 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.8821 | −0.587808 | −0.293904 | − | 0.955835i | \(-0.594955\pi\) | ||||
−0.293904 | + | 0.955835i | \(0.594955\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.38851 | −0.370247 | −0.185123 | − | 0.982715i | \(-0.559268\pi\) | ||||
−0.185123 | + | 0.982715i | \(0.559268\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.9638 | 0.981430 | 0.490715 | − | 0.871320i | \(-0.336736\pi\) | ||||
0.490715 | + | 0.871320i | \(0.336736\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.365307 | −0.0143396 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −34.0819 | −1.33373 | −0.666865 | − | 0.745179i | \(-0.732364\pi\) | ||||
−0.666865 | + | 0.745179i | \(0.732364\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −25.9158 | −1.01262 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.7009 | −0.767440 | −0.383720 | − | 0.923450i | \(-0.625357\pi\) | ||||
−0.383720 | + | 0.923450i | \(0.625357\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.9804 | 0.699358 | 0.349679 | − | 0.936870i | \(-0.386291\pi\) | ||||
0.349679 | + | 0.936870i | \(0.386291\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.79574 | 0.0696359 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.8762 | −0.576009 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −25.6022 | −0.988364 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.6371 | −0.410029 | −0.205015 | − | 0.978759i | \(-0.565724\pi\) | ||||
−0.205015 | + | 0.978759i | \(0.565724\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.0551 | 0.424883 | 0.212441 | − | 0.977174i | \(-0.431859\pi\) | ||||
0.212441 | + | 0.977174i | \(0.431859\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.9202 | 0.419078 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.2786 | 1.00552 | 0.502762 | − | 0.864425i | \(-0.332317\pi\) | ||||
0.502762 | + | 0.864425i | \(0.332317\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.58853 | −0.328151 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.224531 | −0.00855396 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.0629 | −1.10561 | −0.552803 | − | 0.833312i | \(-0.686442\pi\) | ||||
−0.552803 | + | 0.833312i | \(0.686442\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −31.5417 | −1.19644 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −65.5994 | −2.48476 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.7473 | 1.12354 | 0.561771 | − | 0.827293i | \(-0.310120\pi\) | ||||
0.561771 | + | 0.827293i | \(0.310120\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.99238 | 0.301438 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.90854 | −0.184605 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.8047 | 1.15689 | 0.578447 | − | 0.815720i | \(-0.303659\pi\) | ||||
0.578447 | + | 0.815720i | \(0.303659\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −68.6038 | −2.56923 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.209053 | −0.00781812 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29.2904 | −1.09235 | −0.546175 | − | 0.837671i | \(-0.683917\pi\) | ||||
−0.546175 | + | 0.837671i | \(0.683917\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.66015 | −0.210795 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.78437 | 0.140548 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −37.9357 | −1.40696 | −0.703479 | − | 0.710716i | \(-0.748371\pi\) | ||||
−0.703479 | + | 0.710716i | \(0.748371\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 50.2359 | 1.85804 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.8326 | 0.584792 | 0.292396 | − | 0.956297i | \(-0.405547\pi\) | ||||
0.292396 | + | 0.956297i | \(0.405547\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 23.8591 | 0.878861 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.06045 | 0.333294 | 0.166647 | − | 0.986017i | \(-0.446706\pi\) | ||||
0.166647 | + | 0.986017i | \(0.446706\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.42135 | 0.308949 | 0.154475 | − | 0.987997i | \(-0.450631\pi\) | ||||
0.154475 | + | 0.987997i | \(0.450631\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.23853 | −0.228562 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.00787 | 0.329140 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.2016 | −0.700677 | −0.350338 | − | 0.936623i | \(-0.613933\pi\) | ||||
−0.350338 | + | 0.936623i | \(0.613933\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.44793 | −0.198270 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.32193 | −0.338811 | −0.169406 | − | 0.985546i | \(-0.554185\pi\) | ||||
−0.169406 | + | 0.985546i | \(0.554185\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −51.3651 | −1.86198 | −0.930992 | − | 0.365041i | \(-0.881055\pi\) | ||||
−0.930992 | + | 0.365041i | \(0.881055\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.24958 | −0.262452 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.00860367 | 0.000310661 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 43.2738 | 1.56049 | 0.780246 | − | 0.625473i | \(-0.215094\pi\) | ||||
0.780246 | + | 0.625473i | \(0.215094\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.59292 | 0.237131 | 0.118565 | − | 0.992946i | \(-0.462170\pi\) | ||||
0.118565 | + | 0.992946i | \(0.462170\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.4522 | 0.626901 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.7996 | 0.637736 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.3885 | −0.657991 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.22545 | −0.186504 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −51.1075 | −1.82179 | −0.910893 | − | 0.412642i | \(-0.864606\pi\) | ||||
−0.910893 | + | 0.412642i | \(0.864606\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.44309 | −0.157978 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.602981 | 0.0214125 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −37.6794 | −1.33467 | −0.667337 | − | 0.744756i | \(-0.732566\pi\) | ||||
−0.667337 | + | 0.744756i | \(0.732566\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28.8125 | 1.01931 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 28.6876 | 1.01236 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.54419 | 0.301143 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 38.0342 | 1.33721 | 0.668605 | − | 0.743618i | \(-0.266892\pi\) | ||||
0.668605 | + | 0.743618i | \(0.266892\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.6164 | 0.478138 | 0.239069 | − | 0.971003i | \(-0.423158\pi\) | ||||
0.239069 | + | 0.971003i | \(0.423158\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.8277 | 0.694535 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.6309 | −0.476884 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.5818 | −1.06731 | −0.533656 | − | 0.845702i | \(-0.679182\pi\) | ||||
−0.533656 | + | 0.845702i | \(0.679182\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.4303 | −0.642439 | −0.321220 | − | 0.947005i | \(-0.604093\pi\) | ||||
−0.321220 | + | 0.947005i | \(0.604093\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.06070 | 0.0716577 | 0.0358288 | − | 0.999358i | \(-0.488593\pi\) | ||||
0.0358288 | + | 0.999358i | \(0.488593\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 53.5915 | 1.86131 | 0.930655 | − | 0.365897i | \(-0.119238\pi\) | ||||
0.930655 | + | 0.365897i | \(0.119238\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 36.1943 | 1.25406 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.1220 | −0.419498 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.37280 | 0.323585 | 0.161792 | − | 0.986825i | \(-0.448272\pi\) | ||||
0.161792 | + | 0.986825i | \(0.448272\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.6522 | −0.850075 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −23.1959 | −0.797964 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.04403 | −0.138954 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 38.0280 | 1.30358 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.69000 | −0.297540 | −0.148770 | − | 0.988872i | \(-0.547531\pi\) | ||||
−0.148770 | + | 0.988872i | \(0.547531\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.4197 | 0.595045 | 0.297522 | − | 0.954715i | \(-0.403840\pi\) | ||||
0.297522 | + | 0.954715i | \(0.403840\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.0839 | 1.29941 | 0.649703 | − | 0.760188i | \(-0.274893\pi\) | ||||
0.649703 | + | 0.760188i | \(0.274893\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.47779 | −0.0503046 | −0.0251523 | − | 0.999684i | \(-0.508007\pi\) | ||||
−0.0251523 | + | 0.999684i | \(0.508007\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −35.2836 | −1.19968 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.5509 | 0.595374 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.561927 | −0.0190402 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.16161 | −0.275913 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.1183 | 0.544278 | 0.272139 | − | 0.962258i | \(-0.412269\pi\) | ||||
0.272139 | + | 0.962258i | \(0.412269\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.7458 | 0.867399 | 0.433699 | − | 0.901058i | \(-0.357208\pi\) | ||||
0.433699 | + | 0.901058i | \(0.357208\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.3112 | 1.72676 | 0.863380 | − | 0.504554i | \(-0.168343\pi\) | ||||
0.863380 | + | 0.504554i | \(0.168343\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26.4272 | −0.887339 | −0.443670 | − | 0.896190i | \(-0.646324\pi\) | ||||
−0.443670 | + | 0.896190i | \(0.646324\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.904955 | −0.0303512 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.81789 | −0.261616 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 31.3345 | 1.04740 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 20.0507 | 0.668727 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.6230 | 0.786996 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.73865 | −0.190759 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41.6133 | 1.38175 | 0.690873 | − | 0.722976i | \(-0.257226\pi\) | ||||
0.690873 | + | 0.722976i | \(0.257226\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.6569 | −1.61208 | −0.806038 | − | 0.591864i | \(-0.798392\pi\) | ||||
−0.806038 | + | 0.591864i | \(0.798392\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.6595 | −0.385873 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.74451 | −0.321792 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.6597 | 1.07734 | 0.538672 | − | 0.842515i | \(-0.318926\pi\) | ||||
0.538672 | + | 0.842515i | \(0.318926\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.433083 | 0.0142551 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.67397 | −0.318078 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29.0898 | 0.954406 | 0.477203 | − | 0.878793i | \(-0.341651\pi\) | ||||
0.477203 | + | 0.878793i | \(0.341651\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.82086 | −0.321866 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21.9945 | 0.719297 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.3014 | 1.28392 | 0.641960 | − | 0.766738i | \(-0.278122\pi\) | ||||
0.641960 | + | 0.766738i | \(0.278122\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.7356 | −0.578163 | −0.289082 | − | 0.957304i | \(-0.593350\pi\) | ||||
−0.289082 | + | 0.957304i | \(0.593350\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 84.6909 | 2.75792 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −41.3091 | −1.34237 | −0.671183 | − | 0.741292i | \(-0.734213\pi\) | ||||
−0.671183 | + | 0.741292i | \(0.734213\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.675646 | −0.0219324 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.6289 | −0.635842 | −0.317921 | − | 0.948117i | \(-0.602985\pi\) | ||||
−0.317921 | + | 0.948117i | \(0.602985\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.6641 | 0.701033 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.22934 | −0.104281 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 61.4667 | 1.98280 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 20.6134 | 0.663567 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.3193 | 1.42521 | 0.712606 | − | 0.701565i | \(-0.247515\pi\) | ||||
0.712606 | + | 0.701565i | \(0.247515\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.22052 | 0.135443 | 0.0677214 | − | 0.997704i | \(-0.478427\pi\) | ||||
0.0677214 | + | 0.997704i | \(0.478427\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.8599 | −0.380210 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29.3344 | 0.938492 | 0.469246 | − | 0.883068i | \(-0.344526\pi\) | ||||
0.469246 | + | 0.883068i | \(0.344526\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.02309 | −0.192499 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −55.0110 | −1.75458 | −0.877290 | − | 0.479961i | \(-0.840651\pi\) | ||||
−0.877290 | + | 0.479961i | \(0.840651\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.993066 | 0.0316417 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −64.8562 | −2.06231 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.39630 | −0.266717 | −0.133359 | − | 0.991068i | \(-0.542576\pi\) | ||||
−0.133359 | + | 0.991068i | \(0.542576\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 28.3495 | 0.898738 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.7423 | 0.498564 | 0.249282 | − | 0.968431i | \(-0.419805\pi\) | ||||
0.249282 | + | 0.968431i | \(0.419805\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 9036.2.a.i.1.6 | 7 | ||
3.2 | odd | 2 | 1004.2.a.a.1.2 | ✓ | 7 | ||
12.11 | even | 2 | 4016.2.a.g.1.6 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1004.2.a.a.1.2 | ✓ | 7 | 3.2 | odd | 2 | ||
4016.2.a.g.1.6 | 7 | 12.11 | even | 2 | |||
9036.2.a.i.1.6 | 7 | 1.1 | even | 1 | trivial |