Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,6,Mod(1,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.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: | \(51.9643576194\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 110x^{3} + 39x^{2} + 2214x - 1944 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{7} \) |
Twist minimal: | no (minimal twist has level 36) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.900358\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.1 |
$q$-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 | ||||||||
\(5\) | 26.3205 | 0.470835 | 0.235418 | − | 0.971894i | \(-0.424354\pi\) | ||||
0.235418 | + | 0.971894i | \(0.424354\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 63.2575 | 0.487940 | 0.243970 | − | 0.969783i | \(-0.421550\pi\) | ||||
0.243970 | + | 0.969783i | \(0.421550\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −98.2387 | −0.244794 | −0.122397 | − | 0.992481i | \(-0.539058\pi\) | ||||
−0.122397 | + | 0.992481i | \(0.539058\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −738.285 | −1.21162 | −0.605809 | − | 0.795610i | \(-0.707151\pi\) | ||||
−0.605809 | + | 0.795610i | \(0.707151\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −250.060 | −0.209856 | −0.104928 | − | 0.994480i | \(-0.533461\pi\) | ||||
−0.104928 | + | 0.994480i | \(0.533461\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1102.41 | 0.700579 | 0.350290 | − | 0.936641i | \(-0.386083\pi\) | ||||
0.350290 | + | 0.936641i | \(0.386083\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4409.41 | −1.73804 | −0.869022 | − | 0.494774i | \(-0.835251\pi\) | ||||
−0.869022 | + | 0.494774i | \(0.835251\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2432.23 | −0.778314 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7882.12 | 1.74039 | 0.870197 | − | 0.492703i | \(-0.163991\pi\) | ||||
0.870197 | + | 0.492703i | \(0.163991\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4611.29 | −0.861823 | −0.430912 | − | 0.902394i | \(-0.641808\pi\) | ||||
−0.430912 | + | 0.902394i | \(0.641808\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1664.97 | 0.229740 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11896.3 | 1.42859 | 0.714297 | − | 0.699843i | \(-0.246747\pi\) | ||||
0.714297 | + | 0.699843i | \(0.246747\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10081.2 | −0.936594 | −0.468297 | − | 0.883571i | \(-0.655132\pi\) | ||||
−0.468297 | + | 0.883571i | \(0.655132\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7037.98 | 0.580466 | 0.290233 | − | 0.956956i | \(-0.406267\pi\) | ||||
0.290233 | + | 0.956956i | \(0.406267\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −14918.7 | −0.985111 | −0.492555 | − | 0.870281i | \(-0.663937\pi\) | ||||
−0.492555 | + | 0.870281i | \(0.663937\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −12805.5 | −0.761914 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −22451.7 | −1.09789 | −0.548947 | − | 0.835857i | \(-0.684971\pi\) | ||||
−0.548947 | + | 0.835857i | \(0.684971\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2585.69 | −0.115258 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10810.5 | −0.404311 | −0.202156 | − | 0.979353i | \(-0.564795\pi\) | ||||
−0.202156 | + | 0.979353i | \(0.564795\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1189.29 | −0.0409227 | −0.0204614 | − | 0.999791i | \(-0.506514\pi\) | ||||
−0.0204614 | + | 0.999791i | \(0.506514\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −19432.0 | −0.570473 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 59180.5 | 1.61061 | 0.805307 | − | 0.592858i | \(-0.202000\pi\) | ||||
0.805307 | + | 0.592858i | \(0.202000\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14326.6 | −0.337284 | −0.168642 | − | 0.985677i | \(-0.553938\pi\) | ||||
−0.168642 | + | 0.985677i | \(0.553938\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −53098.2 | −1.16620 | −0.583099 | − | 0.812401i | \(-0.698160\pi\) | ||||
−0.583099 | + | 0.812401i | \(0.698160\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6214.33 | −0.119445 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −37391.1 | −0.674063 | −0.337032 | − | 0.941493i | \(-0.609423\pi\) | ||||
−0.337032 | + | 0.941493i | \(0.609423\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −120879. | −1.92600 | −0.962998 | − | 0.269509i | \(-0.913139\pi\) | ||||
−0.962998 | + | 0.269509i | \(0.913139\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6581.71 | −0.0988078 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −97873.2 | −1.30975 | −0.654875 | − | 0.755737i | \(-0.727279\pi\) | ||||
−0.654875 | + | 0.755737i | \(0.727279\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −46702.1 | −0.591198 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 29015.9 | 0.329858 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 106713. | 1.15157 | 0.575784 | − | 0.817602i | \(-0.304697\pi\) | ||||
0.575784 | + | 0.817602i | \(0.304697\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −96472.1 | −0.941019 | −0.470510 | − | 0.882395i | \(-0.655930\pi\) | ||||
−0.470510 | + | 0.882395i | \(0.655930\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 29944.4 | 0.278114 | 0.139057 | − | 0.990284i | \(-0.455593\pi\) | ||||
0.139057 | + | 0.990284i | \(0.455593\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −22758.9 | −0.192173 | −0.0960865 | − | 0.995373i | \(-0.530633\pi\) | ||||
−0.0960865 | + | 0.995373i | \(0.530633\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2671.93 | −0.0215407 | −0.0107703 | − | 0.999942i | \(-0.503428\pi\) | ||||
−0.0107703 | + | 0.999942i | \(0.503428\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −131339. | −0.967606 | −0.483803 | − | 0.875177i | \(-0.660745\pi\) | ||||
−0.483803 | + | 0.875177i | \(0.660745\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −116058. | −0.818332 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −15818.2 | −0.102397 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −151400. | −0.940076 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −146269. | −0.837293 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 236012. | 1.29845 | 0.649223 | − | 0.760598i | \(-0.275094\pi\) | ||||
0.649223 | + | 0.760598i | \(0.275094\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −360366. | −1.83470 | −0.917352 | − | 0.398078i | \(-0.869677\pi\) | ||||
−0.917352 | + | 0.398078i | \(0.869677\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 69735.4 | 0.341841 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 237666. | 1.08185 | 0.540923 | − | 0.841072i | \(-0.318075\pi\) | ||||
0.540923 | + | 0.841072i | \(0.318075\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 163347. | 0.717090 | 0.358545 | − | 0.933513i | \(-0.383273\pi\) | ||||
0.358545 | + | 0.933513i | \(0.383273\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 72528.2 | 0.296597 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 207461. | 0.819440 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −335607. | −1.23841 | −0.619205 | − | 0.785229i | \(-0.712545\pi\) | ||||
−0.619205 | + | 0.785229i | \(0.712545\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −135577. | −0.483886 | −0.241943 | − | 0.970290i | \(-0.577785\pi\) | ||||
−0.241943 | + | 0.970290i | \(0.577785\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −121371. | −0.405777 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −425432. | −1.37747 | −0.688733 | − | 0.725016i | \(-0.741833\pi\) | ||||
−0.688733 | + | 0.725016i | \(0.741833\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −278928. | −0.848062 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −158679. | −0.467789 | −0.233895 | − | 0.972262i | \(-0.575147\pi\) | ||||
−0.233895 | + | 0.972262i | \(0.575147\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 518446. | 1.43851 | 0.719254 | − | 0.694747i | \(-0.244484\pi\) | ||||
0.719254 | + | 0.694747i | \(0.244484\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 173772. | 0.468019 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 153178. | 0.389118 | 0.194559 | − | 0.980891i | \(-0.437672\pi\) | ||||
0.194559 | + | 0.980891i | \(0.437672\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −153857. | −0.379771 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 736845. | 1.71887 | 0.859437 | − | 0.511242i | \(-0.170815\pi\) | ||||
0.859437 | + | 0.511242i | \(0.170815\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 28183.8 | 0.0639445 | 0.0319722 | − | 0.999489i | \(-0.489821\pi\) | ||||
0.0319722 | + | 0.999489i | \(0.489821\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 313118. | 0.672633 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24565.6 | 0.0513716 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −99321.0 | −0.196996 | −0.0984981 | − | 0.995137i | \(-0.531404\pi\) | ||||
−0.0984981 | + | 0.995137i | \(0.531404\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 417272. | 0.806355 | 0.403177 | − | 0.915122i | \(-0.367906\pi\) | ||||
0.403177 | + | 0.915122i | \(0.367906\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −254565. | −0.467340 | −0.233670 | − | 0.972316i | \(-0.575073\pi\) | ||||
−0.233670 | + | 0.972316i | \(0.575073\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −599702. | −1.07350 | −0.536751 | − | 0.843741i | \(-0.680348\pi\) | ||||
−0.536751 | + | 0.843741i | \(0.680348\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 498603. | 0.849209 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −265341. | −0.440982 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −108299. | −0.171498 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 756584. | 1.16991 | 0.584953 | − | 0.811067i | \(-0.301113\pi\) | ||||
0.584953 | + | 0.811067i | \(0.301113\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 185243. | 0.273304 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −291699. | −0.420518 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 184616. | 0.254266 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −111205. | −0.149748 | −0.0748741 | − | 0.997193i | \(-0.523855\pi\) | ||||
−0.0748741 | + | 0.997193i | \(0.523855\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 490760. | 0.632127 | 0.316063 | − | 0.948738i | \(-0.397639\pi\) | ||||
0.316063 | + | 0.948738i | \(0.397639\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 761021. | 0.958977 | 0.479488 | − | 0.877548i | \(-0.340822\pi\) | ||||
0.479488 | + | 0.877548i | \(0.340822\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 356267. | 0.429918 | 0.214959 | − | 0.976623i | \(-0.431038\pi\) | ||||
0.214959 | + | 0.976623i | \(0.431038\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −392667. | −0.463825 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 906239. | 1.02624 | 0.513119 | − | 0.858318i | \(-0.328490\pi\) | ||||
0.513119 | + | 0.858318i | \(0.328490\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 522576. | 0.579571 | 0.289785 | − | 0.957092i | \(-0.406416\pi\) | ||||
0.289785 | + | 0.957092i | \(0.406416\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −337047. | −0.358736 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −813890. | −0.848835 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 625287. | 0.626462 | 0.313231 | − | 0.949677i | \(-0.398589\pi\) | ||||
0.313231 | + | 0.949677i | \(0.398589\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 433175. | 0.425463 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.30221e6 | 1.22984 | 0.614921 | − | 0.788589i | \(-0.289188\pi\) | ||||
0.614921 | + | 0.788589i | \(0.289188\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 752532. | 0.697069 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.43352e6 | 1.27795 | 0.638977 | − | 0.769226i | \(-0.279358\pi\) | ||||
0.638977 | + | 0.769226i | \(0.279358\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −590941. | −0.516927 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.52329e6 | 1.28352 | 0.641758 | − | 0.766907i | \(-0.278205\pi\) | ||||
0.641758 | + | 0.766907i | \(0.278205\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.60134e6 | 1.32453 | 0.662263 | − | 0.749271i | \(-0.269596\pi\) | ||||
0.662263 | + | 0.749271i | \(0.269596\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 238939. | 0.190527 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −893943. | −0.700020 | −0.350010 | − | 0.936746i | \(-0.613822\pi\) | ||||
−0.350010 | + | 0.936746i | \(0.613822\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28400.1 | 0.0214563 | 0.0107281 | − | 0.999942i | \(-0.496585\pi\) | ||||
0.0107281 | + | 0.999942i | \(0.496585\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.10957e6 | −0.823544 | −0.411772 | − | 0.911287i | \(-0.635090\pi\) | ||||
−0.411772 | + | 0.911287i | \(0.635090\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −637709. | −0.457002 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.35733e6 | −0.955960 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.45768e6 | −1.67246 | −0.836230 | − | 0.548378i | \(-0.815245\pi\) | ||||
−0.836230 | + | 0.548378i | \(0.815245\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −284538. | −0.190364 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.25540e6 | 2.10585 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 445205. | 0.283233 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −31302.8 | −0.0192679 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.77336e6 | 1.07387 | 0.536934 | − | 0.843624i | \(-0.319583\pi\) | ||||
0.536934 | + | 0.843624i | \(0.319583\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.50571e6 | −0.882756 | −0.441378 | − | 0.897321i | \(-0.645510\pi\) | ||||
−0.441378 | + | 0.897321i | \(0.645510\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −812705. | −0.468891 | −0.234446 | − | 0.972129i | \(-0.575327\pi\) | ||||
−0.234446 | + | 0.972129i | \(0.575327\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.04760e6 | −0.585525 | −0.292763 | − | 0.956185i | \(-0.594575\pi\) | ||||
−0.292763 | + | 0.956185i | \(0.594575\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −774329. | −0.426038 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −275668. | −0.147021 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.79568e6 | 0.943020 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −943717. | −0.480675 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −68005.3 | −0.0341172 | −0.0170586 | − | 0.999854i | \(-0.505430\pi\) | ||||
−0.0170586 | + | 0.999854i | \(0.505430\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.55766e6 | 0.758334 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −416472. | −0.199761 | −0.0998806 | − | 0.994999i | \(-0.531846\pi\) | ||||
−0.0998806 | + | 0.994999i | \(0.531846\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 453007. | 0.210969 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.87321e6 | −0.859709 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.80740e6 | 1.25164 | 0.625822 | − | 0.779966i | \(-0.284764\pi\) | ||||
0.625822 | + | 0.779966i | \(0.284764\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −481973. | −0.211816 | −0.105908 | − | 0.994376i | \(-0.533775\pi\) | ||||
−0.105908 | + | 0.994376i | \(0.533775\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.00037e6 | −1.70869 | −0.854346 | − | 0.519705i | \(-0.826042\pi\) | ||||
−0.854346 | + | 0.519705i | \(0.826042\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −377082. | −0.158805 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 800858. | 0.327959 | 0.163979 | − | 0.986464i | \(-0.447567\pi\) | ||||
0.163979 | + | 0.986464i | \(0.447567\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.26080e6 | −0.509189 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.39757e6 | −0.549087 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.00972e6 | 1.16644 | 0.583218 | − | 0.812316i | \(-0.301793\pi\) | ||||
0.583218 | + | 0.812316i | \(0.301793\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.42024e6 | −0.535707 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.59331e6 | 0.592962 | 0.296481 | − | 0.955039i | \(-0.404187\pi\) | ||||
0.296481 | + | 0.955039i | \(0.404187\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.81925e6 | −2.10869 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −297930. | −0.106541 | −0.0532703 | − | 0.998580i | \(-0.516965\pi\) | ||||
−0.0532703 | + | 0.998580i | \(0.516965\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.29030e6 | 0.449464 | 0.224732 | − | 0.974421i | \(-0.427849\pi\) | ||||
0.224732 | + | 0.974421i | \(0.427849\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −163564. | −0.0562389 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.99873e6 | −1.67489 | −0.837444 | − | 0.546523i | \(-0.815951\pi\) | ||||
−0.837444 | + | 0.546523i | \(0.815951\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.10262e6 | 0.364740 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −984153. | −0.317373 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −558980. | −0.178000 | −0.0890000 | − | 0.996032i | \(-0.528367\pi\) | ||||
−0.0890000 | + | 0.996032i | \(0.528367\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −94207.2 | −0.0292565 | −0.0146283 | − | 0.999893i | \(-0.504656\pi\) | ||||
−0.0146283 | + | 0.999893i | \(0.504656\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.40445e6 | 1.04420 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.16868e6 | −0.349711 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.46230e6 | 1.61461 | 0.807304 | − | 0.590135i | \(-0.200926\pi\) | ||||
0.807304 | + | 0.590135i | \(0.200926\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −683845. | −0.197280 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.18159e6 | −0.906827 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 836972. | 0.232903 | 0.116452 | − | 0.993196i | \(-0.462848\pi\) | ||||
0.116452 | + | 0.993196i | \(0.462848\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.42809e6 | −1.76757 | −0.883785 | − | 0.467894i | \(-0.845013\pi\) | ||||
−0.883785 | + | 0.467894i | \(0.845013\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 608204. | 0.163334 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −75231.7 | −0.0199678 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.11509e6 | 1.32636 | 0.663178 | − | 0.748462i | \(-0.269207\pi\) | ||||
0.663178 | + | 0.748462i | \(0.269207\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.39089e6 | −0.356512 | −0.178256 | − | 0.983984i | \(-0.557045\pi\) | ||||
−0.178256 | + | 0.983984i | \(0.557045\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.86095e6 | −1.21764 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.52532e6 | −0.873045 | −0.436523 | − | 0.899693i | \(-0.643790\pi\) | ||||
−0.436523 | + | 0.899693i | \(0.643790\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.04432e6 | −0.494924 | −0.247462 | − | 0.968898i | \(-0.579597\pi\) | ||||
−0.247462 | + | 0.968898i | \(0.579597\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.57607e6 | −0.616677 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.70508e6 | −1.80369 | −0.901844 | − | 0.432062i | \(-0.857786\pi\) | ||||
−0.901844 | + | 0.432062i | \(0.857786\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 990361. | 0.229273 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.22922e6 | −0.278357 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.57692e6 | 1.92106 | 0.960529 | − | 0.278179i | \(-0.0897308\pi\) | ||||
0.960529 | + | 0.278179i | \(0.0897308\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.43263e6 | −0.313966 | −0.156983 | − | 0.987601i | \(-0.550177\pi\) | ||||
−0.156983 | + | 0.987601i | \(0.550177\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.94447e6 | 0.638343 | 0.319172 | − | 0.947697i | \(-0.396595\pi\) | ||||
0.319172 | + | 0.947697i | \(0.396595\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.96160e6 | −1.05276 | −0.526380 | − | 0.850249i | \(-0.676451\pi\) | ||||
−0.526380 | + | 0.850249i | \(0.676451\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.74361e6 | 0.785884 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −691402. | −0.142095 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.68130e6 | −0.545271 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 241513. | 0.0480953 | 0.0240476 | − | 0.999711i | \(-0.492345\pi\) | ||||
0.0240476 | + | 0.999711i | \(0.492345\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.78289e6 | −1.73091 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.80875e6 | 0.542199 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 325055. | 0.0621061 | 0.0310530 | − | 0.999518i | \(-0.490114\pi\) | ||||
0.0310530 | + | 0.999518i | \(0.490114\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.98047e6 | −0.932323 | −0.466162 | − | 0.884700i | \(-0.654363\pi\) | ||||
−0.466162 | + | 0.884700i | \(0.654363\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.97100e6 | −0.365233 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −906262. | −0.164575 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.86495e6 | −1.05442 | −0.527209 | − | 0.849736i | \(-0.676761\pi\) | ||||
−0.527209 | + | 0.849736i | \(0.676761\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.36396e6 | 0.240370 | 0.120185 | − | 0.992751i | \(-0.461651\pi\) | ||||
0.120185 | + | 0.992751i | \(0.461651\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.53919e6 | −0.443065 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.70047e6 | −0.633085 | −0.316542 | − | 0.948578i | \(-0.602522\pi\) | ||||
−0.316542 | + | 0.948578i | \(0.602522\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.35885e6 | −0.569035 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 788153. | 0.130946 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.46559e6 | 0.241149 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 285260. | 0.0460412 | 0.0230206 | − | 0.999735i | \(-0.492672\pi\) | ||||
0.0230206 | + | 0.999735i | \(0.492672\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.28809e6 | 1.32495 | 0.662476 | − | 0.749083i | \(-0.269506\pi\) | ||||
0.662476 | + | 0.749083i | \(0.269506\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.15310e6 | 0.180859 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.30065e7 | 2.02080 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.44278e6 | 1.13479 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −599027. | −0.0904819 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.25800e6 | 0.186512 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.29750e7 | 1.90596 | 0.952982 | − | 0.303028i | \(-0.0979975\pi\) | ||||
0.952982 | + | 0.303028i | \(0.0979975\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −70326.5 | −0.0101421 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.31601e6 | −1.33126 | −0.665628 | − | 0.746284i | \(-0.731836\pi\) | ||||
−0.665628 | + | 0.746284i | \(0.731836\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.68929e6 | 1.21928 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.36527e6 | −0.328903 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.18234e6 | 0.571192 | 0.285596 | − | 0.958350i | \(-0.407809\pi\) | ||||
0.285596 | + | 0.958350i | \(0.407809\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.19604e6 | −0.703304 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.31319e6 | 0.440531 | 0.220265 | − | 0.975440i | \(-0.429308\pi\) | ||||
0.220265 | + | 0.975440i | \(0.429308\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.45692e6 | −0.455583 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.85391e6 | 0.757993 | 0.378996 | − | 0.925398i | \(-0.376269\pi\) | ||||
0.378996 | + | 0.925398i | \(0.376269\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.35086e7 | 1.73388 | 0.866941 | − | 0.498411i | \(-0.166083\pi\) | ||||
0.866941 | + | 0.498411i | \(0.166083\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.07247e7 | 1.35274 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.12898e7 | −1.41171 | −0.705855 | − | 0.708356i | \(-0.749437\pi\) | ||||
−0.705855 | + | 0.708356i | \(0.749437\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.64649e6 | −0.939771 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.20563e6 | 0.268758 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.98280e6 | −0.237510 | −0.118755 | − | 0.992924i | \(-0.537890\pi\) | ||||
−0.118755 | + | 0.992924i | \(0.537890\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.08351e6 | −0.603776 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.22629e7 | −1.43204 | −0.716021 | − | 0.698078i | \(-0.754039\pi\) | ||||
−0.716021 | + | 0.698078i | \(0.754039\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −416342. | −0.0482123 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.56995e7 | 1.78780 | 0.893902 | − | 0.448263i | \(-0.147957\pi\) | ||||
0.893902 | + | 0.448263i | \(0.147957\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.31944e6 | −0.600731 | −0.300366 | − | 0.953824i | \(-0.597109\pi\) | ||||
−0.300366 | + | 0.953824i | \(0.597109\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.98493e6 | −0.442621 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.36964e6 | 0.481365 | 0.240682 | − | 0.970604i | \(-0.422629\pi\) | ||||
0.240682 | + | 0.970604i | \(0.422629\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.10142e7 | 1.19358 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.62875e6 | −0.819978 | −0.409989 | − | 0.912091i | \(-0.634467\pi\) | ||||
−0.409989 | + | 0.912091i | \(0.634467\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.43300e7 | 1.51542 | 0.757708 | − | 0.652594i | \(-0.226319\pi\) | ||||
0.757708 | + | 0.652594i | \(0.226319\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.08181e7 | 1.13482 | 0.567408 | − | 0.823437i | \(-0.307946\pi\) | ||||
0.567408 | + | 0.823437i | \(0.307946\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.19121e6 | −0.639080 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.75085e6 | 0.384087 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.97480e6 | −0.299800 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.96579e6 | 0.796444 | 0.398222 | − | 0.917289i | \(-0.369627\pi\) | ||||
0.398222 | + | 0.917289i | \(0.369627\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.21194e6 | 0.611354 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.45411e6 | 0.923149 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.80448e6 | −0.654108 | −0.327054 | − | 0.945006i | \(-0.606056\pi\) | ||||
−0.327054 | + | 0.945006i | \(0.606056\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.32929e6 | −0.508325 | −0.254163 | − | 0.967161i | \(-0.581800\pi\) | ||||
−0.254163 | + | 0.967161i | \(0.581800\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.03021e6 | 0.472417 | 0.236208 | − | 0.971702i | \(-0.424095\pi\) | ||||
0.236208 | + | 0.971702i | \(0.424095\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.06201e6 | 0.0989731 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.13341e7 | 1.04017 | 0.520084 | − | 0.854115i | \(-0.325901\pi\) | ||||
0.520084 | + | 0.854115i | \(0.325901\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.48502e6 | −0.863843 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.82007e6 | −0.342655 | −0.171328 | − | 0.985214i | \(-0.554806\pi\) | ||||
−0.171328 | + | 0.985214i | \(0.554806\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 926573. | 0.0824852 | 0.0412426 | − | 0.999149i | \(-0.486868\pi\) | ||||
0.0412426 | + | 0.999149i | \(0.486868\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.83547e6 | 0.160951 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.47555e7 | −3.02488 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 116835. | 0.0100176 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.90291e6 | 0.417269 | 0.208635 | − | 0.977994i | \(-0.433098\pi\) | ||||
0.208635 | + | 0.977994i | \(0.433098\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.47440e7 | 1.23636 | 0.618179 | − | 0.786037i | \(-0.287871\pi\) | ||||
0.618179 | + | 0.786037i | \(0.287871\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.75041e6 | 0.561896 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.53893e6 | 0.536358 | 0.268179 | − | 0.963369i | \(-0.413578\pi\) | ||||
0.268179 | + | 0.963369i | \(0.413578\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.25548e6 | 0.509371 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.65758e7 | 1.33023 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.09050e7 | −0.868818 | −0.434409 | − | 0.900716i | \(-0.643043\pi\) | ||||
−0.434409 | + | 0.900716i | \(0.643043\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.29937e6 | 0.337631 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.52090e6 | 0.196550 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.89162e7 | 1.45391 | 0.726957 | − | 0.686683i | \(-0.240934\pi\) | ||||
0.726957 | + | 0.686683i | \(0.240934\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.31146e7 | 1.00084 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.10258e6 | −0.459161 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.92732e7 | −1.43992 | −0.719960 | − | 0.694015i | \(-0.755840\pi\) | ||||
−0.719960 | + | 0.694015i | \(0.755840\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.03331e7 | 1.49789 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.90898e6 | 0.139648 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.42859e7 | −1.03059 | −0.515293 | − | 0.857014i | \(-0.672317\pi\) | ||||
−0.515293 | + | 0.857014i | \(0.672317\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.89421e6 | 0.135703 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.91711e7 | −1.35457 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.82771e7 | 1.98426 | 0.992132 | − | 0.125198i | \(-0.0399567\pi\) | ||||
0.992132 | + | 0.125198i | \(0.0399567\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.75992e6 | −0.121815 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.87699e6 | 0.678992 | 0.339496 | − | 0.940607i | \(-0.389743\pi\) | ||||
0.339496 | + | 0.940607i | \(0.389743\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.81381e6 | −0.394269 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.31081e6 | 0.425083 | 0.212542 | − | 0.977152i | \(-0.431826\pi\) | ||||
0.212542 | + | 0.977152i | \(0.431826\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 63059.8 | 0.00419064 | 0.00209532 | − | 0.999998i | \(-0.499333\pi\) | ||||
0.00209532 | + | 0.999998i | \(0.499333\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.83333e6 | −0.583088 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.43967e6 | −0.0937690 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.73837e7 | −1.12471 | −0.562356 | − | 0.826895i | \(-0.690105\pi\) | ||||
−0.562356 | + | 0.826895i | \(0.690105\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.56845e6 | −0.227831 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.43592e6 | 0.598473 | 0.299237 | − | 0.954179i | \(-0.403268\pi\) | ||||
0.299237 | + | 0.954179i | \(0.403268\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.61282e7 | −1.00954 | −0.504771 | − | 0.863254i | \(-0.668423\pi\) | ||||
−0.504771 | + | 0.863254i | \(0.668423\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −169020. | −0.0105106 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.98124e6 | 0.489871 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.56863e7 | −1.56634 | −0.783169 | − | 0.621809i | \(-0.786398\pi\) | ||||
−0.783169 | + | 0.621809i | \(0.786398\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.01235e7 | 1.21131 | 0.605654 | − | 0.795728i | \(-0.292912\pi\) | ||||
0.605654 | + | 0.795728i | \(0.292912\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.12157e7 | 0.670769 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.11135e7 | −0.656158 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.40742e6 | 0.0825652 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.11976e7 | −0.648559 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.75281e6 | 0.331088 | 0.165544 | − | 0.986202i | \(-0.447062\pi\) | ||||
0.165544 | + | 0.986202i | \(0.447062\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.30819e6 | −0.472134 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 878038. | 0.0495827 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.01964e7 | 0.568595 | 0.284298 | − | 0.958736i | \(-0.408240\pi\) | ||||
0.284298 | + | 0.958736i | \(0.408240\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.73056e6 | 0.206732 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.21629e6 | 0.285478 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.34152e6 | −0.399297 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.00420e6 | −0.322540 | −0.161270 | − | 0.986910i | \(-0.551559\pi\) | ||||
−0.161270 | + | 0.986910i | \(0.551559\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.23880e7 | 1.72915 | 0.864574 | − | 0.502506i | \(-0.167589\pi\) | ||||
0.864574 | + | 0.502506i | \(0.167589\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.17651e6 | −0.220252 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.75871e6 | 0.406663 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.56747e7 | −0.811600 | −0.405800 | − | 0.913962i | \(-0.633007\pi\) | ||||
−0.405800 | + | 0.913962i | \(0.633007\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.71466e7 | −1.39706 | −0.698532 | − | 0.715579i | \(-0.746163\pi\) | ||||
−0.698532 | + | 0.715579i | \(0.746163\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.28543e7 | −1.16199 | −0.580997 | − | 0.813906i | \(-0.697337\pi\) | ||||
−0.580997 | + | 0.813906i | \(0.697337\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.05418e7 | −1.03813 | −0.519066 | − | 0.854734i | \(-0.673720\pi\) | ||||
−0.519066 | + | 0.854734i | \(0.673720\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.20214e6 | 0.159893 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.36458e7 | 0.677301 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.47887e7 | 0.725313 | 0.362657 | − | 0.931923i | \(-0.381870\pi\) | ||||
0.362657 | + | 0.931923i | \(0.381870\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.16166e7 | 2.02897 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.57378e6 | 0.220360 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.57719e6 | −0.458701 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.24558e7 | −2.48296 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.05245e7 | −0.495253 | −0.247627 | − | 0.968856i | \(-0.579651\pi\) | ||||
−0.247627 | + | 0.968856i | \(0.579651\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.48671e7 | −0.691473 | −0.345736 | − | 0.938332i | \(-0.612371\pi\) | ||||
−0.345736 | + | 0.938332i | \(0.612371\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.64679e6 | −0.399827 | −0.199913 | − | 0.979814i | \(-0.564066\pi\) | ||||
−0.199913 | + | 0.979814i | \(0.564066\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.38401e7 | −1.08964 | −0.544818 | − | 0.838555i | \(-0.683401\pi\) | ||||
−0.544818 | + | 0.838555i | \(0.683401\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.03172e6 | 0.183210 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.67325e6 | 0.165007 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.36921e7 | −1.95145 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.25261e6 | −0.408549 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38315.7 | −0.00168220 | −0.000841100 | − | 1.00000i | \(-0.500268\pi\) | ||||
−0.000841100 | 1.00000i | \(0.500268\pi\) | ||||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.55072e7 | 1.10719 | 0.553596 | − | 0.832785i | \(-0.313255\pi\) | ||||
0.553596 | + | 0.832785i | \(0.313255\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.37096e7 | −1.45496 | −0.727482 | − | 0.686127i | \(-0.759309\pi\) | ||||
−0.727482 | + | 0.686127i | \(0.759309\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.64222e6 | 0.112761 | 0.0563806 | − | 0.998409i | \(-0.482044\pi\) | ||||
0.0563806 | + | 0.998409i | \(0.482044\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.49295e7 | 0.633564 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.64464e7 | −0.690148 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.93941e7 | 0.809306 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.63467e7 | −1.49991 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.61429e6 | 0.230400 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 741812. | 0.0301073 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.13018e6 | 0.287795 | 0.143897 | − | 0.989593i | \(-0.454037\pi\) | ||||
0.143897 | + | 0.989593i | \(0.454037\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.13154e7 | −1.25015 | −0.625075 | − | 0.780564i | \(-0.714932\pi\) | ||||
−0.625075 | + | 0.780564i | \(0.714932\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.18750e7 | 0.471472 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.27959e7 | −0.895226 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.28042e6 | 0.0890687 | 0.0445344 | − | 0.999008i | \(-0.485820\pi\) | ||||
0.0445344 | + | 0.999008i | \(0.485820\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.05771e7 | 0.408660 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.89346e7 | −1.11189 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.05725e7 | −0.401919 | −0.200959 | − | 0.979600i | \(-0.564406\pi\) | ||||
−0.200959 | + | 0.979600i | \(0.564406\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.41168e7 | −0.533781 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 646579. | 0.0241876 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.99327e7 | −1.48587 | −0.742934 | − | 0.669365i | \(-0.766566\pi\) | ||||
−0.742934 | + | 0.669365i | \(0.766566\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.32632e6 | 0.306534 | 0.153267 | − | 0.988185i | \(-0.451021\pi\) | ||||
0.153267 | + | 0.988185i | \(0.451021\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.44520e7 | 1.62784 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.75667e7 | −0.998873 | −0.499437 | − | 0.866350i | \(-0.666460\pi\) | ||||
−0.499437 | + | 0.866350i | \(0.666460\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.92016e7 | 1.41299 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.81280e7 | 1.35992 | 0.679958 | − | 0.733251i | \(-0.261998\pi\) | ||||
0.679958 | + | 0.733251i | \(0.261998\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.61418e6 | −0.0927528 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.50341e7 | 0.527876 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.36516e6 | −0.257261 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.09828e7 | 0.379660 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.72711e6 | −0.0937857 | −0.0468928 | − | 0.998900i | \(-0.514932\pi\) | ||||
−0.0468928 | + | 0.998900i | \(0.514932\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.26521e7 | −0.430641 | −0.215320 | − | 0.976543i | \(-0.569080\pi\) | ||||
−0.215320 | + | 0.976543i | \(0.569080\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.03329e7 | 0.349897 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.37252e7 | 1.13036 | 0.565182 | − | 0.824967i | \(-0.308806\pi\) | ||||
0.565182 | + | 0.824967i | \(0.308806\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.61493e6 | 0.320619 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.18743e7 | −0.391944 | −0.195972 | − | 0.980610i | \(-0.562786\pi\) | ||||
−0.195972 | + | 0.980610i | \(0.562786\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.70027e6 | −0.220040 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.10333e7 | −1.00888 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.31910e7 | −0.750128 | −0.375064 | − | 0.926999i | \(-0.622379\pi\) | ||||
−0.375064 | + | 0.926999i | \(0.622379\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.57845e7 | −0.505443 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.86264e7 | 1.23068 | 0.615342 | − | 0.788260i | \(-0.289018\pi\) | ||||
0.615342 | + | 0.788260i | \(0.289018\pi\) | |||||||
\(998\) | 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 | 324.6.a.d.1.4 | 5 | ||
3.2 | odd | 2 | 324.6.a.e.1.2 | 5 | |||
9.2 | odd | 6 | 36.6.e.a.13.4 | ✓ | 10 | ||
9.4 | even | 3 | 108.6.e.a.73.2 | 10 | |||
9.5 | odd | 6 | 36.6.e.a.25.4 | yes | 10 | ||
9.7 | even | 3 | 108.6.e.a.37.2 | 10 | |||
36.7 | odd | 6 | 432.6.i.d.145.2 | 10 | |||
36.11 | even | 6 | 144.6.i.d.49.2 | 10 | |||
36.23 | even | 6 | 144.6.i.d.97.2 | 10 | |||
36.31 | odd | 6 | 432.6.i.d.289.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.6.e.a.13.4 | ✓ | 10 | 9.2 | odd | 6 | ||
36.6.e.a.25.4 | yes | 10 | 9.5 | odd | 6 | ||
108.6.e.a.37.2 | 10 | 9.7 | even | 3 | |||
108.6.e.a.73.2 | 10 | 9.4 | even | 3 | |||
144.6.i.d.49.2 | 10 | 36.11 | even | 6 | |||
144.6.i.d.97.2 | 10 | 36.23 | even | 6 | |||
324.6.a.d.1.4 | 5 | 1.1 | even | 1 | trivial | ||
324.6.a.e.1.2 | 5 | 3.2 | odd | 2 | |||
432.6.i.d.145.2 | 10 | 36.7 | odd | 6 | |||
432.6.i.d.289.2 | 10 | 36.31 | odd | 6 |