Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [688,6,Mod(1,688)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(688, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("688.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 688 = 2^{4} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 688.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: | \(110.344068031\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 173x^{6} + 462x^{5} + 9118x^{4} - 14192x^{3} - 167688x^{2} + 106368x + 681984 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(10.9591\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 688.1 |
$q$-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 | ||||||||
\(3\) | 25.1057 | 1.61053 | 0.805264 | − | 0.592916i | \(-0.202023\pi\) | ||||
0.805264 | + | 0.592916i | \(0.202023\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −61.2927 | −1.09644 | −0.548219 | − | 0.836335i | \(-0.684694\pi\) | ||||
−0.548219 | + | 0.836335i | \(0.684694\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 166.001 | 1.28046 | 0.640230 | − | 0.768183i | \(-0.278839\pi\) | ||||
0.640230 | + | 0.768183i | \(0.278839\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 387.294 | 1.59380 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −607.827 | −1.51460 | −0.757301 | − | 0.653066i | \(-0.773482\pi\) | ||||
−0.757301 | + | 0.653066i | \(0.773482\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1039.54 | −1.70602 | −0.853011 | − | 0.521894i | \(-0.825226\pi\) | ||||
−0.853011 | + | 0.521894i | \(0.825226\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1538.79 | −1.76584 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1439.76 | 1.20828 | 0.604138 | − | 0.796880i | \(-0.293517\pi\) | ||||
0.604138 | + | 0.796880i | \(0.293517\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1332.62 | 0.846881 | 0.423440 | − | 0.905924i | \(-0.360822\pi\) | ||||
0.423440 | + | 0.905924i | \(0.360822\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4167.57 | 2.06222 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 437.244 | 0.172347 | 0.0861737 | − | 0.996280i | \(-0.472536\pi\) | ||||
0.0861737 | + | 0.996280i | \(0.472536\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 631.800 | 0.202176 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3622.60 | 0.956336 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −87.2656 | −0.0192685 | −0.00963425 | − | 0.999954i | \(-0.503067\pi\) | ||||
−0.00963425 | + | 0.999954i | \(0.503067\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2654.45 | −0.496101 | −0.248050 | − | 0.968747i | \(-0.579790\pi\) | ||||
−0.248050 | + | 0.968747i | \(0.579790\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −15259.9 | −2.43931 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −10174.7 | −1.40394 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4671.70 | −0.561010 | −0.280505 | − | 0.959853i | \(-0.590502\pi\) | ||||
−0.280505 | + | 0.959853i | \(0.590502\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −26098.4 | −2.74760 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9012.91 | −0.837347 | −0.418674 | − | 0.908137i | \(-0.637505\pi\) | ||||
−0.418674 | + | 0.908137i | \(0.637505\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1849.00 | 0.152499 | ||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −23738.3 | −1.74751 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8623.49 | 0.569427 | 0.284714 | − | 0.958613i | \(-0.408101\pi\) | ||||
0.284714 | + | 0.958613i | \(0.408101\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10749.4 | 0.639577 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 36146.0 | 1.94596 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −28358.3 | −1.38672 | −0.693362 | − | 0.720590i | \(-0.743871\pi\) | ||||
−0.693362 | + | 0.720590i | \(0.743871\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 37255.4 | 1.66067 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 33456.3 | 1.36393 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −48066.0 | −1.79766 | −0.898832 | − | 0.438294i | \(-0.855583\pi\) | ||||
−0.898832 | + | 0.438294i | \(0.855583\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −39750.4 | −1.36778 | −0.683891 | − | 0.729585i | \(-0.739713\pi\) | ||||
−0.683891 | + | 0.729585i | \(0.739713\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 64291.2 | 2.04080 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 63716.5 | 1.87055 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −19233.9 | −0.523456 | −0.261728 | − | 0.965142i | \(-0.584292\pi\) | ||||
−0.261728 | + | 0.965142i | \(0.584292\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10977.3 | 0.277570 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −17008.5 | −0.400424 | −0.200212 | − | 0.979753i | \(-0.564163\pi\) | ||||
−0.200212 | + | 0.979753i | \(0.564163\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 22236.4 | 0.488380 | 0.244190 | − | 0.969727i | \(-0.421478\pi\) | ||||
0.244190 | + | 0.969727i | \(0.421478\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 15861.8 | 0.325610 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −100900. | −1.93939 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −36951.1 | −0.666131 | −0.333066 | − | 0.942904i | \(-0.608083\pi\) | ||||
−0.333066 | + | 0.942904i | \(0.608083\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3164.77 | −0.0535957 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 117990. | 1.87997 | 0.939985 | − | 0.341216i | \(-0.110839\pi\) | ||||
0.939985 | + | 0.341216i | \(0.110839\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −88246.5 | −1.32480 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2190.86 | −0.0310325 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 41537.6 | 0.555861 | 0.277931 | − | 0.960601i | \(-0.410351\pi\) | ||||
0.277931 | + | 0.960601i | \(0.410351\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −172565. | −2.18449 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −66641.7 | −0.798985 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −81679.9 | −0.928552 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 32593.9 | 0.351728 | 0.175864 | − | 0.984415i | \(-0.443728\pi\) | ||||
0.175864 | + | 0.984415i | \(0.443728\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −235408. | −2.41398 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7934.83 | −0.0773988 | −0.0386994 | − | 0.999251i | \(-0.512321\pi\) | ||||
−0.0386994 | + | 0.999251i | \(0.512321\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −132558. | −1.23116 | −0.615579 | − | 0.788075i | \(-0.711078\pi\) | ||||
−0.615579 | + | 0.788075i | \(0.711078\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −255442. | −2.26109 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −120642. | −1.01868 | −0.509342 | − | 0.860564i | \(-0.670111\pi\) | ||||
−0.509342 | + | 0.860564i | \(0.670111\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16769.1 | 0.135190 | 0.0675950 | − | 0.997713i | \(-0.478467\pi\) | ||||
0.0675950 | + | 0.997713i | \(0.478467\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −117286. | −0.903522 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18201.6 | −0.134096 | −0.0670478 | − | 0.997750i | \(-0.521358\pi\) | ||||
−0.0670478 | + | 0.997750i | \(0.521358\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −26799.9 | −0.188968 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −402609. | −2.71906 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 239001. | 1.54715 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 208403. | 1.29402 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −226275. | −1.34857 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 152815. | 0.874764 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 155225. | 0.853987 | 0.426994 | − | 0.904255i | \(-0.359573\pi\) | ||||
0.426994 | + | 0.904255i | \(0.359573\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 46420.4 | 0.245603 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −206749. | −1.05261 | −0.526303 | − | 0.850297i | \(-0.676422\pi\) | ||||
−0.526303 | + | 0.850297i | \(0.676422\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 221216. | 1.08440 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −222039. | −1.04856 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −219188. | −0.997736 | −0.498868 | − | 0.866678i | \(-0.666251\pi\) | ||||
−0.498868 | + | 0.866678i | \(0.666251\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −83047.4 | −0.364577 | −0.182288 | − | 0.983245i | \(-0.558350\pi\) | ||||
−0.182288 | + | 0.983245i | \(0.558350\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 216498. | 0.917079 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 631863. | 2.58394 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5348.75 | 0.0211267 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 269870. | 1.03006 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −505431. | −1.86507 | −0.932537 | − | 0.361074i | \(-0.882410\pi\) | ||||
−0.932537 | + | 0.361074i | \(0.882410\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 222212. | 0.793095 | 0.396548 | − | 0.918014i | \(-0.370208\pi\) | ||||
0.396548 | + | 0.918014i | \(0.370208\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 557609. | 1.92575 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 162698. | 0.543944 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18138.1 | 0.0587275 | 0.0293638 | − | 0.999569i | \(-0.490652\pi\) | ||||
0.0293638 | + | 0.999569i | \(0.490652\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −711953. | −2.23336 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 72583.1 | 0.220684 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 428372. | 1.26285 | 0.631425 | − | 0.775437i | \(-0.282470\pi\) | ||||
0.631425 | + | 0.775437i | \(0.282470\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 935321. | 2.67455 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −590110. | −1.63735 | −0.818676 | − | 0.574256i | \(-0.805291\pi\) | ||||
−0.818676 | + | 0.574256i | \(0.805291\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 709358. | 1.91051 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 516116. | 1.34976 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −194001. | −0.492821 | −0.246410 | − | 0.969166i | \(-0.579251\pi\) | ||||
−0.246410 | + | 0.969166i | \(0.579251\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 104880. | 0.258878 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.20673e6 | −2.89519 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 434140. | 1.01274 | 0.506369 | − | 0.862317i | \(-0.330988\pi\) | ||||
0.506369 | + | 0.862317i | \(0.330988\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −626829. | −1.42217 | −0.711087 | − | 0.703104i | \(-0.751797\pi\) | ||||
−0.711087 | + | 0.703104i | \(0.751797\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −997959. | −2.20285 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 286341. | 0.615112 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −875122. | −1.83006 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 601355. | 1.22455 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 109059. | 0.216310 | 0.108155 | − | 0.994134i | \(-0.465506\pi\) | ||||
0.108155 | + | 0.994134i | \(0.465506\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −31563.2 | −0.0609941 | −0.0304971 | − | 0.999535i | \(-0.509709\pi\) | ||||
−0.0304971 | + | 0.999535i | \(0.509709\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.59964e6 | 3.01257 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −276843. | −0.508238 | −0.254119 | − | 0.967173i | \(-0.581786\pi\) | ||||
−0.254119 | + | 0.967173i | \(0.581786\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 777649. | 1.39204 | 0.696019 | − | 0.718024i | \(-0.254953\pi\) | ||||
0.696019 | + | 0.718024i | \(0.254953\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −482879. | −0.843041 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −14486.2 | −0.0246725 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 552426. | 0.918099 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 169342. | 0.274688 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −810002. | −1.28269 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 89486.6 | 0.138373 | 0.0691866 | − | 0.997604i | \(-0.477960\pi\) | ||||
0.0691866 | + | 0.997604i | \(0.477960\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −427009. | −0.644894 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −113330. | −0.167205 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −440641. | −0.635237 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 558260. | 0.786550 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.49669e6 | −2.06135 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 952284. | 1.28234 | 0.641172 | − | 0.767398i | \(-0.278449\pi\) | ||||
0.641172 | + | 0.767398i | \(0.278449\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 244693. | 0.322229 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 465809. | 0.599988 | 0.299994 | − | 0.953941i | \(-0.403015\pi\) | ||||
0.299994 | + | 0.953941i | \(0.403015\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 477440. | 0.601631 | 0.300815 | − | 0.953682i | \(-0.402741\pi\) | ||||
0.300815 | + | 0.953682i | \(0.402741\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.53316e6 | −3.12344 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 743589. | 0.897312 | 0.448656 | − | 0.893705i | \(-0.351903\pi\) | ||||
0.448656 | + | 0.893705i | \(0.351903\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −528557. | −0.624342 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −927682. | −1.07282 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.27115e6 | −1.43947 | −0.719734 | − | 0.694250i | \(-0.755736\pi\) | ||||
−0.719734 | + | 0.694250i | \(0.755736\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −875960. | −0.971497 | −0.485749 | − | 0.874099i | \(-0.661453\pi\) | ||||
−0.485749 | + | 0.874099i | \(0.661453\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −959745. | −1.04265 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −658858. | −0.701256 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.38532e6 | −1.44480 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.96222e6 | 3.02774 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.19674e6 | 1.19899 | 0.599494 | − | 0.800380i | \(-0.295369\pi\) | ||||
0.599494 | + | 0.800380i | \(0.295369\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −265769. | −0.261038 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.21549e6 | −2.13363 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.31630e6 | −1.24315 | −0.621573 | − | 0.783357i | \(-0.713506\pi\) | ||||
−0.621573 | + | 0.783357i | \(0.713506\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −775507. | −0.718350 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −33797.4 | −0.0307102 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.74612e6 | −1.55663 | −0.778314 | − | 0.627876i | \(-0.783925\pi\) | ||||
−0.778314 | + | 0.627876i | \(0.783925\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.73816e6 | 1.52046 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.04283e6 | 0.895231 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −470733. | −0.396637 | −0.198319 | − | 0.980138i | \(-0.563548\pi\) | ||||
−0.198319 | + | 0.980138i | \(0.563548\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −29459.5 | −0.0243670 | −0.0121835 | − | 0.999926i | \(-0.503878\pi\) | ||||
−0.0121835 | + | 0.999926i | \(0.503878\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.33237e6 | −3.51819 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −384025. | −0.306216 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.01172e6 | 0.792244 | 0.396122 | − | 0.918198i | \(-0.370356\pi\) | ||||
0.396122 | + | 0.918198i | \(0.370356\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.02805e6 | −0.790687 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −74592.9 | −0.0563549 | −0.0281775 | − | 0.999603i | \(-0.508970\pi\) | ||||
−0.0281775 | + | 0.999603i | \(0.508970\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.14789e6 | 0.851993 | 0.425996 | − | 0.904725i | \(-0.359924\pi\) | ||||
0.425996 | + | 0.904725i | \(0.359924\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.05063e6 | −1.49546 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.49615e6 | −1.07219 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 653038. | 0.459932 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 818290. | 0.566467 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.30694e6 | −0.889376 | −0.444688 | − | 0.895686i | \(-0.646685\pi\) | ||||
−0.444688 | + | 0.895686i | \(0.646685\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.94610e6 | 1.97103 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.20191e6 | −1.44847 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −454535. | −0.294028 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 306936. | 0.195268 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −199209. | −0.124653 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.43641e6 | 1.49969 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.50999e6 | 0.914380 | 0.457190 | − | 0.889369i | \(-0.348856\pi\) | ||||
0.457190 | + | 0.889369i | \(0.348856\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.32796e6 | −1.98282 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.69979e6 | −0.996539 | −0.498269 | − | 0.867022i | \(-0.666031\pi\) | ||||
−0.498269 | + | 0.867022i | \(0.666031\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.85190e6 | 1.64541 | 0.822703 | − | 0.568471i | \(-0.192465\pi\) | ||||
0.822703 | + | 0.568471i | \(0.192465\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.94059e6 | −2.23761 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −158403. | −0.0885351 | −0.0442676 | − | 0.999020i | \(-0.514095\pi\) | ||||
−0.0442676 | + | 0.999020i | \(0.514095\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 53042.4 | 0.0291841 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.02880e6 | −1.64062 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.91865e6 | 1.02327 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −656784. | −0.344917 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 421000. | 0.217727 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.43151e6 | 0.729129 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.38726e6 | −0.695968 | −0.347984 | − | 0.937501i | \(-0.613134\pi\) | ||||
−0.347984 | + | 0.937501i | \(0.613134\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.80932e6 | −0.894139 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.17890e6 | 0.573937 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 602990. | 0.289225 | 0.144612 | − | 0.989488i | \(-0.453807\pi\) | ||||
0.144612 | + | 0.989488i | \(0.453807\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −456964. | −0.215965 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.61345e6 | 0.751395 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00557e6 | −0.461507 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −672829. | −0.304339 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.38847e6 | −0.619030 | −0.309515 | − | 0.950895i | \(-0.600167\pi\) | ||||
−0.309515 | + | 0.950895i | \(0.600167\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.90607e6 | 0.837676 | 0.418838 | − | 0.908061i | \(-0.362437\pi\) | ||||
0.418838 | + | 0.908061i | \(0.362437\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.76585e6 | −1.63153 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.53782e6 | −1.08399 | −0.541993 | − | 0.840383i | \(-0.682330\pi\) | ||||
−0.541993 | + | 0.840383i | \(0.682330\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.04250e6 | 0.439040 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.00028e6 | 2.49173 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 589213. | 0.241288 | 0.120644 | − | 0.992696i | \(-0.461504\pi\) | ||||
0.120644 | + | 0.992696i | \(0.461504\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −700223. | −0.282793 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.23209e6 | 2.08405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.36293e6 | −0.535478 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.67673e6 | −0.649826 | −0.324913 | − | 0.945744i | \(-0.605335\pi\) | ||||
−0.324913 | + | 0.945744i | \(0.605335\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.49065e6 | −1.33457 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.70750e6 | −1.77564 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.12665e6 | 1.16361 | 0.581804 | − | 0.813329i | \(-0.302347\pi\) | ||||
0.581804 | + | 0.813329i | \(0.302347\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.83652e6 | 1.40883 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 90716.4 | 0.0328725 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.98431e6 | 0.709596 | 0.354798 | − | 0.934943i | \(-0.384550\pi\) | ||||
0.354798 | + | 0.934943i | \(0.384550\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.89702e6 | 1.37537 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −321813. | −0.112100 | −0.0560502 | − | 0.998428i | \(-0.517851\pi\) | ||||
−0.0560502 | + | 0.998428i | \(0.517851\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.18444e6 | 2.12642 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 716107. | 0.243053 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.34564e6 | −0.450874 | −0.225437 | − | 0.974258i | \(-0.572381\pi\) | ||||
−0.225437 | + | 0.974258i | \(0.572381\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 629525. | 0.208243 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.19057e6 | −1.69525 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.26484e6 | 0.730372 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.40299e6 | 0.446763 | 0.223382 | − | 0.974731i | \(-0.428290\pi\) | ||||
0.223382 | + | 0.974731i | \(0.428290\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.55378e6 | 1.74645 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.44258e6 | 1.06911 | 0.534556 | − | 0.845133i | \(-0.320479\pi\) | ||||
0.534556 | + | 0.845133i | \(0.320479\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.75942e6 | 0.846359 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 193977. | 0.0587643 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.83958e6 | 0.849706 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.44614e6 | 1.90542 | 0.952711 | − | 0.303877i | \(-0.0982811\pi\) | ||||
0.952711 | + | 0.303877i | \(0.0982811\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.50286e6 | −1.60688 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.97902e6 | −2.30184 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.23194e6 | −2.06127 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.08496e6 | −0.587161 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.77865e6 | 0.494943 | 0.247472 | − | 0.968895i | \(-0.420400\pi\) | ||||
0.247472 | + | 0.968895i | \(0.420400\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.37157e6 | −0.927100 | −0.463550 | − | 0.886071i | \(-0.653425\pi\) | ||||
−0.463550 | + | 0.886071i | \(0.653425\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.33983e6 | 0.907555 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 909638. | 0.244285 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.59861e6 | −1.75139 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.58633e7 | 4.16151 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.38644e6 | −0.359508 | −0.179754 | − | 0.983712i | \(-0.557530\pi\) | ||||
−0.179754 | + | 0.983712i | \(0.557530\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.74536e6 | 1.47264 | 0.736322 | − | 0.676632i | \(-0.236561\pi\) | ||||
0.736322 | + | 0.676632i | \(0.236561\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 134284. | 0.0340252 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 582681. | 0.145958 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.14484e6 | 1.27412 | 0.637060 | − | 0.770814i | \(-0.280150\pi\) | ||||
0.637060 | + | 0.770814i | \(0.280150\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.16317e6 | 1.01936 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.65845e6 | 1.36990 | 0.684949 | − | 0.728591i | \(-0.259824\pi\) | ||||
0.684949 | + | 0.728591i | \(0.259824\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.54595e6 | −0.609468 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.26892e7 | −3.00376 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −956361. | −0.223875 | −0.111938 | − | 0.993715i | \(-0.535706\pi\) | ||||
−0.111938 | + | 0.993715i | \(0.535706\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.47829e6 | 1.26825 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.57878e6 | 1.27730 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.05770e7 | 2.39516 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.50698e6 | −1.23345 | −0.616727 | − | 0.787177i | \(-0.711542\pi\) | ||||
−0.616727 | + | 0.787177i | \(0.711542\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.21565e6 | 1.15552 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.10202e6 | 0.460665 | 0.230333 | − | 0.973112i | \(-0.426019\pi\) | ||||
0.230333 | + | 0.973112i | \(0.426019\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.36108e6 | −0.511868 | −0.255934 | − | 0.966694i | \(-0.582383\pi\) | ||||
−0.255934 | + | 0.966694i | \(0.582383\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.08465e6 | 0.876037 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.56485e6 | 1.81730 | 0.908652 | − | 0.417554i | \(-0.137113\pi\) | ||||
0.908652 | + | 0.417554i | \(0.137113\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.19285e6 | −0.670264 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 455368. | 0.0945823 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.12387e6 | −0.230975 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 841950. | 0.171219 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.09830e7 | −2.21016 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.09570e6 | −0.616481 | −0.308241 | − | 0.951308i | \(-0.599740\pi\) | ||||
−0.308241 | + | 0.951308i | \(0.599740\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.85643e6 | 0.957095 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.82225e6 | 0.355418 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.99777e6 | −0.385648 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.69724e6 | 0.897471 | 0.448736 | − | 0.893665i | \(-0.351875\pi\) | ||||
0.448736 | + | 0.893665i | \(0.351875\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.07546e7 | 2.03386 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.40851e6 | −0.825255 | −0.412628 | − | 0.910900i | \(-0.635389\pi\) | ||||
−0.412628 | + | 0.910900i | \(0.635389\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −125641. | −0.0232817 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.44288e7 | 2.64677 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.82343e6 | −0.512726 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.52789e6 | −0.634255 | −0.317127 | − | 0.948383i | \(-0.602718\pi\) | ||||
−0.317127 | + | 0.948383i | \(0.602718\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.48151e7 | −2.63700 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −79054.9 | −0.0139319 | −0.00696593 | − | 0.999976i | \(-0.502217\pi\) | ||||
−0.00696593 | + | 0.999976i | \(0.502217\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 486347. | 0.0848629 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.78089e7 | 3.07693 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 155909. | 0.0266733 | 0.0133366 | − | 0.999911i | \(-0.495755\pi\) | ||||
0.0133366 | + | 0.999911i | \(0.495755\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.69127e6 | 0.625351 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.82754e6 | 0.809903 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.12486e6 | 1.34989 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.24159e6 | −0.862456 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.87052e6 | −0.793702 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.24897e6 | −0.685787 | −0.342893 | − | 0.939374i | \(-0.611407\pi\) | ||||
−0.342893 | + | 0.939374i | \(0.611407\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.30285e6 | −0.208276 | −0.104138 | − | 0.994563i | \(-0.533208\pi\) | ||||
−0.104138 | + | 0.994563i | \(0.533208\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.63307e6 | 0.416931 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.82176e6 | −0.599427 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.24516e6 | −0.970296 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.86157e7 | −2.86512 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.36932e6 | 1.42853 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.39449e6 | 1.11692 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.08994e7 | 1.63104 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.53376e6 | −0.968704 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.58581e6 | 0.232948 | 0.116474 | − | 0.993194i | \(-0.462841\pi\) | ||||
0.116474 | + | 0.993194i | \(0.462841\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.57370e7 | −2.29045 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.02783e6 | −0.148227 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.60569e6 | 0.801052 | 0.400526 | − | 0.916285i | \(-0.368827\pi\) | ||||
0.400526 | + | 0.916285i | \(0.368827\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.53951e7 | −2.17997 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −116292. | −0.0163181 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.13393e6 | −0.852954 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.18878e6 | 0.990656 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −44346.9 | −0.00605655 | −0.00302828 | − | 0.999995i | \(-0.500964\pi\) | ||||
−0.00302828 | + | 0.999995i | \(0.500964\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.92212e6 | −0.260166 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.19705e7 | −2.94736 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.30007e6 | −0.571748 | −0.285874 | − | 0.958267i | \(-0.592284\pi\) | ||||
−0.285874 | + | 0.958267i | \(0.592284\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.11563e6 | 0.147027 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −525355. | −0.0686271 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.54339e6 | 0.847271 | 0.423635 | − | 0.905833i | \(-0.360754\pi\) | ||||
0.423635 | + | 0.905833i | \(0.360754\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.65292e6 | −1.11064 | −0.555319 | − | 0.831637i | \(-0.687404\pi\) | ||||
−0.555319 | + | 0.831637i | \(0.687404\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.73799e6 | 0.348374 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 276251. | 0.0348445 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.48407e6 | 0.435660 | 0.217830 | − | 0.975987i | \(-0.430102\pi\) | ||||
0.217830 | + | 0.975987i | \(0.430102\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −792415. | −0.0982328 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.95865e7 | 2.40723 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.72369e7 | 2.10033 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.46770e7 | 2.98128 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.56208e6 | −0.786043 | −0.393021 | − | 0.919529i | \(-0.628570\pi\) | ||||
−0.393021 | + | 0.919529i | \(0.628570\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.53737e6 | −0.420138 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.95032e6 | −0.818532 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.08785e6 | 0.944488 | 0.472244 | − | 0.881468i | \(-0.343444\pi\) | ||||
0.472244 | + | 0.881468i | \(0.343444\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.46490e7 | −1.69635 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.95234e7 | 2.24192 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.16029e6 | 1.04314 | 0.521569 | − | 0.853209i | \(-0.325347\pi\) | ||||
0.521569 | + | 0.853209i | \(0.325347\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.25891e7 | −1.42171 | −0.710853 | − | 0.703341i | \(-0.751691\pi\) | ||||
−0.710853 | + | 0.703341i | \(0.751691\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.44917e6 | −0.834285 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.27736e7 | −1.41881 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.05315e7 | 1.16017 | 0.580083 | − | 0.814558i | \(-0.303020\pi\) | ||||
0.580083 | + | 0.814558i | \(0.303020\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −363685. | −0.0397358 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.96450e6 | −0.971455 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.50815e6 | 0.269589 | 0.134794 | − | 0.990874i | \(-0.456963\pi\) | ||||
0.134794 | + | 0.990874i | \(0.456963\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.38690e7 | 1.47863 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.04940e7 | 1.10975 | 0.554876 | − | 0.831933i | \(-0.312766\pi\) | ||||
0.554876 | + | 0.831933i | \(0.312766\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.31973e6 | 0.767836 | 0.383918 | − | 0.923367i | \(-0.374574\pi\) | ||||
0.383918 | + | 0.923367i | \(0.374574\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.58396e6 | 0.164822 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.89529e6 | 0.711758 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.13408e7 | −1.16130 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.03356e7 | −2.06580 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.72610e6 | −0.677855 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.30990e6 | 0.630883 | 0.315442 | − | 0.948945i | \(-0.397847\pi\) | ||||
0.315442 | + | 0.948945i | \(0.397847\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.24662e6 | 0.222854 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.51414e6 | −0.936344 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.11744e7 | −1.09113 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.58729e6 | −0.638196 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 176304. | 0.0169479 | 0.00847395 | − | 0.999964i | \(-0.497303\pi\) | ||||
0.00847395 | + | 0.999964i | \(0.497303\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.73829e6 | 0.451954 | 0.225977 | − | 0.974133i | \(-0.427443\pi\) | ||||
0.225977 | + | 0.974133i | \(0.427443\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.84523e6 | −0.269289 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.27894e7 | 1.20113 | 0.600563 | − | 0.799577i | \(-0.294943\pi\) | ||||
0.600563 | + | 0.799577i | \(0.294943\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.92158e7 | 2.72274 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.10626e7 | −1.02307 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.31597e6 | 0.212545 | 0.106272 | − | 0.994337i | \(-0.466108\pi\) | ||||
0.106272 | + | 0.994337i | \(0.466108\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.26722e7 | 1.15412 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.61203e6 | 0.778381 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.32880e6 | 0.388288 | 0.194144 | − | 0.980973i | \(-0.437807\pi\) | ||||
0.194144 | + | 0.980973i | \(0.437807\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.34429e7 | 1.19671 | 0.598355 | − | 0.801231i | \(-0.295821\pi\) | ||||
0.598355 | + | 0.801231i | \(0.295821\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.75754e7 | −3.31986 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.35590e7 | −1.18897 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −38156.4 | −0.00332088 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.39077e7 | 2.06525 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.41614e7 | 2.07164 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.30893e7 | −1.11398 | −0.556991 | − | 0.830518i | \(-0.688044\pi\) | ||||
−0.556991 | + | 0.830518i | \(0.688044\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.28876e6 | 0.193348 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.26746e6 | 0.106283 | 0.0531415 | − | 0.998587i | \(-0.483077\pi\) | ||||
0.0531415 | + | 0.998587i | \(0.483077\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.41062e6 | 0.450373 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.16944e7 | 0.966298 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.77529e7 | 1.45619 | 0.728093 | − | 0.685479i | \(-0.240407\pi\) | ||||
0.728093 | + | 0.685479i | \(0.240407\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.34346e7 | 1.09396 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.19864e7 | 0.968944 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.94797e7 | 2.36578 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.47133e6 | −0.435911 | −0.217955 | − | 0.975959i | \(-0.569939\pi\) | ||||
−0.217955 | + | 0.975959i | \(0.569939\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.90780e7 | −3.09100 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.09020e6 | 0.399736 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.29764e7 | −1.01175 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.86683e7 | 1.44515 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.16242e7 | −0.893443 | −0.446721 | − | 0.894673i | \(-0.647408\pi\) | ||||
−0.446721 | + | 0.894673i | \(0.647408\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.22560e6 | −0.475108 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.32698e7 | −1.00552 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.31719e6 | −0.0991060 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.30447e6 | −0.321591 | −0.160795 | − | 0.986988i | \(-0.551406\pi\) | ||||
−0.160795 | + | 0.986988i | \(0.551406\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.43110e7 | −1.06168 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.16064e6 | −0.0855017 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.87286e7 | −2.83313 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.19130e7 | −2.31830 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.35107e7 | −0.974664 | −0.487332 | − | 0.873217i | \(-0.662030\pi\) | ||||
−0.487332 | + | 0.873217i | \(0.662030\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.20048e7 | −1.57645 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.19915e7 | −1.56462 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −55134.4 | −0.00389563 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.62118e7 | −1.83934 | −0.919668 | − | 0.392697i | \(-0.871542\pi\) | ||||
−0.919668 | + | 0.392697i | \(0.871542\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.33260e7 | −1.62563 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.66211e6 | 0.184260 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.19136e7 | −1.50644 | −0.753222 | − | 0.657766i | \(-0.771501\pi\) | ||||
−0.753222 | + | 0.657766i | \(0.771501\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.65411e7 | −1.12939 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.16909e7 | 0.792827 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.72080e6 | 0.183267 | 0.0916337 | − | 0.995793i | \(-0.470791\pi\) | ||||
0.0916337 | + | 0.995793i | \(0.470791\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.47793e7 | −2.32689 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.79913e6 | 0.385381 | 0.192691 | − | 0.981260i | \(-0.438279\pi\) | ||||
0.192691 | + | 0.981260i | \(0.438279\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.09792e7 | 2.04494 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.56969e7 | 2.99630 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.00267e7 | −1.30438 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.22708e6 | 0.144091 | 0.0720455 | − | 0.997401i | \(-0.477047\pi\) | ||||
0.0720455 | + | 0.997401i | \(0.477047\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.00449e7 | 1.93100 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.36200e7 | −0.869579 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.68706e7 | 1.07002 | 0.535009 | − | 0.844846i | \(-0.320308\pi\) | ||||
0.535009 | + | 0.844846i | \(0.320308\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.67231e6 | −0.420409 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.73683e6 | −0.421691 | −0.210845 | − | 0.977519i | \(-0.567622\pi\) | ||||
−0.210845 | + | 0.977519i | \(0.567622\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.78370e6 | 0.173105 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.41774e7 | −2.11147 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.99668e7 | 3.06685 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.99965e7 | 1.82917 | 0.914587 | − | 0.404390i | \(-0.132516\pi\) | ||||
0.914587 | + | 0.404390i | \(0.132516\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.30466e7 | −2.00212 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.03964e7 | 1.22773 | 0.613867 | − | 0.789409i | \(-0.289613\pi\) | ||||
0.613867 | + | 0.789409i | \(0.289613\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.67708e6 | −0.100300 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.94696e7 | −1.15692 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.20108e7 | −0.709133 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.03382e7 | 0.606482 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −316128. | −0.0184272 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.11173e6 | −0.0643911 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.96285e6 | 0.573386 | 0.286693 | − | 0.958023i | \(-0.407444\pi\) | ||||
0.286693 | + | 0.958023i | \(0.407444\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.38375e7 | −2.50699 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.02149e6 | −0.171704 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.13223e7 | 2.33346 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.36375e7 | 2.44874 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.33007e6 | −0.241462 | −0.120731 | − | 0.992685i | \(-0.538524\pi\) | ||||
−0.120731 | + | 0.992685i | \(0.538524\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.24157e7 | 0.688026 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.60873e7 | 0.885933 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.35159e7 | −0.739701 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.44881e6 | −0.241966 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.18181e7 | −0.638796 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.65045e6 | 0.249818 | 0.124909 | − | 0.992168i | \(-0.460136\pi\) | ||||
0.124909 | + | 0.992168i | \(0.460136\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.23521e7 | 1.19334 | 0.596672 | − | 0.802486i | \(-0.296490\pi\) | ||||
0.596672 | + | 0.802486i | \(0.296490\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −739599. | −0.0392437 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.62561e7 | −1.38464 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.46401e6 | 0.129148 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.68336e7 | −3.48165 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.86450e6 | 0.355427 | 0.177714 | − | 0.984082i | \(-0.443130\pi\) | ||||
0.177714 | + | 0.984082i | \(0.443130\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.78159e7 | 1.94614 | 0.973072 | − | 0.230502i | \(-0.0740369\pi\) | ||||
0.973072 | + | 0.230502i | \(0.0740369\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9.64121e6 | −0.493170 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.11812e7 | −1.58536 | −0.792681 | − | 0.609637i | \(-0.791315\pi\) | ||||
−0.792681 | + | 0.609637i | \(0.791315\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.56161e6 | −0.382145 | −0.191072 | − | 0.981576i | \(-0.561196\pi\) | ||||
−0.191072 | + | 0.981576i | \(0.561196\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.53998e7 | 1.27593 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.54765e7 | 0.772786 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.61695e7 | 1.79525 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.61600e6 | −0.474439 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.20663e7 | −0.591792 | −0.295896 | − | 0.955220i | \(-0.595618\pi\) | ||||
−0.295896 | + | 0.955220i | \(0.595618\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.05035e7 | −0.999629 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.87270e6 | −0.0907612 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.34785e7 | −2.09475 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.45951e7 | 1.65694 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.88186e7 | 1.37216 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.04267e6 | −0.0966886 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.73307e7 | 1.28611 | 0.643055 | − | 0.765820i | \(-0.277667\pi\) | ||||
0.643055 | + | 0.765820i | \(0.277667\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.16341e7 | −1.47993 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.10213e7 | −1.44280 | −0.721402 | − | 0.692516i | \(-0.756502\pi\) | ||||
−0.721402 | + | 0.692516i | \(0.756502\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.98878e7 | −1.38201 | −0.691006 | − | 0.722849i | \(-0.742832\pi\) | ||||
−0.691006 | + | 0.722849i | \(0.742832\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.75619e7 | −1.72679 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.37019e7 | 1.08332 | 0.541660 | − | 0.840598i | \(-0.317796\pi\) | ||||
0.541660 | + | 0.840598i | \(0.317796\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.18909e7 | 0.540347 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.63949e7 | 0.740734 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.24599e7 | 1.00892 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.99945e7 | 0.893027 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.26234e7 | 0.560584 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.53675e7 | 1.12010 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.85645e7 | 1.69312 | 0.846562 | − | 0.532290i | \(-0.178668\pi\) | ||||
0.846562 | + | 0.532290i | \(0.178668\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.28115e7 | −1.43237 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.45951e7 | −1.50167 | −0.750836 | − | 0.660489i | \(-0.770349\pi\) | ||||
−0.750836 | + | 0.660489i | \(0.770349\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.71550e6 | 0.376175 | 0.188088 | − | 0.982152i | \(-0.439771\pi\) | ||||
0.188088 | + | 0.982152i | \(0.439771\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.39638e7 | 3.17439 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.58909e6 | −0.195847 | −0.0979237 | − | 0.995194i | \(-0.531220\pi\) | ||||
−0.0979237 | + | 0.995194i | \(0.531220\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.57675e7 | 1.09350 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.92363e6 | 0.0811761 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.14918e7 | 0.482237 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.66096e7 | −1.11040 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.14114e7 | −0.473541 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 231642. | 0.00955912 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.08290e7 | −1.67555 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.70583e6 | 0.314485 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.84201e7 | 1.55933 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.10880e7 | −0.447544 | −0.223772 | − | 0.974642i | \(-0.571837\pi\) | ||||
−0.223772 | + | 0.974642i | \(0.571837\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.07311e6 | −0.123358 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.54367e7 | −1.41468 | −0.707339 | − | 0.706875i | \(-0.750104\pi\) | ||||
−0.707339 | + | 0.706875i | \(0.750104\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.17177e7 | −2.84740 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.11677e7 | 2.41529 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.43206e7 | −1.34782 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.32990e7 | −1.30060 | −0.650298 | − | 0.759679i | \(-0.725356\pi\) | ||||
−0.650298 | + | 0.759679i | \(0.725356\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.79092e7 | 1.47264 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.76811e7 | 0.683131 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.95158e6 | −0.113423 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.13390e7 | −1.96222 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.43816e7 | 1.30703 | 0.653517 | − | 0.756912i | \(-0.273293\pi\) | ||||
0.653517 | + | 0.756912i | \(0.273293\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.43248e7 | 0.541645 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.26743e7 | −1.60495 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.36386e7 | 2.00654 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.81989e7 | 1.42135 | 0.710677 | − | 0.703518i | \(-0.248389\pi\) | ||||
0.710677 | + | 0.703518i | \(0.248389\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.15988e7 | 2.64997 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.92661e7 | 1.07744 | 0.538718 | − | 0.842486i | \(-0.318909\pi\) | ||||
0.538718 | + | 0.842486i | \(0.318909\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.94085e6 | −0.144315 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.68587e7 | −1.34264 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.49447e6 | −0.162856 | −0.0814280 | − | 0.996679i | \(-0.525948\pi\) | ||||
−0.0814280 | + | 0.996679i | \(0.525948\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.31157e7 | −0.833186 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.97681e6 | −0.142588 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.96508e6 | −0.284091 | −0.142046 | − | 0.989860i | \(-0.545368\pi\) | ||||
−0.142046 | + | 0.989860i | \(0.545368\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.68451e6 | −0.237171 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.33166e6 | 0.0470018 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.63855e7 | −1.27756 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.15831e7 | −0.753884 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.67240e7 | −1.62358 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.93460e6 | 0.0668763 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.91114e6 | −0.134505 | −0.0672523 | − | 0.997736i | \(-0.521423\pi\) | ||||
−0.0672523 | + | 0.997736i | \(0.521423\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.81689e7 | 1.64800 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.98964e7 | 1.01759 | 0.508793 | − | 0.860889i | \(-0.330092\pi\) | ||||
0.508793 | + | 0.860889i | \(0.330092\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.37860e7 | −0.466826 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.64890e7 | −0.555498 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.36187e7 | −1.46196 | −0.730981 | − | 0.682398i | \(-0.760937\pi\) | ||||
−0.730981 | + | 0.682398i | \(0.760937\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.52477e7 | −0.841909 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.49459e6 | 0.215466 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.95377e7 | 0.644895 | 0.322448 | − | 0.946587i | \(-0.395494\pi\) | ||||
0.322448 | + | 0.946587i | \(0.395494\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.69684e7 | 0.557252 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.59390e7 | 1.17428 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 808465. | 0.0262827 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.45462e7 | −1.11742 | −0.558709 | − | 0.829364i | \(-0.688703\pi\) | ||||
−0.558709 | + | 0.829364i | \(0.688703\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.48282e7 | −1.12088 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.76642e7 | −1.52628 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.34457e7 | 1.06562 | 0.532810 | − | 0.846235i | \(-0.321136\pi\) | ||||
0.532810 | + | 0.846235i | \(0.321136\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.69237e7 | −0.536514 |
(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 | 688.6.a.e.1.7 | 8 | ||
4.3 | odd | 2 | 43.6.a.a.1.8 | ✓ | 8 | ||
12.11 | even | 2 | 387.6.a.c.1.1 | 8 | |||
20.19 | odd | 2 | 1075.6.a.a.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.6.a.a.1.8 | ✓ | 8 | 4.3 | odd | 2 | ||
387.6.a.c.1.1 | 8 | 12.11 | even | 2 | |||
688.6.a.e.1.7 | 8 | 1.1 | even | 1 | trivial | ||
1075.6.a.a.1.1 | 8 | 20.19 | odd | 2 |