Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,5,Mod(296,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("531.296");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(54.8894503975\) |
Analytic rank: | \(0\) |
Dimension: | \(76\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 296.1 | ||
Character | \(\chi\) | \(=\) | 531.296 |
Dual form | 531.5.b.a.296.76 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/531\mathbb{Z}\right)^\times\).
\(n\) | \(119\) | \(415\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 7.89147i | − 1.97287i | −0.164159 | − | 0.986434i | \(-0.552491\pi\) | ||||
0.164159 | − | 0.986434i | \(-0.447509\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −46.2753 | −2.89221 | ||||||||
\(5\) | − 30.7341i | − 1.22936i | −0.788775 | − | 0.614682i | \(-0.789285\pi\) | ||||
0.788775 | − | 0.614682i | \(-0.210715\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −38.0387 | −0.776300 | −0.388150 | − | 0.921596i | \(-0.626886\pi\) | ||||
−0.388150 | + | 0.921596i | \(0.626886\pi\) | |||||||
\(8\) | 238.917i | 3.73308i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −242.537 | −2.42537 | ||||||||
\(11\) | 97.9176i | 0.809236i | 0.914486 | + | 0.404618i | \(0.132596\pi\) | ||||
−0.914486 | + | 0.404618i | \(0.867404\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 266.782 | 1.57859 | 0.789296 | − | 0.614013i | \(-0.210446\pi\) | ||||
0.789296 | + | 0.614013i | \(0.210446\pi\) | |||||||
\(14\) | 300.181i | 1.53154i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1145.00 | 4.47266 | ||||||||
\(17\) | − 405.373i | − 1.40268i | −0.712829 | − | 0.701338i | \(-0.752586\pi\) | ||||
0.712829 | − | 0.701338i | \(-0.247414\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 569.314 | 1.57705 | 0.788524 | − | 0.615005i | \(-0.210846\pi\) | ||||
0.788524 | + | 0.615005i | \(0.210846\pi\) | |||||||
\(20\) | 1422.23i | 3.55557i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 772.714 | 1.59652 | ||||||||
\(23\) | 551.399i | 1.04234i | 0.853452 | + | 0.521171i | \(0.174505\pi\) | ||||
−0.853452 | + | 0.521171i | \(0.825495\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −319.583 | −0.511333 | ||||||||
\(26\) | − 2105.30i | − 3.11435i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1760.25 | 2.24522 | ||||||||
\(29\) | 1575.91i | 1.87386i | 0.349522 | + | 0.936928i | \(0.386344\pi\) | ||||
−0.349522 | + | 0.936928i | \(0.613656\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −590.227 | −0.614180 | −0.307090 | − | 0.951681i | \(-0.599355\pi\) | ||||
−0.307090 | + | 0.951681i | \(0.599355\pi\) | |||||||
\(32\) | − 5213.07i | − 5.09089i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3198.99 | −2.76729 | ||||||||
\(35\) | 1169.08i | 0.954355i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1146.09 | 0.837175 | 0.418588 | − | 0.908176i | \(-0.362525\pi\) | ||||
0.418588 | + | 0.908176i | \(0.362525\pi\) | |||||||
\(38\) | − 4492.73i | − 3.11131i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7342.89 | 4.58931 | ||||||||
\(41\) | − 627.996i | − 0.373585i | −0.982399 | − | 0.186792i | \(-0.940191\pi\) | ||||
0.982399 | − | 0.186792i | \(-0.0598092\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 545.964 | 0.295275 | 0.147638 | − | 0.989042i | \(-0.452833\pi\) | ||||
0.147638 | + | 0.989042i | \(0.452833\pi\) | |||||||
\(44\) | − 4531.17i | − 2.34048i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4351.35 | 2.05640 | ||||||||
\(47\) | 831.478i | 0.376405i | 0.982130 | + | 0.188202i | \(0.0602661\pi\) | ||||
−0.982130 | + | 0.188202i | \(0.939734\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −954.056 | −0.397358 | ||||||||
\(50\) | 2521.98i | 1.00879i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −12345.4 | −4.56562 | ||||||||
\(53\) | 4600.66i | 1.63783i | 0.573915 | + | 0.818915i | \(0.305424\pi\) | ||||
−0.573915 | + | 0.818915i | \(0.694576\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3009.41 | 0.994845 | ||||||||
\(56\) | − 9088.09i | − 2.89799i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 12436.3 | 3.69687 | ||||||||
\(59\) | 453.188i | 0.130189i | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4840.16 | 1.30077 | 0.650384 | − | 0.759606i | \(-0.274608\pi\) | ||||
0.650384 | + | 0.759606i | \(0.274608\pi\) | |||||||
\(62\) | 4657.76i | 1.21170i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −22818.8 | −5.57099 | ||||||||
\(65\) | − 8199.30i | − 1.94066i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2866.26 | −0.638508 | −0.319254 | − | 0.947669i | \(-0.603432\pi\) | ||||
−0.319254 | + | 0.947669i | \(0.603432\pi\) | |||||||
\(68\) | 18758.8i | 4.05683i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 9225.80 | 1.88282 | ||||||||
\(71\) | 5595.36i | 1.10997i | 0.831860 | + | 0.554986i | \(0.187276\pi\) | ||||
−0.831860 | + | 0.554986i | \(0.812724\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7462.48 | 1.40035 | 0.700176 | − | 0.713970i | \(-0.253105\pi\) | ||||
0.700176 | + | 0.713970i | \(0.253105\pi\) | |||||||
\(74\) | − 9044.36i | − 1.65164i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −26345.2 | −4.56115 | ||||||||
\(77\) | − 3724.66i | − 0.628211i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −57.5610 | −0.00922303 | −0.00461152 | − | 0.999989i | \(-0.501468\pi\) | ||||
−0.00461152 | + | 0.999989i | \(0.501468\pi\) | |||||||
\(80\) | − 35190.5i | − 5.49852i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4955.81 | −0.737033 | ||||||||
\(83\) | − 7578.24i | − 1.10005i | −0.835148 | − | 0.550025i | \(-0.814618\pi\) | ||||
0.835148 | − | 0.550025i | \(-0.185382\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12458.8 | −1.72440 | ||||||||
\(86\) | − 4308.46i | − 0.582539i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −23394.2 | −3.02094 | ||||||||
\(89\) | − 4901.93i | − 0.618852i | −0.950923 | − | 0.309426i | \(-0.899863\pi\) | ||||
0.950923 | − | 0.309426i | \(-0.100137\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10148.0 | −1.22546 | ||||||||
\(92\) | − 25516.2i | − 3.01467i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6561.59 | 0.742597 | ||||||||
\(95\) | − 17497.3i | − 1.93876i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4492.34 | 0.477452 | 0.238726 | − | 0.971087i | \(-0.423270\pi\) | ||||
0.238726 | + | 0.971087i | \(0.423270\pi\) | |||||||
\(98\) | 7528.90i | 0.783934i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 14788.8 | 1.47888 | ||||||||
\(101\) | 4511.14i | 0.442225i | 0.975248 | + | 0.221112i | \(0.0709688\pi\) | ||||
−0.975248 | + | 0.221112i | \(0.929031\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5735.81 | −0.540655 | −0.270328 | − | 0.962768i | \(-0.587132\pi\) | ||||
−0.270328 | + | 0.962768i | \(0.587132\pi\) | |||||||
\(104\) | 63738.7i | 5.89300i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 36306.0 | 3.23122 | ||||||||
\(107\) | 19027.5i | 1.66193i | 0.556322 | + | 0.830967i | \(0.312212\pi\) | ||||
−0.556322 | + | 0.830967i | \(0.687788\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −872.407 | −0.0734287 | −0.0367144 | − | 0.999326i | \(-0.511689\pi\) | ||||
−0.0367144 | + | 0.999326i | \(0.511689\pi\) | |||||||
\(110\) | − 23748.6i | − 1.96270i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −43554.4 | −3.47213 | ||||||||
\(113\) | − 17682.3i | − 1.38478i | −0.721522 | − | 0.692391i | \(-0.756557\pi\) | ||||
0.721522 | − | 0.692391i | \(-0.243443\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16946.7 | 1.28142 | ||||||||
\(116\) | − 72925.9i | − 5.41958i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3576.32 | 0.256846 | ||||||||
\(119\) | 15419.9i | 1.08890i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5053.14 | 0.345137 | ||||||||
\(122\) | − 38196.0i | − 2.56624i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 27312.9 | 1.77634 | ||||||||
\(125\) | − 9386.70i | − 0.600749i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3736.99 | −0.231694 | −0.115847 | − | 0.993267i | \(-0.536958\pi\) | ||||
−0.115847 | + | 0.993267i | \(0.536958\pi\) | |||||||
\(128\) | 96664.6i | 5.89994i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −64704.5 | −3.82867 | ||||||||
\(131\) | 15398.3i | 0.897284i | 0.893712 | + | 0.448642i | \(0.148092\pi\) | ||||
−0.893712 | + | 0.448642i | \(0.851908\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −21656.0 | −1.22426 | ||||||||
\(134\) | 22619.0i | 1.25969i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 96850.5 | 5.23630 | ||||||||
\(137\) | − 5681.19i | − 0.302690i | −0.988481 | − | 0.151345i | \(-0.951640\pi\) | ||||
0.988481 | − | 0.151345i | \(-0.0483605\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5777.15 | −0.299009 | −0.149504 | − | 0.988761i | \(-0.547768\pi\) | ||||
−0.149504 | + | 0.988761i | \(0.547768\pi\) | |||||||
\(140\) | − 54099.8i | − 2.76019i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 44155.7 | 2.18983 | ||||||||
\(143\) | 26122.7i | 1.27745i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 48434.2 | 2.30365 | ||||||||
\(146\) | − 58889.9i | − 2.76271i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −53035.8 | −2.42128 | ||||||||
\(149\) | 23565.8i | 1.06147i | 0.847537 | + | 0.530737i | \(0.178085\pi\) | ||||
−0.847537 | + | 0.530737i | \(0.821915\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11254.5 | −0.493598 | −0.246799 | − | 0.969067i | \(-0.579379\pi\) | ||||
−0.246799 | + | 0.969067i | \(0.579379\pi\) | |||||||
\(152\) | 136019.i | 5.88724i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −29393.1 | −1.23938 | ||||||||
\(155\) | 18140.1i | 0.755050i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13876.3 | −0.562955 | −0.281478 | − | 0.959568i | \(-0.590825\pi\) | ||||
−0.281478 | + | 0.959568i | \(0.590825\pi\) | |||||||
\(158\) | 454.241i | 0.0181958i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −160219. | −6.25855 | ||||||||
\(161\) | − 20974.5i | − 0.809170i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 26838.6 | 1.01015 | 0.505073 | − | 0.863077i | \(-0.331466\pi\) | ||||
0.505073 | + | 0.863077i | \(0.331466\pi\) | |||||||
\(164\) | 29060.7i | 1.08048i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −59803.5 | −2.17025 | ||||||||
\(167\) | 35538.6i | 1.27429i | 0.770745 | + | 0.637143i | \(0.219884\pi\) | ||||
−0.770745 | + | 0.637143i | \(0.780116\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 42611.7 | 1.49195 | ||||||||
\(170\) | 98318.1i | 3.40201i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −25264.7 | −0.853998 | ||||||||
\(173\) | − 24487.9i | − 0.818200i | −0.912489 | − | 0.409100i | \(-0.865843\pi\) | ||||
0.912489 | − | 0.409100i | \(-0.134157\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12156.5 | 0.396948 | ||||||||
\(176\) | 112116.i | 3.61944i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −38683.4 | −1.22091 | ||||||||
\(179\) | − 13416.1i | − 0.418717i | −0.977839 | − | 0.209358i | \(-0.932862\pi\) | ||||
0.977839 | − | 0.209358i | \(-0.0671375\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21580.7 | 0.658732 | 0.329366 | − | 0.944202i | \(-0.393165\pi\) | ||||
0.329366 | + | 0.944202i | \(0.393165\pi\) | |||||||
\(182\) | 80083.0i | 2.41767i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −131738. | −3.89114 | ||||||||
\(185\) | − 35224.1i | − 1.02919i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 39693.2 | 1.13510 | ||||||||
\(188\) | − 38476.9i | − 1.08864i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −138080. | −3.82492 | ||||||||
\(191\) | − 20485.4i | − 0.561536i | −0.959776 | − | 0.280768i | \(-0.909411\pi\) | ||||
0.959776 | − | 0.280768i | \(-0.0905892\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13149.3 | 0.353011 | 0.176506 | − | 0.984300i | \(-0.443521\pi\) | ||||
0.176506 | + | 0.984300i | \(0.443521\pi\) | |||||||
\(194\) | − 35451.2i | − 0.941949i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 44149.2 | 1.14924 | ||||||||
\(197\) | − 51059.8i | − 1.31567i | −0.753163 | − | 0.657834i | \(-0.771473\pi\) | ||||
0.753163 | − | 0.657834i | \(-0.228527\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26985.3 | 0.681429 | 0.340715 | − | 0.940167i | \(-0.389331\pi\) | ||||
0.340715 | + | 0.940167i | \(0.389331\pi\) | |||||||
\(200\) | − 76353.9i | − 1.90885i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 35599.5 | 0.872451 | ||||||||
\(203\) | − 59945.7i | − 1.45468i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −19300.9 | −0.459271 | ||||||||
\(206\) | 45264.0i | 1.06664i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 305466. | 7.06050 | ||||||||
\(209\) | 55745.9i | 1.27620i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24609.2 | −0.552756 | −0.276378 | − | 0.961049i | \(-0.589134\pi\) | ||||
−0.276378 | + | 0.961049i | \(0.589134\pi\) | |||||||
\(212\) | − 212897.i | − 4.73694i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 150155. | 3.27878 | ||||||||
\(215\) | − 16779.7i | − 0.363001i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 22451.5 | 0.476788 | ||||||||
\(218\) | 6884.57i | 0.144865i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −139261. | −2.87730 | ||||||||
\(221\) | − 108146.i | − 2.21425i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 82301.1 | 1.65499 | 0.827496 | − | 0.561471i | \(-0.189764\pi\) | ||||
0.827496 | + | 0.561471i | \(0.189764\pi\) | |||||||
\(224\) | 198298.i | 3.95206i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −139539. | −2.73199 | ||||||||
\(227\) | − 33434.3i | − 0.648844i | −0.945913 | − | 0.324422i | \(-0.894830\pi\) | ||||
0.945913 | − | 0.324422i | \(-0.105170\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −28896.0 | −0.551020 | −0.275510 | − | 0.961298i | \(-0.588847\pi\) | ||||
−0.275510 | + | 0.961298i | \(0.588847\pi\) | |||||||
\(230\) | − 133735.i | − 2.52806i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −376512. | −6.99525 | ||||||||
\(233\) | − 81940.3i | − 1.50934i | −0.656107 | − | 0.754668i | \(-0.727798\pi\) | ||||
0.656107 | − | 0.754668i | \(-0.272202\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 25554.7 | 0.462738 | ||||||||
\(236\) | − 20971.4i | − 0.376533i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 121686. | 2.14825 | ||||||||
\(239\) | 23743.6i | 0.415673i | 0.978164 | + | 0.207836i | \(0.0666422\pi\) | ||||
−0.978164 | + | 0.207836i | \(0.933358\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 36976.2 | 0.636631 | 0.318315 | − | 0.947985i | \(-0.396883\pi\) | ||||
0.318315 | + | 0.947985i | \(0.396883\pi\) | |||||||
\(242\) | − 39876.7i | − 0.680909i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −223980. | −3.76209 | ||||||||
\(245\) | 29322.0i | 0.488497i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 151883. | 2.48951 | ||||||||
\(248\) | − 141015.i | − 2.29278i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −74074.8 | −1.18520 | ||||||||
\(251\) | 11789.2i | 0.187127i | 0.995613 | + | 0.0935637i | \(0.0298259\pi\) | ||||
−0.995613 | + | 0.0935637i | \(0.970174\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −53991.6 | −0.843501 | ||||||||
\(254\) | 29490.3i | 0.457101i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 397726. | 6.06881 | ||||||||
\(257\) | − 34248.5i | − 0.518532i | −0.965806 | − | 0.259266i | \(-0.916519\pi\) | ||||
0.965806 | − | 0.259266i | \(-0.0834806\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −43595.9 | −0.649899 | ||||||||
\(260\) | 379425.i | 5.61280i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 121515. | 1.77022 | ||||||||
\(263\) | 83903.7i | 1.21302i | 0.795074 | + | 0.606512i | \(0.207432\pi\) | ||||
−0.795074 | + | 0.606512i | \(0.792568\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 141397. | 2.01349 | ||||||||
\(266\) | 170898.i | 2.41531i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 132637. | 1.84670 | ||||||||
\(269\) | 50613.0i | 0.699451i | 0.936852 | + | 0.349726i | \(0.113725\pi\) | ||||
−0.936852 | + | 0.349726i | \(0.886275\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 108503. | 1.47742 | 0.738709 | − | 0.674025i | \(-0.235436\pi\) | ||||
0.738709 | + | 0.674025i | \(0.235436\pi\) | |||||||
\(272\) | − 464153.i | − 6.27369i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −44832.9 | −0.597168 | ||||||||
\(275\) | − 31292.8i | − 0.413790i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −48391.4 | −0.630679 | −0.315339 | − | 0.948979i | \(-0.602118\pi\) | ||||
−0.315339 | + | 0.948979i | \(0.602118\pi\) | |||||||
\(278\) | 45590.2i | 0.589905i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −279314. | −3.56268 | ||||||||
\(281\) | − 104837.i | − 1.32771i | −0.747860 | − | 0.663856i | \(-0.768919\pi\) | ||||
0.747860 | − | 0.663856i | \(-0.231081\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14243.6 | 0.177847 | 0.0889236 | − | 0.996038i | \(-0.471657\pi\) | ||||
0.0889236 | + | 0.996038i | \(0.471657\pi\) | |||||||
\(284\) | − 258927.i | − 3.21027i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 206146. | 2.52025 | ||||||||
\(287\) | 23888.2i | 0.290014i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −80806.6 | −0.967500 | ||||||||
\(290\) | − 382217.i | − 4.54480i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −345329. | −4.05011 | ||||||||
\(293\) | 68975.2i | 0.803448i | 0.915761 | + | 0.401724i | \(0.131589\pi\) | ||||
−0.915761 | + | 0.401724i | \(0.868411\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13928.3 | 0.160049 | ||||||||
\(296\) | 273821.i | 3.12524i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 185969. | 2.09415 | ||||||||
\(299\) | 147103.i | 1.64543i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20767.8 | −0.229222 | ||||||||
\(302\) | 88814.8i | 0.973803i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 651865. | 7.05359 | ||||||||
\(305\) | − 148758.i | − 1.59912i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −93690.0 | −0.994069 | −0.497034 | − | 0.867731i | \(-0.665578\pi\) | ||||
−0.497034 | + | 0.867731i | \(0.665578\pi\) | |||||||
\(308\) | 172360.i | 1.81692i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 143152. | 1.48961 | ||||||||
\(311\) | 22556.7i | 0.233214i | 0.993178 | + | 0.116607i | \(0.0372019\pi\) | ||||
−0.993178 | + | 0.116607i | \(0.962798\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 58390.8 | 0.596013 | 0.298006 | − | 0.954564i | \(-0.403678\pi\) | ||||
0.298006 | + | 0.954564i | \(0.403678\pi\) | |||||||
\(314\) | 109504.i | 1.11064i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2663.65 | 0.0266749 | ||||||||
\(317\) | − 55440.6i | − 0.551708i | −0.961199 | − | 0.275854i | \(-0.911039\pi\) | ||||
0.961199 | − | 0.275854i | \(-0.0889607\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −154310. | −1.51639 | ||||||||
\(320\) | 701314.i | 6.84877i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −165520. | −1.59639 | ||||||||
\(323\) | − 230785.i | − 2.21209i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −85259.1 | −0.807187 | ||||||||
\(326\) | − 211796.i | − 1.99288i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 150039. | 1.39462 | ||||||||
\(329\) | − 31628.4i | − 0.292203i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −110835. | −1.01163 | −0.505814 | − | 0.862643i | \(-0.668808\pi\) | ||||
−0.505814 | + | 0.862643i | \(0.668808\pi\) | |||||||
\(332\) | 350686.i | 3.18157i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 280452. | 2.51400 | ||||||||
\(335\) | 88092.0i | 0.784958i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −53449.4 | −0.470634 | −0.235317 | − | 0.971919i | \(-0.575613\pi\) | ||||
−0.235317 | + | 0.971919i | \(0.575613\pi\) | |||||||
\(338\) | − 336269.i | − 2.94343i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 576534. | 4.98732 | ||||||||
\(341\) | − 57793.6i | − 0.497016i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 127622. | 1.08477 | ||||||||
\(344\) | 130440.i | 1.10229i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −193246. | −1.61420 | ||||||||
\(347\) | 187145.i | 1.55424i | 0.629350 | + | 0.777122i | \(0.283321\pi\) | ||||
−0.629350 | + | 0.777122i | \(0.716679\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 55841.1 | 0.458462 | 0.229231 | − | 0.973372i | \(-0.426379\pi\) | ||||
0.229231 | + | 0.973372i | \(0.426379\pi\) | |||||||
\(350\) | − 95933.0i | − 0.783127i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 510451. | 4.11973 | ||||||||
\(353\) | − 22199.8i | − 0.178155i | −0.996025 | − | 0.0890777i | \(-0.971608\pi\) | ||||
0.996025 | − | 0.0890777i | \(-0.0283919\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 171968. | 1.36456 | ||||||||
\(356\) | 226838.i | 1.78985i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −105873. | −0.826073 | ||||||||
\(359\) | − 245560.i | − 1.90532i | −0.304034 | − | 0.952661i | \(-0.598334\pi\) | ||||
0.304034 | − | 0.952661i | \(-0.401666\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 193797. | 1.48708 | ||||||||
\(362\) | − 170304.i | − 1.29959i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 469604. | 3.54429 | ||||||||
\(365\) | − 229352.i | − 1.72154i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 144668. | 1.07409 | 0.537045 | − | 0.843554i | \(-0.319541\pi\) | ||||
0.537045 | + | 0.843554i | \(0.319541\pi\) | |||||||
\(368\) | 631352.i | 4.66204i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −277970. | −2.03046 | ||||||||
\(371\) | − 175003.i | − 1.27145i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14333.8 | 0.103025 | 0.0515127 | − | 0.998672i | \(-0.483596\pi\) | ||||
0.0515127 | + | 0.998672i | \(0.483596\pi\) | |||||||
\(374\) | − 313238.i | − 2.23940i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −198654. | −1.40515 | ||||||||
\(377\) | 420425.i | 2.95805i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −143982. | −1.00238 | −0.501188 | − | 0.865338i | \(-0.667104\pi\) | ||||
−0.501188 | + | 0.865338i | \(0.667104\pi\) | |||||||
\(380\) | 809695.i | 5.60731i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −161660. | −1.10784 | ||||||||
\(383\) | − 232495.i | − 1.58495i | −0.609903 | − | 0.792476i | \(-0.708791\pi\) | ||||
0.609903 | − | 0.792476i | \(-0.291209\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −114474. | −0.772299 | ||||||||
\(386\) | − 103768.i | − 0.696445i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −207885. | −1.38089 | ||||||||
\(389\) | 138944.i | 0.918206i | 0.888383 | + | 0.459103i | \(0.151829\pi\) | ||||
−0.888383 | + | 0.459103i | \(0.848171\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 223522. | 1.46207 | ||||||||
\(392\) | − 227940.i | − 1.48337i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −402937. | −2.59564 | ||||||||
\(395\) | 1769.08i | 0.0113385i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 145759. | 0.924815 | 0.462407 | − | 0.886668i | \(-0.346986\pi\) | ||||
0.462407 | + | 0.886668i | \(0.346986\pi\) | |||||||
\(398\) | − 212954.i | − 1.34437i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −365923. | −2.28702 | ||||||||
\(401\) | 147498.i | 0.917273i | 0.888624 | + | 0.458637i | \(0.151662\pi\) | ||||
−0.888624 | + | 0.458637i | \(0.848338\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −157462. | −0.969539 | ||||||||
\(404\) | − 208754.i | − 1.27901i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −473060. | −2.86988 | ||||||||
\(407\) | 112223.i | 0.677473i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −199915. | −1.19509 | −0.597543 | − | 0.801837i | \(-0.703856\pi\) | ||||
−0.597543 | + | 0.801837i | \(0.703856\pi\) | |||||||
\(410\) | 152312.i | 0.906082i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 265427. | 1.56369 | ||||||||
\(413\) | − 17238.7i | − 0.101066i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −232910. | −1.35236 | ||||||||
\(416\) | − 1.39075e6i | − 8.03643i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 439917. | 2.51778 | ||||||||
\(419\) | − 58490.7i | − 0.333165i | −0.986028 | − | 0.166582i | \(-0.946727\pi\) | ||||
0.986028 | − | 0.166582i | \(-0.0532732\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 37928.6 | 0.213994 | 0.106997 | − | 0.994259i | \(-0.465876\pi\) | ||||
0.106997 | + | 0.994259i | \(0.465876\pi\) | |||||||
\(422\) | 194203.i | 1.09051i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.09918e6 | −6.11414 | ||||||||
\(425\) | 129551.i | 0.717235i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −184113. | −1.00979 | ||||||||
\(428\) | − 880503.i | − 4.80666i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −132417. | −0.716152 | ||||||||
\(431\) | 175808.i | 0.946419i | 0.880950 | + | 0.473209i | \(0.156905\pi\) | ||||
−0.880950 | + | 0.473209i | \(0.843095\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 266918. | 1.42365 | 0.711823 | − | 0.702359i | \(-0.247870\pi\) | ||||
0.711823 | + | 0.702359i | \(0.247870\pi\) | |||||||
\(434\) | − 177175.i | − 0.940640i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 40370.9 | 0.212371 | ||||||||
\(437\) | 313919.i | 1.64382i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −195586. | −1.01487 | −0.507434 | − | 0.861690i | \(-0.669406\pi\) | ||||
−0.507434 | + | 0.861690i | \(0.669406\pi\) | |||||||
\(440\) | 718998.i | 3.71383i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −853434. | −4.36843 | ||||||||
\(443\) | − 43264.2i | − 0.220455i | −0.993906 | − | 0.110228i | \(-0.964842\pi\) | ||||
0.993906 | − | 0.110228i | \(-0.0351580\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −150656. | −0.760794 | ||||||||
\(446\) | − 649477.i | − 3.26508i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 867997. | 4.32476 | ||||||||
\(449\) | − 12614.8i | − 0.0625731i | −0.999510 | − | 0.0312866i | \(-0.990040\pi\) | ||||
0.999510 | − | 0.0312866i | \(-0.00996045\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 61491.9 | 0.302318 | ||||||||
\(452\) | 818253.i | 4.00508i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −263846. | −1.28008 | ||||||||
\(455\) | 311891.i | 1.50654i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 309312. | 1.48103 | 0.740516 | − | 0.672039i | \(-0.234581\pi\) | ||||
0.740516 | + | 0.672039i | \(0.234581\pi\) | |||||||
\(458\) | 228032.i | 1.08709i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −784215. | −3.70612 | ||||||||
\(461\) | 54977.6i | 0.258692i | 0.991599 | + | 0.129346i | \(0.0412879\pi\) | ||||
−0.991599 | + | 0.129346i | \(0.958712\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −252184. | −1.17640 | −0.588202 | − | 0.808714i | \(-0.700164\pi\) | ||||
−0.588202 | + | 0.808714i | \(0.700164\pi\) | |||||||
\(464\) | 1.80442e6i | 8.38112i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −646630. | −2.97772 | ||||||||
\(467\) | 214523.i | 0.983649i | 0.870694 | + | 0.491825i | \(0.163670\pi\) | ||||
−0.870694 | + | 0.491825i | \(0.836330\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 109029. | 0.495674 | ||||||||
\(470\) | − 201664.i | − 0.912921i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −108274. | −0.486005 | ||||||||
\(473\) | 53459.5i | 0.238948i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −181943. | −0.806397 | ||||||||
\(476\) | − 713560.i | − 3.14932i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 187372. | 0.820068 | ||||||||
\(479\) | 236791.i | 1.03203i | 0.856578 | + | 0.516017i | \(0.172586\pi\) | ||||
−0.856578 | + | 0.516017i | \(0.827414\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 305757. | 1.32156 | ||||||||
\(482\) | − 291796.i | − 1.25599i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −233836. | −0.998207 | ||||||||
\(485\) | − 138068.i | − 0.586961i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 287933. | 1.21404 | 0.607022 | − | 0.794685i | \(-0.292364\pi\) | ||||
0.607022 | + | 0.794685i | \(0.292364\pi\) | |||||||
\(488\) | 1.15639e6i | 4.85586i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 231394. | 0.963740 | ||||||||
\(491\) | 65201.6i | 0.270455i | 0.990815 | + | 0.135228i | \(0.0431766\pi\) | ||||
−0.990815 | + | 0.135228i | \(0.956823\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 638833. | 2.62841 | ||||||||
\(494\) | − 1.19858e6i | − 4.91148i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −675810. | −2.74702 | ||||||||
\(497\) | − 212841.i | − 0.861671i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −255807. | −1.02733 | −0.513666 | − | 0.857990i | \(-0.671713\pi\) | ||||
−0.513666 | + | 0.857990i | \(0.671713\pi\) | |||||||
\(500\) | 434372.i | 1.73749i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 93034.3 | 0.369178 | ||||||||
\(503\) | 175779.i | 0.694753i | 0.937726 | + | 0.347376i | \(0.112927\pi\) | ||||
−0.937726 | + | 0.347376i | \(0.887073\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 138646. | 0.543655 | ||||||||
\(506\) | 426073.i | 1.66412i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 172930. | 0.670106 | ||||||||
\(509\) | 32249.5i | 0.124476i | 0.998061 | + | 0.0622382i | \(0.0198239\pi\) | ||||
−0.998061 | + | 0.0622382i | \(0.980176\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −283863. | −1.08709 | ||||||||
\(512\) | − 1.59201e6i | − 6.07303i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −270271. | −1.02300 | ||||||||
\(515\) | 176285.i | 0.664662i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −81416.3 | −0.304600 | ||||||||
\(518\) | 344036.i | 1.28217i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.95895e6 | 7.24464 | ||||||||
\(521\) | − 454411.i | − 1.67407i | −0.547149 | − | 0.837035i | \(-0.684287\pi\) | ||||
0.547149 | − | 0.837035i | \(-0.315713\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 353992. | 1.29417 | 0.647083 | − | 0.762420i | \(-0.275989\pi\) | ||||
0.647083 | + | 0.762420i | \(0.275989\pi\) | |||||||
\(524\) | − 712561.i | − 2.59513i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 662123. | 2.39314 | ||||||||
\(527\) | 239262.i | 0.861495i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −24199.5 | −0.0864758 | ||||||||
\(530\) | − 1.11583e6i | − 3.97234i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.00214e6 | 3.54082 | ||||||||
\(533\) | − 167538.i | − 0.589738i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 584792. | 2.04312 | ||||||||
\(536\) | − 684799.i | − 2.38360i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 399411. | 1.37992 | ||||||||
\(539\) | − 93418.8i | − 0.321556i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 135948. | 0.464494 | 0.232247 | − | 0.972657i | \(-0.425392\pi\) | ||||
0.232247 | + | 0.972657i | \(0.425392\pi\) | |||||||
\(542\) | − 856248.i | − 2.91475i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.11324e6 | −7.14087 | ||||||||
\(545\) | 26812.6i | 0.0902706i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 270604. | 0.904398 | 0.452199 | − | 0.891917i | \(-0.350640\pi\) | ||||
0.452199 | + | 0.891917i | \(0.350640\pi\) | |||||||
\(548\) | 262899.i | 0.875443i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −246947. | −0.816352 | ||||||||
\(551\) | 897189.i | 2.95516i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2189.54 | 0.00715984 | ||||||||
\(554\) | 381879.i | 1.24425i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 267339. | 0.864796 | ||||||||
\(557\) | 349893.i | 1.12778i | 0.825849 | + | 0.563891i | \(0.190696\pi\) | ||||
−0.825849 | + | 0.563891i | \(0.809304\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 145653. | 0.466119 | ||||||||
\(560\) | 1.33860e6i | 4.26850i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −827322. | −2.61940 | ||||||||
\(563\) | 326045.i | 1.02863i | 0.857601 | + | 0.514316i | \(0.171954\pi\) | ||||
−0.857601 | + | 0.514316i | \(0.828046\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −543449. | −1.70240 | ||||||||
\(566\) | − 112403.i | − 0.350869i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.33683e6 | −4.14361 | ||||||||
\(569\) | 11943.9i | 0.0368912i | 0.999830 | + | 0.0184456i | \(0.00587176\pi\) | ||||
−0.999830 | + | 0.0184456i | \(0.994128\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19985.7 | −0.0612980 | −0.0306490 | − | 0.999530i | \(-0.509757\pi\) | ||||
−0.0306490 | + | 0.999530i | \(0.509757\pi\) | |||||||
\(572\) | − 1.20883e6i | − 3.69466i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 188513. | 0.572159 | ||||||||
\(575\) | − 176218.i | − 0.532984i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 117550. | 0.353078 | 0.176539 | − | 0.984294i | \(-0.443510\pi\) | ||||
0.176539 | + | 0.984294i | \(0.443510\pi\) | |||||||
\(578\) | 637683.i | 1.90875i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.24131e6 | −6.66263 | ||||||||
\(581\) | 288267.i | 0.853969i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −450486. | −1.32539 | ||||||||
\(584\) | 1.78291e6i | 5.22762i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 544316. | 1.58510 | ||||||||
\(587\) | 285221.i | 0.827761i | 0.910331 | + | 0.413881i | \(0.135827\pi\) | ||||
−0.910331 | + | 0.413881i | \(0.864173\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −336024. | −0.968590 | ||||||||
\(590\) | − 109915.i | − 0.315756i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.31228e6 | 3.74440 | ||||||||
\(593\) | 86944.4i | 0.247248i | 0.992329 | + | 0.123624i | \(0.0394516\pi\) | ||||
−0.992329 | + | 0.123624i | \(0.960548\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 473916. | 1.33865 | ||||||||
\(596\) | − 1.09051e6i | − 3.07000i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.16086e6 | 3.24622 | ||||||||
\(599\) | − 216807.i | − 0.604253i | −0.953268 | − | 0.302127i | \(-0.902303\pi\) | ||||
0.953268 | − | 0.302127i | \(-0.0976966\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −69954.0 | −0.193671 | −0.0968353 | − | 0.995300i | \(-0.530872\pi\) | ||||
−0.0968353 | + | 0.995300i | \(0.530872\pi\) | |||||||
\(602\) | 163888.i | 0.452226i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 520807. | 1.42759 | ||||||||
\(605\) | − 155304.i | − 0.424298i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −301673. | −0.818766 | −0.409383 | − | 0.912363i | \(-0.634256\pi\) | ||||
−0.409383 | + | 0.912363i | \(0.634256\pi\) | |||||||
\(608\) | − 2.96787e6i | − 8.02857i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.17392e6 | −3.15484 | ||||||||
\(611\) | 221823.i | 0.594190i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 447345. | 1.19048 | 0.595240 | − | 0.803548i | \(-0.297057\pi\) | ||||
0.595240 | + | 0.803548i | \(0.297057\pi\) | |||||||
\(614\) | 739352.i | 1.96117i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 889884. | 2.34516 | ||||||||
\(617\) | 130266.i | 0.342185i | 0.985255 | + | 0.171093i | \(0.0547297\pi\) | ||||
−0.985255 | + | 0.171093i | \(0.945270\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 367325. | 0.958670 | 0.479335 | − | 0.877632i | \(-0.340878\pi\) | ||||
0.479335 | + | 0.877632i | \(0.340878\pi\) | |||||||
\(620\) | − 839438.i | − 2.18376i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 178006. | 0.460101 | ||||||||
\(623\) | 186463.i | 0.480415i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −488231. | −1.24987 | ||||||||
\(626\) | − 460789.i | − 1.17585i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 642130. | 1.62818 | ||||||||
\(629\) | − 464595.i | − 1.17429i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1458.86 | −0.00366399 | −0.00183199 | − | 0.999998i | \(-0.500583\pi\) | ||||
−0.00183199 | + | 0.999998i | \(0.500583\pi\) | |||||||
\(632\) | − 13752.3i | − 0.0344303i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −437508. | −1.08845 | ||||||||
\(635\) | 114853.i | 0.284835i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −254525. | −0.627266 | ||||||||
\(638\) | 1.21773e6i | 2.99164i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.97090e6 | 7.25317 | ||||||||
\(641\) | 633002.i | 1.54060i | 0.637683 | + | 0.770299i | \(0.279893\pi\) | ||||
−0.637683 | + | 0.770299i | \(0.720107\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −466214. | −1.12762 | −0.563811 | − | 0.825904i | \(-0.690665\pi\) | ||||
−0.563811 | + | 0.825904i | \(0.690665\pi\) | |||||||
\(644\) | 970602.i | 2.34029i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.82123e6 | −4.36415 | ||||||||
\(647\) | − 657916.i | − 1.57167i | −0.618435 | − | 0.785836i | \(-0.712233\pi\) | ||||
0.618435 | − | 0.785836i | \(-0.287767\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −44375.0 | −0.105354 | ||||||||
\(650\) | 672820.i | 1.59247i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.24196e6 | −2.92155 | ||||||||
\(653\) | 185217.i | 0.434366i | 0.976131 | + | 0.217183i | \(0.0696868\pi\) | ||||
−0.976131 | + | 0.217183i | \(0.930313\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 473252. | 1.10309 | ||||||||
\(656\) | − 719056.i | − 1.67092i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −249594. | −0.576478 | ||||||||
\(659\) | 68433.8i | 0.157580i | 0.996891 | + | 0.0787898i | \(0.0251056\pi\) | ||||
−0.996891 | + | 0.0787898i | \(0.974894\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −650096. | −1.48790 | −0.743951 | − | 0.668234i | \(-0.767051\pi\) | ||||
−0.743951 | + | 0.668234i | \(0.767051\pi\) | |||||||
\(662\) | 874651.i | 1.99581i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.81057e6 | 4.10657 | ||||||||
\(665\) | 665576.i | 1.50506i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −868956. | −1.95320 | ||||||||
\(668\) | − 1.64456e6i | − 3.68550i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 695175. | 1.54862 | ||||||||
\(671\) | 473936.i | 1.05263i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −179348. | −0.395973 | −0.197987 | − | 0.980205i | \(-0.563440\pi\) | ||||
−0.197987 | + | 0.980205i | \(0.563440\pi\) | |||||||
\(674\) | 421794.i | 0.928498i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.97187e6 | −4.31504 | ||||||||
\(677\) | − 676369.i | − 1.47573i | −0.674949 | − | 0.737864i | \(-0.735834\pi\) | ||||
0.674949 | − | 0.737864i | \(-0.264166\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −170883. | −0.370646 | ||||||||
\(680\) | − 2.97661e6i | − 6.43731i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −456076. | −0.980548 | ||||||||
\(683\) | − 369112.i | − 0.791255i | −0.918411 | − | 0.395628i | \(-0.870527\pi\) | ||||
0.918411 | − | 0.395628i | \(-0.129473\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −174606. | −0.372116 | ||||||||
\(686\) | − 1.00713e6i | − 2.14011i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 625129. | 1.32067 | ||||||||
\(689\) | 1.22737e6i | 2.58546i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 274828. | 0.575579 | 0.287789 | − | 0.957694i | \(-0.407080\pi\) | ||||
0.287789 | + | 0.957694i | \(0.407080\pi\) | |||||||
\(692\) | 1.13319e6i | 2.36641i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.47685e6 | 3.06632 | ||||||||
\(695\) | 177555.i | 0.367590i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −254573. | −0.524018 | ||||||||
\(698\) | − 440668.i | − 0.904484i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −562548. | −1.14806 | ||||||||
\(701\) | 869321.i | 1.76907i | 0.466478 | + | 0.884533i | \(0.345523\pi\) | ||||
−0.466478 | + | 0.884533i | \(0.654477\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 652487. | 1.32026 | ||||||||
\(704\) | − 2.23436e6i | − 4.50825i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −175189. | −0.351477 | ||||||||
\(707\) | − 171598.i | − 0.343299i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −476697. | −0.948310 | −0.474155 | − | 0.880441i | \(-0.657246\pi\) | ||||
−0.474155 | + | 0.880441i | \(0.657246\pi\) | |||||||
\(710\) | − 1.35708e6i | − 2.69209i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.17115e6 | 2.31022 | ||||||||
\(713\) | − 325450.i | − 0.640185i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 802856. | 1.57045 | ||||||||
\(716\) | 620834.i | 1.21102i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.93783e6 | −3.75895 | ||||||||
\(719\) | − 497774.i | − 0.962885i | −0.876478 | − | 0.481443i | \(-0.840113\pi\) | ||||
0.876478 | − | 0.481443i | \(-0.159887\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 218183. | 0.419711 | ||||||||
\(722\) | − 1.52935e6i | − 2.93381i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −998655. | −1.90519 | ||||||||
\(725\) | − 503636.i | − 0.958165i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 389597. | 0.737134 | 0.368567 | − | 0.929601i | \(-0.379848\pi\) | ||||
0.368567 | + | 0.929601i | \(0.379848\pi\) | |||||||
\(728\) | − 2.42454e6i | − 4.57474i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.80993e6 | −3.39637 | ||||||||
\(731\) | − 221319.i | − 0.414176i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 224707. | 0.418224 | 0.209112 | − | 0.977892i | \(-0.432943\pi\) | ||||
0.209112 | + | 0.977892i | \(0.432943\pi\) | |||||||
\(734\) | − 1.14164e6i | − 2.11904i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.87448e6 | 5.30644 | ||||||||
\(737\) | − 280658.i | − 0.516704i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −908286. | −1.66316 | −0.831579 | − | 0.555406i | \(-0.812563\pi\) | ||||
−0.831579 | + | 0.555406i | \(0.812563\pi\) | |||||||
\(740\) | 1.63001e6i | 2.97664i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.38103e6 | −2.50840 | ||||||||
\(743\) | − 957884.i | − 1.73514i | −0.497312 | − | 0.867572i | \(-0.665679\pi\) | ||||
0.497312 | − | 0.867572i | \(-0.334321\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 724272. | 1.30494 | ||||||||
\(746\) | − 113115.i | − 0.203256i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.83682e6 | −3.28293 | ||||||||
\(749\) | − 723781.i | − 1.29016i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 603841. | 1.07064 | 0.535319 | − | 0.844650i | \(-0.320191\pi\) | ||||
0.535319 | + | 0.844650i | \(0.320191\pi\) | |||||||
\(752\) | 952043.i | 1.68353i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.31777e6 | 5.83585 | ||||||||
\(755\) | 345897.i | 0.606811i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −322660. | −0.563058 | −0.281529 | − | 0.959553i | \(-0.590842\pi\) | ||||
−0.281529 | + | 0.959553i | \(0.590842\pi\) | |||||||
\(758\) | 1.13623e6i | 1.97756i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.18041e6 | 7.23755 | ||||||||
\(761\) | − 884497.i | − 1.52731i | −0.645624 | − | 0.763655i | \(-0.723403\pi\) | ||||
0.645624 | − | 0.763655i | \(-0.276597\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 33185.2 | 0.0570028 | ||||||||
\(764\) | 947968.i | 1.62408i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.83473e6 | −3.12690 | ||||||||
\(767\) | 120902.i | 0.205515i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −998022. | −1.68767 | −0.843835 | − | 0.536603i | \(-0.819707\pi\) | ||||
−0.843835 | + | 0.536603i | \(0.819707\pi\) | |||||||
\(770\) | 903368.i | 1.52364i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −608489. | −1.02098 | ||||||||
\(773\) | − 401722.i | − 0.672305i | −0.941808 | − | 0.336153i | \(-0.890874\pi\) | ||||
0.941808 | − | 0.336153i | \(-0.109126\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 188627. | 0.314051 | ||||||||
\(776\) | 1.07330e6i | 1.78236i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.09647e6 | 1.81150 | ||||||||
\(779\) | − 357527.i | − 0.589161i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −547885. | −0.898229 | ||||||||
\(782\) | − 1.76392e6i | − 2.88447i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.09239e6 | −1.77724 | ||||||||
\(785\) | 426475.i | 0.692077i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −119699. | −0.193259 | −0.0966296 | − | 0.995320i | \(-0.530806\pi\) | ||||
−0.0966296 | + | 0.995320i | \(0.530806\pi\) | |||||||
\(788\) | 2.36281e6i | 3.80519i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 13960.7 | 0.0223693 | ||||||||
\(791\) | 672611.i | 1.07501i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.29127e6 | 2.05338 | ||||||||
\(794\) | − 1.15025e6i | − 1.82454i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.24875e6 | −1.97084 | ||||||||
\(797\) | 572276.i | 0.900925i | 0.892795 | + | 0.450462i | \(0.148741\pi\) | ||||
−0.892795 | + | 0.450462i | \(0.851259\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 337059. | 0.527974 | ||||||||
\(800\) | 1.66601e6i | 2.60314i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.16398e6 | 1.80966 | ||||||||
\(803\) | 730708.i | 1.13322i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −644632. | −0.994764 | ||||||||
\(806\) | 1.24261e6i | 1.91277i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.07779e6 | −1.65086 | ||||||||
\(809\) | 641287.i | 0.979841i | 0.871767 | + | 0.489920i | \(0.162974\pi\) | ||||
−0.871767 | + | 0.489920i | \(0.837026\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −768329. | −1.16817 | −0.584084 | − | 0.811693i | \(-0.698546\pi\) | ||||
−0.584084 | + | 0.811693i | \(0.698546\pi\) | |||||||
\(812\) | 2.77401e6i | 4.20722i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 885602. | 1.33656 | ||||||||
\(815\) | − 824859.i | − 1.24184i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 310825. | 0.465663 | ||||||||
\(818\) | 1.57763e6i | 2.35775i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 893154. | 1.32831 | ||||||||
\(821\) | − 520639.i | − 0.772414i | −0.922412 | − | 0.386207i | \(-0.873785\pi\) | ||||
0.922412 | − | 0.386207i | \(-0.126215\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.20606e6 | 1.78061 | 0.890304 | − | 0.455367i | \(-0.150492\pi\) | ||||
0.890304 | + | 0.455367i | \(0.150492\pi\) | |||||||
\(824\) | − 1.37038e6i | − 2.01831i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −136039. | −0.199389 | ||||||||
\(827\) | 840904.i | 1.22952i | 0.788715 | + | 0.614759i | \(0.210747\pi\) | ||||
−0.788715 | + | 0.614759i | \(0.789253\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −440575. | −0.641079 | −0.320539 | − | 0.947235i | \(-0.603864\pi\) | ||||
−0.320539 | + | 0.947235i | \(0.603864\pi\) | |||||||
\(830\) | 1.83801e6i | 2.66803i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −6.08764e6 | −8.79432 | ||||||||
\(833\) | 386749.i | 0.557364i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.09225e6 | 1.56656 | ||||||||
\(836\) | − 2.57966e6i | − 3.69105i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −461578. | −0.657290 | ||||||||
\(839\) | − 201331.i | − 0.286014i | −0.989722 | − | 0.143007i | \(-0.954323\pi\) | ||||
0.989722 | − | 0.143007i | \(-0.0456771\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.77622e6 | −2.51134 | ||||||||
\(842\) | − 299312.i | − 0.422183i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.13880e6 | 1.59869 | ||||||||
\(845\) | − 1.30963e6i | − 1.83415i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −192215. | −0.267930 | ||||||||
\(848\) | 5.26776e6i | 7.32545i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.02234e6 | 1.41501 | ||||||||
\(851\) | 631954.i | 0.872622i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 736483. | 1.01220 | 0.506098 | − | 0.862476i | \(-0.331087\pi\) | ||||
0.506098 | + | 0.862476i | \(0.331087\pi\) | |||||||
\(854\) | 1.45293e6i | 1.99218i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.54599e6 | −6.20413 | ||||||||
\(857\) | 946536.i | 1.28877i | 0.764701 | + | 0.644385i | \(0.222887\pi\) | ||||
−0.764701 | + | 0.644385i | \(0.777113\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 851046. | 1.15337 | 0.576683 | − | 0.816968i | \(-0.304347\pi\) | ||||
0.576683 | + | 0.816968i | \(0.304347\pi\) | |||||||
\(860\) | 776486.i | 1.04987i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.38738e6 | 1.86716 | ||||||||
\(863\) | 650921.i | 0.873990i | 0.899464 | + | 0.436995i | \(0.143957\pi\) | ||||
−0.899464 | + | 0.436995i | \(0.856043\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −752613. | −1.00587 | ||||||||
\(866\) | − 2.10637e6i | − 2.80866i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.03895e6 | −1.37897 | ||||||||
\(869\) | − 5636.23i | − 0.00746361i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −764668. | −1.00794 | ||||||||
\(872\) | − 208433.i | − 0.274115i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.47728e6 | 3.24304 | ||||||||
\(875\) | 357058.i | 0.466361i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −635629. | −0.826427 | −0.413214 | − | 0.910634i | \(-0.635594\pi\) | ||||
−0.413214 | + | 0.910634i | \(0.635594\pi\) | |||||||
\(878\) | 1.54347e6i | 2.00220i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.44577e6 | 4.44960 | ||||||||
\(881\) | − 639569.i | − 0.824016i | −0.911180 | − | 0.412008i | \(-0.864828\pi\) | ||||
0.911180 | − | 0.412008i | \(-0.135172\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −778181. | −0.998066 | −0.499033 | − | 0.866583i | \(-0.666311\pi\) | ||||
−0.499033 | + | 0.866583i | \(0.666311\pi\) | |||||||
\(884\) | 5.00451e6i | 6.40408i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −341418. | −0.434930 | ||||||||
\(887\) | − 1.21372e6i | − 1.54267i | −0.636432 | − | 0.771333i | \(-0.719590\pi\) | ||||
0.636432 | − | 0.771333i | \(-0.280410\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 142150. | 0.179864 | ||||||||
\(890\) | 1.18890e6i | 1.50095i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.80851e6 | −4.78658 | ||||||||
\(893\) | 473372.i | 0.593608i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −412331. | −0.514755 | ||||||||
\(896\) | − 3.67700e6i | − 4.58013i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −99549.4 | −0.123449 | ||||||||
\(899\) | − 930146.i | − 1.15088i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.86499e6 | 2.29734 | ||||||||
\(902\) | − 485261.i | − 0.596434i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.22460e6 | 5.16950 | ||||||||
\(905\) | − 663263.i | − 0.809821i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.06908e6 | −1.29955 | −0.649776 | − | 0.760126i | \(-0.725137\pi\) | ||||
−0.649776 | + | 0.760126i | \(0.725137\pi\) | |||||||
\(908\) | 1.54718e6i | 1.87659i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.46128e6 | 2.97220 | ||||||||
\(911\) | − 132856.i | − 0.160082i | −0.996792 | − | 0.0800411i | \(-0.974495\pi\) | ||||
0.996792 | − | 0.0800411i | \(-0.0255051\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 742043. | 0.890200 | ||||||||
\(914\) | − 2.44093e6i | − 2.92188i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.33717e6 | 1.59366 | ||||||||
\(917\) | − 585731.i | − 0.696562i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26758.0 | 0.0316828 | 0.0158414 | − | 0.999875i | \(-0.494957\pi\) | ||||
0.0158414 | + | 0.999875i | \(0.494957\pi\) | |||||||
\(920\) | 4.04886e6i | 4.78362i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 433854. | 0.510366 | ||||||||
\(923\) | 1.49274e6i | 1.75219i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −366272. | −0.428076 | ||||||||
\(926\) | 1.99011e6i | 2.32089i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.21534e6 | 9.53959 | ||||||||
\(929\) | − 546397.i | − 0.633107i | −0.948575 | − | 0.316553i | \(-0.897474\pi\) | ||||
0.948575 | − | 0.316553i | \(-0.102526\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −543157. | −0.626652 | ||||||||
\(932\) | 3.79182e6i | 4.36531i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.69290e6 | 1.94061 | ||||||||
\(935\) | − 1.21993e6i | − 1.39545i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.07946e6 | −1.22949 | −0.614747 | − | 0.788725i | \(-0.710742\pi\) | ||||
−0.614747 | + | 0.788725i | \(0.710742\pi\) | |||||||
\(938\) | − 860399.i | − 0.977900i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.18255e6 | −1.33833 | ||||||||
\(941\) | 7295.07i | 0.00823854i | 0.999992 | + | 0.00411927i | \(0.00131121\pi\) | ||||
−0.999992 | + | 0.00411927i | \(0.998689\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 346276. | 0.389403 | ||||||||
\(944\) | 518900.i | 0.582290i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 421874. | 0.471412 | ||||||||
\(947\) | 708201.i | 0.789690i | 0.918748 | + | 0.394845i | \(0.129202\pi\) | ||||
−0.918748 | + | 0.394845i | \(0.870798\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.99086e6 | 2.21059 | ||||||||
\(950\) | 1.43580e6i | 1.59091i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.68407e6 | −4.06494 | ||||||||
\(953\) | 1.78259e6i | 1.96275i | 0.192107 | + | 0.981374i | \(0.438468\pi\) | ||||
−0.192107 | + | 0.981374i | \(0.561532\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −629600. | −0.690332 | ||||||||
\(956\) | − 1.09874e6i | − 1.20221i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.86863e6 | 2.03607 | ||||||||
\(959\) | 216105.i | 0.234978i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −575154. | −0.622783 | ||||||||
\(962\) | − 2.41287e6i | − 2.60726i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.71108e6 | −1.84127 | ||||||||
\(965\) | − 404132.i | − 0.433979i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 794491. | 0.849642 | 0.424821 | − | 0.905277i | \(-0.360337\pi\) | ||||
0.424821 | + | 0.905277i | \(0.360337\pi\) | |||||||
\(968\) | 1.20728e6i | 1.28842i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.08956e6 | −1.15800 | ||||||||
\(971\) | − 1.80995e6i | − 1.91967i | −0.280559 | − | 0.959837i | \(-0.590520\pi\) | ||||
0.280559 | − | 0.959837i | \(-0.409480\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 219755. | 0.232121 | ||||||||
\(974\) | − 2.27222e6i | − 2.39515i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.54198e6 | 5.81789 | ||||||||
\(977\) | − 1.21769e6i | − 1.27570i | −0.770161 | − | 0.637849i | \(-0.779824\pi\) | ||||
0.770161 | − | 0.637849i | \(-0.220176\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 479985. | 0.500798 | ||||||||
\(980\) | − 1.35689e6i | − 1.41283i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 514537. | 0.533572 | ||||||||
\(983\) | − 1.69305e6i | − 1.75211i | −0.482209 | − | 0.876056i | \(-0.660165\pi\) | ||||
0.482209 | − | 0.876056i | \(-0.339835\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.56928e6 | −1.61743 | ||||||||
\(986\) | − 5.04133e6i | − 5.18551i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.02842e6 | −7.20019 | ||||||||
\(989\) | 301044.i | 0.307778i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 392325. | 0.399483 | 0.199742 | − | 0.979849i | \(-0.435990\pi\) | ||||
0.199742 | + | 0.979849i | \(0.435990\pi\) | |||||||
\(992\) | 3.07689e6i | 3.12672i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.67962e6 | −1.69996 | ||||||||
\(995\) | − 829368.i | − 0.837724i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.14366e6 | −1.15055 | −0.575277 | − | 0.817958i | \(-0.695106\pi\) | ||||
−0.575277 | + | 0.817958i | \(0.695106\pi\) | |||||||
\(998\) | 2.01869e6i | 2.02679i | ||||||||
\(999\) | 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 | 531.5.b.a.296.1 | ✓ | 76 | |
3.2 | odd | 2 | inner | 531.5.b.a.296.76 | yes | 76 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
531.5.b.a.296.1 | ✓ | 76 | 1.1 | even | 1 | trivial | |
531.5.b.a.296.76 | yes | 76 | 3.2 | odd | 2 | inner |