Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,6,Mod(199,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.199");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.c (of order \(2\), degree \(1\), not 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: | \(72.1727189158\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{4081})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2041x^{2} + 1040400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.3 | ||
Root | \(31.4414i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.199 |
Dual form | 450.6.c.q.199.2 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −16.0000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 241.648i | − 1.86397i | −0.362500 | − | 0.931984i | \(-0.618077\pi\) | ||||
0.362500 | − | 0.931984i | \(-0.381923\pi\) | |||||||
\(8\) | − 64.0000i | − 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 653.296 | 1.62790 | 0.813951 | − | 0.580933i | \(-0.197312\pi\) | ||||
0.813951 | + | 0.580933i | \(0.197312\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 828.296i | − 1.35934i | −0.733519 | − | 0.679669i | \(-0.762124\pi\) | ||||
0.733519 | − | 0.679669i | \(-0.237876\pi\) | |||||||
\(14\) | 966.592 | 1.31802 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | − 2162.48i | − 1.81481i | −0.420262 | − | 0.907403i | \(-0.638062\pi\) | ||||
0.420262 | − | 0.907403i | \(-0.361938\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1254.24 | −0.797071 | −0.398535 | − | 0.917153i | \(-0.630481\pi\) | ||||
−0.398535 | + | 0.917153i | \(0.630481\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2613.18i | 1.15110i | ||||||||
\(23\) | 3746.48i | 1.47674i | 0.674396 | + | 0.738370i | \(0.264404\pi\) | ||||
−0.674396 | + | 0.738370i | \(0.735596\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3313.18 | 0.961197 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3866.37i | 0.931984i | ||||||||
\(29\) | −2466.70 | −0.544656 | −0.272328 | − | 0.962205i | \(-0.587794\pi\) | ||||
−0.272328 | + | 0.962205i | \(0.587794\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1895.76 | −0.354306 | −0.177153 | − | 0.984183i | \(-0.556689\pi\) | ||||
−0.177153 | + | 0.984183i | \(0.556689\pi\) | |||||||
\(32\) | 1024.00i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8649.92 | 1.28326 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1050.45i | 0.126145i | 0.998009 | + | 0.0630724i | \(0.0200899\pi\) | ||||
−0.998009 | + | 0.0630724i | \(0.979910\pi\) | |||||||
\(38\) | − 5016.96i | − 0.563614i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1960.56 | 0.182146 | 0.0910730 | − | 0.995844i | \(-0.470970\pi\) | ||||
0.0910730 | + | 0.995844i | \(0.470970\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 11017.6i | − 0.908688i | −0.890826 | − | 0.454344i | \(-0.849874\pi\) | ||||
0.890826 | − | 0.454344i | \(-0.150126\pi\) | |||||||
\(44\) | −10452.7 | −0.813951 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −14985.9 | −1.04421 | ||||||||
\(47\) | 23064.8i | 1.52302i | 0.648154 | + | 0.761509i | \(0.275541\pi\) | ||||
−0.648154 | + | 0.761509i | \(0.724459\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −41586.8 | −2.47437 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 13252.7i | 0.679669i | ||||||||
\(53\) | − 27329.4i | − 1.33641i | −0.743977 | − | 0.668205i | \(-0.767063\pi\) | ||||
0.743977 | − | 0.668205i | \(-0.232937\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −15465.5 | −0.659012 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 9866.82i | − 0.385130i | ||||||||
\(59\) | −35225.7 | −1.31744 | −0.658718 | − | 0.752390i | \(-0.728901\pi\) | ||||
−0.658718 | + | 0.752390i | \(0.728901\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2685.33 | 0.0924002 | 0.0462001 | − | 0.998932i | \(-0.485289\pi\) | ||||
0.0462001 | + | 0.998932i | \(0.485289\pi\) | |||||||
\(62\) | − 7583.04i | − 0.250532i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4096.00 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 48125.1i | 1.30974i | 0.755743 | + | 0.654869i | \(0.227276\pi\) | ||||
−0.755743 | + | 0.654869i | \(0.772724\pi\) | |||||||
\(68\) | 34599.7i | 0.907403i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 27237.7 | 0.641245 | 0.320622 | − | 0.947207i | \(-0.396108\pi\) | ||||
0.320622 | + | 0.947207i | \(0.396108\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6547.77i | 0.143809i | 0.997412 | + | 0.0719046i | \(0.0229077\pi\) | ||||
−0.997412 | + | 0.0719046i | \(0.977092\pi\) | |||||||
\(74\) | −4201.78 | −0.0891978 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 20067.8 | 0.398535 | ||||||||
\(77\) | − 157868.i | − 3.03436i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 65037.3 | 1.17245 | 0.586226 | − | 0.810148i | \(-0.300613\pi\) | ||||
0.586226 | + | 0.810148i | \(0.300613\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7842.23i | 0.128797i | ||||||||
\(83\) | − 62567.2i | − 0.996900i | −0.866919 | − | 0.498450i | \(-0.833903\pi\) | ||||
0.866919 | − | 0.498450i | \(-0.166097\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 44070.3 | 0.642539 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − 41811.0i | − 0.575551i | ||||||||
\(89\) | −17926.2 | −0.239891 | −0.119946 | − | 0.992780i | \(-0.538272\pi\) | ||||
−0.119946 | + | 0.992780i | \(0.538272\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −200156. | −2.53376 | ||||||||
\(92\) | − 59943.7i | − 0.738370i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −92259.2 | −1.07694 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 95974.9i | 1.03569i | 0.855475 | + | 0.517843i | \(0.173265\pi\) | ||||
−0.855475 | + | 0.517843i | \(0.826735\pi\) | |||||||
\(98\) | − 166347.i | − 1.74965i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 41533.7 | 0.405133 | 0.202567 | − | 0.979269i | \(-0.435072\pi\) | ||||
0.202567 | + | 0.979269i | \(0.435072\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 41380.4i | 0.384328i | 0.981363 | + | 0.192164i | \(0.0615506\pi\) | ||||
−0.981363 | + | 0.192164i | \(0.938449\pi\) | |||||||
\(104\) | −53011.0 | −0.480598 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 109317. | 0.944985 | ||||||||
\(107\) | − 11403.4i | − 0.0962885i | −0.998840 | − | 0.0481442i | \(-0.984669\pi\) | ||||
0.998840 | − | 0.0481442i | \(-0.0153307\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −98362.4 | −0.792981 | −0.396490 | − | 0.918039i | \(-0.629772\pi\) | ||||
−0.396490 | + | 0.918039i | \(0.629772\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 61861.9i | − 0.465992i | ||||||||
\(113\) | − 10076.8i | − 0.0742377i | −0.999311 | − | 0.0371189i | \(-0.988182\pi\) | ||||
0.999311 | − | 0.0371189i | \(-0.0118180\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 39467.3 | 0.272328 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 140903.i | − 0.931568i | ||||||||
\(119\) | −522559. | −3.38274 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 265745. | 1.65007 | ||||||||
\(122\) | 10741.3i | 0.0653368i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 30332.2 | 0.177153 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 255129.i | − 1.40362i | −0.712362 | − | 0.701812i | \(-0.752374\pi\) | ||||
0.712362 | − | 0.701812i | \(-0.247626\pi\) | |||||||
\(128\) | − 16384.0i | − 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −65433.3 | −0.333135 | −0.166568 | − | 0.986030i | \(-0.553268\pi\) | ||||
−0.166568 | + | 0.986030i | \(0.553268\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 303085.i | 1.48571i | ||||||||
\(134\) | −192500. | −0.926124 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −138399. | −0.641631 | ||||||||
\(137\) | − 67354.0i | − 0.306593i | −0.988180 | − | 0.153296i | \(-0.951011\pi\) | ||||
0.988180 | − | 0.153296i | \(-0.0489889\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 93837.8 | 0.411946 | 0.205973 | − | 0.978558i | \(-0.433964\pi\) | ||||
0.205973 | + | 0.978558i | \(0.433964\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 108951.i | 0.453429i | ||||||||
\(143\) | − 541123.i | − 2.21287i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −26191.1 | −0.101688 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 16807.1i | − 0.0630724i | ||||||||
\(149\) | −432235. | −1.59498 | −0.797489 | − | 0.603334i | \(-0.793839\pi\) | ||||
−0.797489 | + | 0.603334i | \(0.793839\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −255822. | −0.913053 | −0.456527 | − | 0.889710i | \(-0.650907\pi\) | ||||
−0.456527 | + | 0.889710i | \(0.650907\pi\) | |||||||
\(152\) | 80271.4i | 0.281807i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 631471. | 2.14561 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 58837.3i | − 0.190504i | −0.995453 | − | 0.0952519i | \(-0.969634\pi\) | ||||
0.995453 | − | 0.0952519i | \(-0.0303656\pi\) | |||||||
\(158\) | 260149.i | 0.829048i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 905330. | 2.75259 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 155006.i | − 0.456962i | −0.973548 | − | 0.228481i | \(-0.926624\pi\) | ||||
0.973548 | − | 0.228481i | \(-0.0733758\pi\) | |||||||
\(164\) | −31368.9 | −0.0910730 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 250269. | 0.704914 | ||||||||
\(167\) | − 588656.i | − 1.63332i | −0.577121 | − | 0.816658i | \(-0.695824\pi\) | ||||
0.577121 | − | 0.816658i | \(-0.304176\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −314782. | −0.847798 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 176281.i | 0.454344i | ||||||||
\(173\) | − 192049.i | − 0.487862i | −0.969793 | − | 0.243931i | \(-0.921563\pi\) | ||||
0.969793 | − | 0.243931i | \(-0.0784370\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 167244. | 0.406976 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 71704.9i | − 0.169629i | ||||||||
\(179\) | 350715. | 0.818130 | 0.409065 | − | 0.912505i | \(-0.365855\pi\) | ||||
0.409065 | + | 0.912505i | \(0.365855\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 524637. | 1.19032 | 0.595158 | − | 0.803608i | \(-0.297089\pi\) | ||||
0.595158 | + | 0.803608i | \(0.297089\pi\) | |||||||
\(182\) | − 800625.i | − 1.79164i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 239775. | 0.522106 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 1.41274e6i | − 2.95433i | ||||||||
\(188\) | − 369037.i | − 0.761509i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 63662.7 | 0.126270 | 0.0631352 | − | 0.998005i | \(-0.479890\pi\) | ||||
0.0631352 | + | 0.998005i | \(0.479890\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 717477.i | 1.38648i | 0.720705 | + | 0.693242i | \(0.243818\pi\) | ||||
−0.720705 | + | 0.693242i | \(0.756182\pi\) | |||||||
\(194\) | −383900. | −0.732341 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 665389. | 1.23719 | ||||||||
\(197\) | − 287465.i | − 0.527740i | −0.964558 | − | 0.263870i | \(-0.915001\pi\) | ||||
0.964558 | − | 0.263870i | \(-0.0849990\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −643619. | −1.15212 | −0.576058 | − | 0.817409i | \(-0.695410\pi\) | ||||
−0.576058 | + | 0.817409i | \(0.695410\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 166135.i | 0.286472i | ||||||||
\(203\) | 596074.i | 1.01522i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −165522. | −0.271761 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 212044.i | − 0.339834i | ||||||||
\(209\) | −819391. | −1.29755 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −873827. | −1.35120 | −0.675600 | − | 0.737269i | \(-0.736115\pi\) | ||||
−0.675600 | + | 0.737269i | \(0.736115\pi\) | |||||||
\(212\) | 437270.i | 0.668205i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 45613.5 | 0.0680862 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 458107.i | 0.660416i | ||||||||
\(218\) | − 393449.i | − 0.560722i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.79117e6 | −2.46693 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 288496.i | 0.388488i | 0.980953 | + | 0.194244i | \(0.0622254\pi\) | ||||
−0.980953 | + | 0.194244i | \(0.937775\pi\) | |||||||
\(224\) | 247448. | 0.329506 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 40307.0 | 0.0524940 | ||||||||
\(227\) | 125358.i | 0.161469i | 0.996736 | + | 0.0807343i | \(0.0257265\pi\) | ||||
−0.996736 | + | 0.0807343i | \(0.974273\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 698183. | 0.879793 | 0.439897 | − | 0.898048i | \(-0.355015\pi\) | ||||
0.439897 | + | 0.898048i | \(0.355015\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 157869.i | 0.192565i | ||||||||
\(233\) | − 984588.i | − 1.18813i | −0.804416 | − | 0.594066i | \(-0.797522\pi\) | ||||
0.804416 | − | 0.594066i | \(-0.202478\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 563611. | 0.658718 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 2.09024e6i | − 2.39196i | ||||||||
\(239\) | −131049. | −0.148402 | −0.0742011 | − | 0.997243i | \(-0.523641\pi\) | ||||
−0.0742011 | + | 0.997243i | \(0.523641\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.23632e6 | −1.37116 | −0.685579 | − | 0.727998i | \(-0.740451\pi\) | ||||
−0.685579 | + | 0.727998i | \(0.740451\pi\) | |||||||
\(242\) | 1.06298e6i | 1.16677i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −42965.3 | −0.0462001 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.03888e6i | 1.08349i | ||||||||
\(248\) | 121329.i | 0.125266i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 611918. | 0.613068 | 0.306534 | − | 0.951860i | \(-0.400831\pi\) | ||||
0.306534 | + | 0.951860i | \(0.400831\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.44756e6i | 2.40399i | ||||||||
\(254\) | 1.02052e6 | 0.992513 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 1.64515e6i | 1.55372i | 0.629675 | + | 0.776858i | \(0.283188\pi\) | ||||
−0.629675 | + | 0.776858i | \(0.716812\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 253838. | 0.235130 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 261733.i | − 0.235562i | ||||||||
\(263\) | 268273.i | 0.239159i | 0.992825 | + | 0.119580i | \(0.0381547\pi\) | ||||
−0.992825 | + | 0.119580i | \(0.961845\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.21234e6 | −1.05056 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 770001.i | − 0.654869i | ||||||||
\(269\) | 947177. | 0.798087 | 0.399044 | − | 0.916932i | \(-0.369342\pi\) | ||||
0.399044 | + | 0.916932i | \(0.369342\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 609159. | 0.503857 | 0.251929 | − | 0.967746i | \(-0.418935\pi\) | ||||
0.251929 | + | 0.967746i | \(0.418935\pi\) | |||||||
\(272\) | − 553595.i | − 0.453701i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 269416. | 0.216794 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 741976.i | 0.581019i | 0.956872 | + | 0.290510i | \(0.0938249\pi\) | ||||
−0.956872 | + | 0.290510i | \(0.906175\pi\) | |||||||
\(278\) | 375351.i | 0.291290i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −423084. | −0.319639 | −0.159820 | − | 0.987146i | \(-0.551091\pi\) | ||||
−0.159820 | + | 0.987146i | \(0.551091\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 445130.i | 0.330385i | 0.986261 | + | 0.165192i | \(0.0528245\pi\) | ||||
−0.986261 | + | 0.165192i | \(0.947175\pi\) | |||||||
\(284\) | −435803. | −0.320622 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.16449e6 | 1.56473 | ||||||||
\(287\) | − 473765.i | − 0.339514i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.25647e6 | −2.29352 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 104764.i | − 0.0719046i | ||||||||
\(293\) | 2.45992e6i | 1.67399i | 0.547211 | + | 0.836994i | \(0.315689\pi\) | ||||
−0.547211 | + | 0.836994i | \(0.684311\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 67228.5 | 0.0445989 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − 1.72894e6i | − 1.12782i | ||||||||
\(299\) | 3.10320e6 | 2.00739 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.66238e6 | −1.69376 | ||||||||
\(302\) | − 1.02329e6i | − 0.645626i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −321086. | −0.199268 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 374253.i | 0.226631i | 0.993559 | + | 0.113315i | \(0.0361470\pi\) | ||||
−0.993559 | + | 0.113315i | \(0.963853\pi\) | |||||||
\(308\) | 2.52588e6i | 1.51718i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.22568e6 | 1.30485 | 0.652427 | − | 0.757851i | \(-0.273751\pi\) | ||||
0.652427 | + | 0.757851i | \(0.273751\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 3.05869e6i | − 1.76471i | −0.470580 | − | 0.882357i | \(-0.655955\pi\) | ||||
0.470580 | − | 0.882357i | \(-0.344045\pi\) | |||||||
\(314\) | 235349. | 0.134706 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.04060e6 | −0.586226 | ||||||||
\(317\) | 520610.i | 0.290981i | 0.989360 | + | 0.145490i | \(0.0464760\pi\) | ||||
−0.989360 | + | 0.145490i | \(0.953524\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.61149e6 | −0.886646 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.62132e6i | 1.94638i | ||||||||
\(323\) | 2.71227e6i | 1.44653i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 620025. | 0.323121 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 125476.i | − 0.0643983i | ||||||||
\(329\) | 5.57357e6 | 2.83886 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.12755e6 | −1.06736 | −0.533679 | − | 0.845687i | \(-0.679191\pi\) | ||||
−0.533679 | + | 0.845687i | \(0.679191\pi\) | |||||||
\(332\) | 1.00108e6i | 0.498450i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.35462e6 | 1.15493 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 3.08383e6i | − 1.47916i | −0.673067 | − | 0.739581i | \(-0.735024\pi\) | ||||
0.673067 | − | 0.739581i | \(-0.264976\pi\) | |||||||
\(338\) | − 1.25913e6i | − 0.599484i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.23849e6 | −0.576776 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.98799e6i | 2.74819i | ||||||||
\(344\) | −705125. | −0.321270 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 768196. | 0.344970 | ||||||||
\(347\) | 4.04955e6i | 1.80544i | 0.430231 | + | 0.902719i | \(0.358432\pi\) | ||||
−0.430231 | + | 0.902719i | \(0.641568\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 493135. | 0.216722 | 0.108361 | − | 0.994112i | \(-0.465440\pi\) | ||||
0.108361 | + | 0.994112i | \(0.465440\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 668975.i | 0.287775i | ||||||||
\(353\) | − 1.34815e6i | − 0.575841i | −0.957654 | − | 0.287920i | \(-0.907036\pi\) | ||||
0.957654 | − | 0.287920i | \(-0.0929638\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 286820. | 0.119946 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.40286e6i | 0.578505i | ||||||||
\(359\) | −1.64749e6 | −0.674664 | −0.337332 | − | 0.941386i | \(-0.609524\pi\) | ||||
−0.337332 | + | 0.941386i | \(0.609524\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −902980. | −0.364678 | ||||||||
\(362\) | 2.09855e6i | 0.841681i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.20250e6 | 1.26688 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 27918.4i | − 0.0108199i | −0.999985 | − | 0.00540997i | \(-0.998278\pi\) | ||||
0.999985 | − | 0.00540997i | \(-0.00172206\pi\) | |||||||
\(368\) | 959099.i | 0.369185i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.60409e6 | −2.49103 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 2.80536e6i | − 1.04404i | −0.852934 | − | 0.522019i | \(-0.825179\pi\) | ||||
0.852934 | − | 0.522019i | \(-0.174821\pi\) | |||||||
\(374\) | 5.65096e6 | 2.08902 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.47615e6 | 0.538468 | ||||||||
\(377\) | 2.04316e6i | 0.740371i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.70014e6 | −0.607976 | −0.303988 | − | 0.952676i | \(-0.598318\pi\) | ||||
−0.303988 | + | 0.952676i | \(0.598318\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 254651.i | 0.0892867i | ||||||||
\(383\) | − 627913.i | − 0.218727i | −0.994002 | − | 0.109363i | \(-0.965119\pi\) | ||||
0.994002 | − | 0.109363i | \(-0.0348812\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.86991e6 | −0.980392 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 1.53560e6i | − 0.517843i | ||||||||
\(389\) | −3.14339e6 | −1.05323 | −0.526616 | − | 0.850103i | \(-0.676540\pi\) | ||||
−0.526616 | + | 0.850103i | \(0.676540\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.10169e6 | 2.68000 | ||||||||
\(392\) | 2.66156e6i | 0.874823i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.14986e6 | 0.373169 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 1.10773e6i | − 0.352743i | −0.984324 | − | 0.176371i | \(-0.943564\pi\) | ||||
0.984324 | − | 0.176371i | \(-0.0564359\pi\) | |||||||
\(398\) | − 2.57448e6i | − 0.814669i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.41563e6 | 0.750187 | 0.375093 | − | 0.926987i | \(-0.377611\pi\) | ||||
0.375093 | + | 0.926987i | \(0.377611\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.57025e6i | 0.481622i | ||||||||
\(404\) | −664540. | −0.202567 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.38430e6 | −0.717869 | ||||||||
\(407\) | 686252.i | 0.205351i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.69830e6 | −1.09319 | −0.546593 | − | 0.837398i | \(-0.684075\pi\) | ||||
−0.546593 | + | 0.837398i | \(0.684075\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 662087.i | − 0.192164i | ||||||||
\(413\) | 8.51222e6i | 2.45566i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 848175. | 0.240299 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 3.27756e6i | − 0.917509i | ||||||||
\(419\) | 3.45478e6 | 0.961357 | 0.480679 | − | 0.876897i | \(-0.340390\pi\) | ||||
0.480679 | + | 0.876897i | \(0.340390\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.83980e6 | −1.33083 | −0.665415 | − | 0.746474i | \(-0.731745\pi\) | ||||
−0.665415 | + | 0.746474i | \(0.731745\pi\) | |||||||
\(422\) | − 3.49531e6i | − 0.955442i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.74908e6 | −0.472493 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 648905.i | − 0.172231i | ||||||||
\(428\) | 182454.i | 0.0481442i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.54923e6 | −1.43893 | −0.719464 | − | 0.694529i | \(-0.755613\pi\) | ||||
−0.719464 | + | 0.694529i | \(0.755613\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 814302.i | 0.208721i | 0.994540 | + | 0.104360i | \(0.0332795\pi\) | ||||
−0.994540 | + | 0.104360i | \(0.966720\pi\) | |||||||
\(434\) | −1.83243e6 | −0.466984 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.57380e6 | 0.396490 | ||||||||
\(437\) | − 4.69899e6i | − 1.17707i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.02462e6 | 0.996697 | 0.498349 | − | 0.866977i | \(-0.333940\pi\) | ||||
0.498349 | + | 0.866977i | \(0.333940\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 7.16470e6i | − 1.74438i | ||||||||
\(443\) | − 4.46382e6i | − 1.08068i | −0.841446 | − | 0.540341i | \(-0.818295\pi\) | ||||
0.841446 | − | 0.540341i | \(-0.181705\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.15399e6 | −0.274703 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 989791.i | 0.232996i | ||||||||
\(449\) | 4.66889e6 | 1.09294 | 0.546472 | − | 0.837477i | \(-0.315970\pi\) | ||||
0.546472 | + | 0.837477i | \(0.315970\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.28082e6 | 0.296516 | ||||||||
\(452\) | 161228.i | 0.0371189i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −501433. | −0.114176 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 4.71340e6i | − 1.05571i | −0.849335 | − | 0.527854i | \(-0.822997\pi\) | ||||
0.849335 | − | 0.527854i | \(-0.177003\pi\) | |||||||
\(458\) | 2.79273e6i | 0.622108i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.23975e6 | 1.36746 | 0.683731 | − | 0.729734i | \(-0.260356\pi\) | ||||
0.683731 | + | 0.729734i | \(0.260356\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.33992e6i | 0.724076i | 0.932163 | + | 0.362038i | \(0.117919\pi\) | ||||
−0.932163 | + | 0.362038i | \(0.882081\pi\) | |||||||
\(464\) | −631476. | −0.136164 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.93835e6 | 0.840136 | ||||||||
\(467\) | − 722497.i | − 0.153301i | −0.997058 | − | 0.0766503i | \(-0.975578\pi\) | ||||
0.997058 | − | 0.0766503i | \(-0.0244225\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.16293e7 | 2.44131 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.25444e6i | 0.465784i | ||||||||
\(473\) | − 7.19774e6i | − 1.47926i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 8.36095e6 | 1.69137 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − 524197.i | − 0.104936i | ||||||||
\(479\) | 5.37714e6 | 1.07081 | 0.535405 | − | 0.844595i | \(-0.320159\pi\) | ||||
0.535405 | + | 0.844595i | \(0.320159\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 870080. | 0.171473 | ||||||||
\(482\) | − 4.94527e6i | − 0.969556i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.25192e6 | −0.825034 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 1.72084e6i | − 0.328790i | −0.986395 | − | 0.164395i | \(-0.947433\pi\) | ||||
0.986395 | − | 0.164395i | \(-0.0525672\pi\) | |||||||
\(488\) | − 171861.i | − 0.0326684i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.31449e6 | 1.36924 | 0.684621 | − | 0.728899i | \(-0.259968\pi\) | ||||
0.684621 | + | 0.728899i | \(0.259968\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.33420e6i | 0.988444i | ||||||||
\(494\) | −4.15553e6 | −0.766142 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −485314. | −0.0885766 | ||||||||
\(497\) | − 6.58193e6i | − 1.19526i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.29878e6 | 1.31220 | 0.656098 | − | 0.754676i | \(-0.272206\pi\) | ||||
0.656098 | + | 0.754676i | \(0.272206\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.44767e6i | 0.433505i | ||||||||
\(503\) | 923591.i | 0.162764i | 0.996683 | + | 0.0813822i | \(0.0259334\pi\) | ||||
−0.996683 | + | 0.0813822i | \(0.974067\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −9.79025e6 | −1.69988 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.08207e6i | 0.701812i | ||||||||
\(509\) | −8.81318e6 | −1.50778 | −0.753891 | − | 0.657000i | \(-0.771825\pi\) | ||||
−0.753891 | + | 0.657000i | \(0.771825\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.58226e6 | 0.268056 | ||||||||
\(512\) | 262144.i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.58059e6 | −1.09864 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.50682e7i | 2.47933i | ||||||||
\(518\) | 1.01535e6i | 0.166262i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.66995e6 | 0.269531 | 0.134765 | − | 0.990878i | \(-0.456972\pi\) | ||||
0.134765 | + | 0.990878i | \(0.456972\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 2.85438e6i | − 0.456308i | −0.973625 | − | 0.228154i | \(-0.926731\pi\) | ||||
0.973625 | − | 0.228154i | \(-0.0732689\pi\) | |||||||
\(524\) | 1.04693e6 | 0.166568 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.07309e6 | −0.169111 | ||||||||
\(527\) | 4.09954e6i | 0.642997i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.59978e6 | −1.18076 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − 4.84936e6i | − 0.742857i | ||||||||
\(533\) | − 1.62392e6i | − 0.247598i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.08000e6 | 0.463062 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.78871e6i | 0.564333i | ||||||||
\(539\) | −2.71685e7 | −4.02804 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.85655e6 | −1.15409 | −0.577044 | − | 0.816713i | \(-0.695794\pi\) | ||||
−0.577044 | + | 0.816713i | \(0.695794\pi\) | |||||||
\(542\) | 2.43664e6i | 0.356281i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.21438e6 | 0.320815 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 1.07748e7i | − 1.53972i | −0.638213 | − | 0.769860i | \(-0.720326\pi\) | ||||
0.638213 | − | 0.769860i | \(-0.279674\pi\) | |||||||
\(548\) | 1.07766e6i | 0.153296i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.09384e6 | 0.434129 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 1.57161e7i | − 2.18541i | ||||||||
\(554\) | −2.96791e6 | −0.410843 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.50140e6 | −0.205973 | ||||||||
\(557\) | 7.62158e6i | 1.04090i | 0.853893 | + | 0.520448i | \(0.174235\pi\) | ||||
−0.853893 | + | 0.520448i | \(0.825765\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.12581e6 | −1.23521 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 1.69233e6i | − 0.226019i | ||||||||
\(563\) | − 4.25551e6i | − 0.565823i | −0.959146 | − | 0.282911i | \(-0.908700\pi\) | ||||
0.959146 | − | 0.282911i | \(-0.0913003\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.78052e6 | −0.233617 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 1.74321e6i | − 0.226714i | ||||||||
\(569\) | −5.99899e6 | −0.776779 | −0.388389 | − | 0.921495i | \(-0.626968\pi\) | ||||
−0.388389 | + | 0.921495i | \(0.626968\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.20283e6 | 1.18122 | 0.590611 | − | 0.806957i | \(-0.298887\pi\) | ||||
0.590611 | + | 0.806957i | \(0.298887\pi\) | |||||||
\(572\) | 8.65796e6i | 1.10643i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.89506e6 | 0.240073 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.03879e6i | 0.505024i | 0.967594 | + | 0.252512i | \(0.0812568\pi\) | ||||
−0.967594 | + | 0.252512i | \(0.918743\pi\) | |||||||
\(578\) | − 1.30259e7i | − 1.62176i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.51192e7 | −1.85819 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 1.78542e7i | − 2.17555i | ||||||||
\(584\) | 419058. | 0.0508442 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.83969e6 | −1.18369 | ||||||||
\(587\) | − 1.65997e7i | − 1.98840i | −0.107544 | − | 0.994200i | \(-0.534299\pi\) | ||||
0.107544 | − | 0.994200i | \(-0.465701\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.37774e6 | 0.282407 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 268914.i | 0.0315362i | ||||||||
\(593\) | − 1.09900e7i | − 1.28340i | −0.766957 | − | 0.641698i | \(-0.778230\pi\) | ||||
0.766957 | − | 0.641698i | \(-0.221770\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.91577e6 | 0.797489 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.24128e7i | 1.41944i | ||||||||
\(599\) | −4.47167e6 | −0.509217 | −0.254608 | − | 0.967044i | \(-0.581947\pi\) | ||||
−0.254608 | + | 0.967044i | \(0.581947\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.60311e7 | 1.81041 | 0.905206 | − | 0.424974i | \(-0.139717\pi\) | ||||
0.905206 | + | 0.424974i | \(0.139717\pi\) | |||||||
\(602\) | − 1.06495e7i | − 1.19767i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.09316e6 | 0.456527 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 720250.i | − 0.0793435i | −0.999213 | − | 0.0396718i | \(-0.987369\pi\) | ||||
0.999213 | − | 0.0396718i | \(-0.0126312\pi\) | |||||||
\(608\) | − 1.28434e6i | − 0.140904i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.91045e7 | 2.07030 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.46218e7i | 1.57163i | 0.618464 | + | 0.785813i | \(0.287755\pi\) | ||||
−0.618464 | + | 0.785813i | \(0.712245\pi\) | |||||||
\(614\) | −1.49701e6 | −0.160252 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.01035e7 | −1.07281 | ||||||||
\(617\) | − 4.57269e6i | − 0.483569i | −0.970330 | − | 0.241784i | \(-0.922267\pi\) | ||||
0.970330 | − | 0.241784i | \(-0.0777327\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.62486e6 | 0.485145 | 0.242573 | − | 0.970133i | \(-0.422009\pi\) | ||||
0.242573 | + | 0.970133i | \(0.422009\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.90273e6i | 0.922671i | ||||||||
\(623\) | 4.33184e6i | 0.447149i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.22348e7 | 1.24784 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 941397.i | 0.0952519i | ||||||||
\(629\) | 2.27157e6 | 0.228928 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.03670e7 | −1.03653 | −0.518263 | − | 0.855221i | \(-0.673421\pi\) | ||||
−0.518263 | + | 0.855221i | \(0.673421\pi\) | |||||||
\(632\) | − 4.16239e6i | − 0.414524i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.08244e6 | −0.205755 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.44462e7i | 3.36351i | ||||||||
\(638\) | − 6.44595e6i | − 0.626954i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.62432e6 | −0.444532 | −0.222266 | − | 0.974986i | \(-0.571345\pi\) | ||||
−0.222266 | + | 0.974986i | \(0.571345\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1.13460e7i | − 1.08222i | −0.840951 | − | 0.541111i | \(-0.818004\pi\) | ||||
0.840951 | − | 0.541111i | \(-0.181996\pi\) | |||||||
\(644\) | −1.44853e7 | −1.37630 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.08491e7 | −1.02285 | ||||||||
\(647\) | − 1.10482e7i | − 1.03760i | −0.854895 | − | 0.518800i | \(-0.826379\pi\) | ||||
0.854895 | − | 0.518800i | \(-0.173621\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.30128e7 | −2.14466 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.48010e6i | 0.228481i | ||||||||
\(653\) | − 1.37432e6i | − 0.126126i | −0.998010 | − | 0.0630631i | \(-0.979913\pi\) | ||||
0.998010 | − | 0.0630631i | \(-0.0200869\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 501902. | 0.0455365 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.22943e7i | 2.00738i | ||||||||
\(659\) | 1.28061e7 | 1.14869 | 0.574344 | − | 0.818614i | \(-0.305257\pi\) | ||||
0.574344 | + | 0.818614i | \(0.305257\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −104794. | −0.00932894 | −0.00466447 | − | 0.999989i | \(-0.501485\pi\) | ||||
−0.00466447 | + | 0.999989i | \(0.501485\pi\) | |||||||
\(662\) | − 8.51021e6i | − 0.754737i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.00430e6 | −0.352457 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 9.24146e6i | − 0.804315i | ||||||||
\(668\) | 9.41850e6i | 0.816658i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.75432e6 | 0.150419 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 1.80490e7i | − 1.53608i | −0.640400 | − | 0.768042i | \(-0.721231\pi\) | ||||
0.640400 | − | 0.768042i | \(-0.278769\pi\) | |||||||
\(674\) | 1.23353e7 | 1.04593 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.03651e6 | 0.423899 | ||||||||
\(677\) | − 1.29914e7i | − 1.08939i | −0.838633 | − | 0.544697i | \(-0.816645\pi\) | ||||
0.838633 | − | 0.544697i | \(-0.183355\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.31922e7 | 1.93049 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 4.95397e6i | − 0.407842i | ||||||||
\(683\) | − 3.91843e6i | − 0.321411i | −0.987002 | − | 0.160705i | \(-0.948623\pi\) | ||||
0.987002 | − | 0.160705i | \(-0.0513769\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.39520e7 | −1.94326 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 2.82050e6i | − 0.227172i | ||||||||
\(689\) | −2.26368e7 | −1.81663 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.11077e6 | −0.247840 | −0.123920 | − | 0.992292i | \(-0.539547\pi\) | ||||
−0.123920 | + | 0.992292i | \(0.539547\pi\) | |||||||
\(692\) | 3.07278e6i | 0.243931i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.61982e7 | −1.27664 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 4.23967e6i | − 0.330560i | ||||||||
\(698\) | 1.97254e6i | 0.153245i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.94916e7 | 1.49814 | 0.749070 | − | 0.662490i | \(-0.230500\pi\) | ||||
0.749070 | + | 0.662490i | \(0.230500\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 1.31751e6i | − 0.100546i | ||||||||
\(704\) | −2.67590e6 | −0.203488 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.39261e6 | 0.407181 | ||||||||
\(707\) | − 1.00366e7i | − 0.755155i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.13693e6 | 0.607918 | 0.303959 | − | 0.952685i | \(-0.401691\pi\) | ||||
0.303959 | + | 0.952685i | \(0.401691\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.14728e6i | 0.0848143i | ||||||||
\(713\) | − 7.10243e6i | − 0.523218i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.61144e6 | −0.409065 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − 6.58997e6i | − 0.477059i | ||||||||
\(719\) | 1.14993e7 | 0.829566 | 0.414783 | − | 0.909920i | \(-0.363857\pi\) | ||||
0.414783 | + | 0.909920i | \(0.363857\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.99951e6 | 0.716375 | ||||||||
\(722\) | − 3.61192e6i | − 0.257867i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.39419e6 | −0.595158 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 2.10897e7i | − 1.47991i | −0.672658 | − | 0.739953i | \(-0.734848\pi\) | ||||
0.672658 | − | 0.739953i | \(-0.265152\pi\) | |||||||
\(728\) | 1.28100e7i | 0.895820i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.38253e7 | −1.64909 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 2.20274e7i | − 1.51427i | −0.653259 | − | 0.757134i | \(-0.726599\pi\) | ||||
0.653259 | − | 0.757134i | \(-0.273401\pi\) | |||||||
\(734\) | 111673. | 0.00765085 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.83640e6 | −0.261053 | ||||||||
\(737\) | 3.14399e7i | 2.13213i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.26088e7 | 0.849305 | 0.424653 | − | 0.905356i | \(-0.360396\pi\) | ||||
0.424653 | + | 0.905356i | \(0.360396\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − 2.64164e7i | − 1.76142i | ||||||||
\(743\) | − 5.90968e6i | − 0.392728i | −0.980531 | − | 0.196364i | \(-0.937087\pi\) | ||||
0.980531 | − | 0.196364i | \(-0.0629134\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.12214e7 | 0.738247 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.26039e7i | 1.47716i | ||||||||
\(749\) | −2.75561e6 | −0.179479 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.15585e7 | −0.747830 | −0.373915 | − | 0.927463i | \(-0.621985\pi\) | ||||
−0.373915 | + | 0.927463i | \(0.621985\pi\) | |||||||
\(752\) | 5.90459e6i | 0.380755i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8.17265e6 | −0.523521 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.64988e7i | 1.68068i | 0.542057 | + | 0.840342i | \(0.317646\pi\) | ||||
−0.542057 | + | 0.840342i | \(0.682354\pi\) | |||||||
\(758\) | − 6.80056e6i | − 0.429904i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.54716e6 | 0.0968442 | 0.0484221 | − | 0.998827i | \(-0.484581\pi\) | ||||
0.0484221 | + | 0.998827i | \(0.484581\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.37691e7i | 1.47809i | ||||||||
\(764\) | −1.01860e6 | −0.0631352 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.51165e6 | 0.154663 | ||||||||
\(767\) | 2.91773e7i | 1.79084i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.16191e7 | −0.708529 | −0.354265 | − | 0.935145i | \(-0.615269\pi\) | ||||
−0.354265 | + | 0.935145i | \(0.615269\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 1.14796e7i | − 0.693242i | ||||||||
\(773\) | − 1.16233e7i | − 0.699649i | −0.936815 | − | 0.349824i | \(-0.886241\pi\) | ||||
0.936815 | − | 0.349824i | \(-0.113759\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.14239e6 | 0.366171 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 1.25736e7i | − 0.744748i | ||||||||
\(779\) | −2.45901e6 | −0.145183 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.77943e7 | 1.04388 | ||||||||
\(782\) | 3.24068e7i | 1.89504i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.06462e7 | −0.618594 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.03314e7i | 1.17012i | 0.810991 | + | 0.585059i | \(0.198929\pi\) | ||||
−0.810991 | + | 0.585059i | \(0.801071\pi\) | |||||||
\(788\) | 4.59945e6i | 0.263870i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.43503e6 | −0.138377 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 2.22425e6i | − 0.125603i | ||||||||
\(794\) | 4.43092e6 | 0.249427 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.02979e7 | 0.576058 | ||||||||
\(797\) | 6.32170e6i | 0.352523i | 0.984343 | + | 0.176262i | \(0.0564005\pi\) | ||||
−0.984343 | + | 0.176262i | \(0.943599\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.98772e7 | 2.76398 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.66252e6i | 0.530462i | ||||||||
\(803\) | 4.27764e6i | 0.234107i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.28100e6 | −0.340558 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 2.65816e6i | − 0.143236i | ||||||||
\(809\) | 1.84549e7 | 0.991380 | 0.495690 | − | 0.868499i | \(-0.334915\pi\) | ||||
0.495690 | + | 0.868499i | \(0.334915\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.00263e7 | 1.60306 | 0.801530 | − | 0.597954i | \(-0.204020\pi\) | ||||
0.801530 | + | 0.597954i | \(0.204020\pi\) | |||||||
\(812\) | − 9.53719e6i | − 0.507610i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.74501e6 | −0.145205 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.38187e7i | 0.724289i | ||||||||
\(818\) | − 1.47932e7i | − 0.772999i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.51609e7 | −1.30277 | −0.651387 | − | 0.758746i | \(-0.725812\pi\) | ||||
−0.651387 | + | 0.758746i | \(0.725812\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.97388e6i | 0.410365i | 0.978724 | + | 0.205182i | \(0.0657788\pi\) | ||||
−0.978724 | + | 0.205182i | \(0.934221\pi\) | |||||||
\(824\) | 2.64835e6 | 0.135880 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.40489e7 | −1.73641 | ||||||||
\(827\) | 1.37135e7i | 0.697243i | 0.937264 | + | 0.348622i | \(0.113350\pi\) | ||||
−0.937264 | + | 0.348622i | \(0.886650\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.62566e7 | 0.821569 | 0.410785 | − | 0.911732i | \(-0.365255\pi\) | ||||
0.410785 | + | 0.911732i | \(0.365255\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.39270e6i | 0.169917i | ||||||||
\(833\) | 8.99307e7i | 4.49051i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.31103e7 | 0.648777 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.38191e7i | 0.679782i | ||||||||
\(839\) | 2.36734e7 | 1.16106 | 0.580532 | − | 0.814237i | \(-0.302844\pi\) | ||||
0.580532 | + | 0.814237i | \(0.302844\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.44265e7 | −0.703350 | ||||||||
\(842\) | − 1.93592e7i | − 0.941039i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.39812e7 | 0.675600 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 6.42168e7i | − 3.07567i | ||||||||
\(848\) | − 6.99632e6i | − 0.334103i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.93547e6 | −0.186283 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.53714e7i | 1.19391i | 0.802274 | + | 0.596956i | \(0.203623\pi\) | ||||
−0.802274 | + | 0.596956i | \(0.796377\pi\) | |||||||
\(854\) | 2.59562e6 | 0.121786 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −729817. | −0.0340431 | ||||||||
\(857\) | − 2.37850e7i | − 1.10624i | −0.833100 | − | 0.553122i | \(-0.813436\pi\) | ||||
0.833100 | − | 0.553122i | \(-0.186564\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.55700e6 | 0.395675 | 0.197838 | − | 0.980235i | \(-0.436608\pi\) | ||||
0.197838 | + | 0.980235i | \(0.436608\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 2.21969e7i | − 1.01748i | ||||||||
\(863\) | 3.91623e7i | 1.78995i | 0.446113 | + | 0.894977i | \(0.352808\pi\) | ||||
−0.446113 | + | 0.894977i | \(0.647192\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3.25721e6 | −0.147588 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 7.32971e6i | − 0.330208i | ||||||||
\(869\) | 4.24886e7 | 1.90864 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.98618e7 | 1.78038 | ||||||||
\(872\) | 6.29519e6i | 0.280361i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.87960e7 | 0.832311 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 2.35047e7i | − 1.03194i | −0.856605 | − | 0.515972i | \(-0.827431\pi\) | ||||
0.856605 | − | 0.515972i | \(-0.172569\pi\) | |||||||
\(878\) | 1.60985e7i | 0.704771i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.50902e7 | 1.95723 | 0.978617 | − | 0.205691i | \(-0.0659442\pi\) | ||||
0.978617 | + | 0.205691i | \(0.0659442\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 1.95876e7i | − 0.845434i | −0.906262 | − | 0.422717i | \(-0.861076\pi\) | ||||
0.906262 | − | 0.422717i | \(-0.138924\pi\) | |||||||
\(884\) | 2.86588e7 | 1.23347 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.78553e7 | 0.764157 | ||||||||
\(887\) | − 9.54399e6i | − 0.407306i | −0.979043 | − | 0.203653i | \(-0.934719\pi\) | ||||
0.979043 | − | 0.203653i | \(-0.0652815\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.16515e7 | −2.61631 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 4.61594e6i | − 0.194244i | ||||||||
\(893\) | − 2.89288e7i | − 1.21395i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.95916e6 | −0.164753 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.86756e7i | 0.772828i | ||||||||
\(899\) | 4.67628e6 | 0.192975 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.90992e7 | −2.42532 | ||||||||
\(902\) | 5.12330e6i | 0.209668i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −644912. | −0.0262470 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 1.08034e7i | − 0.436054i | −0.975943 | − | 0.218027i | \(-0.930038\pi\) | ||||
0.975943 | − | 0.218027i | \(-0.0699621\pi\) | |||||||
\(908\) | − 2.00573e6i | − 0.0807343i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.88914e7 | −1.55259 | −0.776296 | − | 0.630368i | \(-0.782904\pi\) | ||||
−0.776296 | + | 0.630368i | \(0.782904\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 4.08749e7i | − 1.62286i | ||||||||
\(914\) | 1.88536e7 | 0.746498 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.11709e7 | −0.439897 | ||||||||
\(917\) | 1.58118e7i | 0.620953i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.89714e7 | −1.13157 | −0.565785 | − | 0.824553i | \(-0.691427\pi\) | ||||
−0.565785 | + | 0.824553i | \(0.691427\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.49590e7i | 0.966941i | ||||||||
\(923\) | − 2.25609e7i | − 0.871668i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.33597e7 | −0.511999 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − 2.52590e6i | − 0.0962824i | ||||||||
\(929\) | 3.61023e7 | 1.37245 | 0.686224 | − | 0.727391i | \(-0.259267\pi\) | ||||
0.686224 | + | 0.727391i | \(0.259267\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.21599e7 | 1.97225 | ||||||||
\(932\) | 1.57534e7i | 0.594066i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.88999e6 | 0.108400 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.02966e7i | 0.383129i | 0.981480 | + | 0.191565i | \(0.0613562\pi\) | ||||
−0.981480 | + | 0.191565i | \(0.938644\pi\) | |||||||
\(938\) | 4.65173e7i | 1.72627i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.55696e7 | 0.573195 | 0.286597 | − | 0.958051i | \(-0.407476\pi\) | ||||
0.286597 | + | 0.958051i | \(0.407476\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.34519e6i | 0.268982i | ||||||||
\(944\) | −9.01778e6 | −0.329359 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.87910e7 | 1.04599 | ||||||||
\(947\) | 3.54260e7i | 1.28365i | 0.766850 | + | 0.641826i | \(0.221823\pi\) | ||||
−0.766850 | + | 0.641826i | \(0.778177\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.42350e6 | 0.195485 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.34438e7i | 1.19598i | ||||||||
\(953\) | 5.47490e6i | 0.195274i | 0.995222 | + | 0.0976369i | \(0.0311284\pi\) | ||||
−0.995222 | + | 0.0976369i | \(0.968872\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.09679e6 | 0.0742011 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.15086e7i | 0.757177i | ||||||||
\(959\) | −1.62760e7 | −0.571479 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.50352e7 | −0.874467 | ||||||||
\(962\) | 3.48032e6i | 0.121250i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.97811e7 | 0.685579 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.65533e7i | 0.569269i | 0.958636 | + | 0.284635i | \(0.0918723\pi\) | ||||
−0.958636 | + | 0.284635i | \(0.908128\pi\) | |||||||
\(968\) | − 1.70077e7i | − 0.583387i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.83751e6 | 0.0625435 | 0.0312718 | − | 0.999511i | \(-0.490044\pi\) | ||||
0.0312718 | + | 0.999511i | \(0.490044\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 2.26757e7i | − 0.767855i | ||||||||
\(974\) | 6.88338e6 | 0.232490 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 687445. | 0.0231001 | ||||||||
\(977\) | − 516874.i | − 0.0173240i | −0.999962 | − | 0.00866200i | \(-0.997243\pi\) | ||||
0.999962 | − | 0.00866200i | \(-0.00275723\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.17111e7 | −0.390519 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.92580e7i | 0.968201i | ||||||||
\(983\) | − 4.15798e7i | − 1.37246i | −0.727386 | − | 0.686229i | \(-0.759265\pi\) | ||||
0.727386 | − | 0.686229i | \(-0.240735\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.13368e7 | −0.698935 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 1.66221e7i | − 0.541744i | ||||||||
\(989\) | 4.12771e7 | 1.34190 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.61859e7 | −0.523544 | −0.261772 | − | 0.965130i | \(-0.584307\pi\) | ||||
−0.261772 | + | 0.965130i | \(0.584307\pi\) | |||||||
\(992\) | − 1.94126e6i | − 0.0626331i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.63277e7 | 0.845176 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.74426e7i | 0.874355i | 0.899375 | + | 0.437178i | \(0.144022\pi\) | ||||
−0.899375 | + | 0.437178i | \(0.855978\pi\) | |||||||
\(998\) | 2.91951e7i | 0.927863i | ||||||||
\(999\) | 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 | 450.6.c.q.199.3 | 4 | ||
3.2 | odd | 2 | 450.6.c.p.199.1 | 4 | |||
5.2 | odd | 4 | 450.6.a.ba.1.2 | yes | 2 | ||
5.3 | odd | 4 | 450.6.a.bd.1.1 | yes | 2 | ||
5.4 | even | 2 | inner | 450.6.c.q.199.2 | 4 | ||
15.2 | even | 4 | 450.6.a.bf.1.2 | yes | 2 | ||
15.8 | even | 4 | 450.6.a.y.1.1 | ✓ | 2 | ||
15.14 | odd | 2 | 450.6.c.p.199.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.6.a.y.1.1 | ✓ | 2 | 15.8 | even | 4 | ||
450.6.a.ba.1.2 | yes | 2 | 5.2 | odd | 4 | ||
450.6.a.bd.1.1 | yes | 2 | 5.3 | odd | 4 | ||
450.6.a.bf.1.2 | yes | 2 | 15.2 | even | 4 | ||
450.6.c.p.199.1 | 4 | 3.2 | odd | 2 | |||
450.6.c.p.199.4 | 4 | 15.14 | odd | 2 | |||
450.6.c.q.199.2 | 4 | 5.4 | even | 2 | inner | ||
450.6.c.q.199.3 | 4 | 1.1 | even | 1 | trivial |