Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,6,Mod(1,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(70.7292645375\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 59x^{4} + 122x^{3} + 941x^{2} - 1856x - 2338 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4}\cdot 7^{3} \) |
Twist minimal: | no (minimal twist has level 147) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-0.910122\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.31815 | 0.940126 | 0.470063 | − | 0.882633i | \(-0.344231\pi\) | ||||
0.470063 | + | 0.882633i | \(0.344231\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.71724 | −0.116164 | ||||||||
\(5\) | −103.471 | −1.85094 | −0.925468 | − | 0.378825i | \(-0.876328\pi\) | ||||
−0.925468 | + | 0.378825i | \(0.876328\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −189.950 | −1.04933 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −550.272 | −1.74011 | ||||||||
\(11\) | −653.308 | −1.62793 | −0.813966 | − | 0.580912i | \(-0.802696\pi\) | ||||
−0.813966 | + | 0.580912i | \(0.802696\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −138.055 | −0.226565 | −0.113282 | − | 0.993563i | \(-0.536137\pi\) | ||||
−0.113282 | + | 0.993563i | \(0.536137\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −891.231 | −0.870342 | ||||||||
\(17\) | −1174.38 | −0.985564 | −0.492782 | − | 0.870153i | \(-0.664020\pi\) | ||||
−0.492782 | + | 0.870153i | \(0.664020\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1710.77 | −1.08720 | −0.543599 | − | 0.839345i | \(-0.682939\pi\) | ||||
−0.543599 | + | 0.839345i | \(0.682939\pi\) | |||||||
\(20\) | 384.625 | 0.215012 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3474.39 | −1.53046 | ||||||||
\(23\) | 4020.28 | 1.58466 | 0.792332 | − | 0.610091i | \(-0.208867\pi\) | ||||
0.792332 | + | 0.610091i | \(0.208867\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7581.15 | 2.42597 | ||||||||
\(26\) | −734.196 | −0.213000 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2649.46 | −0.585009 | −0.292505 | − | 0.956264i | \(-0.594489\pi\) | ||||
−0.292505 | + | 0.956264i | \(0.594489\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2874.65 | −0.537255 | −0.268628 | − | 0.963244i | \(-0.586570\pi\) | ||||
−0.268628 | + | 0.963244i | \(0.586570\pi\) | |||||||
\(32\) | 1338.69 | 0.231103 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6245.51 | −0.926554 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2856.87 | 0.343073 | 0.171536 | − | 0.985178i | \(-0.445127\pi\) | ||||
0.171536 | + | 0.985178i | \(0.445127\pi\) | |||||||
\(38\) | −9098.15 | −1.02210 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 19654.2 | 1.94225 | ||||||||
\(41\) | −216.487 | −0.0201128 | −0.0100564 | − | 0.999949i | \(-0.503201\pi\) | ||||
−0.0100564 | + | 0.999949i | \(0.503201\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2928.29 | 0.241514 | 0.120757 | − | 0.992682i | \(-0.461468\pi\) | ||||
0.120757 | + | 0.992682i | \(0.461468\pi\) | |||||||
\(44\) | 2428.50 | 0.189107 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 21380.5 | 1.48978 | ||||||||
\(47\) | −14816.8 | −0.978386 | −0.489193 | − | 0.872176i | \(-0.662709\pi\) | ||||
−0.489193 | + | 0.872176i | \(0.662709\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 40317.7 | 2.28071 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 513.182 | 0.0263186 | ||||||||
\(53\) | −21167.7 | −1.03510 | −0.517552 | − | 0.855652i | \(-0.673157\pi\) | ||||
−0.517552 | + | 0.855652i | \(0.673157\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 67598.1 | 3.01320 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −14090.3 | −0.549982 | ||||||||
\(59\) | −34689.1 | −1.29737 | −0.648684 | − | 0.761058i | \(-0.724680\pi\) | ||||
−0.648684 | + | 0.761058i | \(0.724680\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8753.12 | −0.301189 | −0.150594 | − | 0.988596i | \(-0.548119\pi\) | ||||
−0.150594 | + | 0.988596i | \(0.548119\pi\) | |||||||
\(62\) | −15287.8 | −0.505087 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 35638.7 | 1.08761 | ||||||||
\(65\) | 14284.6 | 0.419357 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12068.5 | −0.328448 | −0.164224 | − | 0.986423i | \(-0.552512\pi\) | ||||
−0.164224 | + | 0.986423i | \(0.552512\pi\) | |||||||
\(68\) | 4365.43 | 0.114487 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 35541.5 | 0.836738 | 0.418369 | − | 0.908277i | \(-0.362602\pi\) | ||||
0.418369 | + | 0.908277i | \(0.362602\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 33485.8 | 0.735450 | 0.367725 | − | 0.929935i | \(-0.380137\pi\) | ||||
0.367725 | + | 0.929935i | \(0.380137\pi\) | |||||||
\(74\) | 15193.3 | 0.322531 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6359.35 | 0.126293 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 43134.8 | 0.777607 | 0.388804 | − | 0.921321i | \(-0.372888\pi\) | ||||
0.388804 | + | 0.921321i | \(0.372888\pi\) | |||||||
\(80\) | 92216.1 | 1.61095 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1151.31 | −0.0189086 | ||||||||
\(83\) | 43338.8 | 0.690529 | 0.345265 | − | 0.938505i | \(-0.387789\pi\) | ||||
0.345265 | + | 0.938505i | \(0.387789\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 121513. | 1.82422 | ||||||||
\(86\) | 15573.1 | 0.227054 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 124096. | 1.70825 | ||||||||
\(89\) | 103533. | 1.38550 | 0.692748 | − | 0.721180i | \(-0.256400\pi\) | ||||
0.692748 | + | 0.721180i | \(0.256400\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −14944.3 | −0.184080 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −78798.1 | −0.919806 | ||||||||
\(95\) | 177015. | 2.01233 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −86294.4 | −0.931223 | −0.465611 | − | 0.884989i | \(-0.654165\pi\) | ||||
−0.465611 | + | 0.884989i | \(0.654165\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −28180.9 | −0.281809 | ||||||||
\(101\) | −182677. | −1.78189 | −0.890944 | − | 0.454114i | \(-0.849956\pi\) | ||||
−0.890944 | + | 0.454114i | \(0.849956\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −40088.2 | −0.372326 | −0.186163 | − | 0.982519i | \(-0.559605\pi\) | ||||
−0.186163 | + | 0.982519i | \(0.559605\pi\) | |||||||
\(104\) | 26223.5 | 0.237742 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −112573. | −0.973129 | ||||||||
\(107\) | 110207. | 0.930575 | 0.465287 | − | 0.885160i | \(-0.345951\pi\) | ||||
0.465287 | + | 0.885160i | \(0.345951\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −222354. | −1.79258 | −0.896289 | − | 0.443471i | \(-0.853747\pi\) | ||||
−0.896289 | + | 0.443471i | \(0.853747\pi\) | |||||||
\(110\) | 359497. | 2.83279 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 153473. | 1.13067 | 0.565335 | − | 0.824861i | \(-0.308747\pi\) | ||||
0.565335 | + | 0.824861i | \(0.308747\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −415981. | −2.93311 | ||||||||
\(116\) | 9848.68 | 0.0679568 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −184482. | −1.21969 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 265761. | 1.65016 | ||||||||
\(122\) | −46550.5 | −0.283155 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 10685.8 | 0.0624095 | ||||||||
\(125\) | −461080. | −2.63938 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 142247. | 0.782591 | 0.391296 | − | 0.920265i | \(-0.372027\pi\) | ||||
0.391296 | + | 0.920265i | \(0.372027\pi\) | |||||||
\(128\) | 146694. | 0.791385 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 75967.6 | 0.394249 | ||||||||
\(131\) | −127000. | −0.646587 | −0.323293 | − | 0.946299i | \(-0.604790\pi\) | ||||
−0.323293 | + | 0.946299i | \(0.604790\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −64182.2 | −0.308782 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 223072. | 1.03419 | ||||||||
\(137\) | −99654.8 | −0.453625 | −0.226812 | − | 0.973938i | \(-0.572830\pi\) | ||||
−0.226812 | + | 0.973938i | \(0.572830\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 23441.9 | 0.102909 | 0.0514547 | − | 0.998675i | \(-0.483614\pi\) | ||||
0.0514547 | + | 0.998675i | \(0.483614\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 189015. | 0.786639 | ||||||||
\(143\) | 90192.2 | 0.368832 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 274141. | 1.08282 | ||||||||
\(146\) | 178082. | 0.691415 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10619.7 | −0.0398526 | ||||||||
\(149\) | −498705. | −1.84025 | −0.920127 | − | 0.391620i | \(-0.871915\pi\) | ||||
−0.920127 | + | 0.391620i | \(0.871915\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −216338. | −0.772130 | −0.386065 | − | 0.922472i | \(-0.626166\pi\) | ||||
−0.386065 | + | 0.922472i | \(0.626166\pi\) | |||||||
\(152\) | 324961. | 1.14083 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 297441. | 0.994426 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 426837. | 1.38201 | 0.691007 | − | 0.722848i | \(-0.257167\pi\) | ||||
0.691007 | + | 0.722848i | \(0.257167\pi\) | |||||||
\(158\) | 229398. | 0.731049 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −138515. | −0.427757 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −273196. | −0.805387 | −0.402694 | − | 0.915335i | \(-0.631926\pi\) | ||||
−0.402694 | + | 0.915335i | \(0.631926\pi\) | |||||||
\(164\) | 804.735 | 0.00233638 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 230483. | 0.649184 | ||||||||
\(167\) | −600365. | −1.66581 | −0.832903 | − | 0.553420i | \(-0.813323\pi\) | ||||
−0.832903 | + | 0.553420i | \(0.813323\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −352234. | −0.948668 | ||||||||
\(170\) | 646226. | 1.71499 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10885.1 | −0.0280552 | ||||||||
\(173\) | 500188. | 1.27063 | 0.635313 | − | 0.772254i | \(-0.280871\pi\) | ||||
0.635313 | + | 0.772254i | \(0.280871\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 582248. | 1.41686 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 550606. | 1.30254 | ||||||||
\(179\) | −289563. | −0.675477 | −0.337739 | − | 0.941240i | \(-0.609662\pi\) | ||||
−0.337739 | + | 0.941240i | \(0.609662\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 168243. | 0.381715 | 0.190858 | − | 0.981618i | \(-0.438873\pi\) | ||||
0.190858 | + | 0.981618i | \(0.438873\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −763652. | −1.66284 | ||||||||
\(185\) | −295602. | −0.635006 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 767229. | 1.60443 | ||||||||
\(188\) | 55077.6 | 0.113653 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 941391. | 1.89185 | ||||||||
\(191\) | 386110. | 0.765822 | 0.382911 | − | 0.923785i | \(-0.374922\pi\) | ||||
0.382911 | + | 0.923785i | \(0.374922\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −339682. | −0.656416 | −0.328208 | − | 0.944606i | \(-0.606445\pi\) | ||||
−0.328208 | + | 0.944606i | \(0.606445\pi\) | |||||||
\(194\) | −458927. | −0.875466 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 460915. | 0.846166 | 0.423083 | − | 0.906091i | \(-0.360948\pi\) | ||||
0.423083 | + | 0.906091i | \(0.360948\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −392888. | −0.703292 | −0.351646 | − | 0.936133i | \(-0.614378\pi\) | ||||
−0.351646 | + | 0.936133i | \(0.614378\pi\) | |||||||
\(200\) | −1.44004e6 | −2.54565 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −971504. | −1.67520 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 22400.0 | 0.0372275 | ||||||||
\(206\) | −213195. | −0.350033 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 123039. | 0.197189 | ||||||||
\(209\) | 1.11766e6 | 1.76988 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −469348. | −0.725752 | −0.362876 | − | 0.931837i | \(-0.618205\pi\) | ||||
−0.362876 | + | 0.931837i | \(0.618205\pi\) | |||||||
\(212\) | 78685.4 | 0.120242 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 586100. | 0.874857 | ||||||||
\(215\) | −302991. | −0.447027 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.18251e6 | −1.68525 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −251278. | −0.350024 | ||||||||
\(221\) | 162128. | 0.223294 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 83059.4 | 0.111848 | 0.0559238 | − | 0.998435i | \(-0.482190\pi\) | ||||
0.0559238 | + | 0.998435i | \(0.482190\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 816194. | 1.06297 | ||||||||
\(227\) | −139769. | −0.180030 | −0.0900152 | − | 0.995940i | \(-0.528692\pi\) | ||||
−0.0900152 | + | 0.995940i | \(0.528692\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 143847. | 0.181264 | 0.0906321 | − | 0.995884i | \(-0.471111\pi\) | ||||
0.0906321 | + | 0.995884i | \(0.471111\pi\) | |||||||
\(230\) | −2.21225e6 | −2.75749 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 503265. | 0.613870 | ||||||||
\(233\) | 372492. | 0.449498 | 0.224749 | − | 0.974417i | \(-0.427844\pi\) | ||||
0.224749 | + | 0.974417i | \(0.427844\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.53310e6 | 1.81093 | ||||||||
\(236\) | 128948. | 0.150707 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 201182. | 0.227822 | 0.113911 | − | 0.993491i | \(-0.463662\pi\) | ||||
0.113911 | + | 0.993491i | \(0.463662\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −42020.6 | −0.0466036 | −0.0233018 | − | 0.999728i | \(-0.507418\pi\) | ||||
−0.0233018 | + | 0.999728i | \(0.507418\pi\) | |||||||
\(242\) | 1.41336e6 | 1.55136 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 32537.4 | 0.0349872 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 236180. | 0.246321 | ||||||||
\(248\) | 546039. | 0.563760 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.45209e6 | −2.48135 | ||||||||
\(251\) | 1.23330e6 | 1.23562 | 0.617809 | − | 0.786329i | \(-0.288021\pi\) | ||||
0.617809 | + | 0.786329i | \(0.288021\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.62648e6 | −2.57972 | ||||||||
\(254\) | 756493. | 0.735734 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −360297. | −0.343606 | ||||||||
\(257\) | −560688. | −0.529528 | −0.264764 | − | 0.964313i | \(-0.585294\pi\) | ||||
−0.264764 | + | 0.964313i | \(0.585294\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −53099.2 | −0.0487141 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −675408. | −0.607873 | ||||||||
\(263\) | 1.44524e6 | 1.28840 | 0.644198 | − | 0.764859i | \(-0.277191\pi\) | ||||
0.644198 | + | 0.764859i | \(0.277191\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.19023e6 | 1.91591 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 44861.5 | 0.0381537 | ||||||||
\(269\) | −417542. | −0.351819 | −0.175910 | − | 0.984406i | \(-0.556287\pi\) | ||||
−0.175910 | + | 0.984406i | \(0.556287\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −428512. | −0.354437 | −0.177219 | − | 0.984172i | \(-0.556710\pi\) | ||||
−0.177219 | + | 0.984172i | \(0.556710\pi\) | |||||||
\(272\) | 1.04664e6 | 0.857778 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −529980. | −0.426465 | ||||||||
\(275\) | −4.95283e6 | −3.94931 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −690887. | −0.541013 | −0.270506 | − | 0.962718i | \(-0.587191\pi\) | ||||
−0.270506 | + | 0.962718i | \(0.587191\pi\) | |||||||
\(278\) | 124667. | 0.0967478 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.91606e6 | −1.44758 | −0.723792 | − | 0.690018i | \(-0.757603\pi\) | ||||
−0.723792 | + | 0.690018i | \(0.757603\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.62417e6 | −1.20550 | −0.602748 | − | 0.797931i | \(-0.705928\pi\) | ||||
−0.602748 | + | 0.797931i | \(0.705928\pi\) | |||||||
\(284\) | −132116. | −0.0971986 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 479656. | 0.346749 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −40699.3 | −0.0286644 | ||||||||
\(290\) | 1.45793e6 | 1.01798 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −124475. | −0.0854326 | ||||||||
\(293\) | 531272. | 0.361533 | 0.180767 | − | 0.983526i | \(-0.442142\pi\) | ||||
0.180767 | + | 0.983526i | \(0.442142\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.58930e6 | 2.40135 | ||||||||
\(296\) | −542661. | −0.359998 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.65219e6 | −1.73007 | ||||||||
\(299\) | −555019. | −0.359029 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.15052e6 | −0.725899 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.52469e6 | 0.946234 | ||||||||
\(305\) | 905690. | 0.557481 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 409059. | 0.247708 | 0.123854 | − | 0.992300i | \(-0.460475\pi\) | ||||
0.123854 | + | 0.992300i | \(0.460475\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.58184e6 | 0.934885 | ||||||||
\(311\) | 308704. | 0.180984 | 0.0904922 | − | 0.995897i | \(-0.471156\pi\) | ||||
0.0904922 | + | 0.995897i | \(0.471156\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 637733. | 0.367941 | 0.183970 | − | 0.982932i | \(-0.441105\pi\) | ||||
0.183970 | + | 0.982932i | \(0.441105\pi\) | |||||||
\(314\) | 2.26998e6 | 1.29927 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −160342. | −0.0903297 | ||||||||
\(317\) | 2.94325e6 | 1.64505 | 0.822525 | − | 0.568729i | \(-0.192565\pi\) | ||||
0.822525 | + | 0.568729i | \(0.192565\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.73092e6 | 0.952356 | ||||||||
\(320\) | −3.68756e6 | −2.01309 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.00909e6 | 1.07150 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.04661e6 | −0.549639 | ||||||||
\(326\) | −1.45290e6 | −0.757165 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 41121.7 | 0.0211051 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.84991e6 | −1.42976 | −0.714878 | − | 0.699249i | \(-0.753518\pi\) | ||||
−0.714878 | + | 0.699249i | \(0.753518\pi\) | |||||||
\(332\) | −161101. | −0.0802144 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.19283e6 | −1.56607 | ||||||||
\(335\) | 1.24874e6 | 0.607937 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.46617e6 | 1.66255 | 0.831277 | − | 0.555859i | \(-0.187611\pi\) | ||||
0.831277 | + | 0.555859i | \(0.187611\pi\) | |||||||
\(338\) | −1.87323e6 | −0.891867 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −451694. | −0.211908 | ||||||||
\(341\) | 1.87803e6 | 0.874615 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −556228. | −0.253429 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.66008e6 | 1.19455 | ||||||||
\(347\) | −15115.3 | −0.00673897 | −0.00336949 | − | 0.999994i | \(-0.501073\pi\) | ||||
−0.00336949 | + | 0.999994i | \(0.501073\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.24698e6 | 1.42698 | 0.713488 | − | 0.700667i | \(-0.247114\pi\) | ||||
0.713488 | + | 0.700667i | \(0.247114\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −874578. | −0.376220 | ||||||||
\(353\) | 1.76786e6 | 0.755110 | 0.377555 | − | 0.925987i | \(-0.376765\pi\) | ||||
0.377555 | + | 0.925987i | \(0.376765\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.67749e6 | −1.54875 | ||||||||
\(356\) | −384858. | −0.160944 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.53994e6 | −0.635034 | ||||||||
\(359\) | 121581. | 0.0497885 | 0.0248942 | − | 0.999690i | \(-0.492075\pi\) | ||||
0.0248942 | + | 0.999690i | \(0.492075\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 450645. | 0.181998 | ||||||||
\(362\) | 894740. | 0.358860 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.46479e6 | −1.36127 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.08841e6 | 0.809378 | 0.404689 | − | 0.914454i | \(-0.367380\pi\) | ||||
0.404689 | + | 0.914454i | \(0.367380\pi\) | |||||||
\(368\) | −3.58300e6 | −1.37920 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.57206e6 | −0.596985 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.29355e6 | −0.853563 | −0.426782 | − | 0.904355i | \(-0.640353\pi\) | ||||
−0.426782 | + | 0.904355i | \(0.640353\pi\) | |||||||
\(374\) | 4.08024e6 | 1.50837 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.81445e6 | 1.02665 | ||||||||
\(377\) | 365771. | 0.132543 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.93812e6 | −1.05068 | −0.525341 | − | 0.850892i | \(-0.676062\pi\) | ||||
−0.525341 | + | 0.850892i | \(0.676062\pi\) | |||||||
\(380\) | −658005. | −0.233760 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.05339e6 | 0.719969 | ||||||||
\(383\) | −5.04605e6 | −1.75774 | −0.878871 | − | 0.477060i | \(-0.841702\pi\) | ||||
−0.878871 | + | 0.477060i | \(0.841702\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.80648e6 | −0.617113 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 320777. | 0.108174 | ||||||||
\(389\) | 1.07621e6 | 0.360599 | 0.180300 | − | 0.983612i | \(-0.442293\pi\) | ||||
0.180300 | + | 0.983612i | \(0.442293\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.72132e6 | −1.56179 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.45122e6 | 0.795502 | ||||||||
\(395\) | −4.46318e6 | −1.43930 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.34345e6 | 1.38312 | 0.691559 | − | 0.722320i | \(-0.256924\pi\) | ||||
0.691559 | + | 0.722320i | \(0.256924\pi\) | |||||||
\(398\) | −2.08944e6 | −0.661183 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.75655e6 | −2.11142 | ||||||||
\(401\) | 704083. | 0.218657 | 0.109328 | − | 0.994006i | \(-0.465130\pi\) | ||||
0.109328 | + | 0.994006i | \(0.465130\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 396859. | 0.121723 | ||||||||
\(404\) | 679054. | 0.206991 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.86642e6 | −0.558499 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.63500e6 | −0.483292 | −0.241646 | − | 0.970365i | \(-0.577687\pi\) | ||||
−0.241646 | + | 0.970365i | \(0.577687\pi\) | |||||||
\(410\) | 119127. | 0.0349986 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 149017. | 0.0432508 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.48429e6 | −1.27813 | ||||||||
\(416\) | −184813. | −0.0523598 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.94390e6 | 1.66391 | ||||||||
\(419\) | 5.92839e6 | 1.64969 | 0.824844 | − | 0.565360i | \(-0.191263\pi\) | ||||
0.824844 | + | 0.565360i | \(0.191263\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.46170e6 | −1.50184 | −0.750918 | − | 0.660395i | \(-0.770389\pi\) | ||||
−0.750918 | + | 0.660395i | \(0.770389\pi\) | |||||||
\(422\) | −2.49606e6 | −0.682299 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.02080e6 | 1.08617 | ||||||||
\(425\) | −8.90311e6 | −2.39095 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −409667. | −0.108099 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.61136e6 | −0.420262 | ||||||||
\(431\) | −3.44526e6 | −0.893366 | −0.446683 | − | 0.894692i | \(-0.647395\pi\) | ||||
−0.446683 | + | 0.894692i | \(0.647395\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.46833e6 | 0.632680 | 0.316340 | − | 0.948646i | \(-0.397546\pi\) | ||||
0.316340 | + | 0.948646i | \(0.397546\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 826541. | 0.208232 | ||||||||
\(437\) | −6.87779e6 | −1.72284 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.13780e6 | −1.52003 | −0.760014 | − | 0.649907i | \(-0.774808\pi\) | ||||
−0.760014 | + | 0.649907i | \(0.774808\pi\) | |||||||
\(440\) | −1.28403e7 | −3.16185 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 862222. | 0.209925 | ||||||||
\(443\) | 1.79219e6 | 0.433885 | 0.216942 | − | 0.976184i | \(-0.430392\pi\) | ||||
0.216942 | + | 0.976184i | \(0.430392\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.07126e7 | −2.56446 | ||||||||
\(446\) | 441723. | 0.105151 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.76014e6 | 0.880213 | 0.440107 | − | 0.897945i | \(-0.354941\pi\) | ||||
0.440107 | + | 0.897945i | \(0.354941\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 141433. | 0.0327423 | ||||||||
\(452\) | −570496. | −0.131343 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −743312. | −0.169251 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.54502e6 | 1.68994 | 0.844968 | − | 0.534817i | \(-0.179620\pi\) | ||||
0.844968 | + | 0.534817i | \(0.179620\pi\) | |||||||
\(458\) | 765000. | 0.170411 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.54630e6 | 0.340721 | ||||||||
\(461\) | −359098. | −0.0786975 | −0.0393487 | − | 0.999226i | \(-0.512528\pi\) | ||||
−0.0393487 | + | 0.999226i | \(0.512528\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −890950. | −0.193153 | −0.0965764 | − | 0.995326i | \(-0.530789\pi\) | ||||
−0.0965764 | + | 0.995326i | \(0.530789\pi\) | |||||||
\(464\) | 2.36128e6 | 0.509158 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.98097e6 | 0.422584 | ||||||||
\(467\) | 7.61319e6 | 1.61538 | 0.807690 | − | 0.589608i | \(-0.200718\pi\) | ||||
0.807690 | + | 0.589608i | \(0.200718\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 8.15328e6 | 1.70250 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.58919e6 | 1.36137 | ||||||||
\(473\) | −1.91307e6 | −0.393169 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.29696e7 | −2.63751 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.06992e6 | 0.214181 | ||||||||
\(479\) | 5.96007e6 | 1.18690 | 0.593448 | − | 0.804872i | \(-0.297766\pi\) | ||||
0.593448 | + | 0.804872i | \(0.297766\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −394404. | −0.0777282 | ||||||||
\(482\) | −223472. | −0.0438132 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −987895. | −0.191689 | ||||||||
\(485\) | 8.92893e6 | 1.72363 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −257827. | −0.0492612 | −0.0246306 | − | 0.999697i | \(-0.507841\pi\) | ||||
−0.0246306 | + | 0.999697i | \(0.507841\pi\) | |||||||
\(488\) | 1.66265e6 | 0.316047 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −592660. | −0.110944 | −0.0554718 | − | 0.998460i | \(-0.517666\pi\) | ||||
−0.0554718 | + | 0.998460i | \(0.517666\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.11146e6 | 0.576564 | ||||||||
\(494\) | 1.25604e6 | 0.231573 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.56198e6 | 0.467596 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.42242e6 | −0.435511 | −0.217755 | − | 0.976003i | \(-0.569874\pi\) | ||||
−0.217755 | + | 0.976003i | \(0.569874\pi\) | |||||||
\(500\) | 1.71394e6 | 0.306600 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.55887e6 | 1.16164 | ||||||||
\(503\) | −2.31849e6 | −0.408588 | −0.204294 | − | 0.978910i | \(-0.565490\pi\) | ||||
−0.204294 | + | 0.978910i | \(0.565490\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.89017e7 | 3.29816 | ||||||||
\(506\) | −1.39680e7 | −2.42527 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −528767. | −0.0909087 | ||||||||
\(509\) | 8.49886e6 | 1.45401 | 0.727003 | − | 0.686634i | \(-0.240913\pi\) | ||||
0.727003 | + | 0.686634i | \(0.240913\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −6.61033e6 | −1.11442 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.98183e6 | −0.497822 | ||||||||
\(515\) | 4.14795e6 | 0.689152 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.67995e6 | 1.59275 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.71335e6 | −0.440046 | ||||||||
\(521\) | 1.16092e6 | 0.187374 | 0.0936868 | − | 0.995602i | \(-0.470135\pi\) | ||||
0.0936868 | + | 0.995602i | \(0.470135\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.22907e6 | 0.196482 | 0.0982411 | − | 0.995163i | \(-0.468678\pi\) | ||||
0.0982411 | + | 0.995163i | \(0.468678\pi\) | |||||||
\(524\) | 472091. | 0.0751099 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.68598e6 | 1.21125 | ||||||||
\(527\) | 3.37592e6 | 0.529499 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.72633e6 | 1.51116 | ||||||||
\(530\) | 1.16480e7 | 1.80120 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 29887.1 | 0.00455686 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.14032e7 | −1.72244 | ||||||||
\(536\) | 2.29241e6 | 0.344652 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.22055e6 | −0.330754 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −790279. | −0.116088 | −0.0580440 | − | 0.998314i | \(-0.518486\pi\) | ||||
−0.0580440 | + | 0.998314i | \(0.518486\pi\) | |||||||
\(542\) | −2.27889e6 | −0.333216 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.57213e6 | −0.227767 | ||||||||
\(545\) | 2.30070e7 | 3.31795 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.74335e6 | 0.249124 | 0.124562 | − | 0.992212i | \(-0.460247\pi\) | ||||
0.124562 | + | 0.992212i | \(0.460247\pi\) | |||||||
\(548\) | 370441. | 0.0526947 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.63399e7 | −3.71285 | ||||||||
\(551\) | 4.53263e6 | 0.636021 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.67424e6 | −0.508620 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −87139.0 | −0.0119543 | ||||||||
\(557\) | 1.01834e7 | 1.39077 | 0.695385 | − | 0.718637i | \(-0.255234\pi\) | ||||
0.695385 | + | 0.718637i | \(0.255234\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −404264. | −0.0547186 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.01899e7 | −1.36091 | ||||||||
\(563\) | 8.57420e6 | 1.14005 | 0.570023 | − | 0.821629i | \(-0.306934\pi\) | ||||
0.570023 | + | 0.821629i | \(0.306934\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.58799e7 | −2.09280 | ||||||||
\(566\) | −8.63760e6 | −1.13332 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.75109e6 | −0.878018 | ||||||||
\(569\) | −2.67960e6 | −0.346968 | −0.173484 | − | 0.984837i | \(-0.555502\pi\) | ||||
−0.173484 | + | 0.984837i | \(0.555502\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.45017e6 | 0.956260 | 0.478130 | − | 0.878289i | \(-0.341315\pi\) | ||||
0.478130 | + | 0.878289i | \(0.341315\pi\) | |||||||
\(572\) | −335266. | −0.0428449 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.04784e7 | 3.84434 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.72891e6 | 0.716362 | 0.358181 | − | 0.933652i | \(-0.383397\pi\) | ||||
0.358181 | + | 0.933652i | \(0.383397\pi\) | |||||||
\(578\) | −216445. | −0.0269481 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.01905e6 | −0.125784 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.38290e7 | 1.68508 | ||||||||
\(584\) | −6.36061e6 | −0.771733 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.82539e6 | 0.339887 | ||||||||
\(587\) | −1.41744e7 | −1.69788 | −0.848942 | − | 0.528486i | \(-0.822760\pi\) | ||||
−0.848942 | + | 0.528486i | \(0.822760\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.91787e6 | 0.584102 | ||||||||
\(590\) | 1.90885e7 | 2.25757 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.54613e6 | −0.298591 | ||||||||
\(593\) | 6.09494e6 | 0.711758 | 0.355879 | − | 0.934532i | \(-0.384182\pi\) | ||||
0.355879 | + | 0.934532i | \(0.384182\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.85380e6 | 0.213771 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.95168e6 | −0.337533 | ||||||||
\(599\) | −1.97464e6 | −0.224865 | −0.112432 | − | 0.993659i | \(-0.535864\pi\) | ||||
−0.112432 | + | 0.993659i | \(0.535864\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.14078e6 | 0.580554 | 0.290277 | − | 0.956943i | \(-0.406253\pi\) | ||||
0.290277 | + | 0.956943i | \(0.406253\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 804180. | 0.0896935 | ||||||||
\(605\) | −2.74984e7 | −3.05435 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.31482e6 | −0.144843 | −0.0724213 | − | 0.997374i | \(-0.523073\pi\) | ||||
−0.0724213 | + | 0.997374i | \(0.523073\pi\) | |||||||
\(608\) | −2.29020e6 | −0.251255 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.81660e6 | 0.524102 | ||||||||
\(611\) | 2.04553e6 | 0.221668 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.34181e7 | 1.44224 | 0.721122 | − | 0.692808i | \(-0.243627\pi\) | ||||
0.721122 | + | 0.692808i | \(0.243627\pi\) | |||||||
\(614\) | 2.17544e6 | 0.232877 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.48394e7 | −1.56929 | −0.784646 | − | 0.619944i | \(-0.787155\pi\) | ||||
−0.784646 | + | 0.619944i | \(0.787155\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.14468e7 | −1.20077 | −0.600383 | − | 0.799713i | \(-0.704985\pi\) | ||||
−0.600383 | + | 0.799713i | \(0.704985\pi\) | |||||||
\(620\) | −1.10566e6 | −0.115516 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.64173e6 | 0.170148 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.40171e7 | 2.45935 | ||||||||
\(626\) | 3.39156e6 | 0.345910 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.58665e6 | −0.160540 | ||||||||
\(629\) | −3.35504e6 | −0.338120 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.11608e7 | −1.11589 | −0.557944 | − | 0.829878i | \(-0.688410\pi\) | ||||
−0.557944 | + | 0.829878i | \(0.688410\pi\) | |||||||
\(632\) | −8.19345e6 | −0.815970 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.56527e7 | 1.54655 | ||||||||
\(635\) | −1.47184e7 | −1.44853 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 9.20528e6 | 0.895334 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.51785e7 | −1.46480 | ||||||||
\(641\) | 1.72150e7 | 1.65486 | 0.827431 | − | 0.561567i | \(-0.189801\pi\) | ||||
0.827431 | + | 0.561567i | \(0.189801\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.73062e6 | −0.260456 | −0.130228 | − | 0.991484i | \(-0.541571\pi\) | ||||
−0.130228 | + | 0.991484i | \(0.541571\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.06846e7 | 1.00735 | ||||||||
\(647\) | 4.39969e6 | 0.413201 | 0.206600 | − | 0.978425i | \(-0.433760\pi\) | ||||
0.206600 | + | 0.978425i | \(0.433760\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.26627e7 | 2.11203 | ||||||||
\(650\) | −5.56605e6 | −0.516730 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.01553e6 | 0.0935567 | ||||||||
\(653\) | −5.60500e6 | −0.514390 | −0.257195 | − | 0.966360i | \(-0.582798\pi\) | ||||
−0.257195 | + | 0.966360i | \(0.582798\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.31408e7 | 1.19679 | ||||||||
\(656\) | 192940. | 0.0175050 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.33959e7 | 1.20159 | 0.600796 | − | 0.799402i | \(-0.294850\pi\) | ||||
0.600796 | + | 0.799402i | \(0.294850\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.87657e6 | 0.167056 | 0.0835279 | − | 0.996505i | \(-0.473381\pi\) | ||||
0.0835279 | + | 0.996505i | \(0.473381\pi\) | |||||||
\(662\) | −1.51563e7 | −1.34415 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.23220e6 | −0.724596 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.06516e7 | −0.927043 | ||||||||
\(668\) | 2.23170e6 | 0.193506 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.64097e6 | 0.571537 | ||||||||
\(671\) | 5.71849e6 | 0.490315 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.82367e6 | 0.240313 | 0.120156 | − | 0.992755i | \(-0.461660\pi\) | ||||
0.120156 | + | 0.992755i | \(0.461660\pi\) | |||||||
\(674\) | 1.84336e7 | 1.56301 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.30934e6 | 0.110201 | ||||||||
\(677\) | −9.31849e6 | −0.781401 | −0.390700 | − | 0.920518i | \(-0.627767\pi\) | ||||
−0.390700 | + | 0.920518i | \(0.627767\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.30814e7 | −1.91421 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9.98766e6 | 0.822248 | ||||||||
\(683\) | 2.13619e7 | 1.75222 | 0.876108 | − | 0.482114i | \(-0.160131\pi\) | ||||
0.876108 | + | 0.482114i | \(0.160131\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.03113e7 | 0.839631 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.60978e6 | −0.210200 | ||||||||
\(689\) | 2.92230e6 | 0.234518 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.10885e7 | 0.883439 | 0.441720 | − | 0.897153i | \(-0.354369\pi\) | ||||
0.441720 | + | 0.897153i | \(0.354369\pi\) | |||||||
\(692\) | −1.85932e6 | −0.147601 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −80385.6 | −0.00633548 | ||||||||
\(695\) | −2.42554e6 | −0.190479 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 254237. | 0.0198224 | ||||||||
\(698\) | 1.72680e7 | 1.34154 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.02256e7 | 1.55456 | 0.777279 | − | 0.629156i | \(-0.216599\pi\) | ||||
0.777279 | + | 0.629156i | \(0.216599\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.88745e6 | −0.372988 | ||||||||
\(704\) | −2.32831e7 | −1.77055 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.40174e6 | 0.709899 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.10834e7 | −1.57516 | −0.787580 | − | 0.616213i | \(-0.788666\pi\) | ||||
−0.787580 | + | 0.616213i | \(0.788666\pi\) | |||||||
\(710\) | −1.95575e7 | −1.45602 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.96661e7 | −1.45385 | ||||||||
\(713\) | −1.15569e7 | −0.851369 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.33224e6 | −0.682686 | ||||||||
\(716\) | 1.07638e6 | 0.0784659 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 646585. | 0.0468074 | ||||||||
\(719\) | 5.88060e6 | 0.424228 | 0.212114 | − | 0.977245i | \(-0.431965\pi\) | ||||
0.212114 | + | 0.977245i | \(0.431965\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.39660e6 | 0.171101 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −625398. | −0.0443414 | ||||||||
\(725\) | −2.00860e7 | −1.41921 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.23778e6 | 0.648233 | 0.324117 | − | 0.946017i | \(-0.394933\pi\) | ||||
0.324117 | + | 0.946017i | \(0.394933\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.84263e7 | −1.27977 | ||||||||
\(731\) | −3.43891e6 | −0.238028 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.75113e6 | 0.532850 | 0.266425 | − | 0.963856i | \(-0.414158\pi\) | ||||
0.266425 | + | 0.963856i | \(0.414158\pi\) | |||||||
\(734\) | 1.11065e7 | 0.760917 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.38192e6 | 0.366220 | ||||||||
\(737\) | 7.88446e6 | 0.534691 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.02902e7 | 0.693125 | 0.346563 | − | 0.938027i | \(-0.387349\pi\) | ||||
0.346563 | + | 0.938027i | \(0.387349\pi\) | |||||||
\(740\) | 1.09882e6 | 0.0737646 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.04494e6 | 0.135897 | 0.0679483 | − | 0.997689i | \(-0.478355\pi\) | ||||
0.0679483 | + | 0.997689i | \(0.478355\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.16012e7 | 3.40619 | ||||||||
\(746\) | −1.21974e7 | −0.802457 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.85197e6 | −0.186377 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.18742e7 | −0.768251 | −0.384125 | − | 0.923281i | \(-0.625497\pi\) | ||||
−0.384125 | + | 0.923281i | \(0.625497\pi\) | |||||||
\(752\) | 1.32052e7 | 0.851531 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.94523e6 | 0.124607 | ||||||||
\(755\) | 2.23846e7 | 1.42916 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.48702e6 | −0.538289 | −0.269145 | − | 0.963100i | \(-0.586741\pi\) | ||||
−0.269145 | + | 0.963100i | \(0.586741\pi\) | |||||||
\(758\) | −1.56254e7 | −0.987772 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.36239e7 | −2.11161 | ||||||||
\(761\) | −2.39932e7 | −1.50185 | −0.750925 | − | 0.660388i | \(-0.770392\pi\) | ||||
−0.750925 | + | 0.660388i | \(0.770392\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1.43526e6 | −0.0889607 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.68357e7 | −1.65250 | ||||||||
\(767\) | 4.78899e6 | 0.293938 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.43194e7 | −1.48299 | −0.741494 | − | 0.670959i | \(-0.765883\pi\) | ||||
−0.741494 | + | 0.670959i | \(0.765883\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.26268e6 | 0.0762517 | ||||||||
\(773\) | 5.38149e6 | 0.323932 | 0.161966 | − | 0.986796i | \(-0.448216\pi\) | ||||
0.161966 | + | 0.986796i | \(0.448216\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.17931e7 | −1.30336 | ||||||||
\(776\) | 1.63916e7 | 0.977164 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.72347e6 | 0.339009 | ||||||||
\(779\) | 370361. | 0.0218666 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.32195e7 | −1.36215 | ||||||||
\(782\) | −2.51087e7 | −1.46828 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.41650e7 | −2.55802 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.80718e7 | 1.61560 | 0.807800 | − | 0.589456i | \(-0.200658\pi\) | ||||
0.807800 | + | 0.589456i | \(0.200658\pi\) | |||||||
\(788\) | −1.71333e6 | −0.0982938 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.37359e7 | −1.35312 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.20841e6 | 0.0682388 | ||||||||
\(794\) | 2.30992e7 | 1.30030 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.46046e6 | 0.0816970 | ||||||||
\(797\) | −1.97055e7 | −1.09886 | −0.549428 | − | 0.835541i | \(-0.685154\pi\) | ||||
−0.549428 | + | 0.835541i | \(0.685154\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.74005e7 | 0.964262 | ||||||||
\(800\) | 1.01488e7 | 0.560648 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.74442e6 | 0.205565 | ||||||||
\(803\) | −2.18765e7 | −1.19726 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.11056e6 | 0.114435 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.46994e7 | 1.86980 | ||||||||
\(809\) | 3.39408e6 | 0.182327 | 0.0911633 | − | 0.995836i | \(-0.470941\pi\) | ||||
0.0911633 | + | 0.995836i | \(0.470941\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.78837e7 | 0.954786 | 0.477393 | − | 0.878690i | \(-0.341582\pi\) | ||||
0.477393 | + | 0.878690i | \(0.341582\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −9.92588e6 | −0.525059 | ||||||||
\(815\) | 2.82677e7 | 1.49072 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.00964e6 | −0.262574 | ||||||||
\(818\) | −8.69518e6 | −0.454355 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −83266.3 | −0.00432449 | ||||||||
\(821\) | −9.26949e6 | −0.479952 | −0.239976 | − | 0.970779i | \(-0.577140\pi\) | ||||
−0.239976 | + | 0.970779i | \(0.577140\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.52579e6 | −0.0785228 | −0.0392614 | − | 0.999229i | \(-0.512501\pi\) | ||||
−0.0392614 | + | 0.999229i | \(0.512501\pi\) | |||||||
\(824\) | 7.61474e6 | 0.390694 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −806595. | −0.0410102 | −0.0205051 | − | 0.999790i | \(-0.506527\pi\) | ||||
−0.0205051 | + | 0.999790i | \(0.506527\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.19275e7 | −1.10816 | −0.554080 | − | 0.832463i | \(-0.686930\pi\) | ||||
−0.554080 | + | 0.832463i | \(0.686930\pi\) | |||||||
\(830\) | −2.38482e7 | −1.20160 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.92010e6 | −0.246414 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.21201e7 | 3.08330 | ||||||||
\(836\) | −4.15462e6 | −0.205596 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.15281e7 | 1.55091 | ||||||||
\(839\) | 2.40115e7 | 1.17765 | 0.588823 | − | 0.808262i | \(-0.299591\pi\) | ||||
0.588823 | + | 0.808262i | \(0.299591\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.34915e7 | −0.657764 | ||||||||
\(842\) | −2.90462e7 | −1.41192 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.74468e6 | 0.0843061 | ||||||||
\(845\) | 3.64458e7 | 1.75593 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.88653e7 | 0.900895 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4.73481e7 | −2.24779 | ||||||||
\(851\) | 1.14854e7 | 0.543654 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.26785e7 | 1.06719 | 0.533594 | − | 0.845741i | \(-0.320841\pi\) | ||||
0.533594 | + | 0.845741i | \(0.320841\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.09339e7 | −0.976484 | ||||||||
\(857\) | −5.07518e6 | −0.236048 | −0.118024 | − | 0.993011i | \(-0.537656\pi\) | ||||
−0.118024 | + | 0.993011i | \(0.537656\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.71405e7 | −0.792577 | −0.396289 | − | 0.918126i | \(-0.629702\pi\) | ||||
−0.396289 | + | 0.918126i | \(0.629702\pi\) | |||||||
\(860\) | 1.12629e6 | 0.0519284 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.83224e7 | −0.839876 | ||||||||
\(863\) | −3.84686e7 | −1.75824 | −0.879122 | − | 0.476597i | \(-0.841870\pi\) | ||||
−0.879122 | + | 0.476597i | \(0.841870\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.17547e7 | −2.35185 | ||||||||
\(866\) | 1.31270e7 | 0.594799 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.81803e7 | −1.26589 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.66611e6 | 0.0744148 | ||||||||
\(872\) | 4.22360e7 | 1.88101 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.65772e7 | −1.61969 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.91671e7 | −0.841504 | −0.420752 | − | 0.907176i | \(-0.638234\pi\) | ||||
−0.420752 | + | 0.907176i | \(0.638234\pi\) | |||||||
\(878\) | −3.26418e7 | −1.42902 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.02455e7 | −2.62252 | ||||||||
\(881\) | −4.15340e7 | −1.80287 | −0.901434 | − | 0.432916i | \(-0.857485\pi\) | ||||
−0.901434 | + | 0.432916i | \(0.857485\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.31950e7 | −1.86437 | −0.932183 | − | 0.361987i | \(-0.882099\pi\) | ||||
−0.932183 | + | 0.361987i | \(0.882099\pi\) | |||||||
\(884\) | −602668. | −0.0259387 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.53113e6 | 0.407906 | ||||||||
\(887\) | −6.87508e6 | −0.293406 | −0.146703 | − | 0.989181i | \(-0.546866\pi\) | ||||
−0.146703 | + | 0.989181i | \(0.546866\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −5.69715e7 | −2.41092 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −308752. | −0.0129926 | ||||||||
\(893\) | 2.53482e7 | 1.06370 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.99613e7 | 1.25027 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.99970e7 | 0.827511 | ||||||||
\(899\) | 7.61628e6 | 0.314299 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.48588e7 | 1.02016 | ||||||||
\(902\) | 752162. | 0.0307819 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.91522e7 | −1.18645 | ||||||||
\(905\) | −1.74081e7 | −0.706531 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.49747e7 | 0.604423 | 0.302212 | − | 0.953241i | \(-0.402275\pi\) | ||||
0.302212 | + | 0.953241i | \(0.402275\pi\) | |||||||
\(908\) | 519554. | 0.0209130 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.13061e7 | −1.24978 | −0.624889 | − | 0.780714i | \(-0.714856\pi\) | ||||
−0.624889 | + | 0.780714i | \(0.714856\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.83136e7 | −1.12414 | ||||||||
\(914\) | 4.01256e7 | 1.58875 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −534713. | −0.0210563 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.46990e7 | 0.574117 | 0.287058 | − | 0.957913i | \(-0.407323\pi\) | ||||
0.287058 | + | 0.957913i | \(0.407323\pi\) | |||||||
\(920\) | 7.90154e7 | 3.07781 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.90974e6 | −0.0739855 | ||||||||
\(923\) | −4.90666e6 | −0.189575 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.16583e7 | 0.832283 | ||||||||
\(926\) | −4.73821e6 | −0.181588 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.54681e6 | −0.135197 | ||||||||
\(929\) | −1.68420e7 | −0.640256 | −0.320128 | − | 0.947374i | \(-0.603726\pi\) | ||||
−0.320128 | + | 0.947374i | \(0.603726\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.38464e6 | −0.0522153 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.04881e7 | 1.51866 | ||||||||
\(935\) | −7.93856e7 | −2.96970 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.22026e7 | −1.19824 | −0.599118 | − | 0.800661i | \(-0.704482\pi\) | ||||
−0.599118 | + | 0.800661i | \(0.704482\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5.69891e6 | −0.210364 | ||||||||
\(941\) | −2.65064e7 | −0.975837 | −0.487919 | − | 0.872889i | \(-0.662244\pi\) | ||||
−0.487919 | + | 0.872889i | \(0.662244\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −870340. | −0.0318720 | ||||||||
\(944\) | 3.09160e7 | 1.12915 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.01740e7 | −0.369628 | ||||||||
\(947\) | 4.98682e7 | 1.80696 | 0.903481 | − | 0.428629i | \(-0.141003\pi\) | ||||
0.903481 | + | 0.428629i | \(0.141003\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.62287e6 | −0.166627 | ||||||||
\(950\) | −6.89745e7 | −2.47959 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.46027e7 | 0.877508 | 0.438754 | − | 0.898607i | \(-0.355420\pi\) | ||||
0.438754 | + | 0.898607i | \(0.355420\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.99510e7 | −1.41749 | ||||||||
\(956\) | −747843. | −0.0264646 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.16966e7 | 1.11583 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.03655e7 | −0.711357 | ||||||||
\(962\) | −2.09750e6 | −0.0730743 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 156200. | 0.00541364 | ||||||||
\(965\) | 3.51471e7 | 1.21498 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.59962e7 | 0.550111 | 0.275056 | − | 0.961428i | \(-0.411304\pi\) | ||||
0.275056 | + | 0.961428i | \(0.411304\pi\) | |||||||
\(968\) | −5.04812e7 | −1.73157 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.74854e7 | 1.62043 | ||||||||
\(971\) | −9.94424e6 | −0.338473 | −0.169236 | − | 0.985576i | \(-0.554130\pi\) | ||||
−0.169236 | + | 0.985576i | \(0.554130\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.37116e6 | −0.0463118 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.80105e6 | 0.262137 | ||||||||
\(977\) | 1.20871e7 | 0.405121 | 0.202561 | − | 0.979270i | \(-0.435074\pi\) | ||||
0.202561 | + | 0.979270i | \(0.435074\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.76392e7 | −2.25549 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.15186e6 | −0.104301 | ||||||||
\(983\) | −3.42776e7 | −1.13143 | −0.565714 | − | 0.824601i | \(-0.691399\pi\) | ||||
−0.565714 | + | 0.824601i | \(0.691399\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.76911e7 | −1.56620 | ||||||||
\(986\) | 1.65472e7 | 0.542043 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −877938. | −0.0286135 | ||||||||
\(989\) | 1.17725e7 | 0.382719 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.50099e7 | −1.13242 | −0.566209 | − | 0.824262i | \(-0.691590\pi\) | ||||
−0.566209 | + | 0.824262i | \(0.691590\pi\) | |||||||
\(992\) | −3.84827e6 | −0.124161 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.06523e7 | 1.30175 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.99230e6 | 0.318367 | 0.159183 | − | 0.987249i | \(-0.449114\pi\) | ||||
0.159183 | + | 0.987249i | \(0.449114\pi\) | |||||||
\(998\) | −1.28828e7 | −0.409435 | ||||||||
\(999\) | 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 | 441.6.a.ba.1.5 | 6 | ||
3.2 | odd | 2 | 147.6.a.o.1.2 | yes | 6 | ||
7.6 | odd | 2 | 441.6.a.bb.1.5 | 6 | |||
21.2 | odd | 6 | 147.6.e.p.67.5 | 12 | |||
21.5 | even | 6 | 147.6.e.q.67.5 | 12 | |||
21.11 | odd | 6 | 147.6.e.p.79.5 | 12 | |||
21.17 | even | 6 | 147.6.e.q.79.5 | 12 | |||
21.20 | even | 2 | 147.6.a.n.1.2 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.6.a.n.1.2 | ✓ | 6 | 21.20 | even | 2 | ||
147.6.a.o.1.2 | yes | 6 | 3.2 | odd | 2 | ||
147.6.e.p.67.5 | 12 | 21.2 | odd | 6 | |||
147.6.e.p.79.5 | 12 | 21.11 | odd | 6 | |||
147.6.e.q.67.5 | 12 | 21.5 | even | 6 | |||
147.6.e.q.79.5 | 12 | 21.17 | even | 6 | |||
441.6.a.ba.1.5 | 6 | 1.1 | even | 1 | trivial | ||
441.6.a.bb.1.5 | 6 | 7.6 | odd | 2 |