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: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 146x^{6} + 5453x^{4} - 40868x^{2} + 3844 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{5}\cdot 7^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-9.54020\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.72287 | 0.304563 | 0.152281 | − | 0.988337i | \(-0.451338\pi\) | ||||
0.152281 | + | 0.988337i | \(0.451338\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −29.0317 | −0.907242 | ||||||||
\(5\) | 73.1337 | 1.30826 | 0.654128 | − | 0.756384i | \(-0.273036\pi\) | ||||
0.654128 | + | 0.756384i | \(0.273036\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −105.150 | −0.580875 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 126.000 | 0.398446 | ||||||||
\(11\) | 193.070 | 0.481099 | 0.240549 | − | 0.970637i | \(-0.422672\pi\) | ||||
0.240549 | + | 0.970637i | \(0.422672\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −151.500 | −0.248631 | −0.124315 | − | 0.992243i | \(-0.539673\pi\) | ||||
−0.124315 | + | 0.992243i | \(0.539673\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 747.857 | 0.730329 | ||||||||
\(17\) | −1760.12 | −1.47713 | −0.738567 | − | 0.674180i | \(-0.764497\pi\) | ||||
−0.738567 | + | 0.674180i | \(0.764497\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1126.79 | −0.716076 | −0.358038 | − | 0.933707i | \(-0.616554\pi\) | ||||
−0.358038 | + | 0.933707i | \(0.616554\pi\) | |||||||
\(20\) | −2123.20 | −1.18690 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 332.635 | 0.146525 | ||||||||
\(23\) | 2413.33 | 0.951254 | 0.475627 | − | 0.879647i | \(-0.342221\pi\) | ||||
0.475627 | + | 0.879647i | \(0.342221\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2223.54 | 0.711532 | ||||||||
\(26\) | −261.015 | −0.0757237 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7729.11 | −1.70661 | −0.853305 | − | 0.521412i | \(-0.825405\pi\) | ||||
−0.853305 | + | 0.521412i | \(0.825405\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8176.75 | 1.52819 | 0.764094 | − | 0.645105i | \(-0.223186\pi\) | ||||
0.764094 | + | 0.645105i | \(0.223186\pi\) | |||||||
\(32\) | 4653.24 | 0.803306 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3032.45 | −0.449880 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5932.38 | 0.712401 | 0.356200 | − | 0.934410i | \(-0.384072\pi\) | ||||
0.356200 | + | 0.934410i | \(0.384072\pi\) | |||||||
\(38\) | −1941.31 | −0.218090 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7689.98 | −0.759932 | ||||||||
\(41\) | −4975.84 | −0.462282 | −0.231141 | − | 0.972920i | \(-0.574246\pi\) | ||||
−0.231141 | + | 0.972920i | \(0.574246\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5652.51 | −0.466198 | −0.233099 | − | 0.972453i | \(-0.574887\pi\) | ||||
−0.233099 | + | 0.972453i | \(0.574887\pi\) | |||||||
\(44\) | −5605.17 | −0.436473 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4157.84 | 0.289716 | ||||||||
\(47\) | −4720.93 | −0.311733 | −0.155867 | − | 0.987778i | \(-0.549817\pi\) | ||||
−0.155867 | + | 0.987778i | \(0.549817\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3830.86 | 0.216706 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4398.32 | 0.225568 | ||||||||
\(53\) | −32072.1 | −1.56833 | −0.784166 | − | 0.620551i | \(-0.786909\pi\) | ||||
−0.784166 | + | 0.620551i | \(0.786909\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14120.0 | 0.629400 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −13316.2 | −0.519770 | ||||||||
\(59\) | 28566.9 | 1.06840 | 0.534200 | − | 0.845358i | \(-0.320613\pi\) | ||||
0.534200 | + | 0.845358i | \(0.320613\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −29003.7 | −0.997994 | −0.498997 | − | 0.866604i | \(-0.666298\pi\) | ||||
−0.498997 | + | 0.866604i | \(0.666298\pi\) | |||||||
\(62\) | 14087.5 | 0.465429 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −15914.5 | −0.485672 | ||||||||
\(65\) | −11079.8 | −0.325273 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −30517.4 | −0.830540 | −0.415270 | − | 0.909698i | \(-0.636313\pi\) | ||||
−0.415270 | + | 0.909698i | \(0.636313\pi\) | |||||||
\(68\) | 51099.3 | 1.34012 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 56944.5 | 1.34062 | 0.670310 | − | 0.742081i | \(-0.266161\pi\) | ||||
0.670310 | + | 0.742081i | \(0.266161\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9726.79 | −0.213630 | −0.106815 | − | 0.994279i | \(-0.534065\pi\) | ||||
−0.106815 | + | 0.994279i | \(0.534065\pi\) | |||||||
\(74\) | 10220.7 | 0.216971 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 32712.7 | 0.649654 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −98483.5 | −1.77540 | −0.887699 | − | 0.460424i | \(-0.847697\pi\) | ||||
−0.887699 | + | 0.460424i | \(0.847697\pi\) | |||||||
\(80\) | 54693.5 | 0.955457 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8572.71 | −0.140794 | ||||||||
\(83\) | −50637.0 | −0.806813 | −0.403406 | − | 0.915021i | \(-0.632174\pi\) | ||||
−0.403406 | + | 0.915021i | \(0.632174\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −128724. | −1.93247 | ||||||||
\(86\) | −9738.52 | −0.141986 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −20301.3 | −0.279458 | ||||||||
\(89\) | −59655.8 | −0.798321 | −0.399161 | − | 0.916881i | \(-0.630698\pi\) | ||||
−0.399161 | + | 0.916881i | \(0.630698\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −70063.0 | −0.863017 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8133.54 | −0.0949423 | ||||||||
\(95\) | −82406.4 | −0.936811 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 134206. | 1.44825 | 0.724124 | − | 0.689670i | \(-0.242244\pi\) | ||||
0.724124 | + | 0.689670i | \(0.242244\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −64553.2 | −0.645532 | ||||||||
\(101\) | −135281. | −1.31957 | −0.659786 | − | 0.751454i | \(-0.729353\pi\) | ||||
−0.659786 | + | 0.751454i | \(0.729353\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −199410. | −1.85205 | −0.926025 | − | 0.377461i | \(-0.876797\pi\) | ||||
−0.926025 | + | 0.377461i | \(0.876797\pi\) | |||||||
\(104\) | 15930.2 | 0.144423 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −55256.0 | −0.477655 | ||||||||
\(107\) | 93298.1 | 0.787795 | 0.393898 | − | 0.919154i | \(-0.371126\pi\) | ||||
0.393898 | + | 0.919154i | \(0.371126\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −41818.7 | −0.337136 | −0.168568 | − | 0.985690i | \(-0.553914\pi\) | ||||
−0.168568 | + | 0.985690i | \(0.553914\pi\) | |||||||
\(110\) | 24326.8 | 0.191692 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −170560. | −1.25655 | −0.628277 | − | 0.777990i | \(-0.716240\pi\) | ||||
−0.628277 | + | 0.777990i | \(0.716240\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 176495. | 1.24448 | ||||||||
\(116\) | 224389. | 1.54831 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 49217.0 | 0.325395 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −123775. | −0.768544 | ||||||||
\(122\) | −49969.4 | −0.303952 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −237385. | −1.38644 | ||||||||
\(125\) | −65927.2 | −0.377389 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −314872. | −1.73231 | −0.866154 | − | 0.499777i | \(-0.833415\pi\) | ||||
−0.866154 | + | 0.499777i | \(0.833415\pi\) | |||||||
\(128\) | −176322. | −0.951223 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −19089.0 | −0.0990660 | ||||||||
\(131\) | −91423.9 | −0.465459 | −0.232729 | − | 0.972542i | \(-0.574766\pi\) | ||||
−0.232729 | + | 0.972542i | \(0.574766\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −52577.4 | −0.252951 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 185076. | 0.858030 | ||||||||
\(137\) | −5959.51 | −0.0271275 | −0.0135637 | − | 0.999908i | \(-0.504318\pi\) | ||||
−0.0135637 | + | 0.999908i | \(0.504318\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13792.3 | 0.0605479 | 0.0302740 | − | 0.999542i | \(-0.490362\pi\) | ||||
0.0302740 | + | 0.999542i | \(0.490362\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 98107.8 | 0.408303 | ||||||||
\(143\) | −29250.2 | −0.119616 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −565258. | −2.23268 | ||||||||
\(146\) | −16758.0 | −0.0650637 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −172227. | −0.646320 | ||||||||
\(149\) | 400637. | 1.47838 | 0.739189 | − | 0.673498i | \(-0.235209\pi\) | ||||
0.739189 | + | 0.673498i | \(0.235209\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 91744.7 | 0.327445 | 0.163723 | − | 0.986506i | \(-0.447650\pi\) | ||||
0.163723 | + | 0.986506i | \(0.447650\pi\) | |||||||
\(152\) | 118482. | 0.415951 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 597996. | 1.99926 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 498424. | 1.61380 | 0.806900 | − | 0.590688i | \(-0.201143\pi\) | ||||
0.806900 | + | 0.590688i | \(0.201143\pi\) | |||||||
\(158\) | −169674. | −0.540720 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 340309. | 1.05093 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −242531. | −0.714988 | −0.357494 | − | 0.933915i | \(-0.616369\pi\) | ||||
−0.357494 | + | 0.933915i | \(0.616369\pi\) | |||||||
\(164\) | 144457. | 0.419401 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −87240.8 | −0.245725 | ||||||||
\(167\) | 525601. | 1.45836 | 0.729181 | − | 0.684321i | \(-0.239901\pi\) | ||||
0.729181 | + | 0.684321i | \(0.239901\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −348341. | −0.938183 | ||||||||
\(170\) | −221775. | −0.588558 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 164102. | 0.422954 | ||||||||
\(173\) | −96423.4 | −0.244944 | −0.122472 | − | 0.992472i | \(-0.539082\pi\) | ||||
−0.122472 | + | 0.992472i | \(0.539082\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 144389. | 0.351360 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −102779. | −0.243139 | ||||||||
\(179\) | 178701. | 0.416865 | 0.208432 | − | 0.978037i | \(-0.433164\pi\) | ||||
0.208432 | + | 0.978037i | \(0.433164\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 224533. | 0.509428 | 0.254714 | − | 0.967016i | \(-0.418019\pi\) | ||||
0.254714 | + | 0.967016i | \(0.418019\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −253760. | −0.552559 | ||||||||
\(185\) | 433857. | 0.932002 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −339827. | −0.710647 | ||||||||
\(188\) | 137057. | 0.282817 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −141975. | −0.285318 | ||||||||
\(191\) | −905785. | −1.79656 | −0.898280 | − | 0.439423i | \(-0.855183\pi\) | ||||
−0.898280 | + | 0.439423i | \(0.855183\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −717637. | −1.38679 | −0.693396 | − | 0.720556i | \(-0.743886\pi\) | ||||
−0.693396 | + | 0.720556i | \(0.743886\pi\) | |||||||
\(194\) | 231219. | 0.441082 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −57173.0 | −0.104960 | −0.0524802 | − | 0.998622i | \(-0.516713\pi\) | ||||
−0.0524802 | + | 0.998622i | \(0.516713\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −263037. | −0.470853 | −0.235426 | − | 0.971892i | \(-0.575649\pi\) | ||||
−0.235426 | + | 0.971892i | \(0.575649\pi\) | |||||||
\(200\) | −233804. | −0.413311 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −233071. | −0.401892 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −363902. | −0.604782 | ||||||||
\(206\) | −343556. | −0.564066 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −113301. | −0.181582 | ||||||||
\(209\) | −217550. | −0.344503 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −495237. | −0.765786 | −0.382893 | − | 0.923793i | \(-0.625072\pi\) | ||||
−0.382893 | + | 0.923793i | \(0.625072\pi\) | |||||||
\(212\) | 931109. | 1.42286 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 160740. | 0.239933 | ||||||||
\(215\) | −413389. | −0.609906 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −72048.1 | −0.102679 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −409927. | −0.571018 | ||||||||
\(221\) | 266659. | 0.367261 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 373295. | 0.502679 | 0.251339 | − | 0.967899i | \(-0.419129\pi\) | ||||
0.251339 | + | 0.967899i | \(0.419129\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −293852. | −0.382700 | ||||||||
\(227\) | −284573. | −0.366547 | −0.183273 | − | 0.983062i | \(-0.558669\pi\) | ||||
−0.183273 | + | 0.983062i | \(0.558669\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 989364. | 1.24672 | 0.623358 | − | 0.781937i | \(-0.285768\pi\) | ||||
0.623358 | + | 0.781937i | \(0.285768\pi\) | |||||||
\(230\) | 304078. | 0.379023 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 812712. | 0.991327 | ||||||||
\(233\) | 602273. | 0.726781 | 0.363391 | − | 0.931637i | \(-0.381619\pi\) | ||||
0.363391 | + | 0.931637i | \(0.381619\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −345259. | −0.407827 | ||||||||
\(236\) | −829347. | −0.969296 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.44372e6 | −1.63489 | −0.817447 | − | 0.576004i | \(-0.804611\pi\) | ||||
−0.817447 | + | 0.576004i | \(0.804611\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −538796. | −0.597560 | −0.298780 | − | 0.954322i | \(-0.596580\pi\) | ||||
−0.298780 | + | 0.954322i | \(0.596580\pi\) | |||||||
\(242\) | −213248. | −0.234070 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 842026. | 0.905422 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 170709. | 0.178039 | ||||||||
\(248\) | −859782. | −0.887685 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −113584. | −0.114939 | ||||||||
\(251\) | −1.63982e6 | −1.64290 | −0.821449 | − | 0.570282i | \(-0.806834\pi\) | ||||
−0.821449 | + | 0.570282i | \(0.806834\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 465942. | 0.457647 | ||||||||
\(254\) | −542483. | −0.527596 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 205484. | 0.195965 | ||||||||
\(257\) | 1.82127e6 | 1.72005 | 0.860026 | − | 0.510251i | \(-0.170447\pi\) | ||||
0.860026 | + | 0.510251i | \(0.170447\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 321665. | 0.295101 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −157511. | −0.141761 | ||||||||
\(263\) | 1.77477e6 | 1.58217 | 0.791085 | − | 0.611706i | \(-0.209517\pi\) | ||||
0.791085 | + | 0.611706i | \(0.209517\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.34555e6 | −2.05178 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 885972. | 0.753500 | ||||||||
\(269\) | 769025. | 0.647977 | 0.323989 | − | 0.946061i | \(-0.394976\pi\) | ||||
0.323989 | + | 0.946061i | \(0.394976\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.81374e6 | 1.50021 | 0.750106 | − | 0.661317i | \(-0.230002\pi\) | ||||
0.750106 | + | 0.661317i | \(0.230002\pi\) | |||||||
\(272\) | −1.31632e6 | −1.07879 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10267.4 | −0.00826202 | ||||||||
\(275\) | 429299. | 0.342317 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.12526e6 | 0.881157 | 0.440578 | − | 0.897714i | \(-0.354773\pi\) | ||||
0.440578 | + | 0.897714i | \(0.354773\pi\) | |||||||
\(278\) | 23762.3 | 0.0184406 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −243202. | −0.183739 | −0.0918696 | − | 0.995771i | \(-0.529284\pi\) | ||||
−0.0918696 | + | 0.995771i | \(0.529284\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.06625e6 | 0.791396 | 0.395698 | − | 0.918381i | \(-0.370503\pi\) | ||||
0.395698 | + | 0.918381i | \(0.370503\pi\) | |||||||
\(284\) | −1.65320e6 | −1.21627 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −50394.3 | −0.0364306 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.67817e6 | 1.18193 | ||||||||
\(290\) | −973865. | −0.679992 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 282385. | 0.193814 | ||||||||
\(293\) | 2.32478e6 | 1.58203 | 0.791013 | − | 0.611799i | \(-0.209554\pi\) | ||||
0.791013 | + | 0.611799i | \(0.209554\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.08921e6 | 1.39774 | ||||||||
\(296\) | −623787. | −0.413816 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 690244. | 0.450259 | ||||||||
\(299\) | −365620. | −0.236511 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 158064. | 0.0997275 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −842678. | −0.522971 | ||||||||
\(305\) | −2.12114e6 | −1.30563 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.37882e6 | −1.44051 | −0.720255 | − | 0.693710i | \(-0.755975\pi\) | ||||
−0.720255 | + | 0.693710i | \(0.755975\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.03027e6 | 0.608900 | ||||||||
\(311\) | 2.22414e6 | 1.30395 | 0.651976 | − | 0.758240i | \(-0.273940\pi\) | ||||
0.651976 | + | 0.758240i | \(0.273940\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.03945e6 | 0.599713 | 0.299857 | − | 0.953984i | \(-0.403061\pi\) | ||||
0.299857 | + | 0.953984i | \(0.403061\pi\) | |||||||
\(314\) | 858718. | 0.491503 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.85915e6 | 1.61072 | ||||||||
\(317\) | −428476. | −0.239485 | −0.119743 | − | 0.992805i | \(-0.538207\pi\) | ||||
−0.119743 | + | 0.992805i | \(0.538207\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.49226e6 | −0.821048 | ||||||||
\(320\) | −1.16389e6 | −0.635383 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.98329e6 | 1.05774 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −336867. | −0.176909 | ||||||||
\(326\) | −417849. | −0.217759 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 523207. | 0.268528 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.79057e6 | 1.39998 | 0.699991 | − | 0.714152i | \(-0.253187\pi\) | ||||
0.699991 | + | 0.714152i | \(0.253187\pi\) | |||||||
\(332\) | 1.47008e6 | 0.731974 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 905541. | 0.444163 | ||||||||
\(335\) | −2.23185e6 | −1.08656 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.30809e6 | 0.627427 | 0.313714 | − | 0.949518i | \(-0.398427\pi\) | ||||
0.313714 | + | 0.949518i | \(0.398427\pi\) | |||||||
\(338\) | −600145. | −0.285735 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.73708e6 | 1.75322 | ||||||||
\(341\) | 1.57869e6 | 0.735209 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 594359. | 0.270802 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −166125. | −0.0746009 | ||||||||
\(347\) | 664031. | 0.296050 | 0.148025 | − | 0.988984i | \(-0.452708\pi\) | ||||
0.148025 | + | 0.988984i | \(0.452708\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.27119e6 | −0.998136 | −0.499068 | − | 0.866563i | \(-0.666324\pi\) | ||||
−0.499068 | + | 0.866563i | \(0.666324\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 898404. | 0.386469 | ||||||||
\(353\) | 1.96361e6 | 0.838723 | 0.419361 | − | 0.907819i | \(-0.362254\pi\) | ||||
0.419361 | + | 0.907819i | \(0.362254\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.16456e6 | 1.75387 | ||||||||
\(356\) | 1.73191e6 | 0.724270 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 307879. | 0.126961 | ||||||||
\(359\) | −2.09222e6 | −0.856783 | −0.428391 | − | 0.903593i | \(-0.640920\pi\) | ||||
−0.428391 | + | 0.903593i | \(0.640920\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.20644e6 | −0.487235 | ||||||||
\(362\) | 386840. | 0.155153 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −711356. | −0.279483 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.33844e6 | −0.518719 | −0.259360 | − | 0.965781i | \(-0.583512\pi\) | ||||
−0.259360 | + | 0.965781i | \(0.583512\pi\) | |||||||
\(368\) | 1.80482e6 | 0.694728 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 747477. | 0.283853 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.32657e6 | −0.493694 | −0.246847 | − | 0.969054i | \(-0.579394\pi\) | ||||
−0.246847 | + | 0.969054i | \(0.579394\pi\) | |||||||
\(374\) | −585477. | −0.216437 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 496404. | 0.181078 | ||||||||
\(377\) | 1.17096e6 | 0.424316 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 863514. | 0.308796 | 0.154398 | − | 0.988009i | \(-0.450656\pi\) | ||||
0.154398 | + | 0.988009i | \(0.450656\pi\) | |||||||
\(380\) | 2.39240e6 | 0.849914 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.56055e6 | −0.547165 | ||||||||
\(383\) | −2.53709e6 | −0.883769 | −0.441884 | − | 0.897072i | \(-0.645690\pi\) | ||||
−0.441884 | + | 0.897072i | \(0.645690\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.23639e6 | −0.422365 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.89624e6 | −1.31391 | ||||||||
\(389\) | −253814. | −0.0850434 | −0.0425217 | − | 0.999096i | \(-0.513539\pi\) | ||||
−0.0425217 | + | 0.999096i | \(0.513539\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.24774e6 | −1.40513 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −98501.4 | −0.0319670 | ||||||||
\(395\) | −7.20246e6 | −2.32267 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.57767e6 | 1.45770 | 0.728850 | − | 0.684673i | \(-0.240055\pi\) | ||||
0.728850 | + | 0.684673i | \(0.240055\pi\) | |||||||
\(398\) | −453179. | −0.143404 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.66289e6 | 0.519653 | ||||||||
\(401\) | 4.38670e6 | 1.36231 | 0.681156 | − | 0.732138i | \(-0.261477\pi\) | ||||
0.681156 | + | 0.732138i | \(0.261477\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.23878e6 | −0.379955 | ||||||||
\(404\) | 3.92744e6 | 1.19717 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.14537e6 | 0.342735 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −222245. | −0.0656936 | −0.0328468 | − | 0.999460i | \(-0.510457\pi\) | ||||
−0.0328468 | + | 0.999460i | \(0.510457\pi\) | |||||||
\(410\) | −626954. | −0.184194 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.78920e6 | 1.68026 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.70327e6 | −1.05552 | ||||||||
\(416\) | −704968. | −0.199727 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −374810. | −0.104923 | ||||||||
\(419\) | −4.33564e6 | −1.20647 | −0.603237 | − | 0.797562i | \(-0.706123\pi\) | ||||
−0.603237 | + | 0.797562i | \(0.706123\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 572536. | 0.157434 | 0.0787168 | − | 0.996897i | \(-0.474918\pi\) | ||||
0.0787168 | + | 0.996897i | \(0.474918\pi\) | |||||||
\(422\) | −853228. | −0.233230 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.37237e6 | 0.911004 | ||||||||
\(425\) | −3.91370e6 | −1.05103 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2.70860e6 | −0.714720 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −712214. | −0.185754 | ||||||||
\(431\) | 3.30224e6 | 0.856279 | 0.428139 | − | 0.903713i | \(-0.359169\pi\) | ||||
0.428139 | + | 0.903713i | \(0.359169\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19285.5 | 0.00494322 | 0.00247161 | − | 0.999997i | \(-0.499213\pi\) | ||||
0.00247161 | + | 0.999997i | \(0.499213\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.21407e6 | 0.305863 | ||||||||
\(437\) | −2.71931e6 | −0.681170 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −376815. | −0.0933182 | −0.0466591 | − | 0.998911i | \(-0.514857\pi\) | ||||
−0.0466591 | + | 0.998911i | \(0.514857\pi\) | |||||||
\(440\) | −1.48471e6 | −0.365602 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 459418. | 0.111854 | ||||||||
\(443\) | −1.24690e6 | −0.301871 | −0.150936 | − | 0.988544i | \(-0.548229\pi\) | ||||
−0.150936 | + | 0.988544i | \(0.548229\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.36285e6 | −1.04441 | ||||||||
\(446\) | 643138. | 0.153097 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.85298e6 | −0.667857 | −0.333928 | − | 0.942598i | \(-0.608374\pi\) | ||||
−0.333928 | + | 0.942598i | \(0.608374\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −960687. | −0.222403 | ||||||||
\(452\) | 4.95165e6 | 1.14000 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −490282. | −0.111636 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.10513e6 | 0.471506 | 0.235753 | − | 0.971813i | \(-0.424244\pi\) | ||||
0.235753 | + | 0.971813i | \(0.424244\pi\) | |||||||
\(458\) | 1.70454e6 | 0.379703 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5.12397e6 | −1.12905 | ||||||||
\(461\) | 8.96535e6 | 1.96478 | 0.982392 | − | 0.186832i | \(-0.0598220\pi\) | ||||
0.982392 | + | 0.186832i | \(0.0598220\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.01066e6 | −1.51987 | −0.759935 | − | 0.649999i | \(-0.774769\pi\) | ||||
−0.759935 | + | 0.649999i | \(0.774769\pi\) | |||||||
\(464\) | −5.78026e6 | −1.24639 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.03764e6 | 0.221350 | ||||||||
\(467\) | −3.26840e6 | −0.693495 | −0.346747 | − | 0.937959i | \(-0.612714\pi\) | ||||
−0.346747 | + | 0.937959i | \(0.612714\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −594836. | −0.124209 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.00380e6 | −0.620606 | ||||||||
\(473\) | −1.09133e6 | −0.224287 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.50546e6 | −0.509511 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.48734e6 | −0.497928 | ||||||||
\(479\) | 4.89425e6 | 0.974646 | 0.487323 | − | 0.873222i | \(-0.337973\pi\) | ||||
0.487323 | + | 0.873222i | \(0.337973\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −898757. | −0.177125 | ||||||||
\(482\) | −928274. | −0.181995 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.59340e6 | 0.697255 | ||||||||
\(485\) | 9.81499e6 | 1.89468 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.60536e6 | −0.879916 | −0.439958 | − | 0.898018i | \(-0.645007\pi\) | ||||
−0.439958 | + | 0.898018i | \(0.645007\pi\) | |||||||
\(488\) | 3.04972e6 | 0.579710 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.58108e6 | 1.04475 | 0.522377 | − | 0.852714i | \(-0.325045\pi\) | ||||
0.522377 | + | 0.852714i | \(0.325045\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.36042e7 | 2.52089 | ||||||||
\(494\) | 294109. | 0.0542240 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.11504e6 | 1.11608 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.49822e6 | −0.269354 | −0.134677 | − | 0.990890i | \(-0.543000\pi\) | ||||
−0.134677 | + | 0.990890i | \(0.543000\pi\) | |||||||
\(500\) | 1.91398e6 | 0.342383 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.82518e6 | −0.500366 | ||||||||
\(503\) | 479890. | 0.0845710 | 0.0422855 | − | 0.999106i | \(-0.486536\pi\) | ||||
0.0422855 | + | 0.999106i | \(0.486536\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.89359e6 | −1.72634 | ||||||||
\(506\) | 802756. | 0.139382 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.14129e6 | 1.57162 | ||||||||
\(509\) | −1.21062e6 | −0.207117 | −0.103558 | − | 0.994623i | \(-0.533023\pi\) | ||||
−0.103558 | + | 0.994623i | \(0.533023\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 5.99634e6 | 1.01091 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.13780e6 | 0.523863 | ||||||||
\(515\) | −1.45836e7 | −2.42296 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −911472. | −0.149974 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.16503e6 | 0.188943 | ||||||||
\(521\) | −69333.1 | −0.0111904 | −0.00559521 | − | 0.999984i | \(-0.501781\pi\) | ||||
−0.00559521 | + | 0.999984i | \(0.501781\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.95346e6 | −1.43132 | −0.715660 | − | 0.698449i | \(-0.753874\pi\) | ||||
−0.715660 | + | 0.698449i | \(0.753874\pi\) | |||||||
\(524\) | 2.65419e6 | 0.422284 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.05770e6 | 0.481870 | ||||||||
\(527\) | −1.43921e7 | −2.25734 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −612203. | −0.0951166 | ||||||||
\(530\) | −4.04107e6 | −0.624895 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 753841. | 0.114938 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.82323e6 | 1.03064 | ||||||||
\(536\) | 3.20889e6 | 0.482439 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.32493e6 | 0.197350 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.38913e6 | −0.350951 | −0.175476 | − | 0.984484i | \(-0.556146\pi\) | ||||
−0.175476 | + | 0.984484i | \(0.556146\pi\) | |||||||
\(542\) | 3.12484e6 | 0.456909 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −8.19027e6 | −1.18659 | ||||||||
\(545\) | −3.05836e6 | −0.441059 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.19431e6 | −1.02807 | −0.514033 | − | 0.857770i | \(-0.671849\pi\) | ||||
−0.514033 | + | 0.857770i | \(0.671849\pi\) | |||||||
\(548\) | 173015. | 0.0246112 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 739626. | 0.104257 | ||||||||
\(551\) | 8.70909e6 | 1.22206 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.93867e6 | 0.268367 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −400414. | −0.0549316 | ||||||||
\(557\) | 753706. | 0.102935 | 0.0514676 | − | 0.998675i | \(-0.483610\pi\) | ||||
0.0514676 | + | 0.998675i | \(0.483610\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 856357. | 0.115911 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −419005. | −0.0559601 | ||||||||
\(563\) | 1.22890e6 | 0.163397 | 0.0816985 | − | 0.996657i | \(-0.473966\pi\) | ||||
0.0816985 | + | 0.996657i | \(0.473966\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.24737e7 | −1.64389 | ||||||||
\(566\) | 1.83701e6 | 0.241030 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.98769e6 | −0.778733 | ||||||||
\(569\) | 4.30545e6 | 0.557491 | 0.278745 | − | 0.960365i | \(-0.410081\pi\) | ||||
0.278745 | + | 0.960365i | \(0.410081\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.96799e6 | −0.509307 | −0.254654 | − | 0.967032i | \(-0.581961\pi\) | ||||
−0.254654 | + | 0.967032i | \(0.581961\pi\) | |||||||
\(572\) | 849185. | 0.108521 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.36612e6 | 0.676848 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 596027. | 0.0745292 | 0.0372646 | − | 0.999305i | \(-0.488136\pi\) | ||||
0.0372646 | + | 0.999305i | \(0.488136\pi\) | |||||||
\(578\) | 2.89126e6 | 0.359971 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.64104e7 | 2.02558 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.19218e6 | −0.754522 | ||||||||
\(584\) | 1.02277e6 | 0.124092 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.00529e6 | 0.481826 | ||||||||
\(587\) | −2.47516e6 | −0.296489 | −0.148244 | − | 0.988951i | \(-0.547362\pi\) | ||||
−0.148244 | + | 0.988951i | \(0.547362\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.21349e6 | −1.09430 | ||||||||
\(590\) | 3.59942e6 | 0.425699 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.43657e6 | 0.520287 | ||||||||
\(593\) | 1.14108e7 | 1.33253 | 0.666267 | − | 0.745713i | \(-0.267891\pi\) | ||||
0.666267 | + | 0.745713i | \(0.267891\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.16312e7 | −1.34125 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −629914. | −0.0720325 | ||||||||
\(599\) | 8.60394e6 | 0.979784 | 0.489892 | − | 0.871783i | \(-0.337036\pi\) | ||||
0.489892 | + | 0.871783i | \(0.337036\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.00463e7 | −1.13454 | −0.567270 | − | 0.823532i | \(-0.692001\pi\) | ||||
−0.567270 | + | 0.823532i | \(0.692001\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.66351e6 | −0.297072 | ||||||||
\(605\) | −9.05211e6 | −1.00545 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.22979e6 | −0.245636 | −0.122818 | − | 0.992429i | \(-0.539193\pi\) | ||||
−0.122818 | + | 0.992429i | \(0.539193\pi\) | |||||||
\(608\) | −5.24323e6 | −0.575228 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.65445e6 | −0.397647 | ||||||||
\(611\) | 715223. | 0.0775065 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.63670e7 | −1.75921 | −0.879607 | − | 0.475701i | \(-0.842194\pi\) | ||||
−0.879607 | + | 0.475701i | \(0.842194\pi\) | |||||||
\(614\) | −4.09840e6 | −0.438726 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.21424e7 | −1.28407 | −0.642037 | − | 0.766674i | \(-0.721910\pi\) | ||||
−0.642037 | + | 0.766674i | \(0.721910\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.12279e7 | 1.17780 | 0.588898 | − | 0.808207i | \(-0.299562\pi\) | ||||
0.588898 | + | 0.808207i | \(0.299562\pi\) | |||||||
\(620\) | −1.73609e7 | −1.81381 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.83190e6 | 0.397135 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.17701e7 | −1.20525 | ||||||||
\(626\) | 1.79084e6 | 0.182650 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.44701e7 | −1.46411 | ||||||||
\(629\) | −1.04417e7 | −1.05231 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.69644e6 | −0.569548 | −0.284774 | − | 0.958595i | \(-0.591918\pi\) | ||||
−0.284774 | + | 0.958595i | \(0.591918\pi\) | |||||||
\(632\) | 1.03555e7 | 1.03128 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −738208. | −0.0729383 | ||||||||
\(635\) | −2.30278e7 | −2.26630 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.57097e6 | −0.250060 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.28951e7 | −1.24444 | ||||||||
\(641\) | 2.96921e6 | 0.285427 | 0.142714 | − | 0.989764i | \(-0.454417\pi\) | ||||
0.142714 | + | 0.989764i | \(0.454417\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.22682e7 | 1.17018 | 0.585091 | − | 0.810968i | \(-0.301059\pi\) | ||||
0.585091 | + | 0.810968i | \(0.301059\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.41694e6 | 0.322149 | ||||||||
\(647\) | 1.21684e6 | 0.114281 | 0.0571404 | − | 0.998366i | \(-0.481802\pi\) | ||||
0.0571404 | + | 0.998366i | \(0.481802\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.51543e6 | 0.514005 | ||||||||
\(650\) | −580377. | −0.0538799 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.04110e6 | 0.648667 | ||||||||
\(653\) | −1.10265e7 | −1.01194 | −0.505969 | − | 0.862552i | \(-0.668865\pi\) | ||||
−0.505969 | + | 0.862552i | \(0.668865\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.68617e6 | −0.608939 | ||||||||
\(656\) | −3.72121e6 | −0.337618 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.32297e7 | −1.18668 | −0.593342 | − | 0.804951i | \(-0.702192\pi\) | ||||
−0.593342 | + | 0.804951i | \(0.702192\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.60257e6 | −0.587773 | −0.293886 | − | 0.955840i | \(-0.594949\pi\) | ||||
−0.293886 | + | 0.955840i | \(0.594949\pi\) | |||||||
\(662\) | 4.80777e6 | 0.426382 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.32446e6 | 0.468657 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.86529e7 | −1.62342 | ||||||||
\(668\) | −1.52591e7 | −1.32309 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.84518e6 | −0.330925 | ||||||||
\(671\) | −5.59975e6 | −0.480134 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.42013e7 | −1.20862 | −0.604310 | − | 0.796749i | \(-0.706551\pi\) | ||||
−0.604310 | + | 0.796749i | \(0.706551\pi\) | |||||||
\(674\) | 2.25367e6 | 0.191091 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.01129e7 | 0.851158 | ||||||||
\(677\) | 1.55878e7 | 1.30712 | 0.653559 | − | 0.756876i | \(-0.273275\pi\) | ||||
0.653559 | + | 0.756876i | \(0.273275\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.35353e7 | 1.12252 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.71987e6 | 0.223917 | ||||||||
\(683\) | 1.37838e7 | 1.13063 | 0.565313 | − | 0.824877i | \(-0.308756\pi\) | ||||
0.565313 | + | 0.824877i | \(0.308756\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −435841. | −0.0354897 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.22727e6 | −0.340478 | ||||||||
\(689\) | 4.85894e6 | 0.389936 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.13345e7 | 0.903043 | 0.451522 | − | 0.892260i | \(-0.350881\pi\) | ||||
0.451522 | + | 0.892260i | \(0.350881\pi\) | |||||||
\(692\) | 2.79934e6 | 0.222224 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.14404e6 | 0.0901657 | ||||||||
\(695\) | 1.00868e6 | 0.0792121 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.75808e6 | 0.682852 | ||||||||
\(698\) | −3.91296e6 | −0.303995 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.21970e6 | −0.324330 | −0.162165 | − | 0.986764i | \(-0.551848\pi\) | ||||
−0.162165 | + | 0.986764i | \(0.551848\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.68455e6 | −0.510133 | ||||||||
\(704\) | −3.07262e6 | −0.233656 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.38304e6 | 0.255444 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.25786e7 | 0.939757 | 0.469878 | − | 0.882731i | \(-0.344298\pi\) | ||||
0.469878 | + | 0.882731i | \(0.344298\pi\) | |||||||
\(710\) | 7.17499e6 | 0.534165 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.27278e6 | 0.463724 | ||||||||
\(713\) | 1.97332e7 | 1.45369 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.13918e6 | −0.156488 | ||||||||
\(716\) | −5.18801e6 | −0.378197 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.60461e6 | −0.260944 | ||||||||
\(719\) | 2.55041e7 | 1.83988 | 0.919938 | − | 0.392065i | \(-0.128239\pi\) | ||||
0.919938 | + | 0.392065i | \(0.128239\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.07854e6 | −0.148393 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.51857e6 | −0.462175 | ||||||||
\(725\) | −1.71860e7 | −1.21431 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.25405e7 | −1.58171 | −0.790857 | − | 0.612001i | \(-0.790365\pi\) | ||||
−0.790857 | + | 0.612001i | \(0.790365\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.22557e6 | −0.0851200 | ||||||||
\(731\) | 9.94909e6 | 0.688637 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.07168e7 | −0.736724 | −0.368362 | − | 0.929682i | \(-0.620081\pi\) | ||||
−0.368362 | + | 0.929682i | \(0.620081\pi\) | |||||||
\(734\) | −2.30595e6 | −0.157983 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.12298e7 | 0.764147 | ||||||||
\(737\) | −5.89200e6 | −0.399571 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.67756e7 | −1.12997 | −0.564987 | − | 0.825100i | \(-0.691119\pi\) | ||||
−0.564987 | + | 0.825100i | \(0.691119\pi\) | |||||||
\(740\) | −1.25956e7 | −0.845551 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.93625e6 | 0.593859 | 0.296929 | − | 0.954899i | \(-0.404037\pi\) | ||||
0.296929 | + | 0.954899i | \(0.404037\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.93001e7 | 1.93409 | ||||||||
\(746\) | −2.28550e6 | −0.150361 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.86577e6 | 0.644729 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.36875e7 | 0.885571 | 0.442785 | − | 0.896628i | \(-0.353990\pi\) | ||||
0.442785 | + | 0.896628i | \(0.353990\pi\) | |||||||
\(752\) | −3.53058e6 | −0.227668 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.01741e6 | 0.129231 | ||||||||
\(755\) | 6.70963e6 | 0.428382 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.97877e7 | 1.25504 | 0.627518 | − | 0.778602i | \(-0.284071\pi\) | ||||
0.627518 | + | 0.778602i | \(0.284071\pi\) | |||||||
\(758\) | 1.48772e6 | 0.0940477 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.66499e6 | 0.544170 | ||||||||
\(761\) | −5.23103e6 | −0.327435 | −0.163718 | − | 0.986507i | \(-0.552349\pi\) | ||||
−0.163718 | + | 0.986507i | \(0.552349\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.62965e7 | 1.62991 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.37107e6 | −0.269163 | ||||||||
\(767\) | −4.32790e6 | −0.265637 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.04244e7 | −0.635673 | −0.317837 | − | 0.948145i | \(-0.602956\pi\) | ||||
−0.317837 | + | 0.948145i | \(0.602956\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.08342e7 | 1.25816 | ||||||||
\(773\) | 8.04863e6 | 0.484477 | 0.242238 | − | 0.970217i | \(-0.422118\pi\) | ||||
0.242238 | + | 0.970217i | \(0.422118\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.81813e7 | 1.08735 | ||||||||
\(776\) | −1.41117e7 | −0.841251 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −437287. | −0.0259011 | ||||||||
\(779\) | 5.60673e6 | 0.331029 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.09943e7 | 0.644971 | ||||||||
\(782\) | −7.31830e6 | −0.427950 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.64516e7 | 2.11126 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.51619e7 | −0.872602 | −0.436301 | − | 0.899801i | \(-0.643712\pi\) | ||||
−0.436301 | + | 0.899801i | \(0.643712\pi\) | |||||||
\(788\) | 1.65983e6 | 0.0952244 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.24089e7 | −0.707400 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.39406e6 | 0.248132 | ||||||||
\(794\) | 7.88672e6 | 0.443961 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.63643e6 | 0.427177 | ||||||||
\(797\) | 1.70525e7 | 0.950915 | 0.475458 | − | 0.879739i | \(-0.342283\pi\) | ||||
0.475458 | + | 0.879739i | \(0.342283\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.30941e6 | 0.460472 | ||||||||
\(800\) | 1.03467e7 | 0.571578 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.55770e6 | 0.414910 | ||||||||
\(803\) | −1.87795e6 | −0.102777 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.13425e6 | −0.115720 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.42247e7 | 0.766506 | ||||||||
\(809\) | 1.81012e7 | 0.972381 | 0.486190 | − | 0.873853i | \(-0.338386\pi\) | ||||
0.486190 | + | 0.873853i | \(0.338386\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.37346e7 | −0.733271 | −0.366636 | − | 0.930365i | \(-0.619490\pi\) | ||||
−0.366636 | + | 0.930365i | \(0.619490\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.97331e6 | 0.104384 | ||||||||
\(815\) | −1.77372e7 | −0.935387 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.36919e6 | 0.333833 | ||||||||
\(818\) | −382898. | −0.0200078 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.05647e7 | 0.548684 | ||||||||
\(821\) | −2.27546e7 | −1.17818 | −0.589089 | − | 0.808068i | \(-0.700513\pi\) | ||||
−0.589089 | + | 0.808068i | \(0.700513\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.91287e6 | 0.458689 | 0.229344 | − | 0.973345i | \(-0.426342\pi\) | ||||
0.229344 | + | 0.973345i | \(0.426342\pi\) | |||||||
\(824\) | 2.09678e7 | 1.07581 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.85147e7 | −1.44979 | −0.724896 | − | 0.688859i | \(-0.758112\pi\) | ||||
−0.724896 | + | 0.688859i | \(0.758112\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.53299e7 | −0.774733 | −0.387366 | − | 0.921926i | \(-0.626615\pi\) | ||||
−0.387366 | + | 0.921926i | \(0.626615\pi\) | |||||||
\(830\) | −6.38024e6 | −0.321471 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.41105e6 | 0.120753 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.84392e7 | 1.90791 | ||||||||
\(836\) | 6.31585e6 | 0.312548 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7.46973e6 | −0.367447 | ||||||||
\(839\) | 2.17291e7 | 1.06571 | 0.532853 | − | 0.846208i | \(-0.321120\pi\) | ||||
0.532853 | + | 0.846208i | \(0.321120\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.92279e7 | 1.91252 | ||||||||
\(842\) | 986403. | 0.0479484 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.43776e7 | 0.694753 | ||||||||
\(845\) | −2.54754e7 | −1.22738 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.39853e7 | −1.14540 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6.74278e6 | −0.320104 | ||||||||
\(851\) | 1.43168e7 | 0.677674 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.60934e7 | −1.22789 | −0.613943 | − | 0.789350i | \(-0.710418\pi\) | ||||
−0.613943 | + | 0.789350i | \(0.710418\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.81025e6 | −0.457610 | ||||||||
\(857\) | 1.07218e7 | 0.498675 | 0.249337 | − | 0.968417i | \(-0.419787\pi\) | ||||
0.249337 | + | 0.968417i | \(0.419787\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.54531e7 | 1.63935 | 0.819675 | − | 0.572829i | \(-0.194154\pi\) | ||||
0.819675 | + | 0.572829i | \(0.194154\pi\) | |||||||
\(860\) | 1.20014e7 | 0.553332 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.68932e6 | 0.260791 | ||||||||
\(863\) | 1.63278e7 | 0.746278 | 0.373139 | − | 0.927775i | \(-0.378281\pi\) | ||||
0.373139 | + | 0.927775i | \(0.378281\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.05180e6 | −0.320450 | ||||||||
\(866\) | 33226.3 | 0.00150552 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.90143e7 | −0.854142 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.62339e6 | 0.206498 | ||||||||
\(872\) | 4.39722e6 | 0.195834 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.68501e6 | −0.207459 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.94566e7 | 0.854216 | 0.427108 | − | 0.904201i | \(-0.359532\pi\) | ||||
0.427108 | + | 0.904201i | \(0.359532\pi\) | |||||||
\(878\) | −649201. | −0.0284213 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.05597e7 | 0.459669 | ||||||||
\(881\) | −4.31688e7 | −1.87383 | −0.936916 | − | 0.349555i | \(-0.886333\pi\) | ||||
−0.936916 | + | 0.349555i | \(0.886333\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.63478e6 | −0.329530 | −0.164765 | − | 0.986333i | \(-0.552687\pi\) | ||||
−0.164765 | + | 0.986333i | \(0.552687\pi\) | |||||||
\(884\) | −7.74157e6 | −0.333195 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.14824e6 | −0.0919387 | ||||||||
\(887\) | 4.08512e6 | 0.174340 | 0.0871698 | − | 0.996193i | \(-0.472218\pi\) | ||||
0.0871698 | + | 0.996193i | \(0.472218\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −7.51661e6 | −0.318088 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.08374e7 | −0.456051 | ||||||||
\(893\) | 5.31950e6 | 0.223225 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.30691e7 | 0.545366 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.91531e6 | −0.203404 | ||||||||
\(899\) | −6.31990e7 | −2.60802 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.64508e7 | 2.31664 | ||||||||
\(902\) | −1.65514e6 | −0.0677357 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.79343e7 | 0.729900 | ||||||||
\(905\) | 1.64209e7 | 0.666462 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.00583e6 | 0.363501 | 0.181751 | − | 0.983345i | \(-0.441824\pi\) | ||||
0.181751 | + | 0.983345i | \(0.441824\pi\) | |||||||
\(908\) | 8.26165e6 | 0.332546 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.17438e7 | 0.868041 | 0.434020 | − | 0.900903i | \(-0.357095\pi\) | ||||
0.434020 | + | 0.900903i | \(0.357095\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.77650e6 | −0.388156 | ||||||||
\(914\) | 3.62685e6 | 0.143603 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.87229e7 | −1.13107 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.84235e7 | −1.50075 | −0.750374 | − | 0.661013i | \(-0.770127\pi\) | ||||
−0.750374 | + | 0.661013i | \(0.770127\pi\) | |||||||
\(920\) | −1.85584e7 | −0.722888 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.54461e7 | 0.598400 | ||||||||
\(923\) | −8.62711e6 | −0.333320 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.31909e7 | 0.506896 | ||||||||
\(926\) | −1.20784e7 | −0.462896 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.59654e7 | −1.37093 | ||||||||
\(929\) | −3.67005e7 | −1.39519 | −0.697594 | − | 0.716493i | \(-0.745746\pi\) | ||||
−0.697594 | + | 0.716493i | \(0.745746\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.74850e7 | −0.659366 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.63102e6 | −0.211213 | ||||||||
\(935\) | −2.48528e7 | −0.929708 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.37847e7 | 0.512919 | 0.256459 | − | 0.966555i | \(-0.417444\pi\) | ||||
0.256459 | + | 0.966555i | \(0.417444\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.00235e7 | 0.369997 | ||||||||
\(941\) | 6.91322e6 | 0.254511 | 0.127255 | − | 0.991870i | \(-0.459383\pi\) | ||||
0.127255 | + | 0.991870i | \(0.459383\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.20083e7 | −0.439747 | ||||||||
\(944\) | 2.13640e7 | 0.780283 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.88022e6 | −0.0683094 | ||||||||
\(947\) | 1.67481e7 | 0.606863 | 0.303431 | − | 0.952853i | \(-0.401868\pi\) | ||||
0.303431 | + | 0.952853i | \(0.401868\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.47361e6 | 0.0531150 | ||||||||
\(950\) | −4.31658e6 | −0.155178 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.09625e7 | 0.390999 | 0.195500 | − | 0.980704i | \(-0.437367\pi\) | ||||
0.195500 | + | 0.980704i | \(0.437367\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.62434e7 | −2.35036 | ||||||||
\(956\) | 4.19138e7 | 1.48324 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.43213e6 | 0.296841 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.82302e7 | 1.33536 | ||||||||
\(962\) | −1.54844e6 | −0.0539456 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.56422e7 | 0.542132 | ||||||||
\(965\) | −5.24835e7 | −1.81428 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.98311e7 | 1.02589 | 0.512947 | − | 0.858420i | \(-0.328554\pi\) | ||||
0.512947 | + | 0.858420i | \(0.328554\pi\) | |||||||
\(968\) | 1.30149e7 | 0.446428 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.69099e7 | 0.577049 | ||||||||
\(971\) | 1.74542e7 | 0.594090 | 0.297045 | − | 0.954864i | \(-0.403999\pi\) | ||||
0.297045 | + | 0.954864i | \(0.403999\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −7.93442e6 | −0.267989 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.16906e7 | −0.728864 | ||||||||
\(977\) | −2.21922e7 | −0.743812 | −0.371906 | − | 0.928270i | \(-0.621296\pi\) | ||||
−0.371906 | + | 0.928270i | \(0.621296\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.15178e7 | −0.384071 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9.61545e6 | 0.318193 | ||||||||
\(983\) | 5.05328e7 | 1.66798 | 0.833988 | − | 0.551783i | \(-0.186052\pi\) | ||||
0.833988 | + | 0.551783i | \(0.186052\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.18127e6 | −0.137315 | ||||||||
\(986\) | 2.34382e7 | 0.767770 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.95598e6 | −0.161524 | ||||||||
\(989\) | −1.36413e7 | −0.443472 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.91699e6 | −0.256080 | −0.128040 | − | 0.991769i | \(-0.540869\pi\) | ||||
−0.128040 | + | 0.991769i | \(0.540869\pi\) | |||||||
\(992\) | 3.80484e7 | 1.22760 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.92369e7 | −0.615995 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.28160e7 | 1.04556 | 0.522778 | − | 0.852469i | \(-0.324896\pi\) | ||||
0.522778 | + | 0.852469i | \(0.324896\pi\) | |||||||
\(998\) | −2.58123e6 | −0.0820352 | ||||||||
\(999\) | 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.be.1.6 | yes | 8 | |
3.2 | odd | 2 | inner | 441.6.a.be.1.3 | ✓ | 8 | |
7.6 | odd | 2 | inner | 441.6.a.be.1.5 | yes | 8 | |
21.20 | even | 2 | inner | 441.6.a.be.1.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.6.a.be.1.3 | ✓ | 8 | 3.2 | odd | 2 | inner | |
441.6.a.be.1.4 | yes | 8 | 21.20 | even | 2 | inner | |
441.6.a.be.1.5 | yes | 8 | 7.6 | odd | 2 | inner | |
441.6.a.be.1.6 | yes | 8 | 1.1 | even | 1 | trivial |