Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [35,6,Mod(1,35)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(35, 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("35.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 35 = 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 35.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: | \(5.61343369345\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 82x^{2} + 58x + 1168 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(8.05190\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 35.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −6.05190 | −1.06984 | −0.534918 | − | 0.844904i | \(-0.679657\pi\) | ||||
−0.534918 | + | 0.844904i | \(0.679657\pi\) | |||||||
\(3\) | 15.9755 | 1.02483 | 0.512416 | − | 0.858738i | \(-0.328751\pi\) | ||||
0.512416 | + | 0.858738i | \(0.328751\pi\) | |||||||
\(4\) | 4.62555 | 0.144548 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | −96.6824 | −1.09640 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | 165.668 | 0.915193 | ||||||||
\(9\) | 12.2177 | 0.0502788 | ||||||||
\(10\) | −151.298 | −0.478445 | ||||||||
\(11\) | 708.632 | 1.76579 | 0.882894 | − | 0.469572i | \(-0.155592\pi\) | ||||
0.882894 | + | 0.469572i | \(0.155592\pi\) | |||||||
\(12\) | 73.8957 | 0.148138 | ||||||||
\(13\) | 1125.20 | 1.84659 | 0.923295 | − | 0.384091i | \(-0.125485\pi\) | ||||
0.923295 | + | 0.384091i | \(0.125485\pi\) | |||||||
\(14\) | 296.543 | 0.404360 | ||||||||
\(15\) | 399.388 | 0.458318 | ||||||||
\(16\) | −1150.62 | −1.12365 | ||||||||
\(17\) | −393.382 | −0.330135 | −0.165068 | − | 0.986282i | \(-0.552784\pi\) | ||||
−0.165068 | + | 0.986282i | \(0.552784\pi\) | |||||||
\(18\) | −73.9406 | −0.0537900 | ||||||||
\(19\) | 1790.32 | 1.13775 | 0.568874 | − | 0.822425i | \(-0.307379\pi\) | ||||
0.568874 | + | 0.822425i | \(0.307379\pi\) | |||||||
\(20\) | 115.639 | 0.0646441 | ||||||||
\(21\) | −782.801 | −0.387350 | ||||||||
\(22\) | −4288.57 | −1.88910 | ||||||||
\(23\) | −3577.80 | −1.41025 | −0.705126 | − | 0.709082i | \(-0.749110\pi\) | ||||
−0.705126 | + | 0.709082i | \(0.749110\pi\) | |||||||
\(24\) | 2646.63 | 0.937918 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −6809.59 | −1.97555 | ||||||||
\(27\) | −3686.87 | −0.973304 | ||||||||
\(28\) | −226.652 | −0.0546342 | ||||||||
\(29\) | −2.14905 | −0.000474518 0 | −0.000237259 | − | 1.00000i | \(-0.500076\pi\) | ||||
−0.000237259 | 1.00000i | \(0.500076\pi\) | ||||||||
\(30\) | −2417.06 | −0.490325 | ||||||||
\(31\) | 8773.75 | 1.63976 | 0.819881 | − | 0.572534i | \(-0.194040\pi\) | ||||
0.819881 | + | 0.572534i | \(0.194040\pi\) | |||||||
\(32\) | 1662.09 | 0.286933 | ||||||||
\(33\) | 11320.8 | 1.80964 | ||||||||
\(34\) | 2380.71 | 0.353191 | ||||||||
\(35\) | −1225.00 | −0.169031 | ||||||||
\(36\) | 56.5138 | 0.00726772 | ||||||||
\(37\) | −4361.88 | −0.523804 | −0.261902 | − | 0.965094i | \(-0.584350\pi\) | ||||
−0.261902 | + | 0.965094i | \(0.584350\pi\) | |||||||
\(38\) | −10834.8 | −1.21720 | ||||||||
\(39\) | 17975.6 | 1.89244 | ||||||||
\(40\) | 4141.69 | 0.409287 | ||||||||
\(41\) | −8413.22 | −0.781633 | −0.390816 | − | 0.920469i | \(-0.627807\pi\) | ||||
−0.390816 | + | 0.920469i | \(0.627807\pi\) | |||||||
\(42\) | 4737.44 | 0.414401 | ||||||||
\(43\) | −18110.5 | −1.49368 | −0.746842 | − | 0.665002i | \(-0.768431\pi\) | ||||
−0.746842 | + | 0.665002i | \(0.768431\pi\) | |||||||
\(44\) | 3277.81 | 0.255242 | ||||||||
\(45\) | 305.443 | 0.0224853 | ||||||||
\(46\) | 21652.5 | 1.50874 | ||||||||
\(47\) | 8209.65 | 0.542101 | 0.271050 | − | 0.962565i | \(-0.412629\pi\) | ||||
0.271050 | + | 0.962565i | \(0.412629\pi\) | |||||||
\(48\) | −18381.8 | −1.15156 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | −3782.44 | −0.213967 | ||||||||
\(51\) | −6284.49 | −0.338333 | ||||||||
\(52\) | 5204.66 | 0.266922 | ||||||||
\(53\) | −14352.5 | −0.701837 | −0.350919 | − | 0.936406i | \(-0.614131\pi\) | ||||
−0.350919 | + | 0.936406i | \(0.614131\pi\) | |||||||
\(54\) | 22312.6 | 1.04128 | ||||||||
\(55\) | 17715.8 | 0.789685 | ||||||||
\(56\) | −8117.71 | −0.345910 | ||||||||
\(57\) | 28601.3 | 1.16600 | ||||||||
\(58\) | 13.0059 | 0.000507656 0 | ||||||||
\(59\) | −10197.8 | −0.381398 | −0.190699 | − | 0.981649i | \(-0.561075\pi\) | ||||
−0.190699 | + | 0.981649i | \(0.561075\pi\) | |||||||
\(60\) | 1847.39 | 0.0662492 | ||||||||
\(61\) | −2878.09 | −0.0990331 | −0.0495165 | − | 0.998773i | \(-0.515768\pi\) | ||||
−0.0495165 | + | 0.998773i | \(0.515768\pi\) | |||||||
\(62\) | −53097.9 | −1.75428 | ||||||||
\(63\) | −598.669 | −0.0190036 | ||||||||
\(64\) | 26761.1 | 0.816683 | ||||||||
\(65\) | 28130.0 | 0.825821 | ||||||||
\(66\) | −68512.2 | −1.93601 | ||||||||
\(67\) | 37314.1 | 1.01551 | 0.507757 | − | 0.861500i | \(-0.330475\pi\) | ||||
0.507757 | + | 0.861500i | \(0.330475\pi\) | |||||||
\(68\) | −1819.61 | −0.0477206 | ||||||||
\(69\) | −57157.3 | −1.44527 | ||||||||
\(70\) | 7413.58 | 0.180835 | ||||||||
\(71\) | −3259.60 | −0.0767393 | −0.0383697 | − | 0.999264i | \(-0.512216\pi\) | ||||
−0.0383697 | + | 0.999264i | \(0.512216\pi\) | |||||||
\(72\) | 2024.08 | 0.0460148 | ||||||||
\(73\) | 6122.54 | 0.134470 | 0.0672348 | − | 0.997737i | \(-0.478582\pi\) | ||||
0.0672348 | + | 0.997737i | \(0.478582\pi\) | |||||||
\(74\) | 26397.7 | 0.560385 | ||||||||
\(75\) | 9984.71 | 0.204966 | ||||||||
\(76\) | 8281.20 | 0.164460 | ||||||||
\(77\) | −34722.9 | −0.667405 | ||||||||
\(78\) | −108787. | −2.02460 | ||||||||
\(79\) | 7549.78 | 0.136103 | 0.0680514 | − | 0.997682i | \(-0.478322\pi\) | ||||
0.0680514 | + | 0.997682i | \(0.478322\pi\) | |||||||
\(80\) | −28765.5 | −0.502513 | ||||||||
\(81\) | −61868.6 | −1.04775 | ||||||||
\(82\) | 50916.0 | 0.836219 | ||||||||
\(83\) | 1977.20 | 0.0315032 | 0.0157516 | − | 0.999876i | \(-0.494986\pi\) | ||||
0.0157516 | + | 0.999876i | \(0.494986\pi\) | |||||||
\(84\) | −3620.89 | −0.0559908 | ||||||||
\(85\) | −9834.55 | −0.147641 | ||||||||
\(86\) | 109603. | 1.59800 | ||||||||
\(87\) | −34.3323 | −0.000486301 0 | ||||||||
\(88\) | 117397. | 1.61604 | ||||||||
\(89\) | −46820.1 | −0.626553 | −0.313276 | − | 0.949662i | \(-0.601427\pi\) | ||||
−0.313276 | + | 0.949662i | \(0.601427\pi\) | |||||||
\(90\) | −1848.51 | −0.0240556 | ||||||||
\(91\) | −55134.7 | −0.697946 | ||||||||
\(92\) | −16549.3 | −0.203850 | ||||||||
\(93\) | 140165. | 1.68048 | ||||||||
\(94\) | −49684.0 | −0.579959 | ||||||||
\(95\) | 44757.9 | 0.508816 | ||||||||
\(96\) | 26552.8 | 0.294058 | ||||||||
\(97\) | 19767.0 | 0.213310 | 0.106655 | − | 0.994296i | \(-0.465986\pi\) | ||||
0.106655 | + | 0.994296i | \(0.465986\pi\) | |||||||
\(98\) | −14530.6 | −0.152834 | ||||||||
\(99\) | 8657.88 | 0.0887817 | ||||||||
\(100\) | 2890.97 | 0.0289097 | ||||||||
\(101\) | 30849.4 | 0.300915 | 0.150458 | − | 0.988616i | \(-0.451925\pi\) | ||||
0.150458 | + | 0.988616i | \(0.451925\pi\) | |||||||
\(102\) | 38033.1 | 0.361961 | ||||||||
\(103\) | −61864.8 | −0.574580 | −0.287290 | − | 0.957844i | \(-0.592754\pi\) | ||||
−0.287290 | + | 0.957844i | \(0.592754\pi\) | |||||||
\(104\) | 186409. | 1.68999 | ||||||||
\(105\) | −19570.0 | −0.173228 | ||||||||
\(106\) | 86859.7 | 0.750851 | ||||||||
\(107\) | −172017. | −1.45249 | −0.726244 | − | 0.687437i | \(-0.758736\pi\) | ||||
−0.726244 | + | 0.687437i | \(0.758736\pi\) | |||||||
\(108\) | −17053.8 | −0.140690 | ||||||||
\(109\) | 155361. | 1.25249 | 0.626246 | − | 0.779625i | \(-0.284590\pi\) | ||||
0.626246 | + | 0.779625i | \(0.284590\pi\) | |||||||
\(110\) | −107214. | −0.844833 | ||||||||
\(111\) | −69683.3 | −0.536811 | ||||||||
\(112\) | 56380.5 | 0.424701 | ||||||||
\(113\) | 83885.7 | 0.618005 | 0.309002 | − | 0.951061i | \(-0.400005\pi\) | ||||
0.309002 | + | 0.951061i | \(0.400005\pi\) | |||||||
\(114\) | −173092. | −1.24743 | ||||||||
\(115\) | −89445.1 | −0.630684 | ||||||||
\(116\) | −9.94056 | −6.85908e−5 0 | ||||||||
\(117\) | 13747.4 | 0.0928443 | ||||||||
\(118\) | 61716.4 | 0.408033 | ||||||||
\(119\) | 19275.7 | 0.124779 | ||||||||
\(120\) | 66165.7 | 0.419450 | ||||||||
\(121\) | 341108. | 2.11801 | ||||||||
\(122\) | 17417.9 | 0.105949 | ||||||||
\(123\) | −134406. | −0.801042 | ||||||||
\(124\) | 40583.4 | 0.237025 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 3623.09 | 0.0203307 | ||||||||
\(127\) | −340623. | −1.87398 | −0.936988 | − | 0.349361i | \(-0.886399\pi\) | ||||
−0.936988 | + | 0.349361i | \(0.886399\pi\) | |||||||
\(128\) | −215142. | −1.16065 | ||||||||
\(129\) | −289325. | −1.53077 | ||||||||
\(130\) | −170240. | −0.883492 | ||||||||
\(131\) | −145084. | −0.738652 | −0.369326 | − | 0.929300i | \(-0.620411\pi\) | ||||
−0.369326 | + | 0.929300i | \(0.620411\pi\) | |||||||
\(132\) | 52364.8 | 0.261580 | ||||||||
\(133\) | −87725.5 | −0.430028 | ||||||||
\(134\) | −225821. | −1.08643 | ||||||||
\(135\) | −92171.8 | −0.435275 | ||||||||
\(136\) | −65170.6 | −0.302137 | ||||||||
\(137\) | −56539.2 | −0.257364 | −0.128682 | − | 0.991686i | \(-0.541075\pi\) | ||||
−0.128682 | + | 0.991686i | \(0.541075\pi\) | |||||||
\(138\) | 345911. | 1.54620 | ||||||||
\(139\) | −285472. | −1.25322 | −0.626610 | − | 0.779333i | \(-0.715558\pi\) | ||||
−0.626610 | + | 0.779333i | \(0.715558\pi\) | |||||||
\(140\) | −5666.30 | −0.0244332 | ||||||||
\(141\) | 131154. | 0.555562 | ||||||||
\(142\) | 19726.8 | 0.0820985 | ||||||||
\(143\) | 797351. | 3.26069 | ||||||||
\(144\) | −14058.0 | −0.0564959 | ||||||||
\(145\) | −53.7264 | −0.000212211 0 | ||||||||
\(146\) | −37053.0 | −0.143860 | ||||||||
\(147\) | 38357.3 | 0.146404 | ||||||||
\(148\) | −20176.1 | −0.0757152 | ||||||||
\(149\) | −216259. | −0.798012 | −0.399006 | − | 0.916948i | \(-0.630645\pi\) | ||||
−0.399006 | + | 0.916948i | \(0.630645\pi\) | |||||||
\(150\) | −60426.5 | −0.219280 | ||||||||
\(151\) | −153200. | −0.546784 | −0.273392 | − | 0.961903i | \(-0.588146\pi\) | ||||
−0.273392 | + | 0.961903i | \(0.588146\pi\) | |||||||
\(152\) | 296597. | 1.04126 | ||||||||
\(153\) | −4806.24 | −0.0165988 | ||||||||
\(154\) | 210140. | 0.714014 | ||||||||
\(155\) | 219344. | 0.733324 | ||||||||
\(156\) | 83147.3 | 0.273550 | ||||||||
\(157\) | 375178. | 1.21475 | 0.607377 | − | 0.794413i | \(-0.292222\pi\) | ||||
0.607377 | + | 0.794413i | \(0.292222\pi\) | |||||||
\(158\) | −45690.6 | −0.145608 | ||||||||
\(159\) | −229288. | −0.719265 | ||||||||
\(160\) | 41552.3 | 0.128320 | ||||||||
\(161\) | 175312. | 0.533025 | ||||||||
\(162\) | 374423. | 1.12092 | ||||||||
\(163\) | −102281. | −0.301527 | −0.150764 | − | 0.988570i | \(-0.548173\pi\) | ||||
−0.150764 | + | 0.988570i | \(0.548173\pi\) | |||||||
\(164\) | −38915.8 | −0.112984 | ||||||||
\(165\) | 283019. | 0.809293 | ||||||||
\(166\) | −11965.8 | −0.0337033 | ||||||||
\(167\) | −397953. | −1.10418 | −0.552091 | − | 0.833784i | \(-0.686170\pi\) | ||||
−0.552091 | + | 0.833784i | \(0.686170\pi\) | |||||||
\(168\) | −129685. | −0.354500 | ||||||||
\(169\) | 894778. | 2.40990 | ||||||||
\(170\) | 59517.7 | 0.157952 | ||||||||
\(171\) | 21873.6 | 0.0572046 | ||||||||
\(172\) | −83770.9 | −0.215910 | ||||||||
\(173\) | −126162. | −0.320488 | −0.160244 | − | 0.987077i | \(-0.551228\pi\) | ||||
−0.160244 | + | 0.987077i | \(0.551228\pi\) | |||||||
\(174\) | 207.776 | 0.000520262 0 | ||||||||
\(175\) | −30625.0 | −0.0755929 | ||||||||
\(176\) | −815367. | −1.98414 | ||||||||
\(177\) | −162916. | −0.390869 | ||||||||
\(178\) | 283351. | 0.670308 | ||||||||
\(179\) | −399204. | −0.931242 | −0.465621 | − | 0.884984i | \(-0.654169\pi\) | ||||
−0.465621 | + | 0.884984i | \(0.654169\pi\) | |||||||
\(180\) | 1412.84 | 0.00325022 | ||||||||
\(181\) | 409529. | 0.929156 | 0.464578 | − | 0.885532i | \(-0.346206\pi\) | ||||
0.464578 | + | 0.885532i | \(0.346206\pi\) | |||||||
\(182\) | 333670. | 0.746687 | ||||||||
\(183\) | −45979.1 | −0.101492 | ||||||||
\(184\) | −592726. | −1.29065 | ||||||||
\(185\) | −109047. | −0.234252 | ||||||||
\(186\) | −848267. | −1.79784 | ||||||||
\(187\) | −278763. | −0.582949 | ||||||||
\(188\) | 37974.2 | 0.0783598 | ||||||||
\(189\) | 180657. | 0.367874 | ||||||||
\(190\) | −270871. | −0.544350 | ||||||||
\(191\) | 491227. | 0.974313 | 0.487156 | − | 0.873315i | \(-0.338034\pi\) | ||||
0.487156 | + | 0.873315i | \(0.338034\pi\) | |||||||
\(192\) | 427523. | 0.836962 | ||||||||
\(193\) | −479243. | −0.926110 | −0.463055 | − | 0.886330i | \(-0.653247\pi\) | ||||
−0.463055 | + | 0.886330i | \(0.653247\pi\) | |||||||
\(194\) | −119628. | −0.228207 | ||||||||
\(195\) | 449391. | 0.846327 | ||||||||
\(196\) | 11105.9 | 0.0206498 | ||||||||
\(197\) | 364897. | 0.669892 | 0.334946 | − | 0.942237i | \(-0.391282\pi\) | ||||
0.334946 | + | 0.942237i | \(0.391282\pi\) | |||||||
\(198\) | −52396.6 | −0.0949818 | ||||||||
\(199\) | −556031. | −0.995329 | −0.497664 | − | 0.867370i | \(-0.665809\pi\) | ||||
−0.497664 | + | 0.867370i | \(0.665809\pi\) | |||||||
\(200\) | 103542. | 0.183039 | ||||||||
\(201\) | 596113. | 1.04073 | ||||||||
\(202\) | −186698. | −0.321930 | ||||||||
\(203\) | 105.304 | 0.000179351 0 | ||||||||
\(204\) | −29069.2 | −0.0489055 | ||||||||
\(205\) | −210331. | −0.349557 | ||||||||
\(206\) | 374400. | 0.614706 | ||||||||
\(207\) | −43712.7 | −0.0709058 | ||||||||
\(208\) | −1.29468e6 | −2.07493 | ||||||||
\(209\) | 1.26868e6 | 2.00902 | ||||||||
\(210\) | 118436. | 0.185326 | ||||||||
\(211\) | 550443. | 0.851150 | 0.425575 | − | 0.904923i | \(-0.360072\pi\) | ||||
0.425575 | + | 0.904923i | \(0.360072\pi\) | |||||||
\(212\) | −66388.0 | −0.101450 | ||||||||
\(213\) | −52073.8 | −0.0786448 | ||||||||
\(214\) | 1.04103e6 | 1.55392 | ||||||||
\(215\) | −452762. | −0.667996 | ||||||||
\(216\) | −610795. | −0.890760 | ||||||||
\(217\) | −429914. | −0.619772 | ||||||||
\(218\) | −940229. | −1.33996 | ||||||||
\(219\) | 97810.8 | 0.137809 | ||||||||
\(220\) | 81945.3 | 0.114148 | ||||||||
\(221\) | −442633. | −0.609625 | ||||||||
\(222\) | 421717. | 0.574300 | ||||||||
\(223\) | 457765. | 0.616425 | 0.308212 | − | 0.951318i | \(-0.400269\pi\) | ||||
0.308212 | + | 0.951318i | \(0.400269\pi\) | |||||||
\(224\) | −81442.5 | −0.108450 | ||||||||
\(225\) | 7636.09 | 0.0100558 | ||||||||
\(226\) | −507668. | −0.661163 | ||||||||
\(227\) | −1.26171e6 | −1.62515 | −0.812575 | − | 0.582857i | \(-0.801935\pi\) | ||||
−0.812575 | + | 0.582857i | \(0.801935\pi\) | |||||||
\(228\) | 132297. | 0.168543 | ||||||||
\(229\) | −37076.2 | −0.0467204 | −0.0233602 | − | 0.999727i | \(-0.507436\pi\) | ||||
−0.0233602 | + | 0.999727i | \(0.507436\pi\) | |||||||
\(230\) | 541313. | 0.674728 | ||||||||
\(231\) | −554718. | −0.683978 | ||||||||
\(232\) | −356.029 | −0.000434275 0 | ||||||||
\(233\) | −101982. | −0.123065 | −0.0615325 | − | 0.998105i | \(-0.519599\pi\) | ||||
−0.0615325 | + | 0.998105i | \(0.519599\pi\) | |||||||
\(234\) | −83197.8 | −0.0993282 | ||||||||
\(235\) | 205241. | 0.242435 | ||||||||
\(236\) | −47170.7 | −0.0551305 | ||||||||
\(237\) | 120612. | 0.139482 | ||||||||
\(238\) | −116655. | −0.133494 | ||||||||
\(239\) | 1.26398e6 | 1.43134 | 0.715672 | − | 0.698437i | \(-0.246121\pi\) | ||||
0.715672 | + | 0.698437i | \(0.246121\pi\) | |||||||
\(240\) | −459545. | −0.514991 | ||||||||
\(241\) | 221950. | 0.246158 | 0.123079 | − | 0.992397i | \(-0.460723\pi\) | ||||
0.123079 | + | 0.992397i | \(0.460723\pi\) | |||||||
\(242\) | −2.06435e6 | −2.26592 | ||||||||
\(243\) | −92475.2 | −0.100464 | ||||||||
\(244\) | −13312.8 | −0.0143151 | ||||||||
\(245\) | 60025.0 | 0.0638877 | ||||||||
\(246\) | 813411. | 0.856983 | ||||||||
\(247\) | 2.01446e6 | 2.10095 | ||||||||
\(248\) | 1.45353e6 | 1.50070 | ||||||||
\(249\) | 31586.8 | 0.0322855 | ||||||||
\(250\) | −94561.0 | −0.0956890 | ||||||||
\(251\) | −513389. | −0.514354 | −0.257177 | − | 0.966364i | \(-0.582792\pi\) | ||||
−0.257177 | + | 0.966364i | \(0.582792\pi\) | |||||||
\(252\) | −2769.18 | −0.00274694 | ||||||||
\(253\) | −2.53534e6 | −2.49021 | ||||||||
\(254\) | 2.06142e6 | 2.00485 | ||||||||
\(255\) | −157112. | −0.151307 | ||||||||
\(256\) | 445667. | 0.425021 | ||||||||
\(257\) | −1.37745e6 | −1.30090 | −0.650450 | − | 0.759549i | \(-0.725420\pi\) | ||||
−0.650450 | + | 0.759549i | \(0.725420\pi\) | |||||||
\(258\) | 1.75096e6 | 1.63768 | ||||||||
\(259\) | 213732. | 0.197979 | ||||||||
\(260\) | 130117. | 0.119371 | ||||||||
\(261\) | −26.2566 | −2.38582e−5 0 | ||||||||
\(262\) | 878032. | 0.790236 | ||||||||
\(263\) | 112502. | 0.100293 | 0.0501465 | − | 0.998742i | \(-0.484031\pi\) | ||||
0.0501465 | + | 0.998742i | \(0.484031\pi\) | |||||||
\(264\) | 1.87548e6 | 1.65616 | ||||||||
\(265\) | −358811. | −0.313871 | ||||||||
\(266\) | 530907. | 0.460060 | ||||||||
\(267\) | −747977. | −0.642111 | ||||||||
\(268\) | 172598. | 0.146791 | ||||||||
\(269\) | −858748. | −0.723577 | −0.361789 | − | 0.932260i | \(-0.617834\pi\) | ||||
−0.361789 | + | 0.932260i | \(0.617834\pi\) | |||||||
\(270\) | 557815. | 0.465672 | ||||||||
\(271\) | −312828. | −0.258751 | −0.129376 | − | 0.991596i | \(-0.541297\pi\) | ||||
−0.129376 | + | 0.991596i | \(0.541297\pi\) | |||||||
\(272\) | 452634. | 0.370958 | ||||||||
\(273\) | −880807. | −0.715276 | ||||||||
\(274\) | 342170. | 0.275338 | ||||||||
\(275\) | 442895. | 0.353158 | ||||||||
\(276\) | −264384. | −0.208912 | ||||||||
\(277\) | 1.08259e6 | 0.847743 | 0.423871 | − | 0.905722i | \(-0.360671\pi\) | ||||
0.423871 | + | 0.905722i | \(0.360671\pi\) | |||||||
\(278\) | 1.72765e6 | 1.34074 | ||||||||
\(279\) | 107195. | 0.0824452 | ||||||||
\(280\) | −202943. | −0.154696 | ||||||||
\(281\) | 1.82814e6 | 1.38116 | 0.690580 | − | 0.723256i | \(-0.257355\pi\) | ||||
0.690580 | + | 0.723256i | \(0.257355\pi\) | |||||||
\(282\) | −793729. | −0.594360 | ||||||||
\(283\) | −1.89318e6 | −1.40516 | −0.702581 | − | 0.711604i | \(-0.747969\pi\) | ||||
−0.702581 | + | 0.711604i | \(0.747969\pi\) | |||||||
\(284\) | −15077.4 | −0.0110926 | ||||||||
\(285\) | 715032. | 0.521451 | ||||||||
\(286\) | −4.82549e6 | −3.48840 | ||||||||
\(287\) | 412248. | 0.295429 | ||||||||
\(288\) | 20307.0 | 0.0144266 | ||||||||
\(289\) | −1.26511e6 | −0.891011 | ||||||||
\(290\) | 325.147 | 0.000227031 0 | ||||||||
\(291\) | 315788. | 0.218607 | ||||||||
\(292\) | 28320.1 | 0.0194374 | ||||||||
\(293\) | 1.82034e6 | 1.23875 | 0.619374 | − | 0.785096i | \(-0.287386\pi\) | ||||
0.619374 | + | 0.785096i | \(0.287386\pi\) | |||||||
\(294\) | −232134. | −0.156629 | ||||||||
\(295\) | −254946. | −0.170566 | ||||||||
\(296\) | −722622. | −0.479382 | ||||||||
\(297\) | −2.61263e6 | −1.71865 | ||||||||
\(298\) | 1.30878e6 | 0.853741 | ||||||||
\(299\) | −4.02574e6 | −2.60416 | ||||||||
\(300\) | 46184.8 | 0.0296276 | ||||||||
\(301\) | 887413. | 0.564559 | ||||||||
\(302\) | 927150. | 0.584969 | ||||||||
\(303\) | 492836. | 0.308387 | ||||||||
\(304\) | −2.05998e6 | −1.27844 | ||||||||
\(305\) | −71952.3 | −0.0442889 | ||||||||
\(306\) | 29086.9 | 0.0177580 | ||||||||
\(307\) | −2.24274e6 | −1.35811 | −0.679053 | − | 0.734089i | \(-0.737609\pi\) | ||||
−0.679053 | + | 0.734089i | \(0.737609\pi\) | |||||||
\(308\) | −160613. | −0.0964724 | ||||||||
\(309\) | −988323. | −0.588848 | ||||||||
\(310\) | −1.32745e6 | −0.784536 | ||||||||
\(311\) | 1.09627e6 | 0.642715 | 0.321358 | − | 0.946958i | \(-0.395861\pi\) | ||||
0.321358 | + | 0.946958i | \(0.395861\pi\) | |||||||
\(312\) | 2.97798e6 | 1.73195 | ||||||||
\(313\) | 216576. | 0.124954 | 0.0624768 | − | 0.998046i | \(-0.480100\pi\) | ||||
0.0624768 | + | 0.998046i | \(0.480100\pi\) | |||||||
\(314\) | −2.27054e6 | −1.29959 | ||||||||
\(315\) | −14966.7 | −0.00849866 | ||||||||
\(316\) | 34921.9 | 0.0196734 | ||||||||
\(317\) | 2.51114e6 | 1.40353 | 0.701767 | − | 0.712407i | \(-0.252395\pi\) | ||||
0.701767 | + | 0.712407i | \(0.252395\pi\) | |||||||
\(318\) | 1.38763e6 | 0.769495 | ||||||||
\(319\) | −1522.89 | −0.000837898 0 | ||||||||
\(320\) | 669027. | 0.365232 | ||||||||
\(321\) | −2.74807e6 | −1.48855 | ||||||||
\(322\) | −1.06097e6 | −0.570250 | ||||||||
\(323\) | −704278. | −0.375611 | ||||||||
\(324\) | −286177. | −0.151451 | ||||||||
\(325\) | 703249. | 0.369318 | ||||||||
\(326\) | 618996. | 0.322585 | ||||||||
\(327\) | 2.48197e6 | 1.28359 | ||||||||
\(328\) | −1.39380e6 | −0.715345 | ||||||||
\(329\) | −402273. | −0.204895 | ||||||||
\(330\) | −1.71281e6 | −0.865811 | ||||||||
\(331\) | 3.25575e6 | 1.63336 | 0.816678 | − | 0.577094i | \(-0.195813\pi\) | ||||
0.816678 | + | 0.577094i | \(0.195813\pi\) | |||||||
\(332\) | 9145.63 | 0.00455374 | ||||||||
\(333\) | −53292.3 | −0.0263362 | ||||||||
\(334\) | 2.40837e6 | 1.18129 | ||||||||
\(335\) | 932852. | 0.454152 | ||||||||
\(336\) | 900708. | 0.435247 | ||||||||
\(337\) | 1.94506e6 | 0.932951 | 0.466475 | − | 0.884534i | \(-0.345524\pi\) | ||||
0.466475 | + | 0.884534i | \(0.345524\pi\) | |||||||
\(338\) | −5.41511e6 | −2.57819 | ||||||||
\(339\) | 1.34012e6 | 0.633350 | ||||||||
\(340\) | −45490.2 | −0.0213413 | ||||||||
\(341\) | 6.21735e6 | 2.89547 | ||||||||
\(342\) | −132377. | −0.0611995 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | −3.00032e6 | −1.36701 | ||||||||
\(345\) | −1.42893e6 | −0.646345 | ||||||||
\(346\) | 763518. | 0.342870 | ||||||||
\(347\) | −474653. | −0.211618 | −0.105809 | − | 0.994386i | \(-0.533743\pi\) | ||||
−0.105809 | + | 0.994386i | \(0.533743\pi\) | |||||||
\(348\) | −158.806 | −7.02940e−5 0 | ||||||||
\(349\) | 137677. | 0.0605059 | 0.0302530 | − | 0.999542i | \(-0.490369\pi\) | ||||
0.0302530 | + | 0.999542i | \(0.490369\pi\) | |||||||
\(350\) | 185340. | 0.0808720 | ||||||||
\(351\) | −4.14846e6 | −1.79729 | ||||||||
\(352\) | 1.17781e6 | 0.506663 | ||||||||
\(353\) | −406419. | −0.173595 | −0.0867975 | − | 0.996226i | \(-0.527663\pi\) | ||||
−0.0867975 | + | 0.996226i | \(0.527663\pi\) | |||||||
\(354\) | 985952. | 0.418165 | ||||||||
\(355\) | −81489.9 | −0.0343189 | ||||||||
\(356\) | −216569. | −0.0905672 | ||||||||
\(357\) | 307940. | 0.127878 | ||||||||
\(358\) | 2.41594e6 | 0.996275 | ||||||||
\(359\) | 95290.6 | 0.0390224 | 0.0195112 | − | 0.999810i | \(-0.493789\pi\) | ||||
0.0195112 | + | 0.999810i | \(0.493789\pi\) | |||||||
\(360\) | 50602.1 | 0.0205784 | ||||||||
\(361\) | 729137. | 0.294470 | ||||||||
\(362\) | −2.47843e6 | −0.994044 | ||||||||
\(363\) | 5.44938e6 | 2.17060 | ||||||||
\(364\) | −255028. | −0.100887 | ||||||||
\(365\) | 153063. | 0.0601366 | ||||||||
\(366\) | 278261. | 0.108580 | ||||||||
\(367\) | 3.53302e6 | 1.36924 | 0.684622 | − | 0.728898i | \(-0.259967\pi\) | ||||
0.684622 | + | 0.728898i | \(0.259967\pi\) | |||||||
\(368\) | 4.11670e6 | 1.58464 | ||||||||
\(369\) | −102791. | −0.0392995 | ||||||||
\(370\) | 659942. | 0.250612 | ||||||||
\(371\) | 703270. | 0.265270 | ||||||||
\(372\) | 648342. | 0.242911 | ||||||||
\(373\) | −367500. | −0.136768 | −0.0683842 | − | 0.997659i | \(-0.521784\pi\) | ||||
−0.0683842 | + | 0.997659i | \(0.521784\pi\) | |||||||
\(374\) | 1.68705e6 | 0.623660 | ||||||||
\(375\) | 249618. | 0.0916637 | ||||||||
\(376\) | 1.36007e6 | 0.496127 | ||||||||
\(377\) | −2418.11 | −0.000876240 0 | ||||||||
\(378\) | −1.09332e6 | −0.393565 | ||||||||
\(379\) | 601916. | 0.215247 | 0.107624 | − | 0.994192i | \(-0.465676\pi\) | ||||
0.107624 | + | 0.994192i | \(0.465676\pi\) | |||||||
\(380\) | 207030. | 0.0735486 | ||||||||
\(381\) | −5.44163e6 | −1.92051 | ||||||||
\(382\) | −2.97286e6 | −1.04235 | ||||||||
\(383\) | −3.09685e6 | −1.07875 | −0.539377 | − | 0.842064i | \(-0.681340\pi\) | ||||
−0.539377 | + | 0.842064i | \(0.681340\pi\) | |||||||
\(384\) | −3.43702e6 | −1.18947 | ||||||||
\(385\) | −868074. | −0.298473 | ||||||||
\(386\) | 2.90033e6 | 0.990786 | ||||||||
\(387\) | −221269. | −0.0751006 | ||||||||
\(388\) | 91433.2 | 0.0308336 | ||||||||
\(389\) | −3.34374e6 | −1.12036 | −0.560181 | − | 0.828370i | \(-0.689269\pi\) | ||||
−0.560181 | + | 0.828370i | \(0.689269\pi\) | |||||||
\(390\) | −2.71967e6 | −0.905430 | ||||||||
\(391\) | 1.40744e6 | 0.465574 | ||||||||
\(392\) | 397768. | 0.130742 | ||||||||
\(393\) | −2.31779e6 | −0.756994 | ||||||||
\(394\) | −2.20832e6 | −0.716674 | ||||||||
\(395\) | 188745. | 0.0608670 | ||||||||
\(396\) | 40047.5 | 0.0128333 | ||||||||
\(397\) | 1.30101e6 | 0.414291 | 0.207146 | − | 0.978310i | \(-0.433583\pi\) | ||||
0.207146 | + | 0.978310i | \(0.433583\pi\) | |||||||
\(398\) | 3.36505e6 | 1.06484 | ||||||||
\(399\) | −1.40146e6 | −0.440706 | ||||||||
\(400\) | −719139. | −0.224731 | ||||||||
\(401\) | −3.95826e6 | −1.22926 | −0.614630 | − | 0.788816i | \(-0.710695\pi\) | ||||
−0.614630 | + | 0.788816i | \(0.710695\pi\) | |||||||
\(402\) | −3.60762e6 | −1.11341 | ||||||||
\(403\) | 9.87220e6 | 3.02797 | ||||||||
\(404\) | 142696. | 0.0434968 | ||||||||
\(405\) | −1.54672e6 | −0.468568 | ||||||||
\(406\) | −637.288 | −0.000191876 0 | ||||||||
\(407\) | −3.09096e6 | −0.924928 | ||||||||
\(408\) | −1.04114e6 | −0.309640 | ||||||||
\(409\) | 2.57625e6 | 0.761516 | 0.380758 | − | 0.924675i | \(-0.375663\pi\) | ||||
0.380758 | + | 0.924675i | \(0.375663\pi\) | |||||||
\(410\) | 1.27290e6 | 0.373968 | ||||||||
\(411\) | −903245. | −0.263755 | ||||||||
\(412\) | −286159. | −0.0830547 | ||||||||
\(413\) | 499694. | 0.144155 | ||||||||
\(414\) | 264545. | 0.0758575 | ||||||||
\(415\) | 49430.0 | 0.0140887 | ||||||||
\(416\) | 1.87018e6 | 0.529848 | ||||||||
\(417\) | −4.56058e6 | −1.28434 | ||||||||
\(418\) | −7.67790e6 | −2.14932 | ||||||||
\(419\) | −1.45659e6 | −0.405324 | −0.202662 | − | 0.979249i | \(-0.564959\pi\) | ||||
−0.202662 | + | 0.979249i | \(0.564959\pi\) | |||||||
\(420\) | −90522.2 | −0.0250399 | ||||||||
\(421\) | 1.97451e6 | 0.542944 | 0.271472 | − | 0.962446i | \(-0.412490\pi\) | ||||
0.271472 | + | 0.962446i | \(0.412490\pi\) | |||||||
\(422\) | −3.33123e6 | −0.910591 | ||||||||
\(423\) | 100303. | 0.0272562 | ||||||||
\(424\) | −2.37774e6 | −0.642316 | ||||||||
\(425\) | −245864. | −0.0660271 | ||||||||
\(426\) | 315146. | 0.0841370 | ||||||||
\(427\) | 141027. | 0.0374310 | ||||||||
\(428\) | −795674. | −0.209955 | ||||||||
\(429\) | 1.27381e7 | 3.34166 | ||||||||
\(430\) | 2.74007e6 | 0.714646 | ||||||||
\(431\) | −7.36508e6 | −1.90978 | −0.954892 | − | 0.296955i | \(-0.904029\pi\) | ||||
−0.954892 | + | 0.296955i | \(0.904029\pi\) | |||||||
\(432\) | 4.24219e6 | 1.09366 | ||||||||
\(433\) | 3.17734e6 | 0.814411 | 0.407205 | − | 0.913337i | \(-0.366503\pi\) | ||||
0.407205 | + | 0.913337i | \(0.366503\pi\) | |||||||
\(434\) | 2.60180e6 | 0.663054 | ||||||||
\(435\) | −858.308 | −0.000217480 0 | ||||||||
\(436\) | 718630. | 0.181046 | ||||||||
\(437\) | −6.40540e6 | −1.60451 | ||||||||
\(438\) | −591942. | −0.147433 | ||||||||
\(439\) | 2.27765e6 | 0.564061 | 0.282030 | − | 0.959405i | \(-0.408992\pi\) | ||||
0.282030 | + | 0.959405i | \(0.408992\pi\) | |||||||
\(440\) | 2.93493e6 | 0.722714 | ||||||||
\(441\) | 29334.8 | 0.00718268 | ||||||||
\(442\) | 2.67877e6 | 0.652199 | ||||||||
\(443\) | 201316. | 0.0487380 | 0.0243690 | − | 0.999703i | \(-0.492242\pi\) | ||||
0.0243690 | + | 0.999703i | \(0.492242\pi\) | |||||||
\(444\) | −322324. | −0.0775952 | ||||||||
\(445\) | −1.17050e6 | −0.280203 | ||||||||
\(446\) | −2.77035e6 | −0.659473 | ||||||||
\(447\) | −3.45486e6 | −0.817827 | ||||||||
\(448\) | −1.31129e6 | −0.308677 | ||||||||
\(449\) | −1.93977e6 | −0.454082 | −0.227041 | − | 0.973885i | \(-0.572905\pi\) | ||||
−0.227041 | + | 0.973885i | \(0.572905\pi\) | |||||||
\(450\) | −46212.9 | −0.0107580 | ||||||||
\(451\) | −5.96188e6 | −1.38020 | ||||||||
\(452\) | 388018. | 0.0893316 | ||||||||
\(453\) | −2.44745e6 | −0.560361 | ||||||||
\(454\) | 7.63572e6 | 1.73864 | ||||||||
\(455\) | −1.37837e6 | −0.312131 | ||||||||
\(456\) | 4.73830e6 | 1.06711 | ||||||||
\(457\) | 5.78748e6 | 1.29628 | 0.648140 | − | 0.761521i | \(-0.275547\pi\) | ||||
0.648140 | + | 0.761521i | \(0.275547\pi\) | |||||||
\(458\) | 224382. | 0.0499832 | ||||||||
\(459\) | 1.45035e6 | 0.321322 | ||||||||
\(460\) | −413733. | −0.0911644 | ||||||||
\(461\) | 1.96920e6 | 0.431556 | 0.215778 | − | 0.976442i | \(-0.430771\pi\) | ||||
0.215778 | + | 0.976442i | \(0.430771\pi\) | |||||||
\(462\) | 3.35710e6 | 0.731744 | ||||||||
\(463\) | 5.43903e6 | 1.17915 | 0.589575 | − | 0.807713i | \(-0.299295\pi\) | ||||
0.589575 | + | 0.807713i | \(0.299295\pi\) | |||||||
\(464\) | 2472.75 | 0.000533194 0 | ||||||||
\(465\) | 3.50413e6 | 0.751533 | ||||||||
\(466\) | 617187. | 0.131659 | ||||||||
\(467\) | −1.77123e6 | −0.375823 | −0.187911 | − | 0.982186i | \(-0.560172\pi\) | ||||
−0.187911 | + | 0.982186i | \(0.560172\pi\) | |||||||
\(468\) | 63589.2 | 0.0134205 | ||||||||
\(469\) | −1.82839e6 | −0.383828 | ||||||||
\(470\) | −1.24210e6 | −0.259365 | ||||||||
\(471\) | 5.99367e6 | 1.24492 | ||||||||
\(472\) | −1.68945e6 | −0.349053 | ||||||||
\(473\) | −1.28337e7 | −2.63753 | ||||||||
\(474\) | −729931. | −0.149223 | ||||||||
\(475\) | 1.11895e6 | 0.227550 | ||||||||
\(476\) | 89160.8 | 0.0180367 | ||||||||
\(477\) | −175355. | −0.0352875 | ||||||||
\(478\) | −7.64946e6 | −1.53130 | ||||||||
\(479\) | 9.35974e6 | 1.86391 | 0.931955 | − | 0.362575i | \(-0.118102\pi\) | ||||
0.931955 | + | 0.362575i | \(0.118102\pi\) | |||||||
\(480\) | 663821. | 0.131507 | ||||||||
\(481\) | −4.90798e6 | −0.967253 | ||||||||
\(482\) | −1.34322e6 | −0.263348 | ||||||||
\(483\) | 2.80071e6 | 0.546261 | ||||||||
\(484\) | 1.57781e6 | 0.306155 | ||||||||
\(485\) | 494175. | 0.0953951 | ||||||||
\(486\) | 559651. | 0.107480 | ||||||||
\(487\) | 801260. | 0.153091 | 0.0765457 | − | 0.997066i | \(-0.475611\pi\) | ||||
0.0765457 | + | 0.997066i | \(0.475611\pi\) | |||||||
\(488\) | −476807. | −0.0906344 | ||||||||
\(489\) | −1.63400e6 | −0.309014 | ||||||||
\(490\) | −363266. | −0.0683493 | ||||||||
\(491\) | 7.25783e6 | 1.35864 | 0.679318 | − | 0.733844i | \(-0.262276\pi\) | ||||
0.679318 | + | 0.733844i | \(0.262276\pi\) | |||||||
\(492\) | −621701. | −0.115789 | ||||||||
\(493\) | 845.399 | 0.000156655 0 | ||||||||
\(494\) | −1.21913e7 | −2.24768 | ||||||||
\(495\) | 216447. | 0.0397044 | ||||||||
\(496\) | −1.00953e7 | −1.84253 | ||||||||
\(497\) | 159720. | 0.0290047 | ||||||||
\(498\) | −191160. | −0.0345402 | ||||||||
\(499\) | −6.82872e6 | −1.22769 | −0.613844 | − | 0.789427i | \(-0.710378\pi\) | ||||
−0.613844 | + | 0.789427i | \(0.710378\pi\) | |||||||
\(500\) | 72274.2 | 0.0129288 | ||||||||
\(501\) | −6.35751e6 | −1.13160 | ||||||||
\(502\) | 3.10698e6 | 0.550274 | ||||||||
\(503\) | 5.24113e6 | 0.923644 | 0.461822 | − | 0.886973i | \(-0.347196\pi\) | ||||
0.461822 | + | 0.886973i | \(0.347196\pi\) | |||||||
\(504\) | −99180.1 | −0.0173919 | ||||||||
\(505\) | 771236. | 0.134573 | ||||||||
\(506\) | 1.53437e7 | 2.66411 | ||||||||
\(507\) | 1.42946e7 | 2.46974 | ||||||||
\(508\) | −1.57557e6 | −0.270881 | ||||||||
\(509\) | 5.13517e6 | 0.878538 | 0.439269 | − | 0.898356i | \(-0.355237\pi\) | ||||
0.439269 | + | 0.898356i | \(0.355237\pi\) | |||||||
\(510\) | 950828. | 0.161874 | ||||||||
\(511\) | −300004. | −0.0508247 | ||||||||
\(512\) | 4.18742e6 | 0.705947 | ||||||||
\(513\) | −6.60067e6 | −1.10737 | ||||||||
\(514\) | 8.33621e6 | 1.39175 | ||||||||
\(515\) | −1.54662e6 | −0.256960 | ||||||||
\(516\) | −1.33829e6 | −0.221271 | ||||||||
\(517\) | 5.81762e6 | 0.957235 | ||||||||
\(518\) | −1.29349e6 | −0.211806 | ||||||||
\(519\) | −2.01550e6 | −0.328446 | ||||||||
\(520\) | 4.66022e6 | 0.755785 | ||||||||
\(521\) | −5.75165e6 | −0.928320 | −0.464160 | − | 0.885751i | \(-0.653644\pi\) | ||||
−0.464160 | + | 0.885751i | \(0.653644\pi\) | |||||||
\(522\) | 158.902 | 2.55243e−5 0 | ||||||||
\(523\) | 3.17862e6 | 0.508142 | 0.254071 | − | 0.967186i | \(-0.418230\pi\) | ||||
0.254071 | + | 0.967186i | \(0.418230\pi\) | |||||||
\(524\) | −671092. | −0.106771 | ||||||||
\(525\) | −489251. | −0.0774699 | ||||||||
\(526\) | −680852. | −0.107297 | ||||||||
\(527\) | −3.45143e6 | −0.541343 | ||||||||
\(528\) | −1.30259e7 | −2.03340 | ||||||||
\(529\) | 6.36433e6 | 0.988812 | ||||||||
\(530\) | 2.17149e6 | 0.335791 | ||||||||
\(531\) | −124595. | −0.0191762 | ||||||||
\(532\) | −405779. | −0.0621599 | ||||||||
\(533\) | −9.46654e6 | −1.44336 | ||||||||
\(534\) | 4.52668e6 | 0.686953 | ||||||||
\(535\) | −4.30043e6 | −0.649572 | ||||||||
\(536\) | 6.18173e6 | 0.929391 | ||||||||
\(537\) | −6.37750e6 | −0.954365 | ||||||||
\(538\) | 5.19706e6 | 0.774109 | ||||||||
\(539\) | 1.70142e6 | 0.252256 | ||||||||
\(540\) | −426345. | −0.0629183 | ||||||||
\(541\) | −9.67662e6 | −1.42145 | −0.710724 | − | 0.703471i | \(-0.751632\pi\) | ||||
−0.710724 | + | 0.703471i | \(0.751632\pi\) | |||||||
\(542\) | 1.89320e6 | 0.276821 | ||||||||
\(543\) | 6.54245e6 | 0.952228 | ||||||||
\(544\) | −653837. | −0.0947267 | ||||||||
\(545\) | 3.88402e6 | 0.560132 | ||||||||
\(546\) | 5.33056e6 | 0.765228 | ||||||||
\(547\) | 3.14094e6 | 0.448840 | 0.224420 | − | 0.974493i | \(-0.427951\pi\) | ||||
0.224420 | + | 0.974493i | \(0.427951\pi\) | |||||||
\(548\) | −261525. | −0.0372016 | ||||||||
\(549\) | −35163.8 | −0.00497926 | ||||||||
\(550\) | −2.68036e6 | −0.377821 | ||||||||
\(551\) | −3847.49 | −0.000539882 0 | ||||||||
\(552\) | −9.46911e6 | −1.32270 | ||||||||
\(553\) | −369939. | −0.0514420 | ||||||||
\(554\) | −6.55172e6 | −0.906945 | ||||||||
\(555\) | −1.74208e6 | −0.240069 | ||||||||
\(556\) | −1.32047e6 | −0.181151 | ||||||||
\(557\) | −532897. | −0.0727788 | −0.0363894 | − | 0.999338i | \(-0.511586\pi\) | ||||
−0.0363894 | + | 0.999338i | \(0.511586\pi\) | |||||||
\(558\) | −648736. | −0.0882028 | ||||||||
\(559\) | −2.03779e7 | −2.75822 | ||||||||
\(560\) | 1.40951e6 | 0.189932 | ||||||||
\(561\) | −4.45339e6 | −0.597425 | ||||||||
\(562\) | −1.10637e7 | −1.47762 | ||||||||
\(563\) | −1.24343e7 | −1.65329 | −0.826645 | − | 0.562724i | \(-0.809753\pi\) | ||||
−0.826645 | + | 0.562724i | \(0.809753\pi\) | |||||||
\(564\) | 606658. | 0.0803056 | ||||||||
\(565\) | 2.09714e6 | 0.276380 | ||||||||
\(566\) | 1.14574e7 | 1.50329 | ||||||||
\(567\) | 3.03156e6 | 0.396013 | ||||||||
\(568\) | −540009. | −0.0702312 | ||||||||
\(569\) | −8.82869e6 | −1.14318 | −0.571591 | − | 0.820538i | \(-0.693674\pi\) | ||||
−0.571591 | + | 0.820538i | \(0.693674\pi\) | |||||||
\(570\) | −4.32730e6 | −0.557867 | ||||||||
\(571\) | −9.42799e6 | −1.21012 | −0.605060 | − | 0.796180i | \(-0.706851\pi\) | ||||
−0.605060 | + | 0.796180i | \(0.706851\pi\) | |||||||
\(572\) | 3.68819e6 | 0.471328 | ||||||||
\(573\) | 7.84761e6 | 0.998506 | ||||||||
\(574\) | −2.49489e6 | −0.316061 | ||||||||
\(575\) | −2.23613e6 | −0.282050 | ||||||||
\(576\) | 326960. | 0.0410618 | ||||||||
\(577\) | 6.92633e6 | 0.866091 | 0.433046 | − | 0.901372i | \(-0.357439\pi\) | ||||
0.433046 | + | 0.901372i | \(0.357439\pi\) | |||||||
\(578\) | 7.65631e6 | 0.953235 | ||||||||
\(579\) | −7.65617e6 | −0.949106 | ||||||||
\(580\) | −248.514 | −3.06748e−5 0 | ||||||||
\(581\) | −96882.7 | −0.0119071 | ||||||||
\(582\) | −1.91112e6 | −0.233873 | ||||||||
\(583\) | −1.01706e7 | −1.23930 | ||||||||
\(584\) | 1.01431e6 | 0.123066 | ||||||||
\(585\) | 343684. | 0.0415212 | ||||||||
\(586\) | −1.10165e7 | −1.32526 | ||||||||
\(587\) | 3.94161e6 | 0.472148 | 0.236074 | − | 0.971735i | \(-0.424139\pi\) | ||||
0.236074 | + | 0.971735i | \(0.424139\pi\) | |||||||
\(588\) | 177423. | 0.0211625 | ||||||||
\(589\) | 1.57078e7 | 1.86564 | ||||||||
\(590\) | 1.54291e6 | 0.182478 | ||||||||
\(591\) | 5.82942e6 | 0.686526 | ||||||||
\(592\) | 5.01887e6 | 0.588575 | ||||||||
\(593\) | 1.13618e7 | 1.32681 | 0.663405 | − | 0.748260i | \(-0.269111\pi\) | ||||
0.663405 | + | 0.748260i | \(0.269111\pi\) | |||||||
\(594\) | 1.58114e7 | 1.83867 | ||||||||
\(595\) | 481893. | 0.0558031 | ||||||||
\(596\) | −1.00032e6 | −0.115351 | ||||||||
\(597\) | −8.88290e6 | −1.02004 | ||||||||
\(598\) | 2.43634e7 | 2.78602 | ||||||||
\(599\) | 9.73442e6 | 1.10852 | 0.554260 | − | 0.832344i | \(-0.313002\pi\) | ||||
0.554260 | + | 0.832344i | \(0.313002\pi\) | |||||||
\(600\) | 1.65414e6 | 0.187584 | ||||||||
\(601\) | −1.24040e7 | −1.40080 | −0.700400 | − | 0.713750i | \(-0.746995\pi\) | ||||
−0.700400 | + | 0.713750i | \(0.746995\pi\) | |||||||
\(602\) | −5.37054e6 | −0.603986 | ||||||||
\(603\) | 455894. | 0.0510588 | ||||||||
\(604\) | −708633. | −0.0790368 | ||||||||
\(605\) | 8.52769e6 | 0.947203 | ||||||||
\(606\) | −2.98260e6 | −0.329924 | ||||||||
\(607\) | −1.36871e7 | −1.50779 | −0.753893 | − | 0.656997i | \(-0.771826\pi\) | ||||
−0.753893 | + | 0.656997i | \(0.771826\pi\) | |||||||
\(608\) | 2.97567e6 | 0.326457 | ||||||||
\(609\) | 1682.28 | 0.000183804 0 | ||||||||
\(610\) | 435449. | 0.0473819 | ||||||||
\(611\) | 9.23748e6 | 1.00104 | ||||||||
\(612\) | −22231.5 | −0.00239933 | ||||||||
\(613\) | 1.10357e7 | 1.18617 | 0.593087 | − | 0.805138i | \(-0.297909\pi\) | ||||
0.593087 | + | 0.805138i | \(0.297909\pi\) | |||||||
\(614\) | 1.35729e7 | 1.45295 | ||||||||
\(615\) | −3.36014e6 | −0.358237 | ||||||||
\(616\) | −5.75247e6 | −0.610805 | ||||||||
\(617\) | −9.49061e6 | −1.00365 | −0.501824 | − | 0.864970i | \(-0.667337\pi\) | ||||
−0.501824 | + | 0.864970i | \(0.667337\pi\) | |||||||
\(618\) | 5.98124e6 | 0.629970 | ||||||||
\(619\) | 950326. | 0.0996887 | 0.0498444 | − | 0.998757i | \(-0.484127\pi\) | ||||
0.0498444 | + | 0.998757i | \(0.484127\pi\) | |||||||
\(620\) | 1.01459e6 | 0.106001 | ||||||||
\(621\) | 1.31909e7 | 1.37260 | ||||||||
\(622\) | −6.63455e6 | −0.687600 | ||||||||
\(623\) | 2.29419e6 | 0.236815 | ||||||||
\(624\) | −2.06832e7 | −2.12645 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −1.31070e6 | −0.133680 | ||||||||
\(627\) | 2.02678e7 | 2.05891 | ||||||||
\(628\) | 1.73541e6 | 0.175591 | ||||||||
\(629\) | 1.71588e6 | 0.172926 | ||||||||
\(630\) | 90577.2 | 0.00909217 | ||||||||
\(631\) | 1.60839e7 | 1.60812 | 0.804061 | − | 0.594547i | \(-0.202668\pi\) | ||||
0.804061 | + | 0.594547i | \(0.202668\pi\) | |||||||
\(632\) | 1.25075e6 | 0.124560 | ||||||||
\(633\) | 8.79362e6 | 0.872285 | ||||||||
\(634\) | −1.51972e7 | −1.50155 | ||||||||
\(635\) | −8.51557e6 | −0.838068 | ||||||||
\(636\) | −1.06058e6 | −0.103969 | ||||||||
\(637\) | 2.70160e6 | 0.263799 | ||||||||
\(638\) | 9216.37 | 0.000896413 0 | ||||||||
\(639\) | −39824.9 | −0.00385836 | ||||||||
\(640\) | −5.37856e6 | −0.519058 | ||||||||
\(641\) | 1.90411e7 | 1.83041 | 0.915204 | − | 0.402991i | \(-0.132029\pi\) | ||||
0.915204 | + | 0.402991i | \(0.132029\pi\) | |||||||
\(642\) | 1.66310e7 | 1.59251 | ||||||||
\(643\) | −1.03943e7 | −0.991439 | −0.495720 | − | 0.868483i | \(-0.665096\pi\) | ||||
−0.495720 | + | 0.868483i | \(0.665096\pi\) | |||||||
\(644\) | 810916. | 0.0770480 | ||||||||
\(645\) | −7.23311e6 | −0.684583 | ||||||||
\(646\) | 4.26223e6 | 0.401842 | ||||||||
\(647\) | −3.14502e6 | −0.295367 | −0.147684 | − | 0.989035i | \(-0.547182\pi\) | ||||
−0.147684 | + | 0.989035i | \(0.547182\pi\) | |||||||
\(648\) | −1.02496e7 | −0.958894 | ||||||||
\(649\) | −7.22652e6 | −0.673468 | ||||||||
\(650\) | −4.25600e6 | −0.395110 | ||||||||
\(651\) | −6.86810e6 | −0.635161 | ||||||||
\(652\) | −473107. | −0.0435853 | ||||||||
\(653\) | 1.83320e7 | 1.68239 | 0.841196 | − | 0.540731i | \(-0.181852\pi\) | ||||
0.841196 | + | 0.540731i | \(0.181852\pi\) | |||||||
\(654\) | −1.50207e7 | −1.37323 | ||||||||
\(655\) | −3.62709e6 | −0.330335 | ||||||||
\(656\) | 9.68044e6 | 0.878285 | ||||||||
\(657\) | 74803.5 | 0.00676097 | ||||||||
\(658\) | 2.43452e6 | 0.219204 | ||||||||
\(659\) | 2.76429e6 | 0.247954 | 0.123977 | − | 0.992285i | \(-0.460435\pi\) | ||||
0.123977 | + | 0.992285i | \(0.460435\pi\) | |||||||
\(660\) | 1.30912e6 | 0.116982 | ||||||||
\(661\) | −4.80051e6 | −0.427350 | −0.213675 | − | 0.976905i | \(-0.568543\pi\) | ||||
−0.213675 | + | 0.976905i | \(0.568543\pi\) | |||||||
\(662\) | −1.97035e7 | −1.74742 | ||||||||
\(663\) | −7.07129e6 | −0.624763 | ||||||||
\(664\) | 327558. | 0.0288315 | ||||||||
\(665\) | −2.19314e6 | −0.192314 | ||||||||
\(666\) | 322520. | 0.0281755 | ||||||||
\(667\) | 7688.90 | 0.000669190 0 | ||||||||
\(668\) | −1.84075e6 | −0.159608 | ||||||||
\(669\) | 7.31304e6 | 0.631731 | ||||||||
\(670\) | −5.64553e6 | −0.485868 | ||||||||
\(671\) | −2.03951e6 | −0.174872 | ||||||||
\(672\) | −1.30109e6 | −0.111143 | ||||||||
\(673\) | −3.73117e6 | −0.317546 | −0.158773 | − | 0.987315i | \(-0.550754\pi\) | ||||
−0.158773 | + | 0.987315i | \(0.550754\pi\) | |||||||
\(674\) | −1.17713e7 | −0.998104 | ||||||||
\(675\) | −2.30429e6 | −0.194661 | ||||||||
\(676\) | 4.13884e6 | 0.348347 | ||||||||
\(677\) | 1.48375e7 | 1.24419 | 0.622096 | − | 0.782941i | \(-0.286281\pi\) | ||||
0.622096 | + | 0.782941i | \(0.286281\pi\) | |||||||
\(678\) | −8.11027e6 | −0.677581 | ||||||||
\(679\) | −968582. | −0.0806236 | ||||||||
\(680\) | −1.62927e6 | −0.135120 | ||||||||
\(681\) | −2.01564e7 | −1.66550 | ||||||||
\(682\) | −3.76268e7 | −3.09768 | ||||||||
\(683\) | 206230. | 0.0169161 | 0.00845804 | − | 0.999964i | \(-0.497308\pi\) | ||||
0.00845804 | + | 0.999964i | \(0.497308\pi\) | |||||||
\(684\) | 101178. | 0.00826883 | ||||||||
\(685\) | −1.41348e6 | −0.115097 | ||||||||
\(686\) | 712001. | 0.0577657 | ||||||||
\(687\) | −592312. | −0.0478805 | ||||||||
\(688\) | 2.08383e7 | 1.67838 | ||||||||
\(689\) | −1.61494e7 | −1.29601 | ||||||||
\(690\) | 8.64777e6 | 0.691483 | ||||||||
\(691\) | 1.44687e7 | 1.15275 | 0.576376 | − | 0.817185i | \(-0.304466\pi\) | ||||
0.576376 | + | 0.817185i | \(0.304466\pi\) | |||||||
\(692\) | −583567. | −0.0463261 | ||||||||
\(693\) | −424236. | −0.0335563 | ||||||||
\(694\) | 2.87255e6 | 0.226396 | ||||||||
\(695\) | −7.13681e6 | −0.560457 | ||||||||
\(696\) | −5687.75 | −0.000445059 0 | ||||||||
\(697\) | 3.30961e6 | 0.258045 | ||||||||
\(698\) | −833208. | −0.0647314 | ||||||||
\(699\) | −1.62922e6 | −0.126121 | ||||||||
\(700\) | −141658. | −0.0109268 | ||||||||
\(701\) | −9.14822e6 | −0.703140 | −0.351570 | − | 0.936162i | \(-0.614352\pi\) | ||||
−0.351570 | + | 0.936162i | \(0.614352\pi\) | |||||||
\(702\) | 2.51061e7 | 1.92281 | ||||||||
\(703\) | −7.80915e6 | −0.595957 | ||||||||
\(704\) | 1.89637e7 | 1.44209 | ||||||||
\(705\) | 3.27884e6 | 0.248455 | ||||||||
\(706\) | 2.45961e6 | 0.185718 | ||||||||
\(707\) | −1.51162e6 | −0.113735 | ||||||||
\(708\) | −753577. | −0.0564995 | ||||||||
\(709\) | 5.64865e6 | 0.422016 | 0.211008 | − | 0.977484i | \(-0.432325\pi\) | ||||
0.211008 | + | 0.977484i | \(0.432325\pi\) | |||||||
\(710\) | 493169. | 0.0367155 | ||||||||
\(711\) | 92241.3 | 0.00684308 | ||||||||
\(712\) | −7.75658e6 | −0.573416 | ||||||||
\(713\) | −3.13907e7 | −2.31248 | ||||||||
\(714\) | −1.86362e6 | −0.136808 | ||||||||
\(715\) | 1.99338e7 | 1.45822 | ||||||||
\(716\) | −1.84654e6 | −0.134610 | ||||||||
\(717\) | 2.01927e7 | 1.46689 | ||||||||
\(718\) | −576690. | −0.0417476 | ||||||||
\(719\) | −5.23347e6 | −0.377544 | −0.188772 | − | 0.982021i | \(-0.560451\pi\) | ||||
−0.188772 | + | 0.982021i | \(0.560451\pi\) | |||||||
\(720\) | −351450. | −0.0252658 | ||||||||
\(721\) | 3.03138e6 | 0.217171 | ||||||||
\(722\) | −4.41267e6 | −0.315034 | ||||||||
\(723\) | 3.54578e6 | 0.252270 | ||||||||
\(724\) | 1.89430e6 | 0.134308 | ||||||||
\(725\) | −1343.16 | −9.49036e−5 0 | ||||||||
\(726\) | −3.29791e7 | −2.32219 | ||||||||
\(727\) | −1.90417e6 | −0.133619 | −0.0668097 | − | 0.997766i | \(-0.521282\pi\) | ||||
−0.0668097 | + | 0.997766i | \(0.521282\pi\) | |||||||
\(728\) | −9.13403e6 | −0.638755 | ||||||||
\(729\) | 1.35567e7 | 0.944792 | ||||||||
\(730\) | −926325. | −0.0643363 | ||||||||
\(731\) | 7.12433e6 | 0.493118 | ||||||||
\(732\) | −212679. | −0.0146705 | ||||||||
\(733\) | 1.99067e6 | 0.136848 | 0.0684242 | − | 0.997656i | \(-0.478203\pi\) | ||||
0.0684242 | + | 0.997656i | \(0.478203\pi\) | |||||||
\(734\) | −2.13815e7 | −1.46487 | ||||||||
\(735\) | 958932. | 0.0654741 | ||||||||
\(736\) | −5.94664e6 | −0.404648 | ||||||||
\(737\) | 2.64419e7 | 1.79318 | ||||||||
\(738\) | 622079. | 0.0420440 | ||||||||
\(739\) | −1.12289e7 | −0.756357 | −0.378178 | − | 0.925733i | \(-0.623449\pi\) | ||||
−0.378178 | + | 0.925733i | \(0.623449\pi\) | |||||||
\(740\) | −504402. | −0.0338608 | ||||||||
\(741\) | 3.21821e7 | 2.15312 | ||||||||
\(742\) | −4.25613e6 | −0.283795 | ||||||||
\(743\) | 9.86132e6 | 0.655335 | 0.327667 | − | 0.944793i | \(-0.393737\pi\) | ||||
0.327667 | + | 0.944793i | \(0.393737\pi\) | |||||||
\(744\) | 2.32208e7 | 1.53796 | ||||||||
\(745\) | −5.40648e6 | −0.356882 | ||||||||
\(746\) | 2.22408e6 | 0.146320 | ||||||||
\(747\) | 24156.9 | 0.00158394 | ||||||||
\(748\) | −1.28943e6 | −0.0842645 | ||||||||
\(749\) | 8.42884e6 | 0.548989 | ||||||||
\(750\) | −1.51066e6 | −0.0980651 | ||||||||
\(751\) | −9.24657e6 | −0.598247 | −0.299124 | − | 0.954214i | \(-0.596694\pi\) | ||||
−0.299124 | + | 0.954214i | \(0.596694\pi\) | |||||||
\(752\) | −9.44620e6 | −0.609134 | ||||||||
\(753\) | −8.20166e6 | −0.527126 | ||||||||
\(754\) | 14634.2 | 0.000937433 0 | ||||||||
\(755\) | −3.82999e6 | −0.244529 | ||||||||
\(756\) | 835637. | 0.0531757 | ||||||||
\(757\) | 5.85772e6 | 0.371526 | 0.185763 | − | 0.982595i | \(-0.440524\pi\) | ||||
0.185763 | + | 0.982595i | \(0.440524\pi\) | |||||||
\(758\) | −3.64274e6 | −0.230279 | ||||||||
\(759\) | −4.05035e7 | −2.55204 | ||||||||
\(760\) | 7.41494e6 | 0.465665 | ||||||||
\(761\) | 1.36326e7 | 0.853329 | 0.426665 | − | 0.904410i | \(-0.359688\pi\) | ||||
0.426665 | + | 0.904410i | \(0.359688\pi\) | |||||||
\(762\) | 3.29322e7 | 2.05463 | ||||||||
\(763\) | −7.61268e6 | −0.473398 | ||||||||
\(764\) | 2.27219e6 | 0.140835 | ||||||||
\(765\) | −120156. | −0.00742321 | ||||||||
\(766\) | 1.87418e7 | 1.15409 | ||||||||
\(767\) | −1.14746e7 | −0.704286 | ||||||||
\(768\) | 7.11977e6 | 0.435575 | ||||||||
\(769\) | 1.95250e7 | 1.19062 | 0.595312 | − | 0.803494i | \(-0.297028\pi\) | ||||
0.595312 | + | 0.803494i | \(0.297028\pi\) | |||||||
\(770\) | 5.25350e6 | 0.319317 | ||||||||
\(771\) | −2.20055e7 | −1.33320 | ||||||||
\(772\) | −2.21676e6 | −0.133868 | ||||||||
\(773\) | 978993. | 0.0589292 | 0.0294646 | − | 0.999566i | \(-0.490620\pi\) | ||||
0.0294646 | + | 0.999566i | \(0.490620\pi\) | |||||||
\(774\) | 1.33910e6 | 0.0803453 | ||||||||
\(775\) | 5.48359e6 | 0.327952 | ||||||||
\(776\) | 3.27475e6 | 0.195220 | ||||||||
\(777\) | 3.41448e6 | 0.202896 | ||||||||
\(778\) | 2.02360e7 | 1.19860 | ||||||||
\(779\) | −1.50623e7 | −0.889301 | ||||||||
\(780\) | 2.07868e6 | 0.122335 | ||||||||
\(781\) | −2.30985e6 | −0.135505 | ||||||||
\(782\) | −8.51771e6 | −0.498088 | ||||||||
\(783\) | 7923.29 | 0.000461850 0 | ||||||||
\(784\) | −2.76264e6 | −0.160522 | ||||||||
\(785\) | 9.37946e6 | 0.543255 | ||||||||
\(786\) | 1.40270e7 | 0.809859 | ||||||||
\(787\) | 2.41473e7 | 1.38974 | 0.694868 | − | 0.719138i | \(-0.255463\pi\) | ||||
0.694868 | + | 0.719138i | \(0.255463\pi\) | |||||||
\(788\) | 1.68785e6 | 0.0968318 | ||||||||
\(789\) | 1.79728e6 | 0.102783 | ||||||||
\(790\) | −1.14226e6 | −0.0651177 | ||||||||
\(791\) | −4.11040e6 | −0.233584 | ||||||||
\(792\) | 1.43433e6 | 0.0812523 | ||||||||
\(793\) | −3.23843e6 | −0.182874 | ||||||||
\(794\) | −7.87362e6 | −0.443224 | ||||||||
\(795\) | −5.73220e6 | −0.321665 | ||||||||
\(796\) | −2.57195e6 | −0.143873 | ||||||||
\(797\) | −2.16881e7 | −1.20942 | −0.604708 | − | 0.796447i | \(-0.706710\pi\) | ||||
−0.604708 | + | 0.796447i | \(0.706710\pi\) | |||||||
\(798\) | 8.48152e6 | 0.471483 | ||||||||
\(799\) | −3.22953e6 | −0.178967 | ||||||||
\(800\) | 1.03881e6 | 0.0573866 | ||||||||
\(801\) | −572036. | −0.0315023 | ||||||||
\(802\) | 2.39550e7 | 1.31511 | ||||||||
\(803\) | 4.33862e6 | 0.237445 | ||||||||
\(804\) | 2.75735e6 | 0.150436 | ||||||||
\(805\) | 4.38281e6 | 0.238376 | ||||||||
\(806\) | −5.97456e7 | −3.23943 | ||||||||
\(807\) | −1.37190e7 | −0.741544 | ||||||||
\(808\) | 5.11075e6 | 0.275395 | ||||||||
\(809\) | 2.18877e7 | 1.17579 | 0.587895 | − | 0.808938i | \(-0.299957\pi\) | ||||
0.587895 | + | 0.808938i | \(0.299957\pi\) | |||||||
\(810\) | 9.36058e6 | 0.501291 | ||||||||
\(811\) | −1.02862e7 | −0.549167 | −0.274583 | − | 0.961563i | \(-0.588540\pi\) | ||||
−0.274583 | + | 0.961563i | \(0.588540\pi\) | |||||||
\(812\) | 487.088 | 2.59249e−5 0 | ||||||||
\(813\) | −4.99759e6 | −0.265176 | ||||||||
\(814\) | 1.87062e7 | 0.989521 | ||||||||
\(815\) | −2.55703e6 | −0.134847 | ||||||||
\(816\) | 7.23107e6 | 0.380169 | ||||||||
\(817\) | −3.24235e7 | −1.69944 | ||||||||
\(818\) | −1.55912e7 | −0.814697 | ||||||||
\(819\) | −673622. | −0.0350918 | ||||||||
\(820\) | −972895. | −0.0505279 | ||||||||
\(821\) | −1.03817e7 | −0.537540 | −0.268770 | − | 0.963204i | \(-0.586617\pi\) | ||||
−0.268770 | + | 0.963204i | \(0.586617\pi\) | |||||||
\(822\) | 5.46635e6 | 0.282175 | ||||||||
\(823\) | −2.02906e7 | −1.04423 | −0.522115 | − | 0.852875i | \(-0.674857\pi\) | ||||
−0.522115 | + | 0.852875i | \(0.674857\pi\) | |||||||
\(824\) | −1.02490e7 | −0.525851 | ||||||||
\(825\) | 7.07548e6 | 0.361927 | ||||||||
\(826\) | −3.02410e6 | −0.154222 | ||||||||
\(827\) | −1.27595e7 | −0.648741 | −0.324370 | − | 0.945930i | \(-0.605152\pi\) | ||||
−0.324370 | + | 0.945930i | \(0.605152\pi\) | |||||||
\(828\) | −202195. | −0.0102493 | ||||||||
\(829\) | 3.54147e7 | 1.78977 | 0.894885 | − | 0.446296i | \(-0.147257\pi\) | ||||
0.894885 | + | 0.446296i | \(0.147257\pi\) | |||||||
\(830\) | −299145. | −0.0150726 | ||||||||
\(831\) | 1.72949e7 | 0.868793 | ||||||||
\(832\) | 3.01115e7 | 1.50808 | ||||||||
\(833\) | −944510. | −0.0471622 | ||||||||
\(834\) | 2.76002e7 | 1.37403 | ||||||||
\(835\) | −9.94882e6 | −0.493805 | ||||||||
\(836\) | 5.86832e6 | 0.290401 | ||||||||
\(837\) | −3.23477e7 | −1.59599 | ||||||||
\(838\) | 8.81515e6 | 0.433630 | ||||||||
\(839\) | 3.26655e7 | 1.60208 | 0.801040 | − | 0.598611i | \(-0.204280\pi\) | ||||
0.801040 | + | 0.598611i | \(0.204280\pi\) | |||||||
\(840\) | −3.24212e6 | −0.158537 | ||||||||
\(841\) | −2.05111e7 | −1.00000 | ||||||||
\(842\) | −1.19496e7 | −0.580861 | ||||||||
\(843\) | 2.92056e7 | 1.41546 | ||||||||
\(844\) | 2.54610e6 | 0.123032 | ||||||||
\(845\) | 2.23695e7 | 1.07774 | ||||||||
\(846\) | −607026. | −0.0291596 | ||||||||
\(847\) | −1.67143e7 | −0.800533 | ||||||||
\(848\) | 1.65143e7 | 0.788623 | ||||||||
\(849\) | −3.02446e7 | −1.44005 | ||||||||
\(850\) | 1.48794e6 | 0.0706381 | ||||||||
\(851\) | 1.56059e7 | 0.738697 | ||||||||
\(852\) | −240870. | −0.0113680 | ||||||||
\(853\) | −3.13879e7 | −1.47703 | −0.738516 | − | 0.674236i | \(-0.764473\pi\) | ||||
−0.738516 | + | 0.674236i | \(0.764473\pi\) | |||||||
\(854\) | −853480. | −0.0400450 | ||||||||
\(855\) | 546841. | 0.0255827 | ||||||||
\(856\) | −2.84977e7 | −1.32931 | ||||||||
\(857\) | −2.68286e7 | −1.24780 | −0.623902 | − | 0.781502i | \(-0.714454\pi\) | ||||
−0.623902 | + | 0.781502i | \(0.714454\pi\) | |||||||
\(858\) | −7.70898e7 | −3.57502 | ||||||||
\(859\) | −3.01479e7 | −1.39404 | −0.697019 | − | 0.717053i | \(-0.745491\pi\) | ||||
−0.697019 | + | 0.717053i | \(0.745491\pi\) | |||||||
\(860\) | −2.09427e6 | −0.0965578 | ||||||||
\(861\) | 6.58588e6 | 0.302765 | ||||||||
\(862\) | 4.45727e7 | 2.04315 | ||||||||
\(863\) | 6.05947e6 | 0.276954 | 0.138477 | − | 0.990366i | \(-0.455779\pi\) | ||||
0.138477 | + | 0.990366i | \(0.455779\pi\) | |||||||
\(864\) | −6.12792e6 | −0.279273 | ||||||||
\(865\) | −3.15404e6 | −0.143327 | ||||||||
\(866\) | −1.92289e7 | −0.871285 | ||||||||
\(867\) | −2.02108e7 | −0.913135 | ||||||||
\(868\) | −1.98859e6 | −0.0895871 | ||||||||
\(869\) | 5.35001e6 | 0.240329 | ||||||||
\(870\) | 5194.40 | 0.000232668 0 | ||||||||
\(871\) | 4.19858e7 | 1.87524 | ||||||||
\(872\) | 2.57382e7 | 1.14627 | ||||||||
\(873\) | 241508. | 0.0107250 | ||||||||
\(874\) | 3.87649e7 | 1.71656 | ||||||||
\(875\) | −765625. | −0.0338062 | ||||||||
\(876\) | 452429. | 0.0199200 | ||||||||
\(877\) | −6.94230e6 | −0.304792 | −0.152396 | − | 0.988319i | \(-0.548699\pi\) | ||||
−0.152396 | + | 0.988319i | \(0.548699\pi\) | |||||||
\(878\) | −1.37841e7 | −0.603452 | ||||||||
\(879\) | 2.90809e7 | 1.26951 | ||||||||
\(880\) | −2.03842e7 | −0.887333 | ||||||||
\(881\) | 9.89661e6 | 0.429583 | 0.214791 | − | 0.976660i | \(-0.431093\pi\) | ||||
0.214791 | + | 0.976660i | \(0.431093\pi\) | |||||||
\(882\) | −177531. | −0.00768429 | ||||||||
\(883\) | −1.02503e7 | −0.442419 | −0.221209 | − | 0.975226i | \(-0.571000\pi\) | ||||
−0.221209 | + | 0.975226i | \(0.571000\pi\) | |||||||
\(884\) | −2.04742e6 | −0.0881204 | ||||||||
\(885\) | −4.07290e6 | −0.174802 | ||||||||
\(886\) | −1.21834e6 | −0.0521417 | ||||||||
\(887\) | 8.61386e6 | 0.367611 | 0.183806 | − | 0.982963i | \(-0.441158\pi\) | ||||
0.183806 | + | 0.982963i | \(0.441158\pi\) | |||||||
\(888\) | −1.15443e7 | −0.491286 | ||||||||
\(889\) | 1.66905e7 | 0.708297 | ||||||||
\(890\) | 7.08377e6 | 0.299771 | ||||||||
\(891\) | −4.38421e7 | −1.85011 | ||||||||
\(892\) | 2.11741e6 | 0.0891033 | ||||||||
\(893\) | 1.46979e7 | 0.616774 | ||||||||
\(894\) | 2.09085e7 | 0.874941 | ||||||||
\(895\) | −9.98010e6 | −0.416464 | ||||||||
\(896\) | 1.05420e7 | 0.438684 | ||||||||
\(897\) | −6.43133e7 | −2.66882 | ||||||||
\(898\) | 1.17393e7 | 0.485794 | ||||||||
\(899\) | −18855.3 | −0.000778096 0 | ||||||||
\(900\) | 35321.1 | 0.00145354 | ||||||||
\(901\) | 5.64600e6 | 0.231701 | ||||||||
\(902\) | 3.60807e7 | 1.47659 | ||||||||
\(903\) | 1.41769e7 | 0.578578 | ||||||||
\(904\) | 1.38971e7 | 0.565593 | ||||||||
\(905\) | 1.02382e7 | 0.415531 | ||||||||
\(906\) | 1.48117e7 | 0.599494 | ||||||||
\(907\) | −1.87395e6 | −0.0756380 | −0.0378190 | − | 0.999285i | \(-0.512041\pi\) | ||||
−0.0378190 | + | 0.999285i | \(0.512041\pi\) | |||||||
\(908\) | −5.83608e6 | −0.234913 | ||||||||
\(909\) | 376911. | 0.0151296 | ||||||||
\(910\) | 8.34175e6 | 0.333929 | ||||||||
\(911\) | 4.93810e7 | 1.97135 | 0.985676 | − | 0.168649i | \(-0.0539405\pi\) | ||||
0.985676 | + | 0.168649i | \(0.0539405\pi\) | |||||||
\(912\) | −3.29093e7 | −1.31018 | ||||||||
\(913\) | 1.40111e6 | 0.0556280 | ||||||||
\(914\) | −3.50253e7 | −1.38681 | ||||||||
\(915\) | −1.14948e6 | −0.0453887 | ||||||||
\(916\) | −171498. | −0.00675336 | ||||||||
\(917\) | 7.10909e6 | 0.279184 | ||||||||
\(918\) | −8.77737e6 | −0.343762 | ||||||||
\(919\) | −3.25462e7 | −1.27119 | −0.635597 | − | 0.772021i | \(-0.719246\pi\) | ||||
−0.635597 | + | 0.772021i | \(0.719246\pi\) | |||||||
\(920\) | −1.48181e7 | −0.577197 | ||||||||
\(921\) | −3.58290e7 | −1.39183 | ||||||||
\(922\) | −1.19174e7 | −0.461694 | ||||||||
\(923\) | −3.66769e6 | −0.141706 | ||||||||
\(924\) | −2.56588e6 | −0.0988680 | ||||||||
\(925\) | −2.72617e6 | −0.104761 | ||||||||
\(926\) | −3.29165e7 | −1.26150 | ||||||||
\(927\) | −755848. | −0.0288892 | ||||||||
\(928\) | −3571.93 | −0.000136155 0 | ||||||||
\(929\) | 1.13881e6 | 0.0432923 | 0.0216462 | − | 0.999766i | \(-0.493109\pi\) | ||||
0.0216462 | + | 0.999766i | \(0.493109\pi\) | |||||||
\(930\) | −2.12067e7 | −0.804017 | ||||||||
\(931\) | 4.29855e6 | 0.162535 | ||||||||
\(932\) | −471724. | −0.0177889 | ||||||||
\(933\) | 1.75136e7 | 0.658674 | ||||||||
\(934\) | 1.07193e7 | 0.402068 | ||||||||
\(935\) | −6.96907e6 | −0.260703 | ||||||||
\(936\) | 2.27749e6 | 0.0849704 | ||||||||
\(937\) | 3.02967e7 | 1.12732 | 0.563658 | − | 0.826008i | \(-0.309393\pi\) | ||||
0.563658 | + | 0.826008i | \(0.309393\pi\) | |||||||
\(938\) | 1.10652e7 | 0.410633 | ||||||||
\(939\) | 3.45991e6 | 0.128056 | ||||||||
\(940\) | 949354. | 0.0350436 | ||||||||
\(941\) | −2.34042e7 | −0.861628 | −0.430814 | − | 0.902441i | \(-0.641773\pi\) | ||||
−0.430814 | + | 0.902441i | \(0.641773\pi\) | |||||||
\(942\) | −3.62731e7 | −1.33186 | ||||||||
\(943\) | 3.01009e7 | 1.10230 | ||||||||
\(944\) | 1.17339e7 | 0.428559 | ||||||||
\(945\) | 4.51642e6 | 0.164518 | ||||||||
\(946\) | 7.76680e7 | 2.82172 | ||||||||
\(947\) | 4.77998e7 | 1.73201 | 0.866006 | − | 0.500034i | \(-0.166679\pi\) | ||||
0.866006 | + | 0.500034i | \(0.166679\pi\) | |||||||
\(948\) | 557896. | 0.0201620 | ||||||||
\(949\) | 6.88907e6 | 0.248310 | ||||||||
\(950\) | −6.77177e6 | −0.243441 | ||||||||
\(951\) | 4.01168e7 | 1.43838 | ||||||||
\(952\) | 3.19336e6 | 0.114197 | ||||||||
\(953\) | −5.13376e7 | −1.83106 | −0.915532 | − | 0.402246i | \(-0.868230\pi\) | ||||
−0.915532 | + | 0.402246i | \(0.868230\pi\) | |||||||
\(954\) | 1.06123e6 | 0.0377519 | ||||||||
\(955\) | 1.22807e7 | 0.435726 | ||||||||
\(956\) | 5.84658e6 | 0.206899 | ||||||||
\(957\) | −24329.0 | −0.000858704 0 | ||||||||
\(958\) | −5.66442e7 | −1.99408 | ||||||||
\(959\) | 2.77042e6 | 0.0972746 | ||||||||
\(960\) | 1.06881e7 | 0.374301 | ||||||||
\(961\) | 4.83495e7 | 1.68882 | ||||||||
\(962\) | 2.97026e7 | 1.03480 | ||||||||
\(963\) | −2.10166e6 | −0.0730293 | ||||||||
\(964\) | 1.02664e6 | 0.0355817 | ||||||||
\(965\) | −1.19811e7 | −0.414169 | ||||||||
\(966\) | −1.69496e7 | −0.584409 | ||||||||
\(967\) | 1.30795e6 | 0.0449807 | 0.0224904 | − | 0.999747i | \(-0.492840\pi\) | ||||
0.0224904 | + | 0.999747i | \(0.492840\pi\) | |||||||
\(968\) | 5.65105e7 | 1.93839 | ||||||||
\(969\) | −1.12512e7 | −0.384938 | ||||||||
\(970\) | −2.99070e6 | −0.102057 | ||||||||
\(971\) | −1.92507e7 | −0.655236 | −0.327618 | − | 0.944810i | \(-0.606246\pi\) | ||||
−0.327618 | + | 0.944810i | \(0.606246\pi\) | |||||||
\(972\) | −427749. | −0.0145219 | ||||||||
\(973\) | 1.39882e7 | 0.473673 | ||||||||
\(974\) | −4.84915e6 | −0.163783 | ||||||||
\(975\) | 1.12348e7 | 0.378489 | ||||||||
\(976\) | 3.31160e6 | 0.111279 | ||||||||
\(977\) | 4.79097e6 | 0.160578 | 0.0802892 | − | 0.996772i | \(-0.474416\pi\) | ||||
0.0802892 | + | 0.996772i | \(0.474416\pi\) | |||||||
\(978\) | 9.88879e6 | 0.330595 | ||||||||
\(979\) | −3.31782e7 | −1.10636 | ||||||||
\(980\) | 277649. | 0.00923486 | ||||||||
\(981\) | 1.89816e6 | 0.0629738 | ||||||||
\(982\) | −4.39237e7 | −1.45352 | ||||||||
\(983\) | 4.02177e7 | 1.32750 | 0.663748 | − | 0.747956i | \(-0.268965\pi\) | ||||
0.663748 | + | 0.747956i | \(0.268965\pi\) | |||||||
\(984\) | −2.22667e7 | −0.733107 | ||||||||
\(985\) | 9.12242e6 | 0.299585 | ||||||||
\(986\) | −5116.28 | −0.000167595 0 | ||||||||
\(987\) | −6.42652e6 | −0.209983 | ||||||||
\(988\) | 9.31800e6 | 0.303690 | ||||||||
\(989\) | 6.47957e7 | 2.10647 | ||||||||
\(990\) | −1.30992e6 | −0.0424772 | ||||||||
\(991\) | 7.65202e6 | 0.247510 | 0.123755 | − | 0.992313i | \(-0.460506\pi\) | ||||
0.123755 | + | 0.992313i | \(0.460506\pi\) | |||||||
\(992\) | 1.45828e7 | 0.470502 | ||||||||
\(993\) | 5.20123e7 | 1.67391 | ||||||||
\(994\) | −966611. | −0.0310303 | ||||||||
\(995\) | −1.39008e7 | −0.445125 | ||||||||
\(996\) | 146106. | 0.00466682 | ||||||||
\(997\) | 3.97848e7 | 1.26759 | 0.633796 | − | 0.773500i | \(-0.281496\pi\) | ||||
0.633796 | + | 0.773500i | \(0.281496\pi\) | |||||||
\(998\) | 4.13268e7 | 1.31342 | ||||||||
\(999\) | 1.60817e7 | 0.509821 |
(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 | 35.6.a.d.1.1 | ✓ | 4 | |
3.2 | odd | 2 | 315.6.a.l.1.4 | 4 | |||
4.3 | odd | 2 | 560.6.a.v.1.2 | 4 | |||
5.2 | odd | 4 | 175.6.b.f.99.2 | 8 | |||
5.3 | odd | 4 | 175.6.b.f.99.7 | 8 | |||
5.4 | even | 2 | 175.6.a.f.1.4 | 4 | |||
7.6 | odd | 2 | 245.6.a.e.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.6.a.d.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
175.6.a.f.1.4 | 4 | 5.4 | even | 2 | |||
175.6.b.f.99.2 | 8 | 5.2 | odd | 4 | |||
175.6.b.f.99.7 | 8 | 5.3 | odd | 4 | |||
245.6.a.e.1.1 | 4 | 7.6 | odd | 2 | |||
315.6.a.l.1.4 | 4 | 3.2 | odd | 2 | |||
560.6.a.v.1.2 | 4 | 4.3 | odd | 2 |