Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [354,6,Mod(1,354)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(354, 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("354.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 354 = 2 \cdot 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 354.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: | \(56.7758722138\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 358x^{4} - 404x^{3} + 26492x^{2} - 11664x - 353376 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(17.2905\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 354.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −0.707107 | ||||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | −75.0224 | −1.34204 | −0.671021 | − | 0.741439i | \(-0.734144\pi\) | ||||
−0.671021 | + | 0.741439i | \(0.734144\pi\) | |||||||
\(6\) | 36.0000 | 0.408248 | ||||||||
\(7\) | 17.7979 | 0.137285 | 0.0686426 | − | 0.997641i | \(-0.478133\pi\) | ||||
0.0686426 | + | 0.997641i | \(0.478133\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 300.090 | 0.948966 | ||||||||
\(11\) | 485.600 | 1.21003 | 0.605016 | − | 0.796213i | \(-0.293167\pi\) | ||||
0.605016 | + | 0.796213i | \(0.293167\pi\) | |||||||
\(12\) | −144.000 | −0.288675 | ||||||||
\(13\) | −507.251 | −0.832462 | −0.416231 | − | 0.909259i | \(-0.636649\pi\) | ||||
−0.416231 | + | 0.909259i | \(0.636649\pi\) | |||||||
\(14\) | −71.1916 | −0.0970753 | ||||||||
\(15\) | 675.201 | 0.774828 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −346.426 | −0.290729 | −0.145364 | − | 0.989378i | \(-0.546435\pi\) | ||||
−0.145364 | + | 0.989378i | \(0.546435\pi\) | |||||||
\(18\) | −324.000 | −0.235702 | ||||||||
\(19\) | −1662.38 | −1.05644 | −0.528222 | − | 0.849106i | \(-0.677141\pi\) | ||||
−0.528222 | + | 0.849106i | \(0.677141\pi\) | |||||||
\(20\) | −1200.36 | −0.671021 | ||||||||
\(21\) | −160.181 | −0.0792616 | ||||||||
\(22\) | −1942.40 | −0.855622 | ||||||||
\(23\) | −593.797 | −0.234055 | −0.117028 | − | 0.993129i | \(-0.537337\pi\) | ||||
−0.117028 | + | 0.993129i | \(0.537337\pi\) | |||||||
\(24\) | 576.000 | 0.204124 | ||||||||
\(25\) | 2503.36 | 0.801075 | ||||||||
\(26\) | 2029.00 | 0.588640 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 284.766 | 0.0686426 | ||||||||
\(29\) | −6931.65 | −1.53053 | −0.765265 | − | 0.643716i | \(-0.777392\pi\) | ||||
−0.765265 | + | 0.643716i | \(0.777392\pi\) | |||||||
\(30\) | −2700.81 | −0.547886 | ||||||||
\(31\) | −7789.67 | −1.45584 | −0.727922 | − | 0.685660i | \(-0.759514\pi\) | ||||
−0.727922 | + | 0.685660i | \(0.759514\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | −4370.40 | −0.698613 | ||||||||
\(34\) | 1385.70 | 0.205576 | ||||||||
\(35\) | −1335.24 | −0.184242 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | 4846.32 | 0.581980 | 0.290990 | − | 0.956726i | \(-0.406015\pi\) | ||||
0.290990 | + | 0.956726i | \(0.406015\pi\) | |||||||
\(38\) | 6649.53 | 0.747019 | ||||||||
\(39\) | 4565.26 | 0.480622 | ||||||||
\(40\) | 4801.43 | 0.474483 | ||||||||
\(41\) | 14695.2 | 1.36526 | 0.682629 | − | 0.730765i | \(-0.260836\pi\) | ||||
0.682629 | + | 0.730765i | \(0.260836\pi\) | |||||||
\(42\) | 640.724 | 0.0560464 | ||||||||
\(43\) | −15929.6 | −1.31381 | −0.656907 | − | 0.753972i | \(-0.728135\pi\) | ||||
−0.656907 | + | 0.753972i | \(0.728135\pi\) | |||||||
\(44\) | 7769.60 | 0.605016 | ||||||||
\(45\) | −6076.81 | −0.447347 | ||||||||
\(46\) | 2375.19 | 0.165502 | ||||||||
\(47\) | 22466.5 | 1.48351 | 0.741756 | − | 0.670669i | \(-0.233993\pi\) | ||||
0.741756 | + | 0.670669i | \(0.233993\pi\) | |||||||
\(48\) | −2304.00 | −0.144338 | ||||||||
\(49\) | −16490.2 | −0.981153 | ||||||||
\(50\) | −10013.4 | −0.566445 | ||||||||
\(51\) | 3117.83 | 0.167852 | ||||||||
\(52\) | −8116.01 | −0.416231 | ||||||||
\(53\) | −16983.6 | −0.830501 | −0.415250 | − | 0.909707i | \(-0.636306\pi\) | ||||
−0.415250 | + | 0.909707i | \(0.636306\pi\) | |||||||
\(54\) | 2916.00 | 0.136083 | ||||||||
\(55\) | −36430.9 | −1.62391 | ||||||||
\(56\) | −1139.07 | −0.0485376 | ||||||||
\(57\) | 14961.4 | 0.609938 | ||||||||
\(58\) | 27726.6 | 1.08225 | ||||||||
\(59\) | 3481.00 | 0.130189 | ||||||||
\(60\) | 10803.2 | 0.387414 | ||||||||
\(61\) | −5681.13 | −0.195484 | −0.0977418 | − | 0.995212i | \(-0.531162\pi\) | ||||
−0.0977418 | + | 0.995212i | \(0.531162\pi\) | |||||||
\(62\) | 31158.7 | 1.02944 | ||||||||
\(63\) | 1441.63 | 0.0457617 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 38055.2 | 1.11720 | ||||||||
\(66\) | 17481.6 | 0.493994 | ||||||||
\(67\) | −60959.7 | −1.65904 | −0.829518 | − | 0.558480i | \(-0.811385\pi\) | ||||
−0.829518 | + | 0.558480i | \(0.811385\pi\) | |||||||
\(68\) | −5542.81 | −0.145364 | ||||||||
\(69\) | 5344.18 | 0.135132 | ||||||||
\(70\) | 5340.96 | 0.130279 | ||||||||
\(71\) | 32944.4 | 0.775596 | 0.387798 | − | 0.921744i | \(-0.373236\pi\) | ||||
0.387798 | + | 0.921744i | \(0.373236\pi\) | |||||||
\(72\) | −5184.00 | −0.117851 | ||||||||
\(73\) | 74404.5 | 1.63415 | 0.817075 | − | 0.576532i | \(-0.195594\pi\) | ||||
0.817075 | + | 0.576532i | \(0.195594\pi\) | |||||||
\(74\) | −19385.3 | −0.411522 | ||||||||
\(75\) | −22530.2 | −0.462501 | ||||||||
\(76\) | −26598.1 | −0.528222 | ||||||||
\(77\) | 8642.66 | 0.166120 | ||||||||
\(78\) | −18261.0 | −0.339851 | ||||||||
\(79\) | −36190.1 | −0.652412 | −0.326206 | − | 0.945299i | \(-0.605770\pi\) | ||||
−0.326206 | + | 0.945299i | \(0.605770\pi\) | |||||||
\(80\) | −19205.7 | −0.335510 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −58780.7 | −0.965383 | ||||||||
\(83\) | −70280.2 | −1.11979 | −0.559896 | − | 0.828563i | \(-0.689159\pi\) | ||||
−0.559896 | + | 0.828563i | \(0.689159\pi\) | |||||||
\(84\) | −2562.90 | −0.0396308 | ||||||||
\(85\) | 25989.7 | 0.390170 | ||||||||
\(86\) | 63718.4 | 0.929006 | ||||||||
\(87\) | 62384.8 | 0.883651 | ||||||||
\(88\) | −31078.4 | −0.427811 | ||||||||
\(89\) | 25275.7 | 0.338243 | 0.169121 | − | 0.985595i | \(-0.445907\pi\) | ||||
0.169121 | + | 0.985595i | \(0.445907\pi\) | |||||||
\(90\) | 24307.3 | 0.316322 | ||||||||
\(91\) | −9028.00 | −0.114285 | ||||||||
\(92\) | −9500.76 | −0.117028 | ||||||||
\(93\) | 70107.0 | 0.840531 | ||||||||
\(94\) | −89866.1 | −1.04900 | ||||||||
\(95\) | 124716. | 1.41779 | ||||||||
\(96\) | 9216.00 | 0.102062 | ||||||||
\(97\) | 25544.4 | 0.275656 | 0.137828 | − | 0.990456i | \(-0.455988\pi\) | ||||
0.137828 | + | 0.990456i | \(0.455988\pi\) | |||||||
\(98\) | 65960.9 | 0.693780 | ||||||||
\(99\) | 39333.6 | 0.403344 | ||||||||
\(100\) | 40053.7 | 0.400537 | ||||||||
\(101\) | 177892. | 1.73521 | 0.867607 | − | 0.497250i | \(-0.165657\pi\) | ||||
0.867607 | + | 0.497250i | \(0.165657\pi\) | |||||||
\(102\) | −12471.3 | −0.118689 | ||||||||
\(103\) | 92651.8 | 0.860520 | 0.430260 | − | 0.902705i | \(-0.358422\pi\) | ||||
0.430260 | + | 0.902705i | \(0.358422\pi\) | |||||||
\(104\) | 32464.1 | 0.294320 | ||||||||
\(105\) | 12017.2 | 0.106372 | ||||||||
\(106\) | 67934.4 | 0.587253 | ||||||||
\(107\) | 55810.0 | 0.471251 | 0.235626 | − | 0.971844i | \(-0.424286\pi\) | ||||
0.235626 | + | 0.971844i | \(0.424286\pi\) | |||||||
\(108\) | −11664.0 | −0.0962250 | ||||||||
\(109\) | 210675. | 1.69842 | 0.849211 | − | 0.528053i | \(-0.177078\pi\) | ||||
0.849211 | + | 0.528053i | \(0.177078\pi\) | |||||||
\(110\) | 145724. | 1.14828 | ||||||||
\(111\) | −43616.9 | −0.336006 | ||||||||
\(112\) | 4556.26 | 0.0343213 | ||||||||
\(113\) | −254472. | −1.87476 | −0.937378 | − | 0.348315i | \(-0.886754\pi\) | ||||
−0.937378 | + | 0.348315i | \(0.886754\pi\) | |||||||
\(114\) | −59845.7 | −0.431292 | ||||||||
\(115\) | 44548.1 | 0.314112 | ||||||||
\(116\) | −110906. | −0.765265 | ||||||||
\(117\) | −41087.3 | −0.277487 | ||||||||
\(118\) | −13924.0 | −0.0920575 | ||||||||
\(119\) | −6165.65 | −0.0399127 | ||||||||
\(120\) | −43212.9 | −0.273943 | ||||||||
\(121\) | 74756.6 | 0.464179 | ||||||||
\(122\) | 22724.5 | 0.138228 | ||||||||
\(123\) | −132256. | −0.788232 | ||||||||
\(124\) | −124635. | −0.727922 | ||||||||
\(125\) | 46637.0 | 0.266966 | ||||||||
\(126\) | −5766.52 | −0.0323584 | ||||||||
\(127\) | 247007. | 1.35894 | 0.679471 | − | 0.733703i | \(-0.262210\pi\) | ||||
0.679471 | + | 0.733703i | \(0.262210\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | 143366. | 0.758530 | ||||||||
\(130\) | −152221. | −0.789979 | ||||||||
\(131\) | 269965. | 1.37445 | 0.687225 | − | 0.726445i | \(-0.258829\pi\) | ||||
0.687225 | + | 0.726445i | \(0.258829\pi\) | |||||||
\(132\) | −69926.4 | −0.349306 | ||||||||
\(133\) | −29586.9 | −0.145034 | ||||||||
\(134\) | 243839. | 1.17312 | ||||||||
\(135\) | 54691.3 | 0.258276 | ||||||||
\(136\) | 22171.2 | 0.102788 | ||||||||
\(137\) | 356377. | 1.62221 | 0.811107 | − | 0.584897i | \(-0.198865\pi\) | ||||
0.811107 | + | 0.584897i | \(0.198865\pi\) | |||||||
\(138\) | −21376.7 | −0.0955527 | ||||||||
\(139\) | −50616.3 | −0.222205 | −0.111102 | − | 0.993809i | \(-0.535438\pi\) | ||||
−0.111102 | + | 0.993809i | \(0.535438\pi\) | |||||||
\(140\) | −21363.9 | −0.0921212 | ||||||||
\(141\) | −202199. | −0.856506 | ||||||||
\(142\) | −131778. | −0.548429 | ||||||||
\(143\) | −246321. | −1.00731 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | 520029. | 2.05403 | ||||||||
\(146\) | −297618. | −1.15552 | ||||||||
\(147\) | 148412. | 0.566469 | ||||||||
\(148\) | 77541.1 | 0.290990 | ||||||||
\(149\) | 73911.6 | 0.272739 | 0.136369 | − | 0.990658i | \(-0.456457\pi\) | ||||
0.136369 | + | 0.990658i | \(0.456457\pi\) | |||||||
\(150\) | 90120.9 | 0.327037 | ||||||||
\(151\) | −43522.5 | −0.155336 | −0.0776679 | − | 0.996979i | \(-0.524747\pi\) | ||||
−0.0776679 | + | 0.996979i | \(0.524747\pi\) | |||||||
\(152\) | 106392. | 0.373510 | ||||||||
\(153\) | −28060.5 | −0.0969096 | ||||||||
\(154\) | −34570.7 | −0.117464 | ||||||||
\(155\) | 584399. | 1.95380 | ||||||||
\(156\) | 73044.1 | 0.240311 | ||||||||
\(157\) | −102497. | −0.331864 | −0.165932 | − | 0.986137i | \(-0.553063\pi\) | ||||
−0.165932 | + | 0.986137i | \(0.553063\pi\) | |||||||
\(158\) | 144760. | 0.461325 | ||||||||
\(159\) | 152852. | 0.479490 | ||||||||
\(160\) | 76822.9 | 0.237242 | ||||||||
\(161\) | −10568.3 | −0.0321323 | ||||||||
\(162\) | −26244.0 | −0.0785674 | ||||||||
\(163\) | −90752.2 | −0.267540 | −0.133770 | − | 0.991012i | \(-0.542708\pi\) | ||||
−0.133770 | + | 0.991012i | \(0.542708\pi\) | |||||||
\(164\) | 235123. | 0.682629 | ||||||||
\(165\) | 327878. | 0.937567 | ||||||||
\(166\) | 281121. | 0.791813 | ||||||||
\(167\) | −59309.4 | −0.164563 | −0.0822815 | − | 0.996609i | \(-0.526221\pi\) | ||||
−0.0822815 | + | 0.996609i | \(0.526221\pi\) | |||||||
\(168\) | 10251.6 | 0.0280232 | ||||||||
\(169\) | −113990. | −0.307007 | ||||||||
\(170\) | −103959. | −0.275892 | ||||||||
\(171\) | −134653. | −0.352148 | ||||||||
\(172\) | −254874. | −0.656907 | ||||||||
\(173\) | −371287. | −0.943179 | −0.471589 | − | 0.881818i | \(-0.656320\pi\) | ||||
−0.471589 | + | 0.881818i | \(0.656320\pi\) | |||||||
\(174\) | −249539. | −0.624836 | ||||||||
\(175\) | 44554.5 | 0.109976 | ||||||||
\(176\) | 124314. | 0.302508 | ||||||||
\(177\) | −31329.0 | −0.0751646 | ||||||||
\(178\) | −101103. | −0.239174 | ||||||||
\(179\) | 7764.45 | 0.0181125 | 0.00905624 | − | 0.999959i | \(-0.497117\pi\) | ||||
0.00905624 | + | 0.999959i | \(0.497117\pi\) | |||||||
\(180\) | −97229.0 | −0.223674 | ||||||||
\(181\) | 207550. | 0.470898 | 0.235449 | − | 0.971887i | \(-0.424344\pi\) | ||||
0.235449 | + | 0.971887i | \(0.424344\pi\) | |||||||
\(182\) | 36112.0 | 0.0808115 | ||||||||
\(183\) | 51130.2 | 0.112863 | ||||||||
\(184\) | 38003.0 | 0.0827511 | ||||||||
\(185\) | −363582. | −0.781041 | ||||||||
\(186\) | −280428. | −0.594345 | ||||||||
\(187\) | −168224. | −0.351791 | ||||||||
\(188\) | 359464. | 0.741756 | ||||||||
\(189\) | −12974.7 | −0.0264205 | ||||||||
\(190\) | −498863. | −1.00253 | ||||||||
\(191\) | 172606. | 0.342351 | 0.171176 | − | 0.985241i | \(-0.445243\pi\) | ||||
0.171176 | + | 0.985241i | \(0.445243\pi\) | |||||||
\(192\) | −36864.0 | −0.0721688 | ||||||||
\(193\) | −912610. | −1.76357 | −0.881783 | − | 0.471655i | \(-0.843657\pi\) | ||||
−0.881783 | + | 0.471655i | \(0.843657\pi\) | |||||||
\(194\) | −102178. | −0.194918 | ||||||||
\(195\) | −342497. | −0.645015 | ||||||||
\(196\) | −263844. | −0.490576 | ||||||||
\(197\) | 346131. | 0.635441 | 0.317721 | − | 0.948184i | \(-0.397083\pi\) | ||||
0.317721 | + | 0.948184i | \(0.397083\pi\) | |||||||
\(198\) | −157334. | −0.285207 | ||||||||
\(199\) | 219663. | 0.393210 | 0.196605 | − | 0.980483i | \(-0.437008\pi\) | ||||
0.196605 | + | 0.980483i | \(0.437008\pi\) | |||||||
\(200\) | −160215. | −0.283223 | ||||||||
\(201\) | 548637. | 0.957845 | ||||||||
\(202\) | −711568. | −1.22698 | ||||||||
\(203\) | −123369. | −0.210119 | ||||||||
\(204\) | 49885.3 | 0.0839261 | ||||||||
\(205\) | −1.10247e6 | −1.83223 | ||||||||
\(206\) | −370607. | −0.608479 | ||||||||
\(207\) | −48097.6 | −0.0780185 | ||||||||
\(208\) | −129856. | −0.208115 | ||||||||
\(209\) | −807253. | −1.27833 | ||||||||
\(210\) | −48068.7 | −0.0752166 | ||||||||
\(211\) | 139453. | 0.215636 | 0.107818 | − | 0.994171i | \(-0.465614\pi\) | ||||
0.107818 | + | 0.994171i | \(0.465614\pi\) | |||||||
\(212\) | −271738. | −0.415250 | ||||||||
\(213\) | −296500. | −0.447791 | ||||||||
\(214\) | −223240. | −0.333225 | ||||||||
\(215\) | 1.19508e6 | 1.76319 | ||||||||
\(216\) | 46656.0 | 0.0680414 | ||||||||
\(217\) | −138640. | −0.199866 | ||||||||
\(218\) | −842698. | −1.20097 | ||||||||
\(219\) | −669640. | −0.943477 | ||||||||
\(220\) | −582894. | −0.811957 | ||||||||
\(221\) | 175725. | 0.242021 | ||||||||
\(222\) | 174468. | 0.237592 | ||||||||
\(223\) | 524085. | 0.705732 | 0.352866 | − | 0.935674i | \(-0.385207\pi\) | ||||
0.352866 | + | 0.935674i | \(0.385207\pi\) | |||||||
\(224\) | −18225.1 | −0.0242688 | ||||||||
\(225\) | 202772. | 0.267025 | ||||||||
\(226\) | 1.01789e6 | 1.32565 | ||||||||
\(227\) | −1.06504e6 | −1.37183 | −0.685914 | − | 0.727683i | \(-0.740597\pi\) | ||||
−0.685914 | + | 0.727683i | \(0.740597\pi\) | |||||||
\(228\) | 239383. | 0.304969 | ||||||||
\(229\) | 77430.1 | 0.0975711 | 0.0487855 | − | 0.998809i | \(-0.484465\pi\) | ||||
0.0487855 | + | 0.998809i | \(0.484465\pi\) | |||||||
\(230\) | −178192. | −0.222111 | ||||||||
\(231\) | −77784.0 | −0.0959092 | ||||||||
\(232\) | 443626. | 0.541124 | ||||||||
\(233\) | 547655. | 0.660872 | 0.330436 | − | 0.943828i | \(-0.392804\pi\) | ||||
0.330436 | + | 0.943828i | \(0.392804\pi\) | |||||||
\(234\) | 164349. | 0.196213 | ||||||||
\(235\) | −1.68549e6 | −1.99094 | ||||||||
\(236\) | 55696.0 | 0.0650945 | ||||||||
\(237\) | 325711. | 0.376670 | ||||||||
\(238\) | 24662.6 | 0.0282226 | ||||||||
\(239\) | 781054. | 0.884477 | 0.442238 | − | 0.896898i | \(-0.354185\pi\) | ||||
0.442238 | + | 0.896898i | \(0.354185\pi\) | |||||||
\(240\) | 172852. | 0.193707 | ||||||||
\(241\) | 1.10849e6 | 1.22938 | 0.614692 | − | 0.788767i | \(-0.289280\pi\) | ||||
0.614692 | + | 0.788767i | \(0.289280\pi\) | |||||||
\(242\) | −299026. | −0.328224 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | −90898.1 | −0.0977418 | ||||||||
\(245\) | 1.23714e6 | 1.31675 | ||||||||
\(246\) | 529026. | 0.557364 | ||||||||
\(247\) | 843244. | 0.879450 | ||||||||
\(248\) | 498539. | 0.514718 | ||||||||
\(249\) | 632521. | 0.646512 | ||||||||
\(250\) | −186548. | −0.188773 | ||||||||
\(251\) | 1.16262e6 | 1.16480 | 0.582402 | − | 0.812901i | \(-0.302113\pi\) | ||||
0.582402 | + | 0.812901i | \(0.302113\pi\) | |||||||
\(252\) | 23066.1 | 0.0228809 | ||||||||
\(253\) | −288348. | −0.283215 | ||||||||
\(254\) | −988030. | −0.960917 | ||||||||
\(255\) | −233907. | −0.225265 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −1.43559e6 | −1.35580 | −0.677902 | − | 0.735152i | \(-0.737111\pi\) | ||||
−0.677902 | + | 0.735152i | \(0.737111\pi\) | |||||||
\(258\) | −573465. | −0.536362 | ||||||||
\(259\) | 86254.3 | 0.0798972 | ||||||||
\(260\) | 608883. | 0.558599 | ||||||||
\(261\) | −561464. | −0.510176 | ||||||||
\(262\) | −1.07986e6 | −0.971882 | ||||||||
\(263\) | −1.89520e6 | −1.68953 | −0.844766 | − | 0.535135i | \(-0.820261\pi\) | ||||
−0.844766 | + | 0.535135i | \(0.820261\pi\) | |||||||
\(264\) | 279706. | 0.246997 | ||||||||
\(265\) | 1.27415e6 | 1.11457 | ||||||||
\(266\) | 118348. | 0.102555 | ||||||||
\(267\) | −227481. | −0.195285 | ||||||||
\(268\) | −975356. | −0.829518 | ||||||||
\(269\) | 1.77716e6 | 1.49742 | 0.748712 | − | 0.662895i | \(-0.230673\pi\) | ||||
0.748712 | + | 0.662895i | \(0.230673\pi\) | |||||||
\(270\) | −218765. | −0.182629 | ||||||||
\(271\) | −760373. | −0.628932 | −0.314466 | − | 0.949269i | \(-0.601825\pi\) | ||||
−0.314466 | + | 0.949269i | \(0.601825\pi\) | |||||||
\(272\) | −88685.0 | −0.0726822 | ||||||||
\(273\) | 81252.0 | 0.0659823 | ||||||||
\(274\) | −1.42551e6 | −1.14708 | ||||||||
\(275\) | 1.21563e6 | 0.969327 | ||||||||
\(276\) | 85506.8 | 0.0675660 | ||||||||
\(277\) | −1.75250e6 | −1.37233 | −0.686165 | − | 0.727446i | \(-0.740707\pi\) | ||||
−0.686165 | + | 0.727446i | \(0.740707\pi\) | |||||||
\(278\) | 202465. | 0.157122 | ||||||||
\(279\) | −630963. | −0.485281 | ||||||||
\(280\) | 85455.4 | 0.0651395 | ||||||||
\(281\) | 138408. | 0.104567 | 0.0522836 | − | 0.998632i | \(-0.483350\pi\) | ||||
0.0522836 | + | 0.998632i | \(0.483350\pi\) | |||||||
\(282\) | 808795. | 0.605642 | ||||||||
\(283\) | −844853. | −0.627068 | −0.313534 | − | 0.949577i | \(-0.601513\pi\) | ||||
−0.313534 | + | 0.949577i | \(0.601513\pi\) | |||||||
\(284\) | 527110. | 0.387798 | ||||||||
\(285\) | −1.12244e6 | −0.818563 | ||||||||
\(286\) | 985284. | 0.712273 | ||||||||
\(287\) | 261543. | 0.187430 | ||||||||
\(288\) | −82944.0 | −0.0589256 | ||||||||
\(289\) | −1.29985e6 | −0.915477 | ||||||||
\(290\) | −2.08012e6 | −1.45242 | ||||||||
\(291\) | −229900. | −0.159150 | ||||||||
\(292\) | 1.19047e6 | 0.817075 | ||||||||
\(293\) | 2.80754e6 | 1.91054 | 0.955271 | − | 0.295733i | \(-0.0955637\pi\) | ||||
0.955271 | + | 0.295733i | \(0.0955637\pi\) | |||||||
\(294\) | −593648. | −0.400554 | ||||||||
\(295\) | −261153. | −0.174719 | ||||||||
\(296\) | −310164. | −0.205761 | ||||||||
\(297\) | −354003. | −0.232871 | ||||||||
\(298\) | −295646. | −0.192855 | ||||||||
\(299\) | 301204. | 0.194842 | ||||||||
\(300\) | −360484. | −0.231250 | ||||||||
\(301\) | −283513. | −0.180367 | ||||||||
\(302\) | 174090. | 0.109839 | ||||||||
\(303\) | −1.60103e6 | −1.00183 | ||||||||
\(304\) | −425570. | −0.264111 | ||||||||
\(305\) | 426212. | 0.262347 | ||||||||
\(306\) | 112242. | 0.0685254 | ||||||||
\(307\) | 712594. | 0.431516 | 0.215758 | − | 0.976447i | \(-0.430778\pi\) | ||||
0.215758 | + | 0.976447i | \(0.430778\pi\) | |||||||
\(308\) | 138283. | 0.0830598 | ||||||||
\(309\) | −833866. | −0.496821 | ||||||||
\(310\) | −2.33760e6 | −1.38155 | ||||||||
\(311\) | 2.03477e6 | 1.19293 | 0.596464 | − | 0.802640i | \(-0.296572\pi\) | ||||
0.596464 | + | 0.802640i | \(0.296572\pi\) | |||||||
\(312\) | −292176. | −0.169926 | ||||||||
\(313\) | 1.04329e6 | 0.601927 | 0.300964 | − | 0.953636i | \(-0.402692\pi\) | ||||
0.300964 | + | 0.953636i | \(0.402692\pi\) | |||||||
\(314\) | 409986. | 0.234663 | ||||||||
\(315\) | −108155. | −0.0614141 | ||||||||
\(316\) | −579042. | −0.326206 | ||||||||
\(317\) | 97044.0 | 0.0542401 | 0.0271200 | − | 0.999632i | \(-0.491366\pi\) | ||||
0.0271200 | + | 0.999632i | \(0.491366\pi\) | |||||||
\(318\) | −611410. | −0.339051 | ||||||||
\(319\) | −3.36601e6 | −1.85199 | ||||||||
\(320\) | −307292. | −0.167755 | ||||||||
\(321\) | −502290. | −0.272077 | ||||||||
\(322\) | 42273.4 | 0.0227210 | ||||||||
\(323\) | 575892. | 0.307139 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | −1.26983e6 | −0.666864 | ||||||||
\(326\) | 363009. | 0.189179 | ||||||||
\(327\) | −1.89607e6 | −0.980585 | ||||||||
\(328\) | −940491. | −0.482692 | ||||||||
\(329\) | 399857. | 0.203664 | ||||||||
\(330\) | −1.31151e6 | −0.662960 | ||||||||
\(331\) | 3.17003e6 | 1.59035 | 0.795177 | − | 0.606377i | \(-0.207378\pi\) | ||||
0.795177 | + | 0.606377i | \(0.207378\pi\) | |||||||
\(332\) | −1.12448e6 | −0.559896 | ||||||||
\(333\) | 392552. | 0.193993 | ||||||||
\(334\) | 237237. | 0.116364 | ||||||||
\(335\) | 4.57334e6 | 2.22650 | ||||||||
\(336\) | −41006.4 | −0.0198154 | ||||||||
\(337\) | −3.75855e6 | −1.80279 | −0.901397 | − | 0.432994i | \(-0.857457\pi\) | ||||
−0.901397 | + | 0.432994i | \(0.857457\pi\) | |||||||
\(338\) | 455958. | 0.217087 | ||||||||
\(339\) | 2.29025e6 | 1.08239 | ||||||||
\(340\) | 415835. | 0.195085 | ||||||||
\(341\) | −3.78266e6 | −1.76162 | ||||||||
\(342\) | 538612. | 0.249006 | ||||||||
\(343\) | −592621. | −0.271983 | ||||||||
\(344\) | 1.01949e6 | 0.464503 | ||||||||
\(345\) | −400933. | −0.181353 | ||||||||
\(346\) | 1.48515e6 | 0.666928 | ||||||||
\(347\) | −2.43095e6 | −1.08381 | −0.541905 | − | 0.840440i | \(-0.682297\pi\) | ||||
−0.541905 | + | 0.840440i | \(0.682297\pi\) | |||||||
\(348\) | 998157. | 0.441826 | ||||||||
\(349\) | 1.14487e6 | 0.503146 | 0.251573 | − | 0.967838i | \(-0.419052\pi\) | ||||
0.251573 | + | 0.967838i | \(0.419052\pi\) | |||||||
\(350\) | −178218. | −0.0777646 | ||||||||
\(351\) | 369786. | 0.160207 | ||||||||
\(352\) | −497255. | −0.213906 | ||||||||
\(353\) | −2.72502e6 | −1.16395 | −0.581974 | − | 0.813207i | \(-0.697720\pi\) | ||||
−0.581974 | + | 0.813207i | \(0.697720\pi\) | |||||||
\(354\) | 125316. | 0.0531494 | ||||||||
\(355\) | −2.47157e6 | −1.04088 | ||||||||
\(356\) | 404412. | 0.169121 | ||||||||
\(357\) | 55490.9 | 0.0230436 | ||||||||
\(358\) | −31057.8 | −0.0128075 | ||||||||
\(359\) | 3.82400e6 | 1.56596 | 0.782982 | − | 0.622045i | \(-0.213698\pi\) | ||||
0.782982 | + | 0.622045i | \(0.213698\pi\) | |||||||
\(360\) | 388916. | 0.158161 | ||||||||
\(361\) | 287413. | 0.116075 | ||||||||
\(362\) | −830201. | −0.332975 | ||||||||
\(363\) | −672809. | −0.267994 | ||||||||
\(364\) | −144448. | −0.0571423 | ||||||||
\(365\) | −5.58200e6 | −2.19310 | ||||||||
\(366\) | −204521. | −0.0798059 | ||||||||
\(367\) | 2.89599e6 | 1.12236 | 0.561179 | − | 0.827695i | \(-0.310348\pi\) | ||||
0.561179 | + | 0.827695i | \(0.310348\pi\) | |||||||
\(368\) | −152012. | −0.0585139 | ||||||||
\(369\) | 1.19031e6 | 0.455086 | ||||||||
\(370\) | 1.45433e6 | 0.552279 | ||||||||
\(371\) | −302272. | −0.114015 | ||||||||
\(372\) | 1.12171e6 | 0.420266 | ||||||||
\(373\) | 799129. | 0.297403 | 0.148701 | − | 0.988882i | \(-0.452491\pi\) | ||||
0.148701 | + | 0.988882i | \(0.452491\pi\) | |||||||
\(374\) | 672898. | 0.248754 | ||||||||
\(375\) | −419733. | −0.154133 | ||||||||
\(376\) | −1.43786e6 | −0.524501 | ||||||||
\(377\) | 3.51608e6 | 1.27411 | ||||||||
\(378\) | 51898.7 | 0.0186821 | ||||||||
\(379\) | −281568. | −0.100690 | −0.0503449 | − | 0.998732i | \(-0.516032\pi\) | ||||
−0.0503449 | + | 0.998732i | \(0.516032\pi\) | |||||||
\(380\) | 1.99545e6 | 0.708896 | ||||||||
\(381\) | −2.22307e6 | −0.784585 | ||||||||
\(382\) | −690423. | −0.242079 | ||||||||
\(383\) | 2.61292e6 | 0.910183 | 0.455092 | − | 0.890445i | \(-0.349606\pi\) | ||||
0.455092 | + | 0.890445i | \(0.349606\pi\) | |||||||
\(384\) | 147456. | 0.0510310 | ||||||||
\(385\) | −648393. | −0.222939 | ||||||||
\(386\) | 3.65044e6 | 1.24703 | ||||||||
\(387\) | −1.29030e6 | −0.437938 | ||||||||
\(388\) | 408711. | 0.137828 | ||||||||
\(389\) | −1.44947e6 | −0.485664 | −0.242832 | − | 0.970068i | \(-0.578076\pi\) | ||||
−0.242832 | + | 0.970068i | \(0.578076\pi\) | |||||||
\(390\) | 1.36999e6 | 0.456094 | ||||||||
\(391\) | 205707. | 0.0680466 | ||||||||
\(392\) | 1.05538e6 | 0.346890 | ||||||||
\(393\) | −2.42968e6 | −0.793539 | ||||||||
\(394\) | −1.38453e6 | −0.449325 | ||||||||
\(395\) | 2.71507e6 | 0.875564 | ||||||||
\(396\) | 629338. | 0.201672 | ||||||||
\(397\) | 4.38919e6 | 1.39768 | 0.698841 | − | 0.715277i | \(-0.253700\pi\) | ||||
0.698841 | + | 0.715277i | \(0.253700\pi\) | |||||||
\(398\) | −878653. | −0.278042 | ||||||||
\(399\) | 266282. | 0.0837355 | ||||||||
\(400\) | 640860. | 0.200269 | ||||||||
\(401\) | −3.73715e6 | −1.16059 | −0.580296 | − | 0.814406i | \(-0.697063\pi\) | ||||
−0.580296 | + | 0.814406i | \(0.697063\pi\) | |||||||
\(402\) | −2.19455e6 | −0.677299 | ||||||||
\(403\) | 3.95131e6 | 1.21193 | ||||||||
\(404\) | 2.84627e6 | 0.867607 | ||||||||
\(405\) | −492222. | −0.149116 | ||||||||
\(406\) | 493475. | 0.148577 | ||||||||
\(407\) | 2.35337e6 | 0.704214 | ||||||||
\(408\) | −199541. | −0.0593447 | ||||||||
\(409\) | 3.02555e6 | 0.894327 | 0.447163 | − | 0.894452i | \(-0.352434\pi\) | ||||
0.447163 | + | 0.894452i | \(0.352434\pi\) | |||||||
\(410\) | 4.40987e6 | 1.29558 | ||||||||
\(411\) | −3.20739e6 | −0.936586 | ||||||||
\(412\) | 1.48243e6 | 0.430260 | ||||||||
\(413\) | 61954.5 | 0.0178730 | ||||||||
\(414\) | 192390. | 0.0551674 | ||||||||
\(415\) | 5.27259e6 | 1.50281 | ||||||||
\(416\) | 519425. | 0.147160 | ||||||||
\(417\) | 455547. | 0.128290 | ||||||||
\(418\) | 3.22901e6 | 0.903918 | ||||||||
\(419\) | −2.98553e6 | −0.830781 | −0.415391 | − | 0.909643i | \(-0.636355\pi\) | ||||
−0.415391 | + | 0.909643i | \(0.636355\pi\) | |||||||
\(420\) | 192275. | 0.0531862 | ||||||||
\(421\) | 1.71749e6 | 0.472268 | 0.236134 | − | 0.971721i | \(-0.424120\pi\) | ||||
0.236134 | + | 0.971721i | \(0.424120\pi\) | |||||||
\(422\) | −557810. | −0.152477 | ||||||||
\(423\) | 1.81979e6 | 0.494504 | ||||||||
\(424\) | 1.08695e6 | 0.293626 | ||||||||
\(425\) | −867228. | −0.232895 | ||||||||
\(426\) | 1.18600e6 | 0.316636 | ||||||||
\(427\) | −101112. | −0.0268370 | ||||||||
\(428\) | 892960. | 0.235626 | ||||||||
\(429\) | 2.21689e6 | 0.581569 | ||||||||
\(430\) | −4.78031e6 | −1.24676 | ||||||||
\(431\) | −367341. | −0.0952525 | −0.0476263 | − | 0.998865i | \(-0.515166\pi\) | ||||
−0.0476263 | + | 0.998865i | \(0.515166\pi\) | |||||||
\(432\) | −186624. | −0.0481125 | ||||||||
\(433\) | 684609. | 0.175478 | 0.0877390 | − | 0.996143i | \(-0.472036\pi\) | ||||
0.0877390 | + | 0.996143i | \(0.472036\pi\) | |||||||
\(434\) | 554559. | 0.141326 | ||||||||
\(435\) | −4.68026e6 | −1.18590 | ||||||||
\(436\) | 3.37079e6 | 0.849211 | ||||||||
\(437\) | 987118. | 0.247267 | ||||||||
\(438\) | 2.67856e6 | 0.667139 | ||||||||
\(439\) | 3.84247e6 | 0.951590 | 0.475795 | − | 0.879556i | \(-0.342160\pi\) | ||||
0.475795 | + | 0.879556i | \(0.342160\pi\) | |||||||
\(440\) | 2.33158e6 | 0.574140 | ||||||||
\(441\) | −1.33571e6 | −0.327051 | ||||||||
\(442\) | −702899. | −0.171134 | ||||||||
\(443\) | 3.26654e6 | 0.790823 | 0.395412 | − | 0.918504i | \(-0.370602\pi\) | ||||
0.395412 | + | 0.918504i | \(0.370602\pi\) | |||||||
\(444\) | −697870. | −0.168003 | ||||||||
\(445\) | −1.89625e6 | −0.453936 | ||||||||
\(446\) | −2.09634e6 | −0.499028 | ||||||||
\(447\) | −665204. | −0.157466 | ||||||||
\(448\) | 72900.2 | 0.0171606 | ||||||||
\(449\) | −300699. | −0.0703909 | −0.0351954 | − | 0.999380i | \(-0.511205\pi\) | ||||
−0.0351954 | + | 0.999380i | \(0.511205\pi\) | |||||||
\(450\) | −811088. | −0.188815 | ||||||||
\(451\) | 7.13598e6 | 1.65201 | ||||||||
\(452\) | −4.07156e6 | −0.937378 | ||||||||
\(453\) | 391703. | 0.0896832 | ||||||||
\(454\) | 4.26014e6 | 0.970028 | ||||||||
\(455\) | 677302. | 0.153375 | ||||||||
\(456\) | −957532. | −0.215646 | ||||||||
\(457\) | 5.51670e6 | 1.23563 | 0.617815 | − | 0.786323i | \(-0.288018\pi\) | ||||
0.617815 | + | 0.786323i | \(0.288018\pi\) | |||||||
\(458\) | −309720. | −0.0689932 | ||||||||
\(459\) | 252544. | 0.0559508 | ||||||||
\(460\) | 712770. | 0.157056 | ||||||||
\(461\) | 2.95614e6 | 0.647848 | 0.323924 | − | 0.946083i | \(-0.394998\pi\) | ||||
0.323924 | + | 0.946083i | \(0.394998\pi\) | |||||||
\(462\) | 311136. | 0.0678180 | ||||||||
\(463\) | 6.61613e6 | 1.43434 | 0.717169 | − | 0.696899i | \(-0.245437\pi\) | ||||
0.717169 | + | 0.696899i | \(0.245437\pi\) | |||||||
\(464\) | −1.77450e6 | −0.382632 | ||||||||
\(465\) | −5.25959e6 | −1.12803 | ||||||||
\(466\) | −2.19062e6 | −0.467307 | ||||||||
\(467\) | 7.18933e6 | 1.52544 | 0.762721 | − | 0.646727i | \(-0.223863\pi\) | ||||
0.762721 | + | 0.646727i | \(0.223863\pi\) | |||||||
\(468\) | −657397. | −0.138744 | ||||||||
\(469\) | −1.08496e6 | −0.227761 | ||||||||
\(470\) | 6.74197e6 | 1.40780 | ||||||||
\(471\) | 922469. | 0.191602 | ||||||||
\(472\) | −222784. | −0.0460287 | ||||||||
\(473\) | −7.73542e6 | −1.58976 | ||||||||
\(474\) | −1.30284e6 | −0.266346 | ||||||||
\(475\) | −4.16154e6 | −0.846291 | ||||||||
\(476\) | −98650.4 | −0.0199564 | ||||||||
\(477\) | −1.37567e6 | −0.276834 | ||||||||
\(478\) | −3.12422e6 | −0.625420 | ||||||||
\(479\) | 890884. | 0.177412 | 0.0887059 | − | 0.996058i | \(-0.471727\pi\) | ||||
0.0887059 | + | 0.996058i | \(0.471727\pi\) | |||||||
\(480\) | −691406. | −0.136972 | ||||||||
\(481\) | −2.45830e6 | −0.484476 | ||||||||
\(482\) | −4.43394e6 | −0.869305 | ||||||||
\(483\) | 95115.1 | 0.0185516 | ||||||||
\(484\) | 1.19610e6 | 0.232090 | ||||||||
\(485\) | −1.91641e6 | −0.369941 | ||||||||
\(486\) | 236196. | 0.0453609 | ||||||||
\(487\) | −2.18101e6 | −0.416712 | −0.208356 | − | 0.978053i | \(-0.566811\pi\) | ||||
−0.208356 | + | 0.978053i | \(0.566811\pi\) | |||||||
\(488\) | 363593. | 0.0691139 | ||||||||
\(489\) | 816770. | 0.154464 | ||||||||
\(490\) | −4.94855e6 | −0.931081 | ||||||||
\(491\) | 8.22986e6 | 1.54060 | 0.770298 | − | 0.637684i | \(-0.220107\pi\) | ||||
0.770298 | + | 0.637684i | \(0.220107\pi\) | |||||||
\(492\) | −2.11610e6 | −0.394116 | ||||||||
\(493\) | 2.40130e6 | 0.444969 | ||||||||
\(494\) | −3.37298e6 | −0.621865 | ||||||||
\(495\) | −2.95090e6 | −0.541305 | ||||||||
\(496\) | −1.99415e6 | −0.363961 | ||||||||
\(497\) | 586341. | 0.106478 | ||||||||
\(498\) | −2.53009e6 | −0.457153 | ||||||||
\(499\) | −7.67960e6 | −1.38066 | −0.690331 | − | 0.723494i | \(-0.742535\pi\) | ||||
−0.690331 | + | 0.723494i | \(0.742535\pi\) | |||||||
\(500\) | 746192. | 0.133483 | ||||||||
\(501\) | 533784. | 0.0950104 | ||||||||
\(502\) | −4.65047e6 | −0.823641 | ||||||||
\(503\) | −732941. | −0.129166 | −0.0645831 | − | 0.997912i | \(-0.520572\pi\) | ||||
−0.0645831 | + | 0.997912i | \(0.520572\pi\) | |||||||
\(504\) | −92264.3 | −0.0161792 | ||||||||
\(505\) | −1.33459e7 | −2.32873 | ||||||||
\(506\) | 1.15339e6 | 0.200263 | ||||||||
\(507\) | 1.02591e6 | 0.177251 | ||||||||
\(508\) | 3.95212e6 | 0.679471 | ||||||||
\(509\) | −3.43769e6 | −0.588128 | −0.294064 | − | 0.955786i | \(-0.595008\pi\) | ||||
−0.294064 | + | 0.955786i | \(0.595008\pi\) | |||||||
\(510\) | 935629. | 0.159286 | ||||||||
\(511\) | 1.32424e6 | 0.224345 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | 1.21188e6 | 0.203313 | ||||||||
\(514\) | 5.74235e6 | 0.958698 | ||||||||
\(515\) | −6.95096e6 | −1.15485 | ||||||||
\(516\) | 2.29386e6 | 0.379265 | ||||||||
\(517\) | 1.09097e7 | 1.79510 | ||||||||
\(518\) | −345017. | −0.0564958 | ||||||||
\(519\) | 3.34158e6 | 0.544545 | ||||||||
\(520\) | −2.43553e6 | −0.394989 | ||||||||
\(521\) | 1.80746e6 | 0.291726 | 0.145863 | − | 0.989305i | \(-0.453404\pi\) | ||||
0.145863 | + | 0.989305i | \(0.453404\pi\) | |||||||
\(522\) | 2.24585e6 | 0.360749 | ||||||||
\(523\) | 7.89318e6 | 1.26182 | 0.630911 | − | 0.775855i | \(-0.282681\pi\) | ||||
0.630911 | + | 0.775855i | \(0.282681\pi\) | |||||||
\(524\) | 4.31944e6 | 0.687225 | ||||||||
\(525\) | −400991. | −0.0634945 | ||||||||
\(526\) | 7.58082e6 | 1.19468 | ||||||||
\(527\) | 2.69854e6 | 0.423255 | ||||||||
\(528\) | −1.11882e6 | −0.174653 | ||||||||
\(529\) | −6.08375e6 | −0.945218 | ||||||||
\(530\) | −5.09660e6 | −0.788117 | ||||||||
\(531\) | 281961. | 0.0433963 | ||||||||
\(532\) | −473390. | −0.0725171 | ||||||||
\(533\) | −7.45414e6 | −1.13653 | ||||||||
\(534\) | 909926. | 0.138087 | ||||||||
\(535\) | −4.18700e6 | −0.632439 | ||||||||
\(536\) | 3.90142e6 | 0.586558 | ||||||||
\(537\) | −69880.0 | −0.0104572 | ||||||||
\(538\) | −7.10862e6 | −1.05884 | ||||||||
\(539\) | −8.00766e6 | −1.18723 | ||||||||
\(540\) | 875061. | 0.129138 | ||||||||
\(541\) | −1.31054e7 | −1.92512 | −0.962559 | − | 0.271071i | \(-0.912622\pi\) | ||||
−0.962559 | + | 0.271071i | \(0.912622\pi\) | |||||||
\(542\) | 3.04149e6 | 0.444722 | ||||||||
\(543\) | −1.86795e6 | −0.271873 | ||||||||
\(544\) | 354740. | 0.0513941 | ||||||||
\(545\) | −1.58053e7 | −2.27935 | ||||||||
\(546\) | −325008. | −0.0466565 | ||||||||
\(547\) | −1.07610e7 | −1.53774 | −0.768872 | − | 0.639403i | \(-0.779181\pi\) | ||||
−0.768872 | + | 0.639403i | \(0.779181\pi\) | |||||||
\(548\) | 5.70203e6 | 0.811107 | ||||||||
\(549\) | −460172. | −0.0651612 | ||||||||
\(550\) | −4.86253e6 | −0.685418 | ||||||||
\(551\) | 1.15230e7 | 1.61692 | ||||||||
\(552\) | −342027. | −0.0477764 | ||||||||
\(553\) | −644108. | −0.0895665 | ||||||||
\(554\) | 7.00999e6 | 0.970383 | ||||||||
\(555\) | 3.27224e6 | 0.450934 | ||||||||
\(556\) | −809860. | −0.111102 | ||||||||
\(557\) | 3.89845e6 | 0.532420 | 0.266210 | − | 0.963915i | \(-0.414229\pi\) | ||||
0.266210 | + | 0.963915i | \(0.414229\pi\) | |||||||
\(558\) | 2.52385e6 | 0.343146 | ||||||||
\(559\) | 8.08030e6 | 1.09370 | ||||||||
\(560\) | −341822. | −0.0460606 | ||||||||
\(561\) | 1.51402e6 | 0.203107 | ||||||||
\(562\) | −553632. | −0.0739402 | ||||||||
\(563\) | −5.32082e6 | −0.707469 | −0.353735 | − | 0.935346i | \(-0.615088\pi\) | ||||
−0.353735 | + | 0.935346i | \(0.615088\pi\) | |||||||
\(564\) | −3.23518e6 | −0.428253 | ||||||||
\(565\) | 1.90911e7 | 2.51600 | ||||||||
\(566\) | 3.37941e6 | 0.443404 | ||||||||
\(567\) | 116772. | 0.0152539 | ||||||||
\(568\) | −2.10844e6 | −0.274215 | ||||||||
\(569\) | 7.86449e6 | 1.01833 | 0.509166 | − | 0.860668i | \(-0.329954\pi\) | ||||
0.509166 | + | 0.860668i | \(0.329954\pi\) | |||||||
\(570\) | 4.48977e6 | 0.578811 | ||||||||
\(571\) | −4.16368e6 | −0.534425 | −0.267213 | − | 0.963638i | \(-0.586103\pi\) | ||||
−0.267213 | + | 0.963638i | \(0.586103\pi\) | |||||||
\(572\) | −3.94114e6 | −0.503653 | ||||||||
\(573\) | −1.55345e6 | −0.197656 | ||||||||
\(574\) | −1.04617e6 | −0.132533 | ||||||||
\(575\) | −1.48649e6 | −0.187496 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | −7.27913e6 | −0.910206 | −0.455103 | − | 0.890439i | \(-0.650398\pi\) | ||||
−0.455103 | + | 0.890439i | \(0.650398\pi\) | |||||||
\(578\) | 5.19938e6 | 0.647340 | ||||||||
\(579\) | 8.21349e6 | 1.01820 | ||||||||
\(580\) | 8.32046e6 | 1.02702 | ||||||||
\(581\) | −1.25084e6 | −0.153731 | ||||||||
\(582\) | 919600. | 0.112536 | ||||||||
\(583\) | −8.24724e6 | −1.00493 | ||||||||
\(584\) | −4.76189e6 | −0.577759 | ||||||||
\(585\) | 3.08247e6 | 0.372399 | ||||||||
\(586\) | −1.12301e7 | −1.35096 | ||||||||
\(587\) | −1.22184e7 | −1.46359 | −0.731797 | − | 0.681523i | \(-0.761318\pi\) | ||||
−0.731797 | + | 0.681523i | \(0.761318\pi\) | |||||||
\(588\) | 2.37459e6 | 0.283234 | ||||||||
\(589\) | 1.29494e7 | 1.53802 | ||||||||
\(590\) | 1.04461e6 | 0.123545 | ||||||||
\(591\) | −3.11518e6 | −0.366872 | ||||||||
\(592\) | 1.24066e6 | 0.145495 | ||||||||
\(593\) | −1.31282e6 | −0.153309 | −0.0766545 | − | 0.997058i | \(-0.524424\pi\) | ||||
−0.0766545 | + | 0.997058i | \(0.524424\pi\) | |||||||
\(594\) | 1.41601e6 | 0.164665 | ||||||||
\(595\) | 462562. | 0.0535645 | ||||||||
\(596\) | 1.18259e6 | 0.136369 | ||||||||
\(597\) | −1.97697e6 | −0.227020 | ||||||||
\(598\) | −1.20482e6 | −0.137774 | ||||||||
\(599\) | −1.51035e6 | −0.171993 | −0.0859964 | − | 0.996295i | \(-0.527407\pi\) | ||||
−0.0859964 | + | 0.996295i | \(0.527407\pi\) | |||||||
\(600\) | 1.44193e6 | 0.163519 | ||||||||
\(601\) | 7.32636e6 | 0.827374 | 0.413687 | − | 0.910419i | \(-0.364241\pi\) | ||||
0.413687 | + | 0.910419i | \(0.364241\pi\) | |||||||
\(602\) | 1.13405e6 | 0.127539 | ||||||||
\(603\) | −4.93774e6 | −0.553012 | ||||||||
\(604\) | −696360. | −0.0776679 | ||||||||
\(605\) | −5.60842e6 | −0.622948 | ||||||||
\(606\) | 6.40411e6 | 0.708398 | ||||||||
\(607\) | −6.67575e6 | −0.735408 | −0.367704 | − | 0.929943i | \(-0.619856\pi\) | ||||
−0.367704 | + | 0.929943i | \(0.619856\pi\) | |||||||
\(608\) | 1.70228e6 | 0.186755 | ||||||||
\(609\) | 1.11032e6 | 0.121312 | ||||||||
\(610\) | −1.70485e6 | −0.185507 | ||||||||
\(611\) | −1.13962e7 | −1.23497 | ||||||||
\(612\) | −448968. | −0.0484548 | ||||||||
\(613\) | −5.04738e6 | −0.542519 | −0.271260 | − | 0.962506i | \(-0.587440\pi\) | ||||
−0.271260 | + | 0.962506i | \(0.587440\pi\) | |||||||
\(614\) | −2.85038e6 | −0.305128 | ||||||||
\(615\) | 9.92220e6 | 1.05784 | ||||||||
\(616\) | −553131. | −0.0587321 | ||||||||
\(617\) | 8.09696e6 | 0.856267 | 0.428134 | − | 0.903715i | \(-0.359171\pi\) | ||||
0.428134 | + | 0.903715i | \(0.359171\pi\) | |||||||
\(618\) | 3.33546e6 | 0.351306 | ||||||||
\(619\) | 2.22019e6 | 0.232897 | 0.116448 | − | 0.993197i | \(-0.462849\pi\) | ||||
0.116448 | + | 0.993197i | \(0.462849\pi\) | |||||||
\(620\) | 9.35039e6 | 0.976901 | ||||||||
\(621\) | 432878. | 0.0450440 | ||||||||
\(622\) | −8.13908e6 | −0.843528 | ||||||||
\(623\) | 449855. | 0.0464357 | ||||||||
\(624\) | 1.16871e6 | 0.120156 | ||||||||
\(625\) | −1.13218e7 | −1.15935 | ||||||||
\(626\) | −4.17316e6 | −0.425627 | ||||||||
\(627\) | 7.26527e6 | 0.738046 | ||||||||
\(628\) | −1.63994e6 | −0.165932 | ||||||||
\(629\) | −1.67889e6 | −0.169198 | ||||||||
\(630\) | 432618. | 0.0434263 | ||||||||
\(631\) | 1.40361e7 | 1.40338 | 0.701688 | − | 0.712485i | \(-0.252430\pi\) | ||||
0.701688 | + | 0.712485i | \(0.252430\pi\) | |||||||
\(632\) | 2.31617e6 | 0.230662 | ||||||||
\(633\) | −1.25507e6 | −0.124497 | ||||||||
\(634\) | −388176. | −0.0383535 | ||||||||
\(635\) | −1.85311e7 | −1.82376 | ||||||||
\(636\) | 2.44564e6 | 0.239745 | ||||||||
\(637\) | 8.36469e6 | 0.816772 | ||||||||
\(638\) | 1.34640e7 | 1.30955 | ||||||||
\(639\) | 2.66850e6 | 0.258532 | ||||||||
\(640\) | 1.22917e6 | 0.118621 | ||||||||
\(641\) | 376115. | 0.0361556 | 0.0180778 | − | 0.999837i | \(-0.494245\pi\) | ||||
0.0180778 | + | 0.999837i | \(0.494245\pi\) | |||||||
\(642\) | 2.00916e6 | 0.192388 | ||||||||
\(643\) | 1.51655e7 | 1.44653 | 0.723266 | − | 0.690570i | \(-0.242640\pi\) | ||||
0.723266 | + | 0.690570i | \(0.242640\pi\) | |||||||
\(644\) | −169094. | −0.0160662 | ||||||||
\(645\) | −1.07557e7 | −1.01798 | ||||||||
\(646\) | −2.30357e6 | −0.217180 | ||||||||
\(647\) | 1.74275e7 | 1.63672 | 0.818362 | − | 0.574703i | \(-0.194882\pi\) | ||||
0.818362 | + | 0.574703i | \(0.194882\pi\) | |||||||
\(648\) | −419904. | −0.0392837 | ||||||||
\(649\) | 1.69037e6 | 0.157533 | ||||||||
\(650\) | 5.07932e6 | 0.471544 | ||||||||
\(651\) | 1.24776e6 | 0.115393 | ||||||||
\(652\) | −1.45204e6 | −0.133770 | ||||||||
\(653\) | 5.89333e6 | 0.540851 | 0.270426 | − | 0.962741i | \(-0.412836\pi\) | ||||
0.270426 | + | 0.962741i | \(0.412836\pi\) | |||||||
\(654\) | 7.58428e6 | 0.693378 | ||||||||
\(655\) | −2.02534e7 | −1.84457 | ||||||||
\(656\) | 3.76196e6 | 0.341315 | ||||||||
\(657\) | 6.02676e6 | 0.544717 | ||||||||
\(658\) | −1.59943e6 | −0.144012 | ||||||||
\(659\) | −2.41916e6 | −0.216996 | −0.108498 | − | 0.994097i | \(-0.534604\pi\) | ||||
−0.108498 | + | 0.994097i | \(0.534604\pi\) | |||||||
\(660\) | 5.24605e6 | 0.468784 | ||||||||
\(661\) | −2.95209e6 | −0.262800 | −0.131400 | − | 0.991329i | \(-0.541947\pi\) | ||||
−0.131400 | + | 0.991329i | \(0.541947\pi\) | |||||||
\(662\) | −1.26801e7 | −1.12455 | ||||||||
\(663\) | −1.58152e6 | −0.139731 | ||||||||
\(664\) | 4.49793e6 | 0.395906 | ||||||||
\(665\) | 2.21968e6 | 0.194642 | ||||||||
\(666\) | −1.57021e6 | −0.137174 | ||||||||
\(667\) | 4.11600e6 | 0.358229 | ||||||||
\(668\) | −948950. | −0.0822815 | ||||||||
\(669\) | −4.71677e6 | −0.407455 | ||||||||
\(670\) | −1.82934e7 | −1.57437 | ||||||||
\(671\) | −2.75876e6 | −0.236542 | ||||||||
\(672\) | 164025. | 0.0140116 | ||||||||
\(673\) | 2.03480e7 | 1.73174 | 0.865872 | − | 0.500265i | \(-0.166764\pi\) | ||||
0.865872 | + | 0.500265i | \(0.166764\pi\) | |||||||
\(674\) | 1.50342e7 | 1.27477 | ||||||||
\(675\) | −1.82495e6 | −0.154167 | ||||||||
\(676\) | −1.82383e6 | −0.153504 | ||||||||
\(677\) | −1.67007e7 | −1.40044 | −0.700218 | − | 0.713929i | \(-0.746914\pi\) | ||||
−0.700218 | + | 0.713929i | \(0.746914\pi\) | |||||||
\(678\) | −9.16101e6 | −0.765366 | ||||||||
\(679\) | 454638. | 0.0378435 | ||||||||
\(680\) | −1.66334e6 | −0.137946 | ||||||||
\(681\) | 9.58532e6 | 0.792025 | ||||||||
\(682\) | 1.51307e7 | 1.24565 | ||||||||
\(683\) | −9.23369e6 | −0.757397 | −0.378698 | − | 0.925520i | \(-0.623628\pi\) | ||||
−0.378698 | + | 0.925520i | \(0.623628\pi\) | |||||||
\(684\) | −2.15445e6 | −0.176074 | ||||||||
\(685\) | −2.67363e7 | −2.17708 | ||||||||
\(686\) | 2.37048e6 | 0.192321 | ||||||||
\(687\) | −696871. | −0.0563327 | ||||||||
\(688\) | −4.07798e6 | −0.328453 | ||||||||
\(689\) | 8.61495e6 | 0.691360 | ||||||||
\(690\) | 1.60373e6 | 0.128236 | ||||||||
\(691\) | −1.56683e7 | −1.24832 | −0.624159 | − | 0.781297i | \(-0.714558\pi\) | ||||
−0.624159 | + | 0.781297i | \(0.714558\pi\) | |||||||
\(692\) | −5.94059e6 | −0.471589 | ||||||||
\(693\) | 700056. | 0.0553732 | ||||||||
\(694\) | 9.72381e6 | 0.766369 | ||||||||
\(695\) | 3.79735e6 | 0.298208 | ||||||||
\(696\) | −3.99263e6 | −0.312418 | ||||||||
\(697\) | −5.09078e6 | −0.396920 | ||||||||
\(698\) | −4.57950e6 | −0.355778 | ||||||||
\(699\) | −4.92889e6 | −0.381554 | ||||||||
\(700\) | 712872. | 0.0549879 | ||||||||
\(701\) | −1.63457e7 | −1.25634 | −0.628171 | − | 0.778075i | \(-0.716196\pi\) | ||||
−0.628171 | + | 0.778075i | \(0.716196\pi\) | |||||||
\(702\) | −1.47914e6 | −0.113284 | ||||||||
\(703\) | −8.05643e6 | −0.614829 | ||||||||
\(704\) | 1.98902e6 | 0.151254 | ||||||||
\(705\) | 1.51694e7 | 1.14947 | ||||||||
\(706\) | 1.09001e7 | 0.823036 | ||||||||
\(707\) | 3.16611e6 | 0.238219 | ||||||||
\(708\) | −501264. | −0.0375823 | ||||||||
\(709\) | −1.23736e7 | −0.924444 | −0.462222 | − | 0.886764i | \(-0.652948\pi\) | ||||
−0.462222 | + | 0.886764i | \(0.652948\pi\) | |||||||
\(710\) | 9.88627e6 | 0.736015 | ||||||||
\(711\) | −2.93140e6 | −0.217471 | ||||||||
\(712\) | −1.61765e6 | −0.119587 | ||||||||
\(713\) | 4.62548e6 | 0.340748 | ||||||||
\(714\) | −221963. | −0.0162943 | ||||||||
\(715\) | 1.84796e7 | 1.35185 | ||||||||
\(716\) | 124231. | 0.00905624 | ||||||||
\(717\) | −7.02949e6 | −0.510653 | ||||||||
\(718\) | −1.52960e7 | −1.10730 | ||||||||
\(719\) | −2.02502e7 | −1.46086 | −0.730428 | − | 0.682990i | \(-0.760679\pi\) | ||||
−0.730428 | + | 0.682990i | \(0.760679\pi\) | |||||||
\(720\) | −1.55566e6 | −0.111837 | ||||||||
\(721\) | 1.64901e6 | 0.118137 | ||||||||
\(722\) | −1.14965e6 | −0.0820773 | ||||||||
\(723\) | −9.97637e6 | −0.709785 | ||||||||
\(724\) | 3.32081e6 | 0.235449 | ||||||||
\(725\) | −1.73524e7 | −1.22607 | ||||||||
\(726\) | 2.69124e6 | 0.189500 | ||||||||
\(727\) | 1.15577e7 | 0.811030 | 0.405515 | − | 0.914088i | \(-0.367092\pi\) | ||||
0.405515 | + | 0.914088i | \(0.367092\pi\) | |||||||
\(728\) | 577792. | 0.0404057 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 2.23280e7 | 1.55075 | ||||||||
\(731\) | 5.51842e6 | 0.381963 | ||||||||
\(732\) | 818083. | 0.0564313 | ||||||||
\(733\) | 1.55295e7 | 1.06758 | 0.533788 | − | 0.845618i | \(-0.320768\pi\) | ||||
0.533788 | + | 0.845618i | \(0.320768\pi\) | |||||||
\(734\) | −1.15839e7 | −0.793627 | ||||||||
\(735\) | −1.11342e7 | −0.760225 | ||||||||
\(736\) | 608049. | 0.0413755 | ||||||||
\(737\) | −2.96021e7 | −2.00749 | ||||||||
\(738\) | −4.76123e6 | −0.321794 | ||||||||
\(739\) | −8.05265e6 | −0.542410 | −0.271205 | − | 0.962522i | \(-0.587422\pi\) | ||||
−0.271205 | + | 0.962522i | \(0.587422\pi\) | |||||||
\(740\) | −5.81732e6 | −0.390520 | ||||||||
\(741\) | −7.58920e6 | −0.507751 | ||||||||
\(742\) | 1.20909e6 | 0.0806211 | ||||||||
\(743\) | 1.78280e7 | 1.18476 | 0.592381 | − | 0.805658i | \(-0.298188\pi\) | ||||
0.592381 | + | 0.805658i | \(0.298188\pi\) | |||||||
\(744\) | −4.48685e6 | −0.297173 | ||||||||
\(745\) | −5.54502e6 | −0.366027 | ||||||||
\(746\) | −3.19652e6 | −0.210295 | ||||||||
\(747\) | −5.69269e6 | −0.373264 | ||||||||
\(748\) | −2.69159e6 | −0.175896 | ||||||||
\(749\) | 993301. | 0.0646958 | ||||||||
\(750\) | 1.67893e6 | 0.108988 | ||||||||
\(751\) | 2.32701e6 | 0.150556 | 0.0752782 | − | 0.997163i | \(-0.476016\pi\) | ||||
0.0752782 | + | 0.997163i | \(0.476016\pi\) | |||||||
\(752\) | 5.75143e6 | 0.370878 | ||||||||
\(753\) | −1.04636e7 | −0.672500 | ||||||||
\(754\) | −1.40643e7 | −0.900930 | ||||||||
\(755\) | 3.26516e6 | 0.208467 | ||||||||
\(756\) | −207595. | −0.0132103 | ||||||||
\(757\) | −3.09474e6 | −0.196284 | −0.0981418 | − | 0.995172i | \(-0.531290\pi\) | ||||
−0.0981418 | + | 0.995172i | \(0.531290\pi\) | |||||||
\(758\) | 1.12627e6 | 0.0711984 | ||||||||
\(759\) | 2.59513e6 | 0.163514 | ||||||||
\(760\) | −7.98181e6 | −0.501265 | ||||||||
\(761\) | 3.06304e6 | 0.191731 | 0.0958653 | − | 0.995394i | \(-0.469438\pi\) | ||||
0.0958653 | + | 0.995394i | \(0.469438\pi\) | |||||||
\(762\) | 8.89227e6 | 0.554785 | ||||||||
\(763\) | 3.74956e6 | 0.233168 | ||||||||
\(764\) | 2.76169e6 | 0.171176 | ||||||||
\(765\) | 2.10516e6 | 0.130057 | ||||||||
\(766\) | −1.04517e7 | −0.643597 | ||||||||
\(767\) | −1.76574e6 | −0.108377 | ||||||||
\(768\) | −589824. | −0.0360844 | ||||||||
\(769\) | 1.40665e7 | 0.857770 | 0.428885 | − | 0.903359i | \(-0.358906\pi\) | ||||
0.428885 | + | 0.903359i | \(0.358906\pi\) | |||||||
\(770\) | 2.59357e6 | 0.157642 | ||||||||
\(771\) | 1.29203e7 | 0.782774 | ||||||||
\(772\) | −1.46018e7 | −0.881783 | ||||||||
\(773\) | −1.90973e7 | −1.14954 | −0.574768 | − | 0.818317i | \(-0.694908\pi\) | ||||
−0.574768 | + | 0.818317i | \(0.694908\pi\) | |||||||
\(774\) | 5.16119e6 | 0.309669 | ||||||||
\(775\) | −1.95003e7 | −1.16624 | ||||||||
\(776\) | −1.63484e6 | −0.0974590 | ||||||||
\(777\) | −776289. | −0.0461287 | ||||||||
\(778\) | 5.79789e6 | 0.343416 | ||||||||
\(779\) | −2.44290e7 | −1.44232 | ||||||||
\(780\) | −5.47994e6 | −0.322507 | ||||||||
\(781\) | 1.59978e7 | 0.938497 | ||||||||
\(782\) | −822827. | −0.0481162 | ||||||||
\(783\) | 5.05317e6 | 0.294550 | ||||||||
\(784\) | −4.22150e6 | −0.245288 | ||||||||
\(785\) | 7.68953e6 | 0.445375 | ||||||||
\(786\) | 9.71873e6 | 0.561117 | ||||||||
\(787\) | 5.58099e6 | 0.321199 | 0.160600 | − | 0.987020i | \(-0.448657\pi\) | ||||
0.160600 | + | 0.987020i | \(0.448657\pi\) | |||||||
\(788\) | 5.53810e6 | 0.317721 | ||||||||
\(789\) | 1.70568e7 | 0.975452 | ||||||||
\(790\) | −1.08603e7 | −0.619117 | ||||||||
\(791\) | −4.52907e6 | −0.257376 | ||||||||
\(792\) | −2.51735e6 | −0.142604 | ||||||||
\(793\) | 2.88176e6 | 0.162733 | ||||||||
\(794\) | −1.75568e7 | −0.988310 | ||||||||
\(795\) | −1.14674e7 | −0.643495 | ||||||||
\(796\) | 3.51461e6 | 0.196605 | ||||||||
\(797\) | −2.73946e7 | −1.52763 | −0.763817 | − | 0.645433i | \(-0.776677\pi\) | ||||
−0.763817 | + | 0.645433i | \(0.776677\pi\) | |||||||
\(798\) | −1.06513e6 | −0.0592100 | ||||||||
\(799\) | −7.78298e6 | −0.431300 | ||||||||
\(800\) | −2.56344e6 | −0.141611 | ||||||||
\(801\) | 2.04733e6 | 0.112748 | ||||||||
\(802\) | 1.49486e7 | 0.820662 | ||||||||
\(803\) | 3.61308e7 | 1.97737 | ||||||||
\(804\) | 8.77820e6 | 0.478923 | ||||||||
\(805\) | 792863. | 0.0431229 | ||||||||
\(806\) | −1.58053e7 | −0.856967 | ||||||||
\(807\) | −1.59944e7 | −0.864538 | ||||||||
\(808\) | −1.13851e7 | −0.613491 | ||||||||
\(809\) | 2.18484e7 | 1.17368 | 0.586839 | − | 0.809704i | \(-0.300372\pi\) | ||||
0.586839 | + | 0.809704i | \(0.300372\pi\) | |||||||
\(810\) | 1.96889e6 | 0.105441 | ||||||||
\(811\) | −2.22347e7 | −1.18708 | −0.593539 | − | 0.804805i | \(-0.702270\pi\) | ||||
−0.593539 | + | 0.804805i | \(0.702270\pi\) | |||||||
\(812\) | −1.97390e6 | −0.105059 | ||||||||
\(813\) | 6.84336e6 | 0.363114 | ||||||||
\(814\) | −9.41350e6 | −0.497955 | ||||||||
\(815\) | 6.80845e6 | 0.359049 | ||||||||
\(816\) | 798165. | 0.0419631 | ||||||||
\(817\) | 2.64811e7 | 1.38797 | ||||||||
\(818\) | −1.21022e7 | −0.632385 | ||||||||
\(819\) | −731268. | −0.0380949 | ||||||||
\(820\) | −1.76395e7 | −0.916117 | ||||||||
\(821\) | −7.07014e6 | −0.366075 | −0.183038 | − | 0.983106i | \(-0.558593\pi\) | ||||
−0.183038 | + | 0.983106i | \(0.558593\pi\) | |||||||
\(822\) | 1.28296e7 | 0.662266 | ||||||||
\(823\) | 1.64293e7 | 0.845509 | 0.422755 | − | 0.906244i | \(-0.361063\pi\) | ||||
0.422755 | + | 0.906244i | \(0.361063\pi\) | |||||||
\(824\) | −5.92971e6 | −0.304240 | ||||||||
\(825\) | −1.09407e7 | −0.559641 | ||||||||
\(826\) | −247818. | −0.0126381 | ||||||||
\(827\) | −2.82840e7 | −1.43806 | −0.719030 | − | 0.694979i | \(-0.755414\pi\) | ||||
−0.719030 | + | 0.694979i | \(0.755414\pi\) | |||||||
\(828\) | −769562. | −0.0390092 | ||||||||
\(829\) | −5.03085e6 | −0.254247 | −0.127123 | − | 0.991887i | \(-0.540574\pi\) | ||||
−0.127123 | + | 0.991887i | \(0.540574\pi\) | |||||||
\(830\) | −2.10903e7 | −1.06265 | ||||||||
\(831\) | 1.57725e7 | 0.792315 | ||||||||
\(832\) | −2.07770e6 | −0.104058 | ||||||||
\(833\) | 5.71264e6 | 0.285249 | ||||||||
\(834\) | −1.82219e6 | −0.0907147 | ||||||||
\(835\) | 4.44953e6 | 0.220850 | ||||||||
\(836\) | −1.29160e7 | −0.639166 | ||||||||
\(837\) | 5.67867e6 | 0.280177 | ||||||||
\(838\) | 1.19421e7 | 0.587451 | ||||||||
\(839\) | 2.05246e7 | 1.00663 | 0.503316 | − | 0.864102i | \(-0.332113\pi\) | ||||
0.503316 | + | 0.864102i | \(0.332113\pi\) | |||||||
\(840\) | −769099. | −0.0376083 | ||||||||
\(841\) | 2.75366e7 | 1.34252 | ||||||||
\(842\) | −6.86995e6 | −0.333944 | ||||||||
\(843\) | −1.24567e6 | −0.0603719 | ||||||||
\(844\) | 2.23124e6 | 0.107818 | ||||||||
\(845\) | 8.55177e6 | 0.412016 | ||||||||
\(846\) | −7.27915e6 | −0.349667 | ||||||||
\(847\) | 1.33051e6 | 0.0637250 | ||||||||
\(848\) | −4.34780e6 | −0.207625 | ||||||||
\(849\) | 7.60367e6 | 0.362038 | ||||||||
\(850\) | 3.46891e6 | 0.164682 | ||||||||
\(851\) | −2.87773e6 | −0.136215 | ||||||||
\(852\) | −4.74399e6 | −0.223895 | ||||||||
\(853\) | −3.77826e7 | −1.77795 | −0.888974 | − | 0.457957i | \(-0.848581\pi\) | ||||
−0.888974 | + | 0.457957i | \(0.848581\pi\) | |||||||
\(854\) | 404449. | 0.0189766 | ||||||||
\(855\) | 1.01020e7 | 0.472597 | ||||||||
\(856\) | −3.57184e6 | −0.166613 | ||||||||
\(857\) | 1.71644e6 | 0.0798319 | 0.0399159 | − | 0.999203i | \(-0.487291\pi\) | ||||
0.0399159 | + | 0.999203i | \(0.487291\pi\) | |||||||
\(858\) | −8.86756e6 | −0.411231 | ||||||||
\(859\) | 1.12483e7 | 0.520120 | 0.260060 | − | 0.965592i | \(-0.416258\pi\) | ||||
0.260060 | + | 0.965592i | \(0.416258\pi\) | |||||||
\(860\) | 1.91212e7 | 0.881596 | ||||||||
\(861\) | −2.35389e6 | −0.108213 | ||||||||
\(862\) | 1.46936e6 | 0.0673537 | ||||||||
\(863\) | 9.56455e6 | 0.437157 | 0.218579 | − | 0.975819i | \(-0.429858\pi\) | ||||
0.218579 | + | 0.975819i | \(0.429858\pi\) | |||||||
\(864\) | 746496. | 0.0340207 | ||||||||
\(865\) | 2.78548e7 | 1.26578 | ||||||||
\(866\) | −2.73844e6 | −0.124082 | ||||||||
\(867\) | 1.16986e7 | 0.528551 | ||||||||
\(868\) | −2.21824e6 | −0.0999328 | ||||||||
\(869\) | −1.75739e7 | −0.789440 | ||||||||
\(870\) | 1.87210e7 | 0.838556 | ||||||||
\(871\) | 3.09219e7 | 1.38108 | ||||||||
\(872\) | −1.34832e7 | −0.600483 | ||||||||
\(873\) | 2.06910e6 | 0.0918853 | ||||||||
\(874\) | −3.94847e6 | −0.174844 | ||||||||
\(875\) | 830041. | 0.0366505 | ||||||||
\(876\) | −1.07142e7 | −0.471738 | ||||||||
\(877\) | −3.86591e6 | −0.169728 | −0.0848640 | − | 0.996393i | \(-0.527046\pi\) | ||||
−0.0848640 | + | 0.996393i | \(0.527046\pi\) | |||||||
\(878\) | −1.53699e7 | −0.672876 | ||||||||
\(879\) | −2.52678e7 | −1.10305 | ||||||||
\(880\) | −9.32631e6 | −0.405978 | ||||||||
\(881\) | 2.11609e7 | 0.918531 | 0.459265 | − | 0.888299i | \(-0.348113\pi\) | ||||
0.459265 | + | 0.888299i | \(0.348113\pi\) | |||||||
\(882\) | 5.34284e6 | 0.231260 | ||||||||
\(883\) | 2.68330e7 | 1.15816 | 0.579079 | − | 0.815272i | \(-0.303412\pi\) | ||||
0.579079 | + | 0.815272i | \(0.303412\pi\) | |||||||
\(884\) | 2.81160e6 | 0.121010 | ||||||||
\(885\) | 2.35038e6 | 0.100874 | ||||||||
\(886\) | −1.30662e7 | −0.559196 | ||||||||
\(887\) | 2.05930e7 | 0.878840 | 0.439420 | − | 0.898282i | \(-0.355184\pi\) | ||||
0.439420 | + | 0.898282i | \(0.355184\pi\) | |||||||
\(888\) | 2.79148e6 | 0.118796 | ||||||||
\(889\) | 4.39621e6 | 0.186562 | ||||||||
\(890\) | 7.58498e6 | 0.320981 | ||||||||
\(891\) | 3.18602e6 | 0.134448 | ||||||||
\(892\) | 8.38537e6 | 0.352866 | ||||||||
\(893\) | −3.73479e7 | −1.56725 | ||||||||
\(894\) | 2.66082e6 | 0.111345 | ||||||||
\(895\) | −582507. | −0.0243077 | ||||||||
\(896\) | −291601. | −0.0121344 | ||||||||
\(897\) | −2.71084e6 | −0.112492 | ||||||||
\(898\) | 1.20280e6 | 0.0497739 | ||||||||
\(899\) | 5.39952e7 | 2.22821 | ||||||||
\(900\) | 3.24435e6 | 0.133512 | ||||||||
\(901\) | 5.88356e6 | 0.241450 | ||||||||
\(902\) | −2.85439e7 | −1.16815 | ||||||||
\(903\) | 2.55162e6 | 0.104135 | ||||||||
\(904\) | 1.62862e7 | 0.662826 | ||||||||
\(905\) | −1.55709e7 | −0.631965 | ||||||||
\(906\) | −1.56681e6 | −0.0634156 | ||||||||
\(907\) | 4.32278e7 | 1.74480 | 0.872398 | − | 0.488796i | \(-0.162564\pi\) | ||||
0.872398 | + | 0.488796i | \(0.162564\pi\) | |||||||
\(908\) | −1.70406e7 | −0.685914 | ||||||||
\(909\) | 1.44093e7 | 0.578405 | ||||||||
\(910\) | −2.70921e6 | −0.108452 | ||||||||
\(911\) | 1.43100e7 | 0.571271 | 0.285636 | − | 0.958338i | \(-0.407795\pi\) | ||||
0.285636 | + | 0.958338i | \(0.407795\pi\) | |||||||
\(912\) | 3.83013e6 | 0.152485 | ||||||||
\(913\) | −3.41281e7 | −1.35499 | ||||||||
\(914\) | −2.20668e7 | −0.873723 | ||||||||
\(915\) | −3.83591e6 | −0.151466 | ||||||||
\(916\) | 1.23888e6 | 0.0487855 | ||||||||
\(917\) | 4.80480e6 | 0.188692 | ||||||||
\(918\) | −1.01018e6 | −0.0395632 | ||||||||
\(919\) | 2.96906e7 | 1.15966 | 0.579830 | − | 0.814737i | \(-0.303119\pi\) | ||||
0.579830 | + | 0.814737i | \(0.303119\pi\) | |||||||
\(920\) | −2.85108e6 | −0.111055 | ||||||||
\(921\) | −6.41335e6 | −0.249136 | ||||||||
\(922\) | −1.18246e7 | −0.458098 | ||||||||
\(923\) | −1.67111e7 | −0.645654 | ||||||||
\(924\) | −1.24454e6 | −0.0479546 | ||||||||
\(925\) | 1.21321e7 | 0.466209 | ||||||||
\(926\) | −2.64645e7 | −1.01423 | ||||||||
\(927\) | 7.50479e6 | 0.286840 | ||||||||
\(928\) | 7.09801e6 | 0.270562 | ||||||||
\(929\) | 9.42342e6 | 0.358236 | 0.179118 | − | 0.983828i | \(-0.442676\pi\) | ||||
0.179118 | + | 0.983828i | \(0.442676\pi\) | |||||||
\(930\) | 2.10384e7 | 0.797636 | ||||||||
\(931\) | 2.74131e7 | 1.03653 | ||||||||
\(932\) | 8.76248e6 | 0.330436 | ||||||||
\(933\) | −1.83129e7 | −0.688738 | ||||||||
\(934\) | −2.87573e7 | −1.07865 | ||||||||
\(935\) | 1.26206e7 | 0.472118 | ||||||||
\(936\) | 2.62959e6 | 0.0981066 | ||||||||
\(937\) | −1.01301e7 | −0.376935 | −0.188467 | − | 0.982079i | \(-0.560352\pi\) | ||||
−0.188467 | + | 0.982079i | \(0.560352\pi\) | |||||||
\(938\) | 4.33982e6 | 0.161051 | ||||||||
\(939\) | −9.38960e6 | −0.347523 | ||||||||
\(940\) | −2.69679e7 | −0.995468 | ||||||||
\(941\) | −2.81460e6 | −0.103620 | −0.0518099 | − | 0.998657i | \(-0.516499\pi\) | ||||
−0.0518099 | + | 0.998657i | \(0.516499\pi\) | |||||||
\(942\) | −3.68987e6 | −0.135483 | ||||||||
\(943\) | −8.72595e6 | −0.319546 | ||||||||
\(944\) | 891136. | 0.0325472 | ||||||||
\(945\) | 973391. | 0.0354575 | ||||||||
\(946\) | 3.09417e7 | 1.12413 | ||||||||
\(947\) | −1.60727e7 | −0.582388 | −0.291194 | − | 0.956664i | \(-0.594053\pi\) | ||||
−0.291194 | + | 0.956664i | \(0.594053\pi\) | |||||||
\(948\) | 5.21137e6 | 0.188335 | ||||||||
\(949\) | −3.77417e7 | −1.36037 | ||||||||
\(950\) | 1.66461e7 | 0.598418 | ||||||||
\(951\) | −873396. | −0.0313155 | ||||||||
\(952\) | 394602. | 0.0141113 | ||||||||
\(953\) | −5.01184e7 | −1.78758 | −0.893789 | − | 0.448488i | \(-0.851963\pi\) | ||||
−0.893789 | + | 0.448488i | \(0.851963\pi\) | |||||||
\(954\) | 5.50269e6 | 0.195751 | ||||||||
\(955\) | −1.29493e7 | −0.459449 | ||||||||
\(956\) | 1.24969e7 | 0.442238 | ||||||||
\(957\) | 3.02941e7 | 1.06925 | ||||||||
\(958\) | −3.56354e6 | −0.125449 | ||||||||
\(959\) | 6.34276e6 | 0.222706 | ||||||||
\(960\) | 2.76563e6 | 0.0968535 | ||||||||
\(961\) | 3.20497e7 | 1.11948 | ||||||||
\(962\) | 9.83320e6 | 0.342576 | ||||||||
\(963\) | 4.52061e6 | 0.157084 | ||||||||
\(964\) | 1.77358e7 | 0.614692 | ||||||||
\(965\) | 6.84662e7 | 2.36678 | ||||||||
\(966\) | −380461. | −0.0131180 | ||||||||
\(967\) | −2.60892e7 | −0.897211 | −0.448605 | − | 0.893730i | \(-0.648079\pi\) | ||||
−0.448605 | + | 0.893730i | \(0.648079\pi\) | |||||||
\(968\) | −4.78442e6 | −0.164112 | ||||||||
\(969\) | −5.18303e6 | −0.177327 | ||||||||
\(970\) | 7.66562e6 | 0.261588 | ||||||||
\(971\) | −3.47981e7 | −1.18442 | −0.592212 | − | 0.805782i | \(-0.701745\pi\) | ||||
−0.592212 | + | 0.805782i | \(0.701745\pi\) | |||||||
\(972\) | −944784. | −0.0320750 | ||||||||
\(973\) | −900864. | −0.0305054 | ||||||||
\(974\) | 8.72405e6 | 0.294660 | ||||||||
\(975\) | 1.14285e7 | 0.385014 | ||||||||
\(976\) | −1.45437e6 | −0.0488709 | ||||||||
\(977\) | −5.04875e7 | −1.69218 | −0.846092 | − | 0.533038i | \(-0.821050\pi\) | ||||
−0.846092 | + | 0.533038i | \(0.821050\pi\) | |||||||
\(978\) | −3.26708e6 | −0.109223 | ||||||||
\(979\) | 1.22739e7 | 0.409285 | ||||||||
\(980\) | 1.97942e7 | 0.658374 | ||||||||
\(981\) | 1.70646e7 | 0.566141 | ||||||||
\(982\) | −3.29194e7 | −1.08937 | ||||||||
\(983\) | −3.69821e7 | −1.22070 | −0.610348 | − | 0.792134i | \(-0.708970\pi\) | ||||
−0.610348 | + | 0.792134i | \(0.708970\pi\) | |||||||
\(984\) | 8.46442e6 | 0.278682 | ||||||||
\(985\) | −2.59676e7 | −0.852788 | ||||||||
\(986\) | −9.60521e6 | −0.314640 | ||||||||
\(987\) | −3.59871e6 | −0.117586 | ||||||||
\(988\) | 1.34919e7 | 0.439725 | ||||||||
\(989\) | 9.45895e6 | 0.307505 | ||||||||
\(990\) | 1.18036e7 | 0.382760 | ||||||||
\(991\) | 4.47136e7 | 1.44629 | 0.723146 | − | 0.690696i | \(-0.242696\pi\) | ||||
0.723146 | + | 0.690696i | \(0.242696\pi\) | |||||||
\(992\) | 7.97662e6 | 0.257359 | ||||||||
\(993\) | −2.85303e7 | −0.918192 | ||||||||
\(994\) | −2.34536e6 | −0.0752912 | ||||||||
\(995\) | −1.64797e7 | −0.527704 | ||||||||
\(996\) | 1.01203e7 | 0.323256 | ||||||||
\(997\) | 3.12814e7 | 0.996662 | 0.498331 | − | 0.866987i | \(-0.333946\pi\) | ||||
0.498331 | + | 0.866987i | \(0.333946\pi\) | |||||||
\(998\) | 3.07184e7 | 0.976276 | ||||||||
\(999\) | −3.53297e6 | −0.112002 |
(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 | 354.6.a.g.1.1 | ✓ | 6 | |
3.2 | odd | 2 | 1062.6.a.h.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
354.6.a.g.1.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
1062.6.a.h.1.6 | 6 | 3.2 | odd | 2 |