Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,6,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, 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("177.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(28.3879361069\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 331 x^{11} - 41 x^{10} + 41990 x^{9} + 7229 x^{8} - 2592364 x^{7} - 312100 x^{6} + \cdots - 6400833792 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-6.29094\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −6.29094 | −1.11209 | −0.556046 | − | 0.831152i | \(-0.687682\pi\) | ||||
−0.556046 | + | 0.831152i | \(0.687682\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 7.57589 | 0.236747 | ||||||||
\(5\) | 82.0909 | 1.46849 | 0.734243 | − | 0.678886i | \(-0.237537\pi\) | ||||
0.734243 | + | 0.678886i | \(0.237537\pi\) | |||||||
\(6\) | 56.6184 | 0.642066 | ||||||||
\(7\) | 51.5315 | 0.397492 | 0.198746 | − | 0.980051i | \(-0.436313\pi\) | ||||
0.198746 | + | 0.980051i | \(0.436313\pi\) | |||||||
\(8\) | 153.651 | 0.848807 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −516.429 | −1.63309 | ||||||||
\(11\) | 677.894 | 1.68920 | 0.844598 | − | 0.535402i | \(-0.179840\pi\) | ||||
0.844598 | + | 0.535402i | \(0.179840\pi\) | |||||||
\(12\) | −68.1830 | −0.136686 | ||||||||
\(13\) | 290.798 | 0.477236 | 0.238618 | − | 0.971113i | \(-0.423306\pi\) | ||||
0.238618 | + | 0.971113i | \(0.423306\pi\) | |||||||
\(14\) | −324.182 | −0.442047 | ||||||||
\(15\) | −738.818 | −0.847831 | ||||||||
\(16\) | −1209.03 | −1.18070 | ||||||||
\(17\) | 1791.65 | 1.50360 | 0.751800 | − | 0.659392i | \(-0.229186\pi\) | ||||
0.751800 | + | 0.659392i | \(0.229186\pi\) | |||||||
\(18\) | −509.566 | −0.370697 | ||||||||
\(19\) | −766.617 | −0.487186 | −0.243593 | − | 0.969878i | \(-0.578326\pi\) | ||||
−0.243593 | + | 0.969878i | \(0.578326\pi\) | |||||||
\(20\) | 621.912 | 0.347659 | ||||||||
\(21\) | −463.784 | −0.229492 | ||||||||
\(22\) | −4264.59 | −1.87854 | ||||||||
\(23\) | −3880.75 | −1.52966 | −0.764831 | − | 0.644231i | \(-0.777178\pi\) | ||||
−0.764831 | + | 0.644231i | \(0.777178\pi\) | |||||||
\(24\) | −1382.85 | −0.490059 | ||||||||
\(25\) | 3613.92 | 1.15645 | ||||||||
\(26\) | −1829.39 | −0.530730 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 390.397 | 0.0941048 | ||||||||
\(29\) | −4722.12 | −1.04266 | −0.521329 | − | 0.853356i | \(-0.674563\pi\) | ||||
−0.521329 | + | 0.853356i | \(0.674563\pi\) | |||||||
\(30\) | 4647.86 | 0.942866 | ||||||||
\(31\) | 9418.62 | 1.76029 | 0.880143 | − | 0.474709i | \(-0.157447\pi\) | ||||
0.880143 | + | 0.474709i | \(0.157447\pi\) | |||||||
\(32\) | 2689.14 | 0.464236 | ||||||||
\(33\) | −6101.04 | −0.975257 | ||||||||
\(34\) | −11271.2 | −1.67214 | ||||||||
\(35\) | 4230.27 | 0.583711 | ||||||||
\(36\) | 613.647 | 0.0789155 | ||||||||
\(37\) | −10201.3 | −1.22505 | −0.612523 | − | 0.790453i | \(-0.709845\pi\) | ||||
−0.612523 | + | 0.790453i | \(0.709845\pi\) | |||||||
\(38\) | 4822.74 | 0.541795 | ||||||||
\(39\) | −2617.19 | −0.275533 | ||||||||
\(40\) | 12613.3 | 1.24646 | ||||||||
\(41\) | 13038.5 | 1.21135 | 0.605674 | − | 0.795713i | \(-0.292904\pi\) | ||||
0.605674 | + | 0.795713i | \(0.292904\pi\) | |||||||
\(42\) | 2917.64 | 0.255216 | ||||||||
\(43\) | 21726.5 | 1.79192 | 0.895961 | − | 0.444132i | \(-0.146488\pi\) | ||||
0.895961 | + | 0.444132i | \(0.146488\pi\) | |||||||
\(44\) | 5135.65 | 0.399911 | ||||||||
\(45\) | 6649.36 | 0.489496 | ||||||||
\(46\) | 24413.5 | 1.70112 | ||||||||
\(47\) | 3799.78 | 0.250908 | 0.125454 | − | 0.992099i | \(-0.459961\pi\) | ||||
0.125454 | + | 0.992099i | \(0.459961\pi\) | |||||||
\(48\) | 10881.3 | 0.681676 | ||||||||
\(49\) | −14151.5 | −0.842000 | ||||||||
\(50\) | −22734.9 | −1.28608 | ||||||||
\(51\) | −16124.9 | −0.868103 | ||||||||
\(52\) | 2203.06 | 0.112984 | ||||||||
\(53\) | −5749.98 | −0.281175 | −0.140588 | − | 0.990068i | \(-0.544899\pi\) | ||||
−0.140588 | + | 0.990068i | \(0.544899\pi\) | |||||||
\(54\) | 4586.09 | 0.214022 | ||||||||
\(55\) | 55648.9 | 2.48056 | ||||||||
\(56\) | 7917.85 | 0.337394 | ||||||||
\(57\) | 6899.55 | 0.281277 | ||||||||
\(58\) | 29706.5 | 1.15953 | ||||||||
\(59\) | 3481.00 | 0.130189 | ||||||||
\(60\) | −5597.21 | −0.200721 | ||||||||
\(61\) | −34546.5 | −1.18872 | −0.594359 | − | 0.804200i | \(-0.702594\pi\) | ||||
−0.594359 | + | 0.804200i | \(0.702594\pi\) | |||||||
\(62\) | −59252.0 | −1.95760 | ||||||||
\(63\) | 4174.06 | 0.132497 | ||||||||
\(64\) | 21771.9 | 0.664425 | ||||||||
\(65\) | 23871.9 | 0.700815 | ||||||||
\(66\) | 38381.3 | 1.08457 | ||||||||
\(67\) | 48614.6 | 1.32306 | 0.661530 | − | 0.749919i | \(-0.269908\pi\) | ||||
0.661530 | + | 0.749919i | \(0.269908\pi\) | |||||||
\(68\) | 13573.4 | 0.355972 | ||||||||
\(69\) | 34926.7 | 0.883151 | ||||||||
\(70\) | −26612.4 | −0.649140 | ||||||||
\(71\) | 40147.1 | 0.945167 | 0.472583 | − | 0.881286i | \(-0.343322\pi\) | ||||
0.472583 | + | 0.881286i | \(0.343322\pi\) | |||||||
\(72\) | 12445.7 | 0.282936 | ||||||||
\(73\) | −22800.3 | −0.500765 | −0.250382 | − | 0.968147i | \(-0.580556\pi\) | ||||
−0.250382 | + | 0.968147i | \(0.580556\pi\) | |||||||
\(74\) | 64175.9 | 1.36236 | ||||||||
\(75\) | −32525.2 | −0.667679 | ||||||||
\(76\) | −5807.81 | −0.115340 | ||||||||
\(77\) | 34932.9 | 0.671441 | ||||||||
\(78\) | 16464.6 | 0.306417 | ||||||||
\(79\) | −23093.2 | −0.416310 | −0.208155 | − | 0.978096i | \(-0.566746\pi\) | ||||
−0.208155 | + | 0.978096i | \(0.566746\pi\) | |||||||
\(80\) | −99250.7 | −1.73384 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −82024.5 | −1.34713 | ||||||||
\(83\) | −66765.7 | −1.06380 | −0.531898 | − | 0.846808i | \(-0.678521\pi\) | ||||
−0.531898 | + | 0.846808i | \(0.678521\pi\) | |||||||
\(84\) | −3513.58 | −0.0543314 | ||||||||
\(85\) | 147079. | 2.20802 | ||||||||
\(86\) | −136680. | −1.99278 | ||||||||
\(87\) | 42499.0 | 0.601978 | ||||||||
\(88\) | 104159. | 1.43380 | ||||||||
\(89\) | −40387.5 | −0.540470 | −0.270235 | − | 0.962794i | \(-0.587101\pi\) | ||||
−0.270235 | + | 0.962794i | \(0.587101\pi\) | |||||||
\(90\) | −41830.7 | −0.544364 | ||||||||
\(91\) | 14985.3 | 0.189698 | ||||||||
\(92\) | −29400.1 | −0.362142 | ||||||||
\(93\) | −84767.6 | −1.01630 | ||||||||
\(94\) | −23904.2 | −0.279032 | ||||||||
\(95\) | −62932.3 | −0.715426 | ||||||||
\(96\) | −24202.3 | −0.268027 | ||||||||
\(97\) | 75030.3 | 0.809669 | 0.404835 | − | 0.914390i | \(-0.367329\pi\) | ||||
0.404835 | + | 0.914390i | \(0.367329\pi\) | |||||||
\(98\) | 89026.2 | 0.936381 | ||||||||
\(99\) | 54909.4 | 0.563065 | ||||||||
\(100\) | 27378.6 | 0.273786 | ||||||||
\(101\) | 1376.06 | 0.0134225 | 0.00671124 | − | 0.999977i | \(-0.497864\pi\) | ||||
0.00671124 | + | 0.999977i | \(0.497864\pi\) | |||||||
\(102\) | 101441. | 0.965410 | ||||||||
\(103\) | 151296. | 1.40518 | 0.702592 | − | 0.711592i | \(-0.252026\pi\) | ||||
0.702592 | + | 0.711592i | \(0.252026\pi\) | |||||||
\(104\) | 44681.3 | 0.405082 | ||||||||
\(105\) | −38072.4 | −0.337006 | ||||||||
\(106\) | 36172.8 | 0.312692 | ||||||||
\(107\) | −95769.2 | −0.808661 | −0.404331 | − | 0.914613i | \(-0.632495\pi\) | ||||
−0.404331 | + | 0.914613i | \(0.632495\pi\) | |||||||
\(108\) | −5522.82 | −0.0455619 | ||||||||
\(109\) | 113611. | 0.915911 | 0.457956 | − | 0.888975i | \(-0.348582\pi\) | ||||
0.457956 | + | 0.888975i | \(0.348582\pi\) | |||||||
\(110\) | −350084. | −2.75861 | ||||||||
\(111\) | 91811.9 | 0.707280 | ||||||||
\(112\) | −62303.4 | −0.469318 | ||||||||
\(113\) | −191798. | −1.41302 | −0.706508 | − | 0.707705i | \(-0.749731\pi\) | ||||
−0.706508 | + | 0.707705i | \(0.749731\pi\) | |||||||
\(114\) | −43404.7 | −0.312805 | ||||||||
\(115\) | −318574. | −2.24629 | ||||||||
\(116\) | −35774.2 | −0.246846 | ||||||||
\(117\) | 23554.7 | 0.159079 | ||||||||
\(118\) | −21898.8 | −0.144782 | ||||||||
\(119\) | 92326.7 | 0.597668 | ||||||||
\(120\) | −113520. | −0.719645 | ||||||||
\(121\) | 298489. | 1.85338 | ||||||||
\(122\) | 217330. | 1.32196 | ||||||||
\(123\) | −117347. | −0.699372 | ||||||||
\(124\) | 71354.5 | 0.416742 | ||||||||
\(125\) | 40135.6 | 0.229750 | ||||||||
\(126\) | −26258.7 | −0.147349 | ||||||||
\(127\) | −241164. | −1.32680 | −0.663398 | − | 0.748267i | \(-0.730886\pi\) | ||||
−0.663398 | + | 0.748267i | \(0.730886\pi\) | |||||||
\(128\) | −223018. | −1.20314 | ||||||||
\(129\) | −195539. | −1.03457 | ||||||||
\(130\) | −150177. | −0.779371 | ||||||||
\(131\) | −251589. | −1.28089 | −0.640447 | − | 0.768002i | \(-0.721251\pi\) | ||||
−0.640447 | + | 0.768002i | \(0.721251\pi\) | |||||||
\(132\) | −46220.8 | −0.230889 | ||||||||
\(133\) | −39505.0 | −0.193652 | ||||||||
\(134\) | −305831. | −1.47136 | ||||||||
\(135\) | −59844.3 | −0.282610 | ||||||||
\(136\) | 275289. | 1.27627 | ||||||||
\(137\) | 281066. | 1.27940 | 0.639702 | − | 0.768623i | \(-0.279058\pi\) | ||||
0.639702 | + | 0.768623i | \(0.279058\pi\) | |||||||
\(138\) | −219722. | −0.982145 | ||||||||
\(139\) | −184493. | −0.809920 | −0.404960 | − | 0.914334i | \(-0.632715\pi\) | ||||
−0.404960 | + | 0.914334i | \(0.632715\pi\) | |||||||
\(140\) | 32048.1 | 0.138192 | ||||||||
\(141\) | −34198.0 | −0.144862 | ||||||||
\(142\) | −252563. | −1.05111 | ||||||||
\(143\) | 197130. | 0.806146 | ||||||||
\(144\) | −97931.8 | −0.393566 | ||||||||
\(145\) | −387643. | −1.53113 | ||||||||
\(146\) | 143435. | 0.556896 | ||||||||
\(147\) | 127363. | 0.486129 | ||||||||
\(148\) | −77284.1 | −0.290025 | ||||||||
\(149\) | 64871.3 | 0.239379 | 0.119690 | − | 0.992811i | \(-0.461810\pi\) | ||||
0.119690 | + | 0.992811i | \(0.461810\pi\) | |||||||
\(150\) | 204614. | 0.742519 | ||||||||
\(151\) | 331835. | 1.18435 | 0.592175 | − | 0.805809i | \(-0.298269\pi\) | ||||
0.592175 | + | 0.805809i | \(0.298269\pi\) | |||||||
\(152\) | −117791. | −0.413527 | ||||||||
\(153\) | 145124. | 0.501200 | ||||||||
\(154\) | −219761. | −0.746704 | ||||||||
\(155\) | 773183. | 2.58496 | ||||||||
\(156\) | −19827.5 | −0.0652314 | ||||||||
\(157\) | −268495. | −0.869334 | −0.434667 | − | 0.900591i | \(-0.643134\pi\) | ||||
−0.434667 | + | 0.900591i | \(0.643134\pi\) | |||||||
\(158\) | 145278. | 0.462974 | ||||||||
\(159\) | 51749.8 | 0.162336 | ||||||||
\(160\) | 220754. | 0.681724 | ||||||||
\(161\) | −199981. | −0.608028 | ||||||||
\(162\) | −41274.8 | −0.123566 | ||||||||
\(163\) | 529252. | 1.56025 | 0.780124 | − | 0.625625i | \(-0.215156\pi\) | ||||
0.780124 | + | 0.625625i | \(0.215156\pi\) | |||||||
\(164\) | 98778.4 | 0.286782 | ||||||||
\(165\) | −500840. | −1.43215 | ||||||||
\(166\) | 420019. | 1.18304 | ||||||||
\(167\) | 181295. | 0.503030 | 0.251515 | − | 0.967853i | \(-0.419071\pi\) | ||||
0.251515 | + | 0.967853i | \(0.419071\pi\) | |||||||
\(168\) | −71260.6 | −0.194794 | ||||||||
\(169\) | −286729. | −0.772245 | ||||||||
\(170\) | −925262. | −2.45551 | ||||||||
\(171\) | −62096.0 | −0.162395 | ||||||||
\(172\) | 164598. | 0.424231 | ||||||||
\(173\) | 568953. | 1.44531 | 0.722655 | − | 0.691209i | \(-0.242922\pi\) | ||||
0.722655 | + | 0.691209i | \(0.242922\pi\) | |||||||
\(174\) | −267359. | −0.669455 | ||||||||
\(175\) | 186231. | 0.459681 | ||||||||
\(176\) | −819597. | −1.99443 | ||||||||
\(177\) | −31329.0 | −0.0751646 | ||||||||
\(178\) | 254075. | 0.601052 | ||||||||
\(179\) | 474139. | 1.10605 | 0.553023 | − | 0.833166i | \(-0.313474\pi\) | ||||
0.553023 | + | 0.833166i | \(0.313474\pi\) | |||||||
\(180\) | 50374.8 | 0.115886 | ||||||||
\(181\) | 271053. | 0.614974 | 0.307487 | − | 0.951552i | \(-0.400512\pi\) | ||||
0.307487 | + | 0.951552i | \(0.400512\pi\) | |||||||
\(182\) | −94271.5 | −0.210961 | ||||||||
\(183\) | 310918. | 0.686307 | ||||||||
\(184\) | −596279. | −1.29839 | ||||||||
\(185\) | −837436. | −1.79896 | ||||||||
\(186\) | 533268. | 1.13022 | ||||||||
\(187\) | 1.21455e6 | 2.53987 | ||||||||
\(188\) | 28786.7 | 0.0594016 | ||||||||
\(189\) | −37566.5 | −0.0764973 | ||||||||
\(190\) | 395903. | 0.795619 | ||||||||
\(191\) | 768100. | 1.52347 | 0.761736 | − | 0.647888i | \(-0.224348\pi\) | ||||
0.761736 | + | 0.647888i | \(0.224348\pi\) | |||||||
\(192\) | −195947. | −0.383606 | ||||||||
\(193\) | 37462.7 | 0.0723946 | 0.0361973 | − | 0.999345i | \(-0.488476\pi\) | ||||
0.0361973 | + | 0.999345i | \(0.488476\pi\) | |||||||
\(194\) | −472011. | −0.900426 | ||||||||
\(195\) | −214847. | −0.404616 | ||||||||
\(196\) | −107210. | −0.199341 | ||||||||
\(197\) | 600917. | 1.10319 | 0.551593 | − | 0.834113i | \(-0.314020\pi\) | ||||
0.551593 | + | 0.834113i | \(0.314020\pi\) | |||||||
\(198\) | −345431. | −0.626180 | ||||||||
\(199\) | 959.488 | 0.00171754 | 0.000858770 | − | 1.00000i | \(-0.499727\pi\) | ||||
0.000858770 | 1.00000i | \(0.499727\pi\) | ||||||||
\(200\) | 555280. | 0.981606 | ||||||||
\(201\) | −437531. | −0.763869 | ||||||||
\(202\) | −8656.69 | −0.0149270 | ||||||||
\(203\) | −243338. | −0.414448 | ||||||||
\(204\) | −122160. | −0.205520 | ||||||||
\(205\) | 1.07034e6 | 1.77885 | ||||||||
\(206\) | −951792. | −1.56269 | ||||||||
\(207\) | −314340. | −0.509888 | ||||||||
\(208\) | −351585. | −0.563472 | ||||||||
\(209\) | −519685. | −0.822952 | ||||||||
\(210\) | 239511. | 0.374781 | ||||||||
\(211\) | −638539. | −0.987374 | −0.493687 | − | 0.869640i | \(-0.664351\pi\) | ||||
−0.493687 | + | 0.869640i | \(0.664351\pi\) | |||||||
\(212\) | −43561.2 | −0.0665672 | ||||||||
\(213\) | −361324. | −0.545692 | ||||||||
\(214\) | 602478. | 0.899305 | ||||||||
\(215\) | 1.78355e6 | 2.63141 | ||||||||
\(216\) | −112011. | −0.163353 | ||||||||
\(217\) | 485356. | 0.699699 | ||||||||
\(218\) | −714718. | −1.01858 | ||||||||
\(219\) | 205203. | 0.289117 | ||||||||
\(220\) | 421590. | 0.587264 | ||||||||
\(221\) | 521010. | 0.717572 | ||||||||
\(222\) | −577583. | −0.786560 | ||||||||
\(223\) | 1.11924e6 | 1.50717 | 0.753584 | − | 0.657352i | \(-0.228323\pi\) | ||||
0.753584 | + | 0.657352i | \(0.228323\pi\) | |||||||
\(224\) | 138576. | 0.184530 | ||||||||
\(225\) | 292727. | 0.385484 | ||||||||
\(226\) | 1.20659e6 | 1.57140 | ||||||||
\(227\) | 310255. | 0.399626 | 0.199813 | − | 0.979834i | \(-0.435967\pi\) | ||||
0.199813 | + | 0.979834i | \(0.435967\pi\) | |||||||
\(228\) | 52270.3 | 0.0665913 | ||||||||
\(229\) | −576057. | −0.725900 | −0.362950 | − | 0.931809i | \(-0.618230\pi\) | ||||
−0.362950 | + | 0.931809i | \(0.618230\pi\) | |||||||
\(230\) | 2.00413e6 | 2.49808 | ||||||||
\(231\) | −314396. | −0.387657 | ||||||||
\(232\) | −725556. | −0.885015 | ||||||||
\(233\) | 370645. | 0.447269 | 0.223634 | − | 0.974673i | \(-0.428208\pi\) | ||||
0.223634 | + | 0.974673i | \(0.428208\pi\) | |||||||
\(234\) | −148181. | −0.176910 | ||||||||
\(235\) | 311928. | 0.368455 | ||||||||
\(236\) | 26371.7 | 0.0308218 | ||||||||
\(237\) | 207839. | 0.240357 | ||||||||
\(238\) | −580822. | −0.664661 | ||||||||
\(239\) | −457409. | −0.517977 | −0.258988 | − | 0.965880i | \(-0.583389\pi\) | ||||
−0.258988 | + | 0.965880i | \(0.583389\pi\) | |||||||
\(240\) | 893257. | 1.00103 | ||||||||
\(241\) | −1.65108e6 | −1.83115 | −0.915577 | − | 0.402143i | \(-0.868266\pi\) | ||||
−0.915577 | + | 0.402143i | \(0.868266\pi\) | |||||||
\(242\) | −1.87777e6 | −2.06113 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | −261720. | −0.281425 | ||||||||
\(245\) | −1.16171e6 | −1.23647 | ||||||||
\(246\) | 738220. | 0.777765 | ||||||||
\(247\) | −222931. | −0.232503 | ||||||||
\(248\) | 1.44718e6 | 1.49414 | ||||||||
\(249\) | 600892. | 0.614183 | ||||||||
\(250\) | −252491. | −0.255502 | ||||||||
\(251\) | −1.66249e6 | −1.66562 | −0.832810 | − | 0.553560i | \(-0.813269\pi\) | ||||
−0.832810 | + | 0.553560i | \(0.813269\pi\) | |||||||
\(252\) | 31622.2 | 0.0313683 | ||||||||
\(253\) | −2.63073e6 | −2.58390 | ||||||||
\(254\) | 1.51715e6 | 1.47552 | ||||||||
\(255\) | −1.32371e6 | −1.27480 | ||||||||
\(256\) | 706292. | 0.673573 | ||||||||
\(257\) | 1.24468e6 | 1.17551 | 0.587753 | − | 0.809040i | \(-0.300013\pi\) | ||||
0.587753 | + | 0.809040i | \(0.300013\pi\) | |||||||
\(258\) | 1.23012e6 | 1.15053 | ||||||||
\(259\) | −525690. | −0.486945 | ||||||||
\(260\) | 180851. | 0.165916 | ||||||||
\(261\) | −382491. | −0.347552 | ||||||||
\(262\) | 1.58273e6 | 1.42447 | ||||||||
\(263\) | −1.51127e6 | −1.34726 | −0.673632 | − | 0.739067i | \(-0.735267\pi\) | ||||
−0.673632 | + | 0.739067i | \(0.735267\pi\) | |||||||
\(264\) | −937428. | −0.827806 | ||||||||
\(265\) | −472021. | −0.412902 | ||||||||
\(266\) | 248523. | 0.215359 | ||||||||
\(267\) | 363487. | 0.312040 | ||||||||
\(268\) | 368299. | 0.313230 | ||||||||
\(269\) | −111519. | −0.0939658 | −0.0469829 | − | 0.998896i | \(-0.514961\pi\) | ||||
−0.0469829 | + | 0.998896i | \(0.514961\pi\) | |||||||
\(270\) | 376477. | 0.314289 | ||||||||
\(271\) | −281639. | −0.232953 | −0.116477 | − | 0.993193i | \(-0.537160\pi\) | ||||
−0.116477 | + | 0.993193i | \(0.537160\pi\) | |||||||
\(272\) | −2.16617e6 | −1.77530 | ||||||||
\(273\) | −134868. | −0.109522 | ||||||||
\(274\) | −1.76817e6 | −1.42281 | ||||||||
\(275\) | 2.44985e6 | 1.95348 | ||||||||
\(276\) | 264601. | 0.209083 | ||||||||
\(277\) | 2.13042e6 | 1.66827 | 0.834134 | − | 0.551561i | \(-0.185968\pi\) | ||||
0.834134 | + | 0.551561i | \(0.185968\pi\) | |||||||
\(278\) | 1.16063e6 | 0.900705 | ||||||||
\(279\) | 762909. | 0.586762 | ||||||||
\(280\) | 649983. | 0.495458 | ||||||||
\(281\) | −1.74219e6 | −1.31623 | −0.658113 | − | 0.752920i | \(-0.728645\pi\) | ||||
−0.658113 | + | 0.752920i | \(0.728645\pi\) | |||||||
\(282\) | 215138. | 0.161099 | ||||||||
\(283\) | 804963. | 0.597461 | 0.298731 | − | 0.954337i | \(-0.403437\pi\) | ||||
0.298731 | + | 0.954337i | \(0.403437\pi\) | |||||||
\(284\) | 304150. | 0.223765 | ||||||||
\(285\) | 566391. | 0.413051 | ||||||||
\(286\) | −1.24013e6 | −0.896507 | ||||||||
\(287\) | 671895. | 0.481500 | ||||||||
\(288\) | 217821. | 0.154745 | ||||||||
\(289\) | 1.79017e6 | 1.26081 | ||||||||
\(290\) | 2.43864e6 | 1.70275 | ||||||||
\(291\) | −675273. | −0.467463 | ||||||||
\(292\) | −172733. | −0.118554 | ||||||||
\(293\) | 404216. | 0.275070 | 0.137535 | − | 0.990497i | \(-0.456082\pi\) | ||||
0.137535 | + | 0.990497i | \(0.456082\pi\) | |||||||
\(294\) | −801236. | −0.540620 | ||||||||
\(295\) | 285758. | 0.191181 | ||||||||
\(296\) | −1.56744e6 | −1.03983 | ||||||||
\(297\) | −494184. | −0.325086 | ||||||||
\(298\) | −408101. | −0.266212 | ||||||||
\(299\) | −1.12851e6 | −0.730011 | ||||||||
\(300\) | −246408. | −0.158071 | ||||||||
\(301\) | 1.11960e6 | 0.712274 | ||||||||
\(302\) | −2.08755e6 | −1.31711 | ||||||||
\(303\) | −12384.5 | −0.00774948 | ||||||||
\(304\) | 926867. | 0.575219 | ||||||||
\(305\) | −2.83595e6 | −1.74562 | ||||||||
\(306\) | −912966. | −0.557380 | ||||||||
\(307\) | 2.58978e6 | 1.56825 | 0.784127 | − | 0.620601i | \(-0.213111\pi\) | ||||
0.784127 | + | 0.620601i | \(0.213111\pi\) | |||||||
\(308\) | 264648. | 0.158961 | ||||||||
\(309\) | −1.36166e6 | −0.811284 | ||||||||
\(310\) | −4.86405e6 | −2.87471 | ||||||||
\(311\) | 862615. | 0.505727 | 0.252864 | − | 0.967502i | \(-0.418628\pi\) | ||||
0.252864 | + | 0.967502i | \(0.418628\pi\) | |||||||
\(312\) | −402132. | −0.233874 | ||||||||
\(313\) | −1.99901e6 | −1.15333 | −0.576665 | − | 0.816981i | \(-0.695646\pi\) | ||||
−0.576665 | + | 0.816981i | \(0.695646\pi\) | |||||||
\(314\) | 1.68908e6 | 0.966779 | ||||||||
\(315\) | 342652. | 0.194570 | ||||||||
\(316\) | −174952. | −0.0985599 | ||||||||
\(317\) | −1.20570e6 | −0.673895 | −0.336947 | − | 0.941523i | \(-0.609394\pi\) | ||||
−0.336947 | + | 0.941523i | \(0.609394\pi\) | |||||||
\(318\) | −325555. | −0.180533 | ||||||||
\(319\) | −3.20109e6 | −1.76125 | ||||||||
\(320\) | 1.78727e6 | 0.975699 | ||||||||
\(321\) | 861923. | 0.466881 | ||||||||
\(322\) | 1.25807e6 | 0.676183 | ||||||||
\(323\) | −1.37351e6 | −0.732532 | ||||||||
\(324\) | 49705.4 | 0.0263052 | ||||||||
\(325\) | 1.05092e6 | 0.551902 | ||||||||
\(326\) | −3.32949e6 | −1.73514 | ||||||||
\(327\) | −1.02250e6 | −0.528802 | ||||||||
\(328\) | 2.00338e6 | 1.02820 | ||||||||
\(329\) | 195809. | 0.0997338 | ||||||||
\(330\) | 3.15075e6 | 1.59268 | ||||||||
\(331\) | −332094. | −0.166606 | −0.0833031 | − | 0.996524i | \(-0.526547\pi\) | ||||
−0.0833031 | + | 0.996524i | \(0.526547\pi\) | |||||||
\(332\) | −505810. | −0.251850 | ||||||||
\(333\) | −826307. | −0.408348 | ||||||||
\(334\) | −1.14051e6 | −0.559415 | ||||||||
\(335\) | 3.99081e6 | 1.94289 | ||||||||
\(336\) | 560731. | 0.270961 | ||||||||
\(337\) | −2.07718e6 | −0.996319 | −0.498159 | − | 0.867085i | \(-0.665991\pi\) | ||||
−0.498159 | + | 0.867085i | \(0.665991\pi\) | |||||||
\(338\) | 1.80380e6 | 0.858807 | ||||||||
\(339\) | 1.72618e6 | 0.815805 | ||||||||
\(340\) | 1.11425e6 | 0.522740 | ||||||||
\(341\) | 6.38482e6 | 2.97347 | ||||||||
\(342\) | 390642. | 0.180598 | ||||||||
\(343\) | −1.59534e6 | −0.732180 | ||||||||
\(344\) | 3.33829e6 | 1.52100 | ||||||||
\(345\) | 2.86717e6 | 1.29690 | ||||||||
\(346\) | −3.57924e6 | −1.60732 | ||||||||
\(347\) | −2.03249e6 | −0.906160 | −0.453080 | − | 0.891470i | \(-0.649675\pi\) | ||||
−0.453080 | + | 0.891470i | \(0.649675\pi\) | |||||||
\(348\) | 321968. | 0.142516 | ||||||||
\(349\) | −881466. | −0.387384 | −0.193692 | − | 0.981062i | \(-0.562046\pi\) | ||||
−0.193692 | + | 0.981062i | \(0.562046\pi\) | |||||||
\(350\) | −1.17157e6 | −0.511207 | ||||||||
\(351\) | −211992. | −0.0918442 | ||||||||
\(352\) | 1.82295e6 | 0.784185 | ||||||||
\(353\) | −2.95569e6 | −1.26247 | −0.631237 | − | 0.775590i | \(-0.717452\pi\) | ||||
−0.631237 | + | 0.775590i | \(0.717452\pi\) | |||||||
\(354\) | 197089. | 0.0835899 | ||||||||
\(355\) | 3.29571e6 | 1.38797 | ||||||||
\(356\) | −305971. | −0.127954 | ||||||||
\(357\) | −830941. | −0.345064 | ||||||||
\(358\) | −2.98278e6 | −1.23002 | ||||||||
\(359\) | 1.29738e6 | 0.531288 | 0.265644 | − | 0.964071i | \(-0.414416\pi\) | ||||
0.265644 | + | 0.964071i | \(0.414416\pi\) | |||||||
\(360\) | 1.02168e6 | 0.415487 | ||||||||
\(361\) | −1.88840e6 | −0.762650 | ||||||||
\(362\) | −1.70517e6 | −0.683908 | ||||||||
\(363\) | −2.68640e6 | −1.07005 | ||||||||
\(364\) | 113527. | 0.0449102 | ||||||||
\(365\) | −1.87170e6 | −0.735366 | ||||||||
\(366\) | −1.95597e6 | −0.763236 | ||||||||
\(367\) | 1.75493e6 | 0.680132 | 0.340066 | − | 0.940401i | \(-0.389550\pi\) | ||||
0.340066 | + | 0.940401i | \(0.389550\pi\) | |||||||
\(368\) | 4.69196e6 | 1.80607 | ||||||||
\(369\) | 1.05612e6 | 0.403782 | ||||||||
\(370\) | 5.26826e6 | 2.00061 | ||||||||
\(371\) | −296305. | −0.111765 | ||||||||
\(372\) | −642190. | −0.240606 | ||||||||
\(373\) | 1.92485e6 | 0.716349 | 0.358175 | − | 0.933655i | \(-0.383399\pi\) | ||||
0.358175 | + | 0.933655i | \(0.383399\pi\) | |||||||
\(374\) | −7.64067e6 | −2.82457 | ||||||||
\(375\) | −361220. | −0.132646 | ||||||||
\(376\) | 583839. | 0.212972 | ||||||||
\(377\) | −1.37318e6 | −0.497594 | ||||||||
\(378\) | 236328. | 0.0850720 | ||||||||
\(379\) | 3.48628e6 | 1.24671 | 0.623354 | − | 0.781940i | \(-0.285770\pi\) | ||||
0.623354 | + | 0.781940i | \(0.285770\pi\) | |||||||
\(380\) | −476768. | −0.169375 | ||||||||
\(381\) | 2.17048e6 | 0.766025 | ||||||||
\(382\) | −4.83207e6 | −1.69424 | ||||||||
\(383\) | −3.51624e6 | −1.22485 | −0.612423 | − | 0.790530i | \(-0.709805\pi\) | ||||
−0.612423 | + | 0.790530i | \(0.709805\pi\) | |||||||
\(384\) | 2.00716e6 | 0.694631 | ||||||||
\(385\) | 2.86767e6 | 0.986002 | ||||||||
\(386\) | −235676. | −0.0805094 | ||||||||
\(387\) | 1.75985e6 | 0.597307 | ||||||||
\(388\) | 568422. | 0.191686 | ||||||||
\(389\) | −163206. | −0.0546844 | −0.0273422 | − | 0.999626i | \(-0.508704\pi\) | ||||
−0.0273422 | + | 0.999626i | \(0.508704\pi\) | |||||||
\(390\) | 1.35159e6 | 0.449970 | ||||||||
\(391\) | −6.95296e6 | −2.30000 | ||||||||
\(392\) | −2.17439e6 | −0.714696 | ||||||||
\(393\) | 2.26430e6 | 0.739524 | ||||||||
\(394\) | −3.78033e6 | −1.22684 | ||||||||
\(395\) | −1.89574e6 | −0.611346 | ||||||||
\(396\) | 415987. | 0.133304 | ||||||||
\(397\) | −1.26098e6 | −0.401544 | −0.200772 | − | 0.979638i | \(-0.564345\pi\) | ||||
−0.200772 | + | 0.979638i | \(0.564345\pi\) | |||||||
\(398\) | −6036.08 | −0.00191006 | ||||||||
\(399\) | 355545. | 0.111805 | ||||||||
\(400\) | −4.36935e6 | −1.36542 | ||||||||
\(401\) | −2.88395e6 | −0.895628 | −0.447814 | − | 0.894127i | \(-0.647797\pi\) | ||||
−0.447814 | + | 0.894127i | \(0.647797\pi\) | |||||||
\(402\) | 2.75248e6 | 0.849491 | ||||||||
\(403\) | 2.73892e6 | 0.840073 | ||||||||
\(404\) | 10424.9 | 0.00317773 | ||||||||
\(405\) | 538598. | 0.163165 | ||||||||
\(406\) | 1.53082e6 | 0.460904 | ||||||||
\(407\) | −6.91541e6 | −2.06934 | ||||||||
\(408\) | −2.47760e6 | −0.736852 | ||||||||
\(409\) | −2.72417e6 | −0.805241 | −0.402621 | − | 0.915367i | \(-0.631901\pi\) | ||||
−0.402621 | + | 0.915367i | \(0.631901\pi\) | |||||||
\(410\) | −6.73347e6 | −1.97824 | ||||||||
\(411\) | −2.52960e6 | −0.738664 | ||||||||
\(412\) | 1.14620e6 | 0.332673 | ||||||||
\(413\) | 179381. | 0.0517490 | ||||||||
\(414\) | 1.97750e6 | 0.567041 | ||||||||
\(415\) | −5.48086e6 | −1.56217 | ||||||||
\(416\) | 781998. | 0.221550 | ||||||||
\(417\) | 1.66043e6 | 0.467608 | ||||||||
\(418\) | 3.26931e6 | 0.915197 | ||||||||
\(419\) | −2.85576e6 | −0.794669 | −0.397334 | − | 0.917674i | \(-0.630065\pi\) | ||||
−0.397334 | + | 0.917674i | \(0.630065\pi\) | |||||||
\(420\) | −288433. | −0.0797850 | ||||||||
\(421\) | 2.80641e6 | 0.771696 | 0.385848 | − | 0.922562i | \(-0.373909\pi\) | ||||
0.385848 | + | 0.922562i | \(0.373909\pi\) | |||||||
\(422\) | 4.01701e6 | 1.09805 | ||||||||
\(423\) | 307782. | 0.0836359 | ||||||||
\(424\) | −883488. | −0.238663 | ||||||||
\(425\) | 6.47489e6 | 1.73884 | ||||||||
\(426\) | 2.27307e6 | 0.606860 | ||||||||
\(427\) | −1.78023e6 | −0.472506 | ||||||||
\(428\) | −725537. | −0.191448 | ||||||||
\(429\) | −1.77417e6 | −0.465428 | ||||||||
\(430\) | −1.12202e7 | −2.92637 | ||||||||
\(431\) | 3.86257e6 | 1.00157 | 0.500787 | − | 0.865571i | \(-0.333044\pi\) | ||||
0.500787 | + | 0.865571i | \(0.333044\pi\) | |||||||
\(432\) | 881386. | 0.227225 | ||||||||
\(433\) | 67037.6 | 0.0171830 | 0.00859149 | − | 0.999963i | \(-0.497265\pi\) | ||||
0.00859149 | + | 0.999963i | \(0.497265\pi\) | |||||||
\(434\) | −3.05335e6 | −0.778129 | ||||||||
\(435\) | 3.48878e6 | 0.883997 | ||||||||
\(436\) | 860703. | 0.216839 | ||||||||
\(437\) | 2.97505e6 | 0.745230 | ||||||||
\(438\) | −1.29092e6 | −0.321524 | ||||||||
\(439\) | 2.63398e6 | 0.652305 | 0.326152 | − | 0.945317i | \(-0.394248\pi\) | ||||
0.326152 | + | 0.945317i | \(0.394248\pi\) | |||||||
\(440\) | 8.55048e6 | 2.10552 | ||||||||
\(441\) | −1.14627e6 | −0.280667 | ||||||||
\(442\) | −3.27764e6 | −0.798006 | ||||||||
\(443\) | 3.85966e6 | 0.934415 | 0.467208 | − | 0.884148i | \(-0.345260\pi\) | ||||
0.467208 | + | 0.884148i | \(0.345260\pi\) | |||||||
\(444\) | 695557. | 0.167446 | ||||||||
\(445\) | −3.31544e6 | −0.793673 | ||||||||
\(446\) | −7.04108e6 | −1.67611 | ||||||||
\(447\) | −583842. | −0.138206 | ||||||||
\(448\) | 1.12194e6 | 0.264103 | ||||||||
\(449\) | −1.96762e6 | −0.460602 | −0.230301 | − | 0.973119i | \(-0.573971\pi\) | ||||
−0.230301 | + | 0.973119i | \(0.573971\pi\) | |||||||
\(450\) | −1.84153e6 | −0.428694 | ||||||||
\(451\) | 8.83873e6 | 2.04620 | ||||||||
\(452\) | −1.45304e6 | −0.334527 | ||||||||
\(453\) | −2.98652e6 | −0.683785 | ||||||||
\(454\) | −1.95179e6 | −0.444420 | ||||||||
\(455\) | 1.23016e6 | 0.278568 | ||||||||
\(456\) | 1.06012e6 | 0.238750 | ||||||||
\(457\) | 2.80506e6 | 0.628277 | 0.314139 | − | 0.949377i | \(-0.398284\pi\) | ||||
0.314139 | + | 0.949377i | \(0.398284\pi\) | |||||||
\(458\) | 3.62394e6 | 0.807267 | ||||||||
\(459\) | −1.30612e6 | −0.289368 | ||||||||
\(460\) | −2.41348e6 | −0.531801 | ||||||||
\(461\) | −587088. | −0.128662 | −0.0643311 | − | 0.997929i | \(-0.520491\pi\) | ||||
−0.0643311 | + | 0.997929i | \(0.520491\pi\) | |||||||
\(462\) | 1.97785e6 | 0.431110 | ||||||||
\(463\) | −1.11999e6 | −0.242807 | −0.121403 | − | 0.992603i | \(-0.538739\pi\) | ||||
−0.121403 | + | 0.992603i | \(0.538739\pi\) | |||||||
\(464\) | 5.70920e6 | 1.23106 | ||||||||
\(465\) | −6.95865e6 | −1.49243 | ||||||||
\(466\) | −2.33171e6 | −0.497404 | ||||||||
\(467\) | −662714. | −0.140616 | −0.0703079 | − | 0.997525i | \(-0.522398\pi\) | ||||
−0.0703079 | + | 0.997525i | \(0.522398\pi\) | |||||||
\(468\) | 178448. | 0.0376614 | ||||||||
\(469\) | 2.50518e6 | 0.525905 | ||||||||
\(470\) | −1.96232e6 | −0.409755 | ||||||||
\(471\) | 2.41645e6 | 0.501910 | ||||||||
\(472\) | 534858. | 0.110505 | ||||||||
\(473\) | 1.47283e7 | 3.02691 | ||||||||
\(474\) | −1.30750e6 | −0.267298 | ||||||||
\(475\) | −2.77049e6 | −0.563408 | ||||||||
\(476\) | 699457. | 0.141496 | ||||||||
\(477\) | −465748. | −0.0937250 | ||||||||
\(478\) | 2.87753e6 | 0.576037 | ||||||||
\(479\) | −2.14002e6 | −0.426166 | −0.213083 | − | 0.977034i | \(-0.568350\pi\) | ||||
−0.213083 | + | 0.977034i | \(0.568350\pi\) | |||||||
\(480\) | −1.98679e6 | −0.393594 | ||||||||
\(481\) | −2.96653e6 | −0.584636 | ||||||||
\(482\) | 1.03868e7 | 2.03641 | ||||||||
\(483\) | 1.79983e6 | 0.351045 | ||||||||
\(484\) | 2.26132e6 | 0.438781 | ||||||||
\(485\) | 6.15931e6 | 1.18899 | ||||||||
\(486\) | 371474. | 0.0713407 | ||||||||
\(487\) | 8.82596e6 | 1.68632 | 0.843159 | − | 0.537664i | \(-0.180693\pi\) | ||||
0.843159 | + | 0.537664i | \(0.180693\pi\) | |||||||
\(488\) | −5.30808e6 | −1.00899 | ||||||||
\(489\) | −4.76327e6 | −0.900810 | ||||||||
\(490\) | 7.30824e6 | 1.37506 | ||||||||
\(491\) | −338584. | −0.0633816 | −0.0316908 | − | 0.999498i | \(-0.510089\pi\) | ||||
−0.0316908 | + | 0.999498i | \(0.510089\pi\) | |||||||
\(492\) | −889005. | −0.165574 | ||||||||
\(493\) | −8.46040e6 | −1.56774 | ||||||||
\(494\) | 1.40245e6 | 0.258564 | ||||||||
\(495\) | 4.50756e6 | 0.826854 | ||||||||
\(496\) | −1.13874e7 | −2.07837 | ||||||||
\(497\) | 2.06884e6 | 0.375696 | ||||||||
\(498\) | −3.78017e6 | −0.683027 | ||||||||
\(499\) | −4.96188e6 | −0.892062 | −0.446031 | − | 0.895018i | \(-0.647163\pi\) | ||||
−0.446031 | + | 0.895018i | \(0.647163\pi\) | |||||||
\(500\) | 304063. | 0.0543924 | ||||||||
\(501\) | −1.63165e6 | −0.290425 | ||||||||
\(502\) | 1.04586e7 | 1.85232 | ||||||||
\(503\) | −85757.8 | −0.0151131 | −0.00755655 | − | 0.999971i | \(-0.502405\pi\) | ||||
−0.00755655 | + | 0.999971i | \(0.502405\pi\) | |||||||
\(504\) | 641346. | 0.112465 | ||||||||
\(505\) | 112962. | 0.0197107 | ||||||||
\(506\) | 1.65498e7 | 2.87353 | ||||||||
\(507\) | 2.58056e6 | 0.445856 | ||||||||
\(508\) | −1.82703e6 | −0.314114 | ||||||||
\(509\) | −7.60236e6 | −1.30063 | −0.650315 | − | 0.759665i | \(-0.725363\pi\) | ||||
−0.650315 | + | 0.759665i | \(0.725363\pi\) | |||||||
\(510\) | 8.32736e6 | 1.41769 | ||||||||
\(511\) | −1.17494e6 | −0.199050 | ||||||||
\(512\) | 2.69334e6 | 0.454062 | ||||||||
\(513\) | 558864. | 0.0937589 | ||||||||
\(514\) | −7.83021e6 | −1.30727 | ||||||||
\(515\) | 1.24200e7 | 2.06350 | ||||||||
\(516\) | −1.48138e6 | −0.244930 | ||||||||
\(517\) | 2.57585e6 | 0.423832 | ||||||||
\(518\) | 3.30708e6 | 0.541528 | ||||||||
\(519\) | −5.12057e6 | −0.834450 | ||||||||
\(520\) | 3.66793e6 | 0.594857 | ||||||||
\(521\) | −2.25965e6 | −0.364709 | −0.182354 | − | 0.983233i | \(-0.558372\pi\) | ||||
−0.182354 | + | 0.983233i | \(0.558372\pi\) | |||||||
\(522\) | 2.40623e6 | 0.386510 | ||||||||
\(523\) | 6.30058e6 | 1.00722 | 0.503612 | − | 0.863930i | \(-0.332004\pi\) | ||||
0.503612 | + | 0.863930i | \(0.332004\pi\) | |||||||
\(524\) | −1.90601e6 | −0.303247 | ||||||||
\(525\) | −1.67608e6 | −0.265397 | ||||||||
\(526\) | 9.50730e6 | 1.49828 | ||||||||
\(527\) | 1.68749e7 | 2.64676 | ||||||||
\(528\) | 7.37637e6 | 1.15148 | ||||||||
\(529\) | 8.62385e6 | 1.33987 | ||||||||
\(530\) | 2.96946e6 | 0.459184 | ||||||||
\(531\) | 281961. | 0.0433963 | ||||||||
\(532\) | −299285. | −0.0458465 | ||||||||
\(533\) | 3.79158e6 | 0.578099 | ||||||||
\(534\) | −2.28667e6 | −0.347017 | ||||||||
\(535\) | −7.86178e6 | −1.18751 | ||||||||
\(536\) | 7.46965e6 | 1.12302 | ||||||||
\(537\) | −4.26726e6 | −0.638576 | ||||||||
\(538\) | 701562. | 0.104499 | ||||||||
\(539\) | −9.59321e6 | −1.42230 | ||||||||
\(540\) | −453374. | −0.0669070 | ||||||||
\(541\) | −9.75064e6 | −1.43232 | −0.716160 | − | 0.697936i | \(-0.754102\pi\) | ||||
−0.716160 | + | 0.697936i | \(0.754102\pi\) | |||||||
\(542\) | 1.77177e6 | 0.259065 | ||||||||
\(543\) | −2.43947e6 | −0.355056 | ||||||||
\(544\) | 4.81801e6 | 0.698025 | ||||||||
\(545\) | 9.32641e6 | 1.34500 | ||||||||
\(546\) | 848444. | 0.121798 | ||||||||
\(547\) | 6.17092e6 | 0.881823 | 0.440911 | − | 0.897551i | \(-0.354655\pi\) | ||||
0.440911 | + | 0.897551i | \(0.354655\pi\) | |||||||
\(548\) | 2.12933e6 | 0.302894 | ||||||||
\(549\) | −2.79826e6 | −0.396240 | ||||||||
\(550\) | −1.54119e7 | −2.17244 | ||||||||
\(551\) | 3.62005e6 | 0.507968 | ||||||||
\(552\) | 5.36651e6 | 0.749625 | ||||||||
\(553\) | −1.19003e6 | −0.165480 | ||||||||
\(554\) | −1.34023e7 | −1.85527 | ||||||||
\(555\) | 7.53692e6 | 1.03863 | ||||||||
\(556\) | −1.39770e6 | −0.191746 | ||||||||
\(557\) | −4.46667e6 | −0.610023 | −0.305011 | − | 0.952349i | \(-0.598660\pi\) | ||||
−0.305011 | + | 0.952349i | \(0.598660\pi\) | |||||||
\(558\) | −4.79941e6 | −0.652533 | ||||||||
\(559\) | 6.31804e6 | 0.855171 | ||||||||
\(560\) | −5.11454e6 | −0.689187 | ||||||||
\(561\) | −1.09310e7 | −1.46640 | ||||||||
\(562\) | 1.09600e7 | 1.46376 | ||||||||
\(563\) | −2.84216e6 | −0.377901 | −0.188951 | − | 0.981987i | \(-0.560509\pi\) | ||||
−0.188951 | + | 0.981987i | \(0.560509\pi\) | |||||||
\(564\) | −259081. | −0.0342955 | ||||||||
\(565\) | −1.57448e7 | −2.07500 | ||||||||
\(566\) | −5.06397e6 | −0.664431 | ||||||||
\(567\) | 338098. | 0.0441657 | ||||||||
\(568\) | 6.16863e6 | 0.802265 | ||||||||
\(569\) | 2.66553e6 | 0.345146 | 0.172573 | − | 0.984997i | \(-0.444792\pi\) | ||||
0.172573 | + | 0.984997i | \(0.444792\pi\) | |||||||
\(570\) | −3.56313e6 | −0.459351 | ||||||||
\(571\) | −4.62842e6 | −0.594076 | −0.297038 | − | 0.954866i | \(-0.595999\pi\) | ||||
−0.297038 | + | 0.954866i | \(0.595999\pi\) | |||||||
\(572\) | 1.49344e6 | 0.190852 | ||||||||
\(573\) | −6.91290e6 | −0.879576 | ||||||||
\(574\) | −4.22685e6 | −0.535472 | ||||||||
\(575\) | −1.40247e7 | −1.76898 | ||||||||
\(576\) | 1.76352e6 | 0.221475 | ||||||||
\(577\) | 774192. | 0.0968075 | 0.0484038 | − | 0.998828i | \(-0.484587\pi\) | ||||
0.0484038 | + | 0.998828i | \(0.484587\pi\) | |||||||
\(578\) | −1.12618e7 | −1.40214 | ||||||||
\(579\) | −337165. | −0.0417971 | ||||||||
\(580\) | −2.93674e6 | −0.362489 | ||||||||
\(581\) | −3.44054e6 | −0.422850 | ||||||||
\(582\) | 4.24810e6 | 0.519861 | ||||||||
\(583\) | −3.89788e6 | −0.474959 | ||||||||
\(584\) | −3.50328e6 | −0.425053 | ||||||||
\(585\) | 1.93362e6 | 0.233605 | ||||||||
\(586\) | −2.54289e6 | −0.305903 | ||||||||
\(587\) | −1.40973e7 | −1.68865 | −0.844326 | − | 0.535829i | \(-0.819999\pi\) | ||||
−0.844326 | + | 0.535829i | \(0.819999\pi\) | |||||||
\(588\) | 964892. | 0.115089 | ||||||||
\(589\) | −7.22048e6 | −0.857586 | ||||||||
\(590\) | −1.79769e6 | −0.212610 | ||||||||
\(591\) | −5.40825e6 | −0.636925 | ||||||||
\(592\) | 1.23337e7 | 1.44641 | ||||||||
\(593\) | 4.30336e6 | 0.502541 | 0.251270 | − | 0.967917i | \(-0.419152\pi\) | ||||
0.251270 | + | 0.967917i | \(0.419152\pi\) | |||||||
\(594\) | 3.10888e6 | 0.361525 | ||||||||
\(595\) | 7.57919e6 | 0.877668 | ||||||||
\(596\) | 491458. | 0.0566723 | ||||||||
\(597\) | −8635.40 | −0.000991623 0 | ||||||||
\(598\) | 7.09942e6 | 0.811839 | ||||||||
\(599\) | −3.54981e6 | −0.404238 | −0.202119 | − | 0.979361i | \(-0.564783\pi\) | ||||
−0.202119 | + | 0.979361i | \(0.564783\pi\) | |||||||
\(600\) | −4.99752e6 | −0.566731 | ||||||||
\(601\) | −6.16578e6 | −0.696308 | −0.348154 | − | 0.937437i | \(-0.613191\pi\) | ||||
−0.348154 | + | 0.937437i | \(0.613191\pi\) | |||||||
\(602\) | −7.04334e6 | −0.792114 | ||||||||
\(603\) | 3.93778e6 | 0.441020 | ||||||||
\(604\) | 2.51395e6 | 0.280391 | ||||||||
\(605\) | 2.45032e7 | 2.72166 | ||||||||
\(606\) | 77910.2 | 0.00861813 | ||||||||
\(607\) | 9.60415e6 | 1.05800 | 0.529002 | − | 0.848621i | \(-0.322566\pi\) | ||||
0.529002 | + | 0.848621i | \(0.322566\pi\) | |||||||
\(608\) | −2.06154e6 | −0.226169 | ||||||||
\(609\) | 2.19004e6 | 0.239281 | ||||||||
\(610\) | 1.78408e7 | 1.94129 | ||||||||
\(611\) | 1.10497e6 | 0.119742 | ||||||||
\(612\) | 1.09944e6 | 0.118657 | ||||||||
\(613\) | −5.51137e6 | −0.592391 | −0.296195 | − | 0.955127i | \(-0.595718\pi\) | ||||
−0.296195 | + | 0.955127i | \(0.595718\pi\) | |||||||
\(614\) | −1.62921e7 | −1.74404 | ||||||||
\(615\) | −9.63309e6 | −1.02702 | ||||||||
\(616\) | 5.36746e6 | 0.569924 | ||||||||
\(617\) | −8.80831e6 | −0.931493 | −0.465747 | − | 0.884918i | \(-0.654214\pi\) | ||||
−0.465747 | + | 0.884918i | \(0.654214\pi\) | |||||||
\(618\) | 8.56612e6 | 0.902222 | ||||||||
\(619\) | 3.92911e6 | 0.412162 | 0.206081 | − | 0.978535i | \(-0.433929\pi\) | ||||
0.206081 | + | 0.978535i | \(0.433929\pi\) | |||||||
\(620\) | 5.85755e6 | 0.611980 | ||||||||
\(621\) | 2.82906e6 | 0.294384 | ||||||||
\(622\) | −5.42666e6 | −0.562415 | ||||||||
\(623\) | −2.08123e6 | −0.214832 | ||||||||
\(624\) | 3.16427e6 | 0.325321 | ||||||||
\(625\) | −7.99872e6 | −0.819069 | ||||||||
\(626\) | 1.25756e7 | 1.28261 | ||||||||
\(627\) | 4.67716e6 | 0.475131 | ||||||||
\(628\) | −2.03409e6 | −0.205812 | ||||||||
\(629\) | −1.82772e7 | −1.84198 | ||||||||
\(630\) | −2.15560e6 | −0.216380 | ||||||||
\(631\) | 7.24415e6 | 0.724293 | 0.362146 | − | 0.932121i | \(-0.382044\pi\) | ||||
0.362146 | + | 0.932121i | \(0.382044\pi\) | |||||||
\(632\) | −3.54829e6 | −0.353367 | ||||||||
\(633\) | 5.74686e6 | 0.570061 | ||||||||
\(634\) | 7.58500e6 | 0.749432 | ||||||||
\(635\) | −1.97974e7 | −1.94838 | ||||||||
\(636\) | 392051. | 0.0384326 | ||||||||
\(637\) | −4.11523e6 | −0.401833 | ||||||||
\(638\) | 2.01379e7 | 1.95867 | ||||||||
\(639\) | 3.25192e6 | 0.315056 | ||||||||
\(640\) | −1.83078e7 | −1.76679 | ||||||||
\(641\) | −464280. | −0.0446308 | −0.0223154 | − | 0.999751i | \(-0.507104\pi\) | ||||
−0.0223154 | + | 0.999751i | \(0.507104\pi\) | |||||||
\(642\) | −5.42230e6 | −0.519214 | ||||||||
\(643\) | 1.96736e7 | 1.87653 | 0.938265 | − | 0.345918i | \(-0.112433\pi\) | ||||
0.938265 | + | 0.345918i | \(0.112433\pi\) | |||||||
\(644\) | −1.51503e6 | −0.143949 | ||||||||
\(645\) | −1.60520e7 | −1.51925 | ||||||||
\(646\) | 8.64069e6 | 0.814642 | ||||||||
\(647\) | −8.53718e6 | −0.801777 | −0.400889 | − | 0.916127i | \(-0.631299\pi\) | ||||
−0.400889 | + | 0.916127i | \(0.631299\pi\) | |||||||
\(648\) | 1.00810e6 | 0.0943119 | ||||||||
\(649\) | 2.35975e6 | 0.219914 | ||||||||
\(650\) | −6.61128e6 | −0.613765 | ||||||||
\(651\) | −4.36821e6 | −0.403971 | ||||||||
\(652\) | 4.00956e6 | 0.369383 | ||||||||
\(653\) | 5.29534e6 | 0.485971 | 0.242986 | − | 0.970030i | \(-0.421873\pi\) | ||||
0.242986 | + | 0.970030i | \(0.421873\pi\) | |||||||
\(654\) | 6.43246e6 | 0.588075 | ||||||||
\(655\) | −2.06532e7 | −1.88098 | ||||||||
\(656\) | −1.57640e7 | −1.43023 | ||||||||
\(657\) | −1.84683e6 | −0.166922 | ||||||||
\(658\) | −1.23182e6 | −0.110913 | ||||||||
\(659\) | −2.00389e7 | −1.79747 | −0.898734 | − | 0.438495i | \(-0.855512\pi\) | ||||
−0.898734 | + | 0.438495i | \(0.855512\pi\) | |||||||
\(660\) | −3.79431e6 | −0.339057 | ||||||||
\(661\) | 1.65921e6 | 0.147706 | 0.0738530 | − | 0.997269i | \(-0.476470\pi\) | ||||
0.0738530 | + | 0.997269i | \(0.476470\pi\) | |||||||
\(662\) | 2.08918e6 | 0.185281 | ||||||||
\(663\) | −4.68909e6 | −0.414291 | ||||||||
\(664\) | −1.02586e7 | −0.902958 | ||||||||
\(665\) | −3.24300e6 | −0.284376 | ||||||||
\(666\) | 5.19825e6 | 0.454121 | ||||||||
\(667\) | 1.83253e7 | 1.59491 | ||||||||
\(668\) | 1.37347e6 | 0.119091 | ||||||||
\(669\) | −1.00732e7 | −0.870164 | ||||||||
\(670\) | −2.51060e7 | −2.16068 | ||||||||
\(671\) | −2.34188e7 | −2.00798 | ||||||||
\(672\) | −1.24718e6 | −0.106538 | ||||||||
\(673\) | 1.84157e7 | 1.56730 | 0.783649 | − | 0.621204i | \(-0.213356\pi\) | ||||
0.783649 | + | 0.621204i | \(0.213356\pi\) | |||||||
\(674\) | 1.30674e7 | 1.10800 | ||||||||
\(675\) | −2.63455e6 | −0.222560 | ||||||||
\(676\) | −2.17223e6 | −0.182826 | ||||||||
\(677\) | −7.42281e6 | −0.622439 | −0.311219 | − | 0.950338i | \(-0.600737\pi\) | ||||
−0.311219 | + | 0.950338i | \(0.600737\pi\) | |||||||
\(678\) | −1.08593e7 | −0.907250 | ||||||||
\(679\) | 3.86643e6 | 0.321837 | ||||||||
\(680\) | 2.25987e7 | 1.87418 | ||||||||
\(681\) | −2.79229e6 | −0.230724 | ||||||||
\(682\) | −4.01665e7 | −3.30677 | ||||||||
\(683\) | −1.19685e7 | −0.981721 | −0.490860 | − | 0.871238i | \(-0.663318\pi\) | ||||
−0.490860 | + | 0.871238i | \(0.663318\pi\) | |||||||
\(684\) | −470432. | −0.0384465 | ||||||||
\(685\) | 2.30730e7 | 1.87879 | ||||||||
\(686\) | 1.00362e7 | 0.814251 | ||||||||
\(687\) | 5.18451e6 | 0.419099 | ||||||||
\(688\) | −2.62681e7 | −2.11572 | ||||||||
\(689\) | −1.67209e6 | −0.134187 | ||||||||
\(690\) | −1.80372e7 | −1.44227 | ||||||||
\(691\) | −1.41570e7 | −1.12791 | −0.563955 | − | 0.825805i | \(-0.690721\pi\) | ||||
−0.563955 | + | 0.825805i | \(0.690721\pi\) | |||||||
\(692\) | 4.31032e6 | 0.342172 | ||||||||
\(693\) | 2.82957e6 | 0.223814 | ||||||||
\(694\) | 1.27863e7 | 1.00773 | ||||||||
\(695\) | −1.51452e7 | −1.18936 | ||||||||
\(696\) | 6.53000e6 | 0.510964 | ||||||||
\(697\) | 2.33605e7 | 1.82138 | ||||||||
\(698\) | 5.54525e6 | 0.430807 | ||||||||
\(699\) | −3.33581e6 | −0.258231 | ||||||||
\(700\) | 1.41086e6 | 0.108828 | ||||||||
\(701\) | 4.89919e6 | 0.376555 | 0.188278 | − | 0.982116i | \(-0.439710\pi\) | ||||
0.188278 | + | 0.982116i | \(0.439710\pi\) | |||||||
\(702\) | 1.33363e6 | 0.102139 | ||||||||
\(703\) | 7.82051e6 | 0.596825 | ||||||||
\(704\) | 1.47590e7 | 1.12234 | ||||||||
\(705\) | −2.80735e6 | −0.212727 | ||||||||
\(706\) | 1.85941e7 | 1.40399 | ||||||||
\(707\) | 70910.4 | 0.00533533 | ||||||||
\(708\) | −237345. | −0.0177950 | ||||||||
\(709\) | −4.60872e6 | −0.344322 | −0.172161 | − | 0.985069i | \(-0.555075\pi\) | ||||
−0.172161 | + | 0.985069i | \(0.555075\pi\) | |||||||
\(710\) | −2.07331e7 | −1.54354 | ||||||||
\(711\) | −1.87055e6 | −0.138770 | ||||||||
\(712\) | −6.20555e6 | −0.458755 | ||||||||
\(713\) | −3.65513e7 | −2.69264 | ||||||||
\(714\) | 5.22740e6 | 0.383742 | ||||||||
\(715\) | 1.61826e7 | 1.18381 | ||||||||
\(716\) | 3.59203e6 | 0.261853 | ||||||||
\(717\) | 4.11669e6 | 0.299054 | ||||||||
\(718\) | −8.16171e6 | −0.590840 | ||||||||
\(719\) | 2.63345e6 | 0.189978 | 0.0949890 | − | 0.995478i | \(-0.469718\pi\) | ||||
0.0949890 | + | 0.995478i | \(0.469718\pi\) | |||||||
\(720\) | −8.03931e6 | −0.577946 | ||||||||
\(721\) | 7.79650e6 | 0.558549 | ||||||||
\(722\) | 1.18798e7 | 0.848136 | ||||||||
\(723\) | 1.48597e7 | 1.05722 | ||||||||
\(724\) | 2.05346e6 | 0.145593 | ||||||||
\(725\) | −1.70653e7 | −1.20578 | ||||||||
\(726\) | 1.69000e7 | 1.18999 | ||||||||
\(727\) | −1.62754e7 | −1.14207 | −0.571037 | − | 0.820924i | \(-0.693459\pi\) | ||||
−0.571037 | + | 0.820924i | \(0.693459\pi\) | |||||||
\(728\) | 2.30250e6 | 0.161017 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 1.17747e7 | 0.817794 | ||||||||
\(731\) | 3.89264e7 | 2.69433 | ||||||||
\(732\) | 2.35548e6 | 0.162481 | ||||||||
\(733\) | −2.64491e6 | −0.181824 | −0.0909120 | − | 0.995859i | \(-0.528978\pi\) | ||||
−0.0909120 | + | 0.995859i | \(0.528978\pi\) | |||||||
\(734\) | −1.10401e7 | −0.756369 | ||||||||
\(735\) | 1.04554e7 | 0.713874 | ||||||||
\(736\) | −1.04359e7 | −0.710124 | ||||||||
\(737\) | 3.29555e7 | 2.23491 | ||||||||
\(738\) | −6.64398e6 | −0.449043 | ||||||||
\(739\) | 1.63591e7 | 1.10192 | 0.550959 | − | 0.834532i | \(-0.314262\pi\) | ||||
0.550959 | + | 0.834532i | \(0.314262\pi\) | |||||||
\(740\) | −6.34432e6 | −0.425898 | ||||||||
\(741\) | 2.00638e6 | 0.134236 | ||||||||
\(742\) | 1.86404e6 | 0.124293 | ||||||||
\(743\) | 9.62508e6 | 0.639635 | 0.319817 | − | 0.947479i | \(-0.396378\pi\) | ||||
0.319817 | + | 0.947479i | \(0.396378\pi\) | |||||||
\(744\) | −1.30246e7 | −0.862644 | ||||||||
\(745\) | 5.32534e6 | 0.351526 | ||||||||
\(746\) | −1.21091e7 | −0.796646 | ||||||||
\(747\) | −5.40802e6 | −0.354599 | ||||||||
\(748\) | 9.20131e6 | 0.601306 | ||||||||
\(749\) | −4.93514e6 | −0.321436 | ||||||||
\(750\) | 2.27242e6 | 0.147514 | ||||||||
\(751\) | −547839. | −0.0354448 | −0.0177224 | − | 0.999843i | \(-0.505642\pi\) | ||||
−0.0177224 | + | 0.999843i | \(0.505642\pi\) | |||||||
\(752\) | −4.59407e6 | −0.296246 | ||||||||
\(753\) | 1.49624e7 | 0.961646 | ||||||||
\(754\) | 8.63861e6 | 0.553370 | ||||||||
\(755\) | 2.72407e7 | 1.73920 | ||||||||
\(756\) | −284600. | −0.0181105 | ||||||||
\(757\) | −7.62374e6 | −0.483535 | −0.241768 | − | 0.970334i | \(-0.577727\pi\) | ||||
−0.241768 | + | 0.970334i | \(0.577727\pi\) | |||||||
\(758\) | −2.19320e7 | −1.38645 | ||||||||
\(759\) | 2.36766e7 | 1.49181 | ||||||||
\(760\) | −9.66958e6 | −0.607259 | ||||||||
\(761\) | −2.11368e7 | −1.32305 | −0.661527 | − | 0.749922i | \(-0.730091\pi\) | ||||
−0.661527 | + | 0.749922i | \(0.730091\pi\) | |||||||
\(762\) | −1.36543e7 | −0.851890 | ||||||||
\(763\) | 5.85454e6 | 0.364067 | ||||||||
\(764\) | 5.81904e6 | 0.360677 | ||||||||
\(765\) | 1.19134e7 | 0.736005 | ||||||||
\(766\) | 2.21204e7 | 1.36214 | ||||||||
\(767\) | 1.01227e6 | 0.0621309 | ||||||||
\(768\) | −6.35663e6 | −0.388888 | ||||||||
\(769\) | −2.53471e7 | −1.54565 | −0.772827 | − | 0.634617i | \(-0.781158\pi\) | ||||
−0.772827 | + | 0.634617i | \(0.781158\pi\) | |||||||
\(770\) | −1.80404e7 | −1.09652 | ||||||||
\(771\) | −1.12021e7 | −0.678679 | ||||||||
\(772\) | 283814. | 0.0171392 | ||||||||
\(773\) | −2.45392e7 | −1.47711 | −0.738554 | − | 0.674195i | \(-0.764491\pi\) | ||||
−0.738554 | + | 0.674195i | \(0.764491\pi\) | |||||||
\(774\) | −1.10711e7 | −0.664260 | ||||||||
\(775\) | 3.40381e7 | 2.03569 | ||||||||
\(776\) | 1.15285e7 | 0.687253 | ||||||||
\(777\) | 4.73121e6 | 0.281138 | ||||||||
\(778\) | 1.02672e6 | 0.0608140 | ||||||||
\(779\) | −9.99555e6 | −0.590151 | ||||||||
\(780\) | −1.62766e6 | −0.0957915 | ||||||||
\(781\) | 2.72155e7 | 1.59657 | ||||||||
\(782\) | 4.37406e7 | 2.55781 | ||||||||
\(783\) | 3.44242e6 | 0.200659 | ||||||||
\(784\) | 1.71096e7 | 0.994148 | ||||||||
\(785\) | −2.20410e7 | −1.27661 | ||||||||
\(786\) | −1.42446e7 | −0.822418 | ||||||||
\(787\) | −2.27427e7 | −1.30890 | −0.654448 | − | 0.756107i | \(-0.727099\pi\) | ||||
−0.654448 | + | 0.756107i | \(0.727099\pi\) | |||||||
\(788\) | 4.55248e6 | 0.261176 | ||||||||
\(789\) | 1.36014e7 | 0.777843 | ||||||||
\(790\) | 1.19260e7 | 0.679872 | ||||||||
\(791\) | −9.88363e6 | −0.561662 | ||||||||
\(792\) | 8.43686e6 | 0.477934 | ||||||||
\(793\) | −1.00461e7 | −0.567300 | ||||||||
\(794\) | 7.93276e6 | 0.446553 | ||||||||
\(795\) | 4.24819e6 | 0.238389 | ||||||||
\(796\) | 7268.98 | 0.000406622 0 | ||||||||
\(797\) | 2.24707e7 | 1.25306 | 0.626529 | − | 0.779398i | \(-0.284475\pi\) | ||||
0.626529 | + | 0.779398i | \(0.284475\pi\) | |||||||
\(798\) | −2.23671e6 | −0.124338 | ||||||||
\(799\) | 6.80790e6 | 0.377265 | ||||||||
\(800\) | 9.71833e6 | 0.536867 | ||||||||
\(801\) | −3.27138e6 | −0.180157 | ||||||||
\(802\) | 1.81428e7 | 0.996020 | ||||||||
\(803\) | −1.54562e7 | −0.845889 | ||||||||
\(804\) | −3.31469e6 | −0.180843 | ||||||||
\(805\) | −1.64166e7 | −0.892881 | ||||||||
\(806\) | −1.72304e7 | −0.934237 | ||||||||
\(807\) | 1.00367e6 | 0.0542512 | ||||||||
\(808\) | 211432. | 0.0113931 | ||||||||
\(809\) | −3.57608e6 | −0.192104 | −0.0960519 | − | 0.995376i | \(-0.530621\pi\) | ||||
−0.0960519 | + | 0.995376i | \(0.530621\pi\) | |||||||
\(810\) | −3.38829e6 | −0.181455 | ||||||||
\(811\) | 3.19383e7 | 1.70514 | 0.852570 | − | 0.522613i | \(-0.175043\pi\) | ||||
0.852570 | + | 0.522613i | \(0.175043\pi\) | |||||||
\(812\) | −1.84350e6 | −0.0981191 | ||||||||
\(813\) | 2.53475e6 | 0.134496 | ||||||||
\(814\) | 4.35044e7 | 2.30130 | ||||||||
\(815\) | 4.34468e7 | 2.29120 | ||||||||
\(816\) | 1.94956e7 | 1.02497 | ||||||||
\(817\) | −1.66559e7 | −0.872999 | ||||||||
\(818\) | 1.71376e7 | 0.895501 | ||||||||
\(819\) | 1.21381e6 | 0.0632325 | ||||||||
\(820\) | 8.10881e6 | 0.421136 | ||||||||
\(821\) | −3.00431e7 | −1.55556 | −0.777779 | − | 0.628538i | \(-0.783654\pi\) | ||||
−0.777779 | + | 0.628538i | \(0.783654\pi\) | |||||||
\(822\) | 1.59135e7 | 0.821462 | ||||||||
\(823\) | −2.13843e7 | −1.10051 | −0.550256 | − | 0.834996i | \(-0.685470\pi\) | ||||
−0.550256 | + | 0.834996i | \(0.685470\pi\) | |||||||
\(824\) | 2.32467e7 | 1.19273 | ||||||||
\(825\) | −2.20487e7 | −1.12784 | ||||||||
\(826\) | −1.12848e6 | −0.0575496 | ||||||||
\(827\) | −1.64212e7 | −0.834912 | −0.417456 | − | 0.908697i | \(-0.637078\pi\) | ||||
−0.417456 | + | 0.908697i | \(0.637078\pi\) | |||||||
\(828\) | −2.38141e6 | −0.120714 | ||||||||
\(829\) | −1.98607e7 | −1.00371 | −0.501856 | − | 0.864951i | \(-0.667349\pi\) | ||||
−0.501856 | + | 0.864951i | \(0.667349\pi\) | |||||||
\(830\) | 3.44797e7 | 1.73728 | ||||||||
\(831\) | −1.91738e7 | −0.963175 | ||||||||
\(832\) | 6.33123e6 | 0.317088 | ||||||||
\(833\) | −2.53546e7 | −1.26603 | ||||||||
\(834\) | −1.04457e7 | −0.520022 | ||||||||
\(835\) | 1.48826e7 | 0.738693 | ||||||||
\(836\) | −3.93708e6 | −0.194831 | ||||||||
\(837\) | −6.86618e6 | −0.338767 | ||||||||
\(838\) | 1.79654e7 | 0.883744 | ||||||||
\(839\) | 2.18729e7 | 1.07276 | 0.536379 | − | 0.843977i | \(-0.319792\pi\) | ||||
0.536379 | + | 0.843977i | \(0.319792\pi\) | |||||||
\(840\) | −5.84985e6 | −0.286053 | ||||||||
\(841\) | 1.78722e6 | 0.0871342 | ||||||||
\(842\) | −1.76550e7 | −0.858196 | ||||||||
\(843\) | 1.56797e7 | 0.759923 | ||||||||
\(844\) | −4.83751e6 | −0.233757 | ||||||||
\(845\) | −2.35379e7 | −1.13403 | ||||||||
\(846\) | −1.93624e6 | −0.0930108 | ||||||||
\(847\) | 1.53816e7 | 0.736703 | ||||||||
\(848\) | 6.95192e6 | 0.331983 | ||||||||
\(849\) | −7.24467e6 | −0.344944 | ||||||||
\(850\) | −4.07331e7 | −1.93375 | ||||||||
\(851\) | 3.95887e7 | 1.87391 | ||||||||
\(852\) | −2.73735e6 | −0.129191 | ||||||||
\(853\) | 1.85070e7 | 0.870892 | 0.435446 | − | 0.900215i | \(-0.356591\pi\) | ||||
0.435446 | + | 0.900215i | \(0.356591\pi\) | |||||||
\(854\) | 1.11993e7 | 0.525469 | ||||||||
\(855\) | −5.09752e6 | −0.238475 | ||||||||
\(856\) | −1.47150e7 | −0.686397 | ||||||||
\(857\) | −778673. | −0.0362162 | −0.0181081 | − | 0.999836i | \(-0.505764\pi\) | ||||
−0.0181081 | + | 0.999836i | \(0.505764\pi\) | |||||||
\(858\) | 1.11612e7 | 0.517599 | ||||||||
\(859\) | −2.55949e7 | −1.18351 | −0.591754 | − | 0.806119i | \(-0.701564\pi\) | ||||
−0.591754 | + | 0.806119i | \(0.701564\pi\) | |||||||
\(860\) | 1.35120e7 | 0.622978 | ||||||||
\(861\) | −6.04705e6 | −0.277994 | ||||||||
\(862\) | −2.42992e7 | −1.11384 | ||||||||
\(863\) | −2.32218e7 | −1.06137 | −0.530687 | − | 0.847568i | \(-0.678066\pi\) | ||||
−0.530687 | + | 0.847568i | \(0.678066\pi\) | |||||||
\(864\) | −1.96038e6 | −0.0893423 | ||||||||
\(865\) | 4.67058e7 | 2.12242 | ||||||||
\(866\) | −421729. | −0.0191090 | ||||||||
\(867\) | −1.61115e7 | −0.727929 | ||||||||
\(868\) | 3.67701e6 | 0.165651 | ||||||||
\(869\) | −1.56547e7 | −0.703229 | ||||||||
\(870\) | −2.19477e7 | −0.983086 | ||||||||
\(871\) | 1.41370e7 | 0.631412 | ||||||||
\(872\) | 1.74564e7 | 0.777432 | ||||||||
\(873\) | 6.07746e6 | 0.269890 | ||||||||
\(874\) | −1.87158e7 | −0.828763 | ||||||||
\(875\) | 2.06825e6 | 0.0913236 | ||||||||
\(876\) | 1.55459e6 | 0.0684474 | ||||||||
\(877\) | 3.47355e7 | 1.52502 | 0.762508 | − | 0.646979i | \(-0.223968\pi\) | ||||
0.762508 | + | 0.646979i | \(0.223968\pi\) | |||||||
\(878\) | −1.65702e7 | −0.725423 | ||||||||
\(879\) | −3.63794e6 | −0.158812 | ||||||||
\(880\) | −6.72814e7 | −2.92879 | ||||||||
\(881\) | 3.47364e7 | 1.50780 | 0.753902 | − | 0.656987i | \(-0.228169\pi\) | ||||
0.753902 | + | 0.656987i | \(0.228169\pi\) | |||||||
\(882\) | 7.21112e6 | 0.312127 | ||||||||
\(883\) | 1.73501e7 | 0.748859 | 0.374429 | − | 0.927255i | \(-0.377839\pi\) | ||||
0.374429 | + | 0.927255i | \(0.377839\pi\) | |||||||
\(884\) | 3.94712e6 | 0.169883 | ||||||||
\(885\) | −2.57183e6 | −0.110378 | ||||||||
\(886\) | −2.42809e7 | −1.03915 | ||||||||
\(887\) | 2.06179e7 | 0.879904 | 0.439952 | − | 0.898021i | \(-0.354996\pi\) | ||||
0.439952 | + | 0.898021i | \(0.354996\pi\) | |||||||
\(888\) | 1.41069e7 | 0.600345 | ||||||||
\(889\) | −1.24276e7 | −0.527390 | ||||||||
\(890\) | 2.08572e7 | 0.882636 | ||||||||
\(891\) | 4.44766e6 | 0.187688 | ||||||||
\(892\) | 8.47925e6 | 0.356817 | ||||||||
\(893\) | −2.91298e6 | −0.122239 | ||||||||
\(894\) | 3.67291e6 | 0.153697 | ||||||||
\(895\) | 3.89225e7 | 1.62422 | ||||||||
\(896\) | −1.14925e7 | −0.478237 | ||||||||
\(897\) | 1.01566e7 | 0.421472 | ||||||||
\(898\) | 1.23782e7 | 0.512232 | ||||||||
\(899\) | −4.44758e7 | −1.83537 | ||||||||
\(900\) | 2.21767e6 | 0.0912621 | ||||||||
\(901\) | −1.03020e7 | −0.422774 | ||||||||
\(902\) | −5.56039e7 | −2.27556 | ||||||||
\(903\) | −1.00764e7 | −0.411232 | ||||||||
\(904\) | −2.94698e7 | −1.19938 | ||||||||
\(905\) | 2.22509e7 | 0.903082 | ||||||||
\(906\) | 1.87880e7 | 0.760431 | ||||||||
\(907\) | −2.03892e7 | −0.822968 | −0.411484 | − | 0.911417i | \(-0.634989\pi\) | ||||
−0.411484 | + | 0.911417i | \(0.634989\pi\) | |||||||
\(908\) | 2.35046e6 | 0.0946101 | ||||||||
\(909\) | 111461. | 0.00447416 | ||||||||
\(910\) | −7.73884e6 | −0.309793 | ||||||||
\(911\) | −8.86386e6 | −0.353856 | −0.176928 | − | 0.984224i | \(-0.556616\pi\) | ||||
−0.176928 | + | 0.984224i | \(0.556616\pi\) | |||||||
\(912\) | −8.34180e6 | −0.332103 | ||||||||
\(913\) | −4.52601e7 | −1.79696 | ||||||||
\(914\) | −1.76464e7 | −0.698701 | ||||||||
\(915\) | 2.55236e7 | 1.00783 | ||||||||
\(916\) | −4.36415e6 | −0.171854 | ||||||||
\(917\) | −1.29648e7 | −0.509145 | ||||||||
\(918\) | 8.21670e6 | 0.321803 | ||||||||
\(919\) | −2.01939e7 | −0.788736 | −0.394368 | − | 0.918953i | \(-0.629036\pi\) | ||||
−0.394368 | + | 0.918953i | \(0.629036\pi\) | |||||||
\(920\) | −4.89491e7 | −1.90667 | ||||||||
\(921\) | −2.33080e7 | −0.905432 | ||||||||
\(922\) | 3.69334e6 | 0.143084 | ||||||||
\(923\) | 1.16747e7 | 0.451068 | ||||||||
\(924\) | −2.38183e6 | −0.0917764 | ||||||||
\(925\) | −3.68667e7 | −1.41671 | ||||||||
\(926\) | 7.04577e6 | 0.270023 | ||||||||
\(927\) | 1.22550e7 | 0.468395 | ||||||||
\(928\) | −1.26984e7 | −0.484039 | ||||||||
\(929\) | −4.06252e7 | −1.54439 | −0.772194 | − | 0.635387i | \(-0.780841\pi\) | ||||
−0.772194 | + | 0.635387i | \(0.780841\pi\) | |||||||
\(930\) | 4.37764e7 | 1.65971 | ||||||||
\(931\) | 1.08488e7 | 0.410211 | ||||||||
\(932\) | 2.80797e6 | 0.105889 | ||||||||
\(933\) | −7.76354e6 | −0.291982 | ||||||||
\(934\) | 4.16909e6 | 0.156378 | ||||||||
\(935\) | 9.97036e7 | 3.72977 | ||||||||
\(936\) | 3.61919e6 | 0.135027 | ||||||||
\(937\) | 4.97755e7 | 1.85211 | 0.926054 | − | 0.377390i | \(-0.123178\pi\) | ||||
0.926054 | + | 0.377390i | \(0.123178\pi\) | |||||||
\(938\) | −1.57599e7 | −0.584854 | ||||||||
\(939\) | 1.79911e7 | 0.665875 | ||||||||
\(940\) | 2.36313e6 | 0.0872304 | ||||||||
\(941\) | 6.85312e6 | 0.252298 | 0.126149 | − | 0.992011i | \(-0.459738\pi\) | ||||
0.126149 | + | 0.992011i | \(0.459738\pi\) | |||||||
\(942\) | −1.52018e7 | −0.558170 | ||||||||
\(943\) | −5.05992e7 | −1.85295 | ||||||||
\(944\) | −4.20865e6 | −0.153714 | ||||||||
\(945\) | −3.08387e6 | −0.112335 | ||||||||
\(946\) | −9.26547e7 | −3.36620 | ||||||||
\(947\) | 2.46625e7 | 0.893639 | 0.446819 | − | 0.894624i | \(-0.352557\pi\) | ||||
0.446819 | + | 0.894624i | \(0.352557\pi\) | |||||||
\(948\) | 1.57457e6 | 0.0569036 | ||||||||
\(949\) | −6.63029e6 | −0.238983 | ||||||||
\(950\) | 1.74290e7 | 0.626560 | ||||||||
\(951\) | 1.08513e7 | 0.389073 | ||||||||
\(952\) | 1.41861e7 | 0.507305 | ||||||||
\(953\) | 4.33017e7 | 1.54444 | 0.772222 | − | 0.635352i | \(-0.219145\pi\) | ||||
0.772222 | + | 0.635352i | \(0.219145\pi\) | |||||||
\(954\) | 2.92999e6 | 0.104231 | ||||||||
\(955\) | 6.30540e7 | 2.23720 | ||||||||
\(956\) | −3.46528e6 | −0.122629 | ||||||||
\(957\) | 2.88098e7 | 1.01686 | ||||||||
\(958\) | 1.34627e7 | 0.473935 | ||||||||
\(959\) | 1.44838e7 | 0.508552 | ||||||||
\(960\) | −1.60855e7 | −0.563320 | ||||||||
\(961\) | 6.00813e7 | 2.09861 | ||||||||
\(962\) | 1.86622e7 | 0.650169 | ||||||||
\(963\) | −7.75731e6 | −0.269554 | ||||||||
\(964\) | −1.25084e7 | −0.433519 | ||||||||
\(965\) | 3.07535e6 | 0.106311 | ||||||||
\(966\) | −1.13226e7 | −0.390394 | ||||||||
\(967\) | 1.35495e7 | 0.465969 | 0.232984 | − | 0.972480i | \(-0.425151\pi\) | ||||
0.232984 | + | 0.972480i | \(0.425151\pi\) | |||||||
\(968\) | 4.58630e7 | 1.57316 | ||||||||
\(969\) | 1.23616e7 | 0.422928 | ||||||||
\(970\) | −3.87478e7 | −1.32226 | ||||||||
\(971\) | 2.50869e7 | 0.853884 | 0.426942 | − | 0.904279i | \(-0.359591\pi\) | ||||
0.426942 | + | 0.904279i | \(0.359591\pi\) | |||||||
\(972\) | −447349. | −0.0151873 | ||||||||
\(973\) | −9.50719e6 | −0.321936 | ||||||||
\(974\) | −5.55235e7 | −1.87534 | ||||||||
\(975\) | −9.45829e6 | −0.318641 | ||||||||
\(976\) | 4.17679e7 | 1.40352 | ||||||||
\(977\) | −3.14930e7 | −1.05555 | −0.527774 | − | 0.849385i | \(-0.676973\pi\) | ||||
−0.527774 | + | 0.849385i | \(0.676973\pi\) | |||||||
\(978\) | 2.99654e7 | 1.00178 | ||||||||
\(979\) | −2.73784e7 | −0.912959 | ||||||||
\(980\) | −8.80098e6 | −0.292729 | ||||||||
\(981\) | 9.20247e6 | 0.305304 | ||||||||
\(982\) | 2.13001e6 | 0.0704861 | ||||||||
\(983\) | −3.59119e6 | −0.118537 | −0.0592685 | − | 0.998242i | \(-0.518877\pi\) | ||||
−0.0592685 | + | 0.998242i | \(0.518877\pi\) | |||||||
\(984\) | −1.80304e7 | −0.593632 | ||||||||
\(985\) | 4.93298e7 | 1.62001 | ||||||||
\(986\) | 5.32238e7 | 1.74347 | ||||||||
\(987\) | −1.76228e6 | −0.0575813 | ||||||||
\(988\) | −1.68890e6 | −0.0550442 | ||||||||
\(989\) | −8.43151e7 | −2.74104 | ||||||||
\(990\) | −2.83568e7 | −0.919536 | ||||||||
\(991\) | −4.64082e6 | −0.150110 | −0.0750551 | − | 0.997179i | \(-0.523913\pi\) | ||||
−0.0750551 | + | 0.997179i | \(0.523913\pi\) | |||||||
\(992\) | 2.53280e7 | 0.817188 | ||||||||
\(993\) | 2.98885e6 | 0.0961901 | ||||||||
\(994\) | −1.30150e7 | −0.417808 | ||||||||
\(995\) | 78765.3 | 0.00252219 | ||||||||
\(996\) | 4.55229e6 | 0.145406 | ||||||||
\(997\) | 2.99407e7 | 0.953946 | 0.476973 | − | 0.878918i | \(-0.341734\pi\) | ||||
0.476973 | + | 0.878918i | \(0.341734\pi\) | |||||||
\(998\) | 3.12149e7 | 0.992054 | ||||||||
\(999\) | 7.43676e6 | 0.235760 |
(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 | 177.6.a.d.1.4 | ✓ | 13 | |
3.2 | odd | 2 | 531.6.a.e.1.10 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.6.a.d.1.4 | ✓ | 13 | 1.1 | even | 1 | trivial | |
531.6.a.e.1.10 | 13 | 3.2 | odd | 2 |