Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [77,6,Mod(1,77)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(77, 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("77.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 77 = 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 77.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: | \(12.3495541256\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 77.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.353553 | −0.176777 | − | 0.984251i | \(-0.556567\pi\) | ||||
−0.176777 | + | 0.984251i | \(0.556567\pi\) | |||||||
\(3\) | −6.00000 | −0.384900 | −0.192450 | − | 0.981307i | \(-0.561643\pi\) | ||||
−0.192450 | + | 0.981307i | \(0.561643\pi\) | |||||||
\(4\) | −28.0000 | −0.875000 | ||||||||
\(5\) | −74.0000 | −1.32375 | −0.661876 | − | 0.749613i | \(-0.730240\pi\) | ||||
−0.661876 | + | 0.749613i | \(0.730240\pi\) | |||||||
\(6\) | 12.0000 | 0.136083 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | 120.000 | 0.662913 | ||||||||
\(9\) | −207.000 | −0.851852 | ||||||||
\(10\) | 148.000 | 0.468017 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | 168.000 | 0.336788 | ||||||||
\(13\) | 364.000 | 0.597369 | 0.298685 | − | 0.954352i | \(-0.403452\pi\) | ||||
0.298685 | + | 0.954352i | \(0.403452\pi\) | |||||||
\(14\) | 98.0000 | 0.133631 | ||||||||
\(15\) | 444.000 | 0.509512 | ||||||||
\(16\) | 656.000 | 0.640625 | ||||||||
\(17\) | 148.000 | 0.124205 | 0.0621025 | − | 0.998070i | \(-0.480219\pi\) | ||||
0.0621025 | + | 0.998070i | \(0.480219\pi\) | |||||||
\(18\) | 414.000 | 0.301175 | ||||||||
\(19\) | −1320.00 | −0.838861 | −0.419430 | − | 0.907787i | \(-0.637770\pi\) | ||||
−0.419430 | + | 0.907787i | \(0.637770\pi\) | |||||||
\(20\) | 2072.00 | 1.15828 | ||||||||
\(21\) | 294.000 | 0.145479 | ||||||||
\(22\) | −242.000 | −0.106600 | ||||||||
\(23\) | −436.000 | −0.171857 | −0.0859284 | − | 0.996301i | \(-0.527386\pi\) | ||||
−0.0859284 | + | 0.996301i | \(0.527386\pi\) | |||||||
\(24\) | −720.000 | −0.255155 | ||||||||
\(25\) | 2351.00 | 0.752320 | ||||||||
\(26\) | −728.000 | −0.211202 | ||||||||
\(27\) | 2700.00 | 0.712778 | ||||||||
\(28\) | 1372.00 | 0.330719 | ||||||||
\(29\) | 2970.00 | 0.655785 | 0.327892 | − | 0.944715i | \(-0.393662\pi\) | ||||
0.327892 | + | 0.944715i | \(0.393662\pi\) | |||||||
\(30\) | −888.000 | −0.180140 | ||||||||
\(31\) | 8842.00 | 1.65252 | 0.826259 | − | 0.563290i | \(-0.190465\pi\) | ||||
0.826259 | + | 0.563290i | \(0.190465\pi\) | |||||||
\(32\) | −5152.00 | −0.889408 | ||||||||
\(33\) | −726.000 | −0.116052 | ||||||||
\(34\) | −296.000 | −0.0439131 | ||||||||
\(35\) | 3626.00 | 0.500331 | ||||||||
\(36\) | 5796.00 | 0.745370 | ||||||||
\(37\) | 138.000 | 0.0165720 | 0.00828600 | − | 0.999966i | \(-0.497362\pi\) | ||||
0.00828600 | + | 0.999966i | \(0.497362\pi\) | |||||||
\(38\) | 2640.00 | 0.296582 | ||||||||
\(39\) | −2184.00 | −0.229928 | ||||||||
\(40\) | −8880.00 | −0.877532 | ||||||||
\(41\) | 532.000 | 0.0494256 | 0.0247128 | − | 0.999695i | \(-0.492133\pi\) | ||||
0.0247128 | + | 0.999695i | \(0.492133\pi\) | |||||||
\(42\) | −588.000 | −0.0514344 | ||||||||
\(43\) | −20676.0 | −1.70528 | −0.852639 | − | 0.522500i | \(-0.825000\pi\) | ||||
−0.852639 | + | 0.522500i | \(0.825000\pi\) | |||||||
\(44\) | −3388.00 | −0.263822 | ||||||||
\(45\) | 15318.0 | 1.12764 | ||||||||
\(46\) | 872.000 | 0.0607606 | ||||||||
\(47\) | −11722.0 | −0.774029 | −0.387014 | − | 0.922074i | \(-0.626494\pi\) | ||||
−0.387014 | + | 0.922074i | \(0.626494\pi\) | |||||||
\(48\) | −3936.00 | −0.246577 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | −4702.00 | −0.265985 | ||||||||
\(51\) | −888.000 | −0.0478066 | ||||||||
\(52\) | −10192.0 | −0.522698 | ||||||||
\(53\) | 5274.00 | 0.257899 | 0.128950 | − | 0.991651i | \(-0.458839\pi\) | ||||
0.128950 | + | 0.991651i | \(0.458839\pi\) | |||||||
\(54\) | −5400.00 | −0.252005 | ||||||||
\(55\) | −8954.00 | −0.399126 | ||||||||
\(56\) | −5880.00 | −0.250557 | ||||||||
\(57\) | 7920.00 | 0.322878 | ||||||||
\(58\) | −5940.00 | −0.231855 | ||||||||
\(59\) | −27670.0 | −1.03485 | −0.517427 | − | 0.855727i | \(-0.673110\pi\) | ||||
−0.517427 | + | 0.855727i | \(0.673110\pi\) | |||||||
\(60\) | −12432.0 | −0.445823 | ||||||||
\(61\) | 19512.0 | 0.671394 | 0.335697 | − | 0.941970i | \(-0.391028\pi\) | ||||
0.335697 | + | 0.941970i | \(0.391028\pi\) | |||||||
\(62\) | −17684.0 | −0.584253 | ||||||||
\(63\) | 10143.0 | 0.321970 | ||||||||
\(64\) | −10688.0 | −0.326172 | ||||||||
\(65\) | −26936.0 | −0.790769 | ||||||||
\(66\) | 1452.00 | 0.0410305 | ||||||||
\(67\) | 64088.0 | 1.74417 | 0.872087 | − | 0.489351i | \(-0.162766\pi\) | ||||
0.872087 | + | 0.489351i | \(0.162766\pi\) | |||||||
\(68\) | −4144.00 | −0.108679 | ||||||||
\(69\) | 2616.00 | 0.0661477 | ||||||||
\(70\) | −7252.00 | −0.176894 | ||||||||
\(71\) | −3708.00 | −0.0872959 | −0.0436480 | − | 0.999047i | \(-0.513898\pi\) | ||||
−0.0436480 | + | 0.999047i | \(0.513898\pi\) | |||||||
\(72\) | −24840.0 | −0.564703 | ||||||||
\(73\) | −24296.0 | −0.533615 | −0.266807 | − | 0.963750i | \(-0.585969\pi\) | ||||
−0.266807 | + | 0.963750i | \(0.585969\pi\) | |||||||
\(74\) | −276.000 | −0.00585908 | ||||||||
\(75\) | −14106.0 | −0.289568 | ||||||||
\(76\) | 36960.0 | 0.734003 | ||||||||
\(77\) | −5929.00 | −0.113961 | ||||||||
\(78\) | 4368.00 | 0.0812917 | ||||||||
\(79\) | −2200.00 | −0.0396602 | −0.0198301 | − | 0.999803i | \(-0.506313\pi\) | ||||
−0.0198301 | + | 0.999803i | \(0.506313\pi\) | |||||||
\(80\) | −48544.0 | −0.848029 | ||||||||
\(81\) | 34101.0 | 0.577503 | ||||||||
\(82\) | −1064.00 | −0.0174746 | ||||||||
\(83\) | 74424.0 | 1.18582 | 0.592909 | − | 0.805270i | \(-0.297980\pi\) | ||||
0.592909 | + | 0.805270i | \(0.297980\pi\) | |||||||
\(84\) | −8232.00 | −0.127294 | ||||||||
\(85\) | −10952.0 | −0.164417 | ||||||||
\(86\) | 41352.0 | 0.602907 | ||||||||
\(87\) | −17820.0 | −0.252412 | ||||||||
\(88\) | 14520.0 | 0.199876 | ||||||||
\(89\) | 34170.0 | 0.457267 | 0.228634 | − | 0.973513i | \(-0.426574\pi\) | ||||
0.228634 | + | 0.973513i | \(0.426574\pi\) | |||||||
\(90\) | −30636.0 | −0.398681 | ||||||||
\(91\) | −17836.0 | −0.225784 | ||||||||
\(92\) | 12208.0 | 0.150375 | ||||||||
\(93\) | −53052.0 | −0.636055 | ||||||||
\(94\) | 23444.0 | 0.273660 | ||||||||
\(95\) | 97680.0 | 1.11044 | ||||||||
\(96\) | 30912.0 | 0.342333 | ||||||||
\(97\) | 151718. | 1.63722 | 0.818611 | − | 0.574348i | \(-0.194744\pi\) | ||||
0.818611 | + | 0.574348i | \(0.194744\pi\) | |||||||
\(98\) | −4802.00 | −0.0505076 | ||||||||
\(99\) | −25047.0 | −0.256843 | ||||||||
\(100\) | −65828.0 | −0.658280 | ||||||||
\(101\) | 116852. | 1.13981 | 0.569905 | − | 0.821710i | \(-0.306980\pi\) | ||||
0.569905 | + | 0.821710i | \(0.306980\pi\) | |||||||
\(102\) | 1776.00 | 0.0169022 | ||||||||
\(103\) | 103694. | 0.963076 | 0.481538 | − | 0.876425i | \(-0.340078\pi\) | ||||
0.481538 | + | 0.876425i | \(0.340078\pi\) | |||||||
\(104\) | 43680.0 | 0.396004 | ||||||||
\(105\) | −21756.0 | −0.192578 | ||||||||
\(106\) | −10548.0 | −0.0911812 | ||||||||
\(107\) | −97092.0 | −0.819830 | −0.409915 | − | 0.912124i | \(-0.634442\pi\) | ||||
−0.409915 | + | 0.912124i | \(0.634442\pi\) | |||||||
\(108\) | −75600.0 | −0.623681 | ||||||||
\(109\) | 52930.0 | 0.426713 | 0.213356 | − | 0.976974i | \(-0.431560\pi\) | ||||
0.213356 | + | 0.976974i | \(0.431560\pi\) | |||||||
\(110\) | 17908.0 | 0.141112 | ||||||||
\(111\) | −828.000 | −0.00637856 | ||||||||
\(112\) | −32144.0 | −0.242133 | ||||||||
\(113\) | −80526.0 | −0.593253 | −0.296627 | − | 0.954994i | \(-0.595862\pi\) | ||||
−0.296627 | + | 0.954994i | \(0.595862\pi\) | |||||||
\(114\) | −15840.0 | −0.114155 | ||||||||
\(115\) | 32264.0 | 0.227496 | ||||||||
\(116\) | −83160.0 | −0.573812 | ||||||||
\(117\) | −75348.0 | −0.508870 | ||||||||
\(118\) | 55340.0 | 0.365876 | ||||||||
\(119\) | −7252.00 | −0.0469451 | ||||||||
\(120\) | 53280.0 | 0.337762 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −39024.0 | −0.237373 | ||||||||
\(123\) | −3192.00 | −0.0190239 | ||||||||
\(124\) | −247576. | −1.44595 | ||||||||
\(125\) | 57276.0 | 0.327867 | ||||||||
\(126\) | −20286.0 | −0.113833 | ||||||||
\(127\) | 221048. | 1.21612 | 0.608061 | − | 0.793890i | \(-0.291948\pi\) | ||||
0.608061 | + | 0.793890i | \(0.291948\pi\) | |||||||
\(128\) | 186240. | 1.00473 | ||||||||
\(129\) | 124056. | 0.656362 | ||||||||
\(130\) | 53872.0 | 0.279579 | ||||||||
\(131\) | 37572.0 | 0.191287 | 0.0956436 | − | 0.995416i | \(-0.469509\pi\) | ||||
0.0956436 | + | 0.995416i | \(0.469509\pi\) | |||||||
\(132\) | 20328.0 | 0.101545 | ||||||||
\(133\) | 64680.0 | 0.317060 | ||||||||
\(134\) | −128176. | −0.616658 | ||||||||
\(135\) | −199800. | −0.943542 | ||||||||
\(136\) | 17760.0 | 0.0823371 | ||||||||
\(137\) | −290602. | −1.32281 | −0.661405 | − | 0.750029i | \(-0.730039\pi\) | ||||
−0.661405 | + | 0.750029i | \(0.730039\pi\) | |||||||
\(138\) | −5232.00 | −0.0233868 | ||||||||
\(139\) | 367360. | 1.61270 | 0.806352 | − | 0.591435i | \(-0.201439\pi\) | ||||
0.806352 | + | 0.591435i | \(0.201439\pi\) | |||||||
\(140\) | −101528. | −0.437790 | ||||||||
\(141\) | 70332.0 | 0.297924 | ||||||||
\(142\) | 7416.00 | 0.0308638 | ||||||||
\(143\) | 44044.0 | 0.180114 | ||||||||
\(144\) | −135792. | −0.545718 | ||||||||
\(145\) | −219780. | −0.868097 | ||||||||
\(146\) | 48592.0 | 0.188661 | ||||||||
\(147\) | −14406.0 | −0.0549857 | ||||||||
\(148\) | −3864.00 | −0.0145005 | ||||||||
\(149\) | −462730. | −1.70751 | −0.853753 | − | 0.520679i | \(-0.825679\pi\) | ||||
−0.853753 | + | 0.520679i | \(0.825679\pi\) | |||||||
\(150\) | 28212.0 | 0.102378 | ||||||||
\(151\) | −7648.00 | −0.0272964 | −0.0136482 | − | 0.999907i | \(-0.504344\pi\) | ||||
−0.0136482 | + | 0.999907i | \(0.504344\pi\) | |||||||
\(152\) | −158400. | −0.556091 | ||||||||
\(153\) | −30636.0 | −0.105804 | ||||||||
\(154\) | 11858.0 | 0.0402911 | ||||||||
\(155\) | −654308. | −2.18752 | ||||||||
\(156\) | 61152.0 | 0.201187 | ||||||||
\(157\) | −161482. | −0.522847 | −0.261424 | − | 0.965224i | \(-0.584192\pi\) | ||||
−0.261424 | + | 0.965224i | \(0.584192\pi\) | |||||||
\(158\) | 4400.00 | 0.0140220 | ||||||||
\(159\) | −31644.0 | −0.0992656 | ||||||||
\(160\) | 381248. | 1.17736 | ||||||||
\(161\) | 21364.0 | 0.0649558 | ||||||||
\(162\) | −68202.0 | −0.204178 | ||||||||
\(163\) | 179464. | 0.529064 | 0.264532 | − | 0.964377i | \(-0.414782\pi\) | ||||
0.264532 | + | 0.964377i | \(0.414782\pi\) | |||||||
\(164\) | −14896.0 | −0.0432474 | ||||||||
\(165\) | 53724.0 | 0.153624 | ||||||||
\(166\) | −148848. | −0.419250 | ||||||||
\(167\) | 316848. | 0.879144 | 0.439572 | − | 0.898207i | \(-0.355130\pi\) | ||||
0.439572 | + | 0.898207i | \(0.355130\pi\) | |||||||
\(168\) | 35280.0 | 0.0964396 | ||||||||
\(169\) | −238797. | −0.643150 | ||||||||
\(170\) | 21904.0 | 0.0581301 | ||||||||
\(171\) | 273240. | 0.714585 | ||||||||
\(172\) | 578928. | 1.49212 | ||||||||
\(173\) | −175116. | −0.444847 | −0.222423 | − | 0.974950i | \(-0.571397\pi\) | ||||
−0.222423 | + | 0.974950i | \(0.571397\pi\) | |||||||
\(174\) | 35640.0 | 0.0892410 | ||||||||
\(175\) | −115199. | −0.284350 | ||||||||
\(176\) | 79376.0 | 0.193156 | ||||||||
\(177\) | 166020. | 0.398316 | ||||||||
\(178\) | −68340.0 | −0.161668 | ||||||||
\(179\) | −69780.0 | −0.162779 | −0.0813895 | − | 0.996682i | \(-0.525936\pi\) | ||||
−0.0813895 | + | 0.996682i | \(0.525936\pi\) | |||||||
\(180\) | −428904. | −0.986686 | ||||||||
\(181\) | −78638.0 | −0.178417 | −0.0892085 | − | 0.996013i | \(-0.528434\pi\) | ||||
−0.0892085 | + | 0.996013i | \(0.528434\pi\) | |||||||
\(182\) | 35672.0 | 0.0798268 | ||||||||
\(183\) | −117072. | −0.258420 | ||||||||
\(184\) | −52320.0 | −0.113926 | ||||||||
\(185\) | −10212.0 | −0.0219372 | ||||||||
\(186\) | 106104. | 0.224879 | ||||||||
\(187\) | 17908.0 | 0.0374492 | ||||||||
\(188\) | 328216. | 0.677275 | ||||||||
\(189\) | −132300. | −0.269405 | ||||||||
\(190\) | −195360. | −0.392601 | ||||||||
\(191\) | −927208. | −1.83905 | −0.919525 | − | 0.393030i | \(-0.871427\pi\) | ||||
−0.919525 | + | 0.393030i | \(0.871427\pi\) | |||||||
\(192\) | 64128.0 | 0.125544 | ||||||||
\(193\) | 877474. | 1.69567 | 0.847834 | − | 0.530261i | \(-0.177906\pi\) | ||||
0.847834 | + | 0.530261i | \(0.177906\pi\) | |||||||
\(194\) | −303436. | −0.578846 | ||||||||
\(195\) | 161616. | 0.304367 | ||||||||
\(196\) | −67228.0 | −0.125000 | ||||||||
\(197\) | −744602. | −1.36697 | −0.683484 | − | 0.729965i | \(-0.739536\pi\) | ||||
−0.683484 | + | 0.729965i | \(0.739536\pi\) | |||||||
\(198\) | 50094.0 | 0.0908077 | ||||||||
\(199\) | 1.07931e6 | 1.93203 | 0.966014 | − | 0.258489i | \(-0.0832246\pi\) | ||||
0.966014 | + | 0.258489i | \(0.0832246\pi\) | |||||||
\(200\) | 282120. | 0.498722 | ||||||||
\(201\) | −384528. | −0.671333 | ||||||||
\(202\) | −233704. | −0.402984 | ||||||||
\(203\) | −145530. | −0.247863 | ||||||||
\(204\) | 24864.0 | 0.0418307 | ||||||||
\(205\) | −39368.0 | −0.0654273 | ||||||||
\(206\) | −207388. | −0.340499 | ||||||||
\(207\) | 90252.0 | 0.146397 | ||||||||
\(208\) | 238784. | 0.382690 | ||||||||
\(209\) | −159720. | −0.252926 | ||||||||
\(210\) | 43512.0 | 0.0680865 | ||||||||
\(211\) | 728772. | 1.12690 | 0.563450 | − | 0.826150i | \(-0.309474\pi\) | ||||
0.563450 | + | 0.826150i | \(0.309474\pi\) | |||||||
\(212\) | −147672. | −0.225662 | ||||||||
\(213\) | 22248.0 | 0.0336002 | ||||||||
\(214\) | 194184. | 0.289854 | ||||||||
\(215\) | 1.53002e6 | 2.25737 | ||||||||
\(216\) | 324000. | 0.472510 | ||||||||
\(217\) | −433258. | −0.624593 | ||||||||
\(218\) | −105860. | −0.150866 | ||||||||
\(219\) | 145776. | 0.205388 | ||||||||
\(220\) | 250712. | 0.349236 | ||||||||
\(221\) | 53872.0 | 0.0741963 | ||||||||
\(222\) | 1656.00 | 0.00225516 | ||||||||
\(223\) | 38374.0 | 0.0516743 | 0.0258372 | − | 0.999666i | \(-0.491775\pi\) | ||||
0.0258372 | + | 0.999666i | \(0.491775\pi\) | |||||||
\(224\) | 252448. | 0.336165 | ||||||||
\(225\) | −486657. | −0.640865 | ||||||||
\(226\) | 161052. | 0.209747 | ||||||||
\(227\) | 323268. | 0.416388 | 0.208194 | − | 0.978088i | \(-0.433241\pi\) | ||||
0.208194 | + | 0.978088i | \(0.433241\pi\) | |||||||
\(228\) | −221760. | −0.282518 | ||||||||
\(229\) | 813690. | 1.02535 | 0.512673 | − | 0.858584i | \(-0.328655\pi\) | ||||
0.512673 | + | 0.858584i | \(0.328655\pi\) | |||||||
\(230\) | −64528.0 | −0.0804320 | ||||||||
\(231\) | 35574.0 | 0.0438634 | ||||||||
\(232\) | 356400. | 0.434728 | ||||||||
\(233\) | 1.10801e6 | 1.33707 | 0.668537 | − | 0.743679i | \(-0.266921\pi\) | ||||
0.668537 | + | 0.743679i | \(0.266921\pi\) | |||||||
\(234\) | 150696. | 0.179913 | ||||||||
\(235\) | 867428. | 1.02462 | ||||||||
\(236\) | 774760. | 0.905497 | ||||||||
\(237\) | 13200.0 | 0.0152652 | ||||||||
\(238\) | 14504.0 | 0.0165976 | ||||||||
\(239\) | −1.31352e6 | −1.48745 | −0.743724 | − | 0.668487i | \(-0.766942\pi\) | ||||
−0.743724 | + | 0.668487i | \(0.766942\pi\) | |||||||
\(240\) | 291264. | 0.326406 | ||||||||
\(241\) | −1.05607e6 | −1.17125 | −0.585625 | − | 0.810582i | \(-0.699151\pi\) | ||||
−0.585625 | + | 0.810582i | \(0.699151\pi\) | |||||||
\(242\) | −29282.0 | −0.0321412 | ||||||||
\(243\) | −860706. | −0.935059 | ||||||||
\(244\) | −546336. | −0.587469 | ||||||||
\(245\) | −177674. | −0.189107 | ||||||||
\(246\) | 6384.00 | 0.00672597 | ||||||||
\(247\) | −480480. | −0.501110 | ||||||||
\(248\) | 1.06104e6 | 1.09548 | ||||||||
\(249\) | −446544. | −0.456421 | ||||||||
\(250\) | −114552. | −0.115918 | ||||||||
\(251\) | 1.68914e6 | 1.69232 | 0.846159 | − | 0.532931i | \(-0.178909\pi\) | ||||
0.846159 | + | 0.532931i | \(0.178909\pi\) | |||||||
\(252\) | −284004. | −0.281724 | ||||||||
\(253\) | −52756.0 | −0.0518168 | ||||||||
\(254\) | −442096. | −0.429964 | ||||||||
\(255\) | 65712.0 | 0.0632840 | ||||||||
\(256\) | −30464.0 | −0.0290527 | ||||||||
\(257\) | 641938. | 0.606262 | 0.303131 | − | 0.952949i | \(-0.401968\pi\) | ||||
0.303131 | + | 0.952949i | \(0.401968\pi\) | |||||||
\(258\) | −248112. | −0.232059 | ||||||||
\(259\) | −6762.00 | −0.00626363 | ||||||||
\(260\) | 754208. | 0.691923 | ||||||||
\(261\) | −614790. | −0.558632 | ||||||||
\(262\) | −75144.0 | −0.0676303 | ||||||||
\(263\) | −1.10150e6 | −0.981959 | −0.490980 | − | 0.871171i | \(-0.663361\pi\) | ||||
−0.490980 | + | 0.871171i | \(0.663361\pi\) | |||||||
\(264\) | −87120.0 | −0.0769322 | ||||||||
\(265\) | −390276. | −0.341395 | ||||||||
\(266\) | −129360. | −0.112097 | ||||||||
\(267\) | −205020. | −0.176002 | ||||||||
\(268\) | −1.79446e6 | −1.52615 | ||||||||
\(269\) | −2.15147e6 | −1.81282 | −0.906410 | − | 0.422399i | \(-0.861188\pi\) | ||||
−0.906410 | + | 0.422399i | \(0.861188\pi\) | |||||||
\(270\) | 399600. | 0.333592 | ||||||||
\(271\) | −1.08327e6 | −0.896010 | −0.448005 | − | 0.894031i | \(-0.647865\pi\) | ||||
−0.448005 | + | 0.894031i | \(0.647865\pi\) | |||||||
\(272\) | 97088.0 | 0.0795689 | ||||||||
\(273\) | 107016. | 0.0869045 | ||||||||
\(274\) | 581204. | 0.467684 | ||||||||
\(275\) | 284471. | 0.226833 | ||||||||
\(276\) | −73248.0 | −0.0578793 | ||||||||
\(277\) | −2.22372e6 | −1.74133 | −0.870665 | − | 0.491877i | \(-0.836311\pi\) | ||||
−0.870665 | + | 0.491877i | \(0.836311\pi\) | |||||||
\(278\) | −734720. | −0.570177 | ||||||||
\(279\) | −1.83029e6 | −1.40770 | ||||||||
\(280\) | 435120. | 0.331676 | ||||||||
\(281\) | −153018. | −0.115605 | −0.0578025 | − | 0.998328i | \(-0.518409\pi\) | ||||
−0.0578025 | + | 0.998328i | \(0.518409\pi\) | |||||||
\(282\) | −140664. | −0.105332 | ||||||||
\(283\) | 715324. | 0.530929 | 0.265465 | − | 0.964121i | \(-0.414475\pi\) | ||||
0.265465 | + | 0.964121i | \(0.414475\pi\) | |||||||
\(284\) | 103824. | 0.0763839 | ||||||||
\(285\) | −586080. | −0.427410 | ||||||||
\(286\) | −88088.0 | −0.0636798 | ||||||||
\(287\) | −26068.0 | −0.0186811 | ||||||||
\(288\) | 1.06646e6 | 0.757644 | ||||||||
\(289\) | −1.39795e6 | −0.984573 | ||||||||
\(290\) | 439560. | 0.306919 | ||||||||
\(291\) | −910308. | −0.630167 | ||||||||
\(292\) | 680288. | 0.466913 | ||||||||
\(293\) | 347424. | 0.236424 | 0.118212 | − | 0.992988i | \(-0.462284\pi\) | ||||
0.118212 | + | 0.992988i | \(0.462284\pi\) | |||||||
\(294\) | 28812.0 | 0.0194404 | ||||||||
\(295\) | 2.04758e6 | 1.36989 | ||||||||
\(296\) | 16560.0 | 0.0109858 | ||||||||
\(297\) | 326700. | 0.214911 | ||||||||
\(298\) | 925460. | 0.603694 | ||||||||
\(299\) | −158704. | −0.102662 | ||||||||
\(300\) | 394968. | 0.253372 | ||||||||
\(301\) | 1.01312e6 | 0.644535 | ||||||||
\(302\) | 15296.0 | 0.00965074 | ||||||||
\(303\) | −701112. | −0.438713 | ||||||||
\(304\) | −865920. | −0.537395 | ||||||||
\(305\) | −1.44389e6 | −0.888759 | ||||||||
\(306\) | 61272.0 | 0.0374075 | ||||||||
\(307\) | 2.64043e6 | 1.59893 | 0.799463 | − | 0.600715i | \(-0.205117\pi\) | ||||
0.799463 | + | 0.600715i | \(0.205117\pi\) | |||||||
\(308\) | 166012. | 0.0997155 | ||||||||
\(309\) | −622164. | −0.370688 | ||||||||
\(310\) | 1.30862e6 | 0.773407 | ||||||||
\(311\) | −947778. | −0.555656 | −0.277828 | − | 0.960631i | \(-0.589614\pi\) | ||||
−0.277828 | + | 0.960631i | \(0.589614\pi\) | |||||||
\(312\) | −262080. | −0.152422 | ||||||||
\(313\) | −248686. | −0.143480 | −0.0717399 | − | 0.997423i | \(-0.522855\pi\) | ||||
−0.0717399 | + | 0.997423i | \(0.522855\pi\) | |||||||
\(314\) | 322964. | 0.184854 | ||||||||
\(315\) | −750582. | −0.426208 | ||||||||
\(316\) | 61600.0 | 0.0347027 | ||||||||
\(317\) | 2.60904e6 | 1.45825 | 0.729125 | − | 0.684380i | \(-0.239927\pi\) | ||||
0.729125 | + | 0.684380i | \(0.239927\pi\) | |||||||
\(318\) | 63288.0 | 0.0350957 | ||||||||
\(319\) | 359370. | 0.197727 | ||||||||
\(320\) | 790912. | 0.431771 | ||||||||
\(321\) | 582552. | 0.315553 | ||||||||
\(322\) | −42728.0 | −0.0229653 | ||||||||
\(323\) | −195360. | −0.104191 | ||||||||
\(324\) | −954828. | −0.505316 | ||||||||
\(325\) | 855764. | 0.449413 | ||||||||
\(326\) | −358928. | −0.187052 | ||||||||
\(327\) | −317580. | −0.164242 | ||||||||
\(328\) | 63840.0 | 0.0327649 | ||||||||
\(329\) | 574378. | 0.292555 | ||||||||
\(330\) | −107448. | −0.0543142 | ||||||||
\(331\) | 152332. | 0.0764225 | 0.0382112 | − | 0.999270i | \(-0.487834\pi\) | ||||
0.0382112 | + | 0.999270i | \(0.487834\pi\) | |||||||
\(332\) | −2.08387e6 | −1.03759 | ||||||||
\(333\) | −28566.0 | −0.0141169 | ||||||||
\(334\) | −633696. | −0.310824 | ||||||||
\(335\) | −4.74251e6 | −2.30885 | ||||||||
\(336\) | 192864. | 0.0931972 | ||||||||
\(337\) | 206558. | 0.0990757 | 0.0495379 | − | 0.998772i | \(-0.484225\pi\) | ||||
0.0495379 | + | 0.998772i | \(0.484225\pi\) | |||||||
\(338\) | 477594. | 0.227388 | ||||||||
\(339\) | 483156. | 0.228343 | ||||||||
\(340\) | 306656. | 0.143865 | ||||||||
\(341\) | 1.06988e6 | 0.498253 | ||||||||
\(342\) | −546480. | −0.252644 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | −2.48112e6 | −1.13045 | ||||||||
\(345\) | −193584. | −0.0875632 | ||||||||
\(346\) | 350232. | 0.157277 | ||||||||
\(347\) | 2.01807e6 | 0.899730 | 0.449865 | − | 0.893097i | \(-0.351472\pi\) | ||||
0.449865 | + | 0.893097i | \(0.351472\pi\) | |||||||
\(348\) | 498960. | 0.220860 | ||||||||
\(349\) | −580440. | −0.255090 | −0.127545 | − | 0.991833i | \(-0.540710\pi\) | ||||
−0.127545 | + | 0.991833i | \(0.540710\pi\) | |||||||
\(350\) | 230398. | 0.100533 | ||||||||
\(351\) | 982800. | 0.425792 | ||||||||
\(352\) | −623392. | −0.268167 | ||||||||
\(353\) | 572034. | 0.244335 | 0.122167 | − | 0.992510i | \(-0.461016\pi\) | ||||
0.122167 | + | 0.992510i | \(0.461016\pi\) | |||||||
\(354\) | −332040. | −0.140826 | ||||||||
\(355\) | 274392. | 0.115558 | ||||||||
\(356\) | −956760. | −0.400109 | ||||||||
\(357\) | 43512.0 | 0.0180692 | ||||||||
\(358\) | 139560. | 0.0575511 | ||||||||
\(359\) | 4.56544e6 | 1.86959 | 0.934795 | − | 0.355187i | \(-0.115583\pi\) | ||||
0.934795 | + | 0.355187i | \(0.115583\pi\) | |||||||
\(360\) | 1.83816e6 | 0.747527 | ||||||||
\(361\) | −733699. | −0.296312 | ||||||||
\(362\) | 157276. | 0.0630799 | ||||||||
\(363\) | −87846.0 | −0.0349909 | ||||||||
\(364\) | 499408. | 0.197561 | ||||||||
\(365\) | 1.79790e6 | 0.706373 | ||||||||
\(366\) | 234144. | 0.0913651 | ||||||||
\(367\) | 924358. | 0.358241 | 0.179120 | − | 0.983827i | \(-0.442675\pi\) | ||||
0.179120 | + | 0.983827i | \(0.442675\pi\) | |||||||
\(368\) | −286016. | −0.110096 | ||||||||
\(369\) | −110124. | −0.0421033 | ||||||||
\(370\) | 20424.0 | 0.00775598 | ||||||||
\(371\) | −258426. | −0.0974768 | ||||||||
\(372\) | 1.48546e6 | 0.556548 | ||||||||
\(373\) | 4.92021e6 | 1.83110 | 0.915550 | − | 0.402205i | \(-0.131756\pi\) | ||||
0.915550 | + | 0.402205i | \(0.131756\pi\) | |||||||
\(374\) | −35816.0 | −0.0132403 | ||||||||
\(375\) | −343656. | −0.126196 | ||||||||
\(376\) | −1.40664e6 | −0.513113 | ||||||||
\(377\) | 1.08108e6 | 0.391746 | ||||||||
\(378\) | 264600. | 0.0952490 | ||||||||
\(379\) | 3.97540e6 | 1.42162 | 0.710809 | − | 0.703385i | \(-0.248329\pi\) | ||||
0.710809 | + | 0.703385i | \(0.248329\pi\) | |||||||
\(380\) | −2.73504e6 | −0.971638 | ||||||||
\(381\) | −1.32629e6 | −0.468086 | ||||||||
\(382\) | 1.85442e6 | 0.650203 | ||||||||
\(383\) | −982846. | −0.342364 | −0.171182 | − | 0.985239i | \(-0.554759\pi\) | ||||
−0.171182 | + | 0.985239i | \(0.554759\pi\) | |||||||
\(384\) | −1.11744e6 | −0.386720 | ||||||||
\(385\) | 438746. | 0.150856 | ||||||||
\(386\) | −1.75495e6 | −0.599509 | ||||||||
\(387\) | 4.27993e6 | 1.45264 | ||||||||
\(388\) | −4.24810e6 | −1.43257 | ||||||||
\(389\) | −744090. | −0.249317 | −0.124658 | − | 0.992200i | \(-0.539783\pi\) | ||||
−0.124658 | + | 0.992200i | \(0.539783\pi\) | |||||||
\(390\) | −323232. | −0.107610 | ||||||||
\(391\) | −64528.0 | −0.0213455 | ||||||||
\(392\) | 288120. | 0.0947018 | ||||||||
\(393\) | −225432. | −0.0736265 | ||||||||
\(394\) | 1.48920e6 | 0.483296 | ||||||||
\(395\) | 162800. | 0.0525003 | ||||||||
\(396\) | 701316. | 0.224738 | ||||||||
\(397\) | 5.73024e6 | 1.82472 | 0.912360 | − | 0.409388i | \(-0.134258\pi\) | ||||
0.912360 | + | 0.409388i | \(0.134258\pi\) | |||||||
\(398\) | −2.15862e6 | −0.683075 | ||||||||
\(399\) | −388080. | −0.122036 | ||||||||
\(400\) | 1.54226e6 | 0.481955 | ||||||||
\(401\) | 4.26756e6 | 1.32531 | 0.662657 | − | 0.748923i | \(-0.269429\pi\) | ||||
0.662657 | + | 0.748923i | \(0.269429\pi\) | |||||||
\(402\) | 769056. | 0.237352 | ||||||||
\(403\) | 3.21849e6 | 0.987164 | ||||||||
\(404\) | −3.27186e6 | −0.997334 | ||||||||
\(405\) | −2.52347e6 | −0.764471 | ||||||||
\(406\) | 291060. | 0.0876330 | ||||||||
\(407\) | 16698.0 | 0.00499664 | ||||||||
\(408\) | −106560. | −0.0316916 | ||||||||
\(409\) | −5.81772e6 | −1.71967 | −0.859834 | − | 0.510574i | \(-0.829433\pi\) | ||||
−0.859834 | + | 0.510574i | \(0.829433\pi\) | |||||||
\(410\) | 78736.0 | 0.0231320 | ||||||||
\(411\) | 1.74361e6 | 0.509149 | ||||||||
\(412\) | −2.90343e6 | −0.842692 | ||||||||
\(413\) | 1.35583e6 | 0.391138 | ||||||||
\(414\) | −180504. | −0.0517590 | ||||||||
\(415\) | −5.50738e6 | −1.56973 | ||||||||
\(416\) | −1.87533e6 | −0.531305 | ||||||||
\(417\) | −2.20416e6 | −0.620730 | ||||||||
\(418\) | 319440. | 0.0894229 | ||||||||
\(419\) | −4.38823e6 | −1.22111 | −0.610554 | − | 0.791974i | \(-0.709053\pi\) | ||||
−0.610554 | + | 0.791974i | \(0.709053\pi\) | |||||||
\(420\) | 609168. | 0.168505 | ||||||||
\(421\) | −1.48456e6 | −0.408218 | −0.204109 | − | 0.978948i | \(-0.565430\pi\) | ||||
−0.204109 | + | 0.978948i | \(0.565430\pi\) | |||||||
\(422\) | −1.45754e6 | −0.398419 | ||||||||
\(423\) | 2.42645e6 | 0.659358 | ||||||||
\(424\) | 632880. | 0.170965 | ||||||||
\(425\) | 347948. | 0.0934420 | ||||||||
\(426\) | −44496.0 | −0.0118795 | ||||||||
\(427\) | −956088. | −0.253763 | ||||||||
\(428\) | 2.71858e6 | 0.717352 | ||||||||
\(429\) | −264264. | −0.0693258 | ||||||||
\(430\) | −3.06005e6 | −0.798100 | ||||||||
\(431\) | −206448. | −0.0535325 | −0.0267662 | − | 0.999642i | \(-0.508521\pi\) | ||||
−0.0267662 | + | 0.999642i | \(0.508521\pi\) | |||||||
\(432\) | 1.77120e6 | 0.456623 | ||||||||
\(433\) | −5.67867e6 | −1.45555 | −0.727774 | − | 0.685817i | \(-0.759445\pi\) | ||||
−0.727774 | + | 0.685817i | \(0.759445\pi\) | |||||||
\(434\) | 866516. | 0.220827 | ||||||||
\(435\) | 1.31868e6 | 0.334131 | ||||||||
\(436\) | −1.48204e6 | −0.373374 | ||||||||
\(437\) | 575520. | 0.144164 | ||||||||
\(438\) | −291552. | −0.0726157 | ||||||||
\(439\) | −4.43666e6 | −1.09874 | −0.549370 | − | 0.835579i | \(-0.685132\pi\) | ||||
−0.549370 | + | 0.835579i | \(0.685132\pi\) | |||||||
\(440\) | −1.07448e6 | −0.264586 | ||||||||
\(441\) | −497007. | −0.121693 | ||||||||
\(442\) | −107744. | −0.0262324 | ||||||||
\(443\) | 6.17328e6 | 1.49454 | 0.747269 | − | 0.664522i | \(-0.231365\pi\) | ||||
0.747269 | + | 0.664522i | \(0.231365\pi\) | |||||||
\(444\) | 23184.0 | 0.00558124 | ||||||||
\(445\) | −2.52858e6 | −0.605308 | ||||||||
\(446\) | −76748.0 | −0.0182696 | ||||||||
\(447\) | 2.77638e6 | 0.657219 | ||||||||
\(448\) | 523712. | 0.123281 | ||||||||
\(449\) | −4.93105e6 | −1.15431 | −0.577156 | − | 0.816634i | \(-0.695838\pi\) | ||||
−0.577156 | + | 0.816634i | \(0.695838\pi\) | |||||||
\(450\) | 973314. | 0.226580 | ||||||||
\(451\) | 64372.0 | 0.0149024 | ||||||||
\(452\) | 2.25473e6 | 0.519096 | ||||||||
\(453\) | 45888.0 | 0.0105064 | ||||||||
\(454\) | −646536. | −0.147215 | ||||||||
\(455\) | 1.31986e6 | 0.298883 | ||||||||
\(456\) | 950400. | 0.214040 | ||||||||
\(457\) | −4.15030e6 | −0.929585 | −0.464793 | − | 0.885420i | \(-0.653871\pi\) | ||||
−0.464793 | + | 0.885420i | \(0.653871\pi\) | |||||||
\(458\) | −1.62738e6 | −0.362514 | ||||||||
\(459\) | 399600. | 0.0885307 | ||||||||
\(460\) | −903392. | −0.199059 | ||||||||
\(461\) | −4.40345e6 | −0.965029 | −0.482515 | − | 0.875888i | \(-0.660277\pi\) | ||||
−0.482515 | + | 0.875888i | \(0.660277\pi\) | |||||||
\(462\) | −71148.0 | −0.0155081 | ||||||||
\(463\) | 6.82728e6 | 1.48012 | 0.740058 | − | 0.672544i | \(-0.234798\pi\) | ||||
0.740058 | + | 0.672544i | \(0.234798\pi\) | |||||||
\(464\) | 1.94832e6 | 0.420112 | ||||||||
\(465\) | 3.92585e6 | 0.841979 | ||||||||
\(466\) | −2.21603e6 | −0.472727 | ||||||||
\(467\) | 6.88244e6 | 1.46033 | 0.730163 | − | 0.683272i | \(-0.239444\pi\) | ||||
0.730163 | + | 0.683272i | \(0.239444\pi\) | |||||||
\(468\) | 2.10974e6 | 0.445261 | ||||||||
\(469\) | −3.14031e6 | −0.659236 | ||||||||
\(470\) | −1.73486e6 | −0.362259 | ||||||||
\(471\) | 968892. | 0.201244 | ||||||||
\(472\) | −3.32040e6 | −0.686018 | ||||||||
\(473\) | −2.50180e6 | −0.514161 | ||||||||
\(474\) | −26400.0 | −0.00539707 | ||||||||
\(475\) | −3.10332e6 | −0.631092 | ||||||||
\(476\) | 203056. | 0.0410770 | ||||||||
\(477\) | −1.09172e6 | −0.219692 | ||||||||
\(478\) | 2.62704e6 | 0.525892 | ||||||||
\(479\) | 5.02430e6 | 1.00055 | 0.500273 | − | 0.865868i | \(-0.333233\pi\) | ||||
0.500273 | + | 0.865868i | \(0.333233\pi\) | |||||||
\(480\) | −2.28749e6 | −0.453164 | ||||||||
\(481\) | 50232.0 | 0.00989960 | ||||||||
\(482\) | 2.11214e6 | 0.414099 | ||||||||
\(483\) | −128184. | −0.0250015 | ||||||||
\(484\) | −409948. | −0.0795455 | ||||||||
\(485\) | −1.12271e7 | −2.16728 | ||||||||
\(486\) | 1.72141e6 | 0.330593 | ||||||||
\(487\) | −4.51601e6 | −0.862845 | −0.431422 | − | 0.902150i | \(-0.641988\pi\) | ||||
−0.431422 | + | 0.902150i | \(0.641988\pi\) | |||||||
\(488\) | 2.34144e6 | 0.445075 | ||||||||
\(489\) | −1.07678e6 | −0.203637 | ||||||||
\(490\) | 355348. | 0.0668596 | ||||||||
\(491\) | 5.55737e6 | 1.04032 | 0.520159 | − | 0.854070i | \(-0.325873\pi\) | ||||
0.520159 | + | 0.854070i | \(0.325873\pi\) | |||||||
\(492\) | 89376.0 | 0.0166459 | ||||||||
\(493\) | 439560. | 0.0814518 | ||||||||
\(494\) | 960960. | 0.177169 | ||||||||
\(495\) | 1.85348e6 | 0.339996 | ||||||||
\(496\) | 5.80035e6 | 1.05864 | ||||||||
\(497\) | 181692. | 0.0329947 | ||||||||
\(498\) | 893088. | 0.161369 | ||||||||
\(499\) | −3.49744e6 | −0.628780 | −0.314390 | − | 0.949294i | \(-0.601800\pi\) | ||||
−0.314390 | + | 0.949294i | \(0.601800\pi\) | |||||||
\(500\) | −1.60373e6 | −0.286884 | ||||||||
\(501\) | −1.90109e6 | −0.338383 | ||||||||
\(502\) | −3.37828e6 | −0.598325 | ||||||||
\(503\) | 4.61280e6 | 0.812915 | 0.406457 | − | 0.913670i | \(-0.366764\pi\) | ||||
0.406457 | + | 0.913670i | \(0.366764\pi\) | |||||||
\(504\) | 1.21716e6 | 0.213438 | ||||||||
\(505\) | −8.64705e6 | −1.50883 | ||||||||
\(506\) | 105512. | 0.0183200 | ||||||||
\(507\) | 1.43278e6 | 0.247548 | ||||||||
\(508\) | −6.18934e6 | −1.06411 | ||||||||
\(509\) | 7.41609e6 | 1.26876 | 0.634382 | − | 0.773020i | \(-0.281255\pi\) | ||||
0.634382 | + | 0.773020i | \(0.281255\pi\) | |||||||
\(510\) | −131424. | −0.0223743 | ||||||||
\(511\) | 1.19050e6 | 0.201687 | ||||||||
\(512\) | −5.89875e6 | −0.994455 | ||||||||
\(513\) | −3.56400e6 | −0.597922 | ||||||||
\(514\) | −1.28388e6 | −0.214346 | ||||||||
\(515\) | −7.67336e6 | −1.27487 | ||||||||
\(516\) | −3.47357e6 | −0.574317 | ||||||||
\(517\) | −1.41836e6 | −0.233378 | ||||||||
\(518\) | 13524.0 | 0.00221453 | ||||||||
\(519\) | 1.05070e6 | 0.171222 | ||||||||
\(520\) | −3.23232e6 | −0.524211 | ||||||||
\(521\) | 9.75970e6 | 1.57522 | 0.787612 | − | 0.616172i | \(-0.211317\pi\) | ||||
0.787612 | + | 0.616172i | \(0.211317\pi\) | |||||||
\(522\) | 1.22958e6 | 0.197506 | ||||||||
\(523\) | 1.66084e6 | 0.265506 | 0.132753 | − | 0.991149i | \(-0.457618\pi\) | ||||
0.132753 | + | 0.991149i | \(0.457618\pi\) | |||||||
\(524\) | −1.05202e6 | −0.167376 | ||||||||
\(525\) | 691194. | 0.109446 | ||||||||
\(526\) | 2.20299e6 | 0.347175 | ||||||||
\(527\) | 1.30862e6 | 0.205251 | ||||||||
\(528\) | −476256. | −0.0743457 | ||||||||
\(529\) | −6.24625e6 | −0.970465 | ||||||||
\(530\) | 780552. | 0.120701 | ||||||||
\(531\) | 5.72769e6 | 0.881542 | ||||||||
\(532\) | −1.81104e6 | −0.277427 | ||||||||
\(533\) | 193648. | 0.0295253 | ||||||||
\(534\) | 410040. | 0.0622262 | ||||||||
\(535\) | 7.18481e6 | 1.08525 | ||||||||
\(536\) | 7.69056e6 | 1.15623 | ||||||||
\(537\) | 418680. | 0.0626537 | ||||||||
\(538\) | 4.30294e6 | 0.640929 | ||||||||
\(539\) | 290521. | 0.0430730 | ||||||||
\(540\) | 5.59440e6 | 0.825599 | ||||||||
\(541\) | 6.97250e6 | 1.02423 | 0.512113 | − | 0.858918i | \(-0.328863\pi\) | ||||
0.512113 | + | 0.858918i | \(0.328863\pi\) | |||||||
\(542\) | 2.16654e6 | 0.316787 | ||||||||
\(543\) | 471828. | 0.0686727 | ||||||||
\(544\) | −762496. | −0.110469 | ||||||||
\(545\) | −3.91682e6 | −0.564862 | ||||||||
\(546\) | −214032. | −0.0307254 | ||||||||
\(547\) | 3.08503e6 | 0.440850 | 0.220425 | − | 0.975404i | \(-0.429256\pi\) | ||||
0.220425 | + | 0.975404i | \(0.429256\pi\) | |||||||
\(548\) | 8.13686e6 | 1.15746 | ||||||||
\(549\) | −4.03898e6 | −0.571928 | ||||||||
\(550\) | −568942. | −0.0801976 | ||||||||
\(551\) | −3.92040e6 | −0.550112 | ||||||||
\(552\) | 313920. | 0.0438502 | ||||||||
\(553\) | 107800. | 0.0149901 | ||||||||
\(554\) | 4.44744e6 | 0.615653 | ||||||||
\(555\) | 61272.0 | 0.00844364 | ||||||||
\(556\) | −1.02861e7 | −1.41112 | ||||||||
\(557\) | −3.29052e6 | −0.449394 | −0.224697 | − | 0.974429i | \(-0.572139\pi\) | ||||
−0.224697 | + | 0.974429i | \(0.572139\pi\) | |||||||
\(558\) | 3.66059e6 | 0.497697 | ||||||||
\(559\) | −7.52606e6 | −1.01868 | ||||||||
\(560\) | 2.37866e6 | 0.320525 | ||||||||
\(561\) | −107448. | −0.0144142 | ||||||||
\(562\) | 306036. | 0.0408725 | ||||||||
\(563\) | 5.45754e6 | 0.725648 | 0.362824 | − | 0.931858i | \(-0.381813\pi\) | ||||
0.362824 | + | 0.931858i | \(0.381813\pi\) | |||||||
\(564\) | −1.96930e6 | −0.260683 | ||||||||
\(565\) | 5.95892e6 | 0.785320 | ||||||||
\(566\) | −1.43065e6 | −0.187712 | ||||||||
\(567\) | −1.67095e6 | −0.218276 | ||||||||
\(568\) | −444960. | −0.0578696 | ||||||||
\(569\) | 7.28571e6 | 0.943390 | 0.471695 | − | 0.881762i | \(-0.343642\pi\) | ||||
0.471695 | + | 0.881762i | \(0.343642\pi\) | |||||||
\(570\) | 1.17216e6 | 0.151112 | ||||||||
\(571\) | 1.07129e7 | 1.37504 | 0.687519 | − | 0.726166i | \(-0.258700\pi\) | ||||
0.687519 | + | 0.726166i | \(0.258700\pi\) | |||||||
\(572\) | −1.23323e6 | −0.157599 | ||||||||
\(573\) | 5.56325e6 | 0.707851 | ||||||||
\(574\) | 52136.0 | 0.00660477 | ||||||||
\(575\) | −1.02504e6 | −0.129291 | ||||||||
\(576\) | 2.21242e6 | 0.277850 | ||||||||
\(577\) | 4.22024e6 | 0.527713 | 0.263856 | − | 0.964562i | \(-0.415006\pi\) | ||||
0.263856 | + | 0.964562i | \(0.415006\pi\) | |||||||
\(578\) | 2.79591e6 | 0.348099 | ||||||||
\(579\) | −5.26484e6 | −0.652663 | ||||||||
\(580\) | 6.15384e6 | 0.759585 | ||||||||
\(581\) | −3.64678e6 | −0.448197 | ||||||||
\(582\) | 1.82062e6 | 0.222798 | ||||||||
\(583\) | 638154. | 0.0777596 | ||||||||
\(584\) | −2.91552e6 | −0.353740 | ||||||||
\(585\) | 5.57575e6 | 0.673618 | ||||||||
\(586\) | −694848. | −0.0835884 | ||||||||
\(587\) | −6.24180e6 | −0.747678 | −0.373839 | − | 0.927494i | \(-0.621959\pi\) | ||||
−0.373839 | + | 0.927494i | \(0.621959\pi\) | |||||||
\(588\) | 403368. | 0.0481125 | ||||||||
\(589\) | −1.16714e7 | −1.38623 | ||||||||
\(590\) | −4.09516e6 | −0.484329 | ||||||||
\(591\) | 4.46761e6 | 0.526147 | ||||||||
\(592\) | 90528.0 | 0.0106164 | ||||||||
\(593\) | 493664. | 0.0576494 | 0.0288247 | − | 0.999584i | \(-0.490824\pi\) | ||||
0.0288247 | + | 0.999584i | \(0.490824\pi\) | |||||||
\(594\) | −653400. | −0.0759824 | ||||||||
\(595\) | 536648. | 0.0621437 | ||||||||
\(596\) | 1.29564e7 | 1.49407 | ||||||||
\(597\) | −6.47586e6 | −0.743638 | ||||||||
\(598\) | 317408. | 0.0362965 | ||||||||
\(599\) | −8.28890e6 | −0.943908 | −0.471954 | − | 0.881623i | \(-0.656451\pi\) | ||||
−0.471954 | + | 0.881623i | \(0.656451\pi\) | |||||||
\(600\) | −1.69272e6 | −0.191958 | ||||||||
\(601\) | 80612.0 | 0.00910361 | 0.00455180 | − | 0.999990i | \(-0.498551\pi\) | ||||
0.00455180 | + | 0.999990i | \(0.498551\pi\) | |||||||
\(602\) | −2.02625e6 | −0.227877 | ||||||||
\(603\) | −1.32662e7 | −1.48578 | ||||||||
\(604\) | 214144. | 0.0238844 | ||||||||
\(605\) | −1.08343e6 | −0.120341 | ||||||||
\(606\) | 1.40222e6 | 0.155109 | ||||||||
\(607\) | 914168. | 0.100706 | 0.0503529 | − | 0.998731i | \(-0.483965\pi\) | ||||
0.0503529 | + | 0.998731i | \(0.483965\pi\) | |||||||
\(608\) | 6.80064e6 | 0.746089 | ||||||||
\(609\) | 873180. | 0.0954027 | ||||||||
\(610\) | 2.88778e6 | 0.314224 | ||||||||
\(611\) | −4.26681e6 | −0.462381 | ||||||||
\(612\) | 857808. | 0.0925788 | ||||||||
\(613\) | 9.97327e6 | 1.07198 | 0.535990 | − | 0.844224i | \(-0.319939\pi\) | ||||
0.535990 | + | 0.844224i | \(0.319939\pi\) | |||||||
\(614\) | −5.28086e6 | −0.565306 | ||||||||
\(615\) | 236208. | 0.0251830 | ||||||||
\(616\) | −711480. | −0.0755459 | ||||||||
\(617\) | −4.60636e6 | −0.487130 | −0.243565 | − | 0.969885i | \(-0.578317\pi\) | ||||
−0.243565 | + | 0.969885i | \(0.578317\pi\) | |||||||
\(618\) | 1.24433e6 | 0.131058 | ||||||||
\(619\) | 2.51711e6 | 0.264044 | 0.132022 | − | 0.991247i | \(-0.457853\pi\) | ||||
0.132022 | + | 0.991247i | \(0.457853\pi\) | |||||||
\(620\) | 1.83206e7 | 1.91408 | ||||||||
\(621\) | −1.17720e6 | −0.122496 | ||||||||
\(622\) | 1.89556e6 | 0.196454 | ||||||||
\(623\) | −1.67433e6 | −0.172831 | ||||||||
\(624\) | −1.43270e6 | −0.147297 | ||||||||
\(625\) | −1.15853e7 | −1.18633 | ||||||||
\(626\) | 497372. | 0.0507277 | ||||||||
\(627\) | 958320. | 0.0973513 | ||||||||
\(628\) | 4.52150e6 | 0.457492 | ||||||||
\(629\) | 20424.0 | 0.00205833 | ||||||||
\(630\) | 1.50116e6 | 0.150687 | ||||||||
\(631\) | −2.02153e6 | −0.202119 | −0.101059 | − | 0.994880i | \(-0.532223\pi\) | ||||
−0.101059 | + | 0.994880i | \(0.532223\pi\) | |||||||
\(632\) | −264000. | −0.0262912 | ||||||||
\(633\) | −4.37263e6 | −0.433744 | ||||||||
\(634\) | −5.21808e6 | −0.515570 | ||||||||
\(635\) | −1.63576e7 | −1.60984 | ||||||||
\(636\) | 886032. | 0.0868574 | ||||||||
\(637\) | 873964. | 0.0853385 | ||||||||
\(638\) | −718740. | −0.0699069 | ||||||||
\(639\) | 767556. | 0.0743632 | ||||||||
\(640\) | −1.37818e7 | −1.33001 | ||||||||
\(641\) | 1.55870e7 | 1.49837 | 0.749183 | − | 0.662363i | \(-0.230446\pi\) | ||||
0.749183 | + | 0.662363i | \(0.230446\pi\) | |||||||
\(642\) | −1.16510e6 | −0.111565 | ||||||||
\(643\) | −5.88755e6 | −0.561574 | −0.280787 | − | 0.959770i | \(-0.590595\pi\) | ||||
−0.280787 | + | 0.959770i | \(0.590595\pi\) | |||||||
\(644\) | −598192. | −0.0568363 | ||||||||
\(645\) | −9.18014e6 | −0.868861 | ||||||||
\(646\) | 390720. | 0.0368370 | ||||||||
\(647\) | 5.58958e6 | 0.524950 | 0.262475 | − | 0.964939i | \(-0.415461\pi\) | ||||
0.262475 | + | 0.964939i | \(0.415461\pi\) | |||||||
\(648\) | 4.09212e6 | 0.382834 | ||||||||
\(649\) | −3.34807e6 | −0.312020 | ||||||||
\(650\) | −1.71153e6 | −0.158891 | ||||||||
\(651\) | 2.59955e6 | 0.240406 | ||||||||
\(652\) | −5.02499e6 | −0.462931 | ||||||||
\(653\) | 1.76227e7 | 1.61730 | 0.808648 | − | 0.588293i | \(-0.200200\pi\) | ||||
0.808648 | + | 0.588293i | \(0.200200\pi\) | |||||||
\(654\) | 635160. | 0.0580683 | ||||||||
\(655\) | −2.78033e6 | −0.253217 | ||||||||
\(656\) | 348992. | 0.0316633 | ||||||||
\(657\) | 5.02927e6 | 0.454561 | ||||||||
\(658\) | −1.14876e6 | −0.103434 | ||||||||
\(659\) | −9.75566e6 | −0.875071 | −0.437535 | − | 0.899201i | \(-0.644149\pi\) | ||||
−0.437535 | + | 0.899201i | \(0.644149\pi\) | |||||||
\(660\) | −1.50427e6 | −0.134421 | ||||||||
\(661\) | −9.79522e6 | −0.871988 | −0.435994 | − | 0.899950i | \(-0.643603\pi\) | ||||
−0.435994 | + | 0.899950i | \(0.643603\pi\) | |||||||
\(662\) | −304664. | −0.0270194 | ||||||||
\(663\) | −323232. | −0.0285582 | ||||||||
\(664\) | 8.93088e6 | 0.786093 | ||||||||
\(665\) | −4.78632e6 | −0.419708 | ||||||||
\(666\) | 57132.0 | 0.00499107 | ||||||||
\(667\) | −1.29492e6 | −0.112701 | ||||||||
\(668\) | −8.87174e6 | −0.769251 | ||||||||
\(669\) | −230244. | −0.0198895 | ||||||||
\(670\) | 9.48502e6 | 0.816303 | ||||||||
\(671\) | 2.36095e6 | 0.202433 | ||||||||
\(672\) | −1.51469e6 | −0.129390 | ||||||||
\(673\) | −4.72727e6 | −0.402321 | −0.201160 | − | 0.979558i | \(-0.564471\pi\) | ||||
−0.201160 | + | 0.979558i | \(0.564471\pi\) | |||||||
\(674\) | −413116. | −0.0350286 | ||||||||
\(675\) | 6.34770e6 | 0.536237 | ||||||||
\(676\) | 6.68632e6 | 0.562756 | ||||||||
\(677\) | −1.93989e7 | −1.62669 | −0.813344 | − | 0.581783i | \(-0.802355\pi\) | ||||
−0.813344 | + | 0.581783i | \(0.802355\pi\) | |||||||
\(678\) | −966312. | −0.0807315 | ||||||||
\(679\) | −7.43418e6 | −0.618812 | ||||||||
\(680\) | −1.31424e6 | −0.108994 | ||||||||
\(681\) | −1.93961e6 | −0.160268 | ||||||||
\(682\) | −2.13976e6 | −0.176159 | ||||||||
\(683\) | −6.22004e6 | −0.510201 | −0.255100 | − | 0.966915i | \(-0.582109\pi\) | ||||
−0.255100 | + | 0.966915i | \(0.582109\pi\) | |||||||
\(684\) | −7.65072e6 | −0.625262 | ||||||||
\(685\) | 2.15045e7 | 1.75107 | ||||||||
\(686\) | 235298. | 0.0190901 | ||||||||
\(687\) | −4.88214e6 | −0.394656 | ||||||||
\(688\) | −1.35635e7 | −1.09244 | ||||||||
\(689\) | 1.91974e6 | 0.154061 | ||||||||
\(690\) | 387168. | 0.0309583 | ||||||||
\(691\) | 6.04140e6 | 0.481330 | 0.240665 | − | 0.970608i | \(-0.422635\pi\) | ||||
0.240665 | + | 0.970608i | \(0.422635\pi\) | |||||||
\(692\) | 4.90325e6 | 0.389241 | ||||||||
\(693\) | 1.22730e6 | 0.0970775 | ||||||||
\(694\) | −4.03614e6 | −0.318103 | ||||||||
\(695\) | −2.71846e7 | −2.13482 | ||||||||
\(696\) | −2.13840e6 | −0.167327 | ||||||||
\(697\) | 78736.0 | 0.00613891 | ||||||||
\(698\) | 1.16088e6 | 0.0901880 | ||||||||
\(699\) | −6.64808e6 | −0.514640 | ||||||||
\(700\) | 3.22557e6 | 0.248806 | ||||||||
\(701\) | 3.97068e6 | 0.305190 | 0.152595 | − | 0.988289i | \(-0.451237\pi\) | ||||
0.152595 | + | 0.988289i | \(0.451237\pi\) | |||||||
\(702\) | −1.96560e6 | −0.150540 | ||||||||
\(703\) | −182160. | −0.0139016 | ||||||||
\(704\) | −1.29325e6 | −0.0983445 | ||||||||
\(705\) | −5.20457e6 | −0.394377 | ||||||||
\(706\) | −1.14407e6 | −0.0863853 | ||||||||
\(707\) | −5.72575e6 | −0.430808 | ||||||||
\(708\) | −4.64856e6 | −0.348526 | ||||||||
\(709\) | 5.15939e6 | 0.385463 | 0.192732 | − | 0.981252i | \(-0.438265\pi\) | ||||
0.192732 | + | 0.981252i | \(0.438265\pi\) | |||||||
\(710\) | −548784. | −0.0408560 | ||||||||
\(711\) | 455400. | 0.0337846 | ||||||||
\(712\) | 4.10040e6 | 0.303128 | ||||||||
\(713\) | −3.85511e6 | −0.283997 | ||||||||
\(714\) | −87024.0 | −0.00638842 | ||||||||
\(715\) | −3.25926e6 | −0.238426 | ||||||||
\(716\) | 1.95384e6 | 0.142432 | ||||||||
\(717\) | 7.88112e6 | 0.572519 | ||||||||
\(718\) | −9.13088e6 | −0.661000 | ||||||||
\(719\) | −1.26734e7 | −0.914259 | −0.457129 | − | 0.889400i | \(-0.651122\pi\) | ||||
−0.457129 | + | 0.889400i | \(0.651122\pi\) | |||||||
\(720\) | 1.00486e7 | 0.722395 | ||||||||
\(721\) | −5.08101e6 | −0.364009 | ||||||||
\(722\) | 1.46740e6 | 0.104762 | ||||||||
\(723\) | 6.33641e6 | 0.450814 | ||||||||
\(724\) | 2.20186e6 | 0.156115 | ||||||||
\(725\) | 6.98247e6 | 0.493360 | ||||||||
\(726\) | 175692. | 0.0123712 | ||||||||
\(727\) | 1.32783e7 | 0.931762 | 0.465881 | − | 0.884847i | \(-0.345737\pi\) | ||||
0.465881 | + | 0.884847i | \(0.345737\pi\) | |||||||
\(728\) | −2.14032e6 | −0.149675 | ||||||||
\(729\) | −3.12231e6 | −0.217599 | ||||||||
\(730\) | −3.59581e6 | −0.249741 | ||||||||
\(731\) | −3.06005e6 | −0.211804 | ||||||||
\(732\) | 3.27802e6 | 0.226117 | ||||||||
\(733\) | 3.84050e6 | 0.264015 | 0.132007 | − | 0.991249i | \(-0.457858\pi\) | ||||
0.132007 | + | 0.991249i | \(0.457858\pi\) | |||||||
\(734\) | −1.84872e6 | −0.126657 | ||||||||
\(735\) | 1.06604e6 | 0.0727875 | ||||||||
\(736\) | 2.24627e6 | 0.152851 | ||||||||
\(737\) | 7.75465e6 | 0.525888 | ||||||||
\(738\) | 220248. | 0.0148858 | ||||||||
\(739\) | 1.19394e7 | 0.804215 | 0.402107 | − | 0.915592i | \(-0.368278\pi\) | ||||
0.402107 | + | 0.915592i | \(0.368278\pi\) | |||||||
\(740\) | 285936. | 0.0191951 | ||||||||
\(741\) | 2.88288e6 | 0.192877 | ||||||||
\(742\) | 516852. | 0.0344633 | ||||||||
\(743\) | 2.53631e7 | 1.68551 | 0.842754 | − | 0.538298i | \(-0.180933\pi\) | ||||
0.842754 | + | 0.538298i | \(0.180933\pi\) | |||||||
\(744\) | −6.36624e6 | −0.421649 | ||||||||
\(745\) | 3.42420e7 | 2.26031 | ||||||||
\(746\) | −9.84043e6 | −0.647391 | ||||||||
\(747\) | −1.54058e7 | −1.01014 | ||||||||
\(748\) | −501424. | −0.0327681 | ||||||||
\(749\) | 4.75751e6 | 0.309867 | ||||||||
\(750\) | 687312. | 0.0446170 | ||||||||
\(751\) | 1.43903e7 | 0.931046 | 0.465523 | − | 0.885036i | \(-0.345866\pi\) | ||||
0.465523 | + | 0.885036i | \(0.345866\pi\) | |||||||
\(752\) | −7.68963e6 | −0.495862 | ||||||||
\(753\) | −1.01349e7 | −0.651373 | ||||||||
\(754\) | −2.16216e6 | −0.138503 | ||||||||
\(755\) | 565952. | 0.0361337 | ||||||||
\(756\) | 3.70440e6 | 0.235729 | ||||||||
\(757\) | −1.85431e7 | −1.17609 | −0.588047 | − | 0.808827i | \(-0.700103\pi\) | ||||
−0.588047 | + | 0.808827i | \(0.700103\pi\) | |||||||
\(758\) | −7.95080e6 | −0.502618 | ||||||||
\(759\) | 316536. | 0.0199443 | ||||||||
\(760\) | 1.17216e7 | 0.736127 | ||||||||
\(761\) | 6.43123e6 | 0.402562 | 0.201281 | − | 0.979534i | \(-0.435490\pi\) | ||||
0.201281 | + | 0.979534i | \(0.435490\pi\) | |||||||
\(762\) | 2.65258e6 | 0.165493 | ||||||||
\(763\) | −2.59357e6 | −0.161282 | ||||||||
\(764\) | 2.59618e7 | 1.60917 | ||||||||
\(765\) | 2.26706e6 | 0.140059 | ||||||||
\(766\) | 1.96569e6 | 0.121044 | ||||||||
\(767\) | −1.00719e7 | −0.618190 | ||||||||
\(768\) | 182784. | 0.0111824 | ||||||||
\(769\) | 1.48249e7 | 0.904014 | 0.452007 | − | 0.892014i | \(-0.350708\pi\) | ||||
0.452007 | + | 0.892014i | \(0.350708\pi\) | |||||||
\(770\) | −877492. | −0.0533355 | ||||||||
\(771\) | −3.85163e6 | −0.233350 | ||||||||
\(772\) | −2.45693e7 | −1.48371 | ||||||||
\(773\) | 1.96325e7 | 1.18175 | 0.590876 | − | 0.806762i | \(-0.298782\pi\) | ||||
0.590876 | + | 0.806762i | \(0.298782\pi\) | |||||||
\(774\) | −8.55986e6 | −0.513588 | ||||||||
\(775\) | 2.07875e7 | 1.24322 | ||||||||
\(776\) | 1.82062e7 | 1.08534 | ||||||||
\(777\) | 40572.0 | 0.00241087 | ||||||||
\(778\) | 1.48818e6 | 0.0881468 | ||||||||
\(779\) | −702240. | −0.0414612 | ||||||||
\(780\) | −4.52525e6 | −0.266321 | ||||||||
\(781\) | −448668. | −0.0263207 | ||||||||
\(782\) | 129056. | 0.00754677 | ||||||||
\(783\) | 8.01900e6 | 0.467429 | ||||||||
\(784\) | 1.57506e6 | 0.0915179 | ||||||||
\(785\) | 1.19497e7 | 0.692120 | ||||||||
\(786\) | 450864. | 0.0260309 | ||||||||
\(787\) | −9.48639e6 | −0.545964 | −0.272982 | − | 0.962019i | \(-0.588010\pi\) | ||||
−0.272982 | + | 0.962019i | \(0.588010\pi\) | |||||||
\(788\) | 2.08489e7 | 1.19610 | ||||||||
\(789\) | 6.60898e6 | 0.377956 | ||||||||
\(790\) | −325600. | −0.0185617 | ||||||||
\(791\) | 3.94577e6 | 0.224229 | ||||||||
\(792\) | −3.00564e6 | −0.170264 | ||||||||
\(793\) | 7.10237e6 | 0.401070 | ||||||||
\(794\) | −1.14605e7 | −0.645136 | ||||||||
\(795\) | 2.34166e6 | 0.131403 | ||||||||
\(796\) | −3.02207e7 | −1.69052 | ||||||||
\(797\) | 3.32326e7 | 1.85318 | 0.926592 | − | 0.376068i | \(-0.122724\pi\) | ||||
0.926592 | + | 0.376068i | \(0.122724\pi\) | |||||||
\(798\) | 776160. | 0.0431463 | ||||||||
\(799\) | −1.73486e6 | −0.0961383 | ||||||||
\(800\) | −1.21124e7 | −0.669119 | ||||||||
\(801\) | −7.07319e6 | −0.389524 | ||||||||
\(802\) | −8.53512e6 | −0.468569 | ||||||||
\(803\) | −2.93982e6 | −0.160891 | ||||||||
\(804\) | 1.07668e7 | 0.587416 | ||||||||
\(805\) | −1.58094e6 | −0.0859854 | ||||||||
\(806\) | −6.43698e6 | −0.349015 | ||||||||
\(807\) | 1.29088e7 | 0.697755 | ||||||||
\(808\) | 1.40222e7 | 0.755595 | ||||||||
\(809\) | −2.75792e7 | −1.48153 | −0.740764 | − | 0.671766i | \(-0.765536\pi\) | ||||
−0.740764 | + | 0.671766i | \(0.765536\pi\) | |||||||
\(810\) | 5.04695e6 | 0.270281 | ||||||||
\(811\) | −7.76107e6 | −0.414352 | −0.207176 | − | 0.978304i | \(-0.566427\pi\) | ||||
−0.207176 | + | 0.978304i | \(0.566427\pi\) | |||||||
\(812\) | 4.07484e6 | 0.216880 | ||||||||
\(813\) | 6.49961e6 | 0.344874 | ||||||||
\(814\) | −33396.0 | −0.00176658 | ||||||||
\(815\) | −1.32803e7 | −0.700350 | ||||||||
\(816\) | −582528. | −0.0306261 | ||||||||
\(817\) | 2.72923e7 | 1.43049 | ||||||||
\(818\) | 1.16354e7 | 0.607994 | ||||||||
\(819\) | 3.69205e6 | 0.192335 | ||||||||
\(820\) | 1.10230e6 | 0.0572488 | ||||||||
\(821\) | −1.60578e7 | −0.831434 | −0.415717 | − | 0.909494i | \(-0.636469\pi\) | ||||
−0.415717 | + | 0.909494i | \(0.636469\pi\) | |||||||
\(822\) | −3.48722e6 | −0.180012 | ||||||||
\(823\) | 1.04666e6 | 0.0538651 | 0.0269326 | − | 0.999637i | \(-0.491426\pi\) | ||||
0.0269326 | + | 0.999637i | \(0.491426\pi\) | |||||||
\(824\) | 1.24433e7 | 0.638435 | ||||||||
\(825\) | −1.70683e6 | −0.0873081 | ||||||||
\(826\) | −2.71166e6 | −0.138288 | ||||||||
\(827\) | 8.91799e6 | 0.453423 | 0.226711 | − | 0.973962i | \(-0.427203\pi\) | ||||
0.226711 | + | 0.973962i | \(0.427203\pi\) | |||||||
\(828\) | −2.52706e6 | −0.128097 | ||||||||
\(829\) | −2.53821e7 | −1.28275 | −0.641374 | − | 0.767229i | \(-0.721635\pi\) | ||||
−0.641374 | + | 0.767229i | \(0.721635\pi\) | |||||||
\(830\) | 1.10148e7 | 0.554983 | ||||||||
\(831\) | 1.33423e7 | 0.670238 | ||||||||
\(832\) | −3.89043e6 | −0.194845 | ||||||||
\(833\) | 355348. | 0.0177436 | ||||||||
\(834\) | 4.40832e6 | 0.219461 | ||||||||
\(835\) | −2.34468e7 | −1.16377 | ||||||||
\(836\) | 4.47216e6 | 0.221310 | ||||||||
\(837\) | 2.38734e7 | 1.17788 | ||||||||
\(838\) | 8.77646e6 | 0.431727 | ||||||||
\(839\) | −3.10636e7 | −1.52351 | −0.761757 | − | 0.647863i | \(-0.775663\pi\) | ||||
−0.761757 | + | 0.647863i | \(0.775663\pi\) | |||||||
\(840\) | −2.61072e6 | −0.127662 | ||||||||
\(841\) | −1.16902e7 | −0.569946 | ||||||||
\(842\) | 2.96912e6 | 0.144327 | ||||||||
\(843\) | 918108. | 0.0444964 | ||||||||
\(844\) | −2.04056e7 | −0.986038 | ||||||||
\(845\) | 1.76710e7 | 0.851371 | ||||||||
\(846\) | −4.85291e6 | −0.233118 | ||||||||
\(847\) | −717409. | −0.0343604 | ||||||||
\(848\) | 3.45974e6 | 0.165217 | ||||||||
\(849\) | −4.29194e6 | −0.204355 | ||||||||
\(850\) | −695896. | −0.0330367 | ||||||||
\(851\) | −60168.0 | −0.00284801 | ||||||||
\(852\) | −622944. | −0.0294002 | ||||||||
\(853\) | 2.24337e7 | 1.05567 | 0.527835 | − | 0.849347i | \(-0.323004\pi\) | ||||
0.527835 | + | 0.849347i | \(0.323004\pi\) | |||||||
\(854\) | 1.91218e6 | 0.0897187 | ||||||||
\(855\) | −2.02198e7 | −0.945934 | ||||||||
\(856\) | −1.16510e7 | −0.543476 | ||||||||
\(857\) | 4.76449e6 | 0.221597 | 0.110799 | − | 0.993843i | \(-0.464659\pi\) | ||||
0.110799 | + | 0.993843i | \(0.464659\pi\) | |||||||
\(858\) | 528528. | 0.0245104 | ||||||||
\(859\) | 468030. | 0.0216417 | 0.0108208 | − | 0.999941i | \(-0.496556\pi\) | ||||
0.0108208 | + | 0.999941i | \(0.496556\pi\) | |||||||
\(860\) | −4.28407e7 | −1.97520 | ||||||||
\(861\) | 156408. | 0.00719037 | ||||||||
\(862\) | 412896. | 0.0189266 | ||||||||
\(863\) | −1.20487e7 | −0.550697 | −0.275349 | − | 0.961344i | \(-0.588793\pi\) | ||||
−0.275349 | + | 0.961344i | \(0.588793\pi\) | |||||||
\(864\) | −1.39104e7 | −0.633950 | ||||||||
\(865\) | 1.29586e7 | 0.588867 | ||||||||
\(866\) | 1.13573e7 | 0.514614 | ||||||||
\(867\) | 8.38772e6 | 0.378962 | ||||||||
\(868\) | 1.21312e7 | 0.546519 | ||||||||
\(869\) | −266200. | −0.0119580 | ||||||||
\(870\) | −2.63736e6 | −0.118133 | ||||||||
\(871\) | 2.33280e7 | 1.04192 | ||||||||
\(872\) | 6.35160e6 | 0.282873 | ||||||||
\(873\) | −3.14056e7 | −1.39467 | ||||||||
\(874\) | −1.15104e6 | −0.0509697 | ||||||||
\(875\) | −2.80652e6 | −0.123922 | ||||||||
\(876\) | −4.08173e6 | −0.179715 | ||||||||
\(877\) | 3.61718e6 | 0.158807 | 0.0794037 | − | 0.996843i | \(-0.474698\pi\) | ||||
0.0794037 | + | 0.996843i | \(0.474698\pi\) | |||||||
\(878\) | 8.87332e6 | 0.388463 | ||||||||
\(879\) | −2.08454e6 | −0.0909995 | ||||||||
\(880\) | −5.87382e6 | −0.255690 | ||||||||
\(881\) | −2.27025e7 | −0.985448 | −0.492724 | − | 0.870186i | \(-0.663999\pi\) | ||||
−0.492724 | + | 0.870186i | \(0.663999\pi\) | |||||||
\(882\) | 994014. | 0.0430250 | ||||||||
\(883\) | 2.41926e7 | 1.04419 | 0.522097 | − | 0.852886i | \(-0.325150\pi\) | ||||
0.522097 | + | 0.852886i | \(0.325150\pi\) | |||||||
\(884\) | −1.50842e6 | −0.0649218 | ||||||||
\(885\) | −1.22855e7 | −0.527271 | ||||||||
\(886\) | −1.23466e7 | −0.528399 | ||||||||
\(887\) | −4.06125e7 | −1.73321 | −0.866604 | − | 0.498997i | \(-0.833702\pi\) | ||||
−0.866604 | + | 0.498997i | \(0.833702\pi\) | |||||||
\(888\) | −99360.0 | −0.00422843 | ||||||||
\(889\) | −1.08314e7 | −0.459651 | ||||||||
\(890\) | 5.05716e6 | 0.214009 | ||||||||
\(891\) | 4.12622e6 | 0.174124 | ||||||||
\(892\) | −1.07447e6 | −0.0452150 | ||||||||
\(893\) | 1.54730e7 | 0.649302 | ||||||||
\(894\) | −5.55276e6 | −0.232362 | ||||||||
\(895\) | 5.16372e6 | 0.215479 | ||||||||
\(896\) | −9.12576e6 | −0.379751 | ||||||||
\(897\) | 952224. | 0.0395146 | ||||||||
\(898\) | 9.86210e6 | 0.408111 | ||||||||
\(899\) | 2.62607e7 | 1.08370 | ||||||||
\(900\) | 1.36264e7 | 0.560757 | ||||||||
\(901\) | 780552. | 0.0320324 | ||||||||
\(902\) | −128744. | −0.00526879 | ||||||||
\(903\) | −6.07874e6 | −0.248082 | ||||||||
\(904\) | −9.66312e6 | −0.393275 | ||||||||
\(905\) | 5.81921e6 | 0.236180 | ||||||||
\(906\) | −91776.0 | −0.00371457 | ||||||||
\(907\) | −1.98235e7 | −0.800132 | −0.400066 | − | 0.916486i | \(-0.631013\pi\) | ||||
−0.400066 | + | 0.916486i | \(0.631013\pi\) | |||||||
\(908\) | −9.05150e6 | −0.364339 | ||||||||
\(909\) | −2.41884e7 | −0.970950 | ||||||||
\(910\) | −2.63973e6 | −0.105671 | ||||||||
\(911\) | −2.21209e7 | −0.883094 | −0.441547 | − | 0.897238i | \(-0.645570\pi\) | ||||
−0.441547 | + | 0.897238i | \(0.645570\pi\) | |||||||
\(912\) | 5.19552e6 | 0.206844 | ||||||||
\(913\) | 9.00530e6 | 0.357537 | ||||||||
\(914\) | 8.30060e6 | 0.328658 | ||||||||
\(915\) | 8.66333e6 | 0.342083 | ||||||||
\(916\) | −2.27833e7 | −0.897177 | ||||||||
\(917\) | −1.84103e6 | −0.0722998 | ||||||||
\(918\) | −799200. | −0.0313003 | ||||||||
\(919\) | 4.42949e7 | 1.73008 | 0.865038 | − | 0.501706i | \(-0.167294\pi\) | ||||
0.865038 | + | 0.501706i | \(0.167294\pi\) | |||||||
\(920\) | 3.87168e6 | 0.150810 | ||||||||
\(921\) | −1.58426e7 | −0.615427 | ||||||||
\(922\) | 8.80690e6 | 0.341189 | ||||||||
\(923\) | −1.34971e6 | −0.0521479 | ||||||||
\(924\) | −996072. | −0.0383805 | ||||||||
\(925\) | 324438. | 0.0124674 | ||||||||
\(926\) | −1.36546e7 | −0.523300 | ||||||||
\(927\) | −2.14647e7 | −0.820398 | ||||||||
\(928\) | −1.53014e7 | −0.583260 | ||||||||
\(929\) | 1.13166e7 | 0.430207 | 0.215104 | − | 0.976591i | \(-0.430991\pi\) | ||||
0.215104 | + | 0.976591i | \(0.430991\pi\) | |||||||
\(930\) | −7.85170e6 | −0.297684 | ||||||||
\(931\) | −3.16932e6 | −0.119837 | ||||||||
\(932\) | −3.10244e7 | −1.16994 | ||||||||
\(933\) | 5.68667e6 | 0.213872 | ||||||||
\(934\) | −1.37649e7 | −0.516304 | ||||||||
\(935\) | −1.32519e6 | −0.0495735 | ||||||||
\(936\) | −9.04176e6 | −0.337337 | ||||||||
\(937\) | 3.37578e7 | 1.25610 | 0.628052 | − | 0.778172i | \(-0.283853\pi\) | ||||
0.628052 | + | 0.778172i | \(0.283853\pi\) | |||||||
\(938\) | 6.28062e6 | 0.233075 | ||||||||
\(939\) | 1.49212e6 | 0.0552254 | ||||||||
\(940\) | −2.42880e7 | −0.896544 | ||||||||
\(941\) | −3.30036e7 | −1.21503 | −0.607516 | − | 0.794307i | \(-0.707834\pi\) | ||||
−0.607516 | + | 0.794307i | \(0.707834\pi\) | |||||||
\(942\) | −1.93778e6 | −0.0711505 | ||||||||
\(943\) | −231952. | −0.00849413 | ||||||||
\(944\) | −1.81515e7 | −0.662953 | ||||||||
\(945\) | 9.79020e6 | 0.356625 | ||||||||
\(946\) | 5.00359e6 | 0.181783 | ||||||||
\(947\) | 1.92599e7 | 0.697876 | 0.348938 | − | 0.937146i | \(-0.386542\pi\) | ||||
0.348938 | + | 0.937146i | \(0.386542\pi\) | |||||||
\(948\) | −369600. | −0.0133571 | ||||||||
\(949\) | −8.84374e6 | −0.318765 | ||||||||
\(950\) | 6.20664e6 | 0.223125 | ||||||||
\(951\) | −1.56542e7 | −0.561281 | ||||||||
\(952\) | −870240. | −0.0311205 | ||||||||
\(953\) | 1.18503e7 | 0.422665 | 0.211332 | − | 0.977414i | \(-0.432220\pi\) | ||||
0.211332 | + | 0.977414i | \(0.432220\pi\) | |||||||
\(954\) | 2.18344e6 | 0.0776729 | ||||||||
\(955\) | 6.86134e7 | 2.43445 | ||||||||
\(956\) | 3.67786e7 | 1.30152 | ||||||||
\(957\) | −2.15622e6 | −0.0761050 | ||||||||
\(958\) | −1.00486e7 | −0.353746 | ||||||||
\(959\) | 1.42395e7 | 0.499975 | ||||||||
\(960\) | −4.74547e6 | −0.166189 | ||||||||
\(961\) | 4.95518e7 | 1.73082 | ||||||||
\(962\) | −100464. | −0.00350004 | ||||||||
\(963\) | 2.00980e7 | 0.698374 | ||||||||
\(964\) | 2.95699e7 | 1.02484 | ||||||||
\(965\) | −6.49331e7 | −2.24465 | ||||||||
\(966\) | 256368. | 0.00883936 | ||||||||
\(967\) | −1.44196e7 | −0.495892 | −0.247946 | − | 0.968774i | \(-0.579755\pi\) | ||||
−0.247946 | + | 0.968774i | \(0.579755\pi\) | |||||||
\(968\) | 1.75692e6 | 0.0602648 | ||||||||
\(969\) | 1.17216e6 | 0.0401031 | ||||||||
\(970\) | 2.24543e7 | 0.766248 | ||||||||
\(971\) | −1.37494e7 | −0.467990 | −0.233995 | − | 0.972238i | \(-0.575180\pi\) | ||||
−0.233995 | + | 0.972238i | \(0.575180\pi\) | |||||||
\(972\) | 2.40998e7 | 0.818177 | ||||||||
\(973\) | −1.80006e7 | −0.609545 | ||||||||
\(974\) | 9.03202e6 | 0.305062 | ||||||||
\(975\) | −5.13458e6 | −0.172979 | ||||||||
\(976\) | 1.27999e7 | 0.430112 | ||||||||
\(977\) | −9.18802e6 | −0.307954 | −0.153977 | − | 0.988074i | \(-0.549208\pi\) | ||||
−0.153977 | + | 0.988074i | \(0.549208\pi\) | |||||||
\(978\) | 2.15357e6 | 0.0719965 | ||||||||
\(979\) | 4.13457e6 | 0.137871 | ||||||||
\(980\) | 4.97487e6 | 0.165469 | ||||||||
\(981\) | −1.09565e7 | −0.363496 | ||||||||
\(982\) | −1.11147e7 | −0.367808 | ||||||||
\(983\) | −3.43732e7 | −1.13458 | −0.567292 | − | 0.823517i | \(-0.692009\pi\) | ||||
−0.567292 | + | 0.823517i | \(0.692009\pi\) | |||||||
\(984\) | −383040. | −0.0126112 | ||||||||
\(985\) | 5.51005e7 | 1.80953 | ||||||||
\(986\) | −879120. | −0.0287976 | ||||||||
\(987\) | −3.44627e6 | −0.112605 | ||||||||
\(988\) | 1.34534e7 | 0.438471 | ||||||||
\(989\) | 9.01474e6 | 0.293064 | ||||||||
\(990\) | −3.70696e6 | −0.120207 | ||||||||
\(991\) | −4.32179e7 | −1.39791 | −0.698956 | − | 0.715164i | \(-0.746352\pi\) | ||||
−0.698956 | + | 0.715164i | \(0.746352\pi\) | |||||||
\(992\) | −4.55540e7 | −1.46976 | ||||||||
\(993\) | −913992. | −0.0294150 | ||||||||
\(994\) | −363384. | −0.0116654 | ||||||||
\(995\) | −7.98689e7 | −2.55753 | ||||||||
\(996\) | 1.25032e7 | 0.399369 | ||||||||
\(997\) | 2.54793e7 | 0.811801 | 0.405901 | − | 0.913917i | \(-0.366958\pi\) | ||||
0.405901 | + | 0.913917i | \(0.366958\pi\) | |||||||
\(998\) | 6.99488e6 | 0.222307 | ||||||||
\(999\) | 372600. | 0.0118122 |
(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 | 77.6.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 693.6.a.a.1.1 | 1 | |||
7.6 | odd | 2 | 539.6.a.d.1.1 | 1 | |||
11.10 | odd | 2 | 847.6.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.6.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
539.6.a.d.1.1 | 1 | 7.6 | odd | 2 | |||
693.6.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
847.6.a.a.1.1 | 1 | 11.10 | odd | 2 |