Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [80,6,Mod(21,80)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(80, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("80.21");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.l (of order \(4\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(12.8307055850\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 21.3 | ||
Character | \(\chi\) | \(=\) | 80.21 |
Dual form | 80.6.l.a.61.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(21\) | \(31\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.62667 | + | 0.583586i | −0.994664 | + | 0.103164i | ||||
\(3\) | −13.2011 | + | 13.2011i | −0.846853 | + | 0.846853i | −0.989739 | − | 0.142886i | \(-0.954362\pi\) |
0.142886 | + | 0.989739i | \(0.454362\pi\) | |||||||
\(4\) | 31.3189 | − | 6.56730i | 0.978714 | − | 0.205228i | ||||
\(5\) | −17.6777 | − | 17.6777i | −0.316228 | − | 0.316228i | ||||
\(6\) | 66.5744 | − | 81.9824i | 0.754969 | − | 0.929699i | ||||
\(7\) | 190.109i | 1.46642i | 0.680003 | + | 0.733209i | \(0.261978\pi\) | ||||
−0.680003 | + | 0.733209i | \(0.738022\pi\) | |||||||
\(8\) | −172.388 | + | 55.2293i | −0.952320 | + | 0.305102i | ||||
\(9\) | − | 105.540i | − | 0.434319i | ||||||
\(10\) | 109.783 | + | 89.1500i | 0.347164 | + | 0.281917i | ||||
\(11\) | 436.822 | + | 436.822i | 1.08849 | + | 1.08849i | 0.995685 | + | 0.0928004i | \(0.0295818\pi\) |
0.0928004 | + | 0.995685i | \(0.470418\pi\) | |||||||
\(12\) | −326.748 | + | 500.140i | −0.655029 | + | 1.00262i | ||||
\(13\) | −460.621 | + | 460.621i | −0.755937 | + | 0.755937i | −0.975580 | − | 0.219643i | \(-0.929511\pi\) |
0.219643 | + | 0.975580i | \(0.429511\pi\) | |||||||
\(14\) | −110.945 | − | 1069.68i | −0.151282 | − | 1.45859i | ||||
\(15\) | 466.730 | 0.535597 | ||||||||
\(16\) | 937.741 | − | 411.360i | 0.915763 | − | 0.401719i | ||||
\(17\) | −541.113 | −0.454115 | −0.227057 | − | 0.973881i | \(-0.572910\pi\) | ||||
−0.227057 | + | 0.973881i | \(0.572910\pi\) | |||||||
\(18\) | 61.5914 | + | 593.836i | 0.0448063 | + | 0.432002i | ||||
\(19\) | 317.998 | − | 317.998i | 0.202088 | − | 0.202088i | −0.598806 | − | 0.800894i | \(-0.704358\pi\) |
0.800894 | + | 0.598806i | \(0.204358\pi\) | |||||||
\(20\) | −669.739 | − | 437.550i | −0.374395 | − | 0.244598i | ||||
\(21\) | −2509.65 | − | 2509.65i | −1.24184 | − | 1.24184i | ||||
\(22\) | −2712.78 | − | 2202.93i | −1.19497 | − | 0.970384i | ||||
\(23\) | − | 2557.06i | − | 1.00791i | −0.863730 | − | 0.503954i | \(-0.831878\pi\) | ||
0.863730 | − | 0.503954i | \(-0.168122\pi\) | |||||||
\(24\) | 1546.63 | − | 3004.81i | 0.548099 | − | 1.06485i | ||||
\(25\) | 625.000i | 0.200000i | ||||||||
\(26\) | 2322.95 | − | 2860.58i | 0.673918 | − | 0.829890i | ||||
\(27\) | −1814.63 | − | 1814.63i | −0.479049 | − | 0.479049i | ||||
\(28\) | 1248.50 | + | 5954.00i | 0.300950 | + | 1.43520i | ||||
\(29\) | −690.500 | + | 690.500i | −0.152464 | + | 0.152464i | −0.779218 | − | 0.626753i | \(-0.784383\pi\) |
0.626753 | + | 0.779218i | \(0.284383\pi\) | |||||||
\(30\) | −2626.14 | + | 272.377i | −0.532739 | + | 0.0552545i | ||||
\(31\) | −6618.22 | −1.23691 | −0.618453 | − | 0.785821i | \(-0.712240\pi\) | ||||
−0.618453 | + | 0.785821i | \(0.712240\pi\) | |||||||
\(32\) | −5036.30 | + | 2861.84i | −0.869434 | + | 0.494050i | ||||
\(33\) | −11533.1 | −1.84357 | ||||||||
\(34\) | 3044.66 | − | 315.786i | 0.451692 | − | 0.0468485i | ||||
\(35\) | 3360.69 | − | 3360.69i | 0.463722 | − | 0.463722i | ||||
\(36\) | −693.109 | − | 3305.38i | −0.0891344 | − | 0.425074i | ||||
\(37\) | 2981.43 | + | 2981.43i | 0.358031 | + | 0.358031i | 0.863087 | − | 0.505056i | \(-0.168528\pi\) |
−0.505056 | + | 0.863087i | \(0.668528\pi\) | |||||||
\(38\) | −1603.69 | + | 1974.85i | −0.180162 | + | 0.221858i | ||||
\(39\) | − | 12161.4i | − | 1.28034i | ||||||
\(40\) | 4023.75 | + | 2071.10i | 0.397632 | + | 0.204668i | ||||
\(41\) | − | 14704.0i | − | 1.36608i | −0.730383 | − | 0.683038i | \(-0.760658\pi\) | ||
0.730383 | − | 0.683038i | \(-0.239342\pi\) | |||||||
\(42\) | 15585.6 | + | 12656.4i | 1.36333 | + | 1.10710i | ||||
\(43\) | 783.164 | + | 783.164i | 0.0645924 | + | 0.0645924i | 0.738665 | − | 0.674073i | \(-0.235457\pi\) |
−0.674073 | + | 0.738665i | \(0.735457\pi\) | |||||||
\(44\) | 16549.5 | + | 10812.0i | 1.28870 | + | 0.841928i | ||||
\(45\) | −1865.69 | + | 1865.69i | −0.137344 | + | 0.137344i | ||||
\(46\) | 1492.26 | + | 14387.7i | 0.103980 | + | 1.00253i | ||||
\(47\) | 17953.6 | 1.18551 | 0.592757 | − | 0.805381i | \(-0.298039\pi\) | ||||
0.592757 | + | 0.805381i | \(0.298039\pi\) | |||||||
\(48\) | −6948.82 | + | 17809.7i | −0.435319 | + | 1.11571i | ||||
\(49\) | −19334.5 | −1.15038 | ||||||||
\(50\) | −364.741 | − | 3516.67i | −0.0206329 | − | 0.198933i | ||||
\(51\) | 7143.30 | − | 7143.30i | 0.384568 | − | 0.384568i | ||||
\(52\) | −11401.1 | + | 17451.2i | −0.584707 | + | 0.894986i | ||||
\(53\) | 5900.43 | + | 5900.43i | 0.288532 | + | 0.288532i | 0.836500 | − | 0.547967i | \(-0.184598\pi\) |
−0.547967 | + | 0.836500i | \(0.684598\pi\) | |||||||
\(54\) | 11269.3 | + | 9151.35i | 0.525913 | + | 0.427072i | ||||
\(55\) | − | 15444.0i | − | 0.688418i | ||||||
\(56\) | −10499.6 | − | 32772.6i | −0.447406 | − | 1.39650i | ||||
\(57\) | 8395.88i | 0.342278i | ||||||||
\(58\) | 3482.25 | − | 4288.18i | 0.135922 | − | 0.167380i | ||||
\(59\) | −14624.8 | − | 14624.8i | −0.546966 | − | 0.546966i | 0.378596 | − | 0.925562i | \(-0.376407\pi\) |
−0.925562 | + | 0.378596i | \(0.876407\pi\) | |||||||
\(60\) | 14617.5 | − | 3065.16i | 0.524196 | − | 0.109919i | ||||
\(61\) | −34636.5 | + | 34636.5i | −1.19182 | + | 1.19182i | −0.215262 | + | 0.976556i | \(0.569060\pi\) |
−0.976556 | + | 0.215262i | \(0.930940\pi\) | |||||||
\(62\) | 37238.5 | − | 3862.30i | 1.23031 | − | 0.127605i | ||||
\(63\) | 20064.0 | 0.636893 | ||||||||
\(64\) | 26667.5 | − | 19041.8i | 0.813826 | − | 0.581108i | ||||
\(65\) | 16285.4 | 0.478097 | ||||||||
\(66\) | 64892.8 | − | 6730.55i | 1.83374 | − | 0.190191i | ||||
\(67\) | −48789.6 | + | 48789.6i | −1.32782 | + | 1.32782i | −0.420559 | + | 0.907265i | \(0.638166\pi\) |
−0.907265 | + | 0.420559i | \(0.861834\pi\) | |||||||
\(68\) | −16947.0 | + | 3553.65i | −0.444448 | + | 0.0931970i | ||||
\(69\) | 33756.1 | + | 33756.1i | 0.853550 | + | 0.853550i | ||||
\(70\) | −16948.2 | + | 20870.7i | −0.413408 | + | 0.509088i | ||||
\(71\) | 18965.7i | 0.446502i | 0.974761 | + | 0.223251i | \(0.0716669\pi\) | ||||
−0.974761 | + | 0.223251i | \(0.928333\pi\) | |||||||
\(72\) | 5828.87 | + | 18193.8i | 0.132511 | + | 0.413611i | ||||
\(73\) | − | 81785.7i | − | 1.79626i | −0.439726 | − | 0.898132i | \(-0.644924\pi\) | ||
0.439726 | − | 0.898132i | \(-0.355076\pi\) | |||||||
\(74\) | −18515.4 | − | 15035.6i | −0.393056 | − | 0.319184i | ||||
\(75\) | −8250.70 | − | 8250.70i | −0.169371 | − | 0.169371i | ||||
\(76\) | 7870.96 | − | 12047.7i | 0.156312 | − | 0.239261i | ||||
\(77\) | −83043.8 | + | 83043.8i | −1.59617 | + | 1.59617i | ||||
\(78\) | 7097.25 | + | 68428.5i | 0.132085 | + | 1.27350i | ||||
\(79\) | 27688.8 | 0.499156 | 0.249578 | − | 0.968355i | \(-0.419708\pi\) | ||||
0.249578 | + | 0.968355i | \(0.419708\pi\) | |||||||
\(80\) | −23849.0 | − | 9305.19i | −0.416624 | − | 0.162555i | ||||
\(81\) | 73556.5 | 1.24569 | ||||||||
\(82\) | 8581.03 | + | 82734.3i | 0.140930 | + | 1.35879i | ||||
\(83\) | 40272.0 | − | 40272.0i | 0.641665 | − | 0.641665i | −0.309300 | − | 0.950965i | \(-0.600095\pi\) |
0.950965 | + | 0.309300i | \(0.100095\pi\) | |||||||
\(84\) | −95081.1 | − | 62117.9i | −1.47027 | − | 0.960546i | ||||
\(85\) | 9565.61 | + | 9565.61i | 0.143604 | + | 0.143604i | ||||
\(86\) | −4863.65 | − | 3949.56i | −0.0709114 | − | 0.0575841i | ||||
\(87\) | − | 18230.7i | − | 0.258230i | ||||||
\(88\) | −99428.3 | − | 51177.6i | −1.36868 | − | 0.704487i | ||||
\(89\) | 20256.6i | 0.271076i | 0.990772 | + | 0.135538i | \(0.0432764\pi\) | ||||
−0.990772 | + | 0.135538i | \(0.956724\pi\) | |||||||
\(90\) | 9408.85 | − | 11586.4i | 0.122442 | − | 0.150780i | ||||
\(91\) | −87568.3 | − | 87568.3i | −1.10852 | − | 1.10852i | ||||
\(92\) | −16793.0 | − | 80084.2i | −0.206851 | − | 0.986454i | ||||
\(93\) | 87368.0 | − | 87368.0i | 1.04748 | − | 1.04748i | ||||
\(94\) | −101019. | + | 10477.5i | −1.17919 | + | 0.122303i | ||||
\(95\) | −11242.9 | −0.127812 | ||||||||
\(96\) | 28705.2 | − | 104264.i | 0.317895 | − | 1.15467i | ||||
\(97\) | −76865.8 | −0.829476 | −0.414738 | − | 0.909941i | \(-0.636127\pi\) | ||||
−0.414738 | + | 0.909941i | \(0.636127\pi\) | |||||||
\(98\) | 108789. | − | 11283.3i | 1.14424 | − | 0.118679i | ||||
\(99\) | 46101.9 | − | 46101.9i | 0.472750 | − | 0.472750i | ||||
\(100\) | 4104.56 | + | 19574.3i | 0.0410456 | + | 0.195743i | ||||
\(101\) | −11615.5 | − | 11615.5i | −0.113301 | − | 0.113301i | 0.648183 | − | 0.761484i | \(-0.275529\pi\) |
−0.761484 | + | 0.648183i | \(0.775529\pi\) | |||||||
\(102\) | −36024.3 | + | 44361.7i | −0.342842 | + | 0.422190i | ||||
\(103\) | − | 210790.i | − | 1.95775i | −0.204454 | − | 0.978876i | \(-0.565542\pi\) | ||
0.204454 | − | 0.978876i | \(-0.434458\pi\) | |||||||
\(104\) | 53966.0 | − | 104846.i | 0.489257 | − | 0.950532i | ||||
\(105\) | 88729.7i | 0.785409i | ||||||||
\(106\) | −36643.2 | − | 29756.4i | −0.316759 | − | 0.257226i | ||||
\(107\) | 138862. | + | 138862.i | 1.17253 | + | 1.17253i | 0.981605 | + | 0.190922i | \(0.0611478\pi\) |
0.190922 | + | 0.981605i | \(0.438852\pi\) | |||||||
\(108\) | −68749.5 | − | 44915.0i | −0.567166 | − | 0.370537i | ||||
\(109\) | −98758.1 | + | 98758.1i | −0.796171 | + | 0.796171i | −0.982489 | − | 0.186318i | \(-0.940344\pi\) |
0.186318 | + | 0.982489i | \(0.440344\pi\) | |||||||
\(110\) | 9012.90 | + | 86898.2i | 0.0710203 | + | 0.684745i | ||||
\(111\) | −78716.4 | −0.606398 | ||||||||
\(112\) | 78203.4 | + | 178273.i | 0.589088 | + | 1.34289i | ||||
\(113\) | −68434.7 | −0.504174 | −0.252087 | − | 0.967705i | \(-0.581117\pi\) | ||||
−0.252087 | + | 0.967705i | \(0.581117\pi\) | |||||||
\(114\) | −4899.72 | − | 47240.8i | −0.0353109 | − | 0.340452i | ||||
\(115\) | −45202.8 | + | 45202.8i | −0.318729 | + | 0.318729i | ||||
\(116\) | −17090.9 | + | 26160.4i | −0.117929 | + | 0.180509i | ||||
\(117\) | 48613.8 | + | 48613.8i | 0.328318 | + | 0.328318i | ||||
\(118\) | 90823.8 | + | 73754.1i | 0.600475 | + | 0.487620i | ||||
\(119\) | − | 102870.i | − | 0.665922i | ||||||
\(120\) | −80458.8 | + | 25777.2i | −0.510059 | + | 0.163411i | ||||
\(121\) | 220575.i | 1.36960i | ||||||||
\(122\) | 174675. | − | 215102.i | 1.06251 | − | 1.30841i | ||||
\(123\) | 194109. | + | 194109.i | 1.15686 | + | 1.15686i | ||||
\(124\) | −207275. | + | 43463.8i | −1.21058 | + | 0.253848i | ||||
\(125\) | 11048.5 | − | 11048.5i | 0.0632456 | − | 0.0632456i | ||||
\(126\) | −112894. | + | 11709.1i | −0.633495 | + | 0.0657047i | ||||
\(127\) | 186051. | 1.02358 | 0.511791 | − | 0.859110i | \(-0.328982\pi\) | ||||
0.511791 | + | 0.859110i | \(0.328982\pi\) | |||||||
\(128\) | −138936. | + | 122704.i | −0.749534 | + | 0.661966i | ||||
\(129\) | −20677.3 | −0.109401 | ||||||||
\(130\) | −91632.8 | + | 9503.95i | −0.475546 | + | 0.0493226i | ||||
\(131\) | 264913. | − | 264913.i | 1.34873 | − | 1.34873i | 0.461685 | − | 0.887044i | \(-0.347245\pi\) |
0.887044 | − | 0.461685i | \(-0.152755\pi\) | |||||||
\(132\) | −361203. | + | 75741.1i | −1.80433 | + | 0.378353i | ||||
\(133\) | 60454.4 | + | 60454.4i | 0.296346 | + | 0.296346i | ||||
\(134\) | 246050. | − | 302996.i | 1.18375 | − | 1.45772i | ||||
\(135\) | 64157.0i | 0.302977i | ||||||||
\(136\) | 93281.5 | − | 29885.3i | 0.432462 | − | 0.138551i | ||||
\(137\) | − | 188083.i | − | 0.856148i | −0.903744 | − | 0.428074i | \(-0.859192\pi\) | ||
0.903744 | − | 0.428074i | \(-0.140808\pi\) | |||||||
\(138\) | −209634. | − | 170235.i | −0.937052 | − | 0.760940i | ||||
\(139\) | 261616. | + | 261616.i | 1.14849 | + | 1.14849i | 0.986850 | + | 0.161638i | \(0.0516778\pi\) |
0.161638 | + | 0.986850i | \(0.448322\pi\) | |||||||
\(140\) | 83182.2 | − | 127323.i | 0.358683 | − | 0.549020i | ||||
\(141\) | −237008. | + | 237008.i | −1.00396 | + | 1.00396i | ||||
\(142\) | −11068.1 | − | 106714.i | −0.0460631 | − | 0.444119i | ||||
\(143\) | −402419. | −1.64565 | ||||||||
\(144\) | −43414.8 | − | 98968.7i | −0.174474 | − | 0.397733i | ||||
\(145\) | 24412.8 | 0.0964270 | ||||||||
\(146\) | 47729.0 | + | 460181.i | 0.185311 | + | 1.78668i | ||||
\(147\) | 255237. | − | 255237.i | 0.974204 | − | 0.974204i | ||||
\(148\) | 112955. | + | 73795.0i | 0.423887 | + | 0.276932i | ||||
\(149\) | −224725. | − | 224725.i | −0.829251 | − | 0.829251i | 0.158162 | − | 0.987413i | \(-0.449443\pi\) |
−0.987413 | + | 0.158162i | \(0.949443\pi\) | |||||||
\(150\) | 51239.0 | + | 41609.0i | 0.185940 | + | 0.150994i | ||||
\(151\) | 2888.53i | 0.0103094i | 0.999987 | + | 0.00515471i | \(0.00164080\pi\) | ||||
−0.999987 | + | 0.00515471i | \(0.998359\pi\) | |||||||
\(152\) | −37256.4 | + | 72382.0i | −0.130795 | + | 0.254110i | ||||
\(153\) | 57108.8i | 0.197231i | ||||||||
\(154\) | 418797. | − | 515723.i | 1.42299 | − | 1.75233i | ||||
\(155\) | 116995. | + | 116995.i | 0.391144 | + | 0.391144i | ||||
\(156\) | −79867.8 | − | 380883.i | −0.262761 | − | 1.25308i | ||||
\(157\) | −307992. | + | 307992.i | −0.997217 | + | 0.997217i | −0.999996 | − | 0.00277909i | \(-0.999115\pi\) |
0.00277909 | + | 0.999996i | \(0.499115\pi\) | |||||||
\(158\) | −155796. | + | 16158.8i | −0.496493 | + | 0.0514952i | ||||
\(159\) | −155785. | −0.488689 | ||||||||
\(160\) | 139621. | + | 38439.3i | 0.431171 | + | 0.118707i | ||||
\(161\) | 486120. | 1.47802 | ||||||||
\(162\) | −413878. | + | 42926.6i | −1.23904 | + | 0.128511i | ||||
\(163\) | 59729.4 | − | 59729.4i | 0.176084 | − | 0.176084i | −0.613563 | − | 0.789646i | \(-0.710264\pi\) |
0.789646 | + | 0.613563i | \(0.210264\pi\) | |||||||
\(164\) | −96565.3 | − | 460511.i | −0.280357 | − | 1.33700i | ||||
\(165\) | 203878. | + | 203878.i | 0.582989 | + | 0.582989i | ||||
\(166\) | −203095. | + | 250100.i | −0.572044 | + | 0.704438i | ||||
\(167\) | 630406.i | 1.74916i | 0.484883 | + | 0.874579i | \(0.338862\pi\) | ||||
−0.484883 | + | 0.874579i | \(0.661138\pi\) | |||||||
\(168\) | 571241. | + | 294029.i | 1.56152 | + | 0.803742i | ||||
\(169\) | − | 53051.3i | − | 0.142883i | ||||||
\(170\) | −59404.9 | − | 48240.2i | −0.157652 | − | 0.128023i | ||||
\(171\) | −33561.4 | − | 33561.4i | −0.0877707 | − | 0.0877707i | ||||
\(172\) | 29671.1 | + | 19384.5i | 0.0764737 | + | 0.0499614i | ||||
\(173\) | −56816.7 | + | 56816.7i | −0.144331 | + | 0.144331i | −0.775580 | − | 0.631249i | \(-0.782543\pi\) |
0.631249 | + | 0.775580i | \(0.282543\pi\) | |||||||
\(174\) | 10639.2 | + | 102578.i | 0.0266401 | + | 0.256852i | ||||
\(175\) | −118818. | −0.293284 | ||||||||
\(176\) | 589317. | + | 229935.i | 1.43406 | + | 0.559529i | ||||
\(177\) | 386128. | 0.926399 | ||||||||
\(178\) | −11821.5 | − | 113977.i | −0.0279655 | − | 0.269630i | ||||
\(179\) | −4976.81 | + | 4976.81i | −0.0116096 | + | 0.0116096i | −0.712888 | − | 0.701278i | \(-0.752613\pi\) |
0.701278 | + | 0.712888i | \(0.252613\pi\) | |||||||
\(180\) | −46178.8 | + | 70683.9i | −0.106233 | + | 0.162607i | ||||
\(181\) | 197629. | + | 197629.i | 0.448388 | + | 0.448388i | 0.894818 | − | 0.446430i | \(-0.147305\pi\) |
−0.446430 | + | 0.894818i | \(0.647305\pi\) | |||||||
\(182\) | 543822. | + | 441615.i | 1.21697 | + | 0.988246i | ||||
\(183\) | − | 914483.i | − | 2.01859i | ||||||
\(184\) | 141225. | + | 440807.i | 0.307514 | + | 0.959851i | ||||
\(185\) | − | 105409.i | − | 0.226438i | ||||||
\(186\) | −440604. | + | 542578.i | −0.933826 | + | 1.14995i | ||||
\(187\) | −236370. | − | 236370.i | −0.494297 | − | 0.494297i | ||||
\(188\) | 562286. | − | 117907.i | 1.16028 | − | 0.243301i | ||||
\(189\) | 344978. | − | 344978.i | 0.702485 | − | 0.702485i | ||||
\(190\) | 63260.3 | − | 6561.23i | 0.127130 | − | 0.0131856i | ||||
\(191\) | −669691. | −1.32828 | −0.664142 | − | 0.747606i | \(-0.731203\pi\) | ||||
−0.664142 | + | 0.747606i | \(0.731203\pi\) | |||||||
\(192\) | −100668. | + | 603413.i | −0.197078 | + | 1.18130i | ||||
\(193\) | −293474. | −0.567122 | −0.283561 | − | 0.958954i | \(-0.591516\pi\) | ||||
−0.283561 | + | 0.958954i | \(0.591516\pi\) | |||||||
\(194\) | 432499. | − | 44857.8i | 0.825050 | − | 0.0855725i | ||||
\(195\) | −214986. | + | 214986.i | −0.404878 | + | 0.404878i | ||||
\(196\) | −605534. | + | 126975.i | −1.12590 | + | 0.236091i | ||||
\(197\) | −483401. | − | 483401.i | −0.887445 | − | 0.887445i | 0.106832 | − | 0.994277i | \(-0.465929\pi\) |
−0.994277 | + | 0.106832i | \(0.965929\pi\) | |||||||
\(198\) | −232496. | + | 286305.i | −0.421456 | + | 0.518998i | ||||
\(199\) | 617351.i | 1.10509i | 0.833482 | + | 0.552547i | \(0.186344\pi\) | ||||
−0.833482 | + | 0.552547i | \(0.813656\pi\) | |||||||
\(200\) | −34518.3 | − | 107743.i | −0.0610203 | − | 0.190464i | ||||
\(201\) | − | 1.28816e6i | − | 2.24894i | ||||||
\(202\) | 72135.3 | + | 58578.0i | 0.124385 | + | 0.101008i | ||||
\(203\) | −131270. | − | 131270.i | −0.223577 | − | 0.223577i | ||||
\(204\) | 176808. | − | 270632.i | 0.297458 | − | 0.455306i | ||||
\(205\) | −259932. | + | 259932.i | −0.431991 | + | 0.431991i | ||||
\(206\) | 123014. | + | 1.18605e6i | 0.201970 | + | 1.94731i | ||||
\(207\) | −269871. | −0.437754 | ||||||||
\(208\) | −242462. | + | 621425.i | −0.388585 | + | 0.995934i | ||||
\(209\) | 277817. | 0.439940 | ||||||||
\(210\) | −51781.4 | − | 499253.i | −0.0810263 | − | 0.781218i | ||||
\(211\) | −460653. | + | 460653.i | −0.712308 | + | 0.712308i | −0.967018 | − | 0.254710i | \(-0.918020\pi\) |
0.254710 | + | 0.967018i | \(0.418020\pi\) | |||||||
\(212\) | 223545. | + | 146045.i | 0.341606 | + | 0.223176i | ||||
\(213\) | −250369. | − | 250369.i | −0.378121 | − | 0.378121i | ||||
\(214\) | −862367. | − | 700291.i | −1.28723 | − | 1.04531i | ||||
\(215\) | − | 27689.0i | − | 0.0408518i | ||||||
\(216\) | 413042. | + | 212601.i | 0.602366 | + | 0.310049i | ||||
\(217\) | − | 1.25818e6i | − | 1.81382i | ||||||
\(218\) | 498045. | − | 613313.i | 0.709787 | − | 0.874060i | ||||
\(219\) | 1.07966e6 | + | 1.07966e6i | 1.52117 | + | 1.52117i | ||||
\(220\) | −101425. | − | 483688.i | −0.141283 | − | 0.673765i | ||||
\(221\) | 249248. | − | 249248.i | 0.343282 | − | 0.343282i | ||||
\(222\) | 442911. | − | 45937.8i | 0.603163 | − | 0.0625587i | ||||
\(223\) | −1.15488e6 | −1.55516 | −0.777579 | − | 0.628786i | \(-0.783552\pi\) | ||||
−0.777579 | + | 0.628786i | \(0.783552\pi\) | |||||||
\(224\) | −544062. | − | 957446.i | −0.724484 | − | 1.27495i | ||||
\(225\) | 65962.2 | 0.0868638 | ||||||||
\(226\) | 385060. | − | 39937.6i | 0.501484 | − | 0.0520128i | ||||
\(227\) | 148238. | − | 148238.i | 0.190939 | − | 0.190939i | −0.605163 | − | 0.796102i | \(-0.706892\pi\) |
0.796102 | + | 0.605163i | \(0.206892\pi\) | |||||||
\(228\) | 55138.2 | + | 262949.i | 0.0702450 | + | 0.334992i | ||||
\(229\) | 58454.7 | + | 58454.7i | 0.0736599 | + | 0.0736599i | 0.742977 | − | 0.669317i | \(-0.233413\pi\) |
−0.669317 | + | 0.742977i | \(0.733413\pi\) | |||||||
\(230\) | 227962. | − | 280721.i | 0.284147 | − | 0.349910i | ||||
\(231\) | − | 2.19254e6i | − | 2.70345i | ||||||
\(232\) | 80898.3 | − | 157170.i | 0.0986778 | − | 0.191712i | ||||
\(233\) | − | 546820.i | − | 0.659864i | −0.944005 | − | 0.329932i | \(-0.892974\pi\) | ||
0.944005 | − | 0.329932i | \(-0.107026\pi\) | |||||||
\(234\) | −301904. | − | 245163.i | −0.360437 | − | 0.292695i | ||||
\(235\) | −317378. | − | 317378.i | −0.374892 | − | 0.374892i | ||||
\(236\) | −554078. | − | 361987.i | −0.647576 | − | 0.423070i | ||||
\(237\) | −365523. | + | 365523.i | −0.422712 | + | 0.422712i | ||||
\(238\) | 60033.8 | + | 578818.i | 0.0686995 | + | 0.662369i | ||||
\(239\) | −1.20909e6 | −1.36919 | −0.684594 | − | 0.728925i | \(-0.740020\pi\) | ||||
−0.684594 | + | 0.728925i | \(0.740020\pi\) | |||||||
\(240\) | 437672. | − | 191994.i | 0.490480 | − | 0.215159i | ||||
\(241\) | 10734.0 | 0.0119047 | 0.00595236 | − | 0.999982i | \(-0.498105\pi\) | ||||
0.00595236 | + | 0.999982i | \(0.498105\pi\) | |||||||
\(242\) | −128725. | − | 1.24111e6i | −0.141294 | − | 1.36229i | ||||
\(243\) | −530073. | + | 530073.i | −0.575864 | + | 0.575864i | ||||
\(244\) | −857308. | + | 1.31225e6i | −0.921855 | + | 1.41104i | ||||
\(245\) | 341788. | + | 341788.i | 0.363783 | + | 0.363783i | ||||
\(246\) | −1.20547e6 | − | 978907.i | −1.27004 | − | 1.03134i | ||||
\(247\) | 292954.i | 0.305532i | ||||||||
\(248\) | 1.14090e6 | − | 365519.i | 1.17793 | − | 0.377382i | ||||
\(249\) | 1.06327e6i | 1.08679i | ||||||||
\(250\) | −55718.7 | + | 68614.3i | −0.0563834 | + | 0.0694328i | ||||
\(251\) | 290458. | + | 290458.i | 0.291004 | + | 0.291004i | 0.837477 | − | 0.546473i | \(-0.184030\pi\) |
−0.546473 | + | 0.837477i | \(0.684030\pi\) | |||||||
\(252\) | 628382. | − | 131766.i | 0.623336 | − | 0.130708i | ||||
\(253\) | 1.11698e6 | − | 1.11698e6i | 1.09709 | − | 1.09709i | ||||
\(254\) | −1.04685e6 | + | 108577.i | −1.01812 | + | 0.105597i | ||||
\(255\) | −252554. | −0.243222 | ||||||||
\(256\) | 710141. | − | 771499.i | 0.677243 | − | 0.735759i | ||||
\(257\) | −355570. | −0.335809 | −0.167904 | − | 0.985803i | \(-0.553700\pi\) | ||||
−0.167904 | + | 0.985803i | \(0.553700\pi\) | |||||||
\(258\) | 116344. | − | 12067.0i | 0.108817 | − | 0.0112862i | ||||
\(259\) | −566797. | + | 566797.i | −0.525022 | + | 0.525022i | ||||
\(260\) | 510041. | − | 106951.i | 0.467920 | − | 0.0981189i | ||||
\(261\) | 72875.0 | + | 72875.0i | 0.0662182 | + | 0.0662182i | ||||
\(262\) | −1.33598e6 | + | 1.64518e6i | −1.20239 | + | 1.48067i | ||||
\(263\) | 1.59192e6i | 1.41916i | 0.704623 | + | 0.709582i | \(0.251116\pi\) | ||||
−0.704623 | + | 0.709582i | \(0.748884\pi\) | |||||||
\(264\) | 1.98817e6 | − | 636964.i | 1.75567 | − | 0.562477i | ||||
\(265\) | − | 208612.i | − | 0.182484i | ||||||
\(266\) | −375437. | − | 304877.i | −0.325337 | − | 0.264192i | ||||
\(267\) | −267410. | − | 267410.i | −0.229562 | − | 0.229562i | ||||
\(268\) | −1.20762e6 | + | 1.84845e6i | −1.02705 | + | 1.57207i | ||||
\(269\) | −1.42217e6 | + | 1.42217e6i | −1.19831 | + | 1.19831i | −0.223642 | + | 0.974671i | \(0.571795\pi\) |
−0.974671 | + | 0.223642i | \(0.928205\pi\) | |||||||
\(270\) | −37441.1 | − | 360990.i | −0.0312564 | − | 0.301360i | ||||
\(271\) | 1.19243e6 | 0.986300 | 0.493150 | − | 0.869944i | \(-0.335845\pi\) | ||||
0.493150 | + | 0.869944i | \(0.335845\pi\) | |||||||
\(272\) | −507424. | + | 222592.i | −0.415861 | + | 0.182427i | ||||
\(273\) | 2.31200e6 | 1.87751 | ||||||||
\(274\) | 109763. | + | 1.05828e6i | 0.0883241 | + | 0.851580i | ||||
\(275\) | −273014. | + | 273014.i | −0.217697 | + | 0.217697i | ||||
\(276\) | 1.27889e6 | + | 835515.i | 1.01055 | + | 0.660209i | ||||
\(277\) | 532826. | + | 532826.i | 0.417240 | + | 0.417240i | 0.884251 | − | 0.467011i | \(-0.154669\pi\) |
−0.467011 | + | 0.884251i | \(0.654669\pi\) | |||||||
\(278\) | −1.62470e6 | − | 1.31935e6i | −1.26084 | − | 1.02388i | ||||
\(279\) | 698484.i | 0.537212i | ||||||||
\(280\) | −393735. | + | 764951.i | −0.300129 | + | 0.583094i | ||||
\(281\) | 115327.i | 0.0871296i | 0.999051 | + | 0.0435648i | \(0.0138715\pi\) | ||||
−0.999051 | + | 0.0435648i | \(0.986129\pi\) | |||||||
\(282\) | 1.19525e6 | − | 1.47188e6i | 0.895026 | − | 1.10217i | ||||
\(283\) | 169009. | + | 169009.i | 0.125442 | + | 0.125442i | 0.767041 | − | 0.641598i | \(-0.221728\pi\) |
−0.641598 | + | 0.767041i | \(0.721728\pi\) | |||||||
\(284\) | 124553. | + | 593984.i | 0.0916347 | + | 0.436998i | ||||
\(285\) | 148420. | − | 148420.i | 0.108238 | − | 0.108238i | ||||
\(286\) | 2.26428e6 | − | 234846.i | 1.63687 | − | 0.169773i | ||||
\(287\) | 2.79536e6 | 2.00324 | ||||||||
\(288\) | 302037. | + | 531528.i | 0.214575 | + | 0.377611i | ||||
\(289\) | −1.12705e6 | −0.793780 | ||||||||
\(290\) | −137363. | + | 14247.0i | −0.0959124 | + | 0.00994784i | ||||
\(291\) | 1.01472e6 | − | 1.01472e6i | 0.702444 | − | 0.702444i | ||||
\(292\) | −537111. | − | 2.56143e6i | −0.368644 | − | 1.75803i | ||||
\(293\) | −170154. | − | 170154.i | −0.115791 | − | 0.115791i | 0.646837 | − | 0.762628i | \(-0.276091\pi\) |
−0.762628 | + | 0.646837i | \(0.776091\pi\) | |||||||
\(294\) | −1.28718e6 | + | 1.58509e6i | −0.868503 | + | 1.06951i | ||||
\(295\) | 517065.i | 0.345932i | ||||||||
\(296\) | −678625. | − | 349301.i | −0.450195 | − | 0.231724i | ||||
\(297\) | − | 1.58534e6i | − | 1.04287i | ||||||
\(298\) | 1.39560e6 | + | 1.13331e6i | 0.910375 | + | 0.739277i | ||||
\(299\) | 1.17784e6 | + | 1.17784e6i | 0.761916 | + | 0.761916i | ||||
\(300\) | −312587. | − | 204218.i | −0.200525 | − | 0.131006i | ||||
\(301\) | −148887. | + | 148887.i | −0.0947195 | + | 0.0947195i | ||||
\(302\) | −1685.71 | − | 16252.8i | −0.00106357 | − | 0.0102544i | ||||
\(303\) | 306675. | 0.191899 | ||||||||
\(304\) | 167388. | − | 429012.i | 0.103882 | − | 0.266248i | ||||
\(305\) | 1.22459e6 | 0.753772 | ||||||||
\(306\) | −33327.9 | − | 321332.i | −0.0203472 | − | 0.196178i | ||||
\(307\) | −778959. | + | 778959.i | −0.471703 | + | 0.471703i | −0.902465 | − | 0.430762i | \(-0.858245\pi\) |
0.430762 | + | 0.902465i | \(0.358245\pi\) | |||||||
\(308\) | −2.05546e6 | + | 3.14621e6i | −1.23462 | + | 1.88978i | ||||
\(309\) | 2.78267e6 | + | 2.78267e6i | 1.65793 | + | 1.65793i | ||||
\(310\) | −726567. | − | 590014.i | −0.429409 | − | 0.348705i | ||||
\(311\) | 1.12014e6i | 0.656705i | 0.944555 | + | 0.328352i | \(0.106493\pi\) | ||||
−0.944555 | + | 0.328352i | \(0.893507\pi\) | |||||||
\(312\) | 671668. | + | 2.09649e6i | 0.390632 | + | 1.21929i | ||||
\(313\) | − | 3.38921e6i | − | 1.95541i | −0.209980 | − | 0.977706i | \(-0.567340\pi\) | ||
0.209980 | − | 0.977706i | \(-0.432660\pi\) | |||||||
\(314\) | 1.55323e6 | − | 1.91271e6i | 0.889019 | − | 1.09477i | ||||
\(315\) | −354685. | − | 354685.i | −0.201403 | − | 0.201403i | ||||
\(316\) | 867182. | − | 181841.i | 0.488531 | − | 0.102441i | ||||
\(317\) | −1.30797e6 | + | 1.30797e6i | −0.731054 | + | 0.731054i | −0.970829 | − | 0.239774i | \(-0.922927\pi\) |
0.239774 | + | 0.970829i | \(0.422927\pi\) | |||||||
\(318\) | 876550. | − | 90913.9i | 0.486081 | − | 0.0504153i | ||||
\(319\) | −603250. | −0.331910 | ||||||||
\(320\) | −808032. | − | 134804.i | −0.441117 | − | 0.0735918i | ||||
\(321\) | −3.66626e6 | −1.98592 | ||||||||
\(322\) | −2.73524e6 | + | 283693.i | −1.47013 | + | 0.152479i | ||||
\(323\) | −172073. | + | 172073.i | −0.0917712 | + | 0.0917712i | ||||
\(324\) | 2.30371e6 | − | 483067.i | 1.21917 | − | 0.255650i | ||||
\(325\) | −287888. | − | 287888.i | −0.151187 | − | 0.151187i | ||||
\(326\) | −301220. | + | 370935.i | −0.156978 | + | 0.193310i | ||||
\(327\) | − | 2.60744e6i | − | 1.34848i | ||||||
\(328\) | 812089. | + | 2.53479e6i | 0.416792 | + | 1.30094i | ||||
\(329\) | 3.41314e6i | 1.73846i | ||||||||
\(330\) | −1.26613e6 | − | 1.02817e6i | −0.640022 | − | 0.519735i | ||||
\(331\) | 2.48446e6 | + | 2.48446e6i | 1.24641 | + | 1.24641i | 0.957293 | + | 0.289121i | \(0.0933630\pi\) |
0.289121 | + | 0.957293i | \(0.406637\pi\) | |||||||
\(332\) | 996796. | − | 1.52575e6i | 0.496319 | − | 0.759694i | ||||
\(333\) | 314658. | − | 314658.i | 0.155499 | − | 0.155499i | ||||
\(334\) | −367896. | − | 3.54709e6i | −0.180451 | − | 1.73983i | ||||
\(335\) | 1.72497e6 | 0.839790 | ||||||||
\(336\) | −3.38578e6 | − | 1.32103e6i | −1.63610 | − | 0.638360i | ||||
\(337\) | 2.04358e6 | 0.980206 | 0.490103 | − | 0.871665i | \(-0.336959\pi\) | ||||
0.490103 | + | 0.871665i | \(0.336959\pi\) | |||||||
\(338\) | 30960.0 | + | 298502.i | 0.0147404 | + | 0.142120i | ||||
\(339\) | 903415. | − | 903415.i | 0.426961 | − | 0.426961i | ||||
\(340\) | 362404. | + | 236764.i | 0.170018 | + | 0.111075i | ||||
\(341\) | −2.89098e6 | − | 2.89098e6i | −1.34635 | − | 1.34635i | ||||
\(342\) | 208425. | + | 169253.i | 0.0963572 | + | 0.0782476i | ||||
\(343\) | − | 480496.i | − | 0.220523i | ||||||
\(344\) | −178262. | − | 91754.7i | −0.0812199 | − | 0.0418054i | ||||
\(345\) | − | 1.19346e6i | − | 0.539833i | ||||||
\(346\) | 286531. | − | 352846.i | 0.128671 | − | 0.158451i | ||||
\(347\) | −1.42726e6 | − | 1.42726e6i | −0.636325 | − | 0.636325i | 0.313322 | − | 0.949647i | \(-0.398558\pi\) |
−0.949647 | + | 0.313322i | \(0.898558\pi\) | |||||||
\(348\) | −119727. | − | 570966.i | −0.0529960 | − | 0.252733i | ||||
\(349\) | 1.77197e6 | − | 1.77197e6i | 0.778739 | − | 0.778739i | −0.200877 | − | 0.979616i | \(-0.564379\pi\) |
0.979616 | + | 0.200877i | \(0.0643792\pi\) | |||||||
\(350\) | 668551. | − | 69340.7i | 0.291719 | − | 0.0302564i | ||||
\(351\) | 1.67172e6 | 0.724261 | ||||||||
\(352\) | −3.45008e6 | − | 949849.i | −1.48413 | − | 0.408599i | ||||
\(353\) | 836162. | 0.357153 | 0.178576 | − | 0.983926i | \(-0.442851\pi\) | ||||
0.178576 | + | 0.983926i | \(0.442851\pi\) | |||||||
\(354\) | −2.17261e6 | + | 225339.i | −0.921456 | + | 0.0955714i | ||||
\(355\) | 335270. | − | 335270.i | 0.141196 | − | 0.141196i | ||||
\(356\) | 133031. | + | 634414.i | 0.0556325 | + | 0.265306i | ||||
\(357\) | 1.35801e6 | + | 1.35801e6i | 0.563938 | + | 0.563938i | ||||
\(358\) | 25098.5 | − | 30907.3i | 0.0103500 | − | 0.0127454i | ||||
\(359\) | − | 802370.i | − | 0.328578i | −0.986412 | − | 0.164289i | \(-0.947467\pi\) | ||
0.986412 | − | 0.164289i | \(-0.0525330\pi\) | |||||||
\(360\) | 218583. | − | 424664.i | 0.0888914 | − | 0.172699i | ||||
\(361\) | 2.27385e6i | 0.918321i | ||||||||
\(362\) | −1.22733e6 | − | 996659.i | −0.492253 | − | 0.399738i | ||||
\(363\) | −2.91184e6 | − | 2.91184e6i | −1.15985 | − | 1.15985i | ||||
\(364\) | −3.31763e6 | − | 2.16745e6i | −1.31242 | − | 0.857425i | ||||
\(365\) | −1.44578e6 | + | 1.44578e6i | −0.568029 | + | 0.568029i | ||||
\(366\) | 533680. | + | 5.14549e6i | 0.208247 | + | 2.00782i | ||||
\(367\) | −158829. | −0.0615550 | −0.0307775 | − | 0.999526i | \(-0.509798\pi\) | ||||
−0.0307775 | + | 0.999526i | \(0.509798\pi\) | |||||||
\(368\) | −1.05187e6 | − | 2.39786e6i | −0.404896 | − | 0.923005i | ||||
\(369\) | −1.55185e6 | −0.593312 | ||||||||
\(370\) | 61515.5 | + | 593104.i | 0.0233604 | + | 0.225230i | ||||
\(371\) | −1.12173e6 | + | 1.12173e6i | −0.423109 | + | 0.423109i | ||||
\(372\) | 2.16249e6 | − | 3.31004e6i | 0.810210 | − | 1.24015i | ||||
\(373\) | 719302. | + | 719302.i | 0.267694 | + | 0.267694i | 0.828171 | − | 0.560476i | \(-0.189382\pi\) |
−0.560476 | + | 0.828171i | \(0.689382\pi\) | |||||||
\(374\) | 1.46792e6 | + | 1.19203e6i | 0.542653 | + | 0.440666i | ||||
\(375\) | 291706.i | 0.107119i | ||||||||
\(376\) | −3.09499e6 | + | 991564.i | −1.12899 | + | 0.361702i | ||||
\(377\) | − | 636118.i | − | 0.230507i | ||||||
\(378\) | −1.73976e6 | + | 2.14240e6i | −0.626266 | + | 0.771209i | ||||
\(379\) | −733349. | − | 733349.i | −0.262248 | − | 0.262248i | 0.563719 | − | 0.825967i | \(-0.309370\pi\) |
−0.825967 | + | 0.563719i | \(0.809370\pi\) | |||||||
\(380\) | −352116. | + | 73835.7i | −0.125091 | + | 0.0262306i | ||||
\(381\) | −2.45608e6 | + | 2.45608e6i | −0.866824 | + | 0.866824i | ||||
\(382\) | 3.76813e6 | − | 390823.i | 1.32120 | − | 0.137032i | ||||
\(383\) | −3.53928e6 | −1.23287 | −0.616435 | − | 0.787406i | \(-0.711424\pi\) | ||||
−0.616435 | + | 0.787406i | \(0.711424\pi\) | |||||||
\(384\) | 214280. | − | 3.45396e6i | 0.0741574 | − | 1.19533i | ||||
\(385\) | 2.93604e6 | 1.00951 | ||||||||
\(386\) | 1.65128e6 | − | 171268.i | 0.564096 | − | 0.0585069i | ||||
\(387\) | 82654.7 | − | 82654.7i | 0.0280537 | − | 0.0280537i | ||||
\(388\) | −2.40735e6 | + | 504801.i | −0.811820 | + | 0.170232i | ||||
\(389\) | −467653. | − | 467653.i | −0.156693 | − | 0.156693i | 0.624407 | − | 0.781100i | \(-0.285341\pi\) |
−0.781100 | + | 0.624407i | \(0.785341\pi\) | |||||||
\(390\) | 1.08419e6 | − | 1.33512e6i | 0.360948 | − | 0.444486i | ||||
\(391\) | 1.38366e6i | 0.457706i | ||||||||
\(392\) | 3.33304e6 | − | 1.06783e6i | 1.09553 | − | 0.350983i | ||||
\(393\) | 6.99430e6i | 2.28435i | ||||||||
\(394\) | 3.00204e6 | + | 2.43783e6i | 0.974263 | + | 0.791157i | ||||
\(395\) | −489474. | − | 489474.i | −0.157847 | − | 0.157847i | ||||
\(396\) | 1.14109e6 | − | 1.74663e6i | 0.365665 | − | 0.559708i | ||||
\(397\) | 1.28300e6 | − | 1.28300e6i | 0.408555 | − | 0.408555i | −0.472680 | − | 0.881234i | \(-0.656713\pi\) |
0.881234 | + | 0.472680i | \(0.156713\pi\) | |||||||
\(398\) | −360277. | − | 3.47363e6i | −0.114006 | − | 1.09920i | ||||
\(399\) | −1.59613e6 | −0.501923 | ||||||||
\(400\) | 257100. | + | 586088.i | 0.0803438 | + | 0.183153i | ||||
\(401\) | −1.16341e6 | −0.361304 | −0.180652 | − | 0.983547i | \(-0.557821\pi\) | ||||
−0.180652 | + | 0.983547i | \(0.557821\pi\) | |||||||
\(402\) | 751750. | + | 7.24803e6i | 0.232011 | + | 2.23694i | ||||
\(403\) | 3.04849e6 | − | 3.04849e6i | 0.935024 | − | 0.935024i | ||||
\(404\) | −440067. | − | 287502.i | −0.134142 | − | 0.0876369i | ||||
\(405\) | −1.30031e6 | − | 1.30031e6i | −0.393921 | − | 0.393921i | ||||
\(406\) | 815222. | + | 662007.i | 0.245449 | + | 0.199318i | ||||
\(407\) | 2.60470e6i | 0.779422i | ||||||||
\(408\) | −836902. | + | 1.62594e6i | −0.248900 | + | 0.483564i | ||||
\(409\) | 2.33520e6i | 0.690266i | 0.938554 | + | 0.345133i | \(0.112166\pi\) | ||||
−0.938554 | + | 0.345133i | \(0.887834\pi\) | |||||||
\(410\) | 1.31086e6 | − | 1.61424e6i | 0.385120 | − | 0.474252i | ||||
\(411\) | 2.48291e6 | + | 2.48291e6i | 0.725032 | + | 0.725032i | ||||
\(412\) | −1.38432e6 | − | 6.60171e6i | −0.401786 | − | 1.91608i | ||||
\(413\) | 2.78031e6 | − | 2.78031e6i | 0.802081 | − | 0.802081i | ||||
\(414\) | 1.51847e6 | − | 157493.i | 0.435418 | − | 0.0451606i | ||||
\(415\) | −1.42383e6 | −0.405825 | ||||||||
\(416\) | 1.00160e6 | − | 3.63805e6i | 0.283767 | − | 1.03071i | ||||
\(417\) | −6.90724e6 | −1.94520 | ||||||||
\(418\) | −1.56319e6 | + | 162130.i | −0.437593 | + | 0.0453862i | ||||
\(419\) | 591682. | − | 591682.i | 0.164647 | − | 0.164647i | −0.619975 | − | 0.784622i | \(-0.712857\pi\) |
0.784622 | + | 0.619975i | \(0.212857\pi\) | |||||||
\(420\) | 582714. | + | 2.77891e6i | 0.161188 | + | 0.768691i | ||||
\(421\) | −463532. | − | 463532.i | −0.127460 | − | 0.127460i | 0.640499 | − | 0.767959i | \(-0.278728\pi\) |
−0.767959 | + | 0.640499i | \(0.778728\pi\) | |||||||
\(422\) | 2.32311e6 | − | 2.86077e6i | 0.635022 | − | 0.781992i | ||||
\(423\) | − | 1.89481e6i | − | 0.514891i | ||||||
\(424\) | −1.34304e6 | − | 691289.i | −0.362807 | − | 0.186743i | ||||
\(425\) | − | 338195.i | − | 0.0908229i | ||||||
\(426\) | 1.55485e6 | + | 1.26263e6i | 0.415112 | + | 0.337095i | ||||
\(427\) | −6.58472e6 | − | 6.58472e6i | −1.74770 | − | 1.74770i | ||||
\(428\) | 5.26093e6 | + | 3.43704e6i | 1.38820 | + | 0.906934i | ||||
\(429\) | 5.31238e6 | − | 5.31238e6i | 1.39363 | − | 1.39363i | ||||
\(430\) | 16158.9 | + | 155797.i | 0.00421446 | + | 0.0406339i | ||||
\(431\) | −2.47706e6 | −0.642309 | −0.321154 | − | 0.947027i | \(-0.604071\pi\) | ||||
−0.321154 | + | 0.947027i | \(0.604071\pi\) | |||||||
\(432\) | −2.44812e6 | − | 955188.i | −0.631138 | − | 0.246252i | ||||
\(433\) | 3.94915e6 | 1.01224 | 0.506120 | − | 0.862463i | \(-0.331079\pi\) | ||||
0.506120 | + | 0.862463i | \(0.331079\pi\) | |||||||
\(434\) | 734259. | + | 7.07939e6i | 0.187122 | + | 1.80414i | ||||
\(435\) | −322277. | + | 322277.i | −0.0816594 | + | 0.0816594i | ||||
\(436\) | −2.44442e6 | + | 3.74156e6i | −0.615827 | + | 0.942621i | ||||
\(437\) | −813141. | − | 813141.i | −0.203686 | − | 0.203686i | ||||
\(438\) | −6.70499e6 | − | 5.44483e6i | −1.66999 | − | 1.35612i | ||||
\(439\) | − | 2.57617e6i | − | 0.637990i | −0.947756 | − | 0.318995i | \(-0.896655\pi\) | ||
0.947756 | − | 0.318995i | \(-0.103345\pi\) | |||||||
\(440\) | 852960. | + | 2.66236e6i | 0.210038 | + | 0.655595i | ||||
\(441\) | 2.04055e6i | 0.499633i | ||||||||
\(442\) | −1.25698e6 | + | 1.54790e6i | −0.306036 | + | 0.376865i | ||||
\(443\) | −1.36521e6 | − | 1.36521e6i | −0.330514 | − | 0.330514i | 0.522268 | − | 0.852782i | \(-0.325086\pi\) |
−0.852782 | + | 0.522268i | \(0.825086\pi\) | |||||||
\(444\) | −2.46531e6 | + | 516954.i | −0.593491 | + | 0.124450i | ||||
\(445\) | 358090. | − | 358090.i | 0.0857219 | − | 0.0857219i | ||||
\(446\) | 6.49813e6 | − | 673972.i | 1.54686 | − | 0.160437i | ||||
\(447\) | 5.93325e6 | 1.40451 | ||||||||
\(448\) | 3.62001e6 | + | 5.06973e6i | 0.852148 | + | 1.19341i | ||||
\(449\) | −3.34712e6 | −0.783531 | −0.391765 | − | 0.920065i | \(-0.628136\pi\) | ||||
−0.391765 | + | 0.920065i | \(0.628136\pi\) | |||||||
\(450\) | −371148. | + | 38494.6i | −0.0864003 | + | 0.00896126i | ||||
\(451\) | 6.42301e6 | − | 6.42301e6i | 1.48695 | − | 1.48695i | ||||
\(452\) | −2.14330e6 | + | 449431.i | −0.493442 | + | 0.103471i | ||||
\(453\) | −38131.8 | − | 38131.8i | −0.00873056 | − | 0.00873056i | ||||
\(454\) | −747575. | + | 920593.i | −0.170222 | + | 0.209618i | ||||
\(455\) | 3.09601e6i | 0.701090i | ||||||||
\(456\) | −463698. | − | 1.44735e6i | −0.104430 | − | 0.325958i | ||||
\(457\) | 7.96562e6i | 1.78414i | 0.451898 | + | 0.892070i | \(0.350747\pi\) | ||||
−0.451898 | + | 0.892070i | \(0.649253\pi\) | |||||||
\(458\) | −363019. | − | 294792.i | −0.0808659 | − | 0.0656678i | ||||
\(459\) | 981921. | + | 981921.i | 0.217543 | + | 0.217543i | ||||
\(460\) | −1.11884e6 | + | 1.71256e6i | −0.246532 | + | 0.377356i | ||||
\(461\) | −2.11325e6 | + | 2.11325e6i | −0.463126 | + | 0.463126i | −0.899679 | − | 0.436553i | \(-0.856199\pi\) |
0.436553 | + | 0.899679i | \(0.356199\pi\) | |||||||
\(462\) | 1.27954e6 | + | 1.23367e7i | 0.278900 | + | 2.68902i | ||||
\(463\) | −1.33400e6 | −0.289204 | −0.144602 | − | 0.989490i | \(-0.546190\pi\) | ||||
−0.144602 | + | 0.989490i | \(0.546190\pi\) | |||||||
\(464\) | −363466. | + | 931554.i | −0.0783734 | + | 0.200869i | ||||
\(465\) | −3.08892e6 | −0.662483 | ||||||||
\(466\) | 319117. | + | 3.07678e6i | 0.0680745 | + | 0.656343i | ||||
\(467\) | 1.89907e6 | − | 1.89907e6i | 0.402948 | − | 0.402948i | −0.476323 | − | 0.879270i | \(-0.658031\pi\) |
0.879270 | + | 0.476323i | \(0.158031\pi\) | |||||||
\(468\) | 1.84179e6 | + | 1.20327e6i | 0.388709 | + | 0.253949i | ||||
\(469\) | −9.27535e6 | − | 9.27535e6i | −1.94715 | − | 1.94715i | ||||
\(470\) | 1.97100e6 | + | 1.60056e6i | 0.411568 | + | 0.334217i | ||||
\(471\) | − | 8.13167e6i | − | 1.68899i | ||||||
\(472\) | 3.32886e6 | + | 1.71343e6i | 0.687766 | + | 0.354006i | ||||
\(473\) | 684206.i | 0.140616i | ||||||||
\(474\) | 1.84337e6 | − | 2.26999e6i | 0.376848 | − | 0.464065i | ||||
\(475\) | 198749. | + | 198749.i | 0.0404176 | + | 0.0404176i | ||||
\(476\) | −675581. | − | 3.22178e6i | −0.136666 | − | 0.651747i | ||||
\(477\) | 622729. | − | 622729.i | 0.125315 | − | 0.125315i | ||||
\(478\) | 6.80314e6 | − | 705607.i | 1.36188 | − | 0.141251i | ||||
\(479\) | 6.56083e6 | 1.30653 | 0.653266 | − | 0.757129i | \(-0.273399\pi\) | ||||
0.653266 | + | 0.757129i | \(0.273399\pi\) | |||||||
\(480\) | −2.35059e6 | + | 1.33571e6i | −0.465666 | + | 0.264611i | ||||
\(481\) | −2.74662e6 | −0.541297 | ||||||||
\(482\) | −60396.7 | + | 6264.22i | −0.0118412 | + | 0.00122814i | ||||
\(483\) | −6.41733e6 | + | 6.41733e6i | −1.25166 | + | 1.25166i | ||||
\(484\) | 1.44858e6 | + | 6.90817e6i | 0.281080 | + | 1.34045i | ||||
\(485\) | 1.35881e6 | + | 1.35881e6i | 0.262303 | + | 0.262303i | ||||
\(486\) | 2.67320e6 | − | 3.29189e6i | 0.513383 | − | 0.632200i | ||||
\(487\) | 3.54526e6i | 0.677369i | 0.940900 | + | 0.338685i | \(0.109982\pi\) | ||||
−0.940900 | + | 0.338685i | \(0.890018\pi\) | |||||||
\(488\) | 4.05798e6 | − | 7.88389e6i | 0.771367 | − | 1.49862i | ||||
\(489\) | 1.57699e6i | 0.298234i | ||||||||
\(490\) | −2.12259e6 | − | 1.72367e6i | −0.399371 | − | 0.324312i | ||||
\(491\) | 3.02097e6 | + | 3.02097e6i | 0.565514 | + | 0.565514i | 0.930868 | − | 0.365355i | \(-0.119052\pi\) |
−0.365355 | + | 0.930868i | \(0.619052\pi\) | |||||||
\(492\) | 7.35404e6 | + | 4.80450e6i | 1.36966 | + | 0.894819i | ||||
\(493\) | 373638. | − | 373638.i | 0.0692363 | − | 0.0692363i | ||||
\(494\) | −170964. | − | 1.64835e6i | −0.0315201 | − | 0.303902i | ||||
\(495\) | −1.62995e6 | −0.298993 | ||||||||
\(496\) | −6.20618e6 | + | 2.72247e6i | −1.13271 | + | 0.496889i | ||||
\(497\) | −3.60555e6 | −0.654758 | ||||||||
\(498\) | −620511. | − | 5.98268e6i | −0.112118 | − | 1.08099i | ||||
\(499\) | −714396. | + | 714396.i | −0.128436 | + | 0.128436i | −0.768403 | − | 0.639966i | \(-0.778948\pi\) |
0.639966 | + | 0.768403i | \(0.278948\pi\) | |||||||
\(500\) | 273469. | − | 418587.i | 0.0489196 | − | 0.0748791i | ||||
\(501\) | −8.32207e6 | − | 8.32207e6i | −1.48128 | − | 1.48128i | ||||
\(502\) | −1.80382e6 | − | 1.46480e6i | −0.319473 | − | 0.259430i | ||||
\(503\) | 5.36521e6i | 0.945511i | 0.881194 | + | 0.472756i | \(0.156741\pi\) | ||||
−0.881194 | + | 0.472756i | \(0.843259\pi\) | |||||||
\(504\) | −3.45880e6 | + | 1.10812e6i | −0.606526 | + | 0.194317i | ||||
\(505\) | 410670.i | 0.0716580i | ||||||||
\(506\) | −5.63302e6 | + | 6.93673e6i | −0.978059 | + | 1.20442i | ||||
\(507\) | 700337. | + | 700337.i | 0.121001 | + | 0.121001i | ||||
\(508\) | 5.82691e6 | − | 1.22185e6i | 1.00180 | − | 0.210068i | ||||
\(509\) | 660473. | − | 660473.i | 0.112995 | − | 0.112995i | −0.648348 | − | 0.761344i | \(-0.724540\pi\) |
0.761344 | + | 0.648348i | \(0.224540\pi\) | |||||||
\(510\) | 1.42104e6 | − | 147387.i | 0.241924 | − | 0.0250919i | ||||
\(511\) | 1.55482e7 | 2.63407 | ||||||||
\(512\) | −3.54549e6 | + | 4.75540e6i | −0.597726 | + | 0.801701i | ||||
\(513\) | −1.15410e6 | −0.193620 | ||||||||
\(514\) | 2.00067e6 | − | 207506.i | 0.334017 | − | 0.0346435i | ||||
\(515\) | −3.72628e6 | + | 3.72628e6i | −0.619096 | + | 0.619096i | ||||
\(516\) | −647589. | + | 135794.i | −0.107072 | + | 0.0224521i | ||||
\(517\) | 7.84252e6 | + | 7.84252e6i | 1.29041 | + | 1.29041i | ||||
\(518\) | 2.85840e6 | − | 3.51995e6i | 0.468057 | − | 0.576385i | ||||
\(519\) | − | 1.50009e6i | − | 0.244455i | ||||||
\(520\) | −2.80742e6 | + | 899432.i | −0.455301 | + | 0.145868i | ||||
\(521\) | − | 971519.i | − | 0.156804i | −0.996922 | − | 0.0784020i | \(-0.975018\pi\) | ||
0.996922 | − | 0.0784020i | \(-0.0249818\pi\) | |||||||
\(522\) | −452572. | − | 367515.i | −0.0726962 | − | 0.0590335i | ||||
\(523\) | −2.56867e6 | − | 2.56867e6i | −0.410632 | − | 0.410632i | 0.471326 | − | 0.881959i | \(-0.343775\pi\) |
−0.881959 | + | 0.471326i | \(0.843775\pi\) | |||||||
\(524\) | 6.55700e6 | − | 1.00365e7i | 1.04322 | − | 1.59682i | ||||
\(525\) | 1.56853e6 | − | 1.56853e6i | 0.248368 | − | 0.248368i | ||||
\(526\) | −929024. | − | 8.95722e6i | −0.146407 | − | 1.41159i | ||||
\(527\) | 3.58120e6 | 0.561697 | ||||||||
\(528\) | −1.08150e7 | + | 4.74425e6i | −1.68828 | + | 0.740599i | ||||
\(529\) | −102208. | −0.0158798 | ||||||||
\(530\) | 121743. | + | 1.17379e6i | 0.0188258 | + | 0.181510i | ||||
\(531\) | −1.54349e6 | + | 1.54349e6i | −0.237558 | + | 0.237558i | ||||
\(532\) | 2.29038e6 | + | 1.49634e6i | 0.350856 | + | 0.229219i | ||||
\(533\) | 6.77296e6 | + | 6.77296e6i | 1.03267 | + | 1.03267i | ||||
\(534\) | 1.66069e6 | + | 1.34857e6i | 0.252020 | + | 0.204654i | ||||
\(535\) | − | 4.90950e6i | − | 0.741571i | ||||||
\(536\) | 5.71615e6 | − | 1.11054e7i | 0.859392 | − | 1.66963i | ||||
\(537\) | − | 131399.i | − | 0.0196633i | ||||||
\(538\) | 7.17212e6 | − | 8.83203e6i | 1.06830 | − | 1.31554i | ||||
\(539\) | −8.44572e6 | − | 8.44572e6i | −1.25217 | − | 1.25217i | ||||
\(540\) | 421338. | + | 2.00932e6i | 0.0621793 | + | 0.296528i | ||||
\(541\) | −2.32096e6 | + | 2.32096e6i | −0.340937 | + | 0.340937i | −0.856719 | − | 0.515783i | \(-0.827501\pi\) |
0.515783 | + | 0.856719i | \(0.327501\pi\) | |||||||
\(542\) | −6.70940e6 | + | 695885.i | −0.981038 | + | 0.101751i | ||||
\(543\) | −5.21785e6 | −0.759437 | ||||||||
\(544\) | 2.72520e6 | − | 1.54858e6i | 0.394822 | − | 0.224355i | ||||
\(545\) | 3.49163e6 | 0.503543 | ||||||||
\(546\) | −1.30089e7 | + | 1.34925e6i | −1.86749 | + | 0.193692i | ||||
\(547\) | 4.92582e6 | − | 4.92582e6i | 0.703898 | − | 0.703898i | −0.261347 | − | 0.965245i | \(-0.584167\pi\) |
0.965245 | + | 0.261347i | \(0.0841666\pi\) | |||||||
\(548\) | −1.23520e6 | − | 5.89056e6i | −0.175706 | − | 0.837925i | ||||
\(549\) | 3.65552e6 | + | 3.65552e6i | 0.517629 | + | 0.517629i | ||||
\(550\) | 1.37683e6 | − | 1.69548e6i | 0.194077 | − | 0.238994i | ||||
\(551\) | 439156.i | 0.0616225i | ||||||||
\(552\) | −7.68347e6 | − | 3.95483e6i | −1.07327 | − | 0.552433i | ||||
\(553\) | 5.26389e6i | 0.731972i | ||||||||
\(554\) | −3.30899e6 | − | 2.68709e6i | −0.458059 | − | 0.371970i | ||||
\(555\) | 1.39152e6 | + | 1.39152e6i | 0.191760 | + | 0.191760i | ||||
\(556\) | 9.91161e6 | + | 6.47539e6i | 1.35974 | + | 0.888340i | ||||
\(557\) | −5.57524e6 | + | 5.57524e6i | −0.761422 | + | 0.761422i | −0.976579 | − | 0.215157i | \(-0.930974\pi\) |
0.215157 | + | 0.976579i | \(0.430974\pi\) | |||||||
\(558\) | −407626. | − | 3.93014e6i | −0.0554212 | − | 0.534346i | ||||
\(559\) | −721484. | −0.0976557 | ||||||||
\(560\) | 1.76900e6 | − | 4.53391e6i | 0.238373 | − | 0.610946i | ||||
\(561\) | 6.24069e6 | 0.837193 | ||||||||
\(562\) | −67303.3 | − | 648908.i | −0.00898868 | − | 0.0866647i | ||||
\(563\) | −8.90526e6 | + | 8.90526e6i | −1.18406 | + | 1.18406i | −0.205383 | + | 0.978682i | \(0.565844\pi\) |
−0.978682 | + | 0.205383i | \(0.934156\pi\) | |||||||
\(564\) | −5.86631e6 | + | 8.97931e6i | −0.776546 | + | 1.18863i | ||||
\(565\) | 1.20977e6 | + | 1.20977e6i | 0.159434 | + | 0.159434i | ||||
\(566\) | −1.04959e6 | − | 852327.i | −0.137714 | − | 0.111832i | ||||
\(567\) | 1.39838e7i | 1.82670i | ||||||||
\(568\) | −1.04746e6 | − | 3.26947e6i | −0.136228 | − | 0.425213i | ||||
\(569\) | − | 9.17182e6i | − | 1.18761i | −0.804608 | − | 0.593806i | \(-0.797625\pi\) | ||
0.804608 | − | 0.593806i | \(-0.202375\pi\) | |||||||
\(570\) | −748492. | + | 921723.i | −0.0964940 | + | 0.118827i | ||||
\(571\) | −8.05400e6 | − | 8.05400e6i | −1.03376 | − | 1.03376i | −0.999410 | − | 0.0343541i | \(-0.989063\pi\) |
−0.0343541 | − | 0.999410i | \(-0.510937\pi\) | |||||||
\(572\) | −1.26033e7 | + | 2.64280e6i | −1.61062 | + | 0.337734i | ||||
\(573\) | 8.84068e6 | − | 8.84068e6i | 1.12486 | − | 1.12486i | ||||
\(574\) | −1.57286e7 | + | 1.63133e6i | −1.99255 | + | 0.206663i | ||||
\(575\) | 1.59816e6 | 0.201582 | ||||||||
\(576\) | −2.00966e6 | − | 2.81447e6i | −0.252386 | − | 0.353460i | ||||
\(577\) | 6.38833e6 | 0.798818 | 0.399409 | − | 0.916773i | \(-0.369215\pi\) | ||||
0.399409 | + | 0.916773i | \(0.369215\pi\) | |||||||
\(578\) | 6.34156e6 | − | 657733.i | 0.789545 | − | 0.0818899i | ||||
\(579\) | 3.87419e6 | − | 3.87419e6i | 0.480269 | − | 0.480269i | ||||
\(580\) | 764582. | − | 160326.i | 0.0943744 | − | 0.0197895i | ||||
\(581\) | 7.65608e6 | + | 7.65608e6i | 0.940949 | + | 0.940949i | ||||
\(582\) | −5.11730e6 | + | 6.30164e6i | −0.626229 | + | 0.771163i | ||||
\(583\) | 5.15488e6i | 0.628126i | ||||||||
\(584\) | 4.51697e6 | + | 1.40989e7i | 0.548043 | + | 1.71062i | ||||
\(585\) | − | 1.71876e6i | − | 0.207646i | ||||||
\(586\) | 1.05670e6 | + | 858101.i | 0.127118 | + | 0.103227i | ||||
\(587\) | 3.14367e6 | + | 3.14367e6i | 0.376566 | + | 0.376566i | 0.869862 | − | 0.493296i | \(-0.164208\pi\) |
−0.493296 | + | 0.869862i | \(0.664208\pi\) | |||||||
\(588\) | 6.31751e6 | − | 9.66994e6i | 0.753533 | − | 1.15340i | ||||
\(589\) | −2.10458e6 | + | 2.10458e6i | −0.249964 | + | 0.249964i | ||||
\(590\) | −301752. | − | 2.90935e6i | −0.0356878 | − | 0.344086i | ||||
\(591\) | 1.27629e7 | 1.50307 | ||||||||
\(592\) | 4.02225e6 | + | 1.56937e6i | 0.471699 | + | 0.184043i | ||||
\(593\) | −7.90117e6 | −0.922688 | −0.461344 | − | 0.887221i | \(-0.652633\pi\) | ||||
−0.461344 | + | 0.887221i | \(0.652633\pi\) | |||||||
\(594\) | 925184. | + | 8.92020e6i | 0.107588 | + | 1.03731i | ||||
\(595\) | −1.81851e6 | + | 1.81851e6i | −0.210583 | + | 0.210583i | ||||
\(596\) | −8.51397e6 | − | 5.56230e6i | −0.981785 | − | 0.641414i | ||||
\(597\) | −8.14972e6 | − | 8.14972e6i | −0.935852 | − | 0.935852i | ||||
\(598\) | −7.31467e6 | − | 5.93993e6i | −0.836453 | − | 0.679248i | ||||
\(599\) | 7.49192e6i | 0.853152i | 0.904452 | + | 0.426576i | \(0.140280\pi\) | ||||
−0.904452 | + | 0.426576i | \(0.859720\pi\) | |||||||
\(600\) | 1.87801e6 | + | 966644.i | 0.212970 | + | 0.109620i | ||||
\(601\) | − | 8.77293e6i | − | 0.990737i | −0.868683 | − | 0.495369i | \(-0.835033\pi\) | ||
0.868683 | − | 0.495369i | \(-0.164967\pi\) | |||||||
\(602\) | 750848. | − | 924624.i | 0.0844424 | − | 0.103986i | ||||
\(603\) | 5.14923e6 | + | 5.14923e6i | 0.576699 | + | 0.576699i | ||||
\(604\) | 18969.8 | + | 90465.4i | 0.00211578 | + | 0.0100900i | ||||
\(605\) | 3.89926e6 | − | 3.89926e6i | 0.433105 | − | 0.433105i | ||||
\(606\) | −1.72556e6 | + | 178972.i | −0.190875 | + | 0.0197971i | ||||
\(607\) | −752225. | −0.0828660 | −0.0414330 | − | 0.999141i | \(-0.513192\pi\) | ||||
−0.0414330 | + | 0.999141i | \(0.513192\pi\) | |||||||
\(608\) | −691473. | + | 2.51160e6i | −0.0758606 | + | 0.275544i | ||||
\(609\) | 3.46583e6 | 0.378673 | ||||||||
\(610\) | −6.89035e6 | + | 714652.i | −0.749750 | + | 0.0777625i | ||||
\(611\) | −8.26981e6 | + | 8.26981e6i | −0.896174 | + | 0.896174i | ||||
\(612\) | 375050. | + | 1.78858e6i | 0.0404772 | + | 0.193032i | ||||
\(613\) | 3.13608e6 | + | 3.13608e6i | 0.337082 | + | 0.337082i | 0.855268 | − | 0.518186i | \(-0.173392\pi\) |
−0.518186 | + | 0.855268i | \(0.673392\pi\) | |||||||
\(614\) | 3.92836e6 | − | 4.83754e6i | 0.420523 | − | 0.517849i | ||||
\(615\) | − | 6.86278e6i | − | 0.731665i | ||||||
\(616\) | 9.72933e6 | − | 1.89022e7i | 1.03307 | − | 2.00706i | ||||
\(617\) | 2.22134e6i | 0.234911i | 0.993078 | + | 0.117455i | \(0.0374737\pi\) | ||||
−0.993078 | + | 0.117455i | \(0.962526\pi\) | |||||||
\(618\) | −1.72811e7 | − | 1.40332e7i | −1.82012 | − | 1.47804i | ||||
\(619\) | −1.03308e7 | − | 1.03308e7i | −1.08370 | − | 1.08370i | −0.996162 | − | 0.0875338i | \(-0.972101\pi\) |
−0.0875338 | − | 0.996162i | \(-0.527899\pi\) | |||||||
\(620\) | 4.43248e6 | + | 2.89580e6i | 0.463092 | + | 0.302545i | ||||
\(621\) | −4.64012e6 | + | 4.64012e6i | −0.482837 | + | 0.482837i | ||||
\(622\) | −653697. | − | 6.30264e6i | −0.0677486 | − | 0.653201i | ||||
\(623\) | −3.85097e6 | −0.397511 | ||||||||
\(624\) | −5.00274e6 | − | 1.14043e7i | −0.514335 | − | 1.17248i | ||||
\(625\) | −390625. | −0.0400000 | ||||||||
\(626\) | 1.97790e6 | + | 1.90700e7i | 0.201729 | + | 1.94498i | ||||
\(627\) | −3.66750e6 | + | 3.66750e6i | −0.372564 | + | 0.372564i | ||||
\(628\) | −7.62327e6 | + | 1.16686e7i | −0.771334 | + | 1.18065i | ||||
\(629\) | −1.61329e6 | − | 1.61329e6i | −0.162587 | − | 0.162587i | ||||
\(630\) | 2.20269e6 | + | 1.78871e6i | 0.221106 | + | 0.179551i | ||||
\(631\) | − | 2.50673e6i | − | 0.250631i | −0.992117 | − | 0.125315i | \(-0.960006\pi\) | ||
0.992117 | − | 0.125315i | \(-0.0399942\pi\) | |||||||
\(632\) | −4.77323e6 | + | 1.52923e6i | −0.475356 | + | 0.152293i | ||||
\(633\) | − | 1.21623e7i | − | 1.20644i | ||||||
\(634\) | 6.59620e6 | − | 8.12283e6i | 0.651735 | − | 0.802572i | ||||
\(635\) | −3.28895e6 | − | 3.28895e6i | −0.323685 | − | 0.323685i | ||||
\(636\) | −4.87900e6 | + | 1.02308e6i | −0.478286 | + | 0.100293i | ||||
\(637\) | 8.90587e6 | − | 8.90587e6i | 0.869617 | − | 0.869617i | ||||
\(638\) | 3.39429e6 | − | 352049.i | 0.330139 | − | 0.0342414i | ||||
\(639\) | 2.00163e6 | 0.193924 | ||||||||
\(640\) | 4.62520e6 | + | 286944.i | 0.446355 | + | 0.0276915i | ||||
\(641\) | −473959. | −0.0455612 | −0.0227806 | − | 0.999740i | \(-0.507252\pi\) | ||||
−0.0227806 | + | 0.999740i | \(0.507252\pi\) | |||||||
\(642\) | 2.06288e7 | − | 2.13958e6i | 1.97532 | − | 0.204876i | ||||
\(643\) | −9.27956e6 | + | 9.27956e6i | −0.885115 | + | 0.885115i | −0.994049 | − | 0.108934i | \(-0.965256\pi\) |
0.108934 | + | 0.994049i | \(0.465256\pi\) | |||||||
\(644\) | 1.52247e7 | − | 3.19250e6i | 1.44655 | − | 0.303330i | ||||
\(645\) | 365526. | + | 365526.i | 0.0345955 | + | 0.0345955i | ||||
\(646\) | 867779. | − | 1.06862e6i | 0.0818140 | − | 0.100749i | ||||
\(647\) | 1.14608e7i | 1.07635i | 0.842834 | + | 0.538174i | \(0.180886\pi\) | ||||
−0.842834 | + | 0.538174i | \(0.819114\pi\) | |||||||
\(648\) | −1.26803e7 | + | 4.06247e6i | −1.18629 | + | 0.380061i | ||||
\(649\) | − | 1.27769e7i | − | 1.19073i | ||||||
\(650\) | 1.78786e6 | + | 1.45185e6i | 0.165978 | + | 0.134784i | ||||
\(651\) | 1.66094e7 | + | 1.66094e7i | 1.53604 | + | 1.53604i | ||||
\(652\) | 1.47839e6 | − | 2.26292e6i | 0.136198 | − | 0.208473i | ||||
\(653\) | 7.79263e6 | − | 7.79263e6i | 0.715157 | − | 0.715157i | −0.252453 | − | 0.967609i | \(-0.581237\pi\) |
0.967609 | + | 0.252453i | \(0.0812372\pi\) | |||||||
\(654\) | 1.52166e6 | + | 1.46712e7i | 0.139115 | + | 1.34128i | ||||
\(655\) | −9.36608e6 | −0.853011 | ||||||||
\(656\) | −6.04863e6 | − | 1.37885e7i | −0.548779 | − | 1.25100i | ||||
\(657\) | −8.63162e6 | −0.780152 | ||||||||
\(658\) | −1.99186e6 | − | 1.92046e7i | −0.179347 | − | 1.72918i | ||||
\(659\) | 1.08176e7 | − | 1.08176e7i | 0.970327 | − | 0.970327i | −0.0292456 | − | 0.999572i | \(-0.509310\pi\) |
0.999572 | + | 0.0292456i | \(0.00931048\pi\) | |||||||
\(660\) | 7.72415e6 | + | 5.04630e6i | 0.690225 | + | 0.450934i | ||||
\(661\) | −772828. | − | 772828.i | −0.0687985 | − | 0.0687985i | 0.671870 | − | 0.740669i | \(-0.265491\pi\) |
−0.740669 | + | 0.671870i | \(0.765491\pi\) | |||||||
\(662\) | −1.54291e7 | − | 1.25293e7i | −1.36835 | − | 1.11118i | ||||
\(663\) | 6.58071e6i | 0.581419i | ||||||||
\(664\) | −4.71823e6 | + | 9.16662e6i | −0.415297 | + | 0.806843i | ||||
\(665\) | − | 2.13739e6i | − | 0.187426i | ||||||
\(666\) | −1.58685e6 | + | 1.95411e6i | −0.138628 | + | 0.170712i | ||||
\(667\) | 1.76565e6 | + | 1.76565e6i | 0.153670 | + | 0.153670i | ||||
\(668\) | 4.14006e6 | + | 1.97436e7i | 0.358976 | + | 1.71193i | ||||
\(669\) | 1.52457e7 | − | 1.52457e7i | 1.31699 | − | 1.31699i | ||||
\(670\) | −9.70586e6 | + | 1.00667e6i | −0.835309 | + | 0.0866364i | ||||
\(671\) | −3.02600e7 | −2.59455 | ||||||||
\(672\) | 1.98216e7 | + | 5.45713e6i | 1.69323 | + | 0.466166i | ||||
\(673\) | 2.02477e7 | 1.72321 | 0.861603 | − | 0.507583i | \(-0.169461\pi\) | ||||
0.861603 | + | 0.507583i | \(0.169461\pi\) | |||||||
\(674\) | −1.14986e7 | + | 1.19261e6i | −0.974976 | + | 0.101122i | ||||
\(675\) | 1.13415e6 | − | 1.13415e6i | 0.0958097 | − | 0.0958097i | ||||
\(676\) | −348404. | − | 1.66151e6i | −0.0293235 | − | 0.139841i | ||||
\(677\) | −6.86021e6 | − | 6.86021e6i | −0.575262 | − | 0.575262i | 0.358332 | − | 0.933594i | \(-0.383346\pi\) |
−0.933594 | + | 0.358332i | \(0.883346\pi\) | |||||||
\(678\) | −4.55600e6 | + | 5.61044e6i | −0.380636 | + | 0.468730i | ||||
\(679\) | − | 1.46129e7i | − | 1.21636i | ||||||
\(680\) | −2.17730e6 | − | 1.12070e6i | −0.180570 | − | 0.0929429i | ||||
\(681\) | 3.91381e6i | 0.323394i | ||||||||
\(682\) | 1.79537e7 | + | 1.45795e7i | 1.47807 | + | 1.20027i | ||||
\(683\) | 9.81746e6 | + | 9.81746e6i | 0.805281 | + | 0.805281i | 0.983915 | − | 0.178635i | \(-0.0571681\pi\) |
−0.178635 | + | 0.983915i | \(0.557168\pi\) | |||||||
\(684\) | −1.27151e6 | − | 830697.i | −0.103915 | − | 0.0678895i | ||||
\(685\) | −3.32488e6 | + | 3.32488e6i | −0.270738 | + | 0.270738i | ||||
\(686\) | 280411. | + | 2.70359e6i | 0.0227501 | + | 0.219346i | ||||
\(687\) | −1.54334e6 | −0.124758 | ||||||||
\(688\) | 1.05657e6 | + | 412243.i | 0.0850994 | + | 0.0332033i | ||||
\(689\) | −5.43573e6 | −0.436225 | ||||||||
\(690\) | 696485. | + | 6.71519e6i | 0.0556915 | + | 0.536952i | ||||
\(691\) | −6.64037e6 | + | 6.64037e6i | −0.529051 | + | 0.529051i | −0.920289 | − | 0.391238i | \(-0.872047\pi\) |
0.391238 | + | 0.920289i | \(0.372047\pi\) | |||||||
\(692\) | −1.40630e6 | + | 2.15256e6i | −0.111638 | + | 0.170880i | ||||
\(693\) | 8.76440e6 | + | 8.76440e6i | 0.693249 | + | 0.693249i | ||||
\(694\) | 8.86364e6 | + | 7.19778e6i | 0.698575 | + | 0.567283i | ||||
\(695\) | − | 9.24951e6i | − | 0.726368i | ||||||
\(696\) | 1.00687e6 | + | 3.14277e6i | 0.0787863 | + | 0.245917i | ||||
\(697\) | 7.95650e6i | 0.620355i | ||||||||
\(698\) | −8.93618e6 | + | 1.10044e7i | −0.694246 | + | 0.854922i | ||||
\(699\) | 7.21864e6 | + | 7.21864e6i | 0.558808 | + | 0.558808i | ||||
\(700\) | −3.72125e6 | + | 780314.i | −0.287041 | + | 0.0601900i | ||||
\(701\) | −1.66016e7 | + | 1.66016e7i | −1.27601 | + | 1.27601i | −0.333134 | + | 0.942879i | \(0.608106\pi\) |
−0.942879 | + | 0.333134i | \(0.891894\pi\) | |||||||
\(702\) | −9.40621e6 | + | 975592.i | −0.720397 | + | 0.0747180i | ||||
\(703\) | 1.89618e6 | 0.144707 | ||||||||
\(704\) | 1.99668e7 | + | 3.33107e6i | 1.51837 | + | 0.253310i | ||||
\(705\) | 8.37949e6 | 0.634957 | ||||||||
\(706\) | −4.70481e6 | + | 487973.i | −0.355247 | + | 0.0368454i | ||||
\(707\) | 2.20821e6 | − | 2.20821e6i | 0.166147 | − | 0.166147i | ||||
\(708\) | 1.20931e7 | − | 2.53582e6i | 0.906680 | − | 0.190123i | ||||
\(709\) | 1.53831e7 | + | 1.53831e7i | 1.14929 | + | 1.14929i | 0.986693 | + | 0.162597i | \(0.0519869\pi\) |
0.162597 | + | 0.986693i | \(0.448013\pi\) | |||||||
\(710\) | −1.69079e6 | + | 2.08211e6i | −0.125876 | + | 0.155009i | ||||
\(711\) | − | 2.92226e6i | − | 0.216793i | ||||||
\(712\) | −1.11876e6 | − | 3.49200e6i | −0.0827058 | − | 0.258151i | ||||
\(713\) | 1.69232e7i | 1.24669i | ||||||||
\(714\) | −8.43357e6 | − | 6.84854e6i | −0.619107 | − | 0.502750i | ||||
\(715\) | 7.11383e6 | + | 7.11383e6i | 0.520401 | + | 0.520401i | ||||
\(716\) | −123184. | + | 188552.i | −0.00897989 | + | 0.0137451i | ||||
\(717\) | 1.59613e7 | − | 1.59613e7i | 1.15950 | − | 1.15950i | ||||
\(718\) | 468252. | + | 4.51467e6i | 0.0338976 | + | 0.326825i | ||||
\(719\) | 1.07413e7 | 0.774879 | 0.387439 | − | 0.921895i | \(-0.373360\pi\) | ||||
0.387439 | + | 0.921895i | \(0.373360\pi\) | |||||||
\(720\) | −982065. | + | 2.51701e6i | −0.0706007 | + | 0.180948i | ||||
\(721\) | 4.00732e7 | 2.87088 | ||||||||
\(722\) | −1.32699e6 | − | 1.27942e7i | −0.0947381 | − | 0.913421i | ||||
\(723\) | −141701. | + | 141701.i | −0.0100815 | + | 0.0100815i | ||||
\(724\) | 7.48740e6 | + | 4.89162e6i | 0.530865 | + | 0.346822i | ||||
\(725\) | −431562. | − | 431562.i | −0.0304929 | − | 0.0304929i | ||||
\(726\) | 1.80833e7 | + | 1.46847e7i | 1.27332 | + | 1.03401i | ||||
\(727\) | 222223.i | 0.0155939i | 0.999970 | + | 0.00779693i | \(0.00248187\pi\) | ||||
−0.999970 | + | 0.00779693i | \(0.997518\pi\) | |||||||
\(728\) | 1.99321e7 | + | 1.02594e7i | 1.39388 | + | 0.717455i | ||||
\(729\) | 3.87911e6i | 0.270342i | ||||||||
\(730\) | 7.29119e6 | − | 8.97867e6i | 0.506397 | − | 0.623598i | ||||
\(731\) | −423780. | − | 423780.i | −0.0293324 | − | 0.0293324i | ||||
\(732\) | −6.00568e6 | − | 2.86406e7i | −0.414271 | − | 1.97562i | ||||
\(733\) | −1.11978e7 | + | 1.11978e7i | −0.769791 | + | 0.769791i | −0.978070 | − | 0.208279i | \(-0.933214\pi\) |
0.208279 | + | 0.978070i | \(0.433214\pi\) | |||||||
\(734\) | 893676. | − | 92690.2i | 0.0612266 | − | 0.00635029i | ||||
\(735\) | −9.02398e6 | −0.616141 | ||||||||
\(736\) | 7.31790e6 | + | 1.28781e7i | 0.497957 | + | 0.876310i | ||||
\(737\) | −4.26247e7 | −2.89063 | ||||||||
\(738\) | 8.73174e6 | − | 905638.i | 0.590147 | − | 0.0612088i | ||||
\(739\) | −5.74562e6 | + | 5.74562e6i | −0.387013 | + | 0.387013i | −0.873621 | − | 0.486607i | \(-0.838234\pi\) |
0.486607 | + | 0.873621i | \(0.338234\pi\) | |||||||
\(740\) | −692255. | − | 3.30130e6i | −0.0464715 | − | 0.221618i | ||||
\(741\) | −3.86732e6 | − | 3.86732e6i | −0.258741 | − | 0.258741i | ||||
\(742\) | 5.65696e6 | − | 6.96621e6i | 0.377202 | − | 0.464501i | ||||
\(743\) | − | 1.03255e7i | − | 0.686179i | −0.939303 | − | 0.343090i | \(-0.888527\pi\) | ||
0.939303 | − | 0.343090i | \(-0.111473\pi\) | |||||||
\(744\) | −1.02359e7 | + | 1.98865e7i | −0.677947 | + | 1.31712i | ||||
\(745\) | 7.94523e6i | 0.524464i | ||||||||
\(746\) | −4.46705e6 | − | 3.62750e6i | −0.293883 | − | 0.238649i | ||||
\(747\) | −4.25029e6 | − | 4.25029e6i | −0.278687 | − | 0.278687i | ||||
\(748\) | −8.95514e6 | − | 5.85052e6i | −0.585219 | − | 0.382332i | ||||
\(749\) | −2.63989e7 | + | 2.63989e7i | −1.71942 | + | 1.71942i | ||||
\(750\) | −170236. | − | 1.64134e6i | −0.0110509 | − | 0.106548i | ||||
\(751\) | −1.14757e7 | −0.742468 | −0.371234 | − | 0.928539i | \(-0.621065\pi\) | ||||
−0.371234 | + | 0.928539i | \(0.621065\pi\) | |||||||
\(752\) | 1.68358e7 | − | 7.38540e6i | 1.08565 | − | 0.476244i | ||||
\(753\) | −7.66875e6 | −0.492875 | ||||||||
\(754\) | 371230. | + | 3.57923e6i | 0.0237801 | + | 0.229277i | ||||
\(755\) | 51062.5 | − | 51062.5i | 0.00326013 | − | 0.00326013i | ||||
\(756\) | 8.53875e6 | − | 1.30699e7i | 0.543363 | − | 0.831702i | ||||
\(757\) | −9.78035e6 | − | 9.78035e6i | −0.620318 | − | 0.620318i | 0.325294 | − | 0.945613i | \(-0.394537\pi\) |
−0.945613 | + | 0.325294i | \(0.894537\pi\) | |||||||
\(758\) | 4.55429e6 | + | 3.69834e6i | 0.287904 | + | 0.233794i | ||||
\(759\) | 2.94908e7i | 1.85815i | ||||||||
\(760\) | 1.93815e6 | − | 620940.i | 0.121718 | − | 0.0389956i | ||||
\(761\) | 2.22081e6i | 0.139011i | 0.997582 | + | 0.0695054i | \(0.0221421\pi\) | ||||
−0.997582 | + | 0.0695054i | \(0.977858\pi\) | |||||||
\(762\) | 1.23862e7 | − | 1.52529e7i | 0.772773 | − | 0.951624i | ||||
\(763\) | −1.87748e7 | − | 1.87748e7i | −1.16752 | − | 1.16752i | ||||
\(764\) | −2.09740e7 | + | 4.39806e6i | −1.30001 | + | 0.272601i | ||||
\(765\) | 1.00955e6 | − | 1.00955e6i | 0.0623698 | − | 0.0623698i | ||||
\(766\) | 1.99143e7 | − | 2.06547e6i | 1.22629 | − | 0.127188i | ||||
\(767\) | 1.34730e7 | 0.826944 | ||||||||
\(768\) | 809996. | + | 1.95593e7i | 0.0495541 | + | 1.19660i | ||||
\(769\) | −1.41145e7 | −0.860697 | −0.430349 | − | 0.902663i | \(-0.641609\pi\) | ||||
−0.430349 | + | 0.902663i | \(0.641609\pi\) | |||||||
\(770\) | −1.65201e7 | + | 1.71343e6i | −1.00412 | + | 0.104145i | ||||
\(771\) | 4.69392e6 | − | 4.69392e6i | 0.284380 | − | 0.284380i | ||||
\(772\) | −9.19128e6 | + | 1.92733e6i | −0.555051 | + | 0.116389i | ||||
\(773\) | −1.95334e7 | − | 1.95334e7i | −1.17579 | − | 1.17579i | −0.980806 | − | 0.194985i | \(-0.937534\pi\) |
−0.194985 | − | 0.980806i | \(-0.562466\pi\) | |||||||
\(774\) | −416835. | + | 513307.i | −0.0250099 | + | 0.0307982i | ||||
\(775\) | − | 4.13639e6i | − | 0.247381i | ||||||
\(776\) | 1.32508e7 | − | 4.24524e6i | 0.789927 | − | 0.253074i | ||||
\(777\) | − | 1.49647e7i | − | 0.889233i | ||||||
\(778\) | 2.90425e6 | + | 2.35841e6i | 0.172022 | + | 0.139692i | ||||
\(779\) | −4.67584e6 | − | 4.67584e6i | −0.276068 | − | 0.276068i | ||||
\(780\) | −5.32124e6 | + | 8.14499e6i | −0.313167 | + | 0.479352i | ||||
\(781\) | −8.28463e6 | + | 8.28463e6i | −0.486011 | + | 0.486011i | ||||
\(782\) | −807483. | − | 7.78538e6i | −0.0472190 | − | 0.455264i | ||||
\(783\) | 2.50601e6 | 0.146076 | ||||||||
\(784\) | −1.81307e7 | + | 7.95344e6i | −1.05348 | + | 0.462131i | ||||
\(785\) | 1.08891e7 | 0.630695 | ||||||||
\(786\) | −4.08178e6 | − | 3.93546e7i | −0.235664 | − | 2.27216i | ||||
\(787\) | 1.56745e7 | − | 1.56745e7i | 0.902105 | − | 0.902105i | −0.0935131 | − | 0.995618i | \(-0.529810\pi\) |
0.995618 | + | 0.0935131i | \(0.0298097\pi\) | |||||||
\(788\) | −1.83142e7 | − | 1.19649e7i | −1.05068 | − | 0.686427i | ||||
\(789\) | −2.10152e7 | − | 2.10152e7i | −1.20182 | − | 1.20182i | ||||
\(790\) | 3.03976e6 | + | 2.46846e6i | 0.173289 | + | 0.140721i | ||||
\(791\) | − | 1.30101e7i | − | 0.739330i | ||||||
\(792\) | −5.40126e6 | + | 1.04936e7i | −0.305972 | + | 0.594446i | ||||
\(793\) | − | 3.19087e7i | − | 1.80188i | ||||||
\(794\) | −6.47028e6 | + | 7.96776e6i | −0.364226 | + | 0.448523i | ||||
\(795\) | 2.75391e6 | + | 2.75391e6i | 0.154537 | + | 0.154537i | ||||
\(796\) | 4.05433e6 | + | 1.93347e7i | 0.226796 | + | 1.08157i | ||||
\(797\) | 9.69347e6 | − | 9.69347e6i | 0.540547 | − | 0.540547i | −0.383142 | − | 0.923689i | \(-0.625158\pi\) |
0.923689 | + | 0.383142i | \(0.125158\pi\) | |||||||
\(798\) | 8.98091e6 | − | 931481.i | 0.499244 | − | 0.0517806i | ||||
\(799\) | −9.71492e6 | −0.538359 | ||||||||
\(800\) | −1.78865e6 | − | 3.14769e6i | −0.0988100 | − | 0.173887i | ||||
\(801\) | 2.13787e6 | 0.117734 | ||||||||
\(802\) | 6.54613e6 | − | 678951.i | 0.359376 | − | 0.0372737i | ||||
\(803\) | 3.57258e7 | − | 3.57258e7i | 1.95521 | − | 1.95521i | ||||
\(804\) | −8.45970e6 | − | 4.03436e7i | −0.461546 | − | 2.20107i | ||||
\(805\) | −8.59347e6 | − | 8.59347e6i | −0.467390 | − | 0.467390i | ||||
\(806\) | −1.53738e7 | + | 1.89319e7i | −0.833574 | + | 1.02650i | ||||
\(807\) | − | 3.75485e7i | − | 2.02959i | ||||||
\(808\) | 2.64389e6 | + | 1.36086e6i | 0.142467 | + | 0.0733306i | ||||
\(809\) | − | 3.45363e7i | − | 1.85526i | −0.373502 | − | 0.927629i | \(-0.621843\pi\) | ||
0.373502 | − | 0.927629i | \(-0.378157\pi\) | |||||||
\(810\) | 8.07525e6 | + | 6.55756e6i | 0.432457 | + | 0.351180i | ||||
\(811\) | 5.52703e6 | + | 5.52703e6i | 0.295080 | + | 0.295080i | 0.839083 | − | 0.544003i | \(-0.183092\pi\) |
−0.544003 | + | 0.839083i | \(0.683092\pi\) | |||||||
\(812\) | −4.97333e6 | − | 3.24914e6i | −0.264702 | − | 0.172933i | ||||
\(813\) | −1.57414e7 | + | 1.57414e7i | −0.835251 | + | 0.835251i | ||||
\(814\) | −1.52007e6 | − | 1.46558e7i | −0.0804086 | − | 0.775263i | ||||
\(815\) | −2.11175e6 | −0.111365 | ||||||||
\(816\) | 3.76009e6 | − | 9.63703e6i | 0.197685 | − | 0.506662i | ||||
\(817\) | 498090. | 0.0261067 | ||||||||
\(818\) | −1.36279e6 | − | 1.31394e7i | −0.0712109 | − | 0.686583i | ||||
\(819\) | −9.24192e6 | + | 9.24192e6i | −0.481451 | + | 0.481451i | ||||
\(820\) | −6.43372e6 | + | 9.84781e6i | −0.334139 | + | 0.511452i | ||||
\(821\) | −1.00138e7 | − | 1.00138e7i | −0.518493 | − | 0.518493i | 0.398622 | − | 0.917115i | \(-0.369488\pi\) |
−0.917115 | + | 0.398622i | \(0.869488\pi\) | |||||||
\(822\) | −1.54195e7 | − | 1.25215e7i | −0.795961 | − | 0.646366i | ||||
\(823\) | 8.91190e6i | 0.458639i | 0.973351 | + | 0.229319i | \(0.0736500\pi\) | ||||
−0.973351 | + | 0.229319i | \(0.926350\pi\) | |||||||
\(824\) | 1.16418e7 | + | 3.63378e7i | 0.597313 | + | 1.86441i | ||||
\(825\) | − | 7.20817e6i | − | 0.368715i | ||||||
\(826\) | −1.40213e7 | + | 1.72664e7i | −0.715055 | + | 0.880547i | ||||
\(827\) | 1.71368e7 | + | 1.71368e7i | 0.871296 | + | 0.871296i | 0.992614 | − | 0.121317i | \(-0.0387119\pi\) |
−0.121317 | + | 0.992614i | \(0.538712\pi\) | |||||||
\(828\) | −8.45204e6 | + | 1.77232e6i | −0.428436 | + | 0.0898394i | ||||
\(829\) | −7.26943e6 | + | 7.26943e6i | −0.367379 | + | 0.367379i | −0.866520 | − | 0.499142i | \(-0.833649\pi\) |
0.499142 | + | 0.866520i | \(0.333649\pi\) | |||||||
\(830\) | 8.01143e6 | − | 830929.i | 0.403659 | − | 0.0418667i | ||||
\(831\) | −1.40678e7 | −0.706682 | ||||||||
\(832\) | −3.51256e6 | + | 2.10546e7i | −0.175920 | + | 1.05448i | ||||
\(833\) | 1.04621e7 | 0.522405 | ||||||||
\(834\) | 3.88648e7 | − | 4.03097e6i | 1.93482 | − | 0.200676i | ||||
\(835\) | 1.11441e7 | − | 1.11441e7i | 0.553132 | − | 0.553132i | ||||
\(836\) | 8.70092e6 | − | 1.82451e6i | 0.430576 | − | 0.0902880i | ||||
\(837\) | 1.20096e7 | + | 1.20096e7i | 0.592538 | + | 0.592538i | ||||
\(838\) | −2.98390e6 | + | 3.67450e6i | −0.146783 | + | 0.180754i | ||||
\(839\) | 2.46342e7i | 1.20819i | 0.796914 | + | 0.604093i | \(0.206464\pi\) | ||||
−0.796914 | + | 0.604093i | \(0.793536\pi\) | |||||||
\(840\) | −4.90048e6 | − | 1.52960e7i | −0.239629 | − | 0.747960i | ||||
\(841\) | 1.95576e7i | 0.953509i | ||||||||
\(842\) | 2.87865e6 | + | 2.33763e6i | 0.139929 | + | 0.113631i | ||||
\(843\) | −1.52245e6 | − | 1.52245e6i | −0.0737859 | − | 0.0737859i | ||||
\(844\) | −1.14019e7 | + | 1.74524e7i | −0.550960 | + | 0.843331i | ||||
\(845\) | −937824. | + | 937824.i | −0.0451835 | + | 0.0451835i | ||||
\(846\) | 1.10579e6 | + | 1.06615e7i | 0.0531185 | + | 0.512144i | ||||
\(847\) | −4.19334e7 | −2.00841 | ||||||||
\(848\) | 7.96029e6 | + | 3.10588e6i | 0.380136 | + | 0.148318i | ||||
\(849\) | −4.46222e6 | −0.212462 | ||||||||
\(850\) | 197366. | + | 1.90291e6i | 0.00936970 | + | 0.0903383i | ||||
\(851\) | 7.62369e6 | − | 7.62369e6i | 0.360862 | − | 0.360862i | ||||
\(852\) | −9.48551e6 | − | 6.19702e6i | −0.447674 | − | 0.292472i | ||||
\(853\) | 2.29987e7 | + | 2.29987e7i | 1.08226 | + | 1.08226i | 0.996299 | + | 0.0859603i | \(0.0273958\pi\) |
0.0859603 | + | 0.996299i | \(0.472604\pi\) | |||||||
\(854\) | 4.08928e7 | + | 3.32073e7i | 1.91868 | + | 1.55808i | ||||
\(855\) | 1.18657e6i | 0.0555111i | ||||||||
\(856\) | −3.16074e7 | − | 1.62689e7i | −1.47436 | − | 0.758881i | ||||
\(857\) | 1.70677e7i | 0.793823i | 0.917857 | + | 0.396912i | \(0.129918\pi\) | ||||
−0.917857 | + | 0.396912i | \(0.870082\pi\) | |||||||
\(858\) | −2.67908e7 | + | 3.29913e7i | −1.24242 | + | 1.52996i | ||||
\(859\) | −1.32645e7 | − | 1.32645e7i | −0.613351 | − | 0.613351i | 0.330467 | − | 0.943818i | \(-0.392794\pi\) |
−0.943818 | + | 0.330467i | \(0.892794\pi\) | |||||||
\(860\) | −181842. | − | 867189.i | −0.00838394 | − | 0.0399823i | ||||
\(861\) | −3.69019e7 | + | 3.69019e7i | −1.69645 | + | 1.69645i | ||||
\(862\) | 1.39376e7 | − | 1.44558e6i | 0.638881 | − | 0.0662634i | ||||
\(863\) | 1.61706e7 | 0.739094 | 0.369547 | − | 0.929212i | \(-0.379513\pi\) | ||||
0.369547 | + | 0.929212i | \(0.379513\pi\) | |||||||
\(864\) | 1.43322e7 | + | 3.94584e6i | 0.653175 | + | 0.179827i | ||||
\(865\) | 2.00877e6 | 0.0912831 | ||||||||
\(866\) | −2.22206e7 | + | 2.30467e6i | −1.00684 | + | 0.104427i | ||||
\(867\) | 1.48784e7 | − | 1.48784e7i | 0.672215 | − | 0.672215i | ||||
\(868\) | −8.26287e6 | − | 3.94049e7i | −0.372247 | − | 1.77521i | ||||
\(869\) | 1.20951e7 | + | 1.20951e7i | 0.543324 | + | 0.543324i | ||||
\(870\) | 1.62527e6 | − | 2.00142e6i | 0.0727994 | − | 0.0896481i | ||||
\(871\) | − | 4.49471e7i | − | 2.00750i | ||||||
\(872\) | 1.15704e7 | − | 2.24791e7i | 0.515297 | − | 1.00112i | ||||
\(873\) | 8.11238e6i | 0.360257i | ||||||||
\(874\) | 5.04981e6 | + | 4.10074e6i | 0.223613 | + | 0.181586i | ||||
\(875\) | 2.10043e6 | + | 2.10043e6i | 0.0927444 | + | 0.0927444i | ||||
\(876\) | 4.09043e7 | + | 2.67234e7i | 1.80098 | + | 1.17660i | ||||
\(877\) | 1.26350e7 | − | 1.26350e7i | 0.554722 | − | 0.554722i | −0.373078 | − | 0.927800i | \(-0.621698\pi\) |
0.927800 | + | 0.373078i | \(0.121698\pi\) | |||||||
\(878\) | 1.50342e6 | + | 1.44953e7i | 0.0658179 | + | 0.634586i | ||||
\(879\) | 4.49245e6 | 0.196115 | ||||||||
\(880\) | −6.35304e6 | − | 1.44825e7i | −0.276551 | − | 0.630428i | ||||
\(881\) | 7.72392e6 | 0.335273 | 0.167636 | − | 0.985849i | \(-0.446387\pi\) | ||||
0.167636 | + | 0.985849i | \(0.446387\pi\) | |||||||
\(882\) | −1.19084e6 | − | 1.14815e7i | −0.0515443 | − | 0.496967i | ||||
\(883\) | −2.43397e7 | + | 2.43397e7i | −1.05054 | + | 1.05054i | −0.0518872 | + | 0.998653i | \(0.516524\pi\) |
−0.998653 | + | 0.0518872i | \(0.983476\pi\) | |||||||
\(884\) | 6.16928e6 | − | 9.44305e6i | 0.265524 | − | 0.406426i | ||||
\(885\) | −6.82584e6 | − | 6.82584e6i | −0.292953 | − | 0.292953i | ||||
\(886\) | 8.47830e6 | + | 6.88487e6i | 0.362848 | + | 0.294653i | ||||
\(887\) | − | 8.25403e6i | − | 0.352255i | −0.984367 | − | 0.176128i | \(-0.943643\pi\) | ||
0.984367 | − | 0.176128i | \(-0.0563571\pi\) | |||||||
\(888\) | 1.35698e7 | − | 4.34745e6i | 0.577485 | − | 0.185013i | ||||
\(889\) | 3.53700e7i | 1.50100i | ||||||||
\(890\) | −1.80588e6 | + | 2.22383e6i | −0.0764211 | + | 0.0941080i | ||||
\(891\) | 3.21311e7 | + | 3.21311e7i | 1.35591 | + | 1.35591i | ||||
\(892\) | −3.61695e7 | + | 7.58443e6i | −1.52205 | + | 0.319162i | ||||
\(893\) | 5.70921e6 | − | 5.70921e6i | 0.239578 | − | 0.239578i | ||||
\(894\) | −3.33844e7 | + | 3.46256e6i | −1.39701 | + | 0.144895i | ||||
\(895\) | 175957. | 0.00734258 | ||||||||
\(896\) | −2.33272e7 | − | 2.64131e7i | −0.970719 | − | 1.09913i | ||||
\(897\) | −3.10975e7 | −1.29046 | ||||||||
\(898\) | 1.88332e7 | − | 1.95334e6i | 0.779350 | − | 0.0808325i | ||||
\(899\) | 4.56988e6 | − | 4.56988e6i | 0.188584 | − | 0.188584i | ||||
\(900\) | 2.06586e6 | − | 433193.i | 0.0850148 | − | 0.0178269i | ||||
\(901\) | −3.19280e6 | − | 3.19280e6i | −0.131027 | − | 0.131027i | ||||
\(902\) | −3.23918e7 | + | 3.98885e7i | −1.32562 | + | 1.63242i | ||||
\(903\) | − | 3.93094e6i | − | 0.160427i | ||||||
\(904\) | 1.17973e7 | − | 3.77960e6i | 0.480135 | − | 0.153824i | ||||
\(905\) | − | 6.98724e6i | − | 0.283585i | ||||||
\(906\) | 236809. | + | 192302.i | 0.00958466 | + | 0.00778330i | ||||
\(907\) | 1.41287e7 | + | 1.41287e7i | 0.570275 | + | 0.570275i | 0.932205 | − | 0.361930i | \(-0.117882\pi\) |
−0.361930 | + | 0.932205i | \(0.617882\pi\) | |||||||
\(908\) | 3.66911e6 | − | 5.61615e6i | 0.147688 | − | 0.226060i | ||||
\(909\) | −1.22589e6 | + | 1.22589e6i | −0.0492089 | + | 0.0492089i | ||||
\(910\) | −1.80679e6 | − | 1.74202e7i | −0.0723276 | − | 0.697349i | ||||
\(911\) | 2.75193e6 | 0.109861 | 0.0549303 | − | 0.998490i | \(-0.482506\pi\) | ||||
0.0549303 | + | 0.998490i | \(0.482506\pi\) | |||||||
\(912\) | 3.45373e6 | + | 7.87316e6i | 0.137500 | + | 0.313445i | ||||
\(913\) | 3.51834e7 | 1.39689 | ||||||||
\(914\) | −4.64862e6 | − | 4.48199e7i | −0.184060 | − | 1.77462i | ||||
\(915\) | −1.61659e7 | + | 1.61659e7i | −0.638334 | + | 0.638334i | ||||
\(916\) | 2.21463e6 | + | 1.44685e6i | 0.0872090 | + | 0.0569749i | ||||
\(917\) | 5.03623e7 | + | 5.03623e7i | 1.97780 | + | 1.97780i | ||||
\(918\) | −6.09798e6 | − | 4.95191e6i | −0.238825 | − | 0.193939i | ||||
\(919\) | − | 1.39375e7i | − | 0.544373i | −0.962244 | − | 0.272187i | \(-0.912253\pi\) | ||
0.962244 | − | 0.272187i | \(-0.0877468\pi\) | |||||||
\(920\) | 5.29592e6 | − | 1.02890e7i | 0.206287 | − | 0.400776i | ||||
\(921\) | − | 2.05663e7i | − | 0.798926i | ||||||
\(922\) | 1.06573e7 | − | 1.31238e7i | 0.412877 | − | 0.508433i | ||||
\(923\) | −8.73601e6 | − | 8.73601e6i | −0.337527 | − | 0.337527i | ||||
\(924\) | −1.43991e7 | − | 6.86679e7i | −0.554824 | − | 2.64590i | ||||
\(925\) | −1.86339e6 | + | 1.86339e6i | −0.0716061 | + | 0.0716061i | ||||
\(926\) | 7.50600e6 | − | 778506.i | 0.287661 | − | 0.0298356i | ||||
\(927\) | −2.22467e7 | −0.850289 | ||||||||
\(928\) | 1.50146e6 | − | 5.45366e6i | 0.0572326 | − | 0.207883i | ||||
\(929\) | 3.63709e7 | 1.38266 | 0.691330 | − | 0.722539i | \(-0.257025\pi\) | ||||
0.691330 | + | 0.722539i | \(0.257025\pi\) | |||||||
\(930\) | 1.73804e7 | − | 1.80265e6i | 0.658948 | − | 0.0683447i | ||||
\(931\) | −6.14833e6 | + | 6.14833e6i | −0.232479 | + | 0.232479i | ||||
\(932\) | −3.59113e6 | − | 1.71258e7i | −0.135423 | − | 0.645818i | ||||
\(933\) | −1.47871e7 | − | 1.47871e7i | −0.556132 | − | 0.556132i | ||||
\(934\) | −9.57717e6 | + | 1.17937e7i | −0.359228 | + | 0.442368i | ||||
\(935\) | 8.35693e6i | 0.312621i | ||||||||
\(936\) | −1.10653e7 | − | 5.69554e6i | −0.412834 | − | 0.212493i | ||||
\(937\) | 3.20456e7i | 1.19239i | 0.802839 | + | 0.596197i | \(0.203322\pi\) | ||||
−0.802839 | + | 0.596197i | \(0.796678\pi\) | |||||||
\(938\) | 5.76023e7 | + | 4.67764e7i | 2.13763 | + | 1.73588i | ||||
\(939\) | 4.47414e7 | + | 4.47414e7i | 1.65595 | + | 1.65595i | ||||
\(940\) | −1.20242e7 | − | 7.85559e6i | −0.443851 | − | 0.289974i | ||||
\(941\) | 3.10580e7 | − | 3.10580e7i | 1.14340 | − | 1.14340i | 0.155578 | − | 0.987824i | \(-0.450276\pi\) |
0.987824 | − | 0.155578i | \(-0.0497242\pi\) | |||||||
\(942\) | 4.74553e6 | + | 4.57542e7i | 0.174244 | + | 1.67998i | ||||
\(943\) | −3.75989e7 | −1.37688 | ||||||||
\(944\) | −1.97304e7 | − | 7.69822e6i | −0.720618 | − | 0.281164i | ||||
\(945\) | −1.21968e7 | −0.444291 | ||||||||
\(946\) | −399293. | − | 3.84980e6i | −0.0145066 | − | 0.139866i | ||||
\(947\) | 1.18742e7 | − | 1.18742e7i | 0.430257 | − | 0.430257i | −0.458459 | − | 0.888716i | \(-0.651598\pi\) |
0.888716 | + | 0.458459i | \(0.151598\pi\) | |||||||
\(948\) | −9.04728e6 | + | 1.38483e7i | −0.326962 | + | 0.500466i | ||||
\(949\) | 3.76723e7 | + | 3.76723e7i | 1.35786 | + | 1.35786i | ||||
\(950\) | −1.23428e6 | − | 1.00231e6i | −0.0443717 | − | 0.0360323i | ||||
\(951\) | − | 3.45334e7i | − | 1.23819i | ||||||
\(952\) | 5.68146e6 | + | 1.77337e7i | 0.203174 | + | 0.634171i | ||||
\(953\) | − | 6.35853e6i | − | 0.226790i | −0.993550 | − | 0.113395i | \(-0.963827\pi\) | ||
0.993550 | − | 0.113395i | \(-0.0361726\pi\) | |||||||
\(954\) | −3.14047e6 | + | 3.86731e6i | −0.111718 | + | 0.137574i | ||||
\(955\) | 1.18386e7 | + | 1.18386e7i | 0.420040 | + | 0.420040i | ||||
\(956\) | −3.78672e7 | + | 7.94043e6i | −1.34004 | + | 0.280996i | ||||
\(957\) | 7.96359e6 | − | 7.96359e6i | 0.281079 | − | 0.281079i | ||||
\(958\) | −3.69156e7 | + | 3.82881e6i | −1.29956 | + | 0.134788i | ||||
\(959\) | 3.57564e7 | 1.25547 | ||||||||
\(960\) | 1.24465e7 | − | 8.88737e6i | 0.435883 | − | 0.311240i | ||||
\(961\) | 1.51717e7 | 0.529938 | ||||||||
\(962\) | 1.54543e7 | − | 1.60289e6i | 0.538409 | − | 0.0558426i | ||||
\(963\) | 1.46554e7 | − | 1.46554e7i | 0.509251 | − | 0.509251i | ||||
\(964\) | 336177. | − | 70493.4i | 0.0116513 | − | 0.00244318i | ||||
\(965\) | 5.18794e6 | + | 5.18794e6i | 0.179340 | + | 0.179340i | ||||
\(966\) | 3.23632e7 | − | 3.98533e7i | 1.11586 | − | 1.37411i | ||||
\(967\) | 4.24344e7i | 1.45933i | 0.683807 | + | 0.729663i | \(0.260323\pi\) | ||||
−0.683807 | + | 0.729663i | \(0.739677\pi\) | |||||||
\(968\) | −1.21822e7 | − | 3.80246e7i | −0.417867 | − | 1.30430i | ||||
\(969\) | − | 4.54311e6i | − | 0.155433i | ||||||
\(970\) | −8.43855e6 | − | 6.85259e6i | −0.287964 | − | 0.233843i | ||||
\(971\) | 8.42543e6 | + | 8.42543e6i | 0.286777 | + | 0.286777i | 0.835804 | − | 0.549027i | \(-0.185002\pi\) |
−0.549027 | + | 0.835804i | \(0.685002\pi\) | |||||||
\(972\) | −1.31201e7 | + | 2.00824e7i | −0.445423 | + | 0.681790i | ||||
\(973\) | −4.97355e7 | + | 4.97355e7i | −1.68416 | + | 1.68416i | ||||
\(974\) | −2.06896e6 | − | 1.99480e7i | −0.0698805 | − | 0.673755i | ||||
\(975\) | 7.60090e6 | 0.256067 | ||||||||
\(976\) | −1.82320e7 | + | 4.67282e7i | −0.612647 | + | 1.57020i | ||||
\(977\) | 112748. | 0.00377897 | 0.00188949 | − | 0.999998i | \(-0.499399\pi\) | ||||
0.00188949 | + | 0.999998i | \(0.499399\pi\) | |||||||
\(978\) | −920310. | − | 8.87320e6i | −0.0307671 | − | 0.296642i | ||||
\(979\) | −8.84853e6 | + | 8.84853e6i | −0.295063 | + | 0.295063i | ||||
\(980\) | 1.29490e7 | + | 8.45980e6i | 0.430698 | + | 0.281381i | ||||
\(981\) | 1.04229e7 | + | 1.04229e7i | 0.345792 | + | 0.345792i | ||||
\(982\) | −1.87610e7 | − | 1.52350e7i | −0.620837 | − | 0.504155i | ||||
\(983\) | 3.41003e7i | 1.12557i | 0.826602 | + | 0.562787i | \(0.190271\pi\) | ||||
−0.826602 | + | 0.562787i | \(0.809729\pi\) | |||||||
\(984\) | −4.41826e7 | − | 2.27416e7i | −1.45467 | − | 0.748744i | ||||
\(985\) | 1.70908e7i | 0.561270i | ||||||||
\(986\) | −1.88429e6 | + | 2.32039e6i | −0.0617241 | + | 0.0760096i | ||||
\(987\) | −4.50573e7 | − | 4.50573e7i | −1.47222 | − | 1.47222i | ||||
\(988\) | 1.92391e6 | + | 9.17498e6i | 0.0627037 | + | 0.299029i | ||||
\(989\) | 2.00260e6 | − | 2.00260e6i | 0.0651033 | − | 0.0651033i | ||||
\(990\) | 9.17119e6 | − | 951217.i | 0.297398 | − | 0.0308455i | ||||
\(991\) | 1.36375e7 | 0.441113 | 0.220556 | − | 0.975374i | \(-0.429213\pi\) | ||||
0.220556 | + | 0.975374i | \(0.429213\pi\) | |||||||
\(992\) | 3.33313e7 | − | 1.89403e7i | 1.07541 | − | 0.611094i | ||||
\(993\) | −6.55954e7 | −2.11106 | ||||||||
\(994\) | 2.02873e7 | − | 2.10415e6i | 0.651265 | − | 0.0675478i | ||||
\(995\) | 1.09133e7 | − | 1.09133e7i | 0.349461 | − | 0.349461i | ||||
\(996\) | 6.98283e6 | + | 3.33005e7i | 0.223040 | + | 1.06366i | ||||
\(997\) | −1.24966e7 | − | 1.24966e7i | −0.398158 | − | 0.398158i | 0.479425 | − | 0.877583i | \(-0.340845\pi\) |
−0.877583 | + | 0.479425i | \(0.840845\pi\) | |||||||
\(998\) | 3.60276e6 | − | 4.43659e6i | 0.114501 | − | 0.141001i | ||||
\(999\) | − | 1.08204e7i | − | 0.343028i |
(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 | 80.6.l.a.21.3 | ✓ | 80 | |
4.3 | odd | 2 | 320.6.l.a.241.32 | 80 | |||
16.3 | odd | 4 | 320.6.l.a.81.32 | 80 | |||
16.13 | even | 4 | inner | 80.6.l.a.61.3 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.6.l.a.21.3 | ✓ | 80 | 1.1 | even | 1 | trivial | |
80.6.l.a.61.3 | yes | 80 | 16.13 | even | 4 | inner | |
320.6.l.a.81.32 | 80 | 16.3 | odd | 4 | |||
320.6.l.a.241.32 | 80 | 4.3 | odd | 2 |