Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,8,Mod(1,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.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: | \(178.059464526\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4122x^{2} - 49773x + 620550 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-21.7209\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.00000 | 0.707107 | ||||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | 125.000 | 0.447214 | ||||||||
\(6\) | −216.000 | −0.408248 | ||||||||
\(7\) | 206.862 | 0.227949 | 0.113974 | − | 0.993484i | \(-0.463642\pi\) | ||||
0.113974 | + | 0.993484i | \(0.463642\pi\) | |||||||
\(8\) | 512.000 | 0.353553 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 1000.00 | 0.316228 | ||||||||
\(11\) | −4759.55 | −1.07818 | −0.539091 | − | 0.842248i | \(-0.681232\pi\) | ||||
−0.539091 | + | 0.842248i | \(0.681232\pi\) | |||||||
\(12\) | −1728.00 | −0.288675 | ||||||||
\(13\) | −4400.24 | −0.555488 | −0.277744 | − | 0.960655i | \(-0.589587\pi\) | ||||
−0.277744 | + | 0.960655i | \(0.589587\pi\) | |||||||
\(14\) | 1654.89 | 0.161184 | ||||||||
\(15\) | −3375.00 | −0.258199 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | 15564.3 | 0.768349 | 0.384175 | − | 0.923260i | \(-0.374486\pi\) | ||||
0.384175 | + | 0.923260i | \(0.374486\pi\) | |||||||
\(18\) | 5832.00 | 0.235702 | ||||||||
\(19\) | 6859.00 | 0.229416 | ||||||||
\(20\) | 8000.00 | 0.223607 | ||||||||
\(21\) | −5585.27 | −0.131606 | ||||||||
\(22\) | −38076.4 | −0.762389 | ||||||||
\(23\) | 38699.4 | 0.663219 | 0.331609 | − | 0.943417i | \(-0.392408\pi\) | ||||
0.331609 | + | 0.943417i | \(0.392408\pi\) | |||||||
\(24\) | −13824.0 | −0.204124 | ||||||||
\(25\) | 15625.0 | 0.200000 | ||||||||
\(26\) | −35201.9 | −0.392789 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | 13239.2 | 0.113974 | ||||||||
\(29\) | −44138.0 | −0.336062 | −0.168031 | − | 0.985782i | \(-0.553741\pi\) | ||||
−0.168031 | + | 0.985782i | \(0.553741\pi\) | |||||||
\(30\) | −27000.0 | −0.182574 | ||||||||
\(31\) | −135145. | −0.814771 | −0.407385 | − | 0.913256i | \(-0.633559\pi\) | ||||
−0.407385 | + | 0.913256i | \(0.633559\pi\) | |||||||
\(32\) | 32768.0 | 0.176777 | ||||||||
\(33\) | 128508. | 0.622488 | ||||||||
\(34\) | 124515. | 0.543305 | ||||||||
\(35\) | 25857.7 | 0.101942 | ||||||||
\(36\) | 46656.0 | 0.166667 | ||||||||
\(37\) | 137545. | 0.446416 | 0.223208 | − | 0.974771i | \(-0.428347\pi\) | ||||
0.223208 | + | 0.974771i | \(0.428347\pi\) | |||||||
\(38\) | 54872.0 | 0.162221 | ||||||||
\(39\) | 118806. | 0.320711 | ||||||||
\(40\) | 64000.0 | 0.158114 | ||||||||
\(41\) | −159925. | −0.362388 | −0.181194 | − | 0.983447i | \(-0.557996\pi\) | ||||
−0.181194 | + | 0.983447i | \(0.557996\pi\) | |||||||
\(42\) | −44682.2 | −0.0930597 | ||||||||
\(43\) | −455779. | −0.874208 | −0.437104 | − | 0.899411i | \(-0.643996\pi\) | ||||
−0.437104 | + | 0.899411i | \(0.643996\pi\) | |||||||
\(44\) | −304611. | −0.539091 | ||||||||
\(45\) | 91125.0 | 0.149071 | ||||||||
\(46\) | 309595. | 0.468966 | ||||||||
\(47\) | −84818.4 | −0.119165 | −0.0595824 | − | 0.998223i | \(-0.518977\pi\) | ||||
−0.0595824 | + | 0.998223i | \(0.518977\pi\) | |||||||
\(48\) | −110592. | −0.144338 | ||||||||
\(49\) | −780751. | −0.948039 | ||||||||
\(50\) | 125000. | 0.141421 | ||||||||
\(51\) | −420237. | −0.443607 | ||||||||
\(52\) | −281615. | −0.277744 | ||||||||
\(53\) | 76846.2 | 0.0709017 | 0.0354509 | − | 0.999371i | \(-0.488713\pi\) | ||||
0.0354509 | + | 0.999371i | \(0.488713\pi\) | |||||||
\(54\) | −157464. | −0.136083 | ||||||||
\(55\) | −594944. | −0.482177 | ||||||||
\(56\) | 105913. | 0.0805921 | ||||||||
\(57\) | −185193. | −0.132453 | ||||||||
\(58\) | −353104. | −0.237632 | ||||||||
\(59\) | 819764. | 0.519645 | 0.259823 | − | 0.965656i | \(-0.416336\pi\) | ||||
0.259823 | + | 0.965656i | \(0.416336\pi\) | |||||||
\(60\) | −216000. | −0.129099 | ||||||||
\(61\) | −3.35140e6 | −1.89048 | −0.945238 | − | 0.326381i | \(-0.894171\pi\) | ||||
−0.945238 | + | 0.326381i | \(0.894171\pi\) | |||||||
\(62\) | −1.08116e6 | −0.576130 | ||||||||
\(63\) | 150802. | 0.0759829 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | −550030. | −0.248422 | ||||||||
\(66\) | 1.02806e6 | 0.440166 | ||||||||
\(67\) | 1.01099e6 | 0.410661 | 0.205331 | − | 0.978693i | \(-0.434173\pi\) | ||||
0.205331 | + | 0.978693i | \(0.434173\pi\) | |||||||
\(68\) | 996116. | 0.384175 | ||||||||
\(69\) | −1.04488e6 | −0.382909 | ||||||||
\(70\) | 206862. | 0.0720837 | ||||||||
\(71\) | −1.87052e6 | −0.620239 | −0.310119 | − | 0.950698i | \(-0.600369\pi\) | ||||
−0.310119 | + | 0.950698i | \(0.600369\pi\) | |||||||
\(72\) | 373248. | 0.117851 | ||||||||
\(73\) | 4.30803e6 | 1.29613 | 0.648065 | − | 0.761585i | \(-0.275578\pi\) | ||||
0.648065 | + | 0.761585i | \(0.275578\pi\) | |||||||
\(74\) | 1.10036e6 | 0.315664 | ||||||||
\(75\) | −421875. | −0.115470 | ||||||||
\(76\) | 438976. | 0.114708 | ||||||||
\(77\) | −984570. | −0.245770 | ||||||||
\(78\) | 950452. | 0.226777 | ||||||||
\(79\) | 8.30117e6 | 1.89428 | 0.947140 | − | 0.320820i | \(-0.103958\pi\) | ||||
0.947140 | + | 0.320820i | \(0.103958\pi\) | |||||||
\(80\) | 512000. | 0.111803 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −1.27940e6 | −0.256247 | ||||||||
\(83\) | −1.77982e6 | −0.341666 | −0.170833 | − | 0.985300i | \(-0.554646\pi\) | ||||
−0.170833 | + | 0.985300i | \(0.554646\pi\) | |||||||
\(84\) | −357457. | −0.0658031 | ||||||||
\(85\) | 1.94554e6 | 0.343616 | ||||||||
\(86\) | −3.64623e6 | −0.618159 | ||||||||
\(87\) | 1.19173e6 | 0.194026 | ||||||||
\(88\) | −2.43689e6 | −0.381195 | ||||||||
\(89\) | −5.36350e6 | −0.806460 | −0.403230 | − | 0.915099i | \(-0.632113\pi\) | ||||
−0.403230 | + | 0.915099i | \(0.632113\pi\) | |||||||
\(90\) | 729000. | 0.105409 | ||||||||
\(91\) | −910242. | −0.126623 | ||||||||
\(92\) | 2.47676e6 | 0.331609 | ||||||||
\(93\) | 3.64893e6 | 0.470408 | ||||||||
\(94\) | −678548. | −0.0842622 | ||||||||
\(95\) | 857375. | 0.102598 | ||||||||
\(96\) | −884736. | −0.102062 | ||||||||
\(97\) | −5.60450e6 | −0.623499 | −0.311750 | − | 0.950164i | \(-0.600915\pi\) | ||||
−0.311750 | + | 0.950164i | \(0.600915\pi\) | |||||||
\(98\) | −6.24601e6 | −0.670365 | ||||||||
\(99\) | −3.46971e6 | −0.359394 | ||||||||
\(100\) | 1.00000e6 | 0.100000 | ||||||||
\(101\) | 1.70403e7 | 1.64570 | 0.822852 | − | 0.568255i | \(-0.192381\pi\) | ||||
0.822852 | + | 0.568255i | \(0.192381\pi\) | |||||||
\(102\) | −3.36189e6 | −0.313677 | ||||||||
\(103\) | 4.90262e6 | 0.442077 | 0.221038 | − | 0.975265i | \(-0.429055\pi\) | ||||
0.221038 | + | 0.975265i | \(0.429055\pi\) | |||||||
\(104\) | −2.25292e6 | −0.196395 | ||||||||
\(105\) | −698159. | −0.0588561 | ||||||||
\(106\) | 614769. | 0.0501351 | ||||||||
\(107\) | 6.77709e6 | 0.534811 | 0.267405 | − | 0.963584i | \(-0.413834\pi\) | ||||
0.267405 | + | 0.963584i | \(0.413834\pi\) | |||||||
\(108\) | −1.25971e6 | −0.0962250 | ||||||||
\(109\) | −1.44505e7 | −1.06879 | −0.534394 | − | 0.845236i | \(-0.679460\pi\) | ||||
−0.534394 | + | 0.845236i | \(0.679460\pi\) | |||||||
\(110\) | −4.75955e6 | −0.340951 | ||||||||
\(111\) | −3.71372e6 | −0.257738 | ||||||||
\(112\) | 847306. | 0.0569872 | ||||||||
\(113\) | −1.17413e7 | −0.765494 | −0.382747 | − | 0.923853i | \(-0.625022\pi\) | ||||
−0.382747 | + | 0.923853i | \(0.625022\pi\) | |||||||
\(114\) | −1.48154e6 | −0.0936586 | ||||||||
\(115\) | 4.83742e6 | 0.296600 | ||||||||
\(116\) | −2.82483e6 | −0.168031 | ||||||||
\(117\) | −3.20778e6 | −0.185163 | ||||||||
\(118\) | 6.55811e6 | 0.367445 | ||||||||
\(119\) | 3.21966e6 | 0.175144 | ||||||||
\(120\) | −1.72800e6 | −0.0912871 | ||||||||
\(121\) | 3.16618e6 | 0.162475 | ||||||||
\(122\) | −2.68112e7 | −1.33677 | ||||||||
\(123\) | 4.31798e6 | 0.209225 | ||||||||
\(124\) | −8.64931e6 | −0.407385 | ||||||||
\(125\) | 1.95312e6 | 0.0894427 | ||||||||
\(126\) | 1.20642e6 | 0.0537280 | ||||||||
\(127\) | −2.56381e7 | −1.11064 | −0.555320 | − | 0.831637i | \(-0.687404\pi\) | ||||
−0.555320 | + | 0.831637i | \(0.687404\pi\) | |||||||
\(128\) | 2.09715e6 | 0.0883883 | ||||||||
\(129\) | 1.23060e7 | 0.504724 | ||||||||
\(130\) | −4.40024e6 | −0.175661 | ||||||||
\(131\) | −3.44013e7 | −1.33698 | −0.668491 | − | 0.743720i | \(-0.733060\pi\) | ||||
−0.668491 | + | 0.743720i | \(0.733060\pi\) | |||||||
\(132\) | 8.22451e6 | 0.311244 | ||||||||
\(133\) | 1.41887e6 | 0.0522950 | ||||||||
\(134\) | 8.08790e6 | 0.290381 | ||||||||
\(135\) | −2.46038e6 | −0.0860663 | ||||||||
\(136\) | 7.96893e6 | 0.271653 | ||||||||
\(137\) | −4.05482e7 | −1.34725 | −0.673627 | − | 0.739072i | \(-0.735264\pi\) | ||||
−0.673627 | + | 0.739072i | \(0.735264\pi\) | |||||||
\(138\) | −8.35907e6 | −0.270758 | ||||||||
\(139\) | −8.63603e6 | −0.272749 | −0.136374 | − | 0.990657i | \(-0.543545\pi\) | ||||
−0.136374 | + | 0.990657i | \(0.543545\pi\) | |||||||
\(140\) | 1.65489e6 | 0.0509709 | ||||||||
\(141\) | 2.29010e6 | 0.0687998 | ||||||||
\(142\) | −1.49642e7 | −0.438575 | ||||||||
\(143\) | 2.09432e7 | 0.598917 | ||||||||
\(144\) | 2.98598e6 | 0.0833333 | ||||||||
\(145\) | −5.51725e6 | −0.150292 | ||||||||
\(146\) | 3.44643e7 | 0.916503 | ||||||||
\(147\) | 2.10803e7 | 0.547351 | ||||||||
\(148\) | 8.80290e6 | 0.223208 | ||||||||
\(149\) | −9.41371e6 | −0.233136 | −0.116568 | − | 0.993183i | \(-0.537189\pi\) | ||||
−0.116568 | + | 0.993183i | \(0.537189\pi\) | |||||||
\(150\) | −3.37500e6 | −0.0816497 | ||||||||
\(151\) | −7.35199e7 | −1.73774 | −0.868871 | − | 0.495038i | \(-0.835154\pi\) | ||||
−0.868871 | + | 0.495038i | \(0.835154\pi\) | |||||||
\(152\) | 3.51181e6 | 0.0811107 | ||||||||
\(153\) | 1.13464e7 | 0.256116 | ||||||||
\(154\) | −7.87656e6 | −0.173786 | ||||||||
\(155\) | −1.68932e7 | −0.364377 | ||||||||
\(156\) | 7.60362e6 | 0.160356 | ||||||||
\(157\) | 5.40802e7 | 1.11530 | 0.557648 | − | 0.830078i | \(-0.311704\pi\) | ||||
0.557648 | + | 0.830078i | \(0.311704\pi\) | |||||||
\(158\) | 6.64093e7 | 1.33946 | ||||||||
\(159\) | −2.07485e6 | −0.0409351 | ||||||||
\(160\) | 4.09600e6 | 0.0790569 | ||||||||
\(161\) | 8.00543e6 | 0.151180 | ||||||||
\(162\) | 4.25153e6 | 0.0785674 | ||||||||
\(163\) | 5.11902e7 | 0.925828 | 0.462914 | − | 0.886403i | \(-0.346804\pi\) | ||||
0.462914 | + | 0.886403i | \(0.346804\pi\) | |||||||
\(164\) | −1.02352e7 | −0.181194 | ||||||||
\(165\) | 1.60635e7 | 0.278385 | ||||||||
\(166\) | −1.42385e7 | −0.241595 | ||||||||
\(167\) | −3.77401e7 | −0.627040 | −0.313520 | − | 0.949582i | \(-0.601508\pi\) | ||||
−0.313520 | + | 0.949582i | \(0.601508\pi\) | |||||||
\(168\) | −2.85966e6 | −0.0465298 | ||||||||
\(169\) | −4.33864e7 | −0.691433 | ||||||||
\(170\) | 1.55643e7 | 0.242973 | ||||||||
\(171\) | 5.00021e6 | 0.0764719 | ||||||||
\(172\) | −2.91699e7 | −0.437104 | ||||||||
\(173\) | −7.19275e7 | −1.05617 | −0.528085 | − | 0.849192i | \(-0.677090\pi\) | ||||
−0.528085 | + | 0.849192i | \(0.677090\pi\) | |||||||
\(174\) | 9.53381e6 | 0.137197 | ||||||||
\(175\) | 3.23222e6 | 0.0455898 | ||||||||
\(176\) | −1.94951e7 | −0.269545 | ||||||||
\(177\) | −2.21336e7 | −0.300017 | ||||||||
\(178\) | −4.29080e7 | −0.570254 | ||||||||
\(179\) | 1.05740e8 | 1.37801 | 0.689007 | − | 0.724755i | \(-0.258047\pi\) | ||||
0.689007 | + | 0.724755i | \(0.258047\pi\) | |||||||
\(180\) | 5.83200e6 | 0.0745356 | ||||||||
\(181\) | −1.03786e8 | −1.30096 | −0.650482 | − | 0.759522i | \(-0.725433\pi\) | ||||
−0.650482 | + | 0.759522i | \(0.725433\pi\) | |||||||
\(182\) | −7.28193e6 | −0.0895358 | ||||||||
\(183\) | 9.04877e7 | 1.09147 | ||||||||
\(184\) | 1.98141e7 | 0.234483 | ||||||||
\(185\) | 1.71932e7 | 0.199643 | ||||||||
\(186\) | 2.91914e7 | 0.332629 | ||||||||
\(187\) | −7.40792e7 | −0.828420 | ||||||||
\(188\) | −5.42838e6 | −0.0595824 | ||||||||
\(189\) | −4.07166e6 | −0.0438688 | ||||||||
\(190\) | 6.85900e6 | 0.0725476 | ||||||||
\(191\) | −9.31968e7 | −0.967797 | −0.483898 | − | 0.875124i | \(-0.660780\pi\) | ||||
−0.483898 | + | 0.875124i | \(0.660780\pi\) | |||||||
\(192\) | −7.07789e6 | −0.0721688 | ||||||||
\(193\) | −8.30000e7 | −0.831051 | −0.415525 | − | 0.909582i | \(-0.636402\pi\) | ||||
−0.415525 | + | 0.909582i | \(0.636402\pi\) | |||||||
\(194\) | −4.48360e7 | −0.440880 | ||||||||
\(195\) | 1.48508e7 | 0.143426 | ||||||||
\(196\) | −4.99681e7 | −0.474020 | ||||||||
\(197\) | −1.99572e8 | −1.85981 | −0.929905 | − | 0.367799i | \(-0.880112\pi\) | ||||
−0.929905 | + | 0.367799i | \(0.880112\pi\) | |||||||
\(198\) | −2.77577e7 | −0.254130 | ||||||||
\(199\) | −9.87743e7 | −0.888502 | −0.444251 | − | 0.895902i | \(-0.646530\pi\) | ||||
−0.444251 | + | 0.895902i | \(0.646530\pi\) | |||||||
\(200\) | 8.00000e6 | 0.0707107 | ||||||||
\(201\) | −2.72967e7 | −0.237095 | ||||||||
\(202\) | 1.36322e8 | 1.16369 | ||||||||
\(203\) | −9.13047e6 | −0.0766050 | ||||||||
\(204\) | −2.68951e7 | −0.221803 | ||||||||
\(205\) | −1.99906e7 | −0.162065 | ||||||||
\(206\) | 3.92209e7 | 0.312595 | ||||||||
\(207\) | 2.82119e7 | 0.221073 | ||||||||
\(208\) | −1.80234e7 | −0.138872 | ||||||||
\(209\) | −3.26458e7 | −0.247352 | ||||||||
\(210\) | −5.58527e6 | −0.0416176 | ||||||||
\(211\) | −1.15091e8 | −0.843440 | −0.421720 | − | 0.906726i | \(-0.638573\pi\) | ||||
−0.421720 | + | 0.906726i | \(0.638573\pi\) | |||||||
\(212\) | 4.91816e6 | 0.0354509 | ||||||||
\(213\) | 5.05041e7 | 0.358095 | ||||||||
\(214\) | 5.42168e7 | 0.378168 | ||||||||
\(215\) | −5.69724e7 | −0.390958 | ||||||||
\(216\) | −1.00777e7 | −0.0680414 | ||||||||
\(217\) | −2.79564e7 | −0.185726 | ||||||||
\(218\) | −1.15604e8 | −0.755747 | ||||||||
\(219\) | −1.16317e8 | −0.748322 | ||||||||
\(220\) | −3.80764e7 | −0.241089 | ||||||||
\(221\) | −6.84867e7 | −0.426809 | ||||||||
\(222\) | −2.97098e7 | −0.182249 | ||||||||
\(223\) | −2.99317e7 | −0.180744 | −0.0903720 | − | 0.995908i | \(-0.528806\pi\) | ||||
−0.0903720 | + | 0.995908i | \(0.528806\pi\) | |||||||
\(224\) | 6.77845e6 | 0.0402960 | ||||||||
\(225\) | 1.13906e7 | 0.0666667 | ||||||||
\(226\) | −9.39304e7 | −0.541286 | ||||||||
\(227\) | 1.49092e8 | 0.845985 | 0.422992 | − | 0.906133i | \(-0.360980\pi\) | ||||
0.422992 | + | 0.906133i | \(0.360980\pi\) | |||||||
\(228\) | −1.18524e7 | −0.0662266 | ||||||||
\(229\) | −1.98793e7 | −0.109390 | −0.0546948 | − | 0.998503i | \(-0.517419\pi\) | ||||
−0.0546948 | + | 0.998503i | \(0.517419\pi\) | |||||||
\(230\) | 3.86994e7 | 0.209728 | ||||||||
\(231\) | 2.65834e7 | 0.141895 | ||||||||
\(232\) | −2.25987e7 | −0.118816 | ||||||||
\(233\) | −2.38916e8 | −1.23737 | −0.618684 | − | 0.785640i | \(-0.712334\pi\) | ||||
−0.618684 | + | 0.785640i | \(0.712334\pi\) | |||||||
\(234\) | −2.56622e7 | −0.130930 | ||||||||
\(235\) | −1.06023e7 | −0.0532921 | ||||||||
\(236\) | 5.24649e7 | 0.259823 | ||||||||
\(237\) | −2.24131e8 | −1.09366 | ||||||||
\(238\) | 2.57573e7 | 0.123846 | ||||||||
\(239\) | 5.31139e7 | 0.251661 | 0.125830 | − | 0.992052i | \(-0.459841\pi\) | ||||
0.125830 | + | 0.992052i | \(0.459841\pi\) | |||||||
\(240\) | −1.38240e7 | −0.0645497 | ||||||||
\(241\) | 1.05694e8 | 0.486395 | 0.243198 | − | 0.969977i | \(-0.421804\pi\) | ||||
0.243198 | + | 0.969977i | \(0.421804\pi\) | |||||||
\(242\) | 2.53294e7 | 0.114887 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | −2.14489e8 | −0.945238 | ||||||||
\(245\) | −9.75939e7 | −0.423976 | ||||||||
\(246\) | 3.45438e7 | 0.147944 | ||||||||
\(247\) | −3.01812e7 | −0.127438 | ||||||||
\(248\) | −6.91945e7 | −0.288065 | ||||||||
\(249\) | 4.80551e7 | 0.197261 | ||||||||
\(250\) | 1.56250e7 | 0.0632456 | ||||||||
\(251\) | −3.73051e8 | −1.48905 | −0.744526 | − | 0.667594i | \(-0.767324\pi\) | ||||
−0.744526 | + | 0.667594i | \(0.767324\pi\) | |||||||
\(252\) | 9.65135e6 | 0.0379915 | ||||||||
\(253\) | −1.84192e8 | −0.715070 | ||||||||
\(254\) | −2.05105e8 | −0.785342 | ||||||||
\(255\) | −5.25296e7 | −0.198387 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | −2.63207e8 | −0.967235 | −0.483617 | − | 0.875280i | \(-0.660677\pi\) | ||||
−0.483617 | + | 0.875280i | \(0.660677\pi\) | |||||||
\(258\) | 9.84483e7 | 0.356894 | ||||||||
\(259\) | 2.84529e7 | 0.101760 | ||||||||
\(260\) | −3.52019e7 | −0.124211 | ||||||||
\(261\) | −3.21766e7 | −0.112021 | ||||||||
\(262\) | −2.75211e8 | −0.945390 | ||||||||
\(263\) | 8.66354e7 | 0.293664 | 0.146832 | − | 0.989161i | \(-0.453092\pi\) | ||||
0.146832 | + | 0.989161i | \(0.453092\pi\) | |||||||
\(264\) | 6.57961e7 | 0.220083 | ||||||||
\(265\) | 9.60577e6 | 0.0317082 | ||||||||
\(266\) | 1.13509e7 | 0.0369782 | ||||||||
\(267\) | 1.44814e8 | 0.465610 | ||||||||
\(268\) | 6.47032e7 | 0.205331 | ||||||||
\(269\) | 4.47057e8 | 1.40033 | 0.700164 | − | 0.713982i | \(-0.253110\pi\) | ||||
0.700164 | + | 0.713982i | \(0.253110\pi\) | |||||||
\(270\) | −1.96830e7 | −0.0608581 | ||||||||
\(271\) | 1.51318e8 | 0.461848 | 0.230924 | − | 0.972972i | \(-0.425825\pi\) | ||||
0.230924 | + | 0.972972i | \(0.425825\pi\) | |||||||
\(272\) | 6.37514e7 | 0.192087 | ||||||||
\(273\) | 2.45765e7 | 0.0731057 | ||||||||
\(274\) | −3.24385e8 | −0.952652 | ||||||||
\(275\) | −7.43680e7 | −0.215636 | ||||||||
\(276\) | −6.68726e7 | −0.191455 | ||||||||
\(277\) | −1.93832e8 | −0.547956 | −0.273978 | − | 0.961736i | \(-0.588340\pi\) | ||||
−0.273978 | + | 0.961736i | \(0.588340\pi\) | |||||||
\(278\) | −6.90883e7 | −0.192862 | ||||||||
\(279\) | −9.85210e7 | −0.271590 | ||||||||
\(280\) | 1.32392e7 | 0.0360419 | ||||||||
\(281\) | −1.20191e8 | −0.323146 | −0.161573 | − | 0.986861i | \(-0.551657\pi\) | ||||
−0.161573 | + | 0.986861i | \(0.551657\pi\) | |||||||
\(282\) | 1.83208e7 | 0.0486488 | ||||||||
\(283\) | 3.47711e8 | 0.911940 | 0.455970 | − | 0.889995i | \(-0.349292\pi\) | ||||
0.455970 | + | 0.889995i | \(0.349292\pi\) | |||||||
\(284\) | −1.19714e8 | −0.310119 | ||||||||
\(285\) | −2.31491e7 | −0.0592349 | ||||||||
\(286\) | 1.67545e8 | 0.423498 | ||||||||
\(287\) | −3.30824e7 | −0.0826058 | ||||||||
\(288\) | 2.38879e7 | 0.0589256 | ||||||||
\(289\) | −1.68091e8 | −0.409639 | ||||||||
\(290\) | −4.41380e7 | −0.106272 | ||||||||
\(291\) | 1.51321e8 | 0.359977 | ||||||||
\(292\) | 2.75714e8 | 0.648065 | ||||||||
\(293\) | 4.72827e8 | 1.09816 | 0.549079 | − | 0.835770i | \(-0.314978\pi\) | ||||
0.549079 | + | 0.835770i | \(0.314978\pi\) | |||||||
\(294\) | 1.68642e8 | 0.387035 | ||||||||
\(295\) | 1.02470e8 | 0.232392 | ||||||||
\(296\) | 7.04232e7 | 0.157832 | ||||||||
\(297\) | 9.36823e7 | 0.207496 | ||||||||
\(298\) | −7.53097e7 | −0.164852 | ||||||||
\(299\) | −1.70287e8 | −0.368410 | ||||||||
\(300\) | −2.70000e7 | −0.0577350 | ||||||||
\(301\) | −9.42833e7 | −0.199275 | ||||||||
\(302\) | −5.88159e8 | −1.22877 | ||||||||
\(303\) | −4.60087e8 | −0.950148 | ||||||||
\(304\) | 2.80945e7 | 0.0573539 | ||||||||
\(305\) | −4.18925e8 | −0.845447 | ||||||||
\(306\) | 9.07711e7 | 0.181102 | ||||||||
\(307\) | −5.24168e8 | −1.03392 | −0.516959 | − | 0.856010i | \(-0.672936\pi\) | ||||
−0.516959 | + | 0.856010i | \(0.672936\pi\) | |||||||
\(308\) | −6.30125e7 | −0.122885 | ||||||||
\(309\) | −1.32371e8 | −0.255233 | ||||||||
\(310\) | −1.35145e8 | −0.257653 | ||||||||
\(311\) | 3.84447e8 | 0.724728 | 0.362364 | − | 0.932037i | \(-0.381970\pi\) | ||||
0.362364 | + | 0.932037i | \(0.381970\pi\) | |||||||
\(312\) | 6.08289e7 | 0.113389 | ||||||||
\(313\) | 5.87950e8 | 1.08376 | 0.541882 | − | 0.840454i | \(-0.317712\pi\) | ||||
0.541882 | + | 0.840454i | \(0.317712\pi\) | |||||||
\(314\) | 4.32642e8 | 0.788633 | ||||||||
\(315\) | 1.88503e7 | 0.0339806 | ||||||||
\(316\) | 5.31275e8 | 0.947140 | ||||||||
\(317\) | 1.74116e8 | 0.306996 | 0.153498 | − | 0.988149i | \(-0.450946\pi\) | ||||
0.153498 | + | 0.988149i | \(0.450946\pi\) | |||||||
\(318\) | −1.65988e7 | −0.0289455 | ||||||||
\(319\) | 2.10077e8 | 0.362336 | ||||||||
\(320\) | 3.27680e7 | 0.0559017 | ||||||||
\(321\) | −1.82982e8 | −0.308773 | ||||||||
\(322\) | 6.40434e7 | 0.106900 | ||||||||
\(323\) | 1.06756e8 | 0.176271 | ||||||||
\(324\) | 3.40122e7 | 0.0555556 | ||||||||
\(325\) | −6.87538e7 | −0.111098 | ||||||||
\(326\) | 4.09522e8 | 0.654659 | ||||||||
\(327\) | 3.90164e8 | 0.617065 | ||||||||
\(328\) | −8.18817e7 | −0.128123 | ||||||||
\(329\) | −1.75457e7 | −0.0271635 | ||||||||
\(330\) | 1.28508e8 | 0.196848 | ||||||||
\(331\) | 1.35303e8 | 0.205073 | 0.102536 | − | 0.994729i | \(-0.467304\pi\) | ||||
0.102536 | + | 0.994729i | \(0.467304\pi\) | |||||||
\(332\) | −1.13908e8 | −0.170833 | ||||||||
\(333\) | 1.00271e8 | 0.148805 | ||||||||
\(334\) | −3.01921e8 | −0.443385 | ||||||||
\(335\) | 1.26373e8 | 0.183653 | ||||||||
\(336\) | −2.28773e7 | −0.0329016 | ||||||||
\(337\) | 6.48003e8 | 0.922300 | 0.461150 | − | 0.887322i | \(-0.347437\pi\) | ||||
0.461150 | + | 0.887322i | \(0.347437\pi\) | |||||||
\(338\) | −3.47091e8 | −0.488917 | ||||||||
\(339\) | 3.17015e8 | 0.441958 | ||||||||
\(340\) | 1.24515e8 | 0.171808 | ||||||||
\(341\) | 6.43232e8 | 0.878471 | ||||||||
\(342\) | 4.00017e7 | 0.0540738 | ||||||||
\(343\) | −3.31867e8 | −0.444053 | ||||||||
\(344\) | −2.33359e8 | −0.309079 | ||||||||
\(345\) | −1.30610e8 | −0.171242 | ||||||||
\(346\) | −5.75420e8 | −0.746824 | ||||||||
\(347\) | 2.97258e8 | 0.381928 | 0.190964 | − | 0.981597i | \(-0.438839\pi\) | ||||
0.190964 | + | 0.981597i | \(0.438839\pi\) | |||||||
\(348\) | 7.62705e7 | 0.0970128 | ||||||||
\(349\) | −1.30821e9 | −1.64736 | −0.823678 | − | 0.567058i | \(-0.808082\pi\) | ||||
−0.823678 | + | 0.567058i | \(0.808082\pi\) | |||||||
\(350\) | 2.58577e7 | 0.0322368 | ||||||||
\(351\) | 8.66099e7 | 0.106904 | ||||||||
\(352\) | −1.55961e8 | −0.190597 | ||||||||
\(353\) | −1.38083e9 | −1.67082 | −0.835411 | − | 0.549626i | \(-0.814770\pi\) | ||||
−0.835411 | + | 0.549626i | \(0.814770\pi\) | |||||||
\(354\) | −1.77069e8 | −0.212144 | ||||||||
\(355\) | −2.33815e8 | −0.277379 | ||||||||
\(356\) | −3.43264e8 | −0.403230 | ||||||||
\(357\) | −8.69309e7 | −0.101120 | ||||||||
\(358\) | 8.45919e8 | 0.974402 | ||||||||
\(359\) | −4.49561e7 | −0.0512812 | −0.0256406 | − | 0.999671i | \(-0.508163\pi\) | ||||
−0.0256406 | + | 0.999671i | \(0.508163\pi\) | |||||||
\(360\) | 4.66560e7 | 0.0527046 | ||||||||
\(361\) | 4.70459e7 | 0.0526316 | ||||||||
\(362\) | −8.30290e8 | −0.919920 | ||||||||
\(363\) | −8.54867e7 | −0.0938049 | ||||||||
\(364\) | −5.82555e7 | −0.0633114 | ||||||||
\(365\) | 5.38504e8 | 0.579647 | ||||||||
\(366\) | 7.23902e8 | 0.771784 | ||||||||
\(367\) | 2.85156e7 | 0.0301128 | 0.0150564 | − | 0.999887i | \(-0.495207\pi\) | ||||
0.0150564 | + | 0.999887i | \(0.495207\pi\) | |||||||
\(368\) | 1.58513e8 | 0.165805 | ||||||||
\(369\) | −1.16585e8 | −0.120796 | ||||||||
\(370\) | 1.37545e8 | 0.141169 | ||||||||
\(371\) | 1.58965e7 | 0.0161620 | ||||||||
\(372\) | 2.33531e8 | 0.235204 | ||||||||
\(373\) | 1.45520e9 | 1.45192 | 0.725961 | − | 0.687736i | \(-0.241395\pi\) | ||||
0.725961 | + | 0.687736i | \(0.241395\pi\) | |||||||
\(374\) | −5.92634e8 | −0.585781 | ||||||||
\(375\) | −5.27344e7 | −0.0516398 | ||||||||
\(376\) | −4.34270e7 | −0.0421311 | ||||||||
\(377\) | 1.94218e8 | 0.186679 | ||||||||
\(378\) | −3.25733e7 | −0.0310199 | ||||||||
\(379\) | 5.12940e6 | 0.00483982 | 0.00241991 | − | 0.999997i | \(-0.499230\pi\) | ||||
0.00241991 | + | 0.999997i | \(0.499230\pi\) | |||||||
\(380\) | 5.48720e7 | 0.0512989 | ||||||||
\(381\) | 6.92230e8 | 0.641229 | ||||||||
\(382\) | −7.45574e8 | −0.684336 | ||||||||
\(383\) | −1.02289e9 | −0.930321 | −0.465161 | − | 0.885226i | \(-0.654003\pi\) | ||||
−0.465161 | + | 0.885226i | \(0.654003\pi\) | |||||||
\(384\) | −5.66231e7 | −0.0510310 | ||||||||
\(385\) | −1.23071e8 | −0.109912 | ||||||||
\(386\) | −6.64000e8 | −0.587642 | ||||||||
\(387\) | −3.32263e8 | −0.291403 | ||||||||
\(388\) | −3.58688e8 | −0.311750 | ||||||||
\(389\) | 1.14619e9 | 0.987262 | 0.493631 | − | 0.869671i | \(-0.335669\pi\) | ||||
0.493631 | + | 0.869671i | \(0.335669\pi\) | |||||||
\(390\) | 1.18806e8 | 0.101418 | ||||||||
\(391\) | 6.02330e8 | 0.509584 | ||||||||
\(392\) | −3.99745e8 | −0.335183 | ||||||||
\(393\) | 9.28836e8 | 0.771907 | ||||||||
\(394\) | −1.59658e9 | −1.31508 | ||||||||
\(395\) | 1.03765e9 | 0.847148 | ||||||||
\(396\) | −2.22062e8 | −0.179697 | ||||||||
\(397\) | −2.44382e9 | −1.96021 | −0.980105 | − | 0.198478i | \(-0.936400\pi\) | ||||
−0.980105 | + | 0.198478i | \(0.936400\pi\) | |||||||
\(398\) | −7.90194e8 | −0.628266 | ||||||||
\(399\) | −3.83094e7 | −0.0301926 | ||||||||
\(400\) | 6.40000e7 | 0.0500000 | ||||||||
\(401\) | 1.32316e9 | 1.02473 | 0.512364 | − | 0.858768i | \(-0.328770\pi\) | ||||
0.512364 | + | 0.858768i | \(0.328770\pi\) | |||||||
\(402\) | −2.18373e8 | −0.167652 | ||||||||
\(403\) | 5.94672e8 | 0.452595 | ||||||||
\(404\) | 1.09058e9 | 0.822852 | ||||||||
\(405\) | 6.64301e7 | 0.0496904 | ||||||||
\(406\) | −7.30438e7 | −0.0541679 | ||||||||
\(407\) | −6.54654e8 | −0.481318 | ||||||||
\(408\) | −2.15161e8 | −0.156839 | ||||||||
\(409\) | −2.67709e8 | −0.193478 | −0.0967390 | − | 0.995310i | \(-0.530841\pi\) | ||||
−0.0967390 | + | 0.995310i | \(0.530841\pi\) | |||||||
\(410\) | −1.59925e8 | −0.114597 | ||||||||
\(411\) | 1.09480e9 | 0.777837 | ||||||||
\(412\) | 3.13767e8 | 0.221038 | ||||||||
\(413\) | 1.69578e8 | 0.118452 | ||||||||
\(414\) | 2.25695e8 | 0.156322 | ||||||||
\(415\) | −2.22477e8 | −0.152798 | ||||||||
\(416\) | −1.44187e8 | −0.0981973 | ||||||||
\(417\) | 2.33173e8 | 0.157471 | ||||||||
\(418\) | −2.61166e8 | −0.174904 | ||||||||
\(419\) | −7.90101e7 | −0.0524727 | −0.0262364 | − | 0.999656i | \(-0.508352\pi\) | ||||
−0.0262364 | + | 0.999656i | \(0.508352\pi\) | |||||||
\(420\) | −4.46822e7 | −0.0294281 | ||||||||
\(421\) | −4.68482e7 | −0.0305989 | −0.0152995 | − | 0.999883i | \(-0.504870\pi\) | ||||
−0.0152995 | + | 0.999883i | \(0.504870\pi\) | |||||||
\(422\) | −9.20731e8 | −0.596402 | ||||||||
\(423\) | −6.18326e7 | −0.0397216 | ||||||||
\(424\) | 3.93452e7 | 0.0250675 | ||||||||
\(425\) | 2.43192e8 | 0.153670 | ||||||||
\(426\) | 4.04033e8 | 0.253211 | ||||||||
\(427\) | −6.93276e8 | −0.430932 | ||||||||
\(428\) | 4.33734e8 | 0.267405 | ||||||||
\(429\) | −5.65466e8 | −0.345785 | ||||||||
\(430\) | −4.55779e8 | −0.276449 | ||||||||
\(431\) | −1.24607e9 | −0.749675 | −0.374838 | − | 0.927090i | \(-0.622302\pi\) | ||||
−0.374838 | + | 0.927090i | \(0.622302\pi\) | |||||||
\(432\) | −8.06216e7 | −0.0481125 | ||||||||
\(433\) | −2.37190e9 | −1.40407 | −0.702036 | − | 0.712141i | \(-0.747726\pi\) | ||||
−0.702036 | + | 0.712141i | \(0.747726\pi\) | |||||||
\(434\) | −2.23651e8 | −0.131328 | ||||||||
\(435\) | 1.48966e8 | 0.0867709 | ||||||||
\(436\) | −9.24834e8 | −0.534394 | ||||||||
\(437\) | 2.65439e8 | 0.152153 | ||||||||
\(438\) | −9.30535e8 | −0.529143 | ||||||||
\(439\) | 2.34409e9 | 1.32236 | 0.661179 | − | 0.750229i | \(-0.270057\pi\) | ||||
0.661179 | + | 0.750229i | \(0.270057\pi\) | |||||||
\(440\) | −3.04611e8 | −0.170475 | ||||||||
\(441\) | −5.69168e8 | −0.316013 | ||||||||
\(442\) | −5.47894e8 | −0.301799 | ||||||||
\(443\) | 8.56836e8 | 0.468257 | 0.234129 | − | 0.972206i | \(-0.424776\pi\) | ||||
0.234129 | + | 0.972206i | \(0.424776\pi\) | |||||||
\(444\) | −2.37678e8 | −0.128869 | ||||||||
\(445\) | −6.70437e8 | −0.360660 | ||||||||
\(446\) | −2.39453e8 | −0.127805 | ||||||||
\(447\) | 2.54170e8 | 0.134601 | ||||||||
\(448\) | 5.42276e7 | 0.0284936 | ||||||||
\(449\) | 2.19478e9 | 1.14427 | 0.572136 | − | 0.820159i | \(-0.306115\pi\) | ||||
0.572136 | + | 0.820159i | \(0.306115\pi\) | |||||||
\(450\) | 9.11250e7 | 0.0471405 | ||||||||
\(451\) | 7.61172e8 | 0.390720 | ||||||||
\(452\) | −7.51443e8 | −0.382747 | ||||||||
\(453\) | 1.98504e9 | 1.00329 | ||||||||
\(454\) | 1.19273e9 | 0.598201 | ||||||||
\(455\) | −1.13780e8 | −0.0566274 | ||||||||
\(456\) | −9.48188e7 | −0.0468293 | ||||||||
\(457\) | −2.93559e9 | −1.43876 | −0.719382 | − | 0.694615i | \(-0.755575\pi\) | ||||
−0.719382 | + | 0.694615i | \(0.755575\pi\) | |||||||
\(458\) | −1.59034e8 | −0.0773502 | ||||||||
\(459\) | −3.06352e8 | −0.147869 | ||||||||
\(460\) | 3.09595e8 | 0.148300 | ||||||||
\(461\) | 1.22481e9 | 0.582259 | 0.291129 | − | 0.956684i | \(-0.405969\pi\) | ||||
0.291129 | + | 0.956684i | \(0.405969\pi\) | |||||||
\(462\) | 2.12667e8 | 0.100335 | ||||||||
\(463\) | −1.86735e9 | −0.874362 | −0.437181 | − | 0.899374i | \(-0.644023\pi\) | ||||
−0.437181 | + | 0.899374i | \(0.644023\pi\) | |||||||
\(464\) | −1.80789e8 | −0.0840156 | ||||||||
\(465\) | 4.56116e8 | 0.210373 | ||||||||
\(466\) | −1.91133e9 | −0.874951 | ||||||||
\(467\) | 1.86953e9 | 0.849422 | 0.424711 | − | 0.905329i | \(-0.360376\pi\) | ||||
0.424711 | + | 0.905329i | \(0.360376\pi\) | |||||||
\(468\) | −2.05298e8 | −0.0925813 | ||||||||
\(469\) | 2.09135e8 | 0.0936097 | ||||||||
\(470\) | −8.48184e7 | −0.0376832 | ||||||||
\(471\) | −1.46017e9 | −0.643916 | ||||||||
\(472\) | 4.19719e8 | 0.183722 | ||||||||
\(473\) | 2.16931e9 | 0.942555 | ||||||||
\(474\) | −1.79305e9 | −0.773337 | ||||||||
\(475\) | 1.07172e8 | 0.0458831 | ||||||||
\(476\) | 2.06058e8 | 0.0875722 | ||||||||
\(477\) | 5.60209e7 | 0.0236339 | ||||||||
\(478\) | 4.24911e8 | 0.177951 | ||||||||
\(479\) | −4.47751e9 | −1.86150 | −0.930748 | − | 0.365661i | \(-0.880843\pi\) | ||||
−0.930748 | + | 0.365661i | \(0.880843\pi\) | |||||||
\(480\) | −1.10592e8 | −0.0456435 | ||||||||
\(481\) | −6.05233e8 | −0.247979 | ||||||||
\(482\) | 8.45549e8 | 0.343933 | ||||||||
\(483\) | −2.16147e8 | −0.0872837 | ||||||||
\(484\) | 2.02635e8 | 0.0812374 | ||||||||
\(485\) | −7.00562e8 | −0.278837 | ||||||||
\(486\) | −1.14791e8 | −0.0453609 | ||||||||
\(487\) | −3.39583e8 | −0.133228 | −0.0666138 | − | 0.997779i | \(-0.521220\pi\) | ||||
−0.0666138 | + | 0.997779i | \(0.521220\pi\) | |||||||
\(488\) | −1.71591e9 | −0.668384 | ||||||||
\(489\) | −1.38214e9 | −0.534527 | ||||||||
\(490\) | −7.80751e8 | −0.299796 | ||||||||
\(491\) | 1.94382e9 | 0.741090 | 0.370545 | − | 0.928815i | \(-0.379171\pi\) | ||||
0.370545 | + | 0.928815i | \(0.379171\pi\) | |||||||
\(492\) | 2.76351e8 | 0.104612 | ||||||||
\(493\) | −6.86978e8 | −0.258213 | ||||||||
\(494\) | −2.41450e8 | −0.0901120 | ||||||||
\(495\) | −4.33714e8 | −0.160726 | ||||||||
\(496\) | −5.53556e8 | −0.203693 | ||||||||
\(497\) | −3.86940e8 | −0.141383 | ||||||||
\(498\) | 3.84441e8 | 0.139485 | ||||||||
\(499\) | 2.10946e9 | 0.760010 | 0.380005 | − | 0.924984i | \(-0.375922\pi\) | ||||
0.380005 | + | 0.924984i | \(0.375922\pi\) | |||||||
\(500\) | 1.25000e8 | 0.0447214 | ||||||||
\(501\) | 1.01898e9 | 0.362022 | ||||||||
\(502\) | −2.98440e9 | −1.05292 | ||||||||
\(503\) | −1.79602e9 | −0.629252 | −0.314626 | − | 0.949216i | \(-0.601879\pi\) | ||||
−0.314626 | + | 0.949216i | \(0.601879\pi\) | |||||||
\(504\) | 7.72108e7 | 0.0268640 | ||||||||
\(505\) | 2.13003e9 | 0.735981 | ||||||||
\(506\) | −1.47353e9 | −0.505631 | ||||||||
\(507\) | 1.17143e9 | 0.399199 | ||||||||
\(508\) | −1.64084e9 | −0.555320 | ||||||||
\(509\) | −3.43630e9 | −1.15499 | −0.577496 | − | 0.816393i | \(-0.695970\pi\) | ||||
−0.577496 | + | 0.816393i | \(0.695970\pi\) | |||||||
\(510\) | −4.20237e8 | −0.140281 | ||||||||
\(511\) | 8.91167e8 | 0.295451 | ||||||||
\(512\) | 1.34218e8 | 0.0441942 | ||||||||
\(513\) | −1.35006e8 | −0.0441511 | ||||||||
\(514\) | −2.10566e9 | −0.683938 | ||||||||
\(515\) | 6.12827e8 | 0.197703 | ||||||||
\(516\) | 7.87586e8 | 0.252362 | ||||||||
\(517\) | 4.03698e8 | 0.128481 | ||||||||
\(518\) | 2.27623e8 | 0.0719552 | ||||||||
\(519\) | 1.94204e9 | 0.609779 | ||||||||
\(520\) | −2.81615e8 | −0.0878304 | ||||||||
\(521\) | 7.64671e7 | 0.0236888 | 0.0118444 | − | 0.999930i | \(-0.496230\pi\) | ||||
0.0118444 | + | 0.999930i | \(0.496230\pi\) | |||||||
\(522\) | −2.57413e8 | −0.0792106 | ||||||||
\(523\) | 2.55749e9 | 0.781731 | 0.390865 | − | 0.920448i | \(-0.372176\pi\) | ||||
0.390865 | + | 0.920448i | \(0.372176\pi\) | |||||||
\(524\) | −2.20169e9 | −0.668491 | ||||||||
\(525\) | −8.72698e7 | −0.0263213 | ||||||||
\(526\) | 6.93083e8 | 0.207651 | ||||||||
\(527\) | −2.10345e9 | −0.626029 | ||||||||
\(528\) | 5.26369e8 | 0.155622 | ||||||||
\(529\) | −1.90718e9 | −0.560141 | ||||||||
\(530\) | 7.68462e7 | 0.0224211 | ||||||||
\(531\) | 5.97608e8 | 0.173215 | ||||||||
\(532\) | 9.08074e7 | 0.0261475 | ||||||||
\(533\) | 7.03709e8 | 0.201302 | ||||||||
\(534\) | 1.15852e9 | 0.329236 | ||||||||
\(535\) | 8.47137e8 | 0.239175 | ||||||||
\(536\) | 5.17625e8 | 0.145191 | ||||||||
\(537\) | −2.85498e9 | −0.795596 | ||||||||
\(538\) | 3.57646e9 | 0.990182 | ||||||||
\(539\) | 3.71603e9 | 1.02216 | ||||||||
\(540\) | −1.57464e8 | −0.0430331 | ||||||||
\(541\) | −2.25165e8 | −0.0611379 | −0.0305689 | − | 0.999533i | \(-0.509732\pi\) | ||||
−0.0305689 | + | 0.999533i | \(0.509732\pi\) | |||||||
\(542\) | 1.21055e9 | 0.326576 | ||||||||
\(543\) | 2.80223e9 | 0.751112 | ||||||||
\(544\) | 5.10011e8 | 0.135826 | ||||||||
\(545\) | −1.80632e9 | −0.477976 | ||||||||
\(546\) | 1.96612e8 | 0.0516935 | ||||||||
\(547\) | 3.44718e9 | 0.900551 | 0.450275 | − | 0.892890i | \(-0.351326\pi\) | ||||
0.450275 | + | 0.892890i | \(0.351326\pi\) | |||||||
\(548\) | −2.59508e9 | −0.673627 | ||||||||
\(549\) | −2.44317e9 | −0.630159 | ||||||||
\(550\) | −5.94944e8 | −0.152478 | ||||||||
\(551\) | −3.02743e8 | −0.0770980 | ||||||||
\(552\) | −5.34980e8 | −0.135379 | ||||||||
\(553\) | 1.71719e9 | 0.431799 | ||||||||
\(554\) | −1.55065e9 | −0.387464 | ||||||||
\(555\) | −4.64216e8 | −0.115264 | ||||||||
\(556\) | −5.52706e8 | −0.136374 | ||||||||
\(557\) | −3.37891e9 | −0.828483 | −0.414241 | − | 0.910167i | \(-0.635953\pi\) | ||||
−0.414241 | + | 0.910167i | \(0.635953\pi\) | |||||||
\(558\) | −7.88168e8 | −0.192043 | ||||||||
\(559\) | 2.00554e9 | 0.485612 | ||||||||
\(560\) | 1.05913e8 | 0.0254854 | ||||||||
\(561\) | 2.00014e9 | 0.478289 | ||||||||
\(562\) | −9.61525e8 | −0.228499 | ||||||||
\(563\) | 2.10759e9 | 0.497745 | 0.248873 | − | 0.968536i | \(-0.419940\pi\) | ||||
0.248873 | + | 0.968536i | \(0.419940\pi\) | |||||||
\(564\) | 1.46566e8 | 0.0343999 | ||||||||
\(565\) | −1.46766e9 | −0.342339 | ||||||||
\(566\) | 2.78169e9 | 0.644839 | ||||||||
\(567\) | 1.09935e8 | 0.0253276 | ||||||||
\(568\) | −9.57708e8 | −0.219288 | ||||||||
\(569\) | 4.41050e9 | 1.00368 | 0.501840 | − | 0.864960i | \(-0.332657\pi\) | ||||
0.501840 | + | 0.864960i | \(0.332657\pi\) | |||||||
\(570\) | −1.85193e8 | −0.0418854 | ||||||||
\(571\) | 4.94406e9 | 1.11137 | 0.555683 | − | 0.831394i | \(-0.312457\pi\) | ||||
0.555683 | + | 0.831394i | \(0.312457\pi\) | |||||||
\(572\) | 1.34036e9 | 0.299458 | ||||||||
\(573\) | 2.51631e9 | 0.558758 | ||||||||
\(574\) | −2.64659e8 | −0.0584111 | ||||||||
\(575\) | 6.04678e8 | 0.132644 | ||||||||
\(576\) | 1.91103e8 | 0.0416667 | ||||||||
\(577\) | 9.44836e8 | 0.204758 | 0.102379 | − | 0.994745i | \(-0.467355\pi\) | ||||
0.102379 | + | 0.994745i | \(0.467355\pi\) | |||||||
\(578\) | −1.34473e9 | −0.289659 | ||||||||
\(579\) | 2.24100e9 | 0.479807 | ||||||||
\(580\) | −3.53104e8 | −0.0751458 | ||||||||
\(581\) | −3.68176e8 | −0.0778824 | ||||||||
\(582\) | 1.21057e9 | 0.254542 | ||||||||
\(583\) | −3.65754e8 | −0.0764449 | ||||||||
\(584\) | 2.20571e9 | 0.458251 | ||||||||
\(585\) | −4.00972e8 | −0.0828073 | ||||||||
\(586\) | 3.78261e9 | 0.776516 | ||||||||
\(587\) | −3.67002e9 | −0.748919 | −0.374459 | − | 0.927243i | \(-0.622172\pi\) | ||||
−0.374459 | + | 0.927243i | \(0.622172\pi\) | |||||||
\(588\) | 1.34914e9 | 0.273675 | ||||||||
\(589\) | −9.26963e8 | −0.186921 | ||||||||
\(590\) | 8.19764e8 | 0.164326 | ||||||||
\(591\) | 5.38846e9 | 1.07376 | ||||||||
\(592\) | 5.63386e8 | 0.111604 | ||||||||
\(593\) | −2.74952e9 | −0.541458 | −0.270729 | − | 0.962656i | \(-0.587265\pi\) | ||||
−0.270729 | + | 0.962656i | \(0.587265\pi\) | |||||||
\(594\) | 7.49458e8 | 0.146722 | ||||||||
\(595\) | 4.02458e8 | 0.0783269 | ||||||||
\(596\) | −6.02478e8 | −0.116568 | ||||||||
\(597\) | 2.66691e9 | 0.512977 | ||||||||
\(598\) | −1.36229e9 | −0.260505 | ||||||||
\(599\) | −6.51031e9 | −1.23768 | −0.618839 | − | 0.785517i | \(-0.712397\pi\) | ||||
−0.618839 | + | 0.785517i | \(0.712397\pi\) | |||||||
\(600\) | −2.16000e8 | −0.0408248 | ||||||||
\(601\) | 4.32572e9 | 0.812827 | 0.406413 | − | 0.913689i | \(-0.366779\pi\) | ||||
0.406413 | + | 0.913689i | \(0.366779\pi\) | |||||||
\(602\) | −7.54266e8 | −0.140908 | ||||||||
\(603\) | 7.37010e8 | 0.136887 | ||||||||
\(604\) | −4.70527e9 | −0.868871 | ||||||||
\(605\) | 3.95772e8 | 0.0726610 | ||||||||
\(606\) | −3.68070e9 | −0.671856 | ||||||||
\(607\) | 2.42214e9 | 0.439582 | 0.219791 | − | 0.975547i | \(-0.429463\pi\) | ||||
0.219791 | + | 0.975547i | \(0.429463\pi\) | |||||||
\(608\) | 2.24756e8 | 0.0405554 | ||||||||
\(609\) | 2.46523e8 | 0.0442279 | ||||||||
\(610\) | −3.35140e9 | −0.597821 | ||||||||
\(611\) | 3.73222e8 | 0.0661946 | ||||||||
\(612\) | 7.26169e8 | 0.128058 | ||||||||
\(613\) | 4.99809e9 | 0.876381 | 0.438190 | − | 0.898882i | \(-0.355620\pi\) | ||||
0.438190 | + | 0.898882i | \(0.355620\pi\) | |||||||
\(614\) | −4.19334e9 | −0.731091 | ||||||||
\(615\) | 5.39747e8 | 0.0935681 | ||||||||
\(616\) | −5.04100e8 | −0.0868928 | ||||||||
\(617\) | 4.85821e9 | 0.832680 | 0.416340 | − | 0.909209i | \(-0.363313\pi\) | ||||
0.416340 | + | 0.909209i | \(0.363313\pi\) | |||||||
\(618\) | −1.05897e9 | −0.180477 | ||||||||
\(619\) | −3.22430e9 | −0.546410 | −0.273205 | − | 0.961956i | \(-0.588084\pi\) | ||||
−0.273205 | + | 0.961956i | \(0.588084\pi\) | |||||||
\(620\) | −1.08116e9 | −0.182188 | ||||||||
\(621\) | −7.61720e8 | −0.127636 | ||||||||
\(622\) | 3.07557e9 | 0.512460 | ||||||||
\(623\) | −1.10950e9 | −0.183832 | ||||||||
\(624\) | 4.86631e8 | 0.0801778 | ||||||||
\(625\) | 2.44141e8 | 0.0400000 | ||||||||
\(626\) | 4.70360e9 | 0.766338 | ||||||||
\(627\) | 8.81436e8 | 0.142809 | ||||||||
\(628\) | 3.46114e9 | 0.557648 | ||||||||
\(629\) | 2.14080e9 | 0.343004 | ||||||||
\(630\) | 1.50802e8 | 0.0240279 | ||||||||
\(631\) | −3.33117e8 | −0.0527829 | −0.0263915 | − | 0.999652i | \(-0.508402\pi\) | ||||
−0.0263915 | + | 0.999652i | \(0.508402\pi\) | |||||||
\(632\) | 4.25020e9 | 0.669729 | ||||||||
\(633\) | 3.10747e9 | 0.486960 | ||||||||
\(634\) | 1.39293e9 | 0.217079 | ||||||||
\(635\) | −3.20477e9 | −0.496694 | ||||||||
\(636\) | −1.32790e8 | −0.0204676 | ||||||||
\(637\) | 3.43549e9 | 0.526624 | ||||||||
\(638\) | 1.68062e9 | 0.256210 | ||||||||
\(639\) | −1.36361e9 | −0.206746 | ||||||||
\(640\) | 2.62144e8 | 0.0395285 | ||||||||
\(641\) | 5.35301e9 | 0.802777 | 0.401388 | − | 0.915908i | \(-0.368528\pi\) | ||||
0.401388 | + | 0.915908i | \(0.368528\pi\) | |||||||
\(642\) | −1.46385e9 | −0.218336 | ||||||||
\(643\) | 3.59195e9 | 0.532834 | 0.266417 | − | 0.963858i | \(-0.414160\pi\) | ||||
0.266417 | + | 0.963858i | \(0.414160\pi\) | |||||||
\(644\) | 5.12347e8 | 0.0755899 | ||||||||
\(645\) | 1.53825e9 | 0.225720 | ||||||||
\(646\) | 8.54045e8 | 0.124643 | ||||||||
\(647\) | 8.07758e9 | 1.17251 | 0.586254 | − | 0.810127i | \(-0.300602\pi\) | ||||
0.586254 | + | 0.810127i | \(0.300602\pi\) | |||||||
\(648\) | 2.72098e8 | 0.0392837 | ||||||||
\(649\) | −3.90171e9 | −0.560272 | ||||||||
\(650\) | −5.50030e8 | −0.0785579 | ||||||||
\(651\) | 7.54824e8 | 0.107229 | ||||||||
\(652\) | 3.27617e9 | 0.462914 | ||||||||
\(653\) | 7.62872e9 | 1.07215 | 0.536075 | − | 0.844170i | \(-0.319906\pi\) | ||||
0.536075 | + | 0.844170i | \(0.319906\pi\) | |||||||
\(654\) | 3.12132e9 | 0.436331 | ||||||||
\(655\) | −4.30017e9 | −0.597917 | ||||||||
\(656\) | −6.55053e8 | −0.0905969 | ||||||||
\(657\) | 3.14055e9 | 0.432044 | ||||||||
\(658\) | −1.40366e8 | −0.0192075 | ||||||||
\(659\) | −7.79965e9 | −1.06164 | −0.530819 | − | 0.847485i | \(-0.678115\pi\) | ||||
−0.530819 | + | 0.847485i | \(0.678115\pi\) | |||||||
\(660\) | 1.02806e9 | 0.139193 | ||||||||
\(661\) | 8.75949e9 | 1.17971 | 0.589853 | − | 0.807511i | \(-0.299186\pi\) | ||||
0.589853 | + | 0.807511i | \(0.299186\pi\) | |||||||
\(662\) | 1.08242e9 | 0.145008 | ||||||||
\(663\) | 1.84914e9 | 0.246418 | ||||||||
\(664\) | −9.11267e8 | −0.120797 | ||||||||
\(665\) | 1.77358e8 | 0.0233870 | ||||||||
\(666\) | 8.02164e8 | 0.105221 | ||||||||
\(667\) | −1.70811e9 | −0.222883 | ||||||||
\(668\) | −2.41537e9 | −0.313520 | ||||||||
\(669\) | 8.08155e8 | 0.104353 | ||||||||
\(670\) | 1.01099e9 | 0.129863 | ||||||||
\(671\) | 1.59511e10 | 2.03828 | ||||||||
\(672\) | −1.83018e8 | −0.0232649 | ||||||||
\(673\) | −6.97171e9 | −0.881631 | −0.440815 | − | 0.897598i | \(-0.645311\pi\) | ||||
−0.440815 | + | 0.897598i | \(0.645311\pi\) | |||||||
\(674\) | 5.18402e9 | 0.652165 | ||||||||
\(675\) | −3.07547e8 | −0.0384900 | ||||||||
\(676\) | −2.77673e9 | −0.345717 | ||||||||
\(677\) | −5.15536e8 | −0.0638556 | −0.0319278 | − | 0.999490i | \(-0.510165\pi\) | ||||
−0.0319278 | + | 0.999490i | \(0.510165\pi\) | |||||||
\(678\) | 2.53612e9 | 0.312512 | ||||||||
\(679\) | −1.15936e9 | −0.142126 | ||||||||
\(680\) | 9.96116e8 | 0.121487 | ||||||||
\(681\) | −4.02547e9 | −0.488429 | ||||||||
\(682\) | 5.14586e9 | 0.621173 | ||||||||
\(683\) | −7.68537e9 | −0.922980 | −0.461490 | − | 0.887145i | \(-0.652685\pi\) | ||||
−0.461490 | + | 0.887145i | \(0.652685\pi\) | |||||||
\(684\) | 3.20014e8 | 0.0382360 | ||||||||
\(685\) | −5.06852e9 | −0.602510 | ||||||||
\(686\) | −2.65494e9 | −0.313993 | ||||||||
\(687\) | 5.36740e8 | 0.0631562 | ||||||||
\(688\) | −1.86687e9 | −0.218552 | ||||||||
\(689\) | −3.38142e8 | −0.0393851 | ||||||||
\(690\) | −1.04488e9 | −0.121087 | ||||||||
\(691\) | 1.42973e10 | 1.64847 | 0.824233 | − | 0.566251i | \(-0.191607\pi\) | ||||
0.824233 | + | 0.566251i | \(0.191607\pi\) | |||||||
\(692\) | −4.60336e9 | −0.528085 | ||||||||
\(693\) | −7.17751e8 | −0.0819234 | ||||||||
\(694\) | 2.37807e9 | 0.270064 | ||||||||
\(695\) | −1.07950e9 | −0.121977 | ||||||||
\(696\) | 6.10164e8 | 0.0685984 | ||||||||
\(697\) | −2.48913e9 | −0.278440 | ||||||||
\(698\) | −1.04657e10 | −1.16486 | ||||||||
\(699\) | 6.45072e9 | 0.714395 | ||||||||
\(700\) | 2.06862e8 | 0.0227949 | ||||||||
\(701\) | −2.31241e9 | −0.253543 | −0.126771 | − | 0.991932i | \(-0.540461\pi\) | ||||
−0.126771 | + | 0.991932i | \(0.540461\pi\) | |||||||
\(702\) | 6.92879e8 | 0.0755923 | ||||||||
\(703\) | 9.43424e8 | 0.102415 | ||||||||
\(704\) | −1.24769e9 | −0.134773 | ||||||||
\(705\) | 2.86262e8 | 0.0307682 | ||||||||
\(706\) | −1.10467e10 | −1.18145 | ||||||||
\(707\) | 3.52498e9 | 0.375136 | ||||||||
\(708\) | −1.41655e9 | −0.150009 | ||||||||
\(709\) | 4.95543e9 | 0.522179 | 0.261090 | − | 0.965315i | \(-0.415918\pi\) | ||||
0.261090 | + | 0.965315i | \(0.415918\pi\) | |||||||
\(710\) | −1.87052e9 | −0.196137 | ||||||||
\(711\) | 6.05155e9 | 0.631427 | ||||||||
\(712\) | −2.74611e9 | −0.285127 | ||||||||
\(713\) | −5.23005e9 | −0.540371 | ||||||||
\(714\) | −6.95447e8 | −0.0715024 | ||||||||
\(715\) | 2.61790e9 | 0.267844 | ||||||||
\(716\) | 6.76735e9 | 0.689007 | ||||||||
\(717\) | −1.43407e9 | −0.145296 | ||||||||
\(718\) | −3.59649e8 | −0.0362612 | ||||||||
\(719\) | −5.76278e8 | −0.0578204 | −0.0289102 | − | 0.999582i | \(-0.509204\pi\) | ||||
−0.0289102 | + | 0.999582i | \(0.509204\pi\) | |||||||
\(720\) | 3.73248e8 | 0.0372678 | ||||||||
\(721\) | 1.01416e9 | 0.100771 | ||||||||
\(722\) | 3.76367e8 | 0.0372161 | ||||||||
\(723\) | −2.85373e9 | −0.280820 | ||||||||
\(724\) | −6.64232e9 | −0.650482 | ||||||||
\(725\) | −6.89656e8 | −0.0672125 | ||||||||
\(726\) | −6.83894e8 | −0.0663301 | ||||||||
\(727\) | 1.58205e10 | 1.52703 | 0.763517 | − | 0.645788i | \(-0.223471\pi\) | ||||
0.763517 | + | 0.645788i | \(0.223471\pi\) | |||||||
\(728\) | −4.66044e8 | −0.0447679 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 4.30803e9 | 0.409873 | ||||||||
\(731\) | −7.09389e9 | −0.671697 | ||||||||
\(732\) | 5.79121e9 | 0.545734 | ||||||||
\(733\) | 9.97214e9 | 0.935243 | 0.467622 | − | 0.883929i | \(-0.345111\pi\) | ||||
0.467622 | + | 0.883929i | \(0.345111\pi\) | |||||||
\(734\) | 2.28125e8 | 0.0212930 | ||||||||
\(735\) | 2.63504e9 | 0.244783 | ||||||||
\(736\) | 1.26810e9 | 0.117242 | ||||||||
\(737\) | −4.81185e9 | −0.442767 | ||||||||
\(738\) | −9.32684e8 | −0.0854156 | ||||||||
\(739\) | 1.38681e10 | 1.26405 | 0.632023 | − | 0.774950i | \(-0.282225\pi\) | ||||
0.632023 | + | 0.774950i | \(0.282225\pi\) | |||||||
\(740\) | 1.10036e9 | 0.0998217 | ||||||||
\(741\) | 8.14894e8 | 0.0735762 | ||||||||
\(742\) | 1.27172e8 | 0.0114282 | ||||||||
\(743\) | 1.94879e10 | 1.74303 | 0.871515 | − | 0.490368i | \(-0.163138\pi\) | ||||
0.871515 | + | 0.490368i | \(0.163138\pi\) | |||||||
\(744\) | 1.86825e9 | 0.166314 | ||||||||
\(745\) | −1.17671e9 | −0.104262 | ||||||||
\(746\) | 1.16416e10 | 1.02666 | ||||||||
\(747\) | −1.29749e9 | −0.113889 | ||||||||
\(748\) | −4.74107e9 | −0.414210 | ||||||||
\(749\) | 1.40192e9 | 0.121909 | ||||||||
\(750\) | −4.21875e8 | −0.0365148 | ||||||||
\(751\) | 1.83916e10 | 1.58446 | 0.792229 | − | 0.610224i | \(-0.208920\pi\) | ||||
0.792229 | + | 0.610224i | \(0.208920\pi\) | |||||||
\(752\) | −3.47416e8 | −0.0297912 | ||||||||
\(753\) | 1.00724e10 | 0.859704 | ||||||||
\(754\) | 1.55374e9 | 0.132002 | ||||||||
\(755\) | −9.18998e9 | −0.777142 | ||||||||
\(756\) | −2.60586e8 | −0.0219344 | ||||||||
\(757\) | 4.10747e9 | 0.344143 | 0.172072 | − | 0.985084i | \(-0.444954\pi\) | ||||
0.172072 | + | 0.985084i | \(0.444954\pi\) | |||||||
\(758\) | 4.10352e7 | 0.00342227 | ||||||||
\(759\) | 4.97318e9 | 0.412846 | ||||||||
\(760\) | 4.38976e8 | 0.0362738 | ||||||||
\(761\) | −1.47492e10 | −1.21317 | −0.606587 | − | 0.795017i | \(-0.707462\pi\) | ||||
−0.606587 | + | 0.795017i | \(0.707462\pi\) | |||||||
\(762\) | 5.53784e9 | 0.453417 | ||||||||
\(763\) | −2.98926e9 | −0.243629 | ||||||||
\(764\) | −5.96460e9 | −0.483898 | ||||||||
\(765\) | 1.41830e9 | 0.114539 | ||||||||
\(766\) | −8.18311e9 | −0.657836 | ||||||||
\(767\) | −3.60716e9 | −0.288657 | ||||||||
\(768\) | −4.52985e8 | −0.0360844 | ||||||||
\(769\) | −5.32547e9 | −0.422295 | −0.211147 | − | 0.977454i | \(-0.567720\pi\) | ||||
−0.211147 | + | 0.977454i | \(0.567720\pi\) | |||||||
\(770\) | −9.84570e8 | −0.0777193 | ||||||||
\(771\) | 7.10659e9 | 0.558433 | ||||||||
\(772\) | −5.31200e9 | −0.415525 | ||||||||
\(773\) | 1.61135e10 | 1.25476 | 0.627381 | − | 0.778713i | \(-0.284127\pi\) | ||||
0.627381 | + | 0.778713i | \(0.284127\pi\) | |||||||
\(774\) | −2.65810e9 | −0.206053 | ||||||||
\(775\) | −2.11165e9 | −0.162954 | ||||||||
\(776\) | −2.86950e9 | −0.220440 | ||||||||
\(777\) | −7.68228e8 | −0.0587512 | ||||||||
\(778\) | 9.16951e9 | 0.698100 | ||||||||
\(779\) | −1.09693e9 | −0.0831374 | ||||||||
\(780\) | 9.50452e8 | 0.0717132 | ||||||||
\(781\) | 8.90286e9 | 0.668730 | ||||||||
\(782\) | 4.81864e9 | 0.360330 | ||||||||
\(783\) | 8.68768e8 | 0.0646752 | ||||||||
\(784\) | −3.19796e9 | −0.237010 | ||||||||
\(785\) | 6.76003e9 | 0.498775 | ||||||||
\(786\) | 7.43069e9 | 0.545821 | ||||||||
\(787\) | 2.35231e10 | 1.72022 | 0.860109 | − | 0.510111i | \(-0.170396\pi\) | ||||
0.860109 | + | 0.510111i | \(0.170396\pi\) | |||||||
\(788\) | −1.27726e10 | −0.929905 | ||||||||
\(789\) | −2.33915e9 | −0.169547 | ||||||||
\(790\) | 8.30117e9 | 0.599024 | ||||||||
\(791\) | −2.42883e9 | −0.174493 | ||||||||
\(792\) | −1.77649e9 | −0.127065 | ||||||||
\(793\) | 1.47469e10 | 1.05014 | ||||||||
\(794\) | −1.95506e10 | −1.38608 | ||||||||
\(795\) | −2.59356e8 | −0.0183067 | ||||||||
\(796\) | −6.32156e9 | −0.444251 | ||||||||
\(797\) | −7.94400e9 | −0.555821 | −0.277911 | − | 0.960607i | \(-0.589642\pi\) | ||||
−0.277911 | + | 0.960607i | \(0.589642\pi\) | |||||||
\(798\) | −3.06475e8 | −0.0213494 | ||||||||
\(799\) | −1.32014e9 | −0.0915602 | ||||||||
\(800\) | 5.12000e8 | 0.0353553 | ||||||||
\(801\) | −3.90999e9 | −0.268820 | ||||||||
\(802\) | 1.05853e10 | 0.724592 | ||||||||
\(803\) | −2.05043e10 | −1.39746 | ||||||||
\(804\) | −1.74699e9 | −0.118548 | ||||||||
\(805\) | 1.00068e9 | 0.0676097 | ||||||||
\(806\) | 4.75738e9 | 0.320033 | ||||||||
\(807\) | −1.20705e10 | −0.808480 | ||||||||
\(808\) | 8.72462e9 | 0.581844 | ||||||||
\(809\) | −1.14827e10 | −0.762471 | −0.381236 | − | 0.924478i | \(-0.624501\pi\) | ||||
−0.381236 | + | 0.924478i | \(0.624501\pi\) | |||||||
\(810\) | 5.31441e8 | 0.0351364 | ||||||||
\(811\) | −2.98307e9 | −0.196377 | −0.0981883 | − | 0.995168i | \(-0.531305\pi\) | ||||
−0.0981883 | + | 0.995168i | \(0.531305\pi\) | |||||||
\(812\) | −5.84350e8 | −0.0383025 | ||||||||
\(813\) | −4.08559e9 | −0.266648 | ||||||||
\(814\) | −5.23724e9 | −0.340343 | ||||||||
\(815\) | 6.39877e9 | 0.414043 | ||||||||
\(816\) | −1.72129e9 | −0.110902 | ||||||||
\(817\) | −3.12619e9 | −0.200557 | ||||||||
\(818\) | −2.14167e9 | −0.136810 | ||||||||
\(819\) | −6.63566e8 | −0.0422076 | ||||||||
\(820\) | −1.27940e9 | −0.0810323 | ||||||||
\(821\) | 2.47488e10 | 1.56082 | 0.780411 | − | 0.625266i | \(-0.215010\pi\) | ||||
0.780411 | + | 0.625266i | \(0.215010\pi\) | |||||||
\(822\) | 8.75841e9 | 0.550014 | ||||||||
\(823\) | −1.29801e10 | −0.811668 | −0.405834 | − | 0.913947i | \(-0.633019\pi\) | ||||
−0.405834 | + | 0.913947i | \(0.633019\pi\) | |||||||
\(824\) | 2.51014e9 | 0.156298 | ||||||||
\(825\) | 2.00794e9 | 0.124498 | ||||||||
\(826\) | 1.35662e9 | 0.0837585 | ||||||||
\(827\) | 1.63430e10 | 1.00476 | 0.502381 | − | 0.864646i | \(-0.332458\pi\) | ||||
0.502381 | + | 0.864646i | \(0.332458\pi\) | |||||||
\(828\) | 1.80556e9 | 0.110536 | ||||||||
\(829\) | 2.58055e10 | 1.57316 | 0.786579 | − | 0.617490i | \(-0.211850\pi\) | ||||
0.786579 | + | 0.617490i | \(0.211850\pi\) | |||||||
\(830\) | −1.77982e9 | −0.108044 | ||||||||
\(831\) | 5.23346e9 | 0.316363 | ||||||||
\(832\) | −1.15350e9 | −0.0694360 | ||||||||
\(833\) | −1.21519e10 | −0.728426 | ||||||||
\(834\) | 1.86538e9 | 0.111349 | ||||||||
\(835\) | −4.71751e9 | −0.280421 | ||||||||
\(836\) | −2.08933e9 | −0.123676 | ||||||||
\(837\) | 2.66007e9 | 0.156803 | ||||||||
\(838\) | −6.32081e8 | −0.0371038 | ||||||||
\(839\) | −6.76897e9 | −0.395690 | −0.197845 | − | 0.980233i | \(-0.563394\pi\) | ||||
−0.197845 | + | 0.980233i | \(0.563394\pi\) | |||||||
\(840\) | −3.57457e8 | −0.0208088 | ||||||||
\(841\) | −1.53017e10 | −0.887062 | ||||||||
\(842\) | −3.74786e8 | −0.0216367 | ||||||||
\(843\) | 3.24515e9 | 0.186568 | ||||||||
\(844\) | −7.36585e9 | −0.421720 | ||||||||
\(845\) | −5.42330e9 | −0.309218 | ||||||||
\(846\) | −4.94661e8 | −0.0280874 | ||||||||
\(847\) | 6.54961e8 | 0.0370359 | ||||||||
\(848\) | 3.14762e8 | 0.0177254 | ||||||||
\(849\) | −9.38820e9 | −0.526509 | ||||||||
\(850\) | 1.94554e9 | 0.108661 | ||||||||
\(851\) | 5.32292e9 | 0.296072 | ||||||||
\(852\) | 3.23227e9 | 0.179048 | ||||||||
\(853\) | −2.17274e10 | −1.19863 | −0.599317 | − | 0.800512i | \(-0.704561\pi\) | ||||
−0.599317 | + | 0.800512i | \(0.704561\pi\) | |||||||
\(854\) | −5.54621e9 | −0.304715 | ||||||||
\(855\) | 6.25026e8 | 0.0341993 | ||||||||
\(856\) | 3.46987e9 | 0.189084 | ||||||||
\(857\) | −1.72647e10 | −0.936970 | −0.468485 | − | 0.883471i | \(-0.655200\pi\) | ||||
−0.468485 | + | 0.883471i | \(0.655200\pi\) | |||||||
\(858\) | −4.52373e9 | −0.244507 | ||||||||
\(859\) | 2.88521e10 | 1.55311 | 0.776554 | − | 0.630051i | \(-0.216966\pi\) | ||||
0.776554 | + | 0.630051i | \(0.216966\pi\) | |||||||
\(860\) | −3.64623e9 | −0.195479 | ||||||||
\(861\) | 8.93225e8 | 0.0476925 | ||||||||
\(862\) | −9.96859e9 | −0.530101 | ||||||||
\(863\) | 3.79538e9 | 0.201010 | 0.100505 | − | 0.994937i | \(-0.467954\pi\) | ||||
0.100505 | + | 0.994937i | \(0.467954\pi\) | |||||||
\(864\) | −6.44973e8 | −0.0340207 | ||||||||
\(865\) | −8.99093e9 | −0.472333 | ||||||||
\(866\) | −1.89752e10 | −0.992829 | ||||||||
\(867\) | 4.53845e9 | 0.236505 | ||||||||
\(868\) | −1.78921e9 | −0.0928630 | ||||||||
\(869\) | −3.95098e10 | −2.04238 | ||||||||
\(870\) | 1.19173e9 | 0.0613563 | ||||||||
\(871\) | −4.44859e9 | −0.228117 | ||||||||
\(872\) | −7.39867e9 | −0.377873 | ||||||||
\(873\) | −4.08568e9 | −0.207833 | ||||||||
\(874\) | 2.12351e9 | 0.107588 | ||||||||
\(875\) | 4.04027e8 | 0.0203884 | ||||||||
\(876\) | −7.44428e9 | −0.374161 | ||||||||
\(877\) | −2.28605e9 | −0.114443 | −0.0572213 | − | 0.998362i | \(-0.518224\pi\) | ||||
−0.0572213 | + | 0.998362i | \(0.518224\pi\) | |||||||
\(878\) | 1.87527e10 | 0.935048 | ||||||||
\(879\) | −1.27663e10 | −0.634022 | ||||||||
\(880\) | −2.43689e9 | −0.120544 | ||||||||
\(881\) | −4.06251e9 | −0.200161 | −0.100080 | − | 0.994979i | \(-0.531910\pi\) | ||||
−0.100080 | + | 0.994979i | \(0.531910\pi\) | |||||||
\(882\) | −4.55334e9 | −0.223455 | ||||||||
\(883\) | 1.07134e10 | 0.523679 | 0.261840 | − | 0.965111i | \(-0.415671\pi\) | ||||
0.261840 | + | 0.965111i | \(0.415671\pi\) | |||||||
\(884\) | −4.38315e9 | −0.213404 | ||||||||
\(885\) | −2.76670e9 | −0.134172 | ||||||||
\(886\) | 6.85469e9 | 0.331108 | ||||||||
\(887\) | −3.68605e10 | −1.77349 | −0.886745 | − | 0.462259i | \(-0.847039\pi\) | ||||
−0.886745 | + | 0.462259i | \(0.847039\pi\) | |||||||
\(888\) | −1.90143e9 | −0.0911243 | ||||||||
\(889\) | −5.30355e9 | −0.253169 | ||||||||
\(890\) | −5.36350e9 | −0.255025 | ||||||||
\(891\) | −2.52942e9 | −0.119798 | ||||||||
\(892\) | −1.91563e9 | −0.0903720 | ||||||||
\(893\) | −5.81770e8 | −0.0273383 | ||||||||
\(894\) | 2.03336e9 | 0.0951773 | ||||||||
\(895\) | 1.32175e10 | 0.616266 | ||||||||
\(896\) | 4.33821e8 | 0.0201480 | ||||||||
\(897\) | 4.59774e9 | 0.212702 | ||||||||
\(898\) | 1.75583e10 | 0.809123 | ||||||||
\(899\) | 5.96505e9 | 0.273814 | ||||||||
\(900\) | 7.29000e8 | 0.0333333 | ||||||||
\(901\) | 1.19606e9 | 0.0544773 | ||||||||
\(902\) | 6.08938e9 | 0.276280 | ||||||||
\(903\) | 2.54565e9 | 0.115051 | ||||||||
\(904\) | −6.01155e9 | −0.270643 | ||||||||
\(905\) | −1.29733e10 | −0.581808 | ||||||||
\(906\) | 1.58803e10 | 0.709430 | ||||||||
\(907\) | 1.92263e10 | 0.855597 | 0.427798 | − | 0.903874i | \(-0.359289\pi\) | ||||
0.427798 | + | 0.903874i | \(0.359289\pi\) | |||||||
\(908\) | 9.54186e9 | 0.422992 | ||||||||
\(909\) | 1.24224e10 | 0.548568 | ||||||||
\(910\) | −9.10242e8 | −0.0400416 | ||||||||
\(911\) | −2.04778e10 | −0.897366 | −0.448683 | − | 0.893691i | \(-0.648107\pi\) | ||||
−0.448683 | + | 0.893691i | \(0.648107\pi\) | |||||||
\(912\) | −7.58551e8 | −0.0331133 | ||||||||
\(913\) | 8.47114e9 | 0.368378 | ||||||||
\(914\) | −2.34848e10 | −1.01736 | ||||||||
\(915\) | 1.13110e10 | 0.488119 | ||||||||
\(916\) | −1.27227e9 | −0.0546948 | ||||||||
\(917\) | −7.11632e9 | −0.304764 | ||||||||
\(918\) | −2.45082e9 | −0.104559 | ||||||||
\(919\) | −2.68137e10 | −1.13960 | −0.569801 | − | 0.821783i | \(-0.692980\pi\) | ||||
−0.569801 | + | 0.821783i | \(0.692980\pi\) | |||||||
\(920\) | 2.47676e9 | 0.104864 | ||||||||
\(921\) | 1.41525e10 | 0.596933 | ||||||||
\(922\) | 9.79849e9 | 0.411719 | ||||||||
\(923\) | 8.23075e9 | 0.344535 | ||||||||
\(924\) | 1.70134e9 | 0.0709477 | ||||||||
\(925\) | 2.14915e9 | 0.0892832 | ||||||||
\(926\) | −1.49388e10 | −0.618267 | ||||||||
\(927\) | 3.57401e9 | 0.147359 | ||||||||
\(928\) | −1.44631e9 | −0.0594080 | ||||||||
\(929\) | −2.85833e10 | −1.16965 | −0.584827 | − | 0.811158i | \(-0.698837\pi\) | ||||
−0.584827 | + | 0.811158i | \(0.698837\pi\) | |||||||
\(930\) | 3.64893e9 | 0.148756 | ||||||||
\(931\) | −5.35517e9 | −0.217495 | ||||||||
\(932\) | −1.52906e10 | −0.618684 | ||||||||
\(933\) | −1.03801e10 | −0.418422 | ||||||||
\(934\) | 1.49562e10 | 0.600632 | ||||||||
\(935\) | −9.25990e9 | −0.370481 | ||||||||
\(936\) | −1.64238e9 | −0.0654649 | ||||||||
\(937\) | 4.64965e10 | 1.84643 | 0.923213 | − | 0.384288i | \(-0.125553\pi\) | ||||
0.923213 | + | 0.384288i | \(0.125553\pi\) | |||||||
\(938\) | 1.67308e9 | 0.0661921 | ||||||||
\(939\) | −1.58746e10 | −0.625712 | ||||||||
\(940\) | −6.78548e8 | −0.0266460 | ||||||||
\(941\) | −4.13029e10 | −1.61591 | −0.807955 | − | 0.589244i | \(-0.799426\pi\) | ||||
−0.807955 | + | 0.589244i | \(0.799426\pi\) | |||||||
\(942\) | −1.16813e10 | −0.455317 | ||||||||
\(943\) | −6.18901e9 | −0.240342 | ||||||||
\(944\) | 3.35775e9 | 0.129911 | ||||||||
\(945\) | −5.08958e8 | −0.0196187 | ||||||||
\(946\) | 1.73544e10 | 0.666487 | ||||||||
\(947\) | −3.91284e10 | −1.49716 | −0.748578 | − | 0.663047i | \(-0.769263\pi\) | ||||
−0.748578 | + | 0.663047i | \(0.769263\pi\) | |||||||
\(948\) | −1.43444e10 | −0.546832 | ||||||||
\(949\) | −1.89564e10 | −0.719985 | ||||||||
\(950\) | 8.57375e8 | 0.0324443 | ||||||||
\(951\) | −4.70114e9 | −0.177244 | ||||||||
\(952\) | 1.64847e9 | 0.0619229 | ||||||||
\(953\) | −1.91770e10 | −0.717720 | −0.358860 | − | 0.933391i | \(-0.616834\pi\) | ||||
−0.358860 | + | 0.933391i | \(0.616834\pi\) | |||||||
\(954\) | 4.48167e8 | 0.0167117 | ||||||||
\(955\) | −1.16496e10 | −0.432812 | ||||||||
\(956\) | 3.39929e9 | 0.125830 | ||||||||
\(957\) | −5.67208e9 | −0.209195 | ||||||||
\(958\) | −3.58201e10 | −1.31628 | ||||||||
\(959\) | −8.38787e9 | −0.307105 | ||||||||
\(960\) | −8.84736e8 | −0.0322749 | ||||||||
\(961\) | −9.24832e9 | −0.336148 | ||||||||
\(962\) | −4.84186e9 | −0.175347 | ||||||||
\(963\) | 4.94050e9 | 0.178270 | ||||||||
\(964\) | 6.76439e9 | 0.243198 | ||||||||
\(965\) | −1.03750e10 | −0.371657 | ||||||||
\(966\) | −1.72917e9 | −0.0617189 | ||||||||
\(967\) | 3.42399e10 | 1.21770 | 0.608849 | − | 0.793286i | \(-0.291632\pi\) | ||||
0.608849 | + | 0.793286i | \(0.291632\pi\) | |||||||
\(968\) | 1.62108e9 | 0.0574435 | ||||||||
\(969\) | −2.88240e9 | −0.101770 | ||||||||
\(970\) | −5.60450e9 | −0.197168 | ||||||||
\(971\) | −6.42267e9 | −0.225138 | −0.112569 | − | 0.993644i | \(-0.535908\pi\) | ||||
−0.112569 | + | 0.993644i | \(0.535908\pi\) | |||||||
\(972\) | −9.18330e8 | −0.0320750 | ||||||||
\(973\) | −1.78647e9 | −0.0621727 | ||||||||
\(974\) | −2.71666e9 | −0.0942061 | ||||||||
\(975\) | 1.85635e9 | 0.0641422 | ||||||||
\(976\) | −1.37273e10 | −0.472619 | ||||||||
\(977\) | 2.38602e10 | 0.818545 | 0.409272 | − | 0.912412i | \(-0.365783\pi\) | ||||
0.409272 | + | 0.912412i | \(0.365783\pi\) | |||||||
\(978\) | −1.10571e10 | −0.377968 | ||||||||
\(979\) | 2.55278e10 | 0.869510 | ||||||||
\(980\) | −6.24601e9 | −0.211988 | ||||||||
\(981\) | −1.05344e10 | −0.356262 | ||||||||
\(982\) | 1.55506e10 | 0.524030 | ||||||||
\(983\) | −2.08936e10 | −0.701577 | −0.350788 | − | 0.936455i | \(-0.614086\pi\) | ||||
−0.350788 | + | 0.936455i | \(0.614086\pi\) | |||||||
\(984\) | 2.21081e9 | 0.0739721 | ||||||||
\(985\) | −2.49466e10 | −0.831733 | ||||||||
\(986\) | −5.49582e9 | −0.182584 | ||||||||
\(987\) | 4.73734e8 | 0.0156828 | ||||||||
\(988\) | −1.93160e9 | −0.0637188 | ||||||||
\(989\) | −1.76384e10 | −0.579791 | ||||||||
\(990\) | −3.46971e9 | −0.113650 | ||||||||
\(991\) | 3.63659e10 | 1.18696 | 0.593480 | − | 0.804849i | \(-0.297754\pi\) | ||||
0.593480 | + | 0.804849i | \(0.297754\pi\) | |||||||
\(992\) | −4.42845e9 | −0.144033 | ||||||||
\(993\) | −3.65317e9 | −0.118399 | ||||||||
\(994\) | −3.09552e9 | −0.0999727 | ||||||||
\(995\) | −1.23468e10 | −0.397350 | ||||||||
\(996\) | 3.07553e9 | 0.0986306 | ||||||||
\(997\) | 5.24744e9 | 0.167693 | 0.0838464 | − | 0.996479i | \(-0.473279\pi\) | ||||
0.0838464 | + | 0.996479i | \(0.473279\pi\) | |||||||
\(998\) | 1.68757e10 | 0.537408 | ||||||||
\(999\) | −2.70731e9 | −0.0859128 |
(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 | 570.8.a.a.1.3 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.8.a.a.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial |