Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,8,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(55.2921495107\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 6 x^{17} - 1798 x^{16} + 11087 x^{15} + 1326765 x^{14} - 8403720 x^{13} - 518334228 x^{12} + 3375594921 x^{11} + 115310342333 x^{10} + \cdots + 51\!\cdots\!48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(2.80127\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.80127 | 0.335988 | 0.167994 | − | 0.985788i | \(-0.446271\pi\) | ||||
0.167994 | + | 0.985788i | \(0.446271\pi\) | |||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | −113.550 | −0.887112 | ||||||||
\(5\) | −87.8737 | −0.314387 | −0.157193 | − | 0.987568i | \(-0.550245\pi\) | ||||
−0.157193 | + | 0.987568i | \(0.550245\pi\) | |||||||
\(6\) | 102.634 | 0.193983 | ||||||||
\(7\) | 1306.06 | 1.43919 | 0.719596 | − | 0.694393i | \(-0.244327\pi\) | ||||
0.719596 | + | 0.694393i | \(0.244327\pi\) | |||||||
\(8\) | −918.197 | −0.634046 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | −334.031 | −0.105630 | ||||||||
\(11\) | −3799.92 | −0.860796 | −0.430398 | − | 0.902639i | \(-0.641627\pi\) | ||||
−0.430398 | + | 0.902639i | \(0.641627\pi\) | |||||||
\(12\) | −3065.86 | −0.512175 | ||||||||
\(13\) | 8976.87 | 1.13324 | 0.566622 | − | 0.823978i | \(-0.308250\pi\) | ||||
0.566622 | + | 0.823978i | \(0.308250\pi\) | |||||||
\(14\) | 4964.66 | 0.483550 | ||||||||
\(15\) | −2372.59 | −0.181511 | ||||||||
\(16\) | 11044.1 | 0.674081 | ||||||||
\(17\) | −4357.97 | −0.215136 | −0.107568 | − | 0.994198i | \(-0.534306\pi\) | ||||
−0.107568 | + | 0.994198i | \(0.534306\pi\) | |||||||
\(18\) | 2771.12 | 0.111996 | ||||||||
\(19\) | −57085.5 | −1.90936 | −0.954680 | − | 0.297633i | \(-0.903803\pi\) | ||||
−0.954680 | + | 0.297633i | \(0.903803\pi\) | |||||||
\(20\) | 9978.10 | 0.278896 | ||||||||
\(21\) | 35263.5 | 0.830917 | ||||||||
\(22\) | −14444.5 | −0.289217 | ||||||||
\(23\) | 96669.6 | 1.65670 | 0.828348 | − | 0.560214i | \(-0.189281\pi\) | ||||
0.828348 | + | 0.560214i | \(0.189281\pi\) | |||||||
\(24\) | −24791.3 | −0.366067 | ||||||||
\(25\) | −70403.2 | −0.901161 | ||||||||
\(26\) | 34123.5 | 0.380756 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | −148303. | −1.27672 | ||||||||
\(29\) | 22753.4 | 0.173242 | 0.0866212 | − | 0.996241i | \(-0.472393\pi\) | ||||
0.0866212 | + | 0.996241i | \(0.472393\pi\) | |||||||
\(30\) | −9018.85 | −0.0609855 | ||||||||
\(31\) | −53358.6 | −0.321691 | −0.160845 | − | 0.986980i | \(-0.551422\pi\) | ||||
−0.160845 | + | 0.986980i | \(0.551422\pi\) | |||||||
\(32\) | 159511. | 0.860529 | ||||||||
\(33\) | −102598. | −0.496981 | ||||||||
\(34\) | −16565.8 | −0.0722830 | ||||||||
\(35\) | −114768. | −0.452462 | ||||||||
\(36\) | −82778.2 | −0.295704 | ||||||||
\(37\) | 319784. | 1.03789 | 0.518944 | − | 0.854808i | \(-0.326325\pi\) | ||||
0.518944 | + | 0.854808i | \(0.326325\pi\) | |||||||
\(38\) | −216997. | −0.641522 | ||||||||
\(39\) | 242376. | 0.654279 | ||||||||
\(40\) | 80685.4 | 0.199336 | ||||||||
\(41\) | 476338. | 1.07937 | 0.539687 | − | 0.841866i | \(-0.318543\pi\) | ||||
0.539687 | + | 0.841866i | \(0.318543\pi\) | |||||||
\(42\) | 134046. | 0.279178 | ||||||||
\(43\) | 707558. | 1.35713 | 0.678567 | − | 0.734539i | \(-0.262601\pi\) | ||||
0.678567 | + | 0.734539i | \(0.262601\pi\) | |||||||
\(44\) | 431483. | 0.763623 | ||||||||
\(45\) | −64060.0 | −0.104796 | ||||||||
\(46\) | 367467. | 0.556629 | ||||||||
\(47\) | 946330. | 1.32954 | 0.664768 | − | 0.747050i | \(-0.268530\pi\) | ||||
0.664768 | + | 0.747050i | \(0.268530\pi\) | |||||||
\(48\) | 298192. | 0.389181 | ||||||||
\(49\) | 882238. | 1.07127 | ||||||||
\(50\) | −267621. | −0.302779 | ||||||||
\(51\) | −117665. | −0.124209 | ||||||||
\(52\) | −1.01933e6 | −1.00531 | ||||||||
\(53\) | 799926. | 0.738047 | 0.369024 | − | 0.929420i | \(-0.379692\pi\) | ||||
0.369024 | + | 0.929420i | \(0.379692\pi\) | |||||||
\(54\) | 74820.3 | 0.0646608 | ||||||||
\(55\) | 333913. | 0.270623 | ||||||||
\(56\) | −1.19922e6 | −0.912514 | ||||||||
\(57\) | −1.54131e6 | −1.10237 | ||||||||
\(58\) | 86491.9 | 0.0582073 | ||||||||
\(59\) | 205379. | 0.130189 | ||||||||
\(60\) | 269409. | 0.161021 | ||||||||
\(61\) | 539847. | 0.304520 | 0.152260 | − | 0.988340i | \(-0.451345\pi\) | ||||
0.152260 | + | 0.988340i | \(0.451345\pi\) | |||||||
\(62\) | −202830. | −0.108084 | ||||||||
\(63\) | 952114. | 0.479730 | ||||||||
\(64\) | −807306. | −0.384954 | ||||||||
\(65\) | −788832. | −0.356277 | ||||||||
\(66\) | −390002. | −0.166979 | ||||||||
\(67\) | 2.90460e6 | 1.17985 | 0.589923 | − | 0.807460i | \(-0.299158\pi\) | ||||
0.589923 | + | 0.807460i | \(0.299158\pi\) | |||||||
\(68\) | 494849. | 0.190850 | ||||||||
\(69\) | 2.61008e6 | 0.956493 | ||||||||
\(70\) | −436264. | −0.152022 | ||||||||
\(71\) | −523802. | −0.173685 | −0.0868426 | − | 0.996222i | \(-0.527678\pi\) | ||||
−0.0868426 | + | 0.996222i | \(0.527678\pi\) | |||||||
\(72\) | −669366. | −0.211349 | ||||||||
\(73\) | −2.11143e6 | −0.635252 | −0.317626 | − | 0.948216i | \(-0.602886\pi\) | ||||
−0.317626 | + | 0.948216i | \(0.602886\pi\) | |||||||
\(74\) | 1.21558e6 | 0.348718 | ||||||||
\(75\) | −1.90089e6 | −0.520286 | ||||||||
\(76\) | 6.48208e6 | 1.69382 | ||||||||
\(77\) | −4.96291e6 | −1.23885 | ||||||||
\(78\) | 921334. | 0.219830 | ||||||||
\(79\) | −3.80223e6 | −0.867648 | −0.433824 | − | 0.900998i | \(-0.642836\pi\) | ||||
−0.433824 | + | 0.900998i | \(0.642836\pi\) | |||||||
\(80\) | −970490. | −0.211922 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 1.81069e6 | 0.362656 | ||||||||
\(83\) | 1.88881e6 | 0.362589 | 0.181294 | − | 0.983429i | \(-0.441971\pi\) | ||||
0.181294 | + | 0.983429i | \(0.441971\pi\) | |||||||
\(84\) | −4.00418e6 | −0.737117 | ||||||||
\(85\) | 382951. | 0.0676359 | ||||||||
\(86\) | 2.68962e6 | 0.455980 | ||||||||
\(87\) | 614343. | 0.100022 | ||||||||
\(88\) | 3.48908e6 | 0.545785 | ||||||||
\(89\) | 6.48074e6 | 0.974450 | 0.487225 | − | 0.873277i | \(-0.338009\pi\) | ||||
0.487225 | + | 0.873277i | \(0.338009\pi\) | |||||||
\(90\) | −243509. | −0.0352100 | ||||||||
\(91\) | 1.17243e7 | 1.63095 | ||||||||
\(92\) | −1.09769e7 | −1.46967 | ||||||||
\(93\) | −1.44068e6 | −0.185728 | ||||||||
\(94\) | 3.59725e6 | 0.446708 | ||||||||
\(95\) | 5.01631e6 | 0.600278 | ||||||||
\(96\) | 4.30680e6 | 0.496827 | ||||||||
\(97\) | 2.84275e6 | 0.316256 | 0.158128 | − | 0.987419i | \(-0.449454\pi\) | ||||
0.158128 | + | 0.987419i | \(0.449454\pi\) | |||||||
\(98\) | 3.35362e6 | 0.359934 | ||||||||
\(99\) | −2.77014e6 | −0.286932 | ||||||||
\(100\) | 7.99431e6 | 0.799431 | ||||||||
\(101\) | 1.41130e6 | 0.136299 | 0.0681497 | − | 0.997675i | \(-0.478290\pi\) | ||||
0.0681497 | + | 0.997675i | \(0.478290\pi\) | |||||||
\(102\) | −447277. | −0.0417326 | ||||||||
\(103\) | 1.05972e7 | 0.955564 | 0.477782 | − | 0.878478i | \(-0.341441\pi\) | ||||
0.477782 | + | 0.878478i | \(0.341441\pi\) | |||||||
\(104\) | −8.24254e6 | −0.718529 | ||||||||
\(105\) | −3.09874e6 | −0.261229 | ||||||||
\(106\) | 3.04073e6 | 0.247975 | ||||||||
\(107\) | 1.84524e7 | 1.45616 | 0.728082 | − | 0.685490i | \(-0.240412\pi\) | ||||
0.728082 | + | 0.685490i | \(0.240412\pi\) | |||||||
\(108\) | −2.23501e6 | −0.170725 | ||||||||
\(109\) | −1.18614e7 | −0.877289 | −0.438645 | − | 0.898661i | \(-0.644541\pi\) | ||||
−0.438645 | + | 0.898661i | \(0.644541\pi\) | |||||||
\(110\) | 1.26929e6 | 0.0909259 | ||||||||
\(111\) | 8.63417e6 | 0.599225 | ||||||||
\(112\) | 1.44243e7 | 0.970131 | ||||||||
\(113\) | 1.57496e7 | 1.02682 | 0.513412 | − | 0.858142i | \(-0.328381\pi\) | ||||
0.513412 | + | 0.858142i | \(0.328381\pi\) | |||||||
\(114\) | −5.85892e6 | −0.370383 | ||||||||
\(115\) | −8.49472e6 | −0.520843 | ||||||||
\(116\) | −2.58366e6 | −0.153685 | ||||||||
\(117\) | 6.54414e6 | 0.377748 | ||||||||
\(118\) | 780700. | 0.0437419 | ||||||||
\(119\) | −5.69175e6 | −0.309622 | ||||||||
\(120\) | 2.17851e6 | 0.115087 | ||||||||
\(121\) | −5.04777e6 | −0.259030 | ||||||||
\(122\) | 2.05210e6 | 0.102315 | ||||||||
\(123\) | 1.28611e7 | 0.623177 | ||||||||
\(124\) | 6.05889e6 | 0.285376 | ||||||||
\(125\) | 1.30517e7 | 0.597700 | ||||||||
\(126\) | 3.61924e6 | 0.161183 | ||||||||
\(127\) | −1.74843e7 | −0.757417 | −0.378708 | − | 0.925516i | \(-0.623632\pi\) | ||||
−0.378708 | + | 0.925516i | \(0.623632\pi\) | |||||||
\(128\) | −2.34862e7 | −0.989869 | ||||||||
\(129\) | 1.91041e7 | 0.783541 | ||||||||
\(130\) | −2.99856e6 | −0.119705 | ||||||||
\(131\) | 3.83994e7 | 1.49236 | 0.746182 | − | 0.665742i | \(-0.231885\pi\) | ||||
0.746182 | + | 0.665742i | \(0.231885\pi\) | |||||||
\(132\) | 1.16500e7 | 0.440878 | ||||||||
\(133\) | −7.45568e7 | −2.74794 | ||||||||
\(134\) | 1.10412e7 | 0.396413 | ||||||||
\(135\) | −1.72962e6 | −0.0605037 | ||||||||
\(136\) | 4.00148e6 | 0.136406 | ||||||||
\(137\) | −4.77564e7 | −1.58675 | −0.793376 | − | 0.608731i | \(-0.791679\pi\) | ||||
−0.793376 | + | 0.608731i | \(0.791679\pi\) | |||||||
\(138\) | 9.92161e6 | 0.321370 | ||||||||
\(139\) | −9.01121e6 | −0.284598 | −0.142299 | − | 0.989824i | \(-0.545449\pi\) | ||||
−0.142299 | + | 0.989824i | \(0.545449\pi\) | |||||||
\(140\) | 1.30319e7 | 0.401385 | ||||||||
\(141\) | 2.55509e7 | 0.767608 | ||||||||
\(142\) | −1.99111e6 | −0.0583561 | ||||||||
\(143\) | −3.41114e7 | −0.975492 | ||||||||
\(144\) | 8.05118e6 | 0.224694 | ||||||||
\(145\) | −1.99943e6 | −0.0544651 | ||||||||
\(146\) | −8.02609e6 | −0.213437 | ||||||||
\(147\) | 2.38204e7 | 0.618499 | ||||||||
\(148\) | −3.63116e7 | −0.920724 | ||||||||
\(149\) | −1.73883e7 | −0.430631 | −0.215315 | − | 0.976545i | \(-0.569078\pi\) | ||||
−0.215315 | + | 0.976545i | \(0.569078\pi\) | |||||||
\(150\) | −7.22577e6 | −0.174809 | ||||||||
\(151\) | 1.46672e7 | 0.346680 | 0.173340 | − | 0.984862i | \(-0.444544\pi\) | ||||
0.173340 | + | 0.984862i | \(0.444544\pi\) | |||||||
\(152\) | 5.24157e7 | 1.21062 | ||||||||
\(153\) | −3.17696e6 | −0.0717120 | ||||||||
\(154\) | −1.88653e7 | −0.416238 | ||||||||
\(155\) | 4.68882e6 | 0.101135 | ||||||||
\(156\) | −2.75218e7 | −0.580419 | ||||||||
\(157\) | 4.11300e7 | 0.848222 | 0.424111 | − | 0.905610i | \(-0.360587\pi\) | ||||
0.424111 | + | 0.905610i | \(0.360587\pi\) | |||||||
\(158\) | −1.44533e7 | −0.291519 | ||||||||
\(159\) | 2.15980e7 | 0.426112 | ||||||||
\(160\) | −1.40168e7 | −0.270539 | ||||||||
\(161\) | 1.26256e8 | 2.38430 | ||||||||
\(162\) | 2.02015e6 | 0.0373320 | ||||||||
\(163\) | −1.02265e6 | −0.0184957 | −0.00924783 | − | 0.999957i | \(-0.502944\pi\) | ||||
−0.00924783 | + | 0.999957i | \(0.502944\pi\) | |||||||
\(164\) | −5.40884e7 | −0.957526 | ||||||||
\(165\) | 9.01566e6 | 0.156244 | ||||||||
\(166\) | 7.17986e6 | 0.121825 | ||||||||
\(167\) | −4.54084e6 | −0.0754447 | −0.0377224 | − | 0.999288i | \(-0.512010\pi\) | ||||
−0.0377224 | + | 0.999288i | \(0.512010\pi\) | |||||||
\(168\) | −3.23788e7 | −0.526840 | ||||||||
\(169\) | 1.78358e7 | 0.284242 | ||||||||
\(170\) | 1.45570e6 | 0.0227248 | ||||||||
\(171\) | −4.16153e7 | −0.636454 | ||||||||
\(172\) | −8.03435e7 | −1.20393 | ||||||||
\(173\) | 1.45643e7 | 0.213860 | 0.106930 | − | 0.994267i | \(-0.465898\pi\) | ||||
0.106930 | + | 0.994267i | \(0.465898\pi\) | |||||||
\(174\) | 2.33528e6 | 0.0336060 | ||||||||
\(175\) | −9.19505e7 | −1.29694 | ||||||||
\(176\) | −4.19669e7 | −0.580246 | ||||||||
\(177\) | 5.54523e6 | 0.0751646 | ||||||||
\(178\) | 2.46350e7 | 0.327403 | ||||||||
\(179\) | −7.59717e7 | −0.990071 | −0.495036 | − | 0.868873i | \(-0.664845\pi\) | ||||
−0.495036 | + | 0.868873i | \(0.664845\pi\) | |||||||
\(180\) | 7.27403e6 | 0.0929654 | ||||||||
\(181\) | −1.08062e8 | −1.35456 | −0.677281 | − | 0.735724i | \(-0.736842\pi\) | ||||
−0.677281 | + | 0.735724i | \(0.736842\pi\) | |||||||
\(182\) | 4.45672e7 | 0.547981 | ||||||||
\(183\) | 1.45759e7 | 0.175815 | ||||||||
\(184\) | −8.87618e7 | −1.05042 | ||||||||
\(185\) | −2.81006e7 | −0.326298 | ||||||||
\(186\) | −5.47642e6 | −0.0624024 | ||||||||
\(187\) | 1.65599e7 | 0.185188 | ||||||||
\(188\) | −1.07456e8 | −1.17945 | ||||||||
\(189\) | 2.57071e7 | 0.276972 | ||||||||
\(190\) | 1.90683e7 | 0.201686 | ||||||||
\(191\) | −1.32489e8 | −1.37583 | −0.687914 | − | 0.725792i | \(-0.741473\pi\) | ||||
−0.687914 | + | 0.725792i | \(0.741473\pi\) | |||||||
\(192\) | −2.17973e7 | −0.222253 | ||||||||
\(193\) | 1.01108e8 | 1.01236 | 0.506178 | − | 0.862429i | \(-0.331058\pi\) | ||||
0.506178 | + | 0.862429i | \(0.331058\pi\) | |||||||
\(194\) | 1.08061e7 | 0.106258 | ||||||||
\(195\) | −2.12985e7 | −0.205696 | ||||||||
\(196\) | −1.00178e8 | −0.950338 | ||||||||
\(197\) | 1.00275e7 | 0.0934464 | 0.0467232 | − | 0.998908i | \(-0.485122\pi\) | ||||
0.0467232 | + | 0.998908i | \(0.485122\pi\) | |||||||
\(198\) | −1.05300e7 | −0.0964056 | ||||||||
\(199\) | 6.35124e7 | 0.571312 | 0.285656 | − | 0.958332i | \(-0.407789\pi\) | ||||
0.285656 | + | 0.958332i | \(0.407789\pi\) | |||||||
\(200\) | 6.46440e7 | 0.571378 | ||||||||
\(201\) | 7.84243e7 | 0.681184 | ||||||||
\(202\) | 5.36472e6 | 0.0457949 | ||||||||
\(203\) | 2.97173e7 | 0.249329 | ||||||||
\(204\) | 1.33609e7 | 0.110187 | ||||||||
\(205\) | −4.18576e7 | −0.339341 | ||||||||
\(206\) | 4.02827e7 | 0.321058 | ||||||||
\(207\) | 7.04722e7 | 0.552232 | ||||||||
\(208\) | 9.91418e7 | 0.763898 | ||||||||
\(209\) | 2.16920e8 | 1.64357 | ||||||||
\(210\) | −1.17791e7 | −0.0877698 | ||||||||
\(211\) | 2.91443e7 | 0.213582 | 0.106791 | − | 0.994281i | \(-0.465942\pi\) | ||||
0.106791 | + | 0.994281i | \(0.465942\pi\) | |||||||
\(212\) | −9.08319e7 | −0.654731 | ||||||||
\(213\) | −1.41427e7 | −0.100277 | ||||||||
\(214\) | 7.01426e7 | 0.489253 | ||||||||
\(215\) | −6.21758e7 | −0.426665 | ||||||||
\(216\) | −1.80729e7 | −0.122022 | ||||||||
\(217\) | −6.96893e7 | −0.462975 | ||||||||
\(218\) | −4.50883e7 | −0.294758 | ||||||||
\(219\) | −5.70085e7 | −0.366763 | ||||||||
\(220\) | −3.79160e7 | −0.240073 | ||||||||
\(221\) | −3.91210e7 | −0.243802 | ||||||||
\(222\) | 3.28208e7 | 0.201332 | ||||||||
\(223\) | −2.58995e8 | −1.56396 | −0.781979 | − | 0.623305i | \(-0.785789\pi\) | ||||
−0.781979 | + | 0.623305i | \(0.785789\pi\) | |||||||
\(224\) | 2.08330e8 | 1.23847 | ||||||||
\(225\) | −5.13239e7 | −0.300387 | ||||||||
\(226\) | 5.98686e7 | 0.345000 | ||||||||
\(227\) | −2.65429e8 | −1.50612 | −0.753058 | − | 0.657955i | \(-0.771422\pi\) | ||||
−0.753058 | + | 0.657955i | \(0.771422\pi\) | |||||||
\(228\) | 1.75016e8 | 0.977926 | ||||||||
\(229\) | 1.83433e8 | 1.00938 | 0.504688 | − | 0.863302i | \(-0.331607\pi\) | ||||
0.504688 | + | 0.863302i | \(0.331607\pi\) | |||||||
\(230\) | −3.22907e7 | −0.174997 | ||||||||
\(231\) | −1.33999e8 | −0.715250 | ||||||||
\(232\) | −2.08921e7 | −0.109844 | ||||||||
\(233\) | 3.14430e8 | 1.62846 | 0.814232 | − | 0.580540i | \(-0.197159\pi\) | ||||
0.814232 | + | 0.580540i | \(0.197159\pi\) | |||||||
\(234\) | 2.48760e7 | 0.126919 | ||||||||
\(235\) | −8.31576e7 | −0.417989 | ||||||||
\(236\) | −2.33209e7 | −0.115492 | ||||||||
\(237\) | −1.02660e8 | −0.500937 | ||||||||
\(238\) | −2.16359e7 | −0.104029 | ||||||||
\(239\) | −3.42402e7 | −0.162235 | −0.0811173 | − | 0.996705i | \(-0.525849\pi\) | ||||
−0.0811173 | + | 0.996705i | \(0.525849\pi\) | |||||||
\(240\) | −2.62032e7 | −0.122353 | ||||||||
\(241\) | −1.98928e8 | −0.915452 | −0.457726 | − | 0.889093i | \(-0.651336\pi\) | ||||
−0.457726 | + | 0.889093i | \(0.651336\pi\) | |||||||
\(242\) | −1.91879e7 | −0.0870309 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | −6.12999e7 | −0.270144 | ||||||||
\(245\) | −7.75255e7 | −0.336793 | ||||||||
\(246\) | 4.88886e7 | 0.209380 | ||||||||
\(247\) | −5.12449e8 | −2.16377 | ||||||||
\(248\) | 4.89938e7 | 0.203967 | ||||||||
\(249\) | 5.09978e7 | 0.209341 | ||||||||
\(250\) | 4.96131e7 | 0.200820 | ||||||||
\(251\) | −4.06923e8 | −1.62425 | −0.812127 | − | 0.583481i | \(-0.801690\pi\) | ||||
−0.812127 | + | 0.583481i | \(0.801690\pi\) | |||||||
\(252\) | −1.08113e8 | −0.425575 | ||||||||
\(253\) | −3.67337e8 | −1.42608 | ||||||||
\(254\) | −6.64624e7 | −0.254483 | ||||||||
\(255\) | 1.03397e7 | 0.0390496 | ||||||||
\(256\) | 1.40580e7 | 0.0523700 | ||||||||
\(257\) | 1.04442e8 | 0.383804 | 0.191902 | − | 0.981414i | \(-0.438534\pi\) | ||||
0.191902 | + | 0.981414i | \(0.438534\pi\) | |||||||
\(258\) | 7.26196e7 | 0.263260 | ||||||||
\(259\) | 4.17656e8 | 1.49372 | ||||||||
\(260\) | 8.95721e7 | 0.316058 | ||||||||
\(261\) | 1.65873e7 | 0.0577475 | ||||||||
\(262\) | 1.45966e8 | 0.501415 | ||||||||
\(263\) | 2.20493e8 | 0.747393 | 0.373696 | − | 0.927551i | \(-0.378090\pi\) | ||||
0.373696 | + | 0.927551i | \(0.378090\pi\) | |||||||
\(264\) | 9.42051e7 | 0.315109 | ||||||||
\(265\) | −7.02925e7 | −0.232032 | ||||||||
\(266\) | −2.83410e8 | −0.923272 | ||||||||
\(267\) | 1.74980e8 | 0.562599 | ||||||||
\(268\) | −3.29819e8 | −1.04666 | ||||||||
\(269\) | 3.53895e8 | 1.10852 | 0.554258 | − | 0.832345i | \(-0.313002\pi\) | ||||
0.554258 | + | 0.832345i | \(0.313002\pi\) | |||||||
\(270\) | −6.57474e6 | −0.0203285 | ||||||||
\(271\) | −4.86543e8 | −1.48501 | −0.742504 | − | 0.669842i | \(-0.766362\pi\) | ||||
−0.742504 | + | 0.669842i | \(0.766362\pi\) | |||||||
\(272\) | −4.81300e7 | −0.145019 | ||||||||
\(273\) | 3.16556e8 | 0.941632 | ||||||||
\(274\) | −1.81535e8 | −0.533129 | ||||||||
\(275\) | 2.67527e8 | 0.775716 | ||||||||
\(276\) | −2.96376e8 | −0.848517 | ||||||||
\(277\) | −4.24477e8 | −1.19998 | −0.599992 | − | 0.800006i | \(-0.704829\pi\) | ||||
−0.599992 | + | 0.800006i | \(0.704829\pi\) | |||||||
\(278\) | −3.42540e7 | −0.0956213 | ||||||||
\(279\) | −3.88984e7 | −0.107230 | ||||||||
\(280\) | 1.05380e8 | 0.286882 | ||||||||
\(281\) | 5.85274e8 | 1.57357 | 0.786787 | − | 0.617225i | \(-0.211743\pi\) | ||||
0.786787 | + | 0.617225i | \(0.211743\pi\) | |||||||
\(282\) | 9.71258e7 | 0.257907 | ||||||||
\(283\) | 1.23529e8 | 0.323979 | 0.161989 | − | 0.986793i | \(-0.448209\pi\) | ||||
0.161989 | + | 0.986793i | \(0.448209\pi\) | |||||||
\(284\) | 5.94779e7 | 0.154078 | ||||||||
\(285\) | 1.35440e8 | 0.346570 | ||||||||
\(286\) | −1.29667e8 | −0.327753 | ||||||||
\(287\) | 6.22124e8 | 1.55343 | ||||||||
\(288\) | 1.16283e8 | 0.286843 | ||||||||
\(289\) | −3.91347e8 | −0.953716 | ||||||||
\(290\) | −7.60036e6 | −0.0182996 | ||||||||
\(291\) | 7.67544e7 | 0.182590 | ||||||||
\(292\) | 2.39753e8 | 0.563540 | ||||||||
\(293\) | −3.34796e8 | −0.777577 | −0.388788 | − | 0.921327i | \(-0.627106\pi\) | ||||
−0.388788 | + | 0.921327i | \(0.627106\pi\) | |||||||
\(294\) | 9.05477e7 | 0.207808 | ||||||||
\(295\) | −1.80474e7 | −0.0409297 | ||||||||
\(296\) | −2.93625e8 | −0.658069 | ||||||||
\(297\) | −7.47939e7 | −0.165660 | ||||||||
\(298\) | −6.60975e7 | −0.144687 | ||||||||
\(299\) | 8.67791e8 | 1.87744 | ||||||||
\(300\) | 2.15846e8 | 0.461552 | ||||||||
\(301\) | 9.24110e8 | 1.95317 | ||||||||
\(302\) | 5.57541e7 | 0.116480 | ||||||||
\(303\) | 3.81051e7 | 0.0786925 | ||||||||
\(304\) | −6.30460e8 | −1.28706 | ||||||||
\(305\) | −4.74384e7 | −0.0957372 | ||||||||
\(306\) | −1.20765e7 | −0.0240943 | ||||||||
\(307\) | 5.54710e8 | 1.09416 | 0.547081 | − | 0.837080i | \(-0.315739\pi\) | ||||
0.547081 | + | 0.837080i | \(0.315739\pi\) | |||||||
\(308\) | 5.63540e8 | 1.09900 | ||||||||
\(309\) | 2.86124e8 | 0.551695 | ||||||||
\(310\) | 1.78235e7 | 0.0339802 | ||||||||
\(311\) | −4.01552e8 | −0.756973 | −0.378486 | − | 0.925607i | \(-0.623555\pi\) | ||||
−0.378486 | + | 0.925607i | \(0.623555\pi\) | |||||||
\(312\) | −2.22549e8 | −0.414843 | ||||||||
\(313\) | 7.36811e8 | 1.35816 | 0.679080 | − | 0.734064i | \(-0.262379\pi\) | ||||
0.679080 | + | 0.734064i | \(0.262379\pi\) | |||||||
\(314\) | 1.56346e8 | 0.284992 | ||||||||
\(315\) | −8.36659e7 | −0.150821 | ||||||||
\(316\) | 4.31745e8 | 0.769701 | ||||||||
\(317\) | −2.52797e7 | −0.0445722 | −0.0222861 | − | 0.999752i | \(-0.507094\pi\) | ||||
−0.0222861 | + | 0.999752i | \(0.507094\pi\) | |||||||
\(318\) | 8.20997e7 | 0.143168 | ||||||||
\(319\) | −8.64613e7 | −0.149126 | ||||||||
\(320\) | 7.09410e7 | 0.121024 | ||||||||
\(321\) | 4.98216e8 | 0.840717 | ||||||||
\(322\) | 4.79932e8 | 0.801096 | ||||||||
\(323\) | 2.48777e8 | 0.410772 | ||||||||
\(324\) | −6.03453e7 | −0.0985680 | ||||||||
\(325\) | −6.32001e8 | −1.02124 | ||||||||
\(326\) | −3.88736e6 | −0.00621431 | ||||||||
\(327\) | −3.20258e8 | −0.506503 | ||||||||
\(328\) | −4.37372e8 | −0.684373 | ||||||||
\(329\) | 1.23596e9 | 1.91346 | ||||||||
\(330\) | 3.42709e7 | 0.0524961 | ||||||||
\(331\) | 6.96332e8 | 1.05540 | 0.527702 | − | 0.849430i | \(-0.323054\pi\) | ||||
0.527702 | + | 0.849430i | \(0.323054\pi\) | |||||||
\(332\) | −2.14475e8 | −0.321657 | ||||||||
\(333\) | 2.33123e8 | 0.345963 | ||||||||
\(334\) | −1.72609e7 | −0.0253485 | ||||||||
\(335\) | −2.55238e8 | −0.370928 | ||||||||
\(336\) | 3.89455e8 | 0.560105 | ||||||||
\(337\) | −7.32502e8 | −1.04257 | −0.521284 | − | 0.853384i | \(-0.674547\pi\) | ||||
−0.521284 | + | 0.853384i | \(0.674547\pi\) | |||||||
\(338\) | 6.77984e7 | 0.0955017 | ||||||||
\(339\) | 4.25241e8 | 0.592838 | ||||||||
\(340\) | −4.34843e7 | −0.0600006 | ||||||||
\(341\) | 2.02759e8 | 0.276910 | ||||||||
\(342\) | −1.58191e8 | −0.213841 | ||||||||
\(343\) | 7.66587e7 | 0.102573 | ||||||||
\(344\) | −6.49678e8 | −0.860485 | ||||||||
\(345\) | −2.29357e8 | −0.300709 | ||||||||
\(346\) | 5.53629e7 | 0.0718543 | ||||||||
\(347\) | −6.58184e8 | −0.845657 | −0.422828 | − | 0.906210i | \(-0.638963\pi\) | ||||
−0.422828 | + | 0.906210i | \(0.638963\pi\) | |||||||
\(348\) | −6.97589e7 | −0.0887303 | ||||||||
\(349\) | −3.82277e7 | −0.0481381 | −0.0240691 | − | 0.999710i | \(-0.507662\pi\) | ||||
−0.0240691 | + | 0.999710i | \(0.507662\pi\) | |||||||
\(350\) | −3.49528e8 | −0.435757 | ||||||||
\(351\) | 1.76692e8 | 0.218093 | ||||||||
\(352\) | −6.06129e8 | −0.740740 | ||||||||
\(353\) | 8.56374e8 | 1.03622 | 0.518110 | − | 0.855314i | \(-0.326636\pi\) | ||||
0.518110 | + | 0.855314i | \(0.326636\pi\) | |||||||
\(354\) | 2.10789e7 | 0.0252544 | ||||||||
\(355\) | 4.60284e7 | 0.0546043 | ||||||||
\(356\) | −7.35890e8 | −0.864446 | ||||||||
\(357\) | −1.53677e8 | −0.178760 | ||||||||
\(358\) | −2.88789e8 | −0.332652 | ||||||||
\(359\) | 1.50693e9 | 1.71895 | 0.859475 | − | 0.511177i | \(-0.170790\pi\) | ||||
0.859475 | + | 0.511177i | \(0.170790\pi\) | |||||||
\(360\) | 5.88197e7 | 0.0664452 | ||||||||
\(361\) | 2.36488e9 | 2.64566 | ||||||||
\(362\) | −4.10773e8 | −0.455116 | ||||||||
\(363\) | −1.36290e8 | −0.149551 | ||||||||
\(364\) | −1.33130e9 | −1.44684 | ||||||||
\(365\) | 1.85539e8 | 0.199715 | ||||||||
\(366\) | 5.54068e7 | 0.0590716 | ||||||||
\(367\) | −7.69693e8 | −0.812805 | −0.406402 | − | 0.913694i | \(-0.633217\pi\) | ||||
−0.406402 | + | 0.913694i | \(0.633217\pi\) | |||||||
\(368\) | 1.06763e9 | 1.11675 | ||||||||
\(369\) | 3.47251e8 | 0.359791 | ||||||||
\(370\) | −1.06818e8 | −0.109632 | ||||||||
\(371\) | 1.04475e9 | 1.06219 | ||||||||
\(372\) | 1.63590e8 | 0.164762 | ||||||||
\(373\) | −8.69970e8 | −0.868008 | −0.434004 | − | 0.900911i | \(-0.642900\pi\) | ||||
−0.434004 | + | 0.900911i | \(0.642900\pi\) | |||||||
\(374\) | 6.29488e7 | 0.0622209 | ||||||||
\(375\) | 3.52397e8 | 0.345082 | ||||||||
\(376\) | −8.68918e8 | −0.842988 | ||||||||
\(377\) | 2.04255e8 | 0.196326 | ||||||||
\(378\) | 9.77195e7 | 0.0930593 | ||||||||
\(379\) | −6.86916e8 | −0.648136 | −0.324068 | − | 0.946034i | \(-0.605051\pi\) | ||||
−0.324068 | + | 0.946034i | \(0.605051\pi\) | |||||||
\(380\) | −5.69604e8 | −0.532514 | ||||||||
\(381\) | −4.72076e8 | −0.437295 | ||||||||
\(382\) | −5.03627e8 | −0.462261 | ||||||||
\(383\) | 6.92766e8 | 0.630073 | 0.315037 | − | 0.949080i | \(-0.397983\pi\) | ||||
0.315037 | + | 0.949080i | \(0.397983\pi\) | |||||||
\(384\) | −6.34127e8 | −0.571501 | ||||||||
\(385\) | 4.36109e8 | 0.389478 | ||||||||
\(386\) | 3.84337e8 | 0.340139 | ||||||||
\(387\) | 5.15810e8 | 0.452378 | ||||||||
\(388\) | −3.22796e8 | −0.280554 | ||||||||
\(389\) | −1.80412e7 | −0.0155397 | −0.00776985 | − | 0.999970i | \(-0.502473\pi\) | ||||
−0.00776985 | + | 0.999970i | \(0.502473\pi\) | |||||||
\(390\) | −8.09611e7 | −0.0691115 | ||||||||
\(391\) | −4.21283e8 | −0.356415 | ||||||||
\(392\) | −8.10068e8 | −0.679236 | ||||||||
\(393\) | 1.03678e9 | 0.861616 | ||||||||
\(394\) | 3.81174e7 | 0.0313968 | ||||||||
\(395\) | 3.34116e8 | 0.272777 | ||||||||
\(396\) | 3.14551e8 | 0.254541 | ||||||||
\(397\) | 6.47110e8 | 0.519053 | 0.259526 | − | 0.965736i | \(-0.416434\pi\) | ||||
0.259526 | + | 0.965736i | \(0.416434\pi\) | |||||||
\(398\) | 2.41428e8 | 0.191954 | ||||||||
\(399\) | −2.01303e9 | −1.58652 | ||||||||
\(400\) | −7.77543e8 | −0.607455 | ||||||||
\(401\) | −2.37807e8 | −0.184171 | −0.0920853 | − | 0.995751i | \(-0.529353\pi\) | ||||
−0.0920853 | + | 0.995751i | \(0.529353\pi\) | |||||||
\(402\) | 2.98112e8 | 0.228869 | ||||||||
\(403\) | −4.78994e8 | −0.364554 | ||||||||
\(404\) | −1.60253e8 | −0.120913 | ||||||||
\(405\) | −4.66997e7 | −0.0349319 | ||||||||
\(406\) | 1.12963e8 | 0.0837714 | ||||||||
\(407\) | −1.21515e9 | −0.893410 | ||||||||
\(408\) | 1.08040e8 | 0.0787542 | ||||||||
\(409\) | 1.17282e9 | 0.847618 | 0.423809 | − | 0.905752i | \(-0.360693\pi\) | ||||
0.423809 | + | 0.905752i | \(0.360693\pi\) | |||||||
\(410\) | −1.59112e8 | −0.114014 | ||||||||
\(411\) | −1.28942e9 | −0.916112 | ||||||||
\(412\) | −1.20331e9 | −0.847693 | ||||||||
\(413\) | 2.68236e8 | 0.187367 | ||||||||
\(414\) | 2.67883e8 | 0.185543 | ||||||||
\(415\) | −1.65977e8 | −0.113993 | ||||||||
\(416\) | 1.43191e9 | 0.975189 | ||||||||
\(417\) | −2.43303e8 | −0.164313 | ||||||||
\(418\) | 8.24572e8 | 0.552219 | ||||||||
\(419\) | −1.40480e9 | −0.932962 | −0.466481 | − | 0.884531i | \(-0.654478\pi\) | ||||
−0.466481 | + | 0.884531i | \(0.654478\pi\) | |||||||
\(420\) | 3.51863e8 | 0.231740 | ||||||||
\(421\) | −8.16663e8 | −0.533403 | −0.266702 | − | 0.963779i | \(-0.585934\pi\) | ||||
−0.266702 | + | 0.963779i | \(0.585934\pi\) | |||||||
\(422\) | 1.10785e8 | 0.0717609 | ||||||||
\(423\) | 6.89875e8 | 0.443179 | ||||||||
\(424\) | −7.34490e8 | −0.467956 | ||||||||
\(425\) | 3.06815e8 | 0.193872 | ||||||||
\(426\) | −5.37600e7 | −0.0336919 | ||||||||
\(427\) | 7.05070e8 | 0.438263 | ||||||||
\(428\) | −2.09528e9 | −1.29178 | ||||||||
\(429\) | −9.21008e8 | −0.563200 | ||||||||
\(430\) | −2.36347e8 | −0.143354 | ||||||||
\(431\) | 2.46225e9 | 1.48137 | 0.740683 | − | 0.671855i | \(-0.234502\pi\) | ||||
0.740683 | + | 0.671855i | \(0.234502\pi\) | |||||||
\(432\) | 2.17382e8 | 0.129727 | ||||||||
\(433\) | −1.20496e9 | −0.713289 | −0.356645 | − | 0.934240i | \(-0.616079\pi\) | ||||
−0.356645 | + | 0.934240i | \(0.616079\pi\) | |||||||
\(434\) | −2.64908e8 | −0.155554 | ||||||||
\(435\) | −5.39846e7 | −0.0314454 | ||||||||
\(436\) | 1.34687e9 | 0.778254 | ||||||||
\(437\) | −5.51843e9 | −3.16323 | ||||||||
\(438\) | −2.16704e8 | −0.123228 | ||||||||
\(439\) | 7.43862e8 | 0.419630 | 0.209815 | − | 0.977741i | \(-0.432714\pi\) | ||||
0.209815 | + | 0.977741i | \(0.432714\pi\) | |||||||
\(440\) | −3.06598e8 | −0.171587 | ||||||||
\(441\) | 6.43151e8 | 0.357090 | ||||||||
\(442\) | −1.48709e8 | −0.0819143 | ||||||||
\(443\) | 5.65900e8 | 0.309262 | 0.154631 | − | 0.987972i | \(-0.450581\pi\) | ||||
0.154631 | + | 0.987972i | \(0.450581\pi\) | |||||||
\(444\) | −9.80413e8 | −0.531580 | ||||||||
\(445\) | −5.69487e8 | −0.306354 | ||||||||
\(446\) | −9.84510e8 | −0.525470 | ||||||||
\(447\) | −4.69484e8 | −0.248625 | ||||||||
\(448\) | −1.05439e9 | −0.554022 | ||||||||
\(449\) | −1.60627e9 | −0.837443 | −0.418722 | − | 0.908115i | \(-0.637522\pi\) | ||||
−0.418722 | + | 0.908115i | \(0.637522\pi\) | |||||||
\(450\) | −1.95096e8 | −0.100926 | ||||||||
\(451\) | −1.81005e9 | −0.929121 | ||||||||
\(452\) | −1.78838e9 | −0.910909 | ||||||||
\(453\) | 3.96015e8 | 0.200156 | ||||||||
\(454\) | −1.00897e9 | −0.506036 | ||||||||
\(455\) | −1.03026e9 | −0.512750 | ||||||||
\(456\) | 1.41522e9 | 0.698954 | ||||||||
\(457\) | −1.42935e9 | −0.700538 | −0.350269 | − | 0.936649i | \(-0.613910\pi\) | ||||
−0.350269 | + | 0.936649i | \(0.613910\pi\) | |||||||
\(458\) | 6.97277e8 | 0.339138 | ||||||||
\(459\) | −8.57779e7 | −0.0414029 | ||||||||
\(460\) | 9.64579e8 | 0.462046 | ||||||||
\(461\) | 6.78035e8 | 0.322328 | 0.161164 | − | 0.986928i | \(-0.448475\pi\) | ||||
0.161164 | + | 0.986928i | \(0.448475\pi\) | |||||||
\(462\) | −5.09364e8 | −0.240315 | ||||||||
\(463\) | 7.42705e7 | 0.0347763 | 0.0173881 | − | 0.999849i | \(-0.494465\pi\) | ||||
0.0173881 | + | 0.999849i | \(0.494465\pi\) | |||||||
\(464\) | 2.51292e8 | 0.116779 | ||||||||
\(465\) | 1.26598e8 | 0.0583905 | ||||||||
\(466\) | 1.19523e9 | 0.547143 | ||||||||
\(467\) | −8.65991e8 | −0.393464 | −0.196732 | − | 0.980457i | \(-0.563033\pi\) | ||||
−0.196732 | + | 0.980457i | \(0.563033\pi\) | |||||||
\(468\) | −7.43090e8 | −0.335105 | ||||||||
\(469\) | 3.79357e9 | 1.69802 | ||||||||
\(470\) | −3.16104e8 | −0.140439 | ||||||||
\(471\) | 1.11051e9 | 0.489721 | ||||||||
\(472\) | −1.88578e8 | −0.0825458 | ||||||||
\(473\) | −2.68867e9 | −1.16821 | ||||||||
\(474\) | −3.90239e8 | −0.168309 | ||||||||
\(475\) | 4.01900e9 | 1.72064 | ||||||||
\(476\) | 6.46301e8 | 0.274669 | ||||||||
\(477\) | 5.83146e8 | 0.246016 | ||||||||
\(478\) | −1.30156e8 | −0.0545088 | ||||||||
\(479\) | 3.87827e9 | 1.61237 | 0.806183 | − | 0.591666i | \(-0.201530\pi\) | ||||
0.806183 | + | 0.591666i | \(0.201530\pi\) | |||||||
\(480\) | −3.78454e8 | −0.156196 | ||||||||
\(481\) | 2.87066e9 | 1.17618 | ||||||||
\(482\) | −7.56177e8 | −0.307581 | ||||||||
\(483\) | 3.40891e9 | 1.37658 | ||||||||
\(484\) | 5.73176e8 | 0.229789 | ||||||||
\(485\) | −2.49803e8 | −0.0994266 | ||||||||
\(486\) | 5.45440e7 | 0.0215536 | ||||||||
\(487\) | 3.18862e9 | 1.25098 | 0.625492 | − | 0.780231i | \(-0.284898\pi\) | ||||
0.625492 | + | 0.780231i | \(0.284898\pi\) | |||||||
\(488\) | −4.95686e8 | −0.193080 | ||||||||
\(489\) | −2.76115e7 | −0.0106785 | ||||||||
\(490\) | −2.94695e8 | −0.113158 | ||||||||
\(491\) | 1.59045e9 | 0.606364 | 0.303182 | − | 0.952933i | \(-0.401951\pi\) | ||||
0.303182 | + | 0.952933i | \(0.401951\pi\) | |||||||
\(492\) | −1.46039e9 | −0.552828 | ||||||||
\(493\) | −9.91588e7 | −0.0372707 | ||||||||
\(494\) | −1.94796e9 | −0.727000 | ||||||||
\(495\) | 2.43423e8 | 0.0902076 | ||||||||
\(496\) | −5.89300e8 | −0.216846 | ||||||||
\(497\) | −6.84114e8 | −0.249966 | ||||||||
\(498\) | 1.93856e8 | 0.0703359 | ||||||||
\(499\) | −3.98538e9 | −1.43588 | −0.717940 | − | 0.696105i | \(-0.754915\pi\) | ||||
−0.717940 | + | 0.696105i | \(0.754915\pi\) | |||||||
\(500\) | −1.48203e9 | −0.530227 | ||||||||
\(501\) | −1.22603e8 | −0.0435580 | ||||||||
\(502\) | −1.54682e9 | −0.545729 | ||||||||
\(503\) | 4.29501e9 | 1.50479 | 0.752396 | − | 0.658711i | \(-0.228898\pi\) | ||||
0.752396 | + | 0.658711i | \(0.228898\pi\) | |||||||
\(504\) | −8.74229e8 | −0.304171 | ||||||||
\(505\) | −1.24016e8 | −0.0428507 | ||||||||
\(506\) | −1.39635e9 | −0.479144 | ||||||||
\(507\) | 4.81565e8 | 0.164107 | ||||||||
\(508\) | 1.98535e9 | 0.671914 | ||||||||
\(509\) | −2.62335e9 | −0.881746 | −0.440873 | − | 0.897570i | \(-0.645331\pi\) | ||||
−0.440873 | + | 0.897570i | \(0.645331\pi\) | |||||||
\(510\) | 3.93039e7 | 0.0131202 | ||||||||
\(511\) | −2.75764e9 | −0.914248 | ||||||||
\(512\) | 3.05967e9 | 1.00746 | ||||||||
\(513\) | −1.12361e9 | −0.367457 | ||||||||
\(514\) | 3.97013e8 | 0.128954 | ||||||||
\(515\) | −9.31213e8 | −0.300417 | ||||||||
\(516\) | −2.16927e9 | −0.695089 | ||||||||
\(517\) | −3.59598e9 | −1.14446 | ||||||||
\(518\) | 1.58762e9 | 0.501871 | ||||||||
\(519\) | 3.93237e8 | 0.123472 | ||||||||
\(520\) | 7.24303e8 | 0.225896 | ||||||||
\(521\) | −4.65644e9 | −1.44252 | −0.721260 | − | 0.692664i | \(-0.756437\pi\) | ||||
−0.721260 | + | 0.692664i | \(0.756437\pi\) | |||||||
\(522\) | 6.30526e7 | 0.0194024 | ||||||||
\(523\) | −5.16451e9 | −1.57860 | −0.789301 | − | 0.614006i | \(-0.789557\pi\) | ||||
−0.789301 | + | 0.614006i | \(0.789557\pi\) | |||||||
\(524\) | −4.36026e9 | −1.32389 | ||||||||
\(525\) | −2.48266e9 | −0.748790 | ||||||||
\(526\) | 8.38151e8 | 0.251115 | ||||||||
\(527\) | 2.32535e8 | 0.0692073 | ||||||||
\(528\) | −1.13311e9 | −0.335005 | ||||||||
\(529\) | 5.94019e9 | 1.74464 | ||||||||
\(530\) | −2.67200e8 | −0.0779599 | ||||||||
\(531\) | 1.49721e8 | 0.0433963 | ||||||||
\(532\) | 8.46595e9 | 2.43773 | ||||||||
\(533\) | 4.27603e9 | 1.22319 | ||||||||
\(534\) | 6.65145e8 | 0.189026 | ||||||||
\(535\) | −1.62148e9 | −0.457799 | ||||||||
\(536\) | −2.66700e9 | −0.748076 | ||||||||
\(537\) | −2.05124e9 | −0.571618 | ||||||||
\(538\) | 1.34525e9 | 0.372447 | ||||||||
\(539\) | −3.35243e9 | −0.922146 | ||||||||
\(540\) | 1.96399e8 | 0.0536736 | ||||||||
\(541\) | 7.10793e9 | 1.92998 | 0.964990 | − | 0.262288i | \(-0.0844772\pi\) | ||||
0.964990 | + | 0.262288i | \(0.0844772\pi\) | |||||||
\(542\) | −1.84948e9 | −0.498944 | ||||||||
\(543\) | −2.91768e9 | −0.782057 | ||||||||
\(544\) | −6.95144e8 | −0.185131 | ||||||||
\(545\) | 1.04230e9 | 0.275808 | ||||||||
\(546\) | 1.20331e9 | 0.316377 | ||||||||
\(547\) | 4.92835e9 | 1.28750 | 0.643748 | − | 0.765238i | \(-0.277379\pi\) | ||||
0.643748 | + | 0.765238i | \(0.277379\pi\) | |||||||
\(548\) | 5.42275e9 | 1.40763 | ||||||||
\(549\) | 3.93549e8 | 0.101507 | ||||||||
\(550\) | 1.01694e9 | 0.260631 | ||||||||
\(551\) | −1.29889e9 | −0.330782 | ||||||||
\(552\) | −2.39657e9 | −0.606461 | ||||||||
\(553\) | −4.96592e9 | −1.24871 | ||||||||
\(554\) | −1.61355e9 | −0.403179 | ||||||||
\(555\) | −7.58717e8 | −0.188388 | ||||||||
\(556\) | 1.02323e9 | 0.252470 | ||||||||
\(557\) | −5.04922e9 | −1.23803 | −0.619015 | − | 0.785379i | \(-0.712468\pi\) | ||||
−0.619015 | + | 0.785379i | \(0.712468\pi\) | |||||||
\(558\) | −1.47863e8 | −0.0360281 | ||||||||
\(559\) | 6.35166e9 | 1.53796 | ||||||||
\(560\) | −1.26751e9 | −0.304996 | ||||||||
\(561\) | 4.47119e8 | 0.106918 | ||||||||
\(562\) | 2.22478e9 | 0.528701 | ||||||||
\(563\) | −1.36397e9 | −0.322125 | −0.161063 | − | 0.986944i | \(-0.551492\pi\) | ||||
−0.161063 | + | 0.986944i | \(0.551492\pi\) | |||||||
\(564\) | −2.90132e9 | −0.680955 | ||||||||
\(565\) | −1.38398e9 | −0.322820 | ||||||||
\(566\) | 4.69566e8 | 0.108853 | ||||||||
\(567\) | 6.94091e8 | 0.159910 | ||||||||
\(568\) | 4.80953e8 | 0.110124 | ||||||||
\(569\) | −1.81850e9 | −0.413829 | −0.206915 | − | 0.978359i | \(-0.566342\pi\) | ||||
−0.206915 | + | 0.978359i | \(0.566342\pi\) | |||||||
\(570\) | 5.14845e8 | 0.116443 | ||||||||
\(571\) | −9.20531e8 | −0.206925 | −0.103462 | − | 0.994633i | \(-0.532992\pi\) | ||||
−0.103462 | + | 0.994633i | \(0.532992\pi\) | |||||||
\(572\) | 3.87336e9 | 0.865371 | ||||||||
\(573\) | −3.57721e9 | −0.794334 | ||||||||
\(574\) | 2.36486e9 | 0.521932 | ||||||||
\(575\) | −6.80585e9 | −1.49295 | ||||||||
\(576\) | −5.88526e8 | −0.128318 | ||||||||
\(577\) | −6.37038e9 | −1.38054 | −0.690271 | − | 0.723551i | \(-0.742509\pi\) | ||||
−0.690271 | + | 0.723551i | \(0.742509\pi\) | |||||||
\(578\) | −1.48761e9 | −0.320437 | ||||||||
\(579\) | 2.72991e9 | 0.584484 | ||||||||
\(580\) | 2.27036e8 | 0.0483167 | ||||||||
\(581\) | 2.46689e9 | 0.521834 | ||||||||
\(582\) | 2.91764e8 | 0.0613481 | ||||||||
\(583\) | −3.03966e9 | −0.635308 | ||||||||
\(584\) | 1.93871e9 | 0.402779 | ||||||||
\(585\) | −5.75058e8 | −0.118759 | ||||||||
\(586\) | −1.27265e9 | −0.261256 | ||||||||
\(587\) | 4.67433e9 | 0.953863 | 0.476931 | − | 0.878941i | \(-0.341749\pi\) | ||||
0.476931 | + | 0.878941i | \(0.341749\pi\) | |||||||
\(588\) | −2.70482e9 | −0.548678 | ||||||||
\(589\) | 3.04600e9 | 0.614224 | ||||||||
\(590\) | −6.86030e7 | −0.0137519 | ||||||||
\(591\) | 2.70744e8 | 0.0539513 | ||||||||
\(592\) | 3.53174e9 | 0.699620 | ||||||||
\(593\) | 5.82162e9 | 1.14644 | 0.573221 | − | 0.819401i | \(-0.305694\pi\) | ||||
0.573221 | + | 0.819401i | \(0.305694\pi\) | |||||||
\(594\) | −2.84311e8 | −0.0556598 | ||||||||
\(595\) | 5.00156e8 | 0.0973410 | ||||||||
\(596\) | 1.97445e9 | 0.382018 | ||||||||
\(597\) | 1.71484e9 | 0.329847 | ||||||||
\(598\) | 3.29870e9 | 0.630796 | ||||||||
\(599\) | 6.17800e9 | 1.17450 | 0.587251 | − | 0.809405i | \(-0.300210\pi\) | ||||
0.587251 | + | 0.809405i | \(0.300210\pi\) | |||||||
\(600\) | 1.74539e9 | 0.329885 | ||||||||
\(601\) | 8.32412e9 | 1.56415 | 0.782074 | − | 0.623186i | \(-0.214162\pi\) | ||||
0.782074 | + | 0.623186i | \(0.214162\pi\) | |||||||
\(602\) | 3.51279e9 | 0.656242 | ||||||||
\(603\) | 2.11746e9 | 0.393282 | ||||||||
\(604\) | −1.66547e9 | −0.307544 | ||||||||
\(605\) | 4.43566e8 | 0.0814356 | ||||||||
\(606\) | 1.44847e8 | 0.0264397 | ||||||||
\(607\) | −6.60638e9 | −1.19896 | −0.599478 | − | 0.800391i | \(-0.704625\pi\) | ||||
−0.599478 | + | 0.800391i | \(0.704625\pi\) | |||||||
\(608\) | −9.10576e9 | −1.64306 | ||||||||
\(609\) | 8.02366e8 | 0.143950 | ||||||||
\(610\) | −1.80326e8 | −0.0321665 | ||||||||
\(611\) | 8.49509e9 | 1.50669 | ||||||||
\(612\) | 3.60745e8 | 0.0636166 | ||||||||
\(613\) | −5.00900e9 | −0.878293 | −0.439146 | − | 0.898415i | \(-0.644719\pi\) | ||||
−0.439146 | + | 0.898415i | \(0.644719\pi\) | |||||||
\(614\) | 2.10860e9 | 0.367625 | ||||||||
\(615\) | −1.13016e9 | −0.195919 | ||||||||
\(616\) | 4.55693e9 | 0.785488 | ||||||||
\(617\) | 8.30278e9 | 1.42307 | 0.711534 | − | 0.702652i | \(-0.248001\pi\) | ||||
0.711534 | + | 0.702652i | \(0.248001\pi\) | |||||||
\(618\) | 1.08763e9 | 0.185363 | ||||||||
\(619\) | −4.13223e9 | −0.700272 | −0.350136 | − | 0.936699i | \(-0.613865\pi\) | ||||
−0.350136 | + | 0.936699i | \(0.613865\pi\) | |||||||
\(620\) | −5.32418e8 | −0.0897184 | ||||||||
\(621\) | 1.90275e9 | 0.318831 | ||||||||
\(622\) | −1.52641e9 | −0.254333 | ||||||||
\(623\) | 8.46420e9 | 1.40242 | ||||||||
\(624\) | 2.67683e9 | 0.441037 | ||||||||
\(625\) | 4.35335e9 | 0.713252 | ||||||||
\(626\) | 2.80082e9 | 0.456325 | ||||||||
\(627\) | 5.85685e9 | 0.948916 | ||||||||
\(628\) | −4.67032e9 | −0.752468 | ||||||||
\(629\) | −1.39361e9 | −0.223287 | ||||||||
\(630\) | −3.18036e8 | −0.0506739 | ||||||||
\(631\) | 8.48866e8 | 0.134504 | 0.0672522 | − | 0.997736i | \(-0.478577\pi\) | ||||
0.0672522 | + | 0.997736i | \(0.478577\pi\) | |||||||
\(632\) | 3.49120e9 | 0.550129 | ||||||||
\(633\) | 7.86895e8 | 0.123312 | ||||||||
\(634\) | −9.60948e7 | −0.0149757 | ||||||||
\(635\) | 1.53641e9 | 0.238122 | ||||||||
\(636\) | −2.45246e9 | −0.378009 | ||||||||
\(637\) | 7.91974e9 | 1.21401 | ||||||||
\(638\) | −3.28662e8 | −0.0501046 | ||||||||
\(639\) | −3.81852e8 | −0.0578951 | ||||||||
\(640\) | 2.06382e9 | 0.311202 | ||||||||
\(641\) | 4.40906e9 | 0.661216 | 0.330608 | − | 0.943768i | \(-0.392746\pi\) | ||||
0.330608 | + | 0.943768i | \(0.392746\pi\) | |||||||
\(642\) | 1.89385e9 | 0.282470 | ||||||||
\(643\) | −1.11714e10 | −1.65717 | −0.828586 | − | 0.559862i | \(-0.810854\pi\) | ||||
−0.828586 | + | 0.559862i | \(0.810854\pi\) | |||||||
\(644\) | −1.43364e10 | −2.11514 | ||||||||
\(645\) | −1.67875e9 | −0.246335 | ||||||||
\(646\) | 9.45667e8 | 0.138014 | ||||||||
\(647\) | −1.09926e10 | −1.59564 | −0.797818 | − | 0.602899i | \(-0.794012\pi\) | ||||
−0.797818 | + | 0.602899i | \(0.794012\pi\) | |||||||
\(648\) | −4.87968e8 | −0.0704496 | ||||||||
\(649\) | −7.80424e8 | −0.112066 | ||||||||
\(650\) | −2.40240e9 | −0.343122 | ||||||||
\(651\) | −1.88161e9 | −0.267299 | ||||||||
\(652\) | 1.16122e8 | 0.0164077 | ||||||||
\(653\) | −5.52901e9 | −0.777053 | −0.388527 | − | 0.921437i | \(-0.627016\pi\) | ||||
−0.388527 | + | 0.921437i | \(0.627016\pi\) | |||||||
\(654\) | −1.21738e9 | −0.170179 | ||||||||
\(655\) | −3.37430e9 | −0.469179 | ||||||||
\(656\) | 5.26075e9 | 0.727585 | ||||||||
\(657\) | −1.53923e9 | −0.211751 | ||||||||
\(658\) | 4.69821e9 | 0.642898 | ||||||||
\(659\) | −8.17686e9 | −1.11298 | −0.556491 | − | 0.830854i | \(-0.687852\pi\) | ||||
−0.556491 | + | 0.830854i | \(0.687852\pi\) | |||||||
\(660\) | −1.02373e9 | −0.138606 | ||||||||
\(661\) | 1.00210e10 | 1.34960 | 0.674801 | − | 0.737999i | \(-0.264229\pi\) | ||||
0.674801 | + | 0.737999i | \(0.264229\pi\) | |||||||
\(662\) | 2.64694e9 | 0.354603 | ||||||||
\(663\) | −1.05627e9 | −0.140759 | ||||||||
\(664\) | −1.73430e9 | −0.229898 | ||||||||
\(665\) | 6.55158e9 | 0.863914 | ||||||||
\(666\) | 8.86161e8 | 0.116239 | ||||||||
\(667\) | 2.19957e9 | 0.287010 | ||||||||
\(668\) | 5.15614e8 | 0.0669279 | ||||||||
\(669\) | −6.99287e9 | −0.902951 | ||||||||
\(670\) | −9.70229e8 | −0.124627 | ||||||||
\(671\) | −2.05138e9 | −0.262130 | ||||||||
\(672\) | 5.62491e9 | 0.715029 | ||||||||
\(673\) | −1.41401e10 | −1.78814 | −0.894068 | − | 0.447931i | \(-0.852161\pi\) | ||||
−0.894068 | + | 0.447931i | \(0.852161\pi\) | |||||||
\(674\) | −2.78443e9 | −0.350290 | ||||||||
\(675\) | −1.38575e9 | −0.173429 | ||||||||
\(676\) | −2.02526e9 | −0.252154 | ||||||||
\(677\) | 9.91668e9 | 1.22830 | 0.614152 | − | 0.789188i | \(-0.289498\pi\) | ||||
0.614152 | + | 0.789188i | \(0.289498\pi\) | |||||||
\(678\) | 1.61645e9 | 0.199186 | ||||||||
\(679\) | 3.71280e9 | 0.455152 | ||||||||
\(680\) | −3.51625e8 | −0.0428843 | ||||||||
\(681\) | −7.16659e9 | −0.869556 | ||||||||
\(682\) | 7.70740e8 | 0.0930384 | ||||||||
\(683\) | −1.13006e10 | −1.35715 | −0.678575 | − | 0.734531i | \(-0.737402\pi\) | ||||
−0.678575 | + | 0.734531i | \(0.737402\pi\) | |||||||
\(684\) | 4.72543e9 | 0.564606 | ||||||||
\(685\) | 4.19653e9 | 0.498854 | ||||||||
\(686\) | 2.91400e8 | 0.0344632 | ||||||||
\(687\) | 4.95269e9 | 0.582764 | ||||||||
\(688\) | 7.81437e9 | 0.914817 | ||||||||
\(689\) | 7.18083e9 | 0.836388 | ||||||||
\(690\) | −8.71849e8 | −0.101034 | ||||||||
\(691\) | 6.57667e9 | 0.758286 | 0.379143 | − | 0.925338i | \(-0.376219\pi\) | ||||
0.379143 | + | 0.925338i | \(0.376219\pi\) | |||||||
\(692\) | −1.65379e9 | −0.189718 | ||||||||
\(693\) | −3.61796e9 | −0.412950 | ||||||||
\(694\) | −2.50193e9 | −0.284130 | ||||||||
\(695\) | 7.91849e8 | 0.0894737 | ||||||||
\(696\) | −5.64088e8 | −0.0634183 | ||||||||
\(697\) | −2.07587e9 | −0.232212 | ||||||||
\(698\) | −1.45314e8 | −0.0161738 | ||||||||
\(699\) | 8.48960e9 | 0.940194 | ||||||||
\(700\) | 1.04410e10 | 1.15053 | ||||||||
\(701\) | −1.12915e10 | −1.23805 | −0.619027 | − | 0.785370i | \(-0.712473\pi\) | ||||
−0.619027 | + | 0.785370i | \(0.712473\pi\) | |||||||
\(702\) | 6.71653e8 | 0.0732765 | ||||||||
\(703\) | −1.82550e10 | −1.98170 | ||||||||
\(704\) | 3.06770e9 | 0.331366 | ||||||||
\(705\) | −2.24526e9 | −0.241326 | ||||||||
\(706\) | 3.25530e9 | 0.348157 | ||||||||
\(707\) | 1.84323e9 | 0.196161 | ||||||||
\(708\) | −6.29663e8 | −0.0666794 | ||||||||
\(709\) | 4.04329e9 | 0.426062 | 0.213031 | − | 0.977045i | \(-0.431666\pi\) | ||||
0.213031 | + | 0.977045i | \(0.431666\pi\) | |||||||
\(710\) | 1.74966e8 | 0.0183464 | ||||||||
\(711\) | −2.77182e9 | −0.289216 | ||||||||
\(712\) | −5.95060e9 | −0.617846 | ||||||||
\(713\) | −5.15816e9 | −0.532944 | ||||||||
\(714\) | −5.84168e8 | −0.0600612 | ||||||||
\(715\) | 2.99750e9 | 0.306682 | ||||||||
\(716\) | 8.62662e9 | 0.878305 | ||||||||
\(717\) | −9.24485e8 | −0.0936662 | ||||||||
\(718\) | 5.72825e9 | 0.577546 | ||||||||
\(719\) | −1.82139e10 | −1.82748 | −0.913739 | − | 0.406302i | \(-0.866818\pi\) | ||||
−0.913739 | + | 0.406302i | \(0.866818\pi\) | |||||||
\(720\) | −7.07487e8 | −0.0706407 | ||||||||
\(721\) | 1.38405e10 | 1.37524 | ||||||||
\(722\) | 8.98954e9 | 0.888908 | ||||||||
\(723\) | −5.37105e9 | −0.528537 | ||||||||
\(724\) | 1.22705e10 | 1.20165 | ||||||||
\(725\) | −1.60192e9 | −0.156119 | ||||||||
\(726\) | −5.18073e8 | −0.0502473 | ||||||||
\(727\) | 8.36470e9 | 0.807384 | 0.403692 | − | 0.914895i | \(-0.367727\pi\) | ||||
0.403692 | + | 0.914895i | \(0.367727\pi\) | |||||||
\(728\) | −1.07652e10 | −1.03410 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 7.05283e8 | 0.0671016 | ||||||||
\(731\) | −3.08352e9 | −0.291968 | ||||||||
\(732\) | −1.65510e9 | −0.155968 | ||||||||
\(733\) | 1.25663e10 | 1.17853 | 0.589267 | − | 0.807939i | \(-0.299417\pi\) | ||||
0.589267 | + | 0.807939i | \(0.299417\pi\) | |||||||
\(734\) | −2.92581e9 | −0.273092 | ||||||||
\(735\) | −2.09319e9 | −0.194448 | ||||||||
\(736\) | 1.54199e10 | 1.42563 | ||||||||
\(737\) | −1.10373e10 | −1.01561 | ||||||||
\(738\) | 1.31999e9 | 0.120885 | ||||||||
\(739\) | −1.15684e10 | −1.05443 | −0.527214 | − | 0.849733i | \(-0.676763\pi\) | ||||
−0.527214 | + | 0.849733i | \(0.676763\pi\) | |||||||
\(740\) | 3.19084e9 | 0.289463 | ||||||||
\(741\) | −1.38361e10 | −1.24925 | ||||||||
\(742\) | 3.97136e9 | 0.356883 | ||||||||
\(743\) | 1.87018e10 | 1.67272 | 0.836360 | − | 0.548181i | \(-0.184679\pi\) | ||||
0.836360 | + | 0.548181i | \(0.184679\pi\) | |||||||
\(744\) | 1.32283e9 | 0.117760 | ||||||||
\(745\) | 1.52797e9 | 0.135385 | ||||||||
\(746\) | −3.30699e9 | −0.291640 | ||||||||
\(747\) | 1.37694e9 | 0.120863 | ||||||||
\(748\) | −1.88039e9 | −0.164283 | ||||||||
\(749\) | 2.40999e10 | 2.09570 | ||||||||
\(750\) | 1.33955e9 | 0.115943 | ||||||||
\(751\) | −1.25529e10 | −1.08145 | −0.540723 | − | 0.841201i | \(-0.681849\pi\) | ||||
−0.540723 | + | 0.841201i | \(0.681849\pi\) | |||||||
\(752\) | 1.04514e10 | 0.896215 | ||||||||
\(753\) | −1.09869e10 | −0.937763 | ||||||||
\(754\) | 7.76427e8 | 0.0659631 | ||||||||
\(755\) | −1.28886e9 | −0.108992 | ||||||||
\(756\) | −2.91905e9 | −0.245706 | ||||||||
\(757\) | −9.74904e9 | −0.816820 | −0.408410 | − | 0.912799i | \(-0.633917\pi\) | ||||
−0.408410 | + | 0.912799i | \(0.633917\pi\) | |||||||
\(758\) | −2.61115e9 | −0.217766 | ||||||||
\(759\) | −9.91810e9 | −0.823346 | ||||||||
\(760\) | −4.60597e9 | −0.380604 | ||||||||
\(761\) | 1.96148e10 | 1.61338 | 0.806692 | − | 0.590972i | \(-0.201255\pi\) | ||||
0.806692 | + | 0.590972i | \(0.201255\pi\) | |||||||
\(762\) | −1.79449e9 | −0.146926 | ||||||||
\(763\) | −1.54916e10 | −1.26259 | ||||||||
\(764\) | 1.50442e10 | 1.22051 | ||||||||
\(765\) | 2.79171e8 | 0.0225453 | ||||||||
\(766\) | 2.63339e9 | 0.211697 | ||||||||
\(767\) | 1.84366e9 | 0.147536 | ||||||||
\(768\) | 3.79565e8 | 0.0302358 | ||||||||
\(769\) | 1.59863e9 | 0.126767 | 0.0633834 | − | 0.997989i | \(-0.479811\pi\) | ||||
0.0633834 | + | 0.997989i | \(0.479811\pi\) | |||||||
\(770\) | 1.65777e9 | 0.130860 | ||||||||
\(771\) | 2.81994e9 | 0.221590 | ||||||||
\(772\) | −1.14808e10 | −0.898074 | ||||||||
\(773\) | −2.19525e10 | −1.70945 | −0.854725 | − | 0.519081i | \(-0.826274\pi\) | ||||
−0.854725 | + | 0.519081i | \(0.826274\pi\) | |||||||
\(774\) | 1.96073e9 | 0.151993 | ||||||||
\(775\) | 3.75662e9 | 0.289895 | ||||||||
\(776\) | −2.61021e9 | −0.200521 | ||||||||
\(777\) | 1.12767e10 | 0.862400 | ||||||||
\(778\) | −6.85795e7 | −0.00522115 | ||||||||
\(779\) | −2.71920e10 | −2.06091 | ||||||||
\(780\) | 2.41845e9 | 0.182476 | ||||||||
\(781\) | 1.99041e9 | 0.149508 | ||||||||
\(782\) | −1.60141e9 | −0.119751 | ||||||||
\(783\) | 4.47856e8 | 0.0333405 | ||||||||
\(784\) | 9.74356e9 | 0.722123 | ||||||||
\(785\) | −3.61424e9 | −0.266670 | ||||||||
\(786\) | 3.94109e9 | 0.289492 | ||||||||
\(787\) | 2.94002e9 | 0.215000 | 0.107500 | − | 0.994205i | \(-0.465715\pi\) | ||||
0.107500 | + | 0.994205i | \(0.465715\pi\) | |||||||
\(788\) | −1.13863e9 | −0.0828975 | ||||||||
\(789\) | 5.95330e9 | 0.431507 | ||||||||
\(790\) | 1.27006e9 | 0.0916496 | ||||||||
\(791\) | 2.05699e10 | 1.47780 | ||||||||
\(792\) | 2.54354e9 | 0.181928 | ||||||||
\(793\) | 4.84614e9 | 0.345096 | ||||||||
\(794\) | 2.45984e9 | 0.174395 | ||||||||
\(795\) | −1.89790e9 | −0.133964 | ||||||||
\(796\) | −7.21186e9 | −0.506818 | ||||||||
\(797\) | −2.52071e10 | −1.76367 | −0.881836 | − | 0.471556i | \(-0.843693\pi\) | ||||
−0.881836 | + | 0.471556i | \(0.843693\pi\) | |||||||
\(798\) | −7.65207e9 | −0.533051 | ||||||||
\(799\) | −4.12408e9 | −0.286031 | ||||||||
\(800\) | −1.12301e10 | −0.775475 | ||||||||
\(801\) | 4.72446e9 | 0.324817 | ||||||||
\(802\) | −9.03969e8 | −0.0618790 | ||||||||
\(803\) | 8.02325e9 | 0.546822 | ||||||||
\(804\) | −8.90511e9 | −0.604287 | ||||||||
\(805\) | −1.10946e10 | −0.749592 | ||||||||
\(806\) | −1.82078e9 | −0.122486 | ||||||||
\(807\) | 9.55517e9 | 0.640002 | ||||||||
\(808\) | −1.29585e9 | −0.0864201 | ||||||||
\(809\) | −4.67981e9 | −0.310748 | −0.155374 | − | 0.987856i | \(-0.549658\pi\) | ||||
−0.155374 | + | 0.987856i | \(0.549658\pi\) | |||||||
\(810\) | −1.77518e8 | −0.0117367 | ||||||||
\(811\) | 1.13390e10 | 0.746451 | 0.373225 | − | 0.927741i | \(-0.378252\pi\) | ||||
0.373225 | + | 0.927741i | \(0.378252\pi\) | |||||||
\(812\) | −3.37441e9 | −0.221183 | ||||||||
\(813\) | −1.31367e10 | −0.857370 | ||||||||
\(814\) | −4.61912e9 | −0.300175 | ||||||||
\(815\) | 8.98639e7 | 0.00581479 | ||||||||
\(816\) | −1.29951e9 | −0.0837268 | ||||||||
\(817\) | −4.03913e10 | −2.59126 | ||||||||
\(818\) | 4.45820e9 | 0.284789 | ||||||||
\(819\) | 8.54701e9 | 0.543652 | ||||||||
\(820\) | 4.75295e9 | 0.301033 | ||||||||
\(821\) | −2.40573e10 | −1.51721 | −0.758606 | − | 0.651549i | \(-0.774119\pi\) | ||||
−0.758606 | + | 0.651549i | \(0.774119\pi\) | |||||||
\(822\) | −4.90143e9 | −0.307802 | ||||||||
\(823\) | 3.05338e10 | 1.90933 | 0.954666 | − | 0.297681i | \(-0.0962131\pi\) | ||||
0.954666 | + | 0.297681i | \(0.0962131\pi\) | |||||||
\(824\) | −9.73030e9 | −0.605872 | ||||||||
\(825\) | 7.22322e9 | 0.447860 | ||||||||
\(826\) | 1.01964e9 | 0.0629529 | ||||||||
\(827\) | −2.87404e10 | −1.76695 | −0.883473 | − | 0.468482i | \(-0.844801\pi\) | ||||
−0.883473 | + | 0.468482i | \(0.844801\pi\) | |||||||
\(828\) | −8.00214e9 | −0.489892 | ||||||||
\(829\) | −1.64553e10 | −1.00315 | −0.501575 | − | 0.865114i | \(-0.667246\pi\) | ||||
−0.501575 | + | 0.865114i | \(0.667246\pi\) | |||||||
\(830\) | −6.30921e8 | −0.0383003 | ||||||||
\(831\) | −1.14609e10 | −0.692811 | ||||||||
\(832\) | −7.24709e9 | −0.436246 | ||||||||
\(833\) | −3.84477e9 | −0.230469 | ||||||||
\(834\) | −9.24859e8 | −0.0552070 | ||||||||
\(835\) | 3.99021e8 | 0.0237188 | ||||||||
\(836\) | −2.46314e10 | −1.45803 | ||||||||
\(837\) | −1.05026e9 | −0.0619094 | ||||||||
\(838\) | −5.34000e9 | −0.313464 | ||||||||
\(839\) | 1.71860e10 | 1.00463 | 0.502316 | − | 0.864684i | \(-0.332481\pi\) | ||||
0.502316 | + | 0.864684i | \(0.332481\pi\) | |||||||
\(840\) | 2.84525e9 | 0.165632 | ||||||||
\(841\) | −1.67322e10 | −0.969987 | ||||||||
\(842\) | −3.10435e9 | −0.179217 | ||||||||
\(843\) | 1.58024e10 | 0.908503 | ||||||||
\(844\) | −3.30934e9 | −0.189471 | ||||||||
\(845\) | −1.56729e9 | −0.0893618 | ||||||||
\(846\) | 2.62240e9 | 0.148903 | ||||||||
\(847\) | −6.59266e9 | −0.372794 | ||||||||
\(848\) | 8.83449e9 | 0.497503 | ||||||||
\(849\) | 3.33528e9 | 0.187049 | ||||||||
\(850\) | 1.16629e9 | 0.0651386 | ||||||||
\(851\) | 3.09134e10 | 1.71946 | ||||||||
\(852\) | 1.60590e9 | 0.0889571 | ||||||||
\(853\) | −2.96393e9 | −0.163511 | −0.0817555 | − | 0.996652i | \(-0.526053\pi\) | ||||
−0.0817555 | + | 0.996652i | \(0.526053\pi\) | |||||||
\(854\) | 2.68016e9 | 0.147251 | ||||||||
\(855\) | 3.65689e9 | 0.200093 | ||||||||
\(856\) | −1.69430e10 | −0.923276 | ||||||||
\(857\) | −7.20996e9 | −0.391291 | −0.195646 | − | 0.980675i | \(-0.562680\pi\) | ||||
−0.195646 | + | 0.980675i | \(0.562680\pi\) | |||||||
\(858\) | −3.50100e9 | −0.189228 | ||||||||
\(859\) | −2.08163e10 | −1.12054 | −0.560269 | − | 0.828311i | \(-0.689302\pi\) | ||||
−0.560269 | + | 0.828311i | \(0.689302\pi\) | |||||||
\(860\) | 7.06008e9 | 0.378499 | ||||||||
\(861\) | 1.67974e10 | 0.896871 | ||||||||
\(862\) | 9.35968e9 | 0.497720 | ||||||||
\(863\) | 1.95918e9 | 0.103761 | 0.0518807 | − | 0.998653i | \(-0.483478\pi\) | ||||
0.0518807 | + | 0.998653i | \(0.483478\pi\) | |||||||
\(864\) | 3.13965e9 | 0.165609 | ||||||||
\(865\) | −1.27982e9 | −0.0672347 | ||||||||
\(866\) | −4.58038e9 | −0.239656 | ||||||||
\(867\) | −1.05664e10 | −0.550628 | ||||||||
\(868\) | 7.91325e9 | 0.410711 | ||||||||
\(869\) | 1.44482e10 | 0.746868 | ||||||||
\(870\) | −2.05210e8 | −0.0105653 | ||||||||
\(871\) | 2.60743e10 | 1.33705 | ||||||||
\(872\) | 1.08911e10 | 0.556242 | ||||||||
\(873\) | 2.07237e9 | 0.105419 | ||||||||
\(874\) | −2.09770e10 | −1.06281 | ||||||||
\(875\) | 1.70463e10 | 0.860204 | ||||||||
\(876\) | 6.47334e9 | 0.325360 | ||||||||
\(877\) | −3.94405e10 | −1.97444 | −0.987220 | − | 0.159366i | \(-0.949055\pi\) | ||||
−0.987220 | + | 0.159366i | \(0.949055\pi\) | |||||||
\(878\) | 2.82762e9 | 0.140991 | ||||||||
\(879\) | −9.03948e9 | −0.448934 | ||||||||
\(880\) | 3.68778e9 | 0.182422 | ||||||||
\(881\) | 2.19999e10 | 1.08394 | 0.541970 | − | 0.840398i | \(-0.317679\pi\) | ||||
0.541970 | + | 0.840398i | \(0.317679\pi\) | |||||||
\(882\) | 2.44479e9 | 0.119978 | ||||||||
\(883\) | −8.61343e8 | −0.0421031 | −0.0210515 | − | 0.999778i | \(-0.506701\pi\) | ||||
−0.0210515 | + | 0.999778i | \(0.506701\pi\) | |||||||
\(884\) | 4.44220e9 | 0.216279 | ||||||||
\(885\) | −4.87280e8 | −0.0236307 | ||||||||
\(886\) | 2.15114e9 | 0.103908 | ||||||||
\(887\) | 4.62675e9 | 0.222609 | 0.111305 | − | 0.993786i | \(-0.464497\pi\) | ||||
0.111305 | + | 0.993786i | \(0.464497\pi\) | |||||||
\(888\) | −7.92787e9 | −0.379937 | ||||||||
\(889\) | −2.28354e10 | −1.09007 | ||||||||
\(890\) | −2.16477e9 | −0.102931 | ||||||||
\(891\) | −2.01943e9 | −0.0956440 | ||||||||
\(892\) | 2.94090e10 | 1.38741 | ||||||||
\(893\) | −5.40217e10 | −2.53857 | ||||||||
\(894\) | −1.78463e9 | −0.0835348 | ||||||||
\(895\) | 6.67592e9 | 0.311265 | ||||||||
\(896\) | −3.06743e10 | −1.42461 | ||||||||
\(897\) | 2.34304e10 | 1.08394 | ||||||||
\(898\) | −6.10584e9 | −0.281370 | ||||||||
\(899\) | −1.21409e9 | −0.0557305 | ||||||||
\(900\) | 5.82785e9 | 0.266477 | ||||||||
\(901\) | −3.48605e9 | −0.158781 | ||||||||
\(902\) | −6.88047e9 | −0.312173 | ||||||||
\(903\) | 2.49510e10 | 1.12767 | ||||||||
\(904\) | −1.44613e10 | −0.651054 | ||||||||
\(905\) | 9.49583e9 | 0.425856 | ||||||||
\(906\) | 1.50536e9 | 0.0672499 | ||||||||
\(907\) | −5.22593e9 | −0.232562 | −0.116281 | − | 0.993216i | \(-0.537097\pi\) | ||||
−0.116281 | + | 0.993216i | \(0.537097\pi\) | |||||||
\(908\) | 3.01396e10 | 1.33609 | ||||||||
\(909\) | 1.02884e9 | 0.0454331 | ||||||||
\(910\) | −3.91628e9 | −0.172278 | ||||||||
\(911\) | −3.60178e9 | −0.157835 | −0.0789175 | − | 0.996881i | \(-0.525146\pi\) | ||||
−0.0789175 | + | 0.996881i | \(0.525146\pi\) | |||||||
\(912\) | −1.70224e10 | −0.743086 | ||||||||
\(913\) | −7.17732e9 | −0.312115 | ||||||||
\(914\) | −5.43334e9 | −0.235372 | ||||||||
\(915\) | −1.28084e9 | −0.0552739 | ||||||||
\(916\) | −2.08289e10 | −0.895430 | ||||||||
\(917\) | 5.01517e10 | 2.14780 | ||||||||
\(918\) | −3.26065e8 | −0.0139109 | ||||||||
\(919\) | 8.64702e9 | 0.367504 | 0.183752 | − | 0.982973i | \(-0.441176\pi\) | ||||
0.183752 | + | 0.982973i | \(0.441176\pi\) | |||||||
\(920\) | 7.79983e9 | 0.330239 | ||||||||
\(921\) | 1.49772e10 | 0.631715 | ||||||||
\(922\) | 2.57739e9 | 0.108298 | ||||||||
\(923\) | −4.70210e9 | −0.196828 | ||||||||
\(924\) | 1.52156e10 | 0.634507 | ||||||||
\(925\) | −2.25138e10 | −0.935305 | ||||||||
\(926\) | 2.82322e8 | 0.0116844 | ||||||||
\(927\) | 7.72534e9 | 0.318521 | ||||||||
\(928\) | 3.62942e9 | 0.149080 | ||||||||
\(929\) | −2.75239e9 | −0.112630 | −0.0563151 | − | 0.998413i | \(-0.517935\pi\) | ||||
−0.0563151 | + | 0.998413i | \(0.517935\pi\) | |||||||
\(930\) | 4.81234e8 | 0.0196185 | ||||||||
\(931\) | −5.03630e10 | −2.04544 | ||||||||
\(932\) | −3.57036e10 | −1.44463 | ||||||||
\(933\) | −1.08419e10 | −0.437038 | ||||||||
\(934\) | −3.29186e9 | −0.132199 | ||||||||
\(935\) | −1.45518e9 | −0.0582207 | ||||||||
\(936\) | −6.00881e9 | −0.239510 | ||||||||
\(937\) | 2.00871e10 | 0.797678 | 0.398839 | − | 0.917021i | \(-0.369413\pi\) | ||||
0.398839 | + | 0.917021i | \(0.369413\pi\) | |||||||
\(938\) | 1.44204e10 | 0.570515 | ||||||||
\(939\) | 1.98939e10 | 0.784134 | ||||||||
\(940\) | 9.44258e9 | 0.370803 | ||||||||
\(941\) | −5.18639e9 | −0.202909 | −0.101455 | − | 0.994840i | \(-0.532350\pi\) | ||||
−0.101455 | + | 0.994840i | \(0.532350\pi\) | |||||||
\(942\) | 4.22134e9 | 0.164540 | ||||||||
\(943\) | 4.60474e10 | 1.78819 | ||||||||
\(944\) | 2.26823e9 | 0.0877578 | ||||||||
\(945\) | −2.25898e9 | −0.0870764 | ||||||||
\(946\) | −1.02203e10 | −0.392506 | ||||||||
\(947\) | 3.37384e10 | 1.29092 | 0.645460 | − | 0.763794i | \(-0.276666\pi\) | ||||
0.645460 | + | 0.763794i | \(0.276666\pi\) | |||||||
\(948\) | 1.16571e10 | 0.444387 | ||||||||
\(949\) | −1.89540e10 | −0.719895 | ||||||||
\(950\) | 1.52773e10 | 0.578114 | ||||||||
\(951\) | −6.82551e8 | −0.0257338 | ||||||||
\(952\) | 5.22615e9 | 0.196315 | ||||||||
\(953\) | 3.47736e10 | 1.30144 | 0.650720 | − | 0.759318i | \(-0.274467\pi\) | ||||
0.650720 | + | 0.759318i | \(0.274467\pi\) | |||||||
\(954\) | 2.21669e9 | 0.0826582 | ||||||||
\(955\) | 1.16423e10 | 0.432542 | ||||||||
\(956\) | 3.88799e9 | 0.143920 | ||||||||
\(957\) | −2.33445e9 | −0.0860981 | ||||||||
\(958\) | 1.47423e10 | 0.541735 | ||||||||
\(959\) | −6.23725e10 | −2.28364 | ||||||||
\(960\) | 1.91541e9 | 0.0698734 | ||||||||
\(961\) | −2.46655e10 | −0.896515 | ||||||||
\(962\) | 1.09121e10 | 0.395182 | ||||||||
\(963\) | 1.34518e10 | 0.485388 | ||||||||
\(964\) | 2.25883e10 | 0.812109 | ||||||||
\(965\) | −8.88470e9 | −0.318271 | ||||||||
\(966\) | 1.29582e10 | 0.462513 | ||||||||
\(967\) | −4.82322e10 | −1.71532 | −0.857659 | − | 0.514219i | \(-0.828082\pi\) | ||||
−0.857659 | + | 0.514219i | \(0.828082\pi\) | |||||||
\(968\) | 4.63484e9 | 0.164237 | ||||||||
\(969\) | 6.71697e9 | 0.237159 | ||||||||
\(970\) | −9.49569e8 | −0.0334061 | ||||||||
\(971\) | 6.11947e9 | 0.214509 | 0.107255 | − | 0.994232i | \(-0.465794\pi\) | ||||
0.107255 | + | 0.994232i | \(0.465794\pi\) | |||||||
\(972\) | −1.62932e9 | −0.0569083 | ||||||||
\(973\) | −1.17691e10 | −0.409591 | ||||||||
\(974\) | 1.21208e10 | 0.420315 | ||||||||
\(975\) | −1.70640e10 | −0.589610 | ||||||||
\(976\) | 5.96215e9 | 0.205271 | ||||||||
\(977\) | 4.14878e10 | 1.42328 | 0.711638 | − | 0.702546i | \(-0.247954\pi\) | ||||
0.711638 | + | 0.702546i | \(0.247954\pi\) | |||||||
\(978\) | −1.04959e8 | −0.00358783 | ||||||||
\(979\) | −2.46263e10 | −0.838803 | ||||||||
\(980\) | 8.80305e9 | 0.298774 | ||||||||
\(981\) | −8.64695e9 | −0.292430 | ||||||||
\(982\) | 6.04571e9 | 0.203731 | ||||||||
\(983\) | 4.34606e10 | 1.45935 | 0.729674 | − | 0.683795i | \(-0.239672\pi\) | ||||
0.729674 | + | 0.683795i | \(0.239672\pi\) | |||||||
\(984\) | −1.18091e10 | −0.395123 | ||||||||
\(985\) | −8.81158e8 | −0.0293783 | ||||||||
\(986\) | −3.76929e8 | −0.0125225 | ||||||||
\(987\) | 3.33709e10 | 1.10474 | ||||||||
\(988\) | 5.81888e10 | 1.91951 | ||||||||
\(989\) | 6.83994e10 | 2.24836 | ||||||||
\(990\) | 9.25315e8 | 0.0303086 | ||||||||
\(991\) | 2.63085e10 | 0.858694 | 0.429347 | − | 0.903140i | \(-0.358744\pi\) | ||||
0.429347 | + | 0.903140i | \(0.358744\pi\) | |||||||
\(992\) | −8.51129e9 | −0.276824 | ||||||||
\(993\) | 1.88010e10 | 0.609338 | ||||||||
\(994\) | −2.60050e9 | −0.0839855 | ||||||||
\(995\) | −5.58108e9 | −0.179613 | ||||||||
\(996\) | −5.79082e9 | −0.185709 | ||||||||
\(997\) | −4.90773e10 | −1.56837 | −0.784183 | − | 0.620530i | \(-0.786918\pi\) | ||||
−0.784183 | + | 0.620530i | \(0.786918\pi\) | |||||||
\(998\) | −1.51495e10 | −0.482438 | ||||||||
\(999\) | 6.29431e9 | 0.199742 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.8.a.d.1.9 | ✓ | 18 | |
3.2 | odd | 2 | 531.8.a.e.1.10 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.d.1.9 | ✓ | 18 | 1.1 | even | 1 | trivial | |
531.8.a.e.1.10 | 18 | 3.2 | odd | 2 |