Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,8,Mod(1,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, 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("91.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(28.4270373191\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 3 x^{9} - 816 x^{8} + 2298 x^{7} + 213848 x^{6} - 507132 x^{5} - 19919976 x^{4} + \cdots - 7335224320 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-4.83483\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.83483 | 0.427342 | 0.213671 | − | 0.976906i | \(-0.431458\pi\) | ||||
0.213671 | + | 0.976906i | \(0.431458\pi\) | |||||||
\(3\) | 62.4820 | 1.33607 | 0.668037 | − | 0.744128i | \(-0.267135\pi\) | ||||
0.668037 | + | 0.744128i | \(0.267135\pi\) | |||||||
\(4\) | −104.624 | −0.817378 | ||||||||
\(5\) | 314.530 | 1.12530 | 0.562648 | − | 0.826697i | \(-0.309783\pi\) | ||||
0.562648 | + | 0.826697i | \(0.309783\pi\) | |||||||
\(6\) | 302.090 | 0.570961 | ||||||||
\(7\) | −343.000 | −0.377964 | ||||||||
\(8\) | −1124.70 | −0.776643 | ||||||||
\(9\) | 1717.00 | 0.785094 | ||||||||
\(10\) | 1520.70 | 0.480886 | ||||||||
\(11\) | 8467.65 | 1.91818 | 0.959088 | − | 0.283109i | \(-0.0913658\pi\) | ||||
0.959088 | + | 0.283109i | \(0.0913658\pi\) | |||||||
\(12\) | −6537.15 | −1.09208 | ||||||||
\(13\) | −2197.00 | −0.277350 | ||||||||
\(14\) | −1658.35 | −0.161520 | ||||||||
\(15\) | 19652.4 | 1.50348 | ||||||||
\(16\) | 7954.20 | 0.485486 | ||||||||
\(17\) | 11951.4 | 0.589996 | 0.294998 | − | 0.955498i | \(-0.404681\pi\) | ||||
0.294998 | + | 0.955498i | \(0.404681\pi\) | |||||||
\(18\) | 8301.41 | 0.335504 | ||||||||
\(19\) | 6886.88 | 0.230348 | 0.115174 | − | 0.993345i | \(-0.463257\pi\) | ||||
0.115174 | + | 0.993345i | \(0.463257\pi\) | |||||||
\(20\) | −32907.5 | −0.919792 | ||||||||
\(21\) | −21431.3 | −0.504989 | ||||||||
\(22\) | 40939.6 | 0.819718 | ||||||||
\(23\) | 103273. | 1.76987 | 0.884934 | − | 0.465717i | \(-0.154204\pi\) | ||||
0.884934 | + | 0.465717i | \(0.154204\pi\) | |||||||
\(24\) | −70273.5 | −1.03765 | ||||||||
\(25\) | 20803.8 | 0.266289 | ||||||||
\(26\) | −10622.1 | −0.118523 | ||||||||
\(27\) | −29366.4 | −0.287130 | ||||||||
\(28\) | 35886.2 | 0.308940 | ||||||||
\(29\) | −101393. | −0.771993 | −0.385996 | − | 0.922500i | \(-0.626142\pi\) | ||||
−0.385996 | + | 0.922500i | \(0.626142\pi\) | |||||||
\(30\) | 95016.1 | 0.642500 | ||||||||
\(31\) | 240887. | 1.45227 | 0.726137 | − | 0.687551i | \(-0.241314\pi\) | ||||
0.726137 | + | 0.687551i | \(0.241314\pi\) | |||||||
\(32\) | 182419. | 0.984112 | ||||||||
\(33\) | 529076. | 2.56282 | ||||||||
\(34\) | 57783.1 | 0.252130 | ||||||||
\(35\) | −107884. | −0.425322 | ||||||||
\(36\) | −179640. | −0.641719 | ||||||||
\(37\) | −494398. | −1.60461 | −0.802307 | − | 0.596912i | \(-0.796394\pi\) | ||||
−0.802307 | + | 0.596912i | \(0.796394\pi\) | |||||||
\(38\) | 33296.9 | 0.0984376 | ||||||||
\(39\) | −137273. | −0.370560 | ||||||||
\(40\) | −353751. | −0.873952 | ||||||||
\(41\) | −517724. | −1.17315 | −0.586577 | − | 0.809893i | \(-0.699525\pi\) | ||||
−0.586577 | + | 0.809893i | \(0.699525\pi\) | |||||||
\(42\) | −103617. | −0.215803 | ||||||||
\(43\) | 670384. | 1.28583 | 0.642916 | − | 0.765937i | \(-0.277724\pi\) | ||||
0.642916 | + | 0.765937i | \(0.277724\pi\) | |||||||
\(44\) | −885923. | −1.56788 | ||||||||
\(45\) | 540048. | 0.883463 | ||||||||
\(46\) | 499309. | 0.756339 | ||||||||
\(47\) | 390703. | 0.548914 | 0.274457 | − | 0.961599i | \(-0.411502\pi\) | ||||
0.274457 | + | 0.961599i | \(0.411502\pi\) | |||||||
\(48\) | 496995. | 0.648645 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | 100583. | 0.113797 | ||||||||
\(51\) | 746750. | 0.788278 | ||||||||
\(52\) | 229860. | 0.226700 | ||||||||
\(53\) | 316966. | 0.292447 | 0.146224 | − | 0.989252i | \(-0.453288\pi\) | ||||
0.146224 | + | 0.989252i | \(0.453288\pi\) | |||||||
\(54\) | −141982. | −0.122703 | ||||||||
\(55\) | 2.66333e6 | 2.15851 | ||||||||
\(56\) | 385772. | 0.293543 | ||||||||
\(57\) | 430306. | 0.307762 | ||||||||
\(58\) | −490216. | −0.329905 | ||||||||
\(59\) | 2.76489e6 | 1.75265 | 0.876326 | − | 0.481719i | \(-0.159987\pi\) | ||||
0.876326 | + | 0.481719i | \(0.159987\pi\) | |||||||
\(60\) | −2.05613e6 | −1.22891 | ||||||||
\(61\) | 50060.8 | 0.0282386 | 0.0141193 | − | 0.999900i | \(-0.495506\pi\) | ||||
0.0141193 | + | 0.999900i | \(0.495506\pi\) | |||||||
\(62\) | 1.16465e6 | 0.620618 | ||||||||
\(63\) | −588932. | −0.296738 | ||||||||
\(64\) | −136175. | −0.0649334 | ||||||||
\(65\) | −691021. | −0.312101 | ||||||||
\(66\) | 2.55799e6 | 1.09520 | ||||||||
\(67\) | −710978. | −0.288798 | −0.144399 | − | 0.989520i | \(-0.546125\pi\) | ||||
−0.144399 | + | 0.989520i | \(0.546125\pi\) | |||||||
\(68\) | −1.25041e6 | −0.482250 | ||||||||
\(69\) | 6.45272e6 | 2.36467 | ||||||||
\(70\) | −521599. | −0.181758 | ||||||||
\(71\) | −4.81274e6 | −1.59584 | −0.797918 | − | 0.602766i | \(-0.794065\pi\) | ||||
−0.797918 | + | 0.602766i | \(0.794065\pi\) | |||||||
\(72\) | −1.93111e6 | −0.609738 | ||||||||
\(73\) | 319628. | 0.0961645 | 0.0480822 | − | 0.998843i | \(-0.484689\pi\) | ||||
0.0480822 | + | 0.998843i | \(0.484689\pi\) | |||||||
\(74\) | −2.39033e6 | −0.685720 | ||||||||
\(75\) | 1.29987e6 | 0.355782 | ||||||||
\(76\) | −720536. | −0.188282 | ||||||||
\(77\) | −2.90440e6 | −0.725002 | ||||||||
\(78\) | −663691. | −0.158356 | ||||||||
\(79\) | 395221. | 0.0901872 | 0.0450936 | − | 0.998983i | \(-0.485641\pi\) | ||||
0.0450936 | + | 0.998983i | \(0.485641\pi\) | |||||||
\(80\) | 2.50183e6 | 0.546315 | ||||||||
\(81\) | −5.58996e6 | −1.16872 | ||||||||
\(82\) | −2.50311e6 | −0.501339 | ||||||||
\(83\) | −5.55444e6 | −1.06627 | −0.533135 | − | 0.846030i | \(-0.678986\pi\) | ||||
−0.533135 | + | 0.846030i | \(0.678986\pi\) | |||||||
\(84\) | 2.24224e6 | 0.412767 | ||||||||
\(85\) | 3.75908e6 | 0.663919 | ||||||||
\(86\) | 3.24119e6 | 0.549490 | ||||||||
\(87\) | −6.33521e6 | −1.03144 | ||||||||
\(88\) | −9.52355e6 | −1.48974 | ||||||||
\(89\) | −1.22040e7 | −1.83500 | −0.917500 | − | 0.397735i | \(-0.869796\pi\) | ||||
−0.917500 | + | 0.397735i | \(0.869796\pi\) | |||||||
\(90\) | 2.61104e6 | 0.377541 | ||||||||
\(91\) | 753571. | 0.104828 | ||||||||
\(92\) | −1.08049e7 | −1.44665 | ||||||||
\(93\) | 1.50511e7 | 1.94034 | ||||||||
\(94\) | 1.88898e6 | 0.234574 | ||||||||
\(95\) | 2.16613e6 | 0.259210 | ||||||||
\(96\) | 1.13979e7 | 1.31485 | ||||||||
\(97\) | −5.15456e6 | −0.573443 | −0.286721 | − | 0.958014i | \(-0.592565\pi\) | ||||
−0.286721 | + | 0.958014i | \(0.592565\pi\) | |||||||
\(98\) | 568813. | 0.0610489 | ||||||||
\(99\) | 1.45390e7 | 1.50595 | ||||||||
\(100\) | −2.17659e6 | −0.217659 | ||||||||
\(101\) | 5.66908e6 | 0.547504 | 0.273752 | − | 0.961800i | \(-0.411735\pi\) | ||||
0.273752 | + | 0.961800i | \(0.411735\pi\) | |||||||
\(102\) | 3.61041e6 | 0.336865 | ||||||||
\(103\) | −8.15115e6 | −0.735003 | −0.367501 | − | 0.930023i | \(-0.619787\pi\) | ||||
−0.367501 | + | 0.930023i | \(0.619787\pi\) | |||||||
\(104\) | 2.47096e6 | 0.215402 | ||||||||
\(105\) | −6.74079e6 | −0.568261 | ||||||||
\(106\) | 1.53248e6 | 0.124975 | ||||||||
\(107\) | −1.74326e7 | −1.37568 | −0.687841 | − | 0.725861i | \(-0.741441\pi\) | ||||
−0.687841 | + | 0.725861i | \(0.741441\pi\) | |||||||
\(108\) | 3.07245e6 | 0.234694 | ||||||||
\(109\) | 3.93590e6 | 0.291106 | 0.145553 | − | 0.989350i | \(-0.453504\pi\) | ||||
0.145553 | + | 0.989350i | \(0.453504\pi\) | |||||||
\(110\) | 1.28767e7 | 0.922424 | ||||||||
\(111\) | −3.08910e7 | −2.14388 | ||||||||
\(112\) | −2.72829e6 | −0.183496 | ||||||||
\(113\) | −2.61919e7 | −1.70762 | −0.853812 | − | 0.520581i | \(-0.825715\pi\) | ||||
−0.853812 | + | 0.520581i | \(0.825715\pi\) | |||||||
\(114\) | 2.08046e6 | 0.131520 | ||||||||
\(115\) | 3.24825e7 | 1.99162 | ||||||||
\(116\) | 1.06081e7 | 0.631010 | ||||||||
\(117\) | −3.77225e6 | −0.217746 | ||||||||
\(118\) | 1.33678e7 | 0.748982 | ||||||||
\(119\) | −4.09934e6 | −0.222997 | ||||||||
\(120\) | −2.21031e7 | −1.16767 | ||||||||
\(121\) | 5.22139e7 | 2.67940 | ||||||||
\(122\) | 242036. | 0.0120676 | ||||||||
\(123\) | −3.23485e7 | −1.56742 | ||||||||
\(124\) | −2.52027e7 | −1.18706 | ||||||||
\(125\) | −1.80292e7 | −0.825641 | ||||||||
\(126\) | −2.84738e6 | −0.126809 | ||||||||
\(127\) | 5.87479e6 | 0.254495 | 0.127247 | − | 0.991871i | \(-0.459386\pi\) | ||||
0.127247 | + | 0.991871i | \(0.459386\pi\) | |||||||
\(128\) | −2.40080e7 | −1.01186 | ||||||||
\(129\) | 4.18870e7 | 1.71797 | ||||||||
\(130\) | −3.34097e6 | −0.133374 | ||||||||
\(131\) | −1.07603e6 | −0.0418190 | −0.0209095 | − | 0.999781i | \(-0.506656\pi\) | ||||
−0.0209095 | + | 0.999781i | \(0.506656\pi\) | |||||||
\(132\) | −5.53542e7 | −2.09480 | ||||||||
\(133\) | −2.36220e6 | −0.0870634 | ||||||||
\(134\) | −3.43746e6 | −0.123416 | ||||||||
\(135\) | −9.23662e6 | −0.323106 | ||||||||
\(136\) | −1.34418e7 | −0.458216 | ||||||||
\(137\) | −3.97143e7 | −1.31955 | −0.659773 | − | 0.751465i | \(-0.729348\pi\) | ||||
−0.659773 | + | 0.751465i | \(0.729348\pi\) | |||||||
\(138\) | 3.11978e7 | 1.01053 | ||||||||
\(139\) | 2.73886e6 | 0.0865003 | 0.0432501 | − | 0.999064i | \(-0.486229\pi\) | ||||
0.0432501 | + | 0.999064i | \(0.486229\pi\) | |||||||
\(140\) | 1.12873e7 | 0.347649 | ||||||||
\(141\) | 2.44119e7 | 0.733389 | ||||||||
\(142\) | −2.32688e7 | −0.681968 | ||||||||
\(143\) | −1.86034e7 | −0.532006 | ||||||||
\(144\) | 1.36574e7 | 0.381152 | ||||||||
\(145\) | −3.18910e7 | −0.868720 | ||||||||
\(146\) | 1.54535e6 | 0.0410952 | ||||||||
\(147\) | 7.35095e6 | 0.190868 | ||||||||
\(148\) | 5.17261e7 | 1.31158 | ||||||||
\(149\) | 5.33444e7 | 1.32110 | 0.660552 | − | 0.750781i | \(-0.270322\pi\) | ||||
0.660552 | + | 0.750781i | \(0.270322\pi\) | |||||||
\(150\) | 6.28462e6 | 0.152041 | ||||||||
\(151\) | −3.23075e7 | −0.763632 | −0.381816 | − | 0.924238i | \(-0.624701\pi\) | ||||
−0.381816 | + | 0.924238i | \(0.624701\pi\) | |||||||
\(152\) | −7.74567e6 | −0.178898 | ||||||||
\(153\) | 2.05206e7 | 0.463202 | ||||||||
\(154\) | −1.40423e7 | −0.309824 | ||||||||
\(155\) | 7.57662e7 | 1.63424 | ||||||||
\(156\) | 1.43621e7 | 0.302888 | ||||||||
\(157\) | 9.76430e6 | 0.201369 | 0.100684 | − | 0.994918i | \(-0.467897\pi\) | ||||
0.100684 | + | 0.994918i | \(0.467897\pi\) | |||||||
\(158\) | 1.91082e6 | 0.0385408 | ||||||||
\(159\) | 1.98047e7 | 0.390731 | ||||||||
\(160\) | 5.73761e7 | 1.10742 | ||||||||
\(161\) | −3.54227e7 | −0.668947 | ||||||||
\(162\) | −2.70265e7 | −0.499444 | ||||||||
\(163\) | 1.91293e7 | 0.345972 | 0.172986 | − | 0.984924i | \(-0.444658\pi\) | ||||
0.172986 | + | 0.984924i | \(0.444658\pi\) | |||||||
\(164\) | 5.41666e7 | 0.958911 | ||||||||
\(165\) | 1.66410e8 | 2.88393 | ||||||||
\(166\) | −2.68548e7 | −0.455662 | ||||||||
\(167\) | 6.64443e7 | 1.10395 | 0.551976 | − | 0.833860i | \(-0.313874\pi\) | ||||
0.551976 | + | 0.833860i | \(0.313874\pi\) | |||||||
\(168\) | 2.41038e7 | 0.392196 | ||||||||
\(169\) | 4.82681e6 | 0.0769231 | ||||||||
\(170\) | 1.81745e7 | 0.283721 | ||||||||
\(171\) | 1.18248e7 | 0.180845 | ||||||||
\(172\) | −7.01386e7 | −1.05101 | ||||||||
\(173\) | 8.10105e7 | 1.18954 | 0.594771 | − | 0.803895i | \(-0.297243\pi\) | ||||
0.594771 | + | 0.803895i | \(0.297243\pi\) | |||||||
\(174\) | −3.06297e7 | −0.440778 | ||||||||
\(175\) | −7.13571e6 | −0.100648 | ||||||||
\(176\) | 6.73534e7 | 0.931247 | ||||||||
\(177\) | 1.72756e8 | 2.34167 | ||||||||
\(178\) | −5.90041e7 | −0.784174 | ||||||||
\(179\) | −6.95288e7 | −0.906106 | −0.453053 | − | 0.891484i | \(-0.649665\pi\) | ||||
−0.453053 | + | 0.891484i | \(0.649665\pi\) | |||||||
\(180\) | −5.65022e7 | −0.722124 | ||||||||
\(181\) | −1.08438e8 | −1.35927 | −0.679637 | − | 0.733548i | \(-0.737863\pi\) | ||||
−0.679637 | + | 0.733548i | \(0.737863\pi\) | |||||||
\(182\) | 3.64339e6 | 0.0447977 | ||||||||
\(183\) | 3.12790e6 | 0.0377289 | ||||||||
\(184\) | −1.16151e8 | −1.37455 | ||||||||
\(185\) | −1.55503e8 | −1.80566 | ||||||||
\(186\) | 7.27696e7 | 0.829192 | ||||||||
\(187\) | 1.01201e8 | 1.13172 | ||||||||
\(188\) | −4.08771e7 | −0.448670 | ||||||||
\(189\) | 1.00727e7 | 0.108525 | ||||||||
\(190\) | 1.04728e7 | 0.110771 | ||||||||
\(191\) | 6.71166e7 | 0.696968 | 0.348484 | − | 0.937315i | \(-0.386697\pi\) | ||||
0.348484 | + | 0.937315i | \(0.386697\pi\) | |||||||
\(192\) | −8.50850e6 | −0.0867558 | ||||||||
\(193\) | 8.36893e7 | 0.837953 | 0.418976 | − | 0.907997i | \(-0.362389\pi\) | ||||
0.418976 | + | 0.907997i | \(0.362389\pi\) | |||||||
\(194\) | −2.49214e7 | −0.245056 | ||||||||
\(195\) | −4.31764e7 | −0.416990 | ||||||||
\(196\) | −1.23090e7 | −0.116768 | ||||||||
\(197\) | −9.70987e7 | −0.904860 | −0.452430 | − | 0.891800i | \(-0.649443\pi\) | ||||
−0.452430 | + | 0.891800i | \(0.649443\pi\) | |||||||
\(198\) | 7.02934e7 | 0.643556 | ||||||||
\(199\) | 2.29633e7 | 0.206561 | 0.103280 | − | 0.994652i | \(-0.467066\pi\) | ||||
0.103280 | + | 0.994652i | \(0.467066\pi\) | |||||||
\(200\) | −2.33980e7 | −0.206811 | ||||||||
\(201\) | −4.44233e7 | −0.385856 | ||||||||
\(202\) | 2.74090e7 | 0.233972 | ||||||||
\(203\) | 3.47777e7 | 0.291786 | ||||||||
\(204\) | −7.81283e7 | −0.644322 | ||||||||
\(205\) | −1.62840e8 | −1.32014 | ||||||||
\(206\) | −3.94094e7 | −0.314098 | ||||||||
\(207\) | 1.77320e8 | 1.38951 | ||||||||
\(208\) | −1.74754e7 | −0.134650 | ||||||||
\(209\) | 5.83157e7 | 0.441848 | ||||||||
\(210\) | −3.25905e7 | −0.242842 | ||||||||
\(211\) | 7.86028e6 | 0.0576036 | 0.0288018 | − | 0.999585i | \(-0.490831\pi\) | ||||
0.0288018 | + | 0.999585i | \(0.490831\pi\) | |||||||
\(212\) | −3.31624e7 | −0.239040 | ||||||||
\(213\) | −3.00710e8 | −2.13215 | ||||||||
\(214\) | −8.42835e7 | −0.587887 | ||||||||
\(215\) | 2.10856e8 | 1.44694 | ||||||||
\(216\) | 3.30284e7 | 0.222997 | ||||||||
\(217\) | −8.26244e7 | −0.548908 | ||||||||
\(218\) | 1.90294e7 | 0.124402 | ||||||||
\(219\) | 1.99710e7 | 0.128483 | ||||||||
\(220\) | −2.78649e8 | −1.76432 | ||||||||
\(221\) | −2.62573e7 | −0.163635 | ||||||||
\(222\) | −1.49353e8 | −0.916172 | ||||||||
\(223\) | 1.68887e8 | 1.01983 | 0.509916 | − | 0.860224i | \(-0.329676\pi\) | ||||
0.509916 | + | 0.860224i | \(0.329676\pi\) | |||||||
\(224\) | −6.25696e7 | −0.371959 | ||||||||
\(225\) | 3.57202e7 | 0.209062 | ||||||||
\(226\) | −1.26633e8 | −0.729740 | ||||||||
\(227\) | −4.61537e6 | −0.0261888 | −0.0130944 | − | 0.999914i | \(-0.504168\pi\) | ||||
−0.0130944 | + | 0.999914i | \(0.504168\pi\) | |||||||
\(228\) | −4.50205e7 | −0.251558 | ||||||||
\(229\) | −3.10653e8 | −1.70943 | −0.854716 | − | 0.519096i | \(-0.826269\pi\) | ||||
−0.854716 | + | 0.519096i | \(0.826269\pi\) | |||||||
\(230\) | 1.57047e8 | 0.851105 | ||||||||
\(231\) | −1.81473e8 | −0.968657 | ||||||||
\(232\) | 1.14036e8 | 0.599563 | ||||||||
\(233\) | 9.25305e7 | 0.479225 | 0.239612 | − | 0.970869i | \(-0.422980\pi\) | ||||
0.239612 | + | 0.970869i | \(0.422980\pi\) | |||||||
\(234\) | −1.82382e7 | −0.0930521 | ||||||||
\(235\) | 1.22888e8 | 0.617690 | ||||||||
\(236\) | −2.89275e8 | −1.43258 | ||||||||
\(237\) | 2.46942e7 | 0.120497 | ||||||||
\(238\) | −1.98196e7 | −0.0952963 | ||||||||
\(239\) | 2.39451e8 | 1.13455 | 0.567275 | − | 0.823528i | \(-0.307998\pi\) | ||||
0.567275 | + | 0.823528i | \(0.307998\pi\) | |||||||
\(240\) | 1.56319e8 | 0.729917 | ||||||||
\(241\) | 1.76231e8 | 0.811005 | 0.405502 | − | 0.914094i | \(-0.367097\pi\) | ||||
0.405502 | + | 0.914094i | \(0.367097\pi\) | |||||||
\(242\) | 2.52445e8 | 1.14502 | ||||||||
\(243\) | −2.85047e8 | −1.27437 | ||||||||
\(244\) | −5.23759e6 | −0.0230817 | ||||||||
\(245\) | 3.70041e7 | 0.160756 | ||||||||
\(246\) | −1.56399e8 | −0.669826 | ||||||||
\(247\) | −1.51305e7 | −0.0638871 | ||||||||
\(248\) | −2.70926e8 | −1.12790 | ||||||||
\(249\) | −3.47053e8 | −1.42462 | ||||||||
\(250\) | −8.71681e7 | −0.352832 | ||||||||
\(251\) | 2.42360e8 | 0.967393 | 0.483696 | − | 0.875236i | \(-0.339294\pi\) | ||||
0.483696 | + | 0.875236i | \(0.339294\pi\) | |||||||
\(252\) | 6.16166e7 | 0.242547 | ||||||||
\(253\) | 8.74482e8 | 3.39492 | ||||||||
\(254\) | 2.84036e7 | 0.108756 | ||||||||
\(255\) | 2.34875e8 | 0.887046 | ||||||||
\(256\) | −9.86440e7 | −0.367477 | ||||||||
\(257\) | −1.66761e8 | −0.612816 | −0.306408 | − | 0.951900i | \(-0.599127\pi\) | ||||
−0.306408 | + | 0.951900i | \(0.599127\pi\) | |||||||
\(258\) | 2.02516e8 | 0.734160 | ||||||||
\(259\) | 1.69578e8 | 0.606487 | ||||||||
\(260\) | 7.22977e7 | 0.255104 | ||||||||
\(261\) | −1.74091e8 | −0.606087 | ||||||||
\(262\) | −5.20240e6 | −0.0178710 | ||||||||
\(263\) | −3.88876e8 | −1.31815 | −0.659077 | − | 0.752076i | \(-0.729053\pi\) | ||||
−0.659077 | + | 0.752076i | \(0.729053\pi\) | |||||||
\(264\) | −5.95051e8 | −1.99040 | ||||||||
\(265\) | 9.96952e7 | 0.329089 | ||||||||
\(266\) | −1.14208e7 | −0.0372059 | ||||||||
\(267\) | −7.62529e8 | −2.45170 | ||||||||
\(268\) | 7.43857e7 | 0.236057 | ||||||||
\(269\) | −7.59623e7 | −0.237939 | −0.118969 | − | 0.992898i | \(-0.537959\pi\) | ||||
−0.118969 | + | 0.992898i | \(0.537959\pi\) | |||||||
\(270\) | −4.46574e7 | −0.138077 | ||||||||
\(271\) | 4.51789e8 | 1.37893 | 0.689466 | − | 0.724318i | \(-0.257845\pi\) | ||||
0.689466 | + | 0.724318i | \(0.257845\pi\) | |||||||
\(272\) | 9.50642e7 | 0.286435 | ||||||||
\(273\) | 4.70846e7 | 0.140059 | ||||||||
\(274\) | −1.92012e8 | −0.563898 | ||||||||
\(275\) | 1.76160e8 | 0.510789 | ||||||||
\(276\) | −6.75113e8 | −1.93283 | ||||||||
\(277\) | −1.85269e8 | −0.523750 | −0.261875 | − | 0.965102i | \(-0.584341\pi\) | ||||
−0.261875 | + | 0.965102i | \(0.584341\pi\) | |||||||
\(278\) | 1.32419e7 | 0.0369652 | ||||||||
\(279\) | 4.13604e8 | 1.14017 | ||||||||
\(280\) | 1.21337e8 | 0.330323 | ||||||||
\(281\) | −1.75327e8 | −0.471385 | −0.235693 | − | 0.971828i | \(-0.575736\pi\) | ||||
−0.235693 | + | 0.971828i | \(0.575736\pi\) | |||||||
\(282\) | 1.18027e8 | 0.313408 | ||||||||
\(283\) | 5.10613e8 | 1.33918 | 0.669591 | − | 0.742730i | \(-0.266469\pi\) | ||||
0.669591 | + | 0.742730i | \(0.266469\pi\) | |||||||
\(284\) | 5.03530e8 | 1.30440 | ||||||||
\(285\) | 1.35344e8 | 0.346323 | ||||||||
\(286\) | −8.99443e7 | −0.227349 | ||||||||
\(287\) | 1.77579e8 | 0.443411 | ||||||||
\(288\) | 3.13213e8 | 0.772621 | ||||||||
\(289\) | −2.67502e8 | −0.651905 | ||||||||
\(290\) | −1.54187e8 | −0.371241 | ||||||||
\(291\) | −3.22067e8 | −0.766162 | ||||||||
\(292\) | −3.34409e7 | −0.0786028 | ||||||||
\(293\) | 6.87785e8 | 1.59741 | 0.798704 | − | 0.601724i | \(-0.205519\pi\) | ||||
0.798704 | + | 0.601724i | \(0.205519\pi\) | |||||||
\(294\) | 3.55406e7 | 0.0815659 | ||||||||
\(295\) | 8.69639e8 | 1.97225 | ||||||||
\(296\) | 5.56049e8 | 1.24621 | ||||||||
\(297\) | −2.48665e8 | −0.550765 | ||||||||
\(298\) | 2.57911e8 | 0.564563 | ||||||||
\(299\) | −2.26891e8 | −0.490873 | ||||||||
\(300\) | −1.35998e8 | −0.290809 | ||||||||
\(301\) | −2.29942e8 | −0.485999 | ||||||||
\(302\) | −1.56201e8 | −0.326332 | ||||||||
\(303\) | 3.54215e8 | 0.731506 | ||||||||
\(304\) | 5.47796e7 | 0.111831 | ||||||||
\(305\) | 1.57456e7 | 0.0317768 | ||||||||
\(306\) | 9.92137e7 | 0.197946 | ||||||||
\(307\) | −8.22599e8 | −1.62257 | −0.811286 | − | 0.584650i | \(-0.801232\pi\) | ||||
−0.811286 | + | 0.584650i | \(0.801232\pi\) | |||||||
\(308\) | 3.03872e8 | 0.592601 | ||||||||
\(309\) | −5.09301e8 | −0.982018 | ||||||||
\(310\) | 3.66317e8 | 0.698378 | ||||||||
\(311\) | −3.26737e8 | −0.615939 | −0.307969 | − | 0.951396i | \(-0.599649\pi\) | ||||
−0.307969 | + | 0.951396i | \(0.599649\pi\) | |||||||
\(312\) | 1.54391e8 | 0.287793 | ||||||||
\(313\) | −3.79034e8 | −0.698672 | −0.349336 | − | 0.936998i | \(-0.613593\pi\) | ||||
−0.349336 | + | 0.936998i | \(0.613593\pi\) | |||||||
\(314\) | 4.72087e7 | 0.0860534 | ||||||||
\(315\) | −1.85236e8 | −0.333918 | ||||||||
\(316\) | −4.13498e7 | −0.0737171 | ||||||||
\(317\) | −1.32838e8 | −0.234214 | −0.117107 | − | 0.993119i | \(-0.537362\pi\) | ||||
−0.117107 | + | 0.993119i | \(0.537362\pi\) | |||||||
\(318\) | 9.57522e7 | 0.166976 | ||||||||
\(319\) | −8.58557e8 | −1.48082 | ||||||||
\(320\) | −4.28311e7 | −0.0730692 | ||||||||
\(321\) | −1.08922e9 | −1.83801 | ||||||||
\(322\) | −1.71263e8 | −0.285869 | ||||||||
\(323\) | 8.23081e7 | 0.135904 | ||||||||
\(324\) | 5.84846e8 | 0.955288 | ||||||||
\(325\) | −4.57060e7 | −0.0738553 | ||||||||
\(326\) | 9.24866e7 | 0.147849 | ||||||||
\(327\) | 2.45923e8 | 0.388939 | ||||||||
\(328\) | 5.82284e8 | 0.911122 | ||||||||
\(329\) | −1.34011e8 | −0.207470 | ||||||||
\(330\) | 8.04563e8 | 1.23243 | ||||||||
\(331\) | 2.57230e8 | 0.389873 | 0.194937 | − | 0.980816i | \(-0.437550\pi\) | ||||
0.194937 | + | 0.980816i | \(0.437550\pi\) | |||||||
\(332\) | 5.81131e8 | 0.871546 | ||||||||
\(333\) | −8.48882e8 | −1.25977 | ||||||||
\(334\) | 3.21247e8 | 0.471765 | ||||||||
\(335\) | −2.23624e8 | −0.324983 | ||||||||
\(336\) | −1.70469e8 | −0.245165 | ||||||||
\(337\) | 3.24693e8 | 0.462135 | 0.231067 | − | 0.972938i | \(-0.425778\pi\) | ||||
0.231067 | + | 0.972938i | \(0.425778\pi\) | |||||||
\(338\) | 2.33368e7 | 0.0328725 | ||||||||
\(339\) | −1.63652e9 | −2.28151 | ||||||||
\(340\) | −3.93292e8 | −0.542673 | ||||||||
\(341\) | 2.03975e9 | 2.78571 | ||||||||
\(342\) | 5.71708e7 | 0.0772828 | ||||||||
\(343\) | −4.03536e7 | −0.0539949 | ||||||||
\(344\) | −7.53980e8 | −0.998632 | ||||||||
\(345\) | 2.02957e9 | 2.66096 | ||||||||
\(346\) | 3.91672e8 | 0.508342 | ||||||||
\(347\) | −3.43601e8 | −0.441470 | −0.220735 | − | 0.975334i | \(-0.570846\pi\) | ||||
−0.220735 | + | 0.975334i | \(0.570846\pi\) | |||||||
\(348\) | 6.62818e8 | 0.843076 | ||||||||
\(349\) | −1.00954e9 | −1.27127 | −0.635633 | − | 0.771991i | \(-0.719261\pi\) | ||||
−0.635633 | + | 0.771991i | \(0.719261\pi\) | |||||||
\(350\) | −3.44999e7 | −0.0430111 | ||||||||
\(351\) | 6.45181e7 | 0.0796355 | ||||||||
\(352\) | 1.54466e9 | 1.88770 | ||||||||
\(353\) | 9.78169e7 | 0.118359 | 0.0591796 | − | 0.998247i | \(-0.481152\pi\) | ||||
0.0591796 | + | 0.998247i | \(0.481152\pi\) | |||||||
\(354\) | 8.35244e8 | 1.00070 | ||||||||
\(355\) | −1.51375e9 | −1.79579 | ||||||||
\(356\) | 1.27683e9 | 1.49989 | ||||||||
\(357\) | −2.56135e8 | −0.297941 | ||||||||
\(358\) | −3.36160e8 | −0.387218 | ||||||||
\(359\) | 1.47626e9 | 1.68396 | 0.841978 | − | 0.539511i | \(-0.181391\pi\) | ||||
0.841978 | + | 0.539511i | \(0.181391\pi\) | |||||||
\(360\) | −6.07391e8 | −0.686135 | ||||||||
\(361\) | −8.46443e8 | −0.946940 | ||||||||
\(362\) | −5.24280e8 | −0.580876 | ||||||||
\(363\) | 3.26243e9 | 3.57987 | ||||||||
\(364\) | −7.88419e7 | −0.0856845 | ||||||||
\(365\) | 1.00532e8 | 0.108213 | ||||||||
\(366\) | 1.51229e7 | 0.0161232 | ||||||||
\(367\) | −1.45180e8 | −0.153312 | −0.0766559 | − | 0.997058i | \(-0.524424\pi\) | ||||
−0.0766559 | + | 0.997058i | \(0.524424\pi\) | |||||||
\(368\) | 8.21457e8 | 0.859246 | ||||||||
\(369\) | −8.88934e8 | −0.921037 | ||||||||
\(370\) | −7.51829e8 | −0.771637 | ||||||||
\(371\) | −1.08719e8 | −0.110535 | ||||||||
\(372\) | −1.57472e9 | −1.58600 | ||||||||
\(373\) | −1.71209e7 | −0.0170823 | −0.00854114 | − | 0.999964i | \(-0.502719\pi\) | ||||
−0.00854114 | + | 0.999964i | \(0.502719\pi\) | |||||||
\(374\) | 4.89287e8 | 0.483630 | ||||||||
\(375\) | −1.12650e9 | −1.10312 | ||||||||
\(376\) | −4.39423e8 | −0.426310 | ||||||||
\(377\) | 2.22759e8 | 0.214112 | ||||||||
\(378\) | 4.86997e7 | 0.0463773 | ||||||||
\(379\) | 3.62265e8 | 0.341814 | 0.170907 | − | 0.985287i | \(-0.445330\pi\) | ||||
0.170907 | + | 0.985287i | \(0.445330\pi\) | |||||||
\(380\) | −2.26630e8 | −0.211872 | ||||||||
\(381\) | 3.67069e8 | 0.340024 | ||||||||
\(382\) | 3.24497e8 | 0.297844 | ||||||||
\(383\) | 3.36403e8 | 0.305960 | 0.152980 | − | 0.988229i | \(-0.451113\pi\) | ||||
0.152980 | + | 0.988229i | \(0.451113\pi\) | |||||||
\(384\) | −1.50007e9 | −1.35192 | ||||||||
\(385\) | −9.13521e8 | −0.815841 | ||||||||
\(386\) | 4.04623e8 | 0.358093 | ||||||||
\(387\) | 1.15105e9 | 1.00950 | ||||||||
\(388\) | 5.39293e8 | 0.468720 | ||||||||
\(389\) | −7.45679e7 | −0.0642286 | −0.0321143 | − | 0.999484i | \(-0.510224\pi\) | ||||
−0.0321143 | + | 0.999484i | \(0.510224\pi\) | |||||||
\(390\) | −2.08750e8 | −0.178197 | ||||||||
\(391\) | 1.23426e9 | 1.04421 | ||||||||
\(392\) | −1.32320e8 | −0.110949 | ||||||||
\(393\) | −6.72323e7 | −0.0558733 | ||||||||
\(394\) | −4.69455e8 | −0.386685 | ||||||||
\(395\) | 1.24309e8 | 0.101487 | ||||||||
\(396\) | −1.52113e9 | −1.23093 | ||||||||
\(397\) | 1.66485e9 | 1.33539 | 0.667696 | − | 0.744434i | \(-0.267281\pi\) | ||||
0.667696 | + | 0.744434i | \(0.267281\pi\) | |||||||
\(398\) | 1.11023e8 | 0.0882722 | ||||||||
\(399\) | −1.47595e8 | −0.116323 | ||||||||
\(400\) | 1.65478e8 | 0.129280 | ||||||||
\(401\) | 9.52020e8 | 0.737294 | 0.368647 | − | 0.929569i | \(-0.379821\pi\) | ||||
0.368647 | + | 0.929569i | \(0.379821\pi\) | |||||||
\(402\) | −2.14779e8 | −0.164893 | ||||||||
\(403\) | −5.29230e8 | −0.402788 | ||||||||
\(404\) | −5.93124e8 | −0.447518 | ||||||||
\(405\) | −1.75821e9 | −1.31516 | ||||||||
\(406\) | 1.68144e8 | 0.124692 | ||||||||
\(407\) | −4.18639e9 | −3.07793 | ||||||||
\(408\) | −8.39869e8 | −0.612211 | ||||||||
\(409\) | −1.66648e9 | −1.20439 | −0.602197 | − | 0.798348i | \(-0.705708\pi\) | ||||
−0.602197 | + | 0.798348i | \(0.705708\pi\) | |||||||
\(410\) | −7.87301e8 | −0.564154 | ||||||||
\(411\) | −2.48143e9 | −1.76301 | ||||||||
\(412\) | 8.52810e8 | 0.600775 | ||||||||
\(413\) | −9.48357e8 | −0.662440 | ||||||||
\(414\) | 8.57314e8 | 0.593798 | ||||||||
\(415\) | −1.74704e9 | −1.19987 | ||||||||
\(416\) | −4.00774e8 | −0.272943 | ||||||||
\(417\) | 1.71129e8 | 0.115571 | ||||||||
\(418\) | 2.81946e8 | 0.188821 | ||||||||
\(419\) | 7.54096e8 | 0.500815 | 0.250408 | − | 0.968141i | \(-0.419435\pi\) | ||||
0.250408 | + | 0.968141i | \(0.419435\pi\) | |||||||
\(420\) | 7.05251e8 | 0.464484 | ||||||||
\(421\) | 9.66522e8 | 0.631284 | 0.315642 | − | 0.948878i | \(-0.397780\pi\) | ||||
0.315642 | + | 0.948878i | \(0.397780\pi\) | |||||||
\(422\) | 3.80031e7 | 0.0246165 | ||||||||
\(423\) | 6.70837e8 | 0.430949 | ||||||||
\(424\) | −3.56492e8 | −0.227127 | ||||||||
\(425\) | 2.48636e8 | 0.157109 | ||||||||
\(426\) | −1.45388e9 | −0.911160 | ||||||||
\(427\) | −1.71709e7 | −0.0106732 | ||||||||
\(428\) | 1.82387e9 | 1.12445 | ||||||||
\(429\) | −1.16238e9 | −0.710800 | ||||||||
\(430\) | 1.01945e9 | 0.618339 | ||||||||
\(431\) | 1.15524e9 | 0.695025 | 0.347512 | − | 0.937675i | \(-0.387026\pi\) | ||||
0.347512 | + | 0.937675i | \(0.387026\pi\) | |||||||
\(432\) | −2.33587e8 | −0.139398 | ||||||||
\(433\) | −1.01905e9 | −0.603237 | −0.301619 | − | 0.953429i | \(-0.597527\pi\) | ||||
−0.301619 | + | 0.953429i | \(0.597527\pi\) | |||||||
\(434\) | −3.99475e8 | −0.234572 | ||||||||
\(435\) | −1.99261e9 | −1.16067 | ||||||||
\(436\) | −4.11791e8 | −0.237944 | ||||||||
\(437\) | 7.11231e8 | 0.407686 | ||||||||
\(438\) | 9.65563e7 | 0.0549062 | ||||||||
\(439\) | 2.05507e9 | 1.15931 | 0.579655 | − | 0.814862i | \(-0.303187\pi\) | ||||
0.579655 | + | 0.814862i | \(0.303187\pi\) | |||||||
\(440\) | −2.99544e9 | −1.67639 | ||||||||
\(441\) | 2.02004e8 | 0.112156 | ||||||||
\(442\) | −1.26950e8 | −0.0699283 | ||||||||
\(443\) | 1.38350e9 | 0.756079 | 0.378040 | − | 0.925789i | \(-0.376598\pi\) | ||||
0.378040 | + | 0.925789i | \(0.376598\pi\) | |||||||
\(444\) | 3.23195e9 | 1.75236 | ||||||||
\(445\) | −3.83851e9 | −2.06492 | ||||||||
\(446\) | 8.16539e8 | 0.435818 | ||||||||
\(447\) | 3.33306e9 | 1.76509 | ||||||||
\(448\) | 4.67081e7 | 0.0245425 | ||||||||
\(449\) | 1.79991e9 | 0.938404 | 0.469202 | − | 0.883091i | \(-0.344542\pi\) | ||||
0.469202 | + | 0.883091i | \(0.344542\pi\) | |||||||
\(450\) | 1.72701e8 | 0.0893411 | ||||||||
\(451\) | −4.38391e9 | −2.25032 | ||||||||
\(452\) | 2.74031e9 | 1.39578 | ||||||||
\(453\) | −2.01864e9 | −1.02027 | ||||||||
\(454\) | −2.23145e7 | −0.0111916 | ||||||||
\(455\) | 2.37020e8 | 0.117963 | ||||||||
\(456\) | −4.83965e8 | −0.239021 | ||||||||
\(457\) | 1.35945e9 | 0.666279 | 0.333139 | − | 0.942878i | \(-0.391892\pi\) | ||||
0.333139 | + | 0.942878i | \(0.391892\pi\) | |||||||
\(458\) | −1.50196e9 | −0.730513 | ||||||||
\(459\) | −3.50971e8 | −0.169405 | ||||||||
\(460\) | −3.39846e9 | −1.62791 | ||||||||
\(461\) | 9.44068e8 | 0.448797 | 0.224399 | − | 0.974497i | \(-0.427958\pi\) | ||||
0.224399 | + | 0.974497i | \(0.427958\pi\) | |||||||
\(462\) | −8.77390e8 | −0.413948 | ||||||||
\(463\) | −2.11591e8 | −0.0990751 | −0.0495375 | − | 0.998772i | \(-0.515775\pi\) | ||||
−0.0495375 | + | 0.998772i | \(0.515775\pi\) | |||||||
\(464\) | −8.06497e8 | −0.374792 | ||||||||
\(465\) | 4.73403e9 | 2.18346 | ||||||||
\(466\) | 4.47369e8 | 0.204793 | ||||||||
\(467\) | −1.11706e9 | −0.507535 | −0.253768 | − | 0.967265i | \(-0.581670\pi\) | ||||
−0.253768 | + | 0.967265i | \(0.581670\pi\) | |||||||
\(468\) | 3.94670e8 | 0.177981 | ||||||||
\(469\) | 2.43866e8 | 0.109155 | ||||||||
\(470\) | 5.94140e8 | 0.263965 | ||||||||
\(471\) | 6.10093e8 | 0.269044 | ||||||||
\(472\) | −3.10967e9 | −1.36118 | ||||||||
\(473\) | 5.67658e9 | 2.46645 | ||||||||
\(474\) | 1.19392e8 | 0.0514934 | ||||||||
\(475\) | 1.43273e8 | 0.0613392 | ||||||||
\(476\) | 4.28891e8 | 0.182273 | ||||||||
\(477\) | 5.44231e8 | 0.229599 | ||||||||
\(478\) | 1.15770e9 | 0.484842 | ||||||||
\(479\) | −2.45192e9 | −1.01937 | −0.509684 | − | 0.860361i | \(-0.670238\pi\) | ||||
−0.509684 | + | 0.860361i | \(0.670238\pi\) | |||||||
\(480\) | 3.58497e9 | 1.47959 | ||||||||
\(481\) | 1.08619e9 | 0.445040 | ||||||||
\(482\) | 8.52048e8 | 0.346577 | ||||||||
\(483\) | −2.21328e9 | −0.893763 | ||||||||
\(484\) | −5.46285e9 | −2.19008 | ||||||||
\(485\) | −1.62126e9 | −0.645292 | ||||||||
\(486\) | −1.37815e9 | −0.544592 | ||||||||
\(487\) | −3.55244e9 | −1.39372 | −0.696860 | − | 0.717207i | \(-0.745420\pi\) | ||||
−0.696860 | + | 0.717207i | \(0.745420\pi\) | |||||||
\(488\) | −5.63034e7 | −0.0219313 | ||||||||
\(489\) | 1.19523e9 | 0.462245 | ||||||||
\(490\) | 1.78908e8 | 0.0686980 | ||||||||
\(491\) | −8.10999e8 | −0.309197 | −0.154598 | − | 0.987977i | \(-0.549408\pi\) | ||||
−0.154598 | + | 0.987977i | \(0.549408\pi\) | |||||||
\(492\) | 3.38444e9 | 1.28118 | ||||||||
\(493\) | −1.21179e9 | −0.455472 | ||||||||
\(494\) | −7.31532e7 | −0.0273017 | ||||||||
\(495\) | 4.57293e9 | 1.69464 | ||||||||
\(496\) | 1.91607e9 | 0.705058 | ||||||||
\(497\) | 1.65077e9 | 0.603169 | ||||||||
\(498\) | −1.67794e9 | −0.608799 | ||||||||
\(499\) | −3.77182e9 | −1.35894 | −0.679468 | − | 0.733705i | \(-0.737789\pi\) | ||||
−0.679468 | + | 0.733705i | \(0.737789\pi\) | |||||||
\(500\) | 1.88630e9 | 0.674861 | ||||||||
\(501\) | 4.15157e9 | 1.47496 | ||||||||
\(502\) | 1.17177e9 | 0.413408 | ||||||||
\(503\) | −4.69213e9 | −1.64393 | −0.821963 | − | 0.569541i | \(-0.807121\pi\) | ||||
−0.821963 | + | 0.569541i | \(0.807121\pi\) | |||||||
\(504\) | 6.62371e8 | 0.230459 | ||||||||
\(505\) | 1.78309e9 | 0.616104 | ||||||||
\(506\) | 4.22797e9 | 1.45079 | ||||||||
\(507\) | 3.01589e8 | 0.102775 | ||||||||
\(508\) | −6.14646e8 | −0.208019 | ||||||||
\(509\) | 2.19417e9 | 0.737494 | 0.368747 | − | 0.929530i | \(-0.379787\pi\) | ||||
0.368747 | + | 0.929530i | \(0.379787\pi\) | |||||||
\(510\) | 1.13558e9 | 0.379072 | ||||||||
\(511\) | −1.09632e8 | −0.0363468 | ||||||||
\(512\) | 2.59609e9 | 0.854822 | ||||||||
\(513\) | −2.02243e8 | −0.0661398 | ||||||||
\(514\) | −8.06263e8 | −0.261882 | ||||||||
\(515\) | −2.56378e9 | −0.827095 | ||||||||
\(516\) | −4.38240e9 | −1.40423 | ||||||||
\(517\) | 3.30833e9 | 1.05291 | ||||||||
\(518\) | 8.19883e8 | 0.259178 | ||||||||
\(519\) | 5.06170e9 | 1.58932 | ||||||||
\(520\) | 7.77191e8 | 0.242391 | ||||||||
\(521\) | −2.61146e9 | −0.809005 | −0.404503 | − | 0.914537i | \(-0.632555\pi\) | ||||
−0.404503 | + | 0.914537i | \(0.632555\pi\) | |||||||
\(522\) | −8.41701e8 | −0.259007 | ||||||||
\(523\) | −2.69127e9 | −0.822625 | −0.411312 | − | 0.911495i | \(-0.634929\pi\) | ||||
−0.411312 | + | 0.911495i | \(0.634929\pi\) | |||||||
\(524\) | 1.12579e8 | 0.0341819 | ||||||||
\(525\) | −4.45854e8 | −0.134473 | ||||||||
\(526\) | −1.88015e9 | −0.563303 | ||||||||
\(527\) | 2.87895e9 | 0.856835 | ||||||||
\(528\) | 4.20837e9 | 1.24422 | ||||||||
\(529\) | 7.26055e9 | 2.13243 | ||||||||
\(530\) | 4.82009e8 | 0.140634 | ||||||||
\(531\) | 4.74732e9 | 1.37600 | ||||||||
\(532\) | 2.47144e8 | 0.0711638 | ||||||||
\(533\) | 1.13744e9 | 0.325374 | ||||||||
\(534\) | −3.68670e9 | −1.04771 | ||||||||
\(535\) | −5.48306e9 | −1.54805 | ||||||||
\(536\) | 7.99637e8 | 0.224293 | ||||||||
\(537\) | −4.34430e9 | −1.21063 | ||||||||
\(538\) | −3.67265e8 | −0.101681 | ||||||||
\(539\) | 9.96210e8 | 0.274025 | ||||||||
\(540\) | 9.66376e8 | 0.264100 | ||||||||
\(541\) | −4.26647e9 | −1.15845 | −0.579227 | − | 0.815166i | \(-0.696645\pi\) | ||||
−0.579227 | + | 0.815166i | \(0.696645\pi\) | |||||||
\(542\) | 2.18432e9 | 0.589276 | ||||||||
\(543\) | −6.77544e9 | −1.81609 | ||||||||
\(544\) | 2.18017e9 | 0.580622 | ||||||||
\(545\) | 1.23796e9 | 0.327580 | ||||||||
\(546\) | 2.27646e8 | 0.0598530 | ||||||||
\(547\) | 5.32779e9 | 1.39185 | 0.695923 | − | 0.718116i | \(-0.254995\pi\) | ||||
0.695923 | + | 0.718116i | \(0.254995\pi\) | |||||||
\(548\) | 4.15508e9 | 1.07857 | ||||||||
\(549\) | 8.59545e7 | 0.0221700 | ||||||||
\(550\) | 8.51701e8 | 0.218282 | ||||||||
\(551\) | −6.98278e8 | −0.177827 | ||||||||
\(552\) | −7.25737e9 | −1.83651 | ||||||||
\(553\) | −1.35561e8 | −0.0340876 | ||||||||
\(554\) | −8.95744e8 | −0.223820 | ||||||||
\(555\) | −9.71612e9 | −2.41250 | ||||||||
\(556\) | −2.86551e8 | −0.0707035 | ||||||||
\(557\) | 3.19673e9 | 0.783812 | 0.391906 | − | 0.920005i | \(-0.371816\pi\) | ||||
0.391906 | + | 0.920005i | \(0.371816\pi\) | |||||||
\(558\) | 1.99970e9 | 0.487244 | ||||||||
\(559\) | −1.47283e9 | −0.356626 | ||||||||
\(560\) | −8.58128e8 | −0.206488 | ||||||||
\(561\) | 6.32321e9 | 1.51206 | ||||||||
\(562\) | −8.47674e8 | −0.201443 | ||||||||
\(563\) | 2.46611e9 | 0.582417 | 0.291208 | − | 0.956660i | \(-0.405943\pi\) | ||||
0.291208 | + | 0.956660i | \(0.405943\pi\) | |||||||
\(564\) | −2.55408e9 | −0.599457 | ||||||||
\(565\) | −8.23813e9 | −1.92158 | ||||||||
\(566\) | 2.46873e9 | 0.572289 | ||||||||
\(567\) | 1.91736e9 | 0.441735 | ||||||||
\(568\) | 5.41288e9 | 1.23939 | ||||||||
\(569\) | −7.64209e9 | −1.73908 | −0.869539 | − | 0.493864i | \(-0.835584\pi\) | ||||
−0.869539 | + | 0.493864i | \(0.835584\pi\) | |||||||
\(570\) | 6.54365e8 | 0.147999 | ||||||||
\(571\) | −2.39383e9 | −0.538104 | −0.269052 | − | 0.963126i | \(-0.586710\pi\) | ||||
−0.269052 | + | 0.963126i | \(0.586710\pi\) | |||||||
\(572\) | 1.94637e9 | 0.434850 | ||||||||
\(573\) | 4.19358e9 | 0.931201 | ||||||||
\(574\) | 8.58566e8 | 0.189488 | ||||||||
\(575\) | 2.14848e9 | 0.471296 | ||||||||
\(576\) | −2.33813e8 | −0.0509788 | ||||||||
\(577\) | 4.29479e9 | 0.930736 | 0.465368 | − | 0.885117i | \(-0.345922\pi\) | ||||
0.465368 | + | 0.885117i | \(0.345922\pi\) | |||||||
\(578\) | −1.29333e9 | −0.278587 | ||||||||
\(579\) | 5.22908e9 | 1.11957 | ||||||||
\(580\) | 3.33657e9 | 0.710073 | ||||||||
\(581\) | 1.90517e9 | 0.403012 | ||||||||
\(582\) | −1.55714e9 | −0.327414 | ||||||||
\(583\) | 2.68396e9 | 0.560965 | ||||||||
\(584\) | −3.59485e8 | −0.0746854 | ||||||||
\(585\) | −1.18648e9 | −0.245029 | ||||||||
\(586\) | 3.32532e9 | 0.682640 | ||||||||
\(587\) | −4.21222e9 | −0.859563 | −0.429782 | − | 0.902933i | \(-0.641409\pi\) | ||||
−0.429782 | + | 0.902933i | \(0.641409\pi\) | |||||||
\(588\) | −7.69089e8 | −0.156011 | ||||||||
\(589\) | 1.65896e9 | 0.334529 | ||||||||
\(590\) | 4.20455e9 | 0.842826 | ||||||||
\(591\) | −6.06692e9 | −1.20896 | ||||||||
\(592\) | −3.93254e9 | −0.779018 | ||||||||
\(593\) | −1.53014e9 | −0.301328 | −0.150664 | − | 0.988585i | \(-0.548141\pi\) | ||||
−0.150664 | + | 0.988585i | \(0.548141\pi\) | |||||||
\(594\) | −1.20225e9 | −0.235365 | ||||||||
\(595\) | −1.28936e9 | −0.250938 | ||||||||
\(596\) | −5.58113e9 | −1.07984 | ||||||||
\(597\) | 1.43479e9 | 0.275981 | ||||||||
\(598\) | −1.09698e9 | −0.209771 | ||||||||
\(599\) | −5.16267e9 | −0.981478 | −0.490739 | − | 0.871307i | \(-0.663273\pi\) | ||||
−0.490739 | + | 0.871307i | \(0.663273\pi\) | |||||||
\(600\) | −1.46196e9 | −0.276316 | ||||||||
\(601\) | −1.95738e9 | −0.367803 | −0.183901 | − | 0.982945i | \(-0.558873\pi\) | ||||
−0.183901 | + | 0.982945i | \(0.558873\pi\) | |||||||
\(602\) | −1.11173e9 | −0.207688 | ||||||||
\(603\) | −1.22075e9 | −0.226734 | ||||||||
\(604\) | 3.38016e9 | 0.624176 | ||||||||
\(605\) | 1.64228e10 | 3.01511 | ||||||||
\(606\) | 1.71257e9 | 0.312604 | ||||||||
\(607\) | 4.00519e9 | 0.726880 | 0.363440 | − | 0.931618i | \(-0.381602\pi\) | ||||
0.363440 | + | 0.931618i | \(0.381602\pi\) | |||||||
\(608\) | 1.25630e9 | 0.226688 | ||||||||
\(609\) | 2.17298e9 | 0.389847 | ||||||||
\(610\) | 7.61273e7 | 0.0135796 | ||||||||
\(611\) | −8.58374e8 | −0.152241 | ||||||||
\(612\) | −2.14696e9 | −0.378612 | ||||||||
\(613\) | 2.44078e9 | 0.427974 | 0.213987 | − | 0.976837i | \(-0.431355\pi\) | ||||
0.213987 | + | 0.976837i | \(0.431355\pi\) | |||||||
\(614\) | −3.97712e9 | −0.693394 | ||||||||
\(615\) | −1.01745e10 | −1.76381 | ||||||||
\(616\) | 3.26658e9 | 0.563068 | ||||||||
\(617\) | 7.35176e9 | 1.26007 | 0.630033 | − | 0.776569i | \(-0.283042\pi\) | ||||
0.630033 | + | 0.776569i | \(0.283042\pi\) | |||||||
\(618\) | −2.46238e9 | −0.419658 | ||||||||
\(619\) | −4.08633e9 | −0.692495 | −0.346248 | − | 0.938143i | \(-0.612544\pi\) | ||||
−0.346248 | + | 0.938143i | \(0.612544\pi\) | |||||||
\(620\) | −7.92700e9 | −1.33579 | ||||||||
\(621\) | −3.03277e9 | −0.508182 | ||||||||
\(622\) | −1.57972e9 | −0.263217 | ||||||||
\(623\) | 4.18596e9 | 0.693565 | ||||||||
\(624\) | −1.09190e9 | −0.179902 | ||||||||
\(625\) | −7.29602e9 | −1.19538 | ||||||||
\(626\) | −1.83257e9 | −0.298572 | ||||||||
\(627\) | 3.64368e9 | 0.590342 | ||||||||
\(628\) | −1.02158e9 | −0.164595 | ||||||||
\(629\) | −5.90876e9 | −0.946715 | ||||||||
\(630\) | −8.95586e8 | −0.142697 | ||||||||
\(631\) | 2.99656e9 | 0.474811 | 0.237406 | − | 0.971411i | \(-0.423703\pi\) | ||||
0.237406 | + | 0.971411i | \(0.423703\pi\) | |||||||
\(632\) | −4.44504e8 | −0.0700432 | ||||||||
\(633\) | 4.91126e8 | 0.0769627 | ||||||||
\(634\) | −6.42247e8 | −0.100090 | ||||||||
\(635\) | 1.84779e9 | 0.286382 | ||||||||
\(636\) | −2.07205e9 | −0.319375 | ||||||||
\(637\) | −2.58475e8 | −0.0396214 | ||||||||
\(638\) | −4.15097e9 | −0.632816 | ||||||||
\(639\) | −8.26348e9 | −1.25288 | ||||||||
\(640\) | −7.55122e9 | −1.13864 | ||||||||
\(641\) | 3.86937e9 | 0.580279 | 0.290140 | − | 0.956984i | \(-0.406298\pi\) | ||||
0.290140 | + | 0.956984i | \(0.406298\pi\) | |||||||
\(642\) | −5.26620e9 | −0.785461 | ||||||||
\(643\) | −6.05858e9 | −0.898736 | −0.449368 | − | 0.893347i | \(-0.648351\pi\) | ||||
−0.449368 | + | 0.893347i | \(0.648351\pi\) | |||||||
\(644\) | 3.70609e9 | 0.546783 | ||||||||
\(645\) | 1.31747e10 | 1.93322 | ||||||||
\(646\) | 3.97945e8 | 0.0580777 | ||||||||
\(647\) | −1.17641e10 | −1.70763 | −0.853817 | − | 0.520573i | \(-0.825718\pi\) | ||||
−0.853817 | + | 0.520573i | \(0.825718\pi\) | |||||||
\(648\) | 6.28702e9 | 0.907679 | ||||||||
\(649\) | 2.34121e10 | 3.36189 | ||||||||
\(650\) | −2.20981e8 | −0.0315615 | ||||||||
\(651\) | −5.16254e9 | −0.733381 | ||||||||
\(652\) | −2.00139e9 | −0.282790 | ||||||||
\(653\) | −1.25932e9 | −0.176987 | −0.0884934 | − | 0.996077i | \(-0.528205\pi\) | ||||
−0.0884934 | + | 0.996077i | \(0.528205\pi\) | |||||||
\(654\) | 1.18899e9 | 0.166210 | ||||||||
\(655\) | −3.38442e8 | −0.0470587 | ||||||||
\(656\) | −4.11808e9 | −0.569550 | ||||||||
\(657\) | 5.48802e8 | 0.0754982 | ||||||||
\(658\) | −6.47920e8 | −0.0886607 | ||||||||
\(659\) | 9.16362e9 | 1.24729 | 0.623646 | − | 0.781707i | \(-0.285651\pi\) | ||||
0.623646 | + | 0.781707i | \(0.285651\pi\) | |||||||
\(660\) | −1.74105e10 | −2.35727 | ||||||||
\(661\) | 1.30199e10 | 1.75348 | 0.876742 | − | 0.480961i | \(-0.159712\pi\) | ||||
0.876742 | + | 0.480961i | \(0.159712\pi\) | |||||||
\(662\) | 1.24366e9 | 0.166609 | ||||||||
\(663\) | −1.64061e9 | −0.218629 | ||||||||
\(664\) | 6.24708e9 | 0.828111 | ||||||||
\(665\) | −7.42982e8 | −0.0979721 | ||||||||
\(666\) | −4.10420e9 | −0.538355 | ||||||||
\(667\) | −1.04711e10 | −1.36632 | ||||||||
\(668\) | −6.95170e9 | −0.902346 | ||||||||
\(669\) | 1.05524e10 | 1.36257 | ||||||||
\(670\) | −1.08118e9 | −0.138879 | ||||||||
\(671\) | 4.23898e8 | 0.0541667 | ||||||||
\(672\) | −3.90947e9 | −0.496965 | ||||||||
\(673\) | −1.04391e10 | −1.32011 | −0.660053 | − | 0.751219i | \(-0.729466\pi\) | ||||
−0.660053 | + | 0.751219i | \(0.729466\pi\) | |||||||
\(674\) | 1.56984e9 | 0.197490 | ||||||||
\(675\) | −6.10935e8 | −0.0764595 | ||||||||
\(676\) | −5.05002e8 | −0.0628753 | ||||||||
\(677\) | −8.55686e9 | −1.05987 | −0.529937 | − | 0.848037i | \(-0.677784\pi\) | ||||
−0.529937 | + | 0.848037i | \(0.677784\pi\) | |||||||
\(678\) | −7.91230e9 | −0.974987 | ||||||||
\(679\) | 1.76801e9 | 0.216741 | ||||||||
\(680\) | −4.22783e9 | −0.515628 | ||||||||
\(681\) | −2.88378e8 | −0.0349902 | ||||||||
\(682\) | 9.86184e9 | 1.19045 | ||||||||
\(683\) | 1.80307e9 | 0.216540 | 0.108270 | − | 0.994122i | \(-0.465469\pi\) | ||||
0.108270 | + | 0.994122i | \(0.465469\pi\) | |||||||
\(684\) | −1.23716e9 | −0.147819 | ||||||||
\(685\) | −1.24913e10 | −1.48488 | ||||||||
\(686\) | −1.95103e8 | −0.0230743 | ||||||||
\(687\) | −1.94102e10 | −2.28393 | ||||||||
\(688\) | 5.33237e9 | 0.624253 | ||||||||
\(689\) | −6.96375e8 | −0.0811102 | ||||||||
\(690\) | 9.81263e9 | 1.13714 | ||||||||
\(691\) | 1.68072e9 | 0.193786 | 0.0968928 | − | 0.995295i | \(-0.469110\pi\) | ||||
0.0968928 | + | 0.995295i | \(0.469110\pi\) | |||||||
\(692\) | −8.47568e9 | −0.972306 | ||||||||
\(693\) | −4.98686e9 | −0.569195 | ||||||||
\(694\) | −1.66125e9 | −0.188659 | ||||||||
\(695\) | 8.61451e8 | 0.0973384 | ||||||||
\(696\) | 7.12521e9 | 0.801060 | ||||||||
\(697\) | −6.18755e9 | −0.692156 | ||||||||
\(698\) | −4.88097e9 | −0.543266 | ||||||||
\(699\) | 5.78149e9 | 0.640280 | ||||||||
\(700\) | 7.46570e8 | 0.0822673 | ||||||||
\(701\) | −1.60557e10 | −1.76041 | −0.880207 | − | 0.474590i | \(-0.842596\pi\) | ||||
−0.880207 | + | 0.474590i | \(0.842596\pi\) | |||||||
\(702\) | 3.11934e8 | 0.0340316 | ||||||||
\(703\) | −3.40486e9 | −0.369620 | ||||||||
\(704\) | −1.15308e9 | −0.124554 | ||||||||
\(705\) | 7.67826e9 | 0.825279 | ||||||||
\(706\) | 4.72928e8 | 0.0505799 | ||||||||
\(707\) | −1.94449e9 | −0.206937 | ||||||||
\(708\) | −1.80745e10 | −1.91403 | ||||||||
\(709\) | −7.44466e9 | −0.784482 | −0.392241 | − | 0.919862i | \(-0.628300\pi\) | ||||
−0.392241 | + | 0.919862i | \(0.628300\pi\) | |||||||
\(710\) | −7.31871e9 | −0.767416 | ||||||||
\(711\) | 6.78595e8 | 0.0708055 | ||||||||
\(712\) | 1.37258e10 | 1.42514 | ||||||||
\(713\) | 2.48772e10 | 2.57033 | ||||||||
\(714\) | −1.23837e9 | −0.127323 | ||||||||
\(715\) | −5.85133e9 | −0.598664 | ||||||||
\(716\) | 7.27441e9 | 0.740632 | ||||||||
\(717\) | 1.49614e10 | 1.51584 | ||||||||
\(718\) | 7.13744e9 | 0.719626 | ||||||||
\(719\) | 1.47292e10 | 1.47784 | 0.738922 | − | 0.673791i | \(-0.235335\pi\) | ||||
0.738922 | + | 0.673791i | \(0.235335\pi\) | |||||||
\(720\) | 4.29565e9 | 0.428909 | ||||||||
\(721\) | 2.79585e9 | 0.277805 | ||||||||
\(722\) | −4.09240e9 | −0.404667 | ||||||||
\(723\) | 1.10113e10 | 1.08356 | ||||||||
\(724\) | 1.13453e10 | 1.11104 | ||||||||
\(725\) | −2.10935e9 | −0.205573 | ||||||||
\(726\) | 1.57733e10 | 1.52983 | ||||||||
\(727\) | −2.84326e9 | −0.274439 | −0.137219 | − | 0.990541i | \(-0.543817\pi\) | ||||
−0.137219 | + | 0.990541i | \(0.543817\pi\) | |||||||
\(728\) | −8.47541e8 | −0.0814143 | ||||||||
\(729\) | −5.58509e9 | −0.533930 | ||||||||
\(730\) | 4.86057e8 | 0.0462442 | ||||||||
\(731\) | 8.01205e9 | 0.758635 | ||||||||
\(732\) | −3.27255e8 | −0.0308388 | ||||||||
\(733\) | 5.86487e9 | 0.550041 | 0.275020 | − | 0.961438i | \(-0.411315\pi\) | ||||
0.275020 | + | 0.961438i | \(0.411315\pi\) | |||||||
\(734\) | −7.01920e8 | −0.0655166 | ||||||||
\(735\) | 2.31209e9 | 0.214783 | ||||||||
\(736\) | 1.88390e10 | 1.74175 | ||||||||
\(737\) | −6.02031e9 | −0.553966 | ||||||||
\(738\) | −4.29784e9 | −0.393598 | ||||||||
\(739\) | 1.71343e10 | 1.56175 | 0.780873 | − | 0.624690i | \(-0.214775\pi\) | ||||
0.780873 | + | 0.624690i | \(0.214775\pi\) | |||||||
\(740\) | 1.62694e10 | 1.47591 | ||||||||
\(741\) | −9.45382e8 | −0.0853579 | ||||||||
\(742\) | −5.25640e8 | −0.0472361 | ||||||||
\(743\) | 8.14736e9 | 0.728712 | 0.364356 | − | 0.931260i | \(-0.381289\pi\) | ||||
0.364356 | + | 0.931260i | \(0.381289\pi\) | |||||||
\(744\) | −1.69280e10 | −1.50695 | ||||||||
\(745\) | 1.67784e10 | 1.48663 | ||||||||
\(746\) | −8.27766e7 | −0.00729998 | ||||||||
\(747\) | −9.53699e9 | −0.837123 | ||||||||
\(748\) | −1.05881e10 | −0.925040 | ||||||||
\(749\) | 5.97937e9 | 0.519959 | ||||||||
\(750\) | −5.44644e9 | −0.471409 | ||||||||
\(751\) | 1.07000e10 | 0.921815 | 0.460907 | − | 0.887448i | \(-0.347524\pi\) | ||||
0.460907 | + | 0.887448i | \(0.347524\pi\) | |||||||
\(752\) | 3.10773e9 | 0.266490 | ||||||||
\(753\) | 1.51431e10 | 1.29251 | ||||||||
\(754\) | 1.07700e9 | 0.0914992 | ||||||||
\(755\) | −1.01617e10 | −0.859311 | ||||||||
\(756\) | −1.05385e9 | −0.0887059 | ||||||||
\(757\) | −6.06443e9 | −0.508106 | −0.254053 | − | 0.967190i | \(-0.581764\pi\) | ||||
−0.254053 | + | 0.967190i | \(0.581764\pi\) | |||||||
\(758\) | 1.75149e9 | 0.146071 | ||||||||
\(759\) | 5.46394e10 | 4.53586 | ||||||||
\(760\) | −2.43624e9 | −0.201313 | ||||||||
\(761\) | −1.38928e10 | −1.14273 | −0.571364 | − | 0.820697i | \(-0.693586\pi\) | ||||
−0.571364 | + | 0.820697i | \(0.693586\pi\) | |||||||
\(762\) | 1.77471e9 | 0.145307 | ||||||||
\(763\) | −1.35001e9 | −0.110028 | ||||||||
\(764\) | −7.02203e9 | −0.569687 | ||||||||
\(765\) | 6.45435e9 | 0.521239 | ||||||||
\(766\) | 1.62645e9 | 0.130749 | ||||||||
\(767\) | −6.07446e9 | −0.486098 | ||||||||
\(768\) | −6.16347e9 | −0.490977 | ||||||||
\(769\) | 5.83542e9 | 0.462733 | 0.231366 | − | 0.972867i | \(-0.425680\pi\) | ||||
0.231366 | + | 0.972867i | \(0.425680\pi\) | |||||||
\(770\) | −4.41671e9 | −0.348644 | ||||||||
\(771\) | −1.04196e10 | −0.818767 | ||||||||
\(772\) | −8.75595e9 | −0.684924 | ||||||||
\(773\) | −1.21327e10 | −0.944778 | −0.472389 | − | 0.881390i | \(-0.656608\pi\) | ||||
−0.472389 | + | 0.881390i | \(0.656608\pi\) | |||||||
\(774\) | 5.56513e9 | 0.431402 | ||||||||
\(775\) | 5.01138e9 | 0.386724 | ||||||||
\(776\) | 5.79732e9 | 0.445360 | ||||||||
\(777\) | 1.05956e10 | 0.810312 | ||||||||
\(778\) | −3.60523e8 | −0.0274476 | ||||||||
\(779\) | −3.56551e9 | −0.270234 | ||||||||
\(780\) | 4.51731e9 | 0.340838 | ||||||||
\(781\) | −4.07526e10 | −3.06109 | ||||||||
\(782\) | 5.96746e9 | 0.446237 | ||||||||
\(783\) | 2.97754e9 | 0.221662 | ||||||||
\(784\) | 9.35804e8 | 0.0693551 | ||||||||
\(785\) | 3.07116e9 | 0.226599 | ||||||||
\(786\) | −3.25057e8 | −0.0238770 | ||||||||
\(787\) | 6.77656e9 | 0.495562 | 0.247781 | − | 0.968816i | \(-0.420299\pi\) | ||||
0.247781 | + | 0.968816i | \(0.420299\pi\) | |||||||
\(788\) | 1.01589e10 | 0.739613 | ||||||||
\(789\) | −2.42978e10 | −1.76115 | ||||||||
\(790\) | 6.01011e8 | 0.0433698 | ||||||||
\(791\) | 8.98382e9 | 0.645421 | ||||||||
\(792\) | −1.63520e10 | −1.16958 | ||||||||
\(793\) | −1.09984e8 | −0.00783199 | ||||||||
\(794\) | 8.04927e9 | 0.570670 | ||||||||
\(795\) | 6.22916e9 | 0.439688 | ||||||||
\(796\) | −2.40252e9 | −0.168838 | ||||||||
\(797\) | −1.31908e10 | −0.922925 | −0.461462 | − | 0.887160i | \(-0.652675\pi\) | ||||
−0.461462 | + | 0.887160i | \(0.652675\pi\) | |||||||
\(798\) | −7.13596e8 | −0.0497098 | ||||||||
\(799\) | 4.66946e9 | 0.323857 | ||||||||
\(800\) | 3.79501e9 | 0.262058 | ||||||||
\(801\) | −2.09542e10 | −1.44065 | ||||||||
\(802\) | 4.60285e9 | 0.315077 | ||||||||
\(803\) | 2.70650e9 | 0.184460 | ||||||||
\(804\) | 4.64777e9 | 0.315390 | ||||||||
\(805\) | −1.11415e10 | −0.752763 | ||||||||
\(806\) | −2.55873e9 | −0.172128 | ||||||||
\(807\) | −4.74628e9 | −0.317904 | ||||||||
\(808\) | −6.37601e9 | −0.425215 | ||||||||
\(809\) | 3.68694e8 | 0.0244820 | 0.0122410 | − | 0.999925i | \(-0.496103\pi\) | ||||
0.0122410 | + | 0.999925i | \(0.496103\pi\) | |||||||
\(810\) | −8.50063e9 | −0.562022 | ||||||||
\(811\) | 9.58211e9 | 0.630795 | 0.315397 | − | 0.948960i | \(-0.397862\pi\) | ||||
0.315397 | + | 0.948960i | \(0.397862\pi\) | |||||||
\(812\) | −3.63859e9 | −0.238499 | ||||||||
\(813\) | 2.82287e10 | 1.84236 | ||||||||
\(814\) | −2.02405e10 | −1.31533 | ||||||||
\(815\) | 6.01672e9 | 0.389321 | ||||||||
\(816\) | 5.93980e9 | 0.382698 | ||||||||
\(817\) | 4.61685e9 | 0.296189 | ||||||||
\(818\) | −8.05714e9 | −0.514688 | ||||||||
\(819\) | 1.29388e9 | 0.0823003 | ||||||||
\(820\) | 1.70370e10 | 1.07906 | ||||||||
\(821\) | −2.19021e9 | −0.138129 | −0.0690646 | − | 0.997612i | \(-0.522001\pi\) | ||||
−0.0690646 | + | 0.997612i | \(0.522001\pi\) | |||||||
\(822\) | −1.19973e10 | −0.753409 | ||||||||
\(823\) | −1.01062e10 | −0.631957 | −0.315978 | − | 0.948766i | \(-0.602333\pi\) | ||||
−0.315978 | + | 0.948766i | \(0.602333\pi\) | |||||||
\(824\) | 9.16760e9 | 0.570835 | ||||||||
\(825\) | 1.10068e10 | 0.682452 | ||||||||
\(826\) | −4.58514e9 | −0.283089 | ||||||||
\(827\) | −1.63226e10 | −1.00351 | −0.501753 | − | 0.865011i | \(-0.667312\pi\) | ||||
−0.501753 | + | 0.865011i | \(0.667312\pi\) | |||||||
\(828\) | −1.85521e10 | −1.13576 | ||||||||
\(829\) | −2.02220e10 | −1.23277 | −0.616387 | − | 0.787444i | \(-0.711404\pi\) | ||||
−0.616387 | + | 0.787444i | \(0.711404\pi\) | |||||||
\(830\) | −8.44662e9 | −0.512755 | ||||||||
\(831\) | −1.15760e10 | −0.699768 | ||||||||
\(832\) | 2.99177e8 | 0.0180093 | ||||||||
\(833\) | 1.40607e9 | 0.0842851 | ||||||||
\(834\) | 8.27381e8 | 0.0493883 | ||||||||
\(835\) | 2.08987e10 | 1.24227 | ||||||||
\(836\) | −6.10124e9 | −0.361157 | ||||||||
\(837\) | −7.07401e9 | −0.416991 | ||||||||
\(838\) | 3.64592e9 | 0.214020 | ||||||||
\(839\) | −9.25923e9 | −0.541263 | −0.270631 | − | 0.962683i | \(-0.587232\pi\) | ||||
−0.270631 | + | 0.962683i | \(0.587232\pi\) | |||||||
\(840\) | 7.58136e9 | 0.441336 | ||||||||
\(841\) | −6.96942e9 | −0.404027 | ||||||||
\(842\) | 4.67297e9 | 0.269774 | ||||||||
\(843\) | −1.09548e10 | −0.629806 | ||||||||
\(844\) | −8.22377e8 | −0.0470839 | ||||||||
\(845\) | 1.51817e9 | 0.0865612 | ||||||||
\(846\) | 3.24338e9 | 0.184163 | ||||||||
\(847\) | −1.79094e10 | −1.01272 | ||||||||
\(848\) | 2.52121e9 | 0.141979 | ||||||||
\(849\) | 3.19041e10 | 1.78925 | ||||||||
\(850\) | 1.20211e9 | 0.0671395 | ||||||||
\(851\) | −5.10581e10 | −2.83995 | ||||||||
\(852\) | 3.14616e10 | 1.74278 | ||||||||
\(853\) | −1.03242e10 | −0.569552 | −0.284776 | − | 0.958594i | \(-0.591919\pi\) | ||||
−0.284776 | + | 0.958594i | \(0.591919\pi\) | |||||||
\(854\) | −8.30182e7 | −0.00456111 | ||||||||
\(855\) | 3.71924e9 | 0.203504 | ||||||||
\(856\) | 1.96064e10 | 1.06841 | ||||||||
\(857\) | 1.34846e10 | 0.731824 | 0.365912 | − | 0.930649i | \(-0.380757\pi\) | ||||
0.365912 | + | 0.930649i | \(0.380757\pi\) | |||||||
\(858\) | −5.61990e9 | −0.303755 | ||||||||
\(859\) | −7.04555e9 | −0.379262 | −0.189631 | − | 0.981855i | \(-0.560729\pi\) | ||||
−0.189631 | + | 0.981855i | \(0.560729\pi\) | |||||||
\(860\) | −2.20607e10 | −1.18270 | ||||||||
\(861\) | 1.10955e10 | 0.592430 | ||||||||
\(862\) | 5.58537e9 | 0.297014 | ||||||||
\(863\) | 5.76366e9 | 0.305254 | 0.152627 | − | 0.988284i | \(-0.451227\pi\) | ||||
0.152627 | + | 0.988284i | \(0.451227\pi\) | |||||||
\(864\) | −5.35699e9 | −0.282568 | ||||||||
\(865\) | 2.54802e10 | 1.33859 | ||||||||
\(866\) | −4.92693e9 | −0.257789 | ||||||||
\(867\) | −1.67141e10 | −0.870993 | ||||||||
\(868\) | 8.64453e9 | 0.448665 | ||||||||
\(869\) | 3.34659e9 | 0.172995 | ||||||||
\(870\) | −9.63393e9 | −0.496005 | ||||||||
\(871\) | 1.56202e9 | 0.0800982 | ||||||||
\(872\) | −4.42670e9 | −0.226085 | ||||||||
\(873\) | −8.85038e9 | −0.450207 | ||||||||
\(874\) | 3.43868e9 | 0.174221 | ||||||||
\(875\) | 6.18402e9 | 0.312063 | ||||||||
\(876\) | −2.08945e9 | −0.105019 | ||||||||
\(877\) | 2.42411e10 | 1.21354 | 0.606771 | − | 0.794877i | \(-0.292465\pi\) | ||||
0.606771 | + | 0.794877i | \(0.292465\pi\) | |||||||
\(878\) | 9.93588e9 | 0.495423 | ||||||||
\(879\) | 4.29742e10 | 2.13426 | ||||||||
\(880\) | 2.11846e10 | 1.04793 | ||||||||
\(881\) | −1.64052e10 | −0.808285 | −0.404143 | − | 0.914696i | \(-0.632430\pi\) | ||||
−0.404143 | + | 0.914696i | \(0.632430\pi\) | |||||||
\(882\) | 9.76652e8 | 0.0479292 | ||||||||
\(883\) | 2.40299e10 | 1.17460 | 0.587299 | − | 0.809370i | \(-0.300191\pi\) | ||||
0.587299 | + | 0.809370i | \(0.300191\pi\) | |||||||
\(884\) | 2.74716e9 | 0.133752 | ||||||||
\(885\) | 5.43368e10 | 2.63507 | ||||||||
\(886\) | 6.68900e9 | 0.323105 | ||||||||
\(887\) | 2.04477e10 | 0.983813 | 0.491906 | − | 0.870648i | \(-0.336300\pi\) | ||||
0.491906 | + | 0.870648i | \(0.336300\pi\) | |||||||
\(888\) | 3.47430e10 | 1.66503 | ||||||||
\(889\) | −2.01505e9 | −0.0961901 | ||||||||
\(890\) | −1.85585e10 | −0.882427 | ||||||||
\(891\) | −4.73338e10 | −2.24181 | ||||||||
\(892\) | −1.76697e10 | −0.833589 | ||||||||
\(893\) | 2.69072e9 | 0.126441 | ||||||||
\(894\) | 1.61148e10 | 0.754299 | ||||||||
\(895\) | −2.18689e10 | −1.01964 | ||||||||
\(896\) | 8.23474e9 | 0.382447 | ||||||||
\(897\) | −1.41766e10 | −0.655843 | ||||||||
\(898\) | 8.70228e9 | 0.401020 | ||||||||
\(899\) | −2.44242e10 | −1.12114 | ||||||||
\(900\) | −3.73721e9 | −0.170883 | ||||||||
\(901\) | 3.78820e9 | 0.172543 | ||||||||
\(902\) | −2.11954e10 | −0.961655 | ||||||||
\(903\) | −1.43672e10 | −0.649330 | ||||||||
\(904\) | 2.94580e10 | 1.32621 | ||||||||
\(905\) | −3.41070e10 | −1.52959 | ||||||||
\(906\) | −9.75977e9 | −0.436004 | ||||||||
\(907\) | 1.70630e10 | 0.759329 | 0.379664 | − | 0.925124i | \(-0.376040\pi\) | ||||
0.379664 | + | 0.925124i | \(0.376040\pi\) | |||||||
\(908\) | 4.82880e8 | 0.0214062 | ||||||||
\(909\) | 9.73381e9 | 0.429843 | ||||||||
\(910\) | 1.14595e9 | 0.0504106 | ||||||||
\(911\) | −5.54686e9 | −0.243071 | −0.121536 | − | 0.992587i | \(-0.538782\pi\) | ||||
−0.121536 | + | 0.992587i | \(0.538782\pi\) | |||||||
\(912\) | 3.42274e9 | 0.149414 | ||||||||
\(913\) | −4.70331e10 | −2.04529 | ||||||||
\(914\) | 6.57270e9 | 0.284729 | ||||||||
\(915\) | 9.83818e8 | 0.0424562 | ||||||||
\(916\) | 3.25019e10 | 1.39725 | ||||||||
\(917\) | 3.69077e8 | 0.0158061 | ||||||||
\(918\) | −1.69689e9 | −0.0723941 | ||||||||
\(919\) | −1.28731e10 | −0.547115 | −0.273557 | − | 0.961856i | \(-0.588200\pi\) | ||||
−0.273557 | + | 0.961856i | \(0.588200\pi\) | |||||||
\(920\) | −3.65330e10 | −1.54678 | ||||||||
\(921\) | −5.13976e10 | −2.16788 | ||||||||
\(922\) | 4.56441e9 | 0.191790 | ||||||||
\(923\) | 1.05736e10 | 0.442605 | ||||||||
\(924\) | 1.89865e10 | 0.791759 | ||||||||
\(925\) | −1.02854e10 | −0.427291 | ||||||||
\(926\) | −1.02301e9 | −0.0423390 | ||||||||
\(927\) | −1.39955e10 | −0.577046 | ||||||||
\(928\) | −1.84959e10 | −0.759727 | ||||||||
\(929\) | 3.77350e10 | 1.54415 | 0.772075 | − | 0.635531i | \(-0.219219\pi\) | ||||
0.772075 | + | 0.635531i | \(0.219219\pi\) | |||||||
\(930\) | 2.28882e10 | 0.933085 | ||||||||
\(931\) | 8.10234e8 | 0.0329069 | ||||||||
\(932\) | −9.68096e9 | −0.391708 | ||||||||
\(933\) | −2.04152e10 | −0.822940 | ||||||||
\(934\) | −5.40078e9 | −0.216891 | ||||||||
\(935\) | 3.18306e10 | 1.27351 | ||||||||
\(936\) | 4.24265e9 | 0.169111 | ||||||||
\(937\) | −1.35680e10 | −0.538801 | −0.269401 | − | 0.963028i | \(-0.586826\pi\) | ||||
−0.269401 | + | 0.963028i | \(0.586826\pi\) | |||||||
\(938\) | 1.17905e9 | 0.0466468 | ||||||||
\(939\) | −2.36828e10 | −0.933478 | ||||||||
\(940\) | −1.28570e10 | −0.504886 | ||||||||
\(941\) | 1.66279e10 | 0.650541 | 0.325270 | − | 0.945621i | \(-0.394545\pi\) | ||||
0.325270 | + | 0.945621i | \(0.394545\pi\) | |||||||
\(942\) | 2.94969e9 | 0.114974 | ||||||||
\(943\) | −5.34671e10 | −2.07633 | ||||||||
\(944\) | 2.19925e10 | 0.850888 | ||||||||
\(945\) | 3.16816e9 | 0.122122 | ||||||||
\(946\) | 2.74453e10 | 1.05402 | ||||||||
\(947\) | −3.94921e10 | −1.51107 | −0.755536 | − | 0.655107i | \(-0.772624\pi\) | ||||
−0.755536 | + | 0.655107i | \(0.772624\pi\) | |||||||
\(948\) | −2.58362e9 | −0.0984915 | ||||||||
\(949\) | −7.02222e8 | −0.0266712 | ||||||||
\(950\) | 6.92703e8 | 0.0262128 | ||||||||
\(951\) | −8.29996e9 | −0.312928 | ||||||||
\(952\) | 4.61053e9 | 0.173189 | ||||||||
\(953\) | −5.06925e10 | −1.89723 | −0.948613 | − | 0.316439i | \(-0.897513\pi\) | ||||
−0.948613 | + | 0.316439i | \(0.897513\pi\) | |||||||
\(954\) | 2.63126e9 | 0.0981172 | ||||||||
\(955\) | 2.11101e10 | 0.784295 | ||||||||
\(956\) | −2.50524e10 | −0.927357 | ||||||||
\(957\) | −5.36443e10 | −1.97848 | ||||||||
\(958\) | −1.18546e10 | −0.435619 | ||||||||
\(959\) | 1.36220e10 | 0.498741 | ||||||||
\(960\) | −2.67617e9 | −0.0976259 | ||||||||
\(961\) | 3.05142e10 | 1.10910 | ||||||||
\(962\) | 5.25155e9 | 0.190184 | ||||||||
\(963\) | −2.99317e10 | −1.08004 | ||||||||
\(964\) | −1.84381e10 | −0.662898 | ||||||||
\(965\) | 2.63228e10 | 0.942944 | ||||||||
\(966\) | −1.07008e10 | −0.381943 | ||||||||
\(967\) | 4.34587e10 | 1.54555 | 0.772776 | − | 0.634679i | \(-0.218868\pi\) | ||||
0.772776 | + | 0.634679i | \(0.218868\pi\) | |||||||
\(968\) | −5.87249e10 | −2.08093 | ||||||||
\(969\) | 5.14278e9 | 0.181578 | ||||||||
\(970\) | −7.83851e9 | −0.275761 | ||||||||
\(971\) | −2.42378e10 | −0.849623 | −0.424812 | − | 0.905282i | \(-0.639660\pi\) | ||||
−0.424812 | + | 0.905282i | \(0.639660\pi\) | |||||||
\(972\) | 2.98229e10 | 1.04164 | ||||||||
\(973\) | −9.39428e8 | −0.0326940 | ||||||||
\(974\) | −1.71754e10 | −0.595596 | ||||||||
\(975\) | −2.85580e9 | −0.0986762 | ||||||||
\(976\) | 3.98194e8 | 0.0137095 | ||||||||
\(977\) | 5.82477e10 | 1.99824 | 0.999120 | − | 0.0419334i | \(-0.0133517\pi\) | ||||
0.999120 | + | 0.0419334i | \(0.0133517\pi\) | |||||||
\(978\) | 5.77875e9 | 0.197537 | ||||||||
\(979\) | −1.03339e11 | −3.51985 | ||||||||
\(980\) | −3.87153e9 | −0.131399 | ||||||||
\(981\) | 6.75794e9 | 0.228546 | ||||||||
\(982\) | −3.92104e9 | −0.132133 | ||||||||
\(983\) | −3.52029e10 | −1.18207 | −0.591033 | − | 0.806648i | \(-0.701280\pi\) | ||||
−0.591033 | + | 0.806648i | \(0.701280\pi\) | |||||||
\(984\) | 3.63823e10 | 1.21733 | ||||||||
\(985\) | −3.05404e10 | −1.01823 | ||||||||
\(986\) | −5.85878e9 | −0.194643 | ||||||||
\(987\) | −8.37328e9 | −0.277195 | ||||||||
\(988\) | 1.58302e9 | 0.0522199 | ||||||||
\(989\) | 6.92328e10 | 2.27575 | ||||||||
\(990\) | 2.21093e10 | 0.724190 | ||||||||
\(991\) | 2.65405e10 | 0.866266 | 0.433133 | − | 0.901330i | \(-0.357408\pi\) | ||||
0.433133 | + | 0.901330i | \(0.357408\pi\) | |||||||
\(992\) | 4.39424e10 | 1.42920 | ||||||||
\(993\) | 1.60722e10 | 0.520900 | ||||||||
\(994\) | 7.98119e9 | 0.257760 | ||||||||
\(995\) | 7.22263e9 | 0.232442 | ||||||||
\(996\) | 3.63102e10 | 1.16445 | ||||||||
\(997\) | −3.04787e9 | −0.0974009 | −0.0487004 | − | 0.998813i | \(-0.515508\pi\) | ||||
−0.0487004 | + | 0.998813i | \(0.515508\pi\) | |||||||
\(998\) | −1.82361e10 | −0.580731 | ||||||||
\(999\) | 1.45187e10 | 0.460732 |
(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 | 91.8.a.d.1.6 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.8.a.d.1.6 | ✓ | 10 | 1.1 | even | 1 | trivial |