Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,14,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, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
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: | \(189.798744245\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −169.531 | −1.87308 | −0.936538 | − | 0.350567i | \(-0.885989\pi\) | ||||
−0.936538 | + | 0.350567i | \(0.885989\pi\) | |||||||
\(3\) | 729.000 | 0.577350 | ||||||||
\(4\) | 20548.9 | 2.50841 | ||||||||
\(5\) | −21413.6 | −0.612892 | −0.306446 | − | 0.951888i | \(-0.599140\pi\) | ||||
−0.306446 | + | 0.951888i | \(0.599140\pi\) | |||||||
\(6\) | −123588. | −1.08142 | ||||||||
\(7\) | 361154. | 1.16026 | 0.580130 | − | 0.814524i | \(-0.303002\pi\) | ||||
0.580130 | + | 0.814524i | \(0.303002\pi\) | |||||||
\(8\) | −2.09488e6 | −2.82537 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | 3.63027e6 | 1.14799 | ||||||||
\(11\) | −6.55650e6 | −1.11589 | −0.557943 | − | 0.829880i | \(-0.688409\pi\) | ||||
−0.557943 | + | 0.829880i | \(0.688409\pi\) | |||||||
\(12\) | 1.49801e7 | 1.44823 | ||||||||
\(13\) | 3.19555e6 | 0.183617 | 0.0918087 | − | 0.995777i | \(-0.470735\pi\) | ||||
0.0918087 | + | 0.995777i | \(0.470735\pi\) | |||||||
\(14\) | −6.12269e7 | −2.17325 | ||||||||
\(15\) | −1.56105e7 | −0.353854 | ||||||||
\(16\) | 1.86812e8 | 2.78371 | ||||||||
\(17\) | 2.70339e7 | 0.271638 | 0.135819 | − | 0.990734i | \(-0.456633\pi\) | ||||
0.135819 | + | 0.990734i | \(0.456633\pi\) | |||||||
\(18\) | −9.00959e7 | −0.624358 | ||||||||
\(19\) | −6.84109e7 | −0.333601 | −0.166800 | − | 0.985991i | \(-0.553344\pi\) | ||||
−0.166800 | + | 0.985991i | \(0.553344\pi\) | |||||||
\(20\) | −4.40025e8 | −1.53739 | ||||||||
\(21\) | 2.63281e8 | 0.669876 | ||||||||
\(22\) | 1.11153e9 | 2.09014 | ||||||||
\(23\) | −5.78204e8 | −0.814423 | −0.407212 | − | 0.913334i | \(-0.633499\pi\) | ||||
−0.407212 | + | 0.913334i | \(0.633499\pi\) | |||||||
\(24\) | −1.52717e9 | −1.63123 | ||||||||
\(25\) | −7.62162e8 | −0.624363 | ||||||||
\(26\) | −5.41746e8 | −0.343929 | ||||||||
\(27\) | 3.87420e8 | 0.192450 | ||||||||
\(28\) | 7.42131e9 | 2.91041 | ||||||||
\(29\) | 3.44992e9 | 1.07702 | 0.538508 | − | 0.842620i | \(-0.318988\pi\) | ||||
0.538508 | + | 0.842620i | \(0.318988\pi\) | |||||||
\(30\) | 2.64647e9 | 0.662794 | ||||||||
\(31\) | 9.42535e9 | 1.90742 | 0.953710 | − | 0.300727i | \(-0.0972293\pi\) | ||||
0.953710 | + | 0.300727i | \(0.0972293\pi\) | |||||||
\(32\) | −1.45092e10 | −2.38874 | ||||||||
\(33\) | −4.77969e9 | −0.644257 | ||||||||
\(34\) | −4.58309e9 | −0.508798 | ||||||||
\(35\) | −7.73360e9 | −0.711114 | ||||||||
\(36\) | 1.09205e10 | 0.836137 | ||||||||
\(37\) | 1.03645e10 | 0.664103 | 0.332052 | − | 0.943261i | \(-0.392259\pi\) | ||||
0.332052 | + | 0.943261i | \(0.392259\pi\) | |||||||
\(38\) | 1.15978e10 | 0.624859 | ||||||||
\(39\) | 2.32956e9 | 0.106012 | ||||||||
\(40\) | 4.48589e10 | 1.73164 | ||||||||
\(41\) | −2.19371e9 | −0.0721248 | −0.0360624 | − | 0.999350i | \(-0.511482\pi\) | ||||
−0.0360624 | + | 0.999350i | \(0.511482\pi\) | |||||||
\(42\) | −4.46344e10 | −1.25473 | ||||||||
\(43\) | −2.12752e10 | −0.513250 | −0.256625 | − | 0.966511i | \(-0.582611\pi\) | ||||
−0.256625 | + | 0.966511i | \(0.582611\pi\) | |||||||
\(44\) | −1.34729e11 | −2.79910 | ||||||||
\(45\) | −1.13801e10 | −0.204297 | ||||||||
\(46\) | 9.80237e10 | 1.52548 | ||||||||
\(47\) | 3.14969e10 | 0.426219 | 0.213109 | − | 0.977028i | \(-0.431641\pi\) | ||||
0.213109 | + | 0.977028i | \(0.431641\pi\) | |||||||
\(48\) | 1.36186e11 | 1.60718 | ||||||||
\(49\) | 3.35431e10 | 0.346201 | ||||||||
\(50\) | 1.29210e11 | 1.16948 | ||||||||
\(51\) | 1.97077e10 | 0.156830 | ||||||||
\(52\) | 6.56650e10 | 0.460588 | ||||||||
\(53\) | −2.87264e11 | −1.78028 | −0.890138 | − | 0.455691i | \(-0.849392\pi\) | ||||
−0.890138 | + | 0.455691i | \(0.849392\pi\) | |||||||
\(54\) | −6.56799e10 | −0.360473 | ||||||||
\(55\) | 1.40398e11 | 0.683917 | ||||||||
\(56\) | −7.56575e11 | −3.27816 | ||||||||
\(57\) | −4.98715e10 | −0.192604 | ||||||||
\(58\) | −5.84870e11 | −2.01733 | ||||||||
\(59\) | 4.21805e10 | 0.130189 | ||||||||
\(60\) | −3.20779e11 | −0.887610 | ||||||||
\(61\) | −5.01289e10 | −0.124579 | −0.0622894 | − | 0.998058i | \(-0.519840\pi\) | ||||
−0.0622894 | + | 0.998058i | \(0.519840\pi\) | |||||||
\(62\) | −1.59789e12 | −3.57274 | ||||||||
\(63\) | 1.91932e11 | 0.386753 | ||||||||
\(64\) | 9.29400e11 | 1.69057 | ||||||||
\(65\) | −6.84282e10 | −0.112538 | ||||||||
\(66\) | 8.10307e11 | 1.20674 | ||||||||
\(67\) | −5.06275e11 | −0.683755 | −0.341878 | − | 0.939744i | \(-0.611063\pi\) | ||||
−0.341878 | + | 0.939744i | \(0.611063\pi\) | |||||||
\(68\) | 5.55516e11 | 0.681379 | ||||||||
\(69\) | −4.21511e11 | −0.470207 | ||||||||
\(70\) | 1.31109e12 | 1.33197 | ||||||||
\(71\) | −1.47759e12 | −1.36891 | −0.684454 | − | 0.729056i | \(-0.739959\pi\) | ||||
−0.684454 | + | 0.729056i | \(0.739959\pi\) | |||||||
\(72\) | −1.11331e12 | −0.941789 | ||||||||
\(73\) | −5.72451e11 | −0.442731 | −0.221365 | − | 0.975191i | \(-0.571051\pi\) | ||||
−0.221365 | + | 0.975191i | \(0.571051\pi\) | |||||||
\(74\) | −1.75710e12 | −1.24392 | ||||||||
\(75\) | −5.55616e11 | −0.360476 | ||||||||
\(76\) | −1.40577e12 | −0.836807 | ||||||||
\(77\) | −2.36790e12 | −1.29472 | ||||||||
\(78\) | −3.94933e11 | −0.198568 | ||||||||
\(79\) | 1.61549e12 | 0.747702 | 0.373851 | − | 0.927489i | \(-0.378037\pi\) | ||||
0.373851 | + | 0.927489i | \(0.378037\pi\) | |||||||
\(80\) | −4.00031e12 | −1.70612 | ||||||||
\(81\) | 2.82430e11 | 0.111111 | ||||||||
\(82\) | 3.71903e11 | 0.135095 | ||||||||
\(83\) | 2.15856e12 | 0.724697 | 0.362348 | − | 0.932043i | \(-0.381975\pi\) | ||||
0.362348 | + | 0.932043i | \(0.381975\pi\) | |||||||
\(84\) | 5.41014e12 | 1.68032 | ||||||||
\(85\) | −5.78892e11 | −0.166485 | ||||||||
\(86\) | 3.60682e12 | 0.961355 | ||||||||
\(87\) | 2.51499e12 | 0.621816 | ||||||||
\(88\) | 1.37351e13 | 3.15278 | ||||||||
\(89\) | 1.78420e12 | 0.380547 | 0.190274 | − | 0.981731i | \(-0.439062\pi\) | ||||
0.190274 | + | 0.981731i | \(0.439062\pi\) | |||||||
\(90\) | 1.92928e12 | 0.382664 | ||||||||
\(91\) | 1.15409e12 | 0.213044 | ||||||||
\(92\) | −1.18815e13 | −2.04291 | ||||||||
\(93\) | 6.87108e12 | 1.10125 | ||||||||
\(94\) | −5.33972e12 | −0.798339 | ||||||||
\(95\) | 1.46492e12 | 0.204461 | ||||||||
\(96\) | −1.05772e13 | −1.37914 | ||||||||
\(97\) | −3.76742e11 | −0.0459227 | −0.0229613 | − | 0.999736i | \(-0.507309\pi\) | ||||
−0.0229613 | + | 0.999736i | \(0.507309\pi\) | |||||||
\(98\) | −5.68661e12 | −0.648461 | ||||||||
\(99\) | −3.48439e12 | −0.371962 | ||||||||
\(100\) | −1.56616e13 | −1.56616 | ||||||||
\(101\) | −1.25220e13 | −1.17377 | −0.586887 | − | 0.809669i | \(-0.699647\pi\) | ||||
−0.586887 | + | 0.809669i | \(0.699647\pi\) | |||||||
\(102\) | −3.34107e12 | −0.293755 | ||||||||
\(103\) | −3.17368e12 | −0.261892 | −0.130946 | − | 0.991390i | \(-0.541801\pi\) | ||||
−0.130946 | + | 0.991390i | \(0.541801\pi\) | |||||||
\(104\) | −6.69430e12 | −0.518786 | ||||||||
\(105\) | −5.63779e12 | −0.410562 | ||||||||
\(106\) | 4.87002e13 | 3.33459 | ||||||||
\(107\) | −8.62759e12 | −0.555770 | −0.277885 | − | 0.960614i | \(-0.589633\pi\) | ||||
−0.277885 | + | 0.960614i | \(0.589633\pi\) | |||||||
\(108\) | 7.96106e12 | 0.482744 | ||||||||
\(109\) | 1.98524e13 | 1.13381 | 0.566906 | − | 0.823783i | \(-0.308140\pi\) | ||||
0.566906 | + | 0.823783i | \(0.308140\pi\) | |||||||
\(110\) | −2.38019e13 | −1.28103 | ||||||||
\(111\) | 7.55569e12 | 0.383420 | ||||||||
\(112\) | 6.74678e13 | 3.22983 | ||||||||
\(113\) | 3.65518e13 | 1.65158 | 0.825789 | − | 0.563979i | \(-0.190730\pi\) | ||||
0.825789 | + | 0.563979i | \(0.190730\pi\) | |||||||
\(114\) | 8.45479e12 | 0.360762 | ||||||||
\(115\) | 1.23814e13 | 0.499154 | ||||||||
\(116\) | 7.08921e13 | 2.70160 | ||||||||
\(117\) | 1.69825e12 | 0.0612058 | ||||||||
\(118\) | −7.15093e12 | −0.243854 | ||||||||
\(119\) | 9.76338e12 | 0.315170 | ||||||||
\(120\) | 3.27022e13 | 0.999766 | ||||||||
\(121\) | 8.46495e12 | 0.245199 | ||||||||
\(122\) | 8.49842e12 | 0.233345 | ||||||||
\(123\) | −1.59922e12 | −0.0416412 | ||||||||
\(124\) | 1.93681e14 | 4.78459 | ||||||||
\(125\) | 4.24602e13 | 0.995560 | ||||||||
\(126\) | −3.25385e13 | −0.724418 | ||||||||
\(127\) | 6.84567e13 | 1.44774 | 0.723872 | − | 0.689934i | \(-0.242360\pi\) | ||||
0.723872 | + | 0.689934i | \(0.242360\pi\) | |||||||
\(128\) | −3.87033e13 | −0.777827 | ||||||||
\(129\) | −1.55096e13 | −0.296325 | ||||||||
\(130\) | 1.16007e13 | 0.210792 | ||||||||
\(131\) | 5.40307e13 | 0.934065 | 0.467032 | − | 0.884240i | \(-0.345323\pi\) | ||||
0.467032 | + | 0.884240i | \(0.345323\pi\) | |||||||
\(132\) | −9.82173e13 | −1.61606 | ||||||||
\(133\) | −2.47069e13 | −0.387063 | ||||||||
\(134\) | 8.58296e13 | 1.28072 | ||||||||
\(135\) | −8.29606e12 | −0.117951 | ||||||||
\(136\) | −5.66327e13 | −0.767476 | ||||||||
\(137\) | −3.82436e13 | −0.494168 | −0.247084 | − | 0.968994i | \(-0.579472\pi\) | ||||
−0.247084 | + | 0.968994i | \(0.579472\pi\) | |||||||
\(138\) | 7.14593e13 | 0.880734 | ||||||||
\(139\) | −1.12280e14 | −1.32040 | −0.660201 | − | 0.751089i | \(-0.729529\pi\) | ||||
−0.660201 | + | 0.751089i | \(0.729529\pi\) | |||||||
\(140\) | −1.58917e14 | −1.78377 | ||||||||
\(141\) | 2.29613e13 | 0.246077 | ||||||||
\(142\) | 2.50498e14 | 2.56407 | ||||||||
\(143\) | −2.09516e13 | −0.204896 | ||||||||
\(144\) | 9.92794e13 | 0.927904 | ||||||||
\(145\) | −7.38752e13 | −0.660095 | ||||||||
\(146\) | 9.70484e13 | 0.829268 | ||||||||
\(147\) | 2.44529e13 | 0.199879 | ||||||||
\(148\) | 2.12978e14 | 1.66584 | ||||||||
\(149\) | −3.45852e13 | −0.258928 | −0.129464 | − | 0.991584i | \(-0.541326\pi\) | ||||
−0.129464 | + | 0.991584i | \(0.541326\pi\) | |||||||
\(150\) | 9.41944e13 | 0.675199 | ||||||||
\(151\) | −1.39958e14 | −0.960831 | −0.480416 | − | 0.877041i | \(-0.659514\pi\) | ||||
−0.480416 | + | 0.877041i | \(0.659514\pi\) | |||||||
\(152\) | 1.43313e14 | 0.942543 | ||||||||
\(153\) | 1.43669e13 | 0.0905459 | ||||||||
\(154\) | 4.01434e14 | 2.42510 | ||||||||
\(155\) | −2.01830e14 | −1.16904 | ||||||||
\(156\) | 4.78698e13 | 0.265920 | ||||||||
\(157\) | 9.14522e13 | 0.487356 | 0.243678 | − | 0.969856i | \(-0.421646\pi\) | ||||
0.243678 | + | 0.969856i | \(0.421646\pi\) | |||||||
\(158\) | −2.73876e14 | −1.40050 | ||||||||
\(159\) | −2.09415e14 | −1.02784 | ||||||||
\(160\) | 3.10693e14 | 1.46404 | ||||||||
\(161\) | −2.08821e14 | −0.944942 | ||||||||
\(162\) | −4.78807e13 | −0.208119 | ||||||||
\(163\) | −2.06673e14 | −0.863108 | −0.431554 | − | 0.902087i | \(-0.642035\pi\) | ||||
−0.431554 | + | 0.902087i | \(0.642035\pi\) | |||||||
\(164\) | −4.50783e13 | −0.180918 | ||||||||
\(165\) | 1.02350e14 | 0.394860 | ||||||||
\(166\) | −3.65943e14 | −1.35741 | ||||||||
\(167\) | −1.94548e13 | −0.0694016 | −0.0347008 | − | 0.999398i | \(-0.511048\pi\) | ||||
−0.0347008 | + | 0.999398i | \(0.511048\pi\) | |||||||
\(168\) | −5.51543e14 | −1.89264 | ||||||||
\(169\) | −2.92664e14 | −0.966285 | ||||||||
\(170\) | 9.81403e13 | 0.311838 | ||||||||
\(171\) | −3.63563e13 | −0.111200 | ||||||||
\(172\) | −4.37182e14 | −1.28744 | ||||||||
\(173\) | 4.09717e14 | 1.16194 | 0.580971 | − | 0.813925i | \(-0.302673\pi\) | ||||
0.580971 | + | 0.813925i | \(0.302673\pi\) | |||||||
\(174\) | −4.26370e14 | −1.16471 | ||||||||
\(175\) | −2.75258e14 | −0.724423 | ||||||||
\(176\) | −1.22483e15 | −3.10630 | ||||||||
\(177\) | 3.07496e13 | 0.0751646 | ||||||||
\(178\) | −3.02478e14 | −0.712794 | ||||||||
\(179\) | 7.18549e14 | 1.63272 | 0.816360 | − | 0.577543i | \(-0.195988\pi\) | ||||
0.816360 | + | 0.577543i | \(0.195988\pi\) | |||||||
\(180\) | −2.33848e14 | −0.512462 | ||||||||
\(181\) | −4.94149e14 | −1.04459 | −0.522297 | − | 0.852764i | \(-0.674925\pi\) | ||||
−0.522297 | + | 0.852764i | \(0.674925\pi\) | |||||||
\(182\) | −1.95654e14 | −0.399047 | ||||||||
\(183\) | −3.65440e13 | −0.0719256 | ||||||||
\(184\) | 1.21127e15 | 2.30104 | ||||||||
\(185\) | −2.21940e14 | −0.407024 | ||||||||
\(186\) | −1.16486e15 | −2.06272 | ||||||||
\(187\) | −1.77247e14 | −0.303116 | ||||||||
\(188\) | 6.47227e14 | 1.06913 | ||||||||
\(189\) | 1.39918e14 | 0.223292 | ||||||||
\(190\) | −2.48350e14 | −0.382971 | ||||||||
\(191\) | −7.56869e14 | −1.12799 | −0.563993 | − | 0.825780i | \(-0.690735\pi\) | ||||
−0.563993 | + | 0.825780i | \(0.690735\pi\) | |||||||
\(192\) | 6.77533e14 | 0.976050 | ||||||||
\(193\) | 5.42119e13 | 0.0755044 | 0.0377522 | − | 0.999287i | \(-0.487980\pi\) | ||||
0.0377522 | + | 0.999287i | \(0.487980\pi\) | |||||||
\(194\) | 6.38695e13 | 0.0860166 | ||||||||
\(195\) | −4.98841e13 | −0.0649737 | ||||||||
\(196\) | 6.89274e14 | 0.868415 | ||||||||
\(197\) | −3.73102e14 | −0.454775 | −0.227388 | − | 0.973804i | \(-0.573018\pi\) | ||||
−0.227388 | + | 0.973804i | \(0.573018\pi\) | |||||||
\(198\) | 5.90714e14 | 0.696712 | ||||||||
\(199\) | −3.01874e14 | −0.344573 | −0.172286 | − | 0.985047i | \(-0.555115\pi\) | ||||
−0.172286 | + | 0.985047i | \(0.555115\pi\) | |||||||
\(200\) | 1.59664e15 | 1.76405 | ||||||||
\(201\) | −3.69075e14 | −0.394766 | ||||||||
\(202\) | 2.12287e15 | 2.19857 | ||||||||
\(203\) | 1.24595e15 | 1.24962 | ||||||||
\(204\) | 4.04971e14 | 0.393394 | ||||||||
\(205\) | 4.69752e13 | 0.0442047 | ||||||||
\(206\) | 5.38039e14 | 0.490543 | ||||||||
\(207\) | −3.07281e14 | −0.271474 | ||||||||
\(208\) | 5.96966e14 | 0.511138 | ||||||||
\(209\) | 4.48536e14 | 0.372260 | ||||||||
\(210\) | 9.55783e14 | 0.769013 | ||||||||
\(211\) | 1.87437e15 | 1.46225 | 0.731123 | − | 0.682246i | \(-0.238997\pi\) | ||||
0.731123 | + | 0.682246i | \(0.238997\pi\) | |||||||
\(212\) | −5.90295e15 | −4.46566 | ||||||||
\(213\) | −1.07716e15 | −0.790339 | ||||||||
\(214\) | 1.46265e15 | 1.04100 | ||||||||
\(215\) | 4.55578e14 | 0.314567 | ||||||||
\(216\) | −8.11600e14 | −0.543742 | ||||||||
\(217\) | 3.40400e15 | 2.21310 | ||||||||
\(218\) | −3.36561e15 | −2.12371 | ||||||||
\(219\) | −4.17317e14 | −0.255611 | ||||||||
\(220\) | 2.88503e15 | 1.71555 | ||||||||
\(221\) | 8.63880e13 | 0.0498774 | ||||||||
\(222\) | −1.28093e15 | −0.718175 | ||||||||
\(223\) | 1.88601e14 | 0.102698 | 0.0513490 | − | 0.998681i | \(-0.483648\pi\) | ||||
0.0513490 | + | 0.998681i | \(0.483648\pi\) | |||||||
\(224\) | −5.24005e15 | −2.77155 | ||||||||
\(225\) | −4.05044e14 | −0.208121 | ||||||||
\(226\) | −6.19668e15 | −3.09353 | ||||||||
\(227\) | −3.16490e15 | −1.53529 | −0.767647 | − | 0.640873i | \(-0.778573\pi\) | ||||
−0.767647 | + | 0.640873i | \(0.778573\pi\) | |||||||
\(228\) | −1.02480e15 | −0.483131 | ||||||||
\(229\) | 2.86580e15 | 1.31315 | 0.656577 | − | 0.754259i | \(-0.272004\pi\) | ||||
0.656577 | + | 0.754259i | \(0.272004\pi\) | |||||||
\(230\) | −2.09904e15 | −0.934952 | ||||||||
\(231\) | −1.72620e15 | −0.747505 | ||||||||
\(232\) | −7.22718e15 | −3.04297 | ||||||||
\(233\) | −1.63684e14 | −0.0670183 | −0.0335092 | − | 0.999438i | \(-0.510668\pi\) | ||||
−0.0335092 | + | 0.999438i | \(0.510668\pi\) | |||||||
\(234\) | −2.87906e14 | −0.114643 | ||||||||
\(235\) | −6.74462e14 | −0.261226 | ||||||||
\(236\) | 8.66763e14 | 0.326567 | ||||||||
\(237\) | 1.17769e15 | 0.431686 | ||||||||
\(238\) | −1.65520e15 | −0.590337 | ||||||||
\(239\) | −1.56852e15 | −0.544381 | −0.272191 | − | 0.962243i | \(-0.587748\pi\) | ||||
−0.272191 | + | 0.962243i | \(0.587748\pi\) | |||||||
\(240\) | −2.91622e15 | −0.985026 | ||||||||
\(241\) | −1.53250e15 | −0.503835 | −0.251918 | − | 0.967749i | \(-0.581061\pi\) | ||||
−0.251918 | + | 0.967749i | \(0.581061\pi\) | |||||||
\(242\) | −1.43507e15 | −0.459277 | ||||||||
\(243\) | 2.05891e14 | 0.0641500 | ||||||||
\(244\) | −1.03009e15 | −0.312495 | ||||||||
\(245\) | −7.18278e14 | −0.212184 | ||||||||
\(246\) | 2.71117e14 | 0.0779972 | ||||||||
\(247\) | −2.18610e14 | −0.0612549 | ||||||||
\(248\) | −1.97450e16 | −5.38916 | ||||||||
\(249\) | 1.57359e15 | 0.418404 | ||||||||
\(250\) | −7.19834e15 | −1.86476 | ||||||||
\(251\) | −5.07634e15 | −1.28136 | −0.640680 | − | 0.767808i | \(-0.721348\pi\) | ||||
−0.640680 | + | 0.767808i | \(0.721348\pi\) | |||||||
\(252\) | 3.94399e15 | 0.970135 | ||||||||
\(253\) | 3.79099e15 | 0.908803 | ||||||||
\(254\) | −1.16056e16 | −2.71173 | ||||||||
\(255\) | −4.22012e14 | −0.0961200 | ||||||||
\(256\) | −1.05222e15 | −0.233640 | ||||||||
\(257\) | 5.57883e15 | 1.20775 | 0.603876 | − | 0.797078i | \(-0.293622\pi\) | ||||
0.603876 | + | 0.797078i | \(0.293622\pi\) | |||||||
\(258\) | 2.62937e15 | 0.555039 | ||||||||
\(259\) | 3.74317e15 | 0.770532 | ||||||||
\(260\) | −1.40612e15 | −0.282291 | ||||||||
\(261\) | 1.83343e15 | 0.359006 | ||||||||
\(262\) | −9.15990e15 | −1.74957 | ||||||||
\(263\) | 1.41314e15 | 0.263313 | 0.131656 | − | 0.991295i | \(-0.457970\pi\) | ||||
0.131656 | + | 0.991295i | \(0.457970\pi\) | |||||||
\(264\) | 1.00129e16 | 1.82026 | ||||||||
\(265\) | 6.15134e15 | 1.09112 | ||||||||
\(266\) | 4.18859e15 | 0.724998 | ||||||||
\(267\) | 1.30068e15 | 0.219709 | ||||||||
\(268\) | −1.04034e16 | −1.71514 | ||||||||
\(269\) | 4.22038e15 | 0.679144 | 0.339572 | − | 0.940580i | \(-0.389718\pi\) | ||||
0.339572 | + | 0.940580i | \(0.389718\pi\) | |||||||
\(270\) | 1.40644e15 | 0.220931 | ||||||||
\(271\) | −2.83121e15 | −0.434181 | −0.217091 | − | 0.976151i | \(-0.569657\pi\) | ||||
−0.217091 | + | 0.976151i | \(0.569657\pi\) | |||||||
\(272\) | 5.05024e15 | 0.756161 | ||||||||
\(273\) | 8.41328e14 | 0.123001 | ||||||||
\(274\) | 6.48348e15 | 0.925614 | ||||||||
\(275\) | 4.99711e15 | 0.696717 | ||||||||
\(276\) | −8.66158e15 | −1.17947 | ||||||||
\(277\) | 5.67990e15 | 0.755479 | 0.377740 | − | 0.925912i | \(-0.376701\pi\) | ||||
0.377740 | + | 0.925912i | \(0.376701\pi\) | |||||||
\(278\) | 1.90350e16 | 2.47321 | ||||||||
\(279\) | 5.00902e15 | 0.635807 | ||||||||
\(280\) | 1.62010e16 | 2.00916 | ||||||||
\(281\) | −6.84857e15 | −0.829868 | −0.414934 | − | 0.909852i | \(-0.636195\pi\) | ||||
−0.414934 | + | 0.909852i | \(0.636195\pi\) | |||||||
\(282\) | −3.89266e15 | −0.460921 | ||||||||
\(283\) | −1.19895e16 | −1.38736 | −0.693678 | − | 0.720285i | \(-0.744011\pi\) | ||||
−0.693678 | + | 0.720285i | \(0.744011\pi\) | |||||||
\(284\) | −3.03628e16 | −3.43378 | ||||||||
\(285\) | 1.06793e15 | 0.118046 | ||||||||
\(286\) | 3.55196e15 | 0.383785 | ||||||||
\(287\) | −7.92267e14 | −0.0836834 | ||||||||
\(288\) | −7.71077e15 | −0.796245 | ||||||||
\(289\) | −9.17375e15 | −0.926213 | ||||||||
\(290\) | 1.25242e16 | 1.23641 | ||||||||
\(291\) | −2.74645e14 | −0.0265135 | ||||||||
\(292\) | −1.17632e16 | −1.11055 | ||||||||
\(293\) | 1.17508e16 | 1.08499 | 0.542496 | − | 0.840058i | \(-0.317479\pi\) | ||||
0.542496 | + | 0.840058i | \(0.317479\pi\) | |||||||
\(294\) | −4.14554e15 | −0.374389 | ||||||||
\(295\) | −9.03236e14 | −0.0797918 | ||||||||
\(296\) | −2.17123e16 | −1.87633 | ||||||||
\(297\) | −2.54012e15 | −0.214752 | ||||||||
\(298\) | 5.86328e15 | 0.484992 | ||||||||
\(299\) | −1.84768e15 | −0.149542 | ||||||||
\(300\) | −1.14173e16 | −0.904222 | ||||||||
\(301\) | −7.68362e15 | −0.595503 | ||||||||
\(302\) | 2.37273e16 | 1.79971 | ||||||||
\(303\) | −9.12853e15 | −0.677679 | ||||||||
\(304\) | −1.27800e16 | −0.928648 | ||||||||
\(305\) | 1.07344e15 | 0.0763534 | ||||||||
\(306\) | −2.43564e15 | −0.169599 | ||||||||
\(307\) | 1.55258e16 | 1.05841 | 0.529206 | − | 0.848493i | \(-0.322490\pi\) | ||||
0.529206 | + | 0.848493i | \(0.322490\pi\) | |||||||
\(308\) | −4.86578e16 | −3.24768 | ||||||||
\(309\) | −2.31361e15 | −0.151203 | ||||||||
\(310\) | 3.42166e16 | 2.18971 | ||||||||
\(311\) | −2.18300e15 | −0.136808 | −0.0684041 | − | 0.997658i | \(-0.521791\pi\) | ||||
−0.0684041 | + | 0.997658i | \(0.521791\pi\) | |||||||
\(312\) | −4.88014e15 | −0.299521 | ||||||||
\(313\) | −2.13942e16 | −1.28605 | −0.643024 | − | 0.765846i | \(-0.722320\pi\) | ||||
−0.643024 | + | 0.765846i | \(0.722320\pi\) | |||||||
\(314\) | −1.55040e16 | −0.912854 | ||||||||
\(315\) | −4.10995e15 | −0.237038 | ||||||||
\(316\) | 3.31966e16 | 1.87554 | ||||||||
\(317\) | 5.87276e15 | 0.325055 | 0.162528 | − | 0.986704i | \(-0.448035\pi\) | ||||
0.162528 | + | 0.986704i | \(0.448035\pi\) | |||||||
\(318\) | 3.55024e16 | 1.92523 | ||||||||
\(319\) | −2.26194e16 | −1.20183 | ||||||||
\(320\) | −1.99018e16 | −1.03614 | ||||||||
\(321\) | −6.28951e15 | −0.320874 | ||||||||
\(322\) | 3.54016e16 | 1.76995 | ||||||||
\(323\) | −1.84941e15 | −0.0906185 | ||||||||
\(324\) | 5.80362e15 | 0.278712 | ||||||||
\(325\) | −2.43553e15 | −0.114644 | ||||||||
\(326\) | 3.50376e16 | 1.61667 | ||||||||
\(327\) | 1.44724e16 | 0.654606 | ||||||||
\(328\) | 4.59557e15 | 0.203779 | ||||||||
\(329\) | 1.13752e16 | 0.494524 | ||||||||
\(330\) | −1.73516e16 | −0.739602 | ||||||||
\(331\) | −5.76612e15 | −0.240991 | −0.120496 | − | 0.992714i | \(-0.538448\pi\) | ||||
−0.120496 | + | 0.992714i | \(0.538448\pi\) | |||||||
\(332\) | 4.43560e16 | 1.81784 | ||||||||
\(333\) | 5.50810e15 | 0.221368 | ||||||||
\(334\) | 3.29820e15 | 0.129994 | ||||||||
\(335\) | 1.08412e16 | 0.419068 | ||||||||
\(336\) | 4.91840e16 | 1.86474 | ||||||||
\(337\) | −1.33634e16 | −0.496961 | −0.248481 | − | 0.968637i | \(-0.579931\pi\) | ||||
−0.248481 | + | 0.968637i | \(0.579931\pi\) | |||||||
\(338\) | 4.96157e16 | 1.80992 | ||||||||
\(339\) | 2.66463e16 | 0.953539 | ||||||||
\(340\) | −1.18956e16 | −0.417612 | ||||||||
\(341\) | −6.17973e16 | −2.12846 | ||||||||
\(342\) | 6.16354e15 | 0.208286 | ||||||||
\(343\) | −2.28776e16 | −0.758576 | ||||||||
\(344\) | 4.45690e16 | 1.45012 | ||||||||
\(345\) | 9.02605e15 | 0.288187 | ||||||||
\(346\) | −6.94599e16 | −2.17640 | ||||||||
\(347\) | −4.82874e15 | −0.148488 | −0.0742441 | − | 0.997240i | \(-0.523654\pi\) | ||||
−0.0742441 | + | 0.997240i | \(0.523654\pi\) | |||||||
\(348\) | 5.16804e16 | 1.55977 | ||||||||
\(349\) | 3.20684e16 | 0.949974 | 0.474987 | − | 0.879993i | \(-0.342453\pi\) | ||||
0.474987 | + | 0.879993i | \(0.342453\pi\) | |||||||
\(350\) | 4.66648e16 | 1.35690 | ||||||||
\(351\) | 1.23802e15 | 0.0353372 | ||||||||
\(352\) | 9.51294e16 | 2.66555 | ||||||||
\(353\) | −5.60978e16 | −1.54316 | −0.771579 | − | 0.636134i | \(-0.780533\pi\) | ||||
−0.771579 | + | 0.636134i | \(0.780533\pi\) | |||||||
\(354\) | −5.21302e15 | −0.140789 | ||||||||
\(355\) | 3.16404e16 | 0.838993 | ||||||||
\(356\) | 3.66634e16 | 0.954569 | ||||||||
\(357\) | 7.11750e15 | 0.181964 | ||||||||
\(358\) | −1.21817e17 | −3.05821 | ||||||||
\(359\) | −3.53481e16 | −0.871470 | −0.435735 | − | 0.900075i | \(-0.643512\pi\) | ||||
−0.435735 | + | 0.900075i | \(0.643512\pi\) | |||||||
\(360\) | 2.38399e16 | 0.577215 | ||||||||
\(361\) | −3.73729e16 | −0.888711 | ||||||||
\(362\) | 8.37738e16 | 1.95660 | ||||||||
\(363\) | 6.17095e15 | 0.141566 | ||||||||
\(364\) | 2.37152e16 | 0.534401 | ||||||||
\(365\) | 1.22582e16 | 0.271346 | ||||||||
\(366\) | 6.19535e15 | 0.134722 | ||||||||
\(367\) | 4.60564e16 | 0.983922 | 0.491961 | − | 0.870617i | \(-0.336280\pi\) | ||||
0.491961 | + | 0.870617i | \(0.336280\pi\) | |||||||
\(368\) | −1.08015e17 | −2.26712 | ||||||||
\(369\) | −1.16583e15 | −0.0240416 | ||||||||
\(370\) | 3.76258e16 | 0.762386 | ||||||||
\(371\) | −1.03746e17 | −2.06558 | ||||||||
\(372\) | 1.41193e17 | 2.76239 | ||||||||
\(373\) | −9.12768e16 | −1.75490 | −0.877451 | − | 0.479666i | \(-0.840758\pi\) | ||||
−0.877451 | + | 0.479666i | \(0.840758\pi\) | |||||||
\(374\) | 3.00490e16 | 0.567760 | ||||||||
\(375\) | 3.09535e16 | 0.574787 | ||||||||
\(376\) | −6.59824e16 | −1.20422 | ||||||||
\(377\) | 1.10244e16 | 0.197759 | ||||||||
\(378\) | −2.37206e16 | −0.418243 | ||||||||
\(379\) | −2.08075e16 | −0.360633 | −0.180317 | − | 0.983609i | \(-0.557712\pi\) | ||||
−0.180317 | + | 0.983609i | \(0.557712\pi\) | |||||||
\(380\) | 3.01025e16 | 0.512873 | ||||||||
\(381\) | 4.99049e16 | 0.835856 | ||||||||
\(382\) | 1.28313e17 | 2.11280 | ||||||||
\(383\) | −4.14608e16 | −0.671191 | −0.335595 | − | 0.942006i | \(-0.608937\pi\) | ||||
−0.335595 | + | 0.942006i | \(0.608937\pi\) | |||||||
\(384\) | −2.82147e16 | −0.449079 | ||||||||
\(385\) | 5.07053e16 | 0.793521 | ||||||||
\(386\) | −9.19062e15 | −0.141425 | ||||||||
\(387\) | −1.13065e16 | −0.171083 | ||||||||
\(388\) | −7.74162e15 | −0.115193 | ||||||||
\(389\) | 1.25116e17 | 1.83080 | 0.915398 | − | 0.402551i | \(-0.131876\pi\) | ||||
0.915398 | + | 0.402551i | \(0.131876\pi\) | |||||||
\(390\) | 8.45693e15 | 0.121701 | ||||||||
\(391\) | −1.56311e16 | −0.221228 | ||||||||
\(392\) | −7.02689e16 | −0.978146 | ||||||||
\(393\) | 3.93884e16 | 0.539283 | ||||||||
\(394\) | 6.32525e16 | 0.851829 | ||||||||
\(395\) | −3.45934e16 | −0.458261 | ||||||||
\(396\) | −7.16004e16 | −0.933032 | ||||||||
\(397\) | −1.83934e16 | −0.235789 | −0.117894 | − | 0.993026i | \(-0.537614\pi\) | ||||
−0.117894 | + | 0.993026i | \(0.537614\pi\) | |||||||
\(398\) | 5.11771e16 | 0.645411 | ||||||||
\(399\) | −1.80113e16 | −0.223471 | ||||||||
\(400\) | −1.42381e17 | −1.73805 | ||||||||
\(401\) | −1.57173e17 | −1.88773 | −0.943864 | − | 0.330333i | \(-0.892839\pi\) | ||||
−0.943864 | + | 0.330333i | \(0.892839\pi\) | |||||||
\(402\) | 6.25698e16 | 0.739427 | ||||||||
\(403\) | 3.01192e16 | 0.350236 | ||||||||
\(404\) | −2.57313e17 | −2.94431 | ||||||||
\(405\) | −6.04783e15 | −0.0680992 | ||||||||
\(406\) | −2.11228e17 | −2.34063 | ||||||||
\(407\) | −6.79546e16 | −0.741063 | ||||||||
\(408\) | −4.12853e16 | −0.443102 | ||||||||
\(409\) | 3.84365e16 | 0.406015 | 0.203008 | − | 0.979177i | \(-0.434928\pi\) | ||||
0.203008 | + | 0.979177i | \(0.434928\pi\) | |||||||
\(410\) | −7.96377e15 | −0.0827987 | ||||||||
\(411\) | −2.78796e16 | −0.285308 | ||||||||
\(412\) | −6.52157e16 | −0.656931 | ||||||||
\(413\) | 1.52337e16 | 0.151053 | ||||||||
\(414\) | 5.20938e16 | 0.508492 | ||||||||
\(415\) | −4.62225e16 | −0.444161 | ||||||||
\(416\) | −4.63648e16 | −0.438613 | ||||||||
\(417\) | −8.18522e16 | −0.762335 | ||||||||
\(418\) | −7.60409e16 | −0.697271 | ||||||||
\(419\) | −1.88832e17 | −1.70484 | −0.852419 | − | 0.522859i | \(-0.824866\pi\) | ||||
−0.852419 | + | 0.522859i | \(0.824866\pi\) | |||||||
\(420\) | −1.15850e17 | −1.02986 | ||||||||
\(421\) | −4.66069e16 | −0.407959 | −0.203979 | − | 0.978975i | \(-0.565388\pi\) | ||||
−0.203979 | + | 0.978975i | \(0.565388\pi\) | |||||||
\(422\) | −3.17765e17 | −2.73890 | ||||||||
\(423\) | 1.67388e16 | 0.142073 | ||||||||
\(424\) | 6.01783e17 | 5.02993 | ||||||||
\(425\) | −2.06042e16 | −0.169600 | ||||||||
\(426\) | 1.82613e17 | 1.48036 | ||||||||
\(427\) | −1.81042e16 | −0.144544 | ||||||||
\(428\) | −1.77287e17 | −1.39410 | ||||||||
\(429\) | −1.52737e16 | −0.118297 | ||||||||
\(430\) | −7.72348e16 | −0.589207 | ||||||||
\(431\) | −4.58448e16 | −0.344499 | −0.172250 | − | 0.985053i | \(-0.555104\pi\) | ||||
−0.172250 | + | 0.985053i | \(0.555104\pi\) | |||||||
\(432\) | 7.23747e16 | 0.535726 | ||||||||
\(433\) | −1.55194e17 | −1.13163 | −0.565814 | − | 0.824533i | \(-0.691438\pi\) | ||||
−0.565814 | + | 0.824533i | \(0.691438\pi\) | |||||||
\(434\) | −5.77085e17 | −4.14531 | ||||||||
\(435\) | −5.38550e16 | −0.381106 | ||||||||
\(436\) | 4.07945e17 | 2.84406 | ||||||||
\(437\) | 3.95554e16 | 0.271692 | ||||||||
\(438\) | 7.07483e16 | 0.478778 | ||||||||
\(439\) | 2.33386e17 | 1.55617 | 0.778083 | − | 0.628162i | \(-0.216192\pi\) | ||||
0.778083 | + | 0.628162i | \(0.216192\pi\) | |||||||
\(440\) | −2.94117e17 | −1.93232 | ||||||||
\(441\) | 1.78262e16 | 0.115400 | ||||||||
\(442\) | −1.46455e16 | −0.0934241 | ||||||||
\(443\) | −1.78080e17 | −1.11942 | −0.559708 | − | 0.828690i | \(-0.689087\pi\) | ||||
−0.559708 | + | 0.828690i | \(0.689087\pi\) | |||||||
\(444\) | 1.55261e17 | 0.961775 | ||||||||
\(445\) | −3.82061e16 | −0.233235 | ||||||||
\(446\) | −3.19738e16 | −0.192361 | ||||||||
\(447\) | −2.52126e16 | −0.149492 | ||||||||
\(448\) | 3.35656e17 | 1.96150 | ||||||||
\(449\) | 7.79242e15 | 0.0448819 | 0.0224409 | − | 0.999748i | \(-0.492856\pi\) | ||||
0.0224409 | + | 0.999748i | \(0.492856\pi\) | |||||||
\(450\) | 6.86677e16 | 0.389826 | ||||||||
\(451\) | 1.43831e16 | 0.0804829 | ||||||||
\(452\) | 7.51099e17 | 4.14283 | ||||||||
\(453\) | −1.02029e17 | −0.554736 | ||||||||
\(454\) | 5.36550e17 | 2.87572 | ||||||||
\(455\) | −2.47131e16 | −0.130573 | ||||||||
\(456\) | 1.04475e17 | 0.544178 | ||||||||
\(457\) | −2.40369e17 | −1.23431 | −0.617155 | − | 0.786842i | \(-0.711715\pi\) | ||||
−0.617155 | + | 0.786842i | \(0.711715\pi\) | |||||||
\(458\) | −4.85844e17 | −2.45964 | ||||||||
\(459\) | 1.04735e16 | 0.0522767 | ||||||||
\(460\) | 2.54424e17 | 1.25208 | ||||||||
\(461\) | 2.59508e17 | 1.25920 | 0.629599 | − | 0.776920i | \(-0.283219\pi\) | ||||
0.629599 | + | 0.776920i | \(0.283219\pi\) | |||||||
\(462\) | 2.92646e17 | 1.40013 | ||||||||
\(463\) | 5.00655e16 | 0.236190 | 0.118095 | − | 0.993002i | \(-0.462321\pi\) | ||||
0.118095 | + | 0.993002i | \(0.462321\pi\) | |||||||
\(464\) | 6.44486e17 | 2.99810 | ||||||||
\(465\) | −1.47134e17 | −0.674948 | ||||||||
\(466\) | 2.77496e16 | 0.125530 | ||||||||
\(467\) | −2.14821e17 | −0.958332 | −0.479166 | − | 0.877724i | \(-0.659061\pi\) | ||||
−0.479166 | + | 0.877724i | \(0.659061\pi\) | |||||||
\(468\) | 3.48971e16 | 0.153529 | ||||||||
\(469\) | −1.82843e17 | −0.793333 | ||||||||
\(470\) | 1.14343e17 | 0.489296 | ||||||||
\(471\) | 6.66686e16 | 0.281375 | ||||||||
\(472\) | −8.83632e16 | −0.367831 | ||||||||
\(473\) | 1.39491e17 | 0.572728 | ||||||||
\(474\) | −1.99656e17 | −0.808580 | ||||||||
\(475\) | 5.21402e16 | 0.208288 | ||||||||
\(476\) | 2.00627e17 | 0.790576 | ||||||||
\(477\) | −1.52664e17 | −0.593425 | ||||||||
\(478\) | 2.65913e17 | 1.01967 | ||||||||
\(479\) | −3.43840e17 | −1.30069 | −0.650347 | − | 0.759637i | \(-0.725377\pi\) | ||||
−0.650347 | + | 0.759637i | \(0.725377\pi\) | |||||||
\(480\) | 2.26496e17 | 0.845262 | ||||||||
\(481\) | 3.31202e16 | 0.121941 | ||||||||
\(482\) | 2.59806e17 | 0.943721 | ||||||||
\(483\) | −1.52230e17 | −0.545563 | ||||||||
\(484\) | 1.73945e17 | 0.615061 | ||||||||
\(485\) | 8.06739e15 | 0.0281457 | ||||||||
\(486\) | −3.49050e16 | −0.120158 | ||||||||
\(487\) | 2.26271e17 | 0.768583 | 0.384291 | − | 0.923212i | \(-0.374446\pi\) | ||||
0.384291 | + | 0.923212i | \(0.374446\pi\) | |||||||
\(488\) | 1.05014e17 | 0.351981 | ||||||||
\(489\) | −1.50665e17 | −0.498315 | ||||||||
\(490\) | 1.21771e17 | 0.397437 | ||||||||
\(491\) | −2.91151e17 | −0.937754 | −0.468877 | − | 0.883264i | \(-0.655341\pi\) | ||||
−0.468877 | + | 0.883264i | \(0.655341\pi\) | |||||||
\(492\) | −3.28621e16 | −0.104453 | ||||||||
\(493\) | 9.32647e16 | 0.292558 | ||||||||
\(494\) | 3.70613e16 | 0.114735 | ||||||||
\(495\) | 7.46133e16 | 0.227972 | ||||||||
\(496\) | 1.76077e18 | 5.30971 | ||||||||
\(497\) | −5.33637e17 | −1.58829 | ||||||||
\(498\) | −2.66773e17 | −0.783702 | ||||||||
\(499\) | 1.03775e17 | 0.300911 | 0.150455 | − | 0.988617i | \(-0.451926\pi\) | ||||
0.150455 | + | 0.988617i | \(0.451926\pi\) | |||||||
\(500\) | 8.72511e17 | 2.49727 | ||||||||
\(501\) | −1.41825e16 | −0.0400690 | ||||||||
\(502\) | 8.60599e17 | 2.40008 | ||||||||
\(503\) | 2.61519e17 | 0.719965 | 0.359983 | − | 0.932959i | \(-0.382783\pi\) | ||||
0.359983 | + | 0.932959i | \(0.382783\pi\) | |||||||
\(504\) | −4.02075e17 | −1.09272 | ||||||||
\(505\) | 2.68141e17 | 0.719397 | ||||||||
\(506\) | −6.42692e17 | −1.70226 | ||||||||
\(507\) | −2.13352e17 | −0.557885 | ||||||||
\(508\) | 1.40671e18 | 3.63154 | ||||||||
\(509\) | 4.60629e17 | 1.17405 | 0.587024 | − | 0.809569i | \(-0.300299\pi\) | ||||
0.587024 | + | 0.809569i | \(0.300299\pi\) | |||||||
\(510\) | 7.15443e16 | 0.180040 | ||||||||
\(511\) | −2.06743e17 | −0.513682 | ||||||||
\(512\) | 4.95442e17 | 1.21545 | ||||||||
\(513\) | −2.65038e16 | −0.0642015 | ||||||||
\(514\) | −9.45787e17 | −2.26221 | ||||||||
\(515\) | 6.79599e16 | 0.160511 | ||||||||
\(516\) | −3.18706e17 | −0.743304 | ||||||||
\(517\) | −2.06510e17 | −0.475611 | ||||||||
\(518\) | −6.34584e17 | −1.44326 | ||||||||
\(519\) | 2.98684e17 | 0.670847 | ||||||||
\(520\) | 1.43349e17 | 0.317960 | ||||||||
\(521\) | −3.91504e17 | −0.857611 | −0.428806 | − | 0.903397i | \(-0.641066\pi\) | ||||
−0.428806 | + | 0.903397i | \(0.641066\pi\) | |||||||
\(522\) | −3.10824e17 | −0.672444 | ||||||||
\(523\) | −2.55045e17 | −0.544949 | −0.272475 | − | 0.962163i | \(-0.587842\pi\) | ||||
−0.272475 | + | 0.962163i | \(0.587842\pi\) | |||||||
\(524\) | 1.11027e18 | 2.34302 | ||||||||
\(525\) | −2.00663e17 | −0.418246 | ||||||||
\(526\) | −2.39571e17 | −0.493205 | ||||||||
\(527\) | 2.54804e17 | 0.518127 | ||||||||
\(528\) | −8.92901e17 | −1.79342 | ||||||||
\(529\) | −1.69717e17 | −0.336715 | ||||||||
\(530\) | −1.04285e18 | −2.04375 | ||||||||
\(531\) | 2.24165e16 | 0.0433963 | ||||||||
\(532\) | −5.07699e17 | −0.970913 | ||||||||
\(533\) | −7.01011e15 | −0.0132434 | ||||||||
\(534\) | −2.20506e17 | −0.411532 | ||||||||
\(535\) | 1.84747e17 | 0.340627 | ||||||||
\(536\) | 1.06059e18 | 1.93186 | ||||||||
\(537\) | 5.23823e17 | 0.942652 | ||||||||
\(538\) | −7.15487e17 | −1.27209 | ||||||||
\(539\) | −2.19925e17 | −0.386321 | ||||||||
\(540\) | −1.70475e17 | −0.295870 | ||||||||
\(541\) | 2.32630e17 | 0.398918 | 0.199459 | − | 0.979906i | \(-0.436081\pi\) | ||||
0.199459 | + | 0.979906i | \(0.436081\pi\) | |||||||
\(542\) | 4.79978e17 | 0.813254 | ||||||||
\(543\) | −3.60235e17 | −0.603097 | ||||||||
\(544\) | −3.92239e17 | −0.648870 | ||||||||
\(545\) | −4.25111e17 | −0.694904 | ||||||||
\(546\) | −1.42632e17 | −0.230390 | ||||||||
\(547\) | −6.70986e16 | −0.107102 | −0.0535508 | − | 0.998565i | \(-0.517054\pi\) | ||||
−0.0535508 | + | 0.998565i | \(0.517054\pi\) | |||||||
\(548\) | −7.85863e17 | −1.23958 | ||||||||
\(549\) | −2.66405e16 | −0.0415263 | ||||||||
\(550\) | −8.47167e17 | −1.30500 | ||||||||
\(551\) | −2.36012e17 | −0.359293 | ||||||||
\(552\) | 8.83015e17 | 1.32851 | ||||||||
\(553\) | 5.83441e17 | 0.867528 | ||||||||
\(554\) | −9.62922e17 | −1.41507 | ||||||||
\(555\) | −1.61794e17 | −0.234995 | ||||||||
\(556\) | −2.30723e18 | −3.31211 | ||||||||
\(557\) | −3.30516e17 | −0.468958 | −0.234479 | − | 0.972121i | \(-0.575338\pi\) | ||||
−0.234479 | + | 0.972121i | \(0.575338\pi\) | |||||||
\(558\) | −8.49186e17 | −1.19091 | ||||||||
\(559\) | −6.79860e16 | −0.0942416 | ||||||||
\(560\) | −1.44473e18 | −1.97954 | ||||||||
\(561\) | −1.29213e17 | −0.175004 | ||||||||
\(562\) | 1.16105e18 | 1.55440 | ||||||||
\(563\) | 5.93581e17 | 0.785553 | 0.392777 | − | 0.919634i | \(-0.371515\pi\) | ||||
0.392777 | + | 0.919634i | \(0.371515\pi\) | |||||||
\(564\) | 4.71829e17 | 0.617263 | ||||||||
\(565\) | −7.82705e17 | −1.01224 | ||||||||
\(566\) | 2.03259e18 | 2.59862 | ||||||||
\(567\) | 1.02001e17 | 0.128918 | ||||||||
\(568\) | 3.09537e18 | 3.86766 | ||||||||
\(569\) | 4.04856e17 | 0.500116 | 0.250058 | − | 0.968231i | \(-0.419550\pi\) | ||||
0.250058 | + | 0.968231i | \(0.419550\pi\) | |||||||
\(570\) | −1.81047e17 | −0.221109 | ||||||||
\(571\) | 3.47447e17 | 0.419521 | 0.209760 | − | 0.977753i | \(-0.432732\pi\) | ||||
0.209760 | + | 0.977753i | \(0.432732\pi\) | |||||||
\(572\) | −4.30533e17 | −0.513963 | ||||||||
\(573\) | −5.51757e17 | −0.651243 | ||||||||
\(574\) | 1.34314e17 | 0.156745 | ||||||||
\(575\) | 4.40685e17 | 0.508496 | ||||||||
\(576\) | 4.93921e17 | 0.563523 | ||||||||
\(577\) | −6.95052e17 | −0.784106 | −0.392053 | − | 0.919943i | \(-0.628235\pi\) | ||||
−0.392053 | + | 0.919943i | \(0.628235\pi\) | |||||||
\(578\) | 1.55524e18 | 1.73487 | ||||||||
\(579\) | 3.95205e16 | 0.0435925 | ||||||||
\(580\) | −1.51805e18 | −1.65579 | ||||||||
\(581\) | 7.79572e17 | 0.840836 | ||||||||
\(582\) | 4.65609e16 | 0.0496617 | ||||||||
\(583\) | 1.88344e18 | 1.98658 | ||||||||
\(584\) | 1.19922e18 | 1.25088 | ||||||||
\(585\) | −3.63655e16 | −0.0375126 | ||||||||
\(586\) | −1.99212e18 | −2.03227 | ||||||||
\(587\) | −9.96401e17 | −1.00528 | −0.502639 | − | 0.864496i | \(-0.667638\pi\) | ||||
−0.502639 | + | 0.864496i | \(0.667638\pi\) | |||||||
\(588\) | 5.02481e17 | 0.501380 | ||||||||
\(589\) | −6.44796e17 | −0.636316 | ||||||||
\(590\) | 1.53127e17 | 0.149456 | ||||||||
\(591\) | −2.71991e17 | −0.262565 | ||||||||
\(592\) | 1.93620e18 | 1.84867 | ||||||||
\(593\) | −1.57234e18 | −1.48488 | −0.742440 | − | 0.669912i | \(-0.766332\pi\) | ||||
−0.742440 | + | 0.669912i | \(0.766332\pi\) | |||||||
\(594\) | 4.30630e17 | 0.402247 | ||||||||
\(595\) | −2.09069e17 | −0.193165 | ||||||||
\(596\) | −7.10688e17 | −0.649499 | ||||||||
\(597\) | −2.20066e17 | −0.198939 | ||||||||
\(598\) | 3.13240e17 | 0.280104 | ||||||||
\(599\) | 2.19233e18 | 1.93924 | 0.969622 | − | 0.244609i | \(-0.0786595\pi\) | ||||
0.969622 | + | 0.244609i | \(0.0786595\pi\) | |||||||
\(600\) | 1.16395e18 | 1.01848 | ||||||||
\(601\) | −2.21514e18 | −1.91742 | −0.958710 | − | 0.284385i | \(-0.908211\pi\) | ||||
−0.958710 | + | 0.284385i | \(0.908211\pi\) | |||||||
\(602\) | 1.30262e18 | 1.11542 | ||||||||
\(603\) | −2.69056e17 | −0.227918 | ||||||||
\(604\) | −2.87598e18 | −2.41016 | ||||||||
\(605\) | −1.81265e17 | −0.150281 | ||||||||
\(606\) | 1.54757e18 | 1.26934 | ||||||||
\(607\) | 1.51399e18 | 1.22856 | 0.614280 | − | 0.789088i | \(-0.289447\pi\) | ||||
0.614280 | + | 0.789088i | \(0.289447\pi\) | |||||||
\(608\) | 9.92586e17 | 0.796883 | ||||||||
\(609\) | 9.08300e17 | 0.721468 | ||||||||
\(610\) | −1.81982e17 | −0.143016 | ||||||||
\(611\) | 1.00650e17 | 0.0782611 | ||||||||
\(612\) | 2.95224e17 | 0.227126 | ||||||||
\(613\) | −3.48013e17 | −0.264912 | −0.132456 | − | 0.991189i | \(-0.542286\pi\) | ||||
−0.132456 | + | 0.991189i | \(0.542286\pi\) | |||||||
\(614\) | −2.63211e18 | −1.98249 | ||||||||
\(615\) | 3.42449e16 | 0.0255216 | ||||||||
\(616\) | 4.96048e18 | 3.65805 | ||||||||
\(617\) | −3.95948e17 | −0.288925 | −0.144462 | − | 0.989510i | \(-0.546145\pi\) | ||||
−0.144462 | + | 0.989510i | \(0.546145\pi\) | |||||||
\(618\) | 3.92230e17 | 0.283215 | ||||||||
\(619\) | 5.67935e17 | 0.405797 | 0.202899 | − | 0.979200i | \(-0.434964\pi\) | ||||
0.202899 | + | 0.979200i | \(0.434964\pi\) | |||||||
\(620\) | −4.14739e18 | −2.93244 | ||||||||
\(621\) | −2.24008e17 | −0.156736 | ||||||||
\(622\) | 3.70088e17 | 0.256252 | ||||||||
\(623\) | 6.44371e17 | 0.441534 | ||||||||
\(624\) | 4.35188e17 | 0.295106 | ||||||||
\(625\) | 2.11478e16 | 0.0141920 | ||||||||
\(626\) | 3.62698e18 | 2.40886 | ||||||||
\(627\) | 3.26983e17 | 0.214924 | ||||||||
\(628\) | 1.87924e18 | 1.22249 | ||||||||
\(629\) | 2.80191e17 | 0.180395 | ||||||||
\(630\) | 6.96766e17 | 0.443990 | ||||||||
\(631\) | −1.34988e18 | −0.851344 | −0.425672 | − | 0.904878i | \(-0.639962\pi\) | ||||
−0.425672 | + | 0.904878i | \(0.639962\pi\) | |||||||
\(632\) | −3.38426e18 | −2.11253 | ||||||||
\(633\) | 1.36642e18 | 0.844228 | ||||||||
\(634\) | −9.95617e17 | −0.608853 | ||||||||
\(635\) | −1.46590e18 | −0.887312 | ||||||||
\(636\) | −4.30325e18 | −2.57825 | ||||||||
\(637\) | 1.07189e17 | 0.0635686 | ||||||||
\(638\) | 3.83470e18 | 2.25111 | ||||||||
\(639\) | −7.85251e17 | −0.456302 | ||||||||
\(640\) | 8.28776e17 | 0.476724 | ||||||||
\(641\) | −2.93146e18 | −1.66920 | −0.834598 | − | 0.550859i | \(-0.814300\pi\) | ||||
−0.834598 | + | 0.550859i | \(0.814300\pi\) | |||||||
\(642\) | 1.06627e18 | 0.601021 | ||||||||
\(643\) | −2.95486e18 | −1.64879 | −0.824397 | − | 0.566013i | \(-0.808485\pi\) | ||||
−0.824397 | + | 0.566013i | \(0.808485\pi\) | |||||||
\(644\) | −4.29103e18 | −2.37030 | ||||||||
\(645\) | 3.32117e17 | 0.181615 | ||||||||
\(646\) | 3.13533e17 | 0.169735 | ||||||||
\(647\) | 1.50205e18 | 0.805021 | 0.402510 | − | 0.915415i | \(-0.368138\pi\) | ||||
0.402510 | + | 0.915415i | \(0.368138\pi\) | |||||||
\(648\) | −5.91657e17 | −0.313930 | ||||||||
\(649\) | −2.76557e17 | −0.145276 | ||||||||
\(650\) | 4.12898e17 | 0.214737 | ||||||||
\(651\) | 2.48152e18 | 1.27774 | ||||||||
\(652\) | −4.24691e18 | −2.16503 | ||||||||
\(653\) | −2.58043e18 | −1.30243 | −0.651217 | − | 0.758892i | \(-0.725741\pi\) | ||||
−0.651217 | + | 0.758892i | \(0.725741\pi\) | |||||||
\(654\) | −2.45353e18 | −1.22613 | ||||||||
\(655\) | −1.15699e18 | −0.572481 | ||||||||
\(656\) | −4.09811e17 | −0.200775 | ||||||||
\(657\) | −3.04224e17 | −0.147577 | ||||||||
\(658\) | −1.92846e18 | −0.926280 | ||||||||
\(659\) | −1.84356e18 | −0.876804 | −0.438402 | − | 0.898779i | \(-0.644455\pi\) | ||||
−0.438402 | + | 0.898779i | \(0.644455\pi\) | |||||||
\(660\) | 2.10318e18 | 0.990471 | ||||||||
\(661\) | −1.41603e18 | −0.660334 | −0.330167 | − | 0.943922i | \(-0.607105\pi\) | ||||
−0.330167 | + | 0.943922i | \(0.607105\pi\) | |||||||
\(662\) | 9.77538e17 | 0.451395 | ||||||||
\(663\) | 6.29769e16 | 0.0287967 | ||||||||
\(664\) | −4.52193e18 | −2.04753 | ||||||||
\(665\) | 5.29062e17 | 0.237228 | ||||||||
\(666\) | −9.33796e17 | −0.414638 | ||||||||
\(667\) | −1.99476e18 | −0.877147 | ||||||||
\(668\) | −3.99774e17 | −0.174088 | ||||||||
\(669\) | 1.37490e17 | 0.0592927 | ||||||||
\(670\) | −1.83792e18 | −0.784946 | ||||||||
\(671\) | 3.28670e17 | 0.139016 | ||||||||
\(672\) | −3.81999e18 | −1.60016 | ||||||||
\(673\) | 1.59678e18 | 0.662439 | 0.331220 | − | 0.943554i | \(-0.392540\pi\) | ||||
0.331220 | + | 0.943554i | \(0.392540\pi\) | |||||||
\(674\) | 2.26552e18 | 0.930846 | ||||||||
\(675\) | −2.95277e17 | −0.120159 | ||||||||
\(676\) | −6.01391e18 | −2.42384 | ||||||||
\(677\) | 1.26442e18 | 0.504737 | 0.252368 | − | 0.967631i | \(-0.418791\pi\) | ||||
0.252368 | + | 0.967631i | \(0.418791\pi\) | |||||||
\(678\) | −4.51738e18 | −1.78605 | ||||||||
\(679\) | −1.36062e17 | −0.0532822 | ||||||||
\(680\) | 1.21271e18 | 0.470380 | ||||||||
\(681\) | −2.30721e18 | −0.886403 | ||||||||
\(682\) | 1.04766e19 | 3.98677 | ||||||||
\(683\) | 2.94317e18 | 1.10938 | 0.554691 | − | 0.832056i | \(-0.312836\pi\) | ||||
0.554691 | + | 0.832056i | \(0.312836\pi\) | |||||||
\(684\) | −7.47083e17 | −0.278936 | ||||||||
\(685\) | 8.18932e17 | 0.302872 | ||||||||
\(686\) | 3.87847e18 | 1.42087 | ||||||||
\(687\) | 2.08917e18 | 0.758150 | ||||||||
\(688\) | −3.97446e18 | −1.42874 | ||||||||
\(689\) | −9.17965e17 | −0.326890 | ||||||||
\(690\) | −1.53020e18 | −0.539795 | ||||||||
\(691\) | 4.80100e18 | 1.67774 | 0.838870 | − | 0.544333i | \(-0.183217\pi\) | ||||
0.838870 | + | 0.544333i | \(0.183217\pi\) | |||||||
\(692\) | 8.41923e18 | 2.91462 | ||||||||
\(693\) | −1.25840e18 | −0.431572 | ||||||||
\(694\) | 8.18622e17 | 0.278129 | ||||||||
\(695\) | 2.40432e18 | 0.809265 | ||||||||
\(696\) | −5.26862e18 | −1.75686 | ||||||||
\(697\) | −5.93045e16 | −0.0195918 | ||||||||
\(698\) | −5.43660e18 | −1.77937 | ||||||||
\(699\) | −1.19326e17 | −0.0386931 | ||||||||
\(700\) | −5.65624e18 | −1.81715 | ||||||||
\(701\) | 2.27265e18 | 0.723378 | 0.361689 | − | 0.932299i | \(-0.382200\pi\) | ||||
0.361689 | + | 0.932299i | \(0.382200\pi\) | |||||||
\(702\) | −2.09884e17 | −0.0661892 | ||||||||
\(703\) | −7.09042e17 | −0.221545 | ||||||||
\(704\) | −6.09361e18 | −1.88648 | ||||||||
\(705\) | −4.91683e17 | −0.150819 | ||||||||
\(706\) | 9.51034e18 | 2.89045 | ||||||||
\(707\) | −4.52236e18 | −1.36188 | ||||||||
\(708\) | 6.31871e17 | 0.188544 | ||||||||
\(709\) | −4.95978e18 | −1.46643 | −0.733216 | − | 0.679996i | \(-0.761982\pi\) | ||||
−0.733216 | + | 0.679996i | \(0.761982\pi\) | |||||||
\(710\) | −5.36405e18 | −1.57150 | ||||||||
\(711\) | 8.58538e17 | 0.249234 | ||||||||
\(712\) | −3.73769e18 | −1.07519 | ||||||||
\(713\) | −5.44977e18 | −1.55345 | ||||||||
\(714\) | −1.20664e18 | −0.340831 | ||||||||
\(715\) | 4.48649e17 | 0.125579 | ||||||||
\(716\) | 1.47654e19 | 4.09553 | ||||||||
\(717\) | −1.14345e18 | −0.314299 | ||||||||
\(718\) | 5.99262e18 | 1.63233 | ||||||||
\(719\) | 8.04577e17 | 0.217185 | 0.108592 | − | 0.994086i | \(-0.465366\pi\) | ||||
0.108592 | + | 0.994086i | \(0.465366\pi\) | |||||||
\(720\) | −2.12593e18 | −0.568705 | ||||||||
\(721\) | −1.14619e18 | −0.303862 | ||||||||
\(722\) | 6.33589e18 | 1.66462 | ||||||||
\(723\) | −1.11719e18 | −0.290889 | ||||||||
\(724\) | −1.01542e19 | −2.62027 | ||||||||
\(725\) | −2.62940e18 | −0.672449 | ||||||||
\(726\) | −1.04617e18 | −0.265164 | ||||||||
\(727\) | −2.49801e18 | −0.627509 | −0.313755 | − | 0.949504i | \(-0.601587\pi\) | ||||
−0.313755 | + | 0.949504i | \(0.601587\pi\) | |||||||
\(728\) | −2.41767e18 | −0.601926 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | −2.07815e18 | −0.508252 | ||||||||
\(731\) | −5.75151e17 | −0.139418 | ||||||||
\(732\) | −7.50938e17 | −0.180419 | ||||||||
\(733\) | −4.59618e18 | −1.09451 | −0.547256 | − | 0.836965i | \(-0.684328\pi\) | ||||
−0.547256 | + | 0.836965i | \(0.684328\pi\) | |||||||
\(734\) | −7.80801e18 | −1.84296 | ||||||||
\(735\) | −5.23625e17 | −0.122505 | ||||||||
\(736\) | 8.38927e18 | 1.94544 | ||||||||
\(737\) | 3.31939e18 | 0.762992 | ||||||||
\(738\) | 1.97644e17 | 0.0450317 | ||||||||
\(739\) | −4.80740e18 | −1.08573 | −0.542864 | − | 0.839820i | \(-0.682660\pi\) | ||||
−0.542864 | + | 0.839820i | \(0.682660\pi\) | |||||||
\(740\) | −4.56063e18 | −1.02098 | ||||||||
\(741\) | −1.59367e17 | −0.0353655 | ||||||||
\(742\) | 1.75883e19 | 3.86899 | ||||||||
\(743\) | −9.31952e17 | −0.203220 | −0.101610 | − | 0.994824i | \(-0.532399\pi\) | ||||
−0.101610 | + | 0.994824i | \(0.532399\pi\) | |||||||
\(744\) | −1.43941e19 | −3.11143 | ||||||||
\(745\) | 7.40593e17 | 0.158695 | ||||||||
\(746\) | 1.54743e19 | 3.28706 | ||||||||
\(747\) | 1.14715e18 | 0.241566 | ||||||||
\(748\) | −3.64224e18 | −0.760340 | ||||||||
\(749\) | −3.11589e18 | −0.644837 | ||||||||
\(750\) | −5.24759e18 | −1.07662 | ||||||||
\(751\) | −4.00906e18 | −0.815422 | −0.407711 | − | 0.913111i | \(-0.633673\pi\) | ||||
−0.407711 | + | 0.913111i | \(0.633673\pi\) | |||||||
\(752\) | 5.88400e18 | 1.18647 | ||||||||
\(753\) | −3.70065e18 | −0.739794 | ||||||||
\(754\) | −1.86898e18 | −0.370417 | ||||||||
\(755\) | 2.99700e18 | 0.588886 | ||||||||
\(756\) | 2.87517e18 | 0.560108 | ||||||||
\(757\) | −3.00730e18 | −0.580835 | −0.290418 | − | 0.956900i | \(-0.593794\pi\) | ||||
−0.290418 | + | 0.956900i | \(0.593794\pi\) | |||||||
\(758\) | 3.52753e18 | 0.675493 | ||||||||
\(759\) | 2.76363e18 | 0.524697 | ||||||||
\(760\) | −3.06884e18 | −0.577678 | ||||||||
\(761\) | 7.28236e18 | 1.35916 | 0.679582 | − | 0.733600i | \(-0.262161\pi\) | ||||
0.679582 | + | 0.733600i | \(0.262161\pi\) | |||||||
\(762\) | −8.46046e18 | −1.56562 | ||||||||
\(763\) | 7.16977e18 | 1.31551 | ||||||||
\(764\) | −1.55528e19 | −2.82945 | ||||||||
\(765\) | −3.07647e17 | −0.0554949 | ||||||||
\(766\) | 7.02891e18 | 1.25719 | ||||||||
\(767\) | 1.34790e17 | 0.0239049 | ||||||||
\(768\) | −7.67071e17 | −0.134892 | ||||||||
\(769\) | −2.34981e18 | −0.409744 | −0.204872 | − | 0.978789i | \(-0.565678\pi\) | ||||
−0.204872 | + | 0.978789i | \(0.565678\pi\) | |||||||
\(770\) | −8.59614e18 | −1.48633 | ||||||||
\(771\) | 4.06697e18 | 0.697296 | ||||||||
\(772\) | 1.11399e18 | 0.189396 | ||||||||
\(773\) | −5.57007e18 | −0.939061 | −0.469530 | − | 0.882916i | \(-0.655577\pi\) | ||||
−0.469530 | + | 0.882916i | \(0.655577\pi\) | |||||||
\(774\) | 1.91681e18 | 0.320452 | ||||||||
\(775\) | −7.18364e18 | −1.19092 | ||||||||
\(776\) | 7.89229e17 | 0.129748 | ||||||||
\(777\) | 2.72877e18 | 0.444867 | ||||||||
\(778\) | −2.12111e19 | −3.42922 | ||||||||
\(779\) | 1.50074e17 | 0.0240609 | ||||||||
\(780\) | −1.02506e18 | −0.162981 | ||||||||
\(781\) | 9.68780e18 | 1.52754 | ||||||||
\(782\) | 2.64996e18 | 0.414377 | ||||||||
\(783\) | 1.33657e18 | 0.207272 | ||||||||
\(784\) | 6.26625e18 | 0.963725 | ||||||||
\(785\) | −1.95832e18 | −0.298697 | ||||||||
\(786\) | −6.67757e18 | −1.01012 | ||||||||
\(787\) | −9.32424e18 | −1.39887 | −0.699435 | − | 0.714696i | \(-0.746565\pi\) | ||||
−0.699435 | + | 0.714696i | \(0.746565\pi\) | |||||||
\(788\) | −7.66683e18 | −1.14076 | ||||||||
\(789\) | 1.03018e18 | 0.152024 | ||||||||
\(790\) | 5.86467e18 | 0.858357 | ||||||||
\(791\) | 1.32008e19 | 1.91626 | ||||||||
\(792\) | 7.29939e18 | 1.05093 | ||||||||
\(793\) | −1.60189e17 | −0.0228748 | ||||||||
\(794\) | 3.11825e18 | 0.441650 | ||||||||
\(795\) | 4.48433e18 | 0.629957 | ||||||||
\(796\) | −6.20318e18 | −0.864330 | ||||||||
\(797\) | −8.06553e18 | −1.11469 | −0.557345 | − | 0.830281i | \(-0.688180\pi\) | ||||
−0.557345 | + | 0.830281i | \(0.688180\pi\) | |||||||
\(798\) | 3.05348e18 | 0.418578 | ||||||||
\(799\) | 8.51484e17 | 0.115777 | ||||||||
\(800\) | 1.10583e19 | 1.49144 | ||||||||
\(801\) | 9.48197e17 | 0.126849 | ||||||||
\(802\) | 2.66458e19 | 3.53586 | ||||||||
\(803\) | 3.75327e18 | 0.494037 | ||||||||
\(804\) | −7.58408e18 | −0.990236 | ||||||||
\(805\) | 4.47160e18 | 0.579148 | ||||||||
\(806\) | −5.10615e18 | −0.656017 | ||||||||
\(807\) | 3.07666e18 | 0.392104 | ||||||||
\(808\) | 2.62321e19 | 3.31634 | ||||||||
\(809\) | −4.86012e18 | −0.609511 | −0.304756 | − | 0.952431i | \(-0.598575\pi\) | ||||
−0.304756 | + | 0.952431i | \(0.598575\pi\) | |||||||
\(810\) | 1.02530e18 | 0.127555 | ||||||||
\(811\) | 9.37387e18 | 1.15687 | 0.578433 | − | 0.815730i | \(-0.303664\pi\) | ||||
0.578433 | + | 0.815730i | \(0.303664\pi\) | |||||||
\(812\) | 2.56030e19 | 3.13456 | ||||||||
\(813\) | −2.06395e18 | −0.250675 | ||||||||
\(814\) | 1.15204e19 | 1.38807 | ||||||||
\(815\) | 4.42562e18 | 0.528992 | ||||||||
\(816\) | 3.68163e18 | 0.436570 | ||||||||
\(817\) | 1.45546e18 | 0.171220 | ||||||||
\(818\) | −6.51619e18 | −0.760497 | ||||||||
\(819\) | 6.13328e17 | 0.0710146 | ||||||||
\(820\) | 9.65289e17 | 0.110884 | ||||||||
\(821\) | 7.55050e18 | 0.860489 | 0.430245 | − | 0.902712i | \(-0.358427\pi\) | ||||
0.430245 | + | 0.902712i | \(0.358427\pi\) | |||||||
\(822\) | 4.72646e18 | 0.534403 | ||||||||
\(823\) | 2.08667e18 | 0.234075 | 0.117038 | − | 0.993127i | \(-0.462660\pi\) | ||||
0.117038 | + | 0.993127i | \(0.462660\pi\) | |||||||
\(824\) | 6.64849e18 | 0.739939 | ||||||||
\(825\) | 3.64289e18 | 0.402250 | ||||||||
\(826\) | −2.58258e18 | −0.282933 | ||||||||
\(827\) | −1.53200e19 | −1.66523 | −0.832613 | − | 0.553856i | \(-0.813156\pi\) | ||||
−0.832613 | + | 0.553856i | \(0.813156\pi\) | |||||||
\(828\) | −6.31429e18 | −0.680969 | ||||||||
\(829\) | 1.39829e19 | 1.49621 | 0.748107 | − | 0.663578i | \(-0.230963\pi\) | ||||
0.748107 | + | 0.663578i | \(0.230963\pi\) | |||||||
\(830\) | 7.83616e18 | 0.831947 | ||||||||
\(831\) | 4.14065e18 | 0.436176 | ||||||||
\(832\) | 2.96994e18 | 0.310418 | ||||||||
\(833\) | 9.06800e17 | 0.0940413 | ||||||||
\(834\) | 1.38765e19 | 1.42791 | ||||||||
\(835\) | 4.16597e17 | 0.0425357 | ||||||||
\(836\) | 9.21691e18 | 0.933780 | ||||||||
\(837\) | 3.65157e18 | 0.367083 | ||||||||
\(838\) | 3.20129e19 | 3.19329 | ||||||||
\(839\) | −1.92209e18 | −0.190249 | −0.0951244 | − | 0.995465i | \(-0.530325\pi\) | ||||
−0.0951244 | + | 0.995465i | \(0.530325\pi\) | |||||||
\(840\) | 1.18105e19 | 1.15999 | ||||||||
\(841\) | 1.64134e18 | 0.159965 | ||||||||
\(842\) | 7.90133e18 | 0.764137 | ||||||||
\(843\) | −4.99261e18 | −0.479124 | ||||||||
\(844\) | 3.85163e19 | 3.66791 | ||||||||
\(845\) | 6.26697e18 | 0.592228 | ||||||||
\(846\) | −2.83775e18 | −0.266113 | ||||||||
\(847\) | 3.05715e18 | 0.284495 | ||||||||
\(848\) | −5.36642e19 | −4.95577 | ||||||||
\(849\) | −8.74032e18 | −0.800990 | ||||||||
\(850\) | 3.49305e18 | 0.317674 | ||||||||
\(851\) | −5.99277e18 | −0.540861 | ||||||||
\(852\) | −2.21345e19 | −1.98249 | ||||||||
\(853\) | −1.89443e19 | −1.68387 | −0.841937 | − | 0.539575i | \(-0.818585\pi\) | ||||
−0.841937 | + | 0.539575i | \(0.818585\pi\) | |||||||
\(854\) | 3.06924e18 | 0.270741 | ||||||||
\(855\) | 7.78519e17 | 0.0681537 | ||||||||
\(856\) | 1.80738e19 | 1.57025 | ||||||||
\(857\) | 7.63925e18 | 0.658681 | 0.329341 | − | 0.944211i | \(-0.393174\pi\) | ||||
0.329341 | + | 0.944211i | \(0.393174\pi\) | |||||||
\(858\) | 2.58938e18 | 0.221579 | ||||||||
\(859\) | 2.24819e19 | 1.90931 | 0.954656 | − | 0.297712i | \(-0.0962235\pi\) | ||||
0.954656 | + | 0.297712i | \(0.0962235\pi\) | |||||||
\(860\) | 9.36163e18 | 0.789063 | ||||||||
\(861\) | −5.77563e17 | −0.0483146 | ||||||||
\(862\) | 7.77214e18 | 0.645273 | ||||||||
\(863\) | −8.51970e18 | −0.702028 | −0.351014 | − | 0.936370i | \(-0.614163\pi\) | ||||
−0.351014 | + | 0.936370i | \(0.614163\pi\) | |||||||
\(864\) | −5.62115e18 | −0.459712 | ||||||||
\(865\) | −8.77350e18 | −0.712145 | ||||||||
\(866\) | 2.63102e19 | 2.11962 | ||||||||
\(867\) | −6.68766e18 | −0.534749 | ||||||||
\(868\) | 6.99485e19 | 5.55137 | ||||||||
\(869\) | −1.05920e19 | −0.834349 | ||||||||
\(870\) | 9.13012e18 | 0.713841 | ||||||||
\(871\) | −1.61783e18 | −0.125549 | ||||||||
\(872\) | −4.15884e19 | −3.20343 | ||||||||
\(873\) | −2.00216e17 | −0.0153076 | ||||||||
\(874\) | −6.70589e18 | −0.508900 | ||||||||
\(875\) | 1.53347e19 | 1.15511 | ||||||||
\(876\) | −8.57540e18 | −0.641177 | ||||||||
\(877\) | −2.01059e19 | −1.49220 | −0.746099 | − | 0.665835i | \(-0.768076\pi\) | ||||
−0.746099 | + | 0.665835i | \(0.768076\pi\) | |||||||
\(878\) | −3.95663e19 | −2.91482 | ||||||||
\(879\) | 8.56630e18 | 0.626420 | ||||||||
\(880\) | 2.62280e19 | 1.90383 | ||||||||
\(881\) | −1.11063e18 | −0.0800249 | −0.0400125 | − | 0.999199i | \(-0.512740\pi\) | ||||
−0.0400125 | + | 0.999199i | \(0.512740\pi\) | |||||||
\(882\) | −3.02210e18 | −0.216154 | ||||||||
\(883\) | 4.92034e18 | 0.349342 | 0.174671 | − | 0.984627i | \(-0.444114\pi\) | ||||
0.174671 | + | 0.984627i | \(0.444114\pi\) | |||||||
\(884\) | 1.77518e18 | 0.125113 | ||||||||
\(885\) | −6.58459e17 | −0.0460678 | ||||||||
\(886\) | 3.01902e19 | 2.09675 | ||||||||
\(887\) | −2.53874e19 | −1.75031 | −0.875155 | − | 0.483842i | \(-0.839241\pi\) | ||||
−0.875155 | + | 0.483842i | \(0.839241\pi\) | |||||||
\(888\) | −1.58283e19 | −1.08330 | ||||||||
\(889\) | 2.47234e19 | 1.67976 | ||||||||
\(890\) | 6.47714e18 | 0.436866 | ||||||||
\(891\) | −1.85175e18 | −0.123987 | ||||||||
\(892\) | 3.87554e18 | 0.257609 | ||||||||
\(893\) | −2.15473e18 | −0.142187 | ||||||||
\(894\) | 4.27433e18 | 0.280010 | ||||||||
\(895\) | −1.53867e19 | −1.00068 | ||||||||
\(896\) | −1.39778e19 | −0.902481 | ||||||||
\(897\) | −1.34696e18 | −0.0863383 | ||||||||
\(898\) | −1.32106e18 | −0.0840671 | ||||||||
\(899\) | 3.25167e19 | 2.05432 | ||||||||
\(900\) | −8.32321e18 | −0.522053 | ||||||||
\(901\) | −7.76584e18 | −0.483590 | ||||||||
\(902\) | −2.43838e18 | −0.150751 | ||||||||
\(903\) | −5.60136e18 | −0.343814 | ||||||||
\(904\) | −7.65717e19 | −4.66631 | ||||||||
\(905\) | 1.05815e19 | 0.640224 | ||||||||
\(906\) | 1.72972e19 | 1.03906 | ||||||||
\(907\) | −8.19639e18 | −0.488850 | −0.244425 | − | 0.969668i | \(-0.578599\pi\) | ||||
−0.244425 | + | 0.969668i | \(0.578599\pi\) | |||||||
\(908\) | −6.50352e19 | −3.85115 | ||||||||
\(909\) | −6.65470e18 | −0.391258 | ||||||||
\(910\) | 4.18965e18 | 0.244573 | ||||||||
\(911\) | 4.68189e18 | 0.271364 | 0.135682 | − | 0.990752i | \(-0.456677\pi\) | ||||
0.135682 | + | 0.990752i | \(0.456677\pi\) | |||||||
\(912\) | −9.31659e18 | −0.536155 | ||||||||
\(913\) | −1.41526e19 | −0.808678 | ||||||||
\(914\) | 4.07502e19 | 2.31195 | ||||||||
\(915\) | 7.82537e17 | 0.0440827 | ||||||||
\(916\) | 5.88891e19 | 3.29393 | ||||||||
\(917\) | 1.95134e19 | 1.08376 | ||||||||
\(918\) | −1.77558e18 | −0.0979182 | ||||||||
\(919\) | −8.45116e18 | −0.462770 | −0.231385 | − | 0.972862i | \(-0.574326\pi\) | ||||
−0.231385 | + | 0.972862i | \(0.574326\pi\) | |||||||
\(920\) | −2.59376e19 | −1.41029 | ||||||||
\(921\) | 1.13183e19 | 0.611075 | ||||||||
\(922\) | −4.39947e19 | −2.35857 | ||||||||
\(923\) | −4.72170e18 | −0.251355 | ||||||||
\(924\) | −3.54716e19 | −1.87505 | ||||||||
\(925\) | −7.89940e18 | −0.414642 | ||||||||
\(926\) | −8.48767e18 | −0.442402 | ||||||||
\(927\) | −1.68662e18 | −0.0872972 | ||||||||
\(928\) | −5.00556e19 | −2.57271 | ||||||||
\(929\) | 1.21984e19 | 0.622587 | 0.311293 | − | 0.950314i | \(-0.399238\pi\) | ||||
0.311293 | + | 0.950314i | \(0.399238\pi\) | |||||||
\(930\) | 2.49439e19 | 1.26423 | ||||||||
\(931\) | −2.29471e18 | −0.115493 | ||||||||
\(932\) | −3.36353e18 | −0.168109 | ||||||||
\(933\) | −1.59141e18 | −0.0789862 | ||||||||
\(934\) | 3.64188e19 | 1.79503 | ||||||||
\(935\) | 3.79550e18 | 0.185778 | ||||||||
\(936\) | −3.55763e18 | −0.172929 | ||||||||
\(937\) | −3.13677e19 | −1.51417 | −0.757086 | − | 0.653315i | \(-0.773378\pi\) | ||||
−0.757086 | + | 0.653315i | \(0.773378\pi\) | |||||||
\(938\) | 3.09977e19 | 1.48597 | ||||||||
\(939\) | −1.55963e19 | −0.742500 | ||||||||
\(940\) | −1.38595e19 | −0.655262 | ||||||||
\(941\) | 2.61583e19 | 1.22822 | 0.614111 | − | 0.789220i | \(-0.289515\pi\) | ||||
0.614111 | + | 0.789220i | \(0.289515\pi\) | |||||||
\(942\) | −1.13024e19 | −0.527037 | ||||||||
\(943\) | 1.26841e18 | 0.0587401 | ||||||||
\(944\) | 7.87982e18 | 0.362408 | ||||||||
\(945\) | −2.99615e18 | −0.136854 | ||||||||
\(946\) | −2.36481e19 | −1.07276 | ||||||||
\(947\) | 8.37461e18 | 0.377303 | 0.188651 | − | 0.982044i | \(-0.439588\pi\) | ||||
0.188651 | + | 0.982044i | \(0.439588\pi\) | |||||||
\(948\) | 2.42003e19 | 1.08285 | ||||||||
\(949\) | −1.82930e18 | −0.0812931 | ||||||||
\(950\) | −8.83939e18 | −0.390139 | ||||||||
\(951\) | 4.28124e18 | 0.187671 | ||||||||
\(952\) | −2.04531e19 | −0.890471 | ||||||||
\(953\) | −2.89783e19 | −1.25305 | −0.626525 | − | 0.779401i | \(-0.715524\pi\) | ||||
−0.626525 | + | 0.779401i | \(0.715524\pi\) | |||||||
\(954\) | 2.58813e19 | 1.11153 | ||||||||
\(955\) | 1.62073e19 | 0.691334 | ||||||||
\(956\) | −3.22313e19 | −1.36553 | ||||||||
\(957\) | −1.64896e19 | −0.693875 | ||||||||
\(958\) | 5.82916e19 | 2.43630 | ||||||||
\(959\) | −1.38118e19 | −0.573363 | ||||||||
\(960\) | −1.45084e19 | −0.598214 | ||||||||
\(961\) | 6.44197e19 | 2.63825 | ||||||||
\(962\) | −5.61491e18 | −0.228404 | ||||||||
\(963\) | −4.58505e18 | −0.185257 | ||||||||
\(964\) | −3.14911e19 | −1.26383 | ||||||||
\(965\) | −1.16087e18 | −0.0462761 | ||||||||
\(966\) | 2.58078e19 | 1.02188 | ||||||||
\(967\) | −4.09484e19 | −1.61052 | −0.805258 | − | 0.592924i | \(-0.797973\pi\) | ||||
−0.805258 | + | 0.592924i | \(0.797973\pi\) | |||||||
\(968\) | −1.77331e19 | −0.692778 | ||||||||
\(969\) | −1.34822e18 | −0.0523186 | ||||||||
\(970\) | −1.36768e18 | −0.0527189 | ||||||||
\(971\) | −6.74802e18 | −0.258376 | −0.129188 | − | 0.991620i | \(-0.541237\pi\) | ||||
−0.129188 | + | 0.991620i | \(0.541237\pi\) | |||||||
\(972\) | 4.23084e18 | 0.160915 | ||||||||
\(973\) | −4.05504e19 | −1.53201 | ||||||||
\(974\) | −3.83600e19 | −1.43961 | ||||||||
\(975\) | −1.77550e18 | −0.0661897 | ||||||||
\(976\) | −9.36466e18 | −0.346791 | ||||||||
\(977\) | 4.29813e19 | 1.58112 | 0.790560 | − | 0.612384i | \(-0.209789\pi\) | ||||
0.790560 | + | 0.612384i | \(0.209789\pi\) | |||||||
\(978\) | 2.55424e19 | 0.933382 | ||||||||
\(979\) | −1.16981e19 | −0.424647 | ||||||||
\(980\) | −1.47598e19 | −0.532245 | ||||||||
\(981\) | 1.05504e19 | 0.377937 | ||||||||
\(982\) | 4.93593e19 | 1.75648 | ||||||||
\(983\) | 3.22411e19 | 1.13976 | 0.569878 | − | 0.821729i | \(-0.306990\pi\) | ||||
0.569878 | + | 0.821729i | \(0.306990\pi\) | |||||||
\(984\) | 3.35017e18 | 0.117652 | ||||||||
\(985\) | 7.98945e18 | 0.278728 | ||||||||
\(986\) | −1.58113e19 | −0.547984 | ||||||||
\(987\) | 8.29255e18 | 0.285514 | ||||||||
\(988\) | −4.49220e18 | −0.153652 | ||||||||
\(989\) | 1.23014e19 | 0.418003 | ||||||||
\(990\) | −1.26493e19 | −0.427010 | ||||||||
\(991\) | −3.08700e18 | −0.103528 | −0.0517639 | − | 0.998659i | \(-0.516484\pi\) | ||||
−0.0517639 | + | 0.998659i | \(0.516484\pi\) | |||||||
\(992\) | −1.36754e20 | −4.55632 | ||||||||
\(993\) | −4.20350e18 | −0.139136 | ||||||||
\(994\) | 9.04681e19 | 2.97498 | ||||||||
\(995\) | 6.46421e18 | 0.211186 | ||||||||
\(996\) | 3.23355e19 | 1.04953 | ||||||||
\(997\) | 4.33114e19 | 1.39664 | 0.698318 | − | 0.715787i | \(-0.253932\pi\) | ||||
0.698318 | + | 0.715787i | \(0.253932\pi\) | |||||||
\(998\) | −1.75931e19 | −0.563628 | ||||||||
\(999\) | 4.01541e18 | 0.127807 |
(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 | 177.14.a.a.1.1 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.14.a.a.1.1 | ✓ | 30 | 1.1 | even | 1 | trivial |