Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [84,12,Mod(5,84)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(84, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("84.5");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 84 = 2^{2} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 84.k (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(64.5408271670\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 5.7 | ||
Character | \(\chi\) | \(=\) | 84.5 |
Dual form | 84.12.k.b.17.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(43\) | \(73\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −293.330 | + | 301.836i | −0.696930 | + | 0.717140i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2288.66 | − | 3964.07i | 0.327526 | − | 0.567291i | −0.654495 | − | 0.756067i | \(-0.727119\pi\) |
0.982020 | + | 0.188776i | \(0.0604519\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 14878.7 | − | 41904.1i | 0.334600 | − | 0.942360i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5062.60 | − | 177075.i | −0.0285785 | − | 0.999592i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 602411. | − | 347802.i | 1.12780 | − | 0.651137i | 0.184421 | − | 0.982847i | \(-0.440959\pi\) |
0.943381 | + | 0.331710i | \(0.107626\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 801797.i | − | 0.598930i | −0.954107 | − | 0.299465i | \(-0.903192\pi\) | ||
0.954107 | − | 0.299465i | \(-0.0968082\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 525167. | + | 1.85358e6i | 0.178565 | + | 0.630244i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.69093e6 | − | 2.92878e6i | −0.288840 | − | 0.500285i | 0.684693 | − | 0.728831i | \(-0.259936\pi\) |
−0.973533 | + | 0.228546i | \(0.926603\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.34762e6 | + | 1.93275e6i | 0.310164 | + | 0.179073i | 0.647000 | − | 0.762490i | \(-0.276023\pi\) |
−0.336836 | + | 0.941563i | \(0.609357\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.28378e6 | + | 1.67826e7i | 0.442611 | + | 0.896714i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.01711e7 | − | 2.89663e7i | −1.62536 | − | 0.938405i | −0.985451 | − | 0.169958i | \(-0.945637\pi\) |
−0.639913 | − | 0.768447i | \(-0.721030\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.39382e7 | + | 2.41416e7i | 0.285454 | + | 0.494421i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.49325e7 | + | 5.04131e7i | 0.736764 | + | 0.676150i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.26218e8i | 1.14270i | 0.820707 | + | 0.571350i | \(0.193580\pi\) | ||||
−0.820707 | + | 0.571350i | \(0.806420\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.25812e7 | + | 7.26374e6i | −0.0789281 | + | 0.0455692i | −0.538945 | − | 0.842341i | \(-0.681177\pi\) |
0.460017 | + | 0.887910i | \(0.347843\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.17258e7 | + | 2.83850e8i | −0.319043 | + | 1.26259i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.32058e8 | − | 1.54884e8i | −0.425003 | − | 0.498463i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.28757e7 | − | 7.42629e7i | 0.101649 | − | 0.176061i | −0.810715 | − | 0.585441i | \(-0.800922\pi\) |
0.912364 | + | 0.409380i | \(0.134255\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.42011e8 | + | 2.35191e8i | 0.429517 | + | 0.417412i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.77955e7 | −0.0913882 | −0.0456941 | − | 0.998955i | \(-0.514550\pi\) | ||||
−0.0456941 | + | 0.998955i | \(0.514550\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.47763e8 | −0.153281 | −0.0766405 | − | 0.997059i | \(-0.524419\pi\) | ||||
−0.0766405 | + | 0.997059i | \(0.524419\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.13522e8 | − | 3.85194e8i | −0.576420 | − | 0.311180i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.13191e8 | + | 1.96052e8i | −0.0719901 | + | 0.124690i | −0.899773 | − | 0.436357i | \(-0.856268\pi\) |
0.827783 | + | 0.561048i | \(0.189602\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.53458e9 | − | 1.24696e9i | −0.776086 | − | 0.630627i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.38001e9 | + | 3.48714e8i | 0.560076 | + | 0.141525i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.20156e9 | − | 2.42577e9i | 1.38005 | − | 0.796770i | 0.387881 | − | 0.921709i | \(-0.373207\pi\) |
0.992164 | + | 0.124940i | \(0.0398737\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.18400e9i | − | 0.853056i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.56533e9 | + | 4.43499e8i | −0.344583 | + | 0.0976294i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.05171e9 | − | 5.28571e9i | −0.555721 | − | 0.962537i | −0.997847 | − | 0.0655841i | \(-0.979109\pi\) |
0.442126 | − | 0.896953i | \(-0.354224\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.23135e9 | − | 3.02032e9i | −0.793048 | − | 0.457866i | 0.0479866 | − | 0.998848i | \(-0.484720\pi\) |
−0.841034 | + | 0.540982i | \(0.818053\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.49547e9 | − | 2.42250e9i | −0.951538 | − | 0.307532i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.17838e9 | − | 1.83504e9i | −0.339768 | − | 0.196165i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.71415e9 | − | 6.43309e9i | −0.336084 | − | 0.582114i | 0.647609 | − | 0.761973i | \(-0.275769\pi\) |
−0.983692 | + | 0.179859i | \(0.942436\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.34597e10 | − | 6.64677e9i | 1.80573 | − | 0.511612i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.70389e10i | 1.12078i | 0.828230 | + | 0.560389i | \(0.189348\pi\) | ||||
−0.828230 | + | 0.560389i | \(0.810652\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.84429e9 | + | 5.68361e9i | −0.555788 | + | 0.320884i | −0.751453 | − | 0.659787i | \(-0.770647\pi\) |
0.195665 | + | 0.980671i | \(0.437313\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.13753e10 | − | 2.87441e9i | −0.553510 | − | 0.139866i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.61123e9 | − | 3.04183e10i | −0.236243 | − | 1.28067i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.28443e10 | + | 2.22470e10i | −0.469636 | + | 0.813434i | −0.999397 | − | 0.0347131i | \(-0.988948\pi\) |
0.529761 | + | 0.848147i | \(0.322282\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.13298e10 | + | 1.79292e9i | −0.998367 | + | 0.0571337i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.44662e9 | 0.179640 | 0.0898199 | − | 0.995958i | \(-0.471371\pi\) | ||||
0.0898199 | + | 0.995958i | \(0.471371\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.54798e10 | −0.378410 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.80971e10 | − | 3.70234e10i | −0.819475 | − | 0.796381i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.05174e10 | − | 1.82167e10i | 0.199648 | − | 0.345801i | −0.748766 | − | 0.662834i | \(-0.769353\pi\) |
0.948414 | + | 0.317034i | \(0.102687\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.35986e10 | − | 1.19297e10i | −0.564408 | − | 0.200402i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.49797e9 | − | 5.92812e9i | 0.0223279 | − | 0.0883610i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.53231e10 | − | 8.84679e9i | 0.203173 | − | 0.117302i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.27882e11i | − | 1.51205i | −0.654545 | − | 0.756023i | \(-0.727140\pi\) | ||
0.654545 | − | 0.756023i | \(-0.272860\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.46367e10 | − | 1.04911e11i | −0.683102 | − | 1.10873i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.01169e11 | + | 1.75230e11i | 0.957813 | + | 1.65898i | 0.727795 | + | 0.685795i | \(0.240545\pi\) |
0.230019 | + | 0.973186i | \(0.426121\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.84386e11 | − | 1.06456e11i | −1.56720 | − | 0.904823i | −0.996494 | − | 0.0836673i | \(-0.973337\pi\) |
−0.570705 | − | 0.821155i | \(-0.693330\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.54862e10 | + | 5.57217e9i | 0.653664 | + | 0.0426072i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.08969e10 | − | 1.20648e10i | −0.144036 | − | 0.0831594i | 0.426250 | − | 0.904605i | \(-0.359834\pi\) |
−0.570286 | + | 0.821446i | \(0.693168\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.92153e10 | − | 1.71846e11i | −0.617636 | − | 1.06978i | −0.989916 | − | 0.141657i | \(-0.954757\pi\) |
0.372279 | − | 0.928121i | \(-0.378576\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.83849e9 | + | 3.47249e10i | 0.0554182 | + | 0.195598i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 3.09273e11i | − | 1.57910i | −0.613683 | − | 0.789552i | \(-0.710313\pi\) | ||
0.613683 | − | 0.789552i | \(-0.289687\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.29649e11 | + | 1.32588e11i | −1.06470 | + | 0.614703i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.41978e11 | + | 4.05918e9i | −0.598686 | + | 0.0171165i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.47887e11 | + | 2.72805e10i | −0.568095 | + | 0.104796i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.92767e10 | − | 1.71952e11i | 0.347959 | − | 0.602682i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.98864e10 | − | 2.04631e10i | 0.0636911 | − | 0.0655381i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.51100e11 | 1.02903 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.09811e11 | −0.294936 | −0.147468 | − | 0.989067i | \(-0.547112\pi\) | ||||
−0.147468 | + | 0.989067i | \(0.547112\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.33431e10 | − | 4.46000e10i | 0.106826 | − | 0.109924i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.21561e10 | − | 5.56960e10i | 0.0728234 | − | 0.126134i | −0.827314 | − | 0.561739i | \(-0.810132\pi\) |
0.900138 | + | 0.435605i | \(0.143466\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.30798e11 | − | 1.11522e11i | 0.272532 | − | 0.232368i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.25563e11 | − | 1.02378e11i | 0.624883 | − | 0.196503i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.16235e11 | + | 2.98048e11i | −0.913869 | + | 0.527623i | −0.881674 | − | 0.471859i | \(-0.843583\pi\) |
−0.0321951 | + | 0.999482i | \(0.510250\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.33055e11i | 0.707884i | 0.935267 | + | 0.353942i | \(0.115159\pi\) | ||||
−0.935267 | + | 0.353942i | \(0.884841\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.59733e10 | − | 9.16729e10i | −0.0392485 | − | 0.138527i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.78867e11 | − | 4.83011e11i | −0.389986 | − | 0.675475i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.00336e11 | + | 2.88869e11i | 0.648243 | + | 0.374264i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.26512e11 | − | 9.74205e10i | 0.993125 | − | 0.117059i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.89454e11 | + | 2.24851e11i | 0.434442 | + | 0.250825i | 0.701237 | − | 0.712928i | \(-0.252631\pi\) |
−0.266795 | + | 0.963753i | \(0.585965\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.65731e11 | + | 1.49949e12i | 0.897449 | + | 1.55443i | 0.830745 | + | 0.556654i | \(0.187915\pi\) |
0.0667041 | + | 0.997773i | \(0.478752\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.10052e11 | + | 3.14249e11i | −0.491827 | + | 0.303019i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.64968e10i | 0.0597003i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.75857e11 | + | 2.17001e11i | −0.314467 | + | 0.181557i | −0.648924 | − | 0.760854i | \(-0.724780\pi\) |
0.334457 | + | 0.942411i | \(0.391447\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.00257e11 | + | 1.97973e12i | −0.390399 | + | 1.54498i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.96029e12 | + | 1.67139e12i | −1.42816 | + | 1.21769i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.62644e11 | + | 8.01323e11i | −0.314931 | + | 0.545476i | −0.979423 | − | 0.201819i | \(-0.935315\pi\) |
0.664492 | + | 0.747295i | \(0.268648\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.61044e11 | + | 9.33960e11i | 0.611760 | + | 0.594520i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.67140e12 | 0.995724 | 0.497862 | − | 0.867256i | \(-0.334119\pi\) | ||||
0.497862 | + | 0.867256i | \(0.334119\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.14928e12 | 0.641283 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.25293e11 | − | 6.02563e11i | 0.170136 | − | 0.315155i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.09424e12 | − | 1.89528e12i | 0.536859 | − | 0.929867i | −0.462212 | − | 0.886769i | \(-0.652944\pi\) |
0.999071 | − | 0.0430975i | \(-0.0137226\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.21901e12 | − | 2.24870e11i | 0.561435 | − | 0.103567i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.49057e12 | + | 6.29341e11i | 1.07757 | + | 0.272291i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.44064e11 | + | 2.56380e11i | −0.180615 | + | 0.104278i | −0.587582 | − | 0.809165i | \(-0.699920\pi\) |
0.406967 | + | 0.913443i | \(0.366587\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3.75396e12i | − | 1.43634i | −0.695866 | − | 0.718171i | \(-0.744979\pi\) | ||
0.695866 | − | 0.718171i | \(-0.255021\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.44615e12 | − | 6.93058e11i | 0.881053 | − | 0.249625i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.96255e11 | − | 3.39924e11i | −0.0665851 | − | 0.115329i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.03727e12 | − | 1.17622e12i | −0.651509 | − | 0.376149i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.92984e12 | − | 1.55181e12i | 0.883698 | − | 0.468057i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.52254e12 | − | 2.61109e12i | −1.28736 | − | 0.743256i | −0.309176 | − | 0.951005i | \(-0.600053\pi\) |
−0.978182 | + | 0.207749i | \(0.933386\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.68130e12 | + | 2.91209e12i | 0.451939 | + | 0.782781i | 0.998506 | − | 0.0546343i | \(-0.0173993\pi\) |
−0.546568 | + | 0.837415i | \(0.684066\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.48619e12 | − | 4.21078e11i | 0.377472 | − | 0.106948i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.07405e12i | 1.21840i | 0.793016 | + | 0.609201i | \(0.208510\pi\) | ||||
−0.793016 | + | 0.609201i | \(0.791490\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.58573e12 | + | 2.64757e12i | −1.04164 | + | 0.601389i | −0.920296 | − | 0.391222i | \(-0.872053\pi\) |
−0.121340 | + | 0.992611i | \(0.538719\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.03120e12 | + | 7.65953e11i | 0.651684 | + | 0.164674i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.28905e12 | + | 1.87796e12i | 1.07683 | + | 0.382347i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.55161e11 | + | 2.68746e11i | −0.0299320 | + | 0.0518437i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.87520e12 | + | 9.03068e12i | −0.891571 | + | 1.65152i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.68885e12 | 0.466405 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.13706e12 | −0.680986 | −0.340493 | − | 0.940247i | \(-0.610594\pi\) | ||||
−0.340493 | + | 0.940247i | \(0.610594\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.14294e12 | − | 4.99800e12i | −0.803754 | − | 0.781103i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.38178e11 | + | 5.85741e11i | −0.0502034 | + | 0.0869549i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.17189e11 | + | 6.35277e11i | 0.0165332 | + | 0.0896262i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.17211e12 | − | 4.63853e12i | 0.157226 | − | 0.622211i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.34829e12 | + | 1.35579e12i | −0.299636 | + | 0.172995i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 3.07771e12i | − | 0.373724i | −0.982386 | − | 0.186862i | \(-0.940168\pi\) | ||
0.982386 | − | 0.186862i | \(-0.0598317\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.20431e12 | − | 2.59032e12i | 0.486061 | − | 0.299467i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.61808e12 | + | 2.80260e12i | 0.178180 | + | 0.308616i | 0.941257 | − | 0.337691i | \(-0.109646\pi\) |
−0.763078 | + | 0.646307i | \(0.776313\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.11436e13 | − | 6.43374e12i | −1.16931 | − | 0.675101i | −0.215792 | − | 0.976439i | \(-0.569233\pi\) |
−0.953517 | + | 0.301339i | \(0.902567\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.08273e13 | + | 7.22892e12i | 1.08306 | + | 0.723115i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.66048e12 | + | 9.58680e11i | 0.158408 | + | 0.0914569i | 0.577108 | − | 0.816667i | \(-0.304181\pi\) |
−0.418701 | + | 0.908124i | \(0.637514\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.18109e11 | + | 8.97391e11i | 0.0471572 | + | 0.0816787i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.94732e12 | − | 1.04026e13i | −0.256042 | − | 0.903701i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1.04316e13i | − | 0.865289i | −0.901565 | − | 0.432645i | \(-0.857580\pi\) | ||
0.901565 | − | 0.432645i | \(-0.142420\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.93828e13 | + | 1.11906e13i | −1.53575 | + | 0.886668i | −0.536674 | + | 0.843790i | \(0.680320\pi\) |
−0.999080 | + | 0.0428786i | \(0.986347\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.64879e12 | − | 9.98237e12i | 0.654818 | − | 0.755786i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.45513e12 | + | 3.22931e12i | −0.611937 | + | 0.233720i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.54967e12 | − | 2.68411e12i | 0.107252 | − | 0.185766i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.89098e12 | + | 1.94582e12i | −0.125196 | + | 0.128827i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.04993e13 | −0.665201 | −0.332601 | − | 0.943068i | \(-0.607926\pi\) | ||||
−0.332601 | + | 0.943068i | \(0.607926\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.02982e13 | −2.44412 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.54070e12 | − | 4.67237e12i | 0.263725 | − | 0.271373i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.13288e13 | − | 1.96221e13i | 0.630309 | − | 1.09173i | −0.357180 | − | 0.934036i | \(-0.616262\pi\) |
0.987489 | − | 0.157691i | \(-0.0504050\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.47398e12 | − | 2.90160e12i | −0.131901 | − | 0.154700i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.23500e13 | − | 6.38991e11i | 1.14223 | − | 0.0326567i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.74287e13 | − | 1.00625e13i | 0.854102 | − | 0.493116i | −0.00793104 | − | 0.999969i | \(-0.502525\pi\) |
0.862033 | + | 0.506853i | \(0.169191\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2.22070e13i | − | 1.04385i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.41339e12 | + | 8.51805e12i | 0.108847 | + | 0.384174i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.75334e13 | − | 3.03688e13i | −0.758979 | − | 1.31459i | −0.943372 | − | 0.331737i | \(-0.892365\pi\) |
0.184393 | − | 0.982853i | \(-0.440968\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.69535e13 | − | 2.13351e13i | −1.53576 | − | 0.886674i | −0.999080 | − | 0.0428905i | \(-0.986343\pi\) |
−0.536684 | − | 0.843783i | \(-0.680323\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.34563e13 | − | 6.64191e12i | 0.537069 | − | 0.265093i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.67930e13 | + | 9.69545e12i | 0.643871 | + | 0.371739i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.91420e13 | − | 3.31549e13i | −0.705259 | − | 1.22154i | −0.966598 | − | 0.256298i | \(-0.917497\pi\) |
0.261339 | − | 0.965247i | \(-0.415836\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.34992e12 | + | 2.19103e12i | 0.0478062 | + | 0.0775936i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.61830e13i | 0.891526i | 0.895151 | + | 0.445763i | \(0.147068\pi\) | ||||
−0.895151 | + | 0.445763i | \(0.852932\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.27664e13 | + | 1.31442e13i | −0.745535 | + | 0.430435i | −0.824078 | − | 0.566476i | \(-0.808307\pi\) |
0.0785431 | + | 0.996911i | \(0.474973\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.82444e12 | + | 7.22008e12i | −0.0574754 | + | 0.227455i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.00871e12 | + | 2.84091e12i | −0.0305785 | + | 0.0861206i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.14174e13 | − | 1.97756e13i | 0.333143 | − | 0.577021i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.85994e13 | + | 3.75116e13i | 1.08435 | + | 1.05379i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.38647e13 | 0.645630 | 0.322815 | − | 0.946462i | \(-0.395371\pi\) | ||||
0.322815 | + | 0.946462i | \(0.395371\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.79372e13 | −0.728052 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.06257e13 | + | 1.12638e13i | 1.27119 | + | 0.282829i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.32251e13 | + | 4.02271e13i | −0.562039 | + | 0.973480i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.19852e12 | + | 6.19186e12i | −0.0512878 | + | 0.144446i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.25667e13 | − | 2.08637e13i | −1.85725 | − | 0.469307i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.39455e13 | + | 1.38249e13i | −0.519487 | + | 0.299926i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.08703e13i | 1.27393i | 0.770894 | + | 0.636964i | \(0.219810\pi\) | ||||
−0.770894 | + | 0.636964i | \(0.780190\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.62180e13 | − | 2.44278e13i | 1.74111 | − | 0.493303i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.37633e13 | − | 4.11592e13i | −0.463153 | − | 0.802205i | 0.535963 | − | 0.844241i | \(-0.319949\pi\) |
−0.999116 | + | 0.0420369i | \(0.986615\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.37987e13 | − | 7.96666e12i | −0.259623 | − | 0.149893i | 0.364540 | − | 0.931188i | \(-0.381226\pi\) |
−0.624163 | + | 0.781295i | \(0.714560\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.67575e13 | + | 2.41683e13i | −0.486113 | + | 0.439074i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.59916e13 | + | 2.65533e13i | 0.806961 | + | 0.465899i | 0.845899 | − | 0.533343i | \(-0.179064\pi\) |
−0.0389385 | + | 0.999242i | \(0.512398\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.38989e13 | + | 7.60351e13i | 0.744054 | + | 1.28874i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.77129e12 | − | 2.76846e12i | 0.160020 | − | 0.0453379i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.30726e13i | − | 0.206894i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.93567e13 | − | 1.11756e13i | 0.296123 | − | 0.170967i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.09720e13 | + | 2.04608e13i | 1.19763 | + | 0.302628i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.53125e12 | + | 7.66015e12i | 0.0934155 | + | 0.109562i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.74753e13 | + | 6.49092e13i | −0.518432 | + | 0.897950i | 0.481339 | + | 0.876535i | \(0.340151\pi\) |
−0.999771 | + | 0.0214157i | \(0.993183\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.33671e13 | − | 7.21624e12i | −0.178894 | − | 0.0965757i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.40016e13 | −0.440304 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.01593e14 | 1.27321 | 0.636605 | − | 0.771190i | \(-0.280338\pi\) | ||||
0.636605 | + | 0.771190i | \(0.280338\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.33497e13 | + | 9.07189e13i | 1.13244 | + | 1.10052i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.05269e12 | + | 8.75151e12i | −0.0593435 | + | 0.102786i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.50850e13 | + | 4.57518e13i | −0.853956 | + | 0.520344i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.73430e13 | − | 1.08208e14i | 0.301191 | − | 1.19194i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.79188e13 | + | 4.49864e13i | −0.831438 | + | 0.480031i | −0.854345 | − | 0.519707i | \(-0.826041\pi\) |
0.0229067 | + | 0.999738i | \(0.492708\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1.42008e13i | − | 0.146816i | −0.997302 | − | 0.0734078i | \(-0.976613\pi\) | ||
0.997302 | − | 0.0734078i | \(-0.0233875\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.04211e13 | − | 4.40447e13i | 0.404967 | − | 0.441270i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.61013e13 | + | 4.52087e13i | 0.253455 | + | 0.438997i | 0.964475 | − | 0.264175i | \(-0.0850997\pi\) |
−0.711020 | + | 0.703172i | \(0.751766\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.75432e13 | + | 3.89961e13i | 0.635807 | + | 0.367084i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.51453e13 | − | 5.26397e13i | 0.320769 | − | 0.480439i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.72756e13 | + | 2.15211e13i | 0.329918 | + | 0.190478i | 0.655805 | − | 0.754931i | \(-0.272330\pi\) |
−0.325887 | + | 0.945409i | \(0.605663\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.07741e13 | − | 8.79433e13i | −0.435866 | − | 0.754941i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.27805e13 | + | 8.04039e13i | 0.189705 | + | 0.669562i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.20313e13i | 0.420391i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.57969e11 | − | 1.48938e11i | 0.00202257 | − | 0.00116773i | −0.498988 | − | 0.866609i | \(-0.666295\pi\) |
0.501011 | + | 0.865441i | \(0.332962\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.43222e11 | + | 1.20049e13i | 0.00261174 | + | 0.0913508i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.91360e13 | − | 2.12155e14i | −0.289081 | − | 1.56710i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.58739e13 | − | 6.21354e13i | 0.257265 | − | 0.445596i | −0.708243 | − | 0.705968i | \(-0.750512\pi\) |
0.965508 | + | 0.260373i | \(0.0838454\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.02988e14 | + | 1.05975e14i | −0.717158 | + | 0.737955i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.01201e14 | 0.684397 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.42666e13 | 0.225090 | 0.112545 | − | 0.993647i | \(-0.464100\pi\) | ||||
0.112545 | + | 0.993647i | \(0.464100\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.22110e13 | − | 3.31450e13i | 0.205549 | − | 0.211510i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.79381e13 | + | 1.69634e14i | −0.607237 | + | 1.05177i | 0.384457 | + | 0.923143i | \(0.374389\pi\) |
−0.991694 | + | 0.128622i | \(0.958945\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.33422e14 | − | 4.73737e13i | −0.803886 | − | 0.285433i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.48063e11 | + | 2.61650e13i | 0.00438054 | + | 0.153218i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.94244e14 | − | 1.69882e14i | 1.67489 | − | 0.966996i | 0.710048 | − | 0.704153i | \(-0.248673\pi\) |
0.964839 | − | 0.262843i | \(-0.0846602\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.95920e14i | 1.08420i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.37871e12 | + | 2.60431e13i | 0.0397028 | + | 0.140131i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.87924e13 | + | 1.01831e14i | 0.307636 | + | 0.532841i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.05168e14 | − | 1.18454e14i | −1.04415 | − | 0.602840i | −0.123144 | − | 0.992389i | \(-0.539298\pi\) |
−0.921006 | + | 0.389549i | \(0.872631\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.70565e12 | + | 7.21923e13i | −0.0232953 | + | 0.357388i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.22273e14 | − | 7.05942e13i | −0.588892 | − | 0.339997i | 0.175767 | − | 0.984432i | \(-0.443759\pi\) |
−0.764659 | + | 0.644435i | \(0.777093\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.82405e12 | + | 1.00876e13i | 0.0272928 | + | 0.0472724i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.45959e13 | + | 1.28297e14i | −0.294579 | + | 0.585077i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 5.96490e13i | − | 0.264749i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.24831e14 | − | 1.87541e14i | 1.40339 | − | 0.810249i | 0.408654 | − | 0.912690i | \(-0.365998\pi\) |
0.994739 | + | 0.102440i | \(0.0326651\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.14653e13 | − | 2.43244e14i | 0.258523 | − | 1.02309i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.66898e14 | + | 4.92344e13i | −1.09300 | + | 0.201625i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.47541e13 | − | 2.55548e13i | 0.0588366 | − | 0.101908i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.30712e14 | − | 1.27028e14i | −0.507652 | − | 0.493345i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.27845e14 | −1.61849 | −0.809244 | − | 0.587473i | \(-0.800123\pi\) | ||||
−0.809244 | + | 0.587473i | \(0.800123\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.73543e13 | −0.211356 | −0.105678 | − | 0.994400i | \(-0.533701\pi\) | ||||
−0.105678 | + | 0.994400i | \(0.533701\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.52889e13 | + | 1.90507e13i | 0.126697 | + | 0.0683972i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.71370e13 | − | 8.16437e13i | 0.164901 | − | 0.285617i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.04399e14 | + | 1.74276e14i | −0.696829 | + | 0.594135i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.27590e14 | + | 5.75095e13i | 0.756202 | + | 0.191084i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.55755e14 | − | 2.05395e14i | 1.15219 | − | 0.665219i | 0.202773 | − | 0.979226i | \(-0.435005\pi\) |
0.949421 | + | 0.314006i | \(0.101671\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 4.42845e13i | − | 0.139820i | −0.997553 | − | 0.0699098i | \(-0.977729\pi\) | ||
0.997553 | − | 0.0699098i | \(-0.0222711\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.33955e14 | + | 6.62855e13i | −0.720179 | + | 0.204046i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.11969e14 | − | 1.93936e14i | −0.336086 | − | 0.582118i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.01170e14 | − | 1.16146e14i | −0.588856 | − | 0.339976i | 0.175789 | − | 0.984428i | \(-0.443752\pi\) |
−0.764645 | + | 0.644452i | \(0.777086\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.13035e14 | + | 2.78047e14i | −0.608190 | + | 0.793791i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.14033e14 | + | 1.81307e14i | 0.874491 | + | 0.504887i | 0.868838 | − | 0.495097i | \(-0.164867\pi\) |
0.00565271 | + | 0.999984i | \(0.498201\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.81416e13 | − | 8.33837e13i | −0.130780 | − | 0.226517i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.82107e14 | + | 5.15956e13i | −0.482652 | + | 0.136748i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.13315e14i | 0.551653i | 0.961207 | + | 0.275827i | \(0.0889516\pi\) | ||||
−0.961207 | + | 0.275827i | \(0.911048\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.08408e13 | + | 2.35794e13i | −0.103068 | + | 0.0595062i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.06544e14 | − | 1.78536e14i | −1.74020 | − | 0.439730i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.24186e14 | + | 1.05884e14i | −0.298544 | + | 0.254547i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.32103e14 | − | 4.02015e14i | 0.544681 | − | 0.943415i | −0.453946 | − | 0.891029i | \(-0.649984\pi\) |
0.998627 | − | 0.0523856i | \(-0.0166825\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.47620e13 | − | 2.46130e14i | 0.125461 | − | 0.563891i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.21439e14 | 0.495334 | 0.247667 | − | 0.968845i | \(-0.420336\pi\) | ||||
0.247667 | + | 0.968845i | \(0.420336\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.15591e14 | 0.470906 | 0.235453 | − | 0.971886i | \(-0.424343\pi\) | ||||
0.235453 | + | 0.971886i | \(0.424343\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.00711e13 | − | 1.95055e13i | −0.0428134 | − | 0.0416069i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.54765e14 | − | 4.41266e14i | 0.530758 | − | 0.919301i | −0.468597 | − | 0.883412i | \(-0.655240\pi\) |
0.999356 | − | 0.0358887i | \(-0.0114262\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.24834e14 | + | 5.99218e13i | −0.661015 | + | 0.121937i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.47513e13 | − | 1.77100e14i | 0.0889591 | − | 0.352049i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.90138e13 | + | 5.13922e13i | −0.172871 | + | 0.0998069i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.07756e14i | 0.204468i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.50814e14 | − | 7.31709e14i | −0.835884 | − | 1.35671i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.36720e13 | + | 2.36806e13i | 0.0247735 | + | 0.0429090i | 0.878146 | − | 0.478392i | \(-0.158780\pi\) |
−0.853373 | + | 0.521301i | \(0.825447\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.95438e13 | − | 3.43776e13i | −0.105448 | − | 0.0608805i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.05241e13 | − | 1.08195e15i | 0.122075 | − | 1.87284i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.06933e14 | − | 2.92678e14i | −0.857770 | − | 0.495234i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.15564e14 | + | 3.73367e14i | 0.356588 | + | 0.617628i | 0.987388 | − | 0.158317i | \(-0.0506068\pi\) |
−0.630801 | + | 0.775945i | \(0.717273\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.06161e14 | − | 3.74694e14i | −0.171698 | − | 0.606008i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.08798e14i | 1.43721i | 0.695420 | + | 0.718604i | \(0.255218\pi\) | ||||
−0.695420 | + | 0.718604i | \(0.744782\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.69665e14 | − | 2.13426e14i | 0.571676 | − | 0.330057i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.63805e14 | + | 1.61193e13i | −0.852708 | + | 0.0243791i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.13997e14 | + | 2.53516e14i | 1.05618 | + | 0.375012i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.65604e14 | − | 9.79654e14i | 0.818388 | − | 1.41749i | −0.0884818 | − | 0.996078i | \(-0.528202\pi\) |
0.906870 | − | 0.421411i | \(-0.138465\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.90270e14 | + | 5.04487e14i | −0.693949 | + | 0.714073i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.46529e14 | 0.618338 | 0.309169 | − | 0.951007i | \(-0.399949\pi\) | ||||
0.309169 | + | 0.951007i | \(0.399949\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.26166e14 | 1.25483 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.37118e14 | + | 3.46894e14i | −0.446929 | + | 0.459889i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.83062e14 | − | 1.00989e15i | 0.756427 | − | 1.31017i | −0.188235 | − | 0.982124i | \(-0.560277\pi\) |
0.944662 | − | 0.328046i | \(-0.106390\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.16959e13 | + | 4.97081e14i | 0.116422 | + | 0.631120i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.64570e13 | + | 2.74935e14i | 0.107437 | + | 0.341652i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.43994e14 | + | 4.87280e14i | −1.02660 | + | 0.592705i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.57472e14i | 0.187502i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.51091e14 | + | 8.86224e14i | 0.292692 | + | 1.03305i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.78296e14 | + | 3.08818e14i | 0.203486 | + | 0.352448i | 0.949649 | − | 0.313315i | \(-0.101440\pi\) |
−0.746163 | + | 0.665763i | \(0.768106\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.58466e14 | + | 2.06960e14i | 0.400579 | + | 0.231274i | 0.686734 | − | 0.726909i | \(-0.259044\pi\) |
−0.286155 | + | 0.958183i | \(0.592377\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.89699e14 | + | 4.33903e14i | −0.317009 | + | 0.474806i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.25478e13 | + | 2.45650e13i | 0.0455952 | + | 0.0263244i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.20169e15 | + | 2.08139e15i | 1.26121 | + | 2.18447i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.20516e14 | + | 5.67139e14i | −0.946262 | + | 0.583002i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.43583e13i | 0.0547351i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.56517e13 | + | 5.52246e13i | −0.0943511 | + | 0.0544737i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.28723e13 | − | 2.09238e14i | 0.0510939 | − | 0.202201i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.35814e15 | − | 2.17452e14i | −1.28590 | − | 0.205885i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.58141e14 | − | 4.47113e14i | 0.239482 | − | 0.414794i | −0.721084 | − | 0.692848i | \(-0.756356\pi\) |
0.960566 | + | 0.278053i | \(0.0896892\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.13308e15 | + | 1.10115e15i | 1.03006 | + | 1.00103i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.08278e14 | −0.809167 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.96104e15 | 1.71221 | 0.856103 | − | 0.516805i | \(-0.172879\pi\) | ||||
0.856103 | + | 0.516805i | \(0.172879\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.08338e14 | + | 9.41629e14i | −0.435015 | + | 0.805809i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.43947e14 | + | 4.22529e14i | −0.204627 | + | 0.354424i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.41133e14 | + | 8.69235e14i | 0.609407 | + | 0.714741i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.60169e14 | + | 4.04730e13i | 0.129112 | + | 0.0326252i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.64381e15 | + | 9.49057e14i | −1.29912 | + | 0.750047i | −0.980252 | − | 0.197752i | \(-0.936636\pi\) |
−0.318868 | + | 0.947799i | \(0.603303\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.18476e14i | 0.0918046i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.52617e14 | − | 2.69902e14i | 0.723807 | − | 0.205074i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.88117e14 | − | 8.45443e14i | −0.363687 | − | 0.629924i | 0.624878 | − | 0.780723i | \(-0.285149\pi\) |
−0.988565 | + | 0.150799i | \(0.951815\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.22598e15 | − | 7.07820e14i | −0.895812 | − | 0.517197i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.91016e14 | + | 1.33952e15i | −0.280213 | + | 0.959938i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.68583e15 | + | 9.73314e14i | 1.18494 | + | 0.684125i | 0.957152 | − | 0.289586i | \(-0.0935175\pi\) |
0.227787 | + | 0.973711i | \(0.426851\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.01533e15 | + | 1.75861e15i | 0.700018 | + | 1.21247i | 0.968459 | + | 0.249171i | \(0.0801582\pi\) |
−0.268441 | + | 0.963296i | \(0.586508\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.11472e15 | − | 5.99155e14i | 1.43022 | − | 0.405218i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 1.61495e15i | − | 1.07149i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.75093e15 | − | 1.01090e15i | 1.13973 | − | 0.658022i | 0.193364 | − | 0.981127i | \(-0.438060\pi\) |
0.946363 | + | 0.323105i | \(0.104727\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.37215e15 | − | 3.46727e14i | −0.876332 | − | 0.221440i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.59173e13 | − | 2.70140e14i | 0.0601075 | − | 0.169285i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.68738e15 | − | 2.92262e15i | 1.03761 | − | 1.79720i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.08848e14 | + | 5.72100e14i | −0.186375 | + | 0.345235i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.86653e15 | 1.10541 | 0.552707 | − | 0.833376i | \(-0.313595\pi\) | ||||
0.552707 | + | 0.833376i | \(0.313595\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.61559e13 | −0.0326409 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.53153e15 | − | 1.48837e15i | −0.873764 | − | 0.849140i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.19279e14 | + | 3.79802e14i | −0.122799 | + | 0.212695i | −0.920871 | − | 0.389869i | \(-0.872520\pi\) |
0.798071 | + | 0.602563i | \(0.205854\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.30320e14 | + | 6.48669e14i | −0.126616 | + | 0.356599i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.45998e14 | − | 2.16075e15i | 0.294667 | − | 1.16612i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.13916e15 | − | 1.23505e15i | 1.13343 | − | 0.654389i | 0.188638 | − | 0.982047i | \(-0.439593\pi\) |
0.944796 | + | 0.327658i | \(0.106259\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.50056e15i | 0.780627i | 0.920682 | + | 0.390313i | \(0.127633\pi\) | ||||
−0.920682 | + | 0.390313i | \(0.872367\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.12033e15 | + | 6.90249e14i | −0.572272 | + | 0.352582i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.54420e14 | − | 7.87079e14i | −0.227931 | − | 0.394788i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.00707e15 | − | 1.73613e15i | −1.48117 | − | 0.855155i | −0.481400 | − | 0.876501i | \(-0.659872\pi\) |
−0.999772 | + | 0.0213457i | \(0.993205\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.11827e15 | + | 1.04556e15i | −1.02467 | + | 0.505772i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.57194e14 | + | 9.07560e13i | 0.0746809 | + | 0.0431170i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.64528e15 | + | 2.84972e15i | 0.767729 | + | 1.32975i | 0.938791 | + | 0.344486i | \(0.111947\pi\) |
−0.171062 | + | 0.985260i | \(0.554720\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.56040e13 | − | 1.25664e14i | −0.0163187 | − | 0.0575968i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.69767e15i | 0.764336i | 0.924093 | + | 0.382168i | \(0.124822\pi\) | ||||
−0.924093 | + | 0.382168i | \(0.875178\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.28861e15 | + | 7.43979e14i | −0.569932 | + | 0.329050i | −0.757122 | − | 0.653273i | \(-0.773395\pi\) |
0.187190 | + | 0.982324i | \(0.440062\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.29574e15 | − | 4.12048e15i | −0.563008 | − | 1.79037i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.06870e14 | − | 7.11765e14i | −0.259067 | − | 0.303845i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.22972e14 | − | 2.12994e14i | 0.0515783 | − | 0.0893363i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.88720e14 | + | 8.11592e14i | −0.325051 | + | 0.334477i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.90000e14 | −0.117441 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.10684e14 | −0.322619 | −0.161309 | − | 0.986904i | \(-0.551572\pi\) | ||||
−0.161309 | + | 0.986904i | \(0.551572\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.21352e15 | − | 1.24871e15i | 0.474599 | − | 0.488362i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.51321e14 | + | 4.35300e14i | −0.0965990 | + | 0.167314i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.99806e14 | + | 1.23042e15i | −0.377702 | + | 0.464821i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.01715e15 | − | 8.62609e13i | 1.12032 | − | 0.0320302i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.44689e15 | + | 1.41272e15i | −0.893092 | + | 0.515627i | −0.874953 | − | 0.484209i | \(-0.839108\pi\) |
−0.0181392 | + | 0.999835i | \(0.505774\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 2.02025e15i | − | 0.724846i | −0.932014 | − | 0.362423i | \(-0.881950\pi\) | ||
0.932014 | − | 0.362423i | \(-0.118050\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.76001e13 | − | 2.73889e14i | −0.0273706 | − | 0.0966043i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.25398e15 | + | 3.90401e15i | 0.781586 | + | 1.35375i | 0.931018 | + | 0.364974i | \(0.118922\pi\) |
−0.149432 | + | 0.988772i | \(0.547744\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.67676e15 | − | 2.12278e15i | −1.25349 | − | 0.723701i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.26124e14 | − | 1.50974e14i | −0.0757970 | − | 0.0506065i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.22746e15 | + | 1.28602e15i | 0.734153 | + | 0.423864i | 0.819940 | − | 0.572450i | \(-0.194007\pi\) |
−0.0857864 | + | 0.996314i | \(0.527340\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.47188e14 | − | 2.54938e14i | −0.0477031 | − | 0.0826242i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.05626e15 | + | 1.71440e15i | 0.336637 | + | 0.546390i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 4.82477e15i | − | 1.51219i | −0.654462 | − | 0.756095i | \(-0.727105\pi\) | ||
0.654462 | − | 0.756095i | \(-0.272895\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.09492e15 | + | 1.78685e15i | −0.953985 | + | 0.550783i | −0.894317 | − | 0.447435i | \(-0.852338\pi\) |
−0.0596683 | + | 0.998218i | \(0.519004\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.79598e14 | − | 1.10649e15i | 0.0847637 | − | 0.335446i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.42729e14 | − | 7.73728e14i | −0.0425591 | − | 0.230712i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.65607e15 | − | 6.33250e15i | 1.07231 | − | 1.85730i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.28962e14 | + | 9.02782e14i | 0.268012 | + | 0.260459i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.20189e15 | −1.19253 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.71010e13 | 0.0131506 | 0.00657532 | − | 0.999978i | \(-0.497907\pi\) | ||||
0.00657532 | + | 0.999978i | \(0.497907\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.51397e14 | + | 2.02883e15i | −0.123990 | + | 0.557281i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.18334e15 | − | 2.04961e15i | 0.319796 | − | 0.553903i | −0.660649 | − | 0.750695i | \(-0.729719\pi\) |
0.980445 | + | 0.196792i | \(0.0630523\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.35878e15 | − | 1.90272e15i | −1.42489 | − | 0.505931i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.32055e15 | − | 3.33690e14i | −0.345499 | − | 0.0873040i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.20706e15 | + | 1.27425e15i | −0.568198 | + | 0.328049i | −0.756429 | − | 0.654075i | \(-0.773058\pi\) |
0.188231 | + | 0.982125i | \(0.439725\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.72852e15i | 0.691240i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.21067e15 | − | 1.47632e15i | 1.29907 | − | 0.368060i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.94498e15 | − | 3.36880e15i | −0.477209 | − | 0.826551i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.05921e15 | − | 2.92094e15i | −1.22167 | − | 0.705331i | −0.256395 | − | 0.966572i | \(-0.582535\pi\) |
−0.965274 | + | 0.261241i | \(0.915868\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.35790e15 | + | 1.14760e15i | −1.27339 | + | 0.272746i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.71666e15 | + | 9.91115e14i | 0.401576 | + | 0.231850i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.14638e14 | + | 1.98558e14i | 0.0263966 | + | 0.0457202i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.76433e14 | + | 2.19984e14i | −0.175986 | + | 0.0498616i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.09264e13i | 0.00466923i | 0.999997 | + | 0.00233462i | \(0.000743132\pi\) | ||||
−0.999997 | + | 0.00233462i | \(0.999257\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.87063e14 | − | 1.65736e14i | 0.0630555 | − | 0.0364051i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.22841e14 | − | 1.06848e14i | −0.0914403 | − | 0.0231060i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.84813e15 | − | 1.63220e15i | 1.88384 | − | 0.347510i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.49666e14 | + | 1.64487e15i | −0.199075 | + | 0.344808i | −0.948229 | − | 0.317588i | \(-0.897127\pi\) |
0.749154 | + | 0.662396i | \(0.230460\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.00440e15 | + | 2.16177e15i | 0.826523 | + | 0.446198i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.41616e14 | 0.171049 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.55292e15 | −0.510921 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.14862e15 | + | 3.05989e15i | 0.620533 | + | 0.603046i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.94778e14 | + | 6.83776e14i | −0.0766204 | + | 0.132710i | −0.901790 | − | 0.432175i | \(-0.857746\pi\) |
0.825169 | + | 0.564885i | \(0.191080\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.20435e15 | + | 6.14262e15i | −1.37705 | + | 1.17411i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.30780e15 | − | 9.13295e15i | 0.434448 | − | 1.71930i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.04711e15 | + | 1.75925e15i | −0.564974 | + | 0.326188i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 5.66468e15i | − | 1.03451i | −0.855830 | − | 0.517256i | \(-0.826953\pi\) | ||
0.855830 | − | 0.517256i | \(-0.173047\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.76090e14 | + | 5.53864e15i | 0.0856422 | + | 0.996326i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.49857e14 | + | 4.32765e14i | 0.0442737 | + | 0.0766842i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.90786e15 | − | 3.41091e15i | −1.03124 | − | 0.595385i | −0.113898 | − | 0.993492i | \(-0.536334\pi\) |
−0.917339 | + | 0.398107i | \(0.869667\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.50542e15 | − | 3.49931e15i | 0.258867 | − | 0.601731i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.47488e15 | − | 2.58357e15i | −0.758072 | − | 0.437673i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.27003e15 | − | 2.19975e15i | −0.211967 | − | 0.367138i | 0.740363 | − | 0.672208i | \(-0.234654\pi\) |
−0.952330 | + | 0.305069i | \(0.901320\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.55596e14 | + | 1.25508e15i | 0.0584732 | + | 0.206381i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.78015e15i | 0.936485i | 0.883600 | + | 0.468242i | \(0.155113\pi\) | ||||
−0.883600 | + | 0.468242i | \(0.844887\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.78265e15 | − | 1.02922e15i | 0.284582 | − | 0.164303i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.26367e13 | − | 1.14153e15i | −0.00513384 | − | 0.179566i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.16486e14 | + | 6.96157e14i | −0.126561 | + | 0.107909i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.98569e15 | − | 3.43932e15i | 0.303314 | − | 0.525355i | −0.673571 | − | 0.739123i | \(-0.735240\pi\) |
0.976884 | + | 0.213768i | \(0.0685737\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.07974e15 | − | 3.16905e15i | 0.463598 | − | 0.477042i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.92544e15 | 1.17575 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.33721e15 | 1.21897 | 0.609486 | − | 0.792797i | \(-0.291376\pi\) | ||||
0.609486 | + | 0.792797i | \(0.291376\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.18206e16 | − | 1.21634e16i | 1.70338 | − | 1.75278i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.46301e15 | − | 9.46221e15i | 0.775919 | − | 1.34393i | −0.158357 | − | 0.987382i | \(-0.550620\pi\) |
0.934276 | − | 0.356550i | \(-0.116047\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.67724e15 | + | 1.60068e15i | −1.21478 | + | 0.224088i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.83683e13 | + | 2.74109e15i | 0.0108144 | + | 0.378255i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.23807e15 | + | 2.44685e15i | −0.576493 | + | 0.332838i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.91791e15i | 0.927641i | 0.885929 | + | 0.463821i | \(0.153522\pi\) | ||||
−0.885929 | + | 0.463821i | \(0.846478\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.59958e15 | + | 9.17520e15i | 0.343640 | + | 1.21288i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.86294e15 | + | 3.22671e15i | 0.242780 | + | 0.420507i | 0.961505 | − | 0.274787i | \(-0.0886075\pi\) |
−0.718725 | + | 0.695294i | \(0.755274\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.50717e14 | − | 2.02487e14i | −0.0450607 | − | 0.0260158i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.60150e15 | + | 1.04389e14i | 0.202867 | + | 0.0132233i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.26954e14 | − | 1.31032e14i | −0.0283453 | − | 0.0163652i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.92615e15 | + | 1.02644e16i | 0.729780 | + | 1.26402i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.36304e15 | + | 6.93346e15i | −0.772636 | + | 0.841900i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.98656e15i | 0.237859i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.89375e15 | − | 2.24806e15i | 0.459734 | − | 0.265428i | −0.252198 | − | 0.967676i | \(-0.581154\pi\) |
0.711932 | + | 0.702248i | \(0.247820\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.07515e15 | + | 8.21224e15i | −0.241616 | + | 0.956177i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.29598e16 | − | 4.60158e15i | −1.48809 | − | 0.528368i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.42168e15 | + | 4.19448e15i | −0.274230 | + | 0.474980i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.70287e15 | + | 6.51398e15i | 0.748586 | + | 0.727490i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.61510e16 | −1.77901 | −0.889503 | − | 0.456929i | \(-0.848949\pi\) | ||||
−0.889503 | + | 0.456929i | \(0.848949\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.65592e14 | 0.0831745 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.27897e15 | − | 1.77015e15i | −0.351365 | − | 0.189684i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.95354e15 | + | 6.84773e15i | −0.417879 | + | 0.723788i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.13909e15 | + | 1.15960e16i | 0.223024 | + | 1.20901i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.43095e16 | + | 3.61585e15i | 1.47170 | + | 0.371883i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.54933e16 | − | 8.94505e15i | 1.57191 | − | 0.907541i | 0.575971 | − | 0.817470i | \(-0.304624\pi\) |
0.995935 | − | 0.0900709i | \(-0.0287094\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.53671e16i | 1.53808i | 0.639202 | + | 0.769039i | \(0.279265\pi\) | ||||
−0.639202 | + | 0.769039i | \(0.720735\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.72793e16 | − | 4.89567e15i | 1.70619 | − | 0.483408i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.11767e15 | + | 3.66791e15i | 0.206296 | + | 0.357315i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.94653e14 | − | 2.85588e14i | −0.0475422 | − | 0.0274485i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.94235e15 | + | 6.00985e15i | −0.184190 | + | 0.569905i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.39421e15 | − | 1.95965e15i | −0.317578 | − | 0.183354i | 0.332734 | − | 0.943021i | \(-0.392029\pi\) |
−0.650313 | + | 0.759667i | \(0.725362\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.25023e14 | − | 9.09366e14i | −0.0484707 | − | 0.0839537i | 0.840772 | − | 0.541389i | \(-0.182101\pi\) |
−0.889243 | + | 0.457435i | \(0.848768\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.85232e15 | + | 2.22477e15i | −0.715322 | + | 0.202669i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1.47529e15i | − | 0.132616i | −0.997799 | − | 0.0663080i | \(-0.978878\pi\) | ||
0.997799 | − | 0.0663080i | \(-0.0211220\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.14702e16 | − | 6.62231e15i | 1.01747 | − | 0.587435i | 0.104098 | − | 0.994567i | \(-0.466804\pi\) |
0.913369 | + | 0.407132i | \(0.133471\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.56223e16 | + | 3.94758e15i | 1.36753 | + | 0.345561i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.05720e15 | + | 6.60295e15i | −0.0913292 | + | 0.570415i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.82525e15 | − | 6.62553e15i | 0.326125 | − | 0.564865i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.05730e15 | − | 2.35241e14i | −0.0889630 | − | 0.0197935i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.48206e15 | −0.787430 | −0.393715 | − | 0.919233i | \(-0.628810\pi\) | ||||
−0.393715 | + | 0.919233i | \(0.628810\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.73046e15 | −0.305763 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.90295e15 | − | 7.68024e15i | −0.639349 | − | 0.621331i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.63031e15 | − | 4.55583e15i | 0.210037 | − | 0.363794i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.72839e15 | − | 6.71852e15i | −0.451517 | − | 0.529560i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.71067e15 | − | 1.07273e16i | 0.210904 | − | 0.834636i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.30225e15 | + | 2.48390e15i | −0.330433 | + | 0.190775i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1.98483e14i | − | 0.0150489i | −0.999972 | − | 0.00752445i | \(-0.997605\pi\) | ||
0.999972 | − | 0.00752445i | \(-0.00239513\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.64412e15 | − | 2.66854e15i | −0.123061 | − | 0.199738i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.31968e16 | + | 2.28575e16i | 0.975157 | + | 1.68902i | 0.679416 | + | 0.733753i | \(0.262233\pi\) |
0.295741 | + | 0.955268i | \(0.404434\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.60131e15 | + | 1.50186e15i | 0.189771 | + | 0.109564i | 0.591875 | − | 0.806030i | \(-0.298388\pi\) |
−0.402105 | + | 0.915594i | \(0.631721\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.61603e14 | − | 1.13779e15i | −0.0404494 | − | 0.0819490i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.41267e16 | + | 8.15604e15i | 1.00457 | + | 0.579989i | 0.909597 | − | 0.415491i | \(-0.136390\pi\) |
0.0949730 | + | 0.995480i | \(0.469724\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.00869e15 | − | 8.67531e15i | −0.351670 | − | 0.609111i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.61991e15 | + | 9.24695e15i | 0.181627 | + | 0.641053i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.78691e16i | 1.22319i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.15803e15 | + | 2.97799e15i | −0.348646 | + | 0.201291i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.26447e16 | + | 6.47416e14i | −1.51143 | + | 0.0432121i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.22392e15 | − | 1.47125e16i | 0.344312 | − | 0.969712i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.69508e15 | − | 9.86417e15i | 0.370683 | − | 0.642041i | −0.618988 | − | 0.785400i | \(-0.712457\pi\) |
0.989671 | + | 0.143359i | \(0.0457904\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.00021e15 | + | 7.20321e15i | −0.449958 | + | 0.463007i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.01407e15 | 0.381769 | 0.190885 | − | 0.981612i | \(-0.438864\pi\) | ||||
0.190885 | + | 0.981612i | \(0.438864\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.77508e16 | −1.11285 | −0.556423 | − | 0.830899i | \(-0.687826\pi\) | ||||
−0.556423 | + | 0.830899i | \(0.687826\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.19481e15 | − | 8.43245e15i | 0.507401 | − | 0.522115i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.35987e15 | − | 1.10156e16i | 0.388927 | − | 0.673642i | −0.603378 | − | 0.797455i | \(-0.706179\pi\) |
0.992306 | + | 0.123813i | \(0.0395124\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.63385e15 | + | 4.60155e15i | −0.0986855 | + | 0.277936i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.82498e16 | + | 1.19766e16i | −1.08876 | + | 0.714509i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.57839e14 | + | 4.37538e14i | −0.0446574 | + | 0.0257830i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.34707e15i | 0.136615i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.32936e15 | − | 1.88100e16i | −0.306420 | − | 1.08151i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.16815e14 | − | 1.58797e15i | −0.0520719 | − | 0.0901911i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.42091e16 | − | 8.20364e15i | −0.797225 | − | 0.460278i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.22403e15 | − | 2.47985e15i | −0.0678439 | − | 0.137449i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.48810e16 | − | 8.59153e15i | −0.814824 | − | 0.470439i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.38697e15 | − | 5.86641e15i | −0.183219 | − | 0.317345i | 0.759756 | − | 0.650209i | \(-0.225319\pi\) |
−0.942975 | + | 0.332863i | \(0.891985\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.05167e16 | − | 1.88016e16i | 1.63093 | − | 1.00483i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 2.62025e16i | − | 1.38354i | −0.722119 | − | 0.691769i | \(-0.756832\pi\) | ||
0.722119 | − | 0.691769i | \(-0.243168\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.88351e15 | − | 2.24215e15i | 0.202598 | − | 0.116970i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.85106e15 | − | 1.12829e16i | 0.146957 | − | 0.581572i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.85545e15 | − | 2.17615e15i | −0.0944968 | − | 0.110830i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.89457e15 | − | 1.36738e16i | 0.397277 | − | 0.688104i | −0.596112 | − | 0.802901i | \(-0.703289\pi\) |
0.993389 | + | 0.114798i | \(0.0366219\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.83728e16 | − | 1.78551e16i | −0.913584 | − | 0.887837i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.36617e16 | 0.671268 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.39044e15 | 0.116064 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.79171e16 | + | 3.31891e16i | −0.859665 | + | 1.59242i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.27524e14 | − | 7.40493e14i | 0.0202709 | − | 0.0351103i | −0.855712 | − | 0.517452i | \(-0.826880\pi\) |
0.875983 | + | 0.482342i | \(0.160214\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.72712e15 | − | 7.14028e15i | −0.127785 | − | 0.334574i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.93938e16 | + | 4.90061e15i | 0.898078 | + | 0.226935i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.32523e15 | + | 5.38392e15i | −0.426772 | + | 0.246397i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2.08188e16i | − | 0.941647i | −0.882227 | − | 0.470823i | \(-0.843957\pi\) | ||
0.882227 | − | 0.470823i | \(-0.156043\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.45218e15 | − | 1.82807e15i | 0.288433 | − | 0.0817208i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.81954e15 | − | 1.00797e16i | −0.257126 | − | 0.445355i | 0.708345 | − | 0.705866i | \(-0.249442\pi\) |
−0.965471 | + | 0.260511i | \(0.916109\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.40138e15 | + | 1.96379e15i | 0.148539 | + | 0.0857591i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.53908e14 | − | 1.51656e16i | 0.0239091 | − | 0.654615i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.37448e16 | − | 7.93557e15i | −0.586427 | − | 0.338574i | 0.177257 | − | 0.984165i | \(-0.443278\pi\) |
−0.763683 | + | 0.645591i | \(0.776611\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.55710e15 | + | 7.89313e15i | 0.192187 | + | 0.332878i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.15054e16 | + | 6.09305e15i | −0.896510 | + | 0.254005i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 2.14296e16i | − | 0.883085i | −0.897240 | − | 0.441542i | \(-0.854431\pi\) | ||
0.897240 | − | 0.441542i | \(-0.145569\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.07011e16 | + | 1.19518e16i | −0.843285 | + | 0.486871i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.58269e16 | − | 9.05308e15i | −1.44276 | − | 0.364570i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.80853e15 | + | 2.60669e16i | 0.191430 | + | 1.03774i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.25987e16 | + | 2.18216e16i | −0.495847 | + | 0.858832i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.03059e15 | + | 3.76140e15i | −0.0790090 | + | 0.146354i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.53916e16 | 0.592086 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.67370e16 | 0.636549 | 0.318274 | − | 0.947999i | \(-0.396897\pi\) | ||||
0.318274 | + | 0.947999i | \(0.396897\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.94577e15 | + | 3.83458e15i | 0.148372 | + | 0.144190i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.91722e16 | + | 3.32072e16i | −0.712798 | + | 1.23460i | 0.251005 | + | 0.967986i | \(0.419239\pi\) |
−0.963803 | + | 0.266616i | \(0.914094\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.81468e16 | + | 6.44330e15i | 0.667082 | + | 0.236858i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.30470e15 | + | 9.12067e15i | −0.0837700 | + | 0.331514i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.12401e16 | − | 1.22630e16i | 0.763374 | − | 0.440734i | −0.0671319 | − | 0.997744i | \(-0.521385\pi\) |
0.830506 | + | 0.557010i | \(0.188051\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.46320e16i | − | 0.519993i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.99273e16 | + | 1.84385e16i | −1.05169 | + | 0.647957i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.72140e16 | − | 4.71360e16i | −0.945688 | − | 1.63798i | −0.754367 | − | 0.656453i | \(-0.772056\pi\) |
−0.191322 | − | 0.981527i | \(-0.561277\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.01139e16 | + | 1.16128e16i | 0.691189 | + | 0.399058i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.22792e15 | − | 2.75585e14i | −0.143675 | − | 0.00936506i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.41342e15 | + | 4.28014e15i | 0.249137 | + | 0.143840i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.12113e16 | + | 1.94186e16i | 0.372607 | + | 0.645375i | 0.989966 | − | 0.141307i | \(-0.0451306\pi\) |
−0.617359 | + | 0.786682i | \(0.711797\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.59929e15 | − | 3.03512e16i | −0.282645 | − | 0.997596i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.42375e16i | 0.787882i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.68788e15 | − | 4.43860e15i | 0.247163 | − | 0.142700i | −0.371302 | − | 0.928512i | \(-0.621088\pi\) |
0.618465 | + | 0.785813i | \(0.287755\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.09910e15 | − | 1.91795e15i | 0.193935 | − | 0.0609854i |
(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 | 84.12.k.b.5.7 | yes | 56 | |
3.2 | odd | 2 | inner | 84.12.k.b.5.4 | ✓ | 56 | |
7.3 | odd | 6 | inner | 84.12.k.b.17.4 | yes | 56 | |
21.17 | even | 6 | inner | 84.12.k.b.17.7 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.12.k.b.5.4 | ✓ | 56 | 3.2 | odd | 2 | inner | |
84.12.k.b.5.7 | yes | 56 | 1.1 | even | 1 | trivial | |
84.12.k.b.17.4 | yes | 56 | 7.3 | odd | 6 | inner | |
84.12.k.b.17.7 | yes | 56 | 21.17 | even | 6 | inner |