Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,7,Mod(65,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.65");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.h (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: | \(17.4841103551\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 9460 x^{18} + 36670708 x^{16} + 75655761912 x^{14} + 90488614064544 x^{12} + \cdots + 10\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{22}\cdot 3^{8}\cdot 19^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 69.4 | ||
Root | \(21.8702i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.69 |
Dual form | 76.7.h.a.65.4 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −20.4402 | + | 11.8011i | −0.757044 | + | 0.437080i | −0.828233 | − | 0.560383i | \(-0.810654\pi\) |
0.0711895 | + | 0.997463i | \(0.477320\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 15.3686 | + | 26.6192i | 0.122949 | + | 0.212953i | 0.920929 | − | 0.389730i | \(-0.127432\pi\) |
−0.797981 | + | 0.602683i | \(0.794098\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −77.2273 | −0.225152 | −0.112576 | − | 0.993643i | \(-0.535910\pi\) | ||||
−0.112576 | + | 0.993643i | \(0.535910\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −85.9659 | + | 148.897i | −0.117923 | + | 0.204249i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1577.96 | −1.18555 | −0.592774 | − | 0.805369i | \(-0.701967\pi\) | ||||
−0.592774 | + | 0.805369i | \(0.701967\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2818.20 | + | 1627.09i | 1.28275 | + | 0.740596i | 0.977350 | − | 0.211629i | \(-0.0678768\pi\) |
0.305399 | + | 0.952224i | \(0.401210\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −628.274 | − | 362.734i | −0.186155 | − | 0.107477i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3364.22 | − | 5827.00i | −0.684759 | − | 1.18604i | −0.973513 | − | 0.228634i | \(-0.926574\pi\) |
0.288754 | − | 0.957403i | \(-0.406759\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2770.84 | − | 6274.42i | 0.403971 | − | 0.914772i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1578.54 | − | 911.371i | 0.170450 | − | 0.0984095i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2290.31 | − | 3966.93i | 0.188239 | − | 0.326040i | −0.756424 | − | 0.654082i | \(-0.773055\pi\) |
0.944663 | + | 0.328042i | \(0.106389\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7340.11 | − | 12713.4i | 0.469767 | − | 0.813661i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 21264.1i | − | 1.08033i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −22625.8 | − | 13063.0i | −0.927703 | − | 0.535610i | −0.0416188 | − | 0.999134i | \(-0.513251\pi\) |
−0.886084 | + | 0.463524i | \(0.846585\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 25810.7i | − | 0.866391i | −0.901300 | − | 0.433196i | \(-0.857386\pi\) | ||
0.901300 | − | 0.433196i | \(-0.142614\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 32253.9 | − | 18621.8i | 0.897512 | − | 0.518179i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1186.87 | − | 2055.73i | −0.0276822 | − | 0.0479470i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 83385.4i | 1.64621i | 0.567890 | + | 0.823104i | \(0.307760\pi\) | ||||
−0.567890 | + | 0.823104i | \(0.692240\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −76806.0 | −1.29480 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 81159.3 | − | 46857.4i | 1.17757 | − | 0.679871i | 0.222119 | − | 0.975020i | \(-0.428703\pi\) |
0.955451 | + | 0.295149i | \(0.0953693\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −57374.3 | − | 99375.2i | −0.721626 | − | 1.24989i | −0.960348 | − | 0.278804i | \(-0.910062\pi\) |
0.238722 | − | 0.971088i | \(-0.423271\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5284.70 | −0.0579939 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9487.88 | − | 16433.5i | 0.0913852 | − | 0.158284i | −0.816709 | − | 0.577050i | \(-0.804204\pi\) |
0.908094 | + | 0.418766i | \(0.137537\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −111685. | −0.949306 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 137531. | + | 79403.3i | 1.03679 | + | 0.598588i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 59687.5 | + | 34460.6i | 0.400919 | + | 0.231470i | 0.686880 | − | 0.726771i | \(-0.258980\pi\) |
−0.285962 | + | 0.958241i | \(0.592313\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −24251.1 | − | 42004.1i | −0.145762 | − | 0.252467i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 17408.9 | + | 160949.i | 0.0940044 | + | 0.869090i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 17779.2 | − | 10264.8i | 0.0865678 | − | 0.0499799i | −0.456091 | − | 0.889933i | \(-0.650751\pi\) |
0.542659 | + | 0.839953i | \(0.317418\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 39431.6 | − | 68297.5i | 0.173722 | − | 0.300895i | −0.765996 | − | 0.642845i | \(-0.777754\pi\) |
0.939718 | + | 0.341950i | \(0.111087\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6638.91 | − | 11498.9i | 0.0265507 | − | 0.0459871i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 100024.i | 0.364221i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 23781.8 | + | 13730.4i | 0.0790716 | + | 0.0456520i | 0.539015 | − | 0.842296i | \(-0.318797\pi\) |
−0.459943 | + | 0.887948i | \(0.652130\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 108113.i | 0.329102i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −345348. | + | 199387.i | −0.964898 | + | 0.557084i | −0.897677 | − | 0.440654i | \(-0.854747\pi\) |
−0.0672212 | + | 0.997738i | \(0.521413\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 277015. | + | 479804.i | 0.712090 | + | 1.23338i | 0.964071 | + | 0.265644i | \(0.0855845\pi\) |
−0.251981 | + | 0.967732i | \(0.581082\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 346487.i | 0.821302i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 121862. | 0.266929 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −424193. | + | 244908.i | −0.860365 | + | 0.496732i | −0.864134 | − | 0.503261i | \(-0.832133\pi\) |
0.00376977 | + | 0.999993i | \(0.498800\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 188271. | + | 326095.i | 0.354265 | + | 0.613606i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −516880. | −0.903974 | −0.451987 | − | 0.892025i | \(-0.649285\pi\) | ||||
−0.451987 | + | 0.892025i | \(0.649285\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 103407. | − | 179106.i | 0.168380 | − | 0.291644i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 616633. | 0.936416 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −710222. | − | 410047.i | −1.00745 | − | 0.581653i | −0.0970073 | − | 0.995284i | \(-0.530927\pi\) |
−0.910445 | + | 0.413631i | \(0.864260\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −217642. | − | 125656.i | −0.288814 | − | 0.166747i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 304595. | + | 527575.i | 0.378682 | + | 0.655896i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 209604. | − | 22671.6i | 0.244472 | − | 0.0264431i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 429465. | − | 247952.i | 0.470557 | − | 0.271676i | −0.245916 | − | 0.969291i | \(-0.579089\pi\) |
0.716473 | + | 0.697615i | \(0.245755\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 135651. | − | 234955.i | 0.139803 | − | 0.242147i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 127587. | − | 220988.i | 0.123835 | − | 0.214489i | −0.797442 | − | 0.603396i | \(-0.793814\pi\) |
0.921277 | + | 0.388907i | \(0.127147\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 513798.i | − | 0.470198i | −0.971971 | − | 0.235099i | \(-0.924459\pi\) | ||
0.971971 | − | 0.235099i | \(-0.0755415\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 48519.9 | + | 28013.0i | 0.0419133 | + | 0.0241987i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 703986.i | − | 0.574663i | −0.957831 | − | 0.287331i | \(-0.907232\pi\) | ||
0.957831 | − | 0.287331i | \(-0.0927681\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 870559. | − | 502618.i | 0.672231 | − | 0.388113i | −0.124690 | − | 0.992196i | \(-0.539794\pi\) |
0.796922 | + | 0.604083i | \(0.206460\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −984044. | − | 1.70441e6i | −0.719524 | − | 1.24625i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 2.75055e6i | − | 1.90627i | −0.302544 | − | 0.953135i | \(-0.597836\pi\) | ||
0.302544 | − | 0.953135i | \(-0.402164\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 140795. | 0.0925751 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −484538. | + | 279748.i | −0.302531 | + | 0.174667i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 259810. | + | 450004.i | 0.154175 | + | 0.267039i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 718410. | 0.405524 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.10594e6 | + | 1.91555e6i | −0.594315 | + | 1.02938i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 931497. | 0.476927 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.71281e6 | − | 1.56624e6i | −1.32437 | − | 0.764625i | −0.339946 | − | 0.940445i | \(-0.610409\pi\) |
−0.984422 | + | 0.175820i | \(0.943742\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.34548e6 | + | 1.35416e6i | 1.09260 | + | 0.630816i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −959524. | − | 1.66194e6i | −0.426817 | − | 0.739269i | 0.569771 | − | 0.821804i | \(-0.307032\pi\) |
−0.996588 | + | 0.0825343i | \(0.973699\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −213984. | + | 484557.i | −0.0909550 | + | 0.205963i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 566032. | − | 326799.i | 0.230059 | − | 0.132825i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.47741e6 | + | 2.55896e6i | −0.574567 | + | 0.995179i | 0.421521 | + | 0.906818i | \(0.361496\pi\) |
−0.996089 | + | 0.0883610i | \(0.971837\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.71674e6 | − | 2.97347e6i | 0.639233 | − | 1.10718i | −0.346369 | − | 0.938098i | \(-0.612585\pi\) |
0.985601 | − | 0.169085i | \(-0.0540812\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 447872.i | 0.159770i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.44702e6 | − | 2.56749e6i | −1.52076 | − | 0.878012i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 803039.i | − | 0.263410i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.28286e6 | − | 1.31801e6i | 0.718667 | − | 0.414922i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.23720e6 | + | 5.60700e6i | 0.978613 | + | 1.69501i | 0.667456 | + | 0.744649i | \(0.267383\pi\) |
0.311157 | + | 0.950359i | \(0.399284\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.78816e6i | 1.68116i | 0.541686 | + | 0.840581i | \(0.317786\pi\) | ||||
−0.541686 | + | 0.840581i | \(0.682214\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.15683e6 | 0.322995 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 687059. | − | 396674.i | 0.184501 | − | 0.106522i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.04595e6 | − | 1.81164e6i | −0.270278 | − | 0.468136i | 0.698655 | − | 0.715459i | \(-0.253782\pi\) |
−0.968933 | + | 0.247323i | \(0.920449\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.62670e6 | −0.404684 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −176874. | + | 306355.i | −0.0423825 | + | 0.0734087i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 68232.5 | 0.0157554 | 0.00787768 | − | 0.999969i | \(-0.497492\pi\) | ||||
0.00787768 | + | 0.999969i | \(0.497492\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 991393. | + | 572381.i | 0.220696 | + | 0.127419i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.08247e6 | − | 2.93437e6i | −1.09125 | − | 0.630035i | −0.157344 | − | 0.987544i | \(-0.550293\pi\) |
−0.933910 | + | 0.357508i | \(0.883626\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.88143e6 | + | 4.99078e6i | 0.596964 | + | 1.03397i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 696047. | + | 951956.i | 0.139203 | + | 0.190383i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.07177e6 | − | 1.19614e6i | 0.400132 | − | 0.231016i | −0.286409 | − | 0.958108i | \(-0.592462\pi\) |
0.686541 | + | 0.727091i | \(0.259128\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −566857. | + | 981825.i | −0.105769 | + | 0.183198i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −242274. | + | 419630.i | −0.0436904 | + | 0.0756740i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 523538.i | 0.0912828i | 0.998958 | + | 0.0456414i | \(0.0145332\pi\) | ||||
−0.998958 | + | 0.0456414i | \(0.985467\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.77749e6 | + | 1.60358e6i | 0.468399 | + | 0.270430i | 0.715569 | − | 0.698542i | \(-0.246167\pi\) |
−0.247170 | + | 0.968972i | \(0.579501\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.86135e6i | 0.303721i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.21965e6 | + | 1.28152e6i | −0.350566 | + | 0.202399i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.30862e6 | + | 9.19480e6i | 0.811814 | + | 1.40610i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.64217e6i | 0.243238i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.39352e6 | −0.487024 | −0.243512 | − | 0.969898i | \(-0.578299\pi\) | ||||
−0.243512 | + | 0.969898i | \(0.578299\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 252471. | − | 145764.i | 0.0351188 | − | 0.0202759i | −0.482338 | − | 0.875985i | \(-0.660212\pi\) |
0.517457 | + | 0.855709i | \(0.326879\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.18040e6 | − | 2.04451e6i | −0.159194 | − | 0.275731i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.75772e6 | −1.27629 | −0.638145 | − | 0.769916i | \(-0.720298\pi\) | ||||
−0.638145 | + | 0.769916i | \(0.720298\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.24761e6 | + | 5.62502e6i | −0.412101 | + | 0.713780i | −0.995119 | − | 0.0986788i | \(-0.968538\pi\) |
0.583018 | + | 0.812459i | \(0.301872\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −648140. | −0.0798142 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.74733e6 | + | 1.00882e6i | 0.208875 | + | 0.120594i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.49461e6 | + | 1.44026e6i | 0.289562 | + | 0.167178i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 393776. | + | 682041.i | 0.0443955 | + | 0.0768952i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.37228e6 | + | 9.90081e6i | −0.478927 | + | 1.08451i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.20320e7 | − | 6.94670e6i | 1.28083 | − | 0.739488i | 0.303831 | − | 0.952726i | \(-0.401734\pi\) |
0.977000 | + | 0.213238i | \(0.0684010\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.70598e6 | − | 8.15100e6i | 0.486980 | − | 0.843475i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.76352e6 | − | 3.05451e6i | 0.177446 | − | 0.307345i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.99329e6i | 0.195070i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.13245e7 | − | 6.53819e6i | −1.07817 | − | 0.622480i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 2.18955e7i | − | 2.02852i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.01680e6 | + | 587051.i | −0.0916900 | + | 0.0529373i | −0.545144 | − | 0.838342i | \(-0.683525\pi\) |
0.453454 | + | 0.891280i | \(0.350192\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.26200e6 | + | 2.18585e6i | 0.110793 | + | 0.191899i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 983855.i | − | 0.0841112i | −0.999115 | − | 0.0420556i | \(-0.986609\pi\) | ||
0.999115 | − | 0.0420556i | \(-0.0133907\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.22566e6 | 0.268604 | 0.134302 | − | 0.990940i | \(-0.457121\pi\) | ||||
0.134302 | + | 0.990940i | \(0.457121\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.49088e6 | + | 1.43811e6i | −0.202077 | + | 0.116669i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.50061e6 | − | 1.47235e7i | −0.672020 | − | 1.16397i | −0.977330 | − | 0.211720i | \(-0.932093\pi\) |
0.305310 | − | 0.952253i | \(-0.401240\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 583262. | 0.0449428 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.78039e6 | − | 1.00119e7i | 0.434223 | − | 0.752095i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.18180e7 | 1.59816 | 0.799080 | − | 0.601224i | \(-0.205320\pi\) | ||||
0.799080 | + | 0.601224i | \(0.205320\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.09631e7 | − | 1.21031e7i | −1.49763 | − | 0.864657i | −0.497633 | − | 0.867387i | \(-0.665798\pi\) |
−0.999996 | + | 0.00273047i | \(0.999131\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.72810e6 | + | 3.30712e6i | 0.399201 | + | 0.230479i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.71644e6 | − | 2.97296e6i | −0.116716 | − | 0.202158i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.80178e7 | − | 1.31742e7i | 1.19567 | − | 0.874244i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.05651e7 | − | 6.09978e6i | 0.684348 | − | 0.395108i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.55797e6 | + | 1.30908e7i | −0.477952 | + | 0.827837i | −0.999681 | − | 0.0252745i | \(-0.991954\pi\) |
0.521729 | + | 0.853111i | \(0.325287\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.61402e6 | + | 6.25967e6i | −0.223167 | + | 0.386536i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.88127e6i | 0.294383i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.48276e7 | − | 8.56071e6i | −0.873517 | − | 0.504325i | −0.00500133 | − | 0.999987i | \(-0.501592\pi\) |
−0.868515 | + | 0.495662i | \(0.834925\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 6.43963e6i | − | 0.370648i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.89009e6 | − | 2.24594e6i | 0.218795 | − | 0.126321i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.35640e7 | − | 2.34935e7i | −0.745623 | − | 1.29146i | −0.949903 | − | 0.312545i | \(-0.898819\pi\) |
0.204280 | − | 0.978913i | \(-0.434515\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.11845e6i | 0.113836i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.93561e7 | 1.01691 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.97547e7 | + | 1.14054e7i | −1.01488 | + | 0.585939i | −0.912616 | − | 0.408819i | \(-0.865941\pi\) |
−0.102260 | + | 0.994758i | \(0.532608\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.14900e7 | + | 1.99012e7i | 0.577313 | + | 0.999936i | 0.995786 | + | 0.0917066i | \(0.0292322\pi\) |
−0.418473 | + | 0.908229i | \(0.637434\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.93152e6 | 0.291527 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.15824e7 | + | 2.00614e7i | −0.556931 | + | 0.964634i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.56394e6 | 0.167684 | 0.0838420 | − | 0.996479i | \(-0.473281\pi\) | ||||
0.0838420 | + | 0.996479i | \(0.473281\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.84314e6 | + | 2.21884e6i | 0.176959 | + | 0.102167i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.75797e7 | − | 1.01496e7i | −0.792303 | − | 0.457436i | 0.0484697 | − | 0.998825i | \(-0.484566\pi\) |
−0.840773 | + | 0.541388i | \(0.817899\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.87521e6 | + | 1.36403e7i | 0.347458 | + | 0.601816i | 0.985797 | − | 0.167940i | \(-0.0537115\pi\) |
−0.638339 | + | 0.769755i | \(0.720378\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.01679e6 | + | 2.93698e6i | −0.173518 | + | 0.126872i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.26772e6 | + | 3.61867e6i | −0.265133 | + | 0.153075i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.05672e7 | + | 1.83029e7i | −0.437789 | + | 0.758273i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.85223e6 | + | 1.01364e7i | −0.237488 | + | 0.411342i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 2.45322e7i | − | 0.975288i | −0.873042 | − | 0.487644i | \(-0.837856\pi\) | ||
0.873042 | − | 0.487644i | \(-0.162144\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 546483. | + | 315512.i | 0.0212868 | + | 0.0122899i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.35539e7i | 1.28078i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.29091e7 | − | 7.45306e6i | 0.482927 | − | 0.278818i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.43086e6 | + | 7.67448e6i | 0.162476 | + | 0.281416i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.02272e6i | 0.216503i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.42403e6 | 0.0854356 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.39339e7 | − | 8.04477e6i | 0.481569 | − | 0.278034i | −0.239501 | − | 0.970896i | \(-0.576984\pi\) |
0.721070 | + | 0.692862i | \(0.243650\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.06341e6 | + | 1.05021e7i | 0.205514 | + | 0.355961i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.71175e6 | −0.189884 | −0.0949420 | − | 0.995483i | \(-0.530267\pi\) | ||||
−0.0949420 | + | 0.995483i | \(0.530267\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.49327e6 | + | 7.78256e6i | −0.146531 | + | 0.253799i | −0.929943 | − | 0.367704i | \(-0.880144\pi\) |
0.783412 | + | 0.621502i | \(0.213477\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 408123. | 0.0130575 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.80051e6 | − | 1.03952e6i | −0.0565219 | − | 0.0326329i | 0.471473 | − | 0.881881i | \(-0.343723\pi\) |
−0.527995 | + | 0.849248i | \(0.677056\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.57026e7 | + | 2.06129e7i | 1.09984 | + | 0.634991i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.30785e6 | + | 1.43896e7i | 0.251173 | + | 0.435045i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.58828e7 | + | 4.96287e6i | −1.36158 | + | 0.147274i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.13718e7 | − | 2.38860e7i | 1.20519 | − | 0.695815i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.18629e7 | + | 2.05472e7i | −0.339272 | + | 0.587637i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −732724. | + | 1.26911e6i | −0.0205756 | + | 0.0356380i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 2.97731e7i | − | 0.820994i | −0.911862 | − | 0.410497i | \(-0.865355\pi\) | ||
0.911862 | − | 0.410497i | \(-0.134645\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.24159e7 | − | 7.16830e6i | −0.336236 | − | 0.194126i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 844070.i | 0.0224514i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.68887e7 | + | 2.12977e7i | −0.963837 | + | 0.556471i | −0.897352 | − | 0.441316i | \(-0.854512\pi\) |
−0.0664850 | + | 0.997787i | \(0.521178\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.24597e7 | + | 5.62218e7i | 0.833192 | + | 1.44313i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.07283e7i | 1.02715i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.77108e7 | 0.438891 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.87788e6 | + | 1.66154e6i | −0.0700834 | + | 0.0404627i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.87140e7 | − | 6.70546e7i | −0.926572 | − | 1.60487i | −0.789013 | − | 0.614377i | \(-0.789407\pi\) |
−0.137560 | − | 0.990493i | \(-0.543926\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.13837e7 | 0.738291 | 0.369145 | − | 0.929372i | \(-0.379650\pi\) | ||||
0.369145 | + | 0.929372i | \(0.379650\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.45985e7 | − | 5.99264e7i | 0.800085 | − | 1.38579i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.82054e6 | −0.223260 | −0.111630 | − | 0.993750i | \(-0.535607\pi\) | ||||
−0.111630 | + | 0.993750i | \(0.535607\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.06150e7 | − | 6.12858e6i | −0.237266 | − | 0.136986i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.06211e7 | − | 6.13210e6i | −0.233435 | − | 0.134774i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.95871e7 | + | 3.39259e7i | 0.423338 | + | 0.733242i | 0.996264 | − | 0.0863647i | \(-0.0275250\pi\) |
−0.572926 | + | 0.819607i | \(0.694192\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.16908e7 | − | 3.47708e7i | −0.673615 | − | 0.739082i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.46844e7 | + | 8.47806e6i | −0.306999 | + | 0.177246i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.51466e6 | + | 1.47478e7i | −0.175101 | + | 0.303284i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.82447e7 | + | 6.62418e7i | −0.773701 | + | 1.34009i | 0.161821 | + | 0.986820i | \(0.448263\pi\) |
−0.935522 | + | 0.353269i | \(0.885070\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.61125e7i | 0.320690i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.60951e6 | − | 2.66130e6i | −0.0902678 | − | 0.0521161i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 1.59065e6i | − | 0.0306512i | −0.999883 | − | 0.0153256i | \(-0.995122\pi\) | ||
0.999883 | − | 0.0153256i | \(-0.00487847\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.90400e7 | + | 1.09927e7i | −0.361054 | + | 0.208455i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.25093e7 | − | 7.36282e7i | −0.793340 | − | 1.37411i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.73606e7i | 0.502583i | 0.967911 | + | 0.251292i | \(0.0808553\pi\) | ||||
−0.967911 | + | 0.251292i | \(0.919145\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.39339e7 | 1.33681 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.58785e7 | − | 2.07144e7i | 0.638613 | − | 0.368703i | −0.145467 | − | 0.989363i | \(-0.546469\pi\) |
0.784080 | + | 0.620660i | \(0.213135\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.87285e6 | + | 3.24386e6i | 0.0328186 | + | 0.0568435i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.97289e7 | 0.340385 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.53609e7 | − | 7.85673e7i | 0.770606 | − | 1.33473i | −0.166625 | − | 0.986020i | \(-0.553287\pi\) |
0.937231 | − | 0.348709i | \(-0.113380\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.08204e7 | −0.515594 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.92257e7 | + | 2.26470e7i | 0.646239 | + | 0.373106i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.30385e7 | − | 7.52779e6i | −0.211561 | − | 0.122145i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.15730e7 | − | 5.46860e7i | −0.504596 | − | 0.873986i | −0.999986 | − | 0.00531545i | \(-0.998308\pi\) |
0.495390 | − | 0.868671i | \(-0.335025\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.34445e6 | − | 1.24297e7i | −0.0211653 | − | 0.195678i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.51360e7 | + | 2.60593e7i | −0.699986 | + | 0.404137i | −0.807342 | − | 0.590083i | \(-0.799095\pi\) |
0.107356 | + | 0.994221i | \(0.465762\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.19962e7 | − | 7.27396e7i | 0.641646 | − | 1.11136i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.78692e6 | + | 1.00232e7i | −0.0871129 | + | 0.150884i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1.31579e8i | − | 1.95166i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.51917e7 | − | 3.18650e7i | −0.806685 | − | 0.465740i | 0.0391182 | − | 0.999235i | \(-0.487545\pi\) |
−0.845803 | + | 0.533495i | \(0.820878\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 6.97408e7i | − | 1.00453i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.37304e6 | + | 792725.i | −0.0194910 | + | 0.0112531i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.94372e6 | − | 1.37589e7i | −0.111142 | − | 0.192504i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.10378e7i | 1.11758i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.50633e6 | −0.115638 | −0.0578189 | − | 0.998327i | \(-0.518415\pi\) | ||||
−0.0578189 | + | 0.998327i | \(0.518415\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.03004e7 | − | 5.21350e7i | 1.21016 | − | 0.698687i | 0.247367 | − | 0.968922i | \(-0.420435\pi\) |
0.962795 | + | 0.270235i | \(0.0871012\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.63127e6 | + | 2.82544e6i | 0.0215528 | + | 0.0373306i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.87750e7 | −1.28671 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.04519e6 | + | 5.27443e6i | −0.0391139 | + | 0.0677473i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.21197e8 | 1.53504 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.21174e7 | + | 3.00900e7i | 0.650955 | + | 0.375829i | 0.788822 | − | 0.614622i | \(-0.210691\pi\) |
−0.137867 | + | 0.990451i | \(0.544025\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.43557e7 | + | 4.87028e7i | 1.03908 | + | 0.599915i | 0.919574 | − | 0.392918i | \(-0.128534\pi\) |
0.119510 | + | 0.992833i | \(0.461868\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.47678e6 | + | 1.64143e7i | 0.115131 | + | 0.199413i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.85441e7 | − | 2.53621e7i | −0.222209 | − | 0.303907i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.39265e7 | − | 2.53610e7i | 0.519199 | − | 0.299759i | −0.217408 | − | 0.976081i | \(-0.569760\pi\) |
0.736607 | + | 0.676321i | \(0.236427\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.60109e6 | − | 1.66296e7i | 0.111945 | − | 0.193895i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.16568e7 | + | 1.41434e8i | −0.939250 | + | 1.62683i | −0.172376 | + | 0.985031i | \(0.555144\pi\) |
−0.766874 | + | 0.641798i | \(0.778189\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 2.52074e7i | − | 0.286054i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.32338e8 | − | 7.64054e7i | −1.48171 | − | 0.855463i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 6.29869e7i | − | 0.695843i | −0.937524 | − | 0.347922i | \(-0.886887\pi\) | ||
0.937524 | − | 0.347922i | \(-0.113113\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.28067e8 | + | 7.39392e7i | −1.39607 | + | 0.806019i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.83069e7 | − | 1.18311e8i | −0.734801 | − | 1.27271i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 7.72460e6i | − | 0.0820053i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.94545e7 | 0.518152 | 0.259076 | − | 0.965857i | \(-0.416582\pi\) | ||||
0.259076 | + | 0.965857i | \(0.416582\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.23906e8 | + | 7.15370e7i | −1.28131 | + | 0.739763i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.18694e7 | + | 1.24481e8i | 0.733570 | + | 1.27058i | 0.955348 | + | 0.295483i | \(0.0954805\pi\) |
−0.221778 | + | 0.975097i | \(0.571186\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.03473e8 | 1.04252 | 0.521262 | − | 0.853397i | \(-0.325462\pi\) | ||||
0.521262 | + | 0.853397i | \(0.325462\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.36240e6 | + | 1.62162e7i | −0.0931169 | + | 0.161283i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.54867e8 | 1.52058 | 0.760290 | − | 0.649584i | \(-0.225057\pi\) | ||||
0.760290 | + | 0.649584i | \(0.225057\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.83661e6 | − | 1.06036e6i | −0.0178032 | − | 0.0102787i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.27587e7 | + | 2.46868e7i | 0.409225 | + | 0.236266i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.05346e7 | + | 1.56810e8i | 0.855522 | + | 1.48181i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.94313e7 | − | 8.12818e7i | −0.554542 | − | 0.758425i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.02622e7 | + | 5.92488e6i | −0.0945550 | + | 0.0545914i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.38055e7 | + | 1.45155e8i | −0.762546 | + | 1.32077i | 0.178988 | + | 0.983851i | \(0.442718\pi\) |
−0.941534 | + | 0.336917i | \(0.890616\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.35675e8 | + | 2.34997e8i | −1.21918 | + | 2.11167i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 8.34927e6i | − | 0.0740981i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.32005e7 | + | 7.62134e6i | 0.115709 | + | 0.0668045i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.20779e8i | 1.04570i | 0.852425 | + | 0.522849i | \(0.175131\pi\) | ||||
−0.852425 | + | 0.522849i | \(0.824869\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.39469e6 | + | 805222.i | −0.0119275 | + | 0.00688635i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.42386e7 | − | 4.19824e7i | −0.204768 | − | 0.354669i | 0.745291 | − | 0.666740i | \(-0.232311\pi\) |
−0.950059 | + | 0.312071i | \(0.898977\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.75787e8i | 1.46705i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.33906e6 | 0.0687546 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.66703e7 | − | 1.53981e7i | 0.217249 | − | 0.125429i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.53120e7 | − | 9.58031e7i | −0.445161 | − | 0.771042i | 0.552902 | − | 0.833246i | \(-0.313520\pi\) |
−0.998063 | + | 0.0622042i | \(0.980187\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.38516e8 | 1.10150 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.61532e7 | − | 1.31901e8i | 0.598390 | − | 1.03644i | −0.394669 | − | 0.918824i | \(-0.629141\pi\) |
0.993059 | − | 0.117619i | \(-0.0375261\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.84336e6 | 0.0609015 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.17794e8 | − | 6.80084e7i | −0.903856 | − | 0.521841i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.54976e7 | + | 4.35886e7i | 0.572506 | + | 0.330536i | 0.758150 | − | 0.652081i | \(-0.226104\pi\) |
−0.185644 | + | 0.982617i | \(0.559437\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.13931e7 | − | 3.70540e7i | −0.160329 | − | 0.277698i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.33420e8 | − | 5.89192e7i | −0.988252 | − | 0.436420i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.36769e7 | − | 7.89636e6i | 0.100130 | − | 0.0578103i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.49715e7 | + | 2.59315e7i | −0.108342 | + | 0.187653i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.82316e7 | + | 4.88986e7i | −0.201945 | + | 0.349779i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 4.64184e7i | − | 0.328229i | −0.986441 | − | 0.164115i | \(-0.947523\pi\) | ||
0.986441 | − | 0.164115i | \(-0.0524767\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.36597e7 | + | 2.52070e7i | 0.305194 | + | 0.176204i | 0.644774 | − | 0.764373i | \(-0.276952\pi\) |
−0.339580 | + | 0.940577i | \(0.610285\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 2.67583e7i | − | 0.184918i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.50399e8 | + | 8.68327e7i | −1.02757 | + | 0.593269i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.35269e7 | + | 1.10032e8i | 0.429132 | + | 0.743278i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.52970e6i | 0.0235751i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.04964e8 | 2.01404 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.87395e7 | − | 1.08193e7i | 0.122376 | − | 0.0706540i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.17835e6 | − | 1.07012e7i | −0.0398979 | − | 0.0691051i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.76235e8 | 1.12545 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.83173e7 | − | 3.17265e7i | 0.115683 | − | 0.200369i | −0.802370 | − | 0.596827i | \(-0.796428\pi\) |
0.918053 | + | 0.396459i | \(0.129761\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.56965e7 | −0.472798 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.67585e7 | + | 1.54490e7i | 0.165300 | + | 0.0954360i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.52395e8 | − | 8.79852e7i | −0.931126 | − | 0.537586i | −0.0439585 | − | 0.999033i | \(-0.513997\pi\) |
−0.887168 | + | 0.461447i | \(0.847330\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.77954e6 | + | 1.17425e7i | 0.0409716 | + | 0.0709650i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.44655e8 | + | 1.05768e8i | −0.864726 | + | 0.632266i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.27593e7 | − | 1.89136e7i | 0.193713 | − | 0.111840i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.02467e7 | − | 5.23889e7i | 0.176929 | − | 0.306450i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.38942e7 | − | 4.13859e7i | 0.138269 | − | 0.239490i | −0.788572 | − | 0.614942i | \(-0.789179\pi\) |
0.926842 | + | 0.375452i | \(0.122513\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3.73412e8i | − | 2.13773i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.17018e8 | − | 1.25296e8i | −1.22916 | − | 0.709655i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.75359e7i | 0.266377i | 0.991091 | + | 0.133188i | \(0.0425215\pi\) | ||||
−0.991091 | + | 0.133188i | \(0.957478\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.32175e7 | − | 4.22721e7i | 0.405947 | − | 0.234374i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.45397e7 | − | 2.51834e7i | −0.0797637 | − | 0.138155i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.14456e8i | 0.621300i | 0.950524 | + | 0.310650i | \(0.100547\pi\) | ||||
−0.950524 | + | 0.310650i | \(0.899453\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.08831e8 | 1.65887 | 0.829436 | − | 0.558601i | \(-0.188662\pi\) | ||||
0.829436 | + | 0.558601i | \(0.188662\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.93641e7 | − | 4.00474e7i | 0.368698 | − | 0.212868i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.36222e7 | − | 5.82354e7i | −0.176857 | − | 0.306326i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.35527e8 | −1.22607 | −0.613033 | − | 0.790057i | \(-0.710051\pi\) | ||||
−0.613033 | + | 0.790057i | \(0.710051\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.44037e6 | + | 5.95890e6i | −0.0177243 | + | 0.0306994i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.99173e7 | 0.203532 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.41848e7 | − | 5.43776e7i | −0.475308 | − | 0.274419i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.48933e7 | − | 8.59867e6i | −0.0743917 | − | 0.0429501i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.18154e8 | + | 2.04648e8i | 0.584162 | + | 1.01180i | 0.994979 | + | 0.100081i | \(0.0319102\pi\) |
−0.410817 | + | 0.911718i | \(0.634756\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.61947e8 | − | 7.15171e7i | −0.792550 | − | 0.349997i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.99450e8 | − | 1.15152e8i | 0.966208 | − | 0.557840i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.64404e8 | + | 2.84756e8i | −0.788404 | + | 1.36556i | 0.138540 | + | 0.990357i | \(0.455759\pi\) |
−0.926944 | + | 0.375199i | \(0.877574\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.98582e6 | + | 1.38318e7i | −0.0379113 | + | 0.0656643i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 1.53302e8i | − | 0.720484i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.73934e8 | − | 1.00421e8i | −0.809289 | − | 0.467243i | 0.0374200 | − | 0.999300i | \(-0.488086\pi\) |
−0.846709 | + | 0.532057i | \(0.821419\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 6.71399e7i | − | 0.309284i | −0.987971 | − | 0.154642i | \(-0.950578\pi\) | ||
0.987971 | − | 0.154642i | \(-0.0494224\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.08885e6 | + | 2.36070e6i | −0.0186487 | + | 0.0107668i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.10409e7 | + | 1.91235e7i | 0.0498586 | + | 0.0863577i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.51159e8i | 1.12301i | 0.827473 | + | 0.561505i | \(0.189777\pi\) | ||||
−0.827473 | + | 0.561505i | \(0.810223\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.76209e7 | −0.210836 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.34775e7 | − | 3.08753e7i | 0.234449 | − | 0.135359i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.71977e8 | − | 2.97872e8i | −0.746600 | − | 1.29315i | −0.949443 | − | 0.313938i | \(-0.898351\pi\) |
0.202843 | − | 0.979211i | \(-0.434982\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.79870e7 | −0.292281 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.18205e8 | − | 2.04738e8i | 0.503248 | − | 0.871651i | −0.496745 | − | 0.867896i | \(-0.665472\pi\) |
0.999993 | − | 0.00375422i | \(-0.00119501\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.71139e8 | 1.56482 | 0.782411 | − | 0.622762i | \(-0.213990\pi\) | ||||
0.782411 | + | 0.622762i | \(0.213990\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.43530e7 | − | 4.87012e7i | −0.352229 | − | 0.203360i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.48486e7 | + | 3.16668e7i | 0.226830 | + | 0.130961i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00373e8 | − | 1.73852e8i | −0.411130 | − | 0.712098i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.74707e7 | − | 2.53972e8i | −0.111447 | − | 1.03035i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.85887e8 | − | 2.80527e8i | 1.95246 | − | 1.12726i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.09392e7 | + | 1.40191e8i | −0.322159 | + | 0.557996i | −0.980933 | − | 0.194344i | \(-0.937742\pi\) |
0.658774 | + | 0.752341i | \(0.271075\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.63958e8 | + | 2.83984e8i | −0.646430 | + | 1.11965i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 9.62839e7i | − | 0.376039i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.14751e8 | − | 1.81721e8i | −1.21772 | − | 0.703052i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 6.85618e7i | − | 0.262772i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.49604e7 | − | 5.48254e7i | 0.360553 | − | 0.208165i | −0.308771 | − | 0.951137i | \(-0.599918\pi\) |
0.669323 | + | 0.742971i | \(0.266584\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.25704e7 | − | 2.17725e7i | −0.0472840 | − | 0.0818984i | 0.841415 | − | 0.540390i | \(-0.181723\pi\) |
−0.888699 | + | 0.458492i | \(0.848390\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.32464e7i | 0.310232i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.97665e7 | −0.294515 | −0.147258 | − | 0.989098i | \(-0.547045\pi\) | ||||
−0.147258 | + | 0.989098i | \(0.547045\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.80549e7 | + | 1.61975e7i | −0.102630 | + | 0.0592536i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.35231e7 | − | 4.07432e7i | −0.0852612 | − | 0.147677i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.37333e8 | 0.493215 | 0.246607 | − | 0.969115i | \(-0.420684\pi\) | ||||
0.246607 | + | 0.969115i | \(0.420684\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.94931e7 | − | 5.10835e7i | 0.104953 | − | 0.181784i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.52554e7 | −0.335887 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.48871e8 | + | 2.01421e8i | 1.21901 | + | 0.703798i | 0.964707 | − | 0.263325i | \(-0.0848191\pi\) |
0.254308 | + | 0.967123i | \(0.418152\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.46746e8 | + | 1.42459e8i | 0.854369 | + | 0.493270i | 0.862122 | − | 0.506700i | \(-0.169135\pi\) |
−0.00775379 | + | 0.999970i | \(0.502468\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.58392e8 | + | 4.47549e8i | 0.886623 | + | 1.53568i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.61871e7 | + | 1.75087e6i | −0.0550434 | + | 0.00595372i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.03640e8 | + | 5.98365e7i | −0.349260 | + | 0.201645i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.38558e7 | − | 2.39989e7i | 0.0462756 | − | 0.0801517i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.22216e7 | + | 1.07771e8i | −0.205956 | + | 0.356726i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.25275e8i | 0.739038i | 0.929223 | + | 0.369519i | \(0.120478\pi\) | ||||
−0.929223 | + | 0.369519i | \(0.879522\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.70339e8 | − | 1.56081e8i | −0.879019 | − | 0.507502i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 4.96421e8i | − | 1.59987i | −0.600089 | − | 0.799934i | \(-0.704868\pi\) | ||
0.600089 | − | 0.799934i | \(-0.295132\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.31664e7 | + | 1.91486e7i | −0.105947 | + | 0.0611686i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.16106e7 | + | 2.01102e7i | 0.0367633 | + | 0.0636758i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.77653e8i | 1.49917i | 0.661909 | + | 0.749584i | \(0.269747\pi\) | ||||
−0.661909 | + | 0.749584i | \(0.730253\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.08232e7 | −0.282569 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.59332e7 | + | 3.80665e7i | −0.203345 | + | 0.117401i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.12141e8 | + | 1.94234e8i | 0.342852 | + | 0.593837i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.70566e8 | −0.820047 | −0.410024 | − | 0.912075i | \(-0.634480\pi\) | ||||
−0.410024 | + | 0.912075i | \(0.634480\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.04760e7 | + | 1.81449e7i | −0.0314771 | + | 0.0545199i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.05535e8 | 0.314371 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.46076e8 | − | 3.15277e8i | −1.61270 | − | 0.931095i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.47508e8 | + | 2.00634e8i | 1.01750 | + | 0.587453i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.86703e6 | − | 3.23379e6i | −0.00541997 | − | 0.00938767i | 0.863303 | − | 0.504686i | \(-0.168392\pi\) |
−0.868723 | + | 0.495299i | \(0.835059\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.23195e8 | + | 2.31047e8i | 1.50591 | + | 0.665020i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.19220e7 | + | 6.88316e6i | −0.0340237 | + | 0.0196436i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.85324e6 | + | 1.70663e7i | −0.0278818 | + | 0.0482927i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.65430e8 | + | 4.59738e8i | −0.744751 | + | 1.28995i | 0.205560 | + | 0.978644i | \(0.434098\pi\) |
−0.950311 | + | 0.311302i | \(0.899235\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 8.42150e7i | − | 0.234304i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.02389e8 | − | 5.91143e7i | −0.282478 | − | 0.163089i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 1.57835e8i | − | 0.431802i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.45963e8 | + | 2.57477e8i | −1.20988 | + | 0.698523i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.41180e8 | + | 4.17736e8i | 0.648865 | + | 1.12387i | 0.983394 | + | 0.181482i | \(0.0580893\pi\) |
−0.334529 | + | 0.942385i | \(0.608577\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.96793e7i | 0.105866i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.71320e8 | 1.51170 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.32151e8 | + | 1.91768e8i | −0.871609 | + | 0.503224i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.54785e7 | − | 1.13412e8i | −0.170410 | − | 0.295159i | 0.768153 | − | 0.640266i | \(-0.221176\pi\) |
−0.938563 | + | 0.345107i | \(0.887843\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.30610e8 | −1.11148 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.86040e8 | + | 6.68640e8i | −0.988279 | + | 1.71175i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.41677e8 | 1.37540 | 0.687699 | − | 0.725996i | \(-0.258621\pi\) | ||||
0.687699 | + | 0.725996i | \(0.258621\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.01687e7 | + | 4.05119e7i | 0.176718 | + | 0.102028i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.75269e7 | − | 2.16661e7i | −0.0937432 | − | 0.0541226i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.36489e8 | + | 4.09611e8i | 0.585973 | + | 1.01493i | 0.994753 | + | 0.102302i | \(0.0326208\pi\) |
−0.408781 | + | 0.912633i | \(0.634046\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.12817e8 | + | 4.81913e8i | −0.523060 | + | 1.18444i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.54508e8 | − | 2.62410e8i | 1.10809 | − | 0.639757i | 0.169757 | − | 0.985486i | \(-0.445702\pi\) |
0.938334 | + | 0.345729i | \(0.112368\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.95025e7 | + | 1.72343e8i | −0.240638 | + | 0.416798i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.44341e7 | − | 7.69621e7i | 0.106599 | − | 0.184635i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.43670e7i | 0.129387i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.13094e8 | − | 4.11705e8i | −1.68355 | − | 0.972000i | −0.959267 | − | 0.282501i | \(-0.908836\pi\) |
−0.724286 | − | 0.689499i | \(-0.757831\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 3.56771e8i | − | 0.835612i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.54076e8 | + | 8.89558e7i | −0.358009 | + | 0.206697i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.72006e7 | − | 1.51036e8i | −0.201017 | − | 0.348171i | 0.747840 | − | 0.663879i | \(-0.231091\pi\) |
−0.948856 | + | 0.315708i | \(0.897758\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 1.70598e8i | − | 0.390166i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.25630e8 | 1.64650 | 0.823249 | − | 0.567680i | \(-0.192159\pi\) | ||||
0.823249 | + | 0.567680i | \(0.192159\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.72309e7 | + | 3.88158e7i | −0.151355 | + | 0.0873846i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.77789e7 | + | 3.07939e7i | 0.0397119 | + | 0.0687830i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.68071e7 | 0.148060 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.42126e8 | − | 4.19375e8i | 0.532431 | − | 0.922197i | −0.466852 | − | 0.884335i | \(-0.654612\pi\) |
0.999283 | − | 0.0378619i | \(-0.0120547\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.04105e8 | 0.881721 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.22187e8 | − | 2.43750e8i | −0.914043 | − | 0.527723i | −0.0323133 | − | 0.999478i | \(-0.510287\pi\) |
−0.881730 | + | 0.471755i | \(0.843621\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.28142e8 | − | 1.89453e8i | −0.704948 | − | 0.407002i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.59950e7 | + | 1.31627e8i | 0.162003 | + | 0.280597i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.91236e7 | − | 6.39062e8i | −0.146222 | − | 1.35186i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.44946e8 | − | 3.14625e8i | 1.14393 | − | 0.660450i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.77772e8 | + | 4.81115e8i | −0.578633 | + | 1.00222i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.21495e7 | − | 5.56846e7i | 0.0664608 | − | 0.115113i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 3.14248e8i | − | 0.644686i | −0.946623 | − | 0.322343i | \(-0.895529\pi\) | ||
0.946623 | − | 0.322343i | \(-0.104471\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.54500e8 | + | 3.20141e8i | 1.12894 | + | 0.651793i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.12418e8i | 0.429202i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.22252e8 | − | 1.28317e8i | 0.445683 | − | 0.257315i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.50001e7 | − | 4.33014e7i | −0.0497554 | − | 0.0861788i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.43566e8i | 0.678633i | 0.940672 | + | 0.339317i | \(0.110196\pi\) | ||||
−0.940672 | + | 0.339317i | \(0.889804\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.27677e8 | −0.250307 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.22110e8 | − | 7.05001e7i | 0.237604 | − | 0.137180i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.37120e8 | − | 7.57114e8i | −0.844217 | − | 1.46223i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.08732e7 | −0.0208435 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.69193e8 | − | 4.66256e8i | 0.512204 | − | 0.887163i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.39743e8 | 0.263926 | 0.131963 | − | 0.991255i | \(-0.457872\pi\) | ||||
0.131963 | + | 0.991255i | \(0.457872\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.05685e7 | + | 1.76487e7i | 0.0573075 | + | 0.0330865i | 0.528380 | − | 0.849008i | \(-0.322800\pi\) |
−0.471072 | + | 0.882095i | \(0.656133\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.69715e8 | − | 2.71190e8i | −0.874103 | − | 0.504664i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.04864e6 | + | 1.81629e6i | 0.00193710 | + | 0.00335516i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.82496e8 | + | 8.46381e7i | −1.43488 | + | 0.155203i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.74196e7 | − | 2.16042e7i | 0.0681157 | − | 0.0393266i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.09482e8 | − | 7.09244e8i | 0.739955 | − | 1.28164i | −0.212559 | − | 0.977148i | \(-0.568180\pi\) |
0.952515 | − | 0.304492i | \(-0.0984868\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.00075e8 | − | 5.19745e8i | 0.538307 | − | 0.932375i | −0.460688 | − | 0.887562i | \(-0.652397\pi\) |
0.998995 | − | 0.0448133i | \(-0.0142693\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 5.46744e8i | − | 0.973693i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.19418e8 | − | 3.57621e8i | −1.09513 | − | 0.632276i | −0.160195 | − | 0.987085i | \(-0.551212\pi\) |
−0.934939 | + | 0.354809i | \(0.884546\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.10758e8i | 1.07203i | 0.844209 | + | 0.536014i | \(0.180070\pi\) | ||||
−0.844209 | + | 0.536014i | \(0.819930\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.28477e7 | + | 4.20586e7i | −0.126944 | + | 0.0732912i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.75733e8 | + | 6.50788e8i | 0.650046 | + | 1.12591i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 1.80388e8i | − | 0.309848i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.48839e8 | −0.935985 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.95923e8 | − | 1.13116e8i | 0.331741 | − | 0.191531i | −0.324873 | − | 0.945758i | \(-0.605321\pi\) |
0.656614 | + | 0.754227i | \(0.271988\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.38715e7 | + | 7.59877e7i | 0.0737555 | + | 0.127748i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.79108e8 | 0.799744 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.85671e7 | + | 1.53403e8i | −0.146792 | + | 0.254251i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.54809e7 | −0.0913047 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.21941e8 | − | 1.85873e8i | −0.526083 | − | 0.303734i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.30784e8 | + | 1.90978e8i | 0.536730 | + | 0.309881i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.88893e8 | − | 3.27172e8i | −0.304346 | − | 0.527143i | 0.672769 | − | 0.739852i | \(-0.265105\pi\) |
−0.977116 | + | 0.212709i | \(0.931771\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.46430e7 | + | 3.31584e7i | −0.0234279 | + | 0.0530512i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.10139e7 | − | 1.21324e7i | 0.0333859 | − | 0.0192754i | −0.483214 | − | 0.875502i | \(-0.660531\pi\) |
0.516600 | + | 0.856227i | \(0.327197\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.38152e8 | + | 4.12492e8i | −0.375730 | + | 0.650783i | −0.990436 | − | 0.137973i | \(-0.955941\pi\) |
0.614706 | + | 0.788756i | \(0.289275\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.54089e7 | − | 1.47932e8i | 0.133812 | − | 0.231768i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.19370e8i | 0.341307i | 0.985331 | + | 0.170653i | \(0.0545878\pi\) | ||||
−0.985331 | + | 0.170653i | \(0.945412\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.36804e7 | + | 3.67659e7i | 0.0983915 | + | 0.0568064i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 4.98819e8i | − | 0.765395i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.69362e8 | − | 3.86456e8i | 1.02000 | − | 0.588899i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.46813e7 | + | 7.73902e7i | 0.0676194 | + | 0.117120i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.52615e7i | 0.128148i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.19370e7 | −0.107381 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.45206e8 | + | 8.38347e7i | −0.215271 | + | 0.124287i | −0.603759 | − | 0.797167i | \(-0.706331\pi\) |
0.388488 | + | 0.921454i | \(0.372998\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.89508e8 | + | 5.01442e8i | 0.426279 | + | 0.738336i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.61942e7 | −0.0236827 | −0.0118413 | − | 0.999930i | \(-0.503769\pi\) | ||||
−0.0118413 | + | 0.999930i | \(0.503769\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.62142e8 | + | 6.27248e8i | −0.526013 | + | 0.911082i | 0.473528 | + | 0.880779i | \(0.342980\pi\) |
−0.999541 | + | 0.0303026i | \(0.990353\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.48936e7 | −0.0214867 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.22803e8 | − | 4.17311e8i | −1.03574 | − | 0.597983i | −0.117114 | − | 0.993118i | \(-0.537364\pi\) |
−0.918623 | + | 0.395136i | \(0.870698\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.09503e8 | + | 1.20957e8i | 0.298185 | + | 0.172157i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.97085e8 | − | 5.14566e8i | −0.419998 | − | 0.727459i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.68213e7 | − | 1.05065e8i | −0.107877 | − | 0.147539i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.39362e7 | + | 8.04604e6i | −0.0194390 | + | 0.0112231i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.75909e8 | + | 3.04684e8i | −0.243732 | + | 0.422155i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.37164e8 | + | 5.83986e8i | −0.464048 | + | 0.803754i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 4.63732e8i | − | 0.634006i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.81135e8 | − | 1.04578e8i | −0.246003 | − | 0.142030i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.85792e7i | 0.132996i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.51139e8 | − | 3.18200e8i | 0.738651 | − | 0.426460i | −0.0829278 | − | 0.996556i | \(-0.526427\pi\) |
0.821579 | + | 0.570095i | \(0.193094\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.19363e7 | + | 3.79949e7i | 0.0292060 | + | 0.0505863i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 2.53776e8i | − | 0.335656i | −0.985816 | − | 0.167828i | \(-0.946325\pi\) | ||
0.985816 | − | 0.167828i | \(-0.0536754\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.15619e8 | 1.07170 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.95477e7 | + | 2.86064e7i | −0.0646785 | + | 0.0373421i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.41015e7 | + | 1.28347e8i | 0.0960990 | + | 0.166448i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.10261e9 | 1.42061 | 0.710306 | − | 0.703893i | \(-0.248557\pi\) | ||||
0.710306 | + | 0.703893i | \(0.248557\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.89875e8 | + | 3.28873e8i | −0.243046 | + | 0.420968i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.29768e9 | −1.65030 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.06012e9 | + | 6.12058e8i | 1.33946 | + | 0.773335i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.65032e7 | + | 4.41691e7i | 0.0960374 | + | 0.0554472i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.38726e7 | + | 1.62592e8i | 0.117082 | + | 0.202793i | 0.918610 | − | 0.395165i | \(-0.129312\pi\) |
−0.801528 | + | 0.597957i | \(0.795979\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.09461e8 | + | 7.00758e8i | −0.383492 | + | 0.868399i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.16749e8 | − | 6.74052e7i | 0.143750 | − | 0.0829944i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.63172e8 | + | 2.82622e8i | −0.199623 | + | 0.345757i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.47001e8 | − | 6.01023e8i | 0.421805 | − | 0.730588i | −0.574311 | − | 0.818637i | \(-0.694730\pi\) |
0.996116 | + | 0.0880492i | \(0.0280633\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 2.12103e8i | − | 0.256183i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.46330e8 | − | 1.99954e8i | −0.415644 | − | 0.239972i | 0.277568 | − | 0.960706i | \(-0.410472\pi\) |
−0.693212 | + | 0.720734i | \(0.743805\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 4.29271e8i | − | 0.511913i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.37131e7 | + | 2.52378e7i | −0.0517984 | + | 0.0299058i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.24255e8 | − | 5.61626e8i | −0.381800 | − | 0.661298i | 0.609519 | − | 0.792771i | \(-0.291362\pi\) |
−0.991320 | + | 0.131474i | \(0.958029\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.80291e9i | 2.10948i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.90702e7 | 0.0570527 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.87604e8 | − | 4.54723e8i | 0.909974 | − | 0.525374i | 0.0295512 | − | 0.999563i | \(-0.490592\pi\) |
0.880423 | + | 0.474190i | \(0.157259\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.21536e7 | − | 9.03327e7i | −0.0598789 | − | 0.103713i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.73024e8 | −1.11017 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.14097e8 | − | 1.97621e8i | 0.129365 | − | 0.224067i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.21313e8 | 0.249366 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.04822e8 | + | 6.05188e7i | 0.117374 | + | 0.0677659i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.76025e6 | + | 4.48038e6i | 0.00863563 | + | 0.00498578i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.87861e8 | + | 4.98590e8i | 0.318349 | + | 0.551397i | 0.980144 | − | 0.198288i | \(-0.0635383\pi\) |
−0.661795 | + | 0.749685i | \(0.730205\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.79284e8 | − | 6.42911e8i | 0.966402 | − | 0.706610i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.10914e9 | + | 6.40364e8i | −1.21152 | + | 0.699471i | −0.963090 | − | 0.269180i | \(-0.913247\pi\) |
−0.248429 | + | 0.968650i | \(0.579914\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.32579e8 | + | 2.29633e8i | −0.143925 | + | 0.249285i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.63765e8 | + | 9.76470e8i | −0.608253 | + | 1.05353i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.41721e9i | 1.51968i | 0.650112 | + | 0.759838i | \(0.274722\pi\) | ||||
−0.650112 | + | 0.759838i | \(0.725278\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.12071e9 | + | 6.47040e8i | 1.19438 | + | 0.689577i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.72832e8i | 0.183070i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.16009e9 | + | 6.69779e8i | −1.22133 | + | 0.705132i | −0.965200 | − | 0.261511i | \(-0.915779\pi\) |
−0.256125 | + | 0.966644i | \(0.582446\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.49962e8 | − | 2.59742e8i | −0.156918 | − | 0.271790i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 3.45879e7i | − | 0.0359727i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.25619e8 | −0.543353 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.26839e8 | + | 7.32305e7i | −0.130326 | + | 0.0752439i | −0.563746 | − | 0.825948i | \(-0.690640\pi\) |
0.433419 | + | 0.901192i | \(0.357307\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.51357e8 | + | 6.08568e8i | 0.358840 | + | 0.621528i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.99644e8 | −0.202669 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.20649e8 | − | 5.55380e8i | 0.323552 | − | 0.560409i | −0.657666 | − | 0.753310i | \(-0.728456\pi\) |
0.981218 | + | 0.192901i | \(0.0617895\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.77311e9 | 1.77844 |
(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 | 76.7.h.a.69.4 | yes | 20 | |
3.2 | odd | 2 | 684.7.y.c.145.6 | 20 | |||
19.8 | odd | 6 | inner | 76.7.h.a.65.4 | ✓ | 20 | |
57.8 | even | 6 | 684.7.y.c.217.6 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.7.h.a.65.4 | ✓ | 20 | 19.8 | odd | 6 | inner | |
76.7.h.a.69.4 | yes | 20 | 1.1 | even | 1 | trivial | |
684.7.y.c.145.6 | 20 | 3.2 | odd | 2 | |||
684.7.y.c.217.6 | 20 | 57.8 | even | 6 |