Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,8,Mod(5,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 16]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.5");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.i (of order \(9\), degree \(6\), 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: | \(23.7412619368\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{9})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 73.12 | ||
Character | \(\chi\) | \(=\) | 76.73 |
Dual form | 76.8.i.a.25.12 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{2}{9}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 84.9007 | − | 30.9013i | 1.81546 | − | 0.660774i | 0.819288 | − | 0.573383i | \(-0.194369\pi\) |
0.996174 | − | 0.0873915i | \(-0.0278531\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −77.9653 | + | 442.163i | −0.278937 | + | 1.58193i | 0.447235 | + | 0.894417i | \(0.352409\pi\) |
−0.726172 | + | 0.687514i | \(0.758702\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −193.184 | − | 334.604i | −0.212876 | − | 0.368713i | 0.739737 | − | 0.672896i | \(-0.234950\pi\) |
−0.952614 | + | 0.304183i | \(0.901616\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4577.90 | − | 3841.32i | 2.09323 | − | 1.75643i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1898.74 | + | 3288.71i | −0.430121 | + | 0.744992i | −0.996883 | − | 0.0788897i | \(-0.974863\pi\) |
0.566762 | + | 0.823881i | \(0.308196\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 9075.63 | + | 3303.26i | 1.14571 | + | 0.417004i | 0.843973 | − | 0.536386i | \(-0.180211\pi\) |
0.301738 | + | 0.953391i | \(0.402433\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7044.12 | + | 39949.2i | 0.538899 | + | 3.05625i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 21855.6 | + | 18339.1i | 1.07893 | + | 0.905328i | 0.995831 | − | 0.0912134i | \(-0.0290745\pi\) |
0.0830967 | + | 0.996541i | \(0.473519\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4460.62 | − | 29563.1i | 0.149196 | − | 0.988808i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −26741.1 | − | 22438.5i | −0.630104 | − | 0.528720i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 10694.4 | + | 60651.1i | 0.183278 | + | 1.03942i | 0.928148 | + | 0.372211i | \(0.121400\pi\) |
−0.744870 | + | 0.667209i | \(0.767489\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −116016. | − | 42226.4i | −1.48500 | − | 0.540498i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 171168. | − | 296472.i | 1.67360 | − | 2.89875i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 32178.5 | − | 27000.9i | 0.245004 | − | 0.205582i | −0.512014 | − | 0.858977i | \(-0.671100\pi\) |
0.757017 | + | 0.653395i | \(0.226656\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 92451.6 | + | 160131.i | 0.557377 | + | 0.965404i | 0.997714 | + | 0.0675723i | \(0.0215253\pi\) |
−0.440338 | + | 0.897832i | \(0.645141\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −59578.7 | + | 337888.i | −0.288597 | + | 1.63672i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 163011. | − | 59331.2i | 0.642657 | − | 0.233908i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −354058. | −1.14913 | −0.574564 | − | 0.818460i | \(-0.694828\pi\) | ||||
−0.574564 | + | 0.818460i | \(0.694828\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 872603. | 2.35554 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −201193. | + | 73228.2i | −0.455899 | + | 0.165934i | −0.559754 | − | 0.828659i | \(-0.689104\pi\) |
0.103855 | + | 0.994592i | \(0.466882\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 47980.1 | − | 272109.i | 0.0920284 | − | 0.521919i | −0.903589 | − | 0.428400i | \(-0.859077\pi\) |
0.995618 | − | 0.0935188i | \(-0.0298115\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.34157e6 | + | 2.32367e6i | 2.19467 | + | 3.80129i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 84729.7 | − | 71096.6i | 0.119040 | − | 0.0998865i | −0.581324 | − | 0.813672i | \(-0.697465\pi\) |
0.700364 | + | 0.713785i | \(0.253021\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 337132. | − | 583929.i | 0.409367 | − | 0.709045i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.42226e6 | + | 881632.i | 2.55697 | + | 0.930661i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 169985. | + | 964033.i | 0.156836 | + | 0.889460i | 0.957088 | + | 0.289796i | \(0.0935876\pi\) |
−0.800253 | + | 0.599663i | \(0.795301\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.30611e6 | − | 1.09596e6i | −1.05855 | − | 0.888228i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −534828. | − | 2.64777e6i | −0.382518 | − | 1.89373i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −954290. | − | 800744.i | −0.604920 | − | 0.507589i | 0.288103 | − | 0.957600i | \(-0.406976\pi\) |
−0.893023 | + | 0.450011i | \(0.851420\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −611595. | − | 3.46853e6i | −0.344993 | − | 1.95655i | −0.285738 | − | 0.958308i | \(-0.592239\pi\) |
−0.0592542 | − | 0.998243i | \(-0.518872\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.16970e6 | − | 789705.i | −1.09322 | − | 0.397899i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.16816e6 | + | 3.75537e6i | −0.979253 | + | 1.69612i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −307522. | + | 258042.i | −0.124915 | + | 0.104816i | −0.703105 | − | 0.711086i | \(-0.748204\pi\) |
0.578190 | + | 0.815902i | \(0.303759\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.78217e6 | + | 4.81885e6i | 1.01956 | + | 1.76592i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 205419. | − | 1.16499e6i | 0.0681140 | − | 0.386294i | −0.931624 | − | 0.363423i | \(-0.881608\pi\) |
0.999738 | − | 0.0228713i | \(-0.00728079\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.06401e6 | + | 387266.i | −0.320121 | + | 0.116514i | −0.497082 | − | 0.867703i | \(-0.665595\pi\) |
0.176962 | + | 0.984218i | \(0.443373\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.11547e7 | −3.05312 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.46722e6 | 0.366250 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.82833e6 | − | 1.39340e6i | 0.873603 | − | 0.317965i | 0.133978 | − | 0.990984i | \(-0.457225\pi\) |
0.739625 | + | 0.673019i | \(0.235003\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.10142e6 | − | 1.75890e7i | 0.648431 | − | 3.67743i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.42883e6 | + | 4.20686e6i | 0.466255 | + | 0.807578i | 0.999257 | − | 0.0385362i | \(-0.0122695\pi\) |
−0.533002 | + | 0.846114i | \(0.678936\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.81284e6 | + | 8.23395e6i | −1.73312 | + | 1.45426i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.89761e6 | − | 3.28676e6i | 0.308951 | − | 0.535119i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.07859e6 | − | 2.94037e6i | −1.21470 | − | 0.442116i | −0.346371 | − | 0.938098i | \(-0.612586\pi\) |
−0.868333 | + | 0.495981i | \(0.834808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −647980. | − | 3.67488e6i | −0.0901398 | − | 0.511208i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.27975e7 | + | 1.07384e7i | 1.64981 | + | 1.38435i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.27239e7 | + | 4.27721e6i | 1.52261 | + | 0.511833i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.01336e7 | − | 8.50309e6i | −1.12736 | − | 0.945967i | −0.128406 | − | 0.991722i | \(-0.540986\pi\) |
−0.998953 | + | 0.0457550i | \(0.985431\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.94074e6 | + | 2.23491e7i | 0.408183 | + | 2.31492i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.48141e7 | − | 5.39188e6i | −1.43070 | − | 0.520734i | −0.493571 | − | 0.869705i | \(-0.664309\pi\) |
−0.937133 | + | 0.348972i | \(0.886531\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.90761e6 | + | 6.76818e6i | −0.352356 | + | 0.610298i | −0.986662 | − | 0.162784i | \(-0.947953\pi\) |
0.634306 | + | 0.773082i | \(0.281286\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.20063e7 | − | 1.00745e7i | 1.01216 | − | 0.849302i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.91504e6 | − | 5.04899e6i | −0.230039 | − | 0.398439i | 0.727781 | − | 0.685810i | \(-0.240552\pi\) |
−0.957819 | + | 0.287371i | \(0.907219\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.34320e6 | − | 1.32889e7i | 0.173307 | − | 0.982874i | −0.766772 | − | 0.641919i | \(-0.778138\pi\) |
0.940080 | − | 0.340955i | \(-0.110750\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.00598e7 | + | 1.09409e7i | −2.08620 | + | 0.759314i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.03952e7 | −0.677733 | −0.338866 | − | 0.940835i | \(-0.610043\pi\) | ||||
−0.338866 | + | 0.940835i | \(0.610043\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.76515e7 | −1.69541 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.42362e7 | − | 1.97404e7i | 3.13068 | − | 1.13947i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.91417e6 | − | 1.08558e7i | 0.104128 | − | 0.590537i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.53317e6 | + | 4.38757e6i | 0.129991 | + | 0.225152i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.48186e7 | + | 1.24343e7i | −0.718023 | + | 0.602493i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.01777e7 | − | 1.76283e7i | 0.466085 | − | 0.807283i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.06111e6 | − | 1.11415e6i | −0.132607 | − | 0.0482650i | 0.274864 | − | 0.961483i | \(-0.411367\pi\) |
−0.407471 | + | 0.913218i | \(0.633589\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.33498e6 | − | 2.45849e7i | −0.177796 | − | 1.00833i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.92373e6 | + | 3.29240e6i | 0.152493 | + | 0.127957i | 0.715842 | − | 0.698262i | \(-0.246043\pi\) |
−0.563349 | + | 0.826219i | \(0.690487\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.07536e7 | + | 4.21856e6i | −0.396346 | + | 0.155483i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.17744e8 | + | 9.87989e7i | 4.11880 | + | 3.45608i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.40852e6 | − | 1.36594e7i | −0.0800255 | − | 0.453847i | −0.998320 | − | 0.0579484i | \(-0.981544\pi\) |
0.918294 | − | 0.395899i | \(-0.129567\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.76297e7 | + | 1.00564e7i | 0.872618 | + | 0.317607i | 0.739227 | − | 0.673456i | \(-0.235191\pi\) |
0.133391 | + | 0.991063i | \(0.457413\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.99663e6 | − | 8.65442e6i | 0.150110 | − | 0.259999i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.80957e7 | + | 2.35751e7i | −0.803459 | + | 0.674182i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.43001e6 | + | 1.63333e7i | 0.256876 | + | 0.444923i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.05785e7 | − | 5.99938e7i | 0.274672 | − | 1.55774i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.24791e7 | + | 1.18214e7i | −0.804362 | + | 0.292764i | −0.711293 | − | 0.702896i | \(-0.751890\pi\) |
−0.0930694 | + | 0.995660i | \(0.529668\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.57710e6 | 0.179095 | 0.0895475 | − | 0.995983i | \(-0.471458\pi\) | ||||
0.0895475 | + | 0.995983i | \(0.471458\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.70499e8 | 3.84860 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.80120e7 | + | 2.83940e7i | −1.68268 | + | 0.612444i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.42980e7 | + | 8.10879e7i | −0.294867 | + | 1.67227i | 0.372875 | + | 0.927881i | \(0.378372\pi\) |
−0.667742 | + | 0.744392i | \(0.732739\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.42218e7 | + | 7.65943e7i | 0.872461 | + | 1.51115i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.82281e7 | − | 1.52952e7i | 0.344232 | − | 0.288845i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.60257e6 | + | 2.77573e6i | −0.0289842 | + | 0.0502020i | −0.880154 | − | 0.474689i | \(-0.842561\pi\) |
0.851169 | + | 0.524891i | \(0.175894\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.44756e8 | − | 5.26870e7i | −2.50867 | − | 0.913082i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.05387e6 | + | 2.29907e7i | 0.0673538 | + | 0.381983i | 0.999787 | + | 0.0206400i | \(0.00657040\pi\) |
−0.932433 | + | 0.361343i | \(0.882318\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.33873e7 | + | 1.96243e7i | 0.372715 | + | 0.312745i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.31408e7 | − | 1.52472e8i | −1.42447 | − | 2.33186i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.26465e7 | + | 4.41756e7i | 0.773051 | + | 0.648667i | 0.941488 | − | 0.337046i | \(-0.109428\pi\) |
−0.168437 | + | 0.985712i | \(0.553872\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.28329e6 | + | 4.69769e7i | 0.116834 | + | 0.662599i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.05764e8 | − | 3.84949e7i | −1.43361 | − | 0.521792i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.93202e7 | − | 1.20066e8i | 0.903388 | − | 1.56471i | 0.0803207 | − | 0.996769i | \(-0.474406\pi\) |
0.823067 | − | 0.567944i | \(-0.192261\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.14129e7 | − | 5.15315e7i | 0.769811 | − | 0.645948i | −0.170849 | − | 0.985297i | \(-0.554651\pi\) |
0.940661 | + | 0.339349i | \(0.110207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.59107e8 | − | 2.75582e8i | −1.91916 | − | 3.32408i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.76042e7 | − | 1.56551e8i | 0.320534 | − | 1.81784i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.01810e8 | + | 3.70558e7i | −1.13853 | + | 0.414392i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.32268e8 | −1.42508 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.56662e7 | 0.785751 | 0.392876 | − | 0.919592i | \(-0.371480\pi\) | ||||
0.392876 | + | 0.919592i | \(0.371480\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.38506e8 | + | 5.04122e7i | −1.38682 | + | 0.504760i | −0.924238 | − | 0.381817i | \(-0.875298\pi\) |
−0.462580 | + | 0.886578i | \(0.653076\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.80327e7 | + | 3.85833e8i | −0.657047 | + | 3.72630i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.89990e6 | − | 1.19510e7i | −0.0643000 | − | 0.111371i | 0.832083 | − | 0.554651i | \(-0.187148\pi\) |
−0.896383 | + | 0.443280i | \(0.853815\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.84386e6 | − | 7.42088e6i | 0.0795529 | − | 0.0667528i | −0.602144 | − | 0.798387i | \(-0.705687\pi\) |
0.681697 | + | 0.731635i | \(0.261242\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.81350e7 | + | 3.14108e7i | −0.157519 | + | 0.272830i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.52510e7 | − | 5.55090e6i | −0.127956 | − | 0.0465723i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.66927e7 | − | 9.46693e7i | −0.135328 | − | 0.767486i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.81938e8 | + | 2.36574e8i | 2.20932 | + | 1.85384i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.87548e7 | + | 7.08022e7i | 0.672481 | + | 0.536457i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.27857e7 | − | 2.75105e7i | −0.240268 | − | 0.201609i | 0.514700 | − | 0.857370i | \(-0.327903\pi\) |
−0.754968 | + | 0.655762i | \(0.772348\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.85595e7 | − | 1.05256e8i | −0.131595 | − | 0.746310i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.16576e8 | + | 4.24301e7i | 0.799969 | + | 0.291165i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.57203e7 | − | 6.18694e7i | 0.237304 | − | 0.411023i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.83678e7 | + | 6.57584e7i | −0.504177 | + | 0.423055i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.37775e8 | + | 2.38633e8i | 0.858613 | + | 1.48716i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.61825e7 | − | 2.61914e8i | 0.278876 | − | 1.58158i | −0.447500 | − | 0.894284i | \(-0.647686\pi\) |
0.726376 | − | 0.687298i | \(-0.241203\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.93315e8 | + | 2.52346e8i | −4.05781 | + | 1.47692i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.83154e7 | −0.501125 | −0.250563 | − | 0.968100i | \(-0.580616\pi\) | ||||
−0.250563 | + | 0.968100i | \(0.580616\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.24822e8 | 0.686860 | 0.343430 | − | 0.939178i | \(-0.388411\pi\) | ||||
0.343430 | + | 0.939178i | \(0.388411\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.24568e8 | − | 4.53391e7i | 0.664914 | − | 0.242009i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.28974e7 | − | 3.56709e8i | 0.325752 | − | 1.84743i | −0.178586 | − | 0.983924i | \(-0.557152\pi\) |
0.504338 | − | 0.863506i | \(-0.331736\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.48303e7 | + | 4.30074e7i | 0.124809 | + | 0.216175i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.81970e8 | − | 2.36601e8i | 1.37589 | − | 1.15451i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.06201e7 | + | 7.03561e7i | −0.192463 | + | 0.333356i | −0.946066 | − | 0.323974i | \(-0.894981\pi\) |
0.753603 | + | 0.657330i | \(0.228314\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.39338e6 | + | 1.23509e6i | 0.0156161 | + | 0.00568380i | 0.349816 | − | 0.936818i | \(-0.386244\pi\) |
−0.334200 | + | 0.942502i | \(0.608466\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.50203e8 | − | 8.51845e8i | −0.671518 | − | 3.80837i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.31907e8 | + | 1.94593e8i | 1.00747 | + | 0.845370i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.38137e8 | − | 2.53569e8i | 0.583273 | − | 1.07067i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.36207e8 | + | 2.82111e8i | 1.38010 | + | 1.15804i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.22313e7 | + | 4.09644e8i | 0.288315 | + | 1.63512i | 0.693198 | + | 0.720747i | \(0.256201\pi\) |
−0.404883 | + | 0.914369i | \(0.632688\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.19770e8 | − | 7.99897e7i | −0.853191 | − | 0.310536i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.78677e8 | + | 1.00230e9i | −2.18547 | + | 3.78535i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.11031e8 | − | 9.31662e7i | 0.408017 | − | 0.342367i | −0.415565 | − | 0.909563i | \(-0.636416\pi\) |
0.823583 | + | 0.567196i | \(0.191972\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.83982e7 | + | 1.18469e8i | 0.244622 | + | 0.423698i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.35908e7 | − | 2.47215e8i | 0.151758 | − | 0.860665i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.20484e8 | − | 1.53044e8i | 1.42529 | − | 0.518764i | 0.489714 | − | 0.871883i | \(-0.337101\pi\) |
0.935578 | + | 0.353119i | \(0.114879\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.39512e8 | −1.45081 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.76740e8 | −2.49739 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.58319e8 | − | 5.76235e7i | 0.495908 | − | 0.180496i | −0.0819448 | − | 0.996637i | \(-0.526113\pi\) |
0.577852 | + | 0.816141i | \(0.303891\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.92755e7 | + | 4.49594e8i | −0.241962 | + | 1.37223i | 0.585483 | + | 0.810685i | \(0.300905\pi\) |
−0.827445 | + | 0.561547i | \(0.810206\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.68573e8 | − | 2.91976e8i | −0.501438 | − | 0.868517i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.59155e8 | − | 3.01366e8i | 1.04140 | − | 0.873837i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.59498e7 | − | 2.76258e7i | 0.0450895 | − | 0.0780973i | −0.842600 | − | 0.538540i | \(-0.818976\pi\) |
0.887689 | + | 0.460443i | \(0.152309\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.03835e9 | + | 3.77928e8i | 2.86239 | + | 1.04182i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.09372e7 | − | 3.45592e8i | −0.163836 | − | 0.929163i | −0.950256 | − | 0.311470i | \(-0.899179\pi\) |
0.786419 | − | 0.617693i | \(-0.211932\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.57573e8 | + | 2.16129e8i | 0.675535 | + | 0.566841i | 0.914698 | − | 0.404138i | \(-0.132429\pi\) |
−0.239163 | + | 0.970979i | \(0.576873\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.21244e9 | − | 3.00475e7i | 3.10244 | − | 0.0768866i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.33696e7 | + | 5.31734e7i | 0.158232 | + | 0.132772i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.00935e7 | + | 3.97520e8i | 0.170819 | + | 0.968760i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.12311e9 | − | 4.08777e8i | −2.67175 | − | 0.972437i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.85259e8 | − | 3.20878e8i | 0.430272 | − | 0.745253i | −0.566625 | − | 0.823976i | \(-0.691751\pi\) |
0.996896 | + | 0.0787234i | \(0.0250844\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.28461e8 | − | 3.59521e8i | 0.971704 | − | 0.815357i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.50008e8 | + | 1.12585e9i | 1.43970 | + | 2.49363i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.03288e8 | + | 5.85773e8i | −0.223460 | + | 1.26730i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.00318e8 | + | 3.65126e7i | −0.212029 | + | 0.0771721i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.42434e9 | −2.94148 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.58134e9 | 3.19136 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.09870e8 | − | 7.63866e7i | 0.413968 | − | 0.150672i | −0.126636 | − | 0.991949i | \(-0.540418\pi\) |
0.540604 | + | 0.841277i | \(0.318196\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.22613e8 | + | 6.95374e8i | −0.236419 | + | 1.34080i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.68998e7 | − | 2.92713e7i | −0.0318581 | − | 0.0551798i | 0.849657 | − | 0.527336i | \(-0.176809\pi\) |
−0.881515 | + | 0.472156i | \(0.843476\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.70584e8 | + | 3.94867e8i | −0.867425 | + | 0.727856i | −0.963554 | − | 0.267513i | \(-0.913798\pi\) |
0.0961293 | + | 0.995369i | \(0.469354\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.18339e8 | − | 8.97790e8i | 0.934388 | − | 1.61841i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.28156e8 | − | 2.28630e8i | −1.10754 | − | 0.403112i | −0.277450 | − | 0.960740i | \(-0.589489\pi\) |
−0.830091 | + | 0.557628i | \(0.811712\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.76998e7 | + | 1.57093e8i | 0.0477760 | + | 0.270951i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.03510e8 | − | 3.38585e8i | −0.680904 | − | 0.571347i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.39649e8 | − | 5.64316e8i | 1.05617 | − | 0.931781i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.13433e8 | − | 7.66462e8i | −1.47600 | − | 1.23851i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.11707e8 | − | 1.20065e9i | −0.334825 | − | 1.89889i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.01576e7 | − | 1.46162e7i | −0.0621702 | − | 0.0226281i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.53176e8 | − | 7.84923e8i | 0.686861 | − | 1.18968i | −0.285988 | − | 0.958233i | \(-0.592322\pi\) |
0.972848 | − | 0.231444i | \(-0.0743450\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.62084e9 | + | 1.36005e9i | −2.40540 | + | 2.01837i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.01204e7 | − | 1.56093e8i | −0.130968 | − | 0.226844i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.84118e8 | + | 1.04419e9i | −0.262055 | + | 1.48619i | 0.515237 | + | 0.857048i | \(0.327704\pi\) |
−0.777292 | + | 0.629140i | \(0.783407\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.82561e8 | + | 3.21226e8i | −1.23040 | + | 0.447828i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.02166e8 | −0.958958 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.78703e8 | −0.774331 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.34763e9 | + | 8.54467e8i | −3.07796 | + | 1.12029i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.23573e8 | + | 7.00819e8i | −0.158771 | + | 0.900435i | 0.796486 | + | 0.604657i | \(0.206690\pi\) |
−0.955257 | + | 0.295778i | \(0.904421\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.09592e8 | + | 3.63024e8i | 0.263928 | + | 0.457138i | 0.967282 | − | 0.253702i | \(-0.0816484\pi\) |
−0.703354 | + | 0.710840i | \(0.748315\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.53279e9 | − | 2.12526e9i | 3.12625 | − | 2.62323i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.41461e8 | − | 9.37838e8i | 0.655173 | − | 1.13479i | −0.326678 | − | 0.945136i | \(-0.605929\pi\) |
0.981850 | − | 0.189657i | \(-0.0607375\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.99100e8 | + | 1.81657e8i | 0.592091 | + | 0.215503i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.72944e8 | − | 9.80815e8i | −0.201172 | − | 1.14090i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.90074e8 | − | 1.59491e8i | −0.216816 | − | 0.181930i | 0.527911 | − | 0.849300i | \(-0.322976\pi\) |
−0.744726 | + | 0.667370i | \(0.767420\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.54077e8 | − | 2.63739e8i | −0.955481 | − | 0.295053i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.50650e8 | + | 2.94230e8i | 0.384769 | + | 0.322860i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.82793e7 | − | 5.00657e8i | −0.0950242 | − | 0.538909i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.52381e8 | − | 3.10241e8i | −0.900124 | − | 0.327618i | −0.149822 | − | 0.988713i | \(-0.547870\pi\) |
−0.750303 | + | 0.661095i | \(0.770092\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.39749e8 | + | 1.10808e9i | −0.662853 | + | 1.14809i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.89731e8 | − | 2.43113e8i | 0.294568 | − | 0.247172i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.15068e8 | + | 1.99303e8i | 0.114808 | + | 0.198853i | 0.917703 | − | 0.397267i | \(-0.130041\pi\) |
−0.802895 | + | 0.596121i | \(0.796708\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.19357e8 | − | 1.81116e9i | 0.312728 | − | 1.77357i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.81231e8 | − | 1.38757e8i | 0.366432 | − | 0.133370i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.33983e9 | 1.26419 | 0.632095 | − | 0.774891i | \(-0.282195\pi\) | ||||
0.632095 | + | 0.774891i | \(0.282195\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.94320e8 | −0.272635 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.78852e7 | − | 1.37891e7i | 0.0344567 | − | 0.0125412i | −0.324734 | − | 0.945805i | \(-0.605275\pi\) |
0.359191 | + | 0.933264i | \(0.383053\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.14392e8 | + | 6.48751e8i | −0.102161 | + | 0.579383i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.25608e8 | − | 1.43000e9i | −0.724078 | − | 1.25414i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.63319e8 | + | 3.88771e8i | −0.399077 | + | 0.334865i | −0.820137 | − | 0.572168i | \(-0.806103\pi\) |
0.421060 | + | 0.907033i | \(0.361658\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.78551e8 | + | 1.52169e9i | −0.743273 | + | 1.28739i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.34868e8 | + | 1.58279e8i | 0.361396 | + | 0.131537i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.17632e8 | + | 1.80138e9i | 0.259319 | + | 1.47067i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.30741e8 | − | 1.09705e8i | −0.104868 | − | 0.0879950i | 0.588846 | − | 0.808245i | \(-0.299582\pi\) |
−0.693714 | + | 0.720250i | \(0.744027\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.82633e8 | + | 6.90461e8i | −0.616812 | + | 0.544169i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.22259e8 | + | 7.73867e8i | 0.714245 | + | 0.599323i | 0.925787 | − | 0.378046i | \(-0.123404\pi\) |
−0.211541 | + | 0.977369i | \(0.567848\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.10103e8 | + | 1.75868e9i | 0.236014 | + | 1.33850i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.53542e9 | + | 2.74267e9i | 5.63657 | + | 2.05154i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.72264e8 | − | 1.16440e9i | 0.494264 | − | 0.856091i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.10230e8 | + | 5.95954e8i | −0.513296 | + | 0.430706i | −0.862287 | − | 0.506420i | \(-0.830969\pi\) |
0.348991 | + | 0.937126i | \(0.386524\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.26579e8 | − | 1.08527e9i | −0.445174 | − | 0.771064i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.35790e7 | + | 4.74000e8i | −0.0583810 | + | 0.331095i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.04948e9 | + | 7.45950e8i | −1.40759 | + | 0.512320i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.65654e9 | 1.79407 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.44980e9 | 0.962850 | 0.481425 | − | 0.876487i | \(-0.340119\pi\) | ||||
0.481425 | + | 0.876487i | \(0.340119\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.81285e8 | + | 3.57158e8i | −0.640926 | + | 0.233278i | −0.641980 | − | 0.766722i | \(-0.721887\pi\) |
0.00105407 | + | 0.999999i | \(0.499664\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.14780e8 | − | 6.50947e8i | 0.0737349 | − | 0.418172i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.76121e9 | − | 3.05051e9i | −1.11289 | − | 1.92757i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.04243e9 | + | 8.74706e8i | −0.647964 | + | 0.543706i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.65684e9 | + | 2.86974e9i | −1.01317 | + | 1.75486i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.98769e8 | − | 2.54331e8i | −0.420401 | − | 0.153013i | 0.123153 | − | 0.992388i | \(-0.460699\pi\) |
−0.543554 | + | 0.839374i | \(0.682922\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.24327e8 | − | 1.83935e9i | −0.191989 | − | 1.08882i | −0.916642 | − | 0.399709i | \(-0.869111\pi\) |
0.724653 | − | 0.689114i | \(-0.242000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.30534e9 | + | 1.09531e9i | 0.760343 | + | 0.638004i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.84074e9 | − | 4.56182e7i | 1.05513 | − | 0.0261489i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.97015e9 | − | 1.65316e9i | −1.11141 | − | 0.932584i | −0.113271 | − | 0.993564i | \(-0.536133\pi\) |
−0.998139 | + | 0.0609803i | \(0.980577\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.99701e8 | − | 3.96820e9i | −0.388488 | − | 2.20322i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.22390e8 | − | 2.62929e8i | −0.394783 | − | 0.143689i | 0.136997 | − | 0.990571i | \(-0.456255\pi\) |
−0.531781 | + | 0.846882i | \(0.678477\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.92997e9 | − | 3.34281e9i | 1.03822 | − | 1.79826i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.39220e9 | + | 2.00729e9i | −1.26684 | + | 1.06300i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.29957e9 | − | 2.25092e9i | −0.677544 | − | 1.17354i | −0.975718 | − | 0.219029i | \(-0.929711\pi\) |
0.298175 | − | 0.954511i | \(-0.403622\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.41186e8 | − | 8.00706e8i | 0.0724727 | − | 0.411013i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.43301e8 | − | 2.34143e8i | 0.325140 | − | 0.118341i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.67541e9 | 0.833839 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.04468e9 | 0.512010 | 0.256005 | − | 0.966676i | \(-0.417594\pi\) | ||||
0.256005 | + | 0.966676i | \(0.417594\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9.17803e9 | − | 3.34053e9i | 4.43001 | − | 1.61239i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.72741e8 | − | 9.79661e8i | 0.0821186 | − | 0.465717i | −0.915823 | − | 0.401583i | \(-0.868460\pi\) |
0.997941 | − | 0.0641346i | \(-0.0204287\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.23280e9 | − | 2.13527e9i | −0.577244 | − | 0.999815i | −0.995794 | − | 0.0916218i | \(-0.970795\pi\) |
0.418550 | − | 0.908194i | \(-0.362538\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.74586e9 | + | 4.82135e9i | −2.65015 | + | 2.22374i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.16013e9 | + | 3.74146e9i | −0.981457 | + | 1.69993i | −0.324726 | + | 0.945808i | \(0.605272\pi\) |
−0.656731 | + | 0.754125i | \(0.728061\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.45750e8 | + | 5.30486e7i | 0.0652384 | + | 0.0237448i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.29182e9 | + | 7.32625e9i | 0.569675 | + | 3.23079i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.03786e8 | + | 6.74456e8i | 0.349242 | + | 0.293049i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.76584e9 | + | 3.24143e9i | −0.756005 | + | 1.38774i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.48133e9 | + | 3.76028e9i | 1.89057 | + | 1.58638i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.71373e8 | + | 9.71907e8i | 0.0712475 | + | 0.404064i | 0.999485 | + | 0.0320774i | \(0.0102123\pi\) |
−0.928238 | + | 0.371987i | \(0.878677\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.21330e9 | − | 1.16955e9i | −1.31657 | − | 0.479192i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.07494e9 | − | 1.86185e9i | 0.434079 | − | 0.751846i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.54982e9 | − | 3.81775e9i | 1.81092 | − | 1.51954i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.47332e8 | − | 6.01596e8i | −0.136268 | − | 0.236023i | 0.789813 | − | 0.613347i | \(-0.210177\pi\) |
−0.926081 | + | 0.377325i | \(0.876844\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.02855e7 | + | 2.85184e8i | −0.0194474 | + | 0.110292i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.21133e9 | − | 1.53280e9i | 1.60559 | − | 0.584386i | 0.625027 | − | 0.780603i | \(-0.285088\pi\) |
0.980560 | + | 0.196217i | \(0.0628657\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.19845e9 | 0.450461 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.01892e10 | −3.77590 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.29494e8 | + | 1.56323e8i | −0.156931 | + | 0.0571183i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.15724e8 | + | 1.22343e9i | −0.0777223 | + | 0.440785i | 0.920969 | + | 0.389637i | \(0.127399\pi\) |
−0.998691 | + | 0.0511488i | \(0.983712\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.05462e9 | + | 1.82665e9i | 0.374683 | + | 0.648969i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00253e9 | + | 8.41226e8i | −0.351246 | + | 0.294730i | −0.801290 | − | 0.598276i | \(-0.795853\pi\) |
0.450044 | + | 0.893006i | \(0.351408\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.53908e9 | − | 6.12986e9i | 1.22284 | − | 2.11802i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.59202e9 | + | 9.43418e8i | 0.883304 | + | 0.321496i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.41269e8 | + | 4.20395e9i | 0.249152 | + | 1.41301i | 0.810650 | + | 0.585531i | \(0.199114\pi\) |
−0.561498 | + | 0.827478i | \(0.689775\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.35129e8 | + | 2.81207e8i | 0.111106 | + | 0.0932294i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.00112e9 | − | 6.38272e9i | −2.61661 | − | 2.08735i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.68798e9 | − | 2.25549e9i | −0.867164 | − | 0.727637i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.29369e7 | + | 4.13646e8i | 0.0232129 | + | 0.131647i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.83481e9 | + | 2.12370e9i | 1.83207 | + | 0.666818i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.75194e8 | + | 9.96265e8i | −0.178190 | + | 0.308633i | −0.941260 | − | 0.337681i | \(-0.890357\pi\) |
0.763071 | + | 0.646315i | \(0.223691\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.08233e9 | + | 2.58638e9i | −0.942156 | + | 0.790563i | −0.977959 | − | 0.208796i | \(-0.933046\pi\) |
0.0358031 | + | 0.999359i | \(0.488601\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.15491e9 | + | 3.73241e9i | 0.649936 | + | 1.12572i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.16061e8 | + | 5.19524e9i | −0.272639 | + | 1.54621i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.64695e8 | + | 1.32738e8i | −0.107111 | + | 0.0389853i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.44456e9 | −2.15779 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.06784e9 | −0.591524 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.45975e9 | − | 8.95276e8i | 0.694469 | − | 0.252766i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.17513e9 | − | 1.23358e10i | 0.606144 | − | 3.43761i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.28025e9 | + | 2.21746e9i | 0.352155 | + | 0.609951i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.93373e9 | + | 2.46169e9i | −0.796581 | + | 0.668410i | −0.947365 | − | 0.320156i | \(-0.896265\pi\) |
0.150784 | + | 0.988567i | \(0.451820\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.62160e9 | − | 6.27280e9i | 0.970737 | − | 1.68137i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.69319e9 | + | 2.07215e9i | 1.50650 | + | 0.548320i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.02362e9 | + | 5.80521e9i | 0.267412 | + | 1.51657i | 0.762077 | + | 0.647486i | \(0.224180\pi\) |
−0.494665 | + | 0.869084i | \(0.664709\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.61236e10 | − | 1.35293e10i | −4.15870 | − | 3.48956i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.54695e8 | − | 1.07174e9i | −0.166728 | − | 0.272934i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.20581e9 | − | 1.01179e9i | −0.303207 | − | 0.254421i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.49403e9 | − | 1.41443e10i | −0.619264 | − | 3.51202i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.15852e9 | − | 4.21668e8i | −0.284061 | − | 0.103390i | 0.196060 | − | 0.980592i | \(-0.437185\pi\) |
−0.480121 | + | 0.877202i | \(0.659407\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.33430e9 | − | 2.31107e9i | 0.323080 | − | 0.559592i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.49868e9 | + | 6.29214e9i | −1.79314 | + | 1.50462i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.03658e9 | + | 1.79541e9i | 0.244807 | + | 0.424019i | 0.962077 | − | 0.272776i | \(-0.0879419\pi\) |
−0.717270 | + | 0.696795i | \(0.754609\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.10465e8 | − | 4.59637e9i | 0.189045 | − | 1.07213i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.48451e9 | + | 2.36017e9i | −1.49395 | + | 0.543754i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.27567e9 | −1.42813 | −0.714064 | − | 0.700081i | \(-0.753147\pi\) | ||||
−0.714064 | + | 0.700081i | \(0.753147\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.49266e9 | 1.00990 | 0.504948 | − | 0.863150i | \(-0.331512\pi\) | ||||
0.504948 | + | 0.863150i | \(0.331512\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.42412e9 | − | 2.33819e9i | 1.42650 | − | 0.519204i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.32035e9 | − | 7.48809e9i | 0.289636 | − | 1.64261i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.11394e8 | + | 8.85761e8i | 0.110826 | + | 0.191956i | 0.916103 | − | 0.400942i | \(-0.131317\pi\) |
−0.805278 | + | 0.592898i | \(0.797984\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.02015e10 | + | 8.56007e9i | −2.18418 | + | 1.83275i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.38420e8 | − | 1.62539e9i | 0.198509 | − | 0.343828i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.49318e9 | − | 1.27141e9i | −0.730098 | − | 0.265734i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.49992e9 | + | 2.55203e10i | 0.929307 | + | 5.27036i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.15363e9 | + | 2.64621e9i | 0.643542 | + | 0.539996i | 0.905104 | − | 0.425191i | \(-0.139793\pi\) |
−0.261562 | + | 0.965187i | \(0.584237\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.14635e9 | − | 2.01887e9i | 1.03776 | − | 0.407103i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.55108e8 | − | 8.01431e8i | −0.190325 | − | 0.159702i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.91005e8 | + | 4.48601e9i | 0.155772 | + | 0.883424i | 0.958077 | + | 0.286511i | \(0.0924954\pi\) |
−0.802306 | + | 0.596914i | \(0.796394\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.65079e9 | + | 1.69275e9i | 0.905144 | + | 0.329445i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.21535e8 | − | 9.03325e8i | 0.100317 | − | 0.173754i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.40310e9 | − | 5.37284e9i | 1.21730 | − | 1.02143i | 0.218335 | − | 0.975874i | \(-0.429937\pi\) |
0.998962 | − | 0.0455596i | \(-0.0145071\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.72367e9 | + | 2.98548e9i | 0.323887 | + | 0.560988i | 0.981286 | − | 0.192554i | \(-0.0616770\pi\) |
−0.657400 | + | 0.753542i | \(0.728344\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.16586e8 | + | 2.36258e9i | −0.0773739 | + | 0.438809i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.13752e9 | + | 7.77994e8i | −0.392434 | + | 0.142834i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.28916e9 | 0.959901 | 0.479950 | − | 0.877296i | \(-0.340655\pi\) | ||||
0.479950 | + | 0.877296i | \(0.340655\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.46635e9 | −0.263073 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.00383e9 | − | 3.65363e8i | 0.178039 | − | 0.0648007i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.23220e8 | + | 4.66871e9i | −0.144346 | + | 0.818626i | 0.823544 | + | 0.567252i | \(0.191993\pi\) |
−0.967890 | + | 0.251374i | \(0.919118\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.34263e9 | − | 7.52166e9i | −0.752819 | − | 1.30392i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.97266e9 | − | 3.33346e9i | 0.680900 | − | 0.571343i | −0.235370 | − | 0.971906i | \(-0.575630\pi\) |
0.916269 | + | 0.400563i | \(0.131186\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.53062e8 | + | 4.38316e8i | −0.0428854 | + | 0.0742797i | −0.886671 | − | 0.462400i | \(-0.846988\pi\) |
0.843786 | + | 0.536680i | \(0.180322\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.98119e10 | + | 7.21095e9i | 3.31976 | + | 1.20829i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.76794e8 | + | 3.27116e9i | 0.0955680 | + | 0.541993i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.87753e8 | − | 3.25364e8i | −0.0635295 | − | 0.0533076i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.72324e9 | + | 3.26852e9i | 1.57534 | + | 0.529559i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.73817e9 | − | 6.49310e9i | −1.23983 | − | 1.04034i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.98961e9 | + | 1.12836e10i | 0.315257 | + | 1.78791i | 0.570774 | + | 0.821107i | \(0.306643\pi\) |
−0.255517 | + | 0.966805i | \(0.582246\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.63364e9 | − | 1.32254e9i | −0.569415 | − | 0.207250i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.31298e8 | − | 1.26665e9i | 0.113341 | − | 0.196312i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.98855e9 | − | 4.18589e9i | 0.764691 | − | 0.641652i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.53471e9 | − | 6.12229e9i | −0.535921 | − | 0.928242i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.38762e8 | − | 1.35409e9i | 0.0358065 | − | 0.203069i | −0.961656 | − | 0.274257i | \(-0.911568\pi\) |
0.997463 | + | 0.0711884i | \(0.0226792\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.61937e9 | − | 3.13719e9i | 1.27861 | − | 0.465375i | 0.388636 | − | 0.921391i | \(-0.372946\pi\) |
0.889971 | + | 0.456017i | \(0.150724\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.12085e10 | 1.64471 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.00037e10 | −1.45210 | −0.726048 | − | 0.687644i | \(-0.758645\pi\) | ||||
−0.726048 | + | 0.687644i | \(0.758645\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.44537e9 | − | 1.61798e9i | 0.638338 | − | 0.232336i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.12083e9 | − | 6.35656e9i | 0.159224 | − | 0.903002i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.24020e9 | − | 7.34424e9i | −0.595923 | − | 1.03217i | −0.993416 | − | 0.114564i | \(-0.963453\pi\) |
0.397493 | − | 0.917605i | \(-0.369880\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.76169e9 | + | 1.47824e9i | −0.244955 | + | 0.205541i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.38330e9 | + | 5.86005e9i | −0.465438 | + | 0.806162i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.90667e9 | − | 2.87779e9i | −1.07620 | − | 0.391706i | −0.257710 | − | 0.966222i | \(-0.582968\pi\) |
−0.818493 | + | 0.574516i | \(0.805190\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.50044e8 | + | 4.25371e9i | 0.101014 | + | 0.572879i | 0.992738 | + | 0.120299i | \(0.0383852\pi\) |
−0.891724 | + | 0.452580i | \(0.850504\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.90713e10 | + | 1.60027e10i | 2.54146 | + | 2.13254i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.02688e9 | − | 5.08376e9i | −0.135408 | − | 0.670362i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.98177e9 | + | 1.66290e9i | 0.258590 | + | 0.216983i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.17257e9 | − | 2.36638e10i | −0.538780 | − | 3.05558i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.25683e10 | + | 4.57447e9i | 1.60600 | + | 0.584537i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.86370e8 | + | 1.70844e9i | −0.124735 | + | 0.216047i | −0.921629 | − | 0.388072i | \(-0.873141\pi\) |
0.796895 | + | 0.604118i | \(0.206475\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.23772e10 | + | 2.71677e10i | −4.05207 | + | 3.40009i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.21294e9 | + | 3.83292e9i | 0.274100 | + | 0.474754i | 0.969908 | − | 0.243473i | \(-0.0782869\pi\) |
−0.695808 | + | 0.718228i | \(0.744954\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.87524e8 | + | 5.03340e9i | −0.108802 | + | 0.617045i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.49805e9 | + | 2.72907e9i | −0.909773 | + | 0.331130i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.30786e9 | −0.277164 | −0.138582 | − | 0.990351i | \(-0.544254\pi\) | ||||
−0.138582 | + | 0.990351i | \(0.544254\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.22746e9 | 0.740277 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.05975e10 | − | 3.85718e9i | 1.24697 | − | 0.453859i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.64173e9 | + | 9.31070e9i | −0.191220 | + | 1.08446i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.09151e9 | − | 1.22829e10i | −0.817646 | − | 1.41620i | −0.907412 | − | 0.420242i | \(-0.861945\pi\) |
0.0897658 | − | 0.995963i | \(-0.471388\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.71680e9 | − | 5.63606e9i | 0.766648 | − | 0.643294i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.60072e9 | + | 1.14328e10i | −0.745838 | + | 1.29183i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.74014e9 | − | 2.08924e9i | −0.642107 | − | 0.233708i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.68275e9 | − | 3.22285e10i | −0.629344 | − | 3.56919i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.65144e9 | − | 4.74212e9i | −0.619650 | − | 0.519948i | 0.278044 | − | 0.960568i | \(-0.410314\pi\) |
−0.897693 | + | 0.440621i | \(0.854758\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.57932e9 | + | 1.04670e10i | −0.171446 | + | 1.13627i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.43710e9 | + | 2.88407e9i | 0.369428 | + | 0.309987i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.05769e9 | + | 5.99847e9i | 0.112562 | + | 0.638371i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.64243e10 | + | 5.97797e9i | 1.73072 | + | 0.629929i | 0.998681 | − | 0.0513389i | \(-0.0163489\pi\) |
0.732034 | + | 0.681268i | \(0.238571\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.21732e10 | − | 2.10847e10i | 1.27017 | − | 2.20000i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.72340e9 | + | 7.31980e9i | −0.901306 | + | 0.756286i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.23355e9 | − | 1.42609e10i | −0.842395 | − | 1.45907i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.27458e9 | + | 7.22850e9i | −0.129137 | + | 0.732371i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.33088e10 | + | 4.84399e9i | −1.33532 | + | 0.486018i | −0.908337 | − | 0.418239i | \(-0.862647\pi\) |
−0.426987 | + | 0.904258i | \(0.640425\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.01955e9 | 0.300033 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.26267e8 | 0.0321062 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.87337e9 | + | 1.77376e9i | −0.474948 | + | 0.172867i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.24245e8 | + | 3.54027e9i | −0.0602538 | + | 0.341716i | −1.00000 | 0.000156645i | \(-0.999950\pi\) | |
0.939746 | + | 0.341873i | \(0.111061\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.95452e10 | − | 3.38533e10i | −1.86850 | − | 3.23634i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.03886e9 | − | 5.06720e9i | 0.571800 | − | 0.479797i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.87335e9 | + | 1.19050e10i | −0.644621 | + | 1.11652i | 0.339767 | + | 0.940509i | \(0.389652\pi\) |
−0.984389 | + | 0.176007i | \(0.943682\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.57023e10 | + | 9.35487e9i | 2.38763 | + | 0.869025i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.64721e8 | − | 1.50130e9i | −0.0243586 | − | 0.138144i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.12157e10 | − | 9.41113e9i | −1.02229 | − | 0.857800i | −0.0323734 | − | 0.999476i | \(-0.510307\pi\) |
−0.989913 | + | 0.141676i | \(0.954751\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.89235e9 | − | 2.57968e10i | 0.351438 | − | 2.32918i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.54641e10 | + | 1.29760e10i | 1.38314 | + | 1.16059i | 0.968035 | + | 0.250814i | \(0.0806983\pi\) |
0.415101 | + | 0.909775i | \(0.363746\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.69475e9 | − | 1.52827e10i | −0.238766 | − | 1.35411i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.72788e10 | + | 9.92868e9i | 2.39444 | + | 0.871504i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.12628e9 | + | 1.95077e9i | −0.0979396 | + | 0.169636i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.50981e9 | + | 3.78418e9i | −0.388525 | + | 0.326011i | −0.816038 | − | 0.577998i | \(-0.803834\pi\) |
0.427513 | + | 0.904009i | \(0.359390\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.87910e10 | + | 3.25470e10i | 1.60387 | + | 2.77798i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.90750e8 | + | 3.35031e9i | −0.0499562 | + | 0.283316i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.97647e8 | + | 2.17526e8i | −0.0500736 | + | 0.0182253i | −0.366936 | − | 0.930246i | \(-0.619593\pi\) |
0.316862 | + | 0.948472i | \(0.397371\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.11304e10 | −1.75413 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.15726e10 | −0.951888 | −0.475944 | − | 0.879476i | \(-0.657894\pi\) | ||||
−0.475944 | + | 0.879476i | \(0.657894\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.89920e9 | + | 1.78316e9i | −0.399291 | + | 0.145330i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.32930e10 | + | 7.53885e10i | −1.07352 | + | 6.08821i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.01571e9 | − | 1.04195e10i | −0.481397 | − | 0.833804i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.01558e9 | − | 3.36947e9i | 0.318424 | − | 0.267190i | −0.469539 | − | 0.882912i | \(-0.655580\pi\) |
0.787964 | + | 0.615722i | \(0.211135\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.54766e9 | − | 1.13409e10i | 0.514513 | − | 0.891162i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.41366e8 | − | 3.06232e8i | −0.0655174 | − | 0.0238464i | 0.309054 | − | 0.951045i | \(-0.399988\pi\) |
−0.374571 | + | 0.927198i | \(0.622210\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.96412e9 | − | 2.24816e10i | −0.305908 | − | 1.73489i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.46792e9 | + | 7.94453e9i | 0.724071 | + | 0.607568i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.26740e9 | + | 6.27452e9i | 0.0960581 | + | 0.475553i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.44128e9 | + | 2.88758e9i | 0.258489 | + | 0.216898i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.49710e9 | − | 1.41617e10i | −0.185896 | − | 1.05427i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.47393e10 | − | 1.26441e10i | −2.56317 | − | 0.932918i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.12094e9 | − | 7.13767e9i | 0.301359 | − | 0.521969i | −0.675085 | − | 0.737740i | \(-0.735893\pi\) |
0.976444 | + | 0.215771i | \(0.0692263\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.09701e10 | − | 2.59870e10i | 2.24478 | − | 1.88359i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.00818e9 | + | 3.47828e9i | 0.144273 | + | 0.249889i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.90684e9 | − | 3.34993e10i | 0.420629 | − | 2.38550i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.73149e10 | + | 1.35815e10i | −2.63389 | + | 0.958658i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.79861e10 | −1.25844 | −0.629220 | − | 0.777228i | \(-0.716625\pi\) | ||||
−0.629220 | + | 0.777228i | \(0.716625\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.15567e9 | 0.218866 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.82779e10 | + | 1.75717e10i | −3.31921 | + | 1.20809i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.46661e8 | − | 4.23452e9i | 0.0508884 | − | 0.288603i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.34181e9 | + | 9.25229e9i | 0.360913 | + | 0.625120i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.16608e10 | − | 9.78456e9i | 0.781035 | − | 0.655366i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.64687e9 | − | 9.78066e9i | 0.374962 | − | 0.649454i | −0.615359 | − | 0.788247i | \(-0.710989\pi\) |
0.990321 | + | 0.138793i | \(0.0443223\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.82118e9 | + | 1.75477e9i | 0.317380 | + | 0.115517i | 0.495798 | − | 0.868438i | \(-0.334876\pi\) |
−0.178418 | + | 0.983955i | \(0.557098\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.16250e9 | + | 4.06205e10i | 0.467463 | + | 2.65112i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.10238e9 | − | 9.25008e8i | −0.0713314 | − | 0.0598541i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.83035e9 | − | 2.63221e9i | −0.502347 | − | 0.168867i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.70828e10 | − | 1.43341e10i | −1.08659 | − | 0.911754i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.27029e7 | − | 3.55606e8i | −0.00395445 | − | 0.0224268i | 0.982767 | − | 0.184850i | \(-0.0591800\pi\) |
−0.986721 | + | 0.162424i | \(0.948069\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.24385e10 | − | 4.52723e9i | −0.777799 | − | 0.283096i | −0.0775446 | − | 0.996989i | \(-0.524708\pi\) |
−0.700255 | + | 0.713893i | \(0.746930\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.11799e10 | − | 3.66846e10i | 1.31321 | − | 2.27455i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.13323e10 | + | 1.79000e10i | −1.31150 | + | 1.10048i | −0.323470 | + | 0.946238i | \(0.604849\pi\) |
−0.988033 | + | 0.154243i | \(0.950706\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.54226e9 | − | 1.47956e10i | −0.520753 | − | 0.901971i | −0.999709 | − | 0.0241316i | \(-0.992318\pi\) |
0.478956 | − | 0.877839i | \(-0.341015\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.00473e8 | − | 2.83832e9i | 0.0302536 | − | 0.171577i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.80769e10 | − | 6.57947e9i | 1.08360 | − | 0.394397i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.04817e10 | −0.623057 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.32992e10 | 3.73129 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.60977e10 | + | 5.85910e9i | −0.941018 | + | 0.342503i | −0.766568 | − | 0.642163i | \(-0.778037\pi\) |
−0.174450 | + | 0.984666i | \(0.555815\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.68901e9 | + | 1.52501e10i | −0.155886 | + | 0.884071i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.58529e10 | − | 2.74580e10i | −0.911406 | − | 1.57860i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.05005e10 | + | 8.81100e9i | −0.598705 | + | 0.502373i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.78733e8 | − | 1.69521e9i | 0.0553442 | − | 0.0958590i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.85468e10 | + | 1.03902e10i | 1.60096 | + | 0.582703i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.78645e9 | − | 2.14740e10i | −0.210610 | − | 1.19443i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.40531e10 | + | 1.17919e10i | 0.775264 | + | 0.650524i | 0.942051 | − | 0.335469i | \(-0.108895\pi\) |
−0.166787 | + | 0.985993i | \(0.553339\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.46790e10 | − | 2.92959e10i | 4.08618 | − | 1.60297i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.52067e8 | − | 2.95419e8i | −0.0191070 | − | 0.0160327i | 0.633184 | − | 0.774001i | \(-0.281748\pi\) |
−0.652291 | + | 0.757969i | \(0.726192\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.51241e9 | − | 8.57732e9i | −0.0814131 | − | 0.461717i | −0.998073 | − | 0.0620487i | \(-0.980237\pi\) |
0.916660 | − | 0.399668i | \(-0.130875\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.02326e9 | + | 2.55626e9i | 0.374997 | + | 0.136488i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.05087e10 | + | 1.82017e10i | −0.556560 | + | 0.963991i | 0.441220 | + | 0.897399i | \(0.354546\pi\) |
−0.997780 | + | 0.0665919i | \(0.978787\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.36374e10 | + | 1.98342e10i | −1.24178 | + | 1.04198i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.82349e10 | + | 3.15837e10i | 0.950246 | + | 1.64587i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.68651e9 | + | 1.52360e10i | −0.138873 | + | 0.787591i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.64333e9 | + | 1.32606e9i | −0.186825 | + | 0.0679988i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.90537e10 | −4.02135 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.86468e9 | −0.396874 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.25668e9 | + | 4.57394e8i | −0.0629109 | + | 0.0228977i | −0.373284 | − | 0.927717i | \(-0.621768\pi\) |
0.310373 | + | 0.950615i | \(0.399546\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.81307e9 | − | 3.29676e10i | 0.288698 | − | 1.63729i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.61723e10 | + | 2.80113e10i | 0.796814 | + | 1.38012i | 0.921681 | + | 0.387949i | \(0.126816\pi\) |
−0.124867 | + | 0.992173i | \(0.539850\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.81748e10 | − | 1.52505e10i | 0.888397 | − | 0.745454i | −0.0794910 | − | 0.996836i | \(-0.525329\pi\) |
0.967888 | + | 0.251382i | \(0.0808850\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.52670e10 | − | 4.37637e10i | 1.22533 | − | 2.12233i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.80220e9 | − | 2.11183e9i | −0.279164 | − | 0.101607i | 0.198644 | − | 0.980072i | \(-0.436346\pi\) |
−0.477808 | + | 0.878464i | \(0.658569\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.18557e8 | + | 1.23950e9i | 0.0104330 | + | 0.0591683i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.19565e10 | + | 4.35967e10i | 2.46075 | + | 2.06482i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.72389e9 | − | 2.82200e9i | −0.0810082 | − | 0.132610i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.76842e10 | + | 4.00118e10i | 2.22328 | + | 1.86555i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.33198e9 | + | 5.29243e10i | 0.431718 | + | 2.44840i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.29864e9 | + | 2.65649e9i | 0.335029 | + | 0.121941i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.39643e10 | + | 2.41869e10i | −0.636038 | + | 1.10165i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.38875e9 | + | 6.19990e9i | −0.333937 | + | 0.280206i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.79973e10 | + | 3.11722e10i | 0.807116 | + | 1.39797i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.16166e9 | − | 1.79307e10i | 0.140699 | − | 0.797941i | −0.830022 | − | 0.557730i | \(-0.811672\pi\) |
0.970721 | − | 0.240211i | \(-0.0772165\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.85294e10 | + | 3.22221e10i | −3.90943 | + | 1.42292i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.79108e9 | 0.166130 | 0.0830651 | − | 0.996544i | \(-0.473529\pi\) | ||||
0.0830651 | + | 0.996544i | \(0.473529\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.84469e10 | −0.802185 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.34257e11 | − | 4.88655e10i | 5.79379 | − | 2.10877i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.43650e8 | − | 1.94894e9i | 0.0147171 | − | 0.0834651i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.88668e9 | − | 3.26783e9i | −0.0801851 | − | 0.138885i | 0.823144 | − | 0.567832i | \(-0.192218\pi\) |
−0.903329 | + | 0.428948i | \(0.858884\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.54577e10 | − | 1.29706e10i | 0.651983 | − | 0.547079i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.71257e9 | − | 9.89446e9i | 0.239125 | − | 0.414177i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.10764e10 | + | 1.49506e10i | 1.70646 | + | 0.621101i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.11007e9 | + | 4.59945e10i | 0.334384 | + | 1.89639i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.13143e10 | − | 9.49379e9i | −0.462990 | − | 0.388494i | 0.381240 | − | 0.924476i | \(-0.375497\pi\) |
−0.844230 | + | 0.535982i | \(0.819942\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.57589e10 | − | 1.25713e10i | −0.640033 | − | 0.510572i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.33933e9 | − | 1.96293e9i | −0.0942986 | − | 0.0791259i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.44707e9 | − | 4.79057e10i | −0.337960 | − | 1.91667i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.05185e10 | + | 7.46811e9i | 0.814810 | + | 0.296566i | 0.715609 | − | 0.698501i | \(-0.246149\pi\) |
0.0992006 | + | 0.995067i | \(0.468371\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.77510e10 | + | 4.80662e10i | −1.09383 | + | 1.89457i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.28884e9 | + | 6.11607e9i | −0.285164 | + | 0.239281i | −0.774137 | − | 0.633018i | \(-0.781816\pi\) |
0.488973 | + | 0.872299i | \(0.337372\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.59301e9 | − | 1.14194e10i | −0.256031 | − | 0.443459i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.03123e10 | − | 5.84839e10i | 0.397506 | − | 2.25437i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.99665e10 | + | 1.09069e10i | −1.14660 | + | 0.417328i | −0.844293 | − | 0.535883i | \(-0.819979\pi\) |
−0.302307 | + | 0.953211i | \(0.597757\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.09358e10 | −0.415353 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.03959e10 | −2.27706 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.70002e10 | − | 6.18757e9i | 0.636252 | − | 0.231577i | −0.00369811 | − | 0.999993i | \(-0.501177\pi\) |
0.639950 | + | 0.768416i | \(0.278955\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.89933e9 | + | 3.34568e10i | −0.219175 | + | 1.24300i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.20614e9 | + | 1.24814e10i | 0.265773 | + | 0.460332i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.10520e9 | + | 3.44468e9i | −0.150304 | + | 0.126120i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.33830e9 | + | 5.78211e9i | −0.121337 | + | 0.210162i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.27396e10 | − | 1.19162e10i | −1.18136 | − | 0.429978i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.14917e10 | − | 6.51728e10i | −0.411661 | − | 2.33465i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.77435e9 | + | 8.20166e9i | 0.347613 | + | 0.291682i | 0.799831 | − | 0.600226i | \(-0.204923\pi\) |
−0.452218 | + | 0.891907i | \(0.649367\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.68685e10 | − | 6.76769e10i | 1.30174 | − | 2.38950i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.20770e10 | − | 1.85248e10i | −0.773879 | − | 0.649362i | 0.167820 | − | 0.985818i | \(-0.446327\pi\) |
−0.941699 | + | 0.336456i | \(0.890772\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.97270e9 | − | 1.11877e10i | −0.0686540 | − | 0.389356i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.01236e11 | − | 3.68468e10i | −3.49799 | − | 1.27316i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.33723e10 | + | 2.31615e10i | −0.458749 | + | 0.794577i | −0.998895 | − | 0.0469947i | \(-0.985036\pi\) |
0.540146 | + | 0.841571i | \(0.318369\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.50092e10 | − | 2.09852e10i | 0.851843 | − | 0.714781i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.03201e10 | − | 6.98365e10i | −1.36358 | − | 2.36179i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.07202e9 | + | 6.07973e9i | −0.0359970 | + | 0.204149i | −0.997502 | − | 0.0706384i | \(-0.977496\pi\) |
0.961505 | + | 0.274787i | \(0.0886075\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.82223e9 | − | 2.11912e9i | 0.194117 | − | 0.0706527i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.86107e9 | −0.127820 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.70168e10 | 0.559360 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.91092e10 | − | 1.05949e10i | 0.950108 | − | 0.345811i | 0.179959 | − | 0.983674i | \(-0.442404\pi\) |
0.770150 | + | 0.637863i | \(0.220181\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.42198e10 | − | 8.06443e10i | 0.460861 | − | 2.61367i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.59172e9 | + | 4.48900e9i | 0.0834080 | + | 0.144467i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.34730e9 | + | 2.80871e9i | −0.106970 | + | 0.0897583i | −0.694704 | − | 0.719296i | \(-0.744465\pi\) |
0.587734 | + | 0.809054i | \(0.300020\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.06036e10 | + | 1.04968e11i | −1.92318 | + | 3.33104i |
(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 | 76.8.i.a.73.12 | yes | 72 | |
19.6 | even | 9 | inner | 76.8.i.a.25.12 | ✓ | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.8.i.a.25.12 | ✓ | 72 | 19.6 | even | 9 | inner | |
76.8.i.a.73.12 | yes | 72 | 1.1 | even | 1 | trivial |