Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,7,Mod(13,76)]
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, 5]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.13");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.j (of order \(18\), 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: | \(17.4841103551\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 33.10 | ||
Character | \(\chi\) | \(=\) | 76.33 |
Dual form | 76.7.j.a.53.10 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{7}{18}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 48.0588 | + | 8.47406i | 1.77996 | + | 0.313854i | 0.964326 | − | 0.264719i | \(-0.0852793\pi\) |
0.815630 | + | 0.578574i | \(0.196390\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 67.2683 | + | 56.4448i | 0.538147 | + | 0.451559i | 0.870904 | − | 0.491454i | \(-0.163534\pi\) |
−0.332757 | + | 0.943013i | \(0.607979\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −18.9857 | − | 32.8842i | −0.0553518 | − | 0.0958722i | 0.837022 | − | 0.547170i | \(-0.184295\pi\) |
−0.892374 | + | 0.451297i | \(0.850961\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1552.80 | + | 565.174i | 2.13005 | + | 0.775273i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −443.219 | + | 767.678i | −0.332997 | + | 0.576768i | −0.983098 | − | 0.183080i | \(-0.941393\pi\) |
0.650101 | + | 0.759848i | \(0.274727\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2477.96 | − | 436.932i | 1.12789 | − | 0.198877i | 0.421585 | − | 0.906789i | \(-0.361474\pi\) |
0.706300 | + | 0.707912i | \(0.250363\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2754.52 | + | 3282.71i | 0.816153 | + | 0.972654i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1511.07 | + | 549.985i | −0.307566 | + | 0.111945i | −0.491192 | − | 0.871051i | \(-0.663439\pi\) |
0.183626 | + | 0.982996i | \(0.441216\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6769.01 | − | 1107.44i | −0.986880 | − | 0.161457i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −633.766 | − | 1741.26i | −0.0684339 | − | 0.188021i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1870.99 | − | 1569.95i | 0.153776 | − | 0.129033i | −0.562654 | − | 0.826693i | \(-0.690220\pi\) |
0.716429 | + | 0.697660i | \(0.245775\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1374.24 | − | 7793.72i | −0.0879516 | − | 0.498798i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 39027.4 | + | 22532.5i | 1.98280 | + | 1.14477i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7186.37 | + | 19744.4i | −0.294656 | + | 0.809561i | 0.700714 | + | 0.713442i | \(0.252865\pi\) |
−0.995370 | + | 0.0961185i | \(0.969357\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 23317.0 | − | 13462.1i | 0.782685 | − | 0.451883i | −0.0546963 | − | 0.998503i | \(-0.517419\pi\) |
0.837381 | + | 0.546620i | \(0.184086\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −27805.9 | + | 33137.8i | −0.773741 | + | 0.922108i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 579.006 | − | 3283.70i | 0.0135045 | − | 0.0765879i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 26050.1i | 0.514285i | 0.966373 | + | 0.257143i | \(0.0827810\pi\) | ||||
−0.966373 | + | 0.257143i | \(0.917219\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 122791. | 2.07000 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 46849.4 | + | 8260.82i | 0.679756 | + | 0.119859i | 0.502857 | − | 0.864370i | \(-0.332282\pi\) |
0.176899 | + | 0.984229i | \(0.443393\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 66202.0 | + | 55550.1i | 0.832656 | + | 0.698682i | 0.955899 | − | 0.293695i | \(-0.0948849\pi\) |
−0.123243 | + | 0.992377i | \(0.539329\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 72553.3 | + | 125666.i | 0.796195 | + | 1.37905i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −54002.7 | − | 19655.4i | −0.520142 | − | 0.189316i | 0.0685892 | − | 0.997645i | \(-0.478150\pi\) |
−0.588731 | + | 0.808329i | \(0.700372\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 58103.6 | − | 100638.i | 0.493872 | − | 0.855412i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −77280.9 | + | 13626.7i | −0.582588 | + | 0.102726i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −161217. | − | 192130.i | −1.08288 | − | 1.29053i | −0.954306 | − | 0.298832i | \(-0.903403\pi\) |
−0.128579 | − | 0.991699i | \(-0.541042\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −73146.0 | + | 26623.0i | −0.439645 | + | 0.160018i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −315926. | − | 110583.i | −1.70593 | − | 0.597123i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −119006. | − | 326967.i | −0.579447 | − | 1.59202i | −0.789116 | − | 0.614245i | \(-0.789461\pi\) |
0.209669 | − | 0.977772i | \(-0.432761\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −285390. | + | 239471.i | −1.25733 | + | 1.05503i | −0.261370 | + | 0.965239i | \(0.584174\pi\) |
−0.995961 | + | 0.0897876i | \(0.971381\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10895.7 | − | 61792.8i | −0.0435748 | − | 0.247125i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 191351. | + | 110477.i | 0.696772 | + | 0.402282i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 62029.2 | − | 170424.i | 0.206239 | − | 0.566638i | −0.792845 | − | 0.609423i | \(-0.791401\pi\) |
0.999084 | + | 0.0427855i | \(0.0136232\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 103221. | − | 59594.8i | 0.314211 | − | 0.181410i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −425274. | + | 506822.i | −1.18821 | + | 1.41606i | −0.301666 | + | 0.953414i | \(0.597543\pi\) |
−0.886546 | + | 0.462641i | \(0.846902\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 115453. | − | 654764.i | 0.296780 | − | 1.68313i | −0.363097 | − | 0.931751i | \(-0.618281\pi\) |
0.659877 | − | 0.751374i | \(-0.270608\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 386203.i | − | 0.915443i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 33659.2 | 0.0737279 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −167253. | − | 29491.2i | −0.339229 | − | 0.0598152i | 0.00143885 | − | 0.999999i | \(-0.499542\pi\) |
−0.340668 | + | 0.940184i | \(0.610653\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 761859. | + | 639275.i | 1.43357 | + | 1.20291i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −124334. | − | 215353.i | −0.217448 | − | 0.376631i | 0.736579 | − | 0.676351i | \(-0.236440\pi\) |
−0.954027 | + | 0.299720i | \(0.903107\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −132691. | − | 48295.6i | −0.216065 | − | 0.0786413i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −512683. | + | 887994.i | −0.778559 | + | 1.34850i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 692179. | − | 122050.i | 0.981857 | − | 0.173128i | 0.340395 | − | 0.940283i | \(-0.389439\pi\) |
0.641462 | + | 0.767155i | \(0.278328\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −61414.0 | − | 73190.3i | −0.0814973 | − | 0.0971246i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.23466e6 | − | 449381.i | 1.53497 | − | 0.558683i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −392831. | − | 456571.i | −0.458178 | − | 0.532522i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 40294.4 | + | 110708.i | 0.0441499 | + | 0.121301i | 0.959808 | − | 0.280657i | \(-0.0905522\pi\) |
−0.915658 | + | 0.401957i | \(0.868330\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.12210e6 | + | 941556.i | −1.15645 | + | 0.970378i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −80734.6 | − | 457869.i | −0.0783602 | − | 0.444403i | −0.998593 | − | 0.0530311i | \(-0.983112\pi\) |
0.920233 | − | 0.391372i | \(-0.127999\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.74125e6 | − | 1.00531e6i | −1.59349 | − | 0.920000i | −0.992702 | − | 0.120590i | \(-0.961521\pi\) |
−0.600785 | − | 0.799411i | \(-0.705145\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 55652.7 | − | 152904.i | 0.0480749 | − | 0.132085i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −887189. | + | 512219.i | −0.724210 | + | 0.418123i | −0.816300 | − | 0.577628i | \(-0.803979\pi\) |
0.0920900 | + | 0.995751i | \(0.470645\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 629513. | − | 750225.i | 0.486100 | − | 0.579311i | −0.466121 | − | 0.884721i | \(-0.654349\pi\) |
0.952221 | + | 0.305410i | \(0.0987934\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −220750. | + | 1.25194e6i | −0.161411 | + | 0.915405i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 708461.i | 0.490999i | 0.969397 | + | 0.245499i | \(0.0789519\pi\) | ||||
−0.969397 | + | 0.245499i | \(0.921048\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 214474. | 0.141020 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.09473e6 | + | 722012.i | 2.55663 | + | 0.450803i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 46774.5 | + | 39248.5i | 0.0277567 | + | 0.0232907i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 492895. | + | 853718.i | 0.278226 | + | 0.481902i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.18153e6 | + | 794010.i | 1.17232 | + | 0.426688i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.03351e6 | − | 1.79009e6i | 0.529156 | − | 0.916525i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.69467e6 | + | 298817.i | −0.827323 | + | 0.145879i | −0.571248 | − | 0.820777i | \(-0.693541\pi\) |
−0.256075 | + | 0.966657i | \(0.582429\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.71085e6 | + | 3.23067e6i | 1.26281 | + | 1.50496i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.77147e6 | − | 1.00873e6i | 1.23281 | − | 0.448706i | 0.358250 | − | 0.933626i | \(-0.383373\pi\) |
0.874559 | + | 0.484920i | \(0.161151\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 92097.1 | + | 243619.i | 0.0391463 | + | 0.103551i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.35347e6 | + | 3.71862e6i | 0.550105 | + | 1.51140i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.33156e6 | + | 1.95641e6i | −0.906745 | + | 0.760849i | −0.971497 | − | 0.237052i | \(-0.923819\pi\) |
0.0647522 | + | 0.997901i | \(0.479374\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −838508. | − | 4.75541e6i | −0.312221 | − | 1.77070i | −0.587394 | − | 0.809301i | \(-0.699846\pi\) |
0.275173 | − | 0.961395i | \(-0.411265\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.42875e6 | − | 1.40224e6i | −0.866413 | − | 0.500224i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −762858. | + | 2.09593e6i | −0.260877 | + | 0.716753i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.59788e6 | + | 922538.i | −0.524132 | + | 0.302608i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.64521e6 | − | 4.34419e6i | 1.14755 | − | 1.36759i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −27632.1 | + | 156710.i | −0.00835325 | + | 0.0473737i | −0.988699 | − | 0.149911i | \(-0.952101\pi\) |
0.980346 | + | 0.197285i | \(0.0632124\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.66861e6i | 1.35599i | 0.735067 | + | 0.677995i | \(0.237151\pi\) | ||||
−0.735067 | + | 0.677995i | \(0.762849\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.65723e6 | −0.741917 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.32836e6 | + | 410552.i | 0.625251 | + | 0.110249i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.39991e6 | − | 2.85287e6i | −0.878555 | − | 0.737195i | 0.0873266 | − | 0.996180i | \(-0.472168\pi\) |
−0.965881 | + | 0.258985i | \(0.916612\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.11975e6 | − | 1.05997e7i | −1.52245 | − | 2.63696i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −87148.3 | − | 31719.4i | −0.0208824 | − | 0.00760059i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 194573. | − | 337011.i | 0.0449284 | − | 0.0778182i | −0.842687 | − | 0.538404i | \(-0.819027\pi\) |
0.887615 | + | 0.460586i | \(0.152361\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.74091e6 | + | 659624.i | −0.832772 | + | 0.146840i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.27376e6 | + | 3.90151e6i | 0.702906 | + | 0.837691i | 0.992852 | − | 0.119352i | \(-0.0380818\pi\) |
−0.289946 | + | 0.957043i | \(0.593637\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.41368e6 | − | 514538.i | 0.292881 | − | 0.106600i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.88504e6 | − | 5.54530e6i | −1.97693 | − | 1.10901i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.41251e6 | + | 6.62833e6i | 0.465942 | + | 1.28016i | 0.920951 | + | 0.389678i | \(0.127414\pi\) |
−0.455010 | + | 0.890486i | \(0.650364\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −230199. | + | 193160.i | −0.0429526 | + | 0.0360415i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.94856e6 | − | 1.67221e7i | −0.531728 | − | 3.01558i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.44781e6 | − | 1.41324e6i | −0.426795 | − | 0.246410i | 0.271186 | − | 0.962527i | \(-0.412584\pi\) |
−0.697980 | + | 0.716117i | \(0.745918\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.21378e6 | − | 3.33483e6i | 0.204693 | − | 0.562390i | −0.794287 | − | 0.607543i | \(-0.792155\pi\) |
0.998980 | + | 0.0451528i | \(0.0143775\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.57448e7 | + | 9.09027e6i | −2.56912 | + | 1.48328i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.47039e6 | + | 1.75235e6i | −0.232230 | + | 0.276761i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 247524. | − | 1.40378e6i | 0.0378524 | − | 0.214671i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 1.71118e6i | − | 0.253460i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.33312e6 | 0.765388 | 0.382694 | − | 0.923875i | \(-0.374996\pi\) | ||||
0.382694 | + | 0.923875i | \(0.374996\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.16770e7 | + | 2.05898e6i | 1.62428 | + | 0.286404i | 0.910358 | − | 0.413821i | \(-0.135806\pi\) |
0.713922 | + | 0.700226i | \(0.246917\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.25992e6 | + | 6.93089e6i | 1.11397 | + | 0.934728i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.45733e6 | + | 7.72031e6i | 0.583010 | + | 1.00980i | 0.995120 | + | 0.0986685i | \(0.0314583\pi\) |
−0.412111 | + | 0.911134i | \(0.635208\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.34853e6 | + | 854794.i | 0.298014 | + | 0.108468i | 0.486700 | − | 0.873569i | \(-0.338201\pi\) |
−0.188686 | + | 0.982037i | \(0.560423\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.42523e6 | − | 7.66472e6i | 0.544939 | − | 0.943861i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 785715. | − | 138543.i | 0.0939241 | − | 0.0165614i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.68520e6 | + | 3.20010e6i | 0.311685 | + | 0.371451i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.79257e6 | − | 1.38038e6i | 0.427585 | − | 0.155628i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.85031e6 | − | 4.70558e6i | 0.421751 | − | 0.515435i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −410170. | − | 1.12693e6i | −0.0436633 | − | 0.119964i | 0.915945 | − | 0.401305i | \(-0.131443\pi\) |
−0.959608 | + | 0.281341i | \(0.909221\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.47330e7 | + | 2.07534e7i | −2.55940 | + | 2.14759i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.31778e6 | + | 7.47352e6i | 0.132595 | + | 0.751986i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −885376. | − | 511172.i | −0.0866460 | − | 0.0500251i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.10970e7 | − | 3.04888e7i | 1.05651 | − | 2.90274i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.50408e6 | + | 2.02308e6i | −0.324636 | + | 0.187429i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.25368e6 | + | 8.64459e6i | −0.654099 | + | 0.779525i | −0.986526 | − | 0.163604i | \(-0.947688\pi\) |
0.332427 | + | 0.943129i | \(0.392133\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.27088e6 | − | 1.28788e7i | 0.199364 | − | 1.13065i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.60470e7i | 1.37188i | 0.727659 | + | 0.685939i | \(0.240608\pi\) | ||||
−0.727659 | + | 0.685939i | \(0.759392\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.76151e6 | 0.729579 | 0.364790 | − | 0.931090i | \(-0.381141\pi\) | ||||
0.364790 | + | 0.931090i | \(0.381141\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.61762e6 | + | 285231.i | 0.131232 | + | 0.0231398i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.51211e7 | + | 1.26881e7i | 1.19540 | + | 1.00306i | 0.999749 | + | 0.0223896i | \(0.00712744\pi\) |
0.195654 | + | 0.980673i | \(0.437317\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.52323e6 | − | 4.37036e6i | −0.194425 | − | 0.336755i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.78807e6 | − | 2.83463e6i | −0.585039 | − | 0.212937i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.94636e6 | − | 5.10325e6i | 0.215820 | − | 0.373812i | −0.737706 | − | 0.675123i | \(-0.764091\pi\) |
0.953526 | + | 0.301311i | \(0.0974241\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.93878e6 | − | 694513.i | 0.281391 | − | 0.0496169i | −0.0311713 | − | 0.999514i | \(-0.509924\pi\) |
0.312562 | + | 0.949897i | \(0.398813\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00797e7 | + | 1.20125e7i | 0.702470 | + | 0.837171i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.58905e6 | − | 3.49013e6i | 0.652044 | − | 0.237325i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.72572e7 | + | 213409.i | −1.14520 | + | 0.0141619i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.15043e6 | − | 1.14032e7i | −0.268841 | − | 0.738634i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.11946e7 | + | 9.39341e6i | −0.707927 | + | 0.594021i | −0.924017 | − | 0.382352i | \(-0.875114\pi\) |
0.216090 | + | 0.976374i | \(0.430670\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 375955. | + | 2.13215e6i | 0.0232153 | + | 0.131660i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.96771e6 | − | 3.44546e6i | −0.359905 | − | 0.207791i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.61504e6 | + | 4.43730e6i | −0.0951448 | + | 0.261408i | −0.978131 | − | 0.207991i | \(-0.933307\pi\) |
0.882986 | + | 0.469400i | \(0.155530\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 856635. | − | 494579.i | 0.0493057 | − | 0.0284666i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.23180e7 | + | 2.65976e7i | −1.25526 | + | 1.49596i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.31619e6 | + | 7.46448e6i | −0.0723521 | + | 0.410329i | 0.927024 | + | 0.375003i | \(0.122358\pi\) |
−0.999376 | + | 0.0353264i | \(0.988753\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2.20241e7i | − | 1.18348i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.42995e7 | 1.80200 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.13939e7 | + | 3.77232e6i | 1.09909 | + | 0.193799i | 0.693642 | − | 0.720320i | \(-0.256005\pi\) |
0.405446 | + | 0.914119i | \(0.367116\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.45889e6 | + | 7.93695e6i | 0.475261 | + | 0.398791i | 0.848709 | − | 0.528860i | \(-0.177380\pi\) |
−0.373448 | + | 0.927651i | \(0.621825\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.33126e6 | − | 4.03787e6i | −0.114579 | − | 0.198456i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.59216e6 | + | 2.39935e6i | 0.316978 | + | 0.115371i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.45650e6 | − | 5.98683e6i | 0.162629 | − | 0.281681i | −0.773182 | − | 0.634184i | \(-0.781336\pi\) |
0.935811 | + | 0.352503i | \(0.114669\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.38150e7 | − | 7.72577e6i | 2.01749 | − | 0.355737i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.23063e7 | + | 2.65836e7i | 1.00533 | + | 1.19810i | 0.980117 | + | 0.198421i | \(0.0635813\pi\) |
0.0252109 | + | 0.999682i | \(0.491974\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.28921e7 | + | 4.69234e6i | −0.568806 | + | 0.207028i | −0.610382 | − | 0.792107i | \(-0.708984\pi\) |
0.0415764 | + | 0.999135i | \(0.486762\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.50100e7 | − | 2.52711e7i | −0.648403 | − | 1.09167i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −617818. | − | 1.69744e6i | −0.0261345 | − | 0.0718041i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.65096e7 | + | 1.38532e7i | −0.683979 | + | 0.573927i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 998355. | + | 5.66195e6i | 0.0405141 | + | 0.229767i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.15763e7 | + | 1.24571e7i | 0.857776 | + | 0.495237i | 0.863267 | − | 0.504748i | \(-0.168414\pi\) |
−0.00549090 | + | 0.999985i | \(0.501748\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.04502e7 | − | 2.87118e7i | 0.407062 | − | 1.11839i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.45954e7 | + | 1.99736e7i | −1.32053 | + | 0.762409i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.95028e6 | − | 4.70776e6i | 0.147780 | − | 0.176117i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 569828. | − | 3.23165e6i | 0.0208951 | − | 0.118502i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 2.26888e7i | − | 0.815611i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.27146e7 | −1.15303 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.29116e6 | − | 756647.i | −0.148306 | − | 0.0261504i | 0.0990021 | − | 0.995087i | \(-0.468435\pi\) |
−0.247308 | + | 0.968937i | \(0.579546\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.51632e7 | − | 6.30694e7i | −2.54759 | − | 2.13768i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.65524e6 | + | 8.06311e6i | 0.154761 | + | 0.268054i | 0.932972 | − | 0.359949i | \(-0.117206\pi\) |
−0.778211 | + | 0.628003i | \(0.783873\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.35942e7 | − | 1.58670e7i | −1.42166 | − | 0.517442i | −0.487131 | − | 0.873329i | \(-0.661957\pi\) |
−0.934529 | + | 0.355887i | \(0.884179\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.75495e6 | − | 4.77171e6i | 0.0881417 | − | 0.152666i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.89381e7 | + | 6.86583e6i | −1.22235 | + | 0.215534i | −0.747338 | − | 0.664444i | \(-0.768668\pi\) |
−0.475015 | + | 0.879978i | \(0.657557\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.19722e7 | − | 1.42679e7i | −0.368809 | − | 0.439529i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.69778e7 | + | 1.70985e7i | −1.42029 | + | 0.516944i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.08375e7 | − | 2.04944e6i | 0.321605 | − | 0.0608173i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.81065e6 | − | 1.87121e7i | −0.198399 | − | 0.545096i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.66111e7 | − | 3.07204e7i | 1.04706 | − | 0.878584i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 378928. | + | 2.14901e6i | 0.0106407 | + | 0.0603462i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.24089e7 | − | 3.02583e7i | −1.44518 | − | 0.834374i | −0.446990 | − | 0.894539i | \(-0.647504\pi\) |
−0.998188 | + | 0.0601649i | \(0.980837\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.47228e7 | + | 4.04507e7i | −0.398712 | + | 1.09545i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.37921e7 | − | 7.96289e6i | 0.366857 | − | 0.211805i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.67437e7 | − | 5.57070e7i | 1.22133 | − | 1.45553i | 0.371530 | − | 0.928421i | \(-0.378833\pi\) |
0.849801 | − | 0.527104i | \(-0.176722\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.00354e6 | + | 3.40478e7i | −0.154102 | + | 0.873956i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.38665e7i | 0.601903i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.87984e6 | −0.220051 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.03073e7 | + | 1.81746e6i | 0.251009 | + | 0.0442597i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.74415e6 | + | 2.30262e6i | 0.0656779 | + | 0.0551103i | 0.675036 | − | 0.737785i | \(-0.264128\pi\) |
−0.609358 | + | 0.792895i | \(0.708573\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.00092e6 | + | 3.46570e6i | 0.0470710 | + | 0.0815294i | 0.888601 | − | 0.458681i | \(-0.151678\pi\) |
−0.841530 | + | 0.540210i | \(0.818345\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.06554e8 | + | 3.87824e7i | 2.46404 | + | 0.896836i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.40118e7 | − | 4.15897e7i | 0.545885 | − | 0.945501i | −0.452665 | − | 0.891680i | \(-0.649527\pi\) |
0.998551 | − | 0.0538205i | \(-0.0171399\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.72149e7 | + | 1.00885e7i | −1.27886 | + | 0.225498i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.91533e6 | + | 2.28261e6i | 0.0420959 | + | 0.0501679i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.55485e7 | + | 1.29386e7i | −0.768313 | + | 0.279643i | −0.696290 | − | 0.717760i | \(-0.745167\pi\) |
−0.0720221 | + | 0.997403i | \(0.522945\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.45931e7 | + | 1.49925e7i | 0.947863 | + | 0.318678i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.64535e7 | + | 4.52055e7i | 0.343983 | + | 0.945086i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.47244e7 | − | 3.75282e7i | 0.919741 | − | 0.771754i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.43147e6 | + | 2.51321e7i | 0.0896499 | + | 0.508430i | 0.996256 | + | 0.0864518i | \(0.0275529\pi\) |
−0.906606 | + | 0.421978i | \(0.861336\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.80791e7 | + | 3.93055e7i | 1.35499 | + | 0.782302i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.25724e6 | + | 8.94920e6i | −0.0637864 | + | 0.175252i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.11580e7 | + | 2.37626e7i | −0.793099 | + | 0.457896i | −0.841052 | − | 0.540954i | \(-0.818063\pi\) |
0.0479536 | + | 0.998850i | \(0.484730\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.48385e7 | − | 7.72715e7i | 1.22953 | − | 1.46530i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.18061e6 | + | 5.20658e7i | −0.171336 | + | 0.971692i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 4.33231e7i | − | 0.795796i | −0.917430 | − | 0.397898i | \(-0.869740\pi\) | ||
0.917430 | − | 0.397898i | \(-0.130260\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.39762e7 | −1.51838 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.14642e7 | − | 1.43643e7i | −1.45001 | − | 0.255675i | −0.607483 | − | 0.794333i | \(-0.707821\pi\) |
−0.842525 | + | 0.538658i | \(0.818932\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.26420e6 | + | 1.89989e6i | 0.0396764 | + | 0.0332925i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.14032e7 | + | 1.23674e8i | 1.23193 | + | 2.13376i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.02120e8 | + | 3.71685e7i | 1.73484 | + | 0.631431i | 0.998956 | − | 0.0456745i | \(-0.0145437\pi\) |
0.735886 | + | 0.677105i | \(0.236766\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.96375e6 | + | 3.40132e6i | −0.0328516 | + | 0.0569006i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.41741e8 | − | 2.49928e7i | 2.33517 | − | 0.411754i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.58621e6 | − | 1.14244e7i | −0.155545 | − | 0.185371i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.67651e6 | − | 610200.i | 0.0267938 | − | 0.00975216i | −0.328588 | − | 0.944473i | \(-0.606573\pi\) |
0.355382 | + | 0.934721i | \(0.384351\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.36164e6 | + | 1.24885e7i | 0.0371787 | + | 0.196603i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.73049e6 | − | 1.02494e7i | −0.0578540 | − | 0.158953i | 0.907399 | − | 0.420271i | \(-0.138065\pi\) |
−0.965253 | + | 0.261318i | \(0.915843\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.18966e7 | − | 4.35464e7i | 0.792910 | − | 0.665330i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.51652e7 | + | 8.60060e7i | 0.228288 | + | 1.29468i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.99981e7 | − | 1.15459e7i | −0.296623 | − | 0.171255i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.52503e7 | + | 6.93747e7i | −0.369060 | + | 1.01398i | 0.606660 | + | 0.794962i | \(0.292509\pi\) |
−0.975720 | + | 0.219023i | \(0.929713\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.28631e8 | + | 7.42650e7i | −1.85276 | + | 1.06969i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.49262e6 | + | 1.01211e7i | −0.120557 | + | 0.143674i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.79181e6 | − | 2.15044e7i | 0.0530521 | − | 0.300873i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 2.35645e8i | − | 3.24975i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.11060e8 | −1.50978 | −0.754891 | − | 0.655850i | \(-0.772310\pi\) | ||||
−0.754891 | + | 0.655850i | \(0.772310\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.21344e6 | + | 1.09560e6i | 0.0832694 | + | 0.0146826i | 0.215128 | − | 0.976586i | \(-0.430983\pi\) |
−0.131858 | + | 0.991269i | \(0.542094\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.27469e7 | − | 6.10419e7i | −0.961155 | − | 0.806505i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.36301e6 | + | 1.10211e7i | 0.0828888 | + | 0.143568i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.32931e7 | + | 4.83830e6i | 0.170743 | + | 0.0621455i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.44231e7 | + | 9.42636e7i | −0.689305 | + | 1.19391i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.11045e8 | − | 1.95802e7i | 1.38697 | − | 0.244560i | 0.570190 | − | 0.821513i | \(-0.306870\pi\) |
0.816777 | + | 0.576953i | \(0.195759\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.93314e7 | − | 3.49558e7i | −0.361301 | − | 0.430582i | 0.554519 | − | 0.832171i | \(-0.312902\pi\) |
−0.915820 | + | 0.401590i | \(0.868458\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.46100e7 | + | 3.07955e7i | −1.02791 | + | 0.374128i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.44034e7 | + | 8.55498e6i | −0.172591 | + | 0.102512i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.72471e7 | − | 1.02336e8i | −0.440250 | − | 1.20958i | −0.939328 | − | 0.343020i | \(-0.888550\pi\) |
0.499078 | − | 0.866557i | \(-0.333672\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.47102e8 | − | 1.23433e8i | 1.71515 | − | 1.43918i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.20418e7 | + | 1.25005e8i | 0.253534 | + | 1.43786i | 0.799809 | + | 0.600255i | \(0.204934\pi\) |
−0.546275 | + | 0.837606i | \(0.683955\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.34508e7 | + | 3.08598e7i | 0.606560 | + | 0.350198i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.65593e6 | + | 7.29712e6i | −0.0297368 | + | 0.0817013i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.36289e8 | − | 7.86867e7i | 1.50565 | − | 0.869285i | 0.505667 | − | 0.862729i | \(-0.331246\pi\) |
0.999979 | − | 0.00655618i | \(-0.00208691\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.71062e7 | + | 3.23039e7i | −0.295487 | + | 0.352148i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.95621e7 | + | 2.24368e8i | −0.425583 | + | 2.41360i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 8.38989e6i | − | 0.0890681i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.07893e8 | 1.13043 | 0.565214 | − | 0.824944i | \(-0.308794\pi\) | ||||
0.565214 | + | 0.824944i | \(0.308794\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.13657e7 | − | 1.25837e7i | −0.737992 | − | 0.130128i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.90650e6 | − | 8.31254e6i | −0.101115 | − | 0.0848459i | 0.590828 | − | 0.806797i | \(-0.298801\pi\) |
−0.691944 | + | 0.721951i | \(0.743245\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.59240e7 | + | 1.31504e8i | 0.764956 | + | 1.32494i | 0.940270 | + | 0.340429i | \(0.110572\pi\) |
−0.175315 | + | 0.984512i | \(0.556094\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.08419e8 | + | 3.94613e7i | 1.07832 | + | 0.392475i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.91973e7 | − | 5.05711e7i | 0.286676 | − | 0.496537i | −0.686338 | − | 0.727283i | \(-0.740783\pi\) |
0.973014 | + | 0.230745i | \(0.0741163\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.78190e6 | + | 1.19583e6i | −0.0657405 | + | 0.0115918i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.39220e8 | − | 1.65916e8i | −1.33242 | − | 1.58791i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.19865e7 | + | 2.62010e7i | −0.680249 | + | 0.247590i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 671216. | + | 5.42777e7i | 0.00626298 | + | 0.506454i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.41750e8 | − | 3.89456e8i | −1.30608 | − | 3.58842i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.36099e8 | + | 1.14200e8i | −1.23836 | + | 1.03911i | −0.240710 | + | 0.970597i | \(0.577380\pi\) |
−0.997650 | + | 0.0685109i | \(0.978175\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.13821e7 | + | 6.45512e7i | 0.102279 | + | 0.580055i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.91945e6 | − | 2.26290e6i | −0.0347844 | − | 0.0200828i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.53836e6 | + | 9.72155e6i | −0.0310153 | + | 0.0852139i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.52703e7 | − | 2.03633e7i | 0.305367 | − | 0.176304i | −0.339485 | − | 0.940612i | \(-0.610253\pi\) |
0.644851 | + | 0.764308i | \(0.276919\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.22068e7 | − | 1.45475e7i | 0.104394 | − | 0.124412i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.75340e7 | − | 9.94403e7i | 0.148128 | − | 0.840074i | −0.816675 | − | 0.577098i | \(-0.804185\pi\) |
0.964802 | − | 0.262976i | \(-0.0847040\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 3.37876e7i | − | 0.281979i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.28628e8 | −1.06052 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.47405e7 | + | 4.36242e6i | 0.201530 | + | 0.0355352i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −515356. | − | 432435.i | −0.00414768 | − | 0.00348032i | 0.640711 | − | 0.767782i | \(-0.278640\pi\) |
−0.644859 | + | 0.764301i | \(0.723084\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.24271e8 | + | 2.15244e8i | 0.988229 | + | 1.71166i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.24463e7 | − | 2.27286e7i | −0.490685 | − | 0.178595i | 0.0848146 | − | 0.996397i | \(-0.472970\pi\) |
−0.575500 | + | 0.817802i | \(0.695192\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.04134e7 | − | 3.53571e7i | 0.158505 | − | 0.274538i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.23000e7 | − | 1.27484e7i | 0.554772 | − | 0.0978213i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.38810e7 | − | 1.65427e7i | −0.105261 | − | 0.125445i | 0.710842 | − | 0.703352i | \(-0.248314\pi\) |
−0.816103 | + | 0.577907i | \(0.803870\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.37233e7 | + | 8.63458e6i | −0.177792 | + | 0.0647111i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.39223e8 | − | 1.95743e8i | −1.77195 | − | 1.44989i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.03862e7 | − | 1.65910e8i | −0.442096 | − | 1.21465i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.90240e7 | − | 3.27451e7i | 0.282397 | − | 0.236959i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.97737e7 | + | 3.38993e8i | 0.427571 | + | 2.42487i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.19026e7 | − | 5.30600e7i | −0.649852 | − | 0.375192i | 0.138547 | − | 0.990356i | \(-0.455757\pi\) |
−0.788400 | + | 0.615163i | \(0.789090\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.28817e7 | + | 6.28669e7i | −0.159949 | + | 0.439457i | −0.993617 | − | 0.112810i | \(-0.964015\pi\) |
0.833667 | + | 0.552267i | \(0.186237\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.26999e7 | + | 7.33232e6i | −0.0877655 | + | 0.0506714i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.78297e7 | + | 3.31661e7i | −0.190141 | + | 0.226601i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.46703e7 | + | 1.39912e8i | −0.166651 | + | 0.945123i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 5.74974e8i | − | 3.84030i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.19701e8 | 0.790524 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.85918e7 | − | 1.56211e7i | −0.578538 | − | 0.102012i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.05663e8 | − | 8.86618e7i | −0.682339 | − | 0.572550i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.15052e7 | + | 8.92096e7i | 0.328916 | + | 0.569699i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.29585e7 | − | 1.56356e7i | −0.271305 | − | 0.0987469i | 0.202785 | − | 0.979223i | \(-0.435001\pi\) |
−0.474090 | + | 0.880476i | \(0.657223\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.65923e7 | − | 1.49982e8i | 0.540854 | − | 0.936786i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.46926e7 | − | 1.49336e7i | 0.523186 | − | 0.0922518i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.13662e7 | + | 4.92983e7i | 0.252746 | + | 0.301211i | 0.877467 | − | 0.479637i | \(-0.159232\pi\) |
−0.624721 | + | 0.780848i | \(0.714787\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.78498e8 | + | 2.10556e8i | −3.49611 | + | 1.27248i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.05102e7 | − | 1.25691e8i | 0.421500 | − | 0.751365i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.20562e6 | + | 6.05989e6i | 0.0130423 | + | 0.0358335i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.55148e7 | + | 7.17555e7i | −0.500222 | + | 0.419736i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.51532e6 | + | 1.42651e7i | 0.0145555 | + | 0.0825483i | 0.991220 | − | 0.132221i | \(-0.0422110\pi\) |
−0.976665 | + | 0.214770i | \(0.931100\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.88318e8 | + | 1.08725e8i | 1.07809 | + | 0.622437i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.37914e7 | − | 6.53664e7i | 0.134751 | − | 0.370225i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.76845e8 | + | 1.02102e8i | −0.990987 | + | 0.572147i | −0.905569 | − | 0.424199i | \(-0.860556\pi\) |
−0.0854178 | + | 0.996345i | \(0.527223\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.99889e7 | + | 4.76570e7i | −0.221715 | + | 0.264229i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.55763e6 | − | 3.71902e7i | 0.0359747 | − | 0.204023i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.81985e8i | 0.987868i | 0.869499 | + | 0.493934i | \(0.164442\pi\) | ||||
−0.869499 | + | 0.493934i | \(0.835558\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.18975e8 | 0.639068 | 0.319534 | − | 0.947575i | \(-0.396474\pi\) | ||||
0.319534 | + | 0.947575i | \(0.396474\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.56303e8 | + | 4.51932e7i | 1.36236 | + | 0.240220i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.48069e7 | − | 1.24245e7i | −0.0778863 | − | 0.0653544i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.49564e7 | + | 4.32258e7i | 0.129914 | + | 0.225017i | 0.923643 | − | 0.383254i | \(-0.125197\pi\) |
−0.793729 | + | 0.608271i | \(0.791863\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.43737e8 | + | 1.97904e8i | 2.80126 | + | 1.01957i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.72113e6 | + | 8.17724e6i | −0.0240723 | + | 0.0416944i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.18948e8 | − | 3.86065e7i | 1.10493 | − | 0.194830i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.34692e8 | + | 2.79695e8i | 1.17228 | + | 1.39707i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.77795e8 | − | 6.47121e7i | 0.879033 | − | 0.319942i | 0.137214 | − | 0.990541i | \(-0.456185\pi\) |
0.741820 | + | 0.670600i | \(0.233963\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.72741e8 | + | 6.53027e7i | −0.845375 | + | 0.319584i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.48791e8 | + | 4.08801e8i | 0.720801 | + | 1.98038i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.95979e8 | − | 2.48356e8i | 1.41937 | − | 1.19100i | 0.467700 | − | 0.883887i | \(-0.345083\pi\) |
0.951674 | − | 0.307109i | \(-0.0993615\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 931070. | + | 5.28036e6i | 0.00442009 | + | 0.0250676i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.05624e8 | + | 6.09819e7i | 0.496408 | + | 0.286601i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.97544e7 | − | 5.42748e7i | 0.0919143 | − | 0.252533i | −0.885214 | − | 0.465185i | \(-0.845988\pi\) |
0.977128 | + | 0.212652i | \(0.0682101\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.06235e8 | + | 6.13347e7i | −0.489377 | + | 0.282542i | −0.724316 | − | 0.689468i | \(-0.757844\pi\) |
0.234939 | + | 0.972010i | \(0.424511\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.92638e8 | − | 2.29577e8i | 0.878598 | − | 1.04707i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.50318e7 | + | 8.52496e7i | −0.0678805 | + | 0.384969i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1.20152e8i | − | 0.537237i | −0.963247 | − | 0.268618i | \(-0.913433\pi\) | ||
0.963247 | − | 0.268618i | \(-0.0865671\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.89346e7 | 0.172379 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.42405e8 | − | 2.51098e7i | −0.624312 | − | 0.110083i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.68770e7 | − | 3.93344e7i | −0.203506 | − | 0.170762i | 0.535339 | − | 0.844638i | \(-0.320184\pi\) |
−0.738845 | + | 0.673875i | \(0.764628\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.01930e8 | + | 1.76548e8i | 0.438203 | + | 0.758990i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.49180e7 | − | 9.06939e6i | −0.106086 | − | 0.0386120i | 0.288432 | − | 0.957500i | \(-0.406866\pi\) |
−0.394518 | + | 0.918888i | \(0.629088\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.92830e8 | + | 3.33991e8i | −0.813022 | + | 1.40819i | 0.0977184 | + | 0.995214i | \(0.468846\pi\) |
−0.910740 | + | 0.412980i | \(0.864488\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.08395e8 | − | 1.91129e7i | 0.452619 | − | 0.0798089i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.71550e7 | − | 2.04445e7i | −0.0709457 | − | 0.0845498i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.43653e7 | − | 1.97874e7i | 0.222680 | − | 0.0810490i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.24916e8 | − | 1.93517e8i | 0.912470 | − | 0.785084i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.43272e7 | − | 3.93636e7i | −0.0575716 | − | 0.158177i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.46280e8 | + | 2.06653e8i | −0.980258 | + | 0.822534i | −0.984128 | − | 0.177458i | \(-0.943213\pi\) |
0.00386995 | + | 0.999993i | \(0.498768\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.01626e7 | − | 5.76349e7i | −0.0400676 | − | 0.227234i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.30865e8 | − | 7.55547e7i | −0.511094 | − | 0.295080i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00006e8 | − | 2.74766e8i | 0.386910 | − | 1.06303i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.46809e8 | + | 5.46641e8i | −3.62877 | + | 2.09507i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.53986e8 | − | 1.83513e8i | 0.584664 | − | 0.696775i | −0.389907 | − | 0.920854i | \(-0.627493\pi\) |
0.974571 | + | 0.224079i | \(0.0719374\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.38340e7 | − | 3.62021e8i | 0.240115 | − | 1.36176i | −0.591454 | − | 0.806339i | \(-0.701446\pi\) |
0.831569 | − | 0.555421i | \(-0.187443\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.70336e8i | 1.38012i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.83260e8 | −1.78430 | −0.892150 | − | 0.451739i | \(-0.850804\pi\) | ||||
−0.892150 | + | 0.451739i | \(0.850804\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.03751e8 | + | 5.35595e7i | 1.11118 | + | 0.195931i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.82184e7 | − | 3.20691e7i | −0.138526 | − | 0.116237i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.98735e8 | − | 3.44219e8i | −0.713731 | − | 1.23622i | −0.963447 | − | 0.267899i | \(-0.913671\pi\) |
0.249716 | − | 0.968319i | \(-0.419663\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.43370e8 | + | 8.85793e7i | 0.866049 | + | 0.315216i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.49331e8 | − | 9.51469e8i | 1.93704 | − | 3.35505i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.55538e8 | + | 4.50583e7i | −0.892893 | + | 0.157441i | −0.601226 | − | 0.799079i | \(-0.705321\pi\) |
−0.291667 | + | 0.956520i | \(0.594210\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.50816e8 | + | 2.98911e8i | 0.868462 | + | 1.03499i | 0.999051 | + | 0.0435564i | \(0.0138688\pi\) |
−0.130589 | + | 0.991437i | \(0.541687\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.85545e8 | + | 6.75330e7i | −0.636663 | + | 0.231726i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.55579e6 | + | 2.15862e7i | −0.0256930 | + | 0.0734026i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.75520e7 | + | 4.82237e7i | 0.0591492 | + | 0.162511i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.21858e8 | + | 3.53981e8i | −1.40892 | + | 1.18223i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.73461e7 | − | 3.25226e8i | −0.189817 | − | 1.07651i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.14931e8 | − | 2.39561e8i | −1.36123 | − | 0.785905i | −0.371440 | − | 0.928457i | \(-0.621136\pi\) |
−0.989787 | + | 0.142552i | \(0.954469\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.21979e8 | − | 3.35134e8i | 0.396618 | − | 1.08970i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.84922e8 | + | 2.22235e8i | −1.24053 | + | 0.716220i | −0.969202 | − | 0.246267i | \(-0.920796\pi\) |
−0.271328 | + | 0.962487i | \(0.587463\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.87552e6 | − | 3.42691e6i | 0.00918560 | − | 0.0109470i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.35983e8 | + | 7.71198e8i | −0.430570 | + | 2.44188i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 5.54542e8i | − | 1.74049i | −0.492618 | − | 0.870246i | \(-0.663960\pi\) | ||
0.492618 | − | 0.870246i | \(-0.336040\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.67269e8 | −0.831530 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.21068e8 | + | 7.42456e7i | 1.29862 | + | 0.228982i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.83437e8 | − | 4.05652e8i | −1.47803 | − | 1.24021i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.54369e7 | + | 1.47981e8i | 0.258947 | + | 0.448510i | 0.965960 | − | 0.258691i | \(-0.0832911\pi\) |
−0.707013 | + | 0.707201i | \(0.749958\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.22662e7 | + | 1.90233e7i | 0.157044 | + | 0.0571593i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.12014e8 | − | 3.67218e8i | 0.631552 | − | 1.09388i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.53362e7 | + | 1.32838e7i | −0.222487 | + | 0.0392305i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.19181e8 | + | 7.37911e8i | 1.81295 | + | 2.16059i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 844593. | − | 307407.i | 0.00245185 | − | 0.000892400i | −0.340794 | − | 0.940138i | \(-0.610696\pi\) |
0.343246 | + | 0.939246i | \(0.388474\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.88488e7 | − | 1.76333e8i | 0.0830352 | − | 0.507538i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.42286e7 | − | 2.31416e8i | −0.240377 | − | 0.660430i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.35238e7 | + | 1.13478e7i | −0.0382685 | + | 0.0321111i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.32870e7 | − | 7.53541e7i | −0.0372810 | − | 0.211431i | 0.960477 | − | 0.278360i | \(-0.0897909\pi\) |
−0.997758 | + | 0.0669294i | \(0.978680\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.43043e8 | − | 1.40321e8i | −0.676200 | − | 0.390404i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.24911e7 | − | 6.17937e7i | 0.0620500 | − | 0.170481i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.69621e8 | + | 9.79306e7i | −0.464046 | + | 0.267917i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.84844e8 | − | 2.20288e8i | 0.501473 | − | 0.597633i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.06640e7 | + | 1.17191e8i | −0.0555940 | + | 0.315289i | −0.999905 | − | 0.0137643i | \(-0.995619\pi\) |
0.944311 | + | 0.329054i | \(0.106730\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.63459e7i | 0.203695i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.95178e8 | 0.516436 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.63758e8 | + | 2.88750e7i | 0.429723 | + | 0.0757718i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.23119e8 | + | 2.71129e8i | 0.840930 | + | 0.705624i | 0.957773 | − | 0.287527i | \(-0.0928330\pi\) |
−0.116843 | + | 0.993150i | \(0.537277\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.01143e7 | + | 3.48390e7i | 0.0519185 | + | 0.0899254i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.30588e8 | − | 4.75300e7i | −0.334311 | − | 0.121679i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.01560e8 | − | 1.75906e8i | 0.257875 | − | 0.446652i | −0.707798 | − | 0.706415i | \(-0.750311\pi\) |
0.965672 | + | 0.259763i | \(0.0836444\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.90414e8 | − | 8.64732e7i | 1.23510 | − | 0.217781i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.03338e8 | + | 1.23153e8i | 0.258141 | + | 0.307641i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.95342e8 | − | 1.43893e8i | 0.979578 | − | 0.356537i | 0.197902 | − | 0.980222i | \(-0.436587\pi\) |
0.781676 | + | 0.623684i | \(0.214365\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.31170e8 | − | 1.35983e8i | −2.04285 | − | 0.334217i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.00195e8 | + | 5.50032e8i | 0.488076 | + | 1.34098i | 0.902420 | + | 0.430857i | \(0.141789\pi\) |
−0.414344 | + | 0.910120i | \(0.635989\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.07042e7 | + | 8.98190e6i | −0.0258873 | + | 0.0217220i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.13544e7 | − | 4.04671e8i | −0.171182 | − | 0.970823i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.36878e7 | + | 1.94496e7i | 0.0801727 | + | 0.0462877i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.13062e8 | − | 5.85383e8i | 0.503021 | − | 1.38204i | −0.385289 | − | 0.922796i | \(-0.625898\pi\) |
0.888310 | − | 0.459243i | \(-0.151879\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.17601e8 | + | 3.56572e8i | −1.44651 | + | 0.835146i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.63519e8 | + | 3.14049e8i | −0.612309 | + | 0.729721i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.41402e7 | + | 4.77183e8i | −0.193962 | + | 1.10001i | 0.719928 | + | 0.694049i | \(0.244175\pi\) |
−0.913890 | + | 0.405962i | \(0.866936\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.05654e8i | 0.241636i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.73543e8 | 0.847591 | 0.423795 | − | 0.905758i | \(-0.360698\pi\) | ||||
0.423795 | + | 0.905758i | \(0.360698\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.66222e7 | − | 6.45749e6i | −0.0824463 | − | 0.0145375i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.78748e8 | − | 1.49987e8i | −0.399260 | − | 0.335019i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.37755e8 | − | 7.58215e8i | −0.970165 | − | 1.68037i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.95634e8 | − | 1.43999e8i | −0.869990 | − | 0.316650i | −0.131827 | − | 0.991273i | \(-0.542084\pi\) |
−0.738163 | + | 0.674622i | \(0.764306\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.15219e8 | + | 1.99565e8i | −0.251398 | + | 0.435434i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.02327e8 | + | 1.80430e7i | −0.221540 | + | 0.0390634i | −0.283316 | − | 0.959027i | \(-0.591435\pi\) |
0.0617764 | + | 0.998090i | \(0.480323\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.36963e8 | − | 1.63226e8i | −0.294237 | − | 0.350658i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.53600e7 | − | 1.65097e7i | 0.0966962 | − | 0.0351946i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.07976e8 | − | 1.07800e8i | −0.651485 | − | 0.228038i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.00586e8 | − | 5.51106e8i | −0.421064 | − | 1.15686i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.25355e8 | + | 6.08645e8i | −1.51100 | + | 1.26788i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.76769e7 | − | 3.83815e8i | −0.139905 | − | 0.793438i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.69392e7 | + | 5.01944e7i | 0.178357 | + | 0.102975i | 0.586521 | − | 0.809934i | \(-0.300497\pi\) |
−0.408163 | + | 0.912909i | \(0.633831\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.26509e8 | + | 3.47580e8i | −0.257567 | + | 0.707659i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.32971e7 | − | 1.34506e7i | 0.0470731 | − | 0.0271777i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.02554e8 | + | 7.18096e8i | −1.20831 | + | 1.44000i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.86634e8 | − | 1.05845e9i | 0.371440 | − | 2.10654i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 5.80507e8i | − | 1.14665i | −0.819327 | − | 0.573327i | \(-0.805653\pi\) | ||
0.819327 | − | 0.573327i | \(-0.194347\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.24122e7 | 0.181171 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.14380e9 | + | 2.01682e8i | 2.22562 | + | 0.392437i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.51477e8 | + | 3.78834e8i | 0.871945 | + | 0.731649i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.07193e6 | − | 7.05278e6i | −0.00780571 | − | 0.0135199i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.96197e8 | + | 3.62586e8i | 1.89550 | + | 0.689907i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.51011e8 | + | 4.34764e8i | −0.474075 | + | 0.821122i | −0.999559 | − | 0.0296810i | \(-0.990551\pi\) |
0.525484 | + | 0.850803i | \(0.323884\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.62124e8 | − | 6.38522e7i | 0.678883 | − | 0.119705i | 0.176434 | − | 0.984312i | \(-0.443544\pi\) |
0.502448 | + | 0.864607i | \(0.332433\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.87325e8 | + | 4.61596e8i | 0.720781 | + | 0.858994i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.21111e7 | − | 1.16875e7i | 0.0593175 | − | 0.0215898i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.86604e8 | − | 4.49333e8i | −0.708924 | − | 0.823953i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.39985e7 | − | 1.48360e8i | −0.0982947 | − | 0.270063i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.44362e8 | + | 5.40684e8i | −1.16439 | + | 0.977043i | −0.999956 | − | 0.00934391i | \(-0.997026\pi\) |
−0.164439 | + | 0.986387i | \(0.552581\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.46113e8 | + | 8.28647e8i | 0.262113 | + | 1.48652i | 0.777131 | + | 0.629338i | \(0.216674\pi\) |
−0.515018 | + | 0.857179i | \(0.672215\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.96479e8 | + | 1.71172e8i | 0.527998 | + | 0.304840i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.42883e8 | − | 6.67316e8i | 0.429418 | − | 1.17982i | −0.516748 | − | 0.856138i | \(-0.672858\pi\) |
0.946167 | − | 0.323680i | \(-0.104920\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.43876e8 | − | 4.29477e8i | 1.30568 | − | 0.753835i | 0.324309 | − | 0.945951i | \(-0.394868\pi\) |
0.981372 | + | 0.192116i | \(0.0615351\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.16848e8 | − | 2.58429e8i | 0.377878 | − | 0.450338i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.24491e7 | + | 1.84028e8i | −0.0561394 | + | 0.318382i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.47235e8i | 0.768204i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.21333e9 | 2.06921 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.65889e8 | + | 1.17414e8i | 1.12750 | + | 0.198808i | 0.706130 | − | 0.708082i | \(-0.250439\pi\) |
0.421367 | + | 0.906890i | \(0.361550\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.17464e8 | + | 9.85642e7i | 0.197478 | + | 0.165703i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.46741e8 | + | 1.46660e9i | 1.41341 | + | 2.44810i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.24139e8 | + | 4.51829e7i | 0.205749 | + | 0.0748865i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.87159e7 | − | 3.24168e7i | 0.0308006 | − | 0.0533483i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.59342e8 | + | 1.16260e8i | −1.07743 | + | 0.189979i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.08972e7 | + | 4.87394e7i | 0.0663598 | + | 0.0790846i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.57936e8 | + | 5.74841e7i | −0.254469 | + | 0.0926192i | −0.466105 | − | 0.884729i | \(-0.654343\pi\) |
0.211636 | + | 0.977349i | \(0.432121\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.51947e8 | − | 9.30982e8i | −0.563091 | − | 1.48951i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.55088e7 | − | 9.75596e7i | −0.0564149 | − | 0.154999i | 0.908284 | − | 0.418354i | \(-0.137393\pi\) |
−0.964699 | + | 0.263356i | \(0.915171\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.05335e8 | + | 2.56206e8i | −0.481722 | + | 0.404213i | −0.851049 | − | 0.525087i | \(-0.824033\pi\) |
0.369327 | + | 0.929300i | \(0.379588\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.53074e7 | − | 8.68124e7i | −0.0239823 | − | 0.136011i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.63164e8 | − | 2.09673e8i | −0.565028 | − | 0.326219i | 0.190133 | − | 0.981758i | \(-0.439108\pi\) |
−0.755161 | + | 0.655539i | \(0.772441\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.11849e8 | + | 5.82050e8i | −0.327324 | + | 0.899316i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.10824e8 | + | 5.25865e8i | −1.39758 | + | 0.806894i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.67695e7 | − | 1.15325e8i | 0.147462 | − | 0.175738i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.92425e7 | − | 4.49406e8i | 0.119923 | − | 0.680119i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.94681e8i | 0.292605i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.84874e7 | −0.117159 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.48851e8 | − | 4.38791e7i | −0.368927 | − | 0.0650517i | −0.0138885 | − | 0.999904i | \(-0.504421\pi\) |
−0.355038 | + | 0.934852i | \(0.615532\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.31369e8 | + | 7.81511e8i | 1.37137 | + | 1.15072i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.36544e8 | + | 7.56117e8i | 0.638411 | + | 1.10576i | 0.985781 | + | 0.168033i | \(0.0537414\pi\) |
−0.347370 | + | 0.937728i | \(0.612925\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.44076e8 | − | 5.24396e7i | −0.209272 | − | 0.0761688i | 0.235257 | − | 0.971933i | \(-0.424407\pi\) |
−0.444529 | + | 0.895764i | \(0.646629\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.45532e8 | − | 1.29130e9i | 1.07556 | − | 1.86293i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.13594e9 | − | 2.00297e8i | 1.62774 | − | 0.287014i | 0.716097 | − | 0.698001i | \(-0.245927\pi\) |
0.911642 | + | 0.410986i | \(0.134816\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.20009e7 | + | 5.00547e7i | 0.0597796 | + | 0.0712426i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.28428e8 | + | 3.01523e8i | −1.17117 | + | 0.426273i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.43778e8 | + | 1.92852e8i | 0.482751 | + | 0.270813i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.48898e7 | − | 2.33233e8i | −0.118409 | − | 0.325327i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.29740e8 | − | 1.92775e8i | 0.318316 | − | 0.267099i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.82357e7 | + | 5.57122e8i | 0.135204 | + | 0.766781i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.49279e8 | + | 2.01656e8i | 0.477527 | + | 0.275700i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.47705e7 | − | 1.50481e8i | 0.0743846 | − | 0.204370i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.69883e8 | − | 1.55817e8i | 0.364107 | − | 0.210217i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.01287e8 | − | 2.39884e8i | 0.269770 | − | 0.321499i | −0.614103 | − | 0.789226i | \(-0.710482\pi\) |
0.883873 | + | 0.467726i | \(0.154927\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.33411e8 | − | 7.56609e8i | 0.177623 | − | 1.00735i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.32880e8i | 0.572548i | 0.958148 | + | 0.286274i | \(0.0924168\pi\) | ||||
−0.958148 | + | 0.286274i | \(0.907583\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.20429e8 | 0.289638 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.57223e9 | − | 2.77226e8i | −2.05235 | − | 0.361885i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.57894e7 | − | 7.19859e7i | −0.111257 | − | 0.0933554i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.10570e8 | − | 5.37923e8i | −0.400141 | − | 0.693064i | 0.593602 | − | 0.804759i | \(-0.297705\pi\) |
−0.993743 | + | 0.111695i | \(0.964372\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.99816e8 | − | 7.27271e7i | −0.255771 | − | 0.0930931i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.32367e8 | + | 1.44170e9i | −1.05855 | + | 1.83346i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.03027e8 | − | 3.57992e7i | 0.256525 | − | 0.0452322i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.13564e9 | − | 2.54516e9i | −2.68095 | − | 3.19503i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.26804e8 | − | 1.18947e8i | 0.407606 | − | 0.148356i | −0.130076 | − | 0.991504i | \(-0.541522\pi\) |
0.537682 | + | 0.843148i | \(0.319300\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.04754e8 | + | 6.16876e8i | −0.625505 | + | 0.764449i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.55398e8 | + | 4.26952e8i | 0.191338 | + | 0.525696i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.58866e7 | − | 8.04584e7i | 0.117307 | − | 0.0984321i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.30348e8 | − | 7.39238e8i | −0.158447 | − | 0.898598i | −0.955566 | − | 0.294776i | \(-0.904755\pi\) |
0.797119 | − | 0.603822i | \(-0.206356\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.96063e9 | − | 1.13197e9i | −2.36809 | − | 1.36722i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.63392e8 | + | 4.48916e8i | −0.196093 | + | 0.538761i | −0.998300 | − | 0.0582852i | \(-0.981437\pi\) |
0.802207 | + | 0.597046i | \(0.203659\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.00624e8 | − | 5.80952e7i | 0.119996 | − | 0.0692795i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.65871e7 | − | 1.15108e8i | 0.114452 | − | 0.136399i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.39589e7 | + | 1.92591e8i | −0.0399856 | + | 0.226770i | −0.998252 | − | 0.0591085i | \(-0.981174\pi\) |
0.958266 | + | 0.285878i | \(0.0922853\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1.67293e9i | − | 1.95739i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.92950e9 | −2.24338 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.04166e8 | + | 1.83673e7i | 0.120350 | + | 0.0212210i | 0.233499 | − | 0.972357i | \(-0.424982\pi\) |
−0.113149 | + | 0.993578i | \(0.536094\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.58750e8 | + | 3.01027e8i | 0.411891 | + | 0.345617i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.54462e8 | − | 7.87151e8i | −0.518515 | − | 0.898095i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.08601e8 | + | 3.95276e7i | 0.123134 | + | 0.0448172i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.12982e7 | + | 1.40813e8i | −0.0916032 | + | 0.158661i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.66712e9 | + | 2.93959e8i | −1.86676 | + | 0.329160i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.69276e8 | + | 7.97612e8i | 0.744772 | + | 0.887585i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.52946e8 | − | 1.64859e8i | 0.500919 | − | 0.182320i | −0.0791885 | − | 0.996860i | \(-0.525233\pi\) |
0.580107 | + | 0.814540i | \(0.303011\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.38206e8 | − | 6.65563e6i | 0.591530 | − | 0.00731506i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.18042e8 | − | 3.24319e8i | −0.128938 | − | 0.354254i | 0.858379 | − | 0.513016i | \(-0.171472\pi\) |
−0.987317 | + | 0.158762i | \(0.949250\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.40458e8 | + | 1.17858e8i | −0.152478 | + | 0.127945i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.68744e8 | − | 9.56996e8i | −0.182060 | − | 1.03251i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.53353e9 | + | 8.85386e8i | 1.64441 | + | 0.949399i | 0.979240 | + | 0.202705i | \(0.0649734\pi\) |
0.665168 | + | 0.746694i | \(0.268360\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.13092e8 | + | 5.85465e8i | −0.227101 | + | 0.623954i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.40152e9 | − | 8.09167e8i | 1.48454 | − | 0.857099i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.50307e8 | − | 4.17480e8i | 0.368798 | − | 0.439517i | −0.549447 | − | 0.835528i | \(-0.685162\pi\) |
0.918245 | + | 0.396012i | \(0.129606\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.35935e8 | + | 7.70926e8i | −0.142240 | + | 0.806685i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.06490e8i | 0.110753i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.11074e8 | 0.218195 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.63085e8 | − | 8.16544e7i | −0.475817 | − | 0.0838993i | −0.0694034 | − | 0.997589i | \(-0.522110\pi\) |
−0.406413 | + | 0.913689i | \(0.633221\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.26230e9 | − | 1.89830e9i | −2.31048 | − | 1.93872i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.09733e8 | + | 1.90063e8i | 0.111395 | + | 0.192942i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.63595e8 | + | 9.59409e7i | 0.265982 | + | 0.0968096i | 0.471569 | − | 0.881829i | \(-0.343688\pi\) |
−0.205587 | + | 0.978639i | \(0.565910\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.86973e8 | + | 1.01667e9i | −0.588738 | + | 1.01972i |
(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.j.a.33.10 | ✓ | 60 | |
19.15 | odd | 18 | inner | 76.7.j.a.53.10 | yes | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.7.j.a.33.10 | ✓ | 60 | 1.1 | even | 1 | trivial | |
76.7.j.a.53.10 | yes | 60 | 19.15 | odd | 18 | inner |