Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [162,7,Mod(53,162)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(162, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("162.53");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 162 = 2 \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 162.d (of order \(6\), degree \(2\), not 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: | \(37.2687615464\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 18) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 53.1 | ||
Root | \(1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 162.53 |
Dual form | 162.7.d.d.107.1 |
$q$-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 \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).
\(n\) | \(83\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.89898 | + | 2.82843i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 16.0000 | − | 27.7128i | 0.250000 | − | 0.433013i | ||||
\(5\) | 150.644 | + | 86.9741i | 1.20515 | + | 0.695793i | 0.961696 | − | 0.274120i | \(-0.0883864\pi\) |
0.243453 | + | 0.969913i | \(0.421720\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 242.000 | + | 419.156i | 0.705539 | + | 1.22203i | 0.966497 | + | 0.256680i | \(0.0826285\pi\) |
−0.260957 | + | 0.965350i | \(0.584038\pi\) | |||||||
\(8\) | 181.019i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −984.000 | −0.984000 | ||||||||
\(11\) | −1161.06 | + | 670.337i | −0.872320 | + | 0.503634i | −0.868119 | − | 0.496357i | \(-0.834671\pi\) |
−0.00420160 | + | 0.999991i | \(0.501337\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1684.00 | + | 2916.77i | −0.766500 | + | 1.32762i | 0.172950 | + | 0.984931i | \(0.444670\pi\) |
−0.939450 | + | 0.342686i | \(0.888663\pi\) | |||||||
\(14\) | −2371.11 | − | 1368.96i | −0.864106 | − | 0.498892i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −512.000 | − | 886.810i | −0.125000 | − | 0.216506i | ||||
\(17\) | − | 12.7279i | − | 0.00259066i | −0.999999 | − | 0.00129533i | \(-0.999588\pi\) | ||
0.999999 | − | 0.00129533i | \(-0.000412317\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5744.00 | 0.837440 | 0.418720 | − | 0.908115i | \(-0.362479\pi\) | ||||
0.418720 | + | 0.908115i | \(0.362479\pi\) | |||||||
\(20\) | 4820.60 | − | 2783.17i | 0.602574 | − | 0.347897i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3792.00 | − | 6567.94i | 0.356123 | − | 0.616824i | ||||
\(23\) | −2924.69 | − | 1688.57i | −0.240379 | − | 0.138783i | 0.374972 | − | 0.927036i | \(-0.377652\pi\) |
−0.615351 | + | 0.788253i | \(0.710986\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7316.50 | + | 12672.5i | 0.468256 | + | 0.811043i | ||||
\(26\) | − | 19052.3i | − | 1.08399i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 15488.0 | 0.705539 | ||||||||
\(29\) | −25422.0 | + | 14677.4i | −1.04236 | + | 0.601805i | −0.920500 | − | 0.390743i | \(-0.872218\pi\) |
−0.121857 | + | 0.992548i | \(0.538885\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 19898.0 | − | 34464.3i | 0.667920 | − | 1.15687i | −0.310565 | − | 0.950552i | \(-0.600518\pi\) |
0.978485 | − | 0.206319i | \(-0.0661484\pi\) | |||||||
\(32\) | 5016.55 | + | 2896.31i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 36.0000 | + | 62.3538i | 0.000915937 | + | 0.00158645i | ||||
\(35\) | 84191.0i | 1.96364i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 52526.0 | 1.03698 | 0.518489 | − | 0.855085i | \(-0.326495\pi\) | ||||
0.518489 | + | 0.855085i | \(0.326495\pi\) | |||||||
\(38\) | −28139.7 | + | 16246.5i | −0.512825 | + | 0.296080i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −15744.0 | + | 27269.4i | −0.246000 | + | 0.426084i | ||||
\(41\) | −32079.7 | − | 18521.2i | −0.465457 | − | 0.268732i | 0.248879 | − | 0.968535i | \(-0.419938\pi\) |
−0.714336 | + | 0.699803i | \(0.753271\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1900.00 | − | 3290.90i | −0.0238973 | − | 0.0413913i | 0.853829 | − | 0.520553i | \(-0.174274\pi\) |
−0.877727 | + | 0.479162i | \(0.840941\pi\) | |||||||
\(44\) | 42901.6i | 0.503634i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 19104.0 | 0.196269 | ||||||||
\(47\) | −66503.6 | + | 38395.9i | −0.640548 | + | 0.369821i | −0.784826 | − | 0.619717i | \(-0.787248\pi\) |
0.144277 | + | 0.989537i | \(0.453914\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −58303.5 | + | 100985.i | −0.495572 | + | 0.858355i | ||||
\(50\) | −71686.8 | − | 41388.4i | −0.573494 | − | 0.331107i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 53888.0 | + | 93336.8i | 0.383250 | + | 0.663808i | ||||
\(53\) | − | 238738.i | − | 1.60359i | −0.597599 | − | 0.801795i | \(-0.703879\pi\) | ||
0.597599 | − | 0.801795i | \(-0.296121\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −233208. | −1.40170 | ||||||||
\(56\) | −75875.4 | + | 43806.7i | −0.432053 | + | 0.249446i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 83028.0 | − | 143809.i | 0.425540 | − | 0.737057i | ||||
\(59\) | −216368. | − | 124920.i | −1.05351 | − | 0.608243i | −0.129878 | − | 0.991530i | \(-0.541459\pi\) |
−0.923629 | + | 0.383287i | \(0.874792\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6625.00 | − | 11474.8i | −0.0291875 | − | 0.0505542i | 0.851063 | − | 0.525064i | \(-0.175959\pi\) |
−0.880250 | + | 0.474510i | \(0.842625\pi\) | |||||||
\(62\) | 225120.i | 0.944581i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −32768.0 | −0.125000 | ||||||||
\(65\) | −507368. | + | 292929.i | −1.84749 | + | 1.06665i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −84484.0 | + | 146331.i | −0.280899 | + | 0.486531i | −0.971606 | − | 0.236603i | \(-0.923966\pi\) |
0.690707 | + | 0.723134i | \(0.257299\pi\) | |||||||
\(68\) | −352.727 | − | 203.647i | −0.00112179 | − | 0.000647665i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −238128. | − | 412450.i | −0.694251 | − | 1.20248i | ||||
\(71\) | 531467.i | 1.48491i | 0.669894 | + | 0.742457i | \(0.266340\pi\) | ||||
−0.669894 | + | 0.742457i | \(0.733660\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 236144. | 0.607027 | 0.303514 | − | 0.952827i | \(-0.401840\pi\) | ||||
0.303514 | + | 0.952827i | \(0.401840\pi\) | |||||||
\(74\) | −257324. | + | 148566.i | −0.635016 | + | 0.366627i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 91904.0 | − | 159182.i | 0.209360 | − | 0.362622i | ||||
\(77\) | −561952. | − | 324443.i | −1.23091 | − | 0.710668i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 17558.0 | + | 30411.3i | 0.0356118 | + | 0.0616814i | 0.883282 | − | 0.468842i | \(-0.155329\pi\) |
−0.847670 | + | 0.530524i | \(0.821995\pi\) | |||||||
\(80\) | − | 178123.i | − | 0.347897i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 209544. | 0.380044 | ||||||||
\(83\) | 9508.92 | − | 5489.98i | 0.0166302 | − | 0.00960144i | −0.491662 | − | 0.870786i | \(-0.663610\pi\) |
0.508292 | + | 0.861185i | \(0.330277\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1107.00 | − | 1917.38i | 0.00180256 | − | 0.00312213i | ||||
\(86\) | 18616.1 | + | 10748.0i | 0.0292681 | + | 0.0168979i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −121344. | − | 210174.i | −0.178062 | − | 0.308412i | ||||
\(89\) | 129328.i | 0.183453i | 0.995784 | + | 0.0917263i | \(0.0292385\pi\) | ||||
−0.995784 | + | 0.0917263i | \(0.970762\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.63011e6 | −2.16318 | ||||||||
\(92\) | −93590.1 | + | 54034.3i | −0.120189 | + | 0.0693914i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 217200. | − | 376201.i | 0.261503 | − | 0.452936i | ||||
\(95\) | 865297. | + | 499579.i | 1.00924 | + | 0.582685i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 160712. | + | 278361.i | 0.176089 | + | 0.304996i | 0.940538 | − | 0.339689i | \(-0.110322\pi\) |
−0.764448 | + | 0.644685i | \(0.776989\pi\) | |||||||
\(98\) | − | 659629.i | − | 0.700844i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 468256. | 0.468256 | ||||||||
\(101\) | −579181. | + | 334390.i | −0.562147 | + | 0.324556i | −0.754007 | − | 0.656867i | \(-0.771881\pi\) |
0.191860 | + | 0.981422i | \(0.438548\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −996706. | + | 1.72635e6i | −0.912127 | + | 1.57985i | −0.101073 | + | 0.994879i | \(0.532228\pi\) |
−0.811054 | + | 0.584972i | \(0.801106\pi\) | |||||||
\(104\) | −527992. | − | 304837.i | −0.469383 | − | 0.270999i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 675252. | + | 1.16957e6i | 0.566955 | + | 0.981994i | ||||
\(107\) | 260668.i | 0.212783i | 0.994324 | + | 0.106391i | \(0.0339296\pi\) | ||||
−0.994324 | + | 0.106391i | \(0.966070\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 194456. | 0.150156 | 0.0750779 | − | 0.997178i | \(-0.476079\pi\) | ||||
0.0750779 | + | 0.997178i | \(0.476079\pi\) | |||||||
\(110\) | 1.14248e6 | − | 659612.i | 0.858363 | − | 0.495576i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 247808. | − | 429216.i | 0.176385 | − | 0.305508i | ||||
\(113\) | −711784. | − | 410949.i | −0.493302 | − | 0.284808i | 0.232641 | − | 0.972563i | \(-0.425263\pi\) |
−0.725943 | + | 0.687755i | \(0.758596\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −293724. | − | 508745.i | −0.193128 | − | 0.334508i | ||||
\(116\) | 939355.i | 0.601805i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.41331e6 | 0.860185 | ||||||||
\(119\) | 5334.99 | − | 3080.16i | 0.00316587 | − | 0.00182781i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12923.5 | − | 22384.2i | 0.00729498 | − | 0.0126353i | ||||
\(122\) | 64911.5 | + | 37476.7i | 0.0357472 | + | 0.0206387i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −636736. | − | 1.10286e6i | −0.333960 | − | 0.578436i | ||||
\(125\) | − | 172557.i | − | 0.0883490i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.05721e6 | 1.49250 | 0.746250 | − | 0.665666i | \(-0.231852\pi\) | ||||
0.746250 | + | 0.665666i | \(0.231852\pi\) | |||||||
\(128\) | 160530. | − | 92681.9i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.65706e6 | − | 2.87011e6i | 0.754236 | − | 1.30637i | ||||
\(131\) | 2.66206e6 | + | 1.53694e6i | 1.18414 | + | 0.683664i | 0.956969 | − | 0.290191i | \(-0.0937187\pi\) |
0.227172 | + | 0.973855i | \(0.427052\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.39005e6 | + | 2.40763e6i | 0.590847 | + | 1.02338i | ||||
\(134\) | − | 955827.i | − | 0.397251i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2304.00 | 0.000915937 | ||||||||
\(137\) | 3.88336e6 | − | 2.24206e6i | 1.51024 | − | 0.871938i | 0.510312 | − | 0.859990i | \(-0.329530\pi\) |
0.999929 | − | 0.0119482i | \(-0.00380331\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 546164. | − | 945984.i | 0.203366 | − | 0.352241i | −0.746245 | − | 0.665672i | \(-0.768145\pi\) |
0.949611 | + | 0.313431i | \(0.101478\pi\) | |||||||
\(140\) | 2.33317e6 | + | 1.34706e6i | 0.850280 | + | 0.490909i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.50322e6 | − | 2.60365e6i | −0.524996 | − | 0.909321i | ||||
\(143\) | − | 4.51539e6i | − | 1.54414i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.10622e6 | −1.67493 | ||||||||
\(146\) | −1.15686e6 | + | 667916.i | −0.371727 | + | 0.214617i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 840416. | − | 1.45564e6i | 0.259244 | − | 0.449024i | ||||
\(149\) | −1.92333e6 | − | 1.11044e6i | −0.581428 | − | 0.335687i | 0.180273 | − | 0.983617i | \(-0.442302\pi\) |
−0.761701 | + | 0.647929i | \(0.775635\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.03935e6 | + | 3.53226e6i | 0.592327 | + | 1.02594i | 0.993918 | + | 0.110122i | \(0.0351241\pi\) |
−0.401591 | + | 0.915819i | \(0.631543\pi\) | |||||||
\(152\) | 1.03978e6i | 0.296080i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.67066e6 | 1.00504 | ||||||||
\(155\) | 5.99501e6 | − | 3.46122e6i | 1.60989 | − | 0.929468i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.07784e6 | + | 5.33097e6i | −0.795329 | + | 1.37755i | 0.127301 | + | 0.991864i | \(0.459369\pi\) |
−0.922630 | + | 0.385686i | \(0.873965\pi\) | |||||||
\(158\) | −172033. | − | 99323.0i | −0.0436154 | − | 0.0251813i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 503808. | + | 872621.i | 0.123000 | + | 0.213042i | ||||
\(161\) | − | 1.63454e6i | − | 0.391667i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 800696. | 0.184886 | 0.0924432 | − | 0.995718i | \(-0.470532\pi\) | ||||
0.0924432 | + | 0.995718i | \(0.470532\pi\) | |||||||
\(164\) | −1.02655e6 | + | 592680.i | −0.232728 | + | 0.134366i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −31056.0 | + | 53790.6i | −0.00678924 | + | 0.0117593i | ||||
\(167\) | 4.16097e6 | + | 2.40234e6i | 0.893398 | + | 0.515804i | 0.875052 | − | 0.484028i | \(-0.160827\pi\) |
0.0183455 | + | 0.999832i | \(0.494160\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.25831e6 | − | 5.64355e6i | −0.675044 | − | 1.16921i | ||||
\(170\) | 12524.3i | 0.00254921i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −121600. | −0.0238973 | ||||||||
\(173\) | 3.09164e6 | − | 1.78496e6i | 0.597106 | − | 0.344739i | −0.170796 | − | 0.985306i | \(-0.554634\pi\) |
0.767902 | + | 0.640567i | \(0.221301\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.54119e6 | + | 6.13351e6i | −0.660746 | + | 1.14445i | ||||
\(176\) | 1.18892e6 | + | 686425.i | 0.218080 | + | 0.125909i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −365796. | − | 633577.i | −0.0648603 | − | 0.112341i | ||||
\(179\) | 7.43698e6i | 1.29669i | 0.761345 | + | 0.648347i | \(0.224539\pi\) | ||||
−0.761345 | + | 0.648347i | \(0.775461\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.03812e7 | −1.75070 | −0.875350 | − | 0.483491i | \(-0.839369\pi\) | ||||
−0.875350 | + | 0.483491i | \(0.839369\pi\) | |||||||
\(182\) | 7.98589e6 | − | 4.61065e6i | 1.32467 | − | 0.764801i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 305664. | − | 529426.i | 0.0490671 | − | 0.0849868i | ||||
\(185\) | 7.91271e6 | + | 4.56840e6i | 1.24971 | + | 0.721521i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8532.00 | + | 14777.9i | 0.00130475 | + | 0.00225989i | ||||
\(188\) | 2.45734e6i | 0.369821i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.65210e6 | −0.824041 | ||||||||
\(191\) | −1.12532e7 | + | 6.49703e6i | −1.61501 | + | 0.932426i | −0.626825 | + | 0.779160i | \(0.715646\pi\) |
−0.988185 | + | 0.153266i | \(0.951021\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.96598e6 | − | 3.40517e6i | 0.273468 | − | 0.473660i | −0.696279 | − | 0.717771i | \(-0.745163\pi\) |
0.969747 | + | 0.244110i | \(0.0784959\pi\) | |||||||
\(194\) | −1.57465e6 | − | 909124.i | −0.215665 | − | 0.124514i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.86571e6 | + | 3.23151e6i | 0.247786 | + | 0.429178i | ||||
\(197\) | − | 5.37967e6i | − | 0.703651i | −0.936066 | − | 0.351825i | \(-0.885561\pi\) | ||
0.936066 | − | 0.351825i | \(-0.114439\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −565900. | −0.0718093 | −0.0359046 | − | 0.999355i | \(-0.511431\pi\) | ||||
−0.0359046 | + | 0.999355i | \(0.511431\pi\) | |||||||
\(200\) | −2.29398e6 | + | 1.32443e6i | −0.286747 | + | 0.165553i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.89160e6 | − | 3.27634e6i | 0.229496 | − | 0.397498i | ||||
\(203\) | −1.23043e7 | − | 7.10387e6i | −1.47085 | − | 0.849194i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.22174e6 | − | 5.58022e6i | −0.373963 | − | 0.647723i | ||||
\(206\) | − | 1.12764e7i | − | 1.28994i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.44883e6 | 0.383250 | ||||||||
\(209\) | −6.66912e6 | + | 3.85042e6i | −0.730516 | + | 0.421763i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.75825e6 | − | 1.17056e7i | 0.719427 | − | 1.24608i | −0.241799 | − | 0.970326i | \(-0.577738\pi\) |
0.961227 | − | 0.275759i | \(-0.0889291\pi\) | |||||||
\(212\) | −6.61609e6 | − | 3.81980e6i | −0.694375 | − | 0.400897i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −737280. | − | 1.27701e6i | −0.0752300 | − | 0.130302i | ||||
\(215\) | − | 661003.i | − | 0.0665102i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.92613e7 | 1.88497 | ||||||||
\(218\) | −952636. | + | 550005.i | −0.0919512 | + | 0.0530881i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.73133e6 | + | 6.46285e6i | −0.350425 | + | 0.606954i | ||||
\(221\) | 37124.5 | + | 21433.8i | 0.00343941 | + | 0.00198574i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.67742e6 | + | 4.63742e6i | 0.241436 | + | 0.418179i | 0.961123 | − | 0.276119i | \(-0.0890484\pi\) |
−0.719688 | + | 0.694298i | \(0.755715\pi\) | |||||||
\(224\) | 2.80363e6i | 0.249446i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.64935e6 | 0.402779 | ||||||||
\(227\) | 1.17834e7 | − | 6.80317e6i | 1.00738 | − | 0.581612i | 0.0969580 | − | 0.995288i | \(-0.469089\pi\) |
0.910424 | + | 0.413676i | \(0.135755\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.17320e6 | + | 3.76410e6i | −0.180965 | + | 0.313440i | −0.942209 | − | 0.335025i | \(-0.891255\pi\) |
0.761245 | + | 0.648465i | \(0.224589\pi\) | |||||||
\(230\) | 2.87790e6 | + | 1.66155e6i | 0.236533 | + | 0.136562i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.65690e6 | − | 4.60188e6i | −0.212770 | − | 0.368529i | ||||
\(233\) | 2.02333e7i | 1.59956i | 0.600297 | + | 0.799778i | \(0.295049\pi\) | ||||
−0.600297 | + | 0.799778i | \(0.704951\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.33578e7 | −1.02927 | ||||||||
\(236\) | −6.92379e6 | + | 3.99745e6i | −0.526754 | + | 0.304121i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −17424.0 | + | 30179.3i | −0.00129246 | + | 0.00223861i | ||||
\(239\) | −1.76623e7 | − | 1.01973e7i | −1.29376 | − | 0.746953i | −0.314442 | − | 0.949277i | \(-0.601817\pi\) |
−0.979319 | + | 0.202324i | \(0.935151\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.56046e6 | + | 2.70280e6i | 0.111481 | + | 0.193092i | 0.916368 | − | 0.400337i | \(-0.131107\pi\) |
−0.804886 | + | 0.593429i | \(0.797774\pi\) | |||||||
\(242\) | 146213.i | 0.0103167i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −424000. | −0.0291875 | ||||||||
\(245\) | −1.75661e7 | + | 1.01418e7i | −1.19448 | + | 0.689631i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.67290e6 | + | 1.67539e7i | −0.641897 | + | 1.11180i | ||||
\(248\) | 6.23871e6 | + | 3.60192e6i | 0.409016 | + | 0.236145i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 488064. | + | 845352.i | 0.0312361 | + | 0.0541025i | ||||
\(251\) | − | 5.09519e6i | − | 0.322210i | −0.986937 | − | 0.161105i | \(-0.948494\pi\) | ||
0.986937 | − | 0.161105i | \(-0.0515058\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.52765e6 | 0.279583 | ||||||||
\(254\) | −1.49772e7 | + | 8.64710e6i | −0.913966 | + | 0.527678i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −524288. | + | 908093.i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 1.25031e7 | + | 7.21869e6i | 0.736580 | + | 0.425264i | 0.820824 | − | 0.571181i | \(-0.193514\pi\) |
−0.0842448 | + | 0.996445i | \(0.526848\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.27113e7 | + | 2.20166e7i | 0.731628 | + | 1.26722i | ||||
\(260\) | 1.87474e7i | 1.06665i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.73885e7 | −0.966847 | ||||||||
\(263\) | −2.70691e7 | + | 1.56283e7i | −1.48801 | + | 0.859104i | −0.999906 | − | 0.0136808i | \(-0.995645\pi\) |
−0.488105 | + | 0.872785i | \(0.662312\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.07640e7 | − | 3.59643e7i | 1.11577 | − | 1.93256i | ||||
\(266\) | −1.36196e7 | − | 7.86330e6i | −0.723637 | − | 0.417792i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.70349e6 | + | 4.68258e6i | 0.140449 | + | 0.243266i | ||||
\(269\) | − | 251338.i | − | 0.0129122i | −0.999979 | − | 0.00645612i | \(-0.997945\pi\) | ||
0.999979 | − | 0.00645612i | \(-0.00205506\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.96399e7 | 1.48925 | 0.744627 | − | 0.667481i | \(-0.232627\pi\) | ||||
0.744627 | + | 0.667481i | \(0.232627\pi\) | |||||||
\(272\) | −11287.2 | + | 6516.70i | −0.000560895 | + | 0.000323833i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.26830e7 | + | 2.19676e7i | −0.616553 | + | 1.06790i | ||||
\(275\) | −1.69898e7 | − | 9.80904e6i | −0.816938 | − | 0.471660i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.61064e6 | − | 1.14500e7i | −0.311031 | − | 0.538722i | 0.667555 | − | 0.744561i | \(-0.267341\pi\) |
−0.978586 | + | 0.205839i | \(0.934008\pi\) | |||||||
\(278\) | 6.17914e6i | 0.287603i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.52402e7 | −0.694251 | ||||||||
\(281\) | 5.30320e6 | − | 3.06180e6i | 0.239011 | − | 0.137993i | −0.375711 | − | 0.926737i | \(-0.622601\pi\) |
0.614722 | + | 0.788744i | \(0.289268\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.37162e6 | − | 5.83982e6i | 0.148758 | − | 0.257656i | −0.782011 | − | 0.623265i | \(-0.785806\pi\) |
0.930769 | + | 0.365609i | \(0.119139\pi\) | |||||||
\(284\) | 1.47284e7 | + | 8.50347e6i | 0.642987 | + | 0.371229i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.27715e7 | + | 2.21208e7i | 0.545937 | + | 0.945590i | ||||
\(287\) | − | 1.79286e7i | − | 0.758403i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.41374e7 | 0.999993 | ||||||||
\(290\) | 2.50153e7 | − | 1.44426e7i | 1.02568 | − | 0.592176i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.77830e6 | − | 6.54421e6i | 0.151757 | − | 0.262851i | ||||
\(293\) | −8.68096e6 | − | 5.01195e6i | −0.345116 | − | 0.199253i | 0.317416 | − | 0.948286i | \(-0.397185\pi\) |
−0.662532 | + | 0.749034i | \(0.730518\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.17297e7 | − | 3.76369e7i | −0.846422 | − | 1.46605i | ||||
\(296\) | 9.50822e6i | 0.366627i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.25632e7 | 0.474734 | ||||||||
\(299\) | 9.85036e6 | − | 5.68711e6i | 0.368501 | − | 0.212754i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 919600. | − | 1.59279e6i | 0.0337209 | − | 0.0584064i | ||||
\(302\) | −1.99815e7 | − | 1.15363e7i | −0.725450 | − | 0.418839i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.94093e6 | − | 5.09384e6i | −0.104680 | − | 0.181311i | ||||
\(305\) | − | 2.30481e6i | − | 0.0812337i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.23060e6 | −0.180774 | −0.0903871 | − | 0.995907i | \(-0.528810\pi\) | ||||
−0.0903871 | + | 0.995907i | \(0.528810\pi\) | |||||||
\(308\) | −1.79825e7 | + | 1.03822e7i | −0.615456 | + | 0.355334i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.95796e7 | + | 3.39129e7i | −0.657233 | + | 1.13836i | ||||
\(311\) | 2.70392e7 | + | 1.56111e7i | 0.898901 | + | 0.518981i | 0.876844 | − | 0.480776i | \(-0.159645\pi\) |
0.0220578 | + | 0.999757i | \(0.492978\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.12389e7 | − | 1.94664e7i | −0.366515 | − | 0.634822i | 0.622503 | − | 0.782617i | \(-0.286116\pi\) |
−0.989018 | + | 0.147795i | \(0.952782\pi\) | |||||||
\(314\) | − | 3.48218e7i | − | 1.12477i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.12371e6 | 0.0356118 | ||||||||
\(317\) | 2.39206e7 | − | 1.38106e7i | 0.750921 | − | 0.433544i | −0.0751058 | − | 0.997176i | \(-0.523929\pi\) |
0.826026 | + | 0.563631i | \(0.190596\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.96776e7 | − | 3.40827e7i | 0.606179 | − | 1.04993i | ||||
\(320\) | −4.93629e6 | − | 2.84997e6i | −0.150644 | − | 0.0869741i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.62317e6 | + | 8.00756e6i | 0.138475 | + | 0.239846i | ||||
\(323\) | − | 73109.2i | − | 0.00216952i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.92839e7 | −1.43567 | ||||||||
\(326\) | −3.92259e6 | + | 2.26471e6i | −0.113219 | + | 0.0653672i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.35270e6 | − | 5.80705e6i | 0.0950110 | − | 0.164564i | ||||
\(329\) | −3.21878e7 | − | 1.85836e7i | −0.903864 | − | 0.521846i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.88069e6 | + | 4.98950e6i | 0.0794352 | + | 0.137586i | 0.903006 | − | 0.429627i | \(-0.141355\pi\) |
−0.823571 | + | 0.567213i | \(0.808022\pi\) | |||||||
\(332\) | − | 351359.i | − | 0.00960144i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.71793e7 | −0.729456 | ||||||||
\(335\) | −2.54540e7 | + | 1.46958e7i | −0.677050 | + | 0.390895i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.00526e7 | − | 3.47321e7i | 0.523939 | − | 0.907489i | −0.475673 | − | 0.879622i | \(-0.657795\pi\) |
0.999612 | − | 0.0278665i | \(-0.00887132\pi\) | |||||||
\(338\) | 3.19248e7 | + | 1.84318e7i | 0.826756 | + | 0.477328i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −35424.0 | − | 61356.2i | −0.000901282 | − | 0.00156107i | ||||
\(341\) | 5.33535e7i | 1.34555i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 504328. | 0.0124977 | ||||||||
\(344\) | 595716. | − | 343937.i | 0.0146340 | − | 0.00844896i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.00973e7 | + | 1.74890e7i | −0.243767 | + | 0.422217i | ||||
\(347\) | 5.87275e7 | + | 3.39064e7i | 1.40557 | + | 0.811508i | 0.994957 | − | 0.100301i | \(-0.0319804\pi\) |
0.410616 | + | 0.911808i | \(0.365314\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.10319e7 | + | 3.64284e7i | 0.494769 | + | 0.856965i | 0.999982 | − | 0.00602956i | \(-0.00191928\pi\) |
−0.505213 | + | 0.862995i | \(0.668586\pi\) | |||||||
\(350\) | − | 4.00639e7i | − | 0.934436i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7.76602e6 | −0.178062 | ||||||||
\(353\) | 1.52399e7 | − | 8.79878e6i | 0.346465 | − | 0.200032i | −0.316662 | − | 0.948538i | \(-0.602562\pi\) |
0.663127 | + | 0.748507i | \(0.269229\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.62239e7 | + | 8.00621e7i | −1.03319 | + | 1.78954i | ||||
\(356\) | 3.58405e6 | + | 2.06925e6i | 0.0794373 | + | 0.0458632i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.10349e7 | − | 3.64336e7i | −0.458450 | − | 0.794059i | ||||
\(359\) | 1.39920e7i | 0.302410i | 0.988502 | + | 0.151205i | \(0.0483154\pi\) | ||||
−0.988502 | + | 0.151205i | \(0.951685\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.40523e7 | −0.298694 | ||||||||
\(362\) | 5.08572e7 | − | 2.93624e7i | 1.07208 | − | 0.618966i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.60818e7 | + | 4.51750e7i | −0.540796 | + | 0.936686i | ||||
\(365\) | 3.55736e7 | + | 2.05384e7i | 0.731559 | + | 0.422365i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.32927e7 | + | 2.30237e7i | 0.268916 | + | 0.465776i | 0.968582 | − | 0.248694i | \(-0.0800013\pi\) |
−0.699666 | + | 0.714470i | \(0.746668\pi\) | |||||||
\(368\) | 3.45819e6i | 0.0693914i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.16856e7 | −1.02039 | ||||||||
\(371\) | 1.00068e8 | − | 5.77745e7i | 1.95963 | − | 1.13140i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.94146e6 | + | 1.54871e7i | −0.172299 | + | 0.298430i | −0.939223 | − | 0.343307i | \(-0.888453\pi\) |
0.766924 | + | 0.641737i | \(0.221786\pi\) | |||||||
\(374\) | −83596.2 | − | 48264.3i | −0.00159798 | − | 0.000922595i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.95040e6 | − | 1.20384e7i | −0.130751 | − | 0.226468i | ||||
\(377\) | − | 9.88671e7i | − | 1.84513i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.20978e7 | 1.32435 | 0.662177 | − | 0.749347i | \(-0.269633\pi\) | ||||
0.662177 | + | 0.749347i | \(0.269633\pi\) | |||||||
\(380\) | 2.76895e7 | − | 1.59865e7i | 0.504620 | − | 0.291342i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.67527e7 | − | 6.36576e7i | 0.659325 | − | 1.14198i | ||||
\(383\) | 7.52272e6 | + | 4.34324e6i | 0.133899 | + | 0.0773068i | 0.565453 | − | 0.824780i | \(-0.308701\pi\) |
−0.431554 | + | 0.902087i | \(0.642035\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.64363e7 | − | 9.77506e7i | −0.988955 | − | 1.71292i | ||||
\(386\) | 2.22425e7i | 0.386742i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.02856e7 | 0.176089 | ||||||||
\(389\) | 4.28173e7 | − | 2.47206e7i | 0.727395 | − | 0.419962i | −0.0900736 | − | 0.995935i | \(-0.528710\pi\) |
0.817468 | + | 0.575974i | \(0.195377\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21492.0 | + | 37225.2i | −0.000359539 | + | 0.000622741i | ||||
\(392\) | −1.82802e7 | − | 1.05541e7i | −0.303474 | − | 0.175211i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.52160e7 | + | 2.63549e7i | 0.248778 | + | 0.430896i | ||||
\(395\) | 6.10837e6i | 0.0991137i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.56911e7 | 0.250774 | 0.125387 | − | 0.992108i | \(-0.459983\pi\) | ||||
0.125387 | + | 0.992108i | \(0.459983\pi\) | |||||||
\(398\) | 2.77233e6 | − | 1.60061e6i | 0.0439740 | − | 0.0253884i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.49210e6 | − | 1.29767e7i | 0.117064 | − | 0.202761i | ||||
\(401\) | −4.10941e7 | − | 2.37257e7i | −0.637304 | − | 0.367947i | 0.146272 | − | 0.989244i | \(-0.453273\pi\) |
−0.783575 | + | 0.621297i | \(0.786606\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.70165e7 | + | 1.16076e8i | 1.02392 | + | 1.77348i | ||||
\(404\) | 2.14010e7i | 0.324556i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.03711e7 | 1.20094 | ||||||||
\(407\) | −6.09857e7 | + | 3.52101e7i | −0.904576 | + | 0.522257i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.77558e7 | − | 1.00036e8i | 0.844162 | − | 1.46213i | −0.0421850 | − | 0.999110i | \(-0.513432\pi\) |
0.886347 | − | 0.463022i | \(-0.153235\pi\) | |||||||
\(410\) | 3.15665e7 | + | 1.82249e7i | 0.458009 | + | 0.264432i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.18946e7 | + | 5.52431e7i | 0.456064 | + | 0.789925i | ||||
\(413\) | − | 1.20923e8i | − | 1.71656i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.90994e6 | 0.0267225 | ||||||||
\(416\) | −1.68958e7 | + | 9.75477e6i | −0.234692 | + | 0.135499i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.17812e7 | − | 3.77262e7i | 0.298232 | − | 0.516553i | ||||
\(419\) | 1.27040e8 | + | 7.33466e7i | 1.72702 | + | 0.997098i | 0.901577 | + | 0.432618i | \(0.142410\pi\) |
0.825447 | + | 0.564480i | \(0.190923\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.96194e7 | − | 1.20584e8i | −0.933005 | − | 1.61601i | −0.778153 | − | 0.628075i | \(-0.783843\pi\) |
−0.154852 | − | 0.987938i | \(-0.549490\pi\) | |||||||
\(422\) | 7.64609e7i | 1.01742i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.32161e7 | 0.566955 | ||||||||
\(425\) | 161295. | − | 93123.8i | 0.00210114 | − | 0.00121309i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.20650e6 | − | 5.55382e6i | 0.0411858 | − | 0.0713359i | ||||
\(428\) | 7.22384e6 | + | 4.17069e6i | 0.0921376 | + | 0.0531957i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.86960e6 | + | 3.23824e6i | 0.0235149 | + | 0.0407290i | ||||
\(431\) | 1.00392e8i | 1.25391i | 0.779056 | + | 0.626954i | \(0.215699\pi\) | ||||
−0.779056 | + | 0.626954i | \(0.784301\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.00631e7 | −0.493493 | −0.246747 | − | 0.969080i | \(-0.579362\pi\) | ||||
−0.246747 | + | 0.969080i | \(0.579362\pi\) | |||||||
\(434\) | −9.43605e7 | + | 5.44791e7i | −1.15431 | + | 0.666439i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.11130e6 | − | 5.38892e6i | 0.0375389 | − | 0.0650193i | ||||
\(437\) | −1.67994e7 | − | 9.69915e6i | −0.201303 | − | 0.116222i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.92959e7 | + | 1.20024e8i | 0.819057 | + | 1.41865i | 0.906378 | + | 0.422468i | \(0.138836\pi\) |
−0.0873208 | + | 0.996180i | \(0.527831\pi\) | |||||||
\(440\) | − | 4.22152e7i | − | 0.495576i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −242496. | −0.00280826 | ||||||||
\(443\) | 9.65121e7 | − | 5.57213e7i | 1.11012 | − | 0.640929i | 0.171261 | − | 0.985226i | \(-0.445216\pi\) |
0.938861 | + | 0.344296i | \(0.111883\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.12482e7 | + | 1.94825e7i | −0.127645 | + | 0.221088i | ||||
\(446\) | −2.62332e7 | − | 1.51458e7i | −0.295697 | − | 0.170721i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7.92986e6 | − | 1.37349e7i | −0.0881924 | − | 0.152754i | ||||
\(449\) | 6.11166e7i | 0.675181i | 0.941293 | + | 0.337591i | \(0.109612\pi\) | ||||
−0.941293 | + | 0.337591i | \(0.890388\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.96619e7 | 0.541370 | ||||||||
\(452\) | −2.27771e7 | + | 1.31504e7i | −0.246651 | + | 0.142404i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.84845e7 | + | 6.66572e7i | −0.411262 | + | 0.712327i | ||||
\(455\) | −2.45566e8 | − | 1.41778e8i | −2.60696 | − | 1.50513i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.78332e7 | − | 3.08881e7i | −0.186845 | − | 0.323625i | 0.757352 | − | 0.653007i | \(-0.226493\pi\) |
−0.944197 | + | 0.329382i | \(0.893160\pi\) | |||||||
\(458\) | − | 2.45870e7i | − | 0.255923i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.87983e7 | −0.193128 | ||||||||
\(461\) | −1.31621e8 | + | 7.59914e7i | −1.34345 | + | 0.775642i | −0.987312 | − | 0.158791i | \(-0.949241\pi\) |
−0.356139 | + | 0.934433i | \(0.615907\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.74891e7 | + | 9.95740e7i | −0.579218 | + | 1.00324i | 0.416351 | + | 0.909204i | \(0.363309\pi\) |
−0.995569 | + | 0.0940314i | \(0.970025\pi\) | |||||||
\(464\) | 2.60322e7 | + | 1.50297e7i | 0.260589 | + | 0.150451i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.72284e7 | − | 9.91226e7i | −0.565528 | − | 0.979523i | ||||
\(467\) | − | 8.81705e7i | − | 0.865711i | −0.901463 | − | 0.432855i | \(-0.857506\pi\) | ||
0.901463 | − | 0.432855i | \(-0.142494\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.17805e7 | −0.792741 | ||||||||
\(470\) | 6.54396e7 | − | 3.77816e7i | 0.630300 | − | 0.363904i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.26130e7 | − | 3.91669e7i | 0.215046 | − | 0.372471i | ||||
\(473\) | 4.41202e6 | + | 2.54728e6i | 0.0416921 | + | 0.0240710i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.20260e7 | + | 7.27911e7i | 0.392136 | + | 0.679200i | ||||
\(476\) | − | 197130.i | − | 0.00182781i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.15370e8 | 1.05635 | ||||||||
\(479\) | 7.74563e7 | − | 4.47194e7i | 0.704774 | − | 0.406902i | −0.104349 | − | 0.994541i | \(-0.533276\pi\) |
0.809123 | + | 0.587639i | \(0.199943\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.84538e7 | + | 1.53206e8i | −0.794843 | + | 1.37671i | ||||
\(482\) | −1.52894e7 | − | 8.82732e6i | −0.136536 | − | 0.0788293i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −413552. | − | 716293.i | −0.00364749 | − | 0.00631764i | ||||
\(485\) | 5.59111e7i | 0.490087i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.51688e7 | −0.650805 | −0.325403 | − | 0.945576i | \(-0.605500\pi\) | ||||
−0.325403 | + | 0.945576i | \(0.605500\pi\) | |||||||
\(488\) | 2.07717e6 | − | 1.19925e6i | 0.0178736 | − | 0.0103193i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 5.73706e7 | − | 9.93689e7i | 0.487642 | − | 0.844621i | ||||
\(491\) | 3.90424e7 | + | 2.25411e7i | 0.329831 | + | 0.190428i | 0.655766 | − | 0.754964i | \(-0.272346\pi\) |
−0.325935 | + | 0.945392i | \(0.605679\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 186813. | + | 323570.i | 0.00155907 | + | 0.00270039i | ||||
\(494\) | − | 1.09436e8i | − | 0.907780i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.07511e7 | −0.333960 | ||||||||
\(497\) | −2.22768e8 | + | 1.28615e8i | −1.81461 | + | 1.04767i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.57729e7 | + | 7.92810e7i | −0.368389 | + | 0.638069i | −0.989314 | − | 0.145801i | \(-0.953424\pi\) |
0.620925 | + | 0.783870i | \(0.286757\pi\) | |||||||
\(500\) | −4.78203e6 | − | 2.76091e6i | −0.0382562 | − | 0.0220873i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.44114e7 | + | 2.49612e7i | 0.113919 | + | 0.197313i | ||||
\(503\) | 1.61043e8i | 1.26543i | 0.774386 | + | 0.632713i | \(0.218059\pi\) | ||||
−0.774386 | + | 0.632713i | \(0.781941\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.16333e8 | −0.903295 | ||||||||
\(506\) | −2.21809e7 | + | 1.28061e7i | −0.171209 | + | 0.0988476i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.89154e7 | − | 8.47239e7i | 0.373125 | − | 0.646272i | ||||
\(509\) | 2.07841e7 | + | 1.19997e7i | 0.157608 | + | 0.0909951i | 0.576730 | − | 0.816935i | \(-0.304329\pi\) |
−0.419122 | + | 0.907930i | \(0.637662\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.71468e7 | + | 9.89812e7i | 0.428282 | + | 0.741806i | ||||
\(512\) | − | 5.93164e6i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −8.16702e7 | −0.601415 | ||||||||
\(515\) | −3.00295e8 | + | 1.73375e8i | −2.19850 | + | 1.26930i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.14764e7 | − | 8.91597e7i | 0.372509 | − | 0.645204i | ||||
\(518\) | −1.24545e8 | − | 7.19059e7i | −0.896058 | − | 0.517339i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.30258e7 | − | 9.18434e7i | −0.377118 | − | 0.653187i | ||||
\(521\) | 9.00897e7i | 0.637033i | 0.947917 | + | 0.318517i | \(0.103185\pi\) | ||||
−0.947917 | + | 0.318517i | \(0.896815\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.77691e7 | −0.264016 | −0.132008 | − | 0.991249i | \(-0.542143\pi\) | ||||
−0.132008 | + | 0.991249i | \(0.542143\pi\) | |||||||
\(524\) | 8.51858e7 | − | 4.91820e7i | 0.592070 | − | 0.341832i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.84073e7 | − | 1.53126e8i | 0.607478 | − | 1.05218i | ||||
\(527\) | −438660. | − | 253260.i | −0.00299706 | − | 0.00173035i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.83154e7 | − | 1.18326e8i | −0.461479 | − | 0.799304i | ||||
\(530\) | 2.34918e8i | 1.57793i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.89631e7 | 0.590847 | ||||||||
\(533\) | 1.08045e8 | − | 6.23796e7i | 0.713545 | − | 0.411965i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.26714e7 | + | 3.92679e7i | −0.148053 | + | 0.256435i | ||||
\(536\) | −2.64887e7 | − | 1.52932e7i | −0.172015 | − | 0.0993128i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 710892. | + | 1.23130e6i | 0.00456517 | + | 0.00790710i | ||||
\(539\) | − | 1.56332e8i | − | 0.998347i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.54800e7 | 0.160919 | 0.0804595 | − | 0.996758i | \(-0.474361\pi\) | ||||
0.0804595 | + | 0.996758i | \(0.474361\pi\) | |||||||
\(542\) | −1.45205e8 | + | 8.38343e7i | −0.911978 | + | 0.526531i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 36864.0 | − | 63850.3i | 0.000228984 | − | 0.000396612i | ||||
\(545\) | 2.92936e7 | + | 1.69126e7i | 0.180960 | + | 0.104477i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.02608e8 | − | 1.77722e8i | −0.626930 | − | 1.08587i | −0.988164 | − | 0.153399i | \(-0.950978\pi\) |
0.361234 | − | 0.932475i | \(-0.382355\pi\) | |||||||
\(548\) | − | 1.43492e8i | − | 0.871938i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.10977e8 | 0.667027 | ||||||||
\(551\) | −1.46024e8 | + | 8.43071e7i | −0.872911 | + | 0.503975i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.49807e6 | + | 1.47191e7i | −0.0502510 | + | 0.0870373i | ||||
\(554\) | 6.47707e7 | + | 3.73954e7i | 0.380934 | + | 0.219932i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.74772e7 | − | 3.02715e7i | −0.101683 | − | 0.176120i | ||||
\(557\) | 2.41143e8i | 1.39543i | 0.716375 | + | 0.697715i | \(0.245800\pi\) | ||||
−0.716375 | + | 0.697715i | \(0.754200\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.27984e7 | 0.0732690 | ||||||||
\(560\) | 7.46614e7 | − | 4.31058e7i | 0.425140 | − | 0.245455i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.73202e7 | + | 2.99994e7i | −0.0975760 | + | 0.169007i | ||||
\(563\) | −1.46252e8 | − | 8.44386e7i | −0.819552 | − | 0.473168i | 0.0307102 | − | 0.999528i | \(-0.490223\pi\) |
−0.850262 | + | 0.526360i | \(0.823556\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.14838e7 | − | 1.23814e8i | −0.396335 | − | 0.686472i | ||||
\(566\) | 3.81456e7i | 0.210375i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.62058e7 | −0.524996 | ||||||||
\(569\) | 2.11306e8 | − | 1.21998e8i | 1.14703 | − | 0.662238i | 0.198869 | − | 0.980026i | \(-0.436273\pi\) |
0.948162 | + | 0.317788i | \(0.102940\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.20751e8 | + | 2.09147e8i | −0.648608 | + | 1.12342i | 0.334848 | + | 0.942272i | \(0.391315\pi\) |
−0.983456 | + | 0.181149i | \(0.942018\pi\) | |||||||
\(572\) | −1.25134e8 | − | 7.22463e7i | −0.668633 | − | 0.386036i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.07096e7 | + | 8.78317e7i | 0.268136 | + | 0.464425i | ||||
\(575\) | − | 4.94177e7i | − | 0.259944i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.93979e7 | −0.257147 | −0.128573 | − | 0.991700i | \(-0.541040\pi\) | ||||
−0.128573 | + | 0.991700i | \(0.541040\pi\) | |||||||
\(578\) | −1.18249e8 | + | 6.82709e7i | −0.612368 | + | 0.353551i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −8.16996e7 | + | 1.41508e8i | −0.418732 | + | 0.725264i | ||||
\(581\) | 4.60232e6 | + | 2.65715e6i | 0.0234665 | + | 0.0135484i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.60035e8 | + | 2.77188e8i | 0.807623 | + | 1.39884i | ||||
\(584\) | 4.27466e7i | 0.214617i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.67038e7 | 0.281786 | ||||||||
\(587\) | 1.49001e8 | − | 8.60260e7i | 0.736675 | − | 0.425320i | −0.0841840 | − | 0.996450i | \(-0.526828\pi\) |
0.820859 | + | 0.571131i | \(0.193495\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.14294e8 | − | 1.97963e8i | 0.559343 | − | 0.968810i | ||||
\(590\) | 2.12906e8 | + | 1.22922e8i | 1.03665 | + | 0.598511i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.68933e7 | − | 4.65806e7i | −0.129622 | − | 0.224512i | ||||
\(593\) | − | 2.70643e8i | − | 1.29788i | −0.760841 | − | 0.648938i | \(-0.775213\pi\) | ||
0.760841 | − | 0.648938i | \(-0.224787\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.07158e6 | 0.00508712 | ||||||||
\(596\) | −6.15467e7 | + | 3.55340e7i | −0.290714 | + | 0.167844i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.21711e7 | + | 5.57220e7i | −0.150440 | + | 0.260569i | ||||
\(599\) | −1.50082e8 | − | 8.66497e7i | −0.698308 | − | 0.403169i | 0.108409 | − | 0.994106i | \(-0.465425\pi\) |
−0.806717 | + | 0.590938i | \(0.798758\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.15545e8 | + | 3.73335e8i | 0.992921 | + | 1.71979i | 0.599323 | + | 0.800507i | \(0.295437\pi\) |
0.393598 | + | 0.919282i | \(0.371230\pi\) | |||||||
\(602\) | 1.04041e7i | 0.0476886i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.30519e8 | 0.592327 | ||||||||
\(605\) | 3.89369e6 | − | 2.24802e6i | 0.0175831 | − | 0.0101516i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.34953e6 | + | 1.44618e7i | −0.0373332 | + | 0.0646631i | −0.884088 | − | 0.467320i | \(-0.845220\pi\) |
0.846755 | + | 0.531983i | \(0.178553\pi\) | |||||||
\(608\) | 2.88151e7 | + | 1.66364e7i | 0.128206 | + | 0.0740199i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.51900e6 | + | 1.12912e7i | 0.0287205 | + | 0.0497453i | ||||
\(611\) | − | 2.58635e8i | − | 1.13387i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.92321e8 | −0.834920 | −0.417460 | − | 0.908695i | \(-0.637080\pi\) | ||||
−0.417460 | + | 0.908695i | \(0.637080\pi\) | |||||||
\(614\) | 2.56246e7 | − | 1.47944e7i | 0.110701 | − | 0.0639133i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.87305e7 | − | 1.01724e8i | 0.251259 | − | 0.435193i | ||||
\(617\) | −1.61967e8 | − | 9.35117e7i | −0.689558 | − | 0.398117i | 0.113888 | − | 0.993494i | \(-0.463669\pi\) |
−0.803447 | + | 0.595377i | \(0.797003\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.27437e8 | − | 2.20727e8i | −0.537307 | − | 0.930643i | −0.999048 | − | 0.0436278i | \(-0.986108\pi\) |
0.461741 | − | 0.887015i | \(-0.347225\pi\) | |||||||
\(620\) | − | 2.21518e8i | − | 0.929468i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.76619e8 | −0.733950 | ||||||||
\(623\) | −5.42088e7 | + | 3.12975e7i | −0.224185 | + | 0.129433i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.29328e8 | − | 2.24003e8i | 0.529729 | − | 0.917517i | ||||
\(626\) | 1.10118e8 | + | 6.35769e7i | 0.448887 | + | 0.259165i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.84908e7 | + | 1.70591e8i | 0.397665 | + | 0.688775i | ||||
\(629\) | − | 668547.i | − | 0.00268646i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.23602e7 | 0.367618 | 0.183809 | − | 0.982962i | \(-0.441157\pi\) | ||||
0.183809 | + | 0.982962i | \(0.441157\pi\) | |||||||
\(632\) | −5.50504e6 | + | 3.17834e6i | −0.0218077 | + | 0.0125907i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.81243e7 | + | 1.35315e8i | −0.306562 | + | 0.530981i | ||||
\(635\) | 4.60549e8 | + | 2.65898e8i | 1.79869 | + | 1.03847i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.96366e8 | − | 3.40116e8i | −0.759711 | − | 1.31586i | ||||
\(638\) | 2.22627e8i | 0.857267i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.22437e7 | 0.123000 | ||||||||
\(641\) | 3.67771e8 | − | 2.12333e8i | 1.39638 | − | 0.806200i | 0.402368 | − | 0.915478i | \(-0.368187\pi\) |
0.994011 | + | 0.109278i | \(0.0348537\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.87973e8 | + | 3.25579e8i | −0.707071 | + | 1.22468i | 0.258868 | + | 0.965913i | \(0.416650\pi\) |
−0.965939 | + | 0.258770i | \(0.916683\pi\) | |||||||
\(644\) | −4.52976e7 | − | 2.61526e7i | −0.169597 | − | 0.0979168i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 206784. | + | 358160.i | 0.000767042 | + | 0.00132856i | ||||
\(647\) | − | 2.63747e7i | − | 0.0973813i | −0.998814 | − | 0.0486906i | \(-0.984495\pi\) | ||
0.998814 | − | 0.0486906i | \(-0.0155048\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.34955e8 | 1.22533 | ||||||||
\(650\) | 2.41441e8 | − | 1.39396e8i | 0.879166 | − | 0.507587i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.28111e7 | − | 2.21895e7i | 0.0462216 | − | 0.0800581i | ||||
\(653\) | 2.24090e8 | + | 1.29378e8i | 0.804790 | + | 0.464645i | 0.845143 | − | 0.534540i | \(-0.179515\pi\) |
−0.0403536 | + | 0.999185i | \(0.512848\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.67348e8 | + | 4.63060e8i | 0.951377 | + | 1.64783i | ||||
\(656\) | 3.79315e7i | 0.134366i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.10250e8 | 0.738002 | ||||||||
\(659\) | 1.20676e8 | − | 6.96725e7i | 0.421663 | − | 0.243447i | −0.274126 | − | 0.961694i | \(-0.588388\pi\) |
0.695789 | + | 0.718247i | \(0.255055\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.36272e8 | − | 4.09236e8i | 0.818104 | − | 1.41700i | −0.0889731 | − | 0.996034i | \(-0.528359\pi\) |
0.907077 | − | 0.420964i | \(-0.138308\pi\) | |||||||
\(662\) | −2.82249e7 | − | 1.62957e7i | −0.0972878 | − | 0.0561691i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 993792. | + | 1.72130e6i | 0.00339462 | + | 0.00587966i | ||||
\(665\) | 4.83593e8i | 1.64443i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.91354e7 | 0.334081 | ||||||||
\(668\) | 1.33151e8 | − | 7.68747e7i | 0.446699 | − | 0.257902i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8.31323e7 | − | 1.43989e8i | 0.276405 | − | 0.478747i | ||||
\(671\) | 1.53840e7 | + | 8.88197e6i | 0.0509216 | + | 0.0293996i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.74417e8 | − | 4.75304e8i | −0.900254 | − | 1.55929i | −0.827164 | − | 0.561961i | \(-0.810047\pi\) |
−0.0730906 | − | 0.997325i | \(-0.523286\pi\) | |||||||
\(674\) | 2.26869e8i | 0.740961i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.08532e8 | −0.675044 | ||||||||
\(677\) | 8.72609e7 | − | 5.03801e7i | 0.281225 | − | 0.162365i | −0.352753 | − | 0.935717i | \(-0.614754\pi\) |
0.633978 | + | 0.773351i | \(0.281421\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.77846e7 | + | 1.34727e8i | −0.248476 | + | 0.430373i | ||||
\(680\) | 347083. | + | 200388.i | 0.00110384 | + | 0.000637303i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.50906e8 | − | 2.61378e8i | −0.475724 | − | 0.823977i | ||||
\(683\) | 313056.i | 0.000982562i | 1.00000 | 0.000491281i | \(0.000156380\pi\) | |||||
−1.00000 | 0.000491281i | \(0.999844\pi\) | ||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.80005e8 | 2.42675 | ||||||||
\(686\) | −2.47069e6 | + | 1.42645e6i | −0.00765326 | + | 0.00441861i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.94560e6 | + | 3.36988e6i | −0.00597432 | + | 0.0103478i | ||||
\(689\) | 6.96344e8 | + | 4.02034e8i | 2.12895 | + | 1.22915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.86406e8 | + | 3.22865e8i | 0.564971 | + | 0.978558i | 0.997052 | + | 0.0767236i | \(0.0244459\pi\) |
−0.432082 | + | 0.901834i | \(0.642221\pi\) | |||||||
\(692\) | − | 1.14238e8i | − | 0.344739i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.83607e8 | −1.14765 | ||||||||
\(695\) | 1.64552e8 | − | 9.50043e7i | 0.490173 | − | 0.283002i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −235737. | + | 408308.i | −0.000696193 | + | 0.00120584i | ||||
\(698\) | −2.06070e8 | − | 1.18975e8i | −0.605966 | − | 0.349855i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.13318e8 | + | 1.96272e8i | 0.330373 | + | 0.572223i | ||||
\(701\) | − | 6.21170e8i | − | 1.80325i | −0.432517 | − | 0.901626i | \(-0.642374\pi\) | ||
0.432517 | − | 0.901626i | \(-0.357626\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.01709e8 | 0.868406 | ||||||||
\(704\) | 3.80456e7 | − | 2.19656e7i | 0.109040 | − | 0.0629543i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.97734e7 | + | 8.62101e7i | −0.141444 | + | 0.244988i | ||||
\(707\) | −2.80323e8 | − | 1.61845e8i | −0.793234 | − | 0.457974i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.23255e8 | + | 2.13484e8i | 0.345833 | + | 0.599000i | 0.985505 | − | 0.169648i | \(-0.0542631\pi\) |
−0.639672 | + | 0.768648i | \(0.720930\pi\) | |||||||
\(710\) | − | 5.22964e8i | − | 1.46116i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.34109e7 | −0.0648603 | ||||||||
\(713\) | −1.16391e8 | + | 6.71984e7i | −0.321108 | + | 0.185392i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.92722e8 | − | 6.80215e8i | 1.07440 | − | 1.86092i | ||||
\(716\) | 2.06100e8 | + | 1.18992e8i | 0.561485 | + | 0.324173i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.95754e7 | − | 6.85466e7i | −0.106918 | − | 0.185188i | ||||
\(719\) | 9.60389e7i | 0.258381i | 0.991620 | + | 0.129191i | \(0.0412379\pi\) | ||||
−0.991620 | + | 0.129191i | \(0.958762\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.64811e8 | −2.57417 | ||||||||
\(722\) | 6.88421e7 | − | 3.97460e7i | 0.182912 | − | 0.105604i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.66099e8 | + | 2.87692e8i | −0.437675 | + | 0.758075i | ||||
\(725\) | −3.72001e8 | − | 2.14775e8i | −0.976179 | − | 0.563597i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.95685e8 | − | 3.38937e8i | −0.509278 | − | 0.882096i | −0.999942 | − | 0.0107471i | \(-0.996579\pi\) |
0.490664 | − | 0.871349i | \(-0.336754\pi\) | |||||||
\(728\) | − | 2.95082e8i | − | 0.764801i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.32366e8 | −0.597315 | ||||||||
\(731\) | −41886.3 | + | 24183.1i | −0.000107231 | + | 6.19097e-5i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.74539e7 | + | 3.02311e7i | −0.0443181 | + | 0.0767611i | −0.887334 | − | 0.461128i | \(-0.847445\pi\) |
0.843015 | + | 0.537889i | \(0.180778\pi\) | |||||||
\(734\) | −1.30242e8 | − | 7.51951e7i | −0.329353 | − | 0.190152i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.78125e6 | − | 1.69416e7i | −0.0245336 | − | 0.0424934i | ||||
\(737\) | − | 2.26531e8i | − | 0.565881i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.02999e8 | −0.750773 | −0.375386 | − | 0.926868i | \(-0.622490\pi\) | ||||
−0.375386 | + | 0.926868i | \(0.622490\pi\) | |||||||
\(740\) | 2.53207e8 | − | 1.46189e8i | 0.624856 | − | 0.360761i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.26822e8 | + | 5.66072e8i | −0.800018 | + | 1.38567i | ||||
\(743\) | 2.12720e8 | + | 1.22814e8i | 0.518612 | + | 0.299421i | 0.736367 | − | 0.676583i | \(-0.236540\pi\) |
−0.217754 | + | 0.976004i | \(0.569873\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.93159e8 | − | 3.34560e8i | −0.467138 | − | 0.809107i | ||||
\(746\) | − | 1.01161e8i | − | 0.243667i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 546048. | 0.00130475 | ||||||||
\(749\) | −1.09261e8 | + | 6.30816e7i | −0.260027 | + | 0.150127i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.11635e7 | − | 7.12973e7i | 0.0971835 | − | 0.168327i | −0.813334 | − | 0.581797i | \(-0.802350\pi\) |
0.910518 | + | 0.413470i | \(0.135683\pi\) | |||||||
\(752\) | 6.80997e7 | + | 3.93174e7i | 0.160137 | + | 0.0924552i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.79638e8 | + | 4.84348e8i | 0.652353 | + | 1.12991i | ||||
\(755\) | 7.09484e8i | 1.64855i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.03579e8 | −1.39138 | −0.695691 | − | 0.718341i | \(-0.744902\pi\) | ||||
−0.695691 | + | 0.718341i | \(0.744902\pi\) | |||||||
\(758\) | −3.53205e8 | + | 2.03923e8i | −0.810998 | + | 0.468230i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −9.04335e7 | + | 1.56635e8i | −0.206010 | + | 0.356820i | ||||
\(761\) | −2.01769e8 | − | 1.16491e8i | −0.457825 | − | 0.264325i | 0.253304 | − | 0.967387i | \(-0.418483\pi\) |
−0.711129 | + | 0.703061i | \(0.751816\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.70584e7 | + | 8.15075e7i | 0.105941 | + | 0.183495i | ||||
\(764\) | 4.15810e8i | 0.932426i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.91382e7 | −0.109328 | ||||||||
\(767\) | 7.28729e8 | − | 4.20732e8i | 1.61503 | − | 0.932436i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.07898e8 | + | 7.06500e8i | −0.896958 | + | 1.55358i | −0.0655965 | + | 0.997846i | \(0.520895\pi\) |
−0.831362 | + | 0.555731i | \(0.812438\pi\) | |||||||
\(770\) | 5.52961e8 | + | 3.19252e8i | 1.21122 | + | 0.699297i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.29113e7 | − | 1.08966e8i | −0.136734 | − | 0.236830i | ||||
\(773\) | 3.66587e8i | 0.793667i | 0.917891 | + | 0.396833i | \(0.129891\pi\) | ||||
−0.917891 | + | 0.396833i |