Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,8,Mod(67,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.67");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.e (of order \(3\), 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: | \(45.9205987462\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 181x^{6} - 1656x^{5} - 6927x^{4} - 5022x^{3} - 974106x^{2} + 14431284x + 117021996 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{5}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.3 | ||
Root | \(-6.68281 + 0.882730i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.67 |
Dual form | 147.8.e.l.79.3 |
$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 6.10587 | + | 10.5757i | 0.539688 | + | 0.934767i | 0.998921 | + | 0.0464510i | \(0.0147911\pi\) |
−0.459233 | + | 0.888316i | \(0.651876\pi\) | |||||||
\(3\) | −13.5000 | + | 23.3827i | −0.288675 | + | 0.500000i | ||||
\(4\) | −10.5634 | + | 18.2963i | −0.0825263 | + | 0.142940i | ||||
\(5\) | 142.335 | + | 246.532i | 0.509234 | + | 0.882019i | 0.999943 | + | 0.0106955i | \(0.00340453\pi\) |
−0.490709 | + | 0.871324i | \(0.663262\pi\) | |||||||
\(6\) | −329.717 | −0.623178 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1305.11 | 0.901222 | ||||||||
\(9\) | −364.500 | − | 631.333i | −0.166667 | − | 0.288675i | ||||
\(10\) | −1738.16 | + | 3010.58i | −0.549655 | + | 0.952030i | ||||
\(11\) | 3644.47 | − | 6312.42i | 0.825583 | − | 1.42995i | −0.0758906 | − | 0.997116i | \(-0.524180\pi\) |
0.901473 | − | 0.432835i | \(-0.142487\pi\) | |||||||
\(12\) | −285.211 | − | 494.000i | −0.0476466 | − | 0.0825263i | ||||
\(13\) | 8519.49 | 1.07550 | 0.537752 | − | 0.843103i | \(-0.319274\pi\) | ||||
0.537752 | + | 0.843103i | \(0.319274\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7686.10 | −0.588013 | ||||||||
\(16\) | 9320.94 | + | 16144.3i | 0.568905 | + | 0.985373i | ||||
\(17\) | 16729.1 | − | 28975.6i | 0.825848 | − | 1.43041i | −0.0754212 | − | 0.997152i | \(-0.524030\pi\) |
0.901269 | − | 0.433259i | \(-0.142637\pi\) | |||||||
\(18\) | 4451.18 | − | 7709.67i | 0.179896 | − | 0.311589i | ||||
\(19\) | 4453.19 | + | 7713.15i | 0.148948 | + | 0.257985i | 0.930839 | − | 0.365430i | \(-0.119078\pi\) |
−0.781891 | + | 0.623415i | \(0.785745\pi\) | |||||||
\(20\) | −6014.15 | −0.168101 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 89010.8 | 1.78223 | ||||||||
\(23\) | −27201.7 | − | 47114.8i | −0.466175 | − | 0.807440i | 0.533078 | − | 0.846066i | \(-0.321035\pi\) |
−0.999254 | + | 0.0386264i | \(0.987702\pi\) | |||||||
\(24\) | −17619.0 | + | 30517.0i | −0.260160 | + | 0.450611i | ||||
\(25\) | −1456.13 | + | 2522.08i | −0.0186384 | + | 0.0322827i | ||||
\(26\) | 52018.9 | + | 90099.4i | 0.580436 | + | 1.00535i | ||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −32469.4 | −0.247219 | −0.123609 | − | 0.992331i | \(-0.539447\pi\) | ||||
−0.123609 | + | 0.992331i | \(0.539447\pi\) | |||||||
\(30\) | −46930.4 | − | 81285.8i | −0.317343 | − | 0.549655i | ||||
\(31\) | 84535.7 | − | 146420.i | 0.509652 | − | 0.882744i | −0.490285 | − | 0.871562i | \(-0.663107\pi\) |
0.999937 | − | 0.0111818i | \(-0.00355935\pi\) | |||||||
\(32\) | −30298.0 | + | 52477.6i | −0.163451 | + | 0.283106i | ||||
\(33\) | 98400.8 | + | 170435.i | 0.476650 | + | 0.825583i | ||||
\(34\) | 408582. | 1.78280 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 15401.4 | 0.0550175 | ||||||||
\(37\) | −49616.7 | − | 85938.7i | −0.161036 | − | 0.278922i | 0.774205 | − | 0.632935i | \(-0.218150\pi\) |
−0.935240 | + | 0.354013i | \(0.884817\pi\) | |||||||
\(38\) | −54381.2 | + | 94191.1i | −0.160771 | + | 0.278463i | ||||
\(39\) | −115013. | + | 199209.i | −0.310471 | + | 0.537752i | ||||
\(40\) | 185763. | + | 321751.i | 0.458933 | + | 0.794895i | ||||
\(41\) | 235363. | 0.533328 | 0.266664 | − | 0.963790i | \(-0.414079\pi\) | ||||
0.266664 | + | 0.963790i | \(0.414079\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −289312. | −0.554915 | −0.277457 | − | 0.960738i | \(-0.589492\pi\) | ||||
−0.277457 | + | 0.960738i | \(0.589492\pi\) | |||||||
\(44\) | 76995.8 | + | 133361.i | 0.136265 | + | 0.236017i | ||||
\(45\) | 103762. | − | 179722.i | 0.169745 | − | 0.294006i | ||||
\(46\) | 332181. | − | 575354.i | 0.503179 | − | 0.871531i | ||||
\(47\) | 604526. | + | 1.04707e6i | 0.849322 | + | 1.47107i | 0.881815 | + | 0.471596i | \(0.156322\pi\) |
−0.0324932 | + | 0.999472i | \(0.510345\pi\) | |||||||
\(48\) | −503331. | −0.656915 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −35563.7 | −0.0402357 | ||||||||
\(51\) | 451684. | + | 782340.i | 0.476804 | + | 0.825848i | ||||
\(52\) | −89994.5 | + | 155875.i | −0.0887573 | + | 0.153732i | ||||
\(53\) | 98977.7 | − | 171434.i | 0.0913212 | − | 0.158173i | −0.816746 | − | 0.576997i | \(-0.804224\pi\) |
0.908067 | + | 0.418824i | \(0.137558\pi\) | |||||||
\(54\) | 120182. | + | 208161.i | 0.103863 | + | 0.179896i | ||||
\(55\) | 2.07495e6 | 1.68166 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −240472. | −0.171990 | ||||||||
\(58\) | −198254. | − | 343386.i | −0.133421 | − | 0.231092i | ||||
\(59\) | −1.11205e6 | + | 1.92612e6i | −0.704923 | + | 1.22096i | 0.261797 | + | 0.965123i | \(0.415685\pi\) |
−0.966719 | + | 0.255839i | \(0.917648\pi\) | |||||||
\(60\) | 81191.1 | − | 140627.i | 0.0485265 | − | 0.0840504i | ||||
\(61\) | −530377. | − | 918640.i | −0.299178 | − | 0.518192i | 0.676770 | − | 0.736195i | \(-0.263379\pi\) |
−0.975948 | + | 0.218003i | \(0.930046\pi\) | |||||||
\(62\) | 2.06466e6 | 1.10021 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.64618e6 | 0.784959 | ||||||||
\(65\) | 1.21262e6 | + | 2.10033e6i | 0.547683 | + | 0.948615i | ||||
\(66\) | −1.20165e6 | + | 2.08131e6i | −0.514485 | + | 0.891114i | ||||
\(67\) | −1.87235e6 | + | 3.24300e6i | −0.760544 | + | 1.31730i | 0.182026 | + | 0.983294i | \(0.441734\pi\) |
−0.942570 | + | 0.334007i | \(0.891599\pi\) | |||||||
\(68\) | 353430. | + | 612159.i | 0.136308 | + | 0.236093i | ||||
\(69\) | 1.46889e6 | 0.538293 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.99969e6 | −0.994656 | −0.497328 | − | 0.867563i | \(-0.665685\pi\) | ||||
−0.497328 | + | 0.867563i | \(0.665685\pi\) | |||||||
\(72\) | −475712. | − | 823958.i | −0.150204 | − | 0.260160i | ||||
\(73\) | −3.28942e6 | + | 5.69744e6i | −0.989667 | + | 1.71415i | −0.370658 | + | 0.928769i | \(0.620868\pi\) |
−0.619009 | + | 0.785384i | \(0.712465\pi\) | |||||||
\(74\) | 605907. | − | 1.04946e6i | 0.173818 | − | 0.301062i | ||||
\(75\) | −39315.4 | − | 68096.2i | −0.0107609 | − | 0.0186384i | ||||
\(76\) | −188163. | −0.0491684 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.80902e6 | −0.670230 | ||||||||
\(79\) | −3.54939e6 | − | 6.14773e6i | −0.809952 | − | 1.40288i | −0.912897 | − | 0.408191i | \(-0.866160\pi\) |
0.102945 | − | 0.994687i | \(-0.467174\pi\) | |||||||
\(80\) | −2.65340e6 | + | 4.59582e6i | −0.579412 | + | 1.00357i | ||||
\(81\) | −265720. | + | 460241.i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 1.43709e6 | + | 2.48912e6i | 0.287831 | + | 0.498537i | ||||
\(83\) | −441332. | −0.0847212 | −0.0423606 | − | 0.999102i | \(-0.513488\pi\) | ||||
−0.0423606 | + | 0.999102i | \(0.513488\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.52453e6 | 1.68220 | ||||||||
\(86\) | −1.76650e6 | − | 3.05967e6i | −0.299481 | − | 0.518716i | ||||
\(87\) | 438337. | − | 759222.i | 0.0713659 | − | 0.123609i | ||||
\(88\) | 4.75644e6 | − | 8.23839e6i | 0.744033 | − | 1.28870i | ||||
\(89\) | −5.92826e6 | − | 1.02680e7i | −0.891378 | − | 1.54391i | −0.838224 | − | 0.545326i | \(-0.816406\pi\) |
−0.0531544 | − | 0.998586i | \(-0.516928\pi\) | |||||||
\(90\) | 2.53424e6 | 0.366437 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.14937e6 | 0.153887 | ||||||||
\(93\) | 2.28246e6 | + | 3.95334e6i | 0.294248 | + | 0.509652i | ||||
\(94\) | −7.38231e6 | + | 1.27865e7i | −0.916737 | + | 1.58784i | ||||
\(95\) | −1.26769e6 | + | 2.19571e6i | −0.151698 | + | 0.262749i | ||||
\(96\) | −818045. | − | 1.41690e6i | −0.0943687 | − | 0.163451i | ||||
\(97\) | 4.49189e6 | 0.499722 | 0.249861 | − | 0.968282i | \(-0.419615\pi\) | ||||
0.249861 | + | 0.968282i | \(0.419615\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.31364e6 | −0.550388 | ||||||||
\(100\) | −30763.2 | − | 53283.4i | −0.00307632 | − | 0.00532834i | ||||
\(101\) | −4.69201e6 | + | 8.12680e6i | −0.453142 | + | 0.784865i | −0.998579 | − | 0.0532866i | \(-0.983030\pi\) |
0.545437 | + | 0.838152i | \(0.316364\pi\) | |||||||
\(102\) | −5.51586e6 | + | 9.55374e6i | −0.514650 | + | 0.891401i | ||||
\(103\) | 3.53129e6 | + | 6.11637e6i | 0.318422 | + | 0.551523i | 0.980159 | − | 0.198213i | \(-0.0635138\pi\) |
−0.661737 | + | 0.749736i | \(0.730180\pi\) | |||||||
\(104\) | 1.11189e7 | 0.969268 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.41738e6 | 0.197140 | ||||||||
\(107\) | 1.14582e7 | + | 1.98461e7i | 0.904215 | + | 1.56615i | 0.821968 | + | 0.569534i | \(0.192876\pi\) |
0.0822475 | + | 0.996612i | \(0.473790\pi\) | |||||||
\(108\) | −207919. | + | 360126.i | −0.0158822 | + | 0.0275088i | ||||
\(109\) | 7.79104e6 | − | 1.34945e7i | 0.576239 | − | 0.998076i | −0.419666 | − | 0.907678i | \(-0.637853\pi\) |
0.995906 | − | 0.0903975i | \(-0.0288137\pi\) | |||||||
\(110\) | 1.26694e7 | + | 2.19440e7i | 0.907571 | + | 1.57196i | ||||
\(111\) | 2.67930e6 | 0.185948 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.88887e6 | 0.253542 | 0.126771 | − | 0.991932i | \(-0.459539\pi\) | ||||
0.126771 | + | 0.991932i | \(0.459539\pi\) | |||||||
\(114\) | −1.46829e6 | − | 2.54316e6i | −0.0928209 | − | 0.160771i | ||||
\(115\) | 7.74353e6 | − | 1.34122e7i | 0.474785 | − | 0.822351i | ||||
\(116\) | 342986. | − | 594069.i | 0.0204020 | − | 0.0353374i | ||||
\(117\) | −3.10535e6 | − | 5.37863e6i | −0.179251 | − | 0.310471i | ||||
\(118\) | −2.71601e7 | −1.52175 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.00312e7 | −0.529930 | ||||||||
\(121\) | −1.68208e7 | − | 2.91345e7i | −0.863173 | − | 1.49506i | ||||
\(122\) | 6.47683e6 | − | 1.12182e7i | 0.322926 | − | 0.559324i | ||||
\(123\) | −3.17740e6 | + | 5.50341e6i | −0.153958 | + | 0.266664i | ||||
\(124\) | 1.78596e6 | + | 3.09338e6i | 0.0841194 | + | 0.145699i | ||||
\(125\) | 2.14108e7 | 0.980503 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.64571e7 | 1.14612 | 0.573059 | − | 0.819514i | \(-0.305757\pi\) | ||||
0.573059 | + | 0.819514i | \(0.305757\pi\) | |||||||
\(128\) | 1.39295e7 | + | 2.41266e7i | 0.587084 | + | 1.01686i | ||||
\(129\) | 3.90571e6 | − | 6.76488e6i | 0.160190 | − | 0.277457i | ||||
\(130\) | −1.48083e7 | + | 2.56486e7i | −0.591156 | + | 1.02391i | ||||
\(131\) | −3.15884e6 | − | 5.47127e6i | −0.122766 | − | 0.212637i | 0.798092 | − | 0.602536i | \(-0.205843\pi\) |
−0.920857 | + | 0.389899i | \(0.872510\pi\) | |||||||
\(132\) | −4.15777e6 | −0.157345 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.57292e7 | −1.64183 | ||||||||
\(135\) | 2.80158e6 | + | 4.85249e6i | 0.0980021 | + | 0.169745i | ||||
\(136\) | 2.18332e7 | − | 3.78163e7i | 0.744273 | − | 1.28912i | ||||
\(137\) | 384230. | − | 665506.i | 0.0127664 | − | 0.0221121i | −0.859572 | − | 0.511015i | \(-0.829270\pi\) |
0.872338 | + | 0.488903i | \(0.162603\pi\) | |||||||
\(138\) | 8.96888e6 | + | 1.55346e7i | 0.290510 | + | 0.503179i | ||||
\(139\) | 4.86059e7 | 1.53510 | 0.767551 | − | 0.640988i | \(-0.221475\pi\) | ||||
0.767551 | + | 0.640988i | \(0.221475\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.26444e7 | −0.980712 | ||||||||
\(142\) | −1.83157e7 | − | 3.17238e7i | −0.536804 | − | 0.929771i | ||||
\(143\) | 3.10491e7 | − | 5.37786e7i | 0.887917 | − | 1.53792i | ||||
\(144\) | 6.79497e6 | − | 1.17692e7i | 0.189635 | − | 0.328458i | ||||
\(145\) | −4.62154e6 | − | 8.00474e6i | −0.125892 | − | 0.218052i | ||||
\(146\) | −8.03391e7 | −2.13645 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.09648e6 | 0.0531587 | ||||||||
\(149\) | 6.83443e6 | + | 1.18376e7i | 0.169259 | + | 0.293164i | 0.938159 | − | 0.346204i | \(-0.112529\pi\) |
−0.768901 | + | 0.639368i | \(0.779196\pi\) | |||||||
\(150\) | 480109. | − | 831574.i | 0.0116150 | − | 0.0201178i | ||||
\(151\) | −8.37244e6 | + | 1.45015e7i | −0.197894 | + | 0.342763i | −0.947845 | − | 0.318730i | \(-0.896744\pi\) |
0.749951 | + | 0.661493i | \(0.230077\pi\) | |||||||
\(152\) | 5.81190e6 | + | 1.00665e7i | 0.134235 | + | 0.232502i | ||||
\(153\) | −2.43910e7 | −0.550565 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.81296e7 | 1.03813 | ||||||||
\(156\) | −2.42985e6 | − | 4.20863e6i | −0.0512441 | − | 0.0887573i | ||||
\(157\) | −4.86259e6 | + | 8.42225e6i | −0.100281 | + | 0.173692i | −0.911800 | − | 0.410634i | \(-0.865308\pi\) |
0.811519 | + | 0.584325i | \(0.198641\pi\) | |||||||
\(158\) | 4.33443e7 | − | 7.50745e7i | 0.874243 | − | 1.51423i | ||||
\(159\) | 2.67240e6 | + | 4.62873e6i | 0.0527243 | + | 0.0913212i | ||||
\(160\) | −1.72499e7 | −0.332940 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −6.48982e6 | −0.119931 | ||||||||
\(163\) | −7.42421e6 | − | 1.28591e7i | −0.134275 | − | 0.232570i | 0.791046 | − | 0.611757i | \(-0.209537\pi\) |
−0.925320 | + | 0.379187i | \(0.876204\pi\) | |||||||
\(164\) | −2.48622e6 | + | 4.30626e6i | −0.0440136 | + | 0.0762337i | ||||
\(165\) | −2.80118e7 | + | 4.85179e7i | −0.485453 | + | 0.840829i | ||||
\(166\) | −2.69472e6 | − | 4.66738e6i | −0.0457230 | − | 0.0791945i | ||||
\(167\) | −4.88199e7 | −0.811128 | −0.405564 | − | 0.914067i | \(-0.632925\pi\) | ||||
−0.405564 | + | 0.914067i | \(0.632925\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.83322e6 | 0.156708 | ||||||||
\(170\) | 5.81556e7 | + | 1.00728e8i | 0.907863 | + | 1.57246i | ||||
\(171\) | 3.24638e6 | − | 5.62289e6i | 0.0496492 | − | 0.0859950i | ||||
\(172\) | 3.05611e6 | − | 5.29333e6i | 0.0457951 | − | 0.0793194i | ||||
\(173\) | −5.14904e7 | − | 8.91841e7i | −0.756076 | − | 1.30956i | −0.944838 | − | 0.327539i | \(-0.893781\pi\) |
0.188762 | − | 0.982023i | \(-0.439553\pi\) | |||||||
\(174\) | 1.07057e7 | 0.154061 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.35880e8 | 1.87871 | ||||||||
\(177\) | −3.00253e7 | − | 5.20053e7i | −0.406987 | − | 0.704923i | ||||
\(178\) | 7.23944e7 | − | 1.25391e8i | 0.962132 | − | 1.66646i | ||||
\(179\) | 1.66888e7 | − | 2.89059e7i | 0.217491 | − | 0.376705i | −0.736550 | − | 0.676384i | \(-0.763546\pi\) |
0.954040 | + | 0.299679i | \(0.0968795\pi\) | |||||||
\(180\) | 2.19216e6 | + | 3.79693e6i | 0.0280168 | + | 0.0485265i | ||||
\(181\) | −8.05289e7 | −1.00943 | −0.504716 | − | 0.863286i | \(-0.668403\pi\) | ||||
−0.504716 | + | 0.863286i | \(0.668403\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.86403e7 | 0.345461 | ||||||||
\(184\) | −3.55012e7 | − | 6.14900e7i | −0.420128 | − | 0.727682i | ||||
\(185\) | 1.41244e7 | − | 2.44642e7i | 0.164010 | − | 0.284073i | ||||
\(186\) | −2.78729e7 | + | 4.82772e7i | −0.317604 | + | 0.550107i | ||||
\(187\) | −1.21937e8 | − | 2.11201e8i | −1.36361 | − | 2.36184i | ||||
\(188\) | −2.55433e7 | −0.280365 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.09615e7 | −0.327479 | ||||||||
\(191\) | 1.75869e7 | + | 3.04614e7i | 0.182630 | + | 0.316324i | 0.942775 | − | 0.333429i | \(-0.108206\pi\) |
−0.760145 | + | 0.649753i | \(0.774872\pi\) | |||||||
\(192\) | −2.22234e7 | + | 3.84921e7i | −0.226598 | + | 0.392480i | ||||
\(193\) | 4.18332e7 | − | 7.24573e7i | 0.418862 | − | 0.725490i | −0.576963 | − | 0.816770i | \(-0.695763\pi\) |
0.995825 | + | 0.0912801i | \(0.0290959\pi\) | |||||||
\(194\) | 2.74269e7 | + | 4.75048e7i | 0.269694 | + | 0.467123i | ||||
\(195\) | −6.54817e7 | −0.632410 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.57062e8 | −1.46365 | −0.731826 | − | 0.681491i | \(-0.761332\pi\) | ||||
−0.731826 | + | 0.681491i | \(0.761332\pi\) | |||||||
\(198\) | −3.24444e7 | − | 5.61954e7i | −0.297038 | − | 0.514485i | ||||
\(199\) | −8.15296e7 | + | 1.41213e8i | −0.733381 | + | 1.27025i | 0.222049 | + | 0.975036i | \(0.428725\pi\) |
−0.955430 | + | 0.295218i | \(0.904608\pi\) | |||||||
\(200\) | −1.90040e6 | + | 3.29159e6i | −0.0167973 | + | 0.0290938i | ||||
\(201\) | −5.05534e7 | − | 8.75610e7i | −0.439100 | − | 0.760544i | ||||
\(202\) | −1.14595e8 | −0.978221 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.90852e7 | −0.157395 | ||||||||
\(205\) | 3.35004e7 | + | 5.80244e7i | 0.271589 | + | 0.470405i | ||||
\(206\) | −4.31232e7 | + | 7.46916e7i | −0.343697 | + | 0.595301i | ||||
\(207\) | −1.98301e7 | + | 3.43467e7i | −0.155392 | + | 0.269147i | ||||
\(208\) | 7.94097e7 | + | 1.37542e8i | 0.611860 | + | 1.05977i | ||||
\(209\) | 6.49182e7 | 0.491874 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.27246e8 | −1.66536 | −0.832678 | − | 0.553757i | \(-0.813194\pi\) | ||||
−0.832678 | + | 0.553757i | \(0.813194\pi\) | |||||||
\(212\) | 2.09107e6 | + | 3.62185e6i | 0.0150728 | + | 0.0261069i | ||||
\(213\) | 4.04959e7 | − | 7.01409e7i | 0.287132 | − | 0.497328i | ||||
\(214\) | −1.39924e8 | + | 2.42356e8i | −0.975988 | + | 1.69046i | ||||
\(215\) | −4.11792e7 | − | 7.13245e7i | −0.282582 | − | 0.489446i | ||||
\(216\) | 2.56885e7 | 0.173440 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.90285e8 | 1.24396 | ||||||||
\(219\) | −8.88143e7 | − | 1.53831e8i | −0.571384 | − | 0.989667i | ||||
\(220\) | −2.19184e7 | + | 3.79638e7i | −0.138781 | + | 0.240376i | ||||
\(221\) | 1.42523e8 | − | 2.46857e8i | 0.888203 | − | 1.53841i | ||||
\(222\) | 1.63595e7 | + | 2.83355e7i | 0.100354 | + | 0.173818i | ||||
\(223\) | 1.36641e8 | 0.825113 | 0.412557 | − | 0.910932i | \(-0.364636\pi\) | ||||
0.412557 | + | 0.910932i | \(0.364636\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.12303e6 | 0.0124256 | ||||||||
\(226\) | 2.37450e7 | + | 4.11275e7i | 0.136833 | + | 0.237002i | ||||
\(227\) | −4.05401e7 | + | 7.02176e7i | −0.230035 | + | 0.398433i | −0.957818 | − | 0.287375i | \(-0.907218\pi\) |
0.727783 | + | 0.685808i | \(0.240551\pi\) | |||||||
\(228\) | 2.54020e6 | − | 4.39975e6i | 0.0141937 | − | 0.0245842i | ||||
\(229\) | 8.39945e7 | + | 1.45483e8i | 0.462197 | + | 0.800548i | 0.999070 | − | 0.0431147i | \(-0.0137281\pi\) |
−0.536873 | + | 0.843663i | \(0.680395\pi\) | |||||||
\(230\) | 1.89124e8 | 1.02494 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.23761e7 | −0.222799 | ||||||||
\(233\) | 1.35898e8 | + | 2.35382e8i | 0.703828 | + | 1.21907i | 0.967113 | + | 0.254348i | \(0.0818609\pi\) |
−0.263284 | + | 0.964718i | \(0.584806\pi\) | |||||||
\(234\) | 3.79218e7 | − | 6.56825e7i | 0.193479 | − | 0.335115i | ||||
\(235\) | −1.72091e8 | + | 2.98070e8i | −0.865007 | + | 1.49824i | ||||
\(236\) | −2.34939e7 | − | 4.06927e7i | −0.116349 | − | 0.201523i | ||||
\(237\) | 1.91667e8 | 0.935252 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.22573e8 | 1.52839 | 0.764197 | − | 0.644983i | \(-0.223136\pi\) | ||||
0.764197 | + | 0.644983i | \(0.223136\pi\) | |||||||
\(240\) | −7.16417e7 | − | 1.24087e8i | −0.334523 | − | 0.579412i | ||||
\(241\) | −6.50063e7 | + | 1.12594e8i | −0.299155 | + | 0.518151i | −0.975943 | − | 0.218027i | \(-0.930038\pi\) |
0.676788 | + | 0.736178i | \(0.263371\pi\) | |||||||
\(242\) | 2.05411e8 | − | 3.55783e8i | 0.931689 | − | 1.61373i | ||||
\(243\) | −7.17445e6 | − | 1.24265e7i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 2.24103e7 | 0.0987603 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.76031e7 | −0.332358 | ||||||||
\(247\) | 3.79389e7 | + | 6.57121e7i | 0.160194 | + | 0.277464i | ||||
\(248\) | 1.10328e8 | − | 1.91094e8i | 0.459310 | − | 0.795548i | ||||
\(249\) | 5.95798e6 | − | 1.03195e7i | 0.0244569 | − | 0.0423606i | ||||
\(250\) | 1.30732e8 | + | 2.26434e8i | 0.529166 | + | 0.916542i | ||||
\(251\) | −1.58789e8 | −0.633815 | −0.316907 | − | 0.948456i | \(-0.602644\pi\) | ||||
−0.316907 | + | 0.948456i | \(0.602644\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.96544e8 | −1.53947 | ||||||||
\(254\) | 1.61544e8 | + | 2.79802e8i | 0.618546 | + | 1.07135i | ||||
\(255\) | −1.28581e8 | + | 2.22709e8i | −0.485609 | + | 0.841100i | ||||
\(256\) | −6.47481e7 | + | 1.12147e8i | −0.241205 | + | 0.417780i | ||||
\(257\) | 1.38124e8 | + | 2.39238e8i | 0.507579 | + | 0.879152i | 0.999962 | + | 0.00877328i | \(0.00279266\pi\) |
−0.492383 | + | 0.870379i | \(0.663874\pi\) | |||||||
\(258\) | 9.53910e7 | 0.345811 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −5.12375e7 | −0.180793 | ||||||||
\(261\) | 1.18351e7 | + | 2.04990e7i | 0.0412031 | + | 0.0713659i | ||||
\(262\) | 3.85749e7 | − | 6.68137e7i | 0.132511 | − | 0.229515i | ||||
\(263\) | −2.01190e7 | + | 3.48471e7i | −0.0681963 | + | 0.118119i | −0.898107 | − | 0.439776i | \(-0.855058\pi\) |
0.829911 | + | 0.557896i | \(0.188391\pi\) | |||||||
\(264\) | 1.28424e8 | + | 2.22437e8i | 0.429568 | + | 0.744033i | ||||
\(265\) | 5.63520e7 | 0.186015 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.20126e8 | 1.02928 | ||||||||
\(268\) | −3.95566e7 | − | 6.85140e7i | −0.125530 | − | 0.217424i | ||||
\(269\) | −1.92361e8 | + | 3.33179e8i | −0.602537 | + | 1.04362i | 0.389899 | + | 0.920858i | \(0.372510\pi\) |
−0.992436 | + | 0.122767i | \(0.960823\pi\) | |||||||
\(270\) | −3.42122e7 | + | 5.92573e7i | −0.105781 | + | 0.183218i | ||||
\(271\) | 9.78943e7 | + | 1.69558e8i | 0.298789 | + | 0.517518i | 0.975859 | − | 0.218401i | \(-0.0700839\pi\) |
−0.677070 | + | 0.735919i | \(0.736751\pi\) | |||||||
\(272\) | 6.23722e8 | 1.87932 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.38423e6 | 0.0275595 | ||||||||
\(275\) | 1.06136e7 | + | 1.83833e7i | 0.0307751 | + | 0.0533040i | ||||
\(276\) | −1.55165e7 | + | 2.68753e7i | −0.0444233 | + | 0.0769435i | ||||
\(277\) | 1.62603e8 | − | 2.81637e8i | 0.459674 | − | 0.796178i | −0.539270 | − | 0.842133i | \(-0.681300\pi\) |
0.998944 | + | 0.0459547i | \(0.0146330\pi\) | |||||||
\(278\) | 2.96781e8 | + | 5.14040e8i | 0.828476 | + | 1.43496i | ||||
\(279\) | −1.23253e8 | −0.339768 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.42019e8 | 1.72614 | 0.863069 | − | 0.505086i | \(-0.168539\pi\) | ||||
0.863069 | + | 0.505086i | \(0.168539\pi\) | |||||||
\(282\) | −1.99322e8 | − | 3.45237e8i | −0.529279 | − | 0.916737i | ||||
\(283\) | −1.34726e8 | + | 2.33353e8i | −0.353346 | + | 0.612013i | −0.986833 | − | 0.161740i | \(-0.948289\pi\) |
0.633488 | + | 0.773753i | \(0.281623\pi\) | |||||||
\(284\) | 3.16869e7 | − | 5.48833e7i | 0.0820852 | − | 0.142176i | ||||
\(285\) | −3.42277e7 | − | 5.92841e7i | −0.0875831 | − | 0.151698i | ||||
\(286\) | 7.58327e8 | 1.91679 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4.41744e7 | 0.108968 | ||||||||
\(289\) | −3.54553e8 | − | 6.14104e8i | −0.864050 | − | 1.49658i | ||||
\(290\) | 5.64370e7 | − | 9.77518e7i | 0.135885 | − | 0.235360i | ||||
\(291\) | −6.06405e7 | + | 1.05032e8i | −0.144257 | + | 0.249861i | ||||
\(292\) | −6.94946e7 | − | 1.20368e8i | −0.163347 | − | 0.282925i | ||||
\(293\) | −3.00641e7 | −0.0698252 | −0.0349126 | − | 0.999390i | \(-0.511115\pi\) | ||||
−0.0349126 | + | 0.999390i | \(0.511115\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.33134e8 | −1.43588 | ||||||||
\(296\) | −6.47552e7 | − | 1.12159e8i | −0.145129 | − | 0.251371i | ||||
\(297\) | 7.17342e7 | − | 1.24247e8i | 0.158883 | − | 0.275194i | ||||
\(298\) | −8.34603e7 | + | 1.44558e8i | −0.182694 | + | 0.316435i | ||||
\(299\) | −2.31745e8 | − | 4.01394e8i | −0.501373 | − | 0.868404i | ||||
\(300\) | 1.66121e6 | 0.00355222 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.04484e8 | −0.427204 | ||||||||
\(303\) | −1.26684e8 | − | 2.19424e8i | −0.261622 | − | 0.453142i | ||||
\(304\) | −8.30159e7 | + | 1.43788e8i | −0.169474 | + | 0.293538i | ||||
\(305\) | 1.50983e8 | − | 2.61510e8i | 0.304704 | − | 0.527762i | ||||
\(306\) | −1.48928e8 | − | 2.57951e8i | −0.297134 | − | 0.514650i | ||||
\(307\) | −2.00137e8 | −0.394769 | −0.197385 | − | 0.980326i | \(-0.563245\pi\) | ||||
−0.197385 | + | 0.980326i | \(0.563245\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.90690e8 | −0.367682 | ||||||||
\(310\) | 2.93873e8 | + | 5.09004e8i | 0.560266 | + | 0.970409i | ||||
\(311\) | −2.66212e8 | + | 4.61093e8i | −0.501842 | + | 0.869215i | 0.498156 | + | 0.867087i | \(0.334011\pi\) |
−0.999998 | + | 0.00212799i | \(0.999323\pi\) | |||||||
\(312\) | −1.50105e8 | + | 2.59989e8i | −0.279804 | + | 0.484634i | ||||
\(313\) | −2.62148e8 | − | 4.54053e8i | −0.483215 | − | 0.836953i | 0.516599 | − | 0.856227i | \(-0.327198\pi\) |
−0.999814 | + | 0.0192742i | \(0.993864\pi\) | |||||||
\(314\) | −1.18761e8 | −0.216482 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.49974e8 | 0.267369 | ||||||||
\(317\) | 2.47055e8 | + | 4.27912e8i | 0.435599 | + | 0.754480i | 0.997344 | − | 0.0728306i | \(-0.0232033\pi\) |
−0.561745 | + | 0.827310i | \(0.689870\pi\) | |||||||
\(318\) | −3.26346e7 | + | 5.65248e7i | −0.0569094 | + | 0.0985699i | ||||
\(319\) | −1.18334e8 | + | 2.04960e8i | −0.204099 | + | 0.353510i | ||||
\(320\) | 2.34309e8 | + | 4.05835e8i | 0.399728 | + | 0.692349i | ||||
\(321\) | −6.18741e8 | −1.04410 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.97991e8 | 0.492033 | ||||||||
\(324\) | −5.61381e6 | − | 9.72340e6i | −0.00916959 | − | 0.0158822i | ||||
\(325\) | −1.24054e7 | + | 2.14869e7i | −0.0200457 | + | 0.0347201i | ||||
\(326\) | 9.06626e7 | − | 1.57032e8i | 0.144933 | − | 0.251031i | ||||
\(327\) | 2.10358e8 | + | 3.64351e8i | 0.332692 | + | 0.576239i | ||||
\(328\) | 3.07174e8 | 0.480647 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −6.84146e8 | −1.04797 | ||||||||
\(331\) | 1.22105e8 | + | 2.11491e8i | 0.185069 | + | 0.320549i | 0.943600 | − | 0.331088i | \(-0.107416\pi\) |
−0.758531 | + | 0.651637i | \(0.774082\pi\) | |||||||
\(332\) | 4.66195e6 | − | 8.07473e6i | 0.00699172 | − | 0.0121100i | ||||
\(333\) | −3.61706e7 | + | 6.26493e7i | −0.0536786 | + | 0.0929740i | ||||
\(334\) | −2.98088e8 | − | 5.16304e8i | −0.437756 | − | 0.758215i | ||||
\(335\) | −1.06600e9 | −1.54918 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.19277e9 | 1.69766 | 0.848832 | − | 0.528663i | \(-0.177307\pi\) | ||||
0.848832 | + | 0.528663i | \(0.177307\pi\) | |||||||
\(338\) | 6.00404e7 | + | 1.03993e8i | 0.0845736 | + | 0.146486i | ||||
\(339\) | −5.24998e7 | + | 9.09323e7i | −0.0731911 | + | 0.126771i | ||||
\(340\) | −1.00611e8 | + | 1.74264e8i | −0.138826 | + | 0.240453i | ||||
\(341\) | −6.16176e8 | − | 1.06725e9i | −0.841520 | − | 1.45756i | ||||
\(342\) | 7.92878e7 | 0.107180 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.77583e8 | −0.500102 | ||||||||
\(345\) | 2.09075e8 | + | 3.62129e8i | 0.274117 | + | 0.474785i | ||||
\(346\) | 6.28788e8 | − | 1.08909e9i | 0.816090 | − | 1.41351i | ||||
\(347\) | −3.40650e8 | + | 5.90022e8i | −0.437678 | + | 0.758080i | −0.997510 | − | 0.0705257i | \(-0.977532\pi\) |
0.559832 | + | 0.828606i | \(0.310866\pi\) | |||||||
\(348\) | 9.26062e6 | + | 1.60399e7i | 0.0117791 | + | 0.0204020i | ||||
\(349\) | −1.39362e9 | −1.75491 | −0.877457 | − | 0.479656i | \(-0.840761\pi\) | ||||
−0.877457 | + | 0.479656i | \(0.840761\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.67689e8 | 0.206981 | ||||||||
\(352\) | 2.20840e8 | + | 3.82507e8i | 0.269885 | + | 0.467455i | ||||
\(353\) | −5.71873e8 | + | 9.90512e8i | −0.691971 | + | 1.19853i | 0.279220 | + | 0.960227i | \(0.409924\pi\) |
−0.971191 | + | 0.238302i | \(0.923409\pi\) | |||||||
\(354\) | 3.66661e8 | − | 6.35076e8i | 0.439292 | − | 0.760877i | ||||
\(355\) | −4.26962e8 | − | 7.39520e8i | −0.506512 | − | 0.877305i | ||||
\(356\) | 2.50489e8 | 0.294249 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.07600e8 | 0.469508 | ||||||||
\(359\) | 6.57466e7 | + | 1.13876e8i | 0.0749967 | + | 0.129898i | 0.901085 | − | 0.433643i | \(-0.142772\pi\) |
−0.826088 | + | 0.563541i | \(0.809439\pi\) | |||||||
\(360\) | 1.35421e8 | − | 2.34556e8i | 0.152978 | − | 0.264965i | ||||
\(361\) | 4.07274e8 | − | 7.05419e8i | 0.455629 | − | 0.789173i | ||||
\(362\) | −4.91699e8 | − | 8.51648e8i | −0.544778 | − | 0.943583i | ||||
\(363\) | 9.08324e8 | 0.996707 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.87280e9 | −2.01589 | ||||||||
\(366\) | 1.74874e8 | + | 3.02891e8i | 0.186441 | + | 0.322926i | ||||
\(367\) | −3.41381e8 | + | 5.91289e8i | −0.360502 | + | 0.624408i | −0.988044 | − | 0.154175i | \(-0.950728\pi\) |
0.627541 | + | 0.778583i | \(0.284061\pi\) | |||||||
\(368\) | 5.07092e8 | − | 8.78309e8i | 0.530419 | − | 0.918713i | ||||
\(369\) | −8.57897e7 | − | 1.48592e8i | −0.0888879 | − | 0.153958i | ||||
\(370\) | 3.44967e8 | 0.354056 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −9.64420e7 | −0.0971328 | ||||||||
\(373\) | −8.00258e8 | − | 1.38609e9i | −0.798452 | − | 1.38296i | −0.920624 | − | 0.390451i | \(-0.872319\pi\) |
0.122171 | − | 0.992509i | \(-0.461014\pi\) | |||||||
\(374\) | 1.48907e9 | − | 2.57914e9i | 1.47185 | − | 2.54932i | ||||
\(375\) | −2.89046e8 | + | 5.00643e8i | −0.283047 | + | 0.490251i | ||||
\(376\) | 7.88972e8 | + | 1.36654e9i | 0.765427 | + | 1.32576i | ||||
\(377\) | −2.76623e8 | −0.265885 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.79581e7 | −0.0546861 | −0.0273431 | − | 0.999626i | \(-0.508705\pi\) | ||||
−0.0273431 | + | 0.999626i | \(0.508705\pi\) | |||||||
\(380\) | −2.67822e7 | − | 4.63881e7i | −0.0250382 | − | 0.0433675i | ||||
\(381\) | −3.57171e8 | + | 6.18638e8i | −0.330856 | + | 0.573059i | ||||
\(382\) | −2.14766e8 | + | 3.71986e8i | −0.197126 | + | 0.341433i | ||||
\(383\) | 5.13585e8 | + | 8.89555e8i | 0.467107 | + | 0.809054i | 0.999294 | − | 0.0375735i | \(-0.0119628\pi\) |
−0.532187 | + | 0.846627i | \(0.678629\pi\) | |||||||
\(384\) | −7.52193e8 | −0.677907 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.02171e9 | 0.904219 | ||||||||
\(387\) | 1.05454e8 | + | 1.82652e8i | 0.0924858 | + | 0.160190i | ||||
\(388\) | −4.74495e7 | + | 8.21849e7i | −0.0412402 | + | 0.0714301i | ||||
\(389\) | −7.54383e8 | + | 1.30663e9i | −0.649783 | + | 1.12546i | 0.333392 | + | 0.942788i | \(0.391807\pi\) |
−0.983175 | + | 0.182668i | \(0.941527\pi\) | |||||||
\(390\) | −3.99823e8 | − | 6.92513e8i | −0.341304 | − | 0.591156i | ||||
\(391\) | −1.82024e9 | −1.53996 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.70577e8 | 0.141758 | ||||||||
\(394\) | −9.58998e8 | − | 1.66103e9i | −0.789916 | − | 1.36817i | ||||
\(395\) | 1.01041e9 | − | 1.75008e9i | 0.824910 | − | 1.42879i | ||||
\(396\) | 5.61300e7 | − | 9.72199e7i | 0.0454215 | − | 0.0786724i | ||||
\(397\) | −1.74588e8 | − | 3.02395e8i | −0.140038 | − | 0.242554i | 0.787472 | − | 0.616350i | \(-0.211389\pi\) |
−0.927511 | + | 0.373796i | \(0.878056\pi\) | |||||||
\(398\) | −1.99124e9 | −1.58319 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.42898e7 | −0.0424139 | ||||||||
\(401\) | 3.96179e8 | + | 6.86201e8i | 0.306821 | + | 0.531430i | 0.977665 | − | 0.210168i | \(-0.0674012\pi\) |
−0.670844 | + | 0.741599i | \(0.734068\pi\) | |||||||
\(402\) | 6.17345e8 | − | 1.06927e9i | 0.473954 | − | 0.820913i | ||||
\(403\) | 7.20201e8 | − | 1.24742e9i | 0.548133 | − | 0.949394i | ||||
\(404\) | −9.91269e7 | − | 1.71693e8i | −0.0747923 | − | 0.129544i | ||||
\(405\) | −1.51286e8 | −0.113163 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.23308e8 | −0.531793 | ||||||||
\(408\) | 5.89498e8 | + | 1.02104e9i | 0.429706 | + | 0.744273i | ||||
\(409\) | 7.34109e8 | − | 1.27151e9i | 0.530553 | − | 0.918945i | −0.468811 | − | 0.883298i | \(-0.655317\pi\) |
0.999364 | − | 0.0356470i | \(-0.0113492\pi\) | |||||||
\(410\) | −4.09098e8 | + | 7.08579e8i | −0.293146 | + | 0.507744i | ||||
\(411\) | 1.03742e7 | + | 1.79687e7i | 0.00737070 | + | 0.0127664i | ||||
\(412\) | −1.49209e8 | −0.105113 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −4.84320e8 | −0.335452 | ||||||||
\(415\) | −6.28171e7 | − | 1.08802e8i | −0.0431429 | − | 0.0747257i | ||||
\(416\) | −2.58123e8 | + | 4.47083e8i | −0.175793 | + | 0.304482i | ||||
\(417\) | −6.56180e8 | + | 1.13654e9i | −0.443146 | + | 0.767551i | ||||
\(418\) | 3.96382e8 | + | 6.86554e8i | 0.265459 | + | 0.459788i | ||||
\(419\) | 1.76645e9 | 1.17315 | 0.586573 | − | 0.809897i | \(-0.300477\pi\) | ||||
0.586573 | + | 0.809897i | \(0.300477\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.64598e9 | 1.07507 | 0.537537 | − | 0.843240i | \(-0.319355\pi\) | ||||
0.537537 | + | 0.843240i | \(0.319355\pi\) | |||||||
\(422\) | −1.38753e9 | − | 2.40328e9i | −0.898773 | − | 1.55672i | ||||
\(423\) | 4.40699e8 | − | 7.63313e8i | 0.283107 | − | 0.490356i | ||||
\(424\) | 1.29177e8 | − | 2.23741e8i | 0.0823007 | − | 0.142549i | ||||
\(425\) | 4.87192e7 | + | 8.43841e7i | 0.0307850 | + | 0.0533211i | ||||
\(426\) | 9.89050e8 | 0.619848 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −4.84147e8 | −0.298486 | ||||||||
\(429\) | 8.38325e8 | + | 1.45202e9i | 0.512639 | + | 0.887917i | ||||
\(430\) | 5.02870e8 | − | 8.70997e8i | 0.305012 | − | 0.528296i | ||||
\(431\) | −5.88520e8 | + | 1.01935e9i | −0.354072 | + | 0.613270i | −0.986959 | − | 0.160974i | \(-0.948536\pi\) |
0.632887 | + | 0.774244i | \(0.281870\pi\) | |||||||
\(432\) | 1.83464e8 | + | 3.17769e8i | 0.109486 | + | 0.189635i | ||||
\(433\) | 9.32782e8 | 0.552170 | 0.276085 | − | 0.961133i | \(-0.410963\pi\) | ||||
0.276085 | + | 0.961133i | \(0.410963\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.49563e8 | 0.145368 | ||||||||
\(436\) | 1.64599e8 | + | 2.85094e8i | 0.0951098 | + | 0.164735i | ||||
\(437\) | 2.42269e8 | − | 4.19622e8i | 0.138871 | − | 0.240532i | ||||
\(438\) | 1.08458e9 | − | 1.87854e9i | 0.616739 | − | 1.06822i | ||||
\(439\) | 4.95951e8 | + | 8.59013e8i | 0.279778 | + | 0.484589i | 0.971329 | − | 0.237738i | \(-0.0764059\pi\) |
−0.691552 | + | 0.722327i | \(0.743073\pi\) | |||||||
\(440\) | 2.70803e9 | 1.51555 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.48091e9 | 1.91741 | ||||||||
\(443\) | −8.64720e8 | − | 1.49774e9i | −0.472566 | − | 0.818508i | 0.526941 | − | 0.849902i | \(-0.323339\pi\) |
−0.999507 | + | 0.0313936i | \(0.990005\pi\) | |||||||
\(444\) | −2.83025e7 | + | 4.90213e7i | −0.0153456 | + | 0.0265793i | ||||
\(445\) | 1.68760e9 | − | 2.92301e9i | 0.907840 | − | 1.57243i | ||||
\(446\) | 8.34312e8 | + | 1.44507e9i | 0.445304 | + | 0.771289i | ||||
\(447\) | −3.69059e8 | −0.195443 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.43406e8 | 0.387582 | 0.193791 | − | 0.981043i | \(-0.437922\pi\) | ||||
0.193791 | + | 0.981043i | \(0.437922\pi\) | |||||||
\(450\) | 1.29630e7 | + | 2.24525e7i | 0.00670595 | + | 0.0116150i | ||||
\(451\) | 8.57773e8 | − | 1.48571e9i | 0.440306 | − | 0.762632i | ||||
\(452\) | −4.10796e7 | + | 7.11519e7i | −0.0209238 | + | 0.0362412i | ||||
\(453\) | −2.26056e8 | − | 3.91540e8i | −0.114254 | − | 0.197894i | ||||
\(454\) | −9.90131e8 | −0.496589 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.13843e8 | −0.155001 | ||||||||
\(457\) | 1.73265e9 | + | 3.00103e9i | 0.849187 | + | 1.47084i | 0.881935 | + | 0.471372i | \(0.156241\pi\) |
−0.0327472 | + | 0.999464i | \(0.510426\pi\) | |||||||
\(458\) | −1.02572e9 | + | 1.77660e9i | −0.498884 | + | 0.864092i | ||||
\(459\) | 3.29278e8 | − | 5.70326e8i | 0.158935 | − | 0.275283i | ||||
\(460\) | 1.63596e8 | + | 2.83356e8i | 0.0783644 | + | 0.135731i | ||||
\(461\) | −4.98582e8 | −0.237019 | −0.118510 | − | 0.992953i | \(-0.537812\pi\) | ||||
−0.118510 | + | 0.992953i | \(0.537812\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.00802e9 | −0.471994 | −0.235997 | − | 0.971754i | \(-0.575836\pi\) | ||||
−0.235997 | + | 0.971754i | \(0.575836\pi\) | |||||||
\(464\) | −3.02645e8 | − | 5.24197e8i | −0.140644 | − | 0.243602i | ||||
\(465\) | −6.49750e8 | + | 1.12540e9i | −0.299682 | + | 0.519065i | ||||
\(466\) | −1.65955e9 | + | 2.87442e9i | −0.759695 | + | 1.31583i | ||||
\(467\) | −1.95503e8 | − | 3.38622e8i | −0.0888270 | − | 0.153853i | 0.818189 | − | 0.574950i | \(-0.194979\pi\) |
−0.907016 | + | 0.421097i | \(0.861645\pi\) | |||||||
\(468\) | 1.31212e8 | 0.0591716 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4.20305e9 | −1.86733 | ||||||||
\(471\) | −1.31290e8 | − | 2.27401e8i | −0.0578973 | − | 0.100281i | ||||
\(472\) | −1.45134e9 | + | 2.51380e9i | −0.635292 | + | 1.10036i | ||||
\(473\) | −1.05439e9 | + | 1.82626e9i | −0.458128 | + | 0.793501i | ||||
\(474\) | 1.17030e9 | + | 2.02701e9i | 0.504744 | + | 0.874243i | ||||
\(475\) | −2.59376e7 | −0.0111046 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.44309e8 | −0.0608808 | ||||||||
\(478\) | 1.96959e9 | + | 3.41143e9i | 0.824856 | + | 1.42869i | ||||
\(479\) | −1.36998e9 | + | 2.37288e9i | −0.569562 | + | 0.986510i | 0.427047 | + | 0.904229i | \(0.359554\pi\) |
−0.996609 | + | 0.0822808i | \(0.973780\pi\) | |||||||
\(480\) | 2.32873e8 | − | 4.03348e8i | 0.0961115 | − | 0.166470i | ||||
\(481\) | −4.22709e8 | − | 7.32154e8i | −0.173194 | − | 0.299982i | ||||
\(482\) | −1.58768e9 | −0.645800 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.10737e8 | 0.284938 | ||||||||
\(485\) | 6.39354e8 | + | 1.10739e9i | 0.254475 | + | 0.440764i | ||||
\(486\) | 8.76126e7 | − | 1.51749e8i | 0.0346210 | − | 0.0599653i | ||||
\(487\) | 1.29302e9 | − | 2.23957e9i | 0.507286 | − | 0.878646i | −0.492678 | − | 0.870212i | \(-0.663982\pi\) |
0.999964 | − | 0.00843401i | \(-0.00268466\pi\) | |||||||
\(488\) | −6.92200e8 | − | 1.19893e9i | −0.269626 | − | 0.467006i | ||||
\(489\) | 4.00908e8 | 0.155047 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.60025e9 | −0.991357 | −0.495678 | − | 0.868506i | \(-0.665081\pi\) | ||||
−0.495678 | + | 0.868506i | \(0.665081\pi\) | |||||||
\(492\) | −6.71280e7 | − | 1.16269e8i | −0.0254112 | − | 0.0440136i | ||||
\(493\) | −5.43182e8 | + | 9.40819e8i | −0.204165 | + | 0.353624i | ||||
\(494\) | −4.63300e8 | + | 8.02460e8i | −0.172909 | + | 0.299488i | ||||
\(495\) | −7.56319e8 | − | 1.30998e9i | −0.280276 | − | 0.485453i | ||||
\(496\) | 3.15181e9 | 1.15978 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.45515e8 | 0.0527964 | ||||||||
\(499\) | −1.80658e9 | − | 3.12909e9i | −0.650886 | − | 1.12737i | −0.982908 | − | 0.184096i | \(-0.941064\pi\) |
0.332022 | − | 0.943272i | \(-0.392269\pi\) | |||||||
\(500\) | −2.26171e8 | + | 3.91739e8i | −0.0809172 | + | 0.140153i | ||||
\(501\) | 6.59069e8 | − | 1.14154e9i | 0.234152 | − | 0.405564i | ||||
\(502\) | −9.69546e8 | − | 1.67930e9i | −0.342062 | − | 0.592469i | ||||
\(503\) | −1.19103e9 | −0.417286 | −0.208643 | − | 0.977992i | \(-0.566905\pi\) | ||||
−0.208643 | + | 0.977992i | \(0.566905\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.67135e9 | −0.923021 | ||||||||
\(506\) | −2.42125e9 | − | 4.19373e9i | −0.830831 | − | 1.43904i | ||||
\(507\) | −1.32748e8 | + | 2.29927e8i | −0.0452378 | + | 0.0783542i | ||||
\(508\) | −2.79476e8 | + | 4.84067e8i | −0.0945849 | + | 0.163826i | ||||
\(509\) | 5.34378e8 | + | 9.25570e8i | 0.179612 | + | 0.311098i | 0.941748 | − | 0.336320i | \(-0.109182\pi\) |
−0.762135 | + | 0.647418i | \(0.775849\pi\) | |||||||
\(510\) | −3.14040e9 | −1.04831 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.98458e9 | 0.653466 | ||||||||
\(513\) | 8.76522e7 | + | 1.51818e8i | 0.0286650 | + | 0.0496492i | ||||
\(514\) | −1.68674e9 | + | 2.92151e9i | −0.547868 | + | 0.948936i | ||||
\(515\) | −1.00525e9 | + | 1.74115e9i | −0.324303 | + | 0.561708i | ||||
\(516\) | 8.25148e7 | + | 1.42920e8i | 0.0264398 | + | 0.0457951i | ||||
\(517\) | 8.81271e9 | 2.80474 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.78048e9 | 0.873041 | ||||||||
\(520\) | 1.58261e9 | + | 2.74115e9i | 0.493584 | + | 0.854913i | ||||
\(521\) | −2.15780e8 | + | 3.73742e8i | −0.0668466 | + | 0.115782i | −0.897512 | − | 0.440991i | \(-0.854627\pi\) |
0.830665 | + | 0.556773i | \(0.187960\pi\) | |||||||
\(522\) | −1.44527e8 | + | 2.50328e8i | −0.0444736 | + | 0.0770306i | ||||
\(523\) | −1.53697e9 | − | 2.66211e9i | −0.469796 | − | 0.813711i | 0.529607 | − | 0.848243i | \(-0.322339\pi\) |
−0.999404 | + | 0.0345319i | \(0.989006\pi\) | |||||||
\(524\) | 1.33472e8 | 0.0405257 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.91376e8 | −0.147219 | ||||||||
\(527\) | −2.82840e9 | − | 4.89894e9i | −0.841791 | − | 1.45802i | ||||
\(528\) | −1.83438e9 | + | 3.17723e9i | −0.542338 | + | 0.939356i | ||||
\(529\) | 2.22543e8 | − | 3.85455e8i | 0.0653610 | − | 0.113209i | ||||
\(530\) | 3.44078e8 | + | 5.95961e8i | 0.100390 | + | 0.173881i | ||||
\(531\) | 1.62137e9 | 0.469948 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.00517e9 | 0.573596 | ||||||||
\(534\) | 1.95465e9 | + | 3.38555e9i | 0.555487 | + | 0.962132i | ||||
\(535\) | −3.26180e9 | + | 5.64960e9i | −0.920914 | + | 1.59507i | ||||
\(536\) | −2.44362e9 | + | 4.23247e9i | −0.685419 | + | 1.18718i | ||||
\(537\) | 4.50598e8 | + | 7.80459e8i | 0.125568 | + | 0.217491i | ||||
\(538\) | −4.69812e9 | −1.30073 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.18377e8 | −0.0323510 | ||||||||
\(541\) | −4.76287e8 | − | 8.24953e8i | −0.129324 | − | 0.223995i | 0.794091 | − | 0.607799i | \(-0.207947\pi\) |
−0.923415 | + | 0.383804i | \(0.874614\pi\) | |||||||
\(542\) | −1.19546e9 | + | 2.07060e9i | −0.322506 | + | 0.558596i | ||||
\(543\) | 1.08714e9 | − | 1.88298e9i | 0.291398 | − | 0.504716i | ||||
\(544\) | 1.01371e9 | + | 1.75580e9i | 0.269972 | + | 0.467605i | ||||
\(545\) | 4.43576e9 | 1.17376 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.06010e9 | −1.32192 | −0.660958 | − | 0.750423i | \(-0.729850\pi\) | ||||
−0.660958 | + | 0.750423i | \(0.729850\pi\) | |||||||
\(548\) | 8.11752e6 | + | 1.40600e7i | 0.00210713 | + | 0.00364966i | ||||
\(549\) | −3.86645e8 | + | 6.69688e8i | −0.0997261 | + | 0.172731i | ||||
\(550\) | −1.29611e8 | + | 2.24493e8i | −0.0332179 | + | 0.0575351i | ||||
\(551\) | −1.44592e8 | − | 2.50441e8i | −0.0368226 | − | 0.0637787i | ||||
\(552\) | 1.91707e9 | 0.485122 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.97134e9 | 0.992322 | ||||||||
\(555\) | 3.81359e8 | + | 6.60533e8i | 0.0946910 | + | 0.164010i | ||||
\(556\) | −5.13442e8 | + | 8.89307e8i | −0.126686 | + | 0.219427i | ||||
\(557\) | −7.16651e8 | + | 1.24128e9i | −0.175717 | + | 0.304351i | −0.940409 | − | 0.340045i | \(-0.889558\pi\) |
0.764692 | + | 0.644396i | \(0.222891\pi\) | |||||||
\(558\) | −7.52567e8 | − | 1.30348e9i | −0.183369 | − | 0.317604i | ||||
\(559\) | −2.46479e9 | −0.596813 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.58461e9 | 1.57456 | ||||||||
\(562\) | 3.92008e9 | + | 6.78978e9i | 0.931576 | + | 1.61354i | ||||
\(563\) | −5.13648e8 | + | 8.89664e8i | −0.121307 | + | 0.210110i | −0.920283 | − | 0.391253i | \(-0.872042\pi\) |
0.798976 | + | 0.601363i | \(0.205375\pi\) | |||||||
\(564\) | 3.44834e8 | − | 5.97271e8i | 0.0809345 | − | 0.140183i | ||||
\(565\) | 5.53523e8 | + | 9.58731e8i | 0.129112 | + | 0.223628i | ||||
\(566\) | −3.29049e9 | −0.762786 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.91493e9 | −0.896406 | ||||||||
\(569\) | 2.68919e8 | + | 4.65781e8i | 0.0611967 | + | 0.105996i | 0.895001 | − | 0.446065i | \(-0.147175\pi\) |
−0.833804 | + | 0.552061i | \(0.813842\pi\) | |||||||
\(570\) | 4.17980e8 | − | 7.23962e8i | 0.0945351 | − | 0.163740i | ||||
\(571\) | 8.79021e7 | − | 1.52251e8i | 0.0197594 | − | 0.0342242i | −0.855977 | − | 0.517014i | \(-0.827043\pi\) |
0.875736 | + | 0.482790i | \(0.160377\pi\) | |||||||
\(572\) | 6.55965e8 | + | 1.13617e9i | 0.146553 | + | 0.253837i | ||||
\(573\) | −9.49691e8 | −0.210883 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.58437e8 | 0.0347551 | ||||||||
\(576\) | −6.00032e8 | − | 1.03929e9i | −0.130827 | − | 0.226598i | ||||
\(577\) | 3.94062e9 | − | 6.82535e9i | 0.853983 | − | 1.47914i | −0.0236030 | − | 0.999721i | \(-0.507514\pi\) |
0.877586 | − | 0.479420i | \(-0.159153\pi\) | |||||||
\(578\) | 4.32971e9 | − | 7.49928e9i | 0.932635 | − | 1.61537i | ||||
\(579\) | 1.12950e9 | + | 1.95635e9i | 0.241830 | + | 0.418862i | ||||
\(580\) | 1.95276e8 | 0.0415576 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1.48105e9 | −0.311416 | ||||||||
\(583\) | −7.21443e8 | − | 1.24958e9i | −0.150786 | − | 0.261170i | ||||
\(584\) | −4.29305e9 | + | 7.43578e9i | −0.891910 | + | 1.54483i | ||||
\(585\) | 8.84003e8 | − | 1.53114e9i | 0.182561 | − | 0.316205i | ||||
\(586\) | −1.83568e8 | − | 3.17949e8i | −0.0376838 | − | 0.0652703i | ||||
\(587\) | 7.45016e9 | 1.52031 | 0.760155 | − | 0.649742i | \(-0.225123\pi\) | ||||
0.760155 | + | 0.649742i | \(0.225123\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.50581e9 | 0.303646 | ||||||||
\(590\) | −3.86584e9 | − | 6.69583e9i | −0.774928 | − | 1.34222i | ||||
\(591\) | 2.12033e9 | − | 3.67252e9i | 0.422520 | − | 0.731826i | ||||
\(592\) | 9.24949e8 | − | 1.60206e9i | 0.183228 | − | 0.317360i | ||||
\(593\) | −8.85364e8 | − | 1.53350e9i | −0.174353 | − | 0.301989i | 0.765584 | − | 0.643336i | \(-0.222450\pi\) |
−0.939937 | + | 0.341347i | \(0.889117\pi\) | |||||||
\(594\) | 1.75200e9 | 0.342990 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.88778e8 | −0.0558731 | ||||||||
\(597\) | −2.20130e9 | − | 3.81276e9i | −0.423418 | − | 0.733381i | ||||
\(598\) | 2.83001e9 | − | 4.90172e9i | 0.541170 | − | 0.937335i | ||||
\(599\) | 6.86667e8 | − | 1.18934e9i | 0.130543 | − | 0.226107i | −0.793343 | − | 0.608775i | \(-0.791661\pi\) |
0.923886 | + | 0.382668i | \(0.124995\pi\) | |||||||
\(600\) | −5.13109e7 | − | 8.88730e7i | −0.00969795 | − | 0.0167973i | ||||
\(601\) | 2.69227e9 | 0.505892 | 0.252946 | − | 0.967480i | \(-0.418601\pi\) | ||||
0.252946 | + | 0.967480i | \(0.418601\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.72988e9 | 0.507029 | ||||||||
\(604\) | −1.76882e8 | − | 3.06369e8i | −0.0326629 | − | 0.0565738i | ||||
\(605\) | 4.78839e9 | − | 8.29373e9i | 0.879114 | − | 1.52267i | ||||
\(606\) | 1.54704e9 | − | 2.67955e9i | 0.282388 | − | 0.489111i | ||||
\(607\) | 2.85285e9 | + | 4.94128e9i | 0.517748 | + | 0.896766i | 0.999787 | + | 0.0206167i | \(0.00656297\pi\) |
−0.482039 | + | 0.876150i | \(0.660104\pi\) | |||||||
\(608\) | −5.39691e8 | −0.0973828 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.68752e9 | 0.657779 | ||||||||
\(611\) | 5.15025e9 | + | 8.92049e9i | 0.913448 | + | 1.58214i | ||||
\(612\) | 2.57651e8 | − | 4.46264e8i | 0.0454361 | − | 0.0786977i | ||||
\(613\) | −2.63593e9 | + | 4.56556e9i | −0.462191 | + | 0.800539i | −0.999070 | − | 0.0431209i | \(-0.986270\pi\) |
0.536879 | + | 0.843659i | \(0.319603\pi\) | |||||||
\(614\) | −1.22201e9 | − | 2.11659e9i | −0.213052 | − | 0.369017i | ||||
\(615\) | −1.80902e9 | −0.313603 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.13431e9 | −0.365812 | −0.182906 | − | 0.983130i | \(-0.558550\pi\) | ||||
−0.182906 | + | 0.983130i | \(0.558550\pi\) | |||||||
\(618\) | −1.16433e9 | − | 2.01667e9i | −0.198434 | − | 0.343697i | ||||
\(619\) | 5.55040e8 | − | 9.61357e8i | 0.0940604 | − | 0.162917i | −0.815156 | − | 0.579242i | \(-0.803349\pi\) |
0.909216 | + | 0.416325i | \(0.136682\pi\) | |||||||
\(620\) | −5.08411e8 | + | 8.80593e8i | −0.0856730 | + | 0.148390i | ||||
\(621\) | −5.35412e8 | − | 9.27361e8i | −0.0897155 | − | 0.155392i | ||||
\(622\) | −6.50183e9 | −1.08335 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −4.28812e9 | −0.706515 | ||||||||
\(625\) | 3.16128e9 | + | 5.47549e9i | 0.517944 | + | 0.897105i | ||||
\(626\) | 3.20128e9 | − | 5.54478e9i | 0.521571 | − | 0.903387i | ||||
\(627\) | −8.76395e8 | + | 1.51796e9i | −0.141992 | + | 0.245937i | ||||
\(628\) | −1.02731e8 | − | 1.77935e8i | −0.0165516 | − | 0.0286683i | ||||
\(629\) | −3.32016e9 | −0.531964 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.46562e8 | −0.0707585 | −0.0353793 | − | 0.999374i | \(-0.511264\pi\) | ||||
−0.0353793 | + | 0.999374i | \(0.511264\pi\) | |||||||
\(632\) | −4.63235e9 | − | 8.02346e9i | −0.729947 | − | 1.26430i | ||||
\(633\) | 3.06782e9 | − | 5.31362e9i | 0.480747 | − | 0.832678i | ||||
\(634\) | −3.01698e9 | + | 5.22556e9i | −0.470175 | + | 0.814367i | ||||
\(635\) | 3.76578e9 | + | 6.52252e9i | 0.583642 | + | 1.01090i | ||||
\(636\) | −1.12918e8 | −0.0174046 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.89013e9 | −0.440600 | ||||||||
\(639\) | 1.09339e9 | + | 1.89380e9i | 0.165776 | + | 0.287132i | ||||
\(640\) | −3.96532e9 | + | 6.86813e9i | −0.597927 | + | 1.03564i | ||||
\(641\) | −2.16534e9 | + | 3.75048e9i | −0.324731 | + | 0.562450i | −0.981458 | − | 0.191678i | \(-0.938607\pi\) |
0.656727 | + | 0.754128i | \(0.271940\pi\) | |||||||
\(642\) | −3.77795e9 | − | 6.54360e9i | −0.563487 | − | 0.975988i | ||||
\(643\) | −5.12208e9 | −0.759814 | −0.379907 | − | 0.925025i | \(-0.624044\pi\) | ||||
−0.379907 | + | 0.925025i | \(0.624044\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.22368e9 | 0.326297 | ||||||||
\(646\) | 1.81949e9 | + | 3.15146e9i | 0.265544 | + | 0.459936i | ||||
\(647\) | 5.39045e9 | − | 9.33654e9i | 0.782457 | − | 1.35525i | −0.148050 | − | 0.988980i | \(-0.547300\pi\) |
0.930507 | − | 0.366275i | \(-0.119367\pi\) | |||||||
\(648\) | −3.46794e8 | + | 6.00665e8i | −0.0500679 | + | 0.0867201i | ||||
\(649\) | 8.10566e9 | + | 1.40394e10i | 1.16394 | + | 2.01601i | ||||
\(650\) | −3.02984e8 | −0.0432736 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.13699e8 | 0.0443247 | ||||||||
\(653\) | −5.55180e9 | − | 9.61601e9i | −0.780258 | − | 1.35145i | −0.931792 | − | 0.362994i | \(-0.881755\pi\) |
0.151534 | − | 0.988452i | \(-0.451579\pi\) | |||||||
\(654\) | −2.56884e9 | + | 4.44936e9i | −0.359100 | + | 0.621979i | ||||
\(655\) | 8.99228e8 | − | 1.55751e9i | 0.125033 | − | 0.216564i | ||||
\(656\) | 2.19380e9 | + | 3.79978e9i | 0.303413 | + | 0.525526i | ||||
\(657\) | 4.79597e9 | 0.659778 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.33302e9 | −0.725896 | −0.362948 | − | 0.931809i | \(-0.618230\pi\) | ||||
−0.362948 | + | 0.931809i | \(0.618230\pi\) | |||||||
\(660\) | −5.91798e8 | − | 1.02502e9i | −0.0801253 | − | 0.138781i | ||||
\(661\) | 1.49409e9 | − | 2.58784e9i | 0.201221 | − | 0.348524i | −0.747701 | − | 0.664035i | \(-0.768843\pi\) |
0.948922 | + | 0.315511i | \(0.102176\pi\) | |||||||
\(662\) | −1.49111e9 | + | 2.58268e9i | −0.199759 | + | 0.345993i | ||||
\(663\) | 3.84812e9 | + | 6.66514e9i | 0.512804 | + | 0.888203i | ||||
\(664\) | −5.75986e8 | −0.0763526 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.83412e8 | −0.115879 | ||||||||
\(667\) | 8.83224e8 | + | 1.52979e9i | 0.115247 | + | 0.199614i | ||||
\(668\) | 5.15702e8 | − | 8.93223e8i | 0.0669394 | − | 0.115942i | ||||
\(669\) | −1.84465e9 | + | 3.19503e9i | −0.238190 | + | 0.412557i | ||||
\(670\) | −6.50888e9 | − | 1.12737e10i | −0.836074 | − | 1.44812i | ||||
\(671\) | −7.73178e9 | −0.987986 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.02787e10 | −1.29982 | −0.649910 | − | 0.760011i | \(-0.725194\pi\) | ||||
−0.649910 | + | 0.760011i | \(0.725194\pi\) | |||||||
\(674\) | 7.28289e9 | + | 1.26143e10i | 0.916209 | + | 1.58692i | ||||
\(675\) | −2.86609e7 | + | 4.96422e7i | −0.00358696 | + | 0.00621280i | ||||
\(676\) | −1.03872e8 | + | 1.79911e8i | −0.0129326 | + | 0.0223999i | ||||
\(677\) | −4.78417e9 | − | 8.28642e9i | −0.592578 | − | 1.02638i | −0.993884 | − | 0.110432i | \(-0.964777\pi\) |
0.401305 | − | 0.915944i | \(-0.368557\pi\) | |||||||
\(678\) | −1.28223e9 | −0.158001 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.24306e10 | 1.51604 | ||||||||
\(681\) | −1.09458e9 | − | 1.89587e9i | −0.132811 | − | 0.230035i | ||||
\(682\) | 7.52459e9 | − | 1.30330e10i | 0.908317 | − | 1.57325i | ||||
\(683\) | 1.77947e9 | − | 3.08213e9i | 0.213706 | − | 0.370150i | −0.739165 | − | 0.673524i | \(-0.764780\pi\) |
0.952872 | + | 0.303374i | \(0.0981131\pi\) | |||||||
\(684\) | 6.85853e7 | + | 1.18793e8i | 0.00819473 | + | 0.0141937i | ||||
\(685\) | 2.18758e8 | 0.0260044 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.53570e9 | −0.533699 | ||||||||
\(688\) | −2.69666e9 | − | 4.67075e9i | −0.315694 | − | 0.546798i | ||||
\(689\) | 8.43239e8 | − | 1.46053e9i | 0.0982163 | − | 0.170116i | ||||
\(690\) | −2.55318e9 | + | 4.42223e9i | −0.295875 | + | 0.512471i | ||||
\(691\) | −4.72251e9 | − | 8.17963e9i | −0.544502 | − | 0.943106i | −0.998638 | − | 0.0521731i | \(-0.983385\pi\) |
0.454136 | − | 0.890932i | \(-0.349948\pi\) | |||||||
\(692\) | 2.17565e9 | 0.249584 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.31985e9 | −0.944838 | ||||||||
\(695\) | 6.91833e9 | + | 1.19829e10i | 0.781726 | + | 1.35399i | ||||
\(696\) | 5.72077e8 | − | 9.90867e8i | 0.0643165 | − | 0.111399i | ||||
\(697\) | 3.93740e9 | − | 6.81977e9i | 0.440448 | − | 0.762878i | ||||
\(698\) | −8.50927e9 | − | 1.47385e10i | −0.947106 | − | 1.64043i | ||||
\(699\) | −7.33848e9 | −0.812711 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.11584e9 | 0.122345 | 0.0611726 | − | 0.998127i | \(-0.480516\pi\) | ||||
0.0611726 | + | 0.998127i | \(0.480516\pi\) | |||||||
\(702\) | 1.02389e9 | + | 1.77343e9i | 0.111705 | + | 0.193479i | ||||
\(703\) | 4.41906e8 | − | 7.65403e8i | 0.0479718 | − | 0.0830896i | ||||
\(704\) | 5.99946e9 | − | 1.03914e10i | 0.648049 | − | 1.12245i | ||||
\(705\) | −4.64644e9 | − | 8.04788e9i | −0.499412 | − | 0.865007i | ||||
\(706\) | −1.39671e10 | −1.49379 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.26867e9 | 0.134349 | ||||||||
\(709\) | −3.57825e9 | − | 6.19771e9i | −0.377058 | − | 0.653084i | 0.613574 | − | 0.789637i | \(-0.289731\pi\) |
−0.990633 | + | 0.136553i | \(0.956398\pi\) | |||||||
\(710\) | 5.21395e9 | − | 9.03083e9i | 0.546717 | − | 0.946942i | ||||
\(711\) | −2.58751e9 | + | 4.48169e9i | −0.269984 | + | 0.467626i | ||||
\(712\) | −7.73702e9 | − | 1.34009e10i | −0.803330 | − | 1.39141i | ||||
\(713\) | −9.19807e9 | −0.950350 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.76775e10 | 1.80863 | ||||||||
\(716\) | 3.52580e8 | + | 6.10687e8i | 0.0358974 | + | 0.0621761i | ||||
\(717\) | −4.35473e9 | + | 7.54262e9i | −0.441209 | + | 0.764197i | ||||
\(718\) | −8.02880e8 | + | 1.39063e9i | −0.0809497 | + | 0.140209i | ||||
\(719\) | 5.93490e9 | + | 1.02796e10i | 0.595474 | + | 1.03139i | 0.993480 | + | 0.114008i | \(0.0363689\pi\) |
−0.398006 | + | 0.917383i | \(0.630298\pi\) | |||||||
\(720\) | 3.86865e9 | 0.386274 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 9.94705e9 | 0.983590 | ||||||||
\(723\) | −1.75517e9 | − | 3.04004e9i | −0.172717 | − | 0.299155i | ||||
\(724\) | 8.50656e8 | − | 1.47338e9i | 0.0833046 | − | 0.144288i | ||||
\(725\) | 4.72795e7 | − | 8.18905e7i | 0.00460776 | − | 0.00798087i | ||||
\(726\) | 5.54611e9 | + | 9.60614e9i | 0.537911 | + | 0.931689i | ||||
\(727\) | 1.03634e10 | 1.00031 | 0.500153 | − | 0.865937i | \(-0.333277\pi\) | ||||
0.500153 | + | 0.865937i | \(0.333277\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −1.14351e10 | − | 1.98061e10i | −1.08795 | − | 1.88439i | ||||
\(731\) | −4.83991e9 | + | 8.38297e9i | −0.458275 | + | 0.793756i | ||||
\(732\) | −3.02538e8 | + | 5.24012e8i | −0.0285096 | + | 0.0493802i | ||||
\(733\) | 2.30469e9 | + | 3.99183e9i | 0.216146 | + | 0.374376i | 0.953627 | − | 0.300992i | \(-0.0973179\pi\) |
−0.737480 | + | 0.675369i | \(0.763985\pi\) | |||||||
\(734\) | −8.33771e9 | −0.778235 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.29663e9 | 0.304788 | ||||||||
\(737\) | 1.36474e10 | + | 2.36381e10i | 1.25578 | + | 2.17508i | ||||
\(738\) | 1.04764e9 | − | 1.81457e9i | 0.0959435 | − | 0.166179i | ||||
\(739\) | 4.02461e9 | − | 6.97083e9i | 0.366833 | − | 0.635373i | −0.622236 | − | 0.782830i | \(-0.713775\pi\) |
0.989068 | + | 0.147457i | \(0.0471088\pi\) | |||||||
\(740\) | 2.98403e8 | + | 5.16849e8i | 0.0270702 | + | 0.0468870i | ||||
\(741\) | −2.04870e9 | −0.184976 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.41059e10 | −1.26165 | −0.630827 | − | 0.775924i | \(-0.717284\pi\) | ||||
−0.630827 | + | 0.775924i | \(0.717284\pi\) | |||||||
\(744\) | 2.97886e9 | + | 5.15954e9i | 0.265183 | + | 0.459310i | ||||
\(745\) | −1.94556e9 | + | 3.36981e9i | −0.172384 | + | 0.298578i | ||||
\(746\) | 9.77255e9 | − | 1.69265e10i | 0.861830 | − | 1.49273i | ||||
\(747\) | 1.60865e8 | + | 2.78627e8i | 0.0141202 | + | 0.0244569i | ||||
\(748\) | 5.15227e9 | 0.450135 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −7.05952e9 | −0.611028 | ||||||||
\(751\) | −6.68971e9 | − | 1.15869e10i | −0.576325 | − | 0.998225i | −0.995896 | − | 0.0905020i | \(-0.971153\pi\) |
0.419571 | − | 0.907722i | \(-0.362180\pi\) | |||||||
\(752\) | −1.12695e10 | + | 1.95193e10i | −0.966367 | + | 1.67380i | ||||
\(753\) | 2.14365e9 | − | 3.71291e9i | 0.182967 | − | 0.316907i | ||||
\(754\) | −1.68902e9 | − | 2.92547e9i | −0.143495 | − | 0.248540i | ||||
\(755\) | −4.76677e9 | −0.403097 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.36103e10 | 1.14034 | 0.570169 | − | 0.821528i | \(-0.306878\pi\) | ||||
0.570169 | + | 0.821528i | \(0.306878\pi\) | |||||||
\(758\) | −3.53885e8 | − | 6.12947e8i | −0.0295135 | − | 0.0511188i | ||||
\(759\) | 5.35335e9 | − | 9.27227e9i | 0.444405 | − | 0.769733i | ||||
\(760\) | −1.65448e9 | + | 2.86564e9i | −0.136714 | + | 0.236796i | ||||
\(761\) | −5.18088e9 | − | 8.97356e9i | −0.426145 | − | 0.738105i | 0.570381 | − | 0.821380i | \(-0.306795\pi\) |
−0.996527 | + | 0.0832748i | \(0.973462\pi\) | |||||||
\(762\) | −8.72336e9 | −0.714236 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −7.43106e8 | −0.0602871 | ||||||||
\(765\) | −3.47169e9 | − | 6.01315e9i | −0.280367 | − | 0.485609i | ||||
\(766\) | −6.27177e9 | + | 1.08630e10i | −0.504184 | + | 0.873273i | ||||
\(767\) | −9.47408e9 | + | 1.64096e10i | −0.758147 | + | 1.31315i | ||||
\(768\) | −1.74820e9 | − | 3.02797e9i | −0.139260 | − | 0.241205i | ||||
\(769\) | −1.58529e8 | −0.0125709 | −0.00628543 | − | 0.999980i | \(-0.502001\pi\) | ||||
−0.00628543 | + | 0.999980i | \(0.502001\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.45870e9 | −0.586101 | ||||||||
\(772\) | 8.83799e8 | + | 1.53078e9i | 0.0691342 | + | 0.119744i | ||||
\(773\) | −5.35045e9 | + | 9.26725e9i | −0.416641 | + | 0.721643i | −0.995599 | − | 0.0937140i | \(-0.970126\pi\) |
0.578958 | + | 0.815357i | \(0.303459\pi\) | |||||||
\(774\) | −1.28778e9 | + | 2.23050e9i | −0.0998270 | + | 0.172905i | ||||
\(775\) | 2.46189e8 | + | 4.26412e8i | 0.0189982 | + | 0.0329059i | ||||
\(776\) | 5.86241e9 | 0.450360 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.84247e10 | −1.40272 | ||||||||
\(779\) | 1.04812e9 | + | 1.81539e9i | 0.0794379 | + | 0.137591i | ||||
\(780\) | 6.91707e8 | − | 1.19807e9i | 0.0521904 | − | 0.0903965i | ||||
\(781\) | −1.09323e10 | + | 1.89353e10i | −0.821170 | + | 1.42231i | ||||
\(782\) | −1.11141e10 | − | 1.92503e10i | −0.831098 | − | 1.43950i | ||||
\(783\) | −6.39095e8 | −0.0475772 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.76847e9 | −0.204266 | ||||||||
\(786\) | 1.04152e9 | + | 1.80397e9i | 0.0765050 | + | 0.132511i | ||||
\(787\) | 5.40652e8 | − | 9.36436e8i | 0.0395372 | − | 0.0684804i | −0.845580 | − | 0.533849i | \(-0.820745\pi\) |
0.885117 | + | 0.465369i | \(0.154078\pi\) | |||||||
\(788\) | 1.65910e9 | − | 2.87364e9i | 0.120790 | − | 0.209214i | ||||
\(789\) | −5.43213e8 | − | 9.40872e8i | −0.0393732 | − | 0.0681963i | ||||
\(790\) | 2.46777e10 | 1.78078 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −6.93489e9 | −0.496022 | ||||||||
\(793\) | −4.51854e9 | − | 7.82634e9i | −0.321767 | − | 0.557318i | ||||
\(794\) | 2.13202e9 | − | 3.69277e9i | 0.151154 | − | 0.261807i | ||||
\(795\) | −7.60752e8 | + | 1.31766e9i | −0.0536980 | + | 0.0930077i | ||||
\(796\) | −1.72245e9 | − | 2.98338e9i | −0.121046 | − | 0.209659i | ||||
\(797\) | 1.82163e10 | 1.27454 | 0.637272 | − | 0.770639i | \(-0.280063\pi\) | ||||
0.637272 | + | 0.770639i | \(0.280063\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.04526e10 | 2.80564 | ||||||||
\(800\) | −8.82353e7 | − | 1.52828e8i | −0.00609295 | − | 0.0105533i | ||||
\(801\) | −4.32170e9 | + | 7.48540e9i | −0.297126 | + | 0.514638i | ||||
\(802\) | −4.83803e9 | + | 8.37972e9i | −0.331176 | + | 0.573613i | ||||
\(803\) | 2.39764e10 | + | 4.15283e10i | 1.63410 | + | 2.83035i | ||||
\(804\) | 2.13605e9 | 0.144949 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.75898e10 | 1.18328 | ||||||||
\(807\) | −5.19374e9 | − | 8.99582e9i | −0.347875 | − | 0.602537i | ||||
\(808\) | −6.12359e9 | + | 1.06064e10i | −0.408382 | + | 0.707338i | ||||
\(809\) | 1.24301e10 | − | 2.15296e10i | 0.825383 | − | 1.42960i | −0.0762441 | − | 0.997089i | \(-0.524293\pi\) |
0.901627 | − | 0.432515i | \(-0.142374\pi\) | |||||||
\(810\) | −9.23730e8 | − | 1.59995e9i | −0.0610728 | − | 0.105781i | ||||
\(811\) | −2.15538e10 | −1.41890 | −0.709449 | − | 0.704757i | \(-0.751056\pi\) | ||||
−0.709449 | + | 0.704757i | \(0.751056\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.28629e9 | −0.345012 | ||||||||
\(814\) | −4.41642e9 | − | 7.64947e9i | −0.287002 | − | 0.497103i | ||||
\(815\) | 2.11345e9 | − | 3.66061e9i | 0.136754 | − | 0.236866i | ||||
\(816\) | −8.42025e9 | + | 1.45843e10i | −0.542512 | + | 0.939658i | ||||
\(817\) | −1.28836e9 | − | 2.23151e9i | −0.0826533 | − | 0.143160i | ||||
\(818\) | 1.79295e10 | 1.14533 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.41551e9 | −0.0896528 | ||||||||
\(821\) | 5.24010e9 | + | 9.07612e9i | 0.330475 | + | 0.572399i | 0.982605 | − | 0.185708i | \(-0.0594578\pi\) |
−0.652130 | + | 0.758107i | \(0.726124\pi\) | |||||||
\(822\) | −1.26687e8 | + | 2.19429e8i | −0.00795575 | + | 0.0137798i | ||||
\(823\) | 1.89782e9 | − | 3.28711e9i | 0.118674 | − | 0.205549i | −0.800569 | − | 0.599241i | \(-0.795469\pi\) |
0.919242 | + | 0.393692i | \(0.128802\pi\) | |||||||
\(824\) | 4.60872e9 | + | 7.98253e9i | 0.286969 | + | 0.497045i | ||||
\(825\) | −5.73136e8 | −0.0355360 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.11868e9 | 0.314694 | 0.157347 | − | 0.987543i | \(-0.449706\pi\) | ||||
0.157347 | + | 0.987543i | \(0.449706\pi\) | |||||||
\(828\) | −4.18945e8 | − | 7.25633e8i | −0.0256478 | − | 0.0444233i | ||||
\(829\) | 7.69243e9 | − | 1.33237e10i | 0.468946 | − | 0.812238i | −0.530424 | − | 0.847733i | \(-0.677967\pi\) |
0.999370 | + | 0.0354942i | \(0.0113005\pi\) | |||||||
\(830\) | 7.67106e8 | − | 1.32867e9i | 0.0465674 | − | 0.0806571i | ||||
\(831\) | 4.39029e9 | + | 7.60420e9i | 0.265393 | + | 0.459674i | ||||
\(832\) | 1.40246e10 | 0.844227 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1.60262e10 | −0.956642 | ||||||||
\(835\) | −6.94879e9 | − | 1.20357e10i | −0.413054 | − | 0.715430i | ||||
\(836\) | −6.85754e8 | + | 1.18776e9i | −0.0405926 | + | 0.0703084i | ||||
\(837\) | 1.66392e9 | − | 2.88199e9i | 0.0980827 | − | 0.169884i | ||||
\(838\) | 1.07857e10 | + | 1.86814e10i | 0.633132 | + | 1.09662i | ||||
\(839\) | −1.39438e10 | −0.815104 | −0.407552 | − | 0.913182i | \(-0.633618\pi\) | ||||
−0.407552 | + | 0.913182i | \(0.633618\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.61956e10 | −0.938883 | ||||||||
\(842\) | 1.00502e10 | + | 1.74074e10i | 0.580204 | + | 1.00494i | ||||
\(843\) | −8.66725e9 | + | 1.50121e10i | −0.498293 | + | 0.863069i | ||||
\(844\) | 2.40048e9 | − | 4.15775e9i | 0.137436 | − | 0.238046i | ||||
\(845\) | 1.39961e9 | + | 2.42420e9i | 0.0798012 | + | 0.138220i | ||||
\(846\) | 1.07634e10 | 0.611158 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.69026e9 | 0.207812 | ||||||||
\(849\) | −3.63761e9 | − | 6.30053e9i | −0.204004 | − | 0.353346i | ||||
\(850\) | −5.94946e8 | + | 1.03048e9i | −0.0332286 | + | 0.0575536i | ||||
\(851\) | −2.69932e9 | + | 4.67536e9i | −0.150142 | + | 0.260053i | ||||
\(852\) | 8.55545e8 | + | 1.48185e9i | 0.0473919 | + | 0.0820852i | ||||
\(853\) | −2.36230e9 | −0.130321 | −0.0651604 | − | 0.997875i | \(-0.520756\pi\) | ||||
−0.0651604 | + | 0.997875i | \(0.520756\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.84829e9 | 0.101132 | ||||||||
\(856\) | 1.49542e10 | + | 2.59013e10i | 0.814899 | + | 1.41145i | ||||
\(857\) | 6.43636e9 | − | 1.11481e10i | 0.349307 | − | 0.605018i | −0.636820 | − | 0.771013i | \(-0.719750\pi\) |
0.986127 | + | 0.165995i | \(0.0530837\pi\) | |||||||
\(858\) | −1.02374e10 | + | 1.77317e10i | −0.553331 | + | 0.958397i | ||||
\(859\) | 1.02329e10 | + | 1.77238e10i | 0.550835 | + | 0.954074i | 0.998215 | + | 0.0597298i | \(0.0190239\pi\) |
−0.447380 | + | 0.894344i | \(0.647643\pi\) | |||||||
\(860\) | 1.73997e9 | 0.0932816 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.43737e10 | −0.764353 | ||||||||
\(863\) | 1.64337e10 | + | 2.84640e10i | 0.870357 | + | 1.50750i | 0.861628 | + | 0.507540i | \(0.169445\pi\) |
0.00872890 | + | 0.999962i | \(0.497221\pi\) | |||||||
\(864\) | −5.96355e8 | + | 1.03292e9i | −0.0314562 | + | 0.0544838i | ||||
\(865\) | 1.46578e10 | − | 2.53881e10i | 0.770039 | − | 1.33375i | ||||
\(866\) | 5.69545e9 | + | 9.86480e9i | 0.297999 | + | 0.516150i | ||||
\(867\) | 1.91459e10 | 0.997719 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.17427e10 | −2.67473 | ||||||||
\(870\) | 1.52380e9 | + | 2.63930e9i | 0.0784532 | + | 0.135885i | ||||
\(871\) | −1.59514e10 | + | 2.76287e10i | −0.817968 | + | 1.41676i | ||||
\(872\) | 1.01682e10 | − | 1.76118e10i | 0.519320 | − | 0.899488i | ||||
\(873\) | −1.63729e9 | − | 2.83588e9i | −0.0832869 | − | 0.144257i | ||||
\(874\) | 5.91706e9 | 0.299789 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.75271e9 | 0.188617 | ||||||||
\(877\) | −1.14094e10 | − | 1.97617e10i | −0.571168 | − | 0.989293i | −0.996446 | − | 0.0842300i | \(-0.973157\pi\) |
0.425278 | − | 0.905063i | \(-0.360176\pi\) | |||||||
\(878\) | −6.05643e9 | + | 1.04900e10i | −0.301985 | + | 0.523054i | ||||
\(879\) | 4.05866e8 | − | 7.02980e8i | 0.0201568 | − | 0.0349126i | ||||
\(880\) | 1.93405e10 | + | 3.34987e10i | 0.956704 | + | 1.65706i | ||||
\(881\) | 3.68607e10 | 1.81613 | 0.908067 | − | 0.418826i | \(-0.137558\pi\) | ||||
0.908067 | + | 0.418826i | \(0.137558\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.64136e8 | −0.0275754 | −0.0137877 | − | 0.999905i | \(-0.504389\pi\) | ||||
−0.0137877 | + | 0.999905i | \(0.504389\pi\) | |||||||
\(884\) | 3.01105e9 | + | 5.21528e9i | 0.146600 | + | 0.253919i | ||||
\(885\) | 8.54731e9 | − | 1.48044e10i | 0.414503 | − | 0.717941i | ||||
\(886\) | 1.05597e10 | − | 1.82900e10i | 0.510076 | − | 0.883478i | ||||
\(887\) | −1.26134e10 | − | 2.18470e10i | −0.606874 | − | 1.05114i | −0.991752 | − | 0.128169i | \(-0.959090\pi\) |
0.384879 | − | 0.922967i | \(-0.374243\pi\) | |||||||
\(888\) | 3.49678e9 | 0.167580 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 4.12171e10 | 1.95980 | ||||||||
\(891\) | 1.93682e9 | + | 3.35468e9i | 0.0917314 | + | 0.158883i | ||||
\(892\) | −1.44339e9 | + | 2.50002e9i | −0.0680935 | + | 0.117941i | ||||
\(893\) | −5.38414e9 | + | 9.32560e9i | −0.253009 | + | 0.438224i | ||||
\(894\) | −2.25343e9 | − | 3.90305e9i | −0.105478 | − | 0.182694i | ||||
\(895\) | 9.50163e9 | 0.443014 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.25142e10 | 0.578936 | ||||||||
\(898\) | 4.53914e9 | + | 7.86202e9i | 0.209173 | + | 0.362299i | ||||
\(899\) | −2.74482e9 | + | 4.75417e9i | −0.125996 | + | 0.218231i | ||||
\(900\) | −2.24263e7 | + | 3.88436e7i | −0.00102544 | + | 0.00177611i | ||||
\(901\) | −3.31161e9 | − | 5.73587e9i | −0.150835 | − | 0.261254i | ||||
\(902\) | 2.09498e10 | 0.950512 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.07540e9 | 0.228497 | ||||||||
\(905\) | −1.14621e10 | − | 1.98529e10i | −0.514037 | − | 0.890337i | ||||
\(906\) | 2.76054e9 | − | 4.78139e9i | 0.123323 | − | 0.213602i | ||||
\(907\) | −1.53724e10 | + | 2.66257e10i | −0.684092 | + | 1.18488i | 0.289629 | + | 0.957139i | \(0.406468\pi\) |
−0.973721 | + | 0.227744i | \(0.926865\pi\) | |||||||
\(908\) | −8.56480e8 | − | 1.48347e9i | −0.0379679 | − | 0.0657624i | ||||
\(909\) | 6.84095e9 | 0.302095 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.02571e9 | 0.264055 | 0.132027 | − | 0.991246i | \(-0.457851\pi\) | ||||
0.132027 | + | 0.991246i | \(0.457851\pi\) | |||||||
\(912\) | −2.24143e9 | − | 3.88227e9i | −0.0978460 | − | 0.169474i | ||||
\(913\) | −1.60842e9 | + | 2.78587e9i | −0.0699443 | + | 0.121147i | ||||
\(914\) | −2.11587e10 | + | 3.66479e10i | −0.916592 | + | 1.58758i | ||||
\(915\) | 4.07653e9 | + | 7.06076e9i | 0.175921 | + | 0.304704i | ||||
\(916\) | −3.54906e9 | −0.152574 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 8.04212e9 | 0.343100 | ||||||||
\(919\) | 3.86485e9 | + | 6.69411e9i | 0.164259 | + | 0.284504i | 0.936392 | − | 0.350956i | \(-0.114143\pi\) |
−0.772133 | + | 0.635461i | \(0.780810\pi\) | |||||||
\(920\) | 1.01062e10 | − | 1.75044e10i | 0.427887 | − | 0.741121i | ||||
\(921\) | 2.70185e9 | − | 4.67974e9i | 0.113960 | − | 0.197385i | ||||
\(922\) | −3.04428e9 | − | 5.27284e9i | −0.127916 | − | 0.221558i | ||||
\(923\) | −2.55559e10 | −1.06976 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.88993e8 | 0.0120058 | ||||||||
\(926\) | −6.15486e9 | − | 1.06605e10i | −0.254730 | − | 0.441205i | ||||
\(927\) | 2.57431e9 | − | 4.45884e9i | 0.106141 | − | 0.183841i | ||||
\(928\) | 9.83757e8 | − | 1.70392e9i | 0.0404082 | − | 0.0699891i | ||||
\(929\) | 3.00620e9 | + | 5.20690e9i | 0.123016 | + | 0.213071i | 0.920956 | − | 0.389667i | \(-0.127410\pi\) |
−0.797939 | + | 0.602738i | \(0.794077\pi\) | |||||||
\(930\) | −1.58692e10 | −0.646939 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −5.74215e9 | −0.232337 | ||||||||
\(933\) | −7.18773e9 | − | 1.24495e10i | −0.289738 | − | 0.501842i | ||||
\(934\) | 2.38744e9 | − | 4.13516e9i | 0.0958778 | − | 0.166065i | ||||
\(935\) | 3.47119e10 | − | 6.01228e10i | 1.38879 | − | 2.40546i | ||||
\(936\) | −4.05283e9 | − | 7.01970e9i | −0.161545 | − | 0.279804i | ||||
\(937\) | 2.80399e10 | 1.11349 | 0.556746 | − | 0.830683i | \(-0.312050\pi\) | ||||
0.556746 | + | 0.830683i | \(0.312050\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.41560e10 | 0.557969 | ||||||||
\(940\) | −3.63571e9 | − | 6.29723e9i | −0.142772 | − | 0.247288i | ||||
\(941\) | −1.50297e10 | + | 2.60322e10i | −0.588013 | + | 1.01847i | 0.406480 | + | 0.913660i | \(0.366756\pi\) |
−0.994492 | + | 0.104808i | \(0.966577\pi\) | |||||||
\(942\) | 1.60328e9 | − | 2.77696e9i | 0.0624929 | − | 0.108241i | ||||
\(943\) | −6.40228e9 | − | 1.10891e10i | −0.248624 | − | 0.430630i | ||||
\(944\) | −4.14613e10 | −1.60414 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.57519e10 | −0.988985 | ||||||||
\(947\) | 5.66131e9 | + | 9.80568e9i | 0.216617 | + | 0.375191i | 0.953772 | − | 0.300533i | \(-0.0971644\pi\) |
−0.737155 | + | 0.675724i | \(0.763831\pi\) | |||||||
\(948\) | −2.02465e9 | + | 3.50680e9i | −0.0771829 | + | 0.133685i | ||||
\(949\) | −2.80242e10 | + | 4.85393e10i | −1.06439 | + | 1.84358i | ||||
\(950\) | −1.58372e8 | − | 2.74308e8i | −0.00599301 | − | 0.0103802i | ||||
\(951\) | −1.33410e10 | −0.502986 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.35412e10 | 0.881057 | 0.440529 | − | 0.897739i | \(-0.354791\pi\) | ||||
0.440529 | + | 0.897739i | \(0.354791\pi\) | |||||||
\(954\) | −8.81135e8 | − | 1.52617e9i | −0.0328566 | − | 0.0569094i | ||||
\(955\) | −5.00646e9 | + | 8.67145e9i | −0.186003 | + | 0.322166i | ||||
\(956\) | −3.40745e9 | + | 5.90188e9i | −0.126133 | + | 0.218468i | ||||
\(957\) | −3.19501e9 | − | 5.53393e9i | −0.117837 | − | 0.204099i | ||||
\(958\) | −3.34598e10 | −1.22954 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.26527e10 | −0.461566 | ||||||||
\(961\) | −5.36255e8 | − | 9.28822e8i | −0.0194913 | − | 0.0337598i | ||||
\(962\) | 5.16202e9 | − | 8.94088e9i | 0.186942 | − | 0.323793i | ||||
\(963\) | 8.35300e9 | − | 1.44678e10i | 0.301405 | − | 0.522049i | ||||
\(964\) | −1.37337e9 | − | 2.37875e9i | −0.0493762 | − | 0.0855221i | ||||
\(965\) | 2.38174e10 | 0.853194 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.02470e10 | −0.364420 | −0.182210 | − | 0.983260i | \(-0.558325\pi\) | ||||
−0.182210 | + | 0.983260i | \(0.558325\pi\) | |||||||
\(968\) | −2.19530e10 | − | 3.80237e10i | −0.777911 | − | 1.34738i | ||||
\(969\) | −4.02287e9 | + | 6.96782e9i | −0.142038 | + | 0.246016i | ||||
\(970\) | −7.80763e9 | + | 1.35232e10i | −0.274674 | + | 0.475750i | ||||
\(971\) | −1.26563e10 | − | 2.19214e10i | −0.443651 | − | 0.768425i | 0.554307 | − | 0.832313i | \(-0.312984\pi\) |
−0.997957 | + | 0.0638872i | \(0.979650\pi\) | |||||||
\(972\) | 3.03145e8 | 0.0105881 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 3.15800e10 | 1.09511 | ||||||||
\(975\) | −3.34947e8 | − | 5.80145e8i | −0.0115734 | − | 0.0200457i | ||||
\(976\) | 9.88722e9 | − | 1.71252e10i | 0.340408 | − | 0.589604i | ||||
\(977\) | −1.70251e9 | + | 2.94883e9i | −0.0584060 | + | 0.101162i | −0.893750 | − | 0.448565i | \(-0.851935\pi\) |
0.835344 | + | 0.549728i | \(0.185268\pi\) | |||||||
\(978\) | 2.44789e9 | + | 4.23987e9i | 0.0836770 | + | 0.144933i | ||||
\(979\) | −8.64215e10 | −2.94363 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.13593e10 | −0.384160 | ||||||||
\(982\) | −1.58768e10 | − | 2.74994e10i | −0.535023 | − | 0.926688i | ||||
\(983\) | −8.46380e9 | + | 1.46597e10i | −0.284203 | + | 0.492253i | −0.972415 | − | 0.233256i | \(-0.925062\pi\) |
0.688213 | + | 0.725509i | \(0.258395\pi\) | |||||||
\(984\) | −4.14685e9 | + | 7.18255e9i | −0.138751 | + | 0.240323i | ||||
\(985\) | −2.23554e10 | − | 3.87207e10i | −0.745342 | − | 1.29097i | ||||
\(986\) | −1.32664e10 | −0.440742 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.60305e9 | −0.0528808 | ||||||||
\(989\) | 7.86978e9 | + | 1.36309e10i | 0.258688 | + | 0.448060i | ||||
\(990\) | 9.23597e9 | − | 1.59972e10i | 0.302524 | − | 0.523986i | ||||
\(991\) | −9.35993e9 | + | 1.62119e10i | −0.305503 | + | 0.529146i | −0.977373 | − | 0.211523i | \(-0.932158\pi\) |
0.671871 | + | 0.740669i | \(0.265491\pi\) | |||||||
\(992\) | 5.12252e9 | + | 8.87246e9i | 0.166607 | + | 0.288571i | ||||
\(993\) | −6.59365e9 | −0.213699 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.64181e10 | −1.49385 | ||||||||
\(996\) | 1.25873e8 | + | 2.18018e8i | 0.00403667 | + | 0.00699172i | ||||
\(997\) | 2.71939e10 | − | 4.71012e10i | 0.869037 | − | 1.50522i | 0.00605595 | − | 0.999982i | \(-0.498072\pi\) |
0.862982 | − | 0.505235i | \(-0.168594\pi\) | |||||||
\(998\) | 2.20615e10 | − | 3.82116e10i | 0.702551 | − | 1.21685i | ||||
\(999\) | −9.76606e8 | − | 1.69153e9i | −0.0309913 | − | 0.0536786i |
(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 | 147.8.e.l.67.3 | 8 | ||
7.2 | even | 3 | inner | 147.8.e.l.79.3 | 8 | ||
7.3 | odd | 6 | 147.8.a.f.1.2 | ✓ | 4 | ||
7.4 | even | 3 | 147.8.a.g.1.2 | yes | 4 | ||
7.5 | odd | 6 | 147.8.e.m.79.3 | 8 | |||
7.6 | odd | 2 | 147.8.e.m.67.3 | 8 | |||
21.11 | odd | 6 | 441.8.a.u.1.3 | 4 | |||
21.17 | even | 6 | 441.8.a.v.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.8.a.f.1.2 | ✓ | 4 | 7.3 | odd | 6 | ||
147.8.a.g.1.2 | yes | 4 | 7.4 | even | 3 | ||
147.8.e.l.67.3 | 8 | 1.1 | even | 1 | trivial | ||
147.8.e.l.79.3 | 8 | 7.2 | even | 3 | inner | ||
147.8.e.m.67.3 | 8 | 7.6 | odd | 2 | |||
147.8.e.m.79.3 | 8 | 7.5 | odd | 6 | |||
441.8.a.u.1.3 | 4 | 21.11 | odd | 6 | |||
441.8.a.v.1.3 | 4 | 21.17 | even | 6 |