Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [17,10,Mod(4,17)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(17, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("17.4");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 17 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 17.c (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.75560921479\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 13.3 | ||
Character | \(\chi\) | \(=\) | 17.13 |
Dual form | 17.10.c.a.4.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 28.8329i | − | 1.27425i | −0.770762 | − | 0.637123i | \(-0.780124\pi\) | ||
0.770762 | − | 0.637123i | \(-0.219876\pi\) | |||||||
\(3\) | −179.389 | − | 179.389i | −1.27864 | − | 1.27864i | −0.941428 | − | 0.337214i | \(-0.890515\pi\) |
−0.337214 | − | 0.941428i | \(-0.609485\pi\) | |||||||
\(4\) | −319.336 | −0.623703 | ||||||||
\(5\) | −1133.17 | − | 1133.17i | −0.810828 | − | 0.810828i | 0.173930 | − | 0.984758i | \(-0.444353\pi\) |
−0.984758 | + | 0.173930i | \(0.944353\pi\) | |||||||
\(6\) | −5172.29 | + | 5172.29i | −1.62931 | + | 1.62931i | ||||
\(7\) | 4922.20 | − | 4922.20i | 0.774851 | − | 0.774851i | −0.204099 | − | 0.978950i | \(-0.565426\pi\) |
0.978950 | + | 0.204099i | \(0.0654264\pi\) | |||||||
\(8\) | − | 5555.06i | − | 0.479494i | ||||||
\(9\) | 44677.5i | 2.26985i | ||||||||
\(10\) | −32672.5 | + | 32672.5i | −1.03319 | + | 1.03319i | ||||
\(11\) | 44802.3 | − | 44802.3i | 0.922643 | − | 0.922643i | −0.0745727 | − | 0.997216i | \(-0.523759\pi\) |
0.997216 | + | 0.0745727i | \(0.0237593\pi\) | |||||||
\(12\) | 57285.2 | + | 57285.2i | 0.797494 | + | 0.797494i | ||||
\(13\) | 114552. | 1.11239 | 0.556197 | − | 0.831051i | \(-0.312260\pi\) | ||||
0.556197 | + | 0.831051i | \(0.312260\pi\) | |||||||
\(14\) | −141921. | − | 141921.i | −0.987352 | − | 0.987352i | ||||
\(15\) | 406554.i | 2.07352i | ||||||||
\(16\) | −323669. | −1.23470 | ||||||||
\(17\) | −274067. | + | 208507.i | −0.795860 | + | 0.605481i | ||||
\(18\) | 1.28818e6 | 2.89235 | ||||||||
\(19\) | − | 50488.5i | − | 0.0888794i | −0.999012 | − | 0.0444397i | \(-0.985850\pi\) | ||
0.999012 | − | 0.0444397i | \(-0.0141503\pi\) | |||||||
\(20\) | 361861. | + | 361861.i | 0.505716 | + | 0.505716i | ||||
\(21\) | −1.76597e6 | −1.98152 | ||||||||
\(22\) | −1.29178e6 | − | 1.29178e6i | −1.17567 | − | 1.17567i | ||||
\(23\) | 805268. | − | 805268.i | 0.600019 | − | 0.600019i | −0.340298 | − | 0.940317i | \(-0.610528\pi\) |
0.940317 | + | 0.340298i | \(0.110528\pi\) | |||||||
\(24\) | −996514. | + | 996514.i | −0.613102 | + | 0.613102i | ||||
\(25\) | 615007.i | 0.314884i | ||||||||
\(26\) | − | 3.30287e6i | − | 1.41746i | ||||||
\(27\) | 4.48373e6 | − | 4.48373e6i | 1.62369 | − | 1.62369i | ||||
\(28\) | −1.57184e6 | + | 1.57184e6i | −0.483278 | + | 0.483278i | ||||
\(29\) | −1.44158e6 | − | 1.44158e6i | −0.378486 | − | 0.378486i | 0.492070 | − | 0.870556i | \(-0.336240\pi\) |
−0.870556 | + | 0.492070i | \(0.836240\pi\) | |||||||
\(30\) | 1.17221e7 | 2.64217 | ||||||||
\(31\) | 734754. | + | 734754.i | 0.142894 | + | 0.142894i | 0.774935 | − | 0.632041i | \(-0.217783\pi\) |
−0.632041 | + | 0.774935i | \(0.717783\pi\) | |||||||
\(32\) | 6.48811e6i | 1.09381i | ||||||||
\(33\) | −1.60741e7 | −2.35946 | ||||||||
\(34\) | 6.01186e6 | + | 7.90215e6i | 0.771532 | + | 1.01412i | ||||
\(35\) | −1.11554e7 | −1.25654 | ||||||||
\(36\) | − | 1.42671e7i | − | 1.41571i | ||||||
\(37\) | 1.30400e7 | + | 1.30400e7i | 1.14385 | + | 1.14385i | 0.987740 | + | 0.156108i | \(0.0498949\pi\) |
0.156108 | + | 0.987740i | \(0.450105\pi\) | |||||||
\(38\) | −1.45573e6 | −0.113254 | ||||||||
\(39\) | −2.05493e7 | − | 2.05493e7i | −1.42235 | − | 1.42235i | ||||
\(40\) | −6.29480e6 | + | 6.29480e6i | −0.388787 | + | 0.388787i | ||||
\(41\) | 5.63189e6 | − | 5.63189e6i | 0.311263 | − | 0.311263i | −0.534136 | − | 0.845399i | \(-0.679363\pi\) |
0.845399 | + | 0.534136i | \(0.179363\pi\) | |||||||
\(42\) | 5.09182e7i | 2.52494i | ||||||||
\(43\) | 2.09816e7i | 0.935902i | 0.883755 | + | 0.467951i | \(0.155008\pi\) | ||||
−0.883755 | + | 0.467951i | \(0.844992\pi\) | |||||||
\(44\) | −1.43070e7 | + | 1.43070e7i | −0.575456 | + | 0.575456i | ||||
\(45\) | 5.06270e7 | − | 5.06270e7i | 1.84046 | − | 1.84046i | ||||
\(46\) | −2.32182e7 | − | 2.32182e7i | −0.764572 | − | 0.764572i | ||||
\(47\) | 6.43503e6 | 0.192358 | 0.0961790 | − | 0.995364i | \(-0.469338\pi\) | ||||
0.0961790 | + | 0.995364i | \(0.469338\pi\) | |||||||
\(48\) | 5.80624e7 | + | 5.80624e7i | 1.57874 | + | 1.57874i | ||||
\(49\) | − | 8.10258e6i | − | 0.200789i | ||||||
\(50\) | 1.77324e7 | 0.401239 | ||||||||
\(51\) | 8.65682e7 | + | 1.17607e7i | 1.79181 | + | 0.243427i | ||||
\(52\) | −3.65807e7 | −0.693803 | ||||||||
\(53\) | − | 1.61556e7i | − | 0.281242i | −0.990063 | − | 0.140621i | \(-0.955090\pi\) | ||
0.990063 | − | 0.140621i | \(-0.0449099\pi\) | |||||||
\(54\) | −1.29279e8 | − | 1.29279e8i | −2.06898 | − | 2.06898i | ||||
\(55\) | −1.01537e8 | −1.49621 | ||||||||
\(56\) | −2.73431e7 | − | 2.73431e7i | −0.371537 | − | 0.371537i | ||||
\(57\) | −9.05706e6 | + | 9.05706e6i | −0.113645 | + | 0.113645i | ||||
\(58\) | −4.15651e7 | + | 4.15651e7i | −0.482284 | + | 0.482284i | ||||
\(59\) | − | 1.17489e8i | − | 1.26230i | −0.775659 | − | 0.631152i | \(-0.782583\pi\) | ||
0.775659 | − | 0.631152i | \(-0.217417\pi\) | |||||||
\(60\) | − | 1.29827e8i | − | 1.29326i | ||||||
\(61\) | 2.49073e7 | − | 2.49073e7i | 0.230326 | − | 0.230326i | −0.582503 | − | 0.812829i | \(-0.697927\pi\) |
0.812829 | + | 0.582503i | \(0.197927\pi\) | |||||||
\(62\) | 2.11851e7 | − | 2.11851e7i | 0.182082 | − | 0.182082i | ||||
\(63\) | 2.19912e8 | + | 2.19912e8i | 1.75880 | + | 1.75880i | ||||
\(64\) | 2.13528e7 | 0.159091 | ||||||||
\(65\) | −1.29807e8 | − | 1.29807e8i | −0.901959 | − | 0.901959i | ||||
\(66\) | 4.63462e8i | 3.00653i | ||||||||
\(67\) | 2.32033e8 | 1.40674 | 0.703368 | − | 0.710826i | \(-0.251679\pi\) | ||||
0.703368 | + | 0.710826i | \(0.251679\pi\) | |||||||
\(68\) | 8.75195e7 | − | 6.65838e7i | 0.496381 | − | 0.377640i | ||||
\(69\) | −2.88912e8 | −1.53442 | ||||||||
\(70\) | 3.21641e8i | 1.60114i | ||||||||
\(71\) | −5.09689e6 | − | 5.09689e6i | −0.0238036 | − | 0.0238036i | 0.695105 | − | 0.718908i | \(-0.255358\pi\) |
−0.718908 | + | 0.695105i | \(0.755358\pi\) | |||||||
\(72\) | 2.48186e8 | 1.08838 | ||||||||
\(73\) | −2.23490e8 | − | 2.23490e8i | −0.921097 | − | 0.921097i | 0.0760099 | − | 0.997107i | \(-0.475782\pi\) |
−0.997107 | + | 0.0760099i | \(0.975782\pi\) | |||||||
\(74\) | 3.75980e8 | − | 3.75980e8i | 1.45754 | − | 1.45754i | ||||
\(75\) | 1.10325e8 | − | 1.10325e8i | 0.402624 | − | 0.402624i | ||||
\(76\) | 1.61228e7i | 0.0554344i | ||||||||
\(77\) | − | 4.41053e8i | − | 1.42982i | ||||||
\(78\) | −5.92497e8 | + | 5.92497e8i | −1.81243 | + | 1.81243i | ||||
\(79\) | −4.12622e8 | + | 4.12622e8i | −1.19187 | + | 1.19187i | −0.215333 | + | 0.976541i | \(0.569084\pi\) |
−0.976541 | + | 0.215333i | \(0.930916\pi\) | |||||||
\(80\) | 3.66770e8 | + | 3.66770e8i | 1.00113 | + | 1.00113i | ||||
\(81\) | −7.29271e8 | −1.88238 | ||||||||
\(82\) | −1.62384e8 | − | 1.62384e8i | −0.396625 | − | 0.396625i | ||||
\(83\) | 2.61757e8i | 0.605407i | 0.953085 | + | 0.302704i | \(0.0978892\pi\) | ||||
−0.953085 | + | 0.302704i | \(0.902111\pi\) | |||||||
\(84\) | 5.63939e8 | 1.23588 | ||||||||
\(85\) | 5.46837e8 | + | 7.42904e7i | 1.13625 | + | 0.154365i | ||||
\(86\) | 6.04960e8 | 1.19257 | ||||||||
\(87\) | 5.17208e8i | 0.967895i | ||||||||
\(88\) | −2.48880e8 | − | 2.48880e8i | −0.442402 | − | 0.442402i | ||||
\(89\) | 8.28097e7 | 0.139903 | 0.0699513 | − | 0.997550i | \(-0.477716\pi\) | ||||
0.0699513 | + | 0.997550i | \(0.477716\pi\) | |||||||
\(90\) | −1.45972e9 | − | 1.45972e9i | −2.34520 | − | 2.34520i | ||||
\(91\) | 5.63849e8 | − | 5.63849e8i | 0.861939 | − | 0.861939i | ||||
\(92\) | −2.57151e8 | + | 2.57151e8i | −0.374234 | + | 0.374234i | ||||
\(93\) | − | 2.63613e8i | − | 0.365421i | ||||||
\(94\) | − | 1.85541e8i | − | 0.245111i | ||||||
\(95\) | −5.72119e7 | + | 5.72119e7i | −0.0720659 | + | 0.0720659i | ||||
\(96\) | 1.16389e9 | − | 1.16389e9i | 1.39860 | − | 1.39860i | ||||
\(97\) | −1.17934e8 | − | 1.17934e8i | −0.135258 | − | 0.135258i | 0.636236 | − | 0.771494i | \(-0.280490\pi\) |
−0.771494 | + | 0.636236i | \(0.780490\pi\) | |||||||
\(98\) | −2.33621e8 | −0.255855 | ||||||||
\(99\) | 2.00166e9 | + | 2.00166e9i | 2.09426 | + | 2.09426i | ||||
\(100\) | − | 1.96394e8i | − | 0.196394i | ||||||
\(101\) | −1.93499e9 | −1.85026 | −0.925130 | − | 0.379651i | \(-0.876044\pi\) | ||||
−0.925130 | + | 0.379651i | \(0.876044\pi\) | |||||||
\(102\) | 3.39096e8 | − | 2.49601e9i | 0.310185 | − | 2.28321i | ||||
\(103\) | −1.87339e9 | −1.64006 | −0.820031 | − | 0.572319i | \(-0.806044\pi\) | ||||
−0.820031 | + | 0.572319i | \(0.806044\pi\) | |||||||
\(104\) | − | 6.36344e8i | − | 0.533386i | ||||||
\(105\) | 2.00114e9 | + | 2.00114e9i | 1.60667 | + | 1.60667i | ||||
\(106\) | −4.65812e8 | −0.358372 | ||||||||
\(107\) | 1.48763e9 | + | 1.48763e9i | 1.09715 | + | 1.09715i | 0.994742 | + | 0.102412i | \(0.0326561\pi\) |
0.102412 | + | 0.994742i | \(0.467344\pi\) | |||||||
\(108\) | −1.43182e9 | + | 1.43182e9i | −1.01270 | + | 1.01270i | ||||
\(109\) | 7.08084e8 | − | 7.08084e8i | 0.480469 | − | 0.480469i | −0.424812 | − | 0.905281i | \(-0.639660\pi\) |
0.905281 | + | 0.424812i | \(0.139660\pi\) | |||||||
\(110\) | 2.92761e9i | 1.90654i | ||||||||
\(111\) | − | 4.67844e9i | − | 2.92515i | ||||||
\(112\) | −1.59316e9 | + | 1.59316e9i | −0.956707 | + | 0.956707i | ||||
\(113\) | 1.57070e9 | − | 1.57070e9i | 0.906237 | − | 0.906237i | −0.0897295 | − | 0.995966i | \(-0.528600\pi\) |
0.995966 | + | 0.0897295i | \(0.0286003\pi\) | |||||||
\(114\) | 2.61141e8 | + | 2.61141e8i | 0.144812 | + | 0.144812i | ||||
\(115\) | −1.82500e9 | −0.973024 | ||||||||
\(116\) | 4.60350e8 | + | 4.60350e8i | 0.236063 | + | 0.236063i | ||||
\(117\) | 5.11790e9i | 2.52497i | ||||||||
\(118\) | −3.38755e9 | −1.60849 | ||||||||
\(119\) | −3.22700e8 | + | 2.37533e9i | −0.147515 | + | 1.08583i | ||||
\(120\) | 2.25843e9 | 0.994240 | ||||||||
\(121\) | − | 1.65655e9i | − | 0.702540i | ||||||
\(122\) | −7.18149e8 | − | 7.18149e8i | −0.293491 | − | 0.293491i | ||||
\(123\) | −2.02059e9 | −0.795987 | ||||||||
\(124\) | −2.34633e8 | − | 2.34633e8i | −0.0891235 | − | 0.0891235i | ||||
\(125\) | −1.51631e9 | + | 1.51631e9i | −0.555511 | + | 0.555511i | ||||
\(126\) | 6.34069e9 | − | 6.34069e9i | 2.24114 | − | 2.24114i | ||||
\(127\) | − | 1.88159e9i | − | 0.641814i | −0.947111 | − | 0.320907i | \(-0.896012\pi\) | ||
0.947111 | − | 0.320907i | \(-0.103988\pi\) | |||||||
\(128\) | 2.70625e9i | 0.891093i | ||||||||
\(129\) | 3.76386e9 | − | 3.76386e9i | 1.19668 | − | 1.19668i | ||||
\(130\) | −3.74270e9 | + | 3.74270e9i | −1.14932 | + | 1.14932i | ||||
\(131\) | 2.20233e9 | + | 2.20233e9i | 0.653373 | + | 0.653373i | 0.953804 | − | 0.300430i | \(-0.0971303\pi\) |
−0.300430 | + | 0.953804i | \(0.597130\pi\) | |||||||
\(132\) | 5.13303e9 | 1.47160 | ||||||||
\(133\) | −2.48515e8 | − | 2.48515e8i | −0.0688684 | − | 0.0688684i | ||||
\(134\) | − | 6.69017e9i | − | 1.79253i | ||||||
\(135\) | −1.01616e10 | −2.63306 | ||||||||
\(136\) | 1.15827e9 | + | 1.52246e9i | 0.290325 | + | 0.381610i | ||||
\(137\) | 4.16041e9 | 1.00901 | 0.504503 | − | 0.863410i | \(-0.331676\pi\) | ||||
0.504503 | + | 0.863410i | \(0.331676\pi\) | |||||||
\(138\) | 8.33016e9i | 1.95523i | ||||||||
\(139\) | −5.73290e8 | − | 5.73290e8i | −0.130259 | − | 0.130259i | 0.638971 | − | 0.769230i | \(-0.279360\pi\) |
−0.769230 | + | 0.638971i | \(0.779360\pi\) | |||||||
\(140\) | 3.56231e9 | 0.783710 | ||||||||
\(141\) | −1.15437e9 | − | 1.15437e9i | −0.245957 | − | 0.245957i | ||||
\(142\) | −1.46958e8 | + | 1.46958e8i | −0.0303316 | + | 0.0303316i | ||||
\(143\) | 5.13221e9 | − | 5.13221e9i | 1.02634 | − | 1.02634i | ||||
\(144\) | − | 1.44607e10i | − | 2.80258i | ||||||
\(145\) | 3.26711e9i | 0.613773i | ||||||||
\(146\) | −6.44387e9 | + | 6.44387e9i | −1.17370 | + | 1.17370i | ||||
\(147\) | −1.45351e9 | + | 1.45351e9i | −0.256738 | + | 0.256738i | ||||
\(148\) | −4.16413e9 | − | 4.16413e9i | −0.713422 | − | 0.713422i | ||||
\(149\) | −1.33926e9 | −0.222601 | −0.111301 | − | 0.993787i | \(-0.535502\pi\) | ||||
−0.111301 | + | 0.993787i | \(0.535502\pi\) | |||||||
\(150\) | −3.18100e9 | − | 3.18100e9i | −0.513042 | − | 0.513042i | ||||
\(151\) | 3.62654e9i | 0.567671i | 0.958873 | + | 0.283835i | \(0.0916069\pi\) | ||||
−0.958873 | + | 0.283835i | \(0.908393\pi\) | |||||||
\(152\) | −2.80467e8 | −0.0426172 | ||||||||
\(153\) | −9.31557e9 | − | 1.22446e10i | −1.37435 | − | 1.80648i | ||||
\(154\) | −1.27168e10 | −1.82195 | ||||||||
\(155\) | − | 1.66520e9i | − | 0.231725i | ||||||
\(156\) | 6.56215e9 | + | 6.56215e9i | 0.887126 | + | 0.887126i | ||||
\(157\) | 4.56689e9 | 0.599891 | 0.299945 | − | 0.953956i | \(-0.403032\pi\) | ||||
0.299945 | + | 0.953956i | \(0.403032\pi\) | |||||||
\(158\) | 1.18971e10 | + | 1.18971e10i | 1.51874 | + | 1.51874i | ||||
\(159\) | −2.89812e9 | + | 2.89812e9i | −0.359608 | + | 0.359608i | ||||
\(160\) | 7.35211e9 | − | 7.35211e9i | 0.886895 | − | 0.886895i | ||||
\(161\) | − | 7.92738e9i | − | 0.929851i | ||||||
\(162\) | 2.10270e10i | 2.39861i | ||||||||
\(163\) | 1.12494e9 | − | 1.12494e9i | 0.124821 | − | 0.124821i | −0.641937 | − | 0.766758i | \(-0.721869\pi\) |
0.766758 | + | 0.641937i | \(0.221869\pi\) | |||||||
\(164\) | −1.79847e9 | + | 1.79847e9i | −0.194136 | + | 0.194136i | ||||
\(165\) | 1.82146e10 | + | 1.82146e10i | 1.91312 | + | 1.91312i | ||||
\(166\) | 7.54723e9 | 0.771438 | ||||||||
\(167\) | −3.16480e9 | − | 3.16480e9i | −0.314864 | − | 0.314864i | 0.531927 | − | 0.846790i | \(-0.321468\pi\) |
−0.846790 | + | 0.531927i | \(0.821468\pi\) | |||||||
\(168\) | 9.81009e9i | 0.950126i | ||||||||
\(169\) | 2.51770e9 | 0.237418 | ||||||||
\(170\) | 2.14201e9 | − | 1.57669e10i | 0.196699 | − | 1.44786i | ||||
\(171\) | 2.25570e9 | 0.201743 | ||||||||
\(172\) | − | 6.70018e9i | − | 0.583725i | ||||||
\(173\) | −3.39767e9 | − | 3.39767e9i | −0.288386 | − | 0.288386i | 0.548056 | − | 0.836442i | \(-0.315368\pi\) |
−0.836442 | + | 0.548056i | \(0.815368\pi\) | |||||||
\(174\) | 1.49126e10 | 1.23334 | ||||||||
\(175\) | 3.02719e9 | + | 3.02719e9i | 0.243988 | + | 0.243988i | ||||
\(176\) | −1.45011e10 | + | 1.45011e10i | −1.13918 | + | 1.13918i | ||||
\(177\) | −2.10762e10 | + | 2.10762e10i | −1.61403 | + | 1.61403i | ||||
\(178\) | − | 2.38764e9i | − | 0.178270i | ||||||
\(179\) | − | 1.33451e10i | − | 0.971592i | −0.874072 | − | 0.485796i | \(-0.838530\pi\) | ||
0.874072 | − | 0.485796i | \(-0.161470\pi\) | |||||||
\(180\) | −1.61670e10 | + | 1.61670e10i | −1.14790 | + | 1.14790i | ||||
\(181\) | 5.01159e9 | − | 5.01159e9i | 0.347074 | − | 0.347074i | −0.511945 | − | 0.859018i | \(-0.671075\pi\) |
0.859018 | + | 0.511945i | \(0.171075\pi\) | |||||||
\(182\) | −1.62574e10 | − | 1.62574e10i | −1.09832 | − | 1.09832i | ||||
\(183\) | −8.93616e9 | −0.589008 | ||||||||
\(184\) | −4.47331e9 | − | 4.47331e9i | −0.287706 | − | 0.287706i | ||||
\(185\) | − | 2.95529e10i | − | 1.85493i | ||||||
\(186\) | −7.60072e9 | −0.465636 | ||||||||
\(187\) | −2.93724e9 | + | 2.16204e10i | −0.175652 | + | 1.29294i | ||||
\(188\) | −2.05494e9 | −0.119974 | ||||||||
\(189\) | − | 4.41396e10i | − | 2.51623i | ||||||
\(190\) | 1.64958e9 | + | 1.64958e9i | 0.0918297 | + | 0.0918297i | ||||
\(191\) | 3.04732e10 | 1.65679 | 0.828396 | − | 0.560143i | \(-0.189254\pi\) | ||||
0.828396 | + | 0.560143i | \(0.189254\pi\) | |||||||
\(192\) | −3.83045e9 | − | 3.83045e9i | −0.203420 | − | 0.203420i | ||||
\(193\) | 7.47611e9 | − | 7.47611e9i | 0.387854 | − | 0.387854i | −0.486068 | − | 0.873921i | \(-0.661569\pi\) |
0.873921 | + | 0.486068i | \(0.161569\pi\) | |||||||
\(194\) | −3.40037e9 | + | 3.40037e9i | −0.172353 | + | 0.172353i | ||||
\(195\) | 4.65717e10i | 2.30657i | ||||||||
\(196\) | 2.58745e9i | 0.125233i | ||||||||
\(197\) | 9.14937e9 | − | 9.14937e9i | 0.432806 | − | 0.432806i | −0.456776 | − | 0.889582i | \(-0.650996\pi\) |
0.889582 | + | 0.456776i | \(0.150996\pi\) | |||||||
\(198\) | 5.77136e10 | − | 5.77136e10i | 2.66861 | − | 2.66861i | ||||
\(199\) | 1.26061e10 | + | 1.26061e10i | 0.569825 | + | 0.569825i | 0.932079 | − | 0.362254i | \(-0.117993\pi\) |
−0.362254 | + | 0.932079i | \(0.617993\pi\) | |||||||
\(200\) | 3.41640e9 | 0.150985 | ||||||||
\(201\) | −4.16240e10 | − | 4.16240e10i | −1.79871 | − | 1.79871i | ||||
\(202\) | 5.57914e10i | 2.35769i | ||||||||
\(203\) | −1.41916e10 | −0.586540 | ||||||||
\(204\) | −2.76444e10 | − | 3.75562e9i | −1.11756 | − | 0.151826i | ||||
\(205\) | −1.27637e10 | −0.504761 | ||||||||
\(206\) | 5.40152e10i | 2.08984i | ||||||||
\(207\) | 3.59773e10 | + | 3.59773e10i | 1.36195 | + | 1.36195i | ||||
\(208\) | −3.70769e10 | −1.37347 | ||||||||
\(209\) | −2.26200e9 | − | 2.26200e9i | −0.0820040 | − | 0.0820040i | ||||
\(210\) | 5.76987e10 | − | 5.76987e10i | 2.04729 | − | 2.04729i | ||||
\(211\) | 1.19467e10 | − | 1.19467e10i | 0.414931 | − | 0.414931i | −0.468521 | − | 0.883452i | \(-0.655213\pi\) |
0.883452 | + | 0.468521i | \(0.155213\pi\) | |||||||
\(212\) | 5.15905e9i | 0.175412i | ||||||||
\(213\) | 1.82865e9i | 0.0608725i | ||||||||
\(214\) | 4.28927e10 | − | 4.28927e10i | 1.39804 | − | 1.39804i | ||||
\(215\) | 2.37756e10 | − | 2.37756e10i | 0.758855 | − | 0.758855i | ||||
\(216\) | −2.49074e10 | − | 2.49074e10i | −0.778549 | − | 0.778549i | ||||
\(217\) | 7.23322e9 | 0.221443 | ||||||||
\(218\) | −2.04161e10 | − | 2.04161e10i | −0.612236 | − | 0.612236i | ||||
\(219\) | 8.01831e10i | 2.35551i | ||||||||
\(220\) | 3.24244e10 | 0.933191 | ||||||||
\(221\) | −3.13950e10 | + | 2.38849e10i | −0.885309 | + | 0.673533i | ||||
\(222\) | −1.34893e11 | −3.72736 | ||||||||
\(223\) | 1.23092e10i | 0.333319i | 0.986015 | + | 0.166659i | \(0.0532980\pi\) | ||||
−0.986015 | + | 0.166659i | \(0.946702\pi\) | |||||||
\(224\) | 3.19358e10 | + | 3.19358e10i | 0.847543 | + | 0.847543i | ||||
\(225\) | −2.74770e10 | −0.714739 | ||||||||
\(226\) | −4.52880e10 | − | 4.52880e10i | −1.15477 | − | 1.15477i | ||||
\(227\) | 7.91954e9 | − | 7.91954e9i | 0.197963 | − | 0.197963i | −0.601163 | − | 0.799126i | \(-0.705296\pi\) |
0.799126 | + | 0.601163i | \(0.205296\pi\) | |||||||
\(228\) | 2.89225e9 | − | 2.89225e9i | 0.0708808 | − | 0.0708808i | ||||
\(229\) | 5.37234e10i | 1.29093i | 0.763788 | + | 0.645467i | \(0.223337\pi\) | ||||
−0.763788 | + | 0.645467i | \(0.776663\pi\) | |||||||
\(230\) | 5.26202e10i | 1.23987i | ||||||||
\(231\) | −7.91198e10 | + | 7.91198e10i | −1.82823 | + | 1.82823i | ||||
\(232\) | −8.00809e9 | + | 8.00809e9i | −0.181482 | + | 0.181482i | ||||
\(233\) | −2.25957e10 | − | 2.25957e10i | −0.502254 | − | 0.502254i | 0.409884 | − | 0.912138i | \(-0.365569\pi\) |
−0.912138 | + | 0.409884i | \(0.865569\pi\) | |||||||
\(234\) | 1.47564e11 | 3.21743 | ||||||||
\(235\) | −7.29196e9 | − | 7.29196e9i | −0.155969 | − | 0.155969i | ||||
\(236\) | 3.75185e10i | 0.787303i | ||||||||
\(237\) | 1.48039e11 | 3.04796 | ||||||||
\(238\) | 6.84876e10 | + | 9.30437e9i | 1.38362 | + | 0.187971i | ||||
\(239\) | −2.64220e10 | −0.523813 | −0.261906 | − | 0.965093i | \(-0.584351\pi\) | ||||
−0.261906 | + | 0.965093i | \(0.584351\pi\) | |||||||
\(240\) | − | 1.31589e11i | − | 2.56017i | ||||||
\(241\) | −4.33826e10 | − | 4.33826e10i | −0.828398 | − | 0.828398i | 0.158897 | − | 0.987295i | \(-0.449206\pi\) |
−0.987295 | + | 0.158897i | \(0.949206\pi\) | |||||||
\(242\) | −4.77632e10 | −0.895209 | ||||||||
\(243\) | 4.25697e10 | + | 4.25697e10i | 0.783199 | + | 0.783199i | ||||
\(244\) | −7.95380e9 | + | 7.95380e9i | −0.143655 | + | 0.143655i | ||||
\(245\) | −9.18157e9 | + | 9.18157e9i | −0.162806 | + | 0.162806i | ||||
\(246\) | 5.82596e10i | 1.01428i | ||||||||
\(247\) | − | 5.78357e9i | − | 0.0988689i | ||||||
\(248\) | 4.08160e9 | − | 4.08160e9i | 0.0685169 | − | 0.0685169i | ||||
\(249\) | 4.69563e10 | − | 4.69563e10i | 0.774099 | − | 0.774099i | ||||
\(250\) | 4.37196e10 | + | 4.37196e10i | 0.707858 | + | 0.707858i | ||||
\(251\) | −1.01008e11 | −1.60629 | −0.803145 | − | 0.595783i | \(-0.796842\pi\) | ||||
−0.803145 | + | 0.595783i | \(0.796842\pi\) | |||||||
\(252\) | −7.02258e10 | − | 7.02258e10i | −1.09697 | − | 1.09697i | ||||
\(253\) | − | 7.21558e10i | − | 1.10721i | ||||||
\(254\) | −5.42518e10 | −0.817829 | ||||||||
\(255\) | −8.47694e10 | − | 1.11423e11i | −1.25548 | − | 1.65023i | ||||
\(256\) | 8.89617e10 | 1.29456 | ||||||||
\(257\) | 6.24220e10i | 0.892563i | 0.894893 | + | 0.446282i | \(0.147252\pi\) | ||||
−0.894893 | + | 0.446282i | \(0.852748\pi\) | |||||||
\(258\) | −1.08523e11 | − | 1.08523e11i | −1.52487 | − | 1.52487i | ||||
\(259\) | 1.28371e11 | 1.77262 | ||||||||
\(260\) | 4.14520e10 | + | 4.14520e10i | 0.562555 | + | 0.562555i | ||||
\(261\) | 6.44064e10 | − | 6.44064e10i | 0.859106 | − | 0.859106i | ||||
\(262\) | 6.34995e10 | − | 6.34995e10i | 0.832558 | − | 0.832558i | ||||
\(263\) | − | 4.12563e10i | − | 0.531728i | −0.964010 | − | 0.265864i | \(-0.914343\pi\) | ||
0.964010 | − | 0.265864i | \(-0.0856573\pi\) | |||||||
\(264\) | 8.92923e10i | 1.13135i | ||||||||
\(265\) | −1.83069e10 | + | 1.83069e10i | −0.228039 | + | 0.228039i | ||||
\(266\) | −7.16540e9 | + | 7.16540e9i | −0.0877552 | + | 0.0877552i | ||||
\(267\) | −1.48551e10 | − | 1.48551e10i | −0.178885 | − | 0.178885i | ||||
\(268\) | −7.40964e10 | −0.877386 | ||||||||
\(269\) | −5.21630e10 | − | 5.21630e10i | −0.607403 | − | 0.607403i | 0.334864 | − | 0.942267i | \(-0.391310\pi\) |
−0.942267 | + | 0.334864i | \(0.891310\pi\) | |||||||
\(270\) | 2.92989e11i | 3.35517i | ||||||||
\(271\) | 6.04771e10 | 0.681128 | 0.340564 | − | 0.940221i | \(-0.389382\pi\) | ||||
0.340564 | + | 0.940221i | \(0.389382\pi\) | |||||||
\(272\) | 8.87069e10 | − | 6.74871e10i | 0.982646 | − | 0.747586i | ||||
\(273\) | −2.02296e11 | −2.20422 | ||||||||
\(274\) | − | 1.19957e11i | − | 1.28572i | ||||||
\(275\) | 2.75538e10 | + | 2.75538e10i | 0.290525 | + | 0.290525i | ||||
\(276\) | 9.22599e10 | 0.957023 | ||||||||
\(277\) | 4.70878e10 | + | 4.70878e10i | 0.480562 | + | 0.480562i | 0.905311 | − | 0.424749i | \(-0.139638\pi\) |
−0.424749 | + | 0.905311i | \(0.639638\pi\) | |||||||
\(278\) | −1.65296e10 | + | 1.65296e10i | −0.165982 | + | 0.165982i | ||||
\(279\) | −3.28270e10 | + | 3.28270e10i | −0.324348 | + | 0.324348i | ||||
\(280\) | 6.19686e10i | 0.602505i | ||||||||
\(281\) | 1.81317e11i | 1.73484i | 0.497578 | + | 0.867419i | \(0.334223\pi\) | ||||
−0.497578 | + | 0.867419i | \(0.665777\pi\) | |||||||
\(282\) | −3.32838e10 | + | 3.32838e10i | −0.313410 | + | 0.313410i | ||||
\(283\) | 2.20637e10 | − | 2.20637e10i | 0.204474 | − | 0.204474i | −0.597440 | − | 0.801914i | \(-0.703815\pi\) |
0.801914 | + | 0.597440i | \(0.203815\pi\) | |||||||
\(284\) | 1.62762e9 | + | 1.62762e9i | 0.0148464 | + | 0.0148464i | ||||
\(285\) | 2.05263e10 | 0.184293 | ||||||||
\(286\) | −1.47976e11 | − | 1.47976e11i | −1.30781 | − | 1.30781i | ||||
\(287\) | − | 5.54427e10i | − | 0.482365i | ||||||
\(288\) | −2.89873e11 | −2.48280 | ||||||||
\(289\) | 3.16376e10 | − | 1.14290e11i | 0.266786 | − | 0.963756i | ||||
\(290\) | 9.42003e10 | 0.782098 | ||||||||
\(291\) | 4.23118e10i | 0.345894i | ||||||||
\(292\) | 7.13685e10 | + | 7.13685e10i | 0.574491 | + | 0.574491i | ||||
\(293\) | 1.41584e11 | 1.12230 | 0.561151 | − | 0.827713i | \(-0.310359\pi\) | ||||
0.561151 | + | 0.827713i | \(0.310359\pi\) | |||||||
\(294\) | 4.19089e10 | + | 4.19089e10i | 0.327147 | + | 0.327147i | ||||
\(295\) | −1.33135e11 | + | 1.33135e11i | −1.02351 | + | 1.02351i | ||||
\(296\) | 7.24377e10 | − | 7.24377e10i | 0.548469 | − | 0.548469i | ||||
\(297\) | − | 4.01763e11i | − | 2.99617i | ||||||
\(298\) | 3.86149e10i | 0.283649i | ||||||||
\(299\) | 9.22452e10 | − | 9.22452e10i | 0.667457 | − | 0.667457i | ||||
\(300\) | −3.52308e10 | + | 3.52308e10i | −0.251118 | + | 0.251118i | ||||
\(301\) | 1.03276e11 | + | 1.03276e11i | 0.725185 | + | 0.725185i | ||||
\(302\) | 1.04564e11 | 0.723352 | ||||||||
\(303\) | 3.47115e11 | + | 3.47115e11i | 2.36582 | + | 2.36582i | ||||
\(304\) | 1.63415e10i | 0.109739i | ||||||||
\(305\) | −5.64482e10 | −0.373509 | ||||||||
\(306\) | −3.53048e11 | + | 2.68595e11i | −2.30191 | + | 1.75126i | ||||
\(307\) | 1.60774e10 | 0.103299 | 0.0516493 | − | 0.998665i | \(-0.483552\pi\) | ||||
0.0516493 | + | 0.998665i | \(0.483552\pi\) | |||||||
\(308\) | 1.40844e11i | 0.891785i | ||||||||
\(309\) | 3.36064e11 | + | 3.36064e11i | 2.09705 | + | 2.09705i | ||||
\(310\) | −4.80125e10 | −0.295275 | ||||||||
\(311\) | −1.76843e11 | − | 1.76843e11i | −1.07193 | − | 1.07193i | −0.997204 | − | 0.0747254i | \(-0.976192\pi\) |
−0.0747254 | − | 0.997204i | \(-0.523808\pi\) | |||||||
\(312\) | −1.14153e11 | + | 1.14153e11i | −0.682010 | + | 0.682010i | ||||
\(313\) | −1.29944e11 | + | 1.29944e11i | −0.765258 | + | 0.765258i | −0.977268 | − | 0.212009i | \(-0.931999\pi\) |
0.212009 | + | 0.977268i | \(0.431999\pi\) | |||||||
\(314\) | − | 1.31677e11i | − | 0.764408i | ||||||
\(315\) | − | 4.98393e11i | − | 2.85217i | ||||||
\(316\) | 1.31765e11 | − | 1.31765e11i | 0.743376 | − | 0.743376i | ||||
\(317\) | −2.92557e8 | + | 2.92557e8i | −0.00162721 | + | 0.00162721i | −0.707920 | − | 0.706293i | \(-0.750366\pi\) |
0.706293 | + | 0.707920i | \(0.250366\pi\) | |||||||
\(318\) | 8.35613e10 | + | 8.35613e10i | 0.458229 | + | 0.458229i | ||||
\(319\) | −1.29173e11 | −0.698414 | ||||||||
\(320\) | −2.41963e10 | − | 2.41963e10i | −0.128995 | − | 0.128995i | ||||
\(321\) | − | 5.33727e11i | − | 2.80574i | ||||||
\(322\) | −2.28569e11 | −1.18486 | ||||||||
\(323\) | 1.05272e10 | + | 1.38372e10i | 0.0538148 | + | 0.0707356i | ||||
\(324\) | 2.32883e11 | 1.17404 | ||||||||
\(325\) | 7.04504e10i | 0.350274i | ||||||||
\(326\) | −3.24354e10 | − | 3.24354e10i | −0.159052 | − | 0.159052i | ||||
\(327\) | −2.54044e11 | −1.22870 | ||||||||
\(328\) | −3.12855e10 | − | 3.12855e10i | −0.149249 | − | 0.149249i | ||||
\(329\) | 3.16745e10 | − | 3.16745e10i | 0.149049 | − | 0.149049i | ||||
\(330\) | 5.25179e11 | − | 5.25179e11i | 2.43778 | − | 2.43778i | ||||
\(331\) | 2.02135e11i | 0.925586i | 0.886466 | + | 0.462793i | \(0.153153\pi\) | ||||
−0.886466 | + | 0.462793i | \(0.846847\pi\) | |||||||
\(332\) | − | 8.35886e10i | − | 0.377595i | ||||||
\(333\) | −5.82593e11 | + | 5.82593e11i | −2.59637 | + | 2.59637i | ||||
\(334\) | −9.12504e10 | + | 9.12504e10i | −0.401214 | + | 0.401214i | ||||
\(335\) | −2.62932e11 | − | 2.62932e11i | −1.14062 | − | 1.14062i | ||||
\(336\) | 5.71590e11 | 2.44657 | ||||||||
\(337\) | −2.27894e11 | − | 2.27894e11i | −0.962493 | − | 0.962493i | 0.0368290 | − | 0.999322i | \(-0.488274\pi\) |
−0.999322 | + | 0.0368290i | \(0.988274\pi\) | |||||||
\(338\) | − | 7.25926e10i | − | 0.302529i | ||||||
\(339\) | −5.63533e11 | −2.31750 | ||||||||
\(340\) | −1.74625e11 | − | 2.37236e10i | −0.708681 | − | 0.0962777i | ||||
\(341\) | 6.58374e10 | 0.263680 | ||||||||
\(342\) | − | 6.50384e10i | − | 0.257070i | ||||||
\(343\) | 1.58746e11 | + | 1.58746e11i | 0.619269 | + | 0.619269i | ||||
\(344\) | 1.16554e11 | 0.448760 | ||||||||
\(345\) | 3.27385e11 | + | 3.27385e11i | 1.24415 | + | 1.24415i | ||||
\(346\) | −9.79647e10 | + | 9.79647e10i | −0.367475 | + | 0.367475i | ||||
\(347\) | 3.92735e10 | − | 3.92735e10i | 0.145418 | − | 0.145418i | −0.630650 | − | 0.776067i | \(-0.717212\pi\) |
0.776067 | + | 0.630650i | \(0.217212\pi\) | |||||||
\(348\) | − | 1.65163e11i | − | 0.603680i | ||||||
\(349\) | − | 1.80693e11i | − | 0.651968i | −0.945375 | − | 0.325984i | \(-0.894304\pi\) | ||
0.945375 | − | 0.325984i | \(-0.105696\pi\) | |||||||
\(350\) | 8.72827e10 | − | 8.72827e10i | 0.310901 | − | 0.310901i | ||||
\(351\) | 5.13621e11 | − | 5.13621e11i | 1.80618 | − | 1.80618i | ||||
\(352\) | 2.90683e11 | + | 2.90683e11i | 1.00920 | + | 1.00920i | ||||
\(353\) | −1.18291e11 | −0.405475 | −0.202738 | − | 0.979233i | \(-0.564984\pi\) | ||||
−0.202738 | + | 0.979233i | \(0.564984\pi\) | |||||||
\(354\) | 6.07688e11 | + | 6.07688e11i | 2.05668 | + | 2.05668i | ||||
\(355\) | 1.15512e10i | 0.0386012i | ||||||||
\(356\) | −2.64441e10 | −0.0872578 | ||||||||
\(357\) | 4.83995e11 | − | 3.68218e11i | 1.57701 | − | 1.19977i | ||||
\(358\) | −3.84779e11 | −1.23805 | ||||||||
\(359\) | 4.33360e11i | 1.37697i | 0.725251 | + | 0.688484i | \(0.241724\pi\) | ||||
−0.725251 | + | 0.688484i | \(0.758276\pi\) | |||||||
\(360\) | −2.81236e11 | − | 2.81236e11i | −0.882490 | − | 0.882490i | ||||
\(361\) | 3.20139e11 | 0.992100 | ||||||||
\(362\) | −1.44499e11 | − | 1.44499e11i | −0.442257 | − | 0.442257i | ||||
\(363\) | −2.97166e11 | + | 2.97166e11i | −0.898297 | + | 0.898297i | ||||
\(364\) | −1.80057e11 | + | 1.80057e11i | −0.537595 | + | 0.537595i | ||||
\(365\) | 5.06503e11i | 1.49370i | ||||||||
\(366\) | 2.57655e11i | 0.750541i | ||||||||
\(367\) | 2.94968e11 | − | 2.94968e11i | 0.848747 | − | 0.848747i | −0.141230 | − | 0.989977i | \(-0.545106\pi\) |
0.989977 | + | 0.141230i | \(0.0451057\pi\) | |||||||
\(368\) | −2.60640e11 | + | 2.60640e11i | −0.740842 | + | 0.740842i | ||||
\(369\) | 2.51619e11 | + | 2.51619e11i | 0.706520 | + | 0.706520i | ||||
\(370\) | −8.52095e11 | −2.36364 | ||||||||
\(371\) | −7.95210e10 | − | 7.95210e10i | −0.217921 | − | 0.217921i | ||||
\(372\) | 8.41811e10i | 0.227914i | ||||||||
\(373\) | −3.22658e11 | −0.863083 | −0.431542 | − | 0.902093i | \(-0.642030\pi\) | ||||
−0.431542 | + | 0.902093i | \(0.642030\pi\) | |||||||
\(374\) | 6.23380e11 | + | 8.46892e10i | 1.64752 | + | 0.223824i | ||||
\(375\) | 5.44017e11 | 1.42060 | ||||||||
\(376\) | − | 3.57469e10i | − | 0.0922346i | ||||||
\(377\) | −1.65137e11 | − | 1.65137e11i | −0.421025 | − | 0.421025i | ||||
\(378\) | −1.27267e12 | −3.20630 | ||||||||
\(379\) | 3.04808e11 | + | 3.04808e11i | 0.758839 | + | 0.758839i | 0.976111 | − | 0.217272i | \(-0.0697160\pi\) |
−0.217272 | + | 0.976111i | \(0.569716\pi\) | |||||||
\(380\) | 1.82698e10 | − | 1.82698e10i | 0.0449478 | − | 0.0449478i | ||||
\(381\) | −3.37536e11 | + | 3.37536e11i | −0.820651 | + | 0.820651i | ||||
\(382\) | − | 8.78631e11i | − | 2.11116i | ||||||
\(383\) | − | 7.20550e10i | − | 0.171108i | −0.996334 | − | 0.0855539i | \(-0.972734\pi\) | ||
0.996334 | − | 0.0855539i | \(-0.0272660\pi\) | |||||||
\(384\) | 4.85470e11 | − | 4.85470e11i | 1.13939 | − | 1.13939i | ||||
\(385\) | −4.99786e11 | + | 4.99786e11i | −1.15934 | + | 1.15934i | ||||
\(386\) | −2.15558e11 | − | 2.15558e11i | −0.494221 | − | 0.494221i | ||||
\(387\) | −9.37405e11 | −2.12436 | ||||||||
\(388\) | 3.76604e10 | + | 3.76604e10i | 0.0843612 | + | 0.0843612i | ||||
\(389\) | 2.81453e11i | 0.623206i | 0.950212 | + | 0.311603i | \(0.100866\pi\) | ||||
−0.950212 | + | 0.311603i | \(0.899134\pi\) | |||||||
\(390\) | 1.34280e12 | 2.93913 | ||||||||
\(391\) | −5.27934e10 | + | 3.88601e11i | −0.114231 | + | 0.840831i | ||||
\(392\) | −4.50103e10 | −0.0962775 | ||||||||
\(393\) | − | 7.90145e11i | − | 1.67086i | ||||||
\(394\) | −2.63803e11 | − | 2.63803e11i | −0.551501 | − | 0.551501i | ||||
\(395\) | 9.35139e11 | 1.93281 | ||||||||
\(396\) | −6.39201e11 | − | 6.39201e11i | −1.30620 | − | 1.30620i | ||||
\(397\) | 4.33717e11 | − | 4.33717e11i | 0.876292 | − | 0.876292i | −0.116857 | − | 0.993149i | \(-0.537282\pi\) |
0.993149 | + | 0.116857i | \(0.0372819\pi\) | |||||||
\(398\) | 3.63470e11 | − | 3.63470e11i | 0.726097 | − | 0.726097i | ||||
\(399\) | 8.91614e10i | 0.176116i | ||||||||
\(400\) | − | 1.99059e11i | − | 0.388786i | ||||||
\(401\) | −6.40682e11 | + | 6.40682e11i | −1.23735 | + | 1.23735i | −0.276271 | + | 0.961080i | \(0.589099\pi\) |
−0.961080 | + | 0.276271i | \(0.910901\pi\) | |||||||
\(402\) | −1.20014e12 | + | 1.20014e12i | −2.29200 | + | 2.29200i | ||||
\(403\) | 8.41677e10 | + | 8.41677e10i | 0.158954 | + | 0.158954i | ||||
\(404\) | 6.17913e11 | 1.15401 | ||||||||
\(405\) | 8.26385e11 | + | 8.26385e11i | 1.52628 | + | 1.52628i | ||||
\(406\) | 4.09184e11i | 0.747396i | ||||||||
\(407\) | 1.16844e12 | 2.11073 | ||||||||
\(408\) | 6.53315e10 | − | 4.80892e11i | 0.116722 | − | 0.859165i | ||||
\(409\) | 5.05301e11 | 0.892884 | 0.446442 | − | 0.894813i | \(-0.352691\pi\) | ||||
0.446442 | + | 0.894813i | \(0.352691\pi\) | |||||||
\(410\) | 3.68016e11i | 0.643190i | ||||||||
\(411\) | −7.46330e11 | − | 7.46330e11i | −1.29016 | − | 1.29016i | ||||
\(412\) | 5.98241e11 | 1.02291 | ||||||||
\(413\) | −5.78306e11 | − | 5.78306e11i | −0.978098 | − | 0.978098i | ||||
\(414\) | 1.03733e12 | − | 1.03733e12i | 1.73547 | − | 1.73547i | ||||
\(415\) | 2.96615e11 | − | 2.96615e11i | 0.490881 | − | 0.490881i | ||||
\(416\) | 7.43227e11i | 1.21675i | ||||||||
\(417\) | 2.05683e11i | 0.333109i | ||||||||
\(418\) | −6.52201e10 | + | 6.52201e10i | −0.104493 | + | 0.104493i | ||||
\(419\) | 6.04730e11 | − | 6.04730e11i | 0.958514 | − | 0.958514i | −0.0406590 | − | 0.999173i | \(-0.512946\pi\) |
0.999173 | + | 0.0406590i | \(0.0129457\pi\) | |||||||
\(420\) | −6.39037e11 | − | 6.39037e11i | −1.00208 | − | 1.00208i | ||||
\(421\) | −1.94096e11 | −0.301125 | −0.150563 | − | 0.988600i | \(-0.548109\pi\) | ||||
−0.150563 | + | 0.988600i | \(0.548109\pi\) | |||||||
\(422\) | −3.44457e11 | − | 3.44457e11i | −0.528725 | − | 0.528725i | ||||
\(423\) | 2.87501e11i | 0.436624i | ||||||||
\(424\) | −8.97451e10 | −0.134854 | ||||||||
\(425\) | −1.28233e11 | − | 1.68553e11i | −0.190656 | − | 0.250603i | ||||
\(426\) | 5.27252e10 | 0.0775666 | ||||||||
\(427\) | − | 2.45197e11i | − | 0.356936i | ||||||
\(428\) | −4.75054e11 | − | 4.75054e11i | −0.684299 | − | 0.684299i | ||||
\(429\) | −1.84132e12 | −2.62465 | ||||||||
\(430\) | −6.85520e11 | − | 6.85520e11i | −0.966968 | − | 0.966968i | ||||
\(431\) | −1.33430e11 | + | 1.33430e11i | −0.186253 | + | 0.186253i | −0.794074 | − | 0.607821i | \(-0.792044\pi\) |
0.607821 | + | 0.794074i | \(0.292044\pi\) | |||||||
\(432\) | −1.45124e12 | + | 1.45124e12i | −2.00476 | + | 2.00476i | ||||
\(433\) | 2.24845e11i | 0.307389i | 0.988118 | + | 0.153694i | \(0.0491171\pi\) | ||||
−0.988118 | + | 0.153694i | \(0.950883\pi\) | |||||||
\(434\) | − | 2.08555e11i | − | 0.282173i | ||||||
\(435\) | 5.86082e11 | − | 5.86082e11i | 0.784796 | − | 0.784796i | ||||
\(436\) | −2.26117e11 | + | 2.26117e11i | −0.299670 | + | 0.299670i | ||||
\(437\) | −4.06568e10 | − | 4.06568e10i | −0.0533294 | − | 0.0533294i | ||||
\(438\) | 2.31191e12 | 3.00150 | ||||||||
\(439\) | −6.48165e11 | − | 6.48165e11i | −0.832905 | − | 0.832905i | 0.155008 | − | 0.987913i | \(-0.450460\pi\) |
−0.987913 | + | 0.155008i | \(0.950460\pi\) | |||||||
\(440\) | 5.64044e11i | 0.717424i | ||||||||
\(441\) | 3.62003e11 | 0.455762 | ||||||||
\(442\) | 6.88672e11 | + | 9.05208e11i | 0.858246 | + | 1.12810i | ||||
\(443\) | −4.92953e11 | −0.608119 | −0.304060 | − | 0.952653i | \(-0.598342\pi\) | ||||
−0.304060 | + | 0.952653i | \(0.598342\pi\) | |||||||
\(444\) | 1.49399e12i | 1.82442i | ||||||||
\(445\) | −9.38371e10 | − | 9.38371e10i | −0.113437 | − | 0.113437i | ||||
\(446\) | 3.54911e11 | 0.424730 | ||||||||
\(447\) | 2.40249e11 | + | 2.40249e11i | 0.284628 | + | 0.284628i | ||||
\(448\) | 1.05103e11 | − | 1.05103e11i | 0.123272 | − | 0.123272i | ||||
\(449\) | −6.56424e11 | + | 6.56424e11i | −0.762212 | + | 0.762212i | −0.976722 | − | 0.214510i | \(-0.931185\pi\) |
0.214510 | + | 0.976722i | \(0.431185\pi\) | |||||||
\(450\) | 7.92241e11i | 0.910754i | ||||||||
\(451\) | − | 5.04644e11i | − | 0.574369i | ||||||
\(452\) | −5.01583e11 | + | 5.01583e11i | −0.565223 | + | 0.565223i | ||||
\(453\) | 6.50560e11 | − | 6.50560e11i | 0.725847 | − | 0.725847i | ||||
\(454\) | −2.28343e11 | − | 2.28343e11i | −0.252253 | − | 0.252253i | ||||
\(455\) | −1.27787e12 | −1.39777 | ||||||||
\(456\) | 5.03125e10 | + | 5.03125e10i | 0.0544922 | + | 0.0544922i | ||||
\(457\) | − | 1.66023e12i | − | 1.78052i | −0.455456 | − | 0.890258i | \(-0.650524\pi\) | ||
0.455456 | − | 0.890258i | \(-0.349476\pi\) | |||||||
\(458\) | 1.54900e12 | 1.64497 | ||||||||
\(459\) | −2.93953e11 | + | 2.16373e12i | −0.309116 | + | 2.27534i | ||||
\(460\) | 5.82790e11 | 0.606879 | ||||||||
\(461\) | 1.62302e11i | 0.167367i | 0.996492 | + | 0.0836837i | \(0.0266685\pi\) | ||||
−0.996492 | + | 0.0836837i | \(0.973331\pi\) | |||||||
\(462\) | 2.28125e12 | + | 2.28125e12i | 2.32962 | + | 2.32962i | ||||
\(463\) | −7.72644e10 | −0.0781385 | −0.0390692 | − | 0.999237i | \(-0.512439\pi\) | ||||
−0.0390692 | + | 0.999237i | \(0.512439\pi\) | |||||||
\(464\) | 4.66596e11 | + | 4.66596e11i | 0.467315 | + | 0.467315i | ||||
\(465\) | −2.98717e11 | + | 2.98717e11i | −0.296293 | + | 0.296293i | ||||
\(466\) | −6.51499e11 | + | 6.51499e11i | −0.639996 | + | 0.639996i | ||||
\(467\) | 6.91956e11i | 0.673213i | 0.941645 | + | 0.336607i | \(0.109279\pi\) | ||||
−0.941645 | + | 0.336607i | \(0.890721\pi\) | |||||||
\(468\) | − | 1.63433e12i | − | 1.57483i | ||||||
\(469\) | 1.14211e12 | − | 1.14211e12i | 1.09001 | − | 1.09001i | ||||
\(470\) | −2.10248e11 | + | 2.10248e11i | −0.198743 | + | 0.198743i | ||||
\(471\) | −8.19248e11 | − | 8.19248e11i | −0.767045 | − | 0.767045i | ||||
\(472\) | −6.52659e11 | −0.605268 | ||||||||
\(473\) | 9.40024e11 | + | 9.40024e11i | 0.863503 | + | 0.863503i | ||||
\(474\) | − | 4.26840e12i | − | 3.88385i | ||||||
\(475\) | 3.10508e10 | 0.0279867 | ||||||||
\(476\) | 1.03050e11 | − | 7.58528e11i | 0.0920059 | − | 0.677236i | ||||
\(477\) | 7.21790e11 | 0.638378 | ||||||||
\(478\) | 7.61824e11i | 0.667466i | ||||||||
\(479\) | −1.27262e12 | − | 1.27262e12i | −1.10456 | − | 1.10456i | −0.993853 | − | 0.110708i | \(-0.964688\pi\) |
−0.110708 | − | 0.993853i | \(-0.535312\pi\) | |||||||
\(480\) | −2.63777e12 | −2.26804 | ||||||||
\(481\) | 1.49376e12 | + | 1.49376e12i | 1.27241 | + | 1.27241i | ||||
\(482\) | −1.25085e12 | + | 1.25085e12i | −1.05558 | + | 1.05558i | ||||
\(483\) | −1.42208e12 | + | 1.42208e12i | −1.18895 | + | 1.18895i | ||||
\(484\) | 5.28997e11i | 0.438176i | ||||||||
\(485\) | 2.67277e11i | 0.219343i | ||||||||
\(486\) | 1.22741e12 | − | 1.22741e12i | 0.997989 | − | 0.997989i | ||||
\(487\) | 6.08524e11 | − | 6.08524e11i | 0.490227 | − | 0.490227i | −0.418151 | − | 0.908378i | \(-0.637322\pi\) |
0.908378 | + | 0.418151i | \(0.137322\pi\) | |||||||
\(488\) | −1.38361e11 | − | 1.38361e11i | −0.110440 | − | 0.110440i | ||||
\(489\) | −4.03604e11 | −0.319202 | ||||||||
\(490\) | 2.64731e11 | + | 2.64731e11i | 0.207455 | + | 0.207455i | ||||
\(491\) | − | 5.49516e11i | − | 0.426692i | −0.976977 | − | 0.213346i | \(-0.931564\pi\) | ||
0.976977 | − | 0.213346i | \(-0.0684361\pi\) | |||||||
\(492\) | 6.45249e11 | 0.496460 | ||||||||
\(493\) | 6.95671e11 | + | 9.45104e10i | 0.530387 | + | 0.0720557i | ||||
\(494\) | −1.66757e11 | −0.125983 | ||||||||
\(495\) | − | 4.53642e12i | − | 3.39617i | ||||||
\(496\) | −2.37817e11 | − | 2.37817e11i | −0.176431 | − | 0.176431i | ||||
\(497\) | −5.01758e10 | −0.0368885 | ||||||||
\(498\) | −1.35389e12 | − | 1.35389e12i | −0.986393 | − | 0.986393i | ||||
\(499\) | 9.20735e11 | − | 9.20735e11i | 0.664786 | − | 0.664786i | −0.291718 | − | 0.956504i | \(-0.594227\pi\) |
0.956504 | + | 0.291718i | \(0.0942269\pi\) | |||||||
\(500\) | 4.84213e11 | − | 4.84213e11i | 0.346474 | − | 0.346474i | ||||
\(501\) | 1.13546e12i | 0.805196i | ||||||||
\(502\) | 2.91235e12i | 2.04681i | ||||||||
\(503\) | 1.09584e12 | − | 1.09584e12i | 0.763294 | − | 0.763294i | −0.213622 | − | 0.976916i | \(-0.568526\pi\) |
0.976916 | + | 0.213622i | \(0.0685262\pi\) | |||||||
\(504\) | 1.22162e12 | − | 1.22162e12i | 0.843334 | − | 0.843334i | ||||
\(505\) | 2.19267e12 | + | 2.19267e12i | 1.50024 | + | 1.50024i | ||||
\(506\) | −2.08046e12 | −1.41085 | ||||||||
\(507\) | −4.51647e11 | − | 4.51647e11i | −0.303573 | − | 0.303573i | ||||
\(508\) | 6.00861e11i | 0.400302i | ||||||||
\(509\) | −1.50541e12 | −0.994091 | −0.497045 | − | 0.867725i | \(-0.665582\pi\) | ||||
−0.497045 | + | 0.867725i | \(0.665582\pi\) | |||||||
\(510\) | −3.21265e12 | + | 2.44415e12i | −2.10280 | + | 1.59978i | ||||
\(511\) | −2.20013e12 | −1.42743 | ||||||||
\(512\) | − | 1.17942e12i | − | 0.758499i | ||||||
\(513\) | −2.26377e11 | − | 2.26377e11i | −0.144312 | − | 0.144312i | ||||
\(514\) | 1.79981e12 | 1.13735 | ||||||||
\(515\) | 2.12286e12 | + | 2.12286e12i | 1.32981 | + | 1.32981i | ||||
\(516\) | −1.20194e12 | + | 1.20194e12i | −0.746376 | + | 0.746376i | ||||
\(517\) | 2.88304e11 | − | 2.88304e11i | 0.177478 | − | 0.177478i | ||||
\(518\) | − | 3.70130e12i | − | 2.25876i | ||||||
\(519\) | 1.21901e12i | 0.737485i | ||||||||
\(520\) | −7.21084e11 | + | 7.21084e11i | −0.432484 | + | 0.432484i | ||||
\(521\) | −1.53182e12 | + | 1.53182e12i | −0.910833 | + | 0.910833i | −0.996338 | − | 0.0855048i | \(-0.972750\pi\) |
0.0855048 | + | 0.996338i | \(0.472750\pi\) | |||||||
\(522\) | −1.85702e12 | − | 1.85702e12i | −1.09471 | − | 1.09471i | ||||
\(523\) | 2.82309e12 | 1.64994 | 0.824969 | − | 0.565178i | \(-0.191192\pi\) | ||||
0.824969 | + | 0.565178i | \(0.191192\pi\) | |||||||
\(524\) | −7.03283e11 | − | 7.03283e11i | −0.407511 | − | 0.407511i | ||||
\(525\) | − | 1.08609e12i | − | 0.623947i | ||||||
\(526\) | −1.18954e12 | −0.677553 | ||||||||
\(527\) | −3.54573e11 | − | 4.81705e10i | −0.200243 | − | 0.0272040i | ||||
\(528\) | 5.20267e12 | 2.91322 | ||||||||
\(529\) | 5.04240e11i | 0.279954i | ||||||||
\(530\) | 5.27842e11 | + | 5.27842e11i | 0.290578 | + | 0.290578i | ||||
\(531\) | 5.24912e12 | 2.86524 | ||||||||
\(532\) | 7.93597e10 | + | 7.93597e10i | 0.0429534 | + | 0.0429534i | ||||
\(533\) | 6.45146e11 | − | 6.45146e11i | 0.346246 | − | 0.346246i | ||||
\(534\) | −4.28316e11 | + | 4.28316e11i | −0.227944 | + | 0.227944i | ||||
\(535\) | − | 3.37146e12i | − | 1.77921i | ||||||
\(536\) | − | 1.28895e12i | − | 0.674522i | ||||||
\(537\) | −2.39396e12 | + | 2.39396e12i | −1.24232 | + | 1.24232i | ||||
\(538\) | −1.50401e12 | + | 1.50401e12i | −0.773981 | + | 0.773981i | ||||
\(539\) | −3.63015e11 | − | 3.63015e11i | −0.185257 | − | 0.185257i | ||||
\(540\) | 3.24497e12 | 1.64225 | ||||||||
\(541\) | −1.68440e11 | − | 1.68440e11i | −0.0845391 | − | 0.0845391i | 0.663573 | − | 0.748112i | \(-0.269039\pi\) |
−0.748112 | + | 0.663573i | \(0.769039\pi\) | |||||||
\(542\) | − | 1.74373e12i | − | 0.867925i | ||||||
\(543\) | −1.79804e12 | −0.887566 | ||||||||
\(544\) | −1.35282e12 | − | 1.77818e12i | −0.662283 | − | 0.870523i | ||||
\(545\) | −1.60475e12 | −0.779156 | ||||||||
\(546\) | 5.83279e12i | 2.80872i | ||||||||
\(547\) | −1.38372e12 | − | 1.38372e12i | −0.660852 | − | 0.660852i | 0.294729 | − | 0.955581i | \(-0.404771\pi\) |
−0.955581 | + | 0.294729i | \(0.904771\pi\) | |||||||
\(548\) | −1.32857e12 | −0.629320 | ||||||||
\(549\) | 1.11279e12 | + | 1.11279e12i | 0.522805 | + | 0.522805i | ||||
\(550\) | 7.94455e11 | − | 7.94455e11i | 0.370201 | − | 0.370201i | ||||
\(551\) | −7.27835e10 | + | 7.27835e10i | −0.0336396 | + | 0.0336396i | ||||
\(552\) | 1.60492e12i | 0.735746i | ||||||||
\(553\) | 4.06202e12i | 1.84705i | ||||||||
\(554\) | 1.35768e12 | − | 1.35768e12i | 0.612355 | − | 0.612355i | ||||
\(555\) | −5.30145e12 | + | 5.30145e12i | −2.37179 | + | 2.37179i | ||||
\(556\) | 1.83072e11 | + | 1.83072e11i | 0.0812429 | + | 0.0812429i | ||||
\(557\) | 5.54013e11 | 0.243877 | 0.121939 | − | 0.992538i | \(-0.461089\pi\) | ||||
0.121939 | + | 0.992538i | \(0.461089\pi\) | |||||||
\(558\) | 9.46497e11 | + | 9.46497e11i | 0.413300 | + | 0.413300i | ||||
\(559\) | 2.40349e12i | 1.04109i | ||||||||
\(560\) | 3.61064e12 | 1.55145 | ||||||||
\(561\) | 4.40537e12 | − | 3.35155e12i | 1.87780 | − | 1.42861i | ||||
\(562\) | 5.22788e12 | 2.21061 | ||||||||
\(563\) | 6.79128e11i | 0.284881i | 0.989803 | + | 0.142441i | \(0.0454950\pi\) | ||||
−0.989803 | + | 0.142441i | \(0.954505\pi\) | |||||||
\(564\) | 3.68632e11 | + | 3.68632e11i | 0.153404 | + | 0.153404i | ||||
\(565\) | −3.55974e12 | −1.46960 | ||||||||
\(566\) | −6.36159e11 | − | 6.36159e11i | −0.260551 | − | 0.260551i | ||||
\(567\) | −3.58962e12 | + | 3.58962e12i | −1.45856 | + | 1.45856i | ||||
\(568\) | −2.83135e10 | + | 2.83135e10i | −0.0114137 | + | 0.0114137i | ||||
\(569\) | − | 2.62380e12i | − | 1.04936i | −0.851299 | − | 0.524681i | \(-0.824185\pi\) | ||
0.851299 | − | 0.524681i | \(-0.175815\pi\) | |||||||
\(570\) | − | 5.91833e11i | − | 0.234835i | ||||||
\(571\) | 1.63294e12 | − | 1.63294e12i | 0.642847 | − | 0.642847i | −0.308408 | − | 0.951254i | \(-0.599796\pi\) |
0.951254 | + | 0.308408i | \(0.0997961\pi\) | |||||||
\(572\) | −1.63890e12 | + | 1.63890e12i | −0.640133 | + | 0.640133i | ||||
\(573\) | −5.46654e12 | − | 5.46654e12i | −2.11844 | − | 2.11844i | ||||
\(574\) | −1.59857e12 | −0.614651 | ||||||||
\(575\) | 4.95246e11 | + | 4.95246e11i | 0.188936 | + | 0.188936i | ||||
\(576\) | 9.53991e11i | 0.361113i | ||||||||
\(577\) | 4.55996e12 | 1.71266 | 0.856328 | − | 0.516432i | \(-0.172740\pi\) | ||||
0.856328 | + | 0.516432i | \(0.172740\pi\) | |||||||
\(578\) | −3.29531e12 | − | 9.12203e11i | −1.22806 | − | 0.339951i | ||||
\(579\) | −2.68226e12 | −0.991852 | ||||||||
\(580\) | − | 1.04331e12i | − | 0.382812i | ||||||
\(581\) | 1.28842e12 | + | 1.28842e12i | 0.469101 | + | 0.469101i | ||||
\(582\) | 1.21997e12 | 0.440755 | ||||||||
\(583\) | −7.23807e11 | − | 7.23807e11i | −0.259486 | − | 0.259486i | ||||
\(584\) | −1.24150e12 | + | 1.24150e12i | −0.441661 | + | 0.441661i | ||||
\(585\) | 5.79944e12 | − | 5.79944e12i | 2.04731 | − | 2.04731i | ||||
\(586\) | − | 4.08228e12i | − | 1.43009i | ||||||
\(587\) | − | 6.94817e11i | − | 0.241546i | −0.992680 | − | 0.120773i | \(-0.961463\pi\) | ||
0.992680 | − | 0.120773i | \(-0.0385372\pi\) | |||||||
\(588\) | 4.64158e11 | − | 4.64158e11i | 0.160128 | − | 0.160128i | ||||
\(589\) | 3.70966e10 | − | 3.70966e10i | 0.0127003 | − | 0.0127003i | ||||
\(590\) | 3.83866e12 | + | 3.83866e12i | 1.30420 | + | 1.30420i | ||||
\(591\) | −3.28258e12 | −1.10681 | ||||||||
\(592\) | −4.22062e12 | − | 4.22062e12i | −1.41231 | − | 1.41231i | ||||
\(593\) | 3.17510e12i | 1.05441i | 0.849737 | + | 0.527207i | \(0.176761\pi\) | ||||
−0.849737 | + | 0.527207i | \(0.823239\pi\) | |||||||
\(594\) | −1.15840e13 | −3.81785 | ||||||||
\(595\) | 3.05731e12 | − | 2.32597e12i | 1.00003 | − | 0.760812i | ||||
\(596\) | 4.27675e11 | 0.138837 | ||||||||
\(597\) | − | 4.52277e12i | − | 1.45720i | ||||||
\(598\) | −2.65970e12 | − | 2.65970e12i | −0.850505 | − | 0.850505i | ||||
\(599\) | 2.43909e12 | 0.774119 | 0.387060 | − | 0.922055i | \(-0.373491\pi\) | ||||
0.387060 | + | 0.922055i | \(0.373491\pi\) | |||||||
\(600\) | −6.12863e11 | − | 6.12863e11i | −0.193056 | − | 0.193056i | ||||
\(601\) | −1.67326e12 | + | 1.67326e12i | −0.523153 | + | 0.523153i | −0.918522 | − | 0.395369i | \(-0.870617\pi\) |
0.395369 | + | 0.918522i | \(0.370617\pi\) | |||||||
\(602\) | 2.97774e12 | − | 2.97774e12i | 0.924064 | − | 0.924064i | ||||
\(603\) | 1.03666e13i | 3.19308i | ||||||||
\(604\) | − | 1.15809e12i | − | 0.354058i | ||||||
\(605\) | −1.87715e12 | + | 1.87715e12i | −0.569639 | + | 0.569639i | ||||
\(606\) | 1.00083e13 | − | 1.00083e13i | 3.01464 | − | 3.01464i | ||||
\(607\) | 4.25015e12 | + | 4.25015e12i | 1.27074 | + | 1.27074i | 0.945703 | + | 0.325032i | \(0.105375\pi\) |
0.325032 | + | 0.945703i | \(0.394625\pi\) | |||||||
\(608\) | 3.27575e11 | 0.0972176 | ||||||||
\(609\) | 2.54580e12 | + | 2.54580e12i | 0.749975 | + | 0.749975i | ||||
\(610\) | 1.62757e12i | 0.475942i | ||||||||
\(611\) | 7.37146e11 | 0.213978 | ||||||||
\(612\) | 2.97480e12 | + | 3.91015e12i | 0.857188 | + | 1.12671i | ||||
\(613\) | −3.01272e12 | −0.861761 | −0.430880 | − | 0.902409i | \(-0.641797\pi\) | ||||
−0.430880 | + | 0.902409i | \(0.641797\pi\) | |||||||
\(614\) | − | 4.63559e11i | − | 0.131628i | ||||||
\(615\) | 2.28967e12 | + | 2.28967e12i | 0.645409 | + | 0.645409i | ||||
\(616\) | −2.45007e12 | −0.685592 | ||||||||
\(617\) | −7.14533e11 | − | 7.14533e11i | −0.198490 | − | 0.198490i | 0.600862 | − | 0.799352i | \(-0.294824\pi\) |
−0.799352 | + | 0.600862i | \(0.794824\pi\) | |||||||
\(618\) | 9.68971e12 | − | 9.68971e12i | 2.67216 | − | 2.67216i | ||||
\(619\) | −1.29214e11 | + | 1.29214e11i | −0.0353755 | + | 0.0353755i | −0.724573 | − | 0.689198i | \(-0.757963\pi\) |
0.689198 | + | 0.724573i | \(0.257963\pi\) | |||||||
\(620\) | 5.31758e11i | 0.144528i | ||||||||
\(621\) | − | 7.22120e12i | − | 1.94849i | ||||||
\(622\) | −5.09890e12 | + | 5.09890e12i | −1.36590 | + | 1.36590i | ||||
\(623\) | 4.07606e11 | − | 4.07606e11i | 0.108404 | − | 0.108404i | ||||
\(624\) | 6.65118e12 | + | 6.65118e12i | 1.75618 | + | 1.75618i | ||||
\(625\) | 4.63765e12 | 1.21573 | ||||||||
\(626\) | 3.74667e12 | + | 3.74667e12i | 0.975128 | + | 0.975128i | ||||
\(627\) | 8.11555e11i | 0.209708i | ||||||||
\(628\) | −1.45837e12 | −0.374154 | ||||||||
\(629\) | −6.29274e12 | − | 8.54900e11i | −1.60292 | − | 0.217765i | ||||
\(630\) | −1.43701e13 | −3.63436 | ||||||||
\(631\) | 6.42710e11i | 0.161392i | 0.996739 | + | 0.0806962i | \(0.0257143\pi\) | ||||
−0.996739 | + | 0.0806962i | \(0.974286\pi\) | |||||||
\(632\) | 2.29214e12 | + | 2.29214e12i | 0.571497 | + | 0.571497i | ||||
\(633\) | −4.28620e12 | −1.06110 | ||||||||
\(634\) | 8.43527e9 | + | 8.43527e9i | 0.00207347 | + | 0.00207347i | ||||
\(635\) | −2.13216e12 | + | 2.13216e12i | −0.520401 | + | 0.520401i | ||||
\(636\) | 9.25475e11 | − | 9.25475e11i | 0.224289 | − | 0.224289i | ||||
\(637\) | − | 9.28168e11i | − | 0.223357i | ||||||
\(638\) | 3.72443e12i | 0.889951i | ||||||||
\(639\) | 2.27716e11 | − | 2.27716e11i | 0.0540306 | − | 0.0540306i | ||||
\(640\) | 3.06663e12 | − | 3.06663e12i | 0.722523 | − | 0.722523i | ||||
\(641\) | −4.54040e12 | − | 4.54040e12i | −1.06226 | − | 1.06226i | −0.997928 | − | 0.0643359i | \(-0.979507\pi\) |
−0.0643359 | − | 0.997928i | \(-0.520493\pi\) | |||||||
\(642\) | −1.53889e13 | −3.57520 | ||||||||
\(643\) | 4.97107e12 | + | 4.97107e12i | 1.14683 | + | 1.14683i | 0.987172 | + | 0.159663i | \(0.0510409\pi\) |
0.159663 | + | 0.987172i | \(0.448959\pi\) | |||||||
\(644\) | 2.53150e12i | 0.579951i | ||||||||
\(645\) | −8.53015e12 | −1.94061 | ||||||||
\(646\) | 3.98968e11 | − | 3.03530e11i | 0.0901345 | − | 0.0685733i | ||||
\(647\) | 6.41347e12 | 1.43888 | 0.719439 | − | 0.694556i | \(-0.244399\pi\) | ||||
0.719439 | + | 0.694556i | \(0.244399\pi\) | |||||||
\(648\) | 4.05114e12i | 0.902589i | ||||||||
\(649\) | −5.26379e12 | − | 5.26379e12i | −1.16466 | − | 1.16466i | ||||
\(650\) | 2.03129e12 | 0.446336 | ||||||||
\(651\) | −1.29756e12 | − | 1.29756e12i | −0.283147 | − | 0.283147i | ||||
\(652\) | −3.59236e11 | + | 3.59236e11i | −0.0778512 | + | 0.0778512i | ||||
\(653\) | −3.08063e11 | + | 3.08063e11i | −0.0663025 | + | 0.0663025i | −0.739480 | − | 0.673178i | \(-0.764929\pi\) |
0.673178 | + | 0.739480i | \(0.264929\pi\) | |||||||
\(654\) | 7.32484e12i | 1.56566i | ||||||||
\(655\) | − | 4.99121e12i | − | 1.05955i | ||||||
\(656\) | −1.82287e12 | + | 1.82287e12i | −0.384315 | + | 0.384315i | ||||
\(657\) | 9.98498e12 | − | 9.98498e12i | 2.09075 | − | 2.09075i | ||||
\(658\) | −9.13268e11 | − | 9.13268e11i | −0.189925 | − | 0.189925i | ||||
\(659\) | 1.79536e12 | 0.370823 | 0.185412 | − | 0.982661i | \(-0.440638\pi\) | ||||
0.185412 | + | 0.982661i | \(0.440638\pi\) | |||||||
\(660\) | −5.81657e12 | − | 5.81657e12i | −1.19322 | − | 1.19322i | ||||
\(661\) | 1.53076e12i | 0.311889i | 0.987766 | + | 0.155945i | \(0.0498422\pi\) | ||||
−0.987766 | + | 0.155945i | \(0.950158\pi\) | |||||||
\(662\) | 5.82815e12 | 1.17942 | ||||||||
\(663\) | 9.91658e12 | + | 1.34722e12i | 1.99320 | + | 0.270786i | ||||
\(664\) | 1.45408e12 | 0.290289 | ||||||||
\(665\) | 5.63217e11i | 0.111681i | ||||||||
\(666\) | 1.67978e13 | + | 1.67978e13i | 3.30841 | + | 3.30841i | ||||
\(667\) | −2.32172e12 | −0.454197 | ||||||||
\(668\) | 1.01064e12 | + | 1.01064e12i | 0.196381 | + | 0.196381i | ||||
\(669\) | 2.20814e12 | − | 2.20814e12i | 0.426195 | − | 0.426195i | ||||
\(670\) | −7.58108e12 | + | 7.58108e12i | −1.45343 | + | 1.45343i | ||||
\(671\) | − | 2.23181e12i | − | 0.425016i | ||||||
\(672\) | − | 1.14578e13i | − | 2.16741i | ||||||
\(673\) | −7.08953e12 | + | 7.08953e12i | −1.33214 | + | 1.33214i | −0.428687 | + | 0.903453i | \(0.641024\pi\) |
−0.903453 | + | 0.428687i | \(0.858976\pi\) | |||||||
\(674\) | −6.57083e12 | + | 6.57083e12i | −1.22645 | + | 1.22645i | ||||
\(675\) | 2.75752e12 | + | 2.75752e12i | 0.511272 | + | 0.511272i | ||||
\(676\) | −8.03993e11 | −0.148079 | ||||||||
\(677\) | 1.19396e12 | + | 1.19396e12i | 0.218444 | + | 0.218444i | 0.807842 | − | 0.589398i | \(-0.200635\pi\) |
−0.589398 | + | 0.807842i | \(0.700635\pi\) | |||||||
\(678\) | 1.62483e13i | 2.95307i | ||||||||
\(679\) | −1.16099e12 | −0.209610 | ||||||||
\(680\) | 4.12688e11 | − | 3.03771e12i | 0.0740170 | − | 0.544824i | ||||
\(681\) | −2.84135e12 | −0.506247 | ||||||||
\(682\) | − | 1.89828e12i | − | 0.335994i | ||||||
\(683\) | −6.90549e12 | − | 6.90549e12i | −1.21423 | − | 1.21423i | −0.969621 | − | 0.244610i | \(-0.921340\pi\) |
−0.244610 | − | 0.969621i | \(-0.578660\pi\) | |||||||
\(684\) | −7.20327e11 | −0.125828 | ||||||||
\(685\) | −4.71444e12 | − | 4.71444e12i | −0.818130 | − | 0.818130i | ||||
\(686\) | 4.57711e12 | − | 4.57711e12i | 0.789102 | − | 0.789102i | ||||
\(687\) | 9.63737e12 | − | 9.63737e12i | 1.65064 | − | 1.65064i | ||||
\(688\) | − | 6.79108e12i | − | 1.15556i | ||||||
\(689\) | − | 1.85065e12i | − | 0.312852i | ||||||
\(690\) | 9.43946e12 | − | 9.43946e12i | 1.58535 | − | 1.58535i | ||||
\(691\) | −1.66059e12 | + | 1.66059e12i | −0.277084 | + | 0.277084i | −0.831944 | − | 0.554860i | \(-0.812772\pi\) |
0.554860 | + | 0.831944i | \(0.312772\pi\) | |||||||
\(692\) | 1.08500e12 | + | 1.08500e12i | 0.179867 | + | 0.179867i | ||||
\(693\) | 1.97051e13 | 3.24549 | ||||||||
\(694\) | −1.13237e12 | − | 1.13237e12i | −0.185298 | − | 0.185298i | ||||
\(695\) | 1.29927e12i | 0.211235i | ||||||||
\(696\) | 2.87312e12 | 0.464100 | ||||||||
\(697\) | −3.69227e11 | + | 2.71781e12i | −0.0592579 | + | 0.436185i | ||||
\(698\) | −5.20989e12 | −0.830767 | ||||||||
\(699\) | 8.10681e12i | 1.28441i | ||||||||
\(700\) | −9.66692e11 | − | 9.66692e11i | −0.152176 | − | 0.152176i | ||||
\(701\) | 9.78498e12 | 1.53048 | 0.765242 | − | 0.643742i | \(-0.222619\pi\) | ||||
0.765242 | + | 0.643742i | \(0.222619\pi\) | |||||||
\(702\) | −1.48092e13 | − | 1.48092e13i | −2.30151 | − | 2.30151i | ||||
\(703\) | 6.58368e11 | − | 6.58368e11i | 0.101665 | − | 0.101665i | ||||
\(704\) | 9.56657e11 | − | 9.56657e11i | 0.146784 | − | 0.146784i | ||||
\(705\) | 2.61619e12i | 0.398857i | ||||||||
\(706\) | 3.41066e12i | 0.516675i | ||||||||
\(707\) | −9.52442e12 | + | 9.52442e12i | −1.43368 | + | 1.43368i | ||||
\(708\) | 6.73040e12 | − | 6.73040e12i | 1.00668 | − | 1.00668i | ||||
\(709\) | −3.82775e12 | − | 3.82775e12i | −0.568899 | − | 0.568899i | 0.362921 | − | 0.931820i | \(-0.381780\pi\) |
−0.931820 | + | 0.362921i | \(0.881780\pi\) | |||||||
\(710\) | 3.33056e11 | 0.0491875 | ||||||||
\(711\) | −1.84349e13 | − | 1.84349e13i | −2.70538 | − | 2.70538i | ||||
\(712\) | − | 4.60012e11i | − | 0.0670826i | ||||||
\(713\) | 1.18335e12 | 0.171478 | ||||||||
\(714\) | −1.06168e13 | − | 1.39550e13i | −1.52880 | − | 2.00950i | ||||
\(715\) | −1.16313e13 | −1.66437 | ||||||||
\(716\) | 4.26158e12i | 0.605985i | ||||||||
\(717\) | 4.73981e12 | + | 4.73981e12i | 0.669769 | + | 0.669769i | ||||
\(718\) | 1.24950e13 | 1.75460 | ||||||||
\(719\) | −3.47724e11 | − | 3.47724e11i | −0.0485237 | − | 0.0485237i | 0.682429 | − | 0.730952i | \(-0.260924\pi\) |
−0.730952 | + | 0.682429i | \(0.760924\pi\) | |||||||
\(720\) | −1.63864e13 | + | 1.63864e13i | −2.27241 | + | 2.27241i | ||||
\(721\) | −9.22120e12 | + | 9.22120e12i | −1.27080 | + | 1.27080i | ||||
\(722\) | − | 9.23052e12i | − | 1.26418i | ||||||
\(723\) | 1.55647e13i | 2.11845i | ||||||||
\(724\) | −1.60038e12 | + | 1.60038e12i | −0.216471 | + | 0.216471i | ||||
\(725\) | 8.86585e11 | − | 8.86585e11i | 0.119179 | − | 0.119179i | ||||
\(726\) | 8.56817e12 | + | 8.56817e12i | 1.14465 | + | 1.14465i | ||||
\(727\) | −4.85245e11 | −0.0644253 | −0.0322127 | − | 0.999481i | \(-0.510255\pi\) | ||||
−0.0322127 | + | 0.999481i | \(0.510255\pi\) | |||||||
\(728\) | −3.13221e12 | − | 3.13221e12i | −0.413295 | − | 0.413295i | ||||
\(729\) | − | 9.18785e11i | − | 0.120487i | ||||||
\(730\) | 1.46040e13 | 1.90334 | ||||||||
\(731\) | −4.37481e12 | − | 5.75036e12i | −0.566671 | − | 0.744847i | ||||
\(732\) | 2.85364e12 | 0.367366 | ||||||||
\(733\) | − | 4.53070e12i | − | 0.579693i | −0.957073 | − | 0.289846i | \(-0.906396\pi\) | ||
0.957073 | − | 0.289846i | \(-0.0936042\pi\) | |||||||
\(734\) | −8.50480e12 | − | 8.50480e12i | −1.08151 | − | 1.08151i | ||||
\(735\) | 3.29414e12 | 0.416341 | ||||||||
\(736\) | 5.22467e12 | + | 5.22467e12i | 0.656309 | + | 0.656309i | ||||
\(737\) | 1.03956e13 | − | 1.03956e13i | 1.29791 | − | 1.29791i | ||||
\(738\) | 7.25490e12 | − | 7.25490e12i | 0.900281 | − | 0.900281i | ||||
\(739\) | − | 3.39131e12i | − | 0.418281i | −0.977886 | − | 0.209140i | \(-0.932933\pi\) | ||
0.977886 | − | 0.209140i | \(-0.0670665\pi\) | |||||||
\(740\) | 9.43730e12i | 1.15692i | ||||||||
\(741\) | −1.03751e12 | + | 1.03751e12i | −0.126418 | + | 0.126418i | ||||
\(742\) | −2.29282e12 | + | 2.29282e12i | −0.277685 | + | 0.277685i | ||||
\(743\) | 7.73209e12 | + | 7.73209e12i | 0.930780 | + | 0.930780i | 0.997755 | − | 0.0669745i | \(-0.0213346\pi\) |
−0.0669745 | + | 0.997755i | \(0.521335\pi\) | |||||||
\(744\) | −1.46438e12 | −0.175217 | ||||||||
\(745\) | 1.51761e12 | + | 1.51761e12i | 0.180491 | + | 0.180491i | ||||
\(746\) | 9.30316e12i | 1.09978i | ||||||||
\(747\) | −1.16947e13 | −1.37418 | ||||||||
\(748\) | 9.37968e11 | − | 6.90419e12i | 0.109555 | − | 0.806409i | ||||
\(749\) | 1.46448e13 | 1.70026 | ||||||||
\(750\) | − | 1.56856e13i | − | 1.81019i | ||||||
\(751\) | 3.63333e12 | + | 3.63333e12i | 0.416798 | + | 0.416798i | 0.884098 | − | 0.467301i | \(-0.154773\pi\) |
−0.467301 | + | 0.884098i | \(0.654773\pi\) | |||||||
\(752\) | −2.08282e12 | −0.237504 | ||||||||
\(753\) | 1.81197e13 | + | 1.81197e13i | 2.05387 | + | 2.05387i | ||||
\(754\) | −4.76137e12 | + | 4.76137e12i | −0.536489 | + | 0.536489i | ||||
\(755\) | 4.10947e12 | − | 4.10947e12i | 0.460283 | − | 0.460283i | ||||
\(756\) | 1.40954e13i | 1.56938i | ||||||||
\(757\) | 8.25749e12i | 0.913938i | 0.889483 | + | 0.456969i | \(0.151065\pi\) | ||||
−0.889483 | + | 0.456969i | \(0.848935\pi\) | |||||||
\(758\) | 8.78849e12 | − | 8.78849e12i | 0.966947 | − | 0.966947i | ||||
\(759\) | −1.29439e13 | + | 1.29439e13i | −1.41572 | + | 1.41572i | ||||
\(760\) | 3.17815e11 | + | 3.17815e11i | 0.0345552 | + | 0.0345552i | ||||
\(761\) | −1.37466e13 | −1.48581 | −0.742906 | − | 0.669396i | \(-0.766553\pi\) | ||||
−0.742906 | + | 0.669396i | \(0.766553\pi\) | |||||||
\(762\) | 9.73215e12 | + | 9.73215e12i | 1.04571 | + | 1.04571i | ||||
\(763\) | − | 6.97067e12i | − | 0.744585i | ||||||
\(764\) | −9.73119e12 | −1.03335 | ||||||||
\(765\) | −3.31911e12 | + | 2.44313e13i | −0.350385 | + | 2.57911i | ||||
\(766\) | −2.07756e12 | −0.218033 | ||||||||
\(767\) | − | 1.34586e13i | − | 1.40418i | ||||||
\(768\) | −1.59587e13 | − | 1.59587e13i | −1.65528 | − | 1.65528i | ||||
\(769\) | 1.41070e13 | 1.45468 | 0.727338 | − | 0.686280i | \(-0.240757\pi\) | ||||
0.727338 | + | 0.686280i | \(0.240757\pi\) | |||||||
\(770\) | 1.44103e13 | + | 1.44103e13i | 1.47728 | + | 1.47728i | ||||
\(771\) | 1.11978e13 | − | 1.11978e13i | 1.14127 | − | 1.14127i | ||||
\(772\) | −2.38739e12 | + | 2.38739e12i | −0.241906 | + | 0.241906i | ||||
\(773\) | − | 3.76516e12i | − | 0.379294i | −0.981852 | − | 0.189647i | \(-0.939266\pi\) | ||
0.981852 | − | 0.189647i | \(-0.0607343\pi\) | |||||||
\(774\) | 2.70281e13i | 2.70696i | ||||||||
\(775\) | −4.51879e11 | + | 4.51879e11i | −0.0449950 | + | 0.0449950i | ||||
\(776\) | −6.55128e11 | + | 6.55128e11i | −0.0648557 | + | 0.0648557i | ||||
\(777\) | −2.30282e13 | − | 2.30282e13i | −2.26655 | − | 2.26655i | ||||
\(778\) | 8.11509e12 | 0.794118 | ||||||||
\(779\) | −2.84346e11 | − | 2.84346e11i | −0.0276649 | − | 0.0276649i | ||||
\(780\) | − | 1.48720e13i | − | 1.43861i | ||||||
\(781\) | −4.56705e11 | −0.0439244 | ||||||||
\(782\) | 1.12045e13 | + | 1.52219e12i | 1.07143 | + | 0.145558i | ||||
\(783\) | −1.29273e13 | −1.22908 | ||||||||
\(784\) | 2.62255e12i | 0.247914i | ||||||||
\(785\) | −5.17505e12 | − | 5.17505e12i | −0.486408 | − | 0.486408i | ||||
\(786\) | −2.27822e13 | −2.12909 | ||||||||
\(787\) | 4.19600e12 | + | 4.19600e12i | 0.389897 | + | 0.389897i | 0.874651 | − | 0.484754i | \(-0.161091\pi\) |
−0.484754 | + | 0.874651i | \(0.661091\pi\) | |||||||
\(788\) | −2.92172e12 | + | 2.92172e12i | −0.269942 | + | 0.269942i | ||||
\(789\) | −7.40092e12 | + | 7.40092e12i | −0.679890 | + | 0.679890i | ||||
\(790\) | − | 2.69628e13i | − | 2.46287i | ||||||
\(791\) | − | 1.54627e13i | − | 1.40440i | ||||||
\(792\) | 1.11193e13 | − | 1.11193e13i | 1.00419 | − | 1.00419i | ||||
\(793\) | 2.85318e12 | − | 2.85318e12i | 0.256213 | − | 0.256213i | ||||
\(794\) | −1.25053e13 | − | 1.25053e13i | −1.11661 | − | 1.11661i | ||||
\(795\) | 6.56811e12 | 0.583161 | ||||||||
\(796\) | −4.02558e12 | − | 4.02558e12i | −0.355402 | − | 0.355402i | ||||
\(797\) | 1.41517e13i | 1.24235i | 0.783670 | + | 0.621177i | \(0.213345\pi\) | ||||
−0.783670 | + | 0.621177i | \(0.786655\pi\) | |||||||
\(798\) | 2.57078e12 | 0.224415 | ||||||||
\(799\) | −1.76363e12 | + | 1.34175e12i | −0.153090 | + | 0.116469i | ||||
\(800\) | −3.99024e12 | −0.344424 | ||||||||
\(801\) | 3.69973e12i | 0.317558i | ||||||||
\(802\) | 1.84727e13 | + | 1.84727e13i | 1.57669 | + | 1.57669i | ||||
\(803\) | −2.00258e13 | −1.69969 | ||||||||
\(804\) | 1.32920e13 | + | 1.32920e13i | 1.12186 | + | 1.12186i | ||||
\(805\) | −8.98305e12 | + | 8.98305e12i | −0.753949 | + | 0.753949i | ||||
\(806\) | 2.42680e12 | − | 2.42680e12i | 0.202547 | − | 0.202547i | ||||
\(807\) | 1.87149e13i | 1.55330i | ||||||||
\(808\) | 1.07490e13i | 0.887189i | ||||||||
\(809\) | 4.23447e12 | − | 4.23447e12i | 0.347561 | − | 0.347561i | −0.511639 | − | 0.859200i | \(-0.670962\pi\) |
0.859200 | + | 0.511639i | \(0.170962\pi\) | |||||||
\(810\) | 2.38271e13 | − | 2.38271e13i | 1.94486 | − | 1.94486i | ||||
\(811\) | 1.38391e13 | + | 1.38391e13i | 1.12335 | + | 1.12335i | 0.991235 | + | 0.132113i | \(0.0421763\pi\) |
0.132113 | + | 0.991235i | \(0.457824\pi\) | |||||||
\(812\) | 4.53188e12 | 0.365827 | ||||||||
\(813\) | −1.08489e13 | − | 1.08489e13i | −0.870919 | − | 0.870919i | ||||
\(814\) | − | 3.36895e13i | − | 2.68959i | ||||||
\(815\) | −2.54950e12 | −0.202416 | ||||||||
\(816\) | −2.80194e13 | − | 3.80657e12i | −2.21235 | − | 0.300558i | ||||
\(817\) | 1.05933e12 | 0.0831824 | ||||||||
\(818\) | − | 1.45693e13i | − | 1.13775i | ||||||
\(819\) | 2.51914e13 | + | 2.51914e13i | 1.95647 | + | 1.95647i | ||||
\(820\) | 4.07593e12 | 0.314821 | ||||||||
\(821\) | 2.49777e12 | + | 2.49777e12i | 0.191870 | + | 0.191870i | 0.796504 | − | 0.604633i | \(-0.206680\pi\) |
−0.604633 | + | 0.796504i | \(0.706680\pi\) | |||||||
\(822\) | −2.15189e13 | + | 2.15189e13i | −1.64398 | + | 1.64398i | ||||
\(823\) | 1.00995e13 | − | 1.00995e13i | 0.767365 | − | 0.767365i | −0.210277 | − | 0.977642i | \(-0.567437\pi\) |
0.977642 | + | 0.210277i | \(0.0674367\pi\) | |||||||
\(824\) | 1.04068e13i | 0.786401i | ||||||||
\(825\) | − | 9.88566e12i | − | 0.742956i | ||||||
\(826\) | −1.66742e13 | + | 1.66742e13i | −1.24634 | + | 1.24634i | ||||
\(827\) | −1.39869e12 | + | 1.39869e12i | −0.103979 | + | 0.103979i | −0.757182 | − | 0.653203i | \(-0.773425\pi\) |
0.653203 | + | 0.757182i | \(0.273425\pi\) | |||||||
\(828\) | −1.14889e13 | − | 1.14889e13i | −0.849456 | − | 0.849456i | ||||
\(829\) | 1.38516e13 | 1.01860 | 0.509301 | − | 0.860588i | \(-0.329904\pi\) | ||||
0.509301 | + | 0.860588i | \(0.329904\pi\) | |||||||
\(830\) | −8.55226e12 | − | 8.55226e12i | −0.625503 | − | 0.625503i | ||||
\(831\) | − | 1.68940e13i | − | 1.22893i | ||||||
\(832\) | 2.44601e12 | 0.176972 | ||||||||
\(833\) | 1.68944e12 | + | 2.22065e12i | 0.121574 | + | 0.159800i | ||||
\(834\) | 5.93044e12 | 0.424463 | ||||||||
\(835\) | 7.17249e12i | 0.510600i | ||||||||
\(836\) | 7.22339e11 | + | 7.22339e11i | 0.0511462 | + | 0.0511462i | ||||
\(837\) | 6.58887e12 | 0.464030 | ||||||||
\(838\) | −1.74361e13 | − | 1.74361e13i | −1.22138 | − | 1.22138i | ||||
\(839\) | 1.04101e13 | − | 1.04101e13i | 0.725316 | − | 0.725316i | −0.244367 | − | 0.969683i | \(-0.578580\pi\) |
0.969683 | + | 0.244367i | \(0.0785801\pi\) | |||||||
\(840\) | 1.11165e13 | − | 1.11165e13i | 0.770388 | − | 0.770388i | ||||
\(841\) | − | 1.03508e13i | − | 0.713497i | ||||||
\(842\) | 5.59635e12i | 0.383708i | ||||||||
\(843\) | 3.25261e13 | − | 3.25261e13i | 2.21824 | − | 2.21824i | ||||
\(844\) | −3.81501e12 | + | 3.81501e12i | −0.258794 | + | 0.258794i | ||||
\(845\) | −2.85297e12 | − | 2.85297e12i | −0.192505 | − | 0.192505i | ||||
\(846\) | 8.28949e12 | 0.556366 | ||||||||
\(847\) | −8.15389e12 | − | 8.15389e12i | −0.544364 | − | 0.544364i | ||||
\(848\) | 5.22905e12i | 0.347249i | ||||||||
\(849\) | −7.91594e12 | −0.522899 | ||||||||
\(850\) | −4.85988e12 | + | 3.69734e12i | −0.319330 | + | 0.242943i | ||||
\(851\) | 2.10013e13 | 1.37266 | ||||||||
\(852\) | − | 5.83953e11i | − | 0.0379664i | ||||||
\(853\) | −8.42766e12 | − | 8.42766e12i | −0.545050 | − | 0.545050i | 0.379955 | − | 0.925005i | \(-0.375939\pi\) |
−0.925005 | + | 0.379955i | \(0.875939\pi\) | |||||||
\(854\) | −7.06975e12 | −0.454825 | ||||||||
\(855\) | −2.55608e12 | − | 2.55608e12i | −0.163579 | − | 0.163579i | ||||
\(856\) | 8.26387e12 | − | 8.26387e12i | 0.526079 | − | 0.526079i | ||||
\(857\) | −1.89301e13 | + | 1.89301e13i | −1.19878 | + | 1.19878i | −0.224249 | + | 0.974532i | \(0.571993\pi\) |
−0.974532 | + | 0.224249i | \(0.928007\pi\) | |||||||
\(858\) | 5.30905e13i | 3.34445i | ||||||||
\(859\) | − | 1.36188e13i | − | 0.853431i | −0.904386 | − | 0.426716i | \(-0.859671\pi\) | ||
0.904386 | − | 0.426716i | \(-0.140329\pi\) | |||||||
\(860\) | −7.59242e12 | + | 7.59242e12i | −0.473301 | + | 0.473301i | ||||
\(861\) | −9.94578e12 | + | 9.94578e12i | −0.616772 | + | 0.616772i | ||||
\(862\) | 3.84716e12 | + | 3.84716e12i | 0.237333 | + | 0.237333i | ||||
\(863\) | −1.57643e13 | −0.967446 | −0.483723 | − | 0.875221i | \(-0.660716\pi\) | ||||
−0.483723 | + | 0.875221i | \(0.660716\pi\) | |||||||
\(864\) | 2.90909e13 | + | 2.90909e13i | 1.77601 | + | 1.77601i | ||||
\(865\) | 7.70026e12i | 0.467663i | ||||||||
\(866\) | 6.48293e12 | 0.391689 | ||||||||
\(867\) | −2.61777e13 | + | 1.48269e13i | −1.57342 | + | 0.891175i | ||||
\(868\) | −2.30983e12 | −0.138115 | ||||||||
\(869\) | 3.69729e13i | 2.19935i | ||||||||
\(870\) | −1.68985e13 | − | 1.68985e13i | −1.00002 | − | 1.00002i | ||||
\(871\) | 2.65798e13 | 1.56484 | ||||||||
\(872\) | −3.93345e12 | − | 3.93345e12i | −0.230382 | − | 0.230382i | ||||
\(873\) | 5.26898e12 | − | 5.26898e12i | 0.307017 | − | 0.307017i | ||||
\(874\) | −1.17225e12 | + | 1.17225e12i | −0.0679547 | + | 0.0679547i | ||||
\(875\) | 1.49272e13i | 0.860878i | ||||||||
\(876\) | − | 2.56054e13i | − | 1.46914i | ||||||
\(877\) | −1.83130e11 | + | 1.83130e11i | −0.0104535 | + | 0.0104535i | −0.712314 | − | 0.701861i | \(-0.752353\pi\) |
0.701861 | + | 0.712314i | \(0.252353\pi\) | |||||||
\(878\) | −1.86885e13 | + | 1.86885e13i | −1.06133 | + | 1.06133i | ||||
\(879\) | −2.53986e13 | − | 2.53986e13i | −1.43502 | − | 1.43502i | ||||
\(880\) | 3.28643e13 | 1.84737 | ||||||||
\(881\) | −5.24443e12 | − | 5.24443e12i | −0.293296 | − | 0.293296i | 0.545085 | − | 0.838381i | \(-0.316497\pi\) |
−0.838381 | + | 0.545085i | \(0.816497\pi\) | |||||||
\(882\) | − | 1.04376e13i | − | 0.580754i | ||||||
\(883\) | 1.94425e13 | 1.07629 | 0.538146 | − | 0.842852i | \(-0.319125\pi\) | ||||
0.538146 | + | 0.842852i | \(0.319125\pi\) | |||||||
\(884\) | 1.00255e13 | − | 7.62732e12i | 0.552170 | − | 0.420085i | ||||
\(885\) | 4.77657e13 | 2.61741 | ||||||||
\(886\) | 1.42133e13i | 0.774893i | ||||||||
\(887\) | 2.08155e13 | + | 2.08155e13i | 1.12910 | + | 1.12910i | 0.990325 | + | 0.138771i | \(0.0443152\pi\) |
0.138771 | + | 0.990325i | \(0.455685\pi\) | |||||||
\(888\) | −2.59890e13 | −1.40259 | ||||||||
\(889\) | −9.26159e12 | − | 9.26159e12i | −0.497311 | − | 0.497311i | ||||
\(890\) | −2.70560e12 | + | 2.70560e12i | −0.144547 | + | 0.144547i | ||||
\(891\) | −3.26731e13 | + | 3.26731e13i | −1.73676 | + | 1.73676i | ||||
\(892\) | − | 3.93079e12i | − | 0.207892i | ||||||
\(893\) | − | 3.24895e11i | − | 0.0170967i | ||||||
\(894\) | 6.92706e12 | − | 6.92706e12i | 0.362686 | − | 0.362686i | ||||
\(895\) | −1.51222e13 | + | 1.51222e13i | −0.787794 | + | 0.787794i | ||||
\(896\) | 1.33207e13 | + | 1.33207e13i | 0.690465 | + | 0.690465i | ||||
\(897\) | −3.30955e13 | −1.70688 | ||||||||
\(898\) | 1.89266e13 | + | 1.89266e13i | 0.971246 | + | 0.971246i | ||||
\(899\) | − | 2.11842e12i | − | 0.108167i | ||||||
\(900\) | 8.77440e12 | 0.445785 | ||||||||
\(901\) | 3.36855e12 | + | 4.42771e12i | 0.170287 | + | 0.223829i | ||||
\(902\) | −1.45504e13 | −0.731887 | ||||||||
\(903\) | − | 3.70529e13i | − | 1.85450i | ||||||
\(904\) | −8.72536e12 | − | 8.72536e12i | −0.434535 | − | 0.434535i | ||||
\(905\) | −1.13579e13 | −0.562834 | ||||||||
\(906\) | −1.87575e13 | − | 1.87575e13i | −0.924908 | − | 0.924908i | ||||
\(907\) | −2.19209e12 | + | 2.19209e12i | −0.107554 | + | 0.107554i | −0.758836 | − | 0.651282i | \(-0.774231\pi\) |
0.651282 | + | 0.758836i | \(0.274231\pi\) | |||||||
\(908\) | −2.52899e12 | + | 2.52899e12i | −0.123470 | + | 0.123470i | ||||
\(909\) | − | 8.64505e13i | − | 4.19982i | ||||||
\(910\) | 3.68447e13i | 1.78110i | ||||||||
\(911\) | −2.24498e13 | + | 2.24498e13i | −1.07989 | + | 1.07989i | −0.0833713 | + | 0.996519i | \(0.526569\pi\) |
−0.996519 | + | 0.0833713i | \(0.973431\pi\) | |||||||
\(912\) | 2.93149e12 | − | 2.93149e12i | 0.140317 | − | 0.140317i | ||||
\(913\) | 1.17273e13 | + | 1.17273e13i | 0.558575 | + | 0.558575i | ||||
\(914\) | −4.78693e13 | −2.26882 | ||||||||
\(915\) | 1.01262e13 | + | 1.01262e13i | 0.477584 | + | 0.477584i | ||||
\(916\) | − | 1.71558e13i | − | 0.805160i | ||||||
\(917\) | 2.16806e13 | 1.01253 | ||||||||
\(918\) | 6.23866e13 | + | 8.47553e12i | 2.89934 | + | 0.393890i | ||||
\(919\) | −3.86061e13 | −1.78540 | −0.892702 | − | 0.450648i | \(-0.851193\pi\) | ||||
−0.892702 | + | 0.450648i | \(0.851193\pi\) | |||||||
\(920\) | 1.01380e13i | 0.466560i | ||||||||
\(921\) | −2.88411e12 | − | 2.88411e12i | −0.132082 | − | 0.132082i | ||||
\(922\) | 4.67965e12 | 0.213267 | ||||||||
\(923\) | −5.83859e11 | − | 5.83859e11i | −0.0264789 | − | 0.0264789i | ||||
\(924\) | 2.52658e13 | − | 2.52658e13i | 1.14027 | − | 1.14027i | ||||
\(925\) | −8.01967e12 | + | 8.01967e12i | −0.360179 | + | 0.360179i | ||||
\(926\) | 2.22776e12i | 0.0995677i | ||||||||
\(927\) | − | 8.36983e13i | − | 3.72270i | ||||||
\(928\) | 9.35317e12 | − | 9.35317e12i | 0.413993 | − | 0.413993i | ||||
\(929\) | 1.80998e13 | − | 1.80998e13i | 0.797265 | − | 0.797265i | −0.185398 | − | 0.982663i | \(-0.559358\pi\) |
0.982663 | + | 0.185398i | \(0.0593576\pi\) | |||||||
\(930\) | 8.61288e12 | + | 8.61288e12i | 0.377551 | + | 0.377551i | ||||
\(931\) | −4.09087e11 | −0.0178461 | ||||||||
\(932\) | 7.21562e12 | + | 7.21562e12i | 0.313258 | + | 0.313258i | ||||
\(933\) | 6.34472e13i | 2.74123i | ||||||||
\(934\) | 1.99511e13 | 0.857840 | ||||||||
\(935\) | 2.78279e13 | − | 2.11712e13i | 1.19077 | − | 0.905926i | ||||
\(936\) | 2.84303e13 | 1.21071 | ||||||||
\(937\) | − | 2.65934e12i | − | 0.112706i | −0.998411 | − | 0.0563529i | \(-0.982053\pi\) | ||
0.998411 | − | 0.0563529i | \(-0.0179472\pi\) | |||||||
\(938\) | −3.29304e13 | − | 3.29304e13i | −1.38894 | − | 1.38894i | ||||
\(939\) | 4.66211e13 | 1.95698 | ||||||||
\(940\) | 2.32859e12 | + | 2.32859e12i | 0.0972785 | + | 0.0972785i | ||||
\(941\) | 2.92273e13 | − | 2.92273e13i | 1.21516 | − | 1.21516i | 0.245859 | − | 0.969306i | \(-0.420930\pi\) |
0.969306 | − | 0.245859i | \(-0.0790699\pi\) | |||||||
\(942\) | −2.36213e13 | + | 2.36213e13i | −0.977405 | + | 0.977405i | ||||
\(943\) | − | 9.07036e12i | − | 0.373527i | ||||||
\(944\) | 3.80275e13i | 1.55856i | ||||||||
\(945\) | −5.00175e13 | + | 5.00175e13i | −2.04023 | + | 2.04023i | ||||
\(946\) | 2.71036e13 | − | 2.71036e13i | 1.10032 | − | 1.10032i | ||||
\(947\) | 1.46511e13 | + | 1.46511e13i | 0.591966 | + | 0.591966i | 0.938162 | − | 0.346196i | \(-0.112527\pi\) |
−0.346196 | + | 0.938162i | \(0.612527\pi\) | |||||||
\(948\) | −4.72743e13 | −1.90102 | ||||||||
\(949\) | −2.56013e13 | − | 2.56013e13i | −1.02462 | − | 1.02462i | ||||
\(950\) | − | 8.95285e11i | − | 0.0356619i | ||||||
\(951\) | 1.04963e11 | 0.00416124 | ||||||||
\(952\) | 1.31951e13 | + | 1.79262e12i | 0.520650 | + | 0.0707328i | ||||
\(953\) | −2.21831e13 | −0.871174 | −0.435587 | − | 0.900147i | \(-0.643459\pi\) | ||||
−0.435587 | + | 0.900147i | \(0.643459\pi\) | |||||||
\(954\) | − | 2.08113e13i | − | 0.813451i | ||||||
\(955\) | −3.45312e13 | − | 3.45312e13i | −1.34337 | − | 1.34337i | ||||
\(956\) | 8.43751e12 | 0.326704 | ||||||||
\(957\) | 2.31721e13 | + | 2.31721e13i | 0.893022 | + | 0.893022i | ||||
\(958\) | −3.66934e13 | + | 3.66934e13i | −1.40748 | + | 1.40748i | ||||
\(959\) | 2.04784e13 | − | 2.04784e13i | 0.781829 | − | 0.781829i | ||||
\(960\) | 8.68108e12i | 0.329878i | ||||||||
\(961\) | − | 2.53599e13i | − | 0.959163i | ||||||
\(962\) | 4.30693e13 | − | 4.30693e13i | 1.62136 | − | 1.62136i | ||||
\(963\) | −6.64636e13 | + | 6.64636e13i | −2.49038 | + | 2.49038i | ||||
\(964\) | 1.38536e13 | + | 1.38536e13i | 0.516675 | + | 0.516675i | ||||
\(965\) | −1.69434e13 | −0.628965 | ||||||||
\(966\) | 4.10027e13 | + | 4.10027e13i | 1.51501 | + | 1.51501i | ||||
\(967\) | − | 2.63617e13i | − | 0.969514i | −0.874649 | − | 0.484757i | \(-0.838908\pi\) | ||
0.874649 | − | 0.484757i | \(-0.161092\pi\) | |||||||
\(968\) | −9.20224e12 | −0.336864 | ||||||||
\(969\) | 5.93781e11 | − | 4.37070e12i | 0.0216356 | − | 0.159255i | ||||
\(970\) | 7.70636e12 | 0.279497 | ||||||||
\(971\) | 3.49050e12i | 0.126009i | 0.998013 | + | 0.0630045i | \(0.0200682\pi\) | ||||
−0.998013 | + | 0.0630045i | \(0.979932\pi\) | |||||||
\(972\) | −1.35940e13 | − | 1.35940e13i | −0.488484 | − | 0.488484i | ||||
\(973\) | −5.64370e12 | −0.201863 | ||||||||
\(974\) | −1.75455e13 | − | 1.75455e13i | −0.624670 | − | 0.624670i | ||||
\(975\) | 1.26380e13 | − | 1.26380e13i | 0.447876 | − | 0.447876i | ||||
\(976\) | −8.06170e12 | + | 8.06170e12i | −0.284382 | + | 0.284382i | ||||
\(977\) | 1.46631e13i | 0.514875i | 0.966295 | + | 0.257437i | \(0.0828781\pi\) | ||||
−0.966295 | + | 0.257437i | \(0.917122\pi\) | |||||||
\(978\) | 1.16371e13i | 0.406742i | ||||||||
\(979\) | 3.71007e12 | − | 3.71007e12i | 0.129080 | − | 0.129080i | ||||
\(980\) | 2.93201e12 | − | 2.93201e12i | 0.101542 | − | 0.101542i | ||||
\(981\) | 3.16354e13 | + | 3.16354e13i | 1.09059 | + | 1.09059i | ||||
\(982\) | −1.58442e13 | −0.543710 | ||||||||
\(983\) | 7.00196e12 | + | 7.00196e12i | 0.239182 | + | 0.239182i | 0.816511 | − | 0.577329i | \(-0.195905\pi\) |
−0.577329 | + | 0.816511i | \(0.695905\pi\) | |||||||
\(984\) | 1.12245e13i | 0.381671i | ||||||||
\(985\) | −2.07355e13 | −0.701862 | ||||||||
\(986\) | 2.72501e12 | − | 2.00582e13i | 0.0918167 | − | 0.675844i | ||||
\(987\) | −1.13641e13 | −0.381160 | ||||||||
\(988\) | 1.84690e12i | 0.0616649i | ||||||||
\(989\) | 1.68958e13 | + | 1.68958e13i | 0.561559 | + | 0.561559i | ||||
\(990\) | −1.30798e14 | −4.32756 | ||||||||
\(991\) | −3.62679e13 | − | 3.62679e13i | −1.19451 | − | 1.19451i | −0.975786 | − | 0.218728i | \(-0.929809\pi\) |
−0.218728 | − | 0.975786i | \(-0.570191\pi\) | |||||||
\(992\) | −4.76717e12 | + | 4.76717e12i | −0.156300 | + | 0.156300i | ||||
\(993\) | 3.62608e13 | − | 3.62608e13i | 1.18349 | − | 1.18349i | ||||
\(994\) | 1.44671e12i | 0.0470050i | ||||||||
\(995\) | − | 2.85696e13i | − | 0.924060i | ||||||
\(996\) | −1.49948e13 | + | 1.49948e13i | −0.482808 | + | 0.482808i | ||||
\(997\) | −4.99220e12 | + | 4.99220e12i | −0.160016 | + | 0.160016i | −0.782574 | − | 0.622558i | \(-0.786094\pi\) |
0.622558 | + | 0.782574i | \(0.286094\pi\) | |||||||
\(998\) | −2.65475e13 | − | 2.65475e13i | −0.847102 | − | 0.847102i | ||||
\(999\) | 1.16935e14 | 3.71450 |
(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 | 17.10.c.a.13.3 | yes | 24 | |
17.2 | even | 8 | 289.10.a.f.1.19 | 24 | |||
17.4 | even | 4 | inner | 17.10.c.a.4.10 | ✓ | 24 | |
17.15 | even | 8 | 289.10.a.f.1.20 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.10.c.a.4.10 | ✓ | 24 | 17.4 | even | 4 | inner | |
17.10.c.a.13.3 | yes | 24 | 1.1 | even | 1 | trivial | |
289.10.a.f.1.19 | 24 | 17.2 | even | 8 | |||
289.10.a.f.1.20 | 24 | 17.15 | even | 8 |