Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [294,8,Mod(67,294)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(294, 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("294.67");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 294 = 2 \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 294.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: | \(91.8411974923\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 6) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 294.67 |
Dual form | 294.8.e.d.79.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(199\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | − | 6.92820i | −0.353553 | − | 0.612372i | ||||
\(3\) | 13.5000 | − | 23.3827i | 0.288675 | − | 0.500000i | ||||
\(4\) | −32.0000 | + | 55.4256i | −0.250000 | + | 0.433013i | ||||
\(5\) | −57.0000 | − | 98.7269i | −0.203929 | − | 0.353216i | 0.745862 | − | 0.666101i | \(-0.232038\pi\) |
−0.949791 | + | 0.312885i | \(0.898705\pi\) | |||||||
\(6\) | −216.000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 512.000 | 0.353553 | ||||||||
\(9\) | −364.500 | − | 631.333i | −0.166667 | − | 0.288675i | ||||
\(10\) | −456.000 | + | 789.815i | −0.144200 | + | 0.249761i | ||||
\(11\) | −3666.00 | + | 6349.70i | −0.830459 | + | 1.43840i | 0.0672162 | + | 0.997738i | \(0.478588\pi\) |
−0.897675 | + | 0.440658i | \(0.854745\pi\) | |||||||
\(12\) | 864.000 | + | 1496.49i | 0.144338 | + | 0.250000i | ||||
\(13\) | 3802.00 | 0.479966 | 0.239983 | − | 0.970777i | \(-0.422858\pi\) | ||||
0.239983 | + | 0.970777i | \(0.422858\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3078.00 | −0.235477 | ||||||||
\(16\) | −2048.00 | − | 3547.24i | −0.125000 | − | 0.216506i | ||||
\(17\) | −3303.00 | + | 5720.96i | −0.163056 | + | 0.282422i | −0.935963 | − | 0.352098i | \(-0.885469\pi\) |
0.772907 | + | 0.634519i | \(0.218802\pi\) | |||||||
\(18\) | −2916.00 | + | 5050.66i | −0.117851 | + | 0.204124i | ||||
\(19\) | 12430.0 | + | 21529.4i | 0.415751 | + | 0.720102i | 0.995507 | − | 0.0946881i | \(-0.0301854\pi\) |
−0.579756 | + | 0.814790i | \(0.696852\pi\) | |||||||
\(20\) | 7296.00 | 0.203929 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 58656.0 | 1.17445 | ||||||||
\(23\) | −20724.0 | − | 35895.0i | −0.355162 | − | 0.615158i | 0.631984 | − | 0.774982i | \(-0.282241\pi\) |
−0.987146 | + | 0.159823i | \(0.948908\pi\) | |||||||
\(24\) | 6912.00 | − | 11971.9i | 0.102062 | − | 0.176777i | ||||
\(25\) | 32564.5 | − | 56403.4i | 0.416826 | − | 0.721963i | ||||
\(26\) | −15208.0 | − | 26341.0i | −0.169694 | − | 0.293918i | ||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −41610.0 | −0.316814 | −0.158407 | − | 0.987374i | \(-0.550636\pi\) | ||||
−0.158407 | + | 0.987374i | \(0.550636\pi\) | |||||||
\(30\) | 12312.0 | + | 21325.0i | 0.0832538 | + | 0.144200i | ||||
\(31\) | 16576.0 | − | 28710.5i | 0.0999341 | − | 0.173091i | −0.811723 | − | 0.584043i | \(-0.801470\pi\) |
0.911657 | + | 0.410952i | \(0.134803\pi\) | |||||||
\(32\) | −16384.0 | + | 28377.9i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 98982.0 | + | 171442.i | 0.479466 | + | 0.830459i | ||||
\(34\) | 52848.0 | 0.230596 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 46656.0 | 0.166667 | ||||||||
\(37\) | 18233.0 | + | 31580.5i | 0.0591769 | + | 0.102497i | 0.894096 | − | 0.447875i | \(-0.147819\pi\) |
−0.834919 | + | 0.550372i | \(0.814486\pi\) | |||||||
\(38\) | 99440.0 | − | 172235.i | 0.293981 | − | 0.509189i | ||||
\(39\) | 51327.0 | − | 88901.0i | 0.138554 | − | 0.239983i | ||||
\(40\) | −29184.0 | − | 50548.2i | −0.0720999 | − | 0.124881i | ||||
\(41\) | 639078. | 1.44814 | 0.724070 | − | 0.689727i | \(-0.242269\pi\) | ||||
0.724070 | + | 0.689727i | \(0.242269\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −156412. | −0.300006 | −0.150003 | − | 0.988686i | \(-0.547928\pi\) | ||||
−0.150003 | + | 0.988686i | \(0.547928\pi\) | |||||||
\(44\) | −234624. | − | 406381.i | −0.415229 | − | 0.719198i | ||||
\(45\) | −41553.0 | + | 71971.9i | −0.0679765 | + | 0.117739i | ||||
\(46\) | −165792. | + | 287160.i | −0.251137 | + | 0.434983i | ||||
\(47\) | −216888. | − | 375661.i | −0.304714 | − | 0.527781i | 0.672483 | − | 0.740112i | \(-0.265228\pi\) |
−0.977198 | + | 0.212331i | \(0.931894\pi\) | |||||||
\(48\) | −110592. | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −521032. | −0.589480 | ||||||||
\(51\) | 89181.0 | + | 154466.i | 0.0941405 | + | 0.163056i | ||||
\(52\) | −121664. | + | 210728.i | −0.119991 | + | 0.207831i | ||||
\(53\) | −393039. | + | 680764.i | −0.362635 | + | 0.628103i | −0.988394 | − | 0.151914i | \(-0.951456\pi\) |
0.625758 | + | 0.780017i | \(0.284790\pi\) | |||||||
\(54\) | 78732.0 | + | 136368.i | 0.0680414 | + | 0.117851i | ||||
\(55\) | 835848. | 0.677420 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 671220. | 0.480068 | ||||||||
\(58\) | 166440. | + | 288283.i | 0.112011 | + | 0.194008i | ||||
\(59\) | 372570. | − | 645310.i | 0.236171 | − | 0.409059i | −0.723442 | − | 0.690386i | \(-0.757441\pi\) |
0.959612 | + | 0.281326i | \(0.0907742\pi\) | |||||||
\(60\) | 98496.0 | − | 170600.i | 0.0588693 | − | 0.101965i | ||||
\(61\) | −830309. | − | 1.43814e6i | −0.468366 | − | 0.811234i | 0.530980 | − | 0.847384i | \(-0.321824\pi\) |
−0.999346 | + | 0.0361505i | \(0.988490\pi\) | |||||||
\(62\) | −265216. | −0.141328 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | −216714. | − | 375360.i | −0.0978792 | − | 0.169532i | ||||
\(66\) | 791856. | − | 1.37153e6i | 0.339033 | − | 0.587223i | ||||
\(67\) | 1.64542e6 | − | 2.84995e6i | 0.668366 | − | 1.15764i | −0.309995 | − | 0.950738i | \(-0.600327\pi\) |
0.978361 | − | 0.206906i | \(-0.0663394\pi\) | |||||||
\(68\) | −211392. | − | 366142.i | −0.0815281 | − | 0.141211i | ||||
\(69\) | −1.11910e6 | −0.410105 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.71615e6 | 1.89539 | 0.947697 | − | 0.319171i | \(-0.103404\pi\) | ||||
0.947697 | + | 0.319171i | \(0.103404\pi\) | |||||||
\(72\) | −186624. | − | 323242.i | −0.0589256 | − | 0.102062i | ||||
\(73\) | 1.32995e6 | − | 2.30354e6i | 0.400134 | − | 0.693052i | −0.593608 | − | 0.804754i | \(-0.702297\pi\) |
0.993742 | + | 0.111703i | \(0.0356304\pi\) | |||||||
\(74\) | 145864. | − | 252644.i | 0.0418444 | − | 0.0724766i | ||||
\(75\) | −879242. | − | 1.52289e6i | −0.240654 | − | 0.416826i | ||||
\(76\) | −1.59104e6 | −0.415751 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −821232. | −0.195945 | ||||||||
\(79\) | −1.90372e6 | − | 3.29734e6i | −0.434418 | − | 0.752435i | 0.562830 | − | 0.826573i | \(-0.309713\pi\) |
−0.997248 | + | 0.0741382i | \(0.976379\pi\) | |||||||
\(80\) | −233472. | + | 404385.i | −0.0509823 | + | 0.0883040i | ||||
\(81\) | −265720. | + | 460241.i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −2.55631e6 | − | 4.42766e6i | −0.511995 | − | 0.886801i | ||||
\(83\) | −2.22947e6 | −0.427984 | −0.213992 | − | 0.976835i | \(-0.568647\pi\) | ||||
−0.213992 | + | 0.976835i | \(0.568647\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 753084. | 0.133008 | ||||||||
\(86\) | 625648. | + | 1.08365e6i | 0.106068 | + | 0.183716i | ||||
\(87\) | −561735. | + | 972954.i | −0.0914564 | + | 0.158407i | ||||
\(88\) | −1.87699e6 | + | 3.25105e6i | −0.293612 | + | 0.508550i | ||||
\(89\) | 2.99560e6 | + | 5.18854e6i | 0.450422 | + | 0.780154i | 0.998412 | − | 0.0563311i | \(-0.0179402\pi\) |
−0.547990 | + | 0.836485i | \(0.684607\pi\) | |||||||
\(90\) | 664848. | 0.0961332 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.65267e6 | 0.355162 | ||||||||
\(93\) | −447552. | − | 775183.i | −0.0576970 | − | 0.0999341i | ||||
\(94\) | −1.73510e6 | + | 3.00529e6i | −0.215466 | + | 0.373197i | ||||
\(95\) | 1.41702e6 | − | 2.45435e6i | 0.169568 | − | 0.293700i | ||||
\(96\) | 442368. | + | 766204.i | 0.0510310 | + | 0.0883883i | ||||
\(97\) | 4.06013e6 | 0.451688 | 0.225844 | − | 0.974163i | \(-0.427486\pi\) | ||||
0.225844 | + | 0.974163i | \(0.427486\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.34503e6 | 0.553639 | ||||||||
\(100\) | 2.08413e6 | + | 3.60982e6i | 0.208413 | + | 0.360982i | ||||
\(101\) | −8.64097e6 | + | 1.49666e7i | −0.834522 | + | 1.44543i | 0.0598975 | + | 0.998205i | \(0.480923\pi\) |
−0.894419 | + | 0.447229i | \(0.852411\pi\) | |||||||
\(102\) | 713448. | − | 1.23573e6i | 0.0665674 | − | 0.115298i | ||||
\(103\) | −7.18116e6 | − | 1.24381e7i | −0.647536 | − | 1.12157i | −0.983709 | − | 0.179765i | \(-0.942466\pi\) |
0.336173 | − | 0.941800i | \(-0.390867\pi\) | |||||||
\(104\) | 1.94662e6 | 0.169694 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.28862e6 | 0.512844 | ||||||||
\(107\) | −3.22720e6 | − | 5.58968e6i | −0.254673 | − | 0.441107i | 0.710134 | − | 0.704067i | \(-0.248635\pi\) |
−0.964807 | + | 0.262960i | \(0.915301\pi\) | |||||||
\(108\) | 629856. | − | 1.09094e6i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | 442205. | − | 765922.i | 0.0327063 | − | 0.0566489i | −0.849209 | − | 0.528057i | \(-0.822921\pi\) |
0.881915 | + | 0.471408i | \(0.156254\pi\) | |||||||
\(110\) | −3.34339e6 | − | 5.79092e6i | −0.239504 | − | 0.414833i | ||||
\(111\) | 984582. | 0.0683316 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.21325e7 | 0.790999 | 0.395499 | − | 0.918466i | \(-0.370572\pi\) | ||||
0.395499 | + | 0.918466i | \(0.370572\pi\) | |||||||
\(114\) | −2.68488e6 | − | 4.65035e6i | −0.169730 | − | 0.293981i | ||||
\(115\) | −2.36254e6 | + | 4.09203e6i | −0.144856 | + | 0.250898i | ||||
\(116\) | 1.33152e6 | − | 2.30626e6i | 0.0792036 | − | 0.137185i | ||||
\(117\) | −1.38583e6 | − | 2.40033e6i | −0.0799943 | − | 0.138554i | ||||
\(118\) | −5.96112e6 | −0.333996 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.57594e6 | −0.0832538 | ||||||||
\(121\) | −1.71355e7 | − | 2.96796e7i | −0.879323 | − | 1.52303i | ||||
\(122\) | −6.64247e6 | + | 1.15051e7i | −0.331185 | + | 0.573629i | ||||
\(123\) | 8.62755e6 | − | 1.49434e7i | 0.418042 | − | 0.724070i | ||||
\(124\) | 1.06086e6 | + | 1.83747e6i | 0.0499671 | + | 0.0865455i | ||||
\(125\) | −1.63310e7 | −0.747871 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.86806e6 | 0.297524 | 0.148762 | − | 0.988873i | \(-0.452471\pi\) | ||||
0.148762 | + | 0.988873i | \(0.452471\pi\) | |||||||
\(128\) | −1.04858e6 | − | 1.81619e6i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | −2.11156e6 | + | 3.65733e6i | −0.0866044 | + | 0.150003i | ||||
\(130\) | −1.73371e6 | + | 3.00288e6i | −0.0692110 | + | 0.119877i | ||||
\(131\) | −1.97604e7 | − | 3.42260e7i | −0.767973 | − | 1.33017i | −0.938660 | − | 0.344843i | \(-0.887932\pi\) |
0.170687 | − | 0.985325i | \(-0.445401\pi\) | |||||||
\(132\) | −1.26697e7 | −0.479466 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.63267e7 | −0.945212 | ||||||||
\(135\) | 1.12193e6 | + | 1.94324e6i | 0.0392462 | + | 0.0679765i | ||||
\(136\) | −1.69114e6 | + | 2.92913e6i | −0.0576491 | + | 0.0998511i | ||||
\(137\) | −9.58704e6 | + | 1.66052e7i | −0.318539 | + | 0.551725i | −0.980183 | − | 0.198092i | \(-0.936525\pi\) |
0.661645 | + | 0.749818i | \(0.269859\pi\) | |||||||
\(138\) | 4.47638e6 | + | 7.75332e6i | 0.144994 | + | 0.251137i | ||||
\(139\) | −1.32449e7 | −0.418309 | −0.209154 | − | 0.977883i | \(-0.567071\pi\) | ||||
−0.209154 | + | 0.977883i | \(0.567071\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.17120e7 | −0.351854 | ||||||||
\(142\) | −2.28646e7 | − | 3.96027e7i | −0.670123 | − | 1.16069i | ||||
\(143\) | −1.39381e7 | + | 2.41416e7i | −0.398592 | + | 0.690381i | ||||
\(144\) | −1.49299e6 | + | 2.58594e6i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 2.37177e6 | + | 4.10803e6i | 0.0646077 | + | 0.111904i | ||||
\(146\) | −2.12792e7 | −0.565874 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.33382e6 | −0.0591769 | ||||||||
\(149\) | −2.86812e7 | − | 4.96773e7i | −0.710306 | − | 1.23029i | −0.964742 | − | 0.263197i | \(-0.915223\pi\) |
0.254436 | − | 0.967090i | \(-0.418110\pi\) | |||||||
\(150\) | −7.03393e6 | + | 1.21831e7i | −0.170168 | + | 0.294740i | ||||
\(151\) | 1.55436e7 | − | 2.69224e7i | 0.367395 | − | 0.636347i | −0.621762 | − | 0.783206i | \(-0.713583\pi\) |
0.989157 | + | 0.146859i | \(0.0469163\pi\) | |||||||
\(152\) | 6.36416e6 | + | 1.10230e7i | 0.146990 | + | 0.254595i | ||||
\(153\) | 4.81577e6 | 0.108704 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.77933e6 | −0.0815180 | ||||||||
\(156\) | 3.28493e6 | + | 5.68966e6i | 0.0692771 | + | 0.119991i | ||||
\(157\) | −1.68917e7 | + | 2.92573e7i | −0.348358 | + | 0.603373i | −0.985958 | − | 0.166994i | \(-0.946594\pi\) |
0.637600 | + | 0.770367i | \(0.279927\pi\) | |||||||
\(158\) | −1.52298e7 | + | 2.63787e7i | −0.307180 | + | 0.532052i | ||||
\(159\) | 1.06121e7 | + | 1.83806e7i | 0.209368 | + | 0.362635i | ||||
\(160\) | 3.73555e6 | 0.0720999 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 4.25153e6 | 0.0785674 | ||||||||
\(163\) | −3.13329e7 | − | 5.42702e7i | −0.566689 | − | 0.981533i | −0.996890 | − | 0.0788007i | \(-0.974891\pi\) |
0.430202 | − | 0.902733i | \(-0.358442\pi\) | |||||||
\(164\) | −2.04505e7 | + | 3.54213e7i | −0.362035 | + | 0.627063i | ||||
\(165\) | 1.12839e7 | − | 1.95444e7i | 0.195554 | − | 0.338710i | ||||
\(166\) | 8.91787e6 | + | 1.54462e7i | 0.151315 | + | 0.262086i | ||||
\(167\) | −6.27072e7 | −1.04186 | −0.520931 | − | 0.853599i | \(-0.674415\pi\) | ||||
−0.520931 | + | 0.853599i | \(0.674415\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.82933e7 | −0.769633 | ||||||||
\(170\) | −3.01234e6 | − | 5.21752e6i | −0.0470254 | − | 0.0814503i | ||||
\(171\) | 9.06147e6 | − | 1.56949e7i | 0.138584 | − | 0.240034i | ||||
\(172\) | 5.00518e6 | − | 8.66923e6i | 0.0750016 | − | 0.129907i | ||||
\(173\) | −1.35261e7 | − | 2.34278e7i | −0.198614 | − | 0.344010i | 0.749465 | − | 0.662044i | \(-0.230311\pi\) |
−0.948079 | + | 0.318034i | \(0.896977\pi\) | |||||||
\(174\) | 8.98776e6 | 0.129339 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.00319e7 | 0.415229 | ||||||||
\(177\) | −1.00594e7 | − | 1.74234e7i | −0.136353 | − | 0.236171i | ||||
\(178\) | 2.39648e7 | − | 4.15083e7i | 0.318496 | − | 0.551652i | ||||
\(179\) | 6.71404e7 | − | 1.16291e8i | 0.874981 | − | 1.51551i | 0.0181981 | − | 0.999834i | \(-0.494207\pi\) |
0.856783 | − | 0.515677i | \(-0.172460\pi\) | |||||||
\(180\) | −2.65939e6 | − | 4.60620e6i | −0.0339882 | − | 0.0588693i | ||||
\(181\) | −1.14661e8 | −1.43727 | −0.718636 | − | 0.695386i | \(-0.755233\pi\) | ||||
−0.718636 | + | 0.695386i | \(0.755233\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.48367e7 | −0.540822 | ||||||||
\(184\) | −1.06107e7 | − | 1.83783e7i | −0.125569 | − | 0.217491i | ||||
\(185\) | 2.07856e6 | − | 3.60017e6i | 0.0241358 | − | 0.0418045i | ||||
\(186\) | −3.58042e6 | + | 6.20146e6i | −0.0407979 | + | 0.0706641i | ||||
\(187\) | −2.42176e7 | − | 4.19461e7i | −0.270823 | − | 0.469079i | ||||
\(188\) | 2.77617e7 | 0.304714 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.26723e7 | −0.239805 | ||||||||
\(191\) | −8.18026e6 | − | 1.41686e7i | −0.0849474 | − | 0.147133i | 0.820421 | − | 0.571759i | \(-0.193739\pi\) |
−0.905369 | + | 0.424626i | \(0.860406\pi\) | |||||||
\(192\) | 3.53894e6 | − | 6.12963e6i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | 7.70992e7 | − | 1.33540e8i | 0.771968 | − | 1.33709i | −0.164514 | − | 0.986375i | \(-0.552606\pi\) |
0.936483 | − | 0.350714i | \(-0.114061\pi\) | |||||||
\(194\) | −1.62405e7 | − | 2.81294e7i | −0.159696 | − | 0.276601i | ||||
\(195\) | −1.17026e7 | −0.113021 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.32288e7 | 0.775607 | 0.387804 | − | 0.921742i | \(-0.373234\pi\) | ||||
0.387804 | + | 0.921742i | \(0.373234\pi\) | |||||||
\(198\) | −2.13801e7 | − | 3.70314e7i | −0.195741 | − | 0.339033i | ||||
\(199\) | −3.80861e7 | + | 6.59671e7i | −0.342595 | + | 0.593392i | −0.984914 | − | 0.173046i | \(-0.944639\pi\) |
0.642319 | + | 0.766437i | \(0.277972\pi\) | |||||||
\(200\) | 1.66730e7 | − | 2.88785e7i | 0.147370 | − | 0.255253i | ||||
\(201\) | −4.44263e7 | − | 7.69486e7i | −0.385881 | − | 0.668366i | ||||
\(202\) | 1.38256e8 | 1.18019 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.14152e7 | −0.0941405 | ||||||||
\(205\) | −3.64274e7 | − | 6.30942e7i | −0.295318 | − | 0.511506i | ||||
\(206\) | −5.74492e7 | + | 9.95050e7i | −0.457877 | + | 0.793067i | ||||
\(207\) | −1.51078e7 | + | 2.61675e7i | −0.118387 | + | 0.205053i | ||||
\(208\) | −7.78650e6 | − | 1.34866e7i | −0.0599957 | − | 0.103916i | ||||
\(209\) | −1.82274e8 | −1.38106 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.52446e7 | 0.258288 | 0.129144 | − | 0.991626i | \(-0.458777\pi\) | ||||
0.129144 | + | 0.991626i | \(0.458777\pi\) | |||||||
\(212\) | −2.51545e7 | − | 4.35689e7i | −0.181318 | − | 0.314051i | ||||
\(213\) | 7.71681e7 | − | 1.33659e8i | 0.547153 | − | 0.947697i | ||||
\(214\) | −2.58176e7 | + | 4.47174e7i | −0.180081 | + | 0.311909i | ||||
\(215\) | 8.91548e6 | + | 1.54421e7i | 0.0611801 | + | 0.105967i | ||||
\(216\) | −1.00777e7 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7.07528e6 | −0.0462536 | ||||||||
\(219\) | −3.59086e7 | − | 6.21956e7i | −0.231017 | − | 0.400134i | ||||
\(220\) | −2.67471e7 | + | 4.63274e7i | −0.169355 | + | 0.293331i | ||||
\(221\) | −1.25580e7 | + | 2.17511e7i | −0.0782614 | + | 0.135553i | ||||
\(222\) | −3.93833e6 | − | 6.82138e6i | −0.0241589 | − | 0.0418444i | ||||
\(223\) | 1.89131e8 | 1.14208 | 0.571040 | − | 0.820922i | \(-0.306540\pi\) | ||||
0.571040 | + | 0.820922i | \(0.306540\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.74790e7 | −0.277884 | ||||||||
\(226\) | −4.85300e7 | − | 8.40564e7i | −0.279660 | − | 0.484386i | ||||
\(227\) | −8.80501e7 | + | 1.52507e8i | −0.499620 | + | 0.865367i | −1.00000 | 0.000439095i | \(-0.999860\pi\) | |
0.500380 | + | 0.865806i | \(0.333194\pi\) | |||||||
\(228\) | −2.14790e7 | + | 3.72028e7i | −0.120017 | + | 0.207876i | ||||
\(229\) | 3.25198e7 | + | 5.63260e7i | 0.178947 | + | 0.309945i | 0.941520 | − | 0.336957i | \(-0.109398\pi\) |
−0.762573 | + | 0.646902i | \(0.776064\pi\) | |||||||
\(230\) | 3.78006e7 | 0.204857 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.13043e7 | −0.112011 | ||||||||
\(233\) | 1.25659e8 | + | 2.17648e8i | 0.650802 | + | 1.12722i | 0.982929 | + | 0.183987i | \(0.0589005\pi\) |
−0.332127 | + | 0.943235i | \(0.607766\pi\) | |||||||
\(234\) | −1.10866e7 | + | 1.92026e7i | −0.0565645 | + | 0.0979726i | ||||
\(235\) | −2.47252e7 | + | 4.28254e7i | −0.124280 | + | 0.215260i | ||||
\(236\) | 2.38445e7 | + | 4.12999e7i | 0.118085 | + | 0.204530i | ||||
\(237\) | −1.02801e8 | −0.501623 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.13079e8 | 1.00960 | 0.504799 | − | 0.863237i | \(-0.331566\pi\) | ||||
0.504799 | + | 0.863237i | \(0.331566\pi\) | |||||||
\(240\) | 6.30374e6 | + | 1.09184e7i | 0.0294347 | + | 0.0509823i | ||||
\(241\) | 1.28642e8 | − | 2.22814e8i | 0.592001 | − | 1.02538i | −0.401962 | − | 0.915657i | \(-0.631671\pi\) |
0.993963 | − | 0.109719i | \(-0.0349952\pi\) | |||||||
\(242\) | −1.37084e8 | + | 2.37437e8i | −0.621776 | + | 1.07695i | ||||
\(243\) | 7.17445e6 | + | 1.24265e7i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 1.06280e8 | 0.468366 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.38041e8 | −0.591200 | ||||||||
\(247\) | 4.72589e7 | + | 8.18547e7i | 0.199546 | + | 0.345625i | ||||
\(248\) | 8.48691e6 | − | 1.46998e7i | 0.0353320 | − | 0.0611969i | ||||
\(249\) | −3.00978e7 | + | 5.21309e7i | −0.123548 | + | 0.213992i | ||||
\(250\) | 6.53238e7 | + | 1.13144e8i | 0.264412 | + | 0.457975i | ||||
\(251\) | −1.23058e8 | −0.491193 | −0.245596 | − | 0.969372i | \(-0.578984\pi\) | ||||
−0.245596 | + | 0.969372i | \(0.578984\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.03897e8 | 1.17979 | ||||||||
\(254\) | −2.74723e7 | − | 4.75833e7i | −0.105190 | − | 0.182195i | ||||
\(255\) | 1.01666e7 | − | 1.76091e7i | 0.0383961 | − | 0.0665039i | ||||
\(256\) | −8.38861e6 | + | 1.45295e7i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −2.21667e8 | − | 3.83938e8i | −0.814582 | − | 1.41090i | −0.909627 | − | 0.415425i | \(-0.863633\pi\) |
0.0950450 | − | 0.995473i | \(-0.469700\pi\) | |||||||
\(258\) | 3.37850e7 | 0.122477 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.77394e7 | 0.0978792 | ||||||||
\(261\) | 1.51668e7 | + | 2.62697e7i | 0.0528024 | + | 0.0914564i | ||||
\(262\) | −1.58083e8 | + | 2.73808e8i | −0.543039 | + | 0.940571i | ||||
\(263\) | −1.49462e8 | + | 2.58876e8i | −0.506625 | + | 0.877500i | 0.493345 | + | 0.869833i | \(0.335774\pi\) |
−0.999971 | + | 0.00766701i | \(0.997559\pi\) | |||||||
\(264\) | 5.06788e7 | + | 8.77782e7i | 0.169517 | + | 0.293612i | ||||
\(265\) | 8.96129e7 | 0.295808 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.61763e8 | 0.520102 | ||||||||
\(268\) | 1.05307e8 | + | 1.82397e8i | 0.334183 | + | 0.578822i | ||||
\(269\) | 1.04454e8 | − | 1.80920e8i | 0.327184 | − | 0.566699i | −0.654768 | − | 0.755830i | \(-0.727234\pi\) |
0.981952 | + | 0.189131i | \(0.0605670\pi\) | |||||||
\(270\) | 8.97545e6 | − | 1.55459e7i | 0.0277513 | − | 0.0480666i | ||||
\(271\) | −5.63746e6 | − | 9.76437e6i | −0.0172064 | − | 0.0298024i | 0.857294 | − | 0.514827i | \(-0.172144\pi\) |
−0.874500 | + | 0.485025i | \(0.838811\pi\) | |||||||
\(272\) | 2.70582e7 | 0.0815281 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.53393e8 | 0.450482 | ||||||||
\(275\) | 2.38763e8 | + | 4.13549e8i | 0.692313 | + | 1.19912i | ||||
\(276\) | 3.58111e7 | − | 6.20266e7i | 0.102526 | − | 0.177581i | ||||
\(277\) | 3.29482e8 | − | 5.70680e8i | 0.931435 | − | 1.61329i | 0.150565 | − | 0.988600i | \(-0.451891\pi\) |
0.780870 | − | 0.624693i | \(-0.214776\pi\) | |||||||
\(278\) | 5.29796e7 | + | 9.17634e7i | 0.147894 | + | 0.256161i | ||||
\(279\) | −2.41678e7 | −0.0666227 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.05123e8 | −0.282634 | −0.141317 | − | 0.989964i | \(-0.545134\pi\) | ||||
−0.141317 | + | 0.989964i | \(0.545134\pi\) | |||||||
\(282\) | 4.68478e7 | + | 8.11428e7i | 0.124399 | + | 0.215466i | ||||
\(283\) | 1.65081e8 | − | 2.85928e8i | 0.432956 | − | 0.749901i | −0.564171 | − | 0.825658i | \(-0.690804\pi\) |
0.997126 | + | 0.0757570i | \(0.0241373\pi\) | |||||||
\(284\) | −1.82917e8 | + | 3.16821e8i | −0.473849 | + | 0.820730i | ||||
\(285\) | −3.82595e7 | − | 6.62675e7i | −0.0979000 | − | 0.169568i | ||||
\(286\) | 2.23010e8 | 0.563694 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.38879e7 | 0.0589256 | ||||||||
\(289\) | 1.83350e8 | + | 3.17571e8i | 0.446825 | + | 0.773924i | ||||
\(290\) | 1.89742e7 | − | 3.28642e7i | 0.0456846 | − | 0.0791280i | ||||
\(291\) | 5.48117e7 | − | 9.49367e7i | 0.130391 | − | 0.225844i | ||||
\(292\) | 8.51167e7 | + | 1.47427e8i | 0.200067 | + | 0.346526i | ||||
\(293\) | 8.71002e7 | 0.202294 | 0.101147 | − | 0.994871i | \(-0.467749\pi\) | ||||
0.101147 | + | 0.994871i | \(0.467749\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.49460e7 | −0.192649 | ||||||||
\(296\) | 9.33530e6 | + | 1.61692e7i | 0.0209222 | + | 0.0362383i | ||||
\(297\) | 7.21579e7 | − | 1.24981e8i | 0.159822 | − | 0.276820i | ||||
\(298\) | −2.29450e8 | + | 3.97419e8i | −0.502262 | + | 0.869944i | ||||
\(299\) | −7.87926e7 | − | 1.36473e8i | −0.170466 | − | 0.295255i | ||||
\(300\) | 1.12543e8 | 0.240654 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.48698e8 | −0.519575 | ||||||||
\(303\) | 2.33306e8 | + | 4.04098e8i | 0.481811 | + | 0.834522i | ||||
\(304\) | 5.09133e7 | − | 8.81844e7i | 0.103938 | − | 0.180026i | ||||
\(305\) | −9.46552e7 | + | 1.63948e8i | −0.191027 | + | 0.330869i | ||||
\(306\) | −1.92631e7 | − | 3.33647e7i | −0.0384327 | − | 0.0665674i | ||||
\(307\) | 3.91709e8 | 0.772644 | 0.386322 | − | 0.922364i | \(-0.373745\pi\) | ||||
0.386322 | + | 0.922364i | \(0.373745\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.87782e8 | −0.747710 | ||||||||
\(310\) | 1.51173e7 | + | 2.61840e7i | 0.0288210 | + | 0.0499194i | ||||
\(311\) | −1.02468e8 | + | 1.77480e8i | −0.193164 | + | 0.334570i | −0.946297 | − | 0.323298i | \(-0.895208\pi\) |
0.753133 | + | 0.657868i | \(0.228542\pi\) | |||||||
\(312\) | 2.62794e7 | − | 4.55173e7i | 0.0489863 | − | 0.0848468i | ||||
\(313\) | 4.38601e8 | + | 7.59680e8i | 0.808471 | + | 1.40031i | 0.913922 | + | 0.405889i | \(0.133038\pi\) |
−0.105451 | + | 0.994424i | \(0.533629\pi\) | |||||||
\(314\) | 2.70268e8 | 0.492652 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.43676e8 | 0.434418 | ||||||||
\(317\) | 2.20415e8 | + | 3.81770e8i | 0.388628 | + | 0.673124i | 0.992265 | − | 0.124136i | \(-0.0396158\pi\) |
−0.603637 | + | 0.797259i | \(0.706282\pi\) | |||||||
\(318\) | 8.48964e7 | − | 1.47045e8i | 0.148045 | − | 0.256422i | ||||
\(319\) | 1.52542e8 | − | 2.64211e8i | 0.263101 | − | 0.455705i | ||||
\(320\) | −1.49422e7 | − | 2.58807e7i | −0.0254912 | − | 0.0441520i | ||||
\(321\) | −1.74269e8 | −0.294071 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.64225e8 | −0.271163 | ||||||||
\(324\) | −1.70061e7 | − | 2.94555e7i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 1.23810e8 | − | 2.14446e8i | 0.200062 | − | 0.346518i | ||||
\(326\) | −2.50663e8 | + | 4.34162e8i | −0.400709 | + | 0.694049i | ||||
\(327\) | −1.19395e7 | − | 2.06799e7i | −0.0188830 | − | 0.0327063i | ||||
\(328\) | 3.27208e8 | 0.511995 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.80543e8 | −0.276555 | ||||||||
\(331\) | −5.56115e8 | − | 9.63219e8i | −0.842882 | − | 1.45991i | −0.887448 | − | 0.460908i | \(-0.847524\pi\) |
0.0445664 | − | 0.999006i | \(-0.485809\pi\) | |||||||
\(332\) | 7.13430e7 | − | 1.23570e8i | 0.106996 | − | 0.185323i | ||||
\(333\) | 1.32919e7 | − | 2.30222e7i | 0.0197256 | − | 0.0341658i | ||||
\(334\) | 2.50829e8 | + | 4.34448e8i | 0.368354 | + | 0.638007i | ||||
\(335\) | −3.75155e8 | −0.545198 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.88198e8 | 0.410191 | 0.205096 | − | 0.978742i | \(-0.434249\pi\) | ||||
0.205096 | + | 0.978742i | \(0.434249\pi\) | |||||||
\(338\) | 1.93173e8 | + | 3.34586e8i | 0.272106 | + | 0.471302i | ||||
\(339\) | 1.63789e8 | − | 2.83690e8i | 0.228342 | − | 0.395499i | ||||
\(340\) | −2.40987e7 | + | 4.17402e7i | −0.0332520 | + | 0.0575941i | ||||
\(341\) | 1.21535e8 | + | 2.10505e8i | 0.165982 | + | 0.287490i | ||||
\(342\) | −1.44984e8 | −0.195987 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −8.00829e7 | −0.106068 | ||||||||
\(345\) | 6.37885e7 | + | 1.10485e8i | 0.0836326 | + | 0.144856i | ||||
\(346\) | −1.08208e8 | + | 1.87423e8i | −0.140441 | + | 0.243252i | ||||
\(347\) | 5.53003e8 | − | 9.57830e8i | 0.710517 | − | 1.23065i | −0.254146 | − | 0.967166i | \(-0.581794\pi\) |
0.964663 | − | 0.263486i | \(-0.0848722\pi\) | |||||||
\(348\) | −3.59510e7 | − | 6.22690e7i | −0.0457282 | − | 0.0792036i | ||||
\(349\) | 1.32184e9 | 1.66453 | 0.832264 | − | 0.554379i | \(-0.187044\pi\) | ||||
0.832264 | + | 0.554379i | \(0.187044\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.48348e7 | −0.0923695 | ||||||||
\(352\) | −1.20127e8 | − | 2.08067e8i | −0.146806 | − | 0.254275i | ||||
\(353\) | 6.01976e8 | − | 1.04265e9i | 0.728396 | − | 1.26162i | −0.229165 | − | 0.973388i | \(-0.573600\pi\) |
0.957561 | − | 0.288231i | \(-0.0930671\pi\) | |||||||
\(354\) | −8.04751e7 | + | 1.39387e8i | −0.0964162 | + | 0.166998i | ||||
\(355\) | −3.25821e8 | − | 5.64338e8i | −0.386527 | − | 0.669484i | ||||
\(356\) | −3.83437e8 | −0.450422 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.07425e9 | −1.23741 | ||||||||
\(359\) | 6.60286e8 | + | 1.14365e9i | 0.753185 | + | 1.30455i | 0.946272 | + | 0.323373i | \(0.104817\pi\) |
−0.193087 | + | 0.981182i | \(0.561850\pi\) | |||||||
\(360\) | −2.12751e7 | + | 3.68496e7i | −0.0240333 | + | 0.0416269i | ||||
\(361\) | 1.37926e8 | − | 2.38895e8i | 0.154302 | − | 0.267259i | ||||
\(362\) | 4.58642e8 | + | 7.94392e8i | 0.508152 | + | 0.880146i | ||||
\(363\) | −9.25318e8 | −1.01536 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.03228e8 | −0.326396 | ||||||||
\(366\) | 1.79347e8 | + | 3.10638e8i | 0.191210 | + | 0.331185i | ||||
\(367\) | 8.75535e8 | − | 1.51647e9i | 0.924575 | − | 1.60141i | 0.132332 | − | 0.991205i | \(-0.457753\pi\) |
0.792243 | − | 0.610206i | \(-0.208913\pi\) | |||||||
\(368\) | −8.48855e7 | + | 1.47026e8i | −0.0887904 | + | 0.153790i | ||||
\(369\) | −2.32944e8 | − | 4.03471e8i | −0.241357 | − | 0.418042i | ||||
\(370\) | −3.32570e7 | −0.0341332 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 5.72867e7 | 0.0576970 | ||||||||
\(373\) | 2.43973e8 | + | 4.22573e8i | 0.243422 | + | 0.421620i | 0.961687 | − | 0.274150i | \(-0.0883966\pi\) |
−0.718265 | + | 0.695770i | \(0.755063\pi\) | |||||||
\(374\) | −1.93741e8 | + | 3.35569e8i | −0.191501 | + | 0.331689i | ||||
\(375\) | −2.20468e8 | + | 3.81862e8i | −0.215892 | + | 0.373935i | ||||
\(376\) | −1.11047e8 | − | 1.92338e8i | −0.107733 | − | 0.186599i | ||||
\(377\) | −1.58201e8 | −0.152060 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.11007e9 | 1.04740 | 0.523700 | − | 0.851903i | \(-0.324551\pi\) | ||||
0.523700 | + | 0.851903i | \(0.324551\pi\) | |||||||
\(380\) | 9.06893e7 | + | 1.57078e8i | 0.0847839 | + | 0.146850i | ||||
\(381\) | 9.27189e7 | − | 1.60594e8i | 0.0858876 | − | 0.148762i | ||||
\(382\) | −6.54420e7 | + | 1.13349e8i | −0.0600669 | + | 0.104039i | ||||
\(383\) | 9.34558e8 | + | 1.61870e9i | 0.849983 | + | 1.47221i | 0.881222 | + | 0.472702i | \(0.156721\pi\) |
−0.0312391 | + | 0.999512i | \(0.509945\pi\) | |||||||
\(384\) | −5.66231e7 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.23359e9 | −1.09173 | ||||||||
\(387\) | 5.70122e7 | + | 9.87480e7i | 0.0500011 | + | 0.0866044i | ||||
\(388\) | −1.29924e8 | + | 2.25035e8i | −0.112922 | + | 0.195587i | ||||
\(389\) | 1.36948e8 | − | 2.37200e8i | 0.117959 | − | 0.204311i | −0.801000 | − | 0.598665i | \(-0.795698\pi\) |
0.918959 | + | 0.394354i | \(0.129032\pi\) | |||||||
\(390\) | 4.68102e7 | + | 8.10777e7i | 0.0399590 | + | 0.0692110i | ||||
\(391\) | 2.73805e8 | 0.231645 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.06706e9 | −0.886779 | ||||||||
\(394\) | −3.32915e8 | − | 5.76626e8i | −0.274219 | − | 0.474961i | ||||
\(395\) | −2.17024e8 | + | 3.75897e8i | −0.177181 | + | 0.306887i | ||||
\(396\) | −1.71041e8 | + | 2.96252e8i | −0.138410 | + | 0.239733i | ||||
\(397\) | 3.12276e8 | + | 5.40878e8i | 0.250479 | + | 0.433843i | 0.963658 | − | 0.267140i | \(-0.0860785\pi\) |
−0.713179 | + | 0.700982i | \(0.752745\pi\) | |||||||
\(398\) | 6.09378e8 | 0.484502 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.66768e8 | −0.208413 | ||||||||
\(401\) | −2.77750e8 | − | 4.81077e8i | −0.215104 | − | 0.372571i | 0.738201 | − | 0.674581i | \(-0.235676\pi\) |
−0.953305 | + | 0.302010i | \(0.902342\pi\) | |||||||
\(402\) | −3.55410e8 | + | 6.15589e8i | −0.272859 | + | 0.472606i | ||||
\(403\) | 6.30220e7 | − | 1.09157e8i | 0.0479650 | − | 0.0830778i | ||||
\(404\) | −5.53022e8 | − | 9.57862e8i | −0.417261 | − | 0.722717i | ||||
\(405\) | 6.05843e7 | 0.0453176 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.67369e8 | −0.196576 | ||||||||
\(408\) | 4.56607e7 | + | 7.90866e7i | 0.0332837 | + | 0.0576491i | ||||
\(409\) | −1.07885e9 | + | 1.86862e9i | −0.779704 | + | 1.35049i | 0.152409 | + | 0.988318i | \(0.451297\pi\) |
−0.932112 | + | 0.362169i | \(0.882036\pi\) | |||||||
\(410\) | −2.91420e8 | + | 5.04753e8i | −0.208822 | + | 0.361689i | ||||
\(411\) | 2.58850e8 | + | 4.48341e8i | 0.183908 | + | 0.318539i | ||||
\(412\) | 9.19188e8 | 0.647536 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.41725e8 | 0.167425 | ||||||||
\(415\) | 1.27080e8 | + | 2.20108e8i | 0.0872786 | + | 0.151171i | ||||
\(416\) | −6.22920e7 | + | 1.07893e8i | −0.0424234 | + | 0.0734795i | ||||
\(417\) | −1.78806e8 | + | 3.09701e8i | −0.120755 | + | 0.209154i | ||||
\(418\) | 7.29094e8 | + | 1.26283e9i | 0.488277 | + | 0.845721i | ||||
\(419\) | −1.67797e9 | −1.11438 | −0.557191 | − | 0.830384i | \(-0.688121\pi\) | ||||
−0.557191 | + | 0.830384i | \(0.688121\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.25233e8 | −0.343056 | −0.171528 | − | 0.985179i | \(-0.554870\pi\) | ||||
−0.171528 | + | 0.985179i | \(0.554870\pi\) | |||||||
\(422\) | −1.40978e8 | − | 2.44182e8i | −0.0913185 | − | 0.158168i | ||||
\(423\) | −1.58111e8 | + | 2.73857e8i | −0.101571 | + | 0.175927i | ||||
\(424\) | −2.01236e8 | + | 3.48551e8i | −0.128211 | + | 0.222068i | ||||
\(425\) | 2.15121e8 | + | 3.72601e8i | 0.135932 | + | 0.235441i | ||||
\(426\) | −1.23469e9 | −0.773791 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4.13082e8 | 0.254673 | ||||||||
\(429\) | 3.76330e8 | + | 6.51822e8i | 0.230127 | + | 0.398592i | ||||
\(430\) | 7.13239e7 | − | 1.23537e8i | 0.0432609 | − | 0.0749300i | ||||
\(431\) | −8.52965e7 | + | 1.47738e8i | −0.0513169 | + | 0.0888835i | −0.890543 | − | 0.454899i | \(-0.849675\pi\) |
0.839226 | + | 0.543783i | \(0.183009\pi\) | |||||||
\(432\) | 4.03108e7 | + | 6.98203e7i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | 1.68797e9 | 0.999210 | 0.499605 | − | 0.866253i | \(-0.333478\pi\) | ||||
0.499605 | + | 0.866253i | \(0.333478\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.28076e8 | 0.0746026 | ||||||||
\(436\) | 2.83011e7 | + | 4.90190e7i | 0.0163531 | + | 0.0283245i | ||||
\(437\) | 5.15199e8 | − | 8.92350e8i | 0.295318 | − | 0.511505i | ||||
\(438\) | −2.87269e8 | + | 4.97564e8i | −0.163354 | + | 0.282937i | ||||
\(439\) | −5.89248e8 | − | 1.02061e9i | −0.332409 | − | 0.575749i | 0.650575 | − | 0.759442i | \(-0.274528\pi\) |
−0.982984 | + | 0.183693i | \(0.941195\pi\) | |||||||
\(440\) | 4.27954e8 | 0.239504 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.00928e8 | 0.110678 | ||||||||
\(443\) | −3.57877e8 | − | 6.19862e8i | −0.195579 | − | 0.338752i | 0.751511 | − | 0.659720i | \(-0.229325\pi\) |
−0.947090 | + | 0.320968i | \(0.895992\pi\) | |||||||
\(444\) | −3.15066e7 | + | 5.45711e7i | −0.0170829 | + | 0.0295884i | ||||
\(445\) | 3.41499e8 | − | 5.91494e8i | 0.183709 | − | 0.318193i | ||||
\(446\) | −7.56526e8 | − | 1.31034e9i | −0.403786 | − | 0.699378i | ||||
\(447\) | −1.54879e9 | −0.820191 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.37358e9 | −0.716132 | −0.358066 | − | 0.933696i | \(-0.616564\pi\) | ||||
−0.358066 | + | 0.933696i | \(0.616564\pi\) | |||||||
\(450\) | 1.89916e8 | + | 3.28944e8i | 0.0982467 | + | 0.170168i | ||||
\(451\) | −2.34286e9 | + | 4.05795e9i | −1.20262 | + | 2.08300i | ||||
\(452\) | −3.88240e8 | + | 6.72451e8i | −0.197750 | + | 0.342512i | ||||
\(453\) | −4.19678e8 | − | 7.26904e8i | −0.212116 | − | 0.367395i | ||||
\(454\) | 1.40880e9 | 0.706569 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.43665e8 | 0.169730 | ||||||||
\(457\) | −9.23760e8 | − | 1.60000e9i | −0.452744 | − | 0.784175i | 0.545812 | − | 0.837908i | \(-0.316221\pi\) |
−0.998555 | + | 0.0537327i | \(0.982888\pi\) | |||||||
\(458\) | 2.60159e8 | − | 4.50608e8i | 0.126534 | − | 0.219164i | ||||
\(459\) | 6.50129e7 | − | 1.12606e8i | 0.0313802 | − | 0.0543521i | ||||
\(460\) | −1.51202e8 | − | 2.61890e8i | −0.0724279 | − | 0.125449i | ||||
\(461\) | −3.09414e9 | −1.47091 | −0.735455 | − | 0.677573i | \(-0.763032\pi\) | ||||
−0.735455 | + | 0.677573i | \(0.763032\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.00451e9 | 1.40682 | 0.703412 | − | 0.710782i | \(-0.251659\pi\) | ||||
0.703412 | + | 0.710782i | \(0.251659\pi\) | |||||||
\(464\) | 8.52173e7 | + | 1.47601e8i | 0.0396018 | + | 0.0685923i | ||||
\(465\) | −5.10209e7 | + | 8.83708e7i | −0.0235322 | + | 0.0407590i | ||||
\(466\) | 1.00527e9 | − | 1.74119e9i | 0.460186 | − | 0.797066i | ||||
\(467\) | −1.49626e9 | − | 2.59159e9i | −0.679825 | − | 1.17749i | −0.975033 | − | 0.222059i | \(-0.928722\pi\) |
0.295208 | − | 0.955433i | \(-0.404611\pi\) | |||||||
\(468\) | 1.77386e8 | 0.0799943 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.95604e8 | 0.175759 | ||||||||
\(471\) | 4.56077e8 | + | 7.89948e8i | 0.201124 | + | 0.348358i | ||||
\(472\) | 1.90756e8 | − | 3.30399e8i | 0.0834989 | − | 0.144624i | ||||
\(473\) | 5.73406e8 | − | 9.93169e8i | 0.249143 | − | 0.431528i | ||||
\(474\) | 4.11204e8 | + | 7.12225e8i | 0.177351 | + | 0.307180i | ||||
\(475\) | 1.61911e9 | 0.693183 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.73051e8 | 0.241757 | ||||||||
\(478\) | −8.52318e8 | − | 1.47626e9i | −0.356947 | − | 0.618251i | ||||
\(479\) | 9.20207e8 | − | 1.59385e9i | 0.382570 | − | 0.662631i | −0.608858 | − | 0.793279i | \(-0.708372\pi\) |
0.991429 | + | 0.130647i | \(0.0417056\pi\) | |||||||
\(480\) | 5.04300e7 | − | 8.73472e7i | 0.0208135 | − | 0.0360500i | ||||
\(481\) | 6.93219e7 | + | 1.20069e8i | 0.0284029 | + | 0.0491952i | ||||
\(482\) | −2.05827e9 | −0.837216 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.19335e9 | 0.879323 | ||||||||
\(485\) | −2.31427e8 | − | 4.00844e8i | −0.0921124 | − | 0.159543i | ||||
\(486\) | 5.73956e7 | − | 9.94121e7i | 0.0226805 | − | 0.0392837i | ||||
\(487\) | 2.13338e8 | − | 3.69512e8i | 0.0836983 | − | 0.144970i | −0.821137 | − | 0.570730i | \(-0.806660\pi\) |
0.904836 | + | 0.425761i | \(0.139993\pi\) | |||||||
\(488\) | −4.25118e8 | − | 7.36326e8i | −0.165592 | − | 0.286814i | ||||
\(489\) | −1.69198e9 | −0.654356 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.07547e7 | 0.0231630 | 0.0115815 | − | 0.999933i | \(-0.496313\pi\) | ||||
0.0115815 | + | 0.999933i | \(0.496313\pi\) | |||||||
\(492\) | 5.52163e8 | + | 9.56375e8i | 0.209021 | + | 0.362035i | ||||
\(493\) | 1.37438e8 | − | 2.38049e8i | 0.0516585 | − | 0.0894752i | ||||
\(494\) | 3.78071e8 | − | 6.54838e8i | 0.141101 | − | 0.244393i | ||||
\(495\) | −3.04667e8 | − | 5.27698e8i | −0.112903 | − | 0.195554i | ||||
\(496\) | −1.35791e8 | −0.0499671 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 4.81565e8 | 0.174724 | ||||||||
\(499\) | −1.62294e9 | − | 2.81101e9i | −0.584723 | − | 1.01277i | −0.994910 | − | 0.100769i | \(-0.967870\pi\) |
0.410187 | − | 0.912002i | \(-0.365463\pi\) | |||||||
\(500\) | 5.22591e8 | − | 9.05153e8i | 0.186968 | − | 0.323838i | ||||
\(501\) | −8.46548e8 | + | 1.46626e9i | −0.300759 | + | 0.520931i | ||||
\(502\) | 4.92232e8 | + | 8.52571e8i | 0.173663 | + | 0.300793i | ||||
\(503\) | 7.44381e8 | 0.260800 | 0.130400 | − | 0.991461i | \(-0.458374\pi\) | ||||
0.130400 | + | 0.991461i | \(0.458374\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.97014e9 | 0.680734 | ||||||||
\(506\) | −1.21559e9 | − | 2.10546e9i | −0.417118 | − | 0.722470i | ||||
\(507\) | −6.51960e8 | + | 1.12923e9i | −0.222174 | + | 0.384816i | ||||
\(508\) | −2.19778e8 | + | 3.80667e8i | −0.0743809 | + | 0.128831i | ||||
\(509\) | −2.22078e8 | − | 3.84650e8i | −0.0746436 | − | 0.129287i | 0.826288 | − | 0.563248i | \(-0.190449\pi\) |
−0.900931 | + | 0.433962i | \(0.857115\pi\) | |||||||
\(510\) | −1.62666e8 | −0.0543002 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.34218e8 | 0.0441942 | ||||||||
\(513\) | −2.44660e8 | − | 4.23763e8i | −0.0800114 | − | 0.138584i | ||||
\(514\) | −1.77334e9 | + | 3.07151e9i | −0.575997 | + | 0.997656i | ||||
\(515\) | −8.18652e8 | + | 1.41795e9i | −0.264103 | + | 0.457440i | ||||
\(516\) | −1.35140e8 | − | 2.34069e8i | −0.0433022 | − | 0.0750016i | ||||
\(517\) | 3.18045e9 | 1.01221 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.30407e8 | −0.229340 | ||||||||
\(520\) | −1.10958e8 | − | 1.92184e8i | −0.0346055 | − | 0.0599385i | ||||
\(521\) | 1.52481e9 | − | 2.64105e9i | 0.472372 | − | 0.818173i | −0.527128 | − | 0.849786i | \(-0.676731\pi\) |
0.999500 | + | 0.0316130i | \(0.0100644\pi\) | |||||||
\(522\) | 1.21335e8 | − | 2.10158e8i | 0.0373369 | − | 0.0646694i | ||||
\(523\) | −7.01532e8 | − | 1.21509e9i | −0.214433 | − | 0.371409i | 0.738664 | − | 0.674074i | \(-0.235457\pi\) |
−0.953097 | + | 0.302665i | \(0.902124\pi\) | |||||||
\(524\) | 2.52933e9 | 0.767973 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.39140e9 | 0.716476 | ||||||||
\(527\) | 1.09501e8 | + | 1.89661e8i | 0.0325898 | + | 0.0564471i | ||||
\(528\) | 4.05430e8 | − | 7.02226e8i | 0.119866 | − | 0.207615i | ||||
\(529\) | 8.43444e8 | − | 1.46089e9i | 0.247720 | − | 0.429064i | ||||
\(530\) | −3.58452e8 | − | 6.20856e8i | −0.104584 | − | 0.181145i | ||||
\(531\) | −5.43207e8 | −0.157447 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.42977e9 | 0.695058 | ||||||||
\(534\) | −6.47051e8 | − | 1.12072e9i | −0.183884 | − | 0.318496i | ||||
\(535\) | −3.67901e8 | + | 6.37223e8i | −0.103871 | + | 0.179909i | ||||
\(536\) | 8.42454e8 | − | 1.45917e9i | 0.236303 | − | 0.409289i | ||||
\(537\) | −1.81279e9 | − | 3.13985e9i | −0.505171 | − | 0.874981i | ||||
\(538\) | −1.67126e9 | −0.462708 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.43607e8 | −0.0392462 | ||||||||
\(541\) | −2.10553e9 | − | 3.64688e9i | −0.571704 | − | 0.990220i | −0.996391 | − | 0.0848798i | \(-0.972949\pi\) |
0.424688 | − | 0.905340i | \(-0.360384\pi\) | |||||||
\(542\) | −4.50997e7 | + | 7.81150e7i | −0.0121668 | + | 0.0210735i | ||||
\(543\) | −1.54792e9 | + | 2.68107e9i | −0.414905 | + | 0.718636i | ||||
\(544\) | −1.08233e8 | − | 1.87465e8i | −0.0288245 | − | 0.0499256i | ||||
\(545\) | −1.00823e8 | −0.0266791 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.99956e9 | 0.522371 | 0.261185 | − | 0.965289i | \(-0.415887\pi\) | ||||
0.261185 | + | 0.965289i | \(0.415887\pi\) | |||||||
\(548\) | −6.13570e8 | − | 1.06274e9i | −0.159269 | − | 0.275863i | ||||
\(549\) | −6.05295e8 | + | 1.04840e9i | −0.156122 | + | 0.270411i | ||||
\(550\) | 1.91010e9 | − | 3.30840e9i | 0.489539 | − | 0.847907i | ||||
\(551\) | −5.17212e8 | − | 8.95838e8i | −0.131716 | − | 0.228139i | ||||
\(552\) | −5.72977e8 | −0.144994 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −5.27172e9 | −1.31725 | ||||||||
\(555\) | −5.61212e7 | − | 9.72047e7i | −0.0139348 | − | 0.0241358i | ||||
\(556\) | 4.23837e8 | − | 7.34107e8i | 0.104577 | − | 0.181133i | ||||
\(557\) | 1.68702e9 | − | 2.92200e9i | 0.413643 | − | 0.716451i | −0.581642 | − | 0.813445i | \(-0.697589\pi\) |
0.995285 | + | 0.0969937i | \(0.0309227\pi\) | |||||||
\(558\) | 9.66712e7 | + | 1.67439e8i | 0.0235547 | + | 0.0407979i | ||||
\(559\) | −5.94678e8 | −0.143993 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.30775e9 | −0.312719 | ||||||||
\(562\) | 4.20491e8 | + | 7.28312e8i | 0.0999263 | + | 0.173077i | ||||
\(563\) | −2.79011e9 | + | 4.83261e9i | −0.658933 | + | 1.14131i | 0.321959 | + | 0.946754i | \(0.395659\pi\) |
−0.980892 | + | 0.194552i | \(0.937675\pi\) | |||||||
\(564\) | 3.74782e8 | − | 6.49142e8i | 0.0879635 | − | 0.152357i | ||||
\(565\) | −6.91552e8 | − | 1.19780e9i | −0.161308 | − | 0.279393i | ||||
\(566\) | −2.64129e9 | −0.612292 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.92667e9 | 0.670123 | ||||||||
\(569\) | 4.44155e8 | + | 7.69299e8i | 0.101074 | + | 0.175066i | 0.912128 | − | 0.409906i | \(-0.134439\pi\) |
−0.811053 | + | 0.584972i | \(0.801105\pi\) | |||||||
\(570\) | −3.06076e8 | + | 5.30140e8i | −0.0692258 | + | 0.119903i | ||||
\(571\) | 8.95853e8 | − | 1.55166e9i | 0.201377 | − | 0.348796i | −0.747595 | − | 0.664155i | \(-0.768792\pi\) |
0.948972 | + | 0.315359i | \(0.102125\pi\) | |||||||
\(572\) | −8.92040e8 | − | 1.54506e9i | −0.199296 | − | 0.345191i | ||||
\(573\) | −4.41734e8 | −0.0980888 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.69947e9 | −0.592162 | ||||||||
\(576\) | −9.55515e7 | − | 1.65500e8i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 1.91051e9 | − | 3.30911e9i | 0.414033 | − | 0.717126i | −0.581294 | − | 0.813694i | \(-0.697453\pi\) |
0.995326 | + | 0.0965681i | \(0.0307865\pi\) | |||||||
\(578\) | 1.46680e9 | − | 2.54057e9i | 0.315953 | − | 0.547247i | ||||
\(579\) | −2.08168e9 | − | 3.60557e9i | −0.445696 | − | 0.771968i | ||||
\(580\) | −3.03587e8 | −0.0646077 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −8.76987e8 | −0.184401 | ||||||||
\(583\) | −2.88176e9 | − | 4.99136e9i | −0.602307 | − | 1.04323i | ||||
\(584\) | 6.80934e8 | − | 1.17941e9i | 0.141469 | − | 0.245031i | ||||
\(585\) | −1.57985e8 | + | 2.73637e8i | −0.0326264 | + | 0.0565106i | ||||
\(586\) | −3.48401e8 | − | 6.03448e8i | −0.0715217 | − | 0.123879i | ||||
\(587\) | −4.36219e9 | −0.890166 | −0.445083 | − | 0.895489i | \(-0.646826\pi\) | ||||
−0.445083 | + | 0.895489i | \(0.646826\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.24159e8 | 0.166191 | ||||||||
\(590\) | 3.39784e8 | + | 5.88523e8i | 0.0681115 | + | 0.117973i | ||||
\(591\) | 1.12359e9 | − | 1.94611e9i | 0.223899 | − | 0.387804i | ||||
\(592\) | 7.46824e7 | − | 1.29354e8i | 0.0147942 | − | 0.0256243i | ||||
\(593\) | 3.19265e9 | + | 5.52984e9i | 0.628724 | + | 1.08898i | 0.987808 | + | 0.155677i | \(0.0497560\pi\) |
−0.359083 | + | 0.933305i | \(0.616911\pi\) | |||||||
\(594\) | −1.15453e9 | −0.226022 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.67120e9 | 0.710306 | ||||||||
\(597\) | 1.02832e9 | + | 1.78111e9i | 0.197797 | + | 0.342595i | ||||
\(598\) | −6.30341e8 | + | 1.09178e9i | −0.120537 | + | 0.208777i | ||||
\(599\) | −4.02148e8 | + | 6.96542e8i | −0.0764527 | + | 0.132420i | −0.901717 | − | 0.432327i | \(-0.857693\pi\) |
0.825264 | + | 0.564747i | \(0.191026\pi\) | |||||||
\(600\) | −4.50172e8 | − | 7.79720e8i | −0.0850842 | − | 0.147370i | ||||
\(601\) | 4.87162e9 | 0.915403 | 0.457702 | − | 0.889106i | \(-0.348673\pi\) | ||||
0.457702 | + | 0.889106i | \(0.348673\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.39902e9 | −0.445577 | ||||||||
\(604\) | 9.94793e8 | + | 1.72303e9i | 0.183698 | + | 0.318174i | ||||
\(605\) | −1.95345e9 | + | 3.38347e9i | −0.358640 | + | 0.621182i | ||||
\(606\) | 1.86645e9 | − | 3.23279e9i | 0.340692 | − | 0.590096i | ||||
\(607\) | 3.58758e9 | + | 6.21388e9i | 0.651091 | + | 1.12772i | 0.982859 | + | 0.184361i | \(0.0590217\pi\) |
−0.331768 | + | 0.943361i | \(0.607645\pi\) | |||||||
\(608\) | −8.14612e8 | −0.146990 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.51448e9 | 0.270153 | ||||||||
\(611\) | −8.24608e8 | − | 1.42826e9i | −0.146253 | − | 0.253317i | ||||
\(612\) | −1.54105e8 | + | 2.66917e8i | −0.0271760 | + | 0.0470703i | ||||
\(613\) | −1.73945e9 | + | 3.01282e9i | −0.305001 | + | 0.528277i | −0.977261 | − | 0.212038i | \(-0.931990\pi\) |
0.672261 | + | 0.740314i | \(0.265323\pi\) | |||||||
\(614\) | −1.56684e9 | − | 2.71384e9i | −0.273171 | − | 0.473146i | ||||
\(615\) | −1.96708e9 | −0.341004 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.39378e8 | −0.0410286 | −0.0205143 | − | 0.999790i | \(-0.506530\pi\) | ||||
−0.0205143 | + | 0.999790i | \(0.506530\pi\) | |||||||
\(618\) | 1.55113e9 | + | 2.68664e9i | 0.264356 | + | 0.457877i | ||||
\(619\) | −2.76479e9 | + | 4.78876e9i | −0.468539 | + | 0.811533i | −0.999353 | − | 0.0359550i | \(-0.988553\pi\) |
0.530815 | + | 0.847488i | \(0.321886\pi\) | |||||||
\(620\) | 1.20938e8 | − | 2.09472e8i | 0.0203795 | − | 0.0352983i | ||||
\(621\) | 4.07910e8 | + | 7.06522e8i | 0.0683509 | + | 0.118387i | ||||
\(622\) | 1.63949e9 | 0.273175 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −4.20471e8 | −0.0692771 | ||||||||
\(625\) | −1.61324e9 | − | 2.79421e9i | −0.264313 | − | 0.457803i | ||||
\(626\) | 3.50881e9 | − | 6.07744e9i | 0.571676 | − | 0.990171i | ||||
\(627\) | −2.46069e9 | + | 4.26204e9i | −0.398677 | + | 0.690528i | ||||
\(628\) | −1.08107e9 | − | 1.87247e9i | −0.174179 | − | 0.301687i | ||||
\(629\) | −2.40894e8 | −0.0385966 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.13683e9 | −0.972392 | −0.486196 | − | 0.873850i | \(-0.661616\pi\) | ||||
−0.486196 | + | 0.873850i | \(0.661616\pi\) | |||||||
\(632\) | −9.74705e8 | − | 1.68824e9i | −0.153590 | − | 0.266026i | ||||
\(633\) | 4.75802e8 | − | 8.24113e8i | 0.0745612 | − | 0.129144i | ||||
\(634\) | 1.76332e9 | − | 3.05416e9i | 0.274802 | − | 0.475970i | ||||
\(635\) | −3.91480e8 | − | 6.78063e8i | −0.0606738 | − | 0.105090i | ||||
\(636\) | −1.35834e9 | −0.209368 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.44068e9 | −0.372081 | ||||||||
\(639\) | −2.08354e9 | − | 3.60879e9i | −0.315899 | − | 0.547153i | ||||
\(640\) | −1.19538e8 | + | 2.07045e8i | −0.0180250 | + | 0.0312202i | ||||
\(641\) | −5.35190e9 | + | 9.26976e9i | −0.802611 | + | 1.39016i | 0.115282 | + | 0.993333i | \(0.463223\pi\) |
−0.917892 | + | 0.396830i | \(0.870110\pi\) | |||||||
\(642\) | 6.97076e8 | + | 1.20737e9i | 0.103970 | + | 0.180081i | ||||
\(643\) | 1.39803e9 | 0.207385 | 0.103692 | − | 0.994609i | \(-0.466934\pi\) | ||||
0.103692 | + | 0.994609i | \(0.466934\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.81436e8 | 0.0706447 | ||||||||
\(646\) | 6.56901e8 | + | 1.13779e9i | 0.0958707 | + | 0.166053i | ||||
\(647\) | −2.65802e9 | + | 4.60383e9i | −0.385828 | + | 0.668274i | −0.991884 | − | 0.127148i | \(-0.959418\pi\) |
0.606056 | + | 0.795422i | \(0.292751\pi\) | |||||||
\(648\) | −1.36049e8 | + | 2.35644e8i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | 2.73168e9 | + | 4.73141e9i | 0.392260 | + | 0.679414i | ||||
\(650\) | −1.98096e9 | −0.282930 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.01062e9 | 0.566689 | ||||||||
\(653\) | −1.62202e9 | − | 2.80942e9i | −0.227960 | − | 0.394839i | 0.729243 | − | 0.684255i | \(-0.239872\pi\) |
−0.957203 | + | 0.289416i | \(0.906539\pi\) | |||||||
\(654\) | −9.55163e7 | + | 1.65439e8i | −0.0133523 | + | 0.0231268i | ||||
\(655\) | −2.25268e9 | + | 3.90176e9i | −0.313225 | + | 0.542521i | ||||
\(656\) | −1.30883e9 | − | 2.26696e9i | −0.181017 | − | 0.313531i | ||||
\(657\) | −1.93907e9 | −0.266756 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.16506e9 | −0.703034 | −0.351517 | − | 0.936181i | \(-0.614334\pi\) | ||||
−0.351517 | + | 0.936181i | \(0.614334\pi\) | |||||||
\(660\) | 7.22173e8 | + | 1.25084e9i | 0.0977771 | + | 0.169355i | ||||
\(661\) | −1.61258e9 | + | 2.79307e9i | −0.217178 | + | 0.376163i | −0.953944 | − | 0.299985i | \(-0.903018\pi\) |
0.736766 | + | 0.676147i | \(0.236352\pi\) | |||||||
\(662\) | −4.44892e9 | + | 7.70576e9i | −0.596007 | + | 1.03232i | ||||
\(663\) | 3.39066e8 | + | 5.87280e8i | 0.0451843 | + | 0.0782614i | ||||
\(664\) | −1.14149e9 | −0.151315 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.12670e8 | −0.0278963 | ||||||||
\(667\) | 8.62326e8 | + | 1.49359e9i | 0.112520 | + | 0.194891i | ||||
\(668\) | 2.00663e9 | − | 3.47559e9i | 0.260465 | − | 0.451139i | ||||
\(669\) | 2.55327e9 | − | 4.42240e9i | 0.329690 | − | 0.571040i | ||||
\(670\) | 1.50062e9 | + | 2.59915e9i | 0.192757 | + | 0.333864i | ||||
\(671\) | 1.21757e10 | 1.55583 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.00633e9 | −0.253718 | −0.126859 | − | 0.991921i | \(-0.540490\pi\) | ||||
−0.126859 | + | 0.991921i | \(0.540490\pi\) | |||||||
\(674\) | −1.15279e9 | − | 1.99670e9i | −0.145025 | − | 0.251190i | ||||
\(675\) | −6.40967e8 | + | 1.11019e9i | −0.0802181 | + | 0.138942i | ||||
\(676\) | 1.54539e9 | − | 2.67669e9i | 0.192408 | − | 0.333261i | ||||
\(677\) | 5.01055e9 | + | 8.67853e9i | 0.620619 | + | 1.07494i | 0.989371 | + | 0.145416i | \(0.0464520\pi\) |
−0.368751 | + | 0.929528i | \(0.620215\pi\) | |||||||
\(678\) | −2.62062e9 | −0.322924 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3.85579e8 | 0.0470254 | ||||||||
\(681\) | 2.37735e9 | + | 4.11770e9i | 0.288456 | + | 0.499620i | ||||
\(682\) | 9.72282e8 | − | 1.68404e9i | 0.117367 | − | 0.203286i | ||||
\(683\) | 2.92430e9 | − | 5.06504e9i | 0.351196 | − | 0.608290i | −0.635263 | − | 0.772296i | \(-0.719108\pi\) |
0.986459 | + | 0.164006i | \(0.0524416\pi\) | |||||||
\(684\) | 5.79934e8 | + | 1.00448e9i | 0.0692919 | + | 0.120017i | ||||
\(685\) | 2.18584e9 | 0.259838 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.75607e9 | 0.206630 | ||||||||
\(688\) | 3.20332e8 | + | 5.54831e8i | 0.0375008 | + | 0.0649533i | ||||
\(689\) | −1.49433e9 | + | 2.58826e9i | −0.174053 | + | 0.301468i | ||||
\(690\) | 5.10308e8 | − | 8.83879e8i | 0.0591371 | − | 0.102429i | ||||
\(691\) | 1.29343e9 | + | 2.24028e9i | 0.149131 | + | 0.258303i | 0.930907 | − | 0.365257i | \(-0.119019\pi\) |
−0.781775 | + | 0.623560i | \(0.785686\pi\) | |||||||
\(692\) | 1.73134e9 | 0.198614 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.84805e9 | −1.00482 | ||||||||
\(695\) | 7.54959e8 | + | 1.30763e9i | 0.0853054 | + | 0.147753i | ||||
\(696\) | −2.87608e8 | + | 4.98152e8i | −0.0323347 | + | 0.0560054i | ||||
\(697\) | −2.11087e9 | + | 3.65614e9i | −0.236128 | + | 0.408986i | ||||
\(698\) | −5.28737e9 | − | 9.15800e9i | −0.588500 | − | 1.01931i | ||||
\(699\) | 6.78560e9 | 0.751481 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.74460e9 | −0.191286 | −0.0956429 | − | 0.995416i | \(-0.530491\pi\) | ||||
−0.0956429 | + | 0.995416i | \(0.530491\pi\) | |||||||
\(702\) | 2.99339e8 | + | 5.18470e8i | 0.0326575 | + | 0.0565645i | ||||
\(703\) | −4.53272e8 | + | 7.85091e8i | −0.0492057 | + | 0.0852268i | ||||
\(704\) | −9.61020e8 | + | 1.66454e9i | −0.103807 | + | 0.179800i | ||||
\(705\) | 6.67581e8 | + | 1.15628e9i | 0.0717534 | + | 0.124280i | ||||
\(706\) | −9.63161e9 | −1.03011 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.28760e9 | 0.136353 | ||||||||
\(709\) | 5.60254e9 | + | 9.70388e9i | 0.590368 | + | 1.02255i | 0.994183 | + | 0.107707i | \(0.0343508\pi\) |
−0.403814 | + | 0.914841i | \(0.632316\pi\) | |||||||
\(710\) | −2.60657e9 | + | 4.51470e9i | −0.273316 | + | 0.473396i | ||||
\(711\) | −1.38781e9 | + | 2.40376e9i | −0.144806 | + | 0.250812i | ||||
\(712\) | 1.53375e9 | + | 2.65653e9i | 0.159248 | + | 0.275826i | ||||
\(713\) | −1.37408e9 | −0.141971 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.17789e9 | 0.325138 | ||||||||
\(716\) | 4.29699e9 | + | 7.44260e9i | 0.437491 | + | 0.757756i | ||||
\(717\) | 2.87657e9 | − | 4.98237e9i | 0.291446 | − | 0.504799i | ||||
\(718\) | 5.28229e9 | − | 9.14919e9i | 0.532582 | − | 0.922460i | ||||
\(719\) | −4.68284e8 | − | 8.11092e8i | −0.0469849 | − | 0.0813802i | 0.841577 | − | 0.540138i | \(-0.181628\pi\) |
−0.888561 | + | 0.458758i | \(0.848295\pi\) | |||||||
\(720\) | 3.40402e8 | 0.0339882 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.20682e9 | −0.218216 | ||||||||
\(723\) | −3.47333e9 | − | 6.01598e9i | −0.341792 | − | 0.592001i | ||||
\(724\) | 3.66914e9 | − | 6.35513e9i | 0.359318 | − | 0.622357i | ||||
\(725\) | −1.35501e9 | + | 2.34694e9i | −0.132056 | + | 0.228728i | ||||
\(726\) | 3.70127e9 | + | 6.41079e9i | 0.358982 | + | 0.621776i | ||||
\(727\) | −4.20445e9 | −0.405825 | −0.202913 | − | 0.979197i | \(-0.565041\pi\) | ||||
−0.202913 | + | 0.979197i | \(0.565041\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 1.21291e9 | + | 2.10083e9i | 0.115398 | + | 0.199876i | ||||
\(731\) | 5.16629e8 | − | 8.94827e8i | 0.0489179 | − | 0.0847283i | ||||
\(732\) | 1.43477e9 | − | 2.48510e9i | 0.135206 | − | 0.234183i | ||||
\(733\) | −5.77457e9 | − | 1.00018e10i | −0.541571 | − | 0.938029i | −0.998814 | − | 0.0486872i | \(-0.984496\pi\) |
0.457243 | − | 0.889342i | \(-0.348837\pi\) | |||||||
\(734\) | −1.40086e10 | −1.30755 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.35817e9 | 0.125569 | ||||||||
\(737\) | 1.20642e10 | + | 2.08958e10i | 1.11010 | + | 1.92275i | ||||
\(738\) | −1.86355e9 | + | 3.22777e9i | −0.170665 | + | 0.295600i | ||||
\(739\) | 6.98275e9 | − | 1.20945e10i | 0.636460 | − | 1.10238i | −0.349744 | − | 0.936845i | \(-0.613731\pi\) |
0.986204 | − | 0.165535i | \(-0.0529352\pi\) | |||||||
\(740\) | 1.33028e8 | + | 2.30411e8i | 0.0120679 | + | 0.0209022i | ||||
\(741\) | 2.55198e9 | 0.230416 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.43832e10 | 1.28646 | 0.643230 | − | 0.765673i | \(-0.277594\pi\) | ||||
0.643230 | + | 0.765673i | \(0.277594\pi\) | |||||||
\(744\) | −2.29147e8 | − | 3.96894e8i | −0.0203990 | − | 0.0353320i | ||||
\(745\) | −3.26966e9 | + | 5.66321e9i | −0.289705 | + | 0.501783i | ||||
\(746\) | 1.95178e9 | − | 3.38058e9i | 0.172126 | − | 0.298130i | ||||
\(747\) | 8.12641e8 | + | 1.40754e9i | 0.0713307 | + | 0.123548i | ||||
\(748\) | 3.09985e9 | 0.270823 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 3.52749e9 | 0.305317 | ||||||||
\(751\) | 3.35420e8 | + | 5.80965e8i | 0.0288968 | + | 0.0500507i | 0.880112 | − | 0.474766i | \(-0.157467\pi\) |
−0.851215 | + | 0.524817i | \(0.824134\pi\) | |||||||
\(752\) | −8.88373e8 | + | 1.53871e9i | −0.0761786 | + | 0.131945i | ||||
\(753\) | −1.66128e9 | + | 2.87743e9i | −0.141795 | + | 0.245596i | ||||
\(754\) | 6.32805e8 | + | 1.09605e9i | 0.0537613 | + | 0.0931174i | ||||
\(755\) | −3.54395e9 | −0.299691 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.91569e10 | −1.60506 | −0.802529 | − | 0.596613i | \(-0.796513\pi\) | ||||
−0.802529 | + | 0.596613i | \(0.796513\pi\) | |||||||
\(758\) | −4.44027e9 | − | 7.69078e9i | −0.370312 | − | 0.641399i | ||||
\(759\) | 4.10261e9 | − | 7.10592e9i | 0.340576 | − | 0.589894i | ||||
\(760\) | 7.25514e8 | − | 1.25663e9i | 0.0599513 | − | 0.103839i | ||||
\(761\) | 8.95599e9 | + | 1.55122e10i | 0.736660 | + | 1.27593i | 0.953991 | + | 0.299835i | \(0.0969317\pi\) |
−0.217331 | + | 0.976098i | \(0.569735\pi\) | |||||||
\(762\) | −1.48350e9 | −0.121463 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.04707e9 | 0.0849474 | ||||||||
\(765\) | −2.74499e8 | − | 4.75446e8i | −0.0221680 | − | 0.0383961i | ||||
\(766\) | 7.47646e9 | − | 1.29496e10i | 0.601029 | − | 1.04101i | ||||
\(767\) | 1.41651e9 | − | 2.45347e9i | 0.113354 | − | 0.196335i | ||||
\(768\) | 2.26492e8 | + | 3.92296e8i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | 2.14072e10 | 1.69753 | 0.848765 | − | 0.528771i | \(-0.177347\pi\) | ||||
0.848765 | + | 0.528771i | \(0.177347\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.19700e10 | −0.940599 | ||||||||
\(772\) | 4.93435e9 | + | 8.54655e9i | 0.385984 | + | 0.668544i | ||||
\(773\) | −3.77581e8 | + | 6.53990e8i | −0.0294024 | + | 0.0509264i | −0.880352 | − | 0.474321i | \(-0.842694\pi\) |
0.850950 | + | 0.525247i | \(0.176027\pi\) | |||||||
\(774\) | 4.56097e8 | − | 7.89984e8i | 0.0353561 | − | 0.0612385i | ||||
\(775\) | −1.07958e9 | − | 1.86988e9i | −0.0833102 | − | 0.144298i | ||||
\(776\) | 2.07878e9 | 0.159696 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.19116e9 | −0.166819 | ||||||||
\(779\) | 7.94374e9 | + | 1.37590e10i | 0.602066 | + | 1.04281i | ||||
\(780\) | 3.74482e8 | − | 6.48621e8i | 0.0282553 | − | 0.0489396i | ||||
\(781\) | −2.09554e10 | + | 3.62958e10i | −1.57405 | + | 2.72633i | ||||
\(782\) | −1.09522e9 | − | 1.89698e9i | −0.0818990 | − | 0.141853i | ||||
\(783\) | 8.19010e8 | 0.0609709 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.85132e9 | 0.284162 | ||||||||
\(786\) | 4.26825e9 | + | 7.39282e9i | 0.313524 | + | 0.543039i | ||||
\(787\) | 1.02333e10 | − | 1.77245e10i | 0.748347 | − | 1.29617i | −0.200268 | − | 0.979741i | \(-0.564181\pi\) |
0.948615 | − | 0.316434i | \(-0.102485\pi\) | |||||||
\(788\) | −2.66332e9 | + | 4.61301e9i | −0.193902 | + | 0.335848i | ||||
\(789\) | 4.03548e9 | + | 6.98966e9i | 0.292500 | + | 0.506625i | ||||
\(790\) | 3.47239e9 | 0.250572 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2.73665e9 | 0.195741 | ||||||||
\(793\) | −3.15683e9 | − | 5.46780e9i | −0.224800 | − | 0.389364i | ||||
\(794\) | 2.49821e9 | − | 4.32702e9i | 0.177116 | − | 0.306773i | ||||
\(795\) | 1.20977e9 | − | 2.09539e9i | 0.0853924 | − | 0.147904i | ||||
\(796\) | −2.43751e9 | − | 4.22189e9i | −0.171297 | − | 0.296696i | ||||
\(797\) | 1.03098e10 | 0.721348 | 0.360674 | − | 0.932692i | \(-0.382547\pi\) | ||||
0.360674 | + | 0.932692i | \(0.382547\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.86552e9 | 0.198742 | ||||||||
\(800\) | 1.06707e9 | + | 1.84823e9i | 0.0736851 | + | 0.127626i | ||||
\(801\) | 2.18380e9 | − | 3.78245e9i | 0.150141 | − | 0.260051i | ||||
\(802\) | −2.22200e9 | + | 3.84862e9i | −0.152102 | + | 0.263448i | ||||
\(803\) | 9.75119e9 | + | 1.68895e10i | 0.664589 | + | 1.15110i | ||||
\(804\) | 5.68656e9 | 0.385881 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.00835e9 | −0.0678327 | ||||||||
\(807\) | −2.82026e9 | − | 4.88483e9i | −0.188900 | − | 0.327184i | ||||
\(808\) | −4.42418e9 | + | 7.66290e9i | −0.295048 | + | 0.511038i | ||||
\(809\) | 2.08214e8 | − | 3.60637e8i | 0.0138258 | − | 0.0239470i | −0.859030 | − | 0.511926i | \(-0.828932\pi\) |
0.872856 | + | 0.487979i | \(0.162266\pi\) | |||||||
\(810\) | −2.42337e8 | − | 4.19740e8i | −0.0160222 | − | 0.0277513i | ||||
\(811\) | 5.82687e9 | 0.383586 | 0.191793 | − | 0.981435i | \(-0.438570\pi\) | ||||
0.191793 | + | 0.981435i | \(0.438570\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.04423e8 | −0.0198683 | ||||||||
\(814\) | 1.06947e9 | + | 1.85238e9i | 0.0695001 | + | 0.120378i | ||||
\(815\) | −3.57195e9 | + | 6.18681e9i | −0.231129 | + | 0.400327i | ||||
\(816\) | 3.65285e8 | − | 6.32693e8i | 0.0235351 | − | 0.0407641i | ||||
\(817\) | −1.94420e9 | − | 3.36746e9i | −0.124728 | − | 0.216035i | ||||
\(818\) | 1.72616e10 | 1.10267 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.66271e9 | 0.295318 | ||||||||
\(821\) | 1.04166e10 | + | 1.80421e10i | 0.656941 | + | 1.13786i | 0.981403 | + | 0.191957i | \(0.0614833\pi\) |
−0.324462 | + | 0.945899i | \(0.605183\pi\) | |||||||
\(822\) | 2.07080e9 | − | 3.58673e9i | 0.130043 | − | 0.225241i | ||||
\(823\) | −2.11701e9 | + | 3.66677e9i | −0.132381 | + | 0.229290i | −0.924594 | − | 0.380955i | \(-0.875595\pi\) |
0.792213 | + | 0.610244i | \(0.208929\pi\) | |||||||
\(824\) | −3.67675e9 | − | 6.36832e9i | −0.228939 | − | 0.396533i | ||||
\(825\) | 1.28932e10 | 0.799414 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.70597e9 | 0.350800 | 0.175400 | − | 0.984497i | \(-0.443878\pi\) | ||||
0.175400 | + | 0.984497i | \(0.443878\pi\) | |||||||
\(828\) | −9.66899e8 | − | 1.67472e9i | −0.0591936 | − | 0.102526i | ||||
\(829\) | 1.25806e10 | − | 2.17903e10i | 0.766940 | − | 1.32838i | −0.172275 | − | 0.985049i | \(-0.555112\pi\) |
0.939215 | − | 0.343329i | \(-0.111555\pi\) | |||||||
\(830\) | 1.01664e9 | − | 1.76087e9i | 0.0617153 | − | 0.106894i | ||||
\(831\) | −8.89602e9 | − | 1.54084e10i | −0.537764 | − | 0.931435i | ||||
\(832\) | 9.96671e8 | 0.0599957 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2.86090e9 | 0.170774 | ||||||||
\(835\) | 3.57431e9 | + | 6.19089e9i | 0.212466 | + | 0.368002i | ||||
\(836\) | 5.83275e9 | − | 1.01026e10i | 0.345264 | − | 0.598015i | ||||
\(837\) | −3.26265e8 | + | 5.65108e8i | −0.0192323 | + | 0.0333114i | ||||
\(838\) | 6.71187e9 | + | 1.16253e10i | 0.393994 | + | 0.682417i | ||||
\(839\) | −2.27048e10 | −1.32724 | −0.663622 | − | 0.748068i | \(-0.730982\pi\) | ||||
−0.663622 | + | 0.748068i | \(0.730982\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.55185e10 | −0.899629 | ||||||||
\(842\) | 2.10093e9 | + | 3.63892e9i | 0.121289 | + | 0.210078i | ||||
\(843\) | −1.41916e9 | + | 2.45805e9i | −0.0815895 | + | 0.141317i | ||||
\(844\) | −1.12783e9 | + | 1.95345e9i | −0.0645719 | + | 0.111842i | ||||
\(845\) | 2.75272e9 | + | 4.76785e9i | 0.156951 | + | 0.271847i | ||||
\(846\) | 2.52978e9 | 0.143644 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.21978e9 | 0.181318 | ||||||||
\(849\) | −4.45717e9 | − | 7.72005e9i | −0.249967 | − | 0.432956i | ||||
\(850\) | 1.72097e9 | − | 2.98081e9i | 0.0961184 | − | 0.166482i | ||||
\(851\) | 7.55721e8 | − | 1.30895e9i | 0.0420347 | − | 0.0728063i | ||||
\(852\) | 4.93876e9 | + | 8.55418e9i | 0.273577 | + | 0.473849i | ||||
\(853\) | −2.86872e10 | −1.58258 | −0.791292 | − | 0.611439i | \(-0.790591\pi\) | ||||
−0.791292 | + | 0.611439i | \(0.790591\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.06602e9 | −0.113045 | ||||||||
\(856\) | −1.65233e9 | − | 2.86192e9i | −0.0900405 | − | 0.155955i | ||||
\(857\) | 2.67475e9 | − | 4.63280e9i | 0.145161 | − | 0.251426i | −0.784272 | − | 0.620417i | \(-0.786963\pi\) |
0.929433 | + | 0.368991i | \(0.120297\pi\) | |||||||
\(858\) | 3.01064e9 | − | 5.21458e9i | 0.162724 | − | 0.281847i | ||||
\(859\) | −7.01649e9 | − | 1.21529e10i | −0.377697 | − | 0.654191i | 0.613030 | − | 0.790060i | \(-0.289951\pi\) |
−0.990727 | + | 0.135869i | \(0.956617\pi\) | |||||||
\(860\) | −1.14118e9 | −0.0611801 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.36474e9 | 0.0725731 | ||||||||
\(863\) | −1.62497e10 | − | 2.81453e10i | −0.860612 | − | 1.49062i | −0.871339 | − | 0.490682i | \(-0.836748\pi\) |
0.0107265 | − | 0.999942i | \(-0.496586\pi\) | |||||||
\(864\) | 3.22486e8 | − | 5.58563e8i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | −1.54197e9 | + | 2.67077e9i | −0.0810065 | + | 0.140307i | ||||
\(866\) | −6.75188e9 | − | 1.16946e10i | −0.353274 | − | 0.611889i | ||||
\(867\) | 9.90088e9 | 0.515949 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.79162e10 | 1.44307 | ||||||||
\(870\) | −5.12302e8 | − | 8.87334e8i | −0.0263760 | − | 0.0456846i | ||||
\(871\) | 6.25588e9 | − | 1.08355e10i | 0.320793 | − | 0.555630i | ||||
\(872\) | 2.26409e8 | − | 3.92152e8i | 0.0115634 | − | 0.0200284i | ||||
\(873\) | −1.47992e9 | − | 2.56329e9i | −0.0752813 | − | 0.130391i | ||||
\(874\) | −8.24318e9 | −0.417642 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.59630e9 | 0.231017 | ||||||||
\(877\) | 1.69347e10 | + | 2.93318e10i | 0.847772 | + | 1.46838i | 0.883192 | + | 0.469011i | \(0.155390\pi\) |
−0.0354204 | + | 0.999372i | \(0.511277\pi\) | |||||||
\(878\) | −4.71399e9 | + | 8.16486e9i | −0.235048 | + | 0.407116i | ||||
\(879\) | 1.17585e9 | − | 2.03664e9i | 0.0583972 | − | 0.101147i | ||||
\(880\) | −1.71182e9 | − | 2.96495e9i | −0.0846775 | − | 0.146666i | ||||
\(881\) | 1.52708e10 | 0.752397 | 0.376198 | − | 0.926539i | \(-0.377231\pi\) | ||||
0.376198 | + | 0.926539i | \(0.377231\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.12045e10 | −0.547685 | −0.273842 | − | 0.961775i | \(-0.588295\pi\) | ||||
−0.273842 | + | 0.961775i | \(0.588295\pi\) | |||||||
\(884\) | −8.03712e8 | − | 1.39207e9i | −0.0391307 | − | 0.0677764i | ||||
\(885\) | −1.14677e9 | + | 1.98626e9i | −0.0556128 | + | 0.0963243i | ||||
\(886\) | −2.86302e9 | + | 4.95890e9i | −0.138295 | + | 0.239534i | ||||
\(887\) | 3.48616e9 | + | 6.03821e9i | 0.167732 | + | 0.290520i | 0.937622 | − | 0.347657i | \(-0.113022\pi\) |
−0.769890 | + | 0.638176i | \(0.779689\pi\) | |||||||
\(888\) | 5.04106e8 | 0.0241589 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −5.46398e9 | −0.259803 | ||||||||
\(891\) | −1.94826e9 | − | 3.37449e9i | −0.0922732 | − | 0.159822i | ||||
\(892\) | −6.05220e9 | + | 1.04827e10i | −0.285520 | + | 0.494535i | ||||
\(893\) | 5.39184e9 | − | 9.33893e9i | 0.253371 | − | 0.438851i | ||||
\(894\) | 6.19514e9 | + | 1.07303e10i | 0.289981 | + | 0.502262i | ||||
\(895\) | −1.53080e10 | −0.713737 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.25480e9 | −0.196837 | ||||||||
\(898\) | 5.49434e9 | + | 9.51647e9i | 0.253191 | + | 0.438539i | ||||
\(899\) | −6.89727e8 | + | 1.19464e9i | −0.0316606 | + | 0.0548377i | ||||
\(900\) | 1.51933e9 | − | 2.63156e9i | 0.0694709 | − | 0.120327i | ||||
\(901\) | −2.59642e9 | − | 4.49712e9i | −0.118260 | − | 0.204832i | ||||
\(902\) | 3.74858e10 | 1.70076 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.21184e9 | 0.279660 | ||||||||
\(905\) | 6.53565e9 | + | 1.13201e10i | 0.293102 | + | 0.507668i | ||||
\(906\) | −3.35743e9 | + | 5.81523e9i | −0.149988 | + | 0.259788i | ||||
\(907\) | −5.90474e8 | + | 1.02273e9i | −0.0262770 | + | 0.0455130i | −0.878865 | − | 0.477071i | \(-0.841699\pi\) |
0.852588 | + | 0.522584i | \(0.175032\pi\) | |||||||
\(908\) | −5.63521e9 | − | 9.76047e9i | −0.249810 | − | 0.432683i | ||||
\(909\) | 1.25985e10 | 0.556348 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.27915e10 | 0.560541 | 0.280271 | − | 0.959921i | \(-0.409576\pi\) | ||||
0.280271 | + | 0.959921i | \(0.409576\pi\) | |||||||
\(912\) | −1.37466e9 | − | 2.38098e9i | −0.0600085 | − | 0.103938i | ||||
\(913\) | 8.17323e9 | − | 1.41564e10i | 0.355423 | − | 0.615611i | ||||
\(914\) | −7.39008e9 | + | 1.28000e10i | −0.320138 | + | 0.554496i | ||||
\(915\) | 2.55569e9 | + | 4.42659e9i | 0.110290 | + | 0.191027i | ||||
\(916\) | −4.16254e9 | −0.178947 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −1.04021e9 | −0.0443783 | ||||||||
\(919\) | −1.76176e10 | − | 3.05146e10i | −0.748761 | − | 1.29689i | −0.948417 | − | 0.317027i | \(-0.897316\pi\) |
0.199655 | − | 0.979866i | \(-0.436018\pi\) | |||||||
\(920\) | −1.20962e9 | + | 2.09512e9i | −0.0512143 | + | 0.0887057i | ||||
\(921\) | 5.28807e9 | − | 9.15921e9i | 0.223043 | − | 0.386322i | ||||
\(922\) | 1.23765e10 | + | 2.14368e10i | 0.520045 | + | 0.900745i | ||||
\(923\) | 2.17328e10 | 0.909725 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.37499e9 | 0.0986658 | ||||||||
\(926\) | −1.20180e10 | − | 2.08158e10i | −0.497388 | − | 0.861501i | ||||
\(927\) | −5.23506e9 | + | 9.06739e9i | −0.215845 | + | 0.373855i | ||||
\(928\) | 6.81738e8 | − | 1.18081e9i | 0.0280027 | − | 0.0485021i | ||||
\(929\) | −1.08882e10 | − | 1.88590e10i | −0.445556 | − | 0.771725i | 0.552535 | − | 0.833490i | \(-0.313661\pi\) |
−0.998091 | + | 0.0617646i | \(0.980327\pi\) | |||||||
\(930\) | 8.16335e8 | 0.0332796 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.60844e10 | −0.650802 | ||||||||
\(933\) | 2.76664e9 | + | 4.79195e9i | 0.111523 | + | 0.193164i | ||||
\(934\) | −1.19701e10 | + | 2.07328e10i | −0.480709 | + | 0.832613i | ||||
\(935\) | −2.76081e9 | + | 4.78186e9i | −0.110458 | + | 0.191318i | ||||
\(936\) | −7.09544e8 | − | 1.22897e9i | −0.0282823 | − | 0.0489863i | ||||
\(937\) | −1.15795e10 | −0.459833 | −0.229916 | − | 0.973210i | \(-0.573845\pi\) | ||||
−0.229916 | + | 0.973210i | \(0.573845\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.36845e10 | 0.933542 | ||||||||
\(940\) | −1.58241e9 | − | 2.74082e9i | −0.0621402 | − | 0.107630i | ||||
\(941\) | −1.91965e10 | + | 3.32493e10i | −0.751033 | + | 1.30083i | 0.196290 | + | 0.980546i | \(0.437111\pi\) |
−0.947323 | + | 0.320281i | \(0.896223\pi\) | |||||||
\(942\) | 3.64861e9 | − | 6.31959e9i | 0.142216 | − | 0.246326i | ||||
\(943\) | −1.32443e10 | − | 2.29397e10i | −0.514324 | − | 0.890835i | ||||
\(944\) | −3.05209e9 | −0.118085 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.17450e9 | −0.352341 | ||||||||
\(947\) | −5.59205e9 | − | 9.68571e9i | −0.213966 | − | 0.370601i | 0.738986 | − | 0.673721i | \(-0.235305\pi\) |
−0.952952 | + | 0.303120i | \(0.901972\pi\) | |||||||
\(948\) | 3.28963e9 | − | 5.69780e9i | 0.125406 | − | 0.217209i | ||||
\(949\) | 5.05647e9 | − | 8.75806e9i | 0.192050 | − | 0.332641i | ||||
\(950\) | −6.47643e9 | − | 1.12175e10i | −0.245077 | − | 0.424486i | ||||
\(951\) | 1.19024e10 | 0.448749 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.19835e9 | −0.194554 | −0.0972770 | − | 0.995257i | \(-0.531013\pi\) | ||||
−0.0972770 | + | 0.995257i | \(0.531013\pi\) | |||||||
\(954\) | −2.29220e9 | − | 3.97021e9i | −0.0854740 | − | 0.148045i | ||||
\(955\) | −9.32549e8 | + | 1.61522e9i | −0.0346465 | + | 0.0600096i | ||||
\(956\) | −6.81854e9 | + | 1.18101e10i | −0.252400 | + | 0.437169i | ||||
\(957\) | −4.11864e9 | − | 7.13370e9i | −0.151902 | − | 0.263101i | ||||
\(958\) | −1.47233e10 | −0.541036 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −8.06879e8 | −0.0294347 | ||||||||
\(961\) | 1.32068e10 | + | 2.28748e10i | 0.480026 | + | 0.831430i | ||||
\(962\) | 5.54575e8 | − | 9.60552e8i | 0.0200839 | − | 0.0347863i | ||||
\(963\) | −2.35263e9 | + | 4.07488e9i | −0.0848910 | + | 0.147036i | ||||
\(964\) | 8.23308e9 | + | 1.42601e10i | 0.296001 | + | 0.512688i | ||||
\(965\) | −1.75786e10 | −0.629708 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.69243e8 | −0.00957529 | −0.00478765 | − | 0.999989i | \(-0.501524\pi\) | ||||
−0.00478765 | + | 0.999989i | \(0.501524\pi\) | |||||||
\(968\) | −8.77339e9 | − | 1.51960e10i | −0.310888 | − | 0.538473i | ||||
\(969\) | −2.21704e9 | + | 3.84003e9i | −0.0782781 | + | 0.135582i | ||||
\(970\) | −1.85142e9 | + | 3.20675e9i | −0.0651333 | + | 0.112814i | ||||
\(971\) | 2.18642e9 | + | 3.78698e9i | 0.0766418 | + | 0.132747i | 0.901799 | − | 0.432156i | \(-0.142247\pi\) |
−0.825157 | + | 0.564903i | \(0.808914\pi\) | |||||||
\(972\) | −9.18330e8 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −3.41341e9 | −0.118367 | ||||||||
\(975\) | −3.34288e9 | − | 5.79003e9i | −0.115506 | − | 0.200062i | ||||
\(976\) | −3.40095e9 | + | 5.89061e9i | −0.117091 | + | 0.202808i | ||||
\(977\) | 1.87495e10 | − | 3.24752e10i | 0.643220 | − | 1.11409i | −0.341489 | − | 0.939886i | \(-0.610931\pi\) |
0.984710 | − | 0.174204i | \(-0.0557353\pi\) | |||||||
\(978\) | 6.76791e9 | + | 1.17224e10i | 0.231350 | + | 0.400709i | ||||
\(979\) | −4.39276e10 | −1.49623 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.44735e8 | −0.0218042 | ||||||||
\(982\) | −2.43019e8 | − | 4.20921e8i | −0.00818935 | − | 0.0141844i | ||||
\(983\) | −1.53095e10 | + | 2.65168e10i | −0.514071 | + | 0.890397i | 0.485796 | + | 0.874072i | \(0.338530\pi\) |
−0.999867 | + | 0.0163250i | \(0.994803\pi\) | |||||||
\(984\) | 4.41731e9 | − | 7.65100e9i | 0.147800 | − | 0.255997i | ||||
\(985\) | −4.74404e9 | − | 8.21692e9i | −0.158169 | − | 0.273957i | ||||
\(986\) | −2.19901e9 | −0.0730562 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.04913e9 | −0.199546 | ||||||||
\(989\) | 3.24148e9 | + | 5.61441e9i | 0.106551 | + | 0.184551i | ||||
\(990\) | −2.43733e9 | + | 4.22158e9i | −0.0798347 | + | 0.138278i | ||||
\(991\) | 8.63517e9 | − | 1.49565e10i | 0.281847 | − | 0.488173i | −0.689993 | − | 0.723816i | \(-0.742386\pi\) |
0.971840 | + | 0.235643i | \(0.0757197\pi\) | |||||||
\(992\) | 5.43162e8 | + | 9.40785e8i | 0.0176660 | + | 0.0305985i | ||||
\(993\) | −3.00302e10 | −0.973276 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.68363e9 | 0.279461 | ||||||||
\(996\) | −1.92626e9 | − | 3.33638e9i | −0.0617742 | − | 0.106996i | ||||
\(997\) | −1.87539e9 | + | 3.24827e9i | −0.0599319 | + | 0.103805i | −0.894435 | − | 0.447199i | \(-0.852422\pi\) |
0.834503 | + | 0.551004i | \(0.185755\pi\) | |||||||
\(998\) | −1.29835e10 | + | 2.24881e10i | −0.413462 | + | 0.716137i | ||||
\(999\) | −3.58880e8 | − | 6.21599e8i | −0.0113886 | − | 0.0197256i |
(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 | 294.8.e.d.67.1 | 2 | ||
7.2 | even | 3 | inner | 294.8.e.d.79.1 | 2 | ||
7.3 | odd | 6 | 6.8.a.a.1.1 | ✓ | 1 | ||
7.4 | even | 3 | 294.8.a.l.1.1 | 1 | |||
7.5 | odd | 6 | 294.8.e.c.79.1 | 2 | |||
7.6 | odd | 2 | 294.8.e.c.67.1 | 2 | |||
21.17 | even | 6 | 18.8.a.a.1.1 | 1 | |||
28.3 | even | 6 | 48.8.a.b.1.1 | 1 | |||
35.3 | even | 12 | 150.8.c.k.49.1 | 2 | |||
35.17 | even | 12 | 150.8.c.k.49.2 | 2 | |||
35.24 | odd | 6 | 150.8.a.e.1.1 | 1 | |||
56.3 | even | 6 | 192.8.a.n.1.1 | 1 | |||
56.45 | odd | 6 | 192.8.a.f.1.1 | 1 | |||
63.31 | odd | 6 | 162.8.c.d.55.1 | 2 | |||
63.38 | even | 6 | 162.8.c.i.109.1 | 2 | |||
63.52 | odd | 6 | 162.8.c.d.109.1 | 2 | |||
63.59 | even | 6 | 162.8.c.i.55.1 | 2 | |||
84.59 | odd | 6 | 144.8.a.h.1.1 | 1 | |||
105.17 | odd | 12 | 450.8.c.a.199.1 | 2 | |||
105.38 | odd | 12 | 450.8.c.a.199.2 | 2 | |||
105.59 | even | 6 | 450.8.a.ba.1.1 | 1 | |||
168.59 | odd | 6 | 576.8.a.i.1.1 | 1 | |||
168.101 | even | 6 | 576.8.a.h.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.8.a.a.1.1 | ✓ | 1 | 7.3 | odd | 6 | ||
18.8.a.a.1.1 | 1 | 21.17 | even | 6 | |||
48.8.a.b.1.1 | 1 | 28.3 | even | 6 | |||
144.8.a.h.1.1 | 1 | 84.59 | odd | 6 | |||
150.8.a.e.1.1 | 1 | 35.24 | odd | 6 | |||
150.8.c.k.49.1 | 2 | 35.3 | even | 12 | |||
150.8.c.k.49.2 | 2 | 35.17 | even | 12 | |||
162.8.c.d.55.1 | 2 | 63.31 | odd | 6 | |||
162.8.c.d.109.1 | 2 | 63.52 | odd | 6 | |||
162.8.c.i.55.1 | 2 | 63.59 | even | 6 | |||
162.8.c.i.109.1 | 2 | 63.38 | even | 6 | |||
192.8.a.f.1.1 | 1 | 56.45 | odd | 6 | |||
192.8.a.n.1.1 | 1 | 56.3 | even | 6 | |||
294.8.a.l.1.1 | 1 | 7.4 | even | 3 | |||
294.8.e.c.67.1 | 2 | 7.6 | odd | 2 | |||
294.8.e.c.79.1 | 2 | 7.5 | odd | 6 | |||
294.8.e.d.67.1 | 2 | 1.1 | even | 1 | trivial | ||
294.8.e.d.79.1 | 2 | 7.2 | even | 3 | inner | ||
450.8.a.ba.1.1 | 1 | 105.59 | even | 6 | |||
450.8.c.a.199.1 | 2 | 105.17 | odd | 12 | |||
450.8.c.a.199.2 | 2 | 105.38 | odd | 12 | |||
576.8.a.h.1.1 | 1 | 168.101 | even | 6 | |||
576.8.a.i.1.1 | 1 | 168.59 | odd | 6 |