Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(277,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.277");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.k (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: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 553.4 | ||
Character | \(\chi\) | \(=\) | 690.553 |
Dual form | 690.3.k.a.277.4 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.00000i | 0.500000 | − | 0.500000i | ||||
\(3\) | −1.22474 | − | 1.22474i | −0.408248 | − | 0.408248i | ||||
\(4\) | − | 2.00000i | − | 0.500000i | ||||||
\(5\) | −1.90173 | − | 4.62422i | −0.380345 | − | 0.924845i | ||||
\(6\) | −2.44949 | −0.408248 | ||||||||
\(7\) | 2.37572 | − | 2.37572i | 0.339389 | − | 0.339389i | −0.516748 | − | 0.856137i | \(-0.672858\pi\) |
0.856137 | + | 0.516748i | \(0.172858\pi\) | |||||||
\(8\) | −2.00000 | − | 2.00000i | −0.250000 | − | 0.250000i | ||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | −6.52595 | − | 2.72250i | −0.652595 | − | 0.272250i | ||||
\(11\) | −8.18971 | −0.744519 | −0.372260 | − | 0.928129i | \(-0.621417\pi\) | ||||
−0.372260 | + | 0.928129i | \(0.621417\pi\) | |||||||
\(12\) | −2.44949 | + | 2.44949i | −0.204124 | + | 0.204124i | ||||
\(13\) | −7.42310 | − | 7.42310i | −0.571008 | − | 0.571008i | 0.361402 | − | 0.932410i | \(-0.382298\pi\) |
−0.932410 | + | 0.361402i | \(0.882298\pi\) | |||||||
\(14\) | − | 4.75145i | − | 0.339389i | ||||||
\(15\) | −3.33436 | + | 7.99262i | −0.222291 | + | 0.532842i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | 8.23366 | − | 8.23366i | 0.484333 | − | 0.484333i | −0.422179 | − | 0.906512i | \(-0.638735\pi\) |
0.906512 | + | 0.422179i | \(0.138735\pi\) | |||||||
\(18\) | 3.00000 | + | 3.00000i | 0.166667 | + | 0.166667i | ||||
\(19\) | 2.11038i | 0.111073i | 0.998457 | + | 0.0555364i | \(0.0176869\pi\) | ||||
−0.998457 | + | 0.0555364i | \(0.982313\pi\) | |||||||
\(20\) | −9.24845 | + | 3.80345i | −0.462422 | + | 0.190173i | ||||
\(21\) | −5.81931 | −0.277110 | ||||||||
\(22\) | −8.18971 | + | 8.18971i | −0.372260 | + | 0.372260i | ||||
\(23\) | −3.39116 | − | 3.39116i | −0.147442 | − | 0.147442i | ||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | −17.7669 | + | 17.5880i | −0.710675 | + | 0.703521i | ||||
\(26\) | −14.8462 | −0.571008 | ||||||||
\(27\) | 3.67423 | − | 3.67423i | 0.136083 | − | 0.136083i | ||||
\(28\) | −4.75145 | − | 4.75145i | −0.169695 | − | 0.169695i | ||||
\(29\) | 15.8463i | 0.546424i | 0.961954 | + | 0.273212i | \(0.0880860\pi\) | ||||
−0.961954 | + | 0.273212i | \(0.911914\pi\) | |||||||
\(30\) | 4.65826 | + | 11.3270i | 0.155275 | + | 0.377566i | ||||
\(31\) | −15.0787 | −0.486409 | −0.243204 | − | 0.969975i | \(-0.578199\pi\) | ||||
−0.243204 | + | 0.969975i | \(0.578199\pi\) | |||||||
\(32\) | −4.00000 | + | 4.00000i | −0.125000 | + | 0.125000i | ||||
\(33\) | 10.0303 | + | 10.0303i | 0.303949 | + | 0.303949i | ||||
\(34\) | − | 16.4673i | − | 0.484333i | ||||||
\(35\) | −15.5039 | − | 6.46790i | −0.442967 | − | 0.184797i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | −14.2154 | + | 14.2154i | −0.384199 | + | 0.384199i | −0.872612 | − | 0.488413i | \(-0.837576\pi\) |
0.488413 | + | 0.872612i | \(0.337576\pi\) | |||||||
\(38\) | 2.11038 | + | 2.11038i | 0.0555364 | + | 0.0555364i | ||||
\(39\) | 18.1828i | 0.466226i | ||||||||
\(40\) | −5.44499 | + | 13.0519i | −0.136125 | + | 0.326297i | ||||
\(41\) | 7.01600 | 0.171122 | 0.0855609 | − | 0.996333i | \(-0.472732\pi\) | ||||
0.0855609 | + | 0.996333i | \(0.472732\pi\) | |||||||
\(42\) | −5.81931 | + | 5.81931i | −0.138555 | + | 0.138555i | ||||
\(43\) | −3.12385 | − | 3.12385i | −0.0726476 | − | 0.0726476i | 0.669849 | − | 0.742497i | \(-0.266359\pi\) |
−0.742497 | + | 0.669849i | \(0.766359\pi\) | |||||||
\(44\) | 16.3794i | 0.372260i | ||||||||
\(45\) | 13.8727 | − | 5.70518i | 0.308282 | − | 0.126782i | ||||
\(46\) | −6.78233 | −0.147442 | ||||||||
\(47\) | 29.7144 | − | 29.7144i | 0.632221 | − | 0.632221i | −0.316404 | − | 0.948625i | \(-0.602475\pi\) |
0.948625 | + | 0.316404i | \(0.102475\pi\) | |||||||
\(48\) | 4.89898 | + | 4.89898i | 0.102062 | + | 0.102062i | ||||
\(49\) | 37.7119i | 0.769630i | ||||||||
\(50\) | −0.178849 | + | 35.3549i | −0.00357698 | + | 0.707098i | ||||
\(51\) | −20.1683 | −0.395456 | ||||||||
\(52\) | −14.8462 | + | 14.8462i | −0.285504 | + | 0.285504i | ||||
\(53\) | 17.6122 | + | 17.6122i | 0.332306 | + | 0.332306i | 0.853462 | − | 0.521155i | \(-0.174499\pi\) |
−0.521155 | + | 0.853462i | \(0.674499\pi\) | |||||||
\(54\) | − | 7.34847i | − | 0.136083i | ||||||
\(55\) | 15.5746 | + | 37.8710i | 0.283174 | + | 0.688565i | ||||
\(56\) | −9.50289 | −0.169695 | ||||||||
\(57\) | 2.58468 | − | 2.58468i | 0.0453453 | − | 0.0453453i | ||||
\(58\) | 15.8463 | + | 15.8463i | 0.273212 | + | 0.273212i | ||||
\(59\) | − | 26.4258i | − | 0.447895i | −0.974601 | − | 0.223947i | \(-0.928106\pi\) | ||
0.974601 | − | 0.223947i | \(-0.0718944\pi\) | |||||||
\(60\) | 15.9852 | + | 6.66872i | 0.266421 | + | 0.111145i | ||||
\(61\) | −28.1753 | −0.461889 | −0.230945 | − | 0.972967i | \(-0.574182\pi\) | ||||
−0.230945 | + | 0.972967i | \(0.574182\pi\) | |||||||
\(62\) | −15.0787 | + | 15.0787i | −0.243204 | + | 0.243204i | ||||
\(63\) | 7.12717 | + | 7.12717i | 0.113130 | + | 0.113130i | ||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | −20.2094 | + | 48.4428i | −0.310913 | + | 0.745273i | ||||
\(66\) | 20.0606 | 0.303949 | ||||||||
\(67\) | −66.9478 | + | 66.9478i | −0.999221 | + | 0.999221i | −1.00000 | 0.000778970i | \(-0.999752\pi\) | |
0.000778970 | 1.00000i | \(0.499752\pi\) | ||||||||
\(68\) | −16.4673 | − | 16.4673i | −0.242166 | − | 0.242166i | ||||
\(69\) | 8.30662i | 0.120386i | ||||||||
\(70\) | −21.9717 | + | 9.03595i | −0.313882 | + | 0.129085i | ||||
\(71\) | −67.4077 | −0.949405 | −0.474702 | − | 0.880146i | \(-0.657444\pi\) | ||||
−0.474702 | + | 0.880146i | \(0.657444\pi\) | |||||||
\(72\) | 6.00000 | − | 6.00000i | 0.0833333 | − | 0.0833333i | ||||
\(73\) | 16.9909 | + | 16.9909i | 0.232752 | + | 0.232752i | 0.813840 | − | 0.581089i | \(-0.197373\pi\) |
−0.581089 | + | 0.813840i | \(0.697373\pi\) | |||||||
\(74\) | 28.4307i | 0.384199i | ||||||||
\(75\) | 43.3007 | + | 0.219044i | 0.577343 | + | 0.00292059i | ||||
\(76\) | 4.22077 | 0.0555364 | ||||||||
\(77\) | −19.4565 | + | 19.4565i | −0.252682 | + | 0.252682i | ||||
\(78\) | 18.1828 | + | 18.1828i | 0.233113 | + | 0.233113i | ||||
\(79\) | 75.5612i | 0.956471i | 0.878232 | + | 0.478235i | \(0.158723\pi\) | ||||
−0.878232 | + | 0.478235i | \(0.841277\pi\) | |||||||
\(80\) | 7.60691 | + | 18.4969i | 0.0950864 | + | 0.231211i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 7.01600 | − | 7.01600i | 0.0855609 | − | 0.0855609i | ||||
\(83\) | −53.8232 | − | 53.8232i | −0.648473 | − | 0.648473i | 0.304151 | − | 0.952624i | \(-0.401627\pi\) |
−0.952624 | + | 0.304151i | \(0.901627\pi\) | |||||||
\(84\) | 11.6386i | 0.138555i | ||||||||
\(85\) | −53.7325 | − | 22.4161i | −0.632147 | − | 0.263719i | ||||
\(86\) | −6.24770 | −0.0726476 | ||||||||
\(87\) | 19.4077 | − | 19.4077i | 0.223076 | − | 0.223076i | ||||
\(88\) | 16.3794 | + | 16.3794i | 0.186130 | + | 0.186130i | ||||
\(89\) | − | 76.6024i | − | 0.860701i | −0.902662 | − | 0.430351i | \(-0.858390\pi\) | ||
0.902662 | − | 0.430351i | \(-0.141610\pi\) | |||||||
\(90\) | 8.16749 | − | 19.5778i | 0.0907498 | − | 0.217532i | ||||
\(91\) | −35.2705 | −0.387587 | ||||||||
\(92\) | −6.78233 | + | 6.78233i | −0.0737210 | + | 0.0737210i | ||||
\(93\) | 18.4675 | + | 18.4675i | 0.198576 | + | 0.198576i | ||||
\(94\) | − | 59.4288i | − | 0.632221i | ||||||
\(95\) | 9.75888 | − | 4.01337i | 0.102725 | − | 0.0422460i | ||||
\(96\) | 9.79796 | 0.102062 | ||||||||
\(97\) | 34.7900 | − | 34.7900i | 0.358660 | − | 0.358660i | −0.504659 | − | 0.863319i | \(-0.668382\pi\) |
0.863319 | + | 0.504659i | \(0.168382\pi\) | |||||||
\(98\) | 37.7119 | + | 37.7119i | 0.384815 | + | 0.384815i | ||||
\(99\) | − | 24.5691i | − | 0.248173i | ||||||
\(100\) | 35.1760 | + | 35.5337i | 0.351760 | + | 0.355337i | ||||
\(101\) | −0.567660 | −0.00562040 | −0.00281020 | − | 0.999996i | \(-0.500895\pi\) | ||||
−0.00281020 | + | 0.999996i | \(0.500895\pi\) | |||||||
\(102\) | −20.1683 | + | 20.1683i | −0.197728 | + | 0.197728i | ||||
\(103\) | −12.3289 | − | 12.3289i | −0.119698 | − | 0.119698i | 0.644720 | − | 0.764418i | \(-0.276974\pi\) |
−0.764418 | + | 0.644720i | \(0.776974\pi\) | |||||||
\(104\) | 29.6924i | 0.285504i | ||||||||
\(105\) | 11.0667 | + | 26.9098i | 0.105398 | + | 0.256284i | ||||
\(106\) | 35.2245 | 0.332306 | ||||||||
\(107\) | 31.8401 | − | 31.8401i | 0.297571 | − | 0.297571i | −0.542491 | − | 0.840062i | \(-0.682519\pi\) |
0.840062 | + | 0.542491i | \(0.182519\pi\) | |||||||
\(108\) | −7.34847 | − | 7.34847i | −0.0680414 | − | 0.0680414i | ||||
\(109\) | − | 178.228i | − | 1.63512i | −0.575844 | − | 0.817559i | \(-0.695327\pi\) | ||
0.575844 | − | 0.817559i | \(-0.304673\pi\) | |||||||
\(110\) | 53.4456 | + | 22.2965i | 0.485870 | + | 0.202695i | ||||
\(111\) | 34.8204 | 0.313697 | ||||||||
\(112\) | −9.50289 | + | 9.50289i | −0.0848473 | + | 0.0848473i | ||||
\(113\) | −73.7395 | − | 73.7395i | −0.652562 | − | 0.652562i | 0.301047 | − | 0.953609i | \(-0.402664\pi\) |
−0.953609 | + | 0.301047i | \(0.902664\pi\) | |||||||
\(114\) | − | 5.16936i | − | 0.0453453i | ||||||
\(115\) | −9.23243 | + | 22.1306i | −0.0802820 | + | 0.192440i | ||||
\(116\) | 31.6926 | 0.273212 | ||||||||
\(117\) | 22.2693 | − | 22.2693i | 0.190336 | − | 0.190336i | ||||
\(118\) | −26.4258 | − | 26.4258i | −0.223947 | − | 0.223947i | ||||
\(119\) | − | 39.1218i | − | 0.328755i | ||||||
\(120\) | 22.6540 | − | 9.31652i | 0.188783 | − | 0.0776377i | ||||
\(121\) | −53.9286 | −0.445691 | ||||||||
\(122\) | −28.1753 | + | 28.1753i | −0.230945 | + | 0.230945i | ||||
\(123\) | −8.59281 | − | 8.59281i | −0.0698602 | − | 0.0698602i | ||||
\(124\) | 30.1573i | 0.243204i | ||||||||
\(125\) | 115.119 | + | 48.7103i | 0.920949 | + | 0.389683i | ||||
\(126\) | 14.2543 | 0.113130 | ||||||||
\(127\) | 11.2783 | − | 11.2783i | 0.0888056 | − | 0.0888056i | −0.661308 | − | 0.750114i | \(-0.729999\pi\) |
0.750114 | + | 0.661308i | \(0.229999\pi\) | |||||||
\(128\) | 8.00000 | + | 8.00000i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 7.65183i | 0.0593165i | ||||||||
\(130\) | 28.2334 | + | 68.6521i | 0.217180 | + | 0.528093i | ||||
\(131\) | −125.767 | −0.960057 | −0.480028 | − | 0.877253i | \(-0.659374\pi\) | ||||
−0.480028 | + | 0.877253i | \(0.659374\pi\) | |||||||
\(132\) | 20.0606 | − | 20.0606i | 0.151974 | − | 0.151974i | ||||
\(133\) | 5.01369 | + | 5.01369i | 0.0376969 | + | 0.0376969i | ||||
\(134\) | 133.896i | 0.999221i | ||||||||
\(135\) | −23.9779 | − | 10.0031i | −0.177614 | − | 0.0740969i | ||||
\(136\) | −32.9346 | −0.242166 | ||||||||
\(137\) | 89.3505 | − | 89.3505i | 0.652194 | − | 0.652194i | −0.301327 | − | 0.953521i | \(-0.597430\pi\) |
0.953521 | + | 0.301327i | \(0.0974296\pi\) | |||||||
\(138\) | 8.30662 | + | 8.30662i | 0.0601929 | + | 0.0601929i | ||||
\(139\) | − | 61.2074i | − | 0.440341i | −0.975461 | − | 0.220170i | \(-0.929339\pi\) | ||
0.975461 | − | 0.220170i | \(-0.0706613\pi\) | |||||||
\(140\) | −12.9358 | + | 31.0077i | −0.0923985 | + | 0.221484i | ||||
\(141\) | −72.7851 | −0.516206 | ||||||||
\(142\) | −67.4077 | + | 67.4077i | −0.474702 | + | 0.474702i | ||||
\(143\) | 60.7930 | + | 60.7930i | 0.425126 | + | 0.425126i | ||||
\(144\) | − | 12.0000i | − | 0.0833333i | ||||||
\(145\) | 73.2767 | − | 30.1353i | 0.505357 | − | 0.207830i | ||||
\(146\) | 33.9817 | 0.232752 | ||||||||
\(147\) | 46.1874 | − | 46.1874i | 0.314200 | − | 0.314200i | ||||
\(148\) | 28.4307 | + | 28.4307i | 0.192099 | + | 0.192099i | ||||
\(149\) | − | 245.889i | − | 1.65026i | −0.564943 | − | 0.825130i | \(-0.691102\pi\) | ||
0.564943 | − | 0.825130i | \(-0.308898\pi\) | |||||||
\(150\) | 43.5198 | − | 43.0817i | 0.290132 | − | 0.287211i | ||||
\(151\) | −8.23880 | −0.0545616 | −0.0272808 | − | 0.999628i | \(-0.508685\pi\) | ||||
−0.0272808 | + | 0.999628i | \(0.508685\pi\) | |||||||
\(152\) | 4.22077 | − | 4.22077i | 0.0277682 | − | 0.0277682i | ||||
\(153\) | 24.7010 | + | 24.7010i | 0.161444 | + | 0.161444i | ||||
\(154\) | 38.9130i | 0.252682i | ||||||||
\(155\) | 28.6755 | + | 69.7271i | 0.185003 | + | 0.449852i | ||||
\(156\) | 36.3656 | 0.233113 | ||||||||
\(157\) | −57.9326 | + | 57.9326i | −0.368997 | + | 0.368997i | −0.867111 | − | 0.498114i | \(-0.834026\pi\) |
0.498114 | + | 0.867111i | \(0.334026\pi\) | |||||||
\(158\) | 75.5612 | + | 75.5612i | 0.478235 | + | 0.478235i | ||||
\(159\) | − | 43.1410i | − | 0.271327i | ||||||
\(160\) | 26.1038 | + | 10.8900i | 0.163149 | + | 0.0680624i | ||||
\(161\) | −16.1129 | −0.100080 | ||||||||
\(162\) | −9.00000 | + | 9.00000i | −0.0555556 | + | 0.0555556i | ||||
\(163\) | −54.9037 | − | 54.9037i | −0.336832 | − | 0.336832i | 0.518341 | − | 0.855174i | \(-0.326550\pi\) |
−0.855174 | + | 0.518341i | \(0.826550\pi\) | |||||||
\(164\) | − | 14.0320i | − | 0.0855609i | ||||||
\(165\) | 27.3075 | − | 65.4573i | 0.165500 | − | 0.396711i | ||||
\(166\) | −107.646 | −0.648473 | ||||||||
\(167\) | 40.0337 | − | 40.0337i | 0.239723 | − | 0.239723i | −0.577013 | − | 0.816735i | \(-0.695782\pi\) |
0.816735 | + | 0.577013i | \(0.195782\pi\) | |||||||
\(168\) | 11.6386 | + | 11.6386i | 0.0692775 | + | 0.0692775i | ||||
\(169\) | − | 58.7952i | − | 0.347901i | ||||||
\(170\) | −76.1486 | + | 31.3164i | −0.447933 | + | 0.184214i | ||||
\(171\) | −6.33115 | −0.0370243 | ||||||||
\(172\) | −6.24770 | + | 6.24770i | −0.0363238 | + | 0.0363238i | ||||
\(173\) | 72.6221 | + | 72.6221i | 0.419781 | + | 0.419781i | 0.885128 | − | 0.465347i | \(-0.154071\pi\) |
−0.465347 | + | 0.885128i | \(0.654071\pi\) | |||||||
\(174\) | − | 38.8153i | − | 0.223076i | ||||||
\(175\) | −0.424896 | + | 83.9934i | −0.00242798 | + | 0.479962i | ||||
\(176\) | 32.7588 | 0.186130 | ||||||||
\(177\) | −32.3649 | + | 32.3649i | −0.182852 | + | 0.182852i | ||||
\(178\) | −76.6024 | − | 76.6024i | −0.430351 | − | 0.430351i | ||||
\(179\) | − | 294.692i | − | 1.64632i | −0.567808 | − | 0.823161i | \(-0.692208\pi\) | ||
0.567808 | − | 0.823161i | \(-0.307792\pi\) | |||||||
\(180\) | −11.4104 | − | 27.7453i | −0.0633909 | − | 0.154141i | ||||
\(181\) | 15.6531 | 0.0864813 | 0.0432407 | − | 0.999065i | \(-0.486232\pi\) | ||||
0.0432407 | + | 0.999065i | \(0.486232\pi\) | |||||||
\(182\) | −35.2705 | + | 35.2705i | −0.193794 | + | 0.193794i | ||||
\(183\) | 34.5075 | + | 34.5075i | 0.188566 | + | 0.188566i | ||||
\(184\) | 13.5647i | 0.0737210i | ||||||||
\(185\) | 92.7687 | + | 38.7012i | 0.501452 | + | 0.209196i | ||||
\(186\) | 36.9351 | 0.198576 | ||||||||
\(187\) | −67.4313 | + | 67.4313i | −0.360595 | + | 0.360595i | ||||
\(188\) | −59.4288 | − | 59.4288i | −0.316111 | − | 0.316111i | ||||
\(189\) | − | 17.4579i | − | 0.0923700i | ||||||
\(190\) | 5.74551 | − | 13.7723i | 0.0302395 | − | 0.0724855i | ||||
\(191\) | 128.180 | 0.671097 | 0.335548 | − | 0.942023i | \(-0.391078\pi\) | ||||
0.335548 | + | 0.942023i | \(0.391078\pi\) | |||||||
\(192\) | 9.79796 | − | 9.79796i | 0.0510310 | − | 0.0510310i | ||||
\(193\) | −29.7003 | − | 29.7003i | −0.153888 | − | 0.153888i | 0.625964 | − | 0.779852i | \(-0.284706\pi\) |
−0.779852 | + | 0.625964i | \(0.784706\pi\) | |||||||
\(194\) | − | 69.5800i | − | 0.358660i | ||||||
\(195\) | 84.0813 | − | 34.5787i | 0.431186 | − | 0.177327i | ||||
\(196\) | 75.4238 | 0.384815 | ||||||||
\(197\) | 122.742 | − | 122.742i | 0.623057 | − | 0.623057i | −0.323255 | − | 0.946312i | \(-0.604777\pi\) |
0.946312 | + | 0.323255i | \(0.104777\pi\) | |||||||
\(198\) | −24.5691 | − | 24.5691i | −0.124087 | − | 0.124087i | ||||
\(199\) | 10.9495i | 0.0550228i | 0.999621 | + | 0.0275114i | \(0.00875825\pi\) | ||||
−0.999621 | + | 0.0275114i | \(0.991242\pi\) | |||||||
\(200\) | 70.7098 | + | 0.357698i | 0.353549 | + | 0.00178849i | ||||
\(201\) | 163.988 | 0.815860 | ||||||||
\(202\) | −0.567660 | + | 0.567660i | −0.00281020 | + | 0.00281020i | ||||
\(203\) | 37.6464 | + | 37.6464i | 0.185450 | + | 0.185450i | ||||
\(204\) | 40.3365i | 0.197728i | ||||||||
\(205\) | −13.3425 | − | 32.4435i | −0.0650854 | − | 0.158261i | ||||
\(206\) | −24.6578 | −0.119698 | ||||||||
\(207\) | 10.1735 | − | 10.1735i | 0.0491473 | − | 0.0491473i | ||||
\(208\) | 29.6924 | + | 29.6924i | 0.142752 | + | 0.142752i | ||||
\(209\) | − | 17.2834i | − | 0.0826958i | ||||||
\(210\) | 37.9765 | + | 15.8430i | 0.180841 | + | 0.0754431i | ||||
\(211\) | −371.360 | −1.76000 | −0.879999 | − | 0.474975i | \(-0.842457\pi\) | ||||
−0.879999 | + | 0.474975i | \(0.842457\pi\) | |||||||
\(212\) | 35.2245 | − | 35.2245i | 0.166153 | − | 0.166153i | ||||
\(213\) | 82.5573 | + | 82.5573i | 0.387593 | + | 0.387593i | ||||
\(214\) | − | 63.6802i | − | 0.297571i | ||||||
\(215\) | −8.50466 | + | 20.3861i | −0.0395566 | + | 0.0948190i | ||||
\(216\) | −14.6969 | −0.0680414 | ||||||||
\(217\) | −35.8228 | + | 35.8228i | −0.165082 | + | 0.165082i | ||||
\(218\) | −178.228 | − | 178.228i | −0.817559 | − | 0.817559i | ||||
\(219\) | − | 41.6189i | − | 0.190041i | ||||||
\(220\) | 75.7421 | − | 31.1492i | 0.344282 | − | 0.141587i | ||||
\(221\) | −122.239 | −0.553116 | ||||||||
\(222\) | 34.8204 | − | 34.8204i | 0.156849 | − | 0.156849i | ||||
\(223\) | −75.9931 | − | 75.9931i | −0.340776 | − | 0.340776i | 0.515883 | − | 0.856659i | \(-0.327464\pi\) |
−0.856659 | + | 0.515883i | \(0.827464\pi\) | |||||||
\(224\) | 19.0058i | 0.0848473i | ||||||||
\(225\) | −52.7641 | − | 53.3006i | −0.234507 | − | 0.236892i | ||||
\(226\) | −147.479 | −0.652562 | ||||||||
\(227\) | 172.585 | − | 172.585i | 0.760287 | − | 0.760287i | −0.216087 | − | 0.976374i | \(-0.569330\pi\) |
0.976374 | + | 0.216087i | \(0.0693295\pi\) | |||||||
\(228\) | −5.16936 | − | 5.16936i | −0.0226726 | − | 0.0226726i | ||||
\(229\) | − | 73.4614i | − | 0.320792i | −0.987053 | − | 0.160396i | \(-0.948723\pi\) | ||
0.987053 | − | 0.160396i | \(-0.0512772\pi\) | |||||||
\(230\) | 12.8981 | + | 31.3630i | 0.0560789 | + | 0.136361i | ||||
\(231\) | 47.6585 | 0.206314 | ||||||||
\(232\) | 31.6926 | − | 31.6926i | 0.136606 | − | 0.136606i | ||||
\(233\) | 284.973 | + | 284.973i | 1.22306 | + | 1.22306i | 0.966539 | + | 0.256519i | \(0.0825757\pi\) |
0.256519 | + | 0.966539i | \(0.417424\pi\) | |||||||
\(234\) | − | 44.5386i | − | 0.190336i | ||||||
\(235\) | −193.915 | − | 80.8973i | −0.825168 | − | 0.344244i | ||||
\(236\) | −52.8516 | −0.223947 | ||||||||
\(237\) | 92.5432 | − | 92.5432i | 0.390478 | − | 0.390478i | ||||
\(238\) | −39.1218 | − | 39.1218i | −0.164377 | − | 0.164377i | ||||
\(239\) | − | 117.112i | − | 0.490009i | −0.969522 | − | 0.245005i | \(-0.921211\pi\) | ||
0.969522 | − | 0.245005i | \(-0.0787895\pi\) | |||||||
\(240\) | 13.3374 | − | 31.9705i | 0.0555727 | − | 0.133210i | ||||
\(241\) | 178.634 | 0.741219 | 0.370610 | − | 0.928789i | \(-0.379149\pi\) | ||||
0.370610 | + | 0.928789i | \(0.379149\pi\) | |||||||
\(242\) | −53.9286 | + | 53.9286i | −0.222846 | + | 0.222846i | ||||
\(243\) | 11.0227 | + | 11.0227i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 56.3505i | 0.230945i | ||||||||
\(245\) | 174.388 | − | 71.7177i | 0.711788 | − | 0.292725i | ||||
\(246\) | −17.1856 | −0.0698602 | ||||||||
\(247\) | 15.6656 | − | 15.6656i | 0.0634234 | − | 0.0634234i | ||||
\(248\) | 30.1573 | + | 30.1573i | 0.121602 | + | 0.121602i | ||||
\(249\) | 131.839i | 0.529476i | ||||||||
\(250\) | 163.829 | − | 66.4083i | 0.655316 | − | 0.265633i | ||||
\(251\) | −350.780 | −1.39753 | −0.698765 | − | 0.715351i | \(-0.746267\pi\) | ||||
−0.698765 | + | 0.715351i | \(0.746267\pi\) | |||||||
\(252\) | 14.2543 | − | 14.2543i | 0.0565648 | − | 0.0565648i | ||||
\(253\) | 27.7727 | + | 27.7727i | 0.109773 | + | 0.109773i | ||||
\(254\) | − | 22.5566i | − | 0.0888056i | ||||||
\(255\) | 38.3545 | + | 93.2626i | 0.150410 | + | 0.365736i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 108.104 | − | 108.104i | 0.420639 | − | 0.420639i | −0.464785 | − | 0.885424i | \(-0.653868\pi\) |
0.885424 | + | 0.464785i | \(0.153868\pi\) | |||||||
\(258\) | 7.65183 | + | 7.65183i | 0.0296583 | + | 0.0296583i | ||||
\(259\) | 67.5435i | 0.260786i | ||||||||
\(260\) | 96.8855 | + | 40.4187i | 0.372637 | + | 0.155457i | ||||
\(261\) | −47.5388 | −0.182141 | ||||||||
\(262\) | −125.767 | + | 125.767i | −0.480028 | + | 0.480028i | ||||
\(263\) | 78.3826 | + | 78.3826i | 0.298033 | + | 0.298033i | 0.840243 | − | 0.542210i | \(-0.182412\pi\) |
−0.542210 | + | 0.840243i | \(0.682412\pi\) | |||||||
\(264\) | − | 40.1212i | − | 0.151974i | ||||||
\(265\) | 47.9492 | − | 114.937i | 0.180941 | − | 0.433723i | ||||
\(266\) | 10.0274 | 0.0376969 | ||||||||
\(267\) | −93.8184 | + | 93.8184i | −0.351380 | + | 0.351380i | ||||
\(268\) | 133.896 | + | 133.896i | 0.499610 | + | 0.499610i | ||||
\(269\) | − | 326.796i | − | 1.21485i | −0.794376 | − | 0.607427i | \(-0.792202\pi\) | ||
0.794376 | − | 0.607427i | \(-0.207798\pi\) | |||||||
\(270\) | −33.9810 | + | 13.9748i | −0.125855 | + | 0.0517585i | ||||
\(271\) | −312.784 | −1.15419 | −0.577093 | − | 0.816679i | \(-0.695813\pi\) | ||||
−0.577093 | + | 0.816679i | \(0.695813\pi\) | |||||||
\(272\) | −32.9346 | + | 32.9346i | −0.121083 | + | 0.121083i | ||||
\(273\) | 43.1973 | + | 43.1973i | 0.158232 | + | 0.158232i | ||||
\(274\) | − | 178.701i | − | 0.652194i | ||||||
\(275\) | 145.506 | − | 144.041i | 0.529111 | − | 0.523785i | ||||
\(276\) | 16.6132 | 0.0601929 | ||||||||
\(277\) | −64.9224 | + | 64.9224i | −0.234377 | + | 0.234377i | −0.814517 | − | 0.580140i | \(-0.802998\pi\) |
0.580140 | + | 0.814517i | \(0.302998\pi\) | |||||||
\(278\) | −61.2074 | − | 61.2074i | −0.220170 | − | 0.220170i | ||||
\(279\) | − | 45.2360i | − | 0.162136i | ||||||
\(280\) | 18.0719 | + | 43.9435i | 0.0645425 | + | 0.156941i | ||||
\(281\) | −222.033 | −0.790154 | −0.395077 | − | 0.918648i | \(-0.629282\pi\) | ||||
−0.395077 | + | 0.918648i | \(0.629282\pi\) | |||||||
\(282\) | −72.7851 | + | 72.7851i | −0.258103 | + | 0.258103i | ||||
\(283\) | −264.201 | − | 264.201i | −0.933574 | − | 0.933574i | 0.0643532 | − | 0.997927i | \(-0.479502\pi\) |
−0.997927 | + | 0.0643532i | \(0.979502\pi\) | |||||||
\(284\) | 134.815i | 0.474702i | ||||||||
\(285\) | −16.8675 | − | 7.03678i | −0.0591842 | − | 0.0246905i | ||||
\(286\) | 121.586 | 0.425126 | ||||||||
\(287\) | 16.6681 | − | 16.6681i | 0.0580769 | − | 0.0580769i | ||||
\(288\) | −12.0000 | − | 12.0000i | −0.0416667 | − | 0.0416667i | ||||
\(289\) | 153.414i | 0.530843i | ||||||||
\(290\) | 43.1414 | − | 103.412i | 0.148764 | − | 0.356593i | ||||
\(291\) | −85.2178 | −0.292845 | ||||||||
\(292\) | 33.9817 | − | 33.9817i | 0.116376 | − | 0.116376i | ||||
\(293\) | 150.293 | + | 150.293i | 0.512945 | + | 0.512945i | 0.915428 | − | 0.402483i | \(-0.131853\pi\) |
−0.402483 | + | 0.915428i | \(0.631853\pi\) | |||||||
\(294\) | − | 92.3749i | − | 0.314200i | ||||||
\(295\) | −122.199 | + | 50.2546i | −0.414233 | + | 0.170355i | ||||
\(296\) | 56.8614 | 0.192099 | ||||||||
\(297\) | −30.0909 | + | 30.0909i | −0.101316 | + | 0.101316i | ||||
\(298\) | −245.889 | − | 245.889i | −0.825130 | − | 0.825130i | ||||
\(299\) | 50.3459i | 0.168381i | ||||||||
\(300\) | 0.438089 | − | 86.6014i | 0.00146030 | − | 0.288671i | ||||
\(301\) | −14.8428 | −0.0493116 | ||||||||
\(302\) | −8.23880 | + | 8.23880i | −0.0272808 | + | 0.0272808i | ||||
\(303\) | 0.695239 | + | 0.695239i | 0.00229452 | + | 0.00229452i | ||||
\(304\) | − | 8.44153i | − | 0.0277682i | ||||||
\(305\) | 53.5816 | + | 130.289i | 0.175678 | + | 0.427176i | ||||
\(306\) | 49.4020 | 0.161444 | ||||||||
\(307\) | −371.701 | + | 371.701i | −1.21075 | + | 1.21075i | −0.239971 | + | 0.970780i | \(0.577138\pi\) |
−0.970780 | + | 0.239971i | \(0.922862\pi\) | |||||||
\(308\) | 38.9130 | + | 38.9130i | 0.126341 | + | 0.126341i | ||||
\(309\) | 30.1995i | 0.0977331i | ||||||||
\(310\) | 98.4027 | + | 41.0516i | 0.317428 | + | 0.132425i | ||||
\(311\) | 24.8526 | 0.0799118 | 0.0399559 | − | 0.999201i | \(-0.487278\pi\) | ||||
0.0399559 | + | 0.999201i | \(0.487278\pi\) | |||||||
\(312\) | 36.3656 | − | 36.3656i | 0.116556 | − | 0.116556i | ||||
\(313\) | 159.376 | + | 159.376i | 0.509189 | + | 0.509189i | 0.914277 | − | 0.405088i | \(-0.132759\pi\) |
−0.405088 | + | 0.914277i | \(0.632759\pi\) | |||||||
\(314\) | 115.865i | 0.368997i | ||||||||
\(315\) | 19.4037 | − | 46.5116i | 0.0615990 | − | 0.147656i | ||||
\(316\) | 151.122 | 0.478235 | ||||||||
\(317\) | 161.728 | − | 161.728i | 0.510182 | − | 0.510182i | −0.404400 | − | 0.914582i | \(-0.632520\pi\) |
0.914582 | + | 0.404400i | \(0.132520\pi\) | |||||||
\(318\) | −43.1410 | − | 43.1410i | −0.135664 | − | 0.135664i | ||||
\(319\) | − | 129.776i | − | 0.406823i | ||||||
\(320\) | 36.9938 | − | 15.2138i | 0.115606 | − | 0.0475432i | ||||
\(321\) | −77.9920 | −0.242966 | ||||||||
\(322\) | −16.1129 | + | 16.1129i | −0.0500402 | + | 0.0500402i | ||||
\(323\) | 17.3762 | + | 17.3762i | 0.0537962 | + | 0.0537962i | ||||
\(324\) | 18.0000i | 0.0555556i | ||||||||
\(325\) | 262.443 | + | 1.32761i | 0.807516 | + | 0.00408497i | ||||
\(326\) | −109.807 | −0.336832 | ||||||||
\(327\) | −218.284 | + | 218.284i | −0.667534 | + | 0.667534i | ||||
\(328\) | −14.0320 | − | 14.0320i | −0.0427805 | − | 0.0427805i | ||||
\(329\) | − | 141.186i | − | 0.429138i | ||||||
\(330\) | −38.1498 | − | 92.7647i | −0.115606 | − | 0.281105i | ||||
\(331\) | −404.107 | −1.22087 | −0.610434 | − | 0.792067i | \(-0.709005\pi\) | ||||
−0.610434 | + | 0.792067i | \(0.709005\pi\) | |||||||
\(332\) | −107.646 | + | 107.646i | −0.324236 | + | 0.324236i | ||||
\(333\) | −42.6461 | − | 42.6461i | −0.128066 | − | 0.128066i | ||||
\(334\) | − | 80.0673i | − | 0.239723i | ||||||
\(335\) | 436.898 | + | 182.265i | 1.30417 | + | 0.544075i | ||||
\(336\) | 23.2772 | 0.0692775 | ||||||||
\(337\) | −49.6359 | + | 49.6359i | −0.147288 | + | 0.147288i | −0.776905 | − | 0.629618i | \(-0.783212\pi\) |
0.629618 | + | 0.776905i | \(0.283212\pi\) | |||||||
\(338\) | −58.7952 | − | 58.7952i | −0.173950 | − | 0.173950i | ||||
\(339\) | 180.624i | 0.532815i | ||||||||
\(340\) | −44.8322 | + | 107.465i | −0.131859 | + | 0.316073i | ||||
\(341\) | 123.490 | 0.362141 | ||||||||
\(342\) | −6.33115 | + | 6.33115i | −0.0185121 | + | 0.0185121i | ||||
\(343\) | 206.003 | + | 206.003i | 0.600593 | + | 0.600593i | ||||
\(344\) | 12.4954i | 0.0363238i | ||||||||
\(345\) | 38.4117 | − | 15.7969i | 0.111338 | − | 0.0457882i | ||||
\(346\) | 145.244 | 0.419781 | ||||||||
\(347\) | −37.8258 | + | 37.8258i | −0.109008 | + | 0.109008i | −0.759507 | − | 0.650499i | \(-0.774560\pi\) |
0.650499 | + | 0.759507i | \(0.274560\pi\) | |||||||
\(348\) | −38.8153 | − | 38.8153i | −0.111538 | − | 0.111538i | ||||
\(349\) | − | 608.019i | − | 1.74217i | −0.491129 | − | 0.871087i | \(-0.663416\pi\) | ||
0.491129 | − | 0.871087i | \(-0.336584\pi\) | |||||||
\(350\) | 83.5685 | + | 84.4183i | 0.238767 | + | 0.241195i | ||||
\(351\) | −54.5484 | −0.155409 | ||||||||
\(352\) | 32.7588 | − | 32.7588i | 0.0930649 | − | 0.0930649i | ||||
\(353\) | 102.065 | + | 102.065i | 0.289135 | + | 0.289135i | 0.836738 | − | 0.547603i | \(-0.184460\pi\) |
−0.547603 | + | 0.836738i | \(0.684460\pi\) | |||||||
\(354\) | 64.7297i | 0.182852i | ||||||||
\(355\) | 128.191 | + | 311.708i | 0.361102 | + | 0.878052i | ||||
\(356\) | −153.205 | −0.430351 | ||||||||
\(357\) | −47.9142 | + | 47.9142i | −0.134214 | + | 0.134214i | ||||
\(358\) | −294.692 | − | 294.692i | −0.823161 | − | 0.823161i | ||||
\(359\) | 392.739i | 1.09398i | 0.837139 | + | 0.546990i | \(0.184227\pi\) | ||||
−0.837139 | + | 0.546990i | \(0.815773\pi\) | |||||||
\(360\) | −39.1557 | − | 16.3350i | −0.108766 | − | 0.0453749i | ||||
\(361\) | 356.546 | 0.987663 | ||||||||
\(362\) | 15.6531 | − | 15.6531i | 0.0432407 | − | 0.0432407i | ||||
\(363\) | 66.0488 | + | 66.0488i | 0.181953 | + | 0.181953i | ||||
\(364\) | 70.5409i | 0.193794i | ||||||||
\(365\) | 46.2575 | − | 110.882i | 0.126733 | − | 0.303785i | ||||
\(366\) | 69.0150 | 0.188566 | ||||||||
\(367\) | 41.5309 | − | 41.5309i | 0.113163 | − | 0.113163i | −0.648258 | − | 0.761421i | \(-0.724502\pi\) |
0.761421 | + | 0.648258i | \(0.224502\pi\) | |||||||
\(368\) | 13.5647 | + | 13.5647i | 0.0368605 | + | 0.0368605i | ||||
\(369\) | 21.0480i | 0.0570406i | ||||||||
\(370\) | 131.470 | − | 54.0675i | 0.355324 | − | 0.146128i | ||||
\(371\) | 83.6836 | 0.225562 | ||||||||
\(372\) | 36.9351 | − | 36.9351i | 0.0992878 | − | 0.0992878i | ||||
\(373\) | −188.716 | − | 188.716i | −0.505941 | − | 0.505941i | 0.407337 | − | 0.913278i | \(-0.366457\pi\) |
−0.913278 | + | 0.407337i | \(0.866457\pi\) | |||||||
\(374\) | 134.863i | 0.360595i | ||||||||
\(375\) | −81.3332 | − | 200.649i | −0.216889 | − | 0.535063i | ||||
\(376\) | −118.858 | −0.316111 | ||||||||
\(377\) | 117.629 | − | 117.629i | 0.312012 | − | 0.312012i | ||||
\(378\) | −17.4579 | − | 17.4579i | −0.0461850 | − | 0.0461850i | ||||
\(379\) | 143.699i | 0.379152i | 0.981866 | + | 0.189576i | \(0.0607113\pi\) | ||||
−0.981866 | + | 0.189576i | \(0.939289\pi\) | |||||||
\(380\) | −8.02675 | − | 19.5178i | −0.0211230 | − | 0.0513625i | ||||
\(381\) | −27.6261 | −0.0725095 | ||||||||
\(382\) | 128.180 | − | 128.180i | 0.335548 | − | 0.335548i | ||||
\(383\) | 98.2112 | + | 98.2112i | 0.256426 | + | 0.256426i | 0.823599 | − | 0.567173i | \(-0.191963\pi\) |
−0.567173 | + | 0.823599i | \(0.691963\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 126.972 | + | 52.9702i | 0.329798 | + | 0.137585i | ||||
\(386\) | −59.4006 | −0.153888 | ||||||||
\(387\) | 9.37154 | − | 9.37154i | 0.0242159 | − | 0.0242159i | ||||
\(388\) | −69.5800 | − | 69.5800i | −0.179330 | − | 0.179330i | ||||
\(389\) | 244.042i | 0.627357i | 0.949529 | + | 0.313678i | \(0.101561\pi\) | ||||
−0.949529 | + | 0.313678i | \(0.898439\pi\) | |||||||
\(390\) | 49.5026 | − | 118.660i | 0.126930 | − | 0.304257i | ||||
\(391\) | −55.8434 | −0.142822 | ||||||||
\(392\) | 75.4238 | − | 75.4238i | 0.192408 | − | 0.192408i | ||||
\(393\) | 154.033 | + | 154.033i | 0.391941 | + | 0.391941i | ||||
\(394\) | − | 245.484i | − | 0.623057i | ||||||
\(395\) | 349.412 | − | 143.697i | 0.884587 | − | 0.363789i | ||||
\(396\) | −49.1383 | −0.124087 | ||||||||
\(397\) | −168.912 | + | 168.912i | −0.425470 | + | 0.425470i | −0.887082 | − | 0.461612i | \(-0.847271\pi\) |
0.461612 | + | 0.887082i | \(0.347271\pi\) | |||||||
\(398\) | 10.9495 | + | 10.9495i | 0.0275114 | + | 0.0275114i | ||||
\(399\) | − | 12.2810i | − | 0.0307794i | ||||||
\(400\) | 71.0675 | − | 70.3521i | 0.177669 | − | 0.175880i | ||||
\(401\) | −226.855 | −0.565724 | −0.282862 | − | 0.959161i | \(-0.591284\pi\) | ||||
−0.282862 | + | 0.959161i | \(0.591284\pi\) | |||||||
\(402\) | 163.988 | − | 163.988i | 0.407930 | − | 0.407930i | ||||
\(403\) | 111.930 | + | 111.930i | 0.277743 | + | 0.277743i | ||||
\(404\) | 1.13532i | 0.00281020i | ||||||||
\(405\) | 17.1155 | + | 41.6180i | 0.0422606 | + | 0.102761i | ||||
\(406\) | 75.2928 | 0.185450 | ||||||||
\(407\) | 116.420 | − | 116.420i | 0.286043 | − | 0.286043i | ||||
\(408\) | 40.3365 | + | 40.3365i | 0.0988641 | + | 0.0988641i | ||||
\(409\) | − | 193.056i | − | 0.472021i | −0.971751 | − | 0.236010i | \(-0.924160\pi\) | ||
0.971751 | − | 0.236010i | \(-0.0758399\pi\) | |||||||
\(410\) | −45.7860 | − | 19.1010i | −0.111673 | − | 0.0465878i | ||||
\(411\) | −218.863 | −0.532514 | ||||||||
\(412\) | −24.6578 | + | 24.6578i | −0.0598490 | + | 0.0598490i | ||||
\(413\) | −62.7804 | − | 62.7804i | −0.152011 | − | 0.152011i | ||||
\(414\) | − | 20.3470i | − | 0.0491473i | ||||||
\(415\) | −146.533 | + | 351.248i | −0.353093 | + | 0.846380i | ||||
\(416\) | 59.3848 | 0.142752 | ||||||||
\(417\) | −74.9634 | + | 74.9634i | −0.179768 | + | 0.179768i | ||||
\(418\) | −17.2834 | − | 17.2834i | −0.0413479 | − | 0.0413479i | ||||
\(419\) | 418.810i | 0.999546i | 0.866156 | + | 0.499773i | \(0.166583\pi\) | ||||
−0.866156 | + | 0.499773i | \(0.833417\pi\) | |||||||
\(420\) | 53.8196 | − | 22.1335i | 0.128142 | − | 0.0526988i | ||||
\(421\) | 781.367 | 1.85598 | 0.927989 | − | 0.372607i | \(-0.121536\pi\) | ||||
0.927989 | + | 0.372607i | \(0.121536\pi\) | |||||||
\(422\) | −371.360 | + | 371.360i | −0.879999 | + | 0.879999i | ||||
\(423\) | 89.1432 | + | 89.1432i | 0.210740 | + | 0.210740i | ||||
\(424\) | − | 70.4490i | − | 0.166153i | ||||||
\(425\) | −1.47258 | + | 291.100i | −0.00346490 | + | 0.684942i | ||||
\(426\) | 165.115 | 0.387593 | ||||||||
\(427\) | −66.9366 | + | 66.9366i | −0.156760 | + | 0.156760i | ||||
\(428\) | −63.6802 | − | 63.6802i | −0.148785 | − | 0.148785i | ||||
\(429\) | − | 148.912i | − | 0.347114i | ||||||
\(430\) | 11.8814 | + | 28.8907i | 0.0276312 | + | 0.0671878i | ||||
\(431\) | −127.925 | −0.296809 | −0.148404 | − | 0.988927i | \(-0.547414\pi\) | ||||
−0.148404 | + | 0.988927i | \(0.547414\pi\) | |||||||
\(432\) | −14.6969 | + | 14.6969i | −0.0340207 | + | 0.0340207i | ||||
\(433\) | 219.940 | + | 219.940i | 0.507945 | + | 0.507945i | 0.913895 | − | 0.405950i | \(-0.133059\pi\) |
−0.405950 | + | 0.913895i | \(0.633059\pi\) | |||||||
\(434\) | 71.6455i | 0.165082i | ||||||||
\(435\) | −126.653 | − | 52.8372i | −0.291157 | − | 0.121465i | ||||
\(436\) | −356.456 | −0.817559 | ||||||||
\(437\) | 7.15666 | − | 7.15666i | 0.0163768 | − | 0.0163768i | ||||
\(438\) | −41.6189 | − | 41.6189i | −0.0950204 | − | 0.0950204i | ||||
\(439\) | − | 159.575i | − | 0.363496i | −0.983345 | − | 0.181748i | \(-0.941825\pi\) | ||
0.983345 | − | 0.181748i | \(-0.0581754\pi\) | |||||||
\(440\) | 44.5929 | − | 106.891i | 0.101348 | − | 0.242935i | ||||
\(441\) | −113.136 | −0.256543 | ||||||||
\(442\) | −122.239 | + | 122.239i | −0.276558 | + | 0.276558i | ||||
\(443\) | 0.230949 | + | 0.230949i | 0.000521329 | + | 0.000521329i | 0.707367 | − | 0.706846i | \(-0.249883\pi\) |
−0.706846 | + | 0.707367i | \(0.749883\pi\) | |||||||
\(444\) | − | 69.6407i | − | 0.156849i | ||||||
\(445\) | −354.227 | + | 145.677i | −0.796015 | + | 0.327364i | ||||
\(446\) | −151.986 | −0.340776 | ||||||||
\(447\) | −301.151 | + | 301.151i | −0.673716 | + | 0.673716i | ||||
\(448\) | 19.0058 | + | 19.0058i | 0.0424236 | + | 0.0424236i | ||||
\(449\) | − | 717.728i | − | 1.59850i | −0.600997 | − | 0.799251i | \(-0.705230\pi\) | ||
0.600997 | − | 0.799251i | \(-0.294770\pi\) | |||||||
\(450\) | −106.065 | − | 0.536547i | −0.235699 | − | 0.00119233i | ||||
\(451\) | −57.4590 | −0.127404 | ||||||||
\(452\) | −147.479 | + | 147.479i | −0.326281 | + | 0.326281i | ||||
\(453\) | 10.0904 | + | 10.0904i | 0.0222747 | + | 0.0222747i | ||||
\(454\) | − | 345.170i | − | 0.760287i | ||||||
\(455\) | 67.0748 | + | 163.098i | 0.147417 | + | 0.358458i | ||||
\(456\) | −10.3387 | −0.0226726 | ||||||||
\(457\) | 46.2379 | − | 46.2379i | 0.101177 | − | 0.101177i | −0.654706 | − | 0.755883i | \(-0.727208\pi\) |
0.755883 | + | 0.654706i | \(0.227208\pi\) | |||||||
\(458\) | −73.4614 | − | 73.4614i | −0.160396 | − | 0.160396i | ||||
\(459\) | − | 60.5048i | − | 0.131819i | ||||||
\(460\) | 44.2611 | + | 18.4649i | 0.0962199 | + | 0.0401410i | ||||
\(461\) | −88.2710 | −0.191477 | −0.0957386 | − | 0.995407i | \(-0.530521\pi\) | ||||
−0.0957386 | + | 0.995407i | \(0.530521\pi\) | |||||||
\(462\) | 47.6585 | − | 47.6585i | 0.103157 | − | 0.103157i | ||||
\(463\) | 167.771 | + | 167.771i | 0.362357 | + | 0.362357i | 0.864680 | − | 0.502323i | \(-0.167521\pi\) |
−0.502323 | + | 0.864680i | \(0.667521\pi\) | |||||||
\(464\) | − | 63.3851i | − | 0.136606i | ||||||
\(465\) | 50.2778 | − | 120.518i | 0.108124 | − | 0.259179i | ||||
\(466\) | 569.945 | 1.22306 | ||||||||
\(467\) | −62.5685 | + | 62.5685i | −0.133980 | + | 0.133980i | −0.770916 | − | 0.636937i | \(-0.780201\pi\) |
0.636937 | + | 0.770916i | \(0.280201\pi\) | |||||||
\(468\) | −44.5386 | − | 44.5386i | −0.0951679 | − | 0.0951679i | ||||
\(469\) | 318.099i | 0.678249i | ||||||||
\(470\) | −274.812 | + | 113.017i | −0.584706 | + | 0.240462i | ||||
\(471\) | 141.905 | 0.301285 | ||||||||
\(472\) | −52.8516 | + | 52.8516i | −0.111974 | + | 0.111974i | ||||
\(473\) | 25.5834 | + | 25.5834i | 0.0540876 | + | 0.0540876i | ||||
\(474\) | − | 185.086i | − | 0.390478i | ||||||
\(475\) | −37.1175 | − | 37.4949i | −0.0781420 | − | 0.0789366i | ||||
\(476\) | −78.2436 | −0.164377 | ||||||||
\(477\) | −52.8367 | + | 52.8367i | −0.110769 | + | 0.110769i | ||||
\(478\) | −117.112 | − | 117.112i | −0.245005 | − | 0.245005i | ||||
\(479\) | 612.563i | 1.27884i | 0.768858 | + | 0.639419i | \(0.220825\pi\) | ||||
−0.768858 | + | 0.639419i | \(0.779175\pi\) | |||||||
\(480\) | −18.6330 | − | 45.3079i | −0.0388188 | − | 0.0943915i | ||||
\(481\) | 211.044 | 0.438761 | ||||||||
\(482\) | 178.634 | − | 178.634i | 0.370610 | − | 0.370610i | ||||
\(483\) | 19.7342 | + | 19.7342i | 0.0408576 | + | 0.0408576i | ||||
\(484\) | 107.857i | 0.222846i | ||||||||
\(485\) | −227.038 | − | 94.7157i | −0.468119 | − | 0.195290i | ||||
\(486\) | 22.0454 | 0.0453609 | ||||||||
\(487\) | −342.927 | + | 342.927i | −0.704162 | + | 0.704162i | −0.965301 | − | 0.261139i | \(-0.915902\pi\) |
0.261139 | + | 0.965301i | \(0.415902\pi\) | |||||||
\(488\) | 56.3505 | + | 56.3505i | 0.115472 | + | 0.115472i | ||||
\(489\) | 134.486i | 0.275022i | ||||||||
\(490\) | 102.670 | − | 246.106i | 0.209531 | − | 0.502257i | ||||
\(491\) | −850.889 | −1.73297 | −0.866486 | − | 0.499202i | \(-0.833627\pi\) | ||||
−0.866486 | + | 0.499202i | \(0.833627\pi\) | |||||||
\(492\) | −17.1856 | + | 17.1856i | −0.0349301 | + | 0.0349301i | ||||
\(493\) | 130.473 | + | 130.473i | 0.264651 | + | 0.264651i | ||||
\(494\) | − | 31.3312i | − | 0.0634234i | ||||||
\(495\) | −113.613 | + | 46.7238i | −0.229522 | + | 0.0943915i | ||||
\(496\) | 60.3147 | 0.121602 | ||||||||
\(497\) | −160.142 | + | 160.142i | −0.322218 | + | 0.322218i | ||||
\(498\) | 131.839 | + | 131.839i | 0.264738 | + | 0.264738i | ||||
\(499\) | − | 782.522i | − | 1.56818i | −0.620647 | − | 0.784090i | \(-0.713130\pi\) | ||
0.620647 | − | 0.784090i | \(-0.286870\pi\) | |||||||
\(500\) | 97.4207 | − | 230.237i | 0.194841 | − | 0.460475i | ||||
\(501\) | −98.0621 | −0.195733 | ||||||||
\(502\) | −350.780 | + | 350.780i | −0.698765 | + | 0.698765i | ||||
\(503\) | 71.5670 | + | 71.5670i | 0.142280 | + | 0.142280i | 0.774659 | − | 0.632379i | \(-0.217921\pi\) |
−0.632379 | + | 0.774659i | \(0.717921\pi\) | |||||||
\(504\) | − | 28.5087i | − | 0.0565648i | ||||||
\(505\) | 1.07953 | + | 2.62499i | 0.00213769 | + | 0.00519799i | ||||
\(506\) | 55.5453 | 0.109773 | ||||||||
\(507\) | −72.0091 | + | 72.0091i | −0.142030 | + | 0.142030i | ||||
\(508\) | −22.5566 | − | 22.5566i | −0.0444028 | − | 0.0444028i | ||||
\(509\) | 451.402i | 0.886840i | 0.896314 | + | 0.443420i | \(0.146235\pi\) | ||||
−0.896314 | + | 0.443420i | \(0.853765\pi\) | |||||||
\(510\) | 131.617 | + | 54.9080i | 0.258073 | + | 0.107663i | ||||
\(511\) | 80.7312 | 0.157987 | ||||||||
\(512\) | 16.0000 | − | 16.0000i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 7.75404 | + | 7.75404i | 0.0151151 | + | 0.0151151i | ||||
\(514\) | − | 216.209i | − | 0.420639i | ||||||
\(515\) | −33.5654 | + | 80.4578i | −0.0651755 | + | 0.156229i | ||||
\(516\) | 15.3037 | 0.0296583 | ||||||||
\(517\) | −243.352 | + | 243.352i | −0.470701 | + | 0.470701i | ||||
\(518\) | 67.5435 | + | 67.5435i | 0.130393 | + | 0.130393i | ||||
\(519\) | − | 177.887i | − | 0.342749i | ||||||
\(520\) | 137.304 | − | 56.4668i | 0.264047 | − | 0.108590i | ||||
\(521\) | 595.887 | 1.14374 | 0.571869 | − | 0.820345i | \(-0.306219\pi\) | ||||
0.571869 | + | 0.820345i | \(0.306219\pi\) | |||||||
\(522\) | −47.5388 | + | 47.5388i | −0.0910706 | + | 0.0910706i | ||||
\(523\) | 172.420 | + | 172.420i | 0.329674 | + | 0.329674i | 0.852463 | − | 0.522788i | \(-0.175108\pi\) |
−0.522788 | + | 0.852463i | \(0.675108\pi\) | |||||||
\(524\) | 251.535i | 0.480028i | ||||||||
\(525\) | 103.391 | − | 102.350i | 0.196935 | − | 0.194953i | ||||
\(526\) | 156.765 | 0.298033 | ||||||||
\(527\) | −124.153 | + | 124.153i | −0.235584 | + | 0.235584i | ||||
\(528\) | −40.1212 | − | 40.1212i | −0.0759872 | − | 0.0759872i | ||||
\(529\) | 23.0000i | 0.0434783i | ||||||||
\(530\) | −66.9873 | − | 162.886i | −0.126391 | − | 0.307332i | ||||
\(531\) | 79.2774 | 0.149298 | ||||||||
\(532\) | 10.0274 | − | 10.0274i | 0.0188484 | − | 0.0188484i | ||||
\(533\) | −52.0804 | − | 52.0804i | −0.0977119 | − | 0.0977119i | ||||
\(534\) | 187.637i | 0.351380i | ||||||||
\(535\) | −207.787 | − | 86.6845i | −0.388387 | − | 0.162027i | ||||
\(536\) | 267.791 | 0.499610 | ||||||||
\(537\) | −360.922 | + | 360.922i | −0.672108 | + | 0.672108i | ||||
\(538\) | −326.796 | − | 326.796i | −0.607427 | − | 0.607427i | ||||
\(539\) | − | 308.849i | − | 0.573004i | ||||||
\(540\) | −20.0062 | + | 47.9557i | −0.0370485 | + | 0.0888069i | ||||
\(541\) | 576.448 | 1.06552 | 0.532762 | − | 0.846265i | \(-0.321154\pi\) | ||||
0.532762 | + | 0.846265i | \(0.321154\pi\) | |||||||
\(542\) | −312.784 | + | 312.784i | −0.577093 | + | 0.577093i | ||||
\(543\) | −19.1711 | − | 19.1711i | −0.0353059 | − | 0.0353059i | ||||
\(544\) | 65.8693i | 0.121083i | ||||||||
\(545\) | −824.166 | + | 338.941i | −1.51223 | + | 0.621910i | ||||
\(546\) | 86.3946 | 0.158232 | ||||||||
\(547\) | −196.463 | + | 196.463i | −0.359164 | + | 0.359164i | −0.863505 | − | 0.504341i | \(-0.831736\pi\) |
0.504341 | + | 0.863505i | \(0.331736\pi\) | |||||||
\(548\) | −178.701 | − | 178.701i | −0.326097 | − | 0.326097i | ||||
\(549\) | − | 84.5258i | − | 0.153963i | ||||||
\(550\) | 1.46472 | − | 289.546i | 0.00266313 | − | 0.526448i | ||||
\(551\) | −33.4417 | −0.0606928 | ||||||||
\(552\) | 16.6132 | − | 16.6132i | 0.0300965 | − | 0.0300965i | ||||
\(553\) | 179.512 | + | 179.512i | 0.324616 | + | 0.324616i | ||||
\(554\) | 129.845i | 0.234377i | ||||||||
\(555\) | −66.2188 | − | 161.017i | −0.119313 | − | 0.290121i | ||||
\(556\) | −122.415 | −0.220170 | ||||||||
\(557\) | −175.913 | + | 175.913i | −0.315823 | + | 0.315823i | −0.847160 | − | 0.531337i | \(-0.821690\pi\) |
0.531337 | + | 0.847160i | \(0.321690\pi\) | |||||||
\(558\) | −45.2360 | − | 45.2360i | −0.0810681 | − | 0.0810681i | ||||
\(559\) | 46.3773i | 0.0829647i | ||||||||
\(560\) | 62.0154 | + | 25.8716i | 0.110742 | + | 0.0461993i | ||||
\(561\) | 165.172 | 0.294425 | ||||||||
\(562\) | −222.033 | + | 222.033i | −0.395077 | + | 0.395077i | ||||
\(563\) | 385.523 | + | 385.523i | 0.684765 | + | 0.684765i | 0.961070 | − | 0.276305i | \(-0.0891100\pi\) |
−0.276305 | + | 0.961070i | \(0.589110\pi\) | |||||||
\(564\) | 145.570i | 0.258103i | ||||||||
\(565\) | −200.755 | + | 481.220i | −0.355319 | + | 0.851717i | ||||
\(566\) | −528.403 | −0.933574 | ||||||||
\(567\) | −21.3815 | + | 21.3815i | −0.0377099 | + | 0.0377099i | ||||
\(568\) | 134.815 | + | 134.815i | 0.237351 | + | 0.237351i | ||||
\(569\) | 133.135i | 0.233981i | 0.993133 | + | 0.116990i | \(0.0373247\pi\) | ||||
−0.993133 | + | 0.116990i | \(0.962675\pi\) | |||||||
\(570\) | −23.9043 | + | 9.83072i | −0.0419373 | + | 0.0172469i | ||||
\(571\) | −296.967 | −0.520082 | −0.260041 | − | 0.965598i | \(-0.583736\pi\) | ||||
−0.260041 | + | 0.965598i | \(0.583736\pi\) | |||||||
\(572\) | 121.586 | − | 121.586i | 0.212563 | − | 0.212563i | ||||
\(573\) | −156.987 | − | 156.987i | −0.273974 | − | 0.273974i | ||||
\(574\) | − | 33.3361i | − | 0.0580769i | ||||||
\(575\) | 119.894 | + | 0.606507i | 0.208512 | + | 0.00105479i | ||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | −337.682 | + | 337.682i | −0.585237 | + | 0.585237i | −0.936338 | − | 0.351101i | \(-0.885807\pi\) |
0.351101 | + | 0.936338i | \(0.385807\pi\) | |||||||
\(578\) | 153.414 | + | 153.414i | 0.265422 | + | 0.265422i | ||||
\(579\) | 72.7506i | 0.125649i | ||||||||
\(580\) | −60.2706 | − | 146.553i | −0.103915 | − | 0.252678i | ||||
\(581\) | −255.738 | −0.440169 | ||||||||
\(582\) | −85.2178 | + | 85.2178i | −0.146422 | + | 0.146422i | ||||
\(583\) | −144.239 | − | 144.239i | −0.247408 | − | 0.247408i | ||||
\(584\) | − | 67.9635i | − | 0.116376i | ||||||
\(585\) | −145.328 | − | 60.6281i | −0.248424 | − | 0.103638i | ||||
\(586\) | 300.586 | 0.512945 | ||||||||
\(587\) | −389.132 | + | 389.132i | −0.662916 | + | 0.662916i | −0.956066 | − | 0.293150i | \(-0.905296\pi\) |
0.293150 | + | 0.956066i | \(0.405296\pi\) | |||||||
\(588\) | −92.3749 | − | 92.3749i | −0.157100 | − | 0.157100i | ||||
\(589\) | − | 31.8218i | − | 0.0540268i | ||||||
\(590\) | −71.9441 | + | 172.453i | −0.121939 | + | 0.292294i | ||||
\(591\) | −300.656 | −0.508724 | ||||||||
\(592\) | 56.8614 | − | 56.8614i | 0.0960497 | − | 0.0960497i | ||||
\(593\) | −511.328 | − | 511.328i | −0.862273 | − | 0.862273i | 0.129329 | − | 0.991602i | \(-0.458718\pi\) |
−0.991602 | + | 0.129329i | \(0.958718\pi\) | |||||||
\(594\) | 60.1818i | 0.101316i | ||||||||
\(595\) | −180.908 | + | 74.3990i | −0.304047 | + | 0.125040i | ||||
\(596\) | −491.778 | −0.825130 | ||||||||
\(597\) | 13.4104 | − | 13.4104i | 0.0224630 | − | 0.0224630i | ||||
\(598\) | 50.3459 | + | 50.3459i | 0.0841905 | + | 0.0841905i | ||||
\(599\) | − | 163.806i | − | 0.273466i | −0.990608 | − | 0.136733i | \(-0.956340\pi\) | ||
0.990608 | − | 0.136733i | \(-0.0436602\pi\) | |||||||
\(600\) | −86.1633 | − | 87.0395i | −0.143606 | − | 0.145066i | ||||
\(601\) | 686.382 | 1.14207 | 0.571033 | − | 0.820927i | \(-0.306543\pi\) | ||||
0.571033 | + | 0.820927i | \(0.306543\pi\) | |||||||
\(602\) | −14.8428 | + | 14.8428i | −0.0246558 | + | 0.0246558i | ||||
\(603\) | −200.843 | − | 200.843i | −0.333074 | − | 0.333074i | ||||
\(604\) | 16.4776i | 0.0272808i | ||||||||
\(605\) | 102.558 | + | 249.378i | 0.169517 | + | 0.412195i | ||||
\(606\) | 1.39048 | 0.00229452 | ||||||||
\(607\) | −153.299 | + | 153.299i | −0.252553 | + | 0.252553i | −0.822016 | − | 0.569464i | \(-0.807151\pi\) |
0.569464 | + | 0.822016i | \(0.307151\pi\) | |||||||
\(608\) | −8.44153 | − | 8.44153i | −0.0138841 | − | 0.0138841i | ||||
\(609\) | − | 92.2144i | − | 0.151419i | ||||||
\(610\) | 183.870 | + | 76.7070i | 0.301427 | + | 0.125749i | ||||
\(611\) | −441.146 | −0.722006 | ||||||||
\(612\) | 49.4020 | − | 49.4020i | 0.0807222 | − | 0.0807222i | ||||
\(613\) | 713.442 | + | 713.442i | 1.16385 | + | 1.16385i | 0.983625 | + | 0.180228i | \(0.0576834\pi\) |
0.180228 | + | 0.983625i | \(0.442317\pi\) | |||||||
\(614\) | 743.401i | 1.21075i | ||||||||
\(615\) | −23.3939 | + | 56.0762i | −0.0380388 | + | 0.0911808i | ||||
\(616\) | 77.8260 | 0.126341 | ||||||||
\(617\) | 232.838 | − | 232.838i | 0.377372 | − | 0.377372i | −0.492781 | − | 0.870153i | \(-0.664020\pi\) |
0.870153 | + | 0.492781i | \(0.164020\pi\) | |||||||
\(618\) | 30.1995 | + | 30.1995i | 0.0488665 | + | 0.0488665i | ||||
\(619\) | − | 126.186i | − | 0.203854i | −0.994792 | − | 0.101927i | \(-0.967499\pi\) | ||
0.994792 | − | 0.101927i | \(-0.0325009\pi\) | |||||||
\(620\) | 139.454 | − | 57.3510i | 0.224926 | − | 0.0925017i | ||||
\(621\) | −24.9199 | −0.0401286 | ||||||||
\(622\) | 24.8526 | − | 24.8526i | 0.0399559 | − | 0.0399559i | ||||
\(623\) | −181.986 | − | 181.986i | −0.292113 | − | 0.292113i | ||||
\(624\) | − | 72.7312i | − | 0.116556i | ||||||
\(625\) | 6.32319 | − | 624.968i | 0.0101171 | − | 0.999949i | ||||
\(626\) | 318.752 | 0.509189 | ||||||||
\(627\) | −21.1678 | + | 21.1678i | −0.0337604 | + | 0.0337604i | ||||
\(628\) | 115.865 | + | 115.865i | 0.184499 | + | 0.184499i | ||||
\(629\) | 234.089i | 0.372160i | ||||||||
\(630\) | −27.1079 | − | 65.9152i | −0.0430284 | − | 0.104627i | ||||
\(631\) | −632.532 | −1.00243 | −0.501214 | − | 0.865323i | \(-0.667113\pi\) | ||||
−0.501214 | + | 0.865323i | \(0.667113\pi\) | |||||||
\(632\) | 151.122 | − | 151.122i | 0.239118 | − | 0.239118i | ||||
\(633\) | 454.821 | + | 454.821i | 0.718516 | + | 0.718516i | ||||
\(634\) | − | 323.455i | − | 0.510182i | ||||||
\(635\) | −73.6017 | − | 30.7052i | −0.115908 | − | 0.0483546i | ||||
\(636\) | −86.2820 | −0.135664 | ||||||||
\(637\) | 279.939 | − | 279.939i | 0.439465 | − | 0.439465i | ||||
\(638\) | −129.776 | − | 129.776i | −0.203411 | − | 0.203411i | ||||
\(639\) | − | 202.223i | − | 0.316468i | ||||||
\(640\) | 21.7800 | − | 52.2076i | 0.0340312 | − | 0.0815744i | ||||
\(641\) | 216.571 | 0.337864 | 0.168932 | − | 0.985628i | \(-0.445968\pi\) | ||||
0.168932 | + | 0.985628i | \(0.445968\pi\) | |||||||
\(642\) | −77.9920 | + | 77.9920i | −0.121483 | + | 0.121483i | ||||
\(643\) | 763.835 | + | 763.835i | 1.18792 | + | 1.18792i | 0.977641 | + | 0.210283i | \(0.0674385\pi\) |
0.210283 | + | 0.977641i | \(0.432562\pi\) | |||||||
\(644\) | 32.2259i | 0.0500402i | ||||||||
\(645\) | 35.3838 | − | 14.5517i | 0.0548586 | − | 0.0225608i | ||||
\(646\) | 34.7524 | 0.0537962 | ||||||||
\(647\) | 868.923 | − | 868.923i | 1.34300 | − | 1.34300i | 0.449949 | − | 0.893054i | \(-0.351442\pi\) |
0.893054 | − | 0.449949i | \(-0.148558\pi\) | |||||||
\(648\) | 18.0000 | + | 18.0000i | 0.0277778 | + | 0.0277778i | ||||
\(649\) | 216.420i | 0.333466i | ||||||||
\(650\) | 263.770 | − | 261.115i | 0.405801 | − | 0.401716i | ||||
\(651\) | 87.7475 | 0.134789 | ||||||||
\(652\) | −109.807 | + | 109.807i | −0.168416 | + | 0.168416i | ||||
\(653\) | −441.359 | − | 441.359i | −0.675894 | − | 0.675894i | 0.283174 | − | 0.959069i | \(-0.408613\pi\) |
−0.959069 | + | 0.283174i | \(0.908613\pi\) | |||||||
\(654\) | 436.568i | 0.667534i | ||||||||
\(655\) | 239.175 | + | 581.577i | 0.365153 | + | 0.887903i | ||||
\(656\) | −28.0640 | −0.0427805 | ||||||||
\(657\) | −50.9726 | + | 50.9726i | −0.0775839 | + | 0.0775839i | ||||
\(658\) | −141.186 | − | 141.186i | −0.214569 | − | 0.214569i | ||||
\(659\) | − | 333.161i | − | 0.505555i | −0.967524 | − | 0.252778i | \(-0.918656\pi\) | ||
0.967524 | − | 0.252778i | \(-0.0813441\pi\) | |||||||
\(660\) | −130.915 | − | 54.6149i | −0.198355 | − | 0.0827499i | ||||
\(661\) | 1104.51 | 1.67096 | 0.835481 | − | 0.549520i | \(-0.185189\pi\) | ||||
0.835481 | + | 0.549520i | \(0.185189\pi\) | |||||||
\(662\) | −404.107 | + | 404.107i | −0.610434 | + | 0.610434i | ||||
\(663\) | 149.711 | + | 149.711i | 0.225809 | + | 0.225809i | ||||
\(664\) | 215.293i | 0.324236i | ||||||||
\(665\) | 13.6497 | − | 32.7191i | 0.0205259 | − | 0.0492016i | ||||
\(666\) | −85.2921 | −0.128066 | ||||||||
\(667\) | 53.7374 | − | 53.7374i | 0.0805658 | − | 0.0805658i | ||||
\(668\) | −80.0673 | − | 80.0673i | −0.119861 | − | 0.119861i | ||||
\(669\) | 186.144i | 0.278242i | ||||||||
\(670\) | 619.163 | − | 254.633i | 0.924124 | − | 0.380049i | ||||
\(671\) | 230.747 | 0.343886 | ||||||||
\(672\) | 23.2772 | − | 23.2772i | 0.0346387 | − | 0.0346387i | ||||
\(673\) | 166.235 | + | 166.235i | 0.247005 | + | 0.247005i | 0.819740 | − | 0.572735i | \(-0.194118\pi\) |
−0.572735 | + | 0.819740i | \(0.694118\pi\) | |||||||
\(674\) | 99.2719i | 0.147288i | ||||||||
\(675\) | −0.657133 | + | 129.902i | −0.000973531 | + | 0.192448i | ||||
\(676\) | −117.590 | −0.173950 | ||||||||
\(677\) | 56.8084 | − | 56.8084i | 0.0839119 | − | 0.0839119i | −0.663905 | − | 0.747817i | \(-0.731102\pi\) |
0.747817 | + | 0.663905i | \(0.231102\pi\) | |||||||
\(678\) | 180.624 | + | 180.624i | 0.266407 | + | 0.266407i | ||||
\(679\) | − | 165.303i | − | 0.243451i | ||||||
\(680\) | 62.6327 | + | 152.297i | 0.0921069 | + | 0.223966i | ||||
\(681\) | −422.745 | −0.620772 | ||||||||
\(682\) | 123.490 | − | 123.490i | 0.181070 | − | 0.181070i | ||||
\(683\) | −695.233 | − | 695.233i | −1.01791 | − | 1.01791i | −0.999837 | − | 0.0180741i | \(-0.994247\pi\) |
−0.0180741 | − | 0.999837i | \(-0.505753\pi\) | |||||||
\(684\) | 12.6623i | 0.0185121i | ||||||||
\(685\) | −583.097 | − | 243.256i | −0.851237 | − | 0.355119i | ||||
\(686\) | 412.007 | 0.600593 | ||||||||
\(687\) | −89.9715 | + | 89.9715i | −0.130963 | + | 0.130963i | ||||
\(688\) | 12.4954 | + | 12.4954i | 0.0181619 | + | 0.0181619i | ||||
\(689\) | − | 261.475i | − | 0.379499i | ||||||
\(690\) | 22.6147 | − | 54.2086i | 0.0327750 | − | 0.0785632i | ||||
\(691\) | 667.858 | 0.966509 | 0.483255 | − | 0.875480i | \(-0.339455\pi\) | ||||
0.483255 | + | 0.875480i | \(0.339455\pi\) | |||||||
\(692\) | 145.244 | − | 145.244i | 0.209890 | − | 0.209890i | ||||
\(693\) | −58.3695 | − | 58.3695i | −0.0842272 | − | 0.0842272i | ||||
\(694\) | 75.6516i | 0.109008i | ||||||||
\(695\) | −283.037 | + | 116.400i | −0.407247 | + | 0.167482i | ||||
\(696\) | −77.6306 | −0.111538 | ||||||||
\(697\) | 57.7673 | − | 57.7673i | 0.0828800 | − | 0.0828800i | ||||
\(698\) | −608.019 | − | 608.019i | −0.871087 | − | 0.871087i | ||||
\(699\) | − | 698.037i | − | 0.998623i | ||||||
\(700\) | 167.987 | + | 0.849792i | 0.239981 | + | 0.00121399i | ||||
\(701\) | −936.912 | −1.33654 | −0.668268 | − | 0.743920i | \(-0.732964\pi\) | ||||
−0.668268 | + | 0.743920i | \(0.732964\pi\) | |||||||
\(702\) | −54.5484 | + | 54.5484i | −0.0777043 | + | 0.0777043i | ||||
\(703\) | −29.9998 | − | 29.9998i | −0.0426740 | − | 0.0426740i | ||||
\(704\) | − | 65.5177i | − | 0.0930649i | ||||||
\(705\) | 138.417 | + | 336.574i | 0.196337 | + | 0.477411i | ||||
\(706\) | 204.130 | 0.289135 | ||||||||
\(707\) | −1.34860 | + | 1.34860i | −0.00190750 | + | 0.00190750i | ||||
\(708\) | 64.7297 | + | 64.7297i | 0.0914261 | + | 0.0914261i | ||||
\(709\) | 680.289i | 0.959505i | 0.877404 | + | 0.479753i | \(0.159274\pi\) | ||||
−0.877404 | + | 0.479753i | \(0.840726\pi\) | |||||||
\(710\) | 439.900 | + | 183.517i | 0.619577 | + | 0.258475i | ||||
\(711\) | −226.684 | −0.318824 | ||||||||
\(712\) | −153.205 | + | 153.205i | −0.215175 | + | 0.215175i | ||||
\(713\) | 51.1343 | + | 51.1343i | 0.0717171 | + | 0.0717171i | ||||
\(714\) | 95.8284i | 0.134214i | ||||||||
\(715\) | 165.509 | − | 396.732i | 0.231481 | − | 0.554870i | ||||
\(716\) | −589.383 | −0.823161 | ||||||||
\(717\) | −143.433 | + | 143.433i | −0.200045 | + | 0.200045i | ||||
\(718\) | 392.739 | + | 392.739i | 0.546990 | + | 0.546990i | ||||
\(719\) | − | 872.799i | − | 1.21391i | −0.794737 | − | 0.606953i | \(-0.792391\pi\) | ||
0.794737 | − | 0.606953i | \(-0.207609\pi\) | |||||||
\(720\) | −55.4907 | + | 22.8207i | −0.0770704 | + | 0.0316955i | ||||
\(721\) | −58.5801 | −0.0812484 | ||||||||
\(722\) | 356.546 | − | 356.546i | 0.493831 | − | 0.493831i | ||||
\(723\) | −218.781 | − | 218.781i | −0.302601 | − | 0.302601i | ||||
\(724\) | − | 31.3062i | − | 0.0432407i | ||||||
\(725\) | −278.705 | − | 281.539i | −0.384420 | − | 0.388329i | ||||
\(726\) | 132.098 | 0.181953 | ||||||||
\(727\) | 736.548 | − | 736.548i | 1.01313 | − | 1.01313i | 0.0132213 | − | 0.999913i | \(-0.495791\pi\) |
0.999913 | − | 0.0132213i | \(-0.00420860\pi\) | |||||||
\(728\) | 70.5409 | + | 70.5409i | 0.0968969 | + | 0.0968969i | ||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | −64.6240 | − | 157.139i | −0.0885260 | − | 0.215259i | ||||
\(731\) | −51.4414 | −0.0703713 | ||||||||
\(732\) | 69.0150 | − | 69.0150i | 0.0942828 | − | 0.0942828i | ||||
\(733\) | 20.9889 | + | 20.9889i | 0.0286342 | + | 0.0286342i | 0.721279 | − | 0.692645i | \(-0.243555\pi\) |
−0.692645 | + | 0.721279i | \(0.743555\pi\) | |||||||
\(734\) | − | 83.0619i | − | 0.113163i | ||||||
\(735\) | −301.417 | − | 125.745i | −0.410091 | − | 0.171082i | ||||
\(736\) | 27.1293 | 0.0368605 | ||||||||
\(737\) | 548.283 | − | 548.283i | 0.743939 | − | 0.743939i | ||||
\(738\) | 21.0480 | + | 21.0480i | 0.0285203 | + | 0.0285203i | ||||
\(739\) | − | 799.903i | − | 1.08241i | −0.840890 | − | 0.541206i | \(-0.817968\pi\) | ||
0.840890 | − | 0.541206i | \(-0.182032\pi\) | |||||||
\(740\) | 77.4025 | − | 185.537i | 0.104598 | − | 0.250726i | ||||
\(741\) | −38.3727 | −0.0517850 | ||||||||
\(742\) | 83.6836 | − | 83.6836i | 0.112781 | − | 0.112781i | ||||
\(743\) | −293.529 | − | 293.529i | −0.395059 | − | 0.395059i | 0.481427 | − | 0.876486i | \(-0.340119\pi\) |
−0.876486 | + | 0.481427i | \(0.840119\pi\) | |||||||
\(744\) | − | 73.8701i | − | 0.0992878i | ||||||
\(745\) | −1137.04 | + | 467.613i | −1.52623 | + | 0.627669i | ||||
\(746\) | −377.432 | −0.505941 | ||||||||
\(747\) | 161.470 | − | 161.470i | 0.216158 | − | 0.216158i | ||||
\(748\) | 134.863 | + | 134.863i | 0.180298 | + | 0.180298i | ||||
\(749\) | − | 151.286i | − | 0.201985i | ||||||
\(750\) | −281.982 | − | 119.315i | −0.375976 | − | 0.159087i | ||||
\(751\) | 1348.43 | 1.79551 | 0.897757 | − | 0.440491i | \(-0.145196\pi\) | ||||
0.897757 | + | 0.440491i | \(0.145196\pi\) | |||||||
\(752\) | −118.858 | + | 118.858i | −0.158055 | + | 0.158055i | ||||
\(753\) | 429.616 | + | 429.616i | 0.570539 | + | 0.570539i | ||||
\(754\) | − | 235.257i | − | 0.312012i | ||||||
\(755\) | 15.6680 | + | 38.0981i | 0.0207523 | + | 0.0504610i | ||||
\(756\) | −34.9159 | −0.0461850 | ||||||||
\(757\) | 165.657 | − | 165.657i | 0.218834 | − | 0.218834i | −0.589173 | − | 0.808007i | \(-0.700546\pi\) |
0.808007 | + | 0.589173i | \(0.200546\pi\) | |||||||
\(758\) | 143.699 | + | 143.699i | 0.189576 | + | 0.189576i | ||||
\(759\) | − | 68.0289i | − | 0.0896296i | ||||||
\(760\) | −27.5445 | − | 11.4910i | −0.0362428 | − | 0.0151198i | ||||
\(761\) | −650.491 | −0.854785 | −0.427392 | − | 0.904066i | \(-0.640568\pi\) | ||||
−0.427392 | + | 0.904066i | \(0.640568\pi\) | |||||||
\(762\) | −27.6261 | + | 27.6261i | −0.0362547 | + | 0.0362547i | ||||
\(763\) | −423.420 | − | 423.420i | −0.554941 | − | 0.554941i | ||||
\(764\) | − | 256.359i | − | 0.335548i | ||||||
\(765\) | 67.2483 | − | 161.197i | 0.0879063 | − | 0.210716i | ||||
\(766\) | 196.422 | 0.256426 | ||||||||
\(767\) | −196.161 | + | 196.161i | −0.255751 | + | 0.255751i | ||||
\(768\) | −19.5959 | − | 19.5959i | −0.0255155 | − | 0.0255155i | ||||
\(769\) | − | 774.000i | − | 1.00650i | −0.864140 | − | 0.503251i | \(-0.832137\pi\) | ||
0.864140 | − | 0.503251i | \(-0.167863\pi\) | |||||||
\(770\) | 179.942 | − | 74.0019i | 0.233691 | − | 0.0961063i | ||||
\(771\) | −264.800 | −0.343450 | ||||||||
\(772\) | −59.4006 | + | 59.4006i | −0.0769438 | + | 0.0769438i | ||||
\(773\) | −534.474 | − | 534.474i | −0.691429 | − | 0.691429i | 0.271118 | − | 0.962546i | \(-0.412607\pi\) |
−0.962546 | + | 0.271118i | \(0.912607\pi\) | |||||||
\(774\) | − | 18.7431i | − | 0.0242159i | ||||||
\(775\) | 267.901 | − | 265.204i | 0.345678 | − | 0.342199i | ||||
\(776\) | −139.160 | −0.179330 | ||||||||
\(777\) | 82.7236 | − | 82.7236i | 0.106465 | − | 0.106465i | ||||
\(778\) | 244.042 | + | 244.042i | 0.313678 | + | 0.313678i | ||||
\(779\) | 14.8064i | 0.0190070i | ||||||||
\(780\) | −69.1575 | − | 168.163i | −0.0886634 | − | 0.215593i | ||||
\(781\) | 552.050 | 0.706850 | ||||||||
\(782\) | −55.8434 | + | 55.8434i | −0.0714110 | + | 0.0714110i | ||||
\(783\) | 58.2230 | + | 58.2230i | 0.0743588 | + | 0.0743588i | ||||
\(784\) | − | 150.848i | − | 0.192408i | ||||||
\(785\) | 378.065 | + | 157.721i | 0.481611 | + | 0.200919i | ||||
\(786\) | 308.066 | 0.391941 | ||||||||
\(787\) | 491.378 | − | 491.378i | 0.624369 | − | 0.624369i | −0.322277 | − | 0.946646i | \(-0.604448\pi\) |
0.946646 | + | 0.322277i | \(0.104448\pi\) | |||||||
\(788\) | −245.484 | − | 245.484i | −0.311528 | − | 0.311528i | ||||
\(789\) | − | 191.997i | − | 0.243343i | ||||||
\(790\) | 205.715 | − | 493.109i | 0.260399 | − | 0.624188i | ||||
\(791\) | −350.369 | −0.442945 | ||||||||
\(792\) | −49.1383 | + | 49.1383i | −0.0620433 | + | 0.0620433i | ||||
\(793\) | 209.148 | + | 209.148i | 0.263742 | + | 0.263742i | ||||
\(794\) | 337.823i | 0.425470i | ||||||||
\(795\) | −199.494 | + | 82.0424i | −0.250935 | + | 0.103198i | ||||
\(796\) | 21.8991 | 0.0275114 | ||||||||
\(797\) | 697.732 | − | 697.732i | 0.875449 | − | 0.875449i | −0.117611 | − | 0.993060i | \(-0.537524\pi\) |
0.993060 | + | 0.117611i | \(0.0375237\pi\) | |||||||
\(798\) | −12.2810 | − | 12.2810i | −0.0153897 | − | 0.0153897i | ||||
\(799\) | − | 489.316i | − | 0.612411i | ||||||
\(800\) | 0.715396 | − | 141.420i | 0.000894245 | − | 0.176774i | ||||
\(801\) | 229.807 | 0.286900 | ||||||||
\(802\) | −226.855 | + | 226.855i | −0.282862 | + | 0.282862i | ||||
\(803\) | −139.150 | − | 139.150i | −0.173288 | − | 0.173288i | ||||
\(804\) | − | 327.976i | − | 0.407930i | ||||||
\(805\) | 30.6424 | + | 74.5098i | 0.0380651 | + | 0.0925588i | ||||
\(806\) | 223.861 | 0.277743 | ||||||||
\(807\) | −400.241 | + | 400.241i | −0.495962 | + | 0.495962i | ||||
\(808\) | 1.13532 | + | 1.13532i | 0.00140510 | + | 0.00140510i | ||||
\(809\) | − | 666.114i | − | 0.823380i | −0.911324 | − | 0.411690i | \(-0.864939\pi\) | ||
0.911324 | − | 0.411690i | \(-0.135061\pi\) | |||||||
\(810\) | 58.7335 | + | 24.5025i | 0.0725106 | + | 0.0302499i | ||||
\(811\) | 182.199 | 0.224660 | 0.112330 | − | 0.993671i | \(-0.464169\pi\) | ||||
0.112330 | + | 0.993671i | \(0.464169\pi\) | |||||||
\(812\) | 75.2928 | − | 75.2928i | 0.0927251 | − | 0.0927251i | ||||
\(813\) | 383.081 | + | 383.081i | 0.471194 | + | 0.471194i | ||||
\(814\) | − | 232.839i | − | 0.286043i | ||||||
\(815\) | −149.475 | + | 358.298i | −0.183405 | + | 0.439630i | ||||
\(816\) | 80.6731 | 0.0988641 | ||||||||
\(817\) | 6.59252 | − | 6.59252i | 0.00806918 | − | 0.00806918i | ||||
\(818\) | −193.056 | − | 193.056i | −0.236010 | − | 0.236010i | ||||
\(819\) | − | 105.811i | − | 0.129196i | ||||||
\(820\) | −64.8871 | + | 26.6850i | −0.0791306 | + | 0.0325427i | ||||
\(821\) | −840.318 | −1.02353 | −0.511765 | − | 0.859126i | \(-0.671008\pi\) | ||||
−0.511765 | + | 0.859126i | \(0.671008\pi\) | |||||||
\(822\) | −218.863 | + | 218.863i | −0.266257 | + | 0.266257i | ||||
\(823\) | −282.800 | − | 282.800i | −0.343621 | − | 0.343621i | 0.514106 | − | 0.857727i | \(-0.328124\pi\) |
−0.857727 | + | 0.514106i | \(0.828124\pi\) | |||||||
\(824\) | 49.3156i | 0.0598490i | ||||||||
\(825\) | −354.620 | − | 1.79391i | −0.429843 | − | 0.00217444i | ||||
\(826\) | −125.561 | −0.152011 | ||||||||
\(827\) | 1109.73 | − | 1109.73i | 1.34188 | − | 1.34188i | 0.447683 | − | 0.894192i | \(-0.352249\pi\) |
0.894192 | − | 0.447683i | \(-0.147751\pi\) | |||||||
\(828\) | −20.3470 | − | 20.3470i | −0.0245737 | − | 0.0245737i | ||||
\(829\) | 530.827i | 0.640322i | 0.947363 | + | 0.320161i | \(0.103737\pi\) | ||||
−0.947363 | + | 0.320161i | \(0.896263\pi\) | |||||||
\(830\) | 204.714 | + | 497.781i | 0.246644 | + | 0.599736i | ||||
\(831\) | 159.027 | 0.191368 | ||||||||
\(832\) | 59.3848 | − | 59.3848i | 0.0713760 | − | 0.0713760i | ||||
\(833\) | 310.507 | + | 310.507i | 0.372757 | + | 0.372757i | ||||
\(834\) | 149.927i | 0.179768i | ||||||||
\(835\) | −261.258 | − | 108.991i | −0.312883 | − | 0.130529i | ||||
\(836\) | −34.5669 | −0.0413479 | ||||||||
\(837\) | −55.4026 | + | 55.4026i | −0.0661919 | + | 0.0661919i | ||||
\(838\) | 418.810 | + | 418.810i | 0.499773 | + | 0.499773i | ||||
\(839\) | 798.526i | 0.951759i | 0.879510 | + | 0.475880i | \(0.157870\pi\) | ||||
−0.879510 | + | 0.475880i | \(0.842130\pi\) | |||||||
\(840\) | 31.6861 | − | 75.9530i | 0.0377215 | − | 0.0904203i | ||||
\(841\) | 589.895 | 0.701421 | ||||||||
\(842\) | 781.367 | − | 781.367i | 0.927989 | − | 0.927989i | ||||
\(843\) | 271.934 | + | 271.934i | 0.322579 | + | 0.322579i | ||||
\(844\) | 742.719i | 0.879999i | ||||||||
\(845\) | −271.882 | + | 111.812i | −0.321754 | + | 0.132322i | ||||
\(846\) | 178.286 | 0.210740 | ||||||||
\(847\) | −128.119 | + | 128.119i | −0.151263 | + | 0.151263i | ||||
\(848\) | −70.4490 | − | 70.4490i | −0.0830766 | − | 0.0830766i | ||||
\(849\) | 647.159i | 0.762260i | ||||||||
\(850\) | 289.628 | + | 292.573i | 0.340738 | + | 0.344203i | ||||
\(851\) | 96.4132 | 0.113294 | ||||||||
\(852\) | 165.115 | − | 165.115i | 0.193796 | − | 0.193796i | ||||
\(853\) | 366.721 | + | 366.721i | 0.429919 | + | 0.429919i | 0.888601 | − | 0.458681i | \(-0.151678\pi\) |
−0.458681 | + | 0.888601i | \(0.651678\pi\) | |||||||
\(854\) | 133.873i | 0.156760i | ||||||||
\(855\) | 12.0401 | + | 29.2766i | 0.0140820 | + | 0.0342417i | ||||
\(856\) | −127.360 | −0.148785 | ||||||||
\(857\) | 731.186 | − | 731.186i | 0.853192 | − | 0.853192i | −0.137333 | − | 0.990525i | \(-0.543853\pi\) |
0.990525 | + | 0.137333i | \(0.0438530\pi\) | |||||||
\(858\) | −148.912 | − | 148.912i | −0.173557 | − | 0.173557i | ||||
\(859\) | − | 802.675i | − | 0.934429i | −0.884144 | − | 0.467215i | \(-0.845258\pi\) | ||
0.884144 | − | 0.467215i | \(-0.154742\pi\) | |||||||
\(860\) | 40.7722 | + | 17.0093i | 0.0474095 | + | 0.0197783i | ||||
\(861\) | −40.8283 | −0.0474196 | ||||||||
\(862\) | −127.925 | + | 127.925i | −0.148404 | + | 0.148404i | ||||
\(863\) | 715.758 | + | 715.758i | 0.829383 | + | 0.829383i | 0.987431 | − | 0.158048i | \(-0.0505202\pi\) |
−0.158048 | + | 0.987431i | \(0.550520\pi\) | |||||||
\(864\) | 29.3939i | 0.0340207i | ||||||||
\(865\) | 197.713 | − | 473.928i | 0.228570 | − | 0.547893i | ||||
\(866\) | 439.880 | 0.507945 | ||||||||
\(867\) | 187.893 | − | 187.893i | 0.216716 | − | 0.216716i | ||||
\(868\) | 71.6455 | + | 71.6455i | 0.0825409 | + | 0.0825409i | ||||
\(869\) | − | 618.824i | − | 0.712111i | ||||||
\(870\) | −179.491 | + | 73.8161i | −0.206311 | + | 0.0848461i | ||||
\(871\) | 993.920 | 1.14113 | ||||||||
\(872\) | −356.456 | + | 356.456i | −0.408780 | + | 0.408780i | ||||
\(873\) | 104.370 | + | 104.370i | 0.119553 | + | 0.119553i | ||||
\(874\) | − | 14.3133i | − | 0.0163768i | ||||||
\(875\) | 389.212 | − | 157.768i | 0.444814 | − | 0.180306i | ||||
\(876\) | −83.2379 | −0.0950204 | ||||||||
\(877\) | 856.632 | − | 856.632i | 0.976775 | − | 0.976775i | −0.0229612 | − | 0.999736i | \(-0.507309\pi\) |
0.999736 | + | 0.0229612i | \(0.00730941\pi\) | |||||||
\(878\) | −159.575 | − | 159.575i | −0.181748 | − | 0.181748i | ||||
\(879\) | − | 368.141i | − | 0.418818i | ||||||
\(880\) | −62.2984 | − | 151.484i | −0.0707936 | − | 0.172141i | ||||
\(881\) | 1144.37 | 1.29895 | 0.649473 | − | 0.760385i | \(-0.274990\pi\) | ||||
0.649473 | + | 0.760385i | \(0.274990\pi\) | |||||||
\(882\) | −113.136 | + | 113.136i | −0.128272 | + | 0.128272i | ||||
\(883\) | −339.658 | − | 339.658i | −0.384663 | − | 0.384663i | 0.488116 | − | 0.872779i | \(-0.337684\pi\) |
−0.872779 | + | 0.488116i | \(0.837684\pi\) | |||||||
\(884\) | 244.477i | 0.276558i | ||||||||
\(885\) | 211.211 | + | 88.1132i | 0.238657 | + | 0.0995629i | ||||
\(886\) | 0.461898 | 0.000521329 | ||||||||
\(887\) | −700.491 | + | 700.491i | −0.789731 | + | 0.789731i | −0.981450 | − | 0.191719i | \(-0.938594\pi\) |
0.191719 | + | 0.981450i | \(0.438594\pi\) | |||||||
\(888\) | −69.6407 | − | 69.6407i | −0.0784243 | − | 0.0784243i | ||||
\(889\) | − | 53.5883i | − | 0.0602793i | ||||||
\(890\) | −208.550 | + | 499.903i | −0.234326 | + | 0.561689i | ||||
\(891\) | 73.7074 | 0.0827244 | ||||||||
\(892\) | −151.986 | + | 151.986i | −0.170388 | + | 0.170388i | ||||
\(893\) | 62.7087 | + | 62.7087i | 0.0702226 | + | 0.0702226i | ||||
\(894\) | 602.302i | 0.673716i | ||||||||
\(895\) | −1362.72 | + | 560.423i | −1.52259 | + | 0.626171i | ||||
\(896\) | 38.0116 | 0.0424236 | ||||||||
\(897\) | 61.6609 | − | 61.6609i | 0.0687412 | − | 0.0687412i | ||||
\(898\) | −717.728 | − | 717.728i | −0.799251 | − | 0.799251i | ||||
\(899\) | − | 238.941i | − | 0.265785i | ||||||
\(900\) | −106.601 | + | 105.528i | −0.118446 | + | 0.117253i | ||||
\(901\) | 290.026 | 0.321894 | ||||||||
\(902\) | −57.4590 | + | 57.4590i | −0.0637018 | + | 0.0637018i | ||||
\(903\) | 18.1786 | + | 18.1786i | 0.0201314 | + | 0.0201314i | ||||
\(904\) | 294.958i | 0.326281i | ||||||||
\(905\) | −29.7680 | − | 72.3835i | −0.0328928 | − | 0.0799818i | ||||
\(906\) | 20.1809 | 0.0222747 | ||||||||
\(907\) | 902.515 | − | 902.515i | 0.995056 | − | 0.995056i | −0.00493230 | − | 0.999988i | \(-0.501570\pi\) |
0.999988 | + | 0.00493230i | \(0.00157001\pi\) | |||||||
\(908\) | −345.170 | − | 345.170i | −0.380143 | − | 0.380143i | ||||
\(909\) | − | 1.70298i | − | 0.00187347i | ||||||
\(910\) | 230.173 | + | 96.0237i | 0.252938 | + | 0.105521i | ||||
\(911\) | −172.360 | −0.189199 | −0.0945995 | − | 0.995515i | \(-0.530157\pi\) | ||||
−0.0945995 | + | 0.995515i | \(0.530157\pi\) | |||||||
\(912\) | −10.3387 | + | 10.3387i | −0.0113363 | + | 0.0113363i | ||||
\(913\) | 440.797 | + | 440.797i | 0.482800 | + | 0.482800i | ||||
\(914\) | − | 92.4758i | − | 0.101177i | ||||||
\(915\) | 93.9465 | − | 225.194i | 0.102674 | − | 0.246114i | ||||
\(916\) | −146.923 | −0.160396 | ||||||||
\(917\) | −298.789 | + | 298.789i | −0.325833 | + | 0.325833i | ||||
\(918\) | −60.5048 | − | 60.5048i | −0.0659094 | − | 0.0659094i | ||||
\(919\) | 578.120i | 0.629075i | 0.949245 | + | 0.314537i | \(0.101849\pi\) | ||||
−0.949245 | + | 0.314537i | \(0.898151\pi\) | |||||||
\(920\) | 62.7260 | − | 25.7963i | 0.0681804 | − | 0.0280394i | ||||
\(921\) | 910.477 | 0.988574 | ||||||||
\(922\) | −88.2710 | + | 88.2710i | −0.0957386 | + | 0.0957386i | ||||
\(923\) | 500.374 | + | 500.374i | 0.542117 | + | 0.542117i | ||||
\(924\) | − | 95.3169i | − | 0.103157i | ||||||
\(925\) | 2.54240 | − | 502.582i | 0.00274854 | − | 0.543332i | ||||
\(926\) | 335.543 | 0.362357 | ||||||||
\(927\) | 36.9867 | − | 36.9867i | 0.0398994 | − | 0.0398994i | ||||
\(928\) | −63.3851 | − | 63.3851i | −0.0683029 | − | 0.0683029i | ||||
\(929\) | 815.607i | 0.877941i | 0.898501 | + | 0.438971i | \(0.144657\pi\) | ||||
−0.898501 | + | 0.438971i | \(0.855343\pi\) | |||||||
\(930\) | −70.2404 | − | 170.796i | −0.0755273 | − | 0.183652i | ||||
\(931\) | −79.5865 | −0.0854850 | ||||||||
\(932\) | 569.945 | − | 569.945i | 0.611529 | − | 0.611529i | ||||
\(933\) | −30.4381 | − | 30.4381i | −0.0326238 | − | 0.0326238i | ||||
\(934\) | 125.137i | 0.133980i | ||||||||
\(935\) | 440.053 | + | 183.581i | 0.470645 | + | 0.196344i | ||||
\(936\) | −89.0772 | −0.0951679 | ||||||||
\(937\) | 1100.71 | − | 1100.71i | 1.17472 | − | 1.17472i | 0.193646 | − | 0.981072i | \(-0.437969\pi\) |
0.981072 | − | 0.193646i | \(-0.0620312\pi\) | |||||||
\(938\) | 318.099 | + | 318.099i | 0.339125 | + | 0.339125i | ||||
\(939\) | − | 390.390i | − | 0.415751i | ||||||
\(940\) | −161.795 | + | 387.829i | −0.172122 | + | 0.412584i | ||||
\(941\) | 333.594 | 0.354510 | 0.177255 | − | 0.984165i | \(-0.443278\pi\) | ||||
0.177255 | + | 0.984165i | \(0.443278\pi\) | |||||||
\(942\) | 141.905 | − | 141.905i | 0.150642 | − | 0.150642i | ||||
\(943\) | −23.7924 | − | 23.7924i | −0.0252305 | − | 0.0252305i | ||||
\(944\) | 105.703i | 0.111974i | ||||||||
\(945\) | −80.7293 | + | 33.2002i | −0.0854279 | + | 0.0351325i | ||||
\(946\) | 51.1668 | 0.0540876 | ||||||||
\(947\) | −280.909 | + | 280.909i | −0.296631 | + | 0.296631i | −0.839693 | − | 0.543062i | \(-0.817265\pi\) |
0.543062 | + | 0.839693i | \(0.317265\pi\) | |||||||
\(948\) | −185.086 | − | 185.086i | −0.195239 | − | 0.195239i | ||||
\(949\) | − | 252.250i | − | 0.265806i | ||||||
\(950\) | −74.6124 | − | 0.377440i | −0.0785393 | − | 0.000397305i | ||||
\(951\) | −396.150 | −0.416562 | ||||||||
\(952\) | −78.2436 | + | 78.2436i | −0.0821887 | + | 0.0821887i | ||||
\(953\) | −397.498 | − | 397.498i | −0.417102 | − | 0.417102i | 0.467102 | − | 0.884204i | \(-0.345298\pi\) |
−0.884204 | + | 0.467102i | \(0.845298\pi\) | |||||||
\(954\) | 105.673i | 0.110769i | ||||||||
\(955\) | −243.762 | − | 592.731i | −0.255249 | − | 0.620660i | ||||
\(956\) | −234.224 | −0.245005 | ||||||||
\(957\) | −158.943 | + | 158.943i | −0.166085 | + | 0.166085i | ||||
\(958\) | 612.563 | + | 612.563i | 0.639419 | + | 0.639419i | ||||
\(959\) | − | 424.544i | − | 0.442695i | ||||||
\(960\) | −63.9410 | − | 26.6749i | −0.0666052 | − | 0.0277864i | ||||
\(961\) | −733.634 | −0.763406 | ||||||||
\(962\) | 211.044 | − | 211.044i | 0.219380 | − | 0.219380i | ||||
\(963\) | 95.5203 | + | 95.5203i | 0.0991903 | + | 0.0991903i | ||||
\(964\) | − | 357.268i | − | 0.370610i | ||||||
\(965\) | −80.8589 | + | 193.823i | −0.0837916 | + | 0.200853i | ||||
\(966\) | 39.4685 | 0.0408576 | ||||||||
\(967\) | 913.788 | − | 913.788i | 0.944972 | − | 0.944972i | −0.0535914 | − | 0.998563i | \(-0.517067\pi\) |
0.998563 | + | 0.0535914i | \(0.0170668\pi\) | |||||||
\(968\) | 107.857 | + | 107.857i | 0.111423 | + | 0.111423i | ||||
\(969\) | − | 42.5628i | − | 0.0439244i | ||||||
\(970\) | −321.754 | + | 132.322i | −0.331705 | + | 0.136415i | ||||
\(971\) | −642.646 | −0.661839 | −0.330920 | − | 0.943659i | \(-0.607359\pi\) | ||||
−0.330920 | + | 0.943659i | \(0.607359\pi\) | |||||||
\(972\) | 22.0454 | − | 22.0454i | 0.0226805 | − | 0.0226805i | ||||
\(973\) | −145.412 | − | 145.412i | −0.149447 | − | 0.149447i | ||||
\(974\) | 685.854i | 0.704162i | ||||||||
\(975\) | −319.800 | − | 323.051i | −0.328000 | − | 0.331335i | ||||
\(976\) | 112.701 | 0.115472 | ||||||||
\(977\) | 551.397 | − | 551.397i | 0.564377 | − | 0.564377i | −0.366171 | − | 0.930548i | \(-0.619331\pi\) |
0.930548 | + | 0.366171i | \(0.119331\pi\) | |||||||
\(978\) | 134.486 | + | 134.486i | 0.137511 | + | 0.137511i | ||||
\(979\) | 627.352i | 0.640809i | ||||||||
\(980\) | −143.435 | − | 348.776i | −0.146363 | − | 0.355894i | ||||
\(981\) | 534.684 | 0.545040 | ||||||||
\(982\) | −850.889 | + | 850.889i | −0.866486 | + | 0.866486i | ||||
\(983\) | 543.674 | + | 543.674i | 0.553076 | + | 0.553076i | 0.927327 | − | 0.374251i | \(-0.122100\pi\) |
−0.374251 | + | 0.927327i | \(0.622100\pi\) | |||||||
\(984\) | 34.3712i | 0.0349301i | ||||||||
\(985\) | −801.009 | − | 334.165i | −0.813207 | − | 0.339254i | ||||
\(986\) | 260.946 | 0.264651 | ||||||||
\(987\) | −172.917 | + | 172.917i | −0.175195 | + | 0.175195i | ||||
\(988\) | −31.3312 | − | 31.3312i | −0.0317117 | − | 0.0317117i | ||||
\(989\) | 21.1870i | 0.0214226i | ||||||||
\(990\) | −66.8894 | + | 160.337i | −0.0675650 | + | 0.161957i | ||||
\(991\) | −433.622 | −0.437560 | −0.218780 | − | 0.975774i | \(-0.570208\pi\) | ||||
−0.218780 | + | 0.975774i | \(0.570208\pi\) | |||||||
\(992\) | 60.3147 | − | 60.3147i | 0.0608011 | − | 0.0608011i | ||||
\(993\) | 494.929 | + | 494.929i | 0.498417 | + | 0.498417i | ||||
\(994\) | 320.284i | 0.322218i | ||||||||
\(995\) | 50.6331 | − | 20.8230i | 0.0508875 | − | 0.0209277i | ||||
\(996\) | 263.679 | 0.264738 | ||||||||
\(997\) | 104.863 | − | 104.863i | 0.105178 | − | 0.105178i | −0.652559 | − | 0.757738i | \(-0.726305\pi\) |
0.757738 | + | 0.652559i | \(0.226305\pi\) | |||||||
\(998\) | −782.522 | − | 782.522i | −0.784090 | − | 0.784090i | ||||
\(999\) | 104.461i | 0.104566i |
(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 | 690.3.k.a.553.4 | yes | 40 | |
5.2 | odd | 4 | inner | 690.3.k.a.277.4 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.k.a.277.4 | ✓ | 40 | 5.2 | odd | 4 | inner | |
690.3.k.a.553.4 | yes | 40 | 1.1 | even | 1 | trivial |