Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(529,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.ba (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 619.7 | ||
Character | \(\chi\) | \(=\) | 1110.619 |
Dual form | 1110.2.ba.a.529.7 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −0.00696233 | − | 2.23606i | −0.00311365 | − | 0.999995i | ||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | 3.60632 | − | 2.08211i | 1.36306 | − | 0.786963i | 0.373030 | − | 0.927819i | \(-0.378319\pi\) |
0.990030 | + | 0.140856i | \(0.0449855\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 1.93996 | + | 1.11200i | 0.613470 | + | 0.351645i | ||||
\(11\) | 5.62355 | 1.69556 | 0.847782 | − | 0.530346i | \(-0.177938\pi\) | ||||
0.847782 | + | 0.530346i | \(0.177938\pi\) | |||||||
\(12\) | 0.866025 | + | 0.500000i | 0.250000 | + | 0.144338i | ||||
\(13\) | −2.80292 | − | 4.85480i | −0.777391 | − | 1.34648i | −0.933441 | − | 0.358731i | \(-0.883210\pi\) |
0.156050 | − | 0.987749i | \(-0.450124\pi\) | |||||||
\(14\) | 4.16422i | 1.11293i | ||||||||
\(15\) | 1.12406 | + | 1.93300i | 0.290231 | + | 0.499099i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.43213 | − | 2.48053i | 0.347344 | − | 0.601617i | −0.638433 | − | 0.769677i | \(-0.720417\pi\) |
0.985777 | + | 0.168061i | \(0.0537504\pi\) | |||||||
\(18\) | 0.500000 | + | 0.866025i | 0.117851 | + | 0.204124i | ||||
\(19\) | −5.16423 | + | 2.98157i | −1.18475 | + | 0.684018i | −0.957110 | − | 0.289726i | \(-0.906436\pi\) |
−0.227645 | + | 0.973744i | \(0.573103\pi\) | |||||||
\(20\) | −1.93300 | + | 1.12406i | −0.432232 | + | 0.251347i | ||||
\(21\) | −2.08211 | + | 3.60632i | −0.454353 | + | 0.786963i | ||||
\(22\) | −2.81177 | + | 4.87013i | −0.599472 | + | 1.03832i | ||||
\(23\) | −6.24179 | −1.30150 | −0.650752 | − | 0.759291i | \(-0.725546\pi\) | ||||
−0.650752 | + | 0.759291i | \(0.725546\pi\) | |||||||
\(24\) | −0.866025 | + | 0.500000i | −0.176777 | + | 0.102062i | ||||
\(25\) | −4.99990 | + | 0.0311363i | −0.999981 | + | 0.00622727i | ||||
\(26\) | 5.60584 | 1.09940 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −3.60632 | − | 2.08211i | −0.681530 | − | 0.393482i | ||||
\(29\) | − | 9.90800i | − | 1.83987i | −0.392071 | − | 0.919935i | \(-0.628241\pi\) | ||
0.392071 | − | 0.919935i | \(-0.371759\pi\) | |||||||
\(30\) | −2.23606 | + | 0.00696233i | −0.408246 | + | 0.00127114i | ||||
\(31\) | 4.33846i | 0.779210i | 0.920982 | + | 0.389605i | \(0.127388\pi\) | ||||
−0.920982 | + | 0.389605i | \(0.872612\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −4.87013 | + | 2.81177i | −0.847782 | + | 0.489467i | ||||
\(34\) | 1.43213 | + | 2.48053i | 0.245609 | + | 0.425407i | ||||
\(35\) | −4.68082 | − | 8.04944i | −0.791203 | − | 1.36060i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | −2.01692 | + | 5.73864i | −0.331580 | + | 0.943427i | ||||
\(38\) | − | 5.96313i | − | 0.967348i | ||||||
\(39\) | 4.85480 | + | 2.80292i | 0.777391 | + | 0.448827i | ||||
\(40\) | −0.00696233 | − | 2.23606i | −0.00110084 | − | 0.353552i | ||||
\(41\) | −0.470733 | − | 0.815334i | −0.0735162 | − | 0.127334i | 0.826924 | − | 0.562314i | \(-0.190089\pi\) |
−0.900440 | + | 0.434980i | \(0.856755\pi\) | |||||||
\(42\) | −2.08211 | − | 3.60632i | −0.321276 | − | 0.556467i | ||||
\(43\) | 4.29505 | 0.654989 | 0.327495 | − | 0.944853i | \(-0.393796\pi\) | ||||
0.327495 | + | 0.944853i | \(0.393796\pi\) | |||||||
\(44\) | −2.81177 | − | 4.87013i | −0.423891 | − | 0.734200i | ||||
\(45\) | −1.93996 | − | 1.11200i | −0.289193 | − | 0.165767i | ||||
\(46\) | 3.12090 | − | 5.40555i | 0.460151 | − | 0.797005i | ||||
\(47\) | 0.365900i | 0.0533719i | 0.999644 | + | 0.0266860i | \(0.00849542\pi\) | ||||
−0.999644 | + | 0.0266860i | \(0.991505\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 5.17035 | − | 8.95532i | 0.738622 | − | 1.27933i | ||||
\(50\) | 2.47299 | − | 4.34561i | 0.349733 | − | 0.614562i | ||||
\(51\) | 2.86427i | 0.401078i | ||||||||
\(52\) | −2.80292 | + | 4.85480i | −0.388695 | + | 0.673240i | ||||
\(53\) | −3.87603 | − | 2.23783i | −0.532414 | − | 0.307390i | 0.209585 | − | 0.977790i | \(-0.432789\pi\) |
−0.741999 | + | 0.670401i | \(0.766122\pi\) | |||||||
\(54\) | −0.866025 | − | 0.500000i | −0.117851 | − | 0.0680414i | ||||
\(55\) | −0.0391530 | − | 12.5746i | −0.00527939 | − | 1.69555i | ||||
\(56\) | 3.60632 | − | 2.08211i | 0.481915 | − | 0.278233i | ||||
\(57\) | 2.98157 | − | 5.16423i | 0.394918 | − | 0.684018i | ||||
\(58\) | 8.58058 | + | 4.95400i | 1.12669 | + | 0.650492i | ||||
\(59\) | 9.52048 | + | 5.49665i | 1.23946 | + | 0.715603i | 0.968984 | − | 0.247123i | \(-0.0794853\pi\) |
0.270477 | + | 0.962726i | \(0.412819\pi\) | |||||||
\(60\) | 1.11200 | − | 1.93996i | 0.143558 | − | 0.250448i | ||||
\(61\) | 2.20880 | − | 1.27525i | 0.282807 | − | 0.163279i | −0.351886 | − | 0.936043i | \(-0.614460\pi\) |
0.634694 | + | 0.772764i | \(0.281126\pi\) | |||||||
\(62\) | −3.75722 | − | 2.16923i | −0.477167 | − | 0.275492i | ||||
\(63\) | − | 4.16422i | − | 0.524642i | ||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −10.8361 | + | 6.30129i | −1.34405 | + | 0.781579i | ||||
\(66\) | − | 5.62355i | − | 0.692211i | ||||||
\(67\) | 1.92075 | − | 1.10894i | 0.234657 | − | 0.135479i | −0.378062 | − | 0.925780i | \(-0.623409\pi\) |
0.612718 | + | 0.790301i | \(0.290076\pi\) | |||||||
\(68\) | −2.86427 | −0.347344 | ||||||||
\(69\) | 5.40555 | − | 3.12090i | 0.650752 | − | 0.375712i | ||||
\(70\) | 9.31143 | − | 0.0289927i | 1.11293 | − | 0.00346529i | ||||
\(71\) | −6.08527 | − | 10.5400i | −0.722189 | − | 1.25087i | −0.960121 | − | 0.279587i | \(-0.909803\pi\) |
0.237931 | − | 0.971282i | \(-0.423531\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | 11.5997i | 1.35764i | 0.734303 | + | 0.678822i | \(0.237509\pi\) | ||||
−0.734303 | + | 0.678822i | \(0.762491\pi\) | |||||||
\(74\) | −3.96135 | − | 4.61603i | −0.460498 | − | 0.536602i | ||||
\(75\) | 4.31447 | − | 2.52692i | 0.498193 | − | 0.291783i | ||||
\(76\) | 5.16423 | + | 2.98157i | 0.592377 | + | 0.342009i | ||||
\(77\) | 20.2803 | − | 11.7088i | 2.31115 | − | 1.33435i | ||||
\(78\) | −4.85480 | + | 2.80292i | −0.549698 | + | 0.317368i | ||||
\(79\) | −8.57325 | + | 4.94977i | −0.964566 | + | 0.556893i | −0.897575 | − | 0.440861i | \(-0.854673\pi\) |
−0.0669909 | + | 0.997754i | \(0.521340\pi\) | |||||||
\(80\) | 1.93996 | + | 1.11200i | 0.216895 | + | 0.124325i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0.941466 | 0.103968 | ||||||||
\(83\) | 0.157099 | + | 0.0907014i | 0.0172439 | + | 0.00995577i | 0.508597 | − | 0.861005i | \(-0.330164\pi\) |
−0.491353 | + | 0.870960i | \(0.663498\pi\) | |||||||
\(84\) | 4.16422 | 0.454353 | ||||||||
\(85\) | −5.55658 | − | 3.18506i | −0.602695 | − | 0.345469i | ||||
\(86\) | −2.14753 | + | 3.71962i | −0.231574 | + | 0.401097i | ||||
\(87\) | 4.95400 | + | 8.58058i | 0.531125 | + | 0.919935i | ||||
\(88\) | 5.62355 | 0.599472 | ||||||||
\(89\) | −7.38304 | − | 4.26260i | −0.782601 | − | 0.451835i | 0.0547504 | − | 0.998500i | \(-0.482564\pi\) |
−0.837351 | + | 0.546665i | \(0.815897\pi\) | |||||||
\(90\) | 1.93300 | − | 1.12406i | 0.203756 | − | 0.118486i | ||||
\(91\) | −20.2165 | − | 11.6720i | −2.11926 | − | 1.22356i | ||||
\(92\) | 3.12090 | + | 5.40555i | 0.325376 | + | 0.563568i | ||||
\(93\) | −2.16923 | − | 3.75722i | −0.224939 | − | 0.389605i | ||||
\(94\) | −0.316878 | − | 0.182950i | −0.0326835 | − | 0.0188698i | ||||
\(95\) | 6.70291 | + | 11.5267i | 0.687704 | + | 1.18262i | ||||
\(96\) | 0.866025 | + | 0.500000i | 0.0883883 | + | 0.0510310i | ||||
\(97\) | −8.96250 | −0.910004 | −0.455002 | − | 0.890490i | \(-0.650361\pi\) | ||||
−0.455002 | + | 0.890490i | \(0.650361\pi\) | |||||||
\(98\) | 5.17035 | + | 8.95532i | 0.522285 | + | 0.904623i | ||||
\(99\) | 2.81177 | − | 4.87013i | 0.282594 | − | 0.489467i | ||||
\(100\) | 2.52692 | + | 4.31447i | 0.252692 | + | 0.431447i | ||||
\(101\) | 17.5745 | 1.74872 | 0.874362 | − | 0.485274i | \(-0.161280\pi\) | ||||
0.874362 | + | 0.485274i | \(0.161280\pi\) | |||||||
\(102\) | −2.48053 | − | 1.43213i | −0.245609 | − | 0.141802i | ||||
\(103\) | 4.83675 | 0.476579 | 0.238290 | − | 0.971194i | \(-0.423413\pi\) | ||||
0.238290 | + | 0.971194i | \(0.423413\pi\) | |||||||
\(104\) | −2.80292 | − | 4.85480i | −0.274849 | − | 0.476053i | ||||
\(105\) | 8.07843 | + | 4.63061i | 0.788374 | + | 0.451901i | ||||
\(106\) | 3.87603 | − | 2.23783i | 0.376474 | − | 0.217357i | ||||
\(107\) | 13.4925 | − | 7.78991i | 1.30437 | − | 0.753079i | 0.323220 | − | 0.946324i | \(-0.395235\pi\) |
0.981150 | + | 0.193245i | \(0.0619013\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | −1.14051 | − | 0.658472i | −0.109241 | − | 0.0630702i | 0.444384 | − | 0.895836i | \(-0.353423\pi\) |
−0.553625 | + | 0.832766i | \(0.686756\pi\) | |||||||
\(110\) | 10.9095 | + | 6.25338i | 1.04018 | + | 0.596236i | ||||
\(111\) | −1.12262 | − | 5.97827i | −0.106554 | − | 0.567432i | ||||
\(112\) | 4.16422i | 0.393482i | ||||||||
\(113\) | 4.34832 | − | 7.53150i | 0.409055 | − | 0.708504i | −0.585729 | − | 0.810507i | \(-0.699192\pi\) |
0.994784 | + | 0.102003i | \(0.0325250\pi\) | |||||||
\(114\) | 2.98157 | + | 5.16423i | 0.279249 | + | 0.483674i | ||||
\(115\) | 0.0434574 | + | 13.9570i | 0.00405243 | + | 1.30150i | ||||
\(116\) | −8.58058 | + | 4.95400i | −0.796687 | + | 0.459968i | ||||
\(117\) | −5.60584 | −0.518260 | ||||||||
\(118\) | −9.52048 | + | 5.49665i | −0.876431 | + | 0.506008i | ||||
\(119\) | − | 11.9274i | − | 1.09339i | ||||||
\(120\) | 1.12406 | + | 1.93300i | 0.102612 | + | 0.176458i | ||||
\(121\) | 20.6243 | 1.87493 | ||||||||
\(122\) | 2.55050i | 0.230911i | ||||||||
\(123\) | 0.815334 | + | 0.470733i | 0.0735162 | + | 0.0424446i | ||||
\(124\) | 3.75722 | − | 2.16923i | 0.337408 | − | 0.194803i | ||||
\(125\) | 0.104434 | + | 11.1799i | 0.00934083 | + | 0.999956i | ||||
\(126\) | 3.60632 | + | 2.08211i | 0.321276 | + | 0.185489i | ||||
\(127\) | 6.46743 | + | 3.73397i | 0.573892 | + | 0.331336i | 0.758702 | − | 0.651438i | \(-0.225834\pi\) |
−0.184811 | + | 0.982774i | \(0.559167\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −3.71962 | + | 2.14753i | −0.327495 | + | 0.189079i | ||||
\(130\) | −0.0390297 | − | 12.5350i | −0.00342313 | − | 1.09939i | ||||
\(131\) | −4.67400 | − | 2.69853i | −0.408369 | − | 0.235772i | 0.281720 | − | 0.959497i | \(-0.409095\pi\) |
−0.690089 | + | 0.723725i | \(0.742429\pi\) | |||||||
\(132\) | 4.87013 | + | 2.81177i | 0.423891 | + | 0.244733i | ||||
\(133\) | −12.4159 | + | 21.5050i | −1.07659 | + | 1.86472i | ||||
\(134\) | 2.21789i | 0.191596i | ||||||||
\(135\) | 2.23606 | − | 0.00696233i | 0.192449 | − | 0.000599222i | ||||
\(136\) | 1.43213 | − | 2.48053i | 0.122805 | − | 0.212704i | ||||
\(137\) | 3.45444i | 0.295133i | 0.989052 | + | 0.147566i | \(0.0471440\pi\) | ||||
−0.989052 | + | 0.147566i | \(0.952856\pi\) | |||||||
\(138\) | 6.24179i | 0.531337i | ||||||||
\(139\) | 4.16178 | − | 7.20841i | 0.352997 | − | 0.611409i | −0.633776 | − | 0.773517i | \(-0.718496\pi\) |
0.986773 | + | 0.162107i | \(0.0518291\pi\) | |||||||
\(140\) | −4.63061 | + | 8.07843i | −0.391358 | + | 0.682752i | ||||
\(141\) | −0.182950 | − | 0.316878i | −0.0154072 | − | 0.0266860i | ||||
\(142\) | 12.1705 | 1.02133 | ||||||||
\(143\) | −15.7624 | − | 27.3012i | −1.31811 | − | 2.28304i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | −22.1549 | + | 0.0689828i | −1.83986 | + | 0.00572871i | ||||
\(146\) | −10.0456 | − | 5.79986i | −0.831384 | − | 0.480000i | ||||
\(147\) | 10.3407i | 0.852887i | ||||||||
\(148\) | 5.97827 | − | 1.12262i | 0.491411 | − | 0.0922786i | ||||
\(149\) | 9.40193 | 0.770236 | 0.385118 | − | 0.922867i | \(-0.374161\pi\) | ||||
0.385118 | + | 0.922867i | \(0.374161\pi\) | |||||||
\(150\) | 0.0311363 | + | 4.99990i | 0.00254227 | + | 0.408240i | ||||
\(151\) | −5.42704 | − | 9.39991i | −0.441646 | − | 0.764954i | 0.556165 | − | 0.831072i | \(-0.312272\pi\) |
−0.997812 | + | 0.0661176i | \(0.978939\pi\) | |||||||
\(152\) | −5.16423 | + | 2.98157i | −0.418874 | + | 0.241837i | ||||
\(153\) | −1.43213 | − | 2.48053i | −0.115781 | − | 0.200539i | ||||
\(154\) | 23.4177i | 1.88705i | ||||||||
\(155\) | 9.70104 | − | 0.0302058i | 0.779206 | − | 0.00242619i | ||||
\(156\) | − | 5.60584i | − | 0.448827i | ||||||
\(157\) | −13.0906 | − | 7.55789i | −1.04475 | − | 0.603185i | −0.123573 | − | 0.992335i | \(-0.539435\pi\) |
−0.921174 | + | 0.389150i | \(0.872769\pi\) | |||||||
\(158\) | − | 9.89954i | − | 0.787565i | ||||||
\(159\) | 4.47566 | 0.354943 | ||||||||
\(160\) | −1.93300 | + | 1.12406i | −0.152817 | + | 0.0888646i | ||||
\(161\) | −22.5099 | + | 12.9961i | −1.77403 | + | 1.02424i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 2.95761 | − | 5.12274i | 0.231658 | − | 0.401244i | −0.726638 | − | 0.687020i | \(-0.758918\pi\) |
0.958296 | + | 0.285777i | \(0.0922516\pi\) | |||||||
\(164\) | −0.470733 | + | 0.815334i | −0.0367581 | + | 0.0636669i | ||||
\(165\) | 6.32119 | + | 10.8703i | 0.492104 | + | 0.846253i | ||||
\(166\) | −0.157099 | + | 0.0907014i | −0.0121933 | + | 0.00703979i | ||||
\(167\) | 3.04743 | + | 5.27831i | 0.235817 | + | 0.408448i | 0.959510 | − | 0.281675i | \(-0.0908899\pi\) |
−0.723692 | + | 0.690123i | \(0.757557\pi\) | |||||||
\(168\) | −2.08211 | + | 3.60632i | −0.160638 | + | 0.278233i | ||||
\(169\) | −9.21274 | + | 15.9569i | −0.708672 | + | 1.22746i | ||||
\(170\) | 5.53664 | − | 3.21961i | 0.424641 | − | 0.246932i | ||||
\(171\) | 5.96313i | 0.456012i | ||||||||
\(172\) | −2.14753 | − | 3.71962i | −0.163747 | − | 0.283619i | ||||
\(173\) | −6.21546 | − | 3.58850i | −0.472552 | − | 0.272828i | 0.244755 | − | 0.969585i | \(-0.421292\pi\) |
−0.717308 | + | 0.696757i | \(0.754626\pi\) | |||||||
\(174\) | −9.90800 | −0.751124 | ||||||||
\(175\) | −17.9664 | + | 10.5226i | −1.35813 | + | 0.795436i | ||||
\(176\) | −2.81177 | + | 4.87013i | −0.211945 | + | 0.367100i | ||||
\(177\) | −10.9933 | −0.826307 | ||||||||
\(178\) | 7.38304 | − | 4.26260i | 0.553382 | − | 0.319495i | ||||
\(179\) | 22.6831i | 1.69541i | 0.530465 | + | 0.847707i | \(0.322017\pi\) | ||||
−0.530465 | + | 0.847707i | \(0.677983\pi\) | |||||||
\(180\) | 0.00696233 | + | 2.23606i | 0.000518942 | + | 0.166666i | ||||
\(181\) | −5.95683 | − | 10.3175i | −0.442768 | − | 0.766896i | 0.555126 | − | 0.831766i | \(-0.312670\pi\) |
−0.997894 | + | 0.0648700i | \(0.979337\pi\) | |||||||
\(182\) | 20.2165 | − | 11.6720i | 1.49854 | − | 0.865184i | ||||
\(183\) | −1.27525 | + | 2.20880i | −0.0942691 | + | 0.163279i | ||||
\(184\) | −6.24179 | −0.460151 | ||||||||
\(185\) | 12.8460 | + | 4.46999i | 0.944455 | + | 0.328641i | ||||
\(186\) | 4.33846 | 0.318111 | ||||||||
\(187\) | 8.05368 | − | 13.9494i | 0.588943 | − | 1.02008i | ||||
\(188\) | 0.316878 | − | 0.182950i | 0.0231107 | − | 0.0133430i | ||||
\(189\) | 2.08211 | + | 3.60632i | 0.151451 | + | 0.262321i | ||||
\(190\) | −13.3339 | + | 0.0415173i | −0.967343 | + | 0.00301198i | ||||
\(191\) | − | 23.9424i | − | 1.73241i | −0.499690 | − | 0.866204i | \(-0.666553\pi\) | ||
0.499690 | − | 0.866204i | \(-0.333447\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | 16.1408 | 1.16184 | 0.580919 | − | 0.813961i | \(-0.302693\pi\) | ||||
0.580919 | + | 0.813961i | \(0.302693\pi\) | |||||||
\(194\) | 4.48125 | − | 7.76175i | 0.321735 | − | 0.557261i | ||||
\(195\) | 6.23369 | − | 10.8751i | 0.446404 | − | 0.778784i | ||||
\(196\) | −10.3407 | −0.738622 | ||||||||
\(197\) | 21.2832 | + | 12.2879i | 1.51637 | + | 0.875475i | 0.999815 | + | 0.0192182i | \(0.00611772\pi\) |
0.516551 | + | 0.856256i | \(0.327216\pi\) | |||||||
\(198\) | 2.81177 | + | 4.87013i | 0.199824 | + | 0.346105i | ||||
\(199\) | − | 17.4958i | − | 1.24025i | −0.784505 | − | 0.620123i | \(-0.787083\pi\) | ||
0.784505 | − | 0.620123i | \(-0.212917\pi\) | |||||||
\(200\) | −4.99990 | + | 0.0311363i | −0.353547 | + | 0.00220167i | ||||
\(201\) | −1.10894 | + | 1.92075i | −0.0782189 | + | 0.135479i | ||||
\(202\) | −8.78723 | + | 15.2199i | −0.618267 | + | 1.07087i | ||||
\(203\) | −20.6295 | − | 35.7314i | −1.44791 | − | 2.50785i | ||||
\(204\) | 2.48053 | − | 1.43213i | 0.173672 | − | 0.100269i | ||||
\(205\) | −1.81986 | + | 1.05826i | −0.127104 | + | 0.0739123i | ||||
\(206\) | −2.41837 | + | 4.18875i | −0.168496 | + | 0.291844i | ||||
\(207\) | −3.12090 | + | 5.40555i | −0.216917 | + | 0.375712i | ||||
\(208\) | 5.60584 | 0.388695 | ||||||||
\(209\) | −29.0413 | + | 16.7670i | −2.00883 | + | 1.15980i | ||||
\(210\) | −8.04944 | + | 4.68082i | −0.555464 | + | 0.323007i | ||||
\(211\) | 28.4494 | 1.95854 | 0.979268 | − | 0.202571i | \(-0.0649297\pi\) | ||||
0.979268 | + | 0.202571i | \(0.0649297\pi\) | |||||||
\(212\) | 4.47566i | 0.307390i | ||||||||
\(213\) | 10.5400 | + | 6.08527i | 0.722189 | + | 0.416956i | ||||
\(214\) | 15.5798i | 1.06501i | ||||||||
\(215\) | −0.0299036 | − | 9.60398i | −0.00203941 | − | 0.654986i | ||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 9.03314 | + | 15.6459i | 0.613210 | + | 1.06211i | ||||
\(218\) | 1.14051 | − | 0.658472i | 0.0772449 | − | 0.0445974i | ||||
\(219\) | −5.79986 | − | 10.0456i | −0.391918 | − | 0.678822i | ||||
\(220\) | −10.8703 | + | 6.32119i | −0.732877 | + | 0.426175i | ||||
\(221\) | −16.0566 | −1.08009 | ||||||||
\(222\) | 5.73864 | + | 2.01692i | 0.385153 | + | 0.135367i | ||||
\(223\) | 2.89406i | 0.193800i | 0.995294 | + | 0.0969002i | \(0.0308928\pi\) | ||||
−0.995294 | + | 0.0969002i | \(0.969107\pi\) | |||||||
\(224\) | −3.60632 | − | 2.08211i | −0.240957 | − | 0.139117i | ||||
\(225\) | −2.47299 | + | 4.34561i | −0.164866 | + | 0.289707i | ||||
\(226\) | 4.34832 | + | 7.53150i | 0.289246 | + | 0.500988i | ||||
\(227\) | −2.39517 | − | 4.14855i | −0.158973 | − | 0.275349i | 0.775526 | − | 0.631316i | \(-0.217485\pi\) |
−0.934499 | + | 0.355967i | \(0.884152\pi\) | |||||||
\(228\) | −5.96313 | −0.394918 | ||||||||
\(229\) | −0.352183 | − | 0.609999i | −0.0232729 | − | 0.0403099i | 0.854154 | − | 0.520020i | \(-0.174075\pi\) |
−0.877427 | + | 0.479710i | \(0.840742\pi\) | |||||||
\(230\) | −12.1088 | − | 6.94087i | −0.798434 | − | 0.457667i | ||||
\(231\) | −11.7088 | + | 20.2803i | −0.770385 | + | 1.33435i | ||||
\(232\) | − | 9.90800i | − | 0.650492i | ||||||
\(233\) | 15.4170i | 1.01000i | 0.863118 | + | 0.505002i | \(0.168508\pi\) | ||||
−0.863118 | + | 0.505002i | \(0.831492\pi\) | |||||||
\(234\) | 2.80292 | − | 4.85480i | 0.183233 | − | 0.317368i | ||||
\(235\) | 0.818172 | − | 0.00254751i | 0.0533717 | − | 0.000166181i | ||||
\(236\) | − | 10.9933i | − | 0.715603i | ||||||
\(237\) | 4.94977 | − | 8.57325i | 0.321522 | − | 0.556893i | ||||
\(238\) | 10.3295 | + | 5.96372i | 0.669560 | + | 0.386571i | ||||
\(239\) | −6.13569 | − | 3.54245i | −0.396885 | − | 0.229142i | 0.288254 | − | 0.957554i | \(-0.406925\pi\) |
−0.685139 | + | 0.728412i | \(0.740259\pi\) | |||||||
\(240\) | −2.23606 | + | 0.00696233i | −0.144337 | + | 0.000449417i | ||||
\(241\) | −19.6742 | + | 11.3589i | −1.26733 | + | 0.731692i | −0.974481 | − | 0.224468i | \(-0.927936\pi\) |
−0.292846 | + | 0.956160i | \(0.594602\pi\) | |||||||
\(242\) | −10.3121 | + | 17.8611i | −0.662889 | + | 1.14816i | ||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | −2.20880 | − | 1.27525i | −0.141404 | − | 0.0816395i | ||||
\(245\) | −20.0606 | − | 11.4989i | −1.28162 | − | 0.734635i | ||||
\(246\) | −0.815334 | + | 0.470733i | −0.0519838 | + | 0.0300128i | ||||
\(247\) | 28.9498 | + | 16.7142i | 1.84203 | + | 1.06350i | ||||
\(248\) | 4.33846i | 0.275492i | ||||||||
\(249\) | −0.181403 | −0.0114959 | ||||||||
\(250\) | −9.73425 | − | 5.49948i | −0.615648 | − | 0.347818i | ||||
\(251\) | − | 0.437029i | − | 0.0275850i | −0.999905 | − | 0.0137925i | \(-0.995610\pi\) | ||
0.999905 | − | 0.0137925i | \(-0.00439043\pi\) | |||||||
\(252\) | −3.60632 | + | 2.08211i | −0.227177 | + | 0.131161i | ||||
\(253\) | −35.1010 | −2.20678 | ||||||||
\(254\) | −6.46743 | + | 3.73397i | −0.405803 | + | 0.234290i | ||||
\(255\) | 6.40467 | − | 0.0199420i | 0.401076 | − | 0.00124882i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 2.17930 | − | 3.77465i | 0.135941 | − | 0.235456i | −0.790016 | − | 0.613087i | \(-0.789928\pi\) |
0.925956 | + | 0.377630i | \(0.123261\pi\) | |||||||
\(258\) | − | 4.29505i | − | 0.267398i | ||||||
\(259\) | 4.67482 | + | 24.8948i | 0.290479 | + | 1.54689i | ||||
\(260\) | 10.8751 | + | 6.23369i | 0.674447 | + | 0.386597i | ||||
\(261\) | −8.58058 | − | 4.95400i | −0.531125 | − | 0.306645i | ||||
\(262\) | 4.67400 | − | 2.69853i | 0.288761 | − | 0.166716i | ||||
\(263\) | 24.8970 | − | 14.3743i | 1.53522 | − | 0.886358i | 0.536109 | − | 0.844149i | \(-0.319894\pi\) |
0.999109 | − | 0.0422094i | \(-0.0134396\pi\) | |||||||
\(264\) | −4.87013 | + | 2.81177i | −0.299736 | + | 0.173053i | ||||
\(265\) | −4.97693 | + | 8.68262i | −0.305730 | + | 0.533369i | ||||
\(266\) | −12.4159 | − | 21.5050i | −0.761267 | − | 1.31855i | ||||
\(267\) | 8.52520 | 0.521734 | ||||||||
\(268\) | −1.92075 | − | 1.10894i | −0.117328 | − | 0.0677395i | ||||
\(269\) | 2.96047 | 0.180503 | 0.0902516 | − | 0.995919i | \(-0.471233\pi\) | ||||
0.0902516 | + | 0.995919i | \(0.471233\pi\) | |||||||
\(270\) | −1.11200 | + | 1.93996i | −0.0676741 | + | 0.118062i | ||||
\(271\) | −5.51239 | + | 9.54773i | −0.334854 | + | 0.579983i | −0.983457 | − | 0.181143i | \(-0.942020\pi\) |
0.648603 | + | 0.761127i | \(0.275354\pi\) | |||||||
\(272\) | 1.43213 | + | 2.48053i | 0.0868359 | + | 0.150404i | ||||
\(273\) | 23.3440 | 1.41284 | ||||||||
\(274\) | −2.99163 | − | 1.72722i | −0.180731 | − | 0.104345i | ||||
\(275\) | −28.1172 | + | 0.175097i | −1.69553 | + | 0.0105587i | ||||
\(276\) | −5.40555 | − | 3.12090i | −0.325376 | − | 0.187856i | ||||
\(277\) | 5.97624 | + | 10.3511i | 0.359077 | + | 0.621940i | 0.987807 | − | 0.155684i | \(-0.0497581\pi\) |
−0.628730 | + | 0.777624i | \(0.716425\pi\) | |||||||
\(278\) | 4.16178 | + | 7.20841i | 0.249607 | + | 0.432332i | ||||
\(279\) | 3.75722 | + | 2.16923i | 0.224939 | + | 0.129868i | ||||
\(280\) | −4.68082 | − | 8.04944i | −0.279733 | − | 0.481046i | ||||
\(281\) | 4.75144 | + | 2.74325i | 0.283447 | + | 0.163648i | 0.634983 | − | 0.772526i | \(-0.281007\pi\) |
−0.351536 | + | 0.936174i | \(0.614340\pi\) | |||||||
\(282\) | 0.365900 | 0.0217890 | ||||||||
\(283\) | 5.73565 | + | 9.93443i | 0.340949 | + | 0.590541i | 0.984609 | − | 0.174771i | \(-0.0559184\pi\) |
−0.643660 | + | 0.765311i | \(0.722585\pi\) | |||||||
\(284\) | −6.08527 | + | 10.5400i | −0.361095 | + | 0.625434i | ||||
\(285\) | −11.5683 | − | 6.63100i | −0.685245 | − | 0.392787i | ||||
\(286\) | 31.5247 | 1.86410 | ||||||||
\(287\) | −3.39523 | − | 1.96024i | −0.200414 | − | 0.115709i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 4.39798 | + | 7.61753i | 0.258705 | + | 0.448090i | ||||
\(290\) | 11.0177 | − | 19.2212i | 0.646981 | − | 1.12871i | ||||
\(291\) | 7.76175 | − | 4.48125i | 0.455002 | − | 0.262695i | ||||
\(292\) | 10.0456 | − | 5.79986i | 0.587877 | − | 0.339411i | ||||
\(293\) | −8.60014 | + | 4.96530i | −0.502426 | + | 0.290076i | −0.729715 | − | 0.683752i | \(-0.760347\pi\) |
0.227289 | + | 0.973827i | \(0.427014\pi\) | |||||||
\(294\) | −8.95532 | − | 5.17035i | −0.522285 | − | 0.301541i | ||||
\(295\) | 12.2245 | − | 21.3266i | 0.711740 | − | 1.24168i | ||||
\(296\) | −2.01692 | + | 5.73864i | −0.117231 | + | 0.333552i | ||||
\(297\) | 5.62355i | 0.326311i | ||||||||
\(298\) | −4.70096 | + | 8.14231i | −0.272320 | + | 0.471671i | ||||
\(299\) | 17.4953 | + | 30.3027i | 1.01178 | + | 1.75245i | ||||
\(300\) | −4.34561 | − | 2.47299i | −0.250894 | − | 0.142778i | ||||
\(301\) | 15.4893 | − | 8.94276i | 0.892790 | − | 0.515452i | ||||
\(302\) | 10.8541 | 0.624582 | ||||||||
\(303\) | −15.2199 | + | 8.78723i | −0.874362 | + | 0.504813i | ||||
\(304\) | − | 5.96313i | − | 0.342009i | ||||||
\(305\) | −2.86691 | − | 4.93012i | −0.164159 | − | 0.282298i | ||||
\(306\) | 2.86427 | 0.163739 | ||||||||
\(307\) | 1.24701i | 0.0711705i | 0.999367 | + | 0.0355852i | \(0.0113295\pi\) | ||||
−0.999367 | + | 0.0355852i | \(0.988670\pi\) | |||||||
\(308\) | −20.2803 | − | 11.7088i | −1.15558 | − | 0.667173i | ||||
\(309\) | −4.18875 | + | 2.41837i | −0.238290 | + | 0.137577i | ||||
\(310\) | −4.82436 | + | 8.41645i | −0.274005 | + | 0.478022i | ||||
\(311\) | −7.15158 | − | 4.12897i | −0.405529 | − | 0.234132i | 0.283338 | − | 0.959020i | \(-0.408558\pi\) |
−0.688867 | + | 0.724888i | \(0.741892\pi\) | |||||||
\(312\) | 4.85480 | + | 2.80292i | 0.274849 | + | 0.158684i | ||||
\(313\) | −0.958252 | + | 1.65974i | −0.0541636 | + | 0.0938141i | −0.891836 | − | 0.452359i | \(-0.850583\pi\) |
0.837672 | + | 0.546173i | \(0.183916\pi\) | |||||||
\(314\) | 13.0906 | − | 7.55789i | 0.738748 | − | 0.426516i | ||||
\(315\) | −9.31143 | + | 0.0289927i | −0.524640 | + | 0.00163355i | ||||
\(316\) | 8.57325 | + | 4.94977i | 0.482283 | + | 0.278446i | ||||
\(317\) | 1.54711 | + | 0.893227i | 0.0868946 | + | 0.0501686i | 0.542818 | − | 0.839851i | \(-0.317357\pi\) |
−0.455923 | + | 0.890019i | \(0.650691\pi\) | |||||||
\(318\) | −2.23783 | + | 3.87603i | −0.125491 | + | 0.217357i | ||||
\(319\) | − | 55.7181i | − | 3.11962i | ||||||
\(320\) | −0.00696233 | − | 2.23606i | −0.000389206 | − | 0.124999i | ||||
\(321\) | −7.78991 | + | 13.4925i | −0.434790 | + | 0.753079i | ||||
\(322\) | − | 25.9922i | − | 1.44849i | ||||||
\(323\) | 17.0800i | 0.950358i | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | 14.1655 | + | 24.1863i | 0.785760 | + | 1.34161i | ||||
\(326\) | 2.95761 | + | 5.12274i | 0.163807 | + | 0.283722i | ||||
\(327\) | 1.31694 | 0.0728272 | ||||||||
\(328\) | −0.470733 | − | 0.815334i | −0.0259919 | − | 0.0450193i | ||||
\(329\) | 0.761843 | + | 1.31955i | 0.0420017 | + | 0.0727492i | ||||
\(330\) | −12.5746 | + | 0.0391530i | −0.692207 | + | 0.00215530i | ||||
\(331\) | 12.2666 | + | 7.08211i | 0.674232 | + | 0.389268i | 0.797678 | − | 0.603083i | \(-0.206061\pi\) |
−0.123446 | + | 0.992351i | \(0.539395\pi\) | |||||||
\(332\) | − | 0.181403i | − | 0.00995577i | ||||||
\(333\) | 3.96135 | + | 4.61603i | 0.217081 | + | 0.252957i | ||||
\(334\) | −6.09487 | −0.333496 | ||||||||
\(335\) | −2.49304 | − | 4.28718i | −0.136209 | − | 0.234234i | ||||
\(336\) | −2.08211 | − | 3.60632i | −0.113588 | − | 0.196741i | ||||
\(337\) | 8.49393 | − | 4.90397i | 0.462694 | − | 0.267136i | −0.250482 | − | 0.968121i | \(-0.580589\pi\) |
0.713176 | + | 0.700985i | \(0.247256\pi\) | |||||||
\(338\) | −9.21274 | − | 15.9569i | −0.501107 | − | 0.867943i | ||||
\(339\) | 8.69663i | 0.472336i | ||||||||
\(340\) | 0.0199420 | + | 6.40467i | 0.00108151 | + | 0.347342i | ||||
\(341\) | 24.3975i | 1.32120i | ||||||||
\(342\) | −5.16423 | − | 2.98157i | −0.279249 | − | 0.161225i | ||||
\(343\) | − | 13.9114i | − | 0.751147i | ||||||
\(344\) | 4.29505 | 0.231574 | ||||||||
\(345\) | −7.01614 | − | 12.0654i | −0.377736 | − | 0.649579i | ||||
\(346\) | 6.21546 | − | 3.58850i | 0.334145 | − | 0.192919i | ||||
\(347\) | 22.5282 | 1.20938 | 0.604688 | − | 0.796463i | \(-0.293298\pi\) | ||||
0.604688 | + | 0.796463i | \(0.293298\pi\) | |||||||
\(348\) | 4.95400 | − | 8.58058i | 0.265562 | − | 0.459968i | ||||
\(349\) | −0.142907 | + | 0.247523i | −0.00764965 | + | 0.0132496i | −0.869825 | − | 0.493361i | \(-0.835768\pi\) |
0.862175 | + | 0.506610i | \(0.169102\pi\) | |||||||
\(350\) | −0.129659 | − | 20.8207i | −0.00693054 | − | 1.11291i | ||||
\(351\) | 4.85480 | − | 2.80292i | 0.259130 | − | 0.149609i | ||||
\(352\) | −2.81177 | − | 4.87013i | −0.149868 | − | 0.259579i | ||||
\(353\) | −8.58970 | + | 14.8778i | −0.457184 | + | 0.791865i | −0.998811 | − | 0.0487534i | \(-0.984475\pi\) |
0.541627 | + | 0.840619i | \(0.317808\pi\) | |||||||
\(354\) | 5.49665 | − | 9.52048i | 0.292144 | − | 0.506008i | ||||
\(355\) | −23.5257 | + | 13.6804i | −1.24861 | + | 0.726081i | ||||
\(356\) | 8.52520i | 0.451835i | ||||||||
\(357\) | 5.96372 | + | 10.3295i | 0.315634 | + | 0.546693i | ||||
\(358\) | −19.6441 | − | 11.3415i | −1.03822 | − | 0.599419i | ||||
\(359\) | 7.99692 | 0.422061 | 0.211031 | − | 0.977479i | \(-0.432318\pi\) | ||||
0.211031 | + | 0.977479i | \(0.432318\pi\) | |||||||
\(360\) | −1.93996 | − | 1.11200i | −0.102245 | − | 0.0586075i | ||||
\(361\) | 8.27949 | − | 14.3405i | 0.435762 | − | 0.754763i | ||||
\(362\) | 11.9137 | 0.626168 | ||||||||
\(363\) | −17.8611 | + | 10.3121i | −0.937467 | + | 0.541247i | ||||
\(364\) | 23.3440i | 1.22356i | ||||||||
\(365\) | 25.9376 | − | 0.0807611i | 1.35764 | − | 0.00422723i | ||||
\(366\) | −1.27525 | − | 2.20880i | −0.0666583 | − | 0.115456i | ||||
\(367\) | −20.1521 | + | 11.6348i | −1.05193 | + | 0.607332i | −0.923189 | − | 0.384347i | \(-0.874427\pi\) |
−0.128741 | + | 0.991678i | \(0.541093\pi\) | |||||||
\(368\) | 3.12090 | − | 5.40555i | 0.162688 | − | 0.281784i | ||||
\(369\) | −0.941466 | −0.0490108 | ||||||||
\(370\) | −10.2941 | + | 8.88995i | −0.535166 | + | 0.462166i | ||||
\(371\) | −18.6376 | −0.967617 | ||||||||
\(372\) | −2.16923 | + | 3.75722i | −0.112469 | + | 0.194803i | ||||
\(373\) | −19.6815 | + | 11.3631i | −1.01907 | + | 0.588360i | −0.913834 | − | 0.406087i | \(-0.866893\pi\) |
−0.105235 | + | 0.994447i | \(0.533560\pi\) | |||||||
\(374\) | 8.05368 | + | 13.9494i | 0.416446 | + | 0.721305i | ||||
\(375\) | −5.68037 | − | 9.62982i | −0.293333 | − | 0.497282i | ||||
\(376\) | 0.365900i | 0.0188698i | ||||||||
\(377\) | −48.1014 | + | 27.7714i | −2.47735 | + | 1.43030i | ||||
\(378\) | −4.16422 | −0.214184 | ||||||||
\(379\) | −11.1432 | + | 19.3005i | −0.572386 | + | 0.991402i | 0.423934 | + | 0.905693i | \(0.360649\pi\) |
−0.996320 | + | 0.0857086i | \(0.972685\pi\) | |||||||
\(380\) | 6.63100 | − | 11.5683i | 0.340163 | − | 0.593439i | ||||
\(381\) | −7.46795 | −0.382594 | ||||||||
\(382\) | 20.7347 | + | 11.9712i | 1.06088 | + | 0.612499i | ||||
\(383\) | 4.33722 | + | 7.51229i | 0.221622 | + | 0.383860i | 0.955301 | − | 0.295636i | \(-0.0955317\pi\) |
−0.733679 | + | 0.679496i | \(0.762198\pi\) | |||||||
\(384\) | − | 1.00000i | − | 0.0510310i | ||||||
\(385\) | −26.3228 | − | 45.2664i | −1.34154 | − | 2.30699i | ||||
\(386\) | −8.07038 | + | 13.9783i | −0.410772 | + | 0.711477i | ||||
\(387\) | 2.14753 | − | 3.71962i | 0.109165 | − | 0.189079i | ||||
\(388\) | 4.48125 | + | 7.76175i | 0.227501 | + | 0.394043i | ||||
\(389\) | 32.7509 | − | 18.9088i | 1.66054 | − | 0.958712i | 0.688080 | − | 0.725635i | \(-0.258454\pi\) |
0.972458 | − | 0.233077i | \(-0.0748794\pi\) | |||||||
\(390\) | 6.30129 | + | 10.8361i | 0.319078 | + | 0.548707i | ||||
\(391\) | −8.93909 | + | 15.4829i | −0.452069 | + | 0.783006i | ||||
\(392\) | 5.17035 | − | 8.95532i | 0.261142 | − | 0.452312i | ||||
\(393\) | 5.39707 | 0.272246 | ||||||||
\(394\) | −21.2832 | + | 12.2879i | −1.07223 | + | 0.619054i | ||||
\(395\) | 11.1277 | + | 19.1358i | 0.559893 | + | 0.962828i | ||||
\(396\) | −5.62355 | −0.282594 | ||||||||
\(397\) | − | 26.0656i | − | 1.30819i | −0.756411 | − | 0.654097i | \(-0.773049\pi\) | ||
0.756411 | − | 0.654097i | \(-0.226951\pi\) | |||||||
\(398\) | 15.1518 | + | 8.74791i | 0.759492 | + | 0.438493i | ||||
\(399\) | − | 24.8318i | − | 1.24314i | ||||||
\(400\) | 2.47299 | − | 4.34561i | 0.123649 | − | 0.217281i | ||||
\(401\) | 8.98577i | 0.448728i | 0.974505 | + | 0.224364i | \(0.0720305\pi\) | ||||
−0.974505 | + | 0.224364i | \(0.927970\pi\) | |||||||
\(402\) | −1.10894 | − | 1.92075i | −0.0553091 | − | 0.0957982i | ||||
\(403\) | 21.0624 | − | 12.1604i | 1.04919 | − | 0.605751i | ||||
\(404\) | −8.78723 | − | 15.2199i | −0.437181 | − | 0.757220i | ||||
\(405\) | −1.93300 | + | 1.12406i | −0.0960516 | + | 0.0558549i | ||||
\(406\) | 41.2591 | 2.04765 | ||||||||
\(407\) | −11.3422 | + | 32.2715i | −0.562214 | + | 1.59964i | ||||
\(408\) | 2.86427i | 0.141802i | ||||||||
\(409\) | 4.54148 | + | 2.62202i | 0.224561 | + | 0.129651i | 0.608061 | − | 0.793891i | \(-0.291948\pi\) |
−0.383499 | + | 0.923541i | \(0.625281\pi\) | |||||||
\(410\) | −0.00655480 | − | 2.10517i | −0.000323719 | − | 0.103967i | ||||
\(411\) | −1.72722 | − | 2.99163i | −0.0851974 | − | 0.147566i | ||||
\(412\) | −2.41837 | − | 4.18875i | −0.119145 | − | 0.206365i | ||||
\(413\) | 45.7785 | 2.25261 | ||||||||
\(414\) | −3.12090 | − | 5.40555i | −0.153384 | − | 0.265668i | ||||
\(415\) | 0.201720 | − | 0.351915i | 0.00990203 | − | 0.0172748i | ||||
\(416\) | −2.80292 | + | 4.85480i | −0.137425 | + | 0.238026i | ||||
\(417\) | 8.32355i | 0.407606i | ||||||||
\(418\) | − | 33.5340i | − | 1.64020i | ||||||
\(419\) | 4.82659 | − | 8.35990i | 0.235794 | − | 0.408408i | −0.723709 | − | 0.690105i | \(-0.757564\pi\) |
0.959503 | + | 0.281698i | \(0.0908975\pi\) | |||||||
\(420\) | −0.0289927 | − | 9.31143i | −0.00141470 | − | 0.454351i | ||||
\(421\) | 2.40440i | 0.117183i | 0.998282 | + | 0.0585916i | \(0.0186610\pi\) | ||||
−0.998282 | + | 0.0585916i | \(0.981339\pi\) | |||||||
\(422\) | −14.2247 | + | 24.6379i | −0.692447 | + | 1.19935i | ||||
\(423\) | 0.316878 | + | 0.182950i | 0.0154072 | + | 0.00889532i | ||||
\(424\) | −3.87603 | − | 2.23783i | −0.188237 | − | 0.108679i | ||||
\(425\) | −7.08330 | + | 12.4470i | −0.343590 | + | 0.603768i | ||||
\(426\) | −10.5400 | + | 6.08527i | −0.510665 | + | 0.294833i | ||||
\(427\) | 5.31041 | − | 9.19791i | 0.256989 | − | 0.445118i | ||||
\(428\) | −13.4925 | − | 7.78991i | −0.652185 | − | 0.376539i | ||||
\(429\) | 27.3012 | + | 15.7624i | 1.31811 | + | 0.761014i | ||||
\(430\) | 8.33224 | + | 4.77609i | 0.401816 | + | 0.230324i | ||||
\(431\) | −21.2626 | + | 12.2760i | −1.02418 | + | 0.591313i | −0.915313 | − | 0.402742i | \(-0.868057\pi\) |
−0.108871 | + | 0.994056i | \(0.534724\pi\) | |||||||
\(432\) | −0.866025 | − | 0.500000i | −0.0416667 | − | 0.0240563i | ||||
\(433\) | − | 24.7803i | − | 1.19087i | −0.803405 | − | 0.595433i | \(-0.796980\pi\) | ||
0.803405 | − | 0.595433i | \(-0.203020\pi\) | |||||||
\(434\) | −18.0663 | −0.867209 | ||||||||
\(435\) | 19.1522 | − | 11.1372i | 0.918277 | − | 0.533987i | ||||
\(436\) | 1.31694i | 0.0630702i | ||||||||
\(437\) | 32.2340 | − | 18.6103i | 1.54196 | − | 0.890252i | ||||
\(438\) | 11.5997 | 0.554256 | ||||||||
\(439\) | 23.1393 | − | 13.3595i | 1.10438 | − | 0.637614i | 0.167012 | − | 0.985955i | \(-0.446588\pi\) |
0.937368 | + | 0.348341i | \(0.113255\pi\) | |||||||
\(440\) | −0.0391530 | − | 12.5746i | −0.00186655 | − | 0.599469i | ||||
\(441\) | −5.17035 | − | 8.95532i | −0.246207 | − | 0.426444i | ||||
\(442\) | 8.02832 | − | 13.9055i | 0.381868 | − | 0.661415i | ||||
\(443\) | 18.4378i | 0.876008i | 0.898973 | + | 0.438004i | \(0.144314\pi\) | ||||
−0.898973 | + | 0.438004i | \(0.855686\pi\) | |||||||
\(444\) | −4.61603 | + | 3.96135i | −0.219067 | + | 0.187997i | ||||
\(445\) | −9.48002 | + | 16.5386i | −0.449396 | + | 0.784004i | ||||
\(446\) | −2.50633 | − | 1.44703i | −0.118678 | − | 0.0685188i | ||||
\(447\) | −8.14231 | + | 4.70096i | −0.385118 | + | 0.222348i | ||||
\(448\) | 3.60632 | − | 2.08211i | 0.170383 | − | 0.0983704i | ||||
\(449\) | 29.6975 | − | 17.1459i | 1.40151 | − | 0.809164i | 0.406965 | − | 0.913444i | \(-0.366587\pi\) |
0.994548 | + | 0.104280i | \(0.0332539\pi\) | |||||||
\(450\) | −2.52692 | − | 4.31447i | −0.119120 | − | 0.203386i | ||||
\(451\) | −2.64719 | − | 4.58507i | −0.124651 | − | 0.215902i | ||||
\(452\) | −8.69663 | −0.409055 | ||||||||
\(453\) | 9.39991 | + | 5.42704i | 0.441646 | + | 0.254985i | ||||
\(454\) | 4.79034 | 0.224822 | ||||||||
\(455\) | −25.9584 | + | 45.2864i | −1.21695 | + | 2.12306i | ||||
\(456\) | 2.98157 | − | 5.16423i | 0.139625 | − | 0.241837i | ||||
\(457\) | 12.2911 | + | 21.2888i | 0.574954 | + | 0.995849i | 0.996047 | + | 0.0888317i | \(0.0283133\pi\) |
−0.421093 | + | 0.907018i | \(0.638353\pi\) | |||||||
\(458\) | 0.704366 | 0.0329129 | ||||||||
\(459\) | 2.48053 | + | 1.43213i | 0.115781 | + | 0.0668463i | ||||
\(460\) | 12.0654 | − | 7.01614i | 0.562552 | − | 0.327129i | ||||
\(461\) | −9.81068 | − | 5.66420i | −0.456929 | − | 0.263808i | 0.253823 | − | 0.967251i | \(-0.418312\pi\) |
−0.710752 | + | 0.703443i | \(0.751645\pi\) | |||||||
\(462\) | −11.7088 | − | 20.2803i | −0.544744 | − | 0.943525i | ||||
\(463\) | −0.261365 | − | 0.452698i | −0.0121467 | − | 0.0210387i | 0.859888 | − | 0.510482i | \(-0.170533\pi\) |
−0.872035 | + | 0.489444i | \(0.837200\pi\) | |||||||
\(464\) | 8.58058 | + | 4.95400i | 0.398344 | + | 0.229984i | ||||
\(465\) | −8.38624 | + | 4.87668i | −0.388903 | + | 0.226151i | ||||
\(466\) | −13.3515 | − | 7.70852i | −0.618498 | − | 0.357090i | ||||
\(467\) | 1.75438 | 0.0811830 | 0.0405915 | − | 0.999176i | \(-0.487076\pi\) | ||||
0.0405915 | + | 0.999176i | \(0.487076\pi\) | |||||||
\(468\) | 2.80292 | + | 4.85480i | 0.129565 | + | 0.224413i | ||||
\(469\) | 4.61788 | − | 7.99841i | 0.213234 | − | 0.369332i | ||||
\(470\) | −0.406880 | + | 0.709832i | −0.0187680 | + | 0.0327421i | ||||
\(471\) | 15.1158 | 0.696498 | ||||||||
\(472\) | 9.52048 | + | 5.49665i | 0.438216 | + | 0.253004i | ||||
\(473\) | 24.1534 | 1.11058 | ||||||||
\(474\) | 4.94977 | + | 8.57325i | 0.227350 | + | 0.393783i | ||||
\(475\) | 25.7278 | − | 15.0683i | 1.18047 | − | 0.691383i | ||||
\(476\) | −10.3295 | + | 5.96372i | −0.473450 | + | 0.273347i | ||||
\(477\) | −3.87603 | + | 2.23783i | −0.177471 | + | 0.102463i | ||||
\(478\) | 6.13569 | − | 3.54245i | 0.280640 | − | 0.162028i | ||||
\(479\) | −14.0589 | − | 8.11691i | −0.642368 | − | 0.370871i | 0.143158 | − | 0.989700i | \(-0.454274\pi\) |
−0.785526 | + | 0.618829i | \(0.787608\pi\) | |||||||
\(480\) | 1.11200 | − | 1.93996i | 0.0507556 | − | 0.0885468i | ||||
\(481\) | 33.5133 | − | 6.29322i | 1.52807 | − | 0.286946i | ||||
\(482\) | − | 22.7178i | − | 1.03477i | ||||||
\(483\) | 12.9961 | − | 22.5099i | 0.591342 | − | 1.02424i | ||||
\(484\) | −10.3121 | − | 17.8611i | −0.468734 | − | 0.811870i | ||||
\(485\) | 0.0623999 | + | 20.0407i | 0.00283343 | + | 0.909999i | ||||
\(486\) | −0.866025 | + | 0.500000i | −0.0392837 | + | 0.0226805i | ||||
\(487\) | −27.4494 | −1.24385 | −0.621927 | − | 0.783076i | \(-0.713650\pi\) | ||||
−0.621927 | + | 0.783076i | \(0.713650\pi\) | |||||||
\(488\) | 2.20880 | − | 1.27525i | 0.0999875 | − | 0.0577278i | ||||
\(489\) | 5.91523i | 0.267496i | ||||||||
\(490\) | 19.9886 | − | 11.6236i | 0.902993 | − | 0.525099i | ||||
\(491\) | 24.9786 | 1.12727 | 0.563634 | − | 0.826024i | \(-0.309403\pi\) | ||||
0.563634 | + | 0.826024i | \(0.309403\pi\) | |||||||
\(492\) | − | 0.941466i | − | 0.0424446i | ||||||
\(493\) | −24.5771 | − | 14.1896i | −1.10690 | − | 0.639067i | ||||
\(494\) | −28.9498 | + | 16.7142i | −1.30251 | + | 0.752007i | ||||
\(495\) | −10.9095 | − | 6.25338i | −0.490344 | − | 0.281068i | ||||
\(496\) | −3.75722 | − | 2.16923i | −0.168704 | − | 0.0974013i | ||||
\(497\) | −43.8909 | − | 25.3404i | −1.96877 | − | 1.13667i | ||||
\(498\) | 0.0907014 | − | 0.157099i | 0.00406443 | − | 0.00703979i | ||||
\(499\) | 8.21385 | − | 4.74227i | 0.367702 | − | 0.212293i | −0.304752 | − | 0.952432i | \(-0.598574\pi\) |
0.672454 | + | 0.740139i | \(0.265240\pi\) | |||||||
\(500\) | 9.62982 | − | 5.68037i | 0.430659 | − | 0.254034i | ||||
\(501\) | −5.27831 | − | 3.04743i | −0.235817 | − | 0.136149i | ||||
\(502\) | 0.378478 | + | 0.218514i | 0.0168923 | + | 0.00975278i | ||||
\(503\) | 2.11396 | − | 3.66149i | 0.0942569 | − | 0.163258i | −0.815041 | − | 0.579403i | \(-0.803286\pi\) |
0.909298 | + | 0.416145i | \(0.136619\pi\) | |||||||
\(504\) | − | 4.16422i | − | 0.185489i | ||||||
\(505\) | −0.122359 | − | 39.2975i | −0.00544491 | − | 1.74872i | ||||
\(506\) | 17.5505 | − | 30.3984i | 0.780215 | − | 1.35137i | ||||
\(507\) | − | 18.4255i | − | 0.818304i | ||||||
\(508\) | − | 7.46795i | − | 0.331336i | ||||||
\(509\) | 11.0937 | − | 19.2149i | 0.491721 | − | 0.851685i | −0.508234 | − | 0.861219i | \(-0.669701\pi\) |
0.999955 | + | 0.00953382i | \(0.00303475\pi\) | |||||||
\(510\) | −3.18506 | + | 5.55658i | −0.141037 | + | 0.246049i | ||||
\(511\) | 24.1519 | + | 41.8323i | 1.06842 | + | 1.85055i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −2.98157 | − | 5.16423i | −0.131639 | − | 0.228006i | ||||
\(514\) | 2.17930 | + | 3.77465i | 0.0961246 | + | 0.166493i | ||||
\(515\) | −0.0336750 | − | 10.8152i | −0.00148390 | − | 0.476577i | ||||
\(516\) | 3.71962 | + | 2.14753i | 0.163747 | + | 0.0945395i | ||||
\(517\) | 2.05765i | 0.0904955i | ||||||||
\(518\) | −23.8970 | − | 8.39889i | −1.04997 | − | 0.369026i | ||||
\(519\) | 7.17699 | 0.315035 | ||||||||
\(520\) | −10.8361 | + | 6.30129i | −0.475194 | + | 0.276330i | ||||
\(521\) | 1.06382 | + | 1.84258i | 0.0466066 | + | 0.0807250i | 0.888388 | − | 0.459094i | \(-0.151826\pi\) |
−0.841781 | + | 0.539819i | \(0.818493\pi\) | |||||||
\(522\) | 8.58058 | − | 4.95400i | 0.375562 | − | 0.216831i | ||||
\(523\) | −2.71184 | − | 4.69705i | −0.118581 | − | 0.205388i | 0.800625 | − | 0.599166i | \(-0.204501\pi\) |
−0.919205 | + | 0.393778i | \(0.871168\pi\) | |||||||
\(524\) | 5.39707i | 0.235772i | ||||||||
\(525\) | 10.2981 | − | 18.0961i | 0.449444 | − | 0.789777i | ||||
\(526\) | 28.7486i | 1.25350i | ||||||||
\(527\) | 10.7617 | + | 6.21326i | 0.468786 | + | 0.270654i | ||||
\(528\) | − | 5.62355i | − | 0.244733i | ||||||
\(529\) | 15.9600 | 0.693911 | ||||||||
\(530\) | −5.03090 | − | 8.65145i | −0.218528 | − | 0.375795i | ||||
\(531\) | 9.52048 | − | 5.49665i | 0.413154 | − | 0.238534i | ||||
\(532\) | 24.8318 | 1.07659 | ||||||||
\(533\) | −2.63886 | + | 4.57063i | −0.114302 | + | 0.197976i | ||||
\(534\) | −4.26260 | + | 7.38304i | −0.184461 | + | 0.319495i | ||||
\(535\) | −17.5126 | − | 30.1158i | −0.757136 | − | 1.30202i | ||||
\(536\) | 1.92075 | − | 1.10894i | 0.0829637 | − | 0.0478991i | ||||
\(537\) | −11.3415 | − | 19.6441i | −0.489424 | − | 0.847707i | ||||
\(538\) | −1.48024 | + | 2.56384i | −0.0638175 | + | 0.110535i | ||||
\(539\) | 29.0757 | − | 50.3606i | 1.25238 | − | 2.16919i | ||||
\(540\) | −1.12406 | − | 1.93300i | −0.0483718 | − | 0.0831831i | ||||
\(541\) | 7.00976i | 0.301373i | 0.988582 | + | 0.150687i | \(0.0481484\pi\) | ||||
−0.988582 | + | 0.150687i | \(0.951852\pi\) | |||||||
\(542\) | −5.51239 | − | 9.54773i | −0.236777 | − | 0.410110i | ||||
\(543\) | 10.3175 | + | 5.95683i | 0.442768 | + | 0.255632i | ||||
\(544\) | −2.86427 | −0.122805 | ||||||||
\(545\) | −1.46444 | + | 2.55482i | −0.0627298 | + | 0.109437i | ||||
\(546\) | −11.6720 | + | 20.2165i | −0.499514 | + | 0.865184i | ||||
\(547\) | 9.68332 | 0.414029 | 0.207014 | − | 0.978338i | \(-0.433625\pi\) | ||||
0.207014 | + | 0.978338i | \(0.433625\pi\) | |||||||
\(548\) | 2.99163 | − | 1.72722i | 0.127796 | − | 0.0737832i | ||||
\(549\) | − | 2.55050i | − | 0.108853i | ||||||
\(550\) | 13.9070 | − | 24.4377i | 0.592995 | − | 1.04203i | ||||
\(551\) | 29.5414 | + | 51.1672i | 1.25851 | + | 2.17979i | ||||
\(552\) | 5.40555 | − | 3.12090i | 0.230075 | − | 0.132834i | ||||
\(553\) | −20.6119 | + | 35.7009i | −0.876508 | + | 1.51816i | ||||
\(554\) | −11.9525 | −0.507812 | ||||||||
\(555\) | −13.3599 | + | 2.55186i | −0.567098 | + | 0.108320i | ||||
\(556\) | −8.32355 | −0.352997 | ||||||||
\(557\) | −7.32173 | + | 12.6816i | −0.310232 | + | 0.537337i | −0.978412 | − | 0.206662i | \(-0.933740\pi\) |
0.668181 | + | 0.743999i | \(0.267073\pi\) | |||||||
\(558\) | −3.75722 | + | 2.16923i | −0.159056 | + | 0.0918308i | ||||
\(559\) | −12.0387 | − | 20.8516i | −0.509182 | − | 0.881930i | ||||
\(560\) | 9.31143 | − | 0.0289927i | 0.393480 | − | 0.00122516i | ||||
\(561\) | 16.1074i | 0.680053i | ||||||||
\(562\) | −4.75144 | + | 2.74325i | −0.200428 | + | 0.115717i | ||||
\(563\) | −38.3820 | −1.61761 | −0.808804 | − | 0.588079i | \(-0.799885\pi\) | ||||
−0.808804 | + | 0.588079i | \(0.799885\pi\) | |||||||
\(564\) | −0.182950 | + | 0.316878i | −0.00770358 | + | 0.0133430i | ||||
\(565\) | −16.8711 | − | 9.67065i | −0.709775 | − | 0.406847i | ||||
\(566\) | −11.4713 | −0.482174 | ||||||||
\(567\) | −3.60632 | − | 2.08211i | −0.151451 | − | 0.0874403i | ||||
\(568\) | −6.08527 | − | 10.5400i | −0.255332 | − | 0.442249i | ||||
\(569\) | 18.5086i | 0.775922i | 0.921676 | + | 0.387961i | \(0.126820\pi\) | ||||
−0.921676 | + | 0.387961i | \(0.873180\pi\) | |||||||
\(570\) | 11.5267 | − | 6.70291i | 0.482802 | − | 0.280754i | ||||
\(571\) | 13.3669 | − | 23.1522i | 0.559389 | − | 0.968890i | −0.438159 | − | 0.898898i | \(-0.644369\pi\) |
0.997548 | − | 0.0699920i | \(-0.0222974\pi\) | |||||||
\(572\) | −15.7624 | + | 27.3012i | −0.659057 | + | 1.14152i | ||||
\(573\) | 11.9712 | + | 20.7347i | 0.500103 | + | 0.866204i | ||||
\(574\) | 3.39523 | − | 1.96024i | 0.141714 | − | 0.0818186i | ||||
\(575\) | 31.2084 | − | 0.194347i | 1.30148 | − | 0.00810481i | ||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 3.16251 | − | 5.47763i | 0.131657 | − | 0.228037i | −0.792658 | − | 0.609666i | \(-0.791304\pi\) |
0.924315 | + | 0.381629i | \(0.124637\pi\) | |||||||
\(578\) | −8.79596 | −0.365864 | ||||||||
\(579\) | −13.9783 | + | 8.07038i | −0.580919 | + | 0.335394i | ||||
\(580\) | 11.1372 | + | 19.1522i | 0.462446 | + | 0.795251i | ||||
\(581\) | 0.755401 | 0.0313393 | ||||||||
\(582\) | 8.96250i | 0.371507i | ||||||||
\(583\) | −21.7971 | − | 12.5845i | −0.902742 | − | 0.521198i | ||||
\(584\) | 11.5997i | 0.480000i | ||||||||
\(585\) | 0.0390297 | + | 12.5350i | 0.00161368 | + | 0.518258i | ||||
\(586\) | − | 9.93059i | − | 0.410229i | ||||||
\(587\) | −7.49315 | − | 12.9785i | −0.309276 | − | 0.535681i | 0.668929 | − | 0.743327i | \(-0.266753\pi\) |
−0.978204 | + | 0.207646i | \(0.933420\pi\) | |||||||
\(588\) | 8.95532 | − | 5.17035i | 0.369311 | − | 0.213222i | ||||
\(589\) | −12.9354 | − | 22.4048i | −0.532994 | − | 0.923173i | ||||
\(590\) | 12.3571 | + | 21.2501i | 0.508734 | + | 0.874851i | ||||
\(591\) | −24.5757 | −1.01091 | ||||||||
\(592\) | −3.96135 | − | 4.61603i | −0.162811 | − | 0.189718i | ||||
\(593\) | 17.7229i | 0.727791i | 0.931440 | + | 0.363896i | \(0.118554\pi\) | ||||
−0.931440 | + | 0.363896i | \(0.881446\pi\) | |||||||
\(594\) | −4.87013 | − | 2.81177i | −0.199824 | − | 0.115368i | ||||
\(595\) | −26.6704 | + | 0.0830428i | −1.09338 | + | 0.00340442i | ||||
\(596\) | −4.70096 | − | 8.14231i | −0.192559 | − | 0.333522i | ||||
\(597\) | 8.74791 | + | 15.1518i | 0.358028 | + | 0.620123i | ||||
\(598\) | −34.9905 | −1.43087 | ||||||||
\(599\) | −16.2008 | − | 28.0606i | −0.661946 | − | 1.14652i | −0.980104 | − | 0.198486i | \(-0.936397\pi\) |
0.318158 | − | 0.948038i | \(-0.396936\pi\) | |||||||
\(600\) | 4.31447 | − | 2.52692i | 0.176138 | − | 0.103161i | ||||
\(601\) | 16.3395 | − | 28.3009i | 0.666502 | − | 1.15442i | −0.312373 | − | 0.949959i | \(-0.601124\pi\) |
0.978876 | − | 0.204456i | \(-0.0655427\pi\) | |||||||
\(602\) | 17.8855i | 0.728960i | ||||||||
\(603\) | − | 2.21789i | − | 0.0903194i | ||||||
\(604\) | −5.42704 | + | 9.39991i | −0.220823 | + | 0.382477i | ||||
\(605\) | −0.143593 | − | 46.1171i | −0.00583789 | − | 1.87493i | ||||
\(606\) | − | 17.5745i | − | 0.713914i | ||||||
\(607\) | −10.4901 | + | 18.1695i | −0.425782 | + | 0.737476i | −0.996493 | − | 0.0836749i | \(-0.973334\pi\) |
0.570711 | + | 0.821151i | \(0.306668\pi\) | |||||||
\(608\) | 5.16423 | + | 2.98157i | 0.209437 | + | 0.120919i | ||||
\(609\) | 35.7314 | + | 20.6295i | 1.44791 | + | 0.835951i | ||||
\(610\) | 5.70306 | − | 0.0177574i | 0.230910 | − | 0.000718977i | ||||
\(611\) | 1.77637 | − | 1.02559i | 0.0718642 | − | 0.0414908i | ||||
\(612\) | −1.43213 | + | 2.48053i | −0.0578906 | + | 0.100269i | ||||
\(613\) | 18.1752 | + | 10.4935i | 0.734090 | + | 0.423827i | 0.819916 | − | 0.572483i | \(-0.194020\pi\) |
−0.0858268 | + | 0.996310i | \(0.527353\pi\) | |||||||
\(614\) | −1.07994 | − | 0.623504i | −0.0435828 | − | 0.0251626i | ||||
\(615\) | 1.04691 | − | 1.82641i | 0.0422155 | − | 0.0736480i | ||||
\(616\) | 20.2803 | − | 11.7088i | 0.817116 | − | 0.471762i | ||||
\(617\) | 27.7087 | + | 15.9976i | 1.11551 | + | 0.644040i | 0.940251 | − | 0.340482i | \(-0.110590\pi\) |
0.175259 | + | 0.984522i | \(0.443924\pi\) | |||||||
\(618\) | − | 4.83675i | − | 0.194563i | ||||||
\(619\) | −25.6784 | −1.03210 | −0.516051 | − | 0.856558i | \(-0.672598\pi\) | ||||
−0.516051 | + | 0.856558i | \(0.672598\pi\) | |||||||
\(620\) | −4.87668 | − | 8.38624i | −0.195852 | − | 0.336800i | ||||
\(621\) | − | 6.24179i | − | 0.250474i | ||||||
\(622\) | 7.15158 | − | 4.12897i | 0.286752 | − | 0.165556i | ||||
\(623\) | −35.5008 | −1.42231 | ||||||||
\(624\) | −4.85480 | + | 2.80292i | −0.194348 | + | 0.112207i | ||||
\(625\) | 24.9981 | − | 0.311357i | 0.999922 | − | 0.0124543i | ||||
\(626\) | −0.958252 | − | 1.65974i | −0.0382995 | − | 0.0663366i | ||||
\(627\) | 16.7670 | − | 29.0413i | 0.669609 | − | 1.15980i | ||||
\(628\) | 15.1158i | 0.603185i | ||||||||
\(629\) | 11.3464 | + | 13.2215i | 0.452410 | + | 0.527177i | ||||
\(630\) | 4.63061 | − | 8.07843i | 0.184488 | − | 0.321852i | ||||
\(631\) | 5.85446 | + | 3.38007i | 0.233062 | + | 0.134559i | 0.611984 | − | 0.790870i | \(-0.290372\pi\) |
−0.378922 | + | 0.925429i | \(0.623705\pi\) | |||||||
\(632\) | −8.57325 | + | 4.94977i | −0.341026 | + | 0.196891i | ||||
\(633\) | −24.6379 | + | 14.2247i | −0.979268 | + | 0.565380i | ||||
\(634\) | −1.54711 | + | 0.893227i | −0.0614437 | + | 0.0354746i | ||||
\(635\) | 8.30435 | − | 14.4875i | 0.329548 | − | 0.574921i | ||||
\(636\) | −2.23783 | − | 3.87603i | −0.0887357 | − | 0.153695i | ||||
\(637\) | −57.9684 | −2.29679 | ||||||||
\(638\) | 48.2533 | + | 27.8591i | 1.91037 | + | 1.10295i | ||||
\(639\) | −12.1705 | −0.481460 | ||||||||
\(640\) | 1.93996 | + | 1.11200i | 0.0766838 | + | 0.0439556i | ||||
\(641\) | 0.980805 | − | 1.69880i | 0.0387395 | − | 0.0670987i | −0.846006 | − | 0.533174i | \(-0.820999\pi\) |
0.884745 | + | 0.466075i | \(0.154332\pi\) | |||||||
\(642\) | −7.78991 | − | 13.4925i | −0.307443 | − | 0.532507i | ||||
\(643\) | 44.4122 | 1.75145 | 0.875723 | − | 0.482814i | \(-0.160385\pi\) | ||||
0.875723 | + | 0.482814i | \(0.160385\pi\) | |||||||
\(644\) | 22.5099 | + | 12.9961i | 0.887014 | + | 0.512118i | ||||
\(645\) | 4.82789 | + | 8.30234i | 0.190098 | + | 0.326904i | ||||
\(646\) | −14.7917 | − | 8.54001i | −0.581973 | − | 0.336002i | ||||
\(647\) | 10.0345 | + | 17.3803i | 0.394499 | + | 0.683292i | 0.993037 | − | 0.117802i | \(-0.0375850\pi\) |
−0.598538 | + | 0.801094i | \(0.704252\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | 53.5389 | + | 30.9107i | 2.10158 | + | 1.21335i | ||||
\(650\) | −28.0287 | + | 0.174545i | −1.09937 | + | 0.00684624i | ||||
\(651\) | −15.6459 | − | 9.03314i | −0.613210 | − | 0.354037i | ||||
\(652\) | −5.91523 | −0.231658 | ||||||||
\(653\) | 5.72293 | + | 9.91240i | 0.223955 | + | 0.387902i | 0.956006 | − | 0.293349i | \(-0.0947696\pi\) |
−0.732050 | + | 0.681251i | \(0.761436\pi\) | |||||||
\(654\) | −0.658472 | + | 1.14051i | −0.0257483 | + | 0.0445974i | ||||
\(655\) | −6.00153 | + | 10.4701i | −0.234499 | + | 0.409101i | ||||
\(656\) | 0.941466 | 0.0367581 | ||||||||
\(657\) | 10.0456 | + | 5.79986i | 0.391918 | + | 0.226274i | ||||
\(658\) | −1.52369 | −0.0593994 | ||||||||
\(659\) | −1.70920 | − | 2.96042i | −0.0665809 | − | 0.115321i | 0.830813 | − | 0.556551i | \(-0.187876\pi\) |
−0.897394 | + | 0.441230i | \(0.854542\pi\) | |||||||
\(660\) | 6.25338 | − | 10.9095i | 0.243412 | − | 0.424651i | ||||
\(661\) | −6.13183 | + | 3.54021i | −0.238501 | + | 0.137698i | −0.614487 | − | 0.788927i | \(-0.710637\pi\) |
0.375987 | + | 0.926625i | \(0.377304\pi\) | |||||||
\(662\) | −12.2666 | + | 7.08211i | −0.476754 | + | 0.275254i | ||||
\(663\) | 13.9055 | − | 8.02832i | 0.540043 | − | 0.311794i | ||||
\(664\) | 0.157099 | + | 0.0907014i | 0.00609664 | + | 0.00351990i | ||||
\(665\) | 48.1728 | + | 27.6129i | 1.86806 | + | 1.07078i | ||||
\(666\) | −5.97827 | + | 1.12262i | −0.231653 | + | 0.0435006i | ||||
\(667\) | 61.8437i | 2.39460i | ||||||||
\(668\) | 3.04743 | − | 5.27831i | 0.117909 | − | 0.204224i | ||||
\(669\) | −1.44703 | − | 2.50633i | −0.0559454 | − | 0.0969002i | ||||
\(670\) | 4.95932 | − | 0.0154417i | 0.191595 | − | 0.000596564i | ||||
\(671\) | 12.4213 | − | 7.17142i | 0.479518 | − | 0.276850i | ||||
\(672\) | 4.16422 | 0.160638 | ||||||||
\(673\) | −12.4022 | + | 7.16039i | −0.478068 | + | 0.276013i | −0.719611 | − | 0.694377i | \(-0.755680\pi\) |
0.241543 | + | 0.970390i | \(0.422347\pi\) | |||||||
\(674\) | 9.80795i | 0.377788i | ||||||||
\(675\) | −0.0311363 | − | 4.99990i | −0.00119844 | − | 0.192446i | ||||
\(676\) | 18.4255 | 0.708672 | ||||||||
\(677\) | − | 30.6482i | − | 1.17791i | −0.808167 | − | 0.588954i | \(-0.799540\pi\) | ||
0.808167 | − | 0.588954i | \(-0.200460\pi\) | |||||||
\(678\) | −7.53150 | − | 4.34832i | −0.289246 | − | 0.166996i | ||||
\(679\) | −32.3216 | + | 18.6609i | −1.24039 | + | 0.716139i | ||||
\(680\) | −5.55658 | − | 3.18506i | −0.213085 | − | 0.122142i | ||||
\(681\) | 4.14855 | + | 2.39517i | 0.158973 | + | 0.0917830i | ||||
\(682\) | −21.1289 | − | 12.1988i | −0.809066 | − | 0.467115i | ||||
\(683\) | 15.3305 | − | 26.5531i | 0.586604 | − | 1.01603i | −0.408069 | − | 0.912951i | \(-0.633798\pi\) |
0.994673 | − | 0.103077i | \(-0.0328688\pi\) | |||||||
\(684\) | 5.16423 | − | 2.98157i | 0.197459 | − | 0.114003i | ||||
\(685\) | 7.72432 | − | 0.0240509i | 0.295131 | − | 0.000918939i | ||||
\(686\) | 12.0477 | + | 6.95572i | 0.459982 | + | 0.265570i | ||||
\(687\) | 0.609999 | + | 0.352183i | 0.0232729 | + | 0.0134366i | ||||
\(688\) | −2.14753 | + | 3.71962i | −0.0818737 | + | 0.141809i | ||||
\(689\) | 25.0898i | 0.955847i | ||||||||
\(690\) | 13.9570 | − | 0.0434574i | 0.531334 | − | 0.00165440i | ||||
\(691\) | 0.00956990 | − | 0.0165756i | 0.000364056 | − | 0.000630564i | −0.865843 | − | 0.500315i | \(-0.833217\pi\) |
0.866207 | + | 0.499685i | \(0.166551\pi\) | |||||||
\(692\) | 7.17699i | 0.272828i | ||||||||
\(693\) | − | 23.4177i | − | 0.889564i | ||||||
\(694\) | −11.2641 | + | 19.5100i | −0.427579 | + | 0.740588i | ||||
\(695\) | −16.1474 | − | 9.25578i | −0.612505 | − | 0.351092i | ||||
\(696\) | 4.95400 | + | 8.58058i | 0.187781 | + | 0.325246i | ||||
\(697\) | −2.69661 | −0.102141 | ||||||||
\(698\) | −0.142907 | − | 0.247523i | −0.00540912 | − | 0.00936887i | ||||
\(699\) | −7.70852 | − | 13.3515i | −0.291563 | − | 0.505002i | ||||
\(700\) | 18.0961 | + | 10.2981i | 0.683967 | + | 0.389230i | ||||
\(701\) | 5.55582 | + | 3.20765i | 0.209840 | + | 0.121151i | 0.601237 | − | 0.799071i | \(-0.294675\pi\) |
−0.391397 | + | 0.920222i | \(0.628008\pi\) | |||||||
\(702\) | 5.60584i | 0.211579i | ||||||||
\(703\) | −6.69432 | − | 35.6492i | −0.252481 | − | 1.34454i | ||||
\(704\) | 5.62355 | 0.211945 | ||||||||
\(705\) | −0.707284 | + | 0.411292i | −0.0266379 | + | 0.0154902i | ||||
\(706\) | −8.58970 | − | 14.8778i | −0.323278 | − | 0.559933i | ||||
\(707\) | 63.3791 | − | 36.5919i | 2.38362 | − | 1.37618i | ||||
\(708\) | 5.49665 | + | 9.52048i | 0.206577 | + | 0.357802i | ||||
\(709\) | 1.36253i | 0.0511709i | 0.999673 | + | 0.0255855i | \(0.00814500\pi\) | ||||
−0.999673 | + | 0.0255855i | \(0.991855\pi\) | |||||||
\(710\) | −0.0847354 | − | 27.2140i | −0.00318006 | − | 1.02132i | ||||
\(711\) | 9.89954i | 0.371262i | ||||||||
\(712\) | −7.38304 | − | 4.26260i | −0.276691 | − | 0.159748i | ||||
\(713\) | − | 27.0798i | − | 1.01414i | ||||||
\(714\) | −11.9274 | −0.446373 | ||||||||
\(715\) | −60.9373 | + | 35.4356i | −2.27893 | + | 1.32522i | ||||
\(716\) | 19.6441 | − | 11.3415i | 0.734136 | − | 0.423853i | ||||
\(717\) | 7.08489 | 0.264590 | ||||||||
\(718\) | −3.99846 | + | 6.92553i | −0.149221 | + | 0.258459i | ||||
\(719\) | −3.32757 | + | 5.76353i | −0.124098 | + | 0.214943i | −0.921380 | − | 0.388663i | \(-0.872937\pi\) |
0.797282 | + | 0.603607i | \(0.206270\pi\) | |||||||
\(720\) | 1.93300 | − | 1.12406i | 0.0720387 | − | 0.0418912i | ||||
\(721\) | 17.4429 | − | 10.0706i | 0.649606 | − | 0.375050i | ||||
\(722\) | 8.27949 | + | 14.3405i | 0.308131 | + | 0.533698i | ||||
\(723\) | 11.3589 | − | 19.6742i | 0.422442 | − | 0.731692i | ||||
\(724\) | −5.95683 | + | 10.3175i | −0.221384 | + | 0.383448i | ||||
\(725\) | 0.308499 | + | 49.5391i | 0.0114574 | + | 1.83983i | ||||
\(726\) | − | 20.6243i | − | 0.765439i | ||||||
\(727\) | 10.7619 | + | 18.6402i | 0.399137 | + | 0.691325i | 0.993620 | − | 0.112783i | \(-0.0359766\pi\) |
−0.594483 | + | 0.804108i | \(0.702643\pi\) | |||||||
\(728\) | −20.2165 | − | 11.6720i | −0.749272 | − | 0.432592i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −12.8989 | + | 22.5030i | −0.477409 | + | 0.832874i | ||||
\(731\) | 6.15109 | − | 10.6540i | 0.227506 | − | 0.394053i | ||||
\(732\) | 2.55050 | 0.0942691 | ||||||||
\(733\) | 28.2518 | − | 16.3112i | 1.04350 | − | 0.602467i | 0.122680 | − | 0.992446i | \(-0.460851\pi\) |
0.920824 | + | 0.389979i | \(0.127518\pi\) | |||||||
\(734\) | − | 23.2696i | − | 0.858897i | ||||||
\(735\) | 23.1224 | − | 0.0719954i | 0.852883 | − | 0.00265559i | ||||
\(736\) | 3.12090 | + | 5.40555i | 0.115038 | + | 0.199251i | ||||
\(737\) | 10.8014 | − | 6.23620i | 0.397875 | − | 0.229713i | ||||
\(738\) | 0.470733 | − | 0.815334i | 0.0173279 | − | 0.0300128i | ||||
\(739\) | −43.8641 | −1.61357 | −0.806783 | − | 0.590848i | \(-0.798793\pi\) | ||||
−0.806783 | + | 0.590848i | \(0.798793\pi\) | |||||||
\(740\) | −2.55186 | − | 13.3599i | −0.0938082 | − | 0.491121i | ||||
\(741\) | −33.4284 | −1.22802 | ||||||||
\(742\) | 9.31881 | − | 16.1407i | 0.342104 | − | 0.592542i | ||||
\(743\) | −6.39472 | + | 3.69199i | −0.234599 | + | 0.135446i | −0.612692 | − | 0.790322i | \(-0.709913\pi\) |
0.378093 | + | 0.925768i | \(0.376580\pi\) | |||||||
\(744\) | −2.16923 | − | 3.75722i | −0.0795278 | − | 0.137746i | ||||
\(745\) | −0.0654593 | − | 21.0233i | −0.00239824 | − | 0.770232i | ||||
\(746\) | − | 22.7262i | − | 0.832067i | ||||||
\(747\) | 0.157099 | − | 0.0907014i | 0.00574797 | − | 0.00331859i | ||||
\(748\) | −16.1074 | −0.588943 | ||||||||
\(749\) | 32.4389 | − | 56.1858i | 1.18529 | − | 2.05298i | ||||
\(750\) | 11.1799 | − | 0.104434i | 0.408230 | − | 0.00381338i | ||||
\(751\) | 11.2599 | 0.410881 | 0.205440 | − | 0.978670i | \(-0.434137\pi\) | ||||
0.205440 | + | 0.978670i | \(0.434137\pi\) | |||||||
\(752\) | −0.316878 | − | 0.182950i | −0.0115554 | − | 0.00667149i | ||||
\(753\) | 0.218514 | + | 0.378478i | 0.00796311 | + | 0.0137925i | ||||
\(754\) | − | 55.5427i | − | 2.02275i | ||||||
\(755\) | −20.9810 | + | 12.2006i | −0.763575 | + | 0.444026i | ||||
\(756\) | 2.08211 | − | 3.60632i | 0.0757256 | − | 0.131161i | ||||
\(757\) | 14.2380 | − | 24.6609i | 0.517489 | − | 0.896317i | −0.482305 | − | 0.876004i | \(-0.660200\pi\) |
0.999794 | − | 0.0203136i | \(-0.00646647\pi\) | |||||||
\(758\) | −11.1432 | − | 19.3005i | −0.404738 | − | 0.701027i | ||||
\(759\) | 30.3984 | − | 17.5505i | 1.10339 | − | 0.637043i | ||||
\(760\) | 6.70291 | + | 11.5267i | 0.243140 | + | 0.418119i | ||||
\(761\) | −6.86663 | + | 11.8934i | −0.248915 | + | 0.431134i | −0.963225 | − | 0.268696i | \(-0.913407\pi\) |
0.714310 | + | 0.699829i | \(0.246741\pi\) | |||||||
\(762\) | 3.73397 | − | 6.46743i | 0.135268 | − | 0.234290i | ||||
\(763\) | −5.48404 | −0.198536 | ||||||||
\(764\) | −20.7347 | + | 11.9712i | −0.750155 | + | 0.433102i | ||||
\(765\) | −5.53664 | + | 3.21961i | −0.200177 | + | 0.116405i | ||||
\(766\) | −8.67444 | −0.313420 | ||||||||
\(767\) | − | 61.6267i | − | 2.22521i | ||||||
\(768\) | 0.866025 | + | 0.500000i | 0.0312500 | + | 0.0180422i | ||||
\(769\) | − | 45.5375i | − | 1.64212i | −0.570840 | − | 0.821061i | \(-0.693382\pi\) | ||
0.570840 | − | 0.821061i | \(-0.306618\pi\) | |||||||
\(770\) | 52.3633 | − | 0.163042i | 1.88704 | − | 0.00587561i | ||||
\(771\) | 4.35859i | 0.156971i | ||||||||
\(772\) | −8.07038 | − | 13.9783i | −0.290459 | − | 0.503090i | ||||
\(773\) | −39.5623 | + | 22.8413i | −1.42296 | + | 0.821545i | −0.996551 | − | 0.0829869i | \(-0.973554\pi\) |
−0.426407 | + | 0.904532i | \(0.640221\pi\) | |||||||
\(774\) | 2.14753 | + | 3.71962i | 0.0771912 | + | 0.133699i | ||||
\(775\) | −0.135084 | − | 21.6919i | −0.00485235 | − | 0.779195i | ||||
\(776\) | −8.96250 | −0.321735 | ||||||||
\(777\) | −16.4959 | − | 19.2221i | −0.591788 | − | 0.689590i | ||||
\(778\) | 37.8175i | 1.35582i | ||||||||
\(779\) | 4.86194 | + | 2.80704i | 0.174197 | + | 0.100573i | ||||
\(780\) | −12.5350 | + | 0.0390297i | −0.448824 | + | 0.00139749i | ||||
\(781\) | −34.2208 | − | 59.2722i | −1.22452 | − | 2.12093i | ||||
\(782\) | −8.93909 | − | 15.4829i | −0.319661 | − | 0.553669i | ||||
\(783\) | 9.90800 | 0.354083 | ||||||||
\(784\) | 5.17035 | + | 8.95532i | 0.184655 | + | 0.319833i | ||||
\(785\) | −16.8087 | + | 29.3241i | −0.599929 | + | 1.04662i | ||||
\(786\) | −2.69853 | + | 4.67400i | −0.0962535 | + | 0.166716i | ||||
\(787\) | 36.7255i | 1.30912i | 0.756009 | + | 0.654561i | \(0.227147\pi\) | ||||
−0.756009 | + | 0.654561i | \(0.772853\pi\) | |||||||
\(788\) | − | 24.5757i | − | 0.875475i | ||||||
\(789\) | −14.3743 | + | 24.8970i | −0.511739 | + | 0.886358i | ||||
\(790\) | −22.1359 | + | 0.0689239i | −0.787561 | + | 0.00245220i | ||||
\(791\) | − | 36.2147i | − | 1.28765i | ||||||
\(792\) | 2.81177 | − | 4.87013i | 0.0999120 | − | 0.173053i | ||||
\(793\) | −12.3822 | − | 7.14885i | −0.439704 | − | 0.253863i | ||||
\(794\) | 22.5734 | + | 13.0328i | 0.801102 | + | 0.462516i | ||||
\(795\) | −0.0311610 | − | 10.0078i | −0.00110517 | − | 0.354941i | ||||
\(796\) | −15.1518 | + | 8.74791i | −0.537042 | + | 0.310061i | ||||
\(797\) | −11.2290 | + | 19.4492i | −0.397751 | + | 0.688925i | −0.993448 | − | 0.114285i | \(-0.963542\pi\) |
0.595697 | + | 0.803209i | \(0.296876\pi\) | |||||||
\(798\) | 21.5050 | + | 12.4159i | 0.761267 | + | 0.439518i | ||||
\(799\) | 0.907625 | + | 0.524017i | 0.0321095 | + | 0.0185384i | ||||
\(800\) | 2.52692 | + | 4.31447i | 0.0893400 | + | 0.152540i | ||||
\(801\) | −7.38304 | + | 4.26260i | −0.260867 | + | 0.150612i | ||||
\(802\) | −7.78191 | − | 4.49289i | −0.274789 | − | 0.158649i | ||||
\(803\) | 65.2315i | 2.30197i | ||||||||
\(804\) | 2.21789 | 0.0782189 | ||||||||
\(805\) | 29.2167 | + | 50.2429i | 1.02975 | + | 1.77083i | ||||
\(806\) | 24.3207i | 0.856661i | ||||||||
\(807\) | −2.56384 | + | 1.48024i | −0.0902516 | + | 0.0521068i | ||||
\(808\) | 17.5745 | 0.618267 | ||||||||
\(809\) | −15.6803 | + | 9.05301i | −0.551289 | + | 0.318287i | −0.749642 | − | 0.661844i | \(-0.769774\pi\) |
0.198353 | + | 0.980131i | \(0.436441\pi\) | |||||||
\(810\) | −0.00696233 | − | 2.23606i | −0.000244631 | − | 0.0785670i | ||||
\(811\) | 7.95176 | + | 13.7729i | 0.279224 | + | 0.483630i | 0.971192 | − | 0.238298i | \(-0.0765894\pi\) |
−0.691968 | + | 0.721928i | \(0.743256\pi\) | |||||||
\(812\) | −20.6295 | + | 35.7314i | −0.723955 | + | 1.25393i | ||||
\(813\) | − | 11.0248i | − | 0.386656i | ||||||
\(814\) | −22.2768 | − | 25.9584i | −0.780803 | − | 0.909843i | ||||
\(815\) | −11.4753 | − | 6.57772i | −0.401963 | − | 0.230408i | ||||
\(816\) | −2.48053 | − | 1.43213i | −0.0868359 | − | 0.0501347i | ||||
\(817\) | −22.1806 | + | 12.8060i | −0.776002 | + | 0.448025i | ||||
\(818\) | −4.54148 | + | 2.62202i | −0.158789 | + | 0.0916768i | ||||
\(819\) | −20.2165 | + | 11.6720i | −0.706420 | + | 0.407852i | ||||
\(820\) | 1.82641 | + | 1.04691i | 0.0637810 | + | 0.0365597i | ||||
\(821\) | 3.15409 | + | 5.46304i | 0.110078 | + | 0.190661i | 0.915802 | − | 0.401631i | \(-0.131556\pi\) |
−0.805723 | + | 0.592292i | \(0.798223\pi\) | |||||||
\(822\) | 3.45444 | 0.120487 | ||||||||
\(823\) | 26.2973 | + | 15.1827i | 0.916666 | + | 0.529237i | 0.882570 | − | 0.470181i | \(-0.155811\pi\) |
0.0340960 | + | 0.999419i | \(0.489145\pi\) | |||||||
\(824\) | 4.83675 | 0.168496 | ||||||||
\(825\) | 24.2627 | − | 14.2102i | 0.844717 | − | 0.494737i | ||||
\(826\) | −22.8893 | + | 39.6454i | −0.796419 | + | 1.37944i | ||||
\(827\) | −7.21465 | − | 12.4961i | −0.250878 | − | 0.434533i | 0.712890 | − | 0.701276i | \(-0.247386\pi\) |
−0.963768 | + | 0.266743i | \(0.914053\pi\) | |||||||
\(828\) | 6.24179 | 0.216917 | ||||||||
\(829\) | 12.9413 | + | 7.47164i | 0.449468 | + | 0.259501i | 0.707606 | − | 0.706608i | \(-0.249775\pi\) |
−0.258137 | + | 0.966108i | \(0.583109\pi\) | |||||||
\(830\) | 0.203907 | + | 0.350652i | 0.00707773 | + | 0.0121713i | ||||
\(831\) | −10.3511 | − | 5.97624i | −0.359077 | − | 0.207313i | ||||
\(832\) | −2.80292 | − | 4.85480i | −0.0971738 | − | 0.168310i | ||||
\(833\) | −14.8093 | − | 25.6504i | −0.513111 | − | 0.888735i | ||||
\(834\) | −7.20841 | − | 4.16178i | −0.249607 | − | 0.144111i | ||||
\(835\) | 11.7814 | − | 6.85098i | 0.407712 | − | 0.237088i | ||||
\(836\) | 29.0413 | + | 16.7670i | 1.00441 | + | 0.579898i | ||||
\(837\) | −4.33846 | −0.149959 | ||||||||
\(838\) | 4.82659 | + | 8.35990i | 0.166732 | + | 0.288788i | ||||
\(839\) | −6.26033 | + | 10.8432i | −0.216131 | + | 0.374349i | −0.953622 | − | 0.301008i | \(-0.902677\pi\) |
0.737491 | + | 0.675357i | \(0.236010\pi\) | |||||||
\(840\) | 8.07843 | + | 4.63061i | 0.278732 | + | 0.159771i | ||||
\(841\) | −69.1685 | −2.38512 | ||||||||
\(842\) | −2.08227 | − | 1.20220i | −0.0717597 | − | 0.0414305i | ||||
\(843\) | −5.48649 | −0.188965 | ||||||||
\(844\) | −14.2247 | − | 24.6379i | −0.489634 | − | 0.848071i | ||||
\(845\) | 35.7448 | + | 20.4891i | 1.22966 | + | 0.704847i | ||||
\(846\) | −0.316878 | + | 0.182950i | −0.0108945 | + | 0.00628994i | ||||
\(847\) | 74.3777 | − | 42.9420i | 2.55565 | − | 1.47550i | ||||
\(848\) | 3.87603 | − | 2.23783i | 0.133104 | − | 0.0768474i | ||||
\(849\) | −9.93443 | − | 5.73565i | −0.340949 | − | 0.196847i | ||||
\(850\) | −7.23777 | − | 12.3578i | −0.248253 | − | 0.423870i | ||||
\(851\) | 12.5892 | − | 35.8194i | 0.431552 | − | 1.22787i | ||||
\(852\) | − | 12.1705i | − | 0.416956i | ||||||
\(853\) | 12.1760 | − | 21.0894i | 0.416898 | − | 0.722088i | −0.578728 | − | 0.815521i | \(-0.696451\pi\) |
0.995626 | + | 0.0934326i | \(0.0297840\pi\) | |||||||
\(854\) | 5.31041 | + | 9.19791i | 0.181719 | + | 0.314746i | ||||
\(855\) | 13.3339 | − | 0.0415173i | 0.456010 | − | 0.00141986i | ||||
\(856\) | 13.4925 | − | 7.78991i | 0.461165 | − | 0.266253i | ||||
\(857\) | −30.3696 | −1.03741 | −0.518703 | − | 0.854955i | \(-0.673585\pi\) | ||||
−0.518703 | + | 0.854955i | \(0.673585\pi\) | |||||||
\(858\) | −27.3012 | + | 15.7624i | −0.932048 | + | 0.538118i | ||||
\(859\) | 28.1645i | 0.960961i | 0.877005 | + | 0.480480i | \(0.159538\pi\) | ||||
−0.877005 | + | 0.480480i | \(0.840462\pi\) | |||||||
\(860\) | −8.30234 | + | 4.82789i | −0.283107 | + | 0.164630i | ||||
\(861\) | 3.92047 | 0.133609 | ||||||||
\(862\) | − | 24.5520i | − | 0.836243i | ||||||
\(863\) | −15.7408 | − | 9.08796i | −0.535823 | − | 0.309358i | 0.207561 | − | 0.978222i | \(-0.433447\pi\) |
−0.743385 | + | 0.668864i | \(0.766781\pi\) | |||||||
\(864\) | 0.866025 | − | 0.500000i | 0.0294628 | − | 0.0170103i | ||||
\(865\) | −7.98081 | + | 13.9231i | −0.271356 | + | 0.473400i | ||||
\(866\) | 21.4604 | + | 12.3902i | 0.729254 | + | 0.421035i | ||||
\(867\) | −7.61753 | − | 4.39798i | −0.258705 | − | 0.149363i | ||||
\(868\) | 9.03314 | − | 15.6459i | 0.306605 | − | 0.531055i | ||||
\(869\) | −48.2121 | + | 27.8353i | −1.63548 | + | 0.944247i | ||||
\(870\) | 0.0689828 | + | 22.1549i | 0.00233874 | + | 0.751120i | ||||
\(871\) | −10.7674 | − | 6.21657i | −0.364840 | − | 0.210640i | ||||
\(872\) | −1.14051 | − | 0.658472i | −0.0386225 | − | 0.0222987i | ||||
\(873\) | −4.48125 | + | 7.76175i | −0.151667 | + | 0.262695i | ||||
\(874\) | 37.2206i | 1.25901i | ||||||||
\(875\) | 23.6543 | + | 40.1007i | 0.799661 | + | 1.35565i | ||||
\(876\) | −5.79986 | + | 10.0456i | −0.195959 | + | 0.339411i | ||||
\(877\) | 31.8322i | 1.07490i | 0.843297 | + | 0.537448i | \(0.180612\pi\) | ||||
−0.843297 | + | 0.537448i | \(0.819388\pi\) | |||||||
\(878\) | 26.7190i | 0.901722i | ||||||||
\(879\) | 4.96530 | − | 8.60014i | 0.167475 | − | 0.290076i | ||||
\(880\) | 10.9095 | + | 6.25338i | 0.367758 | + | 0.210801i | ||||
\(881\) | 17.5474 | + | 30.3930i | 0.591187 | + | 1.02397i | 0.994073 | + | 0.108716i | \(0.0346739\pi\) |
−0.402886 | + | 0.915250i | \(0.631993\pi\) | |||||||
\(882\) | 10.3407 | 0.348190 | ||||||||
\(883\) | 23.4051 | + | 40.5387i | 0.787643 | + | 1.36424i | 0.927408 | + | 0.374052i | \(0.122032\pi\) |
−0.139765 | + | 0.990185i | \(0.544635\pi\) | |||||||
\(884\) | 8.02832 | + | 13.9055i | 0.270022 | + | 0.467691i | ||||
\(885\) | 0.0765390 | + | 24.5817i | 0.00257283 | + | 0.826303i | ||||
\(886\) | −15.9676 | − | 9.21892i | −0.536443 | − | 0.309716i | ||||
\(887\) | 12.7729i | 0.428872i | 0.976738 | + | 0.214436i | \(0.0687913\pi\) | ||||
−0.976738 | + | 0.214436i | \(0.931209\pi\) | |||||||
\(888\) | −1.12262 | − | 5.97827i | −0.0376726 | − | 0.200618i | ||||
\(889\) | 31.0981 | 1.04300 | ||||||||
\(890\) | −9.58282 | − | 16.4792i | −0.321217 | − | 0.552385i | ||||
\(891\) | −2.81177 | − | 4.87013i | −0.0941979 | − | 0.163156i | ||||
\(892\) | 2.50633 | − | 1.44703i | 0.0839181 | − | 0.0484501i | ||||
\(893\) | −1.09095 | − | 1.88959i | −0.0365074 | − | 0.0632326i | ||||
\(894\) | − | 9.40193i | − | 0.314448i | ||||||
\(895\) | 50.7207 | − | 0.157927i | 1.69541 | − | 0.00527892i | ||||
\(896\) | 4.16422i | 0.139117i | ||||||||
\(897\) | −30.3027 | − | 17.4953i | −1.01178 | − | 0.584149i | ||||
\(898\) | 34.2917i | 1.14433i | ||||||||
\(899\) | 42.9855 | 1.43365 | ||||||||
\(900\) | 4.99990 | − | 0.0311363i | 0.166663 | − | 0.00103788i | ||||
\(901\) | −11.1020 | + | 6.40975i | −0.369861 | + | 0.213540i | ||||
\(902\) | 5.29438 | 0.176284 | ||||||||
\(903\) | −8.94276 | + | 15.4893i | −0.297597 | + | 0.515452i | ||||
\(904\) | 4.34832 | − | 7.53150i | 0.144623 | − | 0.250494i | ||||
\(905\) | −23.0291 | + | 13.3917i | −0.765514 | + | 0.445154i | ||||
\(906\) | −9.39991 | + | 5.42704i | −0.312291 | + | 0.180301i | ||||
\(907\) | −13.8568 | − | 24.0006i | −0.460106 | − | 0.796928i | 0.538859 | − | 0.842396i | \(-0.318855\pi\) |
−0.998966 | + | 0.0454681i | \(0.985522\pi\) | |||||||
\(908\) | −2.39517 | + | 4.14855i | −0.0794864 | + | 0.137675i | ||||
\(909\) | 8.78723 | − | 15.2199i | 0.291454 | − | 0.504813i | ||||
\(910\) | −26.2400 | − | 45.1239i | −0.869846 | − | 1.49584i | ||||
\(911\) | 19.4856i | 0.645587i | 0.946469 | + | 0.322794i | \(0.104622\pi\) | ||||
−0.946469 | + | 0.322794i | \(0.895378\pi\) | |||||||
\(912\) | 2.98157 | + | 5.16423i | 0.0987296 | + | 0.171005i | ||||
\(913\) | 0.883456 | + | 0.510064i | 0.0292381 | + | 0.0168806i | ||||
\(914\) | −24.5822 | −0.813108 | ||||||||
\(915\) | 4.94787 | + | 2.83615i | 0.163572 | + | 0.0937603i | ||||
\(916\) | −0.352183 | + | 0.609999i | −0.0116365 | + | 0.0201549i | ||||
\(917\) | −22.4746 | −0.742175 | ||||||||
\(918\) | −2.48053 | + | 1.43213i | −0.0818697 | + | 0.0472675i | ||||
\(919\) | 28.6717i | 0.945792i | 0.881118 | + | 0.472896i | \(0.156791\pi\) | ||||
−0.881118 | + | 0.472896i | \(0.843209\pi\) | |||||||
\(920\) | 0.0434574 | + | 13.9570i | 0.00143275 | + | 0.460149i | ||||
\(921\) | −0.623504 | − | 1.07994i | −0.0205451 | − | 0.0355852i | ||||
\(922\) | 9.81068 | − | 5.66420i | 0.323097 | − | 0.186540i | ||||
\(923\) | −34.1131 | + | 59.0856i | −1.12285 | + | 1.94483i | ||||
\(924\) | 23.4177 | 0.770385 | ||||||||
\(925\) | 9.90573 | − | 28.7555i | 0.325698 | − | 0.945474i | ||||
\(926\) | 0.522731 | 0.0171780 | ||||||||
\(927\) | 2.41837 | − | 4.18875i | 0.0794298 | − | 0.137577i | ||||
\(928\) | −8.58058 | + | 4.95400i | −0.281671 | + | 0.162623i | ||||
\(929\) | −14.8497 | − | 25.7204i | −0.487201 | − | 0.843858i | 0.512690 | − | 0.858574i | \(-0.328649\pi\) |
−0.999892 | + | 0.0147160i | \(0.995316\pi\) | |||||||
\(930\) | −0.0302058 | − | 9.70104i | −0.000990487 | − | 0.318110i | ||||
\(931\) | 61.6630i | 2.02092i | ||||||||
\(932\) | 13.3515 | − | 7.70852i | 0.437344 | − | 0.252501i | ||||
\(933\) | 8.25793 | 0.270353 | ||||||||
\(934\) | −0.877189 | + | 1.51934i | −0.0287025 | + | 0.0497142i | ||||
\(935\) | −31.2477 | − | 17.9114i | −1.02191 | − | 0.585764i | ||||
\(936\) | −5.60584 | −0.183233 | ||||||||
\(937\) | −38.7008 | − | 22.3439i | −1.26430 | − | 0.729945i | −0.290398 | − | 0.956906i | \(-0.593788\pi\) |
−0.973904 | + | 0.226961i | \(0.927121\pi\) | |||||||
\(938\) | 4.61788 | + | 7.99841i | 0.150779 | + | 0.261157i | ||||
\(939\) | − | 1.91650i | − | 0.0625428i | ||||||
\(940\) | −0.411292 | − | 0.707284i | −0.0134149 | − | 0.0230691i | ||||
\(941\) | −24.6951 | + | 42.7733i | −0.805039 | + | 1.39437i | 0.111226 | + | 0.993795i | \(0.464522\pi\) |
−0.916265 | + | 0.400573i | \(0.868811\pi\) | |||||||
\(942\) | −7.55789 | + | 13.0906i | −0.246249 | + | 0.426516i | ||||
\(943\) | 2.93822 | + | 5.08914i | 0.0956815 | + | 0.165725i | ||||
\(944\) | −9.52048 | + | 5.49665i | −0.309865 | + | 0.178901i | ||||
\(945\) | 8.04944 | − | 4.68082i | 0.261848 | − | 0.152267i | ||||
\(946\) | −12.0767 | + | 20.9175i | −0.392648 | + | 0.680086i | ||||
\(947\) | 14.7814 | − | 25.6022i | 0.480332 | − | 0.831959i | −0.519413 | − | 0.854523i | \(-0.673850\pi\) |
0.999745 | + | 0.0225636i | \(0.00718284\pi\) | |||||||
\(948\) | −9.89954 | −0.321522 | ||||||||
\(949\) | 56.3143 | − | 32.5131i | 1.82804 | − | 1.05542i | ||||
\(950\) | 0.185670 | + | 29.8151i | 0.00602394 | + | 0.967329i | ||||
\(951\) | −1.78645 | −0.0579297 | ||||||||
\(952\) | − | 11.9274i | − | 0.386571i | ||||||
\(953\) | −35.0001 | − | 20.2073i | −1.13376 | − | 0.654578i | −0.188884 | − | 0.981999i | \(-0.560487\pi\) |
−0.944879 | + | 0.327421i | \(0.893820\pi\) | |||||||
\(954\) | − | 4.47566i | − | 0.144905i | ||||||
\(955\) | −53.5365 | + | 0.166695i | −1.73240 | + | 0.00539411i | ||||
\(956\) | 7.08489i | 0.229142i | ||||||||
\(957\) | 27.8591 | + | 48.2533i | 0.900556 | + | 1.55981i | ||||
\(958\) | 14.0589 | − | 8.11691i | 0.454223 | − | 0.262246i | ||||
\(959\) | 7.19252 | + | 12.4578i | 0.232258 | + | 0.402283i | ||||
\(960\) | 1.12406 | + | 1.93300i | 0.0362788 | + | 0.0623873i | ||||
\(961\) | 12.1778 | 0.392832 | ||||||||
\(962\) | −11.3065 | + | 32.1699i | −0.364537 | + | 1.03720i | ||||
\(963\) | − | 15.5798i | − | 0.502052i | ||||||
\(964\) | 19.6742 | + | 11.3589i | 0.633664 | + | 0.365846i | ||||
\(965\) | −0.112377 | − | 36.0917i | −0.00361756 | − | 1.16183i | ||||
\(966\) | 12.9961 | + | 22.5099i | 0.418142 | + | 0.724244i | ||||
\(967\) | −26.2245 | − | 45.4221i | −0.843322 | − | 1.46068i | −0.887071 | − | 0.461633i | \(-0.847264\pi\) |
0.0437492 | − | 0.999043i | \(-0.486070\pi\) | |||||||
\(968\) | 20.6243 | 0.662889 | ||||||||
\(969\) | −8.54001 | − | 14.7917i | −0.274345 | − | 0.475179i | ||||
\(970\) | −17.3869 | − | 9.96629i | −0.558260 | − | 0.319998i | ||||
\(971\) | −29.1830 | + | 50.5464i | −0.936525 | + | 1.62211i | −0.164635 | + | 0.986355i | \(0.552645\pi\) |
−0.771891 | + | 0.635755i | \(0.780689\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | − | 34.6611i | − | 1.11118i | ||||||
\(974\) | 13.7247 | − | 23.7719i | 0.439768 | − | 0.761701i | ||||
\(975\) | −24.3608 | − | 13.8632i | −0.780170 | − | 0.443977i | ||||
\(976\) | 2.55050i | 0.0816395i | ||||||||
\(977\) | −13.3641 | + | 23.1472i | −0.427554 | + | 0.740546i | −0.996655 | − | 0.0817219i | \(-0.973958\pi\) |
0.569101 | + | 0.822268i | \(0.307291\pi\) | |||||||
\(978\) | −5.12274 | − | 2.95761i | −0.163807 | − | 0.0945740i | ||||
\(979\) | −41.5189 | − | 23.9709i | −1.32695 | − | 0.766114i | ||||
\(980\) | 0.0719954 | + | 23.1224i | 0.00229981 | + | 0.738618i | ||||
\(981\) | −1.14051 | + | 0.658472i | −0.0364136 | + | 0.0210234i | ||||
\(982\) | −12.4893 | + | 21.6321i | −0.398550 | + | 0.690308i | ||||
\(983\) | 26.7412 | + | 15.4391i | 0.852913 | + | 0.492429i | 0.861633 | − | 0.507533i | \(-0.169442\pi\) |
−0.00871992 | + | 0.999962i | \(0.502776\pi\) | |||||||
\(984\) | 0.815334 | + | 0.470733i | 0.0259919 | + | 0.0150064i | ||||
\(985\) | 27.3282 | − | 47.6760i | 0.870749 | − | 1.51908i | ||||
\(986\) | 24.5771 | − | 14.1896i | 0.782694 | − | 0.451889i | ||||
\(987\) | −1.31955 | − | 0.761843i | −0.0420017 | − | 0.0242497i | ||||
\(988\) | − | 33.4284i | − | 1.06350i | ||||||
\(989\) | −26.8088 | −0.852471 | ||||||||
\(990\) | 10.8703 | − | 6.32119i | 0.345482 | − | 0.200901i | ||||
\(991\) | 36.8757i | 1.17140i | 0.810530 | + | 0.585698i | \(0.199179\pi\) | ||||
−0.810530 | + | 0.585698i | \(0.800821\pi\) | |||||||
\(992\) | 3.75722 | − | 2.16923i | 0.119292 | − | 0.0688731i | ||||
\(993\) | −14.1642 | −0.449488 | ||||||||
\(994\) | 43.8909 | − | 25.3404i | 1.39213 | − | 0.803749i | ||||
\(995\) | −39.1216 | + | 0.121812i | −1.24024 | + | 0.00386169i | ||||
\(996\) | 0.0907014 | + | 0.157099i | 0.00287398 | + | 0.00497789i | ||||
\(997\) | 12.6457 | − | 21.9029i | 0.400492 | − | 0.693672i | −0.593293 | − | 0.804986i | \(-0.702173\pi\) |
0.993785 | + | 0.111314i | \(0.0355059\pi\) | |||||||
\(998\) | 9.48453i | 0.300228i | ||||||||
\(999\) | −5.73864 | − | 2.01692i | −0.181563 | − | 0.0638125i |
(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 | 1110.2.ba.a.619.7 | yes | 36 | |
5.4 | even | 2 | 1110.2.ba.b.619.12 | yes | 36 | ||
37.11 | even | 6 | 1110.2.ba.b.529.12 | yes | 36 | ||
185.159 | even | 6 | inner | 1110.2.ba.a.529.7 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.ba.a.529.7 | ✓ | 36 | 185.159 | even | 6 | inner | |
1110.2.ba.a.619.7 | yes | 36 | 1.1 | even | 1 | trivial | |
1110.2.ba.b.529.12 | yes | 36 | 37.11 | even | 6 | ||
1110.2.ba.b.619.12 | yes | 36 | 5.4 | even | 2 |