Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [420,2,Mod(239,420)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(420, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("420.239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 420.l (of order \(2\), degree \(1\), 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: | \(3.35371688489\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.386672896.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{6} - 2x^{5} + 2x^{4} - 4x^{3} - 4x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 239.5 | ||
Root | \(-0.835949 - 1.14070i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 420.239 |
Dual form | 420.2.l.f.239.6 |
$q$-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 \(\left(\mathbb{Z}/420\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(241\) | \(281\) | \(337\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.835949 | − | 1.14070i | 0.591105 | − | 0.806595i | ||||
\(3\) | 1.10238 | + | 1.33595i | 0.636459 | + | 0.771310i | ||||
\(4\) | −0.602380 | − | 1.90713i | −0.301190 | − | 0.953564i | ||||
\(5\) | 1.00000 | + | 2.00000i | 0.447214 | + | 0.894427i | ||||
\(6\) | 2.44545 | − | 0.140697i | 0.998349 | − | 0.0574394i | ||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.67901 | − | 0.907128i | −0.947175 | − | 0.320718i | ||||
\(9\) | −0.569517 | + | 2.94545i | −0.189839 | + | 0.981815i | ||||
\(10\) | 3.11734 | + | 0.531200i | 0.985790 | + | 0.167980i | ||||
\(11\) | 2.20476 | 0.664760 | 0.332380 | − | 0.943146i | \(-0.392148\pi\) | ||||
0.332380 | + | 0.943146i | \(0.392148\pi\) | |||||||
\(12\) | 1.88377 | − | 2.90713i | 0.543799 | − | 0.839216i | ||||
\(13\) | 1.89089i | 0.524439i | 0.965008 | + | 0.262219i | \(0.0844544\pi\) | ||||
−0.965008 | + | 0.262219i | \(0.915546\pi\) | |||||||
\(14\) | 0.835949 | − | 1.14070i | 0.223417 | − | 0.304864i | ||||
\(15\) | −1.56952 | + | 3.54071i | −0.405248 | + | 0.914207i | ||||
\(16\) | −3.27428 | + | 2.29763i | −0.818569 | + | 0.574408i | ||||
\(17\) | 1.13903 | 0.276257 | 0.138128 | − | 0.990414i | \(-0.455891\pi\) | ||||
0.138128 | + | 0.990414i | \(0.455891\pi\) | |||||||
\(18\) | 2.88377 | + | 3.11189i | 0.679712 | + | 0.733479i | ||||
\(19\) | − | 8.56279i | − | 1.96444i | −0.187738 | − | 0.982219i | \(-0.560115\pi\) | ||
0.187738 | − | 0.982219i | \(-0.439885\pi\) | |||||||
\(20\) | 3.21188 | − | 3.11189i | 0.718197 | − | 0.695839i | ||||
\(21\) | 1.10238 | + | 1.33595i | 0.240559 | + | 0.291528i | ||||
\(22\) | 1.84307 | − | 2.51496i | 0.392943 | − | 0.536192i | ||||
\(23\) | 3.21899i | 0.671207i | 0.942003 | + | 0.335603i | \(0.108940\pi\) | ||||
−0.942003 | + | 0.335603i | \(0.891060\pi\) | |||||||
\(24\) | −1.74141 | − | 4.57903i | −0.355465 | − | 0.934690i | ||||
\(25\) | −3.00000 | + | 4.00000i | −0.600000 | + | 0.800000i | ||||
\(26\) | 2.15693 | + | 1.58069i | 0.423010 | + | 0.309998i | ||||
\(27\) | −4.56279 | + | 2.48615i | −0.878109 | + | 0.478461i | ||||
\(28\) | −0.602380 | − | 1.90713i | −0.113839 | − | 0.360413i | ||||
\(29\) | − | 1.89089i | − | 0.351130i | −0.984468 | − | 0.175565i | \(-0.943825\pi\) | ||
0.984468 | − | 0.175565i | \(-0.0561752\pi\) | |||||||
\(30\) | 2.72684 | + | 4.75019i | 0.497851 | + | 0.867263i | ||||
\(31\) | − | 5.90658i | − | 1.06085i | −0.847731 | − | 0.530427i | \(-0.822032\pi\) | ||
0.847731 | − | 0.530427i | \(-0.177968\pi\) | |||||||
\(32\) | −0.116226 | + | 5.65566i | −0.0205460 | + | 0.999789i | ||||
\(33\) | 2.43048 | + | 2.94545i | 0.423093 | + | 0.512736i | ||||
\(34\) | 0.952175 | − | 1.29929i | 0.163297 | − | 0.222827i | ||||
\(35\) | 1.00000 | + | 2.00000i | 0.169031 | + | 0.338062i | ||||
\(36\) | 5.96041 | − | 0.688134i | 0.993401 | − | 0.114689i | ||||
\(37\) | − | 0.409519i | − | 0.0673246i | −0.999433 | − | 0.0336623i | \(-0.989283\pi\) | ||
0.999433 | − | 0.0336623i | \(-0.0107171\pi\) | |||||||
\(38\) | −9.76755 | − | 7.15805i | −1.58451 | − | 1.16119i | ||||
\(39\) | −2.52613 | + | 2.08448i | −0.404505 | + | 0.333784i | ||||
\(40\) | −0.864758 | − | 6.26516i | −0.136730 | − | 0.990608i | ||||
\(41\) | − | 4.40952i | − | 0.688651i | −0.938850 | − | 0.344326i | \(-0.888108\pi\) | ||
0.938850 | − | 0.344326i | \(-0.111892\pi\) | |||||||
\(42\) | 2.44545 | − | 0.140697i | 0.377340 | − | 0.0217100i | ||||
\(43\) | −0.934275 | −0.142476 | −0.0712378 | − | 0.997459i | \(-0.522695\pi\) | ||||
−0.0712378 | + | 0.997459i | \(0.522695\pi\) | |||||||
\(44\) | −1.32810 | − | 4.20476i | −0.200219 | − | 0.633891i | ||||
\(45\) | −6.46041 | + | 1.80641i | −0.963061 | + | 0.269284i | ||||
\(46\) | 3.67190 | + | 2.69091i | 0.541392 | + | 0.396754i | ||||
\(47\) | − | 2.67190i | − | 0.389736i | −0.980829 | − | 0.194868i | \(-0.937572\pi\) | ||
0.980829 | − | 0.194868i | \(-0.0624279\pi\) | |||||||
\(48\) | −6.67901 | − | 1.84140i | −0.964033 | − | 0.265784i | ||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.05494 | + | 6.76589i | 0.290613 | + | 0.956841i | ||||
\(51\) | 1.25565 | + | 1.52169i | 0.175826 | + | 0.213079i | ||||
\(52\) | 3.60617 | − | 1.13903i | 0.500086 | − | 0.157956i | ||||
\(53\) | −6.81904 | −0.936667 | −0.468334 | − | 0.883552i | \(-0.655145\pi\) | ||||
−0.468334 | + | 0.883552i | \(0.655145\pi\) | |||||||
\(54\) | −0.978308 | + | 7.28306i | −0.133131 | + | 0.991098i | ||||
\(55\) | 2.20476 | + | 4.40952i | 0.297290 | + | 0.594579i | ||||
\(56\) | −2.67901 | − | 0.907128i | −0.357998 | − | 0.121220i | ||||
\(57\) | 11.4394 | − | 9.43945i | 1.51519 | − | 1.25029i | ||||
\(58\) | −2.15693 | − | 1.58069i | −0.283219 | − | 0.207554i | ||||
\(59\) | −13.5351 | −1.76212 | −0.881060 | − | 0.473005i | \(-0.843169\pi\) | ||||
−0.881060 | + | 0.473005i | \(0.843169\pi\) | |||||||
\(60\) | 7.69803 | + | 0.860420i | 0.993811 | + | 0.111080i | ||||
\(61\) | 12.4694 | 1.59654 | 0.798270 | − | 0.602300i | \(-0.205749\pi\) | ||||
0.798270 | + | 0.602300i | \(0.205749\pi\) | |||||||
\(62\) | −6.73762 | − | 4.93760i | −0.855679 | − | 0.627076i | ||||
\(63\) | −0.569517 | + | 2.94545i | −0.0717524 | + | 0.371091i | ||||
\(64\) | 6.35424 | + | 4.86042i | 0.794280 | + | 0.607552i | ||||
\(65\) | −3.78178 | + | 1.89089i | −0.469072 | + | 0.234536i | ||||
\(66\) | 5.39162 | − | 0.310203i | 0.663663 | − | 0.0381834i | ||||
\(67\) | −10.8475 | −1.32523 | −0.662617 | − | 0.748958i | \(-0.730554\pi\) | ||||
−0.662617 | + | 0.748958i | \(0.730554\pi\) | |||||||
\(68\) | −0.686132 | − | 2.17229i | −0.0832057 | − | 0.263428i | ||||
\(69\) | −4.30041 | + | 3.54855i | −0.517709 | + | 0.427196i | ||||
\(70\) | 3.11734 | + | 0.531200i | 0.372594 | + | 0.0634906i | ||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 4.19764 | − | 7.37427i | 0.494697 | − | 0.869066i | ||||
\(73\) | − | 8.00000i | − | 0.936329i | −0.883641 | − | 0.468165i | \(-0.844915\pi\) | ||
0.883641 | − | 0.468165i | \(-0.155085\pi\) | |||||||
\(74\) | −0.467138 | − | 0.342337i | −0.0543036 | − | 0.0397959i | ||||
\(75\) | −8.65093 | + | 0.401674i | −0.998924 | + | 0.0463813i | ||||
\(76\) | −16.3303 | + | 5.15805i | −1.87322 | + | 0.591669i | ||||
\(77\) | 2.20476 | 0.251256 | ||||||||
\(78\) | 0.266043 | + | 4.62407i | 0.0301234 | + | 0.523573i | ||||
\(79\) | 3.76609i | 0.423718i | 0.977300 | + | 0.211859i | \(0.0679518\pi\) | ||||
−0.977300 | + | 0.211859i | \(0.932048\pi\) | |||||||
\(80\) | −7.86954 | − | 4.25092i | −0.879841 | − | 0.475268i | ||||
\(81\) | −8.35130 | − | 3.35496i | −0.927922 | − | 0.372774i | ||||
\(82\) | −5.02993 | − | 3.68613i | −0.555462 | − | 0.407065i | ||||
\(83\) | 6.84086i | 0.750882i | 0.926846 | + | 0.375441i | \(0.122509\pi\) | ||||
−0.926846 | + | 0.375441i | \(0.877491\pi\) | |||||||
\(84\) | 1.88377 | − | 2.90713i | 0.205537 | − | 0.317194i | ||||
\(85\) | 1.13903 | + | 2.27807i | 0.123546 | + | 0.247091i | ||||
\(86\) | −0.781006 | + | 1.06572i | −0.0842180 | + | 0.114920i | ||||
\(87\) | 2.52613 | − | 2.08448i | 0.270830 | − | 0.223480i | ||||
\(88\) | −5.90658 | − | 2.00000i | −0.629644 | − | 0.213201i | ||||
\(89\) | − | 16.1913i | − | 1.71627i | −0.513420 | − | 0.858137i | \(-0.671622\pi\) | ||
0.513420 | − | 0.858137i | \(-0.328378\pi\) | |||||||
\(90\) | −3.34000 | + | 8.87944i | −0.352067 | + | 0.935975i | ||||
\(91\) | 1.89089i | 0.198219i | ||||||||
\(92\) | 6.13903 | − | 1.93906i | 0.640039 | − | 0.202161i | ||||
\(93\) | 7.89089 | − | 6.51130i | 0.818247 | − | 0.675190i | ||||
\(94\) | −3.04783 | − | 2.23357i | −0.314359 | − | 0.230375i | ||||
\(95\) | 17.1256 | − | 8.56279i | 1.75705 | − | 0.878524i | ||||
\(96\) | −7.68380 | + | 6.07941i | −0.784224 | + | 0.620478i | ||||
\(97\) | 18.4917i | 1.87755i | 0.344532 | + | 0.938774i | \(0.388038\pi\) | ||||
−0.344532 | + | 0.938774i | \(0.611962\pi\) | |||||||
\(98\) | 0.835949 | − | 1.14070i | 0.0844436 | − | 0.115228i | ||||
\(99\) | −1.25565 | + | 6.49400i | −0.126197 | + | 0.652672i | ||||
\(100\) | 9.43565 | + | 3.31187i | 0.943565 | + | 0.331187i | ||||
\(101\) | 14.8789i | 1.48050i | 0.672329 | + | 0.740252i | \(0.265294\pi\) | ||||
−0.672329 | + | 0.740252i | \(0.734706\pi\) | |||||||
\(102\) | 2.78545 | − | 0.160259i | 0.275800 | − | 0.0158680i | ||||
\(103\) | 14.9208 | 1.47019 | 0.735096 | − | 0.677963i | \(-0.237137\pi\) | ||||
0.735096 | + | 0.677963i | \(0.237137\pi\) | |||||||
\(104\) | 1.71528 | − | 5.06572i | 0.168197 | − | 0.496735i | ||||
\(105\) | −1.56952 | + | 3.54071i | −0.153169 | + | 0.345538i | ||||
\(106\) | −5.70037 | + | 7.77846i | −0.553668 | + | 0.755511i | ||||
\(107\) | 0.371487i | 0.0359130i | 0.999839 | + | 0.0179565i | \(0.00571603\pi\) | ||||
−0.999839 | + | 0.0179565i | \(0.994284\pi\) | |||||||
\(108\) | 7.48995 | + | 7.20421i | 0.720720 | + | 0.693226i | ||||
\(109\) | 2.86097 | 0.274031 | 0.137015 | − | 0.990569i | \(-0.456249\pi\) | ||||
0.137015 | + | 0.990569i | \(0.456249\pi\) | |||||||
\(110\) | 6.87299 | + | 1.17117i | 0.655314 | + | 0.111667i | ||||
\(111\) | 0.547097 | − | 0.451446i | 0.0519281 | − | 0.0428493i | ||||
\(112\) | −3.27428 | + | 2.29763i | −0.309390 | + | 0.217106i | ||||
\(113\) | 14.1913 | 1.33501 | 0.667503 | − | 0.744607i | \(-0.267363\pi\) | ||||
0.667503 | + | 0.744607i | \(0.267363\pi\) | |||||||
\(114\) | −1.20476 | − | 20.9398i | −0.112836 | − | 1.96120i | ||||
\(115\) | −6.43799 | + | 3.21899i | −0.600345 | + | 0.300173i | ||||
\(116\) | −3.60617 | + | 1.13903i | −0.334825 | + | 0.105757i | ||||
\(117\) | −5.56952 | − | 1.07690i | −0.514902 | − | 0.0995590i | ||||
\(118\) | −11.3146 | + | 15.4394i | −1.04160 | + | 1.42132i | ||||
\(119\) | 1.13903 | 0.104415 | ||||||||
\(120\) | 7.41664 | − | 8.06185i | 0.677043 | − | 0.735943i | ||||
\(121\) | −6.13903 | −0.558094 | ||||||||
\(122\) | 10.4238 | − | 14.2238i | 0.943722 | − | 1.28776i | ||||
\(123\) | 5.89089 | − | 4.86097i | 0.531164 | − | 0.438298i | ||||
\(124\) | −11.2646 | + | 3.55801i | −1.01159 | + | 0.319518i | ||||
\(125\) | −11.0000 | − | 2.00000i | −0.983870 | − | 0.178885i | ||||
\(126\) | 2.88377 | + | 3.11189i | 0.256907 | + | 0.277229i | ||||
\(127\) | 3.59048 | 0.318604 | 0.159302 | − | 0.987230i | \(-0.449076\pi\) | ||||
0.159302 | + | 0.987230i | \(0.449076\pi\) | |||||||
\(128\) | 10.8561 | − | 3.18520i | 0.959551 | − | 0.281534i | ||||
\(129\) | −1.02993 | − | 1.24814i | −0.0906799 | − | 0.109893i | ||||
\(130\) | −1.00444 | + | 5.89456i | −0.0880954 | + | 0.516987i | ||||
\(131\) | −4.52476 | −0.395330 | −0.197665 | − | 0.980270i | \(-0.563336\pi\) | ||||
−0.197665 | + | 0.980270i | \(0.563336\pi\) | |||||||
\(132\) | 4.15327 | − | 6.40952i | 0.361496 | − | 0.557877i | ||||
\(133\) | − | 8.56279i | − | 0.742488i | ||||||
\(134\) | −9.06796 | + | 12.3737i | −0.783352 | + | 1.06893i | ||||
\(135\) | −9.53510 | − | 6.63942i | −0.820650 | − | 0.571431i | ||||
\(136\) | −3.05149 | − | 1.03325i | −0.261663 | − | 0.0886005i | ||||
\(137\) | −16.4694 | −1.40707 | −0.703537 | − | 0.710659i | \(-0.748397\pi\) | ||||
−0.703537 | + | 0.710659i | \(0.748397\pi\) | |||||||
\(138\) | 0.452903 | + | 7.87187i | 0.0385537 | + | 0.670098i | ||||
\(139\) | − | 12.9723i | − | 1.10030i | −0.835067 | − | 0.550148i | \(-0.814571\pi\) | ||
0.835067 | − | 0.550148i | \(-0.185429\pi\) | |||||||
\(140\) | 3.21188 | − | 3.11189i | 0.271453 | − | 0.263003i | ||||
\(141\) | 3.56952 | − | 2.94545i | 0.300608 | − | 0.248051i | ||||
\(142\) | −6.68759 | + | 9.12558i | −0.561210 | + | 0.765801i | ||||
\(143\) | 4.16896i | 0.348626i | ||||||||
\(144\) | −4.90279 | − | 10.9527i | −0.408566 | − | 0.912729i | ||||
\(145\) | 3.78178 | − | 1.89089i | 0.314060 | − | 0.157030i | ||||
\(146\) | −9.12558 | − | 6.68759i | −0.755238 | − | 0.553469i | ||||
\(147\) | 1.10238 | + | 1.33595i | 0.0909228 | + | 0.110187i | ||||
\(148\) | −0.781006 | + | 0.246686i | −0.0641983 | + | 0.0202775i | ||||
\(149\) | 12.8190i | 1.05018i | 0.851048 | + | 0.525088i | \(0.175968\pi\) | ||||
−0.851048 | + | 0.525088i | \(0.824032\pi\) | |||||||
\(150\) | −6.77355 | + | 10.2039i | −0.553058 | + | 0.833143i | ||||
\(151\) | 5.63464i | 0.458541i | 0.973363 | + | 0.229270i | \(0.0736340\pi\) | ||||
−0.973363 | + | 0.229270i | \(0.926366\pi\) | |||||||
\(152\) | −7.76755 | + | 22.9398i | −0.630031 | + | 1.86067i | ||||
\(153\) | −0.648700 | + | 3.35496i | −0.0524443 | + | 0.271233i | ||||
\(154\) | 1.84307 | − | 2.51496i | 0.148518 | − | 0.202661i | ||||
\(155\) | 11.8132 | − | 5.90658i | 0.948856 | − | 0.474428i | ||||
\(156\) | 5.49706 | + | 3.56201i | 0.440117 | + | 0.285189i | ||||
\(157\) | 12.8190i | 1.02307i | 0.859262 | + | 0.511535i | \(0.170923\pi\) | ||||
−0.859262 | + | 0.511535i | \(0.829077\pi\) | |||||||
\(158\) | 4.29597 | + | 3.14826i | 0.341769 | + | 0.250462i | ||||
\(159\) | −7.51717 | − | 9.10989i | −0.596150 | − | 0.722461i | ||||
\(160\) | −11.4275 | + | 5.42321i | −0.903427 | + | 0.428742i | ||||
\(161\) | 3.21899i | 0.253692i | ||||||||
\(162\) | −10.8083 | + | 6.72173i | −0.849177 | + | 0.528109i | ||||
\(163\) | 5.53510 | 0.433542 | 0.216771 | − | 0.976222i | \(-0.430447\pi\) | ||||
0.216771 | + | 0.976222i | \(0.430447\pi\) | |||||||
\(164\) | −8.40952 | + | 2.65621i | −0.656673 | + | 0.207415i | ||||
\(165\) | −3.46041 | + | 7.80641i | −0.269392 | + | 0.607728i | ||||
\(166\) | 7.80335 | + | 5.71861i | 0.605657 | + | 0.443850i | ||||
\(167\) | − | 16.3222i | − | 1.26305i | −0.775355 | − | 0.631526i | \(-0.782429\pi\) | ||
0.775355 | − | 0.631526i | \(-0.217571\pi\) | |||||||
\(168\) | −1.74141 | − | 4.57903i | −0.134353 | − | 0.353279i | ||||
\(169\) | 9.42453 | 0.724964 | ||||||||
\(170\) | 3.55076 | + | 0.605055i | 0.272331 | + | 0.0464056i | ||||
\(171\) | 25.2212 | + | 4.87666i | 1.92872 | + | 0.372927i | ||||
\(172\) | 0.562788 | + | 1.78178i | 0.0429122 | + | 0.135860i | ||||
\(173\) | 5.13903 | 0.390714 | 0.195357 | − | 0.980732i | \(-0.437414\pi\) | ||||
0.195357 | + | 0.980732i | \(0.437414\pi\) | |||||||
\(174\) | −0.266043 | − | 4.62407i | −0.0201687 | − | 0.350550i | ||||
\(175\) | −3.00000 | + | 4.00000i | −0.226779 | + | 0.302372i | ||||
\(176\) | −7.21899 | + | 5.06572i | −0.544152 | + | 0.381843i | ||||
\(177\) | −14.9208 | − | 18.0822i | −1.12152 | − | 1.35914i | ||||
\(178\) | −18.4694 | − | 13.5351i | −1.38434 | − | 1.01450i | ||||
\(179\) | 14.4380 | 1.07915 | 0.539573 | − | 0.841939i | \(-0.318586\pi\) | ||||
0.539573 | + | 0.841939i | \(0.318586\pi\) | |||||||
\(180\) | 7.33668 | + | 11.2327i | 0.546844 | + | 0.837235i | ||||
\(181\) | 8.68759 | 0.645743 | 0.322872 | − | 0.946443i | \(-0.395352\pi\) | ||||
0.322872 | + | 0.946443i | \(0.395352\pi\) | |||||||
\(182\) | 2.15693 | + | 1.58069i | 0.159883 | + | 0.117168i | ||||
\(183\) | 13.7460 | + | 16.6584i | 1.01613 | + | 1.23143i | ||||
\(184\) | 2.92004 | − | 8.62373i | 0.215268 | − | 0.635750i | ||||
\(185\) | 0.819039 | − | 0.409519i | 0.0602169 | − | 0.0301085i | ||||
\(186\) | −0.831039 | − | 14.4442i | −0.0609348 | − | 1.05910i | ||||
\(187\) | 2.51130 | 0.183644 | ||||||||
\(188\) | −5.09565 | + | 1.60950i | −0.371639 | + | 0.117385i | ||||
\(189\) | −4.56279 | + | 2.48615i | −0.331894 | + | 0.180841i | ||||
\(190\) | 4.54855 | − | 26.6931i | 0.329987 | − | 1.93652i | ||||
\(191\) | 11.7668 | 0.851414 | 0.425707 | − | 0.904861i | \(-0.360025\pi\) | ||||
0.425707 | + | 0.904861i | \(0.360025\pi\) | |||||||
\(192\) | 0.511511 | + | 13.8470i | 0.0369151 | + | 0.999318i | ||||
\(193\) | − | 18.0599i | − | 1.29998i | −0.759944 | − | 0.649988i | \(-0.774774\pi\) | ||
0.759944 | − | 0.649988i | \(-0.225226\pi\) | |||||||
\(194\) | 21.0934 | + | 15.4581i | 1.51442 | + | 1.10983i | ||||
\(195\) | −6.69509 | − | 2.96779i | −0.479446 | − | 0.212528i | ||||
\(196\) | −0.602380 | − | 1.90713i | −0.0430271 | − | 0.136223i | ||||
\(197\) | −16.0599 | −1.14422 | −0.572109 | − | 0.820178i | \(-0.693874\pi\) | ||||
−0.572109 | + | 0.820178i | \(0.693874\pi\) | |||||||
\(198\) | 6.35803 | + | 6.86097i | 0.451845 | + | 0.487588i | ||||
\(199\) | 6.84086i | 0.484936i | 0.970159 | + | 0.242468i | \(0.0779569\pi\) | ||||
−0.970159 | + | 0.242468i | \(0.922043\pi\) | |||||||
\(200\) | 11.6656 | − | 7.99467i | 0.824879 | − | 0.565309i | ||||
\(201\) | −11.9581 | − | 14.4917i | −0.843457 | − | 1.02217i | ||||
\(202\) | 16.9723 | + | 12.4380i | 1.19417 | + | 0.875134i | ||||
\(203\) | − | 1.89089i | − | 0.132715i | ||||||
\(204\) | 2.14568 | − | 3.31132i | 0.150228 | − | 0.231839i | ||||
\(205\) | 8.81904 | − | 4.40952i | 0.615948 | − | 0.307974i | ||||
\(206\) | 12.4730 | − | 17.0201i | 0.869038 | − | 1.18585i | ||||
\(207\) | −9.48137 | − | 1.83327i | −0.659001 | − | 0.127421i | ||||
\(208\) | −4.34457 | − | 6.19130i | −0.301242 | − | 0.429290i | ||||
\(209\) | − | 18.8789i | − | 1.30588i | ||||||
\(210\) | 2.72684 | + | 4.75019i | 0.188170 | + | 0.327795i | ||||
\(211\) | − | 16.3222i | − | 1.12367i | −0.827250 | − | 0.561834i | \(-0.810096\pi\) | ||
0.827250 | − | 0.561834i | \(-0.189904\pi\) | |||||||
\(212\) | 4.10765 | + | 13.0048i | 0.282115 | + | 0.893172i | ||||
\(213\) | −8.81904 | − | 10.6876i | −0.604271 | − | 0.732302i | ||||
\(214\) | 0.423754 | + | 0.310544i | 0.0289672 | + | 0.0212283i | ||||
\(215\) | −0.934275 | − | 1.86855i | −0.0637170 | − | 0.127434i | ||||
\(216\) | 14.4790 | − | 2.52141i | 0.985174 | − | 0.171560i | ||||
\(217\) | − | 5.90658i | − | 0.400965i | ||||||
\(218\) | 2.39162 | − | 3.26349i | 0.161981 | − | 0.221032i | ||||
\(219\) | 10.6876 | − | 8.81904i | 0.722200 | − | 0.595935i | ||||
\(220\) | 7.08142 | − | 6.86097i | 0.477429 | − | 0.462566i | ||||
\(221\) | 2.15379i | 0.144880i | ||||||||
\(222\) | −0.0576182 | − | 1.00146i | −0.00386708 | − | 0.0672134i | ||||
\(223\) | 18.4274 | 1.23399 | 0.616996 | − | 0.786966i | \(-0.288349\pi\) | ||||
0.616996 | + | 0.786966i | \(0.288349\pi\) | |||||||
\(224\) | −0.116226 | + | 5.65566i | −0.00776567 | + | 0.377885i | ||||
\(225\) | −10.0732 | − | 11.1144i | −0.671549 | − | 0.740960i | ||||
\(226\) | 11.8632 | − | 16.1880i | 0.789128 | − | 1.07681i | ||||
\(227\) | 2.67190i | 0.177340i | 0.996061 | + | 0.0886700i | \(0.0282617\pi\) | ||||
−0.996061 | + | 0.0886700i | \(0.971738\pi\) | |||||||
\(228\) | −24.8931 | − | 16.1304i | −1.64859 | − | 1.06826i | ||||
\(229\) | 17.9284 | 1.18474 | 0.592371 | − | 0.805665i | \(-0.298192\pi\) | ||||
0.592371 | + | 0.805665i | \(0.298192\pi\) | |||||||
\(230\) | −1.70993 | + | 10.0347i | −0.112749 | + | 0.661669i | ||||
\(231\) | 2.43048 | + | 2.94545i | 0.159914 | + | 0.193796i | ||||
\(232\) | −1.71528 | + | 5.06572i | −0.112614 | + | 0.332581i | ||||
\(233\) | 17.9731 | 1.17746 | 0.588728 | − | 0.808331i | \(-0.299629\pi\) | ||||
0.588728 | + | 0.808331i | \(0.299629\pi\) | |||||||
\(234\) | −5.88424 | + | 5.45290i | −0.384665 | + | 0.356467i | ||||
\(235\) | 5.34379 | − | 2.67190i | 0.348591 | − | 0.174295i | ||||
\(236\) | 8.15327 | + | 25.8132i | 0.530733 | + | 1.68029i | ||||
\(237\) | −5.03130 | + | 4.15166i | −0.326818 | + | 0.269679i | ||||
\(238\) | 0.952175 | − | 1.29929i | 0.0617203 | − | 0.0842207i | ||||
\(239\) | −24.7055 | −1.59807 | −0.799033 | − | 0.601287i | \(-0.794655\pi\) | ||||
−0.799033 | + | 0.601287i | \(0.794655\pi\) | |||||||
\(240\) | −2.99621 | − | 15.1994i | −0.193404 | − | 0.981119i | ||||
\(241\) | −1.31533 | −0.0847276 | −0.0423638 | − | 0.999102i | \(-0.513489\pi\) | ||||
−0.0423638 | + | 0.999102i | \(0.513489\pi\) | |||||||
\(242\) | −5.13192 | + | 7.00278i | −0.329892 | + | 0.450156i | ||||
\(243\) | −4.72424 | − | 14.8554i | −0.303060 | − | 0.952971i | ||||
\(244\) | −7.51130 | − | 23.7807i | −0.480862 | − | 1.52240i | ||||
\(245\) | 1.00000 | + | 2.00000i | 0.0638877 | + | 0.127775i | ||||
\(246\) | −0.620407 | − | 10.7832i | −0.0395557 | − | 0.687514i | ||||
\(247\) | 16.1913 | 1.03023 | ||||||||
\(248\) | −5.35803 | + | 15.8238i | −0.340235 | + | 1.00481i | ||||
\(249\) | −9.13903 | + | 7.54122i | −0.579163 | + | 0.477906i | ||||
\(250\) | −11.4768 | + | 10.8758i | −0.725858 | + | 0.687844i | ||||
\(251\) | −13.5351 | −0.854328 | −0.427164 | − | 0.904174i | \(-0.640487\pi\) | ||||
−0.427164 | + | 0.904174i | \(0.640487\pi\) | |||||||
\(252\) | 5.96041 | − | 0.688134i | 0.375470 | − | 0.0433484i | ||||
\(253\) | 7.09711i | 0.446191i | ||||||||
\(254\) | 3.00146 | − | 4.09565i | 0.188328 | − | 0.256984i | ||||
\(255\) | −1.78773 | + | 4.03299i | −0.111952 | + | 0.252556i | ||||
\(256\) | 5.44178 | − | 15.0462i | 0.340111 | − | 0.940385i | ||||
\(257\) | 22.3826 | 1.39619 | 0.698094 | − | 0.716006i | \(-0.254032\pi\) | ||||
0.698094 | + | 0.716006i | \(0.254032\pi\) | |||||||
\(258\) | −2.28472 | + | 0.131450i | −0.142240 | + | 0.00818371i | ||||
\(259\) | − | 0.409519i | − | 0.0254463i | ||||||
\(260\) | 5.88424 | + | 6.07331i | 0.364925 | + | 0.376651i | ||||
\(261\) | 5.56952 | + | 1.07690i | 0.344744 | + | 0.0666582i | ||||
\(262\) | −3.78246 | + | 5.16138i | −0.233681 | + | 0.318871i | ||||
\(263\) | 9.49706i | 0.585614i | 0.956172 | + | 0.292807i | \(0.0945893\pi\) | ||||
−0.956172 | + | 0.292807i | \(0.905411\pi\) | |||||||
\(264\) | −3.83940 | − | 10.0957i | −0.236299 | − | 0.621344i | ||||
\(265\) | −6.81904 | − | 13.6381i | −0.418890 | − | 0.837780i | ||||
\(266\) | −9.76755 | − | 7.15805i | −0.598887 | − | 0.438888i | ||||
\(267\) | 21.6307 | − | 17.8490i | 1.32378 | − | 1.09234i | ||||
\(268\) | 6.53432 | + | 20.6876i | 0.399147 | + | 1.26370i | ||||
\(269\) | − | 8.60082i | − | 0.524401i | −0.965013 | − | 0.262201i | \(-0.915552\pi\) | ||
0.965013 | − | 0.262201i | \(-0.0844482\pi\) | |||||||
\(270\) | −15.5444 | + | 5.32644i | −0.946003 | + | 0.324157i | ||||
\(271\) | 12.5059i | 0.759676i | 0.925053 | + | 0.379838i | \(0.124020\pi\) | ||||
−0.925053 | + | 0.379838i | \(0.875980\pi\) | |||||||
\(272\) | −3.72952 | + | 2.61708i | −0.226135 | + | 0.158684i | ||||
\(273\) | −2.52613 | + | 2.08448i | −0.152889 | + | 0.126158i | ||||
\(274\) | −13.7675 | + | 18.7866i | −0.831728 | + | 1.13494i | ||||
\(275\) | −6.61428 | + | 8.81904i | −0.398856 | + | 0.531808i | ||||
\(276\) | 9.35803 | + | 6.06386i | 0.563287 | + | 0.365001i | ||||
\(277\) | 19.2884i | 1.15893i | 0.814998 | + | 0.579464i | \(0.196738\pi\) | ||||
−0.814998 | + | 0.579464i | \(0.803262\pi\) | |||||||
\(278\) | −14.7975 | − | 10.8442i | −0.887494 | − | 0.650391i | ||||
\(279\) | 17.3975 | + | 3.36390i | 1.04156 | + | 0.201392i | ||||
\(280\) | −0.864758 | − | 6.26516i | −0.0516792 | − | 0.374415i | ||||
\(281\) | − | 2.92815i | − | 0.174679i | −0.996179 | − | 0.0873393i | \(-0.972164\pi\) | ||
0.996179 | − | 0.0873393i | \(-0.0278364\pi\) | |||||||
\(282\) | −0.375928 | − | 6.53398i | −0.0223862 | − | 0.389093i | ||||
\(283\) | 7.51717 | 0.446849 | 0.223425 | − | 0.974721i | \(-0.428276\pi\) | ||||
0.223425 | + | 0.974721i | \(0.428276\pi\) | |||||||
\(284\) | 4.81904 | + | 15.2570i | 0.285957 | + | 0.905338i | ||||
\(285\) | 30.3183 | + | 13.4394i | 1.79590 | + | 0.796084i | ||||
\(286\) | 4.75552 | + | 3.48504i | 0.281200 | + | 0.206075i | ||||
\(287\) | − | 4.40952i | − | 0.260286i | ||||||
\(288\) | −16.5922 | − | 3.56333i | −0.977708 | − | 0.209971i | ||||
\(289\) | −15.7026 | −0.923682 | ||||||||
\(290\) | 1.00444 | − | 5.89456i | 0.0589828 | − | 0.346140i | ||||
\(291\) | −24.7040 | + | 20.3849i | −1.44817 | + | 1.19498i | ||||
\(292\) | −15.2570 | + | 4.81904i | −0.892850 | + | 0.282013i | ||||
\(293\) | 14.4245 | 0.842690 | 0.421345 | − | 0.906900i | \(-0.361558\pi\) | ||||
0.421345 | + | 0.906900i | \(0.361558\pi\) | |||||||
\(294\) | 2.44545 | − | 0.140697i | 0.142621 | − | 0.00820562i | ||||
\(295\) | −13.5351 | − | 27.0702i | −0.788044 | − | 1.57609i | ||||
\(296\) | −0.371487 | + | 1.09711i | −0.0215922 | + | 0.0637681i | ||||
\(297\) | −10.0599 | + | 5.48137i | −0.583732 | + | 0.318061i | ||||
\(298\) | 14.6226 | + | 10.7161i | 0.847067 | + | 0.620765i | ||||
\(299\) | −6.08677 | −0.352007 | ||||||||
\(300\) | 5.97719 | + | 16.2565i | 0.345093 | + | 0.938568i | ||||
\(301\) | −0.934275 | −0.0538507 | ||||||||
\(302\) | 6.42742 | + | 4.71027i | 0.369856 | + | 0.271046i | ||||
\(303\) | −19.8774 | + | 16.4022i | −1.14193 | + | 0.942281i | ||||
\(304\) | 19.6741 | + | 28.0369i | 1.12839 | + | 1.60803i | ||||
\(305\) | 12.4694 | + | 24.9387i | 0.713994 | + | 1.42799i | ||||
\(306\) | 3.28472 | + | 3.54455i | 0.187775 | + | 0.202628i | ||||
\(307\) | −21.7114 | −1.23913 | −0.619567 | − | 0.784944i | \(-0.712692\pi\) | ||||
−0.619567 | + | 0.784944i | \(0.712692\pi\) | |||||||
\(308\) | −1.32810 | − | 4.20476i | −0.0756757 | − | 0.239588i | ||||
\(309\) | 16.4484 | + | 19.9334i | 0.935717 | + | 1.13397i | ||||
\(310\) | 3.13758 | − | 18.4128i | 0.178202 | − | 1.04578i | ||||
\(311\) | 19.9284 | 1.13004 | 0.565018 | − | 0.825079i | \(-0.308869\pi\) | ||||
0.565018 | + | 0.825079i | \(0.308869\pi\) | |||||||
\(312\) | 8.65844 | − | 3.29283i | 0.490188 | − | 0.186420i | ||||
\(313\) | − | 18.9281i | − | 1.06988i | −0.844889 | − | 0.534941i | \(-0.820334\pi\) | ||
0.844889 | − | 0.534941i | \(-0.179666\pi\) | |||||||
\(314\) | 14.6226 | + | 10.7161i | 0.825203 | + | 0.604742i | ||||
\(315\) | −6.46041 | + | 1.80641i | −0.364003 | + | 0.101780i | ||||
\(316\) | 7.18242 | − | 2.26862i | 0.404043 | − | 0.127620i | ||||
\(317\) | 0.278070 | 0.0156179 | 0.00780897 | − | 0.999970i | \(-0.497514\pi\) | ||||
0.00780897 | + | 0.999970i | \(0.497514\pi\) | |||||||
\(318\) | −16.6756 | + | 0.959419i | −0.935121 | + | 0.0538016i | ||||
\(319\) | − | 4.16896i | − | 0.233417i | ||||||
\(320\) | −3.36660 | + | 17.5689i | −0.188199 | + | 0.982131i | ||||
\(321\) | −0.496287 | + | 0.409519i | −0.0277000 | + | 0.0228571i | ||||
\(322\) | 3.67190 | + | 2.69091i | 0.204627 | + | 0.149959i | ||||
\(323\) | − | 9.75331i | − | 0.542689i | ||||||
\(324\) | −1.36769 | + | 17.9480i | −0.0759830 | + | 0.997109i | ||||
\(325\) | −7.56357 | − | 5.67267i | −0.419551 | − | 0.314663i | ||||
\(326\) | 4.62706 | − | 6.31387i | 0.256269 | − | 0.349693i | ||||
\(327\) | 3.15387 | + | 3.82210i | 0.174409 | + | 0.211363i | ||||
\(328\) | −4.00000 | + | 11.8132i | −0.220863 | + | 0.652273i | ||||
\(329\) | − | 2.67190i | − | 0.147306i | ||||||
\(330\) | 6.01203 | + | 10.4730i | 0.330951 | + | 0.576522i | ||||
\(331\) | 13.2788i | 0.729871i | 0.931033 | + | 0.364936i | \(0.118909\pi\) | ||||
−0.931033 | + | 0.364936i | \(0.881091\pi\) | |||||||
\(332\) | 13.0464 | − | 4.12079i | 0.716014 | − | 0.226158i | ||||
\(333\) | 1.20622 | + | 0.233228i | 0.0661003 | + | 0.0127808i | ||||
\(334\) | −18.6187 | − | 13.6445i | −1.01877 | − | 0.746596i | ||||
\(335\) | −10.8475 | − | 21.6950i | −0.592663 | − | 1.18533i | ||||
\(336\) | −6.67901 | − | 1.84140i | −0.364370 | − | 0.100457i | ||||
\(337\) | 24.3379i | 1.32577i | 0.748721 | + | 0.662886i | \(0.230668\pi\) | ||||
−0.748721 | + | 0.662886i | \(0.769332\pi\) | |||||||
\(338\) | 7.87842 | − | 10.7505i | 0.428530 | − | 0.584752i | ||||
\(339\) | 15.6442 | + | 18.9589i | 0.849677 | + | 1.02970i | ||||
\(340\) | 3.65844 | − | 3.54455i | 0.198407 | − | 0.192230i | ||||
\(341\) | − | 13.0226i | − | 0.705213i | ||||||
\(342\) | 26.6464 | − | 24.6931i | 1.44087 | − | 1.33525i | ||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 2.50294 | + | 0.847507i | 0.134949 | + | 0.0456945i | ||||
\(345\) | −11.3975 | − | 5.05227i | −0.613622 | − | 0.272005i | ||||
\(346\) | 4.29597 | − | 5.86208i | 0.230953 | − | 0.315147i | ||||
\(347\) | 35.2951i | 1.89474i | 0.320144 | + | 0.947369i | \(0.396269\pi\) | ||||
−0.320144 | + | 0.947369i | \(0.603731\pi\) | |||||||
\(348\) | −5.49706 | − | 3.56201i | −0.294674 | − | 0.190944i | ||||
\(349\) | −11.0942 | −0.593859 | −0.296929 | − | 0.954899i | \(-0.595963\pi\) | ||||
−0.296929 | + | 0.954899i | \(0.595963\pi\) | |||||||
\(350\) | 2.05494 | + | 6.76589i | 0.109841 | + | 0.361652i | ||||
\(351\) | −4.70105 | − | 8.62774i | −0.250923 | − | 0.460515i | ||||
\(352\) | −0.256250 | + | 12.4694i | −0.0136582 | + | 0.664620i | ||||
\(353\) | −21.5216 | −1.14548 | −0.572741 | − | 0.819737i | \(-0.694120\pi\) | ||||
−0.572741 | + | 0.819737i | \(0.694120\pi\) | |||||||
\(354\) | −33.0993 | + | 1.90435i | −1.75921 | + | 0.101215i | ||||
\(355\) | −8.00000 | − | 16.0000i | −0.424596 | − | 0.849192i | ||||
\(356\) | −30.8789 | + | 9.75331i | −1.63658 | + | 0.516925i | ||||
\(357\) | 1.25565 | + | 1.52169i | 0.0664560 | + | 0.0805365i | ||||
\(358\) | 12.0694 | − | 16.4694i | 0.637888 | − | 0.870433i | ||||
\(359\) | 15.5636 | 0.821414 | 0.410707 | − | 0.911767i | \(-0.365282\pi\) | ||||
0.410707 | + | 0.911767i | \(0.365282\pi\) | |||||||
\(360\) | 18.9462 | + | 1.02102i | 0.998551 | + | 0.0538124i | ||||
\(361\) | −54.3213 | −2.85902 | ||||||||
\(362\) | 7.26238 | − | 9.90991i | 0.381702 | − | 0.520853i | ||||
\(363\) | −6.76755 | − | 8.20143i | −0.355204 | − | 0.430464i | ||||
\(364\) | 3.60617 | − | 1.13903i | 0.189015 | − | 0.0597016i | ||||
\(365\) | 16.0000 | − | 8.00000i | 0.837478 | − | 0.418739i | ||||
\(366\) | 30.4932 | − | 1.75440i | 1.59390 | − | 0.0917042i | ||||
\(367\) | −35.7129 | −1.86420 | −0.932100 | − | 0.362201i | \(-0.882026\pi\) | ||||
−0.932100 | + | 0.362201i | \(0.882026\pi\) | |||||||
\(368\) | −7.39606 | − | 10.5399i | −0.385546 | − | 0.549429i | ||||
\(369\) | 12.9880 | + | 2.51130i | 0.676128 | + | 0.130733i | ||||
\(370\) | 0.217537 | − | 1.27661i | 0.0113092 | − | 0.0663679i | ||||
\(371\) | −6.81904 | −0.354027 | ||||||||
\(372\) | −17.1712 | − | 11.1267i | −0.890285 | − | 0.576891i | ||||
\(373\) | 29.0103i | 1.50210i | 0.660246 | + | 0.751049i | \(0.270452\pi\) | ||||
−0.660246 | + | 0.751049i | \(0.729548\pi\) | |||||||
\(374\) | 2.09932 | − | 2.86463i | 0.108553 | − | 0.148127i | ||||
\(375\) | −9.45428 | − | 16.9002i | −0.488217 | − | 0.872722i | ||||
\(376\) | −2.42375 | + | 7.15805i | −0.124996 | + | 0.369148i | ||||
\(377\) | 3.57547 | 0.184146 | ||||||||
\(378\) | −0.978308 | + | 7.28306i | −0.0503187 | + | 0.374600i | ||||
\(379\) | 23.3534i | 1.19958i | 0.800157 | + | 0.599791i | \(0.204750\pi\) | ||||
−0.800157 | + | 0.599791i | \(0.795250\pi\) | |||||||
\(380\) | −26.6464 | − | 27.5026i | −1.36693 | − | 1.41085i | ||||
\(381\) | 3.95807 | + | 4.79670i | 0.202778 | + | 0.245742i | ||||
\(382\) | 9.83642 | − | 13.4223i | 0.503275 | − | 0.686746i | ||||
\(383\) | 14.9169i | 0.762219i | 0.924530 | + | 0.381110i | \(0.124458\pi\) | ||||
−0.924530 | + | 0.381110i | \(0.875542\pi\) | |||||||
\(384\) | 16.2228 | + | 10.9919i | 0.827866 | + | 0.560926i | ||||
\(385\) | 2.20476 | + | 4.40952i | 0.112365 | + | 0.224730i | ||||
\(386\) | −20.6008 | − | 15.0971i | −1.04855 | − | 0.768423i | ||||
\(387\) | 0.532086 | − | 2.75186i | 0.0270474 | − | 0.139885i | ||||
\(388\) | 35.2661 | − | 11.1390i | 1.79036 | − | 0.565499i | ||||
\(389\) | 19.5290i | 0.990158i | 0.868848 | + | 0.495079i | \(0.164861\pi\) | ||||
−0.868848 | + | 0.495079i | \(0.835139\pi\) | |||||||
\(390\) | −8.98210 | + | 5.15616i | −0.454826 | + | 0.261092i | ||||
\(391\) | 3.66655i | 0.185425i | ||||||||
\(392\) | −2.67901 | − | 0.907128i | −0.135311 | − | 0.0458169i | ||||
\(393\) | −4.98800 | − | 6.04484i | −0.251611 | − | 0.304922i | ||||
\(394\) | −13.4252 | + | 18.3194i | −0.676352 | + | 0.922919i | ||||
\(395\) | −7.53218 | + | 3.76609i | −0.378985 | + | 0.189493i | ||||
\(396\) | 13.1413 | − | 1.51717i | 0.660374 | − | 0.0762407i | ||||
\(397\) | − | 3.48429i | − | 0.174871i | −0.996170 | − | 0.0874357i | \(-0.972133\pi\) | ||
0.996170 | − | 0.0874357i | \(-0.0278672\pi\) | |||||||
\(398\) | 7.80335 | + | 5.71861i | 0.391146 | + | 0.286648i | ||||
\(399\) | 11.4394 | − | 9.43945i | 0.572689 | − | 0.472563i | ||||
\(400\) | 0.632306 | − | 19.9900i | 0.0316153 | − | 0.999500i | ||||
\(401\) | 19.2661i | 0.962102i | 0.876693 | + | 0.481051i | \(0.159745\pi\) | ||||
−0.876693 | + | 0.481051i | \(0.840255\pi\) | |||||||
\(402\) | −26.5270 | + | 1.52621i | −1.32305 | + | 0.0761206i | ||||
\(403\) | 11.1687 | 0.556353 | ||||||||
\(404\) | 28.3760 | − | 8.96274i | 1.41176 | − | 0.445913i | ||||
\(405\) | −1.64137 | − | 20.0576i | −0.0815603 | − | 0.996668i | ||||
\(406\) | −2.15693 | − | 1.58069i | −0.107047 | − | 0.0784482i | ||||
\(407\) | − | 0.902892i | − | 0.0447547i | ||||||
\(408\) | −1.98353 | − | 5.21567i | −0.0981995 | − | 0.258214i | ||||
\(409\) | −3.45903 | −0.171038 | −0.0855190 | − | 0.996337i | \(-0.527255\pi\) | ||||
−0.0855190 | + | 0.996337i | \(0.527255\pi\) | |||||||
\(410\) | 2.34234 | − | 13.7460i | 0.115680 | − | 0.678866i | ||||
\(411\) | −18.1555 | − | 22.0022i | −0.895545 | − | 1.08529i | ||||
\(412\) | −8.98800 | − | 28.4559i | −0.442807 | − | 1.40192i | ||||
\(413\) | −13.5351 | −0.666019 | ||||||||
\(414\) | −10.0171 | + | 9.28285i | −0.492316 | + | 0.456227i | ||||
\(415\) | −13.6817 | + | 6.84086i | −0.671609 | + | 0.335805i | ||||
\(416\) | −10.6942 | − | 0.219771i | −0.524328 | − | 0.0107751i | ||||
\(417\) | 17.3303 | − | 14.3004i | 0.848670 | − | 0.700294i | ||||
\(418\) | −21.5351 | − | 15.7818i | −1.05332 | − | 0.771912i | ||||
\(419\) | −11.2839 | −0.551257 | −0.275628 | − | 0.961264i | \(-0.588886\pi\) | ||||
−0.275628 | + | 0.961264i | \(0.588886\pi\) | |||||||
\(420\) | 7.69803 | + | 0.860420i | 0.375625 | + | 0.0419842i | ||||
\(421\) | 9.95807 | 0.485327 | 0.242663 | − | 0.970111i | \(-0.421979\pi\) | ||||
0.242663 | + | 0.970111i | \(0.421979\pi\) | |||||||
\(422\) | −18.6187 | − | 13.6445i | −0.906345 | − | 0.664206i | ||||
\(423\) | 7.86993 | + | 1.52169i | 0.382649 | + | 0.0739872i | ||||
\(424\) | 18.2683 | + | 6.18574i | 0.887187 | + | 0.300406i | ||||
\(425\) | −3.41710 | + | 4.55614i | −0.165754 | + | 0.221005i | ||||
\(426\) | −19.5636 | + | 1.12558i | −0.947858 | + | 0.0545344i | ||||
\(427\) | 12.4694 | 0.603435 | ||||||||
\(428\) | 0.708473 | − | 0.223776i | 0.0342453 | − | 0.0108166i | ||||
\(429\) | −5.56952 | + | 4.59578i | −0.268899 | + | 0.221886i | ||||
\(430\) | −2.91246 | − | 0.496287i | −0.140451 | − | 0.0239331i | ||||
\(431\) | −1.69226 | −0.0815133 | −0.0407566 | − | 0.999169i | \(-0.512977\pi\) | ||||
−0.0407566 | + | 0.999169i | \(0.512977\pi\) | |||||||
\(432\) | 9.22757 | − | 18.6240i | 0.443962 | − | 0.896046i | ||||
\(433\) | − | 12.9387i | − | 0.621796i | −0.950443 | − | 0.310898i | \(-0.899370\pi\) | ||
0.950443 | − | 0.310898i | \(-0.100630\pi\) | |||||||
\(434\) | −6.73762 | − | 4.93760i | −0.323416 | − | 0.237012i | ||||
\(435\) | 6.69509 | + | 2.96779i | 0.321005 | + | 0.142294i | ||||
\(436\) | −1.72339 | − | 5.45623i | −0.0825353 | − | 0.261306i | ||||
\(437\) | 27.5636 | 1.31854 | ||||||||
\(438\) | −1.12558 | − | 19.5636i | −0.0537821 | − | 0.934783i | ||||
\(439\) | 3.10376i | 0.148134i | 0.997253 | + | 0.0740671i | \(0.0235979\pi\) | ||||
−0.997253 | + | 0.0740671i | \(0.976402\pi\) | |||||||
\(440\) | −1.90658 | − | 13.8132i | −0.0908928 | − | 0.658517i | ||||
\(441\) | −0.569517 | + | 2.94545i | −0.0271199 | + | 0.140259i | ||||
\(442\) | 2.45682 | + | 1.80046i | 0.116859 | + | 0.0856391i | ||||
\(443\) | 14.6942i | 0.698144i | 0.937096 | + | 0.349072i | \(0.113503\pi\) | ||||
−0.937096 | + | 0.349072i | \(0.886497\pi\) | |||||||
\(444\) | −1.19053 | − | 0.771442i | −0.0564998 | − | 0.0366110i | ||||
\(445\) | 32.3826 | − | 16.1913i | 1.53508 | − | 0.767541i | ||||
\(446\) | 15.4044 | − | 21.0201i | 0.729419 | − | 0.995332i | ||||
\(447\) | −17.1256 | + | 14.1314i | −0.810012 | + | 0.668395i | ||||
\(448\) | 6.35424 | + | 4.86042i | 0.300209 | + | 0.229633i | ||||
\(449\) | − | 23.8669i | − | 1.12635i | −0.826338 | − | 0.563174i | \(-0.809580\pi\) | ||
0.826338 | − | 0.563174i | \(-0.190420\pi\) | |||||||
\(450\) | −21.0989 | + | 2.19943i | −0.994610 | + | 0.103682i | ||||
\(451\) | − | 9.72193i | − | 0.457788i | ||||||
\(452\) | −8.54855 | − | 27.0646i | −0.402090 | − | 1.27301i | ||||
\(453\) | −7.52759 | + | 6.21151i | −0.353677 | + | 0.291842i | ||||
\(454\) | 3.04783 | + | 2.23357i | 0.143042 | + | 0.104827i | ||||
\(455\) | −3.78178 | + | 1.89089i | −0.177293 | + | 0.0886463i | ||||
\(456\) | −39.2092 | + | 14.9114i | −1.83614 | + | 0.698289i | ||||
\(457\) | − | 28.4723i | − | 1.33188i | −0.746006 | − | 0.665939i | \(-0.768031\pi\) | ||
0.746006 | − | 0.665939i | \(-0.231969\pi\) | |||||||
\(458\) | 14.9872 | − | 20.4509i | 0.700307 | − | 0.955607i | ||||
\(459\) | −5.19717 | + | 2.83182i | −0.242583 | + | 0.132178i | ||||
\(460\) | 10.0171 | + | 10.3390i | 0.467052 | + | 0.482059i | ||||
\(461\) | 23.3007i | 1.08522i | 0.839985 | + | 0.542610i | \(0.182564\pi\) | ||||
−0.839985 | + | 0.542610i | \(0.817436\pi\) | |||||||
\(462\) | 5.39162 | − | 0.310203i | 0.250841 | − | 0.0144320i | ||||
\(463\) | −31.7549 | −1.47577 | −0.737887 | − | 0.674924i | \(-0.764176\pi\) | ||||
−0.737887 | + | 0.674924i | \(0.764176\pi\) | |||||||
\(464\) | 4.34457 | + | 6.19130i | 0.201692 | + | 0.287424i | ||||
\(465\) | 20.9135 | + | 9.27048i | 0.969840 | + | 0.429908i | ||||
\(466\) | 15.0246 | − | 20.5018i | 0.696000 | − | 0.949730i | ||||
\(467\) | − | 6.14714i | − | 0.284456i | −0.989834 | − | 0.142228i | \(-0.954573\pi\) | ||
0.989834 | − | 0.142228i | \(-0.0454266\pi\) | |||||||
\(468\) | 1.30119 | + | 11.2705i | 0.0601474 | + | 0.520978i | ||||
\(469\) | −10.8475 | −0.500891 | ||||||||
\(470\) | 1.41931 | − | 8.32922i | 0.0654680 | − | 0.384198i | ||||
\(471\) | −17.1256 | + | 14.1314i | −0.789105 | + | 0.651143i | ||||
\(472\) | 36.2607 | + | 12.2781i | 1.66903 | + | 0.565144i | ||||
\(473\) | −2.05985 | −0.0947121 | ||||||||
\(474\) | 0.529878 | + | 9.20977i | 0.0243381 | + | 0.423019i | ||||
\(475\) | 34.2512 | + | 25.6884i | 1.57155 | + | 1.17866i | ||||
\(476\) | −0.686132 | − | 2.17229i | −0.0314488 | − | 0.0995665i | ||||
\(477\) | 3.88356 | − | 20.0851i | 0.177816 | − | 0.919634i | ||||
\(478\) | −20.6525 | + | 28.1815i | −0.944625 | + | 1.28899i | ||||
\(479\) | −8.33792 | −0.380969 | −0.190485 | − | 0.981690i | \(-0.561006\pi\) | ||||
−0.190485 | + | 0.981690i | \(0.561006\pi\) | |||||||
\(480\) | −19.8426 | − | 9.28818i | −0.905688 | − | 0.423945i | ||||
\(481\) | 0.774357 | 0.0353076 | ||||||||
\(482\) | −1.09954 | + | 1.50039i | −0.0500829 | + | 0.0683408i | ||||
\(483\) | −4.30041 | + | 3.54855i | −0.195675 | + | 0.161465i | ||||
\(484\) | 3.69803 | + | 11.7079i | 0.168092 | + | 0.532179i | ||||
\(485\) | −36.9834 | + | 18.4917i | −1.67933 | + | 0.839665i | ||||
\(486\) | −20.8947 | − | 7.02938i | −0.947802 | − | 0.318859i | ||||
\(487\) | −19.6532 | −0.890574 | −0.445287 | − | 0.895388i | \(-0.646898\pi\) | ||||
−0.445287 | + | 0.895388i | \(0.646898\pi\) | |||||||
\(488\) | −33.4056 | − | 11.3113i | −1.51220 | − | 0.512039i | ||||
\(489\) | 6.10178 | + | 7.39460i | 0.275932 | + | 0.334396i | ||||
\(490\) | 3.11734 | + | 0.531200i | 0.140827 | + | 0.0239972i | ||||
\(491\) | 14.7609 | 0.666150 | 0.333075 | − | 0.942900i | \(-0.391914\pi\) | ||||
0.333075 | + | 0.942900i | \(0.391914\pi\) | |||||||
\(492\) | −12.8190 | − | 8.30654i | −0.577927 | − | 0.374488i | ||||
\(493\) | − | 2.15379i | − | 0.0970019i | ||||||
\(494\) | 13.5351 | − | 18.4694i | 0.608973 | − | 0.830976i | ||||
\(495\) | −14.2436 | + | 3.98270i | −0.640204 | + | 0.179009i | ||||
\(496\) | 13.5711 | + | 19.3398i | 0.609363 | + | 0.868382i | ||||
\(497\) | −8.00000 | −0.358849 | ||||||||
\(498\) | 0.962489 | + | 16.7289i | 0.0431302 | + | 0.749642i | ||||
\(499\) | 16.8347i | 0.753626i | 0.926289 | + | 0.376813i | \(0.122980\pi\) | ||||
−0.926289 | + | 0.376813i | \(0.877020\pi\) | |||||||
\(500\) | 2.81192 | + | 22.1832i | 0.125753 | + | 0.992062i | ||||
\(501\) | 21.8057 | − | 17.9933i | 0.974205 | − | 0.803881i | ||||
\(502\) | −11.3146 | + | 15.4394i | −0.504997 | + | 0.689096i | ||||
\(503\) | 1.38504i | 0.0617559i | 0.999523 | + | 0.0308779i | \(0.00983032\pi\) | ||||
−0.999523 | + | 0.0308779i | \(0.990170\pi\) | |||||||
\(504\) | 4.19764 | − | 7.37427i | 0.186978 | − | 0.328476i | ||||
\(505\) | −29.7578 | + | 14.8789i | −1.32420 | + | 0.662102i | ||||
\(506\) | 8.09565 | + | 5.93282i | 0.359896 | + | 0.263746i | ||||
\(507\) | 10.3894 | + | 12.5907i | 0.461410 | + | 0.559172i | ||||
\(508\) | −2.16283 | − | 6.84751i | −0.0959602 | − | 0.303809i | ||||
\(509\) | 0.218217i | 0.00967232i | 0.999988 | + | 0.00483616i | \(0.00153940\pi\) | ||||
−0.999988 | + | 0.00483616i | \(0.998461\pi\) | |||||||
\(510\) | 3.10597 | + | 5.41064i | 0.137534 | + | 0.239587i | ||||
\(511\) | − | 8.00000i | − | 0.353899i | ||||||
\(512\) | −12.6141 | − | 18.7852i | −0.557468 | − | 0.830198i | ||||
\(513\) | 21.2884 | + | 39.0702i | 0.939906 | + | 1.72499i | ||||
\(514\) | 18.7107 | − | 25.5318i | 0.825294 | − | 1.12616i | ||||
\(515\) | 14.9208 | + | 29.8416i | 0.657490 | + | 1.31498i | ||||
\(516\) | −1.75996 | + | 2.71606i | −0.0774781 | + | 0.119568i | ||||
\(517\) | − | 5.89089i | − | 0.259081i | ||||||
\(518\) | −0.467138 | − | 0.342337i | −0.0205248 | − | 0.0150414i | ||||
\(519\) | 5.66517 | + | 6.86549i | 0.248673 | + | 0.301361i | ||||
\(520\) | 11.8467 | − | 1.63516i | 0.519514 | − | 0.0717066i | ||||
\(521\) | − | 1.44678i | − | 0.0633844i | −0.999498 | − | 0.0316922i | \(-0.989910\pi\) | ||
0.999498 | − | 0.0316922i | \(-0.0100896\pi\) | |||||||
\(522\) | 5.88424 | − | 5.45290i | 0.257546 | − | 0.238667i | ||||
\(523\) | −6.93719 | −0.303342 | −0.151671 | − | 0.988431i | \(-0.548465\pi\) | ||||
−0.151671 | + | 0.988431i | \(0.548465\pi\) | |||||||
\(524\) | 2.72562 | + | 8.62929i | 0.119069 | + | 0.376972i | ||||
\(525\) | −8.65093 | + | 0.401674i | −0.377558 | + | 0.0175305i | ||||
\(526\) | 10.8333 | + | 7.93906i | 0.472353 | + | 0.346159i | ||||
\(527\) | − | 6.72780i | − | 0.293068i | ||||||
\(528\) | −14.7256 | − | 4.05985i | −0.640850 | − | 0.176682i | ||||
\(529\) | 12.6381 | 0.549482 | ||||||||
\(530\) | −21.2573 | − | 3.62227i | −0.923357 | − | 0.157342i | ||||
\(531\) | 7.70847 | − | 39.8669i | 0.334519 | − | 1.73008i | ||||
\(532\) | −16.3303 | + | 5.15805i | −0.708010 | + | 0.223630i | ||||
\(533\) | 8.33792 | 0.361155 | ||||||||
\(534\) | −2.27807 | − | 39.5949i | −0.0985817 | − | 1.71344i | ||||
\(535\) | −0.742973 | + | 0.371487i | −0.0321215 | + | 0.0160608i | ||||
\(536\) | 29.0606 | + | 9.84008i | 1.25523 | + | 0.425027i | ||||
\(537\) | 15.9161 | + | 19.2884i | 0.686832 | + | 0.832356i | ||||
\(538\) | −9.81093 | − | 7.18984i | −0.422979 | − | 0.309976i | ||||
\(539\) | 2.20476 | 0.0949657 | ||||||||
\(540\) | −6.91848 | + | 22.1841i | −0.297724 | + | 0.954652i | ||||
\(541\) | −19.7997 | −0.851256 | −0.425628 | − | 0.904898i | \(-0.639947\pi\) | ||||
−0.425628 | + | 0.904898i | \(0.639947\pi\) | |||||||
\(542\) | 14.2654 | + | 10.4542i | 0.612751 | + | 0.449048i | ||||
\(543\) | 9.57702 | + | 11.6062i | 0.410989 | + | 0.498069i | ||||
\(544\) | −0.132385 | + | 6.44199i | −0.00567598 | + | 0.276198i | ||||
\(545\) | 2.86097 | + | 5.72193i | 0.122550 | + | 0.245101i | ||||
\(546\) | 0.266043 | + | 4.62407i | 0.0113856 | + | 0.197892i | ||||
\(547\) | −19.1854 | −0.820310 | −0.410155 | − | 0.912016i | \(-0.634525\pi\) | ||||
−0.410155 | + | 0.912016i | \(0.634525\pi\) | |||||||
\(548\) | 9.92082 | + | 31.4092i | 0.423796 | + | 1.34173i | ||||
\(549\) | −7.10152 | + | 36.7279i | −0.303086 | + | 1.56751i | ||||
\(550\) | 4.53065 | + | 14.9172i | 0.193188 | + | 0.636070i | ||||
\(551\) | −16.1913 | −0.689773 | ||||||||
\(552\) | 14.7399 | − | 5.60560i | 0.627370 | − | 0.238590i | ||||
\(553\) | 3.76609i | 0.160150i | ||||||||
\(554\) | 22.0022 | + | 16.1241i | 0.934785 | + | 0.685048i | ||||
\(555\) | 1.44999 | + | 0.642748i | 0.0615486 | + | 0.0272831i | ||||
\(556\) | −24.7399 | + | 7.81426i | −1.04920 | + | 0.331398i | ||||
\(557\) | 21.6532 | 0.917478 | 0.458739 | − | 0.888571i | \(-0.348301\pi\) | ||||
0.458739 | + | 0.888571i | \(0.348301\pi\) | |||||||
\(558\) | 18.3806 | − | 17.0333i | 0.778114 | − | 0.721075i | ||||
\(559\) | − | 1.76661i | − | 0.0747198i | ||||||
\(560\) | −7.86954 | − | 4.25092i | −0.332549 | − | 0.179634i | ||||
\(561\) | 2.76840 | + | 3.35496i | 0.116882 | + | 0.141647i | ||||
\(562\) | −3.34013 | − | 2.44778i | −0.140895 | − | 0.103253i | ||||
\(563\) | − | 20.8424i | − | 0.878403i | −0.898389 | − | 0.439201i | \(-0.855261\pi\) | ||
0.898389 | − | 0.439201i | \(-0.144739\pi\) | |||||||
\(564\) | −7.76755 | − | 5.03325i | −0.327073 | − | 0.211938i | ||||
\(565\) | 14.1913 | + | 28.3826i | 0.597033 | + | 1.19407i | ||||
\(566\) | 6.28397 | − | 8.57482i | 0.264135 | − | 0.360426i | ||||
\(567\) | −8.35130 | − | 3.35496i | −0.350722 | − | 0.140895i | ||||
\(568\) | 21.4321 | + | 7.25703i | 0.899272 | + | 0.304498i | ||||
\(569\) | − | 38.1942i | − | 1.60118i | −0.599209 | − | 0.800592i | \(-0.704518\pi\) | ||
0.599209 | − | 0.800592i | \(-0.295482\pi\) | |||||||
\(570\) | 40.6749 | − | 23.3494i | 1.70368 | − | 0.977997i | ||||
\(571\) | 12.8962i | 0.539691i | 0.962904 | + | 0.269845i | \(0.0869726\pi\) | ||||
−0.962904 | + | 0.269845i | \(0.913027\pi\) | |||||||
\(572\) | 7.95074 | − | 2.51130i | 0.332437 | − | 0.105003i | ||||
\(573\) | 12.9715 | + | 15.7198i | 0.541890 | + | 0.656704i | ||||
\(574\) | −5.02993 | − | 3.68613i | −0.209945 | − | 0.153856i | ||||
\(575\) | −12.8760 | − | 9.65698i | −0.536965 | − | 0.402724i | ||||
\(576\) | −17.9350 | + | 15.9480i | −0.747290 | + | 0.664499i | ||||
\(577\) | − | 5.07185i | − | 0.211144i | −0.994412 | − | 0.105572i | \(-0.966333\pi\) | ||
0.994412 | − | 0.105572i | \(-0.0336673\pi\) | |||||||
\(578\) | −13.1266 | + | 17.9119i | −0.545993 | + | 0.745037i | ||||
\(579\) | 24.1270 | − | 19.9088i | 1.00269 | − | 0.827382i | ||||
\(580\) | −5.88424 | − | 6.07331i | −0.244330 | − | 0.252180i | ||||
\(581\) | 6.84086i | 0.283807i | ||||||||
\(582\) | 2.60173 | + | 45.2205i | 0.107845 | + | 1.87445i | ||||
\(583\) | −15.0343 | −0.622659 | ||||||||
\(584\) | −7.25703 | + | 21.4321i | −0.300298 | + | 0.886867i | ||||
\(585\) | −3.41573 | − | 12.2159i | −0.141223 | − | 0.505067i | ||||
\(586\) | 12.0582 | − | 16.4540i | 0.498118 | − | 0.679709i | ||||
\(587\) | 15.5971i | 0.643762i | 0.946780 | + | 0.321881i | \(0.104315\pi\) | ||||
−0.946780 | + | 0.321881i | \(0.895685\pi\) | |||||||
\(588\) | 1.88377 | − | 2.90713i | 0.0776855 | − | 0.119888i | ||||
\(589\) | −50.5768 | −2.08398 | ||||||||
\(590\) | −42.1935 | − | 7.18984i | −1.73708 | − | 0.296001i | ||||
\(591\) | −17.7041 | − | 21.4551i | −0.728248 | − | 0.882546i | ||||
\(592\) | 0.940924 | + | 1.34088i | 0.0386718 | + | 0.0551098i | ||||
\(593\) | −24.9655 | −1.02521 | −0.512605 | − | 0.858624i | \(-0.671319\pi\) | ||||
−0.512605 | + | 0.858624i | \(0.671319\pi\) | |||||||
\(594\) | −2.15693 | + | 16.0574i | −0.0885001 | + | 0.658843i | ||||
\(595\) | 1.13903 | + | 2.27807i | 0.0466959 | + | 0.0933917i | ||||
\(596\) | 24.4476 | − | 7.72193i | 1.00141 | − | 0.316303i | ||||
\(597\) | −9.13903 | + | 7.54122i | −0.374036 | + | 0.308642i | ||||
\(598\) | −5.08822 | + | 6.94316i | −0.208073 | + | 0.283927i | ||||
\(599\) | 12.0866 | 0.493845 | 0.246923 | − | 0.969035i | \(-0.420581\pi\) | ||||
0.246923 | + | 0.969035i | \(0.420581\pi\) | |||||||
\(600\) | 23.5403 | + | 6.77142i | 0.961031 | + | 0.276442i | ||||
\(601\) | 43.6681 | 1.78126 | 0.890629 | − | 0.454730i | \(-0.150264\pi\) | ||||
0.890629 | + | 0.454730i | \(0.150264\pi\) | |||||||
\(602\) | −0.781006 | + | 1.06572i | −0.0318314 | + | 0.0434357i | ||||
\(603\) | 6.17784 | − | 31.9507i | 0.251581 | − | 1.30113i | ||||
\(604\) | 10.7460 | − | 3.39419i | 0.437248 | − | 0.138108i | ||||
\(605\) | −6.13903 | − | 12.2781i | −0.249587 | − | 0.499175i | ||||
\(606\) | 2.09342 | + | 36.3855i | 0.0850393 | + | 1.47806i | ||||
\(607\) | 40.7055 | 1.65219 | 0.826093 | − | 0.563534i | \(-0.190559\pi\) | ||||
0.826093 | + | 0.563534i | \(0.190559\pi\) | |||||||
\(608\) | 48.4282 | + | 0.995218i | 1.96402 | + | 0.0403614i | ||||
\(609\) | 2.52613 | − | 2.08448i | 0.102364 | − | 0.0844674i | ||||
\(610\) | 38.8713 | + | 6.62373i | 1.57385 | + | 0.268187i | ||||
\(611\) | 5.05227 | 0.204393 | ||||||||
\(612\) | 6.78911 | − | 0.783809i | 0.274434 | − | 0.0316836i | ||||
\(613\) | − | 2.95049i | − | 0.119169i | −0.998223 | − | 0.0595846i | \(-0.981022\pi\) | ||
0.998223 | − | 0.0595846i | \(-0.0189776\pi\) | |||||||
\(614\) | −18.1496 | + | 24.7661i | −0.732458 | + | 0.999479i | ||||
\(615\) | 15.6128 | + | 6.92082i | 0.629570 | + | 0.279074i | ||||
\(616\) | −5.90658 | − | 2.00000i | −0.237983 | − | 0.0805823i | ||||
\(617\) | −15.3124 | −0.616454 | −0.308227 | − | 0.951313i | \(-0.599736\pi\) | ||||
−0.308227 | + | 0.951313i | \(0.599736\pi\) | |||||||
\(618\) | 36.4880 | − | 2.09932i | 1.46776 | − | 0.0844469i | ||||
\(619\) | 0.967840i | 0.0389008i | 0.999811 | + | 0.0194504i | \(0.00619164\pi\) | ||||
−0.999811 | + | 0.0194504i | \(0.993808\pi\) | |||||||
\(620\) | −18.3806 | − | 18.9712i | −0.738184 | − | 0.761902i | ||||
\(621\) | −8.00291 | − | 14.6876i | −0.321146 | − | 0.589393i | ||||
\(622\) | 16.6591 | − | 22.7323i | 0.667970 | − | 0.911481i | ||||
\(623\) | − | 16.1913i | − | 0.648691i | ||||||
\(624\) | 3.48189 | − | 12.6293i | 0.139387 | − | 0.505576i | ||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | −21.5913 | − | 15.8230i | −0.862961 | − | 0.632413i | ||||
\(627\) | 25.2212 | − | 20.8117i | 1.00724 | − | 0.831140i | ||||
\(628\) | 24.4476 | − | 7.72193i | 0.975564 | − | 0.308139i | ||||
\(629\) | − | 0.466457i | − | 0.0185988i | ||||||
\(630\) | −3.34000 | + | 8.87944i | −0.133069 | + | 0.353765i | ||||
\(631\) | − | 5.37278i | − | 0.213887i | −0.994265 | − | 0.106944i | \(-0.965894\pi\) | ||
0.994265 | − | 0.106944i | \(-0.0341064\pi\) | |||||||
\(632\) | 3.41633 | − | 10.0894i | 0.135894 | − | 0.401335i | ||||
\(633\) | 21.8057 | − | 17.9933i | 0.866697 | − | 0.715169i | ||||
\(634\) | 0.232452 | − | 0.317193i | 0.00923184 | − | 0.0125973i | ||||
\(635\) | 3.59048 | + | 7.18096i | 0.142484 | + | 0.284968i | ||||
\(636\) | −12.8455 | + | 19.8238i | −0.509358 | + | 0.786066i | ||||
\(637\) | 1.89089i | 0.0749198i | ||||||||
\(638\) | −4.75552 | − | 3.48504i | −0.188273 | − | 0.137974i | ||||
\(639\) | 4.55614 | − | 23.5636i | 0.180238 | − | 0.932160i | ||||
\(640\) | 17.2265 | + | 18.5270i | 0.680936 | + | 0.732343i | ||||
\(641\) | − | 22.3081i | − | 0.881117i | −0.897724 | − | 0.440558i | \(-0.854781\pi\) | ||
0.897724 | − | 0.440558i | \(-0.145219\pi\) | |||||||
\(642\) | 0.0522671 | + | 0.908450i | 0.00206282 | + | 0.0358537i | ||||
\(643\) | 0.949286 | 0.0374362 | 0.0187181 | − | 0.999825i | \(-0.494041\pi\) | ||||
0.0187181 | + | 0.999825i | \(0.494041\pi\) | |||||||
\(644\) | 6.13903 | − | 1.93906i | 0.241912 | − | 0.0764096i | ||||
\(645\) | 1.46636 | − | 3.30800i | 0.0577379 | − | 0.130252i | ||||
\(646\) | −11.1256 | − | 8.15327i | −0.437730 | − | 0.320786i | ||||
\(647\) | − | 30.1740i | − | 1.18626i | −0.805107 | − | 0.593130i | \(-0.797892\pi\) | ||
0.805107 | − | 0.593130i | \(-0.202108\pi\) | |||||||
\(648\) | 19.3299 | + | 16.5637i | 0.759349 | + | 0.650684i | ||||
\(649\) | −29.8416 | −1.17139 | ||||||||
\(650\) | −12.7936 | + | 3.88567i | −0.501804 | + | 0.152409i | ||||
\(651\) | 7.89089 | − | 6.51130i | 0.309268 | − | 0.255198i | ||||
\(652\) | −3.33423 | − | 10.5561i | −0.130579 | − | 0.413410i | ||||
\(653\) | 2.04468 | 0.0800146 | 0.0400073 | − | 0.999199i | \(-0.487262\pi\) | ||||
0.0400073 | + | 0.999199i | \(0.487262\pi\) | |||||||
\(654\) | 6.99633 | − | 0.402530i | 0.273578 | − | 0.0157402i | ||||
\(655\) | −4.52476 | − | 9.04951i | −0.176797 | − | 0.353594i | ||||
\(656\) | 10.1314 | + | 14.4380i | 0.395567 | + | 0.563709i | ||||
\(657\) | 23.5636 | + | 4.55614i | 0.919302 | + | 0.177752i | ||||
\(658\) | −3.04783 | − | 2.23357i | −0.118817 | − | 0.0870736i | ||||
\(659\) | −13.5054 | −0.526097 | −0.263048 | − | 0.964783i | \(-0.584728\pi\) | ||||
−0.263048 | + | 0.964783i | \(0.584728\pi\) | |||||||
\(660\) | 16.9723 | + | 1.89702i | 0.660646 | + | 0.0738414i | ||||
\(661\) | 11.2286 | 0.436740 | 0.218370 | − | 0.975866i | \(-0.429926\pi\) | ||||
0.218370 | + | 0.975866i | \(0.429926\pi\) | |||||||
\(662\) | 15.1471 | + | 11.1004i | 0.588710 | + | 0.431431i | ||||
\(663\) | −2.87735 | + | 2.37430i | −0.111747 | + | 0.0922100i | ||||
\(664\) | 6.20554 | − | 18.3268i | 0.240822 | − | 0.711216i | ||||
\(665\) | 17.1256 | − | 8.56279i | 0.664101 | − | 0.332051i | ||||
\(666\) | 1.27438 | − | 1.18096i | 0.0493812 | − | 0.0457613i | ||||
\(667\) | 6.08677 | 0.235681 | ||||||||
\(668\) | −31.1286 | + | 9.83218i | −1.20440 | + | 0.380419i | ||||
\(669\) | 20.3140 | + | 24.6181i | 0.785386 | + | 0.951791i | ||||
\(670\) | −33.8154 | − | 5.76220i | −1.30640 | − | 0.222613i | ||||
\(671\) | 27.4920 | 1.06132 | ||||||||
\(672\) | −7.68380 | + | 6.07941i | −0.296409 | + | 0.234518i | ||||
\(673\) | 24.6905i | 0.951749i | 0.879513 | + | 0.475874i | \(0.157868\pi\) | ||||
−0.879513 | + | 0.475874i | \(0.842132\pi\) | |||||||
\(674\) | 27.7622 | + | 20.3453i | 1.06936 | + | 0.783670i | ||||
\(675\) | 3.74375 | − | 25.7096i | 0.144097 | − | 0.989564i | ||||
\(676\) | −5.67715 | − | 17.9738i | −0.218352 | − | 0.691300i | ||||
\(677\) | −26.7771 | −1.02913 | −0.514564 | − | 0.857452i | \(-0.672046\pi\) | ||||
−0.514564 | + | 0.857452i | \(0.672046\pi\) | |||||||
\(678\) | 34.7041 | − | 1.99668i | 1.33280 | − | 0.0766819i | ||||
\(679\) | 18.4917i | 0.709647i | ||||||||
\(680\) | −0.984989 | − | 7.13623i | −0.0377726 | − | 0.273662i | ||||
\(681\) | −3.56952 | + | 2.94545i | −0.136784 | + | 0.112870i | ||||
\(682\) | −14.8548 | − | 10.8862i | −0.568821 | − | 0.416855i | ||||
\(683\) | − | 16.4329i | − | 0.628787i | −0.949293 | − | 0.314394i | \(-0.898199\pi\) | ||
0.949293 | − | 0.314394i | \(-0.101801\pi\) | |||||||
\(684\) | −5.89235 | − | 51.0377i | −0.225300 | − | 1.95148i | ||||
\(685\) | −16.4694 | − | 32.9387i | −0.629262 | − | 1.25852i | ||||
\(686\) | 0.835949 | − | 1.14070i | 0.0319167 | − | 0.0435520i | ||||
\(687\) | 19.7639 | + | 23.9514i | 0.754040 | + | 0.913804i | ||||
\(688\) | 3.05908 | − | 2.14662i | 0.116626 | − | 0.0818391i | ||||
\(689\) | − | 12.8941i | − | 0.491225i | ||||||
\(690\) | −15.2908 | + | 8.77768i | −0.582113 | + | 0.334161i | ||||
\(691\) | 16.6780i | 0.634462i | 0.948348 | + | 0.317231i | \(0.102753\pi\) | ||||
−0.948348 | + | 0.317231i | \(0.897247\pi\) | |||||||
\(692\) | −3.09565 | − | 9.80080i | −0.117679 | − | 0.372570i | ||||
\(693\) | −1.25565 | + | 6.49400i | −0.0476982 | + | 0.246687i | ||||
\(694\) | 40.2610 | + | 29.5049i | 1.52829 | + | 1.11999i | ||||
\(695\) | 25.9446 | − | 12.9723i | 0.984135 | − | 0.492068i | ||||
\(696\) | −8.65844 | + | 3.29283i | −0.328197 | + | 0.124814i | ||||
\(697\) | − | 5.02260i | − | 0.190244i | ||||||
\(698\) | −9.27418 | + | 12.6551i | −0.351033 | + | 0.479003i | ||||
\(699\) | 19.8132 | + | 24.0111i | 0.749403 | + | 0.908184i | ||||
\(700\) | 9.43565 | + | 3.31187i | 0.356634 | + | 0.125177i | ||||
\(701\) | − | 14.1538i | − | 0.534581i | −0.963616 | − | 0.267291i | \(-0.913872\pi\) | ||
0.963616 | − | 0.267291i | \(-0.0861284\pi\) | |||||||
\(702\) | −13.7715 | − | 1.84987i | −0.519771 | − | 0.0698190i | ||||
\(703\) | −3.50663 | −0.132255 | ||||||||
\(704\) | 14.0096 | + | 10.7161i | 0.528005 | + | 0.403877i | ||||
\(705\) | 9.46041 | + | 4.19359i | 0.356300 | + | 0.157940i | ||||
\(706\) | −17.9910 | + | 24.5497i | −0.677100 | + | 0.923939i | ||||
\(707\) | 14.8789i | 0.559578i | ||||||||
\(708\) | −25.4971 | + | 39.3483i | −0.958238 | + | 1.47880i | ||||
\(709\) | 28.4397 | 1.06808 | 0.534038 | − | 0.845461i | \(-0.320674\pi\) | ||||
0.534038 | + | 0.845461i | \(0.320674\pi\) | |||||||
\(710\) | −24.9387 | − | 4.24960i | −0.935934 | − | 0.159485i | ||||
\(711\) | −11.0928 | − | 2.14485i | −0.416013 | − | 0.0804383i | ||||
\(712\) | −14.6876 | + | 43.3767i | −0.550441 | + | 1.62561i | ||||
\(713\) | 19.0133 | 0.712052 | ||||||||
\(714\) | 2.78545 | − | 0.160259i | 0.104243 | − | 0.00599754i | ||||
\(715\) | −8.33792 | + | 4.16896i | −0.311821 | + | 0.155910i | ||||
\(716\) | −8.69715 | − | 27.5351i | −0.325028 | − | 1.02903i | ||||
\(717\) | −27.2349 | − | 33.0053i | −1.01710 | − | 1.23261i | ||||
\(718\) | 13.0103 | − | 17.7533i | 0.485542 | − | 0.662548i | ||||
\(719\) | 35.3453 | 1.31816 | 0.659080 | − | 0.752073i | \(-0.270946\pi\) | ||||
0.659080 | + | 0.752073i | \(0.270946\pi\) | |||||||
\(720\) | 17.0027 | − | 20.7583i | 0.633653 | − | 0.773617i | ||||
\(721\) | 14.9208 | 0.555680 | ||||||||
\(722\) | −45.4099 | + | 61.9642i | −1.68998 | + | 2.30607i | ||||
\(723\) | −1.44999 | − | 1.75721i | −0.0539257 | − | 0.0653513i | ||||
\(724\) | −5.23323 | − | 16.5683i | −0.194491 | − | 0.615758i | ||||
\(725\) | 7.56357 | + | 5.67267i | 0.280904 | + | 0.210678i | ||||
\(726\) | −15.0127 | + | 0.863745i | −0.557173 | + | 0.0320566i | ||||
\(727\) | 15.5636 | 0.577221 | 0.288610 | − | 0.957447i | \(-0.406807\pi\) | ||||
0.288610 | + | 0.957447i | \(0.406807\pi\) | |||||||
\(728\) | 1.71528 | − | 5.06572i | 0.0635725 | − | 0.187748i | ||||
\(729\) | 14.6381 | − | 22.6876i | 0.542151 | − | 0.840281i | ||||
\(730\) | 4.24960 | − | 24.9387i | 0.157285 | − | 0.923024i | ||||
\(731\) | −1.06417 | −0.0393598 | ||||||||
\(732\) | 23.4895 | − | 36.2501i | 0.868196 | − | 1.33984i | ||||
\(733\) | − | 15.2661i | − | 0.563865i | −0.959434 | − | 0.281933i | \(-0.909025\pi\) | ||
0.959434 | − | 0.281933i | \(-0.0909754\pi\) | |||||||
\(734\) | −29.8542 | + | 40.7376i | −1.10194 | + | 1.50365i | ||||
\(735\) | −1.56952 | + | 3.54071i | −0.0578925 | + | 0.130601i | ||||
\(736\) | −18.2055 | − | 0.374131i | −0.671065 | − | 0.0137906i | ||||
\(737\) | −23.9161 | −0.880963 | ||||||||
\(738\) | 13.7219 | − | 12.7161i | 0.505111 | − | 0.468085i | ||||
\(739\) | 9.17265i | 0.337421i | 0.985666 | + | 0.168711i | \(0.0539604\pi\) | ||||
−0.985666 | + | 0.168711i | \(0.946040\pi\) | |||||||
\(740\) | −1.27438 | − | 1.31533i | −0.0468471 | − | 0.0483523i | ||||
\(741\) | 17.8490 | + | 21.6307i | 0.655698 | + | 0.794625i | ||||
\(742\) | −5.70037 | + | 7.77846i | −0.209267 | + | 0.285556i | ||||
\(743\) | 22.9169i | 0.840740i | 0.907353 | + | 0.420370i | \(0.138100\pi\) | ||||
−0.907353 | + | 0.420370i | \(0.861900\pi\) | |||||||
\(744\) | −27.0464 | + | 10.2858i | −0.991569 | + | 0.377096i | ||||
\(745\) | −25.6381 | + | 12.8190i | −0.939306 | + | 0.469653i | ||||
\(746\) | 33.0920 | + | 24.2512i | 1.21158 | + | 0.887898i | ||||
\(747\) | −20.1494 | − | 3.89599i | −0.737227 | − | 0.142547i | ||||
\(748\) | −1.51276 | − | 4.78937i | −0.0553118 | − | 0.175117i | ||||
\(749\) | 0.371487i | 0.0135738i | ||||||||
\(750\) | −27.1813 | − | 3.34322i | −0.992521 | − | 0.122077i | ||||
\(751\) | − | 33.2173i | − | 1.21212i | −0.795420 | − | 0.606059i | \(-0.792750\pi\) | ||
0.795420 | − | 0.606059i | \(-0.207250\pi\) | |||||||
\(752\) | 6.13903 | + | 8.74853i | 0.223868 | + | 0.319026i | ||||
\(753\) | −14.9208 | − | 18.0822i | −0.543745 | − | 0.658952i | ||||
\(754\) | 2.98891 | − | 4.07853i | 0.108850 | − | 0.148531i | ||||
\(755\) | −11.2693 | + | 5.63464i | −0.410131 | + | 0.205066i | ||||
\(756\) | 7.48995 | + | 7.20421i | 0.272407 | + | 0.262015i | ||||
\(757\) | − | 24.8760i | − | 0.904133i | −0.891984 | − | 0.452066i | \(-0.850687\pi\) | ||
0.891984 | − | 0.452066i | \(-0.149313\pi\) | |||||||
\(758\) | 26.6391 | + | 19.5222i | 0.967576 | + | 0.709079i | ||||
\(759\) | −9.48137 | + | 7.82371i | −0.344152 | + | 0.283983i | ||||
\(760\) | −53.6472 | + | 7.40474i | −1.94599 | + | 0.268598i | ||||
\(761\) | 3.15405i | 0.114334i | 0.998365 | + | 0.0571670i | \(0.0182068\pi\) | ||||
−0.998365 | + | 0.0571670i | \(0.981793\pi\) | |||||||
\(762\) | 8.78033 | − | 0.505170i | 0.318078 | − | 0.0183004i | ||||
\(763\) | 2.86097 | 0.103574 | ||||||||
\(764\) | −7.08807 | − | 22.4407i | −0.256437 | − | 0.811878i | ||||
\(765\) | −7.35863 | + | 2.05756i | −0.266052 | + | 0.0743914i | ||||
\(766\) | 17.0157 | + | 12.4698i | 0.614802 | + | 0.450552i | ||||
\(767\) | − | 25.5934i | − | 0.924124i | ||||||
\(768\) | 26.0998 | − | 9.31665i | 0.941796 | − | 0.336186i | ||||
\(769\) | 34.7352 | 1.25258 | 0.626291 | − | 0.779589i | \(-0.284572\pi\) | ||||
0.626291 | + | 0.779589i | \(0.284572\pi\) | |||||||
\(770\) | 6.87299 | + | 1.17117i | 0.247685 | + | 0.0422060i | ||||
\(771\) | 24.6741 | + | 29.9020i | 0.888617 | + | 1.07689i | ||||
\(772\) | −34.4425 | + | 10.8789i | −1.23961 | + | 0.391540i | ||||
\(773\) | −46.5442 | −1.67408 | −0.837040 | − | 0.547142i | \(-0.815716\pi\) | ||||
−0.837040 | + | 0.547142i | \(0.815716\pi\) | |||||||
\(774\) | −2.69424 | − | 2.90736i | −0.0968424 | − | 0.104503i | ||||
\(775\) | 23.6263 | + | 17.7197i | 0.848683 | + | 0.636512i | ||||
\(776\) | 16.7744 | − | 49.5396i | 0.602164 | − | 1.77837i | ||||
\(777\) | 0.547097 | − | 0.451446i | 0.0196270 | − | 0.0161955i | ||||
\(778\) | 22.2766 | + | 16.3252i | 0.798656 | + | 0.585287i | ||||
\(779\) | −37.7578 | −1.35281 | ||||||||
\(780\) | −1.62696 | + | 14.5561i | −0.0582545 | + | 0.521193i | ||||
\(781\) | −17.6381 | −0.631140 | ||||||||
\(782\) | 4.18242 | + | 3.06504i | 0.149563 | + | 0.109606i | ||||
\(783\) | 4.70105 | + | 8.62774i | 0.168002 | + | 0.308330i | ||||
\(784\) | −3.27428 | + | 2.29763i | −0.116938 | + | 0.0820583i | ||||
\(785\) | −25.6381 | + | 12.8190i | −0.915062 | + | 0.457531i | ||||
\(786\) | −11.0650 | + | 0.636620i | −0.394677 | + | 0.0227075i | ||||
\(787\) | 17.6845 | 0.630383 | 0.315192 | − | 0.949028i | \(-0.397931\pi\) | ||||
0.315192 | + | 0.949028i | \(0.397931\pi\) | |||||||
\(788\) | 9.67413 | + | 30.6282i | 0.344627 | + | 1.09108i | ||||
\(789\) | −12.6876 | + | 10.4694i | −0.451690 | + | 0.372719i | ||||
\(790\) | −2.00055 | + | 11.7402i | −0.0711763 | + | 0.417697i | ||||
\(791\) | 14.1913 | 0.504585 | ||||||||
\(792\) | 9.25479 | − | 16.2585i | 0.328855 | − | 0.577720i | ||||
\(793\) | 23.5782i | 0.837287i | ||||||||
\(794\) | −3.97452 | − | 2.91268i | −0.141050 | − | 0.103367i | ||||
\(795\) | 10.7026 | − | 24.1442i | 0.379582 | − | 0.856307i | ||||
\(796\) | 13.0464 | − | 4.12079i | 0.462417 | − | 0.146058i | ||||
\(797\) | −27.5368 | −0.975404 | −0.487702 | − | 0.873010i | \(-0.662165\pi\) | ||||
−0.487702 | + | 0.873010i | \(0.662165\pi\) | |||||||
\(798\) | −1.20476 | − | 20.9398i | −0.0426480 | − | 0.741262i | ||||
\(799\) | − | 3.04338i | − | 0.107667i | ||||||
\(800\) | −22.2740 | − | 17.4319i | −0.787504 | − | 0.616310i | ||||
\(801\) | 47.6906 | + | 9.22123i | 1.68506 | + | 0.325816i | ||||
\(802\) | 21.9767 | + | 16.1054i | 0.776026 | + | 0.568703i | ||||
\(803\) | − | 17.6381i | − | 0.622434i | ||||||
\(804\) | −20.4343 | + | 31.5351i | −0.720661 | + | 1.11216i | ||||
\(805\) | −6.43799 | + | 3.21899i | −0.226909 | + | 0.113455i | ||||
\(806\) | 9.33646 | − | 12.7401i | 0.328863 | − | 0.448751i | ||||
\(807\) | 11.4903 | − | 9.48137i | 0.404476 | − | 0.333760i | ||||
\(808\) | 13.4971 | − | 39.8608i | 0.474825 | − | 1.40230i | ||||
\(809\) | − | 2.15379i | − | 0.0757233i | −0.999283 | − | 0.0378616i | \(-0.987945\pi\) | ||
0.999283 | − | 0.0378616i | \(-0.0120546\pi\) | |||||||
\(810\) | −24.2517 | − | 14.8948i | −0.852118 | − | 0.523349i | ||||
\(811\) | 21.0484i | 0.739108i | 0.929209 | + | 0.369554i | \(0.120490\pi\) | ||||
−0.929209 | + | 0.369554i | \(0.879510\pi\) | |||||||
\(812\) | −3.60617 | + | 1.13903i | −0.126552 | + | 0.0399723i | ||||
\(813\) | −16.7072 | + | 13.7862i | −0.585946 | + | 0.483503i | ||||
\(814\) | −1.02993 | − | 0.754771i | −0.0360989 | − | 0.0264547i | ||||
\(815\) | 5.53510 | + | 11.0702i | 0.193886 | + | 0.387772i | ||||
\(816\) | −7.60763 | − | 2.09742i | −0.266320 | − | 0.0734245i | ||||
\(817\) | 8.00000i | 0.279885i | ||||||||
\(818\) | −2.89157 | + | 3.94571i | −0.101101 | + | 0.137958i | ||||
\(819\) | −5.56952 | − | 1.07690i | −0.194615 | − | 0.0376298i | ||||
\(820\) | −13.7219 | − | 14.1628i | −0.479191 | − | 0.494588i | ||||
\(821\) | − | 44.2048i | − | 1.54276i | −0.636376 | − | 0.771379i | \(-0.719567\pi\) | ||
0.636376 | − | 0.771379i | \(-0.280433\pi\) | |||||||
\(822\) | −40.2750 | + | 2.31719i | −1.40475 | + | 0.0808214i | ||||
\(823\) | −39.0579 | −1.36147 | −0.680737 | − | 0.732528i | \(-0.738340\pi\) | ||||
−0.680737 | + | 0.732528i | \(0.738340\pi\) | |||||||
\(824\) | −39.9731 | − | 13.5351i | −1.39253 | − | 0.471517i | ||||
\(825\) | −19.0732 | + | 0.885594i | −0.664045 | + | 0.0308324i | ||||
\(826\) | −11.3146 | + | 15.4394i | −0.393687 | + | 0.537207i | ||||
\(827\) | − | 5.48481i | − | 0.190725i | −0.995443 | − | 0.0953627i | \(-0.969599\pi\) | ||
0.995443 | − | 0.0953627i | \(-0.0304011\pi\) | |||||||
\(828\) | 2.21510 | + | 19.1865i | 0.0769801 | + | 0.666778i | ||||
\(829\) | −24.3855 | −0.846944 | −0.423472 | − | 0.905909i | \(-0.639189\pi\) | ||||
−0.423472 | + | 0.905909i | \(0.639189\pi\) | |||||||
\(830\) | −3.63386 | + | 21.3253i | −0.126133 | + | 0.740212i | ||||
\(831\) | −25.7683 | + | 21.2632i | −0.893893 | + | 0.737611i | ||||
\(832\) | −9.19053 | + | 12.0152i | −0.318624 | + | 0.416551i | ||||
\(833\) | 1.13903 | 0.0394652 | ||||||||
\(834\) | −1.82517 | − | 31.7231i | −0.0632003 | − | 1.09848i | ||||
\(835\) | 32.6445 | − | 16.3222i | 1.12971 | − | 0.564854i | ||||
\(836\) | −36.0045 | + | 11.3723i | −1.24524 | + | 0.393318i | ||||
\(837\) | 14.6847 | + | 26.9505i | 0.507577 | + | 0.931545i | ||||
\(838\) | −9.43280 | + | 12.8716i | −0.325851 | + | 0.444641i | ||||
\(839\) | −37.5965 | −1.29798 | −0.648988 | − | 0.760799i | \(-0.724807\pi\) | ||||
−0.648988 | + | 0.760799i | \(0.724807\pi\) | |||||||
\(840\) | 7.41664 | − | 8.06185i | 0.255898 | − | 0.278160i | ||||
\(841\) | 25.4245 | 0.876708 | ||||||||
\(842\) | 8.32444 | − | 11.3591i | 0.286879 | − | 0.391462i | ||||
\(843\) | 3.91185 | − | 3.22793i | 0.134731 | − | 0.111176i | ||||
\(844\) | −31.1286 | + | 9.83218i | −1.07149 | + | 0.338438i | ||||
\(845\) | 9.42453 | + | 18.8491i | 0.324214 | + | 0.648427i | ||||
\(846\) | 8.31464 | − | 7.70515i | 0.285863 | − | 0.264908i | ||||
\(847\) | −6.13903 | −0.210940 | ||||||||
\(848\) | 22.3274 | − | 15.6676i | 0.766727 | − | 0.538029i | ||||
\(849\) | 8.28678 | + | 10.0426i | 0.284401 | + | 0.344660i | ||||
\(850\) | 2.34065 | + | 7.70658i | 0.0802837 | + | 0.264333i | ||||
\(851\) | 1.31824 | 0.0451887 | ||||||||
\(852\) | −15.0702 | + | 23.2570i | −0.516296 | + | 0.796773i | ||||
\(853\) | − | 32.9387i | − | 1.12780i | −0.825843 | − | 0.563901i | \(-0.809300\pi\) | ||
0.825843 | − | 0.563901i | \(-0.190700\pi\) | |||||||
\(854\) | 10.4238 | − | 14.2238i | 0.356694 | − | 0.486728i | ||||
\(855\) | 15.4679 | + | 55.3191i | 0.528992 | + | 1.89187i | ||||
\(856\) | 0.336986 | − | 0.995218i | 0.0115179 | − | 0.0340159i | ||||
\(857\) | 41.6833 | 1.42387 | 0.711937 | − | 0.702244i | \(-0.247818\pi\) | ||||
0.711937 | + | 0.702244i | \(0.247818\pi\) | |||||||
\(858\) | 0.586561 | + | 10.1950i | 0.0200249 | + | 0.348050i | ||||
\(859\) | − | 2.44600i | − | 0.0834564i | −0.999129 | − | 0.0417282i | \(-0.986714\pi\) | ||
0.999129 | − | 0.0417282i | \(-0.0132864\pi\) | |||||||
\(860\) | −3.00078 | + | 2.90736i | −0.102326 | + | 0.0991401i | ||||
\(861\) | 5.89089 | − | 4.86097i | 0.200761 | − | 0.165661i | ||||
\(862\) | −1.41464 | + | 1.93036i | −0.0481829 | + | 0.0657482i | ||||
\(863\) | − | 45.2264i | − | 1.53952i | −0.638331 | − | 0.769762i | \(-0.720375\pi\) | ||
0.638331 | − | 0.769762i | \(-0.279625\pi\) | |||||||
\(864\) | −13.5305 | − | 26.0945i | −0.460318 | − | 0.887754i | ||||
\(865\) | 5.13903 | + | 10.2781i | 0.174732 | + | 0.349465i | ||||
\(866\) | −14.7592 | − | 10.8161i | −0.501538 | − | 0.367547i | ||||
\(867\) | −17.3102 | − | 20.9779i | −0.587886 | − | 0.712446i | ||||
\(868\) | −11.2646 | + | 3.55801i | −0.382346 | + | 0.120767i | ||||
\(869\) | 8.30333i | 0.281671i | ||||||||
\(870\) | 8.98210 | − | 5.15616i | 0.304522 | − | 0.174810i | ||||
\(871\) | − | 20.5115i | − | 0.695004i | ||||||
\(872\) | −7.66457 | − | 2.59526i | −0.259555 | − | 0.0878867i | ||||
\(873\) | −54.4663 | − | 10.5314i | −1.84341 | − | 0.356432i | ||||
\(874\) | 23.0417 | − | 31.4417i | 0.779398 | − | 1.06353i | ||||
\(875\) | −11.0000 | − | 2.00000i | −0.371868 | − | 0.0676123i | ||||
\(876\) | −23.2570 | − | 15.0702i | −0.785782 | − | 0.509175i | ||||
\(877\) | − | 11.3723i | − | 0.384014i | −0.981394 | − | 0.192007i | \(-0.938500\pi\) | ||
0.981394 | − | 0.192007i | \(-0.0614996\pi\) | |||||||
\(878\) | 3.54045 | + | 2.59458i | 0.119484 | + | 0.0875629i | ||||
\(879\) | 15.9013 | + | 19.2704i | 0.536338 | + | 0.649976i | ||||
\(880\) | −17.3504 | − | 9.37226i | −0.584883 | − | 0.315939i | ||||
\(881\) | 16.8818i | 0.568762i | 0.958711 | + | 0.284381i | \(0.0917881\pi\) | ||||
−0.958711 | + | 0.284381i | \(0.908212\pi\) | |||||||
\(882\) | 2.88377 | + | 3.11189i | 0.0971017 | + | 0.104783i | ||||
\(883\) | −44.3871 | −1.49374 | −0.746872 | − | 0.664968i | \(-0.768445\pi\) | ||||
−0.746872 | + | 0.664968i | \(0.768445\pi\) | |||||||
\(884\) | 4.10756 | − | 1.29740i | 0.138152 | − | 0.0436363i | ||||
\(885\) | 21.2436 | − | 47.9238i | 0.714095 | − | 1.61094i | ||||
\(886\) | 16.7617 | + | 12.2836i | 0.563119 | + | 0.412677i | ||||
\(887\) | − | 10.8978i | − | 0.365912i | −0.983121 | − | 0.182956i | \(-0.941433\pi\) | ||
0.983121 | − | 0.182956i | \(-0.0585666\pi\) | |||||||
\(888\) | −1.87520 | + | 0.713143i | −0.0629276 | + | 0.0239315i | ||||
\(889\) | 3.59048 | 0.120421 | ||||||||
\(890\) | 8.60082 | − | 50.4738i | 0.288300 | − | 1.69189i | ||||
\(891\) | −18.4126 | − | 7.39689i | −0.616846 | − | 0.247805i | ||||
\(892\) | −11.1003 | − | 35.1435i | −0.371666 | − | 1.17669i | ||||
\(893\) | −22.8789 | −0.765613 | ||||||||
\(894\) | 1.80360 | + | 31.3483i | 0.0603215 | + | 1.04844i | ||||
\(895\) | 14.4380 | + | 28.8760i | 0.482609 | + | 0.965217i | ||||
\(896\) | 10.8561 | − | 3.18520i | 0.362676 | − | 0.106410i | ||||
\(897\) | −6.70993 | − | 8.13161i | −0.224038 | − | 0.271507i | ||||
\(898\) | −27.2249 | − | 19.9515i | −0.908506 | − | 0.665790i | ||||
\(899\) | −11.1687 | −0.372497 | ||||||||
\(900\) | −15.1287 | + | 25.9060i | −0.504290 | + | 0.863535i | ||||
\(901\) | −7.76712 | −0.258760 | ||||||||
\(902\) | −11.0898 | − | 8.12703i | −0.369249 | − | 0.270601i | ||||
\(903\) | −1.02993 | − | 1.24814i | −0.0342738 | − | 0.0415356i | ||||
\(904\) | −38.0187 | − | 12.8733i | −1.26448 | − | 0.428161i | ||||
\(905\) | 8.68759 | + | 17.3752i | 0.288785 | + | 0.577570i | ||||
\(906\) | 0.792778 | + | 13.7792i | 0.0263383 | + | 0.457784i | ||||
\(907\) | 25.4635 | 0.845502 | 0.422751 | − | 0.906246i | \(-0.361065\pi\) | ||||
0.422751 | + | 0.906246i | \(0.361065\pi\) | |||||||
\(908\) | 5.09565 | − | 1.60950i | 0.169105 | − | 0.0534130i | ||||
\(909\) | −43.8250 | − | 8.47379i | −1.45358 | − | 0.281058i | ||||
\(910\) | −1.00444 | + | 5.89456i | −0.0332969 | + | 0.195403i | ||||
\(911\) | 44.4395 | 1.47235 | 0.736174 | − | 0.676792i | \(-0.236631\pi\) | ||||
0.736174 | + | 0.676792i | \(0.236631\pi\) | |||||||
\(912\) | −15.7675 | + | 57.1910i | −0.522116 | + | 1.89378i | ||||
\(913\) | 15.0824i | 0.499156i | ||||||||
\(914\) | −32.4783 | − | 23.8014i | −1.07429 | − | 0.787279i | ||||
\(915\) | −19.5709 | + | 44.1504i | −0.646994 | + | 1.45957i | ||||
\(916\) | −10.7997 | − | 34.1918i | −0.356832 | − | 1.12973i | ||||
\(917\) | −4.52476 | −0.149421 | ||||||||
\(918\) | −1.11433 | + | 8.29565i | −0.0367783 | + | 0.273797i | ||||
\(919\) | − | 4.50906i | − | 0.148740i | −0.997231 | − | 0.0743701i | \(-0.976305\pi\) | ||
0.997231 | − | 0.0743701i | \(-0.0236946\pi\) | |||||||
\(920\) | 20.1675 | − | 2.78365i | 0.664903 | − | 0.0917742i | ||||
\(921\) | −23.9342 | − | 29.0053i | −0.788659 | − | 0.955757i | ||||
\(922\) | 26.5790 | + | 19.4782i | 0.875333 | + | 0.641479i | ||||
\(923\) | − | 15.1271i | − | 0.497916i | ||||||
\(924\) | 4.15327 | − | 6.40952i | 0.136633 | − | 0.210858i | ||||
\(925\) | 1.63808 | + | 1.22856i | 0.0538597 | + | 0.0403947i | ||||
\(926\) | −26.5454 | + | 36.2227i | −0.872337 | + | 1.19035i | ||||
\(927\) | −8.49766 | + | 43.9485i | −0.279100 | + | 1.44346i | ||||
\(928\) | 10.6942 | + | 0.219771i | 0.351056 | + | 0.00721432i | ||||
\(929\) | 10.7323i | 0.352114i | 0.984380 | + | 0.176057i | \(0.0563344\pi\) | ||||
−0.984380 | + | 0.176057i | \(0.943666\pi\) | |||||||
\(930\) | 28.0574 | − | 16.1063i | 0.920039 | − | 0.528147i | ||||
\(931\) | − | 8.56279i | − | 0.280634i | ||||||
\(932\) | −10.8266 | − | 34.2770i | −0.354638 | − | 1.12278i | ||||
\(933\) | 21.9687 | + | 26.6233i | 0.719222 | + | 0.871608i | ||||
\(934\) | −7.01203 | − | 5.13869i | −0.229441 | − | 0.168143i | ||||
\(935\) | 2.51130 | + | 5.02260i | 0.0821282 | + | 0.164256i | ||||
\(936\) | 13.9439 | + | 7.93729i | 0.455772 | + | 0.259438i | ||||
\(937\) | − | 33.6727i | − | 1.10004i | −0.835152 | − | 0.550019i | \(-0.814620\pi\) | ||
0.835152 | − | 0.550019i | \(-0.185380\pi\) | |||||||
\(938\) | −9.06796 | + | 12.3737i | −0.296079 | + | 0.404016i | ||||
\(939\) | 25.2870 | − | 20.8660i | 0.825211 | − | 0.680936i | ||||
\(940\) | −8.31464 | − | 8.58180i | −0.271194 | − | 0.279908i | ||||
\(941\) | 3.98534i | 0.129918i | 0.997888 | + | 0.0649592i | \(0.0206917\pi\) | ||||
−0.997888 | + | 0.0649592i | \(0.979308\pi\) | |||||||
\(942\) | 1.80360 | + | 31.3483i | 0.0587645 | + | 1.02138i | ||||
\(943\) | 14.1942 | 0.462227 | ||||||||
\(944\) | 44.3177 | − | 31.0987i | 1.44242 | − | 1.01218i | ||||
\(945\) | −9.53510 | − | 6.63942i | −0.310177 | − | 0.215980i | ||||
\(946\) | −1.72193 | + | 2.34967i | −0.0559848 | + | 0.0763943i | ||||
\(947\) | − | 2.78256i | − | 0.0904210i | −0.998977 | − | 0.0452105i | \(-0.985604\pi\) | ||
0.998977 | − | 0.0452105i | \(-0.0143959\pi\) | |||||||
\(948\) | 10.9485 | + | 7.09446i | 0.355591 | + | 0.230417i | ||||
\(949\) | 15.1271 | 0.491047 | ||||||||
\(950\) | 57.9348 | − | 17.5960i | 1.87965 | − | 0.570891i | ||||
\(951\) | 0.306538 | + | 0.371487i | 0.00994018 | + | 0.0120463i | ||||
\(952\) | −3.05149 | − | 1.03325i | −0.0988994 | − | 0.0334878i | ||||
\(953\) | 7.44678 | 0.241225 | 0.120612 | − | 0.992700i | \(-0.461514\pi\) | ||||
0.120612 | + | 0.992700i | \(0.461514\pi\) | |||||||
\(954\) | −19.6646 | − | 21.2201i | −0.636664 | − | 0.687026i | ||||
\(955\) | 11.7668 | + | 23.5335i | 0.380764 | + | 0.761528i | ||||
\(956\) | 14.8821 | + | 47.1166i | 0.481322 | + | 1.52386i | ||||
\(957\) | 5.56952 | − | 4.59578i | 0.180037 | − | 0.148560i | ||||
\(958\) | −6.97007 | + | 9.51104i | −0.225193 | + | 0.307288i | ||||
\(959\) | −16.4694 | −0.531824 | ||||||||
\(960\) | −27.1824 | + | 14.8700i | −0.877309 | + | 0.479927i | ||||
\(961\) | −3.88772 | −0.125410 | ||||||||
\(962\) | 0.647322 | − | 0.883306i | 0.0208705 | − | 0.0284789i | ||||
\(963\) | −1.09419 | − | 0.211568i | −0.0352599 | − | 0.00681769i | ||||
\(964\) | 0.792326 | + | 2.50849i | 0.0255191 | + | 0.0807932i | ||||
\(965\) | 36.1197 | − | 18.0599i | 1.16273 | − | 0.581367i | ||||
\(966\) | 0.452903 | + | 7.87187i | 0.0145719 | + | 0.253273i | ||||
\(967\) | 9.25547 | 0.297636 | 0.148818 | − | 0.988865i | \(-0.452453\pi\) | ||||
0.148818 | + | 0.988865i | \(0.452453\pi\) | |||||||
\(968\) | 16.4466 | + | 5.56889i | 0.528613 | + | 0.178991i | ||||
\(969\) | 13.0299 | − | 10.7519i | 0.418582 | − | 0.345399i | ||||
\(970\) | −9.82280 | + | 57.6450i | −0.315391 | + | 1.85087i | ||||
\(971\) | 30.9819 | 0.994256 | 0.497128 | − | 0.867677i | \(-0.334388\pi\) | ||||
0.497128 | + | 0.867677i | \(0.334388\pi\) | |||||||
\(972\) | −25.4853 | + | 17.9583i | −0.817441 | + | 0.576013i | ||||
\(973\) | − | 12.9723i | − | 0.415873i | ||||||
\(974\) | −16.4291 | + | 22.4184i | −0.526422 | + | 0.718332i | ||||
\(975\) | −0.759521 | − | 16.3580i | −0.0243241 | − | 0.523874i | ||||
\(976\) | −40.8282 | + | 28.6500i | −1.30688 | + | 0.917065i | ||||
\(977\) | −5.02551 | −0.160780 | −0.0803902 | − | 0.996763i | \(-0.525617\pi\) | ||||
−0.0803902 | + | 0.996763i | \(0.525617\pi\) | |||||||
\(978\) | 13.5358 | − | 0.778772i | 0.432826 | − | 0.0249024i | ||||
\(979\) | − | 35.6979i | − | 1.14091i | ||||||
\(980\) | 3.21188 | − | 3.11189i | 0.102600 | − | 0.0994056i | ||||
\(981\) | −1.62937 | + | 8.42682i | −0.0520218 | + | 0.269048i | ||||
\(982\) | 12.3394 | − | 16.8377i | 0.393765 | − | 0.537313i | ||||
\(983\) | − | 37.6974i | − | 1.20236i | −0.799113 | − | 0.601180i | \(-0.794697\pi\) | ||
0.799113 | − | 0.601180i | \(-0.205303\pi\) | |||||||
\(984\) | −20.1913 | + | 7.67880i | −0.643675 | + | 0.244791i | ||||
\(985\) | −16.0599 | − | 32.1197i | −0.511709 | − | 1.02342i | ||||
\(986\) | −2.45682 | − | 1.80046i | −0.0782412 | − | 0.0573383i | ||||
\(987\) | 3.56952 | − | 2.94545i | 0.113619 | − | 0.0937546i | ||||
\(988\) | −9.75331 | − | 30.8789i | −0.310294 | − | 0.982388i | ||||
\(989\) | − | 3.00743i | − | 0.0956306i | ||||||
\(990\) | −7.36390 | + | 19.5770i | −0.234040 | + | 0.622199i | ||||
\(991\) | 42.3475i | 1.34521i | 0.740001 | + | 0.672606i | \(0.234825\pi\) | ||||
−0.740001 | + | 0.672606i | \(0.765175\pi\) | |||||||
\(992\) | 33.4056 | + | 0.686498i | 1.06063 | + | 0.0217963i | ||||
\(993\) | −17.7399 | + | 14.6383i | −0.562957 | + | 0.464533i | ||||
\(994\) | −6.68759 | + | 9.12558i | −0.212117 | + | 0.289446i | ||||
\(995\) | −13.6817 | + | 6.84086i | −0.433740 | + | 0.216870i | ||||
\(996\) | 19.8873 | + | 12.8866i | 0.630152 | + | 0.408329i | ||||
\(997\) | 30.7850i | 0.974969i | 0.873132 | + | 0.487485i | \(0.162085\pi\) | ||||
−0.873132 | + | 0.487485i | \(0.837915\pi\) | |||||||
\(998\) | 19.2033 | + | 14.0730i | 0.607871 | + | 0.445472i | ||||
\(999\) | 1.01813 | + | 1.86855i | 0.0322121 | + | 0.0591183i |
(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 | 420.2.l.f.239.5 | yes | 8 | |
3.2 | odd | 2 | 420.2.l.e.239.4 | yes | 8 | ||
4.3 | odd | 2 | 420.2.l.d.239.6 | yes | 8 | ||
5.4 | even | 2 | 420.2.l.c.239.4 | yes | 8 | ||
12.11 | even | 2 | 420.2.l.c.239.3 | ✓ | 8 | ||
15.14 | odd | 2 | 420.2.l.d.239.5 | yes | 8 | ||
20.19 | odd | 2 | 420.2.l.e.239.3 | yes | 8 | ||
60.59 | even | 2 | inner | 420.2.l.f.239.6 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.l.c.239.3 | ✓ | 8 | 12.11 | even | 2 | ||
420.2.l.c.239.4 | yes | 8 | 5.4 | even | 2 | ||
420.2.l.d.239.5 | yes | 8 | 15.14 | odd | 2 | ||
420.2.l.d.239.6 | yes | 8 | 4.3 | odd | 2 | ||
420.2.l.e.239.3 | yes | 8 | 20.19 | odd | 2 | ||
420.2.l.e.239.4 | yes | 8 | 3.2 | odd | 2 | ||
420.2.l.f.239.5 | yes | 8 | 1.1 | even | 1 | trivial | |
420.2.l.f.239.6 | yes | 8 | 60.59 | even | 2 | inner |