Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(49,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, 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("1950.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.y (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 87 x^{10} - 380 x^{9} + 2556 x^{8} - 8010 x^{7} + 29687 x^{6} - 62556 x^{5} + \cdots + 14089 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(0.500000 + 4.99624i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.49 |
Dual form | 1950.2.y.n.199.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 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 | 0 | ||||||||
\(6\) | −0.866025 | − | 0.500000i | −0.353553 | − | 0.204124i | ||||
\(7\) | −2.56511 | + | 4.44290i | −0.969520 | + | 1.67926i | −0.272574 | + | 0.962135i | \(0.587875\pi\) |
−0.696947 | + | 0.717123i | \(0.745459\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.83209 | + | 2.78981i | −1.45693 | + | 0.841159i | −0.998859 | − | 0.0477570i | \(-0.984793\pi\) |
−0.458071 | + | 0.888916i | \(0.651459\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | 1.67900 | + | 3.19076i | 0.465670 | + | 0.884958i | ||||
\(14\) | −5.13022 | −1.37111 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.11081 | + | 0.641326i | 0.269411 | + | 0.155545i | 0.628620 | − | 0.777713i | \(-0.283620\pi\) |
−0.359209 | + | 0.933257i | \(0.616953\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −5.75861 | − | 3.32474i | −1.32112 | − | 0.762747i | −0.337210 | − | 0.941430i | \(-0.609483\pi\) |
−0.983907 | + | 0.178682i | \(0.942817\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 5.13022i | − | 1.11951i | ||||||
\(22\) | −4.83209 | − | 2.78981i | −1.03020 | − | 0.594789i | ||||
\(23\) | 5.94290 | − | 3.43113i | 1.23918 | − | 0.715441i | 0.270253 | − | 0.962789i | \(-0.412892\pi\) |
0.968927 | + | 0.247348i | \(0.0795592\pi\) | |||||||
\(24\) | 0.866025 | − | 0.500000i | 0.176777 | − | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.92378 | + | 3.04944i | −0.377285 | + | 0.598044i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −2.56511 | − | 4.44290i | −0.484760 | − | 0.839629i | ||||
\(29\) | 1.75214 | + | 3.03479i | 0.325364 | + | 0.563546i | 0.981586 | − | 0.191021i | \(-0.0611800\pi\) |
−0.656222 | + | 0.754568i | \(0.727847\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.30618i | 1.13262i | 0.824191 | + | 0.566312i | \(0.191630\pi\) | ||||
−0.824191 | + | 0.566312i | \(0.808370\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 2.78981 | − | 4.83209i | 0.485643 | − | 0.841159i | ||||
\(34\) | 1.28265i | 0.219973i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.500000 | + | 0.866025i | 0.0833333 | + | 0.144338i | ||||
\(37\) | −4.19076 | − | 7.25861i | −0.688957 | − | 1.19331i | −0.972176 | − | 0.234253i | \(-0.924735\pi\) |
0.283218 | − | 0.959055i | \(-0.408598\pi\) | |||||||
\(38\) | − | 6.64947i | − | 1.07869i | ||||||
\(39\) | −3.04944 | − | 1.92378i | −0.488301 | − | 0.308052i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.11081 | − | 0.641326i | 0.173479 | − | 0.100158i | −0.410746 | − | 0.911750i | \(-0.634732\pi\) |
0.584225 | + | 0.811591i | \(0.301398\pi\) | |||||||
\(42\) | 4.44290 | − | 2.56511i | 0.685554 | − | 0.395805i | ||||
\(43\) | 3.77414 | + | 2.17900i | 0.575550 | + | 0.332294i | 0.759363 | − | 0.650667i | \(-0.225511\pi\) |
−0.183813 | + | 0.982961i | \(0.558844\pi\) | |||||||
\(44\) | − | 5.57962i | − | 0.841159i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.94290 | + | 3.43113i | 0.876233 | + | 0.505893i | ||||
\(47\) | 5.02353 | 0.732757 | 0.366379 | − | 0.930466i | \(-0.380598\pi\) | ||||
0.366379 | + | 0.930466i | \(0.380598\pi\) | |||||||
\(48\) | 0.866025 | + | 0.500000i | 0.125000 | + | 0.0721688i | ||||
\(49\) | −9.65957 | − | 16.7309i | −1.37994 | − | 2.39012i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.28265 | −0.179607 | ||||||||
\(52\) | −3.60278 | − | 0.141326i | −0.499616 | − | 0.0195985i | ||||
\(53\) | 6.30618i | 0.866221i | 0.901341 | + | 0.433110i | \(0.142584\pi\) | ||||
−0.901341 | + | 0.433110i | \(0.857416\pi\) | |||||||
\(54\) | −0.866025 | + | 0.500000i | −0.117851 | + | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.56511 | − | 4.44290i | 0.342777 | − | 0.593707i | ||||
\(57\) | 6.64947 | 0.880744 | ||||||||
\(58\) | −1.75214 | + | 3.03479i | −0.230067 | + | 0.398487i | ||||
\(59\) | −1.31571 | − | 0.759628i | −0.171291 | − | 0.0988952i | 0.411903 | − | 0.911228i | \(-0.364864\pi\) |
−0.583195 | + | 0.812332i | \(0.698198\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.19076 | − | 8.99066i | 0.664609 | − | 1.15114i | −0.314782 | − | 0.949164i | \(-0.601931\pi\) |
0.979391 | − | 0.201973i | \(-0.0647352\pi\) | |||||||
\(62\) | −5.46131 | + | 3.15309i | −0.693588 | + | 0.400443i | ||||
\(63\) | 2.56511 | + | 4.44290i | 0.323173 | + | 0.559753i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.57962 | 0.686803 | ||||||||
\(67\) | −1.43555 | − | 2.48644i | −0.175380 | − | 0.303767i | 0.764913 | − | 0.644134i | \(-0.222782\pi\) |
−0.940293 | + | 0.340367i | \(0.889449\pi\) | |||||||
\(68\) | −1.11081 | + | 0.641326i | −0.134706 | + | 0.0777723i | ||||
\(69\) | −3.43113 | + | 5.94290i | −0.413060 | + | 0.715441i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.44775 | + | 5.45466i | 1.12124 | + | 0.647350i | 0.941718 | − | 0.336404i | \(-0.109211\pi\) |
0.179524 | + | 0.983754i | \(0.442544\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | 4.94644 | 0.578937 | 0.289468 | − | 0.957188i | \(-0.406522\pi\) | ||||
0.289468 | + | 0.957188i | \(0.406522\pi\) | |||||||
\(74\) | 4.19076 | − | 7.25861i | 0.487166 | − | 0.843797i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.75861 | − | 3.32474i | 0.660558 | − | 0.381374i | ||||
\(77\) | − | 28.6246i | − | 3.26208i | ||||||
\(78\) | 0.141326 | − | 3.60278i | 0.0160021 | − | 0.407935i | ||||
\(79\) | −10.1485 | −1.14179 | −0.570895 | − | 0.821023i | \(-0.693404\pi\) | ||||
−0.570895 | + | 0.821023i | \(0.693404\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 1.11081 | + | 0.641326i | 0.122668 | + | 0.0708227i | ||||
\(83\) | −17.3887 | −1.90866 | −0.954330 | − | 0.298755i | \(-0.903429\pi\) | ||||
−0.954330 | + | 0.298755i | \(0.903429\pi\) | |||||||
\(84\) | 4.44290 | + | 2.56511i | 0.484760 | + | 0.279876i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.35800i | 0.469935i | ||||||||
\(87\) | −3.03479 | − | 1.75214i | −0.325364 | − | 0.187849i | ||||
\(88\) | 4.83209 | − | 2.78981i | 0.515102 | − | 0.297395i | ||||
\(89\) | −5.57884 | + | 3.22094i | −0.591355 | + | 0.341419i | −0.765633 | − | 0.643277i | \(-0.777574\pi\) |
0.174278 | + | 0.984697i | \(0.444241\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −18.4830 | − | 0.725036i | −1.93755 | − | 0.0760044i | ||||
\(92\) | 6.86227i | 0.715441i | ||||||||
\(93\) | −3.15309 | − | 5.46131i | −0.326960 | − | 0.566312i | ||||
\(94\) | 2.51176 | + | 4.35050i | 0.259069 | + | 0.448720i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | −3.58423 | + | 6.20806i | −0.363923 | + | 0.630333i | −0.988603 | − | 0.150548i | \(-0.951896\pi\) |
0.624680 | + | 0.780881i | \(0.285230\pi\) | |||||||
\(98\) | 9.65957 | − | 16.7309i | 0.975764 | − | 1.69007i | ||||
\(99\) | 5.57962i | 0.560772i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.33175 | − | 12.6990i | −0.729537 | − | 1.26359i | −0.957079 | − | 0.289826i | \(-0.906402\pi\) |
0.227543 | − | 0.973768i | \(-0.426931\pi\) | |||||||
\(102\) | −0.641326 | − | 1.11081i | −0.0635008 | − | 0.109987i | ||||
\(103\) | 4.04929i | 0.398989i | 0.979899 | + | 0.199494i | \(0.0639299\pi\) | ||||
−0.979899 | + | 0.199494i | \(0.936070\pi\) | |||||||
\(104\) | −1.67900 | − | 3.19076i | −0.164639 | − | 0.312880i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.46131 | + | 3.15309i | −0.530450 | + | 0.306255i | ||||
\(107\) | −6.72112 | + | 3.88044i | −0.649755 | + | 0.375136i | −0.788362 | − | 0.615211i | \(-0.789071\pi\) |
0.138608 | + | 0.990347i | \(0.455737\pi\) | |||||||
\(108\) | −0.866025 | − | 0.500000i | −0.0833333 | − | 0.0481125i | ||||
\(109\) | − | 0.792690i | − | 0.0759259i | −0.999279 | − | 0.0379630i | \(-0.987913\pi\) | ||
0.999279 | − | 0.0379630i | \(-0.0120869\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.25861 | + | 4.19076i | 0.688957 | + | 0.397770i | ||||
\(112\) | 5.13022 | 0.484760 | ||||||||
\(113\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(114\) | 3.32474 | + | 5.75861i | 0.311390 | + | 0.539344i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.50427 | −0.325364 | ||||||||
\(117\) | 3.60278 | + | 0.141326i | 0.333077 | + | 0.0130656i | ||||
\(118\) | − | 1.51926i | − | 0.139859i | ||||||
\(119\) | −5.69870 | + | 3.29014i | −0.522399 | + | 0.301607i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.0661 | − | 17.4349i | 0.915096 | − | 1.58499i | ||||
\(122\) | 10.3815 | 0.939899 | ||||||||
\(123\) | −0.641326 | + | 1.11081i | −0.0578265 | + | 0.100158i | ||||
\(124\) | −5.46131 | − | 3.15309i | −0.490440 | − | 0.283156i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.56511 | + | 4.44290i | −0.228518 | + | 0.395805i | ||||
\(127\) | 14.0755 | − | 8.12651i | 1.24900 | − | 0.721111i | 0.278090 | − | 0.960555i | \(-0.410298\pi\) |
0.970910 | + | 0.239444i | \(0.0769652\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −4.35800 | −0.383700 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.04605 | 0.615616 | 0.307808 | − | 0.951448i | \(-0.400405\pi\) | ||||
0.307808 | + | 0.951448i | \(0.400405\pi\) | |||||||
\(132\) | 2.78981 | + | 4.83209i | 0.242822 | + | 0.420579i | ||||
\(133\) | 29.5429 | − | 17.0566i | 2.56170 | − | 1.47900i | ||||
\(134\) | 1.43555 | − | 2.48644i | 0.124012 | − | 0.214796i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.11081 | − | 0.641326i | −0.0952512 | − | 0.0549933i | ||||
\(137\) | 0.444016 | − | 0.769058i | 0.0379348 | − | 0.0657051i | −0.846435 | − | 0.532493i | \(-0.821255\pi\) |
0.884369 | + | 0.466788i | \(0.154589\pi\) | |||||||
\(138\) | −6.86227 | −0.584155 | ||||||||
\(139\) | 0.266279 | − | 0.461208i | 0.0225854 | − | 0.0391191i | −0.854512 | − | 0.519432i | \(-0.826144\pi\) |
0.877097 | + | 0.480313i | \(0.159477\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.35050 | + | 2.51176i | −0.366379 | + | 0.211529i | ||||
\(142\) | 10.9093i | 0.915490i | ||||||||
\(143\) | −17.0147 | − | 10.7340i | −1.42284 | − | 0.897619i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.47322 | + | 4.28374i | 0.204685 | + | 0.354525i | ||||
\(147\) | 16.7309 | + | 9.65957i | 1.37994 | + | 0.796708i | ||||
\(148\) | 8.38153 | 0.688957 | ||||||||
\(149\) | −18.0113 | − | 10.3988i | −1.47554 | − | 0.851905i | −0.475923 | − | 0.879487i | \(-0.657886\pi\) |
−0.999620 | + | 0.0275822i | \(0.991219\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.15400i | 0.175290i | 0.996152 | + | 0.0876448i | \(0.0279341\pi\) | ||||
−0.996152 | + | 0.0876448i | \(0.972066\pi\) | |||||||
\(152\) | 5.75861 | + | 3.32474i | 0.467085 | + | 0.269672i | ||||
\(153\) | 1.11081 | − | 0.641326i | 0.0898037 | − | 0.0518482i | ||||
\(154\) | 24.7897 | − | 14.3123i | 1.99761 | − | 1.15332i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.19076 | − | 1.67900i | 0.255465 | − | 0.134427i | ||||
\(157\) | 7.70236i | 0.614716i | 0.951594 | + | 0.307358i | \(0.0994448\pi\) | ||||
−0.951594 | + | 0.307358i | \(0.900555\pi\) | |||||||
\(158\) | −5.07423 | − | 8.78882i | −0.403684 | − | 0.699201i | ||||
\(159\) | −3.15309 | − | 5.46131i | −0.250056 | − | 0.433110i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 35.2049i | 2.77454i | ||||||||
\(162\) | 0.500000 | − | 0.866025i | 0.0392837 | − | 0.0680414i | ||||
\(163\) | −0.220942 | + | 0.382683i | −0.0173055 | + | 0.0299741i | −0.874548 | − | 0.484938i | \(-0.838842\pi\) |
0.857243 | + | 0.514912i | \(0.172175\pi\) | |||||||
\(164\) | 1.28265i | 0.100158i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.69436 | − | 15.0591i | −0.674813 | − | 1.16881i | ||||
\(167\) | −3.43113 | − | 5.94290i | −0.265509 | − | 0.459875i | 0.702188 | − | 0.711992i | \(-0.252207\pi\) |
−0.967697 | + | 0.252116i | \(0.918873\pi\) | |||||||
\(168\) | 5.13022i | 0.395805i | ||||||||
\(169\) | −7.36193 | + | 10.7146i | −0.566302 | + | 0.824197i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.75861 | + | 3.32474i | −0.440372 | + | 0.254249i | ||||
\(172\) | −3.77414 | + | 2.17900i | −0.287775 | + | 0.166147i | ||||
\(173\) | 19.3036 | + | 11.1449i | 1.46762 | + | 0.847333i | 0.999343 | − | 0.0362472i | \(-0.0115404\pi\) |
0.468280 | + | 0.883580i | \(0.344874\pi\) | |||||||
\(174\) | − | 3.50427i | − | 0.265658i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.83209 | + | 2.78981i | 0.364232 | + | 0.210290i | ||||
\(177\) | 1.51926 | 0.114194 | ||||||||
\(178\) | −5.57884 | − | 3.22094i | −0.418151 | − | 0.241420i | ||||
\(179\) | −0.784447 | − | 1.35870i | −0.0586324 | − | 0.101554i | 0.835219 | − | 0.549917i | \(-0.185341\pi\) |
−0.893852 | + | 0.448363i | \(0.852007\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.4419 | 0.850469 | 0.425234 | − | 0.905083i | \(-0.360192\pi\) | ||||
0.425234 | + | 0.905083i | \(0.360192\pi\) | |||||||
\(182\) | −8.61363 | − | 16.3693i | −0.638484 | − | 1.21337i | ||||
\(183\) | 10.3815i | 0.767424i | ||||||||
\(184\) | −5.94290 | + | 3.43113i | −0.438116 | + | 0.252947i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.15309 | − | 5.46131i | 0.231196 | − | 0.400443i | ||||
\(187\) | −7.15671 | −0.523351 | ||||||||
\(188\) | −2.51176 | + | 4.35050i | −0.183189 | + | 0.317293i | ||||
\(189\) | −4.44290 | − | 2.56511i | −0.323173 | − | 0.186584i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.41092 | + | 7.63995i | −0.319163 | + | 0.552807i | −0.980314 | − | 0.197446i | \(-0.936735\pi\) |
0.661150 | + | 0.750253i | \(0.270069\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | −5.59403 | − | 9.68914i | −0.402667 | − | 0.697440i | 0.591380 | − | 0.806393i | \(-0.298583\pi\) |
−0.994047 | + | 0.108953i | \(0.965250\pi\) | |||||||
\(194\) | −7.16845 | −0.514665 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 19.3191 | 1.37994 | ||||||||
\(197\) | 11.4675 | + | 19.8624i | 0.817029 | + | 1.41514i | 0.907862 | + | 0.419269i | \(0.137714\pi\) |
−0.0908332 | + | 0.995866i | \(0.528953\pi\) | |||||||
\(198\) | −4.83209 | + | 2.78981i | −0.343402 | + | 0.198263i | ||||
\(199\) | −5.52892 | + | 9.57637i | −0.391935 | + | 0.678851i | −0.992705 | − | 0.120571i | \(-0.961527\pi\) |
0.600770 | + | 0.799422i | \(0.294861\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.48644 | + | 1.43555i | 0.175380 | + | 0.101256i | ||||
\(202\) | 7.33175 | − | 12.6990i | 0.515860 | − | 0.893496i | ||||
\(203\) | −17.9777 | −1.26179 | ||||||||
\(204\) | 0.641326 | − | 1.11081i | 0.0449018 | − | 0.0777723i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.50679 | + | 2.02465i | −0.244330 | + | 0.141064i | ||||
\(207\) | − | 6.86227i | − | 0.476961i | ||||||
\(208\) | 1.92378 | − | 3.04944i | 0.133390 | − | 0.211440i | ||||
\(209\) | 37.1015 | 2.56637 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.4171 | − | 23.2391i | −0.923671 | − | 1.59984i | −0.793685 | − | 0.608329i | \(-0.791840\pi\) |
−0.129986 | − | 0.991516i | \(-0.541493\pi\) | |||||||
\(212\) | −5.46131 | − | 3.15309i | −0.375085 | − | 0.216555i | ||||
\(213\) | −10.9093 | −0.747495 | ||||||||
\(214\) | −6.72112 | − | 3.88044i | −0.459446 | − | 0.265261i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −28.0177 | − | 16.1760i | −1.90197 | − | 1.09810i | ||||
\(218\) | 0.686490 | − | 0.396345i | 0.0464949 | − | 0.0268439i | ||||
\(219\) | −4.28374 | + | 2.47322i | −0.289468 | + | 0.167125i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.181273 | + | 4.62112i | −0.0121937 | + | 0.310850i | ||||
\(222\) | 8.38153i | 0.562531i | ||||||||
\(223\) | 0.0345926 | + | 0.0599161i | 0.00231649 | + | 0.00401228i | 0.867181 | − | 0.497993i | \(-0.165929\pi\) |
−0.864865 | + | 0.502005i | \(0.832596\pi\) | |||||||
\(224\) | 2.56511 | + | 4.44290i | 0.171389 | + | 0.296854i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.09599 | + | 5.36241i | −0.205488 | + | 0.355916i | −0.950288 | − | 0.311372i | \(-0.899212\pi\) |
0.744800 | + | 0.667288i | \(0.232545\pi\) | |||||||
\(228\) | −3.32474 | + | 5.75861i | −0.220186 | + | 0.381374i | ||||
\(229\) | − | 17.3857i | − | 1.14888i | −0.818548 | − | 0.574438i | \(-0.805221\pi\) | ||
0.818548 | − | 0.574438i | \(-0.194779\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.3123 | + | 24.7897i | 0.941682 | + | 1.63104i | ||||
\(232\) | −1.75214 | − | 3.03479i | −0.115033 | − | 0.199244i | ||||
\(233\) | 17.7716i | 1.16426i | 0.813097 | + | 0.582128i | \(0.197780\pi\) | ||||
−0.813097 | + | 0.582128i | \(0.802220\pi\) | |||||||
\(234\) | 1.67900 | + | 3.19076i | 0.109760 | + | 0.208587i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.31571 | − | 0.759628i | 0.0856457 | − | 0.0494476i | ||||
\(237\) | 8.78882 | − | 5.07423i | 0.570895 | − | 0.329606i | ||||
\(238\) | −5.69870 | − | 3.29014i | −0.369392 | − | 0.213268i | ||||
\(239\) | 17.1487i | 1.10925i | 0.832099 | + | 0.554627i | \(0.187139\pi\) | ||||
−0.832099 | + | 0.554627i | \(0.812861\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.1831 | − | 8.76597i | −0.978029 | − | 0.564665i | −0.0763547 | − | 0.997081i | \(-0.524328\pi\) |
−0.901675 | + | 0.432415i | \(0.857661\pi\) | |||||||
\(242\) | 20.1321 | 1.29414 | ||||||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 5.19076 | + | 8.99066i | 0.332305 | + | 0.575568i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.28265 | −0.0817790 | ||||||||
\(247\) | 0.939747 | − | 23.9566i | 0.0597947 | − | 1.52432i | ||||
\(248\) | − | 6.30618i | − | 0.400443i | ||||||
\(249\) | 15.0591 | − | 8.69436i | 0.954330 | − | 0.550983i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.10358 | + | 15.7679i | −0.574613 | + | 0.995259i | 0.421470 | + | 0.906842i | \(0.361514\pi\) |
−0.996084 | + | 0.0884170i | \(0.971819\pi\) | |||||||
\(252\) | −5.13022 | −0.323173 | ||||||||
\(253\) | −19.1444 | + | 33.1591i | −1.20360 | + | 2.08469i | ||||
\(254\) | 14.0755 | + | 8.12651i | 0.883177 | + | 0.509902i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 15.2430 | − | 8.80056i | 0.950833 | − | 0.548964i | 0.0574935 | − | 0.998346i | \(-0.481689\pi\) |
0.893340 | + | 0.449382i | \(0.148356\pi\) | |||||||
\(258\) | −2.17900 | − | 3.77414i | −0.135658 | − | 0.234967i | ||||
\(259\) | 42.9991 | 2.67183 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.50427 | 0.216909 | ||||||||
\(262\) | 3.52302 | + | 6.10206i | 0.217653 | + | 0.376986i | ||||
\(263\) | −10.1853 | + | 5.88051i | −0.628055 | + | 0.362608i | −0.779999 | − | 0.625781i | \(-0.784780\pi\) |
0.151943 | + | 0.988389i | \(0.451447\pi\) | |||||||
\(264\) | −2.78981 | + | 4.83209i | −0.171701 | + | 0.297395i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 29.5429 | + | 17.0566i | 1.81139 | + | 1.04581i | ||||
\(267\) | 3.22094 | − | 5.57884i | 0.197118 | − | 0.341419i | ||||
\(268\) | 2.87109 | 0.175380 | ||||||||
\(269\) | −3.20490 | + | 5.55106i | −0.195406 | + | 0.338454i | −0.947034 | − | 0.321134i | \(-0.895936\pi\) |
0.751627 | + | 0.659588i | \(0.229269\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.6919 | − | 7.90503i | 0.831725 | − | 0.480196i | −0.0227182 | − | 0.999742i | \(-0.507232\pi\) |
0.854443 | + | 0.519545i | \(0.173899\pi\) | |||||||
\(272\) | − | 1.28265i | − | 0.0777723i | ||||||
\(273\) | 16.3693 | − | 8.61363i | 0.990716 | − | 0.521320i | ||||
\(274\) | 0.888032 | 0.0536480 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.43113 | − | 5.94290i | −0.206530 | − | 0.357720i | ||||
\(277\) | 4.31832 | + | 2.49319i | 0.259463 | + | 0.149801i | 0.624090 | − | 0.781353i | \(-0.285470\pi\) |
−0.364627 | + | 0.931154i | \(0.618803\pi\) | |||||||
\(278\) | 0.532557 | 0.0319406 | ||||||||
\(279\) | 5.46131 | + | 3.15309i | 0.326960 | + | 0.188771i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.515726i | 0.0307656i | 0.999882 | + | 0.0153828i | \(0.00489670\pi\) | ||||
−0.999882 | + | 0.0153828i | \(0.995103\pi\) | |||||||
\(282\) | −4.35050 | − | 2.51176i | −0.259069 | − | 0.149573i | ||||
\(283\) | −15.5418 | + | 8.97308i | −0.923866 | + | 0.533394i | −0.884866 | − | 0.465845i | \(-0.845750\pi\) |
−0.0389995 | + | 0.999239i | \(0.512417\pi\) | |||||||
\(284\) | −9.44775 | + | 5.45466i | −0.560621 | + | 0.323675i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.788547 | − | 20.1021i | 0.0466278 | − | 1.18866i | ||||
\(287\) | 6.58029i | 0.388422i | ||||||||
\(288\) | −0.500000 | − | 0.866025i | −0.0294628 | − | 0.0510310i | ||||
\(289\) | −7.67740 | − | 13.2976i | −0.451612 | − | 0.782215i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 7.16845i | − | 0.420222i | ||||||
\(292\) | −2.47322 | + | 4.28374i | −0.144734 | + | 0.250687i | ||||
\(293\) | −8.63553 | + | 14.9572i | −0.504493 | + | 0.873808i | 0.495493 | + | 0.868612i | \(0.334987\pi\) |
−0.999987 | + | 0.00519587i | \(0.998346\pi\) | |||||||
\(294\) | 19.3191i | 1.12671i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.19076 | + | 7.25861i | 0.243583 | + | 0.421898i | ||||
\(297\) | −2.78981 | − | 4.83209i | −0.161881 | − | 0.280386i | ||||
\(298\) | − | 20.7976i | − | 1.20478i | ||||||
\(299\) | 20.9261 | + | 13.2015i | 1.21018 | + | 0.763463i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −19.3621 | + | 11.1787i | −1.11601 | + | 0.644332i | ||||
\(302\) | −1.86541 | + | 1.07700i | −0.107343 | + | 0.0619742i | ||||
\(303\) | 12.6990 | + | 7.33175i | 0.729537 | + | 0.421198i | ||||
\(304\) | 6.64947i | 0.381374i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.11081 | + | 0.641326i | 0.0635008 | + | 0.0366622i | ||||
\(307\) | −14.2673 | −0.814279 | −0.407140 | − | 0.913366i | \(-0.633474\pi\) | ||||
−0.407140 | + | 0.913366i | \(0.633474\pi\) | |||||||
\(308\) | 24.7897 | + | 14.3123i | 1.41252 | + | 0.815520i | ||||
\(309\) | −2.02465 | − | 3.50679i | −0.115178 | − | 0.199494i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.1487 | −1.31264 | −0.656320 | − | 0.754483i | \(-0.727888\pi\) | ||||
−0.656320 | + | 0.754483i | \(0.727888\pi\) | |||||||
\(312\) | 3.04944 | + | 1.92378i | 0.172640 | + | 0.108913i | ||||
\(313\) | 14.1122i | 0.797667i | 0.917023 | + | 0.398834i | \(0.130585\pi\) | ||||
−0.917023 | + | 0.398834i | \(0.869415\pi\) | |||||||
\(314\) | −6.67044 | + | 3.85118i | −0.376435 | + | 0.217335i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.07423 | − | 8.78882i | 0.285448 | − | 0.494410i | ||||
\(317\) | −12.1814 | −0.684176 | −0.342088 | − | 0.939668i | \(-0.611134\pi\) | ||||
−0.342088 | + | 0.939668i | \(0.611134\pi\) | |||||||
\(318\) | 3.15309 | − | 5.46131i | 0.176817 | − | 0.306255i | ||||
\(319\) | −16.9330 | − | 9.77625i | −0.948064 | − | 0.547365i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.88044 | − | 6.72112i | 0.216585 | − | 0.375136i | ||||
\(322\) | −30.4884 | + | 17.6025i | −1.69905 | + | 0.980947i | ||||
\(323\) | −4.26448 | − | 7.38630i | −0.237282 | − | 0.410985i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.441885 | −0.0244737 | ||||||||
\(327\) | 0.396345 | + | 0.686490i | 0.0219179 | + | 0.0379630i | ||||
\(328\) | −1.11081 | + | 0.641326i | −0.0613342 | + | 0.0354113i | ||||
\(329\) | −12.8859 | + | 22.3190i | −0.710423 | + | 1.23049i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.86463 | + | 2.23125i | 0.212419 | + | 0.122640i | 0.602435 | − | 0.798168i | \(-0.294197\pi\) |
−0.390016 | + | 0.920808i | \(0.627530\pi\) | |||||||
\(332\) | 8.69436 | − | 15.0591i | 0.477165 | − | 0.826474i | ||||
\(333\) | −8.38153 | −0.459305 | ||||||||
\(334\) | 3.43113 | − | 5.94290i | 0.187743 | − | 0.325181i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.44290 | + | 2.56511i | −0.242380 | + | 0.139938i | ||||
\(337\) | − | 6.04773i | − | 0.329441i | −0.986340 | − | 0.164720i | \(-0.947328\pi\) | ||
0.986340 | − | 0.164720i | \(-0.0526722\pi\) | |||||||
\(338\) | −12.9601 | − | 1.01834i | −0.704934 | − | 0.0553902i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.5930 | − | 30.4720i | −0.952716 | − | 1.65015i | ||||
\(342\) | −5.75861 | − | 3.32474i | −0.311390 | − | 0.179781i | ||||
\(343\) | 63.1999 | 3.41247 | ||||||||
\(344\) | −3.77414 | − | 2.17900i | −0.203488 | − | 0.117484i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 22.2898i | 1.19831i | ||||||||
\(347\) | 5.49627 | + | 3.17327i | 0.295055 | + | 0.170350i | 0.640219 | − | 0.768192i | \(-0.278843\pi\) |
−0.345164 | + | 0.938542i | \(0.612177\pi\) | |||||||
\(348\) | 3.03479 | − | 1.75214i | 0.162682 | − | 0.0939244i | ||||
\(349\) | 24.4438 | − | 14.1126i | 1.30844 | − | 0.755431i | 0.326608 | − | 0.945160i | \(-0.394094\pi\) |
0.981836 | + | 0.189729i | \(0.0607611\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.19076 | + | 1.67900i | −0.170310 | + | 0.0896183i | ||||
\(352\) | 5.57962i | 0.297395i | ||||||||
\(353\) | 8.04696 | + | 13.9378i | 0.428297 | + | 0.741832i | 0.996722 | − | 0.0809033i | \(-0.0257805\pi\) |
−0.568425 | + | 0.822735i | \(0.692447\pi\) | |||||||
\(354\) | 0.759628 | + | 1.31571i | 0.0403738 | + | 0.0699294i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 6.44188i | − | 0.341419i | ||||||
\(357\) | 3.29014 | − | 5.69870i | 0.174133 | − | 0.301607i | ||||
\(358\) | 0.784447 | − | 1.35870i | 0.0414593 | − | 0.0718097i | ||||
\(359\) | 8.79689i | 0.464282i | 0.972682 | + | 0.232141i | \(0.0745731\pi\) | ||||
−0.972682 | + | 0.232141i | \(0.925427\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.6078 | + | 21.8373i | 0.663566 | + | 1.14933i | ||||
\(362\) | 5.72094 | + | 9.90896i | 0.300686 | + | 0.520804i | ||||
\(363\) | 20.1321i | 1.05666i | ||||||||
\(364\) | 9.86942 | − | 15.6443i | 0.517298 | − | 0.819983i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −8.99066 | + | 5.19076i | −0.469950 | + | 0.271326i | ||||
\(367\) | −32.9145 | + | 19.0032i | −1.71812 | + | 0.991958i | −0.795779 | + | 0.605588i | \(0.792938\pi\) |
−0.922344 | + | 0.386371i | \(0.873729\pi\) | |||||||
\(368\) | −5.94290 | − | 3.43113i | −0.309795 | − | 0.178860i | ||||
\(369\) | − | 1.28265i | − | 0.0667722i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −28.0177 | − | 16.1760i | −1.45461 | − | 0.839818i | ||||
\(372\) | 6.30618 | 0.326960 | ||||||||
\(373\) | −14.7361 | − | 8.50787i | −0.763004 | − | 0.440521i | 0.0673691 | − | 0.997728i | \(-0.478540\pi\) |
−0.830373 | + | 0.557207i | \(0.811873\pi\) | |||||||
\(374\) | −3.57836 | − | 6.19789i | −0.185032 | − | 0.320485i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.02353 | −0.259069 | ||||||||
\(377\) | −6.74146 | + | 10.6861i | −0.347203 | + | 0.550360i | ||||
\(378\) | − | 5.13022i | − | 0.263870i | ||||||
\(379\) | −11.0257 | + | 6.36569i | −0.566352 | + | 0.326983i | −0.755691 | − | 0.654928i | \(-0.772699\pi\) |
0.189339 | + | 0.981912i | \(0.439365\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.12651 | + | 14.0755i | −0.416334 | + | 0.721111i | ||||
\(382\) | −8.82185 | −0.451365 | ||||||||
\(383\) | 11.2859 | − | 19.5478i | 0.576683 | − | 0.998845i | −0.419173 | − | 0.907906i | \(-0.637680\pi\) |
0.995857 | − | 0.0909383i | \(-0.0289866\pi\) | |||||||
\(384\) | −0.866025 | − | 0.500000i | −0.0441942 | − | 0.0255155i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.59403 | − | 9.68914i | 0.284729 | − | 0.493164i | ||||
\(387\) | 3.77414 | − | 2.17900i | 0.191850 | − | 0.110765i | ||||
\(388\) | −3.58423 | − | 6.20806i | −0.181961 | − | 0.315167i | ||||
\(389\) | −3.50427 | −0.177674 | −0.0888368 | − | 0.996046i | \(-0.528315\pi\) | ||||
−0.0888368 | + | 0.996046i | \(0.528315\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.80191 | 0.445132 | ||||||||
\(392\) | 9.65957 | + | 16.7309i | 0.487882 | + | 0.845036i | ||||
\(393\) | −6.10206 | + | 3.52302i | −0.307808 | + | 0.177713i | ||||
\(394\) | −11.4675 | + | 19.8624i | −0.577727 | + | 1.00065i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −4.83209 | − | 2.78981i | −0.242822 | − | 0.140193i | ||||
\(397\) | −14.9326 | + | 25.8640i | −0.749445 | + | 1.29808i | 0.198644 | + | 0.980072i | \(0.436346\pi\) |
−0.948089 | + | 0.318005i | \(0.896987\pi\) | |||||||
\(398\) | −11.0578 | −0.554279 | ||||||||
\(399\) | −17.0566 | + | 29.5429i | −0.853899 | + | 1.47900i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −21.7592 | + | 12.5627i | −1.08660 | + | 0.627351i | −0.932670 | − | 0.360730i | \(-0.882528\pi\) |
−0.153934 | + | 0.988081i | \(0.549194\pi\) | |||||||
\(402\) | 2.87109i | 0.143197i | ||||||||
\(403\) | −20.1215 | + | 10.5881i | −1.00232 | + | 0.527429i | ||||
\(404\) | 14.6635 | 0.729537 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.98884 | − | 15.5691i | −0.446109 | − | 0.772683i | ||||
\(407\) | 40.5003 | + | 23.3828i | 2.00752 | + | 1.15904i | ||||
\(408\) | 1.28265 | 0.0635008 | ||||||||
\(409\) | −4.54462 | − | 2.62384i | −0.224717 | − | 0.129740i | 0.383416 | − | 0.923576i | \(-0.374748\pi\) |
−0.608132 | + | 0.793836i | \(0.708081\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.888032i | 0.0438034i | ||||||||
\(412\) | −3.50679 | − | 2.02465i | −0.172767 | − | 0.0997472i | ||||
\(413\) | 6.74990 | − | 3.89706i | 0.332141 | − | 0.191762i | ||||
\(414\) | 5.94290 | − | 3.43113i | 0.292078 | − | 0.168631i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.60278 | + | 0.141326i | 0.176641 | + | 0.00692910i | ||||
\(417\) | 0.532557i | 0.0260794i | ||||||||
\(418\) | 18.5508 | + | 32.1309i | 0.907347 | + | 1.57157i | ||||
\(419\) | −9.01326 | − | 15.6114i | −0.440326 | − | 0.762668i | 0.557387 | − | 0.830253i | \(-0.311804\pi\) |
−0.997714 | + | 0.0675850i | \(0.978471\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.92370i | 0.386178i | 0.981181 | + | 0.193089i | \(0.0618506\pi\) | ||||
−0.981181 | + | 0.193089i | \(0.938149\pi\) | |||||||
\(422\) | 13.4171 | − | 23.2391i | 0.653134 | − | 1.13126i | ||||
\(423\) | 2.51176 | − | 4.35050i | 0.122126 | − | 0.211529i | ||||
\(424\) | − | 6.30618i | − | 0.306255i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.45466 | − | 9.44775i | −0.264279 | − | 0.457745i | ||||
\(427\) | 26.6297 | + | 46.1241i | 1.28870 | + | 2.23210i | ||||
\(428\) | − | 7.76088i | − | 0.375136i | ||||||
\(429\) | 20.1021 | + | 0.788547i | 0.970540 | + | 0.0380714i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.1752 | − | 19.1537i | 1.59800 | − | 0.922603i | 0.606122 | − | 0.795372i | \(-0.292724\pi\) |
0.991873 | − | 0.127231i | \(-0.0406090\pi\) | |||||||
\(432\) | 0.866025 | − | 0.500000i | 0.0416667 | − | 0.0240563i | ||||
\(433\) | −17.3250 | − | 10.0026i | −0.832585 | − | 0.480693i | 0.0221517 | − | 0.999755i | \(-0.492948\pi\) |
−0.854737 | + | 0.519061i | \(0.826282\pi\) | |||||||
\(434\) | − | 32.3521i | − | 1.55295i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.686490 | + | 0.396345i | 0.0328769 | + | 0.0189815i | ||||
\(437\) | −45.6305 | −2.18280 | ||||||||
\(438\) | −4.28374 | − | 2.47322i | −0.204685 | − | 0.118175i | ||||
\(439\) | −5.96660 | − | 10.3345i | −0.284770 | − | 0.493237i | 0.687783 | − | 0.725916i | \(-0.258584\pi\) |
−0.972553 | + | 0.232680i | \(0.925251\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.3191 | −0.919959 | ||||||||
\(442\) | −4.09264 | + | 2.15357i | −0.194667 | + | 0.102435i | ||||
\(443\) | 26.0565i | 1.23798i | 0.785399 | + | 0.618990i | \(0.212458\pi\) | ||||
−0.785399 | + | 0.618990i | \(0.787542\pi\) | |||||||
\(444\) | −7.25861 | + | 4.19076i | −0.344479 | + | 0.198885i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.0345926 | + | 0.0599161i | −0.00163801 | + | 0.00283711i | ||||
\(447\) | 20.7976 | 0.983695 | ||||||||
\(448\) | −2.56511 | + | 4.44290i | −0.121190 | + | 0.209907i | ||||
\(449\) | 14.4966 | + | 8.36959i | 0.684135 | + | 0.394985i | 0.801411 | − | 0.598114i | \(-0.204083\pi\) |
−0.117276 | + | 0.993099i | \(0.537416\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.57836 | + | 6.19789i | −0.168498 | + | 0.291847i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.07700 | − | 1.86541i | −0.0506018 | − | 0.0876448i | ||||
\(454\) | −6.19198 | −0.290604 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.64947 | −0.311390 | ||||||||
\(457\) | −3.55432 | − | 6.15626i | −0.166264 | − | 0.287977i | 0.770840 | − | 0.637029i | \(-0.219837\pi\) |
−0.937103 | + | 0.349052i | \(0.886504\pi\) | |||||||
\(458\) | 15.0564 | − | 8.69283i | 0.703540 | − | 0.406189i | ||||
\(459\) | −0.641326 | + | 1.11081i | −0.0299346 | + | 0.0518482i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.77730 | − | 2.75817i | −0.222501 | − | 0.128461i | 0.384607 | − | 0.923081i | \(-0.374337\pi\) |
−0.607108 | + | 0.794620i | \(0.707670\pi\) | |||||||
\(462\) | −14.3123 | + | 24.7897i | −0.665870 | + | 1.15332i | ||||
\(463\) | 4.98759 | 0.231793 | 0.115896 | − | 0.993261i | \(-0.463026\pi\) | ||||
0.115896 | + | 0.993261i | \(0.463026\pi\) | |||||||
\(464\) | 1.75214 | − | 3.03479i | 0.0813409 | − | 0.140887i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15.3907 | + | 8.88580i | −0.712958 | + | 0.411627i | ||||
\(467\) | 19.7410i | 0.913506i | 0.889594 | + | 0.456753i | \(0.150988\pi\) | ||||
−0.889594 | + | 0.456753i | \(0.849012\pi\) | |||||||
\(468\) | −1.92378 | + | 3.04944i | −0.0889269 | + | 0.140960i | ||||
\(469\) | 14.7293 | 0.680138 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.85118 | − | 6.67044i | −0.177453 | − | 0.307358i | ||||
\(472\) | 1.31571 | + | 0.759628i | 0.0605607 | + | 0.0349647i | ||||
\(473\) | −24.3159 | −1.11805 | ||||||||
\(474\) | 8.78882 | + | 5.07423i | 0.403684 | + | 0.233067i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 6.58029i | − | 0.301607i | ||||||
\(477\) | 5.46131 | + | 3.15309i | 0.250056 | + | 0.144370i | ||||
\(478\) | −14.8512 | + | 8.57433i | −0.679277 | + | 0.392181i | ||||
\(479\) | 7.46188 | − | 4.30812i | 0.340942 | − | 0.196843i | −0.319746 | − | 0.947503i | \(-0.603598\pi\) |
0.660689 | + | 0.750660i | \(0.270264\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.1242 | − | 25.5589i | 0.735202 | − | 1.16539i | ||||
\(482\) | − | 17.5319i | − | 0.798558i | ||||||
\(483\) | −17.6025 | − | 30.4884i | −0.800940 | − | 1.38727i | ||||
\(484\) | 10.0661 | + | 17.4349i | 0.457548 | + | 0.792496i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 9.81026 | − | 16.9919i | 0.444545 | − | 0.769975i | −0.553475 | − | 0.832866i | \(-0.686699\pi\) |
0.998020 | + | 0.0628907i | \(0.0200320\pi\) | |||||||
\(488\) | −5.19076 | + | 8.99066i | −0.234975 | + | 0.406988i | ||||
\(489\) | − | 0.441885i | − | 0.0199827i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.8921 | − | 34.4541i | −0.897718 | − | 1.55489i | −0.830404 | − | 0.557161i | \(-0.811890\pi\) |
−0.0673138 | − | 0.997732i | \(-0.521443\pi\) | |||||||
\(492\) | −0.641326 | − | 1.11081i | −0.0289132 | − | 0.0500792i | ||||
\(493\) | 4.49477i | 0.202434i | ||||||||
\(494\) | 21.2169 | − | 11.1645i | 0.954593 | − | 0.502313i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.46131 | − | 3.15309i | 0.245220 | − | 0.141578i | ||||
\(497\) | −48.4690 | + | 27.9836i | −2.17413 | + | 1.25524i | ||||
\(498\) | 15.0591 | + | 8.69436i | 0.674813 | + | 0.389603i | ||||
\(499\) | 7.84082i | 0.351004i | 0.984479 | + | 0.175502i | \(0.0561548\pi\) | ||||
−0.984479 | + | 0.175502i | \(0.943845\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.94290 | + | 3.43113i | 0.265509 | + | 0.153292i | ||||
\(502\) | −18.2072 | −0.812626 | ||||||||
\(503\) | 6.15215 | + | 3.55194i | 0.274311 | + | 0.158373i | 0.630845 | − | 0.775909i | \(-0.282708\pi\) |
−0.356534 | + | 0.934282i | \(0.616042\pi\) | |||||||
\(504\) | −2.56511 | − | 4.44290i | −0.114259 | − | 0.197902i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −38.2888 | −1.70215 | ||||||||
\(507\) | 1.01834 | − | 12.9601i | 0.0452259 | − | 0.575576i | ||||
\(508\) | 16.2530i | 0.721111i | ||||||||
\(509\) | −34.0477 | + | 19.6575i | −1.50914 | + | 0.871302i | −0.509196 | + | 0.860651i | \(0.670057\pi\) |
−0.999943 | + | 0.0106512i | \(0.996610\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.6882 | + | 21.9765i | −0.561291 | + | 0.972184i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 3.32474 | − | 5.75861i | 0.146791 | − | 0.254249i | ||||
\(514\) | 15.2430 | + | 8.80056i | 0.672341 | + | 0.388176i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.17900 | − | 3.77414i | 0.0959250 | − | 0.166147i | ||||
\(517\) | −24.2741 | + | 14.0147i | −1.06758 | + | 0.616365i | ||||
\(518\) | 21.4995 | + | 37.2383i | 0.944635 | + | 1.63616i | ||||
\(519\) | −22.2898 | −0.978416 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.1840 | 1.71668 | 0.858341 | − | 0.513080i | \(-0.171496\pi\) | ||||
0.858341 | + | 0.513080i | \(0.171496\pi\) | |||||||
\(522\) | 1.75214 | + | 3.03479i | 0.0766889 | + | 0.132829i | ||||
\(523\) | −7.33790 | + | 4.23654i | −0.320864 | + | 0.185251i | −0.651778 | − | 0.758410i | \(-0.725976\pi\) |
0.330914 | + | 0.943661i | \(0.392643\pi\) | |||||||
\(524\) | −3.52302 | + | 6.10206i | −0.153904 | + | 0.266570i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.1853 | − | 5.88051i | −0.444102 | − | 0.256402i | ||||
\(527\) | −4.04432 | + | 7.00497i | −0.176173 | + | 0.305141i | ||||
\(528\) | −5.57962 | −0.242822 | ||||||||
\(529\) | 12.0454 | − | 20.8632i | 0.523712 | − | 0.907095i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.31571 | + | 0.759628i | −0.0570972 | + | 0.0329651i | ||||
\(532\) | 34.1133i | 1.47900i | ||||||||
\(533\) | 3.91137 | + | 2.46755i | 0.169420 | + | 0.106881i | ||||
\(534\) | 6.44188 | 0.278768 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.43555 | + | 2.48644i | 0.0620062 | + | 0.107398i | ||||
\(537\) | 1.35870 | + | 0.784447i | 0.0586324 | + | 0.0338514i | ||||
\(538\) | −6.40981 | −0.276346 | ||||||||
\(539\) | 93.3518 | + | 53.8967i | 4.02095 | + | 2.32149i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.5899i | 0.627269i | 0.949544 | + | 0.313634i | \(0.101547\pi\) | ||||
−0.949544 | + | 0.313634i | \(0.898453\pi\) | |||||||
\(542\) | 13.6919 | + | 7.90503i | 0.588118 | + | 0.339550i | ||||
\(543\) | −9.90896 | + | 5.72094i | −0.425234 | + | 0.245509i | ||||
\(544\) | 1.11081 | − | 0.641326i | 0.0476256 | − | 0.0274966i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 15.6443 | + | 9.86942i | 0.669513 | + | 0.422372i | ||||
\(547\) | − | 14.2246i | − | 0.608200i | −0.952640 | − | 0.304100i | \(-0.901644\pi\) | ||
0.952640 | − | 0.304100i | \(-0.0983557\pi\) | |||||||
\(548\) | 0.444016 | + | 0.769058i | 0.0189674 | + | 0.0328525i | ||||
\(549\) | −5.19076 | − | 8.99066i | −0.221536 | − | 0.383712i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 23.3016i | − | 0.992680i | ||||||
\(552\) | 3.43113 | − | 5.94290i | 0.146039 | − | 0.252947i | ||||
\(553\) | 26.0319 | − | 45.0885i | 1.10699 | − | 1.91736i | ||||
\(554\) | 4.98637i | 0.211851i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.266279 | + | 0.461208i | 0.0112927 | + | 0.0195596i | ||||
\(557\) | −17.4527 | − | 30.2289i | −0.739493 | − | 1.28084i | −0.952724 | − | 0.303838i | \(-0.901732\pi\) |
0.213231 | − | 0.977002i | \(-0.431601\pi\) | |||||||
\(558\) | 6.30618i | 0.266962i | ||||||||
\(559\) | −0.615900 | + | 15.7009i | −0.0260498 | + | 0.664077i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.19789 | − | 3.57836i | 0.261675 | − | 0.151078i | ||||
\(562\) | −0.446632 | + | 0.257863i | −0.0188400 | + | 0.0108773i | ||||
\(563\) | 13.6984 | + | 7.90879i | 0.577320 | + | 0.333316i | 0.760067 | − | 0.649844i | \(-0.225166\pi\) |
−0.182748 | + | 0.983160i | \(0.558499\pi\) | |||||||
\(564\) | − | 5.02353i | − | 0.211529i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −15.5418 | − | 8.97308i | −0.653272 | − | 0.377167i | ||||
\(567\) | 5.13022 | 0.215449 | ||||||||
\(568\) | −9.44775 | − | 5.45466i | −0.396419 | − | 0.228873i | ||||
\(569\) | 0.234472 | + | 0.406118i | 0.00982959 | + | 0.0170253i | 0.870898 | − | 0.491463i | \(-0.163538\pi\) |
−0.861069 | + | 0.508489i | \(0.830204\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.6325 | 0.905292 | 0.452646 | − | 0.891690i | \(-0.350480\pi\) | ||||
0.452646 | + | 0.891690i | \(0.350480\pi\) | |||||||
\(572\) | 17.8032 | − | 9.36816i | 0.744390 | − | 0.391703i | ||||
\(573\) | − | 8.82185i | − | 0.368538i | ||||||
\(574\) | −5.69870 | + | 3.29014i | −0.237859 | + | 0.137328i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | −21.2140 | −0.883149 | −0.441574 | − | 0.897225i | \(-0.645580\pi\) | ||||
−0.441574 | + | 0.897225i | \(0.645580\pi\) | |||||||
\(578\) | 7.67740 | − | 13.2976i | 0.319338 | − | 0.553109i | ||||
\(579\) | 9.68914 | + | 5.59403i | 0.402667 | + | 0.232480i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 44.6040 | − | 77.2563i | 1.85048 | − | 3.20513i | ||||
\(582\) | 6.20806 | − | 3.58423i | 0.257332 | − | 0.148571i | ||||
\(583\) | −17.5930 | − | 30.4720i | −0.728629 | − | 1.26202i | ||||
\(584\) | −4.94644 | −0.204685 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −17.2711 | −0.713461 | ||||||||
\(587\) | 1.18666 | + | 2.05536i | 0.0489788 | + | 0.0848338i | 0.889475 | − | 0.456983i | \(-0.151070\pi\) |
−0.840497 | + | 0.541817i | \(0.817737\pi\) | |||||||
\(588\) | −16.7309 | + | 9.65957i | −0.689969 | + | 0.398354i | ||||
\(589\) | 20.9664 | − | 36.3149i | 0.863905 | − | 1.49633i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19.8624 | − | 11.4675i | −0.817029 | − | 0.471712i | ||||
\(592\) | −4.19076 | + | 7.25861i | −0.172239 | + | 0.298327i | ||||
\(593\) | −2.26258 | −0.0929130 | −0.0464565 | − | 0.998920i | \(-0.514793\pi\) | ||||
−0.0464565 | + | 0.998920i | \(0.514793\pi\) | |||||||
\(594\) | 2.78981 | − | 4.83209i | 0.114467 | − | 0.198263i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 18.0113 | − | 10.3988i | 0.737771 | − | 0.425952i | ||||
\(597\) | − | 11.0578i | − | 0.452567i | ||||||
\(598\) | −0.969820 | + | 24.7232i | −0.0396589 | + | 1.01101i | ||||
\(599\) | 8.04828 | 0.328844 | 0.164422 | − | 0.986390i | \(-0.447424\pi\) | ||||
0.164422 | + | 0.986390i | \(0.447424\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.32625 | − | 2.29713i | −0.0540988 | − | 0.0937019i | 0.837708 | − | 0.546119i | \(-0.183895\pi\) |
−0.891807 | + | 0.452417i | \(0.850562\pi\) | |||||||
\(602\) | −19.3621 | − | 11.1787i | −0.789142 | − | 0.455611i | ||||
\(603\) | −2.87109 | −0.116920 | ||||||||
\(604\) | −1.86541 | − | 1.07700i | −0.0759026 | − | 0.0438224i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 14.6635i | 0.595664i | ||||||||
\(607\) | −1.89971 | − | 1.09680i | −0.0771070 | − | 0.0445177i | 0.460951 | − | 0.887426i | \(-0.347508\pi\) |
−0.538058 | + | 0.842908i | \(0.680842\pi\) | |||||||
\(608\) | −5.75861 | + | 3.32474i | −0.233543 | + | 0.134836i | ||||
\(609\) | 15.5691 | − | 8.98884i | 0.630893 | − | 0.364246i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.43450 | + | 16.0289i | 0.341223 | + | 0.648459i | ||||
\(612\) | 1.28265i | 0.0518482i | ||||||||
\(613\) | 0.0485163 | + | 0.0840326i | 0.00195955 | + | 0.00339405i | 0.867004 | − | 0.498302i | \(-0.166043\pi\) |
−0.865044 | + | 0.501696i | \(0.832710\pi\) | |||||||
\(614\) | −7.13366 | − | 12.3559i | −0.287891 | − | 0.498642i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 28.6246i | 1.15332i | ||||||||
\(617\) | 3.31734 | − | 5.74580i | 0.133551 | − | 0.231317i | −0.791492 | − | 0.611180i | \(-0.790695\pi\) |
0.925043 | + | 0.379862i | \(0.124029\pi\) | |||||||
\(618\) | 2.02465 | − | 3.50679i | 0.0814432 | − | 0.141064i | ||||
\(619\) | 14.0315i | 0.563973i | 0.959418 | + | 0.281987i | \(0.0909934\pi\) | ||||
−0.959418 | + | 0.281987i | \(0.909007\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.43113 | + | 5.94290i | 0.137687 | + | 0.238480i | ||||
\(622\) | −11.5743 | − | 20.0473i | −0.464088 | − | 0.803824i | ||||
\(623\) | − | 33.0483i | − | 1.32405i | ||||||
\(624\) | −0.141326 | + | 3.60278i | −0.00565759 | + | 0.144227i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −12.2215 | + | 7.05609i | −0.488469 | + | 0.282018i | ||||
\(627\) | −32.1309 | + | 18.5508i | −1.28318 | + | 0.740846i | ||||
\(628\) | −6.67044 | − | 3.85118i | −0.266180 | − | 0.153679i | ||||
\(629\) | − | 10.7506i | − | 0.428654i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.1445 | − | 20.8680i | −1.43889 | − | 0.830743i | −0.441116 | − | 0.897450i | \(-0.645417\pi\) |
−0.997773 | + | 0.0667070i | \(0.978751\pi\) | |||||||
\(632\) | 10.1485 | 0.403684 | ||||||||
\(633\) | 23.2391 | + | 13.4171i | 0.923671 | + | 0.533282i | ||||
\(634\) | −6.09070 | − | 10.5494i | −0.241893 | − | 0.418970i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 6.30618 | 0.250056 | ||||||||
\(637\) | 37.1658 | − | 58.9125i | 1.47256 | − | 2.33420i | ||||
\(638\) | − | 19.5525i | − | 0.774091i | ||||||
\(639\) | 9.44775 | − | 5.45466i | 0.373747 | − | 0.215783i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.4382 | + | 31.9358i | −0.728264 | + | 1.26139i | 0.229353 | + | 0.973343i | \(0.426339\pi\) |
−0.957617 | + | 0.288046i | \(0.906994\pi\) | |||||||
\(642\) | 7.76088 | 0.306297 | ||||||||
\(643\) | 10.9694 | − | 18.9996i | 0.432592 | − | 0.749271i | −0.564504 | − | 0.825430i | \(-0.690933\pi\) |
0.997096 | + | 0.0761597i | \(0.0242659\pi\) | |||||||
\(644\) | −30.4884 | − | 17.6025i | −1.20141 | − | 0.693634i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.26448 | − | 7.38630i | 0.167784 | − | 0.290610i | ||||
\(647\) | −1.68214 | + | 0.971183i | −0.0661317 | + | 0.0381811i | −0.532701 | − | 0.846303i | \(-0.678823\pi\) |
0.466570 | + | 0.884485i | \(0.345490\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | 8.47687 | 0.332746 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 32.3521 | 1.26798 | ||||||||
\(652\) | −0.220942 | − | 0.382683i | −0.00865277 | − | 0.0149870i | ||||
\(653\) | −9.14197 | + | 5.27812i | −0.357753 | + | 0.206549i | −0.668095 | − | 0.744076i | \(-0.732890\pi\) |
0.310342 | + | 0.950625i | \(0.399557\pi\) | |||||||
\(654\) | −0.396345 | + | 0.686490i | −0.0154983 | + | 0.0268439i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.11081 | − | 0.641326i | −0.0433698 | − | 0.0250396i | ||||
\(657\) | 2.47322 | − | 4.28374i | 0.0964895 | − | 0.167125i | ||||
\(658\) | −25.7718 | −1.00469 | ||||||||
\(659\) | −0.191440 | + | 0.331584i | −0.00745746 | + | 0.0129167i | −0.869730 | − | 0.493528i | \(-0.835707\pi\) |
0.862273 | + | 0.506444i | \(0.169040\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.5877 | − | 13.0410i | 0.878560 | − | 0.507237i | 0.00837690 | − | 0.999965i | \(-0.497334\pi\) |
0.870183 | + | 0.492728i | \(0.164000\pi\) | |||||||
\(662\) | 4.46249i | 0.173440i | ||||||||
\(663\) | −2.15357 | − | 4.09264i | −0.0836378 | − | 0.158945i | ||||
\(664\) | 17.3887 | 0.674813 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.19076 | − | 7.25861i | −0.162389 | − | 0.281266i | ||||
\(667\) | 20.8255 | + | 12.0236i | 0.806368 | + | 0.465557i | ||||
\(668\) | 6.86227 | 0.265509 | ||||||||
\(669\) | −0.0599161 | − | 0.0345926i | −0.00231649 | − | 0.00133743i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 57.9249i | 2.23617i | ||||||||
\(672\) | −4.44290 | − | 2.56511i | −0.171389 | − | 0.0989512i | ||||
\(673\) | −11.1123 | + | 6.41571i | −0.428349 | + | 0.247307i | −0.698643 | − | 0.715470i | \(-0.746212\pi\) |
0.270294 | + | 0.962778i | \(0.412879\pi\) | |||||||
\(674\) | 5.23749 | − | 3.02387i | 0.201741 | − | 0.116475i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.59812 | − | 11.7329i | −0.215312 | − | 0.451266i | ||||
\(677\) | 22.3408i | 0.858626i | 0.903156 | + | 0.429313i | \(0.141244\pi\) | ||||
−0.903156 | + | 0.429313i | \(0.858756\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.3879 | − | 31.8487i | −0.705661 | − | 1.22224i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 6.19198i | − | 0.237277i | ||||||
\(682\) | 17.5930 | − | 30.4720i | 0.673672 | − | 1.16683i | ||||
\(683\) | 10.1071 | − | 17.5060i | 0.386738 | − | 0.669850i | −0.605271 | − | 0.796020i | \(-0.706935\pi\) |
0.992009 | + | 0.126170i | \(0.0402684\pi\) | |||||||
\(684\) | − | 6.64947i | − | 0.254249i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 31.5999 | + | 54.7327i | 1.20649 | + | 2.08970i | ||||
\(687\) | 8.69283 | + | 15.0564i | 0.331652 | + | 0.574438i | ||||
\(688\) | − | 4.35800i | − | 0.166147i | ||||||
\(689\) | −20.1215 | + | 10.5881i | −0.766569 | + | 0.403373i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.3351 | − | 12.3178i | 0.811625 | − | 0.468592i | −0.0358950 | − | 0.999356i | \(-0.511428\pi\) |
0.847520 | + | 0.530764i | \(0.178095\pi\) | |||||||
\(692\) | −19.3036 | + | 11.1449i | −0.733812 | + | 0.423666i | ||||
\(693\) | −24.7897 | − | 14.3123i | −0.941682 | − | 0.543680i | ||||
\(694\) | 6.34654i | 0.240911i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.03479 | + | 1.75214i | 0.115033 | + | 0.0664146i | ||||
\(697\) | 1.64520 | 0.0623163 | ||||||||
\(698\) | 24.4438 | + | 14.1126i | 0.925210 | + | 0.534170i | ||||
\(699\) | −8.88580 | − | 15.3907i | −0.336092 | − | 0.582128i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 43.4688 | 1.64179 | 0.820897 | − | 0.571076i | \(-0.193474\pi\) | ||||
0.820897 | + | 0.571076i | \(0.193474\pi\) | |||||||
\(702\) | −3.04944 | − | 1.92378i | −0.115094 | − | 0.0726085i | ||||
\(703\) | 55.7327i | 2.10200i | ||||||||
\(704\) | −4.83209 | + | 2.78981i | −0.182116 | + | 0.105145i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.04696 | + | 13.9378i | −0.302851 | + | 0.524554i | ||||
\(707\) | 75.2270 | 2.82920 | ||||||||
\(708\) | −0.759628 | + | 1.31571i | −0.0285486 | + | 0.0494476i | ||||
\(709\) | −4.05937 | − | 2.34368i | −0.152453 | − | 0.0880187i | 0.421833 | − | 0.906674i | \(-0.361387\pi\) |
−0.574286 | + | 0.818655i | \(0.694720\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.07423 | + | 8.78882i | −0.190298 | + | 0.329606i | ||||
\(712\) | 5.57884 | − | 3.22094i | 0.209076 | − | 0.120710i | ||||
\(713\) | 21.6374 | + | 37.4770i | 0.810325 | + | 1.40352i | ||||
\(714\) | 6.58029 | 0.246261 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.56889 | 0.0586324 | ||||||||
\(717\) | −8.57433 | − | 14.8512i | −0.320214 | − | 0.554627i | ||||
\(718\) | −7.61833 | + | 4.39845i | −0.284314 | + | 0.164149i | ||||
\(719\) | −13.6893 | + | 23.7106i | −0.510526 | + | 0.884257i | 0.489400 | + | 0.872060i | \(0.337216\pi\) |
−0.999926 | + | 0.0121971i | \(0.996117\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.9906 | − | 10.3869i | −0.670005 | − | 0.386827i | ||||
\(722\) | −12.6078 | + | 21.8373i | −0.469212 | + | 0.812699i | ||||
\(723\) | 17.5319 | 0.652020 | ||||||||
\(724\) | −5.72094 | + | 9.90896i | −0.212617 | + | 0.368264i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −17.4349 | + | 10.0661i | −0.647071 | + | 0.373586i | ||||
\(727\) | 12.4066i | 0.460136i | 0.973175 | + | 0.230068i | \(0.0738948\pi\) | ||||
−0.973175 | + | 0.230068i | \(0.926105\pi\) | |||||||
\(728\) | 18.4830 | + | 0.725036i | 0.685027 | + | 0.0268716i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.79490 | + | 4.84091i | 0.103373 | + | 0.179047i | ||||
\(732\) | −8.99066 | − | 5.19076i | −0.332305 | − | 0.191856i | ||||
\(733\) | 18.7638 | 0.693056 | 0.346528 | − | 0.938040i | \(-0.387361\pi\) | ||||
0.346528 | + | 0.938040i | \(0.387361\pi\) | |||||||
\(734\) | −32.9145 | − | 19.0032i | −1.21490 | − | 0.701420i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 6.86227i | − | 0.252947i | ||||||
\(737\) | 13.8734 | + | 8.00980i | 0.511033 | + | 0.295045i | ||||
\(738\) | 1.11081 | − | 0.641326i | 0.0408895 | − | 0.0236076i | ||||
\(739\) | −44.5751 | + | 25.7355i | −1.63972 | + | 0.946694i | −0.658794 | + | 0.752324i | \(0.728933\pi\) |
−0.980928 | + | 0.194370i | \(0.937734\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.1645 | + | 21.2169i | 0.410136 | + | 0.779422i | ||||
\(742\) | − | 32.3521i | − | 1.18768i | ||||||
\(743\) | −24.7999 | − | 42.9547i | −0.909819 | − | 1.57585i | −0.814314 | − | 0.580424i | \(-0.802887\pi\) |
−0.0955053 | − | 0.995429i | \(-0.530447\pi\) | |||||||
\(744\) | 3.15309 | + | 5.46131i | 0.115598 | + | 0.200221i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 17.0157i | − | 0.622990i | ||||||
\(747\) | −8.69436 | + | 15.0591i | −0.318110 | + | 0.550983i | ||||
\(748\) | 3.57836 | − | 6.19789i | 0.130838 | − | 0.226617i | ||||
\(749\) | − | 39.8150i | − | 1.45481i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.15058 | + | 8.92107i | 0.187947 | + | 0.325535i | 0.944566 | − | 0.328322i | \(-0.106483\pi\) |
−0.756618 | + | 0.653857i | \(0.773150\pi\) | |||||||
\(752\) | −2.51176 | − | 4.35050i | −0.0915946 | − | 0.158647i | ||||
\(753\) | − | 18.2072i | − | 0.663506i | ||||||
\(754\) | −12.6251 | − | 0.495247i | −0.459780 | − | 0.0180358i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.44290 | − | 2.56511i | 0.161587 | − | 0.0932921i | ||||
\(757\) | −3.83773 | + | 2.21571i | −0.139485 | + | 0.0805314i | −0.568118 | − | 0.822947i | \(-0.692328\pi\) |
0.428634 | + | 0.903478i | \(0.358995\pi\) | |||||||
\(758\) | −11.0257 | − | 6.36569i | −0.400471 | − | 0.231212i | ||||
\(759\) | − | 38.2888i | − | 1.38980i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.89888 | + | 5.71512i | 0.358834 | + | 0.207173i | 0.668569 | − | 0.743650i | \(-0.266907\pi\) |
−0.309735 | + | 0.950823i | \(0.600240\pi\) | |||||||
\(762\) | −16.2530 | −0.588785 | ||||||||
\(763\) | 3.52184 | + | 2.03334i | 0.127499 | + | 0.0736117i | ||||
\(764\) | −4.41092 | − | 7.63995i | −0.159582 | − | 0.276404i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 22.5718 | 0.815553 | ||||||||
\(767\) | 0.214711 | − | 5.47355i | 0.00775277 | − | 0.197638i | ||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | −8.46766 | + | 4.88880i | −0.305352 | + | 0.176295i | −0.644844 | − | 0.764314i | \(-0.723078\pi\) |
0.339493 | + | 0.940609i | \(0.389745\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.80056 | + | 15.2430i | −0.316944 | + | 0.548964i | ||||
\(772\) | 11.1881 | 0.402667 | ||||||||
\(773\) | 3.39593 | − | 5.88192i | 0.122143 | − | 0.211558i | −0.798470 | − | 0.602035i | \(-0.794357\pi\) |
0.920613 | + | 0.390477i | \(0.127690\pi\) | |||||||
\(774\) | 3.77414 | + | 2.17900i | 0.135658 | + | 0.0783225i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.58423 | − | 6.20806i | 0.128666 | − | 0.222856i | ||||
\(777\) | −37.2383 | + | 21.4995i | −1.33592 | + | 0.771291i | ||||
\(778\) | −1.75214 | − | 3.03479i | −0.0628171 | − | 0.108802i | ||||
\(779\) | −8.52897 | −0.305582 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −60.8699 | −2.17809 | ||||||||
\(782\) | 4.40095 | + | 7.62268i | 0.157378 | + | 0.272586i | ||||
\(783\) | −3.03479 | + | 1.75214i | −0.108455 | + | 0.0626163i | ||||
\(784\) | −9.65957 | + | 16.7309i | −0.344985 | + | 0.597531i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −6.10206 | − | 3.52302i | −0.217653 | − | 0.125662i | ||||
\(787\) | 2.50713 | − | 4.34247i | 0.0893694 | − | 0.154792i | −0.817875 | − | 0.575395i | \(-0.804848\pi\) |
0.907245 | + | 0.420603i | \(0.138182\pi\) | |||||||
\(788\) | −22.9351 | −0.817029 | ||||||||
\(789\) | 5.88051 | − | 10.1853i | 0.209352 | − | 0.362608i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 5.57962i | − | 0.198263i | ||||||
\(793\) | 37.4024 | + | 1.46718i | 1.32820 | + | 0.0521012i | ||||
\(794\) | −29.8652 | −1.05988 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.52892 | − | 9.57637i | −0.195967 | − | 0.339425i | ||||
\(797\) | −8.59714 | − | 4.96356i | −0.304526 | − | 0.175818i | 0.339948 | − | 0.940444i | \(-0.389590\pi\) |
−0.644474 | + | 0.764626i | \(0.722924\pi\) | |||||||
\(798\) | −34.1133 | −1.20760 | ||||||||
\(799\) | 5.58019 | + | 3.22172i | 0.197413 | + | 0.113976i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.44188i | 0.227613i | ||||||||
\(802\) | −21.7592 | − | 12.5627i | −0.768345 | − | 0.443604i | ||||
\(803\) | −23.9016 | + | 13.7996i | −0.843470 | + | 0.486978i | ||||
\(804\) | −2.48644 | + | 1.43555i | −0.0876900 | + | 0.0506278i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −19.2303 | − | 12.1317i | −0.677358 | − | 0.427322i | ||||
\(807\) | − | 6.40981i | − | 0.225636i | ||||||
\(808\) | 7.33175 | + | 12.6990i | 0.257930 | + | 0.446748i | ||||
\(809\) | 4.98796 | + | 8.63940i | 0.175367 | + | 0.303745i | 0.940288 | − | 0.340379i | \(-0.110555\pi\) |
−0.764921 | + | 0.644124i | \(0.777222\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.85013i | 0.170311i | 0.996368 | + | 0.0851555i | \(0.0271387\pi\) | ||||
−0.996368 | + | 0.0851555i | \(0.972861\pi\) | |||||||
\(812\) | 8.98884 | − | 15.5691i | 0.315447 | − | 0.546369i | ||||
\(813\) | −7.90503 | + | 13.6919i | −0.277242 | + | 0.480196i | ||||
\(814\) | 46.7657i | 1.63914i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.641326 | + | 1.11081i | 0.0224509 | + | 0.0388861i | ||||
\(817\) | −14.4892 | − | 25.0960i | −0.506913 | − | 0.877998i | ||||
\(818\) | − | 5.24767i | − | 0.183480i | ||||||
\(819\) | −9.86942 | + | 15.6443i | −0.344866 | + | 0.546655i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.9722 | − | 12.6857i | 0.766836 | − | 0.442733i | −0.0649085 | − | 0.997891i | \(-0.520676\pi\) |
0.831745 | + | 0.555158i | \(0.187342\pi\) | |||||||
\(822\) | −0.769058 | + | 0.444016i | −0.0268240 | + | 0.0154868i | ||||
\(823\) | −22.9557 | − | 13.2535i | −0.800184 | − | 0.461986i | 0.0433515 | − | 0.999060i | \(-0.486196\pi\) |
−0.843536 | + | 0.537073i | \(0.819530\pi\) | |||||||
\(824\) | − | 4.04929i | − | 0.141064i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.74990 | + | 3.89706i | 0.234859 | + | 0.135596i | ||||
\(827\) | 21.7678 | 0.756941 | 0.378470 | − | 0.925613i | \(-0.376450\pi\) | ||||
0.378470 | + | 0.925613i | \(0.376450\pi\) | |||||||
\(828\) | 5.94290 | + | 3.43113i | 0.206530 | + | 0.119240i | ||||
\(829\) | −1.09376 | − | 1.89444i | −0.0379878 | − | 0.0657968i | 0.846406 | − | 0.532537i | \(-0.178761\pi\) |
−0.884394 | + | 0.466741i | \(0.845428\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.98637 | −0.172975 | ||||||||
\(832\) | 1.67900 | + | 3.19076i | 0.0582088 | + | 0.110620i | ||||
\(833\) | − | 24.7797i | − | 0.858567i | ||||||
\(834\) | −0.461208 | + | 0.266279i | −0.0159703 | + | 0.00922047i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −18.5508 | + | 32.1309i | −0.641591 | + | 1.11127i | ||||
\(837\) | −6.30618 | −0.217974 | ||||||||
\(838\) | 9.01326 | − | 15.6114i | 0.311358 | − | 0.539288i | ||||
\(839\) | −21.7825 | − | 12.5761i | −0.752016 | − | 0.434177i | 0.0744057 | − | 0.997228i | \(-0.476294\pi\) |
−0.826422 | + | 0.563051i | \(0.809627\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.36004 | − | 14.4800i | 0.288277 | − | 0.499311i | ||||
\(842\) | −6.86213 | + | 3.96185i | −0.236485 | + | 0.136534i | ||||
\(843\) | −0.257863 | − | 0.446632i | −0.00888127 | − | 0.0153828i | ||||
\(844\) | 26.8342 | 0.923671 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.02353 | 0.172712 | ||||||||
\(847\) | 51.6411 | + | 89.4449i | 1.77441 | + | 3.07336i | ||||
\(848\) | 5.46131 | − | 3.15309i | 0.187542 | − | 0.108278i | ||||
\(849\) | 8.97308 | − | 15.5418i | 0.307955 | − | 0.533394i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −49.8106 | − | 28.7581i | −1.70748 | − | 0.985816i | ||||
\(852\) | 5.45466 | − | 9.44775i | 0.186874 | − | 0.323675i | ||||
\(853\) | −36.1721 | −1.23851 | −0.619255 | − | 0.785190i | \(-0.712565\pi\) | ||||
−0.619255 | + | 0.785190i | \(0.712565\pi\) | |||||||
\(854\) | −26.6297 | + | 46.1241i | −0.911251 | + | 1.57833i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.72112 | − | 3.88044i | 0.229723 | − | 0.132631i | ||||
\(857\) | − | 18.5471i | − | 0.633556i | −0.948500 | − | 0.316778i | \(-0.897399\pi\) | ||
0.948500 | − | 0.316778i | \(-0.102601\pi\) | |||||||
\(858\) | 9.36816 | + | 17.8032i | 0.319824 | + | 0.607792i | ||||
\(859\) | 21.5386 | 0.734887 | 0.367443 | − | 0.930046i | \(-0.380233\pi\) | ||||
0.367443 | + | 0.930046i | \(0.380233\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.29014 | − | 5.69870i | −0.112128 | − | 0.194211i | ||||
\(862\) | 33.1752 | + | 19.1537i | 1.12995 | + | 0.652379i | ||||
\(863\) | −32.1136 | −1.09316 | −0.546580 | − | 0.837407i | \(-0.684070\pi\) | ||||
−0.546580 | + | 0.837407i | \(0.684070\pi\) | |||||||
\(864\) | 0.866025 | + | 0.500000i | 0.0294628 | + | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 20.0052i | − | 0.679803i | ||||||
\(867\) | 13.2976 | + | 7.67740i | 0.451612 | + | 0.260738i | ||||
\(868\) | 28.0177 | − | 16.1760i | 0.950984 | − | 0.549051i | ||||
\(869\) | 49.0382 | − | 28.3122i | 1.66351 | − | 0.960427i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.52336 | − | 8.75522i | 0.187152 | − | 0.296659i | ||||
\(872\) | 0.792690i | 0.0268439i | ||||||||
\(873\) | 3.58423 | + | 6.20806i | 0.121308 | + | 0.210111i | ||||
\(874\) | −22.8152 | − | 39.5172i | −0.771737 | − | 1.33669i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 4.94644i | − | 0.167125i | ||||||
\(877\) | 16.0319 | − | 27.7681i | 0.541360 | − | 0.937664i | −0.457466 | − | 0.889227i | \(-0.651243\pi\) |
0.998826 | − | 0.0484365i | \(-0.0154239\pi\) | |||||||
\(878\) | 5.96660 | − | 10.3345i | 0.201363 | − | 0.348771i | ||||
\(879\) | − | 17.2711i | − | 0.582538i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.47244 | + | 16.4067i | 0.319135 | + | 0.552757i | 0.980308 | − | 0.197476i | \(-0.0632745\pi\) |
−0.661173 | + | 0.750233i | \(0.729941\pi\) | |||||||
\(882\) | −9.65957 | − | 16.7309i | −0.325255 | − | 0.563357i | ||||
\(883\) | − | 38.0685i | − | 1.28111i | −0.767914 | − | 0.640554i | \(-0.778705\pi\) | ||
0.767914 | − | 0.640554i | \(-0.221295\pi\) | |||||||
\(884\) | −3.91137 | − | 2.46755i | −0.131554 | − | 0.0829925i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −22.5656 | + | 13.0282i | −0.758105 | + | 0.437692i | ||||
\(887\) | 11.6986 | − | 6.75421i | 0.392802 | − | 0.226784i | −0.290572 | − | 0.956853i | \(-0.593845\pi\) |
0.683373 | + | 0.730069i | \(0.260512\pi\) | |||||||
\(888\) | −7.25861 | − | 4.19076i | −0.243583 | − | 0.140633i | ||||
\(889\) | 83.3815i | 2.79653i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.83209 | + | 2.78981i | 0.161881 | + | 0.0934621i | ||||
\(892\) | −0.0691851 | −0.00231649 | ||||||||
\(893\) | −28.9286 | − | 16.7019i | −0.968058 | − | 0.558908i | ||||
\(894\) | 10.3988 | + | 18.0113i | 0.347789 | + | 0.602388i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −5.13022 | −0.171389 | ||||||||
\(897\) | −24.7232 | − | 0.969820i | −0.825485 | − | 0.0323814i | ||||
\(898\) | 16.7392i | 0.558594i | ||||||||
\(899\) | −19.1379 | + | 11.0493i | −0.638286 | + | 0.368515i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.04432 | + | 7.00497i | −0.134736 | + | 0.233369i | ||||
\(902\) | −7.15671 | −0.238292 | ||||||||
\(903\) | 11.1787 | − | 19.3621i | 0.372005 | − | 0.644332i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.07700 | − | 1.86541i | 0.0357808 | − | 0.0619742i | ||||
\(907\) | 9.41300 | − | 5.43460i | 0.312554 | − | 0.180453i | −0.335515 | − | 0.942035i | \(-0.608910\pi\) |
0.648069 | + | 0.761582i | \(0.275577\pi\) | |||||||
\(908\) | −3.09599 | − | 5.36241i | −0.102744 | − | 0.177958i | ||||
\(909\) | −14.6635 | −0.486358 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.20770 | 0.305065 | 0.152532 | − | 0.988298i | \(-0.451257\pi\) | ||||
0.152532 | + | 0.988298i | \(0.451257\pi\) | |||||||
\(912\) | −3.32474 | − | 5.75861i | −0.110093 | − | 0.190687i | ||||
\(913\) | 84.0238 | − | 48.5112i | 2.78078 | − | 1.60549i | ||||
\(914\) | 3.55432 | − | 6.15626i | 0.117566 | − | 0.203631i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.0564 | + | 8.69283i | 0.497478 | + | 0.287219i | ||||
\(917\) | −18.0739 | + | 31.3049i | −0.596852 | + | 1.03378i | ||||
\(918\) | −1.28265 | −0.0423339 | ||||||||
\(919\) | 0.0963564 | − | 0.166894i | 0.00317850 | − | 0.00550533i | −0.864432 | − | 0.502750i | \(-0.832322\pi\) |
0.867610 | + | 0.497245i | \(0.165655\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.3559 | − | 7.13366i | 0.407140 | − | 0.235062i | ||||
\(922\) | − | 5.51635i | − | 0.181671i | ||||||
\(923\) | −1.54178 | + | 39.3039i | −0.0507482 | + | 1.29370i | ||||
\(924\) | −28.6246 | −0.941682 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.49379 | + | 4.31938i | 0.0819511 | + | 0.141943i | ||||
\(927\) | 3.50679 | + | 2.02465i | 0.115178 | + | 0.0664981i | ||||
\(928\) | 3.50427 | 0.115033 | ||||||||
\(929\) | 10.3702 | + | 5.98725i | 0.340236 | + | 0.196435i | 0.660376 | − | 0.750935i | \(-0.270397\pi\) |
−0.320140 | + | 0.947370i | \(0.603730\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 128.462i | 4.21018i | ||||||||
\(932\) | −15.3907 | − | 8.88580i | −0.504138 | − | 0.291064i | ||||
\(933\) | 20.0473 | − | 11.5743i | 0.656320 | − | 0.378927i | ||||
\(934\) | −17.0962 | + | 9.87051i | −0.559406 | + | 0.322973i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.60278 | − | 0.141326i | −0.117761 | − | 0.00461940i | ||||
\(937\) | − | 32.1031i | − | 1.04876i | −0.851484 | − | 0.524381i | \(-0.824297\pi\) | ||
0.851484 | − | 0.524381i | \(-0.175703\pi\) | |||||||
\(938\) | 7.36467 | + | 12.7560i | 0.240465 | + | 0.416498i | ||||
\(939\) | −7.05609 | − | 12.2215i | −0.230267 | − | 0.398834i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.36756i | 0.207577i | 0.994599 | + | 0.103788i | \(0.0330964\pi\) | ||||
−0.994599 | + | 0.103788i | \(0.966904\pi\) | |||||||
\(942\) | 3.85118 | − | 6.67044i | 0.125478 | − | 0.217335i | ||||
\(943\) | 4.40095 | − | 7.62268i | 0.143315 | − | 0.248229i | ||||
\(944\) | 1.51926i | 0.0494476i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.1580 | − | 21.0582i | −0.395290 | − | 0.684662i | ||||
\(947\) | −29.5983 | − | 51.2658i | −0.961816 | − | 1.66591i | −0.717936 | − | 0.696110i | \(-0.754913\pi\) |
−0.243881 | − | 0.969805i | \(-0.578421\pi\) | |||||||
\(948\) | 10.1485i | 0.329606i | ||||||||
\(949\) | 8.30506 | + | 15.7829i | 0.269594 | + | 0.512335i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.5494 | − | 6.09070i | 0.342088 | − | 0.197505i | ||||
\(952\) | 5.69870 | − | 3.29014i | 0.184696 | − | 0.106634i | ||||
\(953\) | 12.9852 | + | 7.49699i | 0.420631 | + | 0.242851i | 0.695347 | − | 0.718674i | \(-0.255251\pi\) |
−0.274716 | + | 0.961525i | \(0.588584\pi\) | |||||||
\(954\) | 6.30618i | 0.204170i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −14.8512 | − | 8.57433i | −0.480321 | − | 0.277314i | ||||
\(957\) | 19.5525 | 0.632042 | ||||||||
\(958\) | 7.46188 | + | 4.30812i | 0.241083 | + | 0.139189i | ||||
\(959\) | 2.27790 | + | 3.94544i | 0.0735572 | + | 0.127405i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.76794 | −0.282837 | ||||||||
\(962\) | 30.1968 | + | 1.18453i | 0.973584 | + | 0.0381908i | ||||
\(963\) | 7.76088i | 0.250091i | ||||||||
\(964\) | 15.1831 | − | 8.76597i | 0.489015 | − | 0.282333i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 17.6025 | − | 30.4884i | 0.566350 | − | 0.980947i | ||||
\(967\) | 43.4352 | 1.39678 | 0.698390 | − | 0.715717i | \(-0.253900\pi\) | ||||
0.698390 | + | 0.715717i | \(0.253900\pi\) | |||||||
\(968\) | −10.0661 | + | 17.4349i | −0.323535 | + | 0.560380i | ||||
\(969\) | 7.38630 | + | 4.26448i | 0.237282 | + | 0.136995i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.4673 | + | 42.3786i | −0.785192 | + | 1.35999i | 0.143692 | + | 0.989622i | \(0.454103\pi\) |
−0.928884 | + | 0.370370i | \(0.879231\pi\) | |||||||
\(972\) | −0.866025 | + | 0.500000i | −0.0277778 | + | 0.0160375i | ||||
\(973\) | 1.36607 | + | 2.36610i | 0.0437941 | + | 0.0758536i | ||||
\(974\) | 19.6205 | 0.628682 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.3815 | −0.332305 | ||||||||
\(977\) | 26.7331 | + | 46.3031i | 0.855267 | + | 1.48137i | 0.876397 | + | 0.481589i | \(0.159940\pi\) |
−0.0211299 | + | 0.999777i | \(0.506726\pi\) | |||||||
\(978\) | 0.382683 | − | 0.220942i | 0.0122369 | − | 0.00706496i | ||||
\(979\) | 17.9716 | − | 31.1278i | 0.574375 | − | 0.994848i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.686490 | − | 0.396345i | −0.0219179 | − | 0.0126543i | ||||
\(982\) | 19.8921 | − | 34.4541i | 0.634782 | − | 1.09948i | ||||
\(983\) | −26.5785 | −0.847723 | −0.423862 | − | 0.905727i | \(-0.639326\pi\) | ||||
−0.423862 | + | 0.905727i | \(0.639326\pi\) | |||||||
\(984\) | 0.641326 | − | 1.11081i | 0.0204447 | − | 0.0354113i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.89258 | + | 2.24738i | −0.123965 | + | 0.0715713i | ||||
\(987\) | − | 25.7718i | − | 0.820325i | ||||||
\(988\) | 20.2771 | + | 12.7921i | 0.645102 | + | 0.406972i | ||||
\(989\) | 29.9057 | 0.950947 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.1688 | + | 31.4693i | 0.577152 | + | 0.999657i | 0.995804 | + | 0.0915100i | \(0.0291694\pi\) |
−0.418652 | + | 0.908147i | \(0.637497\pi\) | |||||||
\(992\) | 5.46131 | + | 3.15309i | 0.173397 | + | 0.100111i | ||||
\(993\) | −4.46249 | −0.141613 | ||||||||
\(994\) | −48.4690 | − | 27.9836i | −1.53734 | − | 0.887586i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 17.3887i | 0.550983i | ||||||||
\(997\) | 26.3716 | + | 15.2257i | 0.835198 | + | 0.482202i | 0.855629 | − | 0.517590i | \(-0.173171\pi\) |
−0.0204312 | + | 0.999791i | \(0.506504\pi\) | |||||||
\(998\) | −6.79035 | + | 3.92041i | −0.214945 | + | 0.124098i | ||||
\(999\) | 7.25861 | − | 4.19076i | 0.229652 | − | 0.132590i |
(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 | 1950.2.y.n.49.1 | 12 | ||
5.2 | odd | 4 | 1950.2.bc.k.751.1 | yes | 12 | ||
5.3 | odd | 4 | 1950.2.bc.h.751.6 | ✓ | 12 | ||
5.4 | even | 2 | 1950.2.y.m.49.6 | 12 | |||
13.4 | even | 6 | 1950.2.y.m.199.6 | 12 | |||
65.4 | even | 6 | inner | 1950.2.y.n.199.1 | 12 | ||
65.17 | odd | 12 | 1950.2.bc.k.901.1 | yes | 12 | ||
65.43 | odd | 12 | 1950.2.bc.h.901.6 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1950.2.y.m.49.6 | 12 | 5.4 | even | 2 | |||
1950.2.y.m.199.6 | 12 | 13.4 | even | 6 | |||
1950.2.y.n.49.1 | 12 | 1.1 | even | 1 | trivial | ||
1950.2.y.n.199.1 | 12 | 65.4 | even | 6 | inner | ||
1950.2.bc.h.751.6 | ✓ | 12 | 5.3 | odd | 4 | ||
1950.2.bc.h.901.6 | yes | 12 | 65.43 | odd | 12 | ||
1950.2.bc.k.751.1 | yes | 12 | 5.2 | odd | 4 | ||
1950.2.bc.k.901.1 | yes | 12 | 65.17 | odd | 12 |