Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(751,1950)]
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, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.751");
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.bc (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.5708283941\) |
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: | \( x^{12} - 6 x^{11} + 87 x^{10} - 380 x^{9} + 2556 x^{8} - 8010 x^{7} + 29687 x^{6} - 62556 x^{5} + 115386 x^{4} - 135130 x^{3} + 113253 x^{2} - 54888 x + 14089 \) |
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 | 751.6 | ||
Root | \(0.500000 - 4.99624i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.751 |
Dual form | 1950.2.bc.h.901.6 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.866025 | − | 0.500000i | −0.353553 | − | 0.204124i | ||||
\(7\) | 4.44290 | + | 2.56511i | 1.67926 | + | 0.969520i | 0.962135 | + | 0.272574i | \(0.0878748\pi\) |
0.717123 | + | 0.696947i | \(0.245459\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −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 | \(0.651459\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −3.19076 | + | 1.67900i | −0.884958 | + | 0.465670i | ||||
\(14\) | 5.13022 | 1.37111 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0.641326 | − | 1.11081i | 0.155545 | − | 0.269411i | −0.777713 | − | 0.628620i | \(-0.783620\pi\) |
0.933257 | + | 0.359209i | \(0.116953\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 5.75861 | + | 3.32474i | 1.32112 | + | 0.762747i | 0.983907 | − | 0.178682i | \(-0.0571835\pi\) |
0.337210 | + | 0.941430i | \(0.390517\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 5.13022i | − | 1.11951i | ||||||
\(22\) | −2.78981 | + | 4.83209i | −0.594789 | + | 1.03020i | ||||
\(23\) | 3.43113 | + | 5.94290i | 0.715441 | + | 1.23918i | 0.962789 | + | 0.270253i | \(0.0871075\pi\) |
−0.247348 | + | 0.968927i | \(0.579559\pi\) | |||||||
\(24\) | −0.866025 | + | 0.500000i | −0.176777 | + | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.92378 | + | 3.04944i | −0.377285 | + | 0.598044i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.44290 | − | 2.56511i | 0.839629 | − | 0.484760i | ||||
\(29\) | −1.75214 | − | 3.03479i | −0.325364 | − | 0.563546i | 0.656222 | − | 0.754568i | \(-0.272153\pi\) |
−0.981586 | + | 0.191021i | \(0.938820\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.30618i | 1.13262i | 0.824191 | + | 0.566312i | \(0.191630\pi\) | ||||
−0.824191 | + | 0.566312i | \(0.808370\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 4.83209 | + | 2.78981i | 0.841159 | + | 0.485643i | ||||
\(34\) | − | 1.28265i | − | 0.219973i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.500000 | + | 0.866025i | 0.0833333 | + | 0.144338i | ||||
\(37\) | −7.25861 | + | 4.19076i | −1.19331 | + | 0.688957i | −0.959055 | − | 0.283218i | \(-0.908598\pi\) |
−0.234253 | + | 0.972176i | \(0.575265\pi\) | |||||||
\(38\) | 6.64947 | 1.07869 | ||||||||
\(39\) | 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 | \(0.301398\pi\) | |||||||
\(42\) | −2.56511 | − | 4.44290i | −0.395805 | − | 0.685554i | ||||
\(43\) | −2.17900 | + | 3.77414i | −0.332294 | + | 0.575550i | −0.982961 | − | 0.183813i | \(-0.941156\pi\) |
0.650667 | + | 0.759363i | \(0.274489\pi\) | |||||||
\(44\) | 5.57962i | 0.841159i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.94290 | + | 3.43113i | 0.876233 | + | 0.505893i | ||||
\(47\) | − | 5.02353i | − | 0.732757i | −0.930466 | − | 0.366379i | \(-0.880598\pi\) | ||
0.930466 | − | 0.366379i | \(-0.119402\pi\) | |||||||
\(48\) | −0.500000 | + | 0.866025i | −0.0721688 | + | 0.125000i | ||||
\(49\) | 9.65957 | + | 16.7309i | 1.37994 | + | 2.39012i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.28265 | −0.179607 | ||||||||
\(52\) | −0.141326 | + | 3.60278i | −0.0195985 | + | 0.499616i | ||||
\(53\) | −6.30618 | −0.866221 | −0.433110 | − | 0.901341i | \(-0.642584\pi\) | ||||
−0.433110 | + | 0.901341i | \(0.642584\pi\) | |||||||
\(54\) | 0.866025 | − | 0.500000i | 0.117851 | − | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.56511 | − | 4.44290i | 0.342777 | − | 0.593707i | ||||
\(57\) | − | 6.64947i | − | 0.880744i | ||||||
\(58\) | −3.03479 | − | 1.75214i | −0.398487 | − | 0.230067i | ||||
\(59\) | 1.31571 | + | 0.759628i | 0.171291 | + | 0.0988952i | 0.583195 | − | 0.812332i | \(-0.301802\pi\) |
−0.411903 | + | 0.911228i | \(0.635136\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.19076 | − | 8.99066i | 0.664609 | − | 1.15114i | −0.314782 | − | 0.949164i | \(-0.601931\pi\) |
0.979391 | − | 0.201973i | \(-0.0647352\pi\) | |||||||
\(62\) | 3.15309 | + | 5.46131i | 0.400443 | + | 0.693588i | ||||
\(63\) | −4.44290 | + | 2.56511i | −0.559753 | + | 0.323173i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.57962 | 0.686803 | ||||||||
\(67\) | −2.48644 | + | 1.43555i | −0.303767 | + | 0.175380i | −0.644134 | − | 0.764913i | \(-0.722782\pi\) |
0.340367 | + | 0.940293i | \(0.389449\pi\) | |||||||
\(68\) | −0.641326 | − | 1.11081i | −0.0777723 | − | 0.134706i | ||||
\(69\) | 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 | \(0.442544\pi\) | |||||||
\(72\) | 0.866025 | + | 0.500000i | 0.102062 | + | 0.0589256i | ||||
\(73\) | 4.94644i | 0.578937i | 0.957188 | + | 0.289468i | \(0.0934785\pi\) | ||||
−0.957188 | + | 0.289468i | \(0.906522\pi\) | |||||||
\(74\) | −4.19076 | + | 7.25861i | −0.487166 | + | 0.843797i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.75861 | − | 3.32474i | 0.660558 | − | 0.381374i | ||||
\(77\) | −28.6246 | −3.26208 | ||||||||
\(78\) | 3.60278 | + | 0.141326i | 0.407935 | + | 0.0160021i | ||||
\(79\) | 10.1485 | 1.14179 | 0.570895 | − | 0.821023i | \(-0.306596\pi\) | ||||
0.570895 | + | 0.821023i | \(0.306596\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0.641326 | − | 1.11081i | 0.0708227 | − | 0.122668i | ||||
\(83\) | − | 17.3887i | − | 1.90866i | −0.298755 | − | 0.954330i | \(-0.596571\pi\) | ||
0.298755 | − | 0.954330i | \(-0.403429\pi\) | |||||||
\(84\) | −4.44290 | − | 2.56511i | −0.484760 | − | 0.279876i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.35800i | 0.469935i | ||||||||
\(87\) | −1.75214 | + | 3.03479i | −0.187849 | + | 0.325364i | ||||
\(88\) | 2.78981 | + | 4.83209i | 0.297395 | + | 0.515102i | ||||
\(89\) | 5.57884 | − | 3.22094i | 0.591355 | − | 0.341419i | −0.174278 | − | 0.984697i | \(-0.555759\pi\) |
0.765633 | + | 0.643277i | \(0.222426\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −18.4830 | − | 0.725036i | −1.93755 | − | 0.0760044i | ||||
\(92\) | 6.86227 | 0.715441 | ||||||||
\(93\) | 5.46131 | − | 3.15309i | 0.566312 | − | 0.326960i | ||||
\(94\) | −2.51176 | − | 4.35050i | −0.259069 | − | 0.448720i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | 6.20806 | + | 3.58423i | 0.630333 | + | 0.363923i | 0.780881 | − | 0.624680i | \(-0.214770\pi\) |
−0.150548 | + | 0.988603i | \(0.548104\pi\) | |||||||
\(98\) | 16.7309 | + | 9.65957i | 1.69007 | + | 0.975764i | ||||
\(99\) | − | 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 | \(-0.426931\pi\) | |||||||
\(102\) | −1.11081 | + | 0.641326i | −0.109987 | + | 0.0635008i | ||||
\(103\) | −4.04929 | −0.398989 | −0.199494 | − | 0.979899i | \(-0.563930\pi\) | ||||
−0.199494 | + | 0.979899i | \(0.563930\pi\) | |||||||
\(104\) | 1.67900 | + | 3.19076i | 0.164639 | + | 0.312880i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.46131 | + | 3.15309i | −0.530450 | + | 0.306255i | ||||
\(107\) | 3.88044 | + | 6.72112i | 0.375136 | + | 0.649755i | 0.990347 | − | 0.138608i | \(-0.0442626\pi\) |
−0.615211 | + | 0.788362i | \(0.710929\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | 0.792690i | 0.0759259i | 0.999279 | + | 0.0379630i | \(0.0120869\pi\) | ||||
−0.999279 | + | 0.0379630i | \(0.987913\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.25861 | + | 4.19076i | 0.688957 | + | 0.397770i | ||||
\(112\) | − | 5.13022i | − | 0.484760i | ||||||
\(113\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(114\) | −3.32474 | − | 5.75861i | −0.311390 | − | 0.539344i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.50427 | −0.325364 | ||||||||
\(117\) | 0.141326 | − | 3.60278i | 0.0130656 | − | 0.333077i | ||||
\(118\) | 1.51926 | 0.139859 | ||||||||
\(119\) | 5.69870 | − | 3.29014i | 0.522399 | − | 0.301607i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.0661 | − | 17.4349i | 0.915096 | − | 1.58499i | ||||
\(122\) | − | 10.3815i | − | 0.939899i | ||||||
\(123\) | −1.11081 | − | 0.641326i | −0.100158 | − | 0.0578265i | ||||
\(124\) | 5.46131 | + | 3.15309i | 0.490440 | + | 0.283156i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.56511 | + | 4.44290i | −0.228518 | + | 0.395805i | ||||
\(127\) | −8.12651 | − | 14.0755i | −0.721111 | − | 1.24900i | −0.960555 | − | 0.278090i | \(-0.910298\pi\) |
0.239444 | − | 0.970910i | \(-0.423035\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 4.35800 | 0.383700 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.04605 | 0.615616 | 0.307808 | − | 0.951448i | \(-0.400405\pi\) | ||||
0.307808 | + | 0.951448i | \(0.400405\pi\) | |||||||
\(132\) | 4.83209 | − | 2.78981i | 0.420579 | − | 0.242822i | ||||
\(133\) | 17.0566 | + | 29.5429i | 1.47900 | + | 2.56170i | ||||
\(134\) | −1.43555 | + | 2.48644i | −0.124012 | + | 0.214796i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.11081 | − | 0.641326i | −0.0952512 | − | 0.0549933i | ||||
\(137\) | −0.769058 | − | 0.444016i | −0.0657051 | − | 0.0379348i | 0.466788 | − | 0.884369i | \(-0.345411\pi\) |
−0.532493 | + | 0.846435i | \(0.678745\pi\) | |||||||
\(138\) | − | 6.86227i | − | 0.584155i | ||||||
\(139\) | −0.266279 | + | 0.461208i | −0.0225854 | + | 0.0391191i | −0.877097 | − | 0.480313i | \(-0.840523\pi\) |
0.854512 | + | 0.519432i | \(0.173856\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.35050 | + | 2.51176i | −0.366379 | + | 0.211529i | ||||
\(142\) | 10.9093 | 0.915490 | ||||||||
\(143\) | 10.7340 | − | 17.0147i | 0.897619 | − | 1.42284i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.47322 | + | 4.28374i | 0.204685 | + | 0.354525i | ||||
\(147\) | 9.65957 | − | 16.7309i | 0.796708 | − | 1.37994i | ||||
\(148\) | 8.38153i | 0.688957i | ||||||||
\(149\) | 18.0113 | + | 10.3988i | 1.47554 | + | 0.851905i | 0.999620 | − | 0.0275822i | \(-0.00878080\pi\) |
0.475923 | + | 0.879487i | \(0.342114\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.15400i | 0.175290i | 0.996152 | + | 0.0876448i | \(0.0279341\pi\) | ||||
−0.996152 | + | 0.0876448i | \(0.972066\pi\) | |||||||
\(152\) | 3.32474 | − | 5.75861i | 0.269672 | − | 0.467085i | ||||
\(153\) | 0.641326 | + | 1.11081i | 0.0518482 | + | 0.0898037i | ||||
\(154\) | −24.7897 | + | 14.3123i | −1.99761 | + | 1.15332i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.19076 | − | 1.67900i | 0.255465 | − | 0.134427i | ||||
\(157\) | 7.70236 | 0.614716 | 0.307358 | − | 0.951594i | \(-0.400555\pi\) | ||||
0.307358 | + | 0.951594i | \(0.400555\pi\) | |||||||
\(158\) | 8.78882 | − | 5.07423i | 0.699201 | − | 0.403684i | ||||
\(159\) | 3.15309 | + | 5.46131i | 0.250056 | + | 0.433110i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 35.2049i | 2.77454i | ||||||||
\(162\) | −0.866025 | − | 0.500000i | −0.0680414 | − | 0.0392837i | ||||
\(163\) | −0.382683 | − | 0.220942i | −0.0299741 | − | 0.0173055i | 0.484938 | − | 0.874548i | \(-0.338842\pi\) |
−0.514912 | + | 0.857243i | \(0.672175\pi\) | |||||||
\(164\) | − | 1.28265i | − | 0.100158i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.69436 | − | 15.0591i | −0.674813 | − | 1.16881i | ||||
\(167\) | −5.94290 | + | 3.43113i | −0.459875 | + | 0.265509i | −0.711992 | − | 0.702188i | \(-0.752207\pi\) |
0.252116 | + | 0.967697i | \(0.418873\pi\) | |||||||
\(168\) | −5.13022 | −0.395805 | ||||||||
\(169\) | 7.36193 | − | 10.7146i | 0.566302 | − | 0.824197i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.75861 | + | 3.32474i | −0.440372 | + | 0.254249i | ||||
\(172\) | 2.17900 | + | 3.77414i | 0.166147 | + | 0.287775i | ||||
\(173\) | −11.1449 | + | 19.3036i | −0.847333 | + | 1.46762i | 0.0362472 | + | 0.999343i | \(0.488460\pi\) |
−0.883580 | + | 0.468280i | \(0.844874\pi\) | |||||||
\(174\) | 3.50427i | 0.265658i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.83209 | + | 2.78981i | 0.364232 | + | 0.210290i | ||||
\(177\) | − | 1.51926i | − | 0.114194i | ||||||
\(178\) | 3.22094 | − | 5.57884i | 0.241420 | − | 0.418151i | ||||
\(179\) | 0.784447 | + | 1.35870i | 0.0586324 | + | 0.101554i | 0.893852 | − | 0.448363i | \(-0.147993\pi\) |
−0.835219 | + | 0.549917i | \(0.814659\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.4419 | 0.850469 | 0.425234 | − | 0.905083i | \(-0.360192\pi\) | ||||
0.425234 | + | 0.905083i | \(0.360192\pi\) | |||||||
\(182\) | −16.3693 | + | 8.61363i | −1.21337 | + | 0.638484i | ||||
\(183\) | −10.3815 | −0.767424 | ||||||||
\(184\) | 5.94290 | − | 3.43113i | 0.438116 | − | 0.252947i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.15309 | − | 5.46131i | 0.231196 | − | 0.400443i | ||||
\(187\) | 7.15671i | 0.523351i | ||||||||
\(188\) | −4.35050 | − | 2.51176i | −0.317293 | − | 0.183189i | ||||
\(189\) | 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 | \(0.270069\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | 9.68914 | − | 5.59403i | 0.697440 | − | 0.402667i | −0.108953 | − | 0.994047i | \(-0.534750\pi\) |
0.806393 | + | 0.591380i | \(0.201417\pi\) | |||||||
\(194\) | 7.16845 | 0.514665 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 19.3191 | 1.37994 | ||||||||
\(197\) | 19.8624 | − | 11.4675i | 1.41514 | − | 0.817029i | 0.419269 | − | 0.907862i | \(-0.362286\pi\) |
0.995866 | + | 0.0908332i | \(0.0289530\pi\) | |||||||
\(198\) | −2.78981 | − | 4.83209i | −0.198263 | − | 0.343402i | ||||
\(199\) | 5.52892 | − | 9.57637i | 0.391935 | − | 0.678851i | −0.600770 | − | 0.799422i | \(-0.705139\pi\) |
0.992705 | + | 0.120571i | \(0.0384726\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.48644 | + | 1.43555i | 0.175380 | + | 0.101256i | ||||
\(202\) | −12.6990 | − | 7.33175i | −0.893496 | − | 0.515860i | ||||
\(203\) | − | 17.9777i | − | 1.26179i | ||||||
\(204\) | −0.641326 | + | 1.11081i | −0.0449018 | + | 0.0777723i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.50679 | + | 2.02465i | −0.244330 | + | 0.141064i | ||||
\(207\) | −6.86227 | −0.476961 | ||||||||
\(208\) | 3.04944 | + | 1.92378i | 0.211440 | + | 0.133390i | ||||
\(209\) | −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 | \(-0.541493\pi\) | |||||||
\(212\) | −3.15309 | + | 5.46131i | −0.216555 | + | 0.375085i | ||||
\(213\) | − | 10.9093i | − | 0.747495i | ||||||
\(214\) | 6.72112 | + | 3.88044i | 0.459446 | + | 0.265261i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −16.1760 | + | 28.0177i | −1.09810 | + | 1.90197i | ||||
\(218\) | 0.396345 | + | 0.686490i | 0.0268439 | + | 0.0464949i | ||||
\(219\) | 4.28374 | − | 2.47322i | 0.289468 | − | 0.167125i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.181273 | + | 4.62112i | −0.0121937 | + | 0.310850i | ||||
\(222\) | 8.38153 | 0.562531 | ||||||||
\(223\) | −0.0599161 | + | 0.0345926i | −0.00401228 | + | 0.00231649i | −0.502005 | − | 0.864865i | \(-0.667404\pi\) |
0.497993 | + | 0.867181i | \(0.334071\pi\) | |||||||
\(224\) | −2.56511 | − | 4.44290i | −0.171389 | − | 0.296854i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.36241 | + | 3.09599i | 0.355916 | + | 0.205488i | 0.667288 | − | 0.744800i | \(-0.267455\pi\) |
−0.311372 | + | 0.950288i | \(0.600788\pi\) | |||||||
\(228\) | −5.75861 | − | 3.32474i | −0.381374 | − | 0.220186i | ||||
\(229\) | 17.3857i | 1.14888i | 0.818548 | + | 0.574438i | \(0.194779\pi\) | ||||
−0.818548 | + | 0.574438i | \(0.805221\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.3123 | + | 24.7897i | 0.941682 | + | 1.63104i | ||||
\(232\) | −3.03479 | + | 1.75214i | −0.199244 | + | 0.115033i | ||||
\(233\) | −17.7716 | −1.16426 | −0.582128 | − | 0.813097i | \(-0.697780\pi\) | ||||
−0.582128 | + | 0.813097i | \(0.697780\pi\) | |||||||
\(234\) | −1.67900 | − | 3.19076i | −0.109760 | − | 0.208587i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.31571 | − | 0.759628i | 0.0856457 | − | 0.0494476i | ||||
\(237\) | −5.07423 | − | 8.78882i | −0.329606 | − | 0.570895i | ||||
\(238\) | 3.29014 | − | 5.69870i | 0.213268 | − | 0.369392i | ||||
\(239\) | − | 17.1487i | − | 1.10925i | −0.832099 | − | 0.554627i | \(-0.812861\pi\) | ||
0.832099 | − | 0.554627i | \(-0.187139\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.1831 | − | 8.76597i | −0.978029 | − | 0.564665i | −0.0763547 | − | 0.997081i | \(-0.524328\pi\) |
−0.901675 | + | 0.432415i | \(0.857661\pi\) | |||||||
\(242\) | − | 20.1321i | − | 1.29414i | ||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −5.19076 | − | 8.99066i | −0.332305 | − | 0.575568i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.28265 | −0.0817790 | ||||||||
\(247\) | −23.9566 | − | 0.939747i | −1.52432 | − | 0.0597947i | ||||
\(248\) | 6.30618 | 0.400443 | ||||||||
\(249\) | −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 | \(0.971819\pi\) | |||||||
\(252\) | 5.13022i | 0.323173i | ||||||||
\(253\) | −33.1591 | − | 19.1444i | −2.08469 | − | 1.20360i | ||||
\(254\) | −14.0755 | − | 8.12651i | −0.883177 | − | 0.509902i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −8.80056 | − | 15.2430i | −0.548964 | − | 0.950833i | −0.998346 | − | 0.0574935i | \(-0.981689\pi\) |
0.449382 | − | 0.893340i | \(-0.351644\pi\) | |||||||
\(258\) | 3.77414 | − | 2.17900i | 0.234967 | − | 0.135658i | ||||
\(259\) | −42.9991 | −2.67183 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.50427 | 0.216909 | ||||||||
\(262\) | 6.10206 | − | 3.52302i | 0.376986 | − | 0.217653i | ||||
\(263\) | −5.88051 | − | 10.1853i | −0.362608 | − | 0.628055i | 0.625781 | − | 0.779999i | \(-0.284780\pi\) |
−0.988389 | + | 0.151943i | \(0.951447\pi\) | |||||||
\(264\) | 2.78981 | − | 4.83209i | 0.171701 | − | 0.297395i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 29.5429 | + | 17.0566i | 1.81139 | + | 1.04581i | ||||
\(267\) | −5.57884 | − | 3.22094i | −0.341419 | − | 0.197118i | ||||
\(268\) | 2.87109i | 0.175380i | ||||||||
\(269\) | 3.20490 | − | 5.55106i | 0.195406 | − | 0.338454i | −0.751627 | − | 0.659588i | \(-0.770731\pi\) |
0.947034 | + | 0.321134i | \(0.104064\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.6919 | − | 7.90503i | 0.831725 | − | 0.480196i | −0.0227182 | − | 0.999742i | \(-0.507232\pi\) |
0.854443 | + | 0.519545i | \(0.173899\pi\) | |||||||
\(272\) | −1.28265 | −0.0777723 | ||||||||
\(273\) | 8.61363 | + | 16.3693i | 0.521320 | + | 0.990716i | ||||
\(274\) | −0.888032 | −0.0536480 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.43113 | − | 5.94290i | −0.206530 | − | 0.357720i | ||||
\(277\) | 2.49319 | − | 4.31832i | 0.149801 | − | 0.259463i | −0.781353 | − | 0.624090i | \(-0.785470\pi\) |
0.931154 | + | 0.364627i | \(0.118803\pi\) | |||||||
\(278\) | 0.532557i | 0.0319406i | ||||||||
\(279\) | −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 | \(0.995103\pi\) | |||||||
\(282\) | −2.51176 | + | 4.35050i | −0.149573 | + | 0.259069i | ||||
\(283\) | −8.97308 | − | 15.5418i | −0.533394 | − | 0.923866i | −0.999239 | − | 0.0389995i | \(-0.987583\pi\) |
0.465845 | − | 0.884866i | \(-0.345750\pi\) | |||||||
\(284\) | 9.44775 | − | 5.45466i | 0.560621 | − | 0.323675i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.788547 | − | 20.1021i | 0.0466278 | − | 1.18866i | ||||
\(287\) | 6.58029 | 0.388422 | ||||||||
\(288\) | 0.866025 | − | 0.500000i | 0.0510310 | − | 0.0294628i | ||||
\(289\) | 7.67740 | + | 13.2976i | 0.451612 | + | 0.782215i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 7.16845i | − | 0.420222i | ||||||
\(292\) | 4.28374 | + | 2.47322i | 0.250687 | + | 0.144734i | ||||
\(293\) | −14.9572 | − | 8.63553i | −0.873808 | − | 0.504493i | −0.00519587 | − | 0.999987i | \(-0.501654\pi\) |
−0.868612 | + | 0.495493i | \(0.834987\pi\) | |||||||
\(294\) | − | 19.3191i | − | 1.12671i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.19076 | + | 7.25861i | 0.243583 | + | 0.421898i | ||||
\(297\) | −4.83209 | + | 2.78981i | −0.280386 | + | 0.161881i | ||||
\(298\) | 20.7976 | 1.20478 | ||||||||
\(299\) | −20.9261 | − | 13.2015i | −1.21018 | − | 0.763463i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −19.3621 | + | 11.1787i | −1.11601 | + | 0.644332i | ||||
\(302\) | 1.07700 | + | 1.86541i | 0.0619742 | + | 0.107343i | ||||
\(303\) | −7.33175 | + | 12.6990i | −0.421198 | + | 0.729537i | ||||
\(304\) | − | 6.64947i | − | 0.381374i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.11081 | + | 0.641326i | 0.0635008 | + | 0.0366622i | ||||
\(307\) | 14.2673i | 0.814279i | 0.913366 | + | 0.407140i | \(0.133474\pi\) | ||||
−0.913366 | + | 0.407140i | \(0.866526\pi\) | |||||||
\(308\) | −14.3123 | + | 24.7897i | −0.815520 | + | 1.41252i | ||||
\(309\) | 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 | \(0.727888\pi\) | |||||||
\(312\) | 1.92378 | − | 3.04944i | 0.108913 | − | 0.172640i | ||||
\(313\) | −14.1122 | −0.797667 | −0.398834 | − | 0.917023i | \(-0.630585\pi\) | ||||
−0.398834 | + | 0.917023i | \(0.630585\pi\) | |||||||
\(314\) | 6.67044 | − | 3.85118i | 0.376435 | − | 0.217335i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.07423 | − | 8.78882i | 0.285448 | − | 0.494410i | ||||
\(317\) | 12.1814i | 0.684176i | 0.939668 | + | 0.342088i | \(0.111134\pi\) | ||||
−0.939668 | + | 0.342088i | \(0.888866\pi\) | |||||||
\(318\) | 5.46131 | + | 3.15309i | 0.306255 | + | 0.176817i | ||||
\(319\) | 16.9330 | + | 9.77625i | 0.948064 | + | 0.547365i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.88044 | − | 6.72112i | 0.216585 | − | 0.375136i | ||||
\(322\) | 17.6025 | + | 30.4884i | 0.980947 | + | 1.69905i | ||||
\(323\) | 7.38630 | − | 4.26448i | 0.410985 | − | 0.237282i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.441885 | −0.0244737 | ||||||||
\(327\) | 0.686490 | − | 0.396345i | 0.0379630 | − | 0.0219179i | ||||
\(328\) | −0.641326 | − | 1.11081i | −0.0354113 | − | 0.0613342i | ||||
\(329\) | 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 | \(0.627530\pi\) | |||||||
\(332\) | −15.0591 | − | 8.69436i | −0.826474 | − | 0.477165i | ||||
\(333\) | − | 8.38153i | − | 0.459305i | ||||||
\(334\) | −3.43113 | + | 5.94290i | −0.187743 | + | 0.325181i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.44290 | + | 2.56511i | −0.242380 | + | 0.139938i | ||||
\(337\) | −6.04773 | −0.329441 | −0.164720 | − | 0.986340i | \(-0.552672\pi\) | ||||
−0.164720 | + | 0.986340i | \(0.552672\pi\) | |||||||
\(338\) | 1.01834 | − | 12.9601i | 0.0553902 | − | 0.704934i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.5930 | − | 30.4720i | −0.952716 | − | 1.65015i | ||||
\(342\) | −3.32474 | + | 5.75861i | −0.179781 | + | 0.311390i | ||||
\(343\) | 63.1999i | 3.41247i | ||||||||
\(344\) | 3.77414 | + | 2.17900i | 0.203488 | + | 0.117484i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 22.2898i | 1.19831i | ||||||||
\(347\) | 3.17327 | − | 5.49627i | 0.170350 | − | 0.295055i | −0.768192 | − | 0.640219i | \(-0.778843\pi\) |
0.938542 | + | 0.345164i | \(0.112177\pi\) | |||||||
\(348\) | 1.75214 | + | 3.03479i | 0.0939244 | + | 0.162682i | ||||
\(349\) | −24.4438 | + | 14.1126i | −1.30844 | + | 0.755431i | −0.981836 | − | 0.189729i | \(-0.939239\pi\) |
−0.326608 | + | 0.945160i | \(0.605906\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.19076 | + | 1.67900i | −0.170310 | + | 0.0896183i | ||||
\(352\) | 5.57962 | 0.297395 | ||||||||
\(353\) | −13.9378 | + | 8.04696i | −0.741832 | + | 0.428297i | −0.822735 | − | 0.568425i | \(-0.807553\pi\) |
0.0809033 | + | 0.996722i | \(0.474220\pi\) | |||||||
\(354\) | −0.759628 | − | 1.31571i | −0.0403738 | − | 0.0699294i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 6.44188i | − | 0.341419i | ||||||
\(357\) | −5.69870 | − | 3.29014i | −0.301607 | − | 0.174133i | ||||
\(358\) | 1.35870 | + | 0.784447i | 0.0718097 | + | 0.0414593i | ||||
\(359\) | − | 8.79689i | − | 0.464282i | −0.972682 | − | 0.232141i | \(-0.925427\pi\) | ||
0.972682 | − | 0.232141i | \(-0.0745731\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.6078 | + | 21.8373i | 0.663566 | + | 1.14933i | ||||
\(362\) | 9.90896 | − | 5.72094i | 0.520804 | − | 0.300686i | ||||
\(363\) | −20.1321 | −1.05666 | ||||||||
\(364\) | −9.86942 | + | 15.6443i | −0.517298 | + | 0.819983i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −8.99066 | + | 5.19076i | −0.469950 | + | 0.271326i | ||||
\(367\) | 19.0032 | + | 32.9145i | 0.991958 | + | 1.71812i | 0.605588 | + | 0.795779i | \(0.292938\pi\) |
0.386371 | + | 0.922344i | \(0.373729\pi\) | |||||||
\(368\) | 3.43113 | − | 5.94290i | 0.178860 | − | 0.309795i | ||||
\(369\) | 1.28265i | 0.0667722i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −28.0177 | − | 16.1760i | −1.45461 | − | 0.839818i | ||||
\(372\) | − | 6.30618i | − | 0.326960i | ||||||
\(373\) | 8.50787 | − | 14.7361i | 0.440521 | − | 0.763004i | −0.557207 | − | 0.830373i | \(-0.688127\pi\) |
0.997728 | + | 0.0673691i | \(0.0214605\pi\) | |||||||
\(374\) | 3.57836 | + | 6.19789i | 0.185032 | + | 0.320485i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.02353 | −0.259069 | ||||||||
\(377\) | 10.6861 | + | 6.74146i | 0.550360 | + | 0.347203i | ||||
\(378\) | 5.13022 | 0.263870 | ||||||||
\(379\) | 11.0257 | − | 6.36569i | 0.566352 | − | 0.326983i | −0.189339 | − | 0.981912i | \(-0.560635\pi\) |
0.755691 | + | 0.654928i | \(0.227301\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.12651 | + | 14.0755i | −0.416334 | + | 0.721111i | ||||
\(382\) | 8.82185i | 0.451365i | ||||||||
\(383\) | 19.5478 | + | 11.2859i | 0.998845 | + | 0.576683i | 0.907906 | − | 0.419173i | \(-0.137680\pi\) |
0.0909383 | + | 0.995857i | \(0.471013\pi\) | |||||||
\(384\) | 0.866025 | + | 0.500000i | 0.0441942 | + | 0.0255155i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.59403 | − | 9.68914i | 0.284729 | − | 0.493164i | ||||
\(387\) | −2.17900 | − | 3.77414i | −0.110765 | − | 0.191850i | ||||
\(388\) | 6.20806 | − | 3.58423i | 0.315167 | − | 0.181961i | ||||
\(389\) | 3.50427 | 0.177674 | 0.0888368 | − | 0.996046i | \(-0.471685\pi\) | ||||
0.0888368 | + | 0.996046i | \(0.471685\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.80191 | 0.445132 | ||||||||
\(392\) | 16.7309 | − | 9.65957i | 0.845036 | − | 0.487882i | ||||
\(393\) | −3.52302 | − | 6.10206i | −0.177713 | − | 0.307808i | ||||
\(394\) | 11.4675 | − | 19.8624i | 0.577727 | − | 1.00065i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −4.83209 | − | 2.78981i | −0.242822 | − | 0.140193i | ||||
\(397\) | 25.8640 | + | 14.9326i | 1.29808 | + | 0.749445i | 0.980072 | − | 0.198644i | \(-0.0636537\pi\) |
0.318005 | + | 0.948089i | \(0.396987\pi\) | |||||||
\(398\) | − | 11.0578i | − | 0.554279i | ||||||
\(399\) | 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 | \(0.549194\pi\) | |||||||
\(402\) | 2.87109 | 0.143197 | ||||||||
\(403\) | −10.5881 | − | 20.1215i | −0.527429 | − | 1.00232i | ||||
\(404\) | −14.6635 | −0.729537 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.98884 | − | 15.5691i | −0.446109 | − | 0.772683i | ||||
\(407\) | 23.3828 | − | 40.5003i | 1.15904 | − | 2.00752i | ||||
\(408\) | 1.28265i | 0.0635008i | ||||||||
\(409\) | 4.54462 | + | 2.62384i | 0.224717 | + | 0.129740i | 0.608132 | − | 0.793836i | \(-0.291919\pi\) |
−0.383416 | + | 0.923576i | \(0.625252\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.888032i | 0.0438034i | ||||||||
\(412\) | −2.02465 | + | 3.50679i | −0.0997472 | + | 0.172767i | ||||
\(413\) | 3.89706 | + | 6.74990i | 0.191762 | + | 0.332141i | ||||
\(414\) | −5.94290 | + | 3.43113i | −0.292078 | + | 0.168631i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.60278 | + | 0.141326i | 0.176641 | + | 0.00692910i | ||||
\(417\) | 0.532557 | 0.0260794 | ||||||||
\(418\) | −32.1309 | + | 18.5508i | −1.57157 | + | 0.907347i | ||||
\(419\) | 9.01326 | + | 15.6114i | 0.440326 | + | 0.762668i | 0.997714 | − | 0.0675850i | \(-0.0215294\pi\) |
−0.557387 | + | 0.830253i | \(0.688196\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.92370i | 0.386178i | 0.981181 | + | 0.193089i | \(0.0618506\pi\) | ||||
−0.981181 | + | 0.193089i | \(0.938149\pi\) | |||||||
\(422\) | −23.2391 | − | 13.4171i | −1.13126 | − | 0.653134i | ||||
\(423\) | 4.35050 | + | 2.51176i | 0.211529 | + | 0.122126i | ||||
\(424\) | 6.30618i | 0.306255i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.45466 | − | 9.44775i | −0.264279 | − | 0.457745i | ||||
\(427\) | 46.1241 | − | 26.6297i | 2.23210 | − | 1.28870i | ||||
\(428\) | 7.76088 | 0.375136 | ||||||||
\(429\) | −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 | \(-0.0406090\pi\) | |||||||
\(432\) | −0.500000 | − | 0.866025i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | 10.0026 | − | 17.3250i | 0.480693 | − | 0.832585i | −0.519061 | − | 0.854737i | \(-0.673718\pi\) |
0.999755 | + | 0.0221517i | \(0.00705169\pi\) | |||||||
\(434\) | 32.3521i | 1.55295i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.686490 | + | 0.396345i | 0.0328769 | + | 0.0189815i | ||||
\(437\) | 45.6305i | 2.18280i | ||||||||
\(438\) | 2.47322 | − | 4.28374i | 0.118175 | − | 0.204685i | ||||
\(439\) | 5.96660 | + | 10.3345i | 0.284770 | + | 0.493237i | 0.972553 | − | 0.232680i | \(-0.0747493\pi\) |
−0.687783 | + | 0.725916i | \(0.741416\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.3191 | −0.919959 | ||||||||
\(442\) | 2.15357 | + | 4.09264i | 0.102435 | + | 0.194667i | ||||
\(443\) | −26.0565 | −1.23798 | −0.618990 | − | 0.785399i | \(-0.712458\pi\) | ||||
−0.618990 | + | 0.785399i | \(0.712458\pi\) | |||||||
\(444\) | 7.25861 | − | 4.19076i | 0.344479 | − | 0.198885i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.0345926 | + | 0.0599161i | −0.00163801 | + | 0.00283711i | ||||
\(447\) | − | 20.7976i | − | 0.983695i | ||||||
\(448\) | −4.44290 | − | 2.56511i | −0.209907 | − | 0.121190i | ||||
\(449\) | −14.4966 | − | 8.36959i | −0.684135 | − | 0.394985i | 0.117276 | − | 0.993099i | \(-0.462584\pi\) |
−0.801411 | + | 0.598114i | \(0.795917\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.57836 | + | 6.19789i | −0.168498 | + | 0.291847i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.86541 | − | 1.07700i | 0.0876448 | − | 0.0506018i | ||||
\(454\) | 6.19198 | 0.290604 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.64947 | −0.311390 | ||||||||
\(457\) | −6.15626 | + | 3.55432i | −0.287977 | + | 0.166264i | −0.637029 | − | 0.770840i | \(-0.719837\pi\) |
0.349052 | + | 0.937103i | \(0.386504\pi\) | |||||||
\(458\) | 8.69283 | + | 15.0564i | 0.406189 | + | 0.703540i | ||||
\(459\) | 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 | \(0.707670\pi\) | |||||||
\(462\) | 24.7897 | + | 14.3123i | 1.15332 | + | 0.665870i | ||||
\(463\) | 4.98759i | 0.231793i | 0.993261 | + | 0.115896i | \(0.0369741\pi\) | ||||
−0.993261 | + | 0.115896i | \(0.963026\pi\) | |||||||
\(464\) | −1.75214 | + | 3.03479i | −0.0813409 | + | 0.140887i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15.3907 | + | 8.88580i | −0.712958 | + | 0.411627i | ||||
\(467\) | 19.7410 | 0.913506 | 0.456753 | − | 0.889594i | \(-0.349012\pi\) | ||||
0.456753 | + | 0.889594i | \(0.349012\pi\) | |||||||
\(468\) | −3.04944 | − | 1.92378i | −0.140960 | − | 0.0889269i | ||||
\(469\) | −14.7293 | −0.680138 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.85118 | − | 6.67044i | −0.177453 | − | 0.307358i | ||||
\(472\) | 0.759628 | − | 1.31571i | 0.0349647 | − | 0.0605607i | ||||
\(473\) | − | 24.3159i | − | 1.11805i | ||||||
\(474\) | −8.78882 | − | 5.07423i | −0.403684 | − | 0.233067i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 6.58029i | − | 0.301607i | ||||||
\(477\) | 3.15309 | − | 5.46131i | 0.144370 | − | 0.250056i | ||||
\(478\) | −8.57433 | − | 14.8512i | −0.392181 | − | 0.679277i | ||||
\(479\) | −7.46188 | + | 4.30812i | −0.340942 | + | 0.196843i | −0.660689 | − | 0.750660i | \(-0.729736\pi\) |
0.319746 | + | 0.947503i | \(0.396402\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.1242 | − | 25.5589i | 0.735202 | − | 1.16539i | ||||
\(482\) | −17.5319 | −0.798558 | ||||||||
\(483\) | 30.4884 | − | 17.6025i | 1.38727 | − | 0.800940i | ||||
\(484\) | −10.0661 | − | 17.4349i | −0.457548 | − | 0.792496i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | −16.9919 | − | 9.81026i | −0.769975 | − | 0.444545i | 0.0628907 | − | 0.998020i | \(-0.479968\pi\) |
−0.832866 | + | 0.553475i | \(0.813301\pi\) | |||||||
\(488\) | −8.99066 | − | 5.19076i | −0.406988 | − | 0.234975i | ||||
\(489\) | 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 | \(-0.521443\pi\) | |||||||
\(492\) | −1.11081 | + | 0.641326i | −0.0500792 | + | 0.0289132i | ||||
\(493\) | −4.49477 | −0.202434 | ||||||||
\(494\) | −21.2169 | + | 11.1645i | −0.954593 | + | 0.502313i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.46131 | − | 3.15309i | 0.245220 | − | 0.141578i | ||||
\(497\) | 27.9836 | + | 48.4690i | 1.25524 | + | 2.17413i | ||||
\(498\) | −8.69436 | + | 15.0591i | −0.389603 | + | 0.674813i | ||||
\(499\) | − | 7.84082i | − | 0.351004i | −0.984479 | − | 0.175502i | \(-0.943845\pi\) | ||
0.984479 | − | 0.175502i | \(-0.0561548\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.94290 | + | 3.43113i | 0.265509 | + | 0.153292i | ||||
\(502\) | 18.2072i | 0.812626i | ||||||||
\(503\) | −3.55194 | + | 6.15215i | −0.158373 | + | 0.274311i | −0.934282 | − | 0.356534i | \(-0.883958\pi\) |
0.775909 | + | 0.630845i | \(0.217292\pi\) | |||||||
\(504\) | 2.56511 | + | 4.44290i | 0.114259 | + | 0.197902i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −38.2888 | −1.70215 | ||||||||
\(507\) | −12.9601 | − | 1.01834i | −0.575576 | − | 0.0452259i | ||||
\(508\) | −16.2530 | −0.721111 | ||||||||
\(509\) | 34.0477 | − | 19.6575i | 1.50914 | − | 0.871302i | 0.509196 | − | 0.860651i | \(-0.329943\pi\) |
0.999943 | − | 0.0106512i | \(-0.00339045\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.6882 | + | 21.9765i | −0.561291 | + | 0.972184i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 5.75861 | + | 3.32474i | 0.254249 | + | 0.146791i | ||||
\(514\) | −15.2430 | − | 8.80056i | −0.672341 | − | 0.388176i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.17900 | − | 3.77414i | 0.0959250 | − | 0.166147i | ||||
\(517\) | 14.0147 | + | 24.2741i | 0.616365 | + | 1.06758i | ||||
\(518\) | −37.2383 | + | 21.4995i | −1.63616 | + | 0.944635i | ||||
\(519\) | 22.2898 | 0.978416 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.1840 | 1.71668 | 0.858341 | − | 0.513080i | \(-0.171496\pi\) | ||||
0.858341 | + | 0.513080i | \(0.171496\pi\) | |||||||
\(522\) | 3.03479 | − | 1.75214i | 0.132829 | − | 0.0766889i | ||||
\(523\) | −4.23654 | − | 7.33790i | −0.185251 | − | 0.320864i | 0.758410 | − | 0.651778i | \(-0.225976\pi\) |
−0.943661 | + | 0.330914i | \(0.892643\pi\) | |||||||
\(524\) | 3.52302 | − | 6.10206i | 0.153904 | − | 0.266570i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.1853 | − | 5.88051i | −0.444102 | − | 0.256402i | ||||
\(527\) | 7.00497 | + | 4.04432i | 0.305141 | + | 0.176173i | ||||
\(528\) | − | 5.57962i | − | 0.242822i | ||||||
\(529\) | −12.0454 | + | 20.8632i | −0.523712 | + | 0.907095i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.31571 | + | 0.759628i | −0.0570972 | + | 0.0329651i | ||||
\(532\) | 34.1133 | 1.47900 | ||||||||
\(533\) | −2.46755 | + | 3.91137i | −0.106881 | + | 0.169420i | ||||
\(534\) | −6.44188 | −0.278768 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.43555 | + | 2.48644i | 0.0620062 | + | 0.107398i | ||||
\(537\) | 0.784447 | − | 1.35870i | 0.0338514 | − | 0.0586324i | ||||
\(538\) | − | 6.40981i | − | 0.276346i | ||||||
\(539\) | −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 | \(0.898453\pi\) | |||||||
\(542\) | 7.90503 | − | 13.6919i | 0.339550 | − | 0.588118i | ||||
\(543\) | −5.72094 | − | 9.90896i | −0.245509 | − | 0.425234i | ||||
\(544\) | −1.11081 | + | 0.641326i | −0.0476256 | + | 0.0274966i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 15.6443 | + | 9.86942i | 0.669513 | + | 0.422372i | ||||
\(547\) | −14.2246 | −0.608200 | −0.304100 | − | 0.952640i | \(-0.598356\pi\) | ||||
−0.304100 | + | 0.952640i | \(0.598356\pi\) | |||||||
\(548\) | −0.769058 | + | 0.444016i | −0.0328525 | + | 0.0189674i | ||||
\(549\) | 5.19076 | + | 8.99066i | 0.221536 | + | 0.383712i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 23.3016i | − | 0.992680i | ||||||
\(552\) | −5.94290 | − | 3.43113i | −0.252947 | − | 0.146039i | ||||
\(553\) | 45.0885 | + | 26.0319i | 1.91736 | + | 1.10699i | ||||
\(554\) | − | 4.98637i | − | 0.211851i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.266279 | + | 0.461208i | 0.0112927 | + | 0.0195596i | ||||
\(557\) | −30.2289 | + | 17.4527i | −1.28084 | + | 0.739493i | −0.977002 | − | 0.213231i | \(-0.931601\pi\) |
−0.303838 | + | 0.952724i | \(0.598268\pi\) | |||||||
\(558\) | −6.30618 | −0.266962 | ||||||||
\(559\) | 0.615900 | − | 15.7009i | 0.0260498 | − | 0.664077i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.19789 | − | 3.57836i | 0.261675 | − | 0.151078i | ||||
\(562\) | 0.257863 | + | 0.446632i | 0.0108773 | + | 0.0188400i | ||||
\(563\) | −7.90879 | + | 13.6984i | −0.333316 | + | 0.577320i | −0.983160 | − | 0.182748i | \(-0.941501\pi\) |
0.649844 | + | 0.760067i | \(0.274834\pi\) | |||||||
\(564\) | 5.02353i | 0.211529i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −15.5418 | − | 8.97308i | −0.653272 | − | 0.377167i | ||||
\(567\) | − | 5.13022i | − | 0.215449i | ||||||
\(568\) | 5.45466 | − | 9.44775i | 0.228873 | − | 0.396419i | ||||
\(569\) | −0.234472 | − | 0.406118i | −0.00982959 | − | 0.0170253i | 0.861069 | − | 0.508489i | \(-0.169796\pi\) |
−0.870898 | + | 0.491463i | \(0.836462\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.6325 | 0.905292 | 0.452646 | − | 0.891690i | \(-0.350480\pi\) | ||||
0.452646 | + | 0.891690i | \(0.350480\pi\) | |||||||
\(572\) | −9.36816 | − | 17.8032i | −0.391703 | − | 0.744390i | ||||
\(573\) | 8.82185 | 0.368538 | ||||||||
\(574\) | 5.69870 | − | 3.29014i | 0.237859 | − | 0.137328i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 21.2140i | 0.883149i | 0.897225 | + | 0.441574i | \(0.145580\pi\) | ||||
−0.897225 | + | 0.441574i | \(0.854420\pi\) | |||||||
\(578\) | 13.2976 | + | 7.67740i | 0.553109 | + | 0.319338i | ||||
\(579\) | −9.68914 | − | 5.59403i | −0.402667 | − | 0.232480i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 44.6040 | − | 77.2563i | 1.85048 | − | 3.20513i | ||||
\(582\) | −3.58423 | − | 6.20806i | −0.148571 | − | 0.257332i | ||||
\(583\) | 30.4720 | − | 17.5930i | 1.26202 | − | 0.728629i | ||||
\(584\) | 4.94644 | 0.204685 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −17.2711 | −0.713461 | ||||||||
\(587\) | 2.05536 | − | 1.18666i | 0.0848338 | − | 0.0489788i | −0.456983 | − | 0.889475i | \(-0.651070\pi\) |
0.541817 | + | 0.840497i | \(0.317737\pi\) | |||||||
\(588\) | −9.65957 | − | 16.7309i | −0.398354 | − | 0.689969i | ||||
\(589\) | −20.9664 | + | 36.3149i | −0.863905 | + | 1.49633i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19.8624 | − | 11.4675i | −0.817029 | − | 0.471712i | ||||
\(592\) | 7.25861 | + | 4.19076i | 0.298327 | + | 0.172239i | ||||
\(593\) | − | 2.26258i | − | 0.0929130i | −0.998920 | − | 0.0464565i | \(-0.985207\pi\) | ||
0.998920 | − | 0.0464565i | \(-0.0147929\pi\) | |||||||
\(594\) | −2.78981 | + | 4.83209i | −0.114467 | + | 0.198263i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 18.0113 | − | 10.3988i | 0.737771 | − | 0.425952i | ||||
\(597\) | −11.0578 | −0.452567 | ||||||||
\(598\) | −24.7232 | − | 0.969820i | −1.01101 | − | 0.0396589i | ||||
\(599\) | −8.04828 | −0.328844 | −0.164422 | − | 0.986390i | \(-0.552576\pi\) | ||||
−0.164422 | + | 0.986390i | \(0.552576\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.32625 | − | 2.29713i | −0.0540988 | − | 0.0937019i | 0.837708 | − | 0.546119i | \(-0.183895\pi\) |
−0.891807 | + | 0.452417i | \(0.850562\pi\) | |||||||
\(602\) | −11.1787 | + | 19.3621i | −0.455611 | + | 0.789142i | ||||
\(603\) | − | 2.87109i | − | 0.116920i | ||||||
\(604\) | 1.86541 | + | 1.07700i | 0.0759026 | + | 0.0438224i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 14.6635i | 0.595664i | ||||||||
\(607\) | −1.09680 | + | 1.89971i | −0.0445177 | + | 0.0771070i | −0.887426 | − | 0.460951i | \(-0.847508\pi\) |
0.842908 | + | 0.538058i | \(0.180842\pi\) | |||||||
\(608\) | −3.32474 | − | 5.75861i | −0.134836 | − | 0.233543i | ||||
\(609\) | −15.5691 | + | 8.98884i | −0.630893 | + | 0.364246i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.43450 | + | 16.0289i | 0.341223 | + | 0.648459i | ||||
\(612\) | 1.28265 | 0.0518482 | ||||||||
\(613\) | −0.0840326 | + | 0.0485163i | −0.00339405 | + | 0.00195955i | −0.501696 | − | 0.865044i | \(-0.667290\pi\) |
0.498302 | + | 0.867004i | \(0.333957\pi\) | |||||||
\(614\) | 7.13366 | + | 12.3559i | 0.287891 | + | 0.498642i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 28.6246i | 1.15332i | ||||||||
\(617\) | −5.74580 | − | 3.31734i | −0.231317 | − | 0.133551i | 0.379862 | − | 0.925043i | \(-0.375971\pi\) |
−0.611180 | + | 0.791492i | \(0.709305\pi\) | |||||||
\(618\) | 3.50679 | + | 2.02465i | 0.141064 | + | 0.0814432i | ||||
\(619\) | − | 14.0315i | − | 0.563973i | −0.959418 | − | 0.281987i | \(-0.909007\pi\) | ||
0.959418 | − | 0.281987i | \(-0.0909934\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.43113 | + | 5.94290i | 0.137687 | + | 0.238480i | ||||
\(622\) | −20.0473 | + | 11.5743i | −0.803824 | + | 0.464088i | ||||
\(623\) | 33.0483 | 1.32405 | ||||||||
\(624\) | 0.141326 | − | 3.60278i | 0.00565759 | − | 0.144227i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −12.2215 | + | 7.05609i | −0.488469 | + | 0.282018i | ||||
\(627\) | 18.5508 | + | 32.1309i | 0.740846 | + | 1.28318i | ||||
\(628\) | 3.85118 | − | 6.67044i | 0.153679 | − | 0.266180i | ||||
\(629\) | 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 | \(0.978751\pi\) | |||||||
\(632\) | − | 10.1485i | − | 0.403684i | ||||||
\(633\) | −13.4171 | + | 23.2391i | −0.533282 | + | 0.923671i | ||||
\(634\) | 6.09070 | + | 10.5494i | 0.241893 | + | 0.418970i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 6.30618 | 0.250056 | ||||||||
\(637\) | −58.9125 | − | 37.1658i | −2.33420 | − | 1.47256i | ||||
\(638\) | 19.5525 | 0.774091 | ||||||||
\(639\) | −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 | \(0.906994\pi\) | |||||||
\(642\) | − | 7.76088i | − | 0.306297i | ||||||
\(643\) | 18.9996 | + | 10.9694i | 0.749271 | + | 0.432592i | 0.825430 | − | 0.564504i | \(-0.190933\pi\) |
−0.0761597 | + | 0.997096i | \(0.524266\pi\) | |||||||
\(644\) | 30.4884 | + | 17.6025i | 1.20141 | + | 0.693634i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.26448 | − | 7.38630i | 0.167784 | − | 0.290610i | ||||
\(647\) | 0.971183 | + | 1.68214i | 0.0381811 | + | 0.0661317i | 0.884485 | − | 0.466570i | \(-0.154510\pi\) |
−0.846303 | + | 0.532701i | \(0.821177\pi\) | |||||||
\(648\) | −0.866025 | + | 0.500000i | −0.0340207 | + | 0.0196419i | ||||
\(649\) | −8.47687 | −0.332746 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 32.3521 | 1.26798 | ||||||||
\(652\) | −0.382683 | + | 0.220942i | −0.0149870 | + | 0.00865277i | ||||
\(653\) | −5.27812 | − | 9.14197i | −0.206549 | − | 0.357753i | 0.744076 | − | 0.668095i | \(-0.232890\pi\) |
−0.950625 | + | 0.310342i | \(0.899557\pi\) | |||||||
\(654\) | 0.396345 | − | 0.686490i | 0.0154983 | − | 0.0268439i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.11081 | − | 0.641326i | −0.0433698 | − | 0.0250396i | ||||
\(657\) | −4.28374 | − | 2.47322i | −0.167125 | − | 0.0964895i | ||||
\(658\) | − | 25.7718i | − | 1.00469i | ||||||
\(659\) | 0.191440 | − | 0.331584i | 0.00745746 | − | 0.0129167i | −0.862273 | − | 0.506444i | \(-0.830960\pi\) |
0.869730 | + | 0.493528i | \(0.164293\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.5877 | − | 13.0410i | 0.878560 | − | 0.507237i | 0.00837690 | − | 0.999965i | \(-0.497334\pi\) |
0.870183 | + | 0.492728i | \(0.164000\pi\) | |||||||
\(662\) | 4.46249 | 0.173440 | ||||||||
\(663\) | 4.09264 | − | 2.15357i | 0.158945 | − | 0.0836378i | ||||
\(664\) | −17.3887 | −0.674813 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.19076 | − | 7.25861i | −0.162389 | − | 0.281266i | ||||
\(667\) | 12.0236 | − | 20.8255i | 0.465557 | − | 0.806368i | ||||
\(668\) | 6.86227i | 0.265509i | ||||||||
\(669\) | 0.0599161 | + | 0.0345926i | 0.00231649 | + | 0.00133743i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 57.9249i | 2.23617i | ||||||||
\(672\) | −2.56511 | + | 4.44290i | −0.0989512 | + | 0.171389i | ||||
\(673\) | −6.41571 | − | 11.1123i | −0.247307 | − | 0.428349i | 0.715470 | − | 0.698643i | \(-0.246212\pi\) |
−0.962778 | + | 0.270294i | \(0.912879\pi\) | |||||||
\(674\) | −5.23749 | + | 3.02387i | −0.201741 | + | 0.116475i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.59812 | − | 11.7329i | −0.215312 | − | 0.451266i | ||||
\(677\) | 22.3408 | 0.858626 | 0.429313 | − | 0.903156i | \(-0.358756\pi\) | ||||
0.429313 | + | 0.903156i | \(0.358756\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.3879 | + | 31.8487i | 0.705661 | + | 1.22224i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 6.19198i | − | 0.237277i | ||||||
\(682\) | −30.4720 | − | 17.5930i | −1.16683 | − | 0.673672i | ||||
\(683\) | 17.5060 | + | 10.1071i | 0.669850 | + | 0.386738i | 0.796020 | − | 0.605271i | \(-0.206935\pi\) |
−0.126170 | + | 0.992009i | \(0.540268\pi\) | |||||||
\(684\) | 6.64947i | 0.254249i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 31.5999 | + | 54.7327i | 1.20649 | + | 2.08970i | ||||
\(687\) | 15.0564 | − | 8.69283i | 0.574438 | − | 0.331652i | ||||
\(688\) | 4.35800 | 0.166147 | ||||||||
\(689\) | 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 | \(0.178095\pi\) | |||||||
\(692\) | 11.1449 | + | 19.3036i | 0.423666 | + | 0.733812i | ||||
\(693\) | 14.3123 | − | 24.7897i | 0.543680 | − | 0.941682i | ||||
\(694\) | − | 6.34654i | − | 0.240911i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.03479 | + | 1.75214i | 0.115033 | + | 0.0664146i | ||||
\(697\) | − | 1.64520i | − | 0.0623163i | ||||||
\(698\) | −14.1126 | + | 24.4438i | −0.534170 | + | 0.925210i | ||||
\(699\) | 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 | \(0.193474\pi\) | |||||||
\(702\) | −1.92378 | + | 3.04944i | −0.0726085 | + | 0.115094i | ||||
\(703\) | −55.7327 | −2.10200 | ||||||||
\(704\) | 4.83209 | − | 2.78981i | 0.182116 | − | 0.105145i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.04696 | + | 13.9378i | −0.302851 | + | 0.524554i | ||||
\(707\) | − | 75.2270i | − | 2.82920i | ||||||
\(708\) | −1.31571 | − | 0.759628i | −0.0494476 | − | 0.0285486i | ||||
\(709\) | 4.05937 | + | 2.34368i | 0.152453 | + | 0.0880187i | 0.574286 | − | 0.818655i | \(-0.305280\pi\) |
−0.421833 | + | 0.906674i | \(0.638613\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.07423 | + | 8.78882i | −0.190298 | + | 0.329606i | ||||
\(712\) | −3.22094 | − | 5.57884i | −0.120710 | − | 0.209076i | ||||
\(713\) | −37.4770 | + | 21.6374i | −1.40352 | + | 0.810325i | ||||
\(714\) | −6.58029 | −0.246261 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.56889 | 0.0586324 | ||||||||
\(717\) | −14.8512 | + | 8.57433i | −0.554627 | + | 0.320214i | ||||
\(718\) | −4.39845 | − | 7.61833i | −0.164149 | − | 0.284314i | ||||
\(719\) | 13.6893 | − | 23.7106i | 0.510526 | − | 0.884257i | −0.489400 | − | 0.872060i | \(-0.662784\pi\) |
0.999926 | − | 0.0121971i | \(-0.00388256\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.9906 | − | 10.3869i | −0.670005 | − | 0.386827i | ||||
\(722\) | 21.8373 | + | 12.6078i | 0.812699 | + | 0.469212i | ||||
\(723\) | 17.5319i | 0.652020i | ||||||||
\(724\) | 5.72094 | − | 9.90896i | 0.212617 | − | 0.368264i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −17.4349 | + | 10.0661i | −0.647071 | + | 0.373586i | ||||
\(727\) | 12.4066 | 0.460136 | 0.230068 | − | 0.973175i | \(-0.426105\pi\) | ||||
0.230068 | + | 0.973175i | \(0.426105\pi\) | |||||||
\(728\) | −0.725036 | + | 18.4830i | −0.0268716 | + | 0.685027i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.79490 | + | 4.84091i | 0.103373 | + | 0.179047i | ||||
\(732\) | −5.19076 | + | 8.99066i | −0.191856 | + | 0.332305i | ||||
\(733\) | 18.7638i | 0.693056i | 0.938040 | + | 0.346528i | \(0.112639\pi\) | ||||
−0.938040 | + | 0.346528i | \(0.887361\pi\) | |||||||
\(734\) | 32.9145 | + | 19.0032i | 1.21490 | + | 0.701420i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 6.86227i | − | 0.252947i | ||||||
\(737\) | 8.00980 | − | 13.8734i | 0.295045 | − | 0.511033i | ||||
\(738\) | 0.641326 | + | 1.11081i | 0.0236076 | + | 0.0408895i | ||||
\(739\) | 44.5751 | − | 25.7355i | 1.63972 | − | 0.946694i | 0.658794 | − | 0.752324i | \(-0.271067\pi\) |
0.980928 | − | 0.194370i | \(-0.0622663\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.1645 | + | 21.2169i | 0.410136 | + | 0.779422i | ||||
\(742\) | −32.3521 | −1.18768 | ||||||||
\(743\) | 42.9547 | − | 24.7999i | 1.57585 | − | 0.909819i | 0.580424 | − | 0.814314i | \(-0.302887\pi\) |
0.995429 | − | 0.0955053i | \(-0.0304467\pi\) | |||||||
\(744\) | −3.15309 | − | 5.46131i | −0.115598 | − | 0.200221i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 17.0157i | − | 0.622990i | ||||||
\(747\) | 15.0591 | + | 8.69436i | 0.550983 | + | 0.318110i | ||||
\(748\) | 6.19789 | + | 3.57836i | 0.226617 | + | 0.130838i | ||||
\(749\) | 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 | \(0.773150\pi\) | |||||||
\(752\) | −4.35050 | + | 2.51176i | −0.158647 | + | 0.0915946i | ||||
\(753\) | 18.2072 | 0.663506 | ||||||||
\(754\) | 12.6251 | + | 0.495247i | 0.459780 | + | 0.0180358i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.44290 | − | 2.56511i | 0.161587 | − | 0.0932921i | ||||
\(757\) | 2.21571 | + | 3.83773i | 0.0805314 | + | 0.139485i | 0.903478 | − | 0.428634i | \(-0.141005\pi\) |
−0.822947 | + | 0.568118i | \(0.807672\pi\) | |||||||
\(758\) | 6.36569 | − | 11.0257i | 0.231212 | − | 0.400471i | ||||
\(759\) | 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 | \(0.600240\pi\) | |||||||
\(762\) | 16.2530i | 0.588785i | ||||||||
\(763\) | −2.03334 | + | 3.52184i | −0.0736117 | + | 0.127499i | ||||
\(764\) | 4.41092 | + | 7.63995i | 0.159582 | + | 0.276404i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 22.5718 | 0.815553 | ||||||||
\(767\) | −5.47355 | − | 0.214711i | −0.197638 | − | 0.00775277i | ||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 8.46766 | − | 4.88880i | 0.305352 | − | 0.176295i | −0.339493 | − | 0.940609i | \(-0.610255\pi\) |
0.644844 | + | 0.764314i | \(0.276922\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.80056 | + | 15.2430i | −0.316944 | + | 0.548964i | ||||
\(772\) | − | 11.1881i | − | 0.402667i | ||||||
\(773\) | 5.88192 | + | 3.39593i | 0.211558 | + | 0.122143i | 0.602035 | − | 0.798470i | \(-0.294357\pi\) |
−0.390477 | + | 0.920613i | \(0.627690\pi\) | |||||||
\(774\) | −3.77414 | − | 2.17900i | −0.135658 | − | 0.0783225i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.58423 | − | 6.20806i | 0.128666 | − | 0.222856i | ||||
\(777\) | 21.4995 | + | 37.2383i | 0.771291 | + | 1.33592i | ||||
\(778\) | 3.03479 | − | 1.75214i | 0.108802 | − | 0.0628171i | ||||
\(779\) | 8.52897 | 0.305582 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −60.8699 | −2.17809 | ||||||||
\(782\) | 7.62268 | − | 4.40095i | 0.272586 | − | 0.157378i | ||||
\(783\) | −1.75214 | − | 3.03479i | −0.0626163 | − | 0.108455i | ||||
\(784\) | 9.65957 | − | 16.7309i | 0.344985 | − | 0.597531i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −6.10206 | − | 3.52302i | −0.217653 | − | 0.125662i | ||||
\(787\) | −4.34247 | − | 2.50713i | −0.154792 | − | 0.0893694i | 0.420603 | − | 0.907245i | \(-0.361818\pi\) |
−0.575395 | + | 0.817875i | \(0.695152\pi\) | |||||||
\(788\) | − | 22.9351i | − | 0.817029i | ||||||
\(789\) | −5.88051 | + | 10.1853i | −0.209352 | + | 0.362608i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −5.57962 | −0.198263 | ||||||||
\(793\) | −1.46718 | + | 37.4024i | −0.0521012 | + | 1.32820i | ||||
\(794\) | 29.8652 | 1.05988 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.52892 | − | 9.57637i | −0.195967 | − | 0.339425i | ||||
\(797\) | −4.96356 | + | 8.59714i | −0.175818 | + | 0.304526i | −0.940444 | − | 0.339948i | \(-0.889590\pi\) |
0.764626 | + | 0.644474i | \(0.222924\pi\) | |||||||
\(798\) | − | 34.1133i | − | 1.20760i | ||||||
\(799\) | −5.58019 | − | 3.22172i | −0.197413 | − | 0.113976i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.44188i | 0.227613i | ||||||||
\(802\) | −12.5627 | + | 21.7592i | −0.443604 | + | 0.768345i | ||||
\(803\) | −13.7996 | − | 23.9016i | −0.486978 | − | 0.843470i | ||||
\(804\) | 2.48644 | − | 1.43555i | 0.0876900 | − | 0.0506278i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −19.2303 | − | 12.1317i | −0.677358 | − | 0.427322i | ||||
\(807\) | −6.40981 | −0.225636 | ||||||||
\(808\) | −12.6990 | + | 7.33175i | −0.446748 | + | 0.257930i | ||||
\(809\) | −4.98796 | − | 8.63940i | −0.175367 | − | 0.303745i | 0.764921 | − | 0.644124i | \(-0.222778\pi\) |
−0.940288 | + | 0.340379i | \(0.889445\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.85013i | 0.170311i | 0.996368 | + | 0.0851555i | \(0.0271387\pi\) | ||||
−0.996368 | + | 0.0851555i | \(0.972861\pi\) | |||||||
\(812\) | −15.5691 | − | 8.98884i | −0.546369 | − | 0.315447i | ||||
\(813\) | −13.6919 | − | 7.90503i | −0.480196 | − | 0.277242i | ||||
\(814\) | − | 46.7657i | − | 1.63914i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.641326 | + | 1.11081i | 0.0224509 | + | 0.0388861i | ||||
\(817\) | −25.0960 | + | 14.4892i | −0.877998 | + | 0.506913i | ||||
\(818\) | 5.24767 | 0.183480 | ||||||||
\(819\) | 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 | \(0.187342\pi\) | |||||||
\(822\) | 0.444016 | + | 0.769058i | 0.0154868 | + | 0.0268240i | ||||
\(823\) | 13.2535 | − | 22.9557i | 0.461986 | − | 0.800184i | −0.537073 | − | 0.843536i | \(-0.680470\pi\) |
0.999060 | + | 0.0433515i | \(0.0138035\pi\) | |||||||
\(824\) | 4.04929i | 0.141064i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.74990 | + | 3.89706i | 0.234859 | + | 0.135596i | ||||
\(827\) | − | 21.7678i | − | 0.756941i | −0.925613 | − | 0.378470i | \(-0.876450\pi\) | ||
0.925613 | − | 0.378470i | \(-0.123550\pi\) | |||||||
\(828\) | −3.43113 | + | 5.94290i | −0.119240 | + | 0.206530i | ||||
\(829\) | 1.09376 | + | 1.89444i | 0.0379878 | + | 0.0657968i | 0.884394 | − | 0.466741i | \(-0.154572\pi\) |
−0.846406 | + | 0.532537i | \(0.821239\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.98637 | −0.172975 | ||||||||
\(832\) | 3.19076 | − | 1.67900i | 0.110620 | − | 0.0582088i | ||||
\(833\) | 24.7797 | 0.858567 | ||||||||
\(834\) | 0.461208 | − | 0.266279i | 0.0159703 | − | 0.00922047i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −18.5508 | + | 32.1309i | −0.641591 | + | 1.11127i | ||||
\(837\) | 6.30618i | 0.217974i | ||||||||
\(838\) | 15.6114 | + | 9.01326i | 0.539288 | + | 0.311358i | ||||
\(839\) | 21.7825 | + | 12.5761i | 0.752016 | + | 0.434177i | 0.826422 | − | 0.563051i | \(-0.190373\pi\) |
−0.0744057 | + | 0.997228i | \(0.523706\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.36004 | − | 14.4800i | 0.288277 | − | 0.499311i | ||||
\(842\) | 3.96185 | + | 6.86213i | 0.136534 | + | 0.236485i | ||||
\(843\) | 0.446632 | − | 0.257863i | 0.0153828 | − | 0.00888127i | ||||
\(844\) | −26.8342 | −0.923671 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.02353 | 0.172712 | ||||||||
\(847\) | 89.4449 | − | 51.6411i | 3.07336 | − | 1.77441i | ||||
\(848\) | 3.15309 | + | 5.46131i | 0.108278 | + | 0.187542i | ||||
\(849\) | −8.97308 | + | 15.5418i | −0.307955 | + | 0.533394i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −49.8106 | − | 28.7581i | −1.70748 | − | 0.985816i | ||||
\(852\) | −9.44775 | − | 5.45466i | −0.323675 | − | 0.186874i | ||||
\(853\) | − | 36.1721i | − | 1.23851i | −0.785190 | − | 0.619255i | \(-0.787435\pi\) | ||
0.785190 | − | 0.619255i | \(-0.212565\pi\) | |||||||
\(854\) | 26.6297 | − | 46.1241i | 0.911251 | − | 1.57833i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.72112 | − | 3.88044i | 0.229723 | − | 0.132631i | ||||
\(857\) | −18.5471 | −0.633556 | −0.316778 | − | 0.948500i | \(-0.602601\pi\) | ||||
−0.316778 | + | 0.948500i | \(0.602601\pi\) | |||||||
\(858\) | −17.8032 | + | 9.36816i | −0.607792 | + | 0.319824i | ||||
\(859\) | −21.5386 | −0.734887 | −0.367443 | − | 0.930046i | \(-0.619767\pi\) | ||||
−0.367443 | + | 0.930046i | \(0.619767\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.29014 | − | 5.69870i | −0.112128 | − | 0.194211i | ||||
\(862\) | 19.1537 | − | 33.1752i | 0.652379 | − | 1.12995i | ||||
\(863\) | − | 32.1136i | − | 1.09316i | −0.837407 | − | 0.546580i | \(-0.815930\pi\) | ||
0.837407 | − | 0.546580i | \(-0.184070\pi\) | |||||||
\(864\) | −0.866025 | − | 0.500000i | −0.0294628 | − | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 20.0052i | − | 0.679803i | ||||||
\(867\) | 7.67740 | − | 13.2976i | 0.260738 | − | 0.451612i | ||||
\(868\) | 16.1760 | + | 28.0177i | 0.549051 | + | 0.950984i | ||||
\(869\) | −49.0382 | + | 28.3122i | −1.66351 | + | 0.960427i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.52336 | − | 8.75522i | 0.187152 | − | 0.296659i | ||||
\(872\) | 0.792690 | 0.0268439 | ||||||||
\(873\) | −6.20806 | + | 3.58423i | −0.210111 | + | 0.121308i | ||||
\(874\) | 22.8152 | + | 39.5172i | 0.771737 | + | 1.33669i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 4.94644i | − | 0.167125i | ||||||
\(877\) | −27.7681 | − | 16.0319i | −0.937664 | − | 0.541360i | −0.0484365 | − | 0.998826i | \(-0.515424\pi\) |
−0.889227 | + | 0.457466i | \(0.848757\pi\) | |||||||
\(878\) | 10.3345 | + | 5.96660i | 0.348771 | + | 0.201363i | ||||
\(879\) | 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 | \(0.729941\pi\) | |||||||
\(882\) | −16.7309 | + | 9.65957i | −0.563357 | + | 0.325255i | ||||
\(883\) | 38.0685 | 1.28111 | 0.640554 | − | 0.767914i | \(-0.278705\pi\) | ||||
0.640554 | + | 0.767914i | \(0.278705\pi\) | |||||||
\(884\) | 3.91137 | + | 2.46755i | 0.131554 | + | 0.0829925i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −22.5656 | + | 13.0282i | −0.758105 | + | 0.437692i | ||||
\(887\) | −6.75421 | − | 11.6986i | −0.226784 | − | 0.392802i | 0.730069 | − | 0.683373i | \(-0.239488\pi\) |
−0.956853 | + | 0.290572i | \(0.906155\pi\) | |||||||
\(888\) | 4.19076 | − | 7.25861i | 0.140633 | − | 0.243583i | ||||
\(889\) | − | 83.3815i | − | 2.79653i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.83209 | + | 2.78981i | 0.161881 | + | 0.0934621i | ||||
\(892\) | 0.0691851i | 0.00231649i | ||||||||
\(893\) | 16.7019 | − | 28.9286i | 0.558908 | − | 0.968058i | ||||
\(894\) | −10.3988 | − | 18.0113i | −0.347789 | − | 0.602388i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −5.13022 | −0.171389 | ||||||||
\(897\) | −0.969820 | + | 24.7232i | −0.0323814 | + | 0.825485i | ||||
\(898\) | −16.7392 | −0.558594 | ||||||||
\(899\) | 19.1379 | − | 11.0493i | 0.638286 | − | 0.368515i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.04432 | + | 7.00497i | −0.134736 | + | 0.233369i | ||||
\(902\) | 7.15671i | 0.238292i | ||||||||
\(903\) | 19.3621 | + | 11.1787i | 0.644332 | + | 0.372005i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.07700 | − | 1.86541i | 0.0357808 | − | 0.0619742i | ||||
\(907\) | −5.43460 | − | 9.41300i | −0.180453 | − | 0.312554i | 0.761582 | − | 0.648069i | \(-0.224423\pi\) |
−0.942035 | + | 0.335515i | \(0.891090\pi\) | |||||||
\(908\) | 5.36241 | − | 3.09599i | 0.177958 | − | 0.102744i | ||||
\(909\) | 14.6635 | 0.486358 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.20770 | 0.305065 | 0.152532 | − | 0.988298i | \(-0.451257\pi\) | ||||
0.152532 | + | 0.988298i | \(0.451257\pi\) | |||||||
\(912\) | −5.75861 | + | 3.32474i | −0.190687 | + | 0.110093i | ||||
\(913\) | 48.5112 | + | 84.0238i | 1.60549 | + | 2.78078i | ||||
\(914\) | −3.55432 | + | 6.15626i | −0.117566 | + | 0.203631i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.0564 | + | 8.69283i | 0.497478 | + | 0.287219i | ||||
\(917\) | 31.3049 | + | 18.0739i | 1.03378 | + | 0.596852i | ||||
\(918\) | − | 1.28265i | − | 0.0423339i | ||||||
\(919\) | −0.0963564 | + | 0.166894i | −0.00317850 | + | 0.00550533i | −0.867610 | − | 0.497245i | \(-0.834345\pi\) |
0.864432 | + | 0.502750i | \(0.167678\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.3559 | − | 7.13366i | 0.407140 | − | 0.235062i | ||||
\(922\) | −5.51635 | −0.181671 | ||||||||
\(923\) | −39.3039 | − | 1.54178i | −1.29370 | − | 0.0507482i | ||||
\(924\) | 28.6246 | 0.941682 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.49379 | + | 4.31938i | 0.0819511 | + | 0.141943i | ||||
\(927\) | 2.02465 | − | 3.50679i | 0.0664981 | − | 0.115178i | ||||
\(928\) | 3.50427i | 0.115033i | ||||||||
\(929\) | −10.3702 | − | 5.98725i | −0.340236 | − | 0.196435i | 0.320140 | − | 0.947370i | \(-0.396270\pi\) |
−0.660376 | + | 0.750935i | \(0.729603\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 128.462i | 4.21018i | ||||||||
\(932\) | −8.88580 | + | 15.3907i | −0.291064 | + | 0.504138i | ||||
\(933\) | 11.5743 | + | 20.0473i | 0.378927 | + | 0.656320i | ||||
\(934\) | 17.0962 | − | 9.87051i | 0.559406 | − | 0.322973i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.60278 | − | 0.141326i | −0.117761 | − | 0.00461940i | ||||
\(937\) | −32.1031 | −1.04876 | −0.524381 | − | 0.851484i | \(-0.675703\pi\) | ||||
−0.524381 | + | 0.851484i | \(0.675703\pi\) | |||||||
\(938\) | −12.7560 | + | 7.36467i | −0.416498 | + | 0.240465i | ||||
\(939\) | 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 | \(0.966904\pi\) | |||||||
\(942\) | −6.67044 | − | 3.85118i | −0.217335 | − | 0.125478i | ||||
\(943\) | 7.62268 | + | 4.40095i | 0.248229 | + | 0.143315i | ||||
\(944\) | − | 1.51926i | − | 0.0494476i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.1580 | − | 21.0582i | −0.395290 | − | 0.684662i | ||||
\(947\) | −51.2658 | + | 29.5983i | −1.66591 | + | 0.961816i | −0.696110 | + | 0.717936i | \(0.745087\pi\) |
−0.969805 | + | 0.243881i | \(0.921579\pi\) | |||||||
\(948\) | −10.1485 | −0.329606 | ||||||||
\(949\) | −8.30506 | − | 15.7829i | −0.269594 | − | 0.512335i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.5494 | − | 6.09070i | 0.342088 | − | 0.197505i | ||||
\(952\) | −3.29014 | − | 5.69870i | −0.106634 | − | 0.184696i | ||||
\(953\) | −7.49699 | + | 12.9852i | −0.242851 | + | 0.420631i | −0.961525 | − | 0.274716i | \(-0.911416\pi\) |
0.718674 | + | 0.695347i | \(0.244749\pi\) | |||||||
\(954\) | − | 6.30618i | − | 0.204170i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −14.8512 | − | 8.57433i | −0.480321 | − | 0.277314i | ||||
\(957\) | − | 19.5525i | − | 0.632042i | ||||||
\(958\) | −4.30812 | + | 7.46188i | −0.139189 | + | 0.241083i | ||||
\(959\) | −2.27790 | − | 3.94544i | −0.0735572 | − | 0.127405i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.76794 | −0.282837 | ||||||||
\(962\) | 1.18453 | − | 30.1968i | 0.0381908 | − | 0.973584i | ||||
\(963\) | −7.76088 | −0.250091 | ||||||||
\(964\) | −15.1831 | + | 8.76597i | −0.489015 | + | 0.282333i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 17.6025 | − | 30.4884i | 0.566350 | − | 0.980947i | ||||
\(967\) | − | 43.4352i | − | 1.39678i | −0.715717 | − | 0.698390i | \(-0.753900\pi\) | ||
0.715717 | − | 0.698390i | \(-0.246100\pi\) | |||||||
\(968\) | −17.4349 | − | 10.0661i | −0.560380 | − | 0.323535i | ||||
\(969\) | −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 | \(0.879231\pi\) | |||||||
\(972\) | 0.500000 | + | 0.866025i | 0.0160375 | + | 0.0277778i | ||||
\(973\) | −2.36610 | + | 1.36607i | −0.0758536 | + | 0.0437941i | ||||
\(974\) | −19.6205 | −0.628682 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.3815 | −0.332305 | ||||||||
\(977\) | 46.3031 | − | 26.7331i | 1.48137 | − | 0.855267i | 0.481589 | − | 0.876397i | \(-0.340060\pi\) |
0.999777 | + | 0.0211299i | \(0.00672635\pi\) | |||||||
\(978\) | 0.220942 | + | 0.382683i | 0.00706496 | + | 0.0122369i | ||||
\(979\) | −17.9716 | + | 31.1278i | −0.574375 | + | 0.994848i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.686490 | − | 0.396345i | −0.0219179 | − | 0.0126543i | ||||
\(982\) | −34.4541 | − | 19.8921i | −1.09948 | − | 0.634782i | ||||
\(983\) | − | 26.5785i | − | 0.847723i | −0.905727 | − | 0.423862i | \(-0.860674\pi\) | ||
0.905727 | − | 0.423862i | \(-0.139326\pi\) | |||||||
\(984\) | −0.641326 | + | 1.11081i | −0.0204447 | + | 0.0354113i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.89258 | + | 2.24738i | −0.123965 | + | 0.0715713i | ||||
\(987\) | −25.7718 | −0.820325 | ||||||||
\(988\) | −12.7921 | + | 20.2771i | −0.406972 | + | 0.645102i | ||||
\(989\) | −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 | \(0.637497\pi\) | |||||||
\(992\) | 3.15309 | − | 5.46131i | 0.100111 | − | 0.173397i | ||||
\(993\) | − | 4.46249i | − | 0.141613i | ||||||
\(994\) | 48.4690 | + | 27.9836i | 1.53734 | + | 0.887586i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 17.3887i | 0.550983i | ||||||||
\(997\) | 15.2257 | − | 26.3716i | 0.482202 | − | 0.835198i | −0.517590 | − | 0.855629i | \(-0.673171\pi\) |
0.999791 | + | 0.0204312i | \(0.00650390\pi\) | |||||||
\(998\) | −3.92041 | − | 6.79035i | −0.124098 | − | 0.214945i | ||||
\(999\) | −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.bc.h.751.6 | ✓ | 12 | |
5.2 | odd | 4 | 1950.2.y.n.49.1 | 12 | |||
5.3 | odd | 4 | 1950.2.y.m.49.6 | 12 | |||
5.4 | even | 2 | 1950.2.bc.k.751.1 | yes | 12 | ||
13.4 | even | 6 | inner | 1950.2.bc.h.901.6 | yes | 12 | |
65.4 | even | 6 | 1950.2.bc.k.901.1 | yes | 12 | ||
65.17 | odd | 12 | 1950.2.y.m.199.6 | 12 | |||
65.43 | odd | 12 | 1950.2.y.n.199.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1950.2.y.m.49.6 | 12 | 5.3 | odd | 4 | |||
1950.2.y.m.199.6 | 12 | 65.17 | odd | 12 | |||
1950.2.y.n.49.1 | 12 | 5.2 | odd | 4 | |||
1950.2.y.n.199.1 | 12 | 65.43 | odd | 12 | |||
1950.2.bc.h.751.6 | ✓ | 12 | 1.1 | even | 1 | trivial | |
1950.2.bc.h.901.6 | yes | 12 | 13.4 | even | 6 | inner | |
1950.2.bc.k.751.1 | yes | 12 | 5.4 | even | 2 | ||
1950.2.bc.k.901.1 | yes | 12 | 65.4 | even | 6 |