Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [285,2,Mod(106,285)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(285, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("285.106");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 285 = 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 285.i (of order \(3\), 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: | \(2.27573645761\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{10} - x^{9} + 9x^{8} - 2x^{7} + 56x^{6} - 18x^{5} + 125x^{4} + x^{3} + 189x^{2} - 52x + 16 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 106.2 | ||
Root | \(-0.690702 - 1.19633i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 285.106 |
Dual form | 285.2.i.f.121.2 |
$q$-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 \(\left(\mathbb{Z}/285\mathbb{Z}\right)^\times\).
\(n\) | \(172\) | \(191\) | \(211\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.690702 | + | 1.19633i | −0.488400 | + | 0.845933i | −0.999911 | − | 0.0133433i | \(-0.995753\pi\) |
0.511511 | + | 0.859277i | \(0.329086\pi\) | |||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0.0458624 | + | 0.0794360i | 0.0229312 | + | 0.0397180i | ||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0.690702 | + | 1.19633i | 0.281978 | + | 0.488400i | ||||
\(7\) | −4.36264 | −1.64892 | −0.824462 | − | 0.565917i | \(-0.808522\pi\) | ||||
−0.824462 | + | 0.565917i | \(0.808522\pi\) | |||||||
\(8\) | −2.88952 | −1.02160 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −0.690702 | − | 1.19633i | −0.218419 | − | 0.378313i | ||||
\(11\) | −4.31625 | −1.30140 | −0.650699 | − | 0.759336i | \(-0.725524\pi\) | ||||
−0.650699 | + | 0.759336i | \(0.725524\pi\) | |||||||
\(12\) | 0.0917248 | 0.0264787 | ||||||||
\(13\) | 3.18132 | + | 5.51021i | 0.882340 | + | 1.52826i | 0.848732 | + | 0.528823i | \(0.177366\pi\) |
0.0336075 | + | 0.999435i | \(0.489300\pi\) | |||||||
\(14\) | 3.01329 | − | 5.21916i | 0.805334 | − | 1.39488i | ||||
\(15\) | 0.500000 | + | 0.866025i | 0.129099 | + | 0.223607i | ||||
\(16\) | 1.90407 | − | 3.29794i | 0.476017 | − | 0.824486i | ||||
\(17\) | −2.85821 | + | 4.95056i | −0.693217 | + | 1.20069i | 0.277561 | + | 0.960708i | \(0.410474\pi\) |
−0.970778 | + | 0.239979i | \(0.922860\pi\) | |||||||
\(18\) | 1.38140 | 0.325600 | ||||||||
\(19\) | 2.97100 | − | 3.18954i | 0.681594 | − | 0.731730i | ||||
\(20\) | −0.0917248 | −0.0205103 | ||||||||
\(21\) | −2.18132 | + | 3.77816i | −0.476003 | + | 0.824462i | ||||
\(22\) | 2.98124 | − | 5.16366i | 0.635603 | − | 1.10090i | ||||
\(23\) | 0.289678 | + | 0.501738i | 0.0604021 | + | 0.104620i | 0.894645 | − | 0.446777i | \(-0.147428\pi\) |
−0.834243 | + | 0.551397i | \(0.814095\pi\) | |||||||
\(24\) | −1.44476 | + | 2.50239i | −0.294910 | + | 0.510799i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −8.78938 | −1.72374 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.200081 | − | 0.346551i | −0.0378118 | − | 0.0654920i | ||||
\(29\) | 1.77672 | + | 3.07737i | 0.329929 | + | 0.571454i | 0.982497 | − | 0.186276i | \(-0.0596419\pi\) |
−0.652569 | + | 0.757730i | \(0.726309\pi\) | |||||||
\(30\) | −1.38140 | −0.252209 | ||||||||
\(31\) | 1.18345 | 0.212554 | 0.106277 | − | 0.994337i | \(-0.466107\pi\) | ||||
0.106277 | + | 0.994337i | \(0.466107\pi\) | |||||||
\(32\) | −0.259229 | − | 0.448998i | −0.0458257 | − | 0.0793724i | ||||
\(33\) | −2.15812 | + | 3.73798i | −0.375681 | + | 0.650699i | ||||
\(34\) | −3.94834 | − | 6.83872i | −0.677134 | − | 1.17283i | ||||
\(35\) | 2.18132 | − | 3.77816i | 0.368711 | − | 0.638626i | ||||
\(36\) | 0.0458624 | − | 0.0794360i | 0.00764374 | − | 0.0132393i | ||||
\(37\) | −6.54609 | −1.07617 | −0.538086 | − | 0.842890i | \(-0.680852\pi\) | ||||
−0.538086 | + | 0.842890i | \(0.680852\pi\) | |||||||
\(38\) | 1.76367 | + | 5.75732i | 0.286105 | + | 0.933960i | ||||
\(39\) | 6.36264 | 1.01884 | ||||||||
\(40\) | 1.44476 | − | 2.50239i | 0.228436 | − | 0.395663i | ||||
\(41\) | 0.381403 | − | 0.660610i | 0.0595652 | − | 0.103170i | −0.834705 | − | 0.550697i | \(-0.814362\pi\) |
0.894270 | + | 0.447527i | \(0.147695\pi\) | |||||||
\(42\) | −3.01329 | − | 5.21916i | −0.464960 | − | 0.805334i | ||||
\(43\) | 3.18132 | − | 5.51021i | 0.485147 | − | 0.840299i | −0.514707 | − | 0.857366i | \(-0.672099\pi\) |
0.999854 | + | 0.0170666i | \(0.00543274\pi\) | |||||||
\(44\) | −0.197954 | − | 0.342866i | −0.0298426 | − | 0.0516890i | ||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −0.800326 | −0.118002 | ||||||||
\(47\) | 1.36632 | + | 2.36653i | 0.199298 | + | 0.345194i | 0.948301 | − | 0.317372i | \(-0.102800\pi\) |
−0.749003 | + | 0.662567i | \(0.769467\pi\) | |||||||
\(48\) | −1.90407 | − | 3.29794i | −0.274829 | − | 0.476017i | ||||
\(49\) | 12.0327 | 1.71895 | ||||||||
\(50\) | 1.38140 | 0.195360 | ||||||||
\(51\) | 2.85821 | + | 4.95056i | 0.400229 | + | 0.693217i | ||||
\(52\) | −0.291806 | + | 0.505423i | −0.0404662 | + | 0.0700896i | ||||
\(53\) | −2.56853 | − | 4.44882i | −0.352814 | − | 0.611092i | 0.633927 | − | 0.773393i | \(-0.281442\pi\) |
−0.986741 | + | 0.162300i | \(0.948109\pi\) | |||||||
\(54\) | 0.690702 | − | 1.19633i | 0.0939926 | − | 0.162800i | ||||
\(55\) | 2.15812 | − | 3.73798i | 0.291001 | − | 0.504029i | ||||
\(56\) | 12.6059 | 1.68454 | ||||||||
\(57\) | −1.27672 | − | 4.16773i | −0.169106 | − | 0.552029i | ||||
\(58\) | −4.90874 | −0.644549 | ||||||||
\(59\) | −1.91484 | + | 3.31660i | −0.249291 | + | 0.431785i | −0.963329 | − | 0.268322i | \(-0.913531\pi\) |
0.714038 | + | 0.700107i | \(0.246864\pi\) | |||||||
\(60\) | −0.0458624 | + | 0.0794360i | −0.00592081 | + | 0.0102551i | ||||
\(61\) | 6.01053 | + | 10.4105i | 0.769569 | + | 1.33293i | 0.937797 | + | 0.347185i | \(0.112862\pi\) |
−0.168227 | + | 0.985748i | \(0.553804\pi\) | |||||||
\(62\) | −0.817411 | + | 1.41580i | −0.103811 | + | 0.179806i | ||||
\(63\) | 2.18132 | + | 3.77816i | 0.274821 | + | 0.476003i | ||||
\(64\) | 8.33247 | 1.04156 | ||||||||
\(65\) | −6.36264 | −0.789189 | ||||||||
\(66\) | −2.98124 | − | 5.16366i | −0.366965 | − | 0.635603i | ||||
\(67\) | 2.00213 | + | 3.46779i | 0.244599 | + | 0.423658i | 0.962019 | − | 0.272983i | \(-0.0880104\pi\) |
−0.717420 | + | 0.696641i | \(0.754677\pi\) | |||||||
\(68\) | −0.524337 | −0.0635852 | ||||||||
\(69\) | 0.579357 | 0.0697464 | ||||||||
\(70\) | 3.01329 | + | 5.21916i | 0.360156 | + | 0.623809i | ||||
\(71\) | −1.53953 | + | 2.66654i | −0.182708 | + | 0.316460i | −0.942802 | − | 0.333354i | \(-0.891820\pi\) |
0.760094 | + | 0.649814i | \(0.225153\pi\) | |||||||
\(72\) | 1.44476 | + | 2.50239i | 0.170266 | + | 0.294910i | ||||
\(73\) | −4.04320 | + | 7.00303i | −0.473221 | + | 0.819643i | −0.999530 | − | 0.0306504i | \(-0.990242\pi\) |
0.526309 | + | 0.850293i | \(0.323575\pi\) | |||||||
\(74\) | 4.52140 | − | 7.83129i | 0.525602 | − | 0.910369i | ||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0.389622 | + | 0.0897246i | 0.0446927 | + | 0.0102921i | ||||
\(77\) | 18.8303 | 2.14591 | ||||||||
\(78\) | −4.39469 | + | 7.61182i | −0.497601 | + | 0.861869i | ||||
\(79\) | −5.66836 | + | 9.81790i | −0.637741 | + | 1.10460i | 0.348187 | + | 0.937425i | \(0.386798\pi\) |
−0.985927 | + | 0.167174i | \(0.946536\pi\) | |||||||
\(80\) | 1.90407 | + | 3.29794i | 0.212881 | + | 0.368721i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0.526872 | + | 0.912569i | 0.0581833 | + | 0.100776i | ||||
\(83\) | 7.67889 | 0.842868 | 0.421434 | − | 0.906859i | \(-0.361527\pi\) | ||||
0.421434 | + | 0.906859i | \(0.361527\pi\) | |||||||
\(84\) | −0.400163 | −0.0436613 | ||||||||
\(85\) | −2.85821 | − | 4.95056i | −0.310016 | − | 0.536963i | ||||
\(86\) | 4.39469 | + | 7.61182i | 0.473891 | + | 0.820804i | ||||
\(87\) | 3.55344 | 0.380969 | ||||||||
\(88\) | 12.4719 | 1.32951 | ||||||||
\(89\) | −4.92093 | − | 8.52330i | −0.521618 | − | 0.903468i | −0.999684 | − | 0.0251445i | \(-0.991995\pi\) |
0.478066 | − | 0.878324i | \(-0.341338\pi\) | |||||||
\(90\) | −0.690702 | + | 1.19633i | −0.0728063 | + | 0.126104i | ||||
\(91\) | −13.8790 | − | 24.0391i | −1.45491 | − | 2.51998i | ||||
\(92\) | −0.0265707 | + | 0.0460218i | −0.00277019 | + | 0.00479811i | ||||
\(93\) | 0.591725 | − | 1.02490i | 0.0613590 | − | 0.106277i | ||||
\(94\) | −3.77487 | −0.389348 | ||||||||
\(95\) | 1.27672 | + | 4.16773i | 0.130989 | + | 0.427600i | ||||
\(96\) | −0.518458 | −0.0529149 | ||||||||
\(97\) | −1.00000 | + | 1.73205i | −0.101535 | + | 0.175863i | −0.912317 | − | 0.409484i | \(-0.865709\pi\) |
0.810782 | + | 0.585348i | \(0.199042\pi\) | |||||||
\(98\) | −8.31098 | + | 14.3950i | −0.839536 | + | 1.45412i | ||||
\(99\) | 2.15812 | + | 3.73798i | 0.216900 | + | 0.375681i | ||||
\(100\) | 0.0458624 | − | 0.0794360i | 0.00458624 | − | 0.00794360i | ||||
\(101\) | 2.24985 | + | 3.89685i | 0.223868 | + | 0.387751i | 0.955979 | − | 0.293434i | \(-0.0947981\pi\) |
−0.732111 | + | 0.681185i | \(0.761465\pi\) | |||||||
\(102\) | −7.89667 | −0.781887 | ||||||||
\(103\) | −16.0717 | −1.58359 | −0.791796 | − | 0.610785i | \(-0.790854\pi\) | ||||
−0.791796 | + | 0.610785i | \(0.790854\pi\) | |||||||
\(104\) | −9.19248 | − | 15.9218i | −0.901397 | − | 1.56127i | ||||
\(105\) | −2.18132 | − | 3.77816i | −0.212875 | − | 0.368711i | ||||
\(106\) | 7.09634 | 0.689258 | ||||||||
\(107\) | 13.6789 | 1.32239 | 0.661194 | − | 0.750215i | \(-0.270050\pi\) | ||||
0.661194 | + | 0.750215i | \(0.270050\pi\) | |||||||
\(108\) | −0.0458624 | − | 0.0794360i | −0.00441311 | − | 0.00764374i | ||||
\(109\) | 4.48337 | − | 7.76542i | 0.429429 | − | 0.743792i | −0.567394 | − | 0.823447i | \(-0.692048\pi\) |
0.996823 | + | 0.0796541i | \(0.0253816\pi\) | |||||||
\(110\) | 2.98124 | + | 5.16366i | 0.284250 | + | 0.492336i | ||||
\(111\) | −3.27305 | + | 5.66908i | −0.310664 | + | 0.538086i | ||||
\(112\) | −8.30677 | + | 14.3878i | −0.784916 | + | 1.35951i | ||||
\(113\) | 6.42952 | 0.604838 | 0.302419 | − | 0.953175i | \(-0.402206\pi\) | ||||
0.302419 | + | 0.953175i | \(0.402206\pi\) | |||||||
\(114\) | 5.86782 | + | 1.35128i | 0.549571 | + | 0.126559i | ||||
\(115\) | −0.579357 | −0.0540253 | ||||||||
\(116\) | −0.162969 | + | 0.282271i | −0.0151313 | + | 0.0262082i | ||||
\(117\) | 3.18132 | − | 5.51021i | 0.294113 | − | 0.509419i | ||||
\(118\) | −2.64517 | − | 4.58156i | −0.243507 | − | 0.421767i | ||||
\(119\) | 12.4693 | − | 21.5975i | 1.14306 | − | 1.97984i | ||||
\(120\) | −1.44476 | − | 2.50239i | −0.131888 | − | 0.228436i | ||||
\(121\) | 7.63001 | 0.693637 | ||||||||
\(122\) | −16.6059 | −1.50343 | ||||||||
\(123\) | −0.381403 | − | 0.660610i | −0.0343900 | − | 0.0595652i | ||||
\(124\) | 0.0542759 | + | 0.0940086i | 0.00487412 | + | 0.00844222i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −6.02657 | −0.536890 | ||||||||
\(127\) | 3.09172 | + | 5.35502i | 0.274346 | + | 0.475182i | 0.969970 | − | 0.243225i | \(-0.0782052\pi\) |
−0.695624 | + | 0.718406i | \(0.744872\pi\) | |||||||
\(128\) | −5.23680 | + | 9.07040i | −0.462872 | + | 0.801717i | ||||
\(129\) | −3.18132 | − | 5.51021i | −0.280100 | − | 0.485147i | ||||
\(130\) | 4.39469 | − | 7.61182i | 0.385440 | − | 0.667601i | ||||
\(131\) | −8.69872 | + | 15.0666i | −0.760010 | + | 1.31638i | 0.182834 | + | 0.983144i | \(0.441473\pi\) |
−0.942845 | + | 0.333233i | \(0.891860\pi\) | |||||||
\(132\) | −0.395907 | −0.0344593 | ||||||||
\(133\) | −12.9614 | + | 13.9148i | −1.12390 | + | 1.20657i | ||||
\(134\) | −5.53149 | −0.477848 | ||||||||
\(135\) | 0.500000 | − | 0.866025i | 0.0430331 | − | 0.0745356i | ||||
\(136\) | 8.25883 | − | 14.3047i | 0.708189 | − | 1.22662i | ||||
\(137\) | −7.85821 | − | 13.6108i | −0.671372 | − | 1.16285i | −0.977515 | − | 0.210865i | \(-0.932372\pi\) |
0.306143 | − | 0.951985i | \(-0.400961\pi\) | |||||||
\(138\) | −0.400163 | + | 0.693102i | −0.0340641 | + | 0.0590008i | ||||
\(139\) | −3.27672 | − | 5.67545i | −0.277928 | − | 0.481385i | 0.692942 | − | 0.720994i | \(-0.256314\pi\) |
−0.970870 | + | 0.239608i | \(0.922981\pi\) | |||||||
\(140\) | 0.400163 | 0.0338199 | ||||||||
\(141\) | 2.73264 | 0.230130 | ||||||||
\(142\) | −2.12671 | − | 3.68357i | −0.178469 | − | 0.309118i | ||||
\(143\) | −13.7314 | − | 23.7834i | −1.14828 | − | 1.98887i | ||||
\(144\) | −3.80814 | −0.317345 | ||||||||
\(145\) | −3.55344 | −0.295097 | ||||||||
\(146\) | −5.58529 | − | 9.67401i | −0.462242 | − | 0.800627i | ||||
\(147\) | 6.01633 | − | 10.4206i | 0.496219 | − | 0.859476i | ||||
\(148\) | −0.300220 | − | 0.519996i | −0.0246779 | − | 0.0427434i | ||||
\(149\) | −2.87560 | + | 4.98069i | −0.235578 | + | 0.408034i | −0.959441 | − | 0.281911i | \(-0.909032\pi\) |
0.723862 | + | 0.689945i | \(0.242365\pi\) | |||||||
\(150\) | 0.690702 | − | 1.19633i | 0.0563956 | − | 0.0976800i | ||||
\(151\) | −12.6673 | −1.03085 | −0.515425 | − | 0.856935i | \(-0.672366\pi\) | ||||
−0.515425 | + | 0.856935i | \(0.672366\pi\) | |||||||
\(152\) | −8.58475 | + | 9.21622i | −0.696315 | + | 0.747534i | ||||
\(153\) | 5.71641 | 0.462145 | ||||||||
\(154\) | −13.0061 | + | 22.5272i | −1.04806 | + | 1.81529i | ||||
\(155\) | −0.591725 | + | 1.02490i | −0.0475285 | + | 0.0823217i | ||||
\(156\) | 0.291806 | + | 0.505423i | 0.0233632 | + | 0.0404662i | ||||
\(157\) | −0.689434 | + | 1.19414i | −0.0550228 | + | 0.0953024i | −0.892225 | − | 0.451591i | \(-0.850856\pi\) |
0.837202 | + | 0.546894i | \(0.184190\pi\) | |||||||
\(158\) | −7.83030 | − | 13.5625i | −0.622945 | − | 1.07897i | ||||
\(159\) | −5.13706 | −0.407395 | ||||||||
\(160\) | 0.518458 | 0.0409877 | ||||||||
\(161\) | −1.26376 | − | 2.18890i | −0.0995986 | − | 0.172510i | ||||
\(162\) | −0.690702 | − | 1.19633i | −0.0542666 | − | 0.0939926i | ||||
\(163\) | −11.6120 | −0.909523 | −0.454762 | − | 0.890613i | \(-0.650276\pi\) | ||||
−0.454762 | + | 0.890613i | \(0.650276\pi\) | |||||||
\(164\) | 0.0699683 | 0.00546361 | ||||||||
\(165\) | −2.15812 | − | 3.73798i | −0.168010 | − | 0.291001i | ||||
\(166\) | −5.30382 | + | 9.18649i | −0.411657 | + | 0.713010i | ||||
\(167\) | 10.1557 | + | 17.5902i | 0.785871 | + | 1.36117i | 0.928477 | + | 0.371390i | \(0.121119\pi\) |
−0.142606 | + | 0.989780i | \(0.545548\pi\) | |||||||
\(168\) | 6.30296 | − | 10.9171i | 0.486284 | − | 0.842269i | ||||
\(169\) | −13.7416 | + | 23.8012i | −1.05705 | + | 1.83086i | ||||
\(170\) | 7.89667 | 0.605647 | ||||||||
\(171\) | −4.24772 | − | 0.978193i | −0.324831 | − | 0.0748043i | ||||
\(172\) | 0.583613 | 0.0445000 | ||||||||
\(173\) | 6.12545 | − | 10.6096i | 0.465709 | − | 0.806632i | −0.533524 | − | 0.845785i | \(-0.679133\pi\) |
0.999233 | + | 0.0391527i | \(0.0124659\pi\) | |||||||
\(174\) | −2.45437 | + | 4.25109i | −0.186065 | + | 0.322274i | ||||
\(175\) | 2.18132 | + | 3.77816i | 0.164892 | + | 0.285602i | ||||
\(176\) | −8.21843 | + | 14.2347i | −0.619488 | + | 1.07298i | ||||
\(177\) | 1.91484 | + | 3.31660i | 0.143928 | + | 0.249291i | ||||
\(178\) | 13.5956 | 1.01903 | ||||||||
\(179\) | −19.1840 | −1.43388 | −0.716941 | − | 0.697134i | \(-0.754458\pi\) | ||||
−0.716941 | + | 0.697134i | \(0.754458\pi\) | |||||||
\(180\) | 0.0458624 | + | 0.0794360i | 0.00341838 | + | 0.00592081i | ||||
\(181\) | 1.61492 | + | 2.79713i | 0.120036 | + | 0.207909i | 0.919782 | − | 0.392430i | \(-0.128366\pi\) |
−0.799746 | + | 0.600339i | \(0.795032\pi\) | |||||||
\(182\) | 38.3449 | 2.84231 | ||||||||
\(183\) | 12.0211 | 0.888622 | ||||||||
\(184\) | −0.837031 | − | 1.44978i | −0.0617067 | − | 0.106879i | ||||
\(185\) | 3.27305 | − | 5.66908i | 0.240639 | − | 0.416799i | ||||
\(186\) | 0.817411 | + | 1.41580i | 0.0599355 | + | 0.103811i | ||||
\(187\) | 12.3367 | − | 21.3678i | 0.902151 | − | 1.56257i | ||||
\(188\) | −0.125325 | + | 0.217070i | −0.00914029 | + | 0.0158314i | ||||
\(189\) | 4.36264 | 0.317336 | ||||||||
\(190\) | −5.86782 | − | 1.35128i | −0.425696 | − | 0.0980320i | ||||
\(191\) | 27.5509 | 1.99352 | 0.996758 | − | 0.0804642i | \(-0.0256403\pi\) | ||||
0.996758 | + | 0.0804642i | \(0.0256403\pi\) | |||||||
\(192\) | 4.16624 | − | 7.21613i | 0.300672 | − | 0.520780i | ||||
\(193\) | −11.1233 | + | 19.2662i | −0.800674 | + | 1.38681i | 0.118499 | + | 0.992954i | \(0.462192\pi\) |
−0.919173 | + | 0.393854i | \(0.871141\pi\) | |||||||
\(194\) | −1.38140 | − | 2.39266i | −0.0991790 | − | 0.171783i | ||||
\(195\) | −3.18132 | + | 5.51021i | −0.227819 | + | 0.394594i | ||||
\(196\) | 0.551847 | + | 0.955827i | 0.0394176 | + | 0.0682734i | ||||
\(197\) | 12.6627 | 0.902178 | 0.451089 | − | 0.892479i | \(-0.351036\pi\) | ||||
0.451089 | + | 0.892479i | \(0.351036\pi\) | |||||||
\(198\) | −5.96248 | −0.423735 | ||||||||
\(199\) | 4.38478 | + | 7.59466i | 0.310829 | + | 0.538371i | 0.978542 | − | 0.206048i | \(-0.0660602\pi\) |
−0.667713 | + | 0.744418i | \(0.732727\pi\) | |||||||
\(200\) | 1.44476 | + | 2.50239i | 0.102160 | + | 0.176946i | ||||
\(201\) | 4.00426 | 0.282438 | ||||||||
\(202\) | −6.21590 | −0.437349 | ||||||||
\(203\) | −7.75120 | − | 13.4255i | −0.544028 | − | 0.942284i | ||||
\(204\) | −0.262168 | + | 0.454089i | −0.0183555 | + | 0.0317926i | ||||
\(205\) | 0.381403 | + | 0.660610i | 0.0266384 | + | 0.0461390i | ||||
\(206\) | 11.1008 | − | 19.2271i | 0.773426 | − | 1.33961i | ||||
\(207\) | 0.289678 | − | 0.501738i | 0.0201340 | − | 0.0348732i | ||||
\(208\) | 24.2298 | 1.68004 | ||||||||
\(209\) | −12.8236 | + | 13.7668i | −0.887025 | + | 0.952272i | ||||
\(210\) | 6.02657 | 0.415873 | ||||||||
\(211\) | −3.93389 | + | 6.81369i | −0.270820 | + | 0.469074i | −0.969072 | − | 0.246778i | \(-0.920628\pi\) |
0.698252 | + | 0.715852i | \(0.253962\pi\) | |||||||
\(212\) | 0.235598 | − | 0.408067i | 0.0161809 | − | 0.0280262i | ||||
\(213\) | 1.53953 | + | 2.66654i | 0.105487 | + | 0.182708i | ||||
\(214\) | −9.44803 | + | 16.3645i | −0.645854 | + | 1.11865i | ||||
\(215\) | 3.18132 | + | 5.51021i | 0.216964 | + | 0.375793i | ||||
\(216\) | 2.88952 | 0.196607 | ||||||||
\(217\) | −5.16297 | −0.350485 | ||||||||
\(218\) | 6.19334 | + | 10.7272i | 0.419466 | + | 0.726536i | ||||
\(219\) | 4.04320 | + | 7.00303i | 0.273214 | + | 0.473221i | ||||
\(220\) | 0.395907 | 0.0266921 | ||||||||
\(221\) | −36.3715 | −2.44661 | ||||||||
\(222\) | −4.52140 | − | 7.83129i | −0.303456 | − | 0.525602i | ||||
\(223\) | 13.6768 | − | 23.6889i | 0.915864 | − | 1.58632i | 0.110232 | − | 0.993906i | \(-0.464840\pi\) |
0.805631 | − | 0.592417i | \(-0.201826\pi\) | |||||||
\(224\) | 1.13092 | + | 1.95882i | 0.0755631 | + | 0.130879i | ||||
\(225\) | −0.500000 | + | 0.866025i | −0.0333333 | + | 0.0577350i | ||||
\(226\) | −4.44088 | + | 7.69183i | −0.295403 | + | 0.511653i | ||||
\(227\) | −25.0922 | −1.66543 | −0.832713 | − | 0.553704i | \(-0.813214\pi\) | ||||
−0.832713 | + | 0.553704i | \(0.813214\pi\) | |||||||
\(228\) | 0.272515 | − | 0.292560i | 0.0180477 | − | 0.0193753i | ||||
\(229\) | 4.98530 | 0.329438 | 0.164719 | − | 0.986341i | \(-0.447328\pi\) | ||||
0.164719 | + | 0.986341i | \(0.447328\pi\) | |||||||
\(230\) | 0.400163 | − | 0.693102i | 0.0263860 | − | 0.0457018i | ||||
\(231\) | 9.41513 | − | 16.3075i | 0.619470 | − | 1.07295i | ||||
\(232\) | −5.13386 | − | 8.89211i | −0.337055 | − | 0.583796i | ||||
\(233\) | −6.39821 | + | 11.0820i | −0.419161 | + | 0.726007i | −0.995855 | − | 0.0909523i | \(-0.971009\pi\) |
0.576695 | + | 0.816960i | \(0.304342\pi\) | |||||||
\(234\) | 4.39469 | + | 7.61182i | 0.287290 | + | 0.497601i | ||||
\(235\) | −2.73264 | −0.178258 | ||||||||
\(236\) | −0.351277 | −0.0228662 | ||||||||
\(237\) | 5.66836 | + | 9.81790i | 0.368200 | + | 0.637741i | ||||
\(238\) | 17.2252 | + | 29.8349i | 1.11654 | + | 1.93391i | ||||
\(239\) | 12.8049 | 0.828283 | 0.414142 | − | 0.910212i | \(-0.364082\pi\) | ||||
0.414142 | + | 0.910212i | \(0.364082\pi\) | |||||||
\(240\) | 3.80814 | 0.245814 | ||||||||
\(241\) | 0.546395 | + | 0.946383i | 0.0351964 | + | 0.0609619i | 0.883087 | − | 0.469209i | \(-0.155461\pi\) |
−0.847891 | + | 0.530171i | \(0.822128\pi\) | |||||||
\(242\) | −5.27006 | + | 9.12801i | −0.338772 | + | 0.586771i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −0.551315 | + | 0.954905i | −0.0352943 | + | 0.0611315i | ||||
\(245\) | −6.01633 | + | 10.4206i | −0.384369 | + | 0.665747i | ||||
\(246\) | 1.05374 | 0.0671842 | ||||||||
\(247\) | 27.0267 | + | 6.22389i | 1.71967 | + | 0.396017i | ||||
\(248\) | −3.41960 | −0.217145 | ||||||||
\(249\) | 3.83945 | − | 6.65012i | 0.243315 | − | 0.421434i | ||||
\(250\) | −0.690702 | + | 1.19633i | −0.0436838 | + | 0.0756626i | ||||
\(251\) | −3.04764 | − | 5.27867i | −0.192365 | − | 0.333187i | 0.753668 | − | 0.657255i | \(-0.228283\pi\) |
−0.946034 | + | 0.324068i | \(0.894949\pi\) | |||||||
\(252\) | −0.200081 | + | 0.346551i | −0.0126039 | + | 0.0218307i | ||||
\(253\) | −1.25032 | − | 2.16563i | −0.0786072 | − | 0.136152i | ||||
\(254\) | −8.54184 | −0.535963 | ||||||||
\(255\) | −5.71641 | −0.357976 | ||||||||
\(256\) | 1.09835 | + | 1.90239i | 0.0686467 | + | 0.118900i | ||||
\(257\) | −2.31016 | − | 4.00131i | −0.144104 | − | 0.249595i | 0.784934 | − | 0.619579i | \(-0.212697\pi\) |
−0.929038 | + | 0.369984i | \(0.879363\pi\) | |||||||
\(258\) | 8.78938 | 0.547203 | ||||||||
\(259\) | 28.5583 | 1.77452 | ||||||||
\(260\) | −0.291806 | − | 0.505423i | −0.0180971 | − | 0.0313450i | ||||
\(261\) | 1.77672 | − | 3.07737i | 0.109976 | − | 0.190485i | ||||
\(262\) | −12.0164 | − | 20.8131i | −0.742378 | − | 1.28584i | ||||
\(263\) | 15.0247 | − | 26.0236i | 0.926465 | − | 1.60468i | 0.137276 | − | 0.990533i | \(-0.456165\pi\) |
0.789189 | − | 0.614151i | \(-0.210501\pi\) | |||||||
\(264\) | 6.23593 | − | 10.8010i | 0.383795 | − | 0.664753i | ||||
\(265\) | 5.13706 | 0.315567 | ||||||||
\(266\) | −7.69425 | − | 25.1171i | −0.471765 | − | 1.54003i | ||||
\(267\) | −9.84186 | −0.602312 | ||||||||
\(268\) | −0.183645 | + | 0.318082i | −0.0112179 | + | 0.0194300i | ||||
\(269\) | 0.105639 | − | 0.182973i | 0.00644095 | − | 0.0111561i | −0.862787 | − | 0.505568i | \(-0.831283\pi\) |
0.869228 | + | 0.494412i | \(0.164616\pi\) | |||||||
\(270\) | 0.690702 | + | 1.19633i | 0.0420348 | + | 0.0728063i | ||||
\(271\) | 3.70364 | − | 6.41489i | 0.224980 | − | 0.389677i | −0.731333 | − | 0.682020i | \(-0.761102\pi\) |
0.956313 | + | 0.292343i | \(0.0944350\pi\) | |||||||
\(272\) | 10.8844 | + | 18.8524i | 0.659966 | + | 1.14309i | ||||
\(273\) | −27.7579 | −1.67999 | ||||||||
\(274\) | 21.7107 | 1.31159 | ||||||||
\(275\) | 2.15812 | + | 3.73798i | 0.130140 | + | 0.225409i | ||||
\(276\) | 0.0265707 | + | 0.0460218i | 0.00159937 | + | 0.00277019i | ||||
\(277\) | −29.0668 | −1.74646 | −0.873229 | − | 0.487310i | \(-0.837978\pi\) | ||||
−0.873229 | + | 0.487310i | \(0.837978\pi\) | |||||||
\(278\) | 9.05295 | 0.542960 | ||||||||
\(279\) | −0.591725 | − | 1.02490i | −0.0354256 | − | 0.0613590i | ||||
\(280\) | −6.30296 | + | 10.9171i | −0.376674 | + | 0.652419i | ||||
\(281\) | −5.73796 | − | 9.93843i | −0.342298 | − | 0.592877i | 0.642561 | − | 0.766234i | \(-0.277872\pi\) |
−0.984859 | + | 0.173357i | \(0.944539\pi\) | |||||||
\(282\) | −1.88744 | + | 3.26914i | −0.112395 | + | 0.194674i | ||||
\(283\) | 13.6662 | − | 23.6706i | 0.812373 | − | 1.40707i | −0.0988265 | − | 0.995105i | \(-0.531509\pi\) |
0.911199 | − | 0.411966i | \(-0.135158\pi\) | |||||||
\(284\) | −0.282426 | −0.0167589 | ||||||||
\(285\) | 4.24772 | + | 0.978193i | 0.251613 | + | 0.0579431i | ||||
\(286\) | 37.9371 | 2.24327 | ||||||||
\(287\) | −1.66393 | + | 2.88201i | −0.0982185 | + | 0.170119i | ||||
\(288\) | −0.259229 | + | 0.448998i | −0.0152752 | + | 0.0264575i | ||||
\(289\) | −7.83868 | − | 13.5770i | −0.461099 | − | 0.798647i | ||||
\(290\) | 2.45437 | − | 4.25109i | 0.144125 | − | 0.249633i | ||||
\(291\) | 1.00000 | + | 1.73205i | 0.0586210 | + | 0.101535i | ||||
\(292\) | −0.741724 | −0.0434061 | ||||||||
\(293\) | 13.0211 | 0.760698 | 0.380349 | − | 0.924843i | \(-0.375804\pi\) | ||||
0.380349 | + | 0.924843i | \(0.375804\pi\) | |||||||
\(294\) | 8.31098 | + | 14.3950i | 0.484706 | + | 0.839536i | ||||
\(295\) | −1.91484 | − | 3.31660i | −0.111486 | − | 0.193100i | ||||
\(296\) | 18.9150 | 1.09941 | ||||||||
\(297\) | 4.31625 | 0.250454 | ||||||||
\(298\) | −3.97236 | − | 6.88034i | −0.230113 | − | 0.398567i | ||||
\(299\) | −1.84312 | + | 3.19238i | −0.106590 | + | 0.184620i | ||||
\(300\) | −0.0458624 | − | 0.0794360i | −0.00264787 | − | 0.00458624i | ||||
\(301\) | −13.8790 | + | 24.0391i | −0.799971 | + | 1.38559i | ||||
\(302\) | 8.74932 | − | 15.1543i | 0.503467 | − | 0.872030i | ||||
\(303\) | 4.49970 | 0.258501 | ||||||||
\(304\) | −4.86193 | − | 15.8713i | −0.278851 | − | 0.910281i | ||||
\(305\) | −12.0211 | −0.688324 | ||||||||
\(306\) | −3.94834 | + | 6.83872i | −0.225711 | + | 0.390943i | ||||
\(307\) | −2.01267 | + | 3.48604i | −0.114869 | + | 0.198959i | −0.917727 | − | 0.397211i | \(-0.869978\pi\) |
0.802858 | + | 0.596170i | \(0.203312\pi\) | |||||||
\(308\) | 0.863601 | + | 1.49580i | 0.0492082 | + | 0.0852312i | ||||
\(309\) | −8.03585 | + | 13.9185i | −0.457144 | + | 0.791796i | ||||
\(310\) | −0.817411 | − | 1.41580i | −0.0464258 | − | 0.0804119i | ||||
\(311\) | 15.3578 | 0.870860 | 0.435430 | − | 0.900223i | \(-0.356596\pi\) | ||||
0.435430 | + | 0.900223i | \(0.356596\pi\) | |||||||
\(312\) | −18.3850 | −1.04084 | ||||||||
\(313\) | −10.9800 | − | 19.0179i | −0.620625 | − | 1.07495i | −0.989369 | − | 0.145424i | \(-0.953546\pi\) |
0.368744 | − | 0.929531i | \(-0.379788\pi\) | |||||||
\(314\) | −0.952387 | − | 1.64958i | −0.0537463 | − | 0.0930913i | ||||
\(315\) | −4.36264 | −0.245807 | ||||||||
\(316\) | −1.03986 | −0.0584967 | ||||||||
\(317\) | 12.0640 | + | 20.8954i | 0.677580 | + | 1.17360i | 0.975708 | + | 0.219077i | \(0.0703046\pi\) |
−0.298127 | + | 0.954526i | \(0.596362\pi\) | |||||||
\(318\) | 3.54817 | − | 6.14561i | 0.198972 | − | 0.344629i | ||||
\(319\) | −7.66877 | − | 13.2827i | −0.429369 | − | 0.743689i | ||||
\(320\) | −4.16624 | + | 7.21613i | −0.232900 | + | 0.403394i | ||||
\(321\) | 6.83945 | − | 11.8463i | 0.381741 | − | 0.661194i | ||||
\(322\) | 3.49154 | 0.194576 | ||||||||
\(323\) | 7.29826 | + | 23.8245i | 0.406086 | + | 1.32563i | ||||
\(324\) | −0.0917248 | −0.00509582 | ||||||||
\(325\) | 3.18132 | − | 5.51021i | 0.176468 | − | 0.305652i | ||||
\(326\) | 8.02044 | − | 13.8918i | 0.444211 | − | 0.769396i | ||||
\(327\) | −4.48337 | − | 7.76542i | −0.247931 | − | 0.429429i | ||||
\(328\) | −1.10207 | + | 1.90884i | −0.0608517 | + | 0.105398i | ||||
\(329\) | −5.96076 | − | 10.3243i | −0.328627 | − | 0.569199i | ||||
\(330\) | 5.96248 | 0.328224 | ||||||||
\(331\) | −24.8416 | −1.36542 | −0.682710 | − | 0.730690i | \(-0.739199\pi\) | ||||
−0.682710 | + | 0.730690i | \(0.739199\pi\) | |||||||
\(332\) | 0.352173 | + | 0.609981i | 0.0193280 | + | 0.0334771i | ||||
\(333\) | 3.27305 | + | 5.66908i | 0.179362 | + | 0.310664i | ||||
\(334\) | −28.0582 | −1.53528 | ||||||||
\(335\) | −4.00426 | −0.218776 | ||||||||
\(336\) | 8.30677 | + | 14.3878i | 0.453172 | + | 0.784916i | ||||
\(337\) | −0.284651 | + | 0.493031i | −0.0155059 | + | 0.0268571i | −0.873674 | − | 0.486511i | \(-0.838269\pi\) |
0.858168 | + | 0.513368i | \(0.171603\pi\) | |||||||
\(338\) | −18.9827 | − | 32.8790i | −1.03252 | − | 1.78838i | ||||
\(339\) | 3.21476 | − | 5.56813i | 0.174602 | − | 0.302419i | ||||
\(340\) | 0.262168 | − | 0.454089i | 0.0142181 | − | 0.0246264i | ||||
\(341\) | −5.10806 | −0.276617 | ||||||||
\(342\) | 4.10415 | − | 4.40604i | 0.221927 | − | 0.238251i | ||||
\(343\) | −21.9557 | −1.18550 | ||||||||
\(344\) | −9.19248 | + | 15.9218i | −0.495625 | + | 0.858448i | ||||
\(345\) | −0.289678 | + | 0.501738i | −0.0155958 | + | 0.0270127i | ||||
\(346\) | 8.46172 | + | 14.6561i | 0.454905 | + | 0.787918i | ||||
\(347\) | −4.68682 | + | 8.11782i | −0.251602 | + | 0.435787i | −0.963967 | − | 0.266022i | \(-0.914291\pi\) |
0.712365 | + | 0.701809i | \(0.247624\pi\) | |||||||
\(348\) | 0.162969 | + | 0.282271i | 0.00873608 | + | 0.0151313i | ||||
\(349\) | 14.8297 | 0.793815 | 0.396907 | − | 0.917859i | \(-0.370083\pi\) | ||||
0.396907 | + | 0.917859i | \(0.370083\pi\) | |||||||
\(350\) | −6.02657 | −0.322134 | ||||||||
\(351\) | −3.18132 | − | 5.51021i | −0.169806 | − | 0.294113i | ||||
\(352\) | 1.11890 | + | 1.93799i | 0.0596375 | + | 0.103295i | ||||
\(353\) | 31.2650 | 1.66407 | 0.832034 | − | 0.554725i | \(-0.187176\pi\) | ||||
0.832034 | + | 0.554725i | \(0.187176\pi\) | |||||||
\(354\) | −5.29033 | −0.281178 | ||||||||
\(355\) | −1.53953 | − | 2.66654i | −0.0817097 | − | 0.141525i | ||||
\(356\) | 0.451372 | − | 0.781799i | 0.0239226 | − | 0.0414352i | ||||
\(357\) | −12.4693 | − | 21.5975i | −0.659947 | − | 1.14306i | ||||
\(358\) | 13.2504 | − | 22.9504i | 0.700307 | − | 1.21297i | ||||
\(359\) | −5.43561 | + | 9.41475i | −0.286880 | + | 0.496892i | −0.973063 | − | 0.230537i | \(-0.925952\pi\) |
0.686183 | + | 0.727429i | \(0.259285\pi\) | |||||||
\(360\) | −2.88952 | −0.152291 | ||||||||
\(361\) | −1.34631 | − | 18.9522i | −0.0708586 | − | 0.997486i | ||||
\(362\) | −4.46172 | −0.234503 | ||||||||
\(363\) | 3.81500 | − | 6.60778i | 0.200236 | − | 0.346819i | ||||
\(364\) | 1.27305 | − | 2.20498i | 0.0667258 | − | 0.115572i | ||||
\(365\) | −4.04320 | − | 7.00303i | −0.211631 | − | 0.366555i | ||||
\(366\) | −8.30296 | + | 14.3812i | −0.434003 | + | 0.751715i | ||||
\(367\) | 9.36477 | + | 16.2203i | 0.488837 | + | 0.846691i | 0.999918 | − | 0.0128422i | \(-0.00408791\pi\) |
−0.511080 | + | 0.859533i | \(0.670755\pi\) | |||||||
\(368\) | 2.20627 | 0.115010 | ||||||||
\(369\) | −0.762807 | −0.0397101 | ||||||||
\(370\) | 4.52140 | + | 7.83129i | 0.235056 | + | 0.407129i | ||||
\(371\) | 11.2056 | + | 19.4086i | 0.581764 | + | 1.00765i | ||||
\(372\) | 0.108552 | 0.00562815 | ||||||||
\(373\) | 29.3275 | 1.51852 | 0.759259 | − | 0.650788i | \(-0.225561\pi\) | ||||
0.759259 | + | 0.650788i | \(0.225561\pi\) | |||||||
\(374\) | 17.0420 | + | 29.5176i | 0.881221 | + | 1.52632i | ||||
\(375\) | 0.500000 | − | 0.866025i | 0.0258199 | − | 0.0447214i | ||||
\(376\) | −3.94800 | − | 6.83813i | −0.203602 | − | 0.352650i | ||||
\(377\) | −11.3046 | + | 19.5802i | −0.582219 | + | 1.00843i | ||||
\(378\) | −3.01329 | + | 5.21916i | −0.154987 | + | 0.268445i | ||||
\(379\) | −10.6486 | −0.546980 | −0.273490 | − | 0.961875i | \(-0.588178\pi\) | ||||
−0.273490 | + | 0.961875i | \(0.588178\pi\) | |||||||
\(380\) | −0.272515 | + | 0.292560i | −0.0139797 | + | 0.0150080i | ||||
\(381\) | 6.18345 | 0.316788 | ||||||||
\(382\) | −19.0295 | + | 32.9600i | −0.973632 | + | 1.68638i | ||||
\(383\) | −4.63977 | + | 8.03632i | −0.237081 | + | 0.410637i | −0.959876 | − | 0.280426i | \(-0.909524\pi\) |
0.722794 | + | 0.691063i | \(0.242857\pi\) | |||||||
\(384\) | 5.23680 | + | 9.07040i | 0.267239 | + | 0.462872i | ||||
\(385\) | −9.41513 | + | 16.3075i | −0.479839 | + | 0.831106i | ||||
\(386\) | −15.3658 | − | 26.6143i | −0.782098 | − | 1.35463i | ||||
\(387\) | −6.36264 | −0.323431 | ||||||||
\(388\) | −0.183450 | −0.00931325 | ||||||||
\(389\) | −0.666237 | − | 1.15396i | −0.0337796 | − | 0.0585079i | 0.848641 | − | 0.528969i | \(-0.177421\pi\) |
−0.882421 | + | 0.470461i | \(0.844088\pi\) | |||||||
\(390\) | −4.39469 | − | 7.61182i | −0.222534 | − | 0.385440i | ||||
\(391\) | −3.31184 | −0.167487 | ||||||||
\(392\) | −34.7686 | −1.75608 | ||||||||
\(393\) | 8.69872 | + | 15.0666i | 0.438792 | + | 0.760010i | ||||
\(394\) | −8.74613 | + | 15.1487i | −0.440623 | + | 0.763182i | ||||
\(395\) | −5.66836 | − | 9.81790i | −0.285206 | − | 0.493992i | ||||
\(396\) | −0.197954 | + | 0.342866i | −0.00994754 | + | 0.0172297i | ||||
\(397\) | 15.8324 | − | 27.4225i | 0.794605 | − | 1.37630i | −0.128485 | − | 0.991711i | \(-0.541011\pi\) |
0.923090 | − | 0.384584i | \(-0.125655\pi\) | |||||||
\(398\) | −12.1143 | −0.607235 | ||||||||
\(399\) | 5.56988 | + | 18.1823i | 0.278843 | + | 0.910255i | ||||
\(400\) | −3.80814 | −0.190407 | ||||||||
\(401\) | 2.44425 | − | 4.23356i | 0.122060 | − | 0.211414i | −0.798520 | − | 0.601968i | \(-0.794383\pi\) |
0.920580 | + | 0.390554i | \(0.127717\pi\) | |||||||
\(402\) | −2.76575 | + | 4.79041i | −0.137943 | + | 0.238924i | ||||
\(403\) | 3.76493 | + | 6.52106i | 0.187545 | + | 0.324837i | ||||
\(404\) | −0.206367 | + | 0.357438i | −0.0102671 | + | 0.0177832i | ||||
\(405\) | −0.500000 | − | 0.866025i | −0.0248452 | − | 0.0430331i | ||||
\(406\) | 21.4151 | 1.06281 | ||||||||
\(407\) | 28.2546 | 1.40053 | ||||||||
\(408\) | −8.25883 | − | 14.3047i | −0.408873 | − | 0.708189i | ||||
\(409\) | 11.3941 | + | 19.7351i | 0.563400 | + | 0.975837i | 0.997197 | + | 0.0748266i | \(0.0238403\pi\) |
−0.433797 | + | 0.901011i | \(0.642826\pi\) | |||||||
\(410\) | −1.05374 | −0.0520407 | ||||||||
\(411\) | −15.7164 | −0.775233 | ||||||||
\(412\) | −0.737087 | − | 1.27667i | −0.0363137 | − | 0.0628972i | ||||
\(413\) | 8.35377 | − | 14.4692i | 0.411062 | − | 0.711980i | ||||
\(414\) | 0.400163 | + | 0.693102i | 0.0196669 | + | 0.0340641i | ||||
\(415\) | −3.83945 | + | 6.65012i | −0.188471 | + | 0.326441i | ||||
\(416\) | 1.64938 | − | 2.85682i | 0.0808677 | − | 0.140067i | ||||
\(417\) | −6.55344 | −0.320923 | ||||||||
\(418\) | −7.61243 | − | 24.8500i | −0.372336 | − | 1.21545i | ||||
\(419\) | 30.8809 | 1.50863 | 0.754316 | − | 0.656512i | \(-0.227969\pi\) | ||||
0.754316 | + | 0.656512i | \(0.227969\pi\) | |||||||
\(420\) | 0.200081 | − | 0.346551i | 0.00976297 | − | 0.0169100i | ||||
\(421\) | −13.2891 | + | 23.0174i | −0.647671 | + | 1.12180i | 0.336007 | + | 0.941859i | \(0.390923\pi\) |
−0.983678 | + | 0.179939i | \(0.942410\pi\) | |||||||
\(422\) | −5.43429 | − | 9.41246i | −0.264537 | − | 0.458191i | ||||
\(423\) | 1.36632 | − | 2.36653i | 0.0664327 | − | 0.115065i | ||||
\(424\) | 7.42180 | + | 12.8549i | 0.360434 | + | 0.624291i | ||||
\(425\) | 5.71641 | 0.277287 | ||||||||
\(426\) | −4.25342 | −0.206079 | ||||||||
\(427\) | −26.2218 | − | 45.4175i | −1.26896 | − | 2.19791i | ||||
\(428\) | 0.627347 | + | 1.08660i | 0.0303240 | + | 0.0525227i | ||||
\(429\) | −27.4628 | −1.32591 | ||||||||
\(430\) | −8.78938 | −0.423861 | ||||||||
\(431\) | −8.23718 | − | 14.2672i | −0.396771 | − | 0.687228i | 0.596554 | − | 0.802573i | \(-0.296536\pi\) |
−0.993325 | + | 0.115345i | \(0.963203\pi\) | |||||||
\(432\) | −1.90407 | + | 3.29794i | −0.0916095 | + | 0.158672i | ||||
\(433\) | 18.4021 | + | 31.8733i | 0.884346 | + | 1.53173i | 0.846461 | + | 0.532450i | \(0.178729\pi\) |
0.0378851 | + | 0.999282i | \(0.487938\pi\) | |||||||
\(434\) | 3.56607 | − | 6.17662i | 0.171177 | − | 0.296487i | ||||
\(435\) | −1.77672 | + | 3.07737i | −0.0851873 | + | 0.147549i | ||||
\(436\) | 0.822473 | 0.0393893 | ||||||||
\(437\) | 2.46095 | + | 0.566723i | 0.117723 | + | 0.0271100i | ||||
\(438\) | −11.1706 | −0.533751 | ||||||||
\(439\) | −4.79140 | + | 8.29895i | −0.228681 | + | 0.396087i | −0.957417 | − | 0.288707i | \(-0.906775\pi\) |
0.728736 | + | 0.684794i | \(0.240108\pi\) | |||||||
\(440\) | −6.23593 | + | 10.8010i | −0.297287 | + | 0.514915i | ||||
\(441\) | −6.01633 | − | 10.4206i | −0.286492 | − | 0.496219i | ||||
\(442\) | 25.1219 | − | 43.5123i | 1.19492 | − | 2.06967i | ||||
\(443\) | 11.1218 | + | 19.2635i | 0.528412 | + | 0.915236i | 0.999451 | + | 0.0331236i | \(0.0105455\pi\) |
−0.471040 | + | 0.882112i | \(0.656121\pi\) | |||||||
\(444\) | −0.600439 | −0.0284956 | ||||||||
\(445\) | 9.84186 | 0.466549 | ||||||||
\(446\) | 18.8931 | + | 32.7239i | 0.894616 | + | 1.54952i | ||||
\(447\) | 2.87560 | + | 4.98069i | 0.136011 | + | 0.235578i | ||||
\(448\) | −36.3516 | −1.71745 | ||||||||
\(449\) | −0.491188 | −0.0231806 | −0.0115903 | − | 0.999933i | \(-0.503689\pi\) | ||||
−0.0115903 | + | 0.999933i | \(0.503689\pi\) | |||||||
\(450\) | −0.690702 | − | 1.19633i | −0.0325600 | − | 0.0563956i | ||||
\(451\) | −1.64623 | + | 2.85136i | −0.0775180 | + | 0.134265i | ||||
\(452\) | 0.294873 | + | 0.510736i | 0.0138697 | + | 0.0240230i | ||||
\(453\) | −6.33364 | + | 10.9702i | −0.297581 | + | 0.515425i | ||||
\(454\) | 17.3312 | − | 30.0185i | 0.813394 | − | 1.40884i | ||||
\(455\) | 27.7579 | 1.30131 | ||||||||
\(456\) | 3.68911 | + | 12.0427i | 0.172758 | + | 0.563952i | ||||
\(457\) | 13.2607 | 0.620311 | 0.310156 | − | 0.950686i | \(-0.399619\pi\) | ||||
0.310156 | + | 0.950686i | \(0.399619\pi\) | |||||||
\(458\) | −3.44336 | + | 5.96407i | −0.160897 | + | 0.278683i | ||||
\(459\) | 2.85821 | − | 4.95056i | 0.133410 | − | 0.231072i | ||||
\(460\) | −0.0265707 | − | 0.0460218i | −0.00123887 | − | 0.00214578i | ||||
\(461\) | −11.6867 | + | 20.2420i | −0.544305 | + | 0.942763i | 0.454346 | + | 0.890825i | \(0.349873\pi\) |
−0.998650 | + | 0.0519379i | \(0.983460\pi\) | |||||||
\(462\) | 13.0061 | + | 22.5272i | 0.605098 | + | 1.04806i | ||||
\(463\) | −0.981649 | −0.0456211 | −0.0228105 | − | 0.999740i | \(-0.507261\pi\) | ||||
−0.0228105 | + | 0.999740i | \(0.507261\pi\) | |||||||
\(464\) | 13.5320 | 0.628207 | ||||||||
\(465\) | 0.591725 | + | 1.02490i | 0.0274406 | + | 0.0475285i | ||||
\(466\) | −8.83851 | − | 15.3087i | −0.409436 | − | 0.709164i | ||||
\(467\) | −18.8498 | −0.872264 | −0.436132 | − | 0.899883i | \(-0.643652\pi\) | ||||
−0.436132 | + | 0.899883i | \(0.643652\pi\) | |||||||
\(468\) | 0.583613 | 0.0269775 | ||||||||
\(469\) | −8.73457 | − | 15.1287i | −0.403325 | − | 0.698579i | ||||
\(470\) | 1.88744 | − | 3.26914i | 0.0870610 | − | 0.150794i | ||||
\(471\) | 0.689434 | + | 1.19414i | 0.0317675 | + | 0.0550228i | ||||
\(472\) | 5.53296 | − | 9.58337i | 0.254675 | − | 0.441110i | ||||
\(473\) | −13.7314 | + | 23.7834i | −0.631369 | + | 1.09356i | ||||
\(474\) | −15.6606 | −0.719315 | ||||||||
\(475\) | −4.24772 | − | 0.978193i | −0.194899 | − | 0.0448826i | ||||
\(476\) | 2.28750 | 0.104847 | ||||||||
\(477\) | −2.56853 | + | 4.44882i | −0.117605 | + | 0.203697i | ||||
\(478\) | −8.84440 | + | 15.3189i | −0.404533 | + | 0.700672i | ||||
\(479\) | −10.0795 | − | 17.4583i | −0.460546 | − | 0.797688i | 0.538443 | − | 0.842662i | \(-0.319013\pi\) |
−0.998988 | + | 0.0449739i | \(0.985680\pi\) | |||||||
\(480\) | 0.259229 | − | 0.448998i | 0.0118321 | − | 0.0204939i | ||||
\(481\) | −20.8252 | − | 36.0704i | −0.949549 | − | 1.64467i | ||||
\(482\) | −1.50958 | −0.0687596 | ||||||||
\(483\) | −2.52753 | −0.115007 | ||||||||
\(484\) | 0.349931 | + | 0.606098i | 0.0159059 | + | 0.0275499i | ||||
\(485\) | −1.00000 | − | 1.73205i | −0.0454077 | − | 0.0786484i | ||||
\(486\) | −1.38140 | −0.0626617 | ||||||||
\(487\) | 2.79159 | 0.126499 | 0.0632494 | − | 0.997998i | \(-0.479854\pi\) | ||||
0.0632494 | + | 0.997998i | \(0.479854\pi\) | |||||||
\(488\) | −17.3675 | − | 30.0814i | −0.786190 | − | 1.36172i | ||||
\(489\) | −5.80601 | + | 10.0563i | −0.262557 | + | 0.454762i | ||||
\(490\) | −8.31098 | − | 14.3950i | −0.375452 | − | 0.650302i | ||||
\(491\) | −2.88904 | + | 5.00397i | −0.130381 | + | 0.225826i | −0.923823 | − | 0.382819i | \(-0.874953\pi\) |
0.793443 | + | 0.608645i | \(0.208287\pi\) | |||||||
\(492\) | 0.0349842 | − | 0.0605943i | 0.00157721 | − | 0.00273180i | ||||
\(493\) | −20.3129 | −0.914849 | ||||||||
\(494\) | −26.1132 | + | 28.0341i | −1.17489 | + | 1.26131i | ||||
\(495\) | −4.31625 | −0.194001 | ||||||||
\(496\) | 2.25337 | − | 3.90295i | 0.101179 | − | 0.175248i | ||||
\(497\) | 6.71641 | − | 11.6332i | 0.301272 | − | 0.521819i | ||||
\(498\) | 5.30382 | + | 9.18649i | 0.237670 | + | 0.411657i | ||||
\(499\) | −6.39792 | + | 11.0815i | −0.286410 | + | 0.496077i | −0.972950 | − | 0.231015i | \(-0.925795\pi\) |
0.686540 | + | 0.727092i | \(0.259129\pi\) | |||||||
\(500\) | 0.0458624 | + | 0.0794360i | 0.00205103 | + | 0.00355249i | ||||
\(501\) | 20.3114 | 0.907446 | ||||||||
\(502\) | 8.42004 | 0.375805 | ||||||||
\(503\) | −15.8339 | − | 27.4252i | −0.706000 | − | 1.22283i | −0.966329 | − | 0.257308i | \(-0.917164\pi\) |
0.260329 | − | 0.965520i | \(-0.416169\pi\) | |||||||
\(504\) | −6.30296 | − | 10.9171i | −0.280756 | − | 0.486284i | ||||
\(505\) | −4.49970 | −0.200234 | ||||||||
\(506\) | 3.45440 | 0.153567 | ||||||||
\(507\) | 13.7416 | + | 23.8012i | 0.610287 | + | 1.05705i | ||||
\(508\) | −0.283588 | + | 0.491189i | −0.0125822 | + | 0.0217930i | ||||
\(509\) | 2.74405 | + | 4.75283i | 0.121628 | + | 0.210665i | 0.920410 | − | 0.390955i | \(-0.127855\pi\) |
−0.798782 | + | 0.601621i | \(0.794522\pi\) | |||||||
\(510\) | 3.94834 | − | 6.83872i | 0.174835 | − | 0.302823i | ||||
\(511\) | 17.6391 | − | 30.5517i | 0.780306 | − | 1.35153i | ||||
\(512\) | −23.9817 | −1.05985 | ||||||||
\(513\) | −2.97100 | + | 3.18954i | −0.131173 | + | 0.140822i | ||||
\(514\) | 6.38252 | 0.281521 | ||||||||
\(515\) | 8.03585 | − | 13.9185i | 0.354102 | − | 0.613323i | ||||
\(516\) | 0.291806 | − | 0.505423i | 0.0128461 | − | 0.0222500i | ||||
\(517\) | −5.89737 | − | 10.2145i | −0.259366 | − | 0.449235i | ||||
\(518\) | −19.7252 | + | 34.1651i | −0.866678 | + | 1.50113i | ||||
\(519\) | −6.12545 | − | 10.6096i | −0.268877 | − | 0.465709i | ||||
\(520\) | 18.3850 | 0.806234 | ||||||||
\(521\) | 8.28086 | 0.362791 | 0.181396 | − | 0.983410i | \(-0.441939\pi\) | ||||
0.181396 | + | 0.983410i | \(0.441939\pi\) | |||||||
\(522\) | 2.45437 | + | 4.25109i | 0.107425 | + | 0.186065i | ||||
\(523\) | −5.77584 | − | 10.0040i | −0.252560 | − | 0.437446i | 0.711670 | − | 0.702514i | \(-0.247939\pi\) |
−0.964230 | + | 0.265067i | \(0.914606\pi\) | |||||||
\(524\) | −1.59578 | −0.0697118 | ||||||||
\(525\) | 4.36264 | 0.190401 | ||||||||
\(526\) | 20.7552 | + | 35.9491i | 0.904970 | + | 1.56745i | ||||
\(527\) | −3.38254 | + | 5.85874i | −0.147346 | + | 0.255211i | ||||
\(528\) | 8.21843 | + | 14.2347i | 0.357661 | + | 0.619488i | ||||
\(529\) | 11.3322 | − | 19.6279i | 0.492703 | − | 0.853387i | ||||
\(530\) | −3.54817 | + | 6.14561i | −0.154123 | + | 0.266948i | ||||
\(531\) | 3.82968 | 0.166194 | ||||||||
\(532\) | −1.69978 | − | 0.391436i | −0.0736948 | − | 0.0169709i | ||||
\(533\) | 4.85347 | 0.210227 | ||||||||
\(534\) | 6.79779 | − | 11.7741i | 0.294169 | − | 0.509516i | ||||
\(535\) | −6.83945 | + | 11.8463i | −0.295695 | + | 0.512159i | ||||
\(536\) | −5.78518 | − | 10.0202i | −0.249882 | − | 0.432808i | ||||
\(537\) | −9.59201 | + | 16.6139i | −0.413926 | + | 0.716941i | ||||
\(538\) | 0.145931 | + | 0.252759i | 0.00629152 | + | 0.0108972i | ||||
\(539\) | −51.9360 | −2.23704 | ||||||||
\(540\) | 0.0917248 | 0.00394721 | ||||||||
\(541\) | 12.9374 | + | 22.4083i | 0.556224 | + | 0.963409i | 0.997807 | + | 0.0661881i | \(0.0210837\pi\) |
−0.441583 | + | 0.897220i | \(0.645583\pi\) | |||||||
\(542\) | 5.11622 | + | 8.86155i | 0.219760 | + | 0.380636i | ||||
\(543\) | 3.22984 | 0.138606 | ||||||||
\(544\) | 2.96372 | 0.127069 | ||||||||
\(545\) | 4.48337 | + | 7.76542i | 0.192046 | + | 0.332634i | ||||
\(546\) | 19.1725 | − | 33.2077i | 0.820506 | − | 1.42116i | ||||
\(547\) | −3.20287 | − | 5.54753i | −0.136945 | − | 0.237195i | 0.789394 | − | 0.613887i | \(-0.210395\pi\) |
−0.926339 | + | 0.376692i | \(0.877062\pi\) | |||||||
\(548\) | 0.720793 | − | 1.24845i | 0.0307907 | − | 0.0533311i | ||||
\(549\) | 6.01053 | − | 10.4105i | 0.256523 | − | 0.444311i | ||||
\(550\) | −5.96248 | −0.254241 | ||||||||
\(551\) | 15.0940 | + | 3.47595i | 0.643028 | + | 0.148080i | ||||
\(552\) | −1.67406 | −0.0712528 | ||||||||
\(553\) | 24.7291 | − | 42.8320i | 1.05159 | − | 1.82140i | ||||
\(554\) | 20.0765 | − | 34.7736i | 0.852970 | − | 1.47739i | ||||
\(555\) | −3.27305 | − | 5.66908i | −0.138933 | − | 0.240639i | ||||
\(556\) | 0.300557 | − | 0.520580i | 0.0127464 | − | 0.0220775i | ||||
\(557\) | 1.76281 | + | 3.05327i | 0.0746925 | + | 0.129371i | 0.900953 | − | 0.433918i | \(-0.142869\pi\) |
−0.826260 | + | 0.563289i | \(0.809536\pi\) | |||||||
\(558\) | 1.63482 | 0.0692075 | ||||||||
\(559\) | 40.4832 | 1.71226 | ||||||||
\(560\) | −8.30677 | − | 14.3878i | −0.351025 | − | 0.607993i | ||||
\(561\) | −12.3367 | − | 21.3678i | −0.520857 | − | 0.902151i | ||||
\(562\) | 15.8529 | 0.668713 | ||||||||
\(563\) | −30.7179 | −1.29461 | −0.647303 | − | 0.762232i | \(-0.724103\pi\) | ||||
−0.647303 | + | 0.762232i | \(0.724103\pi\) | |||||||
\(564\) | 0.125325 | + | 0.217070i | 0.00527715 | + | 0.00914029i | ||||
\(565\) | −3.21476 | + | 5.56813i | −0.135246 | + | 0.234253i | ||||
\(566\) | 18.8786 | + | 32.6986i | 0.793525 | + | 1.37443i | ||||
\(567\) | 2.18132 | − | 3.77816i | 0.0916069 | − | 0.158668i | ||||
\(568\) | 4.44849 | − | 7.70501i | 0.186654 | − | 0.323295i | ||||
\(569\) | 9.17896 | 0.384802 | 0.192401 | − | 0.981316i | \(-0.438373\pi\) | ||||
0.192401 | + | 0.981316i | \(0.438373\pi\) | |||||||
\(570\) | −4.10415 | + | 4.40604i | −0.171904 | + | 0.184549i | ||||
\(571\) | −7.49001 | −0.313447 | −0.156724 | − | 0.987643i | \(-0.550093\pi\) | ||||
−0.156724 | + | 0.987643i | \(0.550093\pi\) | |||||||
\(572\) | 1.25951 | − | 2.18153i | 0.0526627 | − | 0.0912145i | ||||
\(573\) | 13.7755 | − | 23.8598i | 0.575478 | − | 0.996758i | ||||
\(574\) | −2.29855 | − | 3.98121i | −0.0959398 | − | 0.166173i | ||||
\(575\) | 0.289678 | − | 0.501738i | 0.0120804 | − | 0.0209239i | ||||
\(576\) | −4.16624 | − | 7.21613i | −0.173593 | − | 0.300672i | ||||
\(577\) | 32.6093 | 1.35754 | 0.678771 | − | 0.734350i | \(-0.262513\pi\) | ||||
0.678771 | + | 0.734350i | \(0.262513\pi\) | |||||||
\(578\) | 21.6568 | 0.900803 | ||||||||
\(579\) | 11.1233 | + | 19.2662i | 0.462270 | + | 0.800674i | ||||
\(580\) | −0.162969 | − | 0.282271i | −0.00676694 | − | 0.0117207i | ||||
\(581\) | −33.5003 | −1.38983 | ||||||||
\(582\) | −2.76281 | −0.114522 | ||||||||
\(583\) | 11.0864 | + | 19.2022i | 0.459152 | + | 0.795275i | ||||
\(584\) | 11.6829 | − | 20.2354i | 0.483442 | − | 0.837346i | ||||
\(585\) | 3.18132 | + | 5.51021i | 0.131531 | + | 0.227819i | ||||
\(586\) | −8.99367 | + | 15.5775i | −0.371525 | + | 0.643500i | ||||
\(587\) | 9.19474 | − | 15.9258i | 0.379508 | − | 0.657326i | −0.611483 | − | 0.791258i | \(-0.709427\pi\) |
0.990991 | + | 0.133931i | \(0.0427601\pi\) | |||||||
\(588\) | 1.10369 | 0.0455156 | ||||||||
\(589\) | 3.51603 | − | 3.77466i | 0.144875 | − | 0.155532i | ||||
\(590\) | 5.29033 | 0.217800 | ||||||||
\(591\) | 6.33133 | − | 10.9662i | 0.260436 | − | 0.451089i | ||||
\(592\) | −12.4642 | + | 21.5886i | −0.512276 | + | 0.887288i | ||||
\(593\) | −0.208669 | − | 0.361425i | −0.00856900 | − | 0.0148419i | 0.861709 | − | 0.507403i | \(-0.169394\pi\) |
−0.870278 | + | 0.492561i | \(0.836061\pi\) | |||||||
\(594\) | −2.98124 | + | 5.16366i | −0.122322 | + | 0.211868i | ||||
\(595\) | 12.4693 | + | 21.5975i | 0.511193 | + | 0.885412i | ||||
\(596\) | −0.527528 | −0.0216084 | ||||||||
\(597\) | 8.76955 | 0.358914 | ||||||||
\(598\) | −2.54609 | − | 4.40996i | −0.104118 | − | 0.180337i | ||||
\(599\) | 19.4828 | + | 33.7452i | 0.796045 | + | 1.37879i | 0.922174 | + | 0.386776i | \(0.126411\pi\) |
−0.126129 | + | 0.992014i | \(0.540255\pi\) | |||||||
\(600\) | 2.88952 | 0.117964 | ||||||||
\(601\) | 10.0358 | 0.409367 | 0.204683 | − | 0.978828i | \(-0.434383\pi\) | ||||
0.204683 | + | 0.978828i | \(0.434383\pi\) | |||||||
\(602\) | −19.1725 | − | 33.2077i | −0.781411 | − | 1.35344i | ||||
\(603\) | 2.00213 | − | 3.46779i | 0.0815329 | − | 0.141219i | ||||
\(604\) | −0.580953 | − | 1.00624i | −0.0236386 | − | 0.0409433i | ||||
\(605\) | −3.81500 | + | 6.60778i | −0.155102 | + | 0.268644i | ||||
\(606\) | −3.10795 | + | 5.38313i | −0.126252 | + | 0.218675i | ||||
\(607\) | −6.25423 | −0.253851 | −0.126926 | − | 0.991912i | \(-0.540511\pi\) | ||||
−0.126926 | + | 0.991912i | \(0.540511\pi\) | |||||||
\(608\) | −2.20227 | − | 0.507152i | −0.0893137 | − | 0.0205677i | ||||
\(609\) | −15.5024 | −0.628189 | ||||||||
\(610\) | 8.30296 | − | 14.3812i | 0.336177 | − | 0.582276i | ||||
\(611\) | −8.69340 | + | 15.0574i | −0.351697 | + | 0.609157i | ||||
\(612\) | 0.262168 | + | 0.454089i | 0.0105975 | + | 0.0183555i | ||||
\(613\) | −14.9371 | + | 25.8719i | −0.603306 | + | 1.04496i | 0.389011 | + | 0.921233i | \(0.372817\pi\) |
−0.992317 | + | 0.123723i | \(0.960517\pi\) | |||||||
\(614\) | −2.78031 | − | 4.81563i | −0.112204 | − | 0.194343i | ||||
\(615\) | 0.762807 | 0.0307593 | ||||||||
\(616\) | −54.4103 | −2.19225 | ||||||||
\(617\) | 15.3197 | + | 26.5346i | 0.616749 | + | 1.06824i | 0.990075 | + | 0.140540i | \(0.0448840\pi\) |
−0.373326 | + | 0.927700i | \(0.621783\pi\) | |||||||
\(618\) | −11.1008 | − | 19.2271i | −0.446538 | − | 0.773426i | ||||
\(619\) | 21.1480 | 0.850011 | 0.425006 | − | 0.905191i | \(-0.360272\pi\) | ||||
0.425006 | + | 0.905191i | \(0.360272\pi\) | |||||||
\(620\) | −0.108552 | −0.00435954 | ||||||||
\(621\) | −0.289678 | − | 0.501738i | −0.0116244 | − | 0.0201340i | ||||
\(622\) | −10.6076 | + | 18.3730i | −0.425328 | + | 0.736690i | ||||
\(623\) | 21.4683 | + | 37.1841i | 0.860108 | + | 1.48975i | ||||
\(624\) | 12.1149 | − | 20.9836i | 0.484985 | − | 0.840018i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 30.3356 | 1.21245 | ||||||||
\(627\) | 5.51065 | + | 17.9890i | 0.220074 | + | 0.718410i | ||||
\(628\) | −0.126476 | −0.00504696 | ||||||||
\(629\) | 18.7101 | − | 32.4068i | 0.746020 | − | 1.29214i | ||||
\(630\) | 3.01329 | − | 5.21916i | 0.120052 | − | 0.207936i | ||||
\(631\) | 13.0124 | + | 22.5381i | 0.518014 | + | 0.897227i | 0.999781 | + | 0.0209274i | \(0.00666189\pi\) |
−0.481767 | + | 0.876299i | \(0.660005\pi\) | |||||||
\(632\) | 16.3788 | − | 28.3690i | 0.651515 | − | 1.12846i | ||||
\(633\) | 3.93389 | + | 6.81369i | 0.156358 | + | 0.270820i | ||||
\(634\) | −33.3304 | −1.32372 | ||||||||
\(635\) | −6.18345 | −0.245383 | ||||||||
\(636\) | −0.235598 | − | 0.408067i | −0.00934206 | − | 0.0161809i | ||||
\(637\) | 38.2798 | + | 66.3025i | 1.51670 | + | 2.62700i | ||||
\(638\) | 21.1873 | 0.838815 | ||||||||
\(639\) | 3.07906 | 0.121806 | ||||||||
\(640\) | −5.23680 | − | 9.07040i | −0.207003 | − | 0.358539i | ||||
\(641\) | 9.59982 | − | 16.6274i | 0.379170 | − | 0.656742i | −0.611771 | − | 0.791035i | \(-0.709543\pi\) |
0.990942 | + | 0.134292i | \(0.0428761\pi\) | |||||||
\(642\) | 9.44803 | + | 16.3645i | 0.372884 | + | 0.645854i | ||||
\(643\) | −4.27305 | + | 7.40113i | −0.168513 | + | 0.291872i | −0.937897 | − | 0.346914i | \(-0.887230\pi\) |
0.769385 | + | 0.638786i | \(0.220563\pi\) | |||||||
\(644\) | 0.115919 | − | 0.200777i | 0.00456783 | − | 0.00791172i | ||||
\(645\) | 6.36264 | 0.250529 | ||||||||
\(646\) | −33.5429 | − | 7.72446i | −1.31973 | − | 0.303915i | ||||
\(647\) | −21.6966 | −0.852983 | −0.426492 | − | 0.904492i | \(-0.640251\pi\) | ||||
−0.426492 | + | 0.904492i | \(0.640251\pi\) | |||||||
\(648\) | 1.44476 | − | 2.50239i | 0.0567554 | − | 0.0983033i | ||||
\(649\) | 8.26493 | − | 14.3153i | 0.324427 | − | 0.561924i | ||||
\(650\) | 4.39469 | + | 7.61182i | 0.172374 | + | 0.298560i | ||||
\(651\) | −2.58148 | + | 4.47126i | −0.101176 | + | 0.175243i | ||||
\(652\) | −0.532555 | − | 0.922413i | −0.0208565 | − | 0.0361245i | ||||
\(653\) | −4.39011 | −0.171798 | −0.0858991 | − | 0.996304i | \(-0.527376\pi\) | ||||
−0.0858991 | + | 0.996304i | \(0.527376\pi\) | |||||||
\(654\) | 12.3867 | 0.484358 | ||||||||
\(655\) | −8.69872 | − | 15.0666i | −0.339887 | − | 0.588702i | ||||
\(656\) | −1.45244 | − | 2.51569i | −0.0567081 | − | 0.0982213i | ||||
\(657\) | 8.08640 | 0.315481 | ||||||||
\(658\) | 16.4684 | 0.642006 | ||||||||
\(659\) | 7.57327 | + | 13.1173i | 0.295013 | + | 0.510977i | 0.974988 | − | 0.222258i | \(-0.0713428\pi\) |
−0.679975 | + | 0.733235i | \(0.738009\pi\) | |||||||
\(660\) | 0.197954 | − | 0.342866i | 0.00770534 | − | 0.0133460i | ||||
\(661\) | −3.65794 | − | 6.33574i | −0.142277 | − | 0.246432i | 0.786076 | − | 0.618129i | \(-0.212109\pi\) |
−0.928354 | + | 0.371698i | \(0.878776\pi\) | |||||||
\(662\) | 17.1582 | − | 29.7188i | 0.666871 | − | 1.15505i | ||||
\(663\) | −18.1857 | + | 31.4986i | −0.706276 | + | 1.22331i | ||||
\(664\) | −22.1883 | −0.861072 | ||||||||
\(665\) | −5.56988 | − | 18.1823i | −0.215991 | − | 0.705080i | ||||
\(666\) | −9.04280 | −0.350401 | ||||||||
\(667\) | −1.02936 | + | 1.78290i | −0.0398568 | + | 0.0690340i | ||||
\(668\) | −0.931530 | + | 1.61346i | −0.0360420 | + | 0.0624265i | ||||
\(669\) | −13.6768 | − | 23.6889i | −0.528774 | − | 0.915864i | ||||
\(670\) | 2.76575 | − | 4.79041i | 0.106850 | − | 0.185070i | ||||
\(671\) | −25.9429 | − | 44.9345i | −1.00152 | − | 1.73468i | ||||
\(672\) | 2.26185 | 0.0872527 | ||||||||
\(673\) | 39.7027 | 1.53043 | 0.765213 | − | 0.643777i | \(-0.222634\pi\) | ||||
0.765213 | + | 0.643777i | \(0.222634\pi\) | |||||||
\(674\) | −0.393218 | − | 0.681074i | −0.0151462 | − | 0.0262340i | ||||
\(675\) | 0.500000 | + | 0.866025i | 0.0192450 | + | 0.0333333i | ||||
\(676\) | −2.52090 | −0.0969575 | ||||||||
\(677\) | −9.45197 | −0.363269 | −0.181634 | − | 0.983366i | \(-0.558139\pi\) | ||||
−0.181634 | + | 0.983366i | \(0.558139\pi\) | |||||||
\(678\) | 4.44088 | + | 7.69183i | 0.170551 | + | 0.295403i | ||||
\(679\) | 4.36264 | − | 7.55632i | 0.167423 | − | 0.289985i | ||||
\(680\) | 8.25883 | + | 14.3047i | 0.316712 | + | 0.548561i | ||||
\(681\) | −12.5461 | + | 21.7305i | −0.480767 | + | 0.832713i | ||||
\(682\) | 3.52815 | − | 6.11093i | 0.135100 | − | 0.234000i | ||||
\(683\) | −6.27600 | −0.240145 | −0.120072 | − | 0.992765i | \(-0.538313\pi\) | ||||
−0.120072 | + | 0.992765i | \(0.538313\pi\) | |||||||
\(684\) | −0.117107 | − | 0.382284i | −0.00447770 | − | 0.0146170i | ||||
\(685\) | 15.7164 | 0.600493 | ||||||||
\(686\) | 15.1648 | − | 26.2663i | 0.578996 | − | 1.00285i | ||||
\(687\) | 2.49265 | − | 4.31740i | 0.0951006 | − | 0.164719i | ||||
\(688\) | −12.1149 | − | 20.9836i | −0.461877 | − | 0.799994i | ||||
\(689\) | 16.3426 | − | 28.3063i | 0.622604 | − | 1.07838i | ||||
\(690\) | −0.400163 | − | 0.693102i | −0.0152339 | − | 0.0263860i | ||||
\(691\) | −33.8913 | −1.28929 | −0.644643 | − | 0.764483i | \(-0.722994\pi\) | ||||
−0.644643 | + | 0.764483i | \(0.722994\pi\) | |||||||
\(692\) | 1.12371 | 0.0427171 | ||||||||
\(693\) | −9.41513 | − | 16.3075i | −0.357651 | − | 0.619470i | ||||
\(694\) | −6.47439 | − | 11.2140i | −0.245765 | − | 0.425677i | ||||
\(695\) | 6.55344 | 0.248586 | ||||||||
\(696\) | −10.2677 | −0.389197 | ||||||||
\(697\) | 2.18026 | + | 3.77632i | 0.0825832 | + | 0.143038i | ||||
\(698\) | −10.2429 | + | 17.7412i | −0.387699 | + | 0.671514i | ||||
\(699\) | 6.39821 | + | 11.0820i | 0.242002 | + | 0.419161i | ||||
\(700\) | −0.200081 | + | 0.346551i | −0.00756237 | + | 0.0130984i | ||||
\(701\) | −20.1520 | + | 34.9043i | −0.761131 | + | 1.31832i | 0.181136 | + | 0.983458i | \(0.442022\pi\) |
−0.942268 | + | 0.334860i | \(0.891311\pi\) | |||||||
\(702\) | 8.78938 | 0.331734 | ||||||||
\(703\) | −19.4484 | + | 20.8790i | −0.733512 | + | 0.787467i | ||||
\(704\) | −35.9650 | −1.35548 | ||||||||
\(705\) | −1.36632 | + | 2.36653i | −0.0514585 | + | 0.0891288i | ||||
\(706\) | −21.5948 | + | 37.4033i | −0.812730 | + | 1.40769i | ||||
\(707\) | −9.81529 | − | 17.0006i | −0.369142 | − | 0.639373i | ||||
\(708\) | −0.175638 | + | 0.304215i | −0.00660090 | + | 0.0114331i | ||||
\(709\) | 2.63706 | + | 4.56751i | 0.0990367 | + | 0.171537i | 0.911286 | − | 0.411774i | \(-0.135091\pi\) |
−0.812249 | + | 0.583310i | \(0.801757\pi\) | |||||||
\(710\) | 4.25342 | 0.159628 | ||||||||
\(711\) | 11.3367 | 0.425161 | ||||||||
\(712\) | 14.2191 | + | 24.6282i | 0.532884 | + | 0.922981i | ||||
\(713\) | 0.342820 | + | 0.593782i | 0.0128387 | + | 0.0222373i | ||||
\(714\) | 34.4504 | 1.28927 | ||||||||
\(715\) | 27.4628 | 1.02705 | ||||||||
\(716\) | −0.879826 | − | 1.52390i | −0.0328806 | − | 0.0569509i | ||||
\(717\) | 6.40247 | − | 11.0894i | 0.239105 | − | 0.414142i | ||||
\(718\) | −7.50877 | − | 13.0056i | −0.280225 | − | 0.485364i | ||||
\(719\) | −11.8834 | + | 20.5827i | −0.443176 | + | 0.767604i | −0.997923 | − | 0.0644151i | \(-0.979482\pi\) |
0.554747 | + | 0.832019i | \(0.312815\pi\) | |||||||
\(720\) | 1.90407 | − | 3.29794i | 0.0709604 | − | 0.122907i | ||||
\(721\) | 70.1151 | 2.61122 | ||||||||
\(722\) | 23.6030 | + | 11.4797i | 0.878414 | + | 0.427231i | ||||
\(723\) | 1.09279 | 0.0406413 | ||||||||
\(724\) | −0.148128 | + | 0.256566i | −0.00550515 | + | 0.00953520i | ||||
\(725\) | 1.77672 | − | 3.07737i | 0.0659858 | − | 0.114291i | ||||
\(726\) | 5.27006 | + | 9.12801i | 0.195590 | + | 0.338772i | ||||
\(727\) | 16.9225 | − | 29.3106i | 0.627620 | − | 1.08707i | −0.360408 | − | 0.932795i | \(-0.617363\pi\) |
0.988028 | − | 0.154275i | \(-0.0493040\pi\) | |||||||
\(728\) | 40.1035 | + | 69.4613i | 1.48634 | + | 2.57441i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 11.1706 | 0.413442 | ||||||||
\(731\) | 18.1857 | + | 31.4986i | 0.672624 | + | 1.16502i | ||||
\(732\) | 0.551315 | + | 0.954905i | 0.0203772 | + | 0.0352943i | ||||
\(733\) | 24.6249 | 0.909542 | 0.454771 | − | 0.890608i | \(-0.349721\pi\) | ||||
0.454771 | + | 0.890608i | \(0.349721\pi\) | |||||||
\(734\) | −25.8731 | −0.954992 | ||||||||
\(735\) | 6.01633 | + | 10.4206i | 0.221916 | + | 0.384369i | ||||
\(736\) | 0.150186 | − | 0.260130i | 0.00553594 | − | 0.00958853i | ||||
\(737\) | −8.64168 | − | 14.9678i | −0.318320 | − | 0.551347i | ||||
\(738\) | 0.526872 | − | 0.912569i | 0.0193944 | − | 0.0335921i | ||||
\(739\) | −9.22966 | + | 15.9862i | −0.339518 | + | 0.588063i | −0.984342 | − | 0.176268i | \(-0.943597\pi\) |
0.644824 | + | 0.764331i | \(0.276931\pi\) | |||||||
\(740\) | 0.600439 | 0.0220726 | ||||||||
\(741\) | 18.9034 | − | 20.2939i | 0.694434 | − | 0.745515i | ||||
\(742\) | −30.9588 | −1.13653 | ||||||||
\(743\) | 4.47864 | − | 7.75723i | 0.164305 | − | 0.284585i | −0.772103 | − | 0.635497i | \(-0.780795\pi\) |
0.936408 | + | 0.350912i | \(0.114128\pi\) | |||||||
\(744\) | −1.70980 | + | 2.96146i | −0.0626842 | + | 0.108572i | ||||
\(745\) | −2.87560 | − | 4.98069i | −0.105354 | − | 0.182478i | ||||
\(746\) | −20.2565 | + | 35.0853i | −0.741644 | + | 1.28457i | ||||
\(747\) | −3.83945 | − | 6.65012i | −0.140478 | − | 0.243315i | ||||
\(748\) | 2.26317 | 0.0827497 | ||||||||
\(749\) | −59.6761 | −2.18052 | ||||||||
\(750\) | 0.690702 | + | 1.19633i | 0.0252209 | + | 0.0436838i | ||||
\(751\) | 14.6128 | + | 25.3101i | 0.533228 | + | 0.923578i | 0.999247 | + | 0.0388032i | \(0.0123545\pi\) |
−0.466019 | + | 0.884775i | \(0.654312\pi\) | |||||||
\(752\) | 10.4063 | 0.379477 | ||||||||
\(753\) | −6.09528 | −0.222124 | ||||||||
\(754\) | −15.6163 | − | 27.0482i | −0.568711 | − | 0.985037i | ||||
\(755\) | 6.33364 | − | 10.9702i | 0.230505 | − | 0.399246i | ||||
\(756\) | 0.200081 | + | 0.346551i | 0.00727689 | + | 0.0126039i | ||||
\(757\) | −9.33886 | + | 16.1754i | −0.339427 | + | 0.587904i | −0.984325 | − | 0.176364i | \(-0.943566\pi\) |
0.644898 | + | 0.764268i | \(0.276900\pi\) | |||||||
\(758\) | 7.35499 | − | 12.7392i | 0.267145 | − | 0.462709i | ||||
\(759\) | −2.50065 | −0.0907678 | ||||||||
\(760\) | −3.68911 | − | 12.0427i | −0.133818 | − | 0.436836i | ||||
\(761\) | 41.5952 | 1.50782 | 0.753912 | − | 0.656975i | \(-0.228164\pi\) | ||||
0.753912 | + | 0.656975i | \(0.228164\pi\) | |||||||
\(762\) | −4.27092 | + | 7.39745i | −0.154719 | + | 0.267981i | ||||
\(763\) | −19.5593 | + | 33.8778i | −0.708096 | + | 1.22646i | ||||
\(764\) | 1.26355 | + | 2.18854i | 0.0457137 | + | 0.0791785i | ||||
\(765\) | −2.85821 | + | 4.95056i | −0.103339 | + | 0.178988i | ||||
\(766\) | −6.40940 | − | 11.1014i | −0.231581 | − | 0.401110i | ||||
\(767\) | −24.3669 | −0.879838 | ||||||||
\(768\) | 2.19670 | 0.0792664 | ||||||||
\(769\) | −17.6255 | − | 30.5282i | −0.635590 | − | 1.10087i | −0.986390 | − | 0.164424i | \(-0.947424\pi\) |
0.350800 | − | 0.936450i | \(-0.385910\pi\) | |||||||
\(770\) | −13.0061 | − | 22.5272i | −0.468707 | − | 0.811824i | ||||
\(771\) | −4.62032 | −0.166397 | ||||||||
\(772\) | −2.04057 | −0.0734417 | ||||||||
\(773\) | −23.9762 | − | 41.5280i | −0.862364 | − | 1.49366i | −0.869641 | − | 0.493684i | \(-0.835650\pi\) |
0.00727780 | − | 0.999974i | \(-0.497683\pi\) | |||||||
\(774\) | 4.39469 | − | 7.61182i | 0.157964 | − | 0.273601i | ||||
\(775\) | −0.591725 | − | 1.02490i | −0.0212554 | − | 0.0368154i | ||||
\(776\) | 2.88952 | − | 5.00479i | 0.103728 | − | 0.179661i | ||||
\(777\) | 14.2791 | − | 24.7322i | 0.512261 | − | 0.887262i | ||||
\(778\) | 1.84068 | 0.0659917 | ||||||||
\(779\) | −0.973891 | − | 3.17917i | −0.0348933 | − | 0.113906i | ||||
\(780\) | −0.583613 | −0.0208967 | ||||||||
\(781\) | 6.64499 | − | 11.5095i | 0.237776 | − | 0.411841i | ||||
\(782\) | 2.28750 | − | 3.96206i | 0.0818007 | − | 0.141683i | ||||
\(783\) | −1.77672 | − | 3.07737i | −0.0634948 | − | 0.109976i | ||||
\(784\) | 22.9110 | − | 39.6830i | 0.818250 | − | 1.41725i | ||||
\(785\) | −0.689434 | − | 1.19414i | −0.0246070 | − | 0.0426205i | ||||
\(786\) | −24.0329 | −0.857224 | ||||||||
\(787\) | −5.26074 | −0.187525 | −0.0937626 | − | 0.995595i | \(-0.529889\pi\) | ||||
−0.0937626 | + | 0.995595i | \(0.529889\pi\) | |||||||
\(788\) | 0.580741 | + | 1.00587i | 0.0206880 | + | 0.0358327i | ||||
\(789\) | −15.0247 | − | 26.0236i | −0.534895 | − | 0.926465i | ||||
\(790\) | 15.6606 | 0.557179 | ||||||||
\(791\) | −28.0497 | −0.997333 | ||||||||
\(792\) | −6.23593 | − | 10.8010i | −0.221584 | − | 0.383795i | ||||
\(793\) | −38.2429 | + | 66.2386i | −1.35804 | + | 2.35220i | ||||
\(794\) | 21.8709 | + | 37.8815i | 0.776170 | + | 1.34437i | ||||
\(795\) | 2.56853 | − | 4.44882i | 0.0910963 | − | 0.157783i | ||||
\(796\) | −0.402193 | + | 0.696619i | −0.0142554 | + | 0.0246910i | ||||
\(797\) | −21.0174 | −0.744474 | −0.372237 | − | 0.928138i | \(-0.621409\pi\) | ||||
−0.372237 | + | 0.928138i | \(0.621409\pi\) | |||||||
\(798\) | −25.5992 | − | 5.89515i | −0.906202 | − | 0.208686i | ||||
\(799\) | −15.6209 | −0.552627 | ||||||||
\(800\) | −0.259229 | + | 0.448998i | −0.00916514 | + | 0.0158745i | ||||
\(801\) | −4.92093 | + | 8.52330i | −0.173873 | + | 0.301156i | ||||
\(802\) | 3.37649 | + | 5.84825i | 0.119228 | + | 0.206509i | ||||
\(803\) | 17.4515 | − | 30.2268i | 0.615849 | − | 1.06668i | ||||
\(804\) | 0.183645 | + | 0.318082i | 0.00647665 | + | 0.0112179i | ||||
\(805\) | 2.52753 | 0.0890837 | ||||||||
\(806\) | −10.4018 | −0.366387 | ||||||||
\(807\) | −0.105639 | − | 0.182973i | −0.00371869 | − | 0.00644095i | ||||
\(808\) | −6.50098 | − | 11.2600i | −0.228704 | − | 0.396126i | ||||
\(809\) | 35.3856 | 1.24409 | 0.622046 | − | 0.782981i | \(-0.286302\pi\) | ||||
0.622046 | + | 0.782981i | \(0.286302\pi\) | |||||||
\(810\) | 1.38140 | 0.0485376 | ||||||||
\(811\) | −2.67523 | − | 4.63364i | −0.0939401 | − | 0.162709i | 0.815226 | − | 0.579143i | \(-0.196613\pi\) |
−0.909166 | + | 0.416434i | \(0.863280\pi\) | |||||||
\(812\) | 0.710978 | − | 1.23145i | 0.0249504 | − | 0.0432154i | ||||
\(813\) | −3.70364 | − | 6.41489i | −0.129892 | − | 0.224980i | ||||
\(814\) | −19.5155 | + | 33.8018i | −0.684017 | + | 1.18475i | ||||
\(815\) | 5.80601 | − | 10.0563i | 0.203376 | − | 0.352257i | ||||
\(816\) | 21.7689 | 0.762063 | ||||||||
\(817\) | −8.12332 | − | 26.5178i | −0.284199 | − | 0.927740i | ||||
\(818\) | −31.4796 | −1.10066 | ||||||||
\(819\) | −13.8790 | + | 24.0391i | −0.484971 | + | 0.839994i | ||||
\(820\) | −0.0349842 | + | 0.0605943i | −0.00122170 | + | 0.00211605i | ||||
\(821\) | −3.81886 | − | 6.61446i | −0.133279 | − | 0.230846i | 0.791660 | − | 0.610962i | \(-0.209217\pi\) |
−0.924939 | + | 0.380116i | \(0.875884\pi\) | |||||||
\(822\) | 10.8554 | − | 18.8020i | 0.378624 | − | 0.655796i | ||||
\(823\) | −13.7866 | − | 23.8791i | −0.480570 | − | 0.832372i | 0.519181 | − | 0.854664i | \(-0.326237\pi\) |
−0.999752 | + | 0.0222919i | \(0.992904\pi\) | |||||||
\(824\) | 46.4394 | 1.61779 | ||||||||
\(825\) | 4.31625 | 0.150273 | ||||||||
\(826\) | 11.5399 | + | 19.9877i | 0.401525 | + | 0.695462i | ||||
\(827\) | 9.51585 | + | 16.4819i | 0.330898 | + | 0.573133i | 0.982688 | − | 0.185267i | \(-0.0593149\pi\) |
−0.651790 | + | 0.758400i | \(0.725982\pi\) | |||||||
\(828\) | 0.0531414 | 0.00184679 | ||||||||
\(829\) | −13.7455 | −0.477402 | −0.238701 | − | 0.971093i | \(-0.576722\pi\) | ||||
−0.238701 | + | 0.971093i | \(0.576722\pi\) | |||||||
\(830\) | −5.30382 | − | 9.18649i | −0.184098 | − | 0.318868i | ||||
\(831\) | −14.5334 | + | 25.1726i | −0.504159 | + | 0.873229i | ||||
\(832\) | 26.5083 | + | 45.9137i | 0.919009 | + | 1.59177i | ||||
\(833\) | −34.3918 | + | 59.5684i | −1.19161 | + | 2.06392i | ||||
\(834\) | 4.52647 | − | 7.84008i | 0.156739 | − | 0.271480i | ||||
\(835\) | −20.3114 | −0.702905 | ||||||||
\(836\) | −1.68170 | − | 0.387274i | −0.0581629 | − | 0.0133941i | ||||
\(837\) | −1.18345 | −0.0409060 | ||||||||
\(838\) | −21.3295 | + | 36.9438i | −0.736815 | + | 1.27620i | ||||
\(839\) | −17.1800 | + | 29.7566i | −0.593118 | + | 1.02731i | 0.400691 | + | 0.916213i | \(0.368770\pi\) |
−0.993809 | + | 0.111098i | \(0.964563\pi\) | |||||||
\(840\) | 6.30296 | + | 10.9171i | 0.217473 | + | 0.376674i | ||||
\(841\) | 8.18652 | − | 14.1795i | 0.282294 | − | 0.488947i | ||||
\(842\) | −18.3576 | − | 31.7963i | −0.632644 | − | 1.09577i | ||||
\(843\) | −11.4759 | −0.395251 | ||||||||
\(844\) | −0.721671 | −0.0248409 | ||||||||
\(845\) | −13.7416 | − | 23.8012i | −0.472726 | − | 0.818786i | ||||
\(846\) | 1.88744 | + | 3.26914i | 0.0648914 | + | 0.112395i | ||||
\(847\) | −33.2870 | −1.14375 | ||||||||
\(848\) | −19.5626 | −0.671783 | ||||||||
\(849\) | −13.6662 | − | 23.6706i | −0.469024 | − | 0.812373i | ||||
\(850\) | −3.94834 | + | 6.83872i | −0.135427 | + | 0.234566i | ||||
\(851\) | −1.89626 | − | 3.28442i | −0.0650030 | − | 0.112589i | ||||
\(852\) | −0.141213 | + | 0.244588i | −0.00483788 | + | 0.00837945i | ||||
\(853\) | −22.7147 | + | 39.3431i | −0.777738 | + | 1.34708i | 0.155505 | + | 0.987835i | \(0.450300\pi\) |
−0.933243 | + | 0.359247i | \(0.883034\pi\) | |||||||
\(854\) | 72.4457 | 2.47904 | ||||||||
\(855\) | 2.97100 | − | 3.18954i | 0.101606 | − | 0.109080i | ||||
\(856\) | −39.5254 | −1.35095 | ||||||||
\(857\) | −6.94674 | + | 12.0321i | −0.237296 | + | 0.411009i | −0.959937 | − | 0.280214i | \(-0.909594\pi\) |
0.722641 | + | 0.691223i | \(0.242928\pi\) | |||||||
\(858\) | 18.9686 | − | 32.8545i | 0.647576 | − | 1.12164i | ||||
\(859\) | 1.60333 | + | 2.77705i | 0.0547049 | + | 0.0947517i | 0.892081 | − | 0.451875i | \(-0.149245\pi\) |
−0.837376 | + | 0.546627i | \(0.815912\pi\) | |||||||
\(860\) | −0.291806 | + | 0.505423i | −0.00995051 | + | 0.0172348i | ||||
\(861\) | 1.66393 | + | 2.88201i | 0.0567065 | + | 0.0982185i | ||||
\(862\) | 22.7577 | 0.775132 | ||||||||
\(863\) | 51.7277 | 1.76083 | 0.880416 | − | 0.474201i | \(-0.157263\pi\) | ||||
0.880416 | + | 0.474201i | \(0.157263\pi\) | |||||||
\(864\) | 0.259229 | + | 0.448998i | 0.00881916 | + | 0.0152752i | ||||
\(865\) | 6.12545 | + | 10.6096i | 0.208272 | + | 0.360737i | ||||
\(866\) | −50.8413 | −1.72766 | ||||||||
\(867\) | −15.6774 | −0.532431 | ||||||||
\(868\) | −0.236786 | − | 0.410126i | −0.00803705 | − | 0.0139206i | ||||
\(869\) | 24.4661 | − | 42.3765i | 0.829955 | − | 1.43752i | ||||
\(870\) | −2.45437 | − | 4.25109i | −0.0832109 | − | 0.144125i | ||||
\(871\) | −12.7388 | + | 22.0643i | −0.431639 | + | 0.747620i | ||||
\(872\) | −12.9548 | + | 22.4383i | −0.438704 | + | 0.759857i | ||||
\(873\) | 2.00000 | 0.0676897 | ||||||||
\(874\) | −2.37777 | + | 2.55267i | −0.0804292 | + | 0.0863453i | ||||
\(875\) | −4.36264 | −0.147484 | ||||||||
\(876\) | −0.370862 | + | 0.642352i | −0.0125303 | + | 0.0217031i | ||||
\(877\) | −8.51355 | + | 14.7459i | −0.287482 | + | 0.497933i | −0.973208 | − | 0.229926i | \(-0.926151\pi\) |
0.685726 | + | 0.727860i | \(0.259485\pi\) | |||||||
\(878\) | −6.61885 | − | 11.4642i | −0.223376 | − | 0.386898i | ||||
\(879\) | 6.51053 | − | 11.2766i | 0.219595 | − | 0.380349i | ||||
\(880\) | −8.21843 | − | 14.2347i | −0.277043 | − | 0.479853i | ||||
\(881\) | 12.9112 | 0.434990 | 0.217495 | − | 0.976061i | \(-0.430211\pi\) | ||||
0.217495 | + | 0.976061i | \(0.430211\pi\) | |||||||
\(882\) | 16.6220 | 0.559690 | ||||||||
\(883\) | −12.5102 | − | 21.6684i | −0.421003 | − | 0.729199i | 0.575035 | − | 0.818129i | \(-0.304989\pi\) |
−0.996038 | + | 0.0889302i | \(0.971655\pi\) | |||||||
\(884\) | −1.66808 | − | 2.88921i | −0.0561038 | − | 0.0971746i | ||||
\(885\) | −3.82968 | −0.128733 | ||||||||
\(886\) | −30.7273 | −1.03230 | ||||||||
\(887\) | −5.03634 | − | 8.72319i | −0.169104 | − | 0.292896i | 0.769001 | − | 0.639247i | \(-0.220754\pi\) |
−0.938105 | + | 0.346351i | \(0.887421\pi\) | |||||||
\(888\) | 9.45752 | − | 16.3809i | 0.317374 | − | 0.549707i | ||||
\(889\) | −13.4881 | − | 23.3621i | −0.452376 | − | 0.783539i | ||||
\(890\) | −6.79779 | + | 11.7741i | −0.227862 | + | 0.394669i | ||||
\(891\) | 2.15812 | − | 3.73798i | 0.0722999 | − | 0.125227i | ||||
\(892\) | 2.50900 | 0.0840075 | ||||||||
\(893\) | 11.6075 | + | 2.67304i | 0.388430 | + | 0.0894500i | ||||
\(894\) | −7.94473 | −0.265712 | ||||||||
\(895\) | 9.59201 | − | 16.6139i | 0.320626 | − | 0.555340i | ||||
\(896\) | 22.8463 | − | 39.5709i | 0.763240 | − | 1.32197i | ||||
\(897\) | 1.84312 | + | 3.19238i | 0.0615400 | + | 0.106590i | ||||
\(898\) | 0.339264 | − | 0.587623i | 0.0113214 | − | 0.0196092i | ||||
\(899\) | 2.10266 | + | 3.64191i | 0.0701276 | + | 0.121465i | ||||
\(900\) | −0.0917248 | −0.00305749 | ||||||||
\(901\) | 29.3655 | 0.978307 | ||||||||
\(902\) | −2.27411 | − | 3.93887i | −0.0757196 | − | 0.131150i | ||||
\(903\) | 13.8790 | + | 24.0391i | 0.461863 | + | 0.799971i | ||||
\(904\) | −18.5782 | −0.617902 | ||||||||
\(905\) | −3.22984 | −0.107364 | ||||||||
\(906\) | −8.74932 | − | 15.1543i | −0.290677 | − | 0.503467i | ||||
\(907\) | 3.93231 | − | 6.81096i | 0.130570 | − | 0.226154i | −0.793326 | − | 0.608797i | \(-0.791653\pi\) |
0.923897 | + | 0.382642i | \(0.124986\pi\) | |||||||
\(908\) | −1.15079 | − | 1.99322i | −0.0381903 | − | 0.0661475i | ||||
\(909\) | 2.24985 | − | 3.89685i | 0.0746228 | − | 0.129250i | ||||
\(910\) | −19.1725 | + | 33.2077i | −0.635561 | + | 1.10082i | ||||
\(911\) | −52.2665 | −1.73167 | −0.865833 | − | 0.500333i | \(-0.833211\pi\) | ||||
−0.865833 | + | 0.500333i | \(0.833211\pi\) | |||||||
\(912\) | −16.1759 | − | 3.72509i | −0.535638 | − | 0.123350i | ||||
\(913\) | −33.1440 | −1.09691 | ||||||||
\(914\) | −9.15922 | + | 15.8642i | −0.302960 | + | 0.524742i | ||||
\(915\) | −6.01053 | + | 10.4105i | −0.198702 | + | 0.344162i | ||||
\(916\) | 0.228638 | + | 0.396013i | 0.00755441 | + | 0.0130846i | ||||
\(917\) | 37.9494 | − | 65.7303i | 1.25320 | − | 2.17061i | ||||
\(918\) | 3.94834 | + | 6.83872i | 0.130314 | + | 0.225711i | ||||
\(919\) | 24.2225 | 0.799026 | 0.399513 | − | 0.916728i | \(-0.369179\pi\) | ||||
0.399513 | + | 0.916728i | \(0.369179\pi\) | |||||||
\(920\) | 1.67406 | 0.0551922 | ||||||||
\(921\) | 2.01267 | + | 3.48604i | 0.0663197 | + | 0.114869i | ||||
\(922\) | −16.1441 | − | 27.9623i | −0.531677 | − | 0.920891i | ||||
\(923\) | −19.5909 | −0.644844 | ||||||||
\(924\) | 1.72720 | 0.0568208 | ||||||||
\(925\) | 3.27305 | + | 5.66908i | 0.107617 | + | 0.186398i | ||||
\(926\) | 0.678026 | − | 1.17438i | 0.0222813 | − | 0.0385924i | ||||
\(927\) | 8.03585 | + | 13.9185i | 0.263932 | + | 0.457144i | ||||
\(928\) | 0.921156 | − | 1.59549i | 0.0302384 | − | 0.0523745i | ||||
\(929\) | 21.3993 | − | 37.0647i | 0.702089 | − | 1.21605i | −0.265642 | − | 0.964072i | \(-0.585584\pi\) |
0.967732 | − | 0.251983i | \(-0.0810827\pi\) | |||||||
\(930\) | −1.63482 | −0.0536079 | ||||||||
\(931\) | 35.7490 | − | 38.3786i | 1.17163 | − | 1.25781i | ||||
\(932\) | −1.17375 | −0.0384474 | ||||||||
\(933\) | 7.67889 | − | 13.3002i | 0.251396 | − | 0.435430i | ||||
\(934\) | 13.0196 | − | 22.5506i | 0.426014 | − | 0.737877i | ||||
\(935\) | 12.3367 | + | 21.3678i | 0.403454 | + | 0.698803i | ||||
\(936\) | −9.19248 | + | 15.9218i | −0.300466 | + | 0.520422i | ||||
\(937\) | −5.67783 | − | 9.83429i | −0.185487 | − | 0.321272i | 0.758254 | − | 0.651960i | \(-0.226053\pi\) |
−0.943740 | + | 0.330687i | \(0.892719\pi\) | |||||||
\(938\) | 24.1319 | 0.787935 | ||||||||
\(939\) | −21.9600 | −0.716636 | ||||||||
\(940\) | −0.125325 | − | 0.217070i | −0.00408766 | − | 0.00708004i | ||||
\(941\) | −22.0711 | − | 38.2283i | −0.719498 | − | 1.24621i | −0.961199 | − | 0.275856i | \(-0.911039\pi\) |
0.241701 | − | 0.970351i | \(-0.422295\pi\) | |||||||
\(942\) | −1.90477 | −0.0620609 | ||||||||
\(943\) | 0.441937 | 0.0143915 | ||||||||
\(944\) | 7.29198 | + | 12.6301i | 0.237334 | + | 0.411074i | ||||
\(945\) | −2.18132 | + | 3.77816i | −0.0709584 | + | 0.122904i | ||||
\(946\) | −18.9686 | − | 32.8545i | −0.616721 | − | 1.06819i | ||||
\(947\) | 18.6191 | − | 32.2492i | 0.605038 | − | 1.04796i | −0.387007 | − | 0.922077i | \(-0.626491\pi\) |
0.992045 | − | 0.125880i | \(-0.0401755\pi\) | |||||||
\(948\) | −0.519930 | + | 0.900545i | −0.0168865 | + | 0.0292483i | ||||
\(949\) | −51.4509 | −1.67017 | ||||||||
\(950\) | 4.10415 | − | 4.40604i | 0.133156 | − | 0.142951i | ||||
\(951\) | 24.1279 | 0.782402 | ||||||||
\(952\) | −36.0303 | + | 62.4064i | −1.16775 | + | 2.02260i | ||||
\(953\) | 19.6433 | − | 34.0232i | 0.636310 | − | 1.10212i | −0.349926 | − | 0.936777i | \(-0.613793\pi\) |
0.986236 | − | 0.165344i | \(-0.0528733\pi\) | |||||||
\(954\) | −3.54817 | − | 6.14561i | −0.114876 | − | 0.198972i | ||||
\(955\) | −13.7755 | + | 23.8598i | −0.445764 | + | 0.772085i | ||||
\(956\) | 0.587266 | + | 1.01717i | 0.0189935 | + | 0.0328978i | ||||
\(957\) | −15.3375 | −0.495792 | ||||||||
\(958\) | 27.8478 | 0.899721 | ||||||||
\(959\) | 34.2826 | + | 59.3791i | 1.10704 | + | 1.91745i | ||||
\(960\) | 4.16624 | + | 7.21613i | 0.134465 | + | 0.232900i | ||||
\(961\) | −29.5994 | −0.954821 | ||||||||
\(962\) | 57.5361 | 1.85504 | ||||||||
\(963\) | −6.83945 | − | 11.8463i | −0.220398 | − | 0.381741i | ||||
\(964\) | −0.0501180 | + | 0.0868069i | −0.00161419 | + | 0.00279586i | ||||
\(965\) | −11.1233 | − | 19.2662i | −0.358072 | − | 0.620200i | ||||
\(966\) | 1.74577 | − | 3.02376i | 0.0561692 | − | 0.0972878i | ||||
\(967\) | −10.5429 | + | 18.2608i | −0.339037 | + | 0.587229i | −0.984252 | − | 0.176772i | \(-0.943434\pi\) |
0.645215 | + | 0.764001i | \(0.276768\pi\) | |||||||
\(968\) | −22.0470 | −0.708618 | ||||||||
\(969\) | 24.2817 | + | 5.59175i | 0.780041 | + | 0.179633i | ||||
\(970\) | 2.76281 | 0.0887084 | ||||||||
\(971\) | 12.1226 | − | 20.9969i | 0.389031 | − | 0.673822i | −0.603288 | − | 0.797523i | \(-0.706143\pi\) |
0.992319 | + | 0.123701i | \(0.0394765\pi\) | |||||||
\(972\) | −0.0458624 | + | 0.0794360i | −0.00147104 | + | 0.00254791i | ||||
\(973\) | 14.2952 | + | 24.7600i | 0.458282 | + | 0.793768i | ||||
\(974\) | −1.92815 | + | 3.33966i | −0.0617820 | + | 0.107010i | ||||
\(975\) | −3.18132 | − | 5.51021i | −0.101884 | − | 0.176468i | ||||
\(976\) | 45.7778 | 1.46531 | ||||||||
\(977\) | −51.4540 | −1.64616 | −0.823080 | − | 0.567926i | \(-0.807746\pi\) | ||||
−0.823080 | + | 0.567926i | \(0.807746\pi\) | |||||||
\(978\) | −8.02044 | − | 13.8918i | −0.256465 | − | 0.444211i | ||||
\(979\) | 21.2400 | + | 36.7887i | 0.678832 | + | 1.17577i | ||||
\(980\) | −1.10369 | −0.0352562 | ||||||||
\(981\) | −8.96674 | −0.286286 | ||||||||
\(982\) | −3.99093 | − | 6.91249i | −0.127356 | − | 0.220587i | ||||
\(983\) | −4.56746 | + | 7.91108i | −0.145679 | + | 0.252324i | −0.929626 | − | 0.368504i | \(-0.879870\pi\) |
0.783947 | + | 0.620828i | \(0.213203\pi\) | |||||||
\(984\) | 1.10207 | + | 1.90884i | 0.0351327 | + | 0.0608517i | ||||
\(985\) | −6.33133 | + | 10.9662i | −0.201733 | + | 0.349412i | ||||
\(986\) | 14.0302 | − | 24.3010i | 0.446812 | − | 0.773901i | ||||
\(987\) | −11.9215 | −0.379466 | ||||||||
\(988\) | 0.745111 | + | 2.43234i | 0.0237051 | + | 0.0773830i | ||||
\(989\) | 3.68624 | 0.117216 | ||||||||
\(990\) | 2.98124 | − | 5.16366i | 0.0947500 | − | 0.164112i | ||||
\(991\) | 8.87713 | − | 15.3756i | 0.281991 | − | 0.488424i | −0.689884 | − | 0.723920i | \(-0.742338\pi\) |
0.971875 | + | 0.235497i | \(0.0756717\pi\) | |||||||
\(992\) | −0.306785 | − | 0.531367i | −0.00974042 | − | 0.0168709i | ||||
\(993\) | −12.4208 | + | 21.5135i | −0.394163 | + | 0.682710i | ||||
\(994\) | 9.27807 | + | 16.0701i | 0.294283 | + | 0.509712i | ||||
\(995\) | −8.76955 | −0.278014 | ||||||||
\(996\) | 0.704345 | 0.0223180 | ||||||||
\(997\) | 28.1217 | + | 48.7081i | 0.890622 | + | 1.54260i | 0.839131 | + | 0.543929i | \(0.183064\pi\) |
0.0514903 | + | 0.998673i | \(0.483603\pi\) | |||||||
\(998\) | −8.83810 | − | 15.3080i | −0.279765 | − | 0.484568i | ||||
\(999\) | 6.54609 | 0.207109 |
(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 | 285.2.i.f.106.2 | ✓ | 10 | |
3.2 | odd | 2 | 855.2.k.i.676.4 | 10 | |||
19.7 | even | 3 | inner | 285.2.i.f.121.2 | yes | 10 | |
19.8 | odd | 6 | 5415.2.a.z.1.2 | 5 | |||
19.11 | even | 3 | 5415.2.a.y.1.4 | 5 | |||
57.26 | odd | 6 | 855.2.k.i.406.4 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
285.2.i.f.106.2 | ✓ | 10 | 1.1 | even | 1 | trivial | |
285.2.i.f.121.2 | yes | 10 | 19.7 | even | 3 | inner | |
855.2.k.i.406.4 | 10 | 57.26 | odd | 6 | |||
855.2.k.i.676.4 | 10 | 3.2 | odd | 2 | |||
5415.2.a.y.1.4 | 5 | 19.11 | even | 3 | |||
5415.2.a.z.1.2 | 5 | 19.8 | odd | 6 |