Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(1009,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.1009");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.bb (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1099.13 | ||
Character | \(\chi\) | \(=\) | 1110.1099 |
Dual form | 1110.2.bb.d.1009.13 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0.866025 | + | 0.500000i | 0.500000 | + | 0.288675i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −1.57341 | + | 1.58883i | −0.703649 | + | 0.710548i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 3.59896 | + | 2.07786i | 1.36028 | + | 0.785358i | 0.989661 | − | 0.143427i | \(-0.0458123\pi\) |
0.370619 | + | 0.928785i | \(0.379146\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | −0.568195 | + | 2.16267i | −0.179679 | + | 0.683897i | ||||
\(11\) | 3.62754 | 1.09374 | 0.546872 | − | 0.837216i | \(-0.315818\pi\) | ||||
0.546872 | + | 0.837216i | \(0.315818\pi\) | |||||||
\(12\) | 0.866025 | − | 0.500000i | 0.250000 | − | 0.144338i | ||||
\(13\) | −1.85017 | − | 1.06819i | −0.513144 | − | 0.296264i | 0.220981 | − | 0.975278i | \(-0.429074\pi\) |
−0.734125 | + | 0.679014i | \(0.762407\pi\) | |||||||
\(14\) | 4.15572 | 1.11066 | ||||||||
\(15\) | −2.15703 | + | 0.589266i | −0.556942 | + | 0.152148i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.00089 | + | 0.577862i | −0.242750 | + | 0.140152i | −0.616440 | − | 0.787402i | \(-0.711426\pi\) |
0.373690 | + | 0.927554i | \(0.378092\pi\) | |||||||
\(18\) | 0.866025 | + | 0.500000i | 0.204124 | + | 0.117851i | ||||
\(19\) | −3.73087 | + | 6.46205i | −0.855920 | + | 1.48250i | 0.0198694 | + | 0.999803i | \(0.493675\pi\) |
−0.875789 | + | 0.482694i | \(0.839658\pi\) | |||||||
\(20\) | 0.589266 | + | 2.15703i | 0.131764 | + | 0.482326i | ||||
\(21\) | 2.07786 | + | 3.59896i | 0.453427 | + | 0.785358i | ||||
\(22\) | 3.14154 | − | 1.81377i | 0.669779 | − | 0.386697i | ||||
\(23\) | 0.363708i | 0.0758383i | 0.999281 | + | 0.0379191i | \(0.0120729\pi\) | ||||
−0.999281 | + | 0.0379191i | \(0.987927\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | −0.0487778 | − | 4.99976i | −0.00975556 | − | 0.999952i | ||||
\(26\) | −2.13639 | −0.418980 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 3.59896 | − | 2.07786i | 0.680140 | − | 0.392679i | ||||
\(29\) | −5.15572 | −0.957394 | −0.478697 | − | 0.877980i | \(-0.658891\pi\) | ||||
−0.478697 | + | 0.877980i | \(0.658891\pi\) | |||||||
\(30\) | −1.57341 | + | 1.58883i | −0.287264 | + | 0.290080i | ||||
\(31\) | 3.49115 | 0.627029 | 0.313515 | − | 0.949583i | \(-0.398494\pi\) | ||||
0.313515 | + | 0.949583i | \(0.398494\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 3.14154 | + | 1.81377i | 0.546872 | + | 0.315737i | ||||
\(34\) | −0.577862 | + | 1.00089i | −0.0991025 | + | 0.171651i | ||||
\(35\) | −8.96401 | + | 2.44882i | −1.51519 | + | 0.413927i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 6.08252 | + | 0.0539383i | 0.999961 | + | 0.00886741i | ||||
\(38\) | 7.46174i | 1.21045i | ||||||||
\(39\) | −1.06819 | − | 1.85017i | −0.171048 | − | 0.296264i | ||||
\(40\) | 1.58883 | + | 1.57341i | 0.251216 | + | 0.248778i | ||||
\(41\) | 6.04397 | − | 10.4685i | 0.943910 | − | 1.63490i | 0.185991 | − | 0.982551i | \(-0.440450\pi\) |
0.757919 | − | 0.652349i | \(-0.226216\pi\) | |||||||
\(42\) | 3.59896 | + | 2.07786i | 0.555332 | + | 0.320621i | ||||
\(43\) | 12.3681i | 1.88611i | 0.332634 | + | 0.943056i | \(0.392063\pi\) | ||||
−0.332634 | + | 0.943056i | \(0.607937\pi\) | |||||||
\(44\) | 1.81377 | − | 3.14154i | 0.273436 | − | 0.473605i | ||||
\(45\) | −2.16267 | − | 0.568195i | −0.322392 | − | 0.0847014i | ||||
\(46\) | 0.181854 | + | 0.314980i | 0.0268129 | + | 0.0464413i | ||||
\(47\) | 2.21747i | 0.323451i | 0.986836 | + | 0.161726i | \(0.0517059\pi\) | ||||
−0.986836 | + | 0.161726i | \(0.948294\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 5.13502 | + | 8.89411i | 0.733574 | + | 1.27059i | ||||
\(50\) | −2.54212 | − | 4.30553i | −0.359511 | − | 0.608894i | ||||
\(51\) | −1.15572 | −0.161834 | ||||||||
\(52\) | −1.85017 | + | 1.06819i | −0.256572 | + | 0.148132i | ||||
\(53\) | 9.47411 | − | 5.46988i | 1.30137 | − | 0.751346i | 0.320730 | − | 0.947171i | \(-0.396072\pi\) |
0.980639 | + | 0.195825i | \(0.0627385\pi\) | |||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | −5.70760 | + | 5.76355i | −0.769612 | + | 0.777157i | ||||
\(56\) | 2.07786 | − | 3.59896i | 0.277666 | − | 0.480932i | ||||
\(57\) | −6.46205 | + | 3.73087i | −0.855920 | + | 0.494165i | ||||
\(58\) | −4.46499 | + | 2.57786i | −0.586282 | + | 0.338490i | ||||
\(59\) | −4.88507 | − | 8.46118i | −0.635982 | − | 1.10155i | −0.986306 | − | 0.164924i | \(-0.947262\pi\) |
0.350325 | − | 0.936628i | \(-0.386071\pi\) | |||||||
\(60\) | −0.568195 | + | 2.16267i | −0.0733536 | + | 0.279200i | ||||
\(61\) | −3.12535 | + | 5.41327i | −0.400160 | + | 0.693098i | −0.993745 | − | 0.111674i | \(-0.964379\pi\) |
0.593585 | + | 0.804772i | \(0.297712\pi\) | |||||||
\(62\) | 3.02342 | − | 1.74558i | 0.383975 | − | 0.221688i | ||||
\(63\) | 4.15572i | 0.523572i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 4.60825 | − | 1.25890i | 0.571583 | − | 0.156147i | ||||
\(66\) | 3.62754 | 0.446519 | ||||||||
\(67\) | 13.3985 | + | 7.73561i | 1.63688 | + | 0.945055i | 0.981897 | + | 0.189415i | \(0.0606590\pi\) |
0.654986 | + | 0.755641i | \(0.272674\pi\) | |||||||
\(68\) | 1.15572i | 0.140152i | ||||||||
\(69\) | −0.181854 | + | 0.314980i | −0.0218926 | + | 0.0379191i | ||||
\(70\) | −6.53865 | + | 6.60275i | −0.781518 | + | 0.789179i | ||||
\(71\) | −0.0732348 | + | 0.126846i | −0.00869137 | + | 0.0150539i | −0.870338 | − | 0.492454i | \(-0.836100\pi\) |
0.861647 | + | 0.507508i | \(0.169433\pi\) | |||||||
\(72\) | 0.866025 | − | 0.500000i | 0.102062 | − | 0.0589256i | ||||
\(73\) | − | 9.63375i | − | 1.12754i | −0.825930 | − | 0.563772i | \(-0.809350\pi\) | ||
0.825930 | − | 0.563772i | \(-0.190650\pi\) | |||||||
\(74\) | 5.29459 | − | 2.99455i | 0.615483 | − | 0.348109i | ||||
\(75\) | 2.45764 | − | 4.35431i | 0.283784 | − | 0.502792i | ||||
\(76\) | 3.73087 | + | 6.46205i | 0.427960 | + | 0.741248i | ||||
\(77\) | 13.0554 | + | 7.53753i | 1.48780 | + | 0.858981i | ||||
\(78\) | −1.85017 | − | 1.06819i | −0.209490 | − | 0.120949i | ||||
\(79\) | 7.85583 | − | 13.6067i | 0.883850 | − | 1.53087i | 0.0368247 | − | 0.999322i | \(-0.488276\pi\) |
0.847026 | − | 0.531552i | \(-0.178391\pi\) | |||||||
\(80\) | 2.16267 | + | 0.568195i | 0.241794 | + | 0.0635261i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | − | 12.0879i | − | 1.33489i | ||||||
\(83\) | −11.9781 | + | 6.91556i | −1.31477 | + | 0.759082i | −0.982882 | − | 0.184238i | \(-0.941018\pi\) |
−0.331886 | + | 0.943319i | \(0.607685\pi\) | |||||||
\(84\) | 4.15572 | 0.453427 | ||||||||
\(85\) | 0.656676 | − | 2.49945i | 0.0712265 | − | 0.271104i | ||||
\(86\) | 6.18403 | + | 10.7111i | 0.666841 | + | 1.15500i | ||||
\(87\) | −4.46499 | − | 2.57786i | −0.478697 | − | 0.276376i | ||||
\(88\) | − | 3.62754i | − | 0.386697i | ||||||
\(89\) | −5.67966 | − | 9.83745i | −0.602042 | − | 1.04277i | −0.992511 | − | 0.122152i | \(-0.961021\pi\) |
0.390469 | − | 0.920616i | \(-0.372313\pi\) | |||||||
\(90\) | −2.15703 | + | 0.589266i | −0.227371 | + | 0.0621140i | ||||
\(91\) | −4.43912 | − | 7.68878i | −0.465346 | − | 0.806004i | ||||
\(92\) | 0.314980 | + | 0.181854i | 0.0328389 | + | 0.0189596i | ||||
\(93\) | 3.02342 | + | 1.74558i | 0.313515 | + | 0.181008i | ||||
\(94\) | 1.10873 | + | 1.92038i | 0.114357 | + | 0.198073i | ||||
\(95\) | −4.39694 | − | 16.0952i | −0.451117 | − | 1.65133i | ||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | − | 11.6594i | − | 1.18384i | −0.805998 | − | 0.591919i | \(-0.798371\pi\) | ||
0.805998 | − | 0.591919i | \(-0.201629\pi\) | |||||||
\(98\) | 8.89411 | + | 5.13502i | 0.898441 | + | 0.518715i | ||||
\(99\) | 1.81377 | + | 3.14154i | 0.182291 | + | 0.315737i | ||||
\(100\) | −4.35431 | − | 2.45764i | −0.435431 | − | 0.245764i | ||||
\(101\) | −10.4486 | −1.03968 | −0.519838 | − | 0.854265i | \(-0.674008\pi\) | ||||
−0.519838 | + | 0.854265i | \(0.674008\pi\) | |||||||
\(102\) | −1.00089 | + | 0.577862i | −0.0991025 | + | 0.0572168i | ||||
\(103\) | 9.76260i | 0.961938i | 0.876738 | + | 0.480969i | \(0.159715\pi\) | ||||
−0.876738 | + | 0.480969i | \(0.840285\pi\) | |||||||
\(104\) | −1.06819 | + | 1.85017i | −0.104745 | + | 0.181424i | ||||
\(105\) | −8.98747 | − | 2.36126i | −0.877087 | − | 0.230435i | ||||
\(106\) | 5.46988 | − | 9.47411i | 0.531282 | − | 0.920207i | ||||
\(107\) | −1.06082 | − | 0.612466i | −0.102554 | − | 0.0592093i | 0.447846 | − | 0.894111i | \(-0.352191\pi\) |
−0.550400 | + | 0.834901i | \(0.685525\pi\) | |||||||
\(108\) | 0.866025 | + | 0.500000i | 0.0833333 | + | 0.0481125i | ||||
\(109\) | −4.94812 | − | 8.57040i | −0.473944 | − | 0.820896i | 0.525611 | − | 0.850725i | \(-0.323837\pi\) |
−0.999555 | + | 0.0298295i | \(0.990504\pi\) | |||||||
\(110\) | −2.06115 | + | 7.84518i | −0.196523 | + | 0.748009i | ||||
\(111\) | 5.24065 | + | 3.08797i | 0.497421 | + | 0.293097i | ||||
\(112\) | − | 4.15572i | − | 0.392679i | ||||||
\(113\) | −7.25569 | + | 4.18907i | −0.682558 | + | 0.394075i | −0.800818 | − | 0.598908i | \(-0.795602\pi\) |
0.118260 | + | 0.992983i | \(0.462268\pi\) | |||||||
\(114\) | −3.73087 | + | 6.46205i | −0.349428 | + | 0.605227i | ||||
\(115\) | −0.577871 | − | 0.572260i | −0.0538867 | − | 0.0533636i | ||||
\(116\) | −2.57786 | + | 4.46499i | −0.239348 | + | 0.414564i | ||||
\(117\) | − | 2.13639i | − | 0.197509i | ||||||
\(118\) | −8.46118 | − | 4.88507i | −0.778915 | − | 0.449707i | ||||
\(119\) | −4.80287 | −0.440278 | ||||||||
\(120\) | 0.589266 | + | 2.15703i | 0.0537923 | + | 0.196909i | ||||
\(121\) | 2.15904 | 0.196276 | ||||||||
\(122\) | 6.25070i | 0.565912i | ||||||||
\(123\) | 10.4685 | − | 6.04397i | 0.943910 | − | 0.544967i | ||||
\(124\) | 1.74558 | − | 3.02342i | 0.156757 | − | 0.271512i | ||||
\(125\) | 8.02053 | + | 7.78916i | 0.717378 | + | 0.696684i | ||||
\(126\) | 2.07786 | + | 3.59896i | 0.185111 | + | 0.320621i | ||||
\(127\) | −4.57107 | + | 2.63911i | −0.405617 | + | 0.234183i | −0.688905 | − | 0.724852i | \(-0.741908\pi\) |
0.283288 | + | 0.959035i | \(0.408575\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | −6.18403 | + | 10.7111i | −0.544474 | + | 0.943056i | ||||
\(130\) | 3.36141 | − | 3.39436i | 0.294815 | − | 0.297705i | ||||
\(131\) | −7.60944 | − | 13.1799i | −0.664840 | − | 1.15154i | −0.979329 | − | 0.202275i | \(-0.935167\pi\) |
0.314489 | − | 0.949261i | \(-0.398167\pi\) | |||||||
\(132\) | 3.14154 | − | 1.81377i | 0.273436 | − | 0.157868i | ||||
\(133\) | −26.8545 | + | 15.5045i | −2.32858 | + | 1.34441i | ||||
\(134\) | 15.4712 | 1.33651 | ||||||||
\(135\) | −1.58883 | − | 1.57341i | −0.136745 | − | 0.135417i | ||||
\(136\) | 0.577862 | + | 1.00089i | 0.0495512 | + | 0.0858253i | ||||
\(137\) | − | 6.94371i | − | 0.593241i | −0.954995 | − | 0.296620i | \(-0.904140\pi\) | ||
0.954995 | − | 0.296620i | \(-0.0958596\pi\) | |||||||
\(138\) | 0.363708i | 0.0309609i | ||||||||
\(139\) | −6.89557 | − | 11.9435i | −0.584874 | − | 1.01303i | −0.994891 | − | 0.100954i | \(-0.967811\pi\) |
0.410017 | − | 0.912078i | \(-0.365523\pi\) | |||||||
\(140\) | −2.36126 | + | 8.98747i | −0.199563 | + | 0.759580i | ||||
\(141\) | −1.10873 | + | 1.92038i | −0.0933723 | + | 0.161726i | ||||
\(142\) | 0.146470i | 0.0122915i | ||||||||
\(143\) | −6.71155 | − | 3.87492i | −0.561248 | − | 0.324037i | ||||
\(144\) | 0.500000 | − | 0.866025i | 0.0416667 | − | 0.0721688i | ||||
\(145\) | 8.11205 | − | 8.19158i | 0.673669 | − | 0.680274i | ||||
\(146\) | −4.81687 | − | 8.34307i | −0.398647 | − | 0.690477i | ||||
\(147\) | 10.2700i | 0.847058i | ||||||||
\(148\) | 3.08797 | − | 5.24065i | 0.253830 | − | 0.430779i | ||||
\(149\) | −5.53123 | −0.453136 | −0.226568 | − | 0.973995i | \(-0.572751\pi\) | ||||
−0.226568 | + | 0.973995i | \(0.572751\pi\) | |||||||
\(150\) | −0.0487778 | − | 4.99976i | −0.00398269 | − | 0.408229i | ||||
\(151\) | −11.1149 | + | 19.2515i | −0.904517 | + | 1.56667i | −0.0829517 | + | 0.996554i | \(0.526435\pi\) |
−0.821565 | + | 0.570115i | \(0.806899\pi\) | |||||||
\(152\) | 6.46205 | + | 3.73087i | 0.524142 | + | 0.302613i | ||||
\(153\) | −1.00089 | − | 0.577862i | −0.0809168 | − | 0.0467174i | ||||
\(154\) | 15.0751 | 1.21478 | ||||||||
\(155\) | −5.49300 | + | 5.54685i | −0.441209 | + | 0.445534i | ||||
\(156\) | −2.13639 | −0.171048 | ||||||||
\(157\) | 7.34502 | − | 4.24065i | 0.586197 | − | 0.338441i | −0.177396 | − | 0.984140i | \(-0.556767\pi\) |
0.763592 | + | 0.645699i | \(0.223434\pi\) | |||||||
\(158\) | − | 15.7117i | − | 1.24995i | ||||||
\(159\) | 10.9398 | 0.867579 | ||||||||
\(160\) | 2.15703 | − | 0.589266i | 0.170528 | − | 0.0465855i | ||||
\(161\) | −0.755734 | + | 1.30897i | −0.0595602 | + | 0.103161i | ||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 21.4841 | − | 12.4039i | 1.68277 | − | 0.971546i | 0.722957 | − | 0.690893i | \(-0.242783\pi\) |
0.959810 | − | 0.280652i | \(-0.0905507\pi\) | |||||||
\(164\) | −6.04397 | − | 10.4685i | −0.471955 | − | 0.817450i | ||||
\(165\) | −7.82470 | + | 2.13758i | −0.609152 | + | 0.166411i | ||||
\(166\) | −6.91556 | + | 11.9781i | −0.536752 | + | 0.929681i | ||||
\(167\) | −9.99502 | − | 5.77063i | −0.773438 | − | 0.446545i | 0.0606617 | − | 0.998158i | \(-0.480679\pi\) |
−0.834100 | + | 0.551614i | \(0.814012\pi\) | |||||||
\(168\) | 3.59896 | − | 2.07786i | 0.277666 | − | 0.160311i | ||||
\(169\) | −4.21792 | − | 7.30565i | −0.324455 | − | 0.561973i | ||||
\(170\) | −0.681028 | − | 2.49293i | −0.0522325 | − | 0.191199i | ||||
\(171\) | −7.46174 | −0.570613 | ||||||||
\(172\) | 10.7111 | + | 6.18403i | 0.816711 | + | 0.471528i | ||||
\(173\) | 3.13632 | − | 1.81075i | 0.238450 | − | 0.137669i | −0.376014 | − | 0.926614i | \(-0.622706\pi\) |
0.614464 | + | 0.788945i | \(0.289372\pi\) | |||||||
\(174\) | −5.15572 | −0.390854 | ||||||||
\(175\) | 10.2133 | − | 18.0953i | 0.772050 | − | 1.36788i | ||||
\(176\) | −1.81377 | − | 3.14154i | −0.136718 | − | 0.236803i | ||||
\(177\) | − | 9.77013i | − | 0.734368i | ||||||
\(178\) | −9.83745 | − | 5.67966i | −0.737348 | − | 0.425708i | ||||
\(179\) | 12.5453 | 0.937680 | 0.468840 | − | 0.883283i | \(-0.344672\pi\) | ||||
0.468840 | + | 0.883283i | \(0.344672\pi\) | |||||||
\(180\) | −1.57341 | + | 1.58883i | −0.117275 | + | 0.118425i | ||||
\(181\) | −1.46011 | + | 2.52899i | −0.108529 | + | 0.187979i | −0.915175 | − | 0.403057i | \(-0.867948\pi\) |
0.806645 | + | 0.591036i | \(0.201281\pi\) | |||||||
\(182\) | −7.68878 | − | 4.43912i | −0.569931 | − | 0.329050i | ||||
\(183\) | −5.41327 | + | 3.12535i | −0.400160 | + | 0.231033i | ||||
\(184\) | 0.363708 | 0.0268129 | ||||||||
\(185\) | −9.65599 | + | 9.57924i | −0.709922 | + | 0.704280i | ||||
\(186\) | 3.49115 | 0.255984 | ||||||||
\(187\) | −3.63075 | + | 2.09622i | −0.265507 | + | 0.153291i | ||||
\(188\) | 1.92038 | + | 1.10873i | 0.140058 | + | 0.0808628i | ||||
\(189\) | −2.07786 | + | 3.59896i | −0.151142 | + | 0.261786i | ||||
\(190\) | −11.8554 | − | 11.7404i | −0.860085 | − | 0.851735i | ||||
\(191\) | 20.4211 | 1.47762 | 0.738808 | − | 0.673916i | \(-0.235389\pi\) | ||||
0.738808 | + | 0.673916i | \(0.235389\pi\) | |||||||
\(192\) | −0.866025 | − | 0.500000i | −0.0625000 | − | 0.0360844i | ||||
\(193\) | − | 4.78676i | − | 0.344558i | −0.985048 | − | 0.172279i | \(-0.944887\pi\) | ||
0.985048 | − | 0.172279i | \(-0.0551131\pi\) | |||||||
\(194\) | −5.82972 | − | 10.0974i | −0.418550 | − | 0.724949i | ||||
\(195\) | 4.62031 | + | 1.21388i | 0.330867 | + | 0.0869281i | ||||
\(196\) | 10.2700 | 0.733574 | ||||||||
\(197\) | 3.56459 | − | 2.05802i | 0.253967 | − | 0.146628i | −0.367613 | − | 0.929979i | \(-0.619825\pi\) |
0.621579 | + | 0.783351i | \(0.286491\pi\) | |||||||
\(198\) | 3.14154 | + | 1.81377i | 0.223260 | + | 0.128899i | ||||
\(199\) | −6.59431 | −0.467458 | −0.233729 | − | 0.972302i | \(-0.575093\pi\) | ||||
−0.233729 | + | 0.972302i | \(0.575093\pi\) | |||||||
\(200\) | −4.99976 | + | 0.0487778i | −0.353537 | + | 0.00344911i | ||||
\(201\) | 7.73561 | + | 13.3985i | 0.545628 | + | 0.945055i | ||||
\(202\) | −9.04876 | + | 5.22430i | −0.636668 | + | 0.367581i | ||||
\(203\) | −18.5553 | − | 10.7129i | −1.30232 | − | 0.751897i | ||||
\(204\) | −0.577862 | + | 1.00089i | −0.0404584 | + | 0.0700760i | ||||
\(205\) | 7.12301 | + | 26.0740i | 0.497493 | + | 1.82109i | ||||
\(206\) | 4.88130 | + | 8.45466i | 0.340096 | + | 0.589064i | ||||
\(207\) | −0.314980 | + | 0.181854i | −0.0218926 | + | 0.0126397i | ||||
\(208\) | 2.13639i | 0.148132i | ||||||||
\(209\) | −13.5339 | + | 23.4413i | −0.936157 | + | 1.62147i | ||||
\(210\) | −8.96401 | + | 2.44882i | −0.618575 | + | 0.168985i | ||||
\(211\) | −3.49904 | −0.240884 | −0.120442 | − | 0.992720i | \(-0.538431\pi\) | ||||
−0.120442 | + | 0.992720i | \(0.538431\pi\) | |||||||
\(212\) | − | 10.9398i | − | 0.751346i | ||||||
\(213\) | −0.126846 | + | 0.0732348i | −0.00869137 | + | 0.00501797i | ||||
\(214\) | −1.22493 | −0.0837346 | ||||||||
\(215\) | −19.6508 | − | 19.4600i | −1.34017 | − | 1.32716i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 12.5645 | + | 7.25413i | 0.852935 | + | 0.492442i | ||||
\(218\) | −8.57040 | − | 4.94812i | −0.580461 | − | 0.335129i | ||||
\(219\) | 4.81687 | − | 8.34307i | 0.325494 | − | 0.563772i | ||||
\(220\) | 2.13758 | + | 7.82470i | 0.144116 | + | 0.527541i | ||||
\(221\) | 2.46908 | 0.166088 | ||||||||
\(222\) | 6.08252 | + | 0.0539383i | 0.408232 | + | 0.00362010i | ||||
\(223\) | 11.9286i | 0.798799i | 0.916777 | + | 0.399400i | \(0.130781\pi\) | ||||
−0.916777 | + | 0.399400i | \(0.869219\pi\) | |||||||
\(224\) | −2.07786 | − | 3.59896i | −0.138833 | − | 0.240466i | ||||
\(225\) | 4.30553 | − | 2.54212i | 0.287035 | − | 0.169475i | ||||
\(226\) | −4.18907 | + | 7.25569i | −0.278653 | + | 0.482641i | ||||
\(227\) | 6.93104 | + | 4.00164i | 0.460030 | + | 0.265598i | 0.712057 | − | 0.702122i | \(-0.247764\pi\) |
−0.252027 | + | 0.967720i | \(0.581097\pi\) | |||||||
\(228\) | 7.46174i | 0.494165i | ||||||||
\(229\) | −1.64726 | + | 2.85314i | −0.108854 | + | 0.188541i | −0.915306 | − | 0.402759i | \(-0.868051\pi\) |
0.806452 | + | 0.591299i | \(0.201385\pi\) | |||||||
\(230\) | −0.786581 | − | 0.206657i | −0.0518656 | − | 0.0136265i | ||||
\(231\) | 7.53753 | + | 13.0554i | 0.495933 | + | 0.858981i | ||||
\(232\) | 5.15572i | 0.338490i | ||||||||
\(233\) | − | 9.21492i | − | 0.603690i | −0.953357 | − | 0.301845i | \(-0.902398\pi\) | ||
0.953357 | − | 0.301845i | \(-0.0976024\pi\) | |||||||
\(234\) | −1.06819 | − | 1.85017i | −0.0698301 | − | 0.120949i | ||||
\(235\) | −3.52319 | − | 3.48898i | −0.229827 | − | 0.227596i | ||||
\(236\) | −9.77013 | −0.635982 | ||||||||
\(237\) | 13.6067 | − | 7.85583i | 0.883850 | − | 0.510291i | ||||
\(238\) | −4.15940 | + | 2.40143i | −0.269614 | + | 0.155662i | ||||
\(239\) | 9.36223 | + | 16.2159i | 0.605592 | + | 1.04892i | 0.991958 | + | 0.126570i | \(0.0403970\pi\) |
−0.386366 | + | 0.922346i | \(0.626270\pi\) | |||||||
\(240\) | 1.58883 | + | 1.57341i | 0.102559 | + | 0.101563i | ||||
\(241\) | 8.14642 | − | 14.1100i | 0.524757 | − | 0.908906i | −0.474827 | − | 0.880079i | \(-0.657489\pi\) |
0.999584 | − | 0.0288271i | \(-0.00917722\pi\) | |||||||
\(242\) | 1.86978 | − | 1.07952i | 0.120194 | − | 0.0693942i | ||||
\(243\) | −0.866025 | + | 0.500000i | −0.0555556 | + | 0.0320750i | ||||
\(244\) | 3.12535 | + | 5.41327i | 0.200080 | + | 0.346549i | ||||
\(245\) | −22.2107 | − | 5.83538i | −1.41899 | − | 0.372809i | ||||
\(246\) | 6.04397 | − | 10.4685i | 0.385350 | − | 0.667445i | ||||
\(247\) | 13.8055 | − | 7.97059i | 0.878420 | − | 0.507156i | ||||
\(248\) | − | 3.49115i | − | 0.221688i | ||||||
\(249\) | −13.8311 | −0.876512 | ||||||||
\(250\) | 10.8406 | + | 2.73535i | 0.685618 | + | 0.172999i | ||||
\(251\) | 16.7386 | 1.05653 | 0.528264 | − | 0.849080i | \(-0.322843\pi\) | ||||
0.528264 | + | 0.849080i | \(0.322843\pi\) | |||||||
\(252\) | 3.59896 | + | 2.07786i | 0.226713 | + | 0.130893i | ||||
\(253\) | 1.31936i | 0.0829477i | ||||||||
\(254\) | −2.63911 | + | 4.57107i | −0.165592 | + | 0.286814i | ||||
\(255\) | 1.81842 | − | 1.83625i | 0.113874 | − | 0.114991i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −6.15672 | + | 3.55458i | −0.384046 | + | 0.221729i | −0.679577 | − | 0.733604i | \(-0.737837\pi\) |
0.295531 | + | 0.955333i | \(0.404503\pi\) | |||||||
\(258\) | 12.3681i | 0.770002i | ||||||||
\(259\) | 21.7787 | + | 12.8328i | 1.35326 | + | 0.797389i | ||||
\(260\) | 1.21388 | − | 4.62031i | 0.0752819 | − | 0.286540i | ||||
\(261\) | −2.57786 | − | 4.46499i | −0.159566 | − | 0.276376i | ||||
\(262\) | −13.1799 | − | 7.60944i | −0.814259 | − | 0.470113i | ||||
\(263\) | −6.83430 | − | 3.94578i | −0.421421 | − | 0.243307i | 0.274264 | − | 0.961654i | \(-0.411566\pi\) |
−0.695685 | + | 0.718347i | \(0.744899\pi\) | |||||||
\(264\) | 1.81377 | − | 3.14154i | 0.111630 | − | 0.193348i | ||||
\(265\) | −6.21591 | + | 23.6591i | −0.381840 | + | 1.45337i | ||||
\(266\) | −15.5045 | + | 26.8545i | −0.950639 | + | 1.64656i | ||||
\(267\) | − | 11.3593i | − | 0.695179i | ||||||
\(268\) | 13.3985 | − | 7.73561i | 0.818442 | − | 0.472528i | ||||
\(269\) | −0.806147 | −0.0491516 | −0.0245758 | − | 0.999698i | \(-0.507824\pi\) | ||||
−0.0245758 | + | 0.999698i | \(0.507824\pi\) | |||||||
\(270\) | −2.16267 | − | 0.568195i | −0.131616 | − | 0.0345792i | ||||
\(271\) | −4.63125 | − | 8.02156i | −0.281329 | − | 0.487275i | 0.690384 | − | 0.723443i | \(-0.257442\pi\) |
−0.971712 | + | 0.236168i | \(0.924108\pi\) | |||||||
\(272\) | 1.00089 | + | 0.577862i | 0.0606876 | + | 0.0350380i | ||||
\(273\) | − | 8.87824i | − | 0.537336i | ||||||
\(274\) | −3.47185 | − | 6.01343i | −0.209742 | − | 0.363284i | ||||
\(275\) | −0.176943 | − | 18.1368i | −0.0106701 | − | 1.09369i | ||||
\(276\) | 0.181854 | + | 0.314980i | 0.0109463 | + | 0.0189596i | ||||
\(277\) | 5.54699 | + | 3.20256i | 0.333287 | + | 0.192423i | 0.657299 | − | 0.753630i | \(-0.271699\pi\) |
−0.324013 | + | 0.946053i | \(0.605032\pi\) | |||||||
\(278\) | −11.9435 | − | 6.89557i | −0.716322 | − | 0.413569i | ||||
\(279\) | 1.74558 | + | 3.02342i | 0.104505 | + | 0.181008i | ||||
\(280\) | 2.44882 | + | 8.96401i | 0.146345 | + | 0.535702i | ||||
\(281\) | −4.39344 | − | 7.60967i | −0.262091 | − | 0.453955i | 0.704706 | − | 0.709499i | \(-0.251079\pi\) |
−0.966797 | + | 0.255544i | \(0.917745\pi\) | |||||||
\(282\) | 2.21747i | 0.132048i | ||||||||
\(283\) | 8.33863 | + | 4.81431i | 0.495680 | + | 0.286181i | 0.726928 | − | 0.686714i | \(-0.240947\pi\) |
−0.231248 | + | 0.972895i | \(0.574281\pi\) | |||||||
\(284\) | 0.0732348 | + | 0.126846i | 0.00434569 | + | 0.00752695i | ||||
\(285\) | 4.23972 | − | 16.1373i | 0.251139 | − | 0.955891i | ||||
\(286\) | −7.74984 | −0.458257 | ||||||||
\(287\) | 43.5041 | − | 25.1171i | 2.56796 | − | 1.48261i | ||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | −7.83215 | + | 13.5657i | −0.460715 | + | 0.797981i | ||||
\(290\) | 2.92945 | − | 11.1501i | 0.172023 | − | 0.654759i | ||||
\(291\) | 5.82972 | − | 10.0974i | 0.341744 | − | 0.591919i | ||||
\(292\) | −8.34307 | − | 4.81687i | −0.488241 | − | 0.281886i | ||||
\(293\) | −15.0103 | − | 8.66622i | −0.876913 | − | 0.506286i | −0.00727385 | − | 0.999974i | \(-0.502315\pi\) |
−0.869639 | + | 0.493687i | \(0.835649\pi\) | |||||||
\(294\) | 5.13502 | + | 8.89411i | 0.299480 | + | 0.518715i | ||||
\(295\) | 21.1296 | + | 5.55134i | 1.23021 | + | 0.323211i | ||||
\(296\) | 0.0539383 | − | 6.08252i | 0.00313510 | − | 0.353539i | ||||
\(297\) | 3.62754i | 0.210491i | ||||||||
\(298\) | −4.79019 | + | 2.76562i | −0.277488 | + | 0.160208i | ||||
\(299\) | 0.388511 | − | 0.672920i | 0.0224681 | − | 0.0389160i | ||||
\(300\) | −2.54212 | − | 4.30553i | −0.146770 | − | 0.248580i | ||||
\(301\) | −25.6991 | + | 44.5122i | −1.48127 | + | 2.56564i | ||||
\(302\) | 22.2298i | 1.27918i | ||||||||
\(303\) | −9.04876 | − | 5.22430i | −0.519838 | − | 0.300128i | ||||
\(304\) | 7.46174 | 0.427960 | ||||||||
\(305\) | −3.68332 | − | 13.4829i | −0.210907 | − | 0.772031i | ||||
\(306\) | −1.15572 | −0.0660683 | ||||||||
\(307\) | − | 28.2983i | − | 1.61507i | −0.589820 | − | 0.807535i | \(-0.700801\pi\) | ||
0.589820 | − | 0.807535i | \(-0.299199\pi\) | |||||||
\(308\) | 13.0554 | − | 7.53753i | 0.743899 | − | 0.429490i | ||||
\(309\) | −4.88130 | + | 8.45466i | −0.277687 | + | 0.480969i | ||||
\(310\) | −1.98365 | + | 7.55022i | −0.112664 | + | 0.428823i | ||||
\(311\) | −1.26886 | − | 2.19774i | −0.0719506 | − | 0.124622i | 0.827806 | − | 0.561015i | \(-0.189589\pi\) |
−0.899756 | + | 0.436393i | \(0.856256\pi\) | |||||||
\(312\) | −1.85017 | + | 1.06819i | −0.104745 | + | 0.0604746i | ||||
\(313\) | −9.42952 | + | 5.44413i | −0.532988 | + | 0.307721i | −0.742232 | − | 0.670143i | \(-0.766233\pi\) |
0.209245 | + | 0.977863i | \(0.432900\pi\) | |||||||
\(314\) | 4.24065 | − | 7.34502i | 0.239314 | − | 0.414504i | ||||
\(315\) | −6.60275 | − | 6.53865i | −0.372023 | − | 0.368411i | ||||
\(316\) | −7.85583 | − | 13.6067i | −0.441925 | − | 0.765437i | ||||
\(317\) | −0.878780 | + | 0.507364i | −0.0493572 | + | 0.0284964i | −0.524476 | − | 0.851426i | \(-0.675739\pi\) |
0.475118 | + | 0.879922i | \(0.342405\pi\) | |||||||
\(318\) | 9.47411 | − | 5.46988i | 0.531282 | − | 0.306736i | ||||
\(319\) | −18.7026 | −1.04714 | ||||||||
\(320\) | 1.57341 | − | 1.58883i | 0.0879562 | − | 0.0888184i | ||||
\(321\) | −0.612466 | − | 1.06082i | −0.0341845 | − | 0.0592093i | ||||
\(322\) | 1.51147i | 0.0842308i | ||||||||
\(323\) | − | 8.62370i | − | 0.479836i | ||||||
\(324\) | 0.500000 | + | 0.866025i | 0.0277778 | + | 0.0481125i | ||||
\(325\) | −5.25047 | + | 9.30250i | −0.291244 | + | 0.516010i | ||||
\(326\) | 12.4039 | − | 21.4841i | 0.686986 | − | 1.18990i | ||||
\(327\) | − | 9.89625i | − | 0.547264i | ||||||
\(328\) | −10.4685 | − | 6.04397i | −0.578025 | − | 0.333723i | ||||
\(329\) | −4.60760 | + | 7.98059i | −0.254025 | + | 0.439984i | ||||
\(330\) | −5.70760 | + | 5.76355i | −0.314193 | + | 0.317273i | ||||
\(331\) | −4.88646 | − | 8.46359i | −0.268584 | − | 0.465201i | 0.699912 | − | 0.714229i | \(-0.253222\pi\) |
−0.968496 | + | 0.249028i | \(0.919889\pi\) | |||||||
\(332\) | 13.8311i | 0.759082i | ||||||||
\(333\) | 2.99455 | + | 5.29459i | 0.164100 | + | 0.290142i | ||||
\(334\) | −11.5413 | −0.631509 | ||||||||
\(335\) | −33.3718 | + | 9.11666i | −1.82330 | + | 0.498096i | ||||
\(336\) | 2.07786 | − | 3.59896i | 0.113357 | − | 0.196339i | ||||
\(337\) | −8.78297 | − | 5.07085i | −0.478439 | − | 0.276227i | 0.241327 | − | 0.970444i | \(-0.422417\pi\) |
−0.719766 | + | 0.694217i | \(0.755751\pi\) | |||||||
\(338\) | −7.30565 | − | 4.21792i | −0.397375 | − | 0.229425i | ||||
\(339\) | −8.37815 | −0.455038 | ||||||||
\(340\) | −1.83625 | − | 1.81842i | −0.0995847 | − | 0.0986179i | ||||
\(341\) | 12.6643 | 0.685809 | ||||||||
\(342\) | −6.46205 | + | 3.73087i | −0.349428 | + | 0.201742i | ||||
\(343\) | 13.5894i | 0.733757i | ||||||||
\(344\) | 12.3681 | 0.666841 | ||||||||
\(345\) | −0.214320 | − | 0.784527i | −0.0115386 | − | 0.0422375i | ||||
\(346\) | 1.81075 | − | 3.13632i | 0.0973468 | − | 0.168610i | ||||
\(347\) | − | 16.3722i | − | 0.878906i | −0.898266 | − | 0.439453i | \(-0.855172\pi\) | ||
0.898266 | − | 0.439453i | \(-0.144828\pi\) | |||||||
\(348\) | −4.46499 | + | 2.57786i | −0.239348 | + | 0.138188i | ||||
\(349\) | 7.28289 | + | 12.6143i | 0.389844 | + | 0.675230i | 0.992428 | − | 0.122826i | \(-0.0391956\pi\) |
−0.602584 | + | 0.798055i | \(0.705862\pi\) | |||||||
\(350\) | −0.202707 | − | 20.7776i | −0.0108351 | − | 1.11061i | ||||
\(351\) | 1.06819 | − | 1.85017i | 0.0570160 | − | 0.0987546i | ||||
\(352\) | −3.14154 | − | 1.81377i | −0.167445 | − | 0.0966742i | ||||
\(353\) | −20.7462 | + | 11.9778i | −1.10421 | + | 0.637516i | −0.937324 | − | 0.348460i | \(-0.886705\pi\) |
−0.166887 | + | 0.985976i | \(0.553371\pi\) | |||||||
\(354\) | −4.88507 | − | 8.46118i | −0.259638 | − | 0.449707i | ||||
\(355\) | −0.0863095 | − | 0.315939i | −0.00458083 | − | 0.0167683i | ||||
\(356\) | −11.3593 | −0.602042 | ||||||||
\(357\) | −4.15940 | − | 2.40143i | −0.220139 | − | 0.127097i | ||||
\(358\) | 10.8646 | − | 6.27265i | 0.574210 | − | 0.331520i | ||||
\(359\) | −31.6699 | −1.67147 | −0.835736 | − | 0.549132i | \(-0.814958\pi\) | ||||
−0.835736 | + | 0.549132i | \(0.814958\pi\) | |||||||
\(360\) | −0.568195 | + | 2.16267i | −0.0299465 | + | 0.113983i | ||||
\(361\) | −18.3387 | − | 31.7636i | −0.965197 | − | 1.67177i | ||||
\(362\) | 2.92023i | 0.153484i | ||||||||
\(363\) | 1.86978 | + | 1.07952i | 0.0981382 | + | 0.0566601i | ||||
\(364\) | −8.87824 | −0.465346 | ||||||||
\(365\) | 15.3064 | + | 15.1578i | 0.801174 | + | 0.793396i | ||||
\(366\) | −3.12535 | + | 5.41327i | −0.163365 | + | 0.282956i | ||||
\(367\) | 18.6346 | + | 10.7587i | 0.972720 | + | 0.561600i | 0.900064 | − | 0.435757i | \(-0.143519\pi\) |
0.0726556 | + | 0.997357i | \(0.476853\pi\) | |||||||
\(368\) | 0.314980 | − | 0.181854i | 0.0164195 | − | 0.00947979i | ||||
\(369\) | 12.0879 | 0.629273 | ||||||||
\(370\) | −3.57271 | + | 13.1239i | −0.185736 | + | 0.682277i | ||||
\(371\) | 45.4626 | 2.36030 | ||||||||
\(372\) | 3.02342 | − | 1.74558i | 0.156757 | − | 0.0905039i | ||||
\(373\) | 8.45399 | + | 4.88092i | 0.437731 | + | 0.252724i | 0.702635 | − | 0.711551i | \(-0.252007\pi\) |
−0.264904 | + | 0.964275i | \(0.585340\pi\) | |||||||
\(374\) | −2.09622 | + | 3.63075i | −0.108393 | + | 0.187742i | ||||
\(375\) | 3.05140 | + | 10.7559i | 0.157574 | + | 0.555431i | ||||
\(376\) | 2.21747 | 0.114357 | ||||||||
\(377\) | 9.53895 | + | 5.50732i | 0.491281 | + | 0.283641i | ||||
\(378\) | 4.15572i | 0.213747i | ||||||||
\(379\) | 11.7727 | + | 20.3909i | 0.604722 | + | 1.04741i | 0.992095 | + | 0.125486i | \(0.0400489\pi\) |
−0.387374 | + | 0.921923i | \(0.626618\pi\) | |||||||
\(380\) | −16.1373 | − | 4.23972i | −0.827826 | − | 0.217493i | ||||
\(381\) | −5.27821 | −0.270411 | ||||||||
\(382\) | 17.6852 | − | 10.2105i | 0.904851 | − | 0.522416i | ||||
\(383\) | 5.85258 | + | 3.37899i | 0.299053 | + | 0.172658i | 0.642017 | − | 0.766690i | \(-0.278098\pi\) |
−0.342965 | + | 0.939348i | \(0.611431\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −32.5173 | + | 8.88321i | −1.65723 | + | 0.452730i | ||||
\(386\) | −2.39338 | − | 4.14545i | −0.121820 | − | 0.210998i | ||||
\(387\) | −10.7111 | + | 6.18403i | −0.544474 | + | 0.314352i | ||||
\(388\) | −10.0974 | − | 5.82972i | −0.512617 | − | 0.295959i | ||||
\(389\) | 2.80650 | − | 4.86100i | 0.142295 | − | 0.246462i | −0.786065 | − | 0.618143i | \(-0.787885\pi\) |
0.928361 | + | 0.371681i | \(0.121218\pi\) | |||||||
\(390\) | 4.60825 | − | 1.25890i | 0.233348 | − | 0.0637469i | ||||
\(391\) | −0.210173 | − | 0.364030i | −0.0106289 | − | 0.0184098i | ||||
\(392\) | 8.89411 | − | 5.13502i | 0.449221 | − | 0.259358i | ||||
\(393\) | − | 15.2189i | − | 0.767691i | ||||||
\(394\) | 2.05802 | − | 3.56459i | 0.103681 | − | 0.179581i | ||||
\(395\) | 9.25835 | + | 33.8905i | 0.465838 | + | 1.70522i | ||||
\(396\) | 3.62754 | 0.182291 | ||||||||
\(397\) | 24.5689i | 1.23308i | 0.787324 | + | 0.616540i | \(0.211466\pi\) | ||||
−0.787324 | + | 0.616540i | \(0.788534\pi\) | |||||||
\(398\) | −5.71084 | + | 3.29715i | −0.286258 | + | 0.165271i | ||||
\(399\) | −31.0089 | −1.55239 | ||||||||
\(400\) | −4.30553 | + | 2.54212i | −0.215277 | + | 0.127106i | ||||
\(401\) | 33.1745 | 1.65665 | 0.828327 | − | 0.560245i | \(-0.189293\pi\) | ||||
0.828327 | + | 0.560245i | \(0.189293\pi\) | |||||||
\(402\) | 13.3985 | + | 7.73561i | 0.668255 | + | 0.385817i | ||||
\(403\) | −6.45921 | − | 3.72923i | −0.321756 | − | 0.185766i | ||||
\(404\) | −5.22430 | + | 9.04876i | −0.259919 | + | 0.450193i | ||||
\(405\) | −0.589266 | − | 2.15703i | −0.0292808 | − | 0.107184i | ||||
\(406\) | −21.4258 | −1.06334 | ||||||||
\(407\) | 22.0646 | + | 0.195663i | 1.09370 | + | 0.00969867i | ||||
\(408\) | 1.15572i | 0.0572168i | ||||||||
\(409\) | −13.1498 | − | 22.7761i | −0.650215 | − | 1.12621i | −0.983070 | − | 0.183228i | \(-0.941345\pi\) |
0.332855 | − | 0.942978i | \(-0.391988\pi\) | |||||||
\(410\) | 19.2057 | + | 19.0193i | 0.948503 | + | 0.939295i | ||||
\(411\) | 3.47185 | − | 6.01343i | 0.171254 | − | 0.296620i | ||||
\(412\) | 8.45466 | + | 4.88130i | 0.416531 | + | 0.240484i | ||||
\(413\) | − | 40.6020i | − | 1.99789i | ||||||
\(414\) | −0.181854 | + | 0.314980i | −0.00893763 | + | 0.0154804i | ||||
\(415\) | 7.85877 | − | 29.9122i | 0.385772 | − | 1.46833i | ||||
\(416\) | 1.06819 | + | 1.85017i | 0.0523725 | + | 0.0907119i | ||||
\(417\) | − | 13.7911i | − | 0.675355i | ||||||
\(418\) | 27.0677i | 1.32393i | ||||||||
\(419\) | −16.1912 | − | 28.0440i | −0.790991 | − | 1.37004i | −0.925354 | − | 0.379105i | \(-0.876232\pi\) |
0.134363 | − | 0.990932i | \(-0.457101\pi\) | |||||||
\(420\) | −6.53865 | + | 6.60275i | −0.319053 | + | 0.322181i | ||||
\(421\) | 7.22310 | 0.352032 | 0.176016 | − | 0.984387i | \(-0.443679\pi\) | ||||
0.176016 | + | 0.984387i | \(0.443679\pi\) | |||||||
\(422\) | −3.03026 | + | 1.74952i | −0.147511 | + | 0.0851652i | ||||
\(423\) | −1.92038 | + | 1.10873i | −0.0933723 | + | 0.0539085i | ||||
\(424\) | −5.46988 | − | 9.47411i | −0.265641 | − | 0.460103i | ||||
\(425\) | 2.93799 | + | 4.97600i | 0.142514 | + | 0.241372i | ||||
\(426\) | −0.0732348 | + | 0.126846i | −0.00354824 | + | 0.00614573i | ||||
\(427\) | −22.4960 | + | 12.9881i | −1.08866 | + | 0.628538i | ||||
\(428\) | −1.06082 | + | 0.612466i | −0.0512768 | + | 0.0296046i | ||||
\(429\) | −3.87492 | − | 6.71155i | −0.187083 | − | 0.324037i | ||||
\(430\) | −26.7481 | − | 7.02747i | −1.28991 | − | 0.338895i | ||||
\(431\) | −2.04698 | + | 3.54547i | −0.0985995 | + | 0.170779i | −0.911105 | − | 0.412174i | \(-0.864770\pi\) |
0.812506 | + | 0.582953i | \(0.198103\pi\) | |||||||
\(432\) | 0.866025 | − | 0.500000i | 0.0416667 | − | 0.0240563i | ||||
\(433\) | − | 1.11862i | − | 0.0537574i | −0.999639 | − | 0.0268787i | \(-0.991443\pi\) | ||
0.999639 | − | 0.0268787i | \(-0.00855678\pi\) | |||||||
\(434\) | 14.5083 | 0.696419 | ||||||||
\(435\) | 11.1210 | − | 3.03809i | 0.533213 | − | 0.145665i | ||||
\(436\) | −9.89625 | −0.473944 | ||||||||
\(437\) | −2.35030 | − | 1.35695i | −0.112430 | − | 0.0649115i | ||||
\(438\) | − | 9.63375i | − | 0.460318i | ||||||
\(439\) | −2.98041 | + | 5.16221i | −0.142247 | + | 0.246379i | −0.928342 | − | 0.371726i | \(-0.878766\pi\) |
0.786095 | + | 0.618105i | \(0.212099\pi\) | |||||||
\(440\) | 5.76355 | + | 5.70760i | 0.274767 | + | 0.272099i | ||||
\(441\) | −5.13502 | + | 8.89411i | −0.244525 | + | 0.423529i | ||||
\(442\) | 2.13828 | − | 1.23454i | 0.101708 | − | 0.0587210i | ||||
\(443\) | 10.0305i | 0.476563i | 0.971196 | + | 0.238282i | \(0.0765841\pi\) | ||||
−0.971196 | + | 0.238282i | \(0.923416\pi\) | |||||||
\(444\) | 5.29459 | − | 2.99455i | 0.251270 | − | 0.142115i | ||||
\(445\) | 24.5665 | + | 6.45430i | 1.16456 | + | 0.305963i | ||||
\(446\) | 5.96431 | + | 10.3305i | 0.282418 | + | 0.489163i | ||||
\(447\) | −4.79019 | − | 2.76562i | −0.226568 | − | 0.130809i | ||||
\(448\) | −3.59896 | − | 2.07786i | −0.170035 | − | 0.0981697i | ||||
\(449\) | 7.09889 | − | 12.2956i | 0.335017 | − | 0.580267i | −0.648471 | − | 0.761239i | \(-0.724591\pi\) |
0.983488 | + | 0.180972i | \(0.0579245\pi\) | |||||||
\(450\) | 2.45764 | − | 4.35431i | 0.115854 | − | 0.205264i | ||||
\(451\) | 21.9248 | − | 37.9748i | 1.03240 | − | 1.78816i | ||||
\(452\) | 8.37815i | 0.394075i | ||||||||
\(453\) | −19.2515 | + | 11.1149i | −0.904517 | + | 0.522223i | ||||
\(454\) | 8.00328 | 0.375613 | ||||||||
\(455\) | 19.2007 | + | 5.04457i | 0.900144 | + | 0.236493i | ||||
\(456\) | 3.73087 | + | 6.46205i | 0.174714 | + | 0.302613i | ||||
\(457\) | −9.49114 | − | 5.47971i | −0.443977 | − | 0.256330i | 0.261306 | − | 0.965256i | \(-0.415847\pi\) |
−0.705283 | + | 0.708926i | \(0.749180\pi\) | |||||||
\(458\) | 3.29452i | 0.153943i | ||||||||
\(459\) | −0.577862 | − | 1.00089i | −0.0269723 | − | 0.0467174i | ||||
\(460\) | −0.784527 | + | 0.214320i | −0.0365788 | + | 0.00999274i | ||||
\(461\) | 13.1296 | + | 22.7411i | 0.611506 | + | 1.05916i | 0.990987 | + | 0.133959i | \(0.0427692\pi\) |
−0.379481 | + | 0.925199i | \(0.623897\pi\) | |||||||
\(462\) | 13.0554 | + | 7.53753i | 0.607391 | + | 0.350677i | ||||
\(463\) | −21.8170 | − | 12.5961i | −1.01392 | − | 0.585388i | −0.101584 | − | 0.994827i | \(-0.532391\pi\) |
−0.912338 | + | 0.409439i | \(0.865725\pi\) | |||||||
\(464\) | 2.57786 | + | 4.46499i | 0.119674 | + | 0.207282i | ||||
\(465\) | −7.53051 | + | 2.05721i | −0.349219 | + | 0.0954011i | ||||
\(466\) | −4.60746 | − | 7.98036i | −0.213437 | − | 0.369683i | ||||
\(467\) | 22.8651i | 1.05807i | 0.848600 | + | 0.529035i | \(0.177446\pi\) | ||||
−0.848600 | + | 0.529035i | \(0.822554\pi\) | |||||||
\(468\) | −1.85017 | − | 1.06819i | −0.0855240 | − | 0.0493773i | ||||
\(469\) | 32.1471 | + | 55.6803i | 1.48441 | + | 2.57108i | ||||
\(470\) | −4.79566 | − | 1.25995i | −0.221207 | − | 0.0581174i | ||||
\(471\) | 8.48130 | 0.390798 | ||||||||
\(472\) | −8.46118 | + | 4.88507i | −0.389458 | + | 0.224853i | ||||
\(473\) | 44.8656i | 2.06292i | ||||||||
\(474\) | 7.85583 | − | 13.6067i | 0.360830 | − | 0.624977i | ||||
\(475\) | 32.4907 | + | 18.3382i | 1.49078 | + | 0.841416i | ||||
\(476\) | −2.40143 | + | 4.15940i | −0.110070 | + | 0.190646i | ||||
\(477\) | 9.47411 | + | 5.46988i | 0.433790 | + | 0.250449i | ||||
\(478\) | 16.2159 | + | 9.36223i | 0.741696 | + | 0.428218i | ||||
\(479\) | 12.4085 | + | 21.4922i | 0.566960 | + | 0.982004i | 0.996864 | + | 0.0791292i | \(0.0252140\pi\) |
−0.429904 | + | 0.902874i | \(0.641453\pi\) | |||||||
\(480\) | 2.16267 | + | 0.568195i | 0.0987121 | + | 0.0259344i | ||||
\(481\) | −11.1961 | − | 6.59711i | −0.510497 | − | 0.300802i | ||||
\(482\) | − | 16.2928i | − | 0.742119i | ||||||
\(483\) | −1.30897 | + | 0.755734i | −0.0595602 | + | 0.0343871i | ||||
\(484\) | 1.07952 | − | 1.86978i | 0.0490691 | − | 0.0849902i | ||||
\(485\) | 18.5249 | + | 18.3451i | 0.841173 | + | 0.833006i | ||||
\(486\) | −0.500000 | + | 0.866025i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | 12.1033i | 0.548454i | 0.961665 | + | 0.274227i | \(0.0884220\pi\) | ||||
−0.961665 | + | 0.274227i | \(0.911578\pi\) | |||||||
\(488\) | 5.41327 | + | 3.12535i | 0.245047 | + | 0.141478i | ||||
\(489\) | 24.8077 | 1.12184 | ||||||||
\(490\) | −22.1527 | + | 6.05178i | −1.00076 | + | 0.273392i | ||||
\(491\) | −33.2720 | −1.50154 | −0.750772 | − | 0.660562i | \(-0.770318\pi\) | ||||
−0.750772 | + | 0.660562i | \(0.770318\pi\) | |||||||
\(492\) | − | 12.0879i | − | 0.544967i | ||||||
\(493\) | 5.16029 | − | 2.97930i | 0.232408 | − | 0.134181i | ||||
\(494\) | 7.97059 | − | 13.8055i | 0.358614 | − | 0.621137i | ||||
\(495\) | −7.84518 | − | 2.06115i | −0.352615 | − | 0.0926417i | ||||
\(496\) | −1.74558 | − | 3.02342i | −0.0783786 | − | 0.135756i | ||||
\(497\) | −0.527139 | + | 0.304344i | −0.0236454 | + | 0.0136517i | ||||
\(498\) | −11.9781 | + | 6.91556i | −0.536752 | + | 0.309894i | ||||
\(499\) | −9.98553 | + | 17.2955i | −0.447014 | + | 0.774251i | −0.998190 | − | 0.0601381i | \(-0.980846\pi\) |
0.551176 | + | 0.834389i | \(0.314179\pi\) | |||||||
\(500\) | 10.7559 | − | 3.05140i | 0.481018 | − | 0.136463i | ||||
\(501\) | −5.77063 | − | 9.99502i | −0.257813 | − | 0.446545i | ||||
\(502\) | 14.4960 | − | 8.36928i | 0.646989 | − | 0.373539i | ||||
\(503\) | −2.50589 | + | 1.44678i | −0.111732 | + | 0.0645086i | −0.554825 | − | 0.831967i | \(-0.687215\pi\) |
0.443092 | + | 0.896476i | \(0.353881\pi\) | |||||||
\(504\) | 4.15572 | 0.185111 | ||||||||
\(505\) | 16.4399 | − | 16.6011i | 0.731567 | − | 0.738739i | ||||
\(506\) | 0.659682 | + | 1.14260i | 0.0293264 | + | 0.0507949i | ||||
\(507\) | − | 8.43584i | − | 0.374649i | ||||||
\(508\) | 5.27821i | 0.234183i | ||||||||
\(509\) | −6.90016 | − | 11.9514i | −0.305844 | − | 0.529738i | 0.671605 | − | 0.740910i | \(-0.265605\pi\) |
−0.977449 | + | 0.211172i | \(0.932272\pi\) | |||||||
\(510\) | 0.656676 | − | 2.49945i | 0.0290781 | − | 0.110678i | ||||
\(511\) | 20.0176 | − | 34.6715i | 0.885526 | − | 1.53378i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −6.46205 | − | 3.73087i | −0.285307 | − | 0.164722i | ||||
\(514\) | −3.55458 | + | 6.15672i | −0.156786 | + | 0.271561i | ||||
\(515\) | −15.5111 | − | 15.3605i | −0.683502 | − | 0.676867i | ||||
\(516\) | 6.18403 | + | 10.7111i | 0.272237 | + | 0.471528i | ||||
\(517\) | 8.04396i | 0.353773i | ||||||||
\(518\) | 25.2773 | + | 0.224153i | 1.11062 | + | 0.00984871i | ||||
\(519\) | 3.62151 | 0.158967 | ||||||||
\(520\) | −1.25890 | − | 4.60825i | −0.0552064 | − | 0.202085i | ||||
\(521\) | −4.95593 | + | 8.58393i | −0.217123 | + | 0.376069i | −0.953927 | − | 0.300038i | \(-0.903001\pi\) |
0.736804 | + | 0.676106i | \(0.236334\pi\) | |||||||
\(522\) | −4.46499 | − | 2.57786i | −0.195427 | − | 0.112830i | ||||
\(523\) | 34.6236 | + | 19.9900i | 1.51399 | + | 0.874100i | 0.999866 | + | 0.0163822i | \(0.00521485\pi\) |
0.514120 | + | 0.857718i | \(0.328118\pi\) | |||||||
\(524\) | −15.2189 | −0.664840 | ||||||||
\(525\) | 17.8926 | − | 10.5644i | 0.780897 | − | 0.461067i | ||||
\(526\) | −7.89156 | −0.344089 | ||||||||
\(527\) | −3.49424 | + | 2.01740i | −0.152212 | + | 0.0878794i | ||||
\(528\) | − | 3.62754i | − | 0.157868i | ||||||
\(529\) | 22.8677 | 0.994249 | ||||||||
\(530\) | 6.44642 | + | 23.5974i | 0.280015 | + | 1.02500i | ||||
\(531\) | 4.88507 | − | 8.46118i | 0.211994 | − | 0.367184i | ||||
\(532\) | 31.0089i | 1.34441i | ||||||||
\(533\) | −22.3647 | + | 12.9123i | −0.968724 | + | 0.559293i | ||||
\(534\) | −5.67966 | − | 9.83745i | −0.245783 | − | 0.425708i | ||||
\(535\) | 2.64221 | − | 0.721810i | 0.114233 | − | 0.0312066i | ||||
\(536\) | 7.73561 | − | 13.3985i | 0.334127 | − | 0.578726i | ||||
\(537\) | 10.8646 | + | 6.27265i | 0.468840 | + | 0.270685i | ||||
\(538\) | −0.698143 | + | 0.403073i | −0.0300991 | + | 0.0173777i | ||||
\(539\) | 18.6275 | + | 32.2637i | 0.802342 | + | 1.38970i | ||||
\(540\) | −2.15703 | + | 0.589266i | −0.0928237 | + | 0.0253580i | ||||
\(541\) | −7.11266 | −0.305797 | −0.152899 | − | 0.988242i | \(-0.548861\pi\) | ||||
−0.152899 | + | 0.988242i | \(0.548861\pi\) | |||||||
\(542\) | −8.02156 | − | 4.63125i | −0.344556 | − | 0.198929i | ||||
\(543\) | −2.52899 | + | 1.46011i | −0.108529 | + | 0.0626595i | ||||
\(544\) | 1.15572 | 0.0495512 | ||||||||
\(545\) | 21.4024 | + | 5.62300i | 0.916776 | + | 0.240863i | ||||
\(546\) | −4.43912 | − | 7.68878i | −0.189977 | − | 0.329050i | ||||
\(547\) | 10.4605i | 0.447260i | 0.974674 | + | 0.223630i | \(0.0717907\pi\) | ||||
−0.974674 | + | 0.223630i | \(0.928209\pi\) | |||||||
\(548\) | −6.01343 | − | 3.47185i | −0.256881 | − | 0.148310i | ||||
\(549\) | −6.25070 | −0.266774 | ||||||||
\(550\) | −9.22165 | − | 15.6185i | −0.393213 | − | 0.665975i | ||||
\(551\) | 19.2353 | − | 33.3166i | 0.819452 | − | 1.41933i | ||||
\(552\) | 0.314980 | + | 0.181854i | 0.0134064 | + | 0.00774021i | ||||
\(553\) | 56.5457 | − | 32.6467i | 2.40457 | − | 1.38828i | ||||
\(554\) | 6.40512 | 0.272127 | ||||||||
\(555\) | −13.1520 | + | 3.46788i | −0.558269 | + | 0.147203i | ||||
\(556\) | −13.7911 | −0.584874 | ||||||||
\(557\) | 11.6439 | − | 6.72259i | 0.493367 | − | 0.284845i | −0.232603 | − | 0.972572i | \(-0.574724\pi\) |
0.725970 | + | 0.687726i | \(0.241391\pi\) | |||||||
\(558\) | 3.02342 | + | 1.74558i | 0.127992 | + | 0.0738961i | ||||
\(559\) | 13.2115 | − | 22.8830i | 0.558787 | − | 0.967847i | ||||
\(560\) | 6.60275 | + | 6.53865i | 0.279017 | + | 0.276308i | ||||
\(561\) | −4.19243 | −0.177005 | ||||||||
\(562\) | −7.60967 | − | 4.39344i | −0.320994 | − | 0.185326i | ||||
\(563\) | − | 7.95921i | − | 0.335441i | −0.985835 | − | 0.167720i | \(-0.946359\pi\) | ||
0.985835 | − | 0.167720i | \(-0.0536406\pi\) | |||||||
\(564\) | 1.10873 | + | 1.92038i | 0.0466862 | + | 0.0808628i | ||||
\(565\) | 4.76042 | − | 18.1192i | 0.200272 | − | 0.762280i | ||||
\(566\) | 9.62862 | 0.404721 | ||||||||
\(567\) | −3.59896 | + | 2.07786i | −0.151142 | + | 0.0872620i | ||||
\(568\) | 0.126846 | + | 0.0732348i | 0.00532236 | + | 0.00307287i | ||||
\(569\) | −6.60381 | −0.276846 | −0.138423 | − | 0.990373i | \(-0.544203\pi\) | ||||
−0.138423 | + | 0.990373i | \(0.544203\pi\) | |||||||
\(570\) | −4.39694 | − | 16.0952i | −0.184168 | − | 0.674152i | ||||
\(571\) | 8.02353 | + | 13.8972i | 0.335774 | + | 0.581578i | 0.983633 | − | 0.180182i | \(-0.0576687\pi\) |
−0.647859 | + | 0.761760i | \(0.724335\pi\) | |||||||
\(572\) | −6.71155 | + | 3.87492i | −0.280624 | + | 0.162018i | ||||
\(573\) | 17.6852 | + | 10.2105i | 0.738808 | + | 0.426551i | ||||
\(574\) | 25.1171 | − | 43.5041i | 1.04837 | − | 1.81582i | ||||
\(575\) | 1.81845 | − | 0.0177409i | 0.0758347 | − | 0.000739845i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −21.9490 | + | 12.6723i | −0.913749 | + | 0.527553i | −0.881636 | − | 0.471931i | \(-0.843557\pi\) |
−0.0321136 | + | 0.999484i | \(0.510224\pi\) | |||||||
\(578\) | 15.6643i | 0.651549i | ||||||||
\(579\) | 2.39338 | − | 4.14545i | 0.0994654 | − | 0.172279i | ||||
\(580\) | −3.03809 | − | 11.1210i | −0.126150 | − | 0.461776i | ||||
\(581\) | −57.4783 | −2.38460 | ||||||||
\(582\) | − | 11.6594i | − | 0.483300i | ||||||
\(583\) | 34.3677 | − | 19.8422i | 1.42336 | − | 0.821780i | ||||
\(584\) | −9.63375 | −0.398647 | ||||||||
\(585\) | 3.39436 | + | 3.36141i | 0.140340 | + | 0.138977i | ||||
\(586\) | −17.3324 | −0.715997 | ||||||||
\(587\) | 1.63238 | + | 0.942454i | 0.0673754 | + | 0.0388992i | 0.533309 | − | 0.845920i | \(-0.320948\pi\) |
−0.465934 | + | 0.884820i | \(0.654282\pi\) | |||||||
\(588\) | 8.89411 | + | 5.13502i | 0.366787 | + | 0.211765i | ||||
\(589\) | −13.0250 | + | 22.5600i | −0.536687 | + | 0.929568i | ||||
\(590\) | 21.0744 | − | 5.75720i | 0.867621 | − | 0.237020i | ||||
\(591\) | 4.11603 | 0.169311 | ||||||||
\(592\) | −2.99455 | − | 5.29459i | −0.123075 | − | 0.217606i | ||||
\(593\) | 5.11792i | 0.210168i | 0.994463 | + | 0.105084i | \(0.0335111\pi\) | ||||
−0.994463 | + | 0.105084i | \(0.966489\pi\) | |||||||
\(594\) | 1.81377 | + | 3.14154i | 0.0744199 | + | 0.128899i | ||||
\(595\) | 7.55687 | − | 7.63095i | 0.309801 | − | 0.312839i | ||||
\(596\) | −2.76562 | + | 4.79019i | −0.113284 | + | 0.196214i | ||||
\(597\) | −5.71084 | − | 3.29715i | −0.233729 | − | 0.134943i | ||||
\(598\) | − | 0.777021i | − | 0.0317748i | ||||||
\(599\) | −1.84896 | + | 3.20250i | −0.0755466 | + | 0.130851i | −0.901324 | − | 0.433146i | \(-0.857404\pi\) |
0.825777 | + | 0.563996i | \(0.190737\pi\) | |||||||
\(600\) | −4.35431 | − | 2.45764i | −0.177764 | − | 0.100333i | ||||
\(601\) | −12.3196 | − | 21.3383i | −0.502529 | − | 0.870406i | −0.999996 | − | 0.00292268i | \(-0.999070\pi\) |
0.497467 | − | 0.867483i | \(-0.334264\pi\) | |||||||
\(602\) | 51.3983i | 2.09484i | ||||||||
\(603\) | 15.4712i | 0.630037i | ||||||||
\(604\) | 11.1149 | + | 19.2515i | 0.452258 | + | 0.783334i | ||||
\(605\) | −3.39705 | + | 3.43036i | −0.138110 | + | 0.139464i | ||||
\(606\) | −10.4486 | −0.424446 | ||||||||
\(607\) | 25.1410 | − | 14.5152i | 1.02044 | − | 0.589153i | 0.106211 | − | 0.994344i | \(-0.466128\pi\) |
0.914232 | + | 0.405190i | \(0.132795\pi\) | |||||||
\(608\) | 6.46205 | − | 3.73087i | 0.262071 | − | 0.151307i | ||||
\(609\) | −10.7129 | − | 18.5553i | −0.434108 | − | 0.751897i | ||||
\(610\) | −9.93132 | − | 9.83490i | −0.402107 | − | 0.398204i | ||||
\(611\) | 2.36869 | − | 4.10269i | 0.0958269 | − | 0.165977i | ||||
\(612\) | −1.00089 | + | 0.577862i | −0.0404584 | + | 0.0233587i | ||||
\(613\) | −7.41060 | + | 4.27851i | −0.299311 | + | 0.172807i | −0.642133 | − | 0.766593i | \(-0.721950\pi\) |
0.342822 | + | 0.939400i | \(0.388617\pi\) | |||||||
\(614\) | −14.1491 | − | 24.5070i | −0.571013 | − | 0.989024i | ||||
\(615\) | −6.86831 | + | 26.1423i | −0.276957 | + | 1.05416i | ||||
\(616\) | 7.53753 | − | 13.0554i | 0.303696 | − | 0.526016i | ||||
\(617\) | 18.6337 | − | 10.7581i | 0.750163 | − | 0.433107i | −0.0755901 | − | 0.997139i | \(-0.524084\pi\) |
0.825753 | + | 0.564032i | \(0.190751\pi\) | |||||||
\(618\) | 9.76260i | 0.392709i | ||||||||
\(619\) | 0.00690520 | 0.000277543 | 0.000138772 | − | 1.00000i | \(-0.499956\pi\) | ||||
0.000138772 | 1.00000i | \(0.499956\pi\) | ||||||||
\(620\) | 2.05721 | + | 7.53051i | 0.0826197 | + | 0.302432i | ||||
\(621\) | −0.363708 | −0.0145951 | ||||||||
\(622\) | −2.19774 | − | 1.26886i | −0.0881212 | − | 0.0508768i | ||||
\(623\) | − | 47.2062i | − | 1.89127i | ||||||
\(624\) | −1.06819 | + | 1.85017i | −0.0427620 | + | 0.0740660i | ||||
\(625\) | −24.9952 | + | 0.487755i | −0.999810 | + | 0.0195102i | ||||
\(626\) | −5.44413 | + | 9.42952i | −0.217591 | + | 0.376879i | ||||
\(627\) | −23.4413 | + | 13.5339i | −0.936157 | + | 0.540491i | ||||
\(628\) | − | 8.48130i | − | 0.338441i | ||||||
\(629\) | −6.11908 | + | 3.46087i | −0.243984 | + | 0.137994i | ||||
\(630\) | −8.98747 | − | 2.36126i | −0.358069 | − | 0.0940748i | ||||
\(631\) | −8.60323 | − | 14.9012i | −0.342489 | − | 0.593209i | 0.642405 | − | 0.766365i | \(-0.277937\pi\) |
−0.984894 | + | 0.173157i | \(0.944603\pi\) | |||||||
\(632\) | −13.6067 | − | 7.85583i | −0.541246 | − | 0.312488i | ||||
\(633\) | −3.03026 | − | 1.74952i | −0.120442 | − | 0.0695371i | ||||
\(634\) | −0.507364 | + | 0.878780i | −0.0201500 | + | 0.0349008i | ||||
\(635\) | 2.99905 | − | 11.4150i | 0.119014 | − | 0.452992i | ||||
\(636\) | 5.46988 | − | 9.47411i | 0.216895 | − | 0.375673i | ||||
\(637\) | − | 21.9408i | − | 0.869326i | ||||||
\(638\) | −16.1969 | + | 9.35129i | −0.641242 | + | 0.370221i | ||||
\(639\) | −0.146470 | −0.00579425 | ||||||||
\(640\) | 0.568195 | − | 2.16267i | 0.0224599 | − | 0.0854872i | ||||
\(641\) | 9.46037 | + | 16.3858i | 0.373662 | + | 0.647202i | 0.990126 | − | 0.140182i | \(-0.0447686\pi\) |
−0.616464 | + | 0.787383i | \(0.711435\pi\) | |||||||
\(642\) | −1.06082 | − | 0.612466i | −0.0418673 | − | 0.0241721i | ||||
\(643\) | 42.2666i | 1.66683i | 0.552647 | + | 0.833415i | \(0.313618\pi\) | ||||
−0.552647 | + | 0.833415i | \(0.686382\pi\) | |||||||
\(644\) | 0.755734 | + | 1.30897i | 0.0297801 | + | 0.0515806i | ||||
\(645\) | −7.28808 | − | 26.6783i | −0.286968 | − | 1.05046i | ||||
\(646\) | −4.31185 | − | 7.46835i | −0.169648 | − | 0.293838i | ||||
\(647\) | 36.1233 | + | 20.8558i | 1.42015 | + | 0.819926i | 0.996311 | − | 0.0858109i | \(-0.0273481\pi\) |
0.423841 | + | 0.905736i | \(0.360681\pi\) | |||||||
\(648\) | 0.866025 | + | 0.500000i | 0.0340207 | + | 0.0196419i | ||||
\(649\) | −17.7208 | − | 30.6933i | −0.695601 | − | 1.20482i | ||||
\(650\) | 0.104208 | + | 10.6814i | 0.00408739 | + | 0.418960i | ||||
\(651\) | 7.25413 | + | 12.5645i | 0.284312 | + | 0.492442i | ||||
\(652\) | − | 24.8077i | − | 0.971546i | ||||||
\(653\) | 27.3064 | + | 15.7653i | 1.06858 | + | 0.616946i | 0.927793 | − | 0.373094i | \(-0.121703\pi\) |
0.140788 | + | 0.990040i | \(0.455036\pi\) | |||||||
\(654\) | −4.94812 | − | 8.57040i | −0.193487 | − | 0.335129i | ||||
\(655\) | 32.9134 | + | 8.64728i | 1.28603 | + | 0.337877i | ||||
\(656\) | −12.0879 | −0.471955 | ||||||||
\(657\) | 8.34307 | − | 4.81687i | 0.325494 | − | 0.187924i | ||||
\(658\) | 9.21519i | 0.359246i | ||||||||
\(659\) | −23.8572 | + | 41.3218i | −0.929343 | + | 1.60967i | −0.144919 | + | 0.989443i | \(0.546292\pi\) |
−0.784423 | + | 0.620226i | \(0.787041\pi\) | |||||||
\(660\) | −2.06115 | + | 7.84518i | −0.0802301 | + | 0.305373i | ||||
\(661\) | −18.8385 | + | 32.6293i | −0.732733 | + | 1.26913i | 0.222978 | + | 0.974824i | \(0.428422\pi\) |
−0.955711 | + | 0.294307i | \(0.904911\pi\) | |||||||
\(662\) | −8.46359 | − | 4.88646i | −0.328947 | − | 0.189918i | ||||
\(663\) | 2.13828 | + | 1.23454i | 0.0830440 | + | 0.0479455i | ||||
\(664\) | 6.91556 | + | 11.9781i | 0.268376 | + | 0.464841i | ||||
\(665\) | 17.6191 | − | 67.0621i | 0.683239 | − | 2.60056i | ||||
\(666\) | 5.24065 | + | 3.08797i | 0.203071 | + | 0.119657i | ||||
\(667\) | − | 1.87518i | − | 0.0726071i | ||||||
\(668\) | −9.99502 | + | 5.77063i | −0.386719 | + | 0.223272i | ||||
\(669\) | −5.96431 | + | 10.3305i | −0.230593 | + | 0.399400i | ||||
\(670\) | −24.3425 | + | 24.5812i | −0.940434 | + | 0.949654i | ||||
\(671\) | −11.3373 | + | 19.6368i | −0.437673 | + | 0.758072i | ||||
\(672\) | − | 4.15572i | − | 0.160311i | ||||||
\(673\) | 25.4131 | + | 14.6723i | 0.979603 | + | 0.565574i | 0.902150 | − | 0.431422i | \(-0.141988\pi\) |
0.0774530 | + | 0.996996i | \(0.475321\pi\) | |||||||
\(674\) | −10.1417 | −0.390644 | ||||||||
\(675\) | 4.99976 | − | 0.0487778i | 0.192441 | − | 0.00187746i | ||||
\(676\) | −8.43584 | −0.324455 | ||||||||
\(677\) | − | 20.0254i | − | 0.769639i | −0.922992 | − | 0.384820i | \(-0.874264\pi\) | ||
0.922992 | − | 0.384820i | \(-0.125736\pi\) | |||||||
\(678\) | −7.25569 | + | 4.18907i | −0.278653 | + | 0.160880i | ||||
\(679\) | 24.2267 | − | 41.9619i | 0.929736 | − | 1.61035i | ||||
\(680\) | −2.49945 | − | 0.656676i | −0.0958496 | − | 0.0251824i | ||||
\(681\) | 4.00164 | + | 6.93104i | 0.153343 | + | 0.265598i | ||||
\(682\) | 10.9676 | − | 6.33214i | 0.419971 | − | 0.242470i | ||||
\(683\) | 22.8200 | − | 13.1751i | 0.873183 | − | 0.504133i | 0.00477842 | − | 0.999989i | \(-0.498479\pi\) |
0.868405 | + | 0.495856i | \(0.165146\pi\) | |||||||
\(684\) | −3.73087 | + | 6.46205i | −0.142653 | + | 0.247083i | ||||
\(685\) | 11.0324 | + | 10.9253i | 0.421526 | + | 0.417434i | ||||
\(686\) | 6.79469 | + | 11.7687i | 0.259422 | + | 0.449333i | ||||
\(687\) | −2.85314 | + | 1.64726i | −0.108854 | + | 0.0628469i | ||||
\(688\) | 10.7111 | − | 6.18403i | 0.408355 | − | 0.235764i | ||||
\(689\) | −23.3716 | −0.890386 | ||||||||
\(690\) | −0.577871 | − | 0.572260i | −0.0219992 | − | 0.0217856i | ||||
\(691\) | −16.1086 | − | 27.9009i | −0.612801 | − | 1.06140i | −0.990766 | − | 0.135582i | \(-0.956709\pi\) |
0.377965 | − | 0.925820i | \(-0.376624\pi\) | |||||||
\(692\) | − | 3.62151i | − | 0.137669i | ||||||
\(693\) | 15.0751i | 0.572654i | ||||||||
\(694\) | −8.18610 | − | 14.1787i | −0.310740 | − | 0.538218i | ||||
\(695\) | 29.8257 | + | 7.83605i | 1.13135 | + | 0.297238i | ||||
\(696\) | −2.57786 | + | 4.46499i | −0.0977136 | + | 0.169245i | ||||
\(697\) | 13.9703i | 0.529164i | ||||||||
\(698\) | 12.6143 | + | 7.28289i | 0.477459 | + | 0.275661i | ||||
\(699\) | 4.60746 | − | 7.98036i | 0.174270 | − | 0.301845i | ||||
\(700\) | −10.5644 | − | 17.8926i | −0.399295 | − | 0.676277i | ||||
\(701\) | 19.8955 | + | 34.4600i | 0.751442 | + | 1.30154i | 0.947124 | + | 0.320868i | \(0.103975\pi\) |
−0.195682 | + | 0.980667i | \(0.562692\pi\) | |||||||
\(702\) | − | 2.13639i | − | 0.0806328i | ||||||
\(703\) | −23.0416 | + | 39.1043i | −0.869032 | + | 1.47485i | ||||
\(704\) | −3.62754 | −0.136718 | ||||||||
\(705\) | −1.30668 | − | 4.78314i | −0.0492124 | − | 0.180144i | ||||
\(706\) | −11.9778 | + | 20.7462i | −0.450792 | + | 0.780795i | ||||
\(707\) | −37.6041 | − | 21.7108i | −1.41425 | − | 0.816517i | ||||
\(708\) | −8.46118 | − | 4.88507i | −0.317991 | − | 0.183592i | ||||
\(709\) | −38.2518 | −1.43658 | −0.718288 | − | 0.695746i | \(-0.755074\pi\) | ||||
−0.718288 | + | 0.695746i | \(0.755074\pi\) | |||||||
\(710\) | −0.232716 | − | 0.230456i | −0.00873367 | − | 0.00864888i | ||||
\(711\) | 15.7117 | 0.589234 | ||||||||
\(712\) | −9.83745 | + | 5.67966i | −0.368674 | + | 0.212854i | ||||
\(713\) | 1.26976i | 0.0475528i | ||||||||
\(714\) | −4.80287 | −0.179743 | ||||||||
\(715\) | 16.7166 | − | 4.56671i | 0.625166 | − | 0.170785i | ||||
\(716\) | 6.27265 | − | 10.8646i | 0.234420 | − | 0.406027i | ||||
\(717\) | 18.7245i | 0.699277i | ||||||||
\(718\) | −27.4269 | + | 15.8349i | −1.02356 | + | 0.590954i | ||||
\(719\) | −14.0689 | − | 24.3681i | −0.524681 | − | 0.908775i | −0.999587 | − | 0.0287381i | \(-0.990851\pi\) |
0.474906 | − | 0.880037i | \(-0.342482\pi\) | |||||||
\(720\) | 0.589266 | + | 2.15703i | 0.0219606 | + | 0.0803877i | ||||
\(721\) | −20.2853 | + | 35.1352i | −0.755465 | + | 1.30850i | ||||
\(722\) | −31.7636 | − | 18.3387i | −1.18212 | − | 0.682497i | ||||
\(723\) | 14.1100 | − | 8.14642i | 0.524757 | − | 0.302969i | ||||
\(724\) | 1.46011 | + | 2.52899i | 0.0542647 | + | 0.0939893i | ||||
\(725\) | 0.251485 | + | 25.7774i | 0.00933991 | + | 0.957348i | ||||
\(726\) | 2.15904 | 0.0801295 | ||||||||
\(727\) | 8.63854 | + | 4.98746i | 0.320386 | + | 0.184975i | 0.651564 | − | 0.758593i | \(-0.274113\pi\) |
−0.331179 | + | 0.943568i | \(0.607446\pi\) | |||||||
\(728\) | −7.68878 | + | 4.43912i | −0.284965 | + | 0.164525i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 20.8346 | + | 5.47384i | 0.771125 | + | 0.202596i | ||||
\(731\) | −7.14703 | − | 12.3790i | −0.264343 | − | 0.457855i | ||||
\(732\) | 6.25070i | 0.231033i | ||||||||
\(733\) | −8.08570 | − | 4.66828i | −0.298652 | − | 0.172427i | 0.343185 | − | 0.939268i | \(-0.388494\pi\) |
−0.641837 | + | 0.766841i | \(0.721828\pi\) | |||||||
\(734\) | 21.5174 | 0.794223 | ||||||||
\(735\) | −16.3174 | − | 16.1590i | −0.601875 | − | 0.596032i | ||||
\(736\) | 0.181854 | − | 0.314980i | 0.00670322 | − | 0.0116103i | ||||
\(737\) | 48.6035 | + | 28.0612i | 1.79033 | + | 1.03365i | ||||
\(738\) | 10.4685 | − | 6.04397i | 0.385350 | − | 0.222482i | ||||
\(739\) | 34.3088 | 1.26207 | 0.631035 | − | 0.775754i | \(-0.282630\pi\) | ||||
0.631035 | + | 0.775754i | \(0.282630\pi\) | |||||||
\(740\) | 3.46788 | + | 13.1520i | 0.127482 | + | 0.483475i | ||||
\(741\) | 15.9412 | 0.585614 | ||||||||
\(742\) | 39.3718 | − | 22.7313i | 1.44538 | − | 0.834492i | ||||
\(743\) | −6.05632 | − | 3.49662i | −0.222185 | − | 0.128278i | 0.384777 | − | 0.923010i | \(-0.374278\pi\) |
−0.606962 | + | 0.794731i | \(0.707612\pi\) | |||||||
\(744\) | 1.74558 | − | 3.02342i | 0.0639959 | − | 0.110844i | ||||
\(745\) | 8.70288 | − | 8.78820i | 0.318849 | − | 0.321975i | ||||
\(746\) | 9.76183 | 0.357406 | ||||||||
\(747\) | −11.9781 | − | 6.91556i | −0.438256 | − | 0.253027i | ||||
\(748\) | 4.19243i | 0.153291i | ||||||||
\(749\) | −2.54524 | − | 4.40848i | −0.0930010 | − | 0.161082i | ||||
\(750\) | 8.02053 | + | 7.78916i | 0.292868 | + | 0.284420i | ||||
\(751\) | −3.07125 | −0.112071 | −0.0560357 | − | 0.998429i | \(-0.517846\pi\) | ||||
−0.0560357 | + | 0.998429i | \(0.517846\pi\) | |||||||
\(752\) | 1.92038 | − | 1.10873i | 0.0700292 | − | 0.0404314i | ||||
\(753\) | 14.4960 | + | 8.36928i | 0.528264 | + | 0.304994i | ||||
\(754\) | 11.0146 | 0.401129 | ||||||||
\(755\) | −13.0992 | − | 47.9502i | −0.476730 | − | 1.74509i | ||||
\(756\) | 2.07786 | + | 3.59896i | 0.0755711 | + | 0.130893i | ||||
\(757\) | −26.9227 | + | 15.5438i | −0.978523 | + | 0.564950i | −0.901824 | − | 0.432104i | \(-0.857771\pi\) |
−0.0766990 | + | 0.997054i | \(0.524438\pi\) | |||||||
\(758\) | 20.3909 | + | 11.7727i | 0.740630 | + | 0.427603i | ||||
\(759\) | −0.659682 | + | 1.14260i | −0.0239449 | + | 0.0414738i | ||||
\(760\) | −16.0952 | + | 4.39694i | −0.583833 | + | 0.159494i | ||||
\(761\) | 16.6558 | + | 28.8487i | 0.603772 | + | 1.04576i | 0.992244 | + | 0.124304i | \(0.0396698\pi\) |
−0.388472 | + | 0.921461i | \(0.626997\pi\) | |||||||
\(762\) | −4.57107 | + | 2.63911i | −0.165592 | + | 0.0956047i | ||||
\(763\) | − | 41.1261i | − | 1.48886i | ||||||
\(764\) | 10.2105 | − | 17.6852i | 0.369404 | − | 0.639826i | ||||
\(765\) | 2.49293 | − | 0.681028i | 0.0901320 | − | 0.0246226i | ||||
\(766\) | 6.75798 | 0.244176 | ||||||||
\(767\) | 20.8728i | 0.753673i | ||||||||
\(768\) | −0.866025 | + | 0.500000i | −0.0312500 | + | 0.0180422i | ||||
\(769\) | 33.0922 | 1.19333 | 0.596667 | − | 0.802489i | \(-0.296491\pi\) | ||||
0.596667 | + | 0.802489i | \(0.296491\pi\) | |||||||
\(770\) | −23.7192 | + | 23.9517i | −0.854781 | + | 0.863160i | ||||
\(771\) | −7.10917 | −0.256030 | ||||||||
\(772\) | −4.14545 | − | 2.39338i | −0.149198 | − | 0.0861396i | ||||
\(773\) | 23.9790 | + | 13.8443i | 0.862464 | + | 0.497944i | 0.864837 | − | 0.502053i | \(-0.167422\pi\) |
−0.00237240 | + | 0.999997i | \(0.500755\pi\) | |||||||
\(774\) | −6.18403 | + | 10.7111i | −0.222280 | + | 0.385001i | ||||
\(775\) | −0.170291 | − | 17.4549i | −0.00611702 | − | 0.626999i | ||||
\(776\) | −11.6594 | −0.418550 | ||||||||
\(777\) | 12.4445 | + | 22.0028i | 0.446445 | + | 0.789348i | ||||
\(778\) | − | 5.61300i | − | 0.201236i | ||||||
\(779\) | 45.0985 | + | 78.1129i | 1.61582 | + | 2.79869i | ||||
\(780\) | 3.36141 | − | 3.39436i | 0.120358 | − | 0.121538i | ||||
\(781\) | −0.265662 | + | 0.460140i | −0.00950614 | + | 0.0164651i | ||||
\(782\) | −0.364030 | − | 0.210173i | −0.0130177 | − | 0.00751576i | ||||
\(783\) | − | 5.15572i | − | 0.184251i | ||||||
\(784\) | 5.13502 | − | 8.89411i | 0.183394 | − | 0.317647i | ||||
\(785\) | −4.81903 | + | 18.3423i | −0.171999 | + | 0.654664i | ||||
\(786\) | −7.60944 | − | 13.1799i | −0.271420 | − | 0.470113i | ||||
\(787\) | − | 22.5730i | − | 0.804640i | −0.915499 | − | 0.402320i | \(-0.868204\pi\) | ||
0.915499 | − | 0.402320i | \(-0.131796\pi\) | |||||||
\(788\) | − | 4.11603i | − | 0.146628i | ||||||
\(789\) | −3.94578 | − | 6.83430i | −0.140474 | − | 0.243307i | ||||
\(790\) | 24.9632 | + | 24.7209i | 0.888151 | + | 0.879529i | ||||
\(791\) | −34.8173 | −1.23796 | ||||||||
\(792\) | 3.14154 | − | 1.81377i | 0.111630 | − | 0.0644495i | ||||
\(793\) | 11.5648 | − | 6.67697i | 0.410680 | − | 0.237106i | ||||
\(794\) | 12.2845 | + | 21.2773i | 0.435959 | + | 0.755104i | ||||
\(795\) | −17.2127 | + | 17.3814i | −0.610471 | + | 0.616456i | ||||
\(796\) | −3.29715 | + | 5.71084i | −0.116864 | + | 0.202415i | ||||
\(797\) | −18.4492 | + | 10.6517i | −0.653505 | + | 0.377301i | −0.789798 | − | 0.613367i | \(-0.789814\pi\) |
0.136293 | + | 0.990669i | \(0.456481\pi\) | |||||||
\(798\) | −26.8545 | + | 15.5045i | −0.950639 | + | 0.548852i | ||||
\(799\) | −1.28139 | − | 2.21943i | −0.0453323 | − | 0.0785179i | ||||
\(800\) | −2.45764 | + | 4.35431i | −0.0868906 | + | 0.153948i | ||||
\(801\) | 5.67966 | − | 9.83745i | 0.200681 | − | 0.347589i | ||||
\(802\) | 28.7299 | − | 16.5872i | 1.01449 | − | 0.585716i | ||||
\(803\) | − | 34.9468i | − | 1.23325i | ||||||
\(804\) | 15.4712 | 0.545628 | ||||||||
\(805\) | −0.890656 | − | 3.26028i | −0.0313915 | − | 0.114910i | ||||
\(806\) | −7.45846 | −0.262713 | ||||||||
\(807\) | −0.698143 | − | 0.403073i | −0.0245758 | − | 0.0141889i | ||||
\(808\) | 10.4486i | 0.367581i | ||||||||
\(809\) | 6.26611 | − | 10.8532i | 0.220305 | − | 0.381579i | −0.734596 | − | 0.678505i | \(-0.762628\pi\) |
0.954900 | + | 0.296926i | \(0.0959615\pi\) | |||||||
\(810\) | −1.58883 | − | 1.57341i | −0.0558259 | − | 0.0552839i | ||||
\(811\) | 5.68068 | − | 9.83922i | 0.199476 | − | 0.345502i | −0.748883 | − | 0.662702i | \(-0.769409\pi\) |
0.948358 | + | 0.317201i | \(0.102743\pi\) | |||||||
\(812\) | −18.5553 | + | 10.7129i | −0.651162 | + | 0.375948i | ||||
\(813\) | − | 9.26250i | − | 0.324850i | ||||||
\(814\) | 19.2063 | − | 10.8628i | 0.673181 | − | 0.380743i | ||||
\(815\) | −14.0956 | + | 53.6510i | −0.493748 | + | 1.87931i | ||||
\(816\) | 0.577862 | + | 1.00089i | 0.0202292 | + | 0.0350380i | ||||
\(817\) | −79.9231 | − | 46.1436i | −2.79615 | − | 1.61436i | ||||
\(818\) | −22.7761 | − | 13.1498i | −0.796348 | − | 0.459772i | ||||
\(819\) | 4.43912 | − | 7.68878i | 0.155115 | − | 0.268668i | ||||
\(820\) | 26.1423 | + | 6.86831i | 0.912928 | + | 0.239852i | ||||
\(821\) | −11.6332 | + | 20.1492i | −0.406000 | + | 0.703213i | −0.994437 | − | 0.105330i | \(-0.966410\pi\) |
0.588437 | + | 0.808543i | \(0.299743\pi\) | |||||||
\(822\) | − | 6.94371i | − | 0.242190i | ||||||
\(823\) | 20.1796 | − | 11.6507i | 0.703416 | − | 0.406118i | −0.105202 | − | 0.994451i | \(-0.533549\pi\) |
0.808619 | + | 0.588333i | \(0.200216\pi\) | |||||||
\(824\) | 9.76260 | 0.340096 | ||||||||
\(825\) | 8.91518 | − | 15.7954i | 0.310387 | − | 0.549926i | ||||
\(826\) | −20.3010 | − | 35.1623i | −0.706362 | − | 1.22345i | ||||
\(827\) | 6.85682 | + | 3.95879i | 0.238435 | + | 0.137660i | 0.614457 | − | 0.788950i | \(-0.289375\pi\) |
−0.376022 | + | 0.926611i | \(0.622708\pi\) | |||||||
\(828\) | 0.363708i | 0.0126397i | ||||||||
\(829\) | 1.81551 | + | 3.14455i | 0.0630552 | + | 0.109215i | 0.895830 | − | 0.444398i | \(-0.146582\pi\) |
−0.832774 | + | 0.553612i | \(0.813249\pi\) | |||||||
\(830\) | −8.15021 | − | 29.8341i | −0.282898 | − | 1.03556i | ||||
\(831\) | 3.20256 | + | 5.54699i | 0.111096 | + | 0.192423i | ||||
\(832\) | 1.85017 | + | 1.06819i | 0.0641430 | + | 0.0370330i | ||||
\(833\) | −10.2791 | − | 5.93466i | −0.356151 | − | 0.205624i | ||||
\(834\) | −6.89557 | − | 11.9435i | −0.238774 | − | 0.413569i | ||||
\(835\) | 24.8948 | − | 6.80087i | 0.861520 | − | 0.235354i | ||||
\(836\) | 13.5339 | + | 23.4413i | 0.468079 | + | 0.810736i | ||||
\(837\) | 3.49115i | 0.120672i | ||||||||
\(838\) | −28.0440 | − | 16.1912i | −0.968762 | − | 0.559315i | ||||
\(839\) | 23.1752 | + | 40.1407i | 0.800097 | + | 1.38581i | 0.919552 | + | 0.392969i | \(0.128552\pi\) |
−0.119454 | + | 0.992840i | \(0.538114\pi\) | |||||||
\(840\) | −2.36126 | + | 8.98747i | −0.0814712 | + | 0.310097i | ||||
\(841\) | −2.41852 | −0.0833971 | ||||||||
\(842\) | 6.25539 | − | 3.61155i | 0.215575 | − | 0.124462i | ||||
\(843\) | − | 8.78689i | − | 0.302636i | ||||||
\(844\) | −1.74952 | + | 3.03026i | −0.0602209 | + | 0.104306i | ||||
\(845\) | 18.2440 | + | 4.79320i | 0.627612 | + | 0.164891i | ||||
\(846\) | −1.10873 | + | 1.92038i | −0.0381191 | + | 0.0660242i | ||||
\(847\) | 7.77031 | + | 4.48619i | 0.266991 | + | 0.154147i | ||||
\(848\) | −9.47411 | − | 5.46988i | −0.325342 | − | 0.187836i | ||||
\(849\) | 4.81431 | + | 8.33863i | 0.165227 | + | 0.286181i | ||||
\(850\) | 5.03238 | + | 2.84035i | 0.172609 | + | 0.0974232i | ||||
\(851\) | −0.0196178 | + | 2.21226i | −0.000672489 | + | 0.0758353i | ||||
\(852\) | 0.146470i | 0.00501797i | ||||||||
\(853\) | −14.3566 | + | 8.28879i | −0.491561 | + | 0.283803i | −0.725222 | − | 0.688516i | \(-0.758263\pi\) |
0.233661 | + | 0.972318i | \(0.424929\pi\) | |||||||
\(854\) | −12.9881 | + | 22.4960i | −0.444444 | + | 0.769799i | ||||
\(855\) | 11.7404 | − | 11.8554i | 0.401512 | − | 0.405448i | ||||
\(856\) | −0.612466 | + | 1.06082i | −0.0209336 | + | 0.0362581i | ||||
\(857\) | − | 11.8858i | − | 0.406010i | −0.979178 | − | 0.203005i | \(-0.934929\pi\) | ||
0.979178 | − | 0.203005i | \(-0.0650707\pi\) | |||||||
\(858\) | −6.71155 | − | 3.87492i | −0.229129 | − | 0.132288i | ||||
\(859\) | −0.176667 | −0.00602779 | −0.00301390 | − | 0.999995i | \(-0.500959\pi\) | ||||
−0.00301390 | + | 0.999995i | \(0.500959\pi\) | |||||||
\(860\) | −26.6783 | + | 7.28808i | −0.909721 | + | 0.248521i | ||||
\(861\) | 50.2342 | 1.71198 | ||||||||
\(862\) | 4.09396i | 0.139441i | ||||||||
\(863\) | −22.6023 | + | 13.0494i | −0.769390 | + | 0.444207i | −0.832657 | − | 0.553789i | \(-0.813181\pi\) |
0.0632671 | + | 0.997997i | \(0.479848\pi\) | |||||||
\(864\) | 0.500000 | − | 0.866025i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | −2.05772 | + | 7.83214i | −0.0699646 | + | 0.266301i | ||||
\(866\) | −0.559309 | − | 0.968752i | −0.0190061 | − | 0.0329195i | ||||
\(867\) | −13.5657 | + | 7.83215i | −0.460715 | + | 0.265994i | ||||
\(868\) | 12.5645 | − | 7.25413i | 0.426467 | − | 0.246221i | ||||
\(869\) | 28.4973 | − | 49.3589i | 0.966706 | − | 1.67438i | ||||
\(870\) | 8.11205 | − | 8.19158i | 0.275024 | − | 0.277721i | ||||
\(871\) | −16.5263 | − | 28.6243i | −0.559971 | − | 0.969899i | ||||
\(872\) | −8.57040 | + | 4.94812i | −0.290230 | + | 0.167565i | ||||
\(873\) | 10.0974 | − | 5.82972i | 0.341744 | − | 0.197306i | ||||
\(874\) | −2.71389 | −0.0917987 | ||||||||
\(875\) | 12.6808 | + | 44.6985i | 0.428689 | + | 1.51108i | ||||
\(876\) | −4.81687 | − | 8.34307i | −0.162747 | − | 0.281886i | ||||
\(877\) | 49.2324i | 1.66246i | 0.555930 | + | 0.831229i | \(0.312362\pi\) | ||||
−0.555930 | + | 0.831229i | \(0.687638\pi\) | |||||||
\(878\) | 5.96081i | 0.201168i | ||||||||
\(879\) | −8.66622 | − | 15.0103i | −0.292304 | − | 0.506286i | ||||
\(880\) | 7.84518 | + | 2.06115i | 0.264461 | + | 0.0694813i | ||||
\(881\) | −25.4930 | + | 44.1551i | −0.858880 | + | 1.48762i | 0.0141179 | + | 0.999900i | \(0.495506\pi\) |
−0.872998 | + | 0.487724i | \(0.837827\pi\) | |||||||
\(882\) | 10.2700i | 0.345810i | ||||||||
\(883\) | −11.5905 | − | 6.69179i | −0.390052 | − | 0.225197i | 0.292131 | − | 0.956378i | \(-0.405636\pi\) |
−0.682183 | + | 0.731182i | \(0.738969\pi\) | |||||||
\(884\) | 1.23454 | − | 2.13828i | 0.0415220 | − | 0.0719182i | ||||
\(885\) | 15.5231 | + | 15.3724i | 0.521804 | + | 0.516738i | ||||
\(886\) | 5.01525 | + | 8.68666i | 0.168490 | + | 0.291834i | ||||
\(887\) | 37.4208i | 1.25647i | 0.778025 | + | 0.628233i | \(0.216222\pi\) | ||||
−0.778025 | + | 0.628233i | \(0.783778\pi\) | |||||||
\(888\) | 3.08797 | − | 5.24065i | 0.103626 | − | 0.175865i | ||||
\(889\) | −21.9348 | −0.735669 | ||||||||
\(890\) | 24.5023 | − | 6.69365i | 0.821320 | − | 0.224372i | ||||
\(891\) | −1.81377 | + | 3.14154i | −0.0607636 | + | 0.105246i | ||||
\(892\) | 10.3305 | + | 5.96431i | 0.345890 | + | 0.199700i | ||||
\(893\) | −14.3294 | − | 8.27309i | −0.479515 | − | 0.276848i | ||||
\(894\) | −5.53123 | −0.184992 | ||||||||
\(895\) | −19.7389 | + | 19.9324i | −0.659798 | + | 0.666266i | ||||
\(896\) | −4.15572 | −0.138833 | ||||||||
\(897\) | 0.672920 | − | 0.388511i | 0.0224681 | − | 0.0129720i | ||||
\(898\) | − | 14.1978i | − | 0.473786i | ||||||
\(899\) | −17.9994 | −0.600314 | ||||||||
\(900\) | −0.0487778 | − | 4.99976i | −0.00162593 | − | 0.166659i | ||||
\(901\) | −6.32167 | + | 10.9494i | −0.210605 | + | 0.364779i | ||||
\(902\) | − | 43.8495i | − | 1.46003i | ||||||
\(903\) | −44.5122 | + | 25.6991i | −1.48127 | + | 0.855213i | ||||
\(904\) | 4.18907 | + | 7.25569i | 0.139326 | + | 0.241321i | ||||
\(905\) | −1.72079 | − | 6.29901i | −0.0572010 | − | 0.209386i | ||||
\(906\) | −11.1149 | + | 19.2515i | −0.369267 | + | 0.639590i | ||||
\(907\) | −16.7162 | − | 9.65113i | −0.555054 | − | 0.320460i | 0.196104 | − | 0.980583i | \(-0.437171\pi\) |
−0.751158 | + | 0.660123i | \(0.770504\pi\) | |||||||
\(908\) | 6.93104 | − | 4.00164i | 0.230015 | − | 0.132799i | ||||
\(909\) | −5.22430 | − | 9.04876i | −0.173279 | − | 0.300128i | ||||
\(910\) | 19.1506 | − | 5.23164i | 0.634837 | − | 0.173427i | ||||
\(911\) | 2.02228 | 0.0670011 | 0.0335006 | − | 0.999439i | \(-0.489334\pi\) | ||||
0.0335006 | + | 0.999439i | \(0.489334\pi\) | |||||||
\(912\) | 6.46205 | + | 3.73087i | 0.213980 | + | 0.123541i | ||||
\(913\) | −43.4511 | + | 25.0865i | −1.43802 | + | 0.830241i | ||||
\(914\) | −10.9594 | −0.362506 | ||||||||
\(915\) | 3.55162 | − | 13.5182i | 0.117413 | − | 0.446899i | ||||
\(916\) | 1.64726 | + | 2.85314i | 0.0544270 | + | 0.0942703i | ||||
\(917\) | − | 63.2454i | − | 2.08855i | ||||||
\(918\) | −1.00089 | − | 0.577862i | −0.0330342 | − | 0.0190723i | ||||
\(919\) | −26.5602 | −0.876140 | −0.438070 | − | 0.898941i | \(-0.644338\pi\) | ||||
−0.438070 | + | 0.898941i | \(0.644338\pi\) | |||||||
\(920\) | −0.572260 | + | 0.577871i | −0.0188669 | + | 0.0190518i | ||||
\(921\) | 14.1491 | − | 24.5070i | 0.466230 | − | 0.807535i | ||||
\(922\) | 22.7411 | + | 13.1296i | 0.748938 | + | 0.432400i | ||||
\(923\) | 0.270993 | − | 0.156458i | 0.00891986 | − | 0.00514988i | ||||
\(924\) | 15.0751 | 0.495933 | ||||||||
\(925\) | −0.0270133 | − | 30.4138i | −0.000888193 | − | 1.00000i | ||||
\(926\) | −25.1921 | −0.827864 | ||||||||
\(927\) | −8.45466 | + | 4.88130i | −0.277687 | + | 0.160323i | ||||
\(928\) | 4.46499 | + | 2.57786i | 0.146570 | + | 0.0846225i | ||||
\(929\) | 10.1946 | − | 17.6576i | 0.334475 | − | 0.579327i | −0.648909 | − | 0.760866i | \(-0.724774\pi\) |
0.983384 | + | 0.181539i | \(0.0581078\pi\) | |||||||
\(930\) | −5.49300 | + | 5.54685i | −0.180123 | + | 0.181888i | ||||
\(931\) | −76.6323 | −2.51152 | ||||||||
\(932\) | −7.98036 | − | 4.60746i | −0.261405 | − | 0.150922i | ||||
\(933\) | − | 2.53773i | − | 0.0830814i | ||||||
\(934\) | 11.4326 | + | 19.8018i | 0.374085 | + | 0.647933i | ||||
\(935\) | 2.38212 | − | 9.06686i | 0.0779036 | − | 0.296518i | ||||
\(936\) | −2.13639 | −0.0698301 | ||||||||
\(937\) | −3.69613 | + | 2.13396i | −0.120747 | + | 0.0697134i | −0.559157 | − | 0.829062i | \(-0.688875\pi\) |
0.438410 | + | 0.898775i | \(0.355542\pi\) | |||||||
\(938\) | 55.6803 | + | 32.1471i | 1.81803 | + | 1.04964i | ||||
\(939\) | −10.8883 | −0.355325 | ||||||||
\(940\) | −4.78314 | + | 1.30668i | −0.156009 | + | 0.0426192i | ||||
\(941\) | 19.5603 | + | 33.8794i | 0.637647 | + | 1.10444i | 0.985948 | + | 0.167054i | \(0.0534254\pi\) |
−0.348301 | + | 0.937383i | \(0.613241\pi\) | |||||||
\(942\) | 7.34502 | − | 4.24065i | 0.239314 | − | 0.138168i | ||||
\(943\) | 3.80746 | + | 2.19824i | 0.123988 | + | 0.0715845i | ||||
\(944\) | −4.88507 | + | 8.46118i | −0.158995 | + | 0.275388i | ||||
\(945\) | −2.44882 | − | 8.96401i | −0.0796603 | − | 0.291599i | ||||
\(946\) | 22.4328 | + | 38.8548i | 0.729354 | + | 1.26328i | ||||
\(947\) | −48.8996 | + | 28.2322i | −1.58902 | + | 0.917422i | −0.595554 | + | 0.803315i | \(0.703067\pi\) |
−0.993468 | + | 0.114107i | \(0.963599\pi\) | |||||||
\(948\) | − | 15.7117i | − | 0.510291i | ||||||
\(949\) | −10.2907 | + | 17.8240i | −0.334051 | + | 0.578593i | ||||
\(950\) | 37.3069 | − | 0.363967i | 1.21040 | − | 0.0118086i | ||||
\(951\) | −1.01473 | −0.0329048 | ||||||||
\(952\) | 4.80287i | 0.155662i | ||||||||
\(953\) | −11.4334 | + | 6.60107i | −0.370364 | + | 0.213830i | −0.673617 | − | 0.739080i | \(-0.735260\pi\) |
0.303253 | + | 0.952910i | \(0.401927\pi\) | |||||||
\(954\) | 10.9398 | 0.354188 | ||||||||
\(955\) | −32.1306 | + | 32.4456i | −1.03972 | + | 1.04992i | ||||
\(956\) | 18.7245 | 0.605592 | ||||||||
\(957\) | −16.1969 | − | 9.35129i | −0.523572 | − | 0.302284i | ||||
\(958\) | 21.4922 | + | 12.4085i | 0.694381 | + | 0.400901i | ||||
\(959\) | 14.4281 | − | 24.9901i | 0.465906 | − | 0.806974i | ||||
\(960\) | 2.15703 | − | 0.589266i | 0.0696178 | − | 0.0190185i | ||||
\(961\) | −18.8119 | −0.606835 | ||||||||
\(962\) | −12.9946 | − | 0.115233i | −0.418964 | − | 0.00371527i | ||||
\(963\) | − | 1.22493i | − | 0.0394729i | ||||||
\(964\) | −8.14642 | − | 14.1100i | −0.262379 | − | 0.454453i | ||||
\(965\) | 7.60535 | + | 7.53152i | 0.244825 | + | 0.242448i | ||||
\(966\) | −0.755734 | + | 1.30897i | −0.0243153 | + | 0.0421154i | ||||
\(967\) | −46.3588 | − | 26.7652i | −1.49080 | − | 0.860712i | −0.490853 | − | 0.871243i | \(-0.663315\pi\) |
−0.999945 | + | 0.0105306i | \(0.996648\pi\) | |||||||
\(968\) | − | 2.15904i | − | 0.0693942i | ||||||
\(969\) | 4.31185 | − | 7.46835i | 0.138517 | − | 0.239918i | ||||
\(970\) | 25.2156 | + | 6.62483i | 0.809623 | + | 0.212711i | ||||
\(971\) | −19.2660 | − | 33.3697i | −0.618275 | − | 1.07088i | −0.989800 | − | 0.142461i | \(-0.954498\pi\) |
0.371525 | − | 0.928423i | \(-0.378835\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | − | 57.3121i | − | 1.83734i | ||||||
\(974\) | 6.05167 | + | 10.4818i | 0.193908 | + | 0.335858i | ||||
\(975\) | −9.19829 | + | 5.43097i | −0.294581 | + | 0.173930i | ||||
\(976\) | 6.25070 | 0.200080 | ||||||||
\(977\) | −0.907703 | + | 0.524063i | −0.0290400 | + | 0.0167663i | −0.514450 | − | 0.857521i | \(-0.672004\pi\) |
0.485410 | + | 0.874287i | \(0.338670\pi\) | |||||||
\(978\) | 21.4841 | − | 12.4039i | 0.686986 | − | 0.396632i | ||||
\(979\) | −20.6032 | − | 35.6857i | −0.658480 | − | 1.14052i | ||||
\(980\) | −16.1590 | + | 16.3174i | −0.516179 | + | 0.521239i | ||||
\(981\) | 4.94812 | − | 8.57040i | 0.157981 | − | 0.273632i | ||||
\(982\) | −28.8144 | + | 16.6360i | −0.919504 | + | 0.530876i | ||||
\(983\) | −2.46606 | + | 1.42378i | −0.0786553 | + | 0.0454116i | −0.538812 | − | 0.842426i | \(-0.681127\pi\) |
0.460157 | + | 0.887838i | \(0.347793\pi\) | |||||||
\(984\) | −6.04397 | − | 10.4685i | −0.192675 | − | 0.333723i | ||||
\(985\) | −2.33871 | + | 8.90164i | −0.0745174 | + | 0.283630i | ||||
\(986\) | 2.97930 | − | 5.16029i | 0.0948801 | − | 0.164337i | ||||
\(987\) | −7.98059 | + | 4.60760i | −0.254025 | + | 0.146661i | ||||
\(988\) | − | 15.9412i | − | 0.507156i | ||||||
\(989\) | −4.49836 | −0.143040 | ||||||||
\(990\) | −7.82470 | + | 2.13758i | −0.248685 | + | 0.0679369i | ||||
\(991\) | 2.23806 | 0.0710942 | 0.0355471 | − | 0.999368i | \(-0.488683\pi\) | ||||
0.0355471 | + | 0.999368i | \(0.488683\pi\) | |||||||
\(992\) | −3.02342 | − | 1.74558i | −0.0959938 | − | 0.0554221i | ||||
\(993\) | − | 9.77291i | − | 0.310134i | ||||||
\(994\) | −0.304344 | + | 0.527139i | −0.00965320 | + | 0.0167198i | ||||
\(995\) | 10.3755 | − | 10.4772i | 0.328926 | − | 0.332151i | ||||
\(996\) | −6.91556 | + | 11.9781i | −0.219128 | + | 0.379541i | ||||
\(997\) | 32.0051 | − | 18.4782i | 1.01361 | − | 0.585210i | 0.101365 | − | 0.994849i | \(-0.467679\pi\) |
0.912247 | + | 0.409640i | \(0.134346\pi\) | |||||||
\(998\) | 19.9711i | 0.632173i | ||||||||
\(999\) | −0.0539383 | + | 6.08252i | −0.00170653 | + | 0.192443i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1110.2.bb.d.1099.13 | yes | 28 | |
5.4 | even | 2 | inner | 1110.2.bb.d.1099.2 | yes | 28 | |
37.10 | even | 3 | inner | 1110.2.bb.d.1009.2 | ✓ | 28 | |
185.84 | even | 6 | inner | 1110.2.bb.d.1009.13 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.bb.d.1009.2 | ✓ | 28 | 37.10 | even | 3 | inner | |
1110.2.bb.d.1009.13 | yes | 28 | 185.84 | even | 6 | inner | |
1110.2.bb.d.1099.2 | yes | 28 | 5.4 | even | 2 | inner | |
1110.2.bb.d.1099.13 | yes | 28 | 1.1 | even | 1 | trivial |