Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(43,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("370.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.g (of order \(4\), 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: | \(2.95446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} + 8 x^{18} + 4 x^{17} + 103 x^{16} - 394 x^{15} + 760 x^{14} + 278 x^{13} + 2009 x^{12} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.8 | ||
Root | \(-1.23675 + 1.23675i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.43 |
Dual form | 370.2.g.e.327.8 |
$q$-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 \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(297\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 1.23675 | − | 1.23675i | 0.714039 | − | 0.714039i | −0.253339 | − | 0.967378i | \(-0.581529\pi\) |
0.967378 | + | 0.253339i | \(0.0815287\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.84145 | − | 1.26849i | −0.823522 | − | 0.567285i | ||||
\(6\) | 1.23675 | + | 1.23675i | 0.504902 | + | 0.504902i | ||||
\(7\) | 1.28708 | − | 1.28708i | 0.486471 | − | 0.486471i | −0.420720 | − | 0.907191i | \(-0.638222\pi\) |
0.907191 | + | 0.420720i | \(0.138222\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | − | 0.0591090i | − | 0.0197030i | ||||||
\(10\) | 1.26849 | − | 1.84145i | 0.401131 | − | 0.582318i | ||||
\(11\) | − | 4.27563i | − | 1.28915i | −0.764540 | − | 0.644576i | \(-0.777034\pi\) | ||
0.764540 | − | 0.644576i | \(-0.222966\pi\) | |||||||
\(12\) | −1.23675 | + | 1.23675i | −0.357019 | + | 0.357019i | ||||
\(13\) | − | 1.50964i | − | 0.418700i | −0.977841 | − | 0.209350i | \(-0.932865\pi\) | ||
0.977841 | − | 0.209350i | \(-0.0671348\pi\) | |||||||
\(14\) | 1.28708 | + | 1.28708i | 0.343987 | + | 0.343987i | ||||
\(15\) | −3.84622 | + | 0.708613i | −0.993090 | + | 0.182963i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.12121 | 0.514470 | 0.257235 | − | 0.966349i | \(-0.417189\pi\) | ||||
0.257235 | + | 0.966349i | \(0.417189\pi\) | |||||||
\(18\) | 0.0591090 | 0.0139321 | ||||||||
\(19\) | 0.381960 | − | 0.381960i | 0.0876277 | − | 0.0876277i | −0.661934 | − | 0.749562i | \(-0.730264\pi\) |
0.749562 | + | 0.661934i | \(0.230264\pi\) | |||||||
\(20\) | 1.84145 | + | 1.26849i | 0.411761 | + | 0.283642i | ||||
\(21\) | − | 3.18360i | − | 0.694718i | ||||||
\(22\) | 4.27563 | 0.911568 | ||||||||
\(23\) | − | 8.90184i | − | 1.85616i | −0.372379 | − | 0.928081i | \(-0.621458\pi\) | ||
0.372379 | − | 0.928081i | \(-0.378542\pi\) | |||||||
\(24\) | −1.23675 | − | 1.23675i | −0.252451 | − | 0.252451i | ||||
\(25\) | 1.78188 | + | 4.67171i | 0.356376 | + | 0.934343i | ||||
\(26\) | 1.50964 | 0.296066 | ||||||||
\(27\) | 3.63715 | + | 3.63715i | 0.699970 | + | 0.699970i | ||||
\(28\) | −1.28708 | + | 1.28708i | −0.243235 | + | 0.243235i | ||||
\(29\) | −0.279903 | − | 0.279903i | −0.0519767 | − | 0.0519767i | 0.680641 | − | 0.732617i | \(-0.261702\pi\) |
−0.732617 | + | 0.680641i | \(0.761702\pi\) | |||||||
\(30\) | −0.708613 | − | 3.84622i | −0.129374 | − | 0.702221i | ||||
\(31\) | −1.59328 | + | 1.59328i | −0.286162 | + | 0.286162i | −0.835561 | − | 0.549398i | \(-0.814857\pi\) |
0.549398 | + | 0.835561i | \(0.314857\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −5.28790 | − | 5.28790i | −0.920505 | − | 0.920505i | ||||
\(34\) | 2.12121i | 0.363785i | ||||||||
\(35\) | −4.00274 | + | 0.737449i | −0.676587 | + | 0.124652i | ||||
\(36\) | 0.0591090i | 0.00985149i | ||||||||
\(37\) | −2.28498 | + | 5.63727i | −0.375649 | + | 0.926762i | ||||
\(38\) | 0.381960 | + | 0.381960i | 0.0619621 | + | 0.0619621i | ||||
\(39\) | −1.86705 | − | 1.86705i | −0.298968 | − | 0.298968i | ||||
\(40\) | −1.26849 | + | 1.84145i | −0.200565 | + | 0.291159i | ||||
\(41\) | 0.270882i | 0.0423047i | 0.999776 | + | 0.0211524i | \(0.00673350\pi\) | ||||
−0.999776 | + | 0.0211524i | \(0.993266\pi\) | |||||||
\(42\) | 3.18360 | 0.491240 | ||||||||
\(43\) | 0.302660i | 0.0461552i | 0.999734 | + | 0.0230776i | \(0.00734648\pi\) | ||||
−0.999734 | + | 0.0230776i | \(0.992654\pi\) | |||||||
\(44\) | 4.27563i | 0.644576i | ||||||||
\(45\) | −0.0749790 | + | 0.108846i | −0.0111772 | + | 0.0162258i | ||||
\(46\) | 8.90184 | 1.31250 | ||||||||
\(47\) | −3.17973 | + | 3.17973i | −0.463811 | + | 0.463811i | −0.899902 | − | 0.436091i | \(-0.856362\pi\) |
0.436091 | + | 0.899902i | \(0.356362\pi\) | |||||||
\(48\) | 1.23675 | − | 1.23675i | 0.178510 | − | 0.178510i | ||||
\(49\) | 3.68685i | 0.526692i | ||||||||
\(50\) | −4.67171 | + | 1.78188i | −0.660680 | + | 0.251996i | ||||
\(51\) | 2.62341 | − | 2.62341i | 0.367351 | − | 0.367351i | ||||
\(52\) | 1.50964i | 0.209350i | ||||||||
\(53\) | 9.71066 | + | 9.71066i | 1.33386 | + | 1.33386i | 0.901884 | + | 0.431978i | \(0.142184\pi\) |
0.431978 | + | 0.901884i | \(0.357816\pi\) | |||||||
\(54\) | −3.63715 | + | 3.63715i | −0.494954 | + | 0.494954i | ||||
\(55\) | −5.42359 | + | 7.87337i | −0.731316 | + | 1.06164i | ||||
\(56\) | −1.28708 | − | 1.28708i | −0.171993 | − | 0.171993i | ||||
\(57\) | − | 0.944780i | − | 0.125139i | ||||||
\(58\) | 0.279903 | − | 0.279903i | 0.0367531 | − | 0.0367531i | ||||
\(59\) | 4.06655 | − | 4.06655i | 0.529420 | − | 0.529420i | −0.390979 | − | 0.920399i | \(-0.627864\pi\) |
0.920399 | + | 0.390979i | \(0.127864\pi\) | |||||||
\(60\) | 3.84622 | − | 0.708613i | 0.496545 | − | 0.0914815i | ||||
\(61\) | 4.47102 | − | 4.47102i | 0.572455 | − | 0.572455i | −0.360359 | − | 0.932814i | \(-0.617346\pi\) |
0.932814 | + | 0.360359i | \(0.117346\pi\) | |||||||
\(62\) | −1.59328 | − | 1.59328i | −0.202347 | − | 0.202347i | ||||
\(63\) | −0.0760780 | − | 0.0760780i | −0.00958493 | − | 0.00958493i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −1.91496 | + | 2.77993i | −0.237522 | + | 0.344808i | ||||
\(66\) | 5.28790 | − | 5.28790i | 0.650895 | − | 0.650895i | ||||
\(67\) | 6.17649 | + | 6.17649i | 0.754578 | + | 0.754578i | 0.975330 | − | 0.220752i | \(-0.0708510\pi\) |
−0.220752 | + | 0.975330i | \(0.570851\pi\) | |||||||
\(68\) | −2.12121 | −0.257235 | ||||||||
\(69\) | −11.0094 | − | 11.0094i | −1.32537 | − | 1.32537i | ||||
\(70\) | −0.737449 | − | 4.00274i | −0.0881420 | − | 0.478419i | ||||
\(71\) | −7.90805 | −0.938513 | −0.469256 | − | 0.883062i | \(-0.655478\pi\) | ||||
−0.469256 | + | 0.883062i | \(0.655478\pi\) | |||||||
\(72\) | −0.0591090 | −0.00696606 | ||||||||
\(73\) | −8.32545 | + | 8.32545i | −0.974420 | + | 0.974420i | −0.999681 | − | 0.0252606i | \(-0.991958\pi\) |
0.0252606 | + | 0.999681i | \(0.491958\pi\) | |||||||
\(74\) | −5.63727 | − | 2.28498i | −0.655320 | − | 0.265624i | ||||
\(75\) | 7.98149 | + | 3.57401i | 0.921623 | + | 0.412691i | ||||
\(76\) | −0.381960 | + | 0.381960i | −0.0438138 | + | 0.0438138i | ||||
\(77\) | −5.50309 | − | 5.50309i | −0.627135 | − | 0.627135i | ||||
\(78\) | 1.86705 | − | 1.86705i | 0.211402 | − | 0.211402i | ||||
\(79\) | 2.20061 | − | 2.20061i | 0.247588 | − | 0.247588i | −0.572392 | − | 0.819980i | \(-0.693984\pi\) |
0.819980 | + | 0.572392i | \(0.193984\pi\) | |||||||
\(80\) | −1.84145 | − | 1.26849i | −0.205880 | − | 0.141821i | ||||
\(81\) | 9.17383 | 1.01931 | ||||||||
\(82\) | −0.270882 | −0.0299139 | ||||||||
\(83\) | 10.1305 | + | 10.1305i | 1.11197 | + | 1.11197i | 0.992884 | + | 0.119087i | \(0.0379968\pi\) |
0.119087 | + | 0.992884i | \(0.462003\pi\) | |||||||
\(84\) | 3.18360i | 0.347359i | ||||||||
\(85\) | −3.90611 | − | 2.69073i | −0.423677 | − | 0.291851i | ||||
\(86\) | −0.302660 | −0.0326367 | ||||||||
\(87\) | −0.692342 | −0.0742268 | ||||||||
\(88\) | −4.27563 | −0.455784 | ||||||||
\(89\) | −5.24983 | − | 5.24983i | −0.556481 | − | 0.556481i | 0.371823 | − | 0.928304i | \(-0.378733\pi\) |
−0.928304 | + | 0.371823i | \(0.878733\pi\) | |||||||
\(90\) | −0.108846 | − | 0.0749790i | −0.0114734 | − | 0.00790348i | ||||
\(91\) | −1.94303 | − | 1.94303i | −0.203685 | − | 0.203685i | ||||
\(92\) | 8.90184i | 0.928081i | ||||||||
\(93\) | 3.94099i | 0.408662i | ||||||||
\(94\) | −3.17973 | − | 3.17973i | −0.327964 | − | 0.327964i | ||||
\(95\) | −1.18787 | + | 0.218849i | −0.121873 | + | 0.0224534i | ||||
\(96\) | 1.23675 | + | 1.23675i | 0.126225 | + | 0.126225i | ||||
\(97\) | −12.2566 | −1.24447 | −0.622237 | − | 0.782829i | \(-0.713776\pi\) | ||||
−0.622237 | + | 0.782829i | \(0.713776\pi\) | |||||||
\(98\) | −3.68685 | −0.372428 | ||||||||
\(99\) | −0.252728 | −0.0254001 | ||||||||
\(100\) | −1.78188 | − | 4.67171i | −0.178188 | − | 0.467171i | ||||
\(101\) | − | 19.3052i | − | 1.92094i | −0.278383 | − | 0.960470i | \(-0.589798\pi\) | ||
0.278383 | − | 0.960470i | \(-0.410202\pi\) | |||||||
\(102\) | 2.62341 | + | 2.62341i | 0.259757 | + | 0.259757i | ||||
\(103\) | 10.5846 | 1.04293 | 0.521466 | − | 0.853272i | \(-0.325385\pi\) | ||||
0.521466 | + | 0.853272i | \(0.325385\pi\) | |||||||
\(104\) | −1.50964 | −0.148033 | ||||||||
\(105\) | −4.03835 | + | 5.86244i | −0.394103 | + | 0.572115i | ||||
\(106\) | −9.71066 | + | 9.71066i | −0.943183 | + | 0.943183i | ||||
\(107\) | 2.77915 | − | 2.77915i | 0.268670 | − | 0.268670i | −0.559894 | − | 0.828564i | \(-0.689158\pi\) |
0.828564 | + | 0.559894i | \(0.189158\pi\) | |||||||
\(108\) | −3.63715 | − | 3.63715i | −0.349985 | − | 0.349985i | ||||
\(109\) | −4.14598 | + | 4.14598i | −0.397113 | + | 0.397113i | −0.877213 | − | 0.480101i | \(-0.840600\pi\) |
0.480101 | + | 0.877213i | \(0.340600\pi\) | |||||||
\(110\) | −7.87337 | − | 5.42359i | −0.750696 | − | 0.517119i | ||||
\(111\) | 4.14595 | + | 9.79786i | 0.393516 | + | 0.929972i | ||||
\(112\) | 1.28708 | − | 1.28708i | 0.121618 | − | 0.121618i | ||||
\(113\) | −2.26739 | −0.213298 | −0.106649 | − | 0.994297i | \(-0.534012\pi\) | ||||
−0.106649 | + | 0.994297i | \(0.534012\pi\) | |||||||
\(114\) | 0.944780 | 0.0884867 | ||||||||
\(115\) | −11.2919 | + | 16.3923i | −1.05297 | + | 1.52859i | ||||
\(116\) | 0.279903 | + | 0.279903i | 0.0259884 | + | 0.0259884i | ||||
\(117\) | −0.0892335 | −0.00824964 | ||||||||
\(118\) | 4.06655 | + | 4.06655i | 0.374356 | + | 0.374356i | ||||
\(119\) | 2.73017 | − | 2.73017i | 0.250275 | − | 0.250275i | ||||
\(120\) | 0.708613 | + | 3.84622i | 0.0646872 | + | 0.351110i | ||||
\(121\) | −7.28104 | −0.661913 | ||||||||
\(122\) | 4.47102 | + | 4.47102i | 0.404787 | + | 0.404787i | ||||
\(123\) | 0.335014 | + | 0.335014i | 0.0302072 | + | 0.0302072i | ||||
\(124\) | 1.59328 | − | 1.59328i | 0.143081 | − | 0.143081i | ||||
\(125\) | 2.64477 | − | 10.8630i | 0.236555 | − | 0.971618i | ||||
\(126\) | 0.0760780 | − | 0.0760780i | 0.00677757 | − | 0.00677757i | ||||
\(127\) | −7.95386 | + | 7.95386i | −0.705791 | + | 0.705791i | −0.965647 | − | 0.259857i | \(-0.916325\pi\) |
0.259857 | + | 0.965647i | \(0.416325\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0.374315 | + | 0.374315i | 0.0329566 | + | 0.0329566i | ||||
\(130\) | −2.77993 | − | 1.91496i | −0.243816 | − | 0.167954i | ||||
\(131\) | −6.31669 | + | 6.31669i | −0.551892 | + | 0.551892i | −0.926987 | − | 0.375095i | \(-0.877610\pi\) |
0.375095 | + | 0.926987i | \(0.377610\pi\) | |||||||
\(132\) | 5.28790 | + | 5.28790i | 0.460252 | + | 0.460252i | ||||
\(133\) | − | 0.983227i | − | 0.0852566i | ||||||
\(134\) | −6.17649 | + | 6.17649i | −0.533567 | + | 0.533567i | ||||
\(135\) | −2.08395 | − | 11.3113i | −0.179358 | − | 0.973523i | ||||
\(136\) | − | 2.12121i | − | 0.181893i | ||||||
\(137\) | −3.53660 | + | 3.53660i | −0.302152 | + | 0.302152i | −0.841855 | − | 0.539703i | \(-0.818536\pi\) |
0.539703 | + | 0.841855i | \(0.318536\pi\) | |||||||
\(138\) | 11.0094 | − | 11.0094i | 0.937179 | − | 0.937179i | ||||
\(139\) | 5.70896 | 0.484228 | 0.242114 | − | 0.970248i | \(-0.422159\pi\) | ||||
0.242114 | + | 0.970248i | \(0.422159\pi\) | |||||||
\(140\) | 4.00274 | − | 0.737449i | 0.338293 | − | 0.0623258i | ||||
\(141\) | 7.86507i | 0.662358i | ||||||||
\(142\) | − | 7.90805i | − | 0.663629i | ||||||
\(143\) | −6.45468 | −0.539768 | ||||||||
\(144\) | − | 0.0591090i | − | 0.00492575i | ||||||
\(145\) | 0.160374 | + | 0.870482i | 0.0133184 | + | 0.0722896i | ||||
\(146\) | −8.32545 | − | 8.32545i | −0.689019 | − | 0.689019i | ||||
\(147\) | 4.55971 | + | 4.55971i | 0.376079 | + | 0.376079i | ||||
\(148\) | 2.28498 | − | 5.63727i | 0.187824 | − | 0.463381i | ||||
\(149\) | − | 7.36973i | − | 0.603752i | −0.953347 | − | 0.301876i | \(-0.902387\pi\) | ||
0.953347 | − | 0.301876i | \(-0.0976129\pi\) | |||||||
\(150\) | −3.57401 | + | 7.98149i | −0.291817 | + | 0.651686i | ||||
\(151\) | − | 4.96769i | − | 0.404265i | −0.979358 | − | 0.202132i | \(-0.935213\pi\) | ||
0.979358 | − | 0.202132i | \(-0.0647871\pi\) | |||||||
\(152\) | −0.381960 | − | 0.381960i | −0.0309811 | − | 0.0309811i | ||||
\(153\) | − | 0.125383i | − | 0.0101366i | ||||||
\(154\) | 5.50309 | − | 5.50309i | 0.443451 | − | 0.443451i | ||||
\(155\) | 4.95501 | − | 0.912892i | 0.397996 | − | 0.0733252i | ||||
\(156\) | 1.86705 | + | 1.86705i | 0.149484 | + | 0.149484i | ||||
\(157\) | 8.28379 | − | 8.28379i | 0.661119 | − | 0.661119i | −0.294525 | − | 0.955644i | \(-0.595161\pi\) |
0.955644 | + | 0.294525i | \(0.0951615\pi\) | |||||||
\(158\) | 2.20061 | + | 2.20061i | 0.175071 | + | 0.175071i | ||||
\(159\) | 24.0194 | 1.90486 | ||||||||
\(160\) | 1.26849 | − | 1.84145i | 0.100283 | − | 0.145579i | ||||
\(161\) | −11.4574 | − | 11.4574i | −0.902968 | − | 0.902968i | ||||
\(162\) | 9.17383i | 0.720764i | ||||||||
\(163\) | 19.2629 | 1.50879 | 0.754394 | − | 0.656422i | \(-0.227931\pi\) | ||||
0.754394 | + | 0.656422i | \(0.227931\pi\) | |||||||
\(164\) | − | 0.270882i | − | 0.0211524i | ||||||
\(165\) | 3.02977 | + | 16.4450i | 0.235867 | + | 1.28024i | ||||
\(166\) | −10.1305 | + | 10.1305i | −0.786282 | + | 0.786282i | ||||
\(167\) | 22.3611 | 1.73036 | 0.865178 | − | 0.501466i | \(-0.167206\pi\) | ||||
0.865178 | + | 0.501466i | \(0.167206\pi\) | |||||||
\(168\) | −3.18360 | −0.245620 | ||||||||
\(169\) | 10.7210 | 0.824690 | ||||||||
\(170\) | 2.69073 | − | 3.90611i | 0.206370 | − | 0.299585i | ||||
\(171\) | −0.0225773 | − | 0.0225773i | −0.00172653 | − | 0.00172653i | ||||
\(172\) | − | 0.302660i | − | 0.0230776i | ||||||
\(173\) | 6.44977 | − | 6.44977i | 0.490367 | − | 0.490367i | −0.418055 | − | 0.908422i | \(-0.637288\pi\) |
0.908422 | + | 0.418055i | \(0.137288\pi\) | |||||||
\(174\) | − | 0.692342i | − | 0.0524863i | ||||||
\(175\) | 8.30629 | + | 3.71945i | 0.627897 | + | 0.281164i | ||||
\(176\) | − | 4.27563i | − | 0.322288i | ||||||
\(177\) | − | 10.0586i | − | 0.756053i | ||||||
\(178\) | 5.24983 | − | 5.24983i | 0.393492 | − | 0.393492i | ||||
\(179\) | 8.44973 | + | 8.44973i | 0.631562 | + | 0.631562i | 0.948460 | − | 0.316897i | \(-0.102641\pi\) |
−0.316897 | + | 0.948460i | \(0.602641\pi\) | |||||||
\(180\) | 0.0749790 | − | 0.108846i | 0.00558860 | − | 0.00811292i | ||||
\(181\) | 1.63147 | 0.121266 | 0.0606330 | − | 0.998160i | \(-0.480688\pi\) | ||||
0.0606330 | + | 0.998160i | \(0.480688\pi\) | |||||||
\(182\) | 1.94303 | − | 1.94303i | 0.144027 | − | 0.144027i | ||||
\(183\) | − | 11.0591i | − | 0.817511i | ||||||
\(184\) | −8.90184 | −0.656252 | ||||||||
\(185\) | 11.3585 | − | 7.48229i | 0.835093 | − | 0.550109i | ||||
\(186\) | −3.94099 | −0.288967 | ||||||||
\(187\) | − | 9.06953i | − | 0.663230i | ||||||
\(188\) | 3.17973 | − | 3.17973i | 0.231905 | − | 0.231905i | ||||
\(189\) | 9.36262 | 0.681030 | ||||||||
\(190\) | −0.218849 | − | 1.18787i | −0.0158770 | − | 0.0861773i | ||||
\(191\) | −14.3915 | − | 14.3915i | −1.04133 | − | 1.04133i | −0.999108 | − | 0.0422206i | \(-0.986557\pi\) |
−0.0422206 | − | 0.999108i | \(-0.513443\pi\) | |||||||
\(192\) | −1.23675 | + | 1.23675i | −0.0892549 | + | 0.0892549i | ||||
\(193\) | − | 1.88527i | − | 0.135705i | −0.997695 | − | 0.0678525i | \(-0.978385\pi\) | ||
0.997695 | − | 0.0678525i | \(-0.0216147\pi\) | |||||||
\(194\) | − | 12.2566i | − | 0.879976i | ||||||
\(195\) | 1.06975 | + | 5.80642i | 0.0766066 | + | 0.415807i | ||||
\(196\) | − | 3.68685i | − | 0.263346i | ||||||
\(197\) | −16.9005 | + | 16.9005i | −1.20411 | + | 1.20411i | −0.231210 | + | 0.972904i | \(0.574268\pi\) |
−0.972904 | + | 0.231210i | \(0.925732\pi\) | |||||||
\(198\) | − | 0.252728i | − | 0.0179606i | ||||||
\(199\) | −6.68597 | − | 6.68597i | −0.473956 | − | 0.473956i | 0.429236 | − | 0.903192i | \(-0.358783\pi\) |
−0.903192 | + | 0.429236i | \(0.858783\pi\) | |||||||
\(200\) | 4.67171 | − | 1.78188i | 0.330340 | − | 0.125998i | ||||
\(201\) | 15.2776 | 1.07760 | ||||||||
\(202\) | 19.3052 | 1.35831 | ||||||||
\(203\) | −0.720516 | −0.0505703 | ||||||||
\(204\) | −2.62341 | + | 2.62341i | −0.183676 | + | 0.183676i | ||||
\(205\) | 0.343611 | − | 0.498816i | 0.0239988 | − | 0.0348388i | ||||
\(206\) | 10.5846i | 0.737464i | ||||||||
\(207\) | −0.526178 | −0.0365719 | ||||||||
\(208\) | − | 1.50964i | − | 0.104675i | ||||||
\(209\) | −1.63312 | − | 1.63312i | −0.112965 | − | 0.112965i | ||||
\(210\) | −5.86244 | − | 4.03835i | −0.404547 | − | 0.278673i | ||||
\(211\) | 16.4186 | 1.13030 | 0.565151 | − | 0.824987i | \(-0.308818\pi\) | ||||
0.565151 | + | 0.824987i | \(0.308818\pi\) | |||||||
\(212\) | −9.71066 | − | 9.71066i | −0.666931 | − | 0.666931i | ||||
\(213\) | −9.78029 | + | 9.78029i | −0.670135 | + | 0.670135i | ||||
\(214\) | 2.77915 | + | 2.77915i | 0.189978 | + | 0.189978i | ||||
\(215\) | 0.383920 | − | 0.557333i | 0.0261832 | − | 0.0380098i | ||||
\(216\) | 3.63715 | − | 3.63715i | 0.247477 | − | 0.247477i | ||||
\(217\) | 4.10137i | 0.278419i | ||||||||
\(218\) | −4.14598 | − | 4.14598i | −0.280801 | − | 0.280801i | ||||
\(219\) | 20.5930i | 1.39155i | ||||||||
\(220\) | 5.42359 | − | 7.87337i | 0.365658 | − | 0.530822i | ||||
\(221\) | − | 3.20228i | − | 0.215408i | ||||||
\(222\) | −9.79786 | + | 4.14595i | −0.657590 | + | 0.278258i | ||||
\(223\) | 13.7600 | + | 13.7600i | 0.921436 | + | 0.921436i | 0.997131 | − | 0.0756947i | \(-0.0241175\pi\) |
−0.0756947 | + | 0.997131i | \(0.524117\pi\) | |||||||
\(224\) | 1.28708 | + | 1.28708i | 0.0859967 | + | 0.0859967i | ||||
\(225\) | 0.276140 | − | 0.105325i | 0.0184093 | − | 0.00702167i | ||||
\(226\) | − | 2.26739i | − | 0.150825i | ||||||
\(227\) | 5.23067 | 0.347172 | 0.173586 | − | 0.984819i | \(-0.444465\pi\) | ||||
0.173586 | + | 0.984819i | \(0.444465\pi\) | |||||||
\(228\) | 0.944780i | 0.0625696i | ||||||||
\(229\) | − | 3.12544i | − | 0.206535i | −0.994654 | − | 0.103267i | \(-0.967070\pi\) | ||
0.994654 | − | 0.103267i | \(-0.0329298\pi\) | |||||||
\(230\) | −16.3923 | − | 11.2919i | −1.08088 | − | 0.744564i | ||||
\(231\) | −13.6119 | −0.895597 | ||||||||
\(232\) | −0.279903 | + | 0.279903i | −0.0183766 | + | 0.0183766i | ||||
\(233\) | 7.43576 | − | 7.43576i | 0.487133 | − | 0.487133i | −0.420268 | − | 0.907400i | \(-0.638064\pi\) |
0.907400 | + | 0.420268i | \(0.138064\pi\) | |||||||
\(234\) | − | 0.0892335i | − | 0.00583338i | ||||||
\(235\) | 9.88875 | − | 1.82187i | 0.645071 | − | 0.118845i | ||||
\(236\) | −4.06655 | + | 4.06655i | −0.264710 | + | 0.264710i | ||||
\(237\) | − | 5.44322i | − | 0.353575i | ||||||
\(238\) | 2.73017 | + | 2.73017i | 0.176971 | + | 0.176971i | ||||
\(239\) | −19.2129 | + | 19.2129i | −1.24278 | + | 1.24278i | −0.283939 | + | 0.958842i | \(0.591641\pi\) |
−0.958842 | + | 0.283939i | \(0.908359\pi\) | |||||||
\(240\) | −3.84622 | + | 0.708613i | −0.248272 | + | 0.0457407i | ||||
\(241\) | 19.0019 | + | 19.0019i | 1.22402 | + | 1.22402i | 0.966190 | + | 0.257830i | \(0.0830073\pi\) |
0.257830 | + | 0.966190i | \(0.416993\pi\) | |||||||
\(242\) | − | 7.28104i | − | 0.468043i | ||||||
\(243\) | 0.434298 | − | 0.434298i | 0.0278602 | − | 0.0278602i | ||||
\(244\) | −4.47102 | + | 4.47102i | −0.286228 | + | 0.286228i | ||||
\(245\) | 4.67672 | − | 6.78914i | 0.298785 | − | 0.433743i | ||||
\(246\) | −0.335014 | + | 0.335014i | −0.0213597 | + | 0.0213597i | ||||
\(247\) | −0.576624 | − | 0.576624i | −0.0366897 | − | 0.0366897i | ||||
\(248\) | 1.59328 | + | 1.59328i | 0.101174 | + | 0.101174i | ||||
\(249\) | 25.0579 | 1.58798 | ||||||||
\(250\) | 10.8630 | + | 2.64477i | 0.687038 | + | 0.167270i | ||||
\(251\) | −2.56669 | + | 2.56669i | −0.162008 | + | 0.162008i | −0.783456 | − | 0.621448i | \(-0.786545\pi\) |
0.621448 | + | 0.783456i | \(0.286545\pi\) | |||||||
\(252\) | 0.0760780 | + | 0.0760780i | 0.00479246 | + | 0.00479246i | ||||
\(253\) | −38.0610 | −2.39287 | ||||||||
\(254\) | −7.95386 | − | 7.95386i | −0.499069 | − | 0.499069i | ||||
\(255\) | −8.15865 | + | 1.50312i | −0.510915 | + | 0.0941289i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −13.8993 | −0.867015 | −0.433507 | − | 0.901150i | \(-0.642724\pi\) | ||||
−0.433507 | + | 0.901150i | \(0.642724\pi\) | |||||||
\(258\) | −0.374315 | + | 0.374315i | −0.0233038 | + | 0.0233038i | ||||
\(259\) | 4.31467 | + | 10.1966i | 0.268100 | + | 0.633585i | ||||
\(260\) | 1.91496 | − | 2.77993i | 0.118761 | − | 0.172404i | ||||
\(261\) | −0.0165448 | + | 0.0165448i | −0.00102410 | + | 0.00102410i | ||||
\(262\) | −6.31669 | − | 6.31669i | −0.390246 | − | 0.390246i | ||||
\(263\) | −14.2273 | + | 14.2273i | −0.877290 | + | 0.877290i | −0.993253 | − | 0.115964i | \(-0.963004\pi\) |
0.115964 | + | 0.993253i | \(0.463004\pi\) | |||||||
\(264\) | −5.28790 | + | 5.28790i | −0.325448 | + | 0.325448i | ||||
\(265\) | −5.56385 | − | 30.1996i | −0.341784 | − | 1.85514i | ||||
\(266\) | 0.983227 | 0.0602855 | ||||||||
\(267\) | −12.9855 | −0.794699 | ||||||||
\(268\) | −6.17649 | − | 6.17649i | −0.377289 | − | 0.377289i | ||||
\(269\) | − | 21.4303i | − | 1.30663i | −0.757086 | − | 0.653315i | \(-0.773378\pi\) | ||
0.757086 | − | 0.653315i | \(-0.226622\pi\) | |||||||
\(270\) | 11.3113 | − | 2.08395i | 0.688385 | − | 0.126825i | ||||
\(271\) | −17.5063 | −1.06343 | −0.531717 | − | 0.846922i | \(-0.678453\pi\) | ||||
−0.531717 | + | 0.846922i | \(0.678453\pi\) | |||||||
\(272\) | 2.12121 | 0.128617 | ||||||||
\(273\) | −4.80610 | −0.290878 | ||||||||
\(274\) | −3.53660 | − | 3.53660i | −0.213654 | − | 0.213654i | ||||
\(275\) | 19.9745 | − | 7.61866i | 1.20451 | − | 0.459422i | ||||
\(276\) | 11.0094 | + | 11.0094i | 0.662686 | + | 0.662686i | ||||
\(277\) | 9.92772i | 0.596499i | 0.954488 | + | 0.298249i | \(0.0964027\pi\) | ||||
−0.954488 | + | 0.298249i | \(0.903597\pi\) | |||||||
\(278\) | 5.70896i | 0.342401i | ||||||||
\(279\) | 0.0941773 | + | 0.0941773i | 0.00563825 | + | 0.00563825i | ||||
\(280\) | 0.737449 | + | 4.00274i | 0.0440710 | + | 0.239210i | ||||
\(281\) | 9.25821 | + | 9.25821i | 0.552299 | + | 0.552299i | 0.927104 | − | 0.374805i | \(-0.122290\pi\) |
−0.374805 | + | 0.927104i | \(0.622290\pi\) | |||||||
\(282\) | −7.86507 | −0.468358 | ||||||||
\(283\) | 7.32826 | 0.435620 | 0.217810 | − | 0.975991i | \(-0.430109\pi\) | ||||
0.217810 | + | 0.975991i | \(0.430109\pi\) | |||||||
\(284\) | 7.90805 | 0.469256 | ||||||||
\(285\) | −1.19844 | + | 1.73976i | −0.0709895 | + | 0.103055i | ||||
\(286\) | − | 6.45468i | − | 0.381673i | ||||||
\(287\) | 0.348647 | + | 0.348647i | 0.0205800 | + | 0.0205800i | ||||
\(288\) | 0.0591090 | 0.00348303 | ||||||||
\(289\) | −12.5005 | −0.735321 | ||||||||
\(290\) | −0.870482 | + | 0.160374i | −0.0511165 | + | 0.00941750i | ||||
\(291\) | −15.1584 | + | 15.1584i | −0.888603 | + | 0.888603i | ||||
\(292\) | 8.32545 | − | 8.32545i | 0.487210 | − | 0.487210i | ||||
\(293\) | −12.6098 | − | 12.6098i | −0.736675 | − | 0.736675i | 0.235258 | − | 0.971933i | \(-0.424406\pi\) |
−0.971933 | + | 0.235258i | \(0.924406\pi\) | |||||||
\(294\) | −4.55971 | + | 4.55971i | −0.265928 | + | 0.265928i | ||||
\(295\) | −12.6467 | + | 2.32998i | −0.736321 | + | 0.135657i | ||||
\(296\) | 5.63727 | + | 2.28498i | 0.327660 | + | 0.132812i | ||||
\(297\) | 15.5511 | − | 15.5511i | 0.902368 | − | 0.902368i | ||||
\(298\) | 7.36973 | 0.426917 | ||||||||
\(299\) | −13.4386 | −0.777175 | ||||||||
\(300\) | −7.98149 | − | 3.57401i | −0.460812 | − | 0.206345i | ||||
\(301\) | 0.389548 | + | 0.389548i | 0.0224532 | + | 0.0224532i | ||||
\(302\) | 4.96769 | 0.285858 | ||||||||
\(303\) | −23.8758 | − | 23.8758i | −1.37163 | − | 1.37163i | ||||
\(304\) | 0.381960 | − | 0.381960i | 0.0219069 | − | 0.0219069i | ||||
\(305\) | −13.9046 | + | 2.56173i | −0.796174 | + | 0.146684i | ||||
\(306\) | 0.125383 | 0.00716765 | ||||||||
\(307\) | −17.0291 | − | 17.0291i | −0.971903 | − | 0.971903i | 0.0277133 | − | 0.999616i | \(-0.491177\pi\) |
−0.999616 | + | 0.0277133i | \(0.991177\pi\) | |||||||
\(308\) | 5.50309 | + | 5.50309i | 0.313567 | + | 0.313567i | ||||
\(309\) | 13.0905 | − | 13.0905i | 0.744694 | − | 0.744694i | ||||
\(310\) | 0.912892 | + | 4.95501i | 0.0518488 | + | 0.281426i | ||||
\(311\) | 3.74670 | − | 3.74670i | 0.212456 | − | 0.212456i | −0.592854 | − | 0.805310i | \(-0.701999\pi\) |
0.805310 | + | 0.592854i | \(0.201999\pi\) | |||||||
\(312\) | −1.86705 | + | 1.86705i | −0.105701 | + | 0.105701i | ||||
\(313\) | 14.7056i | 0.831208i | 0.909546 | + | 0.415604i | \(0.136430\pi\) | ||||
−0.909546 | + | 0.415604i | \(0.863570\pi\) | |||||||
\(314\) | 8.28379 | + | 8.28379i | 0.467481 | + | 0.467481i | ||||
\(315\) | 0.0435899 | + | 0.236598i | 0.00245601 | + | 0.0133308i | ||||
\(316\) | −2.20061 | + | 2.20061i | −0.123794 | + | 0.123794i | ||||
\(317\) | −13.6458 | − | 13.6458i | −0.766423 | − | 0.766423i | 0.211052 | − | 0.977475i | \(-0.432311\pi\) |
−0.977475 | + | 0.211052i | \(0.932311\pi\) | |||||||
\(318\) | 24.0194i | 1.34694i | ||||||||
\(319\) | −1.19676 | + | 1.19676i | −0.0670059 | + | 0.0670059i | ||||
\(320\) | 1.84145 | + | 1.26849i | 0.102940 | + | 0.0709106i | ||||
\(321\) | − | 6.87423i | − | 0.383682i | ||||||
\(322\) | 11.4574 | − | 11.4574i | 0.638495 | − | 0.638495i | ||||
\(323\) | 0.810219 | − | 0.810219i | 0.0450818 | − | 0.0450818i | ||||
\(324\) | −9.17383 | −0.509657 | ||||||||
\(325\) | 7.05262 | − | 2.69000i | 0.391209 | − | 0.149214i | ||||
\(326\) | 19.2629i | 1.06687i | ||||||||
\(327\) | 10.2551i | 0.567108i | ||||||||
\(328\) | 0.270882 | 0.0149570 | ||||||||
\(329\) | 8.18513i | 0.451261i | ||||||||
\(330\) | −16.4450 | + | 3.02977i | −0.905269 | + | 0.166783i | ||||
\(331\) | −15.5423 | − | 15.5423i | −0.854280 | − | 0.854280i | 0.136377 | − | 0.990657i | \(-0.456454\pi\) |
−0.990657 | + | 0.136377i | \(0.956454\pi\) | |||||||
\(332\) | −10.1305 | − | 10.1305i | −0.555985 | − | 0.555985i | ||||
\(333\) | 0.333213 | + | 0.135063i | 0.0182600 | + | 0.00740141i | ||||
\(334\) | 22.3611i | 1.22355i | ||||||||
\(335\) | −3.53890 | − | 19.2085i | −0.193351 | − | 1.04947i | ||||
\(336\) | − | 3.18360i | − | 0.173680i | ||||||
\(337\) | −14.8294 | − | 14.8294i | −0.807811 | − | 0.807811i | 0.176491 | − | 0.984302i | \(-0.443525\pi\) |
−0.984302 | + | 0.176491i | \(0.943525\pi\) | |||||||
\(338\) | 10.7210i | 0.583144i | ||||||||
\(339\) | −2.80420 | + | 2.80420i | −0.152303 | + | 0.152303i | ||||
\(340\) | 3.90611 | + | 2.69073i | 0.211838 | + | 0.145925i | ||||
\(341\) | 6.81229 | + | 6.81229i | 0.368906 | + | 0.368906i | ||||
\(342\) | 0.0225773 | − | 0.0225773i | 0.00122084 | − | 0.00122084i | ||||
\(343\) | 13.7548 | + | 13.7548i | 0.742691 | + | 0.742691i | ||||
\(344\) | 0.302660 | 0.0163183 | ||||||||
\(345\) | 6.30795 | + | 34.2384i | 0.339609 | + | 1.84334i | ||||
\(346\) | 6.44977 | + | 6.44977i | 0.346742 | + | 0.346742i | ||||
\(347\) | 8.24738i | 0.442742i | 0.975190 | + | 0.221371i | \(0.0710532\pi\) | ||||
−0.975190 | + | 0.221371i | \(0.928947\pi\) | |||||||
\(348\) | 0.692342 | 0.0371134 | ||||||||
\(349\) | 16.1967i | 0.866991i | 0.901156 | + | 0.433496i | \(0.142720\pi\) | ||||
−0.901156 | + | 0.433496i | \(0.857280\pi\) | |||||||
\(350\) | −3.71945 | + | 8.30629i | −0.198813 | + | 0.443990i | ||||
\(351\) | 5.49080 | − | 5.49080i | 0.293077 | − | 0.293077i | ||||
\(352\) | 4.27563 | 0.227892 | ||||||||
\(353\) | −20.3765 | −1.08453 | −0.542266 | − | 0.840207i | \(-0.682433\pi\) | ||||
−0.542266 | + | 0.840207i | \(0.682433\pi\) | |||||||
\(354\) | 10.0586 | 0.534610 | ||||||||
\(355\) | 14.5623 | + | 10.0313i | 0.772885 | + | 0.532404i | ||||
\(356\) | 5.24983 | + | 5.24983i | 0.278241 | + | 0.278241i | ||||
\(357\) | − | 6.75309i | − | 0.357411i | ||||||
\(358\) | −8.44973 | + | 8.44973i | −0.446582 | + | 0.446582i | ||||
\(359\) | 30.2708i | 1.59763i | 0.601575 | + | 0.798816i | \(0.294540\pi\) | ||||
−0.601575 | + | 0.798816i | \(0.705460\pi\) | |||||||
\(360\) | 0.108846 | + | 0.0749790i | 0.00573670 | + | 0.00395174i | ||||
\(361\) | 18.7082i | 0.984643i | ||||||||
\(362\) | 1.63147i | 0.0857480i | ||||||||
\(363\) | −9.00484 | + | 9.00484i | −0.472632 | + | 0.472632i | ||||
\(364\) | 1.94303 | + | 1.94303i | 0.101843 | + | 0.101843i | ||||
\(365\) | 25.8916 | − | 4.77017i | 1.35523 | − | 0.249682i | ||||
\(366\) | 11.0591 | 0.578067 | ||||||||
\(367\) | 13.0615 | − | 13.0615i | 0.681804 | − | 0.681804i | −0.278603 | − | 0.960406i | \(-0.589871\pi\) |
0.960406 | + | 0.278603i | \(0.0898713\pi\) | |||||||
\(368\) | − | 8.90184i | − | 0.464040i | ||||||
\(369\) | 0.0160116 | 0.000833529 | ||||||||
\(370\) | 7.48229 | + | 11.3585i | 0.388986 | + | 0.590500i | ||||
\(371\) | 24.9968 | 1.29777 | ||||||||
\(372\) | − | 3.94099i | − | 0.204331i | ||||||
\(373\) | 16.1154 | − | 16.1154i | 0.834423 | − | 0.834423i | −0.153695 | − | 0.988118i | \(-0.549117\pi\) |
0.988118 | + | 0.153695i | \(0.0491174\pi\) | |||||||
\(374\) | 9.06953 | 0.468974 | ||||||||
\(375\) | −10.1639 | − | 16.7058i | −0.524863 | − | 0.862683i | ||||
\(376\) | 3.17973 | + | 3.17973i | 0.163982 | + | 0.163982i | ||||
\(377\) | −0.422554 | + | 0.422554i | −0.0217627 | + | 0.0217627i | ||||
\(378\) | 9.36262i | 0.481561i | ||||||||
\(379\) | − | 7.07736i | − | 0.363539i | −0.983341 | − | 0.181770i | \(-0.941817\pi\) | ||
0.983341 | − | 0.181770i | \(-0.0581825\pi\) | |||||||
\(380\) | 1.18787 | − | 0.218849i | 0.0609366 | − | 0.0112267i | ||||
\(381\) | 19.6739i | 1.00792i | ||||||||
\(382\) | 14.3915 | − | 14.3915i | 0.736331 | − | 0.736331i | ||||
\(383\) | − | 17.6507i | − | 0.901911i | −0.892546 | − | 0.450955i | \(-0.851083\pi\) | ||
0.892546 | − | 0.450955i | \(-0.148917\pi\) | |||||||
\(384\) | −1.23675 | − | 1.23675i | −0.0631127 | − | 0.0631127i | ||||
\(385\) | 3.15306 | + | 17.1143i | 0.160695 | + | 0.872223i | ||||
\(386\) | 1.88527 | 0.0959579 | ||||||||
\(387\) | 0.0178899 | 0.000909395 | ||||||||
\(388\) | 12.2566 | 0.622237 | ||||||||
\(389\) | −14.9010 | + | 14.9010i | −0.755508 | + | 0.755508i | −0.975501 | − | 0.219993i | \(-0.929397\pi\) |
0.219993 | + | 0.975501i | \(0.429397\pi\) | |||||||
\(390\) | −5.80642 | + | 1.06975i | −0.294020 | + | 0.0541690i | ||||
\(391\) | − | 18.8827i | − | 0.954939i | ||||||
\(392\) | 3.68685 | 0.186214 | ||||||||
\(393\) | 15.6244i | 0.788144i | ||||||||
\(394\) | −16.9005 | − | 16.9005i | −0.851437 | − | 0.851437i | ||||
\(395\) | −6.84376 | + | 1.26087i | −0.344347 | + | 0.0634412i | ||||
\(396\) | 0.252728 | 0.0127001 | ||||||||
\(397\) | 3.61759 | + | 3.61759i | 0.181562 | + | 0.181562i | 0.792036 | − | 0.610474i | \(-0.209021\pi\) |
−0.610474 | + | 0.792036i | \(0.709021\pi\) | |||||||
\(398\) | 6.68597 | − | 6.68597i | 0.335137 | − | 0.335137i | ||||
\(399\) | −1.21601 | − | 1.21601i | −0.0608765 | − | 0.0608765i | ||||
\(400\) | 1.78188 | + | 4.67171i | 0.0890939 | + | 0.233586i | ||||
\(401\) | −12.9977 | + | 12.9977i | −0.649075 | + | 0.649075i | −0.952770 | − | 0.303694i | \(-0.901780\pi\) |
0.303694 | + | 0.952770i | \(0.401780\pi\) | |||||||
\(402\) | 15.2776i | 0.761976i | ||||||||
\(403\) | 2.40529 | + | 2.40529i | 0.119816 | + | 0.119816i | ||||
\(404\) | 19.3052i | 0.960470i | ||||||||
\(405\) | −16.8932 | − | 11.6369i | −0.839428 | − | 0.578242i | ||||
\(406\) | − | 0.720516i | − | 0.0357586i | ||||||
\(407\) | 24.1029 | + | 9.76975i | 1.19474 | + | 0.484269i | ||||
\(408\) | −2.62341 | − | 2.62341i | −0.129878 | − | 0.129878i | ||||
\(409\) | −1.73592 | − | 1.73592i | −0.0858355 | − | 0.0858355i | 0.662885 | − | 0.748721i | \(-0.269332\pi\) |
−0.748721 | + | 0.662885i | \(0.769332\pi\) | |||||||
\(410\) | 0.498816 | + | 0.343611i | 0.0246348 | + | 0.0169697i | ||||
\(411\) | 8.74779i | 0.431497i | ||||||||
\(412\) | −10.5846 | −0.521466 | ||||||||
\(413\) | − | 10.4680i | − | 0.515095i | ||||||
\(414\) | − | 0.526178i | − | 0.0258603i | ||||||
\(415\) | −5.80442 | − | 31.5053i | −0.284928 | − | 1.54654i | ||||
\(416\) | 1.50964 | 0.0740164 | ||||||||
\(417\) | 7.06057 | − | 7.06057i | 0.345758 | − | 0.345758i | ||||
\(418\) | 1.63312 | − | 1.63312i | 0.0798786 | − | 0.0798786i | ||||
\(419\) | − | 16.7428i | − | 0.817941i | −0.912548 | − | 0.408970i | \(-0.865888\pi\) | ||
0.912548 | − | 0.408970i | \(-0.134112\pi\) | |||||||
\(420\) | 4.03835 | − | 5.86244i | 0.197052 | − | 0.286058i | ||||
\(421\) | −0.463240 | + | 0.463240i | −0.0225770 | + | 0.0225770i | −0.718305 | − | 0.695728i | \(-0.755082\pi\) |
0.695728 | + | 0.718305i | \(0.255082\pi\) | |||||||
\(422\) | 16.4186i | 0.799245i | ||||||||
\(423\) | 0.187950 | + | 0.187950i | 0.00913846 | + | 0.00913846i | ||||
\(424\) | 9.71066 | − | 9.71066i | 0.471592 | − | 0.471592i | ||||
\(425\) | 3.77974 | + | 9.90970i | 0.183345 | + | 0.480691i | ||||
\(426\) | −9.78029 | − | 9.78029i | −0.473857 | − | 0.473857i | ||||
\(427\) | − | 11.5091i | − | 0.556965i | ||||||
\(428\) | −2.77915 | + | 2.77915i | −0.134335 | + | 0.134335i | ||||
\(429\) | −7.98284 | + | 7.98284i | −0.385415 | + | 0.385415i | ||||
\(430\) | 0.557333 | + | 0.383920i | 0.0268770 | + | 0.0185143i | ||||
\(431\) | −27.2475 | + | 27.2475i | −1.31247 | + | 1.31247i | −0.392877 | + | 0.919591i | \(0.628520\pi\) |
−0.919591 | + | 0.392877i | \(0.871480\pi\) | |||||||
\(432\) | 3.63715 | + | 3.63715i | 0.174993 | + | 0.174993i | ||||
\(433\) | 17.1809 | + | 17.1809i | 0.825660 | + | 0.825660i | 0.986913 | − | 0.161253i | \(-0.0515536\pi\) |
−0.161253 | + | 0.986913i | \(0.551554\pi\) | |||||||
\(434\) | −4.10137 | −0.196872 | ||||||||
\(435\) | 1.27491 | + | 0.878227i | 0.0611274 | + | 0.0421078i | ||||
\(436\) | 4.14598 | − | 4.14598i | 0.198556 | − | 0.198556i | ||||
\(437\) | −3.40015 | − | 3.40015i | −0.162651 | − | 0.162651i | ||||
\(438\) | −20.5930 | −0.983973 | ||||||||
\(439\) | −13.3023 | − | 13.3023i | −0.634886 | − | 0.634886i | 0.314404 | − | 0.949289i | \(-0.398195\pi\) |
−0.949289 | + | 0.314404i | \(0.898195\pi\) | |||||||
\(440\) | 7.87337 | + | 5.42359i | 0.375348 | + | 0.258559i | ||||
\(441\) | 0.217926 | 0.0103774 | ||||||||
\(442\) | 3.20228 | 0.152317 | ||||||||
\(443\) | −24.4725 | + | 24.4725i | −1.16272 | + | 1.16272i | −0.178845 | + | 0.983877i | \(0.557236\pi\) |
−0.983877 | + | 0.178845i | \(0.942764\pi\) | |||||||
\(444\) | −4.14595 | − | 9.79786i | −0.196758 | − | 0.464986i | ||||
\(445\) | 3.00796 | + | 16.3267i | 0.142591 | + | 0.773958i | ||||
\(446\) | −13.7600 | + | 13.7600i | −0.651554 | + | 0.651554i | ||||
\(447\) | −9.11453 | − | 9.11453i | −0.431102 | − | 0.431102i | ||||
\(448\) | −1.28708 | + | 1.28708i | −0.0608088 | + | 0.0608088i | ||||
\(449\) | 20.4966 | − | 20.4966i | 0.967296 | − | 0.967296i | −0.0321863 | − | 0.999482i | \(-0.510247\pi\) |
0.999482 | + | 0.0321863i | \(0.0102470\pi\) | |||||||
\(450\) | 0.105325 | + | 0.276140i | 0.00496507 | + | 0.0130174i | ||||
\(451\) | 1.15819 | 0.0545372 | ||||||||
\(452\) | 2.26739 | 0.106649 | ||||||||
\(453\) | −6.14380 | − | 6.14380i | −0.288661 | − | 0.288661i | ||||
\(454\) | 5.23067i | 0.245488i | ||||||||
\(455\) | 1.11329 | + | 6.04271i | 0.0521916 | + | 0.283287i | ||||
\(456\) | −0.944780 | −0.0442434 | ||||||||
\(457\) | −25.3795 | −1.18720 | −0.593601 | − | 0.804759i | \(-0.702294\pi\) | ||||
−0.593601 | + | 0.804759i | \(0.702294\pi\) | |||||||
\(458\) | 3.12544 | 0.146042 | ||||||||
\(459\) | 7.71517 | + | 7.71517i | 0.360113 | + | 0.360113i | ||||
\(460\) | 11.2919 | − | 16.3923i | 0.526486 | − | 0.764295i | ||||
\(461\) | −19.5684 | − | 19.5684i | −0.911392 | − | 0.911392i | 0.0849894 | − | 0.996382i | \(-0.472914\pi\) |
−0.996382 | + | 0.0849894i | \(0.972914\pi\) | |||||||
\(462\) | − | 13.6119i | − | 0.633283i | ||||||
\(463\) | − | 40.3494i | − | 1.87520i | −0.347720 | − | 0.937599i | \(-0.613044\pi\) | ||
0.347720 | − | 0.937599i | \(-0.386956\pi\) | |||||||
\(464\) | −0.279903 | − | 0.279903i | −0.0129942 | − | 0.0129942i | ||||
\(465\) | 4.99910 | − | 7.25714i | 0.231828 | − | 0.336542i | ||||
\(466\) | 7.43576 | + | 7.43576i | 0.344455 | + | 0.344455i | ||||
\(467\) | 6.84915 | 0.316941 | 0.158471 | − | 0.987364i | \(-0.449344\pi\) | ||||
0.158471 | + | 0.987364i | \(0.449344\pi\) | |||||||
\(468\) | 0.0892335 | 0.00412482 | ||||||||
\(469\) | 15.8993 | 0.734161 | ||||||||
\(470\) | 1.82187 | + | 9.88875i | 0.0840364 | + | 0.456134i | ||||
\(471\) | − | 20.4900i | − | 0.944129i | ||||||
\(472\) | −4.06655 | − | 4.06655i | −0.187178 | − | 0.187178i | ||||
\(473\) | 1.29406 | 0.0595011 | ||||||||
\(474\) | 5.44322 | 0.250015 | ||||||||
\(475\) | 2.46501 | + | 1.10380i | 0.113103 | + | 0.0506459i | ||||
\(476\) | −2.73017 | + | 2.73017i | −0.125137 | + | 0.125137i | ||||
\(477\) | 0.573987 | − | 0.573987i | 0.0262811 | − | 0.0262811i | ||||
\(478\) | −19.2129 | − | 19.2129i | −0.878779 | − | 0.878779i | ||||
\(479\) | 30.4703 | − | 30.4703i | 1.39222 | − | 1.39222i | 0.571895 | − | 0.820327i | \(-0.306208\pi\) |
0.820327 | − | 0.571895i | \(-0.193792\pi\) | |||||||
\(480\) | −0.708613 | − | 3.84622i | −0.0323436 | − | 0.175555i | ||||
\(481\) | 8.51028 | + | 3.44951i | 0.388035 | + | 0.157284i | ||||
\(482\) | −19.0019 | + | 19.0019i | −0.865513 | + | 0.865513i | ||||
\(483\) | −28.3399 | −1.28951 | ||||||||
\(484\) | 7.28104 | 0.330956 | ||||||||
\(485\) | 22.5700 | + | 15.5474i | 1.02485 | + | 0.705971i | ||||
\(486\) | 0.434298 | + | 0.434298i | 0.0197001 | + | 0.0197001i | ||||
\(487\) | −38.9294 | −1.76406 | −0.882029 | − | 0.471194i | \(-0.843823\pi\) | ||||
−0.882029 | + | 0.471194i | \(0.843823\pi\) | |||||||
\(488\) | −4.47102 | − | 4.47102i | −0.202393 | − | 0.202393i | ||||
\(489\) | 23.8234 | − | 23.8234i | 1.07733 | − | 1.07733i | ||||
\(490\) | 6.78914 | + | 4.67672i | 0.306702 | + | 0.211273i | ||||
\(491\) | 8.64964 | 0.390353 | 0.195176 | − | 0.980768i | \(-0.437472\pi\) | ||||
0.195176 | + | 0.980768i | \(0.437472\pi\) | |||||||
\(492\) | −0.335014 | − | 0.335014i | −0.0151036 | − | 0.0151036i | ||||
\(493\) | −0.593735 | − | 0.593735i | −0.0267405 | − | 0.0267405i | ||||
\(494\) | 0.576624 | − | 0.576624i | 0.0259435 | − | 0.0259435i | ||||
\(495\) | 0.465387 | + | 0.320583i | 0.0209176 | + | 0.0144091i | ||||
\(496\) | −1.59328 | + | 1.59328i | −0.0715405 | + | 0.0715405i | ||||
\(497\) | −10.1783 | + | 10.1783i | −0.456559 | + | 0.456559i | ||||
\(498\) | 25.0579i | 1.12287i | ||||||||
\(499\) | 10.9240 | + | 10.9240i | 0.489024 | + | 0.489024i | 0.907998 | − | 0.418974i | \(-0.137610\pi\) |
−0.418974 | + | 0.907998i | \(0.637610\pi\) | |||||||
\(500\) | −2.64477 | + | 10.8630i | −0.118278 | + | 0.485809i | ||||
\(501\) | 27.6551 | − | 27.6551i | 1.23554 | − | 1.23554i | ||||
\(502\) | −2.56669 | − | 2.56669i | −0.114557 | − | 0.114557i | ||||
\(503\) | 37.0071i | 1.65007i | 0.565085 | + | 0.825033i | \(0.308843\pi\) | ||||
−0.565085 | + | 0.825033i | \(0.691157\pi\) | |||||||
\(504\) | −0.0760780 | + | 0.0760780i | −0.00338878 | + | 0.00338878i | ||||
\(505\) | −24.4884 | + | 35.5496i | −1.08972 | + | 1.58194i | ||||
\(506\) | − | 38.0610i | − | 1.69202i | ||||||
\(507\) | 13.2592 | − | 13.2592i | 0.588861 | − | 0.588861i | ||||
\(508\) | 7.95386 | − | 7.95386i | 0.352895 | − | 0.352895i | ||||
\(509\) | −1.39333 | −0.0617583 | −0.0308791 | − | 0.999523i | \(-0.509831\pi\) | ||||
−0.0308791 | + | 0.999523i | \(0.509831\pi\) | |||||||
\(510\) | −1.50312 | − | 8.15865i | −0.0665592 | − | 0.361271i | ||||
\(511\) | 21.4311i | 0.948054i | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 2.77849 | 0.122673 | ||||||||
\(514\) | − | 13.8993i | − | 0.613072i | ||||||
\(515\) | −19.4910 | − | 13.4264i | −0.858877 | − | 0.591640i | ||||
\(516\) | −0.374315 | − | 0.374315i | −0.0164783 | − | 0.0164783i | ||||
\(517\) | 13.5953 | + | 13.5953i | 0.597923 | + | 0.597923i | ||||
\(518\) | −10.1966 | + | 4.31467i | −0.448012 | + | 0.189576i | ||||
\(519\) | − | 15.9535i | − | 0.700282i | ||||||
\(520\) | 2.77993 | + | 1.91496i | 0.121908 | + | 0.0839768i | ||||
\(521\) | − | 3.37437i | − | 0.147834i | −0.997264 | − | 0.0739169i | \(-0.976450\pi\) | ||
0.997264 | − | 0.0739169i | \(-0.0235500\pi\) | |||||||
\(522\) | −0.0165448 | − | 0.0165448i | −0.000724146 | − | 0.000724146i | ||||
\(523\) | − | 6.99302i | − | 0.305783i | −0.988243 | − | 0.152892i | \(-0.951141\pi\) | ||
0.988243 | − | 0.152892i | \(-0.0488586\pi\) | |||||||
\(524\) | 6.31669 | − | 6.31669i | 0.275946 | − | 0.275946i | ||||
\(525\) | 14.8729 | − | 5.67279i | 0.649105 | − | 0.247581i | ||||
\(526\) | −14.2273 | − | 14.2273i | −0.620338 | − | 0.620338i | ||||
\(527\) | −3.37969 | + | 3.37969i | −0.147222 | + | 0.147222i | ||||
\(528\) | −5.28790 | − | 5.28790i | −0.230126 | − | 0.230126i | ||||
\(529\) | −56.2427 | −2.44534 | ||||||||
\(530\) | 30.1996 | − | 5.56385i | 1.31179 | − | 0.241678i | ||||
\(531\) | −0.240370 | − | 0.240370i | −0.0104312 | − | 0.0104312i | ||||
\(532\) | 0.983227i | 0.0426283i | ||||||||
\(533\) | 0.408936 | 0.0177130 | ||||||||
\(534\) | − | 12.9855i | − | 0.561937i | ||||||
\(535\) | −8.64297 | + | 1.59235i | −0.373668 | + | 0.0688432i | ||||
\(536\) | 6.17649 | − | 6.17649i | 0.266784 | − | 0.266784i | ||||
\(537\) | 20.9004 | 0.901920 | ||||||||
\(538\) | 21.4303 | 0.923927 | ||||||||
\(539\) | 15.7636 | 0.678986 | ||||||||
\(540\) | 2.08395 | + | 11.3113i | 0.0896790 | + | 0.486762i | ||||
\(541\) | 3.85792 | + | 3.85792i | 0.165865 | + | 0.165865i | 0.785159 | − | 0.619294i | \(-0.212581\pi\) |
−0.619294 | + | 0.785159i | \(0.712581\pi\) | |||||||
\(542\) | − | 17.5063i | − | 0.751962i | ||||||
\(543\) | 2.01772 | − | 2.01772i | 0.0865886 | − | 0.0865886i | ||||
\(544\) | 2.12121i | 0.0909463i | ||||||||
\(545\) | 12.8937 | − | 2.37549i | 0.552307 | − | 0.101755i | ||||
\(546\) | − | 4.80610i | − | 0.205682i | ||||||
\(547\) | 5.76769i | 0.246609i | 0.992369 | + | 0.123304i | \(0.0393491\pi\) | ||||
−0.992369 | + | 0.123304i | \(0.960651\pi\) | |||||||
\(548\) | 3.53660 | − | 3.53660i | 0.151076 | − | 0.151076i | ||||
\(549\) | −0.264277 | − | 0.264277i | −0.0112791 | − | 0.0112791i | ||||
\(550\) | 7.61866 | + | 19.9745i | 0.324861 | + | 0.851717i | ||||
\(551\) | −0.213824 | −0.00910920 | ||||||||
\(552\) | −11.0094 | + | 11.0094i | −0.468590 | + | 0.468590i | ||||
\(553\) | − | 5.66473i | − | 0.240889i | ||||||
\(554\) | −9.92772 | −0.421788 | ||||||||
\(555\) | 4.79391 | − | 23.3014i | 0.203490 | − | 0.989088i | ||||
\(556\) | −5.70896 | −0.242114 | ||||||||
\(557\) | 33.4435i | 1.41705i | 0.705687 | + | 0.708524i | \(0.250639\pi\) | ||||
−0.705687 | + | 0.708524i | \(0.749361\pi\) | |||||||
\(558\) | −0.0941773 | + | 0.0941773i | −0.00398684 | + | 0.00398684i | ||||
\(559\) | 0.456909 | 0.0193252 | ||||||||
\(560\) | −4.00274 | + | 0.737449i | −0.169147 | + | 0.0311629i | ||||
\(561\) | −11.2168 | − | 11.2168i | −0.473572 | − | 0.473572i | ||||
\(562\) | −9.25821 | + | 9.25821i | −0.390534 | + | 0.390534i | ||||
\(563\) | 14.9840i | 0.631500i | 0.948842 | + | 0.315750i | \(0.102256\pi\) | ||||
−0.948842 | + | 0.315750i | \(0.897744\pi\) | |||||||
\(564\) | − | 7.86507i | − | 0.331179i | ||||||
\(565\) | 4.17529 | + | 2.87616i | 0.175656 | + | 0.121001i | ||||
\(566\) | 7.32826i | 0.308030i | ||||||||
\(567\) | 11.8075 | − | 11.8075i | 0.495867 | − | 0.495867i | ||||
\(568\) | 7.90805i | 0.331814i | ||||||||
\(569\) | −8.42505 | − | 8.42505i | −0.353197 | − | 0.353197i | 0.508101 | − | 0.861298i | \(-0.330348\pi\) |
−0.861298 | + | 0.508101i | \(0.830348\pi\) | |||||||
\(570\) | −1.73976 | − | 1.19844i | −0.0728707 | − | 0.0501972i | ||||
\(571\) | −22.3944 | −0.937176 | −0.468588 | − | 0.883417i | \(-0.655237\pi\) | ||||
−0.468588 | + | 0.883417i | \(0.655237\pi\) | |||||||
\(572\) | 6.45468 | 0.269884 | ||||||||
\(573\) | −35.5973 | −1.48710 | ||||||||
\(574\) | −0.348647 | + | 0.348647i | −0.0145523 | + | 0.0145523i | ||||
\(575\) | 41.5868 | − | 15.8620i | 1.73429 | − | 0.661491i | ||||
\(576\) | 0.0591090i | 0.00246287i | ||||||||
\(577\) | −15.1857 | −0.632189 | −0.316094 | − | 0.948728i | \(-0.602372\pi\) | ||||
−0.316094 | + | 0.948728i | \(0.602372\pi\) | |||||||
\(578\) | − | 12.5005i | − | 0.519950i | ||||||
\(579\) | −2.33162 | − | 2.33162i | −0.0968986 | − | 0.0968986i | ||||
\(580\) | −0.160374 | − | 0.870482i | −0.00665918 | − | 0.0361448i | ||||
\(581\) | 26.0776 | 1.08188 | ||||||||
\(582\) | −15.1584 | − | 15.1584i | −0.628337 | − | 0.628337i | ||||
\(583\) | 41.5192 | − | 41.5192i | 1.71955 | − | 1.71955i | ||||
\(584\) | 8.32545 | + | 8.32545i | 0.344510 | + | 0.344510i | ||||
\(585\) | 0.164319 | + | 0.113192i | 0.00679376 | + | 0.00467990i | ||||
\(586\) | 12.6098 | − | 12.6098i | 0.520908 | − | 0.520908i | ||||
\(587\) | − | 36.1936i | − | 1.49387i | −0.664898 | − | 0.746934i | \(-0.731525\pi\) | ||
0.664898 | − | 0.746934i | \(-0.268475\pi\) | |||||||
\(588\) | −4.55971 | − | 4.55971i | −0.188039 | − | 0.188039i | ||||
\(589\) | 1.21714i | 0.0501514i | ||||||||
\(590\) | −2.32998 | − | 12.6467i | −0.0959239 | − | 0.520657i | ||||
\(591\) | 41.8036i | 1.71957i | ||||||||
\(592\) | −2.28498 | + | 5.63727i | −0.0939122 | + | 0.231691i | ||||
\(593\) | 28.1253 | + | 28.1253i | 1.15497 | + | 1.15497i | 0.985543 | + | 0.169424i | \(0.0541906\pi\) |
0.169424 | + | 0.985543i | \(0.445809\pi\) | |||||||
\(594\) | 15.5511 | + | 15.5511i | 0.638070 | + | 0.638070i | ||||
\(595\) | −8.49067 | + | 1.56429i | −0.348083 | + | 0.0641295i | ||||
\(596\) | 7.36973i | 0.301876i | ||||||||
\(597\) | −16.5378 | −0.676846 | ||||||||
\(598\) | − | 13.4386i | − | 0.549545i | ||||||
\(599\) | 8.68551i | 0.354880i | 0.984132 | + | 0.177440i | \(0.0567816\pi\) | ||||
−0.984132 | + | 0.177440i | \(0.943218\pi\) | |||||||
\(600\) | 3.57401 | − | 7.98149i | 0.145908 | − | 0.325843i | ||||
\(601\) | −17.1654 | −0.700191 | −0.350095 | − | 0.936714i | \(-0.613851\pi\) | ||||
−0.350095 | + | 0.936714i | \(0.613851\pi\) | |||||||
\(602\) | −0.389548 | + | 0.389548i | −0.0158768 | + | 0.0158768i | ||||
\(603\) | 0.365086 | − | 0.365086i | 0.0148674 | − | 0.0148674i | ||||
\(604\) | 4.96769i | 0.202132i | ||||||||
\(605\) | 13.4077 | + | 9.23591i | 0.545100 | + | 0.375493i | ||||
\(606\) | 23.8758 | − | 23.8758i | 0.969886 | − | 0.969886i | ||||
\(607\) | − | 40.1612i | − | 1.63009i | −0.579395 | − | 0.815047i | \(-0.696711\pi\) | ||
0.579395 | − | 0.815047i | \(-0.303289\pi\) | |||||||
\(608\) | 0.381960 | + | 0.381960i | 0.0154905 | + | 0.0154905i | ||||
\(609\) | −0.891100 | + | 0.891100i | −0.0361092 | + | 0.0361092i | ||||
\(610\) | −2.56173 | − | 13.9046i | −0.103721 | − | 0.562980i | ||||
\(611\) | 4.80026 | + | 4.80026i | 0.194198 | + | 0.194198i | ||||
\(612\) | 0.125383i | 0.00506830i | ||||||||
\(613\) | 12.5774 | − | 12.5774i | 0.507997 | − | 0.507997i | −0.405914 | − | 0.913911i | \(-0.633047\pi\) |
0.913911 | + | 0.405914i | \(0.133047\pi\) | |||||||
\(614\) | 17.0291 | − | 17.0291i | 0.687239 | − | 0.687239i | ||||
\(615\) | −0.191951 | − | 1.04187i | −0.00774019 | − | 0.0420124i | ||||
\(616\) | −5.50309 | + | 5.50309i | −0.221726 | + | 0.221726i | ||||
\(617\) | 33.9984 | + | 33.9984i | 1.36872 | + | 1.36872i | 0.862264 | + | 0.506459i | \(0.169046\pi\) |
0.506459 | + | 0.862264i | \(0.330954\pi\) | |||||||
\(618\) | 13.0905 | + | 13.0905i | 0.526578 | + | 0.526578i | ||||
\(619\) | 5.28421 | 0.212390 | 0.106195 | − | 0.994345i | \(-0.466133\pi\) | ||||
0.106195 | + | 0.994345i | \(0.466133\pi\) | |||||||
\(620\) | −4.95501 | + | 0.912892i | −0.198998 | + | 0.0366626i | ||||
\(621\) | 32.3773 | − | 32.3773i | 1.29926 | − | 1.29926i | ||||
\(622\) | 3.74670 | + | 3.74670i | 0.150229 | + | 0.150229i | ||||
\(623\) | −13.5139 | −0.541424 | ||||||||
\(624\) | −1.86705 | − | 1.86705i | −0.0747420 | − | 0.0747420i | ||||
\(625\) | −18.6498 | + | 16.6489i | −0.745993 | + | 0.665954i | ||||
\(626\) | −14.7056 | −0.587753 | ||||||||
\(627\) | −4.03953 | −0.161323 | ||||||||
\(628\) | −8.28379 | + | 8.28379i | −0.330559 | + | 0.330559i | ||||
\(629\) | −4.84694 | + | 11.9579i | −0.193260 | + | 0.476791i | ||||
\(630\) | −0.236598 | + | 0.0435899i | −0.00942628 | + | 0.00173666i | ||||
\(631\) | −5.35861 | + | 5.35861i | −0.213323 | + | 0.213323i | −0.805677 | − | 0.592355i | \(-0.798198\pi\) |
0.592355 | + | 0.805677i | \(0.298198\pi\) | |||||||
\(632\) | −2.20061 | − | 2.20061i | −0.0875356 | − | 0.0875356i | ||||
\(633\) | 20.3057 | − | 20.3057i | 0.807080 | − | 0.807080i | ||||
\(634\) | 13.6458 | − | 13.6458i | 0.541943 | − | 0.541943i | ||||
\(635\) | 24.7360 | − | 4.55726i | 0.981618 | − | 0.180849i | ||||
\(636\) | −24.0194 | −0.952430 | ||||||||
\(637\) | 5.56582 | 0.220526 | ||||||||
\(638\) | −1.19676 | − | 1.19676i | −0.0473803 | − | 0.0473803i | ||||
\(639\) | 0.467437i | 0.0184915i | ||||||||
\(640\) | −1.26849 | + | 1.84145i | −0.0501414 | + | 0.0727897i | ||||
\(641\) | 24.0958 | 0.951727 | 0.475864 | − | 0.879519i | \(-0.342136\pi\) | ||||
0.475864 | + | 0.879519i | \(0.342136\pi\) | |||||||
\(642\) | 6.87423 | 0.271304 | ||||||||
\(643\) | 6.55586 | 0.258538 | 0.129269 | − | 0.991610i | \(-0.458737\pi\) | ||||
0.129269 | + | 0.991610i | \(0.458737\pi\) | |||||||
\(644\) | 11.4574 | + | 11.4574i | 0.451484 | + | 0.451484i | ||||
\(645\) | −0.214469 | − | 1.16410i | −0.00844469 | − | 0.0458363i | ||||
\(646\) | 0.810219 | + | 0.810219i | 0.0318776 | + | 0.0318776i | ||||
\(647\) | 6.75259i | 0.265472i | 0.991151 | + | 0.132736i | \(0.0423762\pi\) | ||||
−0.991151 | + | 0.132736i | \(0.957624\pi\) | |||||||
\(648\) | − | 9.17383i | − | 0.360382i | ||||||
\(649\) | −17.3871 | − | 17.3871i | −0.682503 | − | 0.682503i | ||||
\(650\) | 2.69000 | + | 7.05262i | 0.105511 | + | 0.276627i | ||||
\(651\) | 5.07237 | + | 5.07237i | 0.198802 | + | 0.198802i | ||||
\(652\) | −19.2629 | −0.754394 | ||||||||
\(653\) | −18.5694 | −0.726675 | −0.363338 | − | 0.931658i | \(-0.618363\pi\) | ||||
−0.363338 | + | 0.931658i | \(0.618363\pi\) | |||||||
\(654\) | −10.2551 | −0.401006 | ||||||||
\(655\) | 19.6445 | − | 3.61923i | 0.767575 | − | 0.141415i | ||||
\(656\) | 0.270882i | 0.0105762i | ||||||||
\(657\) | 0.492109 | + | 0.492109i | 0.0191990 | + | 0.0191990i | ||||
\(658\) | −8.18513 | −0.319090 | ||||||||
\(659\) | −29.5588 | −1.15145 | −0.575724 | − | 0.817644i | \(-0.695280\pi\) | ||||
−0.575724 | + | 0.817644i | \(0.695280\pi\) | |||||||
\(660\) | −3.02977 | − | 16.4450i | −0.117934 | − | 0.640122i | ||||
\(661\) | −35.1268 | + | 35.1268i | −1.36627 | + | 1.36627i | −0.500587 | + | 0.865686i | \(0.666882\pi\) |
−0.865686 | + | 0.500587i | \(0.833118\pi\) | |||||||
\(662\) | 15.5423 | − | 15.5423i | 0.604067 | − | 0.604067i | ||||
\(663\) | −3.96042 | − | 3.96042i | −0.153810 | − | 0.153810i | ||||
\(664\) | 10.1305 | − | 10.1305i | 0.393141 | − | 0.393141i | ||||
\(665\) | −1.24721 | + | 1.81056i | −0.0483648 | + | 0.0702106i | ||||
\(666\) | −0.135063 | + | 0.333213i | −0.00523358 | + | 0.0129118i | ||||
\(667\) | −2.49165 | + | 2.49165i | −0.0964772 | + | 0.0964772i | ||||
\(668\) | −22.3611 | −0.865178 | ||||||||
\(669\) | 34.0353 | 1.31588 | ||||||||
\(670\) | 19.2085 | − | 3.53890i | 0.742089 | − | 0.136720i | ||||
\(671\) | −19.1164 | − | 19.1164i | −0.737982 | − | 0.737982i | ||||
\(672\) | 3.18360 | 0.122810 | ||||||||
\(673\) | −1.64758 | − | 1.64758i | −0.0635097 | − | 0.0635097i | 0.674639 | − | 0.738148i | \(-0.264300\pi\) |
−0.738148 | + | 0.674639i | \(0.764300\pi\) | |||||||
\(674\) | 14.8294 | − | 14.8294i | 0.571209 | − | 0.571209i | ||||
\(675\) | −10.5108 | + | 23.4727i | −0.404560 | + | 0.903464i | ||||
\(676\) | −10.7210 | −0.412345 | ||||||||
\(677\) | 18.6418 | + | 18.6418i | 0.716461 | + | 0.716461i | 0.967879 | − | 0.251417i | \(-0.0808967\pi\) |
−0.251417 | + | 0.967879i | \(0.580897\pi\) | |||||||
\(678\) | −2.80420 | − | 2.80420i | −0.107695 | − | 0.107695i | ||||
\(679\) | −15.7753 | + | 15.7753i | −0.605400 | + | 0.605400i | ||||
\(680\) | −2.69073 | + | 3.90611i | −0.103185 | + | 0.149792i | ||||
\(681\) | 6.46904 | − | 6.46904i | 0.247894 | − | 0.247894i | ||||
\(682\) | −6.81229 | + | 6.81229i | −0.260856 | + | 0.260856i | ||||
\(683\) | 21.7547i | 0.832421i | 0.909268 | + | 0.416210i | \(0.136642\pi\) | ||||
−0.909268 | + | 0.416210i | \(0.863358\pi\) | |||||||
\(684\) | 0.0225773 | + | 0.0225773i | 0.000863263 | + | 0.000863263i | ||||
\(685\) | 10.9986 | − | 2.02634i | 0.420235 | − | 0.0774225i | ||||
\(686\) | −13.7548 | + | 13.7548i | −0.525162 | + | 0.525162i | ||||
\(687\) | −3.86539 | − | 3.86539i | −0.147474 | − | 0.147474i | ||||
\(688\) | 0.302660i | 0.0115388i | ||||||||
\(689\) | 14.6596 | − | 14.6596i | 0.558488 | − | 0.558488i | ||||
\(690\) | −34.2384 | + | 6.30795i | −1.30343 | + | 0.240140i | ||||
\(691\) | 10.1836i | 0.387401i | 0.981061 | + | 0.193700i | \(0.0620490\pi\) | ||||
−0.981061 | + | 0.193700i | \(0.937951\pi\) | |||||||
\(692\) | −6.44977 | + | 6.44977i | −0.245183 | + | 0.245183i | ||||
\(693\) | −0.325282 | + | 0.325282i | −0.0123564 | + | 0.0123564i | ||||
\(694\) | −8.24738 | −0.313066 | ||||||||
\(695\) | −10.5128 | − | 7.24175i | −0.398772 | − | 0.274695i | ||||
\(696\) | 0.692342i | 0.0262431i | ||||||||
\(697\) | 0.574599i | 0.0217645i | ||||||||
\(698\) | −16.1967 | −0.613056 | ||||||||
\(699\) | − | 18.3924i | − | 0.695663i | ||||||
\(700\) | −8.30629 | − | 3.71945i | −0.313948 | − | 0.140582i | ||||
\(701\) | 10.1893 | + | 10.1893i | 0.384844 | + | 0.384844i | 0.872844 | − | 0.488000i | \(-0.162273\pi\) |
−0.488000 | + | 0.872844i | \(0.662273\pi\) | |||||||
\(702\) | 5.49080 | + | 5.49080i | 0.207237 | + | 0.207237i | ||||
\(703\) | 1.28044 | + | 3.02599i | 0.0482927 | + | 0.114127i | ||||
\(704\) | 4.27563i | 0.161144i | ||||||||
\(705\) | 9.97674 | − | 14.4831i | 0.375746 | − | 0.545466i | ||||
\(706\) | − | 20.3765i | − | 0.766880i | ||||||
\(707\) | −24.8474 | − | 24.8474i | −0.934481 | − | 0.934481i | ||||
\(708\) | 10.0586i | 0.378026i | ||||||||
\(709\) | −35.9766 | + | 35.9766i | −1.35113 | + | 1.35113i | −0.466725 | + | 0.884402i | \(0.654566\pi\) |
−0.884402 | + | 0.466725i | \(0.845434\pi\) | |||||||
\(710\) | −10.0313 | + | 14.5623i | −0.376467 | + | 0.546513i | ||||
\(711\) | −0.130076 | − | 0.130076i | −0.00487822 | − | 0.00487822i | ||||
\(712\) | −5.24983 | + | 5.24983i | −0.196746 | + | 0.196746i | ||||
\(713\) | 14.1831 | + | 14.1831i | 0.531163 | + | 0.531163i | ||||
\(714\) | 6.75309 | 0.252728 | ||||||||
\(715\) | 11.8860 | + | 8.18769i | 0.444510 | + | 0.306202i | ||||
\(716\) | −8.44973 | − | 8.44973i | −0.315781 | − | 0.315781i | ||||
\(717\) | 47.5233i | 1.77479i | ||||||||
\(718\) | −30.2708 | −1.12970 | ||||||||
\(719\) | − | 10.7340i | − | 0.400310i | −0.979764 | − | 0.200155i | \(-0.935855\pi\) | ||
0.979764 | − | 0.200155i | \(-0.0641446\pi\) | |||||||
\(720\) | −0.0749790 | + | 0.108846i | −0.00279430 | + | 0.00405646i | ||||
\(721\) | 13.6232 | − | 13.6232i | 0.507356 | − | 0.507356i | ||||
\(722\) | −18.7082 | −0.696248 | ||||||||
\(723\) | 47.0013 | 1.74800 | ||||||||
\(724\) | −1.63147 | −0.0606330 | ||||||||
\(725\) | 0.808875 | − | 1.80638i | 0.0300408 | − | 0.0670873i | ||||
\(726\) | −9.00484 | − | 9.00484i | −0.334201 | − | 0.334201i | ||||
\(727\) | 14.6699i | 0.544078i | 0.962286 | + | 0.272039i | \(0.0876980\pi\) | ||||
−0.962286 | + | 0.272039i | \(0.912302\pi\) | |||||||
\(728\) | −1.94303 | + | 1.94303i | −0.0720136 | + | 0.0720136i | ||||
\(729\) | 26.4473i | 0.979528i | ||||||||
\(730\) | 4.77017 | + | 25.8916i | 0.176552 | + | 0.958292i | ||||
\(731\) | 0.642006i | 0.0237455i | ||||||||
\(732\) | 11.0591i | 0.408755i | ||||||||
\(733\) | 22.2345 | − | 22.2345i | 0.821249 | − | 0.821249i | −0.165039 | − | 0.986287i | \(-0.552775\pi\) |
0.986287 | + | 0.165039i | \(0.0527748\pi\) | |||||||
\(734\) | 13.0615 | + | 13.0615i | 0.482108 | + | 0.482108i | ||||
\(735\) | −2.61255 | − | 14.1804i | −0.0963652 | − | 0.523053i | ||||
\(736\) | 8.90184 | 0.328126 | ||||||||
\(737\) | 26.4084 | − | 26.4084i | 0.972766 | − | 0.972766i | ||||
\(738\) | 0.0160116i | 0.000589394i | ||||||||
\(739\) | 4.21587 | 0.155083 | 0.0775416 | − | 0.996989i | \(-0.475293\pi\) | ||||
0.0775416 | + | 0.996989i | \(0.475293\pi\) | |||||||
\(740\) | −11.3585 | + | 7.48229i | −0.417547 | + | 0.275054i | ||||
\(741\) | −1.42628 | −0.0523957 | ||||||||
\(742\) | 24.9968i | 0.917662i | ||||||||
\(743\) | −0.649329 | + | 0.649329i | −0.0238216 | + | 0.0238216i | −0.718917 | − | 0.695096i | \(-0.755362\pi\) |
0.695096 | + | 0.718917i | \(0.255362\pi\) | |||||||
\(744\) | 3.94099 | 0.144484 | ||||||||
\(745\) | −9.34842 | + | 13.5710i | −0.342499 | + | 0.497203i | ||||
\(746\) | 16.1154 | + | 16.1154i | 0.590026 | + | 0.590026i | ||||
\(747\) | 0.598806 | − | 0.598806i | 0.0219091 | − | 0.0219091i | ||||
\(748\) | 9.06953i | 0.331615i | ||||||||
\(749\) | − | 7.15397i | − | 0.261400i | ||||||
\(750\) | 16.7058 | − | 10.1639i | 0.610009 | − | 0.371134i | ||||
\(751\) | 25.7790i | 0.940688i | 0.882483 | + | 0.470344i | \(0.155870\pi\) | ||||
−0.882483 | + | 0.470344i | \(0.844130\pi\) | |||||||
\(752\) | −3.17973 | + | 3.17973i | −0.115953 | + | 0.115953i | ||||
\(753\) | 6.34872i | 0.231360i | ||||||||
\(754\) | −0.422554 | − | 0.422554i | −0.0153885 | − | 0.0153885i | ||||
\(755\) | −6.30145 | + | 9.14775i | −0.229333 | + | 0.332921i | ||||
\(756\) | −9.36262 | −0.340515 | ||||||||
\(757\) | 15.9640 | 0.580222 | 0.290111 | − | 0.956993i | \(-0.406308\pi\) | ||||
0.290111 | + | 0.956993i | \(0.406308\pi\) | |||||||
\(758\) | 7.07736 | 0.257061 | ||||||||
\(759\) | −47.0720 | + | 47.0720i | −1.70861 | + | 1.70861i | ||||
\(760\) | 0.218849 | + | 1.18787i | 0.00793848 | + | 0.0430887i | ||||
\(761\) | − | 28.4393i | − | 1.03092i | −0.856912 | − | 0.515462i | \(-0.827620\pi\) | ||
0.856912 | − | 0.515462i | \(-0.172380\pi\) | |||||||
\(762\) | −19.6739 | −0.712710 | ||||||||
\(763\) | 10.6724i | 0.386368i | ||||||||
\(764\) | 14.3915 | + | 14.3915i | 0.520664 | + | 0.520664i | ||||
\(765\) | −0.159046 | + | 0.230886i | −0.00575033 | + | 0.00834770i | ||||
\(766\) | 17.6507 | 0.637747 | ||||||||
\(767\) | −6.13905 | − | 6.13905i | −0.221668 | − | 0.221668i | ||||
\(768\) | 1.23675 | − | 1.23675i | 0.0446274 | − | 0.0446274i | ||||
\(769\) | −21.9651 | − | 21.9651i | −0.792083 | − | 0.792083i | 0.189749 | − | 0.981833i | \(-0.439232\pi\) |
−0.981833 | + | 0.189749i | \(0.939232\pi\) | |||||||
\(770\) | −17.1143 | + | 3.15306i | −0.616755 | + | 0.113629i | ||||
\(771\) | −17.1900 | + | 17.1900i | −0.619082 | + | 0.619082i | ||||
\(772\) | 1.88527i | 0.0678525i | ||||||||
\(773\) | 2.60816 | + | 2.60816i | 0.0938089 | + | 0.0938089i | 0.752454 | − | 0.658645i | \(-0.228870\pi\) |
−0.658645 | + | 0.752454i | \(0.728870\pi\) | |||||||
\(774\) | 0.0178899i | 0.000643040i | ||||||||
\(775\) | −10.2824 | − | 4.60433i | −0.369355 | − | 0.165392i | ||||
\(776\) | 12.2566i | 0.439988i | ||||||||
\(777\) | 17.9468 | + | 7.27447i | 0.643838 | + | 0.260970i | ||||
\(778\) | −14.9010 | − | 14.9010i | −0.534225 | − | 0.534225i | ||||
\(779\) | 0.103466 | + | 0.103466i | 0.00370706 | + | 0.00370706i | ||||
\(780\) | −1.06975 | − | 5.80642i | −0.0383033 | − | 0.207903i | ||||
\(781\) | 33.8119i | 1.20989i | ||||||||
\(782\) | 18.8827 | 0.675244 | ||||||||
\(783\) | − | 2.03610i | − | 0.0727643i | ||||||
\(784\) | 3.68685i | 0.131673i | ||||||||
\(785\) | −25.7621 | + | 4.74630i | −0.919488 | + | 0.169403i | ||||
\(786\) | −15.6244 | −0.557302 | ||||||||
\(787\) | −2.48943 | + | 2.48943i | −0.0887387 | + | 0.0887387i | −0.750083 | − | 0.661344i | \(-0.769986\pi\) |
0.661344 | + | 0.750083i | \(0.269986\pi\) | |||||||
\(788\) | 16.9005 | − | 16.9005i | 0.602057 | − | 0.602057i | ||||
\(789\) | 35.1912i | 1.25284i | ||||||||
\(790\) | −1.26087 | − | 6.84376i | −0.0448597 | − | 0.243490i | ||||
\(791\) | −2.91832 | + | 2.91832i | −0.103763 | + | 0.103763i | ||||
\(792\) | 0.252728i | 0.00898031i | ||||||||
\(793\) | −6.74965 | − | 6.74965i | −0.239687 | − | 0.239687i | ||||
\(794\) | −3.61759 | + | 3.61759i | −0.128384 | + | 0.128384i | ||||
\(795\) | −44.2305 | − | 30.4683i | −1.56869 | − | 1.08060i | ||||
\(796\) | 6.68597 | + | 6.68597i | 0.236978 | + | 0.236978i | ||||
\(797\) | 30.0363i | 1.06394i | 0.846763 | + | 0.531970i | \(0.178548\pi\) | ||||
−0.846763 | + | 0.531970i | \(0.821452\pi\) | |||||||
\(798\) | 1.21601 | − | 1.21601i | 0.0430462 | − | 0.0430462i | ||||
\(799\) | −6.74488 | + | 6.74488i | −0.238617 | + | 0.238617i | ||||
\(800\) | −4.67171 | + | 1.78188i | −0.165170 | + | 0.0629989i | ||||
\(801\) | −0.310312 | + | 0.310312i | −0.0109643 | + | 0.0109643i | ||||
\(802\) | −12.9977 | − | 12.9977i | −0.458965 | − | 0.458965i | ||||
\(803\) | 35.5966 | + | 35.5966i | 1.25618 | + | 1.25618i | ||||
\(804\) | −15.2776 | −0.538798 | ||||||||
\(805\) | 6.56465 | + | 35.6318i | 0.231374 | + | 1.25585i | ||||
\(806\) | −2.40529 | + | 2.40529i | −0.0847227 | + | 0.0847227i | ||||
\(807\) | −26.5040 | − | 26.5040i | −0.932984 | − | 0.932984i | ||||
\(808\) | −19.3052 | −0.679155 | ||||||||
\(809\) | −4.17505 | − | 4.17505i | −0.146787 | − | 0.146787i | 0.629894 | − | 0.776681i | \(-0.283098\pi\) |
−0.776681 | + | 0.629894i | \(0.783098\pi\) | |||||||
\(810\) | 11.6369 | − | 16.8932i | 0.408879 | − | 0.593565i | ||||
\(811\) | 21.0938 | 0.740702 | 0.370351 | − | 0.928892i | \(-0.379237\pi\) | ||||
0.370351 | + | 0.928892i | \(0.379237\pi\) | |||||||
\(812\) | 0.720516 | 0.0252852 | ||||||||
\(813\) | −21.6510 | + | 21.6510i | −0.759334 | + | 0.759334i | ||||
\(814\) | −9.76975 | + | 24.1029i | −0.342430 | + | 0.844807i | ||||
\(815\) | −35.4717 | − | 24.4348i | −1.24252 | − | 0.855912i | ||||
\(816\) | 2.62341 | − | 2.62341i | 0.0918378 | − | 0.0918378i | ||||
\(817\) | 0.115604 | + | 0.115604i | 0.00404447 | + | 0.00404447i | ||||
\(818\) | 1.73592 | − | 1.73592i | 0.0606949 | − | 0.0606949i | ||||
\(819\) | −0.114851 | + | 0.114851i | −0.00401321 | + | 0.00401321i | ||||
\(820\) | −0.343611 | + | 0.498816i | −0.0119994 | + | 0.0174194i | ||||
\(821\) | −27.8919 | −0.973434 | −0.486717 | − | 0.873560i | \(-0.661806\pi\) | ||||
−0.486717 | + | 0.873560i | \(0.661806\pi\) | |||||||
\(822\) | −8.74779 | −0.305114 | ||||||||
\(823\) | 7.17157 | + | 7.17157i | 0.249985 | + | 0.249985i | 0.820964 | − | 0.570979i | \(-0.193436\pi\) |
−0.570979 | + | 0.820964i | \(0.693436\pi\) | |||||||
\(824\) | − | 10.5846i | − | 0.368732i | ||||||
\(825\) | 15.2811 | − | 34.1259i | 0.532021 | − | 1.18811i | ||||
\(826\) | 10.4680 | 0.364227 | ||||||||
\(827\) | 46.4436 | 1.61500 | 0.807501 | − | 0.589866i | \(-0.200819\pi\) | ||||
0.807501 | + | 0.589866i | \(0.200819\pi\) | |||||||
\(828\) | 0.526178 | 0.0182860 | ||||||||
\(829\) | −2.54664 | − | 2.54664i | −0.0884484 | − | 0.0884484i | 0.661498 | − | 0.749947i | \(-0.269921\pi\) |
−0.749947 | + | 0.661498i | \(0.769921\pi\) | |||||||
\(830\) | 31.5053 | − | 5.80442i | 1.09357 | − | 0.201474i | ||||
\(831\) | 12.2781 | + | 12.2781i | 0.425923 | + | 0.425923i | ||||
\(832\) | 1.50964i | 0.0523375i | ||||||||
\(833\) | 7.82059i | 0.270967i | ||||||||
\(834\) | 7.06057 | + | 7.06057i | 0.244488 | + | 0.244488i | ||||
\(835\) | −41.1769 | − | 28.3648i | −1.42498 | − | 0.981604i | ||||
\(836\) | 1.63312 | + | 1.63312i | 0.0564827 | + | 0.0564827i | ||||
\(837\) | −11.5900 | −0.400610 | ||||||||
\(838\) | 16.7428 | 0.578372 | ||||||||
\(839\) | −29.4346 | −1.01619 | −0.508097 | − | 0.861300i | \(-0.669651\pi\) | ||||
−0.508097 | + | 0.861300i | \(0.669651\pi\) | |||||||
\(840\) | 5.86244 | + | 4.03835i | 0.202273 | + | 0.139336i | ||||
\(841\) | − | 28.8433i | − | 0.994597i | ||||||
\(842\) | −0.463240 | − | 0.463240i | −0.0159643 | − | 0.0159643i | ||||
\(843\) | 22.9002 | 0.788725 | ||||||||
\(844\) | −16.4186 | −0.565151 | ||||||||
\(845\) | −19.7421 | − | 13.5994i | −0.679150 | − | 0.467834i | ||||
\(846\) | −0.187950 | + | 0.187950i | −0.00646187 | + | 0.00646187i | ||||
\(847\) | −9.37129 | + | 9.37129i | −0.322001 | + | 0.322001i | ||||
\(848\) | 9.71066 | + | 9.71066i | 0.333466 | + | 0.333466i | ||||
\(849\) | 9.06323 | − | 9.06323i | 0.311049 | − | 0.311049i | ||||
\(850\) | −9.90970 | + | 3.77974i | −0.339900 | + | 0.129644i | ||||
\(851\) | 50.1821 | + | 20.3406i | 1.72022 | + | 0.697265i | ||||
\(852\) | 9.78029 | − | 9.78029i | 0.335067 | − | 0.335067i | ||||
\(853\) | −17.8225 | −0.610230 | −0.305115 | − | 0.952315i | \(-0.598695\pi\) | ||||
−0.305115 | + | 0.952315i | \(0.598695\pi\) | |||||||
\(854\) | 11.5091 | 0.393834 | ||||||||
\(855\) | 0.0129359 | + | 0.0702139i | 0.000442400 | + | 0.00240126i | ||||
\(856\) | −2.77915 | − | 2.77915i | −0.0949892 | − | 0.0949892i | ||||
\(857\) | 42.4300 | 1.44938 | 0.724691 | − | 0.689074i | \(-0.241983\pi\) | ||||
0.724691 | + | 0.689074i | \(0.241983\pi\) | |||||||
\(858\) | −7.98284 | − | 7.98284i | −0.272530 | − | 0.272530i | ||||
\(859\) | 7.52410 | − | 7.52410i | 0.256719 | − | 0.256719i | −0.566999 | − | 0.823718i | \(-0.691896\pi\) |
0.823718 | + | 0.566999i | \(0.191896\pi\) | |||||||
\(860\) | −0.383920 | + | 0.557333i | −0.0130916 | + | 0.0190049i | ||||
\(861\) | 0.862380 | 0.0293898 | ||||||||
\(862\) | −27.2475 | − | 27.2475i | −0.928055 | − | 0.928055i | ||||
\(863\) | −32.3511 | − | 32.3511i | −1.10124 | − | 1.10124i | −0.994261 | − | 0.106983i | \(-0.965881\pi\) |
−0.106983 | − | 0.994261i | \(-0.534119\pi\) | |||||||
\(864\) | −3.63715 | + | 3.63715i | −0.123738 | + | 0.123738i | ||||
\(865\) | −20.0584 | + | 3.69548i | −0.682005 | + | 0.125650i | ||||
\(866\) | −17.1809 | + | 17.1809i | −0.583830 | + | 0.583830i | ||||
\(867\) | −15.4600 | + | 15.4600i | −0.525048 | + | 0.525048i | ||||
\(868\) | − | 4.10137i | − | 0.139209i | ||||||
\(869\) | −9.40901 | − | 9.40901i | −0.319179 | − | 0.319179i | ||||
\(870\) | −0.878227 | + | 1.27491i | −0.0297747 | + | 0.0432236i | ||||
\(871\) | 9.32430 | − | 9.32430i | 0.315942 | − | 0.315942i | ||||
\(872\) | 4.14598 | + | 4.14598i | 0.140401 | + | 0.140401i | ||||
\(873\) | 0.724478i | 0.0245198i | ||||||||
\(874\) | 3.40015 | − | 3.40015i | 0.115012 | − | 0.115012i | ||||
\(875\) | −10.5776 | − | 17.3856i | −0.357586 | − | 0.587741i | ||||
\(876\) | − | 20.5930i | − | 0.695774i | ||||||
\(877\) | 33.8258 | − | 33.8258i | 1.14222 | − | 1.14222i | 0.154171 | − | 0.988044i | \(-0.450729\pi\) |
0.988044 | − | 0.154171i | \(-0.0492707\pi\) | |||||||
\(878\) | 13.3023 | − | 13.3023i | 0.448932 | − | 0.448932i | ||||
\(879\) | −31.1905 | −1.05203 | ||||||||
\(880\) | −5.42359 | + | 7.87337i | −0.182829 | + | 0.265411i | ||||
\(881\) | − | 49.3397i | − | 1.66230i | −0.556050 | − | 0.831149i | \(-0.687684\pi\) | ||
0.556050 | − | 0.831149i | \(-0.312316\pi\) | |||||||
\(882\) | 0.217926i | 0.00733794i | ||||||||
\(883\) | 14.6163 | 0.491878 | 0.245939 | − | 0.969285i | \(-0.420904\pi\) | ||||
0.245939 | + | 0.969285i | \(0.420904\pi\) | |||||||
\(884\) | 3.20228i | 0.107704i | ||||||||
\(885\) | −12.7592 | + | 18.5225i | −0.428897 | + | 0.622626i | ||||
\(886\) | −24.4725 | − | 24.4725i | −0.822169 | − | 0.822169i | ||||
\(887\) | 39.7503 | + | 39.7503i | 1.33468 | + | 1.33468i | 0.901125 | + | 0.433560i | \(0.142743\pi\) |
0.433560 | + | 0.901125i | \(0.357257\pi\) | |||||||
\(888\) | 9.79786 | − | 4.14595i | 0.328795 | − | 0.139129i | ||||
\(889\) | 20.4745i | 0.686693i | ||||||||
\(890\) | −16.3267 | + | 3.00796i | −0.547271 | + | 0.100827i | ||||
\(891\) | − | 39.2239i | − | 1.31405i | ||||||
\(892\) | −13.7600 | − | 13.7600i | −0.460718 | − | 0.460718i | ||||
\(893\) | 2.42906i | 0.0812853i | ||||||||
\(894\) | 9.11453 | − | 9.11453i | 0.304835 | − | 0.304835i | ||||
\(895\) | −4.84138 | − | 26.2781i | −0.161829 | − | 0.878381i | ||||
\(896\) | −1.28708 | − | 1.28708i | −0.0429984 | − | 0.0429984i | ||||
\(897\) | −16.6202 | + | 16.6202i | −0.554933 | + | 0.554933i | ||||
\(898\) | 20.4966 | + | 20.4966i | 0.683981 | + | 0.683981i | ||||
\(899\) | 0.891930 | 0.0297475 | ||||||||
\(900\) | −0.276140 | + | 0.105325i | −0.00920467 | + | 0.00351083i | ||||
\(901\) | 20.5984 | + | 20.5984i | 0.686232 | + | 0.686232i | ||||
\(902\) | 1.15819i | 0.0385636i | ||||||||
\(903\) | 0.963548 | 0.0320649 | ||||||||
\(904\) | 2.26739i | 0.0754124i | ||||||||
\(905\) | −3.00427 | − | 2.06950i | −0.0998652 | − | 0.0687924i | ||||
\(906\) | 6.14380 | − | 6.14380i | 0.204114 | − | 0.204114i | ||||
\(907\) | 9.06842 | 0.301112 | 0.150556 | − | 0.988601i | \(-0.451894\pi\) | ||||
0.150556 | + | 0.988601i | \(0.451894\pi\) | |||||||
\(908\) | −5.23067 | −0.173586 | ||||||||
\(909\) | −1.14111 | −0.0378483 | ||||||||
\(910\) | −6.04271 | + | 1.11329i | −0.200314 | + | 0.0369051i | ||||
\(911\) | 13.7635 | + | 13.7635i | 0.456006 | + | 0.456006i | 0.897342 | − | 0.441336i | \(-0.145495\pi\) |
−0.441336 | + | 0.897342i | \(0.645495\pi\) | |||||||
\(912\) | − | 0.944780i | − | 0.0312848i | ||||||
\(913\) | 43.3145 | − | 43.3145i | 1.43350 | − | 1.43350i | ||||
\(914\) | − | 25.3795i | − | 0.839479i | ||||||
\(915\) | −14.0283 | + | 20.3647i | −0.463761 | + | 0.673238i | ||||
\(916\) | 3.12544i | 0.103267i | ||||||||
\(917\) | 16.2602i | 0.536959i | ||||||||
\(918\) | −7.71517 | + | 7.71517i | −0.254639 | + | 0.254639i | ||||
\(919\) | 20.8694 | + | 20.8694i | 0.688418 | + | 0.688418i | 0.961882 | − | 0.273464i | \(-0.0881696\pi\) |
−0.273464 | + | 0.961882i | \(0.588170\pi\) | |||||||
\(920\) | 16.3923 | + | 11.2919i | 0.540438 | + | 0.372282i | ||||
\(921\) | −42.1216 | −1.38795 | ||||||||
\(922\) | 19.5684 | − | 19.5684i | 0.644452 | − | 0.644452i | ||||
\(923\) | 11.9383i | 0.392955i | ||||||||
\(924\) | 13.6119 | 0.447799 | ||||||||
\(925\) | −30.4073 | − | 0.629852i | −0.999786 | − | 0.0207094i | ||||
\(926\) | 40.3494 | 1.32596 | ||||||||
\(927\) | − | 0.625645i | − | 0.0205489i | ||||||
\(928\) | 0.279903 | − | 0.279903i | 0.00918828 | − | 0.00918828i | ||||
\(929\) | −26.4042 | −0.866294 | −0.433147 | − | 0.901323i | \(-0.642597\pi\) | ||||
−0.433147 | + | 0.901323i | \(0.642597\pi\) | |||||||
\(930\) | 7.25714 | + | 4.99910i | 0.237971 | + | 0.163927i | ||||
\(931\) | 1.40823 | + | 1.40823i | 0.0461528 | + | 0.0461528i | ||||
\(932\) | −7.43576 | + | 7.43576i | −0.243566 | + | 0.243566i | ||||
\(933\) | − | 9.26748i | − | 0.303404i | ||||||
\(934\) | 6.84915i | 0.224111i | ||||||||
\(935\) | −11.5046 | + | 16.7011i | −0.376240 | + | 0.546184i | ||||
\(936\) | 0.0892335i | 0.00291669i | ||||||||
\(937\) | 2.29378 | − | 2.29378i | 0.0749346 | − | 0.0749346i | −0.668646 | − | 0.743581i | \(-0.733126\pi\) |
0.743581 | + | 0.668646i | \(0.233126\pi\) | |||||||
\(938\) | 15.8993i | 0.519130i | ||||||||
\(939\) | 18.1871 | + | 18.1871i | 0.593515 | + | 0.593515i | ||||
\(940\) | −9.88875 | + | 1.82187i | −0.322536 | + | 0.0594227i | ||||
\(941\) | 46.2380 | 1.50732 | 0.753658 | − | 0.657267i | \(-0.228288\pi\) | ||||
0.753658 | + | 0.657267i | \(0.228288\pi\) | |||||||
\(942\) | 20.4900 | 0.667600 | ||||||||
\(943\) | 2.41135 | 0.0785244 | ||||||||
\(944\) | 4.06655 | − | 4.06655i | 0.132355 | − | 0.132355i | ||||
\(945\) | −17.2408 | − | 11.8764i | −0.560843 | − | 0.386338i | ||||
\(946\) | 1.29406i | 0.0420736i | ||||||||
\(947\) | −45.6330 | −1.48287 | −0.741436 | − | 0.671023i | \(-0.765855\pi\) | ||||
−0.741436 | + | 0.671023i | \(0.765855\pi\) | |||||||
\(948\) | 5.44322i | 0.176787i | ||||||||
\(949\) | 12.5685 | + | 12.5685i | 0.407990 | + | 0.407990i | ||||
\(950\) | −1.10380 | + | 2.46501i | −0.0358121 | + | 0.0799756i | ||||
\(951\) | −33.7528 | −1.09451 | ||||||||
\(952\) | −2.73017 | − | 2.73017i | −0.0884854 | − | 0.0884854i | ||||
\(953\) | 17.8564 | − | 17.8564i | 0.578427 | − | 0.578427i | −0.356043 | − | 0.934470i | \(-0.615874\pi\) |
0.934470 | + | 0.356043i | \(0.115874\pi\) | |||||||
\(954\) | 0.573987 | + | 0.573987i | 0.0185835 | + | 0.0185835i | ||||
\(955\) | 8.24577 | + | 44.7565i | 0.266827 | + | 1.44829i | ||||
\(956\) | 19.2129 | − | 19.2129i | 0.621391 | − | 0.621391i | ||||
\(957\) | 2.96020i | 0.0956897i | ||||||||
\(958\) | 30.4703 | + | 30.4703i | 0.984450 | + | 0.984450i | ||||
\(959\) | 9.10378i | 0.293976i | ||||||||
\(960\) | 3.84622 | − | 0.708613i | 0.124136 | − | 0.0228704i | ||||
\(961\) | 25.9229i | 0.836223i | ||||||||
\(962\) | −3.44951 | + | 8.51028i | −0.111217 | + | 0.274382i | ||||
\(963\) | −0.164272 | − | 0.164272i | −0.00529360 | − | 0.00529360i | ||||
\(964\) | −19.0019 | − | 19.0019i | −0.612010 | − | 0.612010i | ||||
\(965\) | −2.39145 | + | 3.47164i | −0.0769834 | + | 0.111756i | ||||
\(966\) | − | 28.3399i | − | 0.911821i | ||||||
\(967\) | 21.9000 | 0.704256 | 0.352128 | − | 0.935952i | \(-0.385458\pi\) | ||||
0.352128 | + | 0.935952i | \(0.385458\pi\) | |||||||
\(968\) | 7.28104i | 0.234022i | ||||||||
\(969\) | − | 2.00408i | − | 0.0643803i | ||||||
\(970\) | −15.5474 | + | 22.5700i | −0.499197 | + | 0.724679i | ||||
\(971\) | −56.4041 | −1.81009 | −0.905047 | − | 0.425313i | \(-0.860164\pi\) | ||||
−0.905047 | + | 0.425313i | \(0.860164\pi\) | |||||||
\(972\) | −0.434298 | + | 0.434298i | −0.0139301 | + | 0.0139301i | ||||
\(973\) | 7.34790 | − | 7.34790i | 0.235563 | − | 0.235563i | ||||
\(974\) | − | 38.9294i | − | 1.24738i | ||||||
\(975\) | 5.39548 | − | 12.0492i | 0.172794 | − | 0.385883i | ||||
\(976\) | 4.47102 | − | 4.47102i | 0.143114 | − | 0.143114i | ||||
\(977\) | − | 39.9367i | − | 1.27769i | −0.769336 | − | 0.638844i | \(-0.779413\pi\) | ||
0.769336 | − | 0.638844i | \(-0.220587\pi\) | |||||||
\(978\) | 23.8234 | + | 23.8234i | 0.761789 | + | 0.761789i | ||||
\(979\) | −22.4464 | + | 22.4464i | −0.717389 | + | 0.717389i | ||||
\(980\) | −4.67672 | + | 6.78914i | −0.149392 | + | 0.216871i | ||||
\(981\) | 0.245065 | + | 0.245065i | 0.00782431 | + | 0.00782431i | ||||
\(982\) | 8.64964i | 0.276021i | ||||||||
\(983\) | 27.5089 | − | 27.5089i | 0.877396 | − | 0.877396i | −0.115868 | − | 0.993265i | \(-0.536965\pi\) |
0.993265 | + | 0.115868i | \(0.0369651\pi\) | |||||||
\(984\) | 0.335014 | − | 0.335014i | 0.0106799 | − | 0.0106799i | ||||
\(985\) | 52.5596 | − | 9.68338i | 1.67469 | − | 0.308538i | ||||
\(986\) | 0.593735 | − | 0.593735i | 0.0189084 | − | 0.0189084i | ||||
\(987\) | 10.1230 | + | 10.1230i | 0.322218 | + | 0.322218i | ||||
\(988\) | 0.576624 | + | 0.576624i | 0.0183448 | + | 0.0183448i | ||||
\(989\) | 2.69423 | 0.0856715 | ||||||||
\(990\) | −0.320583 | + | 0.465387i | −0.0101888 | + | 0.0147910i | ||||
\(991\) | 31.0307 | − | 31.0307i | 0.985721 | − | 0.985721i | −0.0141781 | − | 0.999899i | \(-0.504513\pi\) |
0.999899 | + | 0.0141781i | \(0.00451317\pi\) | |||||||
\(992\) | −1.59328 | − | 1.59328i | −0.0505868 | − | 0.0505868i | ||||
\(993\) | −38.4438 | −1.21998 | ||||||||
\(994\) | −10.1783 | − | 10.1783i | −0.322836 | − | 0.322836i | ||||
\(995\) | 3.83081 | + | 20.7930i | 0.121445 | + | 0.659181i | ||||
\(996\) | −25.0579 | −0.793990 | ||||||||
\(997\) | 44.3360 | 1.40414 | 0.702068 | − | 0.712110i | \(-0.252260\pi\) | ||||
0.702068 | + | 0.712110i | \(0.252260\pi\) | |||||||
\(998\) | −10.9240 | + | 10.9240i | −0.345792 | + | 0.345792i | ||||
\(999\) | −28.8144 | + | 12.1928i | −0.911649 | + | 0.385763i |
(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 | 370.2.g.e.43.8 | ✓ | 20 | |
5.2 | odd | 4 | 370.2.h.e.117.3 | yes | 20 | ||
37.31 | odd | 4 | 370.2.h.e.253.3 | yes | 20 | ||
185.142 | even | 4 | inner | 370.2.g.e.327.8 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.g.e.43.8 | ✓ | 20 | 1.1 | even | 1 | trivial | |
370.2.g.e.327.8 | yes | 20 | 185.142 | even | 4 | inner | |
370.2.h.e.117.3 | yes | 20 | 5.2 | odd | 4 | ||
370.2.h.e.253.3 | yes | 20 | 37.31 | odd | 4 |