Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [722,2,Mod(429,722)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(722, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("722.429");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 722 = 2 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 722.c (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.76519902594\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 2x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 429.1 | ||
Root | \(-0.309017 + 0.535233i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 722.429 |
Dual form | 722.2.c.h.653.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/722\mathbb{Z}\right)^\times\).
\(n\) | \(363\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | −0.618034 | + | 1.07047i | −0.356822 | + | 0.618034i | −0.987428 | − | 0.158069i | \(-0.949473\pi\) |
0.630606 | + | 0.776103i | \(0.282806\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.80902 | − | 3.13331i | 0.809017 | − | 1.40126i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(6\) | −0.618034 | − | 1.07047i | −0.252311 | − | 0.437016i | ||||
\(7\) | −3.23607 | −1.22312 | −0.611559 | − | 0.791199i | \(-0.709457\pi\) | ||||
−0.611559 | + | 0.791199i | \(0.709457\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.736068 | + | 1.27491i | 0.245356 | + | 0.424969i | ||||
\(10\) | 1.80902 | + | 3.13331i | 0.572061 | + | 0.990839i | ||||
\(11\) | −3.23607 | −0.975711 | −0.487856 | − | 0.872924i | \(-0.662221\pi\) | ||||
−0.487856 | + | 0.872924i | \(0.662221\pi\) | |||||||
\(12\) | 1.23607 | 0.356822 | ||||||||
\(13\) | 0.690983 | + | 1.19682i | 0.191644 | + | 0.331937i | 0.945795 | − | 0.324763i | \(-0.105285\pi\) |
−0.754151 | + | 0.656701i | \(0.771951\pi\) | |||||||
\(14\) | 1.61803 | − | 2.80252i | 0.432438 | − | 0.749004i | ||||
\(15\) | 2.23607 | + | 3.87298i | 0.577350 | + | 1.00000i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.69098 | − | 2.92887i | 0.410124 | − | 0.710355i | −0.584779 | − | 0.811192i | \(-0.698819\pi\) |
0.994903 | + | 0.100837i | \(0.0321522\pi\) | |||||||
\(18\) | −1.47214 | −0.346986 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −3.61803 | −0.809017 | ||||||||
\(21\) | 2.00000 | − | 3.46410i | 0.436436 | − | 0.755929i | ||||
\(22\) | 1.61803 | − | 2.80252i | 0.344966 | − | 0.597499i | ||||
\(23\) | −2.61803 | − | 4.53457i | −0.545898 | − | 0.945523i | −0.998550 | − | 0.0538355i | \(-0.982855\pi\) |
0.452652 | − | 0.891687i | \(-0.350478\pi\) | |||||||
\(24\) | −0.618034 | + | 1.07047i | −0.126156 | + | 0.218508i | ||||
\(25\) | −4.04508 | − | 7.00629i | −0.809017 | − | 1.40126i | ||||
\(26\) | −1.38197 | −0.271026 | ||||||||
\(27\) | −5.52786 | −1.06384 | ||||||||
\(28\) | 1.61803 | + | 2.80252i | 0.305780 | + | 0.529626i | ||||
\(29\) | −4.54508 | − | 7.87232i | −0.844001 | − | 1.46185i | −0.886486 | − | 0.462756i | \(-0.846861\pi\) |
0.0424848 | − | 0.999097i | \(-0.486473\pi\) | |||||||
\(30\) | −4.47214 | −0.816497 | ||||||||
\(31\) | 1.23607 | 0.222004 | 0.111002 | − | 0.993820i | \(-0.464594\pi\) | ||||
0.111002 | + | 0.993820i | \(0.464594\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 2.00000 | − | 3.46410i | 0.348155 | − | 0.603023i | ||||
\(34\) | 1.69098 | + | 2.92887i | 0.290001 | + | 0.502297i | ||||
\(35\) | −5.85410 | + | 10.1396i | −0.989524 | + | 1.71391i | ||||
\(36\) | 0.736068 | − | 1.27491i | 0.122678 | − | 0.212485i | ||||
\(37\) | −8.38197 | −1.37799 | −0.688993 | − | 0.724768i | \(-0.741947\pi\) | ||||
−0.688993 | + | 0.724768i | \(0.741947\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.70820 | −0.273532 | ||||||||
\(40\) | 1.80902 | − | 3.13331i | 0.286031 | − | 0.495420i | ||||
\(41\) | 0.427051 | − | 0.739674i | 0.0666942 | − | 0.115518i | −0.830750 | − | 0.556646i | \(-0.812088\pi\) |
0.897444 | + | 0.441128i | \(0.145421\pi\) | |||||||
\(42\) | 2.00000 | + | 3.46410i | 0.308607 | + | 0.534522i | ||||
\(43\) | 4.61803 | − | 7.99867i | 0.704244 | − | 1.21979i | −0.262720 | − | 0.964872i | \(-0.584620\pi\) |
0.966964 | − | 0.254914i | \(-0.0820470\pi\) | |||||||
\(44\) | 1.61803 | + | 2.80252i | 0.243928 | + | 0.422495i | ||||
\(45\) | 5.32624 | 0.793989 | ||||||||
\(46\) | 5.23607 | 0.772016 | ||||||||
\(47\) | −2.23607 | − | 3.87298i | −0.326164 | − | 0.564933i | 0.655583 | − | 0.755123i | \(-0.272423\pi\) |
−0.981747 | + | 0.190190i | \(0.939090\pi\) | |||||||
\(48\) | −0.618034 | − | 1.07047i | −0.0892055 | − | 0.154508i | ||||
\(49\) | 3.47214 | 0.496019 | ||||||||
\(50\) | 8.09017 | 1.14412 | ||||||||
\(51\) | 2.09017 | + | 3.62028i | 0.292682 | + | 0.506941i | ||||
\(52\) | 0.690983 | − | 1.19682i | 0.0958221 | − | 0.165969i | ||||
\(53\) | −3.04508 | − | 5.27424i | −0.418275 | − | 0.724473i | 0.577491 | − | 0.816397i | \(-0.304032\pi\) |
−0.995766 | + | 0.0919239i | \(0.970698\pi\) | |||||||
\(54\) | 2.76393 | − | 4.78727i | 0.376124 | − | 0.651465i | ||||
\(55\) | −5.85410 | + | 10.1396i | −0.789367 | + | 1.36722i | ||||
\(56\) | −3.23607 | −0.432438 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.09017 | 1.19360 | ||||||||
\(59\) | −0.236068 | + | 0.408882i | −0.0307334 | + | 0.0532319i | −0.880983 | − | 0.473148i | \(-0.843118\pi\) |
0.850250 | + | 0.526380i | \(0.176451\pi\) | |||||||
\(60\) | 2.23607 | − | 3.87298i | 0.288675 | − | 0.500000i | ||||
\(61\) | −0.690983 | − | 1.19682i | −0.0884713 | − | 0.153237i | 0.818394 | − | 0.574658i | \(-0.194865\pi\) |
−0.906865 | + | 0.421421i | \(0.861531\pi\) | |||||||
\(62\) | −0.618034 | + | 1.07047i | −0.0784904 | + | 0.135949i | ||||
\(63\) | −2.38197 | − | 4.12569i | −0.300100 | − | 0.519788i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.00000 | 0.620174 | ||||||||
\(66\) | 2.00000 | + | 3.46410i | 0.246183 | + | 0.426401i | ||||
\(67\) | 5.85410 | + | 10.1396i | 0.715192 | + | 1.23875i | 0.962885 | + | 0.269911i | \(0.0869943\pi\) |
−0.247693 | + | 0.968839i | \(0.579672\pi\) | |||||||
\(68\) | −3.38197 | −0.410124 | ||||||||
\(69\) | 6.47214 | 0.779154 | ||||||||
\(70\) | −5.85410 | − | 10.1396i | −0.699699 | − | 1.21191i | ||||
\(71\) | 1.47214 | − | 2.54981i | 0.174710 | − | 0.302607i | −0.765351 | − | 0.643614i | \(-0.777434\pi\) |
0.940061 | + | 0.341006i | \(0.110768\pi\) | |||||||
\(72\) | 0.736068 | + | 1.27491i | 0.0867464 | + | 0.150249i | ||||
\(73\) | 2.80902 | − | 4.86536i | 0.328771 | − | 0.569447i | −0.653498 | − | 0.756929i | \(-0.726699\pi\) |
0.982268 | + | 0.187481i | \(0.0600324\pi\) | |||||||
\(74\) | 4.19098 | − | 7.25900i | 0.487192 | − | 0.843841i | ||||
\(75\) | 10.0000 | 1.15470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.4721 | 1.19341 | ||||||||
\(78\) | 0.854102 | − | 1.47935i | 0.0967080 | − | 0.167503i | ||||
\(79\) | −1.38197 | + | 2.39364i | −0.155483 | + | 0.269305i | −0.933235 | − | 0.359267i | \(-0.883027\pi\) |
0.777752 | + | 0.628572i | \(0.216360\pi\) | |||||||
\(80\) | 1.80902 | + | 3.13331i | 0.202254 | + | 0.350315i | ||||
\(81\) | 1.20820 | − | 2.09267i | 0.134245 | − | 0.232519i | ||||
\(82\) | 0.427051 | + | 0.739674i | 0.0471599 | + | 0.0816833i | ||||
\(83\) | −0.472136 | −0.0518237 | −0.0259118 | − | 0.999664i | \(-0.508249\pi\) | ||||
−0.0259118 | + | 0.999664i | \(0.508249\pi\) | |||||||
\(84\) | −4.00000 | −0.436436 | ||||||||
\(85\) | −6.11803 | − | 10.5967i | −0.663594 | − | 1.14938i | ||||
\(86\) | 4.61803 | + | 7.99867i | 0.497975 | + | 0.862519i | ||||
\(87\) | 11.2361 | 1.20463 | ||||||||
\(88\) | −3.23607 | −0.344966 | ||||||||
\(89\) | 4.42705 | + | 7.66788i | 0.469266 | + | 0.812793i | 0.999383 | − | 0.0351316i | \(-0.0111850\pi\) |
−0.530116 | + | 0.847925i | \(0.677852\pi\) | |||||||
\(90\) | −2.66312 | + | 4.61266i | −0.280717 | + | 0.486217i | ||||
\(91\) | −2.23607 | − | 3.87298i | −0.234404 | − | 0.405999i | ||||
\(92\) | −2.61803 | + | 4.53457i | −0.272949 | + | 0.472761i | ||||
\(93\) | −0.763932 | + | 1.32317i | −0.0792161 | + | 0.137206i | ||||
\(94\) | 4.47214 | 0.461266 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.23607 | 0.126156 | ||||||||
\(97\) | 4.30902 | − | 7.46344i | 0.437514 | − | 0.757797i | −0.559983 | − | 0.828504i | \(-0.689192\pi\) |
0.997497 | + | 0.0707071i | \(0.0225256\pi\) | |||||||
\(98\) | −1.73607 | + | 3.00696i | −0.175369 | + | 0.303749i | ||||
\(99\) | −2.38197 | − | 4.12569i | −0.239397 | − | 0.414647i | ||||
\(100\) | −4.04508 | + | 7.00629i | −0.404508 | + | 0.700629i | ||||
\(101\) | 7.80902 | + | 13.5256i | 0.777026 | + | 1.34585i | 0.933649 | + | 0.358190i | \(0.116606\pi\) |
−0.156622 | + | 0.987659i | \(0.550061\pi\) | |||||||
\(102\) | −4.18034 | −0.413915 | ||||||||
\(103\) | −14.6525 | −1.44375 | −0.721876 | − | 0.692023i | \(-0.756720\pi\) | ||||
−0.721876 | + | 0.692023i | \(0.756720\pi\) | |||||||
\(104\) | 0.690983 | + | 1.19682i | 0.0677565 | + | 0.117358i | ||||
\(105\) | −7.23607 | − | 12.5332i | −0.706168 | − | 1.22312i | ||||
\(106\) | 6.09017 | 0.591530 | ||||||||
\(107\) | −9.41641 | −0.910319 | −0.455159 | − | 0.890410i | \(-0.650418\pi\) | ||||
−0.455159 | + | 0.890410i | \(0.650418\pi\) | |||||||
\(108\) | 2.76393 | + | 4.78727i | 0.265959 | + | 0.460655i | ||||
\(109\) | −5.51722 | + | 9.55611i | −0.528454 | + | 0.915309i | 0.470996 | + | 0.882136i | \(0.343895\pi\) |
−0.999450 | + | 0.0331735i | \(0.989439\pi\) | |||||||
\(110\) | −5.85410 | − | 10.1396i | −0.558167 | − | 0.966773i | ||||
\(111\) | 5.18034 | − | 8.97261i | 0.491696 | − | 0.851643i | ||||
\(112\) | 1.61803 | − | 2.80252i | 0.152890 | − | 0.264813i | ||||
\(113\) | 9.85410 | 0.926996 | 0.463498 | − | 0.886098i | \(-0.346594\pi\) | ||||
0.463498 | + | 0.886098i | \(0.346594\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −18.9443 | −1.76656 | ||||||||
\(116\) | −4.54508 | + | 7.87232i | −0.422001 | + | 0.730926i | ||||
\(117\) | −1.01722 | + | 1.76188i | −0.0940421 | + | 0.162886i | ||||
\(118\) | −0.236068 | − | 0.408882i | −0.0217318 | − | 0.0376406i | ||||
\(119\) | −5.47214 | + | 9.47802i | −0.501630 | + | 0.868848i | ||||
\(120\) | 2.23607 | + | 3.87298i | 0.204124 | + | 0.353553i | ||||
\(121\) | −0.527864 | −0.0479876 | ||||||||
\(122\) | 1.38197 | 0.125117 | ||||||||
\(123\) | 0.527864 | + | 0.914287i | 0.0475959 | + | 0.0824385i | ||||
\(124\) | −0.618034 | − | 1.07047i | −0.0555011 | − | 0.0961307i | ||||
\(125\) | −11.1803 | −1.00000 | ||||||||
\(126\) | 4.76393 | 0.424405 | ||||||||
\(127\) | −5.70820 | − | 9.88690i | −0.506521 | − | 0.877320i | −0.999972 | − | 0.00754646i | \(-0.997598\pi\) |
0.493450 | − | 0.869774i | \(-0.335735\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 5.70820 | + | 9.88690i | 0.502579 | + | 0.870493i | ||||
\(130\) | −2.50000 | + | 4.33013i | −0.219265 | + | 0.379777i | ||||
\(131\) | −2.23607 | + | 3.87298i | −0.195366 | + | 0.338384i | −0.947020 | − | 0.321173i | \(-0.895923\pi\) |
0.751654 | + | 0.659557i | \(0.229256\pi\) | |||||||
\(132\) | −4.00000 | −0.348155 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −11.7082 | −1.01143 | ||||||||
\(135\) | −10.0000 | + | 17.3205i | −0.860663 | + | 1.49071i | ||||
\(136\) | 1.69098 | − | 2.92887i | 0.145001 | − | 0.251148i | ||||
\(137\) | −1.19098 | − | 2.06284i | −0.101753 | − | 0.176241i | 0.810654 | − | 0.585525i | \(-0.199112\pi\) |
−0.912407 | + | 0.409285i | \(0.865778\pi\) | |||||||
\(138\) | −3.23607 | + | 5.60503i | −0.275472 | + | 0.477132i | ||||
\(139\) | 7.00000 | + | 12.1244i | 0.593732 | + | 1.02837i | 0.993724 | + | 0.111856i | \(0.0356795\pi\) |
−0.399992 | + | 0.916519i | \(0.630987\pi\) | |||||||
\(140\) | 11.7082 | 0.989524 | ||||||||
\(141\) | 5.52786 | 0.465530 | ||||||||
\(142\) | 1.47214 | + | 2.54981i | 0.123539 | + | 0.213976i | ||||
\(143\) | −2.23607 | − | 3.87298i | −0.186989 | − | 0.323875i | ||||
\(144\) | −1.47214 | −0.122678 | ||||||||
\(145\) | −32.8885 | −2.73124 | ||||||||
\(146\) | 2.80902 | + | 4.86536i | 0.232476 | + | 0.402660i | ||||
\(147\) | −2.14590 | + | 3.71680i | −0.176991 | + | 0.306557i | ||||
\(148\) | 4.19098 | + | 7.25900i | 0.344497 | + | 0.596686i | ||||
\(149\) | 6.54508 | − | 11.3364i | 0.536194 | − | 0.928716i | −0.462910 | − | 0.886405i | \(-0.653195\pi\) |
0.999105 | − | 0.0423105i | \(-0.0134719\pi\) | |||||||
\(150\) | −5.00000 | + | 8.66025i | −0.408248 | + | 0.707107i | ||||
\(151\) | −14.4721 | −1.17773 | −0.588863 | − | 0.808233i | \(-0.700424\pi\) | ||||
−0.588863 | + | 0.808233i | \(0.700424\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.97871 | 0.402505 | ||||||||
\(154\) | −5.23607 | + | 9.06914i | −0.421934 | + | 0.730812i | ||||
\(155\) | 2.23607 | − | 3.87298i | 0.179605 | − | 0.311086i | ||||
\(156\) | 0.854102 | + | 1.47935i | 0.0683829 | + | 0.118443i | ||||
\(157\) | −4.69098 | + | 8.12502i | −0.374381 | + | 0.648447i | −0.990234 | − | 0.139414i | \(-0.955478\pi\) |
0.615853 | + | 0.787861i | \(0.288812\pi\) | |||||||
\(158\) | −1.38197 | − | 2.39364i | −0.109943 | − | 0.190427i | ||||
\(159\) | 7.52786 | 0.596998 | ||||||||
\(160\) | −3.61803 | −0.286031 | ||||||||
\(161\) | 8.47214 | + | 14.6742i | 0.667698 | + | 1.15649i | ||||
\(162\) | 1.20820 | + | 2.09267i | 0.0949255 | + | 0.164416i | ||||
\(163\) | 10.6525 | 0.834366 | 0.417183 | − | 0.908822i | \(-0.363017\pi\) | ||||
0.417183 | + | 0.908822i | \(0.363017\pi\) | |||||||
\(164\) | −0.854102 | −0.0666942 | ||||||||
\(165\) | −7.23607 | − | 12.5332i | −0.563327 | − | 0.975711i | ||||
\(166\) | 0.236068 | − | 0.408882i | 0.0183224 | − | 0.0317354i | ||||
\(167\) | −6.23607 | − | 10.8012i | −0.482561 | − | 0.835821i | 0.517238 | − | 0.855842i | \(-0.326960\pi\) |
−0.999800 | + | 0.0200206i | \(0.993627\pi\) | |||||||
\(168\) | 2.00000 | − | 3.46410i | 0.154303 | − | 0.267261i | ||||
\(169\) | 5.54508 | − | 9.60437i | 0.426545 | − | 0.738798i | ||||
\(170\) | 12.2361 | 0.938464 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9.23607 | −0.704244 | ||||||||
\(173\) | 0.663119 | − | 1.14856i | 0.0504160 | − | 0.0873231i | −0.839716 | − | 0.543026i | \(-0.817279\pi\) |
0.890132 | + | 0.455703i | \(0.150612\pi\) | |||||||
\(174\) | −5.61803 | + | 9.73072i | −0.425902 | + | 0.737684i | ||||
\(175\) | 13.0902 | + | 22.6728i | 0.989524 | + | 1.71391i | ||||
\(176\) | 1.61803 | − | 2.80252i | 0.121964 | − | 0.211248i | ||||
\(177\) | −0.291796 | − | 0.505406i | −0.0219327 | − | 0.0379886i | ||||
\(178\) | −8.85410 | −0.663643 | ||||||||
\(179\) | 23.4164 | 1.75022 | 0.875112 | − | 0.483920i | \(-0.160787\pi\) | ||||
0.875112 | + | 0.483920i | \(0.160787\pi\) | |||||||
\(180\) | −2.66312 | − | 4.61266i | −0.198497 | − | 0.343807i | ||||
\(181\) | 2.70820 | + | 4.69075i | 0.201299 | + | 0.348660i | 0.948947 | − | 0.315435i | \(-0.102150\pi\) |
−0.747648 | + | 0.664095i | \(0.768817\pi\) | |||||||
\(182\) | 4.47214 | 0.331497 | ||||||||
\(183\) | 1.70820 | 0.126274 | ||||||||
\(184\) | −2.61803 | − | 4.53457i | −0.193004 | − | 0.334293i | ||||
\(185\) | −15.1631 | + | 26.2633i | −1.11481 | + | 1.93092i | ||||
\(186\) | −0.763932 | − | 1.32317i | −0.0560142 | − | 0.0970195i | ||||
\(187\) | −5.47214 | + | 9.47802i | −0.400162 | + | 0.693101i | ||||
\(188\) | −2.23607 | + | 3.87298i | −0.163082 | + | 0.282466i | ||||
\(189\) | 17.8885 | 1.30120 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.52786 | 0.255267 | 0.127634 | − | 0.991821i | \(-0.459262\pi\) | ||||
0.127634 | + | 0.991821i | \(0.459262\pi\) | |||||||
\(192\) | −0.618034 | + | 1.07047i | −0.0446028 | + | 0.0772542i | ||||
\(193\) | −5.76393 | + | 9.98342i | −0.414897 | + | 0.718623i | −0.995418 | − | 0.0956230i | \(-0.969516\pi\) |
0.580521 | + | 0.814245i | \(0.302849\pi\) | |||||||
\(194\) | 4.30902 | + | 7.46344i | 0.309369 | + | 0.535844i | ||||
\(195\) | −3.09017 | + | 5.35233i | −0.221292 | + | 0.383288i | ||||
\(196\) | −1.73607 | − | 3.00696i | −0.124005 | − | 0.214783i | ||||
\(197\) | −4.14590 | −0.295383 | −0.147692 | − | 0.989033i | \(-0.547184\pi\) | ||||
−0.147692 | + | 0.989033i | \(0.547184\pi\) | |||||||
\(198\) | 4.76393 | 0.338558 | ||||||||
\(199\) | −5.23607 | − | 9.06914i | −0.371175 | − | 0.642894i | 0.618572 | − | 0.785728i | \(-0.287712\pi\) |
−0.989747 | + | 0.142834i | \(0.954378\pi\) | |||||||
\(200\) | −4.04508 | − | 7.00629i | −0.286031 | − | 0.495420i | ||||
\(201\) | −14.4721 | −1.02079 | ||||||||
\(202\) | −15.6180 | −1.09888 | ||||||||
\(203\) | 14.7082 | + | 25.4754i | 1.03231 | + | 1.78802i | ||||
\(204\) | 2.09017 | − | 3.62028i | 0.146341 | − | 0.253470i | ||||
\(205\) | −1.54508 | − | 2.67617i | −0.107913 | − | 0.186912i | ||||
\(206\) | 7.32624 | − | 12.6894i | 0.510443 | − | 0.884114i | ||||
\(207\) | 3.85410 | − | 6.67550i | 0.267879 | − | 0.463979i | ||||
\(208\) | −1.38197 | −0.0958221 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 14.4721 | 0.998672 | ||||||||
\(211\) | −3.61803 | + | 6.26662i | −0.249076 | + | 0.431412i | −0.963270 | − | 0.268536i | \(-0.913460\pi\) |
0.714194 | + | 0.699948i | \(0.246793\pi\) | |||||||
\(212\) | −3.04508 | + | 5.27424i | −0.209137 | + | 0.362236i | ||||
\(213\) | 1.81966 | + | 3.15174i | 0.124681 | + | 0.215954i | ||||
\(214\) | 4.70820 | − | 8.15485i | 0.321846 | − | 0.557454i | ||||
\(215\) | −16.7082 | − | 28.9395i | −1.13949 | − | 1.97365i | ||||
\(216\) | −5.52786 | −0.376124 | ||||||||
\(217\) | −4.00000 | −0.271538 | ||||||||
\(218\) | −5.51722 | − | 9.55611i | −0.373673 | − | 0.647221i | ||||
\(219\) | 3.47214 | + | 6.01392i | 0.234625 | + | 0.406383i | ||||
\(220\) | 11.7082 | 0.789367 | ||||||||
\(221\) | 4.67376 | 0.314391 | ||||||||
\(222\) | 5.18034 | + | 8.97261i | 0.347682 | + | 0.602202i | ||||
\(223\) | 13.8541 | − | 23.9960i | 0.927739 | − | 1.60689i | 0.140644 | − | 0.990060i | \(-0.455083\pi\) |
0.787095 | − | 0.616831i | \(-0.211584\pi\) | |||||||
\(224\) | 1.61803 | + | 2.80252i | 0.108109 | + | 0.187251i | ||||
\(225\) | 5.95492 | − | 10.3142i | 0.396994 | − | 0.687614i | ||||
\(226\) | −4.92705 | + | 8.53390i | −0.327743 | + | 0.567667i | ||||
\(227\) | 8.94427 | 0.593652 | 0.296826 | − | 0.954932i | \(-0.404072\pi\) | ||||
0.296826 | + | 0.954932i | \(0.404072\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.38197 | 0.289568 | 0.144784 | − | 0.989463i | \(-0.453751\pi\) | ||||
0.144784 | + | 0.989463i | \(0.453751\pi\) | |||||||
\(230\) | 9.47214 | − | 16.4062i | 0.624574 | − | 1.08179i | ||||
\(231\) | −6.47214 | + | 11.2101i | −0.425835 | + | 0.737568i | ||||
\(232\) | −4.54508 | − | 7.87232i | −0.298399 | − | 0.516843i | ||||
\(233\) | −0.781153 | + | 1.35300i | −0.0511750 | + | 0.0886378i | −0.890478 | − | 0.455026i | \(-0.849630\pi\) |
0.839303 | + | 0.543664i | \(0.182963\pi\) | |||||||
\(234\) | −1.01722 | − | 1.76188i | −0.0664978 | − | 0.115178i | ||||
\(235\) | −16.1803 | −1.05549 | ||||||||
\(236\) | 0.472136 | 0.0307334 | ||||||||
\(237\) | −1.70820 | − | 2.95870i | −0.110960 | − | 0.192188i | ||||
\(238\) | −5.47214 | − | 9.47802i | −0.354706 | − | 0.614369i | ||||
\(239\) | 30.1803 | 1.95220 | 0.976102 | − | 0.217313i | \(-0.0697293\pi\) | ||||
0.976102 | + | 0.217313i | \(0.0697293\pi\) | |||||||
\(240\) | −4.47214 | −0.288675 | ||||||||
\(241\) | −12.7082 | − | 22.0113i | −0.818607 | − | 1.41787i | −0.906708 | − | 0.421758i | \(-0.861413\pi\) |
0.0881010 | − | 0.996112i | \(-0.471920\pi\) | |||||||
\(242\) | 0.263932 | − | 0.457144i | 0.0169662 | − | 0.0293863i | ||||
\(243\) | −6.79837 | − | 11.7751i | −0.436116 | − | 0.755375i | ||||
\(244\) | −0.690983 | + | 1.19682i | −0.0442357 | + | 0.0766184i | ||||
\(245\) | 6.28115 | − | 10.8793i | 0.401288 | − | 0.695051i | ||||
\(246\) | −1.05573 | −0.0673108 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.23607 | 0.0784904 | ||||||||
\(249\) | 0.291796 | − | 0.505406i | 0.0184918 | − | 0.0320288i | ||||
\(250\) | 5.59017 | − | 9.68246i | 0.353553 | − | 0.612372i | ||||
\(251\) | 1.14590 | + | 1.98475i | 0.0723284 | + | 0.125277i | 0.899921 | − | 0.436052i | \(-0.143624\pi\) |
−0.827593 | + | 0.561329i | \(0.810290\pi\) | |||||||
\(252\) | −2.38197 | + | 4.12569i | −0.150050 | + | 0.259894i | ||||
\(253\) | 8.47214 | + | 14.6742i | 0.532639 | + | 0.922557i | ||||
\(254\) | 11.4164 | 0.716329 | ||||||||
\(255\) | 15.1246 | 0.947140 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 9.19098 | + | 15.9192i | 0.573318 | + | 0.993016i | 0.996222 | + | 0.0868412i | \(0.0276773\pi\) |
−0.422904 | + | 0.906174i | \(0.638989\pi\) | |||||||
\(258\) | −11.4164 | −0.710755 | ||||||||
\(259\) | 27.1246 | 1.68544 | ||||||||
\(260\) | −2.50000 | − | 4.33013i | −0.155043 | − | 0.268543i | ||||
\(261\) | 6.69098 | − | 11.5891i | 0.414161 | − | 0.717349i | ||||
\(262\) | −2.23607 | − | 3.87298i | −0.138145 | − | 0.239274i | ||||
\(263\) | −1.47214 | + | 2.54981i | −0.0907758 | + | 0.157228i | −0.907838 | − | 0.419322i | \(-0.862268\pi\) |
0.817062 | + | 0.576550i | \(0.195601\pi\) | |||||||
\(264\) | 2.00000 | − | 3.46410i | 0.123091 | − | 0.213201i | ||||
\(265\) | −22.0344 | −1.35357 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.9443 | −0.669779 | ||||||||
\(268\) | 5.85410 | − | 10.1396i | 0.357596 | − | 0.619375i | ||||
\(269\) | 7.16312 | − | 12.4069i | 0.436743 | − | 0.756461i | −0.560693 | − | 0.828024i | \(-0.689465\pi\) |
0.997436 | + | 0.0715625i | \(0.0227986\pi\) | |||||||
\(270\) | −10.0000 | − | 17.3205i | −0.608581 | − | 1.05409i | ||||
\(271\) | −13.0000 | + | 22.5167i | −0.789694 | + | 1.36779i | 0.136461 | + | 0.990645i | \(0.456427\pi\) |
−0.926155 | + | 0.377144i | \(0.876906\pi\) | |||||||
\(272\) | 1.69098 | + | 2.92887i | 0.102531 | + | 0.177589i | ||||
\(273\) | 5.52786 | 0.334562 | ||||||||
\(274\) | 2.38197 | 0.143900 | ||||||||
\(275\) | 13.0902 | + | 22.6728i | 0.789367 | + | 1.36722i | ||||
\(276\) | −3.23607 | − | 5.60503i | −0.194788 | − | 0.337383i | ||||
\(277\) | −10.0902 | −0.606260 | −0.303130 | − | 0.952949i | \(-0.598032\pi\) | ||||
−0.303130 | + | 0.952949i | \(0.598032\pi\) | |||||||
\(278\) | −14.0000 | −0.839664 | ||||||||
\(279\) | 0.909830 | + | 1.57587i | 0.0544701 | + | 0.0943450i | ||||
\(280\) | −5.85410 | + | 10.1396i | −0.349850 | + | 0.605957i | ||||
\(281\) | 10.4894 | + | 18.1681i | 0.625743 | + | 1.08382i | 0.988397 | + | 0.151894i | \(0.0485373\pi\) |
−0.362654 | + | 0.931924i | \(0.618129\pi\) | |||||||
\(282\) | −2.76393 | + | 4.78727i | −0.164590 | + | 0.285078i | ||||
\(283\) | −11.2361 | + | 19.4614i | −0.667915 | + | 1.15686i | 0.310571 | + | 0.950550i | \(0.399480\pi\) |
−0.978486 | + | 0.206312i | \(0.933854\pi\) | |||||||
\(284\) | −2.94427 | −0.174710 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.47214 | 0.264443 | ||||||||
\(287\) | −1.38197 | + | 2.39364i | −0.0815749 | + | 0.141292i | ||||
\(288\) | 0.736068 | − | 1.27491i | 0.0433732 | − | 0.0751246i | ||||
\(289\) | 2.78115 | + | 4.81710i | 0.163597 | + | 0.283359i | ||||
\(290\) | 16.4443 | − | 28.4823i | 0.965641 | − | 1.67254i | ||||
\(291\) | 5.32624 | + | 9.22531i | 0.312230 | + | 0.540798i | ||||
\(292\) | −5.61803 | −0.328771 | ||||||||
\(293\) | −22.9443 | −1.34042 | −0.670209 | − | 0.742172i | \(-0.733796\pi\) | ||||
−0.670209 | + | 0.742172i | \(0.733796\pi\) | |||||||
\(294\) | −2.14590 | − | 3.71680i | −0.125151 | − | 0.216768i | ||||
\(295\) | 0.854102 | + | 1.47935i | 0.0497277 | + | 0.0861310i | ||||
\(296\) | −8.38197 | −0.487192 | ||||||||
\(297\) | 17.8885 | 1.03800 | ||||||||
\(298\) | 6.54508 | + | 11.3364i | 0.379147 | + | 0.656701i | ||||
\(299\) | 3.61803 | − | 6.26662i | 0.209236 | − | 0.362408i | ||||
\(300\) | −5.00000 | − | 8.66025i | −0.288675 | − | 0.500000i | ||||
\(301\) | −14.9443 | + | 25.8842i | −0.861374 | + | 1.49194i | ||||
\(302\) | 7.23607 | − | 12.5332i | 0.416389 | − | 0.721207i | ||||
\(303\) | −19.3050 | −1.10904 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.00000 | −0.286299 | ||||||||
\(306\) | −2.48936 | + | 4.31169i | −0.142307 | + | 0.246483i | ||||
\(307\) | 5.85410 | − | 10.1396i | 0.334111 | − | 0.578698i | −0.649202 | − | 0.760616i | \(-0.724897\pi\) |
0.983314 | + | 0.181918i | \(0.0582305\pi\) | |||||||
\(308\) | −5.23607 | − | 9.06914i | −0.298353 | − | 0.516762i | ||||
\(309\) | 9.05573 | − | 15.6850i | 0.515162 | − | 0.892287i | ||||
\(310\) | 2.23607 | + | 3.87298i | 0.127000 | + | 0.219971i | ||||
\(311\) | 31.2361 | 1.77123 | 0.885617 | − | 0.464415i | \(-0.153736\pi\) | ||||
0.885617 | + | 0.464415i | \(0.153736\pi\) | |||||||
\(312\) | −1.70820 | −0.0967080 | ||||||||
\(313\) | 7.75329 | + | 13.4291i | 0.438242 | + | 0.759057i | 0.997554 | − | 0.0699000i | \(-0.0222680\pi\) |
−0.559312 | + | 0.828957i | \(0.688935\pi\) | |||||||
\(314\) | −4.69098 | − | 8.12502i | −0.264727 | − | 0.458521i | ||||
\(315\) | −17.2361 | −0.971142 | ||||||||
\(316\) | 2.76393 | 0.155483 | ||||||||
\(317\) | 0.663119 | + | 1.14856i | 0.0372445 | + | 0.0645093i | 0.884047 | − | 0.467398i | \(-0.154809\pi\) |
−0.846802 | + | 0.531908i | \(0.821475\pi\) | |||||||
\(318\) | −3.76393 | + | 6.51932i | −0.211071 | + | 0.365585i | ||||
\(319\) | 14.7082 | + | 25.4754i | 0.823501 | + | 1.42635i | ||||
\(320\) | 1.80902 | − | 3.13331i | 0.101127 | − | 0.175157i | ||||
\(321\) | 5.81966 | − | 10.0799i | 0.324822 | − | 0.562608i | ||||
\(322\) | −16.9443 | −0.944267 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −2.41641 | −0.134245 | ||||||||
\(325\) | 5.59017 | − | 9.68246i | 0.310087 | − | 0.537086i | ||||
\(326\) | −5.32624 | + | 9.22531i | −0.294993 | + | 0.510943i | ||||
\(327\) | −6.81966 | − | 11.8120i | −0.377128 | − | 0.653205i | ||||
\(328\) | 0.427051 | − | 0.739674i | 0.0235799 | − | 0.0408417i | ||||
\(329\) | 7.23607 | + | 12.5332i | 0.398937 | + | 0.690980i | ||||
\(330\) | 14.4721 | 0.796665 | ||||||||
\(331\) | −25.7082 | −1.41305 | −0.706525 | − | 0.707688i | \(-0.749738\pi\) | ||||
−0.706525 | + | 0.707688i | \(0.749738\pi\) | |||||||
\(332\) | 0.236068 | + | 0.408882i | 0.0129559 | + | 0.0224403i | ||||
\(333\) | −6.16970 | − | 10.6862i | −0.338097 | − | 0.585602i | ||||
\(334\) | 12.4721 | 0.682445 | ||||||||
\(335\) | 42.3607 | 2.31441 | ||||||||
\(336\) | 2.00000 | + | 3.46410i | 0.109109 | + | 0.188982i | ||||
\(337\) | 1.19098 | − | 2.06284i | 0.0648770 | − | 0.112370i | −0.831762 | − | 0.555132i | \(-0.812668\pi\) |
0.896639 | + | 0.442762i | \(0.146001\pi\) | |||||||
\(338\) | 5.54508 | + | 9.60437i | 0.301613 | + | 0.522409i | ||||
\(339\) | −6.09017 | + | 10.5485i | −0.330773 | + | 0.572915i | ||||
\(340\) | −6.11803 | + | 10.5967i | −0.331797 | + | 0.574689i | ||||
\(341\) | −4.00000 | −0.216612 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.4164 | 0.616428 | ||||||||
\(344\) | 4.61803 | − | 7.99867i | 0.248988 | − | 0.431259i | ||||
\(345\) | 11.7082 | − | 20.2792i | 0.630349 | − | 1.09180i | ||||
\(346\) | 0.663119 | + | 1.14856i | 0.0356495 | + | 0.0617467i | ||||
\(347\) | 1.32624 | − | 2.29711i | 0.0711962 | − | 0.123315i | −0.828230 | − | 0.560389i | \(-0.810652\pi\) |
0.899426 | + | 0.437073i | \(0.143985\pi\) | |||||||
\(348\) | −5.61803 | − | 9.73072i | −0.301158 | − | 0.521621i | ||||
\(349\) | −33.0902 | −1.77128 | −0.885638 | − | 0.464376i | \(-0.846279\pi\) | ||||
−0.885638 | + | 0.464376i | \(0.846279\pi\) | |||||||
\(350\) | −26.1803 | −1.39940 | ||||||||
\(351\) | −3.81966 | − | 6.61585i | −0.203878 | − | 0.353128i | ||||
\(352\) | 1.61803 | + | 2.80252i | 0.0862415 | + | 0.149375i | ||||
\(353\) | −23.7426 | −1.26369 | −0.631847 | − | 0.775093i | \(-0.717703\pi\) | ||||
−0.631847 | + | 0.775093i | \(0.717703\pi\) | |||||||
\(354\) | 0.583592 | 0.0310176 | ||||||||
\(355\) | −5.32624 | − | 9.22531i | −0.282687 | − | 0.489629i | ||||
\(356\) | 4.42705 | − | 7.66788i | 0.234633 | − | 0.406397i | ||||
\(357\) | −6.76393 | − | 11.7155i | −0.357985 | − | 0.620049i | ||||
\(358\) | −11.7082 | + | 20.2792i | −0.618798 | + | 1.07179i | ||||
\(359\) | −5.76393 | + | 9.98342i | −0.304209 | + | 0.526905i | −0.977085 | − | 0.212850i | \(-0.931725\pi\) |
0.672876 | + | 0.739755i | \(0.265059\pi\) | |||||||
\(360\) | 5.32624 | 0.280717 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −5.41641 | −0.284680 | ||||||||
\(363\) | 0.326238 | − | 0.565061i | 0.0171231 | − | 0.0296580i | ||||
\(364\) | −2.23607 | + | 3.87298i | −0.117202 | + | 0.202999i | ||||
\(365\) | −10.1631 | − | 17.6030i | −0.531962 | − | 0.921385i | ||||
\(366\) | −0.854102 | + | 1.47935i | −0.0446446 | + | 0.0773268i | ||||
\(367\) | −9.41641 | − | 16.3097i | −0.491532 | − | 0.851359i | 0.508420 | − | 0.861109i | \(-0.330230\pi\) |
−0.999952 | + | 0.00975000i | \(0.996896\pi\) | |||||||
\(368\) | 5.23607 | 0.272949 | ||||||||
\(369\) | 1.25735 | 0.0654552 | ||||||||
\(370\) | −15.1631 | − | 26.2633i | −0.788293 | − | 1.36536i | ||||
\(371\) | 9.85410 | + | 17.0678i | 0.511599 | + | 0.886116i | ||||
\(372\) | 1.52786 | 0.0792161 | ||||||||
\(373\) | −18.3262 | −0.948897 | −0.474448 | − | 0.880283i | \(-0.657352\pi\) | ||||
−0.474448 | + | 0.880283i | \(0.657352\pi\) | |||||||
\(374\) | −5.47214 | − | 9.47802i | −0.282957 | − | 0.490097i | ||||
\(375\) | 6.90983 | − | 11.9682i | 0.356822 | − | 0.618034i | ||||
\(376\) | −2.23607 | − | 3.87298i | −0.115316 | − | 0.199734i | ||||
\(377\) | 6.28115 | − | 10.8793i | 0.323496 | − | 0.560311i | ||||
\(378\) | −8.94427 | + | 15.4919i | −0.460044 | + | 0.796819i | ||||
\(379\) | 35.4164 | 1.81922 | 0.909609 | − | 0.415465i | \(-0.136381\pi\) | ||||
0.909609 | + | 0.415465i | \(0.136381\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.1115 | 0.722952 | ||||||||
\(382\) | −1.76393 | + | 3.05522i | −0.0902506 | + | 0.156319i | ||||
\(383\) | 10.3820 | − | 17.9821i | 0.530494 | − | 0.918842i | −0.468873 | − | 0.883265i | \(-0.655340\pi\) |
0.999367 | − | 0.0355766i | \(-0.0113268\pi\) | |||||||
\(384\) | −0.618034 | − | 1.07047i | −0.0315389 | − | 0.0546270i | ||||
\(385\) | 18.9443 | − | 32.8124i | 0.965489 | − | 1.67228i | ||||
\(386\) | −5.76393 | − | 9.98342i | −0.293376 | − | 0.508143i | ||||
\(387\) | 13.5967 | 0.691162 | ||||||||
\(388\) | −8.61803 | −0.437514 | ||||||||
\(389\) | −6.39919 | − | 11.0837i | −0.324452 | − | 0.561967i | 0.656950 | − | 0.753935i | \(-0.271846\pi\) |
−0.981401 | + | 0.191968i | \(0.938513\pi\) | |||||||
\(390\) | −3.09017 | − | 5.35233i | −0.156477 | − | 0.271026i | ||||
\(391\) | −17.7082 | −0.895542 | ||||||||
\(392\) | 3.47214 | 0.175369 | ||||||||
\(393\) | −2.76393 | − | 4.78727i | −0.139422 | − | 0.241486i | ||||
\(394\) | 2.07295 | − | 3.59045i | 0.104434 | − | 0.180884i | ||||
\(395\) | 5.00000 | + | 8.66025i | 0.251577 | + | 0.435745i | ||||
\(396\) | −2.38197 | + | 4.12569i | −0.119698 | + | 0.207324i | ||||
\(397\) | 11.1803 | − | 19.3649i | 0.561125 | − | 0.971897i | −0.436273 | − | 0.899814i | \(-0.643702\pi\) |
0.997399 | − | 0.0720832i | \(-0.0229647\pi\) | |||||||
\(398\) | 10.4721 | 0.524921 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.09017 | 0.404508 | ||||||||
\(401\) | 9.47214 | − | 16.4062i | 0.473016 | − | 0.819288i | −0.526507 | − | 0.850171i | \(-0.676499\pi\) |
0.999523 | + | 0.0308832i | \(0.00983198\pi\) | |||||||
\(402\) | 7.23607 | − | 12.5332i | 0.360902 | − | 0.625101i | ||||
\(403\) | 0.854102 | + | 1.47935i | 0.0425458 | + | 0.0736916i | ||||
\(404\) | 7.80902 | − | 13.5256i | 0.388513 | − | 0.672924i | ||||
\(405\) | −4.37132 | − | 7.57135i | −0.217213 | − | 0.376224i | ||||
\(406\) | −29.4164 | −1.45991 | ||||||||
\(407\) | 27.1246 | 1.34452 | ||||||||
\(408\) | 2.09017 | + | 3.62028i | 0.103479 | + | 0.179231i | ||||
\(409\) | 8.13525 | + | 14.0907i | 0.402262 | + | 0.696739i | 0.993999 | − | 0.109393i | \(-0.0348906\pi\) |
−0.591736 | + | 0.806132i | \(0.701557\pi\) | |||||||
\(410\) | 3.09017 | 0.152613 | ||||||||
\(411\) | 2.94427 | 0.145230 | ||||||||
\(412\) | 7.32624 | + | 12.6894i | 0.360938 | + | 0.625163i | ||||
\(413\) | 0.763932 | − | 1.32317i | 0.0375906 | − | 0.0651089i | ||||
\(414\) | 3.85410 | + | 6.67550i | 0.189419 | + | 0.328083i | ||||
\(415\) | −0.854102 | + | 1.47935i | −0.0419262 | + | 0.0726183i | ||||
\(416\) | 0.690983 | − | 1.19682i | 0.0338782 | − | 0.0586788i | ||||
\(417\) | −17.3050 | −0.847427 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.47214 | −0.316185 | −0.158092 | − | 0.987424i | \(-0.550534\pi\) | ||||
−0.158092 | + | 0.987424i | \(0.550534\pi\) | |||||||
\(420\) | −7.23607 | + | 12.5332i | −0.353084 | + | 0.611559i | ||||
\(421\) | 6.95492 | − | 12.0463i | 0.338962 | − | 0.587099i | −0.645276 | − | 0.763950i | \(-0.723258\pi\) |
0.984238 | + | 0.176851i | \(0.0565909\pi\) | |||||||
\(422\) | −3.61803 | − | 6.26662i | −0.176123 | − | 0.305054i | ||||
\(423\) | 3.29180 | − | 5.70156i | 0.160053 | − | 0.277219i | ||||
\(424\) | −3.04508 | − | 5.27424i | −0.147882 | − | 0.256140i | ||||
\(425\) | −27.3607 | −1.32719 | ||||||||
\(426\) | −3.63932 | −0.176326 | ||||||||
\(427\) | 2.23607 | + | 3.87298i | 0.108211 | + | 0.187427i | ||||
\(428\) | 4.70820 | + | 8.15485i | 0.227580 | + | 0.394179i | ||||
\(429\) | 5.52786 | 0.266888 | ||||||||
\(430\) | 33.4164 | 1.61148 | ||||||||
\(431\) | 3.32624 | + | 5.76121i | 0.160219 | + | 0.277508i | 0.934947 | − | 0.354787i | \(-0.115447\pi\) |
−0.774728 | + | 0.632295i | \(0.782113\pi\) | |||||||
\(432\) | 2.76393 | − | 4.78727i | 0.132980 | − | 0.230328i | ||||
\(433\) | −12.5172 | − | 21.6805i | −0.601539 | − | 1.04190i | −0.992588 | − | 0.121527i | \(-0.961221\pi\) |
0.391049 | − | 0.920370i | \(-0.372112\pi\) | |||||||
\(434\) | 2.00000 | − | 3.46410i | 0.0960031 | − | 0.166282i | ||||
\(435\) | 20.3262 | − | 35.2061i | 0.974569 | − | 1.68800i | ||||
\(436\) | 11.0344 | 0.528454 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −6.94427 | −0.331810 | ||||||||
\(439\) | 14.6180 | − | 25.3192i | 0.697681 | − | 1.20842i | −0.271588 | − | 0.962414i | \(-0.587549\pi\) |
0.969269 | − | 0.246005i | \(-0.0791179\pi\) | |||||||
\(440\) | −5.85410 | + | 10.1396i | −0.279083 | + | 0.483387i | ||||
\(441\) | 2.55573 | + | 4.42665i | 0.121701 | + | 0.210793i | ||||
\(442\) | −2.33688 | + | 4.04760i | −0.111154 | + | 0.192525i | ||||
\(443\) | −4.61803 | − | 7.99867i | −0.219409 | − | 0.380028i | 0.735218 | − | 0.677831i | \(-0.237080\pi\) |
−0.954628 | + | 0.297802i | \(0.903746\pi\) | |||||||
\(444\) | −10.3607 | −0.491696 | ||||||||
\(445\) | 32.0344 | 1.51858 | ||||||||
\(446\) | 13.8541 | + | 23.9960i | 0.656011 | + | 1.13624i | ||||
\(447\) | 8.09017 | + | 14.0126i | 0.382652 | + | 0.662773i | ||||
\(448\) | −3.23607 | −0.152890 | ||||||||
\(449\) | 22.7984 | 1.07592 | 0.537961 | − | 0.842970i | \(-0.319195\pi\) | ||||
0.537961 | + | 0.842970i | \(0.319195\pi\) | |||||||
\(450\) | 5.95492 | + | 10.3142i | 0.280717 | + | 0.486217i | ||||
\(451\) | −1.38197 | + | 2.39364i | −0.0650742 | + | 0.112712i | ||||
\(452\) | −4.92705 | − | 8.53390i | −0.231749 | − | 0.401401i | ||||
\(453\) | 8.94427 | − | 15.4919i | 0.420239 | − | 0.727875i | ||||
\(454\) | −4.47214 | + | 7.74597i | −0.209888 | + | 0.363536i | ||||
\(455\) | −16.1803 | −0.758546 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.2148 | 1.17950 | 0.589749 | − | 0.807587i | \(-0.299227\pi\) | ||||
0.589749 | + | 0.807587i | \(0.299227\pi\) | |||||||
\(458\) | −2.19098 | + | 3.79489i | −0.102378 | + | 0.177324i | ||||
\(459\) | −9.34752 | + | 16.1904i | −0.436305 | + | 0.755703i | ||||
\(460\) | 9.47214 | + | 16.4062i | 0.441641 | + | 0.764944i | ||||
\(461\) | −10.7082 | + | 18.5472i | −0.498731 | + | 0.863827i | −0.999999 | − | 0.00146495i | \(-0.999534\pi\) |
0.501268 | + | 0.865292i | \(0.332867\pi\) | |||||||
\(462\) | −6.47214 | − | 11.2101i | −0.301111 | − | 0.521540i | ||||
\(463\) | −5.05573 | −0.234960 | −0.117480 | − | 0.993075i | \(-0.537482\pi\) | ||||
−0.117480 | + | 0.993075i | \(0.537482\pi\) | |||||||
\(464\) | 9.09017 | 0.422001 | ||||||||
\(465\) | 2.76393 | + | 4.78727i | 0.128174 | + | 0.222004i | ||||
\(466\) | −0.781153 | − | 1.35300i | −0.0361862 | − | 0.0626764i | ||||
\(467\) | −33.3050 | −1.54117 | −0.770585 | − | 0.637338i | \(-0.780036\pi\) | ||||
−0.770585 | + | 0.637338i | \(0.780036\pi\) | |||||||
\(468\) | 2.03444 | 0.0940421 | ||||||||
\(469\) | −18.9443 | − | 32.8124i | −0.874765 | − | 1.51514i | ||||
\(470\) | 8.09017 | − | 14.0126i | 0.373172 | − | 0.646352i | ||||
\(471\) | −5.79837 | − | 10.0431i | −0.267175 | − | 0.462761i | ||||
\(472\) | −0.236068 | + | 0.408882i | −0.0108659 | + | 0.0188203i | ||||
\(473\) | −14.9443 | + | 25.8842i | −0.687138 | + | 1.19016i | ||||
\(474\) | 3.41641 | 0.156921 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 10.9443 | 0.501630 | ||||||||
\(477\) | 4.48278 | − | 7.76440i | 0.205252 | − | 0.355508i | ||||
\(478\) | −15.0902 | + | 26.1369i | −0.690208 | + | 1.19548i | ||||
\(479\) | −3.85410 | − | 6.67550i | −0.176098 | − | 0.305011i | 0.764442 | − | 0.644692i | \(-0.223014\pi\) |
−0.940541 | + | 0.339681i | \(0.889681\pi\) | |||||||
\(480\) | 2.23607 | − | 3.87298i | 0.102062 | − | 0.176777i | ||||
\(481\) | −5.79180 | − | 10.0317i | −0.264083 | − | 0.457405i | ||||
\(482\) | 25.4164 | 1.15769 | ||||||||
\(483\) | −20.9443 | −0.952997 | ||||||||
\(484\) | 0.263932 | + | 0.457144i | 0.0119969 | + | 0.0207793i | ||||
\(485\) | −15.5902 | − | 27.0030i | −0.707913 | − | 1.22614i | ||||
\(486\) | 13.5967 | 0.616761 | ||||||||
\(487\) | −19.2361 | −0.871669 | −0.435835 | − | 0.900027i | \(-0.643547\pi\) | ||||
−0.435835 | + | 0.900027i | \(0.643547\pi\) | |||||||
\(488\) | −0.690983 | − | 1.19682i | −0.0312793 | − | 0.0541774i | ||||
\(489\) | −6.58359 | + | 11.4031i | −0.297720 | + | 0.515667i | ||||
\(490\) | 6.28115 | + | 10.8793i | 0.283754 | + | 0.491476i | ||||
\(491\) | 0.763932 | − | 1.32317i | 0.0344758 | − | 0.0597138i | −0.848273 | − | 0.529560i | \(-0.822357\pi\) |
0.882748 | + | 0.469846i | \(0.155691\pi\) | |||||||
\(492\) | 0.527864 | − | 0.914287i | 0.0237979 | − | 0.0412193i | ||||
\(493\) | −30.7426 | −1.38458 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −17.2361 | −0.774704 | ||||||||
\(496\) | −0.618034 | + | 1.07047i | −0.0277505 | + | 0.0480654i | ||||
\(497\) | −4.76393 | + | 8.25137i | −0.213692 | + | 0.370125i | ||||
\(498\) | 0.291796 | + | 0.505406i | 0.0130757 | + | 0.0226478i | ||||
\(499\) | 17.6525 | − | 30.5750i | 0.790233 | − | 1.36872i | −0.135589 | − | 0.990765i | \(-0.543293\pi\) |
0.925822 | − | 0.377959i | \(-0.123374\pi\) | |||||||
\(500\) | 5.59017 | + | 9.68246i | 0.250000 | + | 0.433013i | ||||
\(501\) | 15.4164 | 0.688754 | ||||||||
\(502\) | −2.29180 | −0.102288 | ||||||||
\(503\) | −3.38197 | − | 5.85774i | −0.150794 | − | 0.261184i | 0.780725 | − | 0.624874i | \(-0.214850\pi\) |
−0.931520 | + | 0.363691i | \(0.881516\pi\) | |||||||
\(504\) | −2.38197 | − | 4.12569i | −0.106101 | − | 0.183773i | ||||
\(505\) | 56.5066 | 2.51451 | ||||||||
\(506\) | −16.9443 | −0.753265 | ||||||||
\(507\) | 6.85410 | + | 11.8717i | 0.304401 | + | 0.527239i | ||||
\(508\) | −5.70820 | + | 9.88690i | −0.253261 | + | 0.438660i | ||||
\(509\) | 21.3435 | + | 36.9680i | 0.946032 | + | 1.63858i | 0.753671 | + | 0.657252i | \(0.228281\pi\) |
0.192361 | + | 0.981324i | \(0.438386\pi\) | |||||||
\(510\) | −7.56231 | + | 13.0983i | −0.334865 | + | 0.580002i | ||||
\(511\) | −9.09017 | + | 15.7446i | −0.402125 | + | 0.696502i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −18.3820 | −0.810794 | ||||||||
\(515\) | −26.5066 | + | 45.9107i | −1.16802 | + | 2.02307i | ||||
\(516\) | 5.70820 | − | 9.88690i | 0.251290 | − | 0.435246i | ||||
\(517\) | 7.23607 | + | 12.5332i | 0.318242 | + | 0.551211i | ||||
\(518\) | −13.5623 | + | 23.4906i | −0.595894 | + | 1.03212i | ||||
\(519\) | 0.819660 | + | 1.41969i | 0.0359791 | + | 0.0623176i | ||||
\(520\) | 5.00000 | 0.219265 | ||||||||
\(521\) | 5.27051 | 0.230905 | 0.115453 | − | 0.993313i | \(-0.463168\pi\) | ||||
0.115453 | + | 0.993313i | \(0.463168\pi\) | |||||||
\(522\) | 6.69098 | + | 11.5891i | 0.292856 | + | 0.507242i | ||||
\(523\) | −2.00000 | − | 3.46410i | −0.0874539 | − | 0.151475i | 0.818980 | − | 0.573822i | \(-0.194540\pi\) |
−0.906434 | + | 0.422347i | \(0.861206\pi\) | |||||||
\(524\) | 4.47214 | 0.195366 | ||||||||
\(525\) | −32.3607 | −1.41234 | ||||||||
\(526\) | −1.47214 | − | 2.54981i | −0.0641882 | − | 0.111177i | ||||
\(527\) | 2.09017 | − | 3.62028i | 0.0910492 | − | 0.157702i | ||||
\(528\) | 2.00000 | + | 3.46410i | 0.0870388 | + | 0.150756i | ||||
\(529\) | −2.20820 | + | 3.82472i | −0.0960089 | + | 0.166292i | ||||
\(530\) | 11.0172 | − | 19.0824i | 0.478557 | − | 0.828886i | ||||
\(531\) | −0.695048 | −0.0301625 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.18034 | 0.0511262 | ||||||||
\(534\) | 5.47214 | − | 9.47802i | 0.236802 | − | 0.410154i | ||||
\(535\) | −17.0344 | + | 29.5045i | −0.736463 | + | 1.27559i | ||||
\(536\) | 5.85410 | + | 10.1396i | 0.252859 | + | 0.437964i | ||||
\(537\) | −14.4721 | + | 25.0665i | −0.624519 | + | 1.08170i | ||||
\(538\) | 7.16312 | + | 12.4069i | 0.308824 | + | 0.534899i | ||||
\(539\) | −11.2361 | −0.483972 | ||||||||
\(540\) | 20.0000 | 0.860663 | ||||||||
\(541\) | 13.3090 | + | 23.0519i | 0.572199 | + | 0.991078i | 0.996340 | + | 0.0854819i | \(0.0272430\pi\) |
−0.424140 | + | 0.905596i | \(0.639424\pi\) | |||||||
\(542\) | −13.0000 | − | 22.5167i | −0.558398 | − | 0.967173i | ||||
\(543\) | −6.69505 | −0.287312 | ||||||||
\(544\) | −3.38197 | −0.145001 | ||||||||
\(545\) | 19.9615 | + | 34.5743i | 0.855056 | + | 1.48100i | ||||
\(546\) | −2.76393 | + | 4.78727i | −0.118285 | + | 0.204876i | ||||
\(547\) | 2.52786 | + | 4.37839i | 0.108084 | + | 0.187206i | 0.914994 | − | 0.403468i | \(-0.132195\pi\) |
−0.806910 | + | 0.590674i | \(0.798862\pi\) | |||||||
\(548\) | −1.19098 | + | 2.06284i | −0.0508763 | + | 0.0881203i | ||||
\(549\) | 1.01722 | − | 1.76188i | 0.0434139 | − | 0.0751951i | ||||
\(550\) | −26.1803 | −1.11633 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 6.47214 | 0.275472 | ||||||||
\(553\) | 4.47214 | − | 7.74597i | 0.190175 | − | 0.329392i | ||||
\(554\) | 5.04508 | − | 8.73834i | 0.214345 | − | 0.371257i | ||||
\(555\) | −18.7426 | − | 32.4632i | −0.795581 | − | 1.37799i | ||||
\(556\) | 7.00000 | − | 12.1244i | 0.296866 | − | 0.514187i | ||||
\(557\) | −2.52786 | − | 4.37839i | −0.107109 | − | 0.185518i | 0.807489 | − | 0.589883i | \(-0.200826\pi\) |
−0.914598 | + | 0.404364i | \(0.867493\pi\) | |||||||
\(558\) | −1.81966 | −0.0770324 | ||||||||
\(559\) | 12.7639 | 0.539857 | ||||||||
\(560\) | −5.85410 | − | 10.1396i | −0.247381 | − | 0.428476i | ||||
\(561\) | −6.76393 | − | 11.7155i | −0.285573 | − | 0.494628i | ||||
\(562\) | −20.9787 | −0.884934 | ||||||||
\(563\) | −26.2918 | −1.10807 | −0.554034 | − | 0.832494i | \(-0.686912\pi\) | ||||
−0.554034 | + | 0.832494i | \(0.686912\pi\) | |||||||
\(564\) | −2.76393 | − | 4.78727i | −0.116383 | − | 0.201580i | ||||
\(565\) | 17.8262 | − | 30.8759i | 0.749955 | − | 1.29896i | ||||
\(566\) | −11.2361 | − | 19.4614i | −0.472287 | − | 0.818025i | ||||
\(567\) | −3.90983 | + | 6.77202i | −0.164197 | + | 0.284398i | ||||
\(568\) | 1.47214 | − | 2.54981i | 0.0617695 | − | 0.106988i | ||||
\(569\) | −7.90983 | −0.331597 | −0.165799 | − | 0.986160i | \(-0.553020\pi\) | ||||
−0.165799 | + | 0.986160i | \(0.553020\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.5410 | −1.36180 | −0.680900 | − | 0.732377i | \(-0.738411\pi\) | ||||
−0.680900 | + | 0.732377i | \(0.738411\pi\) | |||||||
\(572\) | −2.23607 | + | 3.87298i | −0.0934947 | + | 0.161938i | ||||
\(573\) | −2.18034 | + | 3.77646i | −0.0910850 | + | 0.157764i | ||||
\(574\) | −1.38197 | − | 2.39364i | −0.0576821 | − | 0.0999084i | ||||
\(575\) | −21.1803 | + | 36.6854i | −0.883281 | + | 1.52989i | ||||
\(576\) | 0.736068 | + | 1.27491i | 0.0306695 | + | 0.0531211i | ||||
\(577\) | 45.9230 | 1.91180 | 0.955899 | − | 0.293694i | \(-0.0948847\pi\) | ||||
0.955899 | + | 0.293694i | \(0.0948847\pi\) | |||||||
\(578\) | −5.56231 | −0.231361 | ||||||||
\(579\) | −7.12461 | − | 12.3402i | −0.296089 | − | 0.512841i | ||||
\(580\) | 16.4443 | + | 28.4823i | 0.682811 | + | 1.18266i | ||||
\(581\) | 1.52786 | 0.0633865 | ||||||||
\(582\) | −10.6525 | −0.441559 | ||||||||
\(583\) | 9.85410 | + | 17.0678i | 0.408115 | + | 0.706876i | ||||
\(584\) | 2.80902 | − | 4.86536i | 0.116238 | − | 0.201330i | ||||
\(585\) | 3.68034 | + | 6.37454i | 0.152163 | + | 0.263555i | ||||
\(586\) | 11.4721 | − | 19.8703i | 0.473910 | − | 0.820835i | ||||
\(587\) | −1.43769 | + | 2.49016i | −0.0593400 | + | 0.102780i | −0.894169 | − | 0.447729i | \(-0.852233\pi\) |
0.834829 | + | 0.550509i | \(0.185566\pi\) | |||||||
\(588\) | 4.29180 | 0.176991 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −1.70820 | −0.0703256 | ||||||||
\(591\) | 2.56231 | − | 4.43804i | 0.105399 | − | 0.182557i | ||||
\(592\) | 4.19098 | − | 7.25900i | 0.172248 | − | 0.298343i | ||||
\(593\) | 17.4615 | + | 30.2442i | 0.717058 | + | 1.24198i | 0.962161 | + | 0.272483i | \(0.0878449\pi\) |
−0.245103 | + | 0.969497i | \(0.578822\pi\) | |||||||
\(594\) | −8.94427 | + | 15.4919i | −0.366988 | + | 0.635642i | ||||
\(595\) | 19.7984 | + | 34.2918i | 0.811654 | + | 1.40583i | ||||
\(596\) | −13.0902 | −0.536194 | ||||||||
\(597\) | 12.9443 | 0.529774 | ||||||||
\(598\) | 3.61803 | + | 6.26662i | 0.147952 | + | 0.256261i | ||||
\(599\) | −19.5623 | − | 33.8829i | −0.799294 | − | 1.38442i | −0.920076 | − | 0.391739i | \(-0.871874\pi\) |
0.120782 | − | 0.992679i | \(-0.461460\pi\) | |||||||
\(600\) | 10.0000 | 0.408248 | ||||||||
\(601\) | −16.4721 | −0.671912 | −0.335956 | − | 0.941878i | \(-0.609059\pi\) | ||||
−0.335956 | + | 0.941878i | \(0.609059\pi\) | |||||||
\(602\) | −14.9443 | − | 25.8842i | −0.609083 | − | 1.05496i | ||||
\(603\) | −8.61803 | + | 14.9269i | −0.350953 | + | 0.607869i | ||||
\(604\) | 7.23607 | + | 12.5332i | 0.294431 | + | 0.509970i | ||||
\(605\) | −0.954915 | + | 1.65396i | −0.0388228 | + | 0.0672431i | ||||
\(606\) | 9.65248 | − | 16.7186i | 0.392105 | − | 0.679146i | ||||
\(607\) | 47.7771 | 1.93921 | 0.969606 | − | 0.244671i | \(-0.0786801\pi\) | ||||
0.969606 | + | 0.244671i | \(0.0786801\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −36.3607 | −1.47341 | ||||||||
\(610\) | 2.50000 | − | 4.33013i | 0.101222 | − | 0.175322i | ||||
\(611\) | 3.09017 | − | 5.35233i | 0.125015 | − | 0.216532i | ||||
\(612\) | −2.48936 | − | 4.31169i | −0.100626 | − | 0.174290i | ||||
\(613\) | −4.19098 | + | 7.25900i | −0.169272 | + | 0.293188i | −0.938164 | − | 0.346191i | \(-0.887475\pi\) |
0.768892 | + | 0.639379i | \(0.220808\pi\) | |||||||
\(614\) | 5.85410 | + | 10.1396i | 0.236252 | + | 0.409201i | ||||
\(615\) | 3.81966 | 0.154024 | ||||||||
\(616\) | 10.4721 | 0.421934 | ||||||||
\(617\) | −21.4721 | − | 37.1908i | −0.864436 | − | 1.49725i | −0.867606 | − | 0.497251i | \(-0.834343\pi\) |
0.00317081 | − | 0.999995i | \(-0.498991\pi\) | |||||||
\(618\) | 9.05573 | + | 15.6850i | 0.364275 | + | 0.630942i | ||||
\(619\) | 22.3607 | 0.898752 | 0.449376 | − | 0.893343i | \(-0.351646\pi\) | ||||
0.449376 | + | 0.893343i | \(0.351646\pi\) | |||||||
\(620\) | −4.47214 | −0.179605 | ||||||||
\(621\) | 14.4721 | + | 25.0665i | 0.580747 | + | 1.00588i | ||||
\(622\) | −15.6180 | + | 27.0512i | −0.626226 | + | 1.08466i | ||||
\(623\) | −14.3262 | − | 24.8138i | −0.573969 | − | 0.994143i | ||||
\(624\) | 0.854102 | − | 1.47935i | 0.0341914 | − | 0.0592213i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −15.5066 | −0.619767 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.38197 | 0.374381 | ||||||||
\(629\) | −14.1738 | + | 24.5497i | −0.565145 | + | 0.978860i | ||||
\(630\) | 8.61803 | − | 14.9269i | 0.343351 | − | 0.594701i | ||||
\(631\) | 15.5623 | + | 26.9547i | 0.619526 | + | 1.07305i | 0.989572 | + | 0.144037i | \(0.0460083\pi\) |
−0.370047 | + | 0.929013i | \(0.620658\pi\) | |||||||
\(632\) | −1.38197 | + | 2.39364i | −0.0549717 | + | 0.0952137i | ||||
\(633\) | −4.47214 | − | 7.74597i | −0.177751 | − | 0.307875i | ||||
\(634\) | −1.32624 | −0.0526716 | ||||||||
\(635\) | −41.3050 | −1.63914 | ||||||||
\(636\) | −3.76393 | − | 6.51932i | −0.149250 | − | 0.258508i | ||||
\(637\) | 2.39919 | + | 4.15551i | 0.0950592 | + | 0.164647i | ||||
\(638\) | −29.4164 | −1.16461 | ||||||||
\(639\) | 4.33437 | 0.171465 | ||||||||
\(640\) | 1.80902 | + | 3.13331i | 0.0715077 | + | 0.123855i | ||||
\(641\) | −6.63525 | + | 11.4926i | −0.262077 | + | 0.453930i | −0.966794 | − | 0.255558i | \(-0.917741\pi\) |
0.704717 | + | 0.709489i | \(0.251074\pi\) | |||||||
\(642\) | 5.81966 | + | 10.0799i | 0.229684 | + | 0.397824i | ||||
\(643\) | 19.4164 | − | 33.6302i | 0.765708 | − | 1.32625i | −0.174163 | − | 0.984717i | \(-0.555722\pi\) |
0.939871 | − | 0.341529i | \(-0.110945\pi\) | |||||||
\(644\) | 8.47214 | − | 14.6742i | 0.333849 | − | 0.578243i | ||||
\(645\) | 41.3050 | 1.62638 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.0689 | 1.02487 | 0.512437 | − | 0.858725i | \(-0.328743\pi\) | ||||
0.512437 | + | 0.858725i | \(0.328743\pi\) | |||||||
\(648\) | 1.20820 | − | 2.09267i | 0.0474627 | − | 0.0822079i | ||||
\(649\) | 0.763932 | − | 1.32317i | 0.0299870 | − | 0.0519389i | ||||
\(650\) | 5.59017 | + | 9.68246i | 0.219265 | + | 0.379777i | ||||
\(651\) | 2.47214 | − | 4.28187i | 0.0968906 | − | 0.167820i | ||||
\(652\) | −5.32624 | − | 9.22531i | −0.208592 | − | 0.361291i | ||||
\(653\) | −35.3951 | −1.38512 | −0.692559 | − | 0.721361i | \(-0.743517\pi\) | ||||
−0.692559 | + | 0.721361i | \(0.743517\pi\) | |||||||
\(654\) | 13.6393 | 0.533340 | ||||||||
\(655\) | 8.09017 | + | 14.0126i | 0.316109 | + | 0.547517i | ||||
\(656\) | 0.427051 | + | 0.739674i | 0.0166735 | + | 0.0288794i | ||||
\(657\) | 8.27051 | 0.322663 | ||||||||
\(658\) | −14.4721 | −0.564183 | ||||||||
\(659\) | −24.2705 | − | 42.0378i | −0.945445 | − | 1.63756i | −0.754858 | − | 0.655888i | \(-0.772294\pi\) |
−0.190587 | − | 0.981670i | \(-0.561039\pi\) | |||||||
\(660\) | −7.23607 | + | 12.5332i | −0.281664 | + | 0.487856i | ||||
\(661\) | −10.7082 | − | 18.5472i | −0.416501 | − | 0.721401i | 0.579084 | − | 0.815268i | \(-0.303410\pi\) |
−0.995585 | + | 0.0938673i | \(0.970077\pi\) | |||||||
\(662\) | 12.8541 | − | 22.2640i | 0.499589 | − | 0.865313i | ||||
\(663\) | −2.88854 | + | 5.00310i | −0.112182 | + | 0.194304i | ||||
\(664\) | −0.472136 | −0.0183224 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 12.3394 | 0.478142 | ||||||||
\(667\) | −23.7984 | + | 41.2200i | −0.921477 | + | 1.59604i | ||||
\(668\) | −6.23607 | + | 10.8012i | −0.241281 | + | 0.417910i | ||||
\(669\) | 17.1246 | + | 29.6607i | 0.662076 | + | 1.14675i | ||||
\(670\) | −21.1803 | + | 36.6854i | −0.818268 | + | 1.41728i | ||||
\(671\) | 2.23607 | + | 3.87298i | 0.0863224 | + | 0.149515i | ||||
\(672\) | −4.00000 | −0.154303 | ||||||||
\(673\) | −30.3820 | −1.17114 | −0.585569 | − | 0.810622i | \(-0.699129\pi\) | ||||
−0.585569 | + | 0.810622i | \(0.699129\pi\) | |||||||
\(674\) | 1.19098 | + | 2.06284i | 0.0458750 | + | 0.0794577i | ||||
\(675\) | 22.3607 | + | 38.7298i | 0.860663 | + | 1.49071i | ||||
\(676\) | −11.0902 | −0.426545 | ||||||||
\(677\) | 6.61803 | 0.254352 | 0.127176 | − | 0.991880i | \(-0.459409\pi\) | ||||
0.127176 | + | 0.991880i | \(0.459409\pi\) | |||||||
\(678\) | −6.09017 | − | 10.5485i | −0.233892 | − | 0.405112i | ||||
\(679\) | −13.9443 | + | 24.1522i | −0.535132 | + | 0.926876i | ||||
\(680\) | −6.11803 | − | 10.5967i | −0.234616 | − | 0.406367i | ||||
\(681\) | −5.52786 | + | 9.57454i | −0.211828 | + | 0.366897i | ||||
\(682\) | 2.00000 | − | 3.46410i | 0.0765840 | − | 0.132647i | ||||
\(683\) | 20.1803 | 0.772179 | 0.386090 | − | 0.922461i | \(-0.373826\pi\) | ||||
0.386090 | + | 0.922461i | \(0.373826\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.61803 | −0.329278 | ||||||||
\(686\) | −5.70820 | + | 9.88690i | −0.217940 | + | 0.377484i | ||||
\(687\) | −2.70820 | + | 4.69075i | −0.103324 | + | 0.178963i | ||||
\(688\) | 4.61803 | + | 7.99867i | 0.176061 | + | 0.304946i | ||||
\(689\) | 4.20820 | − | 7.28882i | 0.160320 | − | 0.277682i | ||||
\(690\) | 11.7082 | + | 20.2792i | 0.445724 | + | 0.772016i | ||||
\(691\) | −22.3607 | −0.850640 | −0.425320 | − | 0.905043i | \(-0.639839\pi\) | ||||
−0.425320 | + | 0.905043i | \(0.639839\pi\) | |||||||
\(692\) | −1.32624 | −0.0504160 | ||||||||
\(693\) | 7.70820 | + | 13.3510i | 0.292810 | + | 0.507163i | ||||
\(694\) | 1.32624 | + | 2.29711i | 0.0503433 | + | 0.0871972i | ||||
\(695\) | 50.6525 | 1.92136 | ||||||||
\(696\) | 11.2361 | 0.425902 | ||||||||
\(697\) | −1.44427 | − | 2.50155i | −0.0547057 | − | 0.0947531i | ||||
\(698\) | 16.5451 | − | 28.6569i | 0.626241 | − | 1.08468i | ||||
\(699\) | −0.965558 | − | 1.67240i | −0.0365208 | − | 0.0632558i | ||||
\(700\) | 13.0902 | − | 22.6728i | 0.494762 | − | 0.856953i | ||||
\(701\) | −19.3156 | + | 33.4556i | −0.729540 | + | 1.26360i | 0.227538 | + | 0.973769i | \(0.426932\pi\) |
−0.957078 | + | 0.289831i | \(0.906401\pi\) | |||||||
\(702\) | 7.63932 | 0.288328 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −3.23607 | −0.121964 | ||||||||
\(705\) | 10.0000 | − | 17.3205i | 0.376622 | − | 0.652328i | ||||
\(706\) | 11.8713 | − | 20.5617i | 0.446783 | − | 0.773851i | ||||
\(707\) | −25.2705 | − | 43.7698i | −0.950395 | − | 1.64613i | ||||
\(708\) | −0.291796 | + | 0.505406i | −0.0109664 | + | 0.0189943i | ||||
\(709\) | −3.45492 | − | 5.98409i | −0.129752 | − | 0.224737i | 0.793828 | − | 0.608142i | \(-0.208085\pi\) |
−0.923580 | + | 0.383405i | \(0.874751\pi\) | |||||||
\(710\) | 10.6525 | 0.399780 | ||||||||
\(711\) | −4.06888 | −0.152595 | ||||||||
\(712\) | 4.42705 | + | 7.66788i | 0.165911 | + | 0.287366i | ||||
\(713\) | −3.23607 | − | 5.60503i | −0.121192 | − | 0.209910i | ||||
\(714\) | 13.5279 | 0.506268 | ||||||||
\(715\) | −16.1803 | −0.605110 | ||||||||
\(716\) | −11.7082 | − | 20.2792i | −0.437556 | − | 0.757869i | ||||
\(717\) | −18.6525 | + | 32.3070i | −0.696589 | + | 1.20653i | ||||
\(718\) | −5.76393 | − | 9.98342i | −0.215108 | − | 0.372578i | ||||
\(719\) | −6.14590 | + | 10.6450i | −0.229203 | + | 0.396992i | −0.957572 | − | 0.288193i | \(-0.906945\pi\) |
0.728369 | + | 0.685185i | \(0.240279\pi\) | |||||||
\(720\) | −2.66312 | + | 4.61266i | −0.0992486 | + | 0.171904i | ||||
\(721\) | 47.4164 | 1.76588 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 31.4164 | 1.16839 | ||||||||
\(724\) | 2.70820 | − | 4.69075i | 0.100650 | − | 0.174330i | ||||
\(725\) | −36.7705 | + | 63.6884i | −1.36562 | + | 2.36533i | ||||
\(726\) | 0.326238 | + | 0.565061i | 0.0121078 | + | 0.0209714i | ||||
\(727\) | 15.4721 | − | 26.7985i | 0.573830 | − | 0.993902i | −0.422338 | − | 0.906438i | \(-0.638790\pi\) |
0.996168 | − | 0.0874638i | \(-0.0278762\pi\) | |||||||
\(728\) | −2.23607 | − | 3.87298i | −0.0828742 | − | 0.143542i | ||||
\(729\) | 24.0557 | 0.890953 | ||||||||
\(730\) | 20.3262 | 0.752308 | ||||||||
\(731\) | −15.6180 | − | 27.0512i | −0.577654 | − | 1.00053i | ||||
\(732\) | −0.854102 | − | 1.47935i | −0.0315685 | − | 0.0546783i | ||||
\(733\) | −1.09017 | −0.0402663 | −0.0201332 | − | 0.999797i | \(-0.506409\pi\) | ||||
−0.0201332 | + | 0.999797i | \(0.506409\pi\) | |||||||
\(734\) | 18.8328 | 0.695132 | ||||||||
\(735\) | 7.76393 | + | 13.4475i | 0.286377 | + | 0.496019i | ||||
\(736\) | −2.61803 | + | 4.53457i | −0.0965020 | + | 0.167146i | ||||
\(737\) | −18.9443 | − | 32.8124i | −0.697821 | − | 1.20866i | ||||
\(738\) | −0.628677 | + | 1.08890i | −0.0231419 | + | 0.0400830i | ||||
\(739\) | −4.56231 | + | 7.90215i | −0.167827 | + | 0.290685i | −0.937656 | − | 0.347566i | \(-0.887008\pi\) |
0.769829 | + | 0.638251i | \(0.220342\pi\) | |||||||
\(740\) | 30.3262 | 1.11481 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −19.7082 | −0.723511 | ||||||||
\(743\) | 3.05573 | − | 5.29268i | 0.112104 | − | 0.194169i | −0.804515 | − | 0.593933i | \(-0.797574\pi\) |
0.916618 | + | 0.399764i | \(0.130908\pi\) | |||||||
\(744\) | −0.763932 | + | 1.32317i | −0.0280071 | + | 0.0485097i | ||||
\(745\) | −23.6803 | − | 41.0156i | −0.867581 | − | 1.50269i | ||||
\(746\) | 9.16312 | − | 15.8710i | 0.335486 | − | 0.581078i | ||||
\(747\) | −0.347524 | − | 0.601929i | −0.0127152 | − | 0.0220234i | ||||
\(748\) | 10.9443 | 0.400162 | ||||||||
\(749\) | 30.4721 | 1.11343 | ||||||||
\(750\) | 6.90983 | + | 11.9682i | 0.252311 | + | 0.437016i | ||||
\(751\) | −12.0344 | − | 20.8443i | −0.439143 | − | 0.760618i | 0.558481 | − | 0.829518i | \(-0.311385\pi\) |
−0.997624 | + | 0.0688996i | \(0.978051\pi\) | |||||||
\(752\) | 4.47214 | 0.163082 | ||||||||
\(753\) | −2.83282 | −0.103234 | ||||||||
\(754\) | 6.28115 | + | 10.8793i | 0.228746 | + | 0.396200i | ||||
\(755\) | −26.1803 | + | 45.3457i | −0.952800 | + | 1.65030i | ||||
\(756\) | −8.94427 | − | 15.4919i | −0.325300 | − | 0.563436i | ||||
\(757\) | −2.21885 | + | 3.84316i | −0.0806454 | + | 0.139682i | −0.903527 | − | 0.428530i | \(-0.859031\pi\) |
0.822882 | + | 0.568212i | \(0.192365\pi\) | |||||||
\(758\) | −17.7082 | + | 30.6715i | −0.643191 | + | 1.11404i | ||||
\(759\) | −20.9443 | −0.760229 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.3607 | 0.955574 | 0.477787 | − | 0.878476i | \(-0.341439\pi\) | ||||
0.477787 | + | 0.878476i | \(0.341439\pi\) | |||||||
\(762\) | −7.05573 | + | 12.2209i | −0.255602 | + | 0.442716i | ||||
\(763\) | 17.8541 | − | 30.9242i | 0.646362 | − | 1.11953i | ||||
\(764\) | −1.76393 | − | 3.05522i | −0.0638168 | − | 0.110534i | ||||
\(765\) | 9.00658 | − | 15.5999i | 0.325634 | − | 0.564014i | ||||
\(766\) | 10.3820 | + | 17.9821i | 0.375116 | + | 0.649719i | ||||
\(767\) | −0.652476 | −0.0235595 | ||||||||
\(768\) | 1.23607 | 0.0446028 | ||||||||
\(769\) | −19.3713 | − | 33.5521i | −0.698548 | − | 1.20992i | −0.968970 | − | 0.247178i | \(-0.920497\pi\) |
0.270422 | − | 0.962742i | \(-0.412837\pi\) | |||||||
\(770\) | 18.9443 | + | 32.8124i | 0.682704 | + | 1.18248i | ||||
\(771\) | −22.7214 | −0.818290 | ||||||||
\(772\) | 11.5279 | 0.414897 | ||||||||
\(773\) | −4.07295 | − | 7.05455i | −0.146494 | − | 0.253735i | 0.783435 | − | 0.621473i | \(-0.213466\pi\) |
−0.929929 | + | 0.367738i | \(0.880132\pi\) | |||||||
\(774\) | −6.79837 | + | 11.7751i | −0.244363 | + | 0.423248i | ||||
\(775\) | −5.00000 | − | 8.66025i | −0.179605 | − | 0.311086i | ||||
\(776\) | 4.30902 | − | 7.46344i | 0.154685 | − | 0.267922i | ||||
\(777\) | −16.7639 | + | 29.0360i | −0.601403 | + | 1.04166i | ||||
\(778\) | 12.7984 | 0.458844 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 6.18034 | 0.221292 | ||||||||
\(781\) | −4.76393 | + | 8.25137i | −0.170467 | + | 0.295257i | ||||
\(782\) | 8.85410 | − | 15.3358i | 0.316622 | − | 0.548405i | ||||
\(783\) | 25.1246 | + | 43.5171i | 0.897880 | + | 1.55517i | ||||
\(784\) | −1.73607 | + | 3.00696i | −0.0620024 | + | 0.107391i | ||||
\(785\) | 16.9721 | + | 29.3966i | 0.605762 | + | 1.04921i | ||||
\(786\) | 5.52786 | 0.197172 | ||||||||
\(787\) | −28.4721 | −1.01492 | −0.507461 | − | 0.861675i | \(-0.669416\pi\) | ||||
−0.507461 | + | 0.861675i | \(0.669416\pi\) | |||||||
\(788\) | 2.07295 | + | 3.59045i | 0.0738458 | + | 0.127905i | ||||
\(789\) | −1.81966 | − | 3.15174i | −0.0647816 | − | 0.112205i | ||||
\(790\) | −10.0000 | −0.355784 | ||||||||
\(791\) | −31.8885 | −1.13383 | ||||||||
\(792\) | −2.38197 | − | 4.12569i | −0.0846395 | − | 0.146600i | ||||
\(793\) | 0.954915 | − | 1.65396i | 0.0339100 | − | 0.0587339i | ||||
\(794\) | 11.1803 | + | 19.3649i | 0.396775 | + | 0.687235i | ||||
\(795\) | 13.6180 | − | 23.5871i | 0.482982 | − | 0.836549i | ||||
\(796\) | −5.23607 | + | 9.06914i | −0.185588 | + | 0.321447i | ||||
\(797\) | −28.4377 | −1.00731 | −0.503657 | − | 0.863903i | \(-0.668013\pi\) | ||||
−0.503657 | + | 0.863903i | \(0.668013\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.1246 | −0.535070 | ||||||||
\(800\) | −4.04508 | + | 7.00629i | −0.143015 | + | 0.247710i | ||||
\(801\) | −6.51722 | + | 11.2882i | −0.230275 | + | 0.398847i | ||||
\(802\) | 9.47214 | + | 16.4062i | 0.334473 | + | 0.579324i | ||||
\(803\) | −9.09017 | + | 15.7446i | −0.320785 | + | 0.555616i | ||||
\(804\) | 7.23607 | + | 12.5332i | 0.255196 | + | 0.442013i | ||||
\(805\) | 61.3050 | 2.16072 | ||||||||
\(806\) | −1.70820 | −0.0601689 | ||||||||
\(807\) | 8.85410 | + | 15.3358i | 0.311679 | + | 0.539844i | ||||
\(808\) | 7.80902 | + | 13.5256i | 0.274720 | + | 0.475829i | ||||
\(809\) | 2.74265 | 0.0964263 | 0.0482131 | − | 0.998837i | \(-0.484647\pi\) | ||||
0.0482131 | + | 0.998837i | \(0.484647\pi\) | |||||||
\(810\) | 8.74265 | 0.307185 | ||||||||
\(811\) | 2.79837 | + | 4.84693i | 0.0982642 | + | 0.170199i | 0.910966 | − | 0.412481i | \(-0.135338\pi\) |
−0.812702 | + | 0.582679i | \(0.802004\pi\) | |||||||
\(812\) | 14.7082 | − | 25.4754i | 0.516157 | − | 0.894010i | ||||
\(813\) | −16.0689 | − | 27.8321i | −0.563560 | − | 0.976115i | ||||
\(814\) | −13.5623 | + | 23.4906i | −0.475359 | + | 0.823345i | ||||
\(815\) | 19.2705 | − | 33.3775i | 0.675017 | − | 1.16916i | ||||
\(816\) | −4.18034 | −0.146341 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −16.2705 | −0.568885 | ||||||||
\(819\) | 3.29180 | − | 5.70156i | 0.115025 | − | 0.199229i | ||||
\(820\) | −1.54508 | + | 2.67617i | −0.0539567 | + | 0.0934558i | ||||
\(821\) | −9.63525 | − | 16.6888i | −0.336273 | − | 0.582441i | 0.647456 | − | 0.762103i | \(-0.275833\pi\) |
−0.983728 | + | 0.179662i | \(0.942500\pi\) | |||||||
\(822\) | −1.47214 | + | 2.54981i | −0.0513466 | + | 0.0889350i | ||||
\(823\) | 10.4164 | + | 18.0417i | 0.363093 | + | 0.628896i | 0.988468 | − | 0.151429i | \(-0.0483873\pi\) |
−0.625375 | + | 0.780324i | \(0.715054\pi\) | |||||||
\(824\) | −14.6525 | −0.510443 | ||||||||
\(825\) | −32.3607 | −1.12665 | ||||||||
\(826\) | 0.763932 | + | 1.32317i | 0.0265806 | + | 0.0460389i | ||||
\(827\) | −15.2705 | − | 26.4493i | −0.531008 | − | 0.919732i | −0.999345 | − | 0.0361826i | \(-0.988480\pi\) |
0.468338 | − | 0.883550i | \(-0.344853\pi\) | |||||||
\(828\) | −7.70820 | −0.267879 | ||||||||
\(829\) | 9.72949 | 0.337919 | 0.168960 | − | 0.985623i | \(-0.445959\pi\) | ||||
0.168960 | + | 0.985623i | \(0.445959\pi\) | |||||||
\(830\) | −0.854102 | − | 1.47935i | −0.0296463 | − | 0.0513489i | ||||
\(831\) | 6.23607 | − | 10.8012i | 0.216327 | − | 0.374689i | ||||
\(832\) | 0.690983 | + | 1.19682i | 0.0239555 | + | 0.0414922i | ||||
\(833\) | 5.87132 | − | 10.1694i | 0.203429 | − | 0.352350i | ||||
\(834\) | 8.65248 | − | 14.9865i | 0.299611 | − | 0.518941i | ||||
\(835\) | −45.1246 | −1.56160 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.83282 | −0.236177 | ||||||||
\(838\) | 3.23607 | − | 5.60503i | 0.111788 | − | 0.193623i | ||||
\(839\) | 11.0000 | − | 19.0526i | 0.379762 | − | 0.657767i | −0.611265 | − | 0.791426i | \(-0.709339\pi\) |
0.991027 | + | 0.133658i | \(0.0426725\pi\) | |||||||
\(840\) | −7.23607 | − | 12.5332i | −0.249668 | − | 0.432438i | ||||
\(841\) | −26.8156 | + | 46.4460i | −0.924676 | + | 1.60159i | ||||
\(842\) | 6.95492 | + | 12.0463i | 0.239682 | + | 0.415142i | ||||
\(843\) | −25.9311 | −0.893115 | ||||||||
\(844\) | 7.23607 | 0.249076 | ||||||||
\(845\) | −20.0623 | − | 34.7489i | −0.690164 | − | 1.19540i | ||||
\(846\) | 3.29180 | + | 5.70156i | 0.113174 | + | 0.196024i | ||||
\(847\) | 1.70820 | 0.0586946 | ||||||||
\(848\) | 6.09017 | 0.209137 | ||||||||
\(849\) | −13.8885 | − | 24.0557i | −0.476654 | − | 0.825588i | ||||
\(850\) | 13.6803 | − | 23.6950i | 0.469232 | − | 0.812733i | ||||
\(851\) | 21.9443 | + | 38.0086i | 0.752240 | + | 1.30292i | ||||
\(852\) | 1.81966 | − | 3.15174i | 0.0623405 | − | 0.107977i | ||||
\(853\) | 14.5451 | − | 25.1928i | 0.498014 | − | 0.862586i | −0.501983 | − | 0.864877i | \(-0.667396\pi\) |
0.999997 | + | 0.00229146i | \(0.000729395\pi\) | |||||||
\(854\) | −4.47214 | −0.153033 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.41641 | −0.321846 | ||||||||
\(857\) | 2.78115 | − | 4.81710i | 0.0950024 | − | 0.164549i | −0.814607 | − | 0.580013i | \(-0.803047\pi\) |
0.909610 | + | 0.415464i | \(0.136381\pi\) | |||||||
\(858\) | −2.76393 | + | 4.78727i | −0.0943591 | + | 0.163435i | ||||
\(859\) | −14.0344 | − | 24.3084i | −0.478849 | − | 0.829391i | 0.520857 | − | 0.853644i | \(-0.325613\pi\) |
−0.999706 | + | 0.0242533i | \(0.992279\pi\) | |||||||
\(860\) | −16.7082 | + | 28.9395i | −0.569745 | + | 0.986827i | ||||
\(861\) | −1.70820 | − | 2.95870i | −0.0582154 | − | 0.100832i | ||||
\(862\) | −6.65248 | −0.226584 | ||||||||
\(863\) | 25.8885 | 0.881256 | 0.440628 | − | 0.897690i | \(-0.354756\pi\) | ||||
0.440628 | + | 0.897690i | \(0.354756\pi\) | |||||||
\(864\) | 2.76393 | + | 4.78727i | 0.0940309 | + | 0.162866i | ||||
\(865\) | −2.39919 | − | 4.15551i | −0.0815748 | − | 0.141292i | ||||
\(866\) | 25.0344 | 0.850705 | ||||||||
\(867\) | −6.87539 | −0.233500 | ||||||||
\(868\) | 2.00000 | + | 3.46410i | 0.0678844 | + | 0.117579i | ||||
\(869\) | 4.47214 | − | 7.74597i | 0.151707 | − | 0.262764i | ||||
\(870\) | 20.3262 | + | 35.2061i | 0.689124 | + | 1.19360i | ||||
\(871\) | −8.09017 | + | 14.0126i | −0.274125 | + | 0.474798i | ||||
\(872\) | −5.51722 | + | 9.55611i | −0.186837 | + | 0.323611i | ||||
\(873\) | 12.6869 | 0.429387 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 36.1803 | 1.22312 | ||||||||
\(876\) | 3.47214 | − | 6.01392i | 0.117313 | − | 0.203191i | ||||
\(877\) | 0.871323 | − | 1.50918i | 0.0294225 | − | 0.0509612i | −0.850939 | − | 0.525264i | \(-0.823967\pi\) |
0.880362 | + | 0.474303i | \(0.157300\pi\) | |||||||
\(878\) | 14.6180 | + | 25.3192i | 0.493335 | + | 0.854481i | ||||
\(879\) | 14.1803 | − | 24.5611i | 0.478291 | − | 0.828424i | ||||
\(880\) | −5.85410 | − | 10.1396i | −0.197342 | − | 0.341806i | ||||
\(881\) | 5.21478 | 0.175690 | 0.0878452 | − | 0.996134i | \(-0.472002\pi\) | ||||
0.0878452 | + | 0.996134i | \(0.472002\pi\) | |||||||
\(882\) | −5.11146 | −0.172112 | ||||||||
\(883\) | 8.90983 | + | 15.4323i | 0.299840 | + | 0.519338i | 0.976099 | − | 0.217326i | \(-0.0697335\pi\) |
−0.676259 | + | 0.736664i | \(0.736400\pi\) | |||||||
\(884\) | −2.33688 | − | 4.04760i | −0.0785978 | − | 0.136135i | ||||
\(885\) | −2.11146 | −0.0709758 | ||||||||
\(886\) | 9.23607 | 0.310292 | ||||||||
\(887\) | 3.47214 | + | 6.01392i | 0.116583 | + | 0.201928i | 0.918411 | − | 0.395627i | \(-0.129473\pi\) |
−0.801828 | + | 0.597554i | \(0.796139\pi\) | |||||||
\(888\) | 5.18034 | − | 8.97261i | 0.173841 | − | 0.301101i | ||||
\(889\) | 18.4721 | + | 31.9947i | 0.619536 | + | 1.07307i | ||||
\(890\) | −16.0172 | + | 27.7426i | −0.536898 | + | 0.929935i | ||||
\(891\) | −3.90983 | + | 6.77202i | −0.130984 | + | 0.226871i | ||||
\(892\) | −27.7082 | −0.927739 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −16.1803 | −0.541152 | ||||||||
\(895\) | 42.3607 | − | 73.3708i | 1.41596 | − | 2.45252i | ||||
\(896\) | 1.61803 | − | 2.80252i | 0.0540547 | − | 0.0936255i | ||||
\(897\) | 4.47214 | + | 7.74597i | 0.149320 | + | 0.258630i | ||||
\(898\) | −11.3992 | + | 19.7440i | −0.380396 | + | 0.658865i | ||||
\(899\) | −5.61803 | − | 9.73072i | −0.187372 | − | 0.324538i | ||||
\(900\) | −11.9098 | −0.396994 | ||||||||
\(901\) | −20.5967 | −0.686177 | ||||||||
\(902\) | −1.38197 | − | 2.39364i | −0.0460144 | − | 0.0796993i | ||||
\(903\) | −18.4721 | − | 31.9947i | −0.614714 | − | 1.06472i | ||||
\(904\) | 9.85410 | 0.327743 | ||||||||
\(905\) | 19.5967 | 0.651418 | ||||||||
\(906\) | 8.94427 | + | 15.4919i | 0.297154 | + | 0.514685i | ||||
\(907\) | −0.145898 | + | 0.252703i | −0.00484446 | + | 0.00839086i | −0.868437 | − | 0.495799i | \(-0.834875\pi\) |
0.863593 | + | 0.504190i | \(0.168209\pi\) | |||||||
\(908\) | −4.47214 | − | 7.74597i | −0.148413 | − | 0.257059i | ||||
\(909\) | −11.4959 | + | 19.9115i | −0.381296 | + | 0.660424i | ||||
\(910\) | 8.09017 | − | 14.0126i | 0.268187 | − | 0.464513i | ||||
\(911\) | −12.0689 | −0.399860 | −0.199930 | − | 0.979810i | \(-0.564071\pi\) | ||||
−0.199930 | + | 0.979810i | \(0.564071\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.52786 | 0.0505649 | ||||||||
\(914\) | −12.6074 | + | 21.8366i | −0.417015 | + | 0.722292i | ||||
\(915\) | 3.09017 | − | 5.35233i | 0.102158 | − | 0.176943i | ||||
\(916\) | −2.19098 | − | 3.79489i | −0.0723921 | − | 0.125387i | ||||
\(917\) | 7.23607 | − | 12.5332i | 0.238956 | − | 0.413884i | ||||
\(918\) | −9.34752 | − | 16.1904i | −0.308514 | − | 0.534362i | ||||
\(919\) | 45.8885 | 1.51372 | 0.756862 | − | 0.653575i | \(-0.226732\pi\) | ||||
0.756862 | + | 0.653575i | \(0.226732\pi\) | |||||||
\(920\) | −18.9443 | −0.624574 | ||||||||
\(921\) | 7.23607 | + | 12.5332i | 0.238437 | + | 0.412984i | ||||
\(922\) | −10.7082 | − | 18.5472i | −0.352656 | − | 0.610818i | ||||
\(923\) | 4.06888 | 0.133929 | ||||||||
\(924\) | 12.9443 | 0.425835 | ||||||||
\(925\) | 33.9058 | + | 58.7265i | 1.11481 | + | 1.93092i | ||||
\(926\) | 2.52786 | − | 4.37839i | 0.0830708 | − | 0.143883i | ||||
\(927\) | −10.7852 | − | 18.6805i | −0.354233 | − | 0.613550i | ||||
\(928\) | −4.54508 | + | 7.87232i | −0.149200 | + | 0.258422i | ||||
\(929\) | 29.5795 | − | 51.2332i | 0.970473 | − | 1.68091i | 0.276342 | − | 0.961059i | \(-0.410878\pi\) |
0.694131 | − | 0.719849i | \(-0.255789\pi\) | |||||||
\(930\) | −5.52786 | −0.181266 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.56231 | 0.0511750 | ||||||||
\(933\) | −19.3050 | + | 33.4372i | −0.632016 | + | 1.09468i | ||||
\(934\) | 16.6525 | − | 28.8429i | 0.544886 | − | 0.943770i | ||||
\(935\) | 19.7984 | + | 34.2918i | 0.647476 | + | 1.12146i | ||||
\(936\) | −1.01722 | + | 1.76188i | −0.0332489 | + | 0.0575888i | ||||
\(937\) | −7.94427 | − | 13.7599i | −0.259528 | − | 0.449516i | 0.706588 | − | 0.707626i | \(-0.250234\pi\) |
−0.966116 | + | 0.258110i | \(0.916900\pi\) | |||||||
\(938\) | 37.8885 | 1.23710 | ||||||||
\(939\) | −19.1672 | −0.625497 | ||||||||
\(940\) | 8.09017 | + | 14.0126i | 0.263872 | + | 0.457040i | ||||
\(941\) | 13.0000 | + | 22.5167i | 0.423788 | + | 0.734022i | 0.996306 | − | 0.0858697i | \(-0.0273669\pi\) |
−0.572518 | + | 0.819892i | \(0.694034\pi\) | |||||||
\(942\) | 11.5967 | 0.377842 | ||||||||
\(943\) | −4.47214 | −0.145633 | ||||||||
\(944\) | −0.236068 | − | 0.408882i | −0.00768336 | − | 0.0133080i | ||||
\(945\) | 32.3607 | − | 56.0503i | 1.05269 | − | 1.82332i | ||||
\(946\) | −14.9443 | − | 25.8842i | −0.485880 | − | 0.841569i | ||||
\(947\) | −4.09017 | + | 7.08438i | −0.132913 | + | 0.230211i | −0.924798 | − | 0.380458i | \(-0.875766\pi\) |
0.791885 | + | 0.610670i | \(0.209100\pi\) | |||||||
\(948\) | −1.70820 | + | 2.95870i | −0.0554799 | + | 0.0960940i | ||||
\(949\) | 7.76393 | 0.252028 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.63932 | −0.0531586 | ||||||||
\(952\) | −5.47214 | + | 9.47802i | −0.177353 | + | 0.307184i | ||||
\(953\) | 23.9058 | − | 41.4060i | 0.774384 | − | 1.34127i | −0.160757 | − | 0.986994i | \(-0.551393\pi\) |
0.935140 | − | 0.354278i | \(-0.115273\pi\) | |||||||
\(954\) | 4.48278 | + | 7.76440i | 0.145135 | + | 0.251382i | ||||
\(955\) | 6.38197 | − | 11.0539i | 0.206516 | − | 0.357695i | ||||
\(956\) | −15.0902 | − | 26.1369i | −0.488051 | − | 0.845329i | ||||
\(957\) | −36.3607 | −1.17537 | ||||||||
\(958\) | 7.70820 | 0.249041 | ||||||||
\(959\) | 3.85410 | + | 6.67550i | 0.124455 | + | 0.215563i | ||||
\(960\) | 2.23607 | + | 3.87298i | 0.0721688 | + | 0.125000i | ||||
\(961\) | −29.4721 | −0.950714 | ||||||||
\(962\) | 11.5836 | 0.373470 | ||||||||
\(963\) | −6.93112 | − | 12.0050i | −0.223352 | − | 0.386857i | ||||
\(964\) | −12.7082 | + | 22.0113i | −0.409304 | + | 0.708935i | ||||
\(965\) | 20.8541 | + | 36.1204i | 0.671317 | + | 1.16276i | ||||
\(966\) | 10.4721 | − | 18.1383i | 0.336935 | − | 0.583589i | ||||
\(967\) | −4.41641 | + | 7.64944i | −0.142022 | + | 0.245989i | −0.928258 | − | 0.371937i | \(-0.878694\pi\) |
0.786236 | + | 0.617926i | \(0.212027\pi\) | |||||||
\(968\) | −0.527864 | −0.0169662 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 31.1803 | 1.00114 | ||||||||
\(971\) | 30.2705 | − | 52.4301i | 0.971427 | − | 1.68256i | 0.280172 | − | 0.959950i | \(-0.409609\pi\) |
0.691255 | − | 0.722611i | \(-0.257058\pi\) | |||||||
\(972\) | −6.79837 | + | 11.7751i | −0.218058 | + | 0.377687i | ||||
\(973\) | −22.6525 | − | 39.2352i | −0.726205 | − | 1.25782i | ||||
\(974\) | 9.61803 | − | 16.6589i | 0.308182 | − | 0.533786i | ||||
\(975\) | 6.90983 | + | 11.9682i | 0.221292 | + | 0.383288i | ||||
\(976\) | 1.38197 | 0.0442357 | ||||||||
\(977\) | 9.03444 | 0.289037 | 0.144519 | − | 0.989502i | \(-0.453837\pi\) | ||||
0.144519 | + | 0.989502i | \(0.453837\pi\) | |||||||
\(978\) | −6.58359 | − | 11.4031i | −0.210520 | − | 0.364631i | ||||
\(979\) | −14.3262 | − | 24.8138i | −0.457869 | − | 0.793052i | ||||
\(980\) | −12.5623 | −0.401288 | ||||||||
\(981\) | −16.2442 | −0.518637 | ||||||||
\(982\) | 0.763932 | + | 1.32317i | 0.0243781 | + | 0.0422240i | ||||
\(983\) | 9.79837 | − | 16.9713i | 0.312520 | − | 0.541300i | −0.666388 | − | 0.745606i | \(-0.732160\pi\) |
0.978907 | + | 0.204306i | \(0.0654937\pi\) | |||||||
\(984\) | 0.527864 | + | 0.914287i | 0.0168277 | + | 0.0291464i | ||||
\(985\) | −7.50000 | + | 12.9904i | −0.238970 | + | 0.413908i | ||||
\(986\) | 15.3713 | − | 26.6239i | 0.489523 | − | 0.847878i | ||||
\(987\) | −17.8885 | −0.569399 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −48.3607 | −1.53778 | ||||||||
\(990\) | 8.61803 | − | 14.9269i | 0.273899 | − | 0.474407i | ||||
\(991\) | −15.3262 | + | 26.5458i | −0.486854 | + | 0.843256i | −0.999886 | − | 0.0151138i | \(-0.995189\pi\) |
0.513032 | + | 0.858370i | \(0.328522\pi\) | |||||||
\(992\) | −0.618034 | − | 1.07047i | −0.0196226 | − | 0.0339873i | ||||
\(993\) | 15.8885 | − | 27.5198i | 0.504208 | − | 0.873313i | ||||
\(994\) | −4.76393 | − | 8.25137i | −0.151103 | − | 0.261718i | ||||
\(995\) | −37.8885 | −1.20115 | ||||||||
\(996\) | −0.583592 | −0.0184918 | ||||||||
\(997\) | 6.75329 | + | 11.6970i | 0.213879 | + | 0.370449i | 0.952925 | − | 0.303206i | \(-0.0980569\pi\) |
−0.739046 | + | 0.673655i | \(0.764724\pi\) | |||||||
\(998\) | 17.6525 | + | 30.5750i | 0.558779 | + | 0.967834i | ||||
\(999\) | 46.3344 | 1.46595 |
(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 | 722.2.c.h.429.1 | 4 | ||
19.2 | odd | 18 | 722.2.e.q.595.2 | 12 | |||
19.3 | odd | 18 | 722.2.e.q.99.1 | 12 | |||
19.4 | even | 9 | 722.2.e.p.423.2 | 12 | |||
19.5 | even | 9 | 722.2.e.p.389.2 | 12 | |||
19.6 | even | 9 | 722.2.e.p.415.1 | 12 | |||
19.7 | even | 3 | inner | 722.2.c.h.653.1 | 4 | ||
19.8 | odd | 6 | 722.2.a.h.1.1 | ✓ | 2 | ||
19.9 | even | 9 | 722.2.e.p.245.2 | 12 | |||
19.10 | odd | 18 | 722.2.e.q.245.1 | 12 | |||
19.11 | even | 3 | 722.2.a.i.1.2 | yes | 2 | ||
19.12 | odd | 6 | 722.2.c.i.653.2 | 4 | |||
19.13 | odd | 18 | 722.2.e.q.415.2 | 12 | |||
19.14 | odd | 18 | 722.2.e.q.389.1 | 12 | |||
19.15 | odd | 18 | 722.2.e.q.423.1 | 12 | |||
19.16 | even | 9 | 722.2.e.p.99.2 | 12 | |||
19.17 | even | 9 | 722.2.e.p.595.1 | 12 | |||
19.18 | odd | 2 | 722.2.c.i.429.2 | 4 | |||
57.8 | even | 6 | 6498.2.a.bk.1.2 | 2 | |||
57.11 | odd | 6 | 6498.2.a.be.1.2 | 2 | |||
76.11 | odd | 6 | 5776.2.a.be.1.1 | 2 | |||
76.27 | even | 6 | 5776.2.a.t.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
722.2.a.h.1.1 | ✓ | 2 | 19.8 | odd | 6 | ||
722.2.a.i.1.2 | yes | 2 | 19.11 | even | 3 | ||
722.2.c.h.429.1 | 4 | 1.1 | even | 1 | trivial | ||
722.2.c.h.653.1 | 4 | 19.7 | even | 3 | inner | ||
722.2.c.i.429.2 | 4 | 19.18 | odd | 2 | |||
722.2.c.i.653.2 | 4 | 19.12 | odd | 6 | |||
722.2.e.p.99.2 | 12 | 19.16 | even | 9 | |||
722.2.e.p.245.2 | 12 | 19.9 | even | 9 | |||
722.2.e.p.389.2 | 12 | 19.5 | even | 9 | |||
722.2.e.p.415.1 | 12 | 19.6 | even | 9 | |||
722.2.e.p.423.2 | 12 | 19.4 | even | 9 | |||
722.2.e.p.595.1 | 12 | 19.17 | even | 9 | |||
722.2.e.q.99.1 | 12 | 19.3 | odd | 18 | |||
722.2.e.q.245.1 | 12 | 19.10 | odd | 18 | |||
722.2.e.q.389.1 | 12 | 19.14 | odd | 18 | |||
722.2.e.q.415.2 | 12 | 19.13 | odd | 18 | |||
722.2.e.q.423.1 | 12 | 19.15 | odd | 18 | |||
722.2.e.q.595.2 | 12 | 19.2 | odd | 18 | |||
5776.2.a.t.1.2 | 2 | 76.27 | even | 6 | |||
5776.2.a.be.1.1 | 2 | 76.11 | odd | 6 | |||
6498.2.a.be.1.2 | 2 | 57.11 | odd | 6 | |||
6498.2.a.bk.1.2 | 2 | 57.8 | even | 6 |