Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [845,2,Mod(146,845)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(845, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("845.146");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 845 = 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 845.e (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: | \(6.74735897080\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 146.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 845.146 |
Dual form | 845.2.e.e.191.1 |
$q$-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 \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).
\(n\) | \(171\) | \(677\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 1.50000i | −0.612372 | − | 1.06066i | −0.990839 | − | 0.135045i | \(-0.956882\pi\) |
0.378467 | − | 0.925615i | \(-0.376451\pi\) | |||||||
\(3\) | 0.366025 | + | 0.633975i | 0.211325 | + | 0.366025i | 0.952129 | − | 0.305695i | \(-0.0988889\pi\) |
−0.740805 | + | 0.671721i | \(0.765556\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.633975 | − | 1.09808i | 0.258819 | − | 0.448288i | ||||
\(7\) | −1.00000 | + | 1.73205i | −0.377964 | + | 0.654654i | −0.990766 | − | 0.135583i | \(-0.956709\pi\) |
0.612801 | + | 0.790237i | \(0.290043\pi\) | |||||||
\(8\) | −1.73205 | −0.612372 | ||||||||
\(9\) | 1.23205 | − | 2.13397i | 0.410684 | − | 0.711325i | ||||
\(10\) | 0.866025 | + | 1.50000i | 0.273861 | + | 0.474342i | ||||
\(11\) | 0.633975 | + | 1.09808i | 0.191151 | + | 0.331082i | 0.945632 | − | 0.325239i | \(-0.105445\pi\) |
−0.754481 | + | 0.656322i | \(0.772111\pi\) | |||||||
\(12\) | −0.732051 | −0.211325 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 3.46410 | 0.925820 | ||||||||
\(15\) | −0.366025 | − | 0.633975i | −0.0945074 | − | 0.163692i | ||||
\(16\) | 2.50000 | + | 4.33013i | 0.625000 | + | 1.08253i | ||||
\(17\) | −1.73205 | + | 3.00000i | −0.420084 | + | 0.727607i | −0.995947 | − | 0.0899392i | \(-0.971333\pi\) |
0.575863 | + | 0.817546i | \(0.304666\pi\) | |||||||
\(18\) | −4.26795 | −1.00597 | ||||||||
\(19\) | −2.09808 | + | 3.63397i | −0.481332 | + | 0.833691i | −0.999770 | − | 0.0214238i | \(-0.993180\pi\) |
0.518439 | + | 0.855115i | \(0.326513\pi\) | |||||||
\(20\) | 0.500000 | − | 0.866025i | 0.111803 | − | 0.193649i | ||||
\(21\) | −1.46410 | −0.319493 | ||||||||
\(22\) | 1.09808 | − | 1.90192i | 0.234111 | − | 0.405492i | ||||
\(23\) | −2.36603 | − | 4.09808i | −0.493350 | − | 0.854508i | 0.506620 | − | 0.862169i | \(-0.330895\pi\) |
−0.999971 | + | 0.00766135i | \(0.997561\pi\) | |||||||
\(24\) | −0.633975 | − | 1.09808i | −0.129410 | − | 0.224144i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | −1.00000 | − | 1.73205i | −0.188982 | − | 0.327327i | ||||
\(29\) | 4.73205 | + | 8.19615i | 0.878720 | + | 1.52199i | 0.852747 | + | 0.522325i | \(0.174935\pi\) |
0.0259731 | + | 0.999663i | \(0.491732\pi\) | |||||||
\(30\) | −0.633975 | + | 1.09808i | −0.115747 | + | 0.200480i | ||||
\(31\) | −0.196152 | −0.0352300 | −0.0176150 | − | 0.999845i | \(-0.505607\pi\) | ||||
−0.0176150 | + | 0.999845i | \(0.505607\pi\) | |||||||
\(32\) | 2.59808 | − | 4.50000i | 0.459279 | − | 0.795495i | ||||
\(33\) | −0.464102 | + | 0.803848i | −0.0807897 | + | 0.139932i | ||||
\(34\) | 6.00000 | 1.02899 | ||||||||
\(35\) | 1.00000 | − | 1.73205i | 0.169031 | − | 0.292770i | ||||
\(36\) | 1.23205 | + | 2.13397i | 0.205342 | + | 0.355662i | ||||
\(37\) | 2.00000 | + | 3.46410i | 0.328798 | + | 0.569495i | 0.982274 | − | 0.187453i | \(-0.0600231\pi\) |
−0.653476 | + | 0.756948i | \(0.726690\pi\) | |||||||
\(38\) | 7.26795 | 1.17902 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.73205 | 0.273861 | ||||||||
\(41\) | 1.73205 | + | 3.00000i | 0.270501 | + | 0.468521i | 0.968990 | − | 0.247099i | \(-0.0794774\pi\) |
−0.698489 | + | 0.715621i | \(0.746144\pi\) | |||||||
\(42\) | 1.26795 | + | 2.19615i | 0.195649 | + | 0.338874i | ||||
\(43\) | −5.09808 | + | 8.83013i | −0.777449 | + | 1.34658i | 0.155958 | + | 0.987764i | \(0.450153\pi\) |
−0.933408 | + | 0.358818i | \(0.883180\pi\) | |||||||
\(44\) | −1.26795 | −0.191151 | ||||||||
\(45\) | −1.23205 | + | 2.13397i | −0.183663 | + | 0.318114i | ||||
\(46\) | −4.09808 | + | 7.09808i | −0.604228 | + | 1.04655i | ||||
\(47\) | 6.00000 | 0.875190 | 0.437595 | − | 0.899172i | \(-0.355830\pi\) | ||||
0.437595 | + | 0.899172i | \(0.355830\pi\) | |||||||
\(48\) | −1.83013 | + | 3.16987i | −0.264156 | + | 0.457532i | ||||
\(49\) | 1.50000 | + | 2.59808i | 0.214286 | + | 0.371154i | ||||
\(50\) | −0.866025 | − | 1.50000i | −0.122474 | − | 0.212132i | ||||
\(51\) | −2.53590 | −0.355097 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.3923 | −1.42749 | −0.713746 | − | 0.700404i | \(-0.753003\pi\) | ||||
−0.713746 | + | 0.700404i | \(0.753003\pi\) | |||||||
\(54\) | −3.46410 | − | 6.00000i | −0.471405 | − | 0.816497i | ||||
\(55\) | −0.633975 | − | 1.09808i | −0.0854851 | − | 0.148065i | ||||
\(56\) | 1.73205 | − | 3.00000i | 0.231455 | − | 0.400892i | ||||
\(57\) | −3.07180 | −0.406869 | ||||||||
\(58\) | 8.19615 | − | 14.1962i | 1.07621 | − | 1.86405i | ||||
\(59\) | 7.56218 | − | 13.0981i | 0.984512 | − | 1.70522i | 0.340425 | − | 0.940272i | \(-0.389429\pi\) |
0.644086 | − | 0.764953i | \(-0.277238\pi\) | |||||||
\(60\) | 0.732051 | 0.0945074 | ||||||||
\(61\) | −6.19615 | + | 10.7321i | −0.793336 | + | 1.37410i | 0.130554 | + | 0.991441i | \(0.458324\pi\) |
−0.923890 | + | 0.382657i | \(0.875009\pi\) | |||||||
\(62\) | 0.169873 | + | 0.294229i | 0.0215739 | + | 0.0373671i | ||||
\(63\) | 2.46410 | + | 4.26795i | 0.310448 | + | 0.537711i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.60770 | 0.197894 | ||||||||
\(67\) | 7.19615 | + | 12.4641i | 0.879150 | + | 1.52273i | 0.852275 | + | 0.523094i | \(0.175222\pi\) |
0.0268747 | + | 0.999639i | \(0.491444\pi\) | |||||||
\(68\) | −1.73205 | − | 3.00000i | −0.210042 | − | 0.363803i | ||||
\(69\) | 1.73205 | − | 3.00000i | 0.208514 | − | 0.361158i | ||||
\(70\) | −3.46410 | −0.414039 | ||||||||
\(71\) | −0.633975 | + | 1.09808i | −0.0752389 | + | 0.130318i | −0.901190 | − | 0.433424i | \(-0.857305\pi\) |
0.825951 | + | 0.563742i | \(0.190639\pi\) | |||||||
\(72\) | −2.13397 | + | 3.69615i | −0.251491 | + | 0.435596i | ||||
\(73\) | −4.00000 | −0.468165 | −0.234082 | − | 0.972217i | \(-0.575209\pi\) | ||||
−0.234082 | + | 0.972217i | \(0.575209\pi\) | |||||||
\(74\) | 3.46410 | − | 6.00000i | 0.402694 | − | 0.697486i | ||||
\(75\) | 0.366025 | + | 0.633975i | 0.0422650 | + | 0.0732051i | ||||
\(76\) | −2.09808 | − | 3.63397i | −0.240666 | − | 0.416845i | ||||
\(77\) | −2.53590 | −0.288992 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.3923 | 1.39424 | 0.697122 | − | 0.716953i | \(-0.254464\pi\) | ||||
0.697122 | + | 0.716953i | \(0.254464\pi\) | |||||||
\(80\) | −2.50000 | − | 4.33013i | −0.279508 | − | 0.484123i | ||||
\(81\) | −2.23205 | − | 3.86603i | −0.248006 | − | 0.429558i | ||||
\(82\) | 3.00000 | − | 5.19615i | 0.331295 | − | 0.573819i | ||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | 0.732051 | − | 1.26795i | 0.0798733 | − | 0.138345i | ||||
\(85\) | 1.73205 | − | 3.00000i | 0.187867 | − | 0.325396i | ||||
\(86\) | 17.6603 | 1.90435 | ||||||||
\(87\) | −3.46410 | + | 6.00000i | −0.371391 | + | 0.643268i | ||||
\(88\) | −1.09808 | − | 1.90192i | −0.117055 | − | 0.202746i | ||||
\(89\) | −0.464102 | − | 0.803848i | −0.0491947 | − | 0.0852077i | 0.840379 | − | 0.541998i | \(-0.182332\pi\) |
−0.889574 | + | 0.456791i | \(0.848999\pi\) | |||||||
\(90\) | 4.26795 | 0.449881 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.73205 | 0.493350 | ||||||||
\(93\) | −0.0717968 | − | 0.124356i | −0.00744498 | − | 0.0128951i | ||||
\(94\) | −5.19615 | − | 9.00000i | −0.535942 | − | 0.928279i | ||||
\(95\) | 2.09808 | − | 3.63397i | 0.215258 | − | 0.372838i | ||||
\(96\) | 3.80385 | 0.388229 | ||||||||
\(97\) | −1.00000 | + | 1.73205i | −0.101535 | + | 0.175863i | −0.912317 | − | 0.409484i | \(-0.865709\pi\) |
0.810782 | + | 0.585348i | \(0.199042\pi\) | |||||||
\(98\) | 2.59808 | − | 4.50000i | 0.262445 | − | 0.454569i | ||||
\(99\) | 3.12436 | 0.314010 | ||||||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | −6.46410 | − | 11.1962i | −0.643202 | − | 1.11406i | −0.984714 | − | 0.174181i | \(-0.944272\pi\) |
0.341511 | − | 0.939878i | \(-0.389061\pi\) | |||||||
\(102\) | 2.19615 | + | 3.80385i | 0.217451 | + | 0.376637i | ||||
\(103\) | 10.1962 | 1.00466 | 0.502328 | − | 0.864677i | \(-0.332477\pi\) | ||||
0.502328 | + | 0.864677i | \(0.332477\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.46410 | 0.142882 | ||||||||
\(106\) | 9.00000 | + | 15.5885i | 0.874157 | + | 1.51408i | ||||
\(107\) | −0.169873 | − | 0.294229i | −0.0164222 | − | 0.0284442i | 0.857697 | − | 0.514155i | \(-0.171894\pi\) |
−0.874120 | + | 0.485710i | \(0.838561\pi\) | |||||||
\(108\) | −2.00000 | + | 3.46410i | −0.192450 | + | 0.333333i | ||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | −1.09808 | + | 1.90192i | −0.104697 | + | 0.181341i | ||||
\(111\) | −1.46410 | + | 2.53590i | −0.138966 | + | 0.240697i | ||||
\(112\) | −10.0000 | −0.944911 | ||||||||
\(113\) | −7.73205 | + | 13.3923i | −0.727370 | + | 1.25984i | 0.230621 | + | 0.973044i | \(0.425924\pi\) |
−0.957991 | + | 0.286798i | \(0.907409\pi\) | |||||||
\(114\) | 2.66025 | + | 4.60770i | 0.249156 | + | 0.431550i | ||||
\(115\) | 2.36603 | + | 4.09808i | 0.220633 | + | 0.382148i | ||||
\(116\) | −9.46410 | −0.878720 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −26.1962 | −2.41155 | ||||||||
\(119\) | −3.46410 | − | 6.00000i | −0.317554 | − | 0.550019i | ||||
\(120\) | 0.633975 | + | 1.09808i | 0.0578737 | + | 0.100240i | ||||
\(121\) | 4.69615 | − | 8.13397i | 0.426923 | − | 0.739452i | ||||
\(122\) | 21.4641 | 1.94327 | ||||||||
\(123\) | −1.26795 | + | 2.19615i | −0.114327 | + | 0.198020i | ||||
\(124\) | 0.0980762 | − | 0.169873i | 0.00880750 | − | 0.0152550i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 4.26795 | − | 7.39230i | 0.380219 | − | 0.658559i | ||||
\(127\) | −2.90192 | − | 5.02628i | −0.257504 | − | 0.446010i | 0.708069 | − | 0.706144i | \(-0.249567\pi\) |
−0.965573 | + | 0.260134i | \(0.916233\pi\) | |||||||
\(128\) | −6.06218 | − | 10.5000i | −0.535826 | − | 0.928078i | ||||
\(129\) | −7.46410 | −0.657178 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | −0.464102 | − | 0.803848i | −0.0403949 | − | 0.0699660i | ||||
\(133\) | −4.19615 | − | 7.26795i | −0.363853 | − | 0.630211i | ||||
\(134\) | 12.4641 | − | 21.5885i | 1.07673 | − | 1.86496i | ||||
\(135\) | −4.00000 | −0.344265 | ||||||||
\(136\) | 3.00000 | − | 5.19615i | 0.257248 | − | 0.445566i | ||||
\(137\) | 6.46410 | − | 11.1962i | 0.552265 | − | 0.956552i | −0.445845 | − | 0.895110i | \(-0.647097\pi\) |
0.998111 | − | 0.0614418i | \(-0.0195699\pi\) | |||||||
\(138\) | −6.00000 | −0.510754 | ||||||||
\(139\) | 4.19615 | − | 7.26795i | 0.355913 | − | 0.616459i | −0.631361 | − | 0.775489i | \(-0.717503\pi\) |
0.987274 | + | 0.159030i | \(0.0508366\pi\) | |||||||
\(140\) | 1.00000 | + | 1.73205i | 0.0845154 | + | 0.146385i | ||||
\(141\) | 2.19615 | + | 3.80385i | 0.184949 | + | 0.320342i | ||||
\(142\) | 2.19615 | 0.184297 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 12.3205 | 1.02671 | ||||||||
\(145\) | −4.73205 | − | 8.19615i | −0.392975 | − | 0.680653i | ||||
\(146\) | 3.46410 | + | 6.00000i | 0.286691 | + | 0.496564i | ||||
\(147\) | −1.09808 | + | 1.90192i | −0.0905678 | + | 0.156868i | ||||
\(148\) | −4.00000 | −0.328798 | ||||||||
\(149\) | −9.92820 | + | 17.1962i | −0.813350 | + | 1.40876i | 0.0971565 | + | 0.995269i | \(0.469025\pi\) |
−0.910507 | + | 0.413495i | \(0.864308\pi\) | |||||||
\(150\) | 0.633975 | − | 1.09808i | 0.0517638 | − | 0.0896575i | ||||
\(151\) | −12.1962 | −0.992509 | −0.496254 | − | 0.868177i | \(-0.665292\pi\) | ||||
−0.496254 | + | 0.868177i | \(0.665292\pi\) | |||||||
\(152\) | 3.63397 | − | 6.29423i | 0.294754 | − | 0.510529i | ||||
\(153\) | 4.26795 | + | 7.39230i | 0.345043 | + | 0.597632i | ||||
\(154\) | 2.19615 | + | 3.80385i | 0.176971 | + | 0.306523i | ||||
\(155\) | 0.196152 | 0.0157553 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0000 | −0.798087 | −0.399043 | − | 0.916932i | \(-0.630658\pi\) | ||||
−0.399043 | + | 0.916932i | \(0.630658\pi\) | |||||||
\(158\) | −10.7321 | − | 18.5885i | −0.853796 | − | 1.47882i | ||||
\(159\) | −3.80385 | − | 6.58846i | −0.301665 | − | 0.522499i | ||||
\(160\) | −2.59808 | + | 4.50000i | −0.205396 | + | 0.355756i | ||||
\(161\) | 9.46410 | 0.745876 | ||||||||
\(162\) | −3.86603 | + | 6.69615i | −0.303744 | + | 0.526099i | ||||
\(163\) | −3.19615 | + | 5.53590i | −0.250342 | + | 0.433605i | −0.963620 | − | 0.267276i | \(-0.913876\pi\) |
0.713278 | + | 0.700881i | \(0.247210\pi\) | |||||||
\(164\) | −3.46410 | −0.270501 | ||||||||
\(165\) | 0.464102 | − | 0.803848i | 0.0361303 | − | 0.0625794i | ||||
\(166\) | 5.19615 | + | 9.00000i | 0.403300 | + | 0.698535i | ||||
\(167\) | −6.46410 | − | 11.1962i | −0.500207 | − | 0.866384i | −1.00000 | 0.000239271i | \(-0.999924\pi\) | |
0.499793 | − | 0.866145i | \(-0.333409\pi\) | |||||||
\(168\) | 2.53590 | 0.195649 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −6.00000 | −0.460179 | ||||||||
\(171\) | 5.16987 | + | 8.95448i | 0.395350 | + | 0.684766i | ||||
\(172\) | −5.09808 | − | 8.83013i | −0.388725 | − | 0.673291i | ||||
\(173\) | −7.73205 | + | 13.3923i | −0.587857 | + | 1.01820i | 0.406656 | + | 0.913581i | \(0.366695\pi\) |
−0.994513 | + | 0.104617i | \(0.966638\pi\) | |||||||
\(174\) | 12.0000 | 0.909718 | ||||||||
\(175\) | −1.00000 | + | 1.73205i | −0.0755929 | + | 0.130931i | ||||
\(176\) | −3.16987 | + | 5.49038i | −0.238938 | + | 0.413853i | ||||
\(177\) | 11.0718 | 0.832207 | ||||||||
\(178\) | −0.803848 | + | 1.39230i | −0.0602509 | + | 0.104358i | ||||
\(179\) | 2.53590 | + | 4.39230i | 0.189542 | + | 0.328296i | 0.945098 | − | 0.326788i | \(-0.105966\pi\) |
−0.755556 | + | 0.655084i | \(0.772633\pi\) | |||||||
\(180\) | −1.23205 | − | 2.13397i | −0.0918316 | − | 0.159057i | ||||
\(181\) | −20.3923 | −1.51575 | −0.757874 | − | 0.652401i | \(-0.773762\pi\) | ||||
−0.757874 | + | 0.652401i | \(0.773762\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.07180 | −0.670607 | ||||||||
\(184\) | 4.09808 | + | 7.09808i | 0.302114 | + | 0.523277i | ||||
\(185\) | −2.00000 | − | 3.46410i | −0.147043 | − | 0.254686i | ||||
\(186\) | −0.124356 | + | 0.215390i | −0.00911820 | + | 0.0157932i | ||||
\(187\) | −4.39230 | −0.321197 | ||||||||
\(188\) | −3.00000 | + | 5.19615i | −0.218797 | + | 0.378968i | ||||
\(189\) | −4.00000 | + | 6.92820i | −0.290957 | + | 0.503953i | ||||
\(190\) | −7.26795 | −0.527272 | ||||||||
\(191\) | 9.46410 | − | 16.3923i | 0.684798 | − | 1.18611i | −0.288702 | − | 0.957419i | \(-0.593224\pi\) |
0.973500 | − | 0.228686i | \(-0.0734431\pi\) | |||||||
\(192\) | 0.366025 | + | 0.633975i | 0.0264156 | + | 0.0457532i | ||||
\(193\) | 5.00000 | + | 8.66025i | 0.359908 | + | 0.623379i | 0.987945 | − | 0.154805i | \(-0.0494748\pi\) |
−0.628037 | + | 0.778183i | \(0.716141\pi\) | |||||||
\(194\) | 3.46410 | 0.248708 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | −0.464102 | − | 0.803848i | −0.0330659 | − | 0.0572718i | 0.849019 | − | 0.528362i | \(-0.177194\pi\) |
−0.882085 | + | 0.471091i | \(0.843860\pi\) | |||||||
\(198\) | −2.70577 | − | 4.68653i | −0.192291 | − | 0.333057i | ||||
\(199\) | −10.0000 | + | 17.3205i | −0.708881 | + | 1.22782i | 0.256391 | + | 0.966573i | \(0.417466\pi\) |
−0.965272 | + | 0.261245i | \(0.915867\pi\) | |||||||
\(200\) | −1.73205 | −0.122474 | ||||||||
\(201\) | −5.26795 | + | 9.12436i | −0.371572 | + | 0.643582i | ||||
\(202\) | −11.1962 | + | 19.3923i | −0.787759 | + | 1.36444i | ||||
\(203\) | −18.9282 | −1.32850 | ||||||||
\(204\) | 1.26795 | − | 2.19615i | 0.0887742 | − | 0.153761i | ||||
\(205\) | −1.73205 | − | 3.00000i | −0.120972 | − | 0.209529i | ||||
\(206\) | −8.83013 | − | 15.2942i | −0.615224 | − | 1.06560i | ||||
\(207\) | −11.6603 | −0.810444 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.32051 | −0.368027 | ||||||||
\(210\) | −1.26795 | − | 2.19615i | −0.0874968 | − | 0.151549i | ||||
\(211\) | −4.00000 | − | 6.92820i | −0.275371 | − | 0.476957i | 0.694857 | − | 0.719148i | \(-0.255467\pi\) |
−0.970229 | + | 0.242190i | \(0.922134\pi\) | |||||||
\(212\) | 5.19615 | − | 9.00000i | 0.356873 | − | 0.618123i | ||||
\(213\) | −0.928203 | −0.0635994 | ||||||||
\(214\) | −0.294229 | + | 0.509619i | −0.0201131 | + | 0.0348368i | ||||
\(215\) | 5.09808 | − | 8.83013i | 0.347686 | − | 0.602210i | ||||
\(216\) | −6.92820 | −0.471405 | ||||||||
\(217\) | 0.196152 | − | 0.339746i | 0.0133157 | − | 0.0230635i | ||||
\(218\) | −1.73205 | − | 3.00000i | −0.117309 | − | 0.203186i | ||||
\(219\) | −1.46410 | − | 2.53590i | −0.0989348 | − | 0.171360i | ||||
\(220\) | 1.26795 | 0.0854851 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 5.07180 | 0.340397 | ||||||||
\(223\) | −1.00000 | − | 1.73205i | −0.0669650 | − | 0.115987i | 0.830599 | − | 0.556871i | \(-0.187998\pi\) |
−0.897564 | + | 0.440884i | \(0.854665\pi\) | |||||||
\(224\) | 5.19615 | + | 9.00000i | 0.347183 | + | 0.601338i | ||||
\(225\) | 1.23205 | − | 2.13397i | 0.0821367 | − | 0.142265i | ||||
\(226\) | 26.7846 | 1.78169 | ||||||||
\(227\) | −1.73205 | + | 3.00000i | −0.114960 | + | 0.199117i | −0.917764 | − | 0.397127i | \(-0.870007\pi\) |
0.802804 | + | 0.596244i | \(0.203341\pi\) | |||||||
\(228\) | 1.53590 | − | 2.66025i | 0.101717 | − | 0.176180i | ||||
\(229\) | −14.3923 | −0.951070 | −0.475535 | − | 0.879697i | \(-0.657746\pi\) | ||||
−0.475535 | + | 0.879697i | \(0.657746\pi\) | |||||||
\(230\) | 4.09808 | − | 7.09808i | 0.270219 | − | 0.468033i | ||||
\(231\) | −0.928203 | − | 1.60770i | −0.0610713 | − | 0.105779i | ||||
\(232\) | −8.19615 | − | 14.1962i | −0.538104 | − | 0.932023i | ||||
\(233\) | −6.00000 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.00000 | −0.391397 | ||||||||
\(236\) | 7.56218 | + | 13.0981i | 0.492256 | + | 0.852612i | ||||
\(237\) | 4.53590 | + | 7.85641i | 0.294638 | + | 0.510328i | ||||
\(238\) | −6.00000 | + | 10.3923i | −0.388922 | + | 0.673633i | ||||
\(239\) | −3.80385 | −0.246050 | −0.123025 | − | 0.992404i | \(-0.539260\pi\) | ||||
−0.123025 | + | 0.992404i | \(0.539260\pi\) | |||||||
\(240\) | 1.83013 | − | 3.16987i | 0.118134 | − | 0.204614i | ||||
\(241\) | −9.19615 | + | 15.9282i | −0.592376 | + | 1.02603i | 0.401535 | + | 0.915844i | \(0.368477\pi\) |
−0.993911 | + | 0.110182i | \(0.964857\pi\) | |||||||
\(242\) | −16.2679 | −1.04574 | ||||||||
\(243\) | 7.63397 | − | 13.2224i | 0.489720 | − | 0.848219i | ||||
\(244\) | −6.19615 | − | 10.7321i | −0.396668 | − | 0.687049i | ||||
\(245\) | −1.50000 | − | 2.59808i | −0.0958315 | − | 0.165985i | ||||
\(246\) | 4.39230 | 0.280043 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.339746 | 0.0215739 | ||||||||
\(249\) | −2.19615 | − | 3.80385i | −0.139176 | − | 0.241059i | ||||
\(250\) | 0.866025 | + | 1.50000i | 0.0547723 | + | 0.0948683i | ||||
\(251\) | 7.26795 | − | 12.5885i | 0.458749 | − | 0.794576i | −0.540146 | − | 0.841571i | \(-0.681631\pi\) |
0.998895 | + | 0.0469948i | \(0.0149644\pi\) | |||||||
\(252\) | −4.92820 | −0.310448 | ||||||||
\(253\) | 3.00000 | − | 5.19615i | 0.188608 | − | 0.326679i | ||||
\(254\) | −5.02628 | + | 8.70577i | −0.315377 | + | 0.546249i | ||||
\(255\) | 2.53590 | 0.158804 | ||||||||
\(256\) | −9.50000 | + | 16.4545i | −0.593750 | + | 1.02841i | ||||
\(257\) | 3.92820 | + | 6.80385i | 0.245035 | + | 0.424412i | 0.962141 | − | 0.272551i | \(-0.0878673\pi\) |
−0.717107 | + | 0.696963i | \(0.754534\pi\) | |||||||
\(258\) | 6.46410 | + | 11.1962i | 0.402437 | + | 0.697042i | ||||
\(259\) | −8.00000 | −0.497096 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 23.3205 | 1.44350 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.36603 | − | 4.09808i | −0.145895 | − | 0.252698i | 0.783811 | − | 0.620999i | \(-0.213273\pi\) |
−0.929707 | + | 0.368301i | \(0.879940\pi\) | |||||||
\(264\) | 0.803848 | − | 1.39230i | 0.0494734 | − | 0.0856904i | ||||
\(265\) | 10.3923 | 0.638394 | ||||||||
\(266\) | −7.26795 | + | 12.5885i | −0.445627 | + | 0.771848i | ||||
\(267\) | 0.339746 | − | 0.588457i | 0.0207921 | − | 0.0360130i | ||||
\(268\) | −14.3923 | −0.879150 | ||||||||
\(269\) | −3.92820 | + | 6.80385i | −0.239507 | + | 0.414838i | −0.960573 | − | 0.278028i | \(-0.910319\pi\) |
0.721066 | + | 0.692866i | \(0.243652\pi\) | |||||||
\(270\) | 3.46410 | + | 6.00000i | 0.210819 | + | 0.365148i | ||||
\(271\) | 10.4904 | + | 18.1699i | 0.637245 | + | 1.10374i | 0.986035 | + | 0.166540i | \(0.0532595\pi\) |
−0.348789 | + | 0.937201i | \(0.613407\pi\) | |||||||
\(272\) | −17.3205 | −1.05021 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −22.3923 | −1.35277 | ||||||||
\(275\) | 0.633975 | + | 1.09808i | 0.0382301 | + | 0.0662165i | ||||
\(276\) | 1.73205 | + | 3.00000i | 0.104257 | + | 0.180579i | ||||
\(277\) | 2.80385 | − | 4.85641i | 0.168467 | − | 0.291793i | −0.769414 | − | 0.638750i | \(-0.779452\pi\) |
0.937881 | + | 0.346957i | \(0.112785\pi\) | |||||||
\(278\) | −14.5359 | −0.871805 | ||||||||
\(279\) | −0.241670 | + | 0.418584i | −0.0144684 | + | 0.0250600i | ||||
\(280\) | −1.73205 | + | 3.00000i | −0.103510 | + | 0.179284i | ||||
\(281\) | 1.60770 | 0.0959071 | 0.0479535 | − | 0.998850i | \(-0.484730\pi\) | ||||
0.0479535 | + | 0.998850i | \(0.484730\pi\) | |||||||
\(282\) | 3.80385 | − | 6.58846i | 0.226516 | − | 0.392337i | ||||
\(283\) | −0.705771 | − | 1.22243i | −0.0419538 | − | 0.0726660i | 0.844286 | − | 0.535893i | \(-0.180025\pi\) |
−0.886240 | + | 0.463227i | \(0.846692\pi\) | |||||||
\(284\) | −0.633975 | − | 1.09808i | −0.0376195 | − | 0.0651588i | ||||
\(285\) | 3.07180 | 0.181958 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.92820 | −0.408959 | ||||||||
\(288\) | −6.40192 | − | 11.0885i | −0.377237 | − | 0.653394i | ||||
\(289\) | 2.50000 | + | 4.33013i | 0.147059 | + | 0.254713i | ||||
\(290\) | −8.19615 | + | 14.1962i | −0.481295 | + | 0.833627i | ||||
\(291\) | −1.46410 | −0.0858272 | ||||||||
\(292\) | 2.00000 | − | 3.46410i | 0.117041 | − | 0.202721i | ||||
\(293\) | 9.46410 | − | 16.3923i | 0.552899 | − | 0.957649i | −0.445165 | − | 0.895449i | \(-0.646855\pi\) |
0.998064 | − | 0.0622001i | \(-0.0198117\pi\) | |||||||
\(294\) | 3.80385 | 0.221845 | ||||||||
\(295\) | −7.56218 | + | 13.0981i | −0.440287 | + | 0.762599i | ||||
\(296\) | −3.46410 | − | 6.00000i | −0.201347 | − | 0.348743i | ||||
\(297\) | 2.53590 | + | 4.39230i | 0.147148 | + | 0.254867i | ||||
\(298\) | 34.3923 | 1.99229 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.732051 | −0.0422650 | ||||||||
\(301\) | −10.1962 | − | 17.6603i | −0.587696 | − | 1.01792i | ||||
\(302\) | 10.5622 | + | 18.2942i | 0.607785 | + | 1.05271i | ||||
\(303\) | 4.73205 | − | 8.19615i | 0.271849 | − | 0.470857i | ||||
\(304\) | −20.9808 | −1.20333 | ||||||||
\(305\) | 6.19615 | − | 10.7321i | 0.354791 | − | 0.614515i | ||||
\(306\) | 7.39230 | − | 12.8038i | 0.422590 | − | 0.731947i | ||||
\(307\) | 22.7846 | 1.30039 | 0.650193 | − | 0.759769i | \(-0.274688\pi\) | ||||
0.650193 | + | 0.759769i | \(0.274688\pi\) | |||||||
\(308\) | 1.26795 | − | 2.19615i | 0.0722481 | − | 0.125137i | ||||
\(309\) | 3.73205 | + | 6.46410i | 0.212309 | + | 0.367730i | ||||
\(310\) | −0.169873 | − | 0.294229i | −0.00964814 | − | 0.0167111i | ||||
\(311\) | 4.39230 | 0.249065 | 0.124532 | − | 0.992216i | \(-0.460257\pi\) | ||||
0.124532 | + | 0.992216i | \(0.460257\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.39230 | 0.361314 | 0.180657 | − | 0.983546i | \(-0.442178\pi\) | ||||
0.180657 | + | 0.983546i | \(0.442178\pi\) | |||||||
\(314\) | 8.66025 | + | 15.0000i | 0.488726 | + | 0.846499i | ||||
\(315\) | −2.46410 | − | 4.26795i | −0.138836 | − | 0.240472i | ||||
\(316\) | −6.19615 | + | 10.7321i | −0.348561 | + | 0.603725i | ||||
\(317\) | 24.0000 | 1.34797 | 0.673987 | − | 0.738743i | \(-0.264580\pi\) | ||||
0.673987 | + | 0.738743i | \(0.264580\pi\) | |||||||
\(318\) | −6.58846 | + | 11.4115i | −0.369462 | + | 0.639928i | ||||
\(319\) | −6.00000 | + | 10.3923i | −0.335936 | + | 0.581857i | ||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 0.124356 | − | 0.215390i | 0.00694086 | − | 0.0120219i | ||||
\(322\) | −8.19615 | − | 14.1962i | −0.456754 | − | 0.791121i | ||||
\(323\) | −7.26795 | − | 12.5885i | −0.404400 | − | 0.700440i | ||||
\(324\) | 4.46410 | 0.248006 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11.0718 | 0.613210 | ||||||||
\(327\) | 0.732051 | + | 1.26795i | 0.0404825 | + | 0.0701178i | ||||
\(328\) | −3.00000 | − | 5.19615i | −0.165647 | − | 0.286910i | ||||
\(329\) | −6.00000 | + | 10.3923i | −0.330791 | + | 0.572946i | ||||
\(330\) | −1.60770 | −0.0885007 | ||||||||
\(331\) | 14.2942 | − | 24.7583i | 0.785682 | − | 1.36084i | −0.142909 | − | 0.989736i | \(-0.545646\pi\) |
0.928591 | − | 0.371105i | \(-0.121021\pi\) | |||||||
\(332\) | 3.00000 | − | 5.19615i | 0.164646 | − | 0.285176i | ||||
\(333\) | 9.85641 | 0.540128 | ||||||||
\(334\) | −11.1962 | + | 19.3923i | −0.612626 | + | 1.06110i | ||||
\(335\) | −7.19615 | − | 12.4641i | −0.393168 | − | 0.680987i | ||||
\(336\) | −3.66025 | − | 6.33975i | −0.199683 | − | 0.345861i | ||||
\(337\) | −5.60770 | −0.305471 | −0.152735 | − | 0.988267i | \(-0.548808\pi\) | ||||
−0.152735 | + | 0.988267i | \(0.548808\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.3205 | −0.614846 | ||||||||
\(340\) | 1.73205 | + | 3.00000i | 0.0939336 | + | 0.162698i | ||||
\(341\) | −0.124356 | − | 0.215390i | −0.00673424 | − | 0.0116640i | ||||
\(342\) | 8.95448 | − | 15.5096i | 0.484203 | − | 0.838664i | ||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | 8.83013 | − | 15.2942i | 0.476089 | − | 0.824610i | ||||
\(345\) | −1.73205 | + | 3.00000i | −0.0932505 | + | 0.161515i | ||||
\(346\) | 26.7846 | 1.43995 | ||||||||
\(347\) | −5.83013 | + | 10.0981i | −0.312978 | + | 0.542093i | −0.979006 | − | 0.203834i | \(-0.934660\pi\) |
0.666028 | + | 0.745927i | \(0.267993\pi\) | |||||||
\(348\) | −3.46410 | − | 6.00000i | −0.185695 | − | 0.321634i | ||||
\(349\) | −3.19615 | − | 5.53590i | −0.171086 | − | 0.296330i | 0.767714 | − | 0.640793i | \(-0.221394\pi\) |
−0.938800 | + | 0.344463i | \(0.888061\pi\) | |||||||
\(350\) | 3.46410 | 0.185164 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.58846 | 0.351166 | ||||||||
\(353\) | −13.8564 | − | 24.0000i | −0.737502 | − | 1.27739i | −0.953617 | − | 0.301023i | \(-0.902672\pi\) |
0.216115 | − | 0.976368i | \(-0.430661\pi\) | |||||||
\(354\) | −9.58846 | − | 16.6077i | −0.509621 | − | 0.882689i | ||||
\(355\) | 0.633975 | − | 1.09808i | 0.0336479 | − | 0.0582798i | ||||
\(356\) | 0.928203 | 0.0491947 | ||||||||
\(357\) | 2.53590 | − | 4.39230i | 0.134214 | − | 0.232465i | ||||
\(358\) | 4.39230 | − | 7.60770i | 0.232141 | − | 0.402079i | ||||
\(359\) | 8.19615 | 0.432576 | 0.216288 | − | 0.976330i | \(-0.430605\pi\) | ||||
0.216288 | + | 0.976330i | \(0.430605\pi\) | |||||||
\(360\) | 2.13397 | − | 3.69615i | 0.112470 | − | 0.194804i | ||||
\(361\) | 0.696152 | + | 1.20577i | 0.0366396 | + | 0.0634617i | ||||
\(362\) | 17.6603 | + | 30.5885i | 0.928202 | + | 1.60769i | ||||
\(363\) | 6.87564 | 0.360878 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.00000 | 0.209370 | ||||||||
\(366\) | 7.85641 | + | 13.6077i | 0.410661 | + | 0.711286i | ||||
\(367\) | −11.0981 | − | 19.2224i | −0.579315 | − | 1.00340i | −0.995558 | − | 0.0941495i | \(-0.969987\pi\) |
0.416243 | − | 0.909253i | \(-0.363346\pi\) | |||||||
\(368\) | 11.8301 | − | 20.4904i | 0.616688 | − | 1.06813i | ||||
\(369\) | 8.53590 | 0.444361 | ||||||||
\(370\) | −3.46410 | + | 6.00000i | −0.180090 | + | 0.311925i | ||||
\(371\) | 10.3923 | − | 18.0000i | 0.539542 | − | 0.934513i | ||||
\(372\) | 0.143594 | 0.00744498 | ||||||||
\(373\) | 5.00000 | − | 8.66025i | 0.258890 | − | 0.448411i | −0.707055 | − | 0.707159i | \(-0.749977\pi\) |
0.965945 | + | 0.258748i | \(0.0833099\pi\) | |||||||
\(374\) | 3.80385 | + | 6.58846i | 0.196692 | + | 0.340681i | ||||
\(375\) | −0.366025 | − | 0.633975i | −0.0189015 | − | 0.0327383i | ||||
\(376\) | −10.3923 | −0.535942 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 13.8564 | 0.712697 | ||||||||
\(379\) | 16.4904 | + | 28.5622i | 0.847054 | + | 1.46714i | 0.883825 | + | 0.467817i | \(0.154959\pi\) |
−0.0367715 | + | 0.999324i | \(0.511707\pi\) | |||||||
\(380\) | 2.09808 | + | 3.63397i | 0.107629 | + | 0.186419i | ||||
\(381\) | 2.12436 | − | 3.67949i | 0.108834 | − | 0.188506i | ||||
\(382\) | −32.7846 | −1.67741 | ||||||||
\(383\) | 0.464102 | − | 0.803848i | 0.0237145 | − | 0.0410747i | −0.853925 | − | 0.520397i | \(-0.825784\pi\) |
0.877639 | + | 0.479322i | \(0.159117\pi\) | |||||||
\(384\) | 4.43782 | − | 7.68653i | 0.226467 | − | 0.392252i | ||||
\(385\) | 2.53590 | 0.129241 | ||||||||
\(386\) | 8.66025 | − | 15.0000i | 0.440795 | − | 0.763480i | ||||
\(387\) | 12.5622 | + | 21.7583i | 0.638571 | + | 1.10604i | ||||
\(388\) | −1.00000 | − | 1.73205i | −0.0507673 | − | 0.0879316i | ||||
\(389\) | 6.00000 | 0.304212 | 0.152106 | − | 0.988364i | \(-0.451394\pi\) | ||||
0.152106 | + | 0.988364i | \(0.451394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.3923 | 0.828994 | ||||||||
\(392\) | −2.59808 | − | 4.50000i | −0.131223 | − | 0.227284i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.803848 | + | 1.39230i | −0.0404973 | + | 0.0701433i | ||||
\(395\) | −12.3923 | −0.623525 | ||||||||
\(396\) | −1.56218 | + | 2.70577i | −0.0785024 | + | 0.135970i | ||||
\(397\) | 6.39230 | − | 11.0718i | 0.320821 | − | 0.555678i | −0.659837 | − | 0.751409i | \(-0.729375\pi\) |
0.980658 | + | 0.195731i | \(0.0627080\pi\) | |||||||
\(398\) | 34.6410 | 1.73640 | ||||||||
\(399\) | 3.07180 | − | 5.32051i | 0.153782 | − | 0.266359i | ||||
\(400\) | 2.50000 | + | 4.33013i | 0.125000 | + | 0.216506i | ||||
\(401\) | 11.5359 | + | 19.9808i | 0.576075 | + | 0.997792i | 0.995924 | + | 0.0901975i | \(0.0287498\pi\) |
−0.419849 | + | 0.907594i | \(0.637917\pi\) | |||||||
\(402\) | 18.2487 | 0.910163 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 12.9282 | 0.643202 | ||||||||
\(405\) | 2.23205 | + | 3.86603i | 0.110911 | + | 0.192104i | ||||
\(406\) | 16.3923 | + | 28.3923i | 0.813536 | + | 1.40909i | ||||
\(407\) | −2.53590 | + | 4.39230i | −0.125700 | + | 0.217718i | ||||
\(408\) | 4.39230 | 0.217451 | ||||||||
\(409\) | 19.1962 | − | 33.2487i | 0.949189 | − | 1.64404i | 0.202049 | − | 0.979375i | \(-0.435240\pi\) |
0.747139 | − | 0.664668i | \(-0.231427\pi\) | |||||||
\(410\) | −3.00000 | + | 5.19615i | −0.148159 | + | 0.256620i | ||||
\(411\) | 9.46410 | 0.466830 | ||||||||
\(412\) | −5.09808 | + | 8.83013i | −0.251164 | + | 0.435029i | ||||
\(413\) | 15.1244 | + | 26.1962i | 0.744221 | + | 1.28903i | ||||
\(414\) | 10.0981 | + | 17.4904i | 0.496293 | + | 0.859605i | ||||
\(415\) | 6.00000 | 0.294528 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.14359 | 0.300853 | ||||||||
\(418\) | 4.60770 | + | 7.98076i | 0.225370 | + | 0.390352i | ||||
\(419\) | 4.73205 | + | 8.19615i | 0.231176 | + | 0.400408i | 0.958154 | − | 0.286252i | \(-0.0924094\pi\) |
−0.726979 | + | 0.686660i | \(0.759076\pi\) | |||||||
\(420\) | −0.732051 | + | 1.26795i | −0.0357204 | + | 0.0618696i | ||||
\(421\) | 10.7846 | 0.525610 | 0.262805 | − | 0.964849i | \(-0.415352\pi\) | ||||
0.262805 | + | 0.964849i | \(0.415352\pi\) | |||||||
\(422\) | −6.92820 | + | 12.0000i | −0.337260 | + | 0.584151i | ||||
\(423\) | 7.39230 | − | 12.8038i | 0.359426 | − | 0.622544i | ||||
\(424\) | 18.0000 | 0.874157 | ||||||||
\(425\) | −1.73205 | + | 3.00000i | −0.0840168 | + | 0.145521i | ||||
\(426\) | 0.803848 | + | 1.39230i | 0.0389465 | + | 0.0674574i | ||||
\(427\) | −12.3923 | − | 21.4641i | −0.599706 | − | 1.03872i | ||||
\(428\) | 0.339746 | 0.0164222 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −17.6603 | −0.851653 | ||||||||
\(431\) | −9.75833 | − | 16.9019i | −0.470042 | − | 0.814137i | 0.529371 | − | 0.848390i | \(-0.322428\pi\) |
−0.999413 | + | 0.0342535i | \(0.989095\pi\) | |||||||
\(432\) | 10.0000 | + | 17.3205i | 0.481125 | + | 0.833333i | ||||
\(433\) | 3.39230 | − | 5.87564i | 0.163024 | − | 0.282365i | −0.772928 | − | 0.634494i | \(-0.781209\pi\) |
0.935952 | + | 0.352128i | \(0.114542\pi\) | |||||||
\(434\) | −0.679492 | −0.0326167 | ||||||||
\(435\) | 3.46410 | − | 6.00000i | 0.166091 | − | 0.287678i | ||||
\(436\) | −1.00000 | + | 1.73205i | −0.0478913 | + | 0.0829502i | ||||
\(437\) | 19.8564 | 0.949861 | ||||||||
\(438\) | −2.53590 | + | 4.39230i | −0.121170 | + | 0.209872i | ||||
\(439\) | −16.0000 | − | 27.7128i | −0.763638 | − | 1.32266i | −0.940963 | − | 0.338508i | \(-0.890078\pi\) |
0.177325 | − | 0.984152i | \(-0.443256\pi\) | |||||||
\(440\) | 1.09808 | + | 1.90192i | 0.0523487 | + | 0.0906707i | ||||
\(441\) | 7.39230 | 0.352015 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.9808 | 1.66199 | 0.830993 | − | 0.556283i | \(-0.187773\pi\) | ||||
0.830993 | + | 0.556283i | \(0.187773\pi\) | |||||||
\(444\) | −1.46410 | − | 2.53590i | −0.0694832 | − | 0.120348i | ||||
\(445\) | 0.464102 | + | 0.803848i | 0.0220005 | + | 0.0381060i | ||||
\(446\) | −1.73205 | + | 3.00000i | −0.0820150 | + | 0.142054i | ||||
\(447\) | −14.5359 | −0.687524 | ||||||||
\(448\) | −1.00000 | + | 1.73205i | −0.0472456 | + | 0.0818317i | ||||
\(449\) | −13.7321 | + | 23.7846i | −0.648056 | + | 1.12247i | 0.335531 | + | 0.942029i | \(0.391084\pi\) |
−0.983587 | + | 0.180436i | \(0.942249\pi\) | |||||||
\(450\) | −4.26795 | −0.201193 | ||||||||
\(451\) | −2.19615 | + | 3.80385i | −0.103413 | + | 0.179116i | ||||
\(452\) | −7.73205 | − | 13.3923i | −0.363685 | − | 0.629921i | ||||
\(453\) | −4.46410 | − | 7.73205i | −0.209742 | − | 0.363283i | ||||
\(454\) | 6.00000 | 0.281594 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.32051 | 0.249156 | ||||||||
\(457\) | 15.3923 | + | 26.6603i | 0.720022 | + | 1.24711i | 0.960991 | + | 0.276581i | \(0.0892015\pi\) |
−0.240969 | + | 0.970533i | \(0.577465\pi\) | |||||||
\(458\) | 12.4641 | + | 21.5885i | 0.582409 | + | 1.00876i | ||||
\(459\) | −6.92820 | + | 12.0000i | −0.323381 | + | 0.560112i | ||||
\(460\) | −4.73205 | −0.220633 | ||||||||
\(461\) | −1.73205 | + | 3.00000i | −0.0806696 | + | 0.139724i | −0.903538 | − | 0.428508i | \(-0.859039\pi\) |
0.822868 | + | 0.568232i | \(0.192373\pi\) | |||||||
\(462\) | −1.60770 | + | 2.78461i | −0.0747967 | + | 0.129552i | ||||
\(463\) | 18.3923 | 0.854763 | 0.427381 | − | 0.904071i | \(-0.359436\pi\) | ||||
0.427381 | + | 0.904071i | \(0.359436\pi\) | |||||||
\(464\) | −23.6603 | + | 40.9808i | −1.09840 | + | 1.90248i | ||||
\(465\) | 0.0717968 | + | 0.124356i | 0.00332950 | + | 0.00576686i | ||||
\(466\) | 5.19615 | + | 9.00000i | 0.240707 | + | 0.416917i | ||||
\(467\) | 38.1962 | 1.76751 | 0.883754 | − | 0.467953i | \(-0.155008\pi\) | ||||
0.883754 | + | 0.467953i | \(0.155008\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −28.7846 | −1.32915 | ||||||||
\(470\) | 5.19615 | + | 9.00000i | 0.239681 | + | 0.415139i | ||||
\(471\) | −3.66025 | − | 6.33975i | −0.168656 | − | 0.292120i | ||||
\(472\) | −13.0981 | + | 22.6865i | −0.602888 | + | 1.04423i | ||||
\(473\) | −12.9282 | −0.594439 | ||||||||
\(474\) | 7.85641 | − | 13.6077i | 0.360857 | − | 0.625022i | ||||
\(475\) | −2.09808 | + | 3.63397i | −0.0962663 | + | 0.166738i | ||||
\(476\) | 6.92820 | 0.317554 | ||||||||
\(477\) | −12.8038 | + | 22.1769i | −0.586248 | + | 1.01541i | ||||
\(478\) | 3.29423 | + | 5.70577i | 0.150675 | + | 0.260976i | ||||
\(479\) | −9.16987 | − | 15.8827i | −0.418982 | − | 0.725698i | 0.576855 | − | 0.816846i | \(-0.304280\pi\) |
−0.995837 | + | 0.0911480i | \(0.970946\pi\) | |||||||
\(480\) | −3.80385 | −0.173621 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 31.8564 | 1.45102 | ||||||||
\(483\) | 3.46410 | + | 6.00000i | 0.157622 | + | 0.273009i | ||||
\(484\) | 4.69615 | + | 8.13397i | 0.213461 | + | 0.369726i | ||||
\(485\) | 1.00000 | − | 1.73205i | 0.0454077 | − | 0.0786484i | ||||
\(486\) | −26.4449 | −1.19956 | ||||||||
\(487\) | 2.80385 | − | 4.85641i | 0.127054 | − | 0.220065i | −0.795480 | − | 0.605980i | \(-0.792781\pi\) |
0.922534 | + | 0.385915i | \(0.126114\pi\) | |||||||
\(488\) | 10.7321 | − | 18.5885i | 0.485817 | − | 0.841460i | ||||
\(489\) | −4.67949 | −0.211614 | ||||||||
\(490\) | −2.59808 | + | 4.50000i | −0.117369 | + | 0.203289i | ||||
\(491\) | 4.73205 | + | 8.19615i | 0.213554 | + | 0.369887i | 0.952824 | − | 0.303522i | \(-0.0981626\pi\) |
−0.739270 | + | 0.673409i | \(0.764829\pi\) | |||||||
\(492\) | −1.26795 | − | 2.19615i | −0.0571636 | − | 0.0990102i | ||||
\(493\) | −32.7846 | −1.47654 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.12436 | −0.140429 | ||||||||
\(496\) | −0.490381 | − | 0.849365i | −0.0220188 | − | 0.0381376i | ||||
\(497\) | −1.26795 | − | 2.19615i | −0.0568753 | − | 0.0985109i | ||||
\(498\) | −3.80385 | + | 6.58846i | −0.170454 | + | 0.295236i | ||||
\(499\) | 12.9808 | 0.581099 | 0.290549 | − | 0.956860i | \(-0.406162\pi\) | ||||
0.290549 | + | 0.956860i | \(0.406162\pi\) | |||||||
\(500\) | 0.500000 | − | 0.866025i | 0.0223607 | − | 0.0387298i | ||||
\(501\) | 4.73205 | − | 8.19615i | 0.211412 | − | 0.366177i | ||||
\(502\) | −25.1769 | −1.12370 | ||||||||
\(503\) | 12.7583 | − | 22.0981i | 0.568866 | − | 0.985305i | −0.427813 | − | 0.903867i | \(-0.640716\pi\) |
0.996678 | − | 0.0814371i | \(-0.0259510\pi\) | |||||||
\(504\) | −4.26795 | − | 7.39230i | −0.190110 | − | 0.329279i | ||||
\(505\) | 6.46410 | + | 11.1962i | 0.287649 | + | 0.498222i | ||||
\(506\) | −10.3923 | −0.461994 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.80385 | 0.257504 | ||||||||
\(509\) | −16.2679 | − | 28.1769i | −0.721064 | − | 1.24892i | −0.960574 | − | 0.278026i | \(-0.910320\pi\) |
0.239509 | − | 0.970894i | \(-0.423013\pi\) | |||||||
\(510\) | −2.19615 | − | 3.80385i | −0.0972473 | − | 0.168437i | ||||
\(511\) | 4.00000 | − | 6.92820i | 0.176950 | − | 0.306486i | ||||
\(512\) | 8.66025 | 0.382733 | ||||||||
\(513\) | −8.39230 | + | 14.5359i | −0.370529 | + | 0.641776i | ||||
\(514\) | 6.80385 | − | 11.7846i | 0.300105 | − | 0.519797i | ||||
\(515\) | −10.1962 | −0.449296 | ||||||||
\(516\) | 3.73205 | − | 6.46410i | 0.164294 | − | 0.284566i | ||||
\(517\) | 3.80385 | + | 6.58846i | 0.167293 | + | 0.289760i | ||||
\(518\) | 6.92820 | + | 12.0000i | 0.304408 | + | 0.527250i | ||||
\(519\) | −11.3205 | −0.496915 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.60770 | −0.333299 | −0.166650 | − | 0.986016i | \(-0.553295\pi\) | ||||
−0.166650 | + | 0.986016i | \(0.553295\pi\) | |||||||
\(522\) | −20.1962 | − | 34.9808i | −0.883962 | − | 1.53107i | ||||
\(523\) | 6.90192 | + | 11.9545i | 0.301800 | + | 0.522733i | 0.976544 | − | 0.215319i | \(-0.0690792\pi\) |
−0.674744 | + | 0.738052i | \(0.735746\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.46410 | −0.0638986 | ||||||||
\(526\) | −4.09808 | + | 7.09808i | −0.178685 | + | 0.309491i | ||||
\(527\) | 0.339746 | − | 0.588457i | 0.0147996 | − | 0.0256336i | ||||
\(528\) | −4.64102 | −0.201974 | ||||||||
\(529\) | 0.303848 | − | 0.526279i | 0.0132108 | − | 0.0228817i | ||||
\(530\) | −9.00000 | − | 15.5885i | −0.390935 | − | 0.677119i | ||||
\(531\) | −18.6340 | − | 32.2750i | −0.808646 | − | 1.40062i | ||||
\(532\) | 8.39230 | 0.363853 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −1.17691 | −0.0509301 | ||||||||
\(535\) | 0.169873 | + | 0.294229i | 0.00734425 | + | 0.0127206i | ||||
\(536\) | −12.4641 | − | 21.5885i | −0.538367 | − | 0.932479i | ||||
\(537\) | −1.85641 | + | 3.21539i | −0.0801099 | + | 0.138754i | ||||
\(538\) | 13.6077 | 0.586669 | ||||||||
\(539\) | −1.90192 | + | 3.29423i | −0.0819217 | + | 0.141892i | ||||
\(540\) | 2.00000 | − | 3.46410i | 0.0860663 | − | 0.149071i | ||||
\(541\) | −5.60770 | −0.241094 | −0.120547 | − | 0.992708i | \(-0.538465\pi\) | ||||
−0.120547 | + | 0.992708i | \(0.538465\pi\) | |||||||
\(542\) | 18.1699 | − | 31.4711i | 0.780463 | − | 1.35180i | ||||
\(543\) | −7.46410 | − | 12.9282i | −0.320315 | − | 0.554802i | ||||
\(544\) | 9.00000 | + | 15.5885i | 0.385872 | + | 0.668350i | ||||
\(545\) | −2.00000 | −0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.80385 | −0.0771270 | −0.0385635 | − | 0.999256i | \(-0.512278\pi\) | ||||
−0.0385635 | + | 0.999256i | \(0.512278\pi\) | |||||||
\(548\) | 6.46410 | + | 11.1962i | 0.276133 | + | 0.478276i | ||||
\(549\) | 15.2679 | + | 26.4449i | 0.651620 | + | 1.12864i | ||||
\(550\) | 1.09808 | − | 1.90192i | 0.0468221 | − | 0.0810983i | ||||
\(551\) | −39.7128 | −1.69182 | ||||||||
\(552\) | −3.00000 | + | 5.19615i | −0.127688 | + | 0.221163i | ||||
\(553\) | −12.3923 | + | 21.4641i | −0.526974 | + | 0.912746i | ||||
\(554\) | −9.71281 | −0.412658 | ||||||||
\(555\) | 1.46410 | − | 2.53590i | 0.0621477 | − | 0.107643i | ||||
\(556\) | 4.19615 | + | 7.26795i | 0.177957 | + | 0.308230i | ||||
\(557\) | 12.9282 | + | 22.3923i | 0.547786 | + | 0.948792i | 0.998426 | + | 0.0560868i | \(0.0178624\pi\) |
−0.450640 | + | 0.892706i | \(0.648804\pi\) | |||||||
\(558\) | 0.837169 | 0.0354402 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 10.0000 | 0.422577 | ||||||||
\(561\) | −1.60770 | − | 2.78461i | −0.0678769 | − | 0.117566i | ||||
\(562\) | −1.39230 | − | 2.41154i | −0.0587308 | − | 0.101725i | ||||
\(563\) | −8.02628 | + | 13.9019i | −0.338267 | + | 0.585896i | −0.984107 | − | 0.177577i | \(-0.943174\pi\) |
0.645840 | + | 0.763473i | \(0.276507\pi\) | |||||||
\(564\) | −4.39230 | −0.184949 | ||||||||
\(565\) | 7.73205 | − | 13.3923i | 0.325290 | − | 0.563418i | ||||
\(566\) | −1.22243 | + | 2.11731i | −0.0513826 | + | 0.0889973i | ||||
\(567\) | 8.92820 | 0.374949 | ||||||||
\(568\) | 1.09808 | − | 1.90192i | 0.0460743 | − | 0.0798029i | ||||
\(569\) | 4.73205 | + | 8.19615i | 0.198378 | + | 0.343601i | 0.948003 | − | 0.318263i | \(-0.103099\pi\) |
−0.749625 | + | 0.661863i | \(0.769766\pi\) | |||||||
\(570\) | −2.66025 | − | 4.60770i | −0.111426 | − | 0.192995i | ||||
\(571\) | 15.6077 | 0.653162 | 0.326581 | − | 0.945169i | \(-0.394103\pi\) | ||||
0.326581 | + | 0.945169i | \(0.394103\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.8564 | 0.578860 | ||||||||
\(574\) | 6.00000 | + | 10.3923i | 0.250435 | + | 0.433766i | ||||
\(575\) | −2.36603 | − | 4.09808i | −0.0986701 | − | 0.170902i | ||||
\(576\) | 1.23205 | − | 2.13397i | 0.0513355 | − | 0.0889156i | ||||
\(577\) | −4.00000 | −0.166522 | −0.0832611 | − | 0.996528i | \(-0.526534\pi\) | ||||
−0.0832611 | + | 0.996528i | \(0.526534\pi\) | |||||||
\(578\) | 4.33013 | − | 7.50000i | 0.180110 | − | 0.311959i | ||||
\(579\) | −3.66025 | + | 6.33975i | −0.152115 | + | 0.263471i | ||||
\(580\) | 9.46410 | 0.392975 | ||||||||
\(581\) | 6.00000 | − | 10.3923i | 0.248922 | − | 0.431145i | ||||
\(582\) | 1.26795 | + | 2.19615i | 0.0525582 | + | 0.0910334i | ||||
\(583\) | −6.58846 | − | 11.4115i | −0.272866 | − | 0.472618i | ||||
\(584\) | 6.92820 | 0.286691 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −32.7846 | −1.35432 | ||||||||
\(587\) | 7.73205 | + | 13.3923i | 0.319136 | + | 0.552760i | 0.980308 | − | 0.197475i | \(-0.0632740\pi\) |
−0.661172 | + | 0.750234i | \(0.729941\pi\) | |||||||
\(588\) | −1.09808 | − | 1.90192i | −0.0452839 | − | 0.0784340i | ||||
\(589\) | 0.411543 | − | 0.712813i | 0.0169573 | − | 0.0293709i | ||||
\(590\) | 26.1962 | 1.07848 | ||||||||
\(591\) | 0.339746 | − | 0.588457i | 0.0139753 | − | 0.0242059i | ||||
\(592\) | −10.0000 | + | 17.3205i | −0.410997 | + | 0.711868i | ||||
\(593\) | −14.7846 | −0.607131 | −0.303566 | − | 0.952811i | \(-0.598177\pi\) | ||||
−0.303566 | + | 0.952811i | \(0.598177\pi\) | |||||||
\(594\) | 4.39230 | − | 7.60770i | 0.180218 | − | 0.312148i | ||||
\(595\) | 3.46410 | + | 6.00000i | 0.142014 | + | 0.245976i | ||||
\(596\) | −9.92820 | − | 17.1962i | −0.406675 | − | 0.704382i | ||||
\(597\) | −14.6410 | −0.599217 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.3923 | −1.16008 | −0.580039 | − | 0.814589i | \(-0.696963\pi\) | ||||
−0.580039 | + | 0.814589i | \(0.696963\pi\) | |||||||
\(600\) | −0.633975 | − | 1.09808i | −0.0258819 | − | 0.0448288i | ||||
\(601\) | 19.7846 | + | 34.2679i | 0.807031 | + | 1.39782i | 0.914911 | + | 0.403655i | \(0.132260\pi\) |
−0.107880 | + | 0.994164i | \(0.534406\pi\) | |||||||
\(602\) | −17.6603 | + | 30.5885i | −0.719778 | + | 1.24669i | ||||
\(603\) | 35.4641 | 1.44421 | ||||||||
\(604\) | 6.09808 | − | 10.5622i | 0.248127 | − | 0.429769i | ||||
\(605\) | −4.69615 | + | 8.13397i | −0.190926 | + | 0.330693i | ||||
\(606\) | −16.3923 | −0.665892 | ||||||||
\(607\) | 13.4904 | − | 23.3660i | 0.547558 | − | 0.948398i | −0.450883 | − | 0.892583i | \(-0.648891\pi\) |
0.998441 | − | 0.0558149i | \(-0.0177757\pi\) | |||||||
\(608\) | 10.9019 | + | 18.8827i | 0.442131 | + | 0.765794i | ||||
\(609\) | −6.92820 | − | 12.0000i | −0.280745 | − | 0.486265i | ||||
\(610\) | −21.4641 | −0.869056 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −8.53590 | −0.345043 | ||||||||
\(613\) | −13.0000 | − | 22.5167i | −0.525065 | − | 0.909439i | −0.999574 | − | 0.0291886i | \(-0.990708\pi\) |
0.474509 | − | 0.880251i | \(-0.342626\pi\) | |||||||
\(614\) | −19.7321 | − | 34.1769i | −0.796321 | − | 1.37927i | ||||
\(615\) | 1.26795 | − | 2.19615i | 0.0511286 | − | 0.0885574i | ||||
\(616\) | 4.39230 | 0.176971 | ||||||||
\(617\) | 10.8564 | − | 18.8038i | 0.437062 | − | 0.757014i | −0.560399 | − | 0.828223i | \(-0.689352\pi\) |
0.997461 | + | 0.0712084i | \(0.0226855\pi\) | |||||||
\(618\) | 6.46410 | − | 11.1962i | 0.260024 | − | 0.450375i | ||||
\(619\) | −44.9808 | −1.80793 | −0.903965 | − | 0.427607i | \(-0.859357\pi\) | ||||
−0.903965 | + | 0.427607i | \(0.859357\pi\) | |||||||
\(620\) | −0.0980762 | + | 0.169873i | −0.00393884 | + | 0.00682226i | ||||
\(621\) | −9.46410 | − | 16.3923i | −0.379781 | − | 0.657801i | ||||
\(622\) | −3.80385 | − | 6.58846i | −0.152520 | − | 0.264173i | ||||
\(623\) | 1.85641 | 0.0743754 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −5.53590 | − | 9.58846i | −0.221259 | − | 0.383232i | ||||
\(627\) | −1.94744 | − | 3.37307i | −0.0777733 | − | 0.134707i | ||||
\(628\) | 5.00000 | − | 8.66025i | 0.199522 | − | 0.345582i | ||||
\(629\) | −13.8564 | −0.552491 | ||||||||
\(630\) | −4.26795 | + | 7.39230i | −0.170039 | + | 0.294516i | ||||
\(631\) | −8.09808 | + | 14.0263i | −0.322379 | + | 0.558377i | −0.980978 | − | 0.194117i | \(-0.937816\pi\) |
0.658599 | + | 0.752494i | \(0.271149\pi\) | |||||||
\(632\) | −21.4641 | −0.853796 | ||||||||
\(633\) | 2.92820 | − | 5.07180i | 0.116386 | − | 0.201586i | ||||
\(634\) | −20.7846 | − | 36.0000i | −0.825462 | − | 1.42974i | ||||
\(635\) | 2.90192 | + | 5.02628i | 0.115159 | + | 0.199462i | ||||
\(636\) | 7.60770 | 0.301665 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 20.7846 | 0.822871 | ||||||||
\(639\) | 1.56218 | + | 2.70577i | 0.0617988 | + | 0.107039i | ||||
\(640\) | 6.06218 | + | 10.5000i | 0.239629 | + | 0.415049i | ||||
\(641\) | 0.464102 | − | 0.803848i | 0.0183309 | − | 0.0317501i | −0.856714 | − | 0.515791i | \(-0.827498\pi\) |
0.875045 | + | 0.484041i | \(0.160831\pi\) | |||||||
\(642\) | −0.430781 | −0.0170016 | ||||||||
\(643\) | −17.3923 | + | 30.1244i | −0.685886 | + | 1.18799i | 0.287272 | + | 0.957849i | \(0.407252\pi\) |
−0.973158 | + | 0.230140i | \(0.926082\pi\) | |||||||
\(644\) | −4.73205 | + | 8.19615i | −0.186469 | + | 0.322974i | ||||
\(645\) | 7.46410 | 0.293899 | ||||||||
\(646\) | −12.5885 | + | 21.8038i | −0.495286 | + | 0.857861i | ||||
\(647\) | 8.02628 | + | 13.9019i | 0.315546 | + | 0.546541i | 0.979553 | − | 0.201185i | \(-0.0644791\pi\) |
−0.664008 | + | 0.747726i | \(0.731146\pi\) | |||||||
\(648\) | 3.86603 | + | 6.69615i | 0.151872 | + | 0.263050i | ||||
\(649\) | 19.1769 | 0.752760 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.287187 | 0.0112557 | ||||||||
\(652\) | −3.19615 | − | 5.53590i | −0.125171 | − | 0.216803i | ||||
\(653\) | 9.92820 | + | 17.1962i | 0.388521 | + | 0.672937i | 0.992251 | − | 0.124251i | \(-0.0396529\pi\) |
−0.603730 | + | 0.797189i | \(0.706320\pi\) | |||||||
\(654\) | 1.26795 | − | 2.19615i | 0.0495807 | − | 0.0858764i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −8.66025 | + | 15.0000i | −0.338126 | + | 0.585652i | ||||
\(657\) | −4.92820 | + | 8.53590i | −0.192268 | + | 0.333017i | ||||
\(658\) | 20.7846 | 0.810268 | ||||||||
\(659\) | 7.26795 | − | 12.5885i | 0.283119 | − | 0.490377i | −0.689032 | − | 0.724731i | \(-0.741964\pi\) |
0.972151 | + | 0.234354i | \(0.0752975\pi\) | |||||||
\(660\) | 0.464102 | + | 0.803848i | 0.0180651 | + | 0.0312897i | ||||
\(661\) | 15.3923 | + | 26.6603i | 0.598691 | + | 1.03696i | 0.993015 | + | 0.117992i | \(0.0376457\pi\) |
−0.394323 | + | 0.918972i | \(0.629021\pi\) | |||||||
\(662\) | −49.5167 | −1.92452 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10.3923 | 0.403300 | ||||||||
\(665\) | 4.19615 | + | 7.26795i | 0.162720 | + | 0.281839i | ||||
\(666\) | −8.53590 | − | 14.7846i | −0.330759 | − | 0.572892i | ||||
\(667\) | 22.3923 | − | 38.7846i | 0.867034 | − | 1.50175i | ||||
\(668\) | 12.9282 | 0.500207 | ||||||||
\(669\) | 0.732051 | − | 1.26795i | 0.0283027 | − | 0.0490217i | ||||
\(670\) | −12.4641 | + | 21.5885i | −0.481530 | + | 0.834035i | ||||
\(671\) | −15.7128 | −0.606586 | ||||||||
\(672\) | −3.80385 | + | 6.58846i | −0.146737 | + | 0.254155i | ||||
\(673\) | −3.19615 | − | 5.53590i | −0.123203 | − | 0.213393i | 0.797826 | − | 0.602887i | \(-0.205983\pi\) |
−0.921029 | + | 0.389494i | \(0.872650\pi\) | |||||||
\(674\) | 4.85641 | + | 8.41154i | 0.187062 | + | 0.324001i | ||||
\(675\) | 4.00000 | 0.153960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.3923 | −0.399409 | −0.199704 | − | 0.979856i | \(-0.563998\pi\) | ||||
−0.199704 | + | 0.979856i | \(0.563998\pi\) | |||||||
\(678\) | 9.80385 | + | 16.9808i | 0.376514 | + | 0.652142i | ||||
\(679\) | −2.00000 | − | 3.46410i | −0.0767530 | − | 0.132940i | ||||
\(680\) | −3.00000 | + | 5.19615i | −0.115045 | + | 0.199263i | ||||
\(681\) | −2.53590 | −0.0971758 | ||||||||
\(682\) | −0.215390 | + | 0.373067i | −0.00824772 | + | 0.0142855i | ||||
\(683\) | −19.7321 | + | 34.1769i | −0.755026 | + | 1.30774i | 0.190335 | + | 0.981719i | \(0.439042\pi\) |
−0.945361 | + | 0.326024i | \(0.894291\pi\) | |||||||
\(684\) | −10.3397 | −0.395350 | ||||||||
\(685\) | −6.46410 | + | 11.1962i | −0.246981 | + | 0.427783i | ||||
\(686\) | 17.3205 | + | 30.0000i | 0.661300 | + | 1.14541i | ||||
\(687\) | −5.26795 | − | 9.12436i | −0.200985 | − | 0.348116i | ||||
\(688\) | −50.9808 | −1.94362 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 6.00000 | 0.228416 | ||||||||
\(691\) | −22.8827 | − | 39.6340i | −0.870498 | − | 1.50775i | −0.861482 | − | 0.507788i | \(-0.830463\pi\) |
−0.00901639 | − | 0.999959i | \(-0.502870\pi\) | |||||||
\(692\) | −7.73205 | − | 13.3923i | −0.293928 | − | 0.509099i | ||||
\(693\) | −3.12436 | + | 5.41154i | −0.118684 | + | 0.205568i | ||||
\(694\) | 20.1962 | 0.766635 | ||||||||
\(695\) | −4.19615 | + | 7.26795i | −0.159169 | + | 0.275689i | ||||
\(696\) | 6.00000 | − | 10.3923i | 0.227429 | − | 0.393919i | ||||
\(697\) | −12.0000 | −0.454532 | ||||||||
\(698\) | −5.53590 | + | 9.58846i | −0.209537 | + | 0.362928i | ||||
\(699\) | −2.19615 | − | 3.80385i | −0.0830661 | − | 0.143875i | ||||
\(700\) | −1.00000 | − | 1.73205i | −0.0377964 | − | 0.0654654i | ||||
\(701\) | 42.0000 | 1.58632 | 0.793159 | − | 0.609015i | \(-0.208435\pi\) | ||||
0.793159 | + | 0.609015i | \(0.208435\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.7846 | −0.633044 | ||||||||
\(704\) | 0.633975 | + | 1.09808i | 0.0238938 | + | 0.0413853i | ||||
\(705\) | −2.19615 | − | 3.80385i | −0.0827119 | − | 0.143261i | ||||
\(706\) | −24.0000 | + | 41.5692i | −0.903252 | + | 1.56448i | ||||
\(707\) | 25.8564 | 0.972430 | ||||||||
\(708\) | −5.53590 | + | 9.58846i | −0.208052 | + | 0.360356i | ||||
\(709\) | −4.80385 | + | 8.32051i | −0.180412 | + | 0.312483i | −0.942021 | − | 0.335554i | \(-0.891077\pi\) |
0.761609 | + | 0.648037i | \(0.224410\pi\) | |||||||
\(710\) | −2.19615 | −0.0824201 | ||||||||
\(711\) | 15.2679 | − | 26.4449i | 0.572593 | − | 0.991760i | ||||
\(712\) | 0.803848 | + | 1.39230i | 0.0301255 | + | 0.0521788i | ||||
\(713\) | 0.464102 | + | 0.803848i | 0.0173807 | + | 0.0301043i | ||||
\(714\) | −8.78461 | −0.328756 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.07180 | −0.189542 | ||||||||
\(717\) | −1.39230 | − | 2.41154i | −0.0519966 | − | 0.0900607i | ||||
\(718\) | −7.09808 | − | 12.2942i | −0.264898 | − | 0.458817i | ||||
\(719\) | −0.928203 | + | 1.60770i | −0.0346161 | + | 0.0599569i | −0.882814 | − | 0.469722i | \(-0.844354\pi\) |
0.848198 | + | 0.529679i | \(0.177688\pi\) | |||||||
\(720\) | −12.3205 | −0.459158 | ||||||||
\(721\) | −10.1962 | + | 17.6603i | −0.379725 | + | 0.657702i | ||||
\(722\) | 1.20577 | − | 2.08846i | 0.0448742 | − | 0.0777243i | ||||
\(723\) | −13.4641 | −0.500735 | ||||||||
\(724\) | 10.1962 | − | 17.6603i | 0.378937 | − | 0.656338i | ||||
\(725\) | 4.73205 | + | 8.19615i | 0.175744 | + | 0.304397i | ||||
\(726\) | −5.95448 | − | 10.3135i | −0.220992 | − | 0.382769i | ||||
\(727\) | 13.4115 | 0.497407 | 0.248703 | − | 0.968580i | \(-0.419996\pi\) | ||||
0.248703 | + | 0.968580i | \(0.419996\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.21539 | −0.0820515 | ||||||||
\(730\) | −3.46410 | − | 6.00000i | −0.128212 | − | 0.222070i | ||||
\(731\) | −17.6603 | − | 30.5885i | −0.653188 | − | 1.13135i | ||||
\(732\) | 4.53590 | − | 7.85641i | 0.167652 | − | 0.290381i | ||||
\(733\) | 38.0000 | 1.40356 | 0.701781 | − | 0.712393i | \(-0.252388\pi\) | ||||
0.701781 | + | 0.712393i | \(0.252388\pi\) | |||||||
\(734\) | −19.2224 | + | 33.2942i | −0.709513 | + | 1.22891i | ||||
\(735\) | 1.09808 | − | 1.90192i | 0.0405032 | − | 0.0701535i | ||||
\(736\) | −24.5885 | −0.906343 | ||||||||
\(737\) | −9.12436 | + | 15.8038i | −0.336100 | + | 0.582142i | ||||
\(738\) | −7.39230 | − | 12.8038i | −0.272115 | − | 0.471316i | ||||
\(739\) | 3.90192 | + | 6.75833i | 0.143535 | + | 0.248609i | 0.928825 | − | 0.370518i | \(-0.120820\pi\) |
−0.785291 | + | 0.619127i | \(0.787487\pi\) | |||||||
\(740\) | 4.00000 | 0.147043 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −36.0000 | −1.32160 | ||||||||
\(743\) | 21.9282 | + | 37.9808i | 0.804468 | + | 1.39338i | 0.916650 | + | 0.399691i | \(0.130883\pi\) |
−0.112182 | + | 0.993688i | \(0.535784\pi\) | |||||||
\(744\) | 0.124356 | + | 0.215390i | 0.00455910 | + | 0.00789659i | ||||
\(745\) | 9.92820 | − | 17.1962i | 0.363741 | − | 0.630018i | ||||
\(746\) | −17.3205 | −0.634149 | ||||||||
\(747\) | −7.39230 | + | 12.8038i | −0.270470 | + | 0.468468i | ||||
\(748\) | 2.19615 | − | 3.80385i | 0.0802993 | − | 0.139082i | ||||
\(749\) | 0.679492 | 0.0248281 | ||||||||
\(750\) | −0.633975 | + | 1.09808i | −0.0231495 | + | 0.0400961i | ||||
\(751\) | −7.80385 | − | 13.5167i | −0.284766 | − | 0.493230i | 0.687786 | − | 0.725913i | \(-0.258583\pi\) |
−0.972553 | + | 0.232683i | \(0.925249\pi\) | |||||||
\(752\) | 15.0000 | + | 25.9808i | 0.546994 | + | 0.947421i | ||||
\(753\) | 10.6410 | 0.387780 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.1962 | 0.443863 | ||||||||
\(756\) | −4.00000 | − | 6.92820i | −0.145479 | − | 0.251976i | ||||
\(757\) | −9.19615 | − | 15.9282i | −0.334240 | − | 0.578920i | 0.649099 | − | 0.760704i | \(-0.275146\pi\) |
−0.983339 | + | 0.181784i | \(0.941813\pi\) | |||||||
\(758\) | 28.5622 | − | 49.4711i | 1.03743 | − | 1.79687i | ||||
\(759\) | 4.39230 | 0.159431 | ||||||||
\(760\) | −3.63397 | + | 6.29423i | −0.131818 | + | 0.228316i | ||||
\(761\) | −3.92820 | + | 6.80385i | −0.142397 | + | 0.246639i | −0.928399 | − | 0.371585i | \(-0.878814\pi\) |
0.786002 | + | 0.618224i | \(0.212148\pi\) | |||||||
\(762\) | −7.35898 | −0.266588 | ||||||||
\(763\) | −2.00000 | + | 3.46410i | −0.0724049 | + | 0.125409i | ||||
\(764\) | 9.46410 | + | 16.3923i | 0.342399 | + | 0.593053i | ||||
\(765\) | −4.26795 | − | 7.39230i | −0.154308 | − | 0.267269i | ||||
\(766\) | −1.60770 | −0.0580884 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −13.9090 | −0.501897 | ||||||||
\(769\) | 3.39230 | + | 5.87564i | 0.122330 | + | 0.211881i | 0.920686 | − | 0.390304i | \(-0.127630\pi\) |
−0.798356 | + | 0.602185i | \(0.794297\pi\) | |||||||
\(770\) | −2.19615 | − | 3.80385i | −0.0791438 | − | 0.137081i | ||||
\(771\) | −2.87564 | + | 4.98076i | −0.103564 | + | 0.179378i | ||||
\(772\) | −10.0000 | −0.359908 | ||||||||
\(773\) | 3.46410 | − | 6.00000i | 0.124595 | − | 0.215805i | −0.796980 | − | 0.604006i | \(-0.793570\pi\) |
0.921575 | + | 0.388201i | \(0.126903\pi\) | |||||||
\(774\) | 21.7583 | − | 37.6865i | 0.782087 | − | 1.35461i | ||||
\(775\) | −0.196152 | −0.00704600 | ||||||||
\(776\) | 1.73205 | − | 3.00000i | 0.0621770 | − | 0.107694i | ||||
\(777\) | −2.92820 | − | 5.07180i | −0.105049 | − | 0.181950i | ||||
\(778\) | −5.19615 | − | 9.00000i | −0.186291 | − | 0.322666i | ||||
\(779\) | −14.5359 | −0.520803 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.60770 | −0.0575279 | ||||||||
\(782\) | −14.1962 | − | 24.5885i | −0.507653 | − | 0.879281i | ||||
\(783\) | 18.9282 | + | 32.7846i | 0.676439 | + | 1.17163i | ||||
\(784\) | −7.50000 | + | 12.9904i | −0.267857 | + | 0.463942i | ||||
\(785\) | 10.0000 | 0.356915 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.7846 | − | 44.6603i | 0.919122 | − | 1.59197i | 0.118371 | − | 0.992969i | \(-0.462233\pi\) |
0.800752 | − | 0.598997i | \(-0.204434\pi\) | |||||||
\(788\) | 0.928203 | 0.0330659 | ||||||||
\(789\) | 1.73205 | − | 3.00000i | 0.0616626 | − | 0.106803i | ||||
\(790\) | 10.7321 | + | 18.5885i | 0.381829 | + | 0.661348i | ||||
\(791\) | −15.4641 | − | 26.7846i | −0.549840 | − | 0.952351i | ||||
\(792\) | −5.41154 | −0.192291 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −22.1436 | −0.785847 | ||||||||
\(795\) | 3.80385 | + | 6.58846i | 0.134909 | + | 0.233668i | ||||
\(796\) | −10.0000 | − | 17.3205i | −0.354441 | − | 0.613909i | ||||
\(797\) | −14.3205 | + | 24.8038i | −0.507258 | + | 0.878597i | 0.492706 | + | 0.870196i | \(0.336008\pi\) |
−0.999965 | + | 0.00840168i | \(0.997326\pi\) | |||||||
\(798\) | −10.6410 | −0.376688 | ||||||||
\(799\) | −10.3923 | + | 18.0000i | −0.367653 | + | 0.636794i | ||||
\(800\) | 2.59808 | − | 4.50000i | 0.0918559 | − | 0.159099i | ||||
\(801\) | −2.28719 | −0.0808138 | ||||||||
\(802\) | 19.9808 | − | 34.6077i | 0.705545 | − | 1.22204i | ||||
\(803\) | −2.53590 | − | 4.39230i | −0.0894899 | − | 0.155001i | ||||
\(804\) | −5.26795 | − | 9.12436i | −0.185786 | − | 0.321791i | ||||
\(805\) | −9.46410 | −0.333566 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.75129 | −0.202455 | ||||||||
\(808\) | 11.1962 | + | 19.3923i | 0.393879 | + | 0.682219i | ||||
\(809\) | 4.73205 | + | 8.19615i | 0.166370 | + | 0.288161i | 0.937141 | − | 0.348951i | \(-0.113462\pi\) |
−0.770771 | + | 0.637112i | \(0.780129\pi\) | |||||||
\(810\) | 3.86603 | − | 6.69615i | 0.135838 | − | 0.235279i | ||||
\(811\) | 28.1962 | 0.990101 | 0.495050 | − | 0.868864i | \(-0.335150\pi\) | ||||
0.495050 | + | 0.868864i | \(0.335150\pi\) | |||||||
\(812\) | 9.46410 | − | 16.3923i | 0.332125 | − | 0.575257i | ||||
\(813\) | −7.67949 | + | 13.3013i | −0.269332 | + | 0.466496i | ||||
\(814\) | 8.78461 | 0.307900 | ||||||||
\(815\) | 3.19615 | − | 5.53590i | 0.111956 | − | 0.193914i | ||||
\(816\) | −6.33975 | − | 10.9808i | −0.221936 | − | 0.384404i | ||||
\(817\) | −21.3923 | − | 37.0526i | −0.748422 | − | 1.29630i | ||||
\(818\) | −66.4974 | −2.32503 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.46410 | 0.120972 | ||||||||
\(821\) | 20.3205 | + | 35.1962i | 0.709191 | + | 1.22835i | 0.965158 | + | 0.261669i | \(0.0842728\pi\) |
−0.255967 | + | 0.966685i | \(0.582394\pi\) | |||||||
\(822\) | −8.19615 | − | 14.1962i | −0.285874 | − | 0.495148i | ||||
\(823\) | 23.2942 | − | 40.3468i | 0.811986 | − | 1.40640i | −0.0994864 | − | 0.995039i | \(-0.531720\pi\) |
0.911472 | − | 0.411362i | \(-0.134947\pi\) | |||||||
\(824\) | −17.6603 | −0.615224 | ||||||||
\(825\) | −0.464102 | + | 0.803848i | −0.0161579 | + | 0.0279864i | ||||
\(826\) | 26.1962 | − | 45.3731i | 0.911481 | − | 1.57873i | ||||
\(827\) | 18.0000 | 0.625921 | 0.312961 | − | 0.949766i | \(-0.398679\pi\) | ||||
0.312961 | + | 0.949766i | \(0.398679\pi\) | |||||||
\(828\) | 5.83013 | − | 10.0981i | 0.202611 | − | 0.350932i | ||||
\(829\) | 10.1962 | + | 17.6603i | 0.354127 | + | 0.613366i | 0.986968 | − | 0.160916i | \(-0.0514447\pi\) |
−0.632841 | + | 0.774282i | \(0.718111\pi\) | |||||||
\(830\) | −5.19615 | − | 9.00000i | −0.180361 | − | 0.312395i | ||||
\(831\) | 4.10512 | 0.142405 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.3923 | −0.360072 | ||||||||
\(834\) | −5.32051 | − | 9.21539i | −0.184234 | − | 0.319103i | ||||
\(835\) | 6.46410 | + | 11.1962i | 0.223699 | + | 0.387459i | ||||
\(836\) | 2.66025 | − | 4.60770i | 0.0920068 | − | 0.159360i | ||||
\(837\) | −0.784610 | −0.0271201 | ||||||||
\(838\) | 8.19615 | − | 14.1962i | 0.283131 | − | 0.490398i | ||||
\(839\) | −8.83013 | + | 15.2942i | −0.304850 | + | 0.528015i | −0.977228 | − | 0.212193i | \(-0.931940\pi\) |
0.672378 | + | 0.740208i | \(0.265273\pi\) | |||||||
\(840\) | −2.53590 | −0.0874968 | ||||||||
\(841\) | −30.2846 | + | 52.4545i | −1.04430 | + | 1.80878i | ||||
\(842\) | −9.33975 | − | 16.1769i | −0.321869 | − | 0.557493i | ||||
\(843\) | 0.588457 | + | 1.01924i | 0.0202675 | + | 0.0351044i | ||||
\(844\) | 8.00000 | 0.275371 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −25.6077 | −0.880411 | ||||||||
\(847\) | 9.39230 | + | 16.2679i | 0.322723 | + | 0.558973i | ||||
\(848\) | −25.9808 | − | 45.0000i | −0.892183 | − | 1.54531i | ||||
\(849\) | 0.516660 | − | 0.894882i | 0.0177317 | − | 0.0307123i | ||||
\(850\) | 6.00000 | 0.205798 | ||||||||
\(851\) | 9.46410 | − | 16.3923i | 0.324425 | − | 0.561921i | ||||
\(852\) | 0.464102 | − | 0.803848i | 0.0158999 | − | 0.0275394i | ||||
\(853\) | 8.00000 | 0.273915 | 0.136957 | − | 0.990577i | \(-0.456268\pi\) | ||||
0.136957 | + | 0.990577i | \(0.456268\pi\) | |||||||
\(854\) | −21.4641 | + | 37.1769i | −0.734486 | + | 1.27217i | ||||
\(855\) | −5.16987 | − | 8.95448i | −0.176806 | − | 0.306237i | ||||
\(856\) | 0.294229 | + | 0.509619i | 0.0100565 | + | 0.0174184i | ||||
\(857\) | 47.5692 | 1.62493 | 0.812467 | − | 0.583007i | \(-0.198124\pi\) | ||||
0.812467 | + | 0.583007i | \(0.198124\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45.1769 | 1.54142 | 0.770708 | − | 0.637188i | \(-0.219903\pi\) | ||||
0.770708 | + | 0.637188i | \(0.219903\pi\) | |||||||
\(860\) | 5.09808 | + | 8.83013i | 0.173843 | + | 0.301105i | ||||
\(861\) | −2.53590 | − | 4.39230i | −0.0864232 | − | 0.149689i | ||||
\(862\) | −16.9019 | + | 29.2750i | −0.575682 | + | 0.997110i | ||||
\(863\) | 2.78461 | 0.0947892 | 0.0473946 | − | 0.998876i | \(-0.484908\pi\) | ||||
0.0473946 | + | 0.998876i | \(0.484908\pi\) | |||||||
\(864\) | 10.3923 | − | 18.0000i | 0.353553 | − | 0.612372i | ||||
\(865\) | 7.73205 | − | 13.3923i | 0.262898 | − | 0.455352i | ||||
\(866\) | −11.7513 | −0.399325 | ||||||||
\(867\) | −1.83013 | + | 3.16987i | −0.0621544 | + | 0.107655i | ||||
\(868\) | 0.196152 | + | 0.339746i | 0.00665785 | + | 0.0115317i | ||||
\(869\) | 7.85641 | + | 13.6077i | 0.266510 | + | 0.461609i | ||||
\(870\) | −12.0000 | −0.406838 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −3.46410 | −0.117309 | ||||||||
\(873\) | 2.46410 | + | 4.26795i | 0.0833972 | + | 0.144448i | ||||
\(874\) | −17.1962 | − | 29.7846i | −0.581669 | − | 1.00748i | ||||
\(875\) | 1.00000 | − | 1.73205i | 0.0338062 | − | 0.0585540i | ||||
\(876\) | 2.92820 | 0.0989348 | ||||||||
\(877\) | −1.00000 | + | 1.73205i | −0.0337676 | + | 0.0584872i | −0.882415 | − | 0.470471i | \(-0.844084\pi\) |
0.848648 | + | 0.528958i | \(0.177417\pi\) | |||||||
\(878\) | −27.7128 | + | 48.0000i | −0.935262 | + | 1.61992i | ||||
\(879\) | 13.8564 | 0.467365 | ||||||||
\(880\) | 3.16987 | − | 5.49038i | 0.106856 | − | 0.185081i | ||||
\(881\) | 6.33975 | + | 10.9808i | 0.213591 | + | 0.369951i | 0.952836 | − | 0.303486i | \(-0.0981505\pi\) |
−0.739244 | + | 0.673437i | \(0.764817\pi\) | |||||||
\(882\) | −6.40192 | − | 11.0885i | −0.215564 | − | 0.373368i | ||||
\(883\) | 34.1962 | 1.15079 | 0.575396 | − | 0.817875i | \(-0.304848\pi\) | ||||
0.575396 | + | 0.817875i | \(0.304848\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −11.0718 | −0.372174 | ||||||||
\(886\) | −30.2942 | − | 52.4711i | −1.01775 | − | 1.76280i | ||||
\(887\) | −8.95448 | − | 15.5096i | −0.300662 | − | 0.520762i | 0.675624 | − | 0.737246i | \(-0.263874\pi\) |
−0.976286 | + | 0.216484i | \(0.930541\pi\) | |||||||
\(888\) | 2.53590 | − | 4.39230i | 0.0850992 | − | 0.147396i | ||||
\(889\) | 11.6077 | 0.389310 | ||||||||
\(890\) | 0.803848 | − | 1.39230i | 0.0269450 | − | 0.0466702i | ||||
\(891\) | 2.83013 | − | 4.90192i | 0.0948128 | − | 0.164221i | ||||
\(892\) | 2.00000 | 0.0669650 | ||||||||
\(893\) | −12.5885 | + | 21.8038i | −0.421257 | + | 0.729638i | ||||
\(894\) | 12.5885 | + | 21.8038i | 0.421021 | + | 0.729230i | ||||
\(895\) | −2.53590 | − | 4.39230i | −0.0847657 | − | 0.146819i | ||||
\(896\) | 24.2487 | 0.810093 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 47.5692 | 1.58741 | ||||||||
\(899\) | −0.928203 | − | 1.60770i | −0.0309573 | − | 0.0536196i | ||||
\(900\) | 1.23205 | + | 2.13397i | 0.0410684 | + | 0.0711325i | ||||
\(901\) | 18.0000 | − | 31.1769i | 0.599667 | − | 1.03865i | ||||
\(902\) | 7.60770 | 0.253309 | ||||||||
\(903\) | 7.46410 | − | 12.9282i | 0.248390 | − | 0.430224i | ||||
\(904\) | 13.3923 | − | 23.1962i | 0.445421 | − | 0.771493i | ||||
\(905\) | 20.3923 | 0.677863 | ||||||||
\(906\) | −7.73205 | + | 13.3923i | −0.256880 | + | 0.444930i | ||||
\(907\) | −19.8827 | − | 34.4378i | −0.660194 | − | 1.14349i | −0.980565 | − | 0.196197i | \(-0.937141\pi\) |
0.320371 | − | 0.947292i | \(-0.396193\pi\) | |||||||
\(908\) | −1.73205 | − | 3.00000i | −0.0574801 | − | 0.0995585i | ||||
\(909\) | −31.8564 | −1.05661 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.0000 | −1.19273 | −0.596367 | − | 0.802712i | \(-0.703390\pi\) | ||||
−0.596367 | + | 0.802712i | \(0.703390\pi\) | |||||||
\(912\) | −7.67949 | − | 13.3013i | −0.254293 | − | 0.440449i | ||||
\(913\) | −3.80385 | − | 6.58846i | −0.125889 | − | 0.218046i | ||||
\(914\) | 26.6603 | − | 46.1769i | 0.881843 | − | 1.52740i | ||||
\(915\) | 9.07180 | 0.299904 | ||||||||
\(916\) | 7.19615 | − | 12.4641i | 0.237768 | − | 0.411826i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 24.0000 | 0.792118 | ||||||||
\(919\) | 26.5885 | − | 46.0526i | 0.877072 | − | 1.51913i | 0.0225335 | − | 0.999746i | \(-0.492827\pi\) |
0.854539 | − | 0.519388i | \(-0.173840\pi\) | |||||||
\(920\) | −4.09808 | − | 7.09808i | −0.135110 | − | 0.234017i | ||||
\(921\) | 8.33975 | + | 14.4449i | 0.274804 | + | 0.475974i | ||||
\(922\) | 6.00000 | 0.197599 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 1.85641 | 0.0610713 | ||||||||
\(925\) | 2.00000 | + | 3.46410i | 0.0657596 | + | 0.113899i | ||||
\(926\) | −15.9282 | − | 27.5885i | −0.523433 | − | 0.906613i | ||||
\(927\) | 12.5622 | − | 21.7583i | 0.412596 | − | 0.714637i | ||||
\(928\) | 49.1769 | 1.61431 | ||||||||
\(929\) | −25.7321 | + | 44.5692i | −0.844241 | + | 1.46227i | 0.0420373 | + | 0.999116i | \(0.486615\pi\) |
−0.886279 | + | 0.463153i | \(0.846718\pi\) | |||||||
\(930\) | 0.124356 | − | 0.215390i | 0.00407778 | − | 0.00706293i | ||||
\(931\) | −12.5885 | −0.412570 | ||||||||
\(932\) | 3.00000 | − | 5.19615i | 0.0982683 | − | 0.170206i | ||||
\(933\) | 1.60770 | + | 2.78461i | 0.0526336 | + | 0.0911640i | ||||
\(934\) | −33.0788 | − | 57.2942i | −1.08237 | − | 1.87472i | ||||
\(935\) | 4.39230 | 0.143644 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.78461 | −0.221644 | −0.110822 | − | 0.993840i | \(-0.535348\pi\) | ||||
−0.110822 | + | 0.993840i | \(0.535348\pi\) | |||||||
\(938\) | 24.9282 | + | 43.1769i | 0.813935 | + | 1.40978i | ||||
\(939\) | 2.33975 | + | 4.05256i | 0.0763547 | + | 0.132250i | ||||
\(940\) | 3.00000 | − | 5.19615i | 0.0978492 | − | 0.169480i | ||||
\(941\) | −31.1769 | −1.01634 | −0.508169 | − | 0.861257i | \(-0.669678\pi\) | ||||
−0.508169 | + | 0.861257i | \(0.669678\pi\) | |||||||
\(942\) | −6.33975 | + | 10.9808i | −0.206560 | + | 0.357773i | ||||
\(943\) | 8.19615 | − | 14.1962i | 0.266903 | − | 0.462290i | ||||
\(944\) | 75.6218 | 2.46128 | ||||||||
\(945\) | 4.00000 | − | 6.92820i | 0.130120 | − | 0.225374i | ||||
\(946\) | 11.1962 | + | 19.3923i | 0.364018 | + | 0.630498i | ||||
\(947\) | 14.3205 | + | 24.8038i | 0.465354 | + | 0.806017i | 0.999217 | − | 0.0395540i | \(-0.0125937\pi\) |
−0.533863 | + | 0.845571i | \(0.679260\pi\) | |||||||
\(948\) | −9.07180 | −0.294638 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 7.26795 | 0.235803 | ||||||||
\(951\) | 8.78461 | + | 15.2154i | 0.284860 | + | 0.493393i | ||||
\(952\) | 6.00000 | + | 10.3923i | 0.194461 | + | 0.336817i | ||||
\(953\) | 6.46410 | − | 11.1962i | 0.209393 | − | 0.362679i | −0.742131 | − | 0.670255i | \(-0.766185\pi\) |
0.951523 | + | 0.307576i | \(0.0995179\pi\) | |||||||
\(954\) | 44.3538 | 1.43601 | ||||||||
\(955\) | −9.46410 | + | 16.3923i | −0.306251 | + | 0.530443i | ||||
\(956\) | 1.90192 | − | 3.29423i | 0.0615126 | − | 0.106543i | ||||
\(957\) | −8.78461 | −0.283966 | ||||||||
\(958\) | −15.8827 | + | 27.5096i | −0.513146 | + | 0.888795i | ||||
\(959\) | 12.9282 | + | 22.3923i | 0.417473 | + | 0.723085i | ||||
\(960\) | −0.366025 | − | 0.633975i | −0.0118134 | − | 0.0204614i | ||||
\(961\) | −30.9615 | −0.998759 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.837169 | −0.0269774 | ||||||||
\(964\) | −9.19615 | − | 15.9282i | −0.296188 | − | 0.513013i | ||||
\(965\) | −5.00000 | − | 8.66025i | −0.160956 | − | 0.278783i | ||||
\(966\) | 6.00000 | − | 10.3923i | 0.193047 | − | 0.334367i | ||||
\(967\) | −29.6077 | −0.952119 | −0.476060 | − | 0.879413i | \(-0.657935\pi\) | ||||
−0.476060 | + | 0.879413i | \(0.657935\pi\) | |||||||
\(968\) | −8.13397 | + | 14.0885i | −0.261436 | + | 0.452820i | ||||
\(969\) | 5.32051 | − | 9.21539i | 0.170919 | − | 0.296041i | ||||
\(970\) | −3.46410 | −0.111226 | ||||||||
\(971\) | −2.53590 | + | 4.39230i | −0.0813809 | + | 0.140956i | −0.903843 | − | 0.427864i | \(-0.859266\pi\) |
0.822462 | + | 0.568819i | \(0.192600\pi\) | |||||||
\(972\) | 7.63397 | + | 13.2224i | 0.244860 | + | 0.424110i | ||||
\(973\) | 8.39230 | + | 14.5359i | 0.269045 | + | 0.466000i | ||||
\(974\) | −9.71281 | −0.311219 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −61.9615 | −1.98334 | ||||||||
\(977\) | −19.8564 | − | 34.3923i | −0.635263 | − | 1.10031i | −0.986459 | − | 0.164006i | \(-0.947558\pi\) |
0.351197 | − | 0.936302i | \(-0.385775\pi\) | |||||||
\(978\) | 4.05256 | + | 7.01924i | 0.129587 | + | 0.224450i | ||||
\(979\) | 0.588457 | − | 1.01924i | 0.0188072 | − | 0.0325750i | ||||
\(980\) | 3.00000 | 0.0958315 | ||||||||
\(981\) | 2.46410 | − | 4.26795i | 0.0786727 | − | 0.136265i | ||||
\(982\) | 8.19615 | − | 14.1962i | 0.261550 | − | 0.453017i | ||||
\(983\) | −13.6077 | −0.434018 | −0.217009 | − | 0.976170i | \(-0.569630\pi\) | ||||
−0.217009 | + | 0.976170i | \(0.569630\pi\) | |||||||
\(984\) | 2.19615 | − | 3.80385i | 0.0700108 | − | 0.121262i | ||||
\(985\) | 0.464102 | + | 0.803848i | 0.0147875 | + | 0.0256127i | ||||
\(986\) | 28.3923 | + | 49.1769i | 0.904195 | + | 1.56611i | ||||
\(987\) | −8.78461 | −0.279617 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 48.2487 | 1.53422 | ||||||||
\(990\) | 2.70577 | + | 4.68653i | 0.0859951 | + | 0.148948i | ||||
\(991\) | −4.00000 | − | 6.92820i | −0.127064 | − | 0.220082i | 0.795474 | − | 0.605988i | \(-0.207222\pi\) |
−0.922538 | + | 0.385906i | \(0.873889\pi\) | |||||||
\(992\) | −0.509619 | + | 0.882686i | −0.0161804 | + | 0.0280253i | ||||
\(993\) | 20.9282 | 0.664136 | ||||||||
\(994\) | −2.19615 | + | 3.80385i | −0.0696577 | + | 0.120651i | ||||
\(995\) | 10.0000 | − | 17.3205i | 0.317021 | − | 0.549097i | ||||
\(996\) | 4.39230 | 0.139176 | ||||||||
\(997\) | −27.1962 | + | 47.1051i | −0.861311 | + | 1.49183i | 0.00935346 | + | 0.999956i | \(0.497023\pi\) |
−0.870664 | + | 0.491878i | \(0.836311\pi\) | |||||||
\(998\) | −11.2417 | − | 19.4711i | −0.355849 | − | 0.616348i | ||||
\(999\) | 8.00000 | + | 13.8564i | 0.253109 | + | 0.438397i |
(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 | 845.2.e.e.146.1 | 4 | ||
13.2 | odd | 12 | 845.2.c.e.506.1 | 4 | |||
13.3 | even | 3 | 65.2.a.c.1.2 | ✓ | 2 | ||
13.4 | even | 6 | 845.2.e.f.191.2 | 4 | |||
13.5 | odd | 4 | 845.2.m.a.361.2 | 4 | |||
13.6 | odd | 12 | 845.2.m.c.316.2 | 4 | |||
13.7 | odd | 12 | 845.2.m.a.316.2 | 4 | |||
13.8 | odd | 4 | 845.2.m.c.361.2 | 4 | |||
13.9 | even | 3 | inner | 845.2.e.e.191.1 | 4 | ||
13.10 | even | 6 | 845.2.a.d.1.1 | 2 | |||
13.11 | odd | 12 | 845.2.c.e.506.3 | 4 | |||
13.12 | even | 2 | 845.2.e.f.146.2 | 4 | |||
39.23 | odd | 6 | 7605.2.a.be.1.2 | 2 | |||
39.29 | odd | 6 | 585.2.a.k.1.1 | 2 | |||
52.3 | odd | 6 | 1040.2.a.h.1.2 | 2 | |||
65.3 | odd | 12 | 325.2.b.e.274.2 | 4 | |||
65.29 | even | 6 | 325.2.a.g.1.1 | 2 | |||
65.42 | odd | 12 | 325.2.b.e.274.3 | 4 | |||
65.49 | even | 6 | 4225.2.a.w.1.2 | 2 | |||
91.55 | odd | 6 | 3185.2.a.k.1.2 | 2 | |||
104.3 | odd | 6 | 4160.2.a.bj.1.1 | 2 | |||
104.29 | even | 6 | 4160.2.a.y.1.2 | 2 | |||
143.120 | odd | 6 | 7865.2.a.h.1.1 | 2 | |||
156.107 | even | 6 | 9360.2.a.cm.1.2 | 2 | |||
195.29 | odd | 6 | 2925.2.a.z.1.2 | 2 | |||
195.68 | even | 12 | 2925.2.c.v.2224.3 | 4 | |||
195.107 | even | 12 | 2925.2.c.v.2224.2 | 4 | |||
260.159 | odd | 6 | 5200.2.a.ca.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.a.c.1.2 | ✓ | 2 | 13.3 | even | 3 | ||
325.2.a.g.1.1 | 2 | 65.29 | even | 6 | |||
325.2.b.e.274.2 | 4 | 65.3 | odd | 12 | |||
325.2.b.e.274.3 | 4 | 65.42 | odd | 12 | |||
585.2.a.k.1.1 | 2 | 39.29 | odd | 6 | |||
845.2.a.d.1.1 | 2 | 13.10 | even | 6 | |||
845.2.c.e.506.1 | 4 | 13.2 | odd | 12 | |||
845.2.c.e.506.3 | 4 | 13.11 | odd | 12 | |||
845.2.e.e.146.1 | 4 | 1.1 | even | 1 | trivial | ||
845.2.e.e.191.1 | 4 | 13.9 | even | 3 | inner | ||
845.2.e.f.146.2 | 4 | 13.12 | even | 2 | |||
845.2.e.f.191.2 | 4 | 13.4 | even | 6 | |||
845.2.m.a.316.2 | 4 | 13.7 | odd | 12 | |||
845.2.m.a.361.2 | 4 | 13.5 | odd | 4 | |||
845.2.m.c.316.2 | 4 | 13.6 | odd | 12 | |||
845.2.m.c.361.2 | 4 | 13.8 | odd | 4 | |||
1040.2.a.h.1.2 | 2 | 52.3 | odd | 6 | |||
2925.2.a.z.1.2 | 2 | 195.29 | odd | 6 | |||
2925.2.c.v.2224.2 | 4 | 195.107 | even | 12 | |||
2925.2.c.v.2224.3 | 4 | 195.68 | even | 12 | |||
3185.2.a.k.1.2 | 2 | 91.55 | odd | 6 | |||
4160.2.a.y.1.2 | 2 | 104.29 | even | 6 | |||
4160.2.a.bj.1.1 | 2 | 104.3 | odd | 6 | |||
4225.2.a.w.1.2 | 2 | 65.49 | even | 6 | |||
5200.2.a.ca.1.1 | 2 | 260.159 | odd | 6 | |||
7605.2.a.be.1.2 | 2 | 39.23 | odd | 6 | |||
7865.2.a.h.1.1 | 2 | 143.120 | odd | 6 | |||
9360.2.a.cm.1.2 | 2 | 156.107 | even | 6 |