Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(751,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.751");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.bc (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 901.2 | ||
Root | \(0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.901 |
Dual form | 1950.2.bc.f.751.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.866025 | + | 0.500000i | −0.353553 | + | 0.204124i | ||||
\(7\) | 2.53906 | − | 1.46593i | 0.959674 | − | 0.554068i | 0.0636011 | − | 0.997975i | \(-0.479741\pi\) |
0.896073 | + | 0.443908i | \(0.146408\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.992694 | − | 0.573132i | −0.299309 | − | 0.172806i | 0.342824 | − | 0.939400i | \(-0.388617\pi\) |
−0.642132 | + | 0.766594i | \(0.721950\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 1.86250 | − | 3.08725i | 0.516565 | − | 0.856248i | ||||
\(14\) | −2.93185 | −0.783570 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0.276457 | + | 0.478838i | 0.0670507 | + | 0.116135i | 0.897602 | − | 0.440807i | \(-0.145308\pi\) |
−0.830551 | + | 0.556942i | \(0.811974\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 0.723543 | − | 0.417738i | 0.165992 | − | 0.0958356i | −0.414703 | − | 0.909957i | \(-0.636114\pi\) |
0.580695 | + | 0.814121i | \(0.302781\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 2.93185i | − | 0.639782i | ||||||
\(22\) | 0.573132 | + | 0.992694i | 0.122192 | + | 0.211643i | ||||
\(23\) | 0.496476 | − | 0.859921i | 0.103522 | − | 0.179306i | −0.809611 | − | 0.586967i | \(-0.800322\pi\) |
0.913134 | + | 0.407661i | \(0.133655\pi\) | |||||||
\(24\) | −0.866025 | − | 0.500000i | −0.176777 | − | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.15660 | + | 1.74238i | −0.619060 | + | 0.341709i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.53906 | + | 1.46593i | 0.479837 | + | 0.277034i | ||||
\(29\) | 1.03786 | − | 1.79762i | 0.192725 | − | 0.333810i | −0.753427 | − | 0.657531i | \(-0.771601\pi\) |
0.946152 | + | 0.323722i | \(0.104934\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.36673i | − | 0.784288i | −0.919904 | − | 0.392144i | \(-0.871734\pi\) | ||
0.919904 | − | 0.392144i | \(-0.128266\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | −0.992694 | + | 0.573132i | −0.172806 | + | 0.0997695i | ||||
\(34\) | − | 0.552914i | − | 0.0948240i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.500000 | − | 0.866025i | 0.0833333 | − | 0.144338i | ||||
\(37\) | 7.00449 | + | 4.04404i | 1.15153 | + | 0.664836i | 0.949260 | − | 0.314493i | \(-0.101835\pi\) |
0.202271 | + | 0.979330i | \(0.435168\pi\) | |||||||
\(38\) | −0.835475 | −0.135532 | ||||||||
\(39\) | −1.74238 | − | 3.15660i | −0.279005 | − | 0.505460i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.67739 | − | 5.58725i | −1.51136 | − | 0.872581i | −0.999912 | − | 0.0132641i | \(-0.995778\pi\) |
−0.511443 | − | 0.859317i | \(-0.670889\pi\) | |||||||
\(42\) | −1.46593 | + | 2.53906i | −0.226197 | + | 0.391785i | ||||
\(43\) | −3.94036 | − | 6.82490i | −0.600899 | − | 1.04079i | −0.992685 | − | 0.120732i | \(-0.961476\pi\) |
0.391786 | − | 0.920056i | \(-0.371857\pi\) | |||||||
\(44\) | − | 1.14626i | − | 0.172806i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.859921 | + | 0.496476i | −0.126789 | + | 0.0732014i | ||||
\(47\) | 10.9489i | 1.59706i | 0.601957 | + | 0.798528i | \(0.294388\pi\) | ||||
−0.601957 | + | 0.798528i | \(0.705612\pi\) | |||||||
\(48\) | 0.500000 | + | 0.866025i | 0.0721688 | + | 0.125000i | ||||
\(49\) | 0.797877 | − | 1.38196i | 0.113982 | − | 0.197423i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.552914 | 0.0774235 | ||||||||
\(52\) | 3.60488 | + | 0.0693504i | 0.499908 | + | 0.00961716i | ||||
\(53\) | 3.56753 | 0.490037 | 0.245019 | − | 0.969518i | \(-0.421206\pi\) | ||||
0.245019 | + | 0.969518i | \(0.421206\pi\) | |||||||
\(54\) | 0.866025 | + | 0.500000i | 0.117851 | + | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.46593 | − | 2.53906i | −0.195893 | − | 0.339296i | ||||
\(57\) | − | 0.835475i | − | 0.110661i | ||||||
\(58\) | −1.79762 | + | 1.03786i | −0.236039 | + | 0.136277i | ||||
\(59\) | −4.75442 | + | 2.74496i | −0.618972 | + | 0.357364i | −0.776469 | − | 0.630156i | \(-0.782991\pi\) |
0.157497 | + | 0.987520i | \(0.449658\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.43368 | − | 2.48320i | −0.183563 | − | 0.317941i | 0.759528 | − | 0.650474i | \(-0.225430\pi\) |
−0.943091 | + | 0.332533i | \(0.892097\pi\) | |||||||
\(62\) | −2.18336 | + | 3.78170i | −0.277288 | + | 0.480276i | ||||
\(63\) | −2.53906 | − | 1.46593i | −0.319891 | − | 0.184689i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.14626 | 0.141095 | ||||||||
\(67\) | 8.88828 | + | 5.13165i | 1.08588 | + | 0.626931i | 0.932476 | − | 0.361233i | \(-0.117644\pi\) |
0.153401 | + | 0.988164i | \(0.450977\pi\) | |||||||
\(68\) | −0.276457 | + | 0.478838i | −0.0335254 | + | 0.0580676i | ||||
\(69\) | −0.496476 | − | 0.859921i | −0.0597687 | − | 0.103522i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.85992 | − | 5.69263i | 1.17016 | − | 0.675591i | 0.216440 | − | 0.976296i | \(-0.430555\pi\) |
0.953717 | + | 0.300705i | \(0.0972220\pi\) | |||||||
\(72\) | −0.866025 | + | 0.500000i | −0.102062 | + | 0.0589256i | ||||
\(73\) | − | 8.19151i | − | 0.958744i | −0.877612 | − | 0.479372i | \(-0.840865\pi\) | ||
0.877612 | − | 0.479372i | \(-0.159135\pi\) | |||||||
\(74\) | −4.04404 | − | 7.00449i | −0.470110 | − | 0.814255i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.723543 | + | 0.417738i | 0.0829961 | + | 0.0479178i | ||||
\(77\) | −3.36068 | −0.382985 | ||||||||
\(78\) | −0.0693504 | + | 3.60488i | −0.00785238 | + | 0.408173i | ||||
\(79\) | 1.68973 | 0.190109 | 0.0950545 | − | 0.995472i | \(-0.469697\pi\) | ||||
0.0950545 | + | 0.995472i | \(0.469697\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 5.58725 | + | 9.67739i | 0.617008 | + | 1.06869i | ||||
\(83\) | − | 8.77729i | − | 0.963433i | −0.876327 | − | 0.481717i | \(-0.840013\pi\) | ||
0.876327 | − | 0.481717i | \(-0.159987\pi\) | |||||||
\(84\) | 2.53906 | − | 1.46593i | 0.277034 | − | 0.159946i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.88072i | 0.849800i | ||||||||
\(87\) | −1.03786 | − | 1.79762i | −0.111270 | − | 0.192725i | ||||
\(88\) | −0.573132 | + | 0.992694i | −0.0610961 | + | 0.105822i | ||||
\(89\) | −3.93073 | − | 2.26941i | −0.416657 | − | 0.240557i | 0.276989 | − | 0.960873i | \(-0.410663\pi\) |
−0.693646 | + | 0.720316i | \(0.743997\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.203325 | − | 10.5690i | 0.0213142 | − | 1.10793i | ||||
\(92\) | 0.992952 | 0.103522 | ||||||||
\(93\) | −3.78170 | − | 2.18336i | −0.392144 | − | 0.226404i | ||||
\(94\) | 5.47443 | − | 9.48200i | 0.564645 | − | 0.977993i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | 9.19453 | − | 5.30847i | 0.933564 | − | 0.538993i | 0.0456267 | − | 0.998959i | \(-0.485472\pi\) |
0.887937 | + | 0.459965i | \(0.152138\pi\) | |||||||
\(98\) | −1.38196 | + | 0.797877i | −0.139599 | + | 0.0805978i | ||||
\(99\) | 1.14626i | 0.115204i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.07313 | + | 12.2510i | −0.703803 | + | 1.21902i | 0.263319 | + | 0.964709i | \(0.415183\pi\) |
−0.967122 | + | 0.254314i | \(0.918150\pi\) | |||||||
\(102\) | −0.478838 | − | 0.276457i | −0.0474120 | − | 0.0273733i | ||||
\(103\) | −6.72500 | −0.662634 | −0.331317 | − | 0.943519i | \(-0.607493\pi\) | ||||
−0.331317 | + | 0.943519i | \(0.607493\pi\) | |||||||
\(104\) | −3.08725 | − | 1.86250i | −0.302729 | − | 0.182633i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.08957 | − | 1.78376i | −0.300085 | − | 0.173254i | ||||
\(107\) | 0.123385 | − | 0.213709i | 0.0119281 | − | 0.0206600i | −0.860000 | − | 0.510294i | \(-0.829536\pi\) |
0.871928 | + | 0.489634i | \(0.162870\pi\) | |||||||
\(108\) | −0.500000 | − | 0.866025i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | − | 4.13797i | − | 0.396346i | −0.980167 | − | 0.198173i | \(-0.936499\pi\) | ||
0.980167 | − | 0.198173i | \(-0.0635008\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.00449 | − | 4.04404i | 0.664836 | − | 0.383843i | ||||
\(112\) | 2.93185i | 0.277034i | ||||||||
\(113\) | −0.828427 | − | 1.43488i | −0.0779319 | − | 0.134982i | 0.824426 | − | 0.565970i | \(-0.191498\pi\) |
−0.902357 | + | 0.430988i | \(0.858165\pi\) | |||||||
\(114\) | −0.417738 | + | 0.723543i | −0.0391247 | + | 0.0677660i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.07571 | 0.192725 | ||||||||
\(117\) | −3.60488 | − | 0.0693504i | −0.333272 | − | 0.00641144i | ||||
\(118\) | 5.48993 | 0.505389 | ||||||||
\(119\) | 1.40388 | + | 0.810531i | 0.128694 | + | 0.0743013i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.84304 | − | 8.38839i | −0.440276 | − | 0.762581i | ||||
\(122\) | 2.86735i | 0.259598i | ||||||||
\(123\) | −9.67739 | + | 5.58725i | −0.872581 | + | 0.503785i | ||||
\(124\) | 3.78170 | − | 2.18336i | 0.339607 | − | 0.196072i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.46593 | + | 2.53906i | 0.130595 | + | 0.226197i | ||||
\(127\) | 3.80260 | − | 6.58630i | 0.337426 | − | 0.584440i | −0.646521 | − | 0.762896i | \(-0.723777\pi\) |
0.983948 | + | 0.178456i | \(0.0571102\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | −7.88072 | −0.693859 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.45340 | 0.476466 | 0.238233 | − | 0.971208i | \(-0.423432\pi\) | ||||
0.238233 | + | 0.971208i | \(0.423432\pi\) | |||||||
\(132\) | −0.992694 | − | 0.573132i | −0.0864029 | − | 0.0498848i | ||||
\(133\) | 1.22474 | − | 2.12132i | 0.106199 | − | 0.183942i | ||||
\(134\) | −5.13165 | − | 8.88828i | −0.443307 | − | 0.767831i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.478838 | − | 0.276457i | 0.0410600 | − | 0.0237060i | ||||
\(137\) | 0.276333 | − | 0.159541i | 0.0236087 | − | 0.0136305i | −0.488149 | − | 0.872760i | \(-0.662328\pi\) |
0.511758 | + | 0.859130i | \(0.328994\pi\) | |||||||
\(138\) | 0.992952i | 0.0845257i | ||||||||
\(139\) | −5.84046 | − | 10.1160i | −0.495381 | − | 0.858026i | 0.504605 | − | 0.863351i | \(-0.331638\pi\) |
−0.999986 | + | 0.00532505i | \(0.998305\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.48200 | + | 5.47443i | 0.798528 | + | 0.461030i | ||||
\(142\) | −11.3853 | −0.955430 | ||||||||
\(143\) | −3.61829 | + | 1.99723i | −0.302577 | + | 0.167017i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.09575 | + | 7.09405i | −0.338967 | + | 0.587108i | ||||
\(147\) | −0.797877 | − | 1.38196i | −0.0658078 | − | 0.113982i | ||||
\(148\) | 8.08808i | 0.664836i | ||||||||
\(149\) | 4.33221 | − | 2.50120i | 0.354908 | − | 0.204906i | −0.311937 | − | 0.950103i | \(-0.600978\pi\) |
0.666845 | + | 0.745196i | \(0.267644\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.9005i | 1.04983i | 0.851156 | + | 0.524914i | \(0.175902\pi\) | ||||
−0.851156 | + | 0.524914i | \(0.824098\pi\) | |||||||
\(152\) | −0.417738 | − | 0.723543i | −0.0338830 | − | 0.0586871i | ||||
\(153\) | 0.276457 | − | 0.478838i | 0.0223502 | − | 0.0387117i | ||||
\(154\) | 2.91043 | + | 1.68034i | 0.234529 | + | 0.135406i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.86250 | − | 3.08725i | 0.149119 | − | 0.247178i | ||||
\(157\) | 8.66531 | 0.691567 | 0.345784 | − | 0.938314i | \(-0.387613\pi\) | ||||
0.345784 | + | 0.938314i | \(0.387613\pi\) | |||||||
\(158\) | −1.46335 | − | 0.844863i | −0.116418 | − | 0.0672137i | ||||
\(159\) | 1.78376 | − | 3.08957i | 0.141462 | − | 0.245019i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 2.91119i | − | 0.229434i | ||||||
\(162\) | 0.866025 | − | 0.500000i | 0.0680414 | − | 0.0392837i | ||||
\(163\) | 1.59928 | − | 0.923344i | 0.125265 | − | 0.0723219i | −0.436058 | − | 0.899919i | \(-0.643626\pi\) |
0.561323 | + | 0.827597i | \(0.310292\pi\) | |||||||
\(164\) | − | 11.1745i | − | 0.872581i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.38865 | + | 7.60136i | −0.340625 | + | 0.589980i | ||||
\(167\) | −18.8898 | − | 10.9060i | −1.46174 | − | 0.843935i | −0.462647 | − | 0.886543i | \(-0.653100\pi\) |
−0.999092 | + | 0.0426077i | \(0.986433\pi\) | |||||||
\(168\) | −2.93185 | −0.226197 | ||||||||
\(169\) | −6.06218 | − | 11.5000i | −0.466321 | − | 0.884615i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.723543 | − | 0.417738i | −0.0553307 | − | 0.0319452i | ||||
\(172\) | 3.94036 | − | 6.82490i | 0.300450 | − | 0.520394i | ||||
\(173\) | −5.93942 | − | 10.2874i | −0.451565 | − | 0.782134i | 0.546918 | − | 0.837186i | \(-0.315801\pi\) |
−0.998483 | + | 0.0550519i | \(0.982468\pi\) | |||||||
\(174\) | 2.07571i | 0.157359i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.992694 | − | 0.573132i | 0.0748271 | − | 0.0432015i | ||||
\(177\) | 5.48993i | 0.412648i | ||||||||
\(178\) | 2.26941 | + | 3.93073i | 0.170099 | + | 0.294621i | ||||
\(179\) | −4.47746 | + | 7.75519i | −0.334661 | + | 0.579650i | −0.983420 | − | 0.181344i | \(-0.941955\pi\) |
0.648759 | + | 0.760994i | \(0.275288\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.2297 | −1.57799 | −0.788996 | − | 0.614399i | \(-0.789399\pi\) | ||||
−0.788996 | + | 0.614399i | \(0.789399\pi\) | |||||||
\(182\) | −5.46058 | + | 9.05135i | −0.404765 | + | 0.670931i | ||||
\(183\) | −2.86735 | −0.211961 | ||||||||
\(184\) | −0.859921 | − | 0.496476i | −0.0633943 | − | 0.0366007i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.18336 | + | 3.78170i | 0.160092 | + | 0.277288i | ||||
\(187\) | − | 0.633786i | − | 0.0463470i | ||||||
\(188\) | −9.48200 | + | 5.47443i | −0.691546 | + | 0.399264i | ||||
\(189\) | −2.53906 | + | 1.46593i | −0.184689 | + | 0.106630i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.25347 | − | 3.90313i | −0.163055 | − | 0.282420i | 0.772908 | − | 0.634519i | \(-0.218802\pi\) |
−0.935963 | + | 0.352098i | \(0.885468\pi\) | |||||||
\(192\) | −0.500000 | + | 0.866025i | −0.0360844 | + | 0.0625000i | ||||
\(193\) | −2.30090 | − | 1.32843i | −0.165623 | − | 0.0956223i | 0.414898 | − | 0.909868i | \(-0.363817\pi\) |
−0.580520 | + | 0.814246i | \(0.697151\pi\) | |||||||
\(194\) | −10.6169 | −0.762251 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.59575 | 0.113982 | ||||||||
\(197\) | −1.68375 | − | 0.972112i | −0.119962 | − | 0.0692601i | 0.438818 | − | 0.898576i | \(-0.355397\pi\) |
−0.558780 | + | 0.829316i | \(0.688731\pi\) | |||||||
\(198\) | 0.573132 | − | 0.992694i | 0.0407307 | − | 0.0705477i | ||||
\(199\) | 7.50877 | + | 13.0056i | 0.532282 | + | 0.921940i | 0.999290 | + | 0.0376865i | \(0.0119988\pi\) |
−0.467007 | + | 0.884253i | \(0.654668\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.88828 | − | 5.13165i | 0.626931 | − | 0.361959i | ||||
\(202\) | 12.2510 | − | 7.07313i | 0.861979 | − | 0.497664i | ||||
\(203\) | − | 6.08568i | − | 0.427131i | ||||||
\(204\) | 0.276457 | + | 0.478838i | 0.0193559 | + | 0.0335254i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.82402 | + | 3.36250i | 0.405779 | + | 0.234277i | ||||
\(207\) | −0.992952 | −0.0690149 | ||||||||
\(208\) | 1.74238 | + | 3.15660i | 0.120813 | + | 0.218871i | ||||
\(209\) | −0.957676 | −0.0662438 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.379882 | + | 0.657974i | −0.0261521 | + | 0.0452968i | −0.878805 | − | 0.477181i | \(-0.841659\pi\) |
0.852653 | + | 0.522477i | \(0.174992\pi\) | |||||||
\(212\) | 1.78376 | + | 3.08957i | 0.122509 | + | 0.212192i | ||||
\(213\) | − | 11.3853i | − | 0.780105i | ||||||
\(214\) | −0.213709 | + | 0.123385i | −0.0146088 | + | 0.00843441i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | −6.40130 | − | 11.0874i | −0.434549 | − | 0.752660i | ||||
\(218\) | −2.06899 | + | 3.58359i | −0.140129 | + | 0.242711i | ||||
\(219\) | −7.09405 | − | 4.09575i | −0.479372 | − | 0.276765i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.99319 | + | 0.0383448i | 0.134077 | + | 0.00257935i | ||||
\(222\) | −8.08808 | −0.542837 | ||||||||
\(223\) | 18.5939 | + | 10.7352i | 1.24514 | + | 0.718883i | 0.970136 | − | 0.242560i | \(-0.0779871\pi\) |
0.275005 | + | 0.961443i | \(0.411320\pi\) | |||||||
\(224\) | 1.46593 | − | 2.53906i | 0.0979463 | − | 0.169648i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.65685i | 0.110212i | ||||||||
\(227\) | −19.1406 | + | 11.0508i | −1.27041 | + | 0.733471i | −0.975065 | − | 0.221920i | \(-0.928767\pi\) |
−0.295344 | + | 0.955391i | \(0.595434\pi\) | |||||||
\(228\) | 0.723543 | − | 0.417738i | 0.0479178 | − | 0.0276654i | ||||
\(229\) | 21.6368i | 1.42980i | 0.699226 | + | 0.714901i | \(0.253528\pi\) | ||||
−0.699226 | + | 0.714901i | \(0.746472\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.68034 | + | 2.91043i | −0.110558 | + | 0.191492i | ||||
\(232\) | −1.79762 | − | 1.03786i | −0.118019 | − | 0.0681386i | ||||
\(233\) | 5.95668 | 0.390235 | 0.195118 | − | 0.980780i | \(-0.437491\pi\) | ||||
0.195118 | + | 0.980780i | \(0.437491\pi\) | |||||||
\(234\) | 3.08725 | + | 1.86250i | 0.201820 | + | 0.121756i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.75442 | − | 2.74496i | −0.309486 | − | 0.178682i | ||||
\(237\) | 0.844863 | − | 1.46335i | 0.0548798 | − | 0.0950545i | ||||
\(238\) | −0.810531 | − | 1.40388i | −0.0525389 | − | 0.0910001i | ||||
\(239\) | 28.8408i | 1.86556i | 0.360451 | + | 0.932778i | \(0.382623\pi\) | ||||
−0.360451 | + | 0.932778i | \(0.617377\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.95886 | − | 2.86300i | 0.319428 | − | 0.184422i | −0.331709 | − | 0.943382i | \(-0.607625\pi\) |
0.651138 | + | 0.758960i | \(0.274292\pi\) | |||||||
\(242\) | 9.68608i | 0.622645i | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 1.43368 | − | 2.48320i | 0.0917817 | − | 0.158971i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 11.1745 | 0.712460 | ||||||||
\(247\) | 0.0579405 | − | 3.01179i | 0.00368667 | − | 0.191636i | ||||
\(248\) | −4.36673 | −0.277288 | ||||||||
\(249\) | −7.60136 | − | 4.38865i | −0.481717 | − | 0.278119i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.33171 | + | 5.77069i | 0.210296 | + | 0.364243i | 0.951807 | − | 0.306697i | \(-0.0992240\pi\) |
−0.741511 | + | 0.670940i | \(0.765891\pi\) | |||||||
\(252\) | − | 2.93185i | − | 0.184689i | ||||||
\(253\) | −0.985697 | + | 0.569093i | −0.0619703 | + | 0.0357785i | ||||
\(254\) | −6.58630 | + | 3.80260i | −0.413261 | + | 0.238597i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 5.01607 | − | 8.68809i | 0.312894 | − | 0.541948i | −0.666094 | − | 0.745868i | \(-0.732035\pi\) |
0.978988 | + | 0.203920i | \(0.0653682\pi\) | |||||||
\(258\) | 6.82490 | + | 3.94036i | 0.424900 | + | 0.245316i | ||||
\(259\) | 23.7131 | 1.47346 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.07571 | −0.128483 | ||||||||
\(262\) | −4.72279 | − | 2.72670i | −0.291775 | − | 0.168456i | ||||
\(263\) | 12.5202 | − | 21.6856i | 0.772027 | − | 1.33719i | −0.164423 | − | 0.986390i | \(-0.552576\pi\) |
0.936450 | − | 0.350800i | \(-0.114090\pi\) | |||||||
\(264\) | 0.573132 | + | 0.992694i | 0.0352738 | + | 0.0610961i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.12132 | + | 1.22474i | −0.130066 | + | 0.0750939i | ||||
\(267\) | −3.93073 | + | 2.26941i | −0.240557 | + | 0.138886i | ||||
\(268\) | 10.2633i | 0.626931i | ||||||||
\(269\) | −11.6268 | − | 20.1382i | −0.708899 | − | 1.22785i | −0.965266 | − | 0.261269i | \(-0.915859\pi\) |
0.256367 | − | 0.966579i | \(-0.417474\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.32698 | − | 3.07554i | −0.323591 | − | 0.186826i | 0.329401 | − | 0.944190i | \(-0.393153\pi\) |
−0.652992 | + | 0.757365i | \(0.726487\pi\) | |||||||
\(272\) | −0.552914 | −0.0335254 | ||||||||
\(273\) | −9.05135 | − | 5.46058i | −0.547812 | − | 0.330489i | ||||
\(274\) | −0.319082 | −0.0192764 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.496476 | − | 0.859921i | 0.0298843 | − | 0.0517612i | ||||
\(277\) | 3.44464 | + | 5.96629i | 0.206968 | + | 0.358480i | 0.950758 | − | 0.309934i | \(-0.100307\pi\) |
−0.743790 | + | 0.668414i | \(0.766974\pi\) | |||||||
\(278\) | 11.6809i | 0.700575i | ||||||||
\(279\) | −3.78170 | + | 2.18336i | −0.226404 | + | 0.130715i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.545617i | 0.0325488i | 0.999868 | + | 0.0162744i | \(0.00518053\pi\) | ||||
−0.999868 | + | 0.0162744i | \(0.994819\pi\) | |||||||
\(282\) | −5.47443 | − | 9.48200i | −0.325998 | − | 0.564645i | ||||
\(283\) | 4.21329 | − | 7.29764i | 0.250454 | − | 0.433799i | −0.713197 | − | 0.700964i | \(-0.752753\pi\) |
0.963651 | + | 0.267164i | \(0.0860867\pi\) | |||||||
\(284\) | 9.85992 | + | 5.69263i | 0.585079 | + | 0.337795i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.13215 | + | 0.0794938i | 0.244339 | + | 0.00470057i | ||||
\(287\) | −32.7620 | −1.93388 | ||||||||
\(288\) | −0.866025 | − | 0.500000i | −0.0510310 | − | 0.0294628i | ||||
\(289\) | 8.34714 | − | 14.4577i | 0.491008 | − | 0.850452i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 10.6169i | − | 0.622376i | ||||||
\(292\) | 7.09405 | − | 4.09575i | 0.415148 | − | 0.239686i | ||||
\(293\) | −5.87017 | + | 3.38915i | −0.342939 | + | 0.197996i | −0.661571 | − | 0.749883i | \(-0.730110\pi\) |
0.318632 | + | 0.947879i | \(0.396777\pi\) | |||||||
\(294\) | 1.59575i | 0.0930663i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.04404 | − | 7.00449i | 0.235055 | − | 0.407127i | ||||
\(297\) | 0.992694 | + | 0.573132i | 0.0576020 | + | 0.0332565i | ||||
\(298\) | −5.00240 | −0.289781 | ||||||||
\(299\) | −1.73010 | − | 3.13435i | −0.100054 | − | 0.181264i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.0096 | − | 11.5525i | −1.15333 | − | 0.665878i | ||||
\(302\) | 6.45025 | − | 11.1722i | 0.371170 | − | 0.642885i | ||||
\(303\) | 7.07313 | + | 12.2510i | 0.406341 | + | 0.703803i | ||||
\(304\) | 0.835475i | 0.0479178i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.478838 | + | 0.276457i | −0.0273733 | + | 0.0158040i | ||||
\(307\) | 34.6432i | 1.97719i | 0.150601 | + | 0.988595i | \(0.451879\pi\) | ||||
−0.150601 | + | 0.988595i | \(0.548121\pi\) | |||||||
\(308\) | −1.68034 | − | 2.91043i | −0.0957462 | − | 0.165837i | ||||
\(309\) | −3.36250 | + | 5.82402i | −0.191286 | + | 0.331317i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.2203 | 1.14659 | 0.573293 | − | 0.819351i | \(-0.305666\pi\) | ||||
0.573293 | + | 0.819351i | \(0.305666\pi\) | |||||||
\(312\) | −3.15660 | + | 1.74238i | −0.178707 | + | 0.0986430i | ||||
\(313\) | 22.3326 | 1.26231 | 0.631157 | − | 0.775655i | \(-0.282580\pi\) | ||||
0.631157 | + | 0.775655i | \(0.282580\pi\) | |||||||
\(314\) | −7.50438 | − | 4.33266i | −0.423497 | − | 0.244506i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.844863 | + | 1.46335i | 0.0475273 | + | 0.0823196i | ||||
\(317\) | − | 11.4292i | − | 0.641930i | −0.947091 | − | 0.320965i | \(-0.895993\pi\) | ||
0.947091 | − | 0.320965i | \(-0.104007\pi\) | |||||||
\(318\) | −3.08957 | + | 1.78376i | −0.173254 | + | 0.100028i | ||||
\(319\) | −2.06055 | + | 1.18966i | −0.115368 | + | 0.0666080i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.123385 | − | 0.213709i | −0.00688666 | − | 0.0119281i | ||||
\(322\) | −1.45559 | + | 2.52116i | −0.0811171 | + | 0.140499i | ||||
\(323\) | 0.400057 | + | 0.230973i | 0.0222598 | + | 0.0128517i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.84669 | −0.102279 | ||||||||
\(327\) | −3.58359 | − | 2.06899i | −0.198173 | − | 0.114415i | ||||
\(328\) | −5.58725 | + | 9.67739i | −0.308504 | + | 0.534345i | ||||
\(329\) | 16.0502 | + | 27.7998i | 0.884878 | + | 1.53265i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.53602 | − | 0.886823i | 0.0844274 | − | 0.0487442i | −0.457192 | − | 0.889368i | \(-0.651145\pi\) |
0.541619 | + | 0.840624i | \(0.317811\pi\) | |||||||
\(332\) | 7.60136 | − | 4.38865i | 0.417179 | − | 0.240858i | ||||
\(333\) | − | 8.08808i | − | 0.443224i | ||||||
\(334\) | 10.9060 | + | 18.8898i | 0.596752 | + | 1.03361i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.53906 | + | 1.46593i | 0.138517 | + | 0.0799728i | ||||
\(337\) | 12.0024 | 0.653815 | 0.326907 | − | 0.945056i | \(-0.393994\pi\) | ||||
0.326907 | + | 0.945056i | \(0.393994\pi\) | |||||||
\(338\) | −0.500000 | + | 12.9904i | −0.0271964 | + | 0.706584i | ||||
\(339\) | −1.65685 | −0.0899880 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.50271 | + | 4.33483i | −0.135530 | + | 0.234744i | ||||
\(342\) | 0.417738 | + | 0.723543i | 0.0225887 | + | 0.0391247i | ||||
\(343\) | 15.8444i | 0.855520i | ||||||||
\(344\) | −6.82490 | + | 3.94036i | −0.367974 | + | 0.212450i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.8788i | 0.638610i | ||||||||
\(347\) | −13.7793 | − | 23.8664i | −0.739709 | − | 1.28121i | −0.952626 | − | 0.304143i | \(-0.901630\pi\) |
0.212917 | − | 0.977070i | \(-0.431704\pi\) | |||||||
\(348\) | 1.03786 | − | 1.79762i | 0.0556349 | − | 0.0963625i | ||||
\(349\) | 12.2674 | + | 7.08260i | 0.656660 | + | 0.379123i | 0.791003 | − | 0.611812i | \(-0.209559\pi\) |
−0.134343 | + | 0.990935i | \(0.542892\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.86250 | + | 3.08725i | −0.0994130 | + | 0.164785i | ||||
\(352\) | −1.14626 | −0.0610961 | ||||||||
\(353\) | 27.3612 | + | 15.7970i | 1.45629 | + | 0.840790i | 0.998826 | − | 0.0484373i | \(-0.0154241\pi\) |
0.457465 | + | 0.889228i | \(0.348757\pi\) | |||||||
\(354\) | 2.74496 | − | 4.75442i | 0.145893 | − | 0.252694i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 4.53882i | − | 0.240557i | ||||||
\(357\) | 1.40388 | − | 0.810531i | 0.0743013 | − | 0.0428979i | ||||
\(358\) | 7.75519 | − | 4.47746i | 0.409874 | − | 0.236641i | ||||
\(359\) | 12.1714i | 0.642380i | 0.947015 | + | 0.321190i | \(0.104083\pi\) | ||||
−0.947015 | + | 0.321190i | \(0.895917\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.15099 | + | 15.8500i | −0.481631 | + | 0.834209i | ||||
\(362\) | 18.3855 | + | 10.6149i | 0.966318 | + | 0.557904i | ||||
\(363\) | −9.68608 | −0.508387 | ||||||||
\(364\) | 9.25467 | − | 5.10841i | 0.485077 | − | 0.267753i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.48320 | + | 1.43368i | 0.129799 | + | 0.0749394i | ||||
\(367\) | 14.9977 | − | 25.9768i | 0.782873 | − | 1.35598i | −0.147389 | − | 0.989079i | \(-0.547087\pi\) |
0.930262 | − | 0.366897i | \(-0.119580\pi\) | |||||||
\(368\) | 0.496476 | + | 0.859921i | 0.0258806 | + | 0.0448265i | ||||
\(369\) | 11.1745i | 0.581721i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.05816 | − | 5.22973i | 0.470276 | − | 0.271514i | ||||
\(372\) | − | 4.36673i | − | 0.226404i | ||||||
\(373\) | −18.3785 | − | 31.8325i | −0.951604 | − | 1.64823i | −0.741954 | − | 0.670450i | \(-0.766101\pi\) |
−0.209650 | − | 0.977777i | \(-0.567232\pi\) | |||||||
\(374\) | −0.316893 | + | 0.548875i | −0.0163861 | + | 0.0283816i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.9489 | 0.564645 | ||||||||
\(377\) | −3.61669 | − | 6.55219i | −0.186269 | − | 0.337455i | ||||
\(378\) | 2.93185 | 0.150798 | ||||||||
\(379\) | 4.47699 | + | 2.58479i | 0.229967 | + | 0.132772i | 0.610557 | − | 0.791972i | \(-0.290946\pi\) |
−0.380590 | + | 0.924744i | \(0.624279\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.80260 | − | 6.58630i | −0.194813 | − | 0.337426i | ||||
\(382\) | 4.50694i | 0.230595i | ||||||||
\(383\) | −2.42657 | + | 1.40098i | −0.123992 | + | 0.0715867i | −0.560713 | − | 0.828010i | \(-0.689473\pi\) |
0.436721 | + | 0.899597i | \(0.356140\pi\) | |||||||
\(384\) | 0.866025 | − | 0.500000i | 0.0441942 | − | 0.0255155i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.32843 | + | 2.30090i | 0.0676152 | + | 0.117113i | ||||
\(387\) | −3.94036 | + | 6.82490i | −0.200300 | + | 0.346929i | ||||
\(388\) | 9.19453 | + | 5.30847i | 0.466782 | + | 0.269497i | ||||
\(389\) | 11.8936 | 0.603030 | 0.301515 | − | 0.953461i | \(-0.402508\pi\) | ||||
0.301515 | + | 0.953461i | \(0.402508\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.549017 | 0.0277650 | ||||||||
\(392\) | −1.38196 | − | 0.797877i | −0.0697997 | − | 0.0402989i | ||||
\(393\) | 2.72670 | − | 4.72279i | 0.137544 | − | 0.238233i | ||||
\(394\) | 0.972112 | + | 1.68375i | 0.0489743 | + | 0.0848259i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.992694 | + | 0.573132i | −0.0498848 | + | 0.0288010i | ||||
\(397\) | 33.7790 | − | 19.5023i | 1.69532 | − | 0.978792i | 0.745231 | − | 0.666806i | \(-0.232339\pi\) |
0.950087 | − | 0.311986i | \(-0.100994\pi\) | |||||||
\(398\) | − | 15.0175i | − | 0.752761i | ||||||
\(399\) | −1.22474 | − | 2.12132i | −0.0613139 | − | 0.106199i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.4558 | + | 13.5422i | 1.17133 | + | 0.676266i | 0.953992 | − | 0.299831i | \(-0.0969303\pi\) |
0.217335 | + | 0.976097i | \(0.430264\pi\) | |||||||
\(402\) | −10.2633 | −0.511887 | ||||||||
\(403\) | −13.4812 | − | 8.13304i | −0.671545 | − | 0.405136i | ||||
\(404\) | −14.1463 | −0.703803 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.04284 | + | 5.27035i | −0.151014 | + | 0.261563i | ||||
\(407\) | −4.63554 | − | 8.02899i | −0.229775 | − | 0.397982i | ||||
\(408\) | − | 0.552914i | − | 0.0273733i | ||||||
\(409\) | −13.8087 | + | 7.97248i | −0.682798 | + | 0.394214i | −0.800908 | − | 0.598787i | \(-0.795650\pi\) |
0.118110 | + | 0.993000i | \(0.462316\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 0.319082i | − | 0.0157391i | ||||||
\(412\) | −3.36250 | − | 5.82402i | −0.165659 | − | 0.286929i | ||||
\(413\) | −8.04782 | + | 13.9392i | −0.396008 | + | 0.685905i | ||||
\(414\) | 0.859921 | + | 0.496476i | 0.0422628 | + | 0.0244005i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.0693504 | − | 3.60488i | 0.00340018 | − | 0.176744i | ||||
\(417\) | −11.6809 | −0.572017 | ||||||||
\(418\) | 0.829371 | + | 0.478838i | 0.0405659 | + | 0.0234207i | ||||
\(419\) | −9.71670 | + | 16.8298i | −0.474692 | + | 0.822190i | −0.999580 | − | 0.0289808i | \(-0.990774\pi\) |
0.524888 | + | 0.851171i | \(0.324107\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.5769i | 1.05160i | 0.850610 | + | 0.525798i | \(0.176233\pi\) | ||||
−0.850610 | + | 0.525798i | \(0.823767\pi\) | |||||||
\(422\) | 0.657974 | − | 0.379882i | 0.0320297 | − | 0.0184924i | ||||
\(423\) | 9.48200 | − | 5.47443i | 0.461030 | − | 0.266176i | ||||
\(424\) | − | 3.56753i | − | 0.173254i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.69263 | + | 9.85992i | −0.275809 | + | 0.477715i | ||||
\(427\) | −7.28037 | − | 4.20332i | −0.352322 | − | 0.203413i | ||||
\(428\) | 0.246769 | 0.0119281 | ||||||||
\(429\) | −0.0794938 | + | 4.13215i | −0.00383800 | + | 0.199502i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.550541 | + | 0.317855i | 0.0265186 | + | 0.0153105i | 0.513201 | − | 0.858269i | \(-0.328460\pi\) |
−0.486682 | + | 0.873579i | \(0.661793\pi\) | |||||||
\(432\) | 0.500000 | − | 0.866025i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | 5.30090 | + | 9.18143i | 0.254745 | + | 0.441232i | 0.964826 | − | 0.262888i | \(-0.0846751\pi\) |
−0.710081 | + | 0.704120i | \(0.751342\pi\) | |||||||
\(434\) | 12.8026i | 0.614545i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.58359 | − | 2.06899i | 0.171623 | − | 0.0990865i | ||||
\(437\) | − | 0.829587i | − | 0.0396845i | ||||||
\(438\) | 4.09575 | + | 7.09405i | 0.195703 | + | 0.338967i | ||||
\(439\) | −7.65685 | + | 13.2621i | −0.365442 | + | 0.632964i | −0.988847 | − | 0.148935i | \(-0.952415\pi\) |
0.623405 | + | 0.781899i | \(0.285749\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.59575 | −0.0759883 | ||||||||
\(442\) | −1.70698 | − | 1.02980i | −0.0811929 | − | 0.0489828i | ||||
\(443\) | 18.4800 | 0.878009 | 0.439005 | − | 0.898485i | \(-0.355331\pi\) | ||||
0.439005 | + | 0.898485i | \(0.355331\pi\) | |||||||
\(444\) | 7.00449 | + | 4.04404i | 0.332418 | + | 0.191922i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −10.7352 | − | 18.5939i | −0.508327 | − | 0.880448i | ||||
\(447\) | − | 5.00240i | − | 0.236606i | ||||||
\(448\) | −2.53906 | + | 1.46593i | −0.119959 | + | 0.0692585i | ||||
\(449\) | 22.5084 | − | 12.9952i | 1.06224 | − | 0.613283i | 0.136187 | − | 0.990683i | \(-0.456515\pi\) |
0.926050 | + | 0.377400i | \(0.123182\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.40446 | + | 11.0929i | 0.301574 | + | 0.522342i | ||||
\(452\) | 0.828427 | − | 1.43488i | 0.0389659 | − | 0.0674910i | ||||
\(453\) | 11.1722 | + | 6.45025i | 0.524914 | + | 0.303059i | ||||
\(454\) | 22.1017 | 1.03728 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.835475 | −0.0391247 | ||||||||
\(457\) | 35.9475 | + | 20.7543i | 1.68155 | + | 0.970846i | 0.960630 | + | 0.277832i | \(0.0896157\pi\) |
0.720924 | + | 0.693014i | \(0.243718\pi\) | |||||||
\(458\) | 10.8184 | − | 18.7380i | 0.505511 | − | 0.875571i | ||||
\(459\) | −0.276457 | − | 0.478838i | −0.0129039 | − | 0.0223502i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.8532 | − | 7.99818i | 0.645210 | − | 0.372512i | −0.141409 | − | 0.989951i | \(-0.545163\pi\) |
0.786619 | + | 0.617439i | \(0.211830\pi\) | |||||||
\(462\) | 2.91043 | − | 1.68034i | 0.135406 | − | 0.0781764i | ||||
\(463\) | 18.8328i | 0.875232i | 0.899162 | + | 0.437616i | \(0.144177\pi\) | ||||
−0.899162 | + | 0.437616i | \(0.855823\pi\) | |||||||
\(464\) | 1.03786 | + | 1.79762i | 0.0481813 | + | 0.0834524i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.15864 | − | 2.97834i | −0.238969 | − | 0.137969i | ||||
\(467\) | 3.43738 | 0.159063 | 0.0795316 | − | 0.996832i | \(-0.474658\pi\) | ||||
0.0795316 | + | 0.996832i | \(0.474658\pi\) | |||||||
\(468\) | −1.74238 | − | 3.15660i | −0.0805417 | − | 0.145914i | ||||
\(469\) | 30.0905 | 1.38945 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.33266 | − | 7.50438i | 0.199638 | − | 0.345784i | ||||
\(472\) | 2.74496 | + | 4.75442i | 0.126347 | + | 0.218840i | ||||
\(473\) | 9.03339i | 0.415356i | ||||||||
\(474\) | −1.46335 | + | 0.844863i | −0.0672137 | + | 0.0388059i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.62106i | 0.0743013i | ||||||||
\(477\) | −1.78376 | − | 3.08957i | −0.0816729 | − | 0.141462i | ||||
\(478\) | 14.4204 | − | 24.9769i | 0.659574 | − | 1.14242i | ||||
\(479\) | 22.4648 | + | 12.9700i | 1.02644 | + | 0.592617i | 0.915963 | − | 0.401262i | \(-0.131428\pi\) |
0.110479 | + | 0.993878i | \(0.464762\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.5308 | − | 14.0925i | 1.16411 | − | 0.642564i | ||||
\(482\) | −5.72600 | −0.260812 | ||||||||
\(483\) | −2.52116 | − | 1.45559i | −0.114717 | − | 0.0662318i | ||||
\(484\) | 4.84304 | − | 8.38839i | 0.220138 | − | 0.381290i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | −15.6047 | + | 9.00939i | −0.707117 | + | 0.408254i | −0.809993 | − | 0.586440i | \(-0.800529\pi\) |
0.102875 | + | 0.994694i | \(0.467196\pi\) | |||||||
\(488\) | −2.48320 | + | 1.43368i | −0.112409 | + | 0.0648995i | ||||
\(489\) | − | 1.84669i | − | 0.0835101i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.7564 | + | 27.2908i | −0.711075 | + | 1.23162i | 0.253379 | + | 0.967367i | \(0.418458\pi\) |
−0.964454 | + | 0.264251i | \(0.914875\pi\) | |||||||
\(492\) | −9.67739 | − | 5.58725i | −0.436291 | − | 0.251893i | ||||
\(493\) | 1.14769 | 0.0516894 | ||||||||
\(494\) | −1.55607 | + | 2.57932i | −0.0700111 | + | 0.116049i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.78170 | + | 2.18336i | 0.169803 | + | 0.0980360i | ||||
\(497\) | 16.6899 | − | 28.9078i | 0.748646 | − | 1.29669i | ||||
\(498\) | 4.38865 | + | 7.60136i | 0.196660 | + | 0.340625i | ||||
\(499\) | − | 5.57925i | − | 0.249762i | −0.992172 | − | 0.124881i | \(-0.960145\pi\) | ||
0.992172 | − | 0.124881i | \(-0.0398549\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.8898 | + | 10.9060i | −0.843935 | + | 0.487246i | ||||
\(502\) | − | 6.66342i | − | 0.297403i | ||||||
\(503\) | 18.8126 | + | 32.5844i | 0.838812 | + | 1.45286i | 0.890889 | + | 0.454222i | \(0.150083\pi\) |
−0.0520768 | + | 0.998643i | \(0.516584\pi\) | |||||||
\(504\) | −1.46593 | + | 2.53906i | −0.0652975 | + | 0.113099i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.13819 | 0.0505985 | ||||||||
\(507\) | −12.9904 | − | 0.500000i | −0.576923 | − | 0.0222058i | ||||
\(508\) | 7.60521 | 0.337426 | ||||||||
\(509\) | 25.5466 | + | 14.7493i | 1.13233 | + | 0.653753i | 0.944521 | − | 0.328452i | \(-0.106527\pi\) |
0.187813 | + | 0.982205i | \(0.439860\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.0081 | − | 20.7987i | −0.531209 | − | 0.920081i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −0.723543 | + | 0.417738i | −0.0319452 | + | 0.0184436i | ||||
\(514\) | −8.68809 | + | 5.01607i | −0.383215 | + | 0.221249i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3.94036 | − | 6.82490i | −0.173465 | − | 0.300450i | ||||
\(517\) | 6.27515 | − | 10.8689i | 0.275981 | − | 0.478013i | ||||
\(518\) | −20.5361 | − | 11.8565i | −0.902305 | − | 0.520946i | ||||
\(519\) | −11.8788 | −0.521423 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.16676 | −0.138738 | −0.0693692 | − | 0.997591i | \(-0.522099\pi\) | ||||
−0.0693692 | + | 0.997591i | \(0.522099\pi\) | |||||||
\(522\) | 1.79762 | + | 1.03786i | 0.0786797 | + | 0.0454257i | ||||
\(523\) | −15.7956 | + | 27.3587i | −0.690691 | + | 1.19631i | 0.280920 | + | 0.959731i | \(0.409360\pi\) |
−0.971612 | + | 0.236581i | \(0.923973\pi\) | |||||||
\(524\) | 2.72670 | + | 4.72279i | 0.119117 | + | 0.206316i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21.6856 | + | 12.5202i | −0.945536 | + | 0.545906i | ||||
\(527\) | 2.09096 | − | 1.20721i | 0.0910834 | − | 0.0525870i | ||||
\(528\) | − | 1.14626i | − | 0.0498848i | ||||||
\(529\) | 11.0070 | + | 19.0647i | 0.478566 | + | 0.828901i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.75442 | + | 2.74496i | 0.206324 | + | 0.119121i | ||||
\(532\) | 2.44949 | 0.106199 | ||||||||
\(533\) | −35.2734 | + | 19.4702i | −1.52786 | + | 0.843350i | ||||
\(534\) | 4.53882 | 0.196414 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.13165 | − | 8.88828i | 0.221654 | − | 0.383915i | ||||
\(537\) | 4.47746 | + | 7.75519i | 0.193217 | + | 0.334661i | ||||
\(538\) | 23.2536i | 1.00253i | ||||||||
\(539\) | −1.58410 | + | 0.914578i | −0.0682318 | + | 0.0393937i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.1369i | 0.435821i | 0.975969 | + | 0.217911i | \(0.0699241\pi\) | ||||
−0.975969 | + | 0.217911i | \(0.930076\pi\) | |||||||
\(542\) | 3.07554 | + | 5.32698i | 0.132106 | + | 0.228814i | ||||
\(543\) | −10.6149 | + | 18.3855i | −0.455527 | + | 0.788996i | ||||
\(544\) | 0.478838 | + | 0.276457i | 0.0205300 | + | 0.0118530i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 5.10841 | + | 9.25467i | 0.218620 | + | 0.396063i | ||||
\(547\) | −32.1457 | −1.37445 | −0.687225 | − | 0.726445i | \(-0.741171\pi\) | ||||
−0.687225 | + | 0.726445i | \(0.741171\pi\) | |||||||
\(548\) | 0.276333 | + | 0.159541i | 0.0118044 | + | 0.00681525i | ||||
\(549\) | −1.43368 | + | 2.48320i | −0.0611878 | + | 0.105980i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1.73421i | − | 0.0738797i | ||||||
\(552\) | −0.859921 | + | 0.496476i | −0.0366007 | + | 0.0211314i | ||||
\(553\) | 4.29031 | − | 2.47701i | 0.182443 | − | 0.105333i | ||||
\(554\) | − | 6.88928i | − | 0.292697i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.84046 | − | 10.1160i | 0.247691 | − | 0.429013i | ||||
\(557\) | −4.50313 | − | 2.59988i | −0.190804 | − | 0.110161i | 0.401555 | − | 0.915835i | \(-0.368470\pi\) |
−0.592359 | + | 0.805674i | \(0.701803\pi\) | |||||||
\(558\) | 4.36673 | 0.184858 | ||||||||
\(559\) | −28.4091 | − | 0.546531i | −1.20158 | − | 0.0231158i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.548875 | − | 0.316893i | −0.0231735 | − | 0.0133792i | ||||
\(562\) | 0.272809 | − | 0.472519i | 0.0115077 | − | 0.0199320i | ||||
\(563\) | 8.18180 | + | 14.1713i | 0.344822 | + | 0.597249i | 0.985321 | − | 0.170710i | \(-0.0546060\pi\) |
−0.640500 | + | 0.767958i | \(0.721273\pi\) | |||||||
\(564\) | 10.9489i | 0.461030i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −7.29764 | + | 4.21329i | −0.306743 | + | 0.177098i | ||||
\(567\) | 2.93185i | 0.123126i | ||||||||
\(568\) | −5.69263 | − | 9.85992i | −0.238857 | − | 0.413713i | ||||
\(569\) | 7.90761 | − | 13.6964i | 0.331504 | − | 0.574182i | −0.651303 | − | 0.758818i | \(-0.725777\pi\) |
0.982807 | + | 0.184636i | \(0.0591105\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.8170 | −0.787467 | −0.393734 | − | 0.919225i | \(-0.628817\pi\) | ||||
−0.393734 | + | 0.919225i | \(0.628817\pi\) | |||||||
\(572\) | −3.53880 | − | 2.13492i | −0.147965 | − | 0.0892654i | ||||
\(573\) | −4.50694 | −0.188280 | ||||||||
\(574\) | 28.3727 | + | 16.3810i | 1.18425 | + | 0.683729i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.500000 | + | 0.866025i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | 22.3581i | 0.930778i | 0.885106 | + | 0.465389i | \(0.154086\pi\) | ||||
−0.885106 | + | 0.465389i | \(0.845914\pi\) | |||||||
\(578\) | −14.4577 | + | 8.34714i | −0.601360 | + | 0.347195i | ||||
\(579\) | −2.30090 | + | 1.32843i | −0.0956223 | + | 0.0552075i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.8669 | − | 22.2861i | −0.533807 | − | 0.924582i | ||||
\(582\) | −5.30847 | + | 9.19453i | −0.220043 | + | 0.381126i | ||||
\(583\) | −3.54146 | − | 2.04466i | −0.146672 | − | 0.0846813i | ||||
\(584\) | −8.19151 | −0.338967 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.77829 | 0.280009 | ||||||||
\(587\) | 37.1967 | + | 21.4755i | 1.53527 | + | 0.886389i | 0.999106 | + | 0.0422761i | \(0.0134609\pi\) |
0.536165 | + | 0.844113i | \(0.319872\pi\) | |||||||
\(588\) | 0.797877 | − | 1.38196i | 0.0329039 | − | 0.0569912i | ||||
\(589\) | −1.82415 | − | 3.15952i | −0.0751627 | − | 0.130186i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.68375 | + | 0.972112i | −0.0692601 | + | 0.0399873i | ||||
\(592\) | −7.00449 | + | 4.04404i | −0.287883 | + | 0.166209i | ||||
\(593\) | 30.8372i | 1.26633i | 0.774016 | + | 0.633166i | \(0.218245\pi\) | ||||
−0.774016 | + | 0.633166i | \(0.781755\pi\) | |||||||
\(594\) | −0.573132 | − | 0.992694i | −0.0235159 | − | 0.0407307i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.33221 | + | 2.50120i | 0.177454 | + | 0.102453i | ||||
\(597\) | 15.0175 | 0.614627 | ||||||||
\(598\) | −0.0688616 | + | 3.57948i | −0.00281596 | + | 0.146376i | ||||
\(599\) | 9.63447 | 0.393654 | 0.196827 | − | 0.980438i | \(-0.436936\pi\) | ||||
0.196827 | + | 0.980438i | \(0.436936\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.1757 | + | 29.7491i | −0.700609 | + | 1.21349i | 0.267643 | + | 0.963518i | \(0.413755\pi\) |
−0.968253 | + | 0.249973i | \(0.919578\pi\) | |||||||
\(602\) | 11.5525 | + | 20.0096i | 0.470847 | + | 0.815531i | ||||
\(603\) | − | 10.2633i | − | 0.417954i | ||||||
\(604\) | −11.1722 | + | 6.45025i | −0.454588 | + | 0.262457i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | − | 14.1463i | − | 0.574653i | ||||||
\(607\) | 14.7047 | + | 25.4692i | 0.596844 | + | 1.03376i | 0.993284 | + | 0.115704i | \(0.0369124\pi\) |
−0.396439 | + | 0.918061i | \(0.629754\pi\) | |||||||
\(608\) | 0.417738 | − | 0.723543i | 0.0169415 | − | 0.0293435i | ||||
\(609\) | −5.27035 | − | 3.04284i | −0.213565 | − | 0.123302i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 33.8018 | + | 20.3923i | 1.36748 | + | 0.824983i | ||||
\(612\) | 0.552914 | 0.0223502 | ||||||||
\(613\) | 33.2034 | + | 19.1700i | 1.34107 | + | 0.774268i | 0.986965 | − | 0.160938i | \(-0.0514518\pi\) |
0.354106 | + | 0.935205i | \(0.384785\pi\) | |||||||
\(614\) | 17.3216 | − | 30.0019i | 0.699042 | − | 1.21078i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.36068i | 0.135406i | ||||||||
\(617\) | 0.526095 | − | 0.303741i | 0.0211798 | − | 0.0122281i | −0.489373 | − | 0.872075i | \(-0.662774\pi\) |
0.510553 | + | 0.859847i | \(0.329441\pi\) | |||||||
\(618\) | 5.82402 | − | 3.36250i | 0.234277 | − | 0.135260i | ||||
\(619\) | 28.6848i | 1.15294i | 0.817118 | + | 0.576470i | \(0.195570\pi\) | ||||
−0.817118 | + | 0.576470i | \(0.804430\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.496476 | + | 0.859921i | −0.0199229 | + | 0.0345075i | ||||
\(622\) | −17.5113 | − | 10.1101i | −0.702137 | − | 0.405379i | ||||
\(623\) | −13.3071 | −0.533139 | ||||||||
\(624\) | 3.60488 | + | 0.0693504i | 0.144311 | + | 0.00277624i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −19.3406 | − | 11.1663i | −0.773006 | − | 0.446295i | ||||
\(627\) | −0.478838 | + | 0.829371i | −0.0191229 | + | 0.0331219i | ||||
\(628\) | 4.33266 | + | 7.50438i | 0.172892 | + | 0.299457i | ||||
\(629\) | 4.47202i | 0.178311i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.94547 | − | 2.27792i | 0.157067 | − | 0.0906824i | −0.419407 | − | 0.907798i | \(-0.637762\pi\) |
0.576473 | + | 0.817116i | \(0.304429\pi\) | |||||||
\(632\) | − | 1.68973i | − | 0.0672137i | ||||||
\(633\) | 0.379882 | + | 0.657974i | 0.0150989 | + | 0.0261521i | ||||
\(634\) | −5.71462 | + | 9.89801i | −0.226957 | + | 0.393100i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.56753 | 0.141462 | ||||||||
\(637\) | −2.78041 | − | 5.03715i | −0.110164 | − | 0.199579i | ||||
\(638\) | 2.37931 | 0.0941980 | ||||||||
\(639\) | −9.85992 | − | 5.69263i | −0.390052 | − | 0.225197i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.8057 | − | 20.4481i | −0.466297 | − | 0.807650i | 0.532962 | − | 0.846139i | \(-0.321079\pi\) |
−0.999259 | + | 0.0384890i | \(0.987746\pi\) | |||||||
\(642\) | 0.246769i | 0.00973921i | ||||||||
\(643\) | 9.66855 | − | 5.58214i | 0.381290 | − | 0.220138i | −0.297089 | − | 0.954850i | \(-0.596016\pi\) |
0.678379 | + | 0.734712i | \(0.262683\pi\) | |||||||
\(644\) | 2.52116 | − | 1.45559i | 0.0993477 | − | 0.0573584i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.230973 | − | 0.400057i | −0.00908752 | − | 0.0157400i | ||||
\(647\) | −5.68594 | + | 9.84834i | −0.223538 | + | 0.387178i | −0.955880 | − | 0.293758i | \(-0.905094\pi\) |
0.732342 | + | 0.680937i | \(0.238427\pi\) | |||||||
\(648\) | 0.866025 | + | 0.500000i | 0.0340207 | + | 0.0196419i | ||||
\(649\) | 6.29291 | 0.247018 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.8026 | −0.501774 | ||||||||
\(652\) | 1.59928 | + | 0.923344i | 0.0626326 | + | 0.0361609i | ||||
\(653\) | 4.51599 | − | 7.82192i | 0.176724 | − | 0.306096i | −0.764032 | − | 0.645178i | \(-0.776783\pi\) |
0.940757 | + | 0.339082i | \(0.110117\pi\) | |||||||
\(654\) | 2.06899 | + | 3.58359i | 0.0809037 | + | 0.140129i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9.67739 | − | 5.58725i | 0.377839 | − | 0.218145i | ||||
\(657\) | −7.09405 | + | 4.09575i | −0.276765 | + | 0.159791i | ||||
\(658\) | − | 32.1005i | − | 1.25141i | ||||||
\(659\) | −9.57118 | − | 16.5778i | −0.372840 | − | 0.645778i | 0.617161 | − | 0.786837i | \(-0.288283\pi\) |
−0.990001 | + | 0.141059i | \(0.954949\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.6116 | + | 9.01337i | 0.607221 | + | 0.350579i | 0.771877 | − | 0.635772i | \(-0.219318\pi\) |
−0.164656 | + | 0.986351i | \(0.552651\pi\) | |||||||
\(662\) | −1.77365 | −0.0689347 | ||||||||
\(663\) | 1.02980 | − | 1.70698i | 0.0399943 | − | 0.0662937i | ||||
\(664\) | −8.77729 | −0.340625 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.04404 | + | 7.00449i | −0.156703 | + | 0.271418i | ||||
\(667\) | −1.03054 | − | 1.78495i | −0.0399027 | − | 0.0691135i | ||||
\(668\) | − | 21.8121i | − | 0.843935i | ||||||
\(669\) | 18.5939 | − | 10.7352i | 0.718883 | − | 0.415047i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.28674i | 0.126883i | ||||||||
\(672\) | −1.46593 | − | 2.53906i | −0.0565493 | − | 0.0979463i | ||||
\(673\) | −3.91832 | + | 6.78672i | −0.151040 | + | 0.261609i | −0.931610 | − | 0.363459i | \(-0.881596\pi\) |
0.780570 | + | 0.625068i | \(0.214929\pi\) | |||||||
\(674\) | −10.3944 | − | 6.00122i | −0.400378 | − | 0.231158i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.92820 | − | 11.0000i | 0.266469 | − | 0.423077i | ||||
\(677\) | −23.4860 | −0.902641 | −0.451321 | − | 0.892362i | \(-0.649047\pi\) | ||||
−0.451321 | + | 0.892362i | \(0.649047\pi\) | |||||||
\(678\) | 1.43488 | + | 0.828427i | 0.0551062 | + | 0.0318156i | ||||
\(679\) | 15.5636 | − | 26.9570i | 0.597278 | − | 1.03452i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22.1017i | 0.846939i | ||||||||
\(682\) | 4.33483 | − | 2.50271i | 0.165989 | − | 0.0958338i | ||||
\(683\) | −15.4729 | + | 8.93327i | −0.592053 | + | 0.341822i | −0.765909 | − | 0.642949i | \(-0.777711\pi\) |
0.173856 | + | 0.984771i | \(0.444377\pi\) | |||||||
\(684\) | − | 0.835475i | − | 0.0319452i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 7.92222 | − | 13.7217i | 0.302472 | − | 0.523897i | ||||
\(687\) | 18.7380 | + | 10.8184i | 0.714901 | + | 0.412748i | ||||
\(688\) | 7.88072 | 0.300450 | ||||||||
\(689\) | 6.64452 | − | 11.0138i | 0.253136 | − | 0.419594i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.7634 | − | 10.8331i | −0.713795 | − | 0.412109i | 0.0986699 | − | 0.995120i | \(-0.468541\pi\) |
−0.812464 | + | 0.583011i | \(0.801875\pi\) | |||||||
\(692\) | 5.93942 | − | 10.2874i | 0.225783 | − | 0.391067i | ||||
\(693\) | 1.68034 | + | 2.91043i | 0.0638308 | + | 0.110558i | ||||
\(694\) | 27.5585i | 1.04611i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.79762 | + | 1.03786i | −0.0681386 | + | 0.0393398i | ||||
\(697\) | − | 6.17854i | − | 0.234029i | ||||||
\(698\) | −7.08260 | − | 12.2674i | −0.268080 | − | 0.464329i | ||||
\(699\) | 2.97834 | − | 5.15864i | 0.112651 | − | 0.195118i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.8171 | 1.61718 | 0.808590 | − | 0.588372i | \(-0.200231\pi\) | ||||
0.808590 | + | 0.588372i | \(0.200231\pi\) | |||||||
\(702\) | 3.15660 | − | 1.74238i | 0.119138 | − | 0.0657620i | ||||
\(703\) | 6.75739 | 0.254860 | ||||||||
\(704\) | 0.992694 | + | 0.573132i | 0.0374136 | + | 0.0216007i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15.7970 | − | 27.3612i | −0.594528 | − | 1.02975i | ||||
\(707\) | 41.4747i | 1.55982i | ||||||||
\(708\) | −4.75442 | + | 2.74496i | −0.178682 | + | 0.103162i | ||||
\(709\) | 10.7389 | − | 6.20012i | 0.403309 | − | 0.232851i | −0.284602 | − | 0.958646i | \(-0.591861\pi\) |
0.687911 | + | 0.725795i | \(0.258528\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.844863 | − | 1.46335i | −0.0316848 | − | 0.0548798i | ||||
\(712\) | −2.26941 | + | 3.93073i | −0.0850497 | + | 0.147310i | ||||
\(713\) | −3.75504 | − | 2.16798i | −0.140628 | − | 0.0811913i | ||||
\(714\) | −1.62106 | −0.0606667 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.95492 | −0.334661 | ||||||||
\(717\) | 24.9769 | + | 14.4204i | 0.932778 | + | 0.538540i | ||||
\(718\) | 6.08568 | − | 10.5407i | 0.227116 | − | 0.393376i | ||||
\(719\) | 0.822357 | + | 1.42436i | 0.0306687 | + | 0.0531198i | 0.880952 | − | 0.473205i | \(-0.156903\pi\) |
−0.850284 | + | 0.526325i | \(0.823570\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.0752 | + | 9.85835i | −0.635913 | + | 0.367144i | ||||
\(722\) | 15.8500 | − | 9.15099i | 0.589875 | − | 0.340565i | ||||
\(723\) | − | 5.72600i | − | 0.212952i | ||||||
\(724\) | −10.6149 | − | 18.3855i | −0.394498 | − | 0.683290i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 8.38839 | + | 4.84304i | 0.311322 | + | 0.179742i | ||||
\(727\) | −48.0577 | −1.78236 | −0.891180 | − | 0.453650i | \(-0.850122\pi\) | ||||
−0.891180 | + | 0.453650i | \(0.850122\pi\) | |||||||
\(728\) | −10.5690 | − | 0.203325i | −0.391713 | − | 0.00753572i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.17868 | − | 3.77359i | 0.0805814 | − | 0.139571i | ||||
\(732\) | −1.43368 | − | 2.48320i | −0.0529902 | − | 0.0917817i | ||||
\(733\) | − | 5.56731i | − | 0.205633i | −0.994700 | − | 0.102817i | \(-0.967214\pi\) | ||
0.994700 | − | 0.102817i | \(-0.0327855\pi\) | |||||||
\(734\) | −25.9768 | + | 14.9977i | −0.958820 | + | 0.553575i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 0.992952i | − | 0.0366007i | ||||||
\(737\) | −5.88223 | − | 10.1883i | −0.216675 | − | 0.375292i | ||||
\(738\) | 5.58725 | − | 9.67739i | 0.205669 | − | 0.356230i | ||||
\(739\) | −44.1546 | − | 25.4927i | −1.62425 | − | 0.937763i | −0.985765 | − | 0.168132i | \(-0.946227\pi\) |
−0.638489 | − | 0.769631i | \(-0.720440\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.57932 | − | 1.55607i | −0.0947536 | − | 0.0571638i | ||||
\(742\) | −10.4595 | −0.383979 | ||||||||
\(743\) | −35.1316 | − | 20.2832i | −1.28885 | − | 0.744120i | −0.310404 | − | 0.950605i | \(-0.600464\pi\) |
−0.978450 | + | 0.206485i | \(0.933798\pi\) | |||||||
\(744\) | −2.18336 | + | 3.78170i | −0.0800460 | + | 0.138644i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 36.7571i | 1.34577i | ||||||||
\(747\) | −7.60136 | + | 4.38865i | −0.278119 | + | 0.160572i | ||||
\(748\) | 0.548875 | − | 0.316893i | 0.0200688 | − | 0.0115868i | ||||
\(749\) | − | 0.723491i | − | 0.0264358i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.1132 | − | 20.9807i | 0.442018 | − | 0.765597i | −0.555822 | − | 0.831302i | \(-0.687596\pi\) |
0.997839 | + | 0.0657048i | \(0.0209296\pi\) | |||||||
\(752\) | −9.48200 | − | 5.47443i | −0.345773 | − | 0.199632i | ||||
\(753\) | 6.66342 | 0.242829 | ||||||||
\(754\) | −0.143951 | + | 7.48270i | −0.00524240 | + | 0.272504i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.53906 | − | 1.46593i | −0.0923446 | − | 0.0533152i | ||||
\(757\) | 21.0629 | − | 36.4820i | 0.765544 | − | 1.32596i | −0.174415 | − | 0.984672i | \(-0.555803\pi\) |
0.939959 | − | 0.341288i | \(-0.110863\pi\) | |||||||
\(758\) | −2.58479 | − | 4.47699i | −0.0938838 | − | 0.162612i | ||||
\(759\) | 1.13819i | 0.0413135i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.41955 | + | 4.28368i | −0.268959 | + | 0.155283i | −0.628414 | − | 0.777879i | \(-0.716296\pi\) |
0.359456 | + | 0.933162i | \(0.382962\pi\) | |||||||
\(762\) | 7.60521i | 0.275508i | ||||||||
\(763\) | −6.06596 | − | 10.5066i | −0.219602 | − | 0.380363i | ||||
\(764\) | 2.25347 | − | 3.90313i | 0.0815277 | − | 0.141210i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.80196 | 0.101239 | ||||||||
\(767\) | −0.380728 | + | 19.7905i | −0.0137473 | + | 0.714595i | ||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −42.1226 | − | 24.3195i | −1.51898 | − | 0.876983i | −0.999750 | − | 0.0223481i | \(-0.992886\pi\) |
−0.519229 | − | 0.854635i | \(-0.673781\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.01607 | − | 8.68809i | −0.180649 | − | 0.312894i | ||||
\(772\) | − | 2.65685i | − | 0.0956223i | ||||||
\(773\) | 42.1294 | − | 24.3234i | 1.51529 | − | 0.874853i | 0.515450 | − | 0.856919i | \(-0.327625\pi\) |
0.999839 | − | 0.0179335i | \(-0.00570872\pi\) | |||||||
\(774\) | 6.82490 | − | 3.94036i | 0.245316 | − | 0.141633i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.30847 | − | 9.19453i | −0.190563 | − | 0.330065i | ||||
\(777\) | 11.8565 | − | 20.5361i | 0.425351 | − | 0.736729i | ||||
\(778\) | −10.3002 | − | 5.94680i | −0.369279 | − | 0.213203i | ||||
\(779\) | −9.33601 | −0.334497 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.0505 | −0.466984 | ||||||||
\(782\) | −0.475463 | − | 0.274509i | −0.0170025 | − | 0.00981641i | ||||
\(783\) | −1.03786 | + | 1.79762i | −0.0370899 | + | 0.0642417i | ||||
\(784\) | 0.797877 | + | 1.38196i | 0.0284956 | + | 0.0493558i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.72279 | + | 2.72670i | −0.168456 | + | 0.0972583i | ||||
\(787\) | 15.2172 | − | 8.78564i | 0.542434 | − | 0.313174i | −0.203631 | − | 0.979048i | \(-0.565274\pi\) |
0.746065 | + | 0.665874i | \(0.231941\pi\) | |||||||
\(788\) | − | 1.94422i | − | 0.0692601i | ||||||
\(789\) | −12.5202 | − | 21.6856i | −0.445730 | − | 0.772027i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.20685 | − | 2.42883i | −0.149578 | − | 0.0863591i | ||||
\(792\) | 1.14626 | 0.0407307 | ||||||||
\(793\) | −10.3365 | − | 0.198852i | −0.367059 | − | 0.00706144i | ||||
\(794\) | −39.0046 | −1.38422 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.50877 | + | 13.0056i | −0.266141 | + | 0.460970i | ||||
\(797\) | −17.3430 | − | 30.0390i | −0.614321 | − | 1.06403i | −0.990503 | − | 0.137489i | \(-0.956097\pi\) |
0.376183 | − | 0.926546i | \(-0.377237\pi\) | |||||||
\(798\) | 2.44949i | 0.0867110i | ||||||||
\(799\) | −5.24273 | + | 3.02689i | −0.185475 | + | 0.107084i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.53882i | 0.160371i | ||||||||
\(802\) | −13.5422 | − | 23.4558i | −0.478192 | − | 0.828253i | ||||
\(803\) | −4.69482 | + | 8.13166i | −0.165676 | + | 0.286960i | ||||
\(804\) | 8.88828 | + | 5.13165i | 0.313466 | + | 0.180979i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.60852 | + | 13.7840i | 0.267999 | + | 0.485521i | ||||
\(807\) | −23.2536 | −0.818566 | ||||||||
\(808\) | 12.2510 | + | 7.07313i | 0.430990 | + | 0.248832i | ||||
\(809\) | 23.2482 | − | 40.2670i | 0.817362 | − | 1.41571i | −0.0902566 | − | 0.995919i | \(-0.528769\pi\) |
0.907619 | − | 0.419795i | \(-0.137898\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 11.0542i | − | 0.388165i | −0.980985 | − | 0.194082i | \(-0.937827\pi\) | ||
0.980985 | − | 0.194082i | \(-0.0621729\pi\) | |||||||
\(812\) | 5.27035 | − | 3.04284i | 0.184953 | − | 0.106783i | ||||
\(813\) | −5.32698 | + | 3.07554i | −0.186826 | + | 0.107864i | ||||
\(814\) | 9.27108i | 0.324951i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.276457 | + | 0.478838i | −0.00967794 | + | 0.0167627i | ||||
\(817\) | −5.70204 | − | 3.29207i | −0.199489 | − | 0.115175i | ||||
\(818\) | 15.9450 | 0.557502 | ||||||||
\(819\) | −9.25467 | + | 5.10841i | −0.323384 | + | 0.178502i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.7133 | − | 9.07206i | −0.548397 | − | 0.316617i | 0.200078 | − | 0.979780i | \(-0.435880\pi\) |
−0.748475 | + | 0.663163i | \(0.769214\pi\) | |||||||
\(822\) | −0.159541 | + | 0.276333i | −0.00556463 | + | 0.00963821i | ||||
\(823\) | 0.275929 | + | 0.477923i | 0.00961827 | + | 0.0166593i | 0.870794 | − | 0.491647i | \(-0.163605\pi\) |
−0.861176 | + | 0.508307i | \(0.830272\pi\) | |||||||
\(824\) | 6.72500i | 0.234277i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.9392 | − | 8.04782i | 0.485008 | − | 0.280020i | ||||
\(827\) | 34.0321i | 1.18341i | 0.806154 | + | 0.591705i | \(0.201545\pi\) | ||||
−0.806154 | + | 0.591705i | \(0.798455\pi\) | |||||||
\(828\) | −0.496476 | − | 0.859921i | −0.0172537 | − | 0.0298843i | ||||
\(829\) | 13.0638 | − | 22.6271i | 0.453724 | − | 0.785872i | −0.544890 | − | 0.838507i | \(-0.683429\pi\) |
0.998614 | + | 0.0526352i | \(0.0167620\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.88928 | 0.238986 | ||||||||
\(832\) | −1.86250 | + | 3.08725i | −0.0645706 | + | 0.107031i | ||||
\(833\) | 0.882315 | 0.0305704 | ||||||||
\(834\) | 10.1160 | + | 5.84046i | 0.350287 | + | 0.202239i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.478838 | − | 0.829371i | −0.0165610 | − | 0.0286844i | ||||
\(837\) | 4.36673i | 0.150936i | ||||||||
\(838\) | 16.8298 | − | 9.71670i | 0.581376 | − | 0.335658i | ||||
\(839\) | 35.9524 | − | 20.7571i | 1.24121 | − | 0.716616i | 0.271873 | − | 0.962333i | \(-0.412357\pi\) |
0.969342 | + | 0.245717i | \(0.0790235\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.3457 | + | 21.3834i | 0.425714 | + | 0.737359i | ||||
\(842\) | 10.7885 | − | 18.6862i | 0.371795 | − | 0.643968i | ||||
\(843\) | 0.472519 | + | 0.272809i | 0.0162744 | + | 0.00939603i | ||||
\(844\) | −0.759763 | −0.0261521 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −10.9489 | −0.376430 | ||||||||
\(847\) | −24.5935 | − | 14.1991i | −0.845043 | − | 0.487886i | ||||
\(848\) | −1.78376 | + | 3.08957i | −0.0612547 | + | 0.106096i | ||||
\(849\) | −4.21329 | − | 7.29764i | −0.144600 | − | 0.250454i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.95512 | − | 4.01554i | 0.238418 | − | 0.137651i | ||||
\(852\) | 9.85992 | − | 5.69263i | 0.337795 | − | 0.195026i | ||||
\(853\) | − | 18.1928i | − | 0.622908i | −0.950261 | − | 0.311454i | \(-0.899184\pi\) | ||
0.950261 | − | 0.311454i | \(-0.100816\pi\) | |||||||
\(854\) | 4.20332 | + | 7.28037i | 0.143835 | + | 0.249129i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.213709 | − | 0.123385i | −0.00730441 | − | 0.00421720i | ||||
\(857\) | 52.4732 | 1.79245 | 0.896224 | − | 0.443601i | \(-0.146299\pi\) | ||||
0.896224 | + | 0.443601i | \(0.146299\pi\) | |||||||
\(858\) | 2.13492 | − | 3.53880i | 0.0728849 | − | 0.120813i | ||||
\(859\) | −53.9248 | −1.83989 | −0.919945 | − | 0.392047i | \(-0.871767\pi\) | ||||
−0.919945 | + | 0.392047i | \(0.871767\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −16.3810 | + | 28.3727i | −0.558262 | + | 0.966938i | ||||
\(862\) | −0.317855 | − | 0.550541i | −0.0108262 | − | 0.0187515i | ||||
\(863\) | 9.53847i | 0.324693i | 0.986734 | + | 0.162347i | \(0.0519063\pi\) | ||||
−0.986734 | + | 0.162347i | \(0.948094\pi\) | |||||||
\(864\) | −0.866025 | + | 0.500000i | −0.0294628 | + | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 10.6018i | − | 0.360264i | ||||||
\(867\) | −8.34714 | − | 14.4577i | −0.283484 | − | 0.491008i | ||||
\(868\) | 6.40130 | − | 11.0874i | 0.217274 | − | 0.376330i | ||||
\(869\) | −1.67738 | − | 0.968437i | −0.0569013 | − | 0.0328520i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.3971 | − | 17.8826i | 1.09773 | − | 0.605929i | ||||
\(872\) | −4.13797 | −0.140129 | ||||||||
\(873\) | −9.19453 | − | 5.30847i | −0.311188 | − | 0.179664i | ||||
\(874\) | −0.414793 | + | 0.718443i | −0.0140306 | + | 0.0243017i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 8.19151i | − | 0.276765i | ||||||
\(877\) | −39.6842 | + | 22.9117i | −1.34004 | + | 0.773672i | −0.986813 | − | 0.161866i | \(-0.948249\pi\) |
−0.353226 | + | 0.935538i | \(0.614915\pi\) | |||||||
\(878\) | 13.2621 | − | 7.65685i | 0.447573 | − | 0.258406i | ||||
\(879\) | 6.77829i | 0.228626i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.1002 | + | 26.1544i | −0.508740 | + | 0.881164i | 0.491209 | + | 0.871042i | \(0.336555\pi\) |
−0.999949 | + | 0.0101217i | \(0.996778\pi\) | |||||||
\(882\) | 1.38196 | + | 0.797877i | 0.0465331 | + | 0.0268659i | ||||
\(883\) | −22.0417 | −0.741761 | −0.370880 | − | 0.928681i | \(-0.620944\pi\) | ||||
−0.370880 | + | 0.928681i | \(0.620944\pi\) | |||||||
\(884\) | 0.963388 | + | 1.74533i | 0.0324023 | + | 0.0587017i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −16.0041 | − | 9.23998i | −0.537669 | − | 0.310423i | ||||
\(887\) | 13.3918 | − | 23.1953i | 0.449652 | − | 0.778821i | −0.548711 | − | 0.836012i | \(-0.684881\pi\) |
0.998363 | + | 0.0571915i | \(0.0182146\pi\) | |||||||
\(888\) | −4.04404 | − | 7.00449i | −0.135709 | − | 0.235055i | ||||
\(889\) | − | 22.2973i | − | 0.747829i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.992694 | − | 0.573132i | 0.0332565 | − | 0.0192007i | ||||
\(892\) | 21.4704i | 0.718883i | ||||||||
\(893\) | 4.57375 | + | 7.92197i | 0.153055 | + | 0.265099i | ||||
\(894\) | −2.50120 | + | 4.33221i | −0.0836527 | + | 0.144891i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.93185 | 0.0979463 | ||||||||
\(897\) | −3.57948 | − | 0.0688616i | −0.119515 | − | 0.00229922i | ||||
\(898\) | −25.9905 | −0.867313 | ||||||||
\(899\) | −7.84972 | − | 4.53204i | −0.261803 | − | 0.151152i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.986268 | + | 1.70827i | 0.0328574 | + | 0.0569106i | ||||
\(902\) | − | 12.8089i | − | 0.426490i | ||||||
\(903\) | −20.0096 | + | 11.5525i | −0.665878 | + | 0.384445i | ||||
\(904\) | −1.43488 | + | 0.828427i | −0.0477233 | + | 0.0275531i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6.45025 | − | 11.1722i | −0.214295 | − | 0.371170i | ||||
\(907\) | −11.6972 | + | 20.2602i | −0.388400 | + | 0.672729i | −0.992235 | − | 0.124381i | \(-0.960306\pi\) |
0.603834 | + | 0.797110i | \(0.293639\pi\) | |||||||
\(908\) | −19.1406 | − | 11.0508i | −0.635204 | − | 0.366735i | ||||
\(909\) | 14.1463 | 0.469202 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.1351 | 0.965289 | 0.482644 | − | 0.875816i | \(-0.339676\pi\) | ||||
0.482644 | + | 0.875816i | \(0.339676\pi\) | |||||||
\(912\) | 0.723543 | + | 0.417738i | 0.0239589 | + | 0.0138327i | ||||
\(913\) | −5.03055 | + | 8.71317i | −0.166487 | + | 0.288364i | ||||
\(914\) | −20.7543 | − | 35.9475i | −0.686492 | − | 1.18904i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −18.7380 | + | 10.8184i | −0.619123 | + | 0.357451i | ||||
\(917\) | 13.8465 | − | 7.99429i | 0.457252 | − | 0.263995i | ||||
\(918\) | 0.552914i | 0.0182489i | ||||||||
\(919\) | −22.1754 | − | 38.4089i | −0.731499 | − | 1.26699i | −0.956242 | − | 0.292576i | \(-0.905488\pi\) |
0.224743 | − | 0.974418i | \(-0.427846\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 30.0019 | + | 17.3216i | 0.988595 | + | 0.570765i | ||||
\(922\) | −15.9964 | −0.526812 | ||||||||
\(923\) | 0.789572 | − | 41.0425i | 0.0259891 | − | 1.35093i | ||||
\(924\) | −3.36068 | −0.110558 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9.41638 | − | 16.3096i | 0.309441 | − | 0.535968i | ||||
\(927\) | 3.36250 | + | 5.82402i | 0.110439 | + | 0.191286i | ||||
\(928\) | − | 2.07571i | − | 0.0681386i | ||||||
\(929\) | −10.9917 | + | 6.34607i | −0.360626 | + | 0.208208i | −0.669355 | − | 0.742942i | \(-0.733430\pi\) |
0.308729 | + | 0.951150i | \(0.400096\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 1.33321i | − | 0.0436943i | ||||||
\(932\) | 2.97834 | + | 5.15864i | 0.0975588 | + | 0.168977i | ||||
\(933\) | 10.1101 | − | 17.5113i | 0.330991 | − | 0.573293i | ||||
\(934\) | −2.97686 | − | 1.71869i | −0.0974059 | − | 0.0562373i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.0693504 | + | 3.60488i | −0.00226679 | + | 0.117829i | ||||
\(937\) | −47.6859 | −1.55783 | −0.778915 | − | 0.627130i | \(-0.784229\pi\) | ||||
−0.778915 | + | 0.627130i | \(0.784229\pi\) | |||||||
\(938\) | −26.0591 | − | 15.0452i | −0.850861 | − | 0.491245i | ||||
\(939\) | 11.1663 | − | 19.3406i | 0.364399 | − | 0.631157i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 53.8451i | − | 1.75530i | −0.479301 | − | 0.877650i | \(-0.659110\pi\) | ||
0.479301 | − | 0.877650i | \(-0.340890\pi\) | |||||||
\(942\) | −7.50438 | + | 4.33266i | −0.244506 | + | 0.141166i | ||||
\(943\) | −9.60919 | + | 5.54787i | −0.312918 | + | 0.180663i | ||||
\(944\) | − | 5.48993i | − | 0.178682i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.51669 | − | 7.82314i | 0.146850 | − | 0.254352i | ||||
\(947\) | −24.1725 | − | 13.9560i | −0.785500 | − | 0.453509i | 0.0528760 | − | 0.998601i | \(-0.483161\pi\) |
−0.838376 | + | 0.545093i | \(0.816495\pi\) | |||||||
\(948\) | 1.68973 | 0.0548798 | ||||||||
\(949\) | −25.2892 | − | 15.2567i | −0.820922 | − | 0.495253i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.89801 | − | 5.71462i | −0.320965 | − | 0.185309i | ||||
\(952\) | 0.810531 | − | 1.40388i | 0.0262695 | − | 0.0455001i | ||||
\(953\) | 26.6171 | + | 46.1023i | 0.862214 | + | 1.49340i | 0.869787 | + | 0.493427i | \(0.164256\pi\) |
−0.00757307 | + | 0.999971i | \(0.502411\pi\) | |||||||
\(954\) | 3.56753i | 0.115503i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −24.9769 | + | 14.4204i | −0.807810 | + | 0.466389i | ||||
\(957\) | 2.37931i | 0.0769123i | ||||||||
\(958\) | −12.9700 | − | 22.4648i | −0.419043 | − | 0.725804i | ||||
\(959\) | 0.467750 | − | 0.810167i | 0.0151044 | − | 0.0261617i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.9317 | 0.384893 | ||||||||
\(962\) | −29.1566 | − | 0.560911i | −0.940047 | − | 0.0180845i | ||||
\(963\) | −0.246769 | −0.00795203 | ||||||||
\(964\) | 4.95886 | + | 2.86300i | 0.159714 | + | 0.0922110i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.45559 | + | 2.52116i | 0.0468330 | + | 0.0811171i | ||||
\(967\) | 18.2209i | 0.585946i | 0.956121 | + | 0.292973i | \(0.0946446\pi\) | ||||
−0.956121 | + | 0.292973i | \(0.905355\pi\) | |||||||
\(968\) | −8.38839 | + | 4.84304i | −0.269613 | + | 0.155661i | ||||
\(969\) | 0.400057 | − | 0.230973i | 0.0128517 | − | 0.00741993i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.5276 | + | 45.9471i | 0.851311 | + | 1.47451i | 0.880026 | + | 0.474926i | \(0.157525\pi\) |
−0.0287154 | + | 0.999588i | \(0.509142\pi\) | |||||||
\(972\) | −0.500000 | + | 0.866025i | −0.0160375 | + | 0.0277778i | ||||
\(973\) | −29.6585 | − | 17.1234i | −0.950809 | − | 0.548950i | ||||
\(974\) | 18.0188 | 0.577359 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.86735 | 0.0917817 | ||||||||
\(977\) | 49.6962 | + | 28.6921i | 1.58992 | + | 0.917943i | 0.993318 | + | 0.115408i | \(0.0368174\pi\) |
0.596605 | + | 0.802535i | \(0.296516\pi\) | |||||||
\(978\) | −0.923344 | + | 1.59928i | −0.0295253 | + | 0.0511393i | ||||
\(979\) | 2.60134 | + | 4.50566i | 0.0831393 | + | 0.144001i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.58359 | + | 2.06899i | −0.114415 | + | 0.0660576i | ||||
\(982\) | 27.2908 | − | 15.7564i | 0.870886 | − | 0.502806i | ||||
\(983\) | 6.53308i | 0.208373i | 0.994558 | + | 0.104186i | \(0.0332239\pi\) | ||||
−0.994558 | + | 0.104186i | \(0.966776\pi\) | |||||||
\(984\) | 5.58725 | + | 9.67739i | 0.178115 | + | 0.308504i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.993929 | − | 0.573845i | −0.0316532 | − | 0.0182750i | ||||
\(987\) | 32.1005 | 1.02177 | ||||||||
\(988\) | 2.63726 | − | 1.45572i | 0.0839024 | − | 0.0463126i | ||||
\(989\) | −7.82517 | −0.248826 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.9156 | − | 22.3704i | 0.410277 | − | 0.710620i | −0.584643 | − | 0.811291i | \(-0.698765\pi\) |
0.994920 | + | 0.100670i | \(0.0320987\pi\) | |||||||
\(992\) | −2.18336 | − | 3.78170i | −0.0693219 | − | 0.120069i | ||||
\(993\) | − | 1.77365i | − | 0.0562850i | ||||||
\(994\) | −28.9078 | + | 16.6899i | −0.916901 | + | 0.529373i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 8.77729i | − | 0.278119i | ||||||
\(997\) | 11.7814 | + | 20.4060i | 0.373121 | + | 0.646265i | 0.990044 | − | 0.140759i | \(-0.0449542\pi\) |
−0.616923 | + | 0.787024i | \(0.711621\pi\) | |||||||
\(998\) | −2.78963 | + | 4.83178i | −0.0883041 | + | 0.152947i | ||||
\(999\) | −7.00449 | − | 4.04404i | −0.221612 | − | 0.127948i |
(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 | 1950.2.bc.f.901.2 | yes | 8 | |
5.2 | odd | 4 | 1950.2.y.l.199.2 | 8 | |||
5.3 | odd | 4 | 1950.2.y.i.199.3 | 8 | |||
5.4 | even | 2 | 1950.2.bc.e.901.3 | yes | 8 | ||
13.10 | even | 6 | inner | 1950.2.bc.f.751.2 | yes | 8 | |
65.23 | odd | 12 | 1950.2.y.l.49.2 | 8 | |||
65.49 | even | 6 | 1950.2.bc.e.751.3 | ✓ | 8 | ||
65.62 | odd | 12 | 1950.2.y.i.49.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1950.2.y.i.49.3 | 8 | 65.62 | odd | 12 | |||
1950.2.y.i.199.3 | 8 | 5.3 | odd | 4 | |||
1950.2.y.l.49.2 | 8 | 65.23 | odd | 12 | |||
1950.2.y.l.199.2 | 8 | 5.2 | odd | 4 | |||
1950.2.bc.e.751.3 | ✓ | 8 | 65.49 | even | 6 | ||
1950.2.bc.e.901.3 | yes | 8 | 5.4 | even | 2 | ||
1950.2.bc.f.751.2 | yes | 8 | 13.10 | even | 6 | inner | |
1950.2.bc.f.901.2 | yes | 8 | 1.1 | even | 1 | trivial |