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 | 751.3 | ||
Root | \(-0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.751 |
Dual form | 1950.2.bc.e.901.3 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
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 | \(-0.520259\pi\) |
−0.896073 | + | 0.443908i | \(0.853592\pi\) | |||||||
\(8\) | − | 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 | −0.642132 | − | 0.766594i | \(-0.721950\pi\) |
0.342824 | + | 0.939400i | \(0.388617\pi\) | |||||||
\(12\) | −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 | \(-0.854692\pi\) |
0.830551 | + | 0.556942i | \(0.188026\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 0.723543 | + | 0.417738i | 0.165992 | + | 0.0958356i | 0.580695 | − | 0.814121i | \(-0.302781\pi\) |
−0.414703 | + | 0.909957i | \(0.636114\pi\) | |||||||
\(20\) | 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 | \(-0.199678\pi\) |
−0.913134 | + | 0.407661i | \(0.866345\pi\) | |||||||
\(24\) | −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 | 0.946152 | − | 0.323722i | \(-0.104934\pi\) |
−0.753427 | + | 0.657531i | \(0.771601\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.36673i | 0.784288i | 0.919904 | + | 0.392144i | \(0.128266\pi\) | ||||
−0.919904 | + | 0.392144i | \(0.871734\pi\) | |||||||
\(32\) | −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 | \(-0.898165\pi\) |
−0.202271 | + | 0.979330i | \(0.564832\pi\) | |||||||
\(38\) | 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 | −0.511443 | + | 0.859317i | \(0.670889\pi\) |
−0.999912 | + | 0.0132641i | \(0.995778\pi\) | |||||||
\(42\) | 1.46593 | + | 2.53906i | 0.226197 | + | 0.391785i | ||||
\(43\) | 3.94036 | − | 6.82490i | 0.600899 | − | 1.04079i | −0.391786 | − | 0.920056i | \(-0.628143\pi\) |
0.992685 | − | 0.120732i | \(-0.0385240\pi\) | |||||||
\(44\) | 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 | \(-0.578794\pi\) | ||||
−0.245019 | + | 0.969518i | \(0.578794\pi\) | |||||||
\(54\) | 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 | 0.157497 | − | 0.987520i | \(-0.449658\pi\) |
−0.776469 | + | 0.630156i | \(0.782991\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.43368 | + | 2.48320i | −0.183563 | + | 0.317941i | −0.943091 | − | 0.332533i | \(-0.892097\pi\) |
0.759528 | + | 0.650474i | \(0.225430\pi\) | |||||||
\(62\) | 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 | \(-0.882356\pi\) |
−0.153401 | + | 0.988164i | \(0.549023\pi\) | |||||||
\(68\) | 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 | 0.953717 | − | 0.300705i | \(-0.0972220\pi\) |
0.216440 | + | 0.976296i | \(0.430555\pi\) | |||||||
\(72\) | 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 | −0.693646 | − | 0.720316i | \(-0.743997\pi\) |
0.276989 | + | 0.960873i | \(0.410663\pi\) | |||||||
\(90\) | 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 | \(-0.514528\pi\) |
−0.887937 | + | 0.459965i | \(0.847862\pi\) | |||||||
\(98\) | 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 | −0.967122 | − | 0.254314i | \(-0.918150\pi\) |
0.263319 | − | 0.964709i | \(-0.415183\pi\) | |||||||
\(102\) | 0.478838 | − | 0.276457i | 0.0474120 | − | 0.0273733i | ||||
\(103\) | 6.72500 | 0.662634 | 0.331317 | − | 0.943519i | \(-0.392507\pi\) | ||||
0.331317 | + | 0.943519i | \(0.392507\pi\) | |||||||
\(104\) | −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 | \(-0.170464\pi\) |
−0.871928 | + | 0.489634i | \(0.837130\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | 4.13797i | 0.396346i | 0.980167 | + | 0.198173i | \(0.0635008\pi\) | ||||
−0.980167 | + | 0.198173i | \(0.936499\pi\) | |||||||
\(110\) | 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 | \(-0.808502\pi\) |
0.902357 | + | 0.430988i | \(0.141835\pi\) | |||||||
\(114\) | −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 | \(-0.276223\pi\) |
−0.983948 | + | 0.178456i | \(0.942890\pi\) | |||||||
\(128\) | −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 | \(-0.337672\pi\) |
−0.511758 | + | 0.859130i | \(0.671006\pi\) | |||||||
\(138\) | 0.992952i | 0.0845257i | ||||||||
\(139\) | −5.84046 | + | 10.1160i | −0.495381 | + | 0.858026i | −0.999986 | − | 0.00532505i | \(-0.998305\pi\) |
0.504605 | + | 0.863351i | \(0.331638\pi\) | |||||||
\(140\) | 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 | 0.666845 | − | 0.745196i | \(-0.267644\pi\) |
−0.311937 | + | 0.950103i | \(0.600978\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 12.9005i | − | 1.04983i | −0.851156 | − | 0.524914i | \(-0.824098\pi\) | ||
0.851156 | − | 0.524914i | \(-0.175902\pi\) | |||||||
\(152\) | 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 | \(-0.612387\pi\) | ||||
−0.345784 | + | 0.938314i | \(0.612387\pi\) | |||||||
\(158\) | 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 | \(-0.356374\pi\) |
−0.561323 | + | 0.827597i | \(0.689708\pi\) | |||||||
\(164\) | 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 | \(-0.346900\pi\) |
0.999092 | + | 0.0426077i | \(0.0135665\pi\) | |||||||
\(168\) | 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 | \(-0.684199\pi\) |
0.998483 | + | 0.0550519i | \(0.0175324\pi\) | |||||||
\(174\) | − | 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 | 0.648759 | − | 0.760994i | \(-0.275288\pi\) |
−0.983420 | + | 0.181344i | \(0.941955\pi\) | |||||||
\(180\) | 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 | −0.935963 | − | 0.352098i | \(-0.885468\pi\) |
0.772908 | + | 0.634519i | \(0.218802\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | 2.30090 | − | 1.32843i | 0.165623 | − | 0.0956223i | −0.414898 | − | 0.909868i | \(-0.636183\pi\) |
0.580520 | + | 0.814246i | \(0.302849\pi\) | |||||||
\(194\) | −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 | \(-0.644603\pi\) |
0.558780 | + | 0.829316i | \(0.311269\pi\) | |||||||
\(198\) | −0.573132 | − | 0.992694i | −0.0407307 | − | 0.0705477i | ||||
\(199\) | 7.50877 | − | 13.0056i | 0.532282 | − | 0.921940i | −0.467007 | − | 0.884253i | \(-0.654668\pi\) |
0.999290 | − | 0.0376865i | \(-0.0119988\pi\) | |||||||
\(200\) | 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 | 0.852653 | − | 0.522477i | \(-0.174992\pi\) |
−0.878805 | + | 0.477181i | \(0.841659\pi\) | |||||||
\(212\) | −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 | \(-0.922013\pi\) |
−0.275005 | + | 0.961443i | \(0.588680\pi\) | |||||||
\(224\) | 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 | \(-0.0712325\pi\) |
0.295344 | + | 0.955391i | \(0.404566\pi\) | |||||||
\(228\) | −0.723543 | − | 0.417738i | −0.0479178 | − | 0.0276654i | ||||
\(229\) | − | 21.6368i | − | 1.42980i | −0.699226 | − | 0.714901i | \(-0.746472\pi\) | ||
0.699226 | − | 0.714901i | \(-0.253528\pi\) | |||||||
\(230\) | 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 | \(-0.562509\pi\) | ||||
−0.195118 | + | 0.980780i | \(0.562509\pi\) | |||||||
\(234\) | 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 | \(-0.617377\pi\) | ||
0.360451 | − | 0.932778i | \(-0.382623\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.95886 | + | 2.86300i | 0.319428 | + | 0.184422i | 0.651138 | − | 0.758960i | \(-0.274292\pi\) |
−0.331709 | + | 0.943382i | \(0.607625\pi\) | |||||||
\(242\) | 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 | −0.741511 | − | 0.670940i | \(-0.765891\pi\) |
0.951807 | + | 0.306697i | \(0.0992240\pi\) | |||||||
\(252\) | − | 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 | \(-0.267965\pi\) |
−0.978988 | + | 0.203920i | \(0.934632\pi\) | |||||||
\(258\) | −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 | −0.936450 | − | 0.350800i | \(-0.885910\pi\) |
0.164423 | − | 0.986390i | \(-0.447424\pi\) | |||||||
\(264\) | 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 | 0.256367 | + | 0.966579i | \(0.417474\pi\) |
−0.965266 | + | 0.261269i | \(0.915859\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.32698 | + | 3.07554i | −0.323591 | + | 0.186826i | −0.652992 | − | 0.757365i | \(-0.726487\pi\) |
0.329401 | + | 0.944190i | \(0.393153\pi\) | |||||||
\(272\) | 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 | \(-0.899693\pi\) |
0.743790 | + | 0.668414i | \(0.233026\pi\) | |||||||
\(278\) | 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 | \(-0.994819\pi\) | ||
0.999868 | − | 0.0162744i | \(-0.00518053\pi\) | |||||||
\(282\) | 5.47443 | − | 9.48200i | 0.325998 | − | 0.564645i | ||||
\(283\) | −4.21329 | − | 7.29764i | −0.250454 | − | 0.433799i | 0.713197 | − | 0.700964i | \(-0.247247\pi\) |
−0.963651 | + | 0.267164i | \(0.913913\pi\) | |||||||
\(284\) | 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 | \(-0.269890\pi\) |
−0.318632 | + | 0.947879i | \(0.603223\pi\) | |||||||
\(294\) | − | 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 | \(-0.717420\pi\) | ||||
−0.631157 | + | 0.775655i | \(0.717420\pi\) | |||||||
\(314\) | −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 | 0.541619 | − | 0.840624i | \(-0.317811\pi\) |
−0.457192 | + | 0.889368i | \(0.651145\pi\) | |||||||
\(332\) | −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 | \(-0.606006\pi\) | ||||
−0.326907 | + | 0.945056i | \(0.606006\pi\) | |||||||
\(338\) | 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 | −0.212917 | − | 0.977070i | \(-0.568296\pi\) |
0.952626 | − | 0.304143i | \(-0.0983702\pi\) | |||||||
\(348\) | −1.03786 | − | 1.79762i | −0.0556349 | − | 0.0963625i | ||||
\(349\) | 12.2674 | − | 7.08260i | 0.656660 | − | 0.379123i | −0.134343 | − | 0.990935i | \(-0.542892\pi\) |
0.791003 | + | 0.611812i | \(0.209559\pi\) | |||||||
\(350\) | 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 | \(-0.984576\pi\) |
−0.457465 | + | 0.889228i | \(0.651243\pi\) | |||||||
\(354\) | 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 | \(-0.895917\pi\) | ||
0.947015 | − | 0.321190i | \(-0.104083\pi\) | |||||||
\(360\) | 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 | −0.930262 | − | 0.366897i | \(-0.880420\pi\) |
0.147389 | − | 0.989079i | \(-0.452913\pi\) | |||||||
\(368\) | −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 | 0.209650 | − | 0.977777i | \(-0.432768\pi\) |
0.741954 | − | 0.670450i | \(-0.233899\pi\) | |||||||
\(374\) | −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 | −0.380590 | − | 0.924744i | \(-0.624279\pi\) |
0.610557 | + | 0.791972i | \(0.290946\pi\) | |||||||
\(380\) | 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 | \(-0.310527\pi\) |
−0.436721 | + | 0.899597i | \(0.643860\pi\) | |||||||
\(384\) | 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 | −0.950087 | − | 0.311986i | \(-0.899006\pi\) |
−0.745231 | − | 0.666806i | \(-0.767661\pi\) | |||||||
\(398\) | − | 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 | 0.217335 | − | 0.976097i | \(-0.430264\pi\) |
0.953992 | + | 0.299831i | \(0.0969303\pi\) | |||||||
\(402\) | 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 | 0.118110 | − | 0.993000i | \(-0.462316\pi\) |
−0.800908 | + | 0.598787i | \(0.795650\pi\) | |||||||
\(410\) | 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 | 0.524888 | − | 0.851171i | \(-0.324107\pi\) |
−0.999580 | + | 0.0289808i | \(0.990774\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 21.5769i | − | 1.05160i | −0.850610 | − | 0.525798i | \(-0.823767\pi\) | ||
0.850610 | − | 0.525798i | \(-0.176233\pi\) | |||||||
\(422\) | −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 | −0.486682 | − | 0.873579i | \(-0.661793\pi\) |
0.513201 | + | 0.858269i | \(0.328460\pi\) | |||||||
\(432\) | −0.500000 | − | 0.866025i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | −5.30090 | + | 9.18143i | −0.254745 | + | 0.441232i | −0.964826 | − | 0.262888i | \(-0.915325\pi\) |
0.710081 | + | 0.704120i | \(0.248658\pi\) | |||||||
\(434\) | − | 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 | 0.623405 | − | 0.781899i | \(-0.285749\pi\) |
−0.988847 | + | 0.148935i | \(0.952415\pi\) | |||||||
\(440\) | 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 | \(-0.644669\pi\) | ||||
−0.439005 | + | 0.898485i | \(0.644669\pi\) | |||||||
\(444\) | 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 | 0.926050 | − | 0.377400i | \(-0.123182\pi\) |
0.136187 | + | 0.990683i | \(0.456515\pi\) | |||||||
\(450\) | 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 | −0.720924 | + | 0.693014i | \(0.756282\pi\) |
−0.960630 | + | 0.277832i | \(0.910384\pi\) | |||||||
\(458\) | −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 | 0.786619 | − | 0.617439i | \(-0.211830\pi\) |
−0.141409 | + | 0.989951i | \(0.545163\pi\) | |||||||
\(462\) | −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 | \(-0.525342\pi\) | ||||
−0.0795316 | + | 0.996832i | \(0.525342\pi\) | |||||||
\(468\) | 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 | 0.110479 | − | 0.993878i | \(-0.464762\pi\) |
0.915963 | + | 0.401262i | \(0.131428\pi\) | |||||||
\(480\) | 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 | \(-0.199471\pi\) |
−0.102875 | + | 0.994694i | \(0.532804\pi\) | |||||||
\(488\) | 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 | −0.964454 | − | 0.264251i | \(-0.914875\pi\) |
0.253379 | − | 0.967367i | \(-0.418458\pi\) | |||||||
\(492\) | 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 | \(0.0398549\pi\) | ||||
−0.992172 | + | 0.124881i | \(0.960145\pi\) | |||||||
\(500\) | 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 | 0.0520768 | + | 0.998643i | \(0.483416\pi\) |
−0.890889 | + | 0.454222i | \(0.849917\pi\) | |||||||
\(504\) | −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 | 0.187813 | − | 0.982205i | \(-0.439860\pi\) |
0.944521 | + | 0.328452i | \(0.106527\pi\) | |||||||
\(510\) | 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 | 0.971612 | + | 0.236581i | \(0.0760270\pi\) |
−0.280920 | + | 0.959731i | \(0.590640\pi\) | |||||||
\(524\) | 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 | \(-0.930076\pi\) | ||
0.975969 | − | 0.217911i | \(-0.0699241\pi\) | |||||||
\(542\) | −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 | \(-0.258829\pi\) | ||||
0.687225 | + | 0.726445i | \(0.258829\pi\) | |||||||
\(548\) | −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 | \(-0.631530\pi\) |
0.592359 | + | 0.805674i | \(0.298197\pi\) | |||||||
\(558\) | −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 | \(-0.945394\pi\) |
0.640500 | + | 0.767958i | \(0.278727\pi\) | |||||||
\(564\) | − | 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 | 0.982807 | − | 0.184636i | \(-0.0591105\pi\) |
−0.651303 | + | 0.758818i | \(0.725777\pi\) | |||||||
\(570\) | 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 | −0.536165 | + | 0.844113i | \(0.680128\pi\) |
−0.999106 | + | 0.0422761i | \(0.986539\pi\) | |||||||
\(588\) | −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 | −0.968253 | − | 0.249973i | \(-0.919578\pi\) |
0.267643 | − | 0.963518i | \(-0.413755\pi\) | |||||||
\(602\) | −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 | 0.396439 | + | 0.918061i | \(0.370246\pi\) |
−0.993284 | + | 0.115704i | \(0.963088\pi\) | |||||||
\(608\) | −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 | \(-0.948548\pi\) |
−0.354106 | + | 0.935205i | \(0.615215\pi\) | |||||||
\(614\) | 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 | \(-0.337226\pi\) |
−0.510553 | + | 0.859847i | \(0.670559\pi\) | |||||||
\(618\) | −5.82402 | − | 3.36250i | −0.234277 | − | 0.135260i | ||||
\(619\) | − | 28.6848i | − | 1.15294i | −0.817118 | − | 0.576470i | \(-0.804430\pi\) | ||
0.817118 | − | 0.576470i | \(-0.195570\pi\) | |||||||
\(620\) | 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 | 0.576473 | − | 0.817116i | \(-0.304429\pi\) |
−0.419407 | + | 0.907798i | \(0.637762\pi\) | |||||||
\(632\) | − | 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 | −0.999259 | − | 0.0384890i | \(-0.987746\pi\) |
0.532962 | + | 0.846139i | \(0.321079\pi\) | |||||||
\(642\) | 0.246769i | 0.00973921i | ||||||||
\(643\) | −9.66855 | − | 5.58214i | −0.381290 | − | 0.220138i | 0.297089 | − | 0.954850i | \(-0.403984\pi\) |
−0.678379 | + | 0.734712i | \(0.737317\pi\) | |||||||
\(644\) | 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 | \(-0.0949061\pi\) |
−0.732342 | + | 0.680937i | \(0.761573\pi\) | |||||||
\(648\) | −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 | \(-0.223217\pi\) |
−0.940757 | + | 0.339082i | \(0.889883\pi\) | |||||||
\(654\) | 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 | −0.990001 | − | 0.141059i | \(-0.954949\pi\) |
0.617161 | + | 0.786837i | \(0.288283\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.6116 | − | 9.01337i | 0.607221 | − | 0.350579i | −0.164656 | − | 0.986351i | \(-0.552651\pi\) |
0.771877 | + | 0.635772i | \(0.219318\pi\) | |||||||
\(662\) | 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 | \(-0.118404\pi\) |
−0.780570 | + | 0.625068i | \(0.785071\pi\) | |||||||
\(674\) | −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 | \(-0.350953\pi\) | ||||
0.451321 | + | 0.892362i | \(0.350953\pi\) | |||||||
\(678\) | −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 | \(-0.222289\pi\) |
−0.173856 | + | 0.984771i | \(0.555623\pi\) | |||||||
\(684\) | 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 | −0.812464 | − | 0.583011i | \(-0.801875\pi\) |
0.0986699 | + | 0.995120i | \(0.468541\pi\) | |||||||
\(692\) | −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 | 0.687911 | − | 0.725795i | \(-0.258528\pi\) |
−0.284602 | + | 0.958646i | \(0.591861\pi\) | |||||||
\(710\) | 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 | −0.850284 | − | 0.526325i | \(-0.823570\pi\) |
0.880952 | + | 0.473205i | \(0.156903\pi\) | |||||||
\(720\) | 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 | \(-0.149878\pi\) | ||||
0.891180 | + | 0.453650i | \(0.149878\pi\) | |||||||
\(728\) | 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 | −0.638489 | + | 0.769631i | \(0.720440\pi\) |
−0.985765 | + | 0.168132i | \(0.946227\pi\) | |||||||
\(740\) | 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 | \(-0.399536\pi\) |
0.978450 | + | 0.206485i | \(0.0662024\pi\) | |||||||
\(744\) | −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 | 0.997839 | − | 0.0657048i | \(-0.0209296\pi\) |
−0.555822 | + | 0.831302i | \(0.687596\pi\) | |||||||
\(752\) | 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 | −0.939959 | − | 0.341288i | \(-0.889137\pi\) |
0.174415 | − | 0.984672i | \(-0.444197\pi\) | |||||||
\(758\) | 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 | 0.359456 | − | 0.933162i | \(-0.382962\pi\) |
−0.628414 | + | 0.777879i | \(0.716296\pi\) | |||||||
\(762\) | 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 | −0.519229 | + | 0.854635i | \(0.673781\pi\) |
−0.999750 | + | 0.0223481i | \(0.992886\pi\) | |||||||
\(770\) | 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 | −0.999839 | − | 0.0179335i | \(-0.994291\pi\) |
−0.515450 | − | 0.856919i | \(-0.672375\pi\) | |||||||
\(774\) | 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 | \(-0.434726\pi\) |
−0.746065 | + | 0.665874i | \(0.768059\pi\) | |||||||
\(788\) | − | 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 | −0.376183 | − | 0.926546i | \(-0.622763\pi\) |
0.990503 | − | 0.137489i | \(-0.0439032\pi\) | |||||||
\(798\) | 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 | 0.907619 | + | 0.419795i | \(0.137898\pi\) |
−0.0902566 | + | 0.995919i | \(0.528769\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.0542i | 0.388165i | 0.980985 | + | 0.194082i | \(0.0621729\pi\) | ||||
−0.980985 | + | 0.194082i | \(0.937827\pi\) | |||||||
\(812\) | −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 | −0.748475 | − | 0.663163i | \(-0.769214\pi\) |
0.200078 | + | 0.979780i | \(0.435880\pi\) | |||||||
\(822\) | 0.159541 | + | 0.276333i | 0.00556463 | + | 0.00963821i | ||||
\(823\) | −0.275929 | + | 0.477923i | −0.00961827 | + | 0.0166593i | −0.870794 | − | 0.491647i | \(-0.836395\pi\) |
0.861176 | + | 0.508307i | \(0.169728\pi\) | |||||||
\(824\) | − | 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 | 0.998614 | − | 0.0526352i | \(-0.0167620\pi\) |
−0.544890 | + | 0.838507i | \(0.683429\pi\) | |||||||
\(830\) | 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 | 0.969342 | − | 0.245717i | \(-0.0790235\pi\) |
0.271873 | + | 0.962333i | \(0.412357\pi\) | |||||||
\(840\) | 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 | \(-0.853701\pi\) | ||||
−0.896224 | + | 0.443601i | \(0.853701\pi\) | |||||||
\(858\) | −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 | \(-0.0517513\pi\) |
0.353226 | + | 0.935538i | \(0.385085\pi\) | |||||||
\(878\) | −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 | −0.999949 | − | 0.0101217i | \(-0.996778\pi\) |
0.491209 | − | 0.871042i | \(-0.336555\pi\) | |||||||
\(882\) | −1.38196 | + | 0.797877i | −0.0465331 | + | 0.0268659i | ||||
\(883\) | 22.0417 | 0.741761 | 0.370880 | − | 0.928681i | \(-0.379056\pi\) | ||||
0.370880 | + | 0.928681i | \(0.379056\pi\) | |||||||
\(884\) | 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 | \(-0.315119\pi\) |
−0.998363 | + | 0.0571915i | \(0.981785\pi\) | |||||||
\(888\) | 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 | \(-0.0396944\pi\) |
−0.603834 | + | 0.797110i | \(0.706361\pi\) | |||||||
\(908\) | 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 | 0.224743 | + | 0.974418i | \(0.427846\pi\) |
−0.956242 | + | 0.292576i | \(0.905488\pi\) | |||||||
\(920\) | 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 | 0.308729 | − | 0.951150i | \(-0.400096\pi\) |
−0.669355 | + | 0.742942i | \(0.733430\pi\) | |||||||
\(930\) | 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 | \(-0.215771\pi\) | ||||
0.778915 | + | 0.627130i | \(0.215771\pi\) | |||||||
\(938\) | 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 | \(0.340890\pi\) | ||||
−0.479301 | + | 0.877650i | \(0.659110\pi\) | |||||||
\(942\) | 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 | \(-0.516839\pi\) |
0.838376 | + | 0.545093i | \(0.183505\pi\) | |||||||
\(948\) | −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 | 0.00757307 | + | 0.999971i | \(0.497589\pi\) |
−0.869787 | + | 0.493427i | \(0.835744\pi\) | |||||||
\(954\) | − | 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 | −0.0287154 | − | 0.999588i | \(-0.509142\pi\) |
0.880026 | − | 0.474926i | \(-0.157525\pi\) | |||||||
\(972\) | 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 | −0.596605 | + | 0.802535i | \(0.703484\pi\) |
−0.993318 | + | 0.115408i | \(0.963183\pi\) | |||||||
\(978\) | 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 | 0.994920 | − | 0.100670i | \(-0.0320987\pi\) |
−0.584643 | + | 0.811291i | \(0.698765\pi\) | |||||||
\(992\) | 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 | \(-0.955046\pi\) |
0.616923 | + | 0.787024i | \(0.288379\pi\) | |||||||
\(998\) | 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.e.751.3 | ✓ | 8 | |
5.2 | odd | 4 | 1950.2.y.l.49.2 | 8 | |||
5.3 | odd | 4 | 1950.2.y.i.49.3 | 8 | |||
5.4 | even | 2 | 1950.2.bc.f.751.2 | yes | 8 | ||
13.4 | even | 6 | inner | 1950.2.bc.e.901.3 | yes | 8 | |
65.4 | even | 6 | 1950.2.bc.f.901.2 | yes | 8 | ||
65.17 | odd | 12 | 1950.2.y.i.199.3 | 8 | |||
65.43 | odd | 12 | 1950.2.y.l.199.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1950.2.y.i.49.3 | 8 | 5.3 | odd | 4 | |||
1950.2.y.i.199.3 | 8 | 65.17 | odd | 12 | |||
1950.2.y.l.49.2 | 8 | 5.2 | odd | 4 | |||
1950.2.y.l.199.2 | 8 | 65.43 | odd | 12 | |||
1950.2.bc.e.751.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
1950.2.bc.e.901.3 | yes | 8 | 13.4 | even | 6 | inner | |
1950.2.bc.f.751.2 | yes | 8 | 5.4 | even | 2 | ||
1950.2.bc.f.901.2 | yes | 8 | 65.4 | even | 6 |