Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [185,2,Mod(68,185)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(185, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("185.68");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 185 = 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 185.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.47723243739\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} + 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 117.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 185.117 |
Dual form | 185.2.k.b.68.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/185\mathbb{Z}\right)^\times\).
\(n\) | \(76\) | \(112\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | −0.353553 | − | 0.935414i | \(-0.615027\pi\) | ||||
−0.353553 | + | 0.935414i | \(0.615027\pi\) | |||||||
\(3\) | 1.00000 | + | 1.00000i | 0.577350 | + | 0.577350i | 0.934172 | − | 0.356822i | \(-0.116140\pi\) |
−0.356822 | + | 0.934172i | \(0.616140\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.00000 | − | 2.00000i | −0.447214 | − | 0.894427i | ||||
\(6\) | −1.00000 | − | 1.00000i | −0.408248 | − | 0.408248i | ||||
\(7\) | −3.00000 | − | 3.00000i | −1.13389 | − | 1.13389i | −0.989524 | − | 0.144370i | \(-0.953885\pi\) |
−0.144370 | − | 0.989524i | \(-0.546115\pi\) | |||||||
\(8\) | 3.00000 | 1.06066 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 1.00000 | + | 2.00000i | 0.316228 | + | 0.632456i | ||||
\(11\) | − | 2.00000i | − | 0.603023i | −0.953463 | − | 0.301511i | \(-0.902509\pi\) | ||
0.953463 | − | 0.301511i | \(-0.0974911\pi\) | |||||||
\(12\) | −1.00000 | − | 1.00000i | −0.288675 | − | 0.288675i | ||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 3.00000 | + | 3.00000i | 0.801784 | + | 0.801784i | ||||
\(15\) | 1.00000 | − | 3.00000i | 0.258199 | − | 0.774597i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 4.00000i | 0.970143i | 0.874475 | + | 0.485071i | \(0.161206\pi\) | ||||
−0.874475 | + | 0.485071i | \(0.838794\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 3.00000 | − | 3.00000i | 0.688247 | − | 0.688247i | −0.273597 | − | 0.961844i | \(-0.588214\pi\) |
0.961844 | + | 0.273597i | \(0.0882135\pi\) | |||||||
\(20\) | 1.00000 | + | 2.00000i | 0.223607 | + | 0.447214i | ||||
\(21\) | − | 6.00000i | − | 1.30931i | ||||||
\(22\) | 2.00000i | 0.426401i | ||||||||
\(23\) | −8.00000 | −1.66812 | −0.834058 | − | 0.551677i | \(-0.813988\pi\) | ||||
−0.834058 | + | 0.551677i | \(0.813988\pi\) | |||||||
\(24\) | 3.00000 | + | 3.00000i | 0.612372 | + | 0.612372i | ||||
\(25\) | −3.00000 | + | 4.00000i | −0.600000 | + | 0.800000i | ||||
\(26\) | −2.00000 | −0.392232 | ||||||||
\(27\) | 4.00000 | − | 4.00000i | 0.769800 | − | 0.769800i | ||||
\(28\) | 3.00000 | + | 3.00000i | 0.566947 | + | 0.566947i | ||||
\(29\) | −7.00000 | − | 7.00000i | −1.29987 | − | 1.29987i | −0.928477 | − | 0.371391i | \(-0.878881\pi\) |
−0.371391 | − | 0.928477i | \(-0.621119\pi\) | |||||||
\(30\) | −1.00000 | + | 3.00000i | −0.182574 | + | 0.547723i | ||||
\(31\) | 3.00000 | − | 3.00000i | 0.538816 | − | 0.538816i | −0.384365 | − | 0.923181i | \(-0.625580\pi\) |
0.923181 | + | 0.384365i | \(0.125580\pi\) | |||||||
\(32\) | −5.00000 | −0.883883 | ||||||||
\(33\) | 2.00000 | − | 2.00000i | 0.348155 | − | 0.348155i | ||||
\(34\) | − | 4.00000i | − | 0.685994i | ||||||
\(35\) | −3.00000 | + | 9.00000i | −0.507093 | + | 1.52128i | ||||
\(36\) | 1.00000i | 0.166667i | ||||||||
\(37\) | −1.00000 | + | 6.00000i | −0.164399 | + | 0.986394i | ||||
\(38\) | −3.00000 | + | 3.00000i | −0.486664 | + | 0.486664i | ||||
\(39\) | 2.00000 | + | 2.00000i | 0.320256 | + | 0.320256i | ||||
\(40\) | −3.00000 | − | 6.00000i | −0.474342 | − | 0.948683i | ||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 6.00000i | 0.925820i | ||||||||
\(43\) | 12.0000 | 1.82998 | 0.914991 | − | 0.403473i | \(-0.132197\pi\) | ||||
0.914991 | + | 0.403473i | \(0.132197\pi\) | |||||||
\(44\) | 2.00000i | 0.301511i | ||||||||
\(45\) | −2.00000 | + | 1.00000i | −0.298142 | + | 0.149071i | ||||
\(46\) | 8.00000 | 1.17954 | ||||||||
\(47\) | 5.00000 | + | 5.00000i | 0.729325 | + | 0.729325i | 0.970485 | − | 0.241160i | \(-0.0775280\pi\) |
−0.241160 | + | 0.970485i | \(0.577528\pi\) | |||||||
\(48\) | −1.00000 | − | 1.00000i | −0.144338 | − | 0.144338i | ||||
\(49\) | 11.0000i | 1.57143i | ||||||||
\(50\) | 3.00000 | − | 4.00000i | 0.424264 | − | 0.565685i | ||||
\(51\) | −4.00000 | + | 4.00000i | −0.560112 | + | 0.560112i | ||||
\(52\) | −2.00000 | −0.277350 | ||||||||
\(53\) | −3.00000 | + | 3.00000i | −0.412082 | + | 0.412082i | −0.882463 | − | 0.470381i | \(-0.844116\pi\) |
0.470381 | + | 0.882463i | \(0.344116\pi\) | |||||||
\(54\) | −4.00000 | + | 4.00000i | −0.544331 | + | 0.544331i | ||||
\(55\) | −4.00000 | + | 2.00000i | −0.539360 | + | 0.269680i | ||||
\(56\) | −9.00000 | − | 9.00000i | −1.20268 | − | 1.20268i | ||||
\(57\) | 6.00000 | 0.794719 | ||||||||
\(58\) | 7.00000 | + | 7.00000i | 0.919145 | + | 0.919145i | ||||
\(59\) | 7.00000 | − | 7.00000i | 0.911322 | − | 0.911322i | −0.0850540 | − | 0.996376i | \(-0.527106\pi\) |
0.996376 | + | 0.0850540i | \(0.0271063\pi\) | |||||||
\(60\) | −1.00000 | + | 3.00000i | −0.129099 | + | 0.387298i | ||||
\(61\) | 1.00000 | − | 1.00000i | 0.128037 | − | 0.128037i | −0.640184 | − | 0.768221i | \(-0.721142\pi\) |
0.768221 | + | 0.640184i | \(0.221142\pi\) | |||||||
\(62\) | −3.00000 | + | 3.00000i | −0.381000 | + | 0.381000i | ||||
\(63\) | −3.00000 | + | 3.00000i | −0.377964 | + | 0.377964i | ||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | −2.00000 | − | 4.00000i | −0.248069 | − | 0.496139i | ||||
\(66\) | −2.00000 | + | 2.00000i | −0.246183 | + | 0.246183i | ||||
\(67\) | 3.00000 | − | 3.00000i | 0.366508 | − | 0.366508i | −0.499694 | − | 0.866202i | \(-0.666554\pi\) |
0.866202 | + | 0.499694i | \(0.166554\pi\) | |||||||
\(68\) | − | 4.00000i | − | 0.485071i | ||||||
\(69\) | −8.00000 | − | 8.00000i | −0.963087 | − | 0.963087i | ||||
\(70\) | 3.00000 | − | 9.00000i | 0.358569 | − | 1.07571i | ||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | − | 3.00000i | − | 0.353553i | ||||||
\(73\) | 1.00000 | + | 1.00000i | 0.117041 | + | 0.117041i | 0.763202 | − | 0.646160i | \(-0.223626\pi\) |
−0.646160 | + | 0.763202i | \(0.723626\pi\) | |||||||
\(74\) | 1.00000 | − | 6.00000i | 0.116248 | − | 0.697486i | ||||
\(75\) | −7.00000 | + | 1.00000i | −0.808290 | + | 0.115470i | ||||
\(76\) | −3.00000 | + | 3.00000i | −0.344124 | + | 0.344124i | ||||
\(77\) | −6.00000 | + | 6.00000i | −0.683763 | + | 0.683763i | ||||
\(78\) | −2.00000 | − | 2.00000i | −0.226455 | − | 0.226455i | ||||
\(79\) | 3.00000 | − | 3.00000i | 0.337526 | − | 0.337526i | −0.517909 | − | 0.855436i | \(-0.673290\pi\) |
0.855436 | + | 0.517909i | \(0.173290\pi\) | |||||||
\(80\) | 1.00000 | + | 2.00000i | 0.111803 | + | 0.223607i | ||||
\(81\) | 5.00000 | 0.555556 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.00000 | + | 5.00000i | −0.548821 | + | 0.548821i | −0.926100 | − | 0.377279i | \(-0.876860\pi\) |
0.377279 | + | 0.926100i | \(0.376860\pi\) | |||||||
\(84\) | 6.00000i | 0.654654i | ||||||||
\(85\) | 8.00000 | − | 4.00000i | 0.867722 | − | 0.433861i | ||||
\(86\) | −12.0000 | −1.29399 | ||||||||
\(87\) | − | 14.0000i | − | 1.50096i | ||||||
\(88\) | − | 6.00000i | − | 0.639602i | ||||||
\(89\) | 5.00000 | + | 5.00000i | 0.529999 | + | 0.529999i | 0.920572 | − | 0.390573i | \(-0.127723\pi\) |
−0.390573 | + | 0.920572i | \(0.627723\pi\) | |||||||
\(90\) | 2.00000 | − | 1.00000i | 0.210819 | − | 0.105409i | ||||
\(91\) | −6.00000 | − | 6.00000i | −0.628971 | − | 0.628971i | ||||
\(92\) | 8.00000 | 0.834058 | ||||||||
\(93\) | 6.00000 | 0.622171 | ||||||||
\(94\) | −5.00000 | − | 5.00000i | −0.515711 | − | 0.515711i | ||||
\(95\) | −9.00000 | − | 3.00000i | −0.923381 | − | 0.307794i | ||||
\(96\) | −5.00000 | − | 5.00000i | −0.510310 | − | 0.510310i | ||||
\(97\) | − | 8.00000i | − | 0.812277i | −0.913812 | − | 0.406138i | \(-0.866875\pi\) | ||
0.913812 | − | 0.406138i | \(-0.133125\pi\) | |||||||
\(98\) | − | 11.0000i | − | 1.11117i | ||||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | 3.00000 | − | 4.00000i | 0.300000 | − | 0.400000i | ||||
\(101\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(102\) | 4.00000 | − | 4.00000i | 0.396059 | − | 0.396059i | ||||
\(103\) | − | 14.0000i | − | 1.37946i | −0.724066 | − | 0.689730i | \(-0.757729\pi\) | ||
0.724066 | − | 0.689730i | \(-0.242271\pi\) | |||||||
\(104\) | 6.00000 | 0.588348 | ||||||||
\(105\) | −12.0000 | + | 6.00000i | −1.17108 | + | 0.585540i | ||||
\(106\) | 3.00000 | − | 3.00000i | 0.291386 | − | 0.291386i | ||||
\(107\) | −3.00000 | − | 3.00000i | −0.290021 | − | 0.290021i | 0.547068 | − | 0.837088i | \(-0.315744\pi\) |
−0.837088 | + | 0.547068i | \(0.815744\pi\) | |||||||
\(108\) | −4.00000 | + | 4.00000i | −0.384900 | + | 0.384900i | ||||
\(109\) | −3.00000 | + | 3.00000i | −0.287348 | + | 0.287348i | −0.836031 | − | 0.548683i | \(-0.815129\pi\) |
0.548683 | + | 0.836031i | \(0.315129\pi\) | |||||||
\(110\) | 4.00000 | − | 2.00000i | 0.381385 | − | 0.190693i | ||||
\(111\) | −7.00000 | + | 5.00000i | −0.664411 | + | 0.474579i | ||||
\(112\) | 3.00000 | + | 3.00000i | 0.283473 | + | 0.283473i | ||||
\(113\) | − | 4.00000i | − | 0.376288i | −0.982141 | − | 0.188144i | \(-0.939753\pi\) | ||
0.982141 | − | 0.188144i | \(-0.0602472\pi\) | |||||||
\(114\) | −6.00000 | −0.561951 | ||||||||
\(115\) | 8.00000 | + | 16.0000i | 0.746004 | + | 1.49201i | ||||
\(116\) | 7.00000 | + | 7.00000i | 0.649934 | + | 0.649934i | ||||
\(117\) | − | 2.00000i | − | 0.184900i | ||||||
\(118\) | −7.00000 | + | 7.00000i | −0.644402 | + | 0.644402i | ||||
\(119\) | 12.0000 | − | 12.0000i | 1.10004 | − | 1.10004i | ||||
\(120\) | 3.00000 | − | 9.00000i | 0.273861 | − | 0.821584i | ||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | −1.00000 | + | 1.00000i | −0.0905357 | + | 0.0905357i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.00000 | + | 3.00000i | −0.269408 | + | 0.269408i | ||||
\(125\) | 11.0000 | + | 2.00000i | 0.983870 | + | 0.178885i | ||||
\(126\) | 3.00000 | − | 3.00000i | 0.267261 | − | 0.267261i | ||||
\(127\) | 9.00000 | + | 9.00000i | 0.798621 | + | 0.798621i | 0.982878 | − | 0.184257i | \(-0.0589879\pi\) |
−0.184257 | + | 0.982878i | \(0.558988\pi\) | |||||||
\(128\) | 3.00000 | 0.265165 | ||||||||
\(129\) | 12.0000 | + | 12.0000i | 1.05654 | + | 1.05654i | ||||
\(130\) | 2.00000 | + | 4.00000i | 0.175412 | + | 0.350823i | ||||
\(131\) | −5.00000 | + | 5.00000i | −0.436852 | + | 0.436852i | −0.890951 | − | 0.454099i | \(-0.849961\pi\) |
0.454099 | + | 0.890951i | \(0.349961\pi\) | |||||||
\(132\) | −2.00000 | + | 2.00000i | −0.174078 | + | 0.174078i | ||||
\(133\) | −18.0000 | −1.56080 | ||||||||
\(134\) | −3.00000 | + | 3.00000i | −0.259161 | + | 0.259161i | ||||
\(135\) | −12.0000 | − | 4.00000i | −1.03280 | − | 0.344265i | ||||
\(136\) | 12.0000i | 1.02899i | ||||||||
\(137\) | −7.00000 | − | 7.00000i | −0.598050 | − | 0.598050i | 0.341743 | − | 0.939793i | \(-0.388983\pi\) |
−0.939793 | + | 0.341743i | \(0.888983\pi\) | |||||||
\(138\) | 8.00000 | + | 8.00000i | 0.681005 | + | 0.681005i | ||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 3.00000 | − | 9.00000i | 0.253546 | − | 0.760639i | ||||
\(141\) | 10.0000i | 0.842152i | ||||||||
\(142\) | −8.00000 | −0.671345 | ||||||||
\(143\) | − | 4.00000i | − | 0.334497i | ||||||
\(144\) | 1.00000i | 0.0833333i | ||||||||
\(145\) | −7.00000 | + | 21.0000i | −0.581318 | + | 1.74396i | ||||
\(146\) | −1.00000 | − | 1.00000i | −0.0827606 | − | 0.0827606i | ||||
\(147\) | −11.0000 | + | 11.0000i | −0.907265 | + | 0.907265i | ||||
\(148\) | 1.00000 | − | 6.00000i | 0.0821995 | − | 0.493197i | ||||
\(149\) | 16.0000i | 1.31077i | 0.755295 | + | 0.655386i | \(0.227494\pi\) | ||||
−0.755295 | + | 0.655386i | \(0.772506\pi\) | |||||||
\(150\) | 7.00000 | − | 1.00000i | 0.571548 | − | 0.0816497i | ||||
\(151\) | 2.00000i | 0.162758i | 0.996683 | + | 0.0813788i | \(0.0259324\pi\) | ||||
−0.996683 | + | 0.0813788i | \(0.974068\pi\) | |||||||
\(152\) | 9.00000 | − | 9.00000i | 0.729996 | − | 0.729996i | ||||
\(153\) | 4.00000 | 0.323381 | ||||||||
\(154\) | 6.00000 | − | 6.00000i | 0.483494 | − | 0.483494i | ||||
\(155\) | −9.00000 | − | 3.00000i | −0.722897 | − | 0.240966i | ||||
\(156\) | −2.00000 | − | 2.00000i | −0.160128 | − | 0.160128i | ||||
\(157\) | −3.00000 | − | 3.00000i | −0.239426 | − | 0.239426i | 0.577186 | − | 0.816612i | \(-0.304151\pi\) |
−0.816612 | + | 0.577186i | \(0.804151\pi\) | |||||||
\(158\) | −3.00000 | + | 3.00000i | −0.238667 | + | 0.238667i | ||||
\(159\) | −6.00000 | −0.475831 | ||||||||
\(160\) | 5.00000 | + | 10.0000i | 0.395285 | + | 0.790569i | ||||
\(161\) | 24.0000 | + | 24.0000i | 1.89146 | + | 1.89146i | ||||
\(162\) | −5.00000 | −0.392837 | ||||||||
\(163\) | − | 10.0000i | − | 0.783260i | −0.920123 | − | 0.391630i | \(-0.871911\pi\) | ||
0.920123 | − | 0.391630i | \(-0.128089\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.00000 | − | 2.00000i | −0.467099 | − | 0.155700i | ||||
\(166\) | 5.00000 | − | 5.00000i | 0.388075 | − | 0.388075i | ||||
\(167\) | − | 6.00000i | − | 0.464294i | −0.972681 | − | 0.232147i | \(-0.925425\pi\) | ||
0.972681 | − | 0.232147i | \(-0.0745750\pi\) | |||||||
\(168\) | − | 18.0000i | − | 1.38873i | ||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | −8.00000 | + | 4.00000i | −0.613572 | + | 0.306786i | ||||
\(171\) | −3.00000 | − | 3.00000i | −0.229416 | − | 0.229416i | ||||
\(172\) | −12.0000 | −0.914991 | ||||||||
\(173\) | 1.00000 | + | 1.00000i | 0.0760286 | + | 0.0760286i | 0.744099 | − | 0.668070i | \(-0.232879\pi\) |
−0.668070 | + | 0.744099i | \(0.732879\pi\) | |||||||
\(174\) | 14.0000i | 1.06134i | ||||||||
\(175\) | 21.0000 | − | 3.00000i | 1.58745 | − | 0.226779i | ||||
\(176\) | 2.00000i | 0.150756i | ||||||||
\(177\) | 14.0000 | 1.05230 | ||||||||
\(178\) | −5.00000 | − | 5.00000i | −0.374766 | − | 0.374766i | ||||
\(179\) | −7.00000 | − | 7.00000i | −0.523205 | − | 0.523205i | 0.395333 | − | 0.918538i | \(-0.370629\pi\) |
−0.918538 | + | 0.395333i | \(0.870629\pi\) | |||||||
\(180\) | 2.00000 | − | 1.00000i | 0.149071 | − | 0.0745356i | ||||
\(181\) | 10.0000 | 0.743294 | 0.371647 | − | 0.928374i | \(-0.378793\pi\) | ||||
0.371647 | + | 0.928374i | \(0.378793\pi\) | |||||||
\(182\) | 6.00000 | + | 6.00000i | 0.444750 | + | 0.444750i | ||||
\(183\) | 2.00000 | 0.147844 | ||||||||
\(184\) | −24.0000 | −1.76930 | ||||||||
\(185\) | 13.0000 | − | 4.00000i | 0.955779 | − | 0.294086i | ||||
\(186\) | −6.00000 | −0.439941 | ||||||||
\(187\) | 8.00000 | 0.585018 | ||||||||
\(188\) | −5.00000 | − | 5.00000i | −0.364662 | − | 0.364662i | ||||
\(189\) | −24.0000 | −1.74574 | ||||||||
\(190\) | 9.00000 | + | 3.00000i | 0.652929 | + | 0.217643i | ||||
\(191\) | −11.0000 | − | 11.0000i | −0.795932 | − | 0.795932i | 0.186519 | − | 0.982451i | \(-0.440279\pi\) |
−0.982451 | + | 0.186519i | \(0.940279\pi\) | |||||||
\(192\) | 7.00000 | + | 7.00000i | 0.505181 | + | 0.505181i | ||||
\(193\) | 2.00000 | 0.143963 | 0.0719816 | − | 0.997406i | \(-0.477068\pi\) | ||||
0.0719816 | + | 0.997406i | \(0.477068\pi\) | |||||||
\(194\) | 8.00000i | 0.574367i | ||||||||
\(195\) | 2.00000 | − | 6.00000i | 0.143223 | − | 0.429669i | ||||
\(196\) | − | 11.0000i | − | 0.785714i | ||||||
\(197\) | 1.00000 | + | 1.00000i | 0.0712470 | + | 0.0712470i | 0.741832 | − | 0.670585i | \(-0.233957\pi\) |
−0.670585 | + | 0.741832i | \(0.733957\pi\) | |||||||
\(198\) | 2.00000 | 0.142134 | ||||||||
\(199\) | −15.0000 | − | 15.0000i | −1.06332 | − | 1.06332i | −0.997855 | − | 0.0654671i | \(-0.979146\pi\) |
−0.0654671 | − | 0.997855i | \(-0.520854\pi\) | |||||||
\(200\) | −9.00000 | + | 12.0000i | −0.636396 | + | 0.848528i | ||||
\(201\) | 6.00000 | 0.423207 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 42.0000i | 2.94782i | ||||||||
\(204\) | 4.00000 | − | 4.00000i | 0.280056 | − | 0.280056i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 14.0000i | 0.975426i | ||||||||
\(207\) | 8.00000i | 0.556038i | ||||||||
\(208\) | −2.00000 | −0.138675 | ||||||||
\(209\) | −6.00000 | − | 6.00000i | −0.415029 | − | 0.415029i | ||||
\(210\) | 12.0000 | − | 6.00000i | 0.828079 | − | 0.414039i | ||||
\(211\) | 20.0000 | 1.37686 | 0.688428 | − | 0.725304i | \(-0.258301\pi\) | ||||
0.688428 | + | 0.725304i | \(0.258301\pi\) | |||||||
\(212\) | 3.00000 | − | 3.00000i | 0.206041 | − | 0.206041i | ||||
\(213\) | 8.00000 | + | 8.00000i | 0.548151 | + | 0.548151i | ||||
\(214\) | 3.00000 | + | 3.00000i | 0.205076 | + | 0.205076i | ||||
\(215\) | −12.0000 | − | 24.0000i | −0.818393 | − | 1.63679i | ||||
\(216\) | 12.0000 | − | 12.0000i | 0.816497 | − | 0.816497i | ||||
\(217\) | −18.0000 | −1.22192 | ||||||||
\(218\) | 3.00000 | − | 3.00000i | 0.203186 | − | 0.203186i | ||||
\(219\) | 2.00000i | 0.135147i | ||||||||
\(220\) | 4.00000 | − | 2.00000i | 0.269680 | − | 0.134840i | ||||
\(221\) | 8.00000i | 0.538138i | ||||||||
\(222\) | 7.00000 | − | 5.00000i | 0.469809 | − | 0.335578i | ||||
\(223\) | −1.00000 | + | 1.00000i | −0.0669650 | + | 0.0669650i | −0.739796 | − | 0.672831i | \(-0.765078\pi\) |
0.672831 | + | 0.739796i | \(0.265078\pi\) | |||||||
\(224\) | 15.0000 | + | 15.0000i | 1.00223 | + | 1.00223i | ||||
\(225\) | 4.00000 | + | 3.00000i | 0.266667 | + | 0.200000i | ||||
\(226\) | 4.00000i | 0.266076i | ||||||||
\(227\) | − | 2.00000i | − | 0.132745i | −0.997795 | − | 0.0663723i | \(-0.978857\pi\) | ||
0.997795 | − | 0.0663723i | \(-0.0211425\pi\) | |||||||
\(228\) | −6.00000 | −0.397360 | ||||||||
\(229\) | 4.00000i | 0.264327i | 0.991228 | + | 0.132164i | \(0.0421925\pi\) | ||||
−0.991228 | + | 0.132164i | \(0.957808\pi\) | |||||||
\(230\) | −8.00000 | − | 16.0000i | −0.527504 | − | 1.05501i | ||||
\(231\) | −12.0000 | −0.789542 | ||||||||
\(232\) | −21.0000 | − | 21.0000i | −1.37872 | − | 1.37872i | ||||
\(233\) | 1.00000 | + | 1.00000i | 0.0655122 | + | 0.0655122i | 0.739104 | − | 0.673592i | \(-0.235249\pi\) |
−0.673592 | + | 0.739104i | \(0.735249\pi\) | |||||||
\(234\) | 2.00000i | 0.130744i | ||||||||
\(235\) | 5.00000 | − | 15.0000i | 0.326164 | − | 0.978492i | ||||
\(236\) | −7.00000 | + | 7.00000i | −0.455661 | + | 0.455661i | ||||
\(237\) | 6.00000 | 0.389742 | ||||||||
\(238\) | −12.0000 | + | 12.0000i | −0.777844 | + | 0.777844i | ||||
\(239\) | 7.00000 | − | 7.00000i | 0.452792 | − | 0.452792i | −0.443488 | − | 0.896280i | \(-0.646259\pi\) |
0.896280 | + | 0.443488i | \(0.146259\pi\) | |||||||
\(240\) | −1.00000 | + | 3.00000i | −0.0645497 | + | 0.193649i | ||||
\(241\) | 1.00000 | + | 1.00000i | 0.0644157 | + | 0.0644157i | 0.738581 | − | 0.674165i | \(-0.235496\pi\) |
−0.674165 | + | 0.738581i | \(0.735496\pi\) | |||||||
\(242\) | −7.00000 | −0.449977 | ||||||||
\(243\) | −7.00000 | − | 7.00000i | −0.449050 | − | 0.449050i | ||||
\(244\) | −1.00000 | + | 1.00000i | −0.0640184 | + | 0.0640184i | ||||
\(245\) | 22.0000 | − | 11.0000i | 1.40553 | − | 0.702764i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.00000 | − | 6.00000i | 0.381771 | − | 0.381771i | ||||
\(248\) | 9.00000 | − | 9.00000i | 0.571501 | − | 0.571501i | ||||
\(249\) | −10.0000 | −0.633724 | ||||||||
\(250\) | −11.0000 | − | 2.00000i | −0.695701 | − | 0.126491i | ||||
\(251\) | −5.00000 | + | 5.00000i | −0.315597 | + | 0.315597i | −0.847073 | − | 0.531476i | \(-0.821638\pi\) |
0.531476 | + | 0.847073i | \(0.321638\pi\) | |||||||
\(252\) | 3.00000 | − | 3.00000i | 0.188982 | − | 0.188982i | ||||
\(253\) | 16.0000i | 1.00591i | ||||||||
\(254\) | −9.00000 | − | 9.00000i | −0.564710 | − | 0.564710i | ||||
\(255\) | 12.0000 | + | 4.00000i | 0.751469 | + | 0.250490i | ||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | 28.0000i | 1.74659i | 0.487190 | + | 0.873296i | \(0.338022\pi\) | ||||
−0.487190 | + | 0.873296i | \(0.661978\pi\) | |||||||
\(258\) | −12.0000 | − | 12.0000i | −0.747087 | − | 0.747087i | ||||
\(259\) | 21.0000 | − | 15.0000i | 1.30488 | − | 0.932055i | ||||
\(260\) | 2.00000 | + | 4.00000i | 0.124035 | + | 0.248069i | ||||
\(261\) | −7.00000 | + | 7.00000i | −0.433289 | + | 0.433289i | ||||
\(262\) | 5.00000 | − | 5.00000i | 0.308901 | − | 0.308901i | ||||
\(263\) | −7.00000 | − | 7.00000i | −0.431638 | − | 0.431638i | 0.457547 | − | 0.889185i | \(-0.348728\pi\) |
−0.889185 | + | 0.457547i | \(0.848728\pi\) | |||||||
\(264\) | 6.00000 | − | 6.00000i | 0.369274 | − | 0.369274i | ||||
\(265\) | 9.00000 | + | 3.00000i | 0.552866 | + | 0.184289i | ||||
\(266\) | 18.0000 | 1.10365 | ||||||||
\(267\) | 10.0000i | 0.611990i | ||||||||
\(268\) | −3.00000 | + | 3.00000i | −0.183254 | + | 0.183254i | ||||
\(269\) | − | 16.0000i | − | 0.975537i | −0.872973 | − | 0.487769i | \(-0.837811\pi\) | ||
0.872973 | − | 0.487769i | \(-0.162189\pi\) | |||||||
\(270\) | 12.0000 | + | 4.00000i | 0.730297 | + | 0.243432i | ||||
\(271\) | −8.00000 | −0.485965 | −0.242983 | − | 0.970031i | \(-0.578126\pi\) | ||||
−0.242983 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(272\) | − | 4.00000i | − | 0.242536i | ||||||
\(273\) | − | 12.0000i | − | 0.726273i | ||||||
\(274\) | 7.00000 | + | 7.00000i | 0.422885 | + | 0.422885i | ||||
\(275\) | 8.00000 | + | 6.00000i | 0.482418 | + | 0.361814i | ||||
\(276\) | 8.00000 | + | 8.00000i | 0.481543 | + | 0.481543i | ||||
\(277\) | 26.0000 | 1.56219 | 0.781094 | − | 0.624413i | \(-0.214662\pi\) | ||||
0.781094 | + | 0.624413i | \(0.214662\pi\) | |||||||
\(278\) | −4.00000 | −0.239904 | ||||||||
\(279\) | −3.00000 | − | 3.00000i | −0.179605 | − | 0.179605i | ||||
\(280\) | −9.00000 | + | 27.0000i | −0.537853 | + | 1.61356i | ||||
\(281\) | 9.00000 | + | 9.00000i | 0.536895 | + | 0.536895i | 0.922616 | − | 0.385721i | \(-0.126047\pi\) |
−0.385721 | + | 0.922616i | \(0.626047\pi\) | |||||||
\(282\) | − | 10.0000i | − | 0.595491i | ||||||
\(283\) | 22.0000i | 1.30776i | 0.756596 | + | 0.653882i | \(0.226861\pi\) | ||||
−0.756596 | + | 0.653882i | \(0.773139\pi\) | |||||||
\(284\) | −8.00000 | −0.474713 | ||||||||
\(285\) | −6.00000 | − | 12.0000i | −0.355409 | − | 0.710819i | ||||
\(286\) | 4.00000i | 0.236525i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 5.00000i | 0.294628i | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 7.00000 | − | 21.0000i | 0.411054 | − | 1.23316i | ||||
\(291\) | 8.00000 | − | 8.00000i | 0.468968 | − | 0.468968i | ||||
\(292\) | −1.00000 | − | 1.00000i | −0.0585206 | − | 0.0585206i | ||||
\(293\) | 1.00000 | − | 1.00000i | 0.0584206 | − | 0.0584206i | −0.677293 | − | 0.735714i | \(-0.736847\pi\) |
0.735714 | + | 0.677293i | \(0.236847\pi\) | |||||||
\(294\) | 11.0000 | − | 11.0000i | 0.641533 | − | 0.641533i | ||||
\(295\) | −21.0000 | − | 7.00000i | −1.22267 | − | 0.407556i | ||||
\(296\) | −3.00000 | + | 18.0000i | −0.174371 | + | 1.04623i | ||||
\(297\) | −8.00000 | − | 8.00000i | −0.464207 | − | 0.464207i | ||||
\(298\) | − | 16.0000i | − | 0.926855i | ||||||
\(299\) | −16.0000 | −0.925304 | ||||||||
\(300\) | 7.00000 | − | 1.00000i | 0.404145 | − | 0.0577350i | ||||
\(301\) | −36.0000 | − | 36.0000i | −2.07501 | − | 2.07501i | ||||
\(302\) | − | 2.00000i | − | 0.115087i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.00000 | + | 3.00000i | −0.172062 | + | 0.172062i | ||||
\(305\) | −3.00000 | − | 1.00000i | −0.171780 | − | 0.0572598i | ||||
\(306\) | −4.00000 | −0.228665 | ||||||||
\(307\) | −9.00000 | + | 9.00000i | −0.513657 | + | 0.513657i | −0.915645 | − | 0.401988i | \(-0.868319\pi\) |
0.401988 | + | 0.915645i | \(0.368319\pi\) | |||||||
\(308\) | 6.00000 | − | 6.00000i | 0.341882 | − | 0.341882i | ||||
\(309\) | 14.0000 | − | 14.0000i | 0.796432 | − | 0.796432i | ||||
\(310\) | 9.00000 | + | 3.00000i | 0.511166 | + | 0.170389i | ||||
\(311\) | 3.00000 | − | 3.00000i | 0.170114 | − | 0.170114i | −0.616915 | − | 0.787030i | \(-0.711618\pi\) |
0.787030 | + | 0.616915i | \(0.211618\pi\) | |||||||
\(312\) | 6.00000 | + | 6.00000i | 0.339683 | + | 0.339683i | ||||
\(313\) | −30.0000 | −1.69570 | −0.847850 | − | 0.530236i | \(-0.822103\pi\) | ||||
−0.847850 | + | 0.530236i | \(0.822103\pi\) | |||||||
\(314\) | 3.00000 | + | 3.00000i | 0.169300 | + | 0.169300i | ||||
\(315\) | 9.00000 | + | 3.00000i | 0.507093 | + | 0.169031i | ||||
\(316\) | −3.00000 | + | 3.00000i | −0.168763 | + | 0.168763i | ||||
\(317\) | 17.0000 | − | 17.0000i | 0.954815 | − | 0.954815i | −0.0442073 | − | 0.999022i | \(-0.514076\pi\) |
0.999022 | + | 0.0442073i | \(0.0140762\pi\) | |||||||
\(318\) | 6.00000 | 0.336463 | ||||||||
\(319\) | −14.0000 | + | 14.0000i | −0.783850 | + | 0.783850i | ||||
\(320\) | −7.00000 | − | 14.0000i | −0.391312 | − | 0.782624i | ||||
\(321\) | − | 6.00000i | − | 0.334887i | ||||||
\(322\) | −24.0000 | − | 24.0000i | −1.33747 | − | 1.33747i | ||||
\(323\) | 12.0000 | + | 12.0000i | 0.667698 | + | 0.667698i | ||||
\(324\) | −5.00000 | −0.277778 | ||||||||
\(325\) | −6.00000 | + | 8.00000i | −0.332820 | + | 0.443760i | ||||
\(326\) | 10.0000i | 0.553849i | ||||||||
\(327\) | −6.00000 | −0.331801 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 30.0000i | − | 1.65395i | ||||||
\(330\) | 6.00000 | + | 2.00000i | 0.330289 | + | 0.110096i | ||||
\(331\) | −7.00000 | − | 7.00000i | −0.384755 | − | 0.384755i | 0.488057 | − | 0.872812i | \(-0.337706\pi\) |
−0.872812 | + | 0.488057i | \(0.837706\pi\) | |||||||
\(332\) | 5.00000 | − | 5.00000i | 0.274411 | − | 0.274411i | ||||
\(333\) | 6.00000 | + | 1.00000i | 0.328798 | + | 0.0547997i | ||||
\(334\) | 6.00000i | 0.328305i | ||||||||
\(335\) | −9.00000 | − | 3.00000i | −0.491723 | − | 0.163908i | ||||
\(336\) | 6.00000i | 0.327327i | ||||||||
\(337\) | −15.0000 | + | 15.0000i | −0.817102 | + | 0.817102i | −0.985687 | − | 0.168585i | \(-0.946080\pi\) |
0.168585 | + | 0.985687i | \(0.446080\pi\) | |||||||
\(338\) | 9.00000 | 0.489535 | ||||||||
\(339\) | 4.00000 | − | 4.00000i | 0.217250 | − | 0.217250i | ||||
\(340\) | −8.00000 | + | 4.00000i | −0.433861 | + | 0.216930i | ||||
\(341\) | −6.00000 | − | 6.00000i | −0.324918 | − | 0.324918i | ||||
\(342\) | 3.00000 | + | 3.00000i | 0.162221 | + | 0.162221i | ||||
\(343\) | 12.0000 | − | 12.0000i | 0.647939 | − | 0.647939i | ||||
\(344\) | 36.0000 | 1.94099 | ||||||||
\(345\) | −8.00000 | + | 24.0000i | −0.430706 | + | 1.29212i | ||||
\(346\) | −1.00000 | − | 1.00000i | −0.0537603 | − | 0.0537603i | ||||
\(347\) | 4.00000 | 0.214731 | 0.107366 | − | 0.994220i | \(-0.465758\pi\) | ||||
0.107366 | + | 0.994220i | \(0.465758\pi\) | |||||||
\(348\) | 14.0000i | 0.750479i | ||||||||
\(349\) | 32.0000i | 1.71292i | 0.516213 | + | 0.856460i | \(0.327341\pi\) | ||||
−0.516213 | + | 0.856460i | \(0.672659\pi\) | |||||||
\(350\) | −21.0000 | + | 3.00000i | −1.12250 | + | 0.160357i | ||||
\(351\) | 8.00000 | − | 8.00000i | 0.427008 | − | 0.427008i | ||||
\(352\) | 10.0000i | 0.533002i | ||||||||
\(353\) | − | 32.0000i | − | 1.70319i | −0.524202 | − | 0.851594i | \(-0.675636\pi\) | ||
0.524202 | − | 0.851594i | \(-0.324364\pi\) | |||||||
\(354\) | −14.0000 | −0.744092 | ||||||||
\(355\) | −8.00000 | − | 16.0000i | −0.424596 | − | 0.849192i | ||||
\(356\) | −5.00000 | − | 5.00000i | −0.264999 | − | 0.264999i | ||||
\(357\) | 24.0000 | 1.27021 | ||||||||
\(358\) | 7.00000 | + | 7.00000i | 0.369961 | + | 0.369961i | ||||
\(359\) | 34.0000i | 1.79445i | 0.441572 | + | 0.897226i | \(0.354421\pi\) | ||||
−0.441572 | + | 0.897226i | \(0.645579\pi\) | |||||||
\(360\) | −6.00000 | + | 3.00000i | −0.316228 | + | 0.158114i | ||||
\(361\) | 1.00000i | 0.0526316i | ||||||||
\(362\) | −10.0000 | −0.525588 | ||||||||
\(363\) | 7.00000 | + | 7.00000i | 0.367405 | + | 0.367405i | ||||
\(364\) | 6.00000 | + | 6.00000i | 0.314485 | + | 0.314485i | ||||
\(365\) | 1.00000 | − | 3.00000i | 0.0523424 | − | 0.157027i | ||||
\(366\) | −2.00000 | −0.104542 | ||||||||
\(367\) | 17.0000 | + | 17.0000i | 0.887393 | + | 0.887393i | 0.994272 | − | 0.106879i | \(-0.0340858\pi\) |
−0.106879 | + | 0.994272i | \(0.534086\pi\) | |||||||
\(368\) | 8.00000 | 0.417029 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −13.0000 | + | 4.00000i | −0.675838 | + | 0.207950i | ||||
\(371\) | 18.0000 | 0.934513 | ||||||||
\(372\) | −6.00000 | −0.311086 | ||||||||
\(373\) | −3.00000 | − | 3.00000i | −0.155334 | − | 0.155334i | 0.625161 | − | 0.780496i | \(-0.285033\pi\) |
−0.780496 | + | 0.625161i | \(0.785033\pi\) | |||||||
\(374\) | −8.00000 | −0.413670 | ||||||||
\(375\) | 9.00000 | + | 13.0000i | 0.464758 | + | 0.671317i | ||||
\(376\) | 15.0000 | + | 15.0000i | 0.773566 | + | 0.773566i | ||||
\(377\) | −14.0000 | − | 14.0000i | −0.721037 | − | 0.721037i | ||||
\(378\) | 24.0000 | 1.23443 | ||||||||
\(379\) | 14.0000i | 0.719132i | 0.933120 | + | 0.359566i | \(0.117075\pi\) | ||||
−0.933120 | + | 0.359566i | \(0.882925\pi\) | |||||||
\(380\) | 9.00000 | + | 3.00000i | 0.461690 | + | 0.153897i | ||||
\(381\) | 18.0000i | 0.922168i | ||||||||
\(382\) | 11.0000 | + | 11.0000i | 0.562809 | + | 0.562809i | ||||
\(383\) | 8.00000 | 0.408781 | 0.204390 | − | 0.978889i | \(-0.434479\pi\) | ||||
0.204390 | + | 0.978889i | \(0.434479\pi\) | |||||||
\(384\) | 3.00000 | + | 3.00000i | 0.153093 | + | 0.153093i | ||||
\(385\) | 18.0000 | + | 6.00000i | 0.917365 | + | 0.305788i | ||||
\(386\) | −2.00000 | −0.101797 | ||||||||
\(387\) | − | 12.0000i | − | 0.609994i | ||||||
\(388\) | 8.00000i | 0.406138i | ||||||||
\(389\) | 5.00000 | − | 5.00000i | 0.253510 | − | 0.253510i | −0.568898 | − | 0.822408i | \(-0.692630\pi\) |
0.822408 | + | 0.568898i | \(0.192630\pi\) | |||||||
\(390\) | −2.00000 | + | 6.00000i | −0.101274 | + | 0.303822i | ||||
\(391\) | − | 32.0000i | − | 1.61831i | ||||||
\(392\) | 33.0000i | 1.66675i | ||||||||
\(393\) | −10.0000 | −0.504433 | ||||||||
\(394\) | −1.00000 | − | 1.00000i | −0.0503793 | − | 0.0503793i | ||||
\(395\) | −9.00000 | − | 3.00000i | −0.452839 | − | 0.150946i | ||||
\(396\) | 2.00000 | 0.100504 | ||||||||
\(397\) | 5.00000 | − | 5.00000i | 0.250943 | − | 0.250943i | −0.570414 | − | 0.821357i | \(-0.693217\pi\) |
0.821357 | + | 0.570414i | \(0.193217\pi\) | |||||||
\(398\) | 15.0000 | + | 15.0000i | 0.751882 | + | 0.751882i | ||||
\(399\) | −18.0000 | − | 18.0000i | −0.901127 | − | 0.901127i | ||||
\(400\) | 3.00000 | − | 4.00000i | 0.150000 | − | 0.200000i | ||||
\(401\) | 1.00000 | − | 1.00000i | 0.0499376 | − | 0.0499376i | −0.681697 | − | 0.731635i | \(-0.738758\pi\) |
0.731635 | + | 0.681697i | \(0.238758\pi\) | |||||||
\(402\) | −6.00000 | −0.299253 | ||||||||
\(403\) | 6.00000 | − | 6.00000i | 0.298881 | − | 0.298881i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.00000 | − | 10.0000i | −0.248452 | − | 0.496904i | ||||
\(406\) | − | 42.0000i | − | 2.08443i | ||||||
\(407\) | 12.0000 | + | 2.00000i | 0.594818 | + | 0.0991363i | ||||
\(408\) | −12.0000 | + | 12.0000i | −0.594089 | + | 0.594089i | ||||
\(409\) | −3.00000 | − | 3.00000i | −0.148340 | − | 0.148340i | 0.629036 | − | 0.777376i | \(-0.283450\pi\) |
−0.777376 | + | 0.629036i | \(0.783450\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 14.0000i | − | 0.690569i | ||||||
\(412\) | 14.0000i | 0.689730i | ||||||||
\(413\) | −42.0000 | −2.06668 | ||||||||
\(414\) | − | 8.00000i | − | 0.393179i | ||||||
\(415\) | 15.0000 | + | 5.00000i | 0.736321 | + | 0.245440i | ||||
\(416\) | −10.0000 | −0.490290 | ||||||||
\(417\) | 4.00000 | + | 4.00000i | 0.195881 | + | 0.195881i | ||||
\(418\) | 6.00000 | + | 6.00000i | 0.293470 | + | 0.293470i | ||||
\(419\) | 22.0000i | 1.07477i | 0.843337 | + | 0.537385i | \(0.180588\pi\) | ||||
−0.843337 | + | 0.537385i | \(0.819412\pi\) | |||||||
\(420\) | 12.0000 | − | 6.00000i | 0.585540 | − | 0.292770i | ||||
\(421\) | −27.0000 | + | 27.0000i | −1.31590 | + | 1.31590i | −0.398909 | + | 0.916991i | \(0.630611\pi\) |
−0.916991 | + | 0.398909i | \(0.869389\pi\) | |||||||
\(422\) | −20.0000 | −0.973585 | ||||||||
\(423\) | 5.00000 | − | 5.00000i | 0.243108 | − | 0.243108i | ||||
\(424\) | −9.00000 | + | 9.00000i | −0.437079 | + | 0.437079i | ||||
\(425\) | −16.0000 | − | 12.0000i | −0.776114 | − | 0.582086i | ||||
\(426\) | −8.00000 | − | 8.00000i | −0.387601 | − | 0.387601i | ||||
\(427\) | −6.00000 | −0.290360 | ||||||||
\(428\) | 3.00000 | + | 3.00000i | 0.145010 | + | 0.145010i | ||||
\(429\) | 4.00000 | − | 4.00000i | 0.193122 | − | 0.193122i | ||||
\(430\) | 12.0000 | + | 24.0000i | 0.578691 | + | 1.15738i | ||||
\(431\) | 11.0000 | − | 11.0000i | 0.529851 | − | 0.529851i | −0.390677 | − | 0.920528i | \(-0.627759\pi\) |
0.920528 | + | 0.390677i | \(0.127759\pi\) | |||||||
\(432\) | −4.00000 | + | 4.00000i | −0.192450 | + | 0.192450i | ||||
\(433\) | 5.00000 | − | 5.00000i | 0.240285 | − | 0.240285i | −0.576683 | − | 0.816968i | \(-0.695653\pi\) |
0.816968 | + | 0.576683i | \(0.195653\pi\) | |||||||
\(434\) | 18.0000 | 0.864028 | ||||||||
\(435\) | −28.0000 | + | 14.0000i | −1.34250 | + | 0.671249i | ||||
\(436\) | 3.00000 | − | 3.00000i | 0.143674 | − | 0.143674i | ||||
\(437\) | −24.0000 | + | 24.0000i | −1.14808 | + | 1.14808i | ||||
\(438\) | − | 2.00000i | − | 0.0955637i | ||||||
\(439\) | 17.0000 | + | 17.0000i | 0.811366 | + | 0.811366i | 0.984839 | − | 0.173473i | \(-0.0554989\pi\) |
−0.173473 | + | 0.984839i | \(0.555499\pi\) | |||||||
\(440\) | −12.0000 | + | 6.00000i | −0.572078 | + | 0.286039i | ||||
\(441\) | 11.0000 | 0.523810 | ||||||||
\(442\) | − | 8.00000i | − | 0.380521i | ||||||
\(443\) | −11.0000 | − | 11.0000i | −0.522626 | − | 0.522626i | 0.395738 | − | 0.918364i | \(-0.370489\pi\) |
−0.918364 | + | 0.395738i | \(0.870489\pi\) | |||||||
\(444\) | 7.00000 | − | 5.00000i | 0.332205 | − | 0.237289i | ||||
\(445\) | 5.00000 | − | 15.0000i | 0.237023 | − | 0.711068i | ||||
\(446\) | 1.00000 | − | 1.00000i | 0.0473514 | − | 0.0473514i | ||||
\(447\) | −16.0000 | + | 16.0000i | −0.756774 | + | 0.756774i | ||||
\(448\) | −21.0000 | − | 21.0000i | −0.992157 | − | 0.992157i | ||||
\(449\) | 5.00000 | − | 5.00000i | 0.235965 | − | 0.235965i | −0.579212 | − | 0.815177i | \(-0.696640\pi\) |
0.815177 | + | 0.579212i | \(0.196640\pi\) | |||||||
\(450\) | −4.00000 | − | 3.00000i | −0.188562 | − | 0.141421i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 4.00000i | 0.188144i | ||||||||
\(453\) | −2.00000 | + | 2.00000i | −0.0939682 | + | 0.0939682i | ||||
\(454\) | 2.00000i | 0.0938647i | ||||||||
\(455\) | −6.00000 | + | 18.0000i | −0.281284 | + | 0.843853i | ||||
\(456\) | 18.0000 | 0.842927 | ||||||||
\(457\) | − | 32.0000i | − | 1.49690i | −0.663193 | − | 0.748448i | \(-0.730799\pi\) | ||
0.663193 | − | 0.748448i | \(-0.269201\pi\) | |||||||
\(458\) | − | 4.00000i | − | 0.186908i | ||||||
\(459\) | 16.0000 | + | 16.0000i | 0.746816 | + | 0.746816i | ||||
\(460\) | −8.00000 | − | 16.0000i | −0.373002 | − | 0.746004i | ||||
\(461\) | 21.0000 | + | 21.0000i | 0.978068 | + | 0.978068i | 0.999765 | − | 0.0216971i | \(-0.00690694\pi\) |
−0.0216971 | + | 0.999765i | \(0.506907\pi\) | |||||||
\(462\) | 12.0000 | 0.558291 | ||||||||
\(463\) | 40.0000 | 1.85896 | 0.929479 | − | 0.368875i | \(-0.120257\pi\) | ||||
0.929479 | + | 0.368875i | \(0.120257\pi\) | |||||||
\(464\) | 7.00000 | + | 7.00000i | 0.324967 | + | 0.324967i | ||||
\(465\) | −6.00000 | − | 12.0000i | −0.278243 | − | 0.556487i | ||||
\(466\) | −1.00000 | − | 1.00000i | −0.0463241 | − | 0.0463241i | ||||
\(467\) | 38.0000i | 1.75843i | 0.476425 | + | 0.879215i | \(0.341932\pi\) | ||||
−0.476425 | + | 0.879215i | \(0.658068\pi\) | |||||||
\(468\) | 2.00000i | 0.0924500i | ||||||||
\(469\) | −18.0000 | −0.831163 | ||||||||
\(470\) | −5.00000 | + | 15.0000i | −0.230633 | + | 0.691898i | ||||
\(471\) | − | 6.00000i | − | 0.276465i | ||||||
\(472\) | 21.0000 | − | 21.0000i | 0.966603 | − | 0.966603i | ||||
\(473\) | − | 24.0000i | − | 1.10352i | ||||||
\(474\) | −6.00000 | −0.275589 | ||||||||
\(475\) | 3.00000 | + | 21.0000i | 0.137649 | + | 0.963546i | ||||
\(476\) | −12.0000 | + | 12.0000i | −0.550019 | + | 0.550019i | ||||
\(477\) | 3.00000 | + | 3.00000i | 0.137361 | + | 0.137361i | ||||
\(478\) | −7.00000 | + | 7.00000i | −0.320173 | + | 0.320173i | ||||
\(479\) | 23.0000 | − | 23.0000i | 1.05090 | − | 1.05090i | 0.0522635 | − | 0.998633i | \(-0.483356\pi\) |
0.998633 | − | 0.0522635i | \(-0.0166436\pi\) | |||||||
\(480\) | −5.00000 | + | 15.0000i | −0.228218 | + | 0.684653i | ||||
\(481\) | −2.00000 | + | 12.0000i | −0.0911922 | + | 0.547153i | ||||
\(482\) | −1.00000 | − | 1.00000i | −0.0455488 | − | 0.0455488i | ||||
\(483\) | 48.0000i | 2.18408i | ||||||||
\(484\) | −7.00000 | −0.318182 | ||||||||
\(485\) | −16.0000 | + | 8.00000i | −0.726523 | + | 0.363261i | ||||
\(486\) | 7.00000 | + | 7.00000i | 0.317526 | + | 0.317526i | ||||
\(487\) | 2.00000i | 0.0906287i | 0.998973 | + | 0.0453143i | \(0.0144289\pi\) | ||||
−0.998973 | + | 0.0453143i | \(0.985571\pi\) | |||||||
\(488\) | 3.00000 | − | 3.00000i | 0.135804 | − | 0.135804i | ||||
\(489\) | 10.0000 | − | 10.0000i | 0.452216 | − | 0.452216i | ||||
\(490\) | −22.0000 | + | 11.0000i | −0.993859 | + | 0.496929i | ||||
\(491\) | −4.00000 | −0.180517 | −0.0902587 | − | 0.995918i | \(-0.528769\pi\) | ||||
−0.0902587 | + | 0.995918i | \(0.528769\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 28.0000 | − | 28.0000i | 1.26106 | − | 1.26106i | ||||
\(494\) | −6.00000 | + | 6.00000i | −0.269953 | + | 0.269953i | ||||
\(495\) | 2.00000 | + | 4.00000i | 0.0898933 | + | 0.179787i | ||||
\(496\) | −3.00000 | + | 3.00000i | −0.134704 | + | 0.134704i | ||||
\(497\) | −24.0000 | − | 24.0000i | −1.07655 | − | 1.07655i | ||||
\(498\) | 10.0000 | 0.448111 | ||||||||
\(499\) | −27.0000 | − | 27.0000i | −1.20869 | − | 1.20869i | −0.971453 | − | 0.237233i | \(-0.923759\pi\) |
−0.237233 | − | 0.971453i | \(-0.576241\pi\) | |||||||
\(500\) | −11.0000 | − | 2.00000i | −0.491935 | − | 0.0894427i | ||||
\(501\) | 6.00000 | − | 6.00000i | 0.268060 | − | 0.268060i | ||||
\(502\) | 5.00000 | − | 5.00000i | 0.223161 | − | 0.223161i | ||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | −9.00000 | + | 9.00000i | −0.400892 | + | 0.400892i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 16.0000i | − | 0.711287i | ||||||
\(507\) | −9.00000 | − | 9.00000i | −0.399704 | − | 0.399704i | ||||
\(508\) | −9.00000 | − | 9.00000i | −0.399310 | − | 0.399310i | ||||
\(509\) | 30.0000 | 1.32973 | 0.664863 | − | 0.746965i | \(-0.268490\pi\) | ||||
0.664863 | + | 0.746965i | \(0.268490\pi\) | |||||||
\(510\) | −12.0000 | − | 4.00000i | −0.531369 | − | 0.177123i | ||||
\(511\) | − | 6.00000i | − | 0.265424i | ||||||
\(512\) | 11.0000 | 0.486136 | ||||||||
\(513\) | − | 24.0000i | − | 1.05963i | ||||||
\(514\) | − | 28.0000i | − | 1.23503i | ||||||
\(515\) | −28.0000 | + | 14.0000i | −1.23383 | + | 0.616914i | ||||
\(516\) | −12.0000 | − | 12.0000i | −0.528271 | − | 0.528271i | ||||
\(517\) | 10.0000 | − | 10.0000i | 0.439799 | − | 0.439799i | ||||
\(518\) | −21.0000 | + | 15.0000i | −0.922687 | + | 0.659062i | ||||
\(519\) | 2.00000i | 0.0877903i | ||||||||
\(520\) | −6.00000 | − | 12.0000i | −0.263117 | − | 0.526235i | ||||
\(521\) | − | 44.0000i | − | 1.92767i | −0.266491 | − | 0.963837i | \(-0.585864\pi\) | ||
0.266491 | − | 0.963837i | \(-0.414136\pi\) | |||||||
\(522\) | 7.00000 | − | 7.00000i | 0.306382 | − | 0.306382i | ||||
\(523\) | −4.00000 | −0.174908 | −0.0874539 | − | 0.996169i | \(-0.527873\pi\) | ||||
−0.0874539 | + | 0.996169i | \(0.527873\pi\) | |||||||
\(524\) | 5.00000 | − | 5.00000i | 0.218426 | − | 0.218426i | ||||
\(525\) | 24.0000 | + | 18.0000i | 1.04745 | + | 0.785584i | ||||
\(526\) | 7.00000 | + | 7.00000i | 0.305215 | + | 0.305215i | ||||
\(527\) | 12.0000 | + | 12.0000i | 0.522728 | + | 0.522728i | ||||
\(528\) | −2.00000 | + | 2.00000i | −0.0870388 | + | 0.0870388i | ||||
\(529\) | 41.0000 | 1.78261 | ||||||||
\(530\) | −9.00000 | − | 3.00000i | −0.390935 | − | 0.130312i | ||||
\(531\) | −7.00000 | − | 7.00000i | −0.303774 | − | 0.303774i | ||||
\(532\) | 18.0000 | 0.780399 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | − | 10.0000i | − | 0.432742i | ||||||
\(535\) | −3.00000 | + | 9.00000i | −0.129701 | + | 0.389104i | ||||
\(536\) | 9.00000 | − | 9.00000i | 0.388741 | − | 0.388741i | ||||
\(537\) | − | 14.0000i | − | 0.604145i | ||||||
\(538\) | 16.0000i | 0.689809i | ||||||||
\(539\) | 22.0000 | 0.947607 | ||||||||
\(540\) | 12.0000 | + | 4.00000i | 0.516398 | + | 0.172133i | ||||
\(541\) | 1.00000 | + | 1.00000i | 0.0429934 | + | 0.0429934i | 0.728277 | − | 0.685283i | \(-0.240322\pi\) |
−0.685283 | + | 0.728277i | \(0.740322\pi\) | |||||||
\(542\) | 8.00000 | 0.343629 | ||||||||
\(543\) | 10.0000 | + | 10.0000i | 0.429141 | + | 0.429141i | ||||
\(544\) | − | 20.0000i | − | 0.857493i | ||||||
\(545\) | 9.00000 | + | 3.00000i | 0.385518 | + | 0.128506i | ||||
\(546\) | 12.0000i | 0.513553i | ||||||||
\(547\) | 20.0000 | 0.855138 | 0.427569 | − | 0.903983i | \(-0.359370\pi\) | ||||
0.427569 | + | 0.903983i | \(0.359370\pi\) | |||||||
\(548\) | 7.00000 | + | 7.00000i | 0.299025 | + | 0.299025i | ||||
\(549\) | −1.00000 | − | 1.00000i | −0.0426790 | − | 0.0426790i | ||||
\(550\) | −8.00000 | − | 6.00000i | −0.341121 | − | 0.255841i | ||||
\(551\) | −42.0000 | −1.78926 | ||||||||
\(552\) | −24.0000 | − | 24.0000i | −1.02151 | − | 1.02151i | ||||
\(553\) | −18.0000 | −0.765438 | ||||||||
\(554\) | −26.0000 | −1.10463 | ||||||||
\(555\) | 17.0000 | + | 9.00000i | 0.721610 | + | 0.382029i | ||||
\(556\) | −4.00000 | −0.169638 | ||||||||
\(557\) | −14.0000 | −0.593199 | −0.296600 | − | 0.955002i | \(-0.595853\pi\) | ||||
−0.296600 | + | 0.955002i | \(0.595853\pi\) | |||||||
\(558\) | 3.00000 | + | 3.00000i | 0.127000 | + | 0.127000i | ||||
\(559\) | 24.0000 | 1.01509 | ||||||||
\(560\) | 3.00000 | − | 9.00000i | 0.126773 | − | 0.380319i | ||||
\(561\) | 8.00000 | + | 8.00000i | 0.337760 | + | 0.337760i | ||||
\(562\) | −9.00000 | − | 9.00000i | −0.379642 | − | 0.379642i | ||||
\(563\) | −12.0000 | −0.505740 | −0.252870 | − | 0.967500i | \(-0.581374\pi\) | ||||
−0.252870 | + | 0.967500i | \(0.581374\pi\) | |||||||
\(564\) | − | 10.0000i | − | 0.421076i | ||||||
\(565\) | −8.00000 | + | 4.00000i | −0.336563 | + | 0.168281i | ||||
\(566\) | − | 22.0000i | − | 0.924729i | ||||||
\(567\) | −15.0000 | − | 15.0000i | −0.629941 | − | 0.629941i | ||||
\(568\) | 24.0000 | 1.00702 | ||||||||
\(569\) | 25.0000 | + | 25.0000i | 1.04805 | + | 1.04805i | 0.998786 | + | 0.0492690i | \(0.0156892\pi\) |
0.0492690 | + | 0.998786i | \(0.484311\pi\) | |||||||
\(570\) | 6.00000 | + | 12.0000i | 0.251312 | + | 0.502625i | ||||
\(571\) | −28.0000 | −1.17176 | −0.585882 | − | 0.810397i | \(-0.699252\pi\) | ||||
−0.585882 | + | 0.810397i | \(0.699252\pi\) | |||||||
\(572\) | 4.00000i | 0.167248i | ||||||||
\(573\) | − | 22.0000i | − | 0.919063i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.0000 | − | 32.0000i | 1.00087 | − | 1.33449i | ||||
\(576\) | − | 7.00000i | − | 0.291667i | ||||||
\(577\) | 12.0000i | 0.499567i | 0.968302 | + | 0.249783i | \(0.0803594\pi\) | ||||
−0.968302 | + | 0.249783i | \(0.919641\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | 2.00000 | + | 2.00000i | 0.0831172 | + | 0.0831172i | ||||
\(580\) | 7.00000 | − | 21.0000i | 0.290659 | − | 0.871978i | ||||
\(581\) | 30.0000 | 1.24461 | ||||||||
\(582\) | −8.00000 | + | 8.00000i | −0.331611 | + | 0.331611i | ||||
\(583\) | 6.00000 | + | 6.00000i | 0.248495 | + | 0.248495i | ||||
\(584\) | 3.00000 | + | 3.00000i | 0.124141 | + | 0.124141i | ||||
\(585\) | −4.00000 | + | 2.00000i | −0.165380 | + | 0.0826898i | ||||
\(586\) | −1.00000 | + | 1.00000i | −0.0413096 | + | 0.0413096i | ||||
\(587\) | −36.0000 | −1.48588 | −0.742940 | − | 0.669359i | \(-0.766569\pi\) | ||||
−0.742940 | + | 0.669359i | \(0.766569\pi\) | |||||||
\(588\) | 11.0000 | − | 11.0000i | 0.453632 | − | 0.453632i | ||||
\(589\) | − | 18.0000i | − | 0.741677i | ||||||
\(590\) | 21.0000 | + | 7.00000i | 0.864556 | + | 0.288185i | ||||
\(591\) | 2.00000i | 0.0822690i | ||||||||
\(592\) | 1.00000 | − | 6.00000i | 0.0410997 | − | 0.246598i | ||||
\(593\) | −3.00000 | + | 3.00000i | −0.123195 | + | 0.123195i | −0.766016 | − | 0.642821i | \(-0.777764\pi\) |
0.642821 | + | 0.766016i | \(0.277764\pi\) | |||||||
\(594\) | 8.00000 | + | 8.00000i | 0.328244 | + | 0.328244i | ||||
\(595\) | −36.0000 | − | 12.0000i | −1.47586 | − | 0.491952i | ||||
\(596\) | − | 16.0000i | − | 0.655386i | ||||||
\(597\) | − | 30.0000i | − | 1.22782i | ||||||
\(598\) | 16.0000 | 0.654289 | ||||||||
\(599\) | − | 6.00000i | − | 0.245153i | −0.992459 | − | 0.122577i | \(-0.960884\pi\) | ||
0.992459 | − | 0.122577i | \(-0.0391157\pi\) | |||||||
\(600\) | −21.0000 | + | 3.00000i | −0.857321 | + | 0.122474i | ||||
\(601\) | −10.0000 | −0.407909 | −0.203954 | − | 0.978980i | \(-0.565379\pi\) | ||||
−0.203954 | + | 0.978980i | \(0.565379\pi\) | |||||||
\(602\) | 36.0000 | + | 36.0000i | 1.46725 | + | 1.46725i | ||||
\(603\) | −3.00000 | − | 3.00000i | −0.122169 | − | 0.122169i | ||||
\(604\) | − | 2.00000i | − | 0.0813788i | ||||||
\(605\) | −7.00000 | − | 14.0000i | −0.284590 | − | 0.569181i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.0000 | −1.29884 | −0.649420 | − | 0.760430i | \(-0.724988\pi\) | ||||
−0.649420 | + | 0.760430i | \(0.724988\pi\) | |||||||
\(608\) | −15.0000 | + | 15.0000i | −0.608330 | + | 0.608330i | ||||
\(609\) | −42.0000 | + | 42.0000i | −1.70193 | + | 1.70193i | ||||
\(610\) | 3.00000 | + | 1.00000i | 0.121466 | + | 0.0404888i | ||||
\(611\) | 10.0000 | + | 10.0000i | 0.404557 | + | 0.404557i | ||||
\(612\) | −4.00000 | −0.161690 | ||||||||
\(613\) | 21.0000 | + | 21.0000i | 0.848182 | + | 0.848182i | 0.989906 | − | 0.141724i | \(-0.0452646\pi\) |
−0.141724 | + | 0.989906i | \(0.545265\pi\) | |||||||
\(614\) | 9.00000 | − | 9.00000i | 0.363210 | − | 0.363210i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −18.0000 | + | 18.0000i | −0.725241 | + | 0.725241i | ||||
\(617\) | 17.0000 | − | 17.0000i | 0.684394 | − | 0.684394i | −0.276593 | − | 0.960987i | \(-0.589205\pi\) |
0.960987 | + | 0.276593i | \(0.0892054\pi\) | |||||||
\(618\) | −14.0000 | + | 14.0000i | −0.563163 | + | 0.563163i | ||||
\(619\) | −20.0000 | −0.803868 | −0.401934 | − | 0.915669i | \(-0.631662\pi\) | ||||
−0.401934 | + | 0.915669i | \(0.631662\pi\) | |||||||
\(620\) | 9.00000 | + | 3.00000i | 0.361449 | + | 0.120483i | ||||
\(621\) | −32.0000 | + | 32.0000i | −1.28412 | + | 1.28412i | ||||
\(622\) | −3.00000 | + | 3.00000i | −0.120289 | + | 0.120289i | ||||
\(623\) | − | 30.0000i | − | 1.20192i | ||||||
\(624\) | −2.00000 | − | 2.00000i | −0.0800641 | − | 0.0800641i | ||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | 30.0000 | 1.19904 | ||||||||
\(627\) | − | 12.0000i | − | 0.479234i | ||||||
\(628\) | 3.00000 | + | 3.00000i | 0.119713 | + | 0.119713i | ||||
\(629\) | −24.0000 | − | 4.00000i | −0.956943 | − | 0.159490i | ||||
\(630\) | −9.00000 | − | 3.00000i | −0.358569 | − | 0.119523i | ||||
\(631\) | 23.0000 | − | 23.0000i | 0.915616 | − | 0.915616i | −0.0810911 | − | 0.996707i | \(-0.525840\pi\) |
0.996707 | + | 0.0810911i | \(0.0258405\pi\) | |||||||
\(632\) | 9.00000 | − | 9.00000i | 0.358001 | − | 0.358001i | ||||
\(633\) | 20.0000 | + | 20.0000i | 0.794929 | + | 0.794929i | ||||
\(634\) | −17.0000 | + | 17.0000i | −0.675156 | + | 0.675156i | ||||
\(635\) | 9.00000 | − | 27.0000i | 0.357154 | − | 1.07146i | ||||
\(636\) | 6.00000 | 0.237915 | ||||||||
\(637\) | 22.0000i | 0.871672i | ||||||||
\(638\) | 14.0000 | − | 14.0000i | 0.554265 | − | 0.554265i | ||||
\(639\) | − | 8.00000i | − | 0.316475i | ||||||
\(640\) | −3.00000 | − | 6.00000i | −0.118585 | − | 0.237171i | ||||
\(641\) | −18.0000 | −0.710957 | −0.355479 | − | 0.934684i | \(-0.615682\pi\) | ||||
−0.355479 | + | 0.934684i | \(0.615682\pi\) | |||||||
\(642\) | 6.00000i | 0.236801i | ||||||||
\(643\) | − | 10.0000i | − | 0.394362i | −0.980367 | − | 0.197181i | \(-0.936821\pi\) | ||
0.980367 | − | 0.197181i | \(-0.0631786\pi\) | |||||||
\(644\) | −24.0000 | − | 24.0000i | −0.945732 | − | 0.945732i | ||||
\(645\) | 12.0000 | − | 36.0000i | 0.472500 | − | 1.41750i | ||||
\(646\) | −12.0000 | − | 12.0000i | −0.472134 | − | 0.472134i | ||||
\(647\) | −24.0000 | −0.943537 | −0.471769 | − | 0.881722i | \(-0.656384\pi\) | ||||
−0.471769 | + | 0.881722i | \(0.656384\pi\) | |||||||
\(648\) | 15.0000 | 0.589256 | ||||||||
\(649\) | −14.0000 | − | 14.0000i | −0.549548 | − | 0.549548i | ||||
\(650\) | 6.00000 | − | 8.00000i | 0.235339 | − | 0.313786i | ||||
\(651\) | −18.0000 | − | 18.0000i | −0.705476 | − | 0.705476i | ||||
\(652\) | 10.0000i | 0.391630i | ||||||||
\(653\) | 36.0000i | 1.40879i | 0.709809 | + | 0.704394i | \(0.248781\pi\) | ||||
−0.709809 | + | 0.704394i | \(0.751219\pi\) | |||||||
\(654\) | 6.00000 | 0.234619 | ||||||||
\(655\) | 15.0000 | + | 5.00000i | 0.586098 | + | 0.195366i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.00000 | − | 1.00000i | 0.0390137 | − | 0.0390137i | ||||
\(658\) | 30.0000i | 1.16952i | ||||||||
\(659\) | 20.0000 | 0.779089 | 0.389545 | − | 0.921008i | \(-0.372632\pi\) | ||||
0.389545 | + | 0.921008i | \(0.372632\pi\) | |||||||
\(660\) | 6.00000 | + | 2.00000i | 0.233550 | + | 0.0778499i | ||||
\(661\) | 33.0000 | − | 33.0000i | 1.28355 | − | 1.28355i | 0.344919 | − | 0.938633i | \(-0.387906\pi\) |
0.938633 | − | 0.344919i | \(-0.112094\pi\) | |||||||
\(662\) | 7.00000 | + | 7.00000i | 0.272063 | + | 0.272063i | ||||
\(663\) | −8.00000 | + | 8.00000i | −0.310694 | + | 0.310694i | ||||
\(664\) | −15.0000 | + | 15.0000i | −0.582113 | + | 0.582113i | ||||
\(665\) | 18.0000 | + | 36.0000i | 0.698010 | + | 1.39602i | ||||
\(666\) | −6.00000 | − | 1.00000i | −0.232495 | − | 0.0387492i | ||||
\(667\) | 56.0000 | + | 56.0000i | 2.16833 | + | 2.16833i | ||||
\(668\) | 6.00000i | 0.232147i | ||||||||
\(669\) | −2.00000 | −0.0773245 | ||||||||
\(670\) | 9.00000 | + | 3.00000i | 0.347700 | + | 0.115900i | ||||
\(671\) | −2.00000 | − | 2.00000i | −0.0772091 | − | 0.0772091i | ||||
\(672\) | 30.0000i | 1.15728i | ||||||||
\(673\) | −15.0000 | + | 15.0000i | −0.578208 | + | 0.578208i | −0.934409 | − | 0.356202i | \(-0.884072\pi\) |
0.356202 | + | 0.934409i | \(0.384072\pi\) | |||||||
\(674\) | 15.0000 | − | 15.0000i | 0.577778 | − | 0.577778i | ||||
\(675\) | 4.00000 | + | 28.0000i | 0.153960 | + | 1.07772i | ||||
\(676\) | 9.00000 | 0.346154 | ||||||||
\(677\) | −23.0000 | + | 23.0000i | −0.883962 | + | 0.883962i | −0.993935 | − | 0.109973i | \(-0.964924\pi\) |
0.109973 | + | 0.993935i | \(0.464924\pi\) | |||||||
\(678\) | −4.00000 | + | 4.00000i | −0.153619 | + | 0.153619i | ||||
\(679\) | −24.0000 | + | 24.0000i | −0.921035 | + | 0.921035i | ||||
\(680\) | 24.0000 | − | 12.0000i | 0.920358 | − | 0.460179i | ||||
\(681\) | 2.00000 | − | 2.00000i | 0.0766402 | − | 0.0766402i | ||||
\(682\) | 6.00000 | + | 6.00000i | 0.229752 | + | 0.229752i | ||||
\(683\) | 4.00000 | 0.153056 | 0.0765279 | − | 0.997067i | \(-0.475617\pi\) | ||||
0.0765279 | + | 0.997067i | \(0.475617\pi\) | |||||||
\(684\) | 3.00000 | + | 3.00000i | 0.114708 | + | 0.114708i | ||||
\(685\) | −7.00000 | + | 21.0000i | −0.267456 | + | 0.802369i | ||||
\(686\) | −12.0000 | + | 12.0000i | −0.458162 | + | 0.458162i | ||||
\(687\) | −4.00000 | + | 4.00000i | −0.152610 | + | 0.152610i | ||||
\(688\) | −12.0000 | −0.457496 | ||||||||
\(689\) | −6.00000 | + | 6.00000i | −0.228582 | + | 0.228582i | ||||
\(690\) | 8.00000 | − | 24.0000i | 0.304555 | − | 0.913664i | ||||
\(691\) | 46.0000i | 1.74992i | 0.484193 | + | 0.874961i | \(0.339113\pi\) | ||||
−0.484193 | + | 0.874961i | \(0.660887\pi\) | |||||||
\(692\) | −1.00000 | − | 1.00000i | −0.0380143 | − | 0.0380143i | ||||
\(693\) | 6.00000 | + | 6.00000i | 0.227921 | + | 0.227921i | ||||
\(694\) | −4.00000 | −0.151838 | ||||||||
\(695\) | −4.00000 | − | 8.00000i | −0.151729 | − | 0.303457i | ||||
\(696\) | − | 42.0000i | − | 1.59201i | ||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | − | 32.0000i | − | 1.21122i | ||||||
\(699\) | 2.00000i | 0.0756469i | ||||||||
\(700\) | −21.0000 | + | 3.00000i | −0.793725 | + | 0.113389i | ||||
\(701\) | 9.00000 | + | 9.00000i | 0.339925 | + | 0.339925i | 0.856339 | − | 0.516414i | \(-0.172733\pi\) |
−0.516414 | + | 0.856339i | \(0.672733\pi\) | |||||||
\(702\) | −8.00000 | + | 8.00000i | −0.301941 | + | 0.301941i | ||||
\(703\) | 15.0000 | + | 21.0000i | 0.565736 | + | 0.792030i | ||||
\(704\) | − | 14.0000i | − | 0.527645i | ||||||
\(705\) | 20.0000 | − | 10.0000i | 0.753244 | − | 0.376622i | ||||
\(706\) | 32.0000i | 1.20434i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −14.0000 | −0.526152 | ||||||||
\(709\) | −15.0000 | + | 15.0000i | −0.563337 | + | 0.563337i | −0.930254 | − | 0.366917i | \(-0.880413\pi\) |
0.366917 | + | 0.930254i | \(0.380413\pi\) | |||||||
\(710\) | 8.00000 | + | 16.0000i | 0.300235 | + | 0.600469i | ||||
\(711\) | −3.00000 | − | 3.00000i | −0.112509 | − | 0.112509i | ||||
\(712\) | 15.0000 | + | 15.0000i | 0.562149 | + | 0.562149i | ||||
\(713\) | −24.0000 | + | 24.0000i | −0.898807 | + | 0.898807i | ||||
\(714\) | −24.0000 | −0.898177 | ||||||||
\(715\) | −8.00000 | + | 4.00000i | −0.299183 | + | 0.149592i | ||||
\(716\) | 7.00000 | + | 7.00000i | 0.261602 | + | 0.261602i | ||||
\(717\) | 14.0000 | 0.522840 | ||||||||
\(718\) | − | 34.0000i | − | 1.26887i | ||||||
\(719\) | 26.0000i | 0.969636i | 0.874615 | + | 0.484818i | \(0.161114\pi\) | ||||
−0.874615 | + | 0.484818i | \(0.838886\pi\) | |||||||
\(720\) | 2.00000 | − | 1.00000i | 0.0745356 | − | 0.0372678i | ||||
\(721\) | −42.0000 | + | 42.0000i | −1.56416 | + | 1.56416i | ||||
\(722\) | − | 1.00000i | − | 0.0372161i | ||||||
\(723\) | 2.00000i | 0.0743808i | ||||||||
\(724\) | −10.0000 | −0.371647 | ||||||||
\(725\) | 49.0000 | − | 7.00000i | 1.81981 | − | 0.259973i | ||||
\(726\) | −7.00000 | − | 7.00000i | −0.259794 | − | 0.259794i | ||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | −18.0000 | − | 18.0000i | −0.667124 | − | 0.667124i | ||||
\(729\) | − | 29.0000i | − | 1.07407i | ||||||
\(730\) | −1.00000 | + | 3.00000i | −0.0370117 | + | 0.111035i | ||||
\(731\) | 48.0000i | 1.77534i | ||||||||
\(732\) | −2.00000 | −0.0739221 | ||||||||
\(733\) | −3.00000 | − | 3.00000i | −0.110808 | − | 0.110808i | 0.649529 | − | 0.760337i | \(-0.274966\pi\) |
−0.760337 | + | 0.649529i | \(0.774966\pi\) | |||||||
\(734\) | −17.0000 | − | 17.0000i | −0.627481 | − | 0.627481i | ||||
\(735\) | 33.0000 | + | 11.0000i | 1.21722 | + | 0.405741i | ||||
\(736\) | 40.0000 | 1.47442 | ||||||||
\(737\) | −6.00000 | − | 6.00000i | −0.221013 | − | 0.221013i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 44.0000 | 1.61857 | 0.809283 | − | 0.587419i | \(-0.199856\pi\) | ||||
0.809283 | + | 0.587419i | \(0.199856\pi\) | |||||||
\(740\) | −13.0000 | + | 4.00000i | −0.477890 | + | 0.147043i | ||||
\(741\) | 12.0000 | 0.440831 | ||||||||
\(742\) | −18.0000 | −0.660801 | ||||||||
\(743\) | 5.00000 | + | 5.00000i | 0.183432 | + | 0.183432i | 0.792850 | − | 0.609417i | \(-0.208597\pi\) |
−0.609417 | + | 0.792850i | \(0.708597\pi\) | |||||||
\(744\) | 18.0000 | 0.659912 | ||||||||
\(745\) | 32.0000 | − | 16.0000i | 1.17239 | − | 0.586195i | ||||
\(746\) | 3.00000 | + | 3.00000i | 0.109838 | + | 0.109838i | ||||
\(747\) | 5.00000 | + | 5.00000i | 0.182940 | + | 0.182940i | ||||
\(748\) | −8.00000 | −0.292509 | ||||||||
\(749\) | 18.0000i | 0.657706i | ||||||||
\(750\) | −9.00000 | − | 13.0000i | −0.328634 | − | 0.474693i | ||||
\(751\) | − | 22.0000i | − | 0.802791i | −0.915905 | − | 0.401396i | \(-0.868525\pi\) | ||
0.915905 | − | 0.401396i | \(-0.131475\pi\) | |||||||
\(752\) | −5.00000 | − | 5.00000i | −0.182331 | − | 0.182331i | ||||
\(753\) | −10.0000 | −0.364420 | ||||||||
\(754\) | 14.0000 | + | 14.0000i | 0.509850 | + | 0.509850i | ||||
\(755\) | 4.00000 | − | 2.00000i | 0.145575 | − | 0.0727875i | ||||
\(756\) | 24.0000 | 0.872872 | ||||||||
\(757\) | − | 36.0000i | − | 1.30844i | −0.756303 | − | 0.654221i | \(-0.772997\pi\) | ||
0.756303 | − | 0.654221i | \(-0.227003\pi\) | |||||||
\(758\) | − | 14.0000i | − | 0.508503i | ||||||
\(759\) | −16.0000 | + | 16.0000i | −0.580763 | + | 0.580763i | ||||
\(760\) | −27.0000 | − | 9.00000i | −0.979393 | − | 0.326464i | ||||
\(761\) | 8.00000i | 0.290000i | 0.989432 | + | 0.145000i | \(0.0463182\pi\) | ||||
−0.989432 | + | 0.145000i | \(0.953682\pi\) | |||||||
\(762\) | − | 18.0000i | − | 0.652071i | ||||||
\(763\) | 18.0000 | 0.651644 | ||||||||
\(764\) | 11.0000 | + | 11.0000i | 0.397966 | + | 0.397966i | ||||
\(765\) | −4.00000 | − | 8.00000i | −0.144620 | − | 0.289241i | ||||
\(766\) | −8.00000 | −0.289052 | ||||||||
\(767\) | 14.0000 | − | 14.0000i | 0.505511 | − | 0.505511i | ||||
\(768\) | −17.0000 | − | 17.0000i | −0.613435 | − | 0.613435i | ||||
\(769\) | −15.0000 | − | 15.0000i | −0.540914 | − | 0.540914i | 0.382883 | − | 0.923797i | \(-0.374931\pi\) |
−0.923797 | + | 0.382883i | \(0.874931\pi\) | |||||||
\(770\) | −18.0000 | − | 6.00000i | −0.648675 | − | 0.216225i | ||||
\(771\) | −28.0000 | + | 28.0000i | −1.00840 | + | 1.00840i | ||||
\(772\) | −2.00000 | −0.0719816 | ||||||||
\(773\) | −11.0000 | + | 11.0000i | −0.395643 | + | 0.395643i | −0.876693 | − | 0.481050i | \(-0.840255\pi\) |
0.481050 | + | 0.876693i | \(0.340255\pi\) | |||||||
\(774\) | 12.0000i | 0.431331i | ||||||||
\(775\) | 3.00000 | + | 21.0000i | 0.107763 | + | 0.754342i | ||||
\(776\) | − | 24.0000i | − | 0.861550i | ||||||
\(777\) | 36.0000 | + | 6.00000i | 1.29149 | + | 0.215249i | ||||
\(778\) | −5.00000 | + | 5.00000i | −0.179259 | + | 0.179259i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −2.00000 | + | 6.00000i | −0.0716115 | + | 0.214834i | ||||
\(781\) | − | 16.0000i | − | 0.572525i | ||||||
\(782\) | 32.0000i | 1.14432i | ||||||||
\(783\) | −56.0000 | −2.00128 | ||||||||
\(784\) | − | 11.0000i | − | 0.392857i | ||||||
\(785\) | −3.00000 | + | 9.00000i | −0.107075 | + | 0.321224i | ||||
\(786\) | 10.0000 | 0.356688 | ||||||||
\(787\) | −27.0000 | − | 27.0000i | −0.962446 | − | 0.962446i | 0.0368739 | − | 0.999320i | \(-0.488260\pi\) |
−0.999320 | + | 0.0368739i | \(0.988260\pi\) | |||||||
\(788\) | −1.00000 | − | 1.00000i | −0.0356235 | − | 0.0356235i | ||||
\(789\) | − | 14.0000i | − | 0.498413i | ||||||
\(790\) | 9.00000 | + | 3.00000i | 0.320206 | + | 0.106735i | ||||
\(791\) | −12.0000 | + | 12.0000i | −0.426671 | + | 0.426671i | ||||
\(792\) | −6.00000 | −0.213201 | ||||||||
\(793\) | 2.00000 | − | 2.00000i | 0.0710221 | − | 0.0710221i | ||||
\(794\) | −5.00000 | + | 5.00000i | −0.177443 | + | 0.177443i | ||||
\(795\) | 6.00000 | + | 12.0000i | 0.212798 | + | 0.425596i | ||||
\(796\) | 15.0000 | + | 15.0000i | 0.531661 | + | 0.531661i | ||||
\(797\) | −46.0000 | −1.62940 | −0.814702 | − | 0.579880i | \(-0.803099\pi\) | ||||
−0.814702 | + | 0.579880i | \(0.803099\pi\) | |||||||
\(798\) | 18.0000 | + | 18.0000i | 0.637193 | + | 0.637193i | ||||
\(799\) | −20.0000 | + | 20.0000i | −0.707549 | + | 0.707549i | ||||
\(800\) | 15.0000 | − | 20.0000i | 0.530330 | − | 0.707107i | ||||
\(801\) | 5.00000 | − | 5.00000i | 0.176666 | − | 0.176666i | ||||
\(802\) | −1.00000 | + | 1.00000i | −0.0353112 | + | 0.0353112i | ||||
\(803\) | 2.00000 | − | 2.00000i | 0.0705785 | − | 0.0705785i | ||||
\(804\) | −6.00000 | −0.211604 | ||||||||
\(805\) | 24.0000 | − | 72.0000i | 0.845889 | − | 2.53767i | ||||
\(806\) | −6.00000 | + | 6.00000i | −0.211341 | + | 0.211341i | ||||
\(807\) | 16.0000 | − | 16.0000i | 0.563227 | − | 0.563227i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.0000 | + | 25.0000i | 0.878953 | + | 0.878953i | 0.993426 | − | 0.114473i | \(-0.0365180\pi\) |
−0.114473 | + | 0.993426i | \(0.536518\pi\) | |||||||
\(810\) | 5.00000 | + | 10.0000i | 0.175682 | + | 0.351364i | ||||
\(811\) | 20.0000 | 0.702295 | 0.351147 | − | 0.936320i | \(-0.385792\pi\) | ||||
0.351147 | + | 0.936320i | \(0.385792\pi\) | |||||||
\(812\) | − | 42.0000i | − | 1.47391i | ||||||
\(813\) | −8.00000 | − | 8.00000i | −0.280572 | − | 0.280572i | ||||
\(814\) | −12.0000 | − | 2.00000i | −0.420600 | − | 0.0701000i | ||||
\(815\) | −20.0000 | + | 10.0000i | −0.700569 | + | 0.350285i | ||||
\(816\) | 4.00000 | − | 4.00000i | 0.140028 | − | 0.140028i | ||||
\(817\) | 36.0000 | − | 36.0000i | 1.25948 | − | 1.25948i | ||||
\(818\) | 3.00000 | + | 3.00000i | 0.104893 | + | 0.104893i | ||||
\(819\) | −6.00000 | + | 6.00000i | −0.209657 | + | 0.209657i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.0000 | −0.628204 | −0.314102 | − | 0.949389i | \(-0.601703\pi\) | ||||
−0.314102 | + | 0.949389i | \(0.601703\pi\) | |||||||
\(822\) | 14.0000i | 0.488306i | ||||||||
\(823\) | 11.0000 | − | 11.0000i | 0.383436 | − | 0.383436i | −0.488903 | − | 0.872338i | \(-0.662603\pi\) |
0.872338 | + | 0.488903i | \(0.162603\pi\) | |||||||
\(824\) | − | 42.0000i | − | 1.46314i | ||||||
\(825\) | 2.00000 | + | 14.0000i | 0.0696311 | + | 0.487417i | ||||
\(826\) | 42.0000 | 1.46137 | ||||||||
\(827\) | 38.0000i | 1.32139i | 0.750655 | + | 0.660695i | \(0.229738\pi\) | ||||
−0.750655 | + | 0.660695i | \(0.770262\pi\) | |||||||
\(828\) | − | 8.00000i | − | 0.278019i | ||||||
\(829\) | 21.0000 | + | 21.0000i | 0.729360 | + | 0.729360i | 0.970492 | − | 0.241132i | \(-0.0775187\pi\) |
−0.241132 | + | 0.970492i | \(0.577519\pi\) | |||||||
\(830\) | −15.0000 | − | 5.00000i | −0.520658 | − | 0.173553i | ||||
\(831\) | 26.0000 | + | 26.0000i | 0.901930 | + | 0.901930i | ||||
\(832\) | 14.0000 | 0.485363 | ||||||||
\(833\) | −44.0000 | −1.52451 | ||||||||
\(834\) | −4.00000 | − | 4.00000i | −0.138509 | − | 0.138509i | ||||
\(835\) | −12.0000 | + | 6.00000i | −0.415277 | + | 0.207639i | ||||
\(836\) | 6.00000 | + | 6.00000i | 0.207514 | + | 0.207514i | ||||
\(837\) | − | 24.0000i | − | 0.829561i | ||||||
\(838\) | − | 22.0000i | − | 0.759977i | ||||||
\(839\) | 24.0000 | 0.828572 | 0.414286 | − | 0.910147i | \(-0.364031\pi\) | ||||
0.414286 | + | 0.910147i | \(0.364031\pi\) | |||||||
\(840\) | −36.0000 | + | 18.0000i | −1.24212 | + | 0.621059i | ||||
\(841\) | 69.0000i | 2.37931i | ||||||||
\(842\) | 27.0000 | − | 27.0000i | 0.930481 | − | 0.930481i | ||||
\(843\) | 18.0000i | 0.619953i | ||||||||
\(844\) | −20.0000 | −0.688428 | ||||||||
\(845\) | 9.00000 | + | 18.0000i | 0.309609 | + | 0.619219i | ||||
\(846\) | −5.00000 | + | 5.00000i | −0.171904 | + | 0.171904i | ||||
\(847\) | −21.0000 | − | 21.0000i | −0.721569 | − | 0.721569i | ||||
\(848\) | 3.00000 | − | 3.00000i | 0.103020 | − | 0.103020i | ||||
\(849\) | −22.0000 | + | 22.0000i | −0.755038 | + | 0.755038i | ||||
\(850\) | 16.0000 | + | 12.0000i | 0.548795 | + | 0.411597i | ||||
\(851\) | 8.00000 | − | 48.0000i | 0.274236 | − | 1.64542i | ||||
\(852\) | −8.00000 | − | 8.00000i | −0.274075 | − | 0.274075i | ||||
\(853\) | − | 44.0000i | − | 1.50653i | −0.657716 | − | 0.753266i | \(-0.728477\pi\) | ||
0.657716 | − | 0.753266i | \(-0.271523\pi\) | |||||||
\(854\) | 6.00000 | 0.205316 | ||||||||
\(855\) | −3.00000 | + | 9.00000i | −0.102598 | + | 0.307794i | ||||
\(856\) | −9.00000 | − | 9.00000i | −0.307614 | − | 0.307614i | ||||
\(857\) | − | 32.0000i | − | 1.09310i | −0.837427 | − | 0.546550i | \(-0.815941\pi\) | ||
0.837427 | − | 0.546550i | \(-0.184059\pi\) | |||||||
\(858\) | −4.00000 | + | 4.00000i | −0.136558 | + | 0.136558i | ||||
\(859\) | 7.00000 | − | 7.00000i | 0.238837 | − | 0.238837i | −0.577531 | − | 0.816368i | \(-0.695984\pi\) |
0.816368 | + | 0.577531i | \(0.195984\pi\) | |||||||
\(860\) | 12.0000 | + | 24.0000i | 0.409197 | + | 0.818393i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.0000 | + | 11.0000i | −0.374661 | + | 0.374661i | ||||
\(863\) | 15.0000 | − | 15.0000i | 0.510606 | − | 0.510606i | −0.404106 | − | 0.914712i | \(-0.632417\pi\) |
0.914712 | + | 0.404106i | \(0.132417\pi\) | |||||||
\(864\) | −20.0000 | + | 20.0000i | −0.680414 | + | 0.680414i | ||||
\(865\) | 1.00000 | − | 3.00000i | 0.0340010 | − | 0.102003i | ||||
\(866\) | −5.00000 | + | 5.00000i | −0.169907 | + | 0.169907i | ||||
\(867\) | 1.00000 | + | 1.00000i | 0.0339618 | + | 0.0339618i | ||||
\(868\) | 18.0000 | 0.610960 | ||||||||
\(869\) | −6.00000 | − | 6.00000i | −0.203536 | − | 0.203536i | ||||
\(870\) | 28.0000 | − | 14.0000i | 0.949289 | − | 0.474644i | ||||
\(871\) | 6.00000 | − | 6.00000i | 0.203302 | − | 0.203302i | ||||
\(872\) | −9.00000 | + | 9.00000i | −0.304778 | + | 0.304778i | ||||
\(873\) | −8.00000 | −0.270759 | ||||||||
\(874\) | 24.0000 | − | 24.0000i | 0.811812 | − | 0.811812i | ||||
\(875\) | −27.0000 | − | 39.0000i | −0.912767 | − | 1.31844i | ||||
\(876\) | − | 2.00000i | − | 0.0675737i | ||||||
\(877\) | 37.0000 | + | 37.0000i | 1.24940 | + | 1.24940i | 0.955985 | + | 0.293417i | \(0.0947923\pi\) |
0.293417 | + | 0.955985i | \(0.405208\pi\) | |||||||
\(878\) | −17.0000 | − | 17.0000i | −0.573722 | − | 0.573722i | ||||
\(879\) | 2.00000 | 0.0674583 | ||||||||
\(880\) | 4.00000 | − | 2.00000i | 0.134840 | − | 0.0674200i | ||||
\(881\) | 12.0000i | 0.404290i | 0.979356 | + | 0.202145i | \(0.0647913\pi\) | ||||
−0.979356 | + | 0.202145i | \(0.935209\pi\) | |||||||
\(882\) | −11.0000 | −0.370389 | ||||||||
\(883\) | − | 2.00000i | − | 0.0673054i | −0.999434 | − | 0.0336527i | \(-0.989286\pi\) | ||
0.999434 | − | 0.0336527i | \(-0.0107140\pi\) | |||||||
\(884\) | − | 8.00000i | − | 0.269069i | ||||||
\(885\) | −14.0000 | − | 28.0000i | −0.470605 | − | 0.941210i | ||||
\(886\) | 11.0000 | + | 11.0000i | 0.369552 | + | 0.369552i | ||||
\(887\) | −5.00000 | + | 5.00000i | −0.167884 | + | 0.167884i | −0.786048 | − | 0.618165i | \(-0.787876\pi\) |
0.618165 | + | 0.786048i | \(0.287876\pi\) | |||||||
\(888\) | −21.0000 | + | 15.0000i | −0.704714 | + | 0.503367i | ||||
\(889\) | − | 54.0000i | − | 1.81110i | ||||||
\(890\) | −5.00000 | + | 15.0000i | −0.167600 | + | 0.502801i | ||||
\(891\) | − | 10.0000i | − | 0.335013i | ||||||
\(892\) | 1.00000 | − | 1.00000i | 0.0334825 | − | 0.0334825i | ||||
\(893\) | 30.0000 | 1.00391 | ||||||||
\(894\) | 16.0000 | − | 16.0000i | 0.535120 | − | 0.535120i | ||||
\(895\) | −7.00000 | + | 21.0000i | −0.233984 | + | 0.701953i | ||||
\(896\) | −9.00000 | − | 9.00000i | −0.300669 | − | 0.300669i | ||||
\(897\) | −16.0000 | − | 16.0000i | −0.534224 | − | 0.534224i | ||||
\(898\) | −5.00000 | + | 5.00000i | −0.166852 | + | 0.166852i | ||||
\(899\) | −42.0000 | −1.40078 | ||||||||
\(900\) | −4.00000 | − | 3.00000i | −0.133333 | − | 0.100000i | ||||
\(901\) | −12.0000 | − | 12.0000i | −0.399778 | − | 0.399778i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 72.0000i | − | 2.39601i | ||||||
\(904\) | − | 12.0000i | − | 0.399114i | ||||||
\(905\) | −10.0000 | − | 20.0000i | −0.332411 | − | 0.664822i | ||||
\(906\) | 2.00000 | − | 2.00000i | 0.0664455 | − | 0.0664455i | ||||
\(907\) | 14.0000i | 0.464862i | 0.972613 | + | 0.232431i | \(0.0746680\pi\) | ||||
−0.972613 | + | 0.232431i | \(0.925332\pi\) | |||||||
\(908\) | 2.00000i | 0.0663723i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6.00000 | − | 18.0000i | 0.198898 | − | 0.596694i | ||||
\(911\) | −11.0000 | − | 11.0000i | −0.364446 | − | 0.364446i | 0.501001 | − | 0.865447i | \(-0.332965\pi\) |
−0.865447 | + | 0.501001i | \(0.832965\pi\) | |||||||
\(912\) | −6.00000 | −0.198680 | ||||||||
\(913\) | 10.0000 | + | 10.0000i | 0.330952 | + | 0.330952i | ||||
\(914\) | 32.0000i | 1.05847i | ||||||||
\(915\) | −2.00000 | − | 4.00000i | −0.0661180 | − | 0.132236i | ||||
\(916\) | − | 4.00000i | − | 0.132164i | ||||||
\(917\) | 30.0000 | 0.990687 | ||||||||
\(918\) | −16.0000 | − | 16.0000i | −0.528079 | − | 0.528079i | ||||
\(919\) | −3.00000 | − | 3.00000i | −0.0989609 | − | 0.0989609i | 0.655893 | − | 0.754854i | \(-0.272292\pi\) |
−0.754854 | + | 0.655893i | \(0.772292\pi\) | |||||||
\(920\) | 24.0000 | + | 48.0000i | 0.791257 | + | 1.58251i | ||||
\(921\) | −18.0000 | −0.593120 | ||||||||
\(922\) | −21.0000 | − | 21.0000i | −0.691598 | − | 0.691598i | ||||
\(923\) | 16.0000 | 0.526646 | ||||||||
\(924\) | 12.0000 | 0.394771 | ||||||||
\(925\) | −21.0000 | − | 22.0000i | −0.690476 | − | 0.723356i | ||||
\(926\) | −40.0000 | −1.31448 | ||||||||
\(927\) | −14.0000 | −0.459820 | ||||||||
\(928\) | 35.0000 | + | 35.0000i | 1.14893 | + | 1.14893i | ||||
\(929\) | 34.0000 | 1.11550 | 0.557752 | − | 0.830008i | \(-0.311664\pi\) | ||||
0.557752 | + | 0.830008i | \(0.311664\pi\) | |||||||
\(930\) | 6.00000 | + | 12.0000i | 0.196748 | + | 0.393496i | ||||
\(931\) | 33.0000 | + | 33.0000i | 1.08153 | + | 1.08153i | ||||
\(932\) | −1.00000 | − | 1.00000i | −0.0327561 | − | 0.0327561i | ||||
\(933\) | 6.00000 | 0.196431 | ||||||||
\(934\) | − | 38.0000i | − | 1.24340i | ||||||
\(935\) | −8.00000 | − | 16.0000i | −0.261628 | − | 0.523256i | ||||
\(936\) | − | 6.00000i | − | 0.196116i | ||||||
\(937\) | −35.0000 | − | 35.0000i | −1.14340 | − | 1.14340i | −0.987824 | − | 0.155576i | \(-0.950277\pi\) |
−0.155576 | − | 0.987824i | \(-0.549723\pi\) | |||||||
\(938\) | 18.0000 | 0.587721 | ||||||||
\(939\) | −30.0000 | − | 30.0000i | −0.979013 | − | 0.979013i | ||||
\(940\) | −5.00000 | + | 15.0000i | −0.163082 | + | 0.489246i | ||||
\(941\) | −30.0000 | −0.977972 | −0.488986 | − | 0.872292i | \(-0.662633\pi\) | ||||
−0.488986 | + | 0.872292i | \(0.662633\pi\) | |||||||
\(942\) | 6.00000i | 0.195491i | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −7.00000 | + | 7.00000i | −0.227831 | + | 0.227831i | ||||
\(945\) | 24.0000 | + | 48.0000i | 0.780720 | + | 1.56144i | ||||
\(946\) | 24.0000i | 0.780307i | ||||||||
\(947\) | − | 18.0000i | − | 0.584921i | −0.956278 | − | 0.292461i | \(-0.905526\pi\) | ||
0.956278 | − | 0.292461i | \(-0.0944741\pi\) | |||||||
\(948\) | −6.00000 | −0.194871 | ||||||||
\(949\) | 2.00000 | + | 2.00000i | 0.0649227 | + | 0.0649227i | ||||
\(950\) | −3.00000 | − | 21.0000i | −0.0973329 | − | 0.681330i | ||||
\(951\) | 34.0000 | 1.10253 | ||||||||
\(952\) | 36.0000 | − | 36.0000i | 1.16677 | − | 1.16677i | ||||
\(953\) | −7.00000 | − | 7.00000i | −0.226752 | − | 0.226752i | 0.584582 | − | 0.811334i | \(-0.301258\pi\) |
−0.811334 | + | 0.584582i | \(0.801258\pi\) | |||||||
\(954\) | −3.00000 | − | 3.00000i | −0.0971286 | − | 0.0971286i | ||||
\(955\) | −11.0000 | + | 33.0000i | −0.355952 | + | 1.06785i | ||||
\(956\) | −7.00000 | + | 7.00000i | −0.226396 | + | 0.226396i | ||||
\(957\) | −28.0000 | −0.905111 | ||||||||
\(958\) | −23.0000 | + | 23.0000i | −0.743096 | + | 0.743096i | ||||
\(959\) | 42.0000i | 1.35625i | ||||||||
\(960\) | 7.00000 | − | 21.0000i | 0.225924 | − | 0.677772i | ||||
\(961\) | 13.0000i | 0.419355i | ||||||||
\(962\) | 2.00000 | − | 12.0000i | 0.0644826 | − | 0.386896i | ||||
\(963\) | −3.00000 | + | 3.00000i | −0.0966736 | + | 0.0966736i | ||||
\(964\) | −1.00000 | − | 1.00000i | −0.0322078 | − | 0.0322078i | ||||
\(965\) | −2.00000 | − | 4.00000i | −0.0643823 | − | 0.128765i | ||||
\(966\) | − | 48.0000i | − | 1.54437i | ||||||
\(967\) | 2.00000i | 0.0643157i | 0.999483 | + | 0.0321578i | \(0.0102379\pi\) | ||||
−0.999483 | + | 0.0321578i | \(0.989762\pi\) | |||||||
\(968\) | 21.0000 | 0.674966 | ||||||||
\(969\) | 24.0000i | 0.770991i | ||||||||
\(970\) | 16.0000 | − | 8.00000i | 0.513729 | − | 0.256865i | ||||
\(971\) | 36.0000 | 1.15529 | 0.577647 | − | 0.816286i | \(-0.303971\pi\) | ||||
0.577647 | + | 0.816286i | \(0.303971\pi\) | |||||||
\(972\) | 7.00000 | + | 7.00000i | 0.224525 | + | 0.224525i | ||||
\(973\) | −12.0000 | − | 12.0000i | −0.384702 | − | 0.384702i | ||||
\(974\) | − | 2.00000i | − | 0.0640841i | ||||||
\(975\) | −14.0000 | + | 2.00000i | −0.448359 | + | 0.0640513i | ||||
\(976\) | −1.00000 | + | 1.00000i | −0.0320092 | + | 0.0320092i | ||||
\(977\) | 18.0000 | 0.575871 | 0.287936 | − | 0.957650i | \(-0.407031\pi\) | ||||
0.287936 | + | 0.957650i | \(0.407031\pi\) | |||||||
\(978\) | −10.0000 | + | 10.0000i | −0.319765 | + | 0.319765i | ||||
\(979\) | 10.0000 | − | 10.0000i | 0.319601 | − | 0.319601i | ||||
\(980\) | −22.0000 | + | 11.0000i | −0.702764 | + | 0.351382i | ||||
\(981\) | 3.00000 | + | 3.00000i | 0.0957826 | + | 0.0957826i | ||||
\(982\) | 4.00000 | 0.127645 | ||||||||
\(983\) | −15.0000 | − | 15.0000i | −0.478426 | − | 0.478426i | 0.426202 | − | 0.904628i | \(-0.359851\pi\) |
−0.904628 | + | 0.426202i | \(0.859851\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.00000 | − | 3.00000i | 0.0318626 | − | 0.0955879i | ||||
\(986\) | −28.0000 | + | 28.0000i | −0.891702 | + | 0.891702i | ||||
\(987\) | 30.0000 | − | 30.0000i | 0.954911 | − | 0.954911i | ||||
\(988\) | −6.00000 | + | 6.00000i | −0.190885 | + | 0.190885i | ||||
\(989\) | −96.0000 | −3.05262 | ||||||||
\(990\) | −2.00000 | − | 4.00000i | −0.0635642 | − | 0.127128i | ||||
\(991\) | 39.0000 | − | 39.0000i | 1.23888 | − | 1.23888i | 0.278415 | − | 0.960461i | \(-0.410191\pi\) |
0.960461 | − | 0.278415i | \(-0.0898090\pi\) | |||||||
\(992\) | −15.0000 | + | 15.0000i | −0.476250 | + | 0.476250i | ||||
\(993\) | − | 14.0000i | − | 0.444277i | ||||||
\(994\) | 24.0000 | + | 24.0000i | 0.761234 | + | 0.761234i | ||||
\(995\) | −15.0000 | + | 45.0000i | −0.475532 | + | 1.42660i | ||||
\(996\) | 10.0000 | 0.316862 | ||||||||
\(997\) | 28.0000i | 0.886769i | 0.896332 | + | 0.443384i | \(0.146222\pi\) | ||||
−0.896332 | + | 0.443384i | \(0.853778\pi\) | |||||||
\(998\) | 27.0000 | + | 27.0000i | 0.854670 | + | 0.854670i | ||||
\(999\) | 20.0000 | + | 28.0000i | 0.632772 | + | 0.885881i |
(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 | 185.2.k.b.117.1 | yes | 2 | |
5.2 | odd | 4 | 925.2.f.b.43.1 | 2 | |||
5.3 | odd | 4 | 185.2.f.a.43.1 | ✓ | 2 | ||
5.4 | even | 2 | 925.2.k.a.857.1 | 2 | |||
37.31 | odd | 4 | 185.2.f.a.142.1 | yes | 2 | ||
185.68 | even | 4 | inner | 185.2.k.b.68.1 | yes | 2 | |
185.142 | even | 4 | 925.2.k.a.68.1 | 2 | |||
185.179 | odd | 4 | 925.2.f.b.882.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
185.2.f.a.43.1 | ✓ | 2 | 5.3 | odd | 4 | ||
185.2.f.a.142.1 | yes | 2 | 37.31 | odd | 4 | ||
185.2.k.b.68.1 | yes | 2 | 185.68 | even | 4 | inner | |
185.2.k.b.117.1 | yes | 2 | 1.1 | even | 1 | trivial | |
925.2.f.b.43.1 | 2 | 5.2 | odd | 4 | |||
925.2.f.b.882.1 | 2 | 185.179 | odd | 4 | |||
925.2.k.a.68.1 | 2 | 185.142 | even | 4 | |||
925.2.k.a.857.1 | 2 | 5.4 | even | 2 |