Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(89,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.89");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.k (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: | \(3.68908857338\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 353.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.353 |
Dual form | 462.2.k.a.89.1 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0.866025 | − | 1.50000i | 0.500000 | − | 0.866025i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −1.73205 | − | 3.00000i | −0.774597 | − | 1.34164i | −0.935021 | − | 0.354593i | \(-0.884620\pi\) |
0.160424 | − | 0.987048i | \(-0.448714\pi\) | |||||||
\(6\) | 1.73205i | 0.707107i | ||||||||
\(7\) | 2.00000 | − | 1.73205i | 0.755929 | − | 0.654654i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.50000 | − | 2.59808i | −0.500000 | − | 0.866025i | ||||
\(10\) | 3.00000 | + | 1.73205i | 0.948683 | + | 0.547723i | ||||
\(11\) | −0.866025 | − | 0.500000i | −0.261116 | − | 0.150756i | ||||
\(12\) | −0.866025 | − | 1.50000i | −0.250000 | − | 0.433013i | ||||
\(13\) | 3.46410i | 0.960769i | 0.877058 | + | 0.480384i | \(0.159503\pi\) | ||||
−0.877058 | + | 0.480384i | \(0.840497\pi\) | |||||||
\(14\) | −0.866025 | + | 2.50000i | −0.231455 | + | 0.668153i | ||||
\(15\) | −6.00000 | −1.54919 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0.866025 | − | 1.50000i | 0.210042 | − | 0.363803i | −0.741685 | − | 0.670748i | \(-0.765973\pi\) |
0.951727 | + | 0.306944i | \(0.0993066\pi\) | |||||||
\(18\) | 2.59808 | + | 1.50000i | 0.612372 | + | 0.353553i | ||||
\(19\) | −1.50000 | + | 0.866025i | −0.344124 | + | 0.198680i | −0.662094 | − | 0.749421i | \(-0.730332\pi\) |
0.317970 | + | 0.948101i | \(0.396999\pi\) | |||||||
\(20\) | −3.46410 | −0.774597 | ||||||||
\(21\) | −0.866025 | − | 4.50000i | −0.188982 | − | 0.981981i | ||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −2.59808 | + | 1.50000i | −0.541736 | + | 0.312772i | −0.745782 | − | 0.666190i | \(-0.767924\pi\) |
0.204046 | + | 0.978961i | \(0.434591\pi\) | |||||||
\(24\) | 1.50000 | + | 0.866025i | 0.306186 | + | 0.176777i | ||||
\(25\) | −3.50000 | + | 6.06218i | −0.700000 | + | 1.21244i | ||||
\(26\) | −1.73205 | − | 3.00000i | −0.339683 | − | 0.588348i | ||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | −0.500000 | − | 2.59808i | −0.0944911 | − | 0.490990i | ||||
\(29\) | − | 3.00000i | − | 0.557086i | −0.960424 | − | 0.278543i | \(-0.910149\pi\) | ||
0.960424 | − | 0.278543i | \(-0.0898515\pi\) | |||||||
\(30\) | 5.19615 | − | 3.00000i | 0.948683 | − | 0.547723i | ||||
\(31\) | 3.00000 | + | 1.73205i | 0.538816 | + | 0.311086i | 0.744599 | − | 0.667512i | \(-0.232641\pi\) |
−0.205783 | + | 0.978598i | \(0.565974\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | −1.50000 | + | 0.866025i | −0.261116 | + | 0.150756i | ||||
\(34\) | 1.73205i | 0.297044i | ||||||||
\(35\) | −8.66025 | − | 3.00000i | −1.46385 | − | 0.507093i | ||||
\(36\) | −3.00000 | −0.500000 | ||||||||
\(37\) | −3.50000 | − | 6.06218i | −0.575396 | − | 0.996616i | −0.995998 | − | 0.0893706i | \(-0.971514\pi\) |
0.420602 | − | 0.907245i | \(-0.361819\pi\) | |||||||
\(38\) | 0.866025 | − | 1.50000i | 0.140488 | − | 0.243332i | ||||
\(39\) | 5.19615 | + | 3.00000i | 0.832050 | + | 0.480384i | ||||
\(40\) | 3.00000 | − | 1.73205i | 0.474342 | − | 0.273861i | ||||
\(41\) | 6.92820 | 1.08200 | 0.541002 | − | 0.841021i | \(-0.318045\pi\) | ||||
0.541002 | + | 0.841021i | \(0.318045\pi\) | |||||||
\(42\) | 3.00000 | + | 3.46410i | 0.462910 | + | 0.534522i | ||||
\(43\) | 1.00000 | 0.152499 | 0.0762493 | − | 0.997089i | \(-0.475706\pi\) | ||||
0.0762493 | + | 0.997089i | \(0.475706\pi\) | |||||||
\(44\) | −0.866025 | + | 0.500000i | −0.130558 | + | 0.0753778i | ||||
\(45\) | −5.19615 | + | 9.00000i | −0.774597 | + | 1.34164i | ||||
\(46\) | 1.50000 | − | 2.59808i | 0.221163 | − | 0.383065i | ||||
\(47\) | 0.866025 | + | 1.50000i | 0.126323 | + | 0.218797i | 0.922249 | − | 0.386596i | \(-0.126349\pi\) |
−0.795926 | + | 0.605393i | \(0.793016\pi\) | |||||||
\(48\) | −1.73205 | −0.250000 | ||||||||
\(49\) | 1.00000 | − | 6.92820i | 0.142857 | − | 0.989743i | ||||
\(50\) | − | 7.00000i | − | 0.989949i | ||||||
\(51\) | −1.50000 | − | 2.59808i | −0.210042 | − | 0.363803i | ||||
\(52\) | 3.00000 | + | 1.73205i | 0.416025 | + | 0.240192i | ||||
\(53\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(54\) | 4.50000 | − | 2.59808i | 0.612372 | − | 0.353553i | ||||
\(55\) | 3.46410i | 0.467099i | ||||||||
\(56\) | 1.73205 | + | 2.00000i | 0.231455 | + | 0.267261i | ||||
\(57\) | 3.00000i | 0.397360i | ||||||||
\(58\) | 1.50000 | + | 2.59808i | 0.196960 | + | 0.341144i | ||||
\(59\) | −6.06218 | + | 10.5000i | −0.789228 | + | 1.36698i | 0.137212 | + | 0.990542i | \(0.456186\pi\) |
−0.926440 | + | 0.376442i | \(0.877147\pi\) | |||||||
\(60\) | −3.00000 | + | 5.19615i | −0.387298 | + | 0.670820i | ||||
\(61\) | 9.00000 | − | 5.19615i | 1.15233 | − | 0.665299i | 0.202878 | − | 0.979204i | \(-0.434971\pi\) |
0.949454 | + | 0.313905i | \(0.101637\pi\) | |||||||
\(62\) | −3.46410 | −0.439941 | ||||||||
\(63\) | −7.50000 | − | 2.59808i | −0.944911 | − | 0.327327i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 10.3923 | − | 6.00000i | 1.28901 | − | 0.744208i | ||||
\(66\) | 0.866025 | − | 1.50000i | 0.106600 | − | 0.184637i | ||||
\(67\) | 8.00000 | − | 13.8564i | 0.977356 | − | 1.69283i | 0.305424 | − | 0.952217i | \(-0.401202\pi\) |
0.671932 | − | 0.740613i | \(-0.265465\pi\) | |||||||
\(68\) | −0.866025 | − | 1.50000i | −0.105021 | − | 0.181902i | ||||
\(69\) | 5.19615i | 0.625543i | ||||||||
\(70\) | 9.00000 | − | 1.73205i | 1.07571 | − | 0.207020i | ||||
\(71\) | − | 15.0000i | − | 1.78017i | −0.455792 | − | 0.890086i | \(-0.650644\pi\) | ||
0.455792 | − | 0.890086i | \(-0.349356\pi\) | |||||||
\(72\) | 2.59808 | − | 1.50000i | 0.306186 | − | 0.176777i | ||||
\(73\) | −12.0000 | − | 6.92820i | −1.40449 | − | 0.810885i | −0.409644 | − | 0.912245i | \(-0.634347\pi\) |
−0.994850 | + | 0.101361i | \(0.967680\pi\) | |||||||
\(74\) | 6.06218 | + | 3.50000i | 0.704714 | + | 0.406867i | ||||
\(75\) | 6.06218 | + | 10.5000i | 0.700000 | + | 1.21244i | ||||
\(76\) | 1.73205i | 0.198680i | ||||||||
\(77\) | −2.59808 | + | 0.500000i | −0.296078 | + | 0.0569803i | ||||
\(78\) | −6.00000 | −0.679366 | ||||||||
\(79\) | −4.00000 | − | 6.92820i | −0.450035 | − | 0.779484i | 0.548352 | − | 0.836247i | \(-0.315255\pi\) |
−0.998388 | + | 0.0567635i | \(0.981922\pi\) | |||||||
\(80\) | −1.73205 | + | 3.00000i | −0.193649 | + | 0.335410i | ||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | −6.00000 | + | 3.46410i | −0.662589 | + | 0.382546i | ||||
\(83\) | 17.3205 | 1.90117 | 0.950586 | − | 0.310460i | \(-0.100483\pi\) | ||||
0.950586 | + | 0.310460i | \(0.100483\pi\) | |||||||
\(84\) | −4.33013 | − | 1.50000i | −0.472456 | − | 0.163663i | ||||
\(85\) | −6.00000 | −0.650791 | ||||||||
\(86\) | −0.866025 | + | 0.500000i | −0.0933859 | + | 0.0539164i | ||||
\(87\) | −4.50000 | − | 2.59808i | −0.482451 | − | 0.278543i | ||||
\(88\) | 0.500000 | − | 0.866025i | 0.0533002 | − | 0.0923186i | ||||
\(89\) | 5.19615 | + | 9.00000i | 0.550791 | + | 0.953998i | 0.998218 | + | 0.0596775i | \(0.0190072\pi\) |
−0.447427 | + | 0.894321i | \(0.647659\pi\) | |||||||
\(90\) | − | 10.3923i | − | 1.09545i | ||||||
\(91\) | 6.00000 | + | 6.92820i | 0.628971 | + | 0.726273i | ||||
\(92\) | 3.00000i | 0.312772i | ||||||||
\(93\) | 5.19615 | − | 3.00000i | 0.538816 | − | 0.311086i | ||||
\(94\) | −1.50000 | − | 0.866025i | −0.154713 | − | 0.0893237i | ||||
\(95\) | 5.19615 | + | 3.00000i | 0.533114 | + | 0.307794i | ||||
\(96\) | 1.50000 | − | 0.866025i | 0.153093 | − | 0.0883883i | ||||
\(97\) | 15.5885i | 1.58277i | 0.611319 | + | 0.791384i | \(0.290639\pi\) | ||||
−0.611319 | + | 0.791384i | \(0.709361\pi\) | |||||||
\(98\) | 2.59808 | + | 6.50000i | 0.262445 | + | 0.656599i | ||||
\(99\) | 3.00000i | 0.301511i | ||||||||
\(100\) | 3.50000 | + | 6.06218i | 0.350000 | + | 0.606218i | ||||
\(101\) | −2.59808 | + | 4.50000i | −0.258518 | + | 0.447767i | −0.965845 | − | 0.259120i | \(-0.916568\pi\) |
0.707327 | + | 0.706887i | \(0.249901\pi\) | |||||||
\(102\) | 2.59808 | + | 1.50000i | 0.257248 | + | 0.148522i | ||||
\(103\) | 15.0000 | − | 8.66025i | 1.47799 | − | 0.853320i | 0.478303 | − | 0.878195i | \(-0.341252\pi\) |
0.999691 | + | 0.0248745i | \(0.00791862\pi\) | |||||||
\(104\) | −3.46410 | −0.339683 | ||||||||
\(105\) | −12.0000 | + | 10.3923i | −1.17108 | + | 1.01419i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.19615 | + | 3.00000i | −0.502331 | + | 0.290021i | −0.729676 | − | 0.683793i | \(-0.760329\pi\) |
0.227345 | + | 0.973814i | \(0.426996\pi\) | |||||||
\(108\) | −2.59808 | + | 4.50000i | −0.250000 | + | 0.433013i | ||||
\(109\) | −8.00000 | + | 13.8564i | −0.766261 | + | 1.32720i | 0.173316 | + | 0.984866i | \(0.444552\pi\) |
−0.939577 | + | 0.342337i | \(0.888782\pi\) | |||||||
\(110\) | −1.73205 | − | 3.00000i | −0.165145 | − | 0.286039i | ||||
\(111\) | −12.1244 | −1.15079 | ||||||||
\(112\) | −2.50000 | − | 0.866025i | −0.236228 | − | 0.0818317i | ||||
\(113\) | 6.00000i | 0.564433i | 0.959351 | + | 0.282216i | \(0.0910696\pi\) | ||||
−0.959351 | + | 0.282216i | \(0.908930\pi\) | |||||||
\(114\) | −1.50000 | − | 2.59808i | −0.140488 | − | 0.243332i | ||||
\(115\) | 9.00000 | + | 5.19615i | 0.839254 | + | 0.484544i | ||||
\(116\) | −2.59808 | − | 1.50000i | −0.241225 | − | 0.139272i | ||||
\(117\) | 9.00000 | − | 5.19615i | 0.832050 | − | 0.480384i | ||||
\(118\) | − | 12.1244i | − | 1.11614i | ||||||
\(119\) | −0.866025 | − | 4.50000i | −0.0793884 | − | 0.412514i | ||||
\(120\) | − | 6.00000i | − | 0.547723i | ||||||
\(121\) | 0.500000 | + | 0.866025i | 0.0454545 | + | 0.0787296i | ||||
\(122\) | −5.19615 | + | 9.00000i | −0.470438 | + | 0.814822i | ||||
\(123\) | 6.00000 | − | 10.3923i | 0.541002 | − | 0.937043i | ||||
\(124\) | 3.00000 | − | 1.73205i | 0.269408 | − | 0.155543i | ||||
\(125\) | 6.92820 | 0.619677 | ||||||||
\(126\) | 7.79423 | − | 1.50000i | 0.694365 | − | 0.133631i | ||||
\(127\) | 11.0000 | 0.976092 | 0.488046 | − | 0.872818i | \(-0.337710\pi\) | ||||
0.488046 | + | 0.872818i | \(0.337710\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 0.866025 | − | 1.50000i | 0.0762493 | − | 0.132068i | ||||
\(130\) | −6.00000 | + | 10.3923i | −0.526235 | + | 0.911465i | ||||
\(131\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(132\) | 1.73205i | 0.150756i | ||||||||
\(133\) | −1.50000 | + | 4.33013i | −0.130066 | + | 0.375470i | ||||
\(134\) | 16.0000i | 1.38219i | ||||||||
\(135\) | 9.00000 | + | 15.5885i | 0.774597 | + | 1.34164i | ||||
\(136\) | 1.50000 | + | 0.866025i | 0.128624 | + | 0.0742611i | ||||
\(137\) | 15.5885 | + | 9.00000i | 1.33181 | + | 0.768922i | 0.985577 | − | 0.169226i | \(-0.0541268\pi\) |
0.346235 | + | 0.938148i | \(0.387460\pi\) | |||||||
\(138\) | −2.59808 | − | 4.50000i | −0.221163 | − | 0.383065i | ||||
\(139\) | 1.73205i | 0.146911i | 0.997299 | + | 0.0734553i | \(0.0234026\pi\) | ||||
−0.997299 | + | 0.0734553i | \(0.976597\pi\) | |||||||
\(140\) | −6.92820 | + | 6.00000i | −0.585540 | + | 0.507093i | ||||
\(141\) | 3.00000 | 0.252646 | ||||||||
\(142\) | 7.50000 | + | 12.9904i | 0.629386 | + | 1.09013i | ||||
\(143\) | 1.73205 | − | 3.00000i | 0.144841 | − | 0.250873i | ||||
\(144\) | −1.50000 | + | 2.59808i | −0.125000 | + | 0.216506i | ||||
\(145\) | −9.00000 | + | 5.19615i | −0.747409 | + | 0.431517i | ||||
\(146\) | 13.8564 | 1.14676 | ||||||||
\(147\) | −9.52628 | − | 7.50000i | −0.785714 | − | 0.618590i | ||||
\(148\) | −7.00000 | −0.575396 | ||||||||
\(149\) | −7.79423 | + | 4.50000i | −0.638528 | + | 0.368654i | −0.784047 | − | 0.620701i | \(-0.786848\pi\) |
0.145519 | + | 0.989355i | \(0.453515\pi\) | |||||||
\(150\) | −10.5000 | − | 6.06218i | −0.857321 | − | 0.494975i | ||||
\(151\) | 5.50000 | − | 9.52628i | 0.447584 | − | 0.775238i | −0.550645 | − | 0.834740i | \(-0.685618\pi\) |
0.998228 | + | 0.0595022i | \(0.0189513\pi\) | |||||||
\(152\) | −0.866025 | − | 1.50000i | −0.0702439 | − | 0.121666i | ||||
\(153\) | −5.19615 | −0.420084 | ||||||||
\(154\) | 2.00000 | − | 1.73205i | 0.161165 | − | 0.139573i | ||||
\(155\) | − | 12.0000i | − | 0.963863i | ||||||
\(156\) | 5.19615 | − | 3.00000i | 0.416025 | − | 0.240192i | ||||
\(157\) | 4.50000 | + | 2.59808i | 0.359139 | + | 0.207349i | 0.668703 | − | 0.743530i | \(-0.266850\pi\) |
−0.309564 | + | 0.950879i | \(0.600183\pi\) | |||||||
\(158\) | 6.92820 | + | 4.00000i | 0.551178 | + | 0.318223i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 3.46410i | − | 0.273861i | ||||||
\(161\) | −2.59808 | + | 7.50000i | −0.204757 | + | 0.591083i | ||||
\(162\) | − | 9.00000i | − | 0.707107i | ||||||
\(163\) | −7.00000 | − | 12.1244i | −0.548282 | − | 0.949653i | −0.998392 | − | 0.0566798i | \(-0.981949\pi\) |
0.450110 | − | 0.892973i | \(-0.351385\pi\) | |||||||
\(164\) | 3.46410 | − | 6.00000i | 0.270501 | − | 0.468521i | ||||
\(165\) | 5.19615 | + | 3.00000i | 0.404520 | + | 0.233550i | ||||
\(166\) | −15.0000 | + | 8.66025i | −1.16423 | + | 0.672166i | ||||
\(167\) | 24.2487 | 1.87642 | 0.938211 | − | 0.346064i | \(-0.112482\pi\) | ||||
0.938211 | + | 0.346064i | \(0.112482\pi\) | |||||||
\(168\) | 4.50000 | − | 0.866025i | 0.347183 | − | 0.0668153i | ||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 5.19615 | − | 3.00000i | 0.398527 | − | 0.230089i | ||||
\(171\) | 4.50000 | + | 2.59808i | 0.344124 | + | 0.198680i | ||||
\(172\) | 0.500000 | − | 0.866025i | 0.0381246 | − | 0.0660338i | ||||
\(173\) | −10.3923 | − | 18.0000i | −0.790112 | − | 1.36851i | −0.925897 | − | 0.377776i | \(-0.876689\pi\) |
0.135785 | − | 0.990738i | \(-0.456644\pi\) | |||||||
\(174\) | 5.19615 | 0.393919 | ||||||||
\(175\) | 3.50000 | + | 18.1865i | 0.264575 | + | 1.37477i | ||||
\(176\) | 1.00000i | 0.0753778i | ||||||||
\(177\) | 10.5000 | + | 18.1865i | 0.789228 | + | 1.36698i | ||||
\(178\) | −9.00000 | − | 5.19615i | −0.674579 | − | 0.389468i | ||||
\(179\) | −12.9904 | − | 7.50000i | −0.970947 | − | 0.560576i | −0.0714220 | − | 0.997446i | \(-0.522754\pi\) |
−0.899525 | + | 0.436870i | \(0.856087\pi\) | |||||||
\(180\) | 5.19615 | + | 9.00000i | 0.387298 | + | 0.670820i | ||||
\(181\) | − | 13.8564i | − | 1.02994i | −0.857209 | − | 0.514969i | \(-0.827803\pi\) | ||
0.857209 | − | 0.514969i | \(-0.172197\pi\) | |||||||
\(182\) | −8.66025 | − | 3.00000i | −0.641941 | − | 0.222375i | ||||
\(183\) | − | 18.0000i | − | 1.33060i | ||||||
\(184\) | −1.50000 | − | 2.59808i | −0.110581 | − | 0.191533i | ||||
\(185\) | −12.1244 | + | 21.0000i | −0.891400 | + | 1.54395i | ||||
\(186\) | −3.00000 | + | 5.19615i | −0.219971 | + | 0.381000i | ||||
\(187\) | −1.50000 | + | 0.866025i | −0.109691 | + | 0.0633300i | ||||
\(188\) | 1.73205 | 0.126323 | ||||||||
\(189\) | −10.3923 | + | 9.00000i | −0.755929 | + | 0.654654i | ||||
\(190\) | −6.00000 | −0.435286 | ||||||||
\(191\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(192\) | −0.866025 | + | 1.50000i | −0.0625000 | + | 0.108253i | ||||
\(193\) | −2.00000 | + | 3.46410i | −0.143963 | + | 0.249351i | −0.928986 | − | 0.370116i | \(-0.879318\pi\) |
0.785022 | + | 0.619467i | \(0.212651\pi\) | |||||||
\(194\) | −7.79423 | − | 13.5000i | −0.559593 | − | 0.969244i | ||||
\(195\) | − | 20.7846i | − | 1.48842i | ||||||
\(196\) | −5.50000 | − | 4.33013i | −0.392857 | − | 0.309295i | ||||
\(197\) | − | 9.00000i | − | 0.641223i | −0.947211 | − | 0.320612i | \(-0.896112\pi\) | ||
0.947211 | − | 0.320612i | \(-0.103888\pi\) | |||||||
\(198\) | −1.50000 | − | 2.59808i | −0.106600 | − | 0.184637i | ||||
\(199\) | −9.00000 | − | 5.19615i | −0.637993 | − | 0.368345i | 0.145848 | − | 0.989307i | \(-0.453409\pi\) |
−0.783841 | + | 0.620962i | \(0.786742\pi\) | |||||||
\(200\) | −6.06218 | − | 3.50000i | −0.428661 | − | 0.247487i | ||||
\(201\) | −13.8564 | − | 24.0000i | −0.977356 | − | 1.69283i | ||||
\(202\) | − | 5.19615i | − | 0.365600i | ||||||
\(203\) | −5.19615 | − | 6.00000i | −0.364698 | − | 0.421117i | ||||
\(204\) | −3.00000 | −0.210042 | ||||||||
\(205\) | −12.0000 | − | 20.7846i | −0.838116 | − | 1.45166i | ||||
\(206\) | −8.66025 | + | 15.0000i | −0.603388 | + | 1.04510i | ||||
\(207\) | 7.79423 | + | 4.50000i | 0.541736 | + | 0.312772i | ||||
\(208\) | 3.00000 | − | 1.73205i | 0.208013 | − | 0.120096i | ||||
\(209\) | 1.73205 | 0.119808 | ||||||||
\(210\) | 5.19615 | − | 15.0000i | 0.358569 | − | 1.03510i | ||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −22.5000 | − | 12.9904i | −1.54167 | − | 0.890086i | ||||
\(214\) | 3.00000 | − | 5.19615i | 0.205076 | − | 0.355202i | ||||
\(215\) | −1.73205 | − | 3.00000i | −0.118125 | − | 0.204598i | ||||
\(216\) | − | 5.19615i | − | 0.353553i | ||||||
\(217\) | 9.00000 | − | 1.73205i | 0.610960 | − | 0.117579i | ||||
\(218\) | − | 16.0000i | − | 1.08366i | ||||||
\(219\) | −20.7846 | + | 12.0000i | −1.40449 | + | 0.810885i | ||||
\(220\) | 3.00000 | + | 1.73205i | 0.202260 | + | 0.116775i | ||||
\(221\) | 5.19615 | + | 3.00000i | 0.349531 | + | 0.201802i | ||||
\(222\) | 10.5000 | − | 6.06218i | 0.704714 | − | 0.406867i | ||||
\(223\) | 10.3923i | 0.695920i | 0.937509 | + | 0.347960i | \(0.113126\pi\) | ||||
−0.937509 | + | 0.347960i | \(0.886874\pi\) | |||||||
\(224\) | 2.59808 | − | 0.500000i | 0.173591 | − | 0.0334077i | ||||
\(225\) | 21.0000 | 1.40000 | ||||||||
\(226\) | −3.00000 | − | 5.19615i | −0.199557 | − | 0.345643i | ||||
\(227\) | 5.19615 | − | 9.00000i | 0.344881 | − | 0.597351i | −0.640451 | − | 0.767999i | \(-0.721253\pi\) |
0.985332 | + | 0.170648i | \(0.0545860\pi\) | |||||||
\(228\) | 2.59808 | + | 1.50000i | 0.172062 | + | 0.0993399i | ||||
\(229\) | −12.0000 | + | 6.92820i | −0.792982 | + | 0.457829i | −0.841011 | − | 0.541017i | \(-0.818039\pi\) |
0.0480291 | + | 0.998846i | \(0.484706\pi\) | |||||||
\(230\) | −10.3923 | −0.685248 | ||||||||
\(231\) | −1.50000 | + | 4.33013i | −0.0986928 | + | 0.284901i | ||||
\(232\) | 3.00000 | 0.196960 | ||||||||
\(233\) | 23.3827 | − | 13.5000i | 1.53185 | − | 0.884414i | 0.532574 | − | 0.846383i | \(-0.321225\pi\) |
0.999277 | − | 0.0380310i | \(-0.0121086\pi\) | |||||||
\(234\) | −5.19615 | + | 9.00000i | −0.339683 | + | 0.588348i | ||||
\(235\) | 3.00000 | − | 5.19615i | 0.195698 | − | 0.338960i | ||||
\(236\) | 6.06218 | + | 10.5000i | 0.394614 | + | 0.683492i | ||||
\(237\) | −13.8564 | −0.900070 | ||||||||
\(238\) | 3.00000 | + | 3.46410i | 0.194461 | + | 0.224544i | ||||
\(239\) | − | 6.00000i | − | 0.388108i | −0.980991 | − | 0.194054i | \(-0.937836\pi\) | ||
0.980991 | − | 0.194054i | \(-0.0621637\pi\) | |||||||
\(240\) | 3.00000 | + | 5.19615i | 0.193649 | + | 0.335410i | ||||
\(241\) | 18.0000 | + | 10.3923i | 1.15948 | + | 0.669427i | 0.951180 | − | 0.308637i | \(-0.0998729\pi\) |
0.208302 | + | 0.978065i | \(0.433206\pi\) | |||||||
\(242\) | −0.866025 | − | 0.500000i | −0.0556702 | − | 0.0321412i | ||||
\(243\) | 7.79423 | + | 13.5000i | 0.500000 | + | 0.866025i | ||||
\(244\) | − | 10.3923i | − | 0.665299i | ||||||
\(245\) | −22.5167 | + | 9.00000i | −1.43854 | + | 0.574989i | ||||
\(246\) | 12.0000i | 0.765092i | ||||||||
\(247\) | −3.00000 | − | 5.19615i | −0.190885 | − | 0.330623i | ||||
\(248\) | −1.73205 | + | 3.00000i | −0.109985 | + | 0.190500i | ||||
\(249\) | 15.0000 | − | 25.9808i | 0.950586 | − | 1.64646i | ||||
\(250\) | −6.00000 | + | 3.46410i | −0.379473 | + | 0.219089i | ||||
\(251\) | −12.1244 | −0.765283 | −0.382641 | − | 0.923897i | \(-0.624985\pi\) | ||||
−0.382641 | + | 0.923897i | \(0.624985\pi\) | |||||||
\(252\) | −6.00000 | + | 5.19615i | −0.377964 | + | 0.327327i | ||||
\(253\) | 3.00000 | 0.188608 | ||||||||
\(254\) | −9.52628 | + | 5.50000i | −0.597732 | + | 0.345101i | ||||
\(255\) | −5.19615 | + | 9.00000i | −0.325396 | + | 0.563602i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −5.19615 | − | 9.00000i | −0.324127 | − | 0.561405i | 0.657208 | − | 0.753709i | \(-0.271737\pi\) |
−0.981335 | + | 0.192304i | \(0.938404\pi\) | |||||||
\(258\) | 1.73205i | 0.107833i | ||||||||
\(259\) | −17.5000 | − | 6.06218i | −1.08740 | − | 0.376685i | ||||
\(260\) | − | 12.0000i | − | 0.744208i | ||||||
\(261\) | −7.79423 | + | 4.50000i | −0.482451 | + | 0.278543i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.5885 | + | 9.00000i | 0.961225 | + | 0.554964i | 0.896550 | − | 0.442943i | \(-0.146065\pi\) |
0.0646755 | + | 0.997906i | \(0.479399\pi\) | |||||||
\(264\) | −0.866025 | − | 1.50000i | −0.0533002 | − | 0.0923186i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.866025 | − | 4.50000i | −0.0530994 | − | 0.275913i | ||||
\(267\) | 18.0000 | 1.10158 | ||||||||
\(268\) | −8.00000 | − | 13.8564i | −0.488678 | − | 0.846415i | ||||
\(269\) | 6.92820 | − | 12.0000i | 0.422420 | − | 0.731653i | −0.573756 | − | 0.819027i | \(-0.694514\pi\) |
0.996176 | + | 0.0873736i | \(0.0278474\pi\) | |||||||
\(270\) | −15.5885 | − | 9.00000i | −0.948683 | − | 0.547723i | ||||
\(271\) | −9.00000 | + | 5.19615i | −0.546711 | + | 0.315644i | −0.747794 | − | 0.663930i | \(-0.768887\pi\) |
0.201083 | + | 0.979574i | \(0.435554\pi\) | |||||||
\(272\) | −1.73205 | −0.105021 | ||||||||
\(273\) | 15.5885 | − | 3.00000i | 0.943456 | − | 0.181568i | ||||
\(274\) | −18.0000 | −1.08742 | ||||||||
\(275\) | 6.06218 | − | 3.50000i | 0.365563 | − | 0.211058i | ||||
\(276\) | 4.50000 | + | 2.59808i | 0.270868 | + | 0.156386i | ||||
\(277\) | −4.00000 | + | 6.92820i | −0.240337 | + | 0.416275i | −0.960810 | − | 0.277207i | \(-0.910591\pi\) |
0.720473 | + | 0.693482i | \(0.243925\pi\) | |||||||
\(278\) | −0.866025 | − | 1.50000i | −0.0519408 | − | 0.0899640i | ||||
\(279\) | − | 10.3923i | − | 0.622171i | ||||||
\(280\) | 3.00000 | − | 8.66025i | 0.179284 | − | 0.517549i | ||||
\(281\) | 15.0000i | 0.894825i | 0.894328 | + | 0.447412i | \(0.147654\pi\) | ||||
−0.894328 | + | 0.447412i | \(0.852346\pi\) | |||||||
\(282\) | −2.59808 | + | 1.50000i | −0.154713 | + | 0.0893237i | ||||
\(283\) | 15.0000 | + | 8.66025i | 0.891657 | + | 0.514799i | 0.874484 | − | 0.485054i | \(-0.161200\pi\) |
0.0171732 | + | 0.999853i | \(0.494533\pi\) | |||||||
\(284\) | −12.9904 | − | 7.50000i | −0.770837 | − | 0.445043i | ||||
\(285\) | 9.00000 | − | 5.19615i | 0.533114 | − | 0.307794i | ||||
\(286\) | 3.46410i | 0.204837i | ||||||||
\(287\) | 13.8564 | − | 12.0000i | 0.817918 | − | 0.708338i | ||||
\(288\) | − | 3.00000i | − | 0.176777i | ||||||
\(289\) | 7.00000 | + | 12.1244i | 0.411765 | + | 0.713197i | ||||
\(290\) | 5.19615 | − | 9.00000i | 0.305129 | − | 0.528498i | ||||
\(291\) | 23.3827 | + | 13.5000i | 1.37072 | + | 0.791384i | ||||
\(292\) | −12.0000 | + | 6.92820i | −0.702247 | + | 0.405442i | ||||
\(293\) | −8.66025 | −0.505937 | −0.252969 | − | 0.967474i | \(-0.581407\pi\) | ||||
−0.252969 | + | 0.967474i | \(0.581407\pi\) | |||||||
\(294\) | 12.0000 | + | 1.73205i | 0.699854 | + | 0.101015i | ||||
\(295\) | 42.0000 | 2.44533 | ||||||||
\(296\) | 6.06218 | − | 3.50000i | 0.352357 | − | 0.203433i | ||||
\(297\) | 4.50000 | + | 2.59808i | 0.261116 | + | 0.150756i | ||||
\(298\) | 4.50000 | − | 7.79423i | 0.260678 | − | 0.451508i | ||||
\(299\) | −5.19615 | − | 9.00000i | −0.300501 | − | 0.520483i | ||||
\(300\) | 12.1244 | 0.700000 | ||||||||
\(301\) | 2.00000 | − | 1.73205i | 0.115278 | − | 0.0998337i | ||||
\(302\) | 11.0000i | 0.632979i | ||||||||
\(303\) | 4.50000 | + | 7.79423i | 0.258518 | + | 0.447767i | ||||
\(304\) | 1.50000 | + | 0.866025i | 0.0860309 | + | 0.0496700i | ||||
\(305\) | −31.1769 | − | 18.0000i | −1.78518 | − | 1.03068i | ||||
\(306\) | 4.50000 | − | 2.59808i | 0.257248 | − | 0.148522i | ||||
\(307\) | 17.3205i | 0.988534i | 0.869310 | + | 0.494267i | \(0.164563\pi\) | ||||
−0.869310 | + | 0.494267i | \(0.835437\pi\) | |||||||
\(308\) | −0.866025 | + | 2.50000i | −0.0493464 | + | 0.142451i | ||||
\(309\) | − | 30.0000i | − | 1.70664i | ||||||
\(310\) | 6.00000 | + | 10.3923i | 0.340777 | + | 0.590243i | ||||
\(311\) | 11.2583 | − | 19.5000i | 0.638401 | − | 1.10574i | −0.347382 | − | 0.937724i | \(-0.612929\pi\) |
0.985784 | − | 0.168020i | \(-0.0537373\pi\) | |||||||
\(312\) | −3.00000 | + | 5.19615i | −0.169842 | + | 0.294174i | ||||
\(313\) | −25.5000 | + | 14.7224i | −1.44135 | + | 0.832161i | −0.997940 | − | 0.0641600i | \(-0.979563\pi\) |
−0.443406 | + | 0.896321i | \(0.646230\pi\) | |||||||
\(314\) | −5.19615 | −0.293236 | ||||||||
\(315\) | 5.19615 | + | 27.0000i | 0.292770 | + | 1.52128i | ||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | 5.19615 | − | 3.00000i | 0.291845 | − | 0.168497i | −0.346929 | − | 0.937892i | \(-0.612775\pi\) |
0.638774 | + | 0.769395i | \(0.279442\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.50000 | + | 2.59808i | −0.0839839 | + | 0.145464i | ||||
\(320\) | 1.73205 | + | 3.00000i | 0.0968246 | + | 0.167705i | ||||
\(321\) | 10.3923i | 0.580042i | ||||||||
\(322\) | −1.50000 | − | 7.79423i | −0.0835917 | − | 0.434355i | ||||
\(323\) | 3.00000i | 0.166924i | ||||||||
\(324\) | 4.50000 | + | 7.79423i | 0.250000 | + | 0.433013i | ||||
\(325\) | −21.0000 | − | 12.1244i | −1.16487 | − | 0.672538i | ||||
\(326\) | 12.1244 | + | 7.00000i | 0.671506 | + | 0.387694i | ||||
\(327\) | 13.8564 | + | 24.0000i | 0.766261 | + | 1.32720i | ||||
\(328\) | 6.92820i | 0.382546i | ||||||||
\(329\) | 4.33013 | + | 1.50000i | 0.238728 | + | 0.0826977i | ||||
\(330\) | −6.00000 | −0.330289 | ||||||||
\(331\) | −5.00000 | − | 8.66025i | −0.274825 | − | 0.476011i | 0.695266 | − | 0.718752i | \(-0.255287\pi\) |
−0.970091 | + | 0.242742i | \(0.921953\pi\) | |||||||
\(332\) | 8.66025 | − | 15.0000i | 0.475293 | − | 0.823232i | ||||
\(333\) | −10.5000 | + | 18.1865i | −0.575396 | + | 0.996616i | ||||
\(334\) | −21.0000 | + | 12.1244i | −1.14907 | + | 0.663415i | ||||
\(335\) | −55.4256 | −3.02823 | ||||||||
\(336\) | −3.46410 | + | 3.00000i | −0.188982 | + | 0.163663i | ||||
\(337\) | 4.00000 | 0.217894 | 0.108947 | − | 0.994048i | \(-0.465252\pi\) | ||||
0.108947 | + | 0.994048i | \(0.465252\pi\) | |||||||
\(338\) | −0.866025 | + | 0.500000i | −0.0471056 | + | 0.0271964i | ||||
\(339\) | 9.00000 | + | 5.19615i | 0.488813 | + | 0.282216i | ||||
\(340\) | −3.00000 | + | 5.19615i | −0.162698 | + | 0.281801i | ||||
\(341\) | −1.73205 | − | 3.00000i | −0.0937958 | − | 0.162459i | ||||
\(342\) | −5.19615 | −0.280976 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | 1.00000i | 0.0539164i | ||||||||
\(345\) | 15.5885 | − | 9.00000i | 0.839254 | − | 0.484544i | ||||
\(346\) | 18.0000 | + | 10.3923i | 0.967686 | + | 0.558694i | ||||
\(347\) | 20.7846 | + | 12.0000i | 1.11578 | + | 0.644194i | 0.940319 | − | 0.340293i | \(-0.110526\pi\) |
0.175457 | + | 0.984487i | \(0.443860\pi\) | |||||||
\(348\) | −4.50000 | + | 2.59808i | −0.241225 | + | 0.139272i | ||||
\(349\) | 20.7846i | 1.11257i | 0.830990 | + | 0.556287i | \(0.187775\pi\) | ||||
−0.830990 | + | 0.556287i | \(0.812225\pi\) | |||||||
\(350\) | −12.1244 | − | 14.0000i | −0.648074 | − | 0.748331i | ||||
\(351\) | − | 18.0000i | − | 0.960769i | ||||||
\(352\) | −0.500000 | − | 0.866025i | −0.0266501 | − | 0.0461593i | ||||
\(353\) | −1.73205 | + | 3.00000i | −0.0921878 | + | 0.159674i | −0.908431 | − | 0.418034i | \(-0.862719\pi\) |
0.816244 | + | 0.577708i | \(0.196053\pi\) | |||||||
\(354\) | −18.1865 | − | 10.5000i | −0.966603 | − | 0.558069i | ||||
\(355\) | −45.0000 | + | 25.9808i | −2.38835 | + | 1.37892i | ||||
\(356\) | 10.3923 | 0.550791 | ||||||||
\(357\) | −7.50000 | − | 2.59808i | −0.396942 | − | 0.137505i | ||||
\(358\) | 15.0000 | 0.792775 | ||||||||
\(359\) | −5.19615 | + | 3.00000i | −0.274242 | + | 0.158334i | −0.630814 | − | 0.775934i | \(-0.717279\pi\) |
0.356572 | + | 0.934268i | \(0.383946\pi\) | |||||||
\(360\) | −9.00000 | − | 5.19615i | −0.474342 | − | 0.273861i | ||||
\(361\) | −8.00000 | + | 13.8564i | −0.421053 | + | 0.729285i | ||||
\(362\) | 6.92820 | + | 12.0000i | 0.364138 | + | 0.630706i | ||||
\(363\) | 1.73205 | 0.0909091 | ||||||||
\(364\) | 9.00000 | − | 1.73205i | 0.471728 | − | 0.0907841i | ||||
\(365\) | 48.0000i | 2.51243i | ||||||||
\(366\) | 9.00000 | + | 15.5885i | 0.470438 | + | 0.814822i | ||||
\(367\) | −6.00000 | − | 3.46410i | −0.313197 | − | 0.180825i | 0.335159 | − | 0.942162i | \(-0.391210\pi\) |
−0.648356 | + | 0.761337i | \(0.724543\pi\) | |||||||
\(368\) | 2.59808 | + | 1.50000i | 0.135434 | + | 0.0781929i | ||||
\(369\) | −10.3923 | − | 18.0000i | −0.541002 | − | 0.937043i | ||||
\(370\) | − | 24.2487i | − | 1.26063i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 6.00000i | − | 0.311086i | ||||||
\(373\) | −7.00000 | − | 12.1244i | −0.362446 | − | 0.627775i | 0.625917 | − | 0.779890i | \(-0.284725\pi\) |
−0.988363 | + | 0.152115i | \(0.951392\pi\) | |||||||
\(374\) | 0.866025 | − | 1.50000i | 0.0447811 | − | 0.0775632i | ||||
\(375\) | 6.00000 | − | 10.3923i | 0.309839 | − | 0.536656i | ||||
\(376\) | −1.50000 | + | 0.866025i | −0.0773566 | + | 0.0446619i | ||||
\(377\) | 10.3923 | 0.535231 | ||||||||
\(378\) | 4.50000 | − | 12.9904i | 0.231455 | − | 0.668153i | ||||
\(379\) | −20.0000 | −1.02733 | −0.513665 | − | 0.857991i | \(-0.671713\pi\) | ||||
−0.513665 | + | 0.857991i | \(0.671713\pi\) | |||||||
\(380\) | 5.19615 | − | 3.00000i | 0.266557 | − | 0.153897i | ||||
\(381\) | 9.52628 | − | 16.5000i | 0.488046 | − | 0.845321i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.7224 | + | 25.5000i | 0.752281 | + | 1.30299i | 0.946715 | + | 0.322073i | \(0.104380\pi\) |
−0.194434 | + | 0.980916i | \(0.562287\pi\) | |||||||
\(384\) | − | 1.73205i | − | 0.0883883i | ||||||
\(385\) | 6.00000 | + | 6.92820i | 0.305788 | + | 0.353094i | ||||
\(386\) | − | 4.00000i | − | 0.203595i | ||||||
\(387\) | −1.50000 | − | 2.59808i | −0.0762493 | − | 0.132068i | ||||
\(388\) | 13.5000 | + | 7.79423i | 0.685359 | + | 0.395692i | ||||
\(389\) | −15.5885 | − | 9.00000i | −0.790366 | − | 0.456318i | 0.0497253 | − | 0.998763i | \(-0.484165\pi\) |
−0.840091 | + | 0.542445i | \(0.817499\pi\) | |||||||
\(390\) | 10.3923 | + | 18.0000i | 0.526235 | + | 0.911465i | ||||
\(391\) | 5.19615i | 0.262781i | ||||||||
\(392\) | 6.92820 | + | 1.00000i | 0.349927 | + | 0.0505076i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.50000 | + | 7.79423i | 0.226707 | + | 0.392668i | ||||
\(395\) | −13.8564 | + | 24.0000i | −0.697191 | + | 1.20757i | ||||
\(396\) | 2.59808 | + | 1.50000i | 0.130558 | + | 0.0753778i | ||||
\(397\) | −1.50000 | + | 0.866025i | −0.0752828 | + | 0.0434646i | −0.537169 | − | 0.843475i | \(-0.680506\pi\) |
0.461886 | + | 0.886939i | \(0.347173\pi\) | |||||||
\(398\) | 10.3923 | 0.520919 | ||||||||
\(399\) | 5.19615 | + | 6.00000i | 0.260133 | + | 0.300376i | ||||
\(400\) | 7.00000 | 0.350000 | ||||||||
\(401\) | −20.7846 | + | 12.0000i | −1.03793 | + | 0.599251i | −0.919247 | − | 0.393680i | \(-0.871202\pi\) |
−0.118686 | + | 0.992932i | \(0.537868\pi\) | |||||||
\(402\) | 24.0000 | + | 13.8564i | 1.19701 | + | 0.691095i | ||||
\(403\) | −6.00000 | + | 10.3923i | −0.298881 | + | 0.517678i | ||||
\(404\) | 2.59808 | + | 4.50000i | 0.129259 | + | 0.223883i | ||||
\(405\) | 31.1769 | 1.54919 | ||||||||
\(406\) | 7.50000 | + | 2.59808i | 0.372219 | + | 0.128940i | ||||
\(407\) | 7.00000i | 0.346977i | ||||||||
\(408\) | 2.59808 | − | 1.50000i | 0.128624 | − | 0.0742611i | ||||
\(409\) | 12.0000 | + | 6.92820i | 0.593362 | + | 0.342578i | 0.766426 | − | 0.642333i | \(-0.222033\pi\) |
−0.173064 | + | 0.984911i | \(0.555367\pi\) | |||||||
\(410\) | 20.7846 | + | 12.0000i | 1.02648 | + | 0.592638i | ||||
\(411\) | 27.0000 | − | 15.5885i | 1.33181 | − | 0.768922i | ||||
\(412\) | − | 17.3205i | − | 0.853320i | ||||||
\(413\) | 6.06218 | + | 31.5000i | 0.298300 | + | 1.55001i | ||||
\(414\) | −9.00000 | −0.442326 | ||||||||
\(415\) | −30.0000 | − | 51.9615i | −1.47264 | − | 2.55069i | ||||
\(416\) | −1.73205 | + | 3.00000i | −0.0849208 | + | 0.147087i | ||||
\(417\) | 2.59808 | + | 1.50000i | 0.127228 | + | 0.0734553i | ||||
\(418\) | −1.50000 | + | 0.866025i | −0.0733674 | + | 0.0423587i | ||||
\(419\) | −1.73205 | −0.0846162 | −0.0423081 | − | 0.999105i | \(-0.513471\pi\) | ||||
−0.0423081 | + | 0.999105i | \(0.513471\pi\) | |||||||
\(420\) | 3.00000 | + | 15.5885i | 0.146385 | + | 0.760639i | ||||
\(421\) | 5.00000 | 0.243685 | 0.121843 | − | 0.992549i | \(-0.461120\pi\) | ||||
0.121843 | + | 0.992549i | \(0.461120\pi\) | |||||||
\(422\) | −3.46410 | + | 2.00000i | −0.168630 | + | 0.0973585i | ||||
\(423\) | 2.59808 | − | 4.50000i | 0.126323 | − | 0.218797i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.06218 | + | 10.5000i | 0.294059 | + | 0.509325i | ||||
\(426\) | 25.9808 | 1.25877 | ||||||||
\(427\) | 9.00000 | − | 25.9808i | 0.435541 | − | 1.25730i | ||||
\(428\) | 6.00000i | 0.290021i | ||||||||
\(429\) | −3.00000 | − | 5.19615i | −0.144841 | − | 0.250873i | ||||
\(430\) | 3.00000 | + | 1.73205i | 0.144673 | + | 0.0835269i | ||||
\(431\) | 10.3923 | + | 6.00000i | 0.500580 | + | 0.289010i | 0.728953 | − | 0.684564i | \(-0.240007\pi\) |
−0.228373 | + | 0.973574i | \(0.573341\pi\) | |||||||
\(432\) | 2.59808 | + | 4.50000i | 0.125000 | + | 0.216506i | ||||
\(433\) | 8.66025i | 0.416185i | 0.978109 | + | 0.208093i | \(0.0667255\pi\) | ||||
−0.978109 | + | 0.208093i | \(0.933274\pi\) | |||||||
\(434\) | −6.92820 | + | 6.00000i | −0.332564 | + | 0.288009i | ||||
\(435\) | 18.0000i | 0.863034i | ||||||||
\(436\) | 8.00000 | + | 13.8564i | 0.383131 | + | 0.663602i | ||||
\(437\) | 2.59808 | − | 4.50000i | 0.124283 | − | 0.215264i | ||||
\(438\) | 12.0000 | − | 20.7846i | 0.573382 | − | 0.993127i | ||||
\(439\) | 13.5000 | − | 7.79423i | 0.644320 | − | 0.371998i | −0.141957 | − | 0.989873i | \(-0.545339\pi\) |
0.786277 | + | 0.617875i | \(0.212006\pi\) | |||||||
\(440\) | −3.46410 | −0.165145 | ||||||||
\(441\) | −19.5000 | + | 7.79423i | −0.928571 | + | 0.371154i | ||||
\(442\) | −6.00000 | −0.285391 | ||||||||
\(443\) | 7.79423 | − | 4.50000i | 0.370315 | − | 0.213801i | −0.303281 | − | 0.952901i | \(-0.598082\pi\) |
0.673596 | + | 0.739100i | \(0.264749\pi\) | |||||||
\(444\) | −6.06218 | + | 10.5000i | −0.287698 | + | 0.498308i | ||||
\(445\) | 18.0000 | − | 31.1769i | 0.853282 | − | 1.47793i | ||||
\(446\) | −5.19615 | − | 9.00000i | −0.246045 | − | 0.426162i | ||||
\(447\) | 15.5885i | 0.737309i | ||||||||
\(448\) | −2.00000 | + | 1.73205i | −0.0944911 | + | 0.0818317i | ||||
\(449\) | 12.0000i | 0.566315i | 0.959073 | + | 0.283158i | \(0.0913819\pi\) | ||||
−0.959073 | + | 0.283158i | \(0.908618\pi\) | |||||||
\(450\) | −18.1865 | + | 10.5000i | −0.857321 | + | 0.494975i | ||||
\(451\) | −6.00000 | − | 3.46410i | −0.282529 | − | 0.163118i | ||||
\(452\) | 5.19615 | + | 3.00000i | 0.244406 | + | 0.141108i | ||||
\(453\) | −9.52628 | − | 16.5000i | −0.447584 | − | 0.775238i | ||||
\(454\) | 10.3923i | 0.487735i | ||||||||
\(455\) | 10.3923 | − | 30.0000i | 0.487199 | − | 1.40642i | ||||
\(456\) | −3.00000 | −0.140488 | ||||||||
\(457\) | 16.0000 | + | 27.7128i | 0.748448 | + | 1.29635i | 0.948566 | + | 0.316579i | \(0.102534\pi\) |
−0.200118 | + | 0.979772i | \(0.564132\pi\) | |||||||
\(458\) | 6.92820 | − | 12.0000i | 0.323734 | − | 0.560723i | ||||
\(459\) | −4.50000 | + | 7.79423i | −0.210042 | + | 0.363803i | ||||
\(460\) | 9.00000 | − | 5.19615i | 0.419627 | − | 0.242272i | ||||
\(461\) | −8.66025 | −0.403348 | −0.201674 | − | 0.979453i | \(-0.564638\pi\) | ||||
−0.201674 | + | 0.979453i | \(0.564638\pi\) | |||||||
\(462\) | −0.866025 | − | 4.50000i | −0.0402911 | − | 0.209359i | ||||
\(463\) | −4.00000 | −0.185896 | −0.0929479 | − | 0.995671i | \(-0.529629\pi\) | ||||
−0.0929479 | + | 0.995671i | \(0.529629\pi\) | |||||||
\(464\) | −2.59808 | + | 1.50000i | −0.120613 | + | 0.0696358i | ||||
\(465\) | −18.0000 | − | 10.3923i | −0.834730 | − | 0.481932i | ||||
\(466\) | −13.5000 | + | 23.3827i | −0.625375 | + | 1.08318i | ||||
\(467\) | −7.79423 | − | 13.5000i | −0.360674 | − | 0.624705i | 0.627398 | − | 0.778699i | \(-0.284120\pi\) |
−0.988072 | + | 0.153993i | \(0.950787\pi\) | |||||||
\(468\) | − | 10.3923i | − | 0.480384i | ||||||
\(469\) | −8.00000 | − | 41.5692i | −0.369406 | − | 1.91949i | ||||
\(470\) | 6.00000i | 0.276759i | ||||||||
\(471\) | 7.79423 | − | 4.50000i | 0.359139 | − | 0.207349i | ||||
\(472\) | −10.5000 | − | 6.06218i | −0.483302 | − | 0.279034i | ||||
\(473\) | −0.866025 | − | 0.500000i | −0.0398199 | − | 0.0229900i | ||||
\(474\) | 12.0000 | − | 6.92820i | 0.551178 | − | 0.318223i | ||||
\(475\) | − | 12.1244i | − | 0.556304i | ||||||
\(476\) | −4.33013 | − | 1.50000i | −0.198471 | − | 0.0687524i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.00000 | + | 5.19615i | 0.137217 | + | 0.237666i | ||||
\(479\) | −8.66025 | + | 15.0000i | −0.395697 | + | 0.685367i | −0.993190 | − | 0.116507i | \(-0.962830\pi\) |
0.597493 | + | 0.801874i | \(0.296164\pi\) | |||||||
\(480\) | −5.19615 | − | 3.00000i | −0.237171 | − | 0.136931i | ||||
\(481\) | 21.0000 | − | 12.1244i | 0.957518 | − | 0.552823i | ||||
\(482\) | −20.7846 | −0.946713 | ||||||||
\(483\) | 9.00000 | + | 10.3923i | 0.409514 | + | 0.472866i | ||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 46.7654 | − | 27.0000i | 2.12351 | − | 1.22601i | ||||
\(486\) | −13.5000 | − | 7.79423i | −0.612372 | − | 0.353553i | ||||
\(487\) | 13.0000 | − | 22.5167i | 0.589086 | − | 1.02033i | −0.405266 | − | 0.914199i | \(-0.632821\pi\) |
0.994352 | − | 0.106129i | \(-0.0338455\pi\) | |||||||
\(488\) | 5.19615 | + | 9.00000i | 0.235219 | + | 0.407411i | ||||
\(489\) | −24.2487 | −1.09656 | ||||||||
\(490\) | 15.0000 | − | 19.0526i | 0.677631 | − | 0.860707i | ||||
\(491\) | 30.0000i | 1.35388i | 0.736038 | + | 0.676941i | \(0.236695\pi\) | ||||
−0.736038 | + | 0.676941i | \(0.763305\pi\) | |||||||
\(492\) | −6.00000 | − | 10.3923i | −0.270501 | − | 0.468521i | ||||
\(493\) | −4.50000 | − | 2.59808i | −0.202670 | − | 0.117011i | ||||
\(494\) | 5.19615 | + | 3.00000i | 0.233786 | + | 0.134976i | ||||
\(495\) | 9.00000 | − | 5.19615i | 0.404520 | − | 0.233550i | ||||
\(496\) | − | 3.46410i | − | 0.155543i | ||||||
\(497\) | −25.9808 | − | 30.0000i | −1.16540 | − | 1.34568i | ||||
\(498\) | 30.0000i | 1.34433i | ||||||||
\(499\) | 16.0000 | + | 27.7128i | 0.716258 | + | 1.24060i | 0.962472 | + | 0.271380i | \(0.0874801\pi\) |
−0.246214 | + | 0.969216i | \(0.579187\pi\) | |||||||
\(500\) | 3.46410 | − | 6.00000i | 0.154919 | − | 0.268328i | ||||
\(501\) | 21.0000 | − | 36.3731i | 0.938211 | − | 1.62503i | ||||
\(502\) | 10.5000 | − | 6.06218i | 0.468638 | − | 0.270568i | ||||
\(503\) | 17.3205 | 0.772283 | 0.386142 | − | 0.922440i | \(-0.373808\pi\) | ||||
0.386142 | + | 0.922440i | \(0.373808\pi\) | |||||||
\(504\) | 2.59808 | − | 7.50000i | 0.115728 | − | 0.334077i | ||||
\(505\) | 18.0000 | 0.800989 | ||||||||
\(506\) | −2.59808 | + | 1.50000i | −0.115499 | + | 0.0666831i | ||||
\(507\) | 0.866025 | − | 1.50000i | 0.0384615 | − | 0.0666173i | ||||
\(508\) | 5.50000 | − | 9.52628i | 0.244023 | − | 0.422660i | ||||
\(509\) | −3.46410 | − | 6.00000i | −0.153544 | − | 0.265945i | 0.778984 | − | 0.627044i | \(-0.215735\pi\) |
−0.932528 | + | 0.361098i | \(0.882402\pi\) | |||||||
\(510\) | − | 10.3923i | − | 0.460179i | ||||||
\(511\) | −36.0000 | + | 6.92820i | −1.59255 | + | 0.306486i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 7.79423 | − | 4.50000i | 0.344124 | − | 0.198680i | ||||
\(514\) | 9.00000 | + | 5.19615i | 0.396973 | + | 0.229192i | ||||
\(515\) | −51.9615 | − | 30.0000i | −2.28970 | − | 1.32196i | ||||
\(516\) | −0.866025 | − | 1.50000i | −0.0381246 | − | 0.0660338i | ||||
\(517\) | − | 1.73205i | − | 0.0761755i | ||||||
\(518\) | 18.1865 | − | 3.50000i | 0.799070 | − | 0.153781i | ||||
\(519\) | −36.0000 | −1.58022 | ||||||||
\(520\) | 6.00000 | + | 10.3923i | 0.263117 | + | 0.455733i | ||||
\(521\) | −8.66025 | + | 15.0000i | −0.379413 | + | 0.657162i | −0.990977 | − | 0.134033i | \(-0.957207\pi\) |
0.611564 | + | 0.791195i | \(0.290541\pi\) | |||||||
\(522\) | 4.50000 | − | 7.79423i | 0.196960 | − | 0.341144i | ||||
\(523\) | −15.0000 | + | 8.66025i | −0.655904 | + | 0.378686i | −0.790715 | − | 0.612185i | \(-0.790291\pi\) |
0.134810 | + | 0.990871i | \(0.456957\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 30.3109 | + | 10.5000i | 1.32288 | + | 0.458258i | ||||
\(526\) | −18.0000 | −0.784837 | ||||||||
\(527\) | 5.19615 | − | 3.00000i | 0.226348 | − | 0.130682i | ||||
\(528\) | 1.50000 | + | 0.866025i | 0.0652791 | + | 0.0376889i | ||||
\(529\) | −7.00000 | + | 12.1244i | −0.304348 | + | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 36.3731 | 1.57846 | ||||||||
\(532\) | 3.00000 | + | 3.46410i | 0.130066 | + | 0.150188i | ||||
\(533\) | 24.0000i | 1.03956i | ||||||||
\(534\) | −15.5885 | + | 9.00000i | −0.674579 | + | 0.389468i | ||||
\(535\) | 18.0000 | + | 10.3923i | 0.778208 | + | 0.449299i | ||||
\(536\) | 13.8564 | + | 8.00000i | 0.598506 | + | 0.345547i | ||||
\(537\) | −22.5000 | + | 12.9904i | −0.970947 | + | 0.560576i | ||||
\(538\) | 13.8564i | 0.597392i | ||||||||
\(539\) | −4.33013 | + | 5.50000i | −0.186512 | + | 0.236902i | ||||
\(540\) | 18.0000 | 0.774597 | ||||||||
\(541\) | −10.0000 | − | 17.3205i | −0.429934 | − | 0.744667i | 0.566933 | − | 0.823764i | \(-0.308130\pi\) |
−0.996867 | + | 0.0790969i | \(0.974796\pi\) | |||||||
\(542\) | 5.19615 | − | 9.00000i | 0.223194 | − | 0.386583i | ||||
\(543\) | −20.7846 | − | 12.0000i | −0.891953 | − | 0.514969i | ||||
\(544\) | 1.50000 | − | 0.866025i | 0.0643120 | − | 0.0371305i | ||||
\(545\) | 55.4256 | 2.37417 | ||||||||
\(546\) | −12.0000 | + | 10.3923i | −0.513553 | + | 0.444750i | ||||
\(547\) | −25.0000 | −1.06892 | −0.534461 | − | 0.845193i | \(-0.679486\pi\) | ||||
−0.534461 | + | 0.845193i | \(0.679486\pi\) | |||||||
\(548\) | 15.5885 | − | 9.00000i | 0.665906 | − | 0.384461i | ||||
\(549\) | −27.0000 | − | 15.5885i | −1.15233 | − | 0.665299i | ||||
\(550\) | −3.50000 | + | 6.06218i | −0.149241 | + | 0.258492i | ||||
\(551\) | 2.59808 | + | 4.50000i | 0.110682 | + | 0.191706i | ||||
\(552\) | −5.19615 | −0.221163 | ||||||||
\(553\) | −20.0000 | − | 6.92820i | −0.850487 | − | 0.294617i | ||||
\(554\) | − | 8.00000i | − | 0.339887i | ||||||
\(555\) | 21.0000 | + | 36.3731i | 0.891400 | + | 1.54395i | ||||
\(556\) | 1.50000 | + | 0.866025i | 0.0636142 | + | 0.0367277i | ||||
\(557\) | 28.5788 | + | 16.5000i | 1.21092 | + | 0.699127i | 0.962961 | − | 0.269642i | \(-0.0869053\pi\) |
0.247964 | + | 0.968769i | \(0.420239\pi\) | |||||||
\(558\) | 5.19615 | + | 9.00000i | 0.219971 | + | 0.381000i | ||||
\(559\) | 3.46410i | 0.146516i | ||||||||
\(560\) | 1.73205 | + | 9.00000i | 0.0731925 | + | 0.380319i | ||||
\(561\) | 3.00000i | 0.126660i | ||||||||
\(562\) | −7.50000 | − | 12.9904i | −0.316368 | − | 0.547966i | ||||
\(563\) | 15.5885 | − | 27.0000i | 0.656975 | − | 1.13791i | −0.324420 | − | 0.945913i | \(-0.605169\pi\) |
0.981395 | − | 0.192001i | \(-0.0614977\pi\) | |||||||
\(564\) | 1.50000 | − | 2.59808i | 0.0631614 | − | 0.109399i | ||||
\(565\) | 18.0000 | − | 10.3923i | 0.757266 | − | 0.437208i | ||||
\(566\) | −17.3205 | −0.728035 | ||||||||
\(567\) | 4.50000 | + | 23.3827i | 0.188982 | + | 0.981981i | ||||
\(568\) | 15.0000 | 0.629386 | ||||||||
\(569\) | −33.7750 | + | 19.5000i | −1.41592 | + | 0.817483i | −0.995937 | − | 0.0900490i | \(-0.971298\pi\) |
−0.419984 | + | 0.907532i | \(0.637964\pi\) | |||||||
\(570\) | −5.19615 | + | 9.00000i | −0.217643 | + | 0.376969i | ||||
\(571\) | −11.5000 | + | 19.9186i | −0.481260 | + | 0.833567i | −0.999769 | − | 0.0215055i | \(-0.993154\pi\) |
0.518509 | + | 0.855072i | \(0.326487\pi\) | |||||||
\(572\) | −1.73205 | − | 3.00000i | −0.0724207 | − | 0.125436i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.00000 | + | 17.3205i | −0.250435 | + | 0.722944i | ||||
\(575\) | − | 21.0000i | − | 0.875761i | ||||||
\(576\) | 1.50000 | + | 2.59808i | 0.0625000 | + | 0.108253i | ||||
\(577\) | −24.0000 | − | 13.8564i | −0.999133 | − | 0.576850i | −0.0911414 | − | 0.995838i | \(-0.529052\pi\) |
−0.907992 | + | 0.418988i | \(0.862385\pi\) | |||||||
\(578\) | −12.1244 | − | 7.00000i | −0.504307 | − | 0.291162i | ||||
\(579\) | 3.46410 | + | 6.00000i | 0.143963 | + | 0.249351i | ||||
\(580\) | 10.3923i | 0.431517i | ||||||||
\(581\) | 34.6410 | − | 30.0000i | 1.43715 | − | 1.24461i | ||||
\(582\) | −27.0000 | −1.11919 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 6.92820 | − | 12.0000i | 0.286691 | − | 0.496564i | ||||
\(585\) | −31.1769 | − | 18.0000i | −1.28901 | − | 0.744208i | ||||
\(586\) | 7.50000 | − | 4.33013i | 0.309822 | − | 0.178876i | ||||
\(587\) | −10.3923 | −0.428936 | −0.214468 | − | 0.976731i | \(-0.568802\pi\) | ||||
−0.214468 | + | 0.976731i | \(0.568802\pi\) | |||||||
\(588\) | −11.2583 | + | 4.50000i | −0.464286 | + | 0.185577i | ||||
\(589\) | −6.00000 | −0.247226 | ||||||||
\(590\) | −36.3731 | + | 21.0000i | −1.49746 | + | 0.864556i | ||||
\(591\) | −13.5000 | − | 7.79423i | −0.555316 | − | 0.320612i | ||||
\(592\) | −3.50000 | + | 6.06218i | −0.143849 | + | 0.249154i | ||||
\(593\) | 14.7224 | + | 25.5000i | 0.604578 | + | 1.04716i | 0.992118 | + | 0.125307i | \(0.0399915\pi\) |
−0.387540 | + | 0.921853i | \(0.626675\pi\) | |||||||
\(594\) | −5.19615 | −0.213201 | ||||||||
\(595\) | −12.0000 | + | 10.3923i | −0.491952 | + | 0.426043i | ||||
\(596\) | 9.00000i | 0.368654i | ||||||||
\(597\) | −15.5885 | + | 9.00000i | −0.637993 | + | 0.368345i | ||||
\(598\) | 9.00000 | + | 5.19615i | 0.368037 | + | 0.212486i | ||||
\(599\) | −20.7846 | − | 12.0000i | −0.849236 | − | 0.490307i | 0.0111569 | − | 0.999938i | \(-0.496449\pi\) |
−0.860393 | + | 0.509631i | \(0.829782\pi\) | |||||||
\(600\) | −10.5000 | + | 6.06218i | −0.428661 | + | 0.247487i | ||||
\(601\) | 6.92820i | 0.282607i | 0.989966 | + | 0.141304i | \(0.0451294\pi\) | ||||
−0.989966 | + | 0.141304i | \(0.954871\pi\) | |||||||
\(602\) | −0.866025 | + | 2.50000i | −0.0352966 | + | 0.101892i | ||||
\(603\) | −48.0000 | −1.95471 | ||||||||
\(604\) | −5.50000 | − | 9.52628i | −0.223792 | − | 0.387619i | ||||
\(605\) | 1.73205 | − | 3.00000i | 0.0704179 | − | 0.121967i | ||||
\(606\) | −7.79423 | − | 4.50000i | −0.316619 | − | 0.182800i | ||||
\(607\) | 33.0000 | − | 19.0526i | 1.33943 | − | 0.773320i | 0.352706 | − | 0.935734i | \(-0.385262\pi\) |
0.986723 | + | 0.162415i | \(0.0519282\pi\) | |||||||
\(608\) | −1.73205 | −0.0702439 | ||||||||
\(609\) | −13.5000 | + | 2.59808i | −0.547048 | + | 0.105279i | ||||
\(610\) | 36.0000 | 1.45760 | ||||||||
\(611\) | −5.19615 | + | 3.00000i | −0.210214 | + | 0.121367i | ||||
\(612\) | −2.59808 | + | 4.50000i | −0.105021 | + | 0.181902i | ||||
\(613\) | −1.00000 | + | 1.73205i | −0.0403896 | + | 0.0699569i | −0.885514 | − | 0.464614i | \(-0.846193\pi\) |
0.845124 | + | 0.534570i | \(0.179527\pi\) | |||||||
\(614\) | −8.66025 | − | 15.0000i | −0.349499 | − | 0.605351i | ||||
\(615\) | −41.5692 | −1.67623 | ||||||||
\(616\) | −0.500000 | − | 2.59808i | −0.0201456 | − | 0.104679i | ||||
\(617\) | 12.0000i | 0.483102i | 0.970388 | + | 0.241551i | \(0.0776561\pi\) | ||||
−0.970388 | + | 0.241551i | \(0.922344\pi\) | |||||||
\(618\) | 15.0000 | + | 25.9808i | 0.603388 | + | 1.04510i | ||||
\(619\) | 33.0000 | + | 19.0526i | 1.32638 | + | 0.765787i | 0.984738 | − | 0.174042i | \(-0.0556830\pi\) |
0.341644 | + | 0.939829i | \(0.389016\pi\) | |||||||
\(620\) | −10.3923 | − | 6.00000i | −0.417365 | − | 0.240966i | ||||
\(621\) | 13.5000 | − | 7.79423i | 0.541736 | − | 0.312772i | ||||
\(622\) | 22.5167i | 0.902836i | ||||||||
\(623\) | 25.9808 | + | 9.00000i | 1.04090 | + | 0.360577i | ||||
\(624\) | − | 6.00000i | − | 0.240192i | ||||||
\(625\) | 5.50000 | + | 9.52628i | 0.220000 | + | 0.381051i | ||||
\(626\) | 14.7224 | − | 25.5000i | 0.588427 | − | 1.01918i | ||||
\(627\) | 1.50000 | − | 2.59808i | 0.0599042 | − | 0.103757i | ||||
\(628\) | 4.50000 | − | 2.59808i | 0.179570 | − | 0.103675i | ||||
\(629\) | −12.1244 | −0.483430 | ||||||||
\(630\) | −18.0000 | − | 20.7846i | −0.717137 | − | 0.828079i | ||||
\(631\) | −22.0000 | −0.875806 | −0.437903 | − | 0.899022i | \(-0.644279\pi\) | ||||
−0.437903 | + | 0.899022i | \(0.644279\pi\) | |||||||
\(632\) | 6.92820 | − | 4.00000i | 0.275589 | − | 0.159111i | ||||
\(633\) | 3.46410 | − | 6.00000i | 0.137686 | − | 0.238479i | ||||
\(634\) | −3.00000 | + | 5.19615i | −0.119145 | + | 0.206366i | ||||
\(635\) | −19.0526 | − | 33.0000i | −0.756078 | − | 1.30957i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 24.0000 | + | 3.46410i | 0.950915 | + | 0.137253i | ||||
\(638\) | − | 3.00000i | − | 0.118771i | ||||||
\(639\) | −38.9711 | + | 22.5000i | −1.54167 | + | 0.890086i | ||||
\(640\) | −3.00000 | − | 1.73205i | −0.118585 | − | 0.0684653i | ||||
\(641\) | −41.5692 | − | 24.0000i | −1.64189 | − | 0.947943i | −0.980163 | − | 0.198194i | \(-0.936492\pi\) |
−0.661723 | − | 0.749749i | \(-0.730174\pi\) | |||||||
\(642\) | −5.19615 | − | 9.00000i | −0.205076 | − | 0.355202i | ||||
\(643\) | 34.6410i | 1.36611i | 0.730368 | + | 0.683054i | \(0.239349\pi\) | ||||
−0.730368 | + | 0.683054i | \(0.760651\pi\) | |||||||
\(644\) | 5.19615 | + | 6.00000i | 0.204757 | + | 0.236433i | ||||
\(645\) | −6.00000 | −0.236250 | ||||||||
\(646\) | −1.50000 | − | 2.59808i | −0.0590167 | − | 0.102220i | ||||
\(647\) | −5.19615 | + | 9.00000i | −0.204282 | + | 0.353827i | −0.949904 | − | 0.312543i | \(-0.898819\pi\) |
0.745622 | + | 0.666369i | \(0.232153\pi\) | |||||||
\(648\) | −7.79423 | − | 4.50000i | −0.306186 | − | 0.176777i | ||||
\(649\) | 10.5000 | − | 6.06218i | 0.412161 | − | 0.237961i | ||||
\(650\) | 24.2487 | 0.951113 | ||||||||
\(651\) | 5.19615 | − | 15.0000i | 0.203653 | − | 0.587896i | ||||
\(652\) | −14.0000 | −0.548282 | ||||||||
\(653\) | −5.19615 | + | 3.00000i | −0.203341 | + | 0.117399i | −0.598213 | − | 0.801337i | \(-0.704122\pi\) |
0.394872 | + | 0.918736i | \(0.370789\pi\) | |||||||
\(654\) | −24.0000 | − | 13.8564i | −0.938474 | − | 0.541828i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.46410 | − | 6.00000i | −0.135250 | − | 0.234261i | ||||
\(657\) | 41.5692i | 1.62177i | ||||||||
\(658\) | −4.50000 | + | 0.866025i | −0.175428 | + | 0.0337612i | ||||
\(659\) | − | 12.0000i | − | 0.467454i | −0.972302 | − | 0.233727i | \(-0.924908\pi\) | ||
0.972302 | − | 0.233727i | \(-0.0750921\pi\) | |||||||
\(660\) | 5.19615 | − | 3.00000i | 0.202260 | − | 0.116775i | ||||
\(661\) | 25.5000 | + | 14.7224i | 0.991835 | + | 0.572636i | 0.905822 | − | 0.423658i | \(-0.139254\pi\) |
0.0860127 | + | 0.996294i | \(0.472587\pi\) | |||||||
\(662\) | 8.66025 | + | 5.00000i | 0.336590 | + | 0.194331i | ||||
\(663\) | 9.00000 | − | 5.19615i | 0.349531 | − | 0.201802i | ||||
\(664\) | 17.3205i | 0.672166i | ||||||||
\(665\) | 15.5885 | − | 3.00000i | 0.604494 | − | 0.116335i | ||||
\(666\) | − | 21.0000i | − | 0.813733i | ||||||
\(667\) | 4.50000 | + | 7.79423i | 0.174241 | + | 0.301794i | ||||
\(668\) | 12.1244 | − | 21.0000i | 0.469105 | − | 0.812514i | ||||
\(669\) | 15.5885 | + | 9.00000i | 0.602685 | + | 0.347960i | ||||
\(670\) | 48.0000 | − | 27.7128i | 1.85440 | − | 1.07064i | ||||
\(671\) | −10.3923 | −0.401190 | ||||||||
\(672\) | 1.50000 | − | 4.33013i | 0.0578638 | − | 0.167038i | ||||
\(673\) | 22.0000 | 0.848038 | 0.424019 | − | 0.905653i | \(-0.360619\pi\) | ||||
0.424019 | + | 0.905653i | \(0.360619\pi\) | |||||||
\(674\) | −3.46410 | + | 2.00000i | −0.133432 | + | 0.0770371i | ||||
\(675\) | 18.1865 | − | 31.5000i | 0.700000 | − | 1.21244i | ||||
\(676\) | 0.500000 | − | 0.866025i | 0.0192308 | − | 0.0333087i | ||||
\(677\) | 18.1865 | + | 31.5000i | 0.698965 | + | 1.21064i | 0.968826 | + | 0.247744i | \(0.0796891\pi\) |
−0.269860 | + | 0.962899i | \(0.586978\pi\) | |||||||
\(678\) | −10.3923 | −0.399114 | ||||||||
\(679\) | 27.0000 | + | 31.1769i | 1.03616 | + | 1.19646i | ||||
\(680\) | − | 6.00000i | − | 0.230089i | ||||||
\(681\) | −9.00000 | − | 15.5885i | −0.344881 | − | 0.597351i | ||||
\(682\) | 3.00000 | + | 1.73205i | 0.114876 | + | 0.0663237i | ||||
\(683\) | −33.7750 | − | 19.5000i | −1.29236 | − | 0.746147i | −0.313291 | − | 0.949657i | \(-0.601432\pi\) |
−0.979073 | + | 0.203510i | \(0.934765\pi\) | |||||||
\(684\) | 4.50000 | − | 2.59808i | 0.172062 | − | 0.0993399i | ||||
\(685\) | − | 62.3538i | − | 2.38242i | ||||||
\(686\) | 16.4545 | + | 8.50000i | 0.628235 | + | 0.324532i | ||||
\(687\) | 24.0000i | 0.915657i | ||||||||
\(688\) | −0.500000 | − | 0.866025i | −0.0190623 | − | 0.0330169i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −9.00000 | + | 15.5885i | −0.342624 | + | 0.593442i | ||||
\(691\) | 3.00000 | − | 1.73205i | 0.114125 | − | 0.0658903i | −0.441851 | − | 0.897089i | \(-0.645678\pi\) |
0.555976 | + | 0.831198i | \(0.312345\pi\) | |||||||
\(692\) | −20.7846 | −0.790112 | ||||||||
\(693\) | 5.19615 | + | 6.00000i | 0.197386 | + | 0.227921i | ||||
\(694\) | −24.0000 | −0.911028 | ||||||||
\(695\) | 5.19615 | − | 3.00000i | 0.197101 | − | 0.113796i | ||||
\(696\) | 2.59808 | − | 4.50000i | 0.0984798 | − | 0.170572i | ||||
\(697\) | 6.00000 | − | 10.3923i | 0.227266 | − | 0.393637i | ||||
\(698\) | −10.3923 | − | 18.0000i | −0.393355 | − | 0.681310i | ||||
\(699\) | − | 46.7654i | − | 1.76883i | ||||||
\(700\) | 17.5000 | + | 6.06218i | 0.661438 | + | 0.229129i | ||||
\(701\) | 3.00000i | 0.113308i | 0.998394 | + | 0.0566542i | \(0.0180433\pi\) | ||||
−0.998394 | + | 0.0566542i | \(0.981957\pi\) | |||||||
\(702\) | 9.00000 | + | 15.5885i | 0.339683 | + | 0.588348i | ||||
\(703\) | 10.5000 | + | 6.06218i | 0.396015 | + | 0.228639i | ||||
\(704\) | 0.866025 | + | 0.500000i | 0.0326396 | + | 0.0188445i | ||||
\(705\) | −5.19615 | − | 9.00000i | −0.195698 | − | 0.338960i | ||||
\(706\) | − | 3.46410i | − | 0.130373i | ||||||
\(707\) | 2.59808 | + | 13.5000i | 0.0977107 | + | 0.507720i | ||||
\(708\) | 21.0000 | 0.789228 | ||||||||
\(709\) | 14.5000 | + | 25.1147i | 0.544559 | + | 0.943204i | 0.998635 | + | 0.0522406i | \(0.0166363\pi\) |
−0.454076 | + | 0.890963i | \(0.650030\pi\) | |||||||
\(710\) | 25.9808 | − | 45.0000i | 0.975041 | − | 1.68882i | ||||
\(711\) | −12.0000 | + | 20.7846i | −0.450035 | + | 0.779484i | ||||
\(712\) | −9.00000 | + | 5.19615i | −0.337289 | + | 0.194734i | ||||
\(713\) | −10.3923 | −0.389195 | ||||||||
\(714\) | 7.79423 | − | 1.50000i | 0.291692 | − | 0.0561361i | ||||
\(715\) | −12.0000 | −0.448775 | ||||||||
\(716\) | −12.9904 | + | 7.50000i | −0.485473 | + | 0.280288i | ||||
\(717\) | −9.00000 | − | 5.19615i | −0.336111 | − | 0.194054i | ||||
\(718\) | 3.00000 | − | 5.19615i | 0.111959 | − | 0.193919i | ||||
\(719\) | 14.7224 | + | 25.5000i | 0.549054 | + | 0.950990i | 0.998340 | + | 0.0576013i | \(0.0183452\pi\) |
−0.449286 | + | 0.893388i | \(0.648321\pi\) | |||||||
\(720\) | 10.3923 | 0.387298 | ||||||||
\(721\) | 15.0000 | − | 43.3013i | 0.558629 | − | 1.61262i | ||||
\(722\) | − | 16.0000i | − | 0.595458i | ||||||
\(723\) | 31.1769 | − | 18.0000i | 1.15948 | − | 0.669427i | ||||
\(724\) | −12.0000 | − | 6.92820i | −0.445976 | − | 0.257485i | ||||
\(725\) | 18.1865 | + | 10.5000i | 0.675431 | + | 0.389960i | ||||
\(726\) | −1.50000 | + | 0.866025i | −0.0556702 | + | 0.0321412i | ||||
\(727\) | − | 17.3205i | − | 0.642382i | −0.947014 | − | 0.321191i | \(-0.895917\pi\) | ||
0.947014 | − | 0.321191i | \(-0.104083\pi\) | |||||||
\(728\) | −6.92820 | + | 6.00000i | −0.256776 | + | 0.222375i | ||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | −24.0000 | − | 41.5692i | −0.888280 | − | 1.53855i | ||||
\(731\) | 0.866025 | − | 1.50000i | 0.0320311 | − | 0.0554795i | ||||
\(732\) | −15.5885 | − | 9.00000i | −0.576166 | − | 0.332650i | ||||
\(733\) | 3.00000 | − | 1.73205i | 0.110808 | − | 0.0639748i | −0.443572 | − | 0.896239i | \(-0.646289\pi\) |
0.554380 | + | 0.832264i | \(0.312956\pi\) | |||||||
\(734\) | 6.92820 | 0.255725 | ||||||||
\(735\) | −6.00000 | + | 41.5692i | −0.221313 | + | 1.53330i | ||||
\(736\) | −3.00000 | −0.110581 | ||||||||
\(737\) | −13.8564 | + | 8.00000i | −0.510407 | + | 0.294684i | ||||
\(738\) | 18.0000 | + | 10.3923i | 0.662589 | + | 0.382546i | ||||
\(739\) | 14.0000 | − | 24.2487i | 0.514998 | − | 0.892003i | −0.484850 | − | 0.874597i | \(-0.661126\pi\) |
0.999849 | − | 0.0174060i | \(-0.00554079\pi\) | |||||||
\(740\) | 12.1244 | + | 21.0000i | 0.445700 | + | 0.771975i | ||||
\(741\) | −10.3923 | −0.381771 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 36.0000i | − | 1.32071i | −0.750953 | − | 0.660356i | \(-0.770405\pi\) | ||
0.750953 | − | 0.660356i | \(-0.229595\pi\) | |||||||
\(744\) | 3.00000 | + | 5.19615i | 0.109985 | + | 0.190500i | ||||
\(745\) | 27.0000 | + | 15.5885i | 0.989203 | + | 0.571117i | ||||
\(746\) | 12.1244 | + | 7.00000i | 0.443904 | + | 0.256288i | ||||
\(747\) | −25.9808 | − | 45.0000i | −0.950586 | − | 1.64646i | ||||
\(748\) | 1.73205i | 0.0633300i | ||||||||
\(749\) | −5.19615 | + | 15.0000i | −0.189863 | + | 0.548088i | ||||
\(750\) | 12.0000i | 0.438178i | ||||||||
\(751\) | −26.0000 | − | 45.0333i | −0.948753 | − | 1.64329i | −0.748056 | − | 0.663636i | \(-0.769012\pi\) |
−0.200698 | − | 0.979653i | \(-0.564321\pi\) | |||||||
\(752\) | 0.866025 | − | 1.50000i | 0.0315807 | − | 0.0546994i | ||||
\(753\) | −10.5000 | + | 18.1865i | −0.382641 | + | 0.662754i | ||||
\(754\) | −9.00000 | + | 5.19615i | −0.327761 | + | 0.189233i | ||||
\(755\) | −38.1051 | −1.38679 | ||||||||
\(756\) | 2.59808 | + | 13.5000i | 0.0944911 | + | 0.490990i | ||||
\(757\) | 13.0000 | 0.472493 | 0.236247 | − | 0.971693i | \(-0.424083\pi\) | ||||
0.236247 | + | 0.971693i | \(0.424083\pi\) | |||||||
\(758\) | 17.3205 | − | 10.0000i | 0.629109 | − | 0.363216i | ||||
\(759\) | 2.59808 | − | 4.50000i | 0.0943042 | − | 0.163340i | ||||
\(760\) | −3.00000 | + | 5.19615i | −0.108821 | + | 0.188484i | ||||
\(761\) | 17.3205 | + | 30.0000i | 0.627868 | + | 1.08750i | 0.987979 | + | 0.154590i | \(0.0494055\pi\) |
−0.360111 | + | 0.932910i | \(0.617261\pi\) | |||||||
\(762\) | 19.0526i | 0.690201i | ||||||||
\(763\) | 8.00000 | + | 41.5692i | 0.289619 | + | 1.50491i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.00000 | + | 15.5885i | 0.325396 | + | 0.563602i | ||||
\(766\) | −25.5000 | − | 14.7224i | −0.921352 | − | 0.531943i | ||||
\(767\) | −36.3731 | − | 21.0000i | −1.31336 | − | 0.758266i | ||||
\(768\) | 0.866025 | + | 1.50000i | 0.0312500 | + | 0.0541266i | ||||
\(769\) | − | 6.92820i | − | 0.249837i | −0.992167 | − | 0.124919i | \(-0.960133\pi\) | ||
0.992167 | − | 0.124919i | \(-0.0398670\pi\) | |||||||
\(770\) | −8.66025 | − | 3.00000i | −0.312094 | − | 0.108112i | ||||
\(771\) | −18.0000 | −0.648254 | ||||||||
\(772\) | 2.00000 | + | 3.46410i | 0.0719816 | + | 0.124676i | ||||
\(773\) | −6.92820 | + | 12.0000i | −0.249190 | + | 0.431610i | −0.963301 | − | 0.268422i | \(-0.913498\pi\) |
0.714111 | + | 0.700032i | \(0.246831\pi\) | |||||||
\(774\) | 2.59808 | + | 1.50000i | 0.0933859 | + | 0.0539164i | ||||
\(775\) | −21.0000 | + | 12.1244i | −0.754342 | + | 0.435520i | ||||
\(776\) | −15.5885 | −0.559593 | ||||||||
\(777\) | −24.2487 | + | 21.0000i | −0.869918 | + | 0.753371i | ||||
\(778\) | 18.0000 | 0.645331 | ||||||||
\(779\) | −10.3923 | + | 6.00000i | −0.372343 | + | 0.214972i | ||||
\(780\) | −18.0000 | − | 10.3923i | −0.644503 | − | 0.372104i | ||||
\(781\) | −7.50000 | + | 12.9904i | −0.268371 | + | 0.464832i | ||||
\(782\) | −2.59808 | − | 4.50000i | −0.0929070 | − | 0.160920i | ||||
\(783\) | 15.5885i | 0.557086i | ||||||||
\(784\) | −6.50000 | + | 2.59808i | −0.232143 | + | 0.0927884i | ||||
\(785\) | − | 18.0000i | − | 0.642448i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.5000 | − | 18.1865i | −1.12285 | − | 0.648280i | −0.180726 | − | 0.983534i | \(-0.557845\pi\) |
−0.942128 | + | 0.335254i | \(0.891178\pi\) | |||||||
\(788\) | −7.79423 | − | 4.50000i | −0.277658 | − | 0.160306i | ||||
\(789\) | 27.0000 | − | 15.5885i | 0.961225 | − | 0.554964i | ||||
\(790\) | − | 27.7128i | − | 0.985978i | ||||||
\(791\) | 10.3923 | + | 12.0000i | 0.369508 | + | 0.426671i | ||||
\(792\) | −3.00000 | −0.106600 | ||||||||
\(793\) | 18.0000 | + | 31.1769i | 0.639199 | + | 1.10712i | ||||
\(794\) | 0.866025 | − | 1.50000i | 0.0307341 | − | 0.0532330i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.00000 | + | 5.19615i | −0.318997 | + | 0.184173i | ||||
\(797\) | 10.3923 | 0.368114 | 0.184057 | − | 0.982916i | \(-0.441077\pi\) | ||||
0.184057 | + | 0.982916i | \(0.441077\pi\) | |||||||
\(798\) | −7.50000 | − | 2.59808i | −0.265497 | − | 0.0919709i | ||||
\(799\) | 3.00000 | 0.106132 | ||||||||
\(800\) | −6.06218 | + | 3.50000i | −0.214330 | + | 0.123744i | ||||
\(801\) | 15.5885 | − | 27.0000i | 0.550791 | − | 0.953998i | ||||
\(802\) | 12.0000 | − | 20.7846i | 0.423735 | − | 0.733930i | ||||
\(803\) | 6.92820 | + | 12.0000i | 0.244491 | + | 0.423471i | ||||
\(804\) | −27.7128 | −0.977356 | ||||||||
\(805\) | 27.0000 | − | 5.19615i | 0.951625 | − | 0.183140i | ||||
\(806\) | − | 12.0000i | − | 0.422682i | ||||||
\(807\) | −12.0000 | − | 20.7846i | −0.422420 | − | 0.731653i | ||||
\(808\) | −4.50000 | − | 2.59808i | −0.158309 | − | 0.0914000i | ||||
\(809\) | −15.5885 | − | 9.00000i | −0.548061 | − | 0.316423i | 0.200279 | − | 0.979739i | \(-0.435815\pi\) |
−0.748340 | + | 0.663316i | \(0.769149\pi\) | |||||||
\(810\) | −27.0000 | + | 15.5885i | −0.948683 | + | 0.547723i | ||||
\(811\) | 10.3923i | 0.364923i | 0.983213 | + | 0.182462i | \(0.0584065\pi\) | ||||
−0.983213 | + | 0.182462i | \(0.941593\pi\) | |||||||
\(812\) | −7.79423 | + | 1.50000i | −0.273524 | + | 0.0526397i | ||||
\(813\) | 18.0000i | 0.631288i | ||||||||
\(814\) | −3.50000 | − | 6.06218i | −0.122675 | − | 0.212479i | ||||
\(815\) | −24.2487 | + | 42.0000i | −0.849395 | + | 1.47120i | ||||
\(816\) | −1.50000 | + | 2.59808i | −0.0525105 | + | 0.0909509i | ||||
\(817\) | −1.50000 | + | 0.866025i | −0.0524784 | + | 0.0302984i | ||||
\(818\) | −13.8564 | −0.484478 | ||||||||
\(819\) | 9.00000 | − | 25.9808i | 0.314485 | − | 0.907841i | ||||
\(820\) | −24.0000 | −0.838116 | ||||||||
\(821\) | −25.9808 | + | 15.0000i | −0.906735 | + | 0.523504i | −0.879379 | − | 0.476122i | \(-0.842042\pi\) |
−0.0273557 | + | 0.999626i | \(0.508709\pi\) | |||||||
\(822\) | −15.5885 | + | 27.0000i | −0.543710 | + | 0.941733i | ||||
\(823\) | −4.00000 | + | 6.92820i | −0.139431 | + | 0.241502i | −0.927281 | − | 0.374365i | \(-0.877861\pi\) |
0.787850 | + | 0.615867i | \(0.211194\pi\) | |||||||
\(824\) | 8.66025 | + | 15.0000i | 0.301694 | + | 0.522550i | ||||
\(825\) | − | 12.1244i | − | 0.422116i | ||||||
\(826\) | −21.0000 | − | 24.2487i | −0.730683 | − | 0.843721i | ||||
\(827\) | 18.0000i | 0.625921i | 0.949766 | + | 0.312961i | \(0.101321\pi\) | ||||
−0.949766 | + | 0.312961i | \(0.898679\pi\) | |||||||
\(828\) | 7.79423 | − | 4.50000i | 0.270868 | − | 0.156386i | ||||
\(829\) | −19.5000 | − | 11.2583i | −0.677263 | − | 0.391018i | 0.121560 | − | 0.992584i | \(-0.461210\pi\) |
−0.798823 | + | 0.601566i | \(0.794544\pi\) | |||||||
\(830\) | 51.9615 | + | 30.0000i | 1.80361 | + | 1.04132i | ||||
\(831\) | 6.92820 | + | 12.0000i | 0.240337 | + | 0.416275i | ||||
\(832\) | − | 3.46410i | − | 0.120096i | ||||||
\(833\) | −9.52628 | − | 7.50000i | −0.330066 | − | 0.259860i | ||||
\(834\) | −3.00000 | −0.103882 | ||||||||
\(835\) | −42.0000 | − | 72.7461i | −1.45347 | − | 2.51748i | ||||
\(836\) | 0.866025 | − | 1.50000i | 0.0299521 | − | 0.0518786i | ||||
\(837\) | −15.5885 | − | 9.00000i | −0.538816 | − | 0.311086i | ||||
\(838\) | 1.50000 | − | 0.866025i | 0.0518166 | − | 0.0299164i | ||||
\(839\) | −17.3205 | −0.597970 | −0.298985 | − | 0.954258i | \(-0.596648\pi\) | ||||
−0.298985 | + | 0.954258i | \(0.596648\pi\) | |||||||
\(840\) | −10.3923 | − | 12.0000i | −0.358569 | − | 0.414039i | ||||
\(841\) | 20.0000 | 0.689655 | ||||||||
\(842\) | −4.33013 | + | 2.50000i | −0.149226 | + | 0.0861557i | ||||
\(843\) | 22.5000 | + | 12.9904i | 0.774941 | + | 0.447412i | ||||
\(844\) | 2.00000 | − | 3.46410i | 0.0688428 | − | 0.119239i | ||||
\(845\) | −1.73205 | − | 3.00000i | −0.0595844 | − | 0.103203i | ||||
\(846\) | 5.19615i | 0.178647i | ||||||||
\(847\) | 2.50000 | + | 0.866025i | 0.0859010 | + | 0.0297570i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25.9808 | − | 15.0000i | 0.891657 | − | 0.514799i | ||||
\(850\) | −10.5000 | − | 6.06218i | −0.360147 | − | 0.207931i | ||||
\(851\) | 18.1865 | + | 10.5000i | 0.623426 | + | 0.359935i | ||||
\(852\) | −22.5000 | + | 12.9904i | −0.770837 | + | 0.445043i | ||||
\(853\) | 17.3205i | 0.593043i | 0.955026 | + | 0.296521i | \(0.0958266\pi\) | ||||
−0.955026 | + | 0.296521i | \(0.904173\pi\) | |||||||
\(854\) | 5.19615 | + | 27.0000i | 0.177809 | + | 0.923921i | ||||
\(855\) | − | 18.0000i | − | 0.615587i | ||||||
\(856\) | −3.00000 | − | 5.19615i | −0.102538 | − | 0.177601i | ||||
\(857\) | 21.6506 | − | 37.5000i | 0.739572 | − | 1.28098i | −0.213117 | − | 0.977027i | \(-0.568361\pi\) |
0.952688 | − | 0.303949i | \(-0.0983052\pi\) | |||||||
\(858\) | 5.19615 | + | 3.00000i | 0.177394 | + | 0.102418i | ||||
\(859\) | −27.0000 | + | 15.5885i | −0.921228 | + | 0.531871i | −0.884027 | − | 0.467436i | \(-0.845178\pi\) |
−0.0372015 | + | 0.999308i | \(0.511844\pi\) | |||||||
\(860\) | −3.46410 | −0.118125 | ||||||||
\(861\) | −6.00000 | − | 31.1769i | −0.204479 | − | 1.06251i | ||||
\(862\) | −12.0000 | −0.408722 | ||||||||
\(863\) | 31.1769 | − | 18.0000i | 1.06127 | − | 0.612727i | 0.135490 | − | 0.990779i | \(-0.456739\pi\) |
0.925785 | + | 0.378052i | \(0.123406\pi\) | |||||||
\(864\) | −4.50000 | − | 2.59808i | −0.153093 | − | 0.0883883i | ||||
\(865\) | −36.0000 | + | 62.3538i | −1.22404 | + | 2.12009i | ||||
\(866\) | −4.33013 | − | 7.50000i | −0.147144 | − | 0.254860i | ||||
\(867\) | 24.2487 | 0.823529 | ||||||||
\(868\) | 3.00000 | − | 8.66025i | 0.101827 | − | 0.293948i | ||||
\(869\) | 8.00000i | 0.271381i | ||||||||
\(870\) | −9.00000 | − | 15.5885i | −0.305129 | − | 0.528498i | ||||
\(871\) | 48.0000 | + | 27.7128i | 1.62642 | + | 0.939013i | ||||
\(872\) | −13.8564 | − | 8.00000i | −0.469237 | − | 0.270914i | ||||
\(873\) | 40.5000 | − | 23.3827i | 1.37072 | − | 0.791384i | ||||
\(874\) | 5.19615i | 0.175762i | ||||||||
\(875\) | 13.8564 | − | 12.0000i | 0.468432 | − | 0.405674i | ||||
\(876\) | 24.0000i | 0.810885i | ||||||||
\(877\) | 5.00000 | + | 8.66025i | 0.168838 | + | 0.292436i | 0.938012 | − | 0.346604i | \(-0.112665\pi\) |
−0.769174 | + | 0.639040i | \(0.779332\pi\) | |||||||
\(878\) | −7.79423 | + | 13.5000i | −0.263042 | + | 0.455603i | ||||
\(879\) | −7.50000 | + | 12.9904i | −0.252969 | + | 0.438155i | ||||
\(880\) | 3.00000 | − | 1.73205i | 0.101130 | − | 0.0583874i | ||||
\(881\) | 41.5692 | 1.40050 | 0.700251 | − | 0.713896i | \(-0.253071\pi\) | ||||
0.700251 | + | 0.713896i | \(0.253071\pi\) | |||||||
\(882\) | 12.9904 | − | 16.5000i | 0.437409 | − | 0.555584i | ||||
\(883\) | 52.0000 | 1.74994 | 0.874970 | − | 0.484178i | \(-0.160881\pi\) | ||||
0.874970 | + | 0.484178i | \(0.160881\pi\) | |||||||
\(884\) | 5.19615 | − | 3.00000i | 0.174766 | − | 0.100901i | ||||
\(885\) | 36.3731 | − | 63.0000i | 1.22267 | − | 2.11772i | ||||
\(886\) | −4.50000 | + | 7.79423i | −0.151180 | + | 0.261852i | ||||
\(887\) | −17.3205 | − | 30.0000i | −0.581566 | − | 1.00730i | −0.995294 | − | 0.0969010i | \(-0.969107\pi\) |
0.413728 | − | 0.910400i | \(-0.364226\pi\) | |||||||
\(888\) | − | 12.1244i | − | 0.406867i | ||||||
\(889\) | 22.0000 | − | 19.0526i | 0.737856 | − | 0.639002i | ||||
\(890\) | 36.0000i | 1.20672i | ||||||||
\(891\) | 7.79423 | − | 4.50000i | 0.261116 | − | 0.150756i | ||||
\(892\) | 9.00000 | + | 5.19615i | 0.301342 | + | 0.173980i | ||||
\(893\) | −2.59808 | − | 1.50000i | −0.0869413 | − | 0.0501956i | ||||
\(894\) | −7.79423 | − | 13.5000i | −0.260678 | − | 0.451508i | ||||
\(895\) | 51.9615i | 1.73688i | ||||||||
\(896\) | 0.866025 | − | 2.50000i | 0.0289319 | − | 0.0835191i | ||||
\(897\) | −18.0000 | −0.601003 | ||||||||
\(898\) | −6.00000 | − | 10.3923i | −0.200223 | − | 0.346796i | ||||
\(899\) | 5.19615 | − | 9.00000i | 0.173301 | − | 0.300167i | ||||
\(900\) | 10.5000 | − | 18.1865i | 0.350000 | − | 0.606218i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 6.92820 | 0.230684 | ||||||||
\(903\) | −0.866025 | − | 4.50000i | −0.0288195 | − | 0.149751i | ||||
\(904\) | −6.00000 | −0.199557 | ||||||||
\(905\) | −41.5692 | + | 24.0000i | −1.38181 | + | 0.797787i | ||||
\(906\) | 16.5000 | + | 9.52628i | 0.548176 | + | 0.316489i | ||||
\(907\) | 22.0000 | − | 38.1051i | 0.730498 | − | 1.26526i | −0.226173 | − | 0.974087i | \(-0.572621\pi\) |
0.956671 | − | 0.291172i | \(-0.0940453\pi\) | |||||||
\(908\) | −5.19615 | − | 9.00000i | −0.172440 | − | 0.298675i | ||||
\(909\) | 15.5885 | 0.517036 | ||||||||
\(910\) | 6.00000 | + | 31.1769i | 0.198898 | + | 1.03350i | ||||
\(911\) | − | 9.00000i | − | 0.298183i | −0.988823 | − | 0.149092i | \(-0.952365\pi\) | ||
0.988823 | − | 0.149092i | \(-0.0476349\pi\) | |||||||
\(912\) | 2.59808 | − | 1.50000i | 0.0860309 | − | 0.0496700i | ||||
\(913\) | −15.0000 | − | 8.66025i | −0.496428 | − | 0.286613i | ||||
\(914\) | −27.7128 | − | 16.0000i | −0.916658 | − | 0.529233i | ||||
\(915\) | −54.0000 | + | 31.1769i | −1.78518 | + | 1.03068i | ||||
\(916\) | 13.8564i | 0.457829i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 9.00000i | − | 0.297044i | ||||||
\(919\) | 14.5000 | + | 25.1147i | 0.478311 | + | 0.828459i | 0.999691 | − | 0.0248659i | \(-0.00791589\pi\) |
−0.521380 | + | 0.853325i | \(0.674583\pi\) | |||||||
\(920\) | −5.19615 | + | 9.00000i | −0.171312 | + | 0.296721i | ||||
\(921\) | 25.9808 | + | 15.0000i | 0.856095 | + | 0.494267i | ||||
\(922\) | 7.50000 | − | 4.33013i | 0.246999 | − | 0.142605i | ||||
\(923\) | 51.9615 | 1.71033 | ||||||||
\(924\) | 3.00000 | + | 3.46410i | 0.0986928 | + | 0.113961i | ||||
\(925\) | 49.0000 | 1.61111 | ||||||||
\(926\) | 3.46410 | − | 2.00000i | 0.113837 | − | 0.0657241i | ||||
\(927\) | −45.0000 | − | 25.9808i | −1.47799 | − | 0.853320i | ||||
\(928\) | 1.50000 | − | 2.59808i | 0.0492399 | − | 0.0852860i | ||||
\(929\) | 3.46410 | + | 6.00000i | 0.113653 | + | 0.196854i | 0.917241 | − | 0.398333i | \(-0.130411\pi\) |
−0.803587 | + | 0.595187i | \(0.797078\pi\) | |||||||
\(930\) | 20.7846 | 0.681554 | ||||||||
\(931\) | 4.50000 | + | 11.2583i | 0.147482 | + | 0.368977i | ||||
\(932\) | − | 27.0000i | − | 0.884414i | ||||||
\(933\) | −19.5000 | − | 33.7750i | −0.638401 | − | 1.10574i | ||||
\(934\) | 13.5000 | + | 7.79423i | 0.441733 | + | 0.255035i | ||||
\(935\) | 5.19615 | + | 3.00000i | 0.169932 | + | 0.0981105i | ||||
\(936\) | 5.19615 | + | 9.00000i | 0.169842 | + | 0.294174i | ||||
\(937\) | − | 3.46410i | − | 0.113167i | −0.998398 | − | 0.0565836i | \(-0.981979\pi\) | ||
0.998398 | − | 0.0565836i | \(-0.0180208\pi\) | |||||||
\(938\) | 27.7128 | + | 32.0000i | 0.904855 | + | 1.04484i | ||||
\(939\) | 51.0000i | 1.66432i | ||||||||
\(940\) | −3.00000 | − | 5.19615i | −0.0978492 | − | 0.169480i | ||||
\(941\) | −0.866025 | + | 1.50000i | −0.0282316 | + | 0.0488986i | −0.879796 | − | 0.475351i | \(-0.842321\pi\) |
0.851564 | + | 0.524250i | \(0.175654\pi\) | |||||||
\(942\) | −4.50000 | + | 7.79423i | −0.146618 | + | 0.253950i | ||||
\(943\) | −18.0000 | + | 10.3923i | −0.586161 | + | 0.338420i | ||||
\(944\) | 12.1244 | 0.394614 | ||||||||
\(945\) | 45.0000 | + | 15.5885i | 1.46385 | + | 0.507093i | ||||
\(946\) | 1.00000 | 0.0325128 | ||||||||
\(947\) | 2.59808 | − | 1.50000i | 0.0844261 | − | 0.0487435i | −0.457193 | − | 0.889368i | \(-0.651145\pi\) |
0.541619 | + | 0.840624i | \(0.317812\pi\) | |||||||
\(948\) | −6.92820 | + | 12.0000i | −0.225018 | + | 0.389742i | ||||
\(949\) | 24.0000 | − | 41.5692i | 0.779073 | − | 1.34939i | ||||
\(950\) | 6.06218 | + | 10.5000i | 0.196683 | + | 0.340665i | ||||
\(951\) | − | 10.3923i | − | 0.336994i | ||||||
\(952\) | 4.50000 | − | 0.866025i | 0.145846 | − | 0.0280680i | ||||
\(953\) | − | 42.0000i | − | 1.36051i | −0.732974 | − | 0.680257i | \(-0.761868\pi\) | ||
0.732974 | − | 0.680257i | \(-0.238132\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.19615 | − | 3.00000i | −0.168056 | − | 0.0970269i | ||||
\(957\) | 2.59808 | + | 4.50000i | 0.0839839 | + | 0.145464i | ||||
\(958\) | − | 17.3205i | − | 0.559600i | ||||||
\(959\) | 46.7654 | − | 9.00000i | 1.51013 | − | 0.290625i | ||||
\(960\) | 6.00000 | 0.193649 | ||||||||
\(961\) | −9.50000 | − | 16.4545i | −0.306452 | − | 0.530790i | ||||
\(962\) | −12.1244 | + | 21.0000i | −0.390905 | + | 0.677067i | ||||
\(963\) | 15.5885 | + | 9.00000i | 0.502331 | + | 0.290021i | ||||
\(964\) | 18.0000 | − | 10.3923i | 0.579741 | − | 0.334714i | ||||
\(965\) | 13.8564 | 0.446054 | ||||||||
\(966\) | −12.9904 | − | 4.50000i | −0.417959 | − | 0.144785i | ||||
\(967\) | −43.0000 | −1.38279 | −0.691393 | − | 0.722478i | \(-0.743003\pi\) | ||||
−0.691393 | + | 0.722478i | \(0.743003\pi\) | |||||||
\(968\) | −0.866025 | + | 0.500000i | −0.0278351 | + | 0.0160706i | ||||
\(969\) | 4.50000 | + | 2.59808i | 0.144561 | + | 0.0834622i | ||||
\(970\) | −27.0000 | + | 46.7654i | −0.866918 | + | 1.50155i | ||||
\(971\) | 1.73205 | + | 3.00000i | 0.0555842 | + | 0.0962746i | 0.892479 | − | 0.451090i | \(-0.148965\pi\) |
−0.836894 | + | 0.547364i | \(0.815631\pi\) | |||||||
\(972\) | 15.5885 | 0.500000 | ||||||||
\(973\) | 3.00000 | + | 3.46410i | 0.0961756 | + | 0.111054i | ||||
\(974\) | 26.0000i | 0.833094i | ||||||||
\(975\) | −36.3731 | + | 21.0000i | −1.16487 | + | 0.672538i | ||||
\(976\) | −9.00000 | − | 5.19615i | −0.288083 | − | 0.166325i | ||||
\(977\) | −20.7846 | − | 12.0000i | −0.664959 | − | 0.383914i | 0.129205 | − | 0.991618i | \(-0.458757\pi\) |
−0.794164 | + | 0.607704i | \(0.792091\pi\) | |||||||
\(978\) | 21.0000 | − | 12.1244i | 0.671506 | − | 0.387694i | ||||
\(979\) | − | 10.3923i | − | 0.332140i | ||||||
\(980\) | −3.46410 | + | 24.0000i | −0.110657 | + | 0.766652i | ||||
\(981\) | 48.0000 | 1.53252 | ||||||||
\(982\) | −15.0000 | − | 25.9808i | −0.478669 | − | 0.829079i | ||||
\(983\) | −0.866025 | + | 1.50000i | −0.0276219 | + | 0.0478426i | −0.879506 | − | 0.475888i | \(-0.842127\pi\) |
0.851884 | + | 0.523731i | \(0.175460\pi\) | |||||||
\(984\) | 10.3923 | + | 6.00000i | 0.331295 | + | 0.191273i | ||||
\(985\) | −27.0000 | + | 15.5885i | −0.860292 | + | 0.496690i | ||||
\(986\) | 5.19615 | 0.165479 | ||||||||
\(987\) | 6.00000 | − | 5.19615i | 0.190982 | − | 0.165395i | ||||
\(988\) | −6.00000 | −0.190885 | ||||||||
\(989\) | −2.59808 | + | 1.50000i | −0.0826140 | + | 0.0476972i | ||||
\(990\) | −5.19615 | + | 9.00000i | −0.165145 | + | 0.286039i | ||||
\(991\) | 10.0000 | − | 17.3205i | 0.317660 | − | 0.550204i | −0.662339 | − | 0.749204i | \(-0.730436\pi\) |
0.979999 | + | 0.199000i | \(0.0637695\pi\) | |||||||
\(992\) | 1.73205 | + | 3.00000i | 0.0549927 | + | 0.0952501i | ||||
\(993\) | −17.3205 | −0.549650 | ||||||||
\(994\) | 37.5000 | + | 12.9904i | 1.18943 | + | 0.412030i | ||||
\(995\) | 36.0000i | 1.14128i | ||||||||
\(996\) | −15.0000 | − | 25.9808i | −0.475293 | − | 0.823232i | ||||
\(997\) | 33.0000 | + | 19.0526i | 1.04512 | + | 0.603401i | 0.921279 | − | 0.388901i | \(-0.127145\pi\) |
0.123841 | + | 0.992302i | \(0.460479\pi\) | |||||||
\(998\) | −27.7128 | − | 16.0000i | −0.877234 | − | 0.506471i | ||||
\(999\) | 18.1865 | + | 31.5000i | 0.575396 | + | 0.996616i |
(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 | 462.2.k.a.353.1 | yes | 4 | |
3.2 | odd | 2 | inner | 462.2.k.a.353.2 | yes | 4 | |
7.5 | odd | 6 | inner | 462.2.k.a.89.2 | yes | 4 | |
21.5 | even | 6 | inner | 462.2.k.a.89.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.k.a.89.1 | ✓ | 4 | 21.5 | even | 6 | inner | |
462.2.k.a.89.2 | yes | 4 | 7.5 | odd | 6 | inner | |
462.2.k.a.353.1 | yes | 4 | 1.1 | even | 1 | trivial | |
462.2.k.a.353.2 | yes | 4 | 3.2 | odd | 2 | inner |