Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(67,462)]
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([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.i (of order \(3\), 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: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 331.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.331 |
Dual form | 462.2.i.b.67.1 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −2.00000 | − | 1.73205i | −0.755929 | − | 0.654654i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.500000 | − | 0.866025i | −0.150756 | − | 0.261116i | ||||
\(12\) | −0.500000 | + | 0.866025i | −0.144338 | + | 0.250000i | ||||
\(13\) | −4.00000 | −1.10940 | −0.554700 | − | 0.832050i | \(-0.687167\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | −2.50000 | + | 0.866025i | −0.668153 | + | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.50000 | − | 2.59808i | −0.363803 | − | 0.630126i | 0.624780 | − | 0.780801i | \(-0.285189\pi\) |
−0.988583 | + | 0.150675i | \(0.951855\pi\) | |||||||
\(18\) | 0.500000 | + | 0.866025i | 0.117851 | + | 0.204124i | ||||
\(19\) | 0.500000 | − | 0.866025i | 0.114708 | − | 0.198680i | −0.802955 | − | 0.596040i | \(-0.796740\pi\) |
0.917663 | + | 0.397360i | \(0.130073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.500000 | + | 2.59808i | −0.109109 | + | 0.566947i | ||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 1.50000 | − | 2.59808i | 0.312772 | − | 0.541736i | −0.666190 | − | 0.745782i | \(-0.732076\pi\) |
0.978961 | + | 0.204046i | \(0.0654092\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | 2.50000 | + | 4.33013i | 0.500000 | + | 0.866025i | ||||
\(26\) | −2.00000 | + | 3.46410i | −0.392232 | + | 0.679366i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.500000 | + | 2.59808i | −0.0944911 | + | 0.490990i | ||||
\(29\) | −9.00000 | −1.67126 | −0.835629 | − | 0.549294i | \(-0.814897\pi\) | ||||
−0.835629 | + | 0.549294i | \(0.814897\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | − | 1.73205i | −0.179605 | − | 0.311086i | 0.762140 | − | 0.647412i | \(-0.224149\pi\) |
−0.941745 | + | 0.336327i | \(0.890815\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −0.500000 | + | 0.866025i | −0.0870388 | + | 0.150756i | ||||
\(34\) | −3.00000 | −0.514496 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 3.50000 | − | 6.06218i | 0.575396 | − | 0.996616i | −0.420602 | − | 0.907245i | \(-0.638181\pi\) |
0.995998 | − | 0.0893706i | \(-0.0284856\pi\) | |||||||
\(38\) | −0.500000 | − | 0.866025i | −0.0811107 | − | 0.140488i | ||||
\(39\) | 2.00000 | + | 3.46410i | 0.320256 | + | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 2.00000 | + | 1.73205i | 0.308607 | + | 0.267261i | ||||
\(43\) | 11.0000 | 1.67748 | 0.838742 | − | 0.544529i | \(-0.183292\pi\) | ||||
0.838742 | + | 0.544529i | \(0.183292\pi\) | |||||||
\(44\) | −0.500000 | + | 0.866025i | −0.0753778 | + | 0.130558i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.50000 | − | 2.59808i | −0.221163 | − | 0.383065i | ||||
\(47\) | 1.50000 | − | 2.59808i | 0.218797 | − | 0.378968i | −0.735643 | − | 0.677369i | \(-0.763120\pi\) |
0.954441 | + | 0.298401i | \(0.0964533\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | 5.00000 | 0.707107 | ||||||||
\(51\) | −1.50000 | + | 2.59808i | −0.210042 | + | 0.363803i | ||||
\(52\) | 2.00000 | + | 3.46410i | 0.277350 | + | 0.480384i | ||||
\(53\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.00000 | + | 1.73205i | 0.267261 | + | 0.231455i | ||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | −4.50000 | + | 7.79423i | −0.590879 | + | 1.02343i | ||||
\(59\) | −4.50000 | − | 7.79423i | −0.585850 | − | 1.01472i | −0.994769 | − | 0.102151i | \(-0.967427\pi\) |
0.408919 | − | 0.912571i | \(-0.365906\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.00000 | − | 8.66025i | 0.640184 | − | 1.10883i | −0.345207 | − | 0.938527i | \(-0.612191\pi\) |
0.985391 | − | 0.170305i | \(-0.0544754\pi\) | |||||||
\(62\) | −2.00000 | −0.254000 | ||||||||
\(63\) | 2.50000 | − | 0.866025i | 0.314970 | − | 0.109109i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.500000 | + | 0.866025i | 0.0615457 | + | 0.106600i | ||||
\(67\) | 2.00000 | + | 3.46410i | 0.244339 | + | 0.423207i | 0.961946 | − | 0.273241i | \(-0.0880957\pi\) |
−0.717607 | + | 0.696449i | \(0.754762\pi\) | |||||||
\(68\) | −1.50000 | + | 2.59808i | −0.181902 | + | 0.315063i | ||||
\(69\) | −3.00000 | −0.361158 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.00000 | 0.356034 | 0.178017 | − | 0.984027i | \(-0.443032\pi\) | ||||
0.178017 | + | 0.984027i | \(0.443032\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | 2.00000 | + | 3.46410i | 0.234082 | + | 0.405442i | 0.959006 | − | 0.283387i | \(-0.0914581\pi\) |
−0.724923 | + | 0.688830i | \(0.758125\pi\) | |||||||
\(74\) | −3.50000 | − | 6.06218i | −0.406867 | − | 0.704714i | ||||
\(75\) | 2.50000 | − | 4.33013i | 0.288675 | − | 0.500000i | ||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −0.500000 | + | 2.59808i | −0.0569803 | + | 0.296078i | ||||
\(78\) | 4.00000 | 0.452911 | ||||||||
\(79\) | 8.00000 | − | 13.8564i | 0.900070 | − | 1.55897i | 0.0726692 | − | 0.997356i | \(-0.476848\pi\) |
0.827401 | − | 0.561611i | \(-0.189818\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −3.00000 | + | 5.19615i | −0.331295 | + | 0.573819i | ||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 2.50000 | − | 0.866025i | 0.272772 | − | 0.0944911i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.50000 | − | 9.52628i | 0.593080 | − | 1.02725i | ||||
\(87\) | 4.50000 | + | 7.79423i | 0.482451 | + | 0.835629i | ||||
\(88\) | 0.500000 | + | 0.866025i | 0.0533002 | + | 0.0923186i | ||||
\(89\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.00000 | + | 6.92820i | 0.838628 | + | 0.726273i | ||||
\(92\) | −3.00000 | −0.312772 | ||||||||
\(93\) | −1.00000 | + | 1.73205i | −0.103695 | + | 0.179605i | ||||
\(94\) | −1.50000 | − | 2.59808i | −0.154713 | − | 0.267971i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.500000 | − | 0.866025i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | −1.00000 | −0.101535 | −0.0507673 | − | 0.998711i | \(-0.516167\pi\) | ||||
−0.0507673 | + | 0.998711i | \(0.516167\pi\) | |||||||
\(98\) | 6.50000 | + | 2.59808i | 0.656599 | + | 0.262445i | ||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 2.50000 | − | 4.33013i | 0.250000 | − | 0.433013i | ||||
\(101\) | −7.50000 | − | 12.9904i | −0.746278 | − | 1.29259i | −0.949595 | − | 0.313478i | \(-0.898506\pi\) |
0.203317 | − | 0.979113i | \(-0.434828\pi\) | |||||||
\(102\) | 1.50000 | + | 2.59808i | 0.148522 | + | 0.257248i | ||||
\(103\) | 2.00000 | − | 3.46410i | 0.197066 | − | 0.341328i | −0.750510 | − | 0.660859i | \(-0.770192\pi\) |
0.947576 | + | 0.319531i | \(0.103525\pi\) | |||||||
\(104\) | 4.00000 | 0.392232 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.00000 | − | 15.5885i | 0.870063 | − | 1.50699i | 0.00813215 | − | 0.999967i | \(-0.497411\pi\) |
0.861931 | − | 0.507026i | \(-0.169255\pi\) | |||||||
\(108\) | −0.500000 | − | 0.866025i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | 5.00000 | + | 8.66025i | 0.478913 | + | 0.829502i | 0.999708 | − | 0.0241802i | \(-0.00769755\pi\) |
−0.520794 | + | 0.853682i | \(0.674364\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.00000 | −0.664411 | ||||||||
\(112\) | 2.50000 | − | 0.866025i | 0.236228 | − | 0.0818317i | ||||
\(113\) | 12.0000 | 1.12887 | 0.564433 | − | 0.825479i | \(-0.309095\pi\) | ||||
0.564433 | + | 0.825479i | \(0.309095\pi\) | |||||||
\(114\) | −0.500000 | + | 0.866025i | −0.0468293 | + | 0.0811107i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.50000 | + | 7.79423i | 0.417815 | + | 0.723676i | ||||
\(117\) | 2.00000 | − | 3.46410i | 0.184900 | − | 0.320256i | ||||
\(118\) | −9.00000 | −0.828517 | ||||||||
\(119\) | −1.50000 | + | 7.79423i | −0.137505 | + | 0.714496i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | −5.00000 | − | 8.66025i | −0.452679 | − | 0.784063i | ||||
\(123\) | 3.00000 | + | 5.19615i | 0.270501 | + | 0.468521i | ||||
\(124\) | −1.00000 | + | 1.73205i | −0.0898027 | + | 0.155543i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.500000 | − | 2.59808i | 0.0445435 | − | 0.231455i | ||||
\(127\) | −1.00000 | −0.0887357 | −0.0443678 | − | 0.999015i | \(-0.514127\pi\) | ||||
−0.0443678 | + | 0.999015i | \(0.514127\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −5.50000 | − | 9.52628i | −0.484248 | − | 0.838742i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.00000 | + | 15.5885i | −0.786334 | + | 1.36197i | 0.141865 | + | 0.989886i | \(0.454690\pi\) |
−0.928199 | + | 0.372084i | \(0.878643\pi\) | |||||||
\(132\) | 1.00000 | 0.0870388 | ||||||||
\(133\) | −2.50000 | + | 0.866025i | −0.216777 | + | 0.0750939i | ||||
\(134\) | 4.00000 | 0.345547 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.50000 | + | 2.59808i | 0.128624 | + | 0.222783i | ||||
\(137\) | −6.00000 | − | 10.3923i | −0.512615 | − | 0.887875i | −0.999893 | − | 0.0146279i | \(-0.995344\pi\) |
0.487278 | − | 0.873247i | \(-0.337990\pi\) | |||||||
\(138\) | −1.50000 | + | 2.59808i | −0.127688 | + | 0.221163i | ||||
\(139\) | −19.0000 | −1.61156 | −0.805779 | − | 0.592216i | \(-0.798253\pi\) | ||||
−0.805779 | + | 0.592216i | \(0.798253\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.00000 | −0.252646 | ||||||||
\(142\) | 1.50000 | − | 2.59808i | 0.125877 | − | 0.218026i | ||||
\(143\) | 2.00000 | + | 3.46410i | 0.167248 | + | 0.289683i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.00000 | 0.331042 | ||||||||
\(147\) | 5.50000 | − | 4.33013i | 0.453632 | − | 0.357143i | ||||
\(148\) | −7.00000 | −0.575396 | ||||||||
\(149\) | −4.50000 | + | 7.79423i | −0.368654 | + | 0.638528i | −0.989355 | − | 0.145519i | \(-0.953515\pi\) |
0.620701 | + | 0.784047i | \(0.286848\pi\) | |||||||
\(150\) | −2.50000 | − | 4.33013i | −0.204124 | − | 0.353553i | ||||
\(151\) | 9.50000 | + | 16.4545i | 0.773099 | + | 1.33905i | 0.935857 | + | 0.352381i | \(0.114628\pi\) |
−0.162758 | + | 0.986666i | \(0.552039\pi\) | |||||||
\(152\) | −0.500000 | + | 0.866025i | −0.0405554 | + | 0.0702439i | ||||
\(153\) | 3.00000 | 0.242536 | ||||||||
\(154\) | 2.00000 | + | 1.73205i | 0.161165 | + | 0.139573i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.00000 | − | 3.46410i | 0.160128 | − | 0.277350i | ||||
\(157\) | 6.50000 | + | 11.2583i | 0.518756 | + | 0.898513i | 0.999762 | + | 0.0217953i | \(0.00693820\pi\) |
−0.481006 | + | 0.876717i | \(0.659728\pi\) | |||||||
\(158\) | −8.00000 | − | 13.8564i | −0.636446 | − | 1.10236i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.50000 | + | 2.59808i | −0.591083 | + | 0.204757i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −1.00000 | + | 1.73205i | −0.0783260 | + | 0.135665i | −0.902528 | − | 0.430632i | \(-0.858291\pi\) |
0.824202 | + | 0.566296i | \(0.191624\pi\) | |||||||
\(164\) | 3.00000 | + | 5.19615i | 0.234261 | + | 0.405751i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.0000 | 0.928588 | 0.464294 | − | 0.885681i | \(-0.346308\pi\) | ||||
0.464294 | + | 0.885681i | \(0.346308\pi\) | |||||||
\(168\) | 0.500000 | − | 2.59808i | 0.0385758 | − | 0.200446i | ||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.500000 | + | 0.866025i | 0.0382360 | + | 0.0662266i | ||||
\(172\) | −5.50000 | − | 9.52628i | −0.419371 | − | 0.726372i | ||||
\(173\) | 3.00000 | − | 5.19615i | 0.228086 | − | 0.395056i | −0.729155 | − | 0.684349i | \(-0.760087\pi\) |
0.957241 | + | 0.289292i | \(0.0934200\pi\) | |||||||
\(174\) | 9.00000 | 0.682288 | ||||||||
\(175\) | 2.50000 | − | 12.9904i | 0.188982 | − | 0.981981i | ||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −4.50000 | + | 7.79423i | −0.338241 | + | 0.585850i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.50000 | + | 12.9904i | 0.560576 | + | 0.970947i | 0.997446 | + | 0.0714220i | \(0.0227537\pi\) |
−0.436870 | + | 0.899525i | \(0.643913\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 10.0000 | − | 3.46410i | 0.741249 | − | 0.256776i | ||||
\(183\) | −10.0000 | −0.739221 | ||||||||
\(184\) | −1.50000 | + | 2.59808i | −0.110581 | + | 0.191533i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.00000 | + | 1.73205i | 0.0733236 | + | 0.127000i | ||||
\(187\) | −1.50000 | + | 2.59808i | −0.109691 | + | 0.189990i | ||||
\(188\) | −3.00000 | −0.218797 | ||||||||
\(189\) | −2.00000 | − | 1.73205i | −0.145479 | − | 0.125988i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | 5.00000 | + | 8.66025i | 0.359908 | + | 0.623379i | 0.987945 | − | 0.154805i | \(-0.0494748\pi\) |
−0.628037 | + | 0.778183i | \(0.716141\pi\) | |||||||
\(194\) | −0.500000 | + | 0.866025i | −0.0358979 | + | 0.0621770i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.50000 | − | 4.33013i | 0.392857 | − | 0.309295i | ||||
\(197\) | −21.0000 | −1.49619 | −0.748094 | − | 0.663593i | \(-0.769031\pi\) | ||||
−0.748094 | + | 0.663593i | \(0.769031\pi\) | |||||||
\(198\) | 0.500000 | − | 0.866025i | 0.0355335 | − | 0.0615457i | ||||
\(199\) | −10.0000 | − | 17.3205i | −0.708881 | − | 1.22782i | −0.965272 | − | 0.261245i | \(-0.915867\pi\) |
0.256391 | − | 0.966573i | \(-0.417466\pi\) | |||||||
\(200\) | −2.50000 | − | 4.33013i | −0.176777 | − | 0.306186i | ||||
\(201\) | 2.00000 | − | 3.46410i | 0.141069 | − | 0.244339i | ||||
\(202\) | −15.0000 | −1.05540 | ||||||||
\(203\) | 18.0000 | + | 15.5885i | 1.26335 | + | 1.09410i | ||||
\(204\) | 3.00000 | 0.210042 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.00000 | − | 3.46410i | −0.139347 | − | 0.241355i | ||||
\(207\) | 1.50000 | + | 2.59808i | 0.104257 | + | 0.180579i | ||||
\(208\) | 2.00000 | − | 3.46410i | 0.138675 | − | 0.240192i | ||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.50000 | − | 2.59808i | −0.102778 | − | 0.178017i | ||||
\(214\) | −9.00000 | − | 15.5885i | −0.615227 | − | 1.06561i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −1.00000 | + | 5.19615i | −0.0678844 | + | 0.352738i | ||||
\(218\) | 10.0000 | 0.677285 | ||||||||
\(219\) | 2.00000 | − | 3.46410i | 0.135147 | − | 0.234082i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.00000 | + | 10.3923i | 0.403604 | + | 0.699062i | ||||
\(222\) | −3.50000 | + | 6.06218i | −0.234905 | + | 0.406867i | ||||
\(223\) | 8.00000 | 0.535720 | 0.267860 | − | 0.963458i | \(-0.413684\pi\) | ||||
0.267860 | + | 0.963458i | \(0.413684\pi\) | |||||||
\(224\) | 0.500000 | − | 2.59808i | 0.0334077 | − | 0.173591i | ||||
\(225\) | −5.00000 | −0.333333 | ||||||||
\(226\) | 6.00000 | − | 10.3923i | 0.399114 | − | 0.691286i | ||||
\(227\) | −9.00000 | − | 15.5885i | −0.597351 | − | 1.03464i | −0.993210 | − | 0.116331i | \(-0.962887\pi\) |
0.395860 | − | 0.918311i | \(-0.370447\pi\) | |||||||
\(228\) | 0.500000 | + | 0.866025i | 0.0331133 | + | 0.0573539i | ||||
\(229\) | −13.0000 | + | 22.5167i | −0.859064 | + | 1.48794i | 0.0137585 | + | 0.999905i | \(0.495620\pi\) |
−0.872823 | + | 0.488037i | \(0.837713\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.50000 | − | 0.866025i | 0.164488 | − | 0.0569803i | ||||
\(232\) | 9.00000 | 0.590879 | ||||||||
\(233\) | −4.50000 | + | 7.79423i | −0.294805 | + | 0.510617i | −0.974939 | − | 0.222470i | \(-0.928588\pi\) |
0.680135 | + | 0.733087i | \(0.261921\pi\) | |||||||
\(234\) | −2.00000 | − | 3.46410i | −0.130744 | − | 0.226455i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.50000 | + | 7.79423i | −0.292925 | + | 0.507361i | ||||
\(237\) | −16.0000 | −1.03931 | ||||||||
\(238\) | 6.00000 | + | 5.19615i | 0.388922 | + | 0.336817i | ||||
\(239\) | −24.0000 | −1.55243 | −0.776215 | − | 0.630468i | \(-0.782863\pi\) | ||||
−0.776215 | + | 0.630468i | \(0.782863\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.0000 | + | 24.2487i | 0.901819 | + | 1.56200i | 0.825131 | + | 0.564942i | \(0.191101\pi\) |
0.0766885 | + | 0.997055i | \(0.475565\pi\) | |||||||
\(242\) | 0.500000 | + | 0.866025i | 0.0321412 | + | 0.0556702i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −10.0000 | −0.640184 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.00000 | 0.382546 | ||||||||
\(247\) | −2.00000 | + | 3.46410i | −0.127257 | + | 0.220416i | ||||
\(248\) | 1.00000 | + | 1.73205i | 0.0635001 | + | 0.109985i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.0000 | 0.946792 | 0.473396 | − | 0.880850i | \(-0.343028\pi\) | ||||
0.473396 | + | 0.880850i | \(0.343028\pi\) | |||||||
\(252\) | −2.00000 | − | 1.73205i | −0.125988 | − | 0.109109i | ||||
\(253\) | −3.00000 | −0.188608 | ||||||||
\(254\) | −0.500000 | + | 0.866025i | −0.0313728 | + | 0.0543393i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −6.00000 | + | 10.3923i | −0.374270 | + | 0.648254i | −0.990217 | − | 0.139533i | \(-0.955440\pi\) |
0.615948 | + | 0.787787i | \(0.288773\pi\) | |||||||
\(258\) | −11.0000 | −0.684830 | ||||||||
\(259\) | −17.5000 | + | 6.06218i | −1.08740 | + | 0.376685i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.50000 | − | 7.79423i | 0.278543 | − | 0.482451i | ||||
\(262\) | 9.00000 | + | 15.5885i | 0.556022 | + | 0.963058i | ||||
\(263\) | 9.00000 | + | 15.5885i | 0.554964 | + | 0.961225i | 0.997906 | + | 0.0646755i | \(0.0206012\pi\) |
−0.442943 | + | 0.896550i | \(0.646065\pi\) | |||||||
\(264\) | 0.500000 | − | 0.866025i | 0.0307729 | − | 0.0533002i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.500000 | + | 2.59808i | −0.0306570 | + | 0.159298i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.00000 | − | 3.46410i | 0.122169 | − | 0.211604i | ||||
\(269\) | −3.00000 | − | 5.19615i | −0.182913 | − | 0.316815i | 0.759958 | − | 0.649972i | \(-0.225219\pi\) |
−0.942871 | + | 0.333157i | \(0.891886\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | − | 13.8564i | 0.485965 | − | 0.841717i | −0.513905 | − | 0.857847i | \(-0.671801\pi\) |
0.999870 | + | 0.0161307i | \(0.00513477\pi\) | |||||||
\(272\) | 3.00000 | 0.181902 | ||||||||
\(273\) | 2.00000 | − | 10.3923i | 0.121046 | − | 0.628971i | ||||
\(274\) | −12.0000 | −0.724947 | ||||||||
\(275\) | 2.50000 | − | 4.33013i | 0.150756 | − | 0.261116i | ||||
\(276\) | 1.50000 | + | 2.59808i | 0.0902894 | + | 0.156386i | ||||
\(277\) | −16.0000 | − | 27.7128i | −0.961347 | − | 1.66510i | −0.719125 | − | 0.694881i | \(-0.755457\pi\) |
−0.242222 | − | 0.970221i | \(-0.577876\pi\) | |||||||
\(278\) | −9.50000 | + | 16.4545i | −0.569772 | + | 0.986874i | ||||
\(279\) | 2.00000 | 0.119737 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.0000 | −0.894825 | −0.447412 | − | 0.894328i | \(-0.647654\pi\) | ||||
−0.447412 | + | 0.894328i | \(0.647654\pi\) | |||||||
\(282\) | −1.50000 | + | 2.59808i | −0.0893237 | + | 0.154713i | ||||
\(283\) | −10.0000 | − | 17.3205i | −0.594438 | − | 1.02960i | −0.993626 | − | 0.112728i | \(-0.964041\pi\) |
0.399188 | − | 0.916869i | \(-0.369292\pi\) | |||||||
\(284\) | −1.50000 | − | 2.59808i | −0.0890086 | − | 0.154167i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.00000 | 0.236525 | ||||||||
\(287\) | 12.0000 | + | 10.3923i | 0.708338 | + | 0.613438i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.500000 | + | 0.866025i | 0.0293105 | + | 0.0507673i | ||||
\(292\) | 2.00000 | − | 3.46410i | 0.117041 | − | 0.202721i | ||||
\(293\) | 9.00000 | 0.525786 | 0.262893 | − | 0.964825i | \(-0.415323\pi\) | ||||
0.262893 | + | 0.964825i | \(0.415323\pi\) | |||||||
\(294\) | −1.00000 | − | 6.92820i | −0.0583212 | − | 0.404061i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.50000 | + | 6.06218i | −0.203433 | + | 0.352357i | ||||
\(297\) | −0.500000 | − | 0.866025i | −0.0290129 | − | 0.0502519i | ||||
\(298\) | 4.50000 | + | 7.79423i | 0.260678 | + | 0.451508i | ||||
\(299\) | −6.00000 | + | 10.3923i | −0.346989 | + | 0.601003i | ||||
\(300\) | −5.00000 | −0.288675 | ||||||||
\(301\) | −22.0000 | − | 19.0526i | −1.26806 | − | 1.09817i | ||||
\(302\) | 19.0000 | 1.09333 | ||||||||
\(303\) | −7.50000 | + | 12.9904i | −0.430864 | + | 0.746278i | ||||
\(304\) | 0.500000 | + | 0.866025i | 0.0286770 | + | 0.0496700i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.50000 | − | 2.59808i | 0.0857493 | − | 0.148522i | ||||
\(307\) | −4.00000 | −0.228292 | −0.114146 | − | 0.993464i | \(-0.536413\pi\) | ||||
−0.114146 | + | 0.993464i | \(0.536413\pi\) | |||||||
\(308\) | 2.50000 | − | 0.866025i | 0.142451 | − | 0.0493464i | ||||
\(309\) | −4.00000 | −0.227552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.5000 | + | 18.1865i | 0.595400 | + | 1.03126i | 0.993490 | + | 0.113917i | \(0.0363399\pi\) |
−0.398090 | + | 0.917346i | \(0.630327\pi\) | |||||||
\(312\) | −2.00000 | − | 3.46410i | −0.113228 | − | 0.196116i | ||||
\(313\) | 0.500000 | − | 0.866025i | 0.0282617 | − | 0.0489506i | −0.851549 | − | 0.524276i | \(-0.824336\pi\) |
0.879810 | + | 0.475325i | \(0.157669\pi\) | |||||||
\(314\) | 13.0000 | 0.733632 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.0000 | −0.900070 | ||||||||
\(317\) | 6.00000 | − | 10.3923i | 0.336994 | − | 0.583690i | −0.646872 | − | 0.762598i | \(-0.723923\pi\) |
0.983866 | + | 0.178908i | \(0.0572566\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.50000 | + | 7.79423i | 0.251952 | + | 0.436393i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.0000 | −1.00466 | ||||||||
\(322\) | −1.50000 | + | 7.79423i | −0.0835917 | + | 0.434355i | ||||
\(323\) | −3.00000 | −0.166924 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | −10.0000 | − | 17.3205i | −0.554700 | − | 0.960769i | ||||
\(326\) | 1.00000 | + | 1.73205i | 0.0553849 | + | 0.0959294i | ||||
\(327\) | 5.00000 | − | 8.66025i | 0.276501 | − | 0.478913i | ||||
\(328\) | 6.00000 | 0.331295 | ||||||||
\(329\) | −7.50000 | + | 2.59808i | −0.413488 | + | 0.143237i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.00000 | − | 8.66025i | 0.274825 | − | 0.476011i | −0.695266 | − | 0.718752i | \(-0.744713\pi\) |
0.970091 | + | 0.242742i | \(0.0780468\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.50000 | + | 6.06218i | 0.191799 | + | 0.332205i | ||||
\(334\) | 6.00000 | − | 10.3923i | 0.328305 | − | 0.568642i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.00000 | − | 1.73205i | −0.109109 | − | 0.0944911i | ||||
\(337\) | −10.0000 | −0.544735 | −0.272367 | − | 0.962193i | \(-0.587807\pi\) | ||||
−0.272367 | + | 0.962193i | \(0.587807\pi\) | |||||||
\(338\) | 1.50000 | − | 2.59808i | 0.0815892 | − | 0.141317i | ||||
\(339\) | −6.00000 | − | 10.3923i | −0.325875 | − | 0.564433i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.00000 | + | 1.73205i | −0.0541530 | + | 0.0937958i | ||||
\(342\) | 1.00000 | 0.0540738 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | −11.0000 | −0.593080 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.00000 | − | 5.19615i | −0.161281 | − | 0.279347i | ||||
\(347\) | −6.00000 | − | 10.3923i | −0.322097 | − | 0.557888i | 0.658824 | − | 0.752297i | \(-0.271054\pi\) |
−0.980921 | + | 0.194409i | \(0.937721\pi\) | |||||||
\(348\) | 4.50000 | − | 7.79423i | 0.241225 | − | 0.417815i | ||||
\(349\) | 8.00000 | 0.428230 | 0.214115 | − | 0.976808i | \(-0.431313\pi\) | ||||
0.214115 | + | 0.976808i | \(0.431313\pi\) | |||||||
\(350\) | −10.0000 | − | 8.66025i | −0.534522 | − | 0.462910i | ||||
\(351\) | −4.00000 | −0.213504 | ||||||||
\(352\) | 0.500000 | − | 0.866025i | 0.0266501 | − | 0.0461593i | ||||
\(353\) | 12.0000 | + | 20.7846i | 0.638696 | + | 1.10625i | 0.985719 | + | 0.168397i | \(0.0538590\pi\) |
−0.347024 | + | 0.937856i | \(0.612808\pi\) | |||||||
\(354\) | 4.50000 | + | 7.79423i | 0.239172 | + | 0.414259i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.50000 | − | 2.59808i | 0.396942 | − | 0.137505i | ||||
\(358\) | 15.0000 | 0.792775 | ||||||||
\(359\) | 9.00000 | − | 15.5885i | 0.475002 | − | 0.822727i | −0.524588 | − | 0.851356i | \(-0.675781\pi\) |
0.999590 | + | 0.0286287i | \(0.00911406\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | + | 15.5885i | 0.473684 | + | 0.820445i | ||||
\(362\) | −5.00000 | + | 8.66025i | −0.262794 | + | 0.455173i | ||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 2.00000 | − | 10.3923i | 0.104828 | − | 0.544705i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5.00000 | + | 8.66025i | −0.261354 | + | 0.452679i | ||||
\(367\) | 2.00000 | + | 3.46410i | 0.104399 | + | 0.180825i | 0.913493 | − | 0.406855i | \(-0.133375\pi\) |
−0.809093 | + | 0.587680i | \(0.800041\pi\) | |||||||
\(368\) | 1.50000 | + | 2.59808i | 0.0781929 | + | 0.135434i | ||||
\(369\) | 3.00000 | − | 5.19615i | 0.156174 | − | 0.270501i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.00000 | 0.103695 | ||||||||
\(373\) | 11.0000 | − | 19.0526i | 0.569558 | − | 0.986504i | −0.427051 | − | 0.904227i | \(-0.640448\pi\) |
0.996610 | − | 0.0822766i | \(-0.0262191\pi\) | |||||||
\(374\) | 1.50000 | + | 2.59808i | 0.0775632 | + | 0.134343i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.50000 | + | 2.59808i | −0.0773566 | + | 0.133986i | ||||
\(377\) | 36.0000 | 1.85409 | ||||||||
\(378\) | −2.50000 | + | 0.866025i | −0.128586 | + | 0.0445435i | ||||
\(379\) | 14.0000 | 0.719132 | 0.359566 | − | 0.933120i | \(-0.382925\pi\) | ||||
0.359566 | + | 0.933120i | \(0.382925\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.500000 | + | 0.866025i | 0.0256158 | + | 0.0443678i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.50000 | + | 12.9904i | −0.383232 | + | 0.663777i | −0.991522 | − | 0.129937i | \(-0.958522\pi\) |
0.608290 | + | 0.793715i | \(0.291856\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10.0000 | 0.508987 | ||||||||
\(387\) | −5.50000 | + | 9.52628i | −0.279581 | + | 0.484248i | ||||
\(388\) | 0.500000 | + | 0.866025i | 0.0253837 | + | 0.0439658i | ||||
\(389\) | −6.00000 | − | 10.3923i | −0.304212 | − | 0.526911i | 0.672874 | − | 0.739758i | \(-0.265060\pi\) |
−0.977086 | + | 0.212847i | \(0.931726\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.00000 | −0.455150 | ||||||||
\(392\) | −1.00000 | − | 6.92820i | −0.0505076 | − | 0.349927i | ||||
\(393\) | 18.0000 | 0.907980 | ||||||||
\(394\) | −10.5000 | + | 18.1865i | −0.528982 | + | 0.916224i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.500000 | − | 0.866025i | −0.0251259 | − | 0.0435194i | ||||
\(397\) | 6.50000 | − | 11.2583i | 0.326226 | − | 0.565039i | −0.655534 | − | 0.755166i | \(-0.727556\pi\) |
0.981760 | + | 0.190126i | \(0.0608897\pi\) | |||||||
\(398\) | −20.0000 | −1.00251 | ||||||||
\(399\) | 2.00000 | + | 1.73205i | 0.100125 | + | 0.0867110i | ||||
\(400\) | −5.00000 | −0.250000 | ||||||||
\(401\) | 3.00000 | − | 5.19615i | 0.149813 | − | 0.259483i | −0.781345 | − | 0.624099i | \(-0.785466\pi\) |
0.931158 | + | 0.364615i | \(0.118800\pi\) | |||||||
\(402\) | −2.00000 | − | 3.46410i | −0.0997509 | − | 0.172774i | ||||
\(403\) | 4.00000 | + | 6.92820i | 0.199254 | + | 0.345118i | ||||
\(404\) | −7.50000 | + | 12.9904i | −0.373139 | + | 0.646296i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 22.5000 | − | 7.79423i | 1.11666 | − | 0.386821i | ||||
\(407\) | −7.00000 | −0.346977 | ||||||||
\(408\) | 1.50000 | − | 2.59808i | 0.0742611 | − | 0.128624i | ||||
\(409\) | −7.00000 | − | 12.1244i | −0.346128 | − | 0.599511i | 0.639430 | − | 0.768849i | \(-0.279170\pi\) |
−0.985558 | + | 0.169338i | \(0.945837\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.00000 | + | 10.3923i | −0.295958 | + | 0.512615i | ||||
\(412\) | −4.00000 | −0.197066 | ||||||||
\(413\) | −4.50000 | + | 23.3827i | −0.221431 | + | 1.15059i | ||||
\(414\) | 3.00000 | 0.147442 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.00000 | − | 3.46410i | −0.0980581 | − | 0.169842i | ||||
\(417\) | 9.50000 | + | 16.4545i | 0.465217 | + | 0.805779i | ||||
\(418\) | −0.500000 | + | 0.866025i | −0.0244558 | + | 0.0423587i | ||||
\(419\) | 9.00000 | 0.439679 | 0.219839 | − | 0.975536i | \(-0.429447\pi\) | ||||
0.219839 | + | 0.975536i | \(0.429447\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.0000 | 0.828529 | 0.414265 | − | 0.910156i | \(-0.364039\pi\) | ||||
0.414265 | + | 0.910156i | \(0.364039\pi\) | |||||||
\(422\) | −2.00000 | + | 3.46410i | −0.0973585 | + | 0.168630i | ||||
\(423\) | 1.50000 | + | 2.59808i | 0.0729325 | + | 0.126323i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.50000 | − | 12.9904i | 0.363803 | − | 0.630126i | ||||
\(426\) | −3.00000 | −0.145350 | ||||||||
\(427\) | −25.0000 | + | 8.66025i | −1.20983 | + | 0.419099i | ||||
\(428\) | −18.0000 | −0.870063 | ||||||||
\(429\) | 2.00000 | − | 3.46410i | 0.0965609 | − | 0.167248i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.00000 | + | 10.3923i | 0.289010 | + | 0.500580i | 0.973574 | − | 0.228373i | \(-0.0733406\pi\) |
−0.684564 | + | 0.728953i | \(0.740007\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | 29.0000 | 1.39365 | 0.696826 | − | 0.717241i | \(-0.254595\pi\) | ||||
0.696826 | + | 0.717241i | \(0.254595\pi\) | |||||||
\(434\) | 4.00000 | + | 3.46410i | 0.192006 | + | 0.166282i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.00000 | − | 8.66025i | 0.239457 | − | 0.414751i | ||||
\(437\) | −1.50000 | − | 2.59808i | −0.0717547 | − | 0.124283i | ||||
\(438\) | −2.00000 | − | 3.46410i | −0.0955637 | − | 0.165521i | ||||
\(439\) | 18.5000 | − | 32.0429i | 0.882957 | − | 1.52933i | 0.0349192 | − | 0.999390i | \(-0.488883\pi\) |
0.848038 | − | 0.529936i | \(-0.177784\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.50000 | − | 2.59808i | −0.309524 | − | 0.123718i | ||||
\(442\) | 12.0000 | 0.570782 | ||||||||
\(443\) | −1.50000 | + | 2.59808i | −0.0712672 | + | 0.123438i | −0.899457 | − | 0.437009i | \(-0.856038\pi\) |
0.828190 | + | 0.560448i | \(0.189371\pi\) | |||||||
\(444\) | 3.50000 | + | 6.06218i | 0.166103 | + | 0.287698i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.00000 | − | 6.92820i | 0.189405 | − | 0.328060i | ||||
\(447\) | 9.00000 | 0.425685 | ||||||||
\(448\) | −2.00000 | − | 1.73205i | −0.0944911 | − | 0.0818317i | ||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | −2.50000 | + | 4.33013i | −0.117851 | + | 0.204124i | ||||
\(451\) | 3.00000 | + | 5.19615i | 0.141264 | + | 0.244677i | ||||
\(452\) | −6.00000 | − | 10.3923i | −0.282216 | − | 0.488813i | ||||
\(453\) | 9.50000 | − | 16.4545i | 0.446349 | − | 0.773099i | ||||
\(454\) | −18.0000 | −0.844782 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.00000 | 0.0468293 | ||||||||
\(457\) | −1.00000 | + | 1.73205i | −0.0467780 | + | 0.0810219i | −0.888466 | − | 0.458942i | \(-0.848229\pi\) |
0.841688 | + | 0.539964i | \(0.181562\pi\) | |||||||
\(458\) | 13.0000 | + | 22.5167i | 0.607450 | + | 1.05213i | ||||
\(459\) | −1.50000 | − | 2.59808i | −0.0700140 | − | 0.121268i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.0000 | 0.978068 | 0.489034 | − | 0.872265i | \(-0.337349\pi\) | ||||
0.489034 | + | 0.872265i | \(0.337349\pi\) | |||||||
\(462\) | 0.500000 | − | 2.59808i | 0.0232621 | − | 0.120873i | ||||
\(463\) | 8.00000 | 0.371792 | 0.185896 | − | 0.982569i | \(-0.440481\pi\) | ||||
0.185896 | + | 0.982569i | \(0.440481\pi\) | |||||||
\(464\) | 4.50000 | − | 7.79423i | 0.208907 | − | 0.361838i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.50000 | + | 7.79423i | 0.208458 | + | 0.361061i | ||||
\(467\) | 16.5000 | − | 28.5788i | 0.763529 | − | 1.32247i | −0.177492 | − | 0.984122i | \(-0.556798\pi\) |
0.941021 | − | 0.338349i | \(-0.109868\pi\) | |||||||
\(468\) | −4.00000 | −0.184900 | ||||||||
\(469\) | 2.00000 | − | 10.3923i | 0.0923514 | − | 0.479872i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.50000 | − | 11.2583i | 0.299504 | − | 0.518756i | ||||
\(472\) | 4.50000 | + | 7.79423i | 0.207129 | + | 0.358758i | ||||
\(473\) | −5.50000 | − | 9.52628i | −0.252890 | − | 0.438019i | ||||
\(474\) | −8.00000 | + | 13.8564i | −0.367452 | + | 0.636446i | ||||
\(475\) | 5.00000 | 0.229416 | ||||||||
\(476\) | 7.50000 | − | 2.59808i | 0.343762 | − | 0.119083i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12.0000 | + | 20.7846i | −0.548867 | + | 0.950666i | ||||
\(479\) | −3.00000 | − | 5.19615i | −0.137073 | − | 0.237418i | 0.789314 | − | 0.613990i | \(-0.210436\pi\) |
−0.926388 | + | 0.376571i | \(0.877103\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.0000 | + | 24.2487i | −0.638345 | + | 1.10565i | ||||
\(482\) | 28.0000 | 1.27537 | ||||||||
\(483\) | 6.00000 | + | 5.19615i | 0.273009 | + | 0.236433i | ||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.500000 | + | 0.866025i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | 2.00000 | + | 3.46410i | 0.0906287 | + | 0.156973i | 0.907776 | − | 0.419456i | \(-0.137779\pi\) |
−0.817147 | + | 0.576429i | \(0.804446\pi\) | |||||||
\(488\) | −5.00000 | + | 8.66025i | −0.226339 | + | 0.392031i | ||||
\(489\) | 2.00000 | 0.0904431 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −36.0000 | −1.62466 | −0.812329 | − | 0.583200i | \(-0.801800\pi\) | ||||
−0.812329 | + | 0.583200i | \(0.801800\pi\) | |||||||
\(492\) | 3.00000 | − | 5.19615i | 0.135250 | − | 0.234261i | ||||
\(493\) | 13.5000 | + | 23.3827i | 0.608009 | + | 1.05310i | ||||
\(494\) | 2.00000 | + | 3.46410i | 0.0899843 | + | 0.155857i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | −6.00000 | − | 5.19615i | −0.269137 | − | 0.233079i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.00000 | − | 8.66025i | 0.223831 | − | 0.387686i | −0.732137 | − | 0.681157i | \(-0.761477\pi\) |
0.955968 | + | 0.293471i | \(0.0948104\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.00000 | − | 10.3923i | −0.268060 | − | 0.464294i | ||||
\(502\) | 7.50000 | − | 12.9904i | 0.334741 | − | 0.579789i | ||||
\(503\) | 30.0000 | 1.33763 | 0.668817 | − | 0.743427i | \(-0.266801\pi\) | ||||
0.668817 | + | 0.743427i | \(0.266801\pi\) | |||||||
\(504\) | −2.50000 | + | 0.866025i | −0.111359 | + | 0.0385758i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.50000 | + | 2.59808i | −0.0666831 | + | 0.115499i | ||||
\(507\) | −1.50000 | − | 2.59808i | −0.0666173 | − | 0.115385i | ||||
\(508\) | 0.500000 | + | 0.866025i | 0.0221839 | + | 0.0384237i | ||||
\(509\) | 18.0000 | − | 31.1769i | 0.797836 | − | 1.38189i | −0.123187 | − | 0.992384i | \(-0.539311\pi\) |
0.921023 | − | 0.389509i | \(-0.127355\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.00000 | − | 10.3923i | 0.0884748 | − | 0.459728i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0.500000 | − | 0.866025i | 0.0220755 | − | 0.0382360i | ||||
\(514\) | 6.00000 | + | 10.3923i | 0.264649 | + | 0.458385i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.50000 | + | 9.52628i | −0.242124 | + | 0.419371i | ||||
\(517\) | −3.00000 | −0.131940 | ||||||||
\(518\) | −3.50000 | + | 18.1865i | −0.153781 | + | 0.799070i | ||||
\(519\) | −6.00000 | −0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.0000 | + | 25.9808i | 0.657162 | + | 1.13824i | 0.981347 | + | 0.192244i | \(0.0615766\pi\) |
−0.324185 | + | 0.945994i | \(0.605090\pi\) | |||||||
\(522\) | −4.50000 | − | 7.79423i | −0.196960 | − | 0.341144i | ||||
\(523\) | 2.00000 | − | 3.46410i | 0.0874539 | − | 0.151475i | −0.818980 | − | 0.573822i | \(-0.805460\pi\) |
0.906434 | + | 0.422347i | \(0.138794\pi\) | |||||||
\(524\) | 18.0000 | 0.786334 | ||||||||
\(525\) | −12.5000 | + | 4.33013i | −0.545545 | + | 0.188982i | ||||
\(526\) | 18.0000 | 0.784837 | ||||||||
\(527\) | −3.00000 | + | 5.19615i | −0.130682 | + | 0.226348i | ||||
\(528\) | −0.500000 | − | 0.866025i | −0.0217597 | − | 0.0376889i | ||||
\(529\) | 7.00000 | + | 12.1244i | 0.304348 | + | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.00000 | 0.390567 | ||||||||
\(532\) | 2.00000 | + | 1.73205i | 0.0867110 | + | 0.0750939i | ||||
\(533\) | 24.0000 | 1.03956 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.00000 | − | 3.46410i | −0.0863868 | − | 0.149626i | ||||
\(537\) | 7.50000 | − | 12.9904i | 0.323649 | − | 0.560576i | ||||
\(538\) | −6.00000 | −0.258678 | ||||||||
\(539\) | 5.50000 | − | 4.33013i | 0.236902 | − | 0.186512i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.0000 | + | 17.3205i | −0.429934 | + | 0.744667i | −0.996867 | − | 0.0790969i | \(-0.974796\pi\) |
0.566933 | + | 0.823764i | \(0.308130\pi\) | |||||||
\(542\) | −8.00000 | − | 13.8564i | −0.343629 | − | 0.595184i | ||||
\(543\) | 5.00000 | + | 8.66025i | 0.214571 | + | 0.371647i | ||||
\(544\) | 1.50000 | − | 2.59808i | 0.0643120 | − | 0.111392i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −8.00000 | − | 6.92820i | −0.342368 | − | 0.296500i | ||||
\(547\) | −19.0000 | −0.812381 | −0.406191 | − | 0.913788i | \(-0.633143\pi\) | ||||
−0.406191 | + | 0.913788i | \(0.633143\pi\) | |||||||
\(548\) | −6.00000 | + | 10.3923i | −0.256307 | + | 0.443937i | ||||
\(549\) | 5.00000 | + | 8.66025i | 0.213395 | + | 0.369611i | ||||
\(550\) | −2.50000 | − | 4.33013i | −0.106600 | − | 0.184637i | ||||
\(551\) | −4.50000 | + | 7.79423i | −0.191706 | + | 0.332045i | ||||
\(552\) | 3.00000 | 0.127688 | ||||||||
\(553\) | −40.0000 | + | 13.8564i | −1.70097 | + | 0.589234i | ||||
\(554\) | −32.0000 | −1.35955 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.50000 | + | 16.4545i | 0.402890 | + | 0.697826i | ||||
\(557\) | −22.5000 | − | 38.9711i | −0.953356 | − | 1.65126i | −0.738087 | − | 0.674705i | \(-0.764271\pi\) |
−0.215268 | − | 0.976555i | \(-0.569063\pi\) | |||||||
\(558\) | 1.00000 | − | 1.73205i | 0.0423334 | − | 0.0733236i | ||||
\(559\) | −44.0000 | −1.86100 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.00000 | 0.126660 | ||||||||
\(562\) | −7.50000 | + | 12.9904i | −0.316368 | + | 0.547966i | ||||
\(563\) | 18.0000 | + | 31.1769i | 0.758610 | + | 1.31395i | 0.943560 | + | 0.331202i | \(0.107454\pi\) |
−0.184950 | + | 0.982748i | \(0.559212\pi\) | |||||||
\(564\) | 1.50000 | + | 2.59808i | 0.0631614 | + | 0.109399i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −20.0000 | −0.840663 | ||||||||
\(567\) | −0.500000 | + | 2.59808i | −0.0209980 | + | 0.109109i | ||||
\(568\) | −3.00000 | −0.125877 | ||||||||
\(569\) | 10.5000 | − | 18.1865i | 0.440183 | − | 0.762419i | −0.557520 | − | 0.830164i | \(-0.688247\pi\) |
0.997703 | + | 0.0677445i | \(0.0215803\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.5000 | − | 25.1147i | −0.606806 | − | 1.05102i | −0.991763 | − | 0.128085i | \(-0.959117\pi\) |
0.384957 | − | 0.922934i | \(-0.374216\pi\) | |||||||
\(572\) | 2.00000 | − | 3.46410i | 0.0836242 | − | 0.144841i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 15.0000 | − | 5.19615i | 0.626088 | − | 0.216883i | ||||
\(575\) | 15.0000 | 0.625543 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 11.0000 | + | 19.0526i | 0.457936 | + | 0.793168i | 0.998852 | − | 0.0479084i | \(-0.0152556\pi\) |
−0.540916 | + | 0.841077i | \(0.681922\pi\) | |||||||
\(578\) | −4.00000 | − | 6.92820i | −0.166378 | − | 0.288175i | ||||
\(579\) | 5.00000 | − | 8.66025i | 0.207793 | − | 0.359908i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.00000 | 0.0414513 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −2.00000 | − | 3.46410i | −0.0827606 | − | 0.143346i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.50000 | − | 7.79423i | 0.185893 | − | 0.321977i | ||||
\(587\) | 12.0000 | 0.495293 | 0.247647 | − | 0.968850i | \(-0.420343\pi\) | ||||
0.247647 | + | 0.968850i | \(0.420343\pi\) | |||||||
\(588\) | −6.50000 | − | 2.59808i | −0.268055 | − | 0.107143i | ||||
\(589\) | −2.00000 | −0.0824086 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.5000 | + | 18.1865i | 0.431912 | + | 0.748094i | ||||
\(592\) | 3.50000 | + | 6.06218i | 0.143849 | + | 0.249154i | ||||
\(593\) | −4.50000 | + | 7.79423i | −0.184793 | + | 0.320071i | −0.943507 | − | 0.331353i | \(-0.892495\pi\) |
0.758714 | + | 0.651424i | \(0.225828\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.00000 | 0.368654 | ||||||||
\(597\) | −10.0000 | + | 17.3205i | −0.409273 | + | 0.708881i | ||||
\(598\) | 6.00000 | + | 10.3923i | 0.245358 | + | 0.424973i | ||||
\(599\) | −24.0000 | − | 41.5692i | −0.980613 | − | 1.69847i | −0.660006 | − | 0.751260i | \(-0.729446\pi\) |
−0.320607 | − | 0.947212i | \(-0.603887\pi\) | |||||||
\(600\) | −2.50000 | + | 4.33013i | −0.102062 | + | 0.176777i | ||||
\(601\) | 38.0000 | 1.55005 | 0.775026 | − | 0.631929i | \(-0.217737\pi\) | ||||
0.775026 | + | 0.631929i | \(0.217737\pi\) | |||||||
\(602\) | −27.5000 | + | 9.52628i | −1.12082 | + | 0.388262i | ||||
\(603\) | −4.00000 | −0.162893 | ||||||||
\(604\) | 9.50000 | − | 16.4545i | 0.386550 | − | 0.669523i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 7.50000 | + | 12.9904i | 0.304667 | + | 0.527698i | ||||
\(607\) | −16.0000 | + | 27.7128i | −0.649420 | + | 1.12483i | 0.333842 | + | 0.942629i | \(0.391655\pi\) |
−0.983262 | + | 0.182199i | \(0.941678\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 4.50000 | − | 23.3827i | 0.182349 | − | 0.947514i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.00000 | + | 10.3923i | −0.242734 | + | 0.420428i | ||||
\(612\) | −1.50000 | − | 2.59808i | −0.0606339 | − | 0.105021i | ||||
\(613\) | 8.00000 | + | 13.8564i | 0.323117 | + | 0.559655i | 0.981129 | − | 0.193352i | \(-0.0619359\pi\) |
−0.658012 | + | 0.753007i | \(0.728603\pi\) | |||||||
\(614\) | −2.00000 | + | 3.46410i | −0.0807134 | + | 0.139800i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.500000 | − | 2.59808i | 0.0201456 | − | 0.104679i | ||||
\(617\) | 18.0000 | 0.724653 | 0.362326 | − | 0.932051i | \(-0.381983\pi\) | ||||
0.362326 | + | 0.932051i | \(0.381983\pi\) | |||||||
\(618\) | −2.00000 | + | 3.46410i | −0.0804518 | + | 0.139347i | ||||
\(619\) | −7.00000 | − | 12.1244i | −0.281354 | − | 0.487319i | 0.690365 | − | 0.723462i | \(-0.257450\pi\) |
−0.971718 | + | 0.236143i | \(0.924117\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.50000 | − | 2.59808i | 0.0601929 | − | 0.104257i | ||||
\(622\) | 21.0000 | 0.842023 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −4.00000 | −0.160128 | ||||||||
\(625\) | −12.5000 | + | 21.6506i | −0.500000 | + | 0.866025i | ||||
\(626\) | −0.500000 | − | 0.866025i | −0.0199840 | − | 0.0346133i | ||||
\(627\) | 0.500000 | + | 0.866025i | 0.0199681 | + | 0.0345857i | ||||
\(628\) | 6.50000 | − | 11.2583i | 0.259378 | − | 0.449256i | ||||
\(629\) | −21.0000 | −0.837325 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.0000 | −0.636950 | −0.318475 | − | 0.947931i | \(-0.603171\pi\) | ||||
−0.318475 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(632\) | −8.00000 | + | 13.8564i | −0.318223 | + | 0.551178i | ||||
\(633\) | 2.00000 | + | 3.46410i | 0.0794929 | + | 0.137686i | ||||
\(634\) | −6.00000 | − | 10.3923i | −0.238290 | − | 0.412731i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.00000 | − | 27.7128i | −0.158486 | − | 1.09802i | ||||
\(638\) | 9.00000 | 0.356313 | ||||||||
\(639\) | −1.50000 | + | 2.59808i | −0.0593391 | + | 0.102778i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.00000 | − | 15.5885i | −0.355479 | − | 0.615707i | 0.631721 | − | 0.775196i | \(-0.282349\pi\) |
−0.987200 | + | 0.159489i | \(0.949015\pi\) | |||||||
\(642\) | −9.00000 | + | 15.5885i | −0.355202 | + | 0.615227i | ||||
\(643\) | −46.0000 | −1.81406 | −0.907031 | − | 0.421063i | \(-0.861657\pi\) | ||||
−0.907031 | + | 0.421063i | \(0.861657\pi\) | |||||||
\(644\) | 6.00000 | + | 5.19615i | 0.236433 | + | 0.204757i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.50000 | + | 2.59808i | −0.0590167 | + | 0.102220i | ||||
\(647\) | −24.0000 | − | 41.5692i | −0.943537 | − | 1.63425i | −0.758654 | − | 0.651494i | \(-0.774142\pi\) |
−0.184884 | − | 0.982760i | \(-0.559191\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | −4.50000 | + | 7.79423i | −0.176640 | + | 0.305950i | ||||
\(650\) | −20.0000 | −0.784465 | ||||||||
\(651\) | 5.00000 | − | 1.73205i | 0.195965 | − | 0.0678844i | ||||
\(652\) | 2.00000 | 0.0783260 | ||||||||
\(653\) | −12.0000 | + | 20.7846i | −0.469596 | + | 0.813365i | −0.999396 | − | 0.0347583i | \(-0.988934\pi\) |
0.529799 | + | 0.848123i | \(0.322267\pi\) | |||||||
\(654\) | −5.00000 | − | 8.66025i | −0.195515 | − | 0.338643i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.00000 | − | 5.19615i | 0.117130 | − | 0.202876i | ||||
\(657\) | −4.00000 | −0.156055 | ||||||||
\(658\) | −1.50000 | + | 7.79423i | −0.0584761 | + | 0.303851i | ||||
\(659\) | −18.0000 | −0.701180 | −0.350590 | − | 0.936529i | \(-0.614019\pi\) | ||||
−0.350590 | + | 0.936529i | \(0.614019\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.5000 | − | 30.3109i | −0.680671 | − | 1.17896i | −0.974776 | − | 0.223184i | \(-0.928355\pi\) |
0.294105 | − | 0.955773i | \(-0.404978\pi\) | |||||||
\(662\) | −5.00000 | − | 8.66025i | −0.194331 | − | 0.336590i | ||||
\(663\) | 6.00000 | − | 10.3923i | 0.233021 | − | 0.403604i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.00000 | 0.271244 | ||||||||
\(667\) | −13.5000 | + | 23.3827i | −0.522722 | + | 0.905381i | ||||
\(668\) | −6.00000 | − | 10.3923i | −0.232147 | − | 0.402090i | ||||
\(669\) | −4.00000 | − | 6.92820i | −0.154649 | − | 0.267860i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.0000 | −0.386046 | ||||||||
\(672\) | −2.50000 | + | 0.866025i | −0.0964396 | + | 0.0334077i | ||||
\(673\) | 44.0000 | 1.69608 | 0.848038 | − | 0.529936i | \(-0.177784\pi\) | ||||
0.848038 | + | 0.529936i | \(0.177784\pi\) | |||||||
\(674\) | −5.00000 | + | 8.66025i | −0.192593 | + | 0.333581i | ||||
\(675\) | 2.50000 | + | 4.33013i | 0.0962250 | + | 0.166667i | ||||
\(676\) | −1.50000 | − | 2.59808i | −0.0576923 | − | 0.0999260i | ||||
\(677\) | 16.5000 | − | 28.5788i | 0.634147 | − | 1.09837i | −0.352549 | − | 0.935793i | \(-0.614685\pi\) |
0.986695 | − | 0.162581i | \(-0.0519817\pi\) | |||||||
\(678\) | −12.0000 | −0.460857 | ||||||||
\(679\) | 2.00000 | + | 1.73205i | 0.0767530 | + | 0.0664700i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.00000 | + | 15.5885i | −0.344881 | + | 0.597351i | ||||
\(682\) | 1.00000 | + | 1.73205i | 0.0382920 | + | 0.0663237i | ||||
\(683\) | −16.5000 | − | 28.5788i | −0.631355 | − | 1.09354i | −0.987275 | − | 0.159022i | \(-0.949166\pi\) |
0.355920 | − | 0.934516i | \(-0.384168\pi\) | |||||||
\(684\) | 0.500000 | − | 0.866025i | 0.0191180 | − | 0.0331133i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.50000 | − | 16.4545i | −0.324532 | − | 0.628235i | ||||
\(687\) | 26.0000 | 0.991962 | ||||||||
\(688\) | −5.50000 | + | 9.52628i | −0.209686 | + | 0.363186i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.0000 | + | 43.3013i | −0.951045 | + | 1.64726i | −0.207875 | + | 0.978155i | \(0.566655\pi\) |
−0.743170 | + | 0.669102i | \(0.766679\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | −2.00000 | − | 1.73205i | −0.0759737 | − | 0.0657952i | ||||
\(694\) | −12.0000 | −0.455514 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −4.50000 | − | 7.79423i | −0.170572 | − | 0.295439i | ||||
\(697\) | 9.00000 | + | 15.5885i | 0.340899 | + | 0.590455i | ||||
\(698\) | 4.00000 | − | 6.92820i | 0.151402 | − | 0.262236i | ||||
\(699\) | 9.00000 | 0.340411 | ||||||||
\(700\) | −12.5000 | + | 4.33013i | −0.472456 | + | 0.163663i | ||||
\(701\) | −27.0000 | −1.01978 | −0.509888 | − | 0.860241i | \(-0.670313\pi\) | ||||
−0.509888 | + | 0.860241i | \(0.670313\pi\) | |||||||
\(702\) | −2.00000 | + | 3.46410i | −0.0754851 | + | 0.130744i | ||||
\(703\) | −3.50000 | − | 6.06218i | −0.132005 | − | 0.228639i | ||||
\(704\) | −0.500000 | − | 0.866025i | −0.0188445 | − | 0.0326396i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 24.0000 | 0.903252 | ||||||||
\(707\) | −7.50000 | + | 38.9711i | −0.282067 | + | 1.46566i | ||||
\(708\) | 9.00000 | 0.338241 | ||||||||
\(709\) | −17.5000 | + | 30.3109i | −0.657226 | + | 1.13835i | 0.324104 | + | 0.946021i | \(0.394937\pi\) |
−0.981331 | + | 0.192328i | \(0.938396\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.00000 | + | 13.8564i | 0.300023 | + | 0.519656i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.00000 | −0.224702 | ||||||||
\(714\) | 1.50000 | − | 7.79423i | 0.0561361 | − | 0.291692i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.50000 | − | 12.9904i | 0.280288 | − | 0.485473i | ||||
\(717\) | 12.0000 | + | 20.7846i | 0.448148 | + | 0.776215i | ||||
\(718\) | −9.00000 | − | 15.5885i | −0.335877 | − | 0.581756i | ||||
\(719\) | −4.50000 | + | 7.79423i | −0.167822 | + | 0.290676i | −0.937654 | − | 0.347571i | \(-0.887007\pi\) |
0.769832 | + | 0.638247i | \(0.220340\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.0000 | + | 3.46410i | −0.372419 | + | 0.129010i | ||||
\(722\) | 18.0000 | 0.669891 | ||||||||
\(723\) | 14.0000 | − | 24.2487i | 0.520666 | − | 0.901819i | ||||
\(724\) | 5.00000 | + | 8.66025i | 0.185824 | + | 0.321856i | ||||
\(725\) | −22.5000 | − | 38.9711i | −0.835629 | − | 1.44735i | ||||
\(726\) | 0.500000 | − | 0.866025i | 0.0185567 | − | 0.0321412i | ||||
\(727\) | −22.0000 | −0.815935 | −0.407967 | − | 0.912996i | \(-0.633762\pi\) | ||||
−0.407967 | + | 0.912996i | \(0.633762\pi\) | |||||||
\(728\) | −8.00000 | − | 6.92820i | −0.296500 | − | 0.256776i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16.5000 | − | 28.5788i | −0.610275 | − | 1.05703i | ||||
\(732\) | 5.00000 | + | 8.66025i | 0.184805 | + | 0.320092i | ||||
\(733\) | −7.00000 | + | 12.1244i | −0.258551 | + | 0.447823i | −0.965854 | − | 0.259087i | \(-0.916578\pi\) |
0.707303 | + | 0.706910i | \(0.249912\pi\) | |||||||
\(734\) | 4.00000 | 0.147643 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.00000 | 0.110581 | ||||||||
\(737\) | 2.00000 | − | 3.46410i | 0.0736709 | − | 0.127602i | ||||
\(738\) | −3.00000 | − | 5.19615i | −0.110432 | − | 0.191273i | ||||
\(739\) | 2.00000 | + | 3.46410i | 0.0735712 | + | 0.127429i | 0.900464 | − | 0.434930i | \(-0.143227\pi\) |
−0.826893 | + | 0.562360i | \(0.809894\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.00000 | 0.146944 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.00000 | 0.220119 | 0.110059 | − | 0.993925i | \(-0.464896\pi\) | ||||
0.110059 | + | 0.993925i | \(0.464896\pi\) | |||||||
\(744\) | 1.00000 | − | 1.73205i | 0.0366618 | − | 0.0635001i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −11.0000 | − | 19.0526i | −0.402739 | − | 0.697564i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.00000 | 0.109691 | ||||||||
\(749\) | −45.0000 | + | 15.5885i | −1.64426 | + | 0.569590i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | + | 1.73205i | −0.0364905 | + | 0.0632034i | −0.883694 | − | 0.468065i | \(-0.844951\pi\) |
0.847203 | + | 0.531269i | \(0.178285\pi\) | |||||||
\(752\) | 1.50000 | + | 2.59808i | 0.0546994 | + | 0.0947421i | ||||
\(753\) | −7.50000 | − | 12.9904i | −0.273315 | − | 0.473396i | ||||
\(754\) | 18.0000 | − | 31.1769i | 0.655521 | − | 1.13540i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.500000 | + | 2.59808i | −0.0181848 | + | 0.0944911i | ||||
\(757\) | −7.00000 | −0.254419 | −0.127210 | − | 0.991876i | \(-0.540602\pi\) | ||||
−0.127210 | + | 0.991876i | \(0.540602\pi\) | |||||||
\(758\) | 7.00000 | − | 12.1244i | 0.254251 | − | 0.440376i | ||||
\(759\) | 1.50000 | + | 2.59808i | 0.0544466 | + | 0.0943042i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.0000 | + | 25.9808i | −0.543750 | + | 0.941802i | 0.454935 | + | 0.890525i | \(0.349663\pi\) |
−0.998684 | + | 0.0512772i | \(0.983671\pi\) | |||||||
\(762\) | 1.00000 | 0.0362262 | ||||||||
\(763\) | 5.00000 | − | 25.9808i | 0.181012 | − | 0.940567i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.50000 | + | 12.9904i | 0.270986 | + | 0.469362i | ||||
\(767\) | 18.0000 | + | 31.1769i | 0.649942 | + | 1.12573i | ||||
\(768\) | −0.500000 | + | 0.866025i | −0.0180422 | + | 0.0312500i | ||||
\(769\) | 50.0000 | 1.80305 | 0.901523 | − | 0.432731i | \(-0.142450\pi\) | ||||
0.901523 | + | 0.432731i | \(0.142450\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.0000 | 0.432169 | ||||||||
\(772\) | 5.00000 | − | 8.66025i | 0.179954 | − | 0.311689i | ||||
\(773\) | −27.0000 | − | 46.7654i | −0.971123 | − | 1.68203i | −0.692179 | − | 0.721726i | \(-0.743349\pi\) |
−0.278944 | − | 0.960307i | \(-0.589984\pi\) | |||||||
\(774\) | 5.50000 | + | 9.52628i | 0.197693 | + | 0.342415i | ||||
\(775\) | 5.00000 | − | 8.66025i | 0.179605 | − | 0.311086i | ||||
\(776\) | 1.00000 | 0.0358979 | ||||||||
\(777\) | 14.0000 | + | 12.1244i | 0.502247 | + | 0.434959i | ||||
\(778\) | −12.0000 | −0.430221 | ||||||||
\(779\) | −3.00000 | + | 5.19615i | −0.107486 | + | 0.186171i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.50000 | − | 2.59808i | −0.0536742 | − | 0.0929665i | ||||
\(782\) | −4.50000 | + | 7.79423i | −0.160920 | + | 0.278721i | ||||
\(783\) | −9.00000 | −0.321634 | ||||||||
\(784\) | −6.50000 | − | 2.59808i | −0.232143 | − | 0.0927884i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 9.00000 | − | 15.5885i | 0.321019 | − | 0.556022i | ||||
\(787\) | −11.5000 | − | 19.9186i | −0.409931 | − | 0.710021i | 0.584951 | − | 0.811069i | \(-0.301114\pi\) |
−0.994882 | + | 0.101048i | \(0.967780\pi\) | |||||||
\(788\) | 10.5000 | + | 18.1865i | 0.374047 | + | 0.647868i | ||||
\(789\) | 9.00000 | − | 15.5885i | 0.320408 | − | 0.554964i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −24.0000 | − | 20.7846i | −0.853342 | − | 0.739016i | ||||
\(792\) | −1.00000 | −0.0355335 | ||||||||
\(793\) | −20.0000 | + | 34.6410i | −0.710221 | + | 1.23014i | ||||
\(794\) | −6.50000 | − | 11.2583i | −0.230676 | − | 0.399543i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.0000 | + | 17.3205i | −0.354441 | + | 0.613909i | ||||
\(797\) | 42.0000 | 1.48772 | 0.743858 | − | 0.668338i | \(-0.232994\pi\) | ||||
0.743858 | + | 0.668338i | \(0.232994\pi\) | |||||||
\(798\) | 2.50000 | − | 0.866025i | 0.0884990 | − | 0.0306570i | ||||
\(799\) | −9.00000 | −0.318397 | ||||||||
\(800\) | −2.50000 | + | 4.33013i | −0.0883883 | + | 0.153093i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.00000 | − | 5.19615i | −0.105934 | − | 0.183483i | ||||
\(803\) | 2.00000 | − | 3.46410i | 0.0705785 | − | 0.122245i | ||||
\(804\) | −4.00000 | −0.141069 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.00000 | 0.281788 | ||||||||
\(807\) | −3.00000 | + | 5.19615i | −0.105605 | + | 0.182913i | ||||
\(808\) | 7.50000 | + | 12.9904i | 0.263849 | + | 0.457000i | ||||
\(809\) | 3.00000 | + | 5.19615i | 0.105474 | + | 0.182687i | 0.913932 | − | 0.405868i | \(-0.133031\pi\) |
−0.808458 | + | 0.588555i | \(0.799697\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.0000 | 0.702295 | 0.351147 | − | 0.936320i | \(-0.385792\pi\) | ||||
0.351147 | + | 0.936320i | \(0.385792\pi\) | |||||||
\(812\) | 4.50000 | − | 23.3827i | 0.157919 | − | 0.820571i | ||||
\(813\) | −16.0000 | −0.561144 | ||||||||
\(814\) | −3.50000 | + | 6.06218i | −0.122675 | + | 0.212479i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.50000 | − | 2.59808i | −0.0525105 | − | 0.0909509i | ||||
\(817\) | 5.50000 | − | 9.52628i | 0.192421 | − | 0.333282i | ||||
\(818\) | −14.0000 | −0.489499 | ||||||||
\(819\) | −10.0000 | + | 3.46410i | −0.349428 | + | 0.121046i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.0000 | + | 36.3731i | −0.732905 | + | 1.26943i | 0.222731 | + | 0.974880i | \(0.428503\pi\) |
−0.955636 | + | 0.294549i | \(0.904831\pi\) | |||||||
\(822\) | 6.00000 | + | 10.3923i | 0.209274 | + | 0.362473i | ||||
\(823\) | −7.00000 | − | 12.1244i | −0.244005 | − | 0.422628i | 0.717847 | − | 0.696201i | \(-0.245128\pi\) |
−0.961851 | + | 0.273573i | \(0.911795\pi\) | |||||||
\(824\) | −2.00000 | + | 3.46410i | −0.0696733 | + | 0.120678i | ||||
\(825\) | −5.00000 | −0.174078 | ||||||||
\(826\) | 18.0000 | + | 15.5885i | 0.626300 | + | 0.542392i | ||||
\(827\) | 42.0000 | 1.46048 | 0.730242 | − | 0.683189i | \(-0.239408\pi\) | ||||
0.730242 | + | 0.683189i | \(0.239408\pi\) | |||||||
\(828\) | 1.50000 | − | 2.59808i | 0.0521286 | − | 0.0902894i | ||||
\(829\) | 9.50000 | + | 16.4545i | 0.329949 | + | 0.571488i | 0.982501 | − | 0.186256i | \(-0.0596352\pi\) |
−0.652553 | + | 0.757743i | \(0.726302\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.0000 | + | 27.7128i | −0.555034 | + | 0.961347i | ||||
\(832\) | −4.00000 | −0.138675 | ||||||||
\(833\) | 16.5000 | − | 12.9904i | 0.571691 | − | 0.450090i | ||||
\(834\) | 19.0000 | 0.657916 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.500000 | + | 0.866025i | 0.0172929 | + | 0.0299521i | ||||
\(837\) | −1.00000 | − | 1.73205i | −0.0345651 | − | 0.0598684i | ||||
\(838\) | 4.50000 | − | 7.79423i | 0.155450 | − | 0.269247i | ||||
\(839\) | −36.0000 | −1.24286 | −0.621429 | − | 0.783470i | \(-0.713448\pi\) | ||||
−0.621429 | + | 0.783470i | \(0.713448\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 52.0000 | 1.79310 | ||||||||
\(842\) | 8.50000 | − | 14.7224i | 0.292929 | − | 0.507369i | ||||
\(843\) | 7.50000 | + | 12.9904i | 0.258314 | + | 0.447412i | ||||
\(844\) | 2.00000 | + | 3.46410i | 0.0688428 | + | 0.119239i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.00000 | 0.103142 | ||||||||
\(847\) | 2.50000 | − | 0.866025i | 0.0859010 | − | 0.0297570i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.0000 | + | 17.3205i | −0.343199 | + | 0.594438i | ||||
\(850\) | −7.50000 | − | 12.9904i | −0.257248 | − | 0.445566i | ||||
\(851\) | −10.5000 | − | 18.1865i | −0.359935 | − | 0.623426i | ||||
\(852\) | −1.50000 | + | 2.59808i | −0.0513892 | + | 0.0890086i | ||||
\(853\) | 20.0000 | 0.684787 | 0.342393 | − | 0.939557i | \(-0.388762\pi\) | ||||
0.342393 | + | 0.939557i | \(0.388762\pi\) | |||||||
\(854\) | −5.00000 | + | 25.9808i | −0.171096 | + | 0.889043i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.00000 | + | 15.5885i | −0.307614 | + | 0.532803i | ||||
\(857\) | 28.5000 | + | 49.3634i | 0.973541 | + | 1.68622i | 0.684667 | + | 0.728856i | \(0.259948\pi\) |
0.288875 | + | 0.957367i | \(0.406719\pi\) | |||||||
\(858\) | −2.00000 | − | 3.46410i | −0.0682789 | − | 0.118262i | ||||
\(859\) | 20.0000 | − | 34.6410i | 0.682391 | − | 1.18194i | −0.291858 | − | 0.956462i | \(-0.594273\pi\) |
0.974249 | − | 0.225475i | \(-0.0723932\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.00000 | − | 15.5885i | 0.102240 | − | 0.531253i | ||||
\(862\) | 12.0000 | 0.408722 | ||||||||
\(863\) | −12.0000 | + | 20.7846i | −0.408485 | + | 0.707516i | −0.994720 | − | 0.102624i | \(-0.967276\pi\) |
0.586235 | + | 0.810141i | \(0.300609\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 14.5000 | − | 25.1147i | 0.492730 | − | 0.853433i | ||||
\(867\) | −8.00000 | −0.271694 | ||||||||
\(868\) | 5.00000 | − | 1.73205i | 0.169711 | − | 0.0587896i | ||||
\(869\) | −16.0000 | −0.542763 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.00000 | − | 13.8564i | −0.271070 | − | 0.469506i | ||||
\(872\) | −5.00000 | − | 8.66025i | −0.169321 | − | 0.293273i | ||||
\(873\) | 0.500000 | − | 0.866025i | 0.0169224 | − | 0.0293105i | ||||
\(874\) | −3.00000 | −0.101477 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.00000 | −0.135147 | ||||||||
\(877\) | −16.0000 | + | 27.7128i | −0.540282 | + | 0.935795i | 0.458606 | + | 0.888640i | \(0.348349\pi\) |
−0.998888 | + | 0.0471555i | \(0.984984\pi\) | |||||||
\(878\) | −18.5000 | − | 32.0429i | −0.624345 | − | 1.08140i | ||||
\(879\) | −4.50000 | − | 7.79423i | −0.151781 | − | 0.262893i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.0000 | 0.404290 | 0.202145 | − | 0.979356i | \(-0.435209\pi\) | ||||
0.202145 | + | 0.979356i | \(0.435209\pi\) | |||||||
\(882\) | −5.50000 | + | 4.33013i | −0.185195 | + | 0.145803i | ||||
\(883\) | 2.00000 | 0.0673054 | 0.0336527 | − | 0.999434i | \(-0.489286\pi\) | ||||
0.0336527 | + | 0.999434i | \(0.489286\pi\) | |||||||
\(884\) | 6.00000 | − | 10.3923i | 0.201802 | − | 0.349531i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.50000 | + | 2.59808i | 0.0503935 | + | 0.0872841i | ||||
\(887\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(888\) | 7.00000 | 0.234905 | ||||||||
\(889\) | 2.00000 | + | 1.73205i | 0.0670778 | + | 0.0580911i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.500000 | + | 0.866025i | −0.0167506 | + | 0.0290129i | ||||
\(892\) | −4.00000 | − | 6.92820i | −0.133930 | − | 0.231973i | ||||
\(893\) | −1.50000 | − | 2.59808i | −0.0501956 | − | 0.0869413i | ||||
\(894\) | 4.50000 | − | 7.79423i | 0.150503 | − | 0.260678i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.50000 | + | 0.866025i | −0.0835191 | + | 0.0289319i | ||||
\(897\) | 12.0000 | 0.400668 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.00000 | + | 15.5885i | 0.300167 | + | 0.519904i | ||||
\(900\) | 2.50000 | + | 4.33013i | 0.0833333 | + | 0.144338i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 6.00000 | 0.199778 | ||||||||
\(903\) | −5.50000 | + | 28.5788i | −0.183029 | + | 0.951044i | ||||
\(904\) | −12.0000 | −0.399114 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −9.50000 | − | 16.4545i | −0.315616 | − | 0.546664i | ||||
\(907\) | 20.0000 | + | 34.6410i | 0.664089 | + | 1.15024i | 0.979531 | + | 0.201291i | \(0.0645138\pi\) |
−0.315442 | + | 0.948945i | \(0.602153\pi\) | |||||||
\(908\) | −9.00000 | + | 15.5885i | −0.298675 | + | 0.517321i | ||||
\(909\) | 15.0000 | 0.497519 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.00000 | 0.298183 | 0.149092 | − | 0.988823i | \(-0.452365\pi\) | ||||
0.149092 | + | 0.988823i | \(0.452365\pi\) | |||||||
\(912\) | 0.500000 | − | 0.866025i | 0.0165567 | − | 0.0286770i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 1.00000 | + | 1.73205i | 0.0330771 | + | 0.0572911i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 26.0000 | 0.859064 | ||||||||
\(917\) | 45.0000 | − | 15.5885i | 1.48603 | − | 0.514776i | ||||
\(918\) | −3.00000 | −0.0990148 | ||||||||
\(919\) | 3.50000 | − | 6.06218i | 0.115454 | − | 0.199973i | −0.802507 | − | 0.596643i | \(-0.796501\pi\) |
0.917961 | + | 0.396670i | \(0.129834\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.00000 | + | 3.46410i | 0.0659022 | + | 0.114146i | ||||
\(922\) | 10.5000 | − | 18.1865i | 0.345799 | − | 0.598942i | ||||
\(923\) | −12.0000 | −0.394985 | ||||||||
\(924\) | −2.00000 | − | 1.73205i | −0.0657952 | − | 0.0569803i | ||||
\(925\) | 35.0000 | 1.15079 | ||||||||
\(926\) | 4.00000 | − | 6.92820i | 0.131448 | − | 0.227675i | ||||
\(927\) | 2.00000 | + | 3.46410i | 0.0656886 | + | 0.113776i | ||||
\(928\) | −4.50000 | − | 7.79423i | −0.147720 | − | 0.255858i | ||||
\(929\) | −3.00000 | + | 5.19615i | −0.0984268 | + | 0.170480i | −0.911034 | − | 0.412332i | \(-0.864714\pi\) |
0.812607 | + | 0.582812i | \(0.198048\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.50000 | + | 2.59808i | 0.213029 | + | 0.0851485i | ||||
\(932\) | 9.00000 | 0.294805 | ||||||||
\(933\) | 10.5000 | − | 18.1865i | 0.343755 | − | 0.595400i | ||||
\(934\) | −16.5000 | − | 28.5788i | −0.539896 | − | 0.935128i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.00000 | + | 3.46410i | −0.0653720 | + | 0.113228i | ||||
\(937\) | 8.00000 | 0.261349 | 0.130674 | − | 0.991425i | \(-0.458286\pi\) | ||||
0.130674 | + | 0.991425i | \(0.458286\pi\) | |||||||
\(938\) | −8.00000 | − | 6.92820i | −0.261209 | − | 0.226214i | ||||
\(939\) | −1.00000 | −0.0326338 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.5000 | + | 18.1865i | 0.342290 | + | 0.592864i | 0.984858 | − | 0.173365i | \(-0.0554641\pi\) |
−0.642567 | + | 0.766229i | \(0.722131\pi\) | |||||||
\(942\) | −6.50000 | − | 11.2583i | −0.211781 | − | 0.366816i | ||||
\(943\) | −9.00000 | + | 15.5885i | −0.293080 | + | 0.507630i | ||||
\(944\) | 9.00000 | 0.292925 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.0000 | −0.357641 | ||||||||
\(947\) | −1.50000 | + | 2.59808i | −0.0487435 | + | 0.0844261i | −0.889368 | − | 0.457193i | \(-0.848855\pi\) |
0.840624 | + | 0.541619i | \(0.182188\pi\) | |||||||
\(948\) | 8.00000 | + | 13.8564i | 0.259828 | + | 0.450035i | ||||
\(949\) | −8.00000 | − | 13.8564i | −0.259691 | − | 0.449798i | ||||
\(950\) | 2.50000 | − | 4.33013i | 0.0811107 | − | 0.140488i | ||||
\(951\) | −12.0000 | −0.389127 | ||||||||
\(952\) | 1.50000 | − | 7.79423i | 0.0486153 | − | 0.252612i | ||||
\(953\) | 30.0000 | 0.971795 | 0.485898 | − | 0.874016i | \(-0.338493\pi\) | ||||
0.485898 | + | 0.874016i | \(0.338493\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 12.0000 | + | 20.7846i | 0.388108 | + | 0.672222i | ||||
\(957\) | 4.50000 | − | 7.79423i | 0.145464 | − | 0.251952i | ||||
\(958\) | −6.00000 | −0.193851 | ||||||||
\(959\) | −6.00000 | + | 31.1769i | −0.193750 | + | 1.00676i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | − | 23.3827i | 0.435484 | − | 0.754280i | ||||
\(962\) | 14.0000 | + | 24.2487i | 0.451378 | + | 0.781810i | ||||
\(963\) | 9.00000 | + | 15.5885i | 0.290021 | + | 0.502331i | ||||
\(964\) | 14.0000 | − | 24.2487i | 0.450910 | − | 0.780998i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 7.50000 | − | 2.59808i | 0.241309 | − | 0.0835917i | ||||
\(967\) | −37.0000 | −1.18984 | −0.594920 | − | 0.803785i | \(-0.702816\pi\) | ||||
−0.594920 | + | 0.803785i | \(0.702816\pi\) | |||||||
\(968\) | 0.500000 | − | 0.866025i | 0.0160706 | − | 0.0278351i | ||||
\(969\) | 1.50000 | + | 2.59808i | 0.0481869 | + | 0.0834622i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 38.0000 | + | 32.9090i | 1.21822 | + | 1.05501i | ||||
\(974\) | 4.00000 | 0.128168 | ||||||||
\(975\) | −10.0000 | + | 17.3205i | −0.320256 | + | 0.554700i | ||||
\(976\) | 5.00000 | + | 8.66025i | 0.160046 | + | 0.277208i | ||||
\(977\) | 6.00000 | + | 10.3923i | 0.191957 | + | 0.332479i | 0.945899 | − | 0.324462i | \(-0.105183\pi\) |
−0.753942 | + | 0.656941i | \(0.771850\pi\) | |||||||
\(978\) | 1.00000 | − | 1.73205i | 0.0319765 | − | 0.0553849i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.0000 | −0.319275 | ||||||||
\(982\) | −18.0000 | + | 31.1769i | −0.574403 | + | 0.994895i | ||||
\(983\) | 19.5000 | + | 33.7750i | 0.621953 | + | 1.07725i | 0.989122 | + | 0.147100i | \(0.0469940\pi\) |
−0.367168 | + | 0.930155i | \(0.619673\pi\) | |||||||
\(984\) | −3.00000 | − | 5.19615i | −0.0956365 | − | 0.165647i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 27.0000 | 0.859855 | ||||||||
\(987\) | 6.00000 | + | 5.19615i | 0.190982 | + | 0.165395i | ||||
\(988\) | 4.00000 | 0.127257 | ||||||||
\(989\) | 16.5000 | − | 28.5788i | 0.524669 | − | 0.908754i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.00000 | − | 6.92820i | −0.127064 | − | 0.220082i | 0.795474 | − | 0.605988i | \(-0.207222\pi\) |
−0.922538 | + | 0.385906i | \(0.873889\pi\) | |||||||
\(992\) | 1.00000 | − | 1.73205i | 0.0317500 | − | 0.0549927i | ||||
\(993\) | −10.0000 | −0.317340 | ||||||||
\(994\) | −7.50000 | + | 2.59808i | −0.237886 | + | 0.0824060i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.0000 | + | 24.2487i | 0.443384 | + | 0.767964i | 0.997938 | − | 0.0641836i | \(-0.0204443\pi\) |
−0.554554 | + | 0.832148i | \(0.687111\pi\) | |||||||
\(998\) | −5.00000 | − | 8.66025i | −0.158272 | − | 0.274136i | ||||
\(999\) | 3.50000 | − | 6.06218i | 0.110735 | − | 0.191799i |
(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.i.b.331.1 | yes | 2 | |
3.2 | odd | 2 | 1386.2.k.d.793.1 | 2 | |||
7.2 | even | 3 | 3234.2.a.l.1.1 | 1 | |||
7.4 | even | 3 | inner | 462.2.i.b.67.1 | ✓ | 2 | |
7.5 | odd | 6 | 3234.2.a.f.1.1 | 1 | |||
21.2 | odd | 6 | 9702.2.a.bl.1.1 | 1 | |||
21.5 | even | 6 | 9702.2.a.bn.1.1 | 1 | |||
21.11 | odd | 6 | 1386.2.k.d.991.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.i.b.67.1 | ✓ | 2 | 7.4 | even | 3 | inner | |
462.2.i.b.331.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1386.2.k.d.793.1 | 2 | 3.2 | odd | 2 | |||
1386.2.k.d.991.1 | 2 | 21.11 | odd | 6 | |||
3234.2.a.f.1.1 | 1 | 7.5 | odd | 6 | |||
3234.2.a.l.1.1 | 1 | 7.2 | even | 3 | |||
9702.2.a.bl.1.1 | 1 | 21.2 | odd | 6 | |||
9702.2.a.bn.1.1 | 1 | 21.5 | even | 6 |