Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [700,2,Mod(149,700)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(700, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("700.149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 700.r (of order \(6\), degree \(2\), not 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: | \(5.58952814149\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 140) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 149.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 700.149 |
Dual form | 700.2.r.a.249.1 |
$q$-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 \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(477\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | −0.728714 | − | 0.684819i | \(-0.759881\pi\) |
0.228714 | + | 0.973494i | \(0.426548\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.866025 | + | 2.50000i | −0.327327 | + | 0.944911i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | + | 1.73205i | −0.333333 | + | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | − | 5.19615i | −0.904534 | − | 1.56670i | −0.821541 | − | 0.570149i | \(-0.806886\pi\) |
−0.0829925 | − | 0.996550i | \(-0.526448\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.00000i | − | 0.554700i | −0.960769 | − | 0.277350i | \(-0.910544\pi\) | ||
0.960769 | − | 0.277350i | \(-0.0894562\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.19615 | + | 3.00000i | −1.26025 | + | 0.727607i | −0.973123 | − | 0.230285i | \(-0.926034\pi\) |
−0.287129 | + | 0.957892i | \(0.592701\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | − | 6.92820i | 0.917663 | − | 1.58944i | 0.114708 | − | 0.993399i | \(-0.463407\pi\) |
0.802955 | − | 0.596040i | \(-0.203260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.500000 | − | 2.59808i | −0.109109 | − | 0.566947i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.59808 | + | 1.50000i | 0.541736 | + | 0.312772i | 0.745782 | − | 0.666190i | \(-0.232076\pi\) |
−0.204046 | + | 0.978961i | \(0.565409\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.00000i | − | 0.962250i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.00000 | −0.557086 | −0.278543 | − | 0.960424i | \(-0.589851\pi\) | ||||
−0.278543 | + | 0.960424i | \(0.589851\pi\) | |||||||
\(30\) | 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 | 0 | ||||||||
\(33\) | 5.19615 | + | 3.00000i | 0.904534 | + | 0.522233i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.92820 | − | 4.00000i | −1.13899 | − | 0.657596i | −0.192809 | − | 0.981236i | \(-0.561760\pi\) |
−0.946180 | + | 0.323640i | \(0.895093\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | + | 1.73205i | 0.160128 | + | 0.277350i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.00000 | −0.468521 | −0.234261 | − | 0.972174i | \(-0.575267\pi\) | ||||
−0.234261 | + | 0.972174i | \(0.575267\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 5.00000i | − | 0.762493i | −0.924473 | − | 0.381246i | \(-0.875495\pi\) | ||
0.924473 | − | 0.381246i | \(-0.124505\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.50000 | − | 4.33013i | −0.785714 | − | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.00000 | − | 5.19615i | 0.420084 | − | 0.727607i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.3923 | + | 6.00000i | −1.42749 | + | 0.824163i | −0.996922 | − | 0.0783936i | \(-0.975021\pi\) |
−0.430570 | + | 0.902557i | \(0.641688\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.00000i | 1.05963i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.500000 | − | 0.866025i | 0.0640184 | − | 0.110883i | −0.832240 | − | 0.554416i | \(-0.812942\pi\) |
0.896258 | + | 0.443533i | \(0.146275\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.46410 | − | 4.00000i | −0.436436 | − | 0.503953i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.06218 | + | 3.50000i | −0.740613 | + | 0.427593i | −0.822292 | − | 0.569066i | \(-0.807305\pi\) |
0.0816792 | + | 0.996659i | \(0.473972\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.00000 | −0.361158 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.66025 | − | 5.00000i | 1.01361 | − | 0.585206i | 0.101361 | − | 0.994850i | \(-0.467680\pi\) |
0.912245 | + | 0.409644i | \(0.134347\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 15.5885 | − | 3.00000i | 1.77647 | − | 0.341882i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.00000 | + | 3.46410i | −0.225018 | + | 0.389742i | −0.956325 | − | 0.292306i | \(-0.905577\pi\) |
0.731307 | + | 0.682048i | \(0.238911\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 3.00000i | − | 0.329293i | −0.986353 | − | 0.164646i | \(-0.947352\pi\) | ||
0.986353 | − | 0.164646i | \(-0.0526483\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.59808 | − | 1.50000i | 0.278543 | − | 0.160817i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.50000 | + | 2.59808i | −0.159000 | + | 0.275396i | −0.934508 | − | 0.355942i | \(-0.884160\pi\) |
0.775509 | + | 0.631337i | \(0.217494\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.00000 | + | 1.73205i | 0.524142 | + | 0.181568i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.73205 | + | 1.00000i | 0.179605 | + | 0.103695i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 10.0000i | − | 1.01535i | −0.861550 | − | 0.507673i | \(-0.830506\pi\) | ||
0.861550 | − | 0.507673i | \(-0.169494\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.0000 | 1.20605 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.50000 | + | 2.59808i | 0.149256 | + | 0.258518i | 0.930953 | − | 0.365140i | \(-0.118979\pi\) |
−0.781697 | + | 0.623658i | \(0.785646\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.06218 | − | 3.50000i | −0.597324 | − | 0.344865i | 0.170664 | − | 0.985329i | \(-0.445409\pi\) |
−0.767988 | + | 0.640464i | \(0.778742\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.59808 | + | 1.50000i | 0.251166 | + | 0.145010i | 0.620298 | − | 0.784366i | \(-0.287012\pi\) |
−0.369132 | + | 0.929377i | \(0.620345\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.50000 | + | 14.7224i | 0.814152 | + | 1.41015i | 0.909935 | + | 0.414751i | \(0.136131\pi\) |
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.00000 | 0.759326 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.0000i | 1.12887i | 0.825479 | + | 0.564433i | \(0.190905\pi\) | ||||
−0.825479 | + | 0.564433i | \(0.809095\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.46410 | + | 2.00000i | 0.320256 | + | 0.184900i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.00000 | − | 15.5885i | −0.275010 | − | 1.42899i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.5000 | + | 21.6506i | −1.13636 | + | 1.96824i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.59808 | − | 1.50000i | 0.234261 | − | 0.135250i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000i | 0.709885i | 0.934888 | + | 0.354943i | \(0.115500\pi\) | ||||
−0.934888 | + | 0.354943i | \(0.884500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.50000 | + | 4.33013i | 0.220113 | + | 0.381246i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.00000 | + | 10.3923i | −0.524222 | + | 0.907980i | 0.475380 | + | 0.879781i | \(0.342311\pi\) |
−0.999602 | + | 0.0281993i | \(0.991023\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.8564 | + | 16.0000i | 1.20150 | + | 1.38738i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.3923 | + | 6.00000i | −0.887875 | + | 0.512615i | −0.873247 | − | 0.487278i | \(-0.837990\pi\) |
−0.0146279 | + | 0.999893i | \(0.504656\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.00000 | −0.169638 | −0.0848189 | − | 0.996396i | \(-0.527031\pi\) | ||||
−0.0848189 | + | 0.996396i | \(0.527031\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.3923 | + | 6.00000i | −0.869048 | + | 0.501745i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.92820 | + | 1.00000i | 0.571429 | + | 0.0824786i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.50000 | + | 12.9904i | −0.614424 | + | 1.06421i | 0.376061 | + | 0.926595i | \(0.377278\pi\) |
−0.990485 | + | 0.137619i | \(0.956055\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.00000 | + | 8.66025i | 0.406894 | + | 0.704761i | 0.994540 | − | 0.104357i | \(-0.0332784\pi\) |
−0.587646 | + | 0.809118i | \(0.699945\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 12.0000i | − | 0.970143i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.1244 | − | 7.00000i | 0.967629 | − | 0.558661i | 0.0691164 | − | 0.997609i | \(-0.477982\pi\) |
0.898513 | + | 0.438948i | \(0.144649\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.00000 | − | 10.3923i | 0.475831 | − | 0.824163i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.00000 | + | 5.19615i | −0.472866 | + | 0.409514i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.8564 | − | 8.00000i | −1.08532 | − | 0.626608i | −0.152992 | − | 0.988227i | \(-0.548891\pi\) |
−0.932326 | + | 0.361619i | \(0.882224\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 21.0000i | − | 1.62503i | −0.582941 | − | 0.812514i | \(-0.698098\pi\) | ||
0.582941 | − | 0.812514i | \(-0.301902\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.00000 | + | 13.8564i | 0.611775 | + | 1.05963i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.00000 | − | 5.19615i | −0.224231 | − | 0.388379i | 0.731858 | − | 0.681457i | \(-0.238654\pi\) |
−0.956088 | + | 0.293079i | \(0.905320\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.0000 | 1.26360 | 0.631800 | − | 0.775131i | \(-0.282316\pi\) | ||||
0.631800 | + | 0.775131i | \(0.282316\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.00000i | 0.0739221i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 31.1769 | + | 18.0000i | 2.27988 | + | 1.31629i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.5000 | + | 4.33013i | 0.909241 | + | 0.314970i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.00000 | − | 15.5885i | 0.651217 | − | 1.12794i | −0.331611 | − | 0.943416i | \(-0.607592\pi\) |
0.982828 | − | 0.184525i | \(-0.0590746\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.73205 | + | 1.00000i | −0.124676 | + | 0.0719816i | −0.561041 | − | 0.827788i | \(-0.689599\pi\) |
0.436365 | + | 0.899770i | \(0.356266\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 18.0000i | − | 1.28245i | −0.767354 | − | 0.641223i | \(-0.778427\pi\) | ||
0.767354 | − | 0.641223i | \(-0.221573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.0000 | + | 17.3205i | 0.708881 | + | 1.22782i | 0.965272 | + | 0.261245i | \(0.0841331\pi\) |
−0.256391 | + | 0.966573i | \(0.582534\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.50000 | − | 6.06218i | 0.246871 | − | 0.427593i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.59808 | − | 7.50000i | 0.182349 | − | 0.526397i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.19615 | + | 3.00000i | −0.361158 | + | 0.208514i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −48.0000 | −3.32023 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.19615 | − | 1.00000i | 0.352738 | − | 0.0678844i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.00000 | + | 8.66025i | −0.337869 | + | 0.585206i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.00000 | + | 10.3923i | 0.403604 | + | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 8.00000i | − | 0.535720i | −0.963458 | − | 0.267860i | \(-0.913684\pi\) | ||
0.963458 | − | 0.267860i | \(-0.0863164\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.3923 | + | 6.00000i | −0.689761 | + | 0.398234i | −0.803523 | − | 0.595274i | \(-0.797043\pi\) |
0.113761 | + | 0.993508i | \(0.463710\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.00000 | − | 1.73205i | 0.0660819 | − | 0.114457i | −0.831092 | − | 0.556136i | \(-0.812283\pi\) |
0.897173 | + | 0.441679i | \(0.145617\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.0000 | + | 10.3923i | −0.789542 | + | 0.683763i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.19615 | + | 3.00000i | 0.340411 | + | 0.196537i | 0.660454 | − | 0.750867i | \(-0.270364\pi\) |
−0.320043 | + | 0.947403i | \(0.603697\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 4.00000i | − | 0.259828i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.00000 | −0.388108 | −0.194054 | − | 0.980991i | \(-0.562164\pi\) | ||||
−0.194054 | + | 0.980991i | \(0.562164\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.0000 | − | 22.5167i | −0.837404 | − | 1.45043i | −0.892058 | − | 0.451920i | \(-0.850739\pi\) |
0.0546547 | − | 0.998505i | \(-0.482594\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.8564 | + | 8.00000i | 0.888889 | + | 0.513200i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.8564 | − | 8.00000i | −0.881662 | − | 0.509028i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.50000 | + | 2.59808i | 0.0950586 | + | 0.164646i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.0000 | −1.13615 | −0.568075 | − | 0.822977i | \(-0.692312\pi\) | ||||
−0.568075 | + | 0.822977i | \(0.692312\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 18.0000i | − | 1.13165i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.7846 | + | 12.0000i | 1.29651 | + | 0.748539i | 0.979799 | − | 0.199983i | \(-0.0640888\pi\) |
0.316709 | + | 0.948523i | \(0.397422\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.0000 | − | 13.8564i | 0.994192 | − | 0.860995i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.00000 | − | 5.19615i | 0.185695 | − | 0.321634i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.59808 | − | 1.50000i | 0.160204 | − | 0.0924940i | −0.417755 | − | 0.908560i | \(-0.637183\pi\) |
0.577959 | + | 0.816066i | \(0.303849\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 3.00000i | − | 0.183597i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.50000 | − | 12.9904i | −0.457283 | − | 0.792038i | 0.541533 | − | 0.840679i | \(-0.317844\pi\) |
−0.998816 | + | 0.0486418i | \(0.984511\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | − | 13.8564i | 0.485965 | − | 0.841717i | −0.513905 | − | 0.857847i | \(-0.671801\pi\) |
0.999870 | + | 0.0161307i | \(0.00513477\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.19615 | + | 1.00000i | −0.314485 | + | 0.0605228i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.0526 | + | 11.0000i | −1.14476 | + | 0.660926i | −0.947604 | − | 0.319447i | \(-0.896503\pi\) |
−0.197153 | + | 0.980373i | \(0.563170\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.00000 | 0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.3205 | + | 10.0000i | −1.02960 | + | 0.594438i | −0.916869 | − | 0.399188i | \(-0.869292\pi\) |
−0.112728 | + | 0.993626i | \(0.535959\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.59808 | − | 7.50000i | 0.153360 | − | 0.442711i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.50000 | − | 16.4545i | 0.558824 | − | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.00000 | + | 8.66025i | 0.293105 | + | 0.507673i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.0000i | 0.701047i | 0.936554 | + | 0.350524i | \(0.113996\pi\) | ||||
−0.936554 | + | 0.350524i | \(0.886004\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −25.9808 | + | 15.0000i | −1.50756 | + | 0.870388i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.00000 | − | 5.19615i | 0.173494 | − | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.5000 | + | 4.33013i | 0.720488 | + | 0.249584i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.59808 | − | 1.50000i | −0.149256 | − | 0.0861727i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 19.0000i | − | 1.08439i | −0.840254 | − | 0.542194i | \(-0.817594\pi\) | ||
0.840254 | − | 0.542194i | \(-0.182406\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.00000 | 0.398216 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.46410 | − | 2.00000i | −0.195803 | − | 0.113047i | 0.398894 | − | 0.916997i | \(-0.369394\pi\) |
−0.594696 | + | 0.803951i | \(0.702728\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.5885 | − | 9.00000i | −0.875535 | − | 0.505490i | −0.00635137 | − | 0.999980i | \(-0.502022\pi\) |
−0.869184 | + | 0.494489i | \(0.835355\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.00000 | + | 15.5885i | 0.503903 | + | 0.872786i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.00000 | −0.167444 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 48.0000i | 2.67079i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.7224 | − | 8.50000i | −0.814152 | − | 0.470051i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.0000 | − | 19.0526i | 0.604615 | − | 1.04722i | −0.387498 | − | 0.921871i | \(-0.626660\pi\) |
0.992112 | − | 0.125353i | \(-0.0400062\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 13.8564 | − | 8.00000i | 0.759326 | − | 0.438397i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.0000i | 1.08947i | 0.838608 | + | 0.544735i | \(0.183370\pi\) | ||||
−0.838608 | + | 0.544735i | \(0.816630\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.00000 | − | 10.3923i | −0.325875 | − | 0.564433i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.00000 | + | 10.3923i | −0.324918 | + | 0.562775i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.5885 | − | 10.0000i | 0.841698 | − | 0.539949i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.3827 | + | 13.5000i | −1.25525 | + | 0.724718i | −0.972147 | − | 0.234372i | \(-0.924697\pi\) |
−0.283101 | + | 0.959090i | \(0.591363\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.00000 | 0.0535288 | 0.0267644 | − | 0.999642i | \(-0.491480\pi\) | ||||
0.0267644 | + | 0.999642i | \(0.491480\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.0000 | −0.533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.3923 | − | 6.00000i | 0.553127 | − | 0.319348i | −0.197256 | − | 0.980352i | \(-0.563203\pi\) |
0.750382 | + | 0.661004i | \(0.229870\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10.3923 | + | 12.0000i | 0.550019 | + | 0.635107i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.00000 | − | 5.19615i | 0.158334 | − | 0.274242i | −0.775934 | − | 0.630814i | \(-0.782721\pi\) |
0.934268 | + | 0.356572i | \(0.116054\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −22.5000 | − | 38.9711i | −1.18421 | − | 2.05111i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 25.0000i | − | 1.31216i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.33013 | − | 2.50000i | 0.226031 | − | 0.130499i | −0.382709 | − | 0.923869i | \(-0.625009\pi\) |
0.608740 | + | 0.793370i | \(0.291675\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.00000 | − | 5.19615i | 0.156174 | − | 0.270501i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.00000 | − | 31.1769i | −0.311504 | − | 1.61862i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.8564 | − | 8.00000i | −0.717458 | − | 0.414224i | 0.0963587 | − | 0.995347i | \(-0.469280\pi\) |
−0.813816 | + | 0.581122i | \(0.802614\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.00000i | 0.309016i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.00000 | −0.410932 | −0.205466 | − | 0.978664i | \(-0.565871\pi\) | ||||
−0.205466 | + | 0.978664i | \(0.565871\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.00000 | − | 6.92820i | −0.204926 | − | 0.354943i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.59808 | + | 1.50000i | 0.132755 | + | 0.0766464i | 0.564907 | − | 0.825155i | \(-0.308912\pi\) |
−0.432151 | + | 0.901801i | \(0.642245\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.66025 | + | 5.00000i | 0.440225 | + | 0.254164i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.00000 | + | 5.19615i | 0.152106 | + | 0.263455i | 0.932002 | − | 0.362454i | \(-0.118061\pi\) |
−0.779895 | + | 0.625910i | \(0.784728\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.0000 | −0.910299 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 12.0000i | − | 0.605320i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.5167 | − | 13.0000i | −1.13008 | − | 0.652451i | −0.186124 | − | 0.982526i | \(-0.559593\pi\) |
−0.943955 | + | 0.330075i | \(0.892926\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −20.0000 | − | 6.92820i | −1.00125 | − | 0.346844i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.50000 | + | 2.59808i | −0.0749064 | + | 0.129742i | −0.901046 | − | 0.433724i | \(-0.857199\pi\) |
0.826139 | + | 0.563466i | \(0.190532\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.46410 | + | 2.00000i | −0.172559 | + | 0.0996271i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 48.0000i | 2.37927i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.50000 | + | 9.52628i | 0.271957 | + | 0.471044i | 0.969363 | − | 0.245633i | \(-0.0789957\pi\) |
−0.697406 | + | 0.716677i | \(0.745662\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.00000 | − | 10.3923i | 0.295958 | − | 0.512615i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.73205 | − | 1.00000i | 0.0848189 | − | 0.0489702i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.0000 | −1.17248 | −0.586238 | − | 0.810139i | \(-0.699392\pi\) | ||||
−0.586238 | + | 0.810139i | \(0.699392\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.0000 | 1.12095 | 0.560476 | − | 0.828171i | \(-0.310618\pi\) | ||||
0.560476 | + | 0.828171i | \(0.310618\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.73205 | + | 2.00000i | 0.0838198 | + | 0.0967868i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.00000 | − | 10.3923i | 0.289683 | − | 0.501745i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.0000 | − | 25.9808i | −0.722525 | − | 1.25145i | −0.959985 | − | 0.280052i | \(-0.909648\pi\) |
0.237460 | − | 0.971397i | \(-0.423685\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.0000i | 1.34559i | 0.739827 | + | 0.672797i | \(0.234907\pi\) | ||||
−0.739827 | + | 0.672797i | \(0.765093\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.7846 | − | 12.0000i | 0.994263 | − | 0.574038i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.0000 | + | 24.2487i | −0.668184 | + | 1.15733i | 0.310228 | + | 0.950662i | \(0.399595\pi\) |
−0.978412 | + | 0.206666i | \(0.933739\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.0000 | − | 5.19615i | 0.619048 | − | 0.247436i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.79423 | + | 4.50000i | 0.370315 | + | 0.213801i | 0.673596 | − | 0.739100i | \(-0.264749\pi\) |
−0.303281 | + | 0.952901i | \(0.598082\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 15.0000i | − | 0.709476i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.00000 | 0.424736 | 0.212368 | − | 0.977190i | \(-0.431882\pi\) | ||||
0.212368 | + | 0.977190i | \(0.431882\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.00000 | + | 15.5885i | 0.423793 | + | 0.734032i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.66025 | − | 5.00000i | −0.406894 | − | 0.234920i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.46410 | + | 2.00000i | 0.162044 | + | 0.0935561i | 0.578829 | − | 0.815449i | \(-0.303510\pi\) |
−0.416785 | + | 0.909005i | \(0.636843\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 15.0000 | + | 25.9808i | 0.700140 | + | 1.21268i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.0000 | 1.39724 | 0.698620 | − | 0.715493i | \(-0.253798\pi\) | ||||
0.698620 | + | 0.715493i | \(0.253798\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 29.0000i | − | 1.34774i | −0.738848 | − | 0.673872i | \(-0.764630\pi\) | ||
0.738848 | − | 0.673872i | \(-0.235370\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −28.5788 | − | 16.5000i | −1.32247 | − | 0.763529i | −0.338349 | − | 0.941021i | \(-0.609868\pi\) |
−0.984122 | + | 0.177492i | \(0.943202\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.50000 | − | 18.1865i | −0.161615 | − | 0.839776i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.00000 | + | 12.1244i | −0.322543 | + | 0.558661i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −25.9808 | + | 15.0000i | −1.19460 | + | 0.689701i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 24.0000i | − | 1.09888i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.0000 | − | 25.9808i | −0.685367 | − | 1.18709i | −0.973321 | − | 0.229447i | \(-0.926308\pi\) |
0.287954 | − | 0.957644i | \(-0.407025\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.00000 | + | 13.8564i | −0.364769 | + | 0.631798i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.59808 | − | 7.50000i | 0.118217 | − | 0.341262i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.92820 | − | 4.00000i | 0.313947 | − | 0.181257i | −0.334744 | − | 0.942309i | \(-0.608650\pi\) |
0.648691 | + | 0.761052i | \(0.275317\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.0000 | 0.723545 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.00000 | 0.270776 | 0.135388 | − | 0.990793i | \(-0.456772\pi\) | ||||
0.135388 | + | 0.990793i | \(0.456772\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.5885 | − | 9.00000i | 0.702069 | − | 0.405340i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.00000 | − | 1.73205i | 0.0447661 | − | 0.0775372i | −0.842774 | − | 0.538267i | \(-0.819079\pi\) |
0.887540 | + | 0.460730i | \(0.152412\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.5000 | + | 18.1865i | 0.469105 | + | 0.812514i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.00000i | 0.401290i | 0.979664 | + | 0.200645i | \(0.0643038\pi\) | ||||
−0.979664 | + | 0.200645i | \(0.935696\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.79423 | + | 4.50000i | −0.346154 | + | 0.199852i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.5000 | − | 33.7750i | 0.864322 | − | 1.49705i | −0.00339621 | − | 0.999994i | \(-0.501081\pi\) |
0.867719 | − | 0.497056i | \(-0.165586\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.00000 | + | 25.9808i | 0.221187 | + | 1.14932i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −34.6410 | − | 20.0000i | −1.52944 | − | 0.883022i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.0000 | − | 25.9808i | −0.657162 | − | 1.13824i | −0.981347 | − | 0.192244i | \(-0.938423\pi\) |
0.324185 | − | 0.945994i | \(-0.394910\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 38.1051 | + | 22.0000i | 1.66622 | + | 0.961993i | 0.969648 | + | 0.244507i | \(0.0786260\pi\) |
0.696573 | + | 0.717486i | \(0.254707\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.3923 | + | 6.00000i | 0.452696 | + | 0.261364i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | − | 12.1244i | −0.304348 | − | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.00000i | 0.259889i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.19615 | + | 3.00000i | 0.224231 | + | 0.129460i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.00000 | + | 41.5692i | −0.258438 | + | 1.79051i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.50000 | + | 14.7224i | −0.365444 | + | 0.632967i | −0.988847 | − | 0.148933i | \(-0.952416\pi\) |
0.623404 | + | 0.781900i | \(0.285749\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −14.7224 | + | 8.50000i | −0.631800 | + | 0.364770i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 19.0000i | − | 0.812381i | −0.913788 | − | 0.406191i | \(-0.866857\pi\) | ||
0.913788 | − | 0.406191i | \(-0.133143\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.00000 | + | 1.73205i | 0.0426790 | + | 0.0739221i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.0000 | + | 20.7846i | −0.511217 | + | 0.885454i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.92820 | − | 8.00000i | −0.294617 | − | 0.340195i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.9808 | − | 15.0000i | 1.10084 | − | 0.635570i | 0.164399 | − | 0.986394i | \(-0.447432\pi\) |
0.936442 | + | 0.350824i | \(0.114098\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.0000 | −0.422955 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −36.0000 | −1.51992 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.79423 | − | 4.50000i | 0.328488 | − | 0.189652i | −0.326682 | − | 0.945134i | \(-0.605931\pi\) |
0.655169 | + | 0.755482i | \(0.272597\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.59808 | − | 0.500000i | 0.109109 | − | 0.0209980i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.00000 | + | 15.5885i | −0.377300 | + | 0.653502i | −0.990668 | − | 0.136295i | \(-0.956481\pi\) |
0.613369 | + | 0.789797i | \(0.289814\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.00000 | + | 13.8564i | 0.334790 | + | 0.579873i | 0.983444 | − | 0.181210i | \(-0.0580014\pi\) |
−0.648655 | + | 0.761083i | \(0.724668\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.0000i | 0.751961i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.66025 | + | 5.00000i | −0.360531 | + | 0.208153i | −0.669314 | − | 0.742980i | \(-0.733412\pi\) |
0.308783 | + | 0.951133i | \(0.400078\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.00000 | − | 1.73205i | 0.0415586 | − | 0.0719816i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.50000 | + | 2.59808i | 0.311152 | + | 0.107786i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 62.3538 | + | 36.0000i | 2.58243 | + | 1.49097i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.0000i | 0.495293i | 0.968850 | + | 0.247647i | \(0.0796572\pi\) | ||||
−0.968850 | + | 0.247647i | \(0.920343\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.0000 | −0.659269 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.00000 | + | 15.5885i | 0.370211 | + | 0.641223i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.3923 | − | 6.00000i | −0.426761 | − | 0.246390i | 0.271205 | − | 0.962522i | \(-0.412578\pi\) |
−0.697966 | + | 0.716131i | \(0.745911\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −17.3205 | − | 10.0000i | −0.708881 | − | 0.409273i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.0000 | −0.897399 | −0.448699 | − | 0.893683i | \(-0.648113\pi\) | ||||
−0.448699 | + | 0.893683i | \(0.648113\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 14.0000i | − | 0.570124i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.2391 | + | 21.5000i | 1.51149 | + | 0.872658i | 0.999910 | + | 0.0134214i | \(0.00427228\pi\) |
0.511578 | + | 0.859237i | \(0.329061\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.50000 | + | 7.79423i | 0.0607831 | + | 0.315838i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.73205 | + | 1.00000i | −0.0699569 | + | 0.0403896i | −0.534570 | − | 0.845124i | \(-0.679527\pi\) |
0.464614 | + | 0.885514i | \(0.346193\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 12.0000i | − | 0.483102i | −0.970388 | − | 0.241551i | \(-0.922344\pi\) | ||
0.970388 | − | 0.241551i | \(-0.0776561\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.00000 | + | 12.1244i | 0.281354 | + | 0.487319i | 0.971718 | − | 0.236143i | \(-0.0758832\pi\) |
−0.690365 | + | 0.723462i | \(0.742550\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.50000 | − | 12.9904i | 0.300965 | − | 0.521286i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.19615 | − | 6.00000i | −0.208179 | − | 0.240385i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 41.5692 | − | 24.0000i | 1.66011 | − | 0.958468i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 48.0000 | 1.91389 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.0000 | 1.51276 | 0.756378 | − | 0.654135i | \(-0.226967\pi\) | ||||
0.756378 | + | 0.654135i | \(0.226967\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.46410 | − | 2.00000i | 0.137686 | − | 0.0794929i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.66025 | + | 11.0000i | −0.343132 | + | 0.435836i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.5000 | + | 33.7750i | 0.770204 | + | 1.33403i | 0.937451 | + | 0.348117i | \(0.113179\pi\) |
−0.167247 | + | 0.985915i | \(0.553488\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 20.0000i | − | 0.788723i | −0.918955 | − | 0.394362i | \(-0.870966\pi\) | ||
0.918955 | − | 0.394362i | \(-0.129034\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.1865 | − | 10.5000i | 0.714986 | − | 0.412798i | −0.0979182 | − | 0.995194i | \(-0.531218\pi\) |
0.812905 | + | 0.582397i | \(0.197885\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.00000 | + | 3.46410i | −0.156772 | + | 0.135769i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −36.3731 | − | 21.0000i | −1.42339 | − | 0.821794i | −0.426801 | − | 0.904345i | \(-0.640360\pi\) |
−0.996587 | + | 0.0825519i | \(0.973693\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 20.0000i | 0.780274i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.0000 | −0.467454 | −0.233727 | − | 0.972302i | \(-0.575092\pi\) | ||||
−0.233727 | + | 0.972302i | \(0.575092\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.5000 | + | 21.6506i | 0.486194 | + | 0.842112i | 0.999874 | − | 0.0158695i | \(-0.00505163\pi\) |
−0.513680 | + | 0.857982i | \(0.671718\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.3923 | − | 6.00000i | −0.403604 | − | 0.233021i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.79423 | − | 4.50000i | −0.301794 | − | 0.174241i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.00000 | + | 6.92820i | 0.154649 | + | 0.267860i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.00000 | −0.231627 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 32.0000i | − | 1.23351i | −0.787155 | − | 0.616755i | \(-0.788447\pi\) | ||
0.787155 | − | 0.616755i | \(-0.211553\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.5885 | + | 9.00000i | 0.599113 | + | 0.345898i | 0.768693 | − | 0.639618i | \(-0.220908\pi\) |
−0.169580 | + | 0.985517i | \(0.554241\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25.0000 | + | 8.66025i | 0.959412 | + | 0.332350i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.00000 | − | 10.3923i | 0.229920 | − | 0.398234i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.9904 | − | 7.50000i | 0.497063 | − | 0.286980i | −0.230437 | − | 0.973087i | \(-0.574015\pi\) |
0.727500 | + | 0.686108i | \(0.240682\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.00000i | 0.0763048i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.0000 | + | 20.7846i | 0.457164 | + | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.00000 | + | 12.1244i | −0.266293 | + | 0.461232i | −0.967901 | − | 0.251330i | \(-0.919132\pi\) |
0.701609 | + | 0.712562i | \(0.252465\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.3923 | + | 30.0000i | −0.394771 | + | 1.13961i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.5885 | − | 9.00000i | 0.590455 | − | 0.340899i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.00000 | −0.226941 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.0000 | 1.01978 | 0.509888 | − | 0.860241i | \(-0.329687\pi\) | ||||
0.509888 | + | 0.860241i | \(0.329687\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −55.4256 | + | 32.0000i | −2.09042 | + | 1.20690i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.79423 | + | 1.50000i | −0.293132 | + | 0.0564133i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.500000 | + | 0.866025i | −0.0187779 | + | 0.0325243i | −0.875262 | − | 0.483650i | \(-0.839311\pi\) |
0.856484 | + | 0.516174i | \(0.172644\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.00000 | − | 6.92820i | −0.150012 | − | 0.259828i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 6.00000i | − | 0.224702i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.19615 | − | 3.00000i | 0.194054 | − | 0.112037i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.0000 | + | 25.9808i | −0.559406 | + | 0.968919i | 0.438141 | + | 0.898906i | \(0.355637\pi\) |
−0.997546 | + | 0.0700124i | \(0.977696\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.0000 | − | 12.1244i | 0.521387 | − | 0.451535i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 22.5167 | + | 13.0000i | 0.837404 | + | 0.483475i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.0000i | 0.853023i | 0.904482 | + | 0.426511i | \(0.140258\pi\) | ||||
−0.904482 | + | 0.426511i | \(0.859742\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.0000 | + | 25.9808i | 0.554795 | + | 0.960933i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.73205 | + | 1.00000i | 0.0639748 | + | 0.0369358i | 0.531646 | − | 0.846967i | \(-0.321574\pi\) |
−0.467671 | + | 0.883902i | \(0.654907\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 36.3731 | + | 21.0000i | 1.33982 | + | 0.773545i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.0000 | − | 39.8372i | −0.846069 | − | 1.46543i | −0.884690 | − | 0.466180i | \(-0.845630\pi\) |
0.0386212 | − | 0.999254i | \(-0.487703\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.0000 | 0.587775 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 39.0000i | 1.43077i | 0.698730 | + | 0.715386i | \(0.253749\pi\) | ||||
−0.698730 | + | 0.715386i | \(0.746251\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.19615 | + | 3.00000i | 0.190117 | + | 0.109764i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.00000 | + | 5.19615i | −0.219235 | + | 0.189863i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.0000 | + | 17.3205i | −0.364905 | + | 0.632034i | −0.988761 | − | 0.149505i | \(-0.952232\pi\) |
0.623856 | + | 0.781540i | \(0.285565\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.5885 | − | 9.00000i | 0.568075 | − | 0.327978i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.00000i | 0.0726912i | 0.999339 | + | 0.0363456i | \(0.0115717\pi\) | ||||
−0.999339 | + | 0.0363456i | \(0.988428\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.00000 | + | 15.5885i | 0.326679 | + | 0.565825i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.0000 | + | 25.9808i | −0.543750 | + | 0.941802i | 0.454935 | + | 0.890525i | \(0.349663\pi\) |
−0.998684 | + | 0.0512772i | \(0.983671\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −44.1673 | + | 8.50000i | −1.59896 | + | 0.307721i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.0000 | 1.22607 | 0.613036 | − | 0.790055i | \(-0.289948\pi\) | ||||
0.613036 | + | 0.790055i | \(0.289948\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.0000 | −0.864339 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.3731 | − | 21.0000i | 1.30825 | − | 0.755318i | 0.326445 | − | 0.945216i | \(-0.394149\pi\) |
0.981804 | + | 0.189899i | \(0.0608160\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.92820 | + | 20.0000i | −0.248548 | + | 0.717496i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.0000 | + | 20.7846i | −0.429945 | + | 0.744686i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 15.0000i | 0.536056i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.8468 | + | 15.5000i | −0.956985 | + | 0.552515i | −0.895244 | − | 0.445577i | \(-0.852999\pi\) |
−0.0617409 | + | 0.998092i | \(0.519665\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.50000 | + | 2.59808i | −0.0534014 | + | 0.0924940i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30.0000 | − | 10.3923i | −1.06668 | − | 0.369508i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.73205 | − | 1.00000i | −0.0615069 | − | 0.0355110i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 12.0000i | − | 0.425062i | −0.977154 | − | 0.212531i | \(-0.931829\pi\) | ||
0.977154 | − | 0.212531i | \(-0.0681706\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.00000 | − | 5.19615i | −0.106000 | − | 0.183597i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −51.9615 | − | 30.0000i | −1.83368 | − | 1.05868i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.9904 | + | 7.50000i | 0.457283 | + | 0.264013i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −25.5000 | − | 44.1673i | −0.896532 | − | 1.55284i | −0.831897 | − | 0.554930i | \(-0.812745\pi\) |
−0.0646355 | − | 0.997909i | \(-0.520588\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.00000 | 0.0702295 | 0.0351147 | − | 0.999383i | \(-0.488820\pi\) | ||||
0.0351147 | + | 0.999383i | \(0.488820\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.0000i | 0.561144i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −34.6410 | − | 20.0000i | −1.21194 | − | 0.699711i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.00000 | + | 6.92820i | −0.279543 | + | 0.242091i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.00000 | + | 15.5885i | −0.314102 | + | 0.544041i | −0.979246 | − | 0.202674i | \(-0.935037\pi\) |
0.665144 | + | 0.746715i | \(0.268370\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42.4352 | − | 24.5000i | 1.47920 | − | 0.854016i | 0.479477 | − | 0.877555i | \(-0.340826\pi\) |
0.999723 | + | 0.0235383i | \(0.00749316\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 45.0000i | − | 1.56480i | −0.622774 | − | 0.782402i | \(-0.713994\pi\) | ||
0.622774 | − | 0.782402i | \(-0.286006\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.00000 | − | 8.66025i | −0.173657 | − | 0.300783i | 0.766039 | − | 0.642795i | \(-0.222225\pi\) |
−0.939696 | + | 0.342012i | \(0.888892\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.0000 | − | 19.0526i | 0.381586 | − | 0.660926i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 41.5692 | + | 6.00000i | 1.44029 | + | 0.207888i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.66025 | + | 5.00000i | −0.299342 | + | 0.172825i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 42.0000 | 1.45000 | 0.725001 | − | 0.688748i | \(-0.241839\pi\) | ||||
0.725001 | + | 0.688748i | \(0.241839\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.19615 | − | 3.00000i | 0.178965 | − | 0.103325i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −43.3013 | − | 50.0000i | −1.48785 | − | 1.71802i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.0000 | − | 17.3205i | 0.343199 | − | 0.594438i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.0000 | − | 20.7846i | −0.411355 | − | 0.712487i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 32.0000i | − | 1.09566i | −0.836590 | − | 0.547830i | \(-0.815454\pi\) | ||
0.836590 | − | 0.547830i | \(-0.184546\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 36.3731 | − | 21.0000i | 1.24248 | − | 0.717346i | 0.272882 | − | 0.962048i | \(-0.412023\pi\) |
0.969599 | + | 0.244701i | \(0.0786899\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.00000 | + | 3.46410i | −0.0682391 | + | 0.118194i | −0.898126 | − | 0.439738i | \(-0.855071\pi\) |
0.829887 | + | 0.557931i | \(0.188405\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.50000 | + | 7.79423i | 0.0511199 | + | 0.265627i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.5788 | + | 16.5000i | 0.972835 | + | 0.561667i | 0.900099 | − | 0.435685i | \(-0.143494\pi\) |
0.0727356 | + | 0.997351i | \(0.476827\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 19.0000i | 0.645274i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.0000 | 0.814144 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.00000 | + | 12.1244i | 0.237186 | + | 0.410818i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.3205 | + | 10.0000i | 0.586210 | + | 0.338449i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.6410 | + | 20.0000i | 1.16974 | + | 0.675352i | 0.953620 | − | 0.301014i | \(-0.0973250\pi\) |
0.216124 | + | 0.976366i | \(0.430658\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.00000 | − | 10.3923i | −0.202375 | − | 0.350524i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.00000 | 0.303218 | 0.151609 | − | 0.988441i | \(-0.451555\pi\) | ||||
0.151609 | + | 0.988441i | \(0.451555\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.0000i | 0.942275i | 0.882060 | + | 0.471138i | \(0.156156\pi\) | ||||
−0.882060 | + | 0.471138i | \(0.843844\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −49.3634 | − | 28.5000i | −1.65746 | − | 0.956936i | −0.973880 | − | 0.227063i | \(-0.927088\pi\) |
−0.683582 | − | 0.729873i | \(-0.739579\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.0000 | − | 6.92820i | −0.670778 | − | 0.232364i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.00000 | + | 5.19615i | −0.100504 | + | 0.174078i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.00000i | 0.200334i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.00000 | + | 5.19615i | 0.100056 | + | 0.173301i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.0000 | − | 62.3538i | 1.19933 | − | 2.07731i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.9904 | + | 2.50000i | −0.432293 | + | 0.0831948i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.9186 | − | 11.5000i | 0.661386 | − | 0.381851i | −0.131419 | − | 0.991327i | \(-0.541953\pi\) |
0.792805 | + | 0.609476i | \(0.208620\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.00000 | −0.199007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.0000 | 0.993944 | 0.496972 | − | 0.867766i | \(-0.334445\pi\) | ||||
0.496972 | + | 0.867766i | \(0.334445\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.5885 | + | 9.00000i | −0.515903 | + | 0.297857i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −20.7846 | − | 24.0000i | −0.686368 | − | 0.792550i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.00000 | − | 6.92820i | 0.131948 | − | 0.228540i | −0.792480 | − | 0.609898i | \(-0.791210\pi\) |
0.924427 | + | 0.381358i | \(0.124544\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.50000 | + | 16.4545i | 0.313036 | + | 0.542194i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12.1244 | − | 7.00000i | 0.398216 | − | 0.229910i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.5000 | + | 38.9711i | −0.738201 | + | 1.27860i | 0.215104 | + | 0.976591i | \(0.430991\pi\) |
−0.953305 | + | 0.302010i | \(0.902342\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −52.0000 | + | 20.7846i | −1.70423 | + | 0.681188i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.0000i | 1.43742i | 0.695311 | + | 0.718709i | \(0.255266\pi\) | ||||
−0.695311 | + | 0.718709i | \(0.744734\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.00000 | 0.130535 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.0000 | − | 46.7654i | −0.880175 | − | 1.52451i | −0.851146 | − | 0.524929i | \(-0.824092\pi\) |
−0.0290288 | − | 0.999579i | \(-0.509241\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.79423 | − | 4.50000i | −0.253815 | − | 0.146540i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.79423 | − | 4.50000i | −0.253278 | − | 0.146230i | 0.367986 | − | 0.929831i | \(-0.380047\pi\) |
−0.621264 | + | 0.783601i | \(0.713381\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.0000 | − | 17.3205i | −0.324614 | − | 0.562247i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.0000 | 0.583690 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 36.0000i | − | 1.16615i | −0.812417 | − | 0.583077i | \(-0.801849\pi\) | ||
0.812417 | − | 0.583077i | \(-0.198151\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −15.5885 | − | 9.00000i | −0.503903 | − | 0.290929i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.00000 | − | 31.1769i | −0.193750 | − | 1.00676i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | − | 23.3827i | 0.435484 | − | 0.754280i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.19615 | + | 3.00000i | −0.167444 | + | 0.0966736i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 7.00000i | − | 0.225105i | −0.993646 | − | 0.112552i | \(-0.964097\pi\) | ||
0.993646 | − | 0.112552i | \(-0.0359026\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −24.0000 | − | 41.5692i | −0.770991 | − | 1.33540i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.00000 | − | 10.3923i | 0.192549 | − | 0.333505i | −0.753545 | − | 0.657396i | \(-0.771658\pi\) |
0.946094 | + | 0.323891i | \(0.104991\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.73205 | − | 5.00000i | 0.0555270 | − | 0.160293i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −46.7654 | + | 27.0000i | −1.49616 | + | 0.863807i | −0.999990 | − | 0.00442082i | \(-0.998593\pi\) |
−0.496167 | + | 0.868227i | \(0.665259\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.0000 | 0.575282 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −34.0000 | −1.08554 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33.7750 | − | 19.5000i | 1.07725 | − | 0.621953i | 0.147100 | − | 0.989122i | \(-0.453006\pi\) |
0.930155 | + | 0.367168i | \(0.119673\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.50000 | − | 12.9904i | 0.238486 | − | 0.413070i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.0000 | − | 22.5167i | −0.412959 | − | 0.715265i | 0.582253 | − | 0.813008i | \(-0.302171\pi\) |
−0.995212 | + | 0.0977423i | \(0.968838\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22.0000i | 0.698149i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.7128 | − | 16.0000i | 0.877674 | − | 0.506725i | 0.00778294 | − | 0.999970i | \(-0.497523\pi\) |
0.869891 | + | 0.493245i | \(0.164189\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −20.0000 | + | 34.6410i | −0.632772 | + | 1.09599i |
(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 | 700.2.r.a.149.1 | 4 | ||
5.2 | odd | 4 | 700.2.i.b.401.1 | 2 | |||
5.3 | odd | 4 | 140.2.i.a.121.1 | yes | 2 | ||
5.4 | even | 2 | inner | 700.2.r.a.149.2 | 4 | ||
7.2 | even | 3 | 4900.2.e.m.2549.1 | 2 | |||
7.4 | even | 3 | inner | 700.2.r.a.249.2 | 4 | ||
7.5 | odd | 6 | 4900.2.e.n.2549.2 | 2 | |||
15.8 | even | 4 | 1260.2.s.c.541.1 | 2 | |||
20.3 | even | 4 | 560.2.q.f.401.1 | 2 | |||
35.2 | odd | 12 | 4900.2.a.i.1.1 | 1 | |||
35.3 | even | 12 | 980.2.i.f.361.1 | 2 | |||
35.4 | even | 6 | inner | 700.2.r.a.249.1 | 4 | ||
35.9 | even | 6 | 4900.2.e.m.2549.2 | 2 | |||
35.12 | even | 12 | 4900.2.a.q.1.1 | 1 | |||
35.13 | even | 4 | 980.2.i.f.961.1 | 2 | |||
35.18 | odd | 12 | 140.2.i.a.81.1 | ✓ | 2 | ||
35.19 | odd | 6 | 4900.2.e.n.2549.1 | 2 | |||
35.23 | odd | 12 | 980.2.a.g.1.1 | 1 | |||
35.32 | odd | 12 | 700.2.i.b.501.1 | 2 | |||
35.33 | even | 12 | 980.2.a.e.1.1 | 1 | |||
105.23 | even | 12 | 8820.2.a.p.1.1 | 1 | |||
105.53 | even | 12 | 1260.2.s.c.361.1 | 2 | |||
105.68 | odd | 12 | 8820.2.a.a.1.1 | 1 | |||
140.23 | even | 12 | 3920.2.a.k.1.1 | 1 | |||
140.103 | odd | 12 | 3920.2.a.w.1.1 | 1 | |||
140.123 | even | 12 | 560.2.q.f.81.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
140.2.i.a.81.1 | ✓ | 2 | 35.18 | odd | 12 | ||
140.2.i.a.121.1 | yes | 2 | 5.3 | odd | 4 | ||
560.2.q.f.81.1 | 2 | 140.123 | even | 12 | |||
560.2.q.f.401.1 | 2 | 20.3 | even | 4 | |||
700.2.i.b.401.1 | 2 | 5.2 | odd | 4 | |||
700.2.i.b.501.1 | 2 | 35.32 | odd | 12 | |||
700.2.r.a.149.1 | 4 | 1.1 | even | 1 | trivial | ||
700.2.r.a.149.2 | 4 | 5.4 | even | 2 | inner | ||
700.2.r.a.249.1 | 4 | 35.4 | even | 6 | inner | ||
700.2.r.a.249.2 | 4 | 7.4 | even | 3 | inner | ||
980.2.a.e.1.1 | 1 | 35.33 | even | 12 | |||
980.2.a.g.1.1 | 1 | 35.23 | odd | 12 | |||
980.2.i.f.361.1 | 2 | 35.3 | even | 12 | |||
980.2.i.f.961.1 | 2 | 35.13 | even | 4 | |||
1260.2.s.c.361.1 | 2 | 105.53 | even | 12 | |||
1260.2.s.c.541.1 | 2 | 15.8 | even | 4 | |||
3920.2.a.k.1.1 | 1 | 140.23 | even | 12 | |||
3920.2.a.w.1.1 | 1 | 140.103 | odd | 12 | |||
4900.2.a.i.1.1 | 1 | 35.2 | odd | 12 | |||
4900.2.a.q.1.1 | 1 | 35.12 | even | 12 | |||
4900.2.e.m.2549.1 | 2 | 7.2 | even | 3 | |||
4900.2.e.m.2549.2 | 2 | 35.9 | even | 6 | |||
4900.2.e.n.2549.1 | 2 | 35.19 | odd | 6 | |||
4900.2.e.n.2549.2 | 2 | 7.5 | odd | 6 | |||
8820.2.a.a.1.1 | 1 | 105.68 | odd | 12 | |||
8820.2.a.p.1.1 | 1 | 105.23 | even | 12 |