Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1960,2,Mod(361,1960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1960, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1960.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1960.q (of order \(3\), 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: | \(15.6506787962\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1960.361 |
Dual form | 1960.2.q.j.961.1 |
$q$-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 \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).
\(n\) | \(981\) | \(1081\) | \(1177\) | \(1471\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | −0.684819 | − | 0.728714i | \(-0.740119\pi\) |
0.973494 | + | 0.228714i | \(0.0734519\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | + | 1.73205i | 0.333333 | + | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | + | 2.59808i | −0.452267 | + | 0.783349i | −0.998526 | − | 0.0542666i | \(-0.982718\pi\) |
0.546259 | + | 0.837616i | \(0.316051\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | 0.138675 | − | 0.990338i | \(-0.455716\pi\) | ||||
0.138675 | + | 0.990338i | \(0.455716\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.50000 | − | 4.33013i | 0.606339 | − | 1.05021i | −0.385499 | − | 0.922708i | \(-0.625971\pi\) |
0.991838 | − | 0.127502i | \(-0.0406959\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.00000 | + | 5.19615i | 0.688247 | + | 1.19208i | 0.972404 | + | 0.233301i | \(0.0749529\pi\) |
−0.284157 | + | 0.958778i | \(0.591714\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.00000 | −0.928477 | −0.464238 | − | 0.885710i | \(-0.653672\pi\) | ||||
−0.464238 | + | 0.885710i | \(0.653672\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | + | 1.73205i | −0.179605 | + | 0.311086i | −0.941745 | − | 0.336327i | \(-0.890815\pi\) |
0.762140 | + | 0.647412i | \(0.224149\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.50000 | + | 2.59808i | 0.261116 | + | 0.452267i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | + | 3.46410i | 0.328798 | + | 0.569495i | 0.982274 | − | 0.187453i | \(-0.0600231\pi\) |
−0.653476 | + | 0.756948i | \(0.726690\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.500000 | − | 0.866025i | 0.0800641 | − | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.0000 | 1.52499 | 0.762493 | − | 0.646997i | \(-0.223975\pi\) | ||||
0.762493 | + | 0.646997i | \(0.223975\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | − | 1.73205i | 0.149071 | − | 0.258199i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.50000 | + | 7.79423i | 0.656392 | + | 1.13691i | 0.981543 | + | 0.191243i | \(0.0612518\pi\) |
−0.325150 | + | 0.945662i | \(0.605415\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.50000 | − | 4.33013i | −0.350070 | − | 0.606339i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.00000 | + | 5.19615i | −0.412082 | + | 0.713746i | −0.995117 | − | 0.0987002i | \(-0.968532\pi\) |
0.583036 | + | 0.812447i | \(0.301865\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.00000 | 0.404520 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.00000 | 0.794719 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.00000 | − | 5.19615i | 0.390567 | − | 0.676481i | −0.601958 | − | 0.798528i | \(-0.705612\pi\) |
0.992524 | + | 0.122047i | \(0.0389457\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | + | 10.3923i | 0.768221 | + | 1.33060i | 0.938527 | + | 0.345207i | \(0.112191\pi\) |
−0.170305 | + | 0.985391i | \(0.554475\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.500000 | − | 0.866025i | −0.0620174 | − | 0.107417i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.00000 | − | 1.73205i | 0.122169 | − | 0.211604i | −0.798454 | − | 0.602056i | \(-0.794348\pi\) |
0.920623 | + | 0.390453i | \(0.127682\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.00000 | − | 12.1244i | 0.819288 | − | 1.41905i | −0.0869195 | − | 0.996215i | \(-0.527702\pi\) |
0.906208 | − | 0.422833i | \(-0.138964\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.500000 | + | 0.866025i | 0.0577350 | + | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.500000 | − | 0.866025i | −0.0562544 | − | 0.0974355i | 0.836527 | − | 0.547926i | \(-0.184582\pi\) |
−0.892781 | + | 0.450490i | \(0.851249\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0000 | 1.31717 | 0.658586 | − | 0.752506i | \(-0.271155\pi\) | ||||
0.658586 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.00000 | −0.542326 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.50000 | + | 4.33013i | −0.268028 | + | 0.464238i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.00000 | + | 1.73205i | 0.103695 | + | 0.179605i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.00000 | − | 5.19615i | 0.307794 | − | 0.533114i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.00000 | −0.913812 | −0.456906 | − | 0.889515i | \(-0.651042\pi\) | ||||
−0.456906 | + | 0.889515i | \(0.651042\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.00000 | −0.603023 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.00000 | − | 15.5885i | 0.895533 | − | 1.55111i | 0.0623905 | − | 0.998052i | \(-0.480128\pi\) |
0.833143 | − | 0.553058i | \(-0.186539\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.500000 | + | 0.866025i | 0.0492665 | + | 0.0853320i | 0.889607 | − | 0.456727i | \(-0.150978\pi\) |
−0.840341 | + | 0.542059i | \(0.817645\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.00000 | − | 1.73205i | −0.0966736 | − | 0.167444i | 0.813632 | − | 0.581380i | \(-0.197487\pi\) |
−0.910306 | + | 0.413936i | \(0.864154\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.50000 | − | 16.4545i | 0.909935 | − | 1.57605i | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) |
0.814152 | − | 0.580651i | \(-0.197202\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.00000 | 0.379663 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.00000 | −0.376288 | −0.188144 | − | 0.982141i | \(-0.560247\pi\) | ||||
−0.188144 | + | 0.982141i | \(0.560247\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000 | + | 1.73205i | 0.0924500 | + | 0.160128i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.00000 | + | 1.73205i | −0.0901670 | + | 0.156174i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.00000 | −0.532414 | −0.266207 | − | 0.963916i | \(-0.585770\pi\) | ||||
−0.266207 | + | 0.963916i | \(0.585770\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.00000 | − | 8.66025i | 0.440225 | − | 0.762493i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.00000 | + | 13.8564i | 0.698963 | + | 1.21064i | 0.968826 | + | 0.247741i | \(0.0796882\pi\) |
−0.269863 | + | 0.962899i | \(0.586978\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.50000 | − | 4.33013i | −0.215166 | − | 0.372678i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.00000 | + | 3.46410i | −0.170872 | + | 0.295958i | −0.938725 | − | 0.344668i | \(-0.887992\pi\) |
0.767853 | + | 0.640626i | \(0.221325\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.0000 | 1.35710 | 0.678551 | − | 0.734553i | \(-0.262608\pi\) | ||||
0.678551 | + | 0.734553i | \(0.262608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.00000 | 0.757937 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.50000 | + | 2.59808i | −0.125436 | + | 0.217262i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.50000 | + | 4.33013i | 0.207614 | + | 0.359597i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.00000 | − | 15.5885i | −0.737309 | − | 1.27706i | −0.953703 | − | 0.300750i | \(-0.902763\pi\) |
0.216394 | − | 0.976306i | \(-0.430570\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.50000 | + | 7.79423i | −0.366205 | + | 0.634285i | −0.988969 | − | 0.148124i | \(-0.952676\pi\) |
0.622764 | + | 0.782410i | \(0.286010\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.0000 | 0.808452 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.00000 | 0.160644 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.00000 | − | 1.73205i | 0.0798087 | − | 0.138233i | −0.823359 | − | 0.567521i | \(-0.807902\pi\) |
0.903167 | + | 0.429289i | \(0.141236\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.00000 | + | 5.19615i | 0.237915 | + | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.00000 | + | 6.92820i | 0.313304 | + | 0.542659i | 0.979076 | − | 0.203497i | \(-0.0652307\pi\) |
−0.665771 | + | 0.746156i | \(0.731897\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.50000 | − | 2.59808i | 0.116775 | − | 0.202260i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.00000 | −0.386912 | −0.193456 | − | 0.981109i | \(-0.561970\pi\) | ||||
−0.193456 | + | 0.981109i | \(0.561970\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.00000 | + | 10.3923i | −0.458831 | + | 0.794719i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.50000 | − | 12.9904i | −0.570214 | − | 0.987640i | −0.996544 | − | 0.0830722i | \(-0.973527\pi\) |
0.426329 | − | 0.904568i | \(-0.359807\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.00000 | − | 5.19615i | −0.225494 | − | 0.390567i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.0000 | − | 17.3205i | 0.747435 | − | 1.29460i | −0.201613 | − | 0.979465i | \(-0.564618\pi\) |
0.949048 | − | 0.315130i | \(-0.102048\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.0000 | 0.887066 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.00000 | − | 3.46410i | 0.147043 | − | 0.254686i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.50000 | + | 12.9904i | 0.548454 | + | 0.949951i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.5000 | + | 21.6506i | 0.904468 | + | 1.56658i | 0.821629 | + | 0.570022i | \(0.193065\pi\) |
0.0828388 | + | 0.996563i | \(0.473601\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.0000 | + | 20.7846i | −0.863779 | + | 1.49611i | 0.00447566 | + | 0.999990i | \(0.498575\pi\) |
−0.868255 | + | 0.496119i | \(0.834758\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.00000 | −0.0716115 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.00000 | −0.427482 | −0.213741 | − | 0.976890i | \(-0.568565\pi\) | ||||
−0.213741 | + | 0.976890i | \(0.568565\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.0000 | + | 19.0526i | −0.779769 | + | 1.35060i | 0.152305 | + | 0.988334i | \(0.451330\pi\) |
−0.932075 | + | 0.362267i | \(0.882003\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.00000 | − | 1.73205i | −0.0705346 | − | 0.122169i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.00000 | + | 1.73205i | 0.0698430 | + | 0.120972i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −18.0000 | −1.24509 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.0000 | −0.757271 | −0.378636 | − | 0.925546i | \(-0.623607\pi\) | ||||
−0.378636 | + | 0.925546i | \(0.623607\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.00000 | − | 8.66025i | −0.340997 | − | 0.590624i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.00000 | − | 12.1244i | −0.473016 | − | 0.819288i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.50000 | − | 4.33013i | 0.168168 | − | 0.291276i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.0000 | 0.736614 | 0.368307 | − | 0.929704i | \(-0.379937\pi\) | ||||
0.368307 | + | 0.929704i | \(0.379937\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.00000 | −0.133333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.50000 | − | 14.7224i | 0.564165 | − | 0.977162i | −0.432962 | − | 0.901412i | \(-0.642532\pi\) |
0.997127 | − | 0.0757500i | \(-0.0241351\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.00000 | − | 1.73205i | −0.0660819 | − | 0.114457i | 0.831092 | − | 0.556136i | \(-0.187717\pi\) |
−0.897173 | + | 0.441679i | \(0.854383\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.0000 | + | 20.7846i | 0.786146 | + | 1.36165i | 0.928312 | + | 0.371802i | \(0.121260\pi\) |
−0.142166 | + | 0.989843i | \(0.545407\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.50000 | − | 7.79423i | 0.293548 | − | 0.508439i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.00000 | −0.0649570 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.0000 | −0.970269 | −0.485135 | − | 0.874439i | \(-0.661229\pi\) | ||||
−0.485135 | + | 0.874439i | \(0.661229\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.00000 | + | 3.46410i | −0.128831 | + | 0.223142i | −0.923224 | − | 0.384262i | \(-0.874456\pi\) |
0.794393 | + | 0.607404i | \(0.207789\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.00000 | + | 13.8564i | 0.513200 | + | 0.888889i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.00000 | + | 5.19615i | 0.190885 | + | 0.330623i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.00000 | − | 10.3923i | 0.380235 | − | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.50000 | + | 4.33013i | −0.156556 | + | 0.271163i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.00000 | − | 12.1244i | −0.436648 | − | 0.756297i | 0.560781 | − | 0.827964i | \(-0.310501\pi\) |
−0.997429 | + | 0.0716680i | \(0.977168\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.00000 | − | 8.66025i | −0.309492 | − | 0.536056i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.0000 | + | 22.5167i | −0.801614 | + | 1.38844i | 0.116939 | + | 0.993139i | \(0.462692\pi\) |
−0.918553 | + | 0.395298i | \(0.870641\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.00000 | 0.368577 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.00000 | − | 13.8564i | 0.487769 | − | 0.844840i | −0.512132 | − | 0.858906i | \(-0.671144\pi\) |
0.999901 | + | 0.0140665i | \(0.00447764\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.0000 | − | 24.2487i | −0.850439 | − | 1.47300i | −0.880812 | − | 0.473466i | \(-0.843003\pi\) |
0.0303728 | − | 0.999539i | \(-0.490331\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.50000 | − | 2.59808i | −0.0904534 | − | 0.156670i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.00000 | + | 3.46410i | −0.120168 | + | 0.208138i | −0.919834 | − | 0.392308i | \(-0.871677\pi\) |
0.799666 | + | 0.600446i | \(0.205010\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.00000 | −0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.0000 | 1.61068 | 0.805342 | − | 0.592810i | \(-0.201981\pi\) | ||||
0.805342 | + | 0.592810i | \(0.201981\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.500000 | + | 0.866025i | −0.0297219 | + | 0.0514799i | −0.880504 | − | 0.474039i | \(-0.842796\pi\) |
0.850782 | + | 0.525519i | \(0.176129\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.00000 | − | 5.19615i | −0.177705 | − | 0.307794i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.00000 | − | 6.92820i | −0.235294 | − | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.50000 | + | 7.79423i | −0.263795 | + | 0.456906i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −29.0000 | −1.69420 | −0.847099 | − | 0.531435i | \(-0.821653\pi\) | ||||
−0.847099 | + | 0.531435i | \(0.821653\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.00000 | −0.349334 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.50000 | + | 12.9904i | −0.435194 | + | 0.753778i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.00000 | − | 15.5885i | −0.517036 | − | 0.895533i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.00000 | − | 10.3923i | 0.343559 | − | 0.595062i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.0000 | 1.42683 | 0.713413 | − | 0.700744i | \(-0.247149\pi\) | ||||
0.713413 | + | 0.700744i | \(0.247149\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.0000 | + | 19.0526i | −0.623753 | + | 1.08037i | 0.365028 | + | 0.930997i | \(0.381059\pi\) |
−0.988781 | + | 0.149375i | \(0.952274\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.50000 | − | 11.2583i | −0.367402 | − | 0.636358i | 0.621757 | − | 0.783210i | \(-0.286419\pi\) |
−0.989158 | + | 0.146852i | \(0.953086\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.00000 | − | 8.66025i | −0.280828 | − | 0.486408i | 0.690761 | − | 0.723083i | \(-0.257276\pi\) |
−0.971589 | + | 0.236675i | \(0.923942\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.50000 | − | 12.9904i | 0.419919 | − | 0.727322i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.00000 | −0.111629 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 30.0000 | 1.66924 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.500000 | + | 0.866025i | −0.0277350 | + | 0.0480384i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.50000 | − | 16.4545i | −0.525351 | − | 0.909935i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0000 | + | 17.3205i | 0.549650 | + | 0.952021i | 0.998298 | + | 0.0583130i | \(0.0185721\pi\) |
−0.448649 | + | 0.893708i | \(0.648095\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.00000 | + | 6.92820i | −0.219199 | + | 0.379663i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.00000 | −0.109272 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.0000 | 1.74315 | 0.871576 | − | 0.490261i | \(-0.163099\pi\) | ||||
0.871576 | + | 0.490261i | \(0.163099\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.00000 | + | 3.46410i | −0.108625 | + | 0.188144i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.00000 | − | 5.19615i | −0.162459 | − | 0.281387i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.0000 | + | 31.1769i | −0.966291 | + | 1.67366i | −0.260184 | + | 0.965559i | \(0.583783\pi\) |
−0.706107 | + | 0.708105i | \(0.749550\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.00000 | 0.107058 | 0.0535288 | − | 0.998566i | \(-0.482953\pi\) | ||||
0.0535288 | + | 0.998566i | \(0.482953\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.00000 | 0.266880 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.50000 | + | 2.59808i | −0.0798369 | + | 0.138282i | −0.903179 | − | 0.429263i | \(-0.858773\pi\) |
0.823343 | + | 0.567545i | \(0.192107\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.50000 | + | 14.7224i | −0.447368 | + | 0.774865i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.00000 | 0.104973 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.0000 | −0.732793 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.5000 | + | 19.9186i | −0.600295 | + | 1.03974i | 0.392481 | + | 0.919760i | \(0.371617\pi\) |
−0.992776 | + | 0.119982i | \(0.961716\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.00000 | − | 3.46410i | −0.104116 | − | 0.180334i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.0000 | + | 20.7846i | 0.621336 | + | 1.07619i | 0.989237 | + | 0.146321i | \(0.0467433\pi\) |
−0.367901 | + | 0.929865i | \(0.619923\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.500000 | − | 0.866025i | 0.0258199 | − | 0.0447214i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.00000 | −0.257513 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −32.0000 | −1.64373 | −0.821865 | − | 0.569683i | \(-0.807066\pi\) | ||||
−0.821865 | + | 0.569683i | \(0.807066\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.00000 | + | 5.19615i | −0.153695 | + | 0.266207i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.0000 | − | 27.7128i | −0.817562 | − | 1.41606i | −0.907474 | − | 0.420109i | \(-0.861992\pi\) |
0.0899119 | − | 0.995950i | \(-0.471341\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.0000 | + | 17.3205i | 0.508329 | + | 0.880451i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.50000 | − | 12.9904i | 0.380265 | − | 0.658638i | −0.610835 | − | 0.791758i | \(-0.709166\pi\) |
0.991100 | + | 0.133120i | \(0.0424994\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.0000 | 0.807093 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.500000 | + | 0.866025i | −0.0251577 | + | 0.0435745i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.50000 | − | 9.52628i | −0.276037 | − | 0.478110i | 0.694359 | − | 0.719629i | \(-0.255688\pi\) |
−0.970396 | + | 0.241518i | \(0.922355\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.50000 | − | 11.2583i | −0.324595 | − | 0.562214i | 0.656836 | − | 0.754034i | \(-0.271895\pi\) |
−0.981430 | + | 0.191820i | \(0.938561\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.00000 | + | 1.73205i | −0.0498135 | + | 0.0862796i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.0000 | −0.594818 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.0000 | + | 29.4449i | −0.840596 | + | 1.45595i | 0.0487958 | + | 0.998809i | \(0.484462\pi\) |
−0.889392 | + | 0.457146i | \(0.848872\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.00000 | + | 3.46410i | 0.0986527 | + | 0.170872i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.00000 | − | 10.3923i | −0.294528 | − | 0.510138i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.00000 | − | 13.8564i | 0.391762 | − | 0.678551i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.0000 | −1.07477 | −0.537385 | − | 0.843337i | \(-0.680588\pi\) | ||||
−0.537385 | + | 0.843337i | \(0.680588\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.0000 | 0.633581 | 0.316791 | − | 0.948495i | \(-0.397395\pi\) | ||||
0.316791 | + | 0.948495i | \(0.397395\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.00000 | + | 15.5885i | −0.437595 | + | 0.757937i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.50000 | + | 4.33013i | 0.121268 | + | 0.210042i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.50000 | + | 2.59808i | 0.0724207 | + | 0.125436i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.50000 | + | 2.59808i | −0.0722525 | + | 0.125145i | −0.899888 | − | 0.436121i | \(-0.856352\pi\) |
0.827636 | + | 0.561266i | \(0.189685\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.00000 | −0.0961139 | −0.0480569 | − | 0.998845i | \(-0.515303\pi\) | ||||
−0.0480569 | + | 0.998845i | \(0.515303\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.00000 | 0.239732 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.0000 | − | 24.2487i | −0.668184 | − | 1.15733i | −0.978412 | − | 0.206666i | \(-0.933739\pi\) |
0.310228 | − | 0.950662i | \(-0.399595\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.00000 | − | 15.5885i | −0.427603 | − | 0.740630i | 0.569057 | − | 0.822298i | \(-0.307309\pi\) |
−0.996660 | + | 0.0816684i | \(0.973975\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −18.0000 | −0.851371 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.0000 | −1.55737 | −0.778683 | − | 0.627417i | \(-0.784112\pi\) | ||||
−0.778683 | + | 0.627417i | \(0.784112\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.00000 | − | 5.19615i | 0.141264 | − | 0.244677i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.50000 | + | 7.79423i | 0.211428 | + | 0.366205i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.00000 | − | 15.5885i | −0.421002 | − | 0.729197i | 0.575036 | − | 0.818128i | \(-0.304988\pi\) |
−0.996038 | + | 0.0889312i | \(0.971655\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.5000 | − | 21.6506i | 0.583450 | − | 1.01057i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.0000 | 0.558896 | 0.279448 | − | 0.960161i | \(-0.409849\pi\) | ||||
0.279448 | + | 0.960161i | \(0.409849\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 40.0000 | 1.85896 | 0.929479 | − | 0.368875i | \(-0.120257\pi\) | ||||
0.929479 | + | 0.368875i | \(0.120257\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.00000 | − | 1.73205i | 0.0463739 | − | 0.0803219i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.50000 | + | 2.59808i | 0.0694117 | + | 0.120225i | 0.898642 | − | 0.438682i | \(-0.144554\pi\) |
−0.829231 | + | 0.558906i | \(0.811221\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.00000 | − | 1.73205i | −0.0460776 | − | 0.0798087i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15.0000 | + | 25.9808i | −0.689701 | + | 1.19460i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.00000 | −0.275299 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.0000 | −0.549442 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.00000 | − | 3.46410i | 0.0913823 | − | 0.158279i | −0.816711 | − | 0.577047i | \(-0.804205\pi\) |
0.908093 | + | 0.418769i | \(0.137538\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.00000 | + | 3.46410i | 0.0911922 | + | 0.157949i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.50000 | + | 7.79423i | 0.204334 | + | 0.353918i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.0000 | − | 24.2487i | 0.634401 | − | 1.09881i | −0.352241 | − | 0.935909i | \(-0.614580\pi\) |
0.986642 | − | 0.162905i | \(-0.0520863\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.00000 | 0.361773 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.00000 | −0.135388 | −0.0676941 | − | 0.997706i | \(-0.521564\pi\) | ||||
−0.0676941 | + | 0.997706i | \(0.521564\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.5000 | + | 21.6506i | −0.562972 | + | 0.975096i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.00000 | + | 5.19615i | 0.134840 | + | 0.233550i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.50000 | − | 6.06218i | −0.156682 | − | 0.271380i | 0.776989 | − | 0.629515i | \(-0.216746\pi\) |
−0.933670 | + | 0.358134i | \(0.883413\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.50000 | + | 4.33013i | −0.111692 | + | 0.193456i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −39.0000 | −1.73892 | −0.869462 | − | 0.494000i | \(-0.835534\pi\) | ||||
−0.869462 | + | 0.494000i | \(0.835534\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.0000 | −0.800989 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.00000 | + | 10.3923i | −0.266469 | + | 0.461538i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.0000 | − | 34.6410i | −0.886484 | − | 1.53544i | −0.844003 | − | 0.536339i | \(-0.819807\pi\) |
−0.0424816 | − | 0.999097i | \(-0.513526\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 15.0000 | + | 25.9808i | 0.662266 | + | 1.14708i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.500000 | − | 0.866025i | 0.0220326 | − | 0.0381616i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −27.0000 | −1.18746 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.0000 | −0.658427 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.0000 | − | 22.5167i | 0.569540 | − | 0.986473i | −0.427071 | − | 0.904218i | \(-0.640455\pi\) |
0.996611 | − | 0.0822547i | \(-0.0262121\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.00000 | + | 8.66025i | 0.217803 | + | 0.377247i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.5000 | − | 19.9186i | 0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.0000 | 0.520756 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.00000 | −0.0866296 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.00000 | + | 1.73205i | −0.0432338 | + | 0.0748831i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.0000 | − | 17.3205i | −0.431532 | − | 0.747435i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.50000 | − | 12.9904i | −0.322450 | − | 0.558500i | 0.658543 | − | 0.752543i | \(-0.271173\pi\) |
−0.980993 | + | 0.194043i | \(0.937840\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.00000 | + | 8.66025i | −0.214571 | + | 0.371647i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −19.0000 | −0.813871 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.0000 | 0.855138 | 0.427569 | − | 0.903983i | \(-0.359370\pi\) | ||||
0.427569 | + | 0.903983i | \(0.359370\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.0000 | + | 20.7846i | −0.512148 | + | 0.887066i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.0000 | − | 25.9808i | −0.639021 | − | 1.10682i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.00000 | − | 3.46410i | −0.0848953 | − | 0.147043i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.00000 | − | 10.3923i | 0.254228 | − | 0.440336i | −0.710457 | − | 0.703740i | \(-0.751512\pi\) |
0.964686 | + | 0.263404i | \(0.0848453\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.0000 | 0.422955 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.0000 | 0.633300 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.0000 | − | 17.3205i | 0.421450 | − | 0.729972i | −0.574632 | − | 0.818412i | \(-0.694855\pi\) |
0.996082 | + | 0.0884397i | \(0.0281881\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.00000 | + | 3.46410i | 0.0841406 | + | 0.145736i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.00000 | − | 1.73205i | −0.0419222 | − | 0.0726113i | 0.844303 | − | 0.535866i | \(-0.180015\pi\) |
−0.886225 | + | 0.463255i | \(0.846681\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.0000 | + | 31.1769i | −0.753277 | + | 1.30471i | 0.192950 | + | 0.981209i | \(0.438194\pi\) |
−0.946227 | + | 0.323505i | \(0.895139\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 25.0000 | 1.04439 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.50000 | + | 7.79423i | −0.187337 | + | 0.324478i | −0.944362 | − | 0.328909i | \(-0.893319\pi\) |
0.757024 | + | 0.653387i | \(0.226652\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.0000 | + | 20.7846i | 0.498703 | + | 0.863779i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.00000 | − | 15.5885i | −0.372742 | − | 0.645608i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.00000 | − | 1.73205i | 0.0413449 | − | 0.0716115i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.0000 | −0.825488 | −0.412744 | − | 0.910847i | \(-0.635430\pi\) | ||||
−0.412744 | + | 0.910847i | \(0.635430\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.0000 | −0.494451 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.00000 | + | 5.19615i | −0.123404 | + | 0.213741i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.50000 | + | 2.59808i | 0.0615976 | + | 0.106690i | 0.895180 | − | 0.445705i | \(-0.147047\pi\) |
−0.833582 | + | 0.552396i | \(0.813714\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.0000 | + | 19.0526i | 0.450200 | + | 0.779769i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.50000 | − | 14.7224i | 0.347301 | − | 0.601542i | −0.638468 | − | 0.769648i | \(-0.720432\pi\) |
0.985769 | + | 0.168106i | \(0.0537650\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.0000 | 0.897399 | 0.448699 | − | 0.893683i | \(-0.351887\pi\) | ||||
0.448699 | + | 0.893683i | \(0.351887\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.00000 | 0.162893 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.00000 | − | 1.73205i | 0.0406558 | − | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.50000 | − | 11.2583i | −0.263827 | − | 0.456962i | 0.703429 | − | 0.710766i | \(-0.251651\pi\) |
−0.967256 | + | 0.253804i | \(0.918318\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.50000 | + | 7.79423i | 0.182051 | + | 0.315321i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.0000 | + | 19.0526i | −0.444286 | + | 0.769526i | −0.998002 | − | 0.0631797i | \(-0.979876\pi\) |
0.553716 | + | 0.832705i | \(0.313209\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.00000 | 0.0806478 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.0000 | −0.483102 | −0.241551 | − | 0.970388i | \(-0.577656\pi\) | ||||
−0.241551 | + | 0.970388i | \(0.577656\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.0000 | − | 38.1051i | 0.884255 | − | 1.53157i | 0.0376891 | − | 0.999290i | \(-0.488000\pi\) |
0.846566 | − | 0.532284i | \(-0.178666\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.00000 | + | 15.5885i | −0.359425 | + | 0.622543i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.0000 | 0.797452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.0000 | −1.47295 | −0.736473 | − | 0.676467i | \(-0.763510\pi\) | ||||
−0.736473 | + | 0.676467i | \(0.763510\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.50000 | + | 9.52628i | −0.218605 | + | 0.378636i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.00000 | + | 5.19615i | 0.119051 | + | 0.206203i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.00000 | − | 8.66025i | 0.197488 | − | 0.342059i | −0.750225 | − | 0.661182i | \(-0.770055\pi\) |
0.947713 | + | 0.319123i | \(0.103388\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.00000 | −0.354925 | −0.177463 | − | 0.984128i | \(-0.556789\pi\) | ||||
−0.177463 | + | 0.984128i | \(0.556789\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.0000 | −0.393750 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.0000 | − | 17.3205i | 0.393141 | − | 0.680939i | −0.599721 | − | 0.800209i | \(-0.704722\pi\) |
0.992862 | + | 0.119269i | \(0.0380552\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.00000 | + | 15.5885i | 0.353281 | + | 0.611900i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.00000 | + | 12.1244i | 0.273931 | + | 0.474463i | 0.969865 | − | 0.243643i | \(-0.0783426\pi\) |
−0.695934 | + | 0.718106i | \(0.745009\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.00000 | − | 13.8564i | 0.312586 | − | 0.541415i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 28.0000 | 1.09238 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.0000 | −1.28550 | −0.642749 | − | 0.766077i | \(-0.722206\pi\) | ||||
−0.642749 | + | 0.766077i | \(0.722206\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.0000 | + | 38.1051i | −0.855701 | + | 1.48212i | 0.0202925 | + | 0.999794i | \(0.493540\pi\) |
−0.875993 | + | 0.482323i | \(0.839793\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.50000 | − | 4.33013i | −0.0970920 | − | 0.168168i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.50000 | − | 9.52628i | 0.212642 | − | 0.368307i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −36.0000 | −1.38976 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.0000 | −1.54189 | −0.770943 | − | 0.636904i | \(-0.780215\pi\) | ||||
−0.770943 | + | 0.636904i | \(0.780215\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.50000 | + | 4.33013i | −0.0962250 | + | 0.166667i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.50000 | + | 2.59808i | 0.0576497 | + | 0.0998522i | 0.893410 | − | 0.449242i | \(-0.148306\pi\) |
−0.835760 | + | 0.549095i | \(0.814973\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.50000 | − | 14.7224i | −0.325721 | − | 0.564165i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.0000 | − | 31.1769i | 0.688751 | − | 1.19295i | −0.283491 | − | 0.958975i | \(-0.591493\pi\) |
0.972242 | − | 0.233977i | \(-0.0751739\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.00000 | 0.152832 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.00000 | −0.0763048 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.00000 | + | 5.19615i | −0.114291 | + | 0.197958i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.00000 | − | 10.3923i | −0.228251 | − | 0.395342i | 0.729039 | − | 0.684472i | \(-0.239967\pi\) |
−0.957290 | + | 0.289130i | \(0.906634\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.00000 | − | 13.8564i | −0.303457 | − | 0.525603i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.00000 | + | 8.66025i | −0.189389 | + | 0.328031i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 24.0000 | 0.907763 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.0000 | 1.01978 | 0.509888 | − | 0.860241i | \(-0.329687\pi\) | ||||
0.509888 | + | 0.860241i | \(0.329687\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.0000 | + | 20.7846i | −0.452589 | + | 0.783906i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.50000 | − | 7.79423i | −0.169480 | − | 0.293548i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.5000 | − | 23.3827i | −0.507003 | − | 0.878155i | −0.999967 | − | 0.00810550i | \(-0.997420\pi\) |
0.492964 | − | 0.870050i | \(-0.335913\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.00000 | − | 1.73205i | 0.0375029 | − | 0.0649570i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.00000 | 0.112194 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.50000 | + | 12.9904i | −0.280093 | + | 0.485135i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.0000 | − | 20.7846i | −0.447524 | − | 0.775135i | 0.550700 | − | 0.834703i | \(-0.314361\pi\) |
−0.998224 | + | 0.0595683i | \(0.981028\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.00000 | + | 3.46410i | 0.0743808 | + | 0.128831i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.50000 | − | 4.33013i | 0.0928477 | − | 0.160817i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.0000 | 1.18681 | 0.593407 | − | 0.804902i | \(-0.297782\pi\) | ||||
0.593407 | + | 0.804902i | \(0.297782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 25.0000 | − | 43.3013i | 0.924658 | − | 1.60156i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.5000 | + | 44.1673i | 0.941864 | + | 1.63136i | 0.761912 | + | 0.647681i | \(0.224261\pi\) |
0.179952 | + | 0.983675i | \(0.442406\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.00000 | + | 5.19615i | 0.110506 | + | 0.191403i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.5000 | − | 28.5788i | 0.606962 | − | 1.05129i | −0.384776 | − | 0.923010i | \(-0.625721\pi\) |
0.991738 | − | 0.128279i | \(-0.0409454\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.00000 | 0.220416 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 54.0000 | 1.98107 | 0.990534 | − | 0.137268i | \(-0.0438322\pi\) | ||||
0.990534 | + | 0.137268i | \(0.0438322\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.00000 | + | 15.5885i | −0.329734 | + | 0.571117i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.0000 | + | 20.7846i | 0.439057 | + | 0.760469i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.5000 | + | 26.8468i | 0.565603 | + | 0.979653i | 0.996993 | + | 0.0774878i | \(0.0246899\pi\) |
−0.431390 | + | 0.902165i | \(0.641977\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.00000 | + | 10.3923i | −0.218652 | + | 0.378717i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.00000 | 0.327544 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.0000 | 0.872295 | 0.436147 | − | 0.899875i | \(-0.356343\pi\) | ||||
0.436147 | + | 0.899875i | \(0.356343\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.0000 | − | 20.7846i | −0.435000 | − | 0.753442i | 0.562296 | − | 0.826936i | \(-0.309918\pi\) |
−0.997296 | + | 0.0734946i | \(0.976585\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.00000 | − | 8.66025i | −0.180775 | − | 0.313112i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.00000 | − | 5.19615i | 0.108324 | − | 0.187622i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.0000 | −1.22607 | −0.613036 | − | 0.790055i | \(-0.710052\pi\) | ||||
−0.613036 | + | 0.790055i | \(0.710052\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.0000 | −0.504198 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.5000 | − | 19.9186i | 0.413626 | − | 0.716422i | −0.581657 | − | 0.813434i | \(-0.697595\pi\) |
0.995283 | + | 0.0970125i | \(0.0309287\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.00000 | − | 1.73205i | −0.0359211 | − | 0.0622171i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.00000 | − | 10.3923i | −0.214972 | − | 0.372343i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −25.0000 | −0.893427 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.00000 | −0.0713831 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.5000 | − | 38.9711i | 0.802038 | − | 1.38917i | −0.116234 | − | 0.993222i | \(-0.537082\pi\) |
0.918272 | − | 0.395949i | \(-0.129584\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13.0000 | + | 22.5167i | 0.462812 | + | 0.801614i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.00000 | + | 10.3923i | 0.213066 | + | 0.369042i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.00000 | − | 5.19615i | 0.106399 | − | 0.184289i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 39.0000 | 1.38145 | 0.690725 | − | 0.723117i | \(-0.257291\pi\) | ||||
0.690725 | + | 0.723117i | \(0.257291\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 45.0000 | 1.59199 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 21.0000 | + | 36.3731i | 0.741074 | + | 1.28358i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.00000 | − | 13.8564i | −0.281613 | − | 0.487769i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.50000 | − | 2.59808i | 0.0527372 | − | 0.0913435i | −0.838452 | − | 0.544976i | \(-0.816539\pi\) |
0.891189 | + | 0.453632i | \(0.149872\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.0000 | 1.40459 | 0.702295 | − | 0.711886i | \(-0.252159\pi\) | ||||
0.702295 | + | 0.711886i | \(0.252159\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −28.0000 | −0.982003 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.00000 | − | 6.92820i | 0.140114 | − | 0.242684i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30.0000 | + | 51.9615i | 1.04957 | + | 1.81790i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.50000 | − | 4.33013i | −0.0872506 | − | 0.151122i | 0.819097 | − | 0.573654i | \(-0.194475\pi\) |
−0.906348 | + | 0.422532i | \(0.861141\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.0000 | + | 22.5167i | −0.453152 | + | 0.784881i | −0.998580 | − | 0.0532760i | \(-0.983034\pi\) |
0.545428 | + | 0.838157i | \(0.316367\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.00000 | −0.104447 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.00000 | −0.278187 | −0.139094 | − | 0.990279i | \(-0.544419\pi\) | ||||
−0.139094 | + | 0.990279i | \(0.544419\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.00000 | − | 8.66025i | 0.173657 | − | 0.300783i | −0.766039 | − | 0.642795i | \(-0.777775\pi\) |
0.939696 | + | 0.342012i | \(0.111108\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.00000 | + | 3.46410i | 0.0693792 | + | 0.120168i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.50000 | + | 4.33013i | 0.0865161 | + | 0.149850i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.00000 | + | 8.66025i | −0.172825 | + | 0.299342i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −52.0000 | −1.79524 | −0.897620 | − | 0.440771i | \(-0.854705\pi\) | ||||
−0.897620 | + | 0.440771i | \(0.854705\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.5000 | − | 23.3827i | 0.464965 | − | 0.805342i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.00000 | + | 10.3923i | 0.206406 | + | 0.357506i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.500000 | + | 0.866025i | 0.0171600 | + | 0.0297219i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.0000 | −0.753266 | −0.376633 | − | 0.926363i | \(-0.622918\pi\) | ||||
−0.376633 | + | 0.926363i | \(0.622918\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.0000 | 0.410391 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.0000 | − | 32.9090i | 0.649028 | − | 1.12415i | −0.334328 | − | 0.942457i | \(-0.608509\pi\) |
0.983355 | − | 0.181692i | \(-0.0581574\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.0000 | + | 17.3205i | 0.341196 | + | 0.590968i | 0.984655 | − | 0.174512i | \(-0.0558348\pi\) |
−0.643459 | + | 0.765480i | \(0.722501\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.00000 | + | 15.5885i | 0.306364 | + | 0.530637i | 0.977564 | − | 0.210639i | \(-0.0675543\pi\) |
−0.671200 | + | 0.741276i | \(0.734221\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.50000 | + | 12.9904i | −0.255008 | + | 0.441686i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.00000 | −0.271694 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.00000 | 0.101768 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.00000 | − | 1.73205i | 0.0338837 | − | 0.0586883i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.00000 | − | 15.5885i | −0.304604 | − | 0.527589i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.0000 | − | 25.9808i | −0.506514 | − | 0.877308i | −0.999972 | − | 0.00753813i | \(-0.997601\pi\) |
0.493458 | − | 0.869770i | \(-0.335733\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.5000 | + | 25.1147i | −0.489073 | + | 0.847099i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.0000 | 1.21150 | 0.605748 | − | 0.795656i | \(-0.292874\pi\) | ||||
0.605748 | + | 0.795656i | \(0.292874\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.00000 | + | 5.19615i | −0.100844 | + | 0.174667i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.0000 | − | 27.7128i | −0.537227 | − | 0.930505i | −0.999052 | − | 0.0435339i | \(-0.986138\pi\) |
0.461825 | − | 0.886971i | \(-0.347195\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.50000 | − | 2.59808i | −0.0502519 | − | 0.0870388i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −27.0000 | + | 46.7654i | −0.903521 | + | 1.56494i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.0000 | −0.668526 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.00000 | − | 8.66025i | 0.166759 | − | 0.288836i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.0000 | + | 25.9808i | 0.499722 | + | 0.865545i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.00000 | + | 8.66025i | 0.166206 | + | 0.287877i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.0000 | + | 17.3205i | −0.332045 | + | 0.575118i | −0.982913 | − | 0.184073i | \(-0.941072\pi\) |
0.650868 | + | 0.759191i | \(0.274405\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 36.0000 | 1.19404 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.0000 | 0.530104 | 0.265052 | − | 0.964234i | \(-0.414611\pi\) | ||||
0.265052 | + | 0.964234i | \(0.414611\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.0000 | + | 31.1769i | −0.595713 | + | 1.03181i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.00000 | − | 10.3923i | −0.198354 | − | 0.343559i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.50000 | − | 14.7224i | −0.280389 | − | 0.485648i | 0.691091 | − | 0.722767i | \(-0.257130\pi\) |
−0.971481 | + | 0.237119i | \(0.923797\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.5000 | − | 21.6506i | 0.411889 | − | 0.713413i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.00000 | −0.131519 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.00000 | + | 1.73205i | −0.0328443 | + | 0.0568880i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.0000 | + | 36.3731i | 0.688988 | + | 1.19336i | 0.972166 | + | 0.234294i | \(0.0752779\pi\) |
−0.283178 | + | 0.959067i | \(0.591389\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.0000 | + | 19.0526i | 0.360124 | + | 0.623753i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.50000 | − | 12.9904i | 0.245276 | − | 0.424831i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.0000 | 1.40475 | 0.702374 | − | 0.711808i | \(-0.252123\pi\) | ||||
0.702374 | + | 0.711808i | \(0.252123\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −13.0000 | −0.424239 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.00000 | − | 10.3923i | 0.195594 | − | 0.338779i | −0.751501 | − | 0.659732i | \(-0.770670\pi\) |
0.947095 | + | 0.320953i | \(0.104003\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.0000 | + | 22.5167i | 0.422443 | + | 0.731693i | 0.996178 | − | 0.0873481i | \(-0.0278392\pi\) |
−0.573735 | + | 0.819041i | \(0.694506\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.00000 | − | 12.1244i | 0.227230 | − | 0.393573i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.0000 | −0.324272 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34.0000 | −1.10137 | −0.550684 | − | 0.834714i | \(-0.685633\pi\) | ||||
−0.550684 | + | 0.834714i | \(0.685633\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.5000 | − | 21.6506i | 0.404491 | − | 0.700598i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.50000 | − | 12.9904i | −0.242441 | − | 0.419919i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | + | 23.3827i | 0.435484 | + | 0.754280i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.00000 | − | 3.46410i | 0.0644491 | − | 0.111629i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 24.0000 | 0.772587 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −50.0000 | −1.60789 | −0.803946 | − | 0.594703i | \(-0.797270\pi\) | ||||
−0.803946 | + | 0.594703i | \(0.797270\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 15.0000 | − | 25.9808i | 0.481869 | − | 0.834622i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.00000 | + | 12.1244i | 0.224641 | + | 0.389089i | 0.956212 | − | 0.292676i | \(-0.0945458\pi\) |
−0.731571 | + | 0.681765i | \(0.761212\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.500000 | + | 0.866025i | 0.0160128 | + | 0.0277350i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.00000 | − | 15.5885i | 0.287936 | − | 0.498719i | −0.685381 | − | 0.728184i | \(-0.740364\pi\) |
0.973317 | + | 0.229465i | \(0.0736978\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 38.0000 | 1.21325 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17.5000 | − | 30.3109i | 0.558163 | − | 0.966767i | −0.439487 | − | 0.898249i | \(-0.644840\pi\) |
0.997650 | − | 0.0685181i | \(-0.0218271\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.00000 | + | 5.19615i | 0.0955879 | + | 0.165563i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.0000 | + | 31.1769i | −0.571789 | + | 0.990367i | 0.424594 | + | 0.905384i | \(0.360417\pi\) |
−0.996382 | + | 0.0849833i | \(0.972916\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20.0000 | 0.634681 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.0000 | 0.697447 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.50000 | + | 12.9904i | −0.237527 | + | 0.411409i | −0.960004 | − | 0.279986i | \(-0.909670\pi\) |
0.722477 | + | 0.691395i | \(0.243004\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10.0000 | + | 17.3205i | 0.316386 | + | 0.547997i |
(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 | 1960.2.q.j.361.1 | 2 | ||
7.2 | even | 3 | inner | 1960.2.q.j.961.1 | 2 | ||
7.3 | odd | 6 | 1960.2.a.j.1.1 | yes | 1 | ||
7.4 | even | 3 | 1960.2.a.f.1.1 | ✓ | 1 | ||
7.5 | odd | 6 | 1960.2.q.f.961.1 | 2 | |||
7.6 | odd | 2 | 1960.2.q.f.361.1 | 2 | |||
28.3 | even | 6 | 3920.2.a.l.1.1 | 1 | |||
28.11 | odd | 6 | 3920.2.a.x.1.1 | 1 | |||
35.4 | even | 6 | 9800.2.a.bd.1.1 | 1 | |||
35.24 | odd | 6 | 9800.2.a.t.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1960.2.a.f.1.1 | ✓ | 1 | 7.4 | even | 3 | ||
1960.2.a.j.1.1 | yes | 1 | 7.3 | odd | 6 | ||
1960.2.q.f.361.1 | 2 | 7.6 | odd | 2 | |||
1960.2.q.f.961.1 | 2 | 7.5 | odd | 6 | |||
1960.2.q.j.361.1 | 2 | 1.1 | even | 1 | trivial | ||
1960.2.q.j.961.1 | 2 | 7.2 | even | 3 | inner | ||
3920.2.a.l.1.1 | 1 | 28.3 | even | 6 | |||
3920.2.a.x.1.1 | 1 | 28.11 | odd | 6 | |||
9800.2.a.t.1.1 | 1 | 35.24 | odd | 6 | |||
9800.2.a.bd.1.1 | 1 | 35.4 | even | 6 |