Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(889,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.889");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.d (of order \(2\), degree \(1\), 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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 889.2 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1110.889 |
Dual form | 1110.2.d.b.889.1 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.00000 | − | 2.00000i | −0.447214 | − | 0.894427i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | − | 5.00000i | − | 1.88982i | −0.327327 | − | 0.944911i | \(-0.606148\pi\) | ||
0.327327 | − | 0.944911i | \(-0.393852\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 2.00000 | − | 1.00000i | 0.632456 | − | 0.316228i | ||||
\(11\) | 1.00000 | 0.301511 | 0.150756 | − | 0.988571i | \(-0.451829\pi\) | ||||
0.150756 | + | 0.988571i | \(0.451829\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | 5.00000 | 1.33631 | ||||||||
\(15\) | −2.00000 | + | 1.00000i | −0.516398 | + | 0.258199i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 3.00000i | − | 0.727607i | −0.931476 | − | 0.363803i | \(-0.881478\pi\) | ||
0.931476 | − | 0.363803i | \(-0.118522\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | −8.00000 | −1.83533 | −0.917663 | − | 0.397360i | \(-0.869927\pi\) | ||||
−0.917663 | + | 0.397360i | \(0.869927\pi\) | |||||||
\(20\) | 1.00000 | + | 2.00000i | 0.223607 | + | 0.447214i | ||||
\(21\) | −5.00000 | −1.09109 | ||||||||
\(22\) | 1.00000i | 0.213201i | ||||||||
\(23\) | 8.00000i | 1.66812i | 0.551677 | + | 0.834058i | \(0.313988\pi\) | ||||
−0.551677 | + | 0.834058i | \(0.686012\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −3.00000 | + | 4.00000i | −0.600000 | + | 0.800000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 5.00000i | 0.944911i | ||||||||
\(29\) | 5.00000 | 0.928477 | 0.464238 | − | 0.885710i | \(-0.346328\pi\) | ||||
0.464238 | + | 0.885710i | \(0.346328\pi\) | |||||||
\(30\) | −1.00000 | − | 2.00000i | −0.182574 | − | 0.365148i | ||||
\(31\) | 3.00000 | 0.538816 | 0.269408 | − | 0.963026i | \(-0.413172\pi\) | ||||
0.269408 | + | 0.963026i | \(0.413172\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | − | 1.00000i | − | 0.174078i | ||||||
\(34\) | 3.00000 | 0.514496 | ||||||||
\(35\) | −10.0000 | + | 5.00000i | −1.69031 | + | 0.845154i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.00000i | 0.164399i | ||||||||
\(38\) | − | 8.00000i | − | 1.29777i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.00000 | + | 1.00000i | −0.316228 | + | 0.158114i | ||||
\(41\) | −5.00000 | −0.780869 | −0.390434 | − | 0.920631i | \(-0.627675\pi\) | ||||
−0.390434 | + | 0.920631i | \(0.627675\pi\) | |||||||
\(42\) | − | 5.00000i | − | 0.771517i | ||||||
\(43\) | 9.00000i | 1.37249i | 0.727372 | + | 0.686244i | \(0.240742\pi\) | ||||
−0.727372 | + | 0.686244i | \(0.759258\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 1.00000 | + | 2.00000i | 0.149071 | + | 0.298142i | ||||
\(46\) | −8.00000 | −1.17954 | ||||||||
\(47\) | − | 12.0000i | − | 1.75038i | −0.483779 | − | 0.875190i | \(-0.660736\pi\) | ||
0.483779 | − | 0.875190i | \(-0.339264\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | −18.0000 | −2.57143 | ||||||||
\(50\) | −4.00000 | − | 3.00000i | −0.565685 | − | 0.424264i | ||||
\(51\) | −3.00000 | −0.420084 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 5.00000i | − | 0.686803i | −0.939189 | − | 0.343401i | \(-0.888421\pi\) | ||
0.939189 | − | 0.343401i | \(-0.111579\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −1.00000 | − | 2.00000i | −0.134840 | − | 0.269680i | ||||
\(56\) | −5.00000 | −0.668153 | ||||||||
\(57\) | 8.00000i | 1.05963i | ||||||||
\(58\) | 5.00000i | 0.656532i | ||||||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 2.00000 | − | 1.00000i | 0.258199 | − | 0.129099i | ||||
\(61\) | −9.00000 | −1.15233 | −0.576166 | − | 0.817333i | \(-0.695452\pi\) | ||||
−0.576166 | + | 0.817333i | \(0.695452\pi\) | |||||||
\(62\) | 3.00000i | 0.381000i | ||||||||
\(63\) | 5.00000i | 0.629941i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.00000 | 0.123091 | ||||||||
\(67\) | − | 8.00000i | − | 0.977356i | −0.872464 | − | 0.488678i | \(-0.837479\pi\) | ||
0.872464 | − | 0.488678i | \(-0.162521\pi\) | |||||||
\(68\) | 3.00000i | 0.363803i | ||||||||
\(69\) | 8.00000 | 0.963087 | ||||||||
\(70\) | −5.00000 | − | 10.0000i | −0.597614 | − | 1.19523i | ||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | − | 2.00000i | − | 0.234082i | −0.993127 | − | 0.117041i | \(-0.962659\pi\) | ||
0.993127 | − | 0.117041i | \(-0.0373409\pi\) | |||||||
\(74\) | −1.00000 | −0.116248 | ||||||||
\(75\) | 4.00000 | + | 3.00000i | 0.461880 | + | 0.346410i | ||||
\(76\) | 8.00000 | 0.917663 | ||||||||
\(77\) | − | 5.00000i | − | 0.569803i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | −1.00000 | − | 2.00000i | −0.111803 | − | 0.223607i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 5.00000i | − | 0.552158i | ||||||
\(83\) | 4.00000i | 0.439057i | 0.975606 | + | 0.219529i | \(0.0704519\pi\) | ||||
−0.975606 | + | 0.219529i | \(0.929548\pi\) | |||||||
\(84\) | 5.00000 | 0.545545 | ||||||||
\(85\) | −6.00000 | + | 3.00000i | −0.650791 | + | 0.325396i | ||||
\(86\) | −9.00000 | −0.970495 | ||||||||
\(87\) | − | 5.00000i | − | 0.536056i | ||||||
\(88\) | − | 1.00000i | − | 0.106600i | ||||||
\(89\) | 4.00000 | 0.423999 | 0.212000 | − | 0.977270i | \(-0.432002\pi\) | ||||
0.212000 | + | 0.977270i | \(0.432002\pi\) | |||||||
\(90\) | −2.00000 | + | 1.00000i | −0.210819 | + | 0.105409i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 8.00000i | − | 0.834058i | ||||||
\(93\) | − | 3.00000i | − | 0.311086i | ||||||
\(94\) | 12.0000 | 1.23771 | ||||||||
\(95\) | 8.00000 | + | 16.0000i | 0.820783 | + | 1.64157i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | − | 9.00000i | − | 0.913812i | −0.889515 | − | 0.456906i | \(-0.848958\pi\) | ||
0.889515 | − | 0.456906i | \(-0.151042\pi\) | |||||||
\(98\) | − | 18.0000i | − | 1.81827i | ||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 3.00000 | − | 4.00000i | 0.300000 | − | 0.400000i | ||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | − | 3.00000i | − | 0.297044i | ||||||
\(103\) | − | 4.00000i | − | 0.394132i | −0.980390 | − | 0.197066i | \(-0.936859\pi\) | ||
0.980390 | − | 0.197066i | \(-0.0631413\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.00000 | + | 10.0000i | 0.487950 | + | 0.975900i | ||||
\(106\) | 5.00000 | 0.485643 | ||||||||
\(107\) | 2.00000i | 0.193347i | 0.995316 | + | 0.0966736i | \(0.0308203\pi\) | ||||
−0.995316 | + | 0.0966736i | \(0.969180\pi\) | |||||||
\(108\) | − | 1.00000i | − | 0.0962250i | ||||||
\(109\) | −11.0000 | −1.05361 | −0.526804 | − | 0.849987i | \(-0.676610\pi\) | ||||
−0.526804 | + | 0.849987i | \(0.676610\pi\) | |||||||
\(110\) | 2.00000 | − | 1.00000i | 0.190693 | − | 0.0953463i | ||||
\(111\) | 1.00000 | 0.0949158 | ||||||||
\(112\) | − | 5.00000i | − | 0.472456i | ||||||
\(113\) | − | 15.0000i | − | 1.41108i | −0.708669 | − | 0.705541i | \(-0.750704\pi\) | ||
0.708669 | − | 0.705541i | \(-0.249296\pi\) | |||||||
\(114\) | −8.00000 | −0.749269 | ||||||||
\(115\) | 16.0000 | − | 8.00000i | 1.49201 | − | 0.746004i | ||||
\(116\) | −5.00000 | −0.464238 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.00000i | 0.368230i | ||||||||
\(119\) | −15.0000 | −1.37505 | ||||||||
\(120\) | 1.00000 | + | 2.00000i | 0.0912871 | + | 0.182574i | ||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | − | 9.00000i | − | 0.814822i | ||||||
\(123\) | 5.00000i | 0.450835i | ||||||||
\(124\) | −3.00000 | −0.269408 | ||||||||
\(125\) | 11.0000 | + | 2.00000i | 0.983870 | + | 0.178885i | ||||
\(126\) | −5.00000 | −0.445435 | ||||||||
\(127\) | 8.00000i | 0.709885i | 0.934888 | + | 0.354943i | \(0.115500\pi\) | ||||
−0.934888 | + | 0.354943i | \(0.884500\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 9.00000 | 0.792406 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.00000 | −0.524222 | −0.262111 | − | 0.965038i | \(-0.584419\pi\) | ||||
−0.262111 | + | 0.965038i | \(0.584419\pi\) | |||||||
\(132\) | 1.00000i | 0.0870388i | ||||||||
\(133\) | 40.0000i | 3.46844i | ||||||||
\(134\) | 8.00000 | 0.691095 | ||||||||
\(135\) | 2.00000 | − | 1.00000i | 0.172133 | − | 0.0860663i | ||||
\(136\) | −3.00000 | −0.257248 | ||||||||
\(137\) | − | 6.00000i | − | 0.512615i | −0.966595 | − | 0.256307i | \(-0.917494\pi\) | ||
0.966595 | − | 0.256307i | \(-0.0825059\pi\) | |||||||
\(138\) | 8.00000i | 0.681005i | ||||||||
\(139\) | −5.00000 | −0.424094 | −0.212047 | − | 0.977259i | \(-0.568013\pi\) | ||||
−0.212047 | + | 0.977259i | \(0.568013\pi\) | |||||||
\(140\) | 10.0000 | − | 5.00000i | 0.845154 | − | 0.422577i | ||||
\(141\) | −12.0000 | −1.01058 | ||||||||
\(142\) | 6.00000i | 0.503509i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | −5.00000 | − | 10.0000i | −0.415227 | − | 0.830455i | ||||
\(146\) | 2.00000 | 0.165521 | ||||||||
\(147\) | 18.0000i | 1.48461i | ||||||||
\(148\) | − | 1.00000i | − | 0.0821995i | ||||||
\(149\) | 20.0000 | 1.63846 | 0.819232 | − | 0.573462i | \(-0.194400\pi\) | ||||
0.819232 | + | 0.573462i | \(0.194400\pi\) | |||||||
\(150\) | −3.00000 | + | 4.00000i | −0.244949 | + | 0.326599i | ||||
\(151\) | −10.0000 | −0.813788 | −0.406894 | − | 0.913475i | \(-0.633388\pi\) | ||||
−0.406894 | + | 0.913475i | \(0.633388\pi\) | |||||||
\(152\) | 8.00000i | 0.648886i | ||||||||
\(153\) | 3.00000i | 0.242536i | ||||||||
\(154\) | 5.00000 | 0.402911 | ||||||||
\(155\) | −3.00000 | − | 6.00000i | −0.240966 | − | 0.481932i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 11.0000i | − | 0.877896i | −0.898513 | − | 0.438948i | \(-0.855351\pi\) | ||
0.898513 | − | 0.438948i | \(-0.144649\pi\) | |||||||
\(158\) | 8.00000i | 0.636446i | ||||||||
\(159\) | −5.00000 | −0.396526 | ||||||||
\(160\) | 2.00000 | − | 1.00000i | 0.158114 | − | 0.0790569i | ||||
\(161\) | 40.0000 | 3.15244 | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 1.00000i | 0.0783260i | 0.999233 | + | 0.0391630i | \(0.0124692\pi\) | ||||
−0.999233 | + | 0.0391630i | \(0.987531\pi\) | |||||||
\(164\) | 5.00000 | 0.390434 | ||||||||
\(165\) | −2.00000 | + | 1.00000i | −0.155700 | + | 0.0778499i | ||||
\(166\) | −4.00000 | −0.310460 | ||||||||
\(167\) | − | 2.00000i | − | 0.154765i | −0.997001 | − | 0.0773823i | \(-0.975344\pi\) | ||
0.997001 | − | 0.0773823i | \(-0.0246562\pi\) | |||||||
\(168\) | 5.00000i | 0.385758i | ||||||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | −3.00000 | − | 6.00000i | −0.230089 | − | 0.460179i | ||||
\(171\) | 8.00000 | 0.611775 | ||||||||
\(172\) | − | 9.00000i | − | 0.686244i | ||||||
\(173\) | − | 21.0000i | − | 1.59660i | −0.602260 | − | 0.798300i | \(-0.705733\pi\) | ||
0.602260 | − | 0.798300i | \(-0.294267\pi\) | |||||||
\(174\) | 5.00000 | 0.379049 | ||||||||
\(175\) | 20.0000 | + | 15.0000i | 1.51186 | + | 1.13389i | ||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | − | 4.00000i | − | 0.300658i | ||||||
\(178\) | 4.00000i | 0.299813i | ||||||||
\(179\) | 6.00000 | 0.448461 | 0.224231 | − | 0.974536i | \(-0.428013\pi\) | ||||
0.224231 | + | 0.974536i | \(0.428013\pi\) | |||||||
\(180\) | −1.00000 | − | 2.00000i | −0.0745356 | − | 0.149071i | ||||
\(181\) | −12.0000 | −0.891953 | −0.445976 | − | 0.895045i | \(-0.647144\pi\) | ||||
−0.445976 | + | 0.895045i | \(0.647144\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.00000i | 0.665299i | ||||||||
\(184\) | 8.00000 | 0.589768 | ||||||||
\(185\) | 2.00000 | − | 1.00000i | 0.147043 | − | 0.0735215i | ||||
\(186\) | 3.00000 | 0.219971 | ||||||||
\(187\) | − | 3.00000i | − | 0.219382i | ||||||
\(188\) | 12.0000i | 0.875190i | ||||||||
\(189\) | 5.00000 | 0.363696 | ||||||||
\(190\) | −16.0000 | + | 8.00000i | −1.16076 | + | 0.580381i | ||||
\(191\) | −27.0000 | −1.95365 | −0.976826 | − | 0.214036i | \(-0.931339\pi\) | ||||
−0.976826 | + | 0.214036i | \(0.931339\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | − | 10.0000i | − | 0.719816i | −0.932988 | − | 0.359908i | \(-0.882808\pi\) | ||
0.932988 | − | 0.359908i | \(-0.117192\pi\) | |||||||
\(194\) | 9.00000 | 0.646162 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 18.0000 | 1.28571 | ||||||||
\(197\) | 6.00000i | 0.427482i | 0.976890 | + | 0.213741i | \(0.0685649\pi\) | ||||
−0.976890 | + | 0.213741i | \(0.931435\pi\) | |||||||
\(198\) | − | 1.00000i | − | 0.0710669i | ||||||
\(199\) | −16.0000 | −1.13421 | −0.567105 | − | 0.823646i | \(-0.691937\pi\) | ||||
−0.567105 | + | 0.823646i | \(0.691937\pi\) | |||||||
\(200\) | 4.00000 | + | 3.00000i | 0.282843 | + | 0.212132i | ||||
\(201\) | −8.00000 | −0.564276 | ||||||||
\(202\) | − | 6.00000i | − | 0.422159i | ||||||
\(203\) | − | 25.0000i | − | 1.75466i | ||||||
\(204\) | 3.00000 | 0.210042 | ||||||||
\(205\) | 5.00000 | + | 10.0000i | 0.349215 | + | 0.698430i | ||||
\(206\) | 4.00000 | 0.278693 | ||||||||
\(207\) | − | 8.00000i | − | 0.556038i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.00000 | −0.553372 | ||||||||
\(210\) | −10.0000 | + | 5.00000i | −0.690066 | + | 0.345033i | ||||
\(211\) | 3.00000 | 0.206529 | 0.103264 | − | 0.994654i | \(-0.467071\pi\) | ||||
0.103264 | + | 0.994654i | \(0.467071\pi\) | |||||||
\(212\) | 5.00000i | 0.343401i | ||||||||
\(213\) | − | 6.00000i | − | 0.411113i | ||||||
\(214\) | −2.00000 | −0.136717 | ||||||||
\(215\) | 18.0000 | − | 9.00000i | 1.22759 | − | 0.613795i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | − | 15.0000i | − | 1.01827i | ||||||
\(218\) | − | 11.0000i | − | 0.745014i | ||||||
\(219\) | −2.00000 | −0.135147 | ||||||||
\(220\) | 1.00000 | + | 2.00000i | 0.0674200 | + | 0.134840i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1.00000i | 0.0671156i | ||||||||
\(223\) | 23.0000i | 1.54019i | 0.637927 | + | 0.770097i | \(0.279792\pi\) | ||||
−0.637927 | + | 0.770097i | \(0.720208\pi\) | |||||||
\(224\) | 5.00000 | 0.334077 | ||||||||
\(225\) | 3.00000 | − | 4.00000i | 0.200000 | − | 0.266667i | ||||
\(226\) | 15.0000 | 0.997785 | ||||||||
\(227\) | 21.0000i | 1.39382i | 0.717159 | + | 0.696909i | \(0.245442\pi\) | ||||
−0.717159 | + | 0.696909i | \(0.754558\pi\) | |||||||
\(228\) | − | 8.00000i | − | 0.529813i | ||||||
\(229\) | 4.00000 | 0.264327 | 0.132164 | − | 0.991228i | \(-0.457808\pi\) | ||||
0.132164 | + | 0.991228i | \(0.457808\pi\) | |||||||
\(230\) | 8.00000 | + | 16.0000i | 0.527504 | + | 1.05501i | ||||
\(231\) | −5.00000 | −0.328976 | ||||||||
\(232\) | − | 5.00000i | − | 0.328266i | ||||||
\(233\) | 6.00000i | 0.393073i | 0.980497 | + | 0.196537i | \(0.0629694\pi\) | ||||
−0.980497 | + | 0.196537i | \(0.937031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.0000 | + | 12.0000i | −1.56559 | + | 0.782794i | ||||
\(236\) | −4.00000 | −0.260378 | ||||||||
\(237\) | − | 8.00000i | − | 0.519656i | ||||||
\(238\) | − | 15.0000i | − | 0.972306i | ||||||
\(239\) | 19.0000 | 1.22901 | 0.614504 | − | 0.788914i | \(-0.289356\pi\) | ||||
0.614504 | + | 0.788914i | \(0.289356\pi\) | |||||||
\(240\) | −2.00000 | + | 1.00000i | −0.129099 | + | 0.0645497i | ||||
\(241\) | −10.0000 | −0.644157 | −0.322078 | − | 0.946713i | \(-0.604381\pi\) | ||||
−0.322078 | + | 0.946713i | \(0.604381\pi\) | |||||||
\(242\) | − | 10.0000i | − | 0.642824i | ||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 9.00000 | 0.576166 | ||||||||
\(245\) | 18.0000 | + | 36.0000i | 1.14998 | + | 2.29996i | ||||
\(246\) | −5.00000 | −0.318788 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | − | 3.00000i | − | 0.190500i | ||||||
\(249\) | 4.00000 | 0.253490 | ||||||||
\(250\) | −2.00000 | + | 11.0000i | −0.126491 | + | 0.695701i | ||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | − | 5.00000i | − | 0.314970i | ||||||
\(253\) | 8.00000i | 0.502956i | ||||||||
\(254\) | −8.00000 | −0.501965 | ||||||||
\(255\) | 3.00000 | + | 6.00000i | 0.187867 | + | 0.375735i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 26.0000i | − | 1.62184i | −0.585160 | − | 0.810918i | \(-0.698968\pi\) | ||
0.585160 | − | 0.810918i | \(-0.301032\pi\) | |||||||
\(258\) | 9.00000i | 0.560316i | ||||||||
\(259\) | 5.00000 | 0.310685 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.00000 | −0.309492 | ||||||||
\(262\) | − | 6.00000i | − | 0.370681i | ||||||
\(263\) | − | 5.00000i | − | 0.308313i | −0.988046 | − | 0.154157i | \(-0.950734\pi\) | ||
0.988046 | − | 0.154157i | \(-0.0492660\pi\) | |||||||
\(264\) | −1.00000 | −0.0615457 | ||||||||
\(265\) | −10.0000 | + | 5.00000i | −0.614295 | + | 0.307148i | ||||
\(266\) | −40.0000 | −2.45256 | ||||||||
\(267\) | − | 4.00000i | − | 0.244796i | ||||||
\(268\) | 8.00000i | 0.488678i | ||||||||
\(269\) | 4.00000 | 0.243884 | 0.121942 | − | 0.992537i | \(-0.461088\pi\) | ||||
0.121942 | + | 0.992537i | \(0.461088\pi\) | |||||||
\(270\) | 1.00000 | + | 2.00000i | 0.0608581 | + | 0.121716i | ||||
\(271\) | −14.0000 | −0.850439 | −0.425220 | − | 0.905090i | \(-0.639803\pi\) | ||||
−0.425220 | + | 0.905090i | \(0.639803\pi\) | |||||||
\(272\) | − | 3.00000i | − | 0.181902i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.00000 | 0.362473 | ||||||||
\(275\) | −3.00000 | + | 4.00000i | −0.180907 | + | 0.241209i | ||||
\(276\) | −8.00000 | −0.481543 | ||||||||
\(277\) | 32.0000i | 1.92269i | 0.275340 | + | 0.961347i | \(0.411209\pi\) | ||||
−0.275340 | + | 0.961347i | \(0.588791\pi\) | |||||||
\(278\) | − | 5.00000i | − | 0.299880i | ||||||
\(279\) | −3.00000 | −0.179605 | ||||||||
\(280\) | 5.00000 | + | 10.0000i | 0.298807 | + | 0.597614i | ||||
\(281\) | 30.0000 | 1.78965 | 0.894825 | − | 0.446417i | \(-0.147300\pi\) | ||||
0.894825 | + | 0.446417i | \(0.147300\pi\) | |||||||
\(282\) | − | 12.0000i | − | 0.714590i | ||||||
\(283\) | − | 16.0000i | − | 0.951101i | −0.879688 | − | 0.475551i | \(-0.842249\pi\) | ||
0.879688 | − | 0.475551i | \(-0.157751\pi\) | |||||||
\(284\) | −6.00000 | −0.356034 | ||||||||
\(285\) | 16.0000 | − | 8.00000i | 0.947758 | − | 0.473879i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 25.0000i | 1.47570i | ||||||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 8.00000 | 0.470588 | ||||||||
\(290\) | 10.0000 | − | 5.00000i | 0.587220 | − | 0.293610i | ||||
\(291\) | −9.00000 | −0.527589 | ||||||||
\(292\) | 2.00000i | 0.117041i | ||||||||
\(293\) | − | 23.0000i | − | 1.34367i | −0.740699 | − | 0.671837i | \(-0.765505\pi\) | ||
0.740699 | − | 0.671837i | \(-0.234495\pi\) | |||||||
\(294\) | −18.0000 | −1.04978 | ||||||||
\(295\) | −4.00000 | − | 8.00000i | −0.232889 | − | 0.465778i | ||||
\(296\) | 1.00000 | 0.0581238 | ||||||||
\(297\) | 1.00000i | 0.0580259i | ||||||||
\(298\) | 20.0000i | 1.15857i | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4.00000 | − | 3.00000i | −0.230940 | − | 0.173205i | ||||
\(301\) | 45.0000 | 2.59376 | ||||||||
\(302\) | − | 10.0000i | − | 0.575435i | ||||||
\(303\) | 6.00000i | 0.344691i | ||||||||
\(304\) | −8.00000 | −0.458831 | ||||||||
\(305\) | 9.00000 | + | 18.0000i | 0.515339 | + | 1.03068i | ||||
\(306\) | −3.00000 | −0.171499 | ||||||||
\(307\) | 4.00000i | 0.228292i | 0.993464 | + | 0.114146i | \(0.0364132\pi\) | ||||
−0.993464 | + | 0.114146i | \(0.963587\pi\) | |||||||
\(308\) | 5.00000i | 0.284901i | ||||||||
\(309\) | −4.00000 | −0.227552 | ||||||||
\(310\) | 6.00000 | − | 3.00000i | 0.340777 | − | 0.170389i | ||||
\(311\) | 17.0000 | 0.963982 | 0.481991 | − | 0.876176i | \(-0.339914\pi\) | ||||
0.481991 | + | 0.876176i | \(0.339914\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 26.0000i | − | 1.46961i | −0.678280 | − | 0.734803i | \(-0.737274\pi\) | ||
0.678280 | − | 0.734803i | \(-0.262726\pi\) | |||||||
\(314\) | 11.0000 | 0.620766 | ||||||||
\(315\) | 10.0000 | − | 5.00000i | 0.563436 | − | 0.281718i | ||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | − | 11.0000i | − | 0.617822i | −0.951091 | − | 0.308911i | \(-0.900036\pi\) | ||
0.951091 | − | 0.308911i | \(-0.0999645\pi\) | |||||||
\(318\) | − | 5.00000i | − | 0.280386i | ||||||
\(319\) | 5.00000 | 0.279946 | ||||||||
\(320\) | 1.00000 | + | 2.00000i | 0.0559017 | + | 0.111803i | ||||
\(321\) | 2.00000 | 0.111629 | ||||||||
\(322\) | 40.0000i | 2.22911i | ||||||||
\(323\) | 24.0000i | 1.33540i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.00000 | −0.0553849 | ||||||||
\(327\) | 11.0000i | 0.608301i | ||||||||
\(328\) | 5.00000i | 0.276079i | ||||||||
\(329\) | −60.0000 | −3.30791 | ||||||||
\(330\) | −1.00000 | − | 2.00000i | −0.0550482 | − | 0.110096i | ||||
\(331\) | 22.0000 | 1.20923 | 0.604615 | − | 0.796518i | \(-0.293327\pi\) | ||||
0.604615 | + | 0.796518i | \(0.293327\pi\) | |||||||
\(332\) | − | 4.00000i | − | 0.219529i | ||||||
\(333\) | − | 1.00000i | − | 0.0547997i | ||||||
\(334\) | 2.00000 | 0.109435 | ||||||||
\(335\) | −16.0000 | + | 8.00000i | −0.874173 | + | 0.437087i | ||||
\(336\) | −5.00000 | −0.272772 | ||||||||
\(337\) | − | 20.0000i | − | 1.08947i | −0.838608 | − | 0.544735i | \(-0.816630\pi\) | ||
0.838608 | − | 0.544735i | \(-0.183370\pi\) | |||||||
\(338\) | 13.0000i | 0.707107i | ||||||||
\(339\) | −15.0000 | −0.814688 | ||||||||
\(340\) | 6.00000 | − | 3.00000i | 0.325396 | − | 0.162698i | ||||
\(341\) | 3.00000 | 0.162459 | ||||||||
\(342\) | 8.00000i | 0.432590i | ||||||||
\(343\) | 55.0000i | 2.96972i | ||||||||
\(344\) | 9.00000 | 0.485247 | ||||||||
\(345\) | −8.00000 | − | 16.0000i | −0.430706 | − | 0.861411i | ||||
\(346\) | 21.0000 | 1.12897 | ||||||||
\(347\) | − | 28.0000i | − | 1.50312i | −0.659665 | − | 0.751559i | \(-0.729302\pi\) | ||
0.659665 | − | 0.751559i | \(-0.270698\pi\) | |||||||
\(348\) | 5.00000i | 0.268028i | ||||||||
\(349\) | −2.00000 | −0.107058 | −0.0535288 | − | 0.998566i | \(-0.517047\pi\) | ||||
−0.0535288 | + | 0.998566i | \(0.517047\pi\) | |||||||
\(350\) | −15.0000 | + | 20.0000i | −0.801784 | + | 1.06904i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.00000i | 0.0533002i | ||||||||
\(353\) | 19.0000i | 1.01127i | 0.862748 | + | 0.505634i | \(0.168741\pi\) | ||||
−0.862748 | + | 0.505634i | \(0.831259\pi\) | |||||||
\(354\) | 4.00000 | 0.212598 | ||||||||
\(355\) | −6.00000 | − | 12.0000i | −0.318447 | − | 0.636894i | ||||
\(356\) | −4.00000 | −0.212000 | ||||||||
\(357\) | 15.0000i | 0.793884i | ||||||||
\(358\) | 6.00000i | 0.317110i | ||||||||
\(359\) | −18.0000 | −0.950004 | −0.475002 | − | 0.879985i | \(-0.657553\pi\) | ||||
−0.475002 | + | 0.879985i | \(0.657553\pi\) | |||||||
\(360\) | 2.00000 | − | 1.00000i | 0.105409 | − | 0.0527046i | ||||
\(361\) | 45.0000 | 2.36842 | ||||||||
\(362\) | − | 12.0000i | − | 0.630706i | ||||||
\(363\) | 10.0000i | 0.524864i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.00000 | + | 2.00000i | −0.209370 | + | 0.104685i | ||||
\(366\) | −9.00000 | −0.470438 | ||||||||
\(367\) | − | 17.0000i | − | 0.887393i | −0.896177 | − | 0.443696i | \(-0.853667\pi\) | ||
0.896177 | − | 0.443696i | \(-0.146333\pi\) | |||||||
\(368\) | 8.00000i | 0.417029i | ||||||||
\(369\) | 5.00000 | 0.260290 | ||||||||
\(370\) | 1.00000 | + | 2.00000i | 0.0519875 | + | 0.103975i | ||||
\(371\) | −25.0000 | −1.29794 | ||||||||
\(372\) | 3.00000i | 0.155543i | ||||||||
\(373\) | − | 26.0000i | − | 1.34623i | −0.739538 | − | 0.673114i | \(-0.764956\pi\) | ||
0.739538 | − | 0.673114i | \(-0.235044\pi\) | |||||||
\(374\) | 3.00000 | 0.155126 | ||||||||
\(375\) | 2.00000 | − | 11.0000i | 0.103280 | − | 0.568038i | ||||
\(376\) | −12.0000 | −0.618853 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 5.00000i | 0.257172i | ||||||||
\(379\) | −28.0000 | −1.43826 | −0.719132 | − | 0.694874i | \(-0.755460\pi\) | ||||
−0.719132 | + | 0.694874i | \(0.755460\pi\) | |||||||
\(380\) | −8.00000 | − | 16.0000i | −0.410391 | − | 0.820783i | ||||
\(381\) | 8.00000 | 0.409852 | ||||||||
\(382\) | − | 27.0000i | − | 1.38144i | ||||||
\(383\) | 36.0000i | 1.83951i | 0.392488 | + | 0.919757i | \(0.371614\pi\) | ||||
−0.392488 | + | 0.919757i | \(0.628386\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −10.0000 | + | 5.00000i | −0.509647 | + | 0.254824i | ||||
\(386\) | 10.0000 | 0.508987 | ||||||||
\(387\) | − | 9.00000i | − | 0.457496i | ||||||
\(388\) | 9.00000i | 0.456906i | ||||||||
\(389\) | −9.00000 | −0.456318 | −0.228159 | − | 0.973624i | \(-0.573271\pi\) | ||||
−0.228159 | + | 0.973624i | \(0.573271\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.0000 | 1.21373 | ||||||||
\(392\) | 18.0000i | 0.909137i | ||||||||
\(393\) | 6.00000i | 0.302660i | ||||||||
\(394\) | −6.00000 | −0.302276 | ||||||||
\(395\) | −8.00000 | − | 16.0000i | −0.402524 | − | 0.805047i | ||||
\(396\) | 1.00000 | 0.0502519 | ||||||||
\(397\) | 18.0000i | 0.903394i | 0.892171 | + | 0.451697i | \(0.149181\pi\) | ||||
−0.892171 | + | 0.451697i | \(0.850819\pi\) | |||||||
\(398\) | − | 16.0000i | − | 0.802008i | ||||||
\(399\) | 40.0000 | 2.00250 | ||||||||
\(400\) | −3.00000 | + | 4.00000i | −0.150000 | + | 0.200000i | ||||
\(401\) | 14.0000 | 0.699127 | 0.349563 | − | 0.936913i | \(-0.386330\pi\) | ||||
0.349563 | + | 0.936913i | \(0.386330\pi\) | |||||||
\(402\) | − | 8.00000i | − | 0.399004i | ||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 6.00000 | 0.298511 | ||||||||
\(405\) | −1.00000 | − | 2.00000i | −0.0496904 | − | 0.0993808i | ||||
\(406\) | 25.0000 | 1.24073 | ||||||||
\(407\) | 1.00000i | 0.0495682i | ||||||||
\(408\) | 3.00000i | 0.148522i | ||||||||
\(409\) | −20.0000 | −0.988936 | −0.494468 | − | 0.869196i | \(-0.664637\pi\) | ||||
−0.494468 | + | 0.869196i | \(0.664637\pi\) | |||||||
\(410\) | −10.0000 | + | 5.00000i | −0.493865 | + | 0.246932i | ||||
\(411\) | −6.00000 | −0.295958 | ||||||||
\(412\) | 4.00000i | 0.197066i | ||||||||
\(413\) | − | 20.0000i | − | 0.984136i | ||||||
\(414\) | 8.00000 | 0.393179 | ||||||||
\(415\) | 8.00000 | − | 4.00000i | 0.392705 | − | 0.196352i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.00000i | 0.244851i | ||||||||
\(418\) | − | 8.00000i | − | 0.391293i | ||||||
\(419\) | −12.0000 | −0.586238 | −0.293119 | − | 0.956076i | \(-0.594693\pi\) | ||||
−0.293119 | + | 0.956076i | \(0.594693\pi\) | |||||||
\(420\) | −5.00000 | − | 10.0000i | −0.243975 | − | 0.487950i | ||||
\(421\) | 22.0000 | 1.07221 | 0.536107 | − | 0.844150i | \(-0.319894\pi\) | ||||
0.536107 | + | 0.844150i | \(0.319894\pi\) | |||||||
\(422\) | 3.00000i | 0.146038i | ||||||||
\(423\) | 12.0000i | 0.583460i | ||||||||
\(424\) | −5.00000 | −0.242821 | ||||||||
\(425\) | 12.0000 | + | 9.00000i | 0.582086 | + | 0.436564i | ||||
\(426\) | 6.00000 | 0.290701 | ||||||||
\(427\) | 45.0000i | 2.17770i | ||||||||
\(428\) | − | 2.00000i | − | 0.0966736i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 9.00000 | + | 18.0000i | 0.434019 | + | 0.868037i | ||||
\(431\) | −3.00000 | −0.144505 | −0.0722525 | − | 0.997386i | \(-0.523019\pi\) | ||||
−0.0722525 | + | 0.997386i | \(0.523019\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | − | 32.0000i | − | 1.53782i | −0.639356 | − | 0.768911i | \(-0.720799\pi\) | ||
0.639356 | − | 0.768911i | \(-0.279201\pi\) | |||||||
\(434\) | 15.0000 | 0.720023 | ||||||||
\(435\) | −10.0000 | + | 5.00000i | −0.479463 | + | 0.239732i | ||||
\(436\) | 11.0000 | 0.526804 | ||||||||
\(437\) | − | 64.0000i | − | 3.06154i | ||||||
\(438\) | − | 2.00000i | − | 0.0955637i | ||||||
\(439\) | 11.0000 | 0.525001 | 0.262501 | − | 0.964932i | \(-0.415453\pi\) | ||||
0.262501 | + | 0.964932i | \(0.415453\pi\) | |||||||
\(440\) | −2.00000 | + | 1.00000i | −0.0953463 | + | 0.0476731i | ||||
\(441\) | 18.0000 | 0.857143 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 10.0000i | − | 0.475114i | −0.971374 | − | 0.237557i | \(-0.923653\pi\) | ||
0.971374 | − | 0.237557i | \(-0.0763467\pi\) | |||||||
\(444\) | −1.00000 | −0.0474579 | ||||||||
\(445\) | −4.00000 | − | 8.00000i | −0.189618 | − | 0.379236i | ||||
\(446\) | −23.0000 | −1.08908 | ||||||||
\(447\) | − | 20.0000i | − | 0.945968i | ||||||
\(448\) | 5.00000i | 0.236228i | ||||||||
\(449\) | −12.0000 | −0.566315 | −0.283158 | − | 0.959073i | \(-0.591382\pi\) | ||||
−0.283158 | + | 0.959073i | \(0.591382\pi\) | |||||||
\(450\) | 4.00000 | + | 3.00000i | 0.188562 | + | 0.141421i | ||||
\(451\) | −5.00000 | −0.235441 | ||||||||
\(452\) | 15.0000i | 0.705541i | ||||||||
\(453\) | 10.0000i | 0.469841i | ||||||||
\(454\) | −21.0000 | −0.985579 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.00000 | 0.374634 | ||||||||
\(457\) | − | 13.0000i | − | 0.608114i | −0.952654 | − | 0.304057i | \(-0.901659\pi\) | ||
0.952654 | − | 0.304057i | \(-0.0983414\pi\) | |||||||
\(458\) | 4.00000i | 0.186908i | ||||||||
\(459\) | 3.00000 | 0.140028 | ||||||||
\(460\) | −16.0000 | + | 8.00000i | −0.746004 | + | 0.373002i | ||||
\(461\) | −3.00000 | −0.139724 | −0.0698620 | − | 0.997557i | \(-0.522256\pi\) | ||||
−0.0698620 | + | 0.997557i | \(0.522256\pi\) | |||||||
\(462\) | − | 5.00000i | − | 0.232621i | ||||||
\(463\) | − | 20.0000i | − | 0.929479i | −0.885448 | − | 0.464739i | \(-0.846148\pi\) | ||
0.885448 | − | 0.464739i | \(-0.153852\pi\) | |||||||
\(464\) | 5.00000 | 0.232119 | ||||||||
\(465\) | −6.00000 | + | 3.00000i | −0.278243 | + | 0.139122i | ||||
\(466\) | −6.00000 | −0.277945 | ||||||||
\(467\) | 31.0000i | 1.43451i | 0.696811 | + | 0.717254i | \(0.254601\pi\) | ||||
−0.696811 | + | 0.717254i | \(0.745399\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −40.0000 | −1.84703 | ||||||||
\(470\) | −12.0000 | − | 24.0000i | −0.553519 | − | 1.10704i | ||||
\(471\) | −11.0000 | −0.506853 | ||||||||
\(472\) | − | 4.00000i | − | 0.184115i | ||||||
\(473\) | 9.00000i | 0.413820i | ||||||||
\(474\) | 8.00000 | 0.367452 | ||||||||
\(475\) | 24.0000 | − | 32.0000i | 1.10120 | − | 1.46826i | ||||
\(476\) | 15.0000 | 0.687524 | ||||||||
\(477\) | 5.00000i | 0.228934i | ||||||||
\(478\) | 19.0000i | 0.869040i | ||||||||
\(479\) | 36.0000 | 1.64488 | 0.822441 | − | 0.568850i | \(-0.192612\pi\) | ||||
0.822441 | + | 0.568850i | \(0.192612\pi\) | |||||||
\(480\) | −1.00000 | − | 2.00000i | −0.0456435 | − | 0.0912871i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | − | 10.0000i | − | 0.455488i | ||||||
\(483\) | − | 40.0000i | − | 1.82006i | ||||||
\(484\) | 10.0000 | 0.454545 | ||||||||
\(485\) | −18.0000 | + | 9.00000i | −0.817338 | + | 0.408669i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | − | 32.0000i | − | 1.45006i | −0.688718 | − | 0.725029i | \(-0.741826\pi\) | ||
0.688718 | − | 0.725029i | \(-0.258174\pi\) | |||||||
\(488\) | 9.00000i | 0.407411i | ||||||||
\(489\) | 1.00000 | 0.0452216 | ||||||||
\(490\) | −36.0000 | + | 18.0000i | −1.62631 | + | 0.813157i | ||||
\(491\) | 20.0000 | 0.902587 | 0.451294 | − | 0.892375i | \(-0.350963\pi\) | ||||
0.451294 | + | 0.892375i | \(0.350963\pi\) | |||||||
\(492\) | − | 5.00000i | − | 0.225417i | ||||||
\(493\) | − | 15.0000i | − | 0.675566i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.00000 | + | 2.00000i | 0.0449467 | + | 0.0898933i | ||||
\(496\) | 3.00000 | 0.134704 | ||||||||
\(497\) | − | 30.0000i | − | 1.34568i | ||||||
\(498\) | 4.00000i | 0.179244i | ||||||||
\(499\) | 6.00000 | 0.268597 | 0.134298 | − | 0.990941i | \(-0.457122\pi\) | ||||
0.134298 | + | 0.990941i | \(0.457122\pi\) | |||||||
\(500\) | −11.0000 | − | 2.00000i | −0.491935 | − | 0.0894427i | ||||
\(501\) | −2.00000 | −0.0893534 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.0000i | 0.445878i | 0.974832 | + | 0.222939i | \(0.0715651\pi\) | ||||
−0.974832 | + | 0.222939i | \(0.928435\pi\) | |||||||
\(504\) | 5.00000 | 0.222718 | ||||||||
\(505\) | 6.00000 | + | 12.0000i | 0.266996 | + | 0.533993i | ||||
\(506\) | −8.00000 | −0.355643 | ||||||||
\(507\) | − | 13.0000i | − | 0.577350i | ||||||
\(508\) | − | 8.00000i | − | 0.354943i | ||||||
\(509\) | −6.00000 | −0.265945 | −0.132973 | − | 0.991120i | \(-0.542452\pi\) | ||||
−0.132973 | + | 0.991120i | \(0.542452\pi\) | |||||||
\(510\) | −6.00000 | + | 3.00000i | −0.265684 | + | 0.132842i | ||||
\(511\) | −10.0000 | −0.442374 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − | 8.00000i | − | 0.353209i | ||||||
\(514\) | 26.0000 | 1.14681 | ||||||||
\(515\) | −8.00000 | + | 4.00000i | −0.352522 | + | 0.176261i | ||||
\(516\) | −9.00000 | −0.396203 | ||||||||
\(517\) | − | 12.0000i | − | 0.527759i | ||||||
\(518\) | 5.00000i | 0.219687i | ||||||||
\(519\) | −21.0000 | −0.921798 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −39.0000 | −1.70862 | −0.854311 | − | 0.519763i | \(-0.826020\pi\) | ||||
−0.854311 | + | 0.519763i | \(0.826020\pi\) | |||||||
\(522\) | − | 5.00000i | − | 0.218844i | ||||||
\(523\) | − | 44.0000i | − | 1.92399i | −0.273075 | − | 0.961993i | \(-0.588041\pi\) | ||
0.273075 | − | 0.961993i | \(-0.411959\pi\) | |||||||
\(524\) | 6.00000 | 0.262111 | ||||||||
\(525\) | 15.0000 | − | 20.0000i | 0.654654 | − | 0.872872i | ||||
\(526\) | 5.00000 | 0.218010 | ||||||||
\(527\) | − | 9.00000i | − | 0.392046i | ||||||
\(528\) | − | 1.00000i | − | 0.0435194i | ||||||
\(529\) | −41.0000 | −1.78261 | ||||||||
\(530\) | −5.00000 | − | 10.0000i | −0.217186 | − | 0.434372i | ||||
\(531\) | −4.00000 | −0.173585 | ||||||||
\(532\) | − | 40.0000i | − | 1.73422i | ||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 4.00000 | 0.173097 | ||||||||
\(535\) | 4.00000 | − | 2.00000i | 0.172935 | − | 0.0864675i | ||||
\(536\) | −8.00000 | −0.345547 | ||||||||
\(537\) | − | 6.00000i | − | 0.258919i | ||||||
\(538\) | 4.00000i | 0.172452i | ||||||||
\(539\) | −18.0000 | −0.775315 | ||||||||
\(540\) | −2.00000 | + | 1.00000i | −0.0860663 | + | 0.0430331i | ||||
\(541\) | −2.00000 | −0.0859867 | −0.0429934 | − | 0.999075i | \(-0.513689\pi\) | ||||
−0.0429934 | + | 0.999075i | \(0.513689\pi\) | |||||||
\(542\) | − | 14.0000i | − | 0.601351i | ||||||
\(543\) | 12.0000i | 0.514969i | ||||||||
\(544\) | 3.00000 | 0.128624 | ||||||||
\(545\) | 11.0000 | + | 22.0000i | 0.471188 | + | 0.942376i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.0000i | 1.32546i | 0.748857 | + | 0.662732i | \(0.230603\pi\) | ||||
−0.748857 | + | 0.662732i | \(0.769397\pi\) | |||||||
\(548\) | 6.00000i | 0.256307i | ||||||||
\(549\) | 9.00000 | 0.384111 | ||||||||
\(550\) | −4.00000 | − | 3.00000i | −0.170561 | − | 0.127920i | ||||
\(551\) | −40.0000 | −1.70406 | ||||||||
\(552\) | − | 8.00000i | − | 0.340503i | ||||||
\(553\) | − | 40.0000i | − | 1.70097i | ||||||
\(554\) | −32.0000 | −1.35955 | ||||||||
\(555\) | −1.00000 | − | 2.00000i | −0.0424476 | − | 0.0848953i | ||||
\(556\) | 5.00000 | 0.212047 | ||||||||
\(557\) | 26.0000i | 1.10166i | 0.834619 | + | 0.550828i | \(0.185688\pi\) | ||||
−0.834619 | + | 0.550828i | \(0.814312\pi\) | |||||||
\(558\) | − | 3.00000i | − | 0.127000i | ||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −10.0000 | + | 5.00000i | −0.422577 | + | 0.211289i | ||||
\(561\) | −3.00000 | −0.126660 | ||||||||
\(562\) | 30.0000i | 1.26547i | ||||||||
\(563\) | 23.0000i | 0.969334i | 0.874699 | + | 0.484667i | \(0.161059\pi\) | ||||
−0.874699 | + | 0.484667i | \(0.838941\pi\) | |||||||
\(564\) | 12.0000 | 0.505291 | ||||||||
\(565\) | −30.0000 | + | 15.0000i | −1.26211 | + | 0.631055i | ||||
\(566\) | 16.0000 | 0.672530 | ||||||||
\(567\) | − | 5.00000i | − | 0.209980i | ||||||
\(568\) | − | 6.00000i | − | 0.251754i | ||||||
\(569\) | −14.0000 | −0.586911 | −0.293455 | − | 0.955973i | \(-0.594805\pi\) | ||||
−0.293455 | + | 0.955973i | \(0.594805\pi\) | |||||||
\(570\) | 8.00000 | + | 16.0000i | 0.335083 | + | 0.670166i | ||||
\(571\) | 35.0000 | 1.46470 | 0.732352 | − | 0.680926i | \(-0.238422\pi\) | ||||
0.732352 | + | 0.680926i | \(0.238422\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 27.0000i | 1.12794i | ||||||||
\(574\) | −25.0000 | −1.04348 | ||||||||
\(575\) | −32.0000 | − | 24.0000i | −1.33449 | − | 1.00087i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | − | 34.0000i | − | 1.41544i | −0.706494 | − | 0.707719i | \(-0.749724\pi\) | ||
0.706494 | − | 0.707719i | \(-0.250276\pi\) | |||||||
\(578\) | 8.00000i | 0.332756i | ||||||||
\(579\) | −10.0000 | −0.415586 | ||||||||
\(580\) | 5.00000 | + | 10.0000i | 0.207614 | + | 0.415227i | ||||
\(581\) | 20.0000 | 0.829740 | ||||||||
\(582\) | − | 9.00000i | − | 0.373062i | ||||||
\(583\) | − | 5.00000i | − | 0.207079i | ||||||
\(584\) | −2.00000 | −0.0827606 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 23.0000 | 0.950121 | ||||||||
\(587\) | − | 21.0000i | − | 0.866763i | −0.901211 | − | 0.433381i | \(-0.857320\pi\) | ||
0.901211 | − | 0.433381i | \(-0.142680\pi\) | |||||||
\(588\) | − | 18.0000i | − | 0.742307i | ||||||
\(589\) | −24.0000 | −0.988903 | ||||||||
\(590\) | 8.00000 | − | 4.00000i | 0.329355 | − | 0.164677i | ||||
\(591\) | 6.00000 | 0.246807 | ||||||||
\(592\) | 1.00000i | 0.0410997i | ||||||||
\(593\) | − | 36.0000i | − | 1.47834i | −0.673517 | − | 0.739171i | \(-0.735217\pi\) | ||
0.673517 | − | 0.739171i | \(-0.264783\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | 15.0000 | + | 30.0000i | 0.614940 | + | 1.22988i | ||||
\(596\) | −20.0000 | −0.819232 | ||||||||
\(597\) | 16.0000i | 0.654836i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 28.0000 | 1.14405 | 0.572024 | − | 0.820237i | \(-0.306158\pi\) | ||||
0.572024 | + | 0.820237i | \(0.306158\pi\) | |||||||
\(600\) | 3.00000 | − | 4.00000i | 0.122474 | − | 0.163299i | ||||
\(601\) | 25.0000 | 1.01977 | 0.509886 | − | 0.860242i | \(-0.329688\pi\) | ||||
0.509886 | + | 0.860242i | \(0.329688\pi\) | |||||||
\(602\) | 45.0000i | 1.83406i | ||||||||
\(603\) | 8.00000i | 0.325785i | ||||||||
\(604\) | 10.0000 | 0.406894 | ||||||||
\(605\) | 10.0000 | + | 20.0000i | 0.406558 | + | 0.813116i | ||||
\(606\) | −6.00000 | −0.243733 | ||||||||
\(607\) | − | 46.0000i | − | 1.86708i | −0.358470 | − | 0.933541i | \(-0.616702\pi\) | ||
0.358470 | − | 0.933541i | \(-0.383298\pi\) | |||||||
\(608\) | − | 8.00000i | − | 0.324443i | ||||||
\(609\) | −25.0000 | −1.01305 | ||||||||
\(610\) | −18.0000 | + | 9.00000i | −0.728799 | + | 0.364399i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | − | 3.00000i | − | 0.121268i | ||||||
\(613\) | 9.00000i | 0.363507i | 0.983344 | + | 0.181753i | \(0.0581772\pi\) | ||||
−0.983344 | + | 0.181753i | \(0.941823\pi\) | |||||||
\(614\) | −4.00000 | −0.161427 | ||||||||
\(615\) | 10.0000 | − | 5.00000i | 0.403239 | − | 0.201619i | ||||
\(616\) | −5.00000 | −0.201456 | ||||||||
\(617\) | 2.00000i | 0.0805170i | 0.999189 | + | 0.0402585i | \(0.0128181\pi\) | ||||
−0.999189 | + | 0.0402585i | \(0.987182\pi\) | |||||||
\(618\) | − | 4.00000i | − | 0.160904i | ||||||
\(619\) | −17.0000 | −0.683288 | −0.341644 | − | 0.939829i | \(-0.610984\pi\) | ||||
−0.341644 | + | 0.939829i | \(0.610984\pi\) | |||||||
\(620\) | 3.00000 | + | 6.00000i | 0.120483 | + | 0.240966i | ||||
\(621\) | −8.00000 | −0.321029 | ||||||||
\(622\) | 17.0000i | 0.681638i | ||||||||
\(623\) | − | 20.0000i | − | 0.801283i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | 26.0000 | 1.03917 | ||||||||
\(627\) | 8.00000i | 0.319489i | ||||||||
\(628\) | 11.0000i | 0.438948i | ||||||||
\(629\) | 3.00000 | 0.119618 | ||||||||
\(630\) | 5.00000 | + | 10.0000i | 0.199205 | + | 0.398410i | ||||
\(631\) | 15.0000 | 0.597141 | 0.298570 | − | 0.954388i | \(-0.403490\pi\) | ||||
0.298570 | + | 0.954388i | \(0.403490\pi\) | |||||||
\(632\) | − | 8.00000i | − | 0.318223i | ||||||
\(633\) | − | 3.00000i | − | 0.119239i | ||||||
\(634\) | 11.0000 | 0.436866 | ||||||||
\(635\) | 16.0000 | − | 8.00000i | 0.634941 | − | 0.317470i | ||||
\(636\) | 5.00000 | 0.198263 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5.00000i | 0.197952i | ||||||||
\(639\) | −6.00000 | −0.237356 | ||||||||
\(640\) | −2.00000 | + | 1.00000i | −0.0790569 | + | 0.0395285i | ||||
\(641\) | −17.0000 | −0.671460 | −0.335730 | − | 0.941958i | \(-0.608983\pi\) | ||||
−0.335730 | + | 0.941958i | \(0.608983\pi\) | |||||||
\(642\) | 2.00000i | 0.0789337i | ||||||||
\(643\) | − | 19.0000i | − | 0.749287i | −0.927169 | − | 0.374643i | \(-0.877765\pi\) | ||
0.927169 | − | 0.374643i | \(-0.122235\pi\) | |||||||
\(644\) | −40.0000 | −1.57622 | ||||||||
\(645\) | −9.00000 | − | 18.0000i | −0.354375 | − | 0.708749i | ||||
\(646\) | −24.0000 | −0.944267 | ||||||||
\(647\) | 6.00000i | 0.235884i | 0.993020 | + | 0.117942i | \(0.0376297\pi\) | ||||
−0.993020 | + | 0.117942i | \(0.962370\pi\) | |||||||
\(648\) | − | 1.00000i | − | 0.0392837i | ||||||
\(649\) | 4.00000 | 0.157014 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.0000 | −0.587896 | ||||||||
\(652\) | − | 1.00000i | − | 0.0391630i | ||||||
\(653\) | − | 6.00000i | − | 0.234798i | −0.993085 | − | 0.117399i | \(-0.962544\pi\) | ||
0.993085 | − | 0.117399i | \(-0.0374557\pi\) | |||||||
\(654\) | −11.0000 | −0.430134 | ||||||||
\(655\) | 6.00000 | + | 12.0000i | 0.234439 | + | 0.468879i | ||||
\(656\) | −5.00000 | −0.195217 | ||||||||
\(657\) | 2.00000i | 0.0780274i | ||||||||
\(658\) | − | 60.0000i | − | 2.33904i | ||||||
\(659\) | 8.00000 | 0.311636 | 0.155818 | − | 0.987786i | \(-0.450199\pi\) | ||||
0.155818 | + | 0.987786i | \(0.450199\pi\) | |||||||
\(660\) | 2.00000 | − | 1.00000i | 0.0778499 | − | 0.0389249i | ||||
\(661\) | 1.00000 | 0.0388955 | 0.0194477 | − | 0.999811i | \(-0.493809\pi\) | ||||
0.0194477 | + | 0.999811i | \(0.493809\pi\) | |||||||
\(662\) | 22.0000i | 0.855054i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.00000 | 0.155230 | ||||||||
\(665\) | 80.0000 | − | 40.0000i | 3.10227 | − | 1.55113i | ||||
\(666\) | 1.00000 | 0.0387492 | ||||||||
\(667\) | 40.0000i | 1.54881i | ||||||||
\(668\) | 2.00000i | 0.0773823i | ||||||||
\(669\) | 23.0000 | 0.889231 | ||||||||
\(670\) | −8.00000 | − | 16.0000i | −0.309067 | − | 0.618134i | ||||
\(671\) | −9.00000 | −0.347441 | ||||||||
\(672\) | − | 5.00000i | − | 0.192879i | ||||||
\(673\) | − | 32.0000i | − | 1.23351i | −0.787155 | − | 0.616755i | \(-0.788447\pi\) | ||
0.787155 | − | 0.616755i | \(-0.211553\pi\) | |||||||
\(674\) | 20.0000 | 0.770371 | ||||||||
\(675\) | −4.00000 | − | 3.00000i | −0.153960 | − | 0.115470i | ||||
\(676\) | −13.0000 | −0.500000 | ||||||||
\(677\) | 18.0000i | 0.691796i | 0.938272 | + | 0.345898i | \(0.112426\pi\) | ||||
−0.938272 | + | 0.345898i | \(0.887574\pi\) | |||||||
\(678\) | − | 15.0000i | − | 0.576072i | ||||||
\(679\) | −45.0000 | −1.72694 | ||||||||
\(680\) | 3.00000 | + | 6.00000i | 0.115045 | + | 0.230089i | ||||
\(681\) | 21.0000 | 0.804722 | ||||||||
\(682\) | 3.00000i | 0.114876i | ||||||||
\(683\) | 47.0000i | 1.79841i | 0.437533 | + | 0.899203i | \(0.355852\pi\) | ||||
−0.437533 | + | 0.899203i | \(0.644148\pi\) | |||||||
\(684\) | −8.00000 | −0.305888 | ||||||||
\(685\) | −12.0000 | + | 6.00000i | −0.458496 | + | 0.229248i | ||||
\(686\) | −55.0000 | −2.09991 | ||||||||
\(687\) | − | 4.00000i | − | 0.152610i | ||||||
\(688\) | 9.00000i | 0.343122i | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 16.0000 | − | 8.00000i | 0.609110 | − | 0.304555i | ||||
\(691\) | −21.0000 | −0.798878 | −0.399439 | − | 0.916760i | \(-0.630795\pi\) | ||||
−0.399439 | + | 0.916760i | \(0.630795\pi\) | |||||||
\(692\) | 21.0000i | 0.798300i | ||||||||
\(693\) | 5.00000i | 0.189934i | ||||||||
\(694\) | 28.0000 | 1.06287 | ||||||||
\(695\) | 5.00000 | + | 10.0000i | 0.189661 | + | 0.379322i | ||||
\(696\) | −5.00000 | −0.189525 | ||||||||
\(697\) | 15.0000i | 0.568166i | ||||||||
\(698\) | − | 2.00000i | − | 0.0757011i | ||||||
\(699\) | 6.00000 | 0.226941 | ||||||||
\(700\) | −20.0000 | − | 15.0000i | −0.755929 | − | 0.566947i | ||||
\(701\) | 30.0000 | 1.13308 | 0.566542 | − | 0.824033i | \(-0.308281\pi\) | ||||
0.566542 | + | 0.824033i | \(0.308281\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 8.00000i | − | 0.301726i | ||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 12.0000 | + | 24.0000i | 0.451946 | + | 0.903892i | ||||
\(706\) | −19.0000 | −0.715074 | ||||||||
\(707\) | 30.0000i | 1.12827i | ||||||||
\(708\) | 4.00000i | 0.150329i | ||||||||
\(709\) | −3.00000 | −0.112667 | −0.0563337 | − | 0.998412i | \(-0.517941\pi\) | ||||
−0.0563337 | + | 0.998412i | \(0.517941\pi\) | |||||||
\(710\) | 12.0000 | − | 6.00000i | 0.450352 | − | 0.225176i | ||||
\(711\) | −8.00000 | −0.300023 | ||||||||
\(712\) | − | 4.00000i | − | 0.149906i | ||||||
\(713\) | 24.0000i | 0.898807i | ||||||||
\(714\) | −15.0000 | −0.561361 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.00000 | −0.224231 | ||||||||
\(717\) | − | 19.0000i | − | 0.709568i | ||||||
\(718\) | − | 18.0000i | − | 0.671754i | ||||||
\(719\) | −24.0000 | −0.895049 | −0.447524 | − | 0.894272i | \(-0.647694\pi\) | ||||
−0.447524 | + | 0.894272i | \(0.647694\pi\) | |||||||
\(720\) | 1.00000 | + | 2.00000i | 0.0372678 | + | 0.0745356i | ||||
\(721\) | −20.0000 | −0.744839 | ||||||||
\(722\) | 45.0000i | 1.67473i | ||||||||
\(723\) | 10.0000i | 0.371904i | ||||||||
\(724\) | 12.0000 | 0.445976 | ||||||||
\(725\) | −15.0000 | + | 20.0000i | −0.557086 | + | 0.742781i | ||||
\(726\) | −10.0000 | −0.371135 | ||||||||
\(727\) | − | 26.0000i | − | 0.964287i | −0.876092 | − | 0.482143i | \(-0.839858\pi\) | ||
0.876092 | − | 0.482143i | \(-0.160142\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −2.00000 | − | 4.00000i | −0.0740233 | − | 0.148047i | ||||
\(731\) | 27.0000 | 0.998631 | ||||||||
\(732\) | − | 9.00000i | − | 0.332650i | ||||||
\(733\) | 49.0000i | 1.80986i | 0.425564 | + | 0.904928i | \(0.360076\pi\) | ||||
−0.425564 | + | 0.904928i | \(0.639924\pi\) | |||||||
\(734\) | 17.0000 | 0.627481 | ||||||||
\(735\) | 36.0000 | − | 18.0000i | 1.32788 | − | 0.663940i | ||||
\(736\) | −8.00000 | −0.294884 | ||||||||
\(737\) | − | 8.00000i | − | 0.294684i | ||||||
\(738\) | 5.00000i | 0.184053i | ||||||||
\(739\) | 43.0000 | 1.58178 | 0.790890 | − | 0.611958i | \(-0.209618\pi\) | ||||
0.790890 | + | 0.611958i | \(0.209618\pi\) | |||||||
\(740\) | −2.00000 | + | 1.00000i | −0.0735215 | + | 0.0367607i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 25.0000i | − | 0.917779i | ||||||
\(743\) | − | 17.0000i | − | 0.623670i | −0.950136 | − | 0.311835i | \(-0.899056\pi\) | ||
0.950136 | − | 0.311835i | \(-0.100944\pi\) | |||||||
\(744\) | −3.00000 | −0.109985 | ||||||||
\(745\) | −20.0000 | − | 40.0000i | −0.732743 | − | 1.46549i | ||||
\(746\) | 26.0000 | 0.951928 | ||||||||
\(747\) | − | 4.00000i | − | 0.146352i | ||||||
\(748\) | 3.00000i | 0.109691i | ||||||||
\(749\) | 10.0000 | 0.365392 | ||||||||
\(750\) | 11.0000 | + | 2.00000i | 0.401663 | + | 0.0730297i | ||||
\(751\) | −32.0000 | −1.16770 | −0.583848 | − | 0.811863i | \(-0.698454\pi\) | ||||
−0.583848 | + | 0.811863i | \(0.698454\pi\) | |||||||
\(752\) | − | 12.0000i | − | 0.437595i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.0000 | + | 20.0000i | 0.363937 | + | 0.727875i | ||||
\(756\) | −5.00000 | −0.181848 | ||||||||
\(757\) | − | 32.0000i | − | 1.16306i | −0.813525 | − | 0.581530i | \(-0.802454\pi\) | ||
0.813525 | − | 0.581530i | \(-0.197546\pi\) | |||||||
\(758\) | − | 28.0000i | − | 1.01701i | ||||||
\(759\) | 8.00000 | 0.290382 | ||||||||
\(760\) | 16.0000 | − | 8.00000i | 0.580381 | − | 0.290191i | ||||
\(761\) | 47.0000 | 1.70375 | 0.851874 | − | 0.523746i | \(-0.175466\pi\) | ||||
0.851874 | + | 0.523746i | \(0.175466\pi\) | |||||||
\(762\) | 8.00000i | 0.289809i | ||||||||
\(763\) | 55.0000i | 1.99113i | ||||||||
\(764\) | 27.0000 | 0.976826 | ||||||||
\(765\) | 6.00000 | − | 3.00000i | 0.216930 | − | 0.108465i | ||||
\(766\) | −36.0000 | −1.30073 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | 52.0000 | 1.87517 | 0.937584 | − | 0.347759i | \(-0.113057\pi\) | ||||
0.937584 | + | 0.347759i | \(0.113057\pi\) | |||||||
\(770\) | −5.00000 | − | 10.0000i | −0.180187 | − | 0.360375i | ||||
\(771\) | −26.0000 | −0.936367 | ||||||||
\(772\) | 10.0000i | 0.359908i | ||||||||
\(773\) | − | 11.0000i | − | 0.395643i | −0.980238 | − | 0.197821i | \(-0.936613\pi\) | ||
0.980238 | − | 0.197821i | \(-0.0633866\pi\) | |||||||
\(774\) | 9.00000 | 0.323498 | ||||||||
\(775\) | −9.00000 | + | 12.0000i | −0.323290 | + | 0.431053i | ||||
\(776\) | −9.00000 | −0.323081 | ||||||||
\(777\) | − | 5.00000i | − | 0.179374i | ||||||
\(778\) | − | 9.00000i | − | 0.322666i | ||||||
\(779\) | 40.0000 | 1.43315 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.00000 | 0.214697 | ||||||||
\(782\) | 24.0000i | 0.858238i | ||||||||
\(783\) | 5.00000i | 0.178685i | ||||||||
\(784\) | −18.0000 | −0.642857 | ||||||||
\(785\) | −22.0000 | + | 11.0000i | −0.785214 | + | 0.392607i | ||||
\(786\) | −6.00000 | −0.214013 | ||||||||
\(787\) | 26.0000i | 0.926800i | 0.886149 | + | 0.463400i | \(0.153371\pi\) | ||||
−0.886149 | + | 0.463400i | \(0.846629\pi\) | |||||||
\(788\) | − | 6.00000i | − | 0.213741i | ||||||
\(789\) | −5.00000 | −0.178005 | ||||||||
\(790\) | 16.0000 | − | 8.00000i | 0.569254 | − | 0.284627i | ||||
\(791\) | −75.0000 | −2.66669 | ||||||||
\(792\) | 1.00000i | 0.0355335i | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −18.0000 | −0.638796 | ||||||||
\(795\) | 5.00000 | + | 10.0000i | 0.177332 | + | 0.354663i | ||||
\(796\) | 16.0000 | 0.567105 | ||||||||
\(797\) | 24.0000i | 0.850124i | 0.905164 | + | 0.425062i | \(0.139748\pi\) | ||||
−0.905164 | + | 0.425062i | \(0.860252\pi\) | |||||||
\(798\) | 40.0000i | 1.41598i | ||||||||
\(799\) | −36.0000 | −1.27359 | ||||||||
\(800\) | −4.00000 | − | 3.00000i | −0.141421 | − | 0.106066i | ||||
\(801\) | −4.00000 | −0.141333 | ||||||||
\(802\) | 14.0000i | 0.494357i | ||||||||
\(803\) | − | 2.00000i | − | 0.0705785i | ||||||
\(804\) | 8.00000 | 0.282138 | ||||||||
\(805\) | −40.0000 | − | 80.0000i | −1.40981 | − | 2.81963i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 4.00000i | − | 0.140807i | ||||||
\(808\) | 6.00000i | 0.211079i | ||||||||
\(809\) | 36.0000 | 1.26569 | 0.632846 | − | 0.774277i | \(-0.281886\pi\) | ||||
0.632846 | + | 0.774277i | \(0.281886\pi\) | |||||||
\(810\) | 2.00000 | − | 1.00000i | 0.0702728 | − | 0.0351364i | ||||
\(811\) | 8.00000 | 0.280918 | 0.140459 | − | 0.990086i | \(-0.455142\pi\) | ||||
0.140459 | + | 0.990086i | \(0.455142\pi\) | |||||||
\(812\) | 25.0000i | 0.877328i | ||||||||
\(813\) | 14.0000i | 0.491001i | ||||||||
\(814\) | −1.00000 | −0.0350500 | ||||||||
\(815\) | 2.00000 | − | 1.00000i | 0.0700569 | − | 0.0350285i | ||||
\(816\) | −3.00000 | −0.105021 | ||||||||
\(817\) | − | 72.0000i | − | 2.51896i | ||||||
\(818\) | − | 20.0000i | − | 0.699284i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.00000 | − | 10.0000i | −0.174608 | − | 0.349215i | ||||
\(821\) | −30.0000 | −1.04701 | −0.523504 | − | 0.852023i | \(-0.675375\pi\) | ||||
−0.523504 | + | 0.852023i | \(0.675375\pi\) | |||||||
\(822\) | − | 6.00000i | − | 0.209274i | ||||||
\(823\) | 24.0000i | 0.836587i | 0.908312 | + | 0.418294i | \(0.137372\pi\) | ||||
−0.908312 | + | 0.418294i | \(0.862628\pi\) | |||||||
\(824\) | −4.00000 | −0.139347 | ||||||||
\(825\) | 4.00000 | + | 3.00000i | 0.139262 | + | 0.104447i | ||||
\(826\) | 20.0000 | 0.695889 | ||||||||
\(827\) | − | 31.0000i | − | 1.07798i | −0.842314 | − | 0.538988i | \(-0.818807\pi\) | ||
0.842314 | − | 0.538988i | \(-0.181193\pi\) | |||||||
\(828\) | 8.00000i | 0.278019i | ||||||||
\(829\) | 25.0000 | 0.868286 | 0.434143 | − | 0.900844i | \(-0.357051\pi\) | ||||
0.434143 | + | 0.900844i | \(0.357051\pi\) | |||||||
\(830\) | 4.00000 | + | 8.00000i | 0.138842 | + | 0.277684i | ||||
\(831\) | 32.0000 | 1.11007 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 54.0000i | 1.87099i | ||||||||
\(834\) | −5.00000 | −0.173136 | ||||||||
\(835\) | −4.00000 | + | 2.00000i | −0.138426 | + | 0.0692129i | ||||
\(836\) | 8.00000 | 0.276686 | ||||||||
\(837\) | 3.00000i | 0.103695i | ||||||||
\(838\) | − | 12.0000i | − | 0.414533i | ||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 10.0000 | − | 5.00000i | 0.345033 | − | 0.172516i | ||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | 22.0000i | 0.758170i | ||||||||
\(843\) | − | 30.0000i | − | 1.03325i | ||||||
\(844\) | −3.00000 | −0.103264 | ||||||||
\(845\) | −13.0000 | − | 26.0000i | −0.447214 | − | 0.894427i | ||||
\(846\) | −12.0000 | −0.412568 | ||||||||
\(847\) | 50.0000i | 1.71802i | ||||||||
\(848\) | − | 5.00000i | − | 0.171701i | ||||||
\(849\) | −16.0000 | −0.549119 | ||||||||
\(850\) | −9.00000 | + | 12.0000i | −0.308697 | + | 0.411597i | ||||
\(851\) | −8.00000 | −0.274236 | ||||||||
\(852\) | 6.00000i | 0.205557i | ||||||||
\(853\) | 30.0000i | 1.02718i | 0.858036 | + | 0.513590i | \(0.171685\pi\) | ||||
−0.858036 | + | 0.513590i | \(0.828315\pi\) | |||||||
\(854\) | −45.0000 | −1.53987 | ||||||||
\(855\) | −8.00000 | − | 16.0000i | −0.273594 | − | 0.547188i | ||||
\(856\) | 2.00000 | 0.0683586 | ||||||||
\(857\) | 39.0000i | 1.33221i | 0.745856 | + | 0.666107i | \(0.232041\pi\) | ||||
−0.745856 | + | 0.666107i | \(0.767959\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.0000 | −0.818869 | −0.409435 | − | 0.912339i | \(-0.634274\pi\) | ||||
−0.409435 | + | 0.912339i | \(0.634274\pi\) | |||||||
\(860\) | −18.0000 | + | 9.00000i | −0.613795 | + | 0.306897i | ||||
\(861\) | 25.0000 | 0.851998 | ||||||||
\(862\) | − | 3.00000i | − | 0.102180i | ||||||
\(863\) | 37.0000i | 1.25949i | 0.776800 | + | 0.629747i | \(0.216842\pi\) | ||||
−0.776800 | + | 0.629747i | \(0.783158\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −42.0000 | + | 21.0000i | −1.42804 | + | 0.714021i | ||||
\(866\) | 32.0000 | 1.08740 | ||||||||
\(867\) | − | 8.00000i | − | 0.271694i | ||||||
\(868\) | 15.0000i | 0.509133i | ||||||||
\(869\) | 8.00000 | 0.271381 | ||||||||
\(870\) | −5.00000 | − | 10.0000i | −0.169516 | − | 0.339032i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 11.0000i | 0.372507i | ||||||||
\(873\) | 9.00000i | 0.304604i | ||||||||
\(874\) | 64.0000 | 2.16483 | ||||||||
\(875\) | 10.0000 | − | 55.0000i | 0.338062 | − | 1.85934i | ||||
\(876\) | 2.00000 | 0.0675737 | ||||||||
\(877\) | 17.0000i | 0.574049i | 0.957923 | + | 0.287025i | \(0.0926662\pi\) | ||||
−0.957923 | + | 0.287025i | \(0.907334\pi\) | |||||||
\(878\) | 11.0000i | 0.371232i | ||||||||
\(879\) | −23.0000 | −0.775771 | ||||||||
\(880\) | −1.00000 | − | 2.00000i | −0.0337100 | − | 0.0674200i | ||||
\(881\) | −25.0000 | −0.842271 | −0.421136 | − | 0.906998i | \(-0.638368\pi\) | ||||
−0.421136 | + | 0.906998i | \(0.638368\pi\) | |||||||
\(882\) | 18.0000i | 0.606092i | ||||||||
\(883\) | 47.0000i | 1.58168i | 0.612026 | + | 0.790838i | \(0.290355\pi\) | ||||
−0.612026 | + | 0.790838i | \(0.709645\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.00000 | + | 4.00000i | −0.268917 | + | 0.134459i | ||||
\(886\) | 10.0000 | 0.335957 | ||||||||
\(887\) | − | 3.00000i | − | 0.100730i | −0.998731 | − | 0.0503651i | \(-0.983962\pi\) | ||
0.998731 | − | 0.0503651i | \(-0.0160385\pi\) | |||||||
\(888\) | − | 1.00000i | − | 0.0335578i | ||||||
\(889\) | 40.0000 | 1.34156 | ||||||||
\(890\) | 8.00000 | − | 4.00000i | 0.268161 | − | 0.134080i | ||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | − | 23.0000i | − | 0.770097i | ||||||
\(893\) | 96.0000i | 3.21252i | ||||||||
\(894\) | 20.0000 | 0.668900 | ||||||||
\(895\) | −6.00000 | − | 12.0000i | −0.200558 | − | 0.401116i | ||||
\(896\) | −5.00000 | −0.167038 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 12.0000i | − | 0.400445i | ||||||
\(899\) | 15.0000 | 0.500278 | ||||||||
\(900\) | −3.00000 | + | 4.00000i | −0.100000 | + | 0.133333i | ||||
\(901\) | −15.0000 | −0.499722 | ||||||||
\(902\) | − | 5.00000i | − | 0.166482i | ||||||
\(903\) | − | 45.0000i | − | 1.49751i | ||||||
\(904\) | −15.0000 | −0.498893 | ||||||||
\(905\) | 12.0000 | + | 24.0000i | 0.398893 | + | 0.797787i | ||||
\(906\) | −10.0000 | −0.332228 | ||||||||
\(907\) | 52.0000i | 1.72663i | 0.504664 | + | 0.863316i | \(0.331616\pi\) | ||||
−0.504664 | + | 0.863316i | \(0.668384\pi\) | |||||||
\(908\) | − | 21.0000i | − | 0.696909i | ||||||
\(909\) | 6.00000 | 0.199007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −60.0000 | −1.98789 | −0.993944 | − | 0.109885i | \(-0.964952\pi\) | ||||
−0.993944 | + | 0.109885i | \(0.964952\pi\) | |||||||
\(912\) | 8.00000i | 0.264906i | ||||||||
\(913\) | 4.00000i | 0.132381i | ||||||||
\(914\) | 13.0000 | 0.430002 | ||||||||
\(915\) | 18.0000 | − | 9.00000i | 0.595062 | − | 0.297531i | ||||
\(916\) | −4.00000 | −0.132164 | ||||||||
\(917\) | 30.0000i | 0.990687i | ||||||||
\(918\) | 3.00000i | 0.0990148i | ||||||||
\(919\) | −40.0000 | −1.31948 | −0.659739 | − | 0.751495i | \(-0.729333\pi\) | ||||
−0.659739 | + | 0.751495i | \(0.729333\pi\) | |||||||
\(920\) | −8.00000 | − | 16.0000i | −0.263752 | − | 0.527504i | ||||
\(921\) | 4.00000 | 0.131804 | ||||||||
\(922\) | − | 3.00000i | − | 0.0987997i | ||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 5.00000 | 0.164488 | ||||||||
\(925\) | −4.00000 | − | 3.00000i | −0.131519 | − | 0.0986394i | ||||
\(926\) | 20.0000 | 0.657241 | ||||||||
\(927\) | 4.00000i | 0.131377i | ||||||||
\(928\) | 5.00000i | 0.164133i | ||||||||
\(929\) | −25.0000 | −0.820223 | −0.410112 | − | 0.912035i | \(-0.634510\pi\) | ||||
−0.410112 | + | 0.912035i | \(0.634510\pi\) | |||||||
\(930\) | −3.00000 | − | 6.00000i | −0.0983739 | − | 0.196748i | ||||
\(931\) | 144.000 | 4.71941 | ||||||||
\(932\) | − | 6.00000i | − | 0.196537i | ||||||
\(933\) | − | 17.0000i | − | 0.556555i | ||||||
\(934\) | −31.0000 | −1.01435 | ||||||||
\(935\) | −6.00000 | + | 3.00000i | −0.196221 | + | 0.0981105i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | − | 40.0000i | − | 1.30605i | ||||||
\(939\) | −26.0000 | −0.848478 | ||||||||
\(940\) | 24.0000 | − | 12.0000i | 0.782794 | − | 0.391397i | ||||
\(941\) | 30.0000 | 0.977972 | 0.488986 | − | 0.872292i | \(-0.337367\pi\) | ||||
0.488986 | + | 0.872292i | \(0.337367\pi\) | |||||||
\(942\) | − | 11.0000i | − | 0.358399i | ||||||
\(943\) | − | 40.0000i | − | 1.30258i | ||||||
\(944\) | 4.00000 | 0.130189 | ||||||||
\(945\) | −5.00000 | − | 10.0000i | −0.162650 | − | 0.325300i | ||||
\(946\) | −9.00000 | −0.292615 | ||||||||
\(947\) | − | 15.0000i | − | 0.487435i | −0.969846 | − | 0.243717i | \(-0.921633\pi\) | ||
0.969846 | − | 0.243717i | \(-0.0783669\pi\) | |||||||
\(948\) | 8.00000i | 0.259828i | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 32.0000 | + | 24.0000i | 1.03822 | + | 0.778663i | ||||
\(951\) | −11.0000 | −0.356699 | ||||||||
\(952\) | 15.0000i | 0.486153i | ||||||||
\(953\) | − | 22.0000i | − | 0.712650i | −0.934362 | − | 0.356325i | \(-0.884030\pi\) | ||
0.934362 | − | 0.356325i | \(-0.115970\pi\) | |||||||
\(954\) | −5.00000 | −0.161881 | ||||||||
\(955\) | 27.0000 | + | 54.0000i | 0.873699 | + | 1.74740i | ||||
\(956\) | −19.0000 | −0.614504 | ||||||||
\(957\) | − | 5.00000i | − | 0.161627i | ||||||
\(958\) | 36.0000i | 1.16311i | ||||||||
\(959\) | −30.0000 | −0.968751 | ||||||||
\(960\) | 2.00000 | − | 1.00000i | 0.0645497 | − | 0.0322749i | ||||
\(961\) | −22.0000 | −0.709677 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 2.00000i | − | 0.0644491i | ||||||
\(964\) | 10.0000 | 0.322078 | ||||||||
\(965\) | −20.0000 | + | 10.0000i | −0.643823 | + | 0.321911i | ||||
\(966\) | 40.0000 | 1.28698 | ||||||||
\(967\) | 34.0000i | 1.09337i | 0.837340 | + | 0.546683i | \(0.184110\pi\) | ||||
−0.837340 | + | 0.546683i | \(0.815890\pi\) | |||||||
\(968\) | 10.0000i | 0.321412i | ||||||||
\(969\) | 24.0000 | 0.770991 | ||||||||
\(970\) | −9.00000 | − | 18.0000i | −0.288973 | − | 0.577945i | ||||
\(971\) | −5.00000 | −0.160458 | −0.0802288 | − | 0.996776i | \(-0.525565\pi\) | ||||
−0.0802288 | + | 0.996776i | \(0.525565\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 25.0000i | 0.801463i | ||||||||
\(974\) | 32.0000 | 1.02535 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.00000 | −0.288083 | ||||||||
\(977\) | − | 47.0000i | − | 1.50366i | −0.659355 | − | 0.751832i | \(-0.729171\pi\) | ||
0.659355 | − | 0.751832i | \(-0.270829\pi\) | |||||||
\(978\) | 1.00000i | 0.0319765i | ||||||||
\(979\) | 4.00000 | 0.127841 | ||||||||
\(980\) | −18.0000 | − | 36.0000i | −0.574989 | − | 1.14998i | ||||
\(981\) | 11.0000 | 0.351203 | ||||||||
\(982\) | 20.0000i | 0.638226i | ||||||||
\(983\) | − | 15.0000i | − | 0.478426i | −0.970967 | − | 0.239213i | \(-0.923111\pi\) | ||
0.970967 | − | 0.239213i | \(-0.0768894\pi\) | |||||||
\(984\) | 5.00000 | 0.159394 | ||||||||
\(985\) | 12.0000 | − | 6.00000i | 0.382352 | − | 0.191176i | ||||
\(986\) | 15.0000 | 0.477697 | ||||||||
\(987\) | 60.0000i | 1.90982i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −72.0000 | −2.28947 | ||||||||
\(990\) | −2.00000 | + | 1.00000i | −0.0635642 | + | 0.0317821i | ||||
\(991\) | 25.0000 | 0.794151 | 0.397076 | − | 0.917786i | \(-0.370025\pi\) | ||||
0.397076 | + | 0.917786i | \(0.370025\pi\) | |||||||
\(992\) | 3.00000i | 0.0952501i | ||||||||
\(993\) | − | 22.0000i | − | 0.698149i | ||||||
\(994\) | 30.0000 | 0.951542 | ||||||||
\(995\) | 16.0000 | + | 32.0000i | 0.507234 | + | 1.01447i | ||||
\(996\) | −4.00000 | −0.126745 | ||||||||
\(997\) | 60.0000i | 1.90022i | 0.311916 | + | 0.950110i | \(0.399029\pi\) | ||||
−0.311916 | + | 0.950110i | \(0.600971\pi\) | |||||||
\(998\) | 6.00000i | 0.189927i | ||||||||
\(999\) | −1.00000 | −0.0316386 |
(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 | 1110.2.d.b.889.2 | yes | 2 | |
3.2 | odd | 2 | 3330.2.d.e.1999.1 | 2 | |||
5.2 | odd | 4 | 5550.2.a.l.1.1 | 1 | |||
5.3 | odd | 4 | 5550.2.a.be.1.1 | 1 | |||
5.4 | even | 2 | inner | 1110.2.d.b.889.1 | ✓ | 2 | |
15.14 | odd | 2 | 3330.2.d.e.1999.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.d.b.889.1 | ✓ | 2 | 5.4 | even | 2 | inner | |
1110.2.d.b.889.2 | yes | 2 | 1.1 | even | 1 | trivial | |
3330.2.d.e.1999.1 | 2 | 3.2 | odd | 2 | |||
3330.2.d.e.1999.2 | 2 | 15.14 | odd | 2 | |||
5550.2.a.l.1.1 | 1 | 5.2 | odd | 4 | |||
5550.2.a.be.1.1 | 1 | 5.3 | odd | 4 |