Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1815,2,Mod(364,1815)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1815, 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("1815.364");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1815 = 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1815.c (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: | \(14.4928479669\) |
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 | 364.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1815.364 |
Dual form | 1815.2.c.b.364.2 |
$q$-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 \(\left(\mathbb{Z}/1815\mathbb{Z}\right)^\times\).
\(n\) | \(727\) | \(1211\) | \(1696\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | −0.935414 | − | 0.353553i | \(-0.884973\pi\) | ||
0.935414 | − | 0.353553i | \(-0.115027\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | − | 2.00000i | −0.447214 | − | 0.894427i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | − | 4.00000i | − | 1.51186i | −0.654654 | − | 0.755929i | \(-0.727186\pi\) | ||
0.654654 | − | 0.755929i | \(-0.272814\pi\) | |||||||
\(8\) | − | 3.00000i | − | 1.06066i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −2.00000 | + | 1.00000i | −0.632456 | + | 0.316228i | ||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 2.00000i | 0.554700i | 0.960769 | + | 0.277350i | \(0.0894562\pi\) | ||||
−0.960769 | + | 0.277350i | \(0.910544\pi\) | |||||||
\(14\) | −4.00000 | −1.06904 | ||||||||
\(15\) | 2.00000 | − | 1.00000i | 0.516398 | − | 0.258199i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | − | 2.00000i | − | 0.485071i | −0.970143 | − | 0.242536i | \(-0.922021\pi\) | ||
0.970143 | − | 0.242536i | \(-0.0779791\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 8.00000 | 1.83533 | 0.917663 | − | 0.397360i | \(-0.130073\pi\) | ||||
0.917663 | + | 0.397360i | \(0.130073\pi\) | |||||||
\(20\) | −1.00000 | − | 2.00000i | −0.223607 | − | 0.447214i | ||||
\(21\) | 4.00000 | 0.872872 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 4.00000i | − | 0.834058i | −0.908893 | − | 0.417029i | \(-0.863071\pi\) | ||
0.908893 | − | 0.417029i | \(-0.136929\pi\) | |||||||
\(24\) | 3.00000 | 0.612372 | ||||||||
\(25\) | −3.00000 | + | 4.00000i | −0.600000 | + | 0.800000i | ||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | − | 4.00000i | − | 0.755929i | ||||||
\(29\) | 4.00000 | 0.742781 | 0.371391 | − | 0.928477i | \(-0.378881\pi\) | ||||
0.371391 | + | 0.928477i | \(0.378881\pi\) | |||||||
\(30\) | −1.00000 | − | 2.00000i | −0.182574 | − | 0.365148i | ||||
\(31\) | −8.00000 | −1.43684 | −0.718421 | − | 0.695608i | \(-0.755135\pi\) | ||||
−0.718421 | + | 0.695608i | \(0.755135\pi\) | |||||||
\(32\) | − | 5.00000i | − | 0.883883i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | −8.00000 | + | 4.00000i | −1.35225 | + | 0.676123i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 8.00000i | 1.31519i | 0.753371 | + | 0.657596i | \(0.228427\pi\) | ||||
−0.753371 | + | 0.657596i | \(0.771573\pi\) | |||||||
\(38\) | − | 8.00000i | − | 1.29777i | ||||||
\(39\) | −2.00000 | −0.320256 | ||||||||
\(40\) | −6.00000 | + | 3.00000i | −0.948683 | + | 0.474342i | ||||
\(41\) | −12.0000 | −1.87409 | −0.937043 | − | 0.349215i | \(-0.886448\pi\) | ||||
−0.937043 | + | 0.349215i | \(0.886448\pi\) | |||||||
\(42\) | − | 4.00000i | − | 0.617213i | ||||||
\(43\) | − | 8.00000i | − | 1.21999i | −0.792406 | − | 0.609994i | \(-0.791172\pi\) | ||
0.792406 | − | 0.609994i | \(-0.208828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | + | 2.00000i | 0.149071 | + | 0.298142i | ||||
\(46\) | −4.00000 | −0.589768 | ||||||||
\(47\) | − | 4.00000i | − | 0.583460i | −0.956501 | − | 0.291730i | \(-0.905769\pi\) | ||
0.956501 | − | 0.291730i | \(-0.0942309\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | −9.00000 | −1.28571 | ||||||||
\(50\) | 4.00000 | + | 3.00000i | 0.565685 | + | 0.424264i | ||||
\(51\) | 2.00000 | 0.280056 | ||||||||
\(52\) | 2.00000i | 0.277350i | ||||||||
\(53\) | 4.00000i | 0.549442i | 0.961524 | + | 0.274721i | \(0.0885855\pi\) | ||||
−0.961524 | + | 0.274721i | \(0.911414\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −12.0000 | −1.60357 | ||||||||
\(57\) | 8.00000i | 1.05963i | ||||||||
\(58\) | − | 4.00000i | − | 0.525226i | ||||||
\(59\) | 8.00000 | 1.04151 | 0.520756 | − | 0.853706i | \(-0.325650\pi\) | ||||
0.520756 | + | 0.853706i | \(0.325650\pi\) | |||||||
\(60\) | 2.00000 | − | 1.00000i | 0.258199 | − | 0.129099i | ||||
\(61\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(62\) | 8.00000i | 1.01600i | ||||||||
\(63\) | 4.00000i | 0.503953i | ||||||||
\(64\) | −7.00000 | −0.875000 | ||||||||
\(65\) | 4.00000 | − | 2.00000i | 0.496139 | − | 0.248069i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 4.00000i | − | 0.488678i | −0.969690 | − | 0.244339i | \(-0.921429\pi\) | ||
0.969690 | − | 0.244339i | \(-0.0785709\pi\) | |||||||
\(68\) | − | 2.00000i | − | 0.242536i | ||||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | 4.00000 | + | 8.00000i | 0.478091 | + | 0.956183i | ||||
\(71\) | −12.0000 | −1.42414 | −0.712069 | − | 0.702109i | \(-0.752242\pi\) | ||||
−0.712069 | + | 0.702109i | \(0.752242\pi\) | |||||||
\(72\) | 3.00000i | 0.353553i | ||||||||
\(73\) | 2.00000i | 0.234082i | 0.993127 | + | 0.117041i | \(0.0373409\pi\) | ||||
−0.993127 | + | 0.117041i | \(0.962659\pi\) | |||||||
\(74\) | 8.00000 | 0.929981 | ||||||||
\(75\) | −4.00000 | − | 3.00000i | −0.461880 | − | 0.346410i | ||||
\(76\) | 8.00000 | 0.917663 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.00000i | 0.226455i | ||||||||
\(79\) | 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 | ||||||||
\(82\) | 12.0000i | 1.32518i | ||||||||
\(83\) | 4.00000i | 0.439057i | 0.975606 | + | 0.219529i | \(0.0704519\pi\) | ||||
−0.975606 | + | 0.219529i | \(0.929548\pi\) | |||||||
\(84\) | 4.00000 | 0.436436 | ||||||||
\(85\) | −4.00000 | + | 2.00000i | −0.433861 | + | 0.216930i | ||||
\(86\) | −8.00000 | −0.862662 | ||||||||
\(87\) | 4.00000i | 0.428845i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | 2.00000 | − | 1.00000i | 0.210819 | − | 0.105409i | ||||
\(91\) | 8.00000 | 0.838628 | ||||||||
\(92\) | − | 4.00000i | − | 0.417029i | ||||||
\(93\) | − | 8.00000i | − | 0.829561i | ||||||
\(94\) | −4.00000 | −0.412568 | ||||||||
\(95\) | −8.00000 | − | 16.0000i | −0.820783 | − | 1.64157i | ||||
\(96\) | 5.00000 | 0.510310 | ||||||||
\(97\) | − | 8.00000i | − | 0.812277i | −0.913812 | − | 0.406138i | \(-0.866875\pi\) | ||
0.913812 | − | 0.406138i | \(-0.133125\pi\) | |||||||
\(98\) | 9.00000i | 0.909137i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.00000 | + | 4.00000i | −0.300000 | + | 0.400000i | ||||
\(101\) | 4.00000 | 0.398015 | 0.199007 | − | 0.979998i | \(-0.436228\pi\) | ||||
0.199007 | + | 0.979998i | \(0.436228\pi\) | |||||||
\(102\) | − | 2.00000i | − | 0.198030i | ||||||
\(103\) | 12.0000i | 1.18240i | 0.806527 | + | 0.591198i | \(0.201345\pi\) | ||||
−0.806527 | + | 0.591198i | \(0.798655\pi\) | |||||||
\(104\) | 6.00000 | 0.588348 | ||||||||
\(105\) | −4.00000 | − | 8.00000i | −0.390360 | − | 0.780720i | ||||
\(106\) | 4.00000 | 0.388514 | ||||||||
\(107\) | − | 12.0000i | − | 1.16008i | −0.814587 | − | 0.580042i | \(-0.803036\pi\) | ||
0.814587 | − | 0.580042i | \(-0.196964\pi\) | |||||||
\(108\) | − | 1.00000i | − | 0.0962250i | ||||||
\(109\) | −8.00000 | −0.766261 | −0.383131 | − | 0.923694i | \(-0.625154\pi\) | ||||
−0.383131 | + | 0.923694i | \(0.625154\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.00000 | −0.759326 | ||||||||
\(112\) | 4.00000i | 0.377964i | ||||||||
\(113\) | − | 12.0000i | − | 1.12887i | −0.825479 | − | 0.564433i | \(-0.809095\pi\) | ||
0.825479 | − | 0.564433i | \(-0.190905\pi\) | |||||||
\(114\) | 8.00000 | 0.749269 | ||||||||
\(115\) | −8.00000 | + | 4.00000i | −0.746004 | + | 0.373002i | ||||
\(116\) | 4.00000 | 0.371391 | ||||||||
\(117\) | − | 2.00000i | − | 0.184900i | ||||||
\(118\) | − | 8.00000i | − | 0.736460i | ||||||
\(119\) | −8.00000 | −0.733359 | ||||||||
\(120\) | −3.00000 | − | 6.00000i | −0.273861 | − | 0.547723i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 12.0000i | − | 1.08200i | ||||||
\(124\) | −8.00000 | −0.718421 | ||||||||
\(125\) | 11.0000 | + | 2.00000i | 0.983870 | + | 0.178885i | ||||
\(126\) | 4.00000 | 0.356348 | ||||||||
\(127\) | 4.00000i | 0.354943i | 0.984126 | + | 0.177471i | \(0.0567917\pi\) | ||||
−0.984126 | + | 0.177471i | \(0.943208\pi\) | |||||||
\(128\) | − | 3.00000i | − | 0.265165i | ||||||
\(129\) | 8.00000 | 0.704361 | ||||||||
\(130\) | −2.00000 | − | 4.00000i | −0.175412 | − | 0.350823i | ||||
\(131\) | −8.00000 | −0.698963 | −0.349482 | − | 0.936943i | \(-0.613642\pi\) | ||||
−0.349482 | + | 0.936943i | \(0.613642\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 32.0000i | − | 2.77475i | ||||||
\(134\) | −4.00000 | −0.345547 | ||||||||
\(135\) | −2.00000 | + | 1.00000i | −0.172133 | + | 0.0860663i | ||||
\(136\) | −6.00000 | −0.514496 | ||||||||
\(137\) | − | 4.00000i | − | 0.341743i | −0.985293 | − | 0.170872i | \(-0.945342\pi\) | ||
0.985293 | − | 0.170872i | \(-0.0546583\pi\) | |||||||
\(138\) | − | 4.00000i | − | 0.340503i | ||||||
\(139\) | 16.0000 | 1.35710 | 0.678551 | − | 0.734553i | \(-0.262608\pi\) | ||||
0.678551 | + | 0.734553i | \(0.262608\pi\) | |||||||
\(140\) | −8.00000 | + | 4.00000i | −0.676123 | + | 0.338062i | ||||
\(141\) | 4.00000 | 0.336861 | ||||||||
\(142\) | 12.0000i | 1.00702i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −4.00000 | − | 8.00000i | −0.332182 | − | 0.664364i | ||||
\(146\) | 2.00000 | 0.165521 | ||||||||
\(147\) | − | 9.00000i | − | 0.742307i | ||||||
\(148\) | 8.00000i | 0.657596i | ||||||||
\(149\) | 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 | ||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | − | 24.0000i | − | 1.94666i | ||||||
\(153\) | 2.00000i | 0.161690i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.00000 | + | 16.0000i | 0.642575 | + | 1.28515i | ||||
\(156\) | −2.00000 | −0.160128 | ||||||||
\(157\) | 8.00000i | 0.638470i | 0.947676 | + | 0.319235i | \(0.103426\pi\) | ||||
−0.947676 | + | 0.319235i | \(0.896574\pi\) | |||||||
\(158\) | − | 8.00000i | − | 0.636446i | ||||||
\(159\) | −4.00000 | −0.317221 | ||||||||
\(160\) | −10.0000 | + | 5.00000i | −0.790569 | + | 0.395285i | ||||
\(161\) | −16.0000 | −1.26098 | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | 20.0000i | 1.56652i | 0.621694 | + | 0.783260i | \(0.286445\pi\) | ||||
−0.621694 | + | 0.783260i | \(0.713555\pi\) | |||||||
\(164\) | −12.0000 | −0.937043 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.00000 | 0.310460 | ||||||||
\(167\) | − | 24.0000i | − | 1.85718i | −0.371113 | − | 0.928588i | \(-0.621024\pi\) | ||
0.371113 | − | 0.928588i | \(-0.378976\pi\) | |||||||
\(168\) | − | 12.0000i | − | 0.925820i | ||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 2.00000 | + | 4.00000i | 0.153393 | + | 0.306786i | ||||
\(171\) | −8.00000 | −0.611775 | ||||||||
\(172\) | − | 8.00000i | − | 0.609994i | ||||||
\(173\) | 14.0000i | 1.06440i | 0.846619 | + | 0.532200i | \(0.178635\pi\) | ||||
−0.846619 | + | 0.532200i | \(0.821365\pi\) | |||||||
\(174\) | 4.00000 | 0.303239 | ||||||||
\(175\) | 16.0000 | + | 12.0000i | 1.20949 | + | 0.907115i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.00000i | 0.601317i | ||||||||
\(178\) | 6.00000i | 0.449719i | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 1.00000 | + | 2.00000i | 0.0745356 | + | 0.149071i | ||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | − | 8.00000i | − | 0.592999i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −12.0000 | −0.884652 | ||||||||
\(185\) | 16.0000 | − | 8.00000i | 1.17634 | − | 0.588172i | ||||
\(186\) | −8.00000 | −0.586588 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 4.00000i | − | 0.291730i | ||||||
\(189\) | −4.00000 | −0.290957 | ||||||||
\(190\) | −16.0000 | + | 8.00000i | −1.16076 | + | 0.580381i | ||||
\(191\) | 12.0000 | 0.868290 | 0.434145 | − | 0.900843i | \(-0.357051\pi\) | ||||
0.434145 | + | 0.900843i | \(0.357051\pi\) | |||||||
\(192\) | − | 7.00000i | − | 0.505181i | ||||||
\(193\) | − | 6.00000i | − | 0.431889i | −0.976406 | − | 0.215945i | \(-0.930717\pi\) | ||
0.976406 | − | 0.215945i | \(-0.0692831\pi\) | |||||||
\(194\) | −8.00000 | −0.574367 | ||||||||
\(195\) | 2.00000 | + | 4.00000i | 0.143223 | + | 0.286446i | ||||
\(196\) | −9.00000 | −0.642857 | ||||||||
\(197\) | − | 6.00000i | − | 0.427482i | −0.976890 | − | 0.213741i | \(-0.931435\pi\) | ||
0.976890 | − | 0.213741i | \(-0.0685649\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.0000 | 1.13421 | 0.567105 | − | 0.823646i | \(-0.308063\pi\) | ||||
0.567105 | + | 0.823646i | \(0.308063\pi\) | |||||||
\(200\) | 12.0000 | + | 9.00000i | 0.848528 | + | 0.636396i | ||||
\(201\) | 4.00000 | 0.282138 | ||||||||
\(202\) | − | 4.00000i | − | 0.281439i | ||||||
\(203\) | − | 16.0000i | − | 1.12298i | ||||||
\(204\) | 2.00000 | 0.140028 | ||||||||
\(205\) | 12.0000 | + | 24.0000i | 0.838116 | + | 1.67623i | ||||
\(206\) | 12.0000 | 0.836080 | ||||||||
\(207\) | 4.00000i | 0.278019i | ||||||||
\(208\) | − | 2.00000i | − | 0.138675i | ||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −8.00000 | + | 4.00000i | −0.552052 | + | 0.276026i | ||||
\(211\) | 16.0000 | 1.10149 | 0.550743 | − | 0.834675i | \(-0.314345\pi\) | ||||
0.550743 | + | 0.834675i | \(0.314345\pi\) | |||||||
\(212\) | 4.00000i | 0.274721i | ||||||||
\(213\) | − | 12.0000i | − | 0.822226i | ||||||
\(214\) | −12.0000 | −0.820303 | ||||||||
\(215\) | −16.0000 | + | 8.00000i | −1.09119 | + | 0.545595i | ||||
\(216\) | −3.00000 | −0.204124 | ||||||||
\(217\) | 32.0000i | 2.17230i | ||||||||
\(218\) | 8.00000i | 0.541828i | ||||||||
\(219\) | −2.00000 | −0.135147 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.00000 | 0.269069 | ||||||||
\(222\) | 8.00000i | 0.536925i | ||||||||
\(223\) | 4.00000i | 0.267860i | 0.990991 | + | 0.133930i | \(0.0427597\pi\) | ||||
−0.990991 | + | 0.133930i | \(0.957240\pi\) | |||||||
\(224\) | −20.0000 | −1.33631 | ||||||||
\(225\) | 3.00000 | − | 4.00000i | 0.200000 | − | 0.266667i | ||||
\(226\) | −12.0000 | −0.798228 | ||||||||
\(227\) | 12.0000i | 0.796468i | 0.917284 | + | 0.398234i | \(0.130377\pi\) | ||||
−0.917284 | + | 0.398234i | \(0.869623\pi\) | |||||||
\(228\) | 8.00000i | 0.529813i | ||||||||
\(229\) | 22.0000 | 1.45380 | 0.726900 | − | 0.686743i | \(-0.240960\pi\) | ||||
0.726900 | + | 0.686743i | \(0.240960\pi\) | |||||||
\(230\) | 4.00000 | + | 8.00000i | 0.263752 | + | 0.527504i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 12.0000i | − | 0.787839i | ||||||
\(233\) | 6.00000i | 0.393073i | 0.980497 | + | 0.196537i | \(0.0629694\pi\) | ||||
−0.980497 | + | 0.196537i | \(0.937031\pi\) | |||||||
\(234\) | −2.00000 | −0.130744 | ||||||||
\(235\) | −8.00000 | + | 4.00000i | −0.521862 | + | 0.260931i | ||||
\(236\) | 8.00000 | 0.520756 | ||||||||
\(237\) | 8.00000i | 0.519656i | ||||||||
\(238\) | 8.00000i | 0.518563i | ||||||||
\(239\) | −24.0000 | −1.55243 | −0.776215 | − | 0.630468i | \(-0.782863\pi\) | ||||
−0.776215 | + | 0.630468i | \(0.782863\pi\) | |||||||
\(240\) | −2.00000 | + | 1.00000i | −0.129099 | + | 0.0645497i | ||||
\(241\) | −8.00000 | −0.515325 | −0.257663 | − | 0.966235i | \(-0.582952\pi\) | ||||
−0.257663 | + | 0.966235i | \(0.582952\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.00000 | + | 18.0000i | 0.574989 | + | 1.14998i | ||||
\(246\) | −12.0000 | −0.765092 | ||||||||
\(247\) | 16.0000i | 1.01806i | ||||||||
\(248\) | 24.0000i | 1.52400i | ||||||||
\(249\) | −4.00000 | −0.253490 | ||||||||
\(250\) | 2.00000 | − | 11.0000i | 0.126491 | − | 0.695701i | ||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 4.00000i | 0.251976i | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 4.00000 | 0.250982 | ||||||||
\(255\) | −2.00000 | − | 4.00000i | −0.125245 | − | 0.250490i | ||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | 4.00000i | 0.249513i | 0.992187 | + | 0.124757i | \(0.0398150\pi\) | ||||
−0.992187 | + | 0.124757i | \(0.960185\pi\) | |||||||
\(258\) | − | 8.00000i | − | 0.498058i | ||||||
\(259\) | 32.0000 | 1.98838 | ||||||||
\(260\) | 4.00000 | − | 2.00000i | 0.248069 | − | 0.124035i | ||||
\(261\) | −4.00000 | −0.247594 | ||||||||
\(262\) | 8.00000i | 0.494242i | ||||||||
\(263\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.00000 | − | 4.00000i | 0.491436 | − | 0.245718i | ||||
\(266\) | −32.0000 | −1.96205 | ||||||||
\(267\) | − | 6.00000i | − | 0.367194i | ||||||
\(268\) | − | 4.00000i | − | 0.244339i | ||||||
\(269\) | 26.0000 | 1.58525 | 0.792624 | − | 0.609711i | \(-0.208714\pi\) | ||||
0.792624 | + | 0.609711i | \(0.208714\pi\) | |||||||
\(270\) | 1.00000 | + | 2.00000i | 0.0608581 | + | 0.121716i | ||||
\(271\) | −16.0000 | −0.971931 | −0.485965 | − | 0.873978i | \(-0.661532\pi\) | ||||
−0.485965 | + | 0.873978i | \(0.661532\pi\) | |||||||
\(272\) | 2.00000i | 0.121268i | ||||||||
\(273\) | 8.00000i | 0.484182i | ||||||||
\(274\) | −4.00000 | −0.241649 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.00000 | 0.240772 | ||||||||
\(277\) | − | 10.0000i | − | 0.600842i | −0.953807 | − | 0.300421i | \(-0.902873\pi\) | ||
0.953807 | − | 0.300421i | \(-0.0971271\pi\) | |||||||
\(278\) | − | 16.0000i | − | 0.959616i | ||||||
\(279\) | 8.00000 | 0.478947 | ||||||||
\(280\) | 12.0000 | + | 24.0000i | 0.717137 | + | 1.43427i | ||||
\(281\) | −12.0000 | −0.715860 | −0.357930 | − | 0.933748i | \(-0.616517\pi\) | ||||
−0.357930 | + | 0.933748i | \(0.616517\pi\) | |||||||
\(282\) | − | 4.00000i | − | 0.238197i | ||||||
\(283\) | − | 16.0000i | − | 0.951101i | −0.879688 | − | 0.475551i | \(-0.842249\pi\) | ||
0.879688 | − | 0.475551i | \(-0.157751\pi\) | |||||||
\(284\) | −12.0000 | −0.712069 | ||||||||
\(285\) | 16.0000 | − | 8.00000i | 0.947758 | − | 0.473879i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 48.0000i | 2.83335i | ||||||||
\(288\) | 5.00000i | 0.294628i | ||||||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | −8.00000 | + | 4.00000i | −0.469776 | + | 0.234888i | ||||
\(291\) | 8.00000 | 0.468968 | ||||||||
\(292\) | 2.00000i | 0.117041i | ||||||||
\(293\) | − | 6.00000i | − | 0.350524i | −0.984522 | − | 0.175262i | \(-0.943923\pi\) | ||
0.984522 | − | 0.175262i | \(-0.0560772\pi\) | |||||||
\(294\) | −9.00000 | −0.524891 | ||||||||
\(295\) | −8.00000 | − | 16.0000i | −0.465778 | − | 0.931556i | ||||
\(296\) | 24.0000 | 1.39497 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 20.0000i | − | 1.15857i | ||||||
\(299\) | 8.00000 | 0.462652 | ||||||||
\(300\) | −4.00000 | − | 3.00000i | −0.230940 | − | 0.173205i | ||||
\(301\) | −32.0000 | −1.84445 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.00000i | 0.229794i | ||||||||
\(304\) | −8.00000 | −0.458831 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.00000 | 0.114332 | ||||||||
\(307\) | − | 24.0000i | − | 1.36975i | −0.728659 | − | 0.684876i | \(-0.759856\pi\) | ||
0.728659 | − | 0.684876i | \(-0.240144\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.0000 | −0.682656 | ||||||||
\(310\) | 16.0000 | − | 8.00000i | 0.908739 | − | 0.454369i | ||||
\(311\) | 28.0000 | 1.58773 | 0.793867 | − | 0.608091i | \(-0.208065\pi\) | ||||
0.793867 | + | 0.608091i | \(0.208065\pi\) | |||||||
\(312\) | 6.00000i | 0.339683i | ||||||||
\(313\) | − | 16.0000i | − | 0.904373i | −0.891923 | − | 0.452187i | \(-0.850644\pi\) | ||
0.891923 | − | 0.452187i | \(-0.149356\pi\) | |||||||
\(314\) | 8.00000 | 0.451466 | ||||||||
\(315\) | 8.00000 | − | 4.00000i | 0.450749 | − | 0.225374i | ||||
\(316\) | 8.00000 | 0.450035 | ||||||||
\(317\) | 20.0000i | 1.12331i | 0.827371 | + | 0.561656i | \(0.189836\pi\) | ||||
−0.827371 | + | 0.561656i | \(0.810164\pi\) | |||||||
\(318\) | 4.00000i | 0.224309i | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 7.00000 | + | 14.0000i | 0.391312 | + | 0.782624i | ||||
\(321\) | 12.0000 | 0.669775 | ||||||||
\(322\) | 16.0000i | 0.891645i | ||||||||
\(323\) | − | 16.0000i | − | 0.890264i | ||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −8.00000 | − | 6.00000i | −0.443760 | − | 0.332820i | ||||
\(326\) | 20.0000 | 1.10770 | ||||||||
\(327\) | − | 8.00000i | − | 0.442401i | ||||||
\(328\) | 36.0000i | 1.98777i | ||||||||
\(329\) | −16.0000 | −0.882109 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.00000 | 0.219860 | 0.109930 | − | 0.993939i | \(-0.464937\pi\) | ||||
0.109930 | + | 0.993939i | \(0.464937\pi\) | |||||||
\(332\) | 4.00000i | 0.219529i | ||||||||
\(333\) | − | 8.00000i | − | 0.438397i | ||||||
\(334\) | −24.0000 | −1.31322 | ||||||||
\(335\) | −8.00000 | + | 4.00000i | −0.437087 | + | 0.218543i | ||||
\(336\) | −4.00000 | −0.218218 | ||||||||
\(337\) | − | 26.0000i | − | 1.41631i | −0.706057 | − | 0.708155i | \(-0.749528\pi\) | ||
0.706057 | − | 0.708155i | \(-0.250472\pi\) | |||||||
\(338\) | − | 9.00000i | − | 0.489535i | ||||||
\(339\) | 12.0000 | 0.651751 | ||||||||
\(340\) | −4.00000 | + | 2.00000i | −0.216930 | + | 0.108465i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 8.00000i | 0.432590i | ||||||||
\(343\) | 8.00000i | 0.431959i | ||||||||
\(344\) | −24.0000 | −1.29399 | ||||||||
\(345\) | −4.00000 | − | 8.00000i | −0.215353 | − | 0.430706i | ||||
\(346\) | 14.0000 | 0.752645 | ||||||||
\(347\) | − | 12.0000i | − | 0.644194i | −0.946707 | − | 0.322097i | \(-0.895612\pi\) | ||
0.946707 | − | 0.322097i | \(-0.104388\pi\) | |||||||
\(348\) | 4.00000i | 0.214423i | ||||||||
\(349\) | 16.0000 | 0.856460 | 0.428230 | − | 0.903670i | \(-0.359137\pi\) | ||||
0.428230 | + | 0.903670i | \(0.359137\pi\) | |||||||
\(350\) | 12.0000 | − | 16.0000i | 0.641427 | − | 0.855236i | ||||
\(351\) | 2.00000 | 0.106752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 12.0000i | − | 0.638696i | −0.947638 | − | 0.319348i | \(-0.896536\pi\) | ||
0.947638 | − | 0.319348i | \(-0.103464\pi\) | |||||||
\(354\) | 8.00000 | 0.425195 | ||||||||
\(355\) | 12.0000 | + | 24.0000i | 0.636894 | + | 1.27379i | ||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | − | 8.00000i | − | 0.423405i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.0000 | 1.26667 | 0.633336 | − | 0.773877i | \(-0.281685\pi\) | ||||
0.633336 | + | 0.773877i | \(0.281685\pi\) | |||||||
\(360\) | 6.00000 | − | 3.00000i | 0.316228 | − | 0.158114i | ||||
\(361\) | 45.0000 | 2.36842 | ||||||||
\(362\) | 10.0000i | 0.525588i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.00000 | 0.419314 | ||||||||
\(365\) | 4.00000 | − | 2.00000i | 0.209370 | − | 0.104685i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 36.0000i | 1.87918i | 0.342296 | + | 0.939592i | \(0.388796\pi\) | ||||
−0.342296 | + | 0.939592i | \(0.611204\pi\) | |||||||
\(368\) | 4.00000i | 0.208514i | ||||||||
\(369\) | 12.0000 | 0.624695 | ||||||||
\(370\) | −8.00000 | − | 16.0000i | −0.415900 | − | 0.831800i | ||||
\(371\) | 16.0000 | 0.830679 | ||||||||
\(372\) | − | 8.00000i | − | 0.414781i | ||||||
\(373\) | 22.0000i | 1.13912i | 0.821951 | + | 0.569558i | \(0.192886\pi\) | ||||
−0.821951 | + | 0.569558i | \(0.807114\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.00000 | + | 11.0000i | −0.103280 | + | 0.568038i | ||||
\(376\) | −12.0000 | −0.618853 | ||||||||
\(377\) | 8.00000i | 0.412021i | ||||||||
\(378\) | 4.00000i | 0.205738i | ||||||||
\(379\) | 4.00000 | 0.205466 | 0.102733 | − | 0.994709i | \(-0.467241\pi\) | ||||
0.102733 | + | 0.994709i | \(0.467241\pi\) | |||||||
\(380\) | −8.00000 | − | 16.0000i | −0.410391 | − | 0.820783i | ||||
\(381\) | −4.00000 | −0.204926 | ||||||||
\(382\) | − | 12.0000i | − | 0.613973i | ||||||
\(383\) | 36.0000i | 1.83951i | 0.392488 | + | 0.919757i | \(0.371614\pi\) | ||||
−0.392488 | + | 0.919757i | \(0.628386\pi\) | |||||||
\(384\) | 3.00000 | 0.153093 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.00000 | −0.305392 | ||||||||
\(387\) | 8.00000i | 0.406663i | ||||||||
\(388\) | − | 8.00000i | − | 0.406138i | ||||||
\(389\) | −18.0000 | −0.912636 | −0.456318 | − | 0.889817i | \(-0.650832\pi\) | ||||
−0.456318 | + | 0.889817i | \(0.650832\pi\) | |||||||
\(390\) | 4.00000 | − | 2.00000i | 0.202548 | − | 0.101274i | ||||
\(391\) | −8.00000 | −0.404577 | ||||||||
\(392\) | 27.0000i | 1.36371i | ||||||||
\(393\) | − | 8.00000i | − | 0.403547i | ||||||
\(394\) | −6.00000 | −0.302276 | ||||||||
\(395\) | −8.00000 | − | 16.0000i | −0.402524 | − | 0.805047i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.00000i | 0.401508i | 0.979642 | + | 0.200754i | \(0.0643393\pi\) | ||||
−0.979642 | + | 0.200754i | \(0.935661\pi\) | |||||||
\(398\) | − | 16.0000i | − | 0.802008i | ||||||
\(399\) | 32.0000 | 1.60200 | ||||||||
\(400\) | 3.00000 | − | 4.00000i | 0.150000 | − | 0.200000i | ||||
\(401\) | −2.00000 | −0.0998752 | −0.0499376 | − | 0.998752i | \(-0.515902\pi\) | ||||
−0.0499376 | + | 0.998752i | \(0.515902\pi\) | |||||||
\(402\) | − | 4.00000i | − | 0.199502i | ||||||
\(403\) | − | 16.0000i | − | 0.797017i | ||||||
\(404\) | 4.00000 | 0.199007 | ||||||||
\(405\) | −1.00000 | − | 2.00000i | −0.0496904 | − | 0.0993808i | ||||
\(406\) | −16.0000 | −0.794067 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | − | 6.00000i | − | 0.297044i | ||||||
\(409\) | −40.0000 | −1.97787 | −0.988936 | − | 0.148340i | \(-0.952607\pi\) | ||||
−0.988936 | + | 0.148340i | \(0.952607\pi\) | |||||||
\(410\) | 24.0000 | − | 12.0000i | 1.18528 | − | 0.592638i | ||||
\(411\) | 4.00000 | 0.197305 | ||||||||
\(412\) | 12.0000i | 0.591198i | ||||||||
\(413\) | − | 32.0000i | − | 1.57462i | ||||||
\(414\) | 4.00000 | 0.196589 | ||||||||
\(415\) | 8.00000 | − | 4.00000i | 0.392705 | − | 0.196352i | ||||
\(416\) | 10.0000 | 0.490290 | ||||||||
\(417\) | 16.0000i | 0.783523i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.00000 | −0.390826 | −0.195413 | − | 0.980721i | \(-0.562605\pi\) | ||||
−0.195413 | + | 0.980721i | \(0.562605\pi\) | |||||||
\(420\) | −4.00000 | − | 8.00000i | −0.195180 | − | 0.390360i | ||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | − | 16.0000i | − | 0.778868i | ||||||
\(423\) | 4.00000i | 0.194487i | ||||||||
\(424\) | 12.0000 | 0.582772 | ||||||||
\(425\) | 8.00000 | + | 6.00000i | 0.388057 | + | 0.291043i | ||||
\(426\) | −12.0000 | −0.581402 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 12.0000i | − | 0.580042i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.00000 | + | 16.0000i | 0.385794 | + | 0.771589i | ||||
\(431\) | 24.0000 | 1.15604 | 0.578020 | − | 0.816023i | \(-0.303826\pi\) | ||||
0.578020 | + | 0.816023i | \(0.303826\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | − | 16.0000i | − | 0.768911i | −0.923144 | − | 0.384455i | \(-0.874389\pi\) | ||
0.923144 | − | 0.384455i | \(-0.125611\pi\) | |||||||
\(434\) | 32.0000 | 1.53605 | ||||||||
\(435\) | 8.00000 | − | 4.00000i | 0.383571 | − | 0.191785i | ||||
\(436\) | −8.00000 | −0.383131 | ||||||||
\(437\) | − | 32.0000i | − | 1.53077i | ||||||
\(438\) | 2.00000i | 0.0955637i | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.00000 | 0.428571 | ||||||||
\(442\) | − | 4.00000i | − | 0.190261i | ||||||
\(443\) | − | 12.0000i | − | 0.570137i | −0.958507 | − | 0.285069i | \(-0.907984\pi\) | ||
0.958507 | − | 0.285069i | \(-0.0920164\pi\) | |||||||
\(444\) | −8.00000 | −0.379663 | ||||||||
\(445\) | 6.00000 | + | 12.0000i | 0.284427 | + | 0.568855i | ||||
\(446\) | 4.00000 | 0.189405 | ||||||||
\(447\) | 20.0000i | 0.945968i | ||||||||
\(448\) | 28.0000i | 1.32288i | ||||||||
\(449\) | 30.0000 | 1.41579 | 0.707894 | − | 0.706319i | \(-0.249646\pi\) | ||||
0.707894 | + | 0.706319i | \(0.249646\pi\) | |||||||
\(450\) | −4.00000 | − | 3.00000i | −0.188562 | − | 0.141421i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 12.0000i | − | 0.564433i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 12.0000 | 0.563188 | ||||||||
\(455\) | −8.00000 | − | 16.0000i | −0.375046 | − | 0.750092i | ||||
\(456\) | 24.0000 | 1.12390 | ||||||||
\(457\) | 2.00000i | 0.0935561i | 0.998905 | + | 0.0467780i | \(0.0148953\pi\) | ||||
−0.998905 | + | 0.0467780i | \(0.985105\pi\) | |||||||
\(458\) | − | 22.0000i | − | 1.02799i | ||||||
\(459\) | −2.00000 | −0.0933520 | ||||||||
\(460\) | −8.00000 | + | 4.00000i | −0.373002 | + | 0.186501i | ||||
\(461\) | 12.0000 | 0.558896 | 0.279448 | − | 0.960161i | \(-0.409849\pi\) | ||||
0.279448 | + | 0.960161i | \(0.409849\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 28.0000i | − | 1.30127i | −0.759390 | − | 0.650635i | \(-0.774503\pi\) | ||
0.759390 | − | 0.650635i | \(-0.225497\pi\) | |||||||
\(464\) | −4.00000 | −0.185695 | ||||||||
\(465\) | −16.0000 | + | 8.00000i | −0.741982 | + | 0.370991i | ||||
\(466\) | 6.00000 | 0.277945 | ||||||||
\(467\) | 12.0000i | 0.555294i | 0.960683 | + | 0.277647i | \(0.0895545\pi\) | ||||
−0.960683 | + | 0.277647i | \(0.910445\pi\) | |||||||
\(468\) | − | 2.00000i | − | 0.0924500i | ||||||
\(469\) | −16.0000 | −0.738811 | ||||||||
\(470\) | 4.00000 | + | 8.00000i | 0.184506 | + | 0.369012i | ||||
\(471\) | −8.00000 | −0.368621 | ||||||||
\(472\) | − | 24.0000i | − | 1.10469i | ||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 8.00000 | 0.367452 | ||||||||
\(475\) | −24.0000 | + | 32.0000i | −1.10120 | + | 1.46826i | ||||
\(476\) | −8.00000 | −0.366679 | ||||||||
\(477\) | − | 4.00000i | − | 0.183147i | ||||||
\(478\) | 24.0000i | 1.09773i | ||||||||
\(479\) | −24.0000 | −1.09659 | −0.548294 | − | 0.836286i | \(-0.684723\pi\) | ||||
−0.548294 | + | 0.836286i | \(0.684723\pi\) | |||||||
\(480\) | −5.00000 | − | 10.0000i | −0.228218 | − | 0.456435i | ||||
\(481\) | −16.0000 | −0.729537 | ||||||||
\(482\) | 8.00000i | 0.364390i | ||||||||
\(483\) | − | 16.0000i | − | 0.728025i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.0000 | + | 8.00000i | −0.726523 | + | 0.363261i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 20.0000i | 0.906287i | 0.891438 | + | 0.453143i | \(0.149697\pi\) | ||||
−0.891438 | + | 0.453143i | \(0.850303\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −20.0000 | −0.904431 | ||||||||
\(490\) | 18.0000 | − | 9.00000i | 0.813157 | − | 0.406579i | ||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | − | 12.0000i | − | 0.541002i | ||||||
\(493\) | − | 8.00000i | − | 0.360302i | ||||||
\(494\) | 16.0000 | 0.719874 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.00000 | 0.359211 | ||||||||
\(497\) | 48.0000i | 2.15309i | ||||||||
\(498\) | 4.00000i | 0.179244i | ||||||||
\(499\) | 12.0000 | 0.537194 | 0.268597 | − | 0.963253i | \(-0.413440\pi\) | ||||
0.268597 | + | 0.963253i | \(0.413440\pi\) | |||||||
\(500\) | 11.0000 | + | 2.00000i | 0.491935 | + | 0.0894427i | ||||
\(501\) | 24.0000 | 1.07224 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.0000i | 1.07011i | 0.844818 | + | 0.535054i | \(0.179709\pi\) | ||||
−0.844818 | + | 0.535054i | \(0.820291\pi\) | |||||||
\(504\) | 12.0000 | 0.534522 | ||||||||
\(505\) | −4.00000 | − | 8.00000i | −0.177998 | − | 0.355995i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.00000i | 0.399704i | ||||||||
\(508\) | 4.00000i | 0.177471i | ||||||||
\(509\) | −26.0000 | −1.15243 | −0.576215 | − | 0.817298i | \(-0.695471\pi\) | ||||
−0.576215 | + | 0.817298i | \(0.695471\pi\) | |||||||
\(510\) | −4.00000 | + | 2.00000i | −0.177123 | + | 0.0885615i | ||||
\(511\) | 8.00000 | 0.353899 | ||||||||
\(512\) | 11.0000i | 0.486136i | ||||||||
\(513\) | − | 8.00000i | − | 0.353209i | ||||||
\(514\) | 4.00000 | 0.176432 | ||||||||
\(515\) | 24.0000 | − | 12.0000i | 1.05757 | − | 0.528783i | ||||
\(516\) | 8.00000 | 0.352180 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − | 32.0000i | − | 1.40600i | ||||||
\(519\) | −14.0000 | −0.614532 | ||||||||
\(520\) | −6.00000 | − | 12.0000i | −0.263117 | − | 0.526235i | ||||
\(521\) | 22.0000 | 0.963837 | 0.481919 | − | 0.876216i | \(-0.339940\pi\) | ||||
0.481919 | + | 0.876216i | \(0.339940\pi\) | |||||||
\(522\) | 4.00000i | 0.175075i | ||||||||
\(523\) | 24.0000i | 1.04945i | 0.851273 | + | 0.524723i | \(0.175831\pi\) | ||||
−0.851273 | + | 0.524723i | \(0.824169\pi\) | |||||||
\(524\) | −8.00000 | −0.349482 | ||||||||
\(525\) | −12.0000 | + | 16.0000i | −0.523723 | + | 0.698297i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.0000i | 0.696971i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | −4.00000 | − | 8.00000i | −0.173749 | − | 0.347498i | ||||
\(531\) | −8.00000 | −0.347170 | ||||||||
\(532\) | − | 32.0000i | − | 1.38738i | ||||||
\(533\) | − | 24.0000i | − | 1.03956i | ||||||
\(534\) | −6.00000 | −0.259645 | ||||||||
\(535\) | −24.0000 | + | 12.0000i | −1.03761 | + | 0.518805i | ||||
\(536\) | −12.0000 | −0.518321 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 26.0000i | − | 1.12094i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.00000 | + | 1.00000i | −0.0860663 | + | 0.0430331i | ||||
\(541\) | −8.00000 | −0.343947 | −0.171973 | − | 0.985102i | \(-0.555014\pi\) | ||||
−0.171973 | + | 0.985102i | \(0.555014\pi\) | |||||||
\(542\) | 16.0000i | 0.687259i | ||||||||
\(543\) | − | 10.0000i | − | 0.429141i | ||||||
\(544\) | −10.0000 | −0.428746 | ||||||||
\(545\) | 8.00000 | + | 16.0000i | 0.342682 | + | 0.685365i | ||||
\(546\) | 8.00000 | 0.342368 | ||||||||
\(547\) | 8.00000i | 0.342055i | 0.985266 | + | 0.171028i | \(0.0547087\pi\) | ||||
−0.985266 | + | 0.171028i | \(0.945291\pi\) | |||||||
\(548\) | − | 4.00000i | − | 0.170872i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 32.0000 | 1.36325 | ||||||||
\(552\) | − | 12.0000i | − | 0.510754i | ||||||
\(553\) | − | 32.0000i | − | 1.36078i | ||||||
\(554\) | −10.0000 | −0.424859 | ||||||||
\(555\) | 8.00000 | + | 16.0000i | 0.339581 | + | 0.679162i | ||||
\(556\) | 16.0000 | 0.678551 | ||||||||
\(557\) | − | 14.0000i | − | 0.593199i | −0.955002 | − | 0.296600i | \(-0.904147\pi\) | ||
0.955002 | − | 0.296600i | \(-0.0958526\pi\) | |||||||
\(558\) | − | 8.00000i | − | 0.338667i | ||||||
\(559\) | 16.0000 | 0.676728 | ||||||||
\(560\) | 8.00000 | − | 4.00000i | 0.338062 | − | 0.169031i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 12.0000i | 0.506189i | ||||||||
\(563\) | 36.0000i | 1.51722i | 0.651546 | + | 0.758610i | \(0.274121\pi\) | ||||
−0.651546 | + | 0.758610i | \(0.725879\pi\) | |||||||
\(564\) | 4.00000 | 0.168430 | ||||||||
\(565\) | −24.0000 | + | 12.0000i | −1.00969 | + | 0.504844i | ||||
\(566\) | −16.0000 | −0.672530 | ||||||||
\(567\) | − | 4.00000i | − | 0.167984i | ||||||
\(568\) | 36.0000i | 1.51053i | ||||||||
\(569\) | 44.0000 | 1.84458 | 0.922288 | − | 0.386503i | \(-0.126317\pi\) | ||||
0.922288 | + | 0.386503i | \(0.126317\pi\) | |||||||
\(570\) | −8.00000 | − | 16.0000i | −0.335083 | − | 0.670166i | ||||
\(571\) | 40.0000 | 1.67395 | 0.836974 | − | 0.547243i | \(-0.184323\pi\) | ||||
0.836974 | + | 0.547243i | \(0.184323\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.0000i | 0.501307i | ||||||||
\(574\) | 48.0000 | 2.00348 | ||||||||
\(575\) | 16.0000 | + | 12.0000i | 0.667246 | + | 0.500435i | ||||
\(576\) | 7.00000 | 0.291667 | ||||||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | − | 13.0000i | − | 0.540729i | ||||||
\(579\) | 6.00000 | 0.249351 | ||||||||
\(580\) | −4.00000 | − | 8.00000i | −0.166091 | − | 0.332182i | ||||
\(581\) | 16.0000 | 0.663792 | ||||||||
\(582\) | − | 8.00000i | − | 0.331611i | ||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 6.00000 | 0.248282 | ||||||||
\(585\) | −4.00000 | + | 2.00000i | −0.165380 | + | 0.0826898i | ||||
\(586\) | −6.00000 | −0.247858 | ||||||||
\(587\) | 12.0000i | 0.495293i | 0.968850 | + | 0.247647i | \(0.0796572\pi\) | ||||
−0.968850 | + | 0.247647i | \(0.920343\pi\) | |||||||
\(588\) | − | 9.00000i | − | 0.371154i | ||||||
\(589\) | −64.0000 | −2.63707 | ||||||||
\(590\) | −16.0000 | + | 8.00000i | −0.658710 | + | 0.329355i | ||||
\(591\) | 6.00000 | 0.246807 | ||||||||
\(592\) | − | 8.00000i | − | 0.328798i | ||||||
\(593\) | − | 14.0000i | − | 0.574911i | −0.957794 | − | 0.287456i | \(-0.907191\pi\) | ||
0.957794 | − | 0.287456i | \(-0.0928094\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.00000 | + | 16.0000i | 0.327968 | + | 0.655936i | ||||
\(596\) | 20.0000 | 0.819232 | ||||||||
\(597\) | 16.0000i | 0.654836i | ||||||||
\(598\) | − | 8.00000i | − | 0.327144i | ||||||
\(599\) | 12.0000 | 0.490307 | 0.245153 | − | 0.969484i | \(-0.421162\pi\) | ||||
0.245153 | + | 0.969484i | \(0.421162\pi\) | |||||||
\(600\) | −9.00000 | + | 12.0000i | −0.367423 | + | 0.489898i | ||||
\(601\) | 32.0000 | 1.30531 | 0.652654 | − | 0.757656i | \(-0.273656\pi\) | ||||
0.652654 | + | 0.757656i | \(0.273656\pi\) | |||||||
\(602\) | 32.0000i | 1.30422i | ||||||||
\(603\) | 4.00000i | 0.162893i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4.00000 | 0.162489 | ||||||||
\(607\) | − | 20.0000i | − | 0.811775i | −0.913923 | − | 0.405887i | \(-0.866962\pi\) | ||
0.913923 | − | 0.405887i | \(-0.133038\pi\) | |||||||
\(608\) | − | 40.0000i | − | 1.62221i | ||||||
\(609\) | 16.0000 | 0.648353 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.00000 | 0.323645 | ||||||||
\(612\) | 2.00000i | 0.0808452i | ||||||||
\(613\) | − | 42.0000i | − | 1.69636i | −0.529705 | − | 0.848182i | \(-0.677697\pi\) | ||
0.529705 | − | 0.848182i | \(-0.322303\pi\) | |||||||
\(614\) | −24.0000 | −0.968561 | ||||||||
\(615\) | −24.0000 | + | 12.0000i | −0.967773 | + | 0.483887i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 28.0000i | − | 1.12724i | −0.826035 | − | 0.563619i | \(-0.809409\pi\) | ||
0.826035 | − | 0.563619i | \(-0.190591\pi\) | |||||||
\(618\) | 12.0000i | 0.482711i | ||||||||
\(619\) | 36.0000 | 1.44696 | 0.723481 | − | 0.690344i | \(-0.242541\pi\) | ||||
0.723481 | + | 0.690344i | \(0.242541\pi\) | |||||||
\(620\) | 8.00000 | + | 16.0000i | 0.321288 | + | 0.642575i | ||||
\(621\) | −4.00000 | −0.160514 | ||||||||
\(622\) | − | 28.0000i | − | 1.12270i | ||||||
\(623\) | 24.0000i | 0.961540i | ||||||||
\(624\) | 2.00000 | 0.0800641 | ||||||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | −16.0000 | −0.639489 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.00000i | 0.319235i | ||||||||
\(629\) | 16.0000 | 0.637962 | ||||||||
\(630\) | −4.00000 | − | 8.00000i | −0.159364 | − | 0.318728i | ||||
\(631\) | 8.00000 | 0.318475 | 0.159237 | − | 0.987240i | \(-0.449096\pi\) | ||||
0.159237 | + | 0.987240i | \(0.449096\pi\) | |||||||
\(632\) | − | 24.0000i | − | 0.954669i | ||||||
\(633\) | 16.0000i | 0.635943i | ||||||||
\(634\) | 20.0000 | 0.794301 | ||||||||
\(635\) | 8.00000 | − | 4.00000i | 0.317470 | − | 0.158735i | ||||
\(636\) | −4.00000 | −0.158610 | ||||||||
\(637\) | − | 18.0000i | − | 0.713186i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.0000 | 0.474713 | ||||||||
\(640\) | −6.00000 | + | 3.00000i | −0.237171 | + | 0.118585i | ||||
\(641\) | −2.00000 | −0.0789953 | −0.0394976 | − | 0.999220i | \(-0.512576\pi\) | ||||
−0.0394976 | + | 0.999220i | \(0.512576\pi\) | |||||||
\(642\) | − | 12.0000i | − | 0.473602i | ||||||
\(643\) | − | 12.0000i | − | 0.473234i | −0.971603 | − | 0.236617i | \(-0.923961\pi\) | ||
0.971603 | − | 0.236617i | \(-0.0760386\pi\) | |||||||
\(644\) | −16.0000 | −0.630488 | ||||||||
\(645\) | −8.00000 | − | 16.0000i | −0.315000 | − | 0.629999i | ||||
\(646\) | −16.0000 | −0.629512 | ||||||||
\(647\) | − | 28.0000i | − | 1.10079i | −0.834903 | − | 0.550397i | \(-0.814476\pi\) | ||
0.834903 | − | 0.550397i | \(-0.185524\pi\) | |||||||
\(648\) | − | 3.00000i | − | 0.117851i | ||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −6.00000 | + | 8.00000i | −0.235339 | + | 0.313786i | ||||
\(651\) | −32.0000 | −1.25418 | ||||||||
\(652\) | 20.0000i | 0.783260i | ||||||||
\(653\) | − | 28.0000i | − | 1.09572i | −0.836569 | − | 0.547862i | \(-0.815442\pi\) | ||
0.836569 | − | 0.547862i | \(-0.184558\pi\) | |||||||
\(654\) | −8.00000 | −0.312825 | ||||||||
\(655\) | 8.00000 | + | 16.0000i | 0.312586 | + | 0.625172i | ||||
\(656\) | 12.0000 | 0.468521 | ||||||||
\(657\) | − | 2.00000i | − | 0.0780274i | ||||||
\(658\) | 16.0000i | 0.623745i | ||||||||
\(659\) | 24.0000 | 0.934907 | 0.467454 | − | 0.884018i | \(-0.345171\pi\) | ||||
0.467454 | + | 0.884018i | \(0.345171\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.00000 | 0.233373 | 0.116686 | − | 0.993169i | \(-0.462773\pi\) | ||||
0.116686 | + | 0.993169i | \(0.462773\pi\) | |||||||
\(662\) | − | 4.00000i | − | 0.155464i | ||||||
\(663\) | 4.00000i | 0.155347i | ||||||||
\(664\) | 12.0000 | 0.465690 | ||||||||
\(665\) | −64.0000 | + | 32.0000i | −2.48181 | + | 1.24091i | ||||
\(666\) | −8.00000 | −0.309994 | ||||||||
\(667\) | − | 16.0000i | − | 0.619522i | ||||||
\(668\) | − | 24.0000i | − | 0.928588i | ||||||
\(669\) | −4.00000 | −0.154649 | ||||||||
\(670\) | 4.00000 | + | 8.00000i | 0.154533 | + | 0.309067i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | − | 20.0000i | − | 0.771517i | ||||||
\(673\) | − | 38.0000i | − | 1.46479i | −0.680879 | − | 0.732396i | \(-0.738402\pi\) | ||
0.680879 | − | 0.732396i | \(-0.261598\pi\) | |||||||
\(674\) | −26.0000 | −1.00148 | ||||||||
\(675\) | 4.00000 | + | 3.00000i | 0.153960 | + | 0.115470i | ||||
\(676\) | 9.00000 | 0.346154 | ||||||||
\(677\) | 38.0000i | 1.46046i | 0.683202 | + | 0.730229i | \(0.260587\pi\) | ||||
−0.683202 | + | 0.730229i | \(0.739413\pi\) | |||||||
\(678\) | − | 12.0000i | − | 0.460857i | ||||||
\(679\) | −32.0000 | −1.22805 | ||||||||
\(680\) | 6.00000 | + | 12.0000i | 0.230089 | + | 0.460179i | ||||
\(681\) | −12.0000 | −0.459841 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 4.00000i | − | 0.153056i | −0.997067 | − | 0.0765279i | \(-0.975617\pi\) | ||
0.997067 | − | 0.0765279i | \(-0.0243834\pi\) | |||||||
\(684\) | −8.00000 | −0.305888 | ||||||||
\(685\) | −8.00000 | + | 4.00000i | −0.305664 | + | 0.152832i | ||||
\(686\) | 8.00000 | 0.305441 | ||||||||
\(687\) | 22.0000i | 0.839352i | ||||||||
\(688\) | 8.00000i | 0.304997i | ||||||||
\(689\) | −8.00000 | −0.304776 | ||||||||
\(690\) | −8.00000 | + | 4.00000i | −0.304555 | + | 0.152277i | ||||
\(691\) | −20.0000 | −0.760836 | −0.380418 | − | 0.924815i | \(-0.624220\pi\) | ||||
−0.380418 | + | 0.924815i | \(0.624220\pi\) | |||||||
\(692\) | 14.0000i | 0.532200i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.0000 | −0.455514 | ||||||||
\(695\) | −16.0000 | − | 32.0000i | −0.606915 | − | 1.21383i | ||||
\(696\) | 12.0000 | 0.454859 | ||||||||
\(697\) | 24.0000i | 0.909065i | ||||||||
\(698\) | − | 16.0000i | − | 0.605609i | ||||||
\(699\) | −6.00000 | −0.226941 | ||||||||
\(700\) | 16.0000 | + | 12.0000i | 0.604743 | + | 0.453557i | ||||
\(701\) | −12.0000 | −0.453234 | −0.226617 | − | 0.973984i | \(-0.572767\pi\) | ||||
−0.226617 | + | 0.973984i | \(0.572767\pi\) | |||||||
\(702\) | − | 2.00000i | − | 0.0754851i | ||||||
\(703\) | 64.0000i | 2.41381i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.00000 | − | 8.00000i | −0.150649 | − | 0.301297i | ||||
\(706\) | −12.0000 | −0.451626 | ||||||||
\(707\) | − | 16.0000i | − | 0.601742i | ||||||
\(708\) | 8.00000i | 0.300658i | ||||||||
\(709\) | −26.0000 | −0.976450 | −0.488225 | − | 0.872718i | \(-0.662356\pi\) | ||||
−0.488225 | + | 0.872718i | \(0.662356\pi\) | |||||||
\(710\) | 24.0000 | − | 12.0000i | 0.900704 | − | 0.450352i | ||||
\(711\) | −8.00000 | −0.300023 | ||||||||
\(712\) | 18.0000i | 0.674579i | ||||||||
\(713\) | 32.0000i | 1.19841i | ||||||||
\(714\) | −8.00000 | −0.299392 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 24.0000i | − | 0.896296i | ||||||
\(718\) | − | 24.0000i | − | 0.895672i | ||||||
\(719\) | −36.0000 | −1.34257 | −0.671287 | − | 0.741198i | \(-0.734258\pi\) | ||||
−0.671287 | + | 0.741198i | \(0.734258\pi\) | |||||||
\(720\) | −1.00000 | − | 2.00000i | −0.0372678 | − | 0.0745356i | ||||
\(721\) | 48.0000 | 1.78761 | ||||||||
\(722\) | − | 45.0000i | − | 1.67473i | ||||||
\(723\) | − | 8.00000i | − | 0.297523i | ||||||
\(724\) | −10.0000 | −0.371647 | ||||||||
\(725\) | −12.0000 | + | 16.0000i | −0.445669 | + | 0.594225i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.0000i | 1.03846i | 0.854634 | + | 0.519231i | \(0.173782\pi\) | ||||
−0.854634 | + | 0.519231i | \(0.826218\pi\) | |||||||
\(728\) | − | 24.0000i | − | 0.889499i | ||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −2.00000 | − | 4.00000i | −0.0740233 | − | 0.148047i | ||||
\(731\) | −16.0000 | −0.591781 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.0000i | 0.517102i | 0.965998 | + | 0.258551i | \(0.0832450\pi\) | ||||
−0.965998 | + | 0.258551i | \(0.916755\pi\) | |||||||
\(734\) | 36.0000 | 1.32878 | ||||||||
\(735\) | −18.0000 | + | 9.00000i | −0.663940 | + | 0.331970i | ||||
\(736\) | −20.0000 | −0.737210 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | − | 12.0000i | − | 0.441726i | ||||||
\(739\) | 16.0000 | 0.588570 | 0.294285 | − | 0.955718i | \(-0.404919\pi\) | ||||
0.294285 | + | 0.955718i | \(0.404919\pi\) | |||||||
\(740\) | 16.0000 | − | 8.00000i | 0.588172 | − | 0.294086i | ||||
\(741\) | −16.0000 | −0.587775 | ||||||||
\(742\) | − | 16.0000i | − | 0.587378i | ||||||
\(743\) | − | 24.0000i | − | 0.880475i | −0.897881 | − | 0.440237i | \(-0.854894\pi\) | ||
0.897881 | − | 0.440237i | \(-0.145106\pi\) | |||||||
\(744\) | −24.0000 | −0.879883 | ||||||||
\(745\) | −20.0000 | − | 40.0000i | −0.732743 | − | 1.46549i | ||||
\(746\) | 22.0000 | 0.805477 | ||||||||
\(747\) | − | 4.00000i | − | 0.146352i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −48.0000 | −1.75388 | ||||||||
\(750\) | 11.0000 | + | 2.00000i | 0.401663 | + | 0.0730297i | ||||
\(751\) | −16.0000 | −0.583848 | −0.291924 | − | 0.956441i | \(-0.594295\pi\) | ||||
−0.291924 | + | 0.956441i | \(0.594295\pi\) | |||||||
\(752\) | 4.00000i | 0.145865i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.00000 | 0.291343 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.00000 | −0.145479 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | − | 4.00000i | − | 0.145287i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −48.0000 | + | 24.0000i | −1.74114 | + | 0.870572i | ||||
\(761\) | 36.0000 | 1.30500 | 0.652499 | − | 0.757789i | \(-0.273720\pi\) | ||||
0.652499 | + | 0.757789i | \(0.273720\pi\) | |||||||
\(762\) | 4.00000i | 0.144905i | ||||||||
\(763\) | 32.0000i | 1.15848i | ||||||||
\(764\) | 12.0000 | 0.434145 | ||||||||
\(765\) | 4.00000 | − | 2.00000i | 0.144620 | − | 0.0723102i | ||||
\(766\) | 36.0000 | 1.30073 | ||||||||
\(767\) | 16.0000i | 0.577727i | ||||||||
\(768\) | − | 17.0000i | − | 0.613435i | ||||||
\(769\) | 16.0000 | 0.576975 | 0.288487 | − | 0.957484i | \(-0.406848\pi\) | ||||
0.288487 | + | 0.957484i | \(0.406848\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.00000 | −0.144056 | ||||||||
\(772\) | − | 6.00000i | − | 0.215945i | ||||||
\(773\) | 36.0000i | 1.29483i | 0.762138 | + | 0.647415i | \(0.224150\pi\) | ||||
−0.762138 | + | 0.647415i | \(0.775850\pi\) | |||||||
\(774\) | 8.00000 | 0.287554 | ||||||||
\(775\) | 24.0000 | − | 32.0000i | 0.862105 | − | 1.14947i | ||||
\(776\) | −24.0000 | −0.861550 | ||||||||
\(777\) | 32.0000i | 1.14799i | ||||||||
\(778\) | 18.0000i | 0.645331i | ||||||||
\(779\) | −96.0000 | −3.43956 | ||||||||
\(780\) | 2.00000 | + | 4.00000i | 0.0716115 | + | 0.143223i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 8.00000i | 0.286079i | ||||||||
\(783\) | − | 4.00000i | − | 0.142948i | ||||||
\(784\) | 9.00000 | 0.321429 | ||||||||
\(785\) | 16.0000 | − | 8.00000i | 0.571064 | − | 0.285532i | ||||
\(786\) | −8.00000 | −0.285351 | ||||||||
\(787\) | − | 32.0000i | − | 1.14068i | −0.821410 | − | 0.570338i | \(-0.806812\pi\) | ||
0.821410 | − | 0.570338i | \(-0.193188\pi\) | |||||||
\(788\) | − | 6.00000i | − | 0.213741i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −16.0000 | + | 8.00000i | −0.569254 | + | 0.284627i | ||||
\(791\) | −48.0000 | −1.70668 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 8.00000 | 0.283909 | ||||||||
\(795\) | 4.00000 | + | 8.00000i | 0.141865 | + | 0.283731i | ||||
\(796\) | 16.0000 | 0.567105 | ||||||||
\(797\) | 12.0000i | 0.425062i | 0.977154 | + | 0.212531i | \(0.0681706\pi\) | ||||
−0.977154 | + | 0.212531i | \(0.931829\pi\) | |||||||
\(798\) | − | 32.0000i | − | 1.13279i | ||||||
\(799\) | −8.00000 | −0.283020 | ||||||||
\(800\) | 20.0000 | + | 15.0000i | 0.707107 | + | 0.530330i | ||||
\(801\) | 6.00000 | 0.212000 | ||||||||
\(802\) | 2.00000i | 0.0706225i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 4.00000 | 0.141069 | ||||||||
\(805\) | 16.0000 | + | 32.0000i | 0.563926 | + | 1.12785i | ||||
\(806\) | −16.0000 | −0.563576 | ||||||||
\(807\) | 26.0000i | 0.915243i | ||||||||
\(808\) | − | 12.0000i | − | 0.422159i | ||||||
\(809\) | −44.0000 | −1.54696 | −0.773479 | − | 0.633822i | \(-0.781485\pi\) | ||||
−0.773479 | + | 0.633822i | \(0.781485\pi\) | |||||||
\(810\) | −2.00000 | + | 1.00000i | −0.0702728 | + | 0.0351364i | ||||
\(811\) | 8.00000 | 0.280918 | 0.140459 | − | 0.990086i | \(-0.455142\pi\) | ||||
0.140459 | + | 0.990086i | \(0.455142\pi\) | |||||||
\(812\) | − | 16.0000i | − | 0.561490i | ||||||
\(813\) | − | 16.0000i | − | 0.561144i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 40.0000 | − | 20.0000i | 1.40114 | − | 0.700569i | ||||
\(816\) | −2.00000 | −0.0700140 | ||||||||
\(817\) | − | 64.0000i | − | 2.23908i | ||||||
\(818\) | 40.0000i | 1.39857i | ||||||||
\(819\) | −8.00000 | −0.279543 | ||||||||
\(820\) | 12.0000 | + | 24.0000i | 0.419058 | + | 0.838116i | ||||
\(821\) | −20.0000 | −0.698005 | −0.349002 | − | 0.937122i | \(-0.613479\pi\) | ||||
−0.349002 | + | 0.937122i | \(0.613479\pi\) | |||||||
\(822\) | − | 4.00000i | − | 0.139516i | ||||||
\(823\) | − | 20.0000i | − | 0.697156i | −0.937280 | − | 0.348578i | \(-0.886665\pi\) | ||
0.937280 | − | 0.348578i | \(-0.113335\pi\) | |||||||
\(824\) | 36.0000 | 1.25412 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −32.0000 | −1.11342 | ||||||||
\(827\) | 20.0000i | 0.695468i | 0.937593 | + | 0.347734i | \(0.113049\pi\) | ||||
−0.937593 | + | 0.347734i | \(0.886951\pi\) | |||||||
\(828\) | 4.00000i | 0.139010i | ||||||||
\(829\) | 14.0000 | 0.486240 | 0.243120 | − | 0.969996i | \(-0.421829\pi\) | ||||
0.243120 | + | 0.969996i | \(0.421829\pi\) | |||||||
\(830\) | −4.00000 | − | 8.00000i | −0.138842 | − | 0.277684i | ||||
\(831\) | 10.0000 | 0.346896 | ||||||||
\(832\) | − | 14.0000i | − | 0.485363i | ||||||
\(833\) | 18.0000i | 0.623663i | ||||||||
\(834\) | 16.0000 | 0.554035 | ||||||||
\(835\) | −48.0000 | + | 24.0000i | −1.66111 | + | 0.830554i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.00000i | 0.276520i | ||||||||
\(838\) | 8.00000i | 0.276355i | ||||||||
\(839\) | −20.0000 | −0.690477 | −0.345238 | − | 0.938515i | \(-0.612202\pi\) | ||||
−0.345238 | + | 0.938515i | \(0.612202\pi\) | |||||||
\(840\) | −24.0000 | + | 12.0000i | −0.828079 | + | 0.414039i | ||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | 10.0000i | 0.344623i | ||||||||
\(843\) | − | 12.0000i | − | 0.413302i | ||||||
\(844\) | 16.0000 | 0.550743 | ||||||||
\(845\) | −9.00000 | − | 18.0000i | −0.309609 | − | 0.619219i | ||||
\(846\) | 4.00000 | 0.137523 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 4.00000i | − | 0.137361i | ||||||
\(849\) | 16.0000 | 0.549119 | ||||||||
\(850\) | 6.00000 | − | 8.00000i | 0.205798 | − | 0.274398i | ||||
\(851\) | 32.0000 | 1.09695 | ||||||||
\(852\) | − | 12.0000i | − | 0.411113i | ||||||
\(853\) | 6.00000i | 0.205436i | 0.994711 | + | 0.102718i | \(0.0327539\pi\) | ||||
−0.994711 | + | 0.102718i | \(0.967246\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.00000 | + | 16.0000i | 0.273594 | + | 0.547188i | ||||
\(856\) | −36.0000 | −1.23045 | ||||||||
\(857\) | 38.0000i | 1.29806i | 0.760765 | + | 0.649028i | \(0.224824\pi\) | ||||
−0.760765 | + | 0.649028i | \(0.775176\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.00000 | −0.136478 | −0.0682391 | − | 0.997669i | \(-0.521738\pi\) | ||||
−0.0682391 | + | 0.997669i | \(0.521738\pi\) | |||||||
\(860\) | −16.0000 | + | 8.00000i | −0.545595 | + | 0.272798i | ||||
\(861\) | −48.0000 | −1.63584 | ||||||||
\(862\) | − | 24.0000i | − | 0.817443i | ||||||
\(863\) | 36.0000i | 1.22545i | 0.790295 | + | 0.612727i | \(0.209928\pi\) | ||||
−0.790295 | + | 0.612727i | \(0.790072\pi\) | |||||||
\(864\) | −5.00000 | −0.170103 | ||||||||
\(865\) | 28.0000 | − | 14.0000i | 0.952029 | − | 0.476014i | ||||
\(866\) | −16.0000 | −0.543702 | ||||||||
\(867\) | 13.0000i | 0.441503i | ||||||||
\(868\) | 32.0000i | 1.08615i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −4.00000 | − | 8.00000i | −0.135613 | − | 0.271225i | ||||
\(871\) | 8.00000 | 0.271070 | ||||||||
\(872\) | 24.0000i | 0.812743i | ||||||||
\(873\) | 8.00000i | 0.270759i | ||||||||
\(874\) | −32.0000 | −1.08242 | ||||||||
\(875\) | 8.00000 | − | 44.0000i | 0.270449 | − | 1.48747i | ||||
\(876\) | −2.00000 | −0.0675737 | ||||||||
\(877\) | 2.00000i | 0.0675352i | 0.999430 | + | 0.0337676i | \(0.0107506\pi\) | ||||
−0.999430 | + | 0.0337676i | \(0.989249\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.00000 | 0.202375 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.0000 | −1.01073 | −0.505363 | − | 0.862907i | \(-0.668641\pi\) | ||||
−0.505363 | + | 0.862907i | \(0.668641\pi\) | |||||||
\(882\) | − | 9.00000i | − | 0.303046i | ||||||
\(883\) | 4.00000i | 0.134611i | 0.997732 | + | 0.0673054i | \(0.0214402\pi\) | ||||
−0.997732 | + | 0.0673054i | \(0.978560\pi\) | |||||||
\(884\) | 4.00000 | 0.134535 | ||||||||
\(885\) | 16.0000 | − | 8.00000i | 0.537834 | − | 0.268917i | ||||
\(886\) | −12.0000 | −0.403148 | ||||||||
\(887\) | 16.0000i | 0.537227i | 0.963248 | + | 0.268614i | \(0.0865655\pi\) | ||||
−0.963248 | + | 0.268614i | \(0.913434\pi\) | |||||||
\(888\) | 24.0000i | 0.805387i | ||||||||
\(889\) | 16.0000 | 0.536623 | ||||||||
\(890\) | 12.0000 | − | 6.00000i | 0.402241 | − | 0.201120i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.00000i | 0.133930i | ||||||||
\(893\) | − | 32.0000i | − | 1.07084i | ||||||
\(894\) | 20.0000 | 0.668900 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −12.0000 | −0.400892 | ||||||||
\(897\) | 8.00000i | 0.267112i | ||||||||
\(898\) | − | 30.0000i | − | 1.00111i | ||||||
\(899\) | −32.0000 | −1.06726 | ||||||||
\(900\) | 3.00000 | − | 4.00000i | 0.100000 | − | 0.133333i | ||||
\(901\) | 8.00000 | 0.266519 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 32.0000i | − | 1.06489i | ||||||
\(904\) | −36.0000 | −1.19734 | ||||||||
\(905\) | 10.0000 | + | 20.0000i | 0.332411 | + | 0.664822i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 52.0000i | − | 1.72663i | −0.504664 | − | 0.863316i | \(-0.668384\pi\) | ||
0.504664 | − | 0.863316i | \(-0.331616\pi\) | |||||||
\(908\) | 12.0000i | 0.398234i | ||||||||
\(909\) | −4.00000 | −0.132672 | ||||||||
\(910\) | −16.0000 | + | 8.00000i | −0.530395 | + | 0.265197i | ||||
\(911\) | −36.0000 | −1.19273 | −0.596367 | − | 0.802712i | \(-0.703390\pi\) | ||||
−0.596367 | + | 0.802712i | \(0.703390\pi\) | |||||||
\(912\) | − | 8.00000i | − | 0.264906i | ||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 2.00000 | 0.0661541 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 22.0000 | 0.726900 | ||||||||
\(917\) | 32.0000i | 1.05673i | ||||||||
\(918\) | 2.00000i | 0.0660098i | ||||||||
\(919\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(920\) | 12.0000 | + | 24.0000i | 0.395628 | + | 0.791257i | ||||
\(921\) | 24.0000 | 0.790827 | ||||||||
\(922\) | − | 12.0000i | − | 0.395199i | ||||||
\(923\) | − | 24.0000i | − | 0.789970i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32.0000 | − | 24.0000i | −1.05215 | − | 0.789115i | ||||
\(926\) | −28.0000 | −0.920137 | ||||||||
\(927\) | − | 12.0000i | − | 0.394132i | ||||||
\(928\) | − | 20.0000i | − | 0.656532i | ||||||
\(929\) | 18.0000 | 0.590561 | 0.295280 | − | 0.955411i | \(-0.404587\pi\) | ||||
0.295280 | + | 0.955411i | \(0.404587\pi\) | |||||||
\(930\) | 8.00000 | + | 16.0000i | 0.262330 | + | 0.524661i | ||||
\(931\) | −72.0000 | −2.35970 | ||||||||
\(932\) | 6.00000i | 0.196537i | ||||||||
\(933\) | 28.0000i | 0.916679i | ||||||||
\(934\) | 12.0000 | 0.392652 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.00000 | −0.196116 | ||||||||
\(937\) | − | 14.0000i | − | 0.457360i | −0.973502 | − | 0.228680i | \(-0.926559\pi\) | ||
0.973502 | − | 0.228680i | \(-0.0734410\pi\) | |||||||
\(938\) | 16.0000i | 0.522419i | ||||||||
\(939\) | 16.0000 | 0.522140 | ||||||||
\(940\) | −8.00000 | + | 4.00000i | −0.260931 | + | 0.130466i | ||||
\(941\) | 4.00000 | 0.130396 | 0.0651981 | − | 0.997872i | \(-0.479232\pi\) | ||||
0.0651981 | + | 0.997872i | \(0.479232\pi\) | |||||||
\(942\) | 8.00000i | 0.260654i | ||||||||
\(943\) | 48.0000i | 1.56310i | ||||||||
\(944\) | −8.00000 | −0.260378 | ||||||||
\(945\) | 4.00000 | + | 8.00000i | 0.130120 | + | 0.260240i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.0000i | 0.909878i | 0.890523 | + | 0.454939i | \(0.150339\pi\) | ||||
−0.890523 | + | 0.454939i | \(0.849661\pi\) | |||||||
\(948\) | 8.00000i | 0.259828i | ||||||||
\(949\) | −4.00000 | −0.129845 | ||||||||
\(950\) | 32.0000 | + | 24.0000i | 1.03822 | + | 0.778663i | ||||
\(951\) | −20.0000 | −0.648544 | ||||||||
\(952\) | 24.0000i | 0.777844i | ||||||||
\(953\) | 54.0000i | 1.74923i | 0.484817 | + | 0.874616i | \(0.338886\pi\) | ||||
−0.484817 | + | 0.874616i | \(0.661114\pi\) | |||||||
\(954\) | −4.00000 | −0.129505 | ||||||||
\(955\) | −12.0000 | − | 24.0000i | −0.388311 | − | 0.776622i | ||||
\(956\) | −24.0000 | −0.776215 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 24.0000i | 0.775405i | ||||||||
\(959\) | −16.0000 | −0.516667 | ||||||||
\(960\) | −14.0000 | + | 7.00000i | −0.451848 | + | 0.225924i | ||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | 16.0000i | 0.515861i | ||||||||
\(963\) | 12.0000i | 0.386695i | ||||||||
\(964\) | −8.00000 | −0.257663 | ||||||||
\(965\) | −12.0000 | + | 6.00000i | −0.386294 | + | 0.193147i | ||||
\(966\) | −16.0000 | −0.514792 | ||||||||
\(967\) | − | 4.00000i | − | 0.128631i | −0.997930 | − | 0.0643157i | \(-0.979514\pi\) | ||
0.997930 | − | 0.0643157i | \(-0.0204865\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.0000 | 0.513994 | ||||||||
\(970\) | 8.00000 | + | 16.0000i | 0.256865 | + | 0.513729i | ||||
\(971\) | 16.0000 | 0.513464 | 0.256732 | − | 0.966483i | \(-0.417354\pi\) | ||||
0.256732 | + | 0.966483i | \(0.417354\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | − | 64.0000i | − | 2.05175i | ||||||
\(974\) | 20.0000 | 0.640841 | ||||||||
\(975\) | 6.00000 | − | 8.00000i | 0.192154 | − | 0.256205i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 36.0000i | 1.15174i | 0.817541 | + | 0.575871i | \(0.195337\pi\) | ||||
−0.817541 | + | 0.575871i | \(0.804663\pi\) | |||||||
\(978\) | 20.0000i | 0.639529i | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 9.00000 | + | 18.0000i | 0.287494 | + | 0.574989i | ||||
\(981\) | 8.00000 | 0.255420 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.00000i | 0.127580i | 0.997963 | + | 0.0637901i | \(0.0203188\pi\) | ||||
−0.997963 | + | 0.0637901i | \(0.979681\pi\) | |||||||
\(984\) | −36.0000 | −1.14764 | ||||||||
\(985\) | −12.0000 | + | 6.00000i | −0.382352 | + | 0.191176i | ||||
\(986\) | −8.00000 | −0.254772 | ||||||||
\(987\) | − | 16.0000i | − | 0.509286i | ||||||
\(988\) | 16.0000i | 0.509028i | ||||||||
\(989\) | −32.0000 | −1.01754 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(992\) | 40.0000i | 1.27000i | ||||||||
\(993\) | 4.00000i | 0.126936i | ||||||||
\(994\) | 48.0000 | 1.52247 | ||||||||
\(995\) | −16.0000 | − | 32.0000i | −0.507234 | − | 1.01447i | ||||
\(996\) | −4.00000 | −0.126745 | ||||||||
\(997\) | 42.0000i | 1.33015i | 0.746775 | + | 0.665077i | \(0.231601\pi\) | ||||
−0.746775 | + | 0.665077i | \(0.768399\pi\) | |||||||
\(998\) | − | 12.0000i | − | 0.379853i | ||||||
\(999\) | 8.00000 | 0.253109 |
(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 | 1815.2.c.b.364.1 | yes | 2 | |
5.2 | odd | 4 | 9075.2.a.r.1.1 | 1 | |||
5.3 | odd | 4 | 9075.2.a.c.1.1 | 1 | |||
5.4 | even | 2 | inner | 1815.2.c.b.364.2 | yes | 2 | |
11.10 | odd | 2 | 1815.2.c.a.364.2 | yes | 2 | ||
55.32 | even | 4 | 9075.2.a.f.1.1 | 1 | |||
55.43 | even | 4 | 9075.2.a.o.1.1 | 1 | |||
55.54 | odd | 2 | 1815.2.c.a.364.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1815.2.c.a.364.1 | ✓ | 2 | 55.54 | odd | 2 | ||
1815.2.c.a.364.2 | yes | 2 | 11.10 | odd | 2 | ||
1815.2.c.b.364.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1815.2.c.b.364.2 | yes | 2 | 5.4 | even | 2 | inner | |
9075.2.a.c.1.1 | 1 | 5.3 | odd | 4 | |||
9075.2.a.f.1.1 | 1 | 55.32 | even | 4 | |||
9075.2.a.o.1.1 | 1 | 55.43 | even | 4 | |||
9075.2.a.r.1.1 | 1 | 5.2 | odd | 4 |