Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3330,2,Mod(1999,3330)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3330, 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("3330.1999");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3330.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: | \(26.5901838731\) |
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: | no (minimal twist has level 370) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1999.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3330.1999 |
Dual form | 3330.2.d.f.1999.1 |
$q$-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 \(\left(\mathbb{Z}/3330\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 2.00000 | − | 1.00000i | 0.894427 | − | 0.447214i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000i | 0.755929i | 0.925820 | + | 0.377964i | \(0.123376\pi\) | ||||
−0.925820 | + | 0.377964i | \(0.876624\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | + | 2.00000i | 0.316228 | + | 0.632456i | ||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000i | 0.554700i | 0.960769 | + | 0.277350i | \(0.0894562\pi\) | ||||
−0.960769 | + | 0.277350i | \(0.910544\pi\) | |||||||
\(14\) | −2.00000 | −0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 6.00000i | − | 1.45521i | −0.685994 | − | 0.727607i | \(-0.740633\pi\) | ||
0.685994 | − | 0.727607i | \(-0.259367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.00000 | 1.37649 | 0.688247 | − | 0.725476i | \(-0.258380\pi\) | ||||
0.688247 | + | 0.725476i | \(0.258380\pi\) | |||||||
\(20\) | −2.00000 | + | 1.00000i | −0.447214 | + | 0.223607i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 4.00000i | − | 0.834058i | −0.908893 | − | 0.417029i | \(-0.863071\pi\) | ||
0.908893 | − | 0.417029i | \(-0.136929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | − | 4.00000i | 0.600000 | − | 0.800000i | ||||
\(26\) | −2.00000 | −0.392232 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 2.00000i | − | 0.377964i | ||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.00000 | 1.02899 | ||||||||
\(35\) | 2.00000 | + | 4.00000i | 0.338062 | + | 0.676123i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000i | 0.164399i | ||||||||
\(38\) | 6.00000i | 0.973329i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | − | 2.00000i | −0.158114 | − | 0.316228i | ||||
\(41\) | 10.0000 | 1.56174 | 0.780869 | − | 0.624695i | \(-0.214777\pi\) | ||||
0.780869 | + | 0.624695i | \(0.214777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.00000i | − | 0.609994i | −0.952353 | − | 0.304997i | \(-0.901344\pi\) | ||
0.952353 | − | 0.304997i | \(-0.0986555\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.00000 | 0.589768 | ||||||||
\(47\) | − | 2.00000i | − | 0.291730i | −0.989305 | − | 0.145865i | \(-0.953403\pi\) | ||
0.989305 | − | 0.145865i | \(-0.0465965\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | 4.00000 | + | 3.00000i | 0.565685 | + | 0.424264i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 2.00000i | − | 0.277350i | ||||||
\(53\) | − | 2.00000i | − | 0.274721i | −0.990521 | − | 0.137361i | \(-0.956138\pi\) | ||
0.990521 | − | 0.137361i | \(-0.0438619\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.00000 | 0.267261 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.00000 | −0.781133 | −0.390567 | − | 0.920575i | \(-0.627721\pi\) | ||||
−0.390567 | + | 0.920575i | \(0.627721\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(62\) | − | 4.00000i | − | 0.508001i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 2.00000 | + | 4.00000i | 0.248069 | + | 0.496139i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 8.00000i | − | 0.977356i | −0.872464 | − | 0.488678i | \(-0.837479\pi\) | ||
0.872464 | − | 0.488678i | \(-0.162521\pi\) | |||||||
\(68\) | 6.00000i | 0.727607i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.00000 | + | 2.00000i | −0.478091 | + | 0.239046i | ||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.00000i | 0.936329i | 0.883641 | + | 0.468165i | \(0.155085\pi\) | ||||
−0.883641 | + | 0.468165i | \(0.844915\pi\) | |||||||
\(74\) | −1.00000 | −0.116248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.00000 | −0.688247 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 2.00000 | − | 1.00000i | 0.223607 | − | 0.111803i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 10.0000i | 1.10432i | ||||||||
\(83\) | 12.0000i | 1.31717i | 0.752506 | + | 0.658586i | \(0.228845\pi\) | ||||
−0.752506 | + | 0.658586i | \(0.771155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.00000 | − | 12.0000i | −0.650791 | − | 1.30158i | ||||
\(86\) | 4.00000 | 0.431331 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.00000 | −0.419314 | ||||||||
\(92\) | 4.00000i | 0.417029i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.00000 | 0.206284 | ||||||||
\(95\) | 12.0000 | − | 6.00000i | 1.23117 | − | 0.615587i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.0000i | 1.01535i | 0.861550 | + | 0.507673i | \(0.169494\pi\) | ||||
−0.861550 | + | 0.507673i | \(0.830506\pi\) | |||||||
\(98\) | 3.00000i | 0.303046i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.00000 | + | 4.00000i | −0.300000 | + | 0.400000i | ||||
\(101\) | 10.0000 | 0.995037 | 0.497519 | − | 0.867453i | \(-0.334245\pi\) | ||||
0.497519 | + | 0.867453i | \(0.334245\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | 2.00000 | 0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.00000 | 0.194257 | ||||||||
\(107\) | 8.00000i | 0.773389i | 0.922208 | + | 0.386695i | \(0.126383\pi\) | ||||
−0.922208 | + | 0.386695i | \(0.873617\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 20.0000 | 1.91565 | 0.957826 | − | 0.287348i | \(-0.0927736\pi\) | ||||
0.957826 | + | 0.287348i | \(0.0927736\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.00000i | 0.188982i | ||||||||
\(113\) | − | 2.00000i | − | 0.188144i | −0.995565 | − | 0.0940721i | \(-0.970012\pi\) | ||
0.995565 | − | 0.0940721i | \(-0.0299884\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.00000 | − | 8.00000i | −0.373002 | − | 0.746004i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 6.00000i | − | 0.552345i | ||||||
\(119\) | 12.0000 | 1.10004 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.00000 | 0.359211 | ||||||||
\(125\) | 2.00000 | − | 11.0000i | 0.178885 | − | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 22.0000i | − | 1.95218i | −0.217357 | − | 0.976092i | \(-0.569744\pi\) | ||
0.217357 | − | 0.976092i | \(-0.430256\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.00000 | + | 2.00000i | −0.350823 | + | 0.175412i | ||||
\(131\) | −14.0000 | −1.22319 | −0.611593 | − | 0.791173i | \(-0.709471\pi\) | ||||
−0.611593 | + | 0.791173i | \(0.709471\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.0000i | 1.04053i | ||||||||
\(134\) | 8.00000 | 0.691095 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.00000 | −0.514496 | ||||||||
\(137\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.0000 | 1.69638 | 0.848189 | − | 0.529694i | \(-0.177693\pi\) | ||||
0.848189 | + | 0.529694i | \(0.177693\pi\) | |||||||
\(140\) | −2.00000 | − | 4.00000i | −0.169031 | − | 0.338062i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.00000 | −0.662085 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 1.00000i | − | 0.0821995i | ||||||
\(149\) | 14.0000 | 1.14692 | 0.573462 | − | 0.819232i | \(-0.305600\pi\) | ||||
0.573462 | + | 0.819232i | \(0.305600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.0000 | 1.30206 | 0.651031 | − | 0.759051i | \(-0.274337\pi\) | ||||
0.651031 | + | 0.759051i | \(0.274337\pi\) | |||||||
\(152\) | − | 6.00000i | − | 0.486664i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.00000 | + | 4.00000i | −0.642575 | + | 0.321288i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 22.0000i | − | 1.75579i | −0.478852 | − | 0.877896i | \(-0.658947\pi\) | ||
0.478852 | − | 0.877896i | \(-0.341053\pi\) | |||||||
\(158\) | − | 4.00000i | − | 0.318223i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | + | 2.00000i | 0.0790569 | + | 0.158114i | ||||
\(161\) | 8.00000 | 0.630488 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 12.0000i | − | 0.939913i | −0.882690 | − | 0.469956i | \(-0.844270\pi\) | ||
0.882690 | − | 0.469956i | \(-0.155730\pi\) | |||||||
\(164\) | −10.0000 | −0.780869 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.0000 | −0.931381 | ||||||||
\(167\) | 16.0000i | 1.23812i | 0.785345 | + | 0.619059i | \(0.212486\pi\) | ||||
−0.785345 | + | 0.619059i | \(0.787514\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 12.0000 | − | 6.00000i | 0.920358 | − | 0.460179i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.00000i | 0.304997i | ||||||||
\(173\) | − | 2.00000i | − | 0.152057i | −0.997106 | − | 0.0760286i | \(-0.975776\pi\) | ||
0.997106 | − | 0.0760286i | \(-0.0242240\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.00000 | + | 6.00000i | 0.604743 | + | 0.453557i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.00000i | 0.449719i | ||||||||
\(179\) | −14.0000 | −1.04641 | −0.523205 | − | 0.852207i | \(-0.675264\pi\) | ||||
−0.523205 | + | 0.852207i | \(0.675264\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | − | 4.00000i | − | 0.296500i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.00000 | −0.294884 | ||||||||
\(185\) | 1.00000 | + | 2.00000i | 0.0735215 | + | 0.147043i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 2.00000i | 0.145865i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.00000 | + | 12.0000i | 0.435286 | + | 0.870572i | ||||
\(191\) | −4.00000 | −0.289430 | −0.144715 | − | 0.989473i | \(-0.546227\pi\) | ||||
−0.144715 | + | 0.989473i | \(0.546227\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.0000i | 0.719816i | 0.932988 | + | 0.359908i | \(0.117192\pi\) | ||||
−0.932988 | + | 0.359908i | \(0.882808\pi\) | |||||||
\(194\) | −10.0000 | −0.717958 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | − | 10.0000i | − | 0.712470i | −0.934396 | − | 0.356235i | \(-0.884060\pi\) | ||
0.934396 | − | 0.356235i | \(-0.115940\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.0000 | 1.41776 | 0.708881 | − | 0.705328i | \(-0.249200\pi\) | ||||
0.708881 | + | 0.705328i | \(0.249200\pi\) | |||||||
\(200\) | −4.00000 | − | 3.00000i | −0.282843 | − | 0.212132i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.0000i | 0.703598i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.0000 | − | 10.0000i | 1.39686 | − | 0.698430i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.00000i | 0.138675i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.0000 | −1.10149 | −0.550743 | − | 0.834675i | \(-0.685655\pi\) | ||||
−0.550743 | + | 0.834675i | \(0.685655\pi\) | |||||||
\(212\) | 2.00000i | 0.137361i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.00000 | −0.546869 | ||||||||
\(215\) | −4.00000 | − | 8.00000i | −0.272798 | − | 0.545595i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 8.00000i | − | 0.543075i | ||||||
\(218\) | 20.0000i | 1.35457i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000 | 0.807207 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.0000i | 0.937509i | 0.883328 | + | 0.468755i | \(0.155297\pi\) | ||||
−0.883328 | + | 0.468755i | \(0.844703\pi\) | |||||||
\(224\) | −2.00000 | −0.133631 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.00000 | 0.133038 | ||||||||
\(227\) | 20.0000i | 1.32745i | 0.747978 | + | 0.663723i | \(0.231025\pi\) | ||||
−0.747978 | + | 0.663723i | \(0.768975\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.00000 | −0.132164 | −0.0660819 | − | 0.997814i | \(-0.521050\pi\) | ||||
−0.0660819 | + | 0.997814i | \(0.521050\pi\) | |||||||
\(230\) | 8.00000 | − | 4.00000i | 0.527504 | − | 0.263752i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.0000i | 1.57229i | 0.618041 | + | 0.786146i | \(0.287927\pi\) | ||||
−0.618041 | + | 0.786146i | \(0.712073\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.00000 | − | 4.00000i | −0.130466 | − | 0.260931i | ||||
\(236\) | 6.00000 | 0.390567 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 12.0000i | 0.777844i | ||||||||
\(239\) | 28.0000 | 1.81117 | 0.905585 | − | 0.424165i | \(-0.139432\pi\) | ||||
0.905585 | + | 0.424165i | \(0.139432\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.0000 | 0.644157 | 0.322078 | − | 0.946713i | \(-0.395619\pi\) | ||||
0.322078 | + | 0.946713i | \(0.395619\pi\) | |||||||
\(242\) | − | 11.0000i | − | 0.707107i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.00000 | − | 3.00000i | 0.383326 | − | 0.191663i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.0000i | 0.763542i | ||||||||
\(248\) | 4.00000i | 0.254000i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.0000 | + | 2.00000i | 0.695701 | + | 0.126491i | ||||
\(251\) | −2.00000 | −0.126239 | −0.0631194 | − | 0.998006i | \(-0.520105\pi\) | ||||
−0.0631194 | + | 0.998006i | \(0.520105\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 22.0000 | 1.38040 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 30.0000i | − | 1.87135i | −0.352865 | − | 0.935674i | \(-0.614792\pi\) | ||
0.352865 | − | 0.935674i | \(-0.385208\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.00000 | −0.124274 | ||||||||
\(260\) | −2.00000 | − | 4.00000i | −0.124035 | − | 0.248069i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 14.0000i | − | 0.864923i | ||||||
\(263\) | 2.00000i | 0.123325i | 0.998097 | + | 0.0616626i | \(0.0196403\pi\) | ||||
−0.998097 | + | 0.0616626i | \(0.980360\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.00000 | − | 4.00000i | −0.122859 | − | 0.245718i | ||||
\(266\) | −12.0000 | −0.735767 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.00000i | 0.488678i | ||||||||
\(269\) | −10.0000 | −0.609711 | −0.304855 | − | 0.952399i | \(-0.598608\pi\) | ||||
−0.304855 | + | 0.952399i | \(0.598608\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | −0.485965 | −0.242983 | − | 0.970031i | \(-0.578126\pi\) | ||||
−0.242983 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(272\) | − | 6.00000i | − | 0.363803i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.0000i | 1.08152i | 0.841178 | + | 0.540758i | \(0.181862\pi\) | ||||
−0.841178 | + | 0.540758i | \(0.818138\pi\) | |||||||
\(278\) | 20.0000i | 1.19952i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.00000 | − | 2.00000i | 0.239046 | − | 0.119523i | ||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.0000i | 1.66443i | 0.554455 | + | 0.832214i | \(0.312927\pi\) | ||||
−0.554455 | + | 0.832214i | \(0.687073\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 20.0000i | 1.18056i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −19.0000 | −1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 8.00000i | − | 0.468165i | ||||||
\(293\) | − | 6.00000i | − | 0.350524i | −0.984522 | − | 0.175262i | \(-0.943923\pi\) | ||
0.984522 | − | 0.175262i | \(-0.0560772\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.0000 | + | 6.00000i | −0.698667 | + | 0.349334i | ||||
\(296\) | 1.00000 | 0.0581238 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 14.0000i | 0.810998i | ||||||||
\(299\) | 8.00000 | 0.462652 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.00000 | 0.461112 | ||||||||
\(302\) | 16.0000i | 0.920697i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.00000 | 0.344124 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4.00000i | − | 0.228292i | −0.993464 | − | 0.114146i | \(-0.963587\pi\) | ||
0.993464 | − | 0.114146i | \(-0.0364132\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.00000 | − | 8.00000i | −0.227185 | − | 0.454369i | ||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 14.0000i | − | 0.791327i | −0.918396 | − | 0.395663i | \(-0.870515\pi\) | ||
0.918396 | − | 0.395663i | \(-0.129485\pi\) | |||||||
\(314\) | 22.0000 | 1.24153 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.00000 | 0.225018 | ||||||||
\(317\) | − | 6.00000i | − | 0.336994i | −0.985702 | − | 0.168497i | \(-0.946109\pi\) | ||
0.985702 | − | 0.168497i | \(-0.0538913\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −2.00000 | + | 1.00000i | −0.111803 | + | 0.0559017i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.00000i | 0.445823i | ||||||||
\(323\) | − | 36.0000i | − | 2.00309i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.00000 | + | 6.00000i | 0.443760 | + | 0.332820i | ||||
\(326\) | 12.0000 | 0.664619 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 10.0000i | − | 0.552158i | ||||||
\(329\) | 4.00000 | 0.220527 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −34.0000 | −1.86881 | −0.934405 | − | 0.356214i | \(-0.884068\pi\) | ||||
−0.934405 | + | 0.356214i | \(0.884068\pi\) | |||||||
\(332\) | − | 12.0000i | − | 0.658586i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −16.0000 | −0.875481 | ||||||||
\(335\) | −8.00000 | − | 16.0000i | −0.437087 | − | 0.874173i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 8.00000i | − | 0.435788i | −0.975972 | − | 0.217894i | \(-0.930081\pi\) | ||
0.975972 | − | 0.217894i | \(-0.0699187\pi\) | |||||||
\(338\) | 9.00000i | 0.489535i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.00000 | + | 12.0000i | 0.325396 | + | 0.650791i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0000i | 1.07990i | ||||||||
\(344\) | −4.00000 | −0.215666 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.00000 | 0.107521 | ||||||||
\(347\) | 36.0000i | 1.93258i | 0.257454 | + | 0.966291i | \(0.417117\pi\) | ||||
−0.257454 | + | 0.966291i | \(0.582883\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −30.0000 | −1.60586 | −0.802932 | − | 0.596071i | \(-0.796728\pi\) | ||||
−0.802932 | + | 0.596071i | \(0.796728\pi\) | |||||||
\(350\) | −6.00000 | + | 8.00000i | −0.320713 | + | 0.427618i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.0000i | 0.958043i | 0.877803 | + | 0.479022i | \(0.159008\pi\) | ||||
−0.877803 | + | 0.479022i | \(0.840992\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 14.0000i | − | 0.739923i | ||||||
\(359\) | −8.00000 | −0.422224 | −0.211112 | − | 0.977462i | \(-0.567708\pi\) | ||||
−0.211112 | + | 0.977462i | \(0.567708\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | 2.00000i | 0.105118i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.00000 | 0.209657 | ||||||||
\(365\) | 8.00000 | + | 16.0000i | 0.418739 | + | 0.837478i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.0000i | 1.35719i | 0.734513 | + | 0.678594i | \(0.237411\pi\) | ||||
−0.734513 | + | 0.678594i | \(0.762589\pi\) | |||||||
\(368\) | − | 4.00000i | − | 0.208514i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.00000 | + | 1.00000i | −0.103975 | + | 0.0519875i | ||||
\(371\) | 4.00000 | 0.207670 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 34.0000i | − | 1.76045i | −0.474554 | − | 0.880227i | \(-0.657390\pi\) | ||
0.474554 | − | 0.880227i | \(-0.342610\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.00000 | −0.103142 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.0000 | −0.616399 | −0.308199 | − | 0.951322i | \(-0.599726\pi\) | ||||
−0.308199 | + | 0.951322i | \(0.599726\pi\) | |||||||
\(380\) | −12.0000 | + | 6.00000i | −0.615587 | + | 0.307794i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 4.00000i | − | 0.204658i | ||||||
\(383\) | 28.0000i | 1.43073i | 0.698749 | + | 0.715367i | \(0.253740\pi\) | ||||
−0.698749 | + | 0.715367i | \(0.746260\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.0000 | −0.508987 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 10.0000i | − | 0.507673i | ||||||
\(389\) | −16.0000 | −0.811232 | −0.405616 | − | 0.914044i | \(-0.632943\pi\) | ||||
−0.405616 | + | 0.914044i | \(0.632943\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.0000 | −1.21373 | ||||||||
\(392\) | − | 3.00000i | − | 0.151523i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.0000 | 0.503793 | ||||||||
\(395\) | −8.00000 | + | 4.00000i | −0.402524 | + | 0.201262i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 2.00000i | − | 0.100377i | −0.998740 | − | 0.0501886i | \(-0.984018\pi\) | ||
0.998740 | − | 0.0501886i | \(-0.0159822\pi\) | |||||||
\(398\) | 20.0000i | 1.00251i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | − | 4.00000i | 0.150000 | − | 0.200000i | ||||
\(401\) | 2.00000 | 0.0998752 | 0.0499376 | − | 0.998752i | \(-0.484098\pi\) | ||||
0.0499376 | + | 0.998752i | \(0.484098\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 8.00000i | − | 0.398508i | ||||||
\(404\) | −10.0000 | −0.497519 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.0000 | −0.692255 | −0.346128 | − | 0.938187i | \(-0.612504\pi\) | ||||
−0.346128 | + | 0.938187i | \(0.612504\pi\) | |||||||
\(410\) | 10.0000 | + | 20.0000i | 0.493865 | + | 0.987730i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 12.0000i | − | 0.590481i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.0000 | + | 24.0000i | 0.589057 | + | 1.17811i | ||||
\(416\) | −2.00000 | −0.0980581 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.0000 | 0.977064 | 0.488532 | − | 0.872546i | \(-0.337533\pi\) | ||||
0.488532 | + | 0.872546i | \(0.337533\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 36.0000 | 1.75453 | 0.877266 | − | 0.480004i | \(-0.159365\pi\) | ||||
0.877266 | + | 0.480004i | \(0.159365\pi\) | |||||||
\(422\) | − | 16.0000i | − | 0.778868i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.00000 | −0.0971286 | ||||||||
\(425\) | −24.0000 | − | 18.0000i | −1.16417 | − | 0.873128i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 8.00000i | − | 0.386695i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.00000 | − | 4.00000i | 0.385794 | − | 0.192897i | ||||
\(431\) | −20.0000 | −0.963366 | −0.481683 | − | 0.876346i | \(-0.659974\pi\) | ||||
−0.481683 | + | 0.876346i | \(0.659974\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 16.0000i | − | 0.768911i | −0.923144 | − | 0.384455i | \(-0.874389\pi\) | ||
0.923144 | − | 0.384455i | \(-0.125611\pi\) | |||||||
\(434\) | 8.00000 | 0.384012 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −20.0000 | −0.957826 | ||||||||
\(437\) | − | 24.0000i | − | 1.14808i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.00000 | −0.190910 | −0.0954548 | − | 0.995434i | \(-0.530431\pi\) | ||||
−0.0954548 | + | 0.995434i | \(0.530431\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12.0000i | 0.570782i | ||||||||
\(443\) | − | 16.0000i | − | 0.760183i | −0.924949 | − | 0.380091i | \(-0.875893\pi\) | ||
0.924949 | − | 0.380091i | \(-0.124107\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.0000 | − | 6.00000i | 0.568855 | − | 0.284427i | ||||
\(446\) | −14.0000 | −0.662919 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 2.00000i | − | 0.0944911i | ||||||
\(449\) | 30.0000 | 1.41579 | 0.707894 | − | 0.706319i | \(-0.249646\pi\) | ||||
0.707894 | + | 0.706319i | \(0.249646\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 2.00000i | 0.0940721i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −20.0000 | −0.938647 | ||||||||
\(455\) | −8.00000 | + | 4.00000i | −0.375046 | + | 0.187523i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.0000i | 0.467780i | 0.972263 | + | 0.233890i | \(0.0751456\pi\) | ||||
−0.972263 | + | 0.233890i | \(0.924854\pi\) | |||||||
\(458\) | − | 2.00000i | − | 0.0934539i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.00000 | + | 8.00000i | 0.186501 | + | 0.373002i | ||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 4.00000i | − | 0.185896i | −0.995671 | − | 0.0929479i | \(-0.970371\pi\) | ||
0.995671 | − | 0.0929479i | \(-0.0296290\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24.0000 | −1.11178 | ||||||||
\(467\) | − | 36.0000i | − | 1.66588i | −0.553362 | − | 0.832941i | \(-0.686655\pi\) | ||
0.553362 | − | 0.832941i | \(-0.313345\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.0000 | 0.738811 | ||||||||
\(470\) | 4.00000 | − | 2.00000i | 0.184506 | − | 0.0922531i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.00000i | 0.276172i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.0000 | − | 24.0000i | 0.825897 | − | 1.10120i | ||||
\(476\) | −12.0000 | −0.550019 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 28.0000i | 1.28069i | ||||||||
\(479\) | 12.0000 | 0.548294 | 0.274147 | − | 0.961688i | \(-0.411605\pi\) | ||||
0.274147 | + | 0.961688i | \(0.411605\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.00000 | −0.0911922 | ||||||||
\(482\) | 10.0000i | 0.455488i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.0000 | 0.500000 | ||||||||
\(485\) | 10.0000 | + | 20.0000i | 0.454077 | + | 0.908153i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 24.0000i | − | 1.08754i | −0.839233 | − | 0.543772i | \(-0.816996\pi\) | ||
0.839233 | − | 0.543772i | \(-0.183004\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.00000 | + | 6.00000i | 0.135526 | + | 0.271052i | ||||
\(491\) | −24.0000 | −1.08310 | −0.541552 | − | 0.840667i | \(-0.682163\pi\) | ||||
−0.541552 | + | 0.840667i | \(0.682163\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −12.0000 | −0.539906 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.0000 | −1.34298 | −0.671492 | − | 0.741012i | \(-0.734346\pi\) | ||||
−0.671492 | + | 0.741012i | \(0.734346\pi\) | |||||||
\(500\) | −2.00000 | + | 11.0000i | −0.0894427 | + | 0.491935i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 2.00000i | − | 0.0892644i | ||||||
\(503\) | − | 40.0000i | − | 1.78351i | −0.452517 | − | 0.891756i | \(-0.649474\pi\) | ||
0.452517 | − | 0.891756i | \(-0.350526\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.0000 | − | 10.0000i | 0.889988 | − | 0.444994i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 22.0000i | 0.976092i | ||||||||
\(509\) | −18.0000 | −0.797836 | −0.398918 | − | 0.916987i | \(-0.630614\pi\) | ||||
−0.398918 | + | 0.916987i | \(0.630614\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.0000 | −0.707798 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 30.0000 | 1.32324 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − | 2.00000i | − | 0.0878750i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.00000 | − | 2.00000i | 0.175412 | − | 0.0877058i | ||||
\(521\) | −26.0000 | −1.13908 | −0.569540 | − | 0.821963i | \(-0.692879\pi\) | ||||
−0.569540 | + | 0.821963i | \(0.692879\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.00000i | 0.174908i | 0.996169 | + | 0.0874539i | \(0.0278730\pi\) | ||||
−0.996169 | + | 0.0874539i | \(0.972127\pi\) | |||||||
\(524\) | 14.0000 | 0.611593 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.00000 | −0.0872041 | ||||||||
\(527\) | 24.0000i | 1.04546i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | 4.00000 | − | 2.00000i | 0.173749 | − | 0.0868744i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 12.0000i | − | 0.520266i | ||||||
\(533\) | 20.0000i | 0.866296i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.00000 | + | 16.0000i | 0.345870 | + | 0.691740i | ||||
\(536\) | −8.00000 | −0.345547 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 10.0000i | − | 0.431131i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.0000 | −0.687894 | −0.343947 | − | 0.938989i | \(-0.611764\pi\) | ||||
−0.343947 | + | 0.938989i | \(0.611764\pi\) | |||||||
\(542\) | − | 8.00000i | − | 0.343629i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.00000 | 0.257248 | ||||||||
\(545\) | 40.0000 | − | 20.0000i | 1.71341 | − | 0.856706i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.0000i | 1.19719i | 0.801050 | + | 0.598597i | \(0.204275\pi\) | ||||
−0.801050 | + | 0.598597i | \(0.795725\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 8.00000i | − | 0.340195i | ||||||
\(554\) | −18.0000 | −0.764747 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −20.0000 | −0.848189 | ||||||||
\(557\) | − | 30.0000i | − | 1.27114i | −0.772043 | − | 0.635570i | \(-0.780765\pi\) | ||
0.772043 | − | 0.635570i | \(-0.219235\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.00000 | 0.338364 | ||||||||
\(560\) | 2.00000 | + | 4.00000i | 0.0845154 | + | 0.169031i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 6.00000i | − | 0.253095i | ||||||
\(563\) | 4.00000i | 0.168580i | 0.996441 | + | 0.0842900i | \(0.0268622\pi\) | ||||
−0.996441 | + | 0.0842900i | \(0.973138\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.00000 | − | 4.00000i | −0.0841406 | − | 0.168281i | ||||
\(566\) | −28.0000 | −1.17693 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −34.0000 | −1.42535 | −0.712677 | − | 0.701492i | \(-0.752517\pi\) | ||||
−0.712677 | + | 0.701492i | \(0.752517\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.00000 | 0.167395 | 0.0836974 | − | 0.996491i | \(-0.473327\pi\) | ||||
0.0836974 | + | 0.996491i | \(0.473327\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −20.0000 | −0.834784 | ||||||||
\(575\) | −16.0000 | − | 12.0000i | −0.667246 | − | 0.500435i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.0000i | 1.58196i | 0.611842 | + | 0.790980i | \(0.290429\pi\) | ||||
−0.611842 | + | 0.790980i | \(0.709571\pi\) | |||||||
\(578\) | − | 19.0000i | − | 0.790296i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.0000 | −0.995688 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 8.00000 | 0.331042 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.00000 | 0.247858 | ||||||||
\(587\) | 12.0000i | 0.495293i | 0.968850 | + | 0.247647i | \(0.0796572\pi\) | ||||
−0.968850 | + | 0.247647i | \(0.920343\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.0000 | −0.988903 | ||||||||
\(590\) | −6.00000 | − | 12.0000i | −0.247016 | − | 0.494032i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.00000i | 0.0410997i | ||||||||
\(593\) | − | 24.0000i | − | 0.985562i | −0.870153 | − | 0.492781i | \(-0.835980\pi\) | ||
0.870153 | − | 0.492781i | \(-0.164020\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 24.0000 | − | 12.0000i | 0.983904 | − | 0.491952i | ||||
\(596\) | −14.0000 | −0.573462 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 8.00000i | 0.327144i | ||||||||
\(599\) | −8.00000 | −0.326871 | −0.163436 | − | 0.986554i | \(-0.552258\pi\) | ||||
−0.163436 | + | 0.986554i | \(0.552258\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.0000 | −1.06056 | −0.530281 | − | 0.847822i | \(-0.677914\pi\) | ||||
−0.530281 | + | 0.847822i | \(0.677914\pi\) | |||||||
\(602\) | 8.00000i | 0.326056i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −16.0000 | −0.651031 | ||||||||
\(605\) | −22.0000 | + | 11.0000i | −0.894427 | + | 0.447214i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 36.0000i | 1.46119i | 0.682808 | + | 0.730597i | \(0.260758\pi\) | ||||
−0.682808 | + | 0.730597i | \(0.739242\pi\) | |||||||
\(608\) | 6.00000i | 0.243332i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.00000 | 0.161823 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 30.0000i | − | 1.21169i | −0.795583 | − | 0.605844i | \(-0.792835\pi\) | ||
0.795583 | − | 0.605844i | \(-0.207165\pi\) | |||||||
\(614\) | 4.00000 | 0.161427 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.0000i | 0.483102i | 0.970388 | + | 0.241551i | \(0.0776561\pi\) | ||||
−0.970388 | + | 0.241551i | \(0.922344\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.0000 | 1.28619 | 0.643094 | − | 0.765787i | \(-0.277650\pi\) | ||||
0.643094 | + | 0.765787i | \(0.277650\pi\) | |||||||
\(620\) | 8.00000 | − | 4.00000i | 0.321288 | − | 0.160644i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.0000i | 0.480770i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | 14.0000 | 0.559553 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 22.0000i | 0.877896i | ||||||||
\(629\) | 6.00000 | 0.239236 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.00000 | −0.318475 | −0.159237 | − | 0.987240i | \(-0.550904\pi\) | ||||
−0.159237 | + | 0.987240i | \(0.550904\pi\) | |||||||
\(632\) | 4.00000i | 0.159111i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.00000 | 0.238290 | ||||||||
\(635\) | −22.0000 | − | 44.0000i | −0.873043 | − | 1.74609i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.00000i | 0.237729i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.00000 | − | 2.00000i | −0.0395285 | − | 0.0790569i | ||||
\(641\) | −14.0000 | −0.552967 | −0.276483 | − | 0.961019i | \(-0.589169\pi\) | ||||
−0.276483 | + | 0.961019i | \(0.589169\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 44.0000i | − | 1.73519i | −0.497271 | − | 0.867595i | \(-0.665665\pi\) | ||
0.497271 | − | 0.867595i | \(-0.334335\pi\) | |||||||
\(644\) | −8.00000 | −0.315244 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 36.0000 | 1.41640 | ||||||||
\(647\) | − | 16.0000i | − | 0.629025i | −0.949253 | − | 0.314512i | \(-0.898159\pi\) | ||
0.949253 | − | 0.314512i | \(-0.101841\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −6.00000 | + | 8.00000i | −0.235339 | + | 0.313786i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.0000i | 0.469956i | ||||||||
\(653\) | − | 14.0000i | − | 0.547862i | −0.961749 | − | 0.273931i | \(-0.911676\pi\) | ||
0.961749 | − | 0.273931i | \(-0.0883240\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −28.0000 | + | 14.0000i | −1.09405 | + | 0.547025i | ||||
\(656\) | 10.0000 | 0.390434 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.00000i | 0.155936i | ||||||||
\(659\) | −12.0000 | −0.467454 | −0.233727 | − | 0.972302i | \(-0.575092\pi\) | ||||
−0.233727 | + | 0.972302i | \(0.575092\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.0000 | −1.08907 | −0.544537 | − | 0.838737i | \(-0.683295\pi\) | ||||
−0.544537 | + | 0.838737i | \(0.683295\pi\) | |||||||
\(662\) | − | 34.0000i | − | 1.32145i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.0000 | 0.465690 | ||||||||
\(665\) | 12.0000 | + | 24.0000i | 0.465340 | + | 0.930680i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | − | 16.0000i | − | 0.619059i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 16.0000 | − | 8.00000i | 0.618134 | − | 0.309067i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 36.0000i | − | 1.38770i | −0.720121 | − | 0.693849i | \(-0.755914\pi\) | ||
0.720121 | − | 0.693849i | \(-0.244086\pi\) | |||||||
\(674\) | 8.00000 | 0.308148 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | 30.0000i | 1.15299i | 0.817099 | + | 0.576497i | \(0.195581\pi\) | ||||
−0.817099 | + | 0.576497i | \(0.804419\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.0000 | −0.767530 | ||||||||
\(680\) | −12.0000 | + | 6.00000i | −0.460179 | + | 0.230089i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.0000i | 0.765279i | 0.923898 | + | 0.382639i | \(0.124985\pi\) | ||||
−0.923898 | + | 0.382639i | \(0.875015\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −20.0000 | −0.763604 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 4.00000i | − | 0.152499i | ||||||
\(689\) | 4.00000 | 0.152388 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.00000 | 0.152167 | 0.0760836 | − | 0.997101i | \(-0.475758\pi\) | ||||
0.0760836 | + | 0.997101i | \(0.475758\pi\) | |||||||
\(692\) | 2.00000i | 0.0760286i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −36.0000 | −1.36654 | ||||||||
\(695\) | 40.0000 | − | 20.0000i | 1.51729 | − | 0.758643i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 60.0000i | − | 2.27266i | ||||||
\(698\) | − | 30.0000i | − | 1.13552i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.00000 | − | 6.00000i | −0.302372 | − | 0.226779i | ||||
\(701\) | 4.00000 | 0.151078 | 0.0755390 | − | 0.997143i | \(-0.475932\pi\) | ||||
0.0755390 | + | 0.997143i | \(0.475932\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.00000i | 0.226294i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −18.0000 | −0.677439 | ||||||||
\(707\) | 20.0000i | 0.752177i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.0000 | 1.50223 | 0.751116 | − | 0.660171i | \(-0.229516\pi\) | ||||
0.751116 | + | 0.660171i | \(0.229516\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 6.00000i | − | 0.224860i | ||||||
\(713\) | 16.0000i | 0.599205i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 14.0000 | 0.523205 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 8.00000i | − | 0.298557i | ||||||
\(719\) | −16.0000 | −0.596699 | −0.298350 | − | 0.954457i | \(-0.596436\pi\) | ||||
−0.298350 | + | 0.954457i | \(0.596436\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 17.0000i | 0.632674i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.00000 | −0.0743294 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 28.0000i | − | 1.03846i | −0.854634 | − | 0.519231i | \(-0.826218\pi\) | ||
0.854634 | − | 0.519231i | \(-0.173782\pi\) | |||||||
\(728\) | 4.00000i | 0.148250i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −16.0000 | + | 8.00000i | −0.592187 | + | 0.296093i | ||||
\(731\) | −24.0000 | −0.887672 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 38.0000i | − | 1.40356i | −0.712393 | − | 0.701781i | \(-0.752388\pi\) | ||
0.712393 | − | 0.701781i | \(-0.247612\pi\) | |||||||
\(734\) | −26.0000 | −0.959678 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.00000 | 0.147442 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.0000 | 1.32428 | 0.662141 | − | 0.749380i | \(-0.269648\pi\) | ||||
0.662141 | + | 0.749380i | \(0.269648\pi\) | |||||||
\(740\) | −1.00000 | − | 2.00000i | −0.0367607 | − | 0.0735215i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.00000i | 0.146845i | ||||||||
\(743\) | − | 26.0000i | − | 0.953847i | −0.878945 | − | 0.476924i | \(-0.841752\pi\) | ||
0.878945 | − | 0.476924i | \(-0.158248\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 28.0000 | − | 14.0000i | 1.02584 | − | 0.512920i | ||||
\(746\) | 34.0000 | 1.24483 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.0000 | −0.584627 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32.0000 | −1.16770 | −0.583848 | − | 0.811863i | \(-0.698454\pi\) | ||||
−0.583848 | + | 0.811863i | \(0.698454\pi\) | |||||||
\(752\) | − | 2.00000i | − | 0.0729325i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 32.0000 | − | 16.0000i | 1.16460 | − | 0.582300i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 14.0000i | − | 0.508839i | −0.967094 | − | 0.254419i | \(-0.918116\pi\) | ||
0.967094 | − | 0.254419i | \(-0.0818843\pi\) | |||||||
\(758\) | − | 12.0000i | − | 0.435860i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.00000 | − | 12.0000i | −0.217643 | − | 0.435286i | ||||
\(761\) | −34.0000 | −1.23250 | −0.616250 | − | 0.787551i | \(-0.711349\pi\) | ||||
−0.616250 | + | 0.787551i | \(0.711349\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 40.0000i | 1.44810i | ||||||||
\(764\) | 4.00000 | 0.144715 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −28.0000 | −1.01168 | ||||||||
\(767\) | − | 12.0000i | − | 0.433295i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.0000 | −0.360609 | −0.180305 | − | 0.983611i | \(-0.557708\pi\) | ||||
−0.180305 | + | 0.983611i | \(0.557708\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 10.0000i | − | 0.359908i | ||||||
\(773\) | 54.0000i | 1.94225i | 0.238581 | + | 0.971123i | \(0.423318\pi\) | ||||
−0.238581 | + | 0.971123i | \(0.576682\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12.0000 | + | 16.0000i | −0.431053 | + | 0.574737i | ||||
\(776\) | 10.0000 | 0.358979 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 16.0000i | − | 0.573628i | ||||||
\(779\) | 60.0000 | 2.14972 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − | 24.0000i | − | 0.858238i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.00000 | 0.107143 | ||||||||
\(785\) | −22.0000 | − | 44.0000i | −0.785214 | − | 1.57043i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 40.0000i | − | 1.42585i | −0.701242 | − | 0.712923i | \(-0.747371\pi\) | ||
0.701242 | − | 0.712923i | \(-0.252629\pi\) | |||||||
\(788\) | 10.0000i | 0.356235i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.00000 | − | 8.00000i | −0.142314 | − | 0.284627i | ||||
\(791\) | 4.00000 | 0.142224 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 2.00000 | 0.0709773 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −20.0000 | −0.708881 | ||||||||
\(797\) | 6.00000i | 0.212531i | 0.994338 | + | 0.106265i | \(0.0338893\pi\) | ||||
−0.994338 | + | 0.106265i | \(0.966111\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.0000 | −0.424529 | ||||||||
\(800\) | 4.00000 | + | 3.00000i | 0.141421 | + | 0.106066i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.00000i | 0.0706225i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.0000 | − | 8.00000i | 0.563926 | − | 0.281963i | ||||
\(806\) | 8.00000 | 0.281788 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 10.0000i | − | 0.351799i | ||||||
\(809\) | −6.00000 | −0.210949 | −0.105474 | − | 0.994422i | \(-0.533636\pi\) | ||||
−0.105474 | + | 0.994422i | \(0.533636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.0000 | −1.26413 | −0.632065 | − | 0.774915i | \(-0.717793\pi\) | ||||
−0.632065 | + | 0.774915i | \(0.717793\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.0000 | − | 24.0000i | −0.420342 | − | 0.840683i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 24.0000i | − | 0.839654i | ||||||
\(818\) | − | 14.0000i | − | 0.489499i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −20.0000 | + | 10.0000i | −0.698430 | + | 0.349215i | ||||
\(821\) | 50.0000 | 1.74501 | 0.872506 | − | 0.488603i | \(-0.162493\pi\) | ||||
0.872506 | + | 0.488603i | \(0.162493\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 26.0000i | − | 0.906303i | −0.891434 | − | 0.453152i | \(-0.850300\pi\) | ||
0.891434 | − | 0.453152i | \(-0.149700\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.0000 | 0.417533 | ||||||||
\(827\) | 36.0000i | 1.25184i | 0.779886 | + | 0.625921i | \(0.215277\pi\) | ||||
−0.779886 | + | 0.625921i | \(0.784723\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.0000 | 0.694629 | 0.347314 | − | 0.937749i | \(-0.387094\pi\) | ||||
0.347314 | + | 0.937749i | \(0.387094\pi\) | |||||||
\(830\) | −24.0000 | + | 12.0000i | −0.833052 | + | 0.416526i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 2.00000i | − | 0.0693375i | ||||||
\(833\) | − | 18.0000i | − | 0.623663i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.0000 | + | 32.0000i | 0.553703 | + | 1.10741i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 20.0000i | 0.690889i | ||||||||
\(839\) | −48.0000 | −1.65714 | −0.828572 | − | 0.559883i | \(-0.810846\pi\) | ||||
−0.828572 | + | 0.559883i | \(0.810846\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 36.0000i | 1.24064i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 16.0000 | 0.550743 | ||||||||
\(845\) | 18.0000 | − | 9.00000i | 0.619219 | − | 0.309609i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 22.0000i | − | 0.755929i | ||||||
\(848\) | − | 2.00000i | − | 0.0686803i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 18.0000 | − | 24.0000i | 0.617395 | − | 0.823193i | ||||
\(851\) | 4.00000 | 0.137118 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.0000i | 1.02718i | 0.858036 | + | 0.513590i | \(0.171685\pi\) | ||||
−0.858036 | + | 0.513590i | \(0.828315\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.00000 | 0.273434 | ||||||||
\(857\) | − | 2.00000i | − | 0.0683187i | −0.999416 | − | 0.0341593i | \(-0.989125\pi\) | ||
0.999416 | − | 0.0341593i | \(-0.0108754\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.0000 | −0.341196 | −0.170598 | − | 0.985341i | \(-0.554570\pi\) | ||||
−0.170598 | + | 0.985341i | \(0.554570\pi\) | |||||||
\(860\) | 4.00000 | + | 8.00000i | 0.136399 | + | 0.272798i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 20.0000i | − | 0.681203i | ||||||
\(863\) | 6.00000i | 0.204242i | 0.994772 | + | 0.102121i | \(0.0325630\pi\) | ||||
−0.994772 | + | 0.102121i | \(0.967437\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.00000 | − | 4.00000i | −0.0680020 | − | 0.136004i | ||||
\(866\) | 16.0000 | 0.543702 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.00000i | 0.271538i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.0000 | 0.542139 | ||||||||
\(872\) | − | 20.0000i | − | 0.677285i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 24.0000 | 0.811812 | ||||||||
\(875\) | 22.0000 | + | 4.00000i | 0.743736 | + | 0.135225i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.0000i | 1.14810i | 0.818821 | + | 0.574049i | \(0.194628\pi\) | ||||
−0.818821 | + | 0.574049i | \(0.805372\pi\) | |||||||
\(878\) | − | 4.00000i | − | 0.134993i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.0000 | −0.606435 | −0.303218 | − | 0.952921i | \(-0.598061\pi\) | ||||
−0.303218 | + | 0.952921i | \(0.598061\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.0000i | 0.673054i | 0.941674 | + | 0.336527i | \(0.109252\pi\) | ||||
−0.941674 | + | 0.336527i | \(0.890748\pi\) | |||||||
\(884\) | −12.0000 | −0.403604 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.0000 | 0.537531 | ||||||||
\(887\) | − | 50.0000i | − | 1.67884i | −0.543487 | − | 0.839418i | \(-0.682896\pi\) | ||
0.543487 | − | 0.839418i | \(-0.317104\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 44.0000 | 1.47571 | ||||||||
\(890\) | 6.00000 | + | 12.0000i | 0.201120 | + | 0.402241i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 14.0000i | − | 0.468755i | ||||||
\(893\) | − | 12.0000i | − | 0.401565i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −28.0000 | + | 14.0000i | −0.935937 | + | 0.467968i | ||||
\(896\) | 2.00000 | 0.0668153 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 30.0000i | 1.00111i | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.0000 | −0.399778 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.00000 | −0.0665190 | ||||||||
\(905\) | 4.00000 | − | 2.00000i | 0.132964 | − | 0.0664822i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.0000i | 0.664089i | 0.943264 | + | 0.332045i | \(0.107738\pi\) | ||||
−0.943264 | + | 0.332045i | \(0.892262\pi\) | |||||||
\(908\) | − | 20.0000i | − | 0.663723i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.00000 | − | 8.00000i | −0.132599 | − | 0.265197i | ||||
\(911\) | 48.0000 | 1.59031 | 0.795155 | − | 0.606406i | \(-0.207389\pi\) | ||||
0.795155 | + | 0.606406i | \(0.207389\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −10.0000 | −0.330771 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.00000 | 0.0660819 | ||||||||
\(917\) | − | 28.0000i | − | 0.924641i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.00000 | −0.263896 | −0.131948 | − | 0.991257i | \(-0.542123\pi\) | ||||
−0.131948 | + | 0.991257i | \(0.542123\pi\) | |||||||
\(920\) | −8.00000 | + | 4.00000i | −0.263752 | + | 0.131876i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.00000 | + | 3.00000i | 0.131519 | + | 0.0986394i | ||||
\(926\) | 4.00000 | 0.131448 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18.0000 | −0.590561 | −0.295280 | − | 0.955411i | \(-0.595413\pi\) | ||||
−0.295280 | + | 0.955411i | \(0.595413\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.0000 | 0.589926 | ||||||||
\(932\) | − | 24.0000i | − | 0.786146i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 36.0000 | 1.17796 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 4.00000i | − | 0.130674i | −0.997863 | − | 0.0653372i | \(-0.979188\pi\) | ||
0.997863 | − | 0.0653372i | \(-0.0208123\pi\) | |||||||
\(938\) | 16.0000i | 0.522419i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.00000 | + | 4.00000i | 0.0652328 | + | 0.130466i | ||||
\(941\) | 22.0000 | 0.717180 | 0.358590 | − | 0.933495i | \(-0.383258\pi\) | ||||
0.358590 | + | 0.933495i | \(0.383258\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 40.0000i | − | 1.30258i | ||||||
\(944\) | −6.00000 | −0.195283 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.0000i | 0.909878i | 0.890523 | + | 0.454939i | \(0.150339\pi\) | ||||
−0.890523 | + | 0.454939i | \(0.849661\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.0000 | −0.519382 | ||||||||
\(950\) | 24.0000 | + | 18.0000i | 0.778663 | + | 0.583997i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 12.0000i | − | 0.388922i | ||||||
\(953\) | 24.0000i | 0.777436i | 0.921357 | + | 0.388718i | \(0.127082\pi\) | ||||
−0.921357 | + | 0.388718i | \(0.872918\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.00000 | + | 4.00000i | −0.258874 | + | 0.129437i | ||||
\(956\) | −28.0000 | −0.905585 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.0000i | 0.387702i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | − | 2.00000i | − | 0.0644826i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.0000 | −0.322078 | ||||||||
\(965\) | 10.0000 | + | 20.0000i | 0.321911 | + | 0.643823i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.0000i | 0.900419i | 0.892923 | + | 0.450210i | \(0.148651\pi\) | ||||
−0.892923 | + | 0.450210i | \(0.851349\pi\) | |||||||
\(968\) | 11.0000i | 0.353553i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −20.0000 | + | 10.0000i | −0.642161 | + | 0.321081i | ||||
\(971\) | −32.0000 | −1.02693 | −0.513464 | − | 0.858111i | \(-0.671638\pi\) | ||||
−0.513464 | + | 0.858111i | \(0.671638\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 40.0000i | 1.28234i | ||||||||
\(974\) | 24.0000 | 0.769010 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.0000i | 0.575871i | 0.957650 | + | 0.287936i | \(0.0929689\pi\) | ||||
−0.957650 | + | 0.287936i | \(0.907031\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −6.00000 | + | 3.00000i | −0.191663 | + | 0.0958315i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 24.0000i | − | 0.765871i | ||||||
\(983\) | 38.0000i | 1.21201i | 0.795460 | + | 0.606006i | \(0.207229\pi\) | ||||
−0.795460 | + | 0.606006i | \(0.792771\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.0000 | − | 20.0000i | −0.318626 | − | 0.637253i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 12.0000i | − | 0.381771i | ||||||
\(989\) | −16.0000 | −0.508770 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.0000 | 1.52477 | 0.762385 | − | 0.647124i | \(-0.224028\pi\) | ||||
0.762385 | + | 0.647124i | \(0.224028\pi\) | |||||||
\(992\) | − | 4.00000i | − | 0.127000i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 40.0000 | − | 20.0000i | 1.26809 | − | 0.634043i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.0000i | 0.823428i | 0.911313 | + | 0.411714i | \(0.135070\pi\) | ||||
−0.911313 | + | 0.411714i | \(0.864930\pi\) | |||||||
\(998\) | − | 30.0000i | − | 0.949633i | ||||||
\(999\) | 0 | 0 |
(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 | 3330.2.d.f.1999.2 | 2 | ||
3.2 | odd | 2 | 370.2.b.a.149.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 3330.2.d.f.1999.1 | 2 | ||
15.2 | even | 4 | 1850.2.a.j.1.1 | 1 | |||
15.8 | even | 4 | 1850.2.a.e.1.1 | 1 | |||
15.14 | odd | 2 | 370.2.b.a.149.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.b.a.149.1 | ✓ | 2 | 3.2 | odd | 2 | ||
370.2.b.a.149.2 | yes | 2 | 15.14 | odd | 2 | ||
1850.2.a.e.1.1 | 1 | 15.8 | even | 4 | |||
1850.2.a.j.1.1 | 1 | 15.2 | even | 4 | |||
3330.2.d.f.1999.1 | 2 | 5.4 | even | 2 | inner | ||
3330.2.d.f.1999.2 | 2 | 1.1 | even | 1 | trivial |