Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(229,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, 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("570.229");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.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: | \(4.55147291521\) |
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 | 229.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.229 |
Dual form | 570.2.d.b.229.2 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 2.00000 | − | 1.00000i | 0.894427 | − | 0.447214i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −1.00000 | − | 2.00000i | −0.316228 | − | 0.632456i | ||||
\(11\) | −4.00000 | −1.20605 | −0.603023 | − | 0.797724i | \(-0.706037\pi\) | ||||
−0.603023 | + | 0.797724i | \(0.706037\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | − | 4.00000i | − | 1.10940i | −0.832050 | − | 0.554700i | \(-0.812833\pi\) | ||
0.832050 | − | 0.554700i | \(-0.187167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | − | 2.00000i | −0.258199 | − | 0.516398i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 6.00000i | − | 1.45521i | −0.685994 | − | 0.727607i | \(-0.740633\pi\) | ||
0.685994 | − | 0.727607i | \(-0.259367\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −2.00000 | + | 1.00000i | −0.447214 | + | 0.223607i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.00000i | 0.852803i | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 3.00000 | − | 4.00000i | 0.600000 | − | 0.800000i | ||||
\(26\) | −4.00000 | −0.784465 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | −2.00000 | + | 1.00000i | −0.365148 | + | 0.182574i | ||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 4.00000i | 0.696311i | ||||||||
\(34\) | −6.00000 | −1.02899 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 4.00000i | 0.657596i | 0.944400 | + | 0.328798i | \(0.106644\pi\) | ||||
−0.944400 | + | 0.328798i | \(0.893356\pi\) | |||||||
\(38\) | − | 1.00000i | − | 0.162221i | ||||||
\(39\) | −4.00000 | −0.640513 | ||||||||
\(40\) | 1.00000 | + | 2.00000i | 0.158114 | + | 0.316228i | ||||
\(41\) | −12.0000 | −1.87409 | −0.937043 | − | 0.349215i | \(-0.886448\pi\) | ||||
−0.937043 | + | 0.349215i | \(0.886448\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.00000i | 0.914991i | 0.889212 | + | 0.457496i | \(0.151253\pi\) | ||||
−0.889212 | + | 0.457496i | \(0.848747\pi\) | |||||||
\(44\) | 4.00000 | 0.603023 | ||||||||
\(45\) | −2.00000 | + | 1.00000i | −0.298142 | + | 0.149071i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 7.00000 | 1.00000 | ||||||||
\(50\) | −4.00000 | − | 3.00000i | −0.565685 | − | 0.424264i | ||||
\(51\) | −6.00000 | −0.840168 | ||||||||
\(52\) | 4.00000i | 0.554700i | ||||||||
\(53\) | − | 14.0000i | − | 1.92305i | −0.274721 | − | 0.961524i | \(-0.588586\pi\) | ||
0.274721 | − | 0.961524i | \(-0.411414\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −8.00000 | + | 4.00000i | −1.07872 | + | 0.539360i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.00000i | − | 0.132453i | ||||||
\(58\) | − | 2.00000i | − | 0.262613i | ||||||
\(59\) | 10.0000 | 1.30189 | 0.650945 | − | 0.759125i | \(-0.274373\pi\) | ||||
0.650945 | + | 0.759125i | \(0.274373\pi\) | |||||||
\(60\) | 1.00000 | + | 2.00000i | 0.129099 | + | 0.258199i | ||||
\(61\) | −6.00000 | −0.768221 | −0.384111 | − | 0.923287i | \(-0.625492\pi\) | ||||
−0.384111 | + | 0.923287i | \(0.625492\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −4.00000 | − | 8.00000i | −0.496139 | − | 0.992278i | ||||
\(66\) | 4.00000 | 0.492366 | ||||||||
\(67\) | 4.00000i | 0.488678i | 0.969690 | + | 0.244339i | \(0.0785709\pi\) | ||||
−0.969690 | + | 0.244339i | \(0.921429\pi\) | |||||||
\(68\) | 6.00000i | 0.727607i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000 | 1.42414 | 0.712069 | − | 0.702109i | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702109i | \(0.247758\pi\) | |||||||
\(72\) | − | 1.00000i | − | 0.117851i | ||||||
\(73\) | 8.00000i | 0.936329i | 0.883641 | + | 0.468165i | \(0.155085\pi\) | ||||
−0.883641 | + | 0.468165i | \(0.844915\pi\) | |||||||
\(74\) | 4.00000 | 0.464991 | ||||||||
\(75\) | −4.00000 | − | 3.00000i | −0.461880 | − | 0.346410i | ||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.00000i | 0.452911i | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | 2.00000 | − | 1.00000i | 0.223607 | − | 0.111803i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 12.0000i | 1.32518i | ||||||||
\(83\) | 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 | ||||
\(86\) | 6.00000 | 0.646997 | ||||||||
\(87\) | − | 2.00000i | − | 0.214423i | ||||||
\(88\) | − | 4.00000i | − | 0.426401i | ||||||
\(89\) | 8.00000 | 0.847998 | 0.423999 | − | 0.905663i | \(-0.360626\pi\) | ||||
0.423999 | + | 0.905663i | \(0.360626\pi\) | |||||||
\(90\) | 1.00000 | + | 2.00000i | 0.105409 | + | 0.210819i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.00000 | − | 1.00000i | 0.205196 | − | 0.102598i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 10.0000i | 1.01535i | 0.861550 | + | 0.507673i | \(0.169494\pi\) | ||||
−0.861550 | + | 0.507673i | \(0.830506\pi\) | |||||||
\(98\) | − | 7.00000i | − | 0.707107i | ||||||
\(99\) | 4.00000 | 0.402015 | ||||||||
\(100\) | −3.00000 | + | 4.00000i | −0.300000 | + | 0.400000i | ||||
\(101\) | 12.0000 | 1.19404 | 0.597022 | − | 0.802225i | \(-0.296350\pi\) | ||||
0.597022 | + | 0.802225i | \(0.296350\pi\) | |||||||
\(102\) | 6.00000i | 0.594089i | ||||||||
\(103\) | 2.00000i | 0.197066i | 0.995134 | + | 0.0985329i | \(0.0314150\pi\) | ||||
−0.995134 | + | 0.0985329i | \(0.968585\pi\) | |||||||
\(104\) | 4.00000 | 0.392232 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14.0000 | −1.35980 | ||||||||
\(107\) | − | 20.0000i | − | 1.93347i | −0.255774 | − | 0.966736i | \(-0.582330\pi\) | ||
0.255774 | − | 0.966736i | \(-0.417670\pi\) | |||||||
\(108\) | − | 1.00000i | − | 0.0962250i | ||||||
\(109\) | 14.0000 | 1.34096 | 0.670478 | − | 0.741929i | \(-0.266089\pi\) | ||||
0.670478 | + | 0.741929i | \(0.266089\pi\) | |||||||
\(110\) | 4.00000 | + | 8.00000i | 0.381385 | + | 0.762770i | ||||
\(111\) | 4.00000 | 0.379663 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 10.0000i | − | 0.940721i | −0.882474 | − | 0.470360i | \(-0.844124\pi\) | ||
0.882474 | − | 0.470360i | \(-0.155876\pi\) | |||||||
\(114\) | −1.00000 | −0.0936586 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.00000 | −0.185695 | ||||||||
\(117\) | 4.00000i | 0.369800i | ||||||||
\(118\) | − | 10.0000i | − | 0.920575i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.00000 | − | 1.00000i | 0.182574 | − | 0.0912871i | ||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 6.00000i | 0.543214i | ||||||||
\(123\) | 12.0000i | 1.08200i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.00000 | − | 11.0000i | 0.178885 | − | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.0000i | 0.887357i | 0.896186 | + | 0.443678i | \(0.146327\pi\) | ||||
−0.896186 | + | 0.443678i | \(0.853673\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 6.00000 | 0.528271 | ||||||||
\(130\) | −8.00000 | + | 4.00000i | −0.701646 | + | 0.350823i | ||||
\(131\) | −20.0000 | −1.74741 | −0.873704 | − | 0.486458i | \(-0.838289\pi\) | ||||
−0.873704 | + | 0.486458i | \(0.838289\pi\) | |||||||
\(132\) | − | 4.00000i | − | 0.348155i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.00000 | 0.345547 | ||||||||
\(135\) | 1.00000 | + | 2.00000i | 0.0860663 | + | 0.172133i | ||||
\(136\) | 6.00000 | 0.514496 | ||||||||
\(137\) | 6.00000i | 0.512615i | 0.966595 | + | 0.256307i | \(0.0825059\pi\) | ||||
−0.966595 | + | 0.256307i | \(0.917494\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.0000 | 1.01783 | 0.508913 | − | 0.860818i | \(-0.330047\pi\) | ||||
0.508913 | + | 0.860818i | \(0.330047\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 12.0000i | − | 1.00702i | ||||||
\(143\) | 16.0000i | 1.33799i | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 4.00000 | − | 2.00000i | 0.332182 | − | 0.166091i | ||||
\(146\) | 8.00000 | 0.662085 | ||||||||
\(147\) | − | 7.00000i | − | 0.577350i | ||||||
\(148\) | − | 4.00000i | − | 0.328798i | ||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | −3.00000 | + | 4.00000i | −0.244949 | + | 0.326599i | ||||
\(151\) | 16.0000 | 1.30206 | 0.651031 | − | 0.759051i | \(-0.274337\pi\) | ||||
0.651031 | + | 0.759051i | \(0.274337\pi\) | |||||||
\(152\) | 1.00000i | 0.0811107i | ||||||||
\(153\) | 6.00000i | 0.485071i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.00000 | 0.320256 | ||||||||
\(157\) | − | 6.00000i | − | 0.478852i | −0.970915 | − | 0.239426i | \(-0.923041\pi\) | ||
0.970915 | − | 0.239426i | \(-0.0769593\pi\) | |||||||
\(158\) | − | 8.00000i | − | 0.636446i | ||||||
\(159\) | −14.0000 | −1.11027 | ||||||||
\(160\) | −1.00000 | − | 2.00000i | −0.0790569 | − | 0.158114i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | − | 10.0000i | − | 0.783260i | −0.920123 | − | 0.391630i | \(-0.871911\pi\) | ||
0.920123 | − | 0.391630i | \(-0.128089\pi\) | |||||||
\(164\) | 12.0000 | 0.937043 | ||||||||
\(165\) | 4.00000 | + | 8.00000i | 0.311400 | + | 0.622799i | ||||
\(166\) | 12.0000 | 0.931381 | ||||||||
\(167\) | − | 12.0000i | − | 0.928588i | −0.885681 | − | 0.464294i | \(-0.846308\pi\) | ||
0.885681 | − | 0.464294i | \(-0.153692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.00000 | −0.230769 | ||||||||
\(170\) | −12.0000 | + | 6.00000i | −0.920358 | + | 0.460179i | ||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | − | 6.00000i | − | 0.457496i | ||||||
\(173\) | − | 2.00000i | − | 0.152057i | −0.997106 | − | 0.0760286i | \(-0.975776\pi\) | ||
0.997106 | − | 0.0760286i | \(-0.0242240\pi\) | |||||||
\(174\) | −2.00000 | −0.151620 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.00000 | −0.301511 | ||||||||
\(177\) | − | 10.0000i | − | 0.751646i | ||||||
\(178\) | − | 8.00000i | − | 0.599625i | ||||||
\(179\) | −6.00000 | −0.448461 | −0.224231 | − | 0.974536i | \(-0.571987\pi\) | ||||
−0.224231 | + | 0.974536i | \(0.571987\pi\) | |||||||
\(180\) | 2.00000 | − | 1.00000i | 0.149071 | − | 0.0745356i | ||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.00000i | 0.443533i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.00000 | + | 8.00000i | 0.294086 | + | 0.588172i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24.0000i | 1.75505i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.00000 | − | 2.00000i | −0.0725476 | − | 0.145095i | ||||
\(191\) | 6.00000 | 0.434145 | 0.217072 | − | 0.976156i | \(-0.430349\pi\) | ||||
0.217072 | + | 0.976156i | \(0.430349\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | − | 10.0000i | − | 0.719816i | −0.932988 | − | 0.359908i | \(-0.882808\pi\) | ||
0.932988 | − | 0.359908i | \(-0.117192\pi\) | |||||||
\(194\) | 10.0000 | 0.717958 | ||||||||
\(195\) | −8.00000 | + | 4.00000i | −0.572892 | + | 0.286446i | ||||
\(196\) | −7.00000 | −0.500000 | ||||||||
\(197\) | 10.0000i | 0.712470i | 0.934396 | + | 0.356235i | \(0.115940\pi\) | ||||
−0.934396 | + | 0.356235i | \(0.884060\pi\) | |||||||
\(198\) | − | 4.00000i | − | 0.284268i | ||||||
\(199\) | 4.00000 | 0.283552 | 0.141776 | − | 0.989899i | \(-0.454719\pi\) | ||||
0.141776 | + | 0.989899i | \(0.454719\pi\) | |||||||
\(200\) | 4.00000 | + | 3.00000i | 0.282843 | + | 0.212132i | ||||
\(201\) | 4.00000 | 0.282138 | ||||||||
\(202\) | − | 12.0000i | − | 0.844317i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 6.00000 | 0.420084 | ||||||||
\(205\) | −24.0000 | + | 12.0000i | −1.67623 | + | 0.838116i | ||||
\(206\) | 2.00000 | 0.139347 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 4.00000i | − | 0.277350i | ||||||
\(209\) | −4.00000 | −0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.00000 | −0.550743 | −0.275371 | − | 0.961338i | \(-0.588801\pi\) | ||||
−0.275371 | + | 0.961338i | \(0.588801\pi\) | |||||||
\(212\) | 14.0000i | 0.961524i | ||||||||
\(213\) | − | 12.0000i | − | 0.822226i | ||||||
\(214\) | −20.0000 | −1.36717 | ||||||||
\(215\) | 6.00000 | + | 12.0000i | 0.409197 | + | 0.818393i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 14.0000i | − | 0.948200i | ||||||
\(219\) | 8.00000 | 0.540590 | ||||||||
\(220\) | 8.00000 | − | 4.00000i | 0.539360 | − | 0.269680i | ||||
\(221\) | −24.0000 | −1.61441 | ||||||||
\(222\) | − | 4.00000i | − | 0.268462i | ||||||
\(223\) | 10.0000i | 0.669650i | 0.942280 | + | 0.334825i | \(0.108677\pi\) | ||||
−0.942280 | + | 0.334825i | \(0.891323\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.00000 | + | 4.00000i | −0.200000 | + | 0.266667i | ||||
\(226\) | −10.0000 | −0.665190 | ||||||||
\(227\) | 12.0000i | 0.796468i | 0.917284 | + | 0.398234i | \(0.130377\pi\) | ||||
−0.917284 | + | 0.398234i | \(0.869623\pi\) | |||||||
\(228\) | 1.00000i | 0.0662266i | ||||||||
\(229\) | 10.0000 | 0.660819 | 0.330409 | − | 0.943838i | \(-0.392813\pi\) | ||||
0.330409 | + | 0.943838i | \(0.392813\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.00000i | 0.131306i | ||||||||
\(233\) | 14.0000i | 0.917170i | 0.888650 | + | 0.458585i | \(0.151644\pi\) | ||||
−0.888650 | + | 0.458585i | \(0.848356\pi\) | |||||||
\(234\) | 4.00000 | 0.261488 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −10.0000 | −0.650945 | ||||||||
\(237\) | − | 8.00000i | − | 0.519656i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.0000 | −0.646846 | −0.323423 | − | 0.946254i | \(-0.604834\pi\) | ||||
−0.323423 | + | 0.946254i | \(0.604834\pi\) | |||||||
\(240\) | −1.00000 | − | 2.00000i | −0.0645497 | − | 0.129099i | ||||
\(241\) | 26.0000 | 1.67481 | 0.837404 | − | 0.546585i | \(-0.184072\pi\) | ||||
0.837404 | + | 0.546585i | \(0.184072\pi\) | |||||||
\(242\) | − | 5.00000i | − | 0.321412i | ||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 6.00000 | 0.384111 | ||||||||
\(245\) | 14.0000 | − | 7.00000i | 0.894427 | − | 0.447214i | ||||
\(246\) | 12.0000 | 0.765092 | ||||||||
\(247\) | − | 4.00000i | − | 0.254514i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.0000 | 0.760469 | ||||||||
\(250\) | −11.0000 | − | 2.00000i | −0.695701 | − | 0.126491i | ||||
\(251\) | −24.0000 | −1.51487 | −0.757433 | − | 0.652913i | \(-0.773547\pi\) | ||||
−0.757433 | + | 0.652913i | \(0.773547\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 10.0000 | 0.627456 | ||||||||
\(255\) | −12.0000 | + | 6.00000i | −0.751469 | + | 0.375735i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.00000i | 0.124757i | 0.998053 | + | 0.0623783i | \(0.0198685\pi\) | ||||
−0.998053 | + | 0.0623783i | \(0.980131\pi\) | |||||||
\(258\) | − | 6.00000i | − | 0.373544i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.00000 | + | 8.00000i | 0.248069 | + | 0.496139i | ||||
\(261\) | −2.00000 | −0.123797 | ||||||||
\(262\) | 20.0000i | 1.23560i | ||||||||
\(263\) | 16.0000i | 0.986602i | 0.869859 | + | 0.493301i | \(0.164210\pi\) | ||||
−0.869859 | + | 0.493301i | \(0.835790\pi\) | |||||||
\(264\) | −4.00000 | −0.246183 | ||||||||
\(265\) | −14.0000 | − | 28.0000i | −0.860013 | − | 1.72003i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 8.00000i | − | 0.489592i | ||||||
\(268\) | − | 4.00000i | − | 0.244339i | ||||||
\(269\) | 2.00000 | 0.121942 | 0.0609711 | − | 0.998140i | \(-0.480580\pi\) | ||||
0.0609711 | + | 0.998140i | \(0.480580\pi\) | |||||||
\(270\) | 2.00000 | − | 1.00000i | 0.121716 | − | 0.0608581i | ||||
\(271\) | −28.0000 | −1.70088 | −0.850439 | − | 0.526073i | \(-0.823664\pi\) | ||||
−0.850439 | + | 0.526073i | \(0.823664\pi\) | |||||||
\(272\) | − | 6.00000i | − | 0.363803i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.00000 | 0.362473 | ||||||||
\(275\) | −12.0000 | + | 16.0000i | −0.723627 | + | 0.964836i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.0000i | 0.841178i | 0.907251 | + | 0.420589i | \(0.138177\pi\) | ||||
−0.907251 | + | 0.420589i | \(0.861823\pi\) | |||||||
\(278\) | − | 12.0000i | − | 0.719712i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.0000 | 0.715860 | 0.357930 | − | 0.933748i | \(-0.383483\pi\) | ||||
0.357930 | + | 0.933748i | \(0.383483\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 2.00000i | − | 0.118888i | −0.998232 | − | 0.0594438i | \(-0.981067\pi\) | ||
0.998232 | − | 0.0594438i | \(-0.0189327\pi\) | |||||||
\(284\) | −12.0000 | −0.712069 | ||||||||
\(285\) | −1.00000 | − | 2.00000i | −0.0592349 | − | 0.118470i | ||||
\(286\) | 16.0000 | 0.946100 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −19.0000 | −1.11765 | ||||||||
\(290\) | −2.00000 | − | 4.00000i | −0.117444 | − | 0.234888i | ||||
\(291\) | 10.0000 | 0.586210 | ||||||||
\(292\) | − | 8.00000i | − | 0.468165i | ||||||
\(293\) | 14.0000i | 0.817889i | 0.912559 | + | 0.408944i | \(0.134103\pi\) | ||||
−0.912559 | + | 0.408944i | \(0.865897\pi\) | |||||||
\(294\) | −7.00000 | −0.408248 | ||||||||
\(295\) | 20.0000 | − | 10.0000i | 1.16445 | − | 0.582223i | ||||
\(296\) | −4.00000 | −0.232495 | ||||||||
\(297\) | − | 4.00000i | − | 0.232104i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 4.00000 | + | 3.00000i | 0.230940 | + | 0.173205i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 16.0000i | − | 0.920697i | ||||||
\(303\) | − | 12.0000i | − | 0.689382i | ||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −12.0000 | + | 6.00000i | −0.687118 | + | 0.343559i | ||||
\(306\) | 6.00000 | 0.342997 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.00000 | 0.113776 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.0000 | −1.02069 | −0.510343 | − | 0.859971i | \(-0.670482\pi\) | ||||
−0.510343 | + | 0.859971i | \(0.670482\pi\) | |||||||
\(312\) | − | 4.00000i | − | 0.226455i | ||||||
\(313\) | 4.00000i | 0.226093i | 0.993590 | + | 0.113047i | \(0.0360610\pi\) | ||||
−0.993590 | + | 0.113047i | \(0.963939\pi\) | |||||||
\(314\) | −6.00000 | −0.338600 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | − | 18.0000i | − | 1.01098i | −0.862832 | − | 0.505490i | \(-0.831312\pi\) | ||
0.862832 | − | 0.505490i | \(-0.168688\pi\) | |||||||
\(318\) | 14.0000i | 0.785081i | ||||||||
\(319\) | −8.00000 | −0.447914 | ||||||||
\(320\) | −2.00000 | + | 1.00000i | −0.111803 | + | 0.0559017i | ||||
\(321\) | −20.0000 | −1.11629 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 6.00000i | − | 0.333849i | ||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −16.0000 | − | 12.0000i | −0.887520 | − | 0.665640i | ||||
\(326\) | −10.0000 | −0.553849 | ||||||||
\(327\) | − | 14.0000i | − | 0.774202i | ||||||
\(328\) | − | 12.0000i | − | 0.662589i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 8.00000 | − | 4.00000i | 0.440386 | − | 0.220193i | ||||
\(331\) | 8.00000 | 0.439720 | 0.219860 | − | 0.975531i | \(-0.429440\pi\) | ||||
0.219860 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(332\) | − | 12.0000i | − | 0.658586i | ||||||
\(333\) | − | 4.00000i | − | 0.219199i | ||||||
\(334\) | −12.0000 | −0.656611 | ||||||||
\(335\) | 4.00000 | + | 8.00000i | 0.218543 | + | 0.437087i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 18.0000i | − | 0.980522i | −0.871576 | − | 0.490261i | \(-0.836901\pi\) | ||
0.871576 | − | 0.490261i | \(-0.163099\pi\) | |||||||
\(338\) | 3.00000i | 0.163178i | ||||||||
\(339\) | −10.0000 | −0.543125 | ||||||||
\(340\) | 6.00000 | + | 12.0000i | 0.325396 | + | 0.650791i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 1.00000i | 0.0540738i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −6.00000 | −0.323498 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.00000 | −0.107521 | ||||||||
\(347\) | − | 32.0000i | − | 1.71785i | −0.512101 | − | 0.858925i | \(-0.671133\pi\) | ||
0.512101 | − | 0.858925i | \(-0.328867\pi\) | |||||||
\(348\) | 2.00000i | 0.107211i | ||||||||
\(349\) | −34.0000 | −1.81998 | −0.909989 | − | 0.414632i | \(-0.863910\pi\) | ||||
−0.909989 | + | 0.414632i | \(0.863910\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.00000 | 0.213504 | ||||||||
\(352\) | 4.00000i | 0.213201i | ||||||||
\(353\) | 22.0000i | 1.17094i | 0.810693 | + | 0.585471i | \(0.199090\pi\) | ||||
−0.810693 | + | 0.585471i | \(0.800910\pi\) | |||||||
\(354\) | −10.0000 | −0.531494 | ||||||||
\(355\) | 24.0000 | − | 12.0000i | 1.27379 | − | 0.636894i | ||||
\(356\) | −8.00000 | −0.423999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.00000i | 0.317110i | ||||||||
\(359\) | −34.0000 | −1.79445 | −0.897226 | − | 0.441572i | \(-0.854421\pi\) | ||||
−0.897226 | + | 0.441572i | \(0.854421\pi\) | |||||||
\(360\) | −1.00000 | − | 2.00000i | −0.0527046 | − | 0.105409i | ||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 10.0000i | 0.525588i | ||||||||
\(363\) | − | 5.00000i | − | 0.262432i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.00000 | + | 16.0000i | 0.418739 | + | 0.837478i | ||||
\(366\) | 6.00000 | 0.313625 | ||||||||
\(367\) | 12.0000i | 0.626395i | 0.949688 | + | 0.313197i | \(0.101400\pi\) | ||||
−0.949688 | + | 0.313197i | \(0.898600\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12.0000 | 0.624695 | ||||||||
\(370\) | 8.00000 | − | 4.00000i | 0.415900 | − | 0.207950i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.0000i | 0.621336i | 0.950518 | + | 0.310668i | \(0.100553\pi\) | ||||
−0.950518 | + | 0.310668i | \(0.899447\pi\) | |||||||
\(374\) | 24.0000 | 1.24101 | ||||||||
\(375\) | −11.0000 | − | 2.00000i | −0.568038 | − | 0.103280i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 8.00000i | − | 0.412021i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.0000 | −0.616399 | −0.308199 | − | 0.951322i | \(-0.599726\pi\) | ||||
−0.308199 | + | 0.951322i | \(0.599726\pi\) | |||||||
\(380\) | −2.00000 | + | 1.00000i | −0.102598 | + | 0.0512989i | ||||
\(381\) | 10.0000 | 0.512316 | ||||||||
\(382\) | − | 6.00000i | − | 0.306987i | ||||||
\(383\) | 36.0000i | 1.83951i | 0.392488 | + | 0.919757i | \(0.371614\pi\) | ||||
−0.392488 | + | 0.919757i | \(0.628386\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.0000 | −0.508987 | ||||||||
\(387\) | − | 6.00000i | − | 0.304997i | ||||||
\(388\) | − | 10.0000i | − | 0.507673i | ||||||
\(389\) | 4.00000 | 0.202808 | 0.101404 | − | 0.994845i | \(-0.467667\pi\) | ||||
0.101404 | + | 0.994845i | \(0.467667\pi\) | |||||||
\(390\) | 4.00000 | + | 8.00000i | 0.202548 | + | 0.405096i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 7.00000i | 0.353553i | ||||||||
\(393\) | 20.0000i | 1.00887i | ||||||||
\(394\) | 10.0000 | 0.503793 | ||||||||
\(395\) | 16.0000 | − | 8.00000i | 0.805047 | − | 0.402524i | ||||
\(396\) | −4.00000 | −0.201008 | ||||||||
\(397\) | − | 18.0000i | − | 0.903394i | −0.892171 | − | 0.451697i | \(-0.850819\pi\) | ||
0.892171 | − | 0.451697i | \(-0.149181\pi\) | |||||||
\(398\) | − | 4.00000i | − | 0.200502i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | − | 4.00000i | 0.150000 | − | 0.200000i | ||||
\(401\) | 28.0000 | 1.39825 | 0.699127 | − | 0.714998i | \(-0.253572\pi\) | ||||
0.699127 | + | 0.714998i | \(0.253572\pi\) | |||||||
\(402\) | − | 4.00000i | − | 0.199502i | ||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −12.0000 | −0.597022 | ||||||||
\(405\) | 2.00000 | − | 1.00000i | 0.0993808 | − | 0.0496904i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 16.0000i | − | 0.793091i | ||||||
\(408\) | − | 6.00000i | − | 0.297044i | ||||||
\(409\) | 34.0000 | 1.68119 | 0.840596 | − | 0.541663i | \(-0.182205\pi\) | ||||
0.840596 | + | 0.541663i | \(0.182205\pi\) | |||||||
\(410\) | 12.0000 | + | 24.0000i | 0.592638 | + | 1.18528i | ||||
\(411\) | 6.00000 | 0.295958 | ||||||||
\(412\) | − | 2.00000i | − | 0.0985329i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.0000 | + | 24.0000i | 0.589057 | + | 1.17811i | ||||
\(416\) | −4.00000 | −0.196116 | ||||||||
\(417\) | − | 12.0000i | − | 0.587643i | ||||||
\(418\) | 4.00000i | 0.195646i | ||||||||
\(419\) | −8.00000 | −0.390826 | −0.195413 | − | 0.980721i | \(-0.562605\pi\) | ||||
−0.195413 | + | 0.980721i | \(0.562605\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.0000 | −0.682318 | −0.341159 | − | 0.940006i | \(-0.610819\pi\) | ||||
−0.341159 | + | 0.940006i | \(0.610819\pi\) | |||||||
\(422\) | 8.00000i | 0.389434i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 14.0000 | 0.679900 | ||||||||
\(425\) | −24.0000 | − | 18.0000i | −1.16417 | − | 0.873128i | ||||
\(426\) | −12.0000 | −0.581402 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 20.0000i | 0.966736i | ||||||||
\(429\) | 16.0000 | 0.772487 | ||||||||
\(430\) | 12.0000 | − | 6.00000i | 0.578691 | − | 0.289346i | ||||
\(431\) | −12.0000 | −0.578020 | −0.289010 | − | 0.957326i | \(-0.593326\pi\) | ||||
−0.289010 | + | 0.957326i | \(0.593326\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | − | 18.0000i | − | 0.865025i | −0.901628 | − | 0.432512i | \(-0.857627\pi\) | ||
0.901628 | − | 0.432512i | \(-0.142373\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.00000 | − | 4.00000i | −0.0958927 | − | 0.191785i | ||||
\(436\) | −14.0000 | −0.670478 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | − | 8.00000i | − | 0.382255i | ||||||
\(439\) | −16.0000 | −0.763638 | −0.381819 | − | 0.924237i | \(-0.624702\pi\) | ||||
−0.381819 | + | 0.924237i | \(0.624702\pi\) | |||||||
\(440\) | −4.00000 | − | 8.00000i | −0.190693 | − | 0.381385i | ||||
\(441\) | −7.00000 | −0.333333 | ||||||||
\(442\) | 24.0000i | 1.14156i | ||||||||
\(443\) | − | 12.0000i | − | 0.570137i | −0.958507 | − | 0.285069i | \(-0.907984\pi\) | ||
0.958507 | − | 0.285069i | \(-0.0920164\pi\) | |||||||
\(444\) | −4.00000 | −0.189832 | ||||||||
\(445\) | 16.0000 | − | 8.00000i | 0.758473 | − | 0.379236i | ||||
\(446\) | 10.0000 | 0.473514 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 32.0000 | 1.51017 | 0.755087 | − | 0.655625i | \(-0.227595\pi\) | ||||
0.755087 | + | 0.655625i | \(0.227595\pi\) | |||||||
\(450\) | 4.00000 | + | 3.00000i | 0.188562 | + | 0.141421i | ||||
\(451\) | 48.0000 | 2.26023 | ||||||||
\(452\) | 10.0000i | 0.470360i | ||||||||
\(453\) | − | 16.0000i | − | 0.751746i | ||||||
\(454\) | 12.0000 | 0.563188 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.00000 | 0.0468293 | ||||||||
\(457\) | 32.0000i | 1.49690i | 0.663193 | + | 0.748448i | \(0.269201\pi\) | ||||
−0.663193 | + | 0.748448i | \(0.730799\pi\) | |||||||
\(458\) | − | 10.0000i | − | 0.467269i | ||||||
\(459\) | 6.00000 | 0.280056 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.0000 | 1.11779 | 0.558896 | − | 0.829238i | \(-0.311225\pi\) | ||||
0.558896 | + | 0.829238i | \(0.311225\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.0000i | 0.743583i | 0.928316 | + | 0.371792i | \(0.121256\pi\) | ||||
−0.928316 | + | 0.371792i | \(0.878744\pi\) | |||||||
\(464\) | 2.00000 | 0.0928477 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.0000 | 0.648537 | ||||||||
\(467\) | 24.0000i | 1.11059i | 0.831654 | + | 0.555294i | \(0.187394\pi\) | ||||
−0.831654 | + | 0.555294i | \(0.812606\pi\) | |||||||
\(468\) | − | 4.00000i | − | 0.184900i | ||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.00000 | −0.276465 | ||||||||
\(472\) | 10.0000i | 0.460287i | ||||||||
\(473\) | − | 24.0000i | − | 1.10352i | ||||||
\(474\) | −8.00000 | −0.367452 | ||||||||
\(475\) | 3.00000 | − | 4.00000i | 0.137649 | − | 0.183533i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.0000i | 0.641016i | ||||||||
\(478\) | 10.0000i | 0.457389i | ||||||||
\(479\) | −38.0000 | −1.73626 | −0.868132 | − | 0.496333i | \(-0.834679\pi\) | ||||
−0.868132 | + | 0.496333i | \(0.834679\pi\) | |||||||
\(480\) | −2.00000 | + | 1.00000i | −0.0912871 | + | 0.0456435i | ||||
\(481\) | 16.0000 | 0.729537 | ||||||||
\(482\) | − | 26.0000i | − | 1.18427i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.00000 | −0.227273 | ||||||||
\(485\) | 10.0000 | + | 20.0000i | 0.454077 | + | 0.908153i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 18.0000i | 0.815658i | 0.913058 | + | 0.407829i | \(0.133714\pi\) | ||||
−0.913058 | + | 0.407829i | \(0.866286\pi\) | |||||||
\(488\) | − | 6.00000i | − | 0.271607i | ||||||
\(489\) | −10.0000 | −0.452216 | ||||||||
\(490\) | −7.00000 | − | 14.0000i | −0.316228 | − | 0.632456i | ||||
\(491\) | 36.0000 | 1.62466 | 0.812329 | − | 0.583200i | \(-0.198200\pi\) | ||||
0.812329 | + | 0.583200i | \(0.198200\pi\) | |||||||
\(492\) | − | 12.0000i | − | 0.541002i | ||||||
\(493\) | − | 12.0000i | − | 0.540453i | ||||||
\(494\) | −4.00000 | −0.179969 | ||||||||
\(495\) | 8.00000 | − | 4.00000i | 0.359573 | − | 0.179787i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | − | 12.0000i | − | 0.537733i | ||||||
\(499\) | 4.00000 | 0.179065 | 0.0895323 | − | 0.995984i | \(-0.471463\pi\) | ||||
0.0895323 | + | 0.995984i | \(0.471463\pi\) | |||||||
\(500\) | −2.00000 | + | 11.0000i | −0.0894427 | + | 0.491935i | ||||
\(501\) | −12.0000 | −0.536120 | ||||||||
\(502\) | 24.0000i | 1.07117i | ||||||||
\(503\) | 16.0000i | 0.713405i | 0.934218 | + | 0.356702i | \(0.116099\pi\) | ||||
−0.934218 | + | 0.356702i | \(0.883901\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.0000 | − | 12.0000i | 1.06799 | − | 0.533993i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.00000i | 0.133235i | ||||||||
\(508\) | − | 10.0000i | − | 0.443678i | ||||||
\(509\) | −18.0000 | −0.797836 | −0.398918 | − | 0.916987i | \(-0.630614\pi\) | ||||
−0.398918 | + | 0.916987i | \(0.630614\pi\) | |||||||
\(510\) | 6.00000 | + | 12.0000i | 0.265684 | + | 0.531369i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 1.00000i | 0.0441511i | ||||||||
\(514\) | 2.00000 | 0.0882162 | ||||||||
\(515\) | 2.00000 | + | 4.00000i | 0.0881305 | + | 0.176261i | ||||
\(516\) | −6.00000 | −0.264135 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.00000 | −0.0877903 | ||||||||
\(520\) | 8.00000 | − | 4.00000i | 0.350823 | − | 0.175412i | ||||
\(521\) | −12.0000 | −0.525730 | −0.262865 | − | 0.964833i | \(-0.584667\pi\) | ||||
−0.262865 | + | 0.964833i | \(0.584667\pi\) | |||||||
\(522\) | 2.00000i | 0.0875376i | ||||||||
\(523\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(524\) | 20.0000 | 0.873704 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.0000 | 0.697633 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 4.00000i | 0.174078i | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | −28.0000 | + | 14.0000i | −1.21624 | + | 0.608121i | ||||
\(531\) | −10.0000 | −0.433963 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 48.0000i | 2.07911i | ||||||||
\(534\) | −8.00000 | −0.346194 | ||||||||
\(535\) | −20.0000 | − | 40.0000i | −0.864675 | − | 1.72935i | ||||
\(536\) | −4.00000 | −0.172774 | ||||||||
\(537\) | 6.00000i | 0.258919i | ||||||||
\(538\) | − | 2.00000i | − | 0.0862261i | ||||||
\(539\) | −28.0000 | −1.20605 | ||||||||
\(540\) | −1.00000 | − | 2.00000i | −0.0430331 | − | 0.0860663i | ||||
\(541\) | 2.00000 | 0.0859867 | 0.0429934 | − | 0.999075i | \(-0.486311\pi\) | ||||
0.0429934 | + | 0.999075i | \(0.486311\pi\) | |||||||
\(542\) | 28.0000i | 1.20270i | ||||||||
\(543\) | 10.0000i | 0.429141i | ||||||||
\(544\) | −6.00000 | −0.257248 | ||||||||
\(545\) | 28.0000 | − | 14.0000i | 1.19939 | − | 0.599694i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 24.0000i | − | 1.02617i | −0.858339 | − | 0.513083i | \(-0.828503\pi\) | ||
0.858339 | − | 0.513083i | \(-0.171497\pi\) | |||||||
\(548\) | − | 6.00000i | − | 0.256307i | ||||||
\(549\) | 6.00000 | 0.256074 | ||||||||
\(550\) | 16.0000 | + | 12.0000i | 0.682242 | + | 0.511682i | ||||
\(551\) | 2.00000 | 0.0852029 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 14.0000 | 0.594803 | ||||||||
\(555\) | 8.00000 | − | 4.00000i | 0.339581 | − | 0.169791i | ||||
\(556\) | −12.0000 | −0.508913 | ||||||||
\(557\) | 30.0000i | 1.27114i | 0.772043 | + | 0.635570i | \(0.219235\pi\) | ||||
−0.772043 | + | 0.635570i | \(0.780765\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.0000 | 1.01509 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.0000 | 1.01328 | ||||||||
\(562\) | − | 12.0000i | − | 0.506189i | ||||||
\(563\) | − | 36.0000i | − | 1.51722i | −0.651546 | − | 0.758610i | \(-0.725879\pi\) | ||
0.651546 | − | 0.758610i | \(-0.274121\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.0000 | − | 20.0000i | −0.420703 | − | 0.841406i | ||||
\(566\) | −2.00000 | −0.0840663 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.0000i | 0.503509i | ||||||||
\(569\) | −32.0000 | −1.34151 | −0.670755 | − | 0.741679i | \(-0.734030\pi\) | ||||
−0.670755 | + | 0.741679i | \(0.734030\pi\) | |||||||
\(570\) | −2.00000 | + | 1.00000i | −0.0837708 | + | 0.0418854i | ||||
\(571\) | 4.00000 | 0.167395 | 0.0836974 | − | 0.996491i | \(-0.473327\pi\) | ||||
0.0836974 | + | 0.996491i | \(0.473327\pi\) | |||||||
\(572\) | − | 16.0000i | − | 0.668994i | ||||||
\(573\) | − | 6.00000i | − | 0.250654i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 8.00000i | 0.333044i | 0.986038 | + | 0.166522i | \(0.0532537\pi\) | ||||
−0.986038 | + | 0.166522i | \(0.946746\pi\) | |||||||
\(578\) | 19.0000i | 0.790296i | ||||||||
\(579\) | −10.0000 | −0.415586 | ||||||||
\(580\) | −4.00000 | + | 2.00000i | −0.166091 | + | 0.0830455i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − | 10.0000i | − | 0.414513i | ||||||
\(583\) | 56.0000i | 2.31928i | ||||||||
\(584\) | −8.00000 | −0.331042 | ||||||||
\(585\) | 4.00000 | + | 8.00000i | 0.165380 | + | 0.330759i | ||||
\(586\) | 14.0000 | 0.578335 | ||||||||
\(587\) | − | 32.0000i | − | 1.32078i | −0.750922 | − | 0.660391i | \(-0.770391\pi\) | ||
0.750922 | − | 0.660391i | \(-0.229609\pi\) | |||||||
\(588\) | 7.00000i | 0.288675i | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −10.0000 | − | 20.0000i | −0.411693 | − | 0.823387i | ||||
\(591\) | 10.0000 | 0.411345 | ||||||||
\(592\) | 4.00000i | 0.164399i | ||||||||
\(593\) | − | 22.0000i | − | 0.903432i | −0.892162 | − | 0.451716i | \(-0.850812\pi\) | ||
0.892162 | − | 0.451716i | \(-0.149188\pi\) | |||||||
\(594\) | −4.00000 | −0.164122 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 4.00000i | − | 0.163709i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.0000 | 0.490307 | 0.245153 | − | 0.969484i | \(-0.421162\pi\) | ||||
0.245153 | + | 0.969484i | \(0.421162\pi\) | |||||||
\(600\) | 3.00000 | − | 4.00000i | 0.122474 | − | 0.163299i | ||||
\(601\) | −42.0000 | −1.71322 | −0.856608 | − | 0.515968i | \(-0.827432\pi\) | ||||
−0.856608 | + | 0.515968i | \(0.827432\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 4.00000i | − | 0.162893i | ||||||
\(604\) | −16.0000 | −0.651031 | ||||||||
\(605\) | 10.0000 | − | 5.00000i | 0.406558 | − | 0.203279i | ||||
\(606\) | −12.0000 | −0.487467 | ||||||||
\(607\) | − | 30.0000i | − | 1.21766i | −0.793300 | − | 0.608831i | \(-0.791639\pi\) | ||
0.793300 | − | 0.608831i | \(-0.208361\pi\) | |||||||
\(608\) | − | 1.00000i | − | 0.0405554i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.00000 | + | 12.0000i | 0.242933 | + | 0.485866i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | − | 6.00000i | − | 0.242536i | ||||||
\(613\) | − | 46.0000i | − | 1.85792i | −0.370177 | − | 0.928961i | \(-0.620703\pi\) | ||
0.370177 | − | 0.928961i | \(-0.379297\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.0000 | + | 24.0000i | 0.483887 | + | 0.967773i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 6.00000i | − | 0.241551i | −0.992680 | − | 0.120775i | \(-0.961462\pi\) | ||
0.992680 | − | 0.120775i | \(-0.0385381\pi\) | |||||||
\(618\) | − | 2.00000i | − | 0.0804518i | ||||||
\(619\) | 28.0000 | 1.12542 | 0.562708 | − | 0.826656i | \(-0.309760\pi\) | ||||
0.562708 | + | 0.826656i | \(0.309760\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 18.0000i | 0.721734i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −4.00000 | −0.160128 | ||||||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | 4.00000 | 0.159872 | ||||||||
\(627\) | 4.00000i | 0.159745i | ||||||||
\(628\) | 6.00000i | 0.239426i | ||||||||
\(629\) | 24.0000 | 0.956943 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.0000 | 1.11466 | 0.557331 | − | 0.830290i | \(-0.311825\pi\) | ||||
0.557331 | + | 0.830290i | \(0.311825\pi\) | |||||||
\(632\) | 8.00000i | 0.318223i | ||||||||
\(633\) | 8.00000i | 0.317971i | ||||||||
\(634\) | −18.0000 | −0.714871 | ||||||||
\(635\) | 10.0000 | + | 20.0000i | 0.396838 | + | 0.793676i | ||||
\(636\) | 14.0000 | 0.555136 | ||||||||
\(637\) | − | 28.0000i | − | 1.10940i | ||||||
\(638\) | 8.00000i | 0.316723i | ||||||||
\(639\) | −12.0000 | −0.474713 | ||||||||
\(640\) | 1.00000 | + | 2.00000i | 0.0395285 | + | 0.0790569i | ||||
\(641\) | 36.0000 | 1.42191 | 0.710957 | − | 0.703235i | \(-0.248262\pi\) | ||||
0.710957 | + | 0.703235i | \(0.248262\pi\) | |||||||
\(642\) | 20.0000i | 0.789337i | ||||||||
\(643\) | − | 26.0000i | − | 1.02534i | −0.858586 | − | 0.512670i | \(-0.828656\pi\) | ||
0.858586 | − | 0.512670i | \(-0.171344\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.0000 | − | 6.00000i | 0.472500 | − | 0.236250i | ||||
\(646\) | −6.00000 | −0.236067 | ||||||||
\(647\) | 24.0000i | 0.943537i | 0.881722 | + | 0.471769i | \(0.156384\pi\) | ||||
−0.881722 | + | 0.471769i | \(0.843616\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | −40.0000 | −1.57014 | ||||||||
\(650\) | −12.0000 | + | 16.0000i | −0.470679 | + | 0.627572i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.0000i | 0.391630i | ||||||||
\(653\) | 18.0000i | 0.704394i | 0.935926 | + | 0.352197i | \(0.114565\pi\) | ||||
−0.935926 | + | 0.352197i | \(0.885435\pi\) | |||||||
\(654\) | −14.0000 | −0.547443 | ||||||||
\(655\) | −40.0000 | + | 20.0000i | −1.56293 | + | 0.781465i | ||||
\(656\) | −12.0000 | −0.468521 | ||||||||
\(657\) | − | 8.00000i | − | 0.312110i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.0000 | 1.01282 | 0.506408 | − | 0.862294i | \(-0.330973\pi\) | ||||
0.506408 | + | 0.862294i | \(0.330973\pi\) | |||||||
\(660\) | −4.00000 | − | 8.00000i | −0.155700 | − | 0.311400i | ||||
\(661\) | −2.00000 | −0.0777910 | −0.0388955 | − | 0.999243i | \(-0.512384\pi\) | ||||
−0.0388955 | + | 0.999243i | \(0.512384\pi\) | |||||||
\(662\) | − | 8.00000i | − | 0.310929i | ||||||
\(663\) | 24.0000i | 0.932083i | ||||||||
\(664\) | −12.0000 | −0.465690 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.00000 | −0.154997 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 12.0000i | 0.464294i | ||||||||
\(669\) | 10.0000 | 0.386622 | ||||||||
\(670\) | 8.00000 | − | 4.00000i | 0.309067 | − | 0.154533i | ||||
\(671\) | 24.0000 | 0.926510 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.0000i | 1.00223i | 0.865382 | + | 0.501113i | \(0.167076\pi\) | ||||
−0.865382 | + | 0.501113i | \(0.832924\pi\) | |||||||
\(674\) | −18.0000 | −0.693334 | ||||||||
\(675\) | 4.00000 | + | 3.00000i | 0.153960 | + | 0.115470i | ||||
\(676\) | 3.00000 | 0.115385 | ||||||||
\(677\) | 30.0000i | 1.15299i | 0.817099 | + | 0.576497i | \(0.195581\pi\) | ||||
−0.817099 | + | 0.576497i | \(0.804419\pi\) | |||||||
\(678\) | 10.0000i | 0.384048i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 12.0000 | − | 6.00000i | 0.460179 | − | 0.230089i | ||||
\(681\) | 12.0000 | 0.459841 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 12.0000i | − | 0.459167i | −0.973289 | − | 0.229584i | \(-0.926264\pi\) | ||
0.973289 | − | 0.229584i | \(-0.0737364\pi\) | |||||||
\(684\) | 1.00000 | 0.0382360 | ||||||||
\(685\) | 6.00000 | + | 12.0000i | 0.229248 | + | 0.458496i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 10.0000i | − | 0.381524i | ||||||
\(688\) | 6.00000i | 0.228748i | ||||||||
\(689\) | −56.0000 | −2.13343 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.00000 | −0.152167 | −0.0760836 | − | 0.997101i | \(-0.524242\pi\) | ||||
−0.0760836 | + | 0.997101i | \(0.524242\pi\) | |||||||
\(692\) | 2.00000i | 0.0760286i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −32.0000 | −1.21470 | ||||||||
\(695\) | 24.0000 | − | 12.0000i | 0.910372 | − | 0.455186i | ||||
\(696\) | 2.00000 | 0.0758098 | ||||||||
\(697\) | 72.0000i | 2.72719i | ||||||||
\(698\) | 34.0000i | 1.28692i | ||||||||
\(699\) | 14.0000 | 0.529529 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.0000 | 0.755390 | 0.377695 | − | 0.925930i | \(-0.376717\pi\) | ||||
0.377695 | + | 0.925930i | \(0.376717\pi\) | |||||||
\(702\) | − | 4.00000i | − | 0.150970i | ||||||
\(703\) | 4.00000i | 0.150863i | ||||||||
\(704\) | 4.00000 | 0.150756 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 22.0000 | 0.827981 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 10.0000i | 0.375823i | ||||||||
\(709\) | −22.0000 | −0.826227 | −0.413114 | − | 0.910679i | \(-0.635559\pi\) | ||||
−0.413114 | + | 0.910679i | \(0.635559\pi\) | |||||||
\(710\) | −12.0000 | − | 24.0000i | −0.450352 | − | 0.900704i | ||||
\(711\) | −8.00000 | −0.300023 | ||||||||
\(712\) | 8.00000i | 0.299813i | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.0000 | + | 32.0000i | 0.598366 | + | 1.19673i | ||||
\(716\) | 6.00000 | 0.224231 | ||||||||
\(717\) | 10.0000i | 0.373457i | ||||||||
\(718\) | 34.0000i | 1.26887i | ||||||||
\(719\) | −6.00000 | −0.223762 | −0.111881 | − | 0.993722i | \(-0.535688\pi\) | ||||
−0.111881 | + | 0.993722i | \(0.535688\pi\) | |||||||
\(720\) | −2.00000 | + | 1.00000i | −0.0745356 | + | 0.0372678i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 1.00000i | − | 0.0372161i | ||||||
\(723\) | − | 26.0000i | − | 0.966950i | ||||||
\(724\) | 10.0000 | 0.371647 | ||||||||
\(725\) | 6.00000 | − | 8.00000i | 0.222834 | − | 0.297113i | ||||
\(726\) | −5.00000 | −0.185567 | ||||||||
\(727\) | 40.0000i | 1.48352i | 0.670667 | + | 0.741759i | \(0.266008\pi\) | ||||
−0.670667 | + | 0.741759i | \(0.733992\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 16.0000 | − | 8.00000i | 0.592187 | − | 0.296093i | ||||
\(731\) | 36.0000 | 1.33151 | ||||||||
\(732\) | − | 6.00000i | − | 0.221766i | ||||||
\(733\) | − | 26.0000i | − | 0.960332i | −0.877178 | − | 0.480166i | \(-0.840576\pi\) | ||
0.877178 | − | 0.480166i | \(-0.159424\pi\) | |||||||
\(734\) | 12.0000 | 0.442928 | ||||||||
\(735\) | −7.00000 | − | 14.0000i | −0.258199 | − | 0.516398i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 16.0000i | − | 0.589368i | ||||||
\(738\) | − | 12.0000i | − | 0.441726i | ||||||
\(739\) | −20.0000 | −0.735712 | −0.367856 | − | 0.929883i | \(-0.619908\pi\) | ||||
−0.367856 | + | 0.929883i | \(0.619908\pi\) | |||||||
\(740\) | −4.00000 | − | 8.00000i | −0.147043 | − | 0.294086i | ||||
\(741\) | −4.00000 | −0.146944 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 44.0000i | − | 1.61420i | −0.590412 | − | 0.807102i | \(-0.701035\pi\) | ||
0.590412 | − | 0.807102i | \(-0.298965\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 12.0000 | 0.439351 | ||||||||
\(747\) | − | 12.0000i | − | 0.439057i | ||||||
\(748\) | − | 24.0000i | − | 0.877527i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −2.00000 | + | 11.0000i | −0.0730297 | + | 0.401663i | ||||
\(751\) | −8.00000 | −0.291924 | −0.145962 | − | 0.989290i | \(-0.546628\pi\) | ||||
−0.145962 | + | 0.989290i | \(0.546628\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.0000i | 0.874609i | ||||||||
\(754\) | −8.00000 | −0.291343 | ||||||||
\(755\) | 32.0000 | − | 16.0000i | 1.16460 | − | 0.582300i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.00000i | 0.0726912i | 0.999339 | + | 0.0363456i | \(0.0115717\pi\) | ||||
−0.999339 | + | 0.0363456i | \(0.988428\pi\) | |||||||
\(758\) | 12.0000i | 0.435860i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.00000 | + | 2.00000i | 0.0362738 | + | 0.0725476i | ||||
\(761\) | −30.0000 | −1.08750 | −0.543750 | − | 0.839248i | \(-0.682996\pi\) | ||||
−0.543750 | + | 0.839248i | \(0.682996\pi\) | |||||||
\(762\) | − | 10.0000i | − | 0.362262i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −6.00000 | −0.217072 | ||||||||
\(765\) | 6.00000 | + | 12.0000i | 0.216930 | + | 0.433861i | ||||
\(766\) | 36.0000 | 1.30073 | ||||||||
\(767\) | − | 40.0000i | − | 1.44432i | ||||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | −50.0000 | −1.80305 | −0.901523 | − | 0.432731i | \(-0.857550\pi\) | ||||
−0.901523 | + | 0.432731i | \(0.857550\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.00000 | 0.0720282 | ||||||||
\(772\) | 10.0000i | 0.359908i | ||||||||
\(773\) | − | 38.0000i | − | 1.36677i | −0.730061 | − | 0.683383i | \(-0.760508\pi\) | ||
0.730061 | − | 0.683383i | \(-0.239492\pi\) | |||||||
\(774\) | −6.00000 | −0.215666 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −10.0000 | −0.358979 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 4.00000i | − | 0.143407i | ||||||
\(779\) | −12.0000 | −0.429945 | ||||||||
\(780\) | 8.00000 | − | 4.00000i | 0.286446 | − | 0.143223i | ||||
\(781\) | −48.0000 | −1.71758 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.00000i | 0.0714742i | ||||||||
\(784\) | 7.00000 | 0.250000 | ||||||||
\(785\) | −6.00000 | − | 12.0000i | −0.214149 | − | 0.428298i | ||||
\(786\) | 20.0000 | 0.713376 | ||||||||
\(787\) | − | 48.0000i | − | 1.71102i | −0.517790 | − | 0.855508i | \(-0.673245\pi\) | ||
0.517790 | − | 0.855508i | \(-0.326755\pi\) | |||||||
\(788\) | − | 10.0000i | − | 0.356235i | ||||||
\(789\) | 16.0000 | 0.569615 | ||||||||
\(790\) | −8.00000 | − | 16.0000i | −0.284627 | − | 0.569254i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 4.00000i | 0.142134i | ||||||||
\(793\) | 24.0000i | 0.852265i | ||||||||
\(794\) | −18.0000 | −0.638796 | ||||||||
\(795\) | −28.0000 | + | 14.0000i | −0.993058 | + | 0.496529i | ||||
\(796\) | −4.00000 | −0.141776 | ||||||||
\(797\) | 42.0000i | 1.48772i | 0.668338 | + | 0.743858i | \(0.267006\pi\) | ||||
−0.668338 | + | 0.743858i | \(0.732994\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −4.00000 | − | 3.00000i | −0.141421 | − | 0.106066i | ||||
\(801\) | −8.00000 | −0.282666 | ||||||||
\(802\) | − | 28.0000i | − | 0.988714i | ||||||
\(803\) | − | 32.0000i | − | 1.12926i | ||||||
\(804\) | −4.00000 | −0.141069 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 2.00000i | − | 0.0704033i | ||||||
\(808\) | 12.0000i | 0.422159i | ||||||||
\(809\) | −26.0000 | −0.914111 | −0.457056 | − | 0.889438i | \(-0.651096\pi\) | ||||
−0.457056 | + | 0.889438i | \(0.651096\pi\) | |||||||
\(810\) | −1.00000 | − | 2.00000i | −0.0351364 | − | 0.0702728i | ||||
\(811\) | −40.0000 | −1.40459 | −0.702295 | − | 0.711886i | \(-0.747841\pi\) | ||||
−0.702295 | + | 0.711886i | \(0.747841\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 28.0000i | 0.982003i | ||||||||
\(814\) | −16.0000 | −0.560800 | ||||||||
\(815\) | −10.0000 | − | 20.0000i | −0.350285 | − | 0.700569i | ||||
\(816\) | −6.00000 | −0.210042 | ||||||||
\(817\) | 6.00000i | 0.209913i | ||||||||
\(818\) | − | 34.0000i | − | 1.18878i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 24.0000 | − | 12.0000i | 0.838116 | − | 0.419058i | ||||
\(821\) | −4.00000 | −0.139601 | −0.0698005 | − | 0.997561i | \(-0.522236\pi\) | ||||
−0.0698005 | + | 0.997561i | \(0.522236\pi\) | |||||||
\(822\) | − | 6.00000i | − | 0.209274i | ||||||
\(823\) | − | 24.0000i | − | 0.836587i | −0.908312 | − | 0.418294i | \(-0.862628\pi\) | ||
0.908312 | − | 0.418294i | \(-0.137372\pi\) | |||||||
\(824\) | −2.00000 | −0.0696733 | ||||||||
\(825\) | 16.0000 | + | 12.0000i | 0.557048 | + | 0.417786i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 12.0000i | − | 0.417281i | −0.977992 | − | 0.208640i | \(-0.933096\pi\) | ||
0.977992 | − | 0.208640i | \(-0.0669038\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −50.0000 | −1.73657 | −0.868286 | − | 0.496064i | \(-0.834778\pi\) | ||||
−0.868286 | + | 0.496064i | \(0.834778\pi\) | |||||||
\(830\) | 24.0000 | − | 12.0000i | 0.833052 | − | 0.416526i | ||||
\(831\) | 14.0000 | 0.485655 | ||||||||
\(832\) | 4.00000i | 0.138675i | ||||||||
\(833\) | − | 42.0000i | − | 1.45521i | ||||||
\(834\) | −12.0000 | −0.415526 | ||||||||
\(835\) | −12.0000 | − | 24.0000i | −0.415277 | − | 0.830554i | ||||
\(836\) | 4.00000 | 0.138343 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.00000i | 0.276355i | ||||||||
\(839\) | −8.00000 | −0.276191 | −0.138095 | − | 0.990419i | \(-0.544098\pi\) | ||||
−0.138095 | + | 0.990419i | \(0.544098\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 14.0000i | 0.482472i | ||||||||
\(843\) | − | 12.0000i | − | 0.413302i | ||||||
\(844\) | 8.00000 | 0.275371 | ||||||||
\(845\) | −6.00000 | + | 3.00000i | −0.206406 | + | 0.103203i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 14.0000i | − | 0.480762i | ||||||
\(849\) | −2.00000 | −0.0686398 | ||||||||
\(850\) | −18.0000 | + | 24.0000i | −0.617395 | + | 0.823193i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 12.0000i | 0.411113i | ||||||||
\(853\) | − | 50.0000i | − | 1.71197i | −0.517003 | − | 0.855984i | \(-0.672952\pi\) | ||
0.517003 | − | 0.855984i | \(-0.327048\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.00000 | + | 1.00000i | −0.0683986 | + | 0.0341993i | ||||
\(856\) | 20.0000 | 0.683586 | ||||||||
\(857\) | 42.0000i | 1.43469i | 0.696717 | + | 0.717346i | \(0.254643\pi\) | ||||
−0.696717 | + | 0.717346i | \(0.745357\pi\) | |||||||
\(858\) | − | 16.0000i | − | 0.546231i | ||||||
\(859\) | 28.0000 | 0.955348 | 0.477674 | − | 0.878537i | \(-0.341480\pi\) | ||||
0.477674 | + | 0.878537i | \(0.341480\pi\) | |||||||
\(860\) | −6.00000 | − | 12.0000i | −0.204598 | − | 0.409197i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.0000i | 0.408722i | ||||||||
\(863\) | − | 24.0000i | − | 0.816970i | −0.912765 | − | 0.408485i | \(-0.866057\pi\) | ||
0.912765 | − | 0.408485i | \(-0.133943\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −2.00000 | − | 4.00000i | −0.0680020 | − | 0.136004i | ||||
\(866\) | −18.0000 | −0.611665 | ||||||||
\(867\) | 19.0000i | 0.645274i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −32.0000 | −1.08553 | ||||||||
\(870\) | −4.00000 | + | 2.00000i | −0.135613 | + | 0.0678064i | ||||
\(871\) | 16.0000 | 0.542139 | ||||||||
\(872\) | 14.0000i | 0.474100i | ||||||||
\(873\) | − | 10.0000i | − | 0.338449i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.00000 | −0.270295 | ||||||||
\(877\) | 28.0000i | 0.945493i | 0.881199 | + | 0.472746i | \(0.156737\pi\) | ||||
−0.881199 | + | 0.472746i | \(0.843263\pi\) | |||||||
\(878\) | 16.0000i | 0.539974i | ||||||||
\(879\) | 14.0000 | 0.472208 | ||||||||
\(880\) | −8.00000 | + | 4.00000i | −0.269680 | + | 0.134840i | ||||
\(881\) | 42.0000 | 1.41502 | 0.707508 | − | 0.706705i | \(-0.249819\pi\) | ||||
0.707508 | + | 0.706705i | \(0.249819\pi\) | |||||||
\(882\) | 7.00000i | 0.235702i | ||||||||
\(883\) | − | 2.00000i | − | 0.0673054i | −0.999434 | − | 0.0336527i | \(-0.989286\pi\) | ||
0.999434 | − | 0.0336527i | \(-0.0107140\pi\) | |||||||
\(884\) | 24.0000 | 0.807207 | ||||||||
\(885\) | −10.0000 | − | 20.0000i | −0.336146 | − | 0.672293i | ||||
\(886\) | −12.0000 | −0.403148 | ||||||||
\(887\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(888\) | 4.00000i | 0.134231i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −8.00000 | − | 16.0000i | −0.268161 | − | 0.536321i | ||||
\(891\) | −4.00000 | −0.134005 | ||||||||
\(892\) | − | 10.0000i | − | 0.334825i | ||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.0000 | + | 6.00000i | −0.401116 | + | 0.200558i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 32.0000i | − | 1.06785i | ||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 3.00000 | − | 4.00000i | 0.100000 | − | 0.133333i | ||||
\(901\) | −84.0000 | −2.79845 | ||||||||
\(902\) | − | 48.0000i | − | 1.59823i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.0000 | 0.332595 | ||||||||
\(905\) | −20.0000 | + | 10.0000i | −0.664822 | + | 0.332411i | ||||
\(906\) | −16.0000 | −0.531564 | ||||||||
\(907\) | − | 12.0000i | − | 0.398453i | −0.979953 | − | 0.199227i | \(-0.936157\pi\) | ||
0.979953 | − | 0.199227i | \(-0.0638430\pi\) | |||||||
\(908\) | − | 12.0000i | − | 0.398234i | ||||||
\(909\) | −12.0000 | −0.398015 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.0000 | −1.59031 | −0.795155 | − | 0.606406i | \(-0.792611\pi\) | ||||
−0.795155 | + | 0.606406i | \(0.792611\pi\) | |||||||
\(912\) | − | 1.00000i | − | 0.0331133i | ||||||
\(913\) | − | 48.0000i | − | 1.58857i | ||||||
\(914\) | 32.0000 | 1.05847 | ||||||||
\(915\) | 6.00000 | + | 12.0000i | 0.198354 | + | 0.396708i | ||||
\(916\) | −10.0000 | −0.330409 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 6.00000i | − | 0.198030i | ||||||
\(919\) | −4.00000 | −0.131948 | −0.0659739 | − | 0.997821i | \(-0.521015\pi\) | ||||
−0.0659739 | + | 0.997821i | \(0.521015\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 24.0000i | − | 0.790398i | ||||||
\(923\) | − | 48.0000i | − | 1.57994i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.0000 | + | 12.0000i | 0.526077 | + | 0.394558i | ||||
\(926\) | 16.0000 | 0.525793 | ||||||||
\(927\) | − | 2.00000i | − | 0.0656886i | ||||||
\(928\) | − | 2.00000i | − | 0.0656532i | ||||||
\(929\) | 42.0000 | 1.37798 | 0.688988 | − | 0.724773i | \(-0.258055\pi\) | ||||
0.688988 | + | 0.724773i | \(0.258055\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.00000 | 0.229416 | ||||||||
\(932\) | − | 14.0000i | − | 0.458585i | ||||||
\(933\) | 18.0000i | 0.589294i | ||||||||
\(934\) | 24.0000 | 0.785304 | ||||||||
\(935\) | 24.0000 | + | 48.0000i | 0.784884 | + | 1.56977i | ||||
\(936\) | −4.00000 | −0.130744 | ||||||||
\(937\) | 20.0000i | 0.653372i | 0.945133 | + | 0.326686i | \(0.105932\pi\) | ||||
−0.945133 | + | 0.326686i | \(0.894068\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.00000 | 0.130535 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 58.0000 | 1.89075 | 0.945373 | − | 0.325991i | \(-0.105698\pi\) | ||||
0.945373 | + | 0.325991i | \(0.105698\pi\) | |||||||
\(942\) | 6.00000i | 0.195491i | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 10.0000 | 0.325472 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −24.0000 | −0.780307 | ||||||||
\(947\) | − | 40.0000i | − | 1.29983i | −0.760009 | − | 0.649913i | \(-0.774805\pi\) | ||
0.760009 | − | 0.649913i | \(-0.225195\pi\) | |||||||
\(948\) | 8.00000i | 0.259828i | ||||||||
\(949\) | 32.0000 | 1.03876 | ||||||||
\(950\) | −4.00000 | − | 3.00000i | −0.129777 | − | 0.0973329i | ||||
\(951\) | −18.0000 | −0.583690 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42.0000i | 1.36051i | 0.732974 | + | 0.680257i | \(0.238132\pi\) | ||||
−0.732974 | + | 0.680257i | \(0.761868\pi\) | |||||||
\(954\) | 14.0000 | 0.453267 | ||||||||
\(955\) | 12.0000 | − | 6.00000i | 0.388311 | − | 0.194155i | ||||
\(956\) | 10.0000 | 0.323423 | ||||||||
\(957\) | 8.00000i | 0.258603i | ||||||||
\(958\) | 38.0000i | 1.22772i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.00000 | + | 2.00000i | 0.0322749 | + | 0.0645497i | ||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | − | 16.0000i | − | 0.515861i | ||||||
\(963\) | 20.0000i | 0.644491i | ||||||||
\(964\) | −26.0000 | −0.837404 | ||||||||
\(965\) | −10.0000 | − | 20.0000i | −0.321911 | − | 0.643823i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.0000i | 1.41494i | 0.706741 | + | 0.707472i | \(0.250165\pi\) | ||||
−0.706741 | + | 0.707472i | \(0.749835\pi\) | |||||||
\(968\) | 5.00000i | 0.160706i | ||||||||
\(969\) | −6.00000 | −0.192748 | ||||||||
\(970\) | 20.0000 | − | 10.0000i | 0.642161 | − | 0.321081i | ||||
\(971\) | 38.0000 | 1.21948 | 0.609739 | − | 0.792602i | \(-0.291274\pi\) | ||||
0.609739 | + | 0.792602i | \(0.291274\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 18.0000 | 0.576757 | ||||||||
\(975\) | −12.0000 | + | 16.0000i | −0.384308 | + | 0.512410i | ||||
\(976\) | −6.00000 | −0.192055 | ||||||||
\(977\) | − | 34.0000i | − | 1.08776i | −0.839164 | − | 0.543878i | \(-0.816955\pi\) | ||
0.839164 | − | 0.543878i | \(-0.183045\pi\) | |||||||
\(978\) | 10.0000i | 0.319765i | ||||||||
\(979\) | −32.0000 | −1.02272 | ||||||||
\(980\) | −14.0000 | + | 7.00000i | −0.447214 | + | 0.223607i | ||||
\(981\) | −14.0000 | −0.446986 | ||||||||
\(982\) | − | 36.0000i | − | 1.14881i | ||||||
\(983\) | 56.0000i | 1.78612i | 0.449935 | + | 0.893061i | \(0.351447\pi\) | ||||
−0.449935 | + | 0.893061i | \(0.648553\pi\) | |||||||
\(984\) | −12.0000 | −0.382546 | ||||||||
\(985\) | 10.0000 | + | 20.0000i | 0.318626 | + | 0.637253i | ||||
\(986\) | −12.0000 | −0.382158 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.00000i | 0.127257i | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −4.00000 | − | 8.00000i | −0.127128 | − | 0.254257i | ||||
\(991\) | 48.0000 | 1.52477 | 0.762385 | − | 0.647124i | \(-0.224028\pi\) | ||||
0.762385 | + | 0.647124i | \(0.224028\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 8.00000i | − | 0.253872i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.00000 | − | 4.00000i | 0.253617 | − | 0.126809i | ||||
\(996\) | −12.0000 | −0.380235 | ||||||||
\(997\) | 2.00000i | 0.0633406i | 0.999498 | + | 0.0316703i | \(0.0100827\pi\) | ||||
−0.999498 | + | 0.0316703i | \(0.989917\pi\) | |||||||
\(998\) | − | 4.00000i | − | 0.126618i | ||||||
\(999\) | −4.00000 | −0.126554 |
(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 | 570.2.d.b.229.1 | ✓ | 2 | |
3.2 | odd | 2 | 1710.2.d.a.1369.2 | 2 | |||
5.2 | odd | 4 | 2850.2.a.s.1.1 | 1 | |||
5.3 | odd | 4 | 2850.2.a.k.1.1 | 1 | |||
5.4 | even | 2 | inner | 570.2.d.b.229.2 | yes | 2 | |
15.2 | even | 4 | 8550.2.a.j.1.1 | 1 | |||
15.8 | even | 4 | 8550.2.a.bc.1.1 | 1 | |||
15.14 | odd | 2 | 1710.2.d.a.1369.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.d.b.229.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
570.2.d.b.229.2 | yes | 2 | 5.4 | even | 2 | inner | |
1710.2.d.a.1369.1 | 2 | 15.14 | odd | 2 | |||
1710.2.d.a.1369.2 | 2 | 3.2 | odd | 2 | |||
2850.2.a.k.1.1 | 1 | 5.3 | odd | 4 | |||
2850.2.a.s.1.1 | 1 | 5.2 | odd | 4 | |||
8550.2.a.j.1.1 | 1 | 15.2 | even | 4 | |||
8550.2.a.bc.1.1 | 1 | 15.8 | even | 4 |