Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1890,2,Mod(379,1890)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1890, 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("1890.379");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1890.g (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: | \(15.0917259820\) |
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 | 379.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1890.379 |
Dual form | 1890.2.g.k.379.2 |
$q$-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 \(\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(1081\) | \(1541\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.00000 | − | 2.00000i | −0.316228 | − | 0.632456i | ||||
\(11\) | 4.00000 | 1.20605 | 0.603023 | − | 0.797724i | \(-0.293963\pi\) | ||||
0.603023 | + | 0.797724i | \(0.293963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.00000i | 1.66410i | 0.554700 | + | 0.832050i | \(0.312833\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 4.00000i | − | 0.970143i | −0.874475 | − | 0.485071i | \(-0.838794\pi\) | ||
0.874475 | − | 0.485071i | \(-0.161206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | −2.00000 | + | 1.00000i | −0.447214 | + | 0.223607i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 4.00000i | − | 0.852803i | ||||||
\(23\) | 4.00000i | 0.834058i | 0.908893 | + | 0.417029i | \(0.136929\pi\) | ||||
−0.908893 | + | 0.417029i | \(0.863071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | − | 4.00000i | 0.600000 | − | 0.800000i | ||||
\(26\) | 6.00000 | 1.17670 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000i | 0.188982i | ||||||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.00000 | 1.25724 | 0.628619 | − | 0.777714i | \(-0.283621\pi\) | ||||
0.628619 | + | 0.777714i | \(0.283621\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.00000 | −0.685994 | ||||||||
\(35\) | −1.00000 | − | 2.00000i | −0.169031 | − | 0.338062i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000i | 0.164399i | 0.996616 | + | 0.0821995i | \(0.0261945\pi\) | ||||
−0.996616 | + | 0.0821995i | \(0.973806\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | + | 2.00000i | 0.158114 | + | 0.316228i | ||||
\(41\) | 7.00000 | 1.09322 | 0.546608 | − | 0.837389i | \(-0.315919\pi\) | ||||
0.546608 | + | 0.837389i | \(0.315919\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 10.0000i | − | 1.52499i | −0.646997 | − | 0.762493i | \(-0.723975\pi\) | ||
0.646997 | − | 0.762493i | \(-0.276025\pi\) | |||||||
\(44\) | −4.00000 | −0.603023 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.00000 | 0.589768 | ||||||||
\(47\) | 13.0000i | 1.89624i | 0.317905 | + | 0.948122i | \(0.397021\pi\) | ||||
−0.317905 | + | 0.948122i | \(0.602979\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −4.00000 | − | 3.00000i | −0.565685 | − | 0.424264i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 6.00000i | − | 0.832050i | ||||||
\(53\) | 6.00000i | 0.824163i | 0.911147 | + | 0.412082i | \(0.135198\pi\) | ||||
−0.911147 | + | 0.412082i | \(0.864802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.00000 | − | 4.00000i | 1.07872 | − | 0.539360i | ||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 3.00000i | − | 0.393919i | ||||||
\(59\) | −5.00000 | −0.650945 | −0.325472 | − | 0.945552i | \(-0.605523\pi\) | ||||
−0.325472 | + | 0.945552i | \(0.605523\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.00000 | −0.896258 | −0.448129 | − | 0.893969i | \(-0.647910\pi\) | ||||
−0.448129 | + | 0.893969i | \(0.647910\pi\) | |||||||
\(62\) | − | 7.00000i | − | 0.889001i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 6.00000 | + | 12.0000i | 0.744208 | + | 1.48842i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 4.00000i | − | 0.488678i | −0.969690 | − | 0.244339i | \(-0.921429\pi\) | ||
0.969690 | − | 0.244339i | \(-0.0785709\pi\) | |||||||
\(68\) | 4.00000i | 0.485071i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.00000 | + | 1.00000i | −0.239046 | + | 0.119523i | ||||
\(71\) | 3.00000 | 0.356034 | 0.178017 | − | 0.984027i | \(-0.443032\pi\) | ||||
0.178017 | + | 0.984027i | \(0.443032\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 7.00000i | − | 0.819288i | −0.912245 | − | 0.409644i | \(-0.865653\pi\) | ||
0.912245 | − | 0.409644i | \(-0.134347\pi\) | |||||||
\(74\) | 1.00000 | 0.116248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 4.00000i | − | 0.455842i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.0000 | −1.35011 | −0.675053 | − | 0.737769i | \(-0.735879\pi\) | ||||
−0.675053 | + | 0.737769i | \(0.735879\pi\) | |||||||
\(80\) | 2.00000 | − | 1.00000i | 0.223607 | − | 0.111803i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 7.00000i | − | 0.773021i | ||||||
\(83\) | − | 2.00000i | − | 0.219529i | −0.993958 | − | 0.109764i | \(-0.964990\pi\) | ||
0.993958 | − | 0.109764i | \(-0.0350096\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.00000 | − | 8.00000i | −0.433861 | − | 0.867722i | ||||
\(86\) | −10.0000 | −1.07833 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.00000i | 0.426401i | ||||||||
\(89\) | 14.0000 | 1.48400 | 0.741999 | − | 0.670402i | \(-0.233878\pi\) | ||||
0.741999 | + | 0.670402i | \(0.233878\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.00000 | 0.628971 | ||||||||
\(92\) | − | 4.00000i | − | 0.417029i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 13.0000 | 1.34085 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 10.0000i | − | 1.01535i | −0.861550 | − | 0.507673i | \(-0.830506\pi\) | ||
0.861550 | − | 0.507673i | \(-0.169494\pi\) | |||||||
\(98\) | 1.00000i | 0.101015i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.00000 | + | 4.00000i | −0.300000 | + | 0.400000i | ||||
\(101\) | −10.0000 | −0.995037 | −0.497519 | − | 0.867453i | \(-0.665755\pi\) | ||||
−0.497519 | + | 0.867453i | \(0.665755\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 14.0000i | − | 1.37946i | −0.724066 | − | 0.689730i | \(-0.757729\pi\) | ||
0.724066 | − | 0.689730i | \(-0.242271\pi\) | |||||||
\(104\) | −6.00000 | −0.588348 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | − | 9.00000i | − | 0.870063i | −0.900415 | − | 0.435031i | \(-0.856737\pi\) | ||
0.900415 | − | 0.435031i | \(-0.143263\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 20.0000 | 1.91565 | 0.957826 | − | 0.287348i | \(-0.0927736\pi\) | ||||
0.957826 | + | 0.287348i | \(0.0927736\pi\) | |||||||
\(110\) | −4.00000 | − | 8.00000i | −0.381385 | − | 0.762770i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 1.00000i | − | 0.0944911i | ||||||
\(113\) | 3.00000i | 0.282216i | 0.989994 | + | 0.141108i | \(0.0450665\pi\) | ||||
−0.989994 | + | 0.141108i | \(0.954933\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.00000 | + | 8.00000i | 0.373002 | + | 0.746004i | ||||
\(116\) | −3.00000 | −0.278543 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.00000i | 0.460287i | ||||||||
\(119\) | −4.00000 | −0.366679 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 7.00000i | 0.633750i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.00000 | −0.628619 | ||||||||
\(125\) | 2.00000 | − | 11.0000i | 0.178885 | − | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.00000i | 0.621150i | 0.950549 | + | 0.310575i | \(0.100522\pi\) | ||||
−0.950549 | + | 0.310575i | \(0.899478\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 12.0000 | − | 6.00000i | 1.05247 | − | 0.526235i | ||||
\(131\) | −15.0000 | −1.31056 | −0.655278 | − | 0.755388i | \(-0.727449\pi\) | ||||
−0.655278 | + | 0.755388i | \(0.727449\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.00000 | −0.345547 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.00000 | 0.342997 | ||||||||
\(137\) | − | 15.0000i | − | 1.28154i | −0.767734 | − | 0.640768i | \(-0.778616\pi\) | ||
0.767734 | − | 0.640768i | \(-0.221384\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.0000 | 1.18746 | 0.593732 | − | 0.804663i | \(-0.297654\pi\) | ||||
0.593732 | + | 0.804663i | \(0.297654\pi\) | |||||||
\(140\) | 1.00000 | + | 2.00000i | 0.0845154 | + | 0.169031i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 3.00000i | − | 0.251754i | ||||||
\(143\) | 24.0000i | 2.00698i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.00000 | − | 3.00000i | 0.498273 | − | 0.249136i | ||||
\(146\) | −7.00000 | −0.579324 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 1.00000i | − | 0.0821995i | ||||||
\(149\) | 10.0000 | 0.819232 | 0.409616 | − | 0.912258i | \(-0.365663\pi\) | ||||
0.409616 | + | 0.912258i | \(0.365663\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.0000 | −1.13930 | −0.569652 | − | 0.821886i | \(-0.692922\pi\) | ||||
−0.569652 | + | 0.821886i | \(0.692922\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.00000 | −0.322329 | ||||||||
\(155\) | 14.0000 | − | 7.00000i | 1.12451 | − | 0.562254i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0000i | 1.11732i | 0.829396 | + | 0.558661i | \(0.188685\pi\) | ||||
−0.829396 | + | 0.558661i | \(0.811315\pi\) | |||||||
\(158\) | 12.0000i | 0.954669i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.00000 | − | 2.00000i | −0.0790569 | − | 0.158114i | ||||
\(161\) | 4.00000 | 0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 14.0000i | − | 1.09656i | −0.836293 | − | 0.548282i | \(-0.815282\pi\) | ||
0.836293 | − | 0.548282i | \(-0.184718\pi\) | |||||||
\(164\) | −7.00000 | −0.546608 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.00000 | −0.155230 | ||||||||
\(167\) | − | 3.00000i | − | 0.232147i | −0.993241 | − | 0.116073i | \(-0.962969\pi\) | ||
0.993241 | − | 0.116073i | \(-0.0370308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23.0000 | −1.76923 | ||||||||
\(170\) | −8.00000 | + | 4.00000i | −0.613572 | + | 0.306786i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10.0000i | 0.762493i | ||||||||
\(173\) | 17.0000i | 1.29249i | 0.763132 | + | 0.646243i | \(0.223661\pi\) | ||||
−0.763132 | + | 0.646243i | \(0.776339\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.00000 | − | 3.00000i | −0.302372 | − | 0.226779i | ||||
\(176\) | 4.00000 | 0.301511 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 14.0000i | − | 1.04934i | ||||||
\(179\) | 16.0000 | 1.19590 | 0.597948 | − | 0.801535i | \(-0.295983\pi\) | ||||
0.597948 | + | 0.801535i | \(0.295983\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.0000 | 1.70958 | 0.854788 | − | 0.518977i | \(-0.173687\pi\) | ||||
0.854788 | + | 0.518977i | \(0.173687\pi\) | |||||||
\(182\) | − | 6.00000i | − | 0.444750i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.00000 | −0.294884 | ||||||||
\(185\) | 1.00000 | + | 2.00000i | 0.0735215 | + | 0.147043i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 16.0000i | − | 1.17004i | ||||||
\(188\) | − | 13.0000i | − | 0.948122i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.00000i | 0.143963i | 0.997406 | + | 0.0719816i | \(0.0229323\pi\) | ||||
−0.997406 | + | 0.0719816i | \(0.977068\pi\) | |||||||
\(194\) | −10.0000 | −0.717958 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | − | 8.00000i | − | 0.569976i | −0.958531 | − | 0.284988i | \(-0.908010\pi\) | ||
0.958531 | − | 0.284988i | \(-0.0919897\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.0000 | −1.70131 | −0.850657 | − | 0.525720i | \(-0.823796\pi\) | ||||
−0.850657 | + | 0.525720i | \(0.823796\pi\) | |||||||
\(200\) | 4.00000 | + | 3.00000i | 0.282843 | + | 0.212132i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.0000i | 0.703598i | ||||||||
\(203\) | − | 3.00000i | − | 0.210559i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.0000 | − | 7.00000i | 0.977802 | − | 0.488901i | ||||
\(206\) | −14.0000 | −0.975426 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.00000i | 0.416025i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.0000 | −1.03264 | −0.516321 | − | 0.856395i | \(-0.672699\pi\) | ||||
−0.516321 | + | 0.856395i | \(0.672699\pi\) | |||||||
\(212\) | − | 6.00000i | − | 0.412082i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.00000 | −0.615227 | ||||||||
\(215\) | −10.0000 | − | 20.0000i | −0.681994 | − | 1.36399i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 7.00000i | − | 0.475191i | ||||||
\(218\) | − | 20.0000i | − | 1.35457i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −8.00000 | + | 4.00000i | −0.539360 | + | 0.269680i | ||||
\(221\) | 24.0000 | 1.61441 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 4.00000i | − | 0.267860i | −0.990991 | − | 0.133930i | \(-0.957240\pi\) | ||
0.990991 | − | 0.133930i | \(-0.0427597\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.00000 | 0.199557 | ||||||||
\(227\) | − | 16.0000i | − | 1.06196i | −0.847385 | − | 0.530979i | \(-0.821824\pi\) | ||
0.847385 | − | 0.530979i | \(-0.178176\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.0000 | −0.925146 | −0.462573 | − | 0.886581i | \(-0.653074\pi\) | ||||
−0.462573 | + | 0.886581i | \(0.653074\pi\) | |||||||
\(230\) | 8.00000 | − | 4.00000i | 0.527504 | − | 0.263752i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.00000i | 0.196960i | ||||||||
\(233\) | 11.0000i | 0.720634i | 0.932830 | + | 0.360317i | \(0.117331\pi\) | ||||
−0.932830 | + | 0.360317i | \(0.882669\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.0000 | + | 26.0000i | 0.848026 | + | 1.69605i | ||||
\(236\) | 5.00000 | 0.325472 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.00000i | 0.259281i | ||||||||
\(239\) | −13.0000 | −0.840900 | −0.420450 | − | 0.907316i | \(-0.638128\pi\) | ||||
−0.420450 | + | 0.907316i | \(0.638128\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.00000 | −0.128831 | −0.0644157 | − | 0.997923i | \(-0.520518\pi\) | ||||
−0.0644157 | + | 0.997923i | \(0.520518\pi\) | |||||||
\(242\) | − | 5.00000i | − | 0.321412i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.00000 | 0.448129 | ||||||||
\(245\) | −2.00000 | + | 1.00000i | −0.127775 | + | 0.0638877i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 7.00000i | 0.444500i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.0000 | − | 2.00000i | −0.695701 | − | 0.126491i | ||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.0000i | 1.00591i | ||||||||
\(254\) | 7.00000 | 0.439219 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 24.0000i | 1.49708i | 0.663090 | + | 0.748539i | \(0.269245\pi\) | ||||
−0.663090 | + | 0.748539i | \(0.730755\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.00000 | 0.0621370 | ||||||||
\(260\) | −6.00000 | − | 12.0000i | −0.372104 | − | 0.744208i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 15.0000i | 0.926703i | ||||||||
\(263\) | 16.0000i | 0.986602i | 0.869859 | + | 0.493301i | \(0.164210\pi\) | ||||
−0.869859 | + | 0.493301i | \(0.835790\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.00000 | + | 12.0000i | 0.368577 | + | 0.737154i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.00000i | 0.244339i | ||||||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.0000 | −0.668202 | −0.334101 | − | 0.942537i | \(-0.608433\pi\) | ||||
−0.334101 | + | 0.942537i | \(0.608433\pi\) | |||||||
\(272\) | − | 4.00000i | − | 0.242536i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.0000 | −0.906183 | ||||||||
\(275\) | 12.0000 | − | 16.0000i | 0.723627 | − | 0.964836i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 2.00000i | − | 0.120168i | −0.998193 | − | 0.0600842i | \(-0.980863\pi\) | ||
0.998193 | − | 0.0600842i | \(-0.0191369\pi\) | |||||||
\(278\) | − | 14.0000i | − | 0.839664i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.00000 | − | 1.00000i | 0.119523 | − | 0.0597614i | ||||
\(281\) | −24.0000 | −1.43172 | −0.715860 | − | 0.698244i | \(-0.753965\pi\) | ||||
−0.715860 | + | 0.698244i | \(0.753965\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.00000i | 0.416107i | 0.978117 | + | 0.208053i | \(0.0667128\pi\) | ||||
−0.978117 | + | 0.208053i | \(0.933287\pi\) | |||||||
\(284\) | −3.00000 | −0.178017 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 24.0000 | 1.41915 | ||||||||
\(287\) | − | 7.00000i | − | 0.413197i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −3.00000 | − | 6.00000i | −0.176166 | − | 0.352332i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.00000i | 0.409644i | ||||||||
\(293\) | 15.0000i | 0.876309i | 0.898900 | + | 0.438155i | \(0.144368\pi\) | ||||
−0.898900 | + | 0.438155i | \(0.855632\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.0000 | + | 5.00000i | −0.582223 | + | 0.291111i | ||||
\(296\) | −1.00000 | −0.0581238 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 10.0000i | − | 0.579284i | ||||||
\(299\) | −24.0000 | −1.38796 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.0000 | −0.576390 | ||||||||
\(302\) | 14.0000i | 0.805609i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.0000 | + | 7.00000i | −0.801638 | + | 0.400819i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.0000i | 0.684876i | 0.939540 | + | 0.342438i | \(0.111253\pi\) | ||||
−0.939540 | + | 0.342438i | \(0.888747\pi\) | |||||||
\(308\) | 4.00000i | 0.227921i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.00000 | − | 14.0000i | −0.397573 | − | 0.795147i | ||||
\(311\) | 30.0000 | 1.70114 | 0.850572 | − | 0.525859i | \(-0.176256\pi\) | ||||
0.850572 | + | 0.525859i | \(0.176256\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.0000i | 1.46961i | 0.678280 | + | 0.734803i | \(0.262726\pi\) | ||||
−0.678280 | + | 0.734803i | \(0.737274\pi\) | |||||||
\(314\) | 14.0000 | 0.790066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.0000 | 0.675053 | ||||||||
\(317\) | 14.0000i | 0.786318i | 0.919470 | + | 0.393159i | \(0.128618\pi\) | ||||
−0.919470 | + | 0.393159i | \(0.871382\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.0000 | 0.671871 | ||||||||
\(320\) | −2.00000 | + | 1.00000i | −0.111803 | + | 0.0559017i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 4.00000i | − | 0.222911i | ||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 24.0000 | + | 18.0000i | 1.33128 | + | 0.998460i | ||||
\(326\) | −14.0000 | −0.775388 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.00000i | 0.386510i | ||||||||
\(329\) | 13.0000 | 0.716713 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −35.0000 | −1.92377 | −0.961887 | − | 0.273447i | \(-0.911836\pi\) | ||||
−0.961887 | + | 0.273447i | \(0.911836\pi\) | |||||||
\(332\) | 2.00000i | 0.109764i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.00000 | −0.164153 | ||||||||
\(335\) | −4.00000 | − | 8.00000i | −0.218543 | − | 0.437087i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.0000i | 0.871576i | 0.900049 | + | 0.435788i | \(0.143530\pi\) | ||||
−0.900049 | + | 0.435788i | \(0.856470\pi\) | |||||||
\(338\) | 23.0000i | 1.25104i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.00000 | + | 8.00000i | 0.216930 | + | 0.433861i | ||||
\(341\) | 28.0000 | 1.51629 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 10.0000 | 0.539164 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 17.0000 | 0.913926 | ||||||||
\(347\) | − | 27.0000i | − | 1.44944i | −0.689046 | − | 0.724718i | \(-0.741970\pi\) | ||
0.689046 | − | 0.724718i | \(-0.258030\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.00000 | 0.107058 | 0.0535288 | − | 0.998566i | \(-0.482953\pi\) | ||||
0.0535288 | + | 0.998566i | \(0.482953\pi\) | |||||||
\(350\) | −3.00000 | + | 4.00000i | −0.160357 | + | 0.213809i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 4.00000i | − | 0.213201i | ||||||
\(353\) | 32.0000i | 1.70319i | 0.524202 | + | 0.851594i | \(0.324364\pi\) | ||||
−0.524202 | + | 0.851594i | \(0.675636\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.00000 | − | 3.00000i | 0.318447 | − | 0.159223i | ||||
\(356\) | −14.0000 | −0.741999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 16.0000i | − | 0.845626i | ||||||
\(359\) | −12.0000 | −0.633336 | −0.316668 | − | 0.948536i | \(-0.602564\pi\) | ||||
−0.316668 | + | 0.948536i | \(0.602564\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | − | 23.0000i | − | 1.20885i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.00000 | −0.314485 | ||||||||
\(365\) | −7.00000 | − | 14.0000i | −0.366397 | − | 0.732793i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 2.00000i | − | 0.104399i | −0.998637 | − | 0.0521996i | \(-0.983377\pi\) | ||
0.998637 | − | 0.0521996i | \(-0.0166232\pi\) | |||||||
\(368\) | 4.00000i | 0.208514i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.00000 | − | 1.00000i | 0.103975 | − | 0.0519875i | ||||
\(371\) | 6.00000 | 0.311504 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.00000i | 0.155334i | 0.996979 | + | 0.0776671i | \(0.0247471\pi\) | ||||
−0.996979 | + | 0.0776671i | \(0.975253\pi\) | |||||||
\(374\) | −16.0000 | −0.827340 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −13.0000 | −0.670424 | ||||||||
\(377\) | 18.0000i | 0.927047i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.00000 | 0.0513665 | 0.0256833 | − | 0.999670i | \(-0.491824\pi\) | ||||
0.0256833 | + | 0.999670i | \(0.491824\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.00000i | 0.408781i | 0.978889 | + | 0.204390i | \(0.0655212\pi\) | ||||
−0.978889 | + | 0.204390i | \(0.934479\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.00000 | − | 8.00000i | −0.203859 | − | 0.407718i | ||||
\(386\) | 2.00000 | 0.101797 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10.0000i | 0.507673i | ||||||||
\(389\) | 23.0000 | 1.16615 | 0.583073 | − | 0.812420i | \(-0.301850\pi\) | ||||
0.583073 | + | 0.812420i | \(0.301850\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.0000 | 0.809155 | ||||||||
\(392\) | − | 1.00000i | − | 0.0505076i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8.00000 | −0.403034 | ||||||||
\(395\) | −24.0000 | + | 12.0000i | −1.20757 | + | 0.603786i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 14.0000i | − | 0.702640i | −0.936255 | − | 0.351320i | \(-0.885733\pi\) | ||
0.936255 | − | 0.351320i | \(-0.114267\pi\) | |||||||
\(398\) | 24.0000i | 1.20301i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | − | 4.00000i | 0.150000 | − | 0.200000i | ||||
\(401\) | −16.0000 | −0.799002 | −0.399501 | − | 0.916733i | \(-0.630817\pi\) | ||||
−0.399501 | + | 0.916733i | \(0.630817\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 42.0000i | 2.09217i | ||||||||
\(404\) | 10.0000 | 0.497519 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.00000 | −0.148888 | ||||||||
\(407\) | 4.00000i | 0.198273i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.0000 | −0.988936 | −0.494468 | − | 0.869196i | \(-0.664637\pi\) | ||||
−0.494468 | + | 0.869196i | \(0.664637\pi\) | |||||||
\(410\) | −7.00000 | − | 14.0000i | −0.345705 | − | 0.691411i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 14.0000i | 0.689730i | ||||||||
\(413\) | 5.00000i | 0.246034i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.00000 | − | 4.00000i | −0.0981761 | − | 0.196352i | ||||
\(416\) | 6.00000 | 0.294174 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.0000 | −1.22133 | −0.610665 | − | 0.791889i | \(-0.709098\pi\) | ||||
−0.610665 | + | 0.791889i | \(0.709098\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.0000 | −0.974740 | −0.487370 | − | 0.873195i | \(-0.662044\pi\) | ||||
−0.487370 | + | 0.873195i | \(0.662044\pi\) | |||||||
\(422\) | 15.0000i | 0.730189i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | −16.0000 | − | 12.0000i | −0.776114 | − | 0.582086i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.00000i | 0.338754i | ||||||||
\(428\) | 9.00000i | 0.435031i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −20.0000 | + | 10.0000i | −0.964486 | + | 0.482243i | ||||
\(431\) | −11.0000 | −0.529851 | −0.264926 | − | 0.964269i | \(-0.585347\pi\) | ||||
−0.264926 | + | 0.964269i | \(0.585347\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.0000i | 1.39365i | 0.717241 | + | 0.696826i | \(0.245405\pi\) | ||||
−0.717241 | + | 0.696826i | \(0.754595\pi\) | |||||||
\(434\) | −7.00000 | −0.336011 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −20.0000 | −0.957826 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 4.00000 | + | 8.00000i | 0.190693 | + | 0.381385i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 24.0000i | − | 1.14156i | ||||||
\(443\) | 9.00000i | 0.427603i | 0.976877 | + | 0.213801i | \(0.0685846\pi\) | ||||
−0.976877 | + | 0.213801i | \(0.931415\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 28.0000 | − | 14.0000i | 1.32733 | − | 0.663664i | ||||
\(446\) | −4.00000 | −0.189405 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.00000i | 0.0472456i | ||||||||
\(449\) | 36.0000 | 1.69895 | 0.849473 | − | 0.527633i | \(-0.176920\pi\) | ||||
0.849473 | + | 0.527633i | \(0.176920\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.0000 | 1.31847 | ||||||||
\(452\) | − | 3.00000i | − | 0.141108i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −16.0000 | −0.750917 | ||||||||
\(455\) | 12.0000 | − | 6.00000i | 0.562569 | − | 0.281284i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 8.00000i | − | 0.374224i | −0.982339 | − | 0.187112i | \(-0.940087\pi\) | ||
0.982339 | − | 0.187112i | \(-0.0599128\pi\) | |||||||
\(458\) | 14.0000i | 0.654177i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.00000 | − | 8.00000i | −0.186501 | − | 0.373002i | ||||
\(461\) | 36.0000 | 1.67669 | 0.838344 | − | 0.545142i | \(-0.183524\pi\) | ||||
0.838344 | + | 0.545142i | \(0.183524\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 33.0000i | − | 1.53364i | −0.641862 | − | 0.766820i | \(-0.721838\pi\) | ||
0.641862 | − | 0.766820i | \(-0.278162\pi\) | |||||||
\(464\) | 3.00000 | 0.139272 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.0000 | 0.509565 | ||||||||
\(467\) | 18.0000i | 0.832941i | 0.909149 | + | 0.416470i | \(0.136733\pi\) | ||||
−0.909149 | + | 0.416470i | \(0.863267\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.00000 | −0.184703 | ||||||||
\(470\) | 26.0000 | − | 13.0000i | 1.19929 | − | 0.599645i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 5.00000i | − | 0.230144i | ||||||
\(473\) | − | 40.0000i | − | 1.83920i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.00000 | 0.183340 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 13.0000i | 0.594606i | ||||||||
\(479\) | −4.00000 | −0.182765 | −0.0913823 | − | 0.995816i | \(-0.529129\pi\) | ||||
−0.0913823 | + | 0.995816i | \(0.529129\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.00000 | −0.273576 | ||||||||
\(482\) | 2.00000i | 0.0910975i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.00000 | −0.227273 | ||||||||
\(485\) | −10.0000 | − | 20.0000i | −0.454077 | − | 0.908153i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.0000i | 0.951601i | 0.879553 | + | 0.475800i | \(0.157842\pi\) | ||||
−0.879553 | + | 0.475800i | \(0.842158\pi\) | |||||||
\(488\) | − | 7.00000i | − | 0.316875i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.00000 | + | 2.00000i | 0.0451754 | + | 0.0903508i | ||||
\(491\) | 30.0000 | 1.35388 | 0.676941 | − | 0.736038i | \(-0.263305\pi\) | ||||
0.676941 | + | 0.736038i | \(0.263305\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 12.0000i | − | 0.540453i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.00000 | 0.314309 | ||||||||
\(497\) | − | 3.00000i | − | 0.134568i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.00000 | −0.402895 | −0.201448 | − | 0.979499i | \(-0.564565\pi\) | ||||
−0.201448 | + | 0.979499i | \(0.564565\pi\) | |||||||
\(500\) | −2.00000 | + | 11.0000i | −0.0894427 | + | 0.491935i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.0000i | 0.535586i | ||||||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −20.0000 | + | 10.0000i | −0.889988 | + | 0.444994i | ||||
\(506\) | 16.0000 | 0.711287 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 7.00000i | − | 0.310575i | ||||||
\(509\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.00000 | −0.309662 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 24.0000 | 1.05859 | ||||||||
\(515\) | −14.0000 | − | 28.0000i | −0.616914 | − | 1.23383i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 52.0000i | 2.28696i | ||||||||
\(518\) | − | 1.00000i | − | 0.0439375i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −12.0000 | + | 6.00000i | −0.526235 | + | 0.263117i | ||||
\(521\) | 38.0000 | 1.66481 | 0.832405 | − | 0.554168i | \(-0.186963\pi\) | ||||
0.832405 | + | 0.554168i | \(0.186963\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.0000i | 1.22435i | 0.790721 | + | 0.612177i | \(0.209706\pi\) | ||||
−0.790721 | + | 0.612177i | \(0.790294\pi\) | |||||||
\(524\) | 15.0000 | 0.655278 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.0000 | 0.697633 | ||||||||
\(527\) | − | 28.0000i | − | 1.21970i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | 12.0000 | − | 6.00000i | 0.521247 | − | 0.260623i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 42.0000i | 1.81922i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.00000 | − | 18.0000i | −0.389104 | − | 0.778208i | ||||
\(536\) | 4.00000 | 0.172774 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.00000 | −0.172292 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.0000 | −1.37579 | −0.687894 | − | 0.725811i | \(-0.741464\pi\) | ||||
−0.687894 | + | 0.725811i | \(0.741464\pi\) | |||||||
\(542\) | 11.0000i | 0.472490i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.00000 | −0.171499 | ||||||||
\(545\) | 40.0000 | − | 20.0000i | 1.71341 | − | 0.856706i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 32.0000i | − | 1.36822i | −0.729378 | − | 0.684111i | \(-0.760191\pi\) | ||
0.729378 | − | 0.684111i | \(-0.239809\pi\) | |||||||
\(548\) | 15.0000i | 0.640768i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −16.0000 | − | 12.0000i | −0.682242 | − | 0.511682i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.0000i | 0.510292i | ||||||||
\(554\) | −2.00000 | −0.0849719 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.0000 | −0.593732 | ||||||||
\(557\) | − | 12.0000i | − | 0.508456i | −0.967144 | − | 0.254228i | \(-0.918179\pi\) | ||
0.967144 | − | 0.254228i | \(-0.0818214\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 60.0000 | 2.53773 | ||||||||
\(560\) | −1.00000 | − | 2.00000i | −0.0422577 | − | 0.0845154i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 24.0000i | 1.01238i | ||||||||
\(563\) | − | 10.0000i | − | 0.421450i | −0.977545 | − | 0.210725i | \(-0.932418\pi\) | ||
0.977545 | − | 0.210725i | \(-0.0675824\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.00000 | + | 6.00000i | 0.126211 | + | 0.252422i | ||||
\(566\) | 7.00000 | 0.294232 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.00000i | 0.125877i | ||||||||
\(569\) | 20.0000 | 0.838444 | 0.419222 | − | 0.907884i | \(-0.362303\pi\) | ||||
0.419222 | + | 0.907884i | \(0.362303\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.0000 | 0.795125 | 0.397563 | − | 0.917575i | \(-0.369856\pi\) | ||||
0.397563 | + | 0.917575i | \(0.369856\pi\) | |||||||
\(572\) | − | 24.0000i | − | 1.00349i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −7.00000 | −0.292174 | ||||||||
\(575\) | 16.0000 | + | 12.0000i | 0.667246 | + | 0.500435i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 11.0000i | − | 0.457936i | −0.973434 | − | 0.228968i | \(-0.926465\pi\) | ||
0.973434 | − | 0.228968i | \(-0.0735351\pi\) | |||||||
\(578\) | − | 1.00000i | − | 0.0415945i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.00000 | + | 3.00000i | −0.249136 | + | 0.124568i | ||||
\(581\) | −2.00000 | −0.0829740 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.0000i | 0.993978i | ||||||||
\(584\) | 7.00000 | 0.289662 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.0000 | 0.619644 | ||||||||
\(587\) | 18.0000i | 0.742940i | 0.928445 | + | 0.371470i | \(0.121146\pi\) | ||||
−0.928445 | + | 0.371470i | \(0.878854\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 5.00000 | + | 10.0000i | 0.205847 | + | 0.411693i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.00000i | 0.0410997i | ||||||||
\(593\) | 30.0000i | 1.23195i | 0.787765 | + | 0.615976i | \(0.211238\pi\) | ||||
−0.787765 | + | 0.615976i | \(0.788762\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.00000 | + | 4.00000i | −0.327968 | + | 0.163984i | ||||
\(596\) | −10.0000 | −0.409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 24.0000i | 0.981433i | ||||||||
\(599\) | −15.0000 | −0.612883 | −0.306442 | − | 0.951889i | \(-0.599138\pi\) | ||||
−0.306442 | + | 0.951889i | \(0.599138\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 44.0000 | 1.79480 | 0.897399 | − | 0.441221i | \(-0.145454\pi\) | ||||
0.897399 | + | 0.441221i | \(0.145454\pi\) | |||||||
\(602\) | 10.0000i | 0.407570i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 14.0000 | 0.569652 | ||||||||
\(605\) | 10.0000 | − | 5.00000i | 0.406558 | − | 0.203279i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.0000i | 0.568242i | 0.958788 | + | 0.284121i | \(0.0917018\pi\) | ||||
−0.958788 | + | 0.284121i | \(0.908298\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.00000 | + | 14.0000i | 0.283422 | + | 0.566843i | ||||
\(611\) | −78.0000 | −3.15554 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 22.0000i | − | 0.888572i | −0.895885 | − | 0.444286i | \(-0.853457\pi\) | ||
0.895885 | − | 0.444286i | \(-0.146543\pi\) | |||||||
\(614\) | 12.0000 | 0.484281 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.00000 | 0.161165 | ||||||||
\(617\) | − | 31.0000i | − | 1.24801i | −0.781419 | − | 0.624007i | \(-0.785504\pi\) | ||
0.781419 | − | 0.624007i | \(-0.214496\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 40.0000 | 1.60774 | 0.803868 | − | 0.594808i | \(-0.202772\pi\) | ||||
0.803868 | + | 0.594808i | \(0.202772\pi\) | |||||||
\(620\) | −14.0000 | + | 7.00000i | −0.562254 | + | 0.281127i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 30.0000i | − | 1.20289i | ||||||
\(623\) | − | 14.0000i | − | 0.560898i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | 26.0000 | 1.03917 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 14.0000i | − | 0.558661i | ||||||
\(629\) | 4.00000 | 0.159490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.0000 | −1.59237 | −0.796187 | − | 0.605050i | \(-0.793153\pi\) | ||||
−0.796187 | + | 0.605050i | \(0.793153\pi\) | |||||||
\(632\) | − | 12.0000i | − | 0.477334i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 14.0000 | 0.556011 | ||||||||
\(635\) | 7.00000 | + | 14.0000i | 0.277787 | + | 0.555573i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 6.00000i | − | 0.237729i | ||||||
\(638\) | − | 12.0000i | − | 0.475085i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | + | 2.00000i | 0.0395285 | + | 0.0790569i | ||||
\(641\) | −26.0000 | −1.02694 | −0.513469 | − | 0.858108i | \(-0.671640\pi\) | ||||
−0.513469 | + | 0.858108i | \(0.671640\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 39.0000i | 1.53801i | 0.639243 | + | 0.769005i | \(0.279248\pi\) | ||||
−0.639243 | + | 0.769005i | \(0.720752\pi\) | |||||||
\(644\) | −4.00000 | −0.157622 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 33.0000i | 1.29736i | 0.761060 | + | 0.648682i | \(0.224679\pi\) | ||||
−0.761060 | + | 0.648682i | \(0.775321\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.0000 | −0.785069 | ||||||||
\(650\) | 18.0000 | − | 24.0000i | 0.706018 | − | 0.941357i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14.0000i | 0.548282i | ||||||||
\(653\) | − | 14.0000i | − | 0.547862i | −0.961749 | − | 0.273931i | \(-0.911676\pi\) | ||
0.961749 | − | 0.273931i | \(-0.0883240\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −30.0000 | + | 15.0000i | −1.17220 | + | 0.586098i | ||||
\(656\) | 7.00000 | 0.273304 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 13.0000i | − | 0.506793i | ||||||
\(659\) | −26.0000 | −1.01282 | −0.506408 | − | 0.862294i | \(-0.669027\pi\) | ||||
−0.506408 | + | 0.862294i | \(0.669027\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.0000 | −0.739014 | −0.369507 | − | 0.929228i | \(-0.620473\pi\) | ||||
−0.369507 | + | 0.929228i | \(0.620473\pi\) | |||||||
\(662\) | 35.0000i | 1.36031i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.00000 | 0.0776151 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.0000i | 0.464642i | ||||||||
\(668\) | 3.00000i | 0.116073i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8.00000 | + | 4.00000i | −0.309067 | + | 0.154533i | ||||
\(671\) | −28.0000 | −1.08093 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 36.0000i | − | 1.38770i | −0.720121 | − | 0.693849i | \(-0.755914\pi\) | ||
0.720121 | − | 0.693849i | \(-0.244086\pi\) | |||||||
\(674\) | 16.0000 | 0.616297 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 23.0000 | 0.884615 | ||||||||
\(677\) | 29.0000i | 1.11456i | 0.830324 | + | 0.557280i | \(0.188155\pi\) | ||||
−0.830324 | + | 0.557280i | \(0.811845\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.0000 | −0.383765 | ||||||||
\(680\) | 8.00000 | − | 4.00000i | 0.306786 | − | 0.153393i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 28.0000i | − | 1.07218i | ||||||
\(683\) | 1.00000i | 0.0382639i | 0.999817 | + | 0.0191320i | \(0.00609027\pi\) | ||||
−0.999817 | + | 0.0191320i | \(0.993910\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.0000 | − | 30.0000i | −0.573121 | − | 1.14624i | ||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 10.0000i | − | 0.381246i | ||||||
\(689\) | −36.0000 | −1.37149 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.0000 | −1.44559 | −0.722794 | − | 0.691063i | \(-0.757142\pi\) | ||||
−0.722794 | + | 0.691063i | \(0.757142\pi\) | |||||||
\(692\) | − | 17.0000i | − | 0.646243i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −27.0000 | −1.02491 | ||||||||
\(695\) | 28.0000 | − | 14.0000i | 1.06210 | − | 0.531050i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 28.0000i | − | 1.06058i | ||||||
\(698\) | − | 2.00000i | − | 0.0757011i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.00000 | + | 3.00000i | 0.151186 | + | 0.113389i | ||||
\(701\) | −35.0000 | −1.32193 | −0.660966 | − | 0.750416i | \(-0.729853\pi\) | ||||
−0.660966 | + | 0.750416i | \(0.729853\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −4.00000 | −0.150756 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 32.0000 | 1.20434 | ||||||||
\(707\) | 10.0000i | 0.376089i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −48.0000 | −1.80268 | −0.901339 | − | 0.433114i | \(-0.857415\pi\) | ||||
−0.901339 | + | 0.433114i | \(0.857415\pi\) | |||||||
\(710\) | −3.00000 | − | 6.00000i | −0.112588 | − | 0.225176i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 14.0000i | 0.524672i | ||||||||
\(713\) | 28.0000i | 1.04861i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.0000 | + | 48.0000i | 0.897549 | + | 1.79510i | ||||
\(716\) | −16.0000 | −0.597948 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 12.0000i | 0.447836i | ||||||||
\(719\) | 2.00000 | 0.0745874 | 0.0372937 | − | 0.999304i | \(-0.488126\pi\) | ||||
0.0372937 | + | 0.999304i | \(0.488126\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.0000 | −0.521387 | ||||||||
\(722\) | 19.0000i | 0.707107i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −23.0000 | −0.854788 | ||||||||
\(725\) | 9.00000 | − | 12.0000i | 0.334252 | − | 0.445669i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 6.00000i | − | 0.222528i | −0.993791 | − | 0.111264i | \(-0.964510\pi\) | ||
0.993791 | − | 0.111264i | \(-0.0354899\pi\) | |||||||
\(728\) | 6.00000i | 0.222375i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −14.0000 | + | 7.00000i | −0.518163 | + | 0.259082i | ||||
\(731\) | −40.0000 | −1.47945 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 44.0000i | − | 1.62518i | −0.582838 | − | 0.812589i | \(-0.698058\pi\) | ||
0.582838 | − | 0.812589i | \(-0.301942\pi\) | |||||||
\(734\) | −2.00000 | −0.0738213 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.00000 | 0.147442 | ||||||||
\(737\) | − | 16.0000i | − | 0.589368i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.0000 | −0.478213 | −0.239106 | − | 0.970993i | \(-0.576854\pi\) | ||||
−0.239106 | + | 0.970993i | \(0.576854\pi\) | |||||||
\(740\) | −1.00000 | − | 2.00000i | −0.0367607 | − | 0.0735215i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 6.00000i | − | 0.220267i | ||||||
\(743\) | 18.0000i | 0.660356i | 0.943919 | + | 0.330178i | \(0.107109\pi\) | ||||
−0.943919 | + | 0.330178i | \(0.892891\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.0000 | − | 10.0000i | 0.732743 | − | 0.366372i | ||||
\(746\) | 3.00000 | 0.109838 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 16.0000i | 0.585018i | ||||||||
\(749\) | −9.00000 | −0.328853 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.0000 | −0.802791 | −0.401396 | − | 0.915905i | \(-0.631475\pi\) | ||||
−0.401396 | + | 0.915905i | \(0.631475\pi\) | |||||||
\(752\) | 13.0000i | 0.474061i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 18.0000 | 0.655521 | ||||||||
\(755\) | −28.0000 | + | 14.0000i | −1.01902 | + | 0.509512i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.0000i | 0.690567i | 0.938498 | + | 0.345283i | \(0.112217\pi\) | ||||
−0.938498 | + | 0.345283i | \(0.887783\pi\) | |||||||
\(758\) | − | 1.00000i | − | 0.0363216i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.00000 | −0.108750 | −0.0543750 | − | 0.998521i | \(-0.517317\pi\) | ||||
−0.0543750 | + | 0.998521i | \(0.517317\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 20.0000i | − | 0.724049i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.00000 | 0.289052 | ||||||||
\(767\) | − | 30.0000i | − | 1.08324i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.0000 | 0.432731 | 0.216366 | − | 0.976312i | \(-0.430580\pi\) | ||||
0.216366 | + | 0.976312i | \(0.430580\pi\) | |||||||
\(770\) | −8.00000 | + | 4.00000i | −0.288300 | + | 0.144150i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 2.00000i | − | 0.0719816i | ||||||
\(773\) | − | 27.0000i | − | 0.971123i | −0.874203 | − | 0.485561i | \(-0.838615\pi\) | ||
0.874203 | − | 0.485561i | \(-0.161385\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.0000 | − | 28.0000i | 0.754342 | − | 1.00579i | ||||
\(776\) | 10.0000 | 0.358979 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 23.0000i | − | 0.824590i | ||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.0000 | 0.429394 | ||||||||
\(782\) | − | 16.0000i | − | 0.572159i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | 14.0000 | + | 28.0000i | 0.499681 | + | 0.999363i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.00000i | 0.249523i | 0.992187 | + | 0.124762i | \(0.0398166\pi\) | ||||
−0.992187 | + | 0.124762i | \(0.960183\pi\) | |||||||
\(788\) | 8.00000i | 0.284988i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 12.0000 | + | 24.0000i | 0.426941 | + | 0.853882i | ||||
\(791\) | 3.00000 | 0.106668 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 42.0000i | − | 1.49146i | ||||||
\(794\) | −14.0000 | −0.496841 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 24.0000 | 0.850657 | ||||||||
\(797\) | − | 37.0000i | − | 1.31061i | −0.755366 | − | 0.655304i | \(-0.772541\pi\) | ||
0.755366 | − | 0.655304i | \(-0.227459\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 52.0000 | 1.83963 | ||||||||
\(800\) | −4.00000 | − | 3.00000i | −0.141421 | − | 0.106066i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 16.0000i | 0.564980i | ||||||||
\(803\) | − | 28.0000i | − | 0.988099i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.00000 | − | 4.00000i | 0.281963 | − | 0.140981i | ||||
\(806\) | 42.0000 | 1.47939 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 10.0000i | − | 0.351799i | ||||||
\(809\) | 18.0000 | 0.632846 | 0.316423 | − | 0.948618i | \(-0.397518\pi\) | ||||
0.316423 | + | 0.948618i | \(0.397518\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.0000 | −0.491606 | −0.245803 | − | 0.969320i | \(-0.579052\pi\) | ||||
−0.245803 | + | 0.969320i | \(0.579052\pi\) | |||||||
\(812\) | 3.00000i | 0.105279i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.00000 | 0.140200 | ||||||||
\(815\) | −14.0000 | − | 28.0000i | −0.490399 | − | 0.980797i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 20.0000i | 0.699284i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −14.0000 | + | 7.00000i | −0.488901 | + | 0.244451i | ||||
\(821\) | 2.00000 | 0.0698005 | 0.0349002 | − | 0.999391i | \(-0.488889\pi\) | ||||
0.0349002 | + | 0.999391i | \(0.488889\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 51.0000i | − | 1.77775i | −0.458151 | − | 0.888874i | \(-0.651488\pi\) | ||
0.458151 | − | 0.888874i | \(-0.348512\pi\) | |||||||
\(824\) | 14.0000 | 0.487713 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.00000 | 0.173972 | ||||||||
\(827\) | − | 25.0000i | − | 0.869335i | −0.900591 | − | 0.434668i | \(-0.856866\pi\) | ||
0.900591 | − | 0.434668i | \(-0.143134\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.00000 | −0.208389 | −0.104194 | − | 0.994557i | \(-0.533226\pi\) | ||||
−0.104194 | + | 0.994557i | \(0.533226\pi\) | |||||||
\(830\) | −4.00000 | + | 2.00000i | −0.138842 | + | 0.0694210i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 6.00000i | − | 0.208013i | ||||||
\(833\) | 4.00000i | 0.138592i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.00000 | − | 6.00000i | −0.103819 | − | 0.207639i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 25.0000i | 0.863611i | ||||||||
\(839\) | 4.00000 | 0.138095 | 0.0690477 | − | 0.997613i | \(-0.478004\pi\) | ||||
0.0690477 | + | 0.997613i | \(0.478004\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 20.0000i | 0.689246i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 15.0000 | 0.516321 | ||||||||
\(845\) | −46.0000 | + | 23.0000i | −1.58245 | + | 0.791224i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 5.00000i | − | 0.171802i | ||||||
\(848\) | 6.00000i | 0.206041i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −12.0000 | + | 16.0000i | −0.411597 | + | 0.548795i | ||||
\(851\) | −4.00000 | −0.137118 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.0000i | 0.547830i | 0.961754 | + | 0.273915i | \(0.0883186\pi\) | ||||
−0.961754 | + | 0.273915i | \(0.911681\pi\) | |||||||
\(854\) | 7.00000 | 0.239535 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.00000 | 0.307614 | ||||||||
\(857\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.0000 | 1.36478 | 0.682391 | − | 0.730987i | \(-0.260940\pi\) | ||||
0.682391 | + | 0.730987i | \(0.260940\pi\) | |||||||
\(860\) | 10.0000 | + | 20.0000i | 0.340997 | + | 0.681994i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 11.0000i | 0.374661i | ||||||||
\(863\) | 6.00000i | 0.204242i | 0.994772 | + | 0.102121i | \(0.0325630\pi\) | ||||
−0.994772 | + | 0.102121i | \(0.967437\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.0000 | + | 34.0000i | 0.578017 | + | 1.15603i | ||||
\(866\) | 29.0000 | 0.985460 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.00000i | 0.237595i | ||||||||
\(869\) | −48.0000 | −1.62829 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.0000 | 0.813209 | ||||||||
\(872\) | 20.0000i | 0.677285i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.0000 | − | 2.00000i | −0.371868 | − | 0.0676123i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 49.0000i | − | 1.65461i | −0.561751 | − | 0.827306i | \(-0.689872\pi\) | ||
0.561751 | − | 0.827306i | \(-0.310128\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8.00000 | − | 4.00000i | 0.269680 | − | 0.134840i | ||||
\(881\) | −33.0000 | −1.11180 | −0.555899 | − | 0.831250i | \(-0.687626\pi\) | ||||
−0.555899 | + | 0.831250i | \(0.687626\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 54.0000i | − | 1.81724i | −0.417619 | − | 0.908622i | \(-0.637135\pi\) | ||
0.417619 | − | 0.908622i | \(-0.362865\pi\) | |||||||
\(884\) | −24.0000 | −0.807207 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.00000 | 0.302361 | ||||||||
\(887\) | − | 39.0000i | − | 1.30949i | −0.755849 | − | 0.654746i | \(-0.772776\pi\) | ||
0.755849 | − | 0.654746i | \(-0.227224\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.00000 | 0.234772 | ||||||||
\(890\) | −14.0000 | − | 28.0000i | −0.469281 | − | 0.938562i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.00000i | 0.133930i | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 32.0000 | − | 16.0000i | 1.06964 | − | 0.534821i | ||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 36.0000i | − | 1.20134i | ||||||
\(899\) | 21.0000 | 0.700389 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.0000 | 0.799556 | ||||||||
\(902\) | − | 28.0000i | − | 0.932298i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.00000 | −0.0997785 | ||||||||
\(905\) | 46.0000 | − | 23.0000i | 1.52909 | − | 0.764546i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.0000i | 0.796907i | 0.917189 | + | 0.398453i | \(0.130453\pi\) | ||||
−0.917189 | + | 0.398453i | \(0.869547\pi\) | |||||||
\(908\) | 16.0000i | 0.530979i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −6.00000 | − | 12.0000i | −0.198898 | − | 0.397796i | ||||
\(911\) | −9.00000 | −0.298183 | −0.149092 | − | 0.988823i | \(-0.547635\pi\) | ||||
−0.149092 | + | 0.988823i | \(0.547635\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 8.00000i | − | 0.264761i | ||||||
\(914\) | −8.00000 | −0.264616 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.0000 | 0.462573 | ||||||||
\(917\) | 15.0000i | 0.495344i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.0000 | −0.593765 | −0.296883 | − | 0.954914i | \(-0.595947\pi\) | ||||
−0.296883 | + | 0.954914i | \(0.595947\pi\) | |||||||
\(920\) | −8.00000 | + | 4.00000i | −0.263752 | + | 0.131876i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 36.0000i | − | 1.18560i | ||||||
\(923\) | 18.0000i | 0.592477i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.00000 | + | 3.00000i | 0.131519 | + | 0.0986394i | ||||
\(926\) | −33.0000 | −1.08445 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 3.00000i | − | 0.0984798i | ||||||
\(929\) | −42.0000 | −1.37798 | −0.688988 | − | 0.724773i | \(-0.741945\pi\) | ||||
−0.688988 | + | 0.724773i | \(0.741945\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 11.0000i | − | 0.360317i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 18.0000 | 0.588978 | ||||||||
\(935\) | −16.0000 | − | 32.0000i | −0.523256 | − | 1.04651i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.0000i | 0.751377i | 0.926746 | + | 0.375689i | \(0.122594\pi\) | ||||
−0.926746 | + | 0.375689i | \(0.877406\pi\) | |||||||
\(938\) | 4.00000i | 0.130605i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −13.0000 | − | 26.0000i | −0.424013 | − | 0.848026i | ||||
\(941\) | 40.0000 | 1.30396 | 0.651981 | − | 0.758235i | \(-0.273938\pi\) | ||||
0.651981 | + | 0.758235i | \(0.273938\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28.0000i | 0.911805i | ||||||||
\(944\) | −5.00000 | −0.162736 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −40.0000 | −1.30051 | ||||||||
\(947\) | − | 12.0000i | − | 0.389948i | −0.980808 | − | 0.194974i | \(-0.937538\pi\) | ||
0.980808 | − | 0.194974i | \(-0.0624622\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42.0000 | 1.36338 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 4.00000i | − | 0.129641i | ||||||
\(953\) | 38.0000i | 1.23094i | 0.788160 | + | 0.615470i | \(0.211034\pi\) | ||||
−0.788160 | + | 0.615470i | \(0.788966\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 13.0000 | 0.420450 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.00000i | 0.129234i | ||||||||
\(959\) | −15.0000 | −0.484375 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.0000 | 0.580645 | ||||||||
\(962\) | 6.00000i | 0.193448i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.00000 | 0.0644157 | ||||||||
\(965\) | 2.00000 | + | 4.00000i | 0.0643823 | + | 0.128765i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.0000i | 0.932577i | 0.884633 | + | 0.466289i | \(0.154409\pi\) | ||||
−0.884633 | + | 0.466289i | \(0.845591\pi\) | |||||||
\(968\) | 5.00000i | 0.160706i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −20.0000 | + | 10.0000i | −0.642161 | + | 0.321081i | ||||
\(971\) | −33.0000 | −1.05902 | −0.529510 | − | 0.848304i | \(-0.677624\pi\) | ||||
−0.529510 | + | 0.848304i | \(0.677624\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 14.0000i | − | 0.448819i | ||||||
\(974\) | 21.0000 | 0.672883 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.00000 | −0.224065 | ||||||||
\(977\) | 18.0000i | 0.575871i | 0.957650 | + | 0.287936i | \(0.0929689\pi\) | ||||
−0.957650 | + | 0.287936i | \(0.907031\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 56.0000 | 1.78977 | ||||||||
\(980\) | 2.00000 | − | 1.00000i | 0.0638877 | − | 0.0319438i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 30.0000i | − | 0.957338i | ||||||
\(983\) | − | 52.0000i | − | 1.65854i | −0.558846 | − | 0.829271i | \(-0.688756\pi\) | ||
0.558846 | − | 0.829271i | \(-0.311244\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.00000 | − | 16.0000i | −0.254901 | − | 0.509802i | ||||
\(986\) | −12.0000 | −0.382158 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 40.0000 | 1.27193 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.00000 | −0.0635321 | −0.0317660 | − | 0.999495i | \(-0.510113\pi\) | ||||
−0.0317660 | + | 0.999495i | \(0.510113\pi\) | |||||||
\(992\) | − | 7.00000i | − | 0.222250i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.00000 | −0.0951542 | ||||||||
\(995\) | −48.0000 | + | 24.0000i | −1.52170 | + | 0.760851i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.0000i | 0.380044i | 0.981780 | + | 0.190022i | \(0.0608559\pi\) | ||||
−0.981780 | + | 0.190022i | \(0.939144\pi\) | |||||||
\(998\) | 9.00000i | 0.284890i | ||||||||
\(999\) | 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 | 1890.2.g.k.379.1 | yes | 2 | |
3.2 | odd | 2 | 1890.2.g.a.379.2 | yes | 2 | ||
5.2 | odd | 4 | 9450.2.a.dx.1.1 | 1 | |||
5.3 | odd | 4 | 9450.2.a.w.1.1 | 1 | |||
5.4 | even | 2 | inner | 1890.2.g.k.379.2 | yes | 2 | |
15.2 | even | 4 | 9450.2.a.be.1.1 | 1 | |||
15.8 | even | 4 | 9450.2.a.cc.1.1 | 1 | |||
15.14 | odd | 2 | 1890.2.g.a.379.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1890.2.g.a.379.1 | ✓ | 2 | 15.14 | odd | 2 | ||
1890.2.g.a.379.2 | yes | 2 | 3.2 | odd | 2 | ||
1890.2.g.k.379.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1890.2.g.k.379.2 | yes | 2 | 5.4 | even | 2 | inner | |
9450.2.a.w.1.1 | 1 | 5.3 | odd | 4 | |||
9450.2.a.be.1.1 | 1 | 15.2 | even | 4 | |||
9450.2.a.cc.1.1 | 1 | 15.8 | even | 4 | |||
9450.2.a.dx.1.1 | 1 | 5.2 | odd | 4 |