Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [390,2,Mod(79,390)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(390, 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("390.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 390.e (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: | \(3.11416567883\) |
Analytic rank: | \(1\) |
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 | 79.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 390.79 |
Dual form | 390.2.e.a.79.2 |
$q$-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 \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).
\(n\) | \(131\) | \(157\) | \(301\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||
\(11\) | −6.00000 | −1.80907 | −0.904534 | − | 0.426401i | \(-0.859781\pi\) | ||||
−0.904534 | + | 0.426401i | \(0.859781\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 1.00000i | 0.277350i | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | + | 2.00000i | 0.258199 | + | 0.516398i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | −6.00000 | −1.37649 | −0.688247 | − | 0.725476i | \(-0.741620\pi\) | ||||
−0.688247 | + | 0.725476i | \(0.741620\pi\) | |||||||
\(20\) | 2.00000 | − | 1.00000i | 0.447214 | − | 0.223607i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.00000i | 1.27920i | ||||||||
\(23\) | 6.00000i | 1.25109i | 0.780189 | + | 0.625543i | \(0.215123\pi\) | ||||
−0.780189 | + | 0.625543i | \(0.784877\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 3.00000 | − | 4.00000i | 0.600000 | − | 0.800000i | ||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 2.00000 | − | 1.00000i | 0.365148 | − | 0.182574i | ||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 6.00000i | 1.04447i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | − | 10.0000i | − | 1.64399i | −0.569495 | − | 0.821995i | \(-0.692861\pi\) | ||
0.569495 | − | 0.821995i | \(-0.307139\pi\) | |||||||
\(38\) | 6.00000i | 0.973329i | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −1.00000 | − | 2.00000i | −0.158114 | − | 0.316228i | ||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000i | 1.21999i | 0.792406 | + | 0.609994i | \(0.208828\pi\) | ||||
−0.792406 | + | 0.609994i | \(0.791172\pi\) | |||||||
\(44\) | 6.00000 | 0.904534 | ||||||||
\(45\) | 2.00000 | − | 1.00000i | 0.298142 | − | 0.149071i | ||||
\(46\) | 6.00000 | 0.884652 | ||||||||
\(47\) | − | 8.00000i | − | 1.16692i | −0.812142 | − | 0.583460i | \(-0.801699\pi\) | ||
0.812142 | − | 0.583460i | \(-0.198301\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 7.00000 | 1.00000 | ||||||||
\(50\) | −4.00000 | − | 3.00000i | −0.565685 | − | 0.424264i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 1.00000i | − | 0.138675i | ||||||
\(53\) | − | 6.00000i | − | 0.824163i | −0.911147 | − | 0.412082i | \(-0.864802\pi\) | ||
0.911147 | − | 0.412082i | \(-0.135198\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 12.0000 | − | 6.00000i | 1.61808 | − | 0.809040i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.00000i | 0.794719i | ||||||||
\(58\) | 2.00000i | 0.262613i | ||||||||
\(59\) | −10.0000 | −1.30189 | −0.650945 | − | 0.759125i | \(-0.725627\pi\) | ||||
−0.650945 | + | 0.759125i | \(0.725627\pi\) | |||||||
\(60\) | −1.00000 | − | 2.00000i | −0.129099 | − | 0.258199i | ||||
\(61\) | −6.00000 | −0.768221 | −0.384111 | − | 0.923287i | \(-0.625492\pi\) | ||||
−0.384111 | + | 0.923287i | \(0.625492\pi\) | |||||||
\(62\) | − | 4.00000i | − | 0.508001i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −1.00000 | − | 2.00000i | −0.124035 | − | 0.248069i | ||||
\(66\) | 6.00000 | 0.738549 | ||||||||
\(67\) | − | 4.00000i | − | 0.488678i | −0.969690 | − | 0.244339i | \(-0.921429\pi\) | ||
0.969690 | − | 0.244339i | \(-0.0785709\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.00000 | 0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | − | 1.00000i | − | 0.117851i | ||||||
\(73\) | 6.00000i | 0.702247i | 0.936329 | + | 0.351123i | \(0.114200\pi\) | ||||
−0.936329 | + | 0.351123i | \(0.885800\pi\) | |||||||
\(74\) | −10.0000 | −1.16248 | ||||||||
\(75\) | −4.00000 | − | 3.00000i | −0.461880 | − | 0.346410i | ||||
\(76\) | 6.00000 | 0.688247 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 1.00000i | − | 0.113228i | ||||||
\(79\) | −16.0000 | −1.80014 | −0.900070 | − | 0.435745i | \(-0.856485\pi\) | ||||
−0.900070 | + | 0.435745i | \(0.856485\pi\) | |||||||
\(80\) | −2.00000 | + | 1.00000i | −0.223607 | + | 0.111803i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.00000i | 0.662589i | ||||||||
\(83\) | 4.00000i | 0.439057i | 0.975606 | + | 0.219529i | \(0.0704519\pi\) | ||||
−0.975606 | + | 0.219529i | \(0.929548\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.00000 | 0.862662 | ||||||||
\(87\) | 2.00000i | 0.214423i | ||||||||
\(88\) | − | 6.00000i | − | 0.639602i | ||||||
\(89\) | 10.0000 | 1.06000 | 0.529999 | − | 0.847998i | \(-0.322192\pi\) | ||||
0.529999 | + | 0.847998i | \(0.322192\pi\) | |||||||
\(90\) | −1.00000 | − | 2.00000i | −0.105409 | − | 0.210819i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 6.00000i | − | 0.625543i | ||||||
\(93\) | − | 4.00000i | − | 0.414781i | ||||||
\(94\) | −8.00000 | −0.825137 | ||||||||
\(95\) | 12.0000 | − | 6.00000i | 1.23117 | − | 0.615587i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | − | 2.00000i | − | 0.203069i | −0.994832 | − | 0.101535i | \(-0.967625\pi\) | ||
0.994832 | − | 0.101535i | \(-0.0323753\pi\) | |||||||
\(98\) | − | 7.00000i | − | 0.707107i | ||||||
\(99\) | 6.00000 | 0.603023 | ||||||||
\(100\) | −3.00000 | + | 4.00000i | −0.300000 | + | 0.400000i | ||||
\(101\) | −2.00000 | −0.199007 | −0.0995037 | − | 0.995037i | \(-0.531726\pi\) | ||||
−0.0995037 | + | 0.995037i | \(0.531726\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 10.0000i | − | 0.985329i | −0.870219 | − | 0.492665i | \(-0.836023\pi\) | ||
0.870219 | − | 0.492665i | \(-0.163977\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | − | 16.0000i | − | 1.54678i | −0.633932 | − | 0.773389i | \(-0.718560\pi\) | ||
0.633932 | − | 0.773389i | \(-0.281440\pi\) | |||||||
\(108\) | − | 1.00000i | − | 0.0962250i | ||||||
\(109\) | 16.0000 | 1.53252 | 0.766261 | − | 0.642529i | \(-0.222115\pi\) | ||||
0.766261 | + | 0.642529i | \(0.222115\pi\) | |||||||
\(110\) | −6.00000 | − | 12.0000i | −0.572078 | − | 1.14416i | ||||
\(111\) | −10.0000 | −0.949158 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.00000i | 0.752577i | 0.926503 | + | 0.376288i | \(0.122800\pi\) | ||||
−0.926503 | + | 0.376288i | \(0.877200\pi\) | |||||||
\(114\) | 6.00000 | 0.561951 | ||||||||
\(115\) | −6.00000 | − | 12.0000i | −0.559503 | − | 1.11901i | ||||
\(116\) | 2.00000 | 0.185695 | ||||||||
\(117\) | − | 1.00000i | − | 0.0924500i | ||||||
\(118\) | 10.0000i | 0.920575i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.00000 | + | 1.00000i | −0.182574 | + | 0.0912871i | ||||
\(121\) | 25.0000 | 2.27273 | ||||||||
\(122\) | 6.00000i | 0.543214i | ||||||||
\(123\) | 6.00000i | 0.541002i | ||||||||
\(124\) | −4.00000 | −0.359211 | ||||||||
\(125\) | −2.00000 | + | 11.0000i | −0.178885 | + | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.0000i | 1.59724i | 0.601834 | + | 0.798621i | \(0.294437\pi\) | ||||
−0.601834 | + | 0.798621i | \(0.705563\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 8.00000 | 0.704361 | ||||||||
\(130\) | −2.00000 | + | 1.00000i | −0.175412 | + | 0.0877058i | ||||
\(131\) | 12.0000 | 1.04844 | 0.524222 | − | 0.851581i | \(-0.324356\pi\) | ||||
0.524222 | + | 0.851581i | \(0.324356\pi\) | |||||||
\(132\) | − | 6.00000i | − | 0.522233i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.00000 | −0.345547 | ||||||||
\(135\) | −1.00000 | − | 2.00000i | −0.0860663 | − | 0.172133i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 2.00000i | − | 0.170872i | −0.996344 | − | 0.0854358i | \(-0.972772\pi\) | ||
0.996344 | − | 0.0854358i | \(-0.0272282\pi\) | |||||||
\(138\) | − | 6.00000i | − | 0.510754i | ||||||
\(139\) | −8.00000 | −0.678551 | −0.339276 | − | 0.940687i | \(-0.610182\pi\) | ||||
−0.339276 | + | 0.940687i | \(0.610182\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.00000 | −0.673722 | ||||||||
\(142\) | 8.00000i | 0.671345i | ||||||||
\(143\) | − | 6.00000i | − | 0.501745i | ||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 4.00000 | − | 2.00000i | 0.332182 | − | 0.166091i | ||||
\(146\) | 6.00000 | 0.496564 | ||||||||
\(147\) | − | 7.00000i | − | 0.577350i | ||||||
\(148\) | 10.0000i | 0.821995i | ||||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | −3.00000 | + | 4.00000i | −0.244949 | + | 0.326599i | ||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | − | 6.00000i | − | 0.486664i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.00000 | + | 4.00000i | −0.642575 | + | 0.321288i | ||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | 2.00000i | 0.159617i | 0.996810 | + | 0.0798087i | \(0.0254309\pi\) | ||||
−0.996810 | + | 0.0798087i | \(0.974569\pi\) | |||||||
\(158\) | 16.0000i | 1.27289i | ||||||||
\(159\) | −6.00000 | −0.475831 | ||||||||
\(160\) | 1.00000 | + | 2.00000i | 0.0790569 | + | 0.158114i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | 12.0000i | 0.939913i | 0.882690 | + | 0.469956i | \(0.155730\pi\) | ||||
−0.882690 | + | 0.469956i | \(0.844270\pi\) | |||||||
\(164\) | 6.00000 | 0.468521 | ||||||||
\(165\) | −6.00000 | − | 12.0000i | −0.467099 | − | 0.934199i | ||||
\(166\) | 4.00000 | 0.310460 | ||||||||
\(167\) | − | 8.00000i | − | 0.619059i | −0.950890 | − | 0.309529i | \(-0.899829\pi\) | ||
0.950890 | − | 0.309529i | \(-0.100171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.00000 | 0.458831 | ||||||||
\(172\) | − | 8.00000i | − | 0.609994i | ||||||
\(173\) | 18.0000i | 1.36851i | 0.729241 | + | 0.684257i | \(0.239873\pi\) | ||||
−0.729241 | + | 0.684257i | \(0.760127\pi\) | |||||||
\(174\) | 2.00000 | 0.151620 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.00000 | −0.452267 | ||||||||
\(177\) | 10.0000i | 0.751646i | ||||||||
\(178\) | − | 10.0000i | − | 0.749532i | ||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | −2.00000 | + | 1.00000i | −0.149071 | + | 0.0745356i | ||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.00000i | 0.443533i | ||||||||
\(184\) | −6.00000 | −0.442326 | ||||||||
\(185\) | 10.0000 | + | 20.0000i | 0.735215 | + | 1.47043i | ||||
\(186\) | −4.00000 | −0.293294 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 8.00000i | 0.583460i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.00000 | − | 12.0000i | −0.435286 | − | 0.870572i | ||||
\(191\) | −8.00000 | −0.578860 | −0.289430 | − | 0.957199i | \(-0.593466\pi\) | ||||
−0.289430 | + | 0.957199i | \(0.593466\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | 10.0000i | 0.719816i | 0.932988 | + | 0.359908i | \(0.117192\pi\) | ||||
−0.932988 | + | 0.359908i | \(0.882808\pi\) | |||||||
\(194\) | −2.00000 | −0.143592 | ||||||||
\(195\) | −2.00000 | + | 1.00000i | −0.143223 | + | 0.0716115i | ||||
\(196\) | −7.00000 | −0.500000 | ||||||||
\(197\) | 22.0000i | 1.56744i | 0.621117 | + | 0.783718i | \(0.286679\pi\) | ||||
−0.621117 | + | 0.783718i | \(0.713321\pi\) | |||||||
\(198\) | − | 6.00000i | − | 0.426401i | ||||||
\(199\) | −16.0000 | −1.13421 | −0.567105 | − | 0.823646i | \(-0.691937\pi\) | ||||
−0.567105 | + | 0.823646i | \(0.691937\pi\) | |||||||
\(200\) | 4.00000 | + | 3.00000i | 0.282843 | + | 0.212132i | ||||
\(201\) | −4.00000 | −0.282138 | ||||||||
\(202\) | 2.00000i | 0.140720i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.0000 | − | 6.00000i | 0.838116 | − | 0.419058i | ||||
\(206\) | −10.0000 | −0.696733 | ||||||||
\(207\) | − | 6.00000i | − | 0.417029i | ||||||
\(208\) | 1.00000i | 0.0693375i | ||||||||
\(209\) | 36.0000 | 2.49017 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | 6.00000i | 0.412082i | ||||||||
\(213\) | 8.00000i | 0.548151i | ||||||||
\(214\) | −16.0000 | −1.09374 | ||||||||
\(215\) | −8.00000 | − | 16.0000i | −0.545595 | − | 1.09119i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 16.0000i | − | 1.08366i | ||||||
\(219\) | 6.00000 | 0.405442 | ||||||||
\(220\) | −12.0000 | + | 6.00000i | −0.809040 | + | 0.404520i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 10.0000i | 0.671156i | ||||||||
\(223\) | 4.00000i | 0.267860i | 0.990991 | + | 0.133930i | \(0.0427597\pi\) | ||||
−0.990991 | + | 0.133930i | \(0.957240\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.00000 | + | 4.00000i | −0.200000 | + | 0.266667i | ||||
\(226\) | 8.00000 | 0.532152 | ||||||||
\(227\) | 20.0000i | 1.32745i | 0.747978 | + | 0.663723i | \(0.231025\pi\) | ||||
−0.747978 | + | 0.663723i | \(0.768975\pi\) | |||||||
\(228\) | − | 6.00000i | − | 0.397360i | ||||||
\(229\) | −20.0000 | −1.32164 | −0.660819 | − | 0.750546i | \(-0.729791\pi\) | ||||
−0.660819 | + | 0.750546i | \(0.729791\pi\) | |||||||
\(230\) | −12.0000 | + | 6.00000i | −0.791257 | + | 0.395628i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 2.00000i | − | 0.131306i | ||||||
\(233\) | − | 8.00000i | − | 0.524097i | −0.965055 | − | 0.262049i | \(-0.915602\pi\) | ||
0.965055 | − | 0.262049i | \(-0.0843981\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | 8.00000 | + | 16.0000i | 0.521862 | + | 1.04372i | ||||
\(236\) | 10.0000 | 0.650945 | ||||||||
\(237\) | 16.0000i | 1.03931i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28.0000 | 1.81117 | 0.905585 | − | 0.424165i | \(-0.139432\pi\) | ||||
0.905585 | + | 0.424165i | \(0.139432\pi\) | |||||||
\(240\) | 1.00000 | + | 2.00000i | 0.0645497 | + | 0.129099i | ||||
\(241\) | −22.0000 | −1.41714 | −0.708572 | − | 0.705638i | \(-0.750660\pi\) | ||||
−0.708572 | + | 0.705638i | \(0.750660\pi\) | |||||||
\(242\) | − | 25.0000i | − | 1.60706i | ||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 6.00000 | 0.384111 | ||||||||
\(245\) | −14.0000 | + | 7.00000i | −0.894427 | + | 0.447214i | ||||
\(246\) | 6.00000 | 0.382546 | ||||||||
\(247\) | − | 6.00000i | − | 0.381771i | ||||||
\(248\) | 4.00000i | 0.254000i | ||||||||
\(249\) | 4.00000 | 0.253490 | ||||||||
\(250\) | 11.0000 | + | 2.00000i | 0.695701 | + | 0.126491i | ||||
\(251\) | 8.00000 | 0.504956 | 0.252478 | − | 0.967603i | \(-0.418755\pi\) | ||||
0.252478 | + | 0.967603i | \(0.418755\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 36.0000i | − | 2.26330i | ||||||
\(254\) | 18.0000 | 1.12942 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 24.0000i | 1.49708i | 0.663090 | + | 0.748539i | \(0.269245\pi\) | ||||
−0.663090 | + | 0.748539i | \(0.730755\pi\) | |||||||
\(258\) | − | 8.00000i | − | 0.498058i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.00000 | + | 2.00000i | 0.0620174 | + | 0.124035i | ||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | − | 12.0000i | − | 0.741362i | ||||||
\(263\) | − | 6.00000i | − | 0.369976i | −0.982741 | − | 0.184988i | \(-0.940775\pi\) | ||
0.982741 | − | 0.184988i | \(-0.0592246\pi\) | |||||||
\(264\) | −6.00000 | −0.369274 | ||||||||
\(265\) | 6.00000 | + | 12.0000i | 0.368577 | + | 0.737154i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 10.0000i | − | 0.611990i | ||||||
\(268\) | 4.00000i | 0.244339i | ||||||||
\(269\) | −14.0000 | −0.853595 | −0.426798 | − | 0.904347i | \(-0.640358\pi\) | ||||
−0.426798 | + | 0.904347i | \(0.640358\pi\) | |||||||
\(270\) | −2.00000 | + | 1.00000i | −0.121716 | + | 0.0608581i | ||||
\(271\) | −16.0000 | −0.971931 | −0.485965 | − | 0.873978i | \(-0.661532\pi\) | ||||
−0.485965 | + | 0.873978i | \(0.661532\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.00000 | −0.120824 | ||||||||
\(275\) | −18.0000 | + | 24.0000i | −1.08544 | + | 1.44725i | ||||
\(276\) | −6.00000 | −0.361158 | ||||||||
\(277\) | − | 26.0000i | − | 1.56219i | −0.624413 | − | 0.781094i | \(-0.714662\pi\) | ||
0.624413 | − | 0.781094i | \(-0.285338\pi\) | |||||||
\(278\) | 8.00000i | 0.479808i | ||||||||
\(279\) | −4.00000 | −0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.0000 | −0.596550 | −0.298275 | − | 0.954480i | \(-0.596411\pi\) | ||||
−0.298275 | + | 0.954480i | \(0.596411\pi\) | |||||||
\(282\) | 8.00000i | 0.476393i | ||||||||
\(283\) | − | 4.00000i | − | 0.237775i | −0.992908 | − | 0.118888i | \(-0.962067\pi\) | ||
0.992908 | − | 0.118888i | \(-0.0379328\pi\) | |||||||
\(284\) | 8.00000 | 0.474713 | ||||||||
\(285\) | −6.00000 | − | 12.0000i | −0.355409 | − | 0.710819i | ||||
\(286\) | −6.00000 | −0.354787 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 17.0000 | 1.00000 | ||||||||
\(290\) | −2.00000 | − | 4.00000i | −0.117444 | − | 0.234888i | ||||
\(291\) | −2.00000 | −0.117242 | ||||||||
\(292\) | − | 6.00000i | − | 0.351123i | ||||||
\(293\) | − | 14.0000i | − | 0.817889i | −0.912559 | − | 0.408944i | \(-0.865897\pi\) | ||
0.912559 | − | 0.408944i | \(-0.134103\pi\) | |||||||
\(294\) | −7.00000 | −0.408248 | ||||||||
\(295\) | 20.0000 | − | 10.0000i | 1.16445 | − | 0.582223i | ||||
\(296\) | 10.0000 | 0.581238 | ||||||||
\(297\) | − | 6.00000i | − | 0.348155i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.00000 | −0.346989 | ||||||||
\(300\) | 4.00000 | + | 3.00000i | 0.230940 | + | 0.173205i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.00000i | 0.460348i | ||||||||
\(303\) | 2.00000i | 0.114897i | ||||||||
\(304\) | −6.00000 | −0.344124 | ||||||||
\(305\) | 12.0000 | − | 6.00000i | 0.687118 | − | 0.343559i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.0000i | 1.59804i | 0.601302 | + | 0.799022i | \(0.294649\pi\) | ||||
−0.601302 | + | 0.799022i | \(0.705351\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.0000 | −0.568880 | ||||||||
\(310\) | 4.00000 | + | 8.00000i | 0.227185 | + | 0.454369i | ||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 1.00000i | 0.0566139i | ||||||||
\(313\) | − | 16.0000i | − | 0.904373i | −0.891923 | − | 0.452187i | \(-0.850644\pi\) | ||
0.891923 | − | 0.452187i | \(-0.149356\pi\) | |||||||
\(314\) | 2.00000 | 0.112867 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.0000 | 0.900070 | ||||||||
\(317\) | − | 18.0000i | − | 1.01098i | −0.862832 | − | 0.505490i | \(-0.831312\pi\) | ||
0.862832 | − | 0.505490i | \(-0.168688\pi\) | |||||||
\(318\) | 6.00000i | 0.336463i | ||||||||
\(319\) | 12.0000 | 0.671871 | ||||||||
\(320\) | 2.00000 | − | 1.00000i | 0.111803 | − | 0.0559017i | ||||
\(321\) | −16.0000 | −0.893033 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 4.00000 | + | 3.00000i | 0.221880 | + | 0.166410i | ||||
\(326\) | 12.0000 | 0.664619 | ||||||||
\(327\) | − | 16.0000i | − | 0.884802i | ||||||
\(328\) | − | 6.00000i | − | 0.331295i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −12.0000 | + | 6.00000i | −0.660578 | + | 0.330289i | ||||
\(331\) | −26.0000 | −1.42909 | −0.714545 | − | 0.699590i | \(-0.753366\pi\) | ||||
−0.714545 | + | 0.699590i | \(0.753366\pi\) | |||||||
\(332\) | − | 4.00000i | − | 0.219529i | ||||||
\(333\) | 10.0000i | 0.547997i | ||||||||
\(334\) | −8.00000 | −0.437741 | ||||||||
\(335\) | 4.00000 | + | 8.00000i | 0.218543 | + | 0.437087i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 8.00000i | − | 0.435788i | −0.975972 | − | 0.217894i | \(-0.930081\pi\) | ||
0.975972 | − | 0.217894i | \(-0.0699187\pi\) | |||||||
\(338\) | 1.00000i | 0.0543928i | ||||||||
\(339\) | 8.00000 | 0.434500 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.0000 | −1.29967 | ||||||||
\(342\) | − | 6.00000i | − | 0.324443i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −8.00000 | −0.431331 | ||||||||
\(345\) | −12.0000 | + | 6.00000i | −0.646058 | + | 0.323029i | ||||
\(346\) | 18.0000 | 0.967686 | ||||||||
\(347\) | − | 32.0000i | − | 1.71785i | −0.512101 | − | 0.858925i | \(-0.671133\pi\) | ||
0.512101 | − | 0.858925i | \(-0.328867\pi\) | |||||||
\(348\) | − | 2.00000i | − | 0.107211i | ||||||
\(349\) | −8.00000 | −0.428230 | −0.214115 | − | 0.976808i | \(-0.568687\pi\) | ||||
−0.214115 | + | 0.976808i | \(0.568687\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 6.00000i | 0.319801i | ||||||||
\(353\) | − | 10.0000i | − | 0.532246i | −0.963939 | − | 0.266123i | \(-0.914257\pi\) | ||
0.963939 | − | 0.266123i | \(-0.0857428\pi\) | |||||||
\(354\) | 10.0000 | 0.531494 | ||||||||
\(355\) | 16.0000 | − | 8.00000i | 0.849192 | − | 0.424596i | ||||
\(356\) | −10.0000 | −0.529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 12.0000i | − | 0.634220i | ||||||
\(359\) | 12.0000 | 0.633336 | 0.316668 | − | 0.948536i | \(-0.397436\pi\) | ||||
0.316668 | + | 0.948536i | \(0.397436\pi\) | |||||||
\(360\) | 1.00000 | + | 2.00000i | 0.0527046 | + | 0.105409i | ||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | 2.00000i | 0.105118i | ||||||||
\(363\) | − | 25.0000i | − | 1.31216i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.00000 | − | 12.0000i | −0.314054 | − | 0.628109i | ||||
\(366\) | 6.00000 | 0.313625 | ||||||||
\(367\) | − | 6.00000i | − | 0.313197i | −0.987662 | − | 0.156599i | \(-0.949947\pi\) | ||
0.987662 | − | 0.156599i | \(-0.0500529\pi\) | |||||||
\(368\) | 6.00000i | 0.312772i | ||||||||
\(369\) | 6.00000 | 0.312348 | ||||||||
\(370\) | 20.0000 | − | 10.0000i | 1.03975 | − | 0.519875i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.00000i | 0.207390i | ||||||||
\(373\) | − | 10.0000i | − | 0.517780i | −0.965907 | − | 0.258890i | \(-0.916643\pi\) | ||
0.965907 | − | 0.258890i | \(-0.0833568\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.0000 | + | 2.00000i | 0.568038 | + | 0.103280i | ||||
\(376\) | 8.00000 | 0.412568 | ||||||||
\(377\) | − | 2.00000i | − | 0.103005i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.0000 | −1.13006 | −0.565032 | − | 0.825069i | \(-0.691136\pi\) | ||||
−0.565032 | + | 0.825069i | \(0.691136\pi\) | |||||||
\(380\) | −12.0000 | + | 6.00000i | −0.615587 | + | 0.307794i | ||||
\(381\) | 18.0000 | 0.922168 | ||||||||
\(382\) | 8.00000i | 0.409316i | ||||||||
\(383\) | − | 20.0000i | − | 1.02195i | −0.859595 | − | 0.510976i | \(-0.829284\pi\) | ||
0.859595 | − | 0.510976i | \(-0.170716\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10.0000 | 0.508987 | ||||||||
\(387\) | − | 8.00000i | − | 0.406663i | ||||||
\(388\) | 2.00000i | 0.101535i | ||||||||
\(389\) | 14.0000 | 0.709828 | 0.354914 | − | 0.934899i | \(-0.384510\pi\) | ||||
0.354914 | + | 0.934899i | \(0.384510\pi\) | |||||||
\(390\) | 1.00000 | + | 2.00000i | 0.0506370 | + | 0.101274i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 7.00000i | 0.353553i | ||||||||
\(393\) | − | 12.0000i | − | 0.605320i | ||||||
\(394\) | 22.0000 | 1.10834 | ||||||||
\(395\) | 32.0000 | − | 16.0000i | 1.61009 | − | 0.805047i | ||||
\(396\) | −6.00000 | −0.301511 | ||||||||
\(397\) | 18.0000i | 0.903394i | 0.892171 | + | 0.451697i | \(0.149181\pi\) | ||||
−0.892171 | + | 0.451697i | \(0.850819\pi\) | |||||||
\(398\) | 16.0000i | 0.802008i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | − | 4.00000i | 0.150000 | − | 0.200000i | ||||
\(401\) | 14.0000 | 0.699127 | 0.349563 | − | 0.936913i | \(-0.386330\pi\) | ||||
0.349563 | + | 0.936913i | \(0.386330\pi\) | |||||||
\(402\) | 4.00000i | 0.199502i | ||||||||
\(403\) | 4.00000i | 0.199254i | ||||||||
\(404\) | 2.00000 | 0.0995037 | ||||||||
\(405\) | −2.00000 | + | 1.00000i | −0.0993808 | + | 0.0496904i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 60.0000i | 2.97409i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −30.0000 | −1.48340 | −0.741702 | − | 0.670729i | \(-0.765981\pi\) | ||||
−0.741702 | + | 0.670729i | \(0.765981\pi\) | |||||||
\(410\) | −6.00000 | − | 12.0000i | −0.296319 | − | 0.592638i | ||||
\(411\) | −2.00000 | −0.0986527 | ||||||||
\(412\) | 10.0000i | 0.492665i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −6.00000 | −0.294884 | ||||||||
\(415\) | −4.00000 | − | 8.00000i | −0.196352 | − | 0.392705i | ||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | 8.00000i | 0.391762i | ||||||||
\(418\) | − | 36.0000i | − | 1.76082i | ||||||
\(419\) | −28.0000 | −1.36789 | −0.683945 | − | 0.729534i | \(-0.739737\pi\) | ||||
−0.683945 | + | 0.729534i | \(0.739737\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.00000 | −0.389896 | −0.194948 | − | 0.980814i | \(-0.562454\pi\) | ||||
−0.194948 | + | 0.980814i | \(0.562454\pi\) | |||||||
\(422\) | − | 4.00000i | − | 0.194717i | ||||||
\(423\) | 8.00000i | 0.388973i | ||||||||
\(424\) | 6.00000 | 0.291386 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8.00000 | 0.387601 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 16.0000i | 0.773389i | ||||||||
\(429\) | −6.00000 | −0.289683 | ||||||||
\(430\) | −16.0000 | + | 8.00000i | −0.771589 | + | 0.385794i | ||||
\(431\) | −8.00000 | −0.385346 | −0.192673 | − | 0.981263i | \(-0.561716\pi\) | ||||
−0.192673 | + | 0.981263i | \(0.561716\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | 24.0000i | 1.15337i | 0.816968 | + | 0.576683i | \(0.195653\pi\) | ||||
−0.816968 | + | 0.576683i | \(0.804347\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.00000 | − | 4.00000i | −0.0958927 | − | 0.191785i | ||||
\(436\) | −16.0000 | −0.766261 | ||||||||
\(437\) | − | 36.0000i | − | 1.72211i | ||||||
\(438\) | − | 6.00000i | − | 0.286691i | ||||||
\(439\) | −16.0000 | −0.763638 | −0.381819 | − | 0.924237i | \(-0.624702\pi\) | ||||
−0.381819 | + | 0.924237i | \(0.624702\pi\) | |||||||
\(440\) | 6.00000 | + | 12.0000i | 0.286039 | + | 0.572078i | ||||
\(441\) | −7.00000 | −0.333333 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 32.0000i | − | 1.52037i | −0.649709 | − | 0.760183i | \(-0.725109\pi\) | ||
0.649709 | − | 0.760183i | \(-0.274891\pi\) | |||||||
\(444\) | 10.0000 | 0.474579 | ||||||||
\(445\) | −20.0000 | + | 10.0000i | −0.948091 | + | 0.474045i | ||||
\(446\) | 4.00000 | 0.189405 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 34.0000 | 1.60456 | 0.802280 | − | 0.596948i | \(-0.203620\pi\) | ||||
0.802280 | + | 0.596948i | \(0.203620\pi\) | |||||||
\(450\) | 4.00000 | + | 3.00000i | 0.188562 | + | 0.141421i | ||||
\(451\) | 36.0000 | 1.69517 | ||||||||
\(452\) | − | 8.00000i | − | 0.376288i | ||||||
\(453\) | 8.00000i | 0.375873i | ||||||||
\(454\) | 20.0000 | 0.938647 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.00000 | −0.280976 | ||||||||
\(457\) | − | 18.0000i | − | 0.842004i | −0.907060 | − | 0.421002i | \(-0.861678\pi\) | ||
0.907060 | − | 0.421002i | \(-0.138322\pi\) | |||||||
\(458\) | 20.0000i | 0.934539i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.00000 | + | 12.0000i | 0.279751 | + | 0.559503i | ||||
\(461\) | 36.0000 | 1.67669 | 0.838344 | − | 0.545142i | \(-0.183524\pi\) | ||||
0.838344 | + | 0.545142i | \(0.183524\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 16.0000i | − | 0.743583i | −0.928316 | − | 0.371792i | \(-0.878744\pi\) | ||
0.928316 | − | 0.371792i | \(-0.121256\pi\) | |||||||
\(464\) | −2.00000 | −0.0928477 | ||||||||
\(465\) | 4.00000 | + | 8.00000i | 0.185496 | + | 0.370991i | ||||
\(466\) | −8.00000 | −0.370593 | ||||||||
\(467\) | 40.0000i | 1.85098i | 0.378773 | + | 0.925490i | \(0.376346\pi\) | ||||
−0.378773 | + | 0.925490i | \(0.623654\pi\) | |||||||
\(468\) | 1.00000i | 0.0462250i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 16.0000 | − | 8.00000i | 0.738025 | − | 0.369012i | ||||
\(471\) | 2.00000 | 0.0921551 | ||||||||
\(472\) | − | 10.0000i | − | 0.460287i | ||||||
\(473\) | − | 48.0000i | − | 2.20704i | ||||||
\(474\) | 16.0000 | 0.734904 | ||||||||
\(475\) | −18.0000 | + | 24.0000i | −0.825897 | + | 1.10120i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.00000i | 0.274721i | ||||||||
\(478\) | − | 28.0000i | − | 1.28069i | ||||||
\(479\) | −20.0000 | −0.913823 | −0.456912 | − | 0.889512i | \(-0.651044\pi\) | ||||
−0.456912 | + | 0.889512i | \(0.651044\pi\) | |||||||
\(480\) | 2.00000 | − | 1.00000i | 0.0912871 | − | 0.0456435i | ||||
\(481\) | 10.0000 | 0.455961 | ||||||||
\(482\) | 22.0000i | 1.00207i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −25.0000 | −1.13636 | ||||||||
\(485\) | 2.00000 | + | 4.00000i | 0.0908153 | + | 0.181631i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 12.0000i | 0.543772i | 0.962329 | + | 0.271886i | \(0.0876473\pi\) | ||||
−0.962329 | + | 0.271886i | \(0.912353\pi\) | |||||||
\(488\) | − | 6.00000i | − | 0.271607i | ||||||
\(489\) | 12.0000 | 0.542659 | ||||||||
\(490\) | 7.00000 | + | 14.0000i | 0.316228 | + | 0.632456i | ||||
\(491\) | −12.0000 | −0.541552 | −0.270776 | − | 0.962642i | \(-0.587280\pi\) | ||||
−0.270776 | + | 0.962642i | \(0.587280\pi\) | |||||||
\(492\) | − | 6.00000i | − | 0.270501i | ||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −6.00000 | −0.269953 | ||||||||
\(495\) | −12.0000 | + | 6.00000i | −0.539360 | + | 0.269680i | ||||
\(496\) | 4.00000 | 0.179605 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | − | 4.00000i | − | 0.179244i | ||||||
\(499\) | 6.00000 | 0.268597 | 0.134298 | − | 0.990941i | \(-0.457122\pi\) | ||||
0.134298 | + | 0.990941i | \(0.457122\pi\) | |||||||
\(500\) | 2.00000 | − | 11.0000i | 0.0894427 | − | 0.491935i | ||||
\(501\) | −8.00000 | −0.357414 | ||||||||
\(502\) | − | 8.00000i | − | 0.357057i | ||||||
\(503\) | − | 26.0000i | − | 1.15928i | −0.814872 | − | 0.579641i | \(-0.803193\pi\) | ||
0.814872 | − | 0.579641i | \(-0.196807\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.00000 | − | 2.00000i | 0.177998 | − | 0.0889988i | ||||
\(506\) | −36.0000 | −1.60040 | ||||||||
\(507\) | 1.00000i | 0.0444116i | ||||||||
\(508\) | − | 18.0000i | − | 0.798621i | ||||||
\(509\) | −24.0000 | −1.06378 | −0.531891 | − | 0.846813i | \(-0.678518\pi\) | ||||
−0.531891 | + | 0.846813i | \(0.678518\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | − | 6.00000i | − | 0.264906i | ||||||
\(514\) | 24.0000 | 1.05859 | ||||||||
\(515\) | 10.0000 | + | 20.0000i | 0.440653 | + | 0.881305i | ||||
\(516\) | −8.00000 | −0.352180 | ||||||||
\(517\) | 48.0000i | 2.11104i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.0000 | 0.790112 | ||||||||
\(520\) | 2.00000 | − | 1.00000i | 0.0877058 | − | 0.0438529i | ||||
\(521\) | −10.0000 | −0.438108 | −0.219054 | − | 0.975713i | \(-0.570297\pi\) | ||||
−0.219054 | + | 0.975713i | \(0.570297\pi\) | |||||||
\(522\) | − | 2.00000i | − | 0.0875376i | ||||||
\(523\) | 40.0000i | 1.74908i | 0.484955 | + | 0.874539i | \(0.338836\pi\) | ||||
−0.484955 | + | 0.874539i | \(0.661164\pi\) | |||||||
\(524\) | −12.0000 | −0.524222 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.00000 | −0.261612 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 6.00000i | 0.261116i | ||||||||
\(529\) | −13.0000 | −0.565217 | ||||||||
\(530\) | 12.0000 | − | 6.00000i | 0.521247 | − | 0.260623i | ||||
\(531\) | 10.0000 | 0.433963 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 6.00000i | − | 0.259889i | ||||||
\(534\) | −10.0000 | −0.432742 | ||||||||
\(535\) | 16.0000 | + | 32.0000i | 0.691740 | + | 1.38348i | ||||
\(536\) | 4.00000 | 0.172774 | ||||||||
\(537\) | − | 12.0000i | − | 0.517838i | ||||||
\(538\) | 14.0000i | 0.603583i | ||||||||
\(539\) | −42.0000 | −1.80907 | ||||||||
\(540\) | 1.00000 | + | 2.00000i | 0.0430331 | + | 0.0860663i | ||||
\(541\) | 4.00000 | 0.171973 | 0.0859867 | − | 0.996296i | \(-0.472596\pi\) | ||||
0.0859867 | + | 0.996296i | \(0.472596\pi\) | |||||||
\(542\) | 16.0000i | 0.687259i | ||||||||
\(543\) | 2.00000i | 0.0858282i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −32.0000 | + | 16.0000i | −1.37073 | + | 0.685365i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 12.0000i | − | 0.513083i | −0.966533 | − | 0.256541i | \(-0.917417\pi\) | ||
0.966533 | − | 0.256541i | \(-0.0825830\pi\) | |||||||
\(548\) | 2.00000i | 0.0854358i | ||||||||
\(549\) | 6.00000 | 0.256074 | ||||||||
\(550\) | 24.0000 | + | 18.0000i | 1.02336 | + | 0.767523i | ||||
\(551\) | 12.0000 | 0.511217 | ||||||||
\(552\) | 6.00000i | 0.255377i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −26.0000 | −1.10463 | ||||||||
\(555\) | 20.0000 | − | 10.0000i | 0.848953 | − | 0.424476i | ||||
\(556\) | 8.00000 | 0.339276 | ||||||||
\(557\) | 2.00000i | 0.0847427i | 0.999102 | + | 0.0423714i | \(0.0134913\pi\) | ||||
−0.999102 | + | 0.0423714i | \(0.986509\pi\) | |||||||
\(558\) | 4.00000i | 0.169334i | ||||||||
\(559\) | −8.00000 | −0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10.0000i | 0.421825i | ||||||||
\(563\) | − | 24.0000i | − | 1.01148i | −0.862686 | − | 0.505740i | \(-0.831220\pi\) | ||
0.862686 | − | 0.505740i | \(-0.168780\pi\) | |||||||
\(564\) | 8.00000 | 0.336861 | ||||||||
\(565\) | −8.00000 | − | 16.0000i | −0.336563 | − | 0.673125i | ||||
\(566\) | −4.00000 | −0.168133 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 8.00000i | − | 0.335673i | ||||||
\(569\) | −22.0000 | −0.922288 | −0.461144 | − | 0.887325i | \(-0.652561\pi\) | ||||
−0.461144 | + | 0.887325i | \(0.652561\pi\) | |||||||
\(570\) | −12.0000 | + | 6.00000i | −0.502625 | + | 0.251312i | ||||
\(571\) | 4.00000 | 0.167395 | 0.0836974 | − | 0.996491i | \(-0.473327\pi\) | ||||
0.0836974 | + | 0.996491i | \(0.473327\pi\) | |||||||
\(572\) | 6.00000i | 0.250873i | ||||||||
\(573\) | 8.00000i | 0.334205i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.0000 | + | 18.0000i | 1.00087 | + | 0.750652i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 2.00000i | 0.0832611i | 0.999133 | + | 0.0416305i | \(0.0132552\pi\) | ||||
−0.999133 | + | 0.0416305i | \(0.986745\pi\) | |||||||
\(578\) | − | 17.0000i | − | 0.707107i | ||||||
\(579\) | 10.0000 | 0.415586 | ||||||||
\(580\) | −4.00000 | + | 2.00000i | −0.166091 | + | 0.0830455i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 2.00000i | 0.0829027i | ||||||||
\(583\) | 36.0000i | 1.49097i | ||||||||
\(584\) | −6.00000 | −0.248282 | ||||||||
\(585\) | 1.00000 | + | 2.00000i | 0.0413449 | + | 0.0826898i | ||||
\(586\) | −14.0000 | −0.578335 | ||||||||
\(587\) | 12.0000i | 0.495293i | 0.968850 | + | 0.247647i | \(0.0796572\pi\) | ||||
−0.968850 | + | 0.247647i | \(0.920343\pi\) | |||||||
\(588\) | 7.00000i | 0.288675i | ||||||||
\(589\) | −24.0000 | −0.988903 | ||||||||
\(590\) | −10.0000 | − | 20.0000i | −0.411693 | − | 0.823387i | ||||
\(591\) | 22.0000 | 0.904959 | ||||||||
\(592\) | − | 10.0000i | − | 0.410997i | ||||||
\(593\) | 6.00000i | 0.246390i | 0.992382 | + | 0.123195i | \(0.0393141\pi\) | ||||
−0.992382 | + | 0.123195i | \(0.960686\pi\) | |||||||
\(594\) | −6.00000 | −0.246183 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.0000i | 0.654836i | ||||||||
\(598\) | 6.00000i | 0.245358i | ||||||||
\(599\) | −16.0000 | −0.653742 | −0.326871 | − | 0.945069i | \(-0.605994\pi\) | ||||
−0.326871 | + | 0.945069i | \(0.605994\pi\) | |||||||
\(600\) | 3.00000 | − | 4.00000i | 0.122474 | − | 0.163299i | ||||
\(601\) | −10.0000 | −0.407909 | −0.203954 | − | 0.978980i | \(-0.565379\pi\) | ||||
−0.203954 | + | 0.978980i | \(0.565379\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.00000i | 0.162893i | ||||||||
\(604\) | 8.00000 | 0.325515 | ||||||||
\(605\) | −50.0000 | + | 25.0000i | −2.03279 | + | 1.01639i | ||||
\(606\) | 2.00000 | 0.0812444 | ||||||||
\(607\) | − | 2.00000i | − | 0.0811775i | −0.999176 | − | 0.0405887i | \(-0.987077\pi\) | ||
0.999176 | − | 0.0405887i | \(-0.0129233\pi\) | |||||||
\(608\) | 6.00000i | 0.243332i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.00000 | − | 12.0000i | −0.242933 | − | 0.485866i | ||||
\(611\) | 8.00000 | 0.323645 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 38.0000i | − | 1.53481i | −0.641165 | − | 0.767403i | \(-0.721549\pi\) | ||
0.641165 | − | 0.767403i | \(-0.278451\pi\) | |||||||
\(614\) | 28.0000 | 1.12999 | ||||||||
\(615\) | −6.00000 | − | 12.0000i | −0.241943 | − | 0.483887i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.0000i | 0.724653i | 0.932051 | + | 0.362326i | \(0.118017\pi\) | ||||
−0.932051 | + | 0.362326i | \(0.881983\pi\) | |||||||
\(618\) | 10.0000i | 0.402259i | ||||||||
\(619\) | −38.0000 | −1.52735 | −0.763674 | − | 0.645601i | \(-0.776607\pi\) | ||||
−0.763674 | + | 0.645601i | \(0.776607\pi\) | |||||||
\(620\) | 8.00000 | − | 4.00000i | 0.321288 | − | 0.160644i | ||||
\(621\) | −6.00000 | −0.240772 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | −16.0000 | −0.639489 | ||||||||
\(627\) | − | 36.0000i | − | 1.43770i | ||||||
\(628\) | − | 2.00000i | − | 0.0798087i | ||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.0000 | 1.27390 | 0.636950 | − | 0.770905i | \(-0.280196\pi\) | ||||
0.636950 | + | 0.770905i | \(0.280196\pi\) | |||||||
\(632\) | − | 16.0000i | − | 0.636446i | ||||||
\(633\) | − | 4.00000i | − | 0.158986i | ||||||
\(634\) | −18.0000 | −0.714871 | ||||||||
\(635\) | −18.0000 | − | 36.0000i | −0.714308 | − | 1.42862i | ||||
\(636\) | 6.00000 | 0.237915 | ||||||||
\(637\) | 7.00000i | 0.277350i | ||||||||
\(638\) | − | 12.0000i | − | 0.475085i | ||||||
\(639\) | 8.00000 | 0.316475 | ||||||||
\(640\) | −1.00000 | − | 2.00000i | −0.0395285 | − | 0.0790569i | ||||
\(641\) | −42.0000 | −1.65890 | −0.829450 | − | 0.558581i | \(-0.811346\pi\) | ||||
−0.829450 | + | 0.558581i | \(0.811346\pi\) | |||||||
\(642\) | 16.0000i | 0.631470i | ||||||||
\(643\) | 44.0000i | 1.73519i | 0.497271 | + | 0.867595i | \(0.334335\pi\) | ||||
−0.497271 | + | 0.867595i | \(0.665665\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.0000 | + | 8.00000i | −0.629999 | + | 0.315000i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 14.0000i | − | 0.550397i | −0.961387 | − | 0.275198i | \(-0.911256\pi\) | ||
0.961387 | − | 0.275198i | \(-0.0887435\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | 60.0000 | 2.35521 | ||||||||
\(650\) | 3.00000 | − | 4.00000i | 0.117670 | − | 0.156893i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 12.0000i | − | 0.469956i | ||||||
\(653\) | 6.00000i | 0.234798i | 0.993085 | + | 0.117399i | \(0.0374557\pi\) | ||||
−0.993085 | + | 0.117399i | \(0.962544\pi\) | |||||||
\(654\) | −16.0000 | −0.625650 | ||||||||
\(655\) | −24.0000 | + | 12.0000i | −0.937758 | + | 0.468879i | ||||
\(656\) | −6.00000 | −0.234261 | ||||||||
\(657\) | − | 6.00000i | − | 0.234082i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.0000 | 0.467454 | 0.233727 | − | 0.972302i | \(-0.424908\pi\) | ||||
0.233727 | + | 0.972302i | \(0.424908\pi\) | |||||||
\(660\) | 6.00000 | + | 12.0000i | 0.233550 | + | 0.467099i | ||||
\(661\) | −28.0000 | −1.08907 | −0.544537 | − | 0.838737i | \(-0.683295\pi\) | ||||
−0.544537 | + | 0.838737i | \(0.683295\pi\) | |||||||
\(662\) | 26.0000i | 1.01052i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.00000 | −0.155230 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.0000 | 0.387492 | ||||||||
\(667\) | − | 12.0000i | − | 0.464642i | ||||||
\(668\) | 8.00000i | 0.309529i | ||||||||
\(669\) | 4.00000 | 0.154649 | ||||||||
\(670\) | 8.00000 | − | 4.00000i | 0.309067 | − | 0.154533i | ||||
\(671\) | 36.0000 | 1.38976 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 44.0000i | 1.69608i | 0.529936 | + | 0.848038i | \(0.322216\pi\) | ||||
−0.529936 | + | 0.848038i | \(0.677784\pi\) | |||||||
\(674\) | −8.00000 | −0.308148 | ||||||||
\(675\) | 4.00000 | + | 3.00000i | 0.153960 | + | 0.115470i | ||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | − | 38.0000i | − | 1.46046i | −0.683202 | − | 0.730229i | \(-0.739413\pi\) | ||
0.683202 | − | 0.730229i | \(-0.260587\pi\) | |||||||
\(678\) | − | 8.00000i | − | 0.307238i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20.0000 | 0.766402 | ||||||||
\(682\) | 24.0000i | 0.919007i | ||||||||
\(683\) | − | 12.0000i | − | 0.459167i | −0.973289 | − | 0.229584i | \(-0.926264\pi\) | ||
0.973289 | − | 0.229584i | \(-0.0737364\pi\) | |||||||
\(684\) | −6.00000 | −0.229416 | ||||||||
\(685\) | 2.00000 | + | 4.00000i | 0.0764161 | + | 0.152832i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.0000i | 0.763048i | ||||||||
\(688\) | 8.00000i | 0.304997i | ||||||||
\(689\) | 6.00000 | 0.228582 | ||||||||
\(690\) | 6.00000 | + | 12.0000i | 0.228416 | + | 0.456832i | ||||
\(691\) | 22.0000 | 0.836919 | 0.418460 | − | 0.908235i | \(-0.362570\pi\) | ||||
0.418460 | + | 0.908235i | \(0.362570\pi\) | |||||||
\(692\) | − | 18.0000i | − | 0.684257i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −32.0000 | −1.21470 | ||||||||
\(695\) | 16.0000 | − | 8.00000i | 0.606915 | − | 0.303457i | ||||
\(696\) | −2.00000 | −0.0758098 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 8.00000i | 0.302804i | ||||||||
\(699\) | −8.00000 | −0.302588 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.0000 | −0.679851 | −0.339925 | − | 0.940452i | \(-0.610402\pi\) | ||||
−0.339925 | + | 0.940452i | \(0.610402\pi\) | |||||||
\(702\) | 1.00000i | 0.0377426i | ||||||||
\(703\) | 60.0000i | 2.26294i | ||||||||
\(704\) | 6.00000 | 0.226134 | ||||||||
\(705\) | 16.0000 | − | 8.00000i | 0.602595 | − | 0.301297i | ||||
\(706\) | −10.0000 | −0.376355 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − | 10.0000i | − | 0.375823i | ||||||
\(709\) | 44.0000 | 1.65245 | 0.826227 | − | 0.563337i | \(-0.190483\pi\) | ||||
0.826227 | + | 0.563337i | \(0.190483\pi\) | |||||||
\(710\) | −8.00000 | − | 16.0000i | −0.300235 | − | 0.600469i | ||||
\(711\) | 16.0000 | 0.600047 | ||||||||
\(712\) | 10.0000i | 0.374766i | ||||||||
\(713\) | 24.0000i | 0.898807i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.00000 | + | 12.0000i | 0.224387 | + | 0.448775i | ||||
\(716\) | −12.0000 | −0.448461 | ||||||||
\(717\) | − | 28.0000i | − | 1.04568i | ||||||
\(718\) | − | 12.0000i | − | 0.447836i | ||||||
\(719\) | −24.0000 | −0.895049 | −0.447524 | − | 0.894272i | \(-0.647694\pi\) | ||||
−0.447524 | + | 0.894272i | \(0.647694\pi\) | |||||||
\(720\) | 2.00000 | − | 1.00000i | 0.0745356 | − | 0.0372678i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 17.0000i | − | 0.632674i | ||||||
\(723\) | 22.0000i | 0.818189i | ||||||||
\(724\) | 2.00000 | 0.0743294 | ||||||||
\(725\) | −6.00000 | + | 8.00000i | −0.222834 | + | 0.297113i | ||||
\(726\) | −25.0000 | −0.927837 | ||||||||
\(727\) | − | 38.0000i | − | 1.40934i | −0.709534 | − | 0.704671i | \(-0.751095\pi\) | ||
0.709534 | − | 0.704671i | \(-0.248905\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −12.0000 | + | 6.00000i | −0.444140 | + | 0.222070i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | − | 6.00000i | − | 0.221766i | ||||||
\(733\) | − | 26.0000i | − | 0.960332i | −0.877178 | − | 0.480166i | \(-0.840576\pi\) | ||
0.877178 | − | 0.480166i | \(-0.159424\pi\) | |||||||
\(734\) | −6.00000 | −0.221464 | ||||||||
\(735\) | 7.00000 | + | 14.0000i | 0.258199 | + | 0.516398i | ||||
\(736\) | 6.00000 | 0.221163 | ||||||||
\(737\) | 24.0000i | 0.884051i | ||||||||
\(738\) | − | 6.00000i | − | 0.220863i | ||||||
\(739\) | 22.0000 | 0.809283 | 0.404642 | − | 0.914475i | \(-0.367396\pi\) | ||||
0.404642 | + | 0.914475i | \(0.367396\pi\) | |||||||
\(740\) | −10.0000 | − | 20.0000i | −0.367607 | − | 0.735215i | ||||
\(741\) | −6.00000 | −0.220416 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 52.0000i | 1.90769i | 0.300291 | + | 0.953847i | \(0.402916\pi\) | ||||
−0.300291 | + | 0.953847i | \(0.597084\pi\) | |||||||
\(744\) | 4.00000 | 0.146647 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −10.0000 | −0.366126 | ||||||||
\(747\) | − | 4.00000i | − | 0.146352i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.00000 | − | 11.0000i | 0.0730297 | − | 0.401663i | ||||
\(751\) | 32.0000 | 1.16770 | 0.583848 | − | 0.811863i | \(-0.301546\pi\) | ||||
0.583848 | + | 0.811863i | \(0.301546\pi\) | |||||||
\(752\) | − | 8.00000i | − | 0.291730i | ||||||
\(753\) | − | 8.00000i | − | 0.291536i | ||||||
\(754\) | −2.00000 | −0.0728357 | ||||||||
\(755\) | 16.0000 | − | 8.00000i | 0.582300 | − | 0.291150i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 10.0000i | − | 0.363456i | −0.983349 | − | 0.181728i | \(-0.941831\pi\) | ||
0.983349 | − | 0.181728i | \(-0.0581691\pi\) | |||||||
\(758\) | 22.0000i | 0.799076i | ||||||||
\(759\) | −36.0000 | −1.30672 | ||||||||
\(760\) | 6.00000 | + | 12.0000i | 0.217643 | + | 0.435286i | ||||
\(761\) | 30.0000 | 1.08750 | 0.543750 | − | 0.839248i | \(-0.317004\pi\) | ||||
0.543750 | + | 0.839248i | \(0.317004\pi\) | |||||||
\(762\) | − | 18.0000i | − | 0.652071i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 8.00000 | 0.289430 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −20.0000 | −0.722629 | ||||||||
\(767\) | − | 10.0000i | − | 0.361079i | ||||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | 54.0000 | 1.94729 | 0.973645 | − | 0.228069i | \(-0.0732413\pi\) | ||||
0.973645 | + | 0.228069i | \(0.0732413\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.0000 | 0.864339 | ||||||||
\(772\) | − | 10.0000i | − | 0.359908i | ||||||
\(773\) | − | 18.0000i | − | 0.647415i | −0.946157 | − | 0.323708i | \(-0.895071\pi\) | ||
0.946157 | − | 0.323708i | \(-0.104929\pi\) | |||||||
\(774\) | −8.00000 | −0.287554 | ||||||||
\(775\) | 12.0000 | − | 16.0000i | 0.431053 | − | 0.574737i | ||||
\(776\) | 2.00000 | 0.0717958 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 14.0000i | − | 0.501924i | ||||||
\(779\) | 36.0000 | 1.28983 | ||||||||
\(780\) | 2.00000 | − | 1.00000i | 0.0716115 | − | 0.0358057i | ||||
\(781\) | 48.0000 | 1.71758 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 2.00000i | − | 0.0714742i | ||||||
\(784\) | 7.00000 | 0.250000 | ||||||||
\(785\) | −2.00000 | − | 4.00000i | −0.0713831 | − | 0.142766i | ||||
\(786\) | −12.0000 | −0.428026 | ||||||||
\(787\) | 12.0000i | 0.427754i | 0.976861 | + | 0.213877i | \(0.0686091\pi\) | ||||
−0.976861 | + | 0.213877i | \(0.931391\pi\) | |||||||
\(788\) | − | 22.0000i | − | 0.783718i | ||||||
\(789\) | −6.00000 | −0.213606 | ||||||||
\(790\) | −16.0000 | − | 32.0000i | −0.569254 | − | 1.13851i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 6.00000i | 0.213201i | ||||||||
\(793\) | − | 6.00000i | − | 0.213066i | ||||||
\(794\) | 18.0000 | 0.638796 | ||||||||
\(795\) | 12.0000 | − | 6.00000i | 0.425596 | − | 0.212798i | ||||
\(796\) | 16.0000 | 0.567105 | ||||||||
\(797\) | − | 42.0000i | − | 1.48772i | −0.668338 | − | 0.743858i | \(-0.732994\pi\) | ||
0.668338 | − | 0.743858i | \(-0.267006\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −4.00000 | − | 3.00000i | −0.141421 | − | 0.106066i | ||||
\(801\) | −10.0000 | −0.353333 | ||||||||
\(802\) | − | 14.0000i | − | 0.494357i | ||||||
\(803\) | − | 36.0000i | − | 1.27041i | ||||||
\(804\) | 4.00000 | 0.141069 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.00000 | 0.140894 | ||||||||
\(807\) | 14.0000i | 0.492823i | ||||||||
\(808\) | − | 2.00000i | − | 0.0703598i | ||||||
\(809\) | −6.00000 | −0.210949 | −0.105474 | − | 0.994422i | \(-0.533636\pi\) | ||||
−0.105474 | + | 0.994422i | \(0.533636\pi\) | |||||||
\(810\) | 1.00000 | + | 2.00000i | 0.0351364 | + | 0.0702728i | ||||
\(811\) | 2.00000 | 0.0702295 | 0.0351147 | − | 0.999383i | \(-0.488820\pi\) | ||||
0.0351147 | + | 0.999383i | \(0.488820\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.0000i | 0.561144i | ||||||||
\(814\) | 60.0000 | 2.10300 | ||||||||
\(815\) | −12.0000 | − | 24.0000i | −0.420342 | − | 0.840683i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 48.0000i | − | 1.67931i | ||||||
\(818\) | 30.0000i | 1.04893i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.0000 | + | 6.00000i | −0.419058 | + | 0.209529i | ||||
\(821\) | 4.00000 | 0.139601 | 0.0698005 | − | 0.997561i | \(-0.477764\pi\) | ||||
0.0698005 | + | 0.997561i | \(0.477764\pi\) | |||||||
\(822\) | 2.00000i | 0.0697580i | ||||||||
\(823\) | − | 54.0000i | − | 1.88232i | −0.337959 | − | 0.941161i | \(-0.609737\pi\) | ||
0.337959 | − | 0.941161i | \(-0.390263\pi\) | |||||||
\(824\) | 10.0000 | 0.348367 | ||||||||
\(825\) | 24.0000 | + | 18.0000i | 0.835573 | + | 0.626680i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.0000i | 0.695468i | 0.937593 | + | 0.347734i | \(0.113049\pi\) | ||||
−0.937593 | + | 0.347734i | \(0.886951\pi\) | |||||||
\(828\) | 6.00000i | 0.208514i | ||||||||
\(829\) | −26.0000 | −0.903017 | −0.451509 | − | 0.892267i | \(-0.649114\pi\) | ||||
−0.451509 | + | 0.892267i | \(0.649114\pi\) | |||||||
\(830\) | −8.00000 | + | 4.00000i | −0.277684 | + | 0.138842i | ||||
\(831\) | −26.0000 | −0.901930 | ||||||||
\(832\) | − | 1.00000i | − | 0.0346688i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 8.00000 | 0.277017 | ||||||||
\(835\) | 8.00000 | + | 16.0000i | 0.276851 | + | 0.553703i | ||||
\(836\) | −36.0000 | −1.24509 | ||||||||
\(837\) | 4.00000i | 0.138260i | ||||||||
\(838\) | 28.0000i | 0.967244i | ||||||||
\(839\) | 16.0000 | 0.552381 | 0.276191 | − | 0.961103i | \(-0.410928\pi\) | ||||
0.276191 | + | 0.961103i | \(0.410928\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 8.00000i | 0.275698i | ||||||||
\(843\) | 10.0000i | 0.344418i | ||||||||
\(844\) | −4.00000 | −0.137686 | ||||||||
\(845\) | 2.00000 | − | 1.00000i | 0.0688021 | − | 0.0344010i | ||||
\(846\) | 8.00000 | 0.275046 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 6.00000i | − | 0.206041i | ||||||
\(849\) | −4.00000 | −0.137280 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 60.0000 | 2.05677 | ||||||||
\(852\) | − | 8.00000i | − | 0.274075i | ||||||
\(853\) | 14.0000i | 0.479351i | 0.970853 | + | 0.239675i | \(0.0770410\pi\) | ||||
−0.970853 | + | 0.239675i | \(0.922959\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.0000 | + | 6.00000i | −0.410391 | + | 0.205196i | ||||
\(856\) | 16.0000 | 0.546869 | ||||||||
\(857\) | 52.0000i | 1.77629i | 0.459567 | + | 0.888143i | \(0.348005\pi\) | ||||
−0.459567 | + | 0.888143i | \(0.651995\pi\) | |||||||
\(858\) | 6.00000i | 0.204837i | ||||||||
\(859\) | −12.0000 | −0.409435 | −0.204717 | − | 0.978821i | \(-0.565628\pi\) | ||||
−0.204717 | + | 0.978821i | \(0.565628\pi\) | |||||||
\(860\) | 8.00000 | + | 16.0000i | 0.272798 | + | 0.545595i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8.00000i | 0.272481i | ||||||||
\(863\) | − | 32.0000i | − | 1.08929i | −0.838666 | − | 0.544646i | \(-0.816664\pi\) | ||
0.838666 | − | 0.544646i | \(-0.183336\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −18.0000 | − | 36.0000i | −0.612018 | − | 1.22404i | ||||
\(866\) | 24.0000 | 0.815553 | ||||||||
\(867\) | − | 17.0000i | − | 0.577350i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 96.0000 | 3.25658 | ||||||||
\(870\) | −4.00000 | + | 2.00000i | −0.135613 | + | 0.0678064i | ||||
\(871\) | 4.00000 | 0.135535 | ||||||||
\(872\) | 16.0000i | 0.541828i | ||||||||
\(873\) | 2.00000i | 0.0676897i | ||||||||
\(874\) | −36.0000 | −1.21772 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.00000 | −0.202721 | ||||||||
\(877\) | 22.0000i | 0.742887i | 0.928456 | + | 0.371444i | \(0.121137\pi\) | ||||
−0.928456 | + | 0.371444i | \(0.878863\pi\) | |||||||
\(878\) | 16.0000i | 0.539974i | ||||||||
\(879\) | −14.0000 | −0.472208 | ||||||||
\(880\) | 12.0000 | − | 6.00000i | 0.404520 | − | 0.202260i | ||||
\(881\) | −54.0000 | −1.81931 | −0.909653 | − | 0.415369i | \(-0.863653\pi\) | ||||
−0.909653 | + | 0.415369i | \(0.863653\pi\) | |||||||
\(882\) | 7.00000i | 0.235702i | ||||||||
\(883\) | − | 16.0000i | − | 0.538443i | −0.963078 | − | 0.269221i | \(-0.913234\pi\) | ||
0.963078 | − | 0.269221i | \(-0.0867663\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.0000 | − | 20.0000i | −0.336146 | − | 0.672293i | ||||
\(886\) | −32.0000 | −1.07506 | ||||||||
\(887\) | 26.0000i | 0.872995i | 0.899706 | + | 0.436497i | \(0.143781\pi\) | ||||
−0.899706 | + | 0.436497i | \(0.856219\pi\) | |||||||
\(888\) | − | 10.0000i | − | 0.335578i | ||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 10.0000 | + | 20.0000i | 0.335201 | + | 0.670402i | ||||
\(891\) | −6.00000 | −0.201008 | ||||||||
\(892\) | − | 4.00000i | − | 0.133930i | ||||||
\(893\) | 48.0000i | 1.60626i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.0000 | + | 12.0000i | −0.802232 | + | 0.401116i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.00000i | 0.200334i | ||||||||
\(898\) | − | 34.0000i | − | 1.13459i | ||||||
\(899\) | −8.00000 | −0.266815 | ||||||||
\(900\) | 3.00000 | − | 4.00000i | 0.100000 | − | 0.133333i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | − | 36.0000i | − | 1.19867i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.00000 | −0.266076 | ||||||||
\(905\) | 4.00000 | − | 2.00000i | 0.132964 | − | 0.0664822i | ||||
\(906\) | 8.00000 | 0.265782 | ||||||||
\(907\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(908\) | − | 20.0000i | − | 0.663723i | ||||||
\(909\) | 2.00000 | 0.0663358 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.0000 | −0.530104 | −0.265052 | − | 0.964234i | \(-0.585389\pi\) | ||||
−0.265052 | + | 0.964234i | \(0.585389\pi\) | |||||||
\(912\) | 6.00000i | 0.198680i | ||||||||
\(913\) | − | 24.0000i | − | 0.794284i | ||||||
\(914\) | −18.0000 | −0.595387 | ||||||||
\(915\) | −6.00000 | − | 12.0000i | −0.198354 | − | 0.396708i | ||||
\(916\) | 20.0000 | 0.660819 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.0000 | 0.791687 | 0.395843 | − | 0.918318i | \(-0.370452\pi\) | ||||
0.395843 | + | 0.918318i | \(0.370452\pi\) | |||||||
\(920\) | 12.0000 | − | 6.00000i | 0.395628 | − | 0.197814i | ||||
\(921\) | 28.0000 | 0.922631 | ||||||||
\(922\) | − | 36.0000i | − | 1.18560i | ||||||
\(923\) | − | 8.00000i | − | 0.263323i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −40.0000 | − | 30.0000i | −1.31519 | − | 0.986394i | ||||
\(926\) | −16.0000 | −0.525793 | ||||||||
\(927\) | 10.0000i | 0.328443i | ||||||||
\(928\) | 2.00000i | 0.0656532i | ||||||||
\(929\) | −6.00000 | −0.196854 | −0.0984268 | − | 0.995144i | \(-0.531381\pi\) | ||||
−0.0984268 | + | 0.995144i | \(0.531381\pi\) | |||||||
\(930\) | 8.00000 | − | 4.00000i | 0.262330 | − | 0.131165i | ||||
\(931\) | −42.0000 | −1.37649 | ||||||||
\(932\) | 8.00000i | 0.262049i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 40.0000 | 1.30884 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | − | 16.0000i | − | 0.522697i | −0.965244 | − | 0.261349i | \(-0.915833\pi\) | ||
0.965244 | − | 0.261349i | \(-0.0841672\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.0000 | −0.522140 | ||||||||
\(940\) | −8.00000 | − | 16.0000i | −0.260931 | − | 0.521862i | ||||
\(941\) | −24.0000 | −0.782378 | −0.391189 | − | 0.920310i | \(-0.627936\pi\) | ||||
−0.391189 | + | 0.920310i | \(0.627936\pi\) | |||||||
\(942\) | − | 2.00000i | − | 0.0651635i | ||||||
\(943\) | − | 36.0000i | − | 1.17232i | ||||||
\(944\) | −10.0000 | −0.325472 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −48.0000 | −1.56061 | ||||||||
\(947\) | − | 4.00000i | − | 0.129983i | −0.997886 | − | 0.0649913i | \(-0.979298\pi\) | ||
0.997886 | − | 0.0649913i | \(-0.0207020\pi\) | |||||||
\(948\) | − | 16.0000i | − | 0.519656i | ||||||
\(949\) | −6.00000 | −0.194768 | ||||||||
\(950\) | 24.0000 | + | 18.0000i | 0.778663 | + | 0.583997i | ||||
\(951\) | −18.0000 | −0.583690 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.0000i | 1.42530i | 0.701520 | + | 0.712650i | \(0.252505\pi\) | ||||
−0.701520 | + | 0.712650i | \(0.747495\pi\) | |||||||
\(954\) | 6.00000 | 0.194257 | ||||||||
\(955\) | 16.0000 | − | 8.00000i | 0.517748 | − | 0.258874i | ||||
\(956\) | −28.0000 | −0.905585 | ||||||||
\(957\) | − | 12.0000i | − | 0.387905i | ||||||
\(958\) | 20.0000i | 0.646171i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.00000 | − | 2.00000i | −0.0322749 | − | 0.0645497i | ||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | − | 10.0000i | − | 0.322413i | ||||||
\(963\) | 16.0000i | 0.515593i | ||||||||
\(964\) | 22.0000 | 0.708572 | ||||||||
\(965\) | −10.0000 | − | 20.0000i | −0.321911 | − | 0.643823i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 32.0000i | − | 1.02905i | −0.857475 | − | 0.514525i | \(-0.827968\pi\) | ||
0.857475 | − | 0.514525i | \(-0.172032\pi\) | |||||||
\(968\) | 25.0000i | 0.803530i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.00000 | − | 2.00000i | 0.128432 | − | 0.0642161i | ||||
\(971\) | 40.0000 | 1.28366 | 0.641831 | − | 0.766846i | \(-0.278175\pi\) | ||||
0.641831 | + | 0.766846i | \(0.278175\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 12.0000 | 0.384505 | ||||||||
\(975\) | 3.00000 | − | 4.00000i | 0.0960769 | − | 0.128103i | ||||
\(976\) | −6.00000 | −0.192055 | ||||||||
\(977\) | − | 50.0000i | − | 1.59964i | −0.600239 | − | 0.799821i | \(-0.704928\pi\) | ||
0.600239 | − | 0.799821i | \(-0.295072\pi\) | |||||||
\(978\) | − | 12.0000i | − | 0.383718i | ||||||
\(979\) | −60.0000 | −1.91761 | ||||||||
\(980\) | 14.0000 | − | 7.00000i | 0.447214 | − | 0.223607i | ||||
\(981\) | −16.0000 | −0.510841 | ||||||||
\(982\) | 12.0000i | 0.382935i | ||||||||
\(983\) | 12.0000i | 0.382741i | 0.981518 | + | 0.191370i | \(0.0612931\pi\) | ||||
−0.981518 | + | 0.191370i | \(0.938707\pi\) | |||||||
\(984\) | −6.00000 | −0.191273 | ||||||||
\(985\) | −22.0000 | − | 44.0000i | −0.700978 | − | 1.40196i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.00000i | 0.190885i | ||||||||
\(989\) | −48.0000 | −1.52631 | ||||||||
\(990\) | 6.00000 | + | 12.0000i | 0.190693 | + | 0.381385i | ||||
\(991\) | 8.00000 | 0.254128 | 0.127064 | − | 0.991894i | \(-0.459445\pi\) | ||||
0.127064 | + | 0.991894i | \(0.459445\pi\) | |||||||
\(992\) | − | 4.00000i | − | 0.127000i | ||||||
\(993\) | 26.0000i | 0.825085i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 32.0000 | − | 16.0000i | 1.01447 | − | 0.507234i | ||||
\(996\) | −4.00000 | −0.126745 | ||||||||
\(997\) | − | 14.0000i | − | 0.443384i | −0.975117 | − | 0.221692i | \(-0.928842\pi\) | ||
0.975117 | − | 0.221692i | \(-0.0711580\pi\) | |||||||
\(998\) | − | 6.00000i | − | 0.189927i | ||||||
\(999\) | 10.0000 | 0.316386 |
(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 | 390.2.e.a.79.1 | ✓ | 2 | |
3.2 | odd | 2 | 1170.2.e.d.469.2 | 2 | |||
4.3 | odd | 2 | 3120.2.l.a.1249.2 | 2 | |||
5.2 | odd | 4 | 1950.2.a.r.1.1 | 1 | |||
5.3 | odd | 4 | 1950.2.a.i.1.1 | 1 | |||
5.4 | even | 2 | inner | 390.2.e.a.79.2 | yes | 2 | |
15.2 | even | 4 | 5850.2.a.o.1.1 | 1 | |||
15.8 | even | 4 | 5850.2.a.bs.1.1 | 1 | |||
15.14 | odd | 2 | 1170.2.e.d.469.1 | 2 | |||
20.19 | odd | 2 | 3120.2.l.a.1249.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.e.a.79.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
390.2.e.a.79.2 | yes | 2 | 5.4 | even | 2 | inner | |
1170.2.e.d.469.1 | 2 | 15.14 | odd | 2 | |||
1170.2.e.d.469.2 | 2 | 3.2 | odd | 2 | |||
1950.2.a.i.1.1 | 1 | 5.3 | odd | 4 | |||
1950.2.a.r.1.1 | 1 | 5.2 | odd | 4 | |||
3120.2.l.a.1249.1 | 2 | 20.19 | odd | 2 | |||
3120.2.l.a.1249.2 | 2 | 4.3 | odd | 2 | |||
5850.2.a.o.1.1 | 1 | 15.2 | even | 4 | |||
5850.2.a.bs.1.1 | 1 | 15.8 | even | 4 |