Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1280,2,Mod(127,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1280.127");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.o (of order \(4\), degree \(2\), not 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: | \(10.2208514587\) |
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: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 160) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 383.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1280.383 |
Dual form | 1280.2.o.p.127.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.00000 | + | 2.00000i | 1.15470 | + | 1.15470i | 0.985599 | + | 0.169102i | \(0.0540867\pi\) |
0.169102 | + | 0.985599i | \(0.445913\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | − | 2.00000i | 0.447214 | − | 0.894427i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | + | 2.00000i | 0.755929 | + | 0.755929i | 0.975579 | − | 0.219650i | \(-0.0704915\pi\) |
−0.219650 | + | 0.975579i | \(0.570491\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.00000i | 1.66667i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | + | 1.00000i | −0.277350 | + | 0.277350i | −0.832050 | − | 0.554700i | \(-0.812833\pi\) |
0.554700 | + | 0.832050i | \(0.312833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.00000 | − | 2.00000i | 1.54919 | − | 0.516398i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.00000 | + | 5.00000i | −1.21268 | + | 1.21268i | −0.242536 | + | 0.970143i | \(0.577979\pi\) |
−0.970143 | + | 0.242536i | \(0.922021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000i | 0.917663i | 0.888523 | + | 0.458831i | \(0.151732\pi\) | ||||
−0.888523 | + | 0.458831i | \(0.848268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.00000i | 1.74574i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.00000 | − | 2.00000i | 0.417029 | − | 0.417029i | −0.467150 | − | 0.884178i | \(-0.654719\pi\) |
0.884178 | + | 0.467150i | \(0.154719\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.00000 | − | 4.00000i | −0.600000 | − | 0.800000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.00000 | + | 4.00000i | −0.769800 | + | 0.769800i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.00000 | 0.742781 | 0.371391 | − | 0.928477i | \(-0.378881\pi\) | ||||
0.371391 | + | 0.928477i | \(0.378881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.00000i | − | 0.718421i | −0.933257 | − | 0.359211i | \(-0.883046\pi\) | ||
0.933257 | − | 0.359211i | \(-0.116954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.00000 | − | 2.00000i | 1.01419 | − | 0.338062i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | + | 1.00000i | 0.164399 | + | 0.164399i | 0.784512 | − | 0.620113i | \(-0.212913\pi\) |
−0.620113 | + | 0.784512i | \(0.712913\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.00000 | −0.640513 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.00000 | + | 6.00000i | 0.914991 | + | 0.914991i | 0.996660 | − | 0.0816682i | \(-0.0260248\pi\) |
−0.0816682 | + | 0.996660i | \(0.526025\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.0000 | + | 5.00000i | 1.49071 | + | 0.745356i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.00000 | + | 2.00000i | 0.291730 | + | 0.291730i | 0.837763 | − | 0.546033i | \(-0.183863\pi\) |
−0.546033 | + | 0.837763i | \(0.683863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −20.0000 | −2.80056 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.00000 | − | 7.00000i | 0.961524 | − | 0.961524i | −0.0377628 | − | 0.999287i | \(-0.512023\pi\) |
0.999287 | + | 0.0377628i | \(0.0120231\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.00000 | + | 8.00000i | −1.05963 | + | 1.05963i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 4.00000i | − | 0.520756i | −0.965507 | − | 0.260378i | \(-0.916153\pi\) | ||
0.965507 | − | 0.260378i | \(-0.0838471\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.00000i | 0.512148i | 0.966657 | + | 0.256074i | \(0.0824290\pi\) | ||||
−0.966657 | + | 0.256074i | \(0.917571\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10.0000 | + | 10.0000i | −1.25988 | + | 1.25988i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00000 | + | 3.00000i | 0.124035 | + | 0.372104i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.0000 | − | 10.0000i | 1.22169 | − | 1.22169i | 0.254665 | − | 0.967029i | \(-0.418035\pi\) |
0.967029 | − | 0.254665i | \(-0.0819652\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.00000 | 0.963087 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12.0000i | − | 1.42414i | −0.702109 | − | 0.712069i | \(-0.747758\pi\) | ||
0.702109 | − | 0.712069i | \(-0.252242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.00000 | + | 3.00000i | 0.351123 | + | 0.351123i | 0.860527 | − | 0.509404i | \(-0.170134\pi\) |
−0.509404 | + | 0.860527i | \(0.670134\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.00000 | − | 14.0000i | 0.230940 | − | 1.61658i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.0000 | −1.80014 | −0.900070 | − | 0.435745i | \(-0.856485\pi\) | ||||
−0.900070 | + | 0.435745i | \(0.856485\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.00000 | − | 2.00000i | −0.219529 | − | 0.219529i | 0.588771 | − | 0.808300i | \(-0.299612\pi\) |
−0.808300 | + | 0.588771i | \(0.799612\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.00000 | + | 15.0000i | 0.542326 | + | 1.62698i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.00000 | + | 8.00000i | 0.857690 | + | 0.857690i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.00000 | −0.419314 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.00000 | − | 8.00000i | 0.829561 | − | 0.829561i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.00000 | + | 4.00000i | 0.820783 | + | 0.410391i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.00000 | + | 3.00000i | −0.304604 | + | 0.304604i | −0.842812 | − | 0.538208i | \(-0.819101\pi\) |
0.538208 | + | 0.842812i | \(0.319101\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 6.00000i | − | 0.597022i | −0.954406 | − | 0.298511i | \(-0.903510\pi\) | ||
0.954406 | − | 0.298511i | \(-0.0964900\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.00000 | + | 6.00000i | −0.591198 | + | 0.591198i | −0.937955 | − | 0.346757i | \(-0.887283\pi\) |
0.346757 | + | 0.937955i | \(0.387283\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 16.0000 | + | 8.00000i | 1.56144 | + | 0.780720i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.00000 | − | 6.00000i | 0.580042 | − | 0.580042i | −0.354873 | − | 0.934915i | \(-0.615476\pi\) |
0.934915 | + | 0.354873i | \(0.115476\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.0000 | −0.957826 | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||||
−0.478913 | + | 0.877862i | \(0.658969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.00000i | 0.379663i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.00000 | − | 9.00000i | −0.846649 | − | 0.846649i | 0.143065 | − | 0.989713i | \(-0.454304\pi\) |
−0.989713 | + | 0.143065i | \(0.954304\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.00000 | − | 6.00000i | −0.186501 | − | 0.559503i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.00000 | − | 5.00000i | −0.462250 | − | 0.462250i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −20.0000 | −1.83340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.0000 | + | 2.00000i | −0.983870 | + | 0.178885i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.0000 | − | 10.0000i | −0.887357 | − | 0.887357i | 0.106912 | − | 0.994268i | \(-0.465904\pi\) |
−0.994268 | + | 0.106912i | \(0.965904\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 24.0000i | 2.11308i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.00000 | 0.698963 | 0.349482 | − | 0.936943i | \(-0.386358\pi\) | ||||
0.349482 | + | 0.936943i | \(0.386358\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.00000 | + | 8.00000i | −0.693688 | + | 0.693688i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.00000 | + | 12.0000i | 0.344265 | + | 1.03280i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.00000 | + | 1.00000i | −0.0854358 | + | 0.0854358i | −0.748533 | − | 0.663097i | \(-0.769242\pi\) |
0.663097 | + | 0.748533i | \(0.269242\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.0000i | 1.01783i | 0.860818 | + | 0.508913i | \(0.169953\pi\) | ||||
−0.860818 | + | 0.508913i | \(0.830047\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.00000i | 0.673722i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.00000 | − | 8.00000i | 0.332182 | − | 0.664364i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.00000 | + | 2.00000i | −0.164957 | + | 0.164957i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.0000 | −1.47462 | −0.737309 | − | 0.675556i | \(-0.763904\pi\) | ||||
−0.737309 | + | 0.675556i | \(0.763904\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 12.0000i | − | 0.976546i | −0.872691 | − | 0.488273i | \(-0.837627\pi\) | ||
0.872691 | − | 0.488273i | \(-0.162373\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −25.0000 | − | 25.0000i | −2.02113 | − | 2.02113i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.00000 | − | 4.00000i | −0.642575 | − | 0.321288i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.00000 | + | 9.00000i | 0.718278 | + | 0.718278i | 0.968252 | − | 0.249974i | \(-0.0804222\pi\) |
−0.249974 | + | 0.968252i | \(0.580422\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 28.0000 | 2.22054 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.00000 | 0.630488 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.00000 | + | 2.00000i | 0.156652 | + | 0.156652i | 0.781081 | − | 0.624429i | \(-0.214668\pi\) |
−0.624429 | + | 0.781081i | \(0.714668\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.00000 | − | 2.00000i | −0.154765 | − | 0.154765i | 0.625478 | − | 0.780242i | \(-0.284904\pi\) |
−0.780242 | + | 0.625478i | \(0.784904\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.0000i | 0.846154i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −20.0000 | −1.52944 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.0000 | − | 13.0000i | 0.988372 | − | 0.988372i | −0.0115615 | − | 0.999933i | \(-0.503680\pi\) |
0.999933 | + | 0.0115615i | \(0.00368021\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.00000 | − | 14.0000i | 0.151186 | − | 1.05830i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.00000 | − | 8.00000i | 0.601317 | − | 0.601317i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0000i | 0.896922i | 0.893802 | + | 0.448461i | \(0.148028\pi\) | ||||
−0.893802 | + | 0.448461i | \(0.851972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 10.0000i | − | 0.743294i | −0.928374 | − | 0.371647i | \(-0.878793\pi\) | ||
0.928374 | − | 0.371647i | \(-0.121207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.00000 | + | 8.00000i | −0.591377 | + | 0.591377i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.00000 | − | 1.00000i | 0.220564 | − | 0.0735215i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −16.0000 | −1.16383 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 20.0000i | − | 1.44715i | −0.690246 | − | 0.723575i | \(-0.742498\pi\) | ||
0.690246 | − | 0.723575i | \(-0.257502\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.00000 | − | 5.00000i | −0.359908 | − | 0.359908i | 0.503871 | − | 0.863779i | \(-0.331909\pi\) |
−0.863779 | + | 0.503871i | \(0.831909\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.00000 | + | 8.00000i | −0.286446 | + | 0.572892i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.00000 | + | 5.00000i | 0.356235 | + | 0.356235i | 0.862423 | − | 0.506188i | \(-0.168946\pi\) |
−0.506188 | + | 0.862423i | \(0.668946\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.0000 | 1.70131 | 0.850657 | − | 0.525720i | \(-0.176204\pi\) | ||||
0.850657 | + | 0.525720i | \(0.176204\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 40.0000 | 2.82138 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.00000 | + | 8.00000i | 0.561490 | + | 0.561490i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.0000 | + | 10.0000i | 0.695048 | + | 0.695048i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.0000 | 1.10149 | 0.550743 | − | 0.834675i | \(-0.314345\pi\) | ||||
0.550743 | + | 0.834675i | \(0.314345\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 24.0000 | − | 24.0000i | 1.64445 | − | 1.64445i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 18.0000 | − | 6.00000i | 1.22759 | − | 0.409197i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.00000 | − | 8.00000i | 0.543075 | − | 0.543075i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.0000i | 0.810885i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 10.0000i | − | 0.672673i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.0000 | − | 10.0000i | 0.669650 | − | 0.669650i | −0.287985 | − | 0.957635i | \(-0.592985\pi\) |
0.957635 | + | 0.287985i | \(0.0929854\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 20.0000 | − | 15.0000i | 1.33333 | − | 1.00000i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.0000 | + | 10.0000i | −0.663723 | + | 0.663723i | −0.956256 | − | 0.292532i | \(-0.905502\pi\) |
0.292532 | + | 0.956256i | \(0.405502\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.0000 | −1.32164 | −0.660819 | − | 0.750546i | \(-0.729791\pi\) | ||||
−0.660819 | + | 0.750546i | \(0.729791\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.00000 | + | 5.00000i | 0.327561 | + | 0.327561i | 0.851658 | − | 0.524097i | \(-0.175597\pi\) |
−0.524097 | + | 0.851658i | \(0.675597\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.00000 | − | 2.00000i | 0.391397 | − | 0.130466i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −32.0000 | − | 32.0000i | −2.07862 | − | 2.07862i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.00000 | −0.517477 | −0.258738 | − | 0.965947i | \(-0.583307\pi\) | ||||
−0.258738 | + | 0.965947i | \(0.583307\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.0000 | −1.03065 | −0.515325 | − | 0.856995i | \(-0.672329\pi\) | ||||
−0.515325 | + | 0.856995i | \(0.672329\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.0000 | + | 10.0000i | 0.641500 | + | 0.641500i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.00000 | + | 1.00000i | 0.127775 | + | 0.0638877i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.00000 | − | 4.00000i | −0.254514 | − | 0.254514i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 8.00000i | − | 0.506979i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.0000 | 1.51487 | 0.757433 | − | 0.652913i | \(-0.226453\pi\) | ||||
0.757433 | + | 0.652913i | \(0.226453\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −20.0000 | + | 40.0000i | −1.25245 | + | 2.50490i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.00000 | − | 7.00000i | 0.436648 | − | 0.436648i | −0.454234 | − | 0.890882i | \(-0.650087\pi\) |
0.890882 | + | 0.454234i | \(0.150087\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.00000i | 0.248548i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.0000i | 1.23797i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.00000 | − | 6.00000i | 0.369976 | − | 0.369976i | −0.497492 | − | 0.867468i | \(-0.665746\pi\) |
0.867468 | + | 0.497492i | \(0.165746\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.00000 | − | 21.0000i | −0.430007 | − | 1.29002i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.0000 | 0.609711 | 0.304855 | − | 0.952399i | \(-0.401392\pi\) | ||||
0.304855 | + | 0.952399i | \(0.401392\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.0000i | 1.21491i | 0.794353 | + | 0.607457i | \(0.207810\pi\) | ||||
−0.794353 | + | 0.607457i | \(0.792190\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.00000 | − | 8.00000i | −0.484182 | − | 0.484182i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.00000 | − | 9.00000i | −0.540758 | − | 0.540758i | 0.382993 | − | 0.923751i | \(-0.374893\pi\) |
−0.923751 | + | 0.382993i | \(0.874893\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 20.0000 | 1.19737 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.00000 | −0.477240 | −0.238620 | − | 0.971113i | \(-0.576695\pi\) | ||||
−0.238620 | + | 0.971113i | \(0.576695\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.00000 | − | 6.00000i | −0.356663 | − | 0.356663i | 0.505918 | − | 0.862581i | \(-0.331154\pi\) |
−0.862581 | + | 0.505918i | \(0.831154\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.00000 | + | 24.0000i | 0.473879 | + | 1.42164i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 33.0000i | − | 1.94118i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.0000 | −0.703452 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.00000 | − | 5.00000i | 0.292103 | − | 0.292103i | −0.545807 | − | 0.837911i | \(-0.683777\pi\) |
0.837911 | + | 0.545807i | \(0.183777\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.00000 | − | 4.00000i | −0.465778 | − | 0.232889i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.00000i | 0.231326i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.0000i | 1.38334i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.0000 | − | 12.0000i | 0.689382 | − | 0.689382i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.00000 | + | 4.00000i | 0.458079 | + | 0.229039i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.0000 | − | 10.0000i | 0.570730 | − | 0.570730i | −0.361602 | − | 0.932332i | \(-0.617770\pi\) |
0.932332 | + | 0.361602i | \(0.117770\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −24.0000 | −1.36531 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.0000i | 1.58773i | 0.608091 | + | 0.793867i | \(0.291935\pi\) | ||||
−0.608091 | + | 0.793867i | \(0.708065\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.0000 | − | 15.0000i | −0.847850 | − | 0.847850i | 0.142014 | − | 0.989865i | \(-0.454642\pi\) |
−0.989865 | + | 0.142014i | \(0.954642\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.0000 | + | 30.0000i | 0.563436 | + | 1.69031i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.0000 | − | 11.0000i | −0.617822 | − | 0.617822i | 0.327151 | − | 0.944972i | \(-0.393912\pi\) |
−0.944972 | + | 0.327151i | \(0.893912\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 24.0000 | 1.33955 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.0000 | − | 20.0000i | −1.11283 | − | 1.11283i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.00000 | + | 1.00000i | 0.388290 | + | 0.0554700i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −20.0000 | − | 20.0000i | −1.10600 | − | 1.10600i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.00000i | 0.441054i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.00000 | + | 5.00000i | −0.273998 | + | 0.273998i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.0000 | − | 30.0000i | −0.546358 | − | 1.63908i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.0000 | + | 23.0000i | −1.25289 | + | 1.25289i | −0.298471 | + | 0.954419i | \(0.596477\pi\) |
−0.954419 | + | 0.298471i | \(0.903523\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 36.0000i | − | 1.95525i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.0000 | − | 12.0000i | 0.647939 | − | 0.647939i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.00000 | − | 16.0000i | 0.430706 | − | 0.861411i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.0000 | − | 18.0000i | 0.966291 | − | 0.966291i | −0.0331594 | − | 0.999450i | \(-0.510557\pi\) |
0.999450 | + | 0.0331594i | \(0.0105569\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.0000 | −1.07058 | −0.535288 | − | 0.844670i | \(-0.679797\pi\) | ||||
−0.535288 | + | 0.844670i | \(0.679797\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 8.00000i | − | 0.427008i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.00000 | + | 9.00000i | 0.479022 | + | 0.479022i | 0.904819 | − | 0.425797i | \(-0.140006\pi\) |
−0.425797 | + | 0.904819i | \(0.640006\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −24.0000 | − | 12.0000i | −1.27379 | − | 0.636894i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −40.0000 | − | 40.0000i | −2.11702 | − | 2.11702i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.0000 | −0.844448 | −0.422224 | − | 0.906492i | \(-0.638750\pi\) | ||||
−0.422224 | + | 0.906492i | \(0.638750\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −22.0000 | − | 22.0000i | −1.15470 | − | 1.15470i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.00000 | − | 3.00000i | 0.471082 | − | 0.157027i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.0000 | + | 22.0000i | 1.14839 | + | 1.14839i | 0.986869 | + | 0.161521i | \(0.0516401\pi\) |
0.161521 | + | 0.986869i | \(0.448360\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 28.0000 | 1.45369 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.0000 | + | 21.0000i | −1.08734 | + | 1.08734i | −0.0915371 | + | 0.995802i | \(0.529178\pi\) |
−0.995802 | + | 0.0915371i | \(0.970822\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −26.0000 | − | 18.0000i | −1.34263 | − | 0.929516i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.00000 | + | 4.00000i | −0.206010 | + | 0.206010i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 28.0000i | − | 1.43826i | −0.694874 | − | 0.719132i | \(-0.744540\pi\) | ||
0.694874 | − | 0.719132i | \(-0.255460\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 40.0000i | − | 2.04926i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.0000 | + | 22.0000i | −1.12415 | + | 1.12415i | −0.133036 | + | 0.991111i | \(0.542473\pi\) |
−0.991111 | + | 0.133036i | \(0.957527\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −30.0000 | + | 30.0000i | −1.52499 | + | 1.52499i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.0000 | 0.912636 | 0.456318 | − | 0.889817i | \(-0.349168\pi\) | ||||
0.456318 | + | 0.889817i | \(0.349168\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.0000i | 1.01144i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.0000 | + | 16.0000i | 0.807093 | + | 0.807093i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16.0000 | + | 32.0000i | −0.805047 | + | 1.61009i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.0000 | − | 13.0000i | −0.652451 | − | 0.652451i | 0.301131 | − | 0.953583i | \(-0.402636\pi\) |
−0.953583 | + | 0.301131i | \(0.902636\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −32.0000 | −1.60200 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 34.0000 | 1.69788 | 0.848939 | − | 0.528490i | \(-0.177242\pi\) | ||||
0.848939 | + | 0.528490i | \(0.177242\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.00000 | + | 4.00000i | 0.199254 | + | 0.199254i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | + | 2.00000i | −0.0496904 | + | 0.0993808i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.00000i | 0.0988936i | 0.998777 | + | 0.0494468i | \(0.0157458\pi\) | ||||
−0.998777 | + | 0.0494468i | \(0.984254\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.00000 | −0.197305 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.00000 | − | 8.00000i | 0.393654 | − | 0.393654i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.00000 | + | 2.00000i | −0.294528 | + | 0.0981761i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −24.0000 | + | 24.0000i | −1.17529 | + | 1.17529i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 12.0000i | − | 0.586238i | −0.956076 | − | 0.293119i | \(-0.905307\pi\) | ||
0.956076 | − | 0.293119i | \(-0.0946933\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.0000i | 0.974740i | 0.873195 | + | 0.487370i | \(0.162044\pi\) | ||||
−0.873195 | + | 0.487370i | \(0.837956\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.0000 | + | 10.0000i | −0.486217 | + | 0.486217i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 35.0000 | + | 5.00000i | 1.69775 | + | 0.242536i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.00000 | + | 8.00000i | −0.387147 | + | 0.387147i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.00000i | 0.192673i | 0.995349 | + | 0.0963366i | \(0.0307125\pi\) | ||||
−0.995349 | + | 0.0963366i | \(0.969287\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.0000 | − | 19.0000i | −0.913082 | − | 0.913082i | 0.0834318 | − | 0.996513i | \(-0.473412\pi\) |
−0.996513 | + | 0.0834318i | \(0.973412\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 24.0000 | − | 8.00000i | 1.15071 | − | 0.383571i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.00000 | + | 8.00000i | 0.382692 | + | 0.382692i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.0000 | −0.763638 | −0.381819 | − | 0.924237i | \(-0.624702\pi\) | ||||
−0.381819 | + | 0.924237i | \(0.624702\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.00000 | −0.238095 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.0000 | − | 22.0000i | −1.04525 | − | 1.04525i | −0.998926 | − | 0.0463251i | \(-0.985249\pi\) |
−0.0463251 | − | 0.998926i | \(-0.514751\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −36.0000 | − | 36.0000i | −1.70274 | − | 1.70274i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.0000i | 1.22702i | 0.789689 | + | 0.613508i | \(0.210242\pi\) | ||||
−0.789689 | + | 0.613508i | \(0.789758\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 24.0000 | − | 24.0000i | 1.12762 | − | 1.12762i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.00000 | + | 8.00000i | −0.187523 | + | 0.375046i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.0000 | + | 15.0000i | −0.701670 | + | 0.701670i | −0.964769 | − | 0.263099i | \(-0.915256\pi\) |
0.263099 | + | 0.964769i | \(0.415256\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 40.0000i | − | 1.86704i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.0000i | 0.652045i | 0.945362 | + | 0.326023i | \(0.105709\pi\) | ||||
−0.945362 | + | 0.326023i | \(0.894291\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.0000 | − | 22.0000i | 1.02243 | − | 1.02243i | 0.0226840 | − | 0.999743i | \(-0.492779\pi\) |
0.999743 | − | 0.0226840i | \(-0.00722117\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.00000 | − | 24.0000i | −0.370991 | − | 1.11297i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.00000 | + | 2.00000i | −0.0925490 | + | 0.0925490i | −0.751865 | − | 0.659317i | \(-0.770846\pi\) |
0.659317 | + | 0.751865i | \(0.270846\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 40.0000 | 1.84703 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 36.0000i | 1.65879i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.0000 | − | 12.0000i | 0.734130 | − | 0.550598i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 35.0000 | + | 35.0000i | 1.60254 | + | 1.60254i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.0000 | 1.09659 | 0.548294 | − | 0.836286i | \(-0.315277\pi\) | ||||
0.548294 | + | 0.836286i | \(0.315277\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.00000 | −0.0911922 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 16.0000 | + | 16.0000i | 0.728025 | + | 0.728025i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.00000 | + | 9.00000i | 0.136223 | + | 0.408669i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.00000 | − | 6.00000i | −0.271886 | − | 0.271886i | 0.557973 | − | 0.829859i | \(-0.311579\pi\) |
−0.829859 | + | 0.557973i | \(0.811579\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.00000i | 0.361773i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.0000 | 0.722070 | 0.361035 | − | 0.932552i | \(-0.382424\pi\) | ||||
0.361035 | + | 0.932552i | \(0.382424\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.0000 | + | 20.0000i | −0.900755 | + | 0.900755i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 24.0000 | − | 24.0000i | 1.07655 | − | 1.07655i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.00000i | 0.179065i | 0.995984 | + | 0.0895323i | \(0.0285372\pi\) | ||||
−0.995984 | + | 0.0895323i | \(0.971463\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 8.00000i | − | 0.357414i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.0000 | − | 10.0000i | 0.445878 | − | 0.445878i | −0.448104 | − | 0.893982i | \(-0.647900\pi\) |
0.893982 | + | 0.448104i | \(0.147900\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.0000 | − | 6.00000i | −0.533993 | − | 0.266996i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −22.0000 | + | 22.0000i | −0.977054 | + | 0.977054i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −36.0000 | −1.59567 | −0.797836 | − | 0.602875i | \(-0.794022\pi\) | ||||
−0.797836 | + | 0.602875i | \(0.794022\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.0000i | 0.530849i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −16.0000 | − | 16.0000i | −0.706417 | − | 0.706417i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.00000 | + | 18.0000i | 0.264392 | + | 0.793175i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 52.0000 | 2.28255 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.00000 | −0.262865 | −0.131432 | − | 0.991325i | \(-0.541958\pi\) | ||||
−0.131432 | + | 0.991325i | \(0.541958\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.0000 | − | 14.0000i | −0.612177 | − | 0.612177i | 0.331336 | − | 0.943513i | \(-0.392501\pi\) |
−0.943513 | + | 0.331336i | \(0.892501\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 32.0000 | − | 24.0000i | 1.39659 | − | 1.04745i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.0000 | + | 20.0000i | 0.871214 | + | 0.871214i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.0000i | 0.652174i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20.0000 | 0.867926 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.00000 | − | 18.0000i | −0.259403 | − | 0.778208i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −24.0000 | + | 24.0000i | −1.03568 | + | 1.03568i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.0000i | 1.28980i | 0.764267 | + | 0.644900i | \(0.223101\pi\) | ||||
−0.764267 | + | 0.644900i | \(0.776899\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 20.0000 | − | 20.0000i | 0.858282 | − | 0.858282i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.0000 | + | 20.0000i | −0.428353 | + | 0.856706i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.00000 | − | 6.00000i | 0.256541 | − | 0.256541i | −0.567104 | − | 0.823646i | \(-0.691936\pi\) |
0.823646 | + | 0.567104i | \(0.191936\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −20.0000 | −0.853579 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.0000i | 0.681623i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −32.0000 | − | 32.0000i | −1.36078 | − | 1.36078i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.00000 | + | 4.00000i | 0.339581 | + | 0.169791i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.0000 | + | 15.0000i | 0.635570 | + | 0.635570i | 0.949460 | − | 0.313889i | \(-0.101632\pi\) |
−0.313889 | + | 0.949460i | \(0.601632\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.0000 | −0.507546 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.00000 | − | 6.00000i | −0.252870 | − | 0.252870i | 0.569276 | − | 0.822146i | \(-0.307223\pi\) |
−0.822146 | + | 0.569276i | \(0.807223\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −27.0000 | + | 9.00000i | −1.13590 | + | 0.378633i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.00000 | − | 2.00000i | −0.0839921 | − | 0.0839921i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 2.00000i | − | 0.0838444i | −0.999121 | − | 0.0419222i | \(-0.986652\pi\) | ||
0.999121 | − | 0.0419222i | \(-0.0133482\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.0000 | 0.669579 | 0.334790 | − | 0.942293i | \(-0.391335\pi\) | ||||
0.334790 | + | 0.942293i | \(0.391335\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 40.0000 | − | 40.0000i | 1.67102 | − | 1.67102i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.0000 | − | 2.00000i | −0.583840 | − | 0.0834058i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.0000 | − | 15.0000i | 0.624458 | − | 0.624458i | −0.322210 | − | 0.946668i | \(-0.604426\pi\) |
0.946668 | + | 0.322210i | \(0.104426\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 20.0000i | − | 0.831172i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 8.00000i | − | 0.331896i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −15.0000 | + | 5.00000i | −0.620174 | + | 0.206725i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.0000 | + | 14.0000i | −0.577842 | + | 0.577842i | −0.934308 | − | 0.356466i | \(-0.883981\pi\) |
0.356466 | + | 0.934308i | \(0.383981\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.0000 | 0.659269 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.0000i | 0.822690i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.00000 | + | 1.00000i | 0.0410651 | + | 0.0410651i | 0.727341 | − | 0.686276i | \(-0.240756\pi\) |
−0.686276 | + | 0.727341i | \(0.740756\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20.0000 | + | 40.0000i | −0.819920 | + | 1.63984i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 48.0000 | + | 48.0000i | 1.96451 | + | 1.96451i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.00000 | −0.326871 | −0.163436 | − | 0.986554i | \(-0.552258\pi\) | ||||
−0.163436 | + | 0.986554i | \(0.552258\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.00000 | 0.326327 | 0.163163 | − | 0.986599i | \(-0.447830\pi\) | ||||
0.163163 | + | 0.986599i | \(0.447830\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 50.0000 | + | 50.0000i | 2.03616 | + | 2.03616i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11.0000 | + | 22.0000i | −0.447214 | + | 0.894427i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.0000 | + | 18.0000i | 0.730597 | + | 0.730597i | 0.970738 | − | 0.240141i | \(-0.0771936\pi\) |
−0.240141 | + | 0.970738i | \(0.577194\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 32.0000i | 1.29671i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.00000 | −0.161823 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.00000 | − | 9.00000i | 0.363507 | − | 0.363507i | −0.501596 | − | 0.865102i | \(-0.667253\pi\) |
0.865102 | + | 0.501596i | \(0.167253\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.0000 | − | 29.0000i | 1.16750 | − | 1.16750i | 0.184701 | − | 0.982795i | \(-0.440868\pi\) |
0.982795 | − | 0.184701i | \(-0.0591318\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.0000i | 1.12542i | 0.826656 | + | 0.562708i | \(0.190240\pi\) | ||||
−0.826656 | + | 0.562708i | \(0.809760\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 16.0000i | 0.642058i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.0000 | −0.398726 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 4.00000i | − | 0.159237i | −0.996825 | − | 0.0796187i | \(-0.974630\pi\) | ||
0.996825 | − | 0.0796187i | \(-0.0253703\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 32.0000 | + | 32.0000i | 1.27189 | + | 1.27189i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −30.0000 | + | 10.0000i | −1.19051 | + | 0.396838i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | − | 1.00000i | −0.0396214 | − | 0.0396214i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 60.0000 | 2.37356 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −48.0000 | −1.89589 | −0.947943 | − | 0.318440i | \(-0.896841\pi\) | ||||
−0.947943 | + | 0.318440i | \(0.896841\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.0000 | − | 10.0000i | −0.394362 | − | 0.394362i | 0.481877 | − | 0.876239i | \(-0.339955\pi\) |
−0.876239 | + | 0.481877i | \(0.839955\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 48.0000 | + | 24.0000i | 1.89000 | + | 0.944999i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.0000 | + | 10.0000i | 0.393141 | + | 0.393141i | 0.875805 | − | 0.482665i | \(-0.160331\pi\) |
−0.482665 | + | 0.875805i | \(0.660331\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 32.0000 | 1.25418 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.00000 | − | 1.00000i | 0.0391330 | − | 0.0391330i | −0.687270 | − | 0.726403i | \(-0.741191\pi\) |
0.726403 | + | 0.687270i | \(0.241191\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.00000 | − | 16.0000i | 0.312586 | − | 0.625172i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −15.0000 | + | 15.0000i | −0.585206 | + | 0.585206i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.0000i | 0.779089i | 0.921008 | + | 0.389545i | \(0.127368\pi\) | ||||
−0.921008 | + | 0.389545i | \(0.872632\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.0000i | 0.466746i | 0.972387 | + | 0.233373i | \(0.0749763\pi\) | ||||
−0.972387 | + | 0.233373i | \(0.925024\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 20.0000 | − | 20.0000i | 0.776736 | − | 0.776736i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.00000 | + | 24.0000i | 0.310227 | + | 0.930680i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.00000 | − | 8.00000i | 0.309761 | − | 0.309761i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 40.0000 | 1.54649 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.00000 | + | 5.00000i | 0.192736 | + | 0.192736i | 0.796877 | − | 0.604141i | \(-0.206484\pi\) |
−0.604141 | + | 0.796877i | \(0.706484\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 28.0000 | + | 4.00000i | 1.07772 | + | 0.153960i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.00000 | − | 3.00000i | −0.115299 | − | 0.115299i | 0.647103 | − | 0.762402i | \(-0.275980\pi\) |
−0.762402 | + | 0.647103i | \(0.775980\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.0000 | −0.460518 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −40.0000 | −1.53280 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.0000 | + | 22.0000i | 0.841807 | + | 0.841807i | 0.989094 | − | 0.147287i | \(-0.0470541\pi\) |
−0.147287 | + | 0.989094i | \(0.547054\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.00000 | + | 3.00000i | 0.0382080 | + | 0.114624i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −40.0000 | − | 40.0000i | −1.52610 | − | 1.52610i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.0000i | 0.533358i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.0000 | −1.21734 | −0.608669 | − | 0.793424i | \(-0.708296\pi\) | ||||
−0.608669 | + | 0.793424i | \(0.708296\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 24.0000 | + | 12.0000i | 0.910372 | + | 0.455186i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 20.0000i | 0.756469i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 20.0000i | − | 0.755390i | −0.925930 | − | 0.377695i | \(-0.876717\pi\) | ||
0.925930 | − | 0.377695i | \(-0.123283\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.00000 | + | 4.00000i | −0.150863 | + | 0.150863i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16.0000 | + | 8.00000i | 0.602595 | + | 0.301297i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.0000 | − | 12.0000i | 0.451306 | − | 0.451306i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.0000 | −0.450669 | −0.225335 | − | 0.974281i | \(-0.572348\pi\) | ||||
−0.225335 | + | 0.974281i | \(0.572348\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 80.0000i | − | 3.00023i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.00000 | − | 8.00000i | −0.299602 | − | 0.299602i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16.0000 | − | 16.0000i | −0.597531 | − | 0.597531i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.00000 | −0.298350 | −0.149175 | − | 0.988811i | \(-0.547662\pi\) | ||||
−0.149175 | + | 0.988811i | \(0.547662\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.0000 | −0.893807 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −32.0000 | − | 32.0000i | −1.19009 | − | 1.19009i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.0000 | − | 16.0000i | −0.445669 | − | 0.594225i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.0000 | + | 18.0000i | 0.667583 | + | 0.667583i | 0.957156 | − | 0.289573i | \(-0.0935133\pi\) |
−0.289573 | + | 0.957156i | \(0.593513\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 43.0000i | 1.59259i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −60.0000 | −2.21918 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.0000 | − | 21.0000i | 0.775653 | − | 0.775653i | −0.203436 | − | 0.979088i | \(-0.565211\pi\) |
0.979088 | + | 0.203436i | \(0.0652108\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.00000 | + | 6.00000i | 0.0737711 | + | 0.221313i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 44.0000i | 1.61857i | 0.587419 | + | 0.809283i | \(0.300144\pi\) | ||||
−0.587419 | + | 0.809283i | \(0.699856\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 16.0000i | − | 0.587775i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.0000 | − | 30.0000i | 1.10059 | − | 1.10059i | 0.106254 | − | 0.994339i | \(-0.466114\pi\) |
0.994339 | − | 0.106254i | \(-0.0338857\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.0000 | + | 36.0000i | −0.659469 | + | 1.31894i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.0000 | − | 10.0000i | 0.365881 | − | 0.365881i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24.0000 | 0.876941 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 44.0000i | 1.60558i | 0.596260 | + | 0.802791i | \(0.296653\pi\) | ||||
−0.596260 | + | 0.802791i | \(0.703347\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 48.0000 | + | 48.0000i | 1.74922 | + | 1.74922i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −24.0000 | − | 12.0000i | −0.873449 | − | 0.436725i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.00000 | − | 1.00000i | −0.0363456 | − | 0.0363456i | 0.688700 | − | 0.725046i | \(-0.258182\pi\) |
−0.725046 | + | 0.688700i | \(0.758182\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.0000 | 0.797499 | 0.398750 | − | 0.917060i | \(-0.369444\pi\) | ||||
0.398750 | + | 0.917060i | \(0.369444\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.0000 | − | 20.0000i | −0.724049 | − | 0.724049i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −75.0000 | + | 25.0000i | −2.71163 | + | 0.903877i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.00000 | + | 4.00000i | 0.144432 | + | 0.144432i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 40.0000i | − | 1.44244i | −0.692708 | − | 0.721218i | \(-0.743582\pi\) | ||
0.692708 | − | 0.721218i | \(-0.256418\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 28.0000 | 1.00840 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.00000 | − | 1.00000i | 0.0359675 | − | 0.0359675i | −0.688894 | − | 0.724862i | \(-0.741904\pi\) |
0.724862 | + | 0.688894i | \(0.241904\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16.0000 | + | 12.0000i | −0.574737 | + | 0.431053i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.00000 | + | 8.00000i | −0.286998 | + | 0.286998i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −16.0000 | + | 16.0000i | −0.571793 | + | 0.571793i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 27.0000 | − | 9.00000i | 0.963671 | − | 0.321224i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30.0000 | + | 30.0000i | −1.06938 | + | 1.06938i | −0.0719783 | + | 0.997406i | \(0.522931\pi\) |
−0.997406 | + | 0.0719783i | \(0.977069\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 24.0000 | 0.854423 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 36.0000i | − | 1.28001i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.00000 | − | 4.00000i | −0.142044 | − | 0.142044i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 28.0000 | − | 56.0000i | 0.993058 | − | 1.98612i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29.0000 | + | 29.0000i | 1.02723 | + | 1.02723i | 0.999619 | + | 0.0276140i | \(0.00879094\pi\) |
0.0276140 | + | 0.999619i | \(0.491209\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.0000 | −0.707549 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.00000 | − | 16.0000i | 0.281963 | − | 0.563926i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.0000 | + | 20.0000i | 0.704033 | + | 0.704033i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24.0000i | 0.843795i | 0.906644 | + | 0.421898i | \(0.138636\pi\) | ||||
−0.906644 | + | 0.421898i | \(0.861364\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.0000 | 0.842754 | 0.421377 | − | 0.906886i | \(-0.361547\pi\) | ||||
0.421377 | + | 0.906886i | \(0.361547\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −40.0000 | + | 40.0000i | −1.40286 | + | 1.40286i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.00000 | − | 2.00000i | 0.210171 | − | 0.0700569i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.0000 | + | 24.0000i | −0.839654 | + | 0.839654i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 20.0000i | − | 0.698857i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 28.0000i | − | 0.977207i | −0.872506 | − | 0.488603i | \(-0.837507\pi\) | ||
0.872506 | − | 0.488603i | \(-0.162493\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30.0000 | + | 30.0000i | −1.04573 | + | 1.04573i | −0.0468315 | + | 0.998903i | \(0.514912\pi\) |
−0.998903 | + | 0.0468315i | \(0.985088\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.00000 | − | 2.00000i | 0.0695468 | − | 0.0695468i | −0.671478 | − | 0.741025i | \(-0.734340\pi\) |
0.741025 | + | 0.671478i | \(0.234340\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.00000 | −0.208389 | −0.104194 | − | 0.994557i | \(-0.533226\pi\) | ||||
−0.104194 | + | 0.994557i | \(0.533226\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 36.0000i | − | 1.24883i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.00000 | − | 5.00000i | −0.173240 | − | 0.173240i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.00000 | + | 2.00000i | −0.207639 | + | 0.0692129i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.0000 | + | 16.0000i | 0.553041 | + | 0.553041i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.0000 | −0.828572 | −0.414286 | − | 0.910147i | \(-0.635969\pi\) | ||||
−0.414286 | + | 0.910147i | \(0.635969\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −16.0000 | − | 16.0000i | −0.551069 | − | 0.551069i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 22.0000 | + | 11.0000i | 0.756823 | + | 0.378412i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.0000 | − | 22.0000i | −0.755929 | − | 0.755929i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 24.0000i | − | 0.823678i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.00000 | 0.137118 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.0000 | + | 15.0000i | −0.513590 | + | 0.513590i | −0.915625 | − | 0.402034i | \(-0.868303\pi\) |
0.402034 | + | 0.915625i | \(0.368303\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −20.0000 | + | 40.0000i | −0.683986 | + | 1.36797i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.00000 | − | 7.00000i | 0.239115 | − | 0.239115i | −0.577368 | − | 0.816484i | \(-0.695920\pi\) |
0.816484 | + | 0.577368i | \(0.195920\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.0000i | 0.955348i | 0.878537 | + | 0.477674i | \(0.158520\pi\) | ||||
−0.878537 | + | 0.477674i | \(0.841480\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −34.0000 | + | 34.0000i | −1.15737 | + | 1.15737i | −0.172335 | + | 0.985038i | \(0.555131\pi\) |
−0.985038 | + | 0.172335i | \(0.944869\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.0000 | − | 39.0000i | −0.442013 | − | 1.32604i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 66.0000 | − | 66.0000i | 2.24148 | − | 2.24148i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.0000i | 0.677674i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −15.0000 | − | 15.0000i | −0.507673 | − | 0.507673i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −26.0000 | − | 18.0000i | −0.878960 | − | 0.608511i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.0000 | − | 15.0000i | −0.506514 | − | 0.506514i | 0.406941 | − | 0.913455i | \(-0.366596\pi\) |
−0.913455 | + | 0.406941i | \(0.866596\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 20.0000 | 0.674583 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40.0000 | −1.34763 | −0.673817 | − | 0.738898i | \(-0.735346\pi\) | ||||
−0.673817 | + | 0.738898i | \(0.735346\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.0000 | + | 10.0000i | 0.336527 | + | 0.336527i | 0.855058 | − | 0.518532i | \(-0.173521\pi\) |
−0.518532 | + | 0.855058i | \(0.673521\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.00000 | − | 24.0000i | −0.268917 | − | 0.806751i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.0000 | + | 10.0000i | 0.335767 | + | 0.335767i | 0.854772 | − | 0.519004i | \(-0.173697\pi\) |
−0.519004 | + | 0.854772i | \(0.673697\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 40.0000i | − | 1.34156i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.00000 | + | 8.00000i | −0.267710 | + | 0.267710i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.0000 | + | 12.0000i | 0.802232 | + | 0.401116i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.00000 | + | 8.00000i | −0.267112 | + | 0.267112i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 16.0000i | − | 0.533630i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 70.0000i | 2.33204i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −48.0000 | + | 48.0000i | −1.59734 | + | 1.59734i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.0000 | − | 10.0000i | −0.664822 | − | 0.332411i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.00000 | − | 6.00000i | 0.199227 | − | 0.199227i | −0.600442 | − | 0.799668i | \(-0.705009\pi\) |
0.799668 | + | 0.600442i | \(0.205009\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 30.0000 | 0.995037 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 4.00000i | − | 0.132526i | −0.997802 | − | 0.0662630i | \(-0.978892\pi\) | ||
0.997802 | − | 0.0662630i | \(-0.0211076\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.00000 | + | 24.0000i | 0.264472 | + | 0.793416i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.0000 | + | 16.0000i | 0.528367 | + | 0.528367i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.0000 | −0.791687 | −0.395843 | − | 0.918318i | \(-0.629548\pi\) | ||||
−0.395843 | + | 0.918318i | \(0.629548\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 40.0000 | 1.31804 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.0000 | + | 12.0000i | 0.394985 | + | 0.394985i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.00000 | − | 7.00000i | 0.0328798 | − | 0.230159i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −30.0000 | − | 30.0000i | −0.985329 | − | 0.985329i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.00000i | 0.196854i | 0.995144 | + | 0.0984268i | \(0.0313810\pi\) | ||||
−0.995144 | + | 0.0984268i | \(0.968619\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.00000 | −0.131095 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −56.0000 | + | 56.0000i | −1.83336 | + | 1.83336i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.0000 | + | 27.0000i | −0.882052 | + | 0.882052i | −0.993743 | − | 0.111691i | \(-0.964373\pi\) |
0.111691 | + | 0.993743i | \(0.464373\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 60.0000i | − | 1.95803i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 46.0000i | − | 1.49956i | −0.661689 | − | 0.749779i | \(-0.730160\pi\) | ||
0.661689 | − | 0.749779i | \(-0.269840\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −16.0000 | + | 32.0000i | −0.520480 | + | 1.04096i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.0000 | − | 10.0000i | 0.324956 | − | 0.324956i | −0.525708 | − | 0.850665i | \(-0.676200\pi\) |
0.850665 | + | 0.525708i | \(0.176200\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.00000 | −0.194768 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 44.0000i | − | 1.42680i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.00000 | + | 9.00000i | 0.291539 | + | 0.291539i | 0.837688 | − | 0.546149i | \(-0.183907\pi\) |
−0.546149 | + | 0.837688i | \(0.683907\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −40.0000 | − | 20.0000i | −1.29437 | − | 0.647185i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.00000 | −0.129167 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0000 | 0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 30.0000 | + | 30.0000i | 0.966736 | + | 0.966736i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15.0000 | + | 5.00000i | −0.482867 | + | 0.160956i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.0000 | − | 10.0000i | −0.321578 | − | 0.321578i | 0.527794 | − | 0.849372i | \(-0.323019\pi\) |
−0.849372 | + | 0.527794i | \(0.823019\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 80.0000i | − | 2.56997i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.00000 | −0.256732 | −0.128366 | − | 0.991727i | \(-0.540973\pi\) | ||||
−0.128366 | + | 0.991727i | \(0.540973\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.0000 | + | 24.0000i | −0.769405 | + | 0.769405i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12.0000 | + | 16.0000i | 0.384308 | + | 0.512410i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.0000 | − | 21.0000i | 0.671850 | − | 0.671850i | −0.286293 | − | 0.958142i | \(-0.592423\pi\) |
0.958142 | + | 0.286293i | \(0.0924230\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 50.0000i | − | 1.59638i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −34.0000 | + | 34.0000i | −1.08443 | + | 1.08443i | −0.0883413 | + | 0.996090i | \(0.528157\pi\) |
−0.996090 | + | 0.0883413i | \(0.971843\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.0000 | − | 5.00000i | 0.477940 | − | 0.159313i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.0000 | + | 16.0000i | −0.509286 | + | 0.509286i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.0000 | 0.763156 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.00000i | 0.127064i | 0.997980 | + | 0.0635321i | \(0.0202365\pi\) | ||||
−0.997980 | + | 0.0635321i | \(0.979763\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.0000 | − | 48.0000i | 0.760851 | − | 1.52170i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.0000 | − | 21.0000i | −0.665077 | − | 0.665077i | 0.291496 | − | 0.956572i | \(-0.405847\pi\) |
−0.956572 | + | 0.291496i | \(0.905847\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.00000 | −0.253109 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1280.2.o.p.383.1 | 2 | ||
4.3 | odd | 2 | 1280.2.o.b.383.1 | 2 | |||
5.2 | odd | 4 | 1280.2.o.o.127.1 | 2 | |||
8.3 | odd | 2 | 1280.2.o.o.383.1 | 2 | |||
8.5 | even | 2 | 1280.2.o.a.383.1 | 2 | |||
16.3 | odd | 4 | 160.2.n.f.63.1 | yes | 2 | ||
16.5 | even | 4 | 320.2.n.h.63.1 | 2 | |||
16.11 | odd | 4 | 320.2.n.a.63.1 | 2 | |||
16.13 | even | 4 | 160.2.n.a.63.1 | ✓ | 2 | ||
20.7 | even | 4 | 1280.2.o.a.127.1 | 2 | |||
40.27 | even | 4 | inner | 1280.2.o.p.127.1 | 2 | ||
40.37 | odd | 4 | 1280.2.o.b.127.1 | 2 | |||
48.29 | odd | 4 | 1440.2.x.i.703.1 | 2 | |||
48.35 | even | 4 | 1440.2.x.j.703.1 | 2 | |||
80.3 | even | 4 | 800.2.n.j.607.1 | 2 | |||
80.13 | odd | 4 | 800.2.n.a.607.1 | 2 | |||
80.19 | odd | 4 | 800.2.n.a.543.1 | 2 | |||
80.27 | even | 4 | 320.2.n.h.127.1 | 2 | |||
80.29 | even | 4 | 800.2.n.j.543.1 | 2 | |||
80.37 | odd | 4 | 320.2.n.a.127.1 | 2 | |||
80.43 | even | 4 | 1600.2.n.a.1407.1 | 2 | |||
80.53 | odd | 4 | 1600.2.n.n.1407.1 | 2 | |||
80.59 | odd | 4 | 1600.2.n.n.1343.1 | 2 | |||
80.67 | even | 4 | 160.2.n.a.127.1 | yes | 2 | ||
80.69 | even | 4 | 1600.2.n.a.1343.1 | 2 | |||
80.77 | odd | 4 | 160.2.n.f.127.1 | yes | 2 | ||
240.77 | even | 4 | 1440.2.x.j.127.1 | 2 | |||
240.227 | odd | 4 | 1440.2.x.i.127.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.2.n.a.63.1 | ✓ | 2 | 16.13 | even | 4 | ||
160.2.n.a.127.1 | yes | 2 | 80.67 | even | 4 | ||
160.2.n.f.63.1 | yes | 2 | 16.3 | odd | 4 | ||
160.2.n.f.127.1 | yes | 2 | 80.77 | odd | 4 | ||
320.2.n.a.63.1 | 2 | 16.11 | odd | 4 | |||
320.2.n.a.127.1 | 2 | 80.37 | odd | 4 | |||
320.2.n.h.63.1 | 2 | 16.5 | even | 4 | |||
320.2.n.h.127.1 | 2 | 80.27 | even | 4 | |||
800.2.n.a.543.1 | 2 | 80.19 | odd | 4 | |||
800.2.n.a.607.1 | 2 | 80.13 | odd | 4 | |||
800.2.n.j.543.1 | 2 | 80.29 | even | 4 | |||
800.2.n.j.607.1 | 2 | 80.3 | even | 4 | |||
1280.2.o.a.127.1 | 2 | 20.7 | even | 4 | |||
1280.2.o.a.383.1 | 2 | 8.5 | even | 2 | |||
1280.2.o.b.127.1 | 2 | 40.37 | odd | 4 | |||
1280.2.o.b.383.1 | 2 | 4.3 | odd | 2 | |||
1280.2.o.o.127.1 | 2 | 5.2 | odd | 4 | |||
1280.2.o.o.383.1 | 2 | 8.3 | odd | 2 | |||
1280.2.o.p.127.1 | 2 | 40.27 | even | 4 | inner | ||
1280.2.o.p.383.1 | 2 | 1.1 | even | 1 | trivial | ||
1440.2.x.i.127.1 | 2 | 240.227 | odd | 4 | |||
1440.2.x.i.703.1 | 2 | 48.29 | odd | 4 | |||
1440.2.x.j.127.1 | 2 | 240.77 | even | 4 | |||
1440.2.x.j.703.1 | 2 | 48.35 | even | 4 | |||
1600.2.n.a.1343.1 | 2 | 80.69 | even | 4 | |||
1600.2.n.a.1407.1 | 2 | 80.43 | even | 4 | |||
1600.2.n.n.1343.1 | 2 | 80.59 | odd | 4 | |||
1600.2.n.n.1407.1 | 2 | 80.53 | odd | 4 |