Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,2,Mod(63,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.63");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.n (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: | \(2.55521286468\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 160) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 63.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.63 |
Dual form | 320.2.n.h.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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | 0.169102 | − | 0.985599i | \(-0.445913\pi\) |
0.985599 | − | 0.169102i | \(-0.0540867\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000 | + | 1.00000i | 0.894427 | + | 0.447214i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | − | 2.00000i | −0.755929 | − | 0.755929i | 0.219650 | − | 0.975579i | \(-0.429509\pi\) |
−0.975579 | + | 0.219650i | \(0.929509\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 5.00000i | − | 1.66667i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | + | 1.00000i | 0.277350 | + | 0.277350i | 0.832050 | − | 0.554700i | \(-0.187167\pi\) |
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | 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 | ||||||||
\(19\) | 4.00000 | 0.917663 | 0.458831 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458831 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.00000 | −1.74574 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.00000 | + | 2.00000i | −0.417029 | + | 0.417029i | −0.884178 | − | 0.467150i | \(-0.845281\pi\) |
0.467150 | + | 0.884178i | \(0.345281\pi\) | |||||||
\(24\) | 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 | ||||||||
\(29\) | − | 4.00000i | − | 0.742781i | −0.928477 | − | 0.371391i | \(-0.878881\pi\) | ||
0.928477 | − | 0.371391i | \(-0.121119\pi\) | |||||||
\(30\) | 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 | ||||||||
\(35\) | −2.00000 | − | 6.00000i | −0.338062 | − | 1.01419i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | + | 1.00000i | −0.164399 | + | 0.164399i | −0.784512 | − | 0.620113i | \(-0.787087\pi\) |
0.620113 | + | 0.784512i | \(0.287087\pi\) | |||||||
\(38\) | 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 | \(-0.973975\pi\) |
0.0816682 | + | 0.996660i | \(0.473975\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.00000 | − | 10.0000i | 0.745356 | − | 1.49071i | ||||
\(46\) | 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 | ||||||||
\(51\) | 20.0000i | 2.80056i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.00000 | + | 7.00000i | 0.961524 | + | 0.961524i | 0.999287 | − | 0.0377628i | \(-0.0120231\pi\) |
−0.0377628 | + | 0.999287i | \(0.512023\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.00000 | − | 8.00000i | 1.05963 | − | 1.05963i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.00000 | 0.512148 | 0.256074 | − | 0.966657i | \(-0.417571\pi\) | ||||
0.256074 | + | 0.966657i | \(0.417571\pi\) | |||||||
\(62\) | 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 | −0.967029 | − | 0.254665i | \(-0.918035\pi\) |
−0.254665 | − | 0.967029i | \(-0.581965\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.00000i | 0.963087i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000i | 1.42414i | 0.702109 | + | 0.712069i | \(0.252242\pi\) | ||||
−0.702109 | + | 0.712069i | \(0.747758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.00000 | − | 3.00000i | −0.351123 | − | 0.351123i | 0.509404 | − | 0.860527i | \(-0.329866\pi\) |
−0.860527 | + | 0.509404i | \(0.829866\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 14.0000 | + | 2.00000i | 1.61658 | + | 0.230940i | ||||
\(76\) | 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 | −0.808300 | − | 0.588771i | \(-0.799612\pi\) |
0.588771 | + | 0.808300i | \(0.299612\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.0000 | + | 5.00000i | −1.62698 | + | 0.542326i | ||||
\(86\) | 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 | ||||||||
\(91\) | − | 4.00000i | − | 0.419314i | ||||||
\(92\) | 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 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.00000 | − | 6.00000i | 0.591198 | − | 0.591198i | −0.346757 | − | 0.937955i | \(-0.612717\pi\) |
0.937955 | + | 0.346757i | \(0.112717\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −16.0000 | − | 8.00000i | −1.56144 | − | 0.780720i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.00000 | + | 6.00000i | 0.580042 | + | 0.580042i | 0.934915 | − | 0.354873i | \(-0.115476\pi\) |
−0.354873 | + | 0.934915i | \(0.615476\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0000i | 0.957826i | 0.877862 | + | 0.478913i | \(0.158969\pi\) | ||||
−0.877862 | + | 0.478913i | \(0.841031\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | −6.00000 | + | 2.00000i | −0.559503 | + | 0.186501i | ||||
\(116\) | 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 | ||||||||
\(125\) | 2.00000 | + | 11.0000i | 0.178885 | + | 0.983870i | ||||
\(126\) | 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 | ||||||||
\(131\) | − | 8.00000i | − | 0.698963i | −0.936943 | − | 0.349482i | \(-0.886358\pi\) | ||
0.936943 | − | 0.349482i | \(-0.113642\pi\) | |||||||
\(132\) | 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 | −0.663097 | − | 0.748533i | \(-0.730758\pi\) |
0.748533 | + | 0.663097i | \(0.230758\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.0000 | −1.01783 | −0.508913 | − | 0.860818i | \(-0.669953\pi\) | ||||
−0.508913 | + | 0.860818i | \(0.669953\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.00000 | 0.673722 | ||||||||
\(142\) | 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 | ||||||||
\(149\) | − | 18.0000i | − | 1.47462i | −0.675556 | − | 0.737309i | \(-0.736096\pi\) | ||
0.675556 | − | 0.737309i | \(-0.263904\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0000i | 0.976546i | 0.872691 | + | 0.488273i | \(0.162373\pi\) | ||||
−0.872691 | + | 0.488273i | \(0.837627\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 25.0000 | + | 25.0000i | 2.02113 | + | 2.02113i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.00000 | − | 8.00000i | 0.321288 | − | 0.642575i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.00000 | − | 9.00000i | 0.718278 | − | 0.718278i | −0.249974 | − | 0.968252i | \(-0.580422\pi\) |
0.968252 | + | 0.249974i | \(0.0804222\pi\) | |||||||
\(158\) | 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 | −0.624429 | − | 0.781081i | \(-0.714668\pi\) |
0.781081 | + | 0.624429i | \(0.214668\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.00000 | + | 2.00000i | 0.154765 | + | 0.154765i | 0.780242 | − | 0.625478i | \(-0.215096\pi\) |
−0.625478 | + | 0.780242i | \(0.715096\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 11.0000i | − | 0.846154i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 20.0000i | − | 1.52944i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.0000 | − | 13.0000i | −0.988372 | − | 0.988372i | 0.0115615 | − | 0.999933i | \(-0.496320\pi\) |
−0.999933 | + | 0.0115615i | \(0.996320\pi\) | |||||||
\(174\) | 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 | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.0000 | 0.743294 | 0.371647 | − | 0.928374i | \(-0.378793\pi\) | ||||
0.371647 | + | 0.928374i | \(0.378793\pi\) | |||||||
\(182\) | 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 | ||||||||
\(189\) | 16.0000i | 1.16383i | ||||||||
\(190\) | 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 | ||||||||
\(195\) | 8.00000 | + | 4.00000i | 0.572892 | + | 0.286446i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.00000 | + | 5.00000i | −0.356235 | + | 0.356235i | −0.862423 | − | 0.506188i | \(-0.831054\pi\) |
0.506188 | + | 0.862423i | \(0.331054\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.0000 | −1.70131 | −0.850657 | − | 0.525720i | \(-0.823796\pi\) | ||||
−0.850657 | + | 0.525720i | \(0.823796\pi\) | |||||||
\(200\) | 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 | ||||||||
\(211\) | − | 16.0000i | − | 1.10149i | −0.834675 | − | 0.550743i | \(-0.814345\pi\) | ||
0.834675 | − | 0.550743i | \(-0.185655\pi\) | |||||||
\(212\) | 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 | ||||||||
\(219\) | −12.0000 | −0.810885 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.0000 | −0.672673 | ||||||||
\(222\) | 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 | \(-0.0944979\pi\) |
−0.292532 | + | 0.956256i | \(0.594498\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 20.0000i | − | 1.32164i | −0.750546 | − | 0.660819i | \(-0.770209\pi\) | ||
0.750546 | − | 0.660819i | \(-0.229791\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.00000 | − | 5.00000i | −0.327561 | − | 0.327561i | 0.524097 | − | 0.851658i | \(-0.324403\pi\) |
−0.851658 | + | 0.524097i | \(0.824403\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.00000 | + | 6.00000i | 0.130466 | + | 0.391397i | ||||
\(236\) | 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 | ||||||||
\(245\) | −1.00000 | + | 2.00000i | −0.0638877 | + | 0.127775i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.00000 | + | 4.00000i | 0.254514 | + | 0.254514i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.00000i | 0.506979i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.0000i | 1.51487i | 0.652913 | + | 0.757433i | \(0.273547\pi\) | ||||
−0.652913 | + | 0.757433i | \(0.726453\pi\) | |||||||
\(252\) | 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 | ||||||||
\(259\) | 4.00000 | 0.248548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −20.0000 | −1.23797 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.00000 | + | 6.00000i | −0.369976 | + | 0.369976i | −0.867468 | − | 0.497492i | \(-0.834254\pi\) |
0.497492 | + | 0.867468i | \(0.334254\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.00000 | + | 21.0000i | 0.430007 | + | 1.29002i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 10.0000i | − | 0.609711i | −0.952399 | − | 0.304855i | \(-0.901392\pi\) | ||
0.952399 | − | 0.304855i | \(-0.0986081\pi\) | |||||||
\(270\) | 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 | \(-0.625107\pi\) |
0.923751 | + | 0.382993i | \(0.125107\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −20.0000 | −1.19737 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.00000 | 0.477240 | 0.238620 | − | 0.971113i | \(-0.423305\pi\) | ||||
0.238620 | + | 0.971113i | \(0.423305\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.00000 | − | 6.00000i | 0.356663 | − | 0.356663i | −0.505918 | − | 0.862581i | \(-0.668846\pi\) |
0.862581 | + | 0.505918i | \(0.168846\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 24.0000 | − | 8.00000i | 1.42164 | − | 0.473879i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 33.0000i | − | 1.94118i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.0000i | 0.703452i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.00000 | + | 5.00000i | 0.292103 | + | 0.292103i | 0.837911 | − | 0.545807i | \(-0.183777\pi\) |
−0.545807 | + | 0.837911i | \(0.683777\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.00000 | + | 4.00000i | 0.465778 | + | 0.232889i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.00000 | −0.231326 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.0000 | 1.38334 | ||||||||
\(302\) | 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 | \(-0.382230\pi\) |
−0.932332 | + | 0.361602i | \(0.882230\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 24.0000i | − | 1.36531i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 28.0000i | − | 1.58773i | −0.608091 | − | 0.793867i | \(-0.708065\pi\) | ||
0.608091 | − | 0.793867i | \(-0.291935\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.0000 | + | 15.0000i | 0.847850 | + | 0.847850i | 0.989865 | − | 0.142014i | \(-0.0453579\pi\) |
−0.142014 | + | 0.989865i | \(0.545358\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −30.0000 | + | 10.0000i | −1.69031 | + | 0.563436i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.0000 | + | 11.0000i | −0.617822 | + | 0.617822i | −0.944972 | − | 0.327151i | \(-0.893912\pi\) |
0.327151 | + | 0.944972i | \(0.393912\pi\) | |||||||
\(318\) | 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 | ||||||||
\(325\) | −1.00000 | + | 7.00000i | −0.0554700 | + | 0.388290i | ||||
\(326\) | 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 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | 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 | ||||||||
\(339\) | −36.0000 | −1.95525 | ||||||||
\(340\) | 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 | 0.999450 | − | 0.0331594i | \(-0.0105569\pi\) |
−0.0331594 | + | 0.999450i | \(0.510557\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.0000i | 1.07058i | 0.844670 | + | 0.535288i | \(0.179797\pi\) | ||||
−0.844670 | + | 0.535288i | \(0.820203\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | −12.0000 | + | 24.0000i | −0.636894 | + | 1.27379i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 40.0000 | − | 40.0000i | 2.11702 | − | 2.11702i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.0000 | 0.844448 | 0.422224 | − | 0.906492i | \(-0.361250\pi\) | ||||
0.422224 | + | 0.906492i | \(0.361250\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 22.0000 | − | 22.0000i | 1.15470 | − | 1.15470i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.00000 | − | 9.00000i | −0.157027 | − | 0.471082i | ||||
\(366\) | 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 | ||||||||
\(371\) | − | 28.0000i | − | 1.45369i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.0000 | − | 21.0000i | −1.08734 | − | 1.08734i | −0.995802 | − | 0.0915371i | \(-0.970822\pi\) |
−0.0915371 | − | 0.995802i | \(-0.529178\pi\) | |||||||
\(374\) | 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 | ||||||||
\(379\) | 28.0000 | 1.43826 | 0.719132 | − | 0.694874i | \(-0.244540\pi\) | ||||
0.719132 | + | 0.694874i | \(0.244540\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −40.0000 | −2.04926 | ||||||||
\(382\) | 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 | ||||||||
\(389\) | 18.0000i | 0.912636i | 0.889817 | + | 0.456318i | \(0.150832\pi\) | ||||
−0.889817 | + | 0.456318i | \(0.849168\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 20.0000i | − | 1.01144i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.0000 | − | 16.0000i | −0.807093 | − | 0.807093i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −32.0000 | − | 16.0000i | −1.61009 | − | 0.805047i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.0000 | + | 13.0000i | −0.652451 | + | 0.652451i | −0.953583 | − | 0.301131i | \(-0.902636\pi\) |
0.301131 | + | 0.953583i | \(0.402636\pi\) | |||||||
\(398\) | 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 | ||||||||
\(405\) | −2.00000 | − | 1.00000i | −0.0993808 | − | 0.0496904i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 2.00000i | − | 0.0988936i | −0.998777 | − | 0.0494468i | \(-0.984254\pi\) | ||
0.998777 | − | 0.0494468i | \(-0.0157458\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 4.00000i | − | 0.197305i | ||||||
\(412\) | 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 | ||||||||
\(419\) | −12.0000 | −0.586238 | −0.293119 | − | 0.956076i | \(-0.594693\pi\) | ||||
−0.293119 | + | 0.956076i | \(0.594693\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.0000 | −0.974740 | −0.487370 | − | 0.873195i | \(-0.662044\pi\) | ||||
−0.487370 | + | 0.873195i | \(0.662044\pi\) | |||||||
\(422\) | 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 | ||||||||
\(435\) | −8.00000 | − | 24.0000i | −0.383571 | − | 1.15071i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.00000 | + | 8.00000i | −0.382692 | + | 0.382692i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.0000 | 0.763638 | 0.381819 | − | 0.924237i | \(-0.375298\pi\) | ||||
0.381819 | + | 0.924237i | \(0.375298\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.00000 | 0.238095 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.0000 | − | 22.0000i | 1.04525 | − | 1.04525i | 0.0463251 | − | 0.998926i | \(-0.485249\pi\) |
0.998926 | − | 0.0463251i | \(-0.0147510\pi\) | |||||||
\(444\) | 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 | −0.263099 | − | 0.964769i | \(-0.584744\pi\) |
0.964769 | + | 0.263099i | \(0.0847444\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 40.0000 | 1.86704 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.0000 | 0.652045 | 0.326023 | − | 0.945362i | \(-0.394291\pi\) | ||||
0.326023 | + | 0.945362i | \(0.394291\pi\) | |||||||
\(462\) | 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 | \(-0.229154\pi\) |
−0.659317 | + | 0.751865i | \(0.729154\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 40.0000i | 1.84703i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 36.0000i | − | 1.65879i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.0000 | + | 16.0000i | 0.550598 | + | 0.734130i | ||||
\(476\) | 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 | ||||||||
\(485\) | −9.00000 | + | 3.00000i | −0.408669 | + | 0.136223i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.00000 | + | 6.00000i | 0.271886 | + | 0.271886i | 0.829859 | − | 0.557973i | \(-0.188421\pi\) |
−0.557973 | + | 0.829859i | \(0.688421\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 8.00000i | − | 0.361773i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.0000i | 0.722070i | 0.932552 | + | 0.361035i | \(0.117576\pi\) | ||||
−0.932552 | + | 0.361035i | \(0.882424\pi\) | |||||||
\(492\) | 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 | ||||||||
\(499\) | 4.00000 | 0.179065 | 0.0895323 | − | 0.995984i | \(-0.471463\pi\) | ||||
0.0895323 | + | 0.995984i | \(0.471463\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.00000 | 0.357414 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.0000 | + | 10.0000i | −0.445878 | + | 0.445878i | −0.893982 | − | 0.448104i | \(-0.852100\pi\) |
0.448104 | + | 0.893982i | \(0.352100\pi\) | |||||||
\(504\) | 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 | ||||||||
\(509\) | 36.0000i | 1.59567i | 0.602875 | + | 0.797836i | \(0.294022\pi\) | ||||
−0.602875 | + | 0.797836i | \(0.705978\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.0000i | 0.530849i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −16.0000 | − | 16.0000i | −0.706417 | − | 0.706417i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 18.0000 | − | 6.00000i | 0.793175 | − | 0.264392i | ||||
\(516\) | 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 | \(-0.458042\pi\) | ||||
0.131432 | + | 0.991325i | \(0.458042\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.0000 | − | 14.0000i | 0.612177 | − | 0.612177i | −0.331336 | − | 0.943513i | \(-0.607499\pi\) |
0.943513 | + | 0.331336i | \(0.107499\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −24.0000 | − | 32.0000i | −1.04745 | − | 1.39659i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.0000 | + | 20.0000i | 0.871214 | + | 0.871214i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.0000i | 0.652174i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 20.0000i | − | 0.867926i | ||||||
\(532\) | 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 | ||||||||
\(541\) | 30.0000 | 1.28980 | 0.644900 | − | 0.764267i | \(-0.276899\pi\) | ||||
0.644900 | + | 0.764267i | \(0.276899\pi\) | |||||||
\(542\) | 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 | \(-0.308064\pi\) |
−0.823646 | + | 0.567104i | \(0.808064\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 20.0000i | − | 0.853579i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 16.0000i | − | 0.681623i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 32.0000 | + | 32.0000i | 1.36078 | + | 1.36078i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.00000 | + | 8.00000i | −0.169791 | + | 0.339581i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.0000 | − | 15.0000i | 0.635570 | − | 0.635570i | −0.313889 | − | 0.949460i | \(-0.601632\pi\) |
0.949460 | + | 0.313889i | \(0.101632\pi\) | |||||||
\(558\) | 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 | −0.822146 | − | 0.569276i | \(-0.807223\pi\) |
0.569276 | + | 0.822146i | \(0.307223\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.00000 | − | 27.0000i | −0.378633 | − | 1.13590i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.00000 | + | 2.00000i | 0.0839921 | + | 0.0839921i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.00000i | 0.0838444i | 0.999121 | + | 0.0419222i | \(0.0133482\pi\) | ||||
−0.999121 | + | 0.0419222i | \(0.986652\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.0000i | 0.669579i | 0.942293 | + | 0.334790i | \(0.108665\pi\) | ||||
−0.942293 | + | 0.334790i | \(0.891335\pi\) | |||||||
\(572\) | 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 | ||||||||
\(579\) | −20.0000 | −0.831172 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.00000 | 0.331896 | ||||||||
\(582\) | 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 | 0.356466 | − | 0.934308i | \(-0.383981\pi\) |
−0.934308 | + | 0.356466i | \(0.883981\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 16.0000i | − | 0.659269i | ||||||
\(590\) | 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 | ||||||||
\(595\) | 40.0000 | + | 20.0000i | 1.63984 | + | 0.819920i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −48.0000 | + | 48.0000i | −1.96451 | + | 1.96451i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.00000 | 0.326871 | 0.163436 | − | 0.986554i | \(-0.447742\pi\) | ||||
0.163436 | + | 0.986554i | \(0.447742\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.00000 | −0.326327 | −0.163163 | − | 0.986599i | \(-0.552170\pi\) | ||||
−0.163163 | + | 0.986599i | \(0.552170\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −50.0000 | + | 50.0000i | −2.03616 | + | 2.03616i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22.0000 | + | 11.0000i | 0.894427 | + | 0.447214i | ||||
\(606\) | 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 | ||||||||
\(611\) | 4.00000i | 0.161823i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.00000 | + | 9.00000i | 0.363507 | + | 0.363507i | 0.865102 | − | 0.501596i | \(-0.167253\pi\) |
−0.501596 | + | 0.865102i | \(0.667253\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.0000 | + | 29.0000i | −1.16750 | + | 1.16750i | −0.184701 | + | 0.982795i | \(0.559132\pi\) |
−0.982795 | + | 0.184701i | \(0.940868\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.0000 | −1.12542 | −0.562708 | − | 0.826656i | \(-0.690240\pi\) | ||||
−0.562708 | + | 0.826656i | \(0.690240\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 16.0000 | 0.642058 | ||||||||
\(622\) | 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 | ||||||||
\(629\) | − | 10.0000i | − | 0.398726i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.00000i | 0.159237i | 0.996825 | + | 0.0796187i | \(0.0253703\pi\) | ||||
−0.996825 | + | 0.0796187i | \(0.974630\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −32.0000 | − | 32.0000i | −1.27189 | − | 1.27189i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.0000 | − | 30.0000i | −0.396838 | − | 1.19051i | ||||
\(636\) | 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 | −0.876239 | − | 0.481877i | \(-0.839955\pi\) |
0.481877 | + | 0.876239i | \(0.339955\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −24.0000 | + | 48.0000i | −0.944999 | + | 1.89000i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.0000 | − | 10.0000i | −0.393141 | − | 0.393141i | 0.482665 | − | 0.875805i | \(-0.339669\pi\) |
−0.875805 | + | 0.482665i | \(0.839669\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 32.0000i | 1.25418i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.00000 | − | 1.00000i | −0.0391330 | − | 0.0391330i | 0.687270 | − | 0.726403i | \(-0.258809\pi\) |
−0.726403 | + | 0.687270i | \(0.758809\pi\) | |||||||
\(654\) | 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 | ||||||||
\(659\) | 20.0000 | 0.779089 | 0.389545 | − | 0.921008i | \(-0.372632\pi\) | ||||
0.389545 | + | 0.921008i | \(0.372632\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.0000 | −0.466746 | −0.233373 | − | 0.972387i | \(-0.574976\pi\) | ||||
−0.233373 | + | 0.972387i | \(0.574976\pi\) | |||||||
\(662\) | 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 | ||||||||
\(669\) | − | 40.0000i | − | 1.54649i | ||||||
\(670\) | 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 | ||||||||
\(675\) | 4.00000 | − | 28.0000i | 0.153960 | − | 1.07772i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.00000 | − | 3.00000i | 0.115299 | − | 0.115299i | −0.647103 | − | 0.762402i | \(-0.724020\pi\) |
0.762402 | + | 0.647103i | \(0.224020\pi\) | |||||||
\(678\) | 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 | \(-0.952946\pi\) |
0.147287 | + | 0.989094i | \(0.452946\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.00000 | − | 1.00000i | 0.114624 | − | 0.0382080i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −40.0000 | − | 40.0000i | −1.52610 | − | 1.52610i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.0000i | 0.533358i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.0000i | 1.21734i | 0.793424 | + | 0.608669i | \(0.208296\pi\) | ||||
−0.793424 | + | 0.608669i | \(0.791704\pi\) | |||||||
\(692\) | 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 | ||||||||
\(699\) | −20.0000 | −0.756469 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.0000 | −0.755390 | −0.377695 | − | 0.925930i | \(-0.623283\pi\) | ||||
−0.377695 | + | 0.925930i | \(0.623283\pi\) | |||||||
\(702\) | 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 | ||||||||
\(709\) | − | 12.0000i | − | 0.450669i | −0.974281 | − | 0.225335i | \(-0.927652\pi\) | ||
0.974281 | − | 0.225335i | \(-0.0723476\pi\) | |||||||
\(710\) | 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 | ||||||||
\(725\) | 16.0000 | − | 12.0000i | 0.594225 | − | 0.445669i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.0000 | − | 18.0000i | −0.667583 | − | 0.667583i | 0.289573 | − | 0.957156i | \(-0.406487\pi\) |
−0.957156 | + | 0.289573i | \(0.906487\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 43.0000i | − | 1.59259i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 60.0000i | − | 2.21918i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.0000 | − | 21.0000i | −0.775653 | − | 0.775653i | 0.203436 | − | 0.979088i | \(-0.434789\pi\) |
−0.979088 | + | 0.203436i | \(0.934789\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.00000 | + | 6.00000i | 0.0737711 | + | 0.221313i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 44.0000 | 1.61857 | 0.809283 | − | 0.587419i | \(-0.199856\pi\) | ||||
0.809283 | + | 0.587419i | \(0.199856\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.0000 | 0.587775 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.0000 | + | 30.0000i | −1.10059 | + | 1.10059i | −0.106254 | + | 0.994339i | \(0.533886\pi\) |
−0.994339 | + | 0.106254i | \(0.966114\pi\) | |||||||
\(744\) | 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 | ||||||||
\(749\) | − | 24.0000i | − | 0.876941i | ||||||
\(750\) | 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 | ||||||||
\(755\) | −12.0000 | + | 24.0000i | −0.436725 | + | 0.873449i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.00000 | − | 1.00000i | 0.0363456 | − | 0.0363456i | −0.688700 | − | 0.725046i | \(-0.741818\pi\) |
0.725046 | + | 0.688700i | \(0.241818\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.0000 | −0.797499 | −0.398750 | − | 0.917060i | \(-0.630556\pi\) | ||||
−0.398750 | + | 0.917060i | \(0.630556\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.0000 | − | 20.0000i | 0.724049 | − | 0.724049i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 25.0000 | + | 75.0000i | 0.903877 | + | 2.71163i | ||||
\(766\) | 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 | ||||||||
\(771\) | − | 28.0000i | − | 1.00840i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.00000 | + | 1.00000i | 0.0359675 | + | 0.0359675i | 0.724862 | − | 0.688894i | \(-0.241904\pi\) |
−0.688894 | + | 0.724862i | \(0.741904\pi\) | |||||||
\(774\) | 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 | 0.997406 | + | 0.0719783i | \(0.0229312\pi\) |
0.0719783 | + | 0.997406i | \(0.477069\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 24.0000i | 0.854423i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 36.0000i | 1.28001i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.00000 | + | 4.00000i | 0.142044 | + | 0.142044i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 56.0000 | + | 28.0000i | 1.98612 | + | 0.993058i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29.0000 | − | 29.0000i | 1.02723 | − | 1.02723i | 0.0276140 | − | 0.999619i | \(-0.491209\pi\) |
0.999619 | − | 0.0276140i | \(-0.00879094\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.0000 | −0.707549 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.0000 | + | 8.00000i | 0.563926 | + | 0.281963i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20.0000 | − | 20.0000i | −0.704033 | − | 0.704033i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 24.0000i | − | 0.843795i | −0.906644 | − | 0.421898i | \(-0.861364\pi\) | ||
0.906644 | − | 0.421898i | \(-0.138636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.0000i | 0.842754i | 0.906886 | + | 0.421377i | \(0.138453\pi\) | ||||
−0.906886 | + | 0.421377i | \(0.861547\pi\) | |||||||
\(812\) | 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 | ||||||||
\(819\) | −20.0000 | −0.698857 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.0000 | 0.977207 | 0.488603 | − | 0.872506i | \(-0.337507\pi\) | ||||
0.488603 | + | 0.872506i | \(0.337507\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.0000 | − | 30.0000i | 1.04573 | − | 1.04573i | 0.0468315 | − | 0.998903i | \(-0.485088\pi\) |
0.998903 | − | 0.0468315i | \(-0.0149124\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.00000 | + | 2.00000i | 0.0695468 | + | 0.0695468i | 0.741025 | − | 0.671478i | \(-0.234340\pi\) |
−0.671478 | + | 0.741025i | \(0.734340\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.00000i | 0.208389i | 0.994557 | + | 0.104194i | \(0.0332264\pi\) | ||||
−0.994557 | + | 0.104194i | \(0.966774\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 36.0000i | − | 1.24883i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.00000 | − | 5.00000i | −0.173240 | − | 0.173240i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.00000 | + | 6.00000i | 0.0692129 | + | 0.207639i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16.0000 | + | 16.0000i | −0.553041 | + | 0.553041i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.0000 | 0.828572 | 0.414286 | − | 0.910147i | \(-0.364031\pi\) | ||||
0.414286 | + | 0.910147i | \(0.364031\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.0000 | 0.448276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16.0000 | − | 16.0000i | 0.551069 | − | 0.551069i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.0000 | − | 22.0000i | 0.378412 | − | 0.756823i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.0000 | − | 22.0000i | −0.755929 | − | 0.755929i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 24.0000i | − | 0.823678i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 4.00000i | − | 0.137118i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.0000 | − | 15.0000i | −0.513590 | − | 0.513590i | 0.402034 | − | 0.915625i | \(-0.368303\pi\) |
−0.915625 | + | 0.402034i | \(0.868303\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 20.0000 | − | 40.0000i | 0.683986 | − | 1.36797i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.00000 | + | 7.00000i | −0.239115 | + | 0.239115i | −0.816484 | − | 0.577368i | \(-0.804080\pi\) |
0.577368 | + | 0.816484i | \(0.304080\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.0000 | −0.955348 | −0.477674 | − | 0.878537i | \(-0.658520\pi\) | ||||
−0.477674 | + | 0.878537i | \(0.658520\pi\) | |||||||
\(860\) | 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 | ||||||||
\(875\) | 18.0000 | − | 26.0000i | 0.608511 | − | 0.878960i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.0000 | + | 15.0000i | −0.506514 | + | 0.506514i | −0.913455 | − | 0.406941i | \(-0.866596\pi\) |
0.406941 | + | 0.913455i | \(0.366596\pi\) | |||||||
\(878\) | 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 | −0.518532 | − | 0.855058i | \(-0.673521\pi\) |
0.855058 | + | 0.518532i | \(0.173521\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 24.0000 | − | 8.00000i | 0.806751 | − | 0.268917i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.0000 | − | 10.0000i | −0.335767 | − | 0.335767i | 0.519004 | − | 0.854772i | \(-0.326303\pi\) |
−0.854772 | + | 0.519004i | \(0.826303\pi\) | |||||||
\(888\) | 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 | ||||||||
\(899\) | −16.0000 | −0.533630 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −70.0000 | −2.33204 | ||||||||
\(902\) | 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 | 0.799668 | − | 0.600442i | \(-0.205009\pi\) |
−0.600442 | + | 0.799668i | \(0.705009\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 30.0000i | − | 0.995037i | ||||||
\(910\) | 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 | ||||||||
\(915\) | 24.0000 | − | 8.00000i | 0.793416 | − | 0.264472i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16.0000 | + | 16.0000i | −0.528367 | + | 0.528367i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.0000 | 0.791687 | 0.395843 | − | 0.918318i | \(-0.370452\pi\) | ||||
0.395843 | + | 0.918318i | \(0.370452\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −40.0000 | −1.31804 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.0000 | + | 12.0000i | −0.394985 | + | 0.394985i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.00000 | − | 1.00000i | −0.230159 | − | 0.0328798i | ||||
\(926\) | 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 | ||||||||
\(931\) | 4.00000i | 0.131095i | ||||||||
\(932\) | 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 | −0.111691 | − | 0.993743i | \(-0.535627\pi\) |
0.993743 | + | 0.111691i | \(0.0356268\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 60.0000 | 1.95803 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −46.0000 | −1.49956 | −0.749779 | − | 0.661689i | \(-0.769840\pi\) | ||||
−0.749779 | + | 0.661689i | \(0.769840\pi\) | |||||||
\(942\) | 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 | \(-0.323800\pi\) |
−0.850665 | + | 0.525708i | \(0.823800\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 6.00000i | − | 0.194768i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 44.0000i | 1.42680i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.00000 | − | 9.00000i | −0.291539 | − | 0.291539i | 0.546149 | − | 0.837688i | \(-0.316093\pi\) |
−0.837688 | + | 0.546149i | \(0.816093\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.0000 | − | 40.0000i | 0.647185 | − | 1.29437i | ||||
\(956\) | 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 | ||||||||
\(965\) | −5.00000 | − | 15.0000i | −0.160956 | − | 0.482867i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.0000 | + | 10.0000i | 0.321578 | + | 0.321578i | 0.849372 | − | 0.527794i | \(-0.176981\pi\) |
−0.527794 | + | 0.849372i | \(0.676981\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 80.0000i | 2.56997i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 8.00000i | − | 0.256732i | −0.991727 | − | 0.128366i | \(-0.959027\pi\) | ||
0.991727 | − | 0.128366i | \(-0.0409733\pi\) | |||||||
\(972\) | 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 | ||||||||
\(981\) | 50.0000 | 1.59638 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 34.0000 | − | 34.0000i | 1.08443 | − | 1.08443i | 0.0883413 | − | 0.996090i | \(-0.471843\pi\) |
0.996090 | − | 0.0883413i | \(-0.0281566\pi\) | |||||||
\(984\) | 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 | ||||||||
\(989\) | − | 24.0000i | − | 0.763156i | ||||||
\(990\) | 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 | ||||||||
\(995\) | −48.0000 | − | 24.0000i | −1.52170 | − | 0.760851i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.0000 | − | 21.0000i | 0.665077 | − | 0.665077i | −0.291496 | − | 0.956572i | \(-0.594153\pi\) |
0.956572 | + | 0.291496i | \(0.0941528\pi\) | |||||||
\(998\) | 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 | 320.2.n.h.63.1 | 2 | ||
4.3 | odd | 2 | 320.2.n.a.63.1 | 2 | |||
5.2 | odd | 4 | 320.2.n.a.127.1 | 2 | |||
5.3 | odd | 4 | 1600.2.n.n.1407.1 | 2 | |||
5.4 | even | 2 | 1600.2.n.a.1343.1 | 2 | |||
8.3 | odd | 2 | 160.2.n.f.63.1 | yes | 2 | ||
8.5 | even | 2 | 160.2.n.a.63.1 | ✓ | 2 | ||
16.3 | odd | 4 | 1280.2.o.b.383.1 | 2 | |||
16.5 | even | 4 | 1280.2.o.a.383.1 | 2 | |||
16.11 | odd | 4 | 1280.2.o.o.383.1 | 2 | |||
16.13 | even | 4 | 1280.2.o.p.383.1 | 2 | |||
20.3 | even | 4 | 1600.2.n.a.1407.1 | 2 | |||
20.7 | even | 4 | inner | 320.2.n.h.127.1 | 2 | ||
20.19 | odd | 2 | 1600.2.n.n.1343.1 | 2 | |||
24.5 | odd | 2 | 1440.2.x.i.703.1 | 2 | |||
24.11 | even | 2 | 1440.2.x.j.703.1 | 2 | |||
40.3 | even | 4 | 800.2.n.j.607.1 | 2 | |||
40.13 | odd | 4 | 800.2.n.a.607.1 | 2 | |||
40.19 | odd | 2 | 800.2.n.a.543.1 | 2 | |||
40.27 | even | 4 | 160.2.n.a.127.1 | yes | 2 | ||
40.29 | even | 2 | 800.2.n.j.543.1 | 2 | |||
40.37 | odd | 4 | 160.2.n.f.127.1 | yes | 2 | ||
80.27 | even | 4 | 1280.2.o.p.127.1 | 2 | |||
80.37 | odd | 4 | 1280.2.o.b.127.1 | 2 | |||
80.67 | even | 4 | 1280.2.o.a.127.1 | 2 | |||
80.77 | odd | 4 | 1280.2.o.o.127.1 | 2 | |||
120.77 | even | 4 | 1440.2.x.j.127.1 | 2 | |||
120.107 | 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 | 8.5 | even | 2 | ||
160.2.n.a.127.1 | yes | 2 | 40.27 | even | 4 | ||
160.2.n.f.63.1 | yes | 2 | 8.3 | odd | 2 | ||
160.2.n.f.127.1 | yes | 2 | 40.37 | odd | 4 | ||
320.2.n.a.63.1 | 2 | 4.3 | odd | 2 | |||
320.2.n.a.127.1 | 2 | 5.2 | odd | 4 | |||
320.2.n.h.63.1 | 2 | 1.1 | even | 1 | trivial | ||
320.2.n.h.127.1 | 2 | 20.7 | even | 4 | inner | ||
800.2.n.a.543.1 | 2 | 40.19 | odd | 2 | |||
800.2.n.a.607.1 | 2 | 40.13 | odd | 4 | |||
800.2.n.j.543.1 | 2 | 40.29 | even | 2 | |||
800.2.n.j.607.1 | 2 | 40.3 | even | 4 | |||
1280.2.o.a.127.1 | 2 | 80.67 | even | 4 | |||
1280.2.o.a.383.1 | 2 | 16.5 | even | 4 | |||
1280.2.o.b.127.1 | 2 | 80.37 | odd | 4 | |||
1280.2.o.b.383.1 | 2 | 16.3 | odd | 4 | |||
1280.2.o.o.127.1 | 2 | 80.77 | odd | 4 | |||
1280.2.o.o.383.1 | 2 | 16.11 | odd | 4 | |||
1280.2.o.p.127.1 | 2 | 80.27 | even | 4 | |||
1280.2.o.p.383.1 | 2 | 16.13 | even | 4 | |||
1440.2.x.i.127.1 | 2 | 120.107 | odd | 4 | |||
1440.2.x.i.703.1 | 2 | 24.5 | odd | 2 | |||
1440.2.x.j.127.1 | 2 | 120.77 | even | 4 | |||
1440.2.x.j.703.1 | 2 | 24.11 | even | 2 | |||
1600.2.n.a.1343.1 | 2 | 5.4 | even | 2 | |||
1600.2.n.a.1407.1 | 2 | 20.3 | even | 4 | |||
1600.2.n.n.1343.1 | 2 | 20.19 | odd | 2 | |||
1600.2.n.n.1407.1 | 2 | 5.3 | odd | 4 |