Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(543,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.543");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.o (of order \(4\), degree \(2\), 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: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 607.1 | ||
Root | \(0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.607 |
Dual form | 1600.2.o.i.543.1 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | −0.881127 | − | 0.472879i | \(-0.843215\pi\) |
0.472879 | + | 0.881127i | \(0.343215\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.00000i | 0.666667i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.73205 | −0.522233 | −0.261116 | − | 0.965307i | \(-0.584091\pi\) | ||||
−0.261116 | + | 0.965307i | \(0.584091\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.82843 | − | 2.82843i | −0.784465 | − | 0.784465i | 0.196116 | − | 0.980581i | \(-0.437167\pi\) |
−0.980581 | + | 0.196116i | \(0.937167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.22474 | + | 1.22474i | 0.297044 | + | 0.297044i | 0.839855 | − | 0.542811i | \(-0.182640\pi\) |
−0.542811 | + | 0.839855i | \(0.682640\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 5.19615i | − | 1.19208i | −0.802955 | − | 0.596040i | \(-0.796740\pi\) | ||
0.802955 | − | 0.596040i | \(-0.203260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.89898 | − | 4.89898i | −1.02151 | − | 1.02151i | −0.999764 | − | 0.0217443i | \(-0.993078\pi\) |
−0.0217443 | − | 0.999764i | \(-0.506922\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.53553 | − | 3.53553i | −0.680414 | − | 0.680414i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.92820 | 1.28654 | 0.643268 | − | 0.765641i | \(-0.277578\pi\) | ||||
0.643268 | + | 0.765641i | \(0.277578\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000i | 0.718421i | 0.933257 | + | 0.359211i | \(0.116954\pi\) | ||||
−0.933257 | + | 0.359211i | \(0.883046\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.22474 | − | 1.22474i | 0.213201 | − | 0.213201i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.65685 | − | 5.65685i | 0.929981 | − | 0.929981i | −0.0677230 | − | 0.997704i | \(-0.521573\pi\) |
0.997704 | + | 0.0677230i | \(0.0215734\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.00000 | 0.640513 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.00000 | 0.468521 | 0.234261 | − | 0.972174i | \(-0.424733\pi\) | ||||
0.234261 | + | 0.972174i | \(0.424733\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.65685 | + | 5.65685i | −0.862662 | + | 0.862662i | −0.991647 | − | 0.128984i | \(-0.958828\pi\) |
0.128984 | + | 0.991647i | \(0.458828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.89898 | − | 4.89898i | 0.714590 | − | 0.714590i | −0.252902 | − | 0.967492i | \(-0.581385\pi\) |
0.967492 | + | 0.252902i | \(0.0813851\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.00000i | 1.00000i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.73205 | −0.242536 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.48528 | − | 8.48528i | −1.16554 | − | 1.16554i | −0.983243 | − | 0.182300i | \(-0.941646\pi\) |
−0.182300 | − | 0.983243i | \(-0.558354\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.67423 | + | 3.67423i | 0.486664 | + | 0.486664i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 10.3923i | − | 1.35296i | −0.736460 | − | 0.676481i | \(-0.763504\pi\) | ||
0.736460 | − | 0.676481i | \(-0.236496\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.94975 | − | 4.94975i | −0.604708 | − | 0.604708i | 0.336850 | − | 0.941558i | \(-0.390638\pi\) |
−0.941558 | + | 0.336850i | \(0.890638\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.92820 | 0.834058 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12.0000i | − | 1.42414i | −0.702109 | − | 0.712069i | \(-0.747758\pi\) | ||
0.702109 | − | 0.712069i | \(-0.252242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.12372 | − | 6.12372i | 0.716728 | − | 0.716728i | −0.251206 | − | 0.967934i | \(-0.580827\pi\) |
0.967934 | + | 0.251206i | \(0.0808271\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.6066 | + | 10.6066i | −1.16423 | + | 1.16423i | −0.180685 | + | 0.983541i | \(0.557831\pi\) |
−0.983541 | + | 0.180685i | \(0.942169\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.89898 | + | 4.89898i | −0.525226 | + | 0.525226i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.00000i | 0.317999i | 0.987279 | + | 0.159000i | \(0.0508269\pi\) | ||||
−0.987279 | + | 0.159000i | \(0.949173\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.82843 | − | 2.82843i | −0.293294 | − | 0.293294i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 3.46410i | − | 0.348155i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 13.8564i | − | 1.37876i | −0.724398 | − | 0.689382i | \(-0.757882\pi\) | ||
0.724398 | − | 0.689382i | \(-0.242118\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.89898 | − | 4.89898i | −0.482711 | − | 0.482711i | 0.423286 | − | 0.905996i | \(-0.360877\pi\) |
−0.905996 | + | 0.423286i | \(0.860877\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.12132 | + | 2.12132i | 0.205076 | + | 0.205076i | 0.802171 | − | 0.597095i | \(-0.203678\pi\) |
−0.597095 | + | 0.802171i | \(0.703678\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.8564 | 1.32720 | 0.663602 | − | 0.748086i | \(-0.269027\pi\) | ||||
0.663602 | + | 0.748086i | \(0.269027\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.00000i | 0.759326i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.57321 | − | 8.57321i | 0.806500 | − | 0.806500i | −0.177602 | − | 0.984102i | \(-0.556834\pi\) |
0.984102 | + | 0.177602i | \(0.0568340\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.65685 | − | 5.65685i | 0.522976 | − | 0.522976i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.00000 | −0.727273 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.12132 | + | 2.12132i | −0.191273 | + | 0.191273i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.6969 | − | 14.6969i | 1.30414 | − | 1.30414i | 0.378570 | − | 0.925573i | \(-0.376416\pi\) |
0.925573 | − | 0.378570i | \(-0.123584\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 8.00000i | − | 0.704361i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.46410 | −0.302660 | −0.151330 | − | 0.988483i | \(-0.548356\pi\) | ||||
−0.151330 | + | 0.988483i | \(0.548356\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.67423 | − | 3.67423i | −0.313911 | − | 0.313911i | 0.532512 | − | 0.846423i | \(-0.321248\pi\) |
−0.846423 | + | 0.532512i | \(0.821248\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1.73205i | − | 0.146911i | −0.997299 | − | 0.0734553i | \(-0.976597\pi\) | ||
0.997299 | − | 0.0734553i | \(-0.0234026\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.92820i | 0.583460i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.89898 | + | 4.89898i | 0.409673 | + | 0.409673i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.94975 | − | 4.94975i | −0.408248 | − | 0.408248i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.92820 | −0.567581 | −0.283790 | − | 0.958886i | \(-0.591592\pi\) | ||||
−0.283790 | + | 0.958886i | \(0.591592\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 16.0000i | − | 1.30206i | −0.759051 | − | 0.651031i | \(-0.774337\pi\) | ||
0.759051 | − | 0.651031i | \(-0.225663\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.44949 | + | 2.44949i | −0.198030 | + | 0.198030i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.82843 | − | 2.82843i | 0.225733 | − | 0.225733i | −0.585174 | − | 0.810907i | \(-0.698974\pi\) |
0.810907 | + | 0.585174i | \(0.198974\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.0000 | 0.951662 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.94975 | − | 4.94975i | 0.387694 | − | 0.387694i | −0.486170 | − | 0.873864i | \(-0.661606\pi\) |
0.873864 | + | 0.486170i | \(0.161606\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.6969 | + | 14.6969i | −1.13728 | + | 1.13728i | −0.148348 | + | 0.988935i | \(0.547396\pi\) |
−0.988935 | + | 0.148348i | \(0.952604\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.00000i | 0.230769i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.3923 | 0.794719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.34847 | + | 7.34847i | 0.552345 | + | 0.552345i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.19615i | 0.388379i | 0.980964 | + | 0.194189i | \(0.0622076\pi\) | ||||
−0.980964 | + | 0.194189i | \(0.937792\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.92820i | 0.514969i | 0.966282 | + | 0.257485i | \(0.0828937\pi\) | ||||
−0.966282 | + | 0.257485i | \(0.917106\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.12132 | − | 2.12132i | −0.155126 | − | 0.155126i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.0000i | 0.868290i | 0.900843 | + | 0.434145i | \(0.142949\pi\) | ||||
−0.900843 | + | 0.434145i | \(0.857051\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.0227 | + | 11.0227i | −0.793432 | + | 0.793432i | −0.982050 | − | 0.188619i | \(-0.939599\pi\) |
0.188619 | + | 0.982050i | \(0.439599\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.48528 | + | 8.48528i | −0.604551 | + | 0.604551i | −0.941517 | − | 0.336966i | \(-0.890599\pi\) |
0.336966 | + | 0.941517i | \(0.390599\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.0000 | −1.13421 | −0.567105 | − | 0.823646i | \(-0.691937\pi\) | ||||
−0.567105 | + | 0.823646i | \(0.691937\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.00000 | 0.493742 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.79796 | − | 9.79796i | 0.681005 | − | 0.681005i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.00000i | 0.622543i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.66025 | 0.596196 | 0.298098 | − | 0.954535i | \(-0.403648\pi\) | ||||
0.298098 | + | 0.954535i | \(0.403648\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.48528 | + | 8.48528i | 0.581402 | + | 0.581402i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.66025i | 0.585206i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 6.92820i | − | 0.466041i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.79796 | + | 9.79796i | 0.656120 | + | 0.656120i | 0.954460 | − | 0.298340i | \(-0.0964329\pi\) |
−0.298340 | + | 0.954460i | \(0.596433\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.9706 | + | 16.9706i | 1.12638 | + | 1.12638i | 0.990762 | + | 0.135614i | \(0.0433007\pi\) |
0.135614 | + | 0.990762i | \(0.456699\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.8564 | −0.915657 | −0.457829 | − | 0.889041i | \(-0.651373\pi\) | ||||
−0.457829 | + | 0.889041i | \(0.651373\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.65685 | + | 5.65685i | −0.367452 | + | 0.367452i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.0000 | −0.776215 | −0.388108 | − | 0.921614i | \(-0.626871\pi\) | ||||
−0.388108 | + | 0.921614i | \(0.626871\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 0.0644157 | 0.0322078 | − | 0.999481i | \(-0.489746\pi\) | ||||
0.0322078 | + | 0.999481i | \(0.489746\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.3137 | − | 11.3137i | 0.725775 | − | 0.725775i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.6969 | + | 14.6969i | −0.935144 | + | 0.935144i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 15.0000i | − | 0.950586i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −29.4449 | −1.85854 | −0.929272 | − | 0.369397i | \(-0.879564\pi\) | ||||
−0.929272 | + | 0.369397i | \(0.879564\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.48528 | + | 8.48528i | 0.533465 | + | 0.533465i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −19.5959 | − | 19.5959i | −1.22236 | − | 1.22236i | −0.966791 | − | 0.255569i | \(-0.917737\pi\) |
−0.255569 | − | 0.966791i | \(-0.582263\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.8564i | 0.857690i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.6969 | − | 14.6969i | −0.906252 | − | 0.906252i | 0.0897154 | − | 0.995967i | \(-0.471404\pi\) |
−0.995967 | + | 0.0897154i | \(0.971404\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.12132 | − | 2.12132i | −0.129823 | − | 0.129823i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −27.7128 | −1.68968 | −0.844840 | − | 0.535019i | \(-0.820304\pi\) | ||||
−0.844840 | + | 0.535019i | \(0.820304\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.0000i | 1.70088i | 0.526073 | + | 0.850439i | \(0.323664\pi\) | ||||
−0.526073 | + | 0.850439i | \(0.676336\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.82843 | + | 2.82843i | −0.169944 | + | 0.169944i | −0.786955 | − | 0.617011i | \(-0.788343\pi\) |
0.617011 | + | 0.786955i | \(0.288343\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.00000 | −0.478947 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.5061 | − | 20.5061i | 1.21896 | − | 1.21896i | 0.250965 | − | 0.967996i | \(-0.419252\pi\) |
0.967996 | − | 0.250965i | \(-0.0807478\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 14.0000i | − | 0.823529i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.12372 | + | 6.12372i | 0.355335 | + | 0.355335i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 27.7128i | 1.60267i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.79796 | + | 9.79796i | 0.562878 | + | 0.562878i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.94975 | + | 4.94975i | 0.282497 | + | 0.282497i | 0.834104 | − | 0.551607i | \(-0.185985\pi\) |
−0.551607 | + | 0.834104i | \(0.685985\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.92820 | 0.394132 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 24.0000i | − | 1.36092i | −0.732787 | − | 0.680458i | \(-0.761781\pi\) | ||
0.732787 | − | 0.680458i | \(-0.238219\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.5959 | + | 19.5959i | −1.10763 | + | 1.10763i | −0.114165 | + | 0.993462i | \(0.536419\pi\) |
−0.993462 | + | 0.114165i | \(0.963581\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.9706 | + | 16.9706i | −0.953162 | + | 0.953162i | −0.998951 | − | 0.0457894i | \(-0.985420\pi\) |
0.0457894 | + | 0.998951i | \(0.485420\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.0000 | −0.671871 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.00000 | −0.167444 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.36396 | − | 6.36396i | 0.354100 | − | 0.354100i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.79796 | + | 9.79796i | −0.541828 | + | 0.541828i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.4449 | 1.61844 | 0.809218 | − | 0.587508i | \(-0.199891\pi\) | ||||
0.809218 | + | 0.587508i | \(0.199891\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.3137 | + | 11.3137i | 0.619987 | + | 0.619987i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.57321 | + | 8.57321i | 0.467013 | + | 0.467013i | 0.900945 | − | 0.433933i | \(-0.142874\pi\) |
−0.433933 | + | 0.900945i | \(0.642874\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.1244i | 0.658505i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 6.92820i | − | 0.375183i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.0919 | + | 19.0919i | 1.02491 | + | 1.02491i | 0.999682 | + | 0.0252242i | \(0.00802995\pi\) |
0.0252242 | + | 0.999682i | \(0.491970\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.7128 | −1.48343 | −0.741716 | − | 0.670714i | \(-0.765988\pi\) | ||||
−0.741716 | + | 0.670714i | \(0.765988\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 20.0000i | 1.06752i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.5959 | + | 19.5959i | −1.04299 | + | 1.04299i | −0.0439518 | + | 0.999034i | \(0.513995\pi\) |
−0.999034 | + | 0.0439518i | \(0.986005\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.00000 | −0.421053 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.65685 | − | 5.65685i | 0.296908 | − | 0.296908i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.79796 | − | 9.79796i | 0.511449 | − | 0.511449i | −0.403521 | − | 0.914970i | \(-0.632214\pi\) |
0.914970 | + | 0.403521i | \(0.132214\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.00000i | 0.312348i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.7990 | + | 19.7990i | 1.02515 | + | 1.02515i | 0.999675 | + | 0.0254774i | \(0.00811060\pi\) |
0.0254774 | + | 0.999675i | \(0.491889\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −19.5959 | − | 19.5959i | −1.00924 | − | 1.00924i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.73205i | 0.0889695i | 0.999010 | + | 0.0444847i | \(0.0141646\pi\) | ||||
−0.999010 | + | 0.0444847i | \(0.985835\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.7846i | 1.06483i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.5959 | + | 19.5959i | 1.00130 | + | 1.00130i | 0.999999 | + | 0.00130548i | \(0.000415549\pi\) |
0.00130548 | + | 0.999999i | \(0.499584\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.3137 | − | 11.3137i | −0.575108 | − | 0.575108i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.92820 | −0.351274 | −0.175637 | − | 0.984455i | \(-0.556198\pi\) | ||||
−0.175637 | + | 0.984455i | \(0.556198\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 12.0000i | − | 0.606866i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.44949 | − | 2.44949i | 0.123560 | − | 0.123560i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.3137 | − | 11.3137i | 0.567819 | − | 0.567819i | −0.363698 | − | 0.931517i | \(-0.618486\pi\) |
0.931517 | + | 0.363698i | \(0.118486\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.0000 | 0.749064 | 0.374532 | − | 0.927214i | \(-0.377803\pi\) | ||||
0.374532 | + | 0.927214i | \(0.377803\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.3137 | − | 11.3137i | 0.563576 | − | 0.563576i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.79796 | + | 9.79796i | −0.485667 | + | 0.485667i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 5.00000i | − | 0.247234i | −0.992330 | − | 0.123617i | \(-0.960551\pi\) | ||
0.992330 | − | 0.123617i | \(-0.0394494\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.19615 | 0.256307 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.22474 | + | 1.22474i | 0.0599760 | + | 0.0599760i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.0526i | 0.930778i | 0.885106 | + | 0.465389i | \(0.154086\pi\) | ||||
−0.885106 | + | 0.465389i | \(0.845914\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.7128i | 1.35064i | 0.737525 | + | 0.675320i | \(0.235994\pi\) | ||||
−0.737525 | + | 0.675320i | \(0.764006\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.79796 | + | 9.79796i | 0.476393 | + | 0.476393i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.92820 | −0.334497 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.8207 | − | 20.8207i | 1.00058 | − | 1.00058i | 0.000577367 | − | 1.00000i | \(-0.499816\pi\) |
1.00000 | 0.000577367i | \(-0.000183782\pi\) | ||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −25.4558 | + | 25.4558i | −1.21772 | + | 1.21772i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.00000 | −0.190910 | −0.0954548 | − | 0.995434i | \(-0.530431\pi\) | ||||
−0.0954548 | + | 0.995434i | \(0.530431\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.0000 | −0.666667 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.12132 | − | 2.12132i | 0.100787 | − | 0.100787i | −0.654915 | − | 0.755702i | \(-0.727296\pi\) |
0.755702 | + | 0.654915i | \(0.227296\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.89898 | − | 4.89898i | 0.231714 | − | 0.231714i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 39.0000i | − | 1.84052i | −0.391303 | − | 0.920262i | \(-0.627976\pi\) | ||
0.391303 | − | 0.920262i | \(-0.372024\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.19615 | −0.244677 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.3137 | + | 11.3137i | 0.531564 | + | 0.531564i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.67423 | + | 3.67423i | 0.171873 | + | 0.171873i | 0.787802 | − | 0.615929i | \(-0.211219\pi\) |
−0.615929 | + | 0.787802i | \(0.711219\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 8.66025i | − | 0.404226i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 41.5692i | − | 1.93607i | −0.250812 | − | 0.968036i | \(-0.580698\pi\) | ||
0.250812 | − | 0.968036i | \(-0.419302\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.79796 | + | 9.79796i | 0.455350 | + | 0.455350i | 0.897126 | − | 0.441776i | \(-0.145651\pi\) |
−0.441776 | + | 0.897126i | \(0.645651\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.9706 | + | 16.9706i | 0.785304 | + | 0.785304i | 0.980720 | − | 0.195416i | \(-0.0626058\pi\) |
−0.195416 | + | 0.980720i | \(0.562606\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.00000i | 0.184310i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.79796 | − | 9.79796i | 0.450511 | − | 0.450511i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.9706 | − | 16.9706i | 0.777029 | − | 0.777029i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.0000 | −0.548294 | −0.274147 | − | 0.961688i | \(-0.588395\pi\) | ||||
−0.274147 | + | 0.961688i | \(0.588395\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −32.0000 | −1.45907 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.89898 | + | 4.89898i | −0.221994 | + | 0.221994i | −0.809338 | − | 0.587344i | \(-0.800174\pi\) |
0.587344 | + | 0.809338i | \(0.300174\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.00000i | 0.316551i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.3923 | −0.468998 | −0.234499 | − | 0.972116i | \(-0.575345\pi\) | ||||
−0.234499 | + | 0.972116i | \(0.575345\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.48528 | + | 8.48528i | 0.382158 | + | 0.382158i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.2487i | 1.08552i | 0.839887 | + | 0.542761i | \(0.182621\pi\) | ||||
−0.839887 | + | 0.542761i | \(0.817379\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 20.7846i | − | 0.928588i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.5959 | − | 19.5959i | −0.873739 | − | 0.873739i | 0.119139 | − | 0.992878i | \(-0.461987\pi\) |
−0.992878 | + | 0.119139i | \(0.961987\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.12132 | − | 2.12132i | −0.0942111 | − | 0.0942111i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.92820 | 0.307087 | 0.153544 | − | 0.988142i | \(-0.450931\pi\) | ||||
0.153544 | + | 0.988142i | \(0.450931\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −18.3712 | + | 18.3712i | −0.811107 | + | 0.811107i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.48528 | + | 8.48528i | −0.373182 | + | 0.373182i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.00000 | 0.131432 | 0.0657162 | − | 0.997838i | \(-0.479067\pi\) | ||||
0.0657162 | + | 0.997838i | \(0.479067\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.19239 | + | 9.19239i | −0.401955 | + | 0.401955i | −0.878922 | − | 0.476966i | \(-0.841736\pi\) |
0.476966 | + | 0.878922i | \(0.341736\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.89898 | + | 4.89898i | −0.213403 | + | 0.213403i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.0000i | 1.08696i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20.7846 | 0.901975 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.48528 | − | 8.48528i | −0.367538 | − | 0.367538i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.67423 | − | 3.67423i | −0.158555 | − | 0.158555i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 12.1244i | − | 0.522233i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.89898 | − | 4.89898i | −0.210235 | − | 0.210235i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.0208 | − | 12.0208i | −0.513973 | − | 0.513973i | 0.401768 | − | 0.915741i | \(-0.368396\pi\) |
−0.915741 | + | 0.401768i | \(0.868396\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 36.0000i | − | 1.53365i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.48528 | + | 8.48528i | −0.359533 | + | 0.359533i | −0.863641 | − | 0.504108i | \(-0.831821\pi\) |
0.504108 | + | 0.863641i | \(0.331821\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.0000 | 1.35346 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.00000 | 0.126660 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16.9706 | + | 16.9706i | −0.715224 | + | 0.715224i | −0.967623 | − | 0.252399i | \(-0.918780\pi\) |
0.252399 | + | 0.967623i | \(0.418780\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 27.0000i | − | 1.13190i | −0.824440 | − | 0.565949i | \(-0.808510\pi\) | ||
0.824440 | − | 0.565949i | \(-0.191490\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.3923 | 0.434904 | 0.217452 | − | 0.976071i | \(-0.430225\pi\) | ||||
0.217452 | + | 0.976071i | \(0.430225\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.48528 | − | 8.48528i | −0.354478 | − | 0.354478i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.3712 | − | 18.3712i | −0.764802 | − | 0.764802i | 0.212384 | − | 0.977186i | \(-0.431877\pi\) |
−0.977186 | + | 0.212384i | \(0.931877\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 15.5885i | − | 0.647834i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.6969 | + | 14.6969i | 0.608685 | + | 0.608685i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.0919 | + | 19.0919i | 0.788006 | + | 0.788006i | 0.981167 | − | 0.193161i | \(-0.0618739\pi\) |
−0.193161 | + | 0.981167i | \(0.561874\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.7846 | 0.856415 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 12.0000i | − | 0.493614i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 28.1691 | − | 28.1691i | 1.15677 | − | 1.15677i | 0.171601 | − | 0.985167i | \(-0.445106\pi\) |
0.985167 | − | 0.171601i | \(-0.0548940\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.3137 | − | 11.3137i | 0.463039 | − | 0.463039i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.0000 | 0.775026 | 0.387513 | − | 0.921864i | \(-0.373334\pi\) | ||||
0.387513 | + | 0.921864i | \(0.373334\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.89949 | − | 9.89949i | 0.403139 | − | 0.403139i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.5959 | − | 19.5959i | 0.795374 | − | 0.795374i | −0.186988 | − | 0.982362i | \(-0.559873\pi\) |
0.982362 | + | 0.186988i | \(0.0598727\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −27.7128 | −1.12114 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.1421 | − | 14.1421i | −0.571195 | − | 0.571195i | 0.361267 | − | 0.932462i | \(-0.382344\pi\) |
−0.932462 | + | 0.361267i | \(0.882344\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.5959 | + | 19.5959i | 0.788902 | + | 0.788902i | 0.981314 | − | 0.192412i | \(-0.0616311\pi\) |
−0.192412 | + | 0.981314i | \(0.561631\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.3923i | 0.417702i | 0.977947 | + | 0.208851i | \(0.0669724\pi\) | ||||
−0.977947 | + | 0.208851i | \(0.933028\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 34.6410i | 1.39010i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.36396 | − | 6.36396i | −0.254152 | − | 0.254152i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.8564 | 0.552491 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.0000i | 1.11466i | 0.830290 | + | 0.557331i | \(0.188175\pi\) | ||||
−0.830290 | + | 0.557331i | \(0.811825\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.12372 | + | 6.12372i | −0.243396 | + | 0.243396i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.7990 | − | 19.7990i | 0.784465 | − | 0.784465i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 24.0000 | 0.949425 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.0000 | 0.710957 | 0.355479 | − | 0.934684i | \(-0.384318\pi\) | ||||
0.355479 | + | 0.934684i | \(0.384318\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.65685 | + | 5.65685i | −0.223085 | + | 0.223085i | −0.809796 | − | 0.586711i | \(-0.800422\pi\) |
0.586711 | + | 0.809796i | \(0.300422\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.0000i | 0.706562i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.9706 | − | 16.9706i | −0.664109 | − | 0.664109i | 0.292237 | − | 0.956346i | \(-0.405601\pi\) |
−0.956346 | + | 0.292237i | \(0.905601\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.2474 | + | 12.2474i | 0.477818 | + | 0.477818i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 36.3731i | − | 1.41689i | −0.705764 | − | 0.708447i | \(-0.749396\pi\) | ||
0.705764 | − | 0.708447i | \(-0.250604\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.92820i | 0.269476i | 0.990881 | + | 0.134738i | \(0.0430193\pi\) | ||||
−0.990881 | + | 0.134738i | \(0.956981\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.89898 | + | 4.89898i | 0.190261 | + | 0.190261i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −33.9411 | − | 33.9411i | −1.31421 | − | 1.31421i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13.8564 | −0.535720 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.5959 | + | 19.5959i | −0.755367 | + | 0.755367i | −0.975475 | − | 0.220108i | \(-0.929359\pi\) |
0.220108 | + | 0.975475i | \(0.429359\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −24.0000 | −0.919682 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.8198 | + | 31.8198i | −1.21755 | + | 1.21755i | −0.249064 | + | 0.968487i | \(0.580123\pi\) |
−0.968487 | + | 0.249064i | \(0.919877\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.79796 | − | 9.79796i | 0.373815 | − | 0.373815i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 48.0000i | 1.82865i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.19615 | 0.197671 | 0.0988355 | − | 0.995104i | \(-0.468488\pi\) | ||||
0.0988355 | + | 0.995104i | \(0.468488\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.67423 | + | 3.67423i | 0.139172 | + | 0.139172i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 34.6410i | − | 1.30837i | −0.756333 | − | 0.654187i | \(-0.773011\pi\) | ||
0.756333 | − | 0.654187i | \(-0.226989\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −29.3939 | − | 29.3939i | −1.10861 | − | 1.10861i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 41.5692 | 1.56116 | 0.780582 | − | 0.625053i | \(-0.214923\pi\) | ||||
0.780582 | + | 0.625053i | \(0.214923\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16.0000i | 0.600047i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.5959 | − | 19.5959i | 0.733873 | − | 0.733873i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.48528 | − | 8.48528i | 0.316889 | − | 0.316889i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.0000 | −0.895049 | −0.447524 | − | 0.894272i | \(-0.647694\pi\) | ||||
−0.447524 | + | 0.894272i | \(0.647694\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.707107 | + | 0.707107i | −0.0262976 | + | 0.0262976i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.89898 | − | 4.89898i | 0.181693 | − | 0.181693i | −0.610400 | − | 0.792093i | \(-0.708991\pi\) |
0.792093 | + | 0.610400i | \(0.208991\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000i | 0.481481i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.8564 | −0.512498 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.82843 | + | 2.82843i | 0.104470 | + | 0.104470i | 0.757410 | − | 0.652940i | \(-0.226464\pi\) |
−0.652940 | + | 0.757410i | \(0.726464\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.57321 | + | 8.57321i | 0.315798 | + | 0.315798i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 51.9615i | − | 1.91144i | −0.294285 | − | 0.955718i | \(-0.595081\pi\) | ||
0.294285 | − | 0.955718i | \(-0.404919\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 20.7846i | − | 0.763542i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.4949 | − | 24.4949i | −0.898631 | − | 0.898631i | 0.0966845 | − | 0.995315i | \(-0.469176\pi\) |
−0.995315 | + | 0.0966845i | \(0.969176\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −21.2132 | − | 21.2132i | −0.776151 | − | 0.776151i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.00000i | 0.145962i | 0.997333 | + | 0.0729810i | \(0.0232513\pi\) | ||||
−0.997333 | + | 0.0729810i | \(0.976749\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20.8207 | − | 20.8207i | 0.758747 | − | 0.758747i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.2843 | − | 28.2843i | 1.02801 | − | 1.02801i | 0.0284131 | − | 0.999596i | \(-0.490955\pi\) |
0.999596 | − | 0.0284131i | \(-0.00904537\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12.0000 | −0.435572 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.0000 | 0.761249 | 0.380625 | − | 0.924730i | \(-0.375709\pi\) | ||||
0.380625 | + | 0.924730i | \(0.375709\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −29.3939 | + | 29.3939i | −1.06135 | + | 1.06135i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 41.0000i | − | 1.47850i | −0.673432 | − | 0.739249i | \(-0.735181\pi\) | ||
0.673432 | − | 0.739249i | \(-0.264819\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27.7128 | 0.998053 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.4558 | − | 25.4558i | −0.915583 | − | 0.915583i | 0.0811212 | − | 0.996704i | \(-0.474150\pi\) |
−0.996704 | + | 0.0811212i | \(0.974150\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 15.5885i | − | 0.558514i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.7846i | 0.743732i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −24.4949 | − | 24.4949i | −0.875376 | − | 0.875376i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.65685 | − | 5.65685i | −0.201645 | − | 0.201645i | 0.599059 | − | 0.800705i | \(-0.295541\pi\) |
−0.800705 | + | 0.599059i | \(0.795541\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20.7846 | 0.739952 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −25.4558 | + | 25.4558i | −0.901692 | + | 0.901692i | −0.995583 | − | 0.0938903i | \(-0.970070\pi\) |
0.0938903 | + | 0.995583i | \(0.470070\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.0000 | 0.424529 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.00000 | −0.212000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.6066 | + | 10.6066i | −0.374299 | + | 0.374299i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 19.5959 | − | 19.5959i | 0.689809 | − | 0.689809i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 42.0000i | 1.47664i | 0.674450 | + | 0.738321i | \(0.264381\pi\) | ||||
−0.674450 | + | 0.738321i | \(0.735619\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.1051 | −1.33805 | −0.669026 | − | 0.743239i | \(-0.733288\pi\) | ||||
−0.669026 | + | 0.743239i | \(0.733288\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.7990 | − | 19.7990i | −0.694381 | − | 0.694381i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.3939 | + | 29.3939i | 1.02836 | + | 1.02836i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.7846i | 0.725388i | 0.931908 | + | 0.362694i | \(0.118143\pi\) | ||||
−0.931908 | + | 0.362694i | \(0.881857\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.79796 | + | 9.79796i | 0.341535 | + | 0.341535i | 0.856944 | − | 0.515409i | \(-0.172360\pi\) |
−0.515409 | + | 0.856944i | \(0.672360\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.12132 | − | 2.12132i | −0.0737655 | − | 0.0737655i | 0.669261 | − | 0.743027i | \(-0.266611\pi\) |
−0.743027 | + | 0.669261i | \(0.766611\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.6410 | 1.20313 | 0.601566 | − | 0.798823i | \(-0.294544\pi\) | ||||
0.601566 | + | 0.798823i | \(0.294544\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 4.00000i | − | 0.138758i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.57321 | + | 8.57321i | −0.297044 | + | 0.297044i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 14.1421 | − | 14.1421i | 0.488824 | − | 0.488824i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 48.0000 | 1.65714 | 0.828572 | − | 0.559883i | \(-0.189154\pi\) | ||||
0.828572 | + | 0.559883i | \(0.189154\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.0000 | 0.655172 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.24264 | + | 4.24264i | −0.146124 | + | 0.146124i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 29.0000i | 0.995277i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −55.4256 | −1.89997 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31.1127 | − | 31.1127i | −1.06528 | − | 1.06528i | −0.997715 | − | 0.0675635i | \(-0.978477\pi\) |
−0.0675635 | − | 0.997715i | \(-0.521523\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25.7196 | − | 25.7196i | −0.878566 | − | 0.878566i | 0.114820 | − | 0.993386i | \(-0.463371\pi\) |
−0.993386 | + | 0.114820i | \(0.963371\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 43.3013i | − | 1.47742i | −0.674023 | − | 0.738710i | \(-0.735435\pi\) | ||
0.674023 | − | 0.738710i | \(-0.264565\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.89898 | − | 4.89898i | −0.166763 | − | 0.166763i | 0.618792 | − | 0.785555i | \(-0.287622\pi\) |
−0.785555 | + | 0.618792i | \(0.787622\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.89949 | + | 9.89949i | 0.336204 | + | 0.336204i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.8564 | −0.470046 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.0000i | 0.948744i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.65685 | − | 5.65685i | 0.191018 | − | 0.191018i | −0.605118 | − | 0.796136i | \(-0.706874\pi\) |
0.796136 | + | 0.605118i | \(0.206874\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.0000 | 1.01073 | 0.505363 | − | 0.862907i | \(-0.331359\pi\) | ||||
0.505363 | + | 0.862907i | \(0.331359\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.6777 | + | 17.6777i | −0.594901 | + | 0.594901i | −0.938951 | − | 0.344050i | \(-0.888201\pi\) |
0.344050 | + | 0.938951i | \(0.388201\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.5959 | − | 19.5959i | 0.657967 | − | 0.657967i | −0.296932 | − | 0.954899i | \(-0.595963\pi\) |
0.954899 | + | 0.296932i | \(0.0959635\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.73205 | 0.0580259 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −25.4558 | − | 25.4558i | −0.851847 | − | 0.851847i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −19.5959 | − | 19.5959i | −0.654289 | − | 0.654289i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 27.7128i | 0.924274i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 20.7846i | − | 0.692436i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.65685 | + | 5.65685i | 0.187833 | + | 0.187833i | 0.794759 | − | 0.606926i | \(-0.207597\pi\) |
−0.606926 | + | 0.794759i | \(0.707597\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 27.7128 | 0.919176 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 24.0000i | − | 0.795155i | −0.917568 | − | 0.397578i | \(-0.869851\pi\) | ||
0.917568 | − | 0.397578i | \(-0.130149\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.3712 | − | 18.3712i | 0.607997 | − | 0.607997i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.0000 | 0.659739 | 0.329870 | − | 0.944027i | \(-0.392995\pi\) | ||||
0.329870 | + | 0.944027i | \(0.392995\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.00000 | −0.230658 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −33.9411 | + | 33.9411i | −1.11719 | + | 1.11719i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.79796 | − | 9.79796i | 0.321807 | − | 0.321807i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 18.0000i | − | 0.590561i | −0.955411 | − | 0.295280i | \(-0.904587\pi\) | ||
0.955411 | − | 0.295280i | \(-0.0954131\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 36.3731 | 1.19208 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16.9706 | + | 16.9706i | 0.555591 | + | 0.555591i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.7196 | + | 25.7196i | 0.840224 | + | 0.840224i | 0.988888 | − | 0.148664i | \(-0.0474972\pi\) |
−0.148664 | + | 0.988888i | \(0.547497\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 27.7128i | − | 0.904373i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 34.6410i | − | 1.12926i | −0.825342 | − | 0.564632i | \(-0.809018\pi\) | ||
0.825342 | − | 0.564632i | \(-0.190982\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.6969 | − | 14.6969i | −0.478598 | − | 0.478598i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.9706 | − | 16.9706i | −0.551469 | − | 0.551469i | 0.375396 | − | 0.926865i | \(-0.377507\pi\) |
−0.926865 | + | 0.375396i | \(0.877507\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −34.6410 | −1.12449 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 24.0000i | − | 0.778253i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.4722 | + | 13.4722i | −0.436407 | + | 0.436407i | −0.890801 | − | 0.454394i | \(-0.849856\pi\) |
0.454394 | + | 0.890801i | \(0.349856\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.48528 | − | 8.48528i | 0.274290 | − | 0.274290i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0000 | 0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.24264 | + | 4.24264i | −0.136717 | + | 0.136717i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.79796 | − | 9.79796i | 0.315081 | − | 0.315081i | −0.531793 | − | 0.846874i | \(-0.678482\pi\) |
0.846874 | + | 0.531793i | \(0.178482\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.00000i | 0.289122i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.4449 | 0.944931 | 0.472465 | − | 0.881349i | \(-0.343364\pi\) | ||||
0.472465 | + | 0.881349i | \(0.343364\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.22474 | + | 1.22474i | 0.0391831 | + | 0.0391831i | 0.726427 | − | 0.687244i | \(-0.241180\pi\) |
−0.687244 | + | 0.726427i | \(0.741180\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 5.19615i | − | 0.166070i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 27.7128i | 0.884802i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.79796 | − | 9.79796i | −0.312506 | − | 0.312506i | 0.533373 | − | 0.845880i | \(-0.320924\pi\) |
−0.845880 | + | 0.533373i | \(0.820924\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 55.4256 | 1.76243 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 40.0000i | − | 1.27064i | −0.772248 | − | 0.635321i | \(-0.780868\pi\) | ||
0.772248 | − | 0.635321i | \(-0.219132\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20.8207 | + | 20.8207i | −0.660724 | + | 0.660724i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.3137 | − | 11.3137i | 0.358309 | − | 0.358309i | −0.504881 | − | 0.863189i | \(-0.668463\pi\) |
0.863189 | + | 0.504881i | \(0.168463\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −40.0000 | −1.26554 |
(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 | 1600.2.o.i.607.1 | yes | 8 | |
4.3 | odd | 2 | 1600.2.o.h.607.4 | yes | 8 | ||
5.2 | odd | 4 | 1600.2.o.h.543.3 | yes | 8 | ||
5.3 | odd | 4 | 1600.2.o.h.543.1 | ✓ | 8 | ||
5.4 | even | 2 | inner | 1600.2.o.i.607.3 | yes | 8 | |
8.3 | odd | 2 | 1600.2.o.h.607.1 | yes | 8 | ||
8.5 | even | 2 | inner | 1600.2.o.i.607.4 | yes | 8 | |
20.3 | even | 4 | inner | 1600.2.o.i.543.4 | yes | 8 | |
20.7 | even | 4 | inner | 1600.2.o.i.543.2 | yes | 8 | |
20.19 | odd | 2 | 1600.2.o.h.607.2 | yes | 8 | ||
40.3 | even | 4 | inner | 1600.2.o.i.543.1 | yes | 8 | |
40.13 | odd | 4 | 1600.2.o.h.543.4 | yes | 8 | ||
40.19 | odd | 2 | 1600.2.o.h.607.3 | yes | 8 | ||
40.27 | even | 4 | inner | 1600.2.o.i.543.3 | yes | 8 | |
40.29 | even | 2 | inner | 1600.2.o.i.607.2 | yes | 8 | |
40.37 | odd | 4 | 1600.2.o.h.543.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1600.2.o.h.543.1 | ✓ | 8 | 5.3 | odd | 4 | ||
1600.2.o.h.543.2 | yes | 8 | 40.37 | odd | 4 | ||
1600.2.o.h.543.3 | yes | 8 | 5.2 | odd | 4 | ||
1600.2.o.h.543.4 | yes | 8 | 40.13 | odd | 4 | ||
1600.2.o.h.607.1 | yes | 8 | 8.3 | odd | 2 | ||
1600.2.o.h.607.2 | yes | 8 | 20.19 | odd | 2 | ||
1600.2.o.h.607.3 | yes | 8 | 40.19 | odd | 2 | ||
1600.2.o.h.607.4 | yes | 8 | 4.3 | odd | 2 | ||
1600.2.o.i.543.1 | yes | 8 | 40.3 | even | 4 | inner | |
1600.2.o.i.543.2 | yes | 8 | 20.7 | even | 4 | inner | |
1600.2.o.i.543.3 | yes | 8 | 40.27 | even | 4 | inner | |
1600.2.o.i.543.4 | yes | 8 | 20.3 | even | 4 | inner | |
1600.2.o.i.607.1 | yes | 8 | 1.1 | even | 1 | trivial | |
1600.2.o.i.607.2 | yes | 8 | 40.29 | even | 2 | inner | |
1600.2.o.i.607.3 | yes | 8 | 5.4 | even | 2 | inner | |
1600.2.o.i.607.4 | yes | 8 | 8.5 | even | 2 | inner |