Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [280,2,Mod(19,280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(280, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("280.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 280 = 2^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 280.ba (of order \(6\), 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: | \(2.23581125660\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.3317760000.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{6}]$ |
Embedding invariants
Embedding label | 19.2 | ||
Root | \(1.72286 - 0.178197i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 280.19 |
Dual form | 280.2.ba.a.59.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).
\(n\) | \(57\) | \(71\) | \(141\) | \(241\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 1.22474i | −0.500000 | + | 0.866025i | ||||
\(3\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(4\) | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | ||||
\(5\) | 1.93649 | + | 1.11803i | 0.866025 | + | 0.500000i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.41421 | − | 2.23607i | 0.534522 | − | 0.845154i | ||||
\(8\) | 2.82843 | 1.00000 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.500000 | − | 0.866025i | ||||
\(10\) | −2.73861 | + | 1.58114i | −0.866025 | + | 0.500000i | ||||
\(11\) | −3.23861 | − | 5.60944i | −0.976478 | − | 1.69131i | −0.674967 | − | 0.737848i | \(-0.735842\pi\) |
−0.301511 | − | 0.953463i | \(-0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.66291i | 0.738559i | 0.929318 | + | 0.369279i | \(0.120395\pi\) | ||||
−0.929318 | + | 0.369279i | \(0.879605\pi\) | |||||||
\(14\) | 1.73861 | + | 3.31319i | 0.464664 | + | 0.885487i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.500000 | + | 0.866025i | ||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | 2.12132 | + | 3.67423i | 0.500000 | + | 0.866025i | ||||
\(19\) | 7.23861 | + | 4.17922i | 1.66065 | + | 0.958778i | 0.972404 | + | 0.233301i | \(0.0749529\pi\) |
0.688247 | + | 0.725476i | \(0.258380\pi\) | |||||||
\(20\) | − | 4.47214i | − | 1.00000i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 9.16018 | 1.95296 | ||||||||
\(23\) | 0.184829 | − | 0.320133i | 0.0385394 | − | 0.0667523i | −0.846112 | − | 0.533005i | \(-0.821063\pi\) |
0.884652 | + | 0.466252i | \(0.154396\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.50000 | + | 4.33013i | 0.500000 | + | 0.866025i | ||||
\(26\) | −3.26139 | − | 1.88296i | −0.639611 | − | 0.369279i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.28720 | − | 0.213422i | −0.999186 | − | 0.0403329i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(32\) | −2.82843 | − | 4.89898i | −0.500000 | − | 0.866025i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.23861 | − | 2.74899i | 0.885487 | − | 0.464664i | ||||
\(36\) | −6.00000 | −1.00000 | ||||||||
\(37\) | −4.76492 | + | 8.25308i | −0.783348 | + | 1.35680i | 0.146633 | + | 0.989191i | \(0.453156\pi\) |
−0.929981 | + | 0.367607i | \(0.880177\pi\) | |||||||
\(38\) | −10.2369 | + | 5.91030i | −1.66065 | + | 0.958778i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.47723 | + | 3.16228i | 0.866025 | + | 0.500000i | ||||
\(41\) | − | 4.59250i | − | 0.717229i | −0.933486 | − | 0.358614i | \(-0.883249\pi\) | ||
0.933486 | − | 0.358614i | \(-0.116751\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | −6.47723 | + | 11.2189i | −0.976478 | + | 1.69131i | ||||
\(45\) | 5.80948 | − | 3.35410i | 0.866025 | − | 0.500000i | ||||
\(46\) | 0.261387 | + | 0.452736i | 0.0385394 | + | 0.0667523i | ||||
\(47\) | −7.93080 | − | 4.57885i | −1.15683 | − | 0.667893i | −0.206284 | − | 0.978492i | \(-0.566137\pi\) |
−0.950541 | + | 0.310599i | \(0.899470\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | − | 6.32456i | −0.428571 | − | 0.903508i | ||||
\(50\) | −7.07107 | −1.00000 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.61230 | − | 2.66291i | 0.639611 | − | 0.369279i | ||||
\(53\) | 4.39526 | + | 7.61282i | 0.603736 | + | 1.04570i | 0.992250 | + | 0.124258i | \(0.0396551\pi\) |
−0.388514 | + | 0.921443i | \(0.627012\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 14.4835i | − | 1.95296i | ||||||
\(56\) | 4.00000 | − | 6.32456i | 0.534522 | − | 0.845154i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.47723 | + | 3.16228i | −0.713074 | + | 0.411693i | −0.812198 | − | 0.583382i | \(-0.801729\pi\) |
0.0991242 | + | 0.995075i | \(0.468396\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.68815 | − | 7.02834i | −0.464664 | − | 0.885487i | ||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | −2.97723 | + | 5.15671i | −0.369279 | + | 0.639611i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.337449 | + | 8.35979i | −0.0403329 | + | 0.999186i | ||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 4.24264 | − | 7.34847i | 0.500000 | − | 0.866025i | ||||
\(73\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(74\) | −6.73861 | − | 11.6716i | −0.783348 | − | 1.35680i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 16.7169i | − | 1.91756i | ||||||
\(77\) | −17.1232 | − | 0.691190i | −1.95137 | − | 0.0787685i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(80\) | −7.74597 | + | 4.47214i | −0.866025 | + | 0.500000i | ||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 5.62465 | + | 3.24739i | 0.621138 | + | 0.358614i | ||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −9.16018 | − | 15.8659i | −0.976478 | − | 1.69131i | ||||
\(89\) | 10.9545 | + | 6.32456i | 1.16117 | + | 0.670402i | 0.951584 | − | 0.307389i | \(-0.0994552\pi\) |
0.209585 | + | 0.977790i | \(0.432789\pi\) | |||||||
\(90\) | 9.48683i | 1.00000i | ||||||||
\(91\) | 5.95445 | + | 3.76593i | 0.624196 | + | 0.394776i | ||||
\(92\) | −0.739315 | −0.0770789 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11.2158 | − | 6.47547i | 1.15683 | − | 0.667893i | ||||
\(95\) | 9.34501 | + | 16.1860i | 0.958778 | + | 1.66065i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(98\) | 9.86729 | + | 0.797901i | 0.996747 | + | 0.0806002i | ||||
\(99\) | −19.4317 | −1.95296 | ||||||||
\(100\) | 5.00000 | − | 8.66025i | 0.500000 | − | 0.866025i | ||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.87298 | + | 2.23607i | 0.381616 | + | 0.220326i | 0.678521 | − | 0.734581i | \(-0.262621\pi\) |
−0.296905 | + | 0.954907i | \(0.595954\pi\) | |||||||
\(104\) | 7.53185i | 0.738559i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.4317 | −1.20747 | ||||||||
\(107\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(110\) | 17.7386 | + | 10.2414i | 1.69131 | + | 0.976478i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.91754 | + | 9.37112i | 0.464664 | + | 0.885487i | ||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.715838 | − | 0.413289i | 0.0667523 | − | 0.0385394i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.91845 | + | 3.99437i | 0.639611 | + | 0.369279i | ||||
\(118\) | − | 8.94427i | − | 0.823387i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −15.4772 | + | 26.8073i | −1.40702 | + | 2.43703i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803i | 1.00000i | ||||||||
\(126\) | 11.2158 | + | 0.452736i | 0.999186 | + | 0.0403329i | ||||
\(127\) | −17.9507 | −1.59287 | −0.796434 | − | 0.604726i | \(-0.793283\pi\) | ||||
−0.796434 | + | 0.604726i | \(0.793283\pi\) | |||||||
\(128\) | −5.65685 | + | 9.79796i | −0.500000 | + | 0.866025i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.21043 | − | 7.29268i | −0.369279 | − | 0.639611i | ||||
\(131\) | −13.7614 | − | 7.94514i | −1.20234 | − | 0.694170i | −0.241264 | − | 0.970460i | \(-0.577562\pi\) |
−0.961074 | + | 0.276289i | \(0.910895\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 19.5820 | − | 10.2757i | 1.69797 | − | 0.891019i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.9737i | 1.60933i | 0.593732 | + | 0.804663i | \(0.297654\pi\) | ||||
−0.593732 | + | 0.804663i | \(0.702346\pi\) | |||||||
\(140\) | −10.0000 | − | 6.32456i | −0.845154 | − | 0.534522i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.9374 | − | 8.62414i | 1.24913 | − | 0.721187i | ||||
\(144\) | 6.00000 | + | 10.3923i | 0.500000 | + | 0.866025i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 19.0597 | 1.56670 | ||||||||
\(149\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(152\) | 20.4739 | + | 11.8206i | 1.66065 | + | 0.958778i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 12.9545 | − | 20.4828i | 1.04390 | − | 1.65055i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.1677 | − | 10.4891i | 1.44994 | − | 0.837125i | 0.451466 | − | 0.892288i | \(-0.350901\pi\) |
0.998477 | + | 0.0551630i | \(0.0175678\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 12.6491i | − | 1.00000i | ||||||
\(161\) | −0.454451 | − | 0.866025i | −0.0358158 | − | 0.0682524i | ||||
\(162\) | 12.7279 | 1.00000 | ||||||||
\(163\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(164\) | −7.95445 | + | 4.59250i | −0.621138 | + | 0.358614i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.8093i | 1.53289i | 0.642308 | + | 0.766446i | \(0.277977\pi\) | ||||
−0.642308 | + | 0.766446i | \(0.722023\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.90890 | 0.454531 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 21.7158 | − | 12.5376i | 1.66065 | − | 0.958778i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.7800 | − | 13.1521i | −1.73193 | − | 0.999933i | −0.871769 | − | 0.489917i | \(-0.837027\pi\) |
−0.860165 | − | 0.510015i | \(-0.829640\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.2180 | + | 0.533554i | 0.999186 | + | 0.0403329i | ||||
\(176\) | 25.9089 | 1.95296 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −15.4919 | + | 8.94427i | −1.16117 | + | 0.670402i | ||||
\(179\) | 3.76139 | + | 6.51491i | 0.281139 | + | 0.486948i | 0.971666 | − | 0.236360i | \(-0.0759544\pi\) |
−0.690526 | + | 0.723307i | \(0.742621\pi\) | |||||||
\(180\) | −11.6190 | − | 6.70820i | −0.866025 | − | 0.500000i | ||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | −8.82273 | + | 4.62977i | −0.653984 | + | 0.343182i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.522774 | − | 0.905472i | 0.0385394 | − | 0.0667523i | ||||
\(185\) | −18.4545 | + | 10.6547i | −1.35680 | + | 0.783348i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 18.3154i | 1.33579i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −26.4317 | −1.91756 | ||||||||
\(191\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.95445 | + | 11.5207i | −0.568175 | + | 0.822908i | ||||
\(197\) | −27.8502 | −1.98424 | −0.992122 | − | 0.125274i | \(-0.960019\pi\) | ||||
−0.992122 | + | 0.125274i | \(0.960019\pi\) | |||||||
\(198\) | 13.7403 | − | 23.7988i | 0.976478 | − | 1.69131i | ||||
\(199\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(200\) | 7.07107 | + | 12.2474i | 0.500000 | + | 0.866025i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.13458 | − | 8.89335i | 0.358614 | − | 0.621138i | ||||
\(206\) | −5.47723 | + | 3.16228i | −0.381616 | + | 0.220326i | ||||
\(207\) | −0.554486 | − | 0.960398i | −0.0385394 | − | 0.0667523i | ||||
\(208\) | −9.22460 | − | 5.32582i | −0.639611 | − | 0.369279i | ||||
\(209\) | − | 54.1394i | − | 3.74490i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.43168 | −0.373932 | −0.186966 | − | 0.982366i | \(-0.559865\pi\) | ||||
−0.186966 | + | 0.982366i | \(0.559865\pi\) | |||||||
\(212\) | 8.79052 | − | 15.2256i | 0.603736 | − | 1.04570i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −25.0862 | + | 14.4835i | −1.69131 | + | 0.976478i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.3607i | 1.49738i | 0.662919 | + | 0.748691i | \(0.269317\pi\) | ||||
−0.662919 | + | 0.748691i | \(0.730683\pi\) | |||||||
\(224\) | −14.9545 | − | 0.603648i | −0.999186 | − | 0.0403329i | ||||
\(225\) | 15.0000 | 1.00000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(230\) | 1.16896i | 0.0770789i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(234\) | −9.78416 | + | 5.64889i | −0.639611 | + | 0.369279i | ||||
\(235\) | −10.2386 | − | 17.7338i | −0.667893 | − | 1.15683i | ||||
\(236\) | 10.9545 | + | 6.32456i | 0.713074 | + | 0.411693i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.54555 | − | 1.46967i | 0.163973 | − | 0.0946700i | −0.415768 | − | 0.909471i | \(-0.636487\pi\) |
0.579741 | + | 0.814801i | \(0.303154\pi\) | |||||||
\(242\) | −21.8881 | − | 37.9113i | −1.40702 | − | 2.43703i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.26159 | − | 15.6016i | 0.0806002 | − | 0.996747i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.1289 | + | 19.2758i | −0.708114 | + | 1.22649i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −13.6931 | − | 7.90569i | −0.866025 | − | 0.500000i | ||||
\(251\) | 17.5434i | 1.10733i | 0.832739 | + | 0.553666i | \(0.186772\pi\) | ||||
−0.832739 | + | 0.553666i | \(0.813228\pi\) | |||||||
\(252\) | −8.48528 | + | 13.4164i | −0.534522 | + | 0.845154i | ||||
\(253\) | −2.39435 | −0.150532 | ||||||||
\(254\) | 12.6931 | − | 21.9850i | 0.796434 | − | 1.37946i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.7158 | + | 22.3263i | 0.727987 | + | 1.38729i | ||||
\(260\) | 11.9089 | 0.738559 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 19.4615 | − | 11.2361i | 1.20234 | − | 0.694170i | ||||
\(263\) | 4.24264 | + | 7.34847i | 0.261612 | + | 0.453126i | 0.966671 | − | 0.256023i | \(-0.0824124\pi\) |
−0.705058 | + | 0.709150i | \(0.749079\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.6562i | 1.20747i | ||||||||
\(266\) | −1.26139 | + | 31.2489i | −0.0773406 | + | 1.91600i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.1931 | − | 28.0472i | 0.976478 | − | 1.69131i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.65685 | − | 9.79796i | −0.339887 | − | 0.588702i | 0.644524 | − | 0.764584i | \(-0.277056\pi\) |
−0.984411 | + | 0.175882i | \(0.943722\pi\) | |||||||
\(278\) | −23.2379 | − | 13.4164i | −1.39372 | − | 0.804663i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 14.8170 | − | 7.77531i | 0.885487 | − | 0.464664i | ||||
\(281\) | 32.9089 | 1.96318 | 0.981590 | − | 0.190999i | \(-0.0611727\pi\) | ||||
0.981590 | + | 0.190999i | \(0.0611727\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 24.3927i | 1.44237i | ||||||||
\(287\) | −10.2692 | − | 6.49478i | −0.606169 | − | 0.383375i | ||||
\(288\) | −16.9706 | −1.00000 | ||||||||
\(289\) | 8.50000 | − | 14.7224i | 0.500000 | − | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 31.6299i | − | 1.84784i | −0.382584 | − | 0.923921i | \(-0.624966\pi\) | ||
0.382584 | − | 0.923921i | \(-0.375034\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.1421 | −0.823387 | ||||||||
\(296\) | −13.4772 | + | 23.3432i | −0.783348 | + | 1.35680i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.852485 | + | 0.492182i | 0.0493005 | + | 0.0284636i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −28.9545 | + | 16.7169i | −1.66065 | + | 0.958778i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(308\) | 15.9260 | + | 30.3494i | 0.907468 | + | 1.72932i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(314\) | 29.6678i | 1.67425i | ||||||||
\(315\) | 0.715838 | − | 17.7338i | 0.0403329 | − | 0.999186i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.48528 | − | 14.6969i | 0.476581 | − | 0.825462i | −0.523059 | − | 0.852296i | \(-0.675209\pi\) |
0.999640 | + | 0.0268342i | \(0.00854260\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 15.4919 | + | 8.94427i | 0.866025 | + | 0.500000i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.38201 | + | 0.0557857i | 0.0770162 | + | 0.00310882i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −9.00000 | + | 15.5885i | −0.500000 | + | 0.866025i | ||||
\(325\) | −11.5307 | + | 6.65728i | −0.639611 | + | 0.369279i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 12.9896i | − | 0.717229i | ||||||
\(329\) | −21.4545 | + | 11.2583i | −1.18282 | + | 0.620692i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.19306 | − | 15.9229i | 0.505296 | − | 0.875199i | −0.494685 | − | 0.869072i | \(-0.664716\pi\) |
0.999981 | − | 0.00612670i | \(-0.00195020\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 14.2948 | + | 24.7592i | 0.783348 | + | 1.35680i | ||||
\(334\) | −24.2614 | − | 14.0073i | −1.32752 | − | 0.766446i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(338\) | −4.17822 | + | 7.23690i | −0.227265 | + | 0.393635i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 35.4618i | 1.91756i | ||||||||
\(343\) | −18.3848 | − | 2.23607i | −0.992685 | − | 0.120736i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 32.2158 | − | 18.5998i | 1.73193 | − | 0.999933i | ||||
\(347\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | −10.0000 | + | 15.8114i | −0.534522 | + | 0.845154i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −18.3204 | + | 31.7318i | −0.976478 | + | 1.69131i | ||||
\(353\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 25.2982i | − | 1.34080i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.6388 | −0.562279 | ||||||||
\(359\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(360\) | 16.4317 | − | 9.48683i | 0.866025 | − | 0.500000i | ||||
\(361\) | 25.4317 | + | 44.0490i | 1.33851 | + | 2.31837i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.568323 | − | 14.0793i | 0.0297882 | − | 0.737958i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 33.0170 | − | 19.0624i | 1.72347 | − | 0.995047i | 0.812035 | − | 0.583609i | \(-0.198360\pi\) |
0.911438 | − | 0.411438i | \(-0.134973\pi\) | |||||||
\(368\) | 0.739315 | + | 1.28053i | 0.0385394 | + | 0.0667523i | ||||
\(369\) | −11.9317 | − | 6.88876i | −0.621138 | − | 0.358614i | ||||
\(370\) | − | 30.1360i | − | 1.56670i | ||||||
\(371\) | 23.2386 | + | 0.938044i | 1.20649 | + | 0.0487008i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.3137 | + | 19.5959i | −0.585802 | + | 1.01464i | 0.408973 | + | 0.912546i | \(0.365887\pi\) |
−0.994775 | + | 0.102092i | \(0.967446\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −22.4317 | − | 12.9509i | −1.15683 | − | 0.667893i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.4317 | −1.71727 | −0.858635 | − | 0.512588i | \(-0.828687\pi\) | ||||
−0.858635 | + | 0.512588i | \(0.828687\pi\) | |||||||
\(380\) | 18.6900 | − | 32.3721i | 0.958778 | − | 1.66065i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.7677 | + | 12.5676i | 1.11228 | + | 0.642173i | 0.939418 | − | 0.342773i | \(-0.111366\pi\) |
0.172859 | + | 0.984947i | \(0.444700\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −32.3861 | − | 20.4828i | −1.65055 | − | 1.04390i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −8.48528 | − | 17.8885i | −0.428571 | − | 0.903508i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 19.6931 | − | 34.1094i | 0.992122 | − | 1.71841i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 19.4317 | + | 33.6567i | 0.976478 | + | 1.69131i | ||||
\(397\) | 3.87298 | + | 2.23607i | 0.194379 | + | 0.112225i | 0.594031 | − | 0.804442i | \(-0.297536\pi\) |
−0.399652 | + | 0.916667i | \(0.630869\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −20.0000 | −1.00000 | ||||||||
\(401\) | 4.02277 | − | 6.96765i | 0.200888 | − | 0.347948i | −0.747927 | − | 0.663781i | \(-0.768951\pi\) |
0.948815 | + | 0.315833i | \(0.102284\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 20.1246i | − | 1.00000i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 61.7269 | 3.05969 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.8634 | − | 18.9737i | 1.62499 | − | 0.938187i | 0.639430 | − | 0.768849i | \(-0.279170\pi\) |
0.985558 | − | 0.169338i | \(-0.0541630\pi\) | |||||||
\(410\) | 7.26139 | + | 12.5771i | 0.358614 | + | 0.621138i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 8.94427i | − | 0.440653i | ||||||
\(413\) | −0.674899 | + | 16.7196i | −0.0332096 | + | 0.822717i | ||||
\(414\) | 1.56832 | 0.0770789 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 13.0455 | − | 7.53185i | 0.639611 | − | 0.369279i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 66.3070 | + | 38.2824i | 3.24318 | + | 1.87245i | ||||
\(419\) | − | 6.70527i | − | 0.327574i | −0.986496 | − | 0.163787i | \(-0.947629\pi\) | ||
0.986496 | − | 0.163787i | \(-0.0523710\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | 3.84078 | − | 6.65242i | 0.186966 | − | 0.323835i | ||||
\(423\) | −23.7924 | + | 13.7365i | −1.15683 | + | 0.667893i | ||||
\(424\) | 12.4317 | + | 21.5323i | 0.603736 | + | 1.04570i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.67581 | − | 1.54488i | 0.128001 | − | 0.0739015i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(440\) | − | 40.9656i | − | 1.95296i | ||||||
\(441\) | −20.9317 | − | 1.69260i | −0.996747 | − | 0.0806002i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.1421 | + | 24.4949i | 0.670402 | + | 1.16117i | ||||
\(446\) | −27.3861 | − | 15.8114i | −1.29677 | − | 0.748691i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 11.3137 | − | 17.8885i | 0.534522 | − | 0.845154i | ||||
\(449\) | 4.90890 | 0.231665 | 0.115833 | − | 0.993269i | \(-0.463046\pi\) | ||||
0.115833 | + | 0.993269i | \(0.463046\pi\) | |||||||
\(450\) | −10.6066 | + | 18.3712i | −0.500000 | + | 0.866025i | ||||
\(451\) | −25.7614 | + | 14.8733i | −1.21306 | + | 0.700358i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.32031 | + | 13.9500i | 0.343182 | + | 0.653984i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.43168 | − | 0.826579i | −0.0667523 | − | 0.0385394i | ||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −37.7497 | −1.75438 | −0.877189 | − | 0.480146i | \(-0.840584\pi\) | ||||
−0.877189 | + | 0.480146i | \(0.840584\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(468\) | − | 15.9775i | − | 0.738559i | ||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 28.9592 | 1.33579 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −15.4919 | + | 8.94427i | −0.713074 | + | 0.411693i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 41.7922i | 1.91756i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 26.3716 | 1.20747 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21.9772 | − | 12.6886i | −1.00208 | − | 0.578548i | ||||
\(482\) | 4.15686i | 0.189340i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 61.9089 | 2.81404 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.5563 | − | 26.9444i | −0.704925 | − | 1.22097i | −0.966718 | − | 0.255843i | \(-0.917647\pi\) |
0.261793 | − | 0.965124i | \(-0.415686\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 18.2158 | + | 12.5771i | 0.822908 | + | 0.568175i | ||||
\(491\) | 2.00000 | 0.0902587 | 0.0451294 | − | 0.998981i | \(-0.485630\pi\) | ||||
0.0451294 | + | 0.998981i | \(0.485630\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −15.7386 | − | 27.2601i | −0.708114 | − | 1.22649i | ||||
\(495\) | −37.6293 | − | 21.7253i | −1.69131 | − | 0.976478i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.00000 | − | 5.19615i | 0.134298 | − | 0.232612i | −0.791031 | − | 0.611776i | \(-0.790455\pi\) |
0.925329 | + | 0.379165i | \(0.123789\pi\) | |||||||
\(500\) | 19.3649 | − | 11.1803i | 0.866025 | − | 0.500000i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −21.4862 | − | 12.4051i | −0.958978 | − | 0.553666i | ||||
\(503\) | − | 40.2492i | − | 1.79462i | −0.441397 | − | 0.897312i | \(-0.645517\pi\) | ||
0.441397 | − | 0.897312i | \(-0.354483\pi\) | |||||||
\(504\) | −10.4317 | − | 19.8791i | −0.464664 | − | 0.885487i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.69306 | − | 2.93247i | 0.0752659 | − | 0.130364i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 17.9507 | + | 31.0915i | 0.796434 | + | 1.37946i | ||||
\(509\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.6274 | 1.00000 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.00000 | + | 8.66025i | 0.220326 | + | 0.381616i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 59.3164i | 2.60873i | ||||||||
\(518\) | −35.6284 | − | 1.43817i | −1.56542 | − | 0.0631894i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.42087 | + | 14.5854i | −0.369279 | + | 0.639611i | ||||
\(521\) | −39.4545 | + | 22.7790i | −1.72853 | + | 0.997968i | −0.832405 | + | 0.554168i | \(0.813037\pi\) |
−0.896126 | + | 0.443800i | \(0.853630\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(524\) | 31.7806i | 1.38834i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.0000 | −0.523225 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4317 | + | 19.8002i | 0.497029 | + | 0.860880i | ||||
\(530\) | −24.0738 | − | 13.8990i | −1.04570 | − | 0.603736i | ||||
\(531\) | 18.9737i | 0.823387i | ||||||||
\(532\) | −37.3800 | − | 23.6412i | −1.62063 | − | 1.02498i | ||||
\(533\) | 12.2294 | 0.529716 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −25.7614 | + | 37.3111i | −1.10962 | + | 1.60710i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 22.9005 | + | 39.6647i | 0.976478 | + | 1.69131i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 16.0000 | 0.679775 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 32.8634 | − | 18.9737i | 1.39372 | − | 0.804663i | ||||
\(557\) | −5.50423 | − | 9.53361i | −0.233222 | − | 0.403952i | 0.725533 | − | 0.688188i | \(-0.241594\pi\) |
−0.958754 | + | 0.284236i | \(0.908260\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.954451 | + | 23.6451i | −0.0403329 | + | 0.999186i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −23.2701 | + | 40.3050i | −0.981590 | + | 1.70016i | ||||
\(563\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −23.7924 | − | 0.960398i | −0.999186 | − | 0.0403329i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.9772 | + | 29.4054i | −0.711722 | + | 1.23274i | 0.252488 | + | 0.967600i | \(0.418751\pi\) |
−0.964210 | + | 0.265139i | \(0.914582\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.00000 | − | 15.5885i | −0.376638 | − | 0.652357i | 0.613933 | − | 0.789359i | \(-0.289587\pi\) |
−0.990571 | + | 0.137002i | \(0.956253\pi\) | |||||||
\(572\) | −29.8749 | − | 17.2483i | −1.24913 | − | 0.721187i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 15.2158 | − | 7.98459i | 0.635097 | − | 0.333270i | ||||
\(575\) | 1.84829 | 0.0770789 | ||||||||
\(576\) | 12.0000 | − | 20.7846i | 0.500000 | − | 0.866025i | ||||
\(577\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(578\) | 12.0208 | + | 20.8207i | 0.500000 | + | 0.866025i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28.4691 | − | 49.3099i | 1.17907 | − | 2.04221i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.93168 | + | 15.4701i | 0.369279 | + | 0.639611i | ||||
\(586\) | 38.7386 | + | 22.3657i | 1.60028 | + | 0.923921i | ||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 10.0000 | − | 17.3205i | 0.411693 | − | 0.713074i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −19.0597 | − | 33.0123i | −0.783348 | − | 1.35680i | ||||
\(593\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.20560 | + | 0.696051i | −0.0493005 | + | 0.0284636i | ||||
\(599\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 25.2982i | − | 1.03194i | −0.856608 | − | 0.515968i | \(-0.827432\pi\) | ||
0.856608 | − | 0.515968i | \(-0.172568\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −59.9430 | + | 34.6081i | −2.43703 | + | 1.40702i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.1801 | + | 11.0736i | 0.778496 | + | 0.449465i | 0.835897 | − | 0.548886i | \(-0.184948\pi\) |
−0.0574012 | + | 0.998351i | \(0.518281\pi\) | |||||||
\(608\) | − | 47.2824i | − | 1.91756i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.1931 | − | 21.1190i | 0.493279 | − | 0.854384i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.7156 | − | 39.3446i | −0.917475 | − | 1.58911i | −0.803236 | − | 0.595661i | \(-0.796890\pi\) |
−0.114239 | − | 0.993453i | \(-0.536443\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −48.4317 | − | 1.95498i | −1.95137 | − | 0.0787685i | ||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 42.7158 | − | 24.6620i | 1.71689 | − | 0.991250i | 0.792446 | − | 0.609941i | \(-0.208807\pi\) |
0.924448 | − | 0.381308i | \(-0.124526\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 29.6341 | − | 15.5506i | 1.18726 | − | 0.623023i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5000 | + | 21.6506i | −0.500000 | + | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −36.3355 | − | 20.9783i | −1.44994 | − | 0.837125i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 21.2132 | + | 13.4164i | 0.845154 | + | 0.534522i | ||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 12.0000 | + | 20.7846i | 0.476581 | + | 0.825462i | ||||
\(635\) | −34.7614 | − | 20.0695i | −1.37946 | − | 0.796434i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.8417 | − | 7.98873i | 0.667294 | − | 0.316525i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −21.9089 | + | 12.6491i | −0.866025 | + | 0.500000i | ||||
\(641\) | −22.4089 | − | 38.8134i | −0.885098 | − | 1.53304i | −0.845601 | − | 0.533816i | \(-0.820758\pi\) |
−0.0394976 | − | 0.999220i | \(-0.512576\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(644\) | −1.04555 | + | 1.65316i | −0.0412004 | + | 0.0651435i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.90610 | − | 3.40989i | 0.232193 | − | 0.134057i | −0.379390 | − | 0.925237i | \(-0.623866\pi\) |
0.611583 | + | 0.791180i | \(0.290533\pi\) | |||||||
\(648\) | −12.7279 | − | 22.0454i | −0.500000 | − | 0.866025i | ||||
\(649\) | 35.4772 | + | 20.4828i | 1.39260 | + | 0.804020i | ||||
\(650\) | − | 18.8296i | − | 0.738559i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.6644 | + | 25.3995i | −0.573863 | + | 0.993960i | 0.422301 | + | 0.906456i | \(0.361222\pi\) |
−0.996164 | + | 0.0875041i | \(0.972111\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.7659 | − | 30.7714i | −0.694170 | − | 1.20234i | ||||
\(656\) | 15.9089 | + | 9.18501i | 0.621138 | + | 0.358614i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.38201 | − | 34.2371i | 0.0538762 | − | 1.33470i | ||||
\(659\) | −26.0000 | −1.01282 | −0.506408 | − | 0.862294i | \(-0.669027\pi\) | ||||
−0.506408 | + | 0.862294i | \(0.669027\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(662\) | 13.0010 | + | 22.5183i | 0.505296 | + | 0.875199i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 49.4089 | + | 1.99443i | 1.91600 | + | 0.0773406i | ||||
\(666\) | −40.4317 | −1.56670 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 34.3108 | − | 19.8093i | 1.32752 | − | 0.766446i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.90890 | − | 10.2345i | −0.227265 | − | 0.393635i | ||||
\(677\) | 34.0293 | + | 19.6468i | 1.30785 | + | 0.755090i | 0.981738 | − | 0.190240i | \(-0.0609267\pi\) |
0.326116 | + | 0.945330i | \(0.394260\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(684\) | −43.4317 | − | 25.0753i | −1.66065 | − | 0.958778i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 15.7386 | − | 20.9355i | 0.600903 | − | 0.799322i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −20.2723 | + | 11.7042i | −0.772311 | + | 0.445894i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.3861 | − | 15.8114i | −1.04182 | − | 0.601494i | −0.121470 | − | 0.992595i | \(-0.538761\pi\) |
−0.920348 | + | 0.391102i | \(0.872094\pi\) | |||||||
\(692\) | 52.6082i | 1.99987i | ||||||||
\(693\) | −27.4805 | + | 43.4506i | −1.04390 | + | 1.65055i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −21.2132 | + | 36.7423i | −0.804663 | + | 1.39372i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −12.2938 | − | 23.4278i | −0.464664 | − | 0.885487i | ||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −68.9828 | + | 39.8272i | −2.60174 | + | 1.50211i | ||||
\(704\) | −25.9089 | − | 44.8755i | −0.976478 | − | 1.69131i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 30.9839 | + | 17.8885i | 1.16117 | + | 0.670402i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 38.5683 | 1.44237 | ||||||||
\(716\) | 7.52277 | − | 13.0298i | 0.281139 | − | 0.486948i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(720\) | 26.8328i | 1.00000i | ||||||||
\(721\) | 10.4772 | − | 5.49798i | 0.390192 | − | 0.204755i | ||||
\(722\) | −71.9316 | −2.67702 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 48.7764i | − | 1.80902i | −0.426457 | − | 0.904508i | \(-0.640239\pi\) | ||
0.426457 | − | 0.904508i | \(-0.359761\pi\) | |||||||
\(728\) | 16.8417 | + | 10.6516i | 0.624196 | + | 0.394776i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.33085 | + | 2.50041i | 0.159963 | + | 0.0923549i | 0.577845 | − | 0.816147i | \(-0.303894\pi\) |
−0.417881 | + | 0.908502i | \(0.637227\pi\) | |||||||
\(734\) | 53.9165i | 1.99009i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.09110 | −0.0770789 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 16.8739 | − | 9.74217i | 0.621138 | − | 0.358614i | ||||
\(739\) | 10.7614 | + | 18.6393i | 0.395864 | + | 0.685657i | 0.993211 | − | 0.116326i | \(-0.0371118\pi\) |
−0.597347 | + | 0.801983i | \(0.703778\pi\) | |||||||
\(740\) | 36.9089 | + | 21.3094i | 1.35680 | + | 0.783348i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −17.5810 | + | 27.7981i | −0.645420 | + | 1.02050i | ||||
\(743\) | 16.4721 | 0.604302 | 0.302151 | − | 0.953260i | \(-0.402295\pi\) | ||||
0.302151 | + | 0.953260i | \(0.402295\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −16.0000 | − | 27.7128i | −0.585802 | − | 1.01464i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(752\) | 31.7232 | − | 18.3154i | 1.15683 | − | 0.667893i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 45.2548 | 1.64481 | 0.822407 | − | 0.568899i | \(-0.192630\pi\) | ||||
0.822407 | + | 0.568899i | \(0.192630\pi\) | |||||||
\(758\) | 23.6398 | − | 40.9453i | 0.858635 | − | 1.48720i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 26.4317 | + | 45.7810i | 0.958778 | + | 1.66065i | ||||
\(761\) | 5.40890 | + | 3.12283i | 0.196073 | + | 0.113203i | 0.594822 | − | 0.803857i | \(-0.297222\pi\) |
−0.398750 | + | 0.917060i | \(0.630556\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −30.7842 | + | 17.7732i | −1.11228 | + | 0.642173i | ||||
\(767\) | −8.42087 | − | 14.5854i | −0.304060 | − | 0.526647i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 53.0899i | − | 1.91447i | −0.289309 | − | 0.957236i | \(-0.593425\pi\) | ||
0.289309 | − | 0.957236i | \(-0.406575\pi\) | |||||||
\(770\) | 47.9866 | − | 25.1812i | 1.72932 | − | 0.907468i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 47.8662 | − | 27.6356i | 1.72163 | − | 0.993983i | 0.806045 | − | 0.591854i | \(-0.201604\pi\) |
0.915583 | − | 0.402129i | \(-0.131730\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19.1931 | − | 33.2434i | 0.687663 | − | 1.19107i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 27.9089 | + | 2.25681i | 0.996747 | + | 0.0806002i | ||||
\(785\) | 46.9089 | 1.67425 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(788\) | 27.8502 | + | 48.2380i | 0.992122 | + | 1.71841i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −54.9611 | −1.95296 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −5.47723 | + | 3.16228i | −0.194379 | + | 0.112225i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 40.2492i | − | 1.42570i | −0.701316 | − | 0.712850i | \(-0.747404\pi\) | ||
0.701316 | − | 0.712850i | \(-0.252596\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 14.1421 | − | 24.4949i | 0.500000 | − | 0.866025i | ||||
\(801\) | 32.8634 | − | 18.9737i | 1.16117 | − | 0.670402i | ||||
\(802\) | 5.68906 | + | 9.85374i | 0.200888 | + | 0.347948i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.0882050 | − | 2.18514i | 0.00310882 | − | 0.0770162i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.4089 | − | 26.6890i | −0.541748 | − | 0.938335i | −0.998804 | − | 0.0488972i | \(-0.984429\pi\) |
0.457056 | − | 0.889438i | \(-0.348904\pi\) | |||||||
\(810\) | 24.6475 | + | 14.2302i | 0.866025 | + | 0.500000i | ||||
\(811\) | − | 26.7284i | − | 0.938563i | −0.883049 | − | 0.469281i | \(-0.844513\pi\) | ||
0.883049 | − | 0.469281i | \(-0.155487\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −43.6475 | + | 75.5997i | −1.52984 | + | 2.64977i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 53.6656i | 1.87637i | ||||||||
\(819\) | 18.7158 | − | 9.82123i | 0.653984 | − | 0.343182i | ||||
\(820\) | −20.5383 | −0.717229 | ||||||||
\(821\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.0416 | + | 41.6413i | 0.838039 | + | 1.45153i | 0.891532 | + | 0.452957i | \(0.149631\pi\) |
−0.0534937 | + | 0.998568i | \(0.517036\pi\) | |||||||
\(824\) | 10.9545 | + | 6.32456i | 0.381616 | + | 0.220326i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −20.0000 | − | 12.6491i | −0.695889 | − | 0.440119i | ||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | −1.10897 | + | 1.92080i | −0.0385394 | + | 0.0667523i | ||||
\(829\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 21.3033i | 0.738559i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22.1475 | + | 38.3606i | −0.766446 | + | 1.32752i | ||||
\(836\) | −93.7723 | + | 54.1394i | −3.24318 | + | 1.87245i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.21225 | + | 4.74134i | 0.283687 | + | 0.163787i | ||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.43168 | + | 9.40794i | 0.186966 | + | 0.323835i | ||||
\(845\) | 11.4425 | + | 6.60635i | 0.393635 | + | 0.227265i | ||||
\(846\) | − | 38.8528i | − | 1.33579i | ||||||
\(847\) | 38.0549 | + | 72.5194i | 1.30758 | + | 2.49180i | ||||
\(848\) | −35.1621 | −1.20747 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.76139 | + | 3.05081i | 0.0603796 | + | 0.104580i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.9679i | 1.16304i | 0.813533 | + | 0.581519i | \(0.197541\pi\) | ||||
−0.813533 | + | 0.581519i | \(0.802459\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 56.0701 | 1.91756 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 49.2950 | + | 28.4605i | 1.68192 | + | 0.971060i | 0.960381 | + | 0.278691i | \(0.0899005\pi\) |
0.721544 | + | 0.692369i | \(0.243433\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27.2957 | − | 47.2776i | 0.929157 | − | 1.60935i | 0.144421 | − | 0.989516i | \(-0.453868\pi\) |
0.784736 | − | 0.619831i | \(-0.212799\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −29.4089 | − | 50.9377i | −0.999933 | − | 1.73193i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.36957i | 0.147803i | ||||||||
\(875\) | 25.0000 | + | 15.8114i | 0.845154 | + | 0.534522i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.3460 | − | 38.7043i | 0.754570 | − | 1.30695i | −0.191018 | − | 0.981586i | \(-0.561179\pi\) |
0.945588 | − | 0.325366i | \(-0.105488\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 50.1724 | + | 28.9670i | 1.69131 | + | 0.976478i | ||||
\(881\) | 43.9049i | 1.47919i | 0.673050 | + | 0.739597i | \(0.264984\pi\) | ||||
−0.673050 | + | 0.739597i | \(0.735016\pi\) | |||||||
\(882\) | 16.8739 | − | 24.4391i | 0.568175 | − | 0.822908i | ||||
\(883\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.87298 | + | 2.23607i | 0.130042 | + | 0.0750798i | 0.563610 | − | 0.826041i | \(-0.309412\pi\) |
−0.433568 | + | 0.901121i | \(0.642746\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −25.3861 | + | 40.1390i | −0.851423 | + | 1.34622i | ||||
\(890\) | −40.0000 | −1.34080 | ||||||||
\(891\) | −29.1475 | + | 50.4850i | −0.976478 | + | 1.69131i | ||||
\(892\) | 38.7298 | − | 22.3607i | 1.29677 | − | 0.748691i | ||||
\(893\) | −38.2720 | − | 66.2890i | −1.28072 | − | 2.21828i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.8214i | 0.562279i | ||||||||
\(896\) | 13.9089 | + | 26.5055i | 0.464664 | + | 0.885487i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.47112 | + | 6.01215i | −0.115833 | + | 0.200628i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −15.0000 | − | 25.9808i | −0.500000 | − | 0.866025i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | − | 42.0682i | − | 1.40072i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −22.2614 | − | 0.898598i | −0.737958 | − | 0.0297882i | ||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −37.2274 | + | 19.5353i | −1.22936 | + | 0.645112i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(920\) | 2.02470 | − | 1.16896i | 0.0667523 | − | 0.0385394i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −47.6492 | −1.56670 | ||||||||
\(926\) | 26.6931 | − | 46.2337i | 0.877189 | − | 1.51934i | ||||
\(927\) | 11.6190 | − | 6.70820i | 0.381616 | − | 0.220326i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 47.4089 | + | 27.3715i | 1.55544 | + | 0.898031i | 0.997684 | + | 0.0680235i | \(0.0216693\pi\) |
0.557752 | + | 0.830008i | \(0.311664\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.71584 | − | 58.3187i | 0.154555 | − | 1.91132i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 19.5683 | + | 11.2978i | 0.639611 | + | 0.369279i | ||||
\(937\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −20.4772 | + | 35.4676i | −0.667893 | + | 1.15683i | ||||
\(941\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.47021 | − | 0.848827i | −0.0478766 | − | 0.0276416i | ||||
\(944\) | − | 25.2982i | − | 0.823387i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −51.1847 | − | 29.5515i | −1.66065 | − | 0.958778i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | −18.6475 | + | 32.2984i | −0.603736 | + | 1.04570i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.5000 | − | 26.8468i | 0.500000 | − | 0.866025i | ||||
\(962\) | 31.0805 | − | 17.9443i | 1.00208 | − | 0.578548i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.09110 | − | 2.93935i | −0.163973 | − | 0.0946700i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −53.7401 | −1.72817 | −0.864083 | − | 0.503350i | \(-0.832101\pi\) | ||||
−0.864083 | + | 0.503350i | \(0.832101\pi\) | |||||||
\(968\) | −43.7762 | + | 75.8226i | −1.40702 | + | 2.43703i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 49.2386 | + | 28.4279i | 1.58014 | + | 0.912296i | 0.994837 | + | 0.101482i | \(0.0323585\pi\) |
0.585305 | + | 0.810813i | \(0.300975\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 42.4264 | + | 26.8328i | 1.36013 | + | 0.860221i | ||||
\(974\) | 44.0000 | 1.40985 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 81.9311i | − | 2.61853i | ||||||
\(980\) | −28.2843 | + | 13.4164i | −0.903508 | + | 0.428571i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.41421 | + | 2.44949i | −0.0451294 | + | 0.0781664i | ||||
\(983\) | −53.4909 | + | 30.8830i | −1.70609 | + | 0.985014i | −0.766809 | + | 0.641875i | \(0.778157\pi\) |
−0.939285 | + | 0.343138i | \(0.888510\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −53.9317 | − | 31.1375i | −1.71841 | − | 0.992122i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 44.5155 | 1.41623 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 53.2158 | − | 30.7242i | 1.69131 | − | 0.976478i | ||||
\(991\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −42.6028 | + | 24.5967i | −1.34924 | + | 0.778987i | −0.988143 | − | 0.153539i | \(-0.950933\pi\) |
−0.361102 | + | 0.932526i | \(0.617599\pi\) | |||||||
\(998\) | 4.24264 | + | 7.34847i | 0.134298 | + | 0.232612i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 280.2.ba.a.19.2 | ✓ | 8 | |
4.3 | odd | 2 | 1120.2.bq.a.719.3 | 8 | |||
5.4 | even | 2 | inner | 280.2.ba.a.19.3 | yes | 8 | |
7.3 | odd | 6 | inner | 280.2.ba.a.59.2 | yes | 8 | |
8.3 | odd | 2 | inner | 280.2.ba.a.19.3 | yes | 8 | |
8.5 | even | 2 | 1120.2.bq.a.719.2 | 8 | |||
20.19 | odd | 2 | 1120.2.bq.a.719.2 | 8 | |||
28.3 | even | 6 | 1120.2.bq.a.1039.3 | 8 | |||
35.24 | odd | 6 | inner | 280.2.ba.a.59.3 | yes | 8 | |
40.19 | odd | 2 | CM | 280.2.ba.a.19.2 | ✓ | 8 | |
40.29 | even | 2 | 1120.2.bq.a.719.3 | 8 | |||
56.3 | even | 6 | inner | 280.2.ba.a.59.3 | yes | 8 | |
56.45 | odd | 6 | 1120.2.bq.a.1039.2 | 8 | |||
140.59 | even | 6 | 1120.2.bq.a.1039.2 | 8 | |||
280.59 | even | 6 | inner | 280.2.ba.a.59.2 | yes | 8 | |
280.269 | odd | 6 | 1120.2.bq.a.1039.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.ba.a.19.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
280.2.ba.a.19.2 | ✓ | 8 | 40.19 | odd | 2 | CM | |
280.2.ba.a.19.3 | yes | 8 | 5.4 | even | 2 | inner | |
280.2.ba.a.19.3 | yes | 8 | 8.3 | odd | 2 | inner | |
280.2.ba.a.59.2 | yes | 8 | 7.3 | odd | 6 | inner | |
280.2.ba.a.59.2 | yes | 8 | 280.59 | even | 6 | inner | |
280.2.ba.a.59.3 | yes | 8 | 35.24 | odd | 6 | inner | |
280.2.ba.a.59.3 | yes | 8 | 56.3 | even | 6 | inner | |
1120.2.bq.a.719.2 | 8 | 8.5 | even | 2 | |||
1120.2.bq.a.719.2 | 8 | 20.19 | odd | 2 | |||
1120.2.bq.a.719.3 | 8 | 4.3 | odd | 2 | |||
1120.2.bq.a.719.3 | 8 | 40.29 | even | 2 | |||
1120.2.bq.a.1039.2 | 8 | 56.45 | odd | 6 | |||
1120.2.bq.a.1039.2 | 8 | 140.59 | even | 6 | |||
1120.2.bq.a.1039.3 | 8 | 28.3 | even | 6 | |||
1120.2.bq.a.1039.3 | 8 | 280.269 | odd | 6 |