Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [180,2,Mod(61,180)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(180, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("180.61");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 180.i (of order \(3\), 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: | \(1.43730723638\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 61.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 180.61 |
Dual form | 180.2.i.a.121.1 |
$q$-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 \(\left(\mathbb{Z}/180\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(91\) | \(101\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | 0 | ||||||||
\(3\) | 1.50000 | − | 0.866025i | 0.866025 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | − | 0.866025i | 0.188982 | − | 0.327327i | −0.755929 | − | 0.654654i | \(-0.772814\pi\) |
0.944911 | + | 0.327327i | \(0.106148\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | + | 3.46410i | 0.554700 | + | 0.960769i | 0.997927 | + | 0.0643593i | \(0.0205004\pi\) |
−0.443227 | + | 0.896410i | \(0.646166\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.50000 | − | 0.866025i | −0.387298 | − | 0.223607i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.00000 | −1.45521 | −0.727607 | − | 0.685994i | \(-0.759367\pi\) | ||||
−0.727607 | + | 0.685994i | \(0.759367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 1.73205i | − | 0.377964i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.50000 | + | 2.59808i | 0.312772 | + | 0.541736i | 0.978961 | − | 0.204046i | \(-0.0654092\pi\) |
−0.666190 | + | 0.745782i | \(0.732076\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.50000 | + | 2.59808i | −0.278543 | + | 0.482451i | −0.971023 | − | 0.238987i | \(-0.923185\pi\) |
0.692480 | + | 0.721437i | \(0.256518\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.00000 | + | 8.66025i | 0.898027 | + | 1.55543i | 0.830014 | + | 0.557743i | \(0.188333\pi\) |
0.0680129 | + | 0.997684i | \(0.478334\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.0000 | −1.64399 | −0.821995 | − | 0.569495i | \(-0.807139\pi\) | ||||
−0.821995 | + | 0.569495i | \(0.807139\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.00000 | + | 3.46410i | 0.960769 | + | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.50000 | − | 7.79423i | −0.702782 | − | 1.21725i | −0.967486 | − | 0.252924i | \(-0.918608\pi\) |
0.264704 | − | 0.964330i | \(-0.414726\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000 | − | 3.46410i | 0.304997 | − | 0.528271i | −0.672264 | − | 0.740312i | \(-0.734678\pi\) |
0.977261 | + | 0.212041i | \(0.0680112\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.00000 | −0.447214 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.50000 | + | 7.79423i | −0.656392 | + | 1.13691i | 0.325150 | + | 0.945662i | \(0.394585\pi\) |
−0.981543 | + | 0.191243i | \(0.938748\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | + | 5.19615i | 0.428571 | + | 0.742307i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.00000 | + | 5.19615i | −1.26025 | + | 0.727607i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.00000 | − | 1.73205i | 0.397360 | − | 0.229416i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.00000 | + | 5.19615i | 0.390567 | + | 0.676481i | 0.992524 | − | 0.122047i | \(-0.0389457\pi\) |
−0.601958 | + | 0.798528i | \(0.705612\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.500000 | − | 0.866025i | 0.0640184 | − | 0.110883i | −0.832240 | − | 0.554416i | \(-0.812942\pi\) |
0.896258 | + | 0.443533i | \(0.146275\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.50000 | − | 2.59808i | −0.188982 | − | 0.327327i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.00000 | − | 3.46410i | 0.248069 | − | 0.429669i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.50000 | − | 9.52628i | −0.671932 | − | 1.16382i | −0.977356 | − | 0.211604i | \(-0.932131\pi\) |
0.305424 | − | 0.952217i | \(-0.401202\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.50000 | + | 2.59808i | 0.541736 | + | 0.312772i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000 | 1.42414 | 0.712069 | − | 0.702109i | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702109i | \(0.247758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.00000 | −0.468165 | −0.234082 | − | 0.972217i | \(-0.575209\pi\) | ||||
−0.234082 | + | 0.972217i | \(0.575209\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.73205i | 0.200000i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.00000 | − | 8.66025i | 0.562544 | − | 0.974355i | −0.434730 | − | 0.900561i | \(-0.643156\pi\) |
0.997274 | − | 0.0737937i | \(-0.0235106\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.50000 | − | 7.79423i | 0.493939 | − | 0.855528i | −0.506036 | − | 0.862512i | \(-0.668890\pi\) |
0.999976 | + | 0.00698436i | \(0.00222321\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.00000 | + | 5.19615i | 0.325396 | + | 0.563602i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.19615i | 0.557086i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.00000 | 0.953998 | 0.476999 | − | 0.878904i | \(-0.341725\pi\) | ||||
0.476999 | + | 0.878904i | \(0.341725\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000 | 0.419314 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 15.0000 | + | 8.66025i | 1.55543 | + | 0.898027i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | − | 1.73205i | −0.102598 | − | 0.177705i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.00000 | − | 8.66025i | 0.507673 | − | 0.879316i | −0.492287 | − | 0.870433i | \(-0.663839\pi\) |
0.999961 | − | 0.00888289i | \(-0.00282755\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.00000 | − | 15.5885i | 0.895533 | − | 1.55111i | 0.0623905 | − | 0.998052i | \(-0.480128\pi\) |
0.833143 | − | 0.553058i | \(-0.186539\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00000 | − | 6.92820i | −0.394132 | − | 0.682656i | 0.598858 | − | 0.800855i | \(-0.295621\pi\) |
−0.992990 | + | 0.118199i | \(0.962288\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.50000 | + | 0.866025i | −0.146385 | + | 0.0845154i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.00000 | 0.870063 | 0.435031 | − | 0.900415i | \(-0.356737\pi\) | ||||
0.435031 | + | 0.900415i | \(0.356737\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.0000 | −1.81987 | −0.909935 | − | 0.414751i | \(-0.863869\pi\) | ||||
−0.909935 | + | 0.414751i | \(0.863869\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −15.0000 | + | 8.66025i | −1.42374 | + | 0.821995i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000 | + | 10.3923i | 0.564433 | + | 0.977626i | 0.997102 | + | 0.0760733i | \(0.0242383\pi\) |
−0.432670 | + | 0.901553i | \(0.642428\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.50000 | − | 2.59808i | 0.139876 | − | 0.242272i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.0000 | 1.10940 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.00000 | + | 5.19615i | −0.275010 | + | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.50000 | + | 9.52628i | 0.500000 | + | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −13.5000 | − | 7.79423i | −1.21725 | − | 0.702782i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.00000 | −0.621150 | −0.310575 | − | 0.950549i | \(-0.600522\pi\) | ||||
−0.310575 | + | 0.950549i | \(0.600522\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 6.92820i | − | 0.609994i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.00000 | − | 5.19615i | −0.262111 | − | 0.453990i | 0.704692 | − | 0.709514i | \(-0.251085\pi\) |
−0.966803 | + | 0.255524i | \(0.917752\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.00000 | − | 1.73205i | 0.0867110 | − | 0.150188i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.50000 | + | 2.59808i | −0.387298 | + | 0.223607i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.00000 | + | 10.3923i | −0.512615 | + | 0.887875i | 0.487278 | + | 0.873247i | \(0.337990\pi\) |
−0.999893 | + | 0.0146279i | \(0.995344\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.0000 | − | 17.3205i | −0.848189 | − | 1.46911i | −0.882823 | − | 0.469706i | \(-0.844360\pi\) |
0.0346338 | − | 0.999400i | \(-0.488974\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.5885i | 1.31278i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.00000 | 0.249136 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.00000 | + | 5.19615i | 0.742307 | + | 0.428571i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.50000 | − | 7.79423i | −0.368654 | − | 0.638528i | 0.620701 | − | 0.784047i | \(-0.286848\pi\) |
−0.989355 | + | 0.145519i | \(0.953515\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.00000 | + | 6.92820i | −0.325515 | + | 0.563809i | −0.981617 | − | 0.190864i | \(-0.938871\pi\) |
0.656101 | + | 0.754673i | \(0.272204\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.00000 | + | 15.5885i | −0.727607 | + | 1.26025i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.00000 | − | 8.66025i | 0.401610 | − | 0.695608i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.00000 | − | 1.73205i | −0.0798087 | − | 0.138233i | 0.823359 | − | 0.567521i | \(-0.192098\pi\) |
−0.903167 | + | 0.429289i | \(0.858764\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.00000 | + | 5.19615i | −0.713746 | + | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.00000 | 0.236433 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.00000 | −0.313304 | −0.156652 | − | 0.987654i | \(-0.550070\pi\) | ||||
−0.156652 | + | 0.987654i | \(0.550070\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.50000 | + | 12.9904i | 0.580367 | + | 1.00523i | 0.995436 | + | 0.0954356i | \(0.0304244\pi\) |
−0.415068 | + | 0.909790i | \(0.636242\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.50000 | + | 2.59808i | −0.115385 | + | 0.199852i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.00000 | − | 5.19615i | 0.229416 | − | 0.397360i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.500000 | + | 0.866025i | 0.0377964 | + | 0.0654654i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.00000 | + | 5.19615i | 0.676481 | + | 0.390567i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −24.0000 | −1.79384 | −0.896922 | − | 0.442189i | \(-0.854202\pi\) | ||||
−0.896922 | + | 0.442189i | \(0.854202\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.00000 | 0.371647 | 0.185824 | − | 0.982583i | \(-0.440505\pi\) | ||||
0.185824 | + | 0.982583i | \(0.440505\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 1.73205i | − | 0.128037i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.00000 | + | 8.66025i | 0.367607 | + | 0.636715i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.50000 | − | 2.59808i | −0.327327 | − | 0.188982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.00000 | + | 5.19615i | −0.217072 | + | 0.375980i | −0.953912 | − | 0.300088i | \(-0.902984\pi\) |
0.736839 | + | 0.676068i | \(0.236317\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.00000 | + | 3.46410i | 0.143963 | + | 0.249351i | 0.928986 | − | 0.370116i | \(-0.120682\pi\) |
−0.785022 | + | 0.619467i | \(0.787349\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 6.92820i | − | 0.496139i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.0000 | 0.854965 | 0.427482 | − | 0.904024i | \(-0.359401\pi\) | ||||
0.427482 | + | 0.904024i | \(0.359401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.00000 | 0.141776 | 0.0708881 | − | 0.997484i | \(-0.477417\pi\) | ||||
0.0708881 | + | 0.997484i | \(0.477417\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.5000 | − | 9.52628i | −1.16382 | − | 0.671932i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.50000 | + | 2.59808i | 0.105279 | + | 0.182349i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.50000 | + | 7.79423i | −0.314294 | + | 0.544373i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.00000 | 0.625543 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.00000 | + | 3.46410i | 0.137686 | + | 0.238479i | 0.926620 | − | 0.375999i | \(-0.122700\pi\) |
−0.788935 | + | 0.614477i | \(0.789367\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 18.0000 | − | 10.3923i | 1.23334 | − | 0.712069i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.00000 | −0.272798 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.0000 | 0.678844 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.00000 | + | 3.46410i | −0.405442 | + | 0.234082i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.0000 | − | 20.7846i | −0.807207 | − | 1.39812i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.50000 | + | 9.52628i | −0.368307 | + | 0.637927i | −0.989301 | − | 0.145889i | \(-0.953396\pi\) |
0.620994 | + | 0.783815i | \(0.286729\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.50000 | + | 2.59808i | 0.100000 | + | 0.173205i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.00000 | + | 10.3923i | −0.398234 | + | 0.689761i | −0.993508 | − | 0.113761i | \(-0.963710\pi\) |
0.595274 | + | 0.803523i | \(0.297043\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.500000 | + | 0.866025i | 0.0330409 | + | 0.0572286i | 0.882073 | − | 0.471113i | \(-0.156147\pi\) |
−0.849032 | + | 0.528341i | \(0.822814\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −30.0000 | −1.96537 | −0.982683 | − | 0.185296i | \(-0.940675\pi\) | ||||
−0.982683 | + | 0.185296i | \(0.940675\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.00000 | 0.587095 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 17.3205i | − | 1.12509i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.50000 | − | 6.06218i | 0.225455 | − | 0.390499i | −0.731001 | − | 0.682376i | \(-0.760947\pi\) |
0.956456 | + | 0.291877i | \(0.0942799\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.5000 | − | 7.79423i | −0.866025 | − | 0.500000i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.00000 | − | 5.19615i | 0.191663 | − | 0.331970i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.00000 | + | 6.92820i | 0.254514 | + | 0.440831i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 15.5885i | − | 0.987878i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.0000 | 1.13615 | 0.568075 | − | 0.822977i | \(-0.307688\pi\) | ||||
0.568075 | + | 0.822977i | \(0.307688\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.00000 | + | 5.19615i | 0.563602 | + | 0.325396i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.00000 | − | 5.19615i | −0.187135 | − | 0.324127i | 0.757159 | − | 0.653231i | \(-0.226587\pi\) |
−0.944294 | + | 0.329104i | \(0.893253\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.00000 | + | 8.66025i | −0.310685 | + | 0.538122i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.50000 | + | 7.79423i | 0.278543 | + | 0.482451i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.0000 | − | 20.7846i | 0.739952 | − | 1.28163i | −0.212565 | − | 0.977147i | \(-0.568182\pi\) |
0.952517 | − | 0.304487i | \(-0.0984850\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.00000 | + | 5.19615i | 0.184289 | + | 0.319197i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.5000 | − | 7.79423i | 0.826187 | − | 0.476999i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.00000 | 0.548740 | 0.274370 | − | 0.961624i | \(-0.411531\pi\) | ||||
0.274370 | + | 0.961624i | \(0.411531\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.0000 | 0.850439 | 0.425220 | − | 0.905090i | \(-0.360197\pi\) | ||||
0.425220 | + | 0.905090i | \(0.360197\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.00000 | − | 3.46410i | 0.363137 | − | 0.209657i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.00000 | + | 1.73205i | −0.0600842 | + | 0.104069i | −0.894503 | − | 0.447062i | \(-0.852470\pi\) |
0.834419 | + | 0.551131i | \(0.185804\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 30.0000 | 1.79605 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.5000 | + | 28.5788i | −0.984307 | + | 1.70487i | −0.339333 | + | 0.940666i | \(0.610201\pi\) |
−0.644974 | + | 0.764204i | \(0.723132\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.500000 | + | 0.866025i | 0.0297219 | + | 0.0514799i | 0.880504 | − | 0.474039i | \(-0.157204\pi\) |
−0.850782 | + | 0.525519i | \(0.823871\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.00000 | − | 1.73205i | −0.177705 | − | 0.102598i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.00000 | −0.531253 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 17.3205i | − | 1.01535i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.00000 | + | 5.19615i | 0.175262 | + | 0.303562i | 0.940252 | − | 0.340480i | \(-0.110589\pi\) |
−0.764990 | + | 0.644042i | \(0.777256\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.00000 | − | 5.19615i | 0.174667 | − | 0.302532i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.00000 | + | 10.3923i | −0.346989 | + | 0.601003i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.00000 | − | 3.46410i | −0.115278 | − | 0.199667i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 31.1769i | − | 1.79107i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.00000 | −0.0572598 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.0000 | 1.65512 | 0.827559 | − | 0.561379i | \(-0.189729\pi\) | ||||
0.827559 | + | 0.561379i | \(0.189729\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.0000 | − | 6.92820i | −0.682656 | − | 0.394132i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.00000 | − | 15.5885i | −0.510343 | − | 0.883940i | −0.999928 | − | 0.0119847i | \(-0.996185\pi\) |
0.489585 | − | 0.871956i | \(-0.337148\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.00000 | − | 13.8564i | 0.452187 | − | 0.783210i | −0.546335 | − | 0.837567i | \(-0.683977\pi\) |
0.998522 | + | 0.0543564i | \(0.0173107\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.50000 | + | 2.59808i | −0.0845154 | + | 0.146385i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.00000 | − | 10.3923i | 0.336994 | − | 0.583690i | −0.646872 | − | 0.762598i | \(-0.723923\pi\) |
0.983866 | + | 0.178908i | \(0.0572566\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.5000 | − | 7.79423i | 0.753497 | − | 0.435031i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.0000 | −0.667698 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.00000 | −0.221880 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −28.5000 | + | 16.4545i | −1.57605 | + | 0.909935i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.50000 | + | 7.79423i | 0.248093 | + | 0.429710i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.0000 | + | 22.5167i | −0.714545 | + | 1.23763i | 0.248590 | + | 0.968609i | \(0.420033\pi\) |
−0.963135 | + | 0.269019i | \(0.913301\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −15.0000 | + | 25.9808i | −0.821995 | + | 1.42374i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.50000 | + | 9.52628i | −0.300497 | + | 0.520476i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.00000 | − | 6.92820i | −0.217894 | − | 0.377403i | 0.736270 | − | 0.676688i | \(-0.236585\pi\) |
−0.954164 | + | 0.299285i | \(0.903252\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.0000 | + | 10.3923i | 0.977626 | + | 0.564433i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.0000 | 0.701934 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 5.19615i | − | 0.279751i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.0000 | − | 20.7846i | −0.644194 | − | 1.11578i | −0.984487 | − | 0.175457i | \(-0.943860\pi\) |
0.340293 | − | 0.940319i | \(-0.389474\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.5000 | + | 19.9186i | −0.615581 | + | 1.06622i | 0.374701 | + | 0.927146i | \(0.377745\pi\) |
−0.990282 | + | 0.139072i | \(0.955588\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.0000 | − | 10.3923i | 0.960769 | − | 0.554700i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.00000 | + | 10.3923i | −0.319348 | + | 0.553127i | −0.980352 | − | 0.197256i | \(-0.936797\pi\) |
0.661004 | + | 0.750382i | \(0.270130\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.00000 | − | 10.3923i | −0.318447 | − | 0.551566i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10.3923i | 0.550019i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.00000 | −0.316668 | −0.158334 | − | 0.987386i | \(-0.550612\pi\) | ||||
−0.158334 | + | 0.987386i | \(0.550612\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 16.5000 | + | 9.52628i | 0.866025 | + | 0.500000i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.00000 | + | 3.46410i | 0.104685 | + | 0.181319i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.0000 | + | 27.7128i | −0.835193 | + | 1.44660i | 0.0586798 | + | 0.998277i | \(0.481311\pi\) |
−0.893873 | + | 0.448320i | \(0.852022\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −27.0000 | −1.40556 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.00000 | + | 5.19615i | −0.155752 | + | 0.269771i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.00000 | − | 12.1244i | −0.362446 | − | 0.627775i | 0.625917 | − | 0.779890i | \(-0.284725\pi\) |
−0.988363 | + | 0.152115i | \(0.951392\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.50000 | − | 0.866025i | 0.0774597 | − | 0.0447214i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.0000 | −0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.0000 | 0.719132 | 0.359566 | − | 0.933120i | \(-0.382925\pi\) | ||||
0.359566 | + | 0.933120i | \(0.382925\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.5000 | + | 6.06218i | −0.537931 | + | 0.310575i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.0000 | + | 20.7846i | 0.613171 | + | 1.06204i | 0.990702 | + | 0.136047i | \(0.0434398\pi\) |
−0.377531 | + | 0.925997i | \(0.623227\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.00000 | − | 10.3923i | −0.304997 | − | 0.528271i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.50000 | − | 12.9904i | 0.380265 | − | 0.658638i | −0.610835 | − | 0.791758i | \(-0.709166\pi\) |
0.991100 | + | 0.133120i | \(0.0424994\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.00000 | − | 15.5885i | −0.455150 | − | 0.788342i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.00000 | − | 5.19615i | −0.453990 | − | 0.262111i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.0000 | −0.503155 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.0000 | −1.10415 | −0.552074 | − | 0.833795i | \(-0.686163\pi\) | ||||
−0.552074 | + | 0.833795i | \(0.686163\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 3.46410i | − | 0.173422i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.00000 | + | 15.5885i | 0.449439 | + | 0.778450i | 0.998350 | − | 0.0574304i | \(-0.0182907\pi\) |
−0.548911 | + | 0.835881i | \(0.684957\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.0000 | + | 34.6410i | −0.996271 | + | 1.72559i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.50000 | + | 7.79423i | −0.223607 | + | 0.387298i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.00000 | + | 8.66025i | 0.247234 | + | 0.428222i | 0.962757 | − | 0.270367i | \(-0.0871450\pi\) |
−0.715523 | + | 0.698589i | \(0.753812\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.7846i | 1.02523i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.00000 | 0.295241 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.00000 | −0.441793 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −30.0000 | − | 17.3205i | −1.46911 | − | 0.848189i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.00000 | − | 10.3923i | −0.293119 | − | 0.507697i | 0.681426 | − | 0.731887i | \(-0.261360\pi\) |
−0.974546 | + | 0.224189i | \(0.928027\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.0000 | − | 19.0526i | 0.536107 | − | 0.928565i | −0.463002 | − | 0.886357i | \(-0.653228\pi\) |
0.999109 | − | 0.0422075i | \(-0.0134391\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 13.5000 | + | 23.3827i | 0.656392 | + | 1.13691i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.00000 | − | 5.19615i | 0.145521 | − | 0.252050i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.500000 | − | 0.866025i | −0.0241967 | − | 0.0419099i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.00000 | 0.289010 | 0.144505 | − | 0.989504i | \(-0.453841\pi\) | ||||
0.144505 | + | 0.989504i | \(0.453841\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.0000 | 1.24948 | 0.624740 | − | 0.780833i | \(-0.285205\pi\) | ||||
0.624740 | + | 0.780833i | \(0.285205\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.50000 | − | 2.59808i | 0.215758 | − | 0.124568i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.00000 | + | 5.19615i | 0.143509 | + | 0.248566i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.0000 | − | 24.2487i | 0.668184 | − | 1.15733i | −0.310228 | − | 0.950662i | \(-0.600405\pi\) |
0.978412 | − | 0.206666i | \(-0.0662612\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.0000 | 0.857143 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.5000 | − | 23.3827i | 0.641404 | − | 1.11094i | −0.343715 | − | 0.939074i | \(-0.611685\pi\) |
0.985119 | − | 0.171871i | \(-0.0549812\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.50000 | − | 7.79423i | −0.213320 | − | 0.369482i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.5000 | − | 7.79423i | −0.638528 | − | 0.368654i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.0000 | 1.41579 | 0.707894 | − | 0.706319i | \(-0.249646\pi\) | ||||
0.707894 | + | 0.706319i | \(0.249646\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.8564i | 0.651031i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.00000 | − | 3.46410i | −0.0937614 | − | 0.162400i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.00000 | − | 8.66025i | 0.233890 | − | 0.405110i | −0.725059 | − | 0.688686i | \(-0.758188\pi\) |
0.958950 | + | 0.283577i | \(0.0915211\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 31.1769i | 1.45521i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.5000 | + | 28.5788i | −0.768482 | + | 1.33105i | 0.169904 | + | 0.985461i | \(0.445654\pi\) |
−0.938386 | + | 0.345589i | \(0.887679\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.00000 | + | 3.46410i | 0.0929479 | + | 0.160990i | 0.908750 | − | 0.417340i | \(-0.137038\pi\) |
−0.815802 | + | 0.578331i | \(0.803704\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 17.3205i | − | 0.803219i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 36.0000 | 1.66588 | 0.832941 | − | 0.553362i | \(-0.186655\pi\) | ||||
0.832941 | + | 0.553362i | \(0.186655\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.0000 | −0.507933 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.00000 | − | 1.73205i | −0.138233 | − | 0.0798087i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.00000 | + | 1.73205i | −0.0458831 | + | 0.0794719i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.00000 | + | 15.5885i | −0.412082 | + | 0.713746i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.0000 | − | 25.9808i | 0.685367 | − | 1.18709i | −0.287954 | − | 0.957644i | \(-0.592975\pi\) |
0.973321 | − | 0.229447i | \(-0.0736918\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.0000 | − | 34.6410i | −0.911922 | − | 1.57949i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.50000 | − | 2.59808i | 0.204757 | − | 0.118217i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.0000 | −0.454077 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.0000 | −0.725029 | −0.362515 | − | 0.931978i | \(-0.618082\pi\) | ||||
−0.362515 | + | 0.931978i | \(0.618082\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.00000 | + | 3.46410i | −0.271329 | + | 0.156652i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.0000 | + | 20.7846i | 0.541552 | + | 0.937996i | 0.998815 | + | 0.0486647i | \(0.0154966\pi\) |
−0.457263 | + | 0.889332i | \(0.651170\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.00000 | − | 15.5885i | 0.405340 | − | 0.702069i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.00000 | − | 10.3923i | 0.269137 | − | 0.466159i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.00000 | + | 3.46410i | 0.0895323 | + | 0.155074i | 0.907314 | − | 0.420455i | \(-0.138129\pi\) |
−0.817781 | + | 0.575529i | \(0.804796\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 22.5000 | + | 12.9904i | 1.00523 | + | 0.580367i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.00000 | 0.133763 | 0.0668817 | − | 0.997761i | \(-0.478695\pi\) | ||||
0.0668817 | + | 0.997761i | \(0.478695\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.0000 | −0.800989 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.19615i | 0.230769i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.50000 | + | 7.79423i | 0.199459 | + | 0.345473i | 0.948353 | − | 0.317217i | \(-0.102748\pi\) |
−0.748894 | + | 0.662690i | \(0.769415\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.00000 | + | 3.46410i | −0.0884748 | + | 0.153243i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 10.3923i | − | 0.458831i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.00000 | + | 6.92820i | −0.176261 | + | 0.305293i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.0000 | 1.18289 | 0.591446 | − | 0.806345i | \(-0.298557\pi\) | ||||
0.591446 | + | 0.806345i | \(0.298557\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.00000 | −0.306089 | −0.153044 | − | 0.988219i | \(-0.548908\pi\) | ||||
−0.153044 | + | 0.988219i | \(0.548908\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.50000 | + | 0.866025i | 0.0654654 | + | 0.0377964i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −30.0000 | − | 51.9615i | −1.30682 | − | 2.26348i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | − | 12.1244i | 0.304348 | − | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.0000 | 0.781133 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.0000 | − | 31.1769i | 0.779667 | − | 1.35042i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.50000 | − | 7.79423i | −0.194552 | − | 0.336974i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −36.0000 | + | 20.7846i | −1.55351 | + | 0.896922i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.00000 | −0.300954 | −0.150477 | − | 0.988614i | \(-0.548081\pi\) | ||||
−0.150477 | + | 0.988614i | \(0.548081\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.50000 | − | 4.33013i | 0.321856 | − | 0.185824i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.50000 | + | 16.4545i | 0.406935 | + | 0.704833i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.50000 | − | 6.06218i | 0.149649 | − | 0.259200i | −0.781449 | − | 0.623970i | \(-0.785519\pi\) |
0.931098 | + | 0.364770i | \(0.118852\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.50000 | − | 2.59808i | −0.0640184 | − | 0.110883i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.00000 | + | 5.19615i | −0.127804 | + | 0.221364i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.00000 | − | 8.66025i | −0.212622 | − | 0.368271i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 15.0000 | + | 8.66025i | 0.636715 | + | 0.367607i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.00000 | −0.254228 | −0.127114 | − | 0.991888i | \(-0.540571\pi\) | ||||
−0.127114 | + | 0.991888i | \(0.540571\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.0000 | 0.676728 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.5000 | + | 33.7750i | 0.821827 | + | 1.42345i | 0.904320 | + | 0.426855i | \(0.140378\pi\) |
−0.0824933 | + | 0.996592i | \(0.526288\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.00000 | − | 10.3923i | 0.252422 | − | 0.437208i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.00000 | −0.377964 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.00000 | + | 5.19615i | −0.125767 | + | 0.217834i | −0.922032 | − | 0.387113i | \(-0.873472\pi\) |
0.796266 | + | 0.604947i | \(0.206806\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.0000 | − | 27.7128i | −0.669579 | − | 1.15975i | −0.978022 | − | 0.208502i | \(-0.933141\pi\) |
0.308443 | − | 0.951243i | \(-0.400192\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.3923i | 0.434145i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.00000 | −0.125109 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.0000 | 1.58196 | 0.790980 | − | 0.611842i | \(-0.209571\pi\) | ||||
0.790980 | + | 0.611842i | \(0.209571\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.00000 | + | 3.46410i | 0.249351 | + | 0.143963i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.50000 | − | 7.79423i | −0.186691 | − | 0.323359i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.00000 | − | 10.3923i | −0.248069 | − | 0.429669i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.5000 | − | 23.3827i | 0.557205 | − | 0.965107i | −0.440524 | − | 0.897741i | \(-0.645207\pi\) |
0.997728 | − | 0.0673658i | \(-0.0214594\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.0000 | + | 17.3205i | 0.412043 | + | 0.713679i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.0000 | − | 10.3923i | 0.740421 | − | 0.427482i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.00000 | −0.246390 | −0.123195 | − | 0.992382i | \(-0.539314\pi\) | ||||
−0.123195 | + | 0.992382i | \(0.539314\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.00000 | 0.245976 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.00000 | − | 1.73205i | 0.122782 | − | 0.0708881i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.00000 | − | 5.19615i | −0.122577 | − | 0.212309i | 0.798206 | − | 0.602384i | \(-0.205782\pi\) |
−0.920783 | + | 0.390075i | \(0.872449\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.0000 | − | 19.0526i | 0.448699 | − | 0.777170i | −0.549602 | − | 0.835426i | \(-0.685221\pi\) |
0.998302 | + | 0.0582563i | \(0.0185541\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −33.0000 | −1.34386 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.50000 | − | 9.52628i | 0.223607 | − | 0.387298i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.50000 | + | 6.06218i | 0.142061 | + | 0.246056i | 0.928272 | − | 0.371901i | \(-0.121294\pi\) |
−0.786212 | + | 0.617957i | \(0.787961\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.50000 | + | 2.59808i | 0.182349 | + | 0.105279i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −36.0000 | −1.45640 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.0000 | −0.888572 | −0.444286 | − | 0.895885i | \(-0.646543\pi\) | ||||
−0.444286 | + | 0.895885i | \(0.646543\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 15.5885i | 0.628587i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.00000 | + | 10.3923i | 0.241551 | + | 0.418378i | 0.961156 | − | 0.276005i | \(-0.0890106\pi\) |
−0.719605 | + | 0.694383i | \(0.755677\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.0000 | + | 22.5167i | −0.522514 | + | 0.905021i | 0.477143 | + | 0.878826i | \(0.341672\pi\) |
−0.999657 | + | 0.0261952i | \(0.991661\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.5000 | − | 7.79423i | 0.541736 | − | 0.312772i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.50000 | − | 7.79423i | 0.180289 | − | 0.312269i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 60.0000 | 2.39236 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.0000 | −1.59237 | −0.796187 | − | 0.605050i | \(-0.793153\pi\) | ||||
−0.796187 | + | 0.605050i | \(0.793153\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.00000 | + | 3.46410i | 0.238479 | + | 0.137686i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.50000 | + | 6.06218i | 0.138893 | + | 0.240570i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.0000 | + | 20.7846i | −0.475457 | + | 0.823516i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 18.0000 | − | 31.1769i | 0.712069 | − | 1.23334i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.5000 | + | 18.1865i | −0.414725 | + | 0.718325i | −0.995400 | − | 0.0958109i | \(-0.969456\pi\) |
0.580674 | + | 0.814136i | \(0.302789\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.5000 | + | 26.8468i | 0.611260 | + | 1.05873i | 0.991028 | + | 0.133652i | \(0.0426705\pi\) |
−0.379768 | + | 0.925082i | \(0.623996\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.00000 | + | 3.46410i | −0.236250 | + | 0.136399i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.00000 | 0.353827 | 0.176913 | − | 0.984226i | \(-0.443389\pi\) | ||||
0.176913 | + | 0.984226i | \(0.443389\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15.0000 | − | 8.66025i | 0.587896 | − | 0.339422i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.00000 | − | 5.19615i | −0.117399 | − | 0.203341i | 0.801337 | − | 0.598213i | \(-0.204122\pi\) |
−0.918736 | + | 0.394872i | \(0.870789\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.00000 | + | 5.19615i | −0.117220 | + | 0.203030i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.00000 | + | 10.3923i | −0.234082 | + | 0.405442i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.0000 | + | 31.1769i | −0.701180 | + | 1.21448i | 0.266872 | + | 0.963732i | \(0.414010\pi\) |
−0.968052 | + | 0.250748i | \(0.919323\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.00000 | + | 8.66025i | 0.194477 | + | 0.336845i | 0.946729 | − | 0.322031i | \(-0.104366\pi\) |
−0.752252 | + | 0.658876i | \(0.771032\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −36.0000 | − | 20.7846i | −1.39812 | − | 0.807207i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.00000 | −0.0775567 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.00000 | −0.348481 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19.0526i | 0.736614i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.0000 | − | 24.2487i | 0.539660 | − | 0.934719i | −0.459262 | − | 0.888301i | \(-0.651886\pi\) |
0.998922 | − | 0.0464181i | \(-0.0147807\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.50000 | + | 2.59808i | 0.173205 | + | 0.100000i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.00000 | − | 8.66025i | −0.191882 | − | 0.332350i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20.7846i | 0.796468i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.0000 | −0.459167 | −0.229584 | − | 0.973289i | \(-0.573736\pi\) | ||||
−0.229584 | + | 0.973289i | \(0.573736\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.0000 | 0.458496 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.50000 | + | 0.866025i | 0.0572286 | + | 0.0330409i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.0000 | − | 20.7846i | −0.457164 | − | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.00000 | − | 8.66025i | 0.190209 | − | 0.329452i | −0.755110 | − | 0.655598i | \(-0.772417\pi\) |
0.945319 | + | 0.326146i | \(0.105750\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.0000 | + | 17.3205i | −0.379322 | + | 0.657004i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 27.0000 | + | 46.7654i | 1.02270 | + | 1.77136i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −45.0000 | + | 25.9808i | −1.70206 | + | 0.982683i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.0000 | −0.793159 | −0.396580 | − | 0.918000i | \(-0.629803\pi\) | ||||
−0.396580 | + | 0.918000i | \(0.629803\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.0000 | −0.754314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13.5000 | − | 7.79423i | 0.508439 | − | 0.293548i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.00000 | − | 15.5885i | −0.338480 | − | 0.586264i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.5000 | + | 30.3109i | −0.657226 | + | 1.13835i | 0.324104 | + | 0.946021i | \(0.394937\pi\) |
−0.981331 | + | 0.192328i | \(0.938396\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.0000 | − | 25.9808i | −0.562544 | − | 0.974355i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15.0000 | + | 25.9808i | −0.561754 | + | 0.972987i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −42.0000 | −1.56634 | −0.783168 | − | 0.621810i | \(-0.786397\pi\) | ||||
−0.783168 | + | 0.621810i | \(0.786397\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.00000 | −0.297936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 12.1244i | − | 0.450910i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.50000 | − | 2.59808i | −0.0557086 | − | 0.0964901i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.50000 | − | 16.4545i | 0.352335 | − | 0.610263i | −0.634323 | − | 0.773068i | \(-0.718721\pi\) |
0.986658 | + | 0.162805i | \(0.0520543\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.0000 | + | 20.7846i | −0.443836 | + | 0.768747i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.00000 | − | 12.1244i | −0.258551 | − | 0.447823i | 0.707303 | − | 0.706910i | \(-0.249912\pi\) |
−0.965854 | + | 0.259087i | \(0.916578\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 10.3923i | − | 0.383326i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.00000 | 0.0735712 | 0.0367856 | − | 0.999323i | \(-0.488288\pi\) | ||||
0.0367856 | + | 0.999323i | \(0.488288\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.0000 | + | 6.92820i | 0.440831 | + | 0.254514i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.5000 | − | 28.5788i | −0.605326 | − | 1.04846i | −0.992000 | − | 0.126239i | \(-0.959709\pi\) |
0.386674 | − | 0.922217i | \(-0.373624\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.50000 | + | 7.79423i | −0.164867 | + | 0.285558i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.5000 | − | 23.3827i | −0.493939 | − | 0.855528i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.50000 | − | 7.79423i | 0.164426 | − | 0.284795i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.00000 | + | 13.8564i | 0.291924 | + | 0.505627i | 0.974265 | − | 0.225407i | \(-0.0723712\pi\) |
−0.682341 | + | 0.731034i | \(0.739038\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 27.0000 | − | 15.5885i | 0.983935 | − | 0.568075i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.00000 | 0.291150 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.0000 | 0.726912 | 0.363456 | − | 0.931611i | \(-0.381597\pi\) | ||||
0.363456 | + | 0.931611i | \(0.381597\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.5000 | + | 38.9711i | 0.815624 | + | 1.41270i | 0.908879 | + | 0.417061i | \(0.136940\pi\) |
−0.0932544 | + | 0.995642i | \(0.529727\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.50000 | + | 16.4545i | −0.343923 | + | 0.595692i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 18.0000 | 0.650791 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.0000 | + | 20.7846i | −0.433295 | + | 0.750489i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.5000 | + | 26.8468i | 0.558944 | + | 0.968120i | 0.997585 | + | 0.0694574i | \(0.0221268\pi\) |
−0.438641 | + | 0.898663i | \(0.644540\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.00000 | − | 5.19615i | −0.324127 | − | 0.187135i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −36.0000 | −1.29483 | −0.647415 | − | 0.762138i | \(-0.724150\pi\) | ||||
−0.647415 | + | 0.762138i | \(0.724150\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.0000 | −0.359211 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 17.3205i | 0.621370i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.00000 | − | 15.5885i | −0.322458 | − | 0.558514i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 13.5000 | + | 7.79423i | 0.482451 | + | 0.278543i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.00000 | + | 1.73205i | −0.0356915 | + | 0.0618195i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.0000 | + | 34.6410i | 0.712923 | + | 1.23482i | 0.963755 | + | 0.266788i | \(0.0859624\pi\) |
−0.250832 | + | 0.968031i | \(0.580704\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 41.5692i | − | 1.47990i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.0000 | 0.426671 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.00000 | 0.142044 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.00000 | + | 5.19615i | 0.319197 | + | 0.184289i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.0000 | + | 20.7846i | 0.425062 | + | 0.736229i | 0.996426 | − | 0.0844678i | \(-0.0269190\pi\) |
−0.571364 | + | 0.820696i | \(0.693586\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.0000 | − | 46.7654i | 0.955191 | − | 1.65444i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.5000 | − | 23.3827i | 0.476999 | − | 0.826187i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.50000 | − | 2.59808i | −0.0528681 | − | 0.0915702i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.5000 | − | 7.79423i | 0.475223 | − | 0.274370i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −54.0000 | −1.89854 | −0.949269 | − | 0.314464i | \(-0.898175\pi\) | ||||
−0.949269 | + | 0.314464i | \(0.898175\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.0000 | −0.772524 | −0.386262 | − | 0.922389i | \(-0.626234\pi\) | ||||
−0.386262 | + | 0.922389i | \(0.626234\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.0000 | − | 12.1244i | 0.736502 | − | 0.425220i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.00000 | + | 3.46410i | 0.0700569 | + | 0.121342i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.00000 | − | 6.92820i | 0.139942 | − | 0.242387i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.00000 | − | 10.3923i | 0.209657 | − | 0.363137i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.50000 | + | 2.59808i | −0.0523504 | + | 0.0906735i | −0.891013 | − | 0.453978i | \(-0.850005\pi\) |
0.838663 | + | 0.544651i | \(0.183338\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.5000 | + | 42.4352i | 0.854016 | + | 1.47920i | 0.877555 | + | 0.479477i | \(0.159174\pi\) |
−0.0235383 | + | 0.999723i | \(0.507493\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.0000 | 0.938882 | 0.469441 | − | 0.882964i | \(-0.344455\pi\) | ||||
0.469441 | + | 0.882964i | \(0.344455\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.00000 | −0.243120 | −0.121560 | − | 0.992584i | \(-0.538790\pi\) | ||||
−0.121560 | + | 0.992584i | \(0.538790\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.46410i | 0.120168i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.0000 | − | 31.1769i | −0.623663 | − | 1.08022i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.50000 | − | 12.9904i | 0.259548 | − | 0.449551i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 45.0000 | − | 25.9808i | 1.55543 | − | 0.898027i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.0000 | − | 25.9808i | 0.517858 | − | 0.896956i | −0.481927 | − | 0.876211i | \(-0.660063\pi\) |
0.999785 | − | 0.0207443i | \(-0.00660359\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0000 | + | 17.3205i | 0.344828 | + | 0.597259i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 57.1577i | 1.96861i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.00000 | 0.103203 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.0000 | 0.377964 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.50000 | + | 0.866025i | 0.0514799 | + | 0.0297219i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.0000 | − | 25.9808i | −0.514193 | − | 0.890609i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.00000 | − | 3.46410i | 0.0684787 | − | 0.118609i | −0.829753 | − | 0.558131i | \(-0.811519\pi\) |
0.898232 | + | 0.439522i | \(0.144852\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.00000 | −0.205196 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.0000 | − | 41.5692i | 0.819824 | − | 1.41998i | −0.0859870 | − | 0.996296i | \(-0.527404\pi\) |
0.905811 | − | 0.423681i | \(-0.139262\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.0000 | − | 17.3205i | −0.341196 | − | 0.590968i | 0.643459 | − | 0.765480i | \(-0.277499\pi\) |
−0.984655 | + | 0.174512i | \(0.944165\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.5000 | + | 7.79423i | −0.460079 | + | 0.265627i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.0000 | 0.510606 | 0.255303 | − | 0.966861i | \(-0.417825\pi\) | ||||
0.255303 | + | 0.966861i | \(0.417825\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 28.5000 | − | 16.4545i | 0.967911 | − | 0.558824i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.0000 | − | 38.1051i | 0.745442 | − | 1.29114i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −15.0000 | − | 25.9808i | −0.507673 | − | 0.879316i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.500000 | − | 0.866025i | 0.0169031 | − | 0.0292770i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.00000 | + | 3.46410i | 0.0675352 | + | 0.116974i | 0.897816 | − | 0.440371i | \(-0.145153\pi\) |
−0.830281 | + | 0.557346i | \(0.811820\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.00000 | + | 5.19615i | 0.303562 | + | 0.175262i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.0000 | −0.505363 | −0.252681 | − | 0.967550i | \(-0.581312\pi\) | ||||
−0.252681 | + | 0.967550i | \(0.581312\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.0000 | 0.975928 | 0.487964 | − | 0.872864i | \(-0.337740\pi\) | ||||
0.487964 | + | 0.872864i | \(0.337740\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 10.3923i | − | 0.349334i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.0000 | + | 41.5692i | 0.805841 | + | 1.39576i | 0.915722 | + | 0.401813i | \(0.131620\pi\) |
−0.109881 | + | 0.993945i | \(0.535047\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.50000 | + | 6.06218i | −0.117386 | + | 0.203319i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.00000 | + | 15.5885i | −0.301174 | + | 0.521648i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.0000 | + | 20.7846i | 0.401116 | + | 0.694753i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 20.7846i | 0.693978i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −30.0000 | −1.00056 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.0000 | 1.19933 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.00000 | − | 3.46410i | −0.199667 | − | 0.115278i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.50000 | − | 4.33013i | −0.0831028 | − | 0.143938i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.500000 | − | 0.866025i | 0.0166022 | − | 0.0287559i | −0.857605 | − | 0.514309i | \(-0.828048\pi\) |
0.874207 | + | 0.485553i | \(0.161382\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −27.0000 | − | 46.7654i | −0.895533 | − | 1.55111i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.00000 | − | 5.19615i | 0.0993944 | − | 0.172156i | −0.812040 | − | 0.583602i | \(-0.801643\pi\) |
0.911434 | + | 0.411446i | \(0.134976\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.50000 | + | 0.866025i | −0.0495885 | + | 0.0286299i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.00000 | −0.198137 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34.0000 | −1.12156 | −0.560778 | − | 0.827966i | \(-0.689498\pi\) | ||||
−0.560778 | + | 0.827966i | \(0.689498\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 43.5000 | − | 25.1147i | 1.43337 | − | 0.827559i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.0000 | + | 41.5692i | 0.789970 | + | 1.36827i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.00000 | − | 8.66025i | 0.164399 | − | 0.284747i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −24.0000 | −0.788263 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.00000 | + | 5.19615i | −0.0984268 | + | 0.170480i | −0.911034 | − | 0.412332i | \(-0.864714\pi\) |
0.812607 | + | 0.582812i | \(0.198048\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.00000 | + | 10.3923i | 0.196642 | + | 0.340594i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −27.0000 | − | 15.5885i | −0.883940 | − | 0.510343i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.0000 | −0.522697 | −0.261349 | − | 0.965244i | \(-0.584167\pi\) | ||||
−0.261349 | + | 0.965244i | \(0.584167\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 27.7128i | − | 0.904373i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.5000 | − | 38.9711i | −0.733479 | − | 1.27042i | −0.955387 | − | 0.295355i | \(-0.904562\pi\) |
0.221908 | − | 0.975068i | \(-0.428771\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.5000 | − | 23.3827i | 0.439620 | − | 0.761445i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.19615i | 0.169031i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.50000 | + | 12.9904i | −0.243717 | + | 0.422131i | −0.961770 | − | 0.273858i | \(-0.911700\pi\) |
0.718053 | + | 0.695988i | \(0.245034\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.00000 | − | 13.8564i | −0.259691 | − | 0.449798i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 20.7846i | − | 0.673987i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.0000 | 0.777436 | 0.388718 | − | 0.921357i | \(-0.372918\pi\) | ||||
0.388718 | + | 0.921357i | \(0.372918\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.00000 | 0.194155 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.00000 | + | 10.3923i | 0.193750 | + | 0.335585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −34.5000 | + | 59.7558i | −1.11290 | + | 1.92760i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.5000 | − | 23.3827i | 0.435031 | − | 0.753497i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.00000 | − | 3.46410i | 0.0643823 | − | 0.111513i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.500000 | + | 0.866025i | 0.0160789 | + | 0.0278495i | 0.873953 | − | 0.486011i | \(-0.161548\pi\) |
−0.857874 | + | 0.513860i | \(0.828215\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −18.0000 | + | 10.3923i | −0.578243 | + | 0.333849i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.0000 | 1.34784 | 0.673922 | − | 0.738802i | \(-0.264608\pi\) | ||||
0.673922 | + | 0.738802i | \(0.264608\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.0000 | −0.641171 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.00000 | + | 3.46410i | −0.192154 | + | 0.110940i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.0000 | − | 20.7846i | −0.383914 | − | 0.664959i | 0.607704 | − | 0.794164i | \(-0.292091\pi\) |
−0.991618 | + | 0.129205i | \(0.958757\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −28.5000 | + | 49.3634i | −0.909935 | + | 1.57605i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.50000 | + | 7.79423i | −0.143528 | + | 0.248597i | −0.928823 | − | 0.370525i | \(-0.879178\pi\) |
0.785295 | + | 0.619122i | \(0.212511\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.00000 | − | 10.3923i | −0.191176 | − | 0.331126i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13.5000 | + | 7.79423i | 0.429710 | + | 0.248093i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.0000 | 0.381578 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.00000 | 0.0635321 | 0.0317660 | − | 0.999495i | \(-0.489887\pi\) | ||||
0.0317660 | + | 0.999495i | \(0.489887\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 45.0333i | 1.42909i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.00000 | − | 1.73205i | −0.0317021 | − | 0.0549097i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.00000 | − | 8.66025i | 0.158352 | − | 0.274273i | −0.775923 | − | 0.630828i | \(-0.782715\pi\) |
0.934274 | + | 0.356555i | \(0.116049\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 51.9615i | 1.64399i |
(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 | 180.2.i.a.61.1 | ✓ | 2 | |
3.2 | odd | 2 | 540.2.i.a.181.1 | 2 | |||
4.3 | odd | 2 | 720.2.q.a.241.1 | 2 | |||
5.2 | odd | 4 | 900.2.s.a.349.1 | 4 | |||
5.3 | odd | 4 | 900.2.s.a.349.2 | 4 | |||
5.4 | even | 2 | 900.2.i.a.601.1 | 2 | |||
9.2 | odd | 6 | 1620.2.a.b.1.1 | 1 | |||
9.4 | even | 3 | inner | 180.2.i.a.121.1 | yes | 2 | |
9.5 | odd | 6 | 540.2.i.a.361.1 | 2 | |||
9.7 | even | 3 | 1620.2.a.e.1.1 | 1 | |||
12.11 | even | 2 | 2160.2.q.e.721.1 | 2 | |||
15.2 | even | 4 | 2700.2.s.a.2449.2 | 4 | |||
15.8 | even | 4 | 2700.2.s.a.2449.1 | 4 | |||
15.14 | odd | 2 | 2700.2.i.a.1801.1 | 2 | |||
36.7 | odd | 6 | 6480.2.a.t.1.1 | 1 | |||
36.11 | even | 6 | 6480.2.a.h.1.1 | 1 | |||
36.23 | even | 6 | 2160.2.q.e.1441.1 | 2 | |||
36.31 | odd | 6 | 720.2.q.a.481.1 | 2 | |||
45.2 | even | 12 | 8100.2.d.f.649.1 | 2 | |||
45.4 | even | 6 | 900.2.i.a.301.1 | 2 | |||
45.7 | odd | 12 | 8100.2.d.e.649.1 | 2 | |||
45.13 | odd | 12 | 900.2.s.a.49.1 | 4 | |||
45.14 | odd | 6 | 2700.2.i.a.901.1 | 2 | |||
45.22 | odd | 12 | 900.2.s.a.49.2 | 4 | |||
45.23 | even | 12 | 2700.2.s.a.1549.2 | 4 | |||
45.29 | odd | 6 | 8100.2.a.h.1.1 | 1 | |||
45.32 | even | 12 | 2700.2.s.a.1549.1 | 4 | |||
45.34 | even | 6 | 8100.2.a.i.1.1 | 1 | |||
45.38 | even | 12 | 8100.2.d.f.649.2 | 2 | |||
45.43 | odd | 12 | 8100.2.d.e.649.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.2.i.a.61.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
180.2.i.a.121.1 | yes | 2 | 9.4 | even | 3 | inner | |
540.2.i.a.181.1 | 2 | 3.2 | odd | 2 | |||
540.2.i.a.361.1 | 2 | 9.5 | odd | 6 | |||
720.2.q.a.241.1 | 2 | 4.3 | odd | 2 | |||
720.2.q.a.481.1 | 2 | 36.31 | odd | 6 | |||
900.2.i.a.301.1 | 2 | 45.4 | even | 6 | |||
900.2.i.a.601.1 | 2 | 5.4 | even | 2 | |||
900.2.s.a.49.1 | 4 | 45.13 | odd | 12 | |||
900.2.s.a.49.2 | 4 | 45.22 | odd | 12 | |||
900.2.s.a.349.1 | 4 | 5.2 | odd | 4 | |||
900.2.s.a.349.2 | 4 | 5.3 | odd | 4 | |||
1620.2.a.b.1.1 | 1 | 9.2 | odd | 6 | |||
1620.2.a.e.1.1 | 1 | 9.7 | even | 3 | |||
2160.2.q.e.721.1 | 2 | 12.11 | even | 2 | |||
2160.2.q.e.1441.1 | 2 | 36.23 | even | 6 | |||
2700.2.i.a.901.1 | 2 | 45.14 | odd | 6 | |||
2700.2.i.a.1801.1 | 2 | 15.14 | odd | 2 | |||
2700.2.s.a.1549.1 | 4 | 45.32 | even | 12 | |||
2700.2.s.a.1549.2 | 4 | 45.23 | even | 12 | |||
2700.2.s.a.2449.1 | 4 | 15.8 | even | 4 | |||
2700.2.s.a.2449.2 | 4 | 15.2 | even | 4 | |||
6480.2.a.h.1.1 | 1 | 36.11 | even | 6 | |||
6480.2.a.t.1.1 | 1 | 36.7 | odd | 6 | |||
8100.2.a.h.1.1 | 1 | 45.29 | odd | 6 | |||
8100.2.a.i.1.1 | 1 | 45.34 | even | 6 | |||
8100.2.d.e.649.1 | 2 | 45.7 | odd | 12 | |||
8100.2.d.e.649.2 | 2 | 45.43 | odd | 12 | |||
8100.2.d.f.649.1 | 2 | 45.2 | even | 12 | |||
8100.2.d.f.649.2 | 2 | 45.38 | even | 12 |