Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1920,2,Mod(481,1920)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1920, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1920.481");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1920 = 2^{7} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1920.s (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.3312771881\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{20} - 2 x^{18} - 4 x^{17} + 7 x^{16} + 16 x^{15} + 6 x^{14} - 36 x^{13} - 42 x^{12} + 40 x^{11} + \cdots + 1024 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{20} \) |
Twist minimal: | no (minimal twist has level 240) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 481.8 | ||
Root | \(-0.720859 + 1.21670i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1920.481 |
Dual form | 1920.2.s.f.1441.8 |
$q$-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 \(\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(641\) | \(901\) | \(1537\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.707107 | − | 0.707107i | 0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.707107 | − | 0.707107i | −0.316228 | − | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.0588949i | 0.0222602i | 0.999938 | + | 0.0111301i | \(0.00354289\pi\) | ||||
−0.999938 | + | 0.0111301i | \(0.996457\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.23289 | + | 2.23289i | 0.673242 | + | 0.673242i | 0.958462 | − | 0.285220i | \(-0.0920668\pi\) |
−0.285220 | + | 0.958462i | \(0.592067\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.84870 | + | 2.84870i | −0.790087 | + | 0.790087i | −0.981508 | − | 0.191421i | \(-0.938690\pi\) |
0.191421 | + | 0.981508i | \(0.438690\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.98228 | 1.45092 | 0.725458 | − | 0.688267i | \(-0.241628\pi\) | ||||
0.725458 | + | 0.688267i | \(0.241628\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.617238 | + | 0.617238i | −0.141604 | + | 0.141604i | −0.774355 | − | 0.632751i | \(-0.781926\pi\) |
0.632751 | + | 0.774355i | \(0.281926\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.0416450 | + | 0.0416450i | 0.00908769 | + | 0.00908769i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 0.746698i | − | 0.155697i | −0.996965 | − | 0.0778486i | \(-0.975195\pi\) | ||
0.996965 | − | 0.0778486i | \(-0.0248051\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.13987 | − | 1.13987i | 0.211668 | − | 0.211668i | −0.593308 | − | 0.804976i | \(-0.702178\pi\) |
0.804976 | + | 0.593308i | \(0.202178\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.55143 | 1.53588 | 0.767941 | − | 0.640520i | \(-0.221281\pi\) | ||||
0.767941 | + | 0.640520i | \(0.221281\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.15778 | 0.549700 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.0416450 | − | 0.0416450i | 0.00703929 | − | 0.00703929i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.01811 | + | 2.01811i | 0.331774 | + | 0.331774i | 0.853260 | − | 0.521486i | \(-0.174622\pi\) |
−0.521486 | + | 0.853260i | \(0.674622\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.02867i | 0.645104i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.71113i | 1.20428i | 0.798392 | + | 0.602138i | \(0.205684\pi\) | ||||
−0.798392 | + | 0.602138i | \(0.794316\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.94233 | − | 2.94233i | −0.448701 | − | 0.448701i | 0.446221 | − | 0.894923i | \(-0.352769\pi\) |
−0.894923 | + | 0.446221i | \(0.852769\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.707107 | + | 0.707107i | −0.105409 | + | 0.105409i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.789616 | 0.115177 | 0.0575887 | − | 0.998340i | \(-0.481659\pi\) | ||||
0.0575887 | + | 0.998340i | \(0.481659\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.99653 | 0.999504 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.23011 | − | 4.23011i | 0.592334 | − | 0.592334i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.80791 | + | 6.80791i | 0.935138 | + | 0.935138i | 0.998021 | − | 0.0628826i | \(-0.0200294\pi\) |
−0.0628826 | + | 0.998021i | \(0.520029\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.15778i | − | 0.425795i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.872906i | 0.115619i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.36045 | − | 9.36045i | −1.21863 | − | 1.21863i | −0.968113 | − | 0.250514i | \(-0.919401\pi\) |
−0.250514 | − | 0.968113i | \(-0.580599\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.814225 | − | 0.814225i | 0.104251 | − | 0.104251i | −0.653057 | − | 0.757308i | \(-0.726514\pi\) |
0.757308 | + | 0.653057i | \(0.226514\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.0588949 | 0.00742006 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.02867 | 0.499695 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.46701 | − | 5.46701i | 0.667901 | − | 0.667901i | −0.289329 | − | 0.957230i | \(-0.593432\pi\) |
0.957230 | + | 0.289329i | \(0.0934320\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.527995 | − | 0.527995i | −0.0635631 | − | 0.0635631i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.40423i | − | 0.878720i | −0.898311 | − | 0.439360i | \(-0.855205\pi\) | ||
0.898311 | − | 0.439360i | \(-0.144795\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 11.6114i | − | 1.35901i | −0.733670 | − | 0.679506i | \(-0.762194\pi\) | ||
0.733670 | − | 0.679506i | \(-0.237806\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.707107 | + | 0.707107i | 0.0816497 | + | 0.0816497i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.131506 | + | 0.131506i | −0.0149865 | + | 0.0149865i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 17.4027 | 1.95796 | 0.978978 | − | 0.203964i | \(-0.0653827\pi\) | ||||
0.978978 | + | 0.203964i | \(0.0653827\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.55090 | + | 7.55090i | −0.828819 | + | 0.828819i | −0.987354 | − | 0.158534i | \(-0.949323\pi\) |
0.158534 | + | 0.987354i | \(0.449323\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.23011 | − | 4.23011i | −0.458820 | − | 0.458820i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 1.61202i | − | 0.172826i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.3007i | 1.72788i | 0.503599 | + | 0.863938i | \(0.332009\pi\) | ||||
−0.503599 | + | 0.863938i | \(0.667991\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.167774 | − | 0.167774i | −0.0175875 | − | 0.0175875i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.04678 | − | 6.04678i | 0.627021 | − | 0.627021i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.872906 | 0.0895583 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.3159 | 1.25049 | 0.625247 | − | 0.780427i | \(-0.284998\pi\) | ||||
0.625247 | + | 0.780427i | \(0.284998\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.23289 | − | 2.23289i | 0.224414 | − | 0.224414i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.663582 | + | 0.663582i | 0.0660289 | + | 0.0660289i | 0.739350 | − | 0.673321i | \(-0.235133\pi\) |
−0.673321 | + | 0.739350i | \(0.735133\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 14.9036i | − | 1.46850i | −0.678880 | − | 0.734249i | \(-0.737534\pi\) | ||
0.678880 | − | 0.734249i | \(-0.262466\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 0.0588949i | − | 0.00574756i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.43861 | + | 3.43861i | 0.332423 | + | 0.332423i | 0.853506 | − | 0.521083i | \(-0.174472\pi\) |
−0.521083 | + | 0.853506i | \(0.674472\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.0571202 | + | 0.0571202i | −0.00547113 | + | 0.00547113i | −0.709837 | − | 0.704366i | \(-0.751231\pi\) |
0.704366 | + | 0.709837i | \(0.251231\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.85403 | 0.270893 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.9834 | −1.40952 | −0.704759 | − | 0.709447i | \(-0.748945\pi\) | ||||
−0.704759 | + | 0.709447i | \(0.748945\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.527995 | + | 0.527995i | −0.0492358 | + | 0.0492358i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.84870 | + | 2.84870i | 0.263362 | + | 0.263362i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.352326i | 0.0322977i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 1.02840i | − | 0.0934912i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.45259 | + | 5.45259i | 0.491644 | + | 0.491644i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.707107 | − | 0.707107i | 0.0632456 | − | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.74629 | −0.598636 | −0.299318 | − | 0.954153i | \(-0.596759\pi\) | ||||
−0.299318 | + | 0.954153i | \(0.596759\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.16109 | −0.366363 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.2459 | − | 10.2459i | 0.895185 | − | 0.895185i | −0.0998208 | − | 0.995005i | \(-0.531827\pi\) |
0.995005 | + | 0.0998208i | \(0.0318269\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.0363522 | − | 0.0363522i | −0.00315214 | − | 0.00315214i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000i | 0.0860663i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.4514i | 1.66185i | 0.556388 | + | 0.830923i | \(0.312187\pi\) | ||||
−0.556388 | + | 0.830923i | \(0.687813\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.09587 | − | 1.09587i | −0.0929501 | − | 0.0929501i | 0.659103 | − | 0.752053i | \(-0.270936\pi\) |
−0.752053 | + | 0.659103i | \(0.770936\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.558343 | − | 0.558343i | 0.0470210 | − | 0.0470210i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.7217 | −1.06384 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.61202 | −0.133871 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.94729 | − | 4.94729i | 0.408046 | − | 0.408046i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.6510 | + | 13.6510i | 1.11834 | + | 1.11834i | 0.991986 | + | 0.126349i | \(0.0403260\pi\) |
0.126349 | + | 0.991986i | \(0.459674\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 13.4811i | − | 1.09708i | −0.836125 | − | 0.548538i | \(-0.815184\pi\) | ||
0.836125 | − | 0.548538i | \(-0.184816\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 5.98228i | − | 0.483638i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.04678 | − | 6.04678i | −0.485689 | − | 0.485689i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.1090 | + | 11.1090i | −0.886593 | + | 0.886593i | −0.994194 | − | 0.107602i | \(-0.965683\pi\) |
0.107602 | + | 0.994194i | \(0.465683\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.62784 | 0.763537 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.0439767 | 0.00346585 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.97598 | + | 1.97598i | −0.154771 | + | 0.154771i | −0.780245 | − | 0.625474i | \(-0.784906\pi\) |
0.625474 | + | 0.780245i | \(0.284906\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.23289 | − | 2.23289i | −0.173830 | − | 0.173830i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 2.12777i | − | 0.164652i | −0.996605 | − | 0.0823259i | \(-0.973765\pi\) | ||
0.996605 | − | 0.0823259i | \(-0.0262348\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 3.23018i | − | 0.248476i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.617238 | + | 0.617238i | 0.0472014 | + | 0.0472014i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.21877 | − | 9.21877i | 0.700890 | − | 0.700890i | −0.263711 | − | 0.964602i | \(-0.584947\pi\) |
0.964602 | + | 0.263711i | \(0.0849466\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.0588949 | −0.00445204 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −13.2377 | −0.995004 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.02407 | − | 5.02407i | 0.375516 | − | 0.375516i | −0.493965 | − | 0.869482i | \(-0.664453\pi\) |
0.869482 | + | 0.493965i | \(0.164453\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.1363 | + | 15.1363i | 1.12507 | + | 1.12507i | 0.990967 | + | 0.134102i | \(0.0428151\pi\) |
0.134102 | + | 0.990967i | \(0.457185\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 1.15149i | − | 0.0851205i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 2.85403i | − | 0.209833i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.3578 | + | 13.3578i | 0.976817 | + | 0.976817i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.0416450 | − | 0.0416450i | 0.00302923 | − | 0.00302923i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.4425 | −0.900310 | −0.450155 | − | 0.892950i | \(-0.648631\pi\) | ||||
−0.450155 | + | 0.892950i | \(0.648631\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.241933 | 0.0174147 | 0.00870734 | − | 0.999962i | \(-0.497228\pi\) | ||||
0.00870734 | + | 0.999962i | \(0.497228\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.84870 | − | 2.84870i | 0.204000 | − | 0.204000i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.37260 | + | 2.37260i | 0.169041 | + | 0.169041i | 0.786558 | − | 0.617517i | \(-0.211861\pi\) |
−0.617517 | + | 0.786558i | \(0.711861\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.8275i | 1.40553i | 0.711420 | + | 0.702767i | \(0.248052\pi\) | ||||
−0.711420 | + | 0.702767i | \(0.751948\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 7.73152i | − | 0.545339i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.0671324 | + | 0.0671324i | 0.00471177 | + | 0.00471177i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.45259 | − | 5.45259i | 0.380826 | − | 0.380826i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.746698 | −0.0518991 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.75645 | −0.190668 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.54907 | − | 3.54907i | 0.244328 | − | 0.244328i | −0.574310 | − | 0.818638i | \(-0.694730\pi\) |
0.818638 | + | 0.574310i | \(0.194730\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.23558 | − | 5.23558i | −0.358736 | − | 0.358736i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.16109i | 0.283784i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.503636i | 0.0341890i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.21050 | − | 8.21050i | −0.554814 | − | 0.554814i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.0417 | + | 17.0417i | −1.14635 | + | 1.14635i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.6789 | −1.45173 | −0.725864 | − | 0.687838i | \(-0.758560\pi\) | ||||
−0.725864 | + | 0.687838i | \(0.758560\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.2117 | + | 10.2117i | −0.677775 | + | 0.677775i | −0.959496 | − | 0.281721i | \(-0.909095\pi\) |
0.281721 | + | 0.959496i | \(0.409095\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.0933 | − | 17.0933i | −1.12956 | − | 1.12956i | −0.990249 | − | 0.139312i | \(-0.955511\pi\) |
−0.139312 | − | 0.990249i | \(-0.544489\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.185977i | 0.0122364i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 24.2409i | − | 1.58807i | −0.607871 | − | 0.794036i | \(-0.707976\pi\) | ||
0.607871 | − | 0.794036i | \(-0.292024\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.558343 | − | 0.558343i | −0.0364223 | − | 0.0364223i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.3056 | − | 12.3056i | 0.799332 | − | 0.799332i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.0658 | −1.36263 | −0.681317 | − | 0.731989i | \(-0.738592\pi\) | ||||
−0.681317 | + | 0.731989i | \(0.738592\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.0578 | −1.42087 | −0.710434 | − | 0.703764i | \(-0.751501\pi\) | ||||
−0.710434 | + | 0.703764i | \(0.751501\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.707107 | + | 0.707107i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.94729 | − | 4.94729i | −0.316071 | − | 0.316071i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 3.51665i | − | 0.223759i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.6786i | 0.676728i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.22942 | + | 8.22942i | 0.519436 | + | 0.519436i | 0.917401 | − | 0.397964i | \(-0.130283\pi\) |
−0.397964 | + | 0.917401i | \(0.630283\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.66729 | − | 1.66729i | 0.104822 | − | 0.104822i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.98228 | −0.374625 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.32164 | 0.456712 | 0.228356 | − | 0.973578i | \(-0.426665\pi\) | ||||
0.228356 | + | 0.973578i | \(0.426665\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.118856 | + | 0.118856i | −0.00738536 | + | 0.00738536i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.13987 | − | 1.13987i | −0.0705560 | − | 0.0705560i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.6430i | 1.14958i | 0.818302 | + | 0.574788i | \(0.194915\pi\) | ||||
−0.818302 | + | 0.574788i | \(0.805085\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 9.62784i | − | 0.591433i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.5264 | + | 11.5264i | 0.705402 | + | 0.705402i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.22889 | − | 3.22889i | 0.196869 | − | 0.196869i | −0.601787 | − | 0.798656i | \(-0.705544\pi\) |
0.798656 | + | 0.601787i | \(0.205544\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.9381 | 1.69712 | 0.848560 | − | 0.529099i | \(-0.177470\pi\) | ||||
0.848560 | + | 0.529099i | \(0.177470\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.237268 | −0.0143601 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.23289 | + | 2.23289i | −0.134648 | + | 0.134648i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.58682 | + | 1.58682i | 0.0953431 | + | 0.0953431i | 0.753170 | − | 0.657826i | \(-0.228524\pi\) |
−0.657826 | + | 0.753170i | \(0.728524\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 8.55143i | − | 0.511961i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.36028i | 0.379423i | 0.981840 | + | 0.189711i | \(0.0607552\pi\) | ||||
−0.981840 | + | 0.189711i | \(0.939245\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.64115 | + | 3.64115i | 0.216444 | + | 0.216444i | 0.806998 | − | 0.590554i | \(-0.201091\pi\) |
−0.590554 | + | 0.806998i | \(0.701091\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.617238 | − | 0.617238i | 0.0365620 | − | 0.0365620i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.454146 | −0.0268074 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 18.7876 | 1.10516 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.70869 | − | 8.70869i | 0.510512 | − | 0.510512i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.09157 | + | 4.09157i | 0.239032 | + | 0.239032i | 0.816449 | − | 0.577417i | \(-0.195939\pi\) |
−0.577417 | + | 0.816449i | \(0.695939\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.2377i | 0.770727i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 3.15778i | − | 0.183233i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.12712 | + | 2.12712i | 0.123014 | + | 0.123014i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.173288 | − | 0.173288i | 0.00998818 | − | 0.00998818i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.938447 | 0.0539124 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.15149 | −0.0659341 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.832070 | − | 0.832070i | 0.0474887 | − | 0.0474887i | −0.682964 | − | 0.730452i | \(-0.739309\pi\) |
0.730452 | + | 0.682964i | \(0.239309\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.5385 | − | 10.5385i | −0.599512 | − | 0.599512i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.8376i | 0.784657i | 0.919825 | + | 0.392329i | \(0.128330\pi\) | ||||
−0.919825 | + | 0.392329i | \(0.871670\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 5.09179i | − | 0.287805i | −0.989592 | − | 0.143902i | \(-0.954035\pi\) | ||
0.989592 | − | 0.143902i | \(-0.0459651\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.0416450 | − | 0.0416450i | −0.00234643 | − | 0.00234643i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.3055 | + | 16.3055i | −0.915811 | + | 0.915811i | −0.996721 | − | 0.0809105i | \(-0.974217\pi\) |
0.0809105 | + | 0.996721i | \(0.474217\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.09040 | 0.285007 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.86293 | 0.271422 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.69249 | + | 3.69249i | −0.205456 | + | 0.205456i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.84870 | − | 2.84870i | −0.158017 | − | 0.158017i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.0807802i | 0.00446716i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.0465044i | 0.00256387i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.33950 | + | 5.33950i | 0.293485 | + | 0.293485i | 0.838455 | − | 0.544970i | \(-0.183459\pi\) |
−0.544970 | + | 0.838455i | \(0.683459\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.01811 | − | 2.01811i | 0.110591 | − | 0.110591i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.73152 | −0.422418 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.9232 | −0.595023 | −0.297512 | − | 0.954718i | \(-0.596157\pi\) | ||||
−0.297512 | + | 0.954718i | \(0.596157\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.5948 | + | 10.5948i | −0.575433 | + | 0.575433i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.0944 | + | 19.0944i | 1.03402 | + | 1.03402i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.824325i | 0.0445094i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.746698i | 0.0402009i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.5294 | − | 19.5294i | −1.04839 | − | 1.04839i | −0.998768 | − | 0.0496243i | \(-0.984198\pi\) |
−0.0496243 | − | 0.998768i | \(-0.515802\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.27622 | − | 9.27622i | 0.496545 | − | 0.496545i | −0.413816 | − | 0.910361i | \(-0.635804\pi\) |
0.910361 | + | 0.413816i | \(0.135804\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.02867 | 0.215035 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.31510 | 0.176445 | 0.0882225 | − | 0.996101i | \(-0.471881\pi\) | ||||
0.0882225 | + | 0.996101i | \(0.471881\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.23558 | + | 5.23558i | −0.277876 | + | 0.277876i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.249132 | + | 0.249132i | 0.0131855 | + | 0.0131855i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.61854i | 0.243757i | 0.992545 | + | 0.121879i | \(0.0388919\pi\) | ||||
−0.992545 | + | 0.121879i | \(0.961108\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.2380i | 0.959897i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.727191 | − | 0.727191i | −0.0381676 | − | 0.0381676i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.21050 | + | 8.21050i | −0.429757 | + | 0.429757i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.80336 | 0.198534 | 0.0992668 | − | 0.995061i | \(-0.468350\pi\) | ||||
0.0992668 | + | 0.995061i | \(0.468350\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.71113 | 0.401425 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.400951 | + | 0.400951i | −0.0208164 | + | 0.0208164i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.4506 | − | 18.4506i | −0.955338 | − | 0.955338i | 0.0437062 | − | 0.999044i | \(-0.486083\pi\) |
−0.999044 | + | 0.0437062i | \(0.986083\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 1.00000i | − | 0.0516398i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.49428i | 0.334472i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.95913 | + | 2.95913i | 0.152000 | + | 0.152000i | 0.779011 | − | 0.627010i | \(-0.215722\pi\) |
−0.627010 | + | 0.779011i | \(0.715722\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.77035 | + | 4.77035i | −0.244392 | + | 0.244392i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −37.0073 | −1.89099 | −0.945493 | − | 0.325642i | \(-0.894420\pi\) | ||||
−0.945493 | + | 0.325642i | \(0.894420\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.185977 | 0.00947829 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.94233 | + | 2.94233i | −0.149567 | + | 0.149567i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.0915 | − | 18.0915i | −0.917276 | − | 0.917276i | 0.0795542 | − | 0.996831i | \(-0.474650\pi\) |
−0.996831 | + | 0.0795542i | \(0.974650\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 4.46695i | − | 0.225904i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 14.4898i | − | 0.730915i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.3056 | − | 12.3056i | −0.619160 | − | 0.619160i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.0980 | − | 17.0980i | 0.858125 | − | 0.858125i | −0.132992 | − | 0.991117i | \(-0.542458\pi\) |
0.991117 | + | 0.132992i | \(0.0424584\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.0514098 | −0.00257371 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.8173 | 0.540189 | 0.270094 | − | 0.962834i | \(-0.412945\pi\) | ||||
0.270094 | + | 0.962834i | \(0.412945\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −24.3605 | + | 24.3605i | −1.21348 | + | 1.21348i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.707107 | + | 0.707107i | 0.0351364 | + | 0.0351364i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.01241i | 0.446729i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 4.30551i | − | 0.212894i | −0.994318 | − | 0.106447i | \(-0.966053\pi\) | ||
0.994318 | − | 0.106447i | \(-0.0339474\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.7542 | + | 13.7542i | 0.678446 | + | 0.678446i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.551283 | − | 0.551283i | 0.0271269 | − | 0.0271269i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.6786 | 0.524191 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.54979 | −0.0758934 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.3215 | + | 16.3215i | −0.797357 | + | 0.797357i | −0.982678 | − | 0.185321i | \(-0.940667\pi\) |
0.185321 | + | 0.982678i | \(0.440667\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.16177 | − | 7.16177i | −0.349043 | − | 0.349043i | 0.510710 | − | 0.859753i | \(-0.329383\pi\) |
−0.859753 | + | 0.510710i | \(0.829383\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 0.789616i | − | 0.0383925i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.98228i | 0.290183i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.0479538 | + | 0.0479538i | 0.00232064 | + | 0.00232064i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.99558 | + | 8.99558i | −0.434311 | + | 0.434311i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.4255 | 0.694851 | 0.347426 | − | 0.937708i | \(-0.387056\pi\) | ||||
0.347426 | + | 0.937708i | \(0.387056\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −31.3821 | −1.50813 | −0.754063 | − | 0.656802i | \(-0.771909\pi\) | ||||
−0.754063 | + | 0.656802i | \(0.771909\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.13987 | + | 1.13987i | −0.0546524 | + | 0.0546524i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.460890 | + | 0.460890i | 0.0220474 | + | 0.0220474i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.91484i | 0.377755i | 0.982001 | + | 0.188877i | \(0.0604849\pi\) | ||||
−0.982001 | + | 0.188877i | \(0.939515\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 6.99653i | − | 0.333168i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.2877 | − | 11.2877i | −0.536294 | − | 0.536294i | 0.386144 | − | 0.922438i | \(-0.373807\pi\) |
−0.922438 | + | 0.386144i | \(0.873807\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.5264 | − | 11.5264i | 0.546402 | − | 0.546402i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 19.3055 | 0.913117 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.7071 | −0.788458 | −0.394229 | − | 0.919012i | \(-0.628988\pi\) | ||||
−0.394229 | + | 0.919012i | \(0.628988\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.2181 | + | 17.2181i | −0.810769 | + | 0.810769i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.53258 | − | 9.53258i | −0.447880 | − | 0.447880i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.237268i | 0.0111233i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 25.5371i | − | 1.19458i | −0.802027 | − | 0.597288i | \(-0.796245\pi\) | ||
0.802027 | − | 0.597288i | \(-0.203755\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.23011 | − | 4.23011i | −0.197445 | − | 0.197445i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.05719 | − | 1.05719i | 0.0492382 | − | 0.0492382i | −0.682059 | − | 0.731297i | \(-0.738915\pi\) |
0.731297 | + | 0.682059i | \(0.238915\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.8953 | −1.57525 | −0.787623 | − | 0.616157i | \(-0.788688\pi\) | ||||
−0.787623 | + | 0.616157i | \(0.788688\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.55143 | −0.396563 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.8661 | + | 15.8661i | −0.734194 | + | 0.734194i | −0.971448 | − | 0.237253i | \(-0.923753\pi\) |
0.237253 | + | 0.971448i | \(0.423753\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.321979 | + | 0.321979i | 0.0148676 | + | 0.0148676i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.7105i | 0.723900i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 13.1398i | − | 0.604169i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.617238 | − | 0.617238i | −0.0283208 | − | 0.0283208i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.80791 | − | 6.80791i | 0.311713 | − | 0.311713i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.85047 | 0.0845500 | 0.0422750 | − | 0.999106i | \(-0.486539\pi\) | ||||
0.0422750 | + | 0.999106i | \(0.486539\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.4980 | −0.524261 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.0310962 | − | 0.0310962i | 0.00141493 | − | 0.00141493i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.70869 | − | 8.70869i | −0.395441 | − | 0.395441i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.72194i | 0.349915i | 0.984576 | + | 0.174957i | \(0.0559787\pi\) | ||||
−0.984576 | + | 0.174957i | \(0.944021\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.79446i | 0.126370i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.2289 | + | 16.2289i | 0.732399 | + | 0.732399i | 0.971094 | − | 0.238696i | \(-0.0767199\pi\) |
−0.238696 | + | 0.971094i | \(0.576720\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.81900 | − | 6.81900i | 0.307112 | − | 0.307112i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.15778 | −0.141932 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.436071 | 0.0195605 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.2479 | − | 20.2479i | 0.906418 | − | 0.906418i | −0.0895629 | − | 0.995981i | \(-0.528547\pi\) |
0.995981 | + | 0.0895629i | \(0.0285470\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.50456 | − | 1.50456i | −0.0672188 | − | 0.0672188i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 18.2912i | − | 0.815566i | −0.913079 | − | 0.407783i | \(-0.866302\pi\) | ||
0.913079 | − | 0.407783i | \(-0.133698\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 0.938447i | − | 0.0417603i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.28408 | − | 2.28408i | −0.101440 | − | 0.101440i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.0470 | + | 16.0470i | −0.711272 | + | 0.711272i | −0.966801 | − | 0.255529i | \(-0.917750\pi\) |
0.255529 | + | 0.966801i | \(0.417750\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.683853 | 0.0302519 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.872906 | 0.0385398 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.5385 | + | 10.5385i | −0.464380 | + | 0.464380i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.76313 | + | 1.76313i | 0.0775422 | + | 0.0775422i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 13.0373i | − | 0.572275i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 8.02188i | − | 0.351445i | −0.984440 | − | 0.175722i | \(-0.943774\pi\) | ||
0.984440 | − | 0.175722i | \(-0.0562261\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.8339 | − | 31.8339i | −1.39200 | − | 1.39200i | −0.820840 | − | 0.571158i | \(-0.806494\pi\) |
−0.571158 | − | 0.820840i | \(-0.693506\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.0416450 | + | 0.0416450i | −0.00181754 | + | 0.00181754i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 51.1570 | 2.22844 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.4424 | 0.975758 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.36045 | + | 9.36045i | −0.406209 | + | 0.406209i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21.9667 | − | 21.9667i | −0.951483 | − | 0.951483i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 4.86293i | − | 0.210243i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 7.10510i | − | 0.306608i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.6225 | + | 15.6225i | 0.672908 | + | 0.672908i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.7467 | + | 16.7467i | −0.719996 | + | 0.719996i | −0.968604 | − | 0.248608i | \(-0.920027\pi\) |
0.248608 | + | 0.968604i | \(0.420027\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 21.4059 | 0.918616 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.0807802 | 0.00346024 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.8600 | − | 24.8600i | 1.06294 | − | 1.06294i | 0.0650571 | − | 0.997882i | \(-0.479277\pi\) |
0.997882 | − | 0.0650571i | \(-0.0207230\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.814225 | − | 0.814225i | −0.0347503 | − | 0.0347503i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.40714i | 0.0599461i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.02493i | 0.0435845i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.01811 | − | 2.01811i | −0.0856638 | − | 0.0856638i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.0423 | + | 12.0423i | −0.510248 | + | 0.510248i | −0.914603 | − | 0.404354i | \(-0.867496\pi\) |
0.404354 | + | 0.914603i | \(0.367496\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.7636 | 0.709026 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18.8907 | 0.797567 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.2672 | + | 15.2672i | −0.643435 | + | 0.643435i | −0.951398 | − | 0.307963i | \(-0.900353\pi\) |
0.307963 | + | 0.951398i | \(0.400353\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.5948 | + | 10.5948i | 0.445729 | + | 0.445729i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 0.0588949i | − | 0.00247335i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 33.2847i | 1.39537i | 0.716406 | + | 0.697683i | \(0.245786\pi\) | ||||
−0.716406 | + | 0.697683i | \(0.754214\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.4781 | − | 10.4781i | −0.438494 | − | 0.438494i | 0.453011 | − | 0.891505i | \(-0.350350\pi\) |
−0.891505 | + | 0.453011i | \(0.850350\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.79820 | + | 8.79820i | −0.367550 | + | 0.367550i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.746698 | 0.0311394 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −38.6407 | −1.60863 | −0.804316 | − | 0.594202i | \(-0.797468\pi\) | ||||
−0.804316 | + | 0.594202i | \(0.797468\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.171072 | − | 0.171072i | 0.00710952 | − | 0.00710952i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.444710 | − | 0.444710i | −0.0184497 | − | 0.0184497i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 30.4026i | 1.25915i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 4.02867i | − | 0.166565i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.1392 | − | 21.1392i | −0.872507 | − | 0.872507i | 0.120238 | − | 0.992745i | \(-0.461634\pi\) |
−0.992745 | + | 0.120238i | \(0.961634\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.27827 | + | 5.27827i | −0.217487 | + | 0.217487i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.35537 | 0.138021 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.03330 | −0.165628 | −0.0828138 | − | 0.996565i | \(-0.526391\pi\) | ||||
−0.0828138 | + | 0.996565i | \(0.526391\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.249132 | − | 0.249132i | 0.0102134 | − | 0.0102134i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.0202 | + | 14.0202i | 0.573807 | + | 0.573807i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.44275i | 0.263244i | 0.991300 | + | 0.131622i | \(0.0420184\pi\) | ||||
−0.991300 | + | 0.131622i | \(0.957982\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.3011i | 1.48075i | 0.672193 | + | 0.740376i | \(0.265352\pi\) | ||||
−0.672193 | + | 0.740376i | \(0.734648\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.46701 | − | 5.46701i | −0.222634 | − | 0.222634i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.727191 | + | 0.727191i | −0.0295645 | + | 0.0295645i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.5463 | −0.793360 | −0.396680 | − | 0.917957i | \(-0.629838\pi\) | ||||
−0.396680 | + | 0.917957i | \(0.629838\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.0949395 | 0.00384714 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.24938 | + | 2.24938i | −0.0910002 | + | 0.0910002i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.5711 | − | 18.5711i | −0.750080 | − | 0.750080i | 0.224414 | − | 0.974494i | \(-0.427953\pi\) |
−0.974494 | + | 0.224414i | \(0.927953\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 7.71113i | − | 0.310943i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 19.7311i | − | 0.794342i | −0.917745 | − | 0.397171i | \(-0.869992\pi\) | ||
0.917745 | − | 0.397171i | \(-0.130008\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.1910 | + | 22.1910i | 0.891930 | + | 0.891930i | 0.994705 | − | 0.102775i | \(-0.0327721\pi\) |
−0.102775 | + | 0.994705i | \(0.532772\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.527995 | + | 0.527995i | −0.0211877 | + | 0.0211877i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.960031 | −0.0384628 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.94910 | + | 1.94910i | −0.0778397 | + | 0.0778397i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.0729 | + | 12.0729i | 0.481377 | + | 0.481377i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 13.1148i | − | 0.522093i | −0.965326 | − | 0.261046i | \(-0.915932\pi\) | ||
0.965326 | − | 0.261046i | \(-0.0840676\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 5.01914i | − | 0.199493i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.77035 | + | 4.77035i | 0.189305 | + | 0.189305i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.9310 | + | 19.9310i | −0.789696 | + | 0.789696i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.40423 | −0.292907 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.5395 | 1.20624 | 0.603119 | − | 0.797652i | \(-0.293925\pi\) | ||||
0.603119 | + | 0.797652i | \(0.293925\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.01306 | + | 4.01306i | −0.158260 | + | 0.158260i | −0.781795 | − | 0.623535i | \(-0.785696\pi\) |
0.623535 | + | 0.781795i | \(0.285696\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.94233 | + | 2.94233i | 0.115854 | + | 0.115854i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 9.01207i | − | 0.354301i | −0.984184 | − | 0.177151i | \(-0.943312\pi\) | ||
0.984184 | − | 0.177151i | \(-0.0566880\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 41.8017i | − | 1.64086i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.356124 | + | 0.356124i | 0.0139576 | + | 0.0139576i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.2241 | − | 25.2241i | 0.987096 | − | 0.987096i | −0.0128219 | − | 0.999918i | \(-0.504081\pi\) |
0.999918 | + | 0.0128219i | \(0.00408146\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.4898 | −0.566165 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.6114 | −0.453004 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.8387 | − | 15.8387i | 0.616987 | − | 0.616987i | −0.327770 | − | 0.944757i | \(-0.606297\pi\) |
0.944757 | + | 0.327770i | \(0.106297\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.25357 | − | 8.25357i | −0.321027 | − | 0.321027i | 0.528134 | − | 0.849161i | \(-0.322892\pi\) |
−0.849161 | + | 0.528134i | \(0.822892\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 24.1006i | 0.935991i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.0514098i | 0.00199359i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.851136 | − | 0.851136i | −0.0329561 | − | 0.0329561i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.3293 | + | 15.3293i | −0.592666 | + | 0.592666i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.63615 | 0.140372 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.8226 | 1.14958 | 0.574789 | − | 0.818302i | \(-0.305084\pi\) | ||||
0.574789 | + | 0.818302i | \(0.305084\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.707107 | − | 0.707107i | 0.0272166 | − | 0.0272166i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.3009 | − | 11.3009i | −0.434328 | − | 0.434328i | 0.455770 | − | 0.890098i | \(-0.349364\pi\) |
−0.890098 | + | 0.455770i | \(0.849364\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.725347i | 0.0278363i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.4415i | 0.553401i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.7739 | + | 24.7739i | 0.947949 | + | 0.947949i | 0.998711 | − | 0.0507621i | \(-0.0161650\pi\) |
−0.0507621 | + | 0.998711i | \(0.516165\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.7542 | − | 13.7542i | 0.525522 | − | 0.525522i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −24.1736 | −0.922282 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −38.7874 | −1.47768 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.4140 | − | 30.4140i | 1.15700 | − | 1.15700i | 0.171888 | − | 0.985117i | \(-0.445013\pi\) |
0.985117 | − | 0.171888i | \(-0.0549866\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.131506 | + | 0.131506i | 0.00499550 | + | 0.00499550i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.54979i | 0.0587868i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 46.1301i | 1.74730i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −17.1409 | − | 17.1409i | −0.648328 | − | 0.648328i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.35541 | − | 9.35541i | 0.353349 | − | 0.353349i | −0.508005 | − | 0.861354i | \(-0.669617\pi\) |
0.861354 | + | 0.508005i | \(0.169617\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.49130 | −0.0939612 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.789616 | −0.0297387 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.0390816 | + | 0.0390816i | −0.00146982 | + | 0.00146982i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.6531 | − | 15.6531i | −0.587866 | − | 0.587866i | 0.349187 | − | 0.937053i | \(-0.386458\pi\) |
−0.937053 | + | 0.349187i | \(0.886458\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 17.4027i | − | 0.652652i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 6.38533i | − | 0.239133i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.99558 | + | 8.99558i | 0.336416 | + | 0.336416i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −14.8958 | + | 14.8958i | −0.556293 | + | 0.556293i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −51.4373 | −1.91829 | −0.959144 | − | 0.282919i | \(-0.908697\pi\) | ||||
−0.959144 | + | 0.282919i | \(0.908697\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.877748 | 0.0326891 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −15.5972 | + | 15.5972i | −0.580067 | + | 0.580067i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.13987 | + | 1.13987i | 0.0423336 | + | 0.0423336i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.7975i | 0.585898i | 0.956128 | + | 0.292949i | \(0.0946366\pi\) | ||||
−0.956128 | + | 0.292949i | \(0.905363\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.6018 | − | 17.6018i | −0.651028 | − | 0.651028i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.7672 | + | 28.7672i | −1.06254 | + | 1.06254i | −0.0646310 | + | 0.997909i | \(0.520587\pi\) |
−0.997909 | + | 0.0646310i | \(0.979413\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.99653 | −0.258071 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24.4145 | 0.899318 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.12767 | − | 6.12767i | 0.225410 | − | 0.225410i | −0.585362 | − | 0.810772i | \(-0.699048\pi\) |
0.810772 | + | 0.585362i | \(0.199048\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.48665 | − | 2.48665i | −0.0913493 | − | 0.0913493i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 22.0466i | − | 0.808810i | −0.914580 | − | 0.404405i | \(-0.867479\pi\) | ||
0.914580 | − | 0.404405i | \(-0.132521\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 19.3055i | − | 0.707297i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.55090 | + | 7.55090i | 0.276273 | + | 0.276273i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.202517 | + | 0.202517i | −0.00739980 | + | 0.00739980i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.6203 | −1.48226 | −0.741128 | − | 0.671364i | \(-0.765709\pi\) | ||||
−0.741128 | + | 0.671364i | \(0.765709\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.6382 | 0.424118 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.53258 | + | 9.53258i | −0.346926 | + | 0.346926i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.9575 | + | 12.9575i | 0.470949 | + | 0.470949i | 0.902222 | − | 0.431272i | \(-0.141935\pi\) |
−0.431272 | + | 0.902222i | \(0.641935\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 2.35791i | − | 0.0855867i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33.9075i | 1.22915i | 0.788860 | + | 0.614573i | \(0.210672\pi\) | ||||
−0.788860 | + | 0.614573i | \(0.789328\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.00336409 | − | 0.00336409i | −0.000121788 | − | 0.000121788i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.23011 | + | 4.23011i | −0.152940 | + | 0.152940i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 53.3302 | 1.92564 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.30816 | 0.299600 | 0.149800 | − | 0.988716i | \(-0.452137\pi\) | ||||
0.149800 | + | 0.988716i | \(0.452137\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.17718 | − | 5.17718i | 0.186452 | − | 0.186452i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.90838 | − | 9.90838i | −0.356380 | − | 0.356380i | 0.506097 | − | 0.862477i | \(-0.331088\pi\) |
−0.862477 | + | 0.506097i | \(0.831088\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.55143i | 0.307176i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.168088i | 0.00603012i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.75960 | − | 4.75960i | −0.170530 | − | 0.170530i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.5328 | − | 16.5328i | 0.591591 | − | 0.591591i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.61202 | −0.0576087 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.7105 | 0.560730 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.2948 | − | 32.2948i | 1.15119 | − | 1.15119i | 0.164872 | − | 0.986315i | \(-0.447279\pi\) |
0.986315 | − | 0.164872i | \(-0.0527209\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13.1826 | + | 13.1826i | 0.469312 | + | 0.469312i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 0.882445i | − | 0.0313761i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.63897i | 0.164735i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.80791 | − | 6.80791i | −0.241452 | − | 0.241452i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.3637 | − | 21.3637i | 0.756740 | − | 0.756740i | −0.218987 | − | 0.975728i | \(-0.570275\pi\) |
0.975728 | + | 0.218987i | \(0.0702754\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.72370 | 0.167113 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16.3007 | 0.575958 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25.9270 | − | 25.9270i | 0.914944 | − | 0.914944i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.0310962 | − | 0.0310962i | −0.00109600 | − | 0.00109600i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 4.56635i | − | 0.160743i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 37.9895i | − | 1.33564i | −0.744323 | − | 0.667820i | \(-0.767228\pi\) | ||
0.744323 | − | 0.667820i | \(-0.232772\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.45375 | + | 6.45375i | 0.226622 | + | 0.226622i | 0.811280 | − | 0.584658i | \(-0.198771\pi\) |
−0.584658 | + | 0.811280i | \(0.698771\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.7552 | − | 19.7552i | 0.692847 | − | 0.692847i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.79446 | 0.0978857 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.63224 | 0.127076 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.167774 | + | 0.167774i | −0.00586250 | + | 0.00586250i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.5389 | + | 10.5389i | 0.367809 | + | 0.367809i | 0.866677 | − | 0.498869i | \(-0.166251\pi\) |
−0.498869 | + | 0.866677i | \(0.666251\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 35.0064i | − | 1.22025i | −0.792306 | − | 0.610124i | \(-0.791120\pi\) | ||
0.792306 | − | 0.610124i | \(-0.208880\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.15778i | 0.109940i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.0789 | + | 13.0789i | 0.454799 | + | 0.454799i | 0.896944 | − | 0.442145i | \(-0.145782\pi\) |
−0.442145 | + | 0.896944i | \(0.645782\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.3502 | − | 28.3502i | 0.984642 | − | 0.984642i | −0.0152419 | − | 0.999884i | \(-0.504852\pi\) |
0.999884 | + | 0.0152419i | \(0.00485184\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.24411 | 0.0778473 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 41.8552 | 1.45020 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.50456 | + | 1.50456i | −0.0520674 | + | 0.0520674i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.04678 | − | 6.04678i | −0.209007 | − | 0.209007i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 52.5560i | − | 1.81444i | −0.420661 | − | 0.907218i | \(-0.638202\pi\) | ||
0.420661 | − | 0.907218i | \(-0.361798\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.4014i | 0.910393i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.49740 | + | 4.49740i | 0.154899 | + | 0.154899i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.28408 | + | 2.28408i | −0.0785749 | + | 0.0785749i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.0605677 | 0.00208113 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.14937 | 0.176726 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.50691 | − | 1.50691i | 0.0516564 | − | 0.0516564i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.3957 | + | 33.3957i | 1.14345 | + | 1.14345i | 0.987815 | + | 0.155632i | \(0.0497413\pi\) |
0.155632 | + | 0.987815i | \(0.450259\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 0.872906i | − | 0.0298528i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.36548i | 0.217441i | 0.994072 | + | 0.108720i | \(0.0346753\pi\) | ||||
−0.994072 | + | 0.108720i | \(0.965325\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.2446 | + | 30.2446i | 1.03193 | + | 1.03193i | 0.999473 | + | 0.0324590i | \(0.0103338\pi\) |
0.0324590 | + | 0.999473i | \(0.489666\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.321130 | + | 0.321130i | −0.0109441 | + | 0.0109441i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.2067 | 0.551683 | 0.275841 | − | 0.961203i | \(-0.411044\pi\) | ||||
0.275841 | + | 0.961203i | \(0.411044\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.0373 | −0.443282 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.2849 | − | 13.2849i | 0.451178 | − | 0.451178i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 38.8583 | + | 38.8583i | 1.31818 | + | 1.31818i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.1477i | 1.05540i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 12.3159i | − | 0.416832i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.0416450 | + | 0.0416450i | 0.00140786 | + | 0.00140786i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.08871 | − | 7.08871i | 0.239369 | − | 0.239369i | −0.577220 | − | 0.816589i | \(-0.695863\pi\) |
0.816589 | + | 0.577220i | \(0.195863\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.78636 | 0.195169 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −46.7030 | −1.57346 | −0.786731 | − | 0.617296i | \(-0.788228\pi\) | ||||
−0.786731 | + | 0.617296i | \(0.788228\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.6005 | − | 35.6005i | 1.19805 | − | 1.19805i | 0.223303 | − | 0.974749i | \(-0.428316\pi\) |
0.974749 | − | 0.223303i | \(-0.0716840\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.36045 | + | 9.36045i | 0.314648 | + | 0.314648i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.62187i | 0.0880338i | 0.999031 | + | 0.0440169i | \(0.0140156\pi\) | ||||
−0.999031 | + | 0.0440169i | \(0.985984\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 0.397322i | − | 0.0133258i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.23289 | − | 2.23289i | −0.0748046 | − | 0.0748046i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.487381 | + | 0.487381i | −0.0163096 | + | 0.0163096i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.10510 | −0.237497 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.00820 | 0.100441 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.74749 | − | 9.74749i | 0.325097 | − | 0.325097i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 40.7268 | + | 40.7268i | 1.35681 | + | 1.35681i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 0.245067i | − | 0.00815532i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 21.4059i | − | 0.711557i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.1287 | − | 11.1287i | −0.369522 | − | 0.369522i | 0.497781 | − | 0.867303i | \(-0.334148\pi\) |
−0.867303 | + | 0.497781i | \(0.834148\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.663582 | − | 0.663582i | 0.0220096 | − | 0.0220096i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.1961 | 1.33176 | 0.665878 | − | 0.746061i | \(-0.268057\pi\) | ||||
0.665878 | + | 0.746061i | \(0.268057\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −33.7207 | −1.11599 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.814225 | + | 0.814225i | −0.0269175 | + | 0.0269175i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.603429 | + | 0.603429i | 0.0199270 | + | 0.0199270i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.413348i | 0.0136351i | 0.999977 | + | 0.00681755i | \(0.00217011\pi\) | ||||
−0.999977 | + | 0.00681755i | \(0.997830\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 1.17672i | − | 0.0387744i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21.0924 | + | 21.0924i | 0.694266 | + | 0.694266i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.01811 | + | 2.01811i | −0.0663549 | + | 0.0663549i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.9036 | −0.489499 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.8881 | −0.947787 | −0.473893 | − | 0.880582i | \(-0.657152\pi\) | ||||
−0.473893 | + | 0.880582i | \(0.657152\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.31853 | + | 4.31853i | −0.141534 | + | 0.141534i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.78465 | + | 9.78465i | 0.320335 | + | 0.320335i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 18.8907i | − | 0.617793i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.60125i | 0.182985i | 0.995806 | + | 0.0914925i | \(0.0291637\pi\) | ||||
−0.995806 | + | 0.0914925i | \(0.970836\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.60044 | − | 3.60044i | −0.117496 | − | 0.117496i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.8730 | − | 15.8730i | 0.517446 | − | 0.517446i | −0.399352 | − | 0.916798i | \(-0.630765\pi\) |
0.916798 | + | 0.399352i | \(0.130765\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.75788 | 0.187502 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.0588949 | −0.00191585 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.0697 | − | 12.0697i | 0.392214 | − | 0.392214i | −0.483262 | − | 0.875476i | \(-0.660548\pi\) |
0.875476 | + | 0.483262i | \(0.160548\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 33.0774 | + | 33.0774i | 1.07374 | + | 1.07374i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23.0595i | 0.747756i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 5.02008i | − | 0.162616i | −0.996689 | − | 0.0813081i | \(-0.974090\pi\) | ||
0.996689 | − | 0.0813081i | \(-0.0259098\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.79820 | + | 8.79820i | 0.284703 | + | 0.284703i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.59945 | − | 3.59945i | 0.116354 | − | 0.116354i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.14559 | −0.0369930 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 42.1270 | 1.35893 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.43861 | − | 3.43861i | 0.110808 | − | 0.110808i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.171072 | − | 0.171072i | −0.00550701 | − | 0.00550701i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 33.9334i | − | 1.09123i | −0.838038 | − | 0.545613i | \(-0.816297\pi\) | ||
0.838038 | − | 0.545613i | \(-0.183703\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.22197i | 0.167754i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.06974 | + | 1.06974i | 0.0343297 | + | 0.0343297i | 0.724063 | − | 0.689734i | \(-0.242272\pi\) |
−0.689734 | + | 0.724063i | \(0.742272\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.0645409 | − | 0.0645409i | 0.00206909 | − | 0.00206909i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.02867 | −0.129021 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.01239 | −0.0323891 | −0.0161946 | − | 0.999869i | \(-0.505155\pi\) | ||||
−0.0161946 | + | 0.999869i | \(0.505155\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −36.3978 | + | 36.3978i | −1.16328 | + | 1.16328i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.0571202 | + | 0.0571202i | 0.00182371 | + | 0.00182371i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.2297i | 0.868494i | 0.900794 | + | 0.434247i | \(0.142985\pi\) | ||||
−0.900794 | + | 0.434247i | \(0.857015\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 3.35537i | − | 0.106911i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.0328836 | + | 0.0328836i | 0.00104670 | + | 0.00104670i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.19703 | + | 2.19703i | −0.0698616 | + | 0.0698616i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.24865 | −0.0714308 | −0.0357154 | − | 0.999362i | \(-0.511371\pi\) | ||||
−0.0357154 | + | 0.999362i | \(0.511371\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.55119 | 0.239630 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.0202 | − | 14.0202i | 0.444469 | − | 0.444469i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.6266 | + | 11.6266i | 0.368220 | + | 0.368220i | 0.866828 | − | 0.498608i | \(-0.166155\pi\) |
−0.498608 | + | 0.866828i | \(0.666155\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 2.85403i | − | 0.0902976i |
(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 | 1920.2.s.f.481.8 | 20 | ||
4.3 | odd | 2 | 1920.2.s.e.481.3 | 20 | |||
8.3 | odd | 2 | 240.2.s.c.181.4 | yes | 20 | ||
8.5 | even | 2 | 960.2.s.c.241.3 | 20 | |||
16.3 | odd | 4 | 1920.2.s.e.1441.3 | 20 | |||
16.5 | even | 4 | 960.2.s.c.721.3 | 20 | |||
16.11 | odd | 4 | 240.2.s.c.61.4 | ✓ | 20 | ||
16.13 | even | 4 | inner | 1920.2.s.f.1441.8 | 20 | ||
24.5 | odd | 2 | 2880.2.t.d.2161.3 | 20 | |||
24.11 | even | 2 | 720.2.t.d.181.7 | 20 | |||
48.5 | odd | 4 | 2880.2.t.d.721.3 | 20 | |||
48.11 | even | 4 | 720.2.t.d.541.7 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
240.2.s.c.61.4 | ✓ | 20 | 16.11 | odd | 4 | ||
240.2.s.c.181.4 | yes | 20 | 8.3 | odd | 2 | ||
720.2.t.d.181.7 | 20 | 24.11 | even | 2 | |||
720.2.t.d.541.7 | 20 | 48.11 | even | 4 | |||
960.2.s.c.241.3 | 20 | 8.5 | even | 2 | |||
960.2.s.c.721.3 | 20 | 16.5 | even | 4 | |||
1920.2.s.e.481.3 | 20 | 4.3 | odd | 2 | |||
1920.2.s.e.1441.3 | 20 | 16.3 | odd | 4 | |||
1920.2.s.f.481.8 | 20 | 1.1 | even | 1 | trivial | ||
1920.2.s.f.1441.8 | 20 | 16.13 | even | 4 | inner | ||
2880.2.t.d.721.3 | 20 | 48.5 | odd | 4 | |||
2880.2.t.d.2161.3 | 20 | 24.5 | odd | 2 |