Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,2,Mod(31,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2352.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.bl (of order \(6\), 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: | \(18.7808145554\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.339738624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.2 | ||
Root | \(0.662827 - 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.31 |
Dual form | 2352.2.bl.q.607.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1471\) | \(1765\) | \(2257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.521114 | + | 0.300865i | −0.233049 | + | 0.134551i | −0.611978 | − | 0.790875i | \(-0.709626\pi\) |
0.378929 | + | 0.925426i | \(0.376293\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.141713 | − | 0.0818181i | −0.0427281 | − | 0.0246691i | 0.478484 | − | 0.878096i | \(-0.341187\pi\) |
−0.521212 | + | 0.853427i | \(0.674520\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.37849i | 0.937025i | 0.883457 | + | 0.468513i | \(0.155210\pi\) | ||||
−0.883457 | + | 0.468513i | \(0.844790\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 0.601731i | − | 0.155366i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.84677 | + | 1.06623i | 0.447907 | + | 0.258599i | 0.706946 | − | 0.707268i | \(-0.250072\pi\) |
−0.259039 | + | 0.965867i | \(0.583406\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.476834 | − | 0.825901i | −0.109393 | − | 0.189475i | 0.806131 | − | 0.591737i | \(-0.201557\pi\) |
−0.915525 | + | 0.402262i | \(0.868224\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.05870 | − | 3.49799i | 1.26333 | − | 0.729382i | 0.289610 | − | 0.957145i | \(-0.406475\pi\) |
0.973717 | + | 0.227763i | \(0.0731412\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.31896 | + | 4.01656i | −0.463792 | + | 0.803311i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.28897 | −0.239356 | −0.119678 | − | 0.992813i | \(-0.538186\pi\) | ||||
−0.119678 | + | 0.992813i | \(0.538186\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.67725 | + | 2.90508i | −0.301242 | + | 0.521767i | −0.976418 | − | 0.215890i | \(-0.930735\pi\) |
0.675175 | + | 0.737657i | \(0.264068\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.141713 | − | 0.0818181i | 0.0246691 | − | 0.0142427i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.58187 | − | 4.47192i | −0.424456 | − | 0.735179i | 0.571913 | − | 0.820314i | \(-0.306201\pi\) |
−0.996369 | + | 0.0851346i | \(0.972868\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.92586 | − | 1.68925i | −0.468513 | − | 0.270496i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.67896i | 1.04308i | 0.853227 | + | 0.521539i | \(0.174642\pi\) | ||||
−0.853227 | + | 0.521539i | \(0.825358\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.09172i | − | 0.928978i | −0.885579 | − | 0.464489i | \(-0.846238\pi\) | ||
0.885579 | − | 0.464489i | \(-0.153762\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.521114 | + | 0.300865i | 0.0776831 | + | 0.0448504i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.84882 | + | 3.20225i | 0.269678 | + | 0.467096i | 0.968779 | − | 0.247927i | \(-0.0797494\pi\) |
−0.699101 | + | 0.715023i | \(0.746416\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.84677 | + | 1.06623i | −0.258599 | + | 0.149302i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.94028 | + | 12.0209i | −0.953321 | + | 1.65120i | −0.215156 | + | 0.976580i | \(0.569026\pi\) |
−0.738165 | + | 0.674620i | \(0.764307\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.0984649 | 0.0132770 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.953669 | 0.126317 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.02594 | + | 6.97313i | −0.524133 | + | 0.907824i | 0.475473 | + | 0.879730i | \(0.342277\pi\) |
−0.999605 | + | 0.0280937i | \(0.991056\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.157153 | − | 0.0907323i | 0.0201214 | − | 0.0116171i | −0.489906 | − | 0.871776i | \(-0.662969\pi\) |
0.510027 | + | 0.860158i | \(0.329635\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.01647 | − | 1.76058i | −0.126078 | − | 0.218373i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.87476 | − | 4.54649i | −0.962055 | − | 0.555443i | −0.0652500 | − | 0.997869i | \(-0.520784\pi\) |
−0.896805 | + | 0.442426i | \(0.854118\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.99598i | 0.842217i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.36066i | 0.398837i | 0.979914 | + | 0.199419i | \(0.0639054\pi\) | ||||
−0.979914 | + | 0.199419i | \(0.936095\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.5172 | + | 6.07210i | 1.23094 | + | 0.710686i | 0.967227 | − | 0.253914i | \(-0.0817180\pi\) |
0.263717 | + | 0.964600i | \(0.415051\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.31896 | − | 4.01656i | −0.267770 | − | 0.463792i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.05213 | − | 3.49420i | 0.680918 | − | 0.393128i | −0.119283 | − | 0.992860i | \(-0.538059\pi\) |
0.800201 | + | 0.599732i | \(0.204726\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.9788 | −1.42460 | −0.712302 | − | 0.701873i | \(-0.752348\pi\) | ||||
−0.712302 | + | 0.701873i | \(0.752348\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.28317 | −0.139179 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.644486 | − | 1.11628i | 0.0690961 | − | 0.119678i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.8911 | + | 7.44266i | −1.36645 | + | 0.788920i | −0.990473 | − | 0.137709i | \(-0.956026\pi\) |
−0.375977 | + | 0.926629i | \(0.622693\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.67725 | − | 2.90508i | −0.173922 | − | 0.301242i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.496970 | + | 0.286926i | 0.0509881 | + | 0.0294380i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.08274i | 0.922213i | 0.887345 | + | 0.461106i | \(0.152547\pi\) | ||||
−0.887345 | + | 0.461106i | \(0.847453\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.163636i | 0.0164461i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.37548 | + | 4.25824i | 0.733888 | + | 0.423710i | 0.819843 | − | 0.572589i | \(-0.194061\pi\) |
−0.0859551 | + | 0.996299i | \(0.527394\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.38043 | − | 14.5153i | −0.825749 | − | 1.43024i | −0.901346 | − | 0.433100i | \(-0.857420\pi\) |
0.0755973 | − | 0.997138i | \(-0.475914\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.80822 | − | 2.19867i | 0.368154 | − | 0.212554i | −0.304498 | − | 0.952513i | \(-0.598489\pi\) |
0.672652 | + | 0.739959i | \(0.265155\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.77263 | + | 9.99849i | −0.552918 | + | 0.957681i | 0.445145 | + | 0.895459i | \(0.353152\pi\) |
−0.998062 | + | 0.0622227i | \(0.980181\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.16373 | 0.490120 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.09821 | −0.103311 | −0.0516554 | − | 0.998665i | \(-0.516450\pi\) | ||||
−0.0516554 | + | 0.998665i | \(0.516450\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.10485 | + | 3.64571i | −0.196278 | + | 0.339964i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.92586 | − | 1.68925i | 0.270496 | − | 0.156171i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.48661 | − | 9.50309i | −0.498783 | − | 0.863917i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.78415 | − | 3.33948i | −0.521539 | − | 0.301111i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 5.79943i | − | 0.518717i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.22625i | 0.463755i | 0.972745 | + | 0.231877i | \(0.0744868\pi\) | ||||
−0.972745 | + | 0.231877i | \(0.925513\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.27558 | + | 3.04586i | 0.464489 | + | 0.268173i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.2659 | + | 19.5132i | 0.984309 | + | 1.70487i | 0.644966 | + | 0.764211i | \(0.276871\pi\) |
0.339343 | + | 0.940663i | \(0.389795\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.521114 | + | 0.300865i | −0.0448504 | + | 0.0258944i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.29579 | + | 12.6367i | −0.623322 | + | 1.07963i | 0.365541 | + | 0.930795i | \(0.380884\pi\) |
−0.988863 | + | 0.148830i | \(0.952449\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.30816 | −0.704689 | −0.352345 | − | 0.935870i | \(-0.614615\pi\) | ||||
−0.352345 | + | 0.935870i | \(0.614615\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.69764 | −0.311397 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.276422 | − | 0.478777i | 0.0231156 | − | 0.0400373i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.671701 | − | 0.387807i | 0.0557818 | − | 0.0322056i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.40083 | − | 9.35450i | −0.442453 | − | 0.766351i | 0.555418 | − | 0.831571i | \(-0.312558\pi\) |
−0.997871 | + | 0.0652205i | \(0.979225\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.2618 | − | 7.07937i | −0.997854 | − | 0.576111i | −0.0902412 | − | 0.995920i | \(-0.528764\pi\) |
−0.907613 | + | 0.419809i | \(0.862097\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2.13246i | − | 0.172400i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 2.01850i | − | 0.162130i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.946253 | − | 0.546320i | −0.0755192 | − | 0.0436011i | 0.461765 | − | 0.887002i | \(-0.347216\pi\) |
−0.537284 | + | 0.843401i | \(0.680550\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.94028 | − | 12.0209i | −0.550400 | − | 0.953321i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.6627 | + | 9.04284i | −1.22679 | + | 0.708290i | −0.966358 | − | 0.257201i | \(-0.917200\pi\) |
−0.260436 | + | 0.965491i | \(0.583866\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.0492325 | + | 0.0852731i | −0.00383274 | + | 0.00663850i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.0196 | −1.47178 | −0.735889 | − | 0.677103i | \(-0.763235\pi\) | ||||
−0.735889 | + | 0.677103i | \(0.763235\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.58579 | 0.121984 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.476834 | + | 0.825901i | −0.0364644 | + | 0.0631583i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.14939 | + | 4.12770i | −0.543558 | + | 0.313823i | −0.746520 | − | 0.665363i | \(-0.768277\pi\) |
0.202962 | + | 0.979187i | \(0.434943\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.02594 | − | 6.97313i | −0.302608 | − | 0.524133i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.76008 | + | 2.74823i | 0.355785 | + | 0.205413i | 0.667230 | − | 0.744852i | \(-0.267480\pi\) |
−0.311445 | + | 0.950264i | \(0.600813\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.8519i | 0.880946i | 0.897766 | + | 0.440473i | \(0.145189\pi\) | ||||
−0.897766 | + | 0.440473i | \(0.854811\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.181465i | 0.0134143i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.69089 | + | 1.55359i | 0.197838 | + | 0.114222i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.174474 | − | 0.302198i | −0.0127588 | − | 0.0220989i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.0470 | − | 11.5741i | 1.45055 | − | 0.837476i | 0.452038 | − | 0.891999i | \(-0.350697\pi\) |
0.998513 | + | 0.0545227i | \(0.0173637\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.256029 | − | 0.443455i | 0.0184294 | − | 0.0319206i | −0.856664 | − | 0.515875i | \(-0.827467\pi\) |
0.875093 | + | 0.483955i | \(0.160800\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.03294 | 0.145582 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.7934 | −0.911495 | −0.455748 | − | 0.890109i | \(-0.650628\pi\) | ||||
−0.455748 | + | 0.890109i | \(0.650628\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.90360 | − | 13.6894i | 0.560271 | − | 0.970418i | −0.437201 | − | 0.899364i | \(-0.644030\pi\) |
0.997472 | − | 0.0710545i | \(-0.0226364\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.87476 | − | 4.54649i | 0.555443 | − | 0.320685i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.00947 | − | 3.48050i | −0.140347 | − | 0.243089i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.05870 | − | 3.49799i | −0.421109 | − | 0.243127i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.156055i | 0.0107945i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.191712i | 0.0131980i | 0.999978 | + | 0.00659899i | \(0.00210054\pi\) | ||||
−0.999978 | + | 0.00659899i | \(0.997899\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.91042 | − | 1.68033i | −0.199419 | − | 0.115134i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.83279 | + | 3.17448i | 0.124995 | + | 0.216498i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.5172 | + | 6.07210i | −0.710686 | + | 0.410315i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.60226 | + | 6.23929i | −0.242314 | + | 0.419700i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.0111 | 0.670392 | 0.335196 | − | 0.942148i | \(-0.391197\pi\) | ||||
0.335196 | + | 0.942148i | \(0.391197\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.63792 | 0.309195 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.06817 | + | 5.31422i | −0.203641 | + | 0.352717i | −0.949699 | − | 0.313164i | \(-0.898611\pi\) |
0.746058 | + | 0.665881i | \(0.231944\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.17961 | − | 4.72250i | 0.540524 | − | 0.312072i | −0.204767 | − | 0.978811i | \(-0.565644\pi\) |
0.745291 | + | 0.666739i | \(0.232310\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.1108 | + | 19.2445i | 0.727895 | + | 1.26075i | 0.957771 | + | 0.287531i | \(0.0928345\pi\) |
−0.229876 | + | 0.973220i | \(0.573832\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.92689 | − | 1.11249i | −0.125697 | − | 0.0725710i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.98840i | 0.453945i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.7962i | 1.34520i | 0.740008 | + | 0.672598i | \(0.234822\pi\) | ||||
−0.740008 | + | 0.672598i | \(0.765178\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.3063 | + | 6.52769i | 0.728302 | + | 0.420486i | 0.817801 | − | 0.575501i | \(-0.195193\pi\) |
−0.0894984 | + | 0.995987i | \(0.528526\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.79030 | − | 1.61098i | 0.177543 | − | 0.102504i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.48938 | − | 11.2399i | 0.411248 | − | 0.712302i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.8975 | −1.12968 | −0.564839 | − | 0.825201i | \(-0.691062\pi\) | ||||
−0.564839 | + | 0.825201i | \(0.691062\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.14480 | −0.0719727 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.641585 | − | 1.11126i | 0.0401776 | − | 0.0695896i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.78415 | + | 3.33948i | −0.360805 | + | 0.208311i | −0.669434 | − | 0.742872i | \(-0.733463\pi\) |
0.308629 | + | 0.951183i | \(0.400130\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.644486 | + | 1.11628i | 0.0398927 | + | 0.0690961i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.1452 | + | 12.2082i | 1.30387 | + | 0.752790i | 0.981066 | − | 0.193676i | \(-0.0620410\pi\) |
0.322804 | + | 0.946466i | \(0.395374\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 8.35236i | − | 0.513081i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 14.8853i | − | 0.910966i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.992403 | + | 0.572964i | 0.0605079 | + | 0.0349342i | 0.529949 | − | 0.848030i | \(-0.322211\pi\) |
−0.469441 | + | 0.882964i | \(0.655544\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.82578 | − | 4.89440i | −0.171654 | − | 0.297314i | 0.767344 | − | 0.641235i | \(-0.221578\pi\) |
−0.938998 | + | 0.343922i | \(0.888244\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.657254 | − | 0.379466i | 0.0396339 | − | 0.0228826i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.63792 | − | 16.6934i | 0.579087 | − | 1.00301i | −0.416498 | − | 0.909137i | \(-0.636743\pi\) |
0.995584 | − | 0.0938706i | \(-0.0299240\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.35449 | 0.200828 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.80369 | 0.525184 | 0.262592 | − | 0.964907i | \(-0.415423\pi\) | ||||
0.262592 | + | 0.964907i | \(0.415423\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.0725 | + | 22.6423i | −0.777081 | + | 1.34594i | 0.156536 | + | 0.987672i | \(0.449967\pi\) |
−0.933617 | + | 0.358272i | \(0.883366\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.496970 | + | 0.286926i | −0.0294380 | + | 0.0169960i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.22630 | − | 10.7843i | −0.366253 | − | 0.634368i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.86588 | − | 4.54137i | −0.461106 | − | 0.266220i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 18.2640i | − | 1.06699i | −0.845802 | − | 0.533497i | \(-0.820877\pi\) | ||
0.845802 | − | 0.533497i | \(-0.179123\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 4.84506i | − | 0.282090i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.141713 | − | 0.0818181i | −0.00822303 | − | 0.00474757i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.8179 | + | 20.4693i | 0.683449 | + | 1.18377i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.37548 | + | 4.25824i | −0.423710 | + | 0.244629i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.0545964 | + | 0.0945638i | −0.00312618 | + | 0.00541471i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.4472 | 1.22405 | 0.612027 | − | 0.790837i | \(-0.290354\pi\) | ||||
0.612027 | + | 0.790837i | \(0.290354\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.7609 | 0.953492 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.24000 | − | 12.5400i | 0.410543 | − | 0.711081i | −0.584407 | − | 0.811461i | \(-0.698673\pi\) |
0.994949 | + | 0.100380i | \(0.0320060\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.28590 | − | 0.742415i | 0.0726834 | − | 0.0419638i | −0.463218 | − | 0.886244i | \(-0.653305\pi\) |
0.535901 | + | 0.844281i | \(0.319972\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.74541 | + | 9.95135i | 0.322695 | + | 0.558923i | 0.981043 | − | 0.193790i | \(-0.0620780\pi\) |
−0.658348 | + | 0.752713i | \(0.728745\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.182664 | + | 0.105461i | 0.0102272 | + | 0.00590469i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.39735i | 0.245436i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 2.03366i | − | 0.113156i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.5699 | − | 7.83459i | −0.752723 | − | 0.434585i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.77263 | − | 9.99849i | −0.319227 | − | 0.552918i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.2703 | + | 10.5484i | −1.00423 | + | 0.579790i | −0.909496 | − | 0.415713i | \(-0.863532\pi\) |
−0.0947302 | + | 0.995503i | \(0.530199\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.58187 | + | 4.47192i | −0.141485 | + | 0.245060i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.47153 | 0.298942 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.62683 | −0.306513 | −0.153256 | − | 0.988186i | \(-0.548976\pi\) | ||||
−0.153256 | + | 0.988186i | \(0.548976\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.549104 | − | 0.951076i | 0.0298232 | − | 0.0516554i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.475376 | − | 0.274458i | 0.0257430 | − | 0.0148628i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.10485 | − | 3.64571i | −0.113321 | − | 0.196278i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.1108 | + | 12.1883i | 1.13329 | + | 0.654305i | 0.944760 | − | 0.327763i | \(-0.106295\pi\) |
0.188529 | + | 0.982068i | \(0.439628\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 2.84502i | − | 0.152290i | −0.997097 | − | 0.0761451i | \(-0.975739\pi\) | ||
0.997097 | − | 0.0761451i | \(-0.0242612\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.37849i | 0.180331i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.3545 | − | 12.3290i | −1.13659 | − | 0.656208i | −0.191003 | − | 0.981589i | \(-0.561174\pi\) |
−0.945583 | + | 0.325381i | \(0.894507\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.01111 | − | 1.75129i | −0.0536640 | − | 0.0929488i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30.8472 | − | 17.8096i | 1.62805 | − | 0.939957i | 0.643381 | − | 0.765546i | \(-0.277531\pi\) |
0.984673 | − | 0.174411i | \(-0.0558022\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.04526 | − | 15.6668i | 0.476066 | − | 0.824571i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.9732 | 0.575945 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.30754 | −0.382494 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.6338 | − | 20.1504i | 0.607280 | − | 1.05184i | −0.384406 | − | 0.923164i | \(-0.625594\pi\) |
0.991687 | − | 0.128676i | \(-0.0410728\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.78415 | − | 3.33948i | 0.301111 | − | 0.173846i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.9866 | + | 19.0294i | 0.568865 | + | 0.985303i | 0.996679 | + | 0.0814363i | \(0.0259507\pi\) |
−0.427813 | + | 0.903867i | \(0.640716\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.02246 | + | 2.89972i | 0.259358 | + | 0.149741i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 4.35478i | − | 0.224283i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 19.7876i | − | 1.01642i | −0.861233 | − | 0.508211i | \(-0.830307\pi\) | ||
0.861233 | − | 0.508211i | \(-0.169693\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.52607 | − | 2.61313i | −0.231877 | − | 0.133874i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.82843 | + | 11.8272i | 0.348916 | + | 0.604341i | 0.986057 | − | 0.166407i | \(-0.0532164\pi\) |
−0.637141 | + | 0.770747i | \(0.719883\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.27558 | + | 3.04586i | −0.268173 | + | 0.154830i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.52505 | − | 11.3017i | 0.330833 | − | 0.573020i | −0.651842 | − | 0.758354i | \(-0.726004\pi\) |
0.982675 | + | 0.185335i | \(0.0593370\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.9187 | 0.754470 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −22.5319 | −1.13658 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.10257 | + | 3.64175i | −0.105792 | + | 0.183237i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.65172 | − | 3.26302i | 0.283652 | − | 0.163766i | −0.351424 | − | 0.936217i | \(-0.614302\pi\) |
0.635075 | + | 0.772450i | \(0.280969\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.7156 | + | 27.2201i | 0.784797 | + | 1.35931i | 0.929120 | + | 0.369778i | \(0.120566\pi\) |
−0.144323 | + | 0.989531i | \(0.546100\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.81478 | − | 5.66657i | −0.488909 | − | 0.282272i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 0.601731i | − | 0.0299002i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.844973i | 0.0418838i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −30.1568 | − | 17.4110i | −1.49116 | − | 0.860921i | −0.491210 | − | 0.871041i | \(-0.663445\pi\) |
−0.999949 | + | 0.0101207i | \(0.996778\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.29579 | − | 12.6367i | −0.359875 | − | 0.623322i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.76342 | − | 3.90486i | 0.332003 | − | 0.191682i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.15408 | − | 7.19508i | 0.203426 | − | 0.352345i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.9597 | 0.584271 | 0.292135 | − | 0.956377i | \(-0.405634\pi\) | ||||
0.292135 | + | 0.956377i | \(0.405634\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.6274 | 1.10279 | 0.551396 | − | 0.834243i | \(-0.314095\pi\) | ||||
0.551396 | + | 0.834243i | \(0.314095\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.84882 | − | 3.20225i | 0.0898927 | − | 0.155699i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.56516 | + | 4.94510i | −0.415471 | + | 0.239873i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.276422 | + | 0.478777i | 0.0133458 | + | 0.0231156i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.5809 | + | 9.57300i | 0.798675 | + | 0.461115i | 0.843008 | − | 0.537902i | \(-0.180783\pi\) |
−0.0443327 | + | 0.999017i | \(0.514116\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 1.66205i | − | 0.0798730i | −0.999202 | − | 0.0399365i | \(-0.987284\pi\) | ||
0.999202 | − | 0.0399365i | \(-0.0127156\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.775614i | 0.0371878i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.77799 | − | 3.33593i | −0.276399 | − | 0.159579i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.27932 | − | 14.3402i | −0.395151 | − | 0.684421i | 0.597970 | − | 0.801519i | \(-0.295974\pi\) |
−0.993120 | + | 0.117098i | \(0.962641\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.8781 | + | 9.16722i | −0.754391 | + | 0.435548i | −0.827278 | − | 0.561792i | \(-0.810112\pi\) |
0.0728872 | + | 0.997340i | \(0.476779\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.47847 | − | 7.75695i | 0.212300 | − | 0.367715i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.8017 | 0.510901 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.9899 | 0.896187 | 0.448093 | − | 0.893987i | \(-0.352103\pi\) | ||||
0.448093 | + | 0.893987i | \(0.352103\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.546460 | − | 0.946496i | 0.0257318 | − | 0.0445687i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.2618 | − | 7.07937i | 0.576111 | − | 0.332618i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.41976 | + | 14.5835i | 0.393860 | + | 0.682185i | 0.992955 | − | 0.118493i | \(-0.0378062\pi\) |
−0.599095 | + | 0.800678i | \(0.704473\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.84677 | + | 1.06623i | 0.0861998 | + | 0.0497675i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 36.8939i | − | 1.71832i | −0.511708 | − | 0.859160i | \(-0.670987\pi\) | ||
0.511708 | − | 0.859160i | \(-0.329013\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.2394i | 1.63771i | 0.573997 | + | 0.818857i | \(0.305392\pi\) | ||||
−0.573997 | + | 0.818857i | \(0.694608\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.74807 | + | 1.00925i | 0.0810650 | + | 0.0468029i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.9123 | + | 31.0250i | 0.828882 | + | 1.43567i | 0.898916 | + | 0.438122i | \(0.144356\pi\) |
−0.0700331 | + | 0.997545i | \(0.522310\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.946253 | − | 0.546320i | 0.0436011 | − | 0.0251731i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.498413 | + | 0.863276i | −0.0229170 | + | 0.0396935i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.42304 | 0.202943 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.8806 | 0.635547 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.05297 | − | 5.28790i | 0.139494 | − | 0.241610i | −0.787811 | − | 0.615917i | \(-0.788786\pi\) |
0.927305 | + | 0.374306i | \(0.122119\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.1084 | − | 8.72281i | 0.688882 | − | 0.397726i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.73268 | − | 4.73314i | −0.124085 | − | 0.214921i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.7285 | + | 8.50353i | 0.667414 | + | 0.385332i | 0.795096 | − | 0.606484i | \(-0.207420\pi\) |
−0.127682 | + | 0.991815i | \(0.540754\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 18.0857i | − | 0.817863i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 31.2897i | − | 1.41209i | −0.708169 | − | 0.706043i | \(-0.750479\pi\) | ||
0.708169 | − | 0.706043i | \(-0.249521\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.38043 | − | 1.37434i | −0.107209 | − | 0.0618973i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.0492325 | − | 0.0852731i | −0.00221283 | − | 0.00383274i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.4043 | + | 10.6257i | −0.823891 | + | 0.475674i | −0.851756 | − | 0.523938i | \(-0.824462\pi\) |
0.0278654 | + | 0.999612i | \(0.491129\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.50978 | − | 16.4714i | 0.424866 | − | 0.735889i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.728285 | −0.0324726 | −0.0162363 | − | 0.999868i | \(-0.505168\pi\) | ||||
−0.0162363 | + | 0.999868i | \(0.505168\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.12462 | −0.228043 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.792893 | + | 1.37333i | −0.0352136 | + | 0.0609918i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −27.4031 | + | 15.8212i | −1.21462 | + | 0.701263i | −0.963763 | − | 0.266761i | \(-0.914047\pi\) |
−0.250860 | + | 0.968023i | \(0.580713\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.476834 | − | 0.825901i | −0.0210528 | − | 0.0364644i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.73432 | + | 5.04276i | 0.384880 | + | 0.222211i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 0.605068i | − | 0.0266108i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 8.25540i | − | 0.362372i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.4836 | − | 9.51681i | −0.722159 | − | 0.416939i | 0.0933876 | − | 0.995630i | \(-0.470230\pi\) |
−0.815547 | + | 0.578691i | \(0.803564\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.45644 | + | 4.25468i | 0.107413 | + | 0.186044i | 0.914721 | − | 0.404085i | \(-0.132410\pi\) |
−0.807309 | + | 0.590129i | \(0.799077\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.19497 | + | 3.57667i | −0.269857 | + | 0.155802i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.9719 | − | 22.4680i | 0.563995 | − | 0.976869i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.05188 | 0.349422 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −22.5648 | −0.977391 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.32301 | + | 2.29152i | −0.0571987 | + | 0.0990711i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.76008 | + | 2.74823i | −0.205413 | + | 0.118595i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.0443 | + | 24.3254i | 0.603811 | + | 1.04583i | 0.992238 | + | 0.124352i | \(0.0396853\pi\) |
−0.388427 | + | 0.921480i | \(0.626981\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.2641 | − | 5.92596i | −0.440473 | − | 0.254307i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 6.94714i | − | 0.297583i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 18.5886i | − | 0.794792i | −0.917647 | − | 0.397396i | \(-0.869914\pi\) | ||
0.917647 | − | 0.397396i | \(-0.130086\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.157153 | − | 0.0907323i | −0.00670713 | − | 0.00387236i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.614626 | + | 1.06456i | 0.0261840 | + | 0.0453519i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.69089 | + | 1.55359i | −0.114222 | + | 0.0659461i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.9939 | − | 31.1663i | 0.762424 | − | 1.32056i | −0.179174 | − | 0.983817i | \(-0.557342\pi\) |
0.941598 | − | 0.336740i | \(-0.109324\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.5808 | 0.870476 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.348948 | 0.0147326 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.6731 | + | 21.9505i | −0.534109 | + | 0.925105i | 0.465097 | + | 0.885260i | \(0.346020\pi\) |
−0.999206 | + | 0.0398445i | \(0.987314\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.572292 | − | 0.330413i | 0.0240765 | − | 0.0139006i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.82160 | + | 15.2795i | 0.369821 | + | 0.640549i | 0.989537 | − | 0.144277i | \(-0.0460857\pi\) |
−0.619716 | + | 0.784826i | \(0.712752\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.9138 | + | 14.9613i | 1.08446 | + | 0.626112i | 0.932095 | − | 0.362213i | \(-0.117979\pi\) |
0.152362 | + | 0.988325i | \(0.451312\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23.1483i | 0.967034i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 32.4468i | 1.35313i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.36021 | + | 4.24942i | 0.306410 | + | 0.176906i | 0.645319 | − | 0.763913i | \(-0.276725\pi\) |
−0.338909 | + | 0.940819i | \(0.610058\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.256029 | + | 0.443455i | 0.0106402 | + | 0.0184294i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.96706 | − | 1.13568i | 0.0814672 | − | 0.0470351i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.01647 | + | 1.76058i | −0.0420259 | + | 0.0727910i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.1156 | −0.871535 | −0.435767 | − | 0.900059i | \(-0.643523\pi\) | ||||
−0.435767 | + | 0.900059i | \(0.643523\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.19908 | 0.131816 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.39672 | − | 11.0794i | 0.263126 | − | 0.455748i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 31.0085 | − | 17.9027i | 1.27336 | − | 0.735177i | 0.297745 | − | 0.954645i | \(-0.403765\pi\) |
0.975620 | + | 0.219468i | \(0.0704321\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.90360 | + | 13.6894i | 0.323473 | + | 0.560271i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.73895 | + | 5.04544i | 0.357064 | + | 0.206151i | 0.667792 | − | 0.744348i | \(-0.267240\pi\) |
−0.310728 | + | 0.950499i | \(0.600573\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 31.0913i | − | 1.26824i | −0.773234 | − | 0.634120i | \(-0.781362\pi\) | ||
0.773234 | − | 0.634120i | \(-0.218638\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.09299i | 0.370295i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.71830 | + | 3.30146i | 0.232482 | + | 0.134224i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.8573 | − | 18.8053i | −0.440683 | − | 0.763285i | 0.557057 | − | 0.830474i | \(-0.311930\pi\) |
−0.997740 | + | 0.0671889i | \(0.978597\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.8188 | + | 6.24622i | −0.437681 | + | 0.252695i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.1405 | − | 17.5639i | 0.409571 | − | 0.709398i | −0.585270 | − | 0.810838i | \(-0.699012\pi\) |
0.994842 | + | 0.101440i | \(0.0323449\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.01893 | 0.162059 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.1442 | 0.569423 | 0.284712 | − | 0.958613i | \(-0.408102\pi\) | ||||
0.284712 | + | 0.958613i | \(0.408102\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.2581 | − | 36.8201i | 0.854435 | − | 1.47992i | −0.0227335 | − | 0.999742i | \(-0.507237\pi\) |
0.877168 | − | 0.480183i | \(-0.159430\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.05870 | − | 3.49799i | 0.243127 | − | 0.140370i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.84995 | − | 17.0606i | −0.393998 | − | 0.682425i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.135147 | − | 0.0780274i | −0.00539727 | − | 0.00311611i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 11.0115i | − | 0.439056i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 11.2426i | − | 0.447561i | −0.974640 | − | 0.223781i | \(-0.928160\pi\) | ||
0.974640 | − | 0.223781i | \(-0.0718399\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.166027 | − | 0.0958559i | −0.00659899 | − | 0.00380993i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.57240 | − | 2.72347i | −0.0623987 | − | 0.108078i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.91042 | − | 1.68033i | 0.115134 | − | 0.0664729i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.235818 | + | 0.408449i | −0.00931425 | + | 0.0161328i | −0.870645 | − | 0.491912i | \(-0.836298\pi\) |
0.861331 | + | 0.508045i | \(0.169632\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.10040 | 0.0433955 | 0.0216977 | − | 0.999765i | \(-0.493093\pi\) | ||||
0.0216977 | + | 0.999765i | \(0.493093\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.66557 | −0.144332 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.8657 | − | 27.4802i | 0.623746 | − | 1.08036i | −0.365036 | − | 0.930993i | \(-0.618943\pi\) |
0.988782 | − | 0.149366i | \(-0.0477232\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.14106 | − | 0.658789i | 0.0447904 | − | 0.0258597i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.49210 | + | 7.78055i | 0.175790 | + | 0.304477i | 0.940434 | − | 0.339976i | \(-0.110419\pi\) |
−0.764645 | + | 0.644452i | \(0.777085\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.7417 | − | 6.77906i | −0.458785 | − | 0.264880i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 12.1442i | − | 0.473791i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.0679i | 1.01546i | 0.861516 | + | 0.507731i | \(0.169516\pi\) | ||||
−0.861516 | + | 0.507731i | \(0.830484\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.18105 | − | 0.681880i | −0.0459376 | − | 0.0265221i | 0.476855 | − | 0.878982i | \(-0.341777\pi\) |
−0.522793 | + | 0.852460i | \(0.675110\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.60226 | − | 6.23929i | −0.139900 | − | 0.242314i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.80949 | + | 4.50881i | −0.302385 | + | 0.174582i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.00555 | + | 8.66986i | −0.193526 | + | 0.335196i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.0296942 | −0.00114633 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.6874 | −0.681799 | −0.340899 | − | 0.940100i | \(-0.610732\pi\) | ||||
−0.340899 | + | 0.940100i | \(0.610732\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.31896 | + | 4.01656i | −0.0892568 | + | 0.154597i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.88562 | − | 3.97541i | 0.264636 | − | 0.152788i | −0.361812 | − | 0.932251i | \(-0.617842\pi\) |
0.626447 | + | 0.779464i | \(0.284508\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.06817 | − | 5.31422i | −0.117572 | − | 0.203641i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.6132 | + | 9.01431i | 0.597424 | + | 0.344923i | 0.768028 | − | 0.640417i | \(-0.221238\pi\) |
−0.170603 | + | 0.985340i | \(0.554572\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 8.78021i | − | 0.335474i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.44500i | 0.360349i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −40.6126 | − | 23.4477i | −1.54722 | − | 0.893286i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.2488 | + | 38.5361i | 0.846384 | + | 1.46598i | 0.884413 | + | 0.466704i | \(0.154559\pi\) |
−0.0380289 | + | 0.999277i | \(0.512108\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.32950 | − | 2.49964i | 0.164227 | − | 0.0948167i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.12132 | + | 12.3345i | −0.269739 | + | 0.467202i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −22.2217 | −0.840501 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.8785 | −0.448646 | −0.224323 | − | 0.974515i | \(-0.572017\pi\) | ||||
−0.224323 | + | 0.974515i | \(0.572017\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.46224 | + | 4.26473i | −0.0928653 | + | 0.160847i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.92689 | − | 1.11249i | 0.0725710 | − | 0.0418989i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.4321 | − | 21.5331i | −0.466899 | − | 0.808693i | 0.532386 | − | 0.846502i | \(-0.321295\pi\) |
−0.999285 | + | 0.0378090i | \(0.987962\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.05213 | − | 3.49420i | −0.226973 | − | 0.131043i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 23.4680i | 0.878883i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.332663i | 0.0124409i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18.0101 | − | 10.3981i | −0.672598 | − | 0.388325i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.302360 | − | 0.523703i | −0.0112761 | − | 0.0195308i | 0.860332 | − | 0.509734i | \(-0.170256\pi\) |
−0.871608 | + | 0.490203i | \(0.836923\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.3063 | + | 6.52769i | −0.420486 | + | 0.242767i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.98907 | − | 5.17723i | 0.111011 | − | 0.192277i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.7628 | −0.658786 | −0.329393 | − | 0.944193i | \(-0.606844\pi\) | ||||
−0.329393 | + | 0.944193i | \(0.606844\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.49519 | − | 11.2500i | 0.240233 | − | 0.416096i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.4467 | − | 7.76347i | 0.496666 | − | 0.286750i | −0.230670 | − | 0.973032i | \(-0.574092\pi\) |
0.727336 | + | 0.686282i | \(0.240758\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.743971 | + | 1.28860i | 0.0274045 | + | 0.0474660i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.8992 | − | 8.60208i | −0.548077 | − | 0.316433i | 0.200269 | − | 0.979741i | \(-0.435818\pi\) |
−0.748346 | + | 0.663308i | \(0.769152\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.22196i | 0.118362i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 13.1996i | − | 0.484247i | −0.970245 | − | 0.242123i | \(-0.922156\pi\) | ||
0.970245 | − | 0.242123i | \(-0.0778439\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.62889 | + | 3.24984i | 0.206227 | + | 0.119065i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.48938 | + | 11.2399i | 0.237434 | + | 0.411248i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.5756 | + | 10.1473i | −0.641344 | + | 0.370280i | −0.785132 | − | 0.619328i | \(-0.787405\pi\) |
0.143788 | + | 0.989609i | \(0.454072\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.94873 | − | 15.4997i | 0.326110 | − | 0.564839i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.51975 | 0.310065 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.7011 | 0.897778 | 0.448889 | − | 0.893587i | \(-0.351820\pi\) | ||||
0.448889 | + | 0.893587i | \(0.351820\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.572398 | − | 0.991422i | 0.0207767 | − | 0.0359864i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.13548 | + | 2.38762i | −0.149911 | + | 0.0865512i | −0.573079 | − | 0.819500i | \(-0.694251\pi\) |
0.423168 | + | 0.906051i | \(0.360918\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.641585 | + | 1.11126i | 0.0231965 | + | 0.0401776i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −23.5587 | − | 13.6016i | −0.850654 | − | 0.491125i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 14.7721i | − | 0.532696i | −0.963877 | − | 0.266348i | \(-0.914183\pi\) | ||
0.963877 | − | 0.266348i | \(-0.0858170\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 6.67896i | − | 0.240537i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.9715 | + | 18.4588i | 1.14994 | + | 0.663916i | 0.948872 | − | 0.315662i | \(-0.102227\pi\) |
0.201064 | + | 0.979578i | \(0.435560\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.77894 | − | 13.4735i | −0.279428 | − | 0.483983i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.51616 | − | 3.18476i | 0.197637 | − | 0.114106i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.274963 | − | 0.476250i | 0.00983895 | − | 0.0170416i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.28897 | −0.0460641 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.657475 | 0.0234663 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.5199 | + | 32.0774i | −0.660164 | + | 1.14344i | 0.320408 | + | 0.947280i | \(0.396180\pi\) |
−0.980572 | + | 0.196158i | \(0.937153\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −21.1452 | + | 12.2082i | −0.752790 | + | 0.434623i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.306539 | + | 0.530940i | 0.0108855 | + | 0.0188542i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.23336 | + | 4.17618i | 0.256541 | + | 0.148114i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 36.9752i | − | 1.30973i | −0.755746 | − | 0.654865i | \(-0.772725\pi\) | ||
0.755746 | − | 0.654865i | \(-0.227275\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.88509i | 0.278954i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.8911 | + | 7.44266i | 0.455483 | + | 0.262973i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.993616 | − | 1.72099i | −0.0350639 | − | 0.0607325i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.992403 | + | 0.572964i | −0.0349342 | + | 0.0201693i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.67050 | + | 4.62544i | −0.0938898 | + | 0.162622i | −0.909145 | − | 0.416480i | \(-0.863263\pi\) |
0.815255 | + | 0.579102i | \(0.196597\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.4180 | −1.31392 | −0.656961 | − | 0.753924i | \(-0.728159\pi\) | ||||
−0.656961 | + | 0.753924i | \(0.728159\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.65157 | 0.198209 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.44135 | − | 9.42470i | 0.190602 | − | 0.330133i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.03116 | + | 2.90474i | −0.176018 | + | 0.101624i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.1730 | − | 17.6202i | −0.355041 | − | 0.614949i | 0.632084 | − | 0.774900i | \(-0.282200\pi\) |
−0.987125 | + | 0.159951i | \(0.948866\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.1287 | + | 23.1683i | 1.39880 | + | 0.807598i | 0.994267 | − | 0.106926i | \(-0.0341007\pi\) |
0.404533 | + | 0.914523i | \(0.367434\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.758932i | 0.0264226i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.20358i | 0.0766260i | 0.999266 | + | 0.0383130i | \(0.0121984\pi\) | ||||
−0.999266 | + | 0.0383130i | \(0.987802\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.9510 | − | 8.63194i | −0.519268 | − | 0.299800i | 0.217367 | − | 0.976090i | \(-0.430253\pi\) |
−0.736635 | + | 0.676290i | \(0.763587\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.63792 | + | 16.6934i | 0.334336 | + | 0.579087i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.91136 | − | 5.72232i | 0.342997 | − | 0.198029i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.67725 | + | 2.90508i | −0.0579741 | + | 0.100414i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.4781 | 0.603410 | 0.301705 | − | 0.953401i | \(-0.402444\pi\) | ||||
0.301705 | + | 0.953401i | \(0.402444\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.3386 | −0.942709 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.40185 | + | 7.62422i | −0.151608 | + | 0.262592i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.826376 | + | 0.477108i | −0.0284282 | + | 0.0164130i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13.0725 | − | 22.6423i | −0.448648 | − | 0.777081i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −31.2855 | − | 18.0627i | −1.07245 | − | 0.619181i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.7781i | 1.05382i | 0.849920 | + | 0.526912i | \(0.176650\pi\) | ||||
−0.849920 | + | 0.526912i | \(0.823350\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 0.573852i | − | 0.0196253i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.3399 | + | 11.7432i | 0.694797 | + | 0.401142i | 0.805407 | − | 0.592722i | \(-0.201947\pi\) |
−0.110609 | + | 0.993864i | \(0.535280\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.1125 | − | 36.5678i | −0.720348 | − | 1.24768i | −0.960860 | − | 0.277033i | \(-0.910649\pi\) |
0.240513 | − | 0.970646i | \(-0.422684\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.52190 | − | 3.18807i | 0.187968 | − | 0.108523i | −0.403063 | − | 0.915172i | \(-0.632054\pi\) |
0.591031 | + | 0.806649i | \(0.298721\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.48376 | − | 4.30200i | 0.0844505 | − | 0.146273i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12.4526 | 0.422912 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.14356 | −0.0387925 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.3603 | − | 26.6048i | 0.520464 | − | 0.901470i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.86588 | − | 4.54137i | 0.266220 | − | 0.153702i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.10997 | + | 10.5828i | 0.206319 | + | 0.357355i | 0.950552 | − | 0.310565i | \(-0.100518\pi\) |
−0.744233 | + | 0.667920i | \(0.767185\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15.8171 | + | 9.13200i | 0.533497 | + | 0.308015i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45.0545i | 1.51793i | 0.651134 | + | 0.758963i | \(0.274294\pi\) | ||||
−0.651134 | + | 0.758963i | \(0.725706\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.8481i | 0.735246i | 0.929975 | + | 0.367623i | \(0.119828\pi\) | ||||
−0.929975 | + | 0.367623i | \(0.880172\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.19595 | + | 2.42253i | 0.141045 | + | 0.0814325i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.1302 | − | 27.9383i | −0.541599 | − | 0.938078i | −0.998812 | − | 0.0487204i | \(-0.984486\pi\) |
0.457213 | − | 0.889357i | \(-0.348848\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.141713 | − | 0.0818181i | 0.00474757 | − | 0.00274101i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.76316 | − | 3.05389i | 0.0590020 | − | 0.102194i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.30739 | −0.110554 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −23.6359 | −0.789179 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.16192 | − | 3.74456i | 0.0721042 | − | 0.124888i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −25.6342 | + | 14.7999i | −0.853998 | + | 0.493056i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.56583 | − | 6.17620i | −0.118532 | − | 0.205304i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.2097 | − | 8.78132i | −0.505030 | − | 0.291579i | 0.225759 | − | 0.974183i | \(-0.427514\pi\) |
−0.730788 | + | 0.682604i | \(0.760847\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 8.51647i | − | 0.282473i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.475746i | 0.0157622i | 0.999969 | + | 0.00788108i | \(0.00250865\pi\) | ||||
−0.999969 | + | 0.00788108i | \(0.997491\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.83926 | + | 1.06190i | 0.0608707 | + | 0.0351437i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.0545964 | − | 0.0945638i | −0.00180490 | − | 0.00312618i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.4809 | − | 16.4435i | 0.939500 | − | 0.542420i | 0.0496962 | − | 0.998764i | \(-0.484175\pi\) |
0.889803 | + | 0.456344i | \(0.150841\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.7236 | + | 18.5738i | −0.353354 | + | 0.612027i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.3540 | −0.373721 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 23.9490 | 0.787437 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.38043 | + | 14.5153i | −0.275250 | + | 0.476746i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.0677 | + | 6.38992i | −0.363118 | + | 0.209646i | −0.670448 | − | 0.741957i | \(-0.733898\pi\) |
0.307329 | + | 0.951603i | \(0.400565\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.24000 | + | 12.5400i | 0.237027 | + | 0.410543i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.181842 | + | 0.104986i | 0.00594687 | + | 0.00343342i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 4.03304i | − | 0.131754i | −0.997828 | − | 0.0658768i | \(-0.979016\pi\) | ||
0.997828 | − | 0.0658768i | \(-0.0209844\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.48483i | 0.0484556i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 50.8865 | + | 29.3793i | 1.65885 | + | 0.957739i | 0.973246 | + | 0.229766i | \(0.0737960\pi\) |
0.685606 | + | 0.727973i | \(0.259537\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.3629 | + | 40.4658i | 0.760802 | + | 1.31775i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.6092 | + | 6.70260i | −0.377250 | + | 0.217805i | −0.676621 | − | 0.736331i | \(-0.736556\pi\) |
0.299371 | + | 0.954137i | \(0.403223\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.5146 | + | 35.5323i | −0.665931 | + | 1.15343i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.4908 | −0.372616 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.89697 | −0.0614490 | −0.0307245 | − | 0.999528i | \(-0.509781\pi\) | ||||
−0.0307245 | + | 0.999528i | \(0.509781\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.96452 | + | 12.0629i | −0.225367 | + | 0.390346i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.182664 | + | 0.105461i | −0.00590469 | + | 0.00340908i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.87368 | + | 17.1017i | 0.318506 | + | 0.551669i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.80822 | − | 2.19867i | −0.122718 | − | 0.0708513i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.308121i | 0.00991877i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 4.84855i | − | 0.155919i | −0.996957 | − | 0.0779595i | \(-0.975160\pi\) | ||
0.996957 | − | 0.0779595i | \(-0.0248405\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.76121 | + | 1.01683i | 0.0565781 | + | 0.0326654i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.8709 | − | 32.6854i | −0.605596 | − | 1.04892i | −0.991957 | − | 0.126576i | \(-0.959601\pi\) |
0.386361 | − | 0.922348i | \(-0.373732\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13.5699 | − | 7.83459i | 0.434585 | − | 0.250908i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.3343 | + | 21.3636i | −0.394609 | + | 0.683482i | −0.993051 | − | 0.117684i | \(-0.962453\pi\) |
0.598442 | + | 0.801166i | \(0.295787\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.43578 | 0.0778477 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.5453 | 0.368612 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.8750 | + | 32.6925i | −0.602019 | + | 1.04273i | 0.390495 | + | 0.920605i | \(0.372304\pi\) |
−0.992515 | + | 0.122123i | \(0.961030\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.66684 | − | 3.84910i | 0.212423 | − | 0.122643i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21.3088 | − | 36.9079i | −0.677580 | − | 1.17360i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −48.1078 | − | 27.7750i | −1.52819 | − | 0.882303i | −0.999438 | − | 0.0335292i | \(-0.989325\pi\) |
−0.528756 | − | 0.848774i | \(-0.677341\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 21.0967i | − | 0.669484i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.51167i | 0.301540i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.9075 | + | 12.0710i | 0.662148 | + | 0.382291i | 0.793095 | − | 0.609098i | \(-0.208468\pi\) |
−0.130947 | + | 0.991389i | \(0.541802\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.58187 | − | 4.47192i | −0.0816866 | − | 0.141485i |
(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 | 2352.2.bl.q.31.2 | 8 | ||
4.3 | odd | 2 | 2352.2.bl.r.31.2 | 8 | |||
7.2 | even | 3 | 2352.2.bl.o.607.3 | 8 | |||
7.3 | odd | 6 | 2352.2.b.k.1567.5 | yes | 8 | ||
7.4 | even | 3 | 2352.2.b.l.1567.4 | yes | 8 | ||
7.5 | odd | 6 | 2352.2.bl.r.607.2 | 8 | |||
7.6 | odd | 2 | 2352.2.bl.t.31.3 | 8 | |||
21.11 | odd | 6 | 7056.2.b.w.1567.5 | 8 | |||
21.17 | even | 6 | 7056.2.b.x.1567.4 | 8 | |||
28.3 | even | 6 | 2352.2.b.l.1567.5 | yes | 8 | ||
28.11 | odd | 6 | 2352.2.b.k.1567.4 | ✓ | 8 | ||
28.19 | even | 6 | inner | 2352.2.bl.q.607.2 | 8 | ||
28.23 | odd | 6 | 2352.2.bl.t.607.3 | 8 | |||
28.27 | even | 2 | 2352.2.bl.o.31.3 | 8 | |||
84.11 | even | 6 | 7056.2.b.x.1567.5 | 8 | |||
84.59 | odd | 6 | 7056.2.b.w.1567.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2352.2.b.k.1567.4 | ✓ | 8 | 28.11 | odd | 6 | ||
2352.2.b.k.1567.5 | yes | 8 | 7.3 | odd | 6 | ||
2352.2.b.l.1567.4 | yes | 8 | 7.4 | even | 3 | ||
2352.2.b.l.1567.5 | yes | 8 | 28.3 | even | 6 | ||
2352.2.bl.o.31.3 | 8 | 28.27 | even | 2 | |||
2352.2.bl.o.607.3 | 8 | 7.2 | even | 3 | |||
2352.2.bl.q.31.2 | 8 | 1.1 | even | 1 | trivial | ||
2352.2.bl.q.607.2 | 8 | 28.19 | even | 6 | inner | ||
2352.2.bl.r.31.2 | 8 | 4.3 | odd | 2 | |||
2352.2.bl.r.607.2 | 8 | 7.5 | odd | 6 | |||
2352.2.bl.t.31.3 | 8 | 7.6 | odd | 2 | |||
2352.2.bl.t.607.3 | 8 | 28.23 | odd | 6 | |||
7056.2.b.w.1567.4 | 8 | 84.59 | odd | 6 | |||
7056.2.b.w.1567.5 | 8 | 21.11 | odd | 6 | |||
7056.2.b.x.1567.4 | 8 | 21.17 | even | 6 | |||
7056.2.b.x.1567.5 | 8 | 84.11 | even | 6 |