Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [378,2,Mod(377,378)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(378, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("378.377");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 378 = 2 \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 378.d (of order \(2\), degree \(1\), 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: | \(3.01834519640\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 377.4 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 378.377 |
Dual form | 378.2.d.c.377.2 |
$q$-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 \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 3.46410 | 1.54919 | 0.774597 | − | 0.632456i | \(-0.217953\pi\) | ||||
0.774597 | + | 0.632456i | \(0.217953\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | + | 1.73205i | 0.755929 | + | 0.654654i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.46410i | 1.09545i | ||||||||
\(11\) | − | 6.00000i | − | 1.80907i | −0.426401 | − | 0.904534i | \(-0.640219\pi\) | ||
0.426401 | − | 0.904534i | \(-0.359781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.73205i | − | 0.480384i | −0.970725 | − | 0.240192i | \(-0.922790\pi\) | ||
0.970725 | − | 0.240192i | \(-0.0772105\pi\) | |||||||
\(14\) | −1.73205 | + | 2.00000i | −0.462910 | + | 0.534522i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.73205 | −0.420084 | −0.210042 | − | 0.977692i | \(-0.567360\pi\) | ||||
−0.210042 | + | 0.977692i | \(0.567360\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.92820i | 1.58944i | 0.606977 | + | 0.794719i | \(0.292382\pi\) | ||||
−0.606977 | + | 0.794719i | \(0.707618\pi\) | |||||||
\(20\) | −3.46410 | −0.774597 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.00000 | 1.27920 | ||||||||
\(23\) | 3.00000i | 0.625543i | 0.949828 | + | 0.312772i | \(0.101257\pi\) | ||||
−0.949828 | + | 0.312772i | \(0.898743\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.00000 | 1.40000 | ||||||||
\(26\) | 1.73205 | 0.339683 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.00000 | − | 1.73205i | −0.377964 | − | 0.327327i | ||||
\(29\) | − | 3.00000i | − | 0.557086i | −0.960424 | − | 0.278543i | \(-0.910149\pi\) | ||
0.960424 | − | 0.278543i | \(-0.0898515\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.19615i | 0.933257i | 0.884454 | + | 0.466628i | \(0.154531\pi\) | ||||
−0.884454 | + | 0.466628i | \(0.845469\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 1.73205i | − | 0.297044i | ||||||
\(35\) | 6.92820 | + | 6.00000i | 1.17108 | + | 1.01419i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | −6.92820 | −1.12390 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 3.46410i | − | 0.547723i | ||||||
\(41\) | 6.92820 | 1.08200 | 0.541002 | − | 0.841021i | \(-0.318045\pi\) | ||||
0.541002 | + | 0.841021i | \(0.318045\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.0000 | −1.67748 | −0.838742 | − | 0.544529i | \(-0.816708\pi\) | ||||
−0.838742 | + | 0.544529i | \(0.816708\pi\) | |||||||
\(44\) | 6.00000i | 0.904534i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.00000 | −0.442326 | ||||||||
\(47\) | −6.92820 | −1.01058 | −0.505291 | − | 0.862949i | \(-0.668615\pi\) | ||||
−0.505291 | + | 0.862949i | \(0.668615\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | 7.00000i | 0.989949i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.73205i | 0.240192i | ||||||||
\(53\) | − | 3.00000i | − | 0.412082i | −0.978543 | − | 0.206041i | \(-0.933942\pi\) | ||
0.978543 | − | 0.206041i | \(-0.0660580\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 20.7846i | − | 2.80260i | ||||||
\(56\) | 1.73205 | − | 2.00000i | 0.231455 | − | 0.267261i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.00000 | 0.393919 | ||||||||
\(59\) | −8.66025 | −1.12747 | −0.563735 | − | 0.825956i | \(-0.690636\pi\) | ||||
−0.563735 | + | 0.825956i | \(0.690636\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 13.8564i | − | 1.77413i | −0.461644 | − | 0.887066i | \(-0.652740\pi\) | ||
0.461644 | − | 0.887066i | \(-0.347260\pi\) | |||||||
\(62\) | −5.19615 | −0.659912 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 6.00000i | − | 0.744208i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.00000 | −0.855186 | −0.427593 | − | 0.903971i | \(-0.640638\pi\) | ||||
−0.427593 | + | 0.903971i | \(0.640638\pi\) | |||||||
\(68\) | 1.73205 | 0.210042 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.00000 | + | 6.92820i | −0.717137 | + | 0.828079i | ||||
\(71\) | − | 3.00000i | − | 0.356034i | −0.984027 | − | 0.178017i | \(-0.943032\pi\) | ||
0.984027 | − | 0.178017i | \(-0.0569683\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.92820i | 0.810885i | 0.914121 | + | 0.405442i | \(0.132883\pi\) | ||||
−0.914121 | + | 0.405442i | \(0.867117\pi\) | |||||||
\(74\) | − | 2.00000i | − | 0.232495i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 6.92820i | − | 0.794719i | ||||||
\(77\) | 10.3923 | − | 12.0000i | 1.18431 | − | 1.36753i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | 3.46410 | 0.387298 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.92820i | 0.765092i | ||||||||
\(83\) | −3.46410 | −0.380235 | −0.190117 | − | 0.981761i | \(-0.560887\pi\) | ||||
−0.190117 | + | 0.981761i | \(0.560887\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.00000 | −0.650791 | ||||||||
\(86\) | − | 11.0000i | − | 1.18616i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.00000 | −0.639602 | ||||||||
\(89\) | 5.19615 | 0.550791 | 0.275396 | − | 0.961331i | \(-0.411191\pi\) | ||||
0.275396 | + | 0.961331i | \(0.411191\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.00000 | − | 3.46410i | 0.314485 | − | 0.363137i | ||||
\(92\) | − | 3.00000i | − | 0.312772i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 6.92820i | − | 0.714590i | ||||||
\(95\) | 24.0000i | 2.46235i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.92820i | − | 0.703452i | −0.936103 | − | 0.351726i | \(-0.885595\pi\) | ||
0.936103 | − | 0.351726i | \(-0.114405\pi\) | |||||||
\(98\) | −6.92820 | + | 1.00000i | −0.699854 | + | 0.101015i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.00000 | −0.700000 | ||||||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 8.66025i | − | 0.853320i | −0.904412 | − | 0.426660i | \(-0.859690\pi\) | ||
0.904412 | − | 0.426660i | \(-0.140310\pi\) | |||||||
\(104\) | −1.73205 | −0.169842 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.00000 | 0.291386 | ||||||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.00000 | 0.383131 | 0.191565 | − | 0.981480i | \(-0.438644\pi\) | ||||
0.191565 | + | 0.981480i | \(0.438644\pi\) | |||||||
\(110\) | 20.7846 | 1.98173 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.00000 | + | 1.73205i | 0.188982 | + | 0.163663i | ||||
\(113\) | 6.00000i | 0.564433i | 0.959351 | + | 0.282216i | \(0.0910696\pi\) | ||||
−0.959351 | + | 0.282216i | \(0.908930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.3923i | 0.969087i | ||||||||
\(116\) | 3.00000i | 0.278543i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 8.66025i | − | 0.797241i | ||||||
\(119\) | −3.46410 | − | 3.00000i | −0.317554 | − | 0.275010i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −25.0000 | −2.27273 | ||||||||
\(122\) | 13.8564 | 1.25450 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 5.19615i | − | 0.466628i | ||||||
\(125\) | 6.92820 | 0.619677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.0000 | 1.24230 | 0.621150 | − | 0.783692i | \(-0.286666\pi\) | ||||
0.621150 | + | 0.783692i | \(0.286666\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.00000 | 0.526235 | ||||||||
\(131\) | −5.19615 | −0.453990 | −0.226995 | − | 0.973896i | \(-0.572890\pi\) | ||||
−0.226995 | + | 0.973896i | \(0.572890\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.0000 | + | 13.8564i | −1.04053 | + | 1.20150i | ||||
\(134\) | − | 7.00000i | − | 0.604708i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.73205i | 0.148522i | ||||||||
\(137\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 3.46410i | − | 0.293821i | −0.989150 | − | 0.146911i | \(-0.953067\pi\) | ||
0.989150 | − | 0.146911i | \(-0.0469330\pi\) | |||||||
\(140\) | −6.92820 | − | 6.00000i | −0.585540 | − | 0.507093i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.00000 | 0.251754 | ||||||||
\(143\) | −10.3923 | −0.869048 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 10.3923i | − | 0.863034i | ||||||
\(146\) | −6.92820 | −0.573382 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.00000 | 0.164399 | ||||||||
\(149\) | − | 15.0000i | − | 1.22885i | −0.788976 | − | 0.614424i | \(-0.789388\pi\) | ||
0.788976 | − | 0.614424i | \(-0.210612\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | 6.92820 | 0.561951 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 12.0000 | + | 10.3923i | 0.966988 | + | 0.837436i | ||||
\(155\) | 18.0000i | 1.44579i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.5885i | 1.24409i | 0.782980 | + | 0.622047i | \(0.213699\pi\) | ||||
−0.782980 | + | 0.622047i | \(0.786301\pi\) | |||||||
\(158\) | 8.00000i | 0.636446i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.46410i | 0.273861i | ||||||||
\(161\) | −5.19615 | + | 6.00000i | −0.409514 | + | 0.472866i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.0000 | 0.861586 | 0.430793 | − | 0.902451i | \(-0.358234\pi\) | ||||
0.430793 | + | 0.902451i | \(0.358234\pi\) | |||||||
\(164\) | −6.92820 | −0.541002 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 3.46410i | − | 0.268866i | ||||||
\(167\) | −17.3205 | −1.34030 | −0.670151 | − | 0.742225i | \(-0.733770\pi\) | ||||
−0.670151 | + | 0.742225i | \(0.733770\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.0000 | 0.769231 | ||||||||
\(170\) | − | 6.00000i | − | 0.460179i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11.0000 | 0.838742 | ||||||||
\(173\) | −20.7846 | −1.58022 | −0.790112 | − | 0.612962i | \(-0.789978\pi\) | ||||
−0.790112 | + | 0.612962i | \(0.789978\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.0000 | + | 12.1244i | 1.05830 | + | 0.916515i | ||||
\(176\) | − | 6.00000i | − | 0.452267i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.19615i | 0.389468i | ||||||||
\(179\) | − | 6.00000i | − | 0.448461i | −0.974536 | − | 0.224231i | \(-0.928013\pi\) | ||
0.974536 | − | 0.224231i | \(-0.0719869\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1.73205i | − | 0.128742i | −0.997926 | − | 0.0643712i | \(-0.979496\pi\) | ||
0.997926 | − | 0.0643712i | \(-0.0205042\pi\) | |||||||
\(182\) | 3.46410 | + | 3.00000i | 0.256776 | + | 0.222375i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.00000 | 0.221163 | ||||||||
\(185\) | −6.92820 | −0.509372 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.3923i | 0.759961i | ||||||||
\(188\) | 6.92820 | 0.505291 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −24.0000 | −1.74114 | ||||||||
\(191\) | 24.0000i | 1.73658i | 0.496058 | + | 0.868290i | \(0.334780\pi\) | ||||
−0.496058 | + | 0.868290i | \(0.665220\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.0000 | 0.935760 | 0.467880 | − | 0.883792i | \(-0.345018\pi\) | ||||
0.467880 | + | 0.883792i | \(0.345018\pi\) | |||||||
\(194\) | 6.92820 | 0.497416 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.00000 | − | 6.92820i | −0.0714286 | − | 0.494872i | ||||
\(197\) | − | 6.00000i | − | 0.427482i | −0.976890 | − | 0.213741i | \(-0.931435\pi\) | ||
0.976890 | − | 0.213741i | \(-0.0685649\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.66025i | 0.613909i | 0.951724 | + | 0.306955i | \(0.0993100\pi\) | ||||
−0.951724 | + | 0.306955i | \(0.900690\pi\) | |||||||
\(200\) | − | 7.00000i | − | 0.494975i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.19615 | − | 6.00000i | 0.364698 | − | 0.421117i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 24.0000 | 1.67623 | ||||||||
\(206\) | 8.66025 | 0.603388 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 1.73205i | − | 0.120096i | ||||||
\(209\) | 41.5692 | 2.87540 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.00000 | 0.481900 | 0.240950 | − | 0.970538i | \(-0.422541\pi\) | ||||
0.240950 | + | 0.970538i | \(0.422541\pi\) | |||||||
\(212\) | 3.00000i | 0.206041i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −38.1051 | −2.59875 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.00000 | + | 10.3923i | −0.610960 | + | 0.705476i | ||||
\(218\) | 4.00000i | 0.270914i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 20.7846i | 1.40130i | ||||||||
\(221\) | 3.00000i | 0.201802i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 10.3923i | − | 0.695920i | −0.937509 | − | 0.347960i | \(-0.886874\pi\) | ||
0.937509 | − | 0.347960i | \(-0.113126\pi\) | |||||||
\(224\) | −1.73205 | + | 2.00000i | −0.115728 | + | 0.133631i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | −0.399114 | ||||||||
\(227\) | 25.9808 | 1.72440 | 0.862202 | − | 0.506565i | \(-0.169085\pi\) | ||||
0.862202 | + | 0.506565i | \(0.169085\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.7846i | 1.37349i | 0.726900 | + | 0.686743i | \(0.240960\pi\) | ||||
−0.726900 | + | 0.686743i | \(0.759040\pi\) | |||||||
\(230\) | −10.3923 | −0.685248 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.00000 | −0.196960 | ||||||||
\(233\) | 24.0000i | 1.57229i | 0.618041 | + | 0.786146i | \(0.287927\pi\) | ||||
−0.618041 | + | 0.786146i | \(0.712073\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.0000 | −1.56559 | ||||||||
\(236\) | 8.66025 | 0.563735 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.00000 | − | 3.46410i | 0.194461 | − | 0.224544i | ||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 13.8564i | − | 0.892570i | −0.894891 | − | 0.446285i | \(-0.852747\pi\) | ||
0.894891 | − | 0.446285i | \(-0.147253\pi\) | |||||||
\(242\) | − | 25.0000i | − | 1.60706i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 13.8564i | 0.887066i | ||||||||
\(245\) | 3.46410 | + | 24.0000i | 0.221313 | + | 1.53330i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.0000 | 0.763542 | ||||||||
\(248\) | 5.19615 | 0.329956 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.92820i | 0.438178i | ||||||||
\(251\) | 3.46410 | 0.218652 | 0.109326 | − | 0.994006i | \(-0.465131\pi\) | ||||
0.109326 | + | 0.994006i | \(0.465131\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.0000 | 1.13165 | ||||||||
\(254\) | 14.0000i | 0.878438i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −20.7846 | −1.29651 | −0.648254 | − | 0.761424i | \(-0.724501\pi\) | ||||
−0.648254 | + | 0.761424i | \(0.724501\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.00000 | − | 3.46410i | −0.248548 | − | 0.215249i | ||||
\(260\) | 6.00000i | 0.372104i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 5.19615i | − | 0.321019i | ||||||
\(263\) | − | 9.00000i | − | 0.554964i | −0.960731 | − | 0.277482i | \(-0.910500\pi\) | ||
0.960731 | − | 0.277482i | \(-0.0894999\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 10.3923i | − | 0.638394i | ||||||
\(266\) | −13.8564 | − | 12.0000i | −0.849591 | − | 0.735767i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.00000 | 0.427593 | ||||||||
\(269\) | −3.46410 | −0.211210 | −0.105605 | − | 0.994408i | \(-0.533678\pi\) | ||||
−0.105605 | + | 0.994408i | \(0.533678\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 12.1244i | − | 0.736502i | −0.929726 | − | 0.368251i | \(-0.879957\pi\) | ||
0.929726 | − | 0.368251i | \(-0.120043\pi\) | |||||||
\(272\) | −1.73205 | −0.105021 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 42.0000i | − | 2.53270i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.0000 | 1.20168 | 0.600842 | − | 0.799368i | \(-0.294832\pi\) | ||||
0.600842 | + | 0.799368i | \(0.294832\pi\) | |||||||
\(278\) | 3.46410 | 0.207763 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.00000 | − | 6.92820i | 0.358569 | − | 0.414039i | ||||
\(281\) | − | 30.0000i | − | 1.78965i | −0.446417 | − | 0.894825i | \(-0.647300\pi\) | ||
0.446417 | − | 0.894825i | \(-0.352700\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 20.7846i | − | 1.23552i | −0.786368 | − | 0.617758i | \(-0.788041\pi\) | ||
0.786368 | − | 0.617758i | \(-0.211959\pi\) | |||||||
\(284\) | 3.00000i | 0.178017i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 10.3923i | − | 0.614510i | ||||||
\(287\) | 13.8564 | + | 12.0000i | 0.817918 | + | 0.708338i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.0000 | −0.823529 | ||||||||
\(290\) | 10.3923 | 0.610257 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 6.92820i | − | 0.405442i | ||||||
\(293\) | 17.3205 | 1.01187 | 0.505937 | − | 0.862570i | \(-0.331147\pi\) | ||||
0.505937 | + | 0.862570i | \(0.331147\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −30.0000 | −1.74667 | ||||||||
\(296\) | 2.00000i | 0.116248i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 15.0000 | 0.868927 | ||||||||
\(299\) | 5.19615 | 0.300501 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −22.0000 | − | 19.0526i | −1.26806 | − | 1.09817i | ||||
\(302\) | − | 8.00000i | − | 0.460348i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.92820i | 0.397360i | ||||||||
\(305\) | − | 48.0000i | − | 2.74847i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 31.1769i | 1.77936i | 0.456584 | + | 0.889680i | \(0.349073\pi\) | ||||
−0.456584 | + | 0.889680i | \(0.650927\pi\) | |||||||
\(308\) | −10.3923 | + | 12.0000i | −0.592157 | + | 0.683763i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −18.0000 | −1.02233 | ||||||||
\(311\) | 13.8564 | 0.785725 | 0.392862 | − | 0.919597i | \(-0.371485\pi\) | ||||
0.392862 | + | 0.919597i | \(0.371485\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.8564i | 0.783210i | 0.920133 | + | 0.391605i | \(0.128080\pi\) | ||||
−0.920133 | + | 0.391605i | \(0.871920\pi\) | |||||||
\(314\) | −15.5885 | −0.879708 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | 18.0000i | 1.01098i | 0.862832 | + | 0.505490i | \(0.168688\pi\) | ||||
−0.862832 | + | 0.505490i | \(0.831312\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.0000 | −1.00781 | ||||||||
\(320\) | −3.46410 | −0.193649 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.00000 | − | 5.19615i | −0.334367 | − | 0.289570i | ||||
\(323\) | − | 12.0000i | − | 0.667698i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 12.1244i | − | 0.672538i | ||||||
\(326\) | 11.0000i | 0.609234i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 6.92820i | − | 0.382546i | ||||||
\(329\) | −13.8564 | − | 12.0000i | −0.763928 | − | 0.661581i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.0000 | −0.934405 | −0.467202 | − | 0.884150i | \(-0.654738\pi\) | ||||
−0.467202 | + | 0.884150i | \(0.654738\pi\) | |||||||
\(332\) | 3.46410 | 0.190117 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 17.3205i | − | 0.947736i | ||||||
\(335\) | −24.2487 | −1.32485 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.0000 | 0.708155 | 0.354078 | − | 0.935216i | \(-0.384795\pi\) | ||||
0.354078 | + | 0.935216i | \(0.384795\pi\) | |||||||
\(338\) | 10.0000i | 0.543928i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.00000 | 0.325396 | ||||||||
\(341\) | 31.1769 | 1.68832 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 11.0000i | 0.593080i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 20.7846i | − | 1.11739i | ||||||
\(347\) | 18.0000i | 0.966291i | 0.875540 | + | 0.483145i | \(0.160506\pi\) | ||||
−0.875540 | + | 0.483145i | \(0.839494\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 19.0526i | − | 1.01986i | −0.860216 | − | 0.509930i | \(-0.829671\pi\) | ||
0.860216 | − | 0.509930i | \(-0.170329\pi\) | |||||||
\(350\) | −12.1244 | + | 14.0000i | −0.648074 | + | 0.748331i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.00000 | 0.319801 | ||||||||
\(353\) | 8.66025 | 0.460939 | 0.230469 | − | 0.973080i | \(-0.425974\pi\) | ||||
0.230469 | + | 0.973080i | \(0.425974\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 10.3923i | − | 0.551566i | ||||||
\(356\) | −5.19615 | −0.275396 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.00000 | 0.317110 | ||||||||
\(359\) | 27.0000i | 1.42501i | 0.701669 | + | 0.712503i | \(0.252438\pi\) | ||||
−0.701669 | + | 0.712503i | \(0.747562\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −29.0000 | −1.52632 | ||||||||
\(362\) | 1.73205 | 0.0910346 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.00000 | + | 3.46410i | −0.157243 | + | 0.181568i | ||||
\(365\) | 24.0000i | 1.25622i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.0526i | 0.994535i | 0.867597 | + | 0.497268i | \(0.165663\pi\) | ||||
−0.867597 | + | 0.497268i | \(0.834337\pi\) | |||||||
\(368\) | 3.00000i | 0.156386i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 6.92820i | − | 0.360180i | ||||||
\(371\) | 5.19615 | − | 6.00000i | 0.269771 | − | 0.311504i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.00000 | −0.207112 | −0.103556 | − | 0.994624i | \(-0.533022\pi\) | ||||
−0.103556 | + | 0.994624i | \(0.533022\pi\) | |||||||
\(374\) | −10.3923 | −0.537373 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.92820i | 0.357295i | ||||||||
\(377\) | −5.19615 | −0.267615 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.0000 | 0.821865 | 0.410932 | − | 0.911666i | \(-0.365203\pi\) | ||||
0.410932 | + | 0.911666i | \(0.365203\pi\) | |||||||
\(380\) | − | 24.0000i | − | 1.23117i | ||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −24.0000 | −1.22795 | ||||||||
\(383\) | −3.46410 | −0.177007 | −0.0885037 | − | 0.996076i | \(-0.528208\pi\) | ||||
−0.0885037 | + | 0.996076i | \(0.528208\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 36.0000 | − | 41.5692i | 1.83473 | − | 2.11856i | ||||
\(386\) | 13.0000i | 0.661683i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.92820i | 0.351726i | ||||||||
\(389\) | 6.00000i | 0.304212i | 0.988364 | + | 0.152106i | \(0.0486055\pi\) | ||||
−0.988364 | + | 0.152106i | \(0.951394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 5.19615i | − | 0.262781i | ||||||
\(392\) | 6.92820 | − | 1.00000i | 0.349927 | − | 0.0505076i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.00000 | 0.302276 | ||||||||
\(395\) | 27.7128 | 1.39438 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | −8.66025 | −0.434099 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.00000 | 0.350000 | ||||||||
\(401\) | − | 18.0000i | − | 0.898877i | −0.893311 | − | 0.449439i | \(-0.851624\pi\) | ||
0.893311 | − | 0.449439i | \(-0.148376\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.00000 | 0.448322 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.00000 | + | 5.19615i | 0.297775 | + | 0.257881i | ||||
\(407\) | 12.0000i | 0.594818i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 3.46410i | − | 0.171289i | −0.996326 | − | 0.0856444i | \(-0.972705\pi\) | ||
0.996326 | − | 0.0856444i | \(-0.0272949\pi\) | |||||||
\(410\) | 24.0000i | 1.18528i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.66025i | 0.426660i | ||||||||
\(413\) | −17.3205 | − | 15.0000i | −0.852286 | − | 0.738102i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.0000 | −0.589057 | ||||||||
\(416\) | 1.73205 | 0.0849208 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 41.5692i | 2.03322i | ||||||||
\(419\) | 29.4449 | 1.43848 | 0.719238 | − | 0.694764i | \(-0.244491\pi\) | ||||
0.719238 | + | 0.694764i | \(0.244491\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −40.0000 | −1.94948 | −0.974740 | − | 0.223341i | \(-0.928304\pi\) | ||||
−0.974740 | + | 0.223341i | \(0.928304\pi\) | |||||||
\(422\) | 7.00000i | 0.340755i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.00000 | −0.145693 | ||||||||
\(425\) | −12.1244 | −0.588118 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.0000 | − | 27.7128i | 1.16144 | − | 1.34112i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 38.1051i | − | 1.83759i | ||||||
\(431\) | − | 12.0000i | − | 0.578020i | −0.957326 | − | 0.289010i | \(-0.906674\pi\) | ||
0.957326 | − | 0.289010i | \(-0.0933260\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.7846i | 0.998845i | 0.866359 | + | 0.499422i | \(0.166454\pi\) | ||||
−0.866359 | + | 0.499422i | \(0.833546\pi\) | |||||||
\(434\) | −10.3923 | − | 9.00000i | −0.498847 | − | 0.432014i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.00000 | −0.191565 | ||||||||
\(437\) | −20.7846 | −0.994263 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.19615i | 0.247999i | 0.992282 | + | 0.123999i | \(0.0395721\pi\) | ||||
−0.992282 | + | 0.123999i | \(0.960428\pi\) | |||||||
\(440\) | −20.7846 | −0.990867 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.00000 | −0.142695 | ||||||||
\(443\) | − | 18.0000i | − | 0.855206i | −0.903967 | − | 0.427603i | \(-0.859358\pi\) | ||
0.903967 | − | 0.427603i | \(-0.140642\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.0000 | 0.853282 | ||||||||
\(446\) | 10.3923 | 0.492090 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.00000 | − | 1.73205i | −0.0944911 | − | 0.0818317i | ||||
\(449\) | 6.00000i | 0.283158i | 0.989927 | + | 0.141579i | \(0.0452178\pi\) | ||||
−0.989927 | + | 0.141579i | \(0.954782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 41.5692i | − | 1.95742i | ||||||
\(452\) | − | 6.00000i | − | 0.282216i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 25.9808i | 1.21934i | ||||||||
\(455\) | 10.3923 | − | 12.0000i | 0.487199 | − | 0.562569i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.0000 | −0.795226 | −0.397613 | − | 0.917553i | \(-0.630161\pi\) | ||||
−0.397613 | + | 0.917553i | \(0.630161\pi\) | |||||||
\(458\) | −20.7846 | −0.971201 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 10.3923i | − | 0.484544i | ||||||
\(461\) | 6.92820 | 0.322679 | 0.161339 | − | 0.986899i | \(-0.448419\pi\) | ||||
0.161339 | + | 0.986899i | \(0.448419\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.00000 | −0.185896 | −0.0929479 | − | 0.995671i | \(-0.529629\pi\) | ||||
−0.0929479 | + | 0.995671i | \(0.529629\pi\) | |||||||
\(464\) | − | 3.00000i | − | 0.139272i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24.0000 | −1.11178 | ||||||||
\(467\) | −31.1769 | −1.44270 | −0.721348 | − | 0.692573i | \(-0.756477\pi\) | ||||
−0.721348 | + | 0.692573i | \(0.756477\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.0000 | − | 12.1244i | −0.646460 | − | 0.559851i | ||||
\(470\) | − | 24.0000i | − | 1.10704i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.66025i | 0.398621i | ||||||||
\(473\) | 66.0000i | 3.03468i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 48.4974i | 2.22521i | ||||||||
\(476\) | 3.46410 | + | 3.00000i | 0.158777 | + | 0.137505i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.2487 | −1.10795 | −0.553976 | − | 0.832533i | \(-0.686890\pi\) | ||||
−0.553976 | + | 0.832533i | \(0.686890\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.46410i | 0.157949i | ||||||||
\(482\) | 13.8564 | 0.631142 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 25.0000 | 1.13636 | ||||||||
\(485\) | − | 24.0000i | − | 1.08978i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.0000 | 1.26880 | 0.634401 | − | 0.773004i | \(-0.281247\pi\) | ||||
0.634401 | + | 0.773004i | \(0.281247\pi\) | |||||||
\(488\) | −13.8564 | −0.627250 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −24.0000 | + | 3.46410i | −1.08421 | + | 0.156492i | ||||
\(491\) | − | 18.0000i | − | 0.812329i | −0.913800 | − | 0.406164i | \(-0.866866\pi\) | ||
0.913800 | − | 0.406164i | \(-0.133134\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.19615i | 0.234023i | ||||||||
\(494\) | 12.0000i | 0.539906i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.19615i | 0.233314i | ||||||||
\(497\) | 5.19615 | − | 6.00000i | 0.233079 | − | 0.269137i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.0000 | 1.25345 | 0.626726 | − | 0.779240i | \(-0.284395\pi\) | ||||
0.626726 | + | 0.779240i | \(0.284395\pi\) | |||||||
\(500\) | −6.92820 | −0.309839 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.46410i | 0.154610i | ||||||||
\(503\) | 17.3205 | 0.772283 | 0.386142 | − | 0.922440i | \(-0.373808\pi\) | ||||
0.386142 | + | 0.922440i | \(0.373808\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 18.0000i | 0.800198i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −14.0000 | −0.621150 | ||||||||
\(509\) | −3.46410 | −0.153544 | −0.0767718 | − | 0.997049i | \(-0.524461\pi\) | ||||
−0.0767718 | + | 0.997049i | \(0.524461\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.0000 | + | 13.8564i | −0.530849 | + | 0.612971i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 20.7846i | − | 0.916770i | ||||||
\(515\) | − | 30.0000i | − | 1.32196i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 41.5692i | 1.82821i | ||||||||
\(518\) | 3.46410 | − | 4.00000i | 0.152204 | − | 0.175750i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.00000 | −0.263117 | ||||||||
\(521\) | 1.73205 | 0.0758825 | 0.0379413 | − | 0.999280i | \(-0.487920\pi\) | ||||
0.0379413 | + | 0.999280i | \(0.487920\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 17.3205i | − | 0.757373i | −0.925525 | − | 0.378686i | \(-0.876376\pi\) | ||
0.925525 | − | 0.378686i | \(-0.123624\pi\) | |||||||
\(524\) | 5.19615 | 0.226995 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.00000 | 0.392419 | ||||||||
\(527\) | − | 9.00000i | − | 0.392046i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.0000 | 0.608696 | ||||||||
\(530\) | 10.3923 | 0.451413 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 12.0000 | − | 13.8564i | 0.520266 | − | 0.600751i | ||||
\(533\) | − | 12.0000i | − | 0.519778i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 7.00000i | 0.302354i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 3.46410i | − | 0.149348i | ||||||
\(539\) | 41.5692 | − | 6.00000i | 1.79051 | − | 0.258438i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.0000 | 1.63375 | 0.816874 | − | 0.576816i | \(-0.195705\pi\) | ||||
0.816874 | + | 0.576816i | \(0.195705\pi\) | |||||||
\(542\) | 12.1244 | 0.520786 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 1.73205i | − | 0.0742611i | ||||||
\(545\) | 13.8564 | 0.593543 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.00000 | 0.342055 | 0.171028 | − | 0.985266i | \(-0.445291\pi\) | ||||
0.171028 | + | 0.985266i | \(0.445291\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 42.0000 | 1.79089 | ||||||||
\(551\) | 20.7846 | 0.885454 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.0000 | + | 13.8564i | 0.680389 | + | 0.589234i | ||||
\(554\) | 20.0000i | 0.849719i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.46410i | 0.146911i | ||||||||
\(557\) | 39.0000i | 1.65248i | 0.563316 | + | 0.826242i | \(0.309525\pi\) | ||||
−0.563316 | + | 0.826242i | \(0.690475\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.0526i | 0.805837i | ||||||||
\(560\) | 6.92820 | + | 6.00000i | 0.292770 | + | 0.253546i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 30.0000 | 1.26547 | ||||||||
\(563\) | 36.3731 | 1.53294 | 0.766471 | − | 0.642279i | \(-0.222011\pi\) | ||||
0.766471 | + | 0.642279i | \(0.222011\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.7846i | 0.874415i | ||||||||
\(566\) | 20.7846 | 0.873642 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.00000 | −0.125877 | ||||||||
\(569\) | − | 18.0000i | − | 0.754599i | −0.926091 | − | 0.377300i | \(-0.876853\pi\) | ||
0.926091 | − | 0.377300i | \(-0.123147\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 41.0000 | 1.71580 | 0.857898 | − | 0.513820i | \(-0.171770\pi\) | ||||
0.857898 | + | 0.513820i | \(0.171770\pi\) | |||||||
\(572\) | 10.3923 | 0.434524 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −12.0000 | + | 13.8564i | −0.500870 | + | 0.578355i | ||||
\(575\) | 21.0000i | 0.875761i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.1051i | 1.58634i | 0.609002 | + | 0.793168i | \(0.291570\pi\) | ||||
−0.609002 | + | 0.793168i | \(0.708430\pi\) | |||||||
\(578\) | − | 14.0000i | − | 0.582323i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 10.3923i | 0.431517i | ||||||||
\(581\) | −6.92820 | − | 6.00000i | −0.287430 | − | 0.248922i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.0000 | −0.745484 | ||||||||
\(584\) | 6.92820 | 0.286691 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17.3205i | 0.715504i | ||||||||
\(587\) | −25.9808 | −1.07234 | −0.536170 | − | 0.844110i | \(-0.680130\pi\) | ||||
−0.536170 | + | 0.844110i | \(0.680130\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −36.0000 | −1.48335 | ||||||||
\(590\) | − | 30.0000i | − | 1.23508i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.00000 | −0.0821995 | ||||||||
\(593\) | 6.92820 | 0.284507 | 0.142254 | − | 0.989830i | \(-0.454565\pi\) | ||||
0.142254 | + | 0.989830i | \(0.454565\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.0000 | − | 10.3923i | −0.491952 | − | 0.426043i | ||||
\(596\) | 15.0000i | 0.614424i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.19615i | 0.212486i | ||||||||
\(599\) | 9.00000i | 0.367730i | 0.982952 | + | 0.183865i | \(0.0588609\pi\) | ||||
−0.982952 | + | 0.183865i | \(0.941139\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.1769i | 1.27173i | 0.771799 | + | 0.635866i | \(0.219357\pi\) | ||||
−0.771799 | + | 0.635866i | \(0.780643\pi\) | |||||||
\(602\) | 19.0526 | − | 22.0000i | 0.776524 | − | 0.896653i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.00000 | 0.325515 | ||||||||
\(605\) | −86.6025 | −3.52089 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1.73205i | − | 0.0703018i | −0.999382 | − | 0.0351509i | \(-0.988809\pi\) | ||
0.999382 | − | 0.0351509i | \(-0.0111912\pi\) | |||||||
\(608\) | −6.92820 | −0.280976 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 48.0000 | 1.94346 | ||||||||
\(611\) | 12.0000i | 0.485468i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.0000 | −1.13091 | −0.565455 | − | 0.824779i | \(-0.691299\pi\) | ||||
−0.565455 | + | 0.824779i | \(0.691299\pi\) | |||||||
\(614\) | −31.1769 | −1.25820 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.0000 | − | 10.3923i | −0.483494 | − | 0.418718i | ||||
\(617\) | 18.0000i | 0.724653i | 0.932051 | + | 0.362326i | \(0.118017\pi\) | ||||
−0.932051 | + | 0.362326i | \(0.881983\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 38.1051i | − | 1.53157i | −0.643094 | − | 0.765787i | \(-0.722350\pi\) | ||
0.643094 | − | 0.765787i | \(-0.277650\pi\) | |||||||
\(620\) | − | 18.0000i | − | 0.722897i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 13.8564i | 0.555591i | ||||||||
\(623\) | 10.3923 | + | 9.00000i | 0.416359 | + | 0.360577i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | −13.8564 | −0.553813 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 15.5885i | − | 0.622047i | ||||||
\(629\) | 3.46410 | 0.138123 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.00000 | 0.0796187 | 0.0398094 | − | 0.999207i | \(-0.487325\pi\) | ||||
0.0398094 | + | 0.999207i | \(0.487325\pi\) | |||||||
\(632\) | − | 8.00000i | − | 0.318223i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −18.0000 | −0.714871 | ||||||||
\(635\) | 48.4974 | 1.92456 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.0000 | − | 1.73205i | 0.475457 | − | 0.0686264i | ||||
\(638\) | − | 18.0000i | − | 0.712627i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 3.46410i | − | 0.136931i | ||||||
\(641\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.3923i | 0.409832i | 0.978780 | + | 0.204916i | \(0.0656922\pi\) | ||||
−0.978780 | + | 0.204916i | \(0.934308\pi\) | |||||||
\(644\) | 5.19615 | − | 6.00000i | 0.204757 | − | 0.236433i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.0000 | 0.472134 | ||||||||
\(647\) | −10.3923 | −0.408564 | −0.204282 | − | 0.978912i | \(-0.565486\pi\) | ||||
−0.204282 | + | 0.978912i | \(0.565486\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 51.9615i | 2.03967i | ||||||||
\(650\) | 12.1244 | 0.475556 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11.0000 | −0.430793 | ||||||||
\(653\) | 27.0000i | 1.05659i | 0.849060 | + | 0.528296i | \(0.177169\pi\) | ||||
−0.849060 | + | 0.528296i | \(0.822831\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.0000 | −0.703318 | ||||||||
\(656\) | 6.92820 | 0.270501 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 12.0000 | − | 13.8564i | 0.467809 | − | 0.540179i | ||||
\(659\) | − | 48.0000i | − | 1.86981i | −0.354892 | − | 0.934907i | \(-0.615482\pi\) | ||
0.354892 | − | 0.934907i | \(-0.384518\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 48.4974i | − | 1.88633i | −0.332323 | − | 0.943166i | \(-0.607832\pi\) | ||
0.332323 | − | 0.943166i | \(-0.392168\pi\) | |||||||
\(662\) | − | 17.0000i | − | 0.660724i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.46410i | 0.134433i | ||||||||
\(665\) | −41.5692 | + | 48.0000i | −1.61199 | + | 1.86136i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.00000 | 0.348481 | ||||||||
\(668\) | 17.3205 | 0.670151 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 24.2487i | − | 0.936809i | ||||||
\(671\) | −83.1384 | −3.20952 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.0000 | 1.19496 | 0.597481 | − | 0.801883i | \(-0.296168\pi\) | ||||
0.597481 | + | 0.801883i | \(0.296168\pi\) | |||||||
\(674\) | 13.0000i | 0.500741i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.0000 | −0.384615 | ||||||||
\(677\) | 10.3923 | 0.399409 | 0.199704 | − | 0.979856i | \(-0.436002\pi\) | ||||
0.199704 | + | 0.979856i | \(0.436002\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.0000 | − | 13.8564i | 0.460518 | − | 0.531760i | ||||
\(680\) | 6.00000i | 0.230089i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 31.1769i | 1.19383i | ||||||||
\(683\) | − | 42.0000i | − | 1.60709i | −0.595247 | − | 0.803543i | \(-0.702946\pi\) | ||
0.595247 | − | 0.803543i | \(-0.297054\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −15.5885 | − | 10.0000i | −0.595170 | − | 0.381802i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −11.0000 | −0.419371 | ||||||||
\(689\) | −5.19615 | −0.197958 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 10.3923i | − | 0.395342i | −0.980268 | − | 0.197671i | \(-0.936662\pi\) | ||
0.980268 | − | 0.197671i | \(-0.0633378\pi\) | |||||||
\(692\) | 20.7846 | 0.790112 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18.0000 | −0.683271 | ||||||||
\(695\) | − | 12.0000i | − | 0.455186i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.0000 | −0.454532 | ||||||||
\(698\) | 19.0526 | 0.721150 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −14.0000 | − | 12.1244i | −0.529150 | − | 0.458258i | ||||
\(701\) | 30.0000i | 1.13308i | 0.824033 | + | 0.566542i | \(0.191719\pi\) | ||||
−0.824033 | + | 0.566542i | \(0.808281\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 13.8564i | − | 0.522604i | ||||||
\(704\) | 6.00000i | 0.226134i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.66025i | 0.325933i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.0000 | 0.375558 | 0.187779 | − | 0.982211i | \(-0.439871\pi\) | ||||
0.187779 | + | 0.982211i | \(0.439871\pi\) | |||||||
\(710\) | 10.3923 | 0.390016 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 5.19615i | − | 0.194734i | ||||||
\(713\) | −15.5885 | −0.583792 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −36.0000 | −1.34632 | ||||||||
\(716\) | 6.00000i | 0.224231i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −27.0000 | −1.00763 | ||||||||
\(719\) | 6.92820 | 0.258378 | 0.129189 | − | 0.991620i | \(-0.458763\pi\) | ||||
0.129189 | + | 0.991620i | \(0.458763\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.0000 | − | 17.3205i | 0.558629 | − | 0.645049i | ||||
\(722\) | − | 29.0000i | − | 1.07927i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.73205i | 0.0643712i | ||||||||
\(725\) | − | 21.0000i | − | 0.779920i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.9808i | 0.963573i | 0.876289 | + | 0.481787i | \(0.160012\pi\) | ||||
−0.876289 | + | 0.481787i | \(0.839988\pi\) | |||||||
\(728\) | −3.46410 | − | 3.00000i | −0.128388 | − | 0.111187i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −24.0000 | −0.888280 | ||||||||
\(731\) | 19.0526 | 0.704684 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 36.3731i | − | 1.34347i | −0.740792 | − | 0.671735i | \(-0.765549\pi\) | ||
0.740792 | − | 0.671735i | \(-0.234451\pi\) | |||||||
\(734\) | −19.0526 | −0.703243 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.00000 | −0.110581 | ||||||||
\(737\) | 42.0000i | 1.54709i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.0000 | 0.735712 | 0.367856 | − | 0.929883i | \(-0.380092\pi\) | ||||
0.367856 | + | 0.929883i | \(0.380092\pi\) | |||||||
\(740\) | 6.92820 | 0.254686 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.00000 | + | 5.19615i | 0.220267 | + | 0.190757i | ||||
\(743\) | 9.00000i | 0.330178i | 0.986279 | + | 0.165089i | \(0.0527911\pi\) | ||||
−0.986279 | + | 0.165089i | \(0.947209\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 51.9615i | − | 1.90372i | ||||||
\(746\) | − | 4.00000i | − | 0.146450i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 10.3923i | − | 0.379980i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.00000 | −0.0729810 | −0.0364905 | − | 0.999334i | \(-0.511618\pi\) | ||||
−0.0364905 | + | 0.999334i | \(0.511618\pi\) | |||||||
\(752\) | −6.92820 | −0.252646 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 5.19615i | − | 0.189233i | ||||||
\(755\) | −27.7128 | −1.00857 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.00000 | −0.0726912 | −0.0363456 | − | 0.999339i | \(-0.511572\pi\) | ||||
−0.0363456 | + | 0.999339i | \(0.511572\pi\) | |||||||
\(758\) | 16.0000i | 0.581146i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 24.0000 | 0.870572 | ||||||||
\(761\) | −19.0526 | −0.690655 | −0.345327 | − | 0.938482i | \(-0.612232\pi\) | ||||
−0.345327 | + | 0.938482i | \(0.612232\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.00000 | + | 6.92820i | 0.289619 | + | 0.250818i | ||||
\(764\) | − | 24.0000i | − | 0.868290i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 3.46410i | − | 0.125163i | ||||||
\(767\) | 15.0000i | 0.541619i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 3.46410i | − | 0.124919i | −0.998048 | − | 0.0624593i | \(-0.980106\pi\) | ||
0.998048 | − | 0.0624593i | \(-0.0198944\pi\) | |||||||
\(770\) | 41.5692 | + | 36.0000i | 1.49805 | + | 1.29735i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −13.0000 | −0.467880 | ||||||||
\(773\) | −38.1051 | −1.37055 | −0.685273 | − | 0.728286i | \(-0.740317\pi\) | ||||
−0.685273 | + | 0.728286i | \(0.740317\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 36.3731i | 1.30656i | ||||||||
\(776\) | −6.92820 | −0.248708 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.00000 | −0.215110 | ||||||||
\(779\) | 48.0000i | 1.71978i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.0000 | −0.644091 | ||||||||
\(782\) | 5.19615 | 0.185814 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | + | 6.92820i | 0.0357143 | + | 0.247436i | ||||
\(785\) | 54.0000i | 1.92734i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.46410i | 0.123482i | 0.998092 | + | 0.0617409i | \(0.0196653\pi\) | ||||
−0.998092 | + | 0.0617409i | \(0.980335\pi\) | |||||||
\(788\) | 6.00000i | 0.213741i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 27.7128i | 0.985978i | ||||||||
\(791\) | −10.3923 | + | 12.0000i | −0.369508 | + | 0.426671i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.0000 | −0.852265 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 8.66025i | − | 0.306955i | ||||||
\(797\) | 31.1769 | 1.10434 | 0.552171 | − | 0.833731i | \(-0.313799\pi\) | ||||
0.552171 | + | 0.833731i | \(0.313799\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.0000 | 0.424529 | ||||||||
\(800\) | 7.00000i | 0.247487i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 18.0000 | 0.635602 | ||||||||
\(803\) | 41.5692 | 1.46695 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −18.0000 | + | 20.7846i | −0.634417 | + | 0.732561i | ||||
\(806\) | 9.00000i | 0.317011i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 24.0000i | − | 0.843795i | −0.906644 | − | 0.421898i | \(-0.861364\pi\) | ||
0.906644 | − | 0.421898i | \(-0.138636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 31.1769i | − | 1.09477i | −0.836881 | − | 0.547385i | \(-0.815623\pi\) | ||
0.836881 | − | 0.547385i | \(-0.184377\pi\) | |||||||
\(812\) | −5.19615 | + | 6.00000i | −0.182349 | + | 0.210559i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −12.0000 | −0.420600 | ||||||||
\(815\) | 38.1051 | 1.33476 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 76.2102i | − | 2.66626i | ||||||
\(818\) | 3.46410 | 0.121119 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −24.0000 | −0.838116 | ||||||||
\(821\) | 33.0000i | 1.15171i | 0.817553 | + | 0.575854i | \(0.195330\pi\) | ||||
−0.817553 | + | 0.575854i | \(0.804670\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.0000 | 0.488009 | 0.244005 | − | 0.969774i | \(-0.421539\pi\) | ||||
0.244005 | + | 0.969774i | \(0.421539\pi\) | |||||||
\(824\) | −8.66025 | −0.301694 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 15.0000 | − | 17.3205i | 0.521917 | − | 0.602658i | ||||
\(827\) | − | 48.0000i | − | 1.66912i | −0.550914 | − | 0.834562i | \(-0.685721\pi\) | ||
0.550914 | − | 0.834562i | \(-0.314279\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 27.7128i | − | 0.962506i | −0.876582 | − | 0.481253i | \(-0.840182\pi\) | ||
0.876582 | − | 0.481253i | \(-0.159818\pi\) | |||||||
\(830\) | − | 12.0000i | − | 0.416526i | ||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.73205i | 0.0600481i | ||||||||
\(833\) | −1.73205 | − | 12.0000i | −0.0600120 | − | 0.415775i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −60.0000 | −2.07639 | ||||||||
\(836\) | −41.5692 | −1.43770 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 29.4449i | 1.01716i | ||||||||
\(839\) | −17.3205 | −0.597970 | −0.298985 | − | 0.954258i | \(-0.596648\pi\) | ||||
−0.298985 | + | 0.954258i | \(0.596648\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.0000 | 0.689655 | ||||||||
\(842\) | − | 40.0000i | − | 1.37849i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.00000 | −0.240950 | ||||||||
\(845\) | 34.6410 | 1.19169 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −50.0000 | − | 43.3013i | −1.71802 | − | 1.48785i | ||||
\(848\) | − | 3.00000i | − | 0.103020i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 12.1244i | − | 0.415862i | ||||||
\(851\) | − | 6.00000i | − | 0.205677i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 12.1244i | − | 0.415130i | −0.978221 | − | 0.207565i | \(-0.933446\pi\) | ||
0.978221 | − | 0.207565i | \(-0.0665539\pi\) | |||||||
\(854\) | 27.7128 | + | 24.0000i | 0.948313 | + | 0.821263i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.5167 | −0.769154 | −0.384577 | − | 0.923093i | \(-0.625653\pi\) | ||||
−0.384577 | + | 0.923093i | \(0.625653\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45.0333i | 1.53652i | 0.640140 | + | 0.768259i | \(0.278876\pi\) | ||||
−0.640140 | + | 0.768259i | \(0.721124\pi\) | |||||||
\(860\) | 38.1051 | 1.29937 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.0000 | 0.408722 | ||||||||
\(863\) | − | 45.0000i | − | 1.53182i | −0.642949 | − | 0.765909i | \(-0.722289\pi\) | ||
0.642949 | − | 0.765909i | \(-0.277711\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −72.0000 | −2.44807 | ||||||||
\(866\) | −20.7846 | −0.706290 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 9.00000 | − | 10.3923i | 0.305480 | − | 0.352738i | ||||
\(869\) | − | 48.0000i | − | 1.62829i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.1244i | 0.410818i | ||||||||
\(872\) | − | 4.00000i | − | 0.135457i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 20.7846i | − | 0.703050i | ||||||
\(875\) | 13.8564 | + | 12.0000i | 0.468432 | + | 0.405674i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.0000 | 1.08056 | 0.540282 | − | 0.841484i | \(-0.318318\pi\) | ||||
0.540282 | + | 0.841484i | \(0.318318\pi\) | |||||||
\(878\) | −5.19615 | −0.175362 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 20.7846i | − | 0.700649i | ||||||
\(881\) | −5.19615 | −0.175063 | −0.0875314 | − | 0.996162i | \(-0.527898\pi\) | ||||
−0.0875314 | + | 0.996162i | \(0.527898\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.0000 | 0.841317 | 0.420658 | − | 0.907219i | \(-0.361799\pi\) | ||||
0.420658 | + | 0.907219i | \(0.361799\pi\) | |||||||
\(884\) | − | 3.00000i | − | 0.100901i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 18.0000 | 0.604722 | ||||||||
\(887\) | −48.4974 | −1.62838 | −0.814192 | − | 0.580596i | \(-0.802820\pi\) | ||||
−0.814192 | + | 0.580596i | \(0.802820\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28.0000 | + | 24.2487i | 0.939090 | + | 0.813276i | ||||
\(890\) | 18.0000i | 0.603361i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.3923i | 0.347960i | ||||||||
\(893\) | − | 48.0000i | − | 1.60626i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 20.7846i | − | 0.694753i | ||||||
\(896\) | 1.73205 | − | 2.00000i | 0.0578638 | − | 0.0668153i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.00000 | −0.200223 | ||||||||
\(899\) | 15.5885 | 0.519904 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.19615i | 0.173109i | ||||||||
\(902\) | 41.5692 | 1.38410 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.00000 | 0.199557 | ||||||||
\(905\) | − | 6.00000i | − | 0.199447i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.0000 | 0.929725 | 0.464862 | − | 0.885383i | \(-0.346104\pi\) | ||||
0.464862 | + | 0.885383i | \(0.346104\pi\) | |||||||
\(908\) | −25.9808 | −0.862202 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 12.0000 | + | 10.3923i | 0.397796 | + | 0.344502i | ||||
\(911\) | 24.0000i | 0.795155i | 0.917568 | + | 0.397578i | \(0.130149\pi\) | ||||
−0.917568 | + | 0.397578i | \(0.869851\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.7846i | 0.687870i | ||||||||
\(914\) | − | 17.0000i | − | 0.562310i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 20.7846i | − | 0.686743i | ||||||
\(917\) | −10.3923 | − | 9.00000i | −0.343184 | − | 0.297206i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.0000 | −1.05558 | −0.527791 | − | 0.849374i | \(-0.676980\pi\) | ||||
−0.527791 | + | 0.849374i | \(0.676980\pi\) | |||||||
\(920\) | 10.3923 | 0.342624 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.92820i | 0.228168i | ||||||||
\(923\) | −5.19615 | −0.171033 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.0000 | −0.460317 | ||||||||
\(926\) | − | 4.00000i | − | 0.131448i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.00000 | 0.0984798 | ||||||||
\(929\) | −6.92820 | −0.227307 | −0.113653 | − | 0.993520i | \(-0.536255\pi\) | ||||
−0.113653 | + | 0.993520i | \(0.536255\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −48.0000 | + | 6.92820i | −1.57314 | + | 0.227063i | ||||
\(932\) | − | 24.0000i | − | 0.786146i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 31.1769i | − | 1.02014i | ||||||
\(935\) | 36.0000i | 1.17733i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 24.2487i | − | 0.792171i | −0.918214 | − | 0.396085i | \(-0.870368\pi\) | ||
0.918214 | − | 0.396085i | \(-0.129632\pi\) | |||||||
\(938\) | 12.1244 | − | 14.0000i | 0.395874 | − | 0.457116i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 24.0000 | 0.782794 | ||||||||
\(941\) | −24.2487 | −0.790485 | −0.395243 | − | 0.918577i | \(-0.629340\pi\) | ||||
−0.395243 | + | 0.918577i | \(0.629340\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.7846i | 0.676840i | ||||||||
\(944\) | −8.66025 | −0.281867 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −66.0000 | −2.14585 | ||||||||
\(947\) | 12.0000i | 0.389948i | 0.980808 | + | 0.194974i | \(0.0624622\pi\) | ||||
−0.980808 | + | 0.194974i | \(0.937538\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.0000 | 0.389536 | ||||||||
\(950\) | −48.4974 | −1.57346 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.00000 | + | 3.46410i | −0.0972306 | + | 0.112272i | ||||
\(953\) | − | 18.0000i | − | 0.583077i | −0.956559 | − | 0.291539i | \(-0.905833\pi\) | ||
0.956559 | − | 0.291539i | \(-0.0941672\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 83.1384i | 2.69030i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 24.2487i | − | 0.783440i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.00000 | 0.129032 | ||||||||
\(962\) | −3.46410 | −0.111687 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 13.8564i | 0.446285i | ||||||||
\(965\) | 45.0333 | 1.44967 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.00000 | 0.0643157 | 0.0321578 | − | 0.999483i | \(-0.489762\pi\) | ||||
0.0321578 | + | 0.999483i | \(0.489762\pi\) | |||||||
\(968\) | 25.0000i | 0.803530i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 24.0000 | 0.770594 | ||||||||
\(971\) | 22.5167 | 0.722594 | 0.361297 | − | 0.932451i | \(-0.382334\pi\) | ||||
0.361297 | + | 0.932451i | \(0.382334\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.00000 | − | 6.92820i | 0.192351 | − | 0.222108i | ||||
\(974\) | 28.0000i | 0.897178i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 13.8564i | − | 0.443533i | ||||||
\(977\) | − | 24.0000i | − | 0.767828i | −0.923369 | − | 0.383914i | \(-0.874576\pi\) | ||
0.923369 | − | 0.383914i | \(-0.125424\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 31.1769i | − | 0.996419i | ||||||
\(980\) | −3.46410 | − | 24.0000i | −0.110657 | − | 0.766652i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 18.0000 | 0.574403 | ||||||||
\(983\) | 38.1051 | 1.21536 | 0.607682 | − | 0.794180i | \(-0.292099\pi\) | ||||
0.607682 | + | 0.794180i | \(0.292099\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 20.7846i | − | 0.662253i | ||||||
\(986\) | −5.19615 | −0.165479 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12.0000 | −0.381771 | ||||||||
\(989\) | − | 33.0000i | − | 1.04934i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.00000 | −0.0635321 | −0.0317660 | − | 0.999495i | \(-0.510113\pi\) | ||||
−0.0317660 | + | 0.999495i | \(0.510113\pi\) | |||||||
\(992\) | −5.19615 | −0.164978 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.00000 | + | 5.19615i | 0.190308 | + | 0.164812i | ||||
\(995\) | 30.0000i | 0.951064i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46.7654i | 1.48107i | 0.672015 | + | 0.740537i | \(0.265429\pi\) | ||||
−0.672015 | + | 0.740537i | \(0.734571\pi\) | |||||||
\(998\) | 28.0000i | 0.886325i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 378.2.d.c.377.4 | yes | 4 | |
3.2 | odd | 2 | inner | 378.2.d.c.377.1 | ✓ | 4 | |
4.3 | odd | 2 | 3024.2.k.f.1889.3 | 4 | |||
7.6 | odd | 2 | inner | 378.2.d.c.377.3 | yes | 4 | |
9.2 | odd | 6 | 1134.2.m.d.377.1 | 4 | |||
9.4 | even | 3 | 1134.2.m.a.755.1 | 4 | |||
9.5 | odd | 6 | 1134.2.m.a.755.2 | 4 | |||
9.7 | even | 3 | 1134.2.m.d.377.2 | 4 | |||
12.11 | even | 2 | 3024.2.k.f.1889.1 | 4 | |||
21.20 | even | 2 | inner | 378.2.d.c.377.2 | yes | 4 | |
28.27 | even | 2 | 3024.2.k.f.1889.2 | 4 | |||
63.13 | odd | 6 | 1134.2.m.d.755.1 | 4 | |||
63.20 | even | 6 | 1134.2.m.a.377.1 | 4 | |||
63.34 | odd | 6 | 1134.2.m.a.377.2 | 4 | |||
63.41 | even | 6 | 1134.2.m.d.755.2 | 4 | |||
84.83 | odd | 2 | 3024.2.k.f.1889.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.2.d.c.377.1 | ✓ | 4 | 3.2 | odd | 2 | inner | |
378.2.d.c.377.2 | yes | 4 | 21.20 | even | 2 | inner | |
378.2.d.c.377.3 | yes | 4 | 7.6 | odd | 2 | inner | |
378.2.d.c.377.4 | yes | 4 | 1.1 | even | 1 | trivial | |
1134.2.m.a.377.1 | 4 | 63.20 | even | 6 | |||
1134.2.m.a.377.2 | 4 | 63.34 | odd | 6 | |||
1134.2.m.a.755.1 | 4 | 9.4 | even | 3 | |||
1134.2.m.a.755.2 | 4 | 9.5 | odd | 6 | |||
1134.2.m.d.377.1 | 4 | 9.2 | odd | 6 | |||
1134.2.m.d.377.2 | 4 | 9.7 | even | 3 | |||
1134.2.m.d.755.1 | 4 | 63.13 | odd | 6 | |||
1134.2.m.d.755.2 | 4 | 63.41 | even | 6 | |||
3024.2.k.f.1889.1 | 4 | 12.11 | even | 2 | |||
3024.2.k.f.1889.2 | 4 | 28.27 | even | 2 | |||
3024.2.k.f.1889.3 | 4 | 4.3 | odd | 2 | |||
3024.2.k.f.1889.4 | 4 | 84.83 | odd | 2 |