Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1024,2,Mod(129,1024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1024, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1024.129");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1024 = 2^{10} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1024.g (of order \(8\), degree \(4\), 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: | \(8.17668116698\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{8})\) |
Coefficient field: | \(\Q(\zeta_{48})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 897.2 | ||
Root | \(0.130526 - 0.991445i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.897 |
Dual form | 1024.2.g.a.129.2 |
$q$-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 \(\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(1023\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.184592 | − | 0.445644i | −0.106574 | − | 0.257293i | 0.861592 | − | 0.507602i | \(-0.169468\pi\) |
−0.968166 | + | 0.250309i | \(0.919468\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.36603 | − | 0.565826i | −0.610905 | − | 0.253045i | 0.0557103 | − | 0.998447i | \(-0.482258\pi\) |
−0.666615 | + | 0.745402i | \(0.732258\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.135131 | + | 0.135131i | 0.0510746 | + | 0.0510746i | 0.732183 | − | 0.681108i | \(-0.238502\pi\) |
−0.681108 | + | 0.732183i | \(0.738502\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.95680 | − | 1.95680i | 0.652265 | − | 0.652265i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.29398 | + | 3.12395i | −0.390151 | + | 0.941907i | 0.599756 | + | 0.800183i | \(0.295264\pi\) |
−0.989906 | + | 0.141724i | \(0.954736\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.29788 | + | 0.951812i | −0.637316 | + | 0.263985i | −0.677858 | − | 0.735193i | \(-0.737092\pi\) |
0.0405417 | + | 0.999178i | \(0.487092\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.713208i | 0.184150i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 3.11099i | − | 0.754525i | −0.926106 | − | 0.377263i | \(-0.876865\pi\) | ||
0.926106 | − | 0.377263i | \(-0.123135\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.99813 | − | 2.48451i | 1.37607 | − | 0.569985i | 0.432639 | − | 0.901567i | \(-0.357582\pi\) |
0.943426 | + | 0.331582i | \(0.107582\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.0352762 | − | 0.0851642i | 0.00769789 | − | 0.0185844i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.18330 | − | 5.18330i | 1.08079 | − | 1.08079i | 0.0843577 | − | 0.996436i | \(-0.473116\pi\) |
0.996436 | − | 0.0843577i | \(-0.0268838\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.98967 | − | 1.98967i | −0.397934 | − | 0.397934i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.57018 | − | 1.06460i | −0.494631 | − | 0.204883i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.79485 | − | 4.33315i | −0.333295 | − | 0.804646i | −0.998326 | − | 0.0578306i | \(-0.981582\pi\) |
0.665031 | − | 0.746816i | \(-0.268418\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.44503 | −1.33717 | −0.668584 | − | 0.743637i | \(-0.733099\pi\) | ||||
−0.668584 | + | 0.743637i | \(0.733099\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.63103 | 0.283926 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.108131 | − | 0.261052i | −0.0182775 | − | 0.0441259i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.44414 | − | 3.49768i | −1.38821 | − | 0.575015i | −0.441545 | − | 0.897239i | \(-0.645569\pi\) |
−0.946663 | + | 0.322224i | \(0.895569\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.848339 | + | 0.848339i | 0.135843 | + | 0.135843i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.27792 | − | 4.27792i | 0.668098 | − | 0.668098i | −0.289177 | − | 0.957276i | \(-0.593382\pi\) |
0.957276 | + | 0.289177i | \(0.0933817\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.79448 | + | 4.33227i | −0.273656 | + | 0.660664i | −0.999634 | − | 0.0270537i | \(-0.991387\pi\) |
0.725978 | + | 0.687718i | \(0.241387\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.78024 | + | 1.56583i | −0.563525 | + | 0.233420i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.0952i | 1.76426i | 0.471002 | + | 0.882132i | \(0.343892\pi\) | ||||
−0.471002 | + | 0.882132i | \(0.656108\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 6.96348i | − | 0.994783i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.38639 | + | 0.574263i | −0.194134 | + | 0.0804129i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.41956 | − | 3.42713i | 0.194992 | − | 0.470752i | −0.795897 | − | 0.605432i | \(-0.793001\pi\) |
0.990889 | + | 0.134680i | \(0.0430005\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.53523 | − | 3.53523i | 0.476690 | − | 0.476690i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.21441 | − | 2.21441i | −0.293306 | − | 0.293306i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.81074 | − | 1.16425i | −0.365927 | − | 0.151572i | 0.192140 | − | 0.981367i | \(-0.438457\pi\) |
−0.558068 | + | 0.829795i | \(0.688457\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.61571 | − | 8.72911i | −0.462945 | − | 1.11765i | −0.967183 | − | 0.254083i | \(-0.918226\pi\) |
0.504238 | − | 0.863565i | \(-0.331774\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.528846 | 0.0666284 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.67752 | 0.456140 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.96182 | − | 7.15047i | −0.361844 | − | 0.873569i | −0.995031 | − | 0.0995698i | \(-0.968253\pi\) |
0.633186 | − | 0.773999i | \(-0.281747\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.26670 | − | 1.35311i | −0.393265 | − | 0.162896i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.86020 | − | 2.86020i | −0.339444 | − | 0.339444i | 0.516714 | − | 0.856158i | \(-0.327155\pi\) |
−0.856158 | + | 0.516714i | \(0.827155\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.49697 | − | 2.49697i | 0.292249 | − | 0.292249i | −0.545719 | − | 0.837968i | \(-0.683744\pi\) |
0.837968 | + | 0.545719i | \(0.183744\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.519408 | + | 1.25396i | −0.0599760 | + | 0.144795i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.596999 | + | 0.247285i | −0.0680343 | + | 0.0281807i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 8.39967i | − | 0.945036i | −0.881321 | − | 0.472518i | \(-0.843345\pi\) | ||
0.881321 | − | 0.472518i | \(-0.156655\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 6.96008i | − | 0.773342i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.0852 | − | 5.42005i | 1.43628 | − | 0.594928i | 0.477389 | − | 0.878692i | \(-0.341583\pi\) |
0.958894 | + | 0.283764i | \(0.0915832\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.76028 | + | 4.24969i | −0.190929 | + | 0.460943i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.59973 | + | 1.59973i | −0.171509 | + | 0.171509i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.96713 | + | 4.96713i | 0.526514 | + | 0.526514i | 0.919531 | − | 0.393017i | \(-0.128569\pi\) |
−0.393017 | + | 0.919531i | \(0.628569\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.439133 | − | 0.181895i | −0.0460336 | − | 0.0190677i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.37429 | + | 3.31784i | 0.142508 | + | 0.344044i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.59940 | −0.984877 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.87492 | −0.291903 | −0.145952 | − | 0.989292i | \(-0.546624\pi\) | ||||
−0.145952 | + | 0.989292i | \(0.546624\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.58087 | + | 8.64500i | 0.359891 | + | 0.868855i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.24674 | + | 3.00170i | 0.721078 | + | 0.298680i | 0.712880 | − | 0.701286i | \(-0.247390\pi\) |
0.00819809 | + | 0.999966i | \(0.497390\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.12067 | + | 4.12067i | 0.406022 | + | 0.406022i | 0.880349 | − | 0.474327i | \(-0.157308\pi\) |
−0.474327 | + | 0.880349i | \(0.657308\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.0963763 | + | 0.0963763i | −0.00940537 | + | 0.00940537i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.30261 | + | 5.55900i | −0.222602 | + | 0.537409i | −0.995242 | − | 0.0974360i | \(-0.968936\pi\) |
0.772640 | + | 0.634845i | \(0.218936\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.19445 | + | 1.73740i | −0.401756 | + | 0.166413i | −0.574406 | − | 0.818571i | \(-0.694767\pi\) |
0.172650 | + | 0.984983i | \(0.444767\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.40873i | 0.418458i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.86370i | 0.927899i | 0.885862 | + | 0.463950i | \(0.153568\pi\) | ||||
−0.885862 | + | 0.463950i | \(0.846432\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.0134 | + | 4.14767i | −0.933752 | + | 0.386773i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.63397 | + | 6.35898i | −0.243511 | + | 0.587888i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.420390 | − | 0.420390i | 0.0385371 | − | 0.0385371i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.306509 | − | 0.306509i | −0.0278645 | − | 0.0278645i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.69610 | − | 1.11676i | −0.243099 | − | 0.100695i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.42126 | + | 10.6739i | 0.395450 | + | 0.954700i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.4530 | 1.37123 | 0.685614 | − | 0.727965i | \(-0.259534\pi\) | ||||
0.685614 | + | 0.727965i | \(0.259534\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.26190 | 0.199149 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.03911 | − | 14.5797i | −0.527639 | − | 1.27383i | −0.933066 | − | 0.359706i | \(-0.882877\pi\) |
0.405427 | − | 0.914128i | \(-0.367123\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.14626 | + | 0.474798i | 0.0993937 | + | 0.0411702i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.90855 | + | 2.90855i | 0.250328 | + | 0.250328i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.83183 | + | 5.83183i | −0.498247 | + | 0.498247i | −0.910892 | − | 0.412645i | \(-0.864605\pi\) |
0.412645 | + | 0.910892i | \(0.364605\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.02980 | − | 7.31458i | 0.256984 | − | 0.620414i | −0.741752 | − | 0.670674i | \(-0.766005\pi\) |
0.998736 | + | 0.0502598i | \(0.0160049\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.39015 | − | 2.23267i | 0.453932 | − | 0.188025i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 8.41009i | − | 0.703287i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.93477i | 0.575901i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.10323 | + | 1.28540i | −0.255950 | + | 0.106018i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.71965 | − | 6.56583i | 0.222803 | − | 0.537893i | −0.772466 | − | 0.635056i | \(-0.780977\pi\) |
0.995268 | + | 0.0971630i | \(0.0309768\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.7733 | + | 10.7733i | −0.876722 | + | 0.876722i | −0.993194 | − | 0.116472i | \(-0.962842\pi\) |
0.116472 | + | 0.993194i | \(0.462842\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.08757 | − | 6.08757i | −0.492151 | − | 0.492151i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.1701 | + | 4.21260i | 0.816883 | + | 0.338364i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.220757 | + | 0.532954i | 0.0176183 | + | 0.0425344i | 0.932444 | − | 0.361315i | \(-0.117672\pi\) |
−0.914826 | + | 0.403849i | \(0.867672\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.78932 | −0.141902 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.40085 | 0.110402 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.26188 | + | 22.3602i | 0.725447 | + | 1.75138i | 0.657201 | + | 0.753715i | \(0.271740\pi\) |
0.0682454 | + | 0.997669i | \(0.478260\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.22803 | − | 0.922880i | −0.173452 | − | 0.0718461i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.2141 | − | 11.2141i | −0.867770 | − | 0.867770i | 0.124455 | − | 0.992225i | \(-0.460282\pi\) |
−0.992225 | + | 0.124455i | \(0.960282\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.81809 | + | 4.81809i | −0.370623 | + | 0.370623i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.87544 | − | 16.5988i | 0.525778 | − | 1.26934i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.1974 | − | 8.36603i | 1.53558 | − | 0.636057i | 0.554940 | − | 0.831890i | \(-0.312741\pi\) |
0.980637 | + | 0.195833i | \(0.0627410\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 0.537730i | − | 0.0406486i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.46750i | 0.110304i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.1545 | + | 5.86300i | −1.05796 | + | 0.438221i | −0.842727 | − | 0.538342i | \(-0.819051\pi\) |
−0.215233 | + | 0.976563i | \(0.569051\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.03749 | − | 9.74737i | 0.300104 | − | 0.724516i | −0.699843 | − | 0.714296i | \(-0.746747\pi\) |
0.999948 | − | 0.0102198i | \(-0.00325311\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.22264 | + | 3.22264i | −0.238225 | + | 0.238225i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.55583 | + | 9.55583i | 0.702559 | + | 0.702559i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.71858 | + | 4.02557i | 0.710693 | + | 0.294379i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.203449 | − | 0.491170i | −0.0147988 | − | 0.0357274i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.9763 | 1.66250 | 0.831252 | − | 0.555896i | \(-0.187625\pi\) | ||||
0.831252 | + | 0.555896i | \(0.187625\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.2368 | −1.31271 | −0.656355 | − | 0.754452i | \(-0.727903\pi\) | ||||
−0.656355 | + | 0.754452i | \(0.727903\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.678840 | − | 1.63887i | −0.0486128 | − | 0.117362i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.6780 | + | 8.56510i | 1.47324 | + | 0.610238i | 0.967596 | − | 0.252502i | \(-0.0812534\pi\) |
0.505648 | + | 0.862740i | \(0.331253\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.62301 | + | 4.62301i | 0.327717 | + | 0.327717i | 0.851718 | − | 0.524001i | \(-0.175561\pi\) |
−0.524001 | + | 0.851718i | \(0.675561\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.63984 | + | 2.63984i | −0.186200 | + | 0.186200i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.343002 | − | 0.828081i | 0.0240741 | − | 0.0581199i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.26430 | + | 3.42319i | −0.577204 | + | 0.239086i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 20.2853i | − | 1.40993i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.9528i | 1.51851i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.75999 | + | 3.21429i | −0.534220 | + | 0.221281i | −0.633450 | − | 0.773783i | \(-0.718362\pi\) |
0.0992305 | + | 0.995064i | \(0.468362\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.746663 | + | 1.80260i | −0.0511605 | + | 0.123512i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.90262 | − | 4.90262i | 0.334356 | − | 0.334356i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.00605 | − | 1.00605i | −0.0682953 | − | 0.0682953i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.57368 | − | 0.651841i | −0.106340 | − | 0.0440473i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.96108 | + | 7.14867i | 0.199183 | + | 0.480871i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.64899 | −0.445249 | −0.222625 | − | 0.974904i | \(-0.571462\pi\) | ||||
−0.222625 | + | 0.974904i | \(0.571462\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.78675 | −0.519116 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.41272 | + | 5.82482i | 0.160138 | + | 0.386607i | 0.983500 | − | 0.180910i | \(-0.0579043\pi\) |
−0.823362 | + | 0.567517i | \(0.807904\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.0487 | + | 6.23338i | 0.994446 | + | 0.411913i | 0.819758 | − | 0.572711i | \(-0.194108\pi\) |
0.174689 | + | 0.984624i | \(0.444108\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.220402 | + | 0.220402i | 0.0145014 | + | 0.0145014i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −17.8296 | + | 17.8296i | −1.16806 | + | 1.16806i | −0.185390 | + | 0.982665i | \(0.559355\pi\) |
−0.982665 | + | 0.185390i | \(0.940645\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.84377 | − | 16.5223i | 0.446438 | − | 1.07780i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.74326 | + | 1.55051i | −0.243151 | + | 0.100716i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.7833i | 0.956254i | 0.878291 | + | 0.478127i | \(0.158684\pi\) | ||||
−0.878291 | + | 0.478127i | \(0.841316\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.03919i | 0.131356i | 0.997841 | + | 0.0656779i | \(0.0209210\pi\) | ||||
−0.997841 | + | 0.0656779i | \(0.979079\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.8122 | + | 4.47858i | −0.693606 | + | 0.287301i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.94012 | + | 9.51229i | −0.251725 | + | 0.607718i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.4182 | + | 11.4182i | −0.726522 | + | 0.726522i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.83083 | − | 4.83083i | −0.306141 | − | 0.306141i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.03025 | + | 3.32624i | 0.506865 | + | 0.209950i | 0.621436 | − | 0.783465i | \(-0.286549\pi\) |
−0.114571 | + | 0.993415i | \(0.536549\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.48528 | + | 22.8995i | 0.596335 | + | 1.43968i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.21878 | 0.138946 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.91308 | 0.181713 | 0.0908563 | − | 0.995864i | \(-0.471040\pi\) | ||||
0.0908563 | + | 0.995864i | \(0.471040\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.668419 | − | 1.61371i | −0.0415335 | − | 0.100271i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.9913 | − | 4.96694i | −0.742240 | − | 0.307446i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.119315 | + | 0.119315i | 0.00735727 | + | 0.00735727i | 0.710776 | − | 0.703419i | \(-0.248344\pi\) |
−0.703419 | + | 0.710776i | \(0.748344\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.87832 | + | 3.87832i | −0.238243 | + | 0.238243i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.29668 | − | 3.13046i | 0.0793556 | − | 0.191581i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 28.9705 | − | 12.0000i | 1.76636 | − | 0.731651i | 0.770851 | − | 0.637016i | \(-0.219831\pi\) |
0.995512 | − | 0.0946356i | \(-0.0301686\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 18.1938i | − | 1.10520i | −0.833447 | − | 0.552599i | \(-0.813636\pi\) | ||
0.833447 | − | 0.552599i | \(-0.186364\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.229273i | 0.0138762i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.79022 | − | 3.64103i | 0.530070 | − | 0.219562i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.88315 | + | 9.37475i | −0.233316 | + | 0.563274i | −0.996564 | − | 0.0828318i | \(-0.973604\pi\) |
0.763248 | + | 0.646106i | \(0.223604\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −14.5684 | + | 14.5684i | −0.872188 | + | 0.872188i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.5916 | + | 12.5916i | 0.751151 | + | 0.751151i | 0.974694 | − | 0.223543i | \(-0.0717623\pi\) |
−0.223543 | + | 0.974694i | \(0.571762\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.0121 | − | 6.21821i | −0.892376 | − | 0.369634i | −0.111092 | − | 0.993810i | \(-0.535435\pi\) |
−0.781284 | + | 0.624176i | \(0.785435\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.77197 | + | 4.27792i | 0.104963 | + | 0.253402i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.15616 | 0.0682457 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.32175 | 0.430691 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.530686 | + | 1.28119i | 0.0311094 | + | 0.0751047i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.5429 | + | 5.60966i | 0.791186 | + | 0.327720i | 0.741420 | − | 0.671041i | \(-0.234153\pi\) |
0.0497657 | + | 0.998761i | \(0.484153\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.18078 | + | 3.18078i | 0.185192 | + | 0.185192i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.65153 | − | 6.65153i | 0.385961 | − | 0.385961i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.97706 | + | 16.8441i | −0.403494 | + | 0.974121i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.827912 | + | 0.342932i | −0.0477200 | + | 0.0197663i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 3.78356i | − | 0.217360i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.9700i | 0.799923i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.1636 | + | 4.62413i | −0.637143 | + | 0.263913i | −0.677784 | − | 0.735261i | \(-0.737060\pi\) |
0.0406418 | + | 0.999174i | \(0.487060\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.07571 | − | 2.59700i | 0.0611951 | − | 0.147738i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.03317 | + | 5.03317i | −0.285405 | + | 0.285405i | −0.835260 | − | 0.549855i | \(-0.814683\pi\) |
0.549855 | + | 0.835260i | \(0.314683\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.58454 | − | 2.58454i | −0.146087 | − | 0.146087i | 0.630281 | − | 0.776367i | \(-0.282940\pi\) |
−0.776367 | + | 0.630281i | \(0.782940\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.722417 | − | 0.299235i | −0.0407036 | − | 0.0168600i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.21371 | − | 19.8296i | −0.461328 | − | 1.11374i | −0.967853 | − | 0.251518i | \(-0.919070\pi\) |
0.506525 | − | 0.862225i | \(-0.330930\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.8591 | 0.887937 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.90238 | 0.161995 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.72927 | − | 18.6601i | −0.430068 | − | 1.03828i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.46580 | + | 2.67822i | 0.358658 | + | 0.148561i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.54852 | + | 1.54852i | 0.0856336 | + | 0.0856336i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.63443 | + | 1.63443i | −0.0901090 | + | 0.0901090i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.83918 | − | 11.6828i | 0.265986 | − | 0.642146i | −0.733301 | − | 0.679904i | \(-0.762022\pi\) |
0.999287 | + | 0.0377578i | \(0.0120216\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −23.3677 | + | 9.67922i | −1.28054 | + | 0.530418i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.4436i | 0.625231i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 17.3525i | − | 0.945254i | −0.881263 | − | 0.472627i | \(-0.843306\pi\) | ||
0.881263 | − | 0.472627i | \(-0.156694\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.39570 | − | 1.82076i | 0.238742 | − | 0.0988901i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.63375 | − | 23.2579i | 0.521697 | − | 1.25949i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.88689 | − | 1.88689i | 0.101883 | − | 0.101883i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.69677 | + | 3.69677i | 0.199028 | + | 0.199028i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.1152 | + | 6.67513i | 0.865109 | + | 0.358340i | 0.770703 | − | 0.637194i | \(-0.219905\pi\) |
0.0944054 | + | 0.995534i | \(0.469905\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.198581 | − | 0.479418i | −0.0106298 | − | 0.0256626i | 0.918476 | − | 0.395478i | \(-0.129421\pi\) |
−0.929105 | + | 0.369815i | \(0.879421\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.91925 | 0.369322 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.30663 | −0.122769 | −0.0613846 | − | 0.998114i | \(-0.519552\pi\) | ||||
−0.0613846 | + | 0.998114i | \(0.519552\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.28873 | + | 5.52549i | 0.121473 | + | 0.293262i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.264945 | − | 0.109744i | −0.0140224 | − | 0.00580826i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.02599 | − | 6.02599i | −0.318039 | − | 0.318039i | 0.529974 | − | 0.848014i | \(-0.322202\pi\) |
−0.848014 | + | 0.529974i | \(0.822202\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.3698 | − | 16.3698i | 0.861567 | − | 0.861567i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.0800150 | + | 0.193173i | −0.00419970 | + | 0.0101390i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.82378 | + | 1.99808i | −0.252488 | + | 0.104584i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 5.67199i | − | 0.296076i | −0.988982 | − | 0.148038i | \(-0.952704\pi\) | ||
0.988982 | − | 0.148038i | \(-0.0472957\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 16.7420i | − | 0.871555i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.654936 | − | 0.271283i | 0.0340026 | − | 0.0140843i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.3210 | + | 32.1599i | −0.689738 | + | 1.66517i | 0.0555710 | + | 0.998455i | \(0.482302\pi\) |
−0.745309 | + | 0.666719i | \(0.767698\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.94062 | − | 3.94062i | 0.203493 | − | 0.203493i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.24869 | + | 8.24869i | 0.424829 | + | 0.424829i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.90292 | − | 1.20243i | −0.149113 | − | 0.0617647i | 0.306879 | − | 0.951749i | \(-0.400715\pi\) |
−0.455992 | + | 0.889984i | \(0.650715\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.85249 | − | 6.88652i | −0.146138 | − | 0.352807i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −26.6159 | −1.36001 | −0.680004 | − | 0.733208i | \(-0.738022\pi\) | ||||
−0.680004 | + | 0.733208i | \(0.738022\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.955435 | 0.0486935 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.96592 | + | 11.9888i | 0.252432 | + | 0.609425i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.3383 | − | 4.69648i | −0.574875 | − | 0.238121i | 0.0762534 | − | 0.997088i | \(-0.475704\pi\) |
−0.651129 | + | 0.758967i | \(0.725704\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.1252 | − | 16.1252i | −0.815486 | − | 0.815486i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.38259 | + | 5.38259i | −0.271516 | + | 0.271516i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.75275 | + | 11.4742i | −0.239137 | + | 0.577327i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.2139 | − | 5.47337i | 0.663185 | − | 0.274700i | −0.0255930 | − | 0.999672i | \(-0.508147\pi\) |
0.688778 | + | 0.724972i | \(0.258147\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 0.598470i | − | 0.0299610i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.8160i | 0.639999i | 0.947418 | + | 0.320000i | \(0.103683\pi\) | ||||
−0.947418 | + | 0.320000i | \(0.896317\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.1078 | − | 7.08627i | 0.852199 | − | 0.352992i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.93820 | + | 9.50765i | −0.195691 | + | 0.472439i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.8532 | − | 21.8532i | 1.08322 | − | 1.08322i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.5505 | − | 10.5505i | −0.521689 | − | 0.521689i | 0.396392 | − | 0.918081i | \(-0.370262\pi\) |
−0.918081 | + | 0.396392i | \(0.870262\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.67543 | + | 1.52241i | 0.181296 | + | 0.0750951i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.222492 | − | 0.537143i | −0.0109481 | − | 0.0264311i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −20.9415 | −1.02798 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.81897 | −0.187016 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.94989 | − | 21.6069i | −0.437231 | − | 1.05557i | −0.976901 | − | 0.213692i | \(-0.931451\pi\) |
0.539671 | − | 0.841876i | \(-0.318549\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.3466 | − | 14.2268i | −1.67395 | − | 0.693372i | −0.674939 | − | 0.737873i | \(-0.735830\pi\) |
−0.999009 | + | 0.0445009i | \(0.985830\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 23.6678 | + | 23.6678i | 1.15077 | + | 1.15077i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.18983 | + | 6.18983i | −0.300251 | + | 0.300251i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.690976 | − | 1.66816i | 0.0334387 | − | 0.0807281i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.74791 | + | 1.55243i | −0.180951 | + | 0.0749522i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.4006i | 1.31984i | 0.751335 | + | 0.659921i | \(0.229410\pi\) | ||||
−0.751335 | + | 0.659921i | \(0.770590\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 17.6255i | − | 0.847027i | −0.905890 | − | 0.423514i | \(-0.860797\pi\) | ||
0.905890 | − | 0.423514i | \(-0.139203\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.09044 | − | 1.28010i | 0.148175 | − | 0.0613762i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.2122 | − | 43.9681i | 0.871206 | − | 2.10328i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.9463 | − | 12.9463i | 0.617894 | − | 0.617894i | −0.327097 | − | 0.944991i | \(-0.606070\pi\) |
0.944991 | + | 0.327097i | \(0.106070\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.6261 | − | 13.6261i | −0.648862 | − | 0.648862i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −30.8594 | − | 12.7824i | −1.46617 | − | 0.607309i | −0.500191 | − | 0.865915i | \(-0.666737\pi\) |
−0.965983 | + | 0.258606i | \(0.916737\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.97469 | − | 9.59575i | −0.188418 | − | 0.454882i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.42805 | −0.162141 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.0878169 | 0.00414433 | 0.00207217 | − | 0.999998i | \(-0.499340\pi\) | ||||
0.00207217 | + | 0.999998i | \(0.499340\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.82845 | + | 18.8996i | 0.368628 | + | 0.889946i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.78975 | + | 2.81241i | 0.319010 | + | 0.132138i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.496946 | + | 0.496946i | 0.0232972 | + | 0.0232972i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.3331 | − | 11.3331i | 0.530141 | − | 0.530141i | −0.390473 | − | 0.920614i | \(-0.627689\pi\) |
0.920614 | + | 0.390473i | \(0.127689\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.31196 | + | 7.99579i | −0.154589 | + | 0.373211i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.5941 | + | 6.04506i | −0.679713 | + | 0.281546i | −0.695707 | − | 0.718326i | \(-0.744909\pi\) |
0.0159940 | + | 0.999872i | \(0.494909\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.2329i | 0.986779i | 0.869809 | + | 0.493389i | \(0.164242\pi\) | ||||
−0.869809 | + | 0.493389i | \(0.835758\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 5.30986i | − | 0.246239i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.22554 | − | 3.82134i | 0.426907 | − | 0.176831i | −0.158876 | − | 0.987299i | \(-0.550787\pi\) |
0.585783 | + | 0.810468i | \(0.300787\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.566015 | − | 1.36648i | 0.0261361 | − | 0.0630982i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.196758 | − | 0.196758i | 0.00906613 | − | 0.00906613i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.2118 | − | 11.2118i | −0.515517 | − | 0.515517i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.8776 | − | 6.99094i | −0.774399 | − | 0.320766i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.92839 | − | 9.48398i | −0.179869 | − | 0.434241i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.02741 | −0.184017 | −0.0920085 | − | 0.995758i | \(-0.529329\pi\) | ||||
−0.0920085 | + | 0.995758i | \(0.529329\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.7327 | 1.03652 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.258585 | − | 0.624279i | −0.0117660 | − | 0.0284057i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.92721 | + | 1.62670i | 0.178325 | + | 0.0738648i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.69427 | + | 6.69427i | 0.303346 | + | 0.303346i | 0.842322 | − | 0.538975i | \(-0.181188\pi\) |
−0.538975 | + | 0.842322i | \(0.681188\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.25501 | − | 8.25501i | 0.373305 | − | 0.373305i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.1010 | + | 31.6286i | −0.591239 | + | 1.42738i | 0.291068 | + | 0.956702i | \(0.405989\pi\) |
−0.882307 | + | 0.470675i | \(0.844011\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.4804 | + | 5.58376i | −0.607126 | + | 0.251480i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 13.8354i | − | 0.621857i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 0.773002i | − | 0.0346739i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.6636 | − | 6.07387i | 0.656434 | − | 0.271904i | −0.0295034 | − | 0.999565i | \(-0.509393\pi\) |
0.685937 | + | 0.727661i | \(0.259393\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.92746 | + | 7.06750i | −0.130789 | + | 0.315753i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.7932 | − | 16.7932i | 0.748773 | − | 0.748773i | −0.225476 | − | 0.974249i | \(-0.572394\pi\) |
0.974249 | + | 0.225476i | \(0.0723938\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.20080 | − | 8.20080i | −0.364931 | − | 0.364931i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.03654 | + | 1.25778i | 0.134857 | + | 0.0558598i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.68700 | + | 8.90119i | 0.163423 | + | 0.394539i | 0.984285 | − | 0.176589i | \(-0.0565063\pi\) |
−0.820862 | + | 0.571127i | \(0.806506\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.674835 | 0.0298530 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −18.0613 | −0.797424 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.29736 | − | 7.96053i | −0.145299 | − | 0.350783i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −37.7848 | − | 15.6510i | −1.66177 | − | 0.688329i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.45654 | − | 7.45654i | −0.327306 | − | 0.327306i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.4229 | − | 25.4229i | 1.11380 | − | 1.11380i | 0.121167 | − | 0.992632i | \(-0.461336\pi\) |
0.992632 | − | 0.121167i | \(-0.0386636\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.59867 | + | 8.68795i | −0.157359 | + | 0.379897i | −0.982821 | − | 0.184559i | \(-0.940914\pi\) |
0.825463 | + | 0.564457i | \(0.190914\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.239636 | + | 0.0992607i | −0.0104586 | + | 0.00433209i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 23.1614i | 1.00893i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 30.7332i | − | 1.33623i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.77824 | + | 3.22185i | −0.337547 | + | 0.139816i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.75836 | + | 13.9019i | −0.249422 | + | 0.602158i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.29085 | − | 6.29085i | 0.271977 | − | 0.271977i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.22562 | + | 5.22562i | 0.225502 | + | 0.225502i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 21.7536 | + | 9.01063i | 0.936993 | + | 0.388115i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.2665 | − | 29.6140i | −0.527379 | − | 1.27320i | −0.933235 | − | 0.359268i | \(-0.883026\pi\) |
0.405856 | − | 0.913937i | \(-0.366974\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.08915 | −0.218396 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.71279 | 0.287545 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.72724 | − | 11.4126i | −0.202122 | − | 0.487966i | 0.790020 | − | 0.613081i | \(-0.210070\pi\) |
−0.992142 | + | 0.125115i | \(0.960070\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −24.1563 | − | 10.0059i | −1.03097 | − | 0.427040i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21.5315 | − | 21.5315i | −0.917273 | − | 0.917273i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.13505 | − | 1.13505i | 0.0482673 | − | 0.0482673i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.49457 | − | 6.02243i | 0.105889 | − | 0.255638i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.0704 | − | 5.82814i | 0.596180 | − | 0.246946i | −0.0641266 | − | 0.997942i | \(-0.520426\pi\) |
0.660307 | + | 0.750996i | \(0.270426\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 11.6630i | − | 0.493293i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 5.07412i | − | 0.214229i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 43.5982 | − | 18.0589i | 1.83744 | − | 0.761094i | 0.878340 | − | 0.478036i | \(-0.158651\pi\) |
0.959103 | − | 0.283057i | \(-0.0913487\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.58114 | − | 13.4741i | 0.234800 | − | 0.566858i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.940520 | − | 0.940520i | 0.0394981 | − | 0.0394981i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.6968 | + | 16.6968i | 0.699965 | + | 0.699965i | 0.964403 | − | 0.264438i | \(-0.0851863\pi\) |
−0.264438 | + | 0.964403i | \(0.585186\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.7136 | + | 10.6509i | 1.07608 | + | 0.445728i | 0.849133 | − | 0.528179i | \(-0.177125\pi\) |
0.226949 | + | 0.973907i | \(0.427125\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.24123 | − | 10.2392i | −0.177180 | − | 0.427750i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −20.6261 | −0.860168 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 42.1981 | 1.75673 | 0.878365 | − | 0.477991i | \(-0.158635\pi\) | ||||
0.878365 | + | 0.477991i | \(0.158635\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.36636 | + | 8.12710i | 0.139901 | + | 0.337751i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.50062 | + | 1.03579i | 0.103743 | + | 0.0429719i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.86929 | + | 8.86929i | 0.367328 | + | 0.367328i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.19615 | − | 7.19615i | 0.297524 | − | 0.297524i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.18852 | + | 17.3546i | −0.296702 | + | 0.716302i | 0.703284 | + | 0.710909i | \(0.251716\pi\) |
−0.999985 | + | 0.00539239i | \(0.998284\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −44.6563 | + | 18.4972i | −1.84003 | + | 0.762166i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 10.7961i | − | 0.444091i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.516291i | 0.0212015i | 0.999944 | + | 0.0106008i | \(0.00337439\pi\) | ||||
−0.999944 | + | 0.0106008i | \(0.996626\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.812131 | + | 0.336396i | −0.0332941 | + | 0.0137909i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.20685 | − | 2.91359i | 0.0493930 | − | 0.119245i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.6567 | − | 13.6567i | 0.557999 | − | 0.557999i | −0.370738 | − | 0.928737i | \(-0.620895\pi\) |
0.928737 | + | 0.370738i | \(0.120895\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.24556 | − | 3.24556i | −0.132389 | − | 0.132389i | 0.637807 | − | 0.770196i | \(-0.279842\pi\) |
−0.770196 | + | 0.637807i | \(0.779842\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −19.7877 | − | 8.19633i | −0.805817 | − | 0.333780i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.245268 | + | 0.592131i | 0.00997158 | + | 0.0240735i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.8854 | 0.563591 | 0.281795 | − | 0.959475i | \(-0.409070\pi\) | ||||
0.281795 | + | 0.959475i | \(0.409070\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.432345 | −0.0175195 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.5123 | − | 27.7932i | −0.465739 | − | 1.12439i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.9929 | + | 8.69556i | 0.847896 | + | 0.351210i | 0.763962 | − | 0.645261i | \(-0.223251\pi\) |
0.0839342 | + | 0.996471i | \(0.473251\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.05105 | + | 3.05105i | 0.123030 | + | 0.123030i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.1547 | − | 11.1547i | 0.449072 | − | 0.449072i | −0.445974 | − | 0.895046i | \(-0.647143\pi\) |
0.895046 | + | 0.445974i | \(0.147143\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.165589 | − | 0.399768i | 0.00665559 | − | 0.0160680i | −0.920517 | − | 0.390703i | \(-0.872232\pi\) |
0.927172 | + | 0.374635i | \(0.122232\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.8402 | + | 7.80385i | −0.756029 | + | 0.313158i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.34242i | 0.0537830i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 3.01337i | − | 0.120535i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.78313 | − | 4.05231i | 0.390701 | − | 0.161834i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.8812 | + | 26.2696i | −0.433863 | + | 1.04744i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.48708 | + | 8.48708i | −0.337865 | + | 0.337865i | −0.855563 | − | 0.517698i | \(-0.826789\pi\) |
0.517698 | + | 0.855563i | \(0.326789\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.86486 | + | 2.86486i | 0.113868 | + | 0.113868i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −21.1091 | − | 8.74369i | −0.837690 | − | 0.346983i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.62792 | + | 16.0012i | 0.262608 | + | 0.633991i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.1937 | −0.442814 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.4227 | 0.885644 | 0.442822 | − | 0.896610i | \(-0.353977\pi\) | ||||
0.442822 | + | 0.896610i | \(0.353977\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.05780 | + | 9.79639i | 0.160024 | + | 0.386332i | 0.983472 | − | 0.181060i | \(-0.0579527\pi\) |
−0.823448 | + | 0.567391i | \(0.807953\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.08981 | − | 1.27984i | −0.121661 | − | 0.0503937i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.4018 | + | 26.4018i | 1.03796 | + | 1.03796i | 0.999250 | + | 0.0387106i | \(0.0123251\pi\) |
0.0387106 | + | 0.999250i | \(0.487675\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.27410 | − | 7.27410i | 0.285534 | − | 0.285534i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.262632 | + | 0.634051i | −0.0102934 | + | 0.0248504i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26.1421 | − | 10.8284i | 1.02302 | − | 0.423748i | 0.192831 | − | 0.981232i | \(-0.438233\pi\) |
0.830188 | + | 0.557484i | \(0.188233\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.3333i | 0.911708i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 9.77214i | − | 0.381247i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.1434 | + | 6.27260i | −0.589903 | + | 0.244346i | −0.657609 | − | 0.753359i | \(-0.728432\pi\) |
0.0677059 | + | 0.997705i | \(0.478432\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.77294 | − | 16.3513i | 0.263437 | − | 0.635993i | −0.735710 | − | 0.677297i | \(-0.763151\pi\) |
0.999147 | + | 0.0413040i | \(0.0131512\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.63917 | − | 2.63917i | 0.102497 | − | 0.102497i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.29717 | − | 1.29717i | −0.0503022 | − | 0.0503022i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −31.7633 | − | 13.1568i | −1.22988 | − | 0.509433i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.22735 | + | 2.96308i | 0.0474521 | + | 0.114559i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 31.9480 | 1.23334 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −49.6916 | −1.91547 | −0.957735 | − | 0.287654i | \(-0.907125\pi\) | ||||
−0.957735 | + | 0.287654i | \(0.907125\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.99559 | + | 7.23200i | 0.115300 | + | 0.278360i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.7931 | − | 9.44122i | −0.876011 | − | 0.362856i | −0.101063 | − | 0.994880i | \(-0.532224\pi\) |
−0.774948 | + | 0.632024i | \(0.782224\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.388489 | − | 0.388489i | −0.0149088 | − | 0.0149088i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.15043 | − | 2.15043i | 0.0824046 | − | 0.0824046i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.7660 | + | 25.9915i | −0.411950 | + | 0.994535i | 0.572664 | + | 0.819790i | \(0.305910\pi\) |
−0.984614 | + | 0.174745i | \(0.944090\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.2662 | − | 4.66662i | 0.430460 | − | 0.178302i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 7.85700i | − | 0.299763i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.22627i | 0.351493i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.53096 | + | 0.634146i | −0.0582406 | + | 0.0241240i | −0.411614 | − | 0.911358i | \(-0.635035\pi\) |
0.353373 | + | 0.935483i | \(0.385035\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.684318 | + | 1.65209i | −0.0259951 | + | 0.0627577i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.27756 | + | 8.27756i | −0.313986 | + | 0.313986i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.3085 | − | 13.3085i | −0.504097 | − | 0.504097i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.2369 | + | 4.65446i | 0.425017 | + | 0.176048i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.23819 | − | 22.3030i | −0.348921 | − | 0.842371i | −0.996748 | − | 0.0805829i | \(-0.974322\pi\) |
0.647826 | − | 0.761788i | \(-0.275678\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −59.3391 | −2.23802 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.62639 | −0.324888 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.573636 | + | 1.38488i | 0.0215738 | + | 0.0520837i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.3249 | + | 4.69095i | 0.425317 | + | 0.176172i | 0.585066 | − | 0.810985i | \(-0.301068\pi\) |
−0.159749 | + | 0.987158i | \(0.551068\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.4364 | − | 16.4364i | −0.616414 | − | 0.616414i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −38.5899 | + | 38.5899i | −1.44520 | + | 1.44520i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.75865 | + | 11.4884i | −0.177963 | + | 0.429641i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.58811 | − | 2.72888i | 0.246037 | − | 0.101912i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.8205i | 0.701888i | 0.936397 | + | 0.350944i | \(0.114139\pi\) | ||||
−0.936397 | + | 0.350944i | \(0.885861\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.11366i | 0.0414748i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.908754 | − | 0.376418i | 0.0337969 | − | 0.0139991i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.05038 | + | 12.1927i | −0.187566 | + | 0.452825i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.7869 | + | 16.7869i | −0.622593 | + | 0.622593i | −0.946194 | − | 0.323601i | \(-0.895107\pi\) |
0.323601 | + | 0.946194i | \(0.395107\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −10.7729 | − | 10.7729i | −0.398994 | − | 0.398994i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.4776 | + | 5.58262i | 0.498488 | + | 0.206481i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.7909 | + | 30.8799i | 0.472442 | + | 1.14058i | 0.963081 | + | 0.269213i | \(0.0867636\pi\) |
−0.490639 | + | 0.871363i | \(0.663236\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.96641 | 0.183189 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 26.1703 | 0.963995 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.05208 | − | 12.1968i | −0.185844 | − | 0.448667i | 0.803308 | − | 0.595564i | \(-0.203071\pi\) |
−0.989152 | + | 0.146897i | \(0.953071\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.19615 | + | 2.98074i | 0.264357 | + | 0.109500i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.2144 | − | 14.2144i | −0.521476 | − | 0.521476i | 0.396541 | − | 0.918017i | \(-0.370211\pi\) |
−0.918017 | + | 0.396541i | \(0.870211\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.43023 | + | 7.43023i | −0.272223 | + | 0.272223i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.9991 | − | 36.2109i | 0.548787 | − | 1.32489i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.06234 | + | 0.440038i | −0.0388172 | + | 0.0160786i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 17.6604i | − | 0.644438i | −0.946665 | − | 0.322219i | \(-0.895571\pi\) | ||
0.946665 | − | 0.322219i | \(-0.104429\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 4.19263i | − | 0.152788i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.8125 | − | 8.62082i | 0.757444 | − | 0.313744i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.26500 | + | 5.46821i | −0.0823230 | + | 0.198745i | −0.959681 | − | 0.281091i | \(-0.909304\pi\) |
0.877358 | + | 0.479836i | \(0.159304\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.45412 | − | 8.45412i | 0.306865 | − | 0.306865i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.84304 | + | 8.84304i | 0.320560 | + | 0.320560i | 0.848982 | − | 0.528422i | \(-0.177216\pi\) |
−0.528422 | + | 0.848982i | \(0.677216\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.801575 | − | 0.332023i | −0.0290190 | − | 0.0120200i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.87127 | + | 11.7603i | 0.176121 | + | 0.425194i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.56688 | 0.273224 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.3761 | −1.16751 | −0.583755 | − | 0.811930i | \(-0.698417\pi\) | ||||
−0.583755 | + | 0.811930i | \(0.698417\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.537730 | − | 1.29820i | −0.0193659 | − | 0.0467534i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21.7148 | + | 8.99455i | 0.781026 | + | 0.323511i | 0.737329 | − | 0.675533i | \(-0.236087\pi\) |
0.0436963 | + | 0.999045i | \(0.486087\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.8131 | + | 14.8131i | 0.532104 | + | 0.532104i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.595754 | + | 0.595754i | −0.0213726 | + | 0.0213726i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15.0310 | − | 36.2880i | 0.538541 | − | 1.30015i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.6362 | − | 5.23408i | 0.452158 | − | 0.187290i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 13.0478i | 0.466289i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 0.852939i | − | 0.0304427i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −50.7364 | + | 21.0157i | −1.80856 | + | 0.749129i | −0.825869 | + | 0.563862i | \(0.809315\pi\) |
−0.982688 | + | 0.185266i | \(0.940685\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.0311474 | − | 0.0751966i | 0.00110888 | − | 0.00267707i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.33289 | + | 1.33289i | −0.0473921 | + | 0.0473921i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.6169 | + | 16.6169i | 0.590085 | + | 0.590085i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.44425 | + | 1.01244i | 0.0866888 | + | 0.0359077i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.76906 | − | 16.3420i | −0.239772 | − | 0.578862i | 0.757487 | − | 0.652851i | \(-0.226427\pi\) |
−0.997259 | + | 0.0739887i | \(0.976427\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 37.6280 | 1.33118 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 19.4393 | 0.686854 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.56938 | + | 11.0315i | 0.161250 | + | 0.389292i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.91359 | − | 0.792635i | −0.0674452 | − | 0.0279367i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.6954 | − | 10.6954i | −0.376497 | − | 0.376497i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.39282 | + | 4.39282i | −0.154443 | + | 0.154443i | −0.780099 | − | 0.625656i | \(-0.784831\pi\) |
0.625656 | + | 0.780099i | \(0.284831\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.2324 | − | 27.1174i | 0.394422 | − | 0.952219i | −0.594542 | − | 0.804065i | \(-0.702667\pi\) |
0.988964 | − | 0.148155i | \(-0.0473334\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.10798 | + | 3.35844i | −0.284359 | + | 0.117786i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 35.7852i | − | 1.25350i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30.4439i | 1.06510i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.21522 | + | 0.503362i | −0.0424633 | + | 0.0175889i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.8289 | − | 45.4570i | 0.657134 | − | 1.58646i | −0.145077 | − | 0.989420i | \(-0.546343\pi\) |
0.802211 | − | 0.597041i | \(-0.203657\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.4059 | − | 14.4059i | 0.502158 | − | 0.502158i | −0.409950 | − | 0.912108i | \(-0.634454\pi\) |
0.912108 | + | 0.409950i | \(0.134454\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.24521 | − | 3.24521i | −0.112984 | − | 0.112984i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.7434 | + | 5.27851i | 0.443133 | + | 0.183552i | 0.593082 | − | 0.805142i | \(-0.297911\pi\) |
−0.149949 | + | 0.988694i | \(0.547911\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.9104 | − | 48.0679i | −0.691516 | − | 1.66947i | −0.741704 | − | 0.670728i | \(-0.765982\pi\) |
0.0501876 | − | 0.998740i | \(-0.484018\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.89460 | 0.169792 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21.6633 | −0.750589 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.97348 | + | 21.6639i | 0.310540 | + | 0.749710i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 19.1351 | + | 7.92600i | 0.661404 | + | 0.273963i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.48780 | − | 5.48780i | −0.189460 | − | 0.189460i | 0.606003 | − | 0.795463i | \(-0.292772\pi\) |
−0.795463 | + | 0.606003i | \(0.792772\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.95137 | − | 4.95137i | 0.170737 | − | 0.170737i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.28706 | − | 7.93568i | 0.113213 | − | 0.273319i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.30784 | − | 3.85544i | 0.320200 | − | 0.132631i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 0.0828376i | − | 0.00284633i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.83788i | 0.268995i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −61.8981 | + | 25.6390i | −2.12184 | + | 0.878894i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.19878 | + | 19.7936i | −0.280721 | + | 0.677720i | −0.999853 | − | 0.0171533i | \(-0.994540\pi\) |
0.719132 | + | 0.694874i | \(0.244540\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −18.7841 | + | 18.7841i | −0.642401 | + | 0.642401i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.5086 | + | 25.5086i | 0.871358 | + | 0.871358i | 0.992620 | − | 0.121263i | \(-0.0386943\pi\) |
−0.121263 | + | 0.992620i | \(0.538694\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.8638 | + | 8.64207i | 0.711864 | + | 0.294864i | 0.709076 | − | 0.705132i | \(-0.249112\pi\) |
0.00278818 | + | 0.999996i | \(0.499112\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.213417 | − | 0.515234i | −0.00727323 | − | 0.0175591i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.587161 | −0.0199872 | −0.00999360 | − | 0.999950i | \(-0.503181\pi\) | ||||
−0.00999360 | + | 0.999950i | \(0.503181\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −32.3238 | −1.09904 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.35154 | − | 3.26290i | −0.0459006 | − | 0.110814i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26.2402 | + | 10.8690i | 0.890136 | + | 0.368706i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.6118 | + | 13.6118i | 0.461218 | + | 0.461218i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.62562 | + | 5.62562i | −0.190398 | + | 0.190398i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.844919 | + | 2.03982i | −0.0285635 | + | 0.0689583i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.93596 | + | 0.801899i | −0.0653726 | + | 0.0270782i | −0.415130 | − | 0.909762i | \(-0.636264\pi\) |
0.349758 | + | 0.936840i | \(0.386264\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 7.07082i | − | 0.238493i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 6.47745i | − | 0.218231i | −0.994029 | − | 0.109115i | \(-0.965198\pi\) | ||
0.994029 | − | 0.109115i | \(-0.0348018\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.1091 | − | 5.84419i | 0.474810 | − | 0.196673i | −0.132428 | − | 0.991193i | \(-0.542277\pi\) |
0.607238 | + | 0.794520i | \(0.292277\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.830351 | − | 2.00464i | 0.0279119 | − | 0.0673854i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26.9437 | + | 26.9437i | −0.904679 | + | 0.904679i | −0.995837 | − | 0.0911573i | \(-0.970943\pi\) |
0.0911573 | + | 0.995837i | \(0.470943\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.08817 | + | 2.08817i | 0.0700349 | + | 0.0700349i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 21.7430 | + | 9.00623i | 0.728416 | + | 0.301720i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 30.0506 | + | 72.5485i | 1.00560 | + | 2.42774i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.6529 | 0.757203 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.79440 | 0.293636 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.3627 | + | 32.2605i | 0.445672 | + | 1.07595i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.6617 | − | 4.41624i | −0.355194 | − | 0.147126i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.305652 | + | 0.305652i | 0.0101714 | + | 0.0101714i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.0306 | + | 11.0306i | −0.366671 | + | 0.366671i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.84992 | + | 9.29454i | −0.127835 | + | 0.308620i | −0.974819 | − | 0.222998i | \(-0.928416\pi\) |
0.846984 | + | 0.531618i | \(0.178416\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 20.0541 | − | 8.30669i | 0.665153 | − | 0.275515i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.1254i | 0.567389i | 0.958915 | + | 0.283694i | \(0.0915601\pi\) | ||||
−0.958915 | + | 0.283694i | \(0.908440\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 47.8909i | 1.58496i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.22567 | − | 2.57876i | 0.205814 | − | 0.0852511i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.15409 | − | 2.78623i | 0.0381116 | − | 0.0920095i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29.1179 | + | 29.1179i | −0.960510 | + | 0.960510i | −0.999249 | − | 0.0387392i | \(-0.987666\pi\) |
0.0387392 | + | 0.999249i | \(0.487666\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.12144 | + | 4.12144i | 0.135806 | + | 0.135806i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.29477 | + | 3.85002i | 0.305941 | + | 0.126725i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.84182 | + | 23.7603i | 0.323597 | + | 0.781232i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.1266 | 0.529668 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.16235 | 0.0709445 | 0.0354722 | − | 0.999371i | \(-0.488706\pi\) | ||||
0.0354722 | + | 0.999371i | \(0.488706\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.3008 | − | 41.7679i | −0.567011 | − | 1.36889i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.17209 | + | 1.31392i | 0.103850 | + | 0.0430159i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.9981 | − | 10.9981i | −0.359675 | − | 0.359675i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.7802 | + | 26.7802i | −0.874871 | + | 0.874871i | −0.992998 | − | 0.118127i | \(-0.962311\pi\) |
0.118127 | + | 0.992998i | \(0.462311\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.674701 | + | 1.62887i | −0.0220180 | + | 0.0531562i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 39.3660 | − | 16.3059i | 1.28329 | − | 0.531558i | 0.366314 | − | 0.930491i | \(-0.380620\pi\) |
0.916980 | + | 0.398933i | \(0.130620\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 44.3475i | − | 1.44415i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.786068i | 0.0255708i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.12544 | − | 0.466171i | 0.0365718 | − | 0.0151485i | −0.364323 | − | 0.931273i | \(-0.618699\pi\) |
0.400894 | + | 0.916124i | \(0.368699\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.36109 | + | 8.11439i | −0.109106 | + | 0.263404i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.32078 | + | 7.32078i | −0.237393 | + | 0.237393i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −31.4229 | − | 31.4229i | −1.01789 | − | 1.01789i | −0.999837 | − | 0.0180517i | \(-0.994254\pi\) |
−0.0180517 | − | 0.999837i | \(-0.505746\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −31.3862 | − | 13.0006i | −1.01563 | − | 0.420689i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.92746 | − | 7.06750i | −0.0946312 | − | 0.228460i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.57612 | −0.0508955 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.4285 | 0.788017 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.37208 | + | 15.3836i | 0.205337 | + | 0.495728i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 24.9119 | + | 10.3188i | 0.801941 | + | 0.332175i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.7661 | − | 17.7661i | −0.571319 | − | 0.571319i | 0.361178 | − | 0.932497i | \(-0.382375\pi\) |
−0.932497 | + | 0.361178i | \(0.882375\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.88901 | + | 6.88901i | −0.221307 | + | 0.221307i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.2407 | − | 53.6939i | 0.713739 | − | 1.72312i | 0.0232989 | − | 0.999729i | \(-0.492583\pi\) |
0.690440 | − | 0.723390i | \(-0.257417\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.39784 | − | 0.579005i | 0.0448128 | − | 0.0185620i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 3.37583i | − | 0.108113i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.3541i | 0.523215i | 0.965174 | + | 0.261608i | \(0.0842527\pi\) | ||||
−0.965174 | + | 0.261608i | \(0.915747\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −21.9445 | + | 9.08969i | −0.701348 | + | 0.290508i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.80795 | + | 11.6074i | −0.153506 | + | 0.370596i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.23497 | − | 5.23497i | 0.166970 | − | 0.166970i | −0.618676 | − | 0.785646i | \(-0.712331\pi\) |
0.785646 | + | 0.618676i | \(0.212331\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23.4003 | − | 23.4003i | −0.745595 | − | 0.745595i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.03008 | + | 0.426672i | 0.0327877 | + | 0.0135811i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.1541 | + | 31.7568i | 0.418276 | + | 1.00981i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41.6039 | 1.32159 | 0.660796 | − | 0.750566i | \(-0.270219\pi\) | ||||
0.660796 | + | 0.750566i | \(0.270219\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.09966 | −0.193567 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.69933 | − | 8.93098i | −0.117277 | − | 0.283131i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.3764 | + | 12.1681i | 0.930361 | + | 0.385368i | 0.795815 | − | 0.605539i | \(-0.207043\pi\) |
0.134545 | + | 0.990907i | \(0.457043\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 17.9793 | + | 17.9793i | 0.568840 | + | 0.568840i |
(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 | 1024.2.g.a.897.2 | yes | 16 | |
4.3 | odd | 2 | inner | 1024.2.g.a.897.3 | yes | 16 | |
8.3 | odd | 2 | 1024.2.g.f.897.2 | yes | 16 | ||
8.5 | even | 2 | 1024.2.g.f.897.3 | yes | 16 | ||
16.3 | odd | 4 | 1024.2.g.g.385.2 | yes | 16 | ||
16.5 | even | 4 | 1024.2.g.d.385.2 | yes | 16 | ||
16.11 | odd | 4 | 1024.2.g.d.385.3 | yes | 16 | ||
16.13 | even | 4 | 1024.2.g.g.385.3 | yes | 16 | ||
32.3 | odd | 8 | 1024.2.g.f.129.2 | yes | 16 | ||
32.5 | even | 8 | 1024.2.g.g.641.3 | yes | 16 | ||
32.11 | odd | 8 | 1024.2.g.d.641.3 | yes | 16 | ||
32.13 | even | 8 | inner | 1024.2.g.a.129.2 | ✓ | 16 | |
32.19 | odd | 8 | inner | 1024.2.g.a.129.3 | yes | 16 | |
32.21 | even | 8 | 1024.2.g.d.641.2 | yes | 16 | ||
32.27 | odd | 8 | 1024.2.g.g.641.2 | yes | 16 | ||
32.29 | even | 8 | 1024.2.g.f.129.3 | yes | 16 | ||
64.13 | even | 16 | 4096.2.a.i.1.5 | 8 | |||
64.19 | odd | 16 | 4096.2.a.i.1.6 | 8 | |||
64.45 | even | 16 | 4096.2.a.s.1.4 | 8 | |||
64.51 | odd | 16 | 4096.2.a.s.1.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1024.2.g.a.129.2 | ✓ | 16 | 32.13 | even | 8 | inner | |
1024.2.g.a.129.3 | yes | 16 | 32.19 | odd | 8 | inner | |
1024.2.g.a.897.2 | yes | 16 | 1.1 | even | 1 | trivial | |
1024.2.g.a.897.3 | yes | 16 | 4.3 | odd | 2 | inner | |
1024.2.g.d.385.2 | yes | 16 | 16.5 | even | 4 | ||
1024.2.g.d.385.3 | yes | 16 | 16.11 | odd | 4 | ||
1024.2.g.d.641.2 | yes | 16 | 32.21 | even | 8 | ||
1024.2.g.d.641.3 | yes | 16 | 32.11 | odd | 8 | ||
1024.2.g.f.129.2 | yes | 16 | 32.3 | odd | 8 | ||
1024.2.g.f.129.3 | yes | 16 | 32.29 | even | 8 | ||
1024.2.g.f.897.2 | yes | 16 | 8.3 | odd | 2 | ||
1024.2.g.f.897.3 | yes | 16 | 8.5 | even | 2 | ||
1024.2.g.g.385.2 | yes | 16 | 16.3 | odd | 4 | ||
1024.2.g.g.385.3 | yes | 16 | 16.13 | even | 4 | ||
1024.2.g.g.641.2 | yes | 16 | 32.27 | odd | 8 | ||
1024.2.g.g.641.3 | yes | 16 | 32.5 | even | 8 | ||
4096.2.a.i.1.5 | 8 | 64.13 | even | 16 | |||
4096.2.a.i.1.6 | 8 | 64.19 | odd | 16 | |||
4096.2.a.s.1.3 | 8 | 64.51 | odd | 16 | |||
4096.2.a.s.1.4 | 8 | 64.45 | even | 16 |