Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(401,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.401");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.l (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.4767670494822400.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 400) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1201.3 | ||
Root | \(-1.41313 - 0.0554252i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.1201 |
Dual form | 1600.2.l.f.401.3 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.488516 | + | 0.488516i | −0.282045 | + | 0.282045i | −0.833924 | − | 0.551879i | \(-0.813911\pi\) |
0.551879 | + | 0.833924i | \(0.313911\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.71540i | 1.78226i | 0.453753 | + | 0.891128i | \(0.350085\pi\) | ||||
−0.453753 | + | 0.891128i | \(0.649915\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.52270i | 0.840901i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.91360 | + | 3.91360i | 1.17999 | + | 1.17999i | 0.979745 | + | 0.200249i | \(0.0641750\pi\) |
0.200249 | + | 0.979745i | \(0.435825\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.0878822 | − | 0.0878822i | 0.0243741 | − | 0.0243741i | −0.694815 | − | 0.719189i | \(-0.744514\pi\) |
0.719189 | + | 0.694815i | \(0.244514\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.67442 | −1.13371 | −0.566857 | − | 0.823816i | \(-0.691841\pi\) | ||||
−0.566857 | + | 0.823816i | \(0.691841\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.81249 | + | 1.81249i | −0.415813 | + | 0.415813i | −0.883758 | − | 0.467945i | \(-0.844995\pi\) |
0.467945 | + | 0.883758i | \(0.344995\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.30355 | − | 2.30355i | −0.502676 | − | 0.502676i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.63007i | − | 0.339893i | −0.985453 | − | 0.169946i | \(-0.945641\pi\) | ||
0.985453 | − | 0.169946i | \(-0.0543594\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.69793 | − | 2.69793i | −0.519217 | − | 0.519217i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.26362 | − | 3.26362i | 0.606039 | − | 0.606039i | −0.335869 | − | 0.941909i | \(-0.609030\pi\) |
0.941909 | + | 0.335869i | \(0.109030\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.12875 | 0.382334 | 0.191167 | − | 0.981557i | \(-0.438773\pi\) | ||||
0.191167 | + | 0.981557i | \(0.438773\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.82371 | −0.665622 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.97797 | − | 3.97797i | −0.653974 | − | 0.653974i | 0.299973 | − | 0.953948i | \(-0.403022\pi\) |
−0.953948 | + | 0.299973i | \(0.903022\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.0858637i | 0.0137492i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 8.25504i | − | 1.28922i | −0.764511 | − | 0.644611i | \(-0.777020\pi\) | ||
0.764511 | − | 0.644611i | \(-0.222980\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.27336 | + | 2.27336i | 0.346685 | + | 0.346685i | 0.858873 | − | 0.512188i | \(-0.171165\pi\) |
−0.512188 | + | 0.858873i | \(0.671165\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.06129 | −0.592400 | −0.296200 | − | 0.955126i | \(-0.595719\pi\) | ||||
−0.296200 | + | 0.955126i | \(0.595719\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15.2350 | −2.17643 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.28353 | − | 2.28353i | 0.319758 | − | 0.319758i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.03938 | + | 5.03938i | 0.692211 | + | 0.692211i | 0.962718 | − | 0.270507i | \(-0.0871912\pi\) |
−0.270507 | + | 0.962718i | \(0.587191\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.77086i | − | 0.234556i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.16453 | + | 5.16453i | 0.672365 | + | 0.672365i | 0.958261 | − | 0.285896i | \(-0.0922911\pi\) |
−0.285896 | + | 0.958261i | \(0.592291\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.12726 | − | 7.12726i | 0.912552 | − | 0.912552i | −0.0839206 | − | 0.996472i | \(-0.526744\pi\) |
0.996472 | + | 0.0839206i | \(0.0267442\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −11.8956 | −1.49870 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.49920 | + | 7.49920i | −0.916173 | + | 0.916173i | −0.996748 | − | 0.0805758i | \(-0.974324\pi\) |
0.0805758 | + | 0.996748i | \(0.474324\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.796314 | + | 0.796314i | 0.0958649 | + | 0.0958649i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 4.54072i | − | 0.538884i | −0.963017 | − | 0.269442i | \(-0.913161\pi\) | ||
0.963017 | − | 0.269442i | \(-0.0868393\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.30557i | 0.972093i | 0.873933 | + | 0.486047i | \(0.161561\pi\) | ||||
−0.873933 | + | 0.486047i | \(0.838439\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −18.4542 | + | 18.4542i | −2.10305 | + | 2.10305i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.5317 | −1.29742 | −0.648709 | − | 0.761037i | \(-0.724691\pi\) | ||||
−0.648709 | + | 0.761037i | \(0.724691\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.93215 | −0.548017 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.16919 | + | 1.16919i | −0.128335 | + | 0.128335i | −0.768357 | − | 0.640022i | \(-0.778925\pi\) |
0.640022 | + | 0.768357i | \(0.278925\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.18866i | 0.341861i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.24572i | 0.344046i | 0.985093 | + | 0.172023i | \(0.0550304\pi\) | ||||
−0.985093 | + | 0.172023i | \(0.944970\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.414400 | + | 0.414400i | 0.0434409 | + | 0.0434409i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.03993 | + | 1.03993i | −0.107835 | + | 0.107835i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.9581 | 1.41723 | 0.708613 | − | 0.705598i | \(-0.249321\pi\) | ||||
0.708613 | + | 0.705598i | \(0.249321\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.87285 | + | 9.87285i | −0.992258 | + | 0.992258i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.4088 | + | 13.4088i | 1.33422 | + | 1.33422i | 0.901552 | + | 0.432672i | \(0.142429\pi\) |
0.432672 | + | 0.901552i | \(0.357571\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 13.7638i | − | 1.35618i | −0.734977 | − | 0.678092i | \(-0.762807\pi\) | ||
0.734977 | − | 0.678092i | \(-0.237193\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.327996 | − | 0.327996i | −0.0317086 | − | 0.0317086i | 0.691075 | − | 0.722783i | \(-0.257138\pi\) |
−0.722783 | + | 0.691075i | \(0.757138\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.149698 | + | 0.149698i | −0.0143385 | + | 0.0143385i | −0.714240 | − | 0.699901i | \(-0.753227\pi\) |
0.699901 | + | 0.714240i | \(0.253227\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.88660 | 0.368900 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.97999 | −0.562550 | −0.281275 | − | 0.959627i | \(-0.590757\pi\) | ||||
−0.281275 | + | 0.959627i | \(0.590757\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.221701 | + | 0.221701i | 0.0204962 | + | 0.0204962i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 22.0418i | − | 2.02057i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.6325i | 1.78477i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.03272 | + | 4.03272i | 0.363618 | + | 0.363618i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.73076 | −0.242315 | −0.121158 | − | 0.992633i | \(-0.538661\pi\) | ||||
−0.121158 | + | 0.992633i | \(0.538661\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.22115 | −0.195561 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.813555 | − | 0.813555i | 0.0710806 | − | 0.0710806i | −0.670673 | − | 0.741753i | \(-0.733994\pi\) |
0.741753 | + | 0.670673i | \(0.233994\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.54661 | − | 8.54661i | −0.741085 | − | 0.741085i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 0.199812i | − | 0.0170711i | −0.999964 | − | 0.00853557i | \(-0.997283\pi\) | ||
0.999964 | − | 0.00853557i | \(-0.00271699\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.6301 | + | 11.6301i | 0.986448 | + | 0.986448i | 0.999909 | − | 0.0134610i | \(-0.00428488\pi\) |
−0.0134610 | + | 0.999909i | \(0.504285\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.98400 | − | 1.98400i | 0.167083 | − | 0.167083i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.687871 | 0.0575227 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.44256 | − | 7.44256i | 0.613852 | − | 0.613852i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.13384 | − | 1.13384i | −0.0928880 | − | 0.0928880i | 0.659136 | − | 0.752024i | \(-0.270922\pi\) |
−0.752024 | + | 0.659136i | \(0.770922\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 7.12216i | − | 0.579593i | −0.957088 | − | 0.289797i | \(-0.906412\pi\) | ||
0.957088 | − | 0.289797i | \(-0.0935877\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 11.7922i | − | 0.953341i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.32145 | − | 5.32145i | 0.424698 | − | 0.424698i | −0.462120 | − | 0.886818i | \(-0.652911\pi\) |
0.886818 | + | 0.462120i | \(0.152911\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.92363 | −0.390469 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.68643 | 0.605775 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.3010 | + | 12.3010i | −0.963488 | + | 0.963488i | −0.999357 | − | 0.0358685i | \(-0.988580\pi\) |
0.0358685 | + | 0.999357i | \(0.488580\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.86820i | 0.763624i | 0.924240 | + | 0.381812i | \(0.124700\pi\) | ||||
−0.924240 | + | 0.381812i | \(0.875300\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9846i | 0.998812i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.57237 | − | 4.57237i | −0.349658 | − | 0.349658i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.4089 | − | 13.4089i | 1.01946 | − | 1.01946i | 0.0196525 | − | 0.999807i | \(-0.493744\pi\) |
0.999807 | − | 0.0196525i | \(-0.00625599\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.04591 | −0.379274 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.419587 | + | 0.419587i | −0.0313614 | + | 0.0313614i | −0.722614 | − | 0.691252i | \(-0.757059\pi\) |
0.691252 | + | 0.722614i | \(0.257059\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.2605 | − | 14.2605i | −1.05998 | − | 1.05998i | −0.998083 | − | 0.0618956i | \(-0.980285\pi\) |
−0.0618956 | − | 0.998083i | \(-0.519715\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.96356i | 0.514761i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.2938 | − | 18.2938i | −1.33777 | − | 1.33777i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.7218 | − | 12.7218i | 0.925377 | − | 0.925377i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.3304 | −1.25399 | −0.626993 | − | 0.779025i | \(-0.715715\pi\) | ||||
−0.626993 | + | 0.779025i | \(0.715715\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.8667 | −1.21409 | −0.607045 | − | 0.794667i | \(-0.707645\pi\) | ||||
−0.607045 | + | 0.794667i | \(0.707645\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.58908 | + | 3.58908i | 0.255712 | + | 0.255712i | 0.823307 | − | 0.567596i | \(-0.192126\pi\) |
−0.567596 | + | 0.823307i | \(0.692126\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 6.64501i | − | 0.471052i | −0.971868 | − | 0.235526i | \(-0.924319\pi\) | ||
0.971868 | − | 0.235526i | \(-0.0756813\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 7.32695i | − | 0.516803i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.3893 | + | 15.3893i | 1.08012 | + | 1.08012i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.11218 | 0.285816 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −14.1867 | −0.981314 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.90906 | + | 1.90906i | −0.131425 | + | 0.131425i | −0.769759 | − | 0.638334i | \(-0.779624\pi\) |
0.638334 | + | 0.769759i | \(0.279624\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.21821 | + | 2.21821i | 0.151989 | + | 0.151989i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.0379i | 0.681418i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.05740 | − | 4.05740i | −0.274174 | − | 0.274174i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.410798 | + | 0.410798i | −0.0276333 | + | 0.0276333i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.1071 | 1.61433 | 0.807165 | − | 0.590326i | \(-0.201001\pi\) | ||||
0.807165 | + | 0.590326i | \(0.201001\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.67411 | − | 6.67411i | 0.442977 | − | 0.442977i | −0.450035 | − | 0.893011i | \(-0.648588\pi\) |
0.893011 | + | 0.450035i | \(0.148588\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.0807 | + | 16.0807i | 1.06264 | + | 1.06264i | 0.997902 | + | 0.0647388i | \(0.0206214\pi\) |
0.0647388 | + | 0.997902i | \(0.479379\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 18.0303i | − | 1.18631i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.4976i | 1.08079i | 0.841411 | + | 0.540396i | \(0.181726\pi\) | ||||
−0.841411 | + | 0.540396i | \(0.818274\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.63342 | − | 5.63342i | 0.365930 | − | 0.365930i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.25917 | −0.340188 | −0.170094 | − | 0.985428i | \(-0.554407\pi\) | ||||
−0.170094 | + | 0.985428i | \(0.554407\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.1126 | −0.909075 | −0.454538 | − | 0.890728i | \(-0.650196\pi\) | ||||
−0.454538 | + | 0.890728i | \(0.650196\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.5032 | − | 10.5032i | 0.673782 | − | 0.673782i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.318571i | 0.0202702i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 1.14234i | − | 0.0723927i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.98825 | + | 9.98825i | 0.630453 | + | 0.630453i | 0.948182 | − | 0.317729i | \(-0.102920\pi\) |
−0.317729 | + | 0.948182i | \(0.602920\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.37943 | − | 6.37943i | 0.401071 | − | 0.401071i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.44760 | 0.526947 | 0.263474 | − | 0.964667i | \(-0.415132\pi\) | ||||
0.263474 | + | 0.964667i | \(0.415132\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.7577 | − | 18.7577i | 1.16555 | − | 1.16555i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.23315 | + | 8.23315i | 0.509619 | + | 0.509619i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.3064i | 1.12882i | 0.825494 | + | 0.564410i | \(0.190896\pi\) | ||||
−0.825494 | + | 0.564410i | \(0.809104\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.58559 | − | 1.58559i | −0.0970364 | − | 0.0970364i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.5631 | − | 13.5631i | 0.826955 | − | 0.826955i | −0.160140 | − | 0.987094i | \(-0.551194\pi\) |
0.987094 | + | 0.160140i | \(0.0511945\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.24520 | 0.136386 | 0.0681930 | − | 0.997672i | \(-0.478277\pi\) | ||||
0.0681930 | + | 0.997672i | \(0.478277\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.404882 | −0.0245046 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.28255 | − | 7.28255i | −0.437566 | − | 0.437566i | 0.453626 | − | 0.891192i | \(-0.350130\pi\) |
−0.891192 | + | 0.453626i | \(0.850130\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.37020i | 0.321506i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.04084i | 0.360367i | 0.983633 | + | 0.180183i | \(0.0576691\pi\) | ||||
−0.983633 | + | 0.180183i | \(0.942331\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.1350 | − | 15.1350i | −0.899682 | − | 0.899682i | 0.0957259 | − | 0.995408i | \(-0.469483\pi\) |
−0.995408 | + | 0.0957259i | \(0.969483\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 38.9259 | 2.29772 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.85021 | 0.285306 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.81873 | + | 6.81873i | −0.399721 | + | 0.399721i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.7777 | + | 10.7777i | 0.629637 | + | 0.629637i | 0.947977 | − | 0.318339i | \(-0.103125\pi\) |
−0.318339 | + | 0.947977i | \(0.603125\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 21.1172i | − | 1.22534i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.143254 | − | 0.143254i | −0.00828459 | − | 0.00828459i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.7198 | + | 10.7198i | −0.617881 | + | 0.617881i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.1008 | −0.752621 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.94378 | − | 7.94378i | 0.453376 | − | 0.453376i | −0.443098 | − | 0.896473i | \(-0.646120\pi\) |
0.896473 | + | 0.443098i | \(0.146120\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.72382 | + | 6.72382i | 0.382505 | + | 0.382505i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 31.1649i | 1.76720i | 0.468244 | + | 0.883599i | \(0.344887\pi\) | ||||
−0.468244 | + | 0.883599i | \(0.655113\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 5.35842i | − | 0.302876i | −0.988467 | − | 0.151438i | \(-0.951610\pi\) | ||
0.988467 | − | 0.151438i | \(-0.0483903\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.88165 | − | 8.88165i | 0.498843 | − | 0.498843i | −0.412235 | − | 0.911078i | \(-0.635252\pi\) |
0.911078 | + | 0.412235i | \(0.135252\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 25.5450 | 1.43025 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.320463 | 0.0178865 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.47233 | − | 8.47233i | 0.471413 | − | 0.471413i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 0.146260i | − | 0.00808817i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 19.1506i | − | 1.05581i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.07281 | − | 6.07281i | −0.333792 | − | 0.333792i | 0.520233 | − | 0.854025i | \(-0.325845\pi\) |
−0.854025 | + | 0.520233i | \(0.825845\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.0352 | − | 10.0352i | 0.549928 | − | 0.549928i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.0227 | 1.19965 | 0.599827 | − | 0.800130i | \(-0.295236\pi\) | ||||
0.599827 | + | 0.800130i | \(0.295236\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.92132 | − | 2.92132i | 0.158664 | − | 0.158664i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.33106 | + | 8.33106i | 0.451152 | + | 0.451152i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 38.8315i | − | 2.09670i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.8920 | + | 11.8920i | 0.638395 | + | 0.638395i | 0.950159 | − | 0.311765i | \(-0.100920\pi\) |
−0.311765 | + | 0.950159i | \(0.600920\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.65696 | + | 8.65696i | −0.463396 | + | 0.463396i | −0.899767 | − | 0.436371i | \(-0.856264\pi\) |
0.436371 | + | 0.899767i | \(0.356264\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.474200 | −0.0253109 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.6153 | 1.41659 | 0.708296 | − | 0.705916i | \(-0.249464\pi\) | ||||
0.708296 | + | 0.705916i | \(0.249464\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10.7678 | + | 10.7678i | 0.569890 | + | 0.569890i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.85032i | 0.255990i | 0.991775 | + | 0.127995i | \(0.0408542\pi\) | ||||
−0.991775 | + | 0.127995i | \(0.959146\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.4298i | 0.654199i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.59078 | − | 9.59078i | −0.503385 | − | 0.503385i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.6741 | −0.818182 | −0.409091 | − | 0.912494i | \(-0.634154\pi\) | ||||
−0.409091 | + | 0.912494i | \(0.634154\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 20.8250 | 1.08411 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −23.7627 | + | 23.7627i | −1.23370 | + | 1.23370i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.44481 | − | 5.44481i | −0.281922 | − | 0.281922i | 0.551953 | − | 0.833875i | \(-0.313883\pi\) |
−0.833875 | + | 0.551953i | \(0.813883\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 0.573629i | − | 0.0295434i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.4103 | + | 17.4103i | 0.894309 | + | 0.894309i | 0.994925 | − | 0.100616i | \(-0.0320814\pi\) |
−0.100616 | + | 0.994925i | \(0.532081\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.33402 | − | 1.33402i | 0.0683438 | − | 0.0683438i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.04928 | −0.462396 | −0.231198 | − | 0.972907i | \(-0.574265\pi\) | ||||
−0.231198 | + | 0.972907i | \(0.574265\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.73503 | + | 5.73503i | −0.291528 | + | 0.291528i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.3617 | − | 15.3617i | −0.778871 | − | 0.778871i | 0.200768 | − | 0.979639i | \(-0.435656\pi\) |
−0.979639 | + | 0.200768i | \(0.935656\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.61962i | 0.385341i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.794869i | 0.0400959i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.44519 | − | 9.44519i | 0.474041 | − | 0.474041i | −0.429179 | − | 0.903220i | \(-0.641197\pi\) |
0.903220 | + | 0.429179i | \(0.141197\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.35031 | 0.418038 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −21.5765 | −1.07748 | −0.538739 | − | 0.842473i | \(-0.681099\pi\) | ||||
−0.538739 | + | 0.842473i | \(0.681099\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.187079 | − | 0.187079i | 0.00931907 | − | 0.00931907i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 31.1363i | − | 1.54337i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 4.17336i | − | 0.206359i | −0.994663 | − | 0.103180i | \(-0.967098\pi\) | ||
0.994663 | − | 0.103180i | \(-0.0329017\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.0976116 | + | 0.0976116i | 0.00481482 | + | 0.00481482i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −24.3529 | + | 24.3529i | −1.19833 | + | 1.19833i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.3629 | −0.556445 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.1191 | + | 27.1191i | −1.32485 | + | 1.32485i | −0.415060 | + | 0.909794i | \(0.636239\pi\) |
−0.909794 | + | 0.415060i | \(0.863761\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.9594 | − | 26.9594i | −1.31392 | − | 1.31392i | −0.918500 | − | 0.395421i | \(-0.870599\pi\) |
−0.395421 | − | 0.918500i | \(-0.629401\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 10.2454i | − | 0.498150i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 33.6079 | + | 33.6079i | 1.62640 | + | 1.62640i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.336036 | + | 0.336036i | −0.0162240 | + | 0.0162240i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.4059 | 1.07925 | 0.539626 | − | 0.841905i | \(-0.318566\pi\) | ||||
0.539626 | + | 0.841905i | \(0.318566\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.8061 | 0.807649 | 0.403824 | − | 0.914837i | \(-0.367681\pi\) | ||||
0.403824 | + | 0.914837i | \(0.367681\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.95448 | + | 2.95448i | 0.141332 | + | 0.141332i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 9.08322i | − | 0.433519i | −0.976225 | − | 0.216759i | \(-0.930451\pi\) | ||
0.976225 | − | 0.216759i | \(-0.0695487\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 38.4335i | − | 1.83017i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.5397 | + | 12.5397i | 0.595781 | + | 0.595781i | 0.939187 | − | 0.343406i | \(-0.111581\pi\) |
−0.343406 | + | 0.939187i | \(0.611581\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.10780 | 0.0523972 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.0707 | 0.852811 | 0.426406 | − | 0.904532i | \(-0.359780\pi\) | ||||
0.426406 | + | 0.904532i | \(0.359780\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.3069 | − | 32.3069i | 1.52127 | − | 1.52127i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.47929 | + | 3.47929i | 0.163471 | + | 0.163471i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 18.6637i | − | 0.873052i | −0.899692 | − | 0.436526i | \(-0.856209\pi\) | ||
0.899692 | − | 0.436526i | \(-0.143791\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.6113 | + | 12.6113i | 0.588643 | + | 0.588643i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.831229 | + | 0.831229i | −0.0387142 | + | 0.0387142i | −0.726199 | − | 0.687485i | \(-0.758715\pi\) |
0.687485 | + | 0.726199i | \(0.258715\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.82533 | 0.363674 | 0.181837 | − | 0.983329i | \(-0.441796\pi\) | ||||
0.181837 | + | 0.983329i | \(0.441796\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.75068 | − | 8.75068i | 0.404933 | − | 0.404933i | −0.475034 | − | 0.879967i | \(-0.657564\pi\) |
0.879967 | + | 0.475034i | \(0.157564\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −35.3617 | − | 35.3617i | −1.63285 | − | 1.63285i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.19922i | 0.239568i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.7941i | 0.818172i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.7129 | + | 12.7129i | −0.582082 | + | 0.582082i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.10417 | −0.0961421 | −0.0480710 | − | 0.998844i | \(-0.515307\pi\) | ||||
−0.0480710 | + | 0.998844i | \(0.515307\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.699186 | −0.0318801 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.75494 | + | 3.75494i | −0.170856 | + | 0.170856i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.87183i | 0.220764i | 0.993889 | + | 0.110382i | \(0.0352074\pi\) | ||||
−0.993889 | + | 0.110382i | \(0.964793\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 12.0185i | − | 0.543494i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.3582 | − | 14.3582i | −0.647975 | − | 0.647975i | 0.304528 | − | 0.952503i | \(-0.401501\pi\) |
−0.952503 | + | 0.304528i | \(0.901501\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.2555 | + | 15.2555i | −0.687075 | + | 0.687075i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 21.4113 | 0.960429 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.1060 | − | 25.1060i | 1.12390 | − | 1.12390i | 0.132748 | − | 0.991150i | \(-0.457620\pi\) |
0.991150 | − | 0.132748i | \(-0.0423801\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.82077 | − | 4.82077i | −0.215376 | − | 0.215376i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.8868i | 0.842120i | 0.907033 | + | 0.421060i | \(0.138342\pi\) | ||||
−0.907033 | + | 0.421060i | \(0.861658\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.34316 | − | 6.34316i | −0.281710 | − | 0.281710i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.9756 | + | 22.9756i | −1.01837 | + | 1.01837i | −0.0185459 | + | 0.999828i | \(0.505904\pi\) |
−0.999828 | + | 0.0185459i | \(0.994096\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −39.1641 | −1.73252 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.77993 | 0.431794 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.8942 | − | 15.8942i | −0.699028 | − | 0.699028i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.1009i | 0.575066i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.2089i | 0.885367i | 0.896678 | + | 0.442683i | \(0.145973\pi\) | ||||
−0.896678 | + | 0.442683i | \(0.854027\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.93445 | − | 3.93445i | −0.172042 | − | 0.172042i | 0.615834 | − | 0.787876i | \(-0.288819\pi\) |
−0.787876 | + | 0.615834i | \(0.788819\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.95066 | −0.433458 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.3429 | 0.884473 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.0286 | + | 13.0286i | −0.565393 | + | 0.565393i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.725471 | − | 0.725471i | −0.0314237 | − | 0.0314237i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 0.409950i | − | 0.0176906i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −59.6238 | − | 59.6238i | −2.56818 | − | 2.56818i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.17895 | + | 3.17895i | −0.136674 | + | 0.136674i | −0.772134 | − | 0.635460i | \(-0.780811\pi\) |
0.635460 | + | 0.772134i | \(0.280811\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.9330 | 0.597923 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.32918 | + | 1.32918i | −0.0568317 | + | 0.0568317i | −0.734951 | − | 0.678120i | \(-0.762795\pi\) |
0.678120 | + | 0.734951i | \(0.262795\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 17.9800 | + | 17.9800i | 0.767366 | + | 0.767366i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.8306i | 0.503998i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 54.3766i | − | 2.31233i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.9082 | − | 24.9082i | 1.05539 | − | 1.05539i | 0.0570196 | − | 0.998373i | \(-0.481840\pi\) |
0.998373 | − | 0.0570196i | \(-0.0181598\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.399576 | 0.0169003 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.8736 | 0.754625 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.80804 | + | 3.80804i | −0.160490 | + | 0.160490i | −0.782784 | − | 0.622294i | \(-0.786201\pi\) |
0.622294 | + | 0.782784i | \(0.286201\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 23.2571i | − | 0.976706i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 8.43971i | − | 0.353811i | −0.984228 | − | 0.176905i | \(-0.943391\pi\) | ||
0.984228 | − | 0.176905i | \(-0.0566087\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.2821 | + | 21.2821i | 0.890629 | + | 0.890629i | 0.994582 | − | 0.103953i | \(-0.0331491\pi\) |
−0.103953 | + | 0.994582i | \(0.533149\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.46619 | − | 8.46619i | 0.353680 | − | 0.353680i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.3491 | −1.51323 | −0.756615 | − | 0.653860i | \(-0.773148\pi\) | ||||
−0.756615 | + | 0.653860i | \(0.773148\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.23964 | − | 8.23964i | 0.342428 | − | 0.342428i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.51321 | − | 5.51321i | −0.228726 | − | 0.228726i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 39.4442i | 1.63361i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.55994 | + | 6.55994i | 0.270758 | + | 0.270758i | 0.829405 | − | 0.558647i | \(-0.188679\pi\) |
−0.558647 | + | 0.829405i | \(0.688679\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.85833 | + | 3.85833i | −0.158980 | + | 0.158980i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.50665 | −0.144244 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.40974 | −0.0578911 | −0.0289455 | − | 0.999581i | \(-0.509215\pi\) | ||||
−0.0289455 | + | 0.999581i | \(0.509215\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.24619 | + | 3.24619i | 0.132858 | + | 0.132858i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.3593i | 0.954435i | 0.878785 | + | 0.477218i | \(0.158355\pi\) | ||||
−0.878785 | + | 0.477218i | \(0.841645\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 20.4138i | − | 0.832695i | −0.909206 | − | 0.416347i | \(-0.863310\pi\) | ||
0.909206 | − | 0.416347i | \(-0.136690\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −18.9183 | − | 18.9183i | −0.770411 | − | 0.770411i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.758240 | −0.0307760 | −0.0153880 | − | 0.999882i | \(-0.504898\pi\) | ||||
−0.0153880 | + | 0.999882i | \(0.504898\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −15.0358 | −0.609283 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.356915 | + | 0.356915i | −0.0144392 | + | 0.0144392i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.0341 | + | 12.0341i | 0.486052 | + | 0.486052i | 0.907058 | − | 0.421006i | \(-0.138323\pi\) |
−0.421006 | + | 0.907058i | \(0.638323\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.6899i | 1.31605i | 0.752998 | + | 0.658023i | \(0.228607\pi\) | ||||
−0.752998 | + | 0.658023i | \(0.771393\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.3836 | − | 26.3836i | −1.06045 | − | 1.06045i | −0.998052 | − | 0.0623934i | \(-0.980127\pi\) |
−0.0623934 | − | 0.998052i | \(-0.519873\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.39781 | + | 4.39781i | −0.176478 | + | 0.176478i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −15.3049 | −0.613178 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.93042 | − | 6.93042i | 0.276774 | − | 0.276774i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.5947 | + | 18.5947i | 0.741420 | + | 0.741420i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.08765i | 0.242345i | 0.992631 | + | 0.121173i | \(0.0386655\pi\) | ||||
−0.992631 | + | 0.121173i | \(0.961335\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 1.86521i | − | 0.0741354i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.33889 | + | 1.33889i | −0.0530487 | + | 0.0530487i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.4549 | 0.453149 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.1680 | 0.441111 | 0.220555 | − | 0.975374i | \(-0.429213\pi\) | ||||
0.220555 | + | 0.975374i | \(0.429213\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.9585 | − | 21.9585i | 0.865957 | − | 0.865957i | −0.126065 | − | 0.992022i | \(-0.540235\pi\) |
0.992022 | + | 0.126065i | \(0.0402348\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.9848i | 1.45402i | 0.686625 | + | 0.727011i | \(0.259091\pi\) | ||||
−0.686625 | + | 0.727011i | \(0.740909\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 40.4238i | 1.58677i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.90368 | − | 4.90368i | −0.192190 | − | 0.192190i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.4157 | + | 18.4157i | −0.720663 | + | 0.720663i | −0.968740 | − | 0.248077i | \(-0.920201\pi\) |
0.248077 | + | 0.968740i | \(0.420201\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −20.9525 | −0.817435 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.5421 | − | 15.5421i | 0.605434 | − | 0.605434i | −0.336316 | − | 0.941749i | \(-0.609181\pi\) |
0.941749 | + | 0.336316i | \(0.109181\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.6677 | + | 29.6677i | 1.15394 | + | 1.15394i | 0.985755 | + | 0.168185i | \(0.0537906\pi\) |
0.168185 | + | 0.985755i | \(0.446209\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 0.401363i | − | 0.0155877i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.31992 | − | 5.31992i | −0.205988 | − | 0.205988i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.7767 | + | 11.7767i | −0.455313 | + | 0.455313i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 55.7864 | 2.15361 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.2198 | −1.12634 | −0.563171 | − | 0.826340i | \(-0.690419\pi\) | ||||
−0.563171 | + | 0.826340i | \(0.690419\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.2591 | + | 17.2591i | 0.663320 | + | 0.663320i | 0.956161 | − | 0.292841i | \(-0.0946006\pi\) |
−0.292841 | + | 0.956161i | \(0.594601\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 65.8179i | 2.52586i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.52082i | 0.249878i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.10407 | − | 1.10407i | −0.0422459 | − | 0.0422459i | 0.685668 | − | 0.727914i | \(-0.259510\pi\) |
−0.727914 | + | 0.685668i | \(0.759510\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.7113 | −0.599425 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.885743 | 0.0337441 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.4233 | − | 28.4233i | 1.08127 | − | 1.08127i | 0.0848830 | − | 0.996391i | \(-0.472948\pi\) |
0.996391 | − | 0.0848830i | \(-0.0270517\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −46.5545 | − | 46.5545i | −1.76846 | − | 1.76846i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 38.5875i | 1.46161i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.05933 | − | 8.05933i | −0.304832 | − | 0.304832i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.7991 | + | 23.7991i | −0.898880 | + | 0.898880i | −0.995337 | − | 0.0964573i | \(-0.969249\pi\) |
0.0964573 | + | 0.995337i | \(0.469249\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.4200 | 0.543862 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −63.2278 | + | 63.2278i | −2.37793 | + | 2.37793i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.49921 | + | 1.49921i | 0.0563039 | + | 0.0563039i | 0.734698 | − | 0.678394i | \(-0.237324\pi\) |
−0.678394 | + | 0.734698i | \(0.737324\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 29.0911i | − | 1.09100i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 3.47000i | − | 0.129953i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.56919 | − | 2.56919i | 0.0959482 | − | 0.0959482i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.37612 | −0.275083 | −0.137541 | − | 0.990496i | \(-0.543920\pi\) | ||||
−0.137541 | + | 0.990496i | \(0.543920\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 64.9017 | 2.41707 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.89425 | − | 6.89425i | 0.256400 | − | 0.256400i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 30.1470i | − | 1.11809i | −0.829137 | − | 0.559045i | \(-0.811168\pi\) | ||
0.829137 | − | 0.559045i | \(-0.188832\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 4.53447i | − | 0.167943i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.6267 | − | 10.6267i | −0.393041 | − | 0.393041i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.43297 | + | 1.43297i | −0.0529279 | + | 0.0529279i | −0.733075 | − | 0.680147i | \(-0.761916\pi\) |
0.680147 | + | 0.733075i | \(0.261916\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −58.6977 | −2.16216 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.0001 | + | 31.0001i | −1.14036 | + | 1.14036i | −0.151973 | + | 0.988385i | \(0.548563\pi\) |
−0.988385 | + | 0.151973i | \(0.951437\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.155627 | − | 0.155627i | −0.00571710 | − | 0.00571710i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.5395i | 1.41388i | 0.707276 | + | 0.706938i | \(0.249924\pi\) | ||||
−0.707276 | + | 0.706938i | \(0.750076\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.94952 | − | 2.94952i | −0.107917 | − | 0.107917i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.54664 | − | 1.54664i | 0.0565128 | − | 0.0565128i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.9523 | −0.983503 | −0.491751 | − | 0.870736i | \(-0.663643\pi\) | ||||
−0.491751 | + | 0.870736i | \(0.663643\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.75884 | −0.355632 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.0688 | + | 17.0688i | 0.620377 | + | 0.620377i | 0.945628 | − | 0.325251i | \(-0.105449\pi\) |
−0.325251 | + | 0.945628i | \(0.605449\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.23290i | 0.226240i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 6.89608i | − | 0.249983i | −0.992158 | − | 0.124991i | \(-0.960110\pi\) | ||
0.992158 | − | 0.124991i | \(-0.0398903\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.705886 | − | 0.705886i | −0.0255548 | − | 0.0255548i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.907741 | 0.0327766 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.8443 | 0.427117 | 0.213558 | − | 0.976930i | \(-0.431495\pi\) | ||||
0.213558 | + | 0.976930i | \(0.431495\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.12679 | + | 4.12679i | −0.148623 | + | 0.148623i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.58865 | − | 3.58865i | −0.129075 | − | 0.129075i | 0.639618 | − | 0.768693i | \(-0.279093\pi\) |
−0.768693 | + | 0.639618i | \(0.779093\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 18.3269i | 0.657474i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.9622 | + | 14.9622i | 0.536075 | + | 0.536075i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.7705 | − | 17.7705i | 0.635880 | − | 0.635880i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −17.6100 | −0.629332 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.4800 | − | 22.4800i | 0.801326 | − | 0.801326i | −0.181977 | − | 0.983303i | \(-0.558250\pi\) |
0.983303 | + | 0.181977i | \(0.0582497\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.94296 | − | 8.94296i | −0.318378 | − | 0.318378i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 28.1981i | − | 1.00261i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1.25272i | − | 0.0444853i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.67589 | + | 8.67589i | −0.307316 | + | 0.307316i | −0.843867 | − | 0.536552i | \(-0.819727\pi\) |
0.536552 | + | 0.843867i | \(0.319727\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.9842 | 0.671612 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.18800 | −0.289309 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −32.5046 | + | 32.5046i | −1.14706 | + | 1.14706i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.2515i | 0.466476i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 27.9066i | − | 0.981143i | −0.871401 | − | 0.490571i | \(-0.836788\pi\) | ||
0.871401 | − | 0.490571i | \(-0.163212\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.2635 | − | 15.2635i | −0.535974 | − | 0.535974i | 0.386370 | − | 0.922344i | \(-0.373729\pi\) |
−0.922344 | + | 0.386370i | \(0.873729\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.09681 | + | 1.09681i | −0.0384670 | + | 0.0384670i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.24089 | −0.288312 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.04541 | + | 1.04541i | −0.0365295 | + | 0.0365295i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.2883 | + | 25.2883i | 0.882567 | + | 0.882567i | 0.993795 | − | 0.111228i | \(-0.0354782\pi\) |
−0.111228 | + | 0.993795i | \(0.535478\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.12228i | 0.248267i | 0.992266 | + | 0.124133i | \(0.0396151\pi\) | ||||
−0.992266 | + | 0.124133i | \(0.960385\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32.1618 | − | 32.1618i | −1.11837 | − | 1.11837i | −0.991980 | − | 0.126394i | \(-0.959660\pi\) |
−0.126394 | − | 0.991980i | \(-0.540340\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34.9802 | + | 34.9802i | −1.21491 | + | 1.21491i | −0.245522 | + | 0.969391i | \(0.578959\pi\) |
−0.969391 | + | 0.245522i | \(0.921041\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.11529 | 0.246827 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 71.2149 | 2.46745 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.74321 | − | 5.74321i | −0.198514 | − | 0.198514i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 11.1147i | − | 0.383721i | −0.981422 | − | 0.191861i | \(-0.938548\pi\) | ||
0.981422 | − | 0.191861i | \(-0.0614521\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.69754i | 0.265432i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.95105 | − | 2.95105i | −0.101640 | − | 0.101640i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −92.5750 | −3.18092 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14.7874 | 0.507501 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.48436 | + | 6.48436i | −0.222281 | + | 0.222281i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.9107 | + | 28.9107i | 0.989884 | + | 0.989884i | 0.999949 | − | 0.0100656i | \(-0.00320402\pi\) |
−0.0100656 | + | 0.999949i | \(0.503204\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 34.1485i | − | 1.16649i | −0.812296 | − | 0.583245i | \(-0.801783\pi\) | ||
0.812296 | − | 0.583245i | \(-0.198217\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.4589 | − | 20.4589i | −0.698047 | − | 0.698047i | 0.265942 | − | 0.963989i | \(-0.414317\pi\) |
−0.963989 | + | 0.265942i | \(0.914317\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −19.0159 | + | 19.0159i | −0.648060 | + | 0.648060i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 35.3591 | 1.20364 | 0.601818 | − | 0.798633i | \(-0.294443\pi\) | ||||
0.601818 | + | 0.798633i | \(0.294443\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.36940 | + | 2.36940i | −0.0804692 | + | 0.0804692i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −45.1304 | − | 45.1304i | −1.53094 | − | 1.53094i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.31809i | 0.0446618i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 35.2120i | 1.19175i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.15415 | + | 3.15415i | −0.106508 | + | 0.106508i | −0.758353 | − | 0.651845i | \(-0.773995\pi\) |
0.651845 | + | 0.758353i | \(0.273995\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.5301 | −0.355172 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.3066 | 0.684146 | 0.342073 | − | 0.939673i | \(-0.388871\pi\) | ||||
0.342073 | + | 0.939673i | \(0.388871\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.523303 | + | 0.523303i | −0.0176105 | + | 0.0176105i | −0.715857 | − | 0.698247i | \(-0.753964\pi\) |
0.698247 | + | 0.715857i | \(0.253964\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 34.8129i | − | 1.16890i | −0.811429 | − | 0.584452i | \(-0.801310\pi\) | ||
0.811429 | − | 0.584452i | \(-0.198690\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 12.8766i | − | 0.431868i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −19.3024 | − | 19.3024i | −0.646656 | − | 0.646656i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.36103 | − | 7.36103i | 0.246328 | − | 0.246328i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.139964 | 0.00467325 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.94743 | − | 6.94743i | 0.231710 | − | 0.231710i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −23.5562 | − | 23.5562i | −0.784770 | − | 0.784770i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 10.4736i | − | 0.348540i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.3188 | + | 13.3188i | 0.442244 | + | 0.442244i | 0.892766 | − | 0.450521i | \(-0.148762\pi\) |
−0.450521 | + | 0.892766i | \(0.648762\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −33.8264 | + | 33.8264i | −1.12195 | + | 1.12195i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.0117 | 1.55757 | 0.778783 | − | 0.627294i | \(-0.215837\pi\) | ||||
0.778783 | + | 0.627294i | \(0.215837\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.15148 | −0.302870 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.83624 | + | 3.83624i | 0.126684 | + | 0.126684i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 31.3426i | − | 1.03390i | −0.856016 | − | 0.516949i | \(-0.827068\pi\) | ||
0.856016 | − | 0.516949i | \(-0.172932\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.76133i | 0.255745i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.399048 | − | 0.399048i | −0.0131348 | − | 0.0131348i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 34.7219 | 1.14042 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30.3384 | 0.995369 | 0.497685 | − | 0.867358i | \(-0.334184\pi\) | ||||
0.497685 | + | 0.867358i | \(0.334184\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27.6133 | − | 27.6133i | 0.904990 | − | 0.904990i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15.2245 | − | 15.2245i | −0.498429 | − | 0.498429i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.5267i | 0.474565i | 0.971441 | + | 0.237283i | \(0.0762567\pi\) | ||||
−0.971441 | + | 0.237283i | \(0.923743\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.61767 | + | 2.61767i | 0.0854245 | + | 0.0854245i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.2863 | − | 37.2863i | 1.21550 | − | 1.21550i | 0.246307 | − | 0.969192i | \(-0.420783\pi\) |
0.969192 | − | 0.246307i | \(-0.0792172\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.4563 | −0.438197 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.8961 | + | 15.8961i | −0.516553 | + | 0.516553i | −0.916527 | − | 0.399973i | \(-0.869019\pi\) |
0.399973 | + | 0.916527i | \(0.369019\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.729912 | + | 0.729912i | 0.0236939 | + | 0.0236939i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.67765i | 0.281392i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.2248i | 1.07626i | 0.842862 | + | 0.538129i | \(0.180869\pi\) | ||||
−0.842862 | + | 0.538129i | \(0.819131\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.4791 | + | 12.4791i | −0.403393 | + | 0.403393i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.942197 | 0.0304251 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.4684 | −0.853820 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.827438 | − | 0.827438i | 0.0266638 | − | 0.0266638i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.79116i | 0.0576000i | 0.999585 | + | 0.0288000i | \(0.00916859\pi\) | ||||
−0.999585 | + | 0.0288000i | \(0.990831\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.27774i | 0.265919i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.31278 | − | 5.31278i | −0.170495 | − | 0.170495i | 0.616702 | − | 0.787197i | \(-0.288469\pi\) |
−0.787197 | + | 0.616702i | \(0.788469\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −54.8404 | + | 54.8404i | −1.75810 | + | 1.75810i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.81676 | 0.218088 | 0.109044 | − | 0.994037i | \(-0.465221\pi\) | ||||
0.109044 | + | 0.994037i | \(0.465221\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.7025 | + | 12.7025i | −0.405972 | + | 0.405972i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.377643 | − | 0.377643i | −0.0120572 | − | 0.0120572i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 5.49468i | − | 0.175253i | −0.996153 | − | 0.0876265i | \(-0.972072\pi\) | ||
0.996153 | − | 0.0876265i | \(-0.0279282\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.35538 | + | 9.35538i | 0.297785 | + | 0.297785i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.70574 | − | 3.70574i | 0.117836 | − | 0.117836i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −48.7524 | −1.54867 | −0.774335 | − | 0.632775i | \(-0.781916\pi\) | ||||
−0.774335 | + | 0.632775i | \(0.781916\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.93333 | 0.188289 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −42.5246 | − | 42.5246i | −1.34677 | − | 1.34677i | −0.889149 | − | 0.457618i | \(-0.848703\pi\) |
−0.457618 | − | 0.889149i | \(-0.651297\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 21.4646i | 0.679109i |
(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 | 1600.2.l.f.1201.3 | 12 | ||
4.3 | odd | 2 | 400.2.l.g.101.1 | yes | 12 | ||
5.2 | odd | 4 | 1600.2.q.f.49.4 | 12 | |||
5.3 | odd | 4 | 1600.2.q.e.49.3 | 12 | |||
5.4 | even | 2 | 1600.2.l.g.1201.4 | 12 | |||
16.3 | odd | 4 | 400.2.l.g.301.1 | yes | 12 | ||
16.13 | even | 4 | inner | 1600.2.l.f.401.3 | 12 | ||
20.3 | even | 4 | 400.2.q.e.149.4 | 12 | |||
20.7 | even | 4 | 400.2.q.f.149.3 | 12 | |||
20.19 | odd | 2 | 400.2.l.f.101.6 | ✓ | 12 | ||
80.3 | even | 4 | 400.2.q.f.349.3 | 12 | |||
80.13 | odd | 4 | 1600.2.q.f.849.4 | 12 | |||
80.19 | odd | 4 | 400.2.l.f.301.6 | yes | 12 | ||
80.29 | even | 4 | 1600.2.l.g.401.4 | 12 | |||
80.67 | even | 4 | 400.2.q.e.349.4 | 12 | |||
80.77 | odd | 4 | 1600.2.q.e.849.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.l.f.101.6 | ✓ | 12 | 20.19 | odd | 2 | ||
400.2.l.f.301.6 | yes | 12 | 80.19 | odd | 4 | ||
400.2.l.g.101.1 | yes | 12 | 4.3 | odd | 2 | ||
400.2.l.g.301.1 | yes | 12 | 16.3 | odd | 4 | ||
400.2.q.e.149.4 | 12 | 20.3 | even | 4 | |||
400.2.q.e.349.4 | 12 | 80.67 | even | 4 | |||
400.2.q.f.149.3 | 12 | 20.7 | even | 4 | |||
400.2.q.f.349.3 | 12 | 80.3 | even | 4 | |||
1600.2.l.f.401.3 | 12 | 16.13 | even | 4 | inner | ||
1600.2.l.f.1201.3 | 12 | 1.1 | even | 1 | trivial | ||
1600.2.l.g.401.4 | 12 | 80.29 | even | 4 | |||
1600.2.l.g.1201.4 | 12 | 5.4 | even | 2 | |||
1600.2.q.e.49.3 | 12 | 5.3 | odd | 4 | |||
1600.2.q.e.849.3 | 12 | 80.77 | odd | 4 | |||
1600.2.q.f.49.4 | 12 | 5.2 | odd | 4 | |||
1600.2.q.f.849.4 | 12 | 80.13 | odd | 4 |