Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(49,1600)]
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, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.q (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 | 49.4 | ||
Root | \(-1.41313 + 0.0554252i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.49 |
Dual form | 1600.2.q.f.849.4 |
$q$-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 | \(-0.186089\pi\) |
−0.551879 | + | 0.833924i | \(0.686089\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.71540 | −1.78226 | −0.891128 | − | 0.453753i | \(-0.850085\pi\) | ||||
−0.891128 | + | 0.453753i | \(0.850085\pi\) | |||||||
\(8\) | 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 | \(-0.255486\pi\) |
−0.719189 | + | 0.694815i | \(0.755486\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.67442i | − | 1.13371i | −0.823816 | − | 0.566857i | \(-0.808159\pi\) | ||
0.823816 | − | 0.566857i | \(-0.191841\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.81249 | − | 1.81249i | 0.415813 | − | 0.415813i | −0.467945 | − | 0.883758i | \(-0.655005\pi\) |
0.883758 | + | 0.467945i | \(0.155005\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.30355 | − | 2.30355i | −0.502676 | − | 0.502676i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.63007 | −0.339893 | −0.169946 | − | 0.985453i | \(-0.554359\pi\) | ||||
−0.169946 | + | 0.985453i | \(0.554359\pi\) | |||||||
\(24\) | 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 | −0.941909 | − | 0.335869i | \(-0.890970\pi\) |
0.335869 | + | 0.941909i | \(0.390970\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.12875 | 0.382334 | 0.191167 | − | 0.981557i | \(-0.438773\pi\) | ||||
0.191167 | + | 0.981557i | \(0.438773\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.82371i | 0.665622i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.97797 | − | 3.97797i | 0.653974 | − | 0.653974i | −0.299973 | − | 0.953948i | \(-0.596978\pi\) |
0.953948 | + | 0.299973i | \(0.0969778\pi\) | |||||||
\(38\) | 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 | −0.512188 | − | 0.858873i | \(-0.671165\pi\) |
0.858873 | + | 0.512188i | \(0.171165\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 4.06129i | − | 0.592400i | −0.955126 | − | 0.296200i | \(-0.904281\pi\) | ||
0.955126 | − | 0.296200i | \(-0.0957195\pi\) | |||||||
\(48\) | 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 | −0.270507 | − | 0.962718i | \(-0.587191\pi\) |
0.962718 | + | 0.270507i | \(0.0871912\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.77086 | 0.234556 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.16453 | − | 5.16453i | −0.672365 | − | 0.672365i | 0.285896 | − | 0.958261i | \(-0.407709\pi\) |
−0.958261 | + | 0.285896i | \(0.907709\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | 11.8956i | 1.49870i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.49920 | − | 7.49920i | −0.916173 | − | 0.916173i | 0.0805758 | − | 0.996748i | \(-0.474324\pi\) |
−0.996748 | + | 0.0805758i | \(0.974324\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | 8.30557 | 0.972093 | 0.486047 | − | 0.873933i | \(-0.338439\pi\) | ||||
0.486047 | + | 0.873933i | \(0.338439\pi\) | |||||||
\(74\) | 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 | \(-0.275309\pi\) | ||||
0.648709 | + | 0.761037i | \(0.275309\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.93215 | −0.548017 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.16919 | + | 1.16919i | 0.128335 | + | 0.128335i | 0.768357 | − | 0.640022i | \(-0.221075\pi\) |
−0.640022 | + | 0.768357i | \(0.721075\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.18866 | −0.341861 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 3.24572i | − | 0.344046i | −0.985093 | − | 0.172023i | \(-0.944970\pi\) | ||
0.985093 | − | 0.172023i | \(-0.0550304\pi\) | |||||||
\(90\) | 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 | ||||||||
\(97\) | 13.9581i | 1.41723i | 0.705598 | + | 0.708613i | \(0.250679\pi\) | ||||
−0.705598 | + | 0.708613i | \(0.749321\pi\) | |||||||
\(98\) | 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 | ||||||||
\(103\) | −13.7638 | −1.35618 | −0.678092 | − | 0.734977i | \(-0.737193\pi\) | ||||
−0.678092 | + | 0.734977i | \(0.737193\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.327996 | − | 0.327996i | 0.0317086 | − | 0.0317086i | −0.691075 | − | 0.722783i | \(-0.742862\pi\) |
0.722783 | + | 0.691075i | \(0.242862\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.149698 | − | 0.149698i | 0.0143385 | − | 0.0143385i | −0.699901 | − | 0.714240i | \(-0.746773\pi\) |
0.714240 | + | 0.699901i | \(0.246773\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.88660 | 0.368900 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.97999i | 0.562550i | 0.959627 | + | 0.281275i | \(0.0907573\pi\) | ||||
−0.959627 | + | 0.281275i | \(0.909243\pi\) | |||||||
\(114\) | 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 | ||||||||
\(127\) | − | 2.73076i | − | 0.242315i | −0.992633 | − | 0.121158i | \(-0.961339\pi\) | ||
0.992633 | − | 0.121158i | \(-0.0386607\pi\) | |||||||
\(128\) | 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 | ||||||||
\(137\) | 0.199812 | 0.0170711 | 0.00853557 | − | 0.999964i | \(-0.497283\pi\) | ||||
0.00853557 | + | 0.999964i | \(0.497283\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.6301 | − | 11.6301i | −0.986448 | − | 0.986448i | 0.0134610 | − | 0.999909i | \(-0.495715\pi\) |
−0.999909 | + | 0.0134610i | \(0.995715\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.98400 | − | 1.98400i | 0.167083 | − | 0.167083i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 0.687871i | − | 0.0575227i | ||||||
\(144\) | 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 | 0.752024 | − | 0.659136i | \(-0.229078\pi\) |
−0.659136 | + | 0.752024i | \(0.729078\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 7.12216i | − | 0.579593i | −0.957088 | − | 0.289797i | \(-0.906412\pi\) | ||
0.957088 | − | 0.289797i | \(-0.0935877\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.7922 | −0.953341 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.32145 | + | 5.32145i | 0.424698 | + | 0.424698i | 0.886818 | − | 0.462120i | \(-0.152911\pi\) |
−0.462120 | + | 0.886818i | \(0.652911\pi\) | |||||||
\(158\) | 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 | \(-0.0114197\pi\) |
−0.0358685 | + | 0.999357i | \(0.511420\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.86820 | −0.763624 | −0.381812 | − | 0.924240i | \(-0.624700\pi\) | ||||
−0.381812 | + | 0.924240i | \(0.624700\pi\) | |||||||
\(168\) | 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 | −0.999807 | − | 0.0196525i | \(-0.993744\pi\) |
−0.0196525 | − | 0.999807i | \(-0.506256\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 5.04591i | − | 0.379274i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.419587 | − | 0.419587i | 0.0313614 | − | 0.0313614i | −0.691252 | − | 0.722614i | \(-0.742941\pi\) |
0.722614 | + | 0.691252i | \(0.242941\pi\) | |||||||
\(180\) | 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 | ||||||||
\(183\) | 6.96356 | 0.514761 | ||||||||
\(184\) | 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 | ||||||||
\(193\) | 16.8667i | 1.21409i | 0.794667 | + | 0.607045i | \(0.207645\pi\) | ||||
−0.794667 | + | 0.607045i | \(0.792355\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.58908 | + | 3.58908i | −0.255712 | + | 0.255712i | −0.823307 | − | 0.567596i | \(-0.807874\pi\) |
0.567596 | + | 0.823307i | \(0.307874\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.64501i | 0.471052i | 0.971868 | + | 0.235526i | \(0.0756813\pi\) | ||||
−0.971868 | + | 0.235526i | \(0.924319\pi\) | |||||||
\(200\) | 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 | ||||||||
\(207\) | 4.11218i | 0.285816i | ||||||||
\(208\) | 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 | ||||||||
\(217\) | −10.0379 | −0.681418 | ||||||||
\(218\) | 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 | ||||||||
\(223\) | − | 24.1071i | − | 1.61433i | −0.590326 | − | 0.807165i | \(-0.701001\pi\) | ||
0.590326 | − | 0.807165i | \(-0.298999\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.67411 | + | 6.67411i | 0.442977 | + | 0.442977i | 0.893011 | − | 0.450035i | \(-0.148588\pi\) |
−0.450035 | + | 0.893011i | \(0.648588\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.0807 | − | 16.0807i | −1.06264 | − | 1.06264i | −0.997902 | − | 0.0647388i | \(-0.979379\pi\) |
−0.0647388 | − | 0.997902i | \(-0.520621\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 18.0303i | − | 1.18631i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.4976 | 1.08079 | 0.540396 | − | 0.841411i | \(-0.318274\pi\) | ||||
0.540396 | + | 0.841411i | \(0.318274\pi\) | |||||||
\(234\) | 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 | \(-0.445593\pi\) | ||||
0.170094 | + | 0.985428i | \(0.445593\pi\) | |||||||
\(240\) | 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 | ||||||||
\(247\) | −0.318571 | −0.0202702 | ||||||||
\(248\) | 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 | ||||||||
\(257\) | 8.44760i | 0.526947i | 0.964667 | + | 0.263474i | \(0.0848682\pi\) | ||||
−0.964667 | + | 0.263474i | \(0.915132\pi\) | |||||||
\(258\) | 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 | ||||||||
\(263\) | 18.3064 | 1.12882 | 0.564410 | − | 0.825494i | \(-0.309104\pi\) | ||||
0.564410 | + | 0.825494i | \(0.309104\pi\) | |||||||
\(264\) | 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 | −0.987094 | − | 0.160140i | \(-0.948806\pi\) |
0.160140 | + | 0.987094i | \(0.448806\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.24520 | 0.136386 | 0.0681930 | − | 0.997672i | \(-0.478277\pi\) | ||||
0.0681930 | + | 0.997672i | \(0.478277\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.404882i | 0.0245046i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.28255 | − | 7.28255i | 0.437566 | − | 0.437566i | −0.453626 | − | 0.891192i | \(-0.649870\pi\) |
0.891192 | + | 0.453626i | \(0.149870\pi\) | |||||||
\(278\) | 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 | −0.995408 | − | 0.0957259i | \(-0.969483\pi\) |
0.0957259 | + | 0.995408i | \(0.469483\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 38.9259i | 2.29772i | ||||||||
\(288\) | 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 | −0.318339 | − | 0.947977i | \(-0.603125\pi\) |
0.947977 | + | 0.318339i | \(0.103125\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 21.1172 | 1.22534 | ||||||||
\(298\) | 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 | ||||||||
\(303\) | 13.1008i | 0.752621i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.94378 | + | 7.94378i | 0.453376 | + | 0.453376i | 0.896473 | − | 0.443098i | \(-0.146120\pi\) |
−0.443098 | + | 0.896473i | \(0.646120\pi\) | |||||||
\(308\) | 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 | ||||||||
\(313\) | −5.35842 | −0.302876 | −0.151438 | − | 0.988467i | \(-0.548390\pi\) | ||||
−0.151438 | + | 0.988467i | \(0.548390\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.88165 | + | 8.88165i | 0.498843 | + | 0.498843i | 0.911078 | − | 0.412235i | \(-0.135252\pi\) |
−0.412235 | + | 0.911078i | \(0.635252\pi\) | |||||||
\(318\) | 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 | ||||||||
\(327\) | 0.146260 | 0.00808817 | ||||||||
\(328\) | 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 | ||||||||
\(337\) | 22.0227i | 1.19965i | 0.800130 | + | 0.599827i | \(0.204764\pi\) | ||||
−0.800130 | + | 0.599827i | \(0.795236\pi\) | |||||||
\(338\) | 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 | ||||||||
\(343\) | −38.8315 | −2.09670 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.8920 | + | 11.8920i | −0.638395 | + | 0.638395i | −0.950159 | − | 0.311765i | \(-0.899080\pi\) |
0.311765 | + | 0.950159i | \(0.399080\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.65696 | − | 8.65696i | 0.463396 | − | 0.463396i | −0.436371 | − | 0.899767i | \(-0.643736\pi\) |
0.899767 | + | 0.436371i | \(0.143736\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.474200 | −0.0253109 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 26.6153i | − | 1.41659i | −0.705916 | − | 0.708296i | \(-0.749464\pi\) | ||
0.705916 | − | 0.708296i | \(-0.250536\pi\) | |||||||
\(354\) | 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 | \(-0.959146\pi\) | ||
0.991775 | − | 0.127995i | \(-0.0408542\pi\) | |||||||
\(360\) | 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 | ||||||||
\(367\) | − | 15.6741i | − | 0.818182i | −0.912494 | − | 0.409091i | \(-0.865846\pi\) | ||
0.912494 | − | 0.409091i | \(-0.134154\pi\) | |||||||
\(368\) | 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 | −0.833875 | − | 0.551953i | \(-0.813883\pi\) |
0.551953 | + | 0.833875i | \(0.313883\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.573629 | 0.0295434 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.4103 | − | 17.4103i | −0.894309 | − | 0.894309i | 0.100616 | − | 0.994925i | \(-0.467919\pi\) |
−0.994925 | + | 0.100616i | \(0.967919\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.33402 | − | 1.33402i | 0.0683438 | − | 0.0683438i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.04928i | 0.462396i | 0.972907 | + | 0.231198i | \(0.0742646\pi\) | ||||
−0.972907 | + | 0.231198i | \(0.925735\pi\) | |||||||
\(384\) | 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 | 0.979639 | − | 0.200768i | \(-0.0643437\pi\) |
−0.200768 | + | 0.979639i | \(0.564344\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.61962i | 0.385341i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.794869 | 0.0400959 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.44519 | + | 9.44519i | 0.474041 | + | 0.474041i | 0.903220 | − | 0.429179i | \(-0.141197\pi\) |
−0.429179 | + | 0.903220i | \(0.641197\pi\) | |||||||
\(398\) | 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 | ||||||||
\(407\) | 31.1363 | 1.54337 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.17336i | 0.206359i | 0.994663 | + | 0.103180i | \(0.0329017\pi\) | ||||
−0.994663 | + | 0.103180i | \(0.967098\pi\) | |||||||
\(410\) | 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 | ||||||||
\(417\) | − | 11.3629i | − | 0.556445i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.1191 | − | 27.1191i | 1.32485 | − | 1.32485i | 0.415060 | − | 0.909794i | \(-0.363761\pi\) |
0.909794 | − | 0.415060i | \(-0.136239\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | −10.2454 | −0.498150 | ||||||||
\(424\) | 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 | ||||||||
\(433\) | − | 16.8061i | − | 0.807649i | −0.914837 | − | 0.403824i | \(-0.867681\pi\) | ||
0.914837 | − | 0.403824i | \(-0.132319\pi\) | |||||||
\(434\) | 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 | \(0.0695487\pi\) | ||||
−0.976225 | + | 0.216759i | \(0.930451\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 38.4335i | − | 1.83017i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.5397 | − | 12.5397i | 0.595781 | − | 0.595781i | −0.343406 | − | 0.939187i | \(-0.611581\pi\) |
0.939187 | + | 0.343406i | \(0.111581\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.10780i | 0.0523972i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.0707 | −0.852811 | −0.426406 | − | 0.904532i | \(-0.640220\pi\) | ||||
−0.426406 | + | 0.904532i | \(0.640220\pi\) | |||||||
\(450\) | 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 | ||||||||
\(457\) | 18.6637 | 0.873052 | 0.436526 | − | 0.899692i | \(-0.356209\pi\) | ||||
0.436526 | + | 0.899692i | \(0.356209\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | − | 7.82533i | − | 0.363674i | −0.983329 | − | 0.181837i | \(-0.941796\pi\) | ||
0.983329 | − | 0.181837i | \(-0.0582043\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.75068 | + | 8.75068i | 0.404933 | + | 0.404933i | 0.879967 | − | 0.475034i | \(-0.157564\pi\) |
−0.475034 | + | 0.879967i | \(0.657564\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 35.3617 | + | 35.3617i | 1.63285 | + | 1.63285i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.19922i | 0.239568i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.7941 | 0.818172 | ||||||||
\(474\) | 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 | \(-0.484693\pi\) | ||||
0.0480710 | + | 0.998844i | \(0.484693\pi\) | |||||||
\(480\) | 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 | ||||||||
\(487\) | −4.87183 | −0.220764 | −0.110382 | − | 0.993889i | \(-0.535207\pi\) | ||||
−0.110382 | + | 0.993889i | \(0.535207\pi\) | |||||||
\(488\) | 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 | ||||||||
\(497\) | 21.4113i | 0.960429i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.1060 | + | 25.1060i | −1.12390 | + | 1.12390i | −0.132748 | + | 0.991150i | \(0.542380\pi\) |
−0.991150 | + | 0.132748i | \(0.957620\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.82077 | − | 4.82077i | −0.215376 | − | 0.215376i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.8868 | 0.842120 | 0.421060 | − | 0.907033i | \(-0.361658\pi\) | ||||
0.421060 | + | 0.907033i | \(0.361658\pi\) | |||||||
\(504\) | 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 | \(-0.494096\pi\) |
0.999828 | − | 0.0185459i | \(-0.00590369\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −39.1641 | −1.73252 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 9.77993i | − | 0.431794i | ||||||
\(514\) | 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 | −0.787876 | − | 0.615834i | \(-0.788819\pi\) |
0.615834 | + | 0.787876i | \(0.288819\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 9.95066i | − | 0.433458i | ||||||
\(528\) | 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 | ||||||||
\(537\) | 0.409950 | 0.0176906 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | − | 13.9330i | − | 0.597923i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.32918 | − | 1.32918i | −0.0568317 | − | 0.0568317i | 0.678120 | − | 0.734951i | \(-0.262795\pi\) |
−0.734951 | + | 0.678120i | \(0.762795\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −17.9800 | − | 17.9800i | −0.767366 | − | 0.767366i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.8306i | 0.503998i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −54.3766 | −2.31233 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.9082 | + | 24.9082i | 1.05539 | + | 1.05539i | 0.998373 | + | 0.0570196i | \(0.0181598\pi\) |
0.0570196 | + | 0.998373i | \(0.481840\pi\) | |||||||
\(558\) | 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 | \(-0.213799\pi\) |
−0.622294 | + | 0.782784i | \(0.713799\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.2571 | 0.976706 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.43971i | 0.353811i | 0.984228 | + | 0.176905i | \(0.0566087\pi\) | ||||
−0.984228 | + | 0.176905i | \(0.943391\pi\) | |||||||
\(570\) | 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 | ||||||||
\(577\) | − | 36.3491i | − | 1.51323i | −0.653860 | − | 0.756615i | \(-0.726852\pi\) | ||
0.653860 | − | 0.756615i | \(-0.273148\pi\) | |||||||
\(578\) | 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 | ||||||||
\(583\) | 39.4442 | 1.63361 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.55994 | + | 6.55994i | −0.270758 | + | 0.270758i | −0.829405 | − | 0.558647i | \(-0.811321\pi\) |
0.558647 | + | 0.829405i | \(0.311321\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.85833 | − | 3.85833i | 0.158980 | − | 0.158980i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.50665 | −0.144244 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.40974i | 0.0578911i | 0.999581 | + | 0.0289455i | \(0.00921494\pi\) | ||||
−0.999581 | + | 0.0289455i | \(0.990785\pi\) | |||||||
\(594\) | 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 | \(-0.841645\pi\) | ||
0.878785 | − | 0.477218i | \(-0.158355\pi\) | |||||||
\(600\) | 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 | ||||||||
\(607\) | − | 0.758240i | − | 0.0307760i | −0.999882 | − | 0.0153880i | \(-0.995102\pi\) | ||
0.999882 | − | 0.0153880i | \(-0.00489835\pi\) | |||||||
\(608\) | 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 | −0.421006 | − | 0.907058i | \(-0.638323\pi\) |
0.907058 | + | 0.421006i | \(0.138323\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −32.6899 | −1.31605 | −0.658023 | − | 0.752998i | \(-0.728607\pi\) | ||||
−0.658023 | + | 0.752998i | \(0.728607\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.3836 | + | 26.3836i | 1.06045 | + | 1.06045i | 0.998052 | + | 0.0623934i | \(0.0198733\pi\) |
0.0623934 | + | 0.998052i | \(0.480127\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.39781 | + | 4.39781i | −0.176478 | + | 0.176478i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.3049i | 0.613178i | ||||||||
\(624\) | 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 | ||||||||
\(633\) | −1.86521 | −0.0741354 | ||||||||
\(634\) | 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 | \(-0.459765\pi\) |
−0.992022 | + | 0.126065i | \(0.959765\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −36.9848 | −1.45402 | −0.727011 | − | 0.686625i | \(-0.759091\pi\) | ||||
−0.727011 | + | 0.686625i | \(0.759091\pi\) | |||||||
\(648\) | 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 | \(-0.0797986\pi\) |
−0.248077 | + | 0.968740i | \(0.579799\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 20.9525i | − | 0.817435i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.5421 | + | 15.5421i | −0.605434 | + | 0.605434i | −0.941749 | − | 0.336316i | \(-0.890819\pi\) |
0.336316 | + | 0.941749i | \(0.390819\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | −0.401363 | −0.0155877 | ||||||||
\(664\) | 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 | ||||||||
\(673\) | 29.2198i | 1.12634i | 0.826340 | + | 0.563171i | \(0.190419\pi\) | ||||
−0.826340 | + | 0.563171i | \(0.809581\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.2591 | + | 17.2591i | −0.663320 | + | 0.663320i | −0.956161 | − | 0.292841i | \(-0.905399\pi\) |
0.292841 | + | 0.956161i | \(0.405399\pi\) | |||||||
\(678\) | 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 | −0.727914 | − | 0.685668i | \(-0.759510\pi\) |
0.685668 | + | 0.727914i | \(0.259510\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 15.7113i | − | 0.599425i | ||||||
\(688\) | 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 | ||||||||
\(697\) | −38.5875 | −1.46161 | ||||||||
\(698\) | 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 | ||||||||
\(703\) | − | 14.4200i | − | 0.543862i | ||||||
\(704\) | 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 | 0.678394 | − | 0.734698i | \(-0.262676\pi\) |
−0.734698 | + | 0.678394i | \(0.762676\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 29.0911i | − | 1.09100i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.47000 | −0.129953 | ||||||||
\(714\) | 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 | \(-0.456080\pi\) | ||||
0.137541 | + | 0.990496i | \(0.456080\pi\) | |||||||
\(720\) | 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 | ||||||||
\(727\) | 30.1470 | 1.11809 | 0.559045 | − | 0.829137i | \(-0.311168\pi\) | ||||
0.559045 | + | 0.829137i | \(0.311168\pi\) | |||||||
\(728\) | 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 | \(-0.238084\pi\) |
−0.680147 | + | 0.733075i | \(0.738084\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 58.6977i | − | 2.16216i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.0001 | − | 31.0001i | 1.14036 | − | 1.14036i | 0.151973 | − | 0.988385i | \(-0.451437\pi\) |
0.988385 | − | 0.151973i | \(-0.0485626\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.155627 | − | 0.155627i | −0.00571710 | − | 0.00571710i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.5395 | 1.41388 | 0.706938 | − | 0.707276i | \(-0.250076\pi\) | ||||
0.706938 | + | 0.707276i | \(0.250076\pi\) | |||||||
\(744\) | 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 | ||||||||
\(753\) | 9.75884i | 0.355632i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.0688 | + | 17.0688i | −0.620377 | + | 0.620377i | −0.945628 | − | 0.325251i | \(-0.894551\pi\) |
0.325251 | + | 0.945628i | \(0.394551\pi\) | |||||||
\(758\) | 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 | ||||||||
\(767\) | 0.907741i | 0.0327766i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.8443 | −0.427117 | −0.213558 | − | 0.976930i | \(-0.568505\pi\) | ||||
−0.213558 | + | 0.976930i | \(0.568505\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.12679 | + | 4.12679i | −0.148623 | + | 0.148623i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.58865 | + | 3.58865i | −0.129075 | + | 0.129075i | −0.768693 | − | 0.639618i | \(-0.779093\pi\) |
0.639618 | + | 0.768693i | \(0.279093\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −18.3269 | −0.657474 | ||||||||
\(778\) | 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 | ||||||||
\(783\) | 17.6100i | 0.629332i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.4800 | + | 22.4800i | 0.801326 | + | 0.801326i | 0.983303 | − | 0.181977i | \(-0.0582497\pi\) |
−0.181977 | + | 0.983303i | \(0.558250\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.94296 | + | 8.94296i | 0.318378 | + | 0.318378i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 28.1981i | − | 1.00261i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.25272 | −0.0444853 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.67589 | − | 8.67589i | −0.307316 | − | 0.307316i | 0.536552 | − | 0.843867i | \(-0.319727\pi\) |
−0.843867 | + | 0.536552i | \(0.819727\pi\) | |||||||
\(798\) | 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 | ||||||||
\(807\) | −13.2515 | −0.466476 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.9066i | 0.981143i | 0.871401 | + | 0.490571i | \(0.163212\pi\) | ||||
−0.871401 | + | 0.490571i | \(0.836788\pi\) | |||||||
\(810\) | 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 | ||||||||
\(817\) | − | 8.24089i | − | 0.288312i | ||||||
\(818\) | 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 | ||||||||
\(823\) | 7.12228 | 0.248267 | 0.124133 | − | 0.992266i | \(-0.460385\pi\) | ||||
0.124133 | + | 0.992266i | \(0.460385\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.1618 | − | 32.1618i | 1.11837 | − | 1.11837i | 0.126394 | − | 0.991980i | \(-0.459660\pi\) |
0.991980 | − | 0.126394i | \(-0.0403403\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.9802 | − | 34.9802i | 1.21491 | − | 1.21491i | 0.245522 | − | 0.969391i | \(-0.421041\pi\) |
0.969391 | − | 0.245522i | \(-0.0789594\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.11529 | 0.246827 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 71.2149i | − | 2.46745i | ||||||
\(834\) | 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 | \(0.0614521\pi\) | ||||
−0.981422 | + | 0.191861i | \(0.938548\pi\) | |||||||
\(840\) | 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 | ||||||||
\(847\) | − | 92.5750i | − | 3.18092i | ||||||
\(848\) | 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 | −0.0100656 | − | 0.999949i | \(-0.503204\pi\) |
0.999949 | + | 0.0100656i | \(0.00320402\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34.1485 | 1.16649 | 0.583245 | − | 0.812296i | \(-0.301783\pi\) | ||||
0.583245 | + | 0.812296i | \(0.301783\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.4589 | + | 20.4589i | 0.698047 | + | 0.698047i | 0.963989 | − | 0.265942i | \(-0.0856829\pi\) |
−0.265942 | + | 0.963989i | \(0.585683\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −19.0159 | + | 19.0159i | −0.648060 | + | 0.648060i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 35.3591i | − | 1.20364i | −0.798633 | − | 0.601818i | \(-0.794443\pi\) | ||
0.798633 | − | 0.601818i | \(-0.205557\pi\) | |||||||
\(864\) | 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 | ||||||||
\(873\) | 35.2120 | 1.19175 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.15415 | − | 3.15415i | −0.106508 | − | 0.106508i | 0.651845 | − | 0.758353i | \(-0.273995\pi\) |
−0.758353 | + | 0.651845i | \(0.773995\pi\) | |||||||
\(878\) | 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 | \(-0.246036\pi\) |
−0.698247 | + | 0.715857i | \(0.746036\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 34.8129 | 1.16890 | 0.584452 | − | 0.811429i | \(-0.301310\pi\) | ||||
0.584452 | + | 0.811429i | \(0.301310\pi\) | |||||||
\(888\) | 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 | ||||||||
\(897\) | 0.139964i | 0.00467325i | ||||||||
\(898\) | 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 | ||||||||
\(903\) | −10.4736 | −0.348540 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.3188 | + | 13.3188i | −0.442244 | + | 0.442244i | −0.892766 | − | 0.450521i | \(-0.851238\pi\) |
0.450521 | + | 0.892766i | \(0.351238\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | 9.15148i | 0.302870i | ||||||||
\(914\) | 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 | \(0.172932\pi\) | ||||
−0.856016 | + | 0.516949i | \(0.827068\pi\) | |||||||
\(920\) | 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 | ||||||||
\(927\) | 34.7219i | 1.14042i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −30.3384 | −0.995369 | −0.497685 | − | 0.867358i | \(-0.665816\pi\) | ||||
−0.497685 | + | 0.867358i | \(0.665816\pi\) | |||||||
\(930\) | 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 | ||||||||
\(937\) | −14.5267 | −0.474565 | −0.237283 | − | 0.971441i | \(-0.576257\pi\) | ||||
−0.237283 | + | 0.971441i | \(0.576257\pi\) | |||||||
\(938\) | 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 | ||||||||
\(943\) | 13.4563i | 0.438197i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.8961 | − | 15.8961i | −0.516553 | − | 0.516553i | 0.399973 | − | 0.916527i | \(-0.369019\pi\) |
−0.916527 | + | 0.399973i | \(0.869019\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.729912 | − | 0.729912i | −0.0236939 | − | 0.0236939i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.67765i | 0.281392i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.2248 | 1.07626 | 0.538129 | − | 0.842862i | \(-0.319131\pi\) | ||||
0.538129 | + | 0.842862i | \(0.319131\pi\) | |||||||
\(954\) | 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 | ||||||||
\(967\) | −1.79116 | −0.0576000 | −0.0288000 | − | 0.999585i | \(-0.509169\pi\) | ||||
−0.0288000 | + | 0.999585i | \(0.509169\pi\) | |||||||
\(968\) | 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 | ||||||||
\(977\) | 6.81676i | 0.218088i | 0.994037 | + | 0.109044i | \(0.0347789\pi\) | ||||
−0.994037 | + | 0.109044i | \(0.965221\pi\) | |||||||
\(978\) | 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 | ||||||||
\(983\) | −5.49468 | −0.175253 | −0.0876265 | − | 0.996153i | \(-0.527928\pi\) | ||||
−0.0876265 | + | 0.996153i | \(0.527928\pi\) | |||||||
\(984\) | 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 | ||||||||
\(993\) | − | 5.93333i | − | 0.188289i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.5246 | − | 42.5246i | 1.34677 | − | 1.34677i | 0.457618 | − | 0.889149i | \(-0.348703\pi\) |
0.889149 | − | 0.457618i | \(-0.151297\pi\) | |||||||
\(998\) | 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.q.f.49.4 | 12 | ||
4.3 | odd | 2 | 400.2.q.f.149.3 | 12 | |||
5.2 | odd | 4 | 1600.2.l.g.1201.4 | 12 | |||
5.3 | odd | 4 | 1600.2.l.f.1201.3 | 12 | |||
5.4 | even | 2 | 1600.2.q.e.49.3 | 12 | |||
16.3 | odd | 4 | 400.2.q.e.349.4 | 12 | |||
16.13 | even | 4 | 1600.2.q.e.849.3 | 12 | |||
20.3 | even | 4 | 400.2.l.g.101.1 | yes | 12 | ||
20.7 | even | 4 | 400.2.l.f.101.6 | ✓ | 12 | ||
20.19 | odd | 2 | 400.2.q.e.149.4 | 12 | |||
80.3 | even | 4 | 400.2.l.g.301.1 | yes | 12 | ||
80.13 | odd | 4 | 1600.2.l.f.401.3 | 12 | |||
80.19 | odd | 4 | 400.2.q.f.349.3 | 12 | |||
80.29 | even | 4 | inner | 1600.2.q.f.849.4 | 12 | ||
80.67 | even | 4 | 400.2.l.f.301.6 | yes | 12 | ||
80.77 | odd | 4 | 1600.2.l.g.401.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.l.f.101.6 | ✓ | 12 | 20.7 | even | 4 | ||
400.2.l.f.301.6 | yes | 12 | 80.67 | even | 4 | ||
400.2.l.g.101.1 | yes | 12 | 20.3 | even | 4 | ||
400.2.l.g.301.1 | yes | 12 | 80.3 | even | 4 | ||
400.2.q.e.149.4 | 12 | 20.19 | odd | 2 | |||
400.2.q.e.349.4 | 12 | 16.3 | odd | 4 | |||
400.2.q.f.149.3 | 12 | 4.3 | odd | 2 | |||
400.2.q.f.349.3 | 12 | 80.19 | odd | 4 | |||
1600.2.l.f.401.3 | 12 | 80.13 | odd | 4 | |||
1600.2.l.f.1201.3 | 12 | 5.3 | odd | 4 | |||
1600.2.l.g.401.4 | 12 | 80.77 | odd | 4 | |||
1600.2.l.g.1201.4 | 12 | 5.2 | odd | 4 | |||
1600.2.q.e.49.3 | 12 | 5.4 | even | 2 | |||
1600.2.q.e.849.3 | 12 | 16.13 | even | 4 | |||
1600.2.q.f.49.4 | 12 | 1.1 | even | 1 | trivial | ||
1600.2.q.f.849.4 | 12 | 80.29 | even | 4 | inner |