Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4900,2,Mod(2549,4900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4900.2549");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4900 = 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4900.e (of order \(2\), degree \(1\), 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: | \(39.1266969904\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2549.8 | ||
Root | \(-1.14412 - 1.14412i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4900.2549 |
Dual form | 4900.2.e.u.2549.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(1177\) | \(2451\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.28825i | 1.32112i | 0.750774 | + | 0.660560i | \(0.229681\pi\) | ||||
−0.750774 | + | 0.660560i | \(0.770319\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.23607 | −0.745356 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.47214 | −1.64991 | −0.824956 | − | 0.565198i | \(-0.808800\pi\) | ||||
−0.824956 | + | 0.565198i | \(0.808800\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 0.874032i | − 0.242413i | −0.992627 | − | 0.121206i | \(-0.961324\pi\) | ||||
0.992627 | − | 0.121206i | \(-0.0386763\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 4.57649i | − 1.10996i | −0.831863 | − | 0.554981i | \(-0.812725\pi\) | ||||
0.831863 | − | 0.554981i | \(-0.187275\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.99070 | 1.37436 | 0.687181 | − | 0.726486i | \(-0.258848\pi\) | ||||
0.687181 | + | 0.726486i | \(0.258848\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.47214i | 0.723990i | 0.932180 | + | 0.361995i | \(0.117904\pi\) | ||||
−0.932180 | + | 0.361995i | \(0.882096\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.74806i | 0.336415i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.236068 | −0.0438367 | −0.0219184 | − | 0.999760i | \(-0.506977\pi\) | ||||
−0.0219184 | + | 0.999760i | \(0.506977\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.27895 | −1.48694 | −0.743472 | − | 0.668767i | \(-0.766822\pi\) | ||||
−0.743472 | + | 0.668767i | \(0.766822\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 12.5216i | − 2.17973i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.23607i | 0.696405i | 0.937419 | + | 0.348203i | \(0.113208\pi\) | ||||
−0.937419 | + | 0.348203i | \(0.886792\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.11667 | −0.799090 | −0.399545 | − | 0.916714i | \(-0.630832\pi\) | ||||
−0.399545 | + | 0.916714i | \(0.630832\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 3.76393i | − 0.573994i | −0.957931 | − | 0.286997i | \(-0.907343\pi\) | ||||
0.957931 | − | 0.286997i | \(-0.0926570\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 4.91034i | − 0.716247i | −0.933674 | − | 0.358123i | \(-0.883417\pi\) | ||||
0.933674 | − | 0.358123i | \(-0.116583\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.4721 | 1.46639 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 11.7082i | − 1.60825i | −0.594463 | − | 0.804123i | \(-0.702635\pi\) | ||||
0.594463 | − | 0.804123i | \(-0.297365\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 13.7082i | 1.81570i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.95440 | −0.254441 | −0.127220 | − | 0.991874i | \(-0.540606\pi\) | ||||
−0.127220 | + | 0.991874i | \(0.540606\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.53244 | −0.964430 | −0.482215 | − | 0.876053i | \(-0.660168\pi\) | ||||
−0.482215 | + | 0.876053i | \(0.660168\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 13.9443i | − 1.70356i | −0.523896 | − | 0.851782i | \(-0.675522\pi\) | ||||
0.523896 | − | 0.851782i | \(-0.324478\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.94510 | −0.956478 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.7082 | 1.98290 | 0.991449 | − | 0.130491i | \(-0.0416554\pi\) | ||||
0.991449 | + | 0.130491i | \(0.0416554\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 7.53244i | − 0.881605i | −0.897604 | − | 0.440803i | \(-0.854694\pi\) | ||||
0.897604 | − | 0.440803i | \(-0.145306\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.4721 | 1.29072 | 0.645358 | − | 0.763880i | \(-0.276708\pi\) | ||||
0.645358 | + | 0.763880i | \(0.276708\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.7082 | −1.18980 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.1877i | 1.33778i | 0.743362 | + | 0.668889i | \(0.233230\pi\) | ||||
−0.743362 | + | 0.668889i | \(0.766770\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 0.540182i | − 0.0579135i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.86319 | 0.621496 | 0.310748 | − | 0.950492i | \(-0.399420\pi\) | ||||
0.310748 | + | 0.950492i | \(0.399420\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 18.9443i | − 1.96443i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 16.3516i | − 1.66025i | −0.557577 | − | 0.830125i | \(-0.688269\pi\) | ||||
0.557577 | − | 0.830125i | \(-0.311731\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.2361 | 1.22977 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.36861 | −0.335189 | −0.167595 | − | 0.985856i | \(-0.553600\pi\) | ||||
−0.167595 | + | 0.985856i | \(0.553600\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 18.3848i | − 1.81151i | −0.423806 | − | 0.905753i | \(-0.639306\pi\) | ||||
0.423806 | − | 0.905753i | \(-0.360694\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.4721i | 1.20573i | 0.797844 | + | 0.602863i | \(0.205974\pi\) | ||||
−0.797844 | + | 0.602863i | \(0.794026\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.4164 | 1.57241 | 0.786203 | − | 0.617968i | \(-0.212044\pi\) | ||||
0.786203 | + | 0.617968i | \(0.212044\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.69316 | −0.920034 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 13.7639i | − 1.29480i | −0.762150 | − | 0.647401i | \(-0.775856\pi\) | ||||
0.762150 | − | 0.647401i | \(-0.224144\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.95440i | 0.180684i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.9443 | 1.72221 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 11.7082i | − 1.05569i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 11.1803i | − 0.992095i | −0.868295 | − | 0.496047i | \(-0.834784\pi\) | ||||
0.868295 | − | 0.496047i | \(-0.165216\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.61280 | 0.758315 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.16073 | 0.188784 | 0.0943918 | − | 0.995535i | \(-0.469909\pi\) | ||||
0.0943918 | + | 0.995535i | \(0.469909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.0000i | 0.854358i | 0.904167 | + | 0.427179i | \(0.140493\pi\) | ||||
−0.904167 | + | 0.427179i | \(0.859507\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.3609 | 0.878797 | 0.439399 | − | 0.898292i | \(-0.355192\pi\) | ||||
0.439399 | + | 0.898292i | \(0.355192\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.2361 | 0.946248 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.78282i | 0.399960i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.70820 | −0.549557 | −0.274779 | − | 0.961507i | \(-0.588605\pi\) | ||||
−0.274779 | + | 0.961507i | \(0.588605\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.23607 | 0.670242 | 0.335121 | − | 0.942175i | \(-0.391223\pi\) | ||||
0.335121 | + | 0.942175i | \(0.391223\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.2333i | 0.827317i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 9.02546i | − 0.720310i | −0.932892 | − | 0.360155i | \(-0.882724\pi\) | ||||
0.932892 | − | 0.360155i | \(-0.117276\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 26.7912 | 2.12468 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.18034i | 0.170777i | 0.996348 | + | 0.0853887i | \(0.0272132\pi\) | ||||
−0.996348 | + | 0.0853887i | \(0.972787\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 4.11512i | − 0.318438i | −0.987243 | − | 0.159219i | \(-0.949102\pi\) | ||||
0.987243 | − | 0.159219i | \(-0.0508975\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.2361 | 0.941236 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.3956 | −1.02439 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 18.3848i | − 1.39777i | −0.715235 | − | 0.698884i | \(-0.753680\pi\) | ||||
0.715235 | − | 0.698884i | \(-0.246320\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 4.47214i | − 0.336146i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.70820 | −0.127677 | −0.0638386 | − | 0.997960i | \(-0.520334\pi\) | ||||
−0.0638386 | + | 0.997960i | \(0.520334\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.62365 | 0.269344 | 0.134672 | − | 0.990890i | \(-0.457002\pi\) | ||||
0.134672 | + | 0.990890i | \(0.457002\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 17.2361i | − 1.27413i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 25.0432i | 1.83134i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.1803 | −0.881338 | −0.440669 | − | 0.897670i | \(-0.645259\pi\) | ||||
−0.440669 | + | 0.897670i | \(0.645259\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.6525i | 1.12669i | 0.826222 | + | 0.563345i | \(0.190486\pi\) | ||||
−0.826222 | + | 0.563345i | \(0.809514\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.4721i | 1.38733i | 0.720297 | + | 0.693666i | \(0.244006\pi\) | ||||
−0.720297 | + | 0.693666i | \(0.755994\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.6746 | −1.53647 | −0.768235 | − | 0.640168i | \(-0.778865\pi\) | ||||
−0.768235 | + | 0.640168i | \(0.778865\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 31.9079 | 2.25061 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 7.76393i | − 0.539631i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −32.7820 | −2.26757 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.52786 | 0.655925 | 0.327963 | − | 0.944691i | \(-0.393638\pi\) | ||||
0.327963 | + | 0.944691i | \(0.393638\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 38.2325i | 2.61965i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 17.2361 | 1.16471 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.00000 | −0.269069 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.8539i | 0.793795i | 0.917863 | + | 0.396898i | \(0.129913\pi\) | ||||
−0.917863 | + | 0.396898i | \(0.870087\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.40337i | 0.425006i | 0.977160 | + | 0.212503i | \(0.0681616\pi\) | ||||
−0.977160 | + | 0.212503i | \(0.931838\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.57804 | −0.368607 | −0.184304 | − | 0.982869i | \(-0.559003\pi\) | ||||
−0.184304 | + | 0.982869i | \(0.559003\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 10.5279i | − 0.689703i | −0.938657 | − | 0.344852i | \(-0.887929\pi\) | ||||
0.938657 | − | 0.344852i | \(-0.112071\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 26.2511i | 1.70519i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.65248 | −0.559682 | −0.279841 | − | 0.960046i | \(-0.590282\pi\) | ||||
−0.279841 | + | 0.960046i | \(0.590282\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.41421 | 0.0910975 | 0.0455488 | − | 0.998962i | \(-0.485496\pi\) | ||||
0.0455488 | + | 0.998962i | \(0.485496\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 19.2588i | − 1.23545i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 5.23607i | − 0.333163i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −27.8885 | −1.76736 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.74806 | −0.110337 | −0.0551684 | − | 0.998477i | \(-0.517570\pi\) | ||||
−0.0551684 | + | 0.998477i | \(0.517570\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 19.0000i | − 1.19452i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 8.27895i | − 0.516427i | −0.966088 | − | 0.258213i | \(-0.916866\pi\) | ||||
0.966088 | − | 0.258213i | \(-0.0831338\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.527864 | 0.0326740 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.7082i | 0.660296i | 0.943929 | + | 0.330148i | \(0.107099\pi\) | ||||
−0.943929 | + | 0.330148i | \(0.892901\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.4164i | 0.821071i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −32.2418 | −1.96582 | −0.982908 | − | 0.184099i | \(-0.941063\pi\) | ||||
−0.982908 | + | 0.184099i | \(0.941063\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.8369 | 1.50873 | 0.754366 | − | 0.656454i | \(-0.227945\pi\) | ||||
0.754366 | + | 0.656454i | \(0.227945\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.9443i | 1.25842i | 0.777236 | + | 0.629210i | \(0.216621\pi\) | ||||
−0.777236 | + | 0.629210i | \(0.783379\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 18.5123 | 1.10830 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.1246 | −1.43915 | −0.719577 | − | 0.694413i | \(-0.755664\pi\) | ||||
−0.719577 | + | 0.694413i | \(0.755664\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.5672i | 0.628155i | 0.949397 | + | 0.314077i | \(0.101695\pi\) | ||||
−0.949397 | + | 0.314077i | \(0.898305\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.94427 | −0.232016 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 37.4164 | 2.19339 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 19.8477i | − 1.15951i | −0.814789 | − | 0.579757i | \(-0.803147\pi\) | ||||
0.814789 | − | 0.579757i | \(-0.196853\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 9.56564i | − 0.555055i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.03476 | 0.175505 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 7.70820i | − 0.442825i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 18.7186i | − 1.06833i | −0.845381 | − | 0.534164i | \(-0.820626\pi\) | ||||
0.845381 | − | 0.534164i | \(-0.179374\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 42.0689 | 2.39322 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.40802 | 0.533480 | 0.266740 | − | 0.963769i | \(-0.414054\pi\) | ||||
0.266740 | + | 0.963769i | \(0.414054\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 3.57494i | − 0.202068i | −0.994883 | − | 0.101034i | \(-0.967785\pi\) | ||||
0.994883 | − | 0.101034i | \(-0.0322150\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 0.416408i | − 0.0233878i | −0.999932 | − | 0.0116939i | \(-0.996278\pi\) | ||||
0.999932 | − | 0.0116939i | \(-0.00372237\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.29180 | 0.0723267 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −28.5393 | −1.59291 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 27.4164i | − 1.52549i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 37.5648i | 2.07734i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.3607 | −0.954229 | −0.477115 | − | 0.878841i | \(-0.658317\pi\) | ||||
−0.477115 | + | 0.878841i | \(0.658317\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 9.47214i | − 0.519070i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 17.1246i | − 0.932837i | −0.884564 | − | 0.466419i | \(-0.845544\pi\) | ||||
0.884564 | − | 0.466419i | \(-0.154456\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 31.4953 | 1.71059 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 45.3035 | 2.45332 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 25.3607i | 1.36143i | 0.732547 | + | 0.680716i | \(0.238331\pi\) | ||||
−0.732547 | + | 0.680716i | \(0.761669\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −34.9427 | −1.87044 | −0.935219 | − | 0.354069i | \(-0.884798\pi\) | ||||
−0.935219 | + | 0.354069i | \(0.884798\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.52786 | 0.0815513 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 11.7751i | − 0.626724i | −0.949634 | − | 0.313362i | \(-0.898545\pi\) | ||||
0.949634 | − | 0.313362i | \(-0.101455\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.0689 | 1.53420 | 0.767099 | − | 0.641529i | \(-0.221700\pi\) | ||||
0.767099 | + | 0.641529i | \(0.221700\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.8885 | 0.888871 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 43.3491i | 2.27524i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.78437i | 0.301942i | 0.988538 | + | 0.150971i | \(0.0482400\pi\) | ||||
−0.988538 | + | 0.150971i | \(0.951760\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.4412 | 0.595607 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 30.1246i | − 1.55979i | −0.625908 | − | 0.779897i | \(-0.715272\pi\) | ||||
0.625908 | − | 0.779897i | \(-0.284728\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.206331i | 0.0106266i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.1246 | −0.520066 | −0.260033 | − | 0.965600i | \(-0.583734\pi\) | ||||
−0.260033 | + | 0.965600i | \(0.583734\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 25.5834 | 1.31068 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.5958i | 1.10349i | 0.834012 | + | 0.551746i | \(0.186038\pi\) | ||||
−0.834012 | + | 0.551746i | \(0.813962\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.41641i | 0.427830i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.18034 | 0.161250 | 0.0806248 | − | 0.996745i | \(-0.474308\pi\) | ||||
0.0806248 | + | 0.996745i | \(0.474308\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.8902 | 0.803602 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.94427i | 0.249406i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 7.73877i | − 0.388398i | −0.980962 | − | 0.194199i | \(-0.937789\pi\) | ||||
0.980962 | − | 0.194199i | \(-0.0622107\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.708204 | 0.0353660 | 0.0176830 | − | 0.999844i | \(-0.494371\pi\) | ||||
0.0176830 | + | 0.999844i | \(0.494371\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.23607i | 0.360454i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 23.1803i | − 1.14901i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.89949 | 0.489499 | 0.244749 | − | 0.969586i | \(-0.421294\pi\) | ||||
0.244749 | + | 0.969586i | \(0.421294\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.8825 | −1.12871 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 23.7082i | 1.16100i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.4211 | 1.09534 | 0.547671 | − | 0.836694i | \(-0.315515\pi\) | ||||
0.547671 | + | 0.836694i | \(0.315515\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.5967 | 1.49119 | 0.745597 | − | 0.666397i | \(-0.232164\pi\) | ||||
0.745597 | + | 0.666397i | \(0.232164\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.9799i | 0.533859i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.9443 | −0.528394 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.6525 | 0.705785 | 0.352892 | − | 0.935664i | \(-0.385198\pi\) | ||||
0.352892 | + | 0.935664i | \(0.385198\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.41577i | 0.116094i | 0.998314 | + | 0.0580471i | \(0.0184874\pi\) | ||||
−0.998314 | + | 0.0580471i | \(0.981513\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.8005i | 0.995025i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.7565 | −1.13384 | −0.566918 | − | 0.823774i | \(-0.691864\pi\) | ||||
−0.566918 | + | 0.823774i | \(0.691864\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 39.1246i | − 1.85887i | −0.368990 | − | 0.929433i | \(-0.620296\pi\) | ||||
0.368990 | − | 0.929433i | \(-0.379704\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 15.3500i | − 0.726031i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.76393 | −0.460788 | −0.230394 | − | 0.973097i | \(-0.574002\pi\) | ||||
−0.230394 | + | 0.973097i | \(0.574002\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.9991 | 1.31843 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18.8461i | 0.885469i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 25.6525i | − 1.19997i | −0.800010 | − | 0.599986i | \(-0.795173\pi\) | ||||
0.800010 | − | 0.599986i | \(-0.204827\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.00000 | 0.373408 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.0193 | 0.792666 | 0.396333 | − | 0.918107i | \(-0.370282\pi\) | ||||
0.396333 | + | 0.918107i | \(0.370282\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 13.4164i | − 0.623513i | −0.950162 | − | 0.311757i | \(-0.899083\pi\) | ||||
0.950162 | − | 0.311757i | \(-0.100917\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.5595i | 0.812555i | 0.913750 | + | 0.406277i | \(0.133173\pi\) | ||||
−0.913750 | + | 0.406277i | \(0.866827\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 20.6525 | 0.951616 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20.5967i | 0.947039i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 26.1803i | 1.19872i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −27.4102 | −1.25241 | −0.626203 | − | 0.779660i | \(-0.715392\pi\) | ||||
−0.626203 | + | 0.779660i | \(0.715392\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.70246 | 0.168818 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 31.4721i | − 1.42614i | −0.701094 | − | 0.713069i | \(-0.747304\pi\) | ||||
0.701094 | − | 0.713069i | \(-0.252696\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.98915 | −0.225617 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.76393 | 0.0796051 | 0.0398026 | − | 0.999208i | \(-0.487327\pi\) | ||||
0.0398026 | + | 0.999208i | \(0.487327\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.08036i | 0.0486571i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.9443 | 1.20619 | 0.603096 | − | 0.797669i | \(-0.293934\pi\) | ||||
0.603096 | + | 0.797669i | \(0.293934\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.41641 | 0.420694 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.3153i | 0.549110i | 0.961571 | + | 0.274555i | \(0.0885306\pi\) | ||||
−0.961571 | + | 0.274555i | \(0.911469\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 27.9991i | 1.24348i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.0162 | 0.665580 | 0.332790 | − | 0.943001i | \(-0.392010\pi\) | ||||
0.332790 | + | 0.943001i | \(0.392010\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.4721i | 0.462356i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26.8701i | 1.18174i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 42.0689 | 1.84662 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −34.5300 | −1.51279 | −0.756394 | − | 0.654117i | \(-0.773041\pi\) | ||||
−0.756394 | + | 0.654117i | \(0.773041\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.90879i | 0.170919i | 0.996342 | + | 0.0854597i | \(0.0272359\pi\) | ||||
−0.996342 | + | 0.0854597i | \(0.972764\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 37.8885i | 1.65045i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.9443 | 0.475838 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.37016 | 0.189649 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.47214i | 0.193710i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 3.90879i | − 0.168677i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.7082 | −0.460382 | −0.230191 | − | 0.973146i | \(-0.573935\pi\) | ||||
−0.230191 | + | 0.973146i | \(0.573935\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.29180i | 0.355835i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 3.29180i | − 0.140747i | −0.997521 | − | 0.0703735i | \(-0.977581\pi\) | ||||
0.997521 | − | 0.0703735i | \(-0.0224191\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 16.8430 | 0.718844 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.41421 | −0.0602475 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.3475i | 0.607924i | 0.952684 | + | 0.303962i | \(0.0983096\pi\) | ||||
−0.952684 | + | 0.303962i | \(0.901690\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.28980 | −0.139144 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −57.3050 | −2.41942 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 41.6799i | − 1.75660i | −0.478112 | − | 0.878299i | \(-0.658679\pi\) | ||||
0.478112 | − | 0.878299i | \(-0.341321\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.9443 | −1.00380 | −0.501898 | − | 0.864927i | \(-0.667365\pi\) | ||||
−0.501898 | + | 0.864927i | \(0.667365\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.34752 | 0.181938 | 0.0909691 | − | 0.995854i | \(-0.471004\pi\) | ||||
0.0909691 | + | 0.995854i | \(0.471004\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 27.8716i | − 1.16435i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 39.5192i | − 1.64520i | −0.568617 | − | 0.822602i | \(-0.692521\pi\) | ||||
0.568617 | − | 0.822602i | \(-0.307479\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −35.8167 | −1.48849 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 64.0689i | 2.65346i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 36.8971i | − 1.52291i | −0.648221 | − | 0.761453i | \(-0.724487\pi\) | ||||
0.648221 | − | 0.761453i | \(-0.275513\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −49.5967 | −2.04360 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −44.5570 | −1.83283 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 30.5424i | − 1.25423i | −0.778928 | − | 0.627113i | \(-0.784236\pi\) | ||||
0.778928 | − | 0.627113i | \(-0.215764\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 49.5967i | − 2.02986i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.52786 | −0.348439 | −0.174220 | − | 0.984707i | \(-0.555740\pi\) | ||||
−0.174220 | + | 0.984707i | \(0.555740\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.4481 | −1.32359 | −0.661793 | − | 0.749687i | \(-0.730204\pi\) | ||||
−0.661793 | + | 0.749687i | \(0.730204\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 31.1803i | 1.26976i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 5.03786i | − 0.204480i | −0.994760 | − | 0.102240i | \(-0.967399\pi\) | ||||
0.994760 | − | 0.102240i | \(-0.0326010\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.29180 | −0.173627 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 26.8885i | − 1.08602i | −0.839727 | − | 0.543009i | \(-0.817285\pi\) | ||||
0.839727 | − | 0.543009i | \(-0.182715\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 15.3607i | − 0.618398i | −0.950997 | − | 0.309199i | \(-0.899939\pi\) | ||||
0.950997 | − | 0.309199i | \(-0.100061\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.1723 | −1.05195 | −0.525976 | − | 0.850500i | \(-0.676300\pi\) | ||||
−0.525976 | + | 0.850500i | \(0.676300\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.06952 | −0.243561 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 75.0132i | − 2.99574i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19.3863 | 0.772984 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.00000 | −0.0398094 | −0.0199047 | − | 0.999802i | \(-0.506336\pi\) | ||||
−0.0199047 | + | 0.999802i | \(0.506336\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 21.8021i | 0.866555i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −37.3607 | −1.47797 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −39.3607 | −1.55465 | −0.777327 | − | 0.629097i | \(-0.783425\pi\) | ||||
−0.777327 | + | 0.629097i | \(0.783425\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 26.3786i | − 1.04027i | −0.854084 | − | 0.520135i | \(-0.825882\pi\) | ||||
0.854084 | − | 0.520135i | \(-0.174118\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.4729i | 0.490360i | 0.969478 | + | 0.245180i | \(0.0788470\pi\) | ||||
−0.969478 | + | 0.245180i | \(0.921153\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.6947 | 0.419804 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 35.3050i | 1.38159i | 0.723051 | + | 0.690795i | \(0.242739\pi\) | ||||
−0.723051 | + | 0.690795i | \(0.757261\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.8430i | 0.657110i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.4721 | −0.641663 | −0.320832 | − | 0.947136i | \(-0.603962\pi\) | ||||
−0.320832 | + | 0.947136i | \(0.603962\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 44.0957 | 1.71512 | 0.857561 | − | 0.514382i | \(-0.171979\pi\) | ||||
0.857561 | + | 0.514382i | \(0.171979\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 9.15298i | − 0.355472i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 0.819660i | − 0.0317374i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −27.1246 | −1.04870 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 41.2185 | 1.59122 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.29180i | 0.319625i | 0.987147 | + | 0.159813i | \(0.0510890\pi\) | ||||
−0.987147 | + | 0.159813i | \(0.948911\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 30.7788i | − 1.18293i | −0.806332 | − | 0.591464i | \(-0.798550\pi\) | ||||
0.806332 | − | 0.591464i | \(-0.201450\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.6525 | −0.561484 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 9.47214i | − 0.362441i | −0.983442 | − | 0.181221i | \(-0.941995\pi\) | ||||
0.983442 | − | 0.181221i | \(-0.0580048\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 12.7639i | − 0.486974i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.2333 | −0.389859 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.0764 | −1.03003 | −0.515017 | − | 0.857180i | \(-0.672214\pi\) | ||||
−0.515017 | + | 0.857180i | \(0.672214\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.4164i | 0.886960i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 24.0903 | 0.911180 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.2492 | 1.29358 | 0.646788 | − | 0.762670i | \(-0.276112\pi\) | ||||
0.646788 | + | 0.762670i | \(0.276112\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.3770i | 0.957113i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.8885 | 0.596707 | 0.298353 | − | 0.954455i | \(-0.403563\pi\) | ||||
0.298353 | + | 0.954455i | \(0.403563\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −25.6525 | −0.962043 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 28.7456i | − 1.07653i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 19.7990i | − 0.739407i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.6777 | 0.883028 | 0.441514 | − | 0.897254i | \(-0.354441\pi\) | ||||
0.441514 | + | 0.897254i | \(0.354441\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.23607i | 0.120351i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.9473i | 1.40739i | 0.710503 | + | 0.703694i | \(0.248468\pi\) | ||||
−0.710503 | + | 0.703694i | \(0.751532\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 11.9443 | 0.442380 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.2256 | −0.637112 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.1313i | 0.706630i | 0.935504 | + | 0.353315i | \(0.114946\pi\) | ||||
−0.935504 | + | 0.353315i | \(0.885054\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 76.3050i | 2.81073i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.0557 | 0.664191 | 0.332095 | − | 0.943246i | \(-0.392244\pi\) | ||||
0.332095 | + | 0.943246i | \(0.392244\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.9814 | 0.440148 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 46.1803i | 1.69419i | 0.531440 | + | 0.847096i | \(0.321651\pi\) | ||||
−0.531440 | + | 0.847096i | \(0.678349\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 27.2526i | − 0.997121i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.94427 | 0.180419 | 0.0902095 | − | 0.995923i | \(-0.471246\pi\) | ||||
0.0902095 | + | 0.995923i | \(0.471246\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 4.00000i | − 0.145768i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 49.7214i | 1.80715i | 0.428426 | + | 0.903577i | \(0.359068\pi\) | ||||
−0.428426 | + | 0.903577i | \(0.640932\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 43.4767 | 1.57810 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −49.9287 | −1.80992 | −0.904958 | − | 0.425501i | \(-0.860098\pi\) | ||||
−0.904958 | + | 0.425501i | \(0.860098\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.70820i | 0.0616797i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.6854 | −0.601692 | −0.300846 | − | 0.953673i | \(-0.597269\pi\) | ||||
−0.300846 | + | 0.953673i | \(0.597269\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.9443 | 0.682261 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 6.94355i | − 0.249742i | −0.992173 | − | 0.124871i | \(-0.960148\pi\) | ||||
0.992173 | − | 0.124871i | \(-0.0398517\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −30.6525 | −1.09824 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −91.4296 | −3.27161 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 0.412662i | − 0.0147473i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 38.4875i | − 1.37193i | −0.727634 | − | 0.685966i | \(-0.759380\pi\) | ||||
0.727634 | − | 0.685966i | \(-0.240620\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24.5030 | −0.872330 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.58359i | 0.233790i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 14.3972i | − 0.509974i | −0.966944 | − | 0.254987i | \(-0.917929\pi\) | ||||
0.966944 | − | 0.254987i | \(-0.0820712\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.4721 | −0.795007 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13.1105 | −0.463236 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 41.2185i | 1.45457i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 73.7771i | − 2.59708i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.8754 | −0.417516 | −0.208758 | − | 0.977967i | \(-0.566942\pi\) | ||||
−0.208758 | + | 0.977967i | \(0.566942\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.1545 | −0.356574 | −0.178287 | − | 0.983979i | \(-0.557056\pi\) | ||||
−0.178287 | + | 0.983979i | \(0.557056\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 56.8328i | 1.99321i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 22.5486i | − 0.788876i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.5279 | −0.681527 | −0.340764 | − | 0.940149i | \(-0.610686\pi\) | ||||
−0.340764 | + | 0.940149i | \(0.610686\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.0557i | 0.559667i | 0.960048 | + | 0.279834i | \(0.0902793\pi\) | ||||
−0.960048 | + | 0.279834i | \(0.909721\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 47.6525i | − 1.65704i | −0.559960 | − | 0.828519i | \(-0.689184\pi\) | ||||
0.559960 | − | 0.828519i | \(-0.310816\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 43.3491 | 1.50558 | 0.752789 | − | 0.658262i | \(-0.228708\pi\) | ||||
0.752789 | + | 0.658262i | \(0.228708\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −47.9256 | −1.66252 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 14.4721i | − 0.500230i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.5803 | 0.814081 | 0.407040 | − | 0.913410i | \(-0.366561\pi\) | ||||
0.407040 | + | 0.913410i | \(0.366561\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9443 | −0.998078 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 55.2030i | − 1.90129i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −24.1803 | −0.829867 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.7082 | −0.504191 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.255039i | 0.00873237i | 0.999990 | + | 0.00436619i | \(0.00138980\pi\) | ||||
−0.999990 | + | 0.00436619i | \(0.998610\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 6.03941i | − 0.206302i | −0.994666 | − | 0.103151i | \(-0.967107\pi\) | ||||
0.994666 | − | 0.103151i | \(-0.0328926\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.4096 | 0.355170 | 0.177585 | − | 0.984105i | \(-0.443172\pi\) | ||||
0.177585 | + | 0.984105i | \(0.443172\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.87539i | 0.336162i | 0.985773 | + | 0.168081i | \(0.0537570\pi\) | ||||
−0.985773 | + | 0.168081i | \(0.946243\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 9.02546i | − 0.306521i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −62.7771 | −2.12957 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.1877 | −0.412966 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 36.5632i | 1.23748i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44.4296i | 1.50028i | 0.661279 | + | 0.750140i | \(0.270014\pi\) | ||||
−0.661279 | + | 0.750140i | \(0.729986\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 45.4164 | 1.53186 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.7456 | −0.968465 | −0.484233 | − | 0.874939i | \(-0.660901\pi\) | ||||
−0.484233 | + | 0.874939i | \(0.660901\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.05573i | 0.203791i | 0.994795 | + | 0.101896i | \(0.0324908\pi\) | ||||
−0.994795 | + | 0.101896i | \(0.967509\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 48.4658i | − 1.62732i | −0.581339 | − | 0.813661i | \(-0.697471\pi\) | ||||
0.581339 | − | 0.813661i | \(-0.302529\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 58.5967 | 1.96306 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 29.4164i | − 0.984383i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.94427i | 0.231862i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.95440 | 0.0651827 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −53.5825 | −1.78509 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.7771i | 0.922323i | 0.887316 | + | 0.461162i | \(0.152567\pi\) | ||||
−0.887316 | + | 0.461162i | \(0.847433\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.53244 | 0.249835 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.11146 | −0.235613 | −0.117807 | − | 0.993037i | \(-0.537586\pi\) | ||||
−0.117807 | + | 0.993037i | \(0.537586\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 66.6930i | − 2.20722i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.7082 | −0.617127 | −0.308563 | − | 0.951204i | \(-0.599848\pi\) | ||||
−0.308563 | + | 0.951204i | \(0.599848\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 42.8328 | 1.41139 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 14.6035i | − 0.480680i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 41.1096i | 1.35022i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.9991 | −0.918622 | −0.459311 | − | 0.888276i | \(-0.651904\pi\) | ||||
−0.459311 | + | 0.888276i | \(0.651904\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 21.5279i | 0.704791i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 55.6157i | 1.81689i | 0.418009 | + | 0.908443i | \(0.362728\pi\) | ||||
−0.418009 | + | 0.908443i | \(0.637272\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.18034 | 0.266955 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.78593 | 0.221215 | 0.110607 | − | 0.993864i | \(-0.464720\pi\) | ||||
0.110607 | + | 0.993864i | \(0.464720\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 17.7658i | − 0.578534i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 15.7771i | − 0.512686i | −0.966586 | − | 0.256343i | \(-0.917482\pi\) | ||||
0.966586 | − | 0.256343i | \(-0.0825177\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.58359 | −0.213712 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.952843 | 0.0308981 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 55.9017i | − 1.81083i | −0.424524 | − | 0.905417i | \(-0.639558\pi\) | ||||
0.424524 | − | 0.905417i | \(-0.360442\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.95595i | 0.0955522i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.5410 | 1.21100 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 27.8885i | − 0.898696i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 4.58359i | − 0.147398i | −0.997281 | − | 0.0736992i | \(-0.976520\pi\) | ||||
0.997281 | − | 0.0736992i | \(-0.0234805\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 62.7355 | 2.01535 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.4729 | −0.400274 | −0.200137 | − | 0.979768i | \(-0.564139\pi\) | ||||
−0.200137 | + | 0.979768i | \(0.564139\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 6.59675i | − 0.211049i | −0.994417 | − | 0.105524i | \(-0.966348\pi\) | ||||
0.994417 | − | 0.105524i | \(-0.0336521\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −32.0841 | −1.02541 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −36.7082 | −1.17200 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 42.4751i | − 1.35475i | −0.735640 | − | 0.677373i | \(-0.763118\pi\) | ||||
0.735640 | − | 0.677373i | \(-0.236882\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.0689 | 0.415566 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.34752 | 0.138104 | 0.0690518 | − | 0.997613i | \(-0.478003\pi\) | ||||
0.0690518 | + | 0.997613i | \(0.478003\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 39.7255i | − 1.26065i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 9.23179i | − 0.292374i | −0.989257 | − | 0.146187i | \(-0.953300\pi\) | ||||
0.989257 | − | 0.146187i | \(-0.0467001\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.40492 | −0.234281 |
(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 | 4900.2.e.u.2549.8 | 8 | ||
5.2 | odd | 4 | 4900.2.a.bg.1.4 | yes | 4 | ||
5.3 | odd | 4 | 4900.2.a.bi.1.1 | yes | 4 | ||
5.4 | even | 2 | inner | 4900.2.e.u.2549.2 | 8 | ||
7.6 | odd | 2 | inner | 4900.2.e.u.2549.1 | 8 | ||
35.13 | even | 4 | 4900.2.a.bi.1.4 | yes | 4 | ||
35.27 | even | 4 | 4900.2.a.bg.1.1 | ✓ | 4 | ||
35.34 | odd | 2 | inner | 4900.2.e.u.2549.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4900.2.a.bg.1.1 | ✓ | 4 | 35.27 | even | 4 | ||
4900.2.a.bg.1.4 | yes | 4 | 5.2 | odd | 4 | ||
4900.2.a.bi.1.1 | yes | 4 | 5.3 | odd | 4 | ||
4900.2.a.bi.1.4 | yes | 4 | 35.13 | even | 4 | ||
4900.2.e.u.2549.1 | 8 | 7.6 | odd | 2 | inner | ||
4900.2.e.u.2549.2 | 8 | 5.4 | even | 2 | inner | ||
4900.2.e.u.2549.7 | 8 | 35.34 | odd | 2 | inner | ||
4900.2.e.u.2549.8 | 8 | 1.1 | even | 1 | trivial |