Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1120,2,Mod(449,1120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1120, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1120.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1120 = 2^{5} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1120.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.94324502638\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 13x^{8} + 56x^{6} + 97x^{4} + 61x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.7 | ||
Root | \(1.28447i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1120.449 |
Dual form | 1120.2.g.b.449.4 |
$q$-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 \(\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(421\) | \(801\) | \(897\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.63460i | 0.943739i | 0.881668 | + | 0.471869i | \(0.156421\pi\) | ||||
−0.881668 | + | 0.471869i | \(0.843579\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.23081 | + | 0.153266i | −0.997648 | + | 0.0685425i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.328072 | 0.109357 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.24087 | −0.374137 | −0.187069 | − | 0.982347i | \(-0.559899\pi\) | ||||
−0.187069 | + | 0.982347i | \(0.559899\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.20355i | − | 1.16585i | −0.812524 | − | 0.582927i | \(-0.801907\pi\) | ||
0.812524 | − | 0.582927i | \(-0.198093\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.250528 | − | 3.64649i | −0.0646862 | − | 0.941519i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 3.39596i | − | 0.823641i | −0.911265 | − | 0.411821i | \(-0.864893\pi\) | ||
0.911265 | − | 0.411821i | \(-0.135107\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.46162 | 1.48240 | 0.741198 | − | 0.671286i | \(-0.234258\pi\) | ||||
0.741198 | + | 0.671286i | \(0.234258\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.63460 | 0.356700 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.15509i | − | 0.449367i | −0.974432 | − | 0.224683i | \(-0.927865\pi\) | ||
0.974432 | − | 0.224683i | \(-0.0721348\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.95302 | − | 0.683813i | 0.990604 | − | 0.136763i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.44008i | 1.04694i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.96490 | −0.736264 | −0.368132 | − | 0.929773i | \(-0.620003\pi\) | ||||
−0.368132 | + | 0.929773i | \(0.620003\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.0611 | 1.80703 | 0.903516 | − | 0.428555i | \(-0.140977\pi\) | ||||
0.903516 | + | 0.428555i | \(0.140977\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 2.02833i | − | 0.353088i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.153266 | + | 2.23081i | 0.0259066 | + | 0.377076i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.76815i | 1.11268i | 0.830956 | + | 0.556338i | \(0.187794\pi\) | ||||
−0.830956 | + | 0.556338i | \(0.812206\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.87113 | 1.10026 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.131318 | −0.0205084 | −0.0102542 | − | 0.999947i | \(-0.503264\pi\) | ||||
−0.0102542 | + | 0.999947i | \(0.503264\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.40498i | 1.12925i | 0.825348 | + | 0.564625i | \(0.190979\pi\) | ||||
−0.825348 | + | 0.564625i | \(0.809021\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.731866 | + | 0.0502822i | −0.109100 | + | 0.00749562i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 4.82702i | − | 0.704093i | −0.935983 | − | 0.352046i | \(-0.885486\pi\) | ||
0.935983 | − | 0.352046i | \(-0.114514\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.55105 | 0.777302 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 10.0374i | − | 1.37874i | −0.724411 | − | 0.689368i | \(-0.757888\pi\) | ||
0.724411 | − | 0.689368i | \(-0.242112\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.76815 | − | 0.190183i | 0.373257 | − | 0.0256443i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.5622i | 1.39900i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.9864 | 1.43031 | 0.715157 | − | 0.698964i | \(-0.246355\pi\) | ||||
0.715157 | + | 0.698964i | \(0.246355\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.33030 | −0.810512 | −0.405256 | − | 0.914203i | \(-0.632818\pi\) | ||||
−0.405256 | + | 0.914203i | \(0.632818\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 0.328072i | − | 0.0413332i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.644259 | + | 9.37731i | 0.0799105 | + | 1.16311i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 2.65614i | − | 0.324500i | −0.986750 | − | 0.162250i | \(-0.948125\pi\) | ||
0.986750 | − | 0.162250i | \(-0.0518750\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.52271 | 0.424085 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.754563 | −0.0895501 | −0.0447751 | − | 0.998997i | \(-0.514257\pi\) | ||||
−0.0447751 | + | 0.998997i | \(0.514257\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.03736i | − | 0.706619i | −0.935506 | − | 0.353310i | \(-0.885056\pi\) | ||
0.935506 | − | 0.353310i | \(-0.114944\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.11776 | + | 8.09622i | 0.129068 | + | 0.934871i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.24087i | 0.141411i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.6652 | 1.64996 | 0.824980 | − | 0.565162i | \(-0.191186\pi\) | ||||
0.824980 | + | 0.565162i | \(0.191186\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.90815 | −0.878684 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 14.0813i | − | 1.54562i | −0.634639 | − | 0.772809i | \(-0.718851\pi\) | ||
0.634639 | − | 0.772809i | \(-0.281149\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.520484 | + | 7.57574i | 0.0564544 | + | 0.821704i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 6.48105i | − | 0.694841i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.6742 | 1.34346 | 0.671731 | − | 0.740795i | \(-0.265551\pi\) | ||||
0.671731 | + | 0.740795i | \(0.265551\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.20355 | −0.440652 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 16.4459i | 1.70537i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −14.4146 | + | 0.990344i | −1.47891 | + | 0.101607i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.914215i | 0.0928244i | 0.998922 | + | 0.0464122i | \(0.0147788\pi\) | ||||
−0.998922 | + | 0.0464122i | \(0.985221\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.407096 | −0.0409146 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.4818 | 1.34149 | 0.670743 | − | 0.741689i | \(-0.265975\pi\) | ||||
0.670743 | + | 0.741689i | \(0.265975\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.516841i | 0.0509258i | 0.999676 | + | 0.0254629i | \(0.00810597\pi\) | ||||
−0.999676 | + | 0.0254629i | \(0.991894\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.64649 | + | 0.250528i | −0.355861 | + | 0.0244491i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.8486i | 1.82216i | 0.412228 | + | 0.911081i | \(0.364751\pi\) | ||||
−0.412228 | + | 0.911081i | \(0.635249\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.345270 | −0.0330709 | −0.0165354 | − | 0.999863i | \(-0.505264\pi\) | ||||
−0.0165354 | + | 0.999863i | \(0.505264\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.0632 | −1.05008 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 3.77026i | − | 0.354677i | −0.984150 | − | 0.177338i | \(-0.943251\pi\) | ||
0.984150 | − | 0.177338i | \(-0.0567487\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.330301 | + | 4.80759i | 0.0308007 | + | 0.448310i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 1.37907i | − | 0.127495i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.39596 | −0.311307 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.46024 | −0.860021 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 0.214652i | − | 0.0193545i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.9444 | + | 2.28458i | −0.978900 | + | 0.204339i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 5.63895i | − | 0.500376i | −0.968197 | − | 0.250188i | \(-0.919508\pi\) | ||
0.968197 | − | 0.250188i | \(-0.0804924\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.1042 | −1.06572 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.5183 | −0.918987 | −0.459493 | − | 0.888181i | \(-0.651969\pi\) | ||||
−0.459493 | + | 0.888181i | \(0.651969\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 6.46162i | − | 0.560293i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.833777 | − | 12.1358i | −0.0717601 | − | 1.04448i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 6.96632i | − | 0.595173i | −0.954695 | − | 0.297586i | \(-0.903818\pi\) | ||
0.954695 | − | 0.297586i | \(-0.0961816\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.3258 | 0.875827 | 0.437913 | − | 0.899017i | \(-0.355718\pi\) | ||||
0.437913 | + | 0.899017i | \(0.355718\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.89025 | 0.664479 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.21607i | 0.436189i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.84494 | − | 0.607683i | 0.734533 | − | 0.0504654i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 1.63460i | − | 0.134820i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.773875 | 0.0633983 | 0.0316992 | − | 0.999497i | \(-0.489908\pi\) | ||||
0.0316992 | + | 0.999497i | \(0.489908\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.14607 | −0.500160 | −0.250080 | − | 0.968225i | \(-0.580457\pi\) | ||||
−0.250080 | + | 0.968225i | \(0.580457\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 1.11412i | − | 0.0900712i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −22.4445 | + | 1.54202i | −1.80278 | + | 0.123858i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 18.5421i | − | 1.47982i | −0.672707 | − | 0.739909i | \(-0.734869\pi\) | ||
0.672707 | − | 0.739909i | \(-0.265131\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 16.4071 | 1.30117 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.15509 | −0.169845 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 0.993429i | − | 0.0778113i | −0.999243 | − | 0.0389057i | \(-0.987613\pi\) | ||
0.999243 | − | 0.0389057i | \(-0.0123872\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.310874 | + | 4.52483i | 0.0242015 | + | 0.352257i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.22052i | 0.249212i | 0.992206 | + | 0.124606i | \(0.0397666\pi\) | ||||
−0.992206 | + | 0.124606i | \(0.960233\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.66981 | −0.359216 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.11988 | 0.162111 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 15.9187i | − | 1.21028i | −0.796120 | − | 0.605138i | \(-0.793118\pi\) | ||
0.796120 | − | 0.605138i | \(-0.206882\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.683813 | − | 4.95302i | −0.0516914 | − | 0.374413i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 17.9585i | 1.34984i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.84647 | −0.735960 | −0.367980 | − | 0.929834i | \(-0.619951\pi\) | ||||
−0.367980 | + | 0.929834i | \(0.619951\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.6562 | 1.60969 | 0.804845 | − | 0.593484i | \(-0.202248\pi\) | ||||
0.804845 | + | 0.593484i | \(0.202248\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 10.3475i | − | 0.764911i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.03732 | − | 15.0985i | −0.0762656 | − | 1.11006i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.21395i | 0.308155i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.44008 | 0.395707 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.7197 | −1.28215 | −0.641077 | − | 0.767477i | \(-0.721512\pi\) | ||||
−0.641077 | + | 0.767477i | \(0.721512\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 12.0238i | − | 0.865490i | −0.901516 | − | 0.432745i | \(-0.857545\pi\) | ||
0.901516 | − | 0.432745i | \(-0.142455\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −15.3282 | + | 1.05311i | −1.09767 | + | 0.0754147i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 4.12069i | − | 0.293587i | −0.989167 | − | 0.146794i | \(-0.953105\pi\) | ||
0.989167 | − | 0.146794i | \(-0.0468953\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.86868 | 0.699572 | 0.349786 | − | 0.936830i | \(-0.386254\pi\) | ||||
0.349786 | + | 0.936830i | \(0.386254\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.34174 | 0.306243 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.96490i | 0.278282i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.292945 | − | 0.0201265i | 0.0204601 | − | 0.00140569i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 0.707024i | − | 0.0491416i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.01804 | −0.554620 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.93076 | 0.477133 | 0.238567 | − | 0.971126i | \(-0.423322\pi\) | ||||
0.238567 | + | 0.971126i | \(0.423322\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 1.23341i | − | 0.0845119i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.13493 | − | 16.5191i | −0.0774015 | − | 1.12659i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 10.0611i | − | 0.682994i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.86868 | 0.666864 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.2751 | −0.960246 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.0625i | 1.54438i | 0.635391 | + | 0.772191i | \(0.280839\pi\) | ||||
−0.635391 | + | 0.772191i | \(0.719161\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.62495 | − | 0.224340i | 0.108330 | − | 0.0149560i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 2.86073i | − | 0.189873i | −0.995483 | − | 0.0949366i | \(-0.969735\pi\) | ||
0.995483 | − | 0.0949366i | \(-0.0302648\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.5227 | −1.22402 | −0.612009 | − | 0.790851i | \(-0.709638\pi\) | ||||
−0.612009 | + | 0.790851i | \(0.709638\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.02833 | −0.133455 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.1112i | 1.51407i | 0.653376 | + | 0.757033i | \(0.273352\pi\) | ||||
−0.653376 | + | 0.757033i | \(0.726648\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.739815 | + | 10.7681i | 0.0482602 | + | 0.702437i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 23.9717i | 1.55713i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.01270 | −0.582983 | −0.291491 | − | 0.956573i | \(-0.594151\pi\) | ||||
−0.291491 | + | 0.956573i | \(0.594151\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.4415 | −0.801427 | −0.400713 | − | 0.916203i | \(-0.631238\pi\) | ||||
−0.400713 | + | 0.916203i | \(0.631238\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.39354i | 0.217696i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.23081 | − | 0.153266i | 0.142521 | − | 0.00979178i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 27.1617i | − | 1.72826i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 23.0173 | 1.45866 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.3984 | −1.35066 | −0.675329 | − | 0.737517i | \(-0.735998\pi\) | ||||
−0.675329 | + | 0.737517i | \(0.735998\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.67419i | 0.168125i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −12.3833 | + | 0.850785i | −0.775474 | + | 0.0532782i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 27.5737i | − | 1.72000i | −0.510296 | − | 0.859999i | \(-0.670464\pi\) | ||
0.510296 | − | 0.859999i | \(-0.329536\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.76815 | 0.420552 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.30077 | −0.0805159 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.77388i | 0.417695i | 0.977948 | + | 0.208848i | \(0.0669712\pi\) | ||||
−0.977948 | + | 0.208848i | \(0.933029\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.53838 | + | 22.3914i | 0.0945020 | + | 1.37549i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 20.7173i | 1.26788i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.5794 | 0.888922 | 0.444461 | − | 0.895798i | \(-0.353395\pi\) | ||||
0.444461 | + | 0.895798i | \(0.353395\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.3842 | −1.42049 | −0.710244 | − | 0.703956i | \(-0.751415\pi\) | ||||
−0.710244 | + | 0.703956i | \(0.751415\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 6.87113i | − | 0.415860i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.14607 | + | 0.848524i | −0.370622 | + | 0.0511679i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 8.57577i | − | 0.515268i | −0.966243 | − | 0.257634i | \(-0.917057\pi\) | ||
0.966243 | − | 0.257634i | \(-0.0829429\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.30077 | 0.197612 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.49675 | −0.208598 | −0.104299 | − | 0.994546i | \(-0.533260\pi\) | ||||
−0.104299 | + | 0.994546i | \(0.533260\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 18.2952i | − | 1.08754i | −0.839235 | − | 0.543769i | \(-0.816997\pi\) | ||
0.839235 | − | 0.543769i | \(-0.183003\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.61882 | − | 23.5622i | −0.0958906 | − | 1.39571i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.131318i | 0.00775143i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.46746 | 0.321615 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.49438 | −0.0876020 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 30.4752i | 1.78038i | 0.455592 | + | 0.890189i | \(0.349428\pi\) | ||||
−0.455592 | + | 0.890189i | \(0.650572\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24.5087 | + | 1.68384i | −1.42695 | + | 0.0980372i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 6.75044i | − | 0.391700i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.05901 | −0.523896 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.40498 | 0.426816 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 22.0374i | 1.26601i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.1217 | − | 0.970217i | 0.808606 | − | 0.0555545i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 24.8725i | − | 1.41955i | −0.704430 | − | 0.709773i | \(-0.748797\pi\) | ||
0.704430 | − | 0.709773i | \(-0.251203\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.844830 | −0.0480607 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.42579 | −0.421078 | −0.210539 | − | 0.977585i | \(-0.567522\pi\) | ||||
−0.210539 | + | 0.977585i | \(0.567522\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.10594i | 0.458175i | 0.973406 | + | 0.229088i | \(0.0735742\pi\) | ||||
−0.973406 | + | 0.229088i | \(0.926426\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.0502822 | + | 0.731866i | 0.00283308 | + | 0.0412360i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.6010i | 0.820076i | 0.912068 | + | 0.410038i | \(0.134485\pi\) | ||||
−0.912068 | + | 0.410038i | \(0.865515\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.91994 | 0.275464 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −30.8100 | −1.71964 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 21.9434i | − | 1.22096i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.87444 | − | 20.8203i | −0.159445 | − | 1.15490i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 0.564380i | − | 0.0312103i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.82702 | −0.266122 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.7374 | −1.63452 | −0.817258 | − | 0.576271i | \(-0.804507\pi\) | ||||
−0.817258 | + | 0.576271i | \(0.804507\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.22044i | 0.121679i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.407096 | + | 5.92535i | 0.0222420 | + | 0.323736i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.88799i | 0.429686i | 0.976649 | + | 0.214843i | \(0.0689241\pi\) | ||||
−0.976649 | + | 0.214843i | \(0.931076\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.16289 | 0.334722 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.4846 | −0.676078 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.85850 | + | 0.539911i | −0.423087 | + | 0.0290678i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 3.28725i | − | 0.176469i | −0.996100 | − | 0.0882344i | \(-0.971878\pi\) | ||
0.996100 | − | 0.0882344i | \(-0.0281225\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.68073 | −0.357611 | −0.178806 | − | 0.983884i | \(-0.557223\pi\) | ||||
−0.178806 | + | 0.983884i | \(0.557223\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 22.8676 | 1.22058 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.3234i | 1.40105i | 0.713626 | + | 0.700527i | \(0.247052\pi\) | ||||
−0.713626 | + | 0.700527i | \(0.752948\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.68329 | − | 0.115649i | 0.0893395 | − | 0.00613799i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 5.55105i | − | 0.293793i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.27155 | −0.436556 | −0.218278 | − | 0.975887i | \(-0.570044\pi\) | ||||
−0.218278 | + | 0.975887i | \(0.570044\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.7525 | 1.19750 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 15.4637i | − | 0.811635i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.925319 | + | 13.4682i | 0.0484334 | + | 0.704957i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 33.7548i | 1.76198i | 0.473130 | + | 0.880992i | \(0.343124\pi\) | ||||
−0.473130 | + | 0.880992i | \(0.656876\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.0430816 | −0.00224274 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.0374 | −0.521114 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.0582i | 1.45280i | 0.687272 | + | 0.726400i | \(0.258808\pi\) | ||||
−0.687272 | + | 0.726400i | \(0.741192\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.73439 | − | 17.8898i | −0.192843 | − | 0.923826i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.6667i | 0.858377i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.6585 | 0.804322 | 0.402161 | − | 0.915569i | \(-0.368259\pi\) | ||||
0.402161 | + | 0.915569i | \(0.368259\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.21744 | 0.472224 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.6950i | 0.955270i | 0.878558 | + | 0.477635i | \(0.158506\pi\) | ||||
−0.878558 | + | 0.477635i | \(0.841494\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.190183 | − | 2.76815i | −0.00969263 | − | 0.141078i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.42937i | 0.123492i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −33.7798 | −1.71270 | −0.856352 | − | 0.516392i | \(-0.827275\pi\) | ||||
−0.856352 | + | 0.516392i | \(0.827275\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.31859 | −0.370117 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 17.1932i | − | 0.867284i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −32.7152 | + | 2.24767i | −1.64608 | + | 0.113092i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 0.466183i | − | 0.0233971i | −0.999932 | − | 0.0116985i | \(-0.996276\pi\) | ||
0.999932 | − | 0.0116985i | \(-0.00372384\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.5622 | 0.528771 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 33.2221 | 1.65903 | 0.829516 | − | 0.558483i | \(-0.188616\pi\) | ||||
0.829516 | + | 0.558483i | \(0.188616\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 42.2924i | − | 2.10674i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 17.6416 | − | 1.21205i | 0.876617 | − | 0.0602271i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 8.39841i | − | 0.416294i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.4588 | 0.764390 | 0.382195 | − | 0.924082i | \(-0.375168\pi\) | ||||
0.382195 | + | 0.924082i | \(0.375168\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.3872 | 0.561688 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 10.9864i | − | 0.540608i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.15817 | + | 31.4126i | 0.105940 | + | 1.54198i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.8787i | 0.826551i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.0268 | 1.41805 | 0.709025 | − | 0.705183i | \(-0.249135\pi\) | ||||
0.709025 | + | 0.705183i | \(0.249135\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.31745 | −0.259156 | −0.129578 | − | 0.991569i | \(-0.541362\pi\) | ||||
−0.129578 | + | 0.991569i | \(0.541362\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 1.58361i | − | 0.0769977i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.32220 | − | 16.8203i | −0.112643 | − | 0.815902i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.33030i | 0.306345i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.52620 | −0.411649 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.6480 | 0.850073 | 0.425036 | − | 0.905176i | \(-0.360261\pi\) | ||||
0.425036 | + | 0.905176i | \(0.360261\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.5011i | 0.889107i | 0.895752 | + | 0.444554i | \(0.146638\pi\) | ||||
−0.895752 | + | 0.444554i | \(0.853362\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.993321 | + | 14.4580i | 0.0476261 | + | 0.693207i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 13.9254i | − | 0.666140i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.7444 | 0.703711 | 0.351855 | − | 0.936054i | \(-0.385551\pi\) | ||||
0.351855 | + | 0.936054i | \(0.385551\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.328072 | −0.0156225 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 18.0223i | − | 0.856264i | −0.903716 | − | 0.428132i | \(-0.859172\pi\) | ||
0.903716 | − | 0.428132i | \(-0.140828\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −28.2737 | + | 1.94252i | −1.34030 | + | 0.0920842i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.26498i | 0.0598314i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.46746 | 0.116447 | 0.0582233 | − | 0.998304i | \(-0.481456\pi\) | ||||
0.0582233 | + | 0.998304i | \(0.481456\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.162948 | 0.00767294 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 10.0464i | − | 0.472020i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.37731 | − | 0.644259i | 0.439615 | − | 0.0302033i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 1.73587i | − | 0.0812004i | −0.999175 | − | 0.0406002i | \(-0.987073\pi\) | ||
0.999175 | − | 0.0406002i | \(-0.0129270\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 18.4743 | 0.862306 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.00725 | 0.419510 | 0.209755 | − | 0.977754i | \(-0.432733\pi\) | ||||
0.209755 | + | 0.977754i | \(0.432733\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.1293i | 1.81849i | 0.416260 | + | 0.909246i | \(0.363341\pi\) | ||||
−0.416260 | + | 0.909246i | \(0.636659\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.52060 | − | 36.6878i | −0.116890 | − | 1.70135i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 6.47873i | − | 0.299800i | −0.988701 | − | 0.149900i | \(-0.952105\pi\) | ||
0.988701 | − | 0.149900i | \(-0.0478952\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.65614 | −0.122649 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 30.3089 | 1.39656 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 9.18864i | − | 0.422494i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 32.0045 | − | 4.41854i | 1.46847 | − | 0.202736i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 3.29298i | − | 0.150775i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.5651 | −1.03103 | −0.515514 | − | 0.856881i | \(-0.672399\pi\) | ||||
−0.515514 | + | 0.856881i | \(0.672399\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.4502 | 1.29722 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 3.52271i | − | 0.160289i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.140118 | − | 2.03944i | −0.00636242 | − | 0.0926061i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.2500i | 1.77859i | 0.457339 | + | 0.889293i | \(0.348803\pi\) | ||||
−0.457339 | + | 0.889293i | \(0.651197\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.62386 | 0.0734336 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.7793 | 1.52444 | 0.762220 | − | 0.647318i | \(-0.224109\pi\) | ||||
0.762220 | + | 0.647318i | \(0.224109\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.4647i | 0.606418i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.908153 | − | 0.0623938i | 0.0408184 | − | 0.00280439i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.754563i | 0.0338468i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.6529 | 0.521654 | 0.260827 | − | 0.965386i | \(-0.416005\pi\) | ||||
0.260827 | + | 0.965386i | \(0.416005\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.26428 | −0.235191 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.0639i | 0.671668i | 0.941921 | + | 0.335834i | \(0.109018\pi\) | ||||
−0.941921 | + | 0.335834i | \(0.890982\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −30.0753 | + | 2.06629i | −1.33833 | + | 0.0919488i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 7.63329i | − | 0.339006i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.8458 | 0.879649 | 0.439825 | − | 0.898084i | \(-0.355041\pi\) | ||||
0.439825 | + | 0.898084i | \(0.355041\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.03736 | −0.267077 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 35.1517i | 1.55199i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.0792139 | − | 1.15297i | −0.00349058 | − | 0.0508061i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.98971i | 0.263427i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 26.0208 | 1.14218 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.7964 | −0.823484 | −0.411742 | − | 0.911300i | \(-0.635080\pi\) | ||||
−0.411742 | + | 0.911300i | \(0.635080\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 31.0907i | − | 1.35950i | −0.733444 | − | 0.679750i | \(-0.762088\pi\) | ||
0.733444 | − | 0.679750i | \(-0.237912\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.09622 | − | 1.11776i | 0.353348 | − | 0.0487832i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 34.1672i | − | 1.48835i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.3556 | 0.798070 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.60435 | 0.156415 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.552000i | 0.0239098i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.88884 | − | 42.0476i | −0.124895 | − | 1.81788i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 16.0951i | − | 0.694554i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.24087 | 0.0534482 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −35.8816 | −1.54267 | −0.771336 | − | 0.636428i | \(-0.780411\pi\) | ||||
−0.771336 | + | 0.636428i | \(0.780411\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 35.3993i | 1.51913i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.770232 | − | 0.0529181i | 0.0329931 | − | 0.00226676i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 25.4869i | − | 1.08974i | −0.838520 | − | 0.544871i | \(-0.816579\pi\) | ||
0.838520 | − | 0.544871i | \(-0.183421\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.07679 | −0.0886354 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25.6197 | −1.09144 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 14.6652i | − | 0.623626i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 24.6800 | − | 1.69561i | 1.04761 | − | 0.0719748i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 23.5917i | − | 0.999612i | −0.866137 | − | 0.499806i | \(-0.833405\pi\) | ||
0.866137 | − | 0.499806i | \(-0.166595\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.1272 | 1.31654 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.88814 | −0.290818 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 1.25815i | − | 0.0530245i | −0.999648 | − | 0.0265123i | \(-0.991560\pi\) | ||
0.999648 | − | 0.0265123i | \(-0.00844011\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.577852 | + | 8.41074i | 0.0243104 | + | 0.353842i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.90815i | 0.332111i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.4899 | −0.984747 | −0.492373 | − | 0.870384i | \(-0.663871\pi\) | ||||
−0.492373 | + | 0.870384i | \(0.663871\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.0476 | 0.755269 | 0.377634 | − | 0.925955i | \(-0.376738\pi\) | ||||
0.377634 | + | 0.925955i | \(0.376738\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 28.9647i | − | 1.21002i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.47368 | − | 10.6742i | −0.0614565 | − | 0.445144i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 45.4141i | − | 1.89061i | −0.326184 | − | 0.945306i | \(-0.605763\pi\) | ||
0.326184 | − | 0.945306i | \(-0.394237\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.6541 | 0.816796 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.0813 | −0.584189 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.4551i | 0.515837i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.211363 | + | 3.07643i | 0.00873880 | + | 0.127195i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 38.1946i | 1.57646i | 0.615381 | + | 0.788230i | \(0.289002\pi\) | ||||
−0.615381 | + | 0.788230i | \(0.710998\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 65.0112 | 2.67874 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.73569 | 0.277069 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 11.0544i | − | 0.453952i | −0.973900 | − | 0.226976i | \(-0.927116\pi\) | ||
0.973900 | − | 0.226976i | \(-0.0728839\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.57574 | − | 0.520484i | 0.310575 | − | 0.0213378i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.1314i | 0.660213i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.4206 | 0.425773 | 0.212887 | − | 0.977077i | \(-0.431714\pi\) | ||||
0.212887 | + | 0.977077i | \(0.431714\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −31.5047 | −1.28510 | −0.642552 | − | 0.766242i | \(-0.722125\pi\) | ||||
−0.642552 | + | 0.766242i | \(0.722125\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 0.871407i | − | 0.0354864i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21.1040 | − | 1.44993i | 0.857999 | − | 0.0589480i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.9493i | 1.41855i | 0.704932 | + | 0.709275i | \(0.250977\pi\) | ||||
−0.704932 | + | 0.709275i | \(0.749023\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.48105 | −0.262625 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.2906 | −0.820869 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 37.9464i | − | 1.53264i | −0.642460 | − | 0.766319i | \(-0.722086\pi\) | ||
0.642460 | − | 0.766319i | \(-0.277914\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.0328988 | + | 0.478848i | 0.00132661 | + | 0.0193090i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.0081i | 1.08731i | 0.839310 | + | 0.543653i | \(0.182959\pi\) | ||||
−0.839310 | + | 0.543653i | \(0.817041\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.0656 | −1.16825 | −0.584123 | − | 0.811665i | \(-0.698561\pi\) | ||||
−0.584123 | + | 0.811665i | \(0.698561\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.7238 | 0.470462 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 12.6742i | − | 0.507781i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.0648 | − | 6.77388i | 0.962592 | − | 0.270955i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 13.1063i | − | 0.523416i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 22.9844 | 0.916447 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.8146 | 1.54518 | 0.772592 | − | 0.634903i | \(-0.218960\pi\) | ||||
0.772592 | + | 0.634903i | \(0.218960\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.3290i | 0.450289i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.864257 | + | 12.5794i | 0.0342970 | + | 0.499199i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.20355i | 0.166551i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.247551 | −0.00979297 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.2837 | 1.59111 | 0.795555 | − | 0.605881i | \(-0.207179\pi\) | ||||
0.795555 | + | 0.605881i | \(0.207179\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 2.02226i | − | 0.0797500i | −0.999205 | − | 0.0398750i | \(-0.987304\pi\) | ||
0.999205 | − | 0.0398750i | \(-0.0126960\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 27.0022 | − | 1.85516i | 1.06321 | − | 0.0730468i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 8.08779i | − | 0.317964i | −0.987281 | − | 0.158982i | \(-0.949179\pi\) | ||
0.987281 | − | 0.158982i | \(-0.0508212\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.6328 | −0.535133 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.4459 | 0.644568 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.0259i | 0.979338i | 0.871908 | + | 0.489669i | \(0.162882\pi\) | ||||
−0.871908 | + | 0.489669i | \(0.837118\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.4643 | − | 1.61209i | 0.916826 | − | 0.0629896i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 1.98069i | − | 0.0772740i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −35.1054 | −1.36751 | −0.683756 | − | 0.729711i | \(-0.739655\pi\) | ||||
−0.683756 | + | 0.729711i | \(0.739655\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.69197 | −0.299183 | −0.149592 | − | 0.988748i | \(-0.547796\pi\) | ||||
−0.149592 | + | 0.988748i | \(0.547796\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 23.3341i | − | 0.906221i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.990344 | + | 14.4146i | 0.0384039 | + | 0.558976i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.54471i | 0.330853i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −37.6981 | −1.45749 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.85510 | 0.303243 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 4.07019i | − | 0.156894i | −0.996918 | − | 0.0784472i | \(-0.975004\pi\) | ||
0.996918 | − | 0.0784472i | \(-0.0249962\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.71999 | + | 26.9448i | 0.143183 | + | 1.03711i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 32.6451i | − | 1.25465i | −0.778756 | − | 0.627327i | \(-0.784149\pi\) | ||
0.778756 | − | 0.627327i | \(-0.215851\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.914215 | 0.0350843 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.67616 | 0.179191 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.7284i | 1.36711i | 0.729900 | + | 0.683554i | \(0.239567\pi\) | ||||
−0.729900 | + | 0.683554i | \(0.760433\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.06770 | + | 15.5405i | 0.0407946 | + | 0.593773i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 30.2773i | − | 1.15515i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −42.1925 | −1.60741 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.9663 | −1.06389 | −0.531945 | − | 0.846779i | \(-0.678539\pi\) | ||||
−0.531945 | + | 0.846779i | \(0.678539\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.407096i | 0.0154643i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −23.0350 | + | 1.58260i | −0.873767 | + | 0.0600313i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.445949i | 0.0168915i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −37.7777 | −1.42888 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.7996 | −0.747822 | −0.373911 | − | 0.927465i | \(-0.621983\pi\) | ||||
−0.373911 | + | 0.927465i | \(0.621983\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 43.7332i | 1.64943i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −17.6017 | + | 1.20930i | −0.662917 | + | 0.0455451i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 13.4818i | − | 0.507034i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.46892 | −0.318057 | −0.159029 | − | 0.987274i | \(-0.550836\pi\) | ||||
−0.159029 | + | 0.987274i | \(0.550836\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.81123 | 0.180435 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 21.6826i | − | 0.812020i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.799444 | − | 11.6360i | −0.0298975 | − | 0.435164i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 14.7322i | − | 0.550183i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11.2512 | −0.419598 | −0.209799 | − | 0.977745i | \(-0.567281\pi\) | ||||
−0.209799 | + | 0.977745i | \(0.567281\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.516841 | 0.0192482 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 20.3369i | − | 0.756338i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −19.6382 | + | 2.71125i | −0.729346 | + | 0.100693i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 26.2716i | − | 0.974360i | −0.873302 | − | 0.487180i | \(-0.838026\pi\) | ||
0.873302 | − | 0.487180i | \(-0.161974\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.2716 | −1.08413 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 25.1470 | 0.930096 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 48.7804i | 1.80175i | 0.434082 | + | 0.900873i | \(0.357073\pi\) | ||||
−0.434082 | + | 0.900873i | \(0.642927\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.250528 | + | 3.64649i | 0.00924088 | + | 0.134503i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.29594i | 0.121407i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.5871 | 1.38267 | 0.691333 | − | 0.722537i | \(-0.257024\pi\) | ||||
0.691333 | + | 0.722537i | \(0.257024\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 44.3986 | 1.63102 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.2572i | 1.07334i | 0.843792 | + | 0.536671i | \(0.180318\pi\) | ||||
−0.843792 | + | 0.536671i | \(0.819682\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.72637 | + | 0.118608i | −0.0632492 | + | 0.00434548i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 4.61967i | − | 0.169025i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.8486 | 0.688712 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −41.4125 | −1.51116 | −0.755582 | − | 0.655054i | \(-0.772646\pi\) | ||||
−0.755582 | + | 0.655054i | \(0.772646\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 34.9780i | − | 1.27467i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.7107 | − | 0.941980i | 0.498983 | − | 0.0342822i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.1411i | 1.20453i | 0.798295 | + | 0.602266i | \(0.205736\pi\) | ||||
−0.798295 | + | 0.602266i | \(0.794264\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.37124 | −0.158666 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.08166 | 0.256710 | 0.128355 | − | 0.991728i | \(-0.459030\pi\) | ||||
0.128355 | + | 0.991728i | \(0.459030\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.345270i | 0.0124996i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.170756 | + | 2.48539i | 0.00617370 | + | 0.0898594i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 46.1820i | − | 1.66754i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.8844 | −0.753112 | −0.376556 | − | 0.926394i | \(-0.622892\pi\) | ||||
−0.376556 | + | 0.926394i | \(0.622892\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 45.0720 | 1.62323 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 50.0409i | 1.79985i | 0.436049 | + | 0.899923i | \(0.356377\pi\) | ||||
−0.436049 | + | 0.899923i | \(0.643623\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 49.8329 | − | 6.87993i | 1.79005 | − | 0.247134i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.0632i | 0.396892i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.848524 | −0.0304015 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.936316 | 0.0335040 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 21.5694i | − | 0.770827i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.84186 | + | 41.3638i | 0.101430 | + | 1.47634i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 23.0831i | − | 0.822824i | −0.911449 | − | 0.411412i | \(-0.865036\pi\) | ||
0.911449 | − | 0.411412i | \(-0.134964\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.0726 | −0.394195 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.77026 | −0.134055 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26.6097i | 0.944939i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −36.6011 | + | 2.51464i | −1.29811 | + | 0.0891852i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 0.553975i | − | 0.0196228i | −0.999952 | − | 0.00981140i | \(-0.996877\pi\) | ||
0.999952 | − | 0.00981140i | \(-0.00312312\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.3923 | −0.579920 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.15805 | 0.146917 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.49159i | 0.264372i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.80759 | − | 0.330301i | 0.169445 | − | 0.0116416i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23.8316i | 0.838910i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 42.8647 | 1.50704 | 0.753521 | − | 0.657424i | \(-0.228354\pi\) | ||||
0.753521 | + | 0.657424i | \(0.228354\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.28042 | −0.115191 | −0.0575955 | − | 0.998340i | \(-0.518343\pi\) | ||||
−0.0575955 | + | 0.998340i | \(0.518343\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 38.2238i | − | 1.34057i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.152258 | + | 2.21615i | 0.00533338 | + | 0.0776283i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 47.8482i | 1.67400i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.37907 | −0.0481885 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.73361 | −0.269905 | −0.134952 | − | 0.990852i | \(-0.543088\pi\) | ||||
−0.134952 | + | 0.990852i | \(0.543088\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 22.9368i | − | 0.799527i | −0.916618 | − | 0.399764i | \(-0.869092\pi\) | ||
0.916618 | − | 0.399764i | \(-0.130908\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.38700 | − | 10.0464i | −0.0482892 | − | 0.349770i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.4640i | 1.68526i | 0.538494 | + | 0.842629i | \(0.318993\pi\) | ||||
−0.538494 | + | 0.842629i | \(0.681007\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.4482 | 1.19643 | 0.598217 | − | 0.801334i | \(-0.295876\pi\) | ||||
0.598217 | + | 0.801334i | \(0.295876\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.0180 | 0.486278 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.39596i | 0.117663i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.493596 | − | 7.18437i | −0.0170816 | − | 0.248626i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 54.7333i | 1.89186i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.81974 | −0.339015 | −0.169508 | − | 0.985529i | \(-0.554218\pi\) | ||||
−0.169508 | + | 0.985529i | \(0.554218\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.2795 | −0.457915 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 5.71579i | − | 0.196862i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.4175 | − | 0.715722i | 0.358372 | − | 0.0246216i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.46024i | 0.325058i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 29.9054 | 1.02635 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.5860 | 0.500000 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 42.3139i | − | 1.44880i | −0.689380 | − | 0.724400i | \(-0.742117\pi\) | ||
0.689380 | − | 0.724400i | \(-0.257883\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.72904 | + | 0.324904i | −0.161730 | + | 0.0111115i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1.54342i | − | 0.0527224i | −0.999652 | − | 0.0263612i | \(-0.991608\pi\) | ||
0.999652 | − | 0.0263612i | \(-0.00839200\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.41854 | 0.150759 | 0.0753793 | − | 0.997155i | \(-0.475983\pi\) | ||||
0.0753793 | + | 0.997155i | \(0.475983\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.214652 | −0.00731533 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.91388i | 0.167270i | 0.996496 | + | 0.0836352i | \(0.0266530\pi\) | ||||
−0.996496 | + | 0.0836352i | \(0.973347\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.43979 | + | 35.5116i | 0.0829553 | + | 1.20743i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.93713i | 0.303521i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.1976 | −0.617311 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.1652 | −0.378319 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.299928i | 0.0101510i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.28458 | + | 10.9444i | 0.0772330 | + | 0.369989i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 11.7021i | − | 0.395153i | −0.980287 | − | 0.197577i | \(-0.936693\pi\) | ||
0.980287 | − | 0.197577i | \(-0.0633071\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −49.8148 | −1.68021 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.8823 | −1.00676 | −0.503380 | − | 0.864065i | \(-0.667910\pi\) | ||||
−0.503380 | + | 0.864065i | \(0.667910\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 44.6829i | − | 1.50370i | −0.659334 | − | 0.751850i | \(-0.729162\pi\) | ||
0.659334 | − | 0.751850i | \(-0.270838\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.75242 | − | 40.0619i | −0.0925215 | − | 1.34667i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.8523i | 0.532269i | 0.963936 | + | 0.266135i | \(0.0857466\pi\) | ||||
−0.963936 | + | 0.266135i | \(0.914253\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.63895 | −0.189124 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.81301 | 0.328748 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 31.1903i | − | 1.04374i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.9656 | − | 1.50913i | 0.734229 | − | 0.0504445i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 14.8079i | − | 0.494421i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −39.8914 | −1.33045 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −34.0865 | −1.13558 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.1042i | 0.402803i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −48.3108 | + | 3.31915i | −1.60591 | + | 0.110332i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.5453i | 0.881421i | 0.897649 | + | 0.440710i | \(0.145273\pi\) | ||||
−0.897649 | + | 0.440710i | \(0.854727\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.42299 | 0.146701 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.855810 | −0.0283543 | −0.0141771 | − | 0.999899i | \(-0.504513\pi\) | ||||
−0.0141771 | + | 0.999899i | \(0.504513\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.4730i | 0.578273i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.58592 | + | 23.0834i | 0.0524289 | + | 0.763113i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.5183i | 0.347344i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.6925 | −0.451675 | −0.225838 | − | 0.974165i | \(-0.572512\pi\) | ||||
−0.225838 | + | 0.974165i | \(0.572512\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 40.6566 | 1.33968 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.17184i | 0.104402i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.62815 | + | 33.5228i | 0.152173 | + | 1.10222i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.169561i | 0.00556911i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.2648 | −0.828912 | −0.414456 | − | 0.910069i | \(-0.636028\pi\) | ||||
−0.414456 | + | 0.910069i | \(0.636028\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.46162 | −0.211771 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 12.1382i | − | 0.397388i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.645854 | − | 9.40052i | −0.0211217 | − | 0.307430i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 28.8534i | − | 0.942599i | −0.881973 | − | 0.471299i | \(-0.843785\pi\) | ||
0.881973 | − | 0.471299i | \(-0.156215\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −13.2500 | −0.432397 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.28998 | 0.139850 | 0.0699248 | − | 0.997552i | \(-0.477724\pi\) | ||||
0.0699248 | + | 0.997552i | \(0.477724\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.283001i | 0.00921578i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −12.1358 | + | 0.833777i | −0.394777 | + | 0.0271228i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 48.2836i | 1.56901i | 0.620126 | + | 0.784503i | \(0.287082\pi\) | ||||
−0.620126 | + | 0.784503i | \(0.712918\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25.3783 | −0.823815 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.8669 | −0.773937 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 34.2147i | − | 1.10832i | −0.832409 | − | 0.554162i | \(-0.813039\pi\) | ||
0.832409 | − | 0.554162i | \(-0.186961\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 39.5293 | − | 2.71582i | 1.27914 | − | 0.0878820i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.04215i | 0.259966i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.96632 | −0.224954 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 70.2263 | 2.26536 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.18369i | 0.199267i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.84283 | + | 26.8227i | 0.0593228 | + | 0.863454i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 49.1870i | 1.58175i | 0.611980 | + | 0.790873i | \(0.290373\pi\) | ||||
−0.611980 | + | 0.790873i | \(0.709627\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 35.8687 | 1.15227 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.2107 | −0.809051 | −0.404526 | − | 0.914527i | \(-0.632563\pi\) | ||||
−0.404526 | + | 0.914527i | \(0.632563\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 10.3258i | − | 0.331031i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 34.0329 | − | 4.69857i | 1.08992 | − | 0.150475i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 18.0389i | − | 0.577116i | −0.957462 | − | 0.288558i | \(-0.906824\pi\) | ||
0.957462 | − | 0.288558i | \(-0.0931758\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.7271 | −0.502639 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.113274 | −0.00361654 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 51.6099i | − | 1.64610i | −0.567968 | − | 0.823051i | \(-0.692270\pi\) | ||
0.567968 | − | 0.823051i | \(-0.307730\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.631560 | + | 9.19247i | 0.0201232 | + | 0.292897i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 7.89025i | − | 0.251150i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15.9584 | 0.507447 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.4063 | 0.489398 | 0.244699 | − | 0.969599i | \(-0.421311\pi\) | ||||
0.244699 | + | 0.969599i | \(0.421311\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 48.6089i | − | 1.54256i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22.0151 | + | 1.51253i | −0.697927 | + | 0.0479504i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 13.6176i | − | 0.431274i | −0.976474 | − | 0.215637i | \(-0.930817\pi\) | ||
0.976474 | − | 0.215637i | \(-0.0691827\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −36.8193 | −1.16491 |
(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 | 1120.2.g.b.449.7 | yes | 10 | |
4.3 | odd | 2 | 1120.2.g.c.449.4 | yes | 10 | ||
5.2 | odd | 4 | 5600.2.a.bu.1.4 | 5 | |||
5.3 | odd | 4 | 5600.2.a.bw.1.2 | 5 | |||
5.4 | even | 2 | inner | 1120.2.g.b.449.4 | ✓ | 10 | |
8.3 | odd | 2 | 2240.2.g.n.449.7 | 10 | |||
8.5 | even | 2 | 2240.2.g.o.449.4 | 10 | |||
20.3 | even | 4 | 5600.2.a.bv.1.4 | 5 | |||
20.7 | even | 4 | 5600.2.a.bx.1.2 | 5 | |||
20.19 | odd | 2 | 1120.2.g.c.449.7 | yes | 10 | ||
40.19 | odd | 2 | 2240.2.g.n.449.4 | 10 | |||
40.29 | even | 2 | 2240.2.g.o.449.7 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1120.2.g.b.449.4 | ✓ | 10 | 5.4 | even | 2 | inner | |
1120.2.g.b.449.7 | yes | 10 | 1.1 | even | 1 | trivial | |
1120.2.g.c.449.4 | yes | 10 | 4.3 | odd | 2 | ||
1120.2.g.c.449.7 | yes | 10 | 20.19 | odd | 2 | ||
2240.2.g.n.449.4 | 10 | 40.19 | odd | 2 | |||
2240.2.g.n.449.7 | 10 | 8.3 | odd | 2 | |||
2240.2.g.o.449.4 | 10 | 8.5 | even | 2 | |||
2240.2.g.o.449.7 | 10 | 40.29 | even | 2 | |||
5600.2.a.bu.1.4 | 5 | 5.2 | odd | 4 | |||
5600.2.a.bv.1.4 | 5 | 20.3 | even | 4 | |||
5600.2.a.bw.1.2 | 5 | 5.3 | odd | 4 | |||
5600.2.a.bx.1.2 | 5 | 20.7 | even | 4 |