Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(401,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.401");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.l (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 401.7 | ||
Root | \(-1.39563 - 0.228522i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.401 |
Dual form | 1600.2.l.i.1201.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.42313 | + | 1.42313i | 0.821645 | + | 0.821645i | 0.986344 | − | 0.164699i | \(-0.0526652\pi\) |
−0.164699 | + | 0.986344i | \(0.552665\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.690576i | − | 0.261013i | −0.991447 | − | 0.130507i | \(-0.958340\pi\) | ||
0.991447 | − | 0.130507i | \(-0.0416604\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.05061i | 0.350202i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.06057 | − | 3.06057i | 0.922797 | − | 0.922797i | −0.0744292 | − | 0.997226i | \(-0.523713\pi\) |
0.997226 | + | 0.0744292i | \(0.0237135\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.33686 | + | 2.33686i | 0.648128 | + | 0.648128i | 0.952540 | − | 0.304413i | \(-0.0984601\pi\) |
−0.304413 | + | 0.952540i | \(0.598460\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.28770 | 1.28246 | 0.641228 | − | 0.767350i | \(-0.278425\pi\) | ||||
0.641228 | + | 0.767350i | \(0.278425\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.38887 | − | 5.38887i | −1.23629 | − | 1.23629i | −0.961505 | − | 0.274787i | \(-0.911393\pi\) |
−0.274787 | − | 0.961505i | \(-0.588607\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.982780 | − | 0.982780i | 0.214460 | − | 0.214460i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.60841i | − | 0.335376i | −0.985840 | − | 0.167688i | \(-0.946370\pi\) | ||
0.985840 | − | 0.167688i | \(-0.0536301\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.77424 | − | 2.77424i | 0.533903 | − | 0.533903i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.70319 | + | 1.70319i | 0.316274 | + | 0.316274i | 0.847334 | − | 0.531060i | \(-0.178206\pi\) |
−0.531060 | + | 0.847334i | \(0.678206\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.69807 | 0.843798 | 0.421899 | − | 0.906643i | \(-0.361364\pi\) | ||||
0.421899 | + | 0.906643i | \(0.361364\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.71119 | 1.51642 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.89871 | + | 7.89871i | −1.29854 | + | 1.29854i | −0.369185 | + | 0.929356i | \(0.620363\pi\) |
−0.929356 | + | 0.369185i | \(0.879637\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.65131i | 1.06506i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.49891i | − | 0.858785i | −0.903118 | − | 0.429392i | \(-0.858728\pi\) | ||
0.903118 | − | 0.429392i | \(-0.141272\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.256166 | + | 0.256166i | −0.0390650 | + | 0.0390650i | −0.726369 | − | 0.687304i | \(-0.758794\pi\) |
0.687304 | + | 0.726369i | \(0.258794\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.60743 | −0.672063 | −0.336032 | − | 0.941851i | \(-0.609085\pi\) | ||||
−0.336032 | + | 0.941851i | \(0.609085\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.52310 | 0.931872 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.52510 | + | 7.52510i | 1.05372 | + | 1.05372i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.99318 | − | 4.99318i | 0.685866 | − | 0.685866i | −0.275449 | − | 0.961316i | \(-0.588827\pi\) |
0.961316 | + | 0.275449i | \(0.0888266\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 15.3382i | − | 2.03159i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.46478 | + | 1.46478i | −0.190698 | + | 0.190698i | −0.795998 | − | 0.605300i | \(-0.793053\pi\) |
0.605300 | + | 0.795998i | \(0.293053\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.33004 | + | 9.33004i | 1.19459 | + | 1.19459i | 0.975764 | + | 0.218825i | \(0.0702224\pi\) |
0.218825 | + | 0.975764i | \(0.429778\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.725523 | 0.0914074 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.94797 | − | 1.94797i | −0.237982 | − | 0.237982i | 0.578032 | − | 0.816014i | \(-0.303821\pi\) |
−0.816014 | + | 0.578032i | \(0.803821\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.28897 | − | 2.28897i | 0.275560 | − | 0.275560i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.32246i | 0.275625i | 0.990458 | + | 0.137813i | \(0.0440072\pi\) | ||||
−0.990458 | + | 0.137813i | \(0.955993\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.29733i | 0.151841i | 0.997114 | + | 0.0759206i | \(0.0241896\pi\) | ||||
−0.997114 | + | 0.0759206i | \(0.975810\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.11356 | − | 2.11356i | −0.240862 | − | 0.240862i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.01968 | 0.564758 | 0.282379 | − | 0.959303i | \(-0.408876\pi\) | ||||
0.282379 | + | 0.959303i | \(0.408876\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 11.0480 | 1.22756 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.30477 | + | 7.30477i | 0.801802 | + | 0.801802i | 0.983377 | − | 0.181575i | \(-0.0581194\pi\) |
−0.181575 | + | 0.983377i | \(0.558119\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.84772i | 0.519730i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.81564i | 0.192458i | 0.995359 | + | 0.0962290i | \(0.0306781\pi\) | ||||
−0.995359 | + | 0.0962290i | \(0.969322\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.61378 | − | 1.61378i | 0.169170 | − | 0.169170i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.68597 | + | 6.68597i | 0.693303 | + | 0.693303i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.27038 | −0.535126 | −0.267563 | − | 0.963540i | \(-0.586218\pi\) | ||||
−0.267563 | + | 0.963540i | \(0.586218\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.21546 | + | 3.21546i | 0.323165 | + | 0.323165i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.4502 | + | 13.4502i | −1.33834 | + | 1.33834i | −0.440675 | + | 0.897667i | \(0.645261\pi\) |
−0.897667 | + | 0.440675i | \(0.854739\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 2.64310i | − | 0.260432i | −0.991486 | − | 0.130216i | \(-0.958433\pi\) | ||
0.991486 | − | 0.130216i | \(-0.0415671\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.28120 | + | 6.28120i | −0.607227 | + | 0.607227i | −0.942220 | − | 0.334994i | \(-0.891266\pi\) |
0.334994 | + | 0.942220i | \(0.391266\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.89216 | − | 6.89216i | −0.660149 | − | 0.660149i | 0.295266 | − | 0.955415i | \(-0.404592\pi\) |
−0.955415 | + | 0.295266i | \(0.904592\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −22.4818 | −2.13388 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.46108 | −0.607807 | −0.303904 | − | 0.952703i | \(-0.598290\pi\) | ||||
−0.303904 | + | 0.952703i | \(0.598290\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.45512 | + | 2.45512i | −0.226976 | + | 0.226976i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 3.65156i | − | 0.334738i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 7.73420i | − | 0.703109i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.82566 | − | 7.82566i | 0.705616 | − | 0.705616i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.6123 | −1.47411 | −0.737054 | − | 0.675834i | \(-0.763784\pi\) | ||||
−0.737054 | + | 0.675834i | \(0.763784\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.729117 | −0.0641951 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.7719 | + | 11.7719i | 1.02851 | + | 1.02851i | 0.999581 | + | 0.0289318i | \(0.00921056\pi\) |
0.0289318 | + | 0.999581i | \(0.490789\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.72143 | + | 3.72143i | −0.322689 | + | 0.322689i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.41495i | 0.718937i | 0.933157 | + | 0.359469i | \(0.117042\pi\) | ||||
−0.933157 | + | 0.359469i | \(0.882958\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.51845 | − | 1.51845i | 0.128793 | − | 0.128793i | −0.639772 | − | 0.768565i | \(-0.720971\pi\) |
0.768565 | + | 0.639772i | \(0.220971\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.55698 | − | 6.55698i | −0.552198 | − | 0.552198i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.3042 | 1.19618 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.28324 | + | 9.28324i | 0.765668 | + | 0.765668i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.61440 | + | 2.61440i | −0.214180 | + | 0.214180i | −0.806040 | − | 0.591860i | \(-0.798394\pi\) |
0.591860 | + | 0.806040i | \(0.298394\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 12.7143i | − | 1.03467i | −0.855782 | − | 0.517337i | \(-0.826923\pi\) | ||
0.855782 | − | 0.517337i | \(-0.173077\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.55529i | 0.449119i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.17831 | + | 7.17831i | 0.572891 | + | 0.572891i | 0.932935 | − | 0.360044i | \(-0.117238\pi\) |
−0.360044 | + | 0.932935i | \(0.617238\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 14.2119 | 1.12708 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.11073 | −0.0875376 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.05476 | − | 7.05476i | −0.552572 | − | 0.552572i | 0.374611 | − | 0.927182i | \(-0.377776\pi\) |
−0.927182 | + | 0.374611i | \(0.877776\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 3.90586i | − | 0.302244i | −0.988515 | − | 0.151122i | \(-0.951711\pi\) | ||
0.988515 | − | 0.151122i | \(-0.0482887\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 2.07819i | − | 0.159861i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.66158 | − | 5.66158i | 0.432952 | − | 0.432952i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.20139 | − | 8.20139i | −0.623540 | − | 0.623540i | 0.322895 | − | 0.946435i | \(-0.395344\pi\) |
−0.946435 | + | 0.322895i | \(0.895344\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.16914 | −0.313372 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.10363 | + | 3.10363i | 0.231976 | + | 0.231976i | 0.813517 | − | 0.581541i | \(-0.197550\pi\) |
−0.581541 | + | 0.813517i | \(0.697550\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.91041 | + | 1.91041i | −0.141999 | + | 0.141999i | −0.774533 | − | 0.632534i | \(-0.782015\pi\) |
0.632534 | + | 0.774533i | \(0.282015\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 26.5557i | 1.96306i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.1834 | − | 16.1834i | 1.18345 | − | 1.18345i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.91583 | − | 1.91583i | −0.139356 | − | 0.139356i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.61041 | −0.405955 | −0.202977 | − | 0.979183i | \(-0.565062\pi\) | ||||
−0.202977 | + | 0.979183i | \(0.565062\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.90696 | −0.281229 | −0.140615 | − | 0.990064i | \(-0.544908\pi\) | ||||
−0.140615 | + | 0.990064i | \(0.544908\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.608436 | + | 0.608436i | −0.0433493 | + | 0.0433493i | −0.728449 | − | 0.685100i | \(-0.759759\pi\) |
0.685100 | + | 0.728449i | \(0.259759\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 15.5282i | − | 1.10076i | −0.834913 | − | 0.550382i | \(-0.814482\pi\) | ||
0.834913 | − | 0.550382i | \(-0.185518\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 5.54443i | − | 0.391074i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.17618 | − | 1.17618i | 0.0825517 | − | 0.0825517i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.68980 | 0.117449 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −32.9861 | −2.28169 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.14501 | − | 2.14501i | −0.147669 | − | 0.147669i | 0.629407 | − | 0.777076i | \(-0.283298\pi\) |
−0.777076 | + | 0.629407i | \(0.783298\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.30516 | + | 3.30516i | −0.226466 | + | 0.226466i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 3.24437i | − | 0.220242i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.84627 | + | 1.84627i | −0.124760 | + | 0.124760i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.3566 | + | 12.3566i | 0.831196 | + | 0.831196i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.34794 | −0.157230 | −0.0786148 | − | 0.996905i | \(-0.525050\pi\) | ||||
−0.0786148 | + | 0.996905i | \(0.525050\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.1881 | + | 13.1881i | 0.875325 | + | 0.875325i | 0.993047 | − | 0.117722i | \(-0.0375591\pi\) |
−0.117722 | + | 0.993047i | \(0.537559\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.37860 | − | 9.37860i | 0.619755 | − | 0.619755i | −0.325713 | − | 0.945469i | \(-0.605604\pi\) |
0.945469 | + | 0.325713i | \(0.105604\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 6.01574i | − | 0.395807i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 16.3435i | − | 1.07070i | −0.844630 | − | 0.535350i | \(-0.820180\pi\) | ||
0.844630 | − | 0.535350i | \(-0.179820\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.14367 | + | 7.14367i | 0.464031 | + | 0.464031i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.3818 | −1.25371 | −0.626854 | − | 0.779137i | \(-0.715658\pi\) | ||||
−0.626854 | + | 0.779137i | \(0.715658\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.15965 | 0.461193 | 0.230597 | − | 0.973049i | \(-0.425932\pi\) | ||||
0.230597 | + | 0.973049i | \(0.425932\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.40009 | + | 7.40009i | 0.474716 | + | 0.474716i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 25.1861i | − | 1.60255i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 20.7913i | 1.31759i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.4372 | + | 10.4372i | −0.658787 | + | 0.658787i | −0.955093 | − | 0.296306i | \(-0.904245\pi\) |
0.296306 | + | 0.955093i | \(0.404245\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.92264 | − | 4.92264i | −0.309484 | − | 0.309484i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.72152 | −0.356899 | −0.178449 | − | 0.983949i | \(-0.557108\pi\) | ||||
−0.178449 | + | 0.983949i | \(0.557108\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.45466 | + | 5.45466i | 0.338936 | + | 0.338936i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.78938 | + | 1.78938i | −0.110760 | + | 0.110760i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 27.1378i | − | 1.67339i | −0.547669 | − | 0.836695i | \(-0.684485\pi\) | ||
0.547669 | − | 0.836695i | \(-0.315515\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.58390 | + | 2.58390i | −0.158132 | + | 0.158132i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.0770 | + | 13.0770i | 0.797320 | + | 0.797320i | 0.982672 | − | 0.185352i | \(-0.0593426\pi\) |
−0.185352 | + | 0.982672i | \(0.559343\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.55264 | −0.398044 | −0.199022 | − | 0.979995i | \(-0.563777\pi\) | ||||
−0.199022 | + | 0.979995i | \(0.563777\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.59324 | 0.277995 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.2851 | − | 10.2851i | 0.617973 | − | 0.617973i | −0.327038 | − | 0.945011i | \(-0.606051\pi\) |
0.945011 | + | 0.327038i | \(0.106051\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.93582i | 0.295500i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 29.9714i | − | 1.78794i | −0.448124 | − | 0.893971i | \(-0.647908\pi\) | ||
0.448124 | − | 0.893971i | \(-0.352092\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.1176 | + | 19.1176i | −1.13642 | + | 1.13642i | −0.147334 | + | 0.989087i | \(0.547069\pi\) |
−0.989087 | + | 0.147334i | \(0.952931\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.79741 | −0.224154 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.9598 | 0.644695 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.50044 | − | 7.50044i | −0.439684 | − | 0.439684i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.27952 | + | 7.27952i | −0.425274 | + | 0.425274i | −0.887015 | − | 0.461741i | \(-0.847225\pi\) |
0.461741 | + | 0.887015i | \(0.347225\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 16.9815i | − | 0.985369i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.75862 | − | 3.75862i | 0.217366 | − | 0.217366i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.176902 | + | 0.176902i | 0.0101965 | + | 0.0101965i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −38.2827 | −2.19928 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.03304 | + | 7.03304i | 0.401397 | + | 0.401397i | 0.878725 | − | 0.477328i | \(-0.158395\pi\) |
−0.477328 | + | 0.878725i | \(0.658395\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.76147 | − | 3.76147i | 0.213983 | − | 0.213983i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.2833i | 0.809929i | 0.914332 | + | 0.404964i | \(0.132716\pi\) | ||||
−0.914332 | + | 0.404964i | \(0.867284\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 18.4579i | − | 1.04330i | −0.853158 | − | 0.521652i | \(-0.825316\pi\) | ||
0.853158 | − | 0.521652i | \(-0.174684\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.21807 | + | 7.21807i | 0.405407 | + | 0.405407i | 0.880133 | − | 0.474726i | \(-0.157453\pi\) |
−0.474726 | + | 0.880133i | \(0.657453\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.4255 | 0.583714 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.8780 | −0.997850 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −28.4948 | − | 28.4948i | −1.58549 | − | 1.58549i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 19.6169i | − | 1.08482i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.18178i | 0.175417i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.4847 | − | 15.4847i | 0.851116 | − | 0.851116i | −0.139155 | − | 0.990271i | \(-0.544439\pi\) |
0.990271 | + | 0.139155i | \(0.0444385\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.29844 | − | 8.29844i | −0.454752 | − | 0.454752i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.0210 | 1.41746 | 0.708728 | − | 0.705482i | \(-0.249269\pi\) | ||||
0.708728 | + | 0.705482i | \(0.249269\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.19497 | − | 9.19497i | −0.499402 | − | 0.499402i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.3788 | − | 14.3788i | 0.778654 | − | 0.778654i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 9.33873i | − | 0.504244i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.8554 | + | 12.8554i | −0.690115 | + | 0.690115i | −0.962257 | − | 0.272142i | \(-0.912268\pi\) |
0.272142 | + | 0.962257i | \(0.412268\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.0227 | − | 20.0227i | −1.07179 | − | 1.07179i | −0.997216 | − | 0.0745736i | \(-0.976240\pi\) |
−0.0745736 | − | 0.997216i | \(-0.523760\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.9660 | 0.692075 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.7062 | −0.729510 | −0.364755 | − | 0.931104i | \(-0.618847\pi\) | ||||
−0.364755 | + | 0.931104i | \(0.618847\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.19665 | − | 5.19665i | 0.275036 | − | 0.275036i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.3506i | 1.70740i | 0.520764 | + | 0.853700i | \(0.325647\pi\) | ||||
−0.520764 | + | 0.853700i | \(0.674353\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 39.0799i | 2.05684i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.0068 | − | 11.0068i | 0.577706 | − | 0.577706i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.3714 | 0.854582 | 0.427291 | − | 0.904114i | \(-0.359468\pi\) | ||||
0.427291 | + | 0.904114i | \(0.359468\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.77718 | 0.300748 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.44817 | − | 3.44817i | −0.179020 | − | 0.179020i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.5321 | + | 15.5321i | −0.804222 | + | 0.804222i | −0.983752 | − | 0.179530i | \(-0.942542\pi\) |
0.179530 | + | 0.983752i | \(0.442542\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.96022i | 0.409972i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.9538 | + | 24.9538i | −1.28179 | + | 1.28179i | −0.342145 | + | 0.939647i | \(0.611153\pi\) |
−0.939647 | + | 0.342145i | \(0.888847\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −23.6416 | − | 23.6416i | −1.21119 | − | 1.21119i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.24887 | 0.319302 | 0.159651 | − | 0.987174i | \(-0.448963\pi\) | ||||
0.159651 | + | 0.987174i | \(0.448963\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.269130 | − | 0.269130i | −0.0136806 | − | 0.0136806i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.10802 | − | 2.10802i | 0.106881 | − | 0.106881i | −0.651644 | − | 0.758525i | \(-0.725920\pi\) |
0.758525 | + | 0.651644i | \(0.225920\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 8.50478i | − | 0.430105i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 33.5058i | 1.69015i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.4977 | − | 23.4977i | −1.17932 | − | 1.17932i | −0.979919 | − | 0.199397i | \(-0.936102\pi\) |
−0.199397 | − | 0.979919i | \(-0.563898\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.5922 | −0.530271 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.9893 | −1.04816 | −0.524078 | − | 0.851670i | \(-0.675590\pi\) | ||||
−0.524078 | + | 0.851670i | \(0.675590\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.9787 | + | 10.9787i | 0.546889 | + | 0.546889i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 48.3492i | 2.39658i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 18.4025i | − | 0.909944i | −0.890506 | − | 0.454972i | \(-0.849649\pi\) | ||
0.890506 | − | 0.454972i | \(-0.150351\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.9756 | + | 11.9756i | −0.590711 | + | 0.590711i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.01154 | + | 1.01154i | 0.0497746 | + | 0.0497746i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.32190 | 0.211644 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.9331 | − | 14.9331i | −0.729530 | − | 0.729530i | 0.240996 | − | 0.970526i | \(-0.422526\pi\) |
−0.970526 | + | 0.240996i | \(0.922526\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.2680 | + | 16.2680i | −0.792854 | + | 0.792854i | −0.981957 | − | 0.189103i | \(-0.939442\pi\) |
0.189103 | + | 0.981957i | \(0.439442\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 4.84060i | − | 0.235358i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.44310 | − | 6.44310i | 0.311804 | − | 0.311804i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 20.3568 | + | 20.3568i | 0.982836 | + | 0.982836i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.05425 | −0.339791 | −0.169896 | − | 0.985462i | \(-0.554343\pi\) | ||||
−0.169896 | + | 0.985462i | \(0.554343\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.3192 | 0.688139 | 0.344069 | − | 0.938944i | \(-0.388194\pi\) | ||||
0.344069 | + | 0.938944i | \(0.388194\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.66750 | + | 8.66750i | −0.414623 | + | 0.414623i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 25.9047i | − | 1.23637i | −0.786034 | − | 0.618183i | \(-0.787869\pi\) | ||
0.786034 | − | 0.618183i | \(-0.212131\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.85321i | 0.326344i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.1389 | + | 11.1389i | −0.529224 | + | 0.529224i | −0.920341 | − | 0.391117i | \(-0.872089\pi\) |
0.391117 | + | 0.920341i | \(0.372089\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.44127 | −0.351960 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.6659 | 0.597740 | 0.298870 | − | 0.954294i | \(-0.403390\pi\) | ||||
0.298870 | + | 0.954294i | \(0.403390\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.8298 | − | 16.8298i | −0.792484 | − | 0.792484i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18.0941 | − | 18.0941i | 0.850135 | − | 0.850135i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.9442i | 0.792617i | 0.918117 | + | 0.396308i | \(0.129709\pi\) | ||||
−0.918117 | + | 0.396308i | \(0.870291\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 14.6694 | − | 14.6694i | 0.684708 | − | 0.684708i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.1888 | − | 13.1888i | −0.614264 | − | 0.614264i | 0.329790 | − | 0.944054i | \(-0.393022\pi\) |
−0.944054 | + | 0.329790i | \(0.893022\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.0955 | −0.655074 | −0.327537 | − | 0.944838i | \(-0.606219\pi\) | ||||
−0.327537 | + | 0.944838i | \(0.606219\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.0918 | − | 12.0918i | −0.559540 | − | 0.559540i | 0.369636 | − | 0.929177i | \(-0.379482\pi\) |
−0.929177 | + | 0.369636i | \(0.879482\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.34522 | + | 1.34522i | −0.0621165 | + | 0.0621165i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 20.4313i | 0.941427i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.56803i | 0.0720981i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.24587 | + | 5.24587i | 0.240192 | + | 0.240192i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.2523 | −0.651202 | −0.325601 | − | 0.945507i | \(-0.605567\pi\) | ||||
−0.325601 | + | 0.945507i | \(0.605567\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −36.9163 | −1.68324 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.58071 | − | 1.58071i | −0.0719248 | − | 0.0719248i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.0424i | 1.18010i | 0.807368 | + | 0.590048i | \(0.200891\pi\) | ||||
−0.807368 | + | 0.590048i | \(0.799109\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 20.0797i | − | 0.908036i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.46798 | + | 3.46798i | −0.156508 | + | 0.156508i | −0.781017 | − | 0.624509i | \(-0.785299\pi\) |
0.624509 | + | 0.781017i | \(0.285299\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.00595 | + | 9.00595i | 0.405608 | + | 0.405608i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.60383 | 0.0719418 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.30274 | + | 5.30274i | 0.237383 | + | 0.237383i | 0.815766 | − | 0.578383i | \(-0.196316\pi\) |
−0.578383 | + | 0.815766i | \(0.696316\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.55855 | − | 5.55855i | 0.248338 | − | 0.248338i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 28.8492i | 1.28632i | 0.765731 | + | 0.643161i | \(0.222378\pi\) | ||||
−0.765731 | + | 0.643161i | \(0.777622\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.95754 | − | 2.95754i | 0.131349 | − | 0.131349i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.9968 | + | 12.9968i | 0.576072 | + | 0.576072i | 0.933819 | − | 0.357747i | \(-0.116455\pi\) |
−0.357747 | + | 0.933819i | \(0.616455\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.895906 | 0.0396326 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −29.9001 | −1.32012 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.1014 | + | 14.1014i | −0.620178 | + | 0.620178i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 23.3433i | − | 1.02466i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.9833i | 0.612618i | 0.951932 | + | 0.306309i | \(0.0990941\pi\) | ||||
−0.951932 | + | 0.306309i | \(0.900906\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.30689 | + | 6.30689i | −0.275781 | + | 0.275781i | −0.831422 | − | 0.555641i | \(-0.812473\pi\) |
0.555641 | + | 0.831422i | \(0.312473\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 24.8420 | 1.08213 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.4130 | 0.887523 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.53890 | − | 1.53890i | −0.0667827 | − | 0.0667827i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.8502 | − | 12.8502i | 0.556602 | − | 0.556602i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.83375i | 0.381204i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19.9644 | − | 19.9644i | 0.859929 | − | 0.859929i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.89317 | + | 3.89317i | 0.167381 | + | 0.167381i | 0.785827 | − | 0.618446i | \(-0.212238\pi\) |
−0.618446 | + | 0.785827i | \(0.712238\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.43752 | −0.233346 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.8376 | − | 27.8376i | −1.19025 | − | 1.19025i | −0.976997 | − | 0.213251i | \(-0.931595\pi\) |
−0.213251 | − | 0.976997i | \(-0.568405\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.80220 | + | 9.80220i | −0.418348 | + | 0.418348i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 18.3565i | − | 0.782014i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 3.46647i | − | 0.147409i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.50454 | − | 1.50454i | −0.0637492 | − | 0.0637492i | 0.674513 | − | 0.738263i | \(-0.264353\pi\) |
−0.738263 | + | 0.674513i | \(0.764353\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.19725 | −0.0506382 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 46.0622 | 1.94475 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.66663 | − | 6.66663i | −0.280965 | − | 0.280965i | 0.552529 | − | 0.833494i | \(-0.313663\pi\) |
−0.833494 | + | 0.552529i | \(0.813663\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 7.62952i | − | 0.320410i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 8.38187i | − | 0.351386i | −0.984445 | − | 0.175693i | \(-0.943783\pi\) | ||
0.984445 | − | 0.175693i | \(-0.0562167\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.4129 | + | 28.4129i | −1.18904 | + | 1.18904i | −0.211708 | + | 0.977333i | \(0.567903\pi\) |
−0.977333 | + | 0.211708i | \(0.932097\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.98435 | − | 7.98435i | −0.333551 | − | 0.333551i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.2045 | −0.966014 | −0.483007 | − | 0.875616i | \(-0.660455\pi\) | ||||
−0.483007 | + | 0.875616i | \(0.660455\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.56012 | − | 5.56012i | −0.231071 | − | 0.231071i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.04450 | − | 5.04450i | 0.209281 | − | 0.209281i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 30.5640i | − | 1.26583i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.0197 | + | 11.0197i | −0.454832 | + | 0.454832i | −0.896955 | − | 0.442123i | \(-0.854226\pi\) |
0.442123 | + | 0.896955i | \(0.354226\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −25.3173 | − | 25.3173i | −1.04318 | − | 1.04318i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.73177 | −0.0712354 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.98847 | 0.286982 | 0.143491 | − | 0.989652i | \(-0.454167\pi\) | ||||
0.143491 | + | 0.989652i | \(0.454167\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 22.0987 | − | 22.0987i | 0.904438 | − | 0.904438i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.9642i | 1.63289i | 0.577420 | + | 0.816447i | \(0.304059\pi\) | ||||
−0.577420 | + | 0.816447i | \(0.695941\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 21.0830i | − | 0.859993i | −0.902831 | − | 0.429997i | \(-0.858515\pi\) | ||
0.902831 | − | 0.429997i | \(-0.141485\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.04655 | − | 2.04655i | 0.0833418 | − | 0.0833418i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.3189 | 0.905897 | 0.452949 | − | 0.891537i | \(-0.350372\pi\) | ||||
0.452949 | + | 0.891537i | \(0.350372\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.34772 | 0.135656 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.7669 | − | 10.7669i | −0.435583 | − | 0.435583i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.6045 | − | 10.6045i | 0.428312 | − | 0.428312i | −0.459741 | − | 0.888053i | \(-0.652058\pi\) |
0.888053 | + | 0.459741i | \(0.152058\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.7636i | 1.35927i | 0.733550 | + | 0.679635i | \(0.237862\pi\) | ||||
−0.733550 | + | 0.679635i | \(0.762138\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.86777 | + | 4.86777i | −0.195652 | + | 0.195652i | −0.798133 | − | 0.602481i | \(-0.794179\pi\) |
0.602481 | + | 0.798133i | \(0.294179\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.46211 | − | 4.46211i | −0.179058 | − | 0.179058i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.25384 | 0.0502341 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −46.9435 | − | 46.9435i | −1.87474 | − | 1.87474i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −41.7661 | + | 41.7661i | −1.66532 | + | 1.66532i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.1348i | 0.642315i | 0.947026 | + | 0.321157i | \(0.104072\pi\) | ||||
−0.947026 | + | 0.321157i | \(0.895928\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 6.10526i | − | 0.242662i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.2436 | + | 15.2436i | 0.603972 | + | 0.603972i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.43999 | −0.0965245 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.3125 | 0.802296 | 0.401148 | − | 0.916013i | \(-0.368611\pi\) | ||||
0.401148 | + | 0.916013i | \(0.368611\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.78443 | + | 7.78443i | 0.306988 | + | 0.306988i | 0.843740 | − | 0.536752i | \(-0.180349\pi\) |
−0.536752 | + | 0.843740i | \(0.680349\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.7693i | 0.855840i | 0.903817 | + | 0.427920i | \(0.140754\pi\) | ||||
−0.903817 | + | 0.427920i | \(0.859246\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.96611i | 0.351951i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.61717 | − | 4.61717i | 0.180961 | − | 0.180961i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26.3118 | + | 26.3118i | 1.02966 | + | 1.02966i | 0.999546 | + | 0.0301152i | \(0.00958743\pi\) |
0.0301152 | + | 0.999546i | \(0.490413\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.36298 | −0.0531751 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.2389 | + | 20.2389i | 0.788397 | + | 0.788397i | 0.981231 | − | 0.192835i | \(-0.0617681\pi\) |
−0.192835 | + | 0.981231i | \(0.561768\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.81905 | − | 6.81905i | 0.265230 | − | 0.265230i | −0.561945 | − | 0.827175i | \(-0.689947\pi\) |
0.827175 | + | 0.561945i | \(0.189947\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 35.1702i | 1.36590i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.73942 | − | 2.73942i | 0.106071 | − | 0.106071i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.34143 | − | 3.34143i | −0.129187 | − | 0.129187i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 57.1105 | 2.20473 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.19512 | 0.315899 | 0.157949 | − | 0.987447i | \(-0.449512\pi\) | ||||
0.157949 | + | 0.987447i | \(0.449512\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.8834 | + | 12.8834i | −0.495151 | + | 0.495151i | −0.909925 | − | 0.414774i | \(-0.863861\pi\) |
0.414774 | + | 0.909925i | \(0.363861\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.63960i | 0.139675i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 37.5368i | 1.43841i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.0673 | − | 15.0673i | 0.576535 | − | 0.576535i | −0.357412 | − | 0.933947i | \(-0.616341\pi\) |
0.933947 | + | 0.357412i | \(0.116341\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.6940 | 1.01844 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 23.3367 | 0.889058 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.23733 | + | 5.23733i | 0.199237 | + | 0.199237i | 0.799673 | − | 0.600436i | \(-0.205006\pi\) |
−0.600436 | + | 0.799673i | \(0.705006\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.22052 | − | 2.22052i | 0.0843504 | − | 0.0843504i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 29.0766i | − | 1.10135i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 23.2590 | − | 23.2590i | 0.879736 | − | 0.879736i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.7664 | + | 21.7664i | 0.822106 | + | 0.822106i | 0.986410 | − | 0.164303i | \(-0.0525376\pi\) |
−0.164303 | + | 0.986410i | \(0.552538\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 85.1304 | 3.21075 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.28836 | + | 9.28836i | 0.349325 | + | 0.349325i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.9643 | + | 23.9643i | −0.899997 | + | 0.899997i | −0.995435 | − | 0.0954387i | \(-0.969575\pi\) |
0.0954387 | + | 0.995435i | \(0.469575\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.27371i | 0.197779i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 7.55640i | − | 0.282990i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −27.5829 | − | 27.5829i | −1.03010 | − | 1.03010i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 44.4408 | 1.65736 | 0.828681 | − | 0.559721i | \(-0.189092\pi\) | ||||
0.828681 | + | 0.559721i | \(0.189092\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.82526 | −0.0679762 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.1891 | + | 10.1891i | 0.378937 | + | 0.378937i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 46.6543i | − | 1.73031i | −0.501504 | − | 0.865155i | \(-0.667220\pi\) | ||
0.501504 | − | 0.865155i | \(-0.332780\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 12.0815i | − | 0.447464i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.35453 | + | 1.35453i | −0.0500992 | + | 0.0500992i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.4202 | − | 19.4202i | −0.717303 | − | 0.717303i | 0.250749 | − | 0.968052i | \(-0.419323\pi\) |
−0.968052 | + | 0.250749i | \(0.919323\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.9238 | −0.439219 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.5243 | + | 20.5243i | 0.754999 | + | 0.754999i | 0.975408 | − | 0.220409i | \(-0.0707392\pi\) |
−0.220409 | + | 0.975408i | \(0.570739\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 35.8431 | − | 35.8431i | 1.31673 | − | 1.31673i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.9245i | 0.474154i | 0.971491 | + | 0.237077i | \(0.0761893\pi\) | ||||
−0.971491 | + | 0.237077i | \(0.923811\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.67443 | + | 7.67443i | −0.280793 | + | 0.280793i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.33765 | + | 4.33765i | 0.158494 | + | 0.158494i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 52.2694 | 1.90734 | 0.953668 | − | 0.300861i | \(-0.0972740\pi\) | ||||
0.953668 | + | 0.300861i | \(0.0972740\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −29.7069 | −1.08258 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.4514 | − | 34.4514i | 1.25216 | − | 1.25216i | 0.297407 | − | 0.954751i | \(-0.403878\pi\) |
0.954751 | − | 0.297407i | \(-0.0961218\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 14.0111i | − | 0.508572i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 47.7467i | 1.73082i | 0.501067 | + | 0.865408i | \(0.332941\pi\) | ||||
−0.501067 | + | 0.865408i | \(0.667059\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.75956 | + | 4.75956i | −0.172308 | + | 0.172308i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.84595 | −0.247193 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.9108 | −0.645882 | −0.322941 | − | 0.946419i | \(-0.604671\pi\) | ||||
−0.322941 | + | 0.946419i | \(0.604671\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.14247 | − | 8.14247i | −0.293244 | − | 0.293244i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.73170 | + | 3.73170i | −0.134220 | + | 0.134220i | −0.771025 | − | 0.636805i | \(-0.780256\pi\) |
0.636805 | + | 0.771025i | \(0.280256\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 15.5254i | 0.556971i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −29.6329 | + | 29.6329i | −1.06171 | + | 1.06171i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.10805 | + | 7.10805i | 0.254346 | + | 0.254346i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.45012 | 0.337720 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.40160 | + | 2.40160i | 0.0856076 | + | 0.0856076i | 0.748614 | − | 0.663006i | \(-0.230720\pi\) |
−0.663006 | + | 0.748614i | \(0.730720\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 38.6207 | − | 38.6207i | 1.37493 | − | 1.37493i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.46187i | 0.158646i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 43.6060i | 1.54849i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −35.4972 | − | 35.4972i | −1.25738 | − | 1.25738i | −0.952341 | − | 0.305035i | \(-0.901332\pi\) |
−0.305035 | − | 0.952341i | \(-0.598668\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.3627 | −0.861892 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.90753 | −0.0673992 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.97058 | + | 3.97058i | 0.140119 | + | 0.140119i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 37.2206i | 1.31023i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.9182i | 0.419021i | 0.977806 | + | 0.209510i | \(0.0671870\pi\) | ||||
−0.977806 | + | 0.209510i | \(0.932813\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.1494 | − | 22.1494i | 0.777772 | − | 0.777772i | −0.201680 | − | 0.979452i | \(-0.564640\pi\) |
0.979452 | + | 0.201680i | \(0.0646400\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.32527 | − | 9.32527i | −0.327051 | − | 0.327051i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.76090 | 0.0965915 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.69545 | + | 1.69545i | 0.0592436 | + | 0.0592436i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.3909 | − | 13.3909i | 0.467344 | − | 0.467344i | −0.433709 | − | 0.901053i | \(-0.642795\pi\) |
0.901053 | + | 0.433709i | \(0.142795\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 43.9496i | − | 1.53199i | −0.642848 | − | 0.765994i | \(-0.722247\pi\) | ||
0.642848 | − | 0.765994i | \(-0.277753\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.79096 | − | 1.79096i | 0.0622777 | − | 0.0622777i | −0.675282 | − | 0.737560i | \(-0.735978\pi\) |
0.737560 | + | 0.675282i | \(0.235978\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.4979 | + | 13.4979i | 0.468801 | + | 0.468801i | 0.901526 | − | 0.432725i | \(-0.142448\pi\) |
−0.432725 | + | 0.901526i | \(0.642448\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.2742 | 1.01551 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 34.4923 | 1.19509 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 13.0336 | − | 13.0336i | 0.450507 | − | 0.450507i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 14.5332i | − | 0.501741i | −0.968021 | − | 0.250870i | \(-0.919283\pi\) | ||
0.968021 | − | 0.250870i | \(-0.0807168\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 23.1983i | − | 0.799941i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 42.6532 | − | 42.6532i | 1.46905 | − | 1.46905i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.34105 | −0.183521 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −54.4136 | −1.86747 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.7043 | + | 12.7043i | 0.435499 | + | 0.435499i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.5836 | + | 11.5836i | −0.396615 | + | 0.396615i | −0.877037 | − | 0.480423i | \(-0.840483\pi\) |
0.480423 | + | 0.877037i | \(0.340483\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.6443i | 0.534399i | 0.963641 | + | 0.267200i | \(0.0860983\pi\) | ||||
−0.963641 | + | 0.267200i | \(0.913902\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.0947 | + | 12.0947i | −0.412665 | + | 0.412665i | −0.882666 | − | 0.470001i | \(-0.844254\pi\) |
0.470001 | + | 0.882666i | \(0.344254\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.40422 | − | 5.40422i | −0.184175 | − | 0.184175i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.28120 | −0.315936 | −0.157968 | − | 0.987444i | \(-0.550494\pi\) | ||||
−0.157968 | + | 0.987444i | \(0.550494\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15.5973 | + | 15.5973i | 0.529711 | + | 0.529711i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.3631 | − | 15.3631i | 0.521157 | − | 0.521157i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 9.10425i | − | 0.308486i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 5.53709i | − | 0.187402i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.97610 | + | 2.97610i | 0.100496 | + | 0.100496i | 0.755567 | − | 0.655071i | \(-0.227361\pi\) |
−0.655071 | + | 0.755567i | \(0.727361\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −20.7194 | −0.698849 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.3318 | 0.988214 | 0.494107 | − | 0.869401i | \(-0.335495\pi\) | ||||
0.494107 | + | 0.869401i | \(0.335495\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.5597 | + | 35.5597i | 1.19668 | + | 1.19668i | 0.975155 | + | 0.221525i | \(0.0711033\pi\) |
0.221525 | + | 0.975155i | \(0.428897\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 4.51671i | − | 0.151656i | −0.997121 | − | 0.0758282i | \(-0.975840\pi\) | ||
0.997121 | − | 0.0758282i | \(-0.0241601\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.4721i | 0.384762i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 33.8133 | − | 33.8133i | 1.13279 | − | 1.13279i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 24.8289 | + | 24.8289i | 0.830867 | + | 0.830867i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.6980 | 0.357196 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.00169 | + | 8.00169i | 0.266871 | + | 0.266871i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 26.4025 | − | 26.4025i | 0.879594 | − | 0.879594i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.503511i | 0.0167558i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.06769 | + | 5.06769i | −0.168270 | + | 0.168270i | −0.786218 | − | 0.617949i | \(-0.787964\pi\) |
0.617949 | + | 0.786218i | \(0.287964\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14.1308 | − | 14.1308i | −0.468690 | − | 0.468690i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.7140 | −1.21639 | −0.608194 | − | 0.793788i | \(-0.708106\pi\) | ||||
−0.608194 | + | 0.793788i | \(0.708106\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 44.7135 | 1.47980 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.12937 | − | 8.12937i | 0.268456 | − | 0.268456i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 21.5651i | − | 0.711365i | −0.934607 | − | 0.355683i | \(-0.884248\pi\) | ||
0.934607 | − | 0.355683i | \(-0.115752\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.0179i | 0.659612i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.42725 | + | 5.42725i | −0.178640 | + | 0.178640i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.77685 | 0.0912038 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −45.6603 | −1.49807 | −0.749033 | − | 0.662532i | \(-0.769482\pi\) | ||||
−0.749033 | + | 0.662532i | \(0.769482\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −35.1522 | − | 35.1522i | −1.15207 | − | 1.15207i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −20.3269 | + | 20.3269i | −0.665474 | + | 0.665474i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.29807i | 0.0750746i | 0.999295 | + | 0.0375373i | \(0.0119513\pi\) | ||||
−0.999295 | + | 0.0375373i | \(0.988049\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.2681 | − | 26.2681i | 0.857226 | − | 0.857226i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.1999 | − | 24.1999i | −0.788894 | − | 0.788894i | 0.192419 | − | 0.981313i | \(-0.438367\pi\) |
−0.981313 | + | 0.192419i | \(0.938367\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.84448 | −0.288016 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.5182 | + | 24.5182i | 0.796733 | + | 0.796733i | 0.982579 | − | 0.185846i | \(-0.0595025\pi\) |
−0.185846 | + | 0.982579i | \(0.559502\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.03168 | + | 3.03168i | −0.0984125 | + | 0.0984125i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.5445i | 0.666202i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 32.3462i | − | 1.04780i | −0.851781 | − | 0.523898i | \(-0.824477\pi\) | ||
0.851781 | − | 0.523898i | \(-0.175523\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14.8368 | + | 14.8368i | 0.479605 | + | 0.479605i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.81116 | 0.187652 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.92816 | −0.288005 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.59907 | − | 6.59907i | −0.212652 | − | 0.212652i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 14.6983i | − | 0.472665i | −0.971672 | − | 0.236333i | \(-0.924054\pi\) | ||
0.971672 | − | 0.236333i | \(-0.0759455\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 81.1036i | − | 2.60542i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29.1065 | + | 29.1065i | −0.934073 | + | 0.934073i | −0.997957 | − | 0.0638845i | \(-0.979651\pi\) |
0.0638845 | + | 0.997957i | \(0.479651\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.04860 | − | 1.04860i | −0.0336167 | − | 0.0336167i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.3533 | −0.555180 | −0.277590 | − | 0.960700i | \(-0.589536\pi\) | ||||
−0.277590 | + | 0.960700i | \(0.589536\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.55691 | + | 5.55691i | 0.177600 | + | 0.177600i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.24094 | − | 7.24094i | 0.231186 | − | 0.231186i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.5174i | 0.877668i | 0.898568 | + | 0.438834i | \(0.144608\pi\) | ||||
−0.898568 | + | 0.438834i | \(0.855392\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.52809 | + | 4.52809i | −0.144131 | + | 0.144131i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.412020 | + | 0.412020i | 0.0131015 | + | 0.0131015i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.96363 | −0.221207 | −0.110604 | − | 0.993865i | \(-0.535278\pi\) | ||||
−0.110604 | + | 0.993865i | \(0.535278\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 44.0735 | 1.39863 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.7051 | − | 15.7051i | 0.497385 | − | 0.497385i | −0.413238 | − | 0.910623i | \(-0.635602\pi\) |
0.910623 | + | 0.413238i | \(0.135602\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 43.8259i | 1.38659i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1600.2.l.i.401.7 | 16 | ||
4.3 | odd | 2 | 400.2.l.h.301.4 | 16 | |||
5.2 | odd | 4 | 1600.2.q.h.849.7 | 16 | |||
5.3 | odd | 4 | 1600.2.q.g.849.2 | 16 | |||
5.4 | even | 2 | 320.2.l.a.81.2 | 16 | |||
15.14 | odd | 2 | 2880.2.t.c.721.3 | 16 | |||
16.5 | even | 4 | inner | 1600.2.l.i.1201.7 | 16 | ||
16.11 | odd | 4 | 400.2.l.h.101.4 | 16 | |||
20.3 | even | 4 | 400.2.q.h.349.8 | 16 | |||
20.7 | even | 4 | 400.2.q.g.349.1 | 16 | |||
20.19 | odd | 2 | 80.2.l.a.61.5 | yes | 16 | ||
40.19 | odd | 2 | 640.2.l.b.161.2 | 16 | |||
40.29 | even | 2 | 640.2.l.a.161.7 | 16 | |||
60.59 | even | 2 | 720.2.t.c.541.4 | 16 | |||
80.19 | odd | 4 | 640.2.l.b.481.2 | 16 | |||
80.27 | even | 4 | 400.2.q.h.149.8 | 16 | |||
80.29 | even | 4 | 640.2.l.a.481.7 | 16 | |||
80.37 | odd | 4 | 1600.2.q.g.49.2 | 16 | |||
80.43 | even | 4 | 400.2.q.g.149.1 | 16 | |||
80.53 | odd | 4 | 1600.2.q.h.49.7 | 16 | |||
80.59 | odd | 4 | 80.2.l.a.21.5 | ✓ | 16 | ||
80.69 | even | 4 | 320.2.l.a.241.2 | 16 | |||
160.59 | odd | 8 | 5120.2.a.v.1.2 | 8 | |||
160.69 | even | 8 | 5120.2.a.t.1.7 | 8 | |||
160.139 | odd | 8 | 5120.2.a.s.1.7 | 8 | |||
160.149 | even | 8 | 5120.2.a.u.1.2 | 8 | |||
240.59 | even | 4 | 720.2.t.c.181.4 | 16 | |||
240.149 | odd | 4 | 2880.2.t.c.2161.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.2.l.a.21.5 | ✓ | 16 | 80.59 | odd | 4 | ||
80.2.l.a.61.5 | yes | 16 | 20.19 | odd | 2 | ||
320.2.l.a.81.2 | 16 | 5.4 | even | 2 | |||
320.2.l.a.241.2 | 16 | 80.69 | even | 4 | |||
400.2.l.h.101.4 | 16 | 16.11 | odd | 4 | |||
400.2.l.h.301.4 | 16 | 4.3 | odd | 2 | |||
400.2.q.g.149.1 | 16 | 80.43 | even | 4 | |||
400.2.q.g.349.1 | 16 | 20.7 | even | 4 | |||
400.2.q.h.149.8 | 16 | 80.27 | even | 4 | |||
400.2.q.h.349.8 | 16 | 20.3 | even | 4 | |||
640.2.l.a.161.7 | 16 | 40.29 | even | 2 | |||
640.2.l.a.481.7 | 16 | 80.29 | even | 4 | |||
640.2.l.b.161.2 | 16 | 40.19 | odd | 2 | |||
640.2.l.b.481.2 | 16 | 80.19 | odd | 4 | |||
720.2.t.c.181.4 | 16 | 240.59 | even | 4 | |||
720.2.t.c.541.4 | 16 | 60.59 | even | 2 | |||
1600.2.l.i.401.7 | 16 | 1.1 | even | 1 | trivial | ||
1600.2.l.i.1201.7 | 16 | 16.5 | even | 4 | inner | ||
1600.2.q.g.49.2 | 16 | 80.37 | odd | 4 | |||
1600.2.q.g.849.2 | 16 | 5.3 | odd | 4 | |||
1600.2.q.h.49.7 | 16 | 80.53 | odd | 4 | |||
1600.2.q.h.849.7 | 16 | 5.2 | odd | 4 | |||
2880.2.t.c.721.3 | 16 | 15.14 | odd | 2 | |||
2880.2.t.c.2161.2 | 16 | 240.149 | odd | 4 | |||
5120.2.a.s.1.7 | 8 | 160.139 | odd | 8 | |||
5120.2.a.t.1.7 | 8 | 160.69 | even | 8 | |||
5120.2.a.u.1.2 | 8 | 160.149 | even | 8 | |||
5120.2.a.v.1.2 | 8 | 160.59 | odd | 8 |