Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,2,Mod(113,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("448.113");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.m (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: | \(3.57729801055\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.20138089353117696.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3x^{10} - 2x^{9} + 2x^{8} + 4x^{7} + 2x^{6} + 8x^{5} + 8x^{4} - 16x^{3} - 48x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 113.3 | ||
Root | \(0.402577 + 1.35570i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 448.113 |
Dual form | 448.2.m.d.337.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.631188 | + | 0.631188i | −0.364416 | + | 0.364416i | −0.865436 | − | 0.501020i | \(-0.832958\pi\) |
0.501020 | + | 0.865436i | \(0.332958\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.34259 | − | 2.34259i | −1.04764 | − | 1.04764i | −0.998807 | − | 0.0488333i | \(-0.984450\pi\) |
−0.0488333 | − | 0.998807i | \(-0.515550\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.20320i | 0.734401i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.18310 | + | 2.18310i | 0.658229 | + | 0.658229i | 0.954961 | − | 0.296732i | \(-0.0958967\pi\) |
−0.296732 | + | 0.954961i | \(0.595897\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.03390 | + | 4.03390i | −1.11880 | + | 1.11880i | −0.126884 | + | 0.991918i | \(0.540498\pi\) |
−0.991918 | + | 0.126884i | \(0.959502\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.95723 | 0.763555 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.347931 | 0.0843858 | 0.0421929 | − | 0.999109i | \(-0.486566\pi\) | ||||
0.0421929 | + | 0.999109i | \(0.486566\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.26332 | + | 4.26332i | −0.978072 | + | 0.978072i | −0.999765 | − | 0.0216925i | \(-0.993095\pi\) |
0.0216925 | + | 0.999765i | \(0.493095\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.631188 | + | 0.631188i | 0.137736 | + | 0.137736i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.23788i | 1.30069i | 0.759640 | + | 0.650344i | \(0.225375\pi\) | ||||
−0.759640 | + | 0.650344i | \(0.774625\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.97550i | 1.19510i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.28420 | − | 3.28420i | −0.632044 | − | 0.632044i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.21961 | − | 1.21961i | 0.226476 | − | 0.226476i | −0.584743 | − | 0.811219i | \(-0.698805\pi\) |
0.811219 | + | 0.584743i | \(0.198805\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.26238 | 0.226729 | 0.113365 | − | 0.993553i | \(-0.463837\pi\) | ||||
0.113365 | + | 0.993553i | \(0.463837\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.75589 | −0.479739 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.34259 | + | 2.34259i | −0.395971 | + | 0.395971i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.42281 | − | 6.42281i | −1.05590 | − | 1.05590i | −0.998342 | − | 0.0575622i | \(-0.981667\pi\) |
−0.0575622 | − | 0.998342i | \(-0.518333\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 5.09229i | − | 0.815419i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.68519i | 0.419356i | 0.977770 | + | 0.209678i | \(0.0672416\pi\) | ||||
−0.977770 | + | 0.209678i | \(0.932758\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.05478 | − | 4.05478i | −0.618348 | − | 0.618348i | 0.326760 | − | 0.945107i | \(-0.394043\pi\) |
−0.945107 | + | 0.326760i | \(0.894043\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.16121 | − | 5.16121i | 0.769388 | − | 0.769388i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.64498 | −0.677540 | −0.338770 | − | 0.940869i | \(-0.610011\pi\) | ||||
−0.338770 | + | 0.940869i | \(0.610011\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.219610 | + | 0.219610i | −0.0307516 | + | 0.0307516i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.44108 | + | 8.44108i | 1.15947 | + | 1.15947i | 0.984589 | + | 0.174882i | \(0.0559544\pi\) |
0.174882 | + | 0.984589i | \(0.444046\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 10.2282i | − | 1.37917i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 5.38191i | − | 0.712851i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.17776 | + | 5.17776i | 0.674087 | + | 0.674087i | 0.958656 | − | 0.284568i | \(-0.0918503\pi\) |
−0.284568 | + | 0.958656i | \(0.591850\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.00533660 | + | 0.00533660i | −0.000683281 | + | 0.000683281i | −0.707448 | − | 0.706765i | \(-0.750154\pi\) |
0.706765 | + | 0.707448i | \(0.250154\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.20320 | 0.277578 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 18.8996 | 2.34420 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.02011 | + | 3.02011i | −0.368965 | + | 0.368965i | −0.867100 | − | 0.498135i | \(-0.834018\pi\) |
0.498135 | + | 0.867100i | \(0.334018\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.93727 | − | 3.93727i | −0.473992 | − | 0.473992i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.828913i | 0.0983739i | 0.998790 | + | 0.0491869i | \(0.0156630\pi\) | ||||
−0.998790 | + | 0.0491869i | \(0.984337\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.25173i | 0.731709i | 0.930672 | + | 0.365855i | \(0.119223\pi\) | ||||
−0.930672 | + | 0.365855i | \(0.880777\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.77166 | − | 3.77166i | −0.435514 | − | 0.435514i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.18310 | − | 2.18310i | 0.248787 | − | 0.248787i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.755891 | 0.0850443 | 0.0425222 | − | 0.999096i | \(-0.486461\pi\) | ||||
0.0425222 | + | 0.999096i | \(0.486461\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.46372 | −0.273747 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.66586 | − | 3.66586i | 0.402380 | − | 0.402380i | −0.476691 | − | 0.879071i | \(-0.658164\pi\) |
0.879071 | + | 0.476691i | \(0.158164\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.815062 | − | 0.815062i | −0.0884059 | − | 0.0884059i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.53961i | 0.165063i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 6.24461i | − | 0.661928i | −0.943643 | − | 0.330964i | \(-0.892626\pi\) | ||
0.943643 | − | 0.330964i | \(-0.107374\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.03390 | + | 4.03390i | 0.422867 | + | 0.422867i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.796796 | + | 0.796796i | −0.0826239 | + | 0.0826239i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 19.9745 | 2.04934 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.18393 | 0.221745 | 0.110872 | − | 0.993835i | \(-0.464635\pi\) | ||||
0.110872 | + | 0.993835i | \(0.464635\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.80981 | + | 4.80981i | −0.483404 | + | 0.483404i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.75325 | − | 4.75325i | −0.472967 | − | 0.472967i | 0.429907 | − | 0.902873i | \(-0.358546\pi\) |
−0.902873 | + | 0.429907i | \(0.858546\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 15.7259i | − | 1.54952i | −0.632256 | − | 0.774760i | \(-0.717871\pi\) | ||
0.632256 | − | 0.774760i | \(-0.282129\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 2.95723i | − | 0.288597i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.68080 | + | 6.68080i | 0.645857 | + | 0.645857i | 0.951989 | − | 0.306132i | \(-0.0990349\pi\) |
−0.306132 | + | 0.951989i | \(0.599035\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.812507 | + | 0.812507i | −0.0778241 | + | 0.0778241i | −0.744947 | − | 0.667123i | \(-0.767525\pi\) |
0.667123 | + | 0.744947i | \(0.267525\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.10800 | 0.769578 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.5170 | −1.74193 | −0.870966 | − | 0.491343i | \(-0.836506\pi\) | ||||
−0.870966 | + | 0.491343i | \(0.836506\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.6128 | − | 14.6128i | 1.36265 | − | 1.36265i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.88750 | − | 8.88750i | −0.821649 | − | 0.821649i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 0.347931i | − | 0.0318948i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 1.46816i | − | 0.133469i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.69486 | − | 1.69486i | −0.152820 | − | 0.152820i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.28520 | − | 2.28520i | 0.204395 | − | 0.204395i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.7063 | −1.21624 | −0.608121 | − | 0.793845i | \(-0.708076\pi\) | ||||
−0.608121 | + | 0.793845i | \(0.708076\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.11865 | 0.450672 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.52925 | − | 3.52925i | 0.308352 | − | 0.308352i | −0.535918 | − | 0.844270i | \(-0.680034\pi\) |
0.844270 | + | 0.535918i | \(0.180034\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.26332 | + | 4.26332i | 0.369677 | + | 0.369677i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 15.3871i | 1.32431i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 15.6540i | − | 1.33741i | −0.743529 | − | 0.668704i | \(-0.766849\pi\) | ||
0.743529 | − | 0.668704i | \(-0.233151\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.52569 | − | 1.52569i | −0.129408 | − | 0.129408i | 0.639436 | − | 0.768844i | \(-0.279168\pi\) |
−0.768844 | + | 0.639436i | \(0.779168\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.93185 | − | 2.93185i | 0.246907 | − | 0.246907i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −17.6128 | −1.47286 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.71410 | −0.474531 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.631188 | − | 0.631188i | 0.0520595 | − | 0.0520595i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.23788 | + | 9.23788i | 0.756796 | + | 0.756796i | 0.975738 | − | 0.218942i | \(-0.0702604\pi\) |
−0.218942 | + | 0.975738i | \(0.570260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.7266i | 0.954297i | 0.878823 | + | 0.477149i | \(0.158330\pi\) | ||||
−0.878823 | + | 0.477149i | \(0.841670\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.766564i | 0.0619730i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.95723 | − | 2.95723i | −0.237531 | − | 0.237531i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.3818 | + | 10.3818i | −0.828560 | + | 0.828560i | −0.987318 | − | 0.158758i | \(-0.949251\pi\) |
0.158758 | + | 0.987318i | \(0.449251\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.6558 | −0.845061 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.23788 | 0.491614 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.6554 | − | 15.6554i | 1.22623 | − | 1.22623i | 0.260849 | − | 0.965380i | \(-0.415997\pi\) |
0.965380 | − | 0.260849i | \(-0.0840025\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.45593 | + | 6.45593i | 0.502594 | + | 0.502594i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.12023i | 0.164068i | 0.996630 | + | 0.0820341i | \(0.0261416\pi\) | ||||
−0.996630 | + | 0.0820341i | \(0.973858\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 19.5446i | − | 1.50343i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.39296 | − | 9.39296i | −0.718298 | − | 0.718298i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.12654 | − | 2.12654i | 0.161678 | − | 0.161678i | −0.621632 | − | 0.783310i | \(-0.713530\pi\) |
0.783310 | + | 0.621632i | \(0.213530\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.97550 | 0.451705 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.53628 | −0.491297 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.41911 | + | 1.41911i | −0.106070 | + | 0.106070i | −0.758150 | − | 0.652080i | \(-0.773896\pi\) |
0.652080 | + | 0.758150i | \(0.273896\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.3191 | + | 14.3191i | 1.06433 | + | 1.06433i | 0.997783 | + | 0.0665470i | \(0.0211982\pi\) |
0.0665470 | + | 0.997783i | \(0.478802\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 0.00673679i | − | 0.000497998i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 30.0921i | 2.21242i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.759569 | + | 0.759569i | 0.0555452 | + | 0.0555452i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.28420 | + | 3.28420i | −0.238890 | + | 0.238890i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.22279 | −0.450265 | −0.225133 | − | 0.974328i | \(-0.572282\pi\) | ||||
−0.225133 | + | 0.974328i | \(0.572282\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.57618 | 0.113456 | 0.0567280 | − | 0.998390i | \(-0.481933\pi\) | ||||
0.0567280 | + | 0.998390i | \(0.481933\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −11.9292 | + | 11.9292i | −0.854266 | + | 0.854266i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.7183 | + | 10.7183i | 0.763648 | + | 0.763648i | 0.976980 | − | 0.213332i | \(-0.0684315\pi\) |
−0.213332 | + | 0.976980i | \(0.568432\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.5363i | 1.81022i | 0.425180 | + | 0.905109i | \(0.360211\pi\) | ||||
−0.425180 | + | 0.905109i | \(0.639789\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 3.81251i | − | 0.268914i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.21961 | − | 1.21961i | −0.0855998 | − | 0.0855998i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.29031 | − | 6.29031i | 0.439334 | − | 0.439334i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −13.7433 | −0.955226 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −18.6145 | −1.28759 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.19881 | + | 9.19881i | −0.633272 | + | 0.633272i | −0.948887 | − | 0.315615i | \(-0.897789\pi\) |
0.315615 | + | 0.948887i | \(0.397789\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.523200 | − | 0.523200i | −0.0358491 | − | 0.0358491i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 18.9974i | 1.29561i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1.26238i | − | 0.0856956i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.94601 | − | 3.94601i | −0.266647 | − | 0.266647i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.40352 | + | 1.40352i | −0.0944109 | + | 0.0944109i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.7530 | −0.854003 | −0.427001 | − | 0.904251i | \(-0.640430\pi\) | ||||
−0.427001 | + | 0.904251i | \(0.640430\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.1652 | −0.877683 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.2451 | − | 12.2451i | 0.812733 | − | 0.812733i | −0.172310 | − | 0.985043i | \(-0.555123\pi\) |
0.985043 | + | 0.172310i | \(0.0551231\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.93193 | − | 9.93193i | −0.656321 | − | 0.656321i | 0.298187 | − | 0.954508i | \(-0.403618\pi\) |
−0.954508 | + | 0.298187i | \(0.903618\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.75589i | 0.181324i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.3143i | 1.19981i | 0.800072 | + | 0.599905i | \(0.204795\pi\) | ||||
−0.800072 | + | 0.599905i | \(0.795205\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.8813 | + | 10.8813i | 0.709818 | + | 0.709818i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.477109 | + | 0.477109i | −0.0309916 | + | 0.0309916i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.3443 | 1.18660 | 0.593298 | − | 0.804983i | \(-0.297826\pi\) | ||||
0.593298 | + | 0.804983i | \(0.297826\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.4147 | 1.63710 | 0.818552 | − | 0.574433i | \(-0.194777\pi\) | ||||
0.818552 | + | 0.574433i | \(0.194777\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.4077 | − | 11.4077i | 0.731802 | − | 0.731802i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.34259 | + | 2.34259i | 0.149663 | + | 0.149663i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 34.3956i | − | 2.18854i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.62769i | 0.293268i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.9301 | + | 10.9301i | 0.689903 | + | 0.689903i | 0.962210 | − | 0.272307i | \(-0.0877867\pi\) |
−0.272307 | + | 0.962210i | \(0.587787\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.6179 | + | 13.6179i | −0.856150 | + | 0.856150i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.02891 | 0.0644331 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.29652 | 0.143253 | 0.0716265 | − | 0.997432i | \(-0.477181\pi\) | ||||
0.0716265 | + | 0.997432i | \(0.477181\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.42281 | + | 6.42281i | −0.399094 | + | 0.399094i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.68705 | + | 2.68705i | 0.166324 | + | 0.166324i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 11.8508i | − | 0.730749i | −0.930861 | − | 0.365375i | \(-0.880941\pi\) | ||
0.930861 | − | 0.365375i | \(-0.119059\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 39.5481i | − | 2.42942i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.94152 | + | 3.94152i | 0.241217 | + | 0.241217i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.70791 | − | 5.70791i | 0.348017 | − | 0.348017i | −0.511353 | − | 0.859371i | \(-0.670856\pi\) |
0.859371 | + | 0.511353i | \(0.170856\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.1234 | −1.58688 | −0.793441 | − | 0.608648i | \(-0.791712\pi\) | ||||
−0.793441 | + | 0.608648i | \(0.791712\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.09229 | −0.308200 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −13.0451 | + | 13.0451i | −0.786650 | + | 0.786650i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.98274 | + | 1.98274i | 0.119131 | + | 0.119131i | 0.764159 | − | 0.645028i | \(-0.223154\pi\) |
−0.645028 | + | 0.764159i | \(0.723154\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.78127i | 0.166510i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.52475i | 0.389234i | 0.980879 | + | 0.194617i | \(0.0623464\pi\) | ||||
−0.980879 | + | 0.194617i | \(0.937654\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.9578 | + | 13.9578i | 0.829705 | + | 0.829705i | 0.987476 | − | 0.157771i | \(-0.0504307\pi\) |
−0.157771 | + | 0.987476i | \(0.550431\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −12.6076 | + | 12.6076i | −0.746812 | + | 0.746812i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.68519 | 0.158502 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8789 | −0.992879 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.37847 | + | 1.37847i | −0.0808075 | + | 0.0808075i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.57087 | − | 2.57087i | −0.150192 | − | 0.150192i | 0.628012 | − | 0.778204i | \(-0.283869\pi\) |
−0.778204 | + | 0.628012i | \(0.783869\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 24.2588i | − | 1.41240i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 14.3395i | − | 0.832060i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −25.1629 | − | 25.1629i | −1.45521 | − | 1.45521i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.05478 | + | 4.05478i | −0.233713 | + | 0.233713i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.00039 | 0.344714 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.0250030 | 0.00143167 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.8253 | + | 18.8253i | −1.07441 | + | 1.07441i | −0.0774148 | + | 0.996999i | \(0.524667\pi\) |
−0.996999 | + | 0.0774148i | \(0.975333\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.92600 | + | 9.92600i | 0.564670 | + | 0.564670i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.8918i | 1.35478i | 0.735625 | + | 0.677389i | \(0.236889\pi\) | ||||
−0.735625 | + | 0.677389i | \(0.763111\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.0884i | 1.02242i | 0.859457 | + | 0.511208i | \(0.170802\pi\) | ||||
−0.859457 | + | 0.511208i | \(0.829198\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.16121 | − | 5.16121i | −0.290801 | − | 0.290801i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.36465 | + | 5.36465i | −0.301309 | + | 0.301309i | −0.841526 | − | 0.540217i | \(-0.818342\pi\) |
0.540217 | + | 0.841526i | \(0.318342\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.32506 | 0.298146 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.43367 | −0.470722 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.48334 | + | 1.48334i | −0.0825354 | + | 0.0825354i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −24.1046 | − | 24.1046i | −1.33708 | − | 1.33708i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 1.02569i | − | 0.0567207i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.64498i | 0.256086i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.3563 | + | 22.3563i | 1.22881 | + | 1.22881i | 0.964413 | + | 0.264402i | \(0.0851744\pi\) |
0.264402 | + | 0.964413i | \(0.414826\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 14.1508 | − | 14.1508i | 0.775457 | − | 0.775457i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.1498 | 0.773084 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.5086 | 0.626914 | 0.313457 | − | 0.949602i | \(-0.398513\pi\) | ||||
0.313457 | + | 0.949602i | \(0.398513\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.6877 | − | 11.6877i | 0.634789 | − | 0.634789i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.75589 | + | 2.75589i | 0.149240 | + | 0.149240i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 18.4469i | 0.993146i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.3190 | − | 12.3190i | −0.661319 | − | 0.661319i | 0.294372 | − | 0.955691i | \(-0.404890\pi\) |
−0.955691 | + | 0.294372i | \(0.904890\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.251501 | − | 0.251501i | 0.0134625 | − | 0.0134625i | −0.700343 | − | 0.713806i | \(-0.746970\pi\) |
0.713806 | + | 0.700343i | \(0.246970\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 26.4962 | 1.41426 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.6888 | 0.888255 | 0.444128 | − | 0.895964i | \(-0.353514\pi\) | ||||
0.444128 | + | 0.895964i | \(0.353514\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.94181 | − | 1.94181i | 0.103060 | − | 0.103060i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.219610 | + | 0.219610i | 0.0116230 | + | 0.0116230i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.9781i | 0.948849i | 0.880296 | + | 0.474425i | \(0.157344\pi\) | ||||
−0.880296 | + | 0.474425i | \(0.842656\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 17.3518i | − | 0.913251i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.926684 | + | 0.926684i | 0.0486383 | + | 0.0486383i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.6453 | − | 14.6453i | 0.766568 | − | 0.766568i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.6270 | −1.12892 | −0.564461 | − | 0.825460i | \(-0.690916\pi\) | ||||
−0.564461 | + | 0.825460i | \(0.690916\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.91602 | −0.307976 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.44108 | − | 8.44108i | 0.438239 | − | 0.438239i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.1124 | − | 12.1124i | −0.627159 | − | 0.627159i | 0.320194 | − | 0.947352i | \(-0.396252\pi\) |
−0.947352 | + | 0.320194i | \(0.896252\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.88478i | 0.148970i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.83956i | 0.506763i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.34251 | − | 4.34251i | −0.223060 | − | 0.223060i | 0.586726 | − | 0.809786i | \(-0.300417\pi\) |
−0.809786 | + | 0.586726i | \(0.800417\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.65128 | − | 8.65128i | 0.443218 | − | 0.443218i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32.8242 | 1.67724 | 0.838619 | − | 0.544718i | \(-0.183363\pi\) | ||||
0.838619 | + | 0.544718i | \(0.183363\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.2282 | −0.521279 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.93350 | − | 8.93350i | 0.454115 | − | 0.454115i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.234988 | + | 0.234988i | 0.0119143 | + | 0.0119143i | 0.713039 | − | 0.701125i | \(-0.247318\pi\) |
−0.701125 | + | 0.713039i | \(0.747318\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.17035i | 0.109759i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.45524i | 0.224737i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.77075 | − | 1.77075i | −0.0890959 | − | 0.0890959i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.97983 | − | 1.97983i | 0.0993650 | − | 0.0993650i | −0.655677 | − | 0.755042i | \(-0.727617\pi\) |
0.755042 | + | 0.655677i | \(0.227617\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.38191 | −0.269432 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.15044 | −0.257200 | −0.128600 | − | 0.991697i | \(-0.541048\pi\) | ||||
−0.128600 | + | 0.991697i | \(0.541048\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.09229 | + | 5.09229i | −0.253665 | + | 0.253665i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.77150 | + | 5.77150i | 0.286788 | + | 0.286788i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 28.0433i | − | 1.39005i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 0.0729036i | − | 0.00360485i | −0.999998 | − | 0.00180243i | \(-0.999426\pi\) | ||
0.999998 | − | 0.00180243i | \(-0.000573731\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.88058 | + | 9.88058i | 0.487373 | + | 0.487373i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.17776 | − | 5.17776i | 0.254781 | − | 0.254781i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17.1752 | −0.843100 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.92600 | 0.0943165 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.7426 | − | 13.7426i | 0.671370 | − | 0.671370i | −0.286662 | − | 0.958032i | \(-0.592546\pi\) |
0.958032 | + | 0.286662i | \(0.0925456\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.88097 | + | 3.88097i | 0.189147 | + | 0.189147i | 0.795327 | − | 0.606180i | \(-0.207299\pi\) |
−0.606180 | + | 0.795327i | \(0.707299\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 10.2338i | − | 0.497586i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.07906i | 0.100849i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.00533660 | + | 0.00533660i | 0.000258256 | + | 0.000258256i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.1170 | − | 11.1170i | 0.536733 | − | 0.536733i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.8033 | 1.62825 | 0.814125 | − | 0.580690i | \(-0.197217\pi\) | ||||
0.814125 | + | 0.580690i | \(0.197217\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.6931 | 0.898334 | 0.449167 | − | 0.893448i | \(-0.351721\pi\) | ||||
0.449167 | + | 0.893448i | \(0.351721\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.60667 | − | 3.60667i | 0.172927 | − | 0.172927i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −26.5940 | − | 26.5940i | −1.27217 | − | 1.27217i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.03142i | 0.287864i | 0.989588 | + | 0.143932i | \(0.0459747\pi\) | ||||
−0.989588 | + | 0.143932i | \(0.954025\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 2.20320i | − | 0.104914i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.9158 | − | 24.9158i | −1.18378 | − | 1.18378i | −0.978756 | − | 0.205027i | \(-0.934272\pi\) |
−0.205027 | − | 0.978756i | \(-0.565728\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.6286 | + | 14.6286i | −0.693462 | + | 0.693462i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.6617 | −0.551578 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.9883 | 1.03769 | 0.518846 | − | 0.854868i | \(-0.326362\pi\) | ||||
0.518846 | + | 0.854868i | \(0.326362\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.86203 | + | 5.86203i | −0.276032 | + | 0.276032i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.40169 | − | 7.40169i | −0.347762 | − | 0.347762i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 18.8996i | − | 0.886026i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 26.7381i | − | 1.25076i | −0.780322 | − | 0.625378i | \(-0.784945\pi\) | ||
0.780322 | − | 0.625378i | \(-0.215055\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.14268 | − | 1.14268i | −0.0533355 | − | 0.0533355i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.5563 | − | 23.5563i | 1.09713 | − | 1.09713i | 0.102381 | − | 0.994745i | \(-0.467354\pi\) |
0.994745 | − | 0.102381i | \(-0.0326462\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.83629 | 0.457131 | 0.228566 | − | 0.973529i | \(-0.426596\pi\) | ||||
0.228566 | + | 0.973529i | \(0.426596\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.73314 | 0.173120 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.96594 | + | 1.96594i | −0.0909727 | + | 0.0909727i | −0.751129 | − | 0.660156i | \(-0.770490\pi\) |
0.660156 | + | 0.751129i | \(0.270490\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.02011 | + | 3.02011i | 0.139455 | + | 0.139455i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 13.1058i | − | 0.603882i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 17.7040i | − | 0.814029i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −25.4755 | − | 25.4755i | −1.16889 | − | 1.16889i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −18.5974 | + | 18.5974i | −0.851517 | + | 0.851517i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.78688 | −0.173027 | −0.0865136 | − | 0.996251i | \(-0.527573\pi\) | ||||
−0.0865136 | + | 0.996251i | \(0.527573\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 51.8179 | 2.36269 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.93727 | + | 3.93727i | −0.179152 | + | 0.179152i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.11607 | − | 5.11607i | −0.232309 | − | 0.232309i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 16.8200i | − | 0.762186i | −0.924537 | − | 0.381093i | \(-0.875548\pi\) | ||
0.924537 | − | 0.381093i | \(-0.124452\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.7630i | 0.893716i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.41618 | + | 6.41618i | 0.289558 | + | 0.289558i | 0.836906 | − | 0.547347i | \(-0.184362\pi\) |
−0.547347 | + | 0.836906i | \(0.684362\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.424341 | − | 0.424341i | 0.0191113 | − | 0.0191113i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 22.5349 | 1.01287 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.828913 | 0.0371818 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.69302 | − | 4.69302i | 0.210088 | − | 0.210088i | −0.594217 | − | 0.804305i | \(-0.702538\pi\) |
0.804305 | + | 0.594217i | \(0.202538\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.33826 | − | 1.33826i | −0.0597891 | − | 0.0597891i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 4.37360i | − | 0.195009i | −0.995235 | − | 0.0975045i | \(-0.968914\pi\) | ||
0.995235 | − | 0.0975045i | \(-0.0310860\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.2699i | 0.990998i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.3363 | + | 12.3363i | 0.547876 | + | 0.547876i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.93619 | − | 1.93619i | 0.0858200 | − | 0.0858200i | −0.662894 | − | 0.748714i | \(-0.730672\pi\) |
0.748714 | + | 0.662894i | \(0.230672\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.25173 | 0.276560 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 28.0032 | 1.23637 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −36.8394 | + | 36.8394i | −1.62334 | + | 1.62334i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.1404 | − | 10.1404i | −0.445976 | − | 0.445976i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.68449i | 0.117836i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 35.3300i | 1.54783i | 0.633287 | + | 0.773917i | \(0.281705\pi\) | ||||
−0.633287 | + | 0.773917i | \(0.718295\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.3854 | + | 23.3854i | 1.02257 | + | 1.02257i | 0.999739 | + | 0.0228331i | \(0.00726864\pi\) |
0.0228331 | + | 0.999739i | \(0.492731\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.77166 | + | 3.77166i | −0.164609 | + | 0.164609i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.439220 | 0.0191327 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.9111 | −0.691787 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.4077 | + | 11.4077i | −0.495051 | + | 0.495051i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.8318 | − | 10.8318i | −0.469176 | − | 0.469176i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 31.3008i | − | 1.35325i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 1.79146i | − | 0.0773070i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.18310 | − | 2.18310i | −0.0940327 | − | 0.0940327i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.13176 | + | 5.13176i | −0.220631 | + | 0.220631i | −0.808764 | − | 0.588133i | \(-0.799863\pi\) |
0.588133 | + | 0.808764i | \(0.299863\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −18.0761 | −0.775719 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.80675 | 0.163063 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.8157 | + | 16.8157i | −0.718989 | + | 0.718989i | −0.968398 | − | 0.249409i | \(-0.919764\pi\) |
0.249409 | + | 0.968398i | \(0.419764\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.0117576 | − | 0.0117576i | −0.000501803 | − | 0.000501803i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.3992i | 0.443020i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 0.755891i | − | 0.0321437i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −18.9938 | − | 18.9938i | −0.806240 | − | 0.806240i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.0874 | + | 11.0874i | −0.469789 | + | 0.469789i | −0.901846 | − | 0.432057i | \(-0.857788\pi\) |
0.432057 | + | 0.901846i | \(0.357788\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.7131 | 1.38362 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.958861 | −0.0404831 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.2057 | + | 22.2057i | −0.935857 | + | 0.935857i | −0.998063 | − | 0.0622066i | \(-0.980186\pi\) |
0.0622066 | + | 0.998063i | \(0.480186\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 43.3778 | + | 43.3778i | 1.82492 | + | 1.82492i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.46372i | 0.103466i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.317171i | 0.0132965i | 0.999978 | + | 0.00664825i | \(0.00211622\pi\) | ||||
−0.999978 | + | 0.00664825i | \(0.997884\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.80358 | + | 7.80358i | 0.326570 | + | 0.326570i | 0.851280 | − | 0.524711i | \(-0.175827\pi\) |
−0.524711 | + | 0.851280i | \(0.675827\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.92775 | − | 3.92775i | 0.164084 | − | 0.164084i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −37.2744 | −1.55445 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.2699 | −0.427540 | −0.213770 | − | 0.976884i | \(-0.568574\pi\) | ||||
−0.213770 | + | 0.976884i | \(0.568574\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.994867 | + | 0.994867i | −0.0413453 | + | 0.0413453i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.66586 | − | 3.66586i | −0.152086 | − | 0.152086i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 36.8554i | 1.52640i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 41.6396i | 1.72159i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.9965 | + | 27.9965i | 1.15554 | + | 1.15554i | 0.985425 | + | 0.170113i | \(0.0544133\pi\) |
0.170113 | + | 0.985425i | \(0.445587\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.38191 | + | 5.38191i | −0.221758 | + | 0.221758i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.5305 | −0.556572 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −34.5902 | −1.42045 | −0.710225 | − | 0.703974i | \(-0.751407\pi\) | ||||
−0.710225 | + | 0.703974i | \(0.751407\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.815062 | + | 0.815062i | −0.0334143 | + | 0.0334143i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −16.1182 | − | 16.1182i | −0.659673 | − | 0.659673i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 14.0866i | − | 0.575562i | −0.957696 | − | 0.287781i | \(-0.907082\pi\) | ||
0.957696 | − | 0.287781i | \(-0.0929176\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 7.07501i | − | 0.288595i | −0.989534 | − | 0.144298i | \(-0.953908\pi\) | ||
0.989534 | − | 0.144298i | \(-0.0460923\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.65391 | − | 6.65391i | −0.270968 | − | 0.270968i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.43930 | + | 3.43930i | −0.139828 | + | 0.139828i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.99294 | −0.243246 | −0.121623 | − | 0.992576i | \(-0.538810\pi\) | ||||
−0.121623 | + | 0.992576i | \(0.538810\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.53961 | 0.0623880 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.7374 | − | 18.7374i | 0.758033 | − | 0.758033i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.3166 | − | 12.3166i | −0.497464 | − | 0.497464i | 0.413184 | − | 0.910648i | \(-0.364417\pi\) |
−0.910648 | + | 0.413184i | \(0.864417\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.94074i | 0.320201i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 40.3690i | − | 1.62519i | −0.582827 | − | 0.812596i | \(-0.698053\pi\) | ||
0.582827 | − | 0.812596i | \(-0.301947\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.9375 | − | 30.9375i | −1.24348 | − | 1.24348i | −0.958546 | − | 0.284938i | \(-0.908027\pi\) |
−0.284938 | − | 0.958546i | \(-0.591973\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 20.4864 | − | 20.4864i | 0.822092 | − | 0.822092i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.24461 | −0.250185 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.1709 | 0.766836 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11.7492 | − | 11.7492i | 0.469219 | − | 0.469219i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.23470 | − | 2.23470i | −0.0891033 | − | 0.0891033i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.7329i | 0.944792i | 0.881386 | + | 0.472396i | \(0.156611\pi\) | ||||
−0.881386 | + | 0.472396i | \(0.843389\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 11.6124i | − | 0.461550i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 32.1084 | + | 32.1084i | 1.27418 | + | 1.27418i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.03390 | − | 4.03390i | 0.159829 | − | 0.159829i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.82626 | −0.0722459 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.9883 | −0.592000 | −0.296000 | − | 0.955188i | \(-0.595653\pi\) | ||||
−0.296000 | + | 0.955188i | \(0.595653\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.8452 | − | 11.8452i | 0.467130 | − | 0.467130i | −0.433854 | − | 0.900983i | \(-0.642847\pi\) |
0.900983 | + | 0.433854i | \(0.142847\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.9909 | − | 11.9909i | −0.472142 | − | 0.472142i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.12471i | 0.162159i | 0.996708 | + | 0.0810795i | \(0.0258368\pi\) | ||||
−0.996708 | + | 0.0810795i | \(0.974163\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.6071i | 0.887408i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.796796 | + | 0.796796i | 0.0312289 | + | 0.0312289i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.4516 | + | 25.4516i | −0.995997 | + | 0.995997i | −0.999992 | − | 0.00399544i | \(-0.998728\pi\) |
0.00399544 | + | 0.999992i | \(0.498728\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.5352 | −0.646084 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −13.7738 | −0.537368 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.38409 | + | 7.38409i | −0.287643 | + | 0.287643i | −0.836148 | − | 0.548504i | \(-0.815197\pi\) |
0.548504 | + | 0.836148i | \(0.315197\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.0924 | + | 14.0924i | 0.548130 | + | 0.548130i | 0.925900 | − | 0.377770i | \(-0.123309\pi\) |
−0.377770 | + | 0.925900i | \(0.623309\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 1.77177i | − | 0.0688098i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 19.9745i | − | 0.774576i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.60778 | + | 7.60778i | 0.294574 | + | 0.294574i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.04953 | − | 8.04953i | 0.311213 | − | 0.311213i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.0233006 | −0.000899511 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.0089 | −1.34949 | −0.674746 | − | 0.738050i | \(-0.735747\pi\) | ||||
−0.674746 | + | 0.738050i | \(0.735747\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 19.6247 | − | 19.6247i | 0.755356 | − | 0.755356i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.2860 | + | 11.2860i | 0.433755 | + | 0.433755i | 0.889904 | − | 0.456148i | \(-0.150771\pi\) |
−0.456148 | + | 0.889904i | \(0.650771\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 2.18393i | − | 0.0838117i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.4579i | 0.592346i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.4270 | − | 33.4270i | −1.27905 | − | 1.27905i | −0.941201 | − | 0.337848i | \(-0.890301\pi\) |
−0.337848 | − | 0.941201i | \(-0.609699\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −36.6709 | + | 36.6709i | −1.40112 | + | 1.40112i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.5378 | 0.478348 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −68.1009 | −2.59444 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.03700 | − | 5.03700i | 0.191616 | − | 0.191616i | −0.604778 | − | 0.796394i | \(-0.706738\pi\) |
0.796394 | + | 0.604778i | \(0.206738\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.80981 | + | 4.80981i | 0.182710 | + | 0.182710i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.14816i | 0.271145i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.934262i | 0.0353877i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.5598 | − | 11.5598i | −0.437230 | − | 0.437230i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.77330 | − | 1.77330i | 0.0669766 | − | 0.0669766i | −0.672825 | − | 0.739802i | \(-0.734919\pi\) |
0.739802 | + | 0.672825i | \(0.234919\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 54.7650 | 2.06550 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.7363 | −0.517339 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.75325 | + | 4.75325i | −0.178765 | + | 0.178765i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.84781 | − | 8.84781i | −0.332286 | − | 0.332286i | 0.521168 | − | 0.853454i | \(-0.325497\pi\) |
−0.853454 | + | 0.521168i | \(0.825497\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.66538i | 0.0624567i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.87454i | 0.294904i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 41.2596 | + | 41.2596i | 1.54302 | + | 1.54302i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.5787 | + | 11.5787i | −0.432415 | + | 0.432415i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.8257 | 0.441025 | 0.220512 | − | 0.975384i | \(-0.429227\pi\) | ||||
0.220512 | + | 0.975384i | \(0.429227\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.7259 | −0.585663 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −16.0414 | + | 16.0414i | −0.596587 | + | 0.596587i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.28778 | + | 7.28778i | 0.270661 | + | 0.270661i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.7703i | 1.02994i | 0.857207 | + | 0.514972i | \(0.172198\pi\) | ||||
−0.857207 | + | 0.514972i | \(0.827802\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.00960i | 0.259615i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.41078 | − | 1.41078i | −0.0521797 | − | 0.0521797i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.8466 | − | 35.8466i | 1.32402 | − | 1.32402i | 0.413535 | − | 0.910488i | \(-0.364294\pi\) |
0.910488 | − | 0.413535i | \(-0.135706\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.95723 | −0.109079 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.1864 | −0.485726 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.1088 | − | 10.1088i | 0.371860 | − | 0.371860i | −0.496295 | − | 0.868154i | \(-0.665306\pi\) |
0.868154 | + | 0.496295i | \(0.165306\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21.7101 | + | 21.7101i | 0.797539 | + | 0.797539i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.4037i | 1.15209i | 0.817418 | + | 0.576045i | \(0.195405\pi\) | ||||
−0.817418 | + | 0.576045i | \(0.804595\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 43.2812i | − | 1.58570i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.07664 | + | 8.07664i | 0.295509 | + | 0.295509i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.68080 | − | 6.68080i | 0.244111 | − | 0.244111i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.6531 | −0.461717 | −0.230859 | − | 0.972987i | \(-0.574153\pi\) | ||||
−0.230859 | + | 0.972987i | \(0.574153\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.7979 | −0.502824 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 27.4707 | − | 27.4707i | 0.999760 | − | 0.999760i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.6555 | + | 19.6555i | 0.714391 | + | 0.714391i | 0.967451 | − | 0.253060i | \(-0.0814370\pi\) |
−0.253060 | + | 0.967451i | \(0.581437\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 17.1909i | − | 0.623990i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.2754i | 0.444984i | 0.974934 | + | 0.222492i | \(0.0714192\pi\) | ||||
−0.974934 | + | 0.222492i | \(0.928581\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.812507 | + | 0.812507i | 0.0294147 | + | 0.0294147i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.79575 | − | 1.79575i | 0.0649254 | − | 0.0649254i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −41.7731 | −1.50834 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.0633 | 1.58896 | 0.794481 | − | 0.607289i | \(-0.207743\pi\) | ||||
0.794481 | + | 0.607289i | \(0.207743\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.44954 | + | 1.44954i | −0.0522037 | + | 0.0522037i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30.9188 | + | 30.9188i | 1.11207 | + | 1.11207i | 0.992870 | + | 0.119200i | \(0.0380330\pi\) |
0.119200 | + | 0.992870i | \(0.461967\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.54333i | 0.270964i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 8.10800i | − | 0.290873i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.4478 | − | 11.4478i | −0.410161 | − | 0.410161i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.80960 | + | 1.80960i | −0.0647526 | + | 0.0647526i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.01088 | −0.286286 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 48.6408 | 1.73607 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.3994 | + | 13.3994i | −0.477638 | + | 0.477638i | −0.904375 | − | 0.426738i | \(-0.859663\pi\) |
0.426738 | + | 0.904375i | \(0.359663\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.48006 | + | 7.48006i | 0.266297 | + | 0.266297i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.5170i | 0.658388i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 0.0430546i | − | 0.00152891i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 24.9623 | + | 24.9623i | 0.885320 | + | 0.885320i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16.1055 | + | 16.1055i | −0.570485 | + | 0.570485i | −0.932264 | − | 0.361779i | \(-0.882169\pi\) |
0.361779 | + | 0.932264i | \(0.382169\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.61613 | −0.0571747 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.7582 | 0.486121 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.6481 | + | 13.6481i | −0.481632 | + | 0.481632i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.6128 | − | 14.6128i | −0.515034 | − | 0.515034i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.20553i | 0.253647i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 37.6047i | − | 1.32211i | −0.750336 | − | 0.661056i | \(-0.770109\pi\) | ||
0.750336 | − | 0.661056i | \(-0.229891\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.00106 | − | 7.00106i | −0.245841 | − | 0.245841i | 0.573421 | − | 0.819261i | \(-0.305616\pi\) |
−0.819261 | + | 0.573421i | \(0.805616\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.4887 | − | 16.4887i | 0.578286 | − | 0.578286i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −73.3487 | −2.56929 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34.5736 | 1.20958 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.88750 | + | 8.88750i | −0.310554 | + | 0.310554i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.711892 | + | 0.711892i | 0.0248452 | + | 0.0248452i | 0.719420 | − | 0.694575i | \(-0.244408\pi\) |
−0.694575 | + | 0.719420i | \(0.744408\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.0278i | 0.419262i | 0.977781 | + | 0.209631i | \(0.0672263\pi\) | ||||
−0.977781 | + | 0.209631i | \(0.932774\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 16.4678i | − | 0.573336i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.1838 | − | 16.1838i | −0.562764 | − | 0.562764i | 0.367328 | − | 0.930092i | \(-0.380273\pi\) |
−0.930092 | + | 0.367328i | \(0.880273\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.31569 | − | 3.31569i | 0.115159 | − | 0.115159i | −0.647179 | − | 0.762338i | \(-0.724051\pi\) |
0.762338 | + | 0.647179i | \(0.224051\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.50296 | −0.0868267 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.347931 | −0.0120551 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.96684 | − | 4.96684i | 0.171884 | − | 0.171884i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.14589 | − | 4.14589i | −0.143303 | − | 0.143303i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 47.4324i | − | 1.63755i | −0.574116 | − | 0.818774i | \(-0.694654\pi\) | ||
0.574116 | − | 0.818774i | \(-0.305346\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.0251i | 0.897417i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.11834 | − | 4.11834i | −0.141843 | − | 0.141843i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −45.7852 | + | 45.7852i | −1.57506 | + | 1.57506i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.46816 | −0.0504466 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.6200 | −0.604716 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 40.0647 | − | 40.0647i | 1.37340 | − | 1.37340i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.99601 | + | 3.99601i | 0.136821 | + | 0.136821i | 0.772200 | − | 0.635379i | \(-0.219156\pi\) |
−0.635379 | + | 0.772200i | \(0.719156\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 44.0078i | 1.50503i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.1854i | 0.382086i | 0.981582 | + | 0.191043i | \(0.0611869\pi\) | ||||
−0.981582 | + | 0.191043i | \(0.938813\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.0707 | − | 15.0707i | −0.514207 | − | 0.514207i | 0.401606 | − | 0.915813i | \(-0.368452\pi\) |
−0.915813 | + | 0.401606i | \(0.868452\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.69486 | + | 1.69486i | −0.0577606 | + | 0.0577606i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −29.6751 | −1.01015 | −0.505076 | − | 0.863075i | \(-0.668536\pi\) | ||||
−0.505076 | + | 0.863075i | \(0.668536\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.96325 | −0.338761 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.6538 | − | 10.6538i | 0.361821 | − | 0.361821i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.65018 | + | 1.65018i | 0.0559787 | + | 0.0559787i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 24.3656i | − | 0.825596i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.81165i | 0.162850i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.28520 | − | 2.28520i | −0.0772540 | − | 0.0772540i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.85105 | − | 2.85105i | 0.0962730 | − | 0.0962730i | −0.657330 | − | 0.753603i | \(-0.728314\pi\) |
0.753603 | + | 0.657330i | \(0.228314\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.24541 | 0.109465 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.4719 | −0.790789 | −0.395394 | − | 0.918511i | \(-0.629392\pi\) | ||||
−0.395394 | + | 0.918511i | \(0.629392\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.0401 | − | 22.0401i | 0.741710 | − | 0.741710i | −0.231197 | − | 0.972907i | \(-0.574264\pi\) |
0.972907 | + | 0.231197i | \(0.0742642\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15.3119 | + | 15.3119i | 0.514702 | + | 0.514702i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 18.6629i | − | 0.626640i | −0.949648 | − | 0.313320i | \(-0.898559\pi\) | ||
0.949648 | − | 0.313320i | \(-0.101441\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.7063i | 0.459696i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.37854 | − | 5.37854i | −0.180188 | − | 0.180188i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 19.8030 | − | 19.8030i | 0.662683 | − | 0.662683i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.64882 | 0.222246 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 31.7651 | 1.06061 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.53961 | − | 1.53961i | 0.0513487 | − | 0.0513487i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.93692 | + | 2.93692i | 0.0978429 | + | 0.0978429i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 5.11865i | − | 0.170338i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 67.0877i | − | 2.23007i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.95043 | + | 2.95043i | 0.0979673 | + | 0.0979673i | 0.754392 | − | 0.656424i | \(-0.227932\pi\) |
−0.656424 | + | 0.754392i | \(0.727932\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.4724 | − | 10.4724i | 0.347347 | − | 0.347347i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.5648 | 0.880132 | 0.440066 | − | 0.897965i | \(-0.354955\pi\) | ||||
0.440066 | + | 0.897965i | \(0.354955\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.0059 | 0.529717 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.0157816 | + | 0.0157816i | −0.000521723 | + | 0.000521723i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.52925 | − | 3.52925i | −0.116546 | − | 0.116546i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 21.9819i | − | 0.725116i | −0.931961 | − | 0.362558i | \(-0.881904\pi\) | ||
0.931961 | − | 0.362558i | \(-0.118096\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 23.7645i | − | 0.783068i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.34375 | − | 3.34375i | −0.110061 | − | 0.110061i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 38.3795 | − | 38.3795i | 1.26191 | − | 1.26191i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 34.6474 | 1.13797 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.0560 | 0.461163 | 0.230581 | − | 0.973053i | \(-0.425937\pi\) | ||||
0.230581 | + | 0.973053i | \(0.425937\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.26332 | − | 4.26332i | 0.139725 | − | 0.139725i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15.0802 | − | 15.0802i | −0.493704 | − | 0.493704i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 3.55872i | − | 0.116383i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 57.9965i | 1.89466i | 0.320256 | + | 0.947331i | \(0.396231\pi\) | ||||
−0.320256 | + | 0.947331i | \(0.603769\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.4172 | − | 11.4172i | −0.372585 | − | 0.372585i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.4672 | + | 15.4672i | −0.504217 | + | 0.504217i | −0.912745 | − | 0.408529i | \(-0.866042\pi\) |
0.408529 | + | 0.912745i | \(0.366042\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.7499 | −0.545451 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 15.3871 | 0.500542 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.9435 | + | 18.9435i | −0.615580 | + | 0.615580i | −0.944395 | − | 0.328814i | \(-0.893351\pi\) |
0.328814 | + | 0.944395i | \(0.393351\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25.2188 | − | 25.2188i | −0.818638 | − | 0.818638i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 6.77220i | − | 0.219604i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 20.2198i | − | 0.654983i | −0.944854 | − | 0.327491i | \(-0.893797\pi\) | ||
0.944854 | − | 0.327491i | \(-0.106203\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.5775 | + | 14.5775i | 0.471716 | + | 0.471716i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.36111 | + | 3.36111i | −0.108649 | + | 0.108649i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.6540 | −0.505493 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.4064 | −0.948594 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.7192 | + | 14.7192i | −0.474318 | + | 0.474318i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.69236 | − | 3.69236i | −0.118861 | − | 0.118861i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 33.3933i | − | 1.07385i | −0.843628 | − | 0.536927i | \(-0.819585\pi\) | ||
0.843628 | − | 0.536927i | \(-0.180415\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 1.87253i | − | 0.0601545i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.52202 | − | 7.52202i | −0.241393 | − | 0.241393i | 0.576033 | − | 0.817426i | \(-0.304600\pi\) |
−0.817426 | + | 0.576033i | \(0.804600\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.52569 | + | 1.52569i | −0.0489115 | + | 0.0489115i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 30.4290 | 0.974508 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28.2764 | 0.904641 | 0.452321 | − | 0.891855i | \(-0.350596\pi\) | ||||
0.452321 | + | 0.891855i | \(0.350596\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.6326 | − | 13.6326i | 0.435700 | − | 0.435700i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.79012 | − | 1.79012i | −0.0571541 | − | 0.0571541i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.94376i | 0.0619964i | 0.999519 | + | 0.0309982i | \(0.00986862\pi\) | ||||
−0.999519 | + | 0.0309982i | \(0.990131\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 50.2173i | − | 1.60006i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.93185 | − | 2.93185i | −0.0933219 | − | 0.0933219i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25.2932 | − | 25.2932i | 0.804277 | − | 0.804277i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.60542 | 0.273360 | 0.136680 | − | 0.990615i | \(-0.456357\pi\) | ||||
0.136680 | + | 0.990615i | \(0.456357\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −28.2221 | −0.895600 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 59.8211 | − | 59.8211i | 1.89646 | − | 1.89646i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.78348 | + | 7.78348i | 0.246505 | + | 0.246505i | 0.819535 | − | 0.573029i | \(-0.194232\pi\) |
−0.573029 | + | 0.819535i | \(0.694232\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 42.1876i | 1.33476i |
(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 | 448.2.m.d.113.3 | 12 | ||
4.3 | odd | 2 | 112.2.m.d.85.6 | yes | 12 | ||
8.3 | odd | 2 | 896.2.m.g.225.3 | 12 | |||
8.5 | even | 2 | 896.2.m.h.225.4 | 12 | |||
16.3 | odd | 4 | 112.2.m.d.29.6 | ✓ | 12 | ||
16.5 | even | 4 | 896.2.m.h.673.4 | 12 | |||
16.11 | odd | 4 | 896.2.m.g.673.3 | 12 | |||
16.13 | even | 4 | inner | 448.2.m.d.337.3 | 12 | ||
28.3 | even | 6 | 784.2.x.m.373.2 | 24 | |||
28.11 | odd | 6 | 784.2.x.l.373.2 | 24 | |||
28.19 | even | 6 | 784.2.x.m.165.3 | 24 | |||
28.23 | odd | 6 | 784.2.x.l.165.3 | 24 | |||
28.27 | even | 2 | 784.2.m.h.197.6 | 12 | |||
32.3 | odd | 8 | 7168.2.a.bj.1.9 | 12 | |||
32.13 | even | 8 | 7168.2.a.bi.1.9 | 12 | |||
32.19 | odd | 8 | 7168.2.a.bj.1.4 | 12 | |||
32.29 | even | 8 | 7168.2.a.bi.1.4 | 12 | |||
112.3 | even | 12 | 784.2.x.m.765.3 | 24 | |||
112.19 | even | 12 | 784.2.x.m.557.2 | 24 | |||
112.51 | odd | 12 | 784.2.x.l.557.2 | 24 | |||
112.67 | odd | 12 | 784.2.x.l.765.3 | 24 | |||
112.83 | even | 4 | 784.2.m.h.589.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.m.d.29.6 | ✓ | 12 | 16.3 | odd | 4 | ||
112.2.m.d.85.6 | yes | 12 | 4.3 | odd | 2 | ||
448.2.m.d.113.3 | 12 | 1.1 | even | 1 | trivial | ||
448.2.m.d.337.3 | 12 | 16.13 | even | 4 | inner | ||
784.2.m.h.197.6 | 12 | 28.27 | even | 2 | |||
784.2.m.h.589.6 | 12 | 112.83 | even | 4 | |||
784.2.x.l.165.3 | 24 | 28.23 | odd | 6 | |||
784.2.x.l.373.2 | 24 | 28.11 | odd | 6 | |||
784.2.x.l.557.2 | 24 | 112.51 | odd | 12 | |||
784.2.x.l.765.3 | 24 | 112.67 | odd | 12 | |||
784.2.x.m.165.3 | 24 | 28.19 | even | 6 | |||
784.2.x.m.373.2 | 24 | 28.3 | even | 6 | |||
784.2.x.m.557.2 | 24 | 112.19 | even | 12 | |||
784.2.x.m.765.3 | 24 | 112.3 | even | 12 | |||
896.2.m.g.225.3 | 12 | 8.3 | odd | 2 | |||
896.2.m.g.673.3 | 12 | 16.11 | odd | 4 | |||
896.2.m.h.225.4 | 12 | 8.5 | even | 2 | |||
896.2.m.h.673.4 | 12 | 16.5 | even | 4 | |||
7168.2.a.bi.1.4 | 12 | 32.29 | even | 8 | |||
7168.2.a.bi.1.9 | 12 | 32.13 | even | 8 | |||
7168.2.a.bj.1.4 | 12 | 32.19 | odd | 8 | |||
7168.2.a.bj.1.9 | 12 | 32.3 | odd | 8 |