Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(237,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4012.237");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.0359812909\) |
Analytic rank: | \(0\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 237.22 | ||
Character | \(\chi\) | \(=\) | 4012.237 |
Dual form | 4012.2.b.b.237.25 |
$q$-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 \(\left(\mathbb{Z}/4012\mathbb{Z}\right)^\times\).
\(n\) | \(2007\) | \(3129\) | \(3777\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 0.257929i | − | 0.148915i | −0.997224 | − | 0.0744575i | \(-0.976277\pi\) | ||
0.997224 | − | 0.0744575i | \(-0.0237225\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.743469i | 0.332490i | 0.986085 | + | 0.166245i | \(0.0531642\pi\) | ||||
−0.986085 | + | 0.166245i | \(0.946836\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.88975i | − | 1.47019i | −0.677965 | − | 0.735094i | \(-0.737138\pi\) | ||
0.677965 | − | 0.735094i | \(-0.262862\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.93347 | 0.977824 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.06863i | − | 0.322203i | −0.986938 | − | 0.161102i | \(-0.948495\pi\) | ||
0.986938 | − | 0.161102i | \(-0.0515047\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.38084 | 1.49238 | 0.746188 | − | 0.665735i | \(-0.231882\pi\) | ||||
0.746188 | + | 0.665735i | \(0.231882\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.191762 | 0.0495127 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.52521 | − | 3.83063i | −0.369918 | − | 0.929064i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.07847 | 0.706249 | 0.353124 | − | 0.935576i | \(-0.385119\pi\) | ||||
0.353124 | + | 0.935576i | \(0.385119\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00328 | −0.218933 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.73219i | − | 0.361188i | −0.983558 | − | 0.180594i | \(-0.942198\pi\) | ||
0.983558 | − | 0.180594i | \(-0.0578019\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.44725 | 0.889451 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.53041i | − | 0.294528i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.99148i | 0.926894i | 0.886125 | + | 0.463447i | \(0.153388\pi\) | ||||
−0.886125 | + | 0.463447i | \(0.846612\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.18871i | 0.213499i | 0.994286 | + | 0.106750i | \(0.0340443\pi\) | ||||
−0.994286 | + | 0.106750i | \(0.965956\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.275629 | −0.0479809 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.89191 | 0.488823 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.759964i | 0.124937i | 0.998047 | + | 0.0624687i | \(0.0198974\pi\) | ||||
−0.998047 | + | 0.0624687i | \(0.980103\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 1.38787i | − | 0.222237i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.00455i | − | 0.469232i | −0.972088 | − | 0.234616i | \(-0.924617\pi\) | ||
0.972088 | − | 0.234616i | \(-0.0753832\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.92247 | −0.750670 | −0.375335 | − | 0.926889i | \(-0.622472\pi\) | ||||
−0.375335 | + | 0.926889i | \(0.622472\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.18095i | 0.325116i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.80648 | 0.846962 | 0.423481 | − | 0.905905i | \(-0.360808\pi\) | ||||
0.423481 | + | 0.905905i | \(0.360808\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8.13019 | −1.16146 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.988029 | + | 0.393396i | −0.138352 | + | 0.0550864i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.194957 | −0.0267794 | −0.0133897 | − | 0.999910i | \(-0.504262\pi\) | ||||
−0.0133897 | + | 0.999910i | \(0.504262\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.794491 | 0.107129 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.794024i | − | 0.105171i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4.03999i | − | 0.517267i | −0.965975 | − | 0.258634i | \(-0.916728\pi\) | ||
0.965975 | − | 0.258634i | \(-0.0832722\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 11.4105i | − | 1.43759i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.00049i | 0.496200i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.58431 | −0.926571 | −0.463285 | − | 0.886209i | \(-0.653330\pi\) | ||||
−0.463285 | + | 0.886209i | \(0.653330\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.446782 | −0.0537863 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.78151i | 0.804817i | 0.915460 | + | 0.402408i | \(0.131827\pi\) | ||||
−0.915460 | + | 0.402408i | \(0.868173\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.3859i | 1.56670i | 0.621582 | + | 0.783349i | \(0.286490\pi\) | ||||
−0.621582 | + | 0.783349i | \(0.713510\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 1.14707i | − | 0.132453i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.15670 | −0.473699 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 15.2500i | − | 1.71575i | −0.513855 | − | 0.857877i | \(-0.671783\pi\) | ||
0.513855 | − | 0.857877i | \(-0.328217\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.40568 | 0.933965 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.30461 | −0.911550 | −0.455775 | − | 0.890095i | \(-0.650638\pi\) | ||||
−0.455775 | + | 0.890095i | \(0.650638\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.84796 | − | 1.13395i | 0.308904 | − | 0.122994i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.28744 | 0.138029 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.68467 | 0.920573 | 0.460287 | − | 0.887770i | \(-0.347747\pi\) | ||||
0.460287 | + | 0.887770i | \(0.347747\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 20.9302i | − | 2.19408i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.306603 | 0.0317933 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.28875i | 0.234820i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.8560i | 1.30533i | 0.757646 | + | 0.652666i | \(0.226350\pi\) | ||||
−0.757646 | + | 0.652666i | \(0.773650\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 3.13479i | − | 0.315058i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −19.2882 | −1.91924 | −0.959622 | − | 0.281292i | \(-0.909237\pi\) | ||||
−0.959622 | + | 0.281292i | \(0.909237\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.883111 | −0.0870155 | −0.0435077 | − | 0.999053i | \(-0.513853\pi\) | ||||
−0.0435077 | + | 0.999053i | \(0.513853\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 0.745907i | − | 0.0727931i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 1.34714i | − | 0.130233i | −0.997878 | − | 0.0651164i | \(-0.979258\pi\) | ||
0.997878 | − | 0.0651164i | \(-0.0207419\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 6.27922i | − | 0.601440i | −0.953712 | − | 0.300720i | \(-0.902773\pi\) | ||
0.953712 | − | 0.300720i | \(-0.0972270\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.196016 | 0.0186051 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.746838i | 0.0702566i | 0.999383 | + | 0.0351283i | \(0.0111840\pi\) | ||||
−0.999383 | + | 0.0351283i | \(0.988816\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.28783 | 0.120091 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 15.7846 | 1.45928 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.9002 | + | 5.93270i | −1.36590 | + | 0.543850i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.85804 | 0.896185 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.774959 | −0.0698757 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.02374i | 0.628223i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.77455 | 0.867351 | 0.433676 | − | 0.901069i | \(-0.357216\pi\) | ||||
0.433676 | + | 0.901069i | \(0.357216\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.26965i | 0.111786i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 0.740669i | − | 0.0647126i | −0.999476 | − | 0.0323563i | \(-0.989699\pi\) | ||
0.999476 | − | 0.0323563i | \(-0.0103011\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 11.9745i | − | 1.03832i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.13781 | 0.0979275 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.1136 | 1.20581 | 0.602904 | − | 0.797814i | \(-0.294010\pi\) | ||||
0.602904 | + | 0.797814i | \(0.294010\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 17.8860i | − | 1.51707i | −0.651634 | − | 0.758533i | \(-0.725916\pi\) | ||
0.651634 | − | 0.758533i | \(-0.274084\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 1.49766i | − | 0.126125i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 5.75011i | − | 0.480848i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.71101 | −0.308183 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.09701i | 0.172958i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.0717 | −0.907026 | −0.453513 | − | 0.891250i | \(-0.649829\pi\) | ||||
−0.453513 | + | 0.891250i | \(0.649829\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.81005 | 0.472815 | 0.236407 | − | 0.971654i | \(-0.424030\pi\) | ||||
0.236407 | + | 0.971654i | \(0.424030\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.47417 | − | 11.2371i | −0.361715 | − | 0.908462i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.883772 | −0.0709863 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.65644 | −0.132198 | −0.0660990 | − | 0.997813i | \(-0.521055\pi\) | ||||
−0.0660990 | + | 0.997813i | \(0.521055\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.0502850i | 0.00398786i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.73781 | −0.531014 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 7.53886i | − | 0.590489i | −0.955422 | − | 0.295244i | \(-0.904599\pi\) | ||
0.955422 | − | 0.295244i | \(-0.0954011\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 0.204922i | − | 0.0159532i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.20100i | 0.479848i | 0.970792 | + | 0.239924i | \(0.0771225\pi\) | ||||
−0.970792 | + | 0.239924i | \(0.922877\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.9535 | 1.22719 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.03060 | 0.690587 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 15.5964i | − | 1.18577i | −0.805287 | − | 0.592886i | \(-0.797989\pi\) | ||
0.805287 | − | 0.592886i | \(-0.202011\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 17.2987i | − | 1.30766i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 0.257929i | − | 0.0193871i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.7619 | −1.10336 | −0.551678 | − | 0.834057i | \(-0.686012\pi\) | ||||
−0.551678 | + | 0.834057i | \(0.686012\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 7.06277i | − | 0.524971i | −0.964936 | − | 0.262486i | \(-0.915458\pi\) | ||
0.964936 | − | 0.262486i | \(-0.0845423\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.04203 | −0.0770289 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.565010 | −0.0415404 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.09351 | + | 1.62988i | −0.299347 | + | 0.119189i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.95293 | −0.433012 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.18256 | 0.0855667 | 0.0427834 | − | 0.999084i | \(-0.486377\pi\) | ||||
0.0427834 | + | 0.999084i | \(0.486377\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 13.0146i | − | 0.936810i | −0.883514 | − | 0.468405i | \(-0.844829\pi\) | ||
0.883514 | − | 0.468405i | \(-0.155171\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.03184 | 0.0738916 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.2246i | 1.51219i | 0.654463 | + | 0.756094i | \(0.272895\pi\) | ||||
−0.654463 | + | 0.756094i | \(0.727105\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.69732i | 0.332984i | 0.986043 | + | 0.166492i | \(0.0532440\pi\) | ||||
−0.986043 | + | 0.166492i | \(0.946756\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.95621i | 0.137980i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 19.4156 | 1.36271 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.23379 | 0.156015 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 5.08135i | − | 0.353178i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 3.28973i | − | 0.227555i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 16.0940i | − | 1.10796i | −0.832531 | − | 0.553979i | \(-0.813109\pi\) | ||
0.832531 | − | 0.553979i | \(-0.186891\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.74914 | 0.119849 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 3.65971i | − | 0.249590i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.62380 | 0.313884 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.45260 | 0.233305 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.20692 | − | 20.6120i | −0.552057 | − | 1.38651i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.2292 | 0.751961 | 0.375981 | − | 0.926628i | \(-0.377306\pi\) | ||||
0.375981 | + | 0.926628i | \(0.377306\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.0459 | 0.869726 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 7.83388i | − | 0.519953i | −0.965615 | − | 0.259976i | \(-0.916285\pi\) | ||
0.965615 | − | 0.259976i | \(-0.0837147\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.0824 | 0.864507 | 0.432254 | − | 0.901752i | \(-0.357719\pi\) | ||||
0.432254 | + | 0.901752i | \(0.357719\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.07213i | 0.0705410i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.91878i | 0.584289i | 0.956374 | + | 0.292144i | \(0.0943687\pi\) | ||||
−0.956374 | + | 0.292144i | \(0.905631\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.31694i | 0.281606i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.93340 | −0.255502 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.3607 | −0.864235 | −0.432117 | − | 0.901817i | \(-0.642233\pi\) | ||||
−0.432117 | + | 0.901817i | \(0.642233\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 11.5118i | − | 0.741537i | −0.928725 | − | 0.370769i | \(-0.879094\pi\) | ||
0.928725 | − | 0.370769i | \(-0.120906\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 6.75930i | − | 0.433609i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 6.04455i | − | 0.386172i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.5647 | 1.05399 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.14200i | 0.135744i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.9699 | −1.44985 | −0.724924 | − | 0.688829i | \(-0.758125\pi\) | ||||
−0.724924 | + | 0.688829i | \(0.758125\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.85107 | −0.116376 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.292478 | − | 0.734569i | −0.0183157 | − | 0.0460005i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 27.8873 | 1.73956 | 0.869781 | − | 0.493438i | \(-0.164260\pi\) | ||||
0.869781 | + | 0.493438i | \(0.164260\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.95607 | 0.183682 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.6424i | 0.906340i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.47876 | 0.461160 | 0.230580 | − | 0.973053i | \(-0.425938\pi\) | ||||
0.230580 | + | 0.973053i | \(0.425938\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.144945i | − | 0.00890389i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 2.24002i | − | 0.137087i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 17.8671i | − | 1.08937i | −0.838639 | − | 0.544687i | \(-0.816648\pi\) | ||
0.838639 | − | 0.544687i | \(-0.183352\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.9077 | −0.966322 | −0.483161 | − | 0.875531i | \(-0.660511\pi\) | ||||
−0.483161 | + | 0.875531i | \(0.660511\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.39848 | −0.326731 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 4.75245i | − | 0.286584i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.4020i | 1.52626i | 0.646248 | + | 0.763128i | \(0.276337\pi\) | ||||
−0.646248 | + | 0.763128i | \(0.723663\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.48706i | 0.208765i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.99936 | −0.119272 | −0.0596360 | − | 0.998220i | \(-0.518994\pi\) | ||||
−0.0596360 | + | 0.998220i | \(0.518994\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.15354i | 0.544121i | 0.962280 | + | 0.272061i | \(0.0877051\pi\) | ||||
−0.962280 | + | 0.272061i | \(0.912295\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.590333 | 0.0349683 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.6870 | −0.689859 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.3475 | + | 11.6850i | −0.726321 | + | 0.687356i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.31594 | 0.194384 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.0247 | 0.760910 | 0.380455 | − | 0.924799i | \(-0.375767\pi\) | ||||
0.380455 | + | 0.924799i | \(0.375767\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.743469i | 0.0432865i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.63544 | −0.0948978 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 9.32066i | − | 0.539028i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19.1472i | 1.10363i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.97497i | 0.285804i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.00361 | 0.171986 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 33.8115 | 1.92972 | 0.964861 | − | 0.262761i | \(-0.0846330\pi\) | ||||
0.964861 | + | 0.262761i | \(0.0846330\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.227779i | 0.0129579i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.2284i | 0.976934i | 0.872582 | + | 0.488467i | \(0.162444\pi\) | ||||
−0.872582 | + | 0.488467i | \(0.837556\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 13.1560i | − | 0.743619i | −0.928309 | − | 0.371809i | \(-0.878738\pi\) | ||
0.928309 | − | 0.371809i | \(-0.121262\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.48335 | 0.477983 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.3748i | 0.807370i | 0.914898 | + | 0.403685i | \(0.132271\pi\) | ||||
−0.914898 | + | 0.403685i | \(0.867729\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.33403 | 0.298648 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.347465 | −0.0193936 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.69531 | − | 11.7925i | −0.261254 | − | 0.656150i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 23.9300 | 1.32740 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.61959 | −0.0895635 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 22.5858i | − | 1.24519i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.92450 | 0.325640 | 0.162820 | − | 0.986656i | \(-0.447941\pi\) | ||||
0.162820 | + | 0.986656i | \(0.447941\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.22933i | 0.122167i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 5.63870i | − | 0.308075i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.80759i | 0.425306i | 0.977128 | + | 0.212653i | \(0.0682104\pi\) | ||||
−0.977128 | + | 0.212653i | \(0.931790\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.192631 | 0.0104623 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.27029 | 0.0687901 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.39615i | 0.237370i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 0.332169i | − | 0.0178834i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 10.9539i | − | 0.588036i | −0.955800 | − | 0.294018i | \(-0.905008\pi\) | ||
0.955800 | − | 0.294018i | \(-0.0949925\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.4015 | 0.770896 | 0.385448 | − | 0.922729i | \(-0.374047\pi\) | ||||
0.385448 | + | 0.922729i | \(0.374047\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 8.23490i | − | 0.439547i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.52022 | 0.293812 | 0.146906 | − | 0.989150i | \(-0.453069\pi\) | ||||
0.146906 | + | 0.989150i | \(0.453069\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.04184 | −0.267593 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.53021 | + | 3.84319i | 0.0809874 | + | 0.203403i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.41581 | −0.0747236 | −0.0373618 | − | 0.999302i | \(-0.511895\pi\) | ||||
−0.0373618 | + | 0.999302i | \(0.511895\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.52305 | −0.501213 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 2.54267i | − | 0.133456i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.95199 | −0.520911 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 1.47678i | − | 0.0770873i | −0.999257 | − | 0.0385437i | \(-0.987728\pi\) | ||
0.999257 | − | 0.0385437i | \(-0.0122719\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 8.81376i | − | 0.458826i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.758336i | 0.0393708i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −37.0490 | −1.91833 | −0.959163 | − | 0.282854i | \(-0.908719\pi\) | ||||
−0.959163 | + | 0.282854i | \(0.908719\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.81162 | 0.0935518 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 26.8584i | 1.38328i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.5120i | 1.36183i | 0.732363 | + | 0.680914i | \(0.238417\pi\) | ||||
−0.732363 | + | 0.680914i | \(0.761583\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 2.52114i | − | 0.129162i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.3811 | 0.990327 | 0.495163 | − | 0.868800i | \(-0.335108\pi\) | ||||
0.495163 | + | 0.868800i | \(0.335108\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 3.09038i | − | 0.157500i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −14.4399 | −0.734023 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.7416 | −1.05164 | −0.525821 | − | 0.850595i | \(-0.676242\pi\) | ||||
−0.525821 | + | 0.850595i | \(0.676242\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.63540 | + | 2.64196i | −0.335566 | + | 0.133610i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.191040 | −0.00963668 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.3379 | 0.570470 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.228359i | 0.0114610i | 0.999984 | + | 0.00573050i | \(0.00182408\pi\) | ||||
−0.999984 | + | 0.00573050i | \(0.998176\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.08856 | −0.154621 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 15.9903i | − | 0.798518i | −0.916838 | − | 0.399259i | \(-0.869268\pi\) | ||
0.916838 | − | 0.399259i | \(-0.130732\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.39628i | 0.318621i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.24937i | 0.310534i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.812118 | 0.0402552 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.2029 | −1.34510 | −0.672549 | − | 0.740052i | \(-0.734801\pi\) | ||||
−0.672549 | + | 0.740052i | \(0.734801\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 3.64030i | − | 0.179563i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 3.88975i | − | 0.191402i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 6.17423i | − | 0.303081i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.61330 | −0.225914 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.6943i | 1.30410i | 0.758174 | + | 0.652052i | \(0.226092\pi\) | ||||
−0.758174 | + | 0.652052i | \(0.773908\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.1321 | 0.834969 | 0.417484 | − | 0.908684i | \(-0.362912\pi\) | ||||
0.417484 | + | 0.908684i | \(0.362912\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 17.0332 | 0.828180 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.78300 | − | 17.0358i | −0.329024 | − | 0.826357i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.7146 | −0.760480 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.48312 | −0.0716056 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 15.3628i | − | 0.740002i | −0.929031 | − | 0.370001i | \(-0.879357\pi\) | ||
0.929031 | − | 0.370001i | \(-0.120643\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.9398 | −0.621848 | −0.310924 | − | 0.950435i | \(-0.600638\pi\) | ||||
−0.310924 | + | 0.950435i | \(0.600638\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.957176i | 0.0458931i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 5.33250i | − | 0.255088i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2.17164i | − | 0.103647i | −0.998656 | − | 0.0518234i | \(-0.983497\pi\) | ||
0.998656 | − | 0.0518234i | \(-0.0165033\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −23.8497 | −1.13570 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −32.7890 | −1.55785 | −0.778926 | − | 0.627115i | \(-0.784235\pi\) | ||||
−0.778926 | + | 0.627115i | \(0.784235\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.45679i | 0.306081i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.85570i | 0.135070i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 40.2945i | − | 1.90162i | −0.309779 | − | 0.950809i | \(-0.600255\pi\) | ||
0.309779 | − | 0.950809i | \(-0.399745\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.21074 | −0.151188 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 1.49858i | − | 0.0704093i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15.5609 | 0.729507 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.0429 | −0.844010 | −0.422005 | − | 0.906594i | \(-0.638673\pi\) | ||||
−0.422005 | + | 0.906594i | \(0.638673\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.86244 | + | 2.33420i | −0.273635 | + | 0.108951i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.2563 | −0.757132 | −0.378566 | − | 0.925574i | \(-0.623583\pi\) | ||||
−0.378566 | + | 0.925574i | \(0.623583\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.4363 | 1.36802 | 0.684010 | − | 0.729472i | \(-0.260234\pi\) | ||||
0.684010 | + | 0.729472i | \(0.260234\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.227950i | 0.0105709i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.28403 | 0.151967 | 0.0759834 | − | 0.997109i | \(-0.475790\pi\) | ||||
0.0759834 | + | 0.997109i | \(0.475790\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 29.5011i | 1.36223i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.427242i | 0.0196863i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.26028i | 0.241868i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.6907 | 0.628173 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.571902 | −0.0261856 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.52191i | 0.252302i | 0.992011 | + | 0.126151i | \(0.0402624\pi\) | ||||
−0.992011 | + | 0.126151i | \(0.959738\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.08925i | 0.186454i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.73787i | 0.0790760i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.55807 | −0.434009 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 0.694991i | − | 0.0314930i | −0.999876 | − | 0.0157465i | \(-0.994988\pi\) | ||
0.999876 | − | 0.0157465i | \(-0.00501248\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.94449 | −0.0879327 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.58015 | 0.432346 | 0.216173 | − | 0.976355i | \(-0.430642\pi\) | ||||
0.216173 | + | 0.976355i | \(0.430642\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.1205 | − | 7.61306i | 0.861144 | − | 0.342875i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.33062 | 0.104754 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 26.3784 | 1.18323 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 29.3534i | − | 1.31404i | −0.753873 | − | 0.657020i | \(-0.771817\pi\) | ||
0.753873 | − | 0.657020i | \(-0.228183\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.59942 | 0.0714566 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.4103i | 1.17758i | 0.808286 | + | 0.588790i | \(0.200395\pi\) | ||||
−0.808286 | + | 0.588790i | \(0.799605\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 14.3402i | − | 0.638129i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 4.11485i | − | 0.182747i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.5823 | −0.557702 | −0.278851 | − | 0.960334i | \(-0.589954\pi\) | ||||
−0.278851 | + | 0.960334i | \(0.589954\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 52.0678 | 2.30334 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 4.71132i | − | 0.208010i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 0.656566i | − | 0.0289317i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 6.20496i | − | 0.272894i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.02275 | −0.176579 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.80320i | 0.122810i | 0.998113 | + | 0.0614052i | \(0.0195582\pi\) | ||||
−0.998113 | + | 0.0614052i | \(0.980442\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.7693 | −1.08308 | −0.541542 | − | 0.840674i | \(-0.682159\pi\) | ||||
−0.541542 | + | 0.840674i | \(0.682159\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.46183 | −0.194730 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.55352 | − | 1.81304i | 0.198355 | − | 0.0789773i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.9995 | 0.869544 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.93347 | 0.127302 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 16.1670i | − | 0.700271i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.00156 | 0.0433010 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.80751i | 0.164306i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.68814i | 0.374224i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.33667i | 0.229441i | 0.993398 | + | 0.114721i | \(0.0365973\pi\) | ||||
−0.993398 | + | 0.114721i | \(0.963403\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.82169 | −0.0781762 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.66841 | 0.199973 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 44.3628i | 1.89682i | 0.317051 | + | 0.948409i | \(0.397307\pi\) | ||||
−0.317051 | + | 0.948409i | \(0.602693\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 11.8512i | − | 0.505796i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.3661i | 0.654618i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −59.3186 | −2.52248 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.145732i | 0.00618599i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −26.1500 | −1.10801 | −0.554005 | − | 0.832513i | \(-0.686901\pi\) | ||||
−0.554005 | + | 0.832513i | \(0.686901\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −26.4870 | −1.12028 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.420393 | + | 1.05583i | 0.0177490 | + | 0.0445773i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −24.2793 | −1.02325 | −0.511626 | − | 0.859208i | \(-0.670957\pi\) | ||||
−0.511626 | + | 0.859208i | \(0.670957\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.555251 | −0.0233596 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 32.6960i | − | 1.37310i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −40.3777 | −1.69272 | −0.846361 | − | 0.532609i | \(-0.821212\pi\) | ||||
−0.846361 | + | 0.532609i | \(0.821212\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 33.5360i | − | 1.40344i | −0.712455 | − | 0.701718i | \(-0.752417\pi\) | ||
0.712455 | − | 0.701718i | \(-0.247583\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 0.305015i | − | 0.0127422i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 7.70351i | − | 0.321258i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.4051 | 0.474799 | 0.237399 | − | 0.971412i | \(-0.423705\pi\) | ||||
0.237399 | + | 0.971412i | \(0.423705\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.35683 | −0.139505 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 32.3029i | 1.34015i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.208337i | 0.00862842i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 11.7353i | 0.485196i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.59098 | 0.148216 | 0.0741079 | − | 0.997250i | \(-0.476389\pi\) | ||||
0.0741079 | + | 0.997250i | \(0.476389\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.65941i | 0.150784i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.47442 | 0.225188 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.1466 | −0.416671 | −0.208335 | − | 0.978057i | \(-0.566805\pi\) | ||||
−0.208335 | + | 0.978057i | \(0.566805\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.41078 | − | 11.0778i | −0.180824 | − | 0.454148i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.21157 | 0.0495863 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22.7784 | −0.930699 | −0.465349 | − | 0.885127i | \(-0.654071\pi\) | ||||
−0.465349 | + | 0.885127i | \(0.654071\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.7652i | 0.847031i | 0.905889 | + | 0.423516i | \(0.139204\pi\) | ||||
−0.905889 | + | 0.423516i | \(0.860796\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −22.2484 | −0.906024 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.32915i | 0.297972i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.09973i | 0.206992i | 0.994630 | + | 0.103496i | \(0.0330029\pi\) | ||||
−0.994630 | + | 0.103496i | \(0.966997\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 5.00784i | − | 0.202928i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 31.2438 | 1.26399 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.4798 | 0.746394 | 0.373197 | − | 0.927752i | \(-0.378262\pi\) | ||||
0.373197 | + | 0.927752i | \(0.378262\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 0.576158i | − | 0.0232329i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.6400i | 1.39456i | 0.716801 | + | 0.697278i | \(0.245606\pi\) | ||||
−0.716801 | + | 0.697278i | \(0.754394\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.2662i | 0.613600i | 0.951774 | + | 0.306800i | \(0.0992583\pi\) | ||||
−0.951774 | + | 0.306800i | \(0.900742\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.65097 | −0.106380 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 33.7812i | − | 1.35342i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.0143 | 0.680573 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.848515 | −0.0338864 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.91114 | − | 1.15911i | 0.116075 | − | 0.0462166i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.4308 | 0.773527 | 0.386764 | − | 0.922179i | \(-0.373593\pi\) | ||||
0.386764 | + | 0.922179i | \(0.373593\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.15111 | −0.164992 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.26708i | 0.288385i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −43.7472 | −1.73333 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 19.8934i | 0.786969i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.88335i | 0.232378i | 0.993227 | + | 0.116189i | \(0.0370679\pi\) | ||||
−0.993227 | + | 0.116189i | \(0.962932\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 35.3797i | − | 1.39524i | −0.716468 | − | 0.697620i | \(-0.754242\pi\) | ||
0.716468 | − | 0.697620i | \(-0.245758\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.943943 | −0.0371677 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.7400 | 1.05126 | 0.525629 | − | 0.850714i | \(-0.323830\pi\) | ||||
0.525629 | + | 0.850714i | \(0.323830\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.06863i | − | 0.0419473i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 1.19261i | − | 0.0467421i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.6616i | 0.691151i | 0.938391 | + | 0.345576i | \(0.112316\pi\) | ||||
−0.938391 | + | 0.345576i | \(0.887684\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.550665 | 0.0215163 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 39.2671i | 1.53196i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.6308 | 1.15425 | 0.577126 | − | 0.816655i | \(-0.304174\pi\) | ||||
0.577126 | + | 0.816655i | \(0.304174\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.8551 | −0.577797 | −0.288899 | − | 0.957360i | \(-0.593289\pi\) | ||||
−0.288899 | + | 0.957360i | \(0.593289\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.31643 | + | 2.11680i | −0.206473 | + | 0.0822097i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.90266 | 0.345230 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.64621 | 0.334783 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 2.89632i | − | 0.111978i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.31724 | −0.166665 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.9569i | 1.11621i | 0.829772 | + | 0.558103i | \(0.188471\pi\) | ||||
−0.829772 | + | 0.558103i | \(0.811529\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 6.80613i | − | 0.261968i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.8890i | 0.918127i | 0.888403 | + | 0.459064i | \(0.151815\pi\) | ||||
−0.888403 | + | 0.459064i | \(0.848185\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 50.0068 | 1.91908 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.02058 | −0.0774288 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 44.9030i | − | 1.71817i | −0.511835 | − | 0.859084i | \(-0.671034\pi\) | ||
0.511835 | − | 0.859084i | \(-0.328966\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.4930i | 0.400918i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 3.37432i | − | 0.128738i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.04903 | −0.0399650 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.1759i | 0.615362i | 0.951490 | + | 0.307681i | \(0.0995529\pi\) | ||||
−0.951490 | + | 0.307681i | \(0.900447\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12.1936 | −0.463195 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.2977 | 0.504409 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.5093 | + | 4.58257i | −0.435946 | + | 0.173577i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.30041 | 0.0870094 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −47.0965 | −1.77881 | −0.889405 | − | 0.457121i | \(-0.848881\pi\) | ||||
−0.889405 | + | 0.457121i | \(0.848881\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.33952i | 0.0882368i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.11346 | 0.0419354 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 75.0262i | 2.82165i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.5184i | 0.995920i | 0.867200 | + | 0.497960i | \(0.165917\pi\) | ||||
−0.867200 | + | 0.497960i | \(0.834083\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 44.7353i | − | 1.67771i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.05908 | 0.0771133 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.27503 | 0.159877 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.44612i | 0.128698i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 2.10780i | − | 0.0786077i | −0.999227 | − | 0.0393039i | \(-0.987486\pi\) | ||
0.999227 | − | 0.0393039i | \(-0.0125140\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.43508i | 0.127929i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.96921 | −0.110426 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22.1984i | 0.824427i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.9859 | −0.815411 | −0.407706 | − | 0.913113i | \(-0.633671\pi\) | ||||
−0.407706 | + | 0.913113i | \(0.633671\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.4736 | 0.869394 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.50781 | + | 18.8562i | 0.277686 | + | 0.697420i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.7560 | 0.655834 | 0.327917 | − | 0.944706i | \(-0.393653\pi\) | ||||
0.327917 | + | 0.944706i | \(0.393653\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.55906 | −0.0575068 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.10480i | 0.298544i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.86714 | 0.289397 | 0.144699 | − | 0.989476i | \(-0.453779\pi\) | ||||
0.144699 | + | 0.989476i | \(0.453779\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 4.27252i | − | 0.156955i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.6420i | 1.12415i | 0.827087 | + | 0.562074i | \(0.189996\pi\) | ||||
−0.827087 | + | 0.562074i | \(0.810004\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 8.23145i | − | 0.301577i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −24.3614 | −0.891335 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.24004 | −0.191467 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 10.9536i | − | 0.399701i | −0.979826 | − | 0.199850i | \(-0.935954\pi\) | ||
0.979826 | − | 0.199850i | \(-0.0640456\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.92460i | 0.215904i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.31959i | 0.157206i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.9967 | 1.41736 | 0.708680 | − | 0.705531i | \(-0.249291\pi\) | ||||
0.708680 | + | 0.705531i | \(0.249291\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.477444i | 0.0173301i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.4793 | −0.633626 | −0.316813 | − | 0.948488i | \(-0.602613\pi\) | ||||
−0.316813 | + | 0.948488i | \(0.602613\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −24.4246 | −0.884230 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.35440 | − | 3.32641i | 0.302054 | − | 0.120266i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.38084 | 0.194291 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.0463 | 0.578643 | 0.289322 | − | 0.957232i | \(-0.406570\pi\) | ||||
0.289322 | + | 0.957232i | \(0.406570\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 7.19293i | − | 0.259047i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.0208 | −0.396390 | −0.198195 | − | 0.980163i | \(-0.563508\pi\) | ||||
−0.198195 | + | 0.980163i | \(0.563508\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.28651i | 0.189897i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 0.762456i | − | 0.0273530i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 9.24940i | − | 0.331394i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.24690 | 0.259314 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.63902 | 0.272996 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 1.23151i | − | 0.0439545i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 6.19725i | − | 0.220908i | −0.993881 | − | 0.110454i | \(-0.964769\pi\) | ||
0.993881 | − | 0.110454i | \(-0.0352305\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 1.92899i | − | 0.0686737i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.90502 | 0.103290 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 21.7385i | − | 0.771958i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.0373854 | −0.00132592 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.55995 | 0.196944 | 0.0984718 | − | 0.995140i | \(-0.468605\pi\) | ||||
0.0984718 | + | 0.995140i | \(0.468605\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.85612 | − | 22.2425i | −0.313307 | − | 0.786883i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 25.4762 | 0.900159 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.3045 | 0.504795 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 5.00936i | − | 0.176557i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.60842 | −0.162224 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 20.1846i | − | 0.709653i | −0.934932 | − | 0.354826i | \(-0.884540\pi\) | ||
0.934932 | − | 0.354826i | \(-0.115460\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.3147i | 0.362200i | 0.983465 | + | 0.181100i | \(0.0579657\pi\) | ||||
−0.983465 | + | 0.181100i | \(0.942034\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.10304i | 0.143900i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.60491 | 0.196331 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.1537 | −0.530159 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 61.3980i | − | 2.14542i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 54.6366i | 1.90683i | 0.301661 | + | 0.953415i | \(0.402459\pi\) | ||||
−0.301661 | + | 0.953415i | \(0.597541\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 47.6656i | 1.66152i | 0.556633 | + | 0.830759i | \(0.312093\pi\) | ||||
−0.556633 | + | 0.830759i | \(0.687907\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.22579 | −0.0426766 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.9748i | 1.32051i | 0.751040 | + | 0.660257i | \(0.229553\pi\) | ||||
−0.751040 | + | 0.660257i | \(0.770447\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36.7907 | 1.27779 | 0.638897 | − | 0.769292i | \(-0.279391\pi\) | ||||
0.638897 | + | 0.769292i | \(0.279391\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.55189 | 0.227283 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12.4003 | + | 31.1437i | 0.429644 | + | 1.07907i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.61025 | −0.159544 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.81922 | 0.0628815 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.8902i | 0.755732i | 0.925860 | + | 0.377866i | \(0.123342\pi\) | ||||
−0.925860 | + | 0.377866i | \(0.876658\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.08515 | 0.140867 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.515693i | 0.0177614i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.8609i | 0.408028i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 38.3453i | − | 1.31756i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.36096 | 0.0810279 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.31641 | 0.0451258 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.0372i | 1.02845i | 0.857654 | + | 0.514227i | \(0.171921\pi\) | ||||
−0.857654 | + | 0.514227i | \(0.828079\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.71397i | 0.229613i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.8552i | 0.473284i | 0.971597 | + | 0.236642i | \(0.0760469\pi\) | ||||
−0.971597 | + | 0.236642i | \(0.923953\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.0365125 | −0.00124579 | −0.000622896 | − | 1.00000i | \(-0.500198\pi\) | ||||
−0.000622896 | 1.00000i | \(0.500198\pi\) | ||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.01440i | 0.102730i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.02921 | −0.103116 | −0.0515578 | − | 0.998670i | \(-0.516419\pi\) | ||||
−0.0515578 | + | 0.998670i | \(0.516419\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.5954 | 0.394257 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.01391 | + | 3.18476i | 0.102358 | + | 0.108160i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.2965 | −0.552821 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −40.8100 | −1.38279 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 37.7128i | 1.27639i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 27.3206 | 0.923606 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.4458i | 0.893011i | 0.894781 | + | 0.446505i | \(0.147332\pi\) | ||||
−0.894781 | + | 0.446505i | \(0.852668\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 3.35944i | − | 0.113311i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 51.7695i | 1.74416i | 0.489365 | + | 0.872079i | \(0.337229\pi\) | ||||
−0.489365 | + | 0.872079i | \(0.662771\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.1375 | 0.980554 | 0.490277 | − | 0.871567i | \(-0.336896\pi\) | ||||
0.490277 | + | 0.871567i | \(0.336896\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.191762 | 0.00644601 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 19.1149i | − | 0.641816i | −0.947110 | − | 0.320908i | \(-0.896012\pi\) | ||
0.947110 | − | 0.320908i | \(-0.103988\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 38.0206i | − | 1.27517i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 8.98254i | − | 0.300926i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 17.8751 | 0.598166 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 10.9750i | − | 0.366854i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.40407 | −0.0802694 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.93344 | −0.197891 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.297351 | + | 0.746809i | 0.00990620 | + | 0.0248798i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.93861 | 0.164347 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.25095 | 0.174548 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 40.6504i | − | 1.34978i | −0.737920 | − | 0.674888i | \(-0.764192\pi\) | ||
0.737920 | − | 0.674888i | \(-0.235808\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −56.5813 | −1.87668 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.36815i | 0.0784604i | 0.999230 | + | 0.0392302i | \(0.0124906\pi\) | ||||
−0.999230 | + | 0.0392302i | \(0.987509\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.87453i | 0.293704i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 0.774716i | − | 0.0256113i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.88102 | −0.0951397 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22.3213 | −0.736312 | −0.368156 | − | 0.929764i | \(-0.620011\pi\) | ||||
−0.368156 | + | 0.929764i | \(0.620011\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 8.72094i | − | 0.287365i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 36.4902i | 1.20109i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.37975i | 0.111126i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.59058 | −0.0850859 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 53.4007i | − | 1.75202i | −0.482292 | − | 0.876011i | \(-0.660196\pi\) | ||
0.482292 | − | 0.876011i | \(-0.339804\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −25.0285 | −0.820276 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.44370 | 0.145480 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.21177 | − | 3.04340i | −0.0396290 | − | 0.0995299i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.8509 | 1.36721 | 0.683604 | − | 0.729853i | \(-0.260412\pi\) | ||||
0.683604 | + | 0.729853i | \(0.260412\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.39330 | −0.110736 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.3220i | 0.890671i | 0.895364 | + | 0.445336i | \(0.146916\pi\) | ||||
−0.895364 | + | 0.445336i | \(0.853084\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.20446 | −0.169481 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 4.42582i | − | 0.143972i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.25327i | 0.235700i | 0.993031 | + | 0.117850i | \(0.0376002\pi\) | ||||
−0.993031 | + | 0.117850i | \(0.962400\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 72.0273i | 2.33810i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.70768 | 0.120230 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.0526 | 1.23264 | 0.616322 | − | 0.787495i | \(-0.288622\pi\) | ||||
0.616322 | + | 0.787495i | \(0.288622\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.879194i | 0.0284501i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 1.37580i | − | 0.0444732i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 54.8985i | − | 1.77276i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.5870 | 0.954418 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 3.95179i | − | 0.127345i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.67594 | 0.311480 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.03155 | −0.258277 | −0.129139 | − | 0.991627i | \(-0.541221\pi\) | ||||
−0.129139 | + | 0.991627i | \(0.541221\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.04161 | + | 1.21106i | −0.0977107 | + | 0.0389047i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.8859 | 1.21582 | 0.607909 | − | 0.794007i | \(-0.292009\pi\) | ||||
0.607909 | + | 0.794007i | \(0.292009\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −69.5720 | −2.23037 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 6.17222i | − | 0.197669i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43.1772 | −1.38136 | −0.690680 | − | 0.723161i | \(-0.742689\pi\) | ||||
−0.690680 | + | 0.723161i | \(0.742689\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 9.28067i | − | 0.296611i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 18.4199i | − | 0.588103i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 54.6825i | 1.74410i | 0.489416 | + | 0.872050i | \(0.337210\pi\) | ||||
−0.489416 | + | 0.872050i | \(0.662790\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.7798 | −0.502787 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.82552 | −0.185428 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.52668i | 0.271133i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 10.1774i | − | 0.323295i | −0.986849 | − | 0.161647i | \(-0.948319\pi\) | ||
0.986849 | − | 0.161647i | \(-0.0516807\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 1.52810i | − | 0.0484927i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.49231 | −0.110714 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.4228i | 0.646797i | 0.946263 | + | 0.323399i | \(0.104825\pi\) | ||||
−0.946263 | + | 0.323399i | \(0.895175\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.16306 | 0.0367975 |
(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 | 4012.2.b.b.237.22 | ✓ | 46 | |
17.16 | even | 2 | inner | 4012.2.b.b.237.25 | yes | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.b.b.237.22 | ✓ | 46 | 1.1 | even | 1 | trivial | |
4012.2.b.b.237.25 | yes | 46 | 17.16 | even | 2 | inner |