Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(77,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 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("570.77");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.k (of order \(4\), degree \(2\), 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: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 77.1 | ||
Character | \(\chi\) | \(=\) | 570.77 |
Dual form | 570.2.k.b.533.1 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | −1.69896 | − | 0.336929i | −0.980897 | − | 0.194526i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 2.14526 | − | 0.630765i | 0.959389 | − | 0.282087i | ||||
\(6\) | 1.43959 | − | 0.963104i | 0.587712 | − | 0.393186i | ||||
\(7\) | 0.804978 | + | 0.804978i | 0.304253 | + | 0.304253i | 0.842675 | − | 0.538422i | \(-0.180979\pi\) |
−0.538422 | + | 0.842675i | \(0.680979\pi\) | |||||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | 2.77296 | + | 1.14486i | 0.924319 | + | 0.381620i | ||||
\(10\) | −1.07091 | + | 1.96295i | −0.338651 | + | 0.620738i | ||||
\(11\) | − | 3.15590i | − | 0.951539i | −0.879570 | − | 0.475769i | \(-0.842170\pi\) | ||
0.879570 | − | 0.475769i | \(-0.157830\pi\) | |||||||
\(12\) | −0.336929 | + | 1.69896i | −0.0972629 | + | 0.490449i | ||||
\(13\) | −2.72994 | + | 2.72994i | −0.757148 | + | 0.757148i | −0.975802 | − | 0.218654i | \(-0.929833\pi\) |
0.218654 | + | 0.975802i | \(0.429833\pi\) | |||||||
\(14\) | −1.13841 | −0.304253 | ||||||||
\(15\) | −3.85724 | + | 0.348848i | −0.995935 | + | 0.0900721i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 2.04213 | − | 2.04213i | 0.495289 | − | 0.495289i | −0.414679 | − | 0.909968i | \(-0.636106\pi\) |
0.909968 | + | 0.414679i | \(0.136106\pi\) | |||||||
\(18\) | −2.77032 | + | 1.15124i | −0.652970 | + | 0.271350i | ||||
\(19\) | − | 1.00000i | − | 0.229416i | ||||||
\(20\) | −0.630765 | − | 2.14526i | −0.141043 | − | 0.479694i | ||||
\(21\) | −1.09641 | − | 1.63885i | −0.239256 | − | 0.357626i | ||||
\(22\) | 2.23156 | + | 2.23156i | 0.475769 | + | 0.475769i | ||||
\(23\) | −1.82163 | − | 1.82163i | −0.379835 | − | 0.379835i | 0.491207 | − | 0.871043i | \(-0.336556\pi\) |
−0.871043 | + | 0.491207i | \(0.836556\pi\) | |||||||
\(24\) | −0.963104 | − | 1.43959i | −0.196593 | − | 0.293856i | ||||
\(25\) | 4.20427 | − | 2.70631i | 0.840854 | − | 0.541262i | ||||
\(26\) | − | 3.86071i | − | 0.757148i | ||||||
\(27\) | −4.32542 | − | 2.87936i | −0.832428 | − | 0.554134i | ||||
\(28\) | 0.804978 | − | 0.804978i | 0.152127 | − | 0.152127i | ||||
\(29\) | 5.49359 | 1.02013 | 0.510067 | − | 0.860134i | \(-0.329620\pi\) | ||||
0.510067 | + | 0.860134i | \(0.329620\pi\) | |||||||
\(30\) | 2.48081 | − | 2.97415i | 0.452932 | − | 0.543004i | ||||
\(31\) | 5.07413 | 0.911341 | 0.455671 | − | 0.890148i | \(-0.349400\pi\) | ||||
0.455671 | + | 0.890148i | \(0.349400\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | −1.06331 | + | 5.36176i | −0.185099 | + | 0.933362i | ||||
\(34\) | 2.88801i | 0.495289i | ||||||||
\(35\) | 2.23464 | + | 1.21913i | 0.377723 | + | 0.206071i | ||||
\(36\) | 1.14486 | − | 2.77296i | 0.190810 | − | 0.462160i | ||||
\(37\) | 7.25575 | + | 7.25575i | 1.19284 | + | 1.19284i | 0.976267 | + | 0.216570i | \(0.0694871\pi\) |
0.216570 | + | 0.976267i | \(0.430513\pi\) | |||||||
\(38\) | 0.707107 | + | 0.707107i | 0.114708 | + | 0.114708i | ||||
\(39\) | 5.55786 | − | 3.71827i | 0.889970 | − | 0.595400i | ||||
\(40\) | 1.96295 | + | 1.07091i | 0.310369 | + | 0.169326i | ||||
\(41\) | − | 6.31900i | − | 0.986862i | −0.869785 | − | 0.493431i | \(-0.835743\pi\) | ||
0.869785 | − | 0.493431i | \(-0.164257\pi\) | |||||||
\(42\) | 1.93412 | + | 0.383563i | 0.298441 | + | 0.0591851i | ||||
\(43\) | 0.643335 | − | 0.643335i | 0.0981077 | − | 0.0981077i | −0.656349 | − | 0.754457i | \(-0.727900\pi\) |
0.754457 | + | 0.656349i | \(0.227900\pi\) | |||||||
\(44\) | −3.15590 | −0.475769 | ||||||||
\(45\) | 6.67085 | + | 0.706935i | 0.994432 | + | 0.105384i | ||||
\(46\) | 2.57617 | 0.379835 | ||||||||
\(47\) | 3.22573 | − | 3.22573i | 0.470521 | − | 0.470521i | −0.431562 | − | 0.902083i | \(-0.642037\pi\) |
0.902083 | + | 0.431562i | \(0.142037\pi\) | |||||||
\(48\) | 1.69896 | + | 0.336929i | 0.245224 | + | 0.0486315i | ||||
\(49\) | − | 5.70402i | − | 0.814860i | ||||||
\(50\) | −1.05922 | + | 4.88652i | −0.149796 | + | 0.691058i | ||||
\(51\) | −4.15756 | + | 2.78145i | −0.582174 | + | 0.389481i | ||||
\(52\) | 2.72994 | + | 2.72994i | 0.378574 | + | 0.378574i | ||||
\(53\) | 3.16898 | + | 3.16898i | 0.435292 | + | 0.435292i | 0.890424 | − | 0.455132i | \(-0.150408\pi\) |
−0.455132 | + | 0.890424i | \(0.650408\pi\) | |||||||
\(54\) | 5.09455 | − | 1.02252i | 0.693281 | − | 0.139147i | ||||
\(55\) | −1.99063 | − | 6.77022i | −0.268416 | − | 0.912896i | ||||
\(56\) | 1.13841i | 0.152127i | ||||||||
\(57\) | −0.336929 | + | 1.69896i | −0.0446273 | + | 0.225033i | ||||
\(58\) | −3.88456 | + | 3.88456i | −0.510067 | + | 0.510067i | ||||
\(59\) | 1.26612 | 0.164834 | 0.0824171 | − | 0.996598i | \(-0.473736\pi\) | ||||
0.0824171 | + | 0.996598i | \(0.473736\pi\) | |||||||
\(60\) | 0.348848 | + | 3.85724i | 0.0450360 | + | 0.497968i | ||||
\(61\) | 2.70369 | 0.346172 | 0.173086 | − | 0.984907i | \(-0.444626\pi\) | ||||
0.173086 | + | 0.984907i | \(0.444626\pi\) | |||||||
\(62\) | −3.58795 | + | 3.58795i | −0.455671 | + | 0.455671i | ||||
\(63\) | 1.31058 | + | 3.15376i | 0.165118 | + | 0.397336i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −4.13447 | + | 7.57837i | −0.512818 | + | 0.939981i | ||||
\(66\) | −3.03946 | − | 4.54321i | −0.374131 | − | 0.559230i | ||||
\(67\) | 3.86878 | + | 3.86878i | 0.472647 | + | 0.472647i | 0.902770 | − | 0.430123i | \(-0.141530\pi\) |
−0.430123 | + | 0.902770i | \(0.641530\pi\) | |||||||
\(68\) | −2.04213 | − | 2.04213i | −0.247645 | − | 0.247645i | ||||
\(69\) | 2.48112 | + | 3.70864i | 0.298692 | + | 0.446467i | ||||
\(70\) | −2.44219 | + | 0.718070i | −0.291897 | + | 0.0858257i | ||||
\(71\) | 0.944610i | 0.112105i | 0.998428 | + | 0.0560523i | \(0.0178514\pi\) | ||||
−0.998428 | + | 0.0560523i | \(0.982149\pi\) | |||||||
\(72\) | 1.15124 | + | 2.77032i | 0.135675 | + | 0.326485i | ||||
\(73\) | 3.61892 | − | 3.61892i | 0.423563 | − | 0.423563i | −0.462866 | − | 0.886428i | \(-0.653179\pi\) |
0.886428 | + | 0.462866i | \(0.153179\pi\) | |||||||
\(74\) | −10.2612 | −1.19284 | ||||||||
\(75\) | −8.05474 | + | 3.18138i | −0.930081 | + | 0.367354i | ||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 2.54043 | − | 2.54043i | 0.289509 | − | 0.289509i | ||||
\(78\) | −1.30079 | + | 6.55921i | −0.147285 | + | 0.742685i | ||||
\(79\) | − | 15.0264i | − | 1.69060i | −0.534292 | − | 0.845300i | \(-0.679422\pi\) | ||
0.534292 | − | 0.845300i | \(-0.320578\pi\) | |||||||
\(80\) | −2.14526 | + | 0.630765i | −0.239847 | + | 0.0705217i | ||||
\(81\) | 6.37859 | + | 6.34930i | 0.708733 | + | 0.705477i | ||||
\(82\) | 4.46821 | + | 4.46821i | 0.493431 | + | 0.493431i | ||||
\(83\) | −5.54904 | − | 5.54904i | −0.609086 | − | 0.609086i | 0.333621 | − | 0.942707i | \(-0.391729\pi\) |
−0.942707 | + | 0.333621i | \(0.891729\pi\) | |||||||
\(84\) | −1.63885 | + | 1.09641i | −0.178813 | + | 0.119628i | ||||
\(85\) | 3.09279 | − | 5.66900i | 0.335460 | − | 0.614889i | ||||
\(86\) | 0.909814i | 0.0981077i | ||||||||
\(87\) | −9.33342 | − | 1.85095i | −1.00065 | − | 0.198443i | ||||
\(88\) | 2.23156 | − | 2.23156i | 0.237885 | − | 0.237885i | ||||
\(89\) | −3.27340 | −0.346979 | −0.173490 | − | 0.984836i | \(-0.555504\pi\) | ||||
−0.173490 | + | 0.984836i | \(0.555504\pi\) | |||||||
\(90\) | −5.21688 | + | 4.21712i | −0.549908 | + | 0.444524i | ||||
\(91\) | −4.39508 | −0.460729 | ||||||||
\(92\) | −1.82163 | + | 1.82163i | −0.189918 | + | 0.189918i | ||||
\(93\) | −8.62077 | − | 1.70962i | −0.893932 | − | 0.177279i | ||||
\(94\) | 4.56187i | 0.470521i | ||||||||
\(95\) | −0.630765 | − | 2.14526i | −0.0647151 | − | 0.220099i | ||||
\(96\) | −1.43959 | + | 0.963104i | −0.146928 | + | 0.0982964i | ||||
\(97\) | 2.89748 | + | 2.89748i | 0.294195 | + | 0.294195i | 0.838735 | − | 0.544540i | \(-0.183296\pi\) |
−0.544540 | + | 0.838735i | \(0.683296\pi\) | |||||||
\(98\) | 4.03335 | + | 4.03335i | 0.407430 | + | 0.407430i | ||||
\(99\) | 3.61306 | − | 8.75117i | 0.363126 | − | 0.879526i | ||||
\(100\) | −2.70631 | − | 4.20427i | −0.270631 | − | 0.420427i | ||||
\(101\) | 16.8808i | 1.67971i | 0.542813 | + | 0.839853i | \(0.317359\pi\) | ||||
−0.542813 | + | 0.839853i | \(0.682641\pi\) | |||||||
\(102\) | 0.973053 | − | 4.90662i | 0.0963466 | − | 0.485828i | ||||
\(103\) | 1.47281 | − | 1.47281i | 0.145121 | − | 0.145121i | −0.630814 | − | 0.775934i | \(-0.717279\pi\) |
0.775934 | + | 0.630814i | \(0.217279\pi\) | |||||||
\(104\) | −3.86071 | −0.378574 | ||||||||
\(105\) | −3.38581 | − | 2.82418i | −0.330421 | − | 0.275612i | ||||
\(106\) | −4.48161 | −0.435292 | ||||||||
\(107\) | −8.84697 | + | 8.84697i | −0.855269 | + | 0.855269i | −0.990776 | − | 0.135507i | \(-0.956734\pi\) |
0.135507 | + | 0.990776i | \(0.456734\pi\) | |||||||
\(108\) | −2.87936 | + | 4.32542i | −0.277067 | + | 0.416214i | ||||
\(109\) | 6.83921i | 0.655077i | 0.944838 | + | 0.327539i | \(0.106219\pi\) | ||||
−0.944838 | + | 0.327539i | \(0.893781\pi\) | |||||||
\(110\) | 6.19485 | + | 3.37968i | 0.590656 | + | 0.322240i | ||||
\(111\) | −9.88258 | − | 14.7719i | −0.938013 | − | 1.40209i | ||||
\(112\) | −0.804978 | − | 0.804978i | −0.0760633 | − | 0.0760633i | ||||
\(113\) | −14.3560 | − | 14.3560i | −1.35050 | − | 1.35050i | −0.885101 | − | 0.465400i | \(-0.845911\pi\) |
−0.465400 | − | 0.885101i | \(-0.654089\pi\) | |||||||
\(114\) | −0.963104 | − | 1.43959i | −0.0902030 | − | 0.134830i | ||||
\(115\) | −5.05688 | − | 2.75884i | −0.471556 | − | 0.257263i | ||||
\(116\) | − | 5.49359i | − | 0.510067i | ||||||
\(117\) | −10.6954 | + | 4.44461i | −0.988790 | + | 0.410904i | ||||
\(118\) | −0.895279 | + | 0.895279i | −0.0824171 | + | 0.0824171i | ||||
\(119\) | 3.28774 | 0.301386 | ||||||||
\(120\) | −2.97415 | − | 2.48081i | −0.271502 | − | 0.226466i | ||||
\(121\) | 1.04032 | 0.0945742 | ||||||||
\(122\) | −1.91180 | + | 1.91180i | −0.173086 | + | 0.173086i | ||||
\(123\) | −2.12905 | + | 10.7357i | −0.191970 | + | 0.968010i | ||||
\(124\) | − | 5.07413i | − | 0.455671i | ||||||
\(125\) | 7.31221 | − | 8.45764i | 0.654024 | − | 0.756474i | ||||
\(126\) | −3.15677 | − | 1.30332i | −0.281227 | − | 0.116109i | ||||
\(127\) | −1.57598 | − | 1.57598i | −0.139845 | − | 0.139845i | 0.633718 | − | 0.773564i | \(-0.281528\pi\) |
−0.773564 | + | 0.633718i | \(0.781528\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | −1.30976 | + | 0.876246i | −0.115318 | + | 0.0771491i | ||||
\(130\) | −2.43520 | − | 8.28223i | −0.213581 | − | 0.726400i | ||||
\(131\) | − | 19.0035i | − | 1.66034i | −0.557509 | − | 0.830171i | \(-0.688243\pi\) | ||
0.557509 | − | 0.830171i | \(-0.311757\pi\) | |||||||
\(132\) | 5.36176 | + | 1.06331i | 0.466681 | + | 0.0925494i | ||||
\(133\) | 0.804978 | − | 0.804978i | 0.0698004 | − | 0.0698004i | ||||
\(134\) | −5.47128 | −0.472647 | ||||||||
\(135\) | −11.0953 | − | 3.44866i | −0.954936 | − | 0.296813i | ||||
\(136\) | 2.88801 | 0.247645 | ||||||||
\(137\) | −15.2239 | + | 15.2239i | −1.30066 | + | 1.30066i | −0.372720 | + | 0.927944i | \(0.621575\pi\) |
−0.927944 | + | 0.372720i | \(0.878425\pi\) | |||||||
\(138\) | −4.37682 | − | 0.867985i | −0.372580 | − | 0.0738878i | ||||
\(139\) | 15.0510i | 1.27661i | 0.769785 | + | 0.638304i | \(0.220364\pi\) | ||||
−0.769785 | + | 0.638304i | \(0.779636\pi\) | |||||||
\(140\) | 1.21913 | − | 2.23464i | 0.103036 | − | 0.188861i | ||||
\(141\) | −6.56724 | + | 4.39356i | −0.553061 | + | 0.370004i | ||||
\(142\) | −0.667940 | − | 0.667940i | −0.0560523 | − | 0.0560523i | ||||
\(143\) | 8.61540 | + | 8.61540i | 0.720456 | + | 0.720456i | ||||
\(144\) | −2.77296 | − | 1.14486i | −0.231080 | − | 0.0954050i | ||||
\(145\) | 11.7852 | − | 3.46517i | 0.978706 | − | 0.287766i | ||||
\(146\) | 5.11793i | 0.423563i | ||||||||
\(147\) | −1.92185 | + | 9.69093i | −0.158511 | + | 0.799294i | ||||
\(148\) | 7.25575 | − | 7.25575i | 0.596419 | − | 0.596419i | ||||
\(149\) | 13.7188 | 1.12389 | 0.561945 | − | 0.827174i | \(-0.310053\pi\) | ||||
0.561945 | + | 0.827174i | \(0.310053\pi\) | |||||||
\(150\) | 3.44598 | − | 7.94514i | 0.281363 | − | 0.648718i | ||||
\(151\) | −14.9068 | −1.21310 | −0.606549 | − | 0.795046i | \(-0.707447\pi\) | ||||
−0.606549 | + | 0.795046i | \(0.707447\pi\) | |||||||
\(152\) | 0.707107 | − | 0.707107i | 0.0573539 | − | 0.0573539i | ||||
\(153\) | 8.00069 | − | 3.32479i | 0.646818 | − | 0.268793i | ||||
\(154\) | 3.59271i | 0.289509i | ||||||||
\(155\) | 10.8853 | − | 3.20058i | 0.874331 | − | 0.257077i | ||||
\(156\) | −3.71827 | − | 5.55786i | −0.297700 | − | 0.444985i | ||||
\(157\) | 2.63322 | + | 2.63322i | 0.210153 | + | 0.210153i | 0.804333 | − | 0.594179i | \(-0.202523\pi\) |
−0.594179 | + | 0.804333i | \(0.702523\pi\) | |||||||
\(158\) | 10.6253 | + | 10.6253i | 0.845300 | + | 0.845300i | ||||
\(159\) | −4.31626 | − | 6.45170i | −0.342301 | − | 0.511653i | ||||
\(160\) | 1.07091 | − | 1.96295i | 0.0846628 | − | 0.155184i | ||||
\(161\) | − | 2.93274i | − | 0.231132i | ||||||
\(162\) | −8.99998 | + | 0.0207168i | −0.707105 | + | 0.00162767i | ||||
\(163\) | −8.49310 | + | 8.49310i | −0.665231 | + | 0.665231i | −0.956608 | − | 0.291377i | \(-0.905887\pi\) |
0.291377 | + | 0.956608i | \(0.405887\pi\) | |||||||
\(164\) | −6.31900 | −0.493431 | ||||||||
\(165\) | 1.10093 | + | 12.1731i | 0.0857071 | + | 0.947671i | ||||
\(166\) | 7.84753 | 0.609086 | ||||||||
\(167\) | 2.26247 | − | 2.26247i | 0.175075 | − | 0.175075i | −0.614130 | − | 0.789205i | \(-0.710493\pi\) |
0.789205 | + | 0.614130i | \(0.210493\pi\) | |||||||
\(168\) | 0.383563 | − | 1.93412i | 0.0295925 | − | 0.149221i | ||||
\(169\) | − | 1.90511i | − | 0.146547i | ||||||
\(170\) | 1.82165 | + | 6.19552i | 0.139714 | + | 0.475175i | ||||
\(171\) | 1.14486 | − | 2.77296i | 0.0875496 | − | 0.212053i | ||||
\(172\) | −0.643335 | − | 0.643335i | −0.0490539 | − | 0.0490539i | ||||
\(173\) | −6.00022 | − | 6.00022i | −0.456189 | − | 0.456189i | 0.441214 | − | 0.897402i | \(-0.354548\pi\) |
−0.897402 | + | 0.441214i | \(0.854548\pi\) | |||||||
\(174\) | 7.90854 | − | 5.29091i | 0.599545 | − | 0.401103i | ||||
\(175\) | 5.56286 | + | 1.20583i | 0.420513 | + | 0.0911520i | ||||
\(176\) | 3.15590i | 0.237885i | ||||||||
\(177\) | −2.15108 | − | 0.426591i | −0.161685 | − | 0.0320645i | ||||
\(178\) | 2.31464 | − | 2.31464i | 0.173490 | − | 0.173490i | ||||
\(179\) | 10.5263 | 0.786776 | 0.393388 | − | 0.919373i | \(-0.371303\pi\) | ||||
0.393388 | + | 0.919373i | \(0.371303\pi\) | |||||||
\(180\) | 0.706935 | − | 6.67085i | 0.0526919 | − | 0.497216i | ||||
\(181\) | −20.9226 | −1.55516 | −0.777582 | − | 0.628781i | \(-0.783554\pi\) | ||||
−0.777582 | + | 0.628781i | \(0.783554\pi\) | |||||||
\(182\) | 3.10779 | − | 3.10779i | 0.230365 | − | 0.230365i | ||||
\(183\) | −4.59347 | − | 0.910950i | −0.339559 | − | 0.0673394i | ||||
\(184\) | − | 2.57617i | − | 0.189918i | ||||||
\(185\) | 20.1421 | + | 10.9888i | 1.48088 | + | 0.807912i | ||||
\(186\) | 7.30469 | − | 4.88692i | 0.535606 | − | 0.358326i | ||||
\(187\) | −6.44475 | − | 6.44475i | −0.471287 | − | 0.471287i | ||||
\(188\) | −3.22573 | − | 3.22573i | −0.235260 | − | 0.235260i | ||||
\(189\) | −1.16404 | − | 5.79969i | −0.0846717 | − | 0.421866i | ||||
\(190\) | 1.96295 | + | 1.07091i | 0.142407 | + | 0.0776919i | ||||
\(191\) | 24.7912i | 1.79383i | 0.442204 | + | 0.896915i | \(0.354197\pi\) | ||||
−0.442204 | + | 0.896915i | \(0.645803\pi\) | |||||||
\(192\) | 0.336929 | − | 1.69896i | 0.0243157 | − | 0.122612i | ||||
\(193\) | 17.4625 | − | 17.4625i | 1.25698 | − | 1.25698i | 0.304450 | − | 0.952528i | \(-0.401527\pi\) |
0.952528 | − | 0.304450i | \(-0.0984726\pi\) | |||||||
\(194\) | −4.09766 | −0.294195 | ||||||||
\(195\) | 9.57769 | − | 11.4824i | 0.685873 | − | 0.822268i | ||||
\(196\) | −5.70402 | −0.407430 | ||||||||
\(197\) | 1.66630 | − | 1.66630i | 0.118719 | − | 0.118719i | −0.645252 | − | 0.763970i | \(-0.723247\pi\) |
0.763970 | + | 0.645252i | \(0.223247\pi\) | |||||||
\(198\) | 3.63319 | + | 8.74283i | 0.258200 | + | 0.621326i | ||||
\(199\) | 27.4124i | 1.94321i | 0.236606 | + | 0.971606i | \(0.423965\pi\) | ||||
−0.236606 | + | 0.971606i | \(0.576035\pi\) | |||||||
\(200\) | 4.88652 | + | 1.05922i | 0.345529 | + | 0.0748982i | ||||
\(201\) | −5.26942 | − | 7.87642i | −0.371676 | − | 0.555560i | ||||
\(202\) | −11.9366 | − | 11.9366i | −0.839853 | − | 0.839853i | ||||
\(203\) | 4.42222 | + | 4.42222i | 0.310379 | + | 0.310379i | ||||
\(204\) | 2.78145 | + | 4.15756i | 0.194741 | + | 0.291087i | ||||
\(205\) | −3.98580 | − | 13.5559i | −0.278380 | − | 0.946784i | ||||
\(206\) | 2.08287i | 0.145121i | ||||||||
\(207\) | −2.96579 | − | 7.13680i | −0.206137 | − | 0.496042i | ||||
\(208\) | 2.72994 | − | 2.72994i | 0.189287 | − | 0.189287i | ||||
\(209\) | −3.15590 | −0.218298 | ||||||||
\(210\) | 4.39112 | − | 0.397132i | 0.303016 | − | 0.0274047i | ||||
\(211\) | −3.68643 | −0.253785 | −0.126892 | − | 0.991917i | \(-0.540500\pi\) | ||||
−0.126892 | + | 0.991917i | \(0.540500\pi\) | |||||||
\(212\) | 3.16898 | − | 3.16898i | 0.217646 | − | 0.217646i | ||||
\(213\) | 0.318266 | − | 1.60486i | 0.0218073 | − | 0.109963i | ||||
\(214\) | − | 12.5115i | − | 0.855269i | ||||||
\(215\) | 0.974328 | − | 1.78591i | 0.0664486 | − | 0.121798i | ||||
\(216\) | −1.02252 | − | 5.09455i | −0.0695734 | − | 0.346640i | ||||
\(217\) | 4.08457 | + | 4.08457i | 0.277278 | + | 0.277278i | ||||
\(218\) | −4.83605 | − | 4.83605i | −0.327539 | − | 0.327539i | ||||
\(219\) | −7.36773 | + | 4.92910i | −0.497865 | + | 0.333078i | ||||
\(220\) | −6.77022 | + | 1.99063i | −0.456448 | + | 0.134208i | ||||
\(221\) | 11.1498i | 0.750015i | ||||||||
\(222\) | 17.4334 | + | 3.45728i | 1.17005 | + | 0.232038i | ||||
\(223\) | −18.9631 | + | 18.9631i | −1.26987 | + | 1.26987i | −0.323709 | + | 0.946157i | \(0.604930\pi\) |
−0.946157 | + | 0.323709i | \(0.895070\pi\) | |||||||
\(224\) | 1.13841 | 0.0760633 | ||||||||
\(225\) | 14.7566 | − | 2.69118i | 0.983774 | − | 0.179412i | ||||
\(226\) | 20.3025 | 1.35050 | ||||||||
\(227\) | −2.05681 | + | 2.05681i | −0.136515 | + | 0.136515i | −0.772062 | − | 0.635547i | \(-0.780775\pi\) |
0.635547 | + | 0.772062i | \(0.280775\pi\) | |||||||
\(228\) | 1.69896 | + | 0.336929i | 0.112517 | + | 0.0223136i | ||||
\(229\) | 15.8734i | 1.04895i | 0.851427 | + | 0.524473i | \(0.175738\pi\) | ||||
−0.851427 | + | 0.524473i | \(0.824262\pi\) | |||||||
\(230\) | 5.52655 | − | 1.62496i | 0.364410 | − | 0.107147i | ||||
\(231\) | −5.17204 | + | 3.46015i | −0.340295 | + | 0.227661i | ||||
\(232\) | 3.88456 | + | 3.88456i | 0.255034 | + | 0.255034i | ||||
\(233\) | −15.6011 | − | 15.6011i | −1.02206 | − | 1.02206i | −0.999751 | − | 0.0223132i | \(-0.992897\pi\) |
−0.0223132 | − | 0.999751i | \(-0.507103\pi\) | |||||||
\(234\) | 4.41997 | − | 10.7056i | 0.288943 | − | 0.699847i | ||||
\(235\) | 4.88535 | − | 8.95470i | 0.318685 | − | 0.584140i | ||||
\(236\) | − | 1.26612i | − | 0.0824171i | ||||||
\(237\) | −5.06282 | + | 25.5293i | −0.328865 | + | 1.65830i | ||||
\(238\) | −2.32478 | + | 2.32478i | −0.150693 | + | 0.150693i | ||||
\(239\) | 4.84839 | 0.313616 | 0.156808 | − | 0.987629i | \(-0.449880\pi\) | ||||
0.156808 | + | 0.987629i | \(0.449880\pi\) | |||||||
\(240\) | 3.85724 | − | 0.348848i | 0.248984 | − | 0.0225180i | ||||
\(241\) | −17.0520 | −1.09842 | −0.549209 | − | 0.835685i | \(-0.685071\pi\) | ||||
−0.549209 | + | 0.835685i | \(0.685071\pi\) | |||||||
\(242\) | −0.735615 | + | 0.735615i | −0.0472871 | + | 0.0472871i | ||||
\(243\) | −8.69774 | − | 12.9364i | −0.557960 | − | 0.829868i | ||||
\(244\) | − | 2.70369i | − | 0.173086i | ||||||
\(245\) | −3.59790 | − | 12.2366i | −0.229861 | − | 0.781768i | ||||
\(246\) | −6.08585 | − | 9.09679i | −0.388020 | − | 0.579990i | ||||
\(247\) | 2.72994 | + | 2.72994i | 0.173702 | + | 0.173702i | ||||
\(248\) | 3.58795 | + | 3.58795i | 0.227835 | + | 0.227835i | ||||
\(249\) | 7.55799 | + | 11.2973i | 0.478968 | + | 0.715934i | ||||
\(250\) | 0.809943 | + | 11.1510i | 0.0512253 | + | 0.705249i | ||||
\(251\) | 7.93870i | 0.501087i | 0.968105 | + | 0.250543i | \(0.0806092\pi\) | ||||
−0.968105 | + | 0.250543i | \(0.919391\pi\) | |||||||
\(252\) | 3.15376 | − | 1.31058i | 0.198668 | − | 0.0825590i | ||||
\(253\) | −5.74887 | + | 5.74887i | −0.361428 | + | 0.361428i | ||||
\(254\) | 2.22877 | 0.139845 | ||||||||
\(255\) | −7.16459 | + | 8.58938i | −0.448664 | + | 0.537888i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 16.9891 | − | 16.9891i | 1.05975 | − | 1.05975i | 0.0616541 | − | 0.998098i | \(-0.480362\pi\) |
0.998098 | − | 0.0616541i | \(-0.0196376\pi\) | |||||||
\(258\) | 0.306542 | − | 1.54574i | 0.0190845 | − | 0.0962336i | ||||
\(259\) | 11.6814i | 0.725849i | ||||||||
\(260\) | 7.57837 | + | 4.13447i | 0.469990 | + | 0.256409i | ||||
\(261\) | 15.2335 | + | 6.28939i | 0.942930 | + | 0.389304i | ||||
\(262\) | 13.4375 | + | 13.4375i | 0.830171 | + | 0.830171i | ||||
\(263\) | 2.30249 | + | 2.30249i | 0.141977 | + | 0.141977i | 0.774523 | − | 0.632546i | \(-0.217990\pi\) |
−0.632546 | + | 0.774523i | \(0.717990\pi\) | |||||||
\(264\) | −4.54321 | + | 3.03946i | −0.279615 | + | 0.187066i | ||||
\(265\) | 8.79715 | + | 4.79939i | 0.540405 | + | 0.294824i | ||||
\(266\) | 1.13841i | 0.0698004i | ||||||||
\(267\) | 5.56138 | + | 1.10290i | 0.340351 | + | 0.0674965i | ||||
\(268\) | 3.86878 | − | 3.86878i | 0.236323 | − | 0.236323i | ||||
\(269\) | −15.9676 | −0.973559 | −0.486780 | − | 0.873525i | \(-0.661829\pi\) | ||||
−0.486780 | + | 0.873525i | \(0.661829\pi\) | |||||||
\(270\) | 10.2842 | − | 5.40703i | 0.625874 | − | 0.329061i | ||||
\(271\) | −5.91297 | −0.359188 | −0.179594 | − | 0.983741i | \(-0.557478\pi\) | ||||
−0.179594 | + | 0.983741i | \(0.557478\pi\) | |||||||
\(272\) | −2.04213 | + | 2.04213i | −0.123822 | + | 0.123822i | ||||
\(273\) | 7.46708 | + | 1.48083i | 0.451928 | + | 0.0896238i | ||||
\(274\) | − | 21.5298i | − | 1.30066i | ||||||
\(275\) | −8.54083 | − | 13.2682i | −0.515031 | − | 0.800105i | ||||
\(276\) | 3.70864 | − | 2.48112i | 0.223234 | − | 0.149346i | ||||
\(277\) | 17.6393 | + | 17.6393i | 1.05984 | + | 1.05984i | 0.998092 | + | 0.0617480i | \(0.0196675\pi\) |
0.0617480 | + | 0.998092i | \(0.480332\pi\) | |||||||
\(278\) | −10.6426 | − | 10.6426i | −0.638304 | − | 0.638304i | ||||
\(279\) | 14.0704 | + | 5.80917i | 0.842370 | + | 0.347786i | ||||
\(280\) | 0.718070 | + | 2.44219i | 0.0429129 | + | 0.145949i | ||||
\(281\) | 11.7923i | 0.703472i | 0.936099 | + | 0.351736i | \(0.114408\pi\) | ||||
−0.936099 | + | 0.351736i | \(0.885592\pi\) | |||||||
\(282\) | 1.53702 | − | 7.75045i | 0.0915285 | − | 0.461533i | ||||
\(283\) | −4.82604 | + | 4.82604i | −0.286878 | + | 0.286878i | −0.835845 | − | 0.548966i | \(-0.815022\pi\) |
0.548966 | + | 0.835845i | \(0.315022\pi\) | |||||||
\(284\) | 0.944610 | 0.0560523 | ||||||||
\(285\) | 0.348848 | + | 3.85724i | 0.0206640 | + | 0.228483i | ||||
\(286\) | −12.1840 | −0.720456 | ||||||||
\(287\) | 5.08665 | − | 5.08665i | 0.300256 | − | 0.300256i | ||||
\(288\) | 2.77032 | − | 1.15124i | 0.163242 | − | 0.0678374i | ||||
\(289\) | 8.65941i | 0.509377i | ||||||||
\(290\) | −5.88314 | + | 10.7836i | −0.345470 | + | 0.633236i | ||||
\(291\) | −3.94648 | − | 5.89897i | −0.231346 | − | 0.345804i | ||||
\(292\) | −3.61892 | − | 3.61892i | −0.211781 | − | 0.211781i | ||||
\(293\) | −11.3784 | − | 11.3784i | −0.664732 | − | 0.664732i | 0.291760 | − | 0.956492i | \(-0.405759\pi\) |
−0.956492 | + | 0.291760i | \(0.905759\pi\) | |||||||
\(294\) | −5.49357 | − | 8.21147i | −0.320391 | − | 0.478903i | ||||
\(295\) | 2.71614 | − | 0.798621i | 0.158140 | − | 0.0464975i | ||||
\(296\) | 10.2612i | 0.596419i | ||||||||
\(297\) | −9.08698 | + | 13.6506i | −0.527280 | + | 0.792087i | ||||
\(298\) | −9.70068 | + | 9.70068i | −0.561945 | + | 0.561945i | ||||
\(299\) | 9.94585 | 0.575183 | ||||||||
\(300\) | 3.18138 | + | 8.05474i | 0.183677 | + | 0.465041i | ||||
\(301\) | 1.03574 | 0.0596992 | ||||||||
\(302\) | 10.5407 | − | 10.5407i | 0.606549 | − | 0.606549i | ||||
\(303\) | 5.68764 | − | 28.6799i | 0.326746 | − | 1.64762i | ||||
\(304\) | 1.00000i | 0.0573539i | ||||||||
\(305\) | 5.80011 | − | 1.70539i | 0.332113 | − | 0.0976504i | ||||
\(306\) | −3.30636 | + | 8.00832i | −0.189012 | + | 0.457805i | ||||
\(307\) | 3.22856 | + | 3.22856i | 0.184264 | + | 0.184264i | 0.793211 | − | 0.608947i | \(-0.208408\pi\) |
−0.608947 | + | 0.793211i | \(0.708408\pi\) | |||||||
\(308\) | −2.54043 | − | 2.54043i | −0.144754 | − | 0.144754i | ||||
\(309\) | −2.99849 | + | 2.00602i | −0.170578 | + | 0.114119i | ||||
\(310\) | −5.43393 | + | 9.96024i | −0.308627 | + | 0.565704i | ||||
\(311\) | − | 8.13102i | − | 0.461068i | −0.973064 | − | 0.230534i | \(-0.925953\pi\) | ||
0.973064 | − | 0.230534i | \(-0.0740473\pi\) | |||||||
\(312\) | 6.55921 | + | 1.30079i | 0.371342 | + | 0.0736425i | ||||
\(313\) | 19.8596 | − | 19.8596i | 1.12253 | − | 1.12253i | 0.131173 | − | 0.991359i | \(-0.458126\pi\) |
0.991359 | − | 0.131173i | \(-0.0418744\pi\) | |||||||
\(314\) | −3.72393 | −0.210153 | ||||||||
\(315\) | 4.80082 | + | 5.93895i | 0.270496 | + | 0.334622i | ||||
\(316\) | −15.0264 | −0.845300 | ||||||||
\(317\) | −7.90002 | + | 7.90002i | −0.443709 | + | 0.443709i | −0.893257 | − | 0.449547i | \(-0.851585\pi\) |
0.449547 | + | 0.893257i | \(0.351585\pi\) | |||||||
\(318\) | 7.61409 | + | 1.50998i | 0.426977 | + | 0.0846756i | ||||
\(319\) | − | 17.3372i | − | 0.970698i | ||||||
\(320\) | 0.630765 | + | 2.14526i | 0.0352608 | + | 0.119924i | ||||
\(321\) | 18.0115 | − | 12.0499i | 1.00530 | − | 0.672559i | ||||
\(322\) | 2.07376 | + | 2.07376i | 0.115566 | + | 0.115566i | ||||
\(323\) | −2.04213 | − | 2.04213i | −0.113627 | − | 0.113627i | ||||
\(324\) | 6.34930 | − | 6.37859i | 0.352739 | − | 0.354366i | ||||
\(325\) | −4.08934 | + | 18.8654i | −0.226836 | + | 1.04647i | ||||
\(326\) | − | 12.0111i | − | 0.665231i | ||||||
\(327\) | 2.30432 | − | 11.6196i | 0.127429 | − | 0.642563i | ||||
\(328\) | 4.46821 | − | 4.46821i | 0.246715 | − | 0.246715i | ||||
\(329\) | 5.19328 | 0.286315 | ||||||||
\(330\) | −9.38612 | − | 7.82917i | −0.516689 | − | 0.430982i | ||||
\(331\) | 29.2265 | 1.60643 | 0.803217 | − | 0.595687i | \(-0.203120\pi\) | ||||
0.803217 | + | 0.595687i | \(0.203120\pi\) | |||||||
\(332\) | −5.54904 | + | 5.54904i | −0.304543 | + | 0.304543i | ||||
\(333\) | 11.8131 | + | 28.4267i | 0.647352 | + | 1.55777i | ||||
\(334\) | 3.19962i | 0.175075i | ||||||||
\(335\) | 10.7398 | + | 5.85925i | 0.586779 | + | 0.320125i | ||||
\(336\) | 1.09641 | + | 1.63885i | 0.0598140 | + | 0.0894065i | ||||
\(337\) | −10.9958 | − | 10.9958i | −0.598982 | − | 0.598982i | 0.341060 | − | 0.940042i | \(-0.389214\pi\) |
−0.940042 | + | 0.341060i | \(0.889214\pi\) | |||||||
\(338\) | 1.34711 | + | 1.34711i | 0.0732734 | + | 0.0732734i | ||||
\(339\) | 19.5534 | + | 29.2273i | 1.06200 | + | 1.58741i | ||||
\(340\) | −5.66900 | − | 3.09279i | −0.307445 | − | 0.167730i | ||||
\(341\) | − | 16.0134i | − | 0.867176i | ||||||
\(342\) | 1.15124 | + | 2.77032i | 0.0622519 | + | 0.149802i | ||||
\(343\) | 10.2265 | − | 10.2265i | 0.552177 | − | 0.552177i | ||||
\(344\) | 0.909814 | 0.0490539 | ||||||||
\(345\) | 7.66192 | + | 6.39098i | 0.412504 | + | 0.344079i | ||||
\(346\) | 8.48560 | 0.456189 | ||||||||
\(347\) | 19.5400 | − | 19.5400i | 1.04896 | − | 1.04896i | 0.0502218 | − | 0.998738i | \(-0.484007\pi\) |
0.998738 | − | 0.0502218i | \(-0.0159928\pi\) | |||||||
\(348\) | −1.85095 | + | 9.33342i | −0.0992213 | + | 0.500324i | ||||
\(349\) | − | 33.9607i | − | 1.81787i | −0.416934 | − | 0.908937i | \(-0.636895\pi\) | ||
0.416934 | − | 0.908937i | \(-0.363105\pi\) | |||||||
\(350\) | −4.78619 | + | 3.08089i | −0.255832 | + | 0.164681i | ||||
\(351\) | 19.6686 | − | 3.94764i | 1.04983 | − | 0.210709i | ||||
\(352\) | −2.23156 | − | 2.23156i | −0.118942 | − | 0.118942i | ||||
\(353\) | −17.4613 | − | 17.4613i | −0.929372 | − | 0.929372i | 0.0682931 | − | 0.997665i | \(-0.478245\pi\) |
−0.997665 | + | 0.0682931i | \(0.978245\pi\) | |||||||
\(354\) | 1.82269 | − | 1.21940i | 0.0968750 | − | 0.0648104i | ||||
\(355\) | 0.595827 | + | 2.02643i | 0.0316232 | + | 0.107552i | ||||
\(356\) | 3.27340i | 0.173490i | ||||||||
\(357\) | −5.58575 | − | 1.10773i | −0.295629 | − | 0.0586275i | ||||
\(358\) | −7.44325 | + | 7.44325i | −0.393388 | + | 0.393388i | ||||
\(359\) | −25.1531 | −1.32753 | −0.663766 | − | 0.747940i | \(-0.731043\pi\) | ||||
−0.663766 | + | 0.747940i | \(0.731043\pi\) | |||||||
\(360\) | 4.21712 | + | 5.21688i | 0.222262 | + | 0.274954i | ||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 14.7945 | − | 14.7945i | 0.777582 | − | 0.777582i | ||||
\(363\) | −1.76746 | − | 0.350513i | −0.0927676 | − | 0.0183971i | ||||
\(364\) | 4.39508i | 0.230365i | ||||||||
\(365\) | 5.48083 | − | 10.0462i | 0.286880 | − | 0.525843i | ||||
\(366\) | 3.89221 | − | 2.60393i | 0.203449 | − | 0.136110i | ||||
\(367\) | −3.86210 | − | 3.86210i | −0.201600 | − | 0.201600i | 0.599085 | − | 0.800685i | \(-0.295531\pi\) |
−0.800685 | + | 0.599085i | \(0.795531\pi\) | |||||||
\(368\) | 1.82163 | + | 1.82163i | 0.0949589 | + | 0.0949589i | ||||
\(369\) | 7.23436 | − | 17.5223i | 0.376606 | − | 0.912175i | ||||
\(370\) | −22.0129 | + | 6.47239i | −1.14440 | + | 0.336484i | ||||
\(371\) | 5.10191i | 0.264878i | ||||||||
\(372\) | −1.70962 | + | 8.62077i | −0.0886397 | + | 0.446966i | ||||
\(373\) | −6.37524 | + | 6.37524i | −0.330098 | + | 0.330098i | −0.852623 | − | 0.522526i | \(-0.824990\pi\) |
0.522526 | + | 0.852623i | \(0.324990\pi\) | |||||||
\(374\) | 9.11425 | 0.471287 | ||||||||
\(375\) | −15.2728 | + | 11.9055i | −0.788684 | + | 0.614799i | ||||
\(376\) | 4.56187 | 0.235260 | ||||||||
\(377\) | −14.9972 | + | 14.9972i | −0.772393 | + | 0.772393i | ||||
\(378\) | 4.92411 | + | 3.27790i | 0.253269 | + | 0.168597i | ||||
\(379\) | 14.0745i | 0.722958i | 0.932380 | + | 0.361479i | \(0.117728\pi\) | ||||
−0.932380 | + | 0.361479i | \(0.882272\pi\) | |||||||
\(380\) | −2.14526 | + | 0.630765i | −0.110049 | + | 0.0323576i | ||||
\(381\) | 2.14654 | + | 3.20852i | 0.109970 | + | 0.164378i | ||||
\(382\) | −17.5300 | − | 17.5300i | −0.896915 | − | 0.896915i | ||||
\(383\) | 5.66358 | + | 5.66358i | 0.289396 | + | 0.289396i | 0.836841 | − | 0.547446i | \(-0.184400\pi\) |
−0.547446 | + | 0.836841i | \(0.684400\pi\) | |||||||
\(384\) | 0.963104 | + | 1.43959i | 0.0491482 | + | 0.0734640i | ||||
\(385\) | 3.84746 | − | 7.05229i | 0.196085 | − | 0.359418i | ||||
\(386\) | 24.6957i | 1.25698i | ||||||||
\(387\) | 2.52047 | − | 1.04741i | 0.128123 | − | 0.0532430i | ||||
\(388\) | 2.89748 | − | 2.89748i | 0.147097 | − | 0.147097i | ||||
\(389\) | 1.77092 | 0.0897890 | 0.0448945 | − | 0.998992i | \(-0.485705\pi\) | ||||
0.0448945 | + | 0.998992i | \(0.485705\pi\) | |||||||
\(390\) | 1.34680 | + | 14.8917i | 0.0681979 | + | 0.754071i | ||||
\(391\) | −7.44000 | −0.376257 | ||||||||
\(392\) | 4.03335 | − | 4.03335i | 0.203715 | − | 0.203715i | ||||
\(393\) | −6.40282 | + | 32.2862i | −0.322980 | + | 1.62863i | ||||
\(394\) | 2.35650i | 0.118719i | ||||||||
\(395\) | −9.47811 | − | 32.2355i | −0.476896 | − | 1.62194i | ||||
\(396\) | −8.75117 | − | 3.61306i | −0.439763 | − | 0.181563i | ||||
\(397\) | −13.5159 | − | 13.5159i | −0.678345 | − | 0.678345i | 0.281281 | − | 0.959626i | \(-0.409241\pi\) |
−0.959626 | + | 0.281281i | \(0.909241\pi\) | |||||||
\(398\) | −19.3835 | − | 19.3835i | −0.971606 | − | 0.971606i | ||||
\(399\) | −1.63885 | + | 1.09641i | −0.0820451 | + | 0.0548891i | ||||
\(400\) | −4.20427 | + | 2.70631i | −0.210214 | + | 0.135315i | ||||
\(401\) | 33.0944i | 1.65266i | 0.563188 | + | 0.826329i | \(0.309575\pi\) | ||||
−0.563188 | + | 0.826329i | \(0.690425\pi\) | |||||||
\(402\) | 9.29551 | + | 1.84343i | 0.463618 | + | 0.0919420i | ||||
\(403\) | −13.8521 | + | 13.8521i | −0.690020 | + | 0.690020i | ||||
\(404\) | 16.8808 | 0.839853 | ||||||||
\(405\) | 17.6886 | + | 9.59749i | 0.878956 | + | 0.476903i | ||||
\(406\) | −6.25397 | −0.310379 | ||||||||
\(407\) | 22.8984 | − | 22.8984i | 1.13503 | − | 1.13503i | ||||
\(408\) | −4.90662 | − | 0.973053i | −0.242914 | − | 0.0481733i | ||||
\(409\) | 12.5812i | 0.622098i | 0.950394 | + | 0.311049i | \(0.100680\pi\) | ||||
−0.950394 | + | 0.311049i | \(0.899320\pi\) | |||||||
\(410\) | 12.4038 | + | 6.76707i | 0.612582 | + | 0.334202i | ||||
\(411\) | 30.9942 | − | 20.7355i | 1.52883 | − | 1.02280i | ||||
\(412\) | −1.47281 | − | 1.47281i | −0.0725603 | − | 0.0725603i | ||||
\(413\) | 1.01919 | + | 1.01919i | 0.0501513 | + | 0.0501513i | ||||
\(414\) | 7.14361 | + | 2.94935i | 0.351089 | + | 0.144953i | ||||
\(415\) | −15.4043 | − | 8.40399i | −0.756166 | − | 0.412536i | ||||
\(416\) | 3.86071i | 0.189287i | ||||||||
\(417\) | 5.07111 | − | 25.5711i | 0.248333 | − | 1.25222i | ||||
\(418\) | 2.23156 | − | 2.23156i | 0.109149 | − | 0.109149i | ||||
\(419\) | −33.5096 | −1.63705 | −0.818525 | − | 0.574471i | \(-0.805208\pi\) | ||||
−0.818525 | + | 0.574471i | \(0.805208\pi\) | |||||||
\(420\) | −2.82418 | + | 3.38581i | −0.137806 | + | 0.165211i | ||||
\(421\) | −29.7747 | −1.45113 | −0.725564 | − | 0.688154i | \(-0.758421\pi\) | ||||
−0.725564 | + | 0.688154i | \(0.758421\pi\) | |||||||
\(422\) | 2.60670 | − | 2.60670i | 0.126892 | − | 0.126892i | ||||
\(423\) | 12.6378 | − | 5.25180i | 0.614472 | − | 0.255351i | ||||
\(424\) | 4.48161i | 0.217646i | ||||||||
\(425\) | 3.05903 | − | 14.1123i | 0.148385 | − | 0.684547i | ||||
\(426\) | 0.909759 | + | 1.35986i | 0.0440779 | + | 0.0658852i | ||||
\(427\) | 2.17641 | + | 2.17641i | 0.105324 | + | 0.105324i | ||||
\(428\) | 8.84697 | + | 8.84697i | 0.427634 | + | 0.427634i | ||||
\(429\) | −11.7345 | − | 17.5400i | −0.566546 | − | 0.846840i | ||||
\(430\) | 0.573879 | + | 1.95179i | 0.0276749 | + | 0.0941235i | ||||
\(431\) | 16.7696i | 0.807763i | 0.914811 | + | 0.403882i | \(0.132339\pi\) | ||||
−0.914811 | + | 0.403882i | \(0.867661\pi\) | |||||||
\(432\) | 4.32542 | + | 2.87936i | 0.208107 | + | 0.138533i | ||||
\(433\) | −0.841474 | + | 0.841474i | −0.0404387 | + | 0.0404387i | −0.727037 | − | 0.686598i | \(-0.759103\pi\) |
0.686598 | + | 0.727037i | \(0.259103\pi\) | |||||||
\(434\) | −5.77645 | −0.277278 | ||||||||
\(435\) | −21.1901 | + | 1.91643i | −1.01599 | + | 0.0918857i | ||||
\(436\) | 6.83921 | 0.327539 | ||||||||
\(437\) | −1.82163 | + | 1.82163i | −0.0871402 | + | 0.0871402i | ||||
\(438\) | 1.72438 | − | 8.69517i | 0.0823939 | − | 0.415471i | ||||
\(439\) | − | 32.4072i | − | 1.54671i | −0.633973 | − | 0.773355i | \(-0.718577\pi\) | ||
0.633973 | − | 0.773355i | \(-0.281423\pi\) | |||||||
\(440\) | 3.37968 | − | 6.19485i | 0.161120 | − | 0.295328i | ||||
\(441\) | 6.53030 | − | 15.8170i | 0.310967 | − | 0.753191i | ||||
\(442\) | −7.88408 | − | 7.88408i | −0.375007 | − | 0.375007i | ||||
\(443\) | 15.3966 | + | 15.3966i | 0.731515 | + | 0.731515i | 0.970920 | − | 0.239405i | \(-0.0769523\pi\) |
−0.239405 | + | 0.970920i | \(0.576952\pi\) | |||||||
\(444\) | −14.7719 | + | 9.88258i | −0.701044 | + | 0.469007i | ||||
\(445\) | −7.02228 | + | 2.06474i | −0.332888 | + | 0.0978782i | ||||
\(446\) | − | 26.8179i | − | 1.26987i | ||||||
\(447\) | −23.3078 | − | 4.62227i | −1.10242 | − | 0.218626i | ||||
\(448\) | −0.804978 | + | 0.804978i | −0.0380316 | + | 0.0380316i | ||||
\(449\) | −3.69496 | −0.174376 | −0.0871879 | − | 0.996192i | \(-0.527788\pi\) | ||||
−0.0871879 | + | 0.996192i | \(0.527788\pi\) | |||||||
\(450\) | −8.53155 | + | 12.3375i | −0.402181 | + | 0.581593i | ||||
\(451\) | −19.9421 | −0.939037 | ||||||||
\(452\) | −14.3560 | + | 14.3560i | −0.675250 | + | 0.675250i | ||||
\(453\) | 25.3261 | + | 5.02253i | 1.18992 | + | 0.235979i | ||||
\(454\) | − | 2.90877i | − | 0.136515i | ||||||
\(455\) | −9.42858 | + | 2.77226i | −0.442019 | + | 0.129966i | ||||
\(456\) | −1.43959 | + | 0.963104i | −0.0674151 | + | 0.0451015i | ||||
\(457\) | 6.23351 | + | 6.23351i | 0.291591 | + | 0.291591i | 0.837709 | − | 0.546117i | \(-0.183895\pi\) |
−0.546117 | + | 0.837709i | \(0.683895\pi\) | |||||||
\(458\) | −11.2242 | − | 11.2242i | −0.524473 | − | 0.524473i | ||||
\(459\) | −14.7131 | + | 2.95303i | −0.686749 | + | 0.137836i | ||||
\(460\) | −2.75884 | + | 5.05688i | −0.128632 | + | 0.235778i | ||||
\(461\) | − | 3.01803i | − | 0.140563i | −0.997527 | − | 0.0702817i | \(-0.977610\pi\) | ||
0.997527 | − | 0.0702817i | \(-0.0223898\pi\) | |||||||
\(462\) | 1.21049 | − | 6.10388i | 0.0563169 | − | 0.283978i | ||||
\(463\) | 17.1200 | − | 17.1200i | 0.795634 | − | 0.795634i | −0.186770 | − | 0.982404i | \(-0.559802\pi\) |
0.982404 | + | 0.186770i | \(0.0598018\pi\) | |||||||
\(464\) | −5.49359 | −0.255034 | ||||||||
\(465\) | −19.5722 | + | 1.77010i | −0.907637 | + | 0.0820864i | ||||
\(466\) | 22.0633 | 1.02206 | ||||||||
\(467\) | −3.42627 | + | 3.42627i | −0.158549 | + | 0.158549i | −0.781923 | − | 0.623375i | \(-0.785761\pi\) |
0.623375 | + | 0.781923i | \(0.285761\pi\) | |||||||
\(468\) | 4.44461 | + | 10.6954i | 0.205452 | + | 0.494395i | ||||
\(469\) | 6.22857i | 0.287608i | ||||||||
\(470\) | 2.87747 | + | 9.78639i | 0.132728 | + | 0.451413i | ||||
\(471\) | −3.58653 | − | 5.36094i | −0.165259 | − | 0.247019i | ||||
\(472\) | 0.895279 | + | 0.895279i | 0.0412085 | + | 0.0412085i | ||||
\(473\) | −2.03030 | − | 2.03030i | −0.0933533 | − | 0.0933533i | ||||
\(474\) | −14.4720 | − | 21.6319i | −0.664720 | − | 0.993585i | ||||
\(475\) | −2.70631 | − | 4.20427i | −0.124174 | − | 0.192905i | ||||
\(476\) | − | 3.28774i | − | 0.150693i | ||||||
\(477\) | 5.15941 | + | 12.4155i | 0.236233 | + | 0.568465i | ||||
\(478\) | −3.42833 | + | 3.42833i | −0.156808 | + | 0.156808i | ||||
\(479\) | 18.0199 | 0.823349 | 0.411674 | − | 0.911331i | \(-0.364944\pi\) | ||||
0.411674 | + | 0.911331i | \(0.364944\pi\) | |||||||
\(480\) | −2.48081 | + | 2.97415i | −0.113233 | + | 0.135751i | ||||
\(481\) | −39.6155 | −1.80631 | ||||||||
\(482\) | 12.0576 | − | 12.0576i | 0.549209 | − | 0.549209i | ||||
\(483\) | −0.988124 | + | 4.98262i | −0.0449612 | + | 0.226717i | ||||
\(484\) | − | 1.04032i | − | 0.0472871i | ||||||
\(485\) | 8.04348 | + | 4.38822i | 0.365236 | + | 0.199259i | ||||
\(486\) | 15.2976 | + | 2.99715i | 0.693914 | + | 0.135954i | ||||
\(487\) | −3.32991 | − | 3.32991i | −0.150893 | − | 0.150893i | 0.627624 | − | 0.778517i | \(-0.284028\pi\) |
−0.778517 | + | 0.627624i | \(0.784028\pi\) | |||||||
\(488\) | 1.91180 | + | 1.91180i | 0.0865429 | + | 0.0865429i | ||||
\(489\) | 17.2910 | − | 11.5679i | 0.781928 | − | 0.523119i | ||||
\(490\) | 11.1967 | + | 6.10849i | 0.505814 | + | 0.275953i | ||||
\(491\) | 40.7725i | 1.84004i | 0.391873 | + | 0.920020i | \(0.371827\pi\) | ||||
−0.391873 | + | 0.920020i | \(0.628173\pi\) | |||||||
\(492\) | 10.7357 | + | 2.12905i | 0.484005 | + | 0.0959851i | ||||
\(493\) | 11.2186 | − | 11.2186i | 0.505262 | − | 0.505262i | ||||
\(494\) | −3.86071 | −0.173702 | ||||||||
\(495\) | 2.23102 | − | 21.0525i | 0.100277 | − | 0.946240i | ||||
\(496\) | −5.07413 | −0.227835 | ||||||||
\(497\) | −0.760391 | + | 0.760391i | −0.0341082 | + | 0.0341082i | ||||
\(498\) | −13.3327 | − | 2.64406i | −0.597451 | − | 0.118483i | ||||
\(499\) | − | 28.4698i | − | 1.27449i | −0.770663 | − | 0.637243i | \(-0.780075\pi\) | ||
0.770663 | − | 0.637243i | \(-0.219925\pi\) | |||||||
\(500\) | −8.45764 | − | 7.31221i | −0.378237 | − | 0.327012i | ||||
\(501\) | −4.60615 | + | 3.08157i | −0.205788 | + | 0.137674i | ||||
\(502\) | −5.61351 | − | 5.61351i | −0.250543 | − | 0.250543i | ||||
\(503\) | 19.2777 | + | 19.2777i | 0.859549 | + | 0.859549i | 0.991285 | − | 0.131736i | \(-0.0420551\pi\) |
−0.131736 | + | 0.991285i | \(0.542055\pi\) | |||||||
\(504\) | −1.30332 | + | 3.15677i | −0.0580545 | + | 0.140614i | ||||
\(505\) | 10.6478 | + | 36.2138i | 0.473823 | + | 1.61149i | ||||
\(506\) | − | 8.13012i | − | 0.361428i | ||||||
\(507\) | −0.641885 | + | 3.23671i | −0.0285071 | + | 0.143747i | ||||
\(508\) | −1.57598 | + | 1.57598i | −0.0699227 | + | 0.0699227i | ||||
\(509\) | −30.9140 | −1.37024 | −0.685120 | − | 0.728431i | \(-0.740250\pi\) | ||||
−0.685120 | + | 0.728431i | \(0.740250\pi\) | |||||||
\(510\) | −1.00747 | − | 11.1397i | −0.0446117 | − | 0.493276i | ||||
\(511\) | 5.82630 | 0.257740 | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | −2.87936 | + | 4.32542i | −0.127127 | + | 0.190972i | ||||
\(514\) | 24.0262i | 1.05975i | ||||||||
\(515\) | 2.23057 | − | 4.08856i | 0.0982905 | − | 0.180164i | ||||
\(516\) | 0.876246 | + | 1.30976i | 0.0385746 | + | 0.0576591i | ||||
\(517\) | −10.1801 | − | 10.1801i | −0.447719 | − | 0.447719i | ||||
\(518\) | −8.26002 | − | 8.26002i | −0.362924 | − | 0.362924i | ||||
\(519\) | 8.17252 | + | 12.2158i | 0.358734 | + | 0.536215i | ||||
\(520\) | −8.28223 | + | 2.43520i | −0.363200 | + | 0.106791i | ||||
\(521\) | 24.0255i | 1.05258i | 0.850306 | + | 0.526289i | \(0.176417\pi\) | ||||
−0.850306 | + | 0.526289i | \(0.823583\pi\) | |||||||
\(522\) | −15.2190 | + | 6.32444i | −0.666117 | + | 0.276813i | ||||
\(523\) | −28.0008 | + | 28.0008i | −1.22439 | + | 1.22439i | −0.258331 | + | 0.966056i | \(0.583172\pi\) |
−0.966056 | + | 0.258331i | \(0.916828\pi\) | |||||||
\(524\) | −19.0035 | −0.830171 | ||||||||
\(525\) | −9.04483 | − | 3.92295i | −0.394749 | − | 0.171211i | ||||
\(526\) | −3.25621 | −0.141977 | ||||||||
\(527\) | 10.3620 | − | 10.3620i | 0.451377 | − | 0.451377i | ||||
\(528\) | 1.06331 | − | 5.36176i | 0.0462747 | − | 0.233340i | ||||
\(529\) | − | 16.3634i | − | 0.711450i | ||||||
\(530\) | −9.61421 | + | 2.82684i | −0.417615 | + | 0.122790i | ||||
\(531\) | 3.51088 | + | 1.44952i | 0.152359 | + | 0.0629040i | ||||
\(532\) | −0.804978 | − | 0.804978i | −0.0349002 | − | 0.0349002i | ||||
\(533\) | 17.2505 | + | 17.2505i | 0.747200 | + | 0.747200i | ||||
\(534\) | −4.71236 | + | 3.15262i | −0.203924 | + | 0.136427i | ||||
\(535\) | −13.3987 | + | 24.5594i | −0.579276 | + | 1.06180i | ||||
\(536\) | 5.47128i | 0.236323i | ||||||||
\(537\) | −17.8839 | − | 3.54663i | −0.771746 | − | 0.153048i | ||||
\(538\) | 11.2908 | − | 11.2908i | 0.486780 | − | 0.486780i | ||||
\(539\) | −18.0013 | −0.775371 | ||||||||
\(540\) | −3.44866 | + | 11.0953i | −0.148407 | + | 0.477468i | ||||
\(541\) | 30.2843 | 1.30202 | 0.651012 | − | 0.759067i | \(-0.274345\pi\) | ||||
0.651012 | + | 0.759067i | \(0.274345\pi\) | |||||||
\(542\) | 4.18110 | − | 4.18110i | 0.179594 | − | 0.179594i | ||||
\(543\) | 35.5467 | + | 7.04942i | 1.52546 | + | 0.302520i | ||||
\(544\) | − | 2.88801i | − | 0.123822i | ||||||
\(545\) | 4.31393 | + | 14.6719i | 0.184788 | + | 0.628474i | ||||
\(546\) | −6.32713 | + | 4.23292i | −0.270776 | + | 0.181152i | ||||
\(547\) | −20.9852 | − | 20.9852i | −0.897263 | − | 0.897263i | 0.0979302 | − | 0.995193i | \(-0.468778\pi\) |
−0.995193 | + | 0.0979302i | \(0.968778\pi\) | |||||||
\(548\) | 15.2239 | + | 15.2239i | 0.650332 | + | 0.650332i | ||||
\(549\) | 7.49721 | + | 3.09534i | 0.319973 | + | 0.132106i | ||||
\(550\) | 15.4213 | + | 3.34279i | 0.657568 | + | 0.142537i | ||||
\(551\) | − | 5.49359i | − | 0.234035i | ||||||
\(552\) | −0.867985 | + | 4.37682i | −0.0369439 | + | 0.186290i | ||||
\(553\) | 12.0959 | − | 12.0959i | 0.514370 | − | 0.514370i | ||||
\(554\) | −24.9457 | −1.05984 | ||||||||
\(555\) | −30.5183 | − | 25.4560i | −1.29543 | − | 1.08055i | ||||
\(556\) | 15.0510 | 0.638304 | ||||||||
\(557\) | −19.6777 | + | 19.6777i | −0.833770 | + | 0.833770i | −0.988030 | − | 0.154260i | \(-0.950701\pi\) |
0.154260 | + | 0.988030i | \(0.450701\pi\) | |||||||
\(558\) | −14.0569 | + | 5.84154i | −0.595078 | + | 0.247292i | ||||
\(559\) | 3.51253i | 0.148564i | ||||||||
\(560\) | −2.23464 | − | 1.21913i | −0.0944307 | − | 0.0515178i | ||||
\(561\) | 8.77798 | + | 13.1208i | 0.370606 | + | 0.553961i | ||||
\(562\) | −8.33844 | − | 8.33844i | −0.351736 | − | 0.351736i | ||||
\(563\) | −11.9658 | − | 11.9658i | −0.504296 | − | 0.504296i | 0.408474 | − | 0.912770i | \(-0.366061\pi\) |
−0.912770 | + | 0.408474i | \(0.866061\pi\) | |||||||
\(564\) | 4.39356 | + | 6.56724i | 0.185002 | + | 0.276531i | ||||
\(565\) | −39.8526 | − | 21.7421i | −1.67661 | − | 0.914697i | ||||
\(566\) | − | 6.82505i | − | 0.286878i | ||||||
\(567\) | 0.0235843 | + | 10.2457i | 0.000990446 | + | 0.430278i | ||||
\(568\) | −0.667940 | + | 0.667940i | −0.0280262 | + | 0.0280262i | ||||
\(569\) | −27.2399 | −1.14195 | −0.570977 | − | 0.820966i | \(-0.693436\pi\) | ||||
−0.570977 | + | 0.820966i | \(0.693436\pi\) | |||||||
\(570\) | −2.97415 | − | 2.48081i | −0.124574 | − | 0.103910i | ||||
\(571\) | 6.63803 | 0.277793 | 0.138896 | − | 0.990307i | \(-0.455644\pi\) | ||||
0.138896 | + | 0.990307i | \(0.455644\pi\) | |||||||
\(572\) | 8.61540 | − | 8.61540i | 0.360228 | − | 0.360228i | ||||
\(573\) | 8.35287 | − | 42.1194i | 0.348946 | − | 1.75956i | ||||
\(574\) | 7.19361i | 0.300256i | ||||||||
\(575\) | −12.5885 | − | 2.72873i | −0.524977 | − | 0.113796i | ||||
\(576\) | −1.14486 | + | 2.77296i | −0.0477025 | + | 0.115540i | ||||
\(577\) | 24.2437 | + | 24.2437i | 1.00928 | + | 1.00928i | 0.999957 | + | 0.00932364i | \(0.00296785\pi\) |
0.00932364 | + | 0.999957i | \(0.497032\pi\) | |||||||
\(578\) | −6.12313 | − | 6.12313i | −0.254689 | − | 0.254689i | ||||
\(579\) | −35.5518 | + | 23.7845i | −1.47748 | + | 0.988452i | ||||
\(580\) | −3.46517 | − | 11.7852i | −0.143883 | − | 0.489353i | ||||
\(581\) | − | 8.93371i | − | 0.370633i | ||||||
\(582\) | 6.96178 | + | 1.38062i | 0.288575 | + | 0.0572285i | ||||
\(583\) | 10.0010 | − | 10.0010i | 0.414197 | − | 0.414197i | ||||
\(584\) | 5.11793 | 0.211781 | ||||||||
\(585\) | −20.1409 | + | 16.2811i | −0.832723 | + | 0.673141i | ||||
\(586\) | 16.0915 | 0.664732 | ||||||||
\(587\) | −30.9059 | + | 30.9059i | −1.27562 | + | 1.27562i | −0.332528 | + | 0.943093i | \(0.607902\pi\) |
−0.943093 | + | 0.332528i | \(0.892098\pi\) | |||||||
\(588\) | 9.69093 | + | 1.92185i | 0.399647 | + | 0.0792557i | ||||
\(589\) | − | 5.07413i | − | 0.209076i | ||||||
\(590\) | −1.35589 | + | 2.48531i | −0.0558213 | + | 0.102319i | ||||
\(591\) | −3.39240 | + | 2.26955i | −0.139545 | + | 0.0933570i | ||||
\(592\) | −7.25575 | − | 7.25575i | −0.298209 | − | 0.298209i | ||||
\(593\) | −25.3962 | − | 25.3962i | −1.04290 | − | 1.04290i | −0.999038 | − | 0.0438587i | \(-0.986035\pi\) |
−0.0438587 | − | 0.999038i | \(-0.513965\pi\) | |||||||
\(594\) | −3.22695 | − | 16.0779i | −0.132404 | − | 0.659683i | ||||
\(595\) | 7.05305 | − | 2.07379i | 0.289147 | − | 0.0850171i | ||||
\(596\) | − | 13.7188i | − | 0.561945i | ||||||
\(597\) | 9.23601 | − | 46.5726i | 0.378005 | − | 1.90609i | ||||
\(598\) | −7.03278 | + | 7.03278i | −0.287592 | + | 0.287592i | ||||
\(599\) | 24.9746 | 1.02043 | 0.510217 | − | 0.860046i | \(-0.329565\pi\) | ||||
0.510217 | + | 0.860046i | \(0.329565\pi\) | |||||||
\(600\) | −7.94514 | − | 3.44598i | −0.324359 | − | 0.140682i | ||||
\(601\) | 32.6339 | 1.33116 | 0.665582 | − | 0.746325i | \(-0.268183\pi\) | ||||
0.665582 | + | 0.746325i | \(0.268183\pi\) | |||||||
\(602\) | −0.732380 | + | 0.732380i | −0.0298496 | + | 0.0298496i | ||||
\(603\) | 6.29876 | + | 15.1572i | 0.256505 | + | 0.617248i | ||||
\(604\) | 14.9068i | 0.606549i | ||||||||
\(605\) | 2.23175 | − | 0.656195i | 0.0907335 | − | 0.0266781i | ||||
\(606\) | 16.2580 | + | 24.3016i | 0.660437 | + | 0.987183i | ||||
\(607\) | −8.92349 | − | 8.92349i | −0.362193 | − | 0.362193i | 0.502427 | − | 0.864620i | \(-0.332441\pi\) |
−0.864620 | + | 0.502427i | \(0.832441\pi\) | |||||||
\(608\) | −0.707107 | − | 0.707107i | −0.0286770 | − | 0.0286770i | ||||
\(609\) | −6.02322 | − | 9.00317i | −0.244073 | − | 0.364827i | ||||
\(610\) | −2.89540 | + | 5.30719i | −0.117231 | + | 0.214882i | ||||
\(611\) | 17.6121i | 0.712508i | ||||||||
\(612\) | −3.32479 | − | 8.00069i | −0.134397 | − | 0.323409i | ||||
\(613\) | −3.94769 | + | 3.94769i | −0.159446 | + | 0.159446i | −0.782321 | − | 0.622875i | \(-0.785964\pi\) |
0.622875 | + | 0.782321i | \(0.285964\pi\) | |||||||
\(614\) | −4.56587 | −0.184264 | ||||||||
\(615\) | 2.20437 | + | 24.3739i | 0.0888887 | + | 0.982850i | ||||
\(616\) | 3.59271 | 0.144754 | ||||||||
\(617\) | 4.00994 | − | 4.00994i | 0.161434 | − | 0.161434i | −0.621768 | − | 0.783202i | \(-0.713585\pi\) |
0.783202 | + | 0.621768i | \(0.213585\pi\) | |||||||
\(618\) | 0.701779 | − | 3.53873i | 0.0282297 | − | 0.142348i | ||||
\(619\) | 13.4636i | 0.541147i | 0.962699 | + | 0.270573i | \(0.0872133\pi\) | ||||
−0.962699 | + | 0.270573i | \(0.912787\pi\) | |||||||
\(620\) | −3.20058 | − | 10.8853i | −0.128539 | − | 0.437165i | ||||
\(621\) | 2.63417 | + | 13.1244i | 0.105706 | + | 0.526665i | ||||
\(622\) | 5.74950 | + | 5.74950i | 0.230534 | + | 0.230534i | ||||
\(623\) | −2.63501 | − | 2.63501i | −0.105570 | − | 0.105570i | ||||
\(624\) | −5.55786 | + | 3.71827i | −0.222492 | + | 0.148850i | ||||
\(625\) | 10.3518 | − | 22.7561i | 0.414072 | − | 0.910244i | ||||
\(626\) | 28.0858i | 1.12253i | ||||||||
\(627\) | 5.36176 | + | 1.06331i | 0.214128 | + | 0.0424646i | ||||
\(628\) | 2.63322 | − | 2.63322i | 0.105077 | − | 0.105077i | ||||
\(629\) | 29.6344 | 1.18160 | ||||||||
\(630\) | −7.59417 | − | 0.804783i | −0.302559 | − | 0.0320633i | ||||
\(631\) | 24.4689 | 0.974092 | 0.487046 | − | 0.873376i | \(-0.338074\pi\) | ||||
0.487046 | + | 0.873376i | \(0.338074\pi\) | |||||||
\(632\) | 10.6253 | − | 10.6253i | 0.422650 | − | 0.422650i | ||||
\(633\) | 6.26312 | + | 1.24207i | 0.248937 | + | 0.0493677i | ||||
\(634\) | − | 11.1723i | − | 0.443709i | ||||||
\(635\) | −4.37495 | − | 2.38681i | −0.173615 | − | 0.0947177i | ||||
\(636\) | −6.45170 | + | 4.31626i | −0.255826 | + | 0.171151i | ||||
\(637\) | 15.5716 | + | 15.5716i | 0.616970 | + | 0.616970i | ||||
\(638\) | 12.2593 | + | 12.2593i | 0.485349 | + | 0.485349i | ||||
\(639\) | −1.08145 | + | 2.61937i | −0.0427814 | + | 0.103620i | ||||
\(640\) | −1.96295 | − | 1.07091i | −0.0775922 | − | 0.0423314i | ||||
\(641\) | − | 14.3767i | − | 0.567845i | −0.958847 | − | 0.283922i | \(-0.908364\pi\) | ||
0.958847 | − | 0.283922i | \(-0.0916358\pi\) | |||||||
\(642\) | −4.21549 | + | 21.2566i | −0.166372 | + | 0.838931i | ||||
\(643\) | 2.63234 | − | 2.63234i | 0.103809 | − | 0.103809i | −0.653294 | − | 0.757104i | \(-0.726614\pi\) |
0.757104 | + | 0.653294i | \(0.226614\pi\) | |||||||
\(644\) | −2.93274 | −0.115566 | ||||||||
\(645\) | −2.25707 | + | 2.70593i | −0.0888722 | + | 0.106546i | ||||
\(646\) | 2.88801 | 0.113627 | ||||||||
\(647\) | −7.51216 | + | 7.51216i | −0.295333 | + | 0.295333i | −0.839183 | − | 0.543849i | \(-0.816966\pi\) |
0.543849 | + | 0.839183i | \(0.316966\pi\) | |||||||
\(648\) | 0.0207168 | + | 8.99998i | 0.000813834 | + | 0.353552i | ||||
\(649\) | − | 3.99573i | − | 0.156846i | ||||||
\(650\) | −10.4483 | − | 16.2315i | −0.409815 | − | 0.636651i | ||||
\(651\) | −5.56332 | − | 8.31574i | −0.218044 | − | 0.325919i | ||||
\(652\) | 8.49310 | + | 8.49310i | 0.332616 | + | 0.332616i | ||||
\(653\) | −7.41773 | − | 7.41773i | −0.290278 | − | 0.290278i | 0.546912 | − | 0.837190i | \(-0.315803\pi\) |
−0.837190 | + | 0.546912i | \(0.815803\pi\) | |||||||
\(654\) | 6.58687 | + | 9.84568i | 0.257567 | + | 0.384996i | ||||
\(655\) | −11.9867 | − | 40.7674i | −0.468360 | − | 1.59291i | ||||
\(656\) | 6.31900i | 0.246715i | ||||||||
\(657\) | 14.1783 | − | 5.89196i | 0.553147 | − | 0.229867i | ||||
\(658\) | −3.67220 | + | 3.67220i | −0.143157 | + | 0.143157i | ||||
\(659\) | 31.2034 | 1.21551 | 0.607755 | − | 0.794124i | \(-0.292070\pi\) | ||||
0.607755 | + | 0.794124i | \(0.292070\pi\) | |||||||
\(660\) | 12.1731 | − | 1.10093i | 0.473835 | − | 0.0428535i | ||||
\(661\) | −27.3601 | −1.06418 | −0.532092 | − | 0.846687i | \(-0.678594\pi\) | ||||
−0.532092 | + | 0.846687i | \(0.678594\pi\) | |||||||
\(662\) | −20.6663 | + | 20.6663i | −0.803217 | + | 0.803217i | ||||
\(663\) | 3.75668 | − | 18.9431i | 0.145897 | − | 0.735687i | ||||
\(664\) | − | 7.84753i | − | 0.304543i | ||||||
\(665\) | 1.21913 | − | 2.23464i | 0.0472760 | − | 0.0866555i | ||||
\(666\) | −28.4538 | − | 11.7476i | −1.10256 | − | 0.455210i | ||||
\(667\) | −10.0073 | − | 10.0073i | −0.387483 | − | 0.387483i | ||||
\(668\) | −2.26247 | − | 2.26247i | −0.0875377 | − | 0.0875377i | ||||
\(669\) | 38.6069 | − | 25.8285i | 1.49263 | − | 0.998586i | ||||
\(670\) | −11.7373 | + | 3.45109i | −0.453452 | + | 0.133327i | ||||
\(671\) | − | 8.53256i | − | 0.329396i | ||||||
\(672\) | −1.93412 | − | 0.383563i | −0.0746103 | − | 0.0147963i | ||||
\(673\) | −20.4515 | + | 20.4515i | −0.788346 | + | 0.788346i | −0.981223 | − | 0.192877i | \(-0.938218\pi\) |
0.192877 | + | 0.981223i | \(0.438218\pi\) | |||||||
\(674\) | 15.5505 | 0.598982 | ||||||||
\(675\) | −25.9777 | − | 0.399710i | −0.999882 | − | 0.0153848i | ||||
\(676\) | −1.90511 | −0.0732734 | ||||||||
\(677\) | 26.1264 | − | 26.1264i | 1.00412 | − | 1.00412i | 0.00412796 | − | 0.999991i | \(-0.498686\pi\) |
0.999991 | − | 0.00412796i | \(-0.00131397\pi\) | |||||||
\(678\) | −34.4932 | − | 6.84049i | −1.32470 | − | 0.262707i | ||||
\(679\) | 4.66482i | 0.179019i | ||||||||
\(680\) | 6.19552 | − | 1.82165i | 0.237587 | − | 0.0698572i | ||||
\(681\) | 4.18744 | − | 2.80144i | 0.160463 | − | 0.107352i | ||||
\(682\) | 11.3232 | + | 11.3232i | 0.433588 | + | 0.433588i | ||||
\(683\) | 17.6171 | + | 17.6171i | 0.674101 | + | 0.674101i | 0.958659 | − | 0.284558i | \(-0.0918468\pi\) |
−0.284558 | + | 0.958659i | \(0.591847\pi\) | |||||||
\(684\) | −2.77296 | − | 1.14486i | −0.106027 | − | 0.0437748i | ||||
\(685\) | −23.0565 | + | 42.2619i | −0.880943 | + | 1.61474i | ||||
\(686\) | 14.4624i | 0.552177i | ||||||||
\(687\) | 5.34821 | − | 26.9684i | 0.204047 | − | 1.02891i | ||||
\(688\) | −0.643335 | + | 0.643335i | −0.0245269 | + | 0.0245269i | ||||
\(689\) | −17.3022 | −0.659162 | ||||||||
\(690\) | −9.93691 | + | 0.898691i | −0.378292 | + | 0.0342126i | ||||
\(691\) | 31.9422 | 1.21514 | 0.607569 | − | 0.794267i | \(-0.292145\pi\) | ||||
0.607569 | + | 0.794267i | \(0.292145\pi\) | |||||||
\(692\) | −6.00022 | + | 6.00022i | −0.228094 | + | 0.228094i | ||||
\(693\) | 9.95293 | − | 4.13607i | 0.378081 | − | 0.157116i | ||||
\(694\) | 27.6337i | 1.04896i | ||||||||
\(695\) | 9.49363 | + | 32.2882i | 0.360114 | + | 1.22476i | ||||
\(696\) | −5.29091 | − | 7.90854i | −0.200551 | − | 0.299773i | ||||
\(697\) | −12.9042 | − | 12.9042i | −0.488782 | − | 0.488782i | ||||
\(698\) | 24.0138 | + | 24.0138i | 0.908937 | + | 0.908937i | ||||
\(699\) | 21.2493 | + | 31.7622i | 0.803722 | + | 1.20136i | ||||
\(700\) | 1.20583 | − | 5.56286i | 0.0455760 | − | 0.210257i | ||||
\(701\) | − | 25.7033i | − | 0.970801i | −0.874292 | − | 0.485401i | \(-0.838674\pi\) | ||
0.874292 | − | 0.485401i | \(-0.161326\pi\) | |||||||
\(702\) | −11.1164 | + | 16.6992i | −0.419562 | + | 0.630271i | ||||
\(703\) | 7.25575 | − | 7.25575i | 0.273656 | − | 0.273656i | ||||
\(704\) | 3.15590 | 0.118942 | ||||||||
\(705\) | −11.3171 | + | 13.5677i | −0.426228 | + | 0.510989i | ||||
\(706\) | 24.6940 | 0.929372 | ||||||||
\(707\) | −13.5887 | + | 13.5887i | −0.511056 | + | 0.511056i | ||||
\(708\) | −0.426591 | + | 2.15108i | −0.0160323 | + | 0.0808427i | ||||
\(709\) | 33.4122i | 1.25482i | 0.778689 | + | 0.627410i | \(0.215885\pi\) | ||||
−0.778689 | + | 0.627410i | \(0.784115\pi\) | |||||||
\(710\) | −1.85422 | − | 1.01159i | −0.0695876 | − | 0.0379644i | ||||
\(711\) | 17.2031 | − | 41.6675i | 0.645166 | − | 1.56265i | ||||
\(712\) | −2.31464 | − | 2.31464i | −0.0867448 | − | 0.0867448i | ||||
\(713\) | −9.24318 | − | 9.24318i | −0.346160 | − | 0.346160i | ||||
\(714\) | 4.73301 | − | 3.16644i | 0.177128 | − | 0.118501i | ||||
\(715\) | 23.9165 | + | 13.0480i | 0.894428 | + | 0.487966i | ||||
\(716\) | − | 10.5263i | − | 0.393388i | ||||||
\(717\) | −8.23724 | − | 1.63356i | −0.307625 | − | 0.0610065i | ||||
\(718\) | 17.7860 | − | 17.7860i | 0.663766 | − | 0.663766i | ||||
\(719\) | 0.187398 | 0.00698877 | 0.00349439 | − | 0.999994i | \(-0.498888\pi\) | ||||
0.00349439 | + | 0.999994i | \(0.498888\pi\) | |||||||
\(720\) | −6.67085 | − | 0.706935i | −0.248608 | − | 0.0263459i | ||||
\(721\) | 2.37116 | 0.0883068 | ||||||||
\(722\) | 0.707107 | − | 0.707107i | 0.0263158 | − | 0.0263158i | ||||
\(723\) | 28.9708 | + | 5.74532i | 1.07744 | + | 0.213671i | ||||
\(724\) | 20.9226i | 0.777582i | ||||||||
\(725\) | 23.0966 | − | 14.8674i | 0.857785 | − | 0.552160i | ||||
\(726\) | 1.49763 | − | 1.00193i | 0.0555824 | − | 0.0371852i | ||||
\(727\) | 0.711792 | + | 0.711792i | 0.0263989 | + | 0.0263989i | 0.720183 | − | 0.693784i | \(-0.244058\pi\) |
−0.693784 | + | 0.720183i | \(0.744058\pi\) | |||||||
\(728\) | −3.10779 | − | 3.10779i | −0.115182 | − | 0.115182i | ||||
\(729\) | 10.4185 | + | 24.9089i | 0.385871 | + | 0.922553i | ||||
\(730\) | 3.22821 | + | 10.9793i | 0.119481 | + | 0.406361i | ||||
\(731\) | − | 2.62755i | − | 0.0971834i | ||||||
\(732\) | −0.910950 | + | 4.59347i | −0.0336697 | + | 0.169779i | ||||
\(733\) | −12.3766 | + | 12.3766i | −0.457142 | + | 0.457142i | −0.897716 | − | 0.440574i | \(-0.854775\pi\) |
0.440574 | + | 0.897716i | \(0.354775\pi\) | |||||||
\(734\) | 5.46183 | 0.201600 | ||||||||
\(735\) | 1.98983 | + | 22.0018i | 0.0733961 | + | 0.811548i | ||||
\(736\) | −2.57617 | −0.0949589 | ||||||||
\(737\) | 12.2095 | − | 12.2095i | 0.449742 | − | 0.449742i | ||||
\(738\) | 7.27468 | + | 17.5056i | 0.267785 | + | 0.644391i | ||||
\(739\) | − | 0.0763442i | − | 0.00280837i | −0.999999 | − | 0.00140418i | \(-0.999553\pi\) | ||
0.999999 | − | 0.00140418i | \(-0.000446966\pi\) | |||||||
\(740\) | 10.9888 | − | 20.1421i | 0.403956 | − | 0.740439i | ||||
\(741\) | −3.71827 | − | 5.55786i | −0.136594 | − | 0.204173i | ||||
\(742\) | −3.60760 | − | 3.60760i | −0.132439 | − | 0.132439i | ||||
\(743\) | 33.1046 | + | 33.1046i | 1.21449 | + | 1.21449i | 0.969534 | + | 0.244956i | \(0.0787734\pi\) |
0.244956 | + | 0.969534i | \(0.421227\pi\) | |||||||
\(744\) | −4.88692 | − | 7.30469i | −0.179163 | − | 0.267803i | ||||
\(745\) | 29.4304 | − | 8.65336i | 1.07825 | − | 0.317034i | ||||
\(746\) | − | 9.01595i | − | 0.330098i | ||||||
\(747\) | −9.03439 | − | 21.7401i | −0.330551 | − | 0.795430i | ||||
\(748\) | −6.44475 | + | 6.44475i | −0.235643 | + | 0.235643i | ||||
\(749\) | −14.2432 | −0.520436 | ||||||||
\(750\) | 2.38102 | − | 19.2180i | 0.0869424 | − | 0.701741i | ||||
\(751\) | 33.2419 | 1.21301 | 0.606506 | − | 0.795079i | \(-0.292570\pi\) | ||||
0.606506 | + | 0.795079i | \(0.292570\pi\) | |||||||
\(752\) | −3.22573 | + | 3.22573i | −0.117630 | + | 0.117630i | ||||
\(753\) | 2.67478 | − | 13.4876i | 0.0974743 | − | 0.491515i | ||||
\(754\) | − | 21.2092i | − | 0.772393i | ||||||
\(755\) | −31.9789 | + | 9.40269i | −1.16383 | + | 0.342199i | ||||
\(756\) | −5.79969 | + | 1.16404i | −0.210933 | + | 0.0423358i | ||||
\(757\) | 18.1270 | + | 18.1270i | 0.658838 | + | 0.658838i | 0.955105 | − | 0.296267i | \(-0.0957420\pi\) |
−0.296267 | + | 0.955105i | \(0.595742\pi\) | |||||||
\(758\) | −9.95217 | − | 9.95217i | −0.361479 | − | 0.361479i | ||||
\(759\) | 11.7041 | − | 7.83016i | 0.424831 | − | 0.284217i | ||||
\(760\) | 1.07091 | − | 1.96295i | 0.0388460 | − | 0.0712035i | ||||
\(761\) | 16.7931i | 0.608751i | 0.952552 | + | 0.304375i | \(0.0984477\pi\) | ||||
−0.952552 | + | 0.304375i | \(0.901552\pi\) | |||||||
\(762\) | −3.78660 | − | 0.750937i | −0.137174 | − | 0.0272036i | ||||
\(763\) | −5.50541 | + | 5.50541i | −0.199309 | + | 0.199309i | ||||
\(764\) | 24.7912 | 0.896915 | ||||||||
\(765\) | 15.0664 | − | 12.1791i | 0.544727 | − | 0.440336i | ||||
\(766\) | −8.00952 | −0.289396 | ||||||||
\(767\) | −3.45641 | + | 3.45641i | −0.124804 | + | 0.124804i | ||||
\(768\) | −1.69896 | − | 0.336929i | −0.0613061 | − | 0.0121579i | ||||
\(769\) | 0.877088i | 0.0316286i | 0.999875 | + | 0.0158143i | \(0.00503406\pi\) | ||||
−0.999875 | + | 0.0158143i | \(0.994966\pi\) | |||||||
\(770\) | 2.26615 | + | 7.70729i | 0.0816665 | + | 0.277751i | ||||
\(771\) | −34.5880 | + | 23.1398i | −1.24566 | + | 0.833359i | ||||
\(772\) | −17.4625 | − | 17.4625i | −0.628489 | − | 0.628489i | ||||
\(773\) | 19.6669 | + | 19.6669i | 0.707370 | + | 0.707370i | 0.965981 | − | 0.258611i | \(-0.0832649\pi\) |
−0.258611 | + | 0.965981i | \(0.583265\pi\) | |||||||
\(774\) | −1.04161 | + | 2.52288i | −0.0374399 | + | 0.0906829i | ||||
\(775\) | 21.3330 | − | 13.7322i | 0.766305 | − | 0.493274i | ||||
\(776\) | 4.09766i | 0.147097i | ||||||||
\(777\) | 3.93581 | − | 19.8463i | 0.141196 | − | 0.711983i | ||||
\(778\) | −1.25223 | + | 1.25223i | −0.0448945 | + | 0.0448945i | ||||
\(779\) | −6.31900 | −0.226402 | ||||||||
\(780\) | −11.4824 | − | 9.57769i | −0.411134 | − | 0.342936i | ||||
\(781\) | 2.98109 | 0.106672 | ||||||||
\(782\) | 5.26087 | − | 5.26087i | 0.188128 | − | 0.188128i | ||||
\(783\) | −23.7621 | − | 15.8181i | −0.849188 | − | 0.565291i | ||||
\(784\) | 5.70402i | 0.203715i | ||||||||
\(785\) | 7.30987 | + | 3.98799i | 0.260900 | + | 0.142337i | ||||
\(786\) | −18.3023 | − | 27.3573i | −0.652823 | − | 0.975803i | ||||
\(787\) | −34.5105 | − | 34.5105i | −1.23017 | − | 1.23017i | −0.963899 | − | 0.266268i | \(-0.914209\pi\) |
−0.266268 | − | 0.963899i | \(-0.585791\pi\) | |||||||
\(788\) | −1.66630 | − | 1.66630i | −0.0593593 | − | 0.0593593i | ||||
\(789\) | −3.13607 | − | 4.68762i | −0.111647 | − | 0.166884i | ||||
\(790\) | 29.4960 | + | 16.0919i | 1.04942 | + | 0.572524i | ||||
\(791\) | − | 23.1126i | − | 0.821788i | ||||||
\(792\) | 8.74283 | − | 3.63319i | 0.310663 | − | 0.129100i | ||||
\(793\) | −7.38090 | + | 7.38090i | −0.262103 | + | 0.262103i | ||||
\(794\) | 19.1144 | 0.678345 | ||||||||
\(795\) | −13.3290 | − | 11.1180i | −0.472731 | − | 0.394315i | ||||
\(796\) | 27.4124 | 0.971606 | ||||||||
\(797\) | 3.11137 | − | 3.11137i | 0.110210 | − | 0.110210i | −0.649851 | − | 0.760061i | \(-0.725169\pi\) |
0.760061 | + | 0.649851i | \(0.225169\pi\) | |||||||
\(798\) | 0.383563 | − | 1.93412i | 0.0135780 | − | 0.0684671i | ||||
\(799\) | − | 13.1747i | − | 0.466088i | ||||||
\(800\) | 1.05922 | − | 4.88652i | 0.0374491 | − | 0.172764i | ||||
\(801\) | −9.07699 | − | 3.74758i | −0.320720 | − | 0.132414i | ||||
\(802\) | −23.4013 | − | 23.4013i | −0.826329 | − | 0.826329i | ||||
\(803\) | −11.4209 | − | 11.4209i | −0.403036 | − | 0.403036i | ||||
\(804\) | −7.87642 | + | 5.26942i | −0.277780 | + | 0.185838i | ||||
\(805\) | −1.84987 | − | 6.29148i | −0.0651993 | − | 0.221746i | ||||
\(806\) | − | 19.5898i | − | 0.690020i | ||||||
\(807\) | 27.1283 | + | 5.37993i | 0.954962 | + | 0.189382i | ||||
\(808\) | −11.9366 | + | 11.9366i | −0.419927 | + | 0.419927i | ||||
\(809\) | 19.2043 | 0.675189 | 0.337594 | − | 0.941292i | \(-0.390387\pi\) | ||||
0.337594 | + | 0.941292i | \(0.390387\pi\) | |||||||
\(810\) | −19.2942 | + | 5.72131i | −0.677929 | + | 0.201026i | ||||
\(811\) | 33.3734 | 1.17190 | 0.585949 | − | 0.810348i | \(-0.300722\pi\) | ||||
0.585949 | + | 0.810348i | \(0.300722\pi\) | |||||||
\(812\) | 4.42222 | − | 4.42222i | 0.155190 | − | 0.155190i | ||||
\(813\) | 10.0459 | + | 1.99225i | 0.352326 | + | 0.0698713i | ||||
\(814\) | 32.3832i | 1.13503i | ||||||||
\(815\) | −12.8628 | + | 23.5771i | −0.450563 | + | 0.825868i | ||||
\(816\) | 4.15756 | − | 2.78145i | 0.145544 | − | 0.0973703i | ||||
\(817\) | −0.643335 | − | 0.643335i | −0.0225075 | − | 0.0225075i | ||||
\(818\) | −8.89622 | − | 8.89622i | −0.311049 | − | 0.311049i | ||||
\(819\) | −12.1874 | − | 5.03175i | −0.425861 | − | 0.175823i | ||||
\(820\) | −13.5559 | + | 3.98580i | −0.473392 | + | 0.139190i | ||||
\(821\) | 5.97506i | 0.208531i | 0.994549 | + | 0.104266i | \(0.0332492\pi\) | ||||
−0.994549 | + | 0.104266i | \(0.966751\pi\) | |||||||
\(822\) | −7.25401 | + | 36.5784i | −0.253013 | + | 1.27582i | ||||
\(823\) | 19.3849 | − | 19.3849i | 0.675714 | − | 0.675714i | −0.283314 | − | 0.959027i | \(-0.591434\pi\) |
0.959027 | + | 0.283314i | \(0.0914338\pi\) | |||||||
\(824\) | 2.08287 | 0.0725603 | ||||||||
\(825\) | 10.0401 | + | 25.4199i | 0.349552 | + | 0.885008i | ||||
\(826\) | −1.44136 | −0.0501513 | ||||||||
\(827\) | −3.64780 | + | 3.64780i | −0.126846 | + | 0.126846i | −0.767680 | − | 0.640833i | \(-0.778589\pi\) |
0.640833 | + | 0.767680i | \(0.278589\pi\) | |||||||
\(828\) | −7.13680 | + | 2.96579i | −0.248021 | + | 0.103068i | ||||
\(829\) | − | 38.1534i | − | 1.32512i | −0.749008 | − | 0.662561i | \(-0.769470\pi\) | ||
0.749008 | − | 0.662561i | \(-0.230530\pi\) | |||||||
\(830\) | 16.8350 | − | 4.94995i | 0.584351 | − | 0.171815i | ||||
\(831\) | −24.0253 | − | 35.9116i | −0.833428 | − | 1.24576i | ||||
\(832\) | −2.72994 | − | 2.72994i | −0.0946435 | − | 0.0946435i | ||||
\(833\) | −11.6483 | − | 11.6483i | −0.403591 | − | 0.403591i | ||||
\(834\) | 14.4957 | + | 21.6673i | 0.501944 | + | 0.750277i | ||||
\(835\) | 3.42650 | − | 6.28068i | 0.118579 | − | 0.217352i | ||||
\(836\) | 3.15590i | 0.109149i | ||||||||
\(837\) | −21.9478 | − | 14.6103i | −0.758625 | − | 0.505005i | ||||
\(838\) | 23.6948 | − | 23.6948i | 0.818525 | − | 0.818525i | ||||
\(839\) | 13.6311 | 0.470597 | 0.235299 | − | 0.971923i | \(-0.424393\pi\) | ||||
0.235299 | + | 0.971923i | \(0.424393\pi\) | |||||||
\(840\) | −0.397132 | − | 4.39112i | −0.0137024 | − | 0.151508i | ||||
\(841\) | 1.17958 | 0.0406753 | ||||||||
\(842\) | 21.0539 | − | 21.0539i | 0.725564 | − | 0.725564i | ||||
\(843\) | 3.97318 | − | 20.0348i | 0.136843 | − | 0.690033i | ||||
\(844\) | 3.68643i | 0.126892i | ||||||||
\(845\) | −1.20168 | − | 4.08695i | −0.0413389 | − | 0.140595i | ||||
\(846\) | −5.22270 | + | 12.6499i | −0.179560 | + | 0.434912i | ||||
\(847\) | 0.837432 | + | 0.837432i | 0.0287745 | + | 0.0287745i | ||||
\(848\) | −3.16898 | − | 3.16898i | −0.108823 | − | 0.108823i | ||||
\(849\) | 9.82530 | − | 6.57324i | 0.337203 | − | 0.225593i | ||||
\(850\) | 7.81584 | + | 12.1420i | 0.268081 | + | 0.416466i | ||||
\(851\) | − | 26.4345i | − | 0.906164i | ||||||
\(852\) | −1.60486 | − | 0.318266i | −0.0549816 | − | 0.0109036i | ||||
\(853\) | 26.9654 | − | 26.9654i | 0.923279 | − | 0.923279i | −0.0739807 | − | 0.997260i | \(-0.523570\pi\) |
0.997260 | + | 0.0739807i | \(0.0235703\pi\) | |||||||
\(854\) | −3.07791 | −0.105324 | ||||||||
\(855\) | 0.706935 | − | 6.67085i | 0.0241767 | − | 0.228138i | ||||
\(856\) | −12.5115 | −0.427634 | ||||||||
\(857\) | 16.1672 | − | 16.1672i | 0.552261 | − | 0.552261i | −0.374832 | − | 0.927093i | \(-0.622300\pi\) |
0.927093 | + | 0.374832i | \(0.122300\pi\) | |||||||
\(858\) | 20.7002 | + | 4.10514i | 0.706693 | + | 0.140147i | ||||
\(859\) | 48.3103i | 1.64833i | 0.566352 | + | 0.824164i | \(0.308354\pi\) | ||||
−0.566352 | + | 0.824164i | \(0.691646\pi\) | |||||||
\(860\) | −1.78591 | − | 0.974328i | −0.0608992 | − | 0.0332243i | ||||
\(861\) | −10.3559 | + | 6.92820i | −0.352928 | + | 0.236113i | ||||
\(862\) | −11.8579 | − | 11.8579i | −0.403882 | − | 0.403882i | ||||
\(863\) | −5.84818 | − | 5.84818i | −0.199074 | − | 0.199074i | 0.600529 | − | 0.799603i | \(-0.294957\pi\) |
−0.799603 | + | 0.600529i | \(0.794957\pi\) | |||||||
\(864\) | −5.09455 | + | 1.02252i | −0.173320 | + | 0.0347867i | ||||
\(865\) | −16.6568 | − | 9.08730i | −0.566347 | − | 0.308978i | ||||
\(866\) | − | 1.19002i | − | 0.0404387i | ||||||
\(867\) | 2.91761 | − | 14.7120i | 0.0990871 | − | 0.499647i | ||||
\(868\) | 4.08457 | − | 4.08457i | 0.138639 | − | 0.138639i | ||||
\(869\) | −47.4217 | −1.60867 | ||||||||
\(870\) | 13.6286 | − | 16.3388i | 0.462051 | − | 0.553937i | ||||
\(871\) | −21.1231 | −0.715727 | ||||||||
\(872\) | −4.83605 | + | 4.83605i | −0.163769 | + | 0.163769i | ||||
\(873\) | 4.71739 | + | 11.3518i | 0.159659 | + | 0.384201i | ||||
\(874\) | − | 2.57617i | − | 0.0871402i | ||||||
\(875\) | 12.6944 | − | 0.922048i | 0.429148 | − | 0.0311709i | ||||
\(876\) | 4.92910 | + | 7.36773i | 0.166539 | + | 0.248933i | ||||
\(877\) | 25.8898 | + | 25.8898i | 0.874236 | + | 0.874236i | 0.992931 | − | 0.118695i | \(-0.0378711\pi\) |
−0.118695 | + | 0.992931i | \(0.537871\pi\) | |||||||
\(878\) | 22.9153 | + | 22.9153i | 0.773355 | + | 0.773355i | ||||
\(879\) | 15.4978 | + | 23.1652i | 0.522726 | + | 0.781341i | ||||
\(880\) | 1.99063 | + | 6.77022i | 0.0671041 | + | 0.228224i | ||||
\(881\) | 6.15899i | 0.207502i | 0.994603 | + | 0.103751i | \(0.0330845\pi\) | ||||
−0.994603 | + | 0.103751i | \(0.966916\pi\) | |||||||
\(882\) | 6.56669 | + | 15.8019i | 0.221112 | + | 0.532079i | ||||
\(883\) | −5.40089 | + | 5.40089i | −0.181755 | + | 0.181755i | −0.792120 | − | 0.610365i | \(-0.791023\pi\) |
0.610365 | + | 0.792120i | \(0.291023\pi\) | |||||||
\(884\) | 11.1498 | 0.375007 | ||||||||
\(885\) | −4.88371 | + | 0.441681i | −0.164164 | + | 0.0148470i | ||||
\(886\) | −21.7741 | −0.731515 | ||||||||
\(887\) | 9.89729 | − | 9.89729i | 0.332319 | − | 0.332319i | −0.521148 | − | 0.853466i | \(-0.674496\pi\) |
0.853466 | + | 0.521148i | \(0.174496\pi\) | |||||||
\(888\) | 3.45728 | − | 17.4334i | 0.116019 | − | 0.585026i | ||||
\(889\) | − | 2.53726i | − | 0.0850968i | ||||||
\(890\) | 3.50551 | − | 6.42550i | 0.117505 | − | 0.215383i | ||||
\(891\) | 20.0377 | − | 20.1302i | 0.671289 | − | 0.674386i | ||||
\(892\) | 18.9631 | + | 18.9631i | 0.634933 | + | 0.634933i | ||||
\(893\) | −3.22573 | − | 3.22573i | −0.107945 | − | 0.107945i | ||||
\(894\) | 19.7495 | − | 13.2127i | 0.660523 | − | 0.441898i | ||||
\(895\) | 22.5817 | − | 6.63965i | 0.754824 | − | 0.221939i | ||||
\(896\) | − | 1.13841i | − | 0.0380316i | ||||||
\(897\) | −16.8976 | − | 3.35104i | −0.564196 | − | 0.111888i | ||||
\(898\) | 2.61273 | − | 2.61273i | 0.0871879 | − | 0.0871879i | ||||
\(899\) | 27.8752 | 0.929691 | ||||||||
\(900\) | −2.69118 | − | 14.7566i | −0.0897060 | − | 0.491887i | ||||
\(901\) | 12.9429 | 0.431191 | ||||||||
\(902\) | 14.1012 | − | 14.1012i | 0.469518 | − | 0.469518i | ||||
\(903\) | −1.75969 | − | 0.348971i | −0.0585588 | − | 0.0116130i | ||||
\(904\) | − | 20.3025i | − | 0.675250i | ||||||
\(905\) | −44.8844 | + | 13.1972i | −1.49201 | + | 0.438691i | ||||
\(906\) | −21.4597 | + | 14.3568i | −0.712952 | + | 0.476973i | ||||
\(907\) | 23.0626 | + | 23.0626i | 0.765781 | + | 0.765781i | 0.977361 | − | 0.211580i | \(-0.0678609\pi\) |
−0.211580 | + | 0.977361i | \(0.567861\pi\) | |||||||
\(908\) | 2.05681 | + | 2.05681i | 0.0682576 | + | 0.0682576i | ||||
\(909\) | −19.3262 | + | 46.8099i | −0.641009 | + | 1.55259i | ||||
\(910\) | 4.70673 | − | 8.62730i | 0.156027 | − | 0.285992i | ||||
\(911\) | 15.0916i | 0.500006i | 0.968245 | + | 0.250003i | \(0.0804316\pi\) | ||||
−0.968245 | + | 0.250003i | \(0.919568\pi\) | |||||||
\(912\) | 0.336929 | − | 1.69896i | 0.0111568 | − | 0.0562583i | ||||
\(913\) | −17.5122 | + | 17.5122i | −0.579569 | + | 0.579569i | ||||
\(914\) | −8.81552 | −0.291591 | ||||||||
\(915\) | −10.4288 | + | 0.943175i | −0.344765 | + | 0.0311804i | ||||
\(916\) | 15.8734 | 0.524473 | ||||||||
\(917\) | 15.2974 | − | 15.2974i | 0.505164 | − | 0.505164i | ||||
\(918\) | 8.31563 | − | 12.4918i | 0.274457 | − | 0.412292i | ||||
\(919\) | − | 8.47668i | − | 0.279620i | −0.990178 | − | 0.139810i | \(-0.955351\pi\) | ||
0.990178 | − | 0.139810i | \(-0.0446492\pi\) | |||||||
\(920\) | −1.62496 | − | 5.52655i | −0.0535733 | − | 0.182205i | ||||
\(921\) | −4.39741 | − | 6.57300i | −0.144900 | − | 0.216588i | ||||
\(922\) | 2.13407 | + | 2.13407i | 0.0702817 | + | 0.0702817i | ||||
\(923\) | −2.57873 | − | 2.57873i | −0.0848798 | − | 0.0848798i | ||||
\(924\) | 3.46015 | + | 5.17204i | 0.113831 | + | 0.170148i | ||||
\(925\) | 50.1414 | + | 10.8688i | 1.64864 | + | 0.357365i | ||||
\(926\) | 24.2113i | 0.795634i | ||||||||
\(927\) | 5.77021 | − | 2.39788i | 0.189519 | − | 0.0787569i | ||||
\(928\) | 3.88456 | − | 3.88456i | 0.127517 | − | 0.127517i | ||||
\(929\) | −6.96249 | −0.228432 | −0.114216 | − | 0.993456i | \(-0.536436\pi\) | ||||
−0.114216 | + | 0.993456i | \(0.536436\pi\) | |||||||
\(930\) | 12.5880 | − | 15.0912i | 0.412775 | − | 0.494862i | ||||
\(931\) | −5.70402 | −0.186942 | ||||||||
\(932\) | −15.6011 | + | 15.6011i | −0.511032 | + | 0.511032i | ||||
\(933\) | −2.73957 | + | 13.8143i | −0.0896896 | + | 0.452260i | ||||
\(934\) | − | 4.84547i | − | 0.158549i | ||||||
\(935\) | −17.8908 | − | 9.76053i | −0.585091 | − | 0.319204i | ||||
\(936\) | −10.7056 | − | 4.41997i | −0.349923 | − | 0.144471i | ||||
\(937\) | 2.15425 | + | 2.15425i | 0.0703762 | + | 0.0703762i | 0.741419 | − | 0.671043i | \(-0.234153\pi\) |
−0.671043 | + | 0.741419i | \(0.734153\pi\) | |||||||
\(938\) | −4.40426 | − | 4.40426i | −0.143804 | − | 0.143804i | ||||
\(939\) | −40.4321 | + | 27.0495i | −1.31945 | + | 0.882728i | ||||
\(940\) | −8.95470 | − | 4.88535i | −0.292070 | − | 0.159342i | ||||
\(941\) | − | 19.9072i | − | 0.648957i | −0.945893 | − | 0.324479i | \(-0.894811\pi\) | ||
0.945893 | − | 0.324479i | \(-0.105189\pi\) | |||||||
\(942\) | 6.32682 | + | 1.25470i | 0.206139 | + | 0.0408803i | ||||
\(943\) | −11.5109 | + | 11.5109i | −0.374845 | + | 0.374845i | ||||
\(944\) | −1.26612 | −0.0412085 | ||||||||
\(945\) | −6.15542 | − | 11.7076i | −0.200236 | − | 0.380848i | ||||
\(946\) | 2.87128 | 0.0933533 | ||||||||
\(947\) | −27.8351 | + | 27.8351i | −0.904520 | + | 0.904520i | −0.995823 | − | 0.0913033i | \(-0.970897\pi\) |
0.0913033 | + | 0.995823i | \(0.470897\pi\) | |||||||
\(948\) | 25.5293 | + | 5.06282i | 0.829152 | + | 0.164433i | ||||
\(949\) | 19.7588i | 0.641399i | ||||||||
\(950\) | 4.88652 | + | 1.05922i | 0.158540 | + | 0.0343656i | ||||
\(951\) | 16.0836 | − | 10.7601i | 0.521546 | − | 0.348920i | ||||
\(952\) | 2.32478 | + | 2.32478i | 0.0753466 | + | 0.0753466i | ||||
\(953\) | −10.6937 | − | 10.6937i | −0.346402 | − | 0.346402i | 0.512365 | − | 0.858768i | \(-0.328769\pi\) |
−0.858768 | + | 0.512365i | \(0.828769\pi\) | |||||||
\(954\) | −12.4273 | − | 5.13081i | −0.402349 | − | 0.166116i | ||||
\(955\) | 15.6374 | + | 53.1836i | 0.506015 | + | 1.72098i | ||||
\(956\) | − | 4.84839i | − | 0.156808i | ||||||
\(957\) | −5.84141 | + | 29.4553i | −0.188826 | + | 0.952155i | ||||
\(958\) | −12.7420 | + | 12.7420i | −0.411674 | + | 0.411674i | ||||
\(959\) | −24.5098 | −0.791462 | ||||||||
\(960\) | −0.348848 | − | 3.85724i | −0.0112590 | − | 0.124492i | ||||
\(961\) | −5.25318 | −0.169457 | ||||||||
\(962\) | 28.0124 | − | 28.0124i | 0.903155 | − | 0.903155i | ||||
\(963\) | −34.6608 | + | 14.4037i | −1.11693 | + | 0.464154i | ||||
\(964\) | 17.0520i | 0.549209i | ||||||||
\(965\) | 26.4468 | − | 48.4763i | 0.851354 | − | 1.56051i | ||||
\(966\) | −2.82453 | − | 4.22195i | −0.0908779 | − | 0.135839i | ||||
\(967\) | −13.5193 | − | 13.5193i | −0.434750 | − | 0.434750i | 0.455491 | − | 0.890241i | \(-0.349464\pi\) |
−0.890241 | + | 0.455491i | \(0.849464\pi\) | |||||||
\(968\) | 0.735615 | + | 0.735615i | 0.0236436 | + | 0.0236436i | ||||
\(969\) | 2.78145 | + | 4.15756i | 0.0893531 | + | 0.133560i | ||||
\(970\) | −8.79054 | + | 2.58466i | −0.282247 | + | 0.0829885i | ||||
\(971\) | 10.6230i | 0.340909i | 0.985366 | + | 0.170455i | \(0.0545236\pi\) | ||||
−0.985366 | + | 0.170455i | \(0.945476\pi\) | |||||||
\(972\) | −12.9364 | + | 8.69774i | −0.414934 | + | 0.278980i | ||||
\(973\) | −12.1157 | + | 12.1157i | −0.388412 | + | 0.388412i | ||||
\(974\) | 4.70920 | 0.150893 | ||||||||
\(975\) | 13.3040 | − | 30.6739i | 0.426068 | − | 0.982351i | ||||
\(976\) | −2.70369 | −0.0865429 | ||||||||
\(977\) | 4.47372 | − | 4.47372i | 0.143127 | − | 0.143127i | −0.631913 | − | 0.775040i | \(-0.717730\pi\) |
0.775040 | + | 0.631913i | \(0.217730\pi\) | |||||||
\(978\) | −4.04687 | + | 20.4064i | −0.129405 | + | 0.652524i | ||||
\(979\) | 10.3305i | 0.330164i | ||||||||
\(980\) | −12.2366 | + | 3.59790i | −0.390884 | + | 0.114931i | ||||
\(981\) | −7.82993 | + | 18.9648i | −0.249990 | + | 0.605500i | ||||
\(982\) | −28.8305 | − | 28.8305i | −0.920020 | − | 0.920020i | ||||
\(983\) | 31.6740 | + | 31.6740i | 1.01024 | + | 1.01024i | 0.999947 | + | 0.0102974i | \(0.00327781\pi\) |
0.0102974 | + | 0.999947i | \(0.496722\pi\) | |||||||
\(984\) | −9.09679 | + | 6.08585i | −0.289995 | + | 0.194010i | ||||
\(985\) | 2.52359 | − | 4.62568i | 0.0804084 | − | 0.147386i | ||||
\(986\) | 15.8655i | 0.505262i | ||||||||
\(987\) | −8.82320 | − | 1.74977i | −0.280846 | − | 0.0556957i | ||||
\(988\) | 2.72994 | − | 2.72994i | 0.0868509 | − | 0.0868509i | ||||
\(989\) | −2.34383 | −0.0745296 | ||||||||
\(990\) | 13.3088 | + | 16.4639i | 0.422982 | + | 0.523258i | ||||
\(991\) | 12.3131 | 0.391138 | 0.195569 | − | 0.980690i | \(-0.437345\pi\) | ||||
0.195569 | + | 0.980690i | \(0.437345\pi\) | |||||||
\(992\) | 3.58795 | − | 3.58795i | 0.113918 | − | 0.113918i | ||||
\(993\) | −49.6548 | − | 9.84724i | −1.57575 | − | 0.312493i | ||||
\(994\) | − | 1.07535i | − | 0.0341082i | ||||||
\(995\) | 17.2908 | + | 58.8066i | 0.548154 | + | 1.86430i | ||||
\(996\) | 11.2973 | − | 7.55799i | 0.357967 | − | 0.239484i | ||||
\(997\) | −31.6019 | − | 31.6019i | −1.00084 | − | 1.00084i | −1.00000 | 0.000842399i | \(-0.999732\pi\) | |
−0.000842399 | − | 1.00000i | \(-0.500268\pi\) | |||||||
\(998\) | 20.1312 | + | 20.1312i | 0.637243 | + | 0.637243i | ||||
\(999\) | −10.4922 | − | 52.2761i | −0.331959 | − | 1.65394i |
(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 | 570.2.k.b.77.1 | ✓ | 36 | |
3.2 | odd | 2 | inner | 570.2.k.b.77.14 | yes | 36 | |
5.3 | odd | 4 | inner | 570.2.k.b.533.14 | yes | 36 | |
15.8 | even | 4 | inner | 570.2.k.b.533.1 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.k.b.77.1 | ✓ | 36 | 1.1 | even | 1 | trivial | |
570.2.k.b.77.14 | yes | 36 | 3.2 | odd | 2 | inner | |
570.2.k.b.533.1 | yes | 36 | 15.8 | even | 4 | inner | |
570.2.k.b.533.14 | yes | 36 | 5.3 | odd | 4 | inner |