Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [804,2,Mod(671,804)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(804, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("804.671");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 804 = 2^{2} \cdot 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 804.c (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: | \(6.41997232251\) |
Analytic rank: | \(0\) |
Dimension: | \(128\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 671.13 | ||
Character | \(\chi\) | \(=\) | 804.671 |
Dual form | 804.2.c.b.671.14 |
$q$-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 \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).
\(n\) | \(269\) | \(337\) | \(403\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36593 | − | 0.366392i | −0.965856 | − | 0.259078i | ||||
\(3\) | −0.973809 | − | 1.43237i | −0.562229 | − | 0.826982i | ||||
\(4\) | 1.73151 | + | 1.00093i | 0.865757 | + | 0.500464i | ||||
\(5\) | 2.42154i | 1.08294i | 0.840719 | + | 0.541472i | \(0.182133\pi\) | ||||
−0.840719 | + | 0.541472i | \(0.817867\pi\) | |||||||
\(6\) | 0.805342 | + | 2.31331i | 0.328779 | + | 0.944407i | ||||
\(7\) | − | 1.75439i | − | 0.663097i | −0.943438 | − | 0.331549i | \(-0.892429\pi\) | ||
0.943438 | − | 0.331549i | \(-0.107571\pi\) | |||||||
\(8\) | −1.99839 | − | 2.00161i | −0.706538 | − | 0.707675i | ||||
\(9\) | −1.10339 | + | 2.78972i | −0.367798 | + | 0.929906i | ||||
\(10\) | 0.887230 | − | 3.30764i | 0.280567 | − | 1.04597i | ||||
\(11\) | 0.337759 | 0.101838 | 0.0509191 | − | 0.998703i | \(-0.483785\pi\) | ||||
0.0509191 | + | 0.998703i | \(0.483785\pi\) | |||||||
\(12\) | −0.252459 | − | 3.45489i | −0.0728786 | − | 0.997341i | ||||
\(13\) | −1.33945 | −0.371497 | −0.185748 | − | 0.982597i | \(-0.559471\pi\) | ||||
−0.185748 | + | 0.982597i | \(0.559471\pi\) | |||||||
\(14\) | −0.642794 | + | 2.39637i | −0.171794 | + | 0.640457i | ||||
\(15\) | 3.46855 | − | 2.35811i | 0.895575 | − | 0.608862i | ||||
\(16\) | 1.99628 | + | 3.46624i | 0.499071 | + | 0.866561i | ||||
\(17\) | − | 4.05920i | − | 0.984501i | −0.870453 | − | 0.492251i | \(-0.836174\pi\) | ||
0.870453 | − | 0.492251i | \(-0.163826\pi\) | |||||||
\(18\) | 2.52928 | − | 3.40628i | 0.596158 | − | 0.802867i | ||||
\(19\) | 1.16371i | 0.266973i | 0.991051 | + | 0.133486i | \(0.0426172\pi\) | ||||
−0.991051 | + | 0.133486i | \(0.957383\pi\) | |||||||
\(20\) | −2.42378 | + | 4.19292i | −0.541975 | + | 0.937566i | ||||
\(21\) | −2.51294 | + | 1.70844i | −0.548369 | + | 0.372812i | ||||
\(22\) | −0.461354 | − | 0.123752i | −0.0983611 | − | 0.0263840i | ||||
\(23\) | 1.81407 | 0.378259 | 0.189130 | − | 0.981952i | \(-0.439433\pi\) | ||||
0.189130 | + | 0.981952i | \(0.439433\pi\) | |||||||
\(24\) | −0.921002 | + | 4.81163i | −0.187999 | + | 0.982169i | ||||
\(25\) | −0.863832 | −0.172766 | ||||||||
\(26\) | 1.82959 | + | 0.490764i | 0.358813 | + | 0.0962467i | ||||
\(27\) | 5.07041 | − | 1.13618i | 0.975802 | − | 0.218658i | ||||
\(28\) | 1.75602 | − | 3.03775i | 0.331856 | − | 0.574081i | ||||
\(29\) | 8.51104i | 1.58046i | 0.612810 | + | 0.790230i | \(0.290039\pi\) | ||||
−0.612810 | + | 0.790230i | \(0.709961\pi\) | |||||||
\(30\) | −5.60177 | + | 1.95016i | −1.02274 | + | 0.356049i | ||||
\(31\) | 4.75899i | 0.854740i | 0.904077 | + | 0.427370i | \(0.140560\pi\) | ||||
−0.904077 | + | 0.427370i | \(0.859440\pi\) | |||||||
\(32\) | −1.45677 | − | 5.46606i | −0.257524 | − | 0.966272i | ||||
\(33\) | −0.328913 | − | 0.483798i | −0.0572564 | − | 0.0842183i | ||||
\(34\) | −1.48726 | + | 5.54458i | −0.255063 | + | 0.950887i | ||||
\(35\) | 4.24832 | 0.718097 | ||||||||
\(36\) | −4.70285 | + | 3.72602i | −0.783808 | + | 0.621003i | ||||
\(37\) | 6.50846 | 1.06998 | 0.534992 | − | 0.844857i | \(-0.320315\pi\) | ||||
0.534992 | + | 0.844857i | \(0.320315\pi\) | |||||||
\(38\) | 0.426373 | − | 1.58954i | 0.0691668 | − | 0.257857i | ||||
\(39\) | 1.30437 | + | 1.91860i | 0.208866 | + | 0.307221i | ||||
\(40\) | 4.84696 | − | 4.83917i | 0.766372 | − | 0.765140i | ||||
\(41\) | − | 0.0765846i | − | 0.0119605i | −0.999982 | − | 0.00598026i | \(-0.998096\pi\) | ||
0.999982 | − | 0.00598026i | \(-0.00190359\pi\) | |||||||
\(42\) | 4.05846 | − | 1.41288i | 0.626233 | − | 0.218013i | ||||
\(43\) | 9.26180i | 1.41241i | 0.708007 | + | 0.706206i | \(0.249595\pi\) | ||||
−0.708007 | + | 0.706206i | \(0.750405\pi\) | |||||||
\(44\) | 0.584835 | + | 0.338073i | 0.0881671 | + | 0.0509664i | ||||
\(45\) | −6.75540 | − | 2.67191i | −1.00704 | − | 0.398304i | ||||
\(46\) | −2.47789 | − | 0.664660i | −0.365344 | − | 0.0979987i | ||||
\(47\) | −8.82365 | −1.28706 | −0.643531 | − | 0.765420i | \(-0.722531\pi\) | ||||
−0.643531 | + | 0.765420i | \(0.722531\pi\) | |||||||
\(48\) | 3.02096 | − | 6.23488i | 0.436038 | − | 0.899928i | ||||
\(49\) | 3.92212 | 0.560302 | ||||||||
\(50\) | 1.17993 | + | 0.316501i | 0.166868 | + | 0.0447600i | ||||
\(51\) | −5.81430 | + | 3.95289i | −0.814165 | + | 0.553515i | ||||
\(52\) | −2.31928 | − | 1.34069i | −0.321626 | − | 0.185921i | ||||
\(53\) | − | 2.03937i | − | 0.280130i | −0.990142 | − | 0.140065i | \(-0.955269\pi\) | ||
0.990142 | − | 0.140065i | \(-0.0447311\pi\) | |||||||
\(54\) | −7.34210 | − | 0.305820i | −0.999134 | − | 0.0416169i | ||||
\(55\) | 0.817896i | 0.110285i | ||||||||
\(56\) | −3.51160 | + | 3.50596i | −0.469257 | + | 0.468503i | ||||
\(57\) | 1.66686 | − | 1.13323i | 0.220782 | − | 0.150100i | ||||
\(58\) | 3.11837 | − | 11.6255i | 0.409463 | − | 1.52650i | ||||
\(59\) | 14.7468 | 1.91987 | 0.959933 | − | 0.280231i | \(-0.0904110\pi\) | ||||
0.959933 | + | 0.280231i | \(0.0904110\pi\) | |||||||
\(60\) | 8.36614 | − | 0.611338i | 1.08006 | − | 0.0789234i | ||||
\(61\) | 10.1820 | 1.30367 | 0.651835 | − | 0.758361i | \(-0.273999\pi\) | ||||
0.651835 | + | 0.758361i | \(0.273999\pi\) | |||||||
\(62\) | 1.74365 | − | 6.50044i | 0.221444 | − | 0.825556i | ||||
\(63\) | 4.89425 | + | 1.93578i | 0.616618 | + | 0.243886i | ||||
\(64\) | −0.0128704 | + | 7.99999i | −0.00160880 | + | 0.999999i | ||||
\(65\) | − | 3.24353i | − | 0.402310i | ||||||
\(66\) | 0.272011 | + | 0.781343i | 0.0334823 | + | 0.0961767i | ||||
\(67\) | − | 1.00000i | − | 0.122169i | ||||||
\(68\) | 4.06297 | − | 7.02857i | 0.492708 | − | 0.852339i | ||||
\(69\) | −1.76656 | − | 2.59843i | −0.212668 | − | 0.312814i | ||||
\(70\) | −5.80289 | − | 1.55655i | −0.693578 | − | 0.186043i | ||||
\(71\) | 3.10054 | 0.367966 | 0.183983 | − | 0.982929i | \(-0.441101\pi\) | ||||
0.183983 | + | 0.982929i | \(0.441101\pi\) | |||||||
\(72\) | 7.78893 | − | 3.36638i | 0.917934 | − | 0.396732i | ||||
\(73\) | 11.7805 | 1.37880 | 0.689401 | − | 0.724380i | \(-0.257874\pi\) | ||||
0.689401 | + | 0.724380i | \(0.257874\pi\) | |||||||
\(74\) | −8.89008 | − | 2.38464i | −1.03345 | − | 0.277209i | ||||
\(75\) | 0.841207 | + | 1.23733i | 0.0971343 | + | 0.142875i | ||||
\(76\) | −1.16479 | + | 2.01498i | −0.133610 | + | 0.231134i | ||||
\(77\) | − | 0.592561i | − | 0.0675286i | ||||||
\(78\) | −1.07872 | − | 3.09857i | −0.122140 | − | 0.350844i | ||||
\(79\) | − | 4.35094i | − | 0.489519i | −0.969584 | − | 0.244760i | \(-0.921291\pi\) | ||
0.969584 | − | 0.244760i | \(-0.0787091\pi\) | |||||||
\(80\) | −8.39363 | + | 4.83407i | −0.938437 | + | 0.540466i | ||||
\(81\) | −6.56505 | − | 6.15631i | −0.729450 | − | 0.684035i | ||||
\(82\) | −0.0280600 | + | 0.104609i | −0.00309871 | + | 0.0115521i | ||||
\(83\) | 8.52629 | 0.935882 | 0.467941 | − | 0.883760i | \(-0.344996\pi\) | ||||
0.467941 | + | 0.883760i | \(0.344996\pi\) | |||||||
\(84\) | −6.06122 | + | 0.442911i | −0.661334 | + | 0.0483256i | ||||
\(85\) | 9.82950 | 1.06616 | ||||||||
\(86\) | 3.39345 | − | 12.6509i | 0.365925 | − | 1.36419i | ||||
\(87\) | 12.1910 | − | 8.28812i | 1.30701 | − | 0.888580i | ||||
\(88\) | −0.674975 | − | 0.676061i | −0.0719525 | − | 0.0720684i | ||||
\(89\) | − | 0.230176i | − | 0.0243986i | −0.999926 | − | 0.0121993i | \(-0.996117\pi\) | ||
0.999926 | − | 0.0121993i | \(-0.00388326\pi\) | |||||||
\(90\) | 8.24842 | + | 6.12475i | 0.869460 | + | 0.645605i | ||||
\(91\) | 2.34992i | 0.246338i | ||||||||
\(92\) | 3.14109 | + | 1.81575i | 0.327481 | + | 0.189305i | ||||
\(93\) | 6.81666 | − | 4.63435i | 0.706855 | − | 0.480559i | ||||
\(94\) | 12.0525 | + | 3.23291i | 1.24312 | + | 0.333449i | ||||
\(95\) | −2.81796 | −0.289116 | ||||||||
\(96\) | −6.41082 | + | 7.40954i | −0.654302 | + | 0.756233i | ||||
\(97\) | 0.733942 | 0.0745205 | 0.0372603 | − | 0.999306i | \(-0.488137\pi\) | ||||
0.0372603 | + | 0.999306i | \(0.488137\pi\) | |||||||
\(98\) | −5.35732 | − | 1.43703i | −0.541172 | − | 0.145162i | ||||
\(99\) | −0.372681 | + | 0.942252i | −0.0374559 | + | 0.0946999i | ||||
\(100\) | −1.49574 | − | 0.864635i | −0.149574 | − | 0.0864635i | ||||
\(101\) | − | 7.44649i | − | 0.740953i | −0.928842 | − | 0.370477i | \(-0.879194\pi\) | ||
0.928842 | − | 0.370477i | \(-0.120806\pi\) | |||||||
\(102\) | 9.39022 | − | 3.26905i | 0.929770 | − | 0.323684i | ||||
\(103\) | 5.90797i | 0.582130i | 0.956703 | + | 0.291065i | \(0.0940096\pi\) | ||||
−0.956703 | + | 0.291065i | \(0.905990\pi\) | |||||||
\(104\) | 2.67675 | + | 2.68106i | 0.262477 | + | 0.262899i | ||||
\(105\) | −4.13705 | − | 6.08518i | −0.403735 | − | 0.593853i | ||||
\(106\) | −0.747210 | + | 2.78564i | −0.0725754 | + | 0.270565i | ||||
\(107\) | −2.90009 | −0.280362 | −0.140181 | − | 0.990126i | \(-0.544768\pi\) | ||||
−0.140181 | + | 0.990126i | \(0.544768\pi\) | |||||||
\(108\) | 9.91673 | + | 3.10781i | 0.954238 | + | 0.299050i | ||||
\(109\) | −3.34202 | −0.320107 | −0.160054 | − | 0.987108i | \(-0.551167\pi\) | ||||
−0.160054 | + | 0.987108i | \(0.551167\pi\) | |||||||
\(110\) | 0.299670 | − | 1.11719i | 0.0285724 | − | 0.106519i | ||||
\(111\) | −6.33799 | − | 9.32255i | −0.601575 | − | 0.884857i | ||||
\(112\) | 6.08114 | − | 3.50226i | 0.574614 | − | 0.330932i | ||||
\(113\) | 6.51949i | 0.613302i | 0.951822 | + | 0.306651i | \(0.0992084\pi\) | ||||
−0.951822 | + | 0.306651i | \(0.900792\pi\) | |||||||
\(114\) | −2.69202 | + | 0.937182i | −0.252131 | + | 0.0877751i | ||||
\(115\) | 4.39283i | 0.409634i | ||||||||
\(116\) | −8.51894 | + | 14.7370i | −0.790964 | + | 1.36829i | ||||
\(117\) | 1.47794 | − | 3.73669i | 0.136636 | − | 0.345457i | ||||
\(118\) | −20.1430 | − | 5.40309i | −1.85431 | − | 0.497395i | ||||
\(119\) | −7.12143 | −0.652820 | ||||||||
\(120\) | −11.6515 | − | 2.23024i | −1.06363 | − | 0.203592i | ||||
\(121\) | −10.8859 | −0.989629 | ||||||||
\(122\) | −13.9079 | − | 3.73060i | −1.25916 | − | 0.337752i | ||||
\(123\) | −0.109698 | + | 0.0745788i | −0.00989113 | + | 0.00672454i | ||||
\(124\) | −4.76341 | + | 8.24026i | −0.427767 | + | 0.739997i | ||||
\(125\) | 10.0159i | 0.895847i | ||||||||
\(126\) | −5.97594 | − | 4.43735i | −0.532379 | − | 0.395311i | ||||
\(127\) | 13.5743i | 1.20452i | 0.798299 | + | 0.602262i | \(0.205734\pi\) | ||||
−0.798299 | + | 0.602262i | \(0.794266\pi\) | |||||||
\(128\) | 2.94871 | − | 10.9227i | 0.260632 | − | 0.965438i | ||||
\(129\) | 13.2664 | − | 9.01922i | 1.16804 | − | 0.794098i | ||||
\(130\) | −1.18840 | + | 4.43042i | −0.104230 | + | 0.388574i | ||||
\(131\) | 18.1110 | 1.58236 | 0.791182 | − | 0.611580i | \(-0.209466\pi\) | ||||
0.791182 | + | 0.611580i | \(0.209466\pi\) | |||||||
\(132\) | −0.0852703 | − | 1.16692i | −0.00742183 | − | 0.101567i | ||||
\(133\) | 2.04160 | 0.177029 | ||||||||
\(134\) | −0.366392 | + | 1.36593i | −0.0316514 | + | 0.117998i | ||||
\(135\) | 2.75130 | + | 12.2782i | 0.236794 | + | 1.05674i | ||||
\(136\) | −8.12493 | + | 8.11187i | −0.696707 | + | 0.695587i | ||||
\(137\) | 6.99766i | 0.597850i | 0.954277 | + | 0.298925i | \(0.0966281\pi\) | ||||
−0.954277 | + | 0.298925i | \(0.903372\pi\) | |||||||
\(138\) | 1.46095 | + | 4.19651i | 0.124364 | + | 0.357231i | ||||
\(139\) | − | 1.25579i | − | 0.106515i | −0.998581 | − | 0.0532574i | \(-0.983040\pi\) | ||
0.998581 | − | 0.0532574i | \(-0.0169604\pi\) | |||||||
\(140\) | 7.35602 | + | 4.25226i | 0.621697 | + | 0.359382i | ||||
\(141\) | 8.59255 | + | 12.6388i | 0.723623 | + | 1.06438i | ||||
\(142\) | −4.23511 | − | 1.13601i | −0.355403 | − | 0.0953320i | ||||
\(143\) | −0.452412 | −0.0378326 | ||||||||
\(144\) | −11.8725 | + | 1.74444i | −0.989377 | + | 0.145370i | ||||
\(145\) | −20.6098 | −1.71155 | ||||||||
\(146\) | −16.0913 | − | 4.31628i | −1.33173 | − | 0.357218i | ||||
\(147\) | −3.81939 | − | 5.61794i | −0.315018 | − | 0.463360i | ||||
\(148\) | 11.2695 | + | 6.51450i | 0.926346 | + | 0.535489i | ||||
\(149\) | − | 8.81368i | − | 0.722045i | −0.932557 | − | 0.361022i | \(-0.882428\pi\) | ||
0.932557 | − | 0.361022i | \(-0.117572\pi\) | |||||||
\(150\) | −0.695680 | − | 1.99832i | −0.0568021 | − | 0.163162i | ||||
\(151\) | 12.8312i | 1.04419i | 0.852887 | + | 0.522095i | \(0.174849\pi\) | ||||
−0.852887 | + | 0.522095i | \(0.825151\pi\) | |||||||
\(152\) | 2.32929 | − | 2.32554i | 0.188930 | − | 0.188626i | ||||
\(153\) | 11.3240 | + | 4.47890i | 0.915494 | + | 0.362097i | ||||
\(154\) | −0.217109 | + | 0.809395i | −0.0174952 | + | 0.0652229i | ||||
\(155\) | −11.5241 | −0.925635 | ||||||||
\(156\) | 0.338156 | + | 4.62766i | 0.0270742 | + | 0.370509i | ||||
\(157\) | −18.8027 | −1.50062 | −0.750308 | − | 0.661089i | \(-0.770095\pi\) | ||||
−0.750308 | + | 0.661089i | \(0.770095\pi\) | |||||||
\(158\) | −1.59415 | + | 5.94307i | −0.126824 | + | 0.472805i | ||||
\(159\) | −2.92115 | + | 1.98596i | −0.231662 | + | 0.157497i | ||||
\(160\) | 13.2363 | − | 3.52763i | 1.04642 | − | 0.278884i | ||||
\(161\) | − | 3.18258i | − | 0.250823i | ||||||
\(162\) | 6.71175 | + | 10.8145i | 0.527325 | + | 0.849664i | ||||
\(163\) | − | 8.64155i | − | 0.676859i | −0.940992 | − | 0.338429i | \(-0.890104\pi\) | ||
0.940992 | − | 0.338429i | \(-0.109896\pi\) | |||||||
\(164\) | 0.0766558 | − | 0.132607i | 0.00598581 | − | 0.0103549i | ||||
\(165\) | 1.17153 | − | 0.796474i | 0.0912037 | − | 0.0620054i | ||||
\(166\) | −11.6463 | − | 3.12396i | −0.903928 | − | 0.242466i | ||||
\(167\) | 13.8923 | 1.07502 | 0.537509 | − | 0.843258i | \(-0.319365\pi\) | ||||
0.537509 | + | 0.843258i | \(0.319365\pi\) | |||||||
\(168\) | 8.44147 | + | 1.61580i | 0.651274 | + | 0.124661i | ||||
\(169\) | −11.2059 | −0.861990 | ||||||||
\(170\) | −13.4264 | − | 3.60145i | −1.02976 | − | 0.276218i | ||||
\(171\) | −3.24641 | − | 1.28403i | −0.248259 | − | 0.0981920i | ||||
\(172\) | −9.27040 | + | 16.0369i | −0.706861 | + | 1.22280i | ||||
\(173\) | 13.4769i | 1.02463i | 0.858799 | + | 0.512313i | \(0.171211\pi\) | ||||
−0.858799 | + | 0.512313i | \(0.828789\pi\) | |||||||
\(174\) | −19.6887 | + | 6.85430i | −1.49260 | + | 0.519623i | ||||
\(175\) | 1.51550i | 0.114561i | ||||||||
\(176\) | 0.674263 | + | 1.17076i | 0.0508245 | + | 0.0882490i | ||||
\(177\) | −14.3605 | − | 21.1229i | −1.07940 | − | 1.58769i | ||||
\(178\) | −0.0843346 | + | 0.314404i | −0.00632115 | + | 0.0235656i | ||||
\(179\) | −15.6492 | −1.16967 | −0.584837 | − | 0.811151i | \(-0.698841\pi\) | ||||
−0.584837 | + | 0.811151i | \(0.698841\pi\) | |||||||
\(180\) | −9.02268 | − | 11.3881i | −0.672511 | − | 0.848820i | ||||
\(181\) | −1.47999 | −0.110007 | −0.0550033 | − | 0.998486i | \(-0.517517\pi\) | ||||
−0.0550033 | + | 0.998486i | \(0.517517\pi\) | |||||||
\(182\) | 0.860991 | − | 3.20982i | 0.0638209 | − | 0.237928i | ||||
\(183\) | −9.91531 | − | 14.5844i | −0.732961 | − | 1.07811i | ||||
\(184\) | −3.62522 | − | 3.63105i | −0.267255 | − | 0.267685i | ||||
\(185\) | 15.7605i | 1.15873i | ||||||||
\(186\) | −11.0090 | + | 3.83261i | −0.807222 | + | 0.281021i | ||||
\(187\) | − | 1.37103i | − | 0.100260i | ||||||
\(188\) | −15.2783 | − | 8.83185i | −1.11428 | − | 0.644129i | ||||
\(189\) | −1.99330 | − | 8.89548i | −0.144991 | − | 0.647051i | ||||
\(190\) | 3.84913 | + | 1.03248i | 0.279245 | + | 0.0749037i | ||||
\(191\) | −9.98074 | −0.722181 | −0.361090 | − | 0.932531i | \(-0.617595\pi\) | ||||
−0.361090 | + | 0.932531i | \(0.617595\pi\) | |||||||
\(192\) | 11.4715 | − | 7.77202i | 0.827885 | − | 0.560898i | ||||
\(193\) | 10.5987 | 0.762908 | 0.381454 | − | 0.924388i | \(-0.375423\pi\) | ||||
0.381454 | + | 0.924388i | \(0.375423\pi\) | |||||||
\(194\) | −1.00251 | − | 0.268910i | −0.0719761 | − | 0.0193066i | ||||
\(195\) | −4.64595 | + | 3.15858i | −0.332703 | + | 0.226190i | ||||
\(196\) | 6.79120 | + | 3.92576i | 0.485086 | + | 0.280411i | ||||
\(197\) | 0.207828i | 0.0148071i | 0.999973 | + | 0.00740355i | \(0.00235665\pi\) | ||||
−0.999973 | + | 0.00740355i | \(0.997643\pi\) | |||||||
\(198\) | 0.854289 | − | 1.15050i | 0.0607117 | − | 0.0817625i | ||||
\(199\) | − | 5.84910i | − | 0.414632i | −0.978274 | − | 0.207316i | \(-0.933527\pi\) | ||
0.978274 | − | 0.207316i | \(-0.0664728\pi\) | |||||||
\(200\) | 1.72627 | + | 1.72905i | 0.122066 | + | 0.122263i | ||||
\(201\) | −1.43237 | + | 0.973809i | −0.101032 | + | 0.0686872i | ||||
\(202\) | −2.72833 | + | 10.1714i | −0.191965 | + | 0.715655i | ||||
\(203\) | 14.9317 | 1.04800 | ||||||||
\(204\) | −14.0241 | + | 1.02478i | −0.981884 | + | 0.0717491i | ||||
\(205\) | 0.185452 | 0.0129526 | ||||||||
\(206\) | 2.16463 | − | 8.06986i | 0.150817 | − | 0.562254i | ||||
\(207\) | −2.00163 | + | 5.06074i | −0.139123 | + | 0.351746i | ||||
\(208\) | −2.67392 | − | 4.64286i | −0.185403 | − | 0.321925i | ||||
\(209\) | 0.393053i | 0.0271880i | ||||||||
\(210\) | 3.42135 | + | 9.82769i | 0.236095 | + | 0.678175i | ||||
\(211\) | 4.93959i | 0.340055i | 0.985439 | + | 0.170028i | \(0.0543857\pi\) | ||||
−0.985439 | + | 0.170028i | \(0.945614\pi\) | |||||||
\(212\) | 2.04127 | − | 3.53121i | 0.140195 | − | 0.242524i | ||||
\(213\) | −3.01933 | − | 4.44114i | −0.206881 | − | 0.304302i | ||||
\(214\) | 3.96131 | + | 1.06257i | 0.270790 | + | 0.0726357i | ||||
\(215\) | −22.4278 | −1.52956 | ||||||||
\(216\) | −12.4069 | − | 7.87845i | −0.844179 | − | 0.536061i | ||||
\(217\) | 8.34913 | 0.566776 | ||||||||
\(218\) | 4.56495 | + | 1.22449i | 0.309177 | + | 0.0829327i | ||||
\(219\) | −11.4719 | − | 16.8741i | −0.775202 | − | 1.14024i | ||||
\(220\) | −0.818655 | + | 1.41620i | −0.0551937 | + | 0.0954800i | ||||
\(221\) | 5.43710i | 0.365739i | ||||||||
\(222\) | 5.24153 | + | 15.0561i | 0.351789 | + | 1.01050i | ||||
\(223\) | 11.8399i | 0.792860i | 0.918065 | + | 0.396430i | \(0.129751\pi\) | ||||
−0.918065 | + | 0.396430i | \(0.870249\pi\) | |||||||
\(224\) | −9.58960 | + | 2.55575i | −0.640732 | + | 0.170763i | ||||
\(225\) | 0.953147 | − | 2.40985i | 0.0635431 | − | 0.160657i | ||||
\(226\) | 2.38869 | − | 8.90515i | 0.158893 | − | 0.592361i | ||||
\(227\) | 21.9181 | 1.45475 | 0.727377 | − | 0.686239i | \(-0.240739\pi\) | ||||
0.727377 | + | 0.686239i | \(0.240739\pi\) | |||||||
\(228\) | 4.02048 | − | 0.293788i | 0.266263 | − | 0.0194566i | ||||
\(229\) | −4.54827 | −0.300558 | −0.150279 | − | 0.988644i | \(-0.548017\pi\) | ||||
−0.150279 | + | 0.988644i | \(0.548017\pi\) | |||||||
\(230\) | 1.60950 | − | 6.00029i | 0.106127 | − | 0.395647i | ||||
\(231\) | −0.848770 | + | 0.577041i | −0.0558449 | + | 0.0379665i | ||||
\(232\) | 17.0358 | − | 17.0084i | 1.11845 | − | 1.11666i | ||||
\(233\) | − | 26.5742i | − | 1.74093i | −0.492228 | − | 0.870466i | \(-0.663817\pi\) | ||
0.492228 | − | 0.870466i | \(-0.336183\pi\) | |||||||
\(234\) | −3.38785 | + | 4.56254i | −0.221471 | + | 0.298263i | ||||
\(235\) | − | 21.3668i | − | 1.39382i | ||||||
\(236\) | 25.5342 | + | 14.7605i | 1.66214 | + | 0.960824i | ||||
\(237\) | −6.23218 | + | 4.23699i | −0.404824 | + | 0.275222i | ||||
\(238\) | 9.72735 | + | 2.60923i | 0.630530 | + | 0.169131i | ||||
\(239\) | −0.563864 | −0.0364733 | −0.0182366 | − | 0.999834i | \(-0.505805\pi\) | ||||
−0.0182366 | + | 0.999834i | \(0.505805\pi\) | |||||||
\(240\) | 15.0980 | + | 7.31537i | 0.974571 | + | 0.472205i | ||||
\(241\) | −20.6935 | −1.33299 | −0.666494 | − | 0.745510i | \(-0.732206\pi\) | ||||
−0.666494 | + | 0.745510i | \(0.732206\pi\) | |||||||
\(242\) | 14.8694 | + | 3.98851i | 0.955839 | + | 0.256391i | ||||
\(243\) | −2.42504 | + | 15.3987i | −0.155567 | + | 0.987825i | ||||
\(244\) | 17.6303 | + | 10.1914i | 1.12866 | + | 0.652441i | ||||
\(245\) | 9.49754i | 0.606776i | ||||||||
\(246\) | 0.177164 | − | 0.0616768i | 0.0112956 | − | 0.00393237i | ||||
\(247\) | − | 1.55873i | − | 0.0991795i | ||||||
\(248\) | 9.52564 | − | 9.51032i | 0.604879 | − | 0.603906i | ||||
\(249\) | −8.30298 | − | 12.2128i | −0.526180 | − | 0.773957i | ||||
\(250\) | 3.66973 | − | 13.6810i | 0.232094 | − | 0.865260i | ||||
\(251\) | 6.57418 | 0.414959 | 0.207479 | − | 0.978239i | \(-0.433474\pi\) | ||||
0.207479 | + | 0.978239i | \(0.433474\pi\) | |||||||
\(252\) | 6.53689 | + | 8.25063i | 0.411785 | + | 0.519741i | ||||
\(253\) | 0.612718 | 0.0385213 | ||||||||
\(254\) | 4.97351 | − | 18.5415i | 0.312065 | − | 1.16340i | ||||
\(255\) | −9.57206 | − | 14.0795i | −0.599425 | − | 0.881694i | ||||
\(256\) | −8.02970 | + | 13.8392i | −0.501857 | + | 0.864951i | ||||
\(257\) | − | 9.06984i | − | 0.565761i | −0.959155 | − | 0.282881i | \(-0.908710\pi\) | ||
0.959155 | − | 0.282881i | \(-0.0912900\pi\) | |||||||
\(258\) | −21.4255 | + | 7.45891i | −1.33389 | + | 0.464372i | ||||
\(259\) | − | 11.4184i | − | 0.709503i | ||||||
\(260\) | 3.24654 | − | 5.61621i | 0.201342 | − | 0.348303i | ||||
\(261\) | −23.7434 | − | 9.39103i | −1.46968 | − | 0.581290i | ||||
\(262\) | −24.7383 | − | 6.63572i | −1.52834 | − | 0.409956i | ||||
\(263\) | −3.87258 | −0.238794 | −0.119397 | − | 0.992847i | \(-0.538096\pi\) | ||||
−0.119397 | + | 0.992847i | \(0.538096\pi\) | |||||||
\(264\) | −0.311077 | + | 1.62517i | −0.0191455 | + | 0.100022i | ||||
\(265\) | 4.93842 | 0.303365 | ||||||||
\(266\) | −2.78867 | − | 0.748024i | −0.170984 | − | 0.0458643i | ||||
\(267\) | −0.329698 | + | 0.224148i | −0.0201772 | + | 0.0137176i | ||||
\(268\) | 1.00093 | − | 1.73151i | 0.0611415 | − | 0.105769i | ||||
\(269\) | 23.0395i | 1.40474i | 0.711812 | + | 0.702370i | \(0.247875\pi\) | ||||
−0.711812 | + | 0.702370i | \(0.752125\pi\) | |||||||
\(270\) | 0.740555 | − | 17.7792i | 0.0450687 | − | 1.08201i | ||||
\(271\) | − | 0.600063i | − | 0.0364512i | −0.999834 | − | 0.0182256i | \(-0.994198\pi\) | ||
0.999834 | − | 0.0182256i | \(-0.00580172\pi\) | |||||||
\(272\) | 14.0702 | − | 8.10332i | 0.853131 | − | 0.491336i | ||||
\(273\) | 3.36596 | − | 2.28837i | 0.203717 | − | 0.138499i | ||||
\(274\) | 2.56388 | − | 9.55829i | 0.154890 | − | 0.577438i | ||||
\(275\) | −0.291767 | −0.0175942 | ||||||||
\(276\) | −0.457978 | − | 6.26741i | −0.0275670 | − | 0.377254i | ||||
\(277\) | 5.70716 | 0.342910 | 0.171455 | − | 0.985192i | \(-0.445153\pi\) | ||||
0.171455 | + | 0.985192i | \(0.445153\pi\) | |||||||
\(278\) | −0.460111 | + | 1.71532i | −0.0275956 | + | 0.102878i | ||||
\(279\) | −13.2762 | − | 5.25104i | −0.794828 | − | 0.314372i | ||||
\(280\) | −8.48980 | − | 8.50347i | −0.507362 | − | 0.508179i | ||||
\(281\) | − | 13.7301i | − | 0.819070i | −0.912294 | − | 0.409535i | \(-0.865691\pi\) | ||
0.912294 | − | 0.409535i | \(-0.134309\pi\) | |||||||
\(282\) | −7.10605 | − | 20.4119i | −0.423159 | − | 1.21551i | ||||
\(283\) | − | 24.8048i | − | 1.47449i | −0.675625 | − | 0.737245i | \(-0.736126\pi\) | ||
0.675625 | − | 0.737245i | \(-0.263874\pi\) | |||||||
\(284\) | 5.36863 | + | 3.10342i | 0.318570 | + | 0.184154i | ||||
\(285\) | 2.74415 | + | 4.03637i | 0.162550 | + | 0.239094i | ||||
\(286\) | 0.617962 | + | 0.165760i | 0.0365408 | + | 0.00980159i | ||||
\(287\) | −0.134359 | −0.00793098 | ||||||||
\(288\) | 16.8562 | + | 1.96722i | 0.993259 | + | 0.115920i | ||||
\(289\) | 0.522866 | 0.0307568 | ||||||||
\(290\) | 28.1515 | + | 7.55125i | 1.65311 | + | 0.443425i | ||||
\(291\) | −0.714719 | − | 1.05128i | −0.0418976 | − | 0.0616271i | ||||
\(292\) | 20.3981 | + | 11.7914i | 1.19371 | + | 0.690042i | ||||
\(293\) | 14.2943i | 0.835079i | 0.908659 | + | 0.417540i | \(0.137108\pi\) | ||||
−0.908659 | + | 0.417540i | \(0.862892\pi\) | |||||||
\(294\) | 3.15864 | + | 9.07309i | 0.184216 | + | 0.529153i | ||||
\(295\) | 35.7098i | 2.07911i | ||||||||
\(296\) | −13.0064 | − | 13.0274i | −0.755984 | − | 0.757201i | ||||
\(297\) | 1.71258 | − | 0.383755i | 0.0993739 | − | 0.0222677i | ||||
\(298\) | −3.22926 | + | 12.0388i | −0.187066 | + | 0.697392i | ||||
\(299\) | −2.42986 | −0.140522 | ||||||||
\(300\) | 0.218082 | + | 2.98445i | 0.0125910 | + | 0.172307i | ||||
\(301\) | 16.2488 | 0.936566 | ||||||||
\(302\) | 4.70125 | − | 17.5265i | 0.270527 | − | 1.00854i | ||||
\(303\) | −10.6662 | + | 7.25146i | −0.612755 | + | 0.416585i | ||||
\(304\) | −4.03369 | + | 2.32309i | −0.231348 | + | 0.133238i | ||||
\(305\) | 24.6560i | 1.41180i | ||||||||
\(306\) | −13.8268 | − | 10.2669i | −0.790424 | − | 0.586918i | ||||
\(307\) | − | 20.1390i | − | 1.14940i | −0.818366 | − | 0.574698i | \(-0.805120\pi\) | ||
0.818366 | − | 0.574698i | \(-0.194880\pi\) | |||||||
\(308\) | 0.593111 | − | 1.02603i | 0.0337957 | − | 0.0584634i | ||||
\(309\) | 8.46243 | − | 5.75323i | 0.481411 | − | 0.327290i | ||||
\(310\) | 15.7410 | + | 4.22232i | 0.894031 | + | 0.239812i | ||||
\(311\) | 16.6924 | 0.946539 | 0.473270 | − | 0.880918i | \(-0.343074\pi\) | ||||
0.473270 | + | 0.880918i | \(0.343074\pi\) | |||||||
\(312\) | 1.23364 | − | 6.44494i | 0.0698410 | − | 0.364873i | ||||
\(313\) | −28.8533 | −1.63089 | −0.815443 | − | 0.578838i | \(-0.803507\pi\) | ||||
−0.815443 | + | 0.578838i | \(0.803507\pi\) | |||||||
\(314\) | 25.6831 | + | 6.88914i | 1.44938 | + | 0.388776i | ||||
\(315\) | −4.68756 | + | 11.8516i | −0.264114 | + | 0.667762i | ||||
\(316\) | 4.35498 | − | 7.53372i | 0.244987 | − | 0.423805i | ||||
\(317\) | 34.8536i | 1.95757i | 0.204883 | + | 0.978786i | \(0.434318\pi\) | ||||
−0.204883 | + | 0.978786i | \(0.565682\pi\) | |||||||
\(318\) | 4.71772 | − | 1.64239i | 0.264556 | − | 0.0921008i | ||||
\(319\) | 2.87468i | 0.160951i | ||||||||
\(320\) | −19.3723 | − | 0.0311662i | −1.08294 | − | 0.00174224i | ||||
\(321\) | 2.82413 | + | 4.15402i | 0.157628 | + | 0.231855i | ||||
\(322\) | −1.16607 | + | 4.34718i | −0.0649827 | + | 0.242259i | ||||
\(323\) | 4.72372 | 0.262835 | ||||||||
\(324\) | −5.20544 | − | 17.2309i | −0.289191 | − | 0.957271i | ||||
\(325\) | 1.15706 | 0.0641822 | ||||||||
\(326\) | −3.16619 | + | 11.8037i | −0.175359 | + | 0.653748i | ||||
\(327\) | 3.25448 | + | 4.78702i | 0.179973 | + | 0.264723i | ||||
\(328\) | −0.153292 | + | 0.153046i | −0.00846416 | + | 0.00845055i | ||||
\(329\) | 15.4801i | 0.853447i | ||||||||
\(330\) | −1.89205 | + | 0.658685i | −0.104154 | + | 0.0362594i | ||||
\(331\) | 23.5479i | 1.29431i | 0.762360 | + | 0.647154i | \(0.224041\pi\) | ||||
−0.762360 | + | 0.647154i | \(0.775959\pi\) | |||||||
\(332\) | 14.7634 | + | 8.53421i | 0.810246 | + | 0.468376i | ||||
\(333\) | −7.18139 | + | 18.1568i | −0.393538 | + | 0.994984i | ||||
\(334\) | −18.9759 | − | 5.09002i | −1.03831 | − | 0.278513i | ||||
\(335\) | 2.42154 | 0.132303 | ||||||||
\(336\) | −10.9384 | − | 5.29995i | −0.596740 | − | 0.289136i | ||||
\(337\) | −31.7590 | −1.73002 | −0.865010 | − | 0.501754i | \(-0.832688\pi\) | ||||
−0.865010 | + | 0.501754i | \(0.832688\pi\) | |||||||
\(338\) | 15.3064 | + | 4.10574i | 0.832559 | + | 0.223323i | ||||
\(339\) | 9.33835 | − | 6.34873i | 0.507189 | − | 0.344816i | ||||
\(340\) | 17.0199 | + | 9.83863i | 0.923035 | + | 0.533575i | ||||
\(341\) | 1.60739i | 0.0870452i | ||||||||
\(342\) | 3.96391 | + | 2.94335i | 0.214344 | + | 0.159158i | ||||
\(343\) | − | 19.1617i | − | 1.03463i | ||||||
\(344\) | 18.5385 | − | 18.5087i | 0.999528 | − | 0.997922i | ||||
\(345\) | 6.29218 | − | 4.27778i | 0.338760 | − | 0.230308i | ||||
\(346\) | 4.93781 | − | 18.4084i | 0.265458 | − | 0.989642i | ||||
\(347\) | −14.0740 | −0.755533 | −0.377766 | − | 0.925901i | \(-0.623308\pi\) | ||||
−0.377766 | + | 0.925901i | \(0.623308\pi\) | |||||||
\(348\) | 29.4047 | − | 2.14869i | 1.57626 | − | 0.115182i | ||||
\(349\) | 6.22850 | 0.333404 | 0.166702 | − | 0.986007i | \(-0.446688\pi\) | ||||
0.166702 | + | 0.986007i | \(0.446688\pi\) | |||||||
\(350\) | 0.555266 | − | 2.07006i | 0.0296802 | − | 0.110649i | ||||
\(351\) | −6.79157 | + | 1.52186i | −0.362507 | + | 0.0812306i | ||||
\(352\) | −0.492039 | − | 1.84621i | −0.0262258 | − | 0.0984034i | ||||
\(353\) | 14.8595i | 0.790892i | 0.918489 | + | 0.395446i | \(0.129410\pi\) | ||||
−0.918489 | + | 0.395446i | \(0.870590\pi\) | |||||||
\(354\) | 11.8762 | + | 34.1139i | 0.631212 | + | 1.81313i | ||||
\(355\) | 7.50807i | 0.398487i | ||||||||
\(356\) | 0.230390 | − | 0.398553i | 0.0122106 | − | 0.0211233i | ||||
\(357\) | 6.93491 | + | 10.2005i | 0.367034 | + | 0.539870i | ||||
\(358\) | 21.3756 | + | 5.73372i | 1.12974 | + | 0.303037i | ||||
\(359\) | −11.2390 | −0.593174 | −0.296587 | − | 0.955006i | \(-0.595848\pi\) | ||||
−0.296587 | + | 0.955006i | \(0.595848\pi\) | |||||||
\(360\) | 8.15182 | + | 18.8612i | 0.429638 | + | 0.994071i | ||||
\(361\) | 17.6458 | 0.928726 | ||||||||
\(362\) | 2.02156 | + | 0.542255i | 0.106251 | + | 0.0285003i | ||||
\(363\) | 10.6008 | + | 15.5927i | 0.556398 | + | 0.818405i | ||||
\(364\) | −2.35210 | + | 4.06892i | −0.123284 | + | 0.213269i | ||||
\(365\) | 28.5269i | 1.49317i | ||||||||
\(366\) | 8.19998 | + | 23.5541i | 0.428620 | + | 1.23120i | ||||
\(367\) | − | 30.6588i | − | 1.60038i | −0.599749 | − | 0.800188i | \(-0.704733\pi\) | ||
0.599749 | − | 0.800188i | \(-0.295267\pi\) | |||||||
\(368\) | 3.62140 | + | 6.28801i | 0.188778 | + | 0.327785i | ||||
\(369\) | 0.213649 | + | 0.0845030i | 0.0111221 | + | 0.00439905i | ||||
\(370\) | 5.77450 | − | 21.5276i | 0.300202 | − | 1.11917i | ||||
\(371\) | −3.57786 | −0.185753 | ||||||||
\(372\) | 16.4418 | − | 1.20145i | 0.852467 | − | 0.0622923i | ||||
\(373\) | 32.8342 | 1.70009 | 0.850045 | − | 0.526711i | \(-0.176575\pi\) | ||||
0.850045 | + | 0.526711i | \(0.176575\pi\) | |||||||
\(374\) | −0.502335 | + | 1.87273i | −0.0259751 | + | 0.0968366i | ||||
\(375\) | 14.3465 | − | 9.75355i | 0.740849 | − | 0.503671i | ||||
\(376\) | 17.6331 | + | 17.6615i | 0.909358 | + | 0.910822i | ||||
\(377\) | − | 11.4001i | − | 0.587136i | ||||||
\(378\) | −0.536528 | + | 12.8809i | −0.0275960 | + | 0.662523i | ||||
\(379\) | 20.9941i | 1.07840i | 0.842179 | + | 0.539198i | \(0.181273\pi\) | ||||
−0.842179 | + | 0.539198i | \(0.818727\pi\) | |||||||
\(380\) | −4.87933 | − | 2.82057i | −0.250305 | − | 0.144692i | ||||
\(381\) | 19.4435 | − | 13.2188i | 0.996119 | − | 0.677217i | ||||
\(382\) | 13.6330 | + | 3.65686i | 0.697523 | + | 0.187101i | ||||
\(383\) | −29.2172 | −1.49293 | −0.746464 | − | 0.665425i | \(-0.768250\pi\) | ||||
−0.746464 | + | 0.665425i | \(0.768250\pi\) | |||||||
\(384\) | −18.5169 | + | 6.41295i | −0.944934 | + | 0.327260i | ||||
\(385\) | 1.43491 | 0.0731297 | ||||||||
\(386\) | −14.4770 | − | 3.88326i | −0.736860 | − | 0.197653i | ||||
\(387\) | −25.8378 | − | 10.2194i | −1.31341 | − | 0.519482i | ||||
\(388\) | 1.27083 | + | 0.734623i | 0.0645167 | + | 0.0372949i | ||||
\(389\) | − | 15.0341i | − | 0.762259i | −0.924522 | − | 0.381129i | \(-0.875535\pi\) | ||
0.924522 | − | 0.381129i | \(-0.124465\pi\) | |||||||
\(390\) | 7.50330 | − | 2.61215i | 0.379944 | − | 0.132271i | ||||
\(391\) | − | 7.36367i | − | 0.372397i | ||||||
\(392\) | −7.83792 | − | 7.85054i | −0.395875 | − | 0.396512i | ||||
\(393\) | −17.6366 | − | 25.9417i | −0.889651 | − | 1.30859i | ||||
\(394\) | 0.0761463 | − | 0.283877i | 0.00383620 | − | 0.0143015i | ||||
\(395\) | 10.5360 | 0.530122 | ||||||||
\(396\) | −1.58843 | + | 1.25850i | −0.0798216 | + | 0.0632418i | ||||
\(397\) | −14.3972 | −0.722572 | −0.361286 | − | 0.932455i | \(-0.617662\pi\) | ||||
−0.361286 | + | 0.932455i | \(0.617662\pi\) | |||||||
\(398\) | −2.14306 | + | 7.98944i | −0.107422 | + | 0.400475i | ||||
\(399\) | −1.98812 | − | 2.92433i | −0.0995307 | − | 0.146400i | ||||
\(400\) | −1.72445 | − | 2.99425i | −0.0862227 | − | 0.149713i | ||||
\(401\) | − | 8.28541i | − | 0.413754i | −0.978367 | − | 0.206877i | \(-0.933670\pi\) | ||
0.978367 | − | 0.206877i | \(-0.0663300\pi\) | |||||||
\(402\) | 2.31331 | − | 0.805342i | 0.115378 | − | 0.0401668i | ||||
\(403\) | − | 6.37444i | − | 0.317533i | ||||||
\(404\) | 7.45341 | − | 12.8937i | 0.370821 | − | 0.641486i | ||||
\(405\) | 14.9077 | − | 15.8975i | 0.740771 | − | 0.789953i | ||||
\(406\) | −20.3956 | − | 5.47084i | −1.01222 | − | 0.271513i | ||||
\(407\) | 2.19829 | 0.108965 | ||||||||
\(408\) | 19.5314 | + | 3.73854i | 0.966947 | + | 0.185085i | ||||
\(409\) | 24.0722 | 1.19030 | 0.595148 | − | 0.803616i | \(-0.297093\pi\) | ||||
0.595148 | + | 0.803616i | \(0.297093\pi\) | |||||||
\(410\) | −0.253314 | − | 0.0679482i | −0.0125103 | − | 0.00335572i | ||||
\(411\) | 10.0233 | − | 6.81438i | 0.494411 | − | 0.336129i | ||||
\(412\) | −5.91346 | + | 10.2297i | −0.291335 | + | 0.503983i | ||||
\(413\) | − | 25.8716i | − | 1.27306i | ||||||
\(414\) | 4.58830 | − | 6.17922i | 0.225502 | − | 0.303692i | ||||
\(415\) | 20.6467i | 1.01351i | ||||||||
\(416\) | 1.95128 | + | 7.32152i | 0.0956693 | + | 0.358967i | ||||
\(417\) | −1.79876 | + | 1.22290i | −0.0880857 | + | 0.0598856i | ||||
\(418\) | 0.144011 | − | 0.536881i | 0.00704382 | − | 0.0262597i | ||||
\(419\) | −23.6806 | −1.15687 | −0.578436 | − | 0.815728i | \(-0.696337\pi\) | ||||
−0.578436 | + | 0.815728i | \(0.696337\pi\) | |||||||
\(420\) | −1.07253 | − | 14.6775i | −0.0523339 | − | 0.716187i | ||||
\(421\) | 35.4520 | 1.72782 | 0.863912 | − | 0.503643i | \(-0.168007\pi\) | ||||
0.863912 | + | 0.503643i | \(0.168007\pi\) | |||||||
\(422\) | 1.80982 | − | 6.74712i | 0.0881009 | − | 0.328445i | ||||
\(423\) | 9.73596 | − | 24.6155i | 0.473379 | − | 1.19685i | ||||
\(424\) | −4.08203 | + | 4.07547i | −0.198241 | + | 0.197922i | ||||
\(425\) | 3.50647i | 0.170089i | ||||||||
\(426\) | 2.49699 | + | 7.17253i | 0.120980 | + | 0.347510i | ||||
\(427\) | − | 17.8632i | − | 0.864460i | ||||||
\(428\) | −5.02155 | − | 2.90278i | −0.242726 | − | 0.140311i | ||||
\(429\) | 0.440562 | + | 0.648023i | 0.0212706 | + | 0.0312868i | ||||
\(430\) | 30.6347 | + | 8.21735i | 1.47734 | + | 0.396276i | ||||
\(431\) | −29.6967 | −1.43044 | −0.715221 | − | 0.698898i | \(-0.753674\pi\) | ||||
−0.715221 | + | 0.698898i | \(0.753674\pi\) | |||||||
\(432\) | 14.0603 | + | 15.3072i | 0.676474 | + | 0.736466i | ||||
\(433\) | −4.86045 | −0.233578 | −0.116789 | − | 0.993157i | \(-0.537260\pi\) | ||||
−0.116789 | + | 0.993157i | \(0.537260\pi\) | |||||||
\(434\) | −11.4043 | − | 3.05905i | −0.547424 | − | 0.146839i | ||||
\(435\) | 20.0700 | + | 29.5209i | 0.962282 | + | 1.41542i | ||||
\(436\) | −5.78675 | − | 3.34512i | −0.277135 | − | 0.160202i | ||||
\(437\) | 2.11104i | 0.100985i | ||||||||
\(438\) | 9.48732 | + | 27.2520i | 0.453322 | + | 1.30215i | ||||
\(439\) | − | 18.1792i | − | 0.867646i | −0.900998 | − | 0.433823i | \(-0.857164\pi\) | ||
0.900998 | − | 0.433823i | \(-0.142836\pi\) | |||||||
\(440\) | 1.63711 | − | 1.63447i | 0.0780460 | − | 0.0779205i | ||||
\(441\) | −4.32764 | + | 10.9416i | −0.206078 | + | 0.521028i | ||||
\(442\) | 1.99211 | − | 7.42669i | 0.0947550 | − | 0.353252i | ||||
\(443\) | 20.6724 | 0.982177 | 0.491089 | − | 0.871110i | \(-0.336599\pi\) | ||||
0.491089 | + | 0.871110i | \(0.336599\pi\) | |||||||
\(444\) | −1.64312 | − | 22.4860i | −0.0779789 | − | 1.06714i | ||||
\(445\) | 0.557380 | 0.0264223 | ||||||||
\(446\) | 4.33805 | − | 16.1725i | 0.205413 | − | 0.765789i | ||||
\(447\) | −12.6245 | + | 8.58284i | −0.597118 | + | 0.405954i | ||||
\(448\) | 14.0351 | + | 0.0225797i | 0.663096 | + | 0.00106679i | ||||
\(449\) | − | 24.1650i | − | 1.14042i | −0.821499 | − | 0.570209i | \(-0.806862\pi\) | ||
0.821499 | − | 0.570209i | \(-0.193138\pi\) | |||||||
\(450\) | −2.18488 | + | 2.94245i | −0.102996 | + | 0.138709i | ||||
\(451\) | − | 0.0258672i | − | 0.00121804i | ||||||
\(452\) | −6.52554 | + | 11.2886i | −0.306936 | + | 0.530970i | ||||
\(453\) | 18.3791 | − | 12.4952i | 0.863526 | − | 0.587074i | ||||
\(454\) | −29.9385 | − | 8.03060i | −1.40508 | − | 0.376895i | ||||
\(455\) | −5.69041 | −0.266771 | ||||||||
\(456\) | −5.59932 | − | 1.07178i | −0.262212 | − | 0.0501906i | ||||
\(457\) | −21.5576 | −1.00842 | −0.504211 | − | 0.863581i | \(-0.668217\pi\) | ||||
−0.504211 | + | 0.863581i | \(0.668217\pi\) | |||||||
\(458\) | 6.21260 | + | 1.66645i | 0.290296 | + | 0.0778679i | ||||
\(459\) | −4.61198 | − | 20.5818i | −0.215269 | − | 0.960678i | ||||
\(460\) | −4.39691 | + | 7.60625i | −0.205007 | + | 0.354643i | ||||
\(461\) | 18.8531i | 0.878077i | 0.898468 | + | 0.439039i | \(0.144681\pi\) | ||||
−0.898468 | + | 0.439039i | \(0.855319\pi\) | |||||||
\(462\) | 1.37078 | − | 0.477214i | 0.0637745 | − | 0.0222020i | ||||
\(463\) | − | 4.38292i | − | 0.203692i | −0.994800 | − | 0.101846i | \(-0.967525\pi\) | ||
0.994800 | − | 0.101846i | \(-0.0324748\pi\) | |||||||
\(464\) | −29.5013 | + | 16.9904i | −1.36957 | + | 0.788762i | ||||
\(465\) | 11.2222 | + | 16.5068i | 0.520419 | + | 0.765484i | ||||
\(466\) | −9.73656 | + | 36.2984i | −0.451037 | + | 1.68149i | ||||
\(467\) | −25.0496 | −1.15916 | −0.579579 | − | 0.814916i | \(-0.696783\pi\) | ||||
−0.579579 | + | 0.814916i | \(0.696783\pi\) | |||||||
\(468\) | 6.29924 | − | 4.99082i | 0.291182 | − | 0.230701i | ||||
\(469\) | −1.75439 | −0.0810102 | ||||||||
\(470\) | −7.82861 | + | 29.1855i | −0.361107 | + | 1.34623i | ||||
\(471\) | 18.3102 | + | 26.9324i | 0.843689 | + | 1.24098i | ||||
\(472\) | −29.4698 | − | 29.5172i | −1.35646 | − | 1.35864i | ||||
\(473\) | 3.12826i | 0.143837i | ||||||||
\(474\) | 10.0651 | − | 3.50400i | 0.462305 | − | 0.160944i | ||||
\(475\) | − | 1.00525i | − | 0.0461239i | ||||||
\(476\) | −12.3309 | − | 7.12804i | −0.565184 | − | 0.326713i | ||||
\(477\) | 5.68928 | + | 2.25023i | 0.260494 | + | 0.103031i | ||||
\(478\) | 0.770197 | + | 0.206595i | 0.0352280 | + | 0.00944943i | ||||
\(479\) | 12.3441 | 0.564016 | 0.282008 | − | 0.959412i | \(-0.408999\pi\) | ||||
0.282008 | + | 0.959412i | \(0.408999\pi\) | |||||||
\(480\) | −17.9425 | − | 15.5240i | −0.818958 | − | 0.708572i | ||||
\(481\) | −8.71776 | −0.397496 | ||||||||
\(482\) | 28.2659 | + | 7.58194i | 1.28748 | + | 0.345348i | ||||
\(483\) | −4.55865 | + | 3.09923i | −0.207426 | + | 0.141020i | ||||
\(484\) | −18.8491 | − | 10.8960i | −0.856778 | − | 0.495274i | ||||
\(485\) | 1.77727i | 0.0807015i | ||||||||
\(486\) | 8.95438 | − | 20.1450i | 0.406179 | − | 0.913794i | ||||
\(487\) | − | 33.9623i | − | 1.53898i | −0.638659 | − | 0.769490i | \(-0.720511\pi\) | ||
0.638659 | − | 0.769490i | \(-0.279489\pi\) | |||||||
\(488\) | −20.3476 | − | 20.3804i | −0.921092 | − | 0.922575i | ||||
\(489\) | −12.3779 | + | 8.41522i | −0.559750 | + | 0.380549i | ||||
\(490\) | 3.47982 | − | 12.9730i | 0.157202 | − | 0.586058i | ||||
\(491\) | −4.55227 | −0.205441 | −0.102721 | − | 0.994710i | \(-0.532755\pi\) | ||||
−0.102721 | + | 0.994710i | \(0.532755\pi\) | |||||||
\(492\) | −0.264592 | + | 0.0193345i | −0.0119287 | + | 0.000871665i | ||||
\(493\) | 34.5480 | 1.55597 | ||||||||
\(494\) | −0.571105 | + | 2.12911i | −0.0256952 | + | 0.0957932i | ||||
\(495\) | −2.28170 | − | 0.902461i | −0.102555 | − | 0.0405626i | ||||
\(496\) | −16.4958 | + | 9.50030i | −0.740685 | + | 0.426576i | ||||
\(497\) | − | 5.43956i | − | 0.243997i | ||||||
\(498\) | 6.86658 | + | 19.7240i | 0.307699 | + | 0.883853i | ||||
\(499\) | − | 22.9604i | − | 1.02785i | −0.857836 | − | 0.513923i | \(-0.828192\pi\) | ||
0.857836 | − | 0.513923i | \(-0.171808\pi\) | |||||||
\(500\) | −10.0252 | + | 17.3426i | −0.448340 | + | 0.775586i | ||||
\(501\) | −13.5284 | − | 19.8990i | −0.604406 | − | 0.889020i | ||||
\(502\) | −8.97985 | − | 2.40873i | −0.400790 | − | 0.107507i | ||||
\(503\) | 2.01888 | 0.0900173 | 0.0450087 | − | 0.998987i | \(-0.485668\pi\) | ||||
0.0450087 | + | 0.998987i | \(0.485668\pi\) | |||||||
\(504\) | −5.90595 | − | 13.6648i | −0.263072 | − | 0.608680i | ||||
\(505\) | 18.0319 | 0.802411 | ||||||||
\(506\) | −0.836929 | − | 0.224495i | −0.0372060 | − | 0.00998001i | ||||
\(507\) | 10.9124 | + | 16.0510i | 0.484636 | + | 0.712850i | ||||
\(508\) | −13.5869 | + | 23.5041i | −0.602821 | + | 1.04282i | ||||
\(509\) | 27.2643i | 1.20847i | 0.796807 | + | 0.604234i | \(0.206521\pi\) | ||||
−0.796807 | + | 0.604234i | \(0.793479\pi\) | |||||||
\(510\) | 7.91611 | + | 22.7387i | 0.350531 | + | 1.00689i | ||||
\(511\) | − | 20.6676i | − | 0.914280i | ||||||
\(512\) | 16.0386 | − | 15.9613i | 0.708811 | − | 0.705398i | ||||
\(513\) | 1.32218 | + | 5.90048i | 0.0583756 | + | 0.260512i | ||||
\(514\) | −3.32311 | + | 12.3887i | −0.146576 | + | 0.546444i | ||||
\(515\) | −14.3064 | −0.630414 | ||||||||
\(516\) | 31.9985 | − | 2.33822i | 1.40866 | − | 0.102935i | ||||
\(517\) | −2.98027 | −0.131072 | ||||||||
\(518\) | −4.18360 | + | 15.5967i | −0.183817 | + | 0.685278i | ||||
\(519\) | 19.3039 | − | 13.1239i | 0.847347 | − | 0.576074i | ||||
\(520\) | −6.49227 | + | 6.48183i | −0.284705 | + | 0.284247i | ||||
\(521\) | − | 19.6443i | − | 0.860631i | −0.902679 | − | 0.430316i | \(-0.858402\pi\) | ||
0.902679 | − | 0.430316i | \(-0.141598\pi\) | |||||||
\(522\) | 28.9910 | + | 21.5268i | 1.26890 | + | 0.942204i | ||||
\(523\) | − | 23.6600i | − | 1.03458i | −0.855810 | − | 0.517291i | \(-0.826941\pi\) | ||
0.855810 | − | 0.517291i | \(-0.173059\pi\) | |||||||
\(524\) | 31.3594 | + | 18.1278i | 1.36994 | + | 0.791917i | ||||
\(525\) | 2.17076 | − | 1.47581i | 0.0947398 | − | 0.0644095i | ||||
\(526\) | 5.28967 | + | 1.41888i | 0.230640 | + | 0.0618662i | ||||
\(527\) | 19.3177 | 0.841493 | ||||||||
\(528\) | 1.02036 | − | 2.10589i | 0.0444054 | − | 0.0916471i | ||||
\(529\) | −19.7092 | −0.856920 | ||||||||
\(530\) | −6.74552 | − | 1.80939i | −0.293007 | − | 0.0785951i | ||||
\(531\) | −16.2715 | + | 41.1393i | −0.706122 | + | 1.78529i | ||||
\(532\) | 3.53505 | + | 2.04349i | 0.153264 | + | 0.0885966i | ||||
\(533\) | 0.102581i | 0.00444329i | ||||||||
\(534\) | 0.532470 | − | 0.185370i | 0.0230422 | − | 0.00802176i | ||||
\(535\) | − | 7.02267i | − | 0.303617i | ||||||
\(536\) | −2.00161 | + | 1.99839i | −0.0864563 | + | 0.0863173i | ||||
\(537\) | 15.2393 | + | 22.4155i | 0.657624 | + | 0.967298i | ||||
\(538\) | 8.44146 | − | 31.4702i | 0.363937 | − | 1.35678i | ||||
\(539\) | 1.32473 | 0.0570602 | ||||||||
\(540\) | −7.52568 | + | 24.0137i | −0.323854 | + | 1.03339i | ||||
\(541\) | 20.6306 | 0.886978 | 0.443489 | − | 0.896280i | \(-0.353741\pi\) | ||||
0.443489 | + | 0.896280i | \(0.353741\pi\) | |||||||
\(542\) | −0.219858 | + | 0.819642i | −0.00944371 | + | 0.0352067i | ||||
\(543\) | 1.44122 | + | 2.11990i | 0.0618489 | + | 0.0909735i | ||||
\(544\) | −22.1878 | + | 5.91335i | −0.951296 | + | 0.253533i | ||||
\(545\) | − | 8.09281i | − | 0.346658i | ||||||
\(546\) | −5.43610 | + | 1.89249i | −0.232644 | + | 0.0809910i | ||||
\(547\) | − | 30.6770i | − | 1.31165i | −0.754912 | − | 0.655826i | \(-0.772320\pi\) | ||
0.754912 | − | 0.655826i | \(-0.227680\pi\) | |||||||
\(548\) | −7.00416 | + | 12.1165i | −0.299203 | + | 0.517593i | ||||
\(549\) | −11.2347 | + | 28.4049i | −0.479487 | + | 1.21229i | ||||
\(550\) | 0.398533 | + | 0.106901i | 0.0169935 | + | 0.00455828i | ||||
\(551\) | −9.90436 | −0.421940 | ||||||||
\(552\) | −1.67076 | + | 8.72862i | −0.0711123 | + | 0.371515i | ||||
\(553\) | −7.63325 | −0.324599 | ||||||||
\(554\) | −7.79556 | − | 2.09106i | −0.331202 | − | 0.0888404i | ||||
\(555\) | 22.5749 | − | 15.3477i | 0.958250 | − | 0.651472i | ||||
\(556\) | 1.25696 | − | 2.17442i | 0.0533068 | − | 0.0922159i | ||||
\(557\) | − | 41.7157i | − | 1.76755i | −0.467910 | − | 0.883776i | \(-0.654993\pi\) | ||
0.467910 | − | 0.883776i | \(-0.345007\pi\) | |||||||
\(558\) | 16.2104 | + | 12.0368i | 0.686243 | + | 0.509560i | ||||
\(559\) | − | 12.4057i | − | 0.524706i | ||||||
\(560\) | 8.48084 | + | 14.7257i | 0.358381 | + | 0.622275i | ||||
\(561\) | −1.96383 | + | 1.33512i | −0.0829131 | + | 0.0563690i | ||||
\(562\) | −5.03060 | + | 18.7543i | −0.212203 | + | 0.791104i | ||||
\(563\) | 37.7631 | 1.59152 | 0.795762 | − | 0.605610i | \(-0.207071\pi\) | ||||
0.795762 | + | 0.605610i | \(0.207071\pi\) | |||||||
\(564\) | 2.22761 | + | 30.4847i | 0.0937993 | + | 1.28364i | ||||
\(565\) | −15.7872 | −0.664171 | ||||||||
\(566\) | −9.08826 | + | 33.8815i | −0.382008 | + | 1.42415i | ||||
\(567\) | −10.8006 | + | 11.5177i | −0.453581 | + | 0.483696i | ||||
\(568\) | −6.19609 | − | 6.20607i | −0.259982 | − | 0.260401i | ||||
\(569\) | − | 3.56714i | − | 0.149542i | −0.997201 | − | 0.0747712i | \(-0.976177\pi\) | ||
0.997201 | − | 0.0747712i | \(-0.0238226\pi\) | |||||||
\(570\) | −2.26942 | − | 6.51882i | −0.0950555 | − | 0.273043i | ||||
\(571\) | − | 7.04923i | − | 0.295001i | −0.989062 | − | 0.147501i | \(-0.952877\pi\) | ||
0.989062 | − | 0.147501i | \(-0.0471228\pi\) | |||||||
\(572\) | −0.783357 | − | 0.452832i | −0.0327538 | − | 0.0189339i | ||||
\(573\) | 9.71933 | + | 14.2962i | 0.406031 | + | 0.597230i | ||||
\(574\) | 0.183525 | + | 0.0492281i | 0.00766019 | + | 0.00205474i | ||||
\(575\) | −1.56705 | −0.0653506 | ||||||||
\(576\) | −22.3035 | − | 8.86304i | −0.929313 | − | 0.369293i | ||||
\(577\) | −31.1050 | −1.29492 | −0.647459 | − | 0.762100i | \(-0.724168\pi\) | ||||
−0.647459 | + | 0.762100i | \(0.724168\pi\) | |||||||
\(578\) | −0.714197 | − | 0.191574i | −0.0297067 | − | 0.00796842i | ||||
\(579\) | −10.3211 | − | 15.1813i | −0.428929 | − | 0.630911i | ||||
\(580\) | −35.6861 | − | 20.6289i | −1.48179 | − | 0.856569i | ||||
\(581\) | − | 14.9584i | − | 0.620581i | ||||||
\(582\) | 0.591074 | + | 1.69784i | 0.0245008 | + | 0.0703777i | ||||
\(583\) | − | 0.688817i | − | 0.0285279i | ||||||
\(584\) | −23.5420 | − | 23.5799i | −0.974176 | − | 0.975745i | ||||
\(585\) | 9.04853 | + | 3.57889i | 0.374110 | + | 0.147969i | ||||
\(586\) | 5.23730 | − | 19.5249i | 0.216351 | − | 0.806567i | ||||
\(587\) | 21.9550 | 0.906178 | 0.453089 | − | 0.891465i | \(-0.350322\pi\) | ||||
0.453089 | + | 0.891465i | \(0.350322\pi\) | |||||||
\(588\) | −0.990173 | − | 13.5505i | −0.0408340 | − | 0.558812i | ||||
\(589\) | −5.53807 | −0.228192 | ||||||||
\(590\) | 13.0838 | − | 48.7770i | 0.538651 | − | 2.00812i | ||||
\(591\) | 0.297687 | − | 0.202384i | 0.0122452 | − | 0.00832498i | ||||
\(592\) | 12.9927 | + | 22.5599i | 0.533998 | + | 0.927206i | ||||
\(593\) | 16.2319i | 0.666564i | 0.942827 | + | 0.333282i | \(0.108156\pi\) | ||||
−0.942827 | + | 0.333282i | \(0.891844\pi\) | |||||||
\(594\) | −2.47986 | − | 0.103294i | −0.101750 | − | 0.00423819i | ||||
\(595\) | − | 17.2448i | − | 0.706967i | ||||||
\(596\) | 8.82186 | − | 15.2610i | 0.361358 | − | 0.625115i | ||||
\(597\) | −8.37810 | + | 5.69590i | −0.342893 | + | 0.233118i | ||||
\(598\) | 3.31901 | + | 0.890279i | 0.135724 | + | 0.0364062i | ||||
\(599\) | 14.6050 | 0.596743 | 0.298371 | − | 0.954450i | \(-0.403557\pi\) | ||||
0.298371 | + | 0.954450i | \(0.403557\pi\) | |||||||
\(600\) | 0.795592 | − | 4.15644i | 0.0324799 | − | 0.169686i | ||||
\(601\) | 31.2179 | 1.27341 | 0.636703 | − | 0.771109i | \(-0.280298\pi\) | ||||
0.636703 | + | 0.771109i | \(0.280298\pi\) | |||||||
\(602\) | −22.1947 | − | 5.95343i | −0.904588 | − | 0.242644i | ||||
\(603\) | 2.78972 | + | 1.10339i | 0.113606 | + | 0.0449337i | ||||
\(604\) | −12.8431 | + | 22.2174i | −0.522580 | + | 0.904015i | ||||
\(605\) | − | 26.3606i | − | 1.07171i | ||||||
\(606\) | 17.2261 | − | 5.99697i | 0.699761 | − | 0.243610i | ||||
\(607\) | 34.1317i | 1.38536i | 0.721244 | + | 0.692681i | \(0.243571\pi\) | ||||
−0.721244 | + | 0.692681i | \(0.756429\pi\) | |||||||
\(608\) | 6.36089 | − | 1.69526i | 0.257968 | − | 0.0687518i | ||||
\(609\) | −14.5406 | − | 21.3878i | −0.589215 | − | 0.866676i | ||||
\(610\) | 9.03377 | − | 33.6784i | 0.365767 | − | 1.36360i | ||||
\(611\) | 11.8188 | 0.478139 | ||||||||
\(612\) | 15.1247 | + | 19.0898i | 0.611378 | + | 0.771660i | ||||
\(613\) | 38.0864 | 1.53829 | 0.769147 | − | 0.639072i | \(-0.220681\pi\) | ||||
0.769147 | + | 0.639072i | \(0.220681\pi\) | |||||||
\(614\) | −7.37878 | + | 27.5085i | −0.297783 | + | 1.11015i | ||||
\(615\) | −0.180595 | − | 0.265637i | −0.00728230 | − | 0.0107115i | ||||
\(616\) | −1.18608 | + | 1.18417i | −0.0477883 | + | 0.0477115i | ||||
\(617\) | 31.6358i | 1.27361i | 0.771025 | + | 0.636805i | \(0.219744\pi\) | ||||
−0.771025 | + | 0.636805i | \(0.780256\pi\) | |||||||
\(618\) | −13.6670 | + | 4.75794i | −0.549767 | + | 0.191392i | ||||
\(619\) | 7.59864i | 0.305415i | 0.988271 | + | 0.152708i | \(0.0487993\pi\) | ||||
−0.988271 | + | 0.152708i | \(0.951201\pi\) | |||||||
\(620\) | −19.9541 | − | 11.5348i | −0.801375 | − | 0.463247i | ||||
\(621\) | 9.19808 | − | 2.06111i | 0.369106 | − | 0.0827093i | ||||
\(622\) | −22.8006 | − | 6.11596i | −0.914221 | − | 0.245228i | ||||
\(623\) | −0.403819 | −0.0161787 | ||||||||
\(624\) | −4.04643 | + | 8.35132i | −0.161987 | + | 0.334320i | ||||
\(625\) | −28.5730 | −1.14292 | ||||||||
\(626\) | 39.4115 | + | 10.5716i | 1.57520 | + | 0.422527i | ||||
\(627\) | 0.562999 | − | 0.382758i | 0.0224840 | − | 0.0152859i | ||||
\(628\) | −32.5571 | − | 18.8201i | −1.29917 | − | 0.751004i | ||||
\(629\) | − | 26.4191i | − | 1.05340i | ||||||
\(630\) | 10.7452 | − | 14.4709i | 0.428099 | − | 0.576536i | ||||
\(631\) | 24.2502i | 0.965384i | 0.875790 | + | 0.482692i | \(0.160341\pi\) | ||||
−0.875790 | + | 0.482692i | \(0.839659\pi\) | |||||||
\(632\) | −8.70889 | + | 8.69489i | −0.346421 | + | 0.345864i | ||||
\(633\) | 7.07534 | − | 4.81021i | 0.281220 | − | 0.191189i | ||||
\(634\) | 12.7701 | − | 47.6075i | 0.507164 | − | 1.89073i | ||||
\(635\) | −32.8706 | −1.30443 | ||||||||
\(636\) | −7.04581 | + | 0.514858i | −0.279385 | + | 0.0204155i | ||||
\(637\) | −5.25348 | −0.208151 | ||||||||
\(638\) | 1.05326 | − | 3.92661i | 0.0416989 | − | 0.155456i | ||||
\(639\) | −3.42112 | + | 8.64963i | −0.135337 | + | 0.342174i | ||||
\(640\) | 26.4497 | + | 7.14040i | 1.04552 | + | 0.282249i | ||||
\(641\) | − | 3.70656i | − | 0.146400i | −0.997317 | − | 0.0732001i | \(-0.976679\pi\) | ||
0.997317 | − | 0.0732001i | \(-0.0233212\pi\) | |||||||
\(642\) | −2.33556 | − | 6.70882i | −0.0921773 | − | 0.264776i | ||||
\(643\) | 3.33117i | 0.131368i | 0.997840 | + | 0.0656842i | \(0.0209230\pi\) | ||||
−0.997840 | + | 0.0656842i | \(0.979077\pi\) | |||||||
\(644\) | 3.18554 | − | 5.51069i | 0.125528 | − | 0.217152i | ||||
\(645\) | 21.8404 | + | 32.1250i | 0.859963 | + | 1.26492i | ||||
\(646\) | −6.45226 | − | 1.73073i | −0.253861 | − | 0.0680948i | ||||
\(647\) | −5.05294 | −0.198652 | −0.0993258 | − | 0.995055i | \(-0.531669\pi\) | ||||
−0.0993258 | + | 0.995055i | \(0.531669\pi\) | |||||||
\(648\) | 0.797003 | + | 25.4434i | 0.0313092 | + | 0.999510i | ||||
\(649\) | 4.98085 | 0.195516 | ||||||||
\(650\) | −1.58046 | − | 0.423938i | −0.0619908 | − | 0.0166282i | ||||
\(651\) | −8.13045 | − | 11.9591i | −0.318658 | − | 0.468713i | ||||
\(652\) | 8.64958 | − | 14.9630i | 0.338744 | − | 0.585995i | ||||
\(653\) | 25.1373i | 0.983700i | 0.870680 | + | 0.491850i | \(0.163679\pi\) | ||||
−0.870680 | + | 0.491850i | \(0.836321\pi\) | |||||||
\(654\) | −2.69147 | − | 7.73114i | −0.105245 | − | 0.302311i | ||||
\(655\) | 43.8564i | 1.71361i | ||||||||
\(656\) | 0.265461 | − | 0.152885i | 0.0103645 | − | 0.00596914i | ||||
\(657\) | −12.9985 | + | 32.8643i | −0.507121 | + | 1.28216i | ||||
\(658\) | 5.67179 | − | 21.1447i | 0.221109 | − | 0.824307i | ||||
\(659\) | −28.1599 | −1.09695 | −0.548477 | − | 0.836166i | \(-0.684792\pi\) | ||||
−0.548477 | + | 0.836166i | \(0.684792\pi\) | |||||||
\(660\) | 2.82574 | − | 0.206485i | 0.109992 | − | 0.00803742i | ||||
\(661\) | −45.2959 | −1.76181 | −0.880904 | − | 0.473295i | \(-0.843064\pi\) | ||||
−0.880904 | + | 0.473295i | \(0.843064\pi\) | |||||||
\(662\) | 8.62774 | − | 32.1647i | 0.335327 | − | 1.25011i | ||||
\(663\) | 7.78797 | − | 5.29470i | 0.302460 | − | 0.205629i | ||||
\(664\) | −17.0389 | − | 17.0663i | −0.661236 | − | 0.662301i | ||||
\(665\) | 4.94380i | 0.191712i | ||||||||
\(666\) | 16.4617 | − | 22.1696i | 0.637879 | − | 0.859055i | ||||
\(667\) | 15.4396i | 0.597824i | ||||||||
\(668\) | 24.0547 | + | 13.9052i | 0.930704 | + | 0.538008i | ||||
\(669\) | 16.9592 | − | 11.5298i | 0.655681 | − | 0.445769i | ||||
\(670\) | −3.30764 | − | 0.887230i | −0.127785 | − | 0.0342767i | ||||
\(671\) | 3.43906 | 0.132763 | ||||||||
\(672\) | 12.9992 | + | 11.2471i | 0.501456 | + | 0.433866i | ||||
\(673\) | −29.2754 | −1.12848 | −0.564242 | − | 0.825609i | \(-0.690832\pi\) | ||||
−0.564242 | + | 0.825609i | \(0.690832\pi\) | |||||||
\(674\) | 43.3804 | + | 11.6362i | 1.67095 | + | 0.448210i | ||||
\(675\) | −4.37999 | + | 0.981468i | −0.168586 | + | 0.0377767i | ||||
\(676\) | −19.4031 | − | 11.2163i | −0.746274 | − | 0.431395i | ||||
\(677\) | − | 21.5652i | − | 0.828818i | −0.910091 | − | 0.414409i | \(-0.863988\pi\) | ||
0.910091 | − | 0.414409i | \(-0.136012\pi\) | |||||||
\(678\) | −15.0816 | + | 5.25041i | −0.579206 | + | 0.201641i | ||||
\(679\) | − | 1.28762i | − | 0.0494143i | ||||||
\(680\) | −19.6432 | − | 19.6748i | −0.753282 | − | 0.754495i | ||||
\(681\) | −21.3440 | − | 31.3949i | −0.817904 | − | 1.20305i | ||||
\(682\) | 0.588935 | − | 2.19558i | 0.0225515 | − | 0.0840732i | ||||
\(683\) | 5.80503 | 0.222123 | 0.111062 | − | 0.993814i | \(-0.464575\pi\) | ||||
0.111062 | + | 0.993814i | \(0.464575\pi\) | |||||||
\(684\) | −4.33599 | − | 5.47274i | −0.165791 | − | 0.209255i | ||||
\(685\) | −16.9451 | −0.647438 | ||||||||
\(686\) | −7.02067 | + | 26.1734i | −0.268050 | + | 0.999306i | ||||
\(687\) | 4.42914 | + | 6.51482i | 0.168982 | + | 0.248556i | ||||
\(688\) | −32.1037 | + | 18.4892i | −1.22394 | + | 0.704893i | ||||
\(689\) | 2.73164i | 0.104067i | ||||||||
\(690\) | −10.1620 | + | 3.53773i | −0.386861 | + | 0.134679i | ||||
\(691\) | 39.6635i | 1.50887i | 0.656374 | + | 0.754436i | \(0.272089\pi\) | ||||
−0.656374 | + | 0.754436i | \(0.727911\pi\) | |||||||
\(692\) | −13.4894 | + | 23.3354i | −0.512789 | + | 0.887077i | ||||
\(693\) | 1.65308 | + | 0.653828i | 0.0627952 | + | 0.0248369i | ||||
\(694\) | 19.2241 | + | 5.15660i | 0.729736 | + | 0.195742i | ||||
\(695\) | 3.04094 | 0.115349 | ||||||||
\(696\) | −40.9520 | − | 7.83869i | −1.55228 | − | 0.297125i | ||||
\(697\) | −0.310873 | −0.0117751 | ||||||||
\(698\) | −8.50768 | − | 2.28207i | −0.322020 | − | 0.0863777i | ||||
\(699\) | −38.0642 | + | 25.8782i | −1.43972 | + | 0.978802i | ||||
\(700\) | −1.51691 | + | 2.62411i | −0.0573337 | + | 0.0991820i | ||||
\(701\) | − | 43.4754i | − | 1.64204i | −0.570896 | − | 0.821022i | \(-0.693404\pi\) | ||
0.570896 | − | 0.821022i | \(-0.306596\pi\) | |||||||
\(702\) | 9.83439 | + | 0.409632i | 0.371175 | + | 0.0154605i | ||||
\(703\) | 7.57394i | 0.285656i | ||||||||
\(704\) | −0.00434710 | + | 2.70207i | −0.000163838 | + | 0.101838i | ||||
\(705\) | −30.6052 | + | 20.8072i | −1.15266 | + | 0.783643i | ||||
\(706\) | 5.44440 | − | 20.2970i | 0.204903 | − | 0.763888i | ||||
\(707\) | −13.0640 | −0.491324 | ||||||||
\(708\) | −3.72295 | − | 50.9484i | −0.139917 | − | 1.91476i | ||||
\(709\) | −17.2998 | −0.649706 | −0.324853 | − | 0.945765i | \(-0.605315\pi\) | ||||
−0.324853 | + | 0.945765i | \(0.605315\pi\) | |||||||
\(710\) | 2.75089 | − | 10.2555i | 0.103239 | − | 0.384881i | ||||
\(711\) | 12.1379 | + | 4.80080i | 0.455207 | + | 0.180044i | ||||
\(712\) | −0.460722 | + | 0.459982i | −0.0172663 | + | 0.0172385i | ||||
\(713\) | 8.63314i | 0.323314i | ||||||||
\(714\) | −5.73518 | − | 16.4741i | −0.214634 | − | 0.616528i | ||||
\(715\) | − | 1.09553i | − | 0.0409705i | ||||||
\(716\) | −27.0967 | − | 15.6637i | −1.01265 | − | 0.585380i | ||||
\(717\) | 0.549095 | + | 0.807664i | 0.0205063 | + | 0.0301628i | ||||
\(718\) | 15.3517 | + | 4.11789i | 0.572921 | + | 0.153678i | ||||
\(719\) | 15.7041 | 0.585662 | 0.292831 | − | 0.956164i | \(-0.405403\pi\) | ||||
0.292831 | + | 0.956164i | \(0.405403\pi\) | |||||||
\(720\) | −4.22421 | − | 28.7497i | −0.157427 | − | 1.07144i | ||||
\(721\) | 10.3649 | 0.386009 | ||||||||
\(722\) | −24.1029 | − | 6.46527i | −0.897016 | − | 0.240612i | ||||
\(723\) | 20.1515 | + | 29.6409i | 0.749444 | + | 1.10236i | ||||
\(724\) | −2.56262 | − | 1.48136i | −0.0952390 | − | 0.0550544i | ||||
\(725\) | − | 7.35211i | − | 0.273051i | ||||||
\(726\) | −8.76688 | − | 25.1826i | −0.325370 | − | 0.934612i | ||||
\(727\) | 18.6188i | 0.690534i | 0.938505 | + | 0.345267i | \(0.112212\pi\) | ||||
−0.938505 | + | 0.345267i | \(0.887788\pi\) | |||||||
\(728\) | 4.70362 | − | 4.69606i | 0.174328 | − | 0.174047i | ||||
\(729\) | 24.4182 | − | 11.5218i | 0.904378 | − | 0.426733i | ||||
\(730\) | 10.4520 | − | 38.9656i | 0.386846 | − | 1.44218i | ||||
\(731\) | 37.5955 | 1.39052 | ||||||||
\(732\) | −2.57053 | − | 35.1777i | −0.0950097 | − | 1.30020i | ||||
\(733\) | 37.1929 | 1.37375 | 0.686875 | − | 0.726776i | \(-0.258982\pi\) | ||||
0.686875 | + | 0.726776i | \(0.258982\pi\) | |||||||
\(734\) | −11.2331 | + | 41.8777i | −0.414622 | + | 1.54573i | ||||
\(735\) | 13.6040 | − | 9.24879i | 0.501792 | − | 0.341147i | ||||
\(736\) | −2.64269 | − | 9.91581i | −0.0974108 | − | 0.365502i | ||||
\(737\) | − | 0.337759i | − | 0.0124415i | ||||||
\(738\) | −0.260868 | − | 0.193704i | −0.00960270 | − | 0.00713035i | ||||
\(739\) | − | 47.8820i | − | 1.76137i | −0.473703 | − | 0.880685i | \(-0.657083\pi\) | ||
0.473703 | − | 0.880685i | \(-0.342917\pi\) | |||||||
\(740\) | −15.7751 | + | 27.2895i | −0.579904 | + | 1.00318i | ||||
\(741\) | −2.23268 | + | 1.51790i | −0.0820197 | + | 0.0557616i | ||||
\(742\) | 4.88709 | + | 1.31090i | 0.179411 | + | 0.0481246i | ||||
\(743\) | 9.47111 | 0.347461 | 0.173731 | − | 0.984793i | \(-0.444418\pi\) | ||||
0.173731 | + | 0.984793i | \(0.444418\pi\) | |||||||
\(744\) | −22.8985 | − | 4.38304i | −0.839500 | − | 0.160690i | ||||
\(745\) | 21.3426 | 0.781934 | ||||||||
\(746\) | −44.8491 | − | 12.0302i | −1.64204 | − | 0.440456i | ||||
\(747\) | −9.40785 | + | 23.7859i | −0.344215 | + | 0.870282i | ||||
\(748\) | 1.37231 | − | 2.37396i | 0.0501765 | − | 0.0868007i | ||||
\(749\) | 5.08789i | 0.185907i | ||||||||
\(750\) | −23.1699 | + | 8.06620i | −0.846044 | + | 0.294536i | ||||
\(751\) | 14.4388i | 0.526880i | 0.964676 | + | 0.263440i | \(0.0848570\pi\) | ||||
−0.964676 | + | 0.263440i | \(0.915143\pi\) | |||||||
\(752\) | −17.6145 | − | 30.5849i | −0.642335 | − | 1.11532i | ||||
\(753\) | −6.40199 | − | 9.41669i | −0.233302 | − | 0.343163i | ||||
\(754\) | −4.17691 | + | 15.5717i | −0.152114 | + | 0.567089i | ||||
\(755\) | −31.0713 | −1.13080 | ||||||||
\(756\) | 5.45232 | − | 17.3978i | 0.198299 | − | 0.632752i | ||||
\(757\) | −44.9004 | −1.63193 | −0.815966 | − | 0.578100i | \(-0.803794\pi\) | ||||
−0.815966 | + | 0.578100i | \(0.803794\pi\) | |||||||
\(758\) | 7.69208 | − | 28.6765i | 0.279389 | − | 1.04158i | ||||
\(759\) | −0.596670 | − | 0.877642i | −0.0216578 | − | 0.0318564i | ||||
\(760\) | 5.63138 | + | 5.64045i | 0.204272 | + | 0.204601i | ||||
\(761\) | − | 2.80263i | − | 0.101595i | −0.998709 | − | 0.0507976i | \(-0.983824\pi\) | ||
0.998709 | − | 0.0507976i | \(-0.0161763\pi\) | |||||||
\(762\) | −31.4016 | + | 10.9319i | −1.13756 | + | 0.396022i | ||||
\(763\) | 5.86320i | 0.212262i | ||||||||
\(764\) | −17.2818 | − | 9.99001i | −0.625233 | − | 0.361426i | ||||
\(765\) | −10.8458 | + | 27.4215i | −0.392131 | + | 0.991428i | ||||
\(766\) | 39.9086 | + | 10.7049i | 1.44195 | + | 0.386785i | ||||
\(767\) | −19.7526 | −0.713224 | ||||||||
\(768\) | 27.6423 | − | 1.97520i | 0.997457 | − | 0.0712740i | ||||
\(769\) | −35.1082 | −1.26603 | −0.633017 | − | 0.774138i | \(-0.718184\pi\) | ||||
−0.633017 | + | 0.774138i | \(0.718184\pi\) | |||||||
\(770\) | −1.95998 | − | 0.525738i | −0.0706328 | − | 0.0189463i | ||||
\(771\) | −12.9914 | + | 8.83229i | −0.467874 | + | 0.318087i | ||||
\(772\) | 18.3517 | + | 10.6085i | 0.660493 | + | 0.381808i | ||||
\(773\) | 10.8115i | 0.388864i | 0.980916 | + | 0.194432i | \(0.0622863\pi\) | ||||
−0.980916 | + | 0.194432i | \(0.937714\pi\) | |||||||
\(774\) | 31.5482 | + | 23.4257i | 1.13398 | + | 0.842020i | ||||
\(775\) | − | 4.11097i | − | 0.147670i | ||||||
\(776\) | −1.46670 | − | 1.46906i | −0.0526516 | − | 0.0527363i | ||||
\(777\) | −16.3554 | + | 11.1193i | −0.586746 | + | 0.398903i | ||||
\(778\) | −5.50837 | + | 20.5355i | −0.197484 | + | 0.736232i | ||||
\(779\) | 0.0891221 | 0.00319313 | ||||||||
\(780\) | −11.2060 | + | 0.818857i | −0.401240 | + | 0.0293198i | ||||
\(781\) | 1.04724 | 0.0374730 | ||||||||
\(782\) | −2.69799 | + | 10.0582i | −0.0964799 | + | 0.359682i | ||||
\(783\) | 9.67006 | + | 43.1545i | 0.345580 | + | 1.54222i | ||||
\(784\) | 7.82966 | + | 13.5950i | 0.279631 | + | 0.485536i | ||||
\(785\) | − | 45.5313i | − | 1.62508i | ||||||
\(786\) | 14.5855 | + | 41.8964i | 0.520249 | + | 1.49440i | ||||
\(787\) | 52.1256i | 1.85808i | 0.369984 | + | 0.929038i | \(0.379363\pi\) | ||||
−0.369984 | + | 0.929038i | \(0.620637\pi\) | |||||||
\(788\) | −0.208021 | + | 0.359856i | −0.00741043 | + | 0.0128194i | ||||
\(789\) | 3.77115 | + | 5.54699i | 0.134257 | + | 0.197478i | ||||
\(790\) | −14.3914 | − | 3.86029i | −0.512022 | − | 0.137343i | ||||
\(791\) | 11.4377 | 0.406679 | ||||||||
\(792\) | 2.63078 | − | 1.13703i | 0.0934808 | − | 0.0404025i | ||||
\(793\) | −13.6383 | −0.484309 | ||||||||
\(794\) | 19.6655 | + | 5.27500i | 0.697901 | + | 0.187203i | ||||
\(795\) | −4.80907 | − | 7.07366i | −0.170560 | − | 0.250877i | ||||
\(796\) | 5.85453 | − | 10.1278i | 0.207508 | − | 0.358970i | ||||
\(797\) | 3.59649i | 0.127394i | 0.997969 | + | 0.0636972i | \(0.0202892\pi\) | ||||
−0.997969 | + | 0.0636972i | \(0.979711\pi\) | |||||||
\(798\) | 1.64418 | + | 4.72285i | 0.0582034 | + | 0.167187i | ||||
\(799\) | 35.8170i | 1.26711i | ||||||||
\(800\) | 1.25841 | + | 4.72176i | 0.0444915 | + | 0.166939i | ||||
\(801\) | 0.642126 | + | 0.253975i | 0.0226884 | + | 0.00897376i | ||||
\(802\) | −3.03571 | + | 11.3173i | −0.107195 | + | 0.399627i | ||||
\(803\) | 3.97897 | 0.140415 | ||||||||
\(804\) | −3.45489 | + | 0.252459i | −0.121845 | + | 0.00890354i | ||||
\(805\) | 7.70674 | 0.271627 | ||||||||
\(806\) | −2.33554 | + | 8.70702i | −0.0822659 | + | 0.306692i | ||||
\(807\) | 33.0011 | − | 22.4360i | 1.16169 | − | 0.789785i | ||||
\(808\) | −14.9050 | + | 14.8810i | −0.524354 | + | 0.523512i | ||||
\(809\) | 32.6512i | 1.14795i | 0.818871 | + | 0.573977i | \(0.194600\pi\) | ||||
−0.818871 | + | 0.573977i | \(0.805400\pi\) | |||||||
\(810\) | −26.1876 | + | 16.2527i | −0.920138 | + | 0.571063i | ||||
\(811\) | 23.0323i | 0.808774i | 0.914588 | + | 0.404387i | \(0.132515\pi\) | ||||
−0.914588 | + | 0.404387i | \(0.867485\pi\) | |||||||
\(812\) | 25.8544 | + | 14.9456i | 0.907312 | + | 0.524486i | ||||
\(813\) | −0.859515 | + | 0.584347i | −0.0301445 | + | 0.0204939i | ||||
\(814\) | −3.00270 | − | 0.805435i | −0.105245 | − | 0.0282305i | ||||
\(815\) | 20.9258 | 0.733000 | ||||||||
\(816\) | −25.3087 | − | 12.2627i | −0.885981 | − | 0.429280i | ||||
\(817\) | −10.7780 | −0.377075 | ||||||||
\(818\) | −32.8809 | − | 8.81987i | −1.14965 | − | 0.308380i | ||||
\(819\) | −6.55561 | − | 2.59289i | −0.229072 | − | 0.0906027i | ||||
\(820\) | 0.321113 | + | 0.185625i | 0.0112138 | + | 0.00648229i | ||||
\(821\) | − | 8.07470i | − | 0.281809i | −0.990023 | − | 0.140905i | \(-0.954999\pi\) | ||
0.990023 | − | 0.140905i | \(-0.0450011\pi\) | |||||||
\(822\) | −16.1878 | + | 5.63551i | −0.564614 | + | 0.196561i | ||||
\(823\) | − | 32.4055i | − | 1.12958i | −0.825233 | − | 0.564792i | \(-0.808956\pi\) | ||
0.825233 | − | 0.564792i | \(-0.191044\pi\) | |||||||
\(824\) | 11.8254 | − | 11.8064i | 0.411959 | − | 0.411297i | ||||
\(825\) | 0.284125 | + | 0.417920i | 0.00989198 | + | 0.0145501i | ||||
\(826\) | −9.47913 | + | 35.3387i | −0.329821 | + | 1.22959i | ||||
\(827\) | 11.9691 | 0.416208 | 0.208104 | − | 0.978107i | \(-0.433271\pi\) | ||||
0.208104 | + | 0.978107i | \(0.433271\pi\) | |||||||
\(828\) | −8.53129 | + | 6.75925i | −0.296483 | + | 0.234900i | ||||
\(829\) | 55.5986 | 1.93102 | 0.965510 | − | 0.260365i | \(-0.0838428\pi\) | ||||
0.965510 | + | 0.260365i | \(0.0838428\pi\) | |||||||
\(830\) | 7.56478 | − | 28.2019i | 0.262577 | − | 0.978902i | ||||
\(831\) | −5.55768 | − | 8.17479i | −0.192794 | − | 0.283580i | ||||
\(832\) | 0.0172393 | − | 10.7156i | 0.000597665 | − | 0.371496i | ||||
\(833\) | − | 15.9207i | − | 0.551618i | ||||||
\(834\) | 2.90504 | − | 1.01134i | 0.100593 | − | 0.0350198i | ||||
\(835\) | 33.6407i | 1.16418i | ||||||||
\(836\) | −0.393418 | + | 0.680576i | −0.0136066 | + | 0.0235382i | ||||
\(837\) | 5.40706 | + | 24.1301i | 0.186895 | + | 0.834057i | ||||
\(838\) | 32.3459 | + | 8.67636i | 1.11737 | + | 0.299720i | ||||
\(839\) | 18.0545 | 0.623309 | 0.311655 | − | 0.950195i | \(-0.399117\pi\) | ||||
0.311655 | + | 0.950195i | \(0.399117\pi\) | |||||||
\(840\) | −3.91271 | + | 20.4413i | −0.135001 | + | 0.705292i | ||||
\(841\) | −43.4378 | −1.49786 | ||||||||
\(842\) | −48.4248 | − | 12.9893i | −1.66883 | − | 0.447641i | ||||
\(843\) | −19.6667 | + | 13.3705i | −0.677356 | + | 0.460504i | ||||
\(844\) | −4.94418 | + | 8.55297i | −0.170186 | + | 0.294405i | ||||
\(845\) | − | 27.1354i | − | 0.933487i | ||||||
\(846\) | −22.3175 | + | 30.0558i | −0.767292 | + | 1.03334i | ||||
\(847\) | 19.0981i | 0.656220i | ||||||||
\(848\) | 7.06897 | − | 4.07117i | 0.242749 | − | 0.139805i | ||||
\(849\) | −35.5297 | + | 24.1551i | −1.21938 | + | 0.829001i | ||||
\(850\) | 1.28474 | − | 4.78958i | 0.0440663 | − | 0.164281i | ||||
\(851\) | 11.8068 | 0.404731 | ||||||||
\(852\) | −0.782759 | − | 10.7120i | −0.0268169 | − | 0.366988i | ||||
\(853\) | 48.4263 | 1.65808 | 0.829042 | − | 0.559187i | \(-0.188887\pi\) | ||||
0.829042 | + | 0.559187i | \(0.188887\pi\) | |||||||
\(854\) | −6.54492 | + | 24.3998i | −0.223963 | + | 0.834944i | ||||
\(855\) | 3.10932 | − | 7.86131i | 0.106336 | − | 0.268851i | ||||
\(856\) | 5.79551 | + | 5.80484i | 0.198087 | + | 0.198405i | ||||
\(857\) | − | 43.2895i | − | 1.47874i | −0.673299 | − | 0.739370i | \(-0.735123\pi\) | ||
0.673299 | − | 0.739370i | \(-0.264877\pi\) | |||||||
\(858\) | −0.364346 | − | 1.04657i | −0.0124386 | − | 0.0357293i | ||||
\(859\) | 0.598378i | 0.0204164i | 0.999948 | + | 0.0102082i | \(0.00324943\pi\) | ||||
−0.999948 | + | 0.0102082i | \(0.996751\pi\) | |||||||
\(860\) | −38.8340 | − | 22.4486i | −1.32423 | − | 0.765491i | ||||
\(861\) | 0.130840 | + | 0.192453i | 0.00445902 | + | 0.00655878i | ||||
\(862\) | 40.5636 | + | 10.8806i | 1.38160 | + | 0.370596i | ||||
\(863\) | 20.3469 | 0.692618 | 0.346309 | − | 0.938120i | \(-0.387435\pi\) | ||||
0.346309 | + | 0.938120i | \(0.387435\pi\) | |||||||
\(864\) | −13.5969 | − | 26.0600i | −0.462575 | − | 0.886580i | ||||
\(865\) | −32.6347 | −1.10961 | ||||||||
\(866\) | 6.63903 | + | 1.78083i | 0.225603 | + | 0.0605151i | ||||
\(867\) | −0.509172 | − | 0.748940i | −0.0172924 | − | 0.0254353i | ||||
\(868\) | 14.4566 | + | 8.35688i | 0.490690 | + | 0.283651i | ||||
\(869\) | − | 1.46957i | − | 0.0498518i | ||||||
\(870\) | −16.5979 | − | 47.6769i | −0.562722 | − | 1.61640i | ||||
\(871\) | 1.33945i | 0.0453856i | ||||||||
\(872\) | 6.67865 | + | 6.68941i | 0.226168 | + | 0.226532i | ||||
\(873\) | −0.809827 | + | 2.04749i | −0.0274085 | + | 0.0692971i | ||||
\(874\) | 0.773469 | − | 2.88353i | 0.0261630 | − | 0.0975370i | ||||
\(875\) | 17.5718 | 0.594034 | ||||||||
\(876\) | −2.97409 | − | 40.7003i | −0.100485 | − | 1.37514i | ||||
\(877\) | −39.1455 | −1.32185 | −0.660924 | − | 0.750453i | \(-0.729836\pi\) | ||||
−0.660924 | + | 0.750453i | \(0.729836\pi\) | |||||||
\(878\) | −6.66071 | + | 24.8315i | −0.224788 | + | 0.838021i | ||||
\(879\) | 20.4747 | − | 13.9199i | 0.690596 | − | 0.469506i | ||||
\(880\) | −2.83503 | + | 1.63275i | −0.0955687 | + | 0.0550400i | ||||
\(881\) | − | 52.0716i | − | 1.75434i | −0.480183 | − | 0.877168i | \(-0.659430\pi\) | ||
0.480183 | − | 0.877168i | \(-0.340570\pi\) | |||||||
\(882\) | 9.92015 | − | 13.3598i | 0.334029 | − | 0.449848i | ||||
\(883\) | − | 24.2954i | − | 0.817606i | −0.912623 | − | 0.408803i | \(-0.865946\pi\) | ||
0.912623 | − | 0.408803i | \(-0.134054\pi\) | |||||||
\(884\) | −5.44215 | + | 9.41442i | −0.183039 | + | 0.316641i | ||||
\(885\) | 51.1498 | − | 34.7745i | 1.71938 | − | 1.16893i | ||||
\(886\) | −28.2370 | − | 7.57421i | −0.948642 | − | 0.254461i | ||||
\(887\) | −23.5018 | −0.789112 | −0.394556 | − | 0.918872i | \(-0.629102\pi\) | ||||
−0.394556 | + | 0.918872i | \(0.629102\pi\) | |||||||
\(888\) | −5.99430 | + | 31.3163i | −0.201156 | + | 1.05090i | ||||
\(889\) | 23.8146 | 0.798716 | ||||||||
\(890\) | −0.761340 | − | 0.204219i | −0.0255202 | − | 0.00684544i | ||||
\(891\) | −2.21740 | − | 2.07935i | −0.0742858 | − | 0.0696609i | ||||
\(892\) | −11.8509 | + | 20.5010i | −0.396798 | + | 0.686424i | ||||
\(893\) | − | 10.2681i | − | 0.343610i | ||||||
\(894\) | 20.3888 | − | 7.09802i | 0.681904 | − | 0.237393i | ||||
\(895\) | − | 37.8950i | − | 1.26669i | ||||||
\(896\) | −19.1627 | − | 5.17319i | −0.640179 | − | 0.172824i | ||||
\(897\) | 2.36621 | + | 3.48046i | 0.0790056 | + | 0.116209i | ||||
\(898\) | −8.85387 | + | 33.0077i | −0.295457 | + | 1.10148i | ||||
\(899\) | −40.5040 | −1.35088 | ||||||||
\(900\) | 4.06247 | − | 3.21865i | 0.135416 | − | 0.107288i | ||||
\(901\) | −8.27824 | −0.275788 | ||||||||
\(902\) | −0.00947751 | + | 0.0353327i | −0.000315567 | + | 0.00117645i | ||||
\(903\) | −15.8232 | − | 23.2744i | −0.526564 | − | 0.774523i | ||||
\(904\) | 13.0495 | − | 13.0285i | 0.434019 | − | 0.433321i | ||||
\(905\) | − | 3.58384i | − | 0.119131i | ||||||
\(906\) | −29.6827 | + | 10.3335i | −0.986140 | + | 0.343308i | ||||
\(907\) | 43.2105i | 1.43478i | 0.696672 | + | 0.717390i | \(0.254663\pi\) | ||||
−0.696672 | + | 0.717390i | \(0.745337\pi\) | |||||||
\(908\) | 37.9514 | + | 21.9384i | 1.25946 | + | 0.728052i | ||||
\(909\) | 20.7736 | + | 8.21641i | 0.689017 | + | 0.272521i | ||||
\(910\) | 7.77269 | + | 2.08492i | 0.257662 | + | 0.0691144i | ||||
\(911\) | 32.6334 | 1.08119 | 0.540596 | − | 0.841282i | \(-0.318199\pi\) | ||||
0.540596 | + | 0.841282i | \(0.318199\pi\) | |||||||
\(912\) | 7.25558 | + | 3.51552i | 0.240256 | + | 0.116410i | ||||
\(913\) | 2.87983 | 0.0953085 | ||||||||
\(914\) | 29.4461 | + | 7.89852i | 0.973990 | + | 0.261260i | ||||
\(915\) | 35.3167 | − | 24.0103i | 1.16753 | − | 0.793755i | ||||
\(916\) | −7.87539 | − | 4.55249i | −0.260210 | − | 0.150419i | ||||
\(917\) | − | 31.7737i | − | 1.04926i | ||||||
\(918\) | −1.24139 | + | 29.8031i | −0.0409719 | + | 0.983649i | ||||
\(919\) | 31.6193i | 1.04303i | 0.853243 | + | 0.521513i | \(0.174632\pi\) | ||||
−0.853243 | + | 0.521513i | \(0.825368\pi\) | |||||||
\(920\) | 8.79273 | − | 8.77859i | 0.289888 | − | 0.289422i | ||||
\(921\) | −28.8466 | + | 19.6116i | −0.950529 | + | 0.646223i | ||||
\(922\) | 6.90762 | − | 25.7520i | 0.227490 | − | 0.848096i | ||||
\(923\) | −4.15302 | −0.136698 | ||||||||
\(924\) | −2.04723 | + | 0.149597i | −0.0673490 | + | 0.00492139i | ||||
\(925\) | −5.62222 | −0.184857 | ||||||||
\(926\) | −1.60587 | + | 5.98675i | −0.0527720 | + | 0.196737i | ||||
\(927\) | −16.4816 | − | 6.51882i | −0.541326 | − | 0.214106i | ||||
\(928\) | 46.5219 | − | 12.3987i | 1.52715 | − | 0.407006i | ||||
\(929\) | 13.3308i | 0.437370i | 0.975796 | + | 0.218685i | \(0.0701767\pi\) | ||||
−0.975796 | + | 0.218685i | \(0.929823\pi\) | |||||||
\(930\) | −9.28081 | − | 26.6588i | −0.304330 | − | 0.874176i | ||||
\(931\) | 4.56419i | 0.149585i | ||||||||
\(932\) | 26.5989 | − | 46.0136i | 0.871275 | − | 1.50722i | ||||
\(933\) | −16.2552 | − | 23.9098i | −0.532172 | − | 0.782771i | ||||
\(934\) | 34.2160 | + | 9.17797i | 1.11958 | + | 0.300312i | ||||
\(935\) | 3.32000 | 0.108576 | ||||||||
\(936\) | −10.4329 | + | 4.50911i | −0.341010 | + | 0.147385i | ||||
\(937\) | 12.1995 | 0.398539 | 0.199269 | − | 0.979945i | \(-0.436143\pi\) | ||||
0.199269 | + | 0.979945i | \(0.436143\pi\) | |||||||
\(938\) | 2.39637 | + | 0.642794i | 0.0782442 | + | 0.0209880i | ||||
\(939\) | 28.0976 | + | 41.3288i | 0.916931 | + | 1.34871i | ||||
\(940\) | 21.3866 | − | 36.9969i | 0.697555 | − | 1.20671i | ||||
\(941\) | − | 16.5447i | − | 0.539342i | −0.962953 | − | 0.269671i | \(-0.913085\pi\) | ||
0.962953 | − | 0.269671i | \(-0.0869150\pi\) | |||||||
\(942\) | −15.1426 | − | 43.4965i | −0.493371 | − | 1.41719i | ||||
\(943\) | − | 0.138930i | − | 0.00452418i | ||||||
\(944\) | 29.4387 | + | 51.1159i | 0.958149 | + | 1.66368i | ||||
\(945\) | 21.5407 | − | 4.82685i | 0.700720 | − | 0.157017i | ||||
\(946\) | 1.14617 | − | 4.27297i | 0.0372651 | − | 0.138926i | ||||
\(947\) | −46.4875 | −1.51064 | −0.755321 | − | 0.655355i | \(-0.772519\pi\) | ||||
−0.755321 | + | 0.655355i | \(0.772519\pi\) | |||||||
\(948\) | −15.0320 | + | 1.09843i | −0.488218 | + | 0.0356755i | ||||
\(949\) | −15.7794 | −0.512221 | ||||||||
\(950\) | −0.368314 | + | 1.37310i | −0.0119497 | + | 0.0445491i | ||||
\(951\) | 49.9234 | − | 33.9407i | 1.61888 | − | 1.10060i | ||||
\(952\) | 14.2314 | + | 14.2543i | 0.461242 | + | 0.461985i | ||||
\(953\) | − | 27.7409i | − | 0.898617i | −0.893377 | − | 0.449309i | \(-0.851670\pi\) | ||
0.893377 | − | 0.449309i | \(-0.148330\pi\) | |||||||
\(954\) | −6.94667 | − | 5.15816i | −0.224907 | − | 0.167002i | ||||
\(955\) | − | 24.1687i | − | 0.782081i | ||||||
\(956\) | −0.976338 | − | 0.564387i | −0.0315770 | − | 0.0182536i | ||||
\(957\) | 4.11762 | − | 2.79939i | 0.133104 | − | 0.0904914i | ||||
\(958\) | −16.8611 | − | 4.52278i | −0.544759 | − | 0.146124i | ||||
\(959\) | 12.2766 | 0.396433 | ||||||||
\(960\) | 18.8202 | + | 27.7787i | 0.607420 | + | 0.896553i | ||||
\(961\) | 8.35200 | 0.269419 | ||||||||
\(962\) | 11.9078 | + | 3.19411i | 0.383924 | + | 0.102982i | ||||
\(963\) | 3.19994 | − | 8.09043i | 0.103117 | − | 0.260711i | ||||
\(964\) | −35.8312 | − | 20.7128i | −1.15404 | − | 0.667113i | ||||
\(965\) | 25.6650i | 0.826187i | ||||||||
\(966\) | 7.36232 | − | 2.56307i | 0.236879 | − | 0.0824653i | ||||
\(967\) | − | 36.3700i | − | 1.16958i | −0.811184 | − | 0.584791i | \(-0.801177\pi\) | ||
0.811184 | − | 0.584791i | \(-0.198823\pi\) | |||||||
\(968\) | 21.7543 | + | 21.7893i | 0.699210 | + | 0.700336i | ||||
\(969\) | −4.60000 | − | 6.76614i | −0.147773 | − | 0.217360i | ||||
\(970\) | 0.651175 | − | 2.42762i | 0.0209080 | − | 0.0779461i | ||||
\(971\) | 52.5091 | 1.68510 | 0.842548 | − | 0.538621i | \(-0.181055\pi\) | ||||
0.842548 | + | 0.538621i | \(0.181055\pi\) | |||||||
\(972\) | −19.6120 | + | 24.2357i | −0.629054 | + | 0.777361i | ||||
\(973\) | −2.20315 | −0.0706296 | ||||||||
\(974\) | −12.4435 | + | 46.3901i | −0.398716 | + | 1.48643i | ||||
\(975\) | −1.12676 | − | 1.65734i | −0.0360851 | − | 0.0530775i | ||||
\(976\) | 20.3261 | + | 35.2933i | 0.650624 | + | 1.12971i | ||||
\(977\) | 26.6635i | 0.853040i | 0.904478 | + | 0.426520i | \(0.140261\pi\) | ||||
−0.904478 | + | 0.426520i | \(0.859739\pi\) | |||||||
\(978\) | 19.9906 | − | 6.95940i | 0.639230 | − | 0.222537i | ||||
\(979\) | − | 0.0777441i | − | 0.00248471i | ||||||
\(980\) | −9.50636 | + | 16.4451i | −0.303670 | + | 0.525320i | ||||
\(981\) | 3.68756 | − | 9.32328i | 0.117735 | − | 0.297669i | ||||
\(982\) | 6.21807 | + | 1.66791i | 0.198427 | + | 0.0532253i | ||||
\(983\) | 44.2612 | 1.41171 | 0.705857 | − | 0.708354i | \(-0.250562\pi\) | ||||
0.705857 | + | 0.708354i | \(0.250562\pi\) | |||||||
\(984\) | 0.368497 | + | 0.0705346i | 0.0117472 | + | 0.00224856i | ||||
\(985\) | −0.503262 | −0.0160353 | ||||||||
\(986\) | −47.1901 | − | 12.6581i | −1.50284 | − | 0.403117i | ||||
\(987\) | 22.1733 | − | 15.0747i | 0.705785 | − | 0.479832i | ||||
\(988\) | 1.56018 | − | 2.69896i | 0.0496358 | − | 0.0858654i | ||||
\(989\) | 16.8015i | 0.534258i | ||||||||
\(990\) | 2.78598 | + | 2.06869i | 0.0885442 | + | 0.0657473i | ||||
\(991\) | 19.8598i | 0.630867i | 0.948948 | + | 0.315433i | \(0.102150\pi\) | ||||
−0.948948 | + | 0.315433i | \(0.897850\pi\) | |||||||
\(992\) | 26.0129 | − | 6.93278i | 0.825911 | − | 0.220116i | ||||
\(993\) | 33.7293 | − | 22.9311i | 1.07037 | − | 0.727697i | ||||
\(994\) | −1.99301 | + | 7.43004i | −0.0632144 | + | 0.235667i | ||||
\(995\) | 14.1638 | 0.449022 | ||||||||
\(996\) | −2.15254 | − | 29.4574i | −0.0682058 | − | 0.933393i | ||||
\(997\) | −10.9554 | −0.346961 | −0.173480 | − | 0.984837i | \(-0.555501\pi\) | ||||
−0.173480 | + | 0.984837i | \(0.555501\pi\) | |||||||
\(998\) | −8.41248 | + | 31.3622i | −0.266292 | + | 0.992752i | ||||
\(999\) | 33.0006 | − | 7.39477i | 1.04409 | − | 0.233960i |
(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 | 804.2.c.b.671.13 | ✓ | 128 | |
3.2 | odd | 2 | inner | 804.2.c.b.671.116 | yes | 128 | |
4.3 | odd | 2 | inner | 804.2.c.b.671.115 | yes | 128 | |
12.11 | even | 2 | inner | 804.2.c.b.671.14 | yes | 128 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
804.2.c.b.671.13 | ✓ | 128 | 1.1 | even | 1 | trivial | |
804.2.c.b.671.14 | yes | 128 | 12.11 | even | 2 | inner | |
804.2.c.b.671.115 | yes | 128 | 4.3 | odd | 2 | inner | |
804.2.c.b.671.116 | yes | 128 | 3.2 | odd | 2 | inner |